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# Math Subscript Calculator

The graphing calculator's CAS functionality, or "Computational Algebra System," allows you to manipulate equations and solve for any variable within the equation. Math teachers know that typing math notation in Google Docs takes a bit of work. TI-Nspire™ Student Software provides students with the ability to work beyond the classroom by taking what they’ve started in class on their handhelds and. ) Type the Title and Description of your quiz. Smarter Balanced and Desmos are proud to offer calculators that are both free to students and include cutting edge accessibility features. In order to calculate log-1 (y) on the calculator, enter the base b (10 is the default value, enter e for e constant), enter the logarithm value y and press the = or calculate button:. TI-Nspire™ software delivers enhanced graphing capabilities and other functionality that are unique to TI-Nspire™ math and science learning technology on desktop and laptop computers. Camera Math of photography settings and EV A few math details about EV, f/stop, shutter speed, and ISO. Al(NO 3) 3 Parentheses - in some chemical formulas it is necessary to use parentheses. This is a "sandbox" where you can try out math entry. All the examples can be cut and pasted into the calculator. What Is a Subscript in Chemistry? In a molecular formula, a subscript is written immediately after the letter denoting an element and refers to the amount of atoms that element has. Base five numeration system The main difference between base five numeration system and our familiar base 10 numeration system is that grouping is done in groups of 5 instead of 10. 0 (which is still available on 32-bit Office versions until the January 2018 update) and MathType. 9952 molecular mass = 310. I am going to first convert 821 and 17, both written in base 10, to base 7. Designed for GNOME. Pre-Algebra. Home›Calculators›Math Calculators› Base calculator Base Calculator. When you were first learning calculus, you learned how to calculate a derivative and how to calculate an integral. The difference is that a conventional variable takes on only one value. Determine ux and sigma(x) from the given parameters of the population and sample size u = 76, sigma. This free exponent calculator determines the result of exponentiation, including expressions that use the irrational number e as a base. The new MyScript© Calculator 2 makes daily math fun and easy! Calculator 2 turns your device into an interactive piece of paper. It also provides the step by step solution on how it derived the answer. Examples: • the number 1 here: A 1 (pronounced "A sub 1" or just "A 1"). 1 Basics Deﬁnition 2. Dining out with a group of friends, going on a date, or having dinner with a few out-of-town relatives should be a joyful occasion. Number of monthly visits to simulation-math. When you were first learning calculus, you learned how to calculate a derivative and how to calculate an integral. Type the expression for which you want the antiderivative. Suppose that a simple random sample of size n is drawn from a large population with mean muμ and standard deviation sigmaσ. - Answered by a verified Math Tutor or Teacher We use cookies to give you the best possible experience on our website. This calculator will generate a step by step explanation on how to apply t - test. Chemists have developed a shorthand to indicate phases by placing an abbreviation in parentheses as a subscript following the formula for the chemical. The multiple suffixes are assigned to the symbolic variables from left to right. If I put 3% of my paycheck into my 401k and my employer matches 3% (automatic 3% raise for doing nothing!!!) and I avoid 15%. Not sure if I can find a workaround there or not. Single Subscript Notation X3 X3 14 3 12 2 1 X Single Subscript Notation Single subscript notation extends naturally to a situation where there are two or more lists. numbers that come in integers and are not likely to be available in amounts smaller than integers. Virial Equation Calculator. Online and live voting winner. Type 119/120 4. The graphing calculator's CAS functionality, or "Computational Algebra System," allows you to manipulate equations and solve for any variable within the equation. For higher nested subscripts, we simply extend this to a_{b_{c_{d_e}}} etc. The t-test for dependent means (also called a repeated-measures t-test, paired samples t-test, matched pairs t-test and matched samples t-test) is used to compare the means of two sets of scores that are directly related to each other. A small letter or number placed slightly lower than the normal text. Critical Z-value calculator-- Enter α For t-distribution critical values, use our t-value distribution calculator For F-distribution critical values, use our F-value distribution calculator. In mathematics, a norm is a function from a vector space over the real or complex numbers to the nonnegative real numbers that satisfies certain properties pertaining to scalability and additivity, and takes the value zero if only the input vector is zero. You don't understand the concept of taxation and time value of money. Calculus II Calculators; Math Problem Solver (all calculators) Trapezoidal Rule Calculator. Z Score Calculator Further Information The z score test for two population proportions is used when you want to know whether two populations or groups (e. Enter a chemical equation to balance [Chemical Equations Examples: H 2 + O 2 = H 2 O Na 2 + Cl 2 = NaCl. Calculator that converts integers from one base to another, up to base 36. Kindler bless his heart, got him to try an after-school program, it was like a miracle!. Learn how to easily spot a superscript when you are looking at math problems. Exam acceptance The TI-30X IIS scientific calculator is approved for use on SAT ®, ACT ® and AP ® exams. Pass or Fail. For example I have seen this in math class calculated by one of my class mates without the help of a calculator. It includes Greek and Latin letters, mathematica…. The reason it must be multiplied by volume before estimating an actual outward flow rate is that the divergence at a point is a number which doesn't care about the size of the volume you happen to be thinking about around that point. This table explains the meaning of every subscript symbol. We are here to assist you with your math questions. Exponents on a Scientific Calculator Date: 08/21/97 at 17:10:08 From: David Brownfield Subject: Using a scientific calculator This is my first year in Algebra. Array Subscripts. While some exercises have a tool from which you can choose a math symbol, there are a limited number of symbols available in the tool. On any page, click or tap the Draw tab. A subscript is used to indicate the base of a logarithm. Al(NO 3) 3 Parentheses - in some chemical formulas it is necessary to use parentheses. It also shows plots, alternate forms and other relevant information to enhance your mathematical intuition. The notes were written by Sigurd Angenent, starting from an extensive collection of notes and problems compiled by Joel Robbin. Unfortunately, the TI-83 graphing calculator does not support subscripts. The LHS consists of the reactants and the RHS consists of the products. I'd like to answer the original question which involves a comma in the subscript: How can I write v 1,2 with 1,2 as subscripts? plot(1:10, 11:20 , main=expression(v["1,2"])) Also, I'd like to add the reference for those looking to find the full expression syntax in R plotting: For more information see the ?plotmath help page. A pseudonorm or seminorm satisfies the same properties, except that it may have a zero value for some nonzero vectors. Determine ux and sigma(x) from the given parameters of the population and sample size u = 76, sigma. Subscripts Coefficient. Homework Check: Our algebra calculator can help you check your homework. Doing some math? It's not so hard with an HTML plus sign or minus sign. Looks like a real calculator!. It looks like these are spread out across different ranges, and not all characters are available. The Distance Formula itself is actually derived from the Pythagorean Theorem which is where is the longest side of a right triangle (also known as the hypotenuse) and and Read more Distance Formula. To use the calculator, you enter the math problem that you want to calculate into the text box. - José Carlos Santos Apr 29 at 9:10 I'm sorry, I may have added the subscript part to the problem description while you were already busy trying / typing out the