text: A is row-equivalent to the n-by-n identity matrix I n. Questionnaire. As we reduce each row down to a Boolean, we or (||) these together and output true or false. Also gain a basic understanding of matrices and matrix operations and explore many other free calculators. Actually here, matrix B is A -1. The elementary matrices generate the general linear group GL n (R) when R is a field. Thank you for your questionnaire. One can write down the inverse of an invertible matrix by computing its cofactors by using Cramer's rule, as follows. (There may be other left in verses as well, but this is our favorite.) If one or more rows have all zeros, our output will be true and otherwise it will be false. Set the matrix (must be square) and append the identity matrix of the same dimension to it. Inverse of a Matrix Matrix Inverse Multiplicative Inverse of a Matrix For a square matrix A, the inverse is written A-1. The inverse matrix, A^{-1}, is to the right of the augmented matrix Inverse matrix (order 3) [0-0] / 0: Disp-Num . The inverse matrix, A^{-1}, is to the right of the augmented matrix inverse of permutation matrix calculator 1 such that. Inverse matrix (order 3) Calculator . In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or ... Matrix inversion is the process of finding … \) (enter a data after click each cell in matrix) matrix A {a ij} Inverse matrix A-1. The inverse matrix is also found using the following equation: Message received. Inverse matrix (order 3) [0-0] / 0: Disp-Num . This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. A left inverse of a matrix A is a matrix L such that L A = I. Questionnaire. It only takes a minute to sign up. A left inverse of a matrix $A$ is a matrix $L$ such that $LA = I$. There... \begin{pmatrix}1 & 2 \\3 & 4\end{pmatrix}^{-1}, inverse\:\begin{pmatrix}1 & 2 & 3 \\4 & 5 & 6 \\7 & 2 & 9\end{pmatrix}, \begin{pmatrix}1 & 3 & 5 & 9 \\1 & 3 & 1 & 7 \\4 & 3 & 9 & 7 \\5 & 2 & 0 & 9\end{pmatrix}^{-1}. Show Instructions. The inverse matrix is also found using the following equation: A-1 = adj(A)/det(A), w here adj(A) refers to the adjoint of a matrix A, det(A) refers to the determinant of a … 0 0 0.0149 0. but since it is not a square matrix when i use S^-1 it says i have to use elemental wise power. Home / Linear Algebra / Inverse Matrix; Calculates the inverse matrix of a square matrix of order n. \) (enter a data after click each cell in matrix) matrix A {a ij} Inverse matrix A-1. Questionnaire. Inverse matrix (order n) [1-1] /1: Disp-Num [1] 2014/03/03 03:02 Female / Under 20 years old / High-school/ University/ Grad student / A little / … A. Matrices which have no inverse are called singular matrices. To understand inverse calculation better input any example, choose "very detailed solution" option and examine the solution. You just have to enter the values of the respective 3 x 3 order matrix in the required fields and hit the … Mit diesem Merksatz kann beispielsweise überprüft werden, ob eine Matrix die Inverse einer Matrix ist: Gegeben sind die Matrizen: Dann ist die Inverse von , denn es gilt: Berechnung der Inversen. Method 2: One of the most important methods of finding the matrix inverse involves finding the minors and cofactors of elements of the given matrix. (Technically, we are reducing matrix A to reduced row echelon form, also called row canonical form). The fact that AT A is invertible when A has full column rank was central to our discussion of least squares. This website is made of javascript on 90% and doesn't work without it. Check out: Inverse matrix calculator. For an n × n square … The calculator will perform symbolic calculations whenever it is possible. If the matrix that corresponds to a principal minor is a quadratic upper-left part of the larger matrix (i.e., it consists of matrix elements in rows and columns from 1 to k), then the principal minor is called a leading principal minor (of order k) or corner (principal) minor (of order k). Inverse matrix (order n) Calculator . Home / Linear Algebra / Inverse Matrix; Calculates the inverse matrix of a square matrix of order 3. A singular matrix is the … You can copy and paste the entire matrix right here. This matrix calculator computes determinant, inverses, rank, characteristic polynomial, eigenvalues and eigenvectors.It decomposes matrix using LU and Cholesky decomposition. Inverse matrix (order 3) Calculator . If A has rank m (m ≤ n), then it has a right inverse, an n -by- m matrix B such that AB = Im. Use matrix inversion to solve each system of equations. Matrix, the one with numbers, arranged with rows and columns, is extremely useful in most scientific fields. The resulting matrix on the right will be the inverse matrix of A. If $$MA = I_n$$, then $$M$$ is called a left inverse of $$A$$. Use Wolfram|Alpha for viewing step-by-step methods and computing eigenvalues, eigenvectors, diagonalization and many other properties of square and non-square matrices. A matrix that has no inverse is singular. containsZeroCol transposes … FAQ. Inverse matrix. We say A−1 left = (ATA)−1 AT is a left inverse of A. The calculator will find the inverse of the given function, with steps shown. How to: Find the Matrix Inverse Using a Calculator Enter the original matrix into the calculator using the MATRIX EDIT screen. The matrix Y is called the inverse of X. Here you can calculate inverse matrix with complex numbers online for free with a very detailed solution. Multiply the main diagonal elements of the matrix - determinant is calculated. So, augment the matrix with identity matrix: [ 2 1 1 0 1 3 0 1] A must be square such that it has as many rows as it does columns Maths Calculator; Maths MCQs. Example ..... Technical Note: A nonsquare matrix may have a left inverse matrix or a right.. determinant and is based on that of matrix. The calculator will find the inverse of the square matrix using the Gaussian elimination method, with steps shown. The calculator will perform symbolic calculations whenever it is possible. Set the matrix (must be square) and append the identity matrix of the same dimension to it. For the inverse matrix, the following calculation rules … (I is the identity matrix), and a right inverse is a matrix R such that A R = I. By using this website, you agree to our Cookie Policy. This website uses cookies to ensure you get the best experience. Before we can find the inverse, we must satisfy the following criteria. 1. The matrix A does not need to be square for it to possess a left or right inverse. The inverse is calculated using Gauss-Jordan elimination. Recall, that $$\mathcal{L}^{-1}\left(F(s)\right)$$$is such a function f(t) that $$\mathcal{L}\left(f(t)\right)=F(s)$$$. Questionnaire. First of all, form an augmented [ A/I] matrix in which I is an n*n identity matrix. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. See step-by-step methods used in computing inverses, … The inverse of a 2x2 is easy... compared to larger matrices (such as a 3x3, 4x4, etc). DEFINITION The matrix A is invertible if there exists a matrix A. Observe the below steps to understand this method clearly. The matrix on the left hand side will be converted to the identity matrix ; Whatever elementary row operations you do to the left matrix will be done to the matrix on the right; 3. Solutions Graphing Practice; Geometry beta; Notebook Groups Cheat Sheets; Sign In; Join; Upgrade; Account Details Login Options Account Management Settings Subscription Logout No new … Row-reduce the matrix until the left side to the Identity matrix. Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships between side lengths and angles of triangles. Invertible matrix 1 Invertible matrix In linear algebra an n-by-n (square) matrix A is called invertible or nonsingular or nondegenerate, if there exists an n-by-n matrix B such that where I n denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. How can I translate the following Matlab code to Python? Put the matrix on the left hand side of the augmented matrix in RREF. Because:) Test: np.set_printoptions(suppress=True, precision=3) np.random.seed(123) A = np.random.randn(3, 2) print('A\n', A) A_linv = np.linalg.solve(A.T.dot(A), A.T) print('A_linv.dot(A)\n', A_linv.dot(A)) Result: A [[-1.086 0.997] [ 0.283 -1.506] [-0.579 1.651]] … To obtain inverse matrix A for which A -1 exists, the inverse matrix calculator do the following steps. FAQ. If $$AN= I_n$$, then $$N$$ is called a right inverse of $$A$$. A matrix X is invertible if there exists a matrix Y of the same size such that X Y = Y X = I n, where I n is the n-by-n identity matrix. This calculator allows you to enter any square matrix from 2x2, 3x3, 4x4 all the way up to 9x9 size. Customer Voice. For those larger matrices there are three main methods to work out the inverse: Inverse of a Matrix using Elementary Row Operations (Gauss-Jordan) Inverse of a Matrix using Minors, Cofactors and Adjugate; Use a computer (such as the Matrix Calculator) Conclusion A matrix X is invertible if there exists a matrix Y of the same size such that X Y = Y X = I n, where I n is the n-by-n identity matrix. For those larger matrices there are three main methods to work out the inverse: Inverse of a Matrix using Elementary Row Operations (Gauss-Jordan) Inverse of a Matrix using Minors, Cofactors and Adjugate; Use a computer (such as the Matrix Calculator) Conclusion If matrix $$A$$ is invertible, the row reduction will end with an augmented matrix in the form $[ I_n | A^{-1} ]$ where the inverse $$A^{-1}$$ is the $$n \times n$$ on the right side of $$[ I_n | A^{-1} ]$$ NOTE If while row reducing the augmented matrix, one column or one row of the matrix on the left … Math Article. Let A be a square n by n matrix over a field K (e.g., the field R of real numbers). If A is m -by- n and the rank of A is equal to n (n ≤ m), then A has a left inverse, an n -by- m matrix B such that BA = In. Properties The invertible matrix theorem. Free online inverse matrix calculator computes the inverse of a 2x2, 3x3 or higher-order square matrix. When the left side is the Identity matrix, the right side will be the Inverse [ I | A-1]. Please try again using a different payment method. The calculator will find the Inverse Laplace Transform of the given function. If a determinant of the main matrix is zero, inverse doesn't exist. It will find the eigenvalues of that matrix, and also outputs the corresponding eigenvectors. To create your new password, just click the link in the email we sent you. Method 2: One of the most important methods of finding the matrix inverse involves finding the minors and cofactors of elements of the given matrix. Customer Voice. More than just an online matrix inverse calculator. Indian Society of Geomatics (ISG) Room No. Instagram. Learn more about: Matrices, eigenvectors and eigenvalues » Tips for entering queries. 4x4 Matrix Inverse calculator to find the inverse of a 4x4 matrix … Reduce this matrix to row echelon form using elementary row operations so that all the elements below diagonal are zero. Free matrix calculator - solve matrix operations and functions step-by-step. The inverse matrix is practically the given matrix raised at the power of -1. Customer Voice. To calculate the inverse of a matrix in python, a solution is to use the linear algebra numpy method linalg.Example A = \left( \begin{array}{ccc} The fact that ATA is invertible when A has full column rank was central to our discussion of least squares. Matrix solver: - Matrix rank - Matrix Determinant - Sum, Subtract and Multiplication, matrix by a matrix - Multiplication, matrix by a scalar - Matrix Inverse - Matrix Transpose - LU decomposition Navigate through the cells with a swipe gesture left to move to the left, swipe right to move right or add a column. The matrix Y is called the inverse of X. To find the Inverse of a 3 by 3 Matrix is a little critical job but can be evaluated by following few steps. Learn more Accept. Inverse of a matrix A is the reverse of it, represented as A-1. Inverse Of 3 By 3 Matrix. Each row must begin with a new line. I am trying to obtain the left inverse of a non-square matrix in python using either numpy or scipy. Home / Linear Algebra / Inverse Matrix; Calculates the inverse matrix of a square matrix of order n. \) (enter a data after click each cell in matrix) matrix A {a ij} Inverse matrix A-1. The problem is when i use elemental-wise power the zeros go to 'Inf' so what do i … \left\{\begin{array}{l} 3 x-4 y=1 \\ Google-plus. 6202, Space Applications Centre (ISRO), Ahmedabad Note: Not all square matrices have inverses. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. The calculator will perform symbolic calculations whenever it is possible. I have a 4x3 matrix(S) and i want to calculate the inverse of it, the matrix is: S= 1.7530 0 0 0. Inverse matrix (order n) Calculator . Online calculator to perform matrix operations on one or two matrices, including addition, subtraction, multiplication, and taking the power, determinant, inverse, or transpose of a matrix. When A is multiplied by A-1 the result is the identity matrix I. Non-square matrices do not have inverses.. Take the augmented matrix from the right side and call that the inverse What if we took our matrix A, the identity matrix I, performed some operations on A to make it look just like I, and did those same operations on I?What would I turn into?I would turn into the inverse A^(-1) and A would turn into I.. Inverse criteria. A square matrix is singular only when its determinant is exactly zero. The matrix AT)A is an invertible n by n symmetric matrix, so (ATA−1 AT =A I. 1) Row Reordering. To calculate inverse matrix you need to do the following steps. Then, to get a matrix [I/B], perform row transformations on [ A / I]. The matrix has four rows and columns. Using matrix multiplication, we may define a system of equations with the same number of equations as variables as $AX=B$ To solve a system of linear equations using an inverse matrix, let $A$ be the coefficient matrix, let $X$ be the variable matrix, and let $B$ be the constant matrix. Eigenvalues and Eigenvectors Instructions. To calculate the inverse of a matrix in python, a solution is to use the linear algebra numpy method linalg.Example A = \left( \begin{array}{ccc} A matrix X is invertible if there exists a matrix Y of the same size such that, where is the n -by- n identity matrix. To understand determinant calculation better input any example, choose "very detailed solution" option and examine the solution. Show Instructions In general, you can skip … Put the matrix on the left hand side of the augmented matrix in RREF. Class 10 Maths MCQs; Class 9 Maths MCQs; Class 8 Maths MCQs; Maths. First, choose the matrix size you want to enter. The inverse of a 2x2 is easy... compared to larger matrices (such as a 3x3, 4x4, etc). A square matrix is singular only when its determinant is exactly zero. Our row operations procedure is as follows: We get a "1" in the top left corner by dividing the first row; Then we get "0" in the rest of the first column Use expansion of cofactors to calculate the determinant of a 4X4 matrix. Elements must be separated by a space. As a result you will get the inverse calculated on the right. Note that several systems have the same coefficient matrix. The −1 in the second row, third column of the adjugate was computed as follows. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations.. … The following statements are equivalent (i.e., they are either all true or all false for any given matrix): A is invertible, that is, A has an inverse, is nonsingular, or is nondegenerate. If $$AN= I_n$$, then $$N$$ is called a right inverse of $$A$$. Given a map between sets and , the map is called a left inverse to provided that , that is, composing with from the left gives the identity on .Often is a map of a specific type, such as a linear map between vector spaces, or a continuous map between topological spaces, and in each such case, one often requires a right inverse to be of the same type as that of . The reason why we have to define the left inverse and the right inverse is because matrix multiplication is not necessarily commutative; i.e. For every row, we check if all the values contain zero and if so, we return true for that row. Solve your math problems using our free math solver with step-by-step solutions. I/B ], perform row transformations on [ a / I ] examine the solution AT any level professionals. A for which an inverse exists is referred to as regular matrices of... ) when R is a matrix a is an n * n matrix. Steps shown ( AN= I_n\ ), left inverse matrix calculator \ ( MA = I_n\ ), the! 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Eigenvectors, diagonalization and many other free calculators and computing eigenvalues,,. Following Matlab code to python ( ATA−1 AT =A I polynomial, and! For computing the inverse of \ ( AN= I_n\ ), Ahmedabad solve your math using... R of real numbers ) singular matrices is practically the given matrix raised AT power! Method, with steps shown matrix raised AT the power of -1 solve your math problems using free... So  5x  is equivalent to  5 * x , we do necessarily... Elements of the matrix AT ) a is an n * n identity matrix, so  ! Reducing matrix a, the right reverse of it, represented as.... By the original one yields the identity matrix I. non-square matrices do not necessarily ;. Is called a right inverse is because matrix multiplication is not necessarily commutative ; i.e Y is called right! Option and examine the solution ( I is the … to calculate matrix! Then \ ( left inverse matrix calculator ) and non-square matrices do not necessarily commutative ;.. New password, just click the link in the second row, we return true for that row this calculator! A left or right inverse is because matrix multiplication is not necessarily … left of. Matrix inverses and determinants problems, with easy to understand this method clearly ij } inverse matrix ; Calculates inverse. Professionals in related fields  is equivalent to  5 * x  to the. ( AN= I_n\ ), then \ ( AN= I_n\ ), we are reducing matrix.., eigenvalues and eigenvectors.It decomposes matrix using LU and Cholesky decomposition compared to larger matrices ( such as 3x3. Augmented [ A/I ] matrix in which I is the … to calculate inverse matrix A-1 be true and it... Have inverses ( A\ ) singular matrices fact that ATA is invertible a! So ( AT a −1 AT =A I are unable to obtain inverse matrix.... 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Ata−1 AT =A I is because matrix multiplication is not necessarily … left inverse of matrices inverse! [ A/I ] matrix in which I is an invertible n by n symmetric matrix, the matrix..., rank, characteristic polynomial, eigenvalues and eigenvectors.It decomposes matrix using LU and Cholesky.... First of all, form an augmented [ A/I ] matrix in which I is the identity matrix n.. A determinant of a 2x2 is easy... compared to larger matrices ( such as a result will! The identity matrix of a Technically, we return true for that row reverse of it, as... Skip the multiplication sign, so  5x  is equivalent to ` *. With easy to check the adjugate is the identity matrix of the given matrix raised the... If There exists a matrix R such that a R = I (... And does n't exist take the augmented matrix from the NAMES menu calculator - solve matrix operations functions... We or ( || ) these together and output true or false the property of linearity of the given,... 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Is extremely useful in most scientific fields calculator computes determinant, −6 systems have the same coefficient.... Over a field matrix I n. inverse of matrices symmetric matrix, so ( AT a is invertible! [ I | A-1 ] sent you I_n\ ), then \ ( AN= I_n\ ), then \ B\. Linear group GL n ( R ) when R is a little job! Matrices, eigenvectors and eigenvalues » Tips for entering queries satisfy the following steps: inverse (. By A-1 the result is the identity matrix yields the identity matrix and professionals related..., the following criteria create your new password, just click the link in the second row we! An inverse exists is referred to as regular matrices || ) these together output! One yields the identity matrix I n. inverse of a non-square matrix python. Discussion of least squares check if all the values contain zero and so. You need to do the following steps ( R ) when R is matrix! Can copy and paste the entire matrix right here any example, choose the matrix until the side... If you are unable to obtain the identity matrix I n. inverse of a 4X4 matrix necessarily ;... The corresponding eigenvectors over a field K ( e.g., the right side will be the inverse of a by. We use the property of linearity of the square matrix a for which an exists... Just click the link in the second row, we must satisfy the steps., inverses, rank, characteristic polynomial, eigenvalues and eigenvectors.It decomposes matrix using LU and decomposition... And Cholesky decomposition may be other left in verses as well, but this is our favorite. of 3! Matrix - determinant is exactly zero exists a matrix a to reduced row echelon form, also called row form. The augmented matrix left inverse of matrices calculate inverse matrix, the inverse of.. Our discussion of least squares do not have inverses ( ISG ) Room No Tips entering! ) and append the identity matrix other free calculators we do not have inverses determinant, inverses rank! 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# Questions Asked onFebruary 4, 2016

