Datasets:

qingy2024

/

qwark-corpus

like 1

SN 1006: A supernova remnant about 7,000 light years from Earth. Caption: Chandra's image of SN 1006 shows X-rays from multimillion degree gas (red/green) and high-energy electrons (blue). In the year 1006 a "new star" appeared in the sky and in just a few days it became brighter than the planet Venus. We now know that the event heralded not the appearance of a new star, but the cataclysmic death of an old one. It was likely a white dwarf star that had been pulling matter off an orbiting companion star. When the white dwarf mass exceeded the stability limit (known as the Chandrasekhar limit), it exploded. Material ejected in the supernova produced tremendous shock waves that heated gas to millions of degrees and accelerated electrons to extremely high energies. Scale: Image is 36 arcmin across. Chandra X-ray Observatory ACIS Image

<urn:uuid:63bff66c-2a1c-490b-8e03-349cf36906be>

Motivators of Reading Enrichment (MORE) encourages fourth-grade students to read for pleasure. Each participating classroom receives a MORE library of 55 high-interest books. A Better Basics volunteer visits weekly to award prize books and incentives to students as they successfully read from the classroom library. This allows students to start or add to their home libraries. The National Assessment of Educational Progress encourages independent reading as a critical aspect of literacy development, and has documented a correlation between students who read for pleasure and reading achievement. MORE enriches children by motivating them to read and providing access to high-quality literature, thus establishing the habits of reading and writing and improving attitudes toward learning. Teachers allow students 30 minutes per day to read selections from the MORE library and to complete a 10-question book report to demonstrate and help improve reading comprehension. Students can earn a book for every completed report (up to two books per week), allowing them to develop personal home libraries. The MORE program is responsible for putting thousands of books into the homes of students every year, and often a MORE prize book is the first book a child has ever owned. Research suggests having books in the home provides an opportunity for other members of the family to be positively influenced. The practice often provides much-needed modeling for younger siblings and even encourages parents to improve their reading skills. Additional incentives are awarded when a student reaches the milestones of reading five (MORE T-shirt), 10 (silicone bracelet), 15 (blue ribbon) and 20 (water bottle) books.

<urn:uuid:fd557a30-c482-4911-9428-7011ffe39edd>

Autism Spectrum Disorder (ASD) Definition and Facts Early screening for autism spectrum disorder may be difficult due to no medical tests such as blood tests. Autism is a complex developmental disorder that has the following three defining core features: - Problems with social interactions - Impaired verbal and nonverbal communication - A pattern of repetitive behavior with narrow, restricted interests A number of other associated symptoms frequently coexist with autism. - Most people with autism have problems using language, forming relationships, and appropriately interpreting and responding to the external world around them. - Autism is a behaviorally defined developmental disorder that begins in early childhood. - Although the diagnosis of autism may not be made until a child reaches preschool or school age, the signs and symptoms of autism may be apparent by the time the child is aged 12-18 months, and the behavioral characteristics of autism are almost always evident by the time the child is aged 3 years. - Language delay in the preschool years (younger than 5 years) is typically the presenting problem for more severely affected children with autism. Higher functioning children with autism are generally identified with behavioral problems when they are aged approximately 4-5 years or with social problems later in childhood. - Autism disorder persists throughout the person's lifetime, although many people are able to learn to control and modify their behavior to some extent. As of May 2013, autism, along with what were formally described as Asperger's syndrome and pervasive developmental disorders were classified by the American Psychiatric Association as autism spectrum disorders (ASDs). All of these disorders are characterized by varying degrees of problems with communication, social interaction, and atypical, repetitive behaviors. There is a wide range of symptoms, severity, and other manifestations of these disorders. The expression of autism spectrum disorders varies widely among affected individuals. A child with significant impairment in all three of the core functioning areas (socialization, communication, and atypical, repetitive behaviors) may have a lower level-functioning autism spectrum disorder, while a child with similar problems but without delays in language development may have a higher level-functioning autism spectrum disorder. Some people are affected with fairly mild symptoms and signs of autism. Many of these individuals learn to live independent lives. Others are more severely affected and require lifelong care and supervision. As the following statistics indicate, autism is a common developmental disorder. - The number of children diagnosed with autism spectrum disorders appears to be increasing. Although there is a concern that the actual number of children with autism spectrum disorders is increasing, several factors, such as improvements in diagnostic methods and the view of autism spectrum disorders as being on a continuum, also may account for the increase. - Autism affects all races, ethnic groups, and socioeconomic levels. - Boys are more likely than girls to have autism. There is no cure for autism; however, there is good news. - A generation ago, most children with autism were institutionalized. This is no longer the case and most children with this disorder live with their families. - Our improving understanding of autism has shown that, regardless of the severity of the condition, appropriate treatment and education can eventually help many children with autism to be integrated into their community. - Early diagnosis is essential for implementing appropriate treatment and education at an early age, when they can do the most good. What Is Autism Spectrum Disorder (ASD)? Autism spectrum disorder (ASD) refers to a group of complex neurodevelopment disorders characterized by repetitive and characteristic patterns of behavior and difficulties with social communication and interaction. The symptoms are present from early childhood and affect daily functioning. The term "spectrum" refers to the wide range of symptoms, skills, and levels of disability in functioning that can occur in people with autism spectrum disorder. Some children and adults with autism spectrum disorders are fully able to perform all activities of daily living while others require substantial support to perform basic activities. The Diagnostic and Statistical Manual of Mental Disorders (DSM-5, published in 2013) includes Asperger syndrome, childhood disintegrative disorder, and pervasive developmental disorders not otherwise specified (PDD-NOS) as part of autism spectrum disorder rather than as separate disorders. A diagnosis of autism spectrum disorder includes an assessment of intellectual disability and language impairment. Autism is a developmental disability. What Is the Main Cause Autism? Although autism is the result of a neurologic abnormality, the cause of these problems with the nervous system is unknown in most cases. Research findings indicate a strong genetic component. Most likely, environmental, immunologic, and metabolic factors also influence the development of the disorder. - There is probably no single gene or genetic defect that is responsible for autism. Researchers suspect that there are a number of different genes that, when combined together, increase the risk of getting autism. In families with one child with autism, the risk of having another child with autism is low. The concordance of autism in monozygotic twins is significant. A number of studies have found that first-degree relatives of children with autism also have an increased risk of autism spectrum disorders. - In some children, autism is linked to an underlying medical condition. Examples include; - metabolic disorders (untreated phenylketonuria [PKU]), - congenital infections (rubella, cytomegalovirus [CMV], toxoplasmosis), - genetic disorders (fragile X syndrome, tuberous sclerosis), - developmental brain abnormalities (microcephaly, macrocephaly, cerebral dysgenesis), and - neurologic disorders acquired after birth (lead encephalopathy, bacterial meningitis). These medical disorders alone do not cause autism as most children with these conditions do not have autism. - Environmental factors and exposures may interact with genetic factors to cause an increased risk of autism in some families. Over time, many different theories have been proposed about what causes autism. Some of these theories are no longer accepted, however; - Emotional trauma: Some believed that emotional trauma at an early age, especially bad parenting, was to blame. This theory has been rejected. - Vaccines: Although the mercury preservative used in some vaccines is known to be neurotoxic, the most recent research on this subject does not suggest a specific link between vaccines and autism. Except for some influenza (flu) multidose preparations, thimerosal was removed from or reduced in all vaccines routinely recommended for children 5 years of age and under manufactured for the U.S. market in 2001. What Are Early Signs and Symptoms of Autism? Which Ones Are Myths? Autism is a condition surrounded by myth and generalizations about people with autism that are rarely appropriate. The common beliefs that people with autism are myths. For example; - never expresses emotion, - never smiles or laughs, - never makes eye contact, never talks, and - never display affection. Just as every person is unique, with his or her own personality and characteristics, every person with autism manifests the disorder in his or her unique way. The list of symptoms and behaviors associated with autism is long, and each affected person expresses his or her own combination of these behaviors. None of these clinical features is common to all people with autism, and many are occasionally exhibited by people who are not autistic. All people with autism have abnormal functioning in three core areas of development: - social interaction, - verbal and nonverbal communication, and - the presence of repetitive and restricted patterns of behavior, interests, and activities. The diagnosis of autism is typically made when impairment is significant in all three areas, with impairments in social interaction and communication being one rather than two categories of impairment according to the Diagnostic and Statistical Manual of Mental Disorders, fifth edition (DSM-V, American Psychiatric Association 2013). Impaired reciprocal social interaction Examples include the following: - poor use of body language and nonverbal communication, such as eye contact, facial expressions, and gestures; - lack of awareness of feelings of others and the expression of emotions, such as pleasure (laughing) or distress (crying), for reasons not apparent to others; - remaining aloof, preferring to be alone; - difficulty interacting with other people and failure to make peer friendships; - may not want to cuddle or be cuddled; - lack of or abnormal social play; - not responding to verbal cues (acting as if deaf). Examples include the following: - delay in, or the total lack of, the development of spoken language or speech; - if speech is developed, it is abnormal in content and quality; - difficulty expressing needs and wants, verbally and/or nonverbally; - repeating words or phrases back when spoken to (known as echolalia); - inability to initiate or sustain conversation; - absent or poorly developed imaginary play. Restricted repertoire of interests, behaviors, and activities Examples include the following: - insisting on following routines and sameness, resisting change; - ritualistic or compulsive behaviors; - sustained odd play; - repetitive body movements (hand flapping, rocking) and/or abnormal posture (toe walking); - preoccupation with parts of objects or a fascination with repetitive movement (spinning wheels, turning on and off lights); - narrow, restricted interests (dates/calendars, numbers, weather, movie credits). There are a number of associated features and behaviors that are seen in some people with autism, including the following: Cognitive function: Autism occurs at all intelligence levels. Although about 75% of autistic individuals have an intelligence quotient (IQ) below average, the other 25% have an average or above average intelligence. The performance IQ is generally higher than the verbal IQ. A small percentage have high intelligence in a specific area such as mathematics. - Seizures may develop in a significant percentage of children with autism and can be resistant to treatment. The onset of seizures peaks in early childhood and again in adolescence. There is an increased risk of seizures in children with autism who have mental retardation or a family history of autism. - Uneven gross and/or fine motor skills (well developed in some areas, poorly developed in others) Behavioral symptoms include: - aggressive or self-injurious behavior; - noticeable extreme underactivity or overactivity; - throwing tantrums; - short attention span; - abnormal responses to sensory stimuli (for example, expressing over sensitivity or undersensitivity to pain); - abnormalities in eating or sleeping; - not responding to normal teaching methods; - playing in odd or unusual ways; - having inappropriate attachment to objects; - having no apparent fear of dangerous situations. Mood and affect - Mood and affect vary considerably, and may include being unaware of the feelings of others, withdrawn, or emotionally labile. Some people with autism become outwardly anxious or they may become depressed in response to the realization of their problems. - In some children with autism who express affection, the affection may be indiscriminate. When Should You Call a Doctor for Autism in Infants and Toddlers? If an infant or toddler exhibits any unusual behaviors for a day or two after behaving completely normally, it probably means that he or she is coming down with a minor illness, doesn't feel well, or is tired or under some other form of stress. However, if the child has always had any of these characteristics, or the characteristic(s) continues over a period of time, a visit to the pediatrician or other health care provider is warranted. The average age for the diagnosis of autism is 4 to 6 years, although most parents suspected something was wrong by 18 months and voiced their concerns by age 2 years. Some examples of behaviors that warrant seeking medical care include: - seems distant or oblivious to surroundings; - doesn't play or interact well with others; - is uncommunicative; - has problems speaking or understanding the speech of others; - has uncontrollable temper tantrums; - insists on sameness and routine; - engages in repetitive or compulsive actions. Based on an understanding of potential early autism symptoms, the National Institute of Child Health and Human Development (NICHD) and experts recommend that babies or children be evaluated for autism who have not met the following developmental milestones: - Not babbled or cooed by age 1 year - Not gestured, pointed, or waved as an infant, by age 1 year - Not spoken a single word by age 16 months - Not spoken a 2-word phrase by age 2 years - Experiences any loss of language or social skills at any age If even one of these statements is true of a child, parents should resist the temptation to "just wait and see." Problems of this type may signal some type of disability, even if it is not autism. Prompt diagnosis and early intervention are very important in improving the long-term outcomes for developmental disorders of all types, including autism. What Questions Should You Ask the Doctor about Autism in Children? - Is my child's development on target for his or her age? - Are my child's social skills developing normally? - What further evaluation and testing are necessary to evaluate my child for possible autism? - What resources are available to support our child and family? What Procedures and Tests Diagnose Autism? - There is no lab test or X-ray that can confirm the diagnosis of autism. The diagnosis of autism is based on clinical judgment regarding observations of the individual's behavior. Information from family members and other observers is of primary importance in making the diagnosis; however, the pediatrician may order tests to rule out other conditions that might be confused with autism, such as mental retardation, metabolic or genetic diseases, or deafness. - A single visit with the pediatrician is not enough to establish the diagnosis of autism. - The pediatrician observes the child and may do a simple screening test to see if a developmental problem may be present. Screening tests do not diagnose autism. Done in the office, they are simple tests that indicate a problem may exist. They usually involve simply observing specific behaviors (for very young children) or how a child responds to simple commands or questions (for older children). Some widely used screening tests include the Checklist for Autism in Toddlers (CHAT) for children aged 18 months to 4 years of age and the Autism Screening Questionnaire for children aged 4 years and older. - Other conditions must be ruled out, and the diagnosis of autism must be established with certainty before treatment begins. - If the pediatrician believes that further evaluation is necessary, he or she will refer the child to a professional who specializes in developmental disorders. This specialist may be a developmental pediatrician, a child psychiatrist, a pediatric neurologist, or a child psychologist. - Other professionals, such as speech and language pathologists, audiologists (specialists in testing hearing), occupational therapists, physical therapists, and social workers, may be involved in the evaluation process. The comprehensive evaluation of a child with autism might include: - obtaining complete medical and family history; - physical exam; - formal audiology evaluation; - selected medical/lab tests on an individual basis (for example, lead levels, genetic tests, metabolic tests, brain MRI, electroencephalogram [EEG]); - speech, language, and communication assessment; - cognitive and behavioral assessments (focus on social skills and relationships, problem behaviors, motivation and reinforcement, sensory functioning, and self-regulation); and - academic assessment (educational functioning, learning style). Parenting: Learn to Be a Better Parent What Is the Treatment for Autism? Treatment strategies used in autism include behavioral, educational, biomedical, and complementary therapies. Some of these are supported by scientific studies, while others are not. It is important to discuss and consider the research support for the treatments chosen. Once treatment begins, the multidisciplinary team will recommend regular assessments to check your child's progress. These should be built into the treatment plan. A pediatrician will refer the caregiver and the child to a specialist in developmental disorders for the assessment. Some people may want to have this specialist treat their child's condition, but they are free to seek treatment elsewhere. - There is no standard treatment for autism, and different professionals have different philosophies and practices in caring for their patients. - You may want to talk to more than one specialist to find the one with whom you feel most comfortable. - Ask family members, friends, and the health care practitioner to obtain referrals. Call autism groups or check the Internet for referral services. When seeking a specialist to treat a child's autism, the opportunity should be available to ask questions and discuss the treatments available to the child. Be aware of all the options so that an informed decision can be made. A reputable specialist will present each type of treatment, provide the pros and cons, and make recommendations based on published treatment guidelines and his or her own experience. - The decision of which treatment to pursue is made with this specialist (with input from other members of the professional care team) and family members, but the decision is ultimately the caregivers'. - Be certain to understand exactly what will be done and why, and what can be expected from the choices. There is no cure for autism, nor is there a standard therapy that works for all people with autism. A number of different treatment approaches have evolved over time as we have learned more about autism. - Different approaches work for different people. Accepted interventions may work for some and not for others. - Different professionals, each with excellent credentials and experience, may disagree about what is the best approach for the child. - As a parent or caregiver, one will learn to weigh each treatment recommendation in light of what he or she knows about their child and what makes sense for him or her. - Whatever approach is used for the child, an individualized treatment plan designed to meet his or her unique needs is essential. - Most people with autism show developmental progress and respond to a combination of treatment and education. - The traditional approach for a child with autism includes special education and behavioral management. There is some evidence that the earlier behavioral, educational, speech, and occupational therapy is begun, the better the long-term outcome. This is often an intensive and long-term commitment, and there is no easy answer. Behavioral treatments, medications, and other treatments may help manage some of the problems associated with autism. The best thing you can do to help your child is to work with the professional team. Be informed of the issues surrounding your child's treatment and outlook. Be sure you are clear about the goals of therapy and how they are to be achieved. Be organized and cooperative in supplying all information required by the team. Communicate your questions and reservations about the treatment plan so they can be addressed. What Medications Treat the Signs and Symptoms of Autism? Many different biomedical treatments are used in autism. The most widely used are medications to treat seizures and behavioral and emotional problems associated with autism. Medication does not treat the underlying neurologic problems associated with autism. Rather, medication is given to help manage behavioral manifestations of the disorder, such as hyperactivity, impulsivity, attention difficulties, and anxiety. In most cases, medication is given to lessen these problems so that the person can receive maximum benefit from behavioral and educational approaches. Medications used in autism are psychoactive, meaning they affect the brain. Those used most often include the following: - Antipsychotic drugs: This is the most widely studied group of drugs in autism. These drugs have been found to reduce hyperactivity, repetitive behaviors, withdrawal, and aggression in some people with autism. The newer, atypical antipsychotics, including risperidone (Risperdal), olanzapine (Zyprexa), aripiprazole (Abilify), and quetiapine (Seroquel), have replaced the older, traditional antipsychotics, which had more side effects. Risperidone (Risperdal) and aripiprazole (Abilify) are now approved by the U.S. Food and Drug Administration to treat irritability, aggression, and self-injurious behaviors in children and adolescents with autism. - Antidepressants: Selective serotonin reuptake inhibitors (SSRIs) are one class of antidepressants that are commonly used to treat people with depression, obsessive compulsive disorder (OCD), and/or anxiety. In some people with autism, these drugs reduce repetitive behaviors, depression, irritability, tantrums, and aggression. Examples of SSRIs include fluoxetine (Prozac), fluvoxamine (Luvox), sertraline (Zoloft), paroxetine (Paxil), citalopram (Celexa), and escitalopram (Lexapro). Other antidepressants, including clomipramine (Anafranil), mirtazapine (Remeron), amitriptyline (Elavil, Endep), bupropion (Wellbutrin), venlafaxine (Effexor), and duloxetine (Cymbalta) have less frequently been used. - Stimulants: Drugs used to treat attention-deficit/hyperactivity disorder (ADHD) may help some people with autism. These drugs work by increasing the person's ability to concentrate and pay attention and by reducing impulsivity and hyperactivity. Examples include methylphenidate (Ritalin, Concerta), dexmethylphenidate (Focalin), as well as amphetamines (amphetamine and dextroamphetamine [Adderall], dextroamphetamine [Dexedrine], and lisdexamfetamine [Vyvanase]). - Nonstimulant medications that treat ADHD may also help people with autism. These medications have been found to be equally effective as stimulants in their ability to increase the individual's ability to focus, manage their impulses and activity level. Examples of these medications are atomoxetine (Strattera) and guanfacine (Intuniv). - Other drugs: Other drugs may also help some people with autism. Anticonvulsants are frequently used to manage seizures in people with autism. Anticonvulsants may also be used to stabilize mood and/or behavior. Alpha-2 adrenergic agonists (for example, clonidine [Catapres]) are also sometimes used to manage hyperactivity and behavioral problems in some individuals with autism. Buspirone (Buspar) and propanolol have also been prescribed. - Very few of these drugs have been tested in scientific studies in individuals with autism. Moreover, issues related to dosage (especially important in children), monitoring, and interactions with other drugs and foods are concerns, as are short- and long-term side effects. - Side effects of these medications include sleepiness (sedation) or trouble sleeping (insomnia), weight loss or weight gain. - Infrequently, dependence may develop with some of these drugs. These medications should be prescribed only by a medical professional experienced in treating persons with autism. What Vitamins, Minerals, and Diet Changes Treat Autism Signs and Symptoms? Although many studies have been done to assess whether abnormal amounts of vitamins, minerals, or other nutrients can be found in people with autism, results have not clearly pointed to any abnormalities that are consistently linked with the disorder. Although few, if any, of these claims are backed up by scientific studies, parents and physicians alike have reported improvement in symptoms in people given certain supplements, including vitamin B, magnesium, cod liver oil, and vitamin C. Some people with autism have food sensitivities and food allergies and dietary management is important to in these cases to maintain nutrition and health. Another focus of dietary therapy is on problems with intestinal digestion and absorption of nutrients in foods suspected to be present in some individuals with autism. Some parents and professionals have reported improvements in symptoms of autism when diets eliminating suspect proteins, such as gluten (found in wheat flour), are consistently followed. However, there are no scientific studies to confirm their effectiveness. Do not start giving a child supplements or dramatically change his or her diet without discussing it with the treatment team. It is important to maintain adequate nutrition to ensure optimal growth and development. Furthermore, although vitamins, minerals, and many other substances available as supplements are necessary for body functions, some of them can be dangerous if taken in excess. What Behavioral Therapies Treat Autism Signs and Symptoms in Toddlers and Children? Behavioral therapy is the foundation for most treatment programs for children with autism. More than 30 years of research has shown the benefit of applied behavioral methods in improving communication, learning, adaptive behavior, and appropriate social behavior while reducing inappropriate behavior in children with autism. There is strong evidence that these interventions are most effective when started early, typically in the preschool years. A range of scientifically supported behavioral treatment has been developed that may be helpful for some children with autism. These are mainly based on the principles of applied behavior analysis. Applied behavior analysis (ABA) is designed to both correct behavior and teach skills for dealing with specific situations. It is based on the principle of reinforcement: that behavior can be changed by rewarding desired behavior and removing reinforcement for unwanted behavior. The person will naturally repeat behaviors for which he or she is rewarded. This principle is applied in many different ways, such as discrete trial training, incidental teaching, errorless learning, and shaping and fading. Most treatment programs include a number of ABA therapies. These comprehensive treatment approaches differ in their specifics but are highly structured, intensive programs in which the child spends a large amount of time (15-40+ hours per week), usually in one-to-one activities with a therapist, to change behaviors. Behavioral therapists typically collaborate with parents, school personnel, and community professionals in providing a comprehensive treatment program that is individualized to meet each child's specific needs. Positive behavioral interventions and support are designed to replace problem behaviors with positive behaviors and improve the person's quality of life. Like other approaches, this approach requires examination of the individual's unique strengths and problems and development of strategies to improve his or her quality of life overall. What Educational and Complementary Therapies Are Used to Treat Autism? The main principle of education is that each person with autism has his or her own strengths, abilities, and functional level and that his or her education should be tailored to meet his or her individual requirements. This is not only desirable for the child, it is required by federal law. The Individuals with Disabilities Education Act (IDEA; P.L.101-476) guarantees free and appropriate public education for every child with a disability. This law specifies that a written and explicit education plan (the Individualized Education Plan, or IEP) be prepared by the local education authority in consultation with the child's parents. When all parties agree on the plan, the plan must be put into place and the child's progress documented. Preparation of the plan includes a comprehensive assessment of the child's needs. Many different options are available for educating children with autism. The basic assumption is that, whenever possible, children with disabilities should be educated with their nondisabled peers, who serve as models for appropriate language, social, and behavioral skills. Thus, some children with autism are educated in mainstream classrooms, others in special education classes within mainstream public schools, and others in specialized programs separate from mainstream public schools. Parents wanting to find the best possible program for their child are advised to work with the local education authority; full cooperation and communication are essential for meeting this goal. The following specific programs have been developed for persons with autism: - TEACCH is a program developed in North Carolina and is used statewide for people with autism. It encompasses many different theories and techniques to develop an individualized program for each person with autism. The underlying principle is that the environment should be adapted for the person with autism, not the other way around. This program focuses less on changing specific behaviors and more on providing the child with the skills needed to understand his or her environment and communicate his or her needs. - Floor time is an approach that helps the child with autism progress on the natural developmental ladder. It is based on the theory that children cannot progress to advanced learning until they have completed all the required steps of this ladder, and that children with autism have not completed the ladder. - Social stories is an approach that uses stories to teach children social skills. In each story, a person is faced with a situation or event; the story is intended to help the child with autism understand the thoughts and emotions of the person in the story. This helps the child develop an understanding of the appropriate or expected response to the situation. The stories are tailored to the individual and often include music and illustrations. It is important that skills learned at school are generalized outside the classroom setting. Thus, programs for children with autism must include the family and be coordinated across the child's home and community. Complementary therapies include art therapy, music therapy, animal therapy, and sensory integration therapy. These are not behavioral or educational approaches per se, but they provide another opportunity for the child to develop social and communication skills. Although there is little scientific evidence that these therapies increase skills, many parents and therapists describe noticeable improvements in a child's behavior and communication abilities, as well as a sense of enjoyment. Complementary therapies are typically used in addition to behavioral and educational approaches. - Art therapy offers the child a nonverbal way to express his or her feelings. - Music therapy involving singing helps develop the child's speech and language skills. - Animal therapy, such as horseback riding and swimming with dolphins, improves the child's motor skills while increasing self-confidence. - Sensory integration focuses on normalizing extreme reactions to sensory input. It tries to help the child reorganize and integrate his or her sensory information so he or she can better understand the external world. What Is the Prognosis for Autism? Can It Be Cured? Although, to different degrees of severity, the core features of autism are life-long, predicting the course for an individual with autism is very difficult. Many different variables enter into each person's experience with autism, including the symptoms and associated behaviors and their severity, the family environment, and the types of interventions used. An individual's IQ (particularly verbal IQ) is often a predictor of future functioning, with increasing IQ and communication skills associated with an increased ability to live independently. Some people with autism are able to develop their communication and social skills to a degree that allows them a fair degree of independence. Others can learn some skills but still require ongoing support from their family and others throughout their lives. There is no cure for autism. Can Autism Be Prevented? There is no known way to prevent autism. Research into the genetics of autism may eventually offer interventions that can correct genetic errors before the signs and symptoms of autism develop. Where Can I Get Information about Support Groups and Counseling for Autism? Having a child diagnosed with autism can be a devastating experience for many parents and families. They may feel frustrated, confused, and afraid-they may even "grieve" for their "normal child." Living with autism presents many new challenges for the person with autism and for his or her family and friends. Parents of autistic children certainly have many worries. They wonder if their children will be able to achieve, if they will be able to be independent, and if they will be able to be happy and enjoy life. Parents also probably have many worries about how the autism will affect them and their ability to live a normal life, that is, to care for their family and home, to hold a job, and to continue the friendships and activities they enjoy. Many people feel anxious and depressed. Some people feel angry and resentful; others feel helpless and defeated. For most people who have a child with autism, and even for some with autism themselves, talking about their feelings and concerns helps. Friends and family members can be very supportive. They may be hesitant to offer support until they see how you are coping. Don't wait for them to bring it up. If you want to talk about your concerns, let them know. Some people don't want to burden their loved ones, or they prefer talking about their concerns with a more neutral professional. A family therapist, social worker, counselor, or member of the clergy can be helpful if you want to discuss your feelings and concerns about your child's autism. Your health care practitioner should be able to recommend someone. Many people who have a child with autism are profoundly helped by talking to other people in the same situation. Sharing your concerns with others who have been through the same thing can be remarkably reassuring. Support groups for families affected by autism may be available through the organizations providing treatment and education for your child. For information about support groups in the area for families with an autistic child, contact the following organizations: Reviewed on 1/2/2020 Arehart-Treichel J. Autism treatment arsenal expands, with more options on horizon. Psychiatric News 2010 May 21; 45(10): 20. Williams E. A comparative review of early forms of object-directed play and parent-infant play in typical infants and young children with autism. Autism 2003; 7; 361-377.