answer. HTML Arrows offers all the html symbol codes you need to simplify your site design. Use your graphing calculator to figure out what the base log equals. Superscipt Dear Dr. First, details of EV and EV Chart for page evchart. subscript 10 and just use log. CO + H 2 O --> CO 2 + H 2. Binary variables are a sub-type of dichotomous variable; variables assigned either a 0 or a 1 are said to be in a binary state. No need to even type your math problem. Use the second law to simplify the following. For example, you can use superscript to write square units like m 2 or inch 2, ordinal numbers such as 1 st, 2 nd, or 3 rd, or exponents in math such as 2 3 or 5 2. For the intents of this calculator, "power of a matrix" means to raise a given matrix to a given power. Mean Absolute Deviation Calculator Instructions. To learn more about how to use subscripts, check out our documentation. Input of the form in a notebook is interpreted as Subscript [x, y]. Welcome to our free collection of online calculation tools. You will be able to answer these questions by simply entering the road surface type, units, and speed or distance below. Dig deeper into specific steps Our solver does what a calculator won't: breaking down key steps into smaller sub-steps to show you every part of the solution. Let's take a look. Symbolab has a handy online graphing calculator that is easy to use. Math Objectives Table of Contents. Given that log subscript 10 =0. Exact Numbers. Click on the calculator's keys to browse through the apps. Calculators with newer operating systems actually have a summation function, which can by reached by pressing MATH 0. A degree 1 polynomial is a linear function, a degree 2 polynomial is a quadratic function, a degree 3 polynomial a cubic. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. That, however, does not mean you cannot solve such a log. Our free anti-derivative calculator is provided by Mathway and will give the antiderivative of any expression. Subscripts have many scientific applications, including mathematics, computer science , and chemistry. The new MyScript© Calculator 2 makes daily math fun and easy! Calculator 2 turns your device into an interactive piece of paper. SPECIFY MATRIX DIMENSIONS: Please select the size of the matrix from the popup menus, then click on the "Submit" button. The simplest notation for defining a sequence is a variable with the subscript n surrounded by braces. Number base calculator with decimals: binary,decimal,octal,hex. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. To open the calculator, select the calculator icon. with superscript and subscript. When you enter your plain text into the calculator or the response field, follow these guidelines. Symbolab's Graphing Calculator offers a color map, parameter sliders, table that shows the points for each function, graph and grid settings, and function properties. In a notebook, a subscript can be created using or. Note that you can select from various types of questions: text, paragraph text, multiple choice, check boxes, etc. 54 cm or 1 gallon = 231 cubic inches or 1 foot = 12 inches or 1 meter = 100 centimeters. How to use the calculator. Home›Calculators›Math Calculators› Base calculator Base Calculator. Special cases − This method returns the positive square root of a. Take care that numbers in any base, other than 10, are said by naming the separate digits. The chain rule states formally that. 6434 b 1 = 1. Entering commands from the keyboard. a n = a n-1 + 5. Snap a pic of your math problem With our mobile app, you can take a photo of your equation and get started, stat. the subscript g after H2O indicates that it is water vapour, a gas, which is what the subscript g stands for. Basically, it shows how many different possible subsets can be made from the larger set. Most calculators have an "EE" button, to help you. The calculus calculator can be used. Tip 1: Insert Math Equation. High School Math Solutions – Logarithmic Equation Calculator. Some of these blocks are dedicated to, or primarily contain, mathematical characters while others are a mix of mathematical and non-mathematical characters. It also generates a normal curve and shades in the area that represents the p-value. Unfortunately, the TI-83 graphing calculator does not support subscripts. Binomial Coefficient Calculator. Welcome to ti 84 plus Questions and Answer. How To Write Subscripts In Microsoft Office Formulas Super User. Start with vectors. The trick here is to forget math and think phonetics. Basically, it shows how many different possible subsets can be made from the larger set. Enter numbers separated by comma, space or line break: If your text contains other extraneous content, you can use our Number Extractor to extract numbers before calculation. Some PowerPoint. Answer to How do you find t Subscript alpha divided by 2t/2 on your calculator. Mastering Physics is the teaching and learning platform that empowers you to reach every student. The good news is there’s a trick that makes calculating logarithms easy and will amaze your friends with your mental math skills. If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. 87% probability that the average CFL bulb for 20 randomly chosen bulbs would be less than or equal to 150 days. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. I worked on a math quiz in Math for set theory where questions are pulled into a text file within Flash. Here are examples of balanced equations you can review or use for homework. zip: 3k: 03-05-28: Algebra2 Finals Notes This is a great program with four pages of review topics on your calculator! If you're in algebra 2 you REALLY need this!. The calculator will approximate the integral using the Trapezoidal Rule, with steps shown. You also learned some notation for how to represent those things: f'(x) meant the derivative, and so did dy/dx , and the integral was represented by something like. Vector or subscript notation When to use the “vectorize” operator rather than subscripts. Exponents are entered using the caret symbol, which is above the number 6 on the keyboard. Mathematical modes. Many people need to type degree symbol in latex and in this article, we will guide you how to insert degree symbol in latex. Z-Critical Values Calculator. This is a "sandbox" where you can try out math entry. Back == Calculating Mean and Standard Deviation How To Video Input Data: (Use Tab or 'Arrow' keys on keyboard to help with data input. This is a converter for Decimal conversion to Hexadecimal (Hex), Octal or Binary and all other number bases from 2 to 36. This requires only typing both commands after 'Mt'. The calculator of sequence makes it possible to calculate online the terms of the sequence, defined by recurrence and its first term, until the indicated index. As its name suggests, the application is distributed as part of the GNOME project. HTML math is powerful enough to describe the range of math expressions you can create in common word processing packages, as well as being suitable for rendering to speech. Basic Math. Scientific Notation on Your Calculator. You should choose a calculator that will take you through several years of the math classes you anticipate taking. Every equations have two sides-a Left Hand Side (LHS) and a Right Hand Side (RHS) like 2x + 5y = 7, Now we can select x or y to find the transposition equation as per selection. Title: Chair, Department of Math and Science, Associate Professor of Science Department: Math & Science Phone: 706-385-1457 Email: donnie. The total load on the wall can be. Under age 65 or 65 and over. That, however, does not mean you cannot solve such a log. Some equations may require numbers to be entered in superscript or subscript form. The t-test for dependent means (also called a repeated-measures t-test, paired samples t-test, matched pairs t-test and matched samples t-test) is used to compare the means of two sets of scores that are directly related to each other. The total load on the wall can be. The bad news is that pH and sound intensity problems from general chemistry and physics will require you to work with logarithms without a calculator. 