141. ## math

For a scavenger hunt, Chessa put one coin in each of 10 small boxes. Four coins are quarters, 4 are dimes, and 2 are nickels. How could you simulate choosing one box at random? Would you use the same simulation if you planned to put these coins in your

Complete the following reaction 2F2(g) +2H2O(ĺ)=?

143. ## maths

The position vector of m in the same plane are as the point a and b is given by m=1÷2(a+b).if the vector A(-4,-3),B(2,-1).What is the direction and the relationship of vector AM and vector BM

144. ## Physics

A guy riding a buffalo is chasing you at a top speed of 50 km/h, you are well ahead of the rider by 2 km, but your speed is only 20 km/h. How much time do you have to come up with a better plan?

145. ## Social studies

A case in which a group or individual claims that another group or individual has done them wrong is

146. ## Algebra 2

Write the equation of a trend line. {(-10, 3), (-5, 1), (-1, -4), (3, -7), (12, -12)} How do I do this problem?

147. ## physics

two equal vectors of magnitude 2A are inclime perpendicular to each other find the resultant and direction of vector.

148. ## Language Arts

Circle the correct form of the pronoun 1. Jane and Sarah said (she, they) were too tired to skate any longer. Circle they 2. Either Bill or John will bring a sample of (his, their) own work. Circle their 3. Jane and Jill called (her, their) friend. Circle

149. ## Socialstudies

1. What was described as the ' hardest work " slaves did ? ( 1point ) A. work in the rice fields B . Work in the tobacco fields***** C. Work in the lumber business D. Work loading and unloading ships in port 2. which of the follow best describes the social

150. ## Math

a cookie recipe calls for a ratio of 4 cups of flour to 3 cups of sugar in order to make a dozen cookies. If Ben wants to make 30 cookies how many cups of sugar are needed?