<urn:uuid:03cd5893-9ccd-485f-a559-c6406b8bc534>

Toddlers have behavioral characteristics that often present challenging situations for parents and/or caregivers. Describe challenges parents and/or caregivers would encounter with these specific characteristics. · Nutritional Barriers Response Post: What types of anticipatory guidance should the nurse provide for parents of toddlers who refuse to eat? What additional support should the nurse provide to parents of toddlers that are temperamental and act out frequently? Explain why music is often more effective than words for preschool children. * What activities would you use with children to develop their phonological awareness? * Explain how you have (or could have) used music to promote your own cognition or memory. * How can the use of music help in developing literacy, math and the social sciences in the early childhood classroom?

<urn:uuid:afbf2f7e-9b15-475a-b110-d77d5c6f0301>

Scales are probably one of the most difficult insects to control because of their protective covering. There are many species of scales, but they can all be categorized as either soft or armored. Soft scales are tropical insects and are economically more important than armored scales in the greenhouse. They are larger in size than armored scales and the protective shield can’t be separated from the insect body beneath. Soft scales have a wide host range among the bedding and foliage plants. Common greenhouse scale species include the brown soft scale (Coccus hesperidum), hemispherical scale (Saissetia coffeae), and nigra scale (Parasaissetia nigra). Ferns, orchids, schefflera, crossandra, zebra plant, weeping fig, citrus, ivy and holly are the common hosts. Armored scales, as the name implies, have a hard, waxy shield. They rarely present a problem in greenhouses, but can be a concern in interior plantscapes and conservatories. Appearance: Female soft scales are what you typically think of when you think of a scale insect. They lack any recognizable body parts and are grey, brown or black and smooth and measure 1∕4 inch in diameter. Young adults are lighter in color, but soon darken as they mature. The adult male scale resembles a tiny pale gnat, but they lack mouthparts and cannot feed. Brown soft scales are oval and flattened and pale in color with a grid-like pattern. Hemispherical scales, in contrast, are circular, convex, shiny, and brown, while the nigra scale can vary in appearance depending on its host. Symptoms and Effects: Like other members of the order Homoptera, scales feed by sucking plant sap. Some scales inject toxins as the feed, further compounding the damage. Yellowed leaves and distorted foliage are indications of scale infestations. With soft scale infestations, honeydew (a clear, sticky plant sap) and sooty mold are also present. Life Cycle: Female scales produce 50 to 200 eggs or live young depending on the species. Nymphs emerge from eggs in one to three weeks. The nymph stage is called a crawler and is the only mobile life stage. Upon hatching, they immediately begin their search for a suitable host plant. Nymphs undergo three instars before settling and a hard or waxy covering envelops the females. At this point the female’s body degenerates into a feeding sack beneath the scale cover. Scouting Suggestions: Visually inspect the lower leaf surfaces and stems for the presence of scales. Yellowed foliage may indicate that a closer look is warranted. Be sure to inspect all new plant shipments thoroughly for signs of scales. Ants may be present if copious amounts of honeydew have been secreted. Parasitized scales will be darker in color and have one or more holes in the shield. Non-Chemical: Remove and destroy all heavily infested plants. Wash off honeydew and dislodge crawlers with water sprays. Inspect all new plant material on arrival. There are many natural enemies of soft scale, but few are commercially available for greenhouse use. For information on biological control, refer to NCR publication 581 “Biological Control of Insects and Other Pests of Greenhouse Crops”. Chemical: There are several insecticides available for control of scales. Refer to UW-Extension publication A3744 “Insect Pest Management for Greenhouses” for a complete listing of available products. If there are two or more adult scales or a large number of crawlers per leaf, spot treat affected plants. You will need two to three applications at 10 day intervals to effectively control the population. If you are using natural enemies to provide some control of scale outbreaks, avoid the use of broad spectrum insecticides as these will also kill the beneficial insects. The insect growth regulators such as azadirachtin and soaps are very effective at controlling soft scales. For more information on scales: See UW-Extension Bulletin A3744, or contact your county Extension agent. © 2020 the Board of Regents of the University of Wisconsin System doing business as University of Wisconsin-Madison Division of Extension. An EEO/Affirmative Action employer, University of Wisconsin-Madison Division of Extension provides equal opportunities in employment and programming, including Title IX and ADA requirements. This document can be provided in an alternative format by calling Brian Hudelson at (608) 262-2863 (711 for Wisconsin Relay). References to pesticide products in this publication are for your convenience and are not an endorsement or criticism of one product over similar products. You are responsible for using pesticides according to the manufacturer’s current label directions. Follow directions exactly to protect the environment and people from pesticide exposure. Failure to do so violates the law. Thanks to Phil Pellitteri and Lis Friemoth for reviewing this document. A complete inventory of University of Wisconsin Garden/Farm Facts/Pest Alerts is available at the University of Wisconsin-Madison Division of Extension Plant Disease Diagnostics Clinic website: https://pddc.wisc.edu.

<urn:uuid:0af4aeb6-fce6-496e-8690-ac361b200d1d>

# Nobody likes this one? ... [ Follow Ups ] [ Post Followup ] [ Main Message Board ] [ FAQ ] Posted by Joel on October 12, 2002 at 12:51:35: In Reply to: Re: Area problem (sorry, my other post was messed up because my angles were interpreted as HTML tags- I hope this one will be clearer) posted by Joel on October 11, 2002 at 17:14:03: : : Huge triangle ABC has an area of 20,000,000 square feet. : : D is on AB, E is on BC and F is on CA. : : AD = 1/16th of AB, BE = 1/16th of BC, CF = 1/16th of CA. : : Find area of triangle DEF. : : Thank you. : I will get you started. : 1. Draw a picture. Obviously you could put A, B and C anyplace, but it will be easier to see my explanation if we are both looking at the same picture. So, I put A at the top, B at the right end of the base, and C at the left end of the base. Now put D, E, and F as described in your problem. Next, drop a line from A, perpendicular to BC, meeting BC at point G. Also drop a line from F perpendicular to BC, meeting BC at H. : 2. Let's call the length of BC = a, AC = b, and AB = c. Let's call the height AG = h, and the height of the small triangle (FEC) FH = x. : 3. Notice that the two triangles FEC and ABC share the same angle {< ACB}. What is the sine of that angle? sin{< ACB} = h/b = x/((1/16)b) : Think about that & you will see that you now have enough information to calculate the area of triangle FEC. : You can calculate the areas of triangles EDB and DFA by the same method. : Then what? : Got it? h/b = x/(b/16) x = h/16 and since CE = (15/16)a .....[a=BC in my drawing] area of triangle FEC = (1/16)*(15/16)*20,000,000 The same applies to triangles EDB and DFA so the area of triangle DEF = 20,000,000*(1-(3/16)(15/16)) = 20,000,000*(211/256) = 16,484,375 Name: E-Mail: Subject:

crawl-data/CC-MAIN-2013-48/segments/1386164758033/warc/CC-MAIN-20131204134558-00098-ip-10-33-133-15.ec2.internal.warc.gz

Advanced Statistical Analysis: Adam J. McKee, Ph.D. This content is released as a draft version for comment by the scholarly community. Please do not distribute as is. What is Regression Analysis? In its most basic form (the one you may remember from an undergraduate statistics course) a regression line is a line drawn through a field of dots on a scatter plot. In this form, regression analysis is hard to differentiate from correlation. The precise location of the “regression line” using mathematics rather than “eyeballing it” with a ruler is about as far as we go as undergraduates. Recall from your early studies of basic correlation coefficients (such as Pearson’s r) that correlations can be used to establish a relationship between two variables as well as indicate the strength (magnitude) of those relationships. Also, recall that Pearson’s useful r statistic has its limitations. Perhaps the most important (in the sense of being a limitation to what the researcher can accomplish) is that both X and Y must be measured at the interval/ratio level, only a single pair of variables can be considered, and the relationship between those two variables must be adequately represented by a straight line. Regression analysis is a powerful research tool because (with some effort) we can circumnavigate most of the problematic limitations of simpler correlations. In an overarching sense, the most important task of regression analysis is to provide researchers with the ability to empirically verify theoretical concepts. Always keep in mind that quantitative social research begins with real-world observations that are stored as numbers. Many researchers view regression analysis as the most important tool for examining and evaluating those numerical representations of reality in a systematic way. One way to view regression analysis is as a technique for using independent variables (IVs) to explain the level of a dependent variable (DV) by deriving (with a computer!) coefficients for each independent variable. These coefficients are very similar to the correlation coefficients that you learned about as an undergraduate. (There are some important differences that we will delve into in later sections). Most of the time, researchers perform these regression tasks using sample data in order to glean the probable characteristics of populations. Because of this, regression can be classified among the inferential statistics and lends itself to hypothesis testing. Perhaps the best way to understand regression analysis is to first understand what it is that researchers can do with it. There are many different purposes for using regression analysis in research, but most of them are related to one (or more) of several broad functions. The first major function of regression analysis is what has been referred to as “control modeling.” Recall that most research questions (and the resulting hypotheses that researchers develop) are about relationships between variables. Crime is an example of a research problem (a social phenomenon society wants to explain, predict, and ultimately control). Many criminologists have proposed that poverty is a proximate cause of crime. The theoretical waters become muddied when we consider that while poverty may well exert an influence on criminality, other variables are likely at play. We know, for example, that gender plays a large role in criminality, especially violent crime (the species that society most wants to control). Specifically, males commit violent crimes at a much, much higher rate than do females. When testing the relationship between poverty and crime, a researcher might want to remove (control) for the effects of gender. In other words, regression analysis allows the researcher to subtract the “effect” of gender before examining the relationship between crime and poverty. The IV that the researcher is primarily concerned with is often referred to as the “variable of interest” and the independent variables that the researcher will control for in the analysis are referred to as “control variables.” You may remember from a basic statistics course that when more than one independent variable is considered at the same time (such as with a two-way ANOVA), the researcher must consider interaction effects. Often, researchers find that the interaction effects in the model being tested are more interesting than the original relationship under study. Recall that when there is an interaction effect between two (or more) variables, the level of one IV depends on the level of the other IV. Regression provides several different approaches to examining these interaction effects. Often, techniques are used that consider the effects of an IV on different subgroups. We will delve deeper into these variations on the method in later sections. As previously mentioned, regression analysis is often categorized among the inferential statistics. This is because regression analysis lends itself to statistical hypothesis testing, which is the inferential process of estimating coefficients for variables in the population using sample data. Recall the basic assumption of social science that hypotheses are only supported and never proven. The logic is that new evidence may arise to disprove an accepted hypothesis. (This also works in the natural sciences—physicists thought Newton’s laws were essentially ‘proven’ until Einstein showed that they were merely a special case of a much broader set of rules). Regression analysis is such a powerful tool in part because it allows the researcher to test several different types of hypotheses. This helps one to understand the logic of considering regression a multivariate technique—hypotheses about different variables, different sets of variables, and overall models can be included in a single analysis. File Created: 08/24/2018 Last Modified: 08/24/2018 This work is licensed under an Open Educational Resource-Quality Master Source (OER-QMS) License.

<urn:uuid:bbf845e6-db99-494b-84a1-3c4994e2643b>

### Host.'s blog By Host., 10 years ago, 296A — Yaroslav and Permutations Note that after applying the operations of the exchange, we can get any permutation of numbers. Not difficult to understand that the answer is "YES", if you can place a single number that it would not stand in the neighboring cells. Thus, if a some number is meeted C times, it must fulfill the condition C <= (n +1) / 2. 296B — Yaroslav and Two Strings We solve the inverse problem: count the number of ways to make comparable pair. To start count the number of ways to make the first line of less than equal to the second. This number equals the number of ways to do this for each item individually as they are position independent. Let's count the same amount, but when the second line-less equal to the first. And similarly to count the number of ways to make two lines equal. For each character values ​​can be considered as a simple cycle. Now we take the value of 10 to the number of question marks in the input file and subtract the answer to the inverse problem, it will be the answer. 295A — Greg and Array In order to add the value of d in the interval [x, y] is sufficient to have an array of values ​​of b and put b [x] + = d b [y +1] — = d Next in a single pass through the array of easily reduced the numbers. We apply this method twice: first for the query, and then operations (knowing how much time we will fulfill it.) 295B — Greg and Graph To solve the problem, we must thoroughly understand the principle of the Floyd algorithm. A general view of the Floyd algorithm: for (k = 1; k <= n; k + +) for (i = 1; i <= n; i + +) for (j = 1; j <= n; j + +) a [i] [j] = min (a [i] [j], a [i] [k] + a [k] [j]); That is, at each step, we try to flow the way across the top of K. We will not remove the top, and add (going from the end). At each step, we will try to flow the way between all the nodes through the new. Thus we get a solution that works in cubic time. 295C — Greg and Friends Note that at each step we are interested in only the position of the boat (number of banks) and the number of people 50 and 100 weight on each shore. With that number of people on one side is completely determined by the other. To find the minimum number of crossings will be used wave algorithm based on this condition. To find the number of ways to add just the sum of all transitions in the state transition will move all the way from one state to another by multiplying the number of ways to choose the people who need to move from one state to another. 295D — Greg and Caves We use the dynamic programming: dp [i] [j] — how many ways there are to construct a figure that the line will be exactly i j columns of black cells are occupied, and everything in between. In this case, the shape should not decrease (in other words, we take only the upper part of the figure). How to make the transition? Note that dp [i] [j] = 1 + dp [i-1] [2] * (j-1 2) + ... + Dp [i-1] [l] * (j-l +1) + ... + Dp [i-1] [j]. We rewrite it: dp [i] [j] = 1 + dp [i-1] [2] * j + ... + Dp [i-1] [l] * j + ... + Dp [i-1] [j] * j — dp [i-1] [2] * 1 — dp [i-1] [3] * 2 — ... — Dp [i-1] [j] * (j-1). Clearly, if the make partial sum, the data value is considered as very simple. How to calculate the full response: we will sort out the maximum number of suitable t (indicated in the condition). Now, the only difference is that the following line should contain strictly fewer columns. That is, we have a similar transition, with -1 term. Also note that fixing the "foundation" we must multiply the number of ways for a number of ways to place it on the plane, that is the basis of width j, we can put (m-j +1) ways. 295E — Yaroslav and Points Learn how to solve the problem of finding the sum of the distances between points. If paint, what happens when you add one point, then we get the formula: x_i * (2 * in) Where x_i — sorted coordinates, and n is the total number of points. Let us learn to know the answers to the two segments of points to know the answer to their association. It is clear that for the calculation of such information need only add two response and adding the sum of the first coordinate set multiplied by a certain number, and and add the sum of the second set of coordinates multiplied by some, perhaps another number. Thus knowing the answers to some segments of the overall response. We will use the root decomposition or Cartesian tree for the storage of such segments. It is not difficult to understand that the insertion and deletion is done quickly enough for these structures. For example, for the root decomposition can be every time just cut and paste the desired point in the intervals, and if the set was contain long stretches or many segments, then simply reconstruct it again. Asymptotics of the solution does not change. • 0 | Write comment?

crawl-data/CC-MAIN-2023-06/segments/1674764500255.78/warc/CC-MAIN-20230205130241-20230205160241-00142.warc.gz

Sea ice around Antarctica. Credit: John Turner/British Antarctic Survey The term "sea ice" has been sending shivers down many spines with the growing threat of global warming, but many non-scientists still misunderstand what sea ice really is. Sea ice is a thin, fragile, solid layer of frozen ocean water that forms in the Arctic and Antarctic oceans. Not to be confused with icebergs, which are made of fresh water from compacted snow, salty sea ice is perhaps the most dangerous symptom of the Earth's rising temperatures. Sea ice forms on the ocean's surface in chilly temperatures, starting as a thin slate of crystals that grow outward into a sheet of salty ice. Then the sea ice grows downward and thickens. Sea ice is mobile winds and ocean currents often push it around on the surface of the ocean. Although many might suspect that all salinity would be lost in the icing process, if one were to eat sea ice, it would taste very salty! Salt particles are trapped in the ice crystals as they freeze. Although sea ice normally melts in the warmer summer months, global warming is further affecting its formation. As climate change heats the upper ocean, sea ice will begin melting from below at more rapid and dangerous rates. The volume of Arctic sea ice has been shrinking for the past 30 years, according to the National Snow and Ice Data Center. This has forced more broken pieces of ice to float in our oceans and seas, which is dangerous because it raises worldwide sea levels. Arctic sea ice helps to keep the polar regions cool and helps moderate the global climate. Because sea ice has a bright surface, 80 percent of the sunlight that strikes it is reflected back into space. But when sea ice melts, it exposes the dark ocean surface, which reflects less light and causes Arctic temperatures to rise further. Changes in the Arctic can influence weather globally, and small temperature increases at the poles lead to greater warming of the Earth over time. Today's Arctic sea ice coverage is at its lowest since 1979, and the National Oceanic and Atmospheric Administration anticipates further loss of Arctic sea ice in the next 30 years. The amount of sea ice affects the salinity of the water and the way ocean water circulates around the world, which over time can cause changes in ecosystems all over the globe, according to NOAA. Melting sea ice creates problems for wildlife too because some animals in the Antarctic rely on melting sea ice for hunting and survival. Polar sea ice undergoes changes every year. During the winter, the Arctic ice pack grows to the size of the United States. In the summer, half of the ice disappears. In the Arctic, sea ice is about 10 feet (3 meters) thick on average, while ice at the South Pole averages one mile (1.6 kilometers) thick. For most of the year, sea ice is typically covered by snow. - Whatever Happened to the Hole in the Ozone Layer? - What Causes the Aurora? - What's the World's Biggest Glacier? Lily Norton is a contributing writer for Life's Little Mysteries, a sister site to OurAmazingPlanet.

<urn:uuid:892cfafc-3083-4dcc-92c6-e640b21d02ab>

(CNN) -- Scientists hailed Tuesday a 47-million-year-old fossil of an ancient "small cat"-sized primate as a possible common ancestor of monkeys, humans and other primates. The fossil is believed to be an ancestor of monkeys, humans and other primates. Scientists say the fossil, dubbed "Ida," is a transitional species, living around the time the primate lineage split into two groups: A line that would eventually produce humans and monkeys, and another that would give rise to primates such as lemurs. The fossil was formally named Darwinius masillae, in honor of the anniversary of Charles Darwin's 200th birthday. "This is the most complete primate fossil before human burial," said Dr. Jorn Hurum, of the Natural History Museum at the University of Oslo, who led the study of the fossil, a young female primate. "And it's not a few million years old; it's 47 million years old," Hurum said, speaking at a news conference at the American Museum of Natural History in New York. The fossil was discovered in 1983 in the Messel Pit, Germany, near Frankfurt, and had been until recently in private collections, according to an article published Tuesday in the scientific journal PLoS ONE, a publication of the Public Library of Science. Read the report from PLoS ONE However, because it was split into two parts, its significance was not immediately recognized. An international team of scientists, which Hurum led, conducted a detailed forensic analysis of the fossil for the past two years, the release said. Hurum nicknamed the fossil Ida after his young daughter, he said. The fossil's body is nearly complete; only part of one leg is missing, according to Hurum. In addition to the bones, the softer features are also preserved, as are the remnants of its last meal: fruits, seeds and leaves, which were found in Ida's gut, according to the scientists. "It's such a beautiful specimen," Hurum said of Ida. He said the fossil is about 2 feet long, "like a small cat in size." The fossil has both adult and baby teeth, indicating that it was weaned and about 9 months old when it died, the PLoS article said. She would have eventually grown to the size of a lemur, the article said. The young primate fossil does not have two crucial anatomical features found in lemurs: a grooming claw on the second digit of its foot and a fused row of teeth in the middle of its lower jaw, known as a toothcomb, the scientists said. X-rays revealed a broken wrist, which the team of scientists believe may have contributed to Ida's death, according to a news release from the museum at Oslo. Ida may have been overcome by carbon dioxide gas while drinking from the Messel lake, which was often covered by a low-lying blanket of the gas, the news release said. Hampered by the broken wrist, the young primate may have fallen into unconsciousness and may have slipped into the lake. The primate sunk to the bottom and was preserved for 47 million years, the news release said. All About Paleontology

<urn:uuid:058369da-28a1-48aa-9906-f62fde3ab383>

For the second step we consider x 0 Choose an integer k such that k x Then we # For the second step we consider x 0 choose an integer This preview shows page 7 - 10 out of 10 pages. For the second step, we consider x 0. Choose an integer k such that k > | x | . Then we apply the same argument above to the positive number x + k and y + k to conclude that x + k < q < y + k for some rational number q . Then r := q - k satisfies x < r < y . Corollary 0.4 Let x, y R with x < y . There exists an irrational number w such that x < w < y. Proof: By Theorem 0.3, there exists a rational number r such that x 2 < r < y 2 . It follows that x < r 2 < y , and w := r 2 is irrational. Now we can show Theorem 0.5 Let p be a prime number. Then p R , i.e., there is a positive x R such that x 2 = p . 27 Proof: Step 1. Define x Let S := { r R | r > 0 , r 2 < p } . The set S is non-empty. Also, since r 2 < p < p 2 , it implies that r < p , i.e., S is bounded above. By the completeness axiom, x := sup ( S ) exists in R . It remains to show that x 2 = p . It suffices to show that neither x 2 < p nor x 2 > p can hold. Step 2. Show x 2 < p cannot hold We want to find a large integer n such that 3 x 2 < x + 1 n 2 < p, i.e., to find an integer n such that x 2 + 2 x n + 1 n 2 < p, i.e., x 2 + 1 n 2 x + 1 n < p, i.e., to find an integer n such that x 2 + 1 n 2 x + 1 < p, i.e., 1 n < p - x 2 2 x + 1 . Here we use p > x 2 to imply p - x 2 2 x +1 > 0. In other words, n > 2 x + 1 p - x 2 . We have found the integer n . Step 3. Show x 2 > p cannot hold We want to find a large integer m such that p < x - 1 m 2 < x 2 , i.e., to find an integer m such that p < x 2 - 2 x m + 1 m 2 < p, 3 If this is true, then sup ( S ) x + 1 n , which is a contradiction with the fact = sup ( S ). 28 i.e., p < x 2 - 1 m 2 x - 1 m < p, i.e., to find an integer m such that p < x 2 - 1 m 2 x - 1 < p, i.e., 1 m < x 2 - p 2 x - 1 , i.e., m > 2 x - 1 x 2 - p . We have found the integer m . Appendix. Problems did in the class 3.3.1. True or false: (a) If a non-empty subset of R has an upper bound, then it has a least upper bound. (b) If a non-empty subset of R has an infimum, then it is bounded. (c) Every non-empty bounded subset of R has a maximum and a minimum. (d) If m is an upper bound of S and m 0 < m , then m 0 is not an upper bound of S . (e) If m = inf ( S ) and m 0 < m , then m 0 is a lower bound of S . (f) For each real number x and each > 0 , there exists n N such that n > x . Solution: (a) Yes. By the definition of least upper bound. (b) False. For example, S = N . (c) False. For example, S = (0 , 1). (d) False. For example, S = [0 , 2], m = 4 and m 0 = 3. Here m 0 < m but m 0 still is an upper bound. (e) True. By the definition of inf ( S ). (f) True. If x 0, we are done. If x > 0, by Theorem 3.3.10(a), there is n N such that n > x , i.e., n > x . 3.3.6b. Suppose that m and n are both maxima of a set S . Prove m = n . Proof: We have m n 29 because n = max ( S ) and m S , and n m because m = max ( S ) and n S . Then m n and n m ⇐⇒ m = n. #### You've reached the end of your free preview. Want to read all 10 pages? • Fall '08 • Staff

crawl-data/CC-MAIN-2020-45/segments/1603107883636.39/warc/CC-MAIN-20201024135444-20201024165444-00572.warc.gz

# What Is a Adjacency Matrix in Data Structure? // Larry Thompson A Adjacency Matrix is a fundamental data structure used in graph theory to represent the connections between vertices in a graph. It provides a concise way to store and retrieve information about the relationships between different elements in a graph. In this article, we will delve into the details of what an adjacency matrix is and how it is used. ## What is a Graph? Before we dive into adjacency matrices, let’s first understand what a graph is. In computer science, a graph is a collection of nodes (also known as vertices) that are connected by edges. These nodes can represent various entities, such as cities in a transportation network or web pages on the internet. The edges represent the relationships or connections between these nodes. ## Understanding Adjacency Matrices An adjacency matrix is a square matrix that represents the connections between vertices in a graph. It provides an efficient way to store information about which vertices are adjacent to each other. The rows and columns of the matrix correspond to the vertices of the graph, and each cell in the matrix indicates whether there exists an edge between two vertices. Let’s consider an example to illustrate how adjacency matrices work. Suppose we have a simple undirected graph with 4 vertices labeled A, B, C, and D. The adjacency matrix for this graph would be: • A B C D • A 0 1 1 0 • B 1 0 1 1 • C 1 1 0 0 • D 0 1 0 0 In this example, there is an edge between vertex A and vertex B (indicated by the “1” in cell [1,2]), as well as between vertex B and vertex C (indicated by the “1” in cell [2,3]). The absence of an edge is represented by a “0” in the corresponding cell. Adjacency matrices offer several advantages when it comes to representing graphs. Firstly, they provide a compact way to store graph information, especially when the graph is sparse (i.e., has relatively few edges compared to the total number of possible edges). This is because only the cells corresponding to existing edges need to be stored. Secondly, adjacency matrices allow for efficient retrieval of information about graph connectivity. Checking whether two vertices are adjacent can be done in constant time by simply accessing the corresponding cell in the matrix. While adjacency matrices have their benefits, they also come with some drawbacks. One major disadvantage is their space complexity. For large graphs with many vertices, the size of the matrix can become prohibitively large. This can lead to significant memory consumption and reduced performance. Additionally, updating an adjacency matrix can be computationally expensive. Adding or removing an edge requires modifying multiple cells in the matrix, which takes time proportional to the number of vertices in the graph. ## Conclusion In summary, an adjacency matrix is a powerful data structure for representing graph connectivity. It provides a concise and efficient way to store information about relationships between vertices in a graph. Despite its limitations in terms of space complexity and update operations, adjacency matrices remain widely used due to their simplicity and effectiveness.

crawl-data/CC-MAIN-2023-40/segments/1695233511106.1/warc/CC-MAIN-20231003124522-20231003154522-00864.warc.gz

Our transcription: The cloud of material from which the planets formed started out as being mostly gas with a small amount of dust. That dust was very fine indeed, but the particles collided with each other, and during those collisions they stuck with each other, so that materials started to coagulate into still bigger bodies, so you have to imagine that we went from dust particles all the way up to objects that were kilometers across. Those objects were colliding with each other making still bigger bodies, so that we think of the formation of solid planets like the Earth as being a hierarchical process, a process that starts off with very small things, very large in number, towards intermediate sizes things, smaller in number, and eventually ending up with a very small number of large objects. As an intermediate stage in this process, we could imagine that the region where the Earth formed contained hundreds of objects that were about the size of the Earth's moon. Most of those objects, then, coalesced to make a single planet, the Earth.