87% probability that the average CFL bulb for 20 randomly chosen bulbs would be less than or equal to 150 days. This means, for example, that you cannot put one symbol over another. Calculator Use. It enables users to handwrite equations directly into a Word document, using a stylus, a finger, or even the mouse. These goals and objectives are in addition to the regular math curriculum. Male or Female. In InputForm, Subscript [x, y] formats literally as Subscript [x, y]. Although most of this document provides instructions pertaining to Word, the procedures for inserting and editing equations in Word are the same as for PowerPoint. A few other ways one can find this answer is to ask a math teacher or check out a book in the library on it. This calculator computes the mean absolute deviation from a data set: You do not need to specify whether the data is for an entire population or from a sample. The mathematical expressions calculator is a powerful algebraic calculation tool, it is able to analyze the type of expression to calculate and use the appropriate calculator to determine the result. Use 2nd to access the yellow options above the keys Use ALPHA to access the green options above the keys 2nd QUIT will back you out of a menu. Reuse previous results wi…. first find the first partial derivative C Subscript x (x,y). All tools to write a mathematical equation are accessible on the left side of the screen. In a notebook, a subscript can be created using or. These goals and objectives are in addition to the regular math curriculum. This also works in cases where you want your Mac to perform calculations, like in Spotlight. The binary logarithm of x is the power to which the number 2 must be raised to obtain the value x. A pseudonorm or seminorm satisfies the same properties, except that it may have a zero value for some nonzero vectors. ccpvirus will be the excuse to have it pushed worldwide; it will be presented as a digital. Convert a number from base 4 to base 10. = Log 37/log 2 Now use your calculator and round to hundredths. The geometric sequence definition is that a collection of numbers, in which all but the first one, are obtained by multiplying the previous one by a fixed, non-zero number called the common ratio. Dig deeper into specific steps Our solver does what a calculator won't: breaking down key steps into smaller sub-steps to show you every part of the solution. The toolbox provides functions in common mathematical areas such as calculus, linear algebra, algebraic and ordinary differential equations, equation. I’ve already shared how to insert math equation in PPT, and it is the same with MS Word. Instructions on balancing chemical equations: Enter an equation of a chemical reaction and click 'Balance'. It is used throughout IntMath. About Log Base 2 Calculator. subscript 10 and just use log. 00 (second decimal place) or = 0. Recursive sequence calculator: recursive_sequence. Smarter Balanced and Desmos are proud to offer calculators that are both free to students and include cutting edge accessibility features. Z Score Calculator Further Information The z score test for two population proportions is used when you want to know whether two populations or groups (e. The simplest is to use a slash character between numbers. Geometric sequence sequence definition. You might need: Calculator Problem Find lim  x → − 3 g ( x ) \\displaystyle \\lim_{x\\to -3}g(x) x → − 3 lim g ( x ) limit, start subscript, x, \\to, minus, 3, end subscript, g, left parenthesis, x, right parenthesis for g ( x ) = 7 x + 22 g(x)=\\sqrt{7x+22} g ( x ) = 7 x + 2 2 g, left parenthesis, x, right parenthesis, equals. LateX pmatrix, bmatrix, vmatrix, Vmatrix. Mathematical operators and symbols are in multiple Unicode blocks. The following examples provide strange behavior:. Use superscript and subscript keyboard shortcuts. , the exponent or power) and 100 is the number. Dig deeper into specific steps Our solver does what a calculator won’t: breaking down key steps into smaller sub-steps to show you every part of the solution. Now you would be wondering with the footnote, yes it is also considered as a subscript. Math 152 Chapter 1 Handout Helene Payne 10. This tutorial shows how to insert superscripts and subscripts in Microsoft Word using three different tools: 1. Symbolic Math Toolbox™ provides functions for solving, plotting, and manipulating symbolic math equations. The t-test for dependent means (also called a repeated-measures t-test, paired samples t-test, matched pairs t-test and matched samples t-test) is used to compare the means of two sets of scores that are directly related to each other. Math Formula Sheet, bash calculator command, How to solve integral equation on calculator. Subscripts appear at or below the baseline, while superscripts are above. Designed for GNOME. How to Create Math Expressions Using Google Forms. Home » Conversion Calcs » Binary to Decimal Converter Binary to Decimal Converter to Convert Base 2 to Base 10 This calculator will convert binary numbers into decimal numbers and display an interactive conversion chart to show how it arrived at the result. subscript 10 and just use log. To Find A Logarithm. When choosing a scientific calculator, consider what math classes besides algebra you'll be using it for. A small number of superscript characters were introduced to Unicode for general usage in math, phonetics, and related fields. These shortcuts allow you to add effects such as bold type, italics, subscript or. Logarithmic equations are equations involving logarithms. Base converter; This tool converts numbers in different bases (eg: decimal, binary, hexa). For K-12 kids, teachers and parents. Find the median values. If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. Check out all of our online calculators here!. If your course offers the calculator tool, the calculator appears as a small icon on all pages in the body of the course. Subscripts appear at or below the baseline, while superscripts are above. Partner with ConvertIt. Unlike some of the numeric methods of class StrictMath, all implementations of the equivalent functions of class Math are not defined to return the bit-for-bit same results. Learn how to easily spot a superscript when you are looking at math problems. Microsoft Mathematics Add-in for Microsoft Word and Microsoft OneNote makes it easy to plot graphs in 2D and 3D, solve equations or inequalities, and simplify algebraic expressions in your Word documents and OneNote notebooks. This option is available with the word. Define the four cases for the right, top, left, and bottom squares in the plot by using a switch statement. For this calculator, the order of the items chosen in the subset does not matter. Math 221 – 1st Semester Calculus Lecture notes version 1. 52 with a 05 in the upper right portion of. Phone support is available Monday-Friday, 9:00AM-10:00PM ET. SciKey is a Scientific Keyboard that brings you the essential scientific characters for your iPad, iPhone, and iPod touch. A few other ways one can find this answer is to ask a math teacher or check out a book in the library on it. First, a Quick Summary of Exposure Computing. Both will give you the same answer. Scientific calculator with arbitrary precision and portrait and landscape mode. Like previous examples, we have a simple worksheet that highlights several cell references. Students who are visually impaired or blind have the same opportunities as their peers to use online calculators. Math · Algebra II · Logarithms · Solving exponential equations with logarithms Solving exponential equations using logarithms Learn how to solve any exponential equation of the form a⋅b^(cx)=d. Most calculators have an "EE" button, to help you. A similar member function, vector::at, has the same behavior as this operator function, except that vector::at is bound-checked and signals if the requested position is out of range by throwing an out_of_range exception. HTML Math Permitted Context: %text Content Model: %math The element is used to include math expressions in the current line. The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions. Using Google products, like Google Docs, at work or school? Try powerful tips, tutorials, and templates. The EE means " x 10 to the power of". In that case we use subscripts: P_1, P_2, P_3, and so on. In case you need to have advice on factoring or radical expressions, Solve-variable. The dummy subscript ican have any of the integer values 1;2or3:For i= 1 we focus attention on the A1 component of the vector A:~ Setting i=2focuses attention on the second component A2 of the vector A~and similarly when i= 3 we can focus attention on the third component of A:~ The subscript iis a dummy subscript and may be replaced by another. isinf (x) ¶ Return True if x is a positive or negative infinity, and False otherwise. In addition it provide a graph of the curve with shaded and filled area. The LATEX and Python ﬁles which were used