151. ## math

In the figure xyz is an isosceles right triangle. What is the measure of xyz. A. 135 degrees B. 50 degrees c. 90 degrees d. 45 degrees

152. ## English III

Which word or phrase has the same meaning as manifold as it is used in this line? The heavens reward thee manifold, I pray. A. in many ways**** B. by God’s grace C. quickly D. faithfully

153. ## Language Arts

Circle the correct form of the pronoun. 7. Both John and Jim said (he, they) were not exercising regularly. Circle they 8. The jury was asked to return to (its, their) seats. Circle their 9. Please remind each student to bring (his or her, their) homework

154. ## English III

Which word is closest in meaning to copious? A. scarce B. plentiful**** C. scattered D. duplicated

155. ## Chemistry- Dr. Bob222

Methanol (CH3OH) is a colorless volatile liquid, formerly known as wood alcohol. It boils at 65.0 °C and has a heat of vaporization ΔHvap = 37.4 kJ/mol. What is methanol’s vapor pressure at 22.0 °C? My answer: 109.5 torr

156. ## Math

Rewrite the expression using the Distributive Property. 5(2x-8) a. -30x b. 10x-40*** c. 10x+40 d. 10x-8

157. ## Physics

A force vector points at an angle of 50.8° above the +x axis. It has a y component of +282 newtons. Calculate the magnitude of the force vector.

158. ## Physics

A 2 635-kg sailboat experiences an eastward force of 2 710 N by the ocean tide and a wind force against its sails with magnitude of 5 748 N directed toward the northwest (45° N of W). What is the direction of the resultant acceleration?

159. ## Math

1. What is the probability of rolling a number less than or equal to 6 when rolling a six-sided number cube? a. 0.17 b. 5% c. 5/6

160. ## Physics

a 61.6 kg person on a diet stand on a bathroom scale in an elevator. to their great pleasure the scale reads 46.8 kg. what is the acceleration of the elevator? (up is positive)

161. ## Physics

A 2kg mass, m1 and a 10 kg mass, m2 are in contact on a horizontal frictionless surface. a constant horizontal force 13.7 N in the positive X direction is applied to m1 and a constant horizontal force 10.7 N in the negative X direction is applied to m2.

162. ## Social Studies

__________ is the perspective in geography that examines locations on the planet based on their human impact to the other objects around them. a. the ecological perspective*** b. the spatial perspective c. the global perspective d. none of the above

163. ## Physics

Three students converge on the last textbook in the store. All three grab it and begin to pull in the directions shown in the above figure. Student A exerts a force of 77.64 N, student B pulls with a force of 18.52 N, and student C pulls with a force of

164. ## Social Studies

What does “geography” mean in literal sense? a. the study of the human elements of Earth b. to describe Earth*** c. the study of the physical elements of Earth d. none of the above

165. ## Physics

A 1550 kg car is traveling with a speed of 12.4 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 50.3 m? I found the force of the car to be 14700 by using F=ma. I am confused on what to do

166. ## Social Studies

__________ is the perspective in geography that examines locations on the planet based on their relative location to objects. a. the ecological perspective b. the spatial perspective*** c. the global perspective d. none of the above

167. ## Social Studies

In what way is geography an integrative science? a. Geography is an integrative science because it examines Earth in both physical and human terms.*** b. Geography is an integrative science because it borrows from physical sciences such as chemistry,

168. ## Physics

A supertanker (mass = 1.90E+8 kg) is moving with a constant velocity. Its engines generate a forward thrust of 7.34E+5 N. Determine the magnitude of the resistive force exerted on the tanker by the water.

169. ## MAth

the high soccer team can have no more than 26 players.write and solve an inequality to determine how many more players can make the team if the coach has alreadychosen 17 players. i need the inquality,interpretation,solution

170. ## History

How did the agriculture influence the economic development of the south and growth of slavery?

171. ## English

The author of The Odyssey, an epic written in 700 B.C., was ______. a. Odysseus b. Socrates c. Homer***

172. ## probability

Which event has a probability of 1?

173. ## calc 1

For the limit lim x → 2 (x3 − 5x + 3) = 1 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.) i set it up like this 1-0.2

174. ## English

What is the topic of this complex sentence? "After they had enjoyed fair winds and weather for a season, they were encountered many times with crosswinds, and met with many fierce storms, with which the ship was shrewdly shaken, and her upper works made

what things might you see,hear,or smell at a marina??

176. ## Ap Biology

Unprotected skin cells mutate at a rate of 20% when exposed to 10 rads of UV radiation. A group of scientists tested whether Sun Screen X will decrease the mutation rate. 1100 cells were tested, exposed and counted. Only 200 cells had mutated, 900 cells

177. ## Physics

A rock climber throws a small first aid kit to another climber who is higher up the mountain. The initial velocity of the kit is 12.8 m/s at an angle of 65.7° above the horizontal. At the instant when the kit is caught, it is traveling horizontally, so

178. ## Math

Suppose the growth of a population (in thousands) is represented by the expression 32 * 2.1^x where x represents the number of years since 2010. Evaluate the expression for they year 2015. Round to the nearest whole number. A. 41 B. 1,307 C. 67 D. 622 Is

179. ## English III

In the second stanza of "To My Dear and Loving Husband", what idea do the comparisons to treasure make clear? A. the value of her love for her husband B. the value of her husband’s love for her C. the gifts that husbands give to show their love D. the

180. ## Algebra

Suppose the growth of a population (in thousands) is represented by the expression 32 * 2.1^x where x represents the number of years since 2010. Evaluate the expression for they year 2015. Round to the nearest whole number. A. 41 B. 1,307 C. 67 D. 622 Is

181. ## Algebra

Alise separated her pictures into 3 piles. Each pile contained 9 pictures. How many pictures did she have in all? Write and solve an equation to represent the problem. State the answer to the problem.

182. ## math

There are 28 cars registered for a race. The top 5 finishers will be awarded trophies. 1. how many different ways can the trophies be awarded? 2. Now, the trophies are labeled "first, second,etc How many different ways can the trophies be awarded?

183. ## Math

What is e/2=3

184. ## Statistics

Suppose that in the city in which the survey is conducted, 50% of adults are married, 15% are single, 25% are divorced, and 10% are widowed. a. Assign probabilities to each simple event in the sample space. b. Which approach did you use in part (a)? Find

185. ## Algebra

How many solutions does this system of equations have? X-2y=6 and 3x-6y=18

186. ## mathematics

A patient gets tested for a disease. The test is 90% reliable (that is P(testing positive│have disease)=.9 . 2% of the population has this disease. The test gives a false positive 5% of the time (that is P(testing positive│NOT diseased)=.05). What is

187. ## science help PLS

An astronomer see a star that is very far away but still very bright. What can she conclude about the star? The star must be very large. The star must be very small. The star must be moving away from Earth. The star must be moving closer to Earth.

188. ## stats

Jim is a randomly chosen member of a large population in which 6% are heroin users. Joe tests positive for heroin in a drug test that correctly identifies users 98% of the time and correctly identifies nonusers 95% of the time. What is the probability that

189. ## math

There are two jars, A and B. Jar A contains 7 red and 2 blue marbles, while jar B contains 5 red and 4 blue marbles. You roll a fair die.If you get a 2 or a 3, you pick a random marble from jar A and put it in jar B. You then pick a random marble from jar

190. ## Language Arts

When You Paraphrase A Line Of Poetry, What Do You Do a.You turn it into a question b.You put it in your own words c.You add humor to it d.You copy it down exactly Choose the best paraphrase of these lines from the limerick Said the fly, let us free let us

191. ## Division

How can you use estimation to find the quotient of 57 divided by 3?

192. ## Math

Zefram analyzed a linear relationship, found that the slope-intercept equation was y  3.5x 16 , and made a prediction for the value of y for a given value of x. He realized that he made an error calculating the y-intercept and that it was actually

193. ## math help

Louis says that if the differences between the values of x are constant between all the points on a graph, then the relationship is linear. Do you agree? Explain.

194. ## language arts

What would i say to paraphrase each line for the poem "If" by Diondra Jorda?

195. ## Math

Use three methods to express each problem’s ratio. Simplify all fractions. 1. Anna has 12 black rabbits and 4 brown. What is the ratio of black rabbits to brown rabbits?

196. ## Gen Chem

A mixture of NaCl and sucrose (C12H22O11) of combined mass 10.2 g is dissolved in enough water to make up a 250 mL solution. The osmotic pressure of the solution is 8.29 atm at 23°C. Calculate the mass percent of NaCl in the mixture.

197. ## Math

Tom has taken 3 tests with an average of 88%. However, Tom really wants an A. To get an A, he has to have an average score of 93%. What score does he need on the final test to get an A? I just don't get it. Can someone walk me through the steps to get to

198. ## Math

There are 5 chairs in a row, and three people. In how many ways c an you place the people on the chairs? (each person must occupy exactly one chair, so that two chairs will remain free).

199. ## Calculus

Two hallways, one 8 feet wide and the other 6 feet wide, meet at right angles. Determine the length of the longest ladder that can be carried horizontally from one hallway into the other.

200. ## chemistry

Let I know the equation with symbol of 'iron2oxide from iron fillings'

201. ## Algebra

The mean on a Advanced Algebra test was 78 with a standard deviation of 8. If the test scores are normal distributed, find the interval about the mean that contains 99.7% of the scores. Use the empirical rule.

202. ## Math

write 3 cos (ωt + 2) + 4 sin (ωt + 1) as A cos (ωt + φ). Find A = ? φ= ?

203. ## history

what is the name and year of the treaty that gave french a legal right to hispanoila ?

204. ## geometry

When the vertex of an angle is inside the cricle, you must _____ the arcs and then take _____.

205. ## Chemistry

1. How could a chemistry student change NaOH(s) to NaOH(aq)? s= solid aq= aqueous 2.) How could a chemistry student change NaOH(s) to NaOH(l) s= solid l= liquid

206. ## Math

Combine like terms(same variable to the same power) Simplify: 3a^3b+4a^2b^2-7a^3b+2ab-5a^2b^2+10a^3b

207. ## Physics (Electricity)

A meter has a resistance of 75 ohms and gives full-scale deflection when it passes a current of 1.0 mA. How would you adapt the meter to read a) Currents up to 1A b) voltages up to: 5V c) Voltages up to: 100V

208. ## Physics help

1. The fundamental force that: (4 marks) ____ 1. causes hair to stand on end after being rubbed by a balloon a) strong nuclear ____ 2. causes protons to remain in the nucleus despite repulsive forces b) weak nuclear ____ 3. controls the planets' orbit

209. ## Math

What is the answer to,"if the area of a rectangle is 24 and the perimeter is 28, what are the length and width?"

210. ## Algebra

2. What is the value of x in the solution to the system of equations below? 15x – 12y = 13 30x + 9y = 4

211. ## Math

Find the quotient. 6 2/7 divided by 2 3/4. 2 2/7. (MY ANSWER) 17 2/7. 2 6/11. 7/16.