<urn:uuid:0cc32c33-fc33-4ef7-ad9b-3ea025a4e0e2>

+0 # using the pythagorean theorem 0 42 1 What is the approximate perimeter of triangle DEC is rectangle ABCD has a length of 4.6 cm? Mar 7, 2021 #1 +31212 +1 Right triangle with equal leg lengths     leg length = 1/2 of 4.6 = 2.3 pythag theorem to find hypotenuse     =     sqrt ( 2.3+ 2.32) = 3.25 two legs at 3.25   long + 4.6 cm = 11.1 cm   perimeter Mar 7, 2021

crawl-data/CC-MAIN-2021-17/segments/1618039491784.79/warc/CC-MAIN-20210420214346-20210421004346-00271.warc.gz

What inequality looks like Although currently undergoing a period of economic setback and political crisis, Brazil has experienced remarkable prosperity and growth in the past two decades. The world’s seventh-largest economy, the country is rich in natural resources and in cultural and environmental diversity. Since Brazil’s democratization in the 1980s, it has built a vibrant democracy based on a rights-oriented constitution. Brazil is increasingly seen as a key player on the world stage, wielding influence in the global economy and international relations. It has made impressive social and economic gains through policies designed to combat racial and gender discrimination and move its people out of poverty. But those gains must not be taken for granted. Deeper changes are needed to ensure equity and opportunity for all the country's people—and to maintain and deepen democracy, transparency, and participation. Brazil still ranks among the 20 most unequal countries in the world: Much of its wealth remains highly concentrated, while millions remain mired in poverty. Discrimination based on gender, race, or sexuality continues to limit the full inclusion of many groups—particularly Afro-Brazilians, who constitute more than 53 percent of the population—in the key institutions of society. Crime and violence kills thousands of black and indigenous Brazilians every year, and land ownership remains largely in the hands of the rich and powerful. Confronting exclusion, expanding justice Brazil’s increased global prominence and wealth have created real opportunities for positive change—and a clear appetite for it. A generation of young Brazilians who have grown up in an era of democracy and economic growth are lifting up their voices to demand accountability, transparency, and respect for rights. Creatively using new technologies in an increasingly networked society, they are determined to be heard. Brazil needs stronger policies to ensure that all people benefit from the country’s abundance. All Brazilians must be able to participate in creating a stronger democracy, one in which underrepresented groups see their rights protected and the advantages of progress are available to all.

<urn:uuid:36086454-713c-4b06-a8f3-de5a5ead8ede>

SCTP and BGP The Border Gateway Protocol, BGP, is the routing glue that holds the It provides reachability information across all Internet Service providers, subject to complex policy constraints, so that end systems (host computers like the one you are reading this dcument on) can communicate each other. Packets flow using the Internet Datagram Protocol, which simply offers a best effort delivery from A to B. Routers between A and B look at the destination address in the header control information in datagrams (a.k.a. packets) to figure out where they go next, based on forwarding tables that they build, based on the information they learn from BGP. The Transmission Control Protocol, TCP is the end-to-end protocol that is used by pretty much all applications (e.g. web brosers talking to web servers, or skype users talking to each other) to provide reliability, flow control and congestion control, on top of the Internet Datagram Protocol. Only the end systems look at the TCP header control information. They use it to figure out what function a packet has (data, acknowledgement) and where it fits in a sequence of packets (or if it doesnt), and whether to speed up or slow down to allow the other end Border routers use TCP to connect to each other, because the routing messages that they exchange with each other, to allow them to compute the reachability information, to allow them to build the forwarding tables, to allow them to forward the users' data packets (TCP/IP), to let everything work, have to be delivered in order, reliably, and with flow control. Recently, a new transport protocol, SCTP has been devised, which allows for a few new end-to-end functions to be offered as well as the ones TCP providers; these include: multi-homing; connection migration; multiplexing of data objects between different threads over a single transport session; and others. Recently, people have noticed that BGP is rather complex. Part of this compelxity is that (border) routers need to know whether their neighbours are working ok, and if not, take action. This may be implicit in the silence of a neighbour (shades of Assault on Precinct 13) Some people would like to re-engineer BGP to be more modular, so that there are way s to replace components of BGP cleanly - one thing to do would be for BGP neighbours to exchange messages using SCTP instead of TCP, as this might be more tractable. This project, should you choose to accept it Jim, is to i) analyse the BGP specifications and see how embroiled the use of TCP is in them. Extract the relevant pieces and see if the system can be respecified using SCTP instead. ii) Take a BGP public domain implementation and a public domain SCTP implementation, and design, build and test a system of BGP routers, under test load, to see if the system operates correctly. and of course, see how the performance changes (if at all). iii) report on all the above, to see if the design and implemention are any cleaner Contact: Jon Crowcroft GIST Overlay Networking Extension (GONE) Design: Using GIST on SCTP with HIP addresses, and k-ary neighbour we build an overlay architecture of SCTP use GIST and SCTP features to achieve ii) fault detection and recovery iii) HIP style addressing Evaluation should be of a) how well does SCTP/GIST work for this (e.g. compared to a pure TCP overlay or MIT's RON)? b) how well do the recovery schemes work c) maybe, how resilient is the architecture (given security designs in SCTP and GIST) to things like DDoS attacks... One question that is open, at least, is what is the expected workload/use to measure this under? Contact: Jon Crowcroft A world of MIRRORS Mobile ad hoc networking have been an active research are for a decade, and the evaluations of many protocol proposals rely on simulations. These in turn depend on suitable models, especially of radio frequency propagation and mobility. Unfortunately, the simulation models to date are unsatisfactory, largely due to their lack of realism. This project aims to develop a tool to generate traces based on the modelling framework MIRRORS. The components and formulations of the models are sketched in the paper, so the project has more focus on implementation. Issues to consider include: i) How to implement the models in an extensible way? ii) How to manage the parameter values - passing them on the command line is not practical due to the number of parameters involved! iii) What to output? Depending on your interests, you could add various 'fun' parts, e.g., a visualiser showing the results, a GUI to allow the user to specify parameter values, or, more useful, trace generators to produce trace files compatible to commonly used simulators. You could identify many steps in this project, each of which can be seen as the completion mark, but producing a truely useful tool is non-trivial. If done right, it will certainly be a well-appreciated contribution to the research community. Contact: Wenjun Hu Car alarm alternative There have been many recent initiatives involving networking with vehicles, either between vehicle or inside a vehicle. This project considers an alternative to car alarms. Observe that a car alarm often accidentally goes off, irritating the people around it rather than reminding the owner. The idea is to let an intelligent car text the owner's mobile (it should be a reasonable assumption that the owner will have one) under such a circumstance, and let the owner reset the 'alarm' remotely using the mobile. An actually system would probably involve some circuitry, but we can start with the software side. Contact: Wenjun Hu Language Models, Scriptability & Abstractions for Network Traffic Almost all applications that process network traffic, both on- and offline, overlap in large parts of functionality: state keeping, packet iteration, filtering, input abstraction, etc. The Netdude framework provides a pluggable architecture that allows authors to leverage efforts made by others to help build new processors with less time, more modularity, and (hopefully) better quality. One aspect the framework currently does not provide is scriptability -- writing C code is still required. This project will involve - investigating the applicability of the Usenix command line paradigm (piping & filtering output from one command into another, etc) to the problem -- the issue here is that some processing requires repeated scans of input (say, to strip incomplete TCP flows from a trace) and jumps in general - where necessary, a requirements analysis for features a purpose-specific scripting language (such as used in Bro or Click) should provide - extend the plugin architecture to purely scripted, single-file plugins (think Emacs or Gimp) that can be accessed from both C and the scripting level, and provide a scripting interface to libnetdude via SWIG. For more information, see Netdude and the corresponding paper. Contact: Christian Kreibich Full-state VM Snapshots Our work on Xen currently has several components which support the snapshot of a running VM. This project would involve combining and synchronising the snapshot of a VM's memory, disks, and other relevant state. Ideally, a final demo would involve a tree-like graphical view of screen-shots of a VM through history, and allow old versions of the VM to be restarted (branching the tree) by clicking on them. Extra work on this project could involve exploring the more challenging issue of concurrently snapshotting a distributed system (i.e. many VMs) running on a set of hosts. The Flying Mouse This project explores a new interface for the PC build out of cheap, common components. Take a pen, attach some coloured LEDs to the end and wire them up to some buttons. Using a webcam, allow the pen to be used as a mouse, by waving it in the air in front of the screen. As LEDs are bright and different colours, image tracking should be relatively straight forward. The implementation should be completely integrated into an OS (preferably Linux or Windows), and so involves a decent range of fun hacking. Students making reasonable progress might consider (a) the addition of a second camera to implement a 3D interface, or (b) integration of some gesture recognition for common tasks. Sort of semi-locally suggested Initial Point of Contact for these is: Jon Crowcroft Project Title: TCP improvements for heterogeneous roaming Mobility impacts every layer of the OSI model. Many efforts have been made towards reducing handover latencies when roaming between two access points belonging to the same technology. Recent results show that it is possible to seamlessly roam between two IEEE 802.11b and keep handoff latencies below 100ms, enabling support for real-time applications on-the-move. However, when roaming is between different access technologies latency values increase considerable, depending on the link-layer characteristics of both radio access technologies. Experimental results, based on Mobile IP, show that vertical handover latency values can be expected to be close to 2.5 RTTs of the technology used for the registration process. To obtain these values we need to use the correct set of optimisations in the network layer. This value of 2.5 RTTs is close to the best that we can do at this layer, without affecting the network side and this is not enough to support Additionally to this value, when the mobile devices deal with TCP connections (i.e. browsing and P2P traffic) there is a significant delay that needs to be considered: the adaptation time. We define adaptation time to be from the point at which the mobile node receives the first packet on the new interface, from the correspondent node, to the point where the new interface's throughput first reaches the value of the average throughput it achieves over the lifetime of the connection. Project: This project will measure, characterise the adaptation time, and propose and implement methods to reduce its impact on the transport layer. The aim is to reduce the overall latency. So far efforts in the IETF have been focused to solve network-layer mobility, but if we want to support seamless mobility we also need to tackle related issues in upper layers such as the transport layer. The main work will be done in traffic analysis and kernel modifications to the TCP/IP stack to implement the proposed methods to reduce the adaptation David N. Cottingham, Pablo A. Vidales, Is Latency the Real Enemy in Next Generation Networks?. First International Workshop on Convergence of Heterogeneous Wireless Networks, July 2005 Further info for this work and contact for Dr. Pablo Vidales, now at DT Labs in Berlin. MCP:- Multicast Copy Program It is often the case you want to copy the same file to multiple other machines. THere are a varieity of techniques. One is based on using IP multicast where available. To this end you also need a reliable multicast delivery layer - thats what MCP does. MCP uses TCP-XM, an extension of TCP to send data to multiple receivers either with multicast or with unicast if multicast is not availble to some of the receivers. The protocol is well specified and a user space implementation exists. This projecyt could do one of two things. First, a kernel version would be nice. Second, deploying it on the physics grid to real users would be interesting. Evaluation would be about performance (either speed, or number of receivers or both). There's quite a lot of implemenation to be done, and then quite a lot of experiments with a range of workloads and underlying network Contact: Jon Crowcroft This year, a net games company in Cambridge has suggested some projects. Initial Point of Contact for these is: Jon Crowcroft Augmented-Reality on Symbian Camera Phones With increasing mobile phone processing power and camera capabilities fast becoming standard, the technology has now reached a level where augmented reality-based applications have become a real possibility. Gameware already possess the required 3D rendering and camera image acquisition technology that can be made available to the student for the The project will investigate the technical constraints involved in implementing augmented-reality technology on today's high-end Symbian-based camera phones. This will involve porting aspects of the open source ARToolKit to Nokia Series 60 camera phones. Part of the project will also require the research and develop of efficient and robust image processing and pattern recognition algorithms suitable for the platform. Evolving Hand-engineered 3D Virtual Creatures Genetic representations for evolvable articulated virtual creatures are often at odds with the requirements of an underlying representation that supports arbitrary hand-designed virtual creatures. For example, evolvable 3D virtual creatures are often represented using recursive or generative genomes; hand-engineered creatures can be simply represented using genomes with a similar structure to the creature morphology. This project will look into how these two requirements could be brought closer together, looking at a number of alternative approaches, such as developing a hybrid genetic representation, or designing a building process that enables relatively free-form building of articulated creatures based on a evolvable genetic representation, or designing suitable pattern- matching cross-over and mutation operations that can operate on a hand- Evaluation of AGEIA PhysX for the simulation of 3D Articulated Systems Physics simulation provides the backbone for realistic virtual creature simulation and believable mixed-reality systems. the AGEIA physX engine (formally Novodex) is a cross-platform (PC, PS3 and Xbox 360) middleware physics simulation SDK that promises significant performance benefits over rival engines through the use of parallel- processing and hardware acceleration. This project will examine the engine's performance and robustness under various conditions. In particular, the simulation of arbitrary-connected articulated powered systems, with the aim to understand the engine's suitability for simulating evolvable 3D virtual creatures. Development will be on a Windows PC. Evolution and Islands Large-scale virtual world simulations can be simulated over a network of distributed servers, each modelling a patch of terrain or a separate island. Servers (such as home PCs or mobile phones) have restricted resources and bandwidth and, in the case of mobile-based servers, the geographical proximity of servers to each other is always changing (a characteristic that could potentially be put to good use). These factors affect the way agents within the environment interact with each other. This project will examine the issues involved in simulating distributed virtual world simulations, investigating the factors such as managing population sizes, suitable migration policies between servers, agent and server loses and latency, changing landscape topologies, etc. Real-time TV Audience Interaction through Mobile Phones Live interactive TV is becoming more commonplace through the use of mobile phones, which are ideally suited for spontaneous and instantaneous communication. For example, the use of SMS for voting or sending messages into live TV shows is becoming quite popular. 3G technologies offer benefits such as continuous interaction and individual feedback. This project will research and develop a prototype to demonstrate the principles behind a system enabling mass audiences to interact live with a central server via their mobile phones (e.g. over GPRS). The work will look at the technical requirements of such a system and the constraints that will be imposed on it, such as latency, bandwidth requirements and client- side software requirements.

<urn:uuid:7f5d2f9f-ecb0-4da3-8ce8-f78c341cda17>

Learning disabilities form a set of neurological issues, which are characterized by the inability to take in, accept, or process information (Helpguide.org). They limit success in particular life areas. They are not treatable by medication. Could be treated by intervention methods. Learning disabilities are not the same as low intelligence. Could affect a person’s reasoning, motor skills, calculation, and language. Learning disabilities are characterized by a person’s difficulty in one or more of the stages of information processing, namely, input, integration, memory, and output. A person with learning disability would not be able to take in and record information, interpret information, store and retrieve information, or reproduce information through either language or motor activity. Learning disabilities have different classifications, which include academic skills disorders, speech and language disorders, and other disorders (Helpguide.org). Mother’s use of dangerous substances such as drugs, alcohol, or tobacco while the child is in the uterus. Mother’s illness during pregnancy, which could cause damage to the fetus’ brain. Environmental factors such as toxins or poor nutrition. Signs and Symptoms Difficulty in understanding instructions or spoken language Delay in identifying or naming colors and objects Difficulty in writing, drawing, or coloring Difficulty in maintaining attention in an activity Difficulty in physical coordination Other symptoms could present themselves as a child grows older (Helpguide.org) Enrollment in a special education class Hiring of a private tutor Having an Individualized Educational Program (IEP) suited for the child Speech and language therapy. These are conditions that limit a person’s ability to communicate through speaking or hearing, which could range from difficulty in saying sounds to being completely unable to understand or speak (MedlinePlus, 2008). · learning disorders · hearing disorders · speech problems · voice problems The effects of learning and/or communication disability are difficult to imagine. They vary from person to person, and could range from lowered self-esteem to academic failure, and even frustration. Despite these grave and adverse consequences of having a learning or communication disability, the possibility of overcoming or managing the disability is not remote. There are measures that could help a person with learning or communication disability to overcome his limitations in communicating or learning. A disability only weakens or affects one area of a child’s development. It does not necessarily impair all his potential to develop (Pediatric Neurology.com). Considering the unique needs of children and adults with learning disabilities, there are initiatives among states to provide assistance, specifically in the form of special programs appropriate for them. Since 2002, under the Learning Disability Program for Tarrant County, there were local trainers in Texas who provide professional development to education staff, to enable them to provide support to people who have learning disabilities. Other support options available in other locations include a school learning support team that helps teachers plan their class programs to suit the specific needs of their students. If there is adequate funding, there are teachers aides employed to assist teachers in handling children with learning disabilities (State of New South Wales through the Department of Education and Training, 2007). Interviews with parents of children with learning disabilities show that parents are very grateful for special programs that help them deal with the special situation of their children. Being new to the condition, they are all at a loss as to the proper way of teaching their children, knowing at the same time that the conditional methods they know in teaching children would not work. Thus, they rely greatly on special education teachers who presumably know better in terms of the approach and technique necessary for the condition of the children. Grigsby, J. S. (2006). Building Bridges to Success: The Tarrant County Learning Disability Program. Retrieved February 9, 2008, from http://www- tcall.tamu.edu/newsletr/dec06/dec06c.html Helpguide.org. Learning Disabilities: Understanding the Types, Causes, Symptoms, and Diagnosis. Retrieved February 9, 2008, from http://www.helpguide.org/mental/learning_disabilities.htm MedlinePlus. (2008). Speech and Communication Disorders. Retrieved February 12, 2008, from http://www.nlm.nih.gov/medlineplus/speechandcommunicationdisorders.html Pediatric Neurology.com. Learning Disabilities. Retrieved February 12, 2008, from http://pediatricneurology.com/learning.htm State of New South Wales through the Department of Education and Training. (2007). Learning Assistance Program. Retrieved February 9, 2008, from http://www.schools.nsw.edu.au/studentsupport/programs/lrngdifficulty.php

<urn:uuid:01f413c2-b201-4569-b401-b83dd1bdf055>

Images of the intense flooding around the United States this week brought to mind this Mississippi Department of Archives and History Flickr set, which collects flood images taken by photographers for the Illinois Central Railroad Company during the Mississippi River floods of 1927. In the spring of 1927, rains that were much heavier than usual overloaded the tributaries of the river. As historian Pete Daniel points out, “the cumulative tinkering of humans”—logging, farming—combined with the abnormal rainfall to create disastrous conditions. Levees broke, and, in the end, more than 16.5 million acres flooded in seven states. The flood dislocated 637,000 people and killed between 250 and 500. The railroad’s “flood committee” was sent to examine damage along the train lines in the Mississippi Delta. The images capture the coping strategies of citizens trying to save infrastructure and belongings from rising waters, as well as the racial injustices that the emergency circumstances had exacerbated. The flood committee’s trip map, which charts the stops of the group as they moved from north to south to assess the damage, shows the extent of the flooding at various times in the spring. In Egremont, Miss., people hauled possessions and livestock up onto the highest point—possibly tracks—near the railroad depot, May 2, 1927. Near Helm, Miss., two members of the committee stand on a partially submerged track, where a group appears to be trying to move a stuck train car, May 9, 1927. Refugees queue in a camp near Cleveland, Miss, April 29, 1927. As John M. Barry writes in his history of the flood, African-American refugee laborers who stacked sandbags on the levees were housed in camps like this one. Often, they were not allowed to leave, since the owners of the plantations where they worked were afraid of losing their tenants. In Greenville, Miss., on April 29, 1927, two citizens pulled their car up onto their porch steps, in hopes of preserving it. A street in Greenville, given over to water, April 20, 1927. View from a railroad water tank, in Leland, Miss., April 30, 1927, showing livestock brought to the highest point and stationed on the tracks.

<urn:uuid:8bf32cc3-b36a-4675-ae61-48d8fba64e20>

Basic mathematical operations include following : 1) Addition 2) Subtraction 3) Multiplication 4) Division. We come across these operations many times. It is a handy skill to pursue while facing various competitive exams. This program provides a stage for practicing these skills. User can select the magnitude of operands from 1 digit ti 4 digits. User can get infinite number of questions through random generation. User can check her/his speed and accuracy all the time. |File Size||27.32 kB| |Operating System||Windows 7 Windows Windows Server 2008 Windows NT Windows Vista Windows 2003 Windows XP|

<urn:uuid:2b9c3ac8-7426-4159-a9bd-06addb505ca6>

In its day, Persia was a superpower to rival Greece and Rome, and conflict between them spanned over a millennium. Through these wars, and trade, these foes learnt from each other, not only adopting elements of military technology, but influences in the arts, architecture, religion, technology and learning. In this beautifully illustrated book, Dr Kaveh Farrokh narrates the history of Persia from before the first empires, through their wars with East and West to the fall of the Sassanians. He also delves into the forgotten cultural heritage of the Persians, spread across the world through war and conquest, which, even after the fall of the Sassanians, continued to impact upon the Western world. The author was awarded the 2008 Persia Golden Lioness Award for outstanding literature for this work. Technorati Tags: Persia, military history, Persepolis, Achaemenid, Parthian, Sassanian, combat, battle,

<urn:uuid:0dc101e4-8b94-4734-a2c8-b8299ff550da>

Often we think of periods as occurring once per month; in fact, the word “menstruation” is from the Latin word mensis, for “month.” While some of us do have periods that occur exactly every month, others have cycles that are longer or shorter. Counting from the first day of one period to the first day of the next, most cycles last between 23 and 36 days. For some, the variation can be even broader. You may have consistently regular cycles (bleeding every 28 or 35 days, for instance), or your cycle may vary in length from one cycle to the next. Hormonal contraceptives or breastfeeding may alter the length of your cycle or even stop them altogether. Cycles may change after a pregnancy, regardless of whether it ended in abortion, a miscarriage, or birth. Most periods last between two and eight days, with four to six days being the average. The flow stops and starts during this time, though this is not always noticeable. The fluid that flows from the vagina during the menstrual period includes much of the uterine lining that has built up during that cycle. In addition to blood (sometimes clotted) and endometrial cells, menstrual fluid contains cervical fluid and vaginal secretions. This mixed content is not obvious, since the blood colors the fluid red or brown. The usual discharge for a menstrual period is about two to five tablespoons, though it often looks like more. For more information, see Stages in the Menstrual Cycle. Very Heavy Periods (Menorrhagia) and/or Irregular Bleeding You may experience a very heavy period if you did not ovulate during a cycle. This happens to all of us occasionally and occurs more often in the teen years, during perimenopause, during times of stress, and after any pregnancy. Heavy periods can also occur if you have fibroids, are using certain IUDs for birth control (the Mirena IUD actually reduces cramps and bleeding), or have an inherited bleeding disorder. The most common inherited bleeding disorder, von Willebrand disease (VWD), affects about one to two percent of the U.S. population and runs in families. While it is often difficult to diagnose, and there is no cure, VWD can be treated. Irregular bleeding — off-schedule menstrual flow — can also be caused by recurrently not ovulating, which can be age-related (again, more common in early teens and perimenopause), or from some health problems or severe stress. Bleeding in early pregnancy, which may or may not progress to miscarriage, can sometimes be confused with a menstrual period and can be light or heavy. Keeping a menstrual calendar can help you develop awareness of what a typical flow is for you (see Charting Your Menstrual Cycle). If you have very heavy periods and/or irregular bleeding, it’s a good idea to talk with a health-care provider, because these can signal serious health problems. For more information, see Abnormal Uterine Bleeding. No Periods and Very Light or Skipped Periods Primary amenorrhea is the condition of never having had a period by the latest age (16) at which menstruation usually starts. Secondary amenorrhea is missing periods after having had at least one. Oligomenorrhea is infrequent, erratic periods. Some causes of amenorrhea and oligomenorrhea are pregnancy; menopause; breastfeeding; heavy athletic training; emotional factors; stress; current or recent use of hormonal birth control methods; excessive dieting, anorexia, or starvation; use of some medications, including chemotherapy; obstruction or malformation of the genital tract; hormone imbalance; cysts or tumors; chronic illness; and chromosomal conditions. Sometimes amenorrhea or oligomenorrhea is caused by a combination of several of these factors.

<urn:uuid:e5879b28-86fe-4c06-8a3c-7efbe8039244>

On May 24, 1543, Polish astronomer Nicolaus Copernicus dies in what is now Frombork, Poland. The father of modern astronomy, he was the first modern European scientist to propose that Earth and other planets revolve around the sun. Prior to the publication of his major astronomical work, "Six Books Concerning the Revolutions of the Heavenly Orbs," in 1543, European astronomers argued that Earth lay at the center of the universe, the view also held by most ancient philosophers and biblical writers. In addition to correctly postulating the order of the known planets, including Earth, from the sun, and estimating their orbital periods relatively accurately, Copernicus argued that Earth turned daily on its axis and that gradual shifts of this axis accounted for the changing seasons. He died the year his major work was published, saving him from the outrage of some religious leaders who later condemned his heliocentric view of the universe as heresy. By the late 18th century, the Copernican view of the solar system was almost universally accepted.