to produce these notes are available at the. Example - Hurricane Wind Load acting on a Wall Surface. Hex calculator. How do input subscripts into a program with a TI-84 Plus? Like Y(sub 1)=y Thanks A website about ti 84 plus graphing calculator, questions and answers, faq ti 84 plus, forum ti 84 plus, guidebooks, downloads, community forum, assembly tutorials, basic, z80, ti 84 plus help, calculator usage. Examples: • the number 1 here: A 1 (pronounced "A sub 1" or just "A 1") • the letter m here: x m (pronounced "x sub m" or just "x m") Often used when we have a list of values. It is an online math tool which determines the number of combinations and permutations that result when we choose r objects from a set. When writing "vec * matrix", vec is interpreted as row vector (a 4 * 1 matrix), and the multiplication works out as 4 dot products of vec with the columns of the matrix. Definition: Geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by a constant. in messaging systems). Like the Combinations Calculator the Permutations Calculator finds the number of subsets that can be taken from a larger set. Calculator Use. Guidelines to use the calculator If you select a n, n is the nth term of the sequence If you select S n, n is the first n term of the sequence For more information on how to find the common difference or sum, see this lesson Geometric sequence. Basically, it shows how many different possible subsets can be made from the larger set. A base log is a log where the subscript small number next to the log is present. Or - from the table above the wind load per square metre is 735 N/m 2. Also learn a method to find the inverse of logarithmic functions that you can easily use. When one of these modes is active clicking the number buttons will enter. to access the standard math curriculum. Golden Spiral Using Fibonacci Numbers. I am going to first convert 821 and 17, both written in base 10, to base 7. Find the inter-quartile range, examples and step by step solutions, how to draw a cumulative frequency curve for grouped data, How to find median and quartiles from the cumulative frequency diagram. Home » Mathematics Statistics and Analysis Calculators » T-Value Calculator Student T-Value Calculator You can use this T-Value Calculator to calculate the Student's t-value based on the significance level and the degrees of freedom in the standard deviation. No need to even type your math problem. Welcome to ti 84 plus Questions and Answer. Dig deeper into specific steps Our solver does what a calculator won’t: breaking down key steps into smaller sub-steps to show you every part of the solution. HTML Math Permitted Context: %text Content Model: %math The element is used to include math expressions in the current line. Sequence calculator: sequence. 1 ∗ 10 ^ -2 = 2182. Click the 'Calculate' button to execute the calculation. L a T e X allows two writing modes for mathematical expressions: the inline mode and the display mode. const calculator = {displayValue: ' 0 ', firstOperand: null, waitingForSecondOperand: false, operator: null,}; The calculator object consists of everything that we need to construct a valid expression: displayValue holds a string value that represents the input of the user or the result of an operation. 183x10 3 - 1. Description of the Subscript mode of the RedCrab Calculator. before a subscript to indicate a. 52 with a 05 in the upper right portion of. A molecular formula, or empirical formula, is noted as a series of letters and numbers that represent a compound, or a molecule. Statistics. Find the upper and lower quartiles. Interactive Open Source Numerical Library of C/C++ functions for Engineering, Finance, Maths, Science and Statistics. Canonical implementations. For higher nested subscripts, we simply extend this to a_{b_{c_{d_e}}} etc. About Log Base 2 Calculator. Note 3: For all coloring, the color will apply only to the text immediately following the command until the next space is encountered. Like previous examples, we have a simple worksheet that highlights several cell references. Subscript Generator. The reason it must be multiplied by volume before estimating an actual outward flow rate is that the divergence at a point is a number which doesn't care about the size of the volume you happen to be thinking about around that point. These shortcuts allow you to add effects such as bold type, italics, subscript or. So, for example, it could be used to test whether subjects' galvanic skin responses are different under two conditions. It is actually converting your text into a subset of the Unicode standard. 28) Find the standardized test statistic t for a sample with n = 12, x = 22. If your course offers the calculator tool, the calculator appears as a small icon on all pages in the body of the course. Proceed to the second number and enter the values as; 56 multiplied by 10 with subscript of 5. Enter numbers separated by comma, space or line break: If your text contains other extraneous content, you can use our Number Extractor to extract numbers before calculation. How to Create Math Expressions Using Google Forms. ) Go to Google Forms. Phone support is available Monday-Friday, 9:00AM-10:00PM ET. How to Get Subscript and Superscript Numbers in Google Sheets. Subscript [x, y] formats as in StandardForm and TraditionalForm. One of the most popular Simulink submissions at. If you are struggling to understand what a geometric sequences is, don't fret! We will explain what this means in more simple terms later on and take a look at. The results are in! And the groups have different numbers. Some PowerPoint. Simply enter your problem and click Answer to find out if you worked the problem correctly. Thus, if the life of a CFL light bulb is 160 days, there is a 13. Binary variables are a sub-type of dichotomous variable; variables assigned either a 0 or a 1 are said to be in a binary state. Tip 1: Insert Math Equation. Keely's Graphing Calculator Guide Detailed steps to basic functions on the TI-84, TI-86, and TI-89 calculators. A small letter or number placed slightly lower than the normal text. Anti-logarithm calculator. Metzler, T. Help is always 100% free!. For help in using the calculator, read the Frequently-Asked Questions or review the Sample Problems. Membership is free, and members add resources to the database and rate them. For full step-by-step work, you'll need to upgrade to their premium membership. The calculus calculator can be used. Log base 2, also known as the binary logarithm, is the logarithm to the base 2. Step-by-step math courses covering Pre-Algebra through Calculus 3. Useful keys! Calculator help from Clark College mathematics faculty: Prof. I installed 3. In essence, if a raised to power y gives x, then the logarithm of x with base a is equal to y. Note that further math-related Excel functions are also provided in the Excel Statistical Functions and Excel Engineering Functions categories. How to subscript x n 1 in microsoft word equation super user how to enter sub and superscripts in equation editor ms one how to write subscripts in microsoft office formulas super user how to write superscripts before symbols in equation mode ms How To Subscript X N 1 In Microsoft Word Equation Super User How To Enter… Read More ». Designed for GNOME. Many people need to type degree symbol in latex and in this article, we will guide you how to insert degree symbol in latex. find log subscript 10 24. Recursive sequence calculator: recursive_sequence. I have tried variations, including paste(). Some equations may require numbers to be entered in superscript or subscript form. Watch the Video on how to use subscripts and superscripts; Practice by typing the following: 3x 2 - 7x + 2 = 15. The mathematical expressions calculator is a powerful algebraic calculation tool, it is able to analyze the type of expression to calculate and use the appropriate calculator to determine the result. You will need to get assistance from your school if you are having problems entering the answers into your online assignment. We indicate the base with the subscript 10 in log 10. 0 (Fall 2007) This is a self contained set of lecture notes for Math 221. That, however, does not mean you cannot solve such a log. Faster than a calculator | Arthur Benjamin Three Ways to Insert Superscripts and Subscripts in Microsoft Word - Duration: 6:04. The annotation only turns the first symbol into a subscript, as shown in the figure below. 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This article explains the basic commands to display equations.