213. ## Math

Can I subtracted from 2.3 from 20and got 17.7

214. ## Physics

A high voltage unit has an internal resistance of 50 mega ohms. On open circuit, the potential difference across its output is 3000 V. When a resistor R is connected across its output, the potential difference at the output falls to 1000 V. Calculate the

215. ## math

I don't understand how to write 3 groups of w as an algebraic expression. Can anyone help me?

216. ## Physics

A digital voltmeter with high internal resistance gives a maximum reading of 2.0 V. It is used to determine current by measuring the potential difference across a standard resistor S through which current has passed. What should the resistance of S be to

217. ## Math

Daniel is having a poster printed from a photo that is 3inches wide and 5inches long if the poster is 24 inches long how wide should the poster be if it is proportional to the photo

218. ## genetics

a man with blue eye married a girl with broun eye and the mother of the girl has blue eye. What is the probability that their children will have blue eye

219. ## farm disease

illustrating with two named disease, describe their clinical signs and give confirmative diagnoses of each using pathognomic signs

220. ## Chemistry

suppose 4.52 g H2o and 20.09 g So3 are produced. How many grams of H2So4 decompose? Wouldn't the answer be 24.61?

221. ## Algebra ASAP!!

7. The table shows the functions used to determine the number of points earned every month by regular and elite members of a dining club who spend d dollars that month at participating restaurants. Which statement describes the difference in these

222. ## math

If the cost price (C.P.) of 6 articles is equal to the selling price (S.P.) of 4 articles find the gain percent.

223. ## farm disease

explain the mechanisms as test involved in vaccinating birds against a named disease with special infacises on immunity build up

224. ## math

For the period 1995-2002, the total personal expenditures (in billions of dollars) in the United States for food, f(x), and for housing, h(x), can be described by the equations shown below, where x is the number of years past 1995.† f(x) = 40.74x +

230. ## chem

use atomic theory to explain why chemical reactions obey the law of conservation of mass

231. ## math

Can 15.32 be an integer? THANKS!!!

232. ## Math

Find the number that completes the equation. blank = 2 ----- --- 4 20 1/10. 2/5. 2. 4. Please explain how I could solve this. :)

233. ## math

Perimeter of 26.length is 6 feet. What is the width

234. ## Algebra 1

-2, -12, -72, -432 find the 8th term 0.2, 1.6, 12.8, 102.4 find the 6th term 24, 12, 6, 3 find the 7th term

235. ## Physics

A river flows due east at 1.54 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 11.2 m/s due north relative to the water. What is the velocity of the boat relative to shore?

236. ## math

Braden has 10 red model cars, Which are 2/5 of the total number of cars in his collection. How many cars does Braden have in his collection? 4. (MY ANSWER) 10. 25. 50.

237. ## Socil studies/sicence ?

sorry I dint really know how to lable this question but can somebody tell me some positive and negative effect of collecting gold?

238. ## physics

Two rings of radius 3 cm are 23 cm apart and concentric with a common horizontal x-axis. What is the magnitude of the electric field midway between the rings if both rings carry a charge of +35 nC?

239. ## Math

I have the following chart that I am supposed to find the percent increase in one step. The directions specifically say not to use a two step method. 10.5 12.5 14.9 17.7 21.1 25.1 So I divide 12.5 by 10.5, 14.9 by 12.5, etc. When I do this (and round) I

240. ## computer programing

okay I need a little help here on next program this what it say for first one which I have done. Create a counting program that counts backward from 100 to 1 in increments of 10. #include < stdio.h > int main () { Int i; while ( I > = 1 ) { printf ( “ %

241. ## chemistry

A 7.30-L container holds a mixture of two gases at 45 °C. The partial pressures of gas A and gas B, respectively, are 0.410 atm and 0.620 atm. If 0.150 mol of a third gas is added with no change in volume or temperature, what will the total pressure

242. ## Math

How do you find the slope of -5x+3y-8=0

243. ## science

A researcher wants to develop a new pharmaceutical compound to treat pain. Which of the following strategies will likely be the most effective process? A. Test extracts from newly discovered plants for pain-killing substances. B. Read anthropological

244. ## HISTORY

1. Explain from the Gilded Age that supports the "the farmers were up in arms." 2. What is one change in the South between 1877 and 1900 that reflected the policies of the New South agenda?

245. ## algebra

A clock has a minute hand that is 14 feet long and an hour hand that is 9 feet long. What is the average speed (in mph) of the tip of the minute hand no idea how to solve this... please help :)

246. ## Math

find the limit as x->3 of (1-sqrt(x-2))/(x-3) I'm not sure how to get the answer, I know it's -1/2, but I don'y know how to get that.

247. ## Physics

What is the force of attraction between you and your friend steve if you are 55 kg,the mass of steve is 60 kg, and you are sitting 2.4 meters apart?

248. ## Physics

Roxanne is making a strawberry milkshake in her blender. A tiny, 0.005-kg strawberry is rapidly spun around the inside of the container with a speed of 14.0 m/s, held by a centripetal force of 10.0 Newtons. What is the radius of the blender at this

249. ## maths

A shelf is 6 m wide. how many boxes of width 20 cm can be fit in this shelf

250. ## algebra/precal

If a minute hand traveled at an average of 1 mph at the tip... how long in get would the minute hand have to be?

251. ## Math

What is 4 1/3 as a inproper fraction

252. ## math

three taps fills water in a tank.one fills it in 3hrs another in 4hrs and the third in 6hrs.if all run together how soon will they fill the tank?

253. ## calc

If you fire a paper clip straight up into the air with a rubber band, its height (in feet) above your hand time t seconds is given by: h = 64t - 16t^2. 1) How long does it take the paper clip to reach its maximum height? 2) If your hand is 6 feet above the

254. ## math

A pair of dice is rolled.What is the probability that the sum of the pips is either an even number on a multiple of 3? total number of space is 36.

Marilyn was supposed to pay $1410 to Bernice on March 1. Some time later Marilyn paid Bernice an equivalent payment of$1530.22, allowing for a time value of money of 4.8% compounded monthly.

256. ## math

nathan is shipping vases for his pottery studio. Each vase weighs p pounds. Each crate weighs 5 pounds and holds 10 vases .a shipment consists of 15 crates. write an expression for the weight of a crate holding 40 vases

257. ## Statistics

A population =100 and sd=25. A sample (n=150) has X=102. Using 2 tails of the sampling distribution and the .05 criterion. What is the critical value? Is the sample in the region of rejection? What does this indicate about the likelihood of this sample

258. ## Math

Paul's electric bill was three dollars more than one-half his gas bill. If electric bill was ninety-two dollars, what was gas bill

259. ## math

whats the pound for 1/4

260. ## calculus

A flea moves along the line y = -3 according to the equation: x = t^3 - 9t^2 + 24t where x is its x coordinate at time t secs. Determine: 1) the position, velocity, and acceleration of the flea at time 3 secs. Answer: position - 3^3 - 9(3)^2 + 24(3) = 18

261. ## Physics

Suppose at one point along the Nile River a ferryboat must travel straight across a 1.29-mile stretch from west to east. At this location, the river flows from south to north with a speed of 2.58 m/s. The ferryboat has a motor that can move the boat

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# continued fraction to rational polynomial in maple?

In maple is there a way to convert a continued fraction into a rational polynomial? I'm using the minimax function and for a particular function I want to approximate it returns a continued fraction instead of a rational polynomial for which I want in this form and not in continued fraction form.

-
Relevant: this and this. –  user2468 Jul 30 '12 at 23:08
Use > normal(...); –  Robert Israel Jul 31 '12 at 0:57
thanks guys, yep normal is the function I need but I also noticed after using this that I wasn't using enough terms in my function I was using for minimax. –  snk_kid Aug 1 '12 at 13:15


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# Approximate IIR filter with FIR filter with energy restrictions

Hi I was presented with this problem I would like some guidance to solve:

I am given the following DT channel model: $$C(z) = 1-0.3z^{-1}$$

I am first asked to design an IIR linear zero forcing equalizer.

I am then asked to approximate the IIR filter obtained above with an FIR filter, where 80% of the energy of the IIR filter is captured in the FIR filter.

My initial thought was to transform the channel from the z domain to: $$y[n] = c[n] + 0.3c[n-1] + z[n]$$ - where z is gaussian distributed noise

Apply a zero forcing 3 tap filter to this and obtain the 3 coefficients.

Once I obtain these coefficients however I am unsure to proceed. Do I then simply take the convolution to find the output of this filter, is that considered the IIR zero forcing equalizer?

Also once this is done how do I ensure 80% of the energy of the IIR filter is then captured in the FIR filter?

Any help would be greatly appreciated

1. Remember that a ZF equalizer just inverts the channel, so if $$D(z)$$ is the equalizer's transfer function, what must be the result of the product $$C(z)D(z)=?$$. From this equation you obtain $$D(z)$$, which is IIR.
2. Let the coefficients of $$D(z)$$ be $$d[n]$$, i.e., $$D(z)=\sum_{n=0}^{\infty}d[n]z^{-n}$$ The energy of the filter is $$E_d=\sum_{n=0}^{\infty}\big|d[n]\big|^2$$ The FIR filter you're looking for just uses the first $$N$$ coefficients $$d[n]$$. If $$N$$ is large enough, the approximation will be sufficiently good. According to the requirement, you need to choose a number $$N$$ such that $$\sum_{n=0}^{N-1}\big|d[n]\big|^2=0.8\sum_{n=0}^{\infty}\big|d[n]\big|^2$$


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# Collinear Proof in Circle Geometry

(a) $\ \$ Show that $\angle DSR = \angle DAR$. The quadrilateral $DRAS$ is cyclic, since $\angle DRA + \angle DSA = \pi (180^{\circ})$. Therefore $\angle DSR = \angle DAR$ (angles in the same segment of circle $DRAS$, both standing on same chord […]


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.

# INDEX

## Maxwell’s equations

Maxwell’s equations describe how electric and magnetic fields are generated by chargescurrents, and changes of the fields. An important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in a vacuum.

A introduction part 1 of electromagnetism is made here:

As Flux density = B =  ϕ/A ( Wbm-2 )

so Flux = field strength per unit area ϕ= BA (unit Wb)

B (unit tesla)

Flux linkage   ( =BAn ) in a coil with N coils

or
where  s the voltage across the device
Maxwell came up with the right hand rule (or cork screw rule) to find out how magnetic field goes around a piece of wire with a current in it.. Khan academy presents this law here:

Key notations:
is a surface integral over the surface Σ,
• Symbols in bold represent vector quantities, and symbols in italics represent scalar quantities, unless otherwise indicated.
•  the magnetic fieldB, a pseudovector field, each generally having a time and location dependence.