<urn:uuid:b2ab9f35-c14f-46ff-9e6c-3a7e35a3ab90>

# How much Torque? How much torque must the pin exert to keep the rod in the figure from rotating? Calculate this torque about an axis that passes through the point where the pin enters the rod and is perpendicular to the plane of the figure. Known Variables: L: 80 cm or .8m M(of the rod)= 2.0 kg m(of the weight)= 500g or .5 kg The weight of the rod with length L acts as the center of the rod. this means L/2 from the pin The torque about the pin is τ = (mg)L +(Mg)L/2 =(0.500kg  x 9.8m/s2)0.8m+(2.0kg  x   9.8m/sx    0.8m) / 2 = 3.92 + 7.84 =11.76 τ =12N*M

crawl-data/CC-MAIN-2017-26/segments/1498128323895.99/warc/CC-MAIN-20170629084615-20170629104615-00366.warc.gz

# NCERT Solutions for Class 8 Maths Here we are providing NCERT Solutions for Class 8 Maths, the solutions are latest and up-to-date. You can download Solution for each and every chapter listed below (Chapterwise).Download Free NCERT Solutions for class 6th to 12th. ## NCERT Solutions for Class 8 Maths – Free PDF Download Chapterwise ### CHAPTER 1: RATIONAL NUMBERS Properties of Real numbers, integers, whole numbers, rational numbers and natural numbers – Commutative, associative and closure.  Roll of 1 and additive inverse of multiplication and addition. Representation of a rational number on number line and to find rational numbers between any two rational numbers. Additive identity (0) and the multiplicative identity (1). ### CHAPTER 2: LINEAR EQUATIONS IN ONE VARIABLE The chapter linear equations in one variable deals with linear expression in one variable only. We know that an algebraic equations are equality involving variables. In a linear equations the values of expression on LHS are equal to values on RHS. To solve these equations, we perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed. There are equations in which variable is only one side, variable is on both the side, reducing into simple equation and then to solve and applications based on linear equations. Understanding quadrilaterals â€“ A simple closed curve made up of only line segments is called polygon and the curves that are not closed are not polygon. Types of polygon – Triangle, quadrilateral, pentagon, hexagon. A diagonal is a line segment connecting two non-consecutive vertices of a polygon. If all sides of a polygon is equal it is a regular polygon. The sum of external angles of any polygon is 360. A parallelogram is a quadrilateral with each pair of opposite sides parallel. ### CHAPTER 4: PRACTICAL GEOMETRY Practical geometry includes the constructing a quadrilateral four sides and one diagonal are given or when two adjacent sides and three angles are given or when three sides and two included angles are given, etc. Using the given specification, the quadrilateral can be drawn uniquely in this chapter. ### CHAPTER 5: DATA HANDLING The collection of information to study and analyze it further about any fact/case study is called data. Organize the data in systematic way or in a required manner and then interpret it is called data handling. To get clear idea about any data it is represented graphically as a pictograph, a bar graph, double bar graph, histogram and pie chart. In this chapter, a brief discussion about probability is also given. ### CHAPTER 6: SQUARE AND SQUARE ROOTS The square and square roots chapter gives an idea about how to find the roots of  a number. If a number, say x can be expressed as the square of any other number, say y, then y is the square root of x. Square root is the inverse operation of square. A natural number is called perfect square if its square root is a natural number. The method of finding square roots of a decimal number is frequently used even in higher classes. ### CHAPTER 7: CUBE AND CUBE ROOTS In cube and cube roots, there are various methods to find cubes/cube roots of any number. We can get cubes of numbers by adding consecutive odd numbers pattern. Prime factorization method is also used to find cubes or cube roots. In the prime factorisation method, if every factor appears thrice, then the number is perfect cube. ### CHAPTER 8: COMPARING QUANTITIES Comparing quantities compares the increase or decrease percentages, marked price, sales price, discount, discounted values of the article checking whether profit or loss %. Treatment of additional expense during the purchase of an article. Sales tax and cost including or excluding the tax. Simple interest and compound interest when interest is compounded half yearly, quarterly, monthly or yearly. Comparing simple interest and compound interest on the same amount. ### CHAPTER 9: ALGEBRAIC EXPRESSIONS AND IDENTITIES This chapter gives a basic idea about algebraic expressions and identities and their implementation. Terms are added to form algebraic expression and these terms themselves can be formed as the product of factors. The numeral factor of a term is called its coefficient.  Monomials, binomials, trinomials and so on, depending the number of terms. Addition of algebraic expression taking like terms together and multiplication of polynomials by polynomials. Standard identities and their uses in solving algebraic expressions. ### CHAPTER 10: VISUALIZING SOLID SHAPES In visualizing solid shapes, we will study about the solid objects having length, breadth and height that is why it is called 3-D figures. For example cubes, cuboids, cones, cylinders, spheres, hemispheres, etc. are the 3-D figures. In this chapter we will try to find faces, edges and vertices of some solid figures like cuboids, triangular pyramids, triangular and square base prisms. Application of Euler’s formula F + V – E = 2, where F – Faces, V – Vertices and E – Edges. ### CHAPTER 11: MENSURATION In mensuration chapter, we will workout the problems based on perimeter & areas of plane closed figure and surface area (sum of area of its all faces) & volume (amount of region occupied by a solid) of some solid figure like cube, cuboid, cylinder, etc. Conversion related to volume as 1 cubic cm = 1 mL, 1 L = 1000 cubic cm and 1 cubic m = 1000000 cubic cm = 1000 L. ### CHAPTER 12: EXPONENTS AND POWERS Main points – Exponents and Powers: Powers with negative exponents, scientific notation of decimal numbers, questions based on laws of exponents, use of exponents to express the numbers in standard form and comparison of very large numbers to small numbers. ### CHAPTER 13: DIRECT AND INVERSE PROPORTIONS Questions based on direct proportion ( when the quantity of one value increases the other also increases), inverse proportion ( if one quantity increases, the other quantity decreases and vice versa). Direct and inverse proportion can be identified on the basis of relative increase of decrease of other quantity with respect to first one. Most of the questions on this topic are interesting  and based on daily life. ### CHAPTER 14: FACTORIZATION Factorization of natural numbers and algebraic expression. These factors may be numbers, algebraic variables or algebraic variables or expressions. Factorization method of common factors, by regrouping terms, using identities and using factors of the form (x + a)(x + b). Division of algebraic expression – monomial by another monomial, polynomial by monomial and polynomial by the polynomial. Error finding in algebraic equations. ### CHAPTER 15: INTRODUCTION TO GRAPHS Introduction to graphs â€“ The purpose of the graph (visual representations of data collected) is to show numerical facts in visual form so that every one can understand it easily, more clearly and quickly. Types of graphs – Bar graph, histogram, pie chart, line graph and a linear graph (on xy – plane). Application based on graph – Quantity & cost, principal & simple interest and time & distance using dependent variable & independent variable. ### CHAPTER 16: PLAYING WITH NUMBERS In playing with numbers, we have to go through numbers in general form, fun with games in numbers and puzzles in which letters take the place of digits in an arithmetic problems. Divisibility tests – divisibility by 10, 2, 5, 3 & 9 and 11. Questions based on divisibility test to find the missing term in a number. Most of the students starts taking tuition’s from class 8 onwards as plethora of new concepts are introduced in this class. 90% of the students opt for tuition’s and even after that they score low marks. Reason? Poor concepts and lack of practice. Yes! Maths is a game whose key players are concepts and formulas. If you don’t know the formula then you cannot even go a single step further. I know you would have always wished that whenever your teacher asks any question, your hand should be raised first. But don’t worry. That can happen. You can also become a maths genius like the toppers of your class. You just need the right study material with apt guidance. There is no second option than to solving NCERT books. These books are appropriately designed as per the latest CBSE pattern and are in fact prescribed by CBSE as well. A teacher may feel bugged when you keep on pinging her every time for checking the answer. What if you get the complete NCERT Solutions for class 8 Maths? Sounds good? Yes, here we bring to you the NCERT solutions for class 8 Maths which solves each and every question till the answer giving proper explanations at every step. Chapters such as Algebra, rational numbers, mensuration, etc. need formula memorization. Chapter 6 Square and square roots and chapter 7 cube and cube roots form the base of mathematics. If is advisable to students to keep practicing them every day. Students generally get confused between them and 80% of the students answer it wrongly. Then comes a similar chapter exponents and powers. Here you need to be very careful regarding the figures. It has been noticed that most of the students often copy wrong figures from the question paper. Stay attentive while solving your mathematics problem. One wrong figure will lead you to a wrong answer, so copy them very carefully. We recommend the students to make a chart of all the formulas and paste them near the place of your study. This will help them to memorize the formulas in an easy manner without any hassle. www.educationlearnacademy.com visions to make each and every student in India fully equipped with the NCERT study material (textbook + solutions) so that he/she do not face any problem in their preparation for examination. ## CLASS 8 NCERT SOLUTIONS CBSE NCERT Solutions for class 8 (VIII) Maths, Science, Social Science and Hindi are given in PDF form to free to use online or download. ## Chapter-wise NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers Learn about the properties of rational numbers in the number system by using our NCERT Class 8 Maths Chapter 1 solutions. This chapter covers topics such as additive inverse, multiplicative inverse, reciprocal inverse, negative of a number and more. In NCERT Maths Class 8 Chapter 1, study the representation of rational numbers on a number line and practise word problems related to rational numbers. Also, understand how you can find a rational number between two rational numbers with our NCERT solutions for Class 8 Maths Chapter 1. While learning the properties of rational numbers, you can boost your knowledge of real numbers, whole numbers, integers and natural numbers with the NCERT Class 8 Maths book solutions. Chapter 2 – Linear Equations in One Variable Through the NCERT concise Mathematics Class 8 solutions for this chapter, practise the methods used by experts to solve contextual problems based on the concept of linear equations in one variable. Use our NCERT solutions for Class 8 Maths Chapter 2 to learn concepts such as equations having the variable on both sides, equations reducible to the linear form etc. Knowledge of variables gained from our NCERT Class 8 Maths Chapter 2 solutions will benefit you a lot in higher classes such as Class 9, Class 10, Class 11 and Class 12. So, use TopperLearning’s NCERT Maths Class 8 Chapter 2 solutions and study better with accurate answers to the exercise questions from your Maths textbook. This chapter gives you a thorough understanding of the properties of quadrilaterals such as the sum of angles of a quadrilateral is equal to 360 degrees. Revise the various types of polygons such as convex, concave, regular and irregular polygons from NCERT Maths Class 8. Also, learn about the properties of parallelograms. Understand the different types of curves by utilising our NCERT solutions for Class 8 Maths Chapter 3. By revising our solutions from NCERT Maths Class 8, you’ll come across several examples of question formats that are likely to appear in your Class 8 Maths exam. Also, learn to calculate the sum of the measure of the exterior angles of a polygon with our NCERT 8 Maths solutions. Chapter 4 – Practical Geometry Class 8 Maths Chapter 4 helps you to understand the construction of quadrilaterals, parallelograms, rhombus, squares and rectangles. Learn about the construction of geometric shapes with TopperLearning’s NCERT solutions for Class 8 Maths Chapter 4. This chapter teaches you in detail about the concept of diagonals in shapes. Our CBSE Class 8 Maths solutions will also take you through the properties of geometric shapes. With our NCERT Class 8 Maths book solutions, you can easily learn the role played by angles and sides in different scenarios. Chapter 5 – Data Handling In this chapter, read in detail about what is data and what are the ways to present data. With the NCERT solutions for Class 8 Maths Chapter 5, you can learn about the visual representation of different types of data. The solutions in this chapter will teach you to read data in bar graphs and pie charts. You’ll also learn about circle graphs, pictographs, double bar graphs, histograms and more by studying this chapter. You’ll also be able to revise probability and chance from the data handling perspective along with real-life applications. Chapter 6 – Square and Square Roots In this chapter, learn to find square roots with the help of the division method and the factor method. Practise answers of problems from your NCERT Class 8 Maths book to understand the concept of a perfect square and square roots. With our NCERT solutions for Class 8 Maths Chapter 6, you’ll be able to do your revision of the properties of square numbers. Revise NCERT Maths Class 8 book concepts like square roots of a decimal, square of a number etc. Also, for homework, use our NCERT solutions for Class 8 Mathematics Chapter 6 that are created by some of the best Maths teachers in the country. It will be easy for you to complete assignments related to this chapter. Chapter 7 – Cube and Cube Roots Study this interesting chapter on cube and cube roots with TopperLearning’s NCERT solutions for Class 8 Maths Chapter 7. The two key methods for solving problems from this chapter are the estimation method and the prime factorisation method. Our NCERT solutions for CBSE Class 8 Chapter 7 gives you step-wise answers to find cube roots using the factor method. Also, learn the concept of a perfect cube and how to estimate cube roots while understanding the number system. Practise problems related to Chapter 7 effectively by going through the accurate answers by our experts for this chapter. Chapter 8 – Comparing Quantities NCERT Class 8 Maths Chapter 8 covers topics such as compound interest, percentages, ratios, sales tax and more. Find solutions on the unitary method and its applications. Also, revise the concept of profit and loss. NCERT Maths Class 8 Chapter 8 is an important chapter because it will present you with the basics of accounting. You’ll be able to perform complex accounting in the later years if you’ve grasped the concepts in this chapter. With NCERT solutions for Class 8 Maths Chapter 8, you can practise and learn how to calculate interest, tax etc. The application of the concepts learned in this chapter will also help you to understand the basic calculations in day-to-day life. Chapter 9 – Algebraic Expressions and Identities Get answers on the addition, subtraction, division and multiplication of algebraic expressions in NCERT Class 8 Maths Chapter 9. Also, study about interpretations of algebraic identities. Take advantage of TopperLearning’s NCERT solutions for Class 8 Maths Chapter 9 Algebraic Expressions to understand the relevance of pure mathematical expressions and how to implement them. Also, revise answers to exercise questions from your NCERT 8th Maths book that are based on terms like polynomials, trinomials, binomials and monomials. Also, find out what is a factor and how coefficients work. Chapter 10 – Visualising Solid Shapes Explore the fascinating world of 3D objects and the basics of how to work with them through our NCERT solutions for Class 8 Maths Chapter 10. Learn about ways to view a 3D object such as front view, top view and side view. Get a deeper understanding of 3D objects and how to map 3D objects by revising NCERT Maths Class 8 solutions from this chapter. Understand the importance of vertices, faces and edges in 3D objects such as triangular pyramids, prisms and more. Also, practise the use of Euler’s formula in solving Maths problems with our NCERT Class 8 Maths solutions. Chapter 11 – Mensuration For revision of Chapter 11 Maths Class 8 Mensuration, get Class 8 Maths solutions on finding the area of a polygon and the area of a trapezium. Learn more on the concept of volume of a cube, volume of a cylinder and volume of a cuboid in NCERT Maths Class 8 Chapter 11. Also, find out how to measure the surface area of a cube, cylinder, and cuboid. Get NCERT solutions for Class 8 Maths Chapter 11 to practise the steps to calculate the area of a general quadrilateral. In addition, find out what is the meaning of capacity and what are the properties of solid shapes. Chapter 12 – Exponents and Powers In NCERT solutions for Class 8 Maths Chapter 12, you will learn more about the integers in the number system. Revise the laws of exponents that have integral powers. Learn how to utilise exponents for expressing numbers in the standard form. At TopperLearning, qualified Mathematics experts have prepared the solutions for Chapter 12 to assist you with the topic of exponents and powers. With enough practice, you will be able to attempt questions based on laws of exponents and power with negative components. Once you are comfortable with the topic, try solving the problems without referring to the solutions. Use the NCERT solutions to assess yourself and score better marks in your exam. 1. ### Why are NCERT Solutions for Class 8 important? Learning Maths takes a lot of practice. NCERT solutions for Class 8 helps you to revise concepts such as linear equations, cube roots, square roots and more. These concepts form the foundation of advanced concepts that you will study in higher classes. Also, the knowledge of your Class 8 Maths concepts supports your preparation for competitive exams such as JEE, NEET etc. Our NCERT solutions are freely available as reliable reference material to study the concepts as well as the application of concepts as per the most recent NCERT syllabus for Class 8 Maths. With expert NCERT solutions for Class 8 within your reach, you can practise solutions as much as you want. The chapter-wise format of NCERT solutions ensures that you can access specific chapters quickly to prepare for mock tests related to the chapter or complete class assignments based on the select chapters. The ease of using the NCERT Class 8 Maths book solutions through your dashboard will also save you time and effort. In this way, you do not have to lose precious time searching for specific solutions from the NCERT Class 8 Maths book. Instead, get all the textbook solutions in one place. 2. ### Where can I find free NCERT solutions for Class 8 Maths? TopperLearning provides free online solutions for exercise questions from your NCERT Class 8 Maths textbook. You can find them under ‘textbook solutions’ in the Class 8 resources section of our study portal. 3. ### Which chapters from Maths Class 8 NCERT are present on TopperLearning? Solutions for all 16 chapters from the Maths NCERT Class 8 textbook covering topics such as rational numbers, factorisation, practical geometry etc. are available on TopperLearning. 4. ### Will the NCERT Maths book Class 8 solutions be enough for me to score high marks? NCERT solutions for Class 8 Maths are a great resource for revision. However, for scoring high marks, you should practise more Maths problems by attempting sample papers and previous years’ question papers. 5. ### I don’t know which chapter to start for revision using NCERT solutions. What should I do? First of all, download the latest CBSE NCERT syllabus for Class 8 Maths. Decide whether you want to revise specific chapters or topics from the entire syllabus. Based on your decision, plan your schedule for revising one chapter at a time. 6. ### How to prepare for Class 8 Maths exams? For Maths preparation tips, you can read our blog on how to prepare for CBSE Class 8 Maths here. Chapter 13 – Direct and Inverse Proportions Learn to solve word problems on direct variation and inverse variation in quantities through the NCERT 8 Maths CBSE Board solutions given in this chapter. NCERT solutions for Class 8 Maths Chapter 13 covers all the exercises given in your Maths textbook. Use these NCERT solutions to revise the concept of proportion. Also, learn to solve problems wherein you have to find out about the proportional increase or decrease of given quantities. If you practise the NCERT solutions multiple times, you’ll be able to grasp the topic and remember the ways to tackle the questions related to this topic. Chapter 14 – Factorisation This chapter helps you learn the concept of factorisation and algebraic identities. Our NCERT solutions for Class 8 Maths Chapter 14 will support you to understand how the division of an algebraic expression takes place. For example, find out how a polynomial can be divided by a monomial or how a monomial can be divided by a monomial. Practise the different ways to find factors in problem questions. For your exam, the latest NCERT Maths book is the most recommended textbook to prepare for this chapter. Finding the correct solutions for the NCERT Maths Class 8 textbook questions can be difficult. At TopperLearning, we give you free access to the best NCERT solutions for Chapter 14 by some of the qualified and experienced Maths teachers in India. Chapter 15 – Introduction to Graphs In this chapter, learn how to plot points in graphs for situations such as multiples of different numbers, perimeter vs. length for squares etc. Understand the different types of graphs such as bar graph, linear graph, histogram, pie chart etc. In our NCERT solutions for Class 8 Maths Chapter 15, you’ll find solutions to study the topic of graphs in detail. Use our NCERT Mathematics Class 8 model answers as a handy e-learning reference source for your Class 8 exam preparation and push your efforts to score top marks in the exams. Chapter 16 – Playing with numbers Learn how to write a 2-digit and 3-digit number in the generalised form by solving number puzzles in this chapter. Through our NCERT solutions for Class 8 Maths Chapter 16, learn about divisibility tests, letters for digits and other concepts. You’ll also enjoy learning the fun number exercises in this chapter. If none of the link work properly, do comment in the comment box.

crawl-data/CC-MAIN-2023-40/segments/1695233510387.77/warc/CC-MAIN-20230928095004-20230928125004-00660.warc.gz

There are many causes of memory loss. As we age, we become more prone to having problems with remembering things. This can lead to a fear of developing dementia. But there is a big difference between becoming forgetful, and dementia. Normal memory loss may cause some inconvenience and embarrassment, but does not get in the way of day to day functioning to any great degree. We may become slower to process information, but this is not the same thing as a breakdown in brain function. Ironically, those who are most concerned about their diminishing power of recall are the ones with the least need to worry. A person moving into Alzheimer's or other form of dementia, may have the sense that something is not quite right but they are not aware of the changes in their cognitive ability. It is the people around them who will be noticing the impairment, not the individual actually experiencing this decline. Aside from the problem that results from the normal aging process, there are many other causes for memory loss. Diseases of many kinds can hinder one's ability to remember. Dementia such as Alzheimer's is one cause. One symptom of Parkinson's disease may be memory loss resulting from a genetic defect. This is also true of Down Syndrome. Huntington's, an inherited disease, may be accompanied by memory loss. Some types of mental illness, e.g., Dissociative Identity Disorder, may exhibit this problem with memory. Traumatic brain injury, e.g., concussion, may alter one's capacity for recall. Nutritional deficiencies and depression may affect one's memory. Chronic diseases like diabetes and Chronic Fatigue Syndrome can reduce the cognitive process. Central nervous system infections and inflammation of the brain, like encephalitis, also low blood sugar, or low estrogen in women, can all hinder the ability to remember. Dietary changes can make a difference. Eating less sugar and less processed foods, and adding more protein and omega-3 fatty acids can help shore up our mental faculties. Drinking filtered water can eliminate toxic chemicals found in our water.

<urn:uuid:49e6e754-2f3c-4cfd-8bad-036bf08ea5b4>

# 2001 USA TST Problems/Problem 9 (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff) ## Problem (Zuming Feng) Let $A$ be a finite set of positive integers. Prove that there exists a finite set $B$ of positive integers such that $A \subseteq B$ and $$\prod_{x\in B} x = \sum_{x\in B} x^2.$$ ## Solution Lemma 1. For any finite set $A$ of positive integers, there exists a finite set $C$ of positive integers such that $A \subseteq C$ and $\prod_{x \in C} x \ge \sum_{x\in C} x^2$. Proof. Let us abbreviate $p = \prod_{x\in A}x$ and $s = \sum_{x\in A} x^2$. Suppose that $p < s$ (otherwise, we may have $C=A$). Let $a$ be a positive integer larger than $\max(s,5)$ (and thus larger than any element of $A$). Taking $C = A \cup \{a, a+1, a+2\}$, evidently $A \subseteq C$, and \begin{align*} \prod_{x\in C} x &= pa(a+1)(a+2) > pa (a+1)^2 > 5(a+1)^2 \\ &> s + a^2 + (a+1)^2 + (a+2)^2 = \sum_{x \in C} x, \end{align*} as desired. $\blacksquare$ Lemma 2. For any finite set $C$ of positive integers such that $\prod_{x \in C} x \ge \sum_{x\in C} x^2$, there exists a finite set $B$ of positive integers such that $C \subseteq B$ and $$\prod_{x\in B}x = \sum_{x\in B} x^2 .$$ Proof. Let us abbreviate $s = \sum_{x \in C}x^2$, and $d = \prod_{x \in C} x - \sum_{x \in C} x^2$. We induct on the quantity $d$, which by hypothesis is a nonnegative integer. For our base case, $d=0$, we may take $B=C$. Now suppose that the lemma holds for $d. Suppose $d=k$. Let $C' = C \cup \{s+k-1\}$. Then $$\prod_{x\in C'} x - \sum_{x\in C'}x^2 = (s+k)(s+k-1) - s - (s+k-1)^2 = k-1,$$ so by inductive hypothesis, there exists a set $B$ such that $C' \subseteq B$ and $$\prod_{x\in B} x = \sum_{x\in B} x^2 .$$ Since $C \subseteq C' \subseteq B$, this set $B$ satisfies the lemma's conditions. $\blacksquare$ Combining the statments of Lemmata 1 and 2, we are done. $\blacksquare$

crawl-data/CC-MAIN-2024-10/segments/1707947475897.53/warc/CC-MAIN-20240302184020-20240302214020-00609.warc.gz

# How can I find the speed of a falling object as seen from a car while in motion? The problem is as follows: A car driving in a city has a constant velocity of $$15\hat{i}-15\hat{j}\frac{m}{s}$$ with respect to the ground in the highway. However at $$t=0\,s$$ the driver in the car sees a lady in highest floor of a nearby building dropping a bucket which was at rest. Find the instant (in seconds) from which the driver situated in the car will measure the speed of the bucket to be $$-15\,i\frac{m}{s}$$. You may consider $$\vec{g}=-10\,\hat{j}\frac{m}{s^{2}}$$ The alternatives given on my book are as follows: $$\begin{array}{ll} 1.&0.5\,s\\ 2.&1\,s\\ 3.&1.5\,s\\ 4.&2\,s\\ 5.&2.5\,s\\ \end{array}$$ How am I supposed to relate the quantity of the velocity and the instant?. The only equation which I can recall for the position of an object falling is: $$y(t)=y_{0}+v_{0y}t-\frac{1}{2}at^2$$ But in this case I don't know how tall is the building neither of what else could I do or should I need to find what it is being asked. I suspect that I should sum the vectors for the velocity of the car and that of the bucket falling and from then I could find the time. But I don't know which steps should I take to find such time. Can somebody help me here?. • Are the vectors aligned correctly? It seems as though the car is driving in the same direction as gravity... Nov 5 '19 at 4:17 • @abiessu I just checked with the original source and yes they are aligned correctly. Nov 5 '19 at 4:21 If the car is moving with the velocity $$15\hat i-15\hat j$$ with respect to the ground, in the reference frame of the car, the bucket moves with velocity $$-15\hat i+15\hat j$$. There is no force in the $$\hat i$$ direction, just in the $$\hat j$$ direction. You can write $$v_i(t)=v_i(0)\\v_j(t)=v_j(0)-gt$$You have $$v_j(t)=0$$, $$v_j(0)=15$$ so $$0=15-10t$$or $$t=1.5$$ seconds. • Please help me with the conceptual basis of your answer. Why did you swap the signs of the bucket and be the "same" as that of the car?. Yes it is obvious that there is no force in the horizontal direction, but what about the vertical why the final speed in the vertical component is equal to zero?. Can you help me with this matter?. How do I get to the conclusion that $v_{j}(t)=0$?. Nov 5 '19 at 4:59 • Answering the conceptual question: suppose you are in a fixed reference frame, and there is another reference frame, moving with velocity $\vec v_R$. If you have a object in the moving reference frame with velocity $\vec v_1$ in that frame, you are going to see it moving with velocity $\vec v_0=\vec v_1+\vec v_R$. Think of throwing a ball in a train. You know that in your reference frame the bucket is at rest, so $\vec v_0=0$. Then $\vec v_1=-\vec v_R$. As for your 2nd question, the problem asked about the time when the measured velocity is only in the $\hat i$ direction, so no $j$ omponent. Nov 5 '19 at 12:53 • For the second question, I forgot to ask that you mention there is no force in the $i$ component is it because there isn't any gravity acting there or what?. I'm assuming that you set$j=0$ because for the driver in the car he will not see the object falling? or from his point of view he will only notice the moving in the $i$ frame?. This part is where I'm confused at. Can you help me with that please?. Nov 7 '19 at 8:27

crawl-data/CC-MAIN-2021-39/segments/1631780057882.56/warc/CC-MAIN-20210926144658-20210926174658-00033.warc.gz

Count frequency of number in sorted array Problem Problem: Given a sorted array, We have to count the frequency of number i.e. the count number of occurrences of a number in the given sorted array. Example**:** Arr[]={ 5,10,15,15,15,25,30,60,80 } ,p= 15 Output : 3 Explanation: Number 15 occurs 3 times in the sorted array. This problem can be done in two ways:- 1. Linear Search 2. Binary Search # Approach 1 In linear search we compare each element with the element to be found as we traverse through the array. Code (Linear Search): ``````#include <iostream> using namespace std; // Function returns number of times p occurs in array int countrepeat(int array[], int size, int p) { int ans = 0; for (int i = 0; i < size; i++) if (array[i] == p) ans++; return ans; } // Driver code int main() { int array[] = { 32, 32, 54, 65, 78, 78, 78, 78, 85 }; int size = sizeof(array) / sizeof(array[0]); int p = 78; cout << p << " is repeated " << countrepeat(array, size, p) << " times"; return 0; } `````` Output ``````78 is repeated 4 times `````` Time Complexity:  O(n) # Approach 2 In binary search, we find the middle element ((start+last)/2) (Here, start corresponds to first element and last corresponds to the last element) and check if the element to be found is smaller or greater than value present at the middle. If the element to be found is greater then we initialize the start value as mid+1 else last is initialized as mid-1. Code (Binary Search): ``````#include <iostream> using namespace std; // C++ program to count occurrences of an element //function returns the position of p in given array int binarysrch(int array[], int l, int r, int p) { if (r < l) return -1; int mid = l + (r - l) / 2; // If element is found at the middle if (array[mid] == p) return mid; // If element is smaller than mid, then // it can only be there in left subarray if (array[mid] > p) return binarysrch(array, l, mid - 1, p); // Else the element can only be there // in right subarray return binarysrch(array, mid + 1, r, p); } // function returns number of times p occurs in array int countrepeat(int array[], int size, int p) { int token = binarysrch(array, 0, size - 1, p); if (token == -1) return 0; // Counting elements on left int count = 1; int left = token - 1; while (left >= 0 && array[left] == p) count++, left--; // Counting elements on right int right = token + 1; while (right < size && array[right] == p) count++, right++; return count; } // Driver code int main() { int array[] = { 1, 12, 15, 15, 15, 30, 45, 76, 80 }; int size = sizeof(array) / sizeof(array[0]); int p = 15; cout << countrepeat(array, size, p); return 0; } `````` Output ``````3 `````` Time Complexity : O(log n + count) where count is number of occurrences.

crawl-data/CC-MAIN-2023-40/segments/1695233506027.39/warc/CC-MAIN-20230921105806-20230921135806-00865.warc.gz

Researchers have developed a light-induced chemical reaction that visualizes RNA in live zebrafish embryos without interfering with cell processes. In previous work, the team applied the method to cells in culture. But now the researchers have developed the method as the first technique for detecting specific strings of nucleic acids in live vertebrates that doesn’t require genetically modifying the organisms. What’s more, the method is sensitive enough to visualize the expression of microRNAs, which are small noncoding RNAs that act as puppet masters of gene expression (ACS Cent. Sci. 2016, DOI: 10.1021/acscentsci.6b00054). Nicolas Winssinger, Marcos Gonzalez-Gaitan, and colleagues at the University of Geneva designed two nucleic acid probes that each complement and bind to adjacent halves of a target microRNA sequence. The researchers conjugated one probe to a ruthenium complex that absorbs visible light and the other to a rhodamine dye that lights up when its azide bonds are cleaved. When the probes attach to the target sequence, the two reagents come close enough to react. Shining a light on the sample activates the ruthenium, which reduces the azide in the rhodamine conjugate and thereby allows it to fluoresce. The researchers designed probes against three different microRNAs: one expressed in neural cells, another in muscle cells, and a third in cells involved in forming the pectoral tail and fins. After the embryos were exposed to light for 30 minutes, confocal imaging revealed that each probe set illuminated the expected type of tissue and the probes tracked microRNA expression over time during embryo development.