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# Find hole size for allowable leak in pressure vessel

bgaw
TL;DR Summary
Need to find the hole size for an an allowable leak in a small, low pressure vessel.
Hello, all. I am completely new here so please be gentle.

I have a small, cylindrical, sealed ("no leak") pressure vessel with an approximate volume of 27 cm3. It has a constant supply of air pressure at 8"WC. I'm trying to figure out how big of a hole it can have if there is an allowable leak/flow rate of 1.00 sccm.

I feel like this isn't that hard of a problem and I should probably know how to do it, but alas I've been out or school for awhile and I do not. And I haven't been able to find anything in my internet searches that seem to tackle this problem. Most of what I can find deals with water and the Bernoulli equation, but I don't think that applies here. I'm pretty sure I'm missing some information/data. I'm not necessarily looking for an exact answer, but mostly just how to do this as I may need to do other versions of this in the future. Thank you in advance.

Welcome to PF.
How long is the hole, how thick is the cylinder wall ?
What shape is the hole ?

Homework Helper
Haello @bgaw ,
.. to find anything in my internet searches
Funny, a search for 'orifice air flow' yields a lot of useful stuff ! Even a calculator, but perhaps it's more useful to look through the equations to see if they apply for your range of ##\Delta p##

##\ ##

bgaw
Welcome to PF.
How long is the hole, how thick is the cylinder wall ?
What shape is the hole ?
The wall thickness is 0.06". And the hole will be round.

Homework Helper
Expanding: google search for 'vapour leak flow' has this in fourth place, with some formulas on page 8/9.

Incidentally, the calculator gives me a worst case initial guess of 19 ##\mu\textsf {m}##:

Where I am assuming sccm is 10-6 Nm3/min

##\ ##

Homework Helper
The wall thickness is 0.06". And the hole will be round.
So the 19 ##\mu##m is ##<<## 1500 ##\mu##m (0.06") and you want to include a pressure drop over the narrow channel ...

##\ ##

FluidDroog
I understand the Problem as follows:
• The sealed volume is estimated to have a leak of 1 sccm of Air.
• The leak flow channel is assumed circular.
• The upstream pressure of the flow channel is 8"water column (8psig = 156.5 kPaA).
• The donstream pressure of the flow channel is 0" water column (0 psig = 101.325 kPaA).
• The temperature of the system is isothermal at T= 22 deg. Celsius (295.15 Kelvin)
The goal is:
What is the diameter, D, of a flow channel if the channel length, L, is 0.06"?

Solution:
First I would use Poiseuille, equation #3 from reference [1]. For this you will need approximations for the viscosity and molecular weight of an Air mixture, which can be found using free software CoolProp [2].
Molecular weight = 2.897E-02 kg/mol and viscosity = 1.831E-05 Pa*s.

$$mdot =\frac{ \pi * M * R^4 * (P_1^2 - P2^2)}{16*\mu*L*R*T}$$
$$sccm = mdot * 60e3 * V_m / M$$
Where Vm is the standard molar volume defined in NIST codata [3].
By substitution and algebraic re-organization. The Diameter is found to be:
D = 23.38 micrometers

The next step is to identify if Poiseuille is accurate at these conditions. Poiseuille assumes incompressible, which means the Mach# < 0.3 [4]. To do that, we need the speed of sound for Air, roughly 345 m/s.
$$Mach = \frac {velocity} {speed of sound}$$

Where the velocity of the gas is found from
$$velocity = \frac {mdot}{Area * Density}$$
Where density is calculated at the average pressure in the channel, 1.516 kg/m3 [2]

I estimate the Mach # to be 0.1, thus Poiseuille is accurate and the problem is finished. This number agrees well with BvU's answer of 19 micron. The diameter is larger due to the friction along the micro channel.
If the Mach # was large, then BvU's recommendation for Orifice flow calculator or other equations would need to be considered.

References:
[1] Calibration of laminar flow meter for process gases. https://tsapps.nist.gov/publication...8560&msclkid=c048ffcdac0711ecae5f6f6526f549c4
[2] [Link spam redacted by the Mentors]
[3] Standard Molar Volume https://physics.nist.gov/cgi-bin/cuu/Value?mvolstd|search_for=molar+volume
[4] Compressible Flow https://en.wikipedia.org/wiki/Compressible_flow?msclkid=867dcdb2ac0911ec9db4f69c0927b111

Last edited by a moderator:
cjl

format: plain


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# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$

Proposition 3.3.9.1. Let $X$ be the inverse limit of a tower of simplicial sets

$\cdots \xrightarrow {q_3} X(3) \xrightarrow {q_2} X(2) \xrightarrow {q_1} X(1) \xrightarrow {q_0} X(0).$

If each of the morphisms $q_ n$ is a Kan fibration, then the canonical map $q: X \rightarrow X(0)$ is a Kan fibration.

Proof. This is a special case of Proposition 1.4.4.14 (which guarantees that the collection of all Kan fibrations is closed under transfinite composition in the opposite of the category of simplicial sets). $\square$


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AVILA, ARTUR / Matemàticas / Investigadores

# Centro Internacional de Investigación Científica

## Matemàticas / AVILA, ARTUR

arturccr.jussieu.fr

### Puesto

Chargé de Recherche, CNRS U.M.R. 7599, "Probabilités et Modèles Aléatoires", Laboratoire de Probabilités, Université Paris VI, Paris, France.