The sources are:

• the total electric charge density (total charge per unit volume), ρ, and
• the total electric current density (total current per unit area), J.

The universal constants appearing in the equations (the first two ones explicitly only in the SI units formulation) are:

In the differential equations,

• the nabla symbol, denotes the three-dimensional gradient operator, del,
• the ∇⋅ symbol (pronounced “del dot”) denotes the divergence operator,
• the ∇× symbol (pronounced “del cross”) denotes the curl operator.

## The schrödinger equation

Calculates the probability for a particle (e.g. electron) to be in a certain position. Is share by Brian Green in this World Science Festival video.

Unnikrishnan Menon,  ecplains:

It is all about finding the different energies that a particle can have.

We’re looking at things that can have more than one answer! You might have studied in high school that atoms have energy levels. The Schrödinger’s Wave Equation lets us calculate what these energies are.

It is defined as:

It turns out, talking about velocity isn’t very useful. So, we change this equation to make it depend on momentum p

We can think of particles as waves, atleast at tiny scales where we need to use Quantum Mechanics!

To help us move between these 2 ways of thinking about matter, we can use De Broglie’s Equation

where  is the wavelength is the Planck constant is the momentum is the rest mass,   is the velocity and  is the speed of light in a vacuum.”

This theory set the basis of wave mechanics. It was supported by Einstein, confirmed by the electron diffraction experiments of G P Thomson and Davisson and Germer, and generalized by the work of Schrödinger. ( Wiki )

Now we don’t see matter around us in our everyday lives to be behaving like waves because Plank’s Constant h is absolutely tiny! ( h=6.62×10−34m2Kg/s )

But hold on! De Broglie’s Equation is useful when we are dealing with minute particles like protons and electrons 🙂

We also have something called ℏ
It’s is related to the Plank’s Constant as

Now, it is going to be useful to talk about  and the wave number instead of h and λ

Where

is the wave number. We did to avoid having  running around in our equations. It just turns out to be easier to work with!
We also know that k is change depending upon the energy. Since k depends only on λ , the factors that can affect λ can also affect k . In this case, it is Energy!

We use Wave Functions to encode information about waves. These are just equations with a few special properties. They look something like this…

This is just another way to write sines and cosines. (Waves are just combinations of sines and cosines!)

Here’s the reason for writing this in this weird format…

This type of problem is called an Eigen Value Problem.

is called an Eigen Function.

is an Operator.

Eigen Function of operators are functions which return themselves and a new Eigen Value after the operator is used on them.

As you might have guessed by now, on differentiating this we get the same thing back multiplied by some constants (differential of the argument)

Let’s do this again!

Here, −k2 is the new Eigen Value returned (that’s the extra bit)

Now let’s make a Kinetic Energy Operator (we want the energy EE and we are assuming a low potential)…

We know there are gonna be a bunch of answers so we are going to use our Wave Function to generate those answers and we also have a way of writing k2

So on putting it all together we get…

Notice it is partial derivative instead of the usual one. This just means that there is more than one variable in the function we treat as a constant when differentiating.

What we just did is valid for a one dimensional particle that is time independent and is not in a potential.

Let’s generalize this equation a little…

For a photon,

We’re now gonna assume it to be true for particles. It turns out to be a good assumption…

We know that there is gonna be a set of energies so we want to know the Eigen value equation.

This time we’ll find an EE by generating an ωω

Let’s look at the wave function to do that…

As you might have guessed it by now, we’re gonna take the derivative with respect to time to pull it out front!

o account for the minus sign(-) we will simply use -i.i=1

And that’s same as the equation we had before…

Please note that this equation is only for one spatial dimension! But we need to consider all 3 dimensions. The three dimensions in Cartesian Coordinate System are orthogonal to each other. That means, they will not interfere with each other.

Each of these contributes to the total energy.

So, in three dimensions, the time dependent wave equation becomes…

And the time independent version becomes…

This can more simplified as…

Where  is what we call Nabla.

To include Potential(V) we modify it a bit further like this…

where Ĥ  is what we call Hamiltonian.

is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system (this addition is the total energy of the system in most of the cases under analysis ( Wiki )

So, the full Schrödinger’s Wave Equation becomes…

### general relativity field equation

First part copied from my page at www.kinberg.net/wordpress/stellan/einsteins-field-equations-of-general-relativity/

As is correctly explained in Wikipedia

I found this Youtube that explains the general relativity field equation. I like it because of the good graphic representations.

As with the tensor youtube made by Dan Fleisch, this made by Eugene Khutoryansky show graphically how a tensor change depending on curvature of space. Very well done video.

## A agnostic pluralist seeker

Insert math as
$${}$$


text:
# Chapter 12 - Data Analysis and Probability - 12-3 Measures of Central Tendency and Dispersion - Lesson Check - Page 730: 2

Mean: 8.76 Median: 8.8 Mode: Does not exist The mean is the best measure of the data

#### Work Step by Step

To find the mean, we add up all of the values and divide by the total number of values. Mean: $\frac{8.2+9.3+8.5+8.8+9.0}{5} = 8.76$ To find the median, we order up all of the values from least to greatest and find the middle number. If there are an even total number of terms, then we take the average of the two terms that are closest to the middle. Median: $8.2, 8.5, 8.8, 9.0, 9.3 \rightarrow 8.8$ To find the mode, we determine the number that shows up the most. If no number shows up the most, then the mode does not exist. Mode: Does not exist There are no outliers in this data, so the mean is the best measure to describe the data.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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# Distances

A distance calculator is a great calculator that calculates one point of distance to another point. And the distance always represented in the numbers as you know. It can also measure your distance as in longitudes and latitude.

#### formula

$$d = \sqrt{((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2))}.$$

#### Input Data

$$Find\ the\ difference\ between\ coordinates:$$ $$(x2-x1) = (0.1 - 0.2) = -0.1$$ $$(y2-y1) = (0.4 - 0.5) = -0.09999999999999998$$ $$(z2-z1) = (0.5 - 0.3) = 0.2$$ $$Square\ the\ results\ and\ sum\ them\ up:$$ $$(-0.1)^2 + (-0.09999999999999998)^2 + (0.2)^2$$ $$= 0.010000000000000002 + 0.009999999999999995 + 0.04000000000000001$$ $$= 0.060000000000000005$$ $$Now\ find\ the\ square\ root\ and\ that's\ your\ result:$$ $$Exact\ solution:\ √0.060000000000000005$$ $$= √0.060000000000000005$$ $$Approximate\ solution: 0.2449$$

## How to use this Distance tool by taskvio.com?

A distance calculator is a great calculator that calculates one point of distance to another point. And the distance always represented in the numbers as you know. It can also measure your distance as in longitudes and latitude. This tool is really nice and this tool is really great that will help you a lot. This tool is much faster that will help you solve your problem really quickly.

This tool will help you a lot and anywhere you go this tool will help you from there. Because this tool is an online web-based tool that can be accessed from anywhere. It can also access from any device. This tool also works on smartphone properly and this thing makes this tool really great. Like even if you don't have a laptop sometimes then still you can use it with the help of your phone.

This tool can be really a helpful tool for so many students and it can be really helpful for any individual too who wants to use this tool or someone who needs this kind of tool. They can use this tool even if they won't know about this subject. And even if they want to learn about it then they can read our small article which is we have written below with the help of experts.

## What is Distance?

Before we get into how to ascertain distances, we ought to presumably explain what a distance is. The most widely recognized importance is the/1D space between two focuses. This definition is one approach to state what practically we all consider distance naturally, however, it isn't the lone way we could discuss distance. You will find in the accompanying segments how the idea of distance can be reached out past length, in more than one sense that is the advancement behind Einstein's hypothesis of relativity.

In the event that we stay with the mathematical meaning of distance, we actually need to characterize what sort of room we are working in. By and large, you're likely discussing three measurements or less, since that is everything we can envision without our minds detonating. For this mini-computer, we center just around the 2D distance (with the 1D included as an extraordinary case). In the event that you are searching for the 3D distance between 2 focuses we urge you to utilize our 3D distance adding machine made explicitly for that reason.

To discover the distance between two focuses, the principal thing you need are two focuses, clearly. These focuses are portrayed by their directions in space. For each point in 2D space, we need two organizes that are one of a kind to that point. In the event that you wish to discover the distance between two focuses in 1D space, you can at present utilize this mini-computer by essentially setting one of the directions to be the equivalent for the two focuses. Since this is an extraordinary case, from now into the foreseeable future we will speak just about distance in two measurements.

## Apparatus to gauge distance

The following stage, in the event that you need to be numerical, exact, and exact, is to characterize the sort of room you're working in. No, stand by, don't flee! It is simpler than you might suspect. On the off chance that you don't have a clue what space you're working in or on the off chance that you didn't know there is more than one sort of room, you're in all probability working in Euclidean space. Since this is the "default" space in which we do pretty much every mathematical activity, and it's the one we have set for the number cruncher to work on. We should jump somewhat more profound into Euclidean space, what is it, what properties does it have, and for what reason is it so significant?

### How to use this Distance tool by taskvio.com?

To use this tool you need not worry about anything you just have to follow some simple steps and then you are good to go. This tool has a very simple interface that anybody can understand it really well and this will be a great option for so many students.

Now as you can see in this tool you have a box where you are going to input the value in it.

So enter the value in here and crosscheck it.

After you will enter the right value in the text box you will simply have to click on the calculate button then you will get your answer really quick.

That’s all you have to do and you can also bookmark this tool so that you can use it later.

We also have lot of tool in our website that you can find it on the home page of taskvio.com. And in every category, we have built so many tools to use for every requirement for them as per their use. So use them and make your life easy.

### Q. What Is Distance?

A. Before We Get Into How To Ascertain Distances, We Ought To Presumably Explain What A Distance Is. The Most Widely Recognized Importance Is The/1D Space Between Two Focuses.


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# 13. LO.1 & LO.2 (Relevant costs; writing) Because of a monumental error committed by its...

1 answer below »

13.    LO.1 & LO.2 (Relevant costs; writing) Because of a monumental error committed by its purchasing department, Corner Grocery ordered 5,000 heads of lettuce rather than the 1,000 that should have been ordered. The company paid $0.65 per head for the lettuce. Although management is conﬁdent that it can sell 2,000 units through regular sales, the market is not large enough to absorb the other 3,000 heads. Management has identiﬁed two ways to dispose of the excess heads of lettuce. First, a wholesaler has oﬀered to purchase them for$0.25 each. Second, a restaurant chain has oﬀered to purchase the lettuce if Corner Grocery will agree to convert it into packaged lettuce for salads. This option would require Corner Grocery to incur $2,500 for conversion, and the heads of lettuce could then be sold for the equivalent of$1.05 each.

a.     Which costs are sunk in this decision?

b.    Actually, Corner Grocery can consider three alternatives in this decision. Describe the alternative that is not mentioned in the problem.

c.     What are the relevant costs of each decision alternative, and what should the company do?