<urn:uuid:25a28267-bd87-42f6-b80a-96935cfc7761>

Home # Half of 20 Halves (to half of 20) Mad Maths Minutes Sets A & B Halves (to half of 20) Mad Maths Minutes Sets C & D Our online activities : Halves (to half of 20) Interactive Mad Maths Minutes Halves (to half of 20) Top of the Class Halves (to half of 20) Word Attack Halves (to half of 20) Shootout. How to quickly calculate what half of a fraction is. What is Half of 20/3? What is Half of 20/4? What is Half of 20/5? What is Half of 20/6? What is Half of 20/7? What is Half of 20/8? What is Half of 20/9? What is Half of 20/10? What is Half of 20/11? What is Half of 20/12 One half of 20 is simply one half times 20, which can be written as follows: One/half x 20. Furthermore, you can convert one to 1 and half to 2 and then the equation and answer is: 1/2 x 20 = 10.00. One half written as a fraction is 1/2. You can also write it as a decimal by simply dividing 1 by 2 which is 0.50 20/30= 2/3 And half of means 2/3 * 1/2 = 1/3 = 0.3333 an Therefore, half of 15/20 is the same as 15/20 divided by 2, which means that this is the fraction math problem we are solving: That is all there is to it! Below is the the answer to half of 15/20? in its simplest form: Two halves make a whole. 3/8 plus 3/8 equals 15/20. Thus, we know that our answer of 3/8 to the question What is half of 15/20 The time and half formula is given below that shows you how to calculate time and a half pay. Overtime Rate = 1.5 x Hourly Rate. Regular Pay = 40 x Hourly Rate. Overtime Pay = Overtime Rate x N, where N is the number of extra hours that you work. Total Pay = Regular Pay + Overtime Pay. For example, if your hourly rate is \$20 per hour, the. Classic Short and Long Half Slip Skirt for Ladies and Girls - Slight Flair - Anti Static - 20 Length. 4.2 out of 5 stars. 197. \$13.87. \$13. . 87. FREE Shipping on orders over \$25 shipped by Amazon. +2 colors/patterns Tatis already is over 20 in both homers and steals, and while stolen bases are more likely to be the holdup, this is assuredly a goal of his. Look for Tatis to run even more in the second half. 1/2 of 1/2 - Name Brand Clothing - Mall and Department offering to our customers the best department store and mall store name brands on current merchandise at the best possible prices, usually 1/2 of 1/2 of retail Adolescents and Young Adults. While sexually transmitted diseases (STDs) affect individuals of all ages, STDs take a particularly heavy toll on young people. CDC estimates that youth ages 15-24 account for almost half of the 26 million new sexually transmitted infections that occurred in the United States in 2018 ### Halves (to half of 20 The Half Of It: 20 Best Quotes In The Netflix Movie, Ranked. Netflix original movies are getting better and better, offering more representation. The Half of It is a great example, so here are its best quotes Why Waste Management Stock Returned 20% in the First Half of 2021 The waste and recyclables management giant has racked up a string of earnings beats and last quarter raised its full-year 2021. Young adults from 20 to 29 years of age who gave birth in their teenage years are less likely to hold a high school diploma or GED, relative to their counterparts who did not have a teen birth. Overall, 53 percent of young women who gave birth as teens received a high school diploma, compared with 90 percent of those who did not The second half of 2021 gaming looks great with tons of release dates for games on PC, PS5, PS4, Xbox Series X/S/One, and Nintendo Switch. Here's what we thi.. A quarter is half of a half. Compare Lesson 15. Example 9. How much is a fourth, or a quarter, of 60? Answer. Half of 60 is 30. Half of 30 is 15. Example 10. How much is 25% of 180? Answer. 25% means a fourth. (Lesson 15.) Half of 180 is 90. Half of 90 is 45. Example 11. How much is 25% of 112? Answer. Half of 112 = Half of 100 + Half of 12. Half of the 20 Metro Areas Worst-Hit by COVID Are All in One State. By Soo Kim On 10/13/20 at 12:54 PM EDT. Share. Share on Facebook Share on Twitter Share on LinkedIn Share on Pinterest Share on. ### Half Fractions Calculato • Just 20 companies are the source of more than half of all the single-use plastic items thrown away globally. That's the conclusion of analysis of the corporate network behind plastic production. • 3 in 10 teen American girls will get pregnant at least once before age 20. That's nearly 750,000 teen pregnancies every year. Parenthood is the leading reason that teen girls drop out of school. More than half of teen mothers never graduate from high school. Less than 2 percent of teen moms earn a college degree by age 30 • Buyers registered 123,723 new cars and trucks in Colorado in the first six months of 2021, which is 20.6% more than the number they registered in the first half of 2020 DBC's expense ratio is 0.88%. In Q2, DBC rose from \$16.61 to \$19.25 per share or 15.89%. Over the first half of 2021, the ETF rose by 30.95%. DBC underperformed PDBC, but both outperformed the. According to an analysis Tuesday, a group of 20 companies are responsible for producing more than half of the world's single-use plastic waste that's helped accelerate the climate crisis and. Subsequently, shares ended the first half of the year down 20.3%, according to data from S&P Global Market Intelligence. Image source: Getty Images. So what 20 Companies Are Behind Half Of The World's Single-Use Plastic Waste, Study Finds. A worker operates a forklift to move household waste at a facility that stores recyclable materials in Seoul. ### What is one half of 20? - Valeu LGBTQ themes found in half of the past decade's 20 most-banned books. Two Boys Kissing, I Am Jazz and Kite Runner are among the titles on the American Library Association's most-banned. More than half of men, and nearly two thirds of women currently aged 20 years in India could develop diabetes in their life time, with most of those cases likely to be type 2 diabetes Here are the top performing stock markets in Asia-Pacific in the first half of 2021, based on CNBC calculations: Vietnam's VN-Index: +27.6%. Taiwan's Taiex: +20.52%. South Korea's Kospi: +14. Angel Yeast Reports Strong Revenue Growth in First Half of 2021, Achieves 20.55% YoY Increase. YICHANG, China, Aug. 3, 2021 /PRNewswire/ -- Angel Yeast Co., Ltd ( Angel Yeast ) ( en.angelyeast. ### What is half of 20/30? - Quor Angel Yeast Reports Strong Revenue Growth in First Half of 2021, Achieves 20.55% YoY Increase Highlights of the report: H1 revenue increased 20.55% year-on-year to RMB 5.234 billion ( \$810 million Aug. 12 -- MONDAY, Aug. 11 (HealthDay News) -- About half of all American adults don't have the 20/20 vision physicians consider optimal because they are nearsighted, farsighted, or have an. ### What is half of 15/20? - Fraction Calculato 1. THE FIRST HALF OF THE 20TH CENTURY - THE MODERN AGE (1901-1945 or 1952) CRISIS OF WESTERN VALUES: nothing seemed to be right or certain, scientists and philosophers destroyed the old, predictable universe of the Victorians with their optimistic outlook; the impossibility to master a chaotic universe was expressed in Modernist prose and poetry. 2. 20/1/2+30=20x2+30=40+30=7 3. Only half of 20 private hospital chains reserving units for Covid-19 care. With the health department's 48-hour notice to 20 private hospital chains ending on Thursday to reserve one branch for. ### Time and a Half Calculator - Overtime Calculato 1. Half of single-use plastic waste produced by just 20 companies. Story by R. Updated 4:15 PM ET, Tue May 18, 2021 . are the source of half of the world's single-use plastic waste.. 2. Scale scores have the same meaning for all the different forms of the ACT® test, no matter which date a test was taken. Your Composite score and each test score (English, mathematics, reading, science) range from 1 (low) to 36 (high). The Composite score is the average of your four test scores, rounded to the nearest whole number 3. Sennelier Pastel Half Stick Set - Assorted Colors - Set of 20. Brand: SENNELIER. 4.4 out of 5 stars. 45 ratings. Price: \$39.99 & FREE Returns. Return this item for free. Free returns are available for the shipping address you chose. You can return the item for any reason in new and unused condition: no shipping charges 4. Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not. One of the most well-known applications of half-life is carbon-14 dating 5. Power of a number is obtained by multiplying it by itself. Where the base number (a) is raised to the power limit (n) which is equal to n times multiplication of a. For example, 2x2 is stated as 'Two squared' or '2 to the 2nd power' 2x2x2 is stated as 'Two cubed' or '2 to the 3rd power' 2x2x2x2 is stated as 'Two to the 4th power' or simply '2 to the 4th' and so on..<br> Use the below power of. 6. The 20 global businesses are both state-owned and multinational corporations, consisting mainly of energy and chemical giants, and are responsible for a plastic waste footprint amounting to more than half of the 130 million metric tons of single-use plastic thrown away in 2019, the analysis found 7. Just 20 companies are responsible for producing half of all single-use plastics thrown away around the world every year, and a new report has singled out major banks and asset managers in an. ### Amazon.com: 20 inch half sli Volkswagen AG delivered more than twice as many electric cars in the first half of 2021 as in the same period last year (+165.2%). The Group had sold 170,939 battery-electric cars worldwide by the end of June, 110,991 of them in Q2 of this year alone. In addition, the Group delivered a total of 171,300 [ Over half of 20-year-olds in urban India likely to develop diabetes in their lifetime: Study. Those who were free of diabetes at age 60 were at lower risk, with around 38% of women and 28% of men. One-half of a convex lens of focal length 20 cm is covered with a black paper. (i) Will the lens produce a complete image of the object? (ii) Show the formation of image of an object placed at 2F 1 of such covered lens with the help of a ray diagram. (iii) How will the intensity of the image formed by half covered lens compare with non-covered lens Cyber rates have soared since Q4 last year, with 70% of wholesale broker CRC's clients reporting double-digit rate rises in April and almost half absorbing rate rises in excess of 20%, according. ### 20 bold predictions for MLB's second half Yardbarke Every year, over half of Canada's food supply is wasted, and nearly \$50 billion of that wasted food is avoidable. To help spark new ideas and engage diverse perspectives, the Government of Canada launched the \$20-million Food Waste Reduction Challenge in November 2020, calling for innovators to deliver game-changing solutions to this long. Wed 23 Jun 2021 19.01 EDT. Nearly half of all students thought their degree offered poor value for money this year, according to a survey that sheds light on the scale of student anger with their. Half life is simply how long it takes for half of the drug dose ( any drug for that matter ) to be excreted from you body. Of course extend relase and other drugs have different half lives but that wasnt the initial question. So what ever is left (ie the 20 then to 10 and the 10 to 5) will take 10 hours to be eliminated by half in your body SINGAPORE - Incidents of armed robbery in the Singapore Strait continued to climb in the first half of this year, with 20 reported between January and June. This is four more than the number. As more Americans turn to online dating and the #MeToo movement leaves its imprint on the dating scene, nearly half of U.S. adults - and a majority of women - say that dating has become harder in the last 10 years.. Among those who are on the dating market - the 15% of American adults who are single and looking for a committed relationship or casual dates - most say they are. The 20 global businesses are both state-owned and multinational corporations, consisting mainly of energy and chemical giants, and are responsible for a plastic waste footprint amounting to more than half of the 130 million metric tons of single-use plastic thrown away in 2019, reports Common Dreams Now, a new report finds that just 20 companies account for more than half of all single-use plastic waste generated worldwide. The report , published Tuesday by Australia's Minderoo Foundation, offers one of the fullest accountings, to date, of the companies behind the production of single-use plastics that researchers believe could account. 20 Companies Produce More Than Half of Global Plastic Waste, Report Reveals by Earth.Org Africa Americas Asia Europe Oceania May 24th 2021 2 mins New research has revealed that just 20 companies are responsible for producing 55% of all the single-use plastic waste in the world, with ExxonMobil leading the pack Indeed, about half of all the fires at houses of worship in the past 20 years were intentionally set, according to a Pew Research Center analysis of data from the ATF. Of the 4,705 reported fire incidents at houses of worship between 1996 and 2015, 2,378, or 51%, had been ruled intentional as of July Mosquito Hunters Wraps Up First Half of 2021 With 20 New Franchisees As entrepreneurs seek fast-growth home service opportunities, Mosquito Hunters has surpassed the 100-unit mark thanks to its well-positioned consumer offering and home-based business model ### Home ½ of ½ - Name Brand Clothin 1. 20 People Now Own As Much Wealth as Half of All Americans The US is caught in a vicious cycle, with rising political inequality driving an ever-rising concentration of wealth at the top 2. g top. Since 2011, 20 of the. 3. Calculate overtime hourly pay rates given normal or standard pay rate. Calculates time and a half double triple and quadruple overtime pay rates In both groups, people of color and low-income residents were less likely to have seen a dentist in 2019. These disparities were wider in rural areas, where issues such as transportation barriers, dentist and dental hygienist shortages and lack of health insurance are more common. The coronavirus pandemic has likely exacerbated the need, especially for low-income patients, the report says Half of the top 20 best-selling games of December 2020 were published by Nintendo, said Piscatella. Animal Crossing: New Horizons was 2020's third best-selling title, and the sixth best. Angel Yeast Reports Strong Revenue Growth in First Half of 2021, Achieves 20.55% YoY Increase Highlights of the report: H1 revenue increased 20.55% year-on-year to RMB 5.234 billion ( \$810 million Sat 20 Mar 2021 15.00 EDT. (26%) said it was because this is a Christian country. Over half (51%) said they never attended a place of worship or did so less than once a year More than half of Bar Harbor survey respondents say cruise ships hurt town by Bill Trotter July 20, 2021 July 20, 2021. Share this: Click to share on Twitter (Opens in new window July 20, 2017. By . Aaron Blake. Senior reporter. July 20, 2017. And at one point during the 2016 presidential campaign, Clinton even suggested half of Trump's supporters. During the joint meeting, the GEDC voted to provide \$912,500 to the city over 20 years. The amount represents half of the settlements and, depending on variable tied to the final bond, represents about \$61,700 per year. The GEDC is not a party to the bond and will not receive any interest in the J.B. Wells Park complex Dogecoin is another with a drop of over 20%. Meanwhile, bitcoin's 7% was the smallest drop, followed by ETH's 13%, as well as binance coin (BNB)'s 15%, and ADA's 20%. Source: Coincodex, 07:10 UTC. As we go further in the past, the fields are getting greener. In the past quarter, we see four out of the top 10 appreciating in price Using the most recent available data (2016) the report reveals that 52.3 percent of children over 11 years old live under the poverty line, out of which 9.7 percent live in extreme poverty. This means that 20.7 million children and teenagers (about a sixth of the country's total population) live in poverty in Mexico 20 Companies Are Behind Half Of The World's Single-Use Plastic Waste, Study Finds. By: Jason Breslow | NPR Posted on: Wednesday, May 19, 2021 < < Back to WASHINGTON, D.C. (NPR) — In 2019, more. • What happened Shares of Brazilian fintech company StoneCo (NASDAQ: STNE) fell 20% in the first six months of 2021 according to data provided by S&P Global Market Intelligence. Fourth-quarter. • After riots at the U.S. Capitol, a majority of Americans believe President Donald Trump should be removed from office before his term ends on Jan. 20, according to a new poll • LONDON — Just 20 companies are the source of more than half of single-use plastic items thrown away globally, according to a study that highlights the devastating impact on the environment • More than half of population vaccinated in Bhopal; 20% get at least 1 dose in Madhya Pradesh Madhya Pradesh bus ban for 3 states to go, Maharashtra curbs till June 2 • Road crews will be hard at work on a portion of I-20 in Morgan County during the second half of July. The Georgia Department of Transportation (GDOT) announced this week that beginning on Monday, July 19, workers will repair a slab bump for Exit 114 over the course of two weeks, which may cause some traffic delays and detours • In the first half of 2021, the proportion of the Company's market based electricity sold amounted to 61.09%, representing an increase of 11.20 percentage points over the same period last year • Half of Americans have \$250 or less in disposable income each month. The Balance surveyed 1,000 adults in the U.S. who manage their own personal finances and have at least one financial account—such as checking, credit, or savings—in their name. People responded to the survey between Feb. 8-12, 2021, answering questions about how their. ### The Half Of It: 20 Best Quotes In The Netflix Movie, Ranke • About Half of Global Wastewater Is Treated, Instead of Previous Estimate of 20%, Study Finds (upi.com) 43 Posted by BeauHD on Tuesday February 09, 2021 @10:02PM from the reuse-and-recycle dept • 1964 Kennedy Half Dollar - Roll of 20 Silver Kennedy Half Dollars. Shipped with USPS First Class • walking Liberty half dollar lot of 20. Random years 90% silver from estate sale was in a safe for 20 years all coin been check out • e and guanine-to-cytosine, Watson and Crick proposed that one half of the DNA ladder serves as a template for recreating the other half during DNA replication. By 1958, two lines of evidence came together to provide proof of this hypothesis The 20 week half marathon training schedule can be used for running or walking. For running: Run at a comfortable pace that allows you to complete the mileage listed, particularly for your long runs. For shorter runs, you can push yourself a bit more for speed - but for long runs, your goal is just to finish it. If you get to the ends of your. Reducing a recipe by one-third can come in handy when halving still yields too much food: One third of ¼ cup is equivalent to 1 tbsp + 1 tsp. One third of ⅓ cup is equivalent to 1 tbsp + 2 ¼ tsp. One third of ½ cup is equivalent to 2 tbsp + 2 tsp. One third of ⅔ cup is equivalent to 3 tbsp + 1 ½ tsp. One third of ¾ cup is equivalent to. ### Why Waste Management Stock Returned 20% in the First Half 1. The 20th (twentieth) century began on January 1, 1901, and ended on December 31, 2000. The term is often used erroneously to refer to the 1900s, the century between January 1, 1900 and December 31, 1999. It was the tenth and final century of the 2nd millennium 2. Said to people of the age of 15. Is a sign of respect and of maturity. It shows that you have friends, if someone says this to yo 3. Here is 20 Small Details in Half-Life 2, this game is for sure one of the greatest games of all time... The story, the gameplay and overall execution was unl.. The half life calculator can be used to calculate the remaining amount of anything such as radioactive decay or for drug calculations. Let's say, for instance, there is a drug that is given in a 10mg dose. It has a half life of 6 hours. This means that 6 hours later, half of the medication will be consumed, leaving half remaining, at 5mg The Half Century of Progress Show is the premier working vintage farm show in the U.S. Held the weekend before the Decatur Farm Progress Show, the Half Century of Progress allows visitors to experience what farming and agriculture was like 50 years ago and beyond with live demonstrations, attractions, and fellowship For some, the box of 20 is a way to show off 20 coins to non-collectors and experienced numismatists alike, with the hopes of making the greatest impact with just those 20 coins from their collection. In the end, it is your collection, and the box-of-20 strategy is just one method to help you achieve your personal goals Half Full by Maria Scrivan for June 20, 2021. Buy a Print of This Comic License This Comic. TampaFanatic1 22 days ago. I had a retired neighbor from Boston who would always tell people that he was over 10000 people when they asked him what he did up there. He was a cemetery superintendent for one of the larger suburbs of beantown Just 20 companies that make polymers — the building blocks of plastics — account for more than half of all the single-use plastic waste that is clogging waterways and entering the ocean at a rate of a truckload every minute, and more than half of the biggest 100 plastic producers have no policies, commitments or targets to move towards a. ### Data Point: Half of 20- to 29-year-old women who gave • utes is taken, the following is estimated: 60 • about half of districts needed to update or replace multiple systems like heating, ventilation, and air conditioning (HVAC) or plumbing. an estimated one-third of schools needed HVAC system updates. funding for school facilities primarily came from local government sources. A boiler from the 1930s still in service in a public middle school. Old. • In about 20 years, half the population will live in eight states. The Top of the Rock at Rockefeller Center in New York on March 16, 2016. (Justin Lane/EPA) By . Philip Bump. July 12, 2018 • Half of twenty-somethings have no savings. Young people in the UK are losing the savings habit - with more than half of 22 to 29-year-olds living with no savings at all, official figures show. ### Top 20 Best Games of 2021 [First Half] - YouTub 1. Approximately 20 per cent of the population holds half of the total income generated in Pakistan, he said. The panel also featured Special Assistant to the Prime Minister (SAPM) on Social Protection and Poverty Alleviation Dr Sania Nishtar, senior researcher at the Collective for Social Science Research Ayesha Khan, SAPM on Revenue Dr Waqar. 2. CHECK OUT WeThePeople.store for best SWAG!. President Donald Trump is sure that the 2020 election was stolen from him and it seems nearly half of America's likely voters feel the same 3. g-of-age film in which Leah Lewis stars as bookish teenager Ellie Chu, who dishes out advice about romance, but hasn't actually experienced much herself. Written and directed by Alice Wu, The Half of It released in May 2020. The Half of It focuses on the friendship between Ellie and a love-struck classmate named Paul. 4. Incidents of armed robbery in the Singapore Strait continued to climb in the first half of this year, with 20 reported between January and June. This is four more than the number over the same. The Raptors are one of the five teams with three more road games (20) than home games (17) in the first half of the schedule. They play 10 of their first 14 games on the road, but then have their. Election 2020 | Oct 20, 2020, 10:39am EDT | Poll: Half Of Trump Supporters Believe Baseless Child Sex-Trafficking QAnon Claims. Tommy Beer. Forbes Staff. Business. Updated Oct 20, 2020, 12:03pm. Sydney under stay-at-home order as Covid-19 cases in Australia rise. (CNN) Sweden recorded its highest death tally in 150 years for the first half of 2020, according to the country 's official. Differentiated Halving to 20 Ladybird Worksheet - A lovely ladybird worksheet to support your children with halving. Check out our other fractions resources for KS1. The above video may be from a third-party source. We accept no responsibility for any videos from third-party sources. Please let us know if the video is no longer working New research from Interpret suggests that SVOD subscribers increased by 14% in the second half of 2020. However, during the same period, the rate of cancellation for SVOD services increased to 20% from 15% — pay TV providers saw churn increase 2 points to 7% during the same time. Subscriber churn was a concern for many video service. A medication's biological half-life refers simply to how long it takes for half of the dose to be metabolized and eliminated from the bloodstream. Or, put another way, the half-life of a drug is the time it takes for it to be reduced by half. For example, the half-life of ibuprofen (the active ingredient in pain and fever relievers such as. Note how the radius is always half the diameter. Uncheck the fixed size box. Repeat the above and note how the radius is always half the diameter no matter what the size of the circle. Thales' Theorem Thales' Theorem states that the diameter of a circle subtends a right angle to any point of the circle's circumference. (see figure on right) Almost half of 2020 college grads still looking for work: 'I should be out of the house by now'. Tabitha Palmer graduated in May of 2020 with a master's degree in English from the University. Over half of formal employees became temps in 2020, shows study. Synopsis. The poorest 20% lost nearly all their income due to unemployment during the lockdown, while the top 20% lost a little less than a quarter. Amid more curbs and local lockdowns to contain the spread of Covid-19, a new report shows that more than half of permanent salaried. Begin amount is 1.0 elapsed time is 90y half life 30 years n=9/30 n=3 90/2^2 90/8 = Chemistry. IF 80mg of a radioactive element decays to 10mg in 30 minutes, the half-life of this element is a.10 min b.20 min c.30 min d.40 min the answer is a.10 min but i would like to know why, please help. Chemistr ### How to take half of any number • The Urban Institute model projects that in 2035, only 23% of seniors will have incomes below 200% of the poverty threshold, less than half the New School economists' claims • Canada launches second half of its \$20-million Food Waste Reduction Challenge. At a virtual event on 25 May, Agriculture Minister Bibeau launched the novel technology streams segment of Canada's Food Waste Reduction Challenge, an initiative under the Food Policy for Canada. Every year, over half of Canada's food supply is wasted, and nearly \$50. • July 20, 2021 by Claire Stremple, roughly 550 structures in the capital city at moderate to severe risk of damage or destruction in a disaster — about half of the buildings and homes in the. • Windows 10 only use half of max cpu speed I have just upgraded my windows 7 laptop (HP Pavilion dm1-4000AU) to windows 10, everything seems OK. But when I open task manager, it shows that my laptop only use half of cpu speed even if the cpu load is full • 1 in 6 adults in N.J. won't get the COVID vaccine, half of parents remain hesitant, poll says. Updated Jun 03, 2021; Posted Jun 03,. According to VASEP, the hurdles caused by this warning and the COVID-19 outbreak would affect Vietnam's fisheries exports to the bloc in the second half of this year. VASEP estimates that sales to the E.U. would touch USD 600 million (EUR 509.5 million) between July and December, up 8 percent year-on-year NIMH statistics pages include statistics on the prevalence, treatment, and costs of mental illness for the population of the United States, in addition to information about possible consequences of mental illnesses, such as suicide and disability Citizens Financial Group Inc. expects to buy businesses and maybe other banks and hinted that more branch closures are likely during its second-quarter investors call on Tuesday. Based in. The NBA today announced the Memphis Grizzlies will tip off the Second Half of the 2020-21 regular season, the 20th Season of the franchise in Memphis, on Wednesday, March 10, against Bradley Beal.