Artur Avila received his Ph.D. in 2001 under the direction of Welington de Melo at the Instituto Nacional de Matemática Pura e Aplicada (IMPA), in Rio de Janeiro, Brazil. His thesis, "Bifurcations of unimodal maps: the topological and metric picture," generalized the regular or stochastic dichotomy from the quadratic family to any non-trivial family of real analytic unimodal maps. Since then he has made numerous outstanding contributions to one-dimensional and holomorphic dynamics, spectral theory of the Schroedinger operator, and ergodic theory of interval exchange transformations and the associated Teichmüller flow.

Cours Peccot at the Collège de France, 2005.
Bronze medal of the CNRS, 2006.
Salem prize, 2006.
Wolff Memorial Lectures at Caltech, 2008.
EMS prize, 2008.

On the dynamics of the renormalization operator.
A. Avila, Marco Martens and Welington de Melo.
In Global Analysis of Dynamical Systems: Festschrift dedicated to Floris Takens for his 60th birthday'', Ed. H.Broer, B. Krauskopf, G. Vegter, Institute of Physics Publishing, Bristol and Philadelphia, pp. 449-460, 2001.

Bifurcations d'applications unimodales.
C. R. Acad. Sci. Paris, Ser. I 334 (2002), 483-488. (French/English).
There is a corrigendum (which only affects the french version).

Infinitesimal perturbations of rational maps.
Nonlinearity 15 (2002), 695-704.

A formula with some applications to the theory of Lyapunov exponents.
A. Avila, Jairo Bochi.
Israel Journal of Mathematics 131 (2002), 125-137.

Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative.
A. Avila, Carlos Gustavo Moreira.
Astérisque 286 (2003), 81-118.

Regular or stochastic dynamics in real analytic families of unimodal maps.
A. Avila, Mikhail Lyubich and W. de Melo.
Inventiones Mathematicae 154 (2003), 451-550.

Bifurcations of unimodal maps.
A. Avila, C. G. Moreira.
In Dynamical Systems. Part II: Topological Geometrical and Ergodic Properties of Dynamics.'' Pubblicazioni della Classe di Scienze, Scuola Normale Superieure, Pisa. Centro di Ricerca Matematica Ennio De Giorgi'': Proceedings, pp. 1-22, 2003.

Robust transitivity and topological mixing for C^1-flows.
Flavio Abdenur, A. Avila and J. Bochi.
Proceedings of the American Mathematical Society 132 (2004), 699-705.

Convergence of an exact quantization scheme.
Communications in Mathematical Physics 249 (2004), 305-318.

Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family.
A. Avila, C. G. Moreira.
Bulletin of the Brazilian Mathematical Society 35 (2004), 291-331.

Siegel disks with smooth boundaries.
A. Avila, Xavier Buff and Arnaud Chéritat.
Acta Mathematica 193 (2004), 1-30.

Statistical properties of unimodal maps: the quadratic family.
A. Avila, C. G. Moreira.
Annals of Mathematics 161 (2005), 831-881.

Statistical properties of unimodal maps: physical measures, periodic points and pathological laminations.
A. Avila, C. G. Moreira.
Publications Mathématiques de l'IHÉS 101 (2005), 1-67.

Generic singular spectrum for ergodic Schrödinger operators.
A. Avila, David Damanik.
Duke Mathematical Journal 130 (2005), 393-400.

Dynamics in the moduli space of Abelian differentials.
A. Avila, Marcelo Viana.
Portugaliae Mathematica 62 (2005), 531-547.

Phase-Parameter relation and sharp statistical properties for general families of unimodal maps.
A. Avila, C. G. Moreira.
Contemporary Mathematics 389 (2005), 1-42.

Smoothness of solenoidal attractors.
A. Avila, Sébastien Gouëzel, Masato Tsujii.
Discrete and Continuous Dynamical Systems 15 (2006), 21-35.

Examples of Feigenbaum Julia sets with small Hausdorff dimension.
A. Avila, M. Lyubich.
In Dynamics on the Riemann Sphere. A Bodil Branner Festschrift'', Ed. Poul G. Hjorth, Carsten Lunde Petersen, European Mathematical Society (EMS), Zürich, pp. 71-87, 2006.

Solving the Ten Martini Problem.
A. Avila, Svetlana Jitomirskaya.
Lecture Notes in Physics 690 (2006), 5-16.

A generic $C^1$ map has no absolutely continuous invariant measure.
A. Avila, J. Bochi.
Nonlinearity 19 (2006), 2717-2725.

Reducibility or non-uniform hyperbolicity for quasiperiodic Schrödinger cocycles.
A. Avila, Raphaël Krikorian.
Annals of Mathematics 164 (2006), 911-940.

Exponential mixing for the Teichmüller flow.
A. Avila, S. Gouëzel and Jean-Christophe Yoccoz.
Publications Mathématiques de l'IHÉS 104, 143-211.

Weak mixing for interval exchange transformations and translation flows.
A. Avila, Giovanni Forni.
Annals of Mathematics 165 (2007), 637-664.

Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture.
A. Avila, M. Viana.
Acta Mathematica 198 (2007), 1-56.

Generic expanding maps without absolutely continuous invariant $\sigma$-finite measure.
A. Avila, J. Bochi.
Mathematical Research Letters 14 (2007), 721-730.

Simplicity of Lyapunov spectra: a sufficient criterion.
A. Avila, M. Viana.
Portugaliae Mathematica 64 (2007), 311-376.

A uniform dichotomy for generic SL(2,R) cocycles over a minimal base.
A. Avila, J. Bochi.
Bulletin de la Société Mathématique de France 135 (2007), 407-417.

Exponential decay of correlations for the Rauzy-Veech-Zorich induction map.
A. Avila, Alexander Bufetov.
Fields Institute Communications 51 (2007), 203-211.

Hausdorff dimension and conformal measures of Feigenbaum Julia sets.
A. Avila, M. Lyubich.
Journal of the American Mathematical Society 21 (2008), 305-363.

Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling.
A. Avila, D. Damanik.
Inventiones Mathematicae 172 (2008), 439-453.

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## Generate Code for `fsolve`

This example shows how to generate C code for solving systems of nonlinear equations with `fsolve`.

### Equation to Solve

The system of nonlinear equations to solve is

`$\begin{array}{c}{e}^{-{e}^{-\left({x}_{1}+{x}_{2}\right)}}={x}_{2}\left(1+{x}_{1}^{2}\right)\\ {x}_{1}\mathrm{cos}\left({x}_{2}\right)+{x}_{2}\mathrm{sin}\left({x}_{1}\right)=\frac{1}{2}.\end{array}$`

Convert the equations to the form F(x) = 0.