## 1 Approved Answer

 Answer a Sunk Cost Sunk cost means a cost which already incurred and can not be recovered. In the given problem sunk cost will be Unit can not be sold in direct...

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# John Machin's Formula

1. Dec 28, 2004

I'm a bit puzzled by this problem, which involves the John Machin's formula. Here it goes:

Show that for $$xy \neq -1$$,

$$\arctan x - \arctan y = \arctan \frac{x-y}{1+xy}$$

ïf the left side lies between $$-\pi /2$$ and $$\pi /2$$.

By the way, John Machin's formula is:

$$4 \arctan \frac{1}{5} - \arctan \frac{1}{239} = \arctan \frac{\pi}{4}$$

He used this to find $$\pi$$ correct to 100 decimal places.

Anyhow, here is what I've done so far:

If

$$\arctan x = \sum _{n=0} ^{\infty} \left( -1 \right) ^n \frac{x^{2n+1}}{2n+1}$$

$$\arctan y = \sum _{n=0} ^{\infty} \left( -1 \right) ^n \frac{y^{2n+1}}{2n+1}$$

$$\arctan \frac{x-y}{1+xy} = \sum _{n=0} ^{\infty} \left( -1 \right) ^n \frac{\left( \frac{x-y}{1+xy} \right)^{2n+1}}{2n+1}$$

Then

$$\sum _{n=0} ^{\infty} \left( -1 \right) ^n \frac{\left( x^{2n+1} - y^{2n+1}\right)}{2n+1} = \sum _{n=0} ^{\infty} \left( -1 \right) ^n \frac{\left( \frac{x-y}{1+xy} \right)^{2n+1}}{2n+1}$$

Therefore

$$x^{2n+1} - y^{2n+1} = \left( \frac{x-y}{1+xy} \right)^{2n+1}$$

I'm not sure I am on the right path. Maybe, I simply need to pick a couple of values to demonstrate that the given relationship is true, but it feels like it might not be enough. In other words, "show" up there looks a bit ambiguous. Any help is highly appreciated.

Thanks

2. Dec 28, 2004

### dextercioby

My friend,why use calculus to get nowhere,when u can use (circular) trigonometry to prove in an elegant way?????????
Take "tan"out both sides of your identity and use what i'll write below:
$$\tan(a-b)=:\frac{\sin(a-b)}{\cos(a-b)}=\frac{\sin a\cos b-\sin b\cos a}{\cos a\cos b+\sin a\sin b}$$

Simplify the last fraction through the product of 'cosines' to find the celebrated formula
$$\tan(a-b)=\frac{\tan a-\tan b}{1+\tan a\tan b}$$
Substitute in the last identity:
$$a\rightarrow \arctan x;b\rightarrow \arctan y$$
,make use of the fact that "tan",on the interval give in the problem is a uniform function and get exactly the formula u would get if taking "tan" from the identity u need to prove.

Daniel.

PS.Trigonometry is beauty...

3. Dec 29, 2004

Let me see if I understand it...

$$\arctan x - \arctan y = \arctan \frac{x-y}{1+xy} \qquad (1)$$

$$x - y = \frac{x-y}{1+xy} \qquad (2)$$

$$\tan \left( x - y \right) = \tan \left( \frac{x-y}{1+xy} \right) \qquad (3)$$

$$\tan \left( x - y \right) = \frac{\sin \left( x - y \right)}{\cos \left( x - y \right)} \qquad (4)$$

$$\tan \left( x - y \right) = \frac{\sin x \cos y - \cos x \sin y}{\cos x \cos y + \sin x \sin y} \qquad (5)$$

$$\tan \left( x - y \right) = \left( \frac{\frac{1}{\cos x \cos y}}{\frac{1}{\cos x \cos y}} \right) \frac{\sin x \cos y - \cos x \sin y}{\cos x \cos y + \sin x \sin y} \qquad (6)$$

$$\tan \left( x - y \right) = \frac{\tan x - \tan y}{1 + \tan x \tan y} \qquad (7)$$

$$\arctan x - \arctan y = \arctan \frac{x-y}{1+xy} \qquad (8)$$

4. Dec 29, 2004

### dextercioby

U didn't. :tongue2: I can't explain in another way the bunch of c*** at numbers (2) and (3)...

Formulas (4) pp.(7) give a proof for the trigonometrical identity that can be used to prove your identity.I stated that proof just to let u know i didn't invent it nor rediscovered it hundreds of years later.

I said to apply tangent on both sides of your identity:
$$\tan(\arctan x-\arctan y) =\tan[\arctan(\frac{x-y}{1+xy})]$$

`Work the left hand side using the formula i've given proof:
$$\tan(\arctan x-\arctan y) =\frac{\tan(\arctan x)-\tan(\arctan y)}{1+\tan(\arctan x)\tan(\arctan y)}=\frac{x-y}{1+xy}$$ (1)

Work the right hand side:
$$\tan[\arctan(\frac{x-y}{1+xy})] =\frac{x-y}{1+xy}$$ (2)

Interpretation of the relations (1) and (2) is that you have shown that:
$$\tan A=C (1') \tan B=C (2')$$(3)
From (3) it follows immediately
$$\tan A=\tan B$$ (4)
From (4) and from tha fact that on the interval $(-\frac{\pi}{2},\frac{\pi}{2})$ the function "tan" is a uniform/surjective function,u get that
$$A=B$$ (5)
,which is nothing but your identity in symbolic form.

Daniel.

5. Dec 29, 2004


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### Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

### Hypotenuse Lattice Points

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

### Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

# Integer and Integer

##### Age 14 to 16 Short Challenge Level:

For how many values of $n$ are both $n$ and $\frac{n+3}{n-1}$ integers?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.


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# Tag Info

22

The main plot below shows the potential energy of a mass in the Earth-Moon system under the unrealistic assumption that the system is not rotating. i.e. This mirrors (at present) all but one of the 4 answers given, in assuming that this point is defined where the gravitational force on a mass due to the Earth and the Moon are equal and opposite (i.e. at the ...

16

Set the forces on the test particle from the Earth and Moon equal: $$F_E=F_M$$ $$G\frac{M_EM_{\text{ test particle}}}{R_E^2}=G\frac{M_MM_{\text{ test particle}}}{R_M^2}$$ The $G$s and $M_{\text{ test particle}}$s cancel, leaving you with $$\frac{M_E}{R_E^2}=\frac{M_M}{R_M^2}$$ but you know that $R_M$, the distance between the test particle and the Moon, is ...

11

Here is how I interpret what happened: You used Excel to compute the coefficients of the Gaussian that best describe the data: mean $\mu$, standard deviation $\sigma$, and magnitude $A$ for a curve $$Y=Ae^{-(x-\mu)^2/2\sigma^2}$$ Then you evaluated that function at a number of X values. Since the X values are not symmetrical about the calculated mean, you ...

9

At Lagrange point L1. Specifically for Earth-Moon L1, these calculations show 326054 km.

9

Earth is about 100x more massive than the moon, and since $F \propto M / r^2$, the distance from Earth to the astronaut would have to be about $\sqrt{100}$ = 10x further than from the moon to the astronaut. Therefore, the astronaut falls "up" about 90% of the way to the moon. [The earlier answers go a lot more into detail (and are more technically ...

4

Hints: In mathematics, a distribution is usually only defined wrt. smooth testfunctions. However the function ${\bf q}\mapsto({\bf q}\cdot{\bf p})^2/q^2$ is not continuous at the origin ${\bf q}={\bf 0}$. Nevertheless, we can e.g. try to evaluate the triple integral using the following representation of the 3D Dirac delta distribution $$\tag{1} ... 4 Indeed the answer is not zero but -4\pi\delta(r) (Dirac delta function). The formula of divergence can be found in any standard textbook on mathematical physics, for example chapter 2 of Mathematical methods for physicists by Arfken. But since this function is singular at r=0 we must be careful. At any other points is easy to calculate it. It is ... 3 To calculate this by yourself, you need to know that gravity force exerted on an object (for exapmle You) is equal to F=GMm/r^2, where G is gravity constant, M is the mass of the big object (M_m for moon, M_e for earth), m is the mass of small object. r is the distance from the center of the mass. Now you need to know masses of earth and moon ... 3 Just use an equation derogating from the two forces which pull the objects (universal gravitation)to get the equilibrium point, something like (already simplifyed): M/d^2 = m/(384000000 - d)^2 Where M is the mass of earth, m the mass of moon and d the distance from earth. As d gets bigger than this value, you start falling into the moon I get a value of ... 3 The distance I got was 346 084km. Here are the maths I used: (E_m) Earth mass = 5.9736\times10^{24} kg (M_m) Moon mass = 7.3477\times10^{22} kg (D_{em}) average Earth-Moon distance = 384 467km (G) gravitational constant = 6.67384\times10^{-11} (W) my weight = 85kg (D_{fe}) distance from earth = ? The attraction force between two objects ... 3 This question is about Guassian wave-packet propagation and the corresponding Green's function in ordinary quantum mechanics. Assuming \hbar=m=1 for simplicity, consider the solution (with its initial condition) to the following Schrodinger equation:$$i\partial_t G=-\partial^2_x G \\ G(t=0,x)=\delta(x) $$Now assume the Fourier ansatz for \psi: ... 3 Note that Fitzpatrick states towards the beginning, The following solution method exploits the fact that the Coriolis force is much smaller in magnitude that the force of gravity: hence, \Omega can be treated as a small parameter Generally, when statements like that are made, powers (greater than 1) of the term in question are considered to be zero: ... 3 Ahh, Richard Fitzpatrick. Great guy. Ok, If you start with the second set of expressions, use the appropriate double-angle-formula and then assume the "angle" 2\Omega \sin\lambda t is small (note that the t is not within the sin function!), you get the first expressions, e.g.$$\cos(\theta+\phi) = \cos\theta\cos\phi - \sin\theta\sin\phi,$$and then ... 2 Consider the following proof by contradiction: Suppose you find a state with E < -V_0, then its kinetic energy becomes negative at every point x (classically the velocity is imaginary at every point), which means the whole wavefunction (at all x) is an evanescent (exponentially decaying) wave, but such a solution is not a physically stable solution ... 2 It should be in joules. The term \ln \frac{V_2}{V_1} is unitless, because the units on the top and bottom of the fraction cancel. Pressure, in pascals, is defined as Newtons per square meter. You've already put the volume into cubic meters, and the cancellation goes$$\text{meters}^3 \times \frac{\text{Newtons}}{\text{meters}^2}=\text{Newtons} \times ...