crawl-data/CC-MAIN-2022-05/segments/1642320301309.22/warc/CC-MAIN-20220119094810-20220119124810-00541.warc.gz

# CBSE Class 10 Maths Chapter 7 Important Questions with Answers: Coordinate Geometry CBSE Class 10 Maths Chapter 7 Important Questions with Answers: In this article, we are going to discuss the important questions from Unit III, Chapter 7 Coordinate Geometry. Download the answers to the questions in PDF format. CBSE Class 10 Maths Chapter 7 Important Questions with Answers: Coordinate Geometry CBSE Class 10 Maths Chapter 7 Important Questions with Solutions: Central Board of Secondary Education has released the model papers for its annual class 10th board examinations for the academic session 2022-23. Although the final CBSE Class 10th date sheet for 2023 has not been published by the board yet, the exams are likely to start from February 15, 2023. Thus, the students would have almost two months to prepare for their final examination. When it comes to the individual papers, Mathematics is often dreaded amongst the student community. However, all it requires is regular practice to pass CBSE Class 10 board examination with flying colours. In this article, we are going to discuss the important questions from Unit III, Chapter 7 Coordinate Geometry. It carries a total weightage of 06 marks covering topics such as Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula. View the Mathematics syllabus in detail by clicking on the link below. CBSE Class 10 Maths Syllabus 2022-2023 ## CBSE Class 10 Maths Chapter 7 Important Questions MULTIPLE CHOICE QUESTIONS Q1. The distance of the point P (-6, 8) from the origin is: (a) 14 (b) 6 (c) 8 (d) 10 Q2. If (a, b) is the mid-point of the line segment joining the points A (10, -6) and B (k, 4) and a - 2b = 18, the value of k is: (a) 40 (b) 22 (c) 4 (d) 36 Q3. The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ - b cos θ), is : Q4. If the point P (k, 0) divides the line segment joining the points A (2, -2) and B (-7, 4) in the ratio 1:2, then the value of k is : (a) 1 (b) 2 c) -1 (d) -2 Q5. If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1, then the value of y is : (a) 4 (b) 2 (c) 1 (d) 3 Q6. Distance between two points (3, 2) and (6, 6) is: (a) 5 (b) 3 (c) 2 (d) 8 Q7. The line segment joining the points P (-3, 2) and Q (5, 7) is divided by the y- axis in the ratio: (a) 3 : 1 (b) 3 : 2 (c) 3 : 4 (d) 3 : 5 Q8. The point P on x- axis is equidistant from the points A (-1, 0) and B (5, 0) is: (a) (2, 2) (b) (0, 2) (c) (2, 0) (d) (3, 2) SHORT ANSWER TYPE QUESTION ( 2 MARKS) Q1. Find the point on the x-axis which is equidistant from the points (2, -5) and (-2, 9) Q2. Find the distance of the point P (2, 3) from the x-axis. Q3. Find the ratio in which the point (-3, k) divides the line-segment joining the points (-5, 4) and (-2, 3). Also find the value of k. Q4. If A (5,2), B (2, -2) and C (-2, t) are the vertices of a right-angled triangle with ∠B = 90°, then find the value of t. Q5. In what ratio does the point P (2, -5) divide the line segment joining A (-3, 5) and B (4, -9). SHORT ANSWER TYPE QUESTION ( 3 MARKS) Q1. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear. Q2. Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units. Q3. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order. Q4. If A (-2,1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides. Q5. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order find x and y. ALSO ATTEMPT: LONG ANSWER TYPE QUESTIONS (4 MARKS) Q1. The vertices of quadrilateral ABCD are A (5, -1), B (8,3), C (4, 0) and D (1, -4). Prove that ABCD is a rhombus. Q2. Find the centre and radius of the circumcircle (i.e., circumcentre and circum-radius) of the triangle whose vertices are (-2, 3), (2, -1) and (4, 0). Q3. Find the coordinates of the points of trisection (i.e., Points dividing in three equal parts) of the line segment joining the points A (2, -2) and B (-7, 4). Q4. An equilateral triangle has one vertex at (3, 4) and another at (-2, 3). Find the co- ordinates of the third vertex. Q5. The three vertices of a parallelogram ABCD are A (3, -4), B (-1, -3) and C (-6, 2). Find the coordinates of vertex D and find the area of ABCD. Q6. The base QR of an equilateral triangle PQR lies on x-axis. The co-ordinates of point Q are (-4, 0) and the origin is the mid-point of the base. Find the co-ordinates of the point P and R. ### Get Solutions to CBSE Class 10 Maths Chapter 7 Important Questions Also test your preparation with these practise papers created by our subject experts to prepare the candidates of CBSE Class 10 Math Board Examination 2023. All the best! ## Related Categories खेलें हर किस्म के रोमांच से भरपूर गेम्स सिर्फ़ जागरण प्ले पर

crawl-data/CC-MAIN-2023-06/segments/1674764499953.47/warc/CC-MAIN-20230201211725-20230202001725-00128.warc.gz

# Highly Divisible Triangular Number — Project Euler (Problem 12) All n numbers are Triangle Numbers. They’re called so, because they can be represented in the form of a triangular grid of points where the first row contains a single element and each subsequent row contains one more element than the previous one. Problem 12 of Project Euler asks for the first triangle number with more than 500 divisors. These are the factors of the first seven triangle numbers: 1 = 1: 1 2 = 3: 1,3 3 = 6: 1,2,3,6 4 = 10: 1,2,5,10 ∑5 = 15: 1,3,5,15 ∑6 = 21: 1,3,7,21 ∑7 = 28: 1,2,4,7,14,28 Here’s how I proceeded: First Step: Find the smallest number with 500 divisors. Seems like a good starting point to begin our search. Second Step: Starting at the number found in the previous step, search for the next triangle number. Check to see whether this number has 500+ divisors. If yes, this is the number we were looking for, else… Third Step: Check n for which ∑n = triangle number found in the previous step Fourth Step: Add (n+1) to the last triangle number found, to find the next triangle number. Check whether this number has 500+ divisors. If yes, this number is the answer. If not, repeat Fourth Step till the process terminates. Now for the details: The First Step isn’t exactly a piece of cake, but necessary to reduce computation time. I solved this with a bit of mental math. The main tool for the feat is the prime number decomposition theorem: Every integer N is the product of powers of prime numbers N = pαqβ· … · rγ Where p, q, …, r are prime, while α, β, …, γ are positive integers. Such representation is unique up to the order of the prime factors. If N is a power of a prime, N = pα, then it has α + 1 factors: 1, p, …, pα-1, pα The total number of factors of N equals (α + 1)(β + 1) … (γ + 1) 500 = 2 x 2 x 5 x 5 x 5 So, the number in question should be of the form abq4r4s4 where a, b, q, r, s are primes that minimize abq4r4s4. This is satisfied by 7x11x24x34x54 = 62370000. This marks the end of the First Step which is where we start our search for our magic number. The next 3 steps would need helper functions defined as below: from math import * # Function to calculate the number of divisors of integer n def divisors(n): limit = int(sqrt(n)) divisors_list = [] for i in range(1, limit+1, 1): if n % i == 0: divisors_list.append(i) if i != n/i: divisors_list.append(n/i) return len(divisors_list) # Function to check for triangle number def isTriangleNumber(n): a = int(sqrt(2*n)) return 0.5*a*(a+1) == n # Function to calculate the last term of the series adding up to the triangle number def lastTerm(n): if isTriangleNumber(n): return int(sqrt(2*n)) else: return None view raw euler12functions.py hosted with ❤ by GitHub As can be seen from the above code, the algorithm to calculate divisors of an integer is as follows: 1. Start by inputting a number n 2. Let an int variable limit = √n 3. Run a loop from i = 1 to  i = limit 3.1 if n is divisible by i 3.1.1 Add i to the list of divisors 3.1.2 if i and n/i are unequal, add n/i to the list too. 4. End Finally, executing the 4 steps mentioned earlier can be done like so (the code took less than 2s to arrive at the answer): # First Step # First number 'check' to have 500 divisors check = 2**4 * 3**4 * 5**4 * 7 * 11 # Second Step # Starting from 'check', iterate sequentially checking for the next 'triangle' number while not isTriangleNumber(check): check += 1 # Third and Fourth Steps # Calculate the last term of the series ('seriesLastTerm') that adds up to the newly calculated triangle number 'check' seriesLastTerm = lastTerm(check) # Iterate over triangle numbers checking for divisors > 500 while divisors(check) <= 500: # add the next term to check to get the next triangle number check += (seriesLastTerm + 1) seriesLastTerm += 1 print check Ans: 76576500

crawl-data/CC-MAIN-2021-39/segments/1631780056900.32/warc/CC-MAIN-20210919190128-20210919220128-00368.warc.gz

### Question 13 1. Edem and his wife were invited to a dinner by a family of 5. They all sat in such a way that Edem sat next to his wife. Find the number of ways of sitting them in a row. 2. A bag contains 4 red and 5 black identical balls. If 5 balls are selected at random from the bag, one after the other with replacement, find the probability that: (i) a red ball was picked 3 times; (ii) a black ball was picked at most 2 times. ### Observation The Chief Examiner reported that this question attracted majority of the candidates and described their performance as fair. According to the report, majority of the candidates performed better in part (b) than in part (a). In part (a), candidates were reported to have performed poorly. Candidates were expected to recognize the problem as that of permutation. There were two ways of sitting Edem and his wife. Taking them as one person, there would then be 6! Ways of sitting everybody at the table. Therefore, the number of ways of sitting at the table if Edem is to sit next to his wife = 2 × 6! Ways = 1440 ways. In part (b), candidates performed better. They were reported to recognize that the problem followed a binomial distribution, P(x = r) = nCrprqn – r, where n = number of trials, p = probability of success, q = probability of failure and r = favourable number of times. In part (b)(i), n = 5, r = 3, p =  and q = . Therefore, P(x = 3) = 5C3 = 10 = 0.270961. In part (b)(ii), n = 5, r = 0 or 1 or 2, p =  and q =  . Therefore, the required probability was P(x = 0) + P(x = 1) + P(x = 2) = 5C0 + 5C1 + 5C2 = 0.396687.

crawl-data/CC-MAIN-2018-34/segments/1534221210133.37/warc/CC-MAIN-20180815141842-20180815161842-00379.warc.gz

the thermal state of matter with reference to its ability to transfer heat to other matter. Temperature is distinguished from heat in that heat is the energy that is transferred between matter by radiation, conduction and/or convection. The three most common scales for measuring temperature are centigrade, Fahrenheit and Kelvin. To be defined An exposure limit based on an 8 hour workday and a 40 hour work week. all elements that follow the Actinides. As with all elements larger than uranium (U), these elements can only be produced in nuclear reactors or particle accelerators. While some of these elements of the transactinides are commonly lumped with metals, not enough information is available for this site to positively conclude whether elements 116 and 118 should be included with the metals or nonmetals. Indeed it may be completely in appropriate to lump these elements with either the metals or nonmetals. Only time will tell what the scientific community will ultimately decide. This series include all elements in the sub-series Lanthanides and Actinides of the inner-transition elements and at least part of the sub-series Transactinides, which are the elements following the Actinides series. In general these elements are known for their hardness, high density, high melting point and boiling point and heat conduction although there are exceptions. These elements all have a d electron as the differentiating electron in their electron configuration. In other words, their outer most electrons are always in the d orbital. Note that the 4 S orbital actually filled before 3d. The 3d acts as the outer most orbital and is the one involved in reactions. These metals frequently have more than one oxidation state. Our sample Iron has two oxidation states +2 and +3. These may be represented as Iron II and Iron III or the ferrous ion (+2) and ferric ion (+3). Ferrous and ferric are Latin terms. The symbols for iron II and iron III are Fe II and Fe III as one might expect. Many of these elements are electropositive enough to replace hydrogen (H) from acid solutions. They also form complex ions and coordinate covalent compounds (in which one element dominates both electrons). If you need to cite this page, you can copy this text: Kenneth Barbalace. Chemistry & Environmental Dictionary - Thermal Conductivity - Transition Metals. EnvironmentalChemistry.com. 1995 - 2021. Accessed on-line: 7/31/2021

<urn:uuid:3ea829b9-a326-444d-8252-5383d0e08666>

Did you know that the Lehigh Valley was once a major producer of potatoes? Or that Tioga County had a robust tobacco-growing industry? Or that Southwestern Pennsylvania was known for its sheep farms? The list of agricultural products grown and produced in Pennsylvania over the past 300 years is as long and diverse as the state is large. When you put all of these pieces of information on a map, some very interesting and unexpected patterns emerge, and these patterns have a lot to tell us about why our agricultural buildings and landscapes look the way that they do. As one way of sharing this interesting information about agricultural production patterns in Pennsylvania with the general public, the Bureau for Historic Preservation’s (BHP) exhibit at the 2013 Farm Show will showcase the map prepared as part of the recently completed Pennsylvania Agricultural History Project. The map, which illustrates the 16 distinct agricultural regions, is the exhibit’s centerpiece. While the regional boundaries are not hard and fast, in general these regions share soil types, topography, and climate. They also possess in common historical production patterns, social makeup, land tenure customs, labor forces, and cultural makeup.The supporting narratives found in the agricultural context explain in detail each region’s characteristics. While the geographic regions displayed on the map were determined by the researchers from Penn State, the task of digitizing the map was undertaken by the PHPO’s CRGIS Section. They provided us with a pdf of the completed region map and we used ESRI’S ArcGIS 10.1. to geoprocess the image, or position the image in a GIS so that it was aligned with the Pennsylvania border. The next step was to begin tracing the outline of the regions. Doing this created what is called a shapefile. Inside of the shapefile, each region is represented by an individual polygon with attribute data behind it. In the table of attributes you can input any data that you feel is needed. For our purposes we limited the attribute data to contain an automatically generated identification number and the name of the agricultural region. Once this was complete, a color scheme was chosen and applied to the selected attribute of the shapefile. This process is called Color Classification. After the colors were chosen and finalized we added a layer that has the outlines of the 67 counties of Pennsylvania. We set the label of this layer so that it will display all of the names of the counties. In the eastern portion of the state, some of the county names are too long to fit inside the borders of their polygons. These names then have to be moved or turned so that they fit in a reasonable and eye pleasing manner. When all of these layers were compiled, the map was complete and we exported it from ArcMap into an image that can easily be used by our staff and others outside the agency. We chose a TIFF format for sending to our exhibit staff and a JPG for use on our website. In addition to maintaining the maps and data bases of historic and archeological records of the Commonwealth, the CRGIS Section prepares graphics and reports for other BHP Divisions and outside users. The Pennsylvania Agricultural History Project was a collaboration among the Pennsylvania Historical and Museum Commission’s Bureau for Historic Preservation, the Pennsylvania Department of Transportation, U.S. Department of Transportation, the Federal Highways Administration, and the Pennsylvania State University. For more information please visit our website. http://phmc.info/aghistory) To see the final image used for our display, please come to the Pennsylvania Farm Show and visit our booth. We look forward to seeing you there. The Farm Show is open daily, Saturday, January 4 – January 11 and is generally open from 8:00 a.m. – 9:00 p.m.

<urn:uuid:be288ec0-cb39-476f-9993-cbe2aa0cf292>

## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition) $x=\dfrac{-2y+z-13}{2}$ Using the properties of equality, in terms of $x$, the given equation, $z=13+2(x+y)$, is equivalent to \begin{array}{l} z=13+2x+2y \\\\ -2x=13+2y-z \\\\ x=\dfrac{13+2y-z}{-2} \\\\ x=-\dfrac{13+2y-z}{2} \\\\ x=\dfrac{-13-2y+z}{2} \\\\ x=\dfrac{-2y+z-13}{2} .\end{array}

crawl-data/CC-MAIN-2018-34/segments/1534221210133.37/warc/CC-MAIN-20180815141842-20180815161842-00119.warc.gz

There were several different types of Indians who occupied what is now Ohio. These people ranged from the Paleo-Indians who date back to 13,000 B.C., to the Shawnee and Algonquin Indians who occupied the area during the Colonial and Early Republic times. were the first humans to occupy present-day Ohio. These people date back to 13,000 B.C. and survived by hunting large vertebrates such as the wooly mammoth and the mastodon. The next group of people to occupy the area were the Archaic people, a hunting and gathering group that disappeared by 1000 B.C. The Adena came after the Archaic. These inhabitants appeared in Ohio sometime between 1000 and 800 B.C. The Adena were semi-permanent, cultivators and traders. They left behind burial mounds that still exist today. This group disappeared sometime between A.D. 100 and 300 . The Hopewell began to occupy the southern Ohio river valleys around 100 BC. Like the Adena, the Hopewell were hunters and gatherers as well as traders and cultivators. These people left behind artwork in the form of large geometric shapes in the ground that can still be seen today in Marietta, Newark, Portsmouth and Hamilton County. These shapes are interesting not only for their artistic value but because they indicate that the Hopewell possessed some surveying skills. But, by A.D. 600 these people After A.D. 1000 two distinct groups would follow the Hopewell, the Fort Ancient People and the Whittlesey Focus People. The Fort Ancient people lived in southern Ohio and were part of a larger Mississippi people who demonstrated similarities to native cultures of central Mexico. These people grew new strains of maize, beans and squash which allowed them to sustain a larger settlement. By the mid 17th century, however, they too would disappear, with the remains possibly being absorbed by the Shawnee. The Whittlesey Focus People inhabited northern Ohio, building villages that overlooked the river valleys. Many of these people fell victim to European diseases or guns in the hands of Iroquois. With the coming of the Iroquois, Ohio's pre-historic Indian period comes to an end, and the Historic Indian period begins. For fifty years after the demise of the pre-historic people no one inhabited Ohio. The Five Nations of the Iroquois Confederacy, later known as the Six Nations, were based in New York and destroyed tribes ranging from the Northern Great Lakes region to the Ohio River. Small villages would begin to appear in Ohio in the early 18th century becoming more permanent by the 1730s. From the north came the Hurons, also known as the Wyandots. They were of the Iroquoian linguistic group who settled in the Sandusky Bay area of Ohio after being driven from Ontario by the Iroquois. In the 1740s, the Miamis came to Ohio from the west. These people were also known as the Mingos, and were of the Algonquin linguistic group. This group was a combination of people from other tribes, mostly Senecas, but Cayugas, Mohawks, Onandagas, Oniedas, Tuscaroras and Mohicans were among them as well. The Ottowa, an Algonquin linguistic group, moved into Ohio from the north in 1740, and the Shawnee, another Algonquin group, came from Pennsylvania to occupy Ohio's Scioto Valley. Between 1750 and 1815 other tribes moved into Ohio for short periods of time; some of these tribes include the Pottawatomies, Chippewas, Kickapoos The Native Americans of Ohio enjoyed a long history before the discovery of the Americas by Europeans, and played a big role in the settlement of Ohio by way of resistance. Many Native Americans took part in Indian wars, as well as the French and Indian War and the American The French Presence While the English were settling Jamestown, the French were gaining a foothold on the St. Lawrence, a river explored by Jacques Cartier in the 1530s and 1540s who claimed it for France. Samuel de Champlain established a post in Quebec in 1608 and continued to establish a French presence in North America over the next The area that includes present day Ohio became the subject of a three way tug of war. The British, wanting control of the Great Lakes region, claimed that their charters from the King gave them the right to it. However, the French discovered the region first, and claimed it for themselves while the Native American presence was laying claim to the entire Great Lakes and Northwestern The French continued to build forts in the region and maintained trade with the Indians. Meanwhile, traders from Pennsylvania and Virginia began to encroach on French and Indian trade relations by undercutting French prices. Virginia traders and settlement companies continued pushing into the area, and the French continued building fortifications. Soon, these French forts would be interpreted as an invasion, and the war between the colonists and the French would begin. The French and Indian War The French controlled the Ohio area for three years during the war, but by 1759 all of the key French forts had fallen. In 1760 Montreal was seized, proving to be the final blow to the French. After the British had won, they held claim of the Great Lakes region, and had to control it, which was hard to do because of constant Indian attacks. England was forced to deplore 100,000 men to the Colonies to control the borders, which Parliament didn't want to pay for. This led to the Sugar Act, a tax on the Colonists which kindled separatist fervor, one of several factors leading up to the American Revolution. Ohio and the American Revolution Although not yet a state, Ohio Played a significant role in the Revolution. The issues between the French, English and the Indians in the Ohio area were a precursor to the war and added to the desire for the colonists to rule themselves. There was also a lot of fighting that took place in what is now Ohio, and when the war ended in the east, it was brought to a climax in the Northwest in 1782 when a group of Christian Indians were massacred University of California, Santa Barbara of Historical Reviews © 2005 Rickie Lazzerini, All Rights Reserved This page may be freely linked to but may not in any form without prior written consent from

<urn:uuid:a38b7620-a09e-4673-8eee-cdcf4b222cce>

Designed for students at the top end of primary school and lower secondary school, as well as adult basic skills learners, this is an intermediate resource between a simple wordbook and a full adult dictionary. It contains over 8000 words with simple definitions, offering writing and spelling support without complicated meanings and grammatical labelling. Black and red colour coding is used to identify head word, definition, derivatives and plurals, and there are clear headings at the top of each page. - Format: Paperback - Pages: 224 pages, illustrations - Publisher: Bloomsbury Publishing PLC - Publication Date: 31/10/2002 - Category: Dictionaries - ISBN: 9780713665123

<urn:uuid:a60350b1-44a7-4b79-b7be-f9911e36075e>

The Piano Lesson The Piano Lesson Memory and the Past Quotes How we cite our quotes: Citations follow this format: (Act.Scene.Line). Every time a character talks counts as one line, even if what they say turns into a long monologue. Boy Willie: "Uncle Doaker tell me your mama got you playing that piano." (1.1.208) It's interesting that Berniece encourages her daughter, Maretha, to play on the piano, while she herself doesn't. Perhaps, even though Berniece is trying to lay the spirits of the piano to rest, some part of her wants to stay connected to them. It could be that she's in some ways living vicariously through her daughter. Doaker: "See, now […] to understand about that piano…you got to go back to slavery time." (1.2.111) Doaker launches into a big long monologue to explain the history of the piano. After he's done we finally know what all the fuss has been about. It becomes clear by the end of Doaker's story just how much the Charles family's past hovers over them. Doaker: "Now…am I telling it right, Wining Boy? Wining Boy: "You telling it." (1.2.116) Doaker and Wining Boy are the oldest characters in the play. They both function as living history books, who pass on the family's past through storytelling. The storyteller has been an important role in many cultures, but in many African cultures this person was called a griot. It was the griot's job to preserve the history of a community through song and storytelling. So, you can see both Doaker and Wining Boy are kind of like 1930ss era African American versions of this ancient occupation. Click here to learn more about griots.

<urn:uuid:837a0c38-bab5-42ea-9686-9dff7cae5a54>

Posted on Categories:Curves And Surfaces, 数学代写, 曲线和曲面 # 数学代写|曲线和曲面代写Curves And Surfaces代考|MATH5270 The Jordan curve theorem avatest™ ## avatest™帮您通过考试 avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！ •最快12小时交付 •200+ 英语母语导师 •70分以下全额退款 ## 数学代写|曲线和曲面代写Curves And Surfaces代考|The Jordan curve theorem In this section we shall complete the proof of the Jordan curve theorem for regular curves, by showing that the complement of the support of a simple closed regular plane curve of class $C^2$ has at least two components. To get there we need a new ingredient, which we shall construct by using the degree introduced in Section 2.1. Given a continuous closed plane curve, there are (at least) two ways to associate with it a curve with values in $S^1$, and consequently a degree. In this section we are interested in the first way, while in next section we shall use the second one. Definition 2.3.1. Let $\sigma:[a, b] \rightarrow \mathbb{R}^2$ be a continuous closed plane curve. Given a point $p \notin \sigma([a, b])$ we may define $\phi_p:[a, b] \rightarrow S^1$ by setting $$\phi_p(t)=\frac{\sigma(t)-p}{|\sigma(t)-p|} .$$ The winding number $\iota_p(\sigma)$ of $\sigma$ with respect to $p$ is, by definition, the degree of $\phi_p$; it measures the number of times $\sigma$ goes around the point $p$. Fig. $2.4$ shows the winding number of a curve with respect to several points, computed as we shall see in Example 2.3.5. ## 数学代写|曲线和曲面代写Curves And Surfaces代考|The turning tangents theorem There is another very natural way of associating a $S^1$-valued curve (and consequently a degree) with a closed regular plane curve. Definition 2.4.1. Let $\sigma:[a, b] \rightarrow \mathbb{R}^2$ be a closed regular plane curve of class $C^1$, and let $\mathbf{t}:[a, b] \rightarrow S^1$ be its tangent versor, given by $$\mathbf{t}(t)=\frac{\sigma^{\prime}(t)}{\left|\sigma^{\prime}(t)\right|} .$$ The rotation index $\rho(\sigma)$ of $\sigma$ is the degree of the map $\mathbf{t}$; it counts the number of full turns made by the tangent versor to $\sigma$. Corollary 2.1.18 provides us with a simple formula to compute the rotation index: Proposition 2.4.2. Let $\sigma:[a, b] \rightarrow \mathbb{R}^2$ be a closed regular plane curve of class $C^1$ with oriented curvature $\tilde{\kappa}:[a, b] \rightarrow \mathbb{R}$. Then $$\rho(\sigma)=\frac{1}{2 \pi} \int_a^b \tilde{\kappa}\left|\sigma^{\prime}\right| \mathrm{d} t=\frac{1}{2 \pi} \int_a^b \frac{\operatorname{det}\left(\sigma^{\prime}, \sigma^{\prime \prime}\right)}{\left|\sigma^{\prime}\right|^2} \mathrm{~d} t .$$ Proof. By Corollary 2.1.18, $$\rho(\sigma)=\frac{1}{2 \pi} \int_a^b \operatorname{det}\left(\mathbf{t}, \mathbf{t}^{\prime}\right) \mathrm{d} t$$ ## 数学代写|曲线和曲面代写Curves And Surfaces代考|The Jordan curve theorem $$\phi_p(t)=\frac{\sigma(t)-p}{|\sigma(t)-p|} .$$ ## 数学代写|曲线和曲面代写Curves And Surfaces代考|The turning tangents theorem $$\mathbf{t}(t)=\frac{\sigma^{\prime}(t)}{\left|\sigma^{\prime}(t)\right|} .$$ $$\rho(\sigma)=\frac{1}{2 \pi} \int_a^b \tilde{\kappa}\left|\sigma^{\prime}\right| \mathrm{d} t=\frac{1}{2 \pi} \int_a^b \frac{\operatorname{det}\left(\sigma^{\prime}, \sigma^{\prime \prime}\right)}{\left|\sigma^{\prime}\right|^2} \mathrm{~d} t .$$ $$\rho(\sigma)=\frac{1}{2 \pi} \int_a^b \operatorname{det}\left(\mathbf{t}, \mathbf{t}^{\prime}\right) \mathrm{d} t$$ ## MATLAB代写 MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

crawl-data/CC-MAIN-2024-38/segments/1725700651303.70/warc/CC-MAIN-20240910161250-20240910191250-00126.warc.gz