`$\begin{array}{c}{e}^{-{e}^{-\left({x}_{1}+{x}_{2}\right)}}-{x}_{2}\left(1+{x}_{1}^{2}\right)=0\\ {x}_{1}\mathrm{cos}\left({x}_{2}\right)+{x}_{2}\mathrm{sin}\left({x}_{1}\right)-\frac{1}{2}=0.\end{array}$`

### Code Generation Steps

1. Write a function that computes the left side of the two equations. For code generation, your program must allocate all arrays when they are created, and must not change their sizes after creation.

```function F = root2d(x) F = zeros(2,1); % Allocate return array F(1) = exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1)^2); F(2) = x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5; end```
2. Write a function that sets up the problem and calls `fsolve`. The function must refer to `root2d` as a function handle, not as a name.

```function [x,fval] = solveroot options = optimoptions('fsolve','Algorithm','levenberg-marquardt','Display','off'); fun = @root2d; rng default x0 = rand(2,1); [x,fval] = fsolve(fun,x0,options); end```
3. Create a configuration for code generation. In this case, use `'mex'`.

`cfg = coder.config('mex');`
4. Generate code for the `solveroot` function.

`codegen -config cfg solveroot`
5. Test the generated code by running the generated file, which is named `solveroot_mex.mexw64` or similar.

`[x,fval] = solveroot_mex`
```x = 0.3532 0.6061 fval = 1.0e-14 * -0.1998 -0.1887```


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# 1.2.1 Whole Numbers, PT3 Practice

Question 1:
 Solve 8 × 2 ÷ 4 + 12.

 Solution:

8 × 2 ÷ 4 + 12
 = 16 ÷ 4 + 12
 = 4 + 12
 = 16

Question 2:
 Solve 7(6 + 5) – 3(13 – 9).

 Solution:

7(6 + 5) – 3(13 – 9)
 = 7(11) – 3(4)
 = 77 – 12
 = 65

Question 3:
 Solve 64 + (136 – 87) × (28 ÷ 4).

 Solution:

64 + (136 – 87) × (28 ÷ 4)
 = 64 + 49 × 7
 = 64 + 343
 = 407

Question 4:
 Solve 84 ÷ 4 – 9 + 6 × 7

 Solution:

84 ÷ 4 – 9 + 6 × 7
 = 21 – 9 + 42
 = 12 + 42
 = 54

Question 5:
 Solve 92 + 13 × 5 – 42

 Solution:

92 + 13 × 5 – 42
 = 92 + (13 × 5) – 42
 = 92 + 65 – 42
 = 157 – 42
 = 115


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# Partial Function Extension with Applications to Learning and Property Testing

Speaker:

## Time:

Tuesday, 20 October 2020, 14:00 to 15:00

Partial function extension is a basic problem that underpins multiple research topics in optimization, including learning, property testing, and game theory. Here, we are given a partial function consisting of $n$ points from a domain and a function value at each point. Our objective is to determine if this partial function can be extended to a function defined on the domain, that additionally satisfies a given property, such as linearity. We formally study partial function extension for various complement-free functions.

Our contributions are twofold. Firstly, for the properties studied, we give a combinatorial characterization and bounds on the complexity of partial function extension. Secondly, we develop new connections between partial function extension and learning and property testing, and use these to give new results for these problems.


text:
# Extending Functions on Closed Submanifolds of C^n

Functions on an algebraic subvariety X of A^n are the same as functions on A^n restricted to X. So the statement that functions on X extend to all of A^n follows by the definition. My question is: does the analogous statement hold for C^n and closed complex submanifolds (maybe even closed analytic subvarieties), and if so, how is this proved?

-


text:
# Show that f is not integrable

1. Jan 10, 2009

### snipez90

1. The problem statement, all variables and given/known data
Let f(x) = 0, if x is rational; 2 + x, if x is irrational, for all x in [0,1]. Show that f is not integrable

2. Relevant equations
density of rationals/irrationals, equation for L(f,P) and U(f,P), Darboux Integrability criterion

3. The attempt at a solution
L(f,P) = 0 because on any subinterval formed from two consecutive points in the partition of [0,1], there exists a rational x.

For U(f,P), I was thinking that I could just pick any irrational x so that sup{ f(x): x is an element of the subinterval from two consecutive points in the partition of [0,1] } = 2 + x. Then note that since $$2+x \geq 2$$, $$U(f,P) \geq 2(b-a) > 0$$ so that

$$sup {L(f,P)} \neq inf {U(f,P)}$$

I left a few steps in demonstrating U(f,P) > 0 but is this a good approach?

2. Jan 10, 2009

### Dick

Sort of. 2+x>=2. x<=1. Can you show any U(f,P)>=2 and any L(f,P)<=1?

3. Jan 10, 2009

### snipez90

Hmm I was really lax about the bounds. U(f,P) >= 2(b-a) = 2. L(f,P) = 0, no matter what, I think, so L(f,P) is certainly <= 1.

As for U(f,P), could I just say that 2+x >= 2 for any x in [0,1] so that U(f,P) >= 2*SUMMATION{bunch of points that cancel out to give b -a}?

4. Jan 10, 2009

### Dick

Sure U(f,P)>=2, but why do you think L(f,P)=0? Take the partition P of the intervals [0,1/2] and [1/2,1]. Then L(f,P)=1/4, I think.

5. Jan 10, 2009

### snipez90

Sorry, here's my reasoning. The definition of L(f,P) is the summation of a bunch of products, each of which is of the form m*(d-c), where d and c are consecutive points in the partition and c < d. The quantity m is equal to inf{f(x) : c <= x <= d}. But assuming the density of the rationals, the quantity m will always be 0. Therefore, the summation of these products will yield 0 as well.

6. Jan 10, 2009

### Dick

Oooops. Right. I misread the problem. Somehow I read it as f(x)=x for x rational instead of f(x)=0. So, yes, L(f,P)=0, U(f,P)>=2.

7. Jan 10, 2009

### snipez90

Haha ok. Actually when you suggested x <= 1 I thought to myself did I put x instead of 0? Thanks for your help though. Especially in noting that it's probably a good idea to use the best bounds possible (I sometimes forget that b and a are given endpoints and leave b-a as b-a).


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## Dissertations, Theses, and Capstone Projects

6-2022

Dissertation

Ph.D.

Physics

#### Committee Members

Sarang Gopalakrishnan

David J. Schwab

Anatoly Kuklov

Tzu-Chieh Wei

E. Miles Stoudenmire

Sriram Ganeshan

#### Subject Categories

Condensed Matter Physics

#### Keywords

Statistical Mechanics, Critical Phenomena, Complex Temperatures, Tensor Networks, Quantum Circuits with Measurements, Modulated Correlations and Non-unitary Quantum Dynamics.

#### Abstract

This thesis explores several aspects of the 2D Ising Model at both real and complex temperatures utilizing tensor network algorithms. We briefly discuss the importance of tensor networks in the context of forming efficient representations of wavefunctions and partition functions for quantum and classical many-body systems respectively, followed by a brief review of the tensor network renormalization algorithms to compute the one point and two point correlation functions. We use the Tensor Renormalization Group (TRG) to study critical phenomena and examine feasibility of accurate estimations of universal critical data for three critical points for three critical points in two dimensions -- the critical points for the isotropic and the anisotropic square lattice Ising models, and the Yang-Lee critical endpoint. The latter two exhibit appreciable corrections to scaling, making a clear case for uniform convergence in bond dimension apparent in our results. We are able to reproduce exactly known values to within 1 percent with modest effort of bond dimension 28.

We analytically continue into the complex temperature plane to identify and study novel phases and phase transitions of the 2D isotropic as well as the 2D anisotropic Ising model. Regions of the phase space that lie in the complex coupling plane cannot be studied using standard Quantum Monte Carlo techniques (phase problem for complex coupling). Tensor networks provides us with a powerful tool to analyze and study regions of phase space in complex coupling planes. Evidence from tensor network renormalization techniques for the infinte 2D isotropic Ising model suggest the presence of only the standard paramagnetic (PM) and the ferromagnetic (FM) phases in the complex temperature plane. On the other hand, evidence from magnetization using tensor network renormalization techniques for the 2D anisotropic Ising model, and also numerical evidence based on the exact Onsager solution for the infinte 2D anisotropic Ising model suggests the presence of novel phases in certain regions of the complex temperature $\tanh(\beta)$ plane that exhibits quasi-long range modulated correlations. Phase transitions from the paramagnetic (PM) phase to these novel phases (which we label as non-ferromagnet or NFM phase) exhibit a one-sided square root singularity akin to a commensurate-incommensurate phase transition.

In this thesis, we also present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases. These phases can range from ferromagnetic order to spin-density waves to time crystals. The corresponding time crystals for the quantum circuit presented in this thesis are incommensurate with the drive frequency, a behavior that is a deviation from the time crystal that have been found in unitary circuits. The period of the incommensurate time-crystal phase can be tuned by adjusting the parameters for the quantum circuit. We demonstrate that these novel phases, including the inherently non-equilibrium dynamical phases, correspond to the complex-temperature equilibrium phases of the exactly solvable infinite square-lattice anisotropic Ising model with doubly periodic boundary conditions. We also present a quantum circuit and briefly discuss special dual unitary points in the complex temperature plane for the square-lattice isotropic Ising Model and its implications in quantum information theory.

COinS


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# Enhanced Dividend Yield

The enhanced dividend yield strategy was developed by Jim O'Shaughnessy to provide a fixed income strategy based on stocks instead of bonds. O'Shaugnessy argued that while bonds appeal to investors because of their inherent principal protection advantage, they have a number of important disadvantages.

• First of all, bond yield remains fixed, i.e. you will receive the same coupon over the entire period until maturity. This is ok in periods of low inflation, but between 1970 and 2010 inflation has on average been at 4,45%. That means that something that cost 1 dollar in 1970 costs \$5,75 in 2010.
• Secondly, with bonds your principal doesn't depreciate, but it also won't appreciate. When the bond matures, you will get back the principal amount, and due to inflation this will be worth a lot less.

To remedy these issues of the traditional fixed income strategies, O'Shaugnessy designed a quantitative investing strategy based on stocks, with as primary objectives a growing yearly income combined with capital appreciation. The results of his study show that by implementing the enhanced dividend yield strategy, yearly income would have increased by 10%per annum and between 1962 and 2009, the principal increased by 5538%. What's more, this strategy never had a five-year period in which it lost money, very enticing for risk-averse investors.

### How does it work?

O'Shaughnessy created a dividend yield strategy with a twist. Sometimes high yielding stocks are value traps and this strategy tries to get rid of these stocks in 2 ways.

1. First he limits the stock universe to market leading companies, that accourding to O'Shaughnessy have the following characteristics:
1. Non-utility stocks
2. Shares outstanding > dataset average
3. Cash flow > dataset average
4. Sales > 1.5 times dataset average
2. Next he excludes the bottom half of these stocks ranked by their EBITDA/EV. This way he only keeps the 50% of market leaders with the best financial conditions.

Finally, he builds a portfolio in which he overweights the stocks with the highest dividend yield, in the following manner:

• 25% of stocks with highest yield get 1.5 times the weight,
• the next 25% by yield get 1.25% the weight,
• the next 25% get 0.75 the weight,
• and the final 25 get 0.5 times the weight

The portfolio should be rebalanced every year.

You can read more about this strategy and the results by clicking on this link. This strategy is quite cumbersome to calculate for small investors, but with our screener it becomes a breeze. Just select the high dividend yield template screen, select your countries, and the screener will show the list of stocks for the dataset of the selected countries.


text:
# The insulation resistance of a cable of length 10 km is 1 MΩ. its resistance for 50 km length will be

1. 1 MΩ
2. 5 MΩ
3. 0.2 MΩ
4. 2 MΩ

Option 3 : 0.2 MΩ
Free
CT 1: Network Theory 1
11207
10 Questions 10 Marks 10 Mins

## Detailed Solution

Concept:

Insulation resistance is inversely proportional to length of the cable

$$R = \frac{\rho }{{2\pi l}}\log \frac{{{r_2}}}{{{r_1}}}$$

$$\Rightarrow R \propto \frac{1}{l}$$

where,

r= radius of cable, r1 = radius of core conductor, l = length of cable

Calculation:

Given

l1 = 10 km, R1 = 1 MΩ, l2 = 50 km

$$\Rightarrow \frac{{{R_1}}}{{{R_2}}} = \frac{{{l_2}}}{{{l_1}}}$$

$$\Rightarrow \frac{{1 }}{{{R_2}}} = \frac{50}{10} \Rightarrow {R_2} = 0.2\;M{\rm{Ω }}$$


text:
1. ## Differentiable Function Question

Show that there exists a differentiable function f : R → R such that
(f(x))^5 + f(x) + x = 0 for all x ∈ R.
[Hint: If f exists and has an inverse function g what equation must g satisfy? ]

I haven't got a clue how to start this one. Any help would be greatly appreciated.

Thanks

2. Originally Posted by DeFacto
Show that there exists a differentiable function f : R → R such that
(f(x))^5 + f(x) + x = 0 for all x ∈ R.
[Hint: If f exists and has an inverse function g what equation must g satisfy? ]
I think you'll find this easier if you write y = f(x). Then $y^5+y+x=0$. The hint suggests that you should consider the inverse function, in other words that you should look at x as a function of y. Then $x = -y^5-y$, and $\tfrac{dx}{dy} = -5y^4-1<0$ for all y. Now use the inverse function theorem to conclude that y is a differentiable function of x.