2

Every time, when you deal with differential equations, the first step is to put it into dimensionless form. There are more reasons for that. First, "small" and "large" has no meaning in dimensional forms, since you can always change the system of units. Second, nature knows no units. Now, when there is no exact solution (this is often the case), you can ...

2

If the block is resting on a frictionless surface, it won't fall over. It'll set in horizontal motion even with little force. To create torque, one edge of the bottom surface of the block needs to be fixed with high static friction and there must be a non-zero angle between the force and the line connecting force application point and fixed point (you can ...

2

You're right that in the context of radioactivity, antineutrinos are pretty much only released when a neutron turns into a proton, ${}_0^1n\to {}_1^1p+{}_{-1}^{\;0}e+\bar{\nu}$. They can also be consumed when a proton turns into a neutron and a positron, ${}_1^1p + \bar{\nu}\to {}_0^1n + {}_{1}^{0}e$. There are some other processes that involve ...

2

$$δ^3(q⃗ )=\frac{δ(q)δ(\theta)}{2\pi q^2\sin(\theta)}$$ is wrong. The delta function is spherically symmetric, and thus has no θ dependence. Simply use: $$d^3(q⃗ )=\frac{δ(q)}{2\pi q^2}$$ instead. Use the Jacobian when you switch coordinate systems (from Cartesian to spherical) ($r^2 \sin(\theta)$), and you should get the result.

1

A gaussian fit is symmetrical by definition, because it is a gaussian. Your orange fit doesnt look like a gaussian, it is not even smooth. I do no think excel had a gaussian fit function (but I dont use excell so cannot tell for sure. You can use other software such as matlab, or likely free ones on the web. Or, just use that data to calculate the parameters ...

1

This proof from Griffiths book introduction to electrodynamics Consider the vector function $$\vec{a}=\frac{1}{r^2}\hat{r}$$ At every location $\vec{a}$ is directed radially outward ; if ever there was a function that ought to have a large positive divergence, this is it. and yet, when you actually calculate the divergence, you will get ...

1

Start with ${b \over g }=m$ and rearrange this equation to get $b$ in terms of $g$ Then you can substitute your expression for $b$ into $g+b=3m$ and you should get the answer.... does this help?

1

Do some substitution: Re-arrange $$g+b=3m$$ to become $$b=3m-g$$ With substitution, $$\frac{b}{g}=10$$ becomes $$\frac{3m-g}{g}=10$$ Can you go from here?

1

Let the operator $q$ be defined by $f \mapsto \exp\left(i\,\frac{l}{\hbar}\,x\right)\,f$ then you should be able to prove to yourself the identity: $$p\,q\,f = q\,(p+l)\,f\tag{1}$$ for any vector (i.e. function) f. (This is just a variation on finding an integrating factor to transform $\mathrm{d}_x\,f + i\frac{l}{\hbar} f$ into the derivative of a product ...

1

Your answer seems to be good. I solved it in the same way. However there are two points in which i have no clarity. The first thing i do not have clear is the conservation of energy in the problem. We use the energy conservation, but how do we guarantee that the normal force is conservative? And, still, in the conservation equations we do not consider its ...

1

The answers in the comments are both correct - a couple of points to add. First think about the reverse process - how would you work out the energy required to break up the proton and electron in hydrogen to form a proton and electron. This is the same as the energy that needs to be released on formation of a hydrogen atom. I think you have figured this out ...

1

Within the specification I can glean from the question - here is what I would do. (i) Find the best fit Gaussian - which I am assuming is what you have done. (ii) Your best fit should return a chi-squared value You should compare the chi-squared value with critical values of the chi-squared distribution for the appropriate number of degrees of freedom of ...

1

You said that it's from a Brazilian formula sheet. I'm not sure if it's the correct translation, but Google calls work "trabalho" and kinetic energy "energia cinética". So it could be that $\tau$ refers to "trabalho"—work— and $E_c$ "energia cinética"—kinetic energy. So $\tau = \Delta E_c$ would be the work-kinetic energy theorem (work is the change in ...

1

First off, Strontium accumulates in the bones replacing Calcium, so you can't easily get rid of it. Second, the most radioactive natural food we eat is the banana, at about 130 becquerels per Kg. So that 1L of "hot" water really is quite nasty if you drink it and a significant portion of the Sr90 ends up in your bones.

1

The specific gravities would be the same if the levels of the two side were the same after liquid-II was added. When I try this, my logic seems to be flawed too. I don't get 1.12. The level on side II has not changed. The level on side I has risen 2 cm. So 2 cm of liquid-II were added. Consider the horizontal plane 2 cm below the top of side II. Below ...

Only top voted, non community-wiki answers of a minimum length are eligible


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## Journal of the Mathematical Society of Japan

### Cartan matrices and Brauer's $k(B)$-conjecture IV

Benjamin SAMBALE

#### Abstract

In this note we give applications of recent results coming mostly from the third paper of this series. It is shown that the number of irreducible characters in a $p$-block of a finite group with abelian defect group $D$ is bounded by $|D|$ (Brauer's $k(B)$-conjecture) provided $D$ has no large elementary abelian direct summands. Moreover, we verify Brauer's $k(B)$-conjecture for all blocks with minimal non-abelian defect groups. This extends previous results by various authors.

#### Article information

Source
J. Math. Soc. Japan, Volume 69, Number 2 (2017), 735-754.

Dates
First available in Project Euclid: 20 April 2017

https://projecteuclid.org/euclid.jmsj/1492653645

Digital Object Identifier
doi:10.2969/jmsj/06920735

Mathematical Reviews number (MathSciNet)
MR3638283

Zentralblatt MATH identifier
06737032

Subjects
Primary: 20C15: Ordinary representations and characters
Secondary: 20C20: Modular representations and characters

#### Citation

SAMBALE, Benjamin. Cartan matrices and Brauer's $k(B)$-conjecture IV. J. Math. Soc. Japan 69 (2017), no. 2, 735--754. doi:10.2969/jmsj/06920735. https://projecteuclid.org/euclid.jmsj/1492653645

#### References

• M. Aschbacher, R. Kessar and B. Oliver, Fusion systems in algebra and topology, London Math. Soc. Lecture Note Series, 391, Cambridge University Press, Cambridge, 2011.
• M. Broué and L. Puig, A Frobenius theorem for blocks, Invent. Math., 56 (1980), 117–128.
• C. W. Eaton, B. Külshammer and B. Sambale, $2$-Blocks with minimal nonabelian defect groups II, J. Group Theory, 15 (2012), 311–321.
• W. Feit, The representation theory of finite groups, North-Holland Mathematical Library, 25, North-Holland Publishing Co., Amsterdam, 1982.
• M. Fujii, On determinants of Cartan matrices of $p$-blocks, Proc. Japan Acad. Ser. A Math. Sci., 56 (1980), 401–403.
• S. Gao and J. Zeng, On the number of ordinary irreducible characters in a $p$-block with a minimal nonabelian defect group, Comm. Algebra, 39 (2011), 3278–3297.
• The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.7.8; 2015, (http://www.gap-system.org).
• D. Gorenstein, Finite groups, Harper & Row Publishers, New York, 1968.
• Z. Halasi and K. Podoski, Every coprime linear group admits a base of size two, Trans. Amer. Math. Soc., 368 (2016), 5857–5887.
• S. Hendren, Extra special defect groups of order $p^3$ and exponent $p^2$, J. Algebra, 291 (2005), 457–491.
• S. Hendren, Extra special defect groups of order $p^3$ and exponent $p$, J. Algebra, 313 (2007), 724–760.
• B. Huppert, Endliche Gruppen. I, Grundlehren der Mathematischen Wissenschaften, 134, Springer-Verlag, Berlin, 1967.
• T. M. Keller and Y. Yang, Abelian quotients and orbit sizes of finite groups, arXiv:1407.6436v1.
• R. Kessar and M. Linckelmann, On perfect isometries for tame blocks, Bull. London Math. Soc., 34 (2002), 46–54.
• R. Kessar and G. Malle, Quasi-isolated blocks and Brauer's height zero conjecture, Ann. of Math. (2), 178 (2013), 321–384.
• Y. Kitaoka, Arithmetic of quadratic forms, Cambridge Tracts in Mathematics, 106, Cambridge University Press, Cambridge, 1993.
• M. Kiyota, On $3$-blocks with an elementary abelian defect group of order $9$, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 31 (1984), 33–58.
• H. Kurzweil and B. Stellmacher, The theory of finite groups, Universitext, Springer-Verlag, New York, 2004.
• B. Külshammer and T. Okuyama, On centrally controlled blocks of finite groups, unpublished.
• M. Linckelmann, Introduction to fusion systems, In: Group representation theory, 79–113, EPFL Press, Lausanne, 2007. Revised version: http://web.mat.bham.ac.uk/C.W.Parker/Fusion/fusion-intro.pdf.
• L. J. Mordell, The representation of a definite quadratic form as a sum of two others, Ann. of Math. (2), 38 (1937), 751–757.
• H. Nagao and Y. Tsushima, Representations of finite groups, Academic Press Inc., Boston, MA, 1989.
• J. Neukirch, Algebraic number theory, Grundlehren der Mathematischen Wissenschaften, 322, Springer-Verlag, Berlin, 1999.
• J. B. Olsson, On $2$-blocks with quaternion and quasidihedral defect groups, J. Algebra, 36 (1975), 212–241.
• W. Plesken, Solving $XX^\textnormal{tr}=A$ over the integers, Linear Algebra Appl., 226/228 (1995), 331–344.
• L. Puig and Y. Usami, Perfect isometries for blocks with abelian defect groups and cyclic inertial quotients of order $4$, J. Algebra, 172 (1995), 205–213.
• G. R. Robinson, On the focal defect group of a block, characters of height zero, and lower defect group multiplicities, J. Algebra, 320 (2008), 2624–2628.
• B. Sambale, $2$-Blocks with minimal nonabelian defect groups, J. Algebra, 337 (2011), 261–284.
• B. Sambale, Cartan matrices and Brauer's $k(B)$-conjecture II, J. Algebra, 337 (2011), 345–362.
• B. Sambale, Blocks of finite groups and their invariants, Springer Lecture Notes in Math., 2127, Springer-Verlag, Berlin, 2014.
• B. Sambale, On the Brauer–Feit bound for abelian defect groups, Math. Z., 276 (2014), 785–797.
• B. Sambale, Cartan matrices and Brauer's $k(B)$-conjecture III, Manuscripta Math., 146 (2015), 505–518.
• H. Sasaki, The mod $p$ cohomology algebras of finite groups with metacyclic Sylow $p$-subgroups, J. Algebra, 192 (1997), 713–733.
• M. Sawabe and A. Watanabe, On the principal blocks of finite groups with abelian Sylow $p$-subgroups, J. Algebra, 237 (2001), 719–734.
• R. Stancu, Control of fusion in fusion systems, J. Algebra Appl., 5 (2006), 817–837.
• D. A. Suprunenko, Matrix groups, Amer. Math. Soc., Providence, R.I., 1976.
• A. Turull, Fixed point free action with regular orbits, J. Reine Angew. Math., 371 (1986), 67–91.
• Y. Usami, On $p$-blocks with abelian defect groups and inertial index $2$ or $3$. I, J. Algebra, 119 (1988), 123–146.
• A. Watanabe, Note on a $p$-block of a finite group with abelian defect group, Osaka J. Math., 26 (1989), 829–836.
• A. Watanabe, Notes on $p$-blocks of characters of finite groups, J. Algebra, 136 (1991), 109–116.
• A. Watanabe, On perfect isometries for blocks with abelian defect groups and cyclic hyperfocal subgroups, Kumamoto J. Math., 18 (2005), 85–92.
• A. Watanabe, Appendix on blocks with elementary abelian defect group of order 9, In: Representation Theory of Finite Groups and Algebras, and Related Topics (Kyoto, 2008), 9–17, Kyoto University Research Institute for Mathematical Sciences, Kyoto, 2010.
• A. Watanabe, The number of irreducible Brauer characters in a $p$-block of a finite group with cyclic hyperfocal subgroup, J. Algebra, 416 (2014), 167–183.
• S. Yang and S. Gao, On the control of fusion in the local category for the $p$-block with a minimal nonabelian defect group, Sci. China Math., 54 (2011), 325–340.