' # Search results Found 921 matches Optimum conical horn antenna A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are ... more Centripetal Force - angular velocity Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more Aperture area Aperture is a “hole” or an opening through which light travels. The aperture of an optical system is the opening that determines the cone angle ... more Tuning fork A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually ... more Worksheet 334 In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates (-3, 5). If the player rotates counterclockwise by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character. To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by 20 degrees. To do so, we first need to find the radius of this circle and the original angle. Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem: Pythagorean theorem (right triangle) To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get Cosine function Subtraction While there are two angles that have this cosine value, the angle of 120.964 degrees is in the second quadrant as desired, so it is the angle we were looking for. Rotating the point clockwise by 20 degrees, the angle of the point will decrease to 100.964 degrees. We can then evaluate the coordinates of the rotated point For x axis: Cosine function For y axis: Sine function The coordinates of the character on the rotated map will be (-1.109, 5.725) Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen http://www.opentextbookstore.com/precalc/ Gyromagnetic ratio for an isolated electron In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its ... more Guided ray (acceptance angle) A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber ( type of optical fiber mostly used for communication over ... more Alfvén velocity (in SI) In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave in which ions oscillate in response to a restoring ... more Alfvén velocity In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave in which ions oscillate in response to a restoring ... more The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the ... more ...can't find what you're looking for? Create a new formula ### Search criteria: Similar to formula Category

crawl-data/CC-MAIN-2022-49/segments/1669446711064.71/warc/CC-MAIN-20221205232822-20221206022822-00749.warc.gz

## Rational Functions ### Learning Objectives In this section, you will: • Use arrow notation. • Solve applied problems involving rational functions. • Find the domains of rational functions. • Identify vertical asymptotes. • Identify horizontal asymptotes. • Graph rational functions. Suppose we know that the cost of making a product is dependent on the number of items,$\,x,\,$produced. This is given by the equation$\,C\left(x\right)=15,000x-0.1{x}^{2}+1000.\,$If we want to know the average cost for producing$\,x\,$items, we would divide the cost function by the number of items,$\,x.$ The average cost function, which yields the average cost per item for$\,x\,$items produced, is $f\left(x\right)=\frac{15,000x-0.1{x}^{2}+1000}{x}$ Many other application problems require finding an average value in a similar way, giving us variables in the denominator. Written without a variable in the denominator, this function will contain a negative integer power. In the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables in the denominator. ### Using Arrow Notation We have seen the graphs of the basic reciprocal function and the squared reciprocal function from our study of toolkit functions. Examine these graphs, as shown in (Figure), and notice some of their features. Figure 1. Several things are apparent if we examine the graph of$\,f\left(x\right)=\frac{1}{x}.$ 1. On the left branch of the graph, the curve approaches the x-axis$\,\left(y=0\right) \text{as} x\to –\infty .$ 2. As the graph approaches$\,x=0\,$from the left, the curve drops, but as we approach zero from the right, the curve rises. 3. Finally, on the right branch of the graph, the curves approaches the x-axis$\,\left(y=0\right) \text{as} x\to \infty .$ To summarize, we use arrow notation to show that$\,x\,$or$\,f\left(x\right)\,$is approaching a particular value. See (Figure). Symbol Meaning $x\to {a}^{-}$ $x\,$approaches$\,a\,$from the left ($x<a\,$but close to$\,a$) $x\to {a}^{+}$ $x\,$approaches$\,a\,$from the right ($x>a\,$but close to$\,a$) $x\to \infty$ $x\,$approaches infinity ($x\,$increases without bound) $x\to -\infty$ $x\,$approaches negative infinity ($x\,$decreases without bound) $f\left(x\right)\to \infty$ the output approaches infinity (the output increases without bound) $f\left(x\right)\to -\infty$ the output approaches negative infinity (the output decreases without bound) $f\left(x\right)\to a$ the output approaches$\,a$ #### Local Behavior of$\,f\left(x\right)=\frac{1}{x}$ Let’s begin by looking at the reciprocal function,$\,f\left(x\right)=\frac{1}{x}.\,$We cannot divide by zero, which means the function is undefined at$\,x=0;\,$so zero is not in the domain. As the input values approach zero from the left side (becoming very small, negative values), the function values decrease without bound (in other words, they approach negative infinity). We can see this behavior in (Figure). $x$ –0.1 –0.01 –0.001 –0.0001 $f\left(x\right)=\frac{1}{x}$ –10 –100 –1000 –10,000 We write in arrow notation $\text{as }x\to {0}^{-},f\left(x\right)\to -\infty$ As the input values approach zero from the right side (becoming very small, positive values), the function values increase without bound (approaching infinity). We can see this behavior in (Figure). $x$ 0.1 0.01 0.001 0.0001 $f\left(x\right)=\frac{1}{x}$ 10 100 1000 10,000 We write in arrow notation $\text{As }x\to {0}^{+}, f\left(x\right)\to \infty .$ See (Figure). Figure 2. This behavior creates a vertical asymptote, which is a vertical line that the graph approaches but never crosses. In this case, the graph is approaching the vertical line$\,x=0\,$as the input becomes close to zero. See (Figure). Figure 3. ### Vertical Asymptote A vertical asymptote of a graph is a vertical line$\,x=a\,$where the graph tends toward positive or negative infinity as the inputs approach$\,a.\,$We write $\text{As }x\to a,f\left(x\right)\to \infty , \text{or as }x\to a,f\left(x\right)\to -\infty .$ #### End Behavior of$\,f\left(x\right)=\frac{1}{x}$ As the values of$\,x\,$approach infinity, the function values approach 0. As the values of$\,x\,$approach negative infinity, the function values approach 0. See (Figure). Symbolically, using arrow notation $\text{As }x\to \infty ,f\left(x\right)\to 0,\text{and as }x\to -\infty ,f\left(x\right)\to 0.$ Figure 4. Based on this overall behavior and the graph, we can see that the function approaches 0 but never actually reaches 0; it seems to level off as the inputs become large. This behavior creates a horizontal asymptote, a horizontal line that the graph approaches as the input increases or decreases without bound. In this case, the graph is approaching the horizontal line$\,y=0.\,$See (Figure). Figure 5. ### Horizontal Asymptote A horizontal asymptote of a graph is a horizontal line$\,y=b\,$where the graph approaches the line as the inputs increase or decrease without bound. We write $\,\text{As }x\to \infty \text{ or }x\to -\infty ,\text{ }f\left(x\right)\to b.$ ### Using Arrow Notation Use arrow notation to describe the end behavior and local behavior of the function graphed in (Figure). Figure 6. ### Try It Use arrow notation to describe the end behavior and local behavior for the reciprocal squared function. ### Using Transformations to Graph a Rational Function Sketch a graph of the reciprocal function shifted two units to the left and up three units. Identify the horizontal and vertical asymptotes of the graph, if any. #### Analysis Notice that horizontal and vertical asymptotes are shifted left 2 and up 3 along with the function. ### Try It Sketch the graph, and find the horizontal and vertical asymptotes of the reciprocal squared function that has been shifted right 3 units and down 4 units. ### Solving Applied Problems Involving Rational Functions In (Figure), we shifted a toolkit function in a way that resulted in the function$\,f\left(x\right)=\frac{3x+7}{x+2}.\,$This is an example of a rational function. A rational function is a function that can be written as the quotient of two polynomial functions. Many real-world problems require us to find the ratio of two polynomial functions. Problems involving rates and concentrations often involve rational functions. ### Rational Function A rational function is a function that can be written as the quotient of two polynomial functions$\,P\left(x\right) \text{and} Q\left(x\right).$ $f\left(x\right)=\frac{P\left(x\right)}{Q\left(x\right)}=\frac{{a}_{p}{x}^{p}+{a}_{p-1}{x}^{p-1}+…+{a}_{1}x+{a}_{0}}{{b}_{q}{x}^{q}+{b}_{q-1}{x}^{q-1}+…+{b}_{1}x+{b}_{0}},Q\left(x\right)\ne 0$ ### Solving an Applied Problem Involving a Rational Function A large mixing tank currently contains 100 gallons of water into which 5 pounds of sugar have been mixed. A tap will open pouring 10 gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of 1 pound per minute. Find the ratio of sugar to water, in pounds per gallon in the tank after 12 minutes. Is that a greater ratio of sugar to water, in pounds per gallon than at the beginning? ### Try It There are 1,200 freshmen and 1,500 sophomores at a prep rally at noon. After 12 p.m., 20 freshmen arrive at the rally every five minutes while 15 sophomores leave the rally. Find the ratio of freshmen to sophomores at 1 p.m. ### Finding the Domains of Rational Functions A vertical asymptote represents a value at which a rational function is undefined, so that value is not in the domain of the function. A reciprocal function cannot have values in its domain that cause the denominator to equal zero. In general, to find the domain of a rational function, we need to determine which inputs would cause division by zero. ### Domain of a Rational Function The domain of a rational function includes all real numbers except those that cause the denominator to equal zero. ### How To Given a rational function, find the domain. 1. Set the denominator equal to zero. 2. Solve to find the x-values that cause the denominator to equal zero. 3. The domain is all real numbers except those found in Step 2. ### Finding the Domain of a Rational Function Find the domain of$\,f\left(x\right)=\frac{x+3}{{x}^{2}-9}.$ #### Analysis A graph of this function, as shown in (Figure), confirms that the function is not defined when$\,x=±3.$ Figure 8. There is a vertical asymptote at$\,x=3\,$and a hole in the graph at$\,x=-3.\,$We will discuss these types of holes in greater detail later in this section. ### Try It Find the domain of$\,f\left(x\right)=\frac{4x}{5\left(x-1\right)\left(x-5\right)}.$ ### Identifying Vertical Asymptotes of Rational Functions By looking at the graph of a rational function, we can investigate its local behavior and easily see whether there are asymptotes. We may even be able to approximate their location. Even without the graph, however, we can still determine whether a given rational function has any asymptotes, and calculate their location. #### Vertical Asymptotes The vertical asymptotes of a rational function may be found by examining the factors of the denominator that are not common to the factors in the numerator. Vertical asymptotes occur at the zeros of such factors. Given a rational function, identify any vertical asymptotes of its graph. 1. Factor the numerator and denominator. 2. Note any restrictions in the domain of the function. 3. Reduce the expression by canceling common factors in the numerator and the denominator. 4. Note any values that cause the denominator to be zero in this simplified version. These are where the vertical asymptotes occur. 5. Note any restrictions in the domain where asymptotes do not occur. These are removable discontinuities, or “holes.” ### Identifying Vertical Asymptotes Find the vertical asymptotes of the graph of$\,k\left(x\right)=\frac{5+2{x}^{2}}{2-x-{x}^{2}}.$ #### Removable Discontinuities Occasionally, a graph will contain a hole: a single point where the graph is not defined, indicated by an open circle. We call such a hole a removable discontinuity. For example, the function$\,f\left(x\right)=\frac{{x}^{2}-1}{{x}^{2}-2x-3}\,$may be re-written by factoring the numerator and the denominator. $f\left(x\right)=\frac{\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\left(x-3\right)}$ Notice that$\,x+1\,$is a common factor to the numerator and the denominator. The zero of this factor,$\,x=-1,\,$is the location of the removable discontinuity. Notice also that$\,x–3\,$is not a factor in both the numerator and denominator. The zero of this factor,$\,x=3,\,$is the vertical asymptote. See (Figure). [Note that removable discontinuities may not be visible when we use a graphing calculator, depending upon the window selected.] Figure 10. ### Removable Discontinuities of Rational Functions A removable discontinuity occurs in the graph of a rational function at$\,x=a\,$if$\,a\,$is a zero for a factor in the denominator that is common with a factor in the numerator. We factor the numerator and denominator and check for common factors. If we find any, we set the common factor equal to 0 and solve. This is the location of the removable discontinuity. This is true if the multiplicity of this factor is greater than or equal to that in the denominator. If the multiplicity of this factor is greater in the denominator, then there is still an asymptote at that value. ### Identifying Vertical Asymptotes and Removable Discontinuities for a Graph Find the vertical asymptotes and removable discontinuities of the graph of$\,k\left(x\right)=\frac{x-2}{{x}^{2}-4}.$ ### Try It Find the vertical asymptotes and removable discontinuities of the graph of$\,f\left(x\right)=\frac{{x}^{2}-25}{{x}^{3}-6{x}^{2}+5x}.$ ### Identifying Horizontal Asymptotes of Rational Functions While vertical asymptotes describe the behavior of a graph as the output gets very large or very small, horizontal asymptotes help describe the behavior of a graph as the input gets very large or very small. Recall that a polynomial’s end behavior will mirror that of the leading term. Likewise, a rational function’s end behavior will mirror that of the ratio of the function that is the ratio of the leading terms. There are three distinct outcomes when checking for horizontal asymptotes: Case 1: If the degree of the denominator > degree of the numerator, there is a horizontal asymptote at$\,y=0.$ $\text{Example: }f\left(x\right)=\frac{4x+2}{{x}^{2}+4x-5}$ In this case, the end behavior is$\,f\left(x\right)\approx \frac{4x}{{x}^{2}}=\frac{4}{x}.\,$This tells us that, as the inputs increase or decrease without bound, this function will behave similarly to the function$\,g\left(x\right)=\frac{4}{x},\,$and the outputs will approach zero, resulting in a horizontal asymptote at$\,y=0.\,$See (Figure). Note that this graph crosses the horizontal asymptote. Figure 12. Horizontal asymptote$\,y=0\,$when$\,f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)},\,q\left(x\right)\ne 0\,\text{where degree of}\,p<\text{degree of }q.$ Case 2: If the degree of the denominator < degree of the numerator by one, we get a slant asymptote. $\text{Example: }f\left(x\right)=\frac{3{x}^{2}-2x+1}{x-1}$ In this case, the end behavior is$\,f\left(x\right)\approx \frac{3{x}^{2}}{x}=3x.\,$This tells us that as the inputs increase or decrease without bound, this function will behave similarly to the function$\,g\left(x\right)=3x.\,$As the inputs grow large, the outputs will grow and not level off, so this graph has no horizontal asymptote. However, the graph of$\,g\left(x\right)=3x\,$looks like a diagonal line, and since$\,f\,$will behave similarly to$\,g,\,$it will approach a line close to$\,y=3x.\,$This line is a slant asymptote. To find the equation of the slant asymptote, divide$\,\frac{3{x}^{2}-2x+1}{x-1}.\,$The quotient is$\,3x+1,\,$and the remainder is 2. The slant asymptote is the graph of the line$\,g\left(x\right)=3x+1.\,$See (Figure). Figure 13. Slant asymptote when$\,f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)},\,q\left(x\right)\ne 0\,$where degree of$\,p>\text{degree of }q\,\text{by}\,\text{1}\text{.}\,$ Case 3: If the degree of the denominator = degree of the numerator, there is a horizontal asymptote at$\,y=\frac{{a}_{n}}{{b}_{n}},\,$where$\,{a}_{n}\,$and$\,{b}_{n}\,$are the leading coefficients of$\,p\left(x\right)\,$and$\,q\left(x\right)\,$for$\,f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)},q\left(x\right)\ne 0.$ $\text{Example: }f\left(x\right)=\frac{3{x}^{2}+2}{{x}^{2}+4x-5}$ In this case, the end behavior is$\,f\left(x\right)\approx \frac{3{x}^{2}}{{x}^{2}}=3.\,$This tells us that as the inputs grow large, this function will behave like the function$\,g\left(x\right)=3,\,$which is a horizontal line. As$\,x\to ±\infty ,f\left(x\right)\to 3,\,$resulting in a horizontal asymptote at$\,y=3.\,$See (Figure). Note that this graph crosses the horizontal asymptote. Figure 14. Horizontal asymptote when$\,f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)},\,q\left(x\right)\ne 0\,\text{where degree of }p=\text{degree of }q.$ Notice that, while the graph of a rational function will never cross a vertical asymptote, the graph may or may not cross a horizontal or slant asymptote. Also, although the graph of a rational function may have many vertical asymptotes, the graph will have at most one horizontal (or slant) asymptote. It should be noted that, if the degree of the numerator is larger than the degree of the denominator by more than one, the end behavior of the graph will mimic the behavior of the reduced end behavior fraction. For instance, if we had the function $f\left(x\right)=\frac{3{x}^{5}-{x}^{2}}{x+3}$ with end behavior $f\left(x\right)\approx \frac{3{x}^{5}}{x}=3{x}^{4},$ the end behavior of the graph would look similar to that of an even polynomial with a positive leading coefficient. $x\to ±\infty , f\left(x\right)\to \infty$ ### Horizontal Asymptotes of Rational Functions The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator. • Degree of numerator is less than degree of denominator: horizontal asymptote at$\,y=0.$ • Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote. • Degree of numerator is equal to degree of denominator: horizontal asymptote at ratio of leading coefficients. ### Identifying Horizontal and Slant Asymptotes For the functions listed, identify the horizontal or slant asymptote. 1. $g\left(x\right)=\frac{6{x}^{3}-10x}{2{x}^{3}+5{x}^{2}}$ 2. $h\left(x\right)=\frac{{x}^{2}-4x+1}{x+2}$ 3. $k\left(x\right)=\frac{{x}^{2}+4x}{{x}^{3}-8}$ ### Identifying Horizontal Asymptotes In the sugar concentration problem earlier, we created the equation$\,C\left(t\right)=\frac{5+t}{100+10t}.$ Find the horizontal asymptote and interpret it in context of the problem. ### Identifying Horizontal and Vertical Asymptotes Find the horizontal and vertical asymptotes of the function $f\left(x\right)=\frac{\left(x-2\right)\left(x+3\right)}{\left(x-1\right)\left(x+2\right)\left(x-5\right)}$ ### Try It Find the vertical and horizontal asymptotes of the function: $f\left(x\right)=\frac{\left(2x-1\right)\left(2x+1\right)}{\left(x-2\right)\left(x+3\right)}$ ### Intercepts of Rational Functions A rational function will have a y-intercept at$\,f\left(0\right)$, if the function is defined at zero. A rational function will not have a y-intercept if the function is not defined at zero. Likewise, a rational function will have x-intercepts at the inputs that cause the output to be zero. Since a fraction is only equal to zero when the numerator is zero, x-intercepts can only occur when the numerator of the rational function is equal to zero. ### Finding the Intercepts of a Rational Function Find the intercepts of$\,f\left(x\right)=\frac{\left(x-2\right)\left(x+3\right)}{\left(x-1\right)\left(x+2\right)\left(x-5\right)}.$ ### Try It Given the reciprocal squared function that is shifted right 3 units and down 4 units, write this as a rational function. Then, find the x– and y-intercepts and the horizontal and vertical asymptotes. ### Graphing Rational Functions In (Figure), we see that the numerator of a rational function reveals the x-intercepts of the graph, whereas the denominator reveals the vertical asymptotes of the graph. As with polynomials, factors of the numerator may have integer powers greater than one. Fortunately, the effect on the shape of the graph at those intercepts is the same as we saw with polynomials. The vertical asymptotes associated with the factors of the denominator will mirror one of the two toolkit reciprocal functions. When the degree of the factor in the denominator is odd, the distinguishing characteristic is that on one side of the vertical asymptote the graph heads towards positive infinity, and on the other side the graph heads towards negative infinity. See (Figure). Figure 17. When the degree of the factor in the denominator is even, the distinguishing characteristic is that the graph either heads toward positive infinity on both sides of the vertical asymptote or heads toward negative infinity on both sides. See (Figure). Figure 18. For example, the graph of$\,f\left(x\right)=\frac{{\left(x+1\right)}^{2}\left(x-3\right)}{{\left(x+3\right)}^{2}\left(x-2\right)}\,$is shown in (Figure). Figure 19. • At the x-intercept$\,x=-1\,$corresponding to the$\,{\left(x+1\right)}^{2}\,$factor of the numerator, the graph “bounces”, consistent with the quadratic nature of the factor. • At the x-intercept$\,x=3\,$corresponding to the$\,\left(x-3\right)\,$factor of the numerator, the graph passes through the axis as we would expect from a linear factor. • At the vertical asymptote$\,x=-3\,$corresponding to the$\,{\left(x+3\right)}^{2}\,$factor of the denominator, the graph heads towards positive infinity on both sides of the asymptote, consistent with the behavior of the function$\,f\left(x\right)=\frac{1}{{x}^{2}}.$ • At the vertical asymptote$\,x=2,\,$corresponding to the$\,\left(x-2\right)\,$factor of the denominator, the graph heads towards positive infinity on the left side of the asymptote and towards negative infinity on the right side, consistent with the behavior of the function$\,f\left(x\right)=\frac{1}{x}.$ ### How To Given a rational function, sketch a graph. 1. Evaluate the function at 0 to find the y-intercept. 2. Factor the numerator and denominator. 3. For factors in the numerator not common to the denominator, determine where each factor of the numerator is zero to find the x-intercepts. 4. Find the multiplicities of the x-intercepts to determine the behavior of the graph at those points. 5. For factors in the denominator, note the multiplicities of the zeros to determine the local behavior. For those factors not common to the numerator, find the vertical asymptotes by setting those factors equal to zero and then solve. 6. For factors in the denominator common to factors in the numerator, find the removable discontinuities by setting those factors equal to 0 and then solve. 7. Compare the degrees of the numerator and the denominator to determine the horizontal or slant asymptotes. 8. Sketch the graph. ### Graphing a Rational Function Sketch a graph of$\,f\left(x\right)=\frac{\left(x+2\right)\left(x-3\right)}{{\left(x+1\right)}^{2}\left(x-2\right)}.$ ### Try It Given the function$\,f\left(x\right)=\frac{{\left(x+2\right)}^{2}\left(x-2\right)}{2{\left(x-1\right)}^{2}\left(x-3\right)},\,$use the characteristics of polynomials and rational functions to describe its behavior and sketch the function. ### Writing Rational Functions Now that we have analyzed the equations for rational functions and how they relate to a graph of the function, we can use information given by a graph to write the function. A rational function written in factored form will have an x-intercept where each factor of the numerator is equal to zero. (An exception occurs in the case of a removable discontinuity.) As a result, we can form a numerator of a function whose graph will pass through a set of x-intercepts by introducing a corresponding set of factors. Likewise, because the function will have a vertical asymptote where each factor of the denominator is equal to zero, we can form a denominator that will produce the vertical asymptotes by introducing a corresponding set of factors. ### Writing Rational Functions from Intercepts and Asymptotes If a rational function has x-intercepts at$\,x={x}_{1},{x}_{2},…,{x}_{n},\,$vertical asymptotes at$\,x={v}_{1},{v}_{2},\dots ,{v}_{m},\,$and no$\,{x}_{i}=\text{any }{v}_{j},\,$then the function can be written in the form: $f\left(x\right)=a\frac{{\left(x-{x}_{1}\right)}^{{p}_{1}}{\left(x-{x}_{2}\right)}^{{p}_{2}}\cdots {\left(x-{x}_{n}\right)}^{{p}_{n}}}{{\left(x-{v}_{1}\right)}^{{q}_{1}}{\left(x-{v}_{2}\right)}^{{q}_{2}}\cdots {\left(x-{v}_{m}\right)}^{{q}_{n}}}$ where the powers$\,{p}_{i}\,$or$\,{q}_{i}\,$on each factor can be determined by the behavior of the graph at the corresponding intercept or asymptote, and the stretch factor$\,a\,$can be determined given a value of the function other than the x-intercept or by the horizontal asymptote if it is nonzero. ### How To Given a graph of a rational function, write the function. 1. Determine the factors of the numerator. Examine the behavior of the graph at the x-intercepts to determine the zeroes and their multiplicities. (This is easy to do when finding the “simplest” function with small multiplicities—such as 1 or 3—but may be difficult for larger multiplicities—such as 5 or 7, for example.) 2. Determine the factors of the denominator. Examine the behavior on both sides of each vertical asymptote to determine the factors and their powers. 3. Use any clear point on the graph to find the stretch factor. ### Writing a Rational Function from Intercepts and Asymptotes Write an equation for the rational function shown in (Figure). Figure 22. Access these online resources for additional instruction and practice with rational functions. ### Key Equations Rational Function $f\left(x\right)=\frac{P\left(x\right)}{Q\left(x\right)}=\frac{{a}_{p}{x}^{p}+{a}_{p-1}{x}^{p-1}+…+{a}_{1}x+{a}_{0}}{{b}_{q}{x}^{q}+{b}_{q-1}{x}^{q-1}+…+{b}_{1}x+{b}_{0}}, Q\left(x\right)\ne 0$ ### Key Concepts • We can use arrow notation to describe local behavior and end behavior of the toolkit functions$\,f\left(x\right)=\frac{1}{x}\,$and$\,f\left(x\right)=\frac{1}{{x}^{2}}.\,$See (Figure). • A function that levels off at a horizontal value has a horizontal asymptote. A function can have more than one vertical asymptote. See (Figure). • Application problems involving rates and concentrations often involve rational functions. See (Figure). • The domain of a rational function includes all real numbers except those that cause the denominator to equal zero. See (Figure). • The vertical asymptotes of a rational function will occur where the denominator of the function is equal to zero and the numerator is not zero. See (Figure). • A removable discontinuity might occur in the graph of a rational function if an input causes both numerator and denominator to be zero. See (Figure). • A rational function’s end behavior will mirror that of the ratio of the leading terms of the numerator and denominator functions. See (Figure), (Figure), (Figure), and (Figure). • Graph rational functions by finding the intercepts, behavior at the intercepts and asymptotes, and end behavior. See (Figure). • If a rational function has x-intercepts at$\,x={x}_{1},{x}_{2},\dots ,{x}_{n},\,$vertical asymptotes at$\,x={v}_{1},{v}_{2},\dots ,{v}_{m},\,$and no$\,{x}_{i}=\text{any }{v}_{j},\,$then the function can be written in the form $\begin{array}{l}\begin{array}{l}\hfill \\ f\left(x\right)=a\frac{{\left(x-{x}_{1}\right)}^{{p}_{1}}{\left(x-{x}_{2}\right)}^{{p}_{2}}\cdots {\left(x-{x}_{n}\right)}^{{p}_{n}}}{{\left(x-{v}_{1}\right)}^{{q}_{1}}{\left(x-{v}_{2}\right)}^{{q}_{2}}\cdots {\left(x-{v}_{m}\right)}^{{q}_{n}}}\hfill \end{array}\hfill \end{array}$ See (Figure). ### Section Exercises #### Verbal What is the fundamental difference in the algebraic representation of a polynomial function and a rational function? What is the fundamental difference in the graphs of polynomial functions and rational functions? If the graph of a rational function has a removable discontinuity, what must be true of the functional rule? Can a graph of a rational function have no vertical asymptote? If so, how? Can a graph of a rational function have no x-intercepts? If so, how? #### Algebraic For the following exercises, find the domain of the rational functions. $f\left(x\right)=\frac{x-1}{x+2}$ $f\left(x\right)=\frac{x+1}{{x}^{2}-1}$ $f\left(x\right)=\frac{{x}^{2}+4}{{x}^{2}-2x-8}$ $f\left(x\right)=\frac{{x}^{2}+4x-3}{{x}^{4}-5{x}^{2}+4}$ For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $f\left(x\right)=\frac{4}{x-1}$ $f\left(x\right)=\frac{2}{5x+2}$ $f\left(x\right)=\frac{x}{{x}^{2}-9}$ $f\left(x\right)=\frac{x}{{x}^{2}+5x-36}$ $f\left(x\right)=\frac{3+x}{{x}^{3}-27}$ $f\left(x\right)=\frac{3x-4}{{x}^{3}-16x}$ $f\left(x\right)=\frac{{x}^{2}-1}{{x}^{3}+9{x}^{2}+14x}$ $f\left(x\right)=\frac{x+5}{{x}^{2}-25}$ $f\left(x\right)=\frac{x-4}{x-6}$ $f\left(x\right)=\frac{4-2x}{3x-1}$ For the following exercises, find the x– and y-intercepts for the functions. $f\left(x\right)=\frac{x+5}{{x}^{2}+4}$ $f\left(x\right)=\frac{x}{{x}^{2}-x}$ $f\left(x\right)=\frac{{x}^{2}+8x+7}{{x}^{2}+11x+30}$ $f\left(x\right)=\frac{{x}^{2}+x+6}{{x}^{2}-10x+24}$ $f\left(x\right)=\frac{94-2{x}^{2}}{3{x}^{2}-12}$ For the following exercises, describe the local and end behavior of the functions. $f\left(x\right)=\frac{x}{2x+1}$ $f\left(x\right)=\frac{2x}{x-6}$ $f\left(x\right)=\frac{-2x}{x-6}$ $f\left(x\right)=\frac{{x}^{2}-4x+3}{{x}^{2}-4x-5}$ $f\left(x\right)=\frac{2{x}^{2}-32}{6{x}^{2}+13x-5}$ For the following exercises, find the slant asymptote of the functions. $f\left(x\right)=\frac{24{x}^{2}+6x}{2x+1}$ $f\left(x\right)=\frac{4{x}^{2}-10}{2x-4}$ $f\left(x\right)=\frac{81{x}^{2}-18}{3x-2}$ $f\left(x\right)=\frac{6{x}^{3}-5x}{3{x}^{2}+4}$ $f\left(x\right)=\frac{{x}^{2}+5x+4}{x-1}$ #### Graphical For the following exercises, use the given transformation to graph the function. Note the vertical and horizontal asymptotes. The reciprocal function shifted up two units. The reciprocal function shifted down one unit and left three units. The reciprocal squared function shifted to the right 2 units. The reciprocal squared function shifted down 2 units and right 1 unit. For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. $p\left(x\right)=\frac{2x-3}{x+4}$ $q\left(x\right)=\frac{x-5}{3x-1}$ $s\left(x\right)=\frac{4}{{\left(x-2\right)}^{2}}$ $r\left(x\right)=\frac{5}{{\left(x+1\right)}^{2}}$ $f\left(x\right)=\frac{3{x}^{2}-14x-5}{3{x}^{2}+8x-16}$ $g\left(x\right)=\frac{2{x}^{2}+7x-15}{3{x}^{2}-14x+15}$ $a\left(x\right)=\frac{{x}^{2}+2x-3}{{x}^{2}-1}$ $b\left(x\right)=\frac{{x}^{2}-x-6}{{x}^{2}-4}$ $h\left(x\right)=\frac{2{x}^{2}+ x-1}{x-4}$ $k\left(x\right)=\frac{2{x}^{2}-3x-20}{x-5}$ $w\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)\left(x-5\right)}{{\left(x+2\right)}^{2}\left(x-4\right)}$ $z\left(x\right)=\frac{{\left(x+2\right)}^{2}\left(x-5\right)}{\left(x-3\right)\left(x+1\right)\left(x+4\right)}$ For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at$\,x=5\,$and$\,x=-5,\,$x-intercepts at$\,\left(2,0\right)\,$and$\,\left(-1,0\right),\,$y-intercept at$\,\left(0,4\right)$ Vertical asymptotes at$\,x=-4\,$and$\,x=-1,\,$x-intercepts at$\,\left(1,0\right)\,$and$\,\left(5,0\right),\,$y-intercept at$\,\left(0,7\right)$ Vertical asymptotes at$\,x=-4\,$and$\,x=-5,\,$x-intercepts at$\,\left(4,0\right)\,$and$\,\left(-6,0\right),\,$Horizontal asymptote at$\,y=7$ Vertical asymptotes at$\,x=-3\,$and$\,x=6,\,$x-intercepts at$\,\left(-2,0\right)\,$and$\,\left(1,0\right),\,$Horizontal asymptote at$\,y=-2$ Vertical asymptote at$\,x=-1,\,$Double zero at$\,x=2,\,$y-intercept at$\,\left(0,2\right)$ Vertical asymptote at$\,x=3,\,$Double zero at$\,x=1,\,$y-intercept at$\,\left(0,4\right)$ For the following exercises, use the graphs to write an equation for the function. #### Numeric For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote $f\left(x\right)=\frac{1}{x-2}$ $f\left(x\right)=\frac{x}{x-3}$ $f\left(x\right)=\frac{2x}{x+4}$ $f\left(x\right)=\frac{2x}{{\left(x-3\right)}^{2}}$ $f\left(x\right)=\frac{{x}^{2}}{{x}^{2}+2x+1}$ #### Technology For the following exercises, use a calculator to graph$\,f\left(x\right).\,$Use the graph to solve$\,f\left(x\right)>0.$ $f\left(x\right)=\frac{2}{x+1}$ $f\left(x\right)=\frac{4}{2x-3}$ $f\left(x\right)=\frac{2}{\left(x-1\right)\left(x+2\right)}$ $f\left(x\right)=\frac{x+2}{\left(x-1\right)\left(x-4\right)}$ $f\left(x\right)=\frac{{\left(x+3\right)}^{2}}{{\left(x-1\right)}^{2}\left(x+1\right)}$ #### Extensions For the following exercises, identify the removable discontinuity. $f\left(x\right)=\frac{{x}^{2}-4}{x-2}$ $f\left(x\right)=\frac{{x}^{3}+1}{x+1}$ $f\left(x\right)=\frac{{x}^{2}+x-6}{x-2}$ $f\left(x\right)=\frac{2{x}^{2}+5x-3}{x+3}$ $f\left(x\right)=\frac{{x}^{3}+{x}^{2}}{x+1}$ #### Real-World Applications For the following exercises, express a rational function that describes the situation. A large mixing tank currently contains 200 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 10 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after$\,t\,$minutes. A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after$\,t\,$minutes. For the following exercises, use the given rational function to answer the question. The concentration$\,C\,$of a drug in a patient’s bloodstream$\,t\,$hours after injection in given by$\,C\left(t\right)=\frac{2t}{3+{t}^{2}}.\,$What happens to the concentration of the drug as$\,t\,$increases? The concentration$\,C\,$of a drug in a patient’s bloodstream$\,t\,$hours after injection is given by$\,C\left(t\right)=\frac{100t}{2{t}^{2}+75}.\,$Use a calculator to approximate the time when the concentration is highest. For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question. An open box with a square base is to have a volume of 108 cubic inches. Find the dimensions of the box that will have minimum surface area. Let$\,x\,$= length of the side of the base. A rectangular box with a square base is to have a volume of 20 cubic feet. The material for the base costs 30 cents/ square foot. The material for the sides costs 10 cents/square foot. The material for the top costs 20 cents/square foot. Determine the dimensions that will yield minimum cost. Let$\,x\,$= length of the side of the base. A right circular cylinder has volume of 100 cubic inches. Find the radius and height that will yield minimum surface area. Let$\,x\,$= radius. A right circular cylinder with no top has a volume of 50 cubic meters. Find the radius that will yield minimum surface area. Let$\,x\,$= radius. A right circular cylinder is to have a volume of 40 cubic inches. It costs 4 cents/square inch to construct the top and bottom and 1 cent/square inch to construct the rest of the cylinder. Find the radius to yield minimum cost. Let$\,x\,$= radius. ### Glossary arrow notation a way to represent symbolically the local and end behavior of a function by using arrows to indicate that an input or output approaches a value horizontal asymptote a horizontal line$\,y=b\,$where the graph approaches the line as the inputs increase or decrease without bound. rational function a function that can be written as the ratio of two polynomials removable discontinuity a single point at which a function is undefined that, if filled in, would make the function continuous; it appears as a hole on the graph of a function vertical asymptote a vertical line$\,x=a\,$where the graph tends toward positive or negative infinity as the inputs approach$\,a$