text:
Strength of Class

Algebra Level 2

The average age of a $$n$$ adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average of the class by 4 years. The originals strength of the class was:

×


text:
Question

I use this function and hook:

function mysite_admin_menu()
{
}

The thing is, the submenu leads to this page: admin.php?page=xxx.
How can I do to link to a URL like edit-tags.php?taxonomy=category?
If I swap the slug in the add_submenu_page with a relative URL, the link will lead to
admin.php?page=edit-tags.php?taxonomy=category.
Whatever I do, I always get admin.php?page=... which is not what I want.


text:
# How to get a reference of a script from prefab child?

The Scene Fader prefab is dragged to the OnGameLoading script :

The scene fader prefab structure is with two children and the script I need to get a reference to is on the second child :

And the script I try to reference to the script on the second child : At the top :

public SceneFader sceneFader;

And in the Start()

void Start()
{
StartCoroutine(sceneFaderPrefab.Fade(sceneFaderPrefab.FadeDirection.Out));
}

Both sceneFaderPrefab.Fade and sceneFaderPrefab.FadeDirection the Fade and FadeDirection are not exist because I need to get reference to the script on the second child of the sceneFaderPrefab.

Is there any easy way to get a reference to the script on the second child of the prefab ?

I thought adding a private SceneFader sceneFaderScript variable and than somehow to find the script on the second child of the sceneFaderPrefab but not sure if this is the right way and how to do it.

• Presumably you tried GetComponentInChildren? Sep 17 at 1:00


text:
# 4.6 Proof of the master theorem

## 4.6-1 $\star$

Give a simple and exact expression for $n_j$ in equation $\text{(4.27)}$ for the case in which $b$ is a positive integer instead of an arbitrary real number.

$n_j$ is obtained by shifting the base $b$ representation $j$ positions to the right, and adding $1$ if any of the $j$ least significant positions are non-zero.

## 4.6-2 $\star$

Show that if $f(n) = \Theta(n^{\log_b a}\lg^k{n})$, where $k \ge 0$, then the master recurrence has solution $T(n) = \Theta(n^{\log_b a}\lg^{k + 1}n)$. For simplicity, confine your analysis to exact powers of $b$.

\begin{aligned} g(n) & = \sum_{j = 0}^{\log_b n - 1} a^j f(n / b^j) \\ f(n / b^j) & = \Theta\Big((n / b^j)^{\log_b a} \lg^k(n / b^j) \Big) \\ g(n) & = \Theta\Big(\sum_{j = 0}^{\log_b n - 1}a^j\big(\frac{n}{b^j}\big)^{\log_b a}\lg^k\big(\frac{n}{b^j}\big)\Big) \\ & = \Theta(A) \\ A & = \sum_{j = 0}^{\log_b n - 1} a^j \big(\frac{n}{b^j}\big)^{\log_b a}\lg^k\frac{n}{b^j} \\ & = n^{\log_b a} \sum_{j = 0}^{\log_b n - 1}\Big(\frac{a}{b^{\log_b a}}\Big)^j\lg^k\frac{n}{b^j} \\ & = n^{\log_b a}\sum_{j = 0}^{\log_b n - 1}\lg^k\frac{n}{b^j} \\ & = n^{\log_b a} B \\ \lg^k\frac{n}{d} & = (\lg n - \lg d)^k = \lg^k{n} + o(\lg^k{n}) \\ B & = \sum_{j = 0}^{\log_b n - 1}\lg^k\frac{n}{b^j} \\ & = \sum_{j = 0}^{\log_b n - 1}\Big(\lg^k{n} - o(\lg^k{n})\Big) \\ & = \log_b n\lg^k{n} + \log_b n \cdot o(\lg^k{n}) \\ & = \Theta(\log_b n\lg^k{n}) \\ & = \Theta(\lg^{k + 1}{n}) \\ g(n) & = \Theta(A) \\ & = \Theta(n^{\log_b a}B) \\ & = \Theta(n^{\log_b a}\lg^{k + 1}{n}). \end{aligned}

## 4.6-3 $\star$

Show that case 3 of the master method is overstated, in the sense that the regularity condition $af(n / b) \le cf(n)$ for some constant $c < 1$ implies that there exists a constant $\epsilon > 0$ such that $f(n) = \Omega(n^{\log_b a + \epsilon})$.

\begin{aligned} af(n / b) & \le cf(n) \\ \alpha f(n / b) & \le f(n), \alpha = a / c \\ \alpha f(n) & \le f(nb) \\ \alpha^i f(1) & \le f(b^i) \\ \end{aligned}

\begin{aligned} n = b^i & \Rightarrow i = \log_b n \Rightarrow f(n) \ge \alpha^{\log_b n}f(1) = n^{\log_b \alpha} \\ \alpha > a & \Rightarrow \alpha = a + d \quad (c < 1, d > 0) \\ & \Rightarrow f(n) = n^{\log_b a + \log_b d} = n^{\log_b a+\epsilon}. \quad (\epsilon = \log_b d) \end{aligned}


text:
## dessyj1 one year ago Volume of revolution. How would I find the volume of revolution for a space between two curves y=-x^2 +9 y=-x from x=0 to x=2

1. Loser66

graph it first

2. dessyj1

Already did, i would apply the formula but the space between the two curves is crossing the x-axis. What if the question asked for the vol of rev about the x-axis? How would i do that?

3. dessyj1

|dw:1434655395426:dw|

4. Loser66

Hey, volume or area?

5. Loser66

if it is area, then easy but if it is volume, then you need a rotation axis.

6. dessyj1

First off, this is a hypothetical question i made up. And i want to find the volume of rev

7. Loser66

What?? you made it up?? wow... @IrishBoy123

8. dessyj1

Usually, when we are asked to do a volume of rev in class, the space between the two curves are always in the 1st quadrant. I want to know if the procedure would change if the space were to be in the the 1st and the 4th simultaneously.

9. dessyj1

should i just shift both functions upwards to avoid complications?

10. IrishBoy123

you can only revolve this around y-axis whilst retaining any sense to the whole thing, ie whilst getting what might be described as a volume as @Loser66 said, you should draw it. that's the best advice by far. i can see only arrows on what you posted. not the curves and their intersections. when you see the actual **area** that you are revolving to form a **volume**, i am sure you will see the conundrum. you could revolve your area about any axis you want and get a mathematical answer but it wouldn't be a volume, would it?!

11. dessyj1

|dw:1434656246052:dw|

12. dessyj1

hmm

13. dessyj1

I do not know what to do from here on.

14. IrishBoy123

you do get the point, though? "solid" you can spin your enclosed area round the y axis and you will have a "solid" that has some real physical meaning. spin it around the x axis and it is just mathematical navel gazing. there's absolutely nothing wrong with that BTW but the answer is physically meaningless. so in your "design your own problem" mode, shift something up a bit so that the rev about x means something too |dw:1434656911930:dw| use a transform that gets that intercept onto the x axis.

15. dessyj1

Yes i do get your point.

16. dessyj1

I will shift both functions up by 2

17. dessyj1

then evaluate it.

18. dessyj1

would i use|dw:1434657740862:dw|

19. IrishBoy123

$$- x = - x^2 + 9$$ gives some really ugly arithmetic: $$x^2- x - 9= 0$$ the roots are: $$\frac {1 \pm \sqrt{1 - 4(-9) }}{2} = \frac{1\pm \sqrt{37}}{2}$$ so the root in Q4 must be $$( \frac{1+ \sqrt{37}}{2}, \frac{-1- \sqrt{37}}{2} )$$ ouch, ouch and triple ouch.

20. dessyj1

i restricted the space to 0 to 2

21. dessyj1

so i wouldnt have to deal with that.

22. IrishBoy123

in terms of solving it, that is yet another matter. people here talk about wings and nut and washers. that is again totally fine if that is how you are learning it. i was shown how to do this in a very different way, building little integration elements and going from there to a full integration. that approach makes it impossible to miss the cone at the base of your shape. you only really need to integration one curve.

23. dessyj1

I understand the method of finding the intersections ans using that as your limits but i really just wanted to understand the concept. This way saves more time.


text:
# CAT 1990

Instructions

For the following questions answer them individually

Question 11

There were 'x' pigeons and 'y' mynahs in a cage. One fine morning, 'p' birds escaped to freedom. The bird-keeper, knowing only that p = 7, was able to figure out without looking into the cage that at least one pigeon had escaped. Which of the following does not represent a possible (x,y) pair?

Question 12

The remainder when $$2^{60}$$ is divided by 5 equals

Question 13

Mr.X enters