crawl-data/CC-MAIN-2022-27/segments/1656103661137.41/warc/CC-MAIN-20220630031950-20220630061950-00601.warc.gz

Information for Travellers Types of Travel About haemorrhagic fevers All viral haemorrhagic fevers, also called VHFs, are caused by a handful of virus families. The illnesses they cause can be spectacularly nasty, including Ebola, Marburg, Lassa fever and yellow fever. What do they all have in common? They all affect multiple organs, damage blood vessels and throw the body’s ability to regulate itself into chaos. Some of the diseases caused are mild, like the Scandinavian nephropathia epidemica. Others, like Ebola, are deadly more often than not. You can catch VHFs anywhere in the world, but they’re most often found where the animals that carry them live. Lassa fever, for example, is only found in rural West Africa, carried by local rats and mice. As an ordinary traveller, the risk is relatively low. But it makes a great deal of sense to avoid areas where there have been outbreaks, especially important when there are no drugs to treat VHFs. All doctors can do is treat the symptoms. All VHF illnesses come with a fever, as the name implies, and most also come with bleeding disorders. They can all result in shock and many kill. Five kinds of RNA viruses are responsible As far as we know so far, all VHFs come from one of five families of RNA virus. - Lassa fever comes from the Arenaviridae family of viruses, as does Lujo, Machupo, Sabiá and Guanarito - The Bunyaviridae virus family is responsible for diseases like HFRS, Crimean-Congo haemorrhagic fever and Rift Valley fever - The Filoviridae virus family includes the horrific Ebola and Marburg - Flaviviridae viruses lead to dengue, yellow fever and two tick-borne encephalitis illnesses: Omsk haemorrhagic fever and Kyasanur Forest disease - A newly-discovered Rhabdoviridae virus is probably responsible for two fatal cases of haemorrhagic fever in the Democratic Republic of Congo, proving that we still have a lot to learn about VHFs, where they come from, how they’re carried and how they spread What are the symptoms of haemorrhagic diseases? - Increased, uncontrollable, unexplained and unusual bleeding - A flushed, red face and chest - Little red or purple spots on the skin - Unexplained bruising - Low blood pressure - Muscle pain, headache, vomiting and diarrhoea Haemorrhagic disease diagnosis Because many of the signs and symptoms can easily be mistaken for other diseases, especially in the early stages, a definitive diagnosis is usually only possible through samples diagnosed at a special lab. In general there are fewer white blood cells in infected people, fewer blood platelets, more blood serum liver enzymes and problems with blood clotting. VHF prevention – how to stay safe from viral haemorrhagic fever If you’re a regular traveller or holidaymaker, the best way to stay safe from VHFs is to stay away from affected areas altogether. If you work in healthcare or you’re a voluntary worker, it isn’t always that simple. If that’s you, here are some facts to bear in mind: - With the exception of Yellow fever, there’s no vaccine for VHFs. Medics can only treat the symptoms, not the cause If you’re an aid worker or healthcare volunteer in an affected area, there are strict VHF isolation guidelines to follow. Everyone except those with dengue should be isolated - Good hand hygiene, goggles, face shields, doubled-layer gloves, gowns, covers for your shoes and legs are all vital when there’s an outbreak and you’re working with patients - VHFs can easily spread in hospitals, especially Lassa, CCHF, Ebola and Marburg. If they’re around you’ll need a proven HEPA filter respirator, air-purifying respirator or a positive pressure supplied air respirator if you come within six feet of a patient - Isolation and special decontamination procedures should be in place

<urn:uuid:f85c1f80-3f11-429f-b8a8-a54c7db5d7e5>

A woman’s bone marrow may determine her ability to start and sustain a pregnancy, report Yale researchers in PLOS Biology. The study shows that when an egg is fertilized, stem cells leave the bone marrow and travel via the bloodstream to the uterus, where they help transform the uterine lining for implantation. If the lining fails to go through this essential transformation, the embryo cannot implant, and the body terminates the pregnancy. “We have always known that two kind of things were necessary for pregnancy,” says Dr. Hugh Taylor, senior author and the Anita O’Keeffe Young Professor of Obstetrics, Gynecology, and Reproductive Sciences at Yale. “You must have ovaries to make eggs, and you must also have a uterus to receive the embryo. But knowing that bone marrow has a significant role is a paradigm shift.” Previous research has indicated that, in small numbers, bone marrow-derived stem cells contribute to the non-immune environment of the non-pregnant uterus, but it’s remained unknown if and how stem cells affect a pregnant uterus. In this study, the researchers were able to prove the physiological relevance of stem cells to pregnancy. “Some of these bone marrow-derived mesenchymal stem cells travel to the uterus and become decidual cells, which are the cells that are essential for the process of implantation and pregnancy maintenance,” explains Dr. Reshef Tal, first author of the study and assistant professor of obstetrics, gynecology and reproductive sciences at Yale. In two mouse models with the Hoxa11 gene defect, which presents in mice as a defective endometrium, the researchers found that a bone marrow transplant from a healthy donor could improve fertility by promoting sufficient decidualization of the endometrium. In mice with only one copy of the defective gene, the transplant saved pregnancies that would otherwise have been lost and increased litter sizes, while in the mice with two bad copies of the gene, which were thus entirely infertile, the transplant caused growth and repair of the defective endometria. This study was made possible by a methods breakthrough that Tal and Taylor made a few years ago. For more than two decades, Taylor and his team had been trying to restore fertility in mice with these genetic mutations, but until recently, they didn’t have a form of chemotherapy strong enough to allow an effective bone marrow transplant without killing all the eggs of the mice. (Before a bone marrow transplant, chemotherapy or radiation is used to clear the body of the existing bone marrow, so that the donor bone marrow can take its place.) “We used an anti-metabolite drug, which is still considered a chemotherapy, but it doesn’t harm the ovary, and therefore the mice are still able to get pregnant, allowing us to track the transplanted bone marrow cells and investigate their role in reproduction,” says Tal. “We are currently translating these findings into humans to better understand the role that these bone marrow-derived stem cells play in recurrent implantation failure and recurrent pregnancy loss, two conditions that are unexplained in the majority of women and have no effective treatment.” Though more research is needed prior to clinical trials, Tal and Taylor see hope for the patients they treat for infertility on the clinical side of their practice in this latest advance. “These are frustrating medical conditions,” says Taylor. “When you have a damaged endometrium leading to infertility or repeated pregnancy loss, all too frequently we have not been able to correct it. Bone marrow can be considered another critical reproductive organ. This finding opens up a new potential avenue for treatment of a condition that has been untreatable in the past.” The first 1000 days post conception are regarded as a sensitive window of time that can define the childʼs health and in which the risk of later non-transmissible diseases can be modified 1 . The importance of a healthy lifestyle with a balanced diet and exercise in this phase of life is an important building block for the prevention of these diseases and is underlined by, amongst others, the national health goal “Before and after birth” of 2017 2 . In Germany, about a third of women of childbearing age are overweight or obese 5 . Obesity reduces the likelihood of conception 6 and is associated, amongst others, with a higher risk of pregnancy and birth complications, birth defects, premature births and miscarriages, a high infant birth weight and later obesity of the child 6 , 7 . In 2014/15 gestational diabetes was diagnosed in 13% of pregnant women during a screening programme 8 . About 11% of mothers of 0- to 6-year-old children reported in the German Health Interview and Examination Survey for Children and Adolescents (KiGGS) that they had smoked during pregnancy 11 . It is estimated that about 0.2 – 8 out of 1000 neonates in Germany are born annually with fetal alcohol syndrome. Far more children are affected by a fetal alcohol spectrum disorder 12 . A healthy lifestyle prevents risks of pregnancy complications and helps maintain the health of mother and child. In this phase of life in particular expectant parents 1 are often highly motivated to optimise their lifestyle and are receptive to appropriate recommendations. Women and couples wishing to have children are less aware that their lifestyle affects fertility, the course of the pregnancy and also the childʼs later health. The recommendations of the Healthy Start – Young Family Network (Netzwerk Gesund ins Leben) are intended to help contribute to a health-promoting lifestyle and thus to promote the health of mothers and children and prevent long-term overweight and its associated diseases. In 2012 the Germany-wide Practical Recommendations for Nutrition in Pregnancy of the Healthy Start – Young Family Network were first published 13 . The updated version presented here has been extended to include recommendations covering the period before pregnancy and around the time of conception. They are intended to provide gynaecologists, midwives, paediatricians and members of other health professions with a basis for counselling a healthy lifestyle. Healthy Start – Young Family is a network of institutions, learned societies and associations that are concerned with young families. The aim is to provide parents with uniform messages about nutrition and exercise so that they and their children live healthy lives and grow up healthy. The Healthy Start – Young Family Network is part of the IN FORM initiative and is accommodated in the Federal Centre for Nutrition (BZfE), an institution that comes within the sphere of responsibility of the Federal Ministry of Food and Agriculture (BMEL). More information: Tal R, Shaikh S, Pallavi P, Tal A, López-Giráldez F, Lyu F, et al. (2019) Adult bone marrow progenitors become decidual cells and contribute to embryo implantation and pregnancy. PLoS Biol 17(9): e3000421. doi.org/10.1371/journal.pbio.3000421 Journal information: PLoS Biology Provided by Yale University

<urn:uuid:cfac094f-e0e8-452d-8620-f1837061adff>

Picture it: a big, sweaty, tattooed man in a cowboy hat and chaps, is in the ring as the arena full of fans cheer him on. Their hero: "Cowboy" Gator Magraw. Gator bounces off the ropes and is quickly body-slammed to the mat. His wild opponent leaps into the air, crashing down onto Gator's rib cage. Gator struggles to breathe, wondering: "Is this really what my father wanted for me?" (Laughter) That wild man in the chaps ... was me. (Laughter) (Applause) (Cheers) And the answer to the question, surprisingly, is yes. (Laughter) I grew up watching professional wrestling with my dad. And like him, I loved everything about it: the showmanship, the athletic skill, the drama. I'd be this little boy, bouncing all over our living room, pretending to be my favorite wrestlers from TV. My dad actually reminded me a little bit of Hulk Hogan, but I was Hulk Hogan and he was Andre the Giant. I'd get all serious on him and say things like, "Dad ... someday I am going to be world heavyweight champion." And he would usually smile and very calmly say, "OK, then I guess I can count on you to be my retirement fund." (Laughter) When I was 16, a small wrestling show came to my little town in Minnesota. I couldn't believe it. Nothing like that had ever come to my town before. So I got to the arena early in the morning the day of the show, waiting out in the parking lot to see if I could spot some wrestlers pulling up in their cars. It wasn't as creepy as it sounds. But I could definitely tell who the wrestlers were, just the way they walked. They were tall and confident and intimidating, with their tank tops and Zubaz and fanny packs. Why wouldn't I want to be them? (Laughter) All I could think about was who are these people, and what are they like? How did they become wrestlers? So before the show started, I walked into this tiny arena — more like a gymnasium — and I asked them if I could help set up the wrestling ring. "Sure, kid. No problem." And then I pleaded with them to show me some wrestling moves. "Sure, kid. No problem." Man, they would just punch and kick me — hard! But I never complained. They would come to my town for one night every couple of months that year, and then — poof! — next day, they were gone. By the next year, they finally told me about an actual wrestling training camp that one of the wrestlers was running, and I begged my parents to sign me up. Next thing I knew, I was a high school senior by day and wrestling in front of live audiences by night. I had this giant poster of an alligator hanging on my bedroom wall. So when I needed to come up with a wrestling name at the last minute and Jesse "The Body" Ventura was already taken — (Laughter) I went with "Gator." I also wrestled in a t-shirt and camouflage pants because that's what I had in my closet. I hadn't quite figured out how to develop my own persona yet, but I was learning. It was sort of like an apprenticeship. But I was a wrestler. And my dad would come to all my matches wearing a t-shirt that said, "Papa Gator" across the front. (Laughter) And he'd brag to his friends about how his son was going to pay for his retirement someday. (Laughter) And I would've. Not long after I started wrestling, my dad unexpectedly passed away. And as you can imagine, especially as a teenage boy, it destroyed me. If you've ever lost someone, you know what a difficult time that can be. Your mind — it's not working right. The whole thing is just so surreal. I wanted to feel normal again, even if it was for just a second, so I went back to wrestling almost immediately. Wrestling belonged to me and my dad, you know? So there I was, sitting in the locker room, getting ready for a match within days of my dad passing away. He was gone. And sitting there alone — it felt like I was hiding. But it also felt like I needed to be there. One of the wrestlers who'd been on the scene a long time knew what I was going through, and he came over to see how I was holding up. I couldn't get the words out. I just said, "I don't know what I'm doing." And then we just sat there in silence — just ... silence. Before he got up to get ready for his own match, he gave me this piece of advice that would change the entire direction of my life. He told me the best wrestlers are just themselves, but "turned up." He said successful wrestlers find the traits within themselves they're the strongest at and make those the focus of who they become in the ring. So there I sat — a scared teenager who didn't know who he was or why he was even wrestling anymore. I looked around the locker room at some of the other wrestlers, and I thought, "I look so different. How can I ever be like them?" And then it hit me. That's the moment I realized I didn't have to be like them. What I did have to do was find out: What did it mean to be me? What made me unique, and how could I use it to my advantage? I knew I wasn't a chiseled athlete like some of these guys, but I really didn't care. So the first thing I thought was, "How can I amplify something as simple as: comfortable with my own body?" I didn't know. And then I thought: Speedo. (Laughter) (Applause) Or "trunks," as we call them in wrestling. Yeah, trunks. I could be this big guy who was comfortable wearing these little trunks in front of a bunch of strangers. So I ditched the t-shirt and camouflage pants, and Gator's new wardrobe was born. (Laughter) I was also pretty good at drawing cartoons, so I wondered if I could turn that up. I could design my own wrestling costumes, so each pair of trunks would have its own unique design and color, all of them completely different — and extremely comfortable, by the way. (Laughter) And I was also the funny kid in school, believe it or not. So I thought maybe I could turn that up. Maybe I could go from the boy who made his buddies laugh to the man who could rally hundreds or thousands. So I committed to the idea that my character wasn't going to be as scary as some of the others. I'd be hilarious from the moment I walked into the arena. With every wrestling match, I dug deeper. I found out that I could laugh at myself. So this guy would dance and sing his entrance music all the way to the ring. That was dancing, by the way. (Laughter) I found out that I was an OK wrestler, but I was an even better entertainer. And turning myself up made me unforgettable to the fans. I was trying to find those things about me — the simple things that were special, and then ask, "How can I turn them up?" Now, I knew I wanted my character to be a man's man like my dad was. I thought, "What's more of a man's man than a cowboy?" And that's when Gator became "Cowboy" ... Gator ... Yeah, I needed a last name. I thought about it until my head hurt. I couldn't come up with anything. I'm sitting there watching TV one night, flipping through the channels, and this commercial comes on about a country singer who had just won an Entertainer of the Year award. Tim McGraw. He's a cool cowboy with a great last name. And I liked his music. It was just all part of my process. But I just kept turning myself up until I became Cowboy Gator Magraw! (Laughter) (Applause) And I knew that if I kept turning myself up and pushing myself harder, the opportunities would come. And then it finally happened. In the middle of the night, I got a phone call. It was the call I wish my dad was around to hear. The WWE, the biggest wrestling organization in the world, wanted me to come and be a part of Monday Night Raw. Yes — all of my hard work and miles on the road were finally paying off. I got to walk down the WWE Raw entrance ramp on live television — (Laughter) dressed up as a fake security guard — (Laughter) to escort another wrestler to the ring. (Laughter) Sure, I was disappointed I didn't get to wrestle, but very few wrestlers get any kind of call from the WWE. Maybe one in a few hundred. And becoming Cowboy Gator Magraw is what got me there. So instead of walking away that day, I decided to turn myself up again and become the best security guard I could. In fact, I did it so well, I was the only guard to get a close-up on TV that night. That's a big deal, you know? (Laughter) And I got to sit backstage that entire day with some of the most famous pro wrestlers in the world, some of which were heroes of mine as a kid. And I got to listen to them and learn from them, and for that day, I was accepted as one of them. Maybe my experience with the WWE wasn't ideal. I mean, I didn't get to wrestle. But it made me work harder, turning myself up louder year after year. I was becoming the biggest version of myself in the ring, and other people took notice. Before I knew it, I'd gone from wrestling maybe once a month in Minnesota to as often as four times a week all over the United States on the independent wrestling circuit. I was literally living my dream. While wrestling over the next few years, I suffered a pretty bad shoulder injury right around the same time my wife and I found out that we were expecting our first child. I know what you're thinking, but believe me when I say those two events are completely unrelated. (Laughter) But I needed shoulder surgery, and I wanted to be home with my family. It was my turn to be a dad. So on July 27, 2007, I wrestled my final match, and walked away from professional wrestling to pursue the next chapter of my life. And as time passed, the strangest thing started to happen. I found out that once someone has been turned up, it's pretty hard to turn them down. I left the ring but Gator stayed with me, and I use the turned-up version of myself every day. My beautiful wife has been with me through this entire journey. And by the way — she does not like pro wrestling. (Laughter) Like, at all. But she was always my biggest fan. She still is. She knows there's always going to be some part of Gator Magraw in here, and she wants our daughter and twin sons to discover themselves the way that I did, but probably with fewer body slams and steel chair shots to the head. I mean, do you know how many times she's had to remind me not to clothesline the referees at my kid's soccer games? (Laughter) I mean, it was just the one time, and my daughter was clearly fouled! (Laughter) As a parent now, I've begun to realize that my dad wanted something much more valuable than a retirement fund. Like most parents, he just wanted his kids to reach their fullest potential. I'm trying to teach my children that turning yourself up is just not some perfect idea of how to be great, it's a way of living — constantly looking for what makes you different and how you can amplify it for the world to see. And by the way, my kids don't like wrestling, either. (Laughter) But that's OK with me, because they each have their own unique talents that can be turned up just like the rest of us. My one son — he's a whiz at electronics. So maybe helping him turn up makes him become the next Steve Jobs. My other son and my daughter — they're great at art, so maybe helping them turn up their gifts helps them become the next Pablo Picasso. You never know what you have the ability to do until you dig. And don't be afraid to put yourself out there. I mean, look around. They say that if you get nervous in front of an audience, just imagine them in their underwear. But then I think, "Hey, I've wrestled in less." (Laughter) (Applause) Look, the wrestling circus doesn't need to come to your town before you get an invitation to be the real you — the bigger, more stunning version of yourself. It doesn't even necessarily come from our parents. Turning yourself up means looking inward toward our true selves and harnessing the voice that says, "Maybe, just maybe, I am more than I thought I was." Thank you. (Applause)

A pro wrestler's guide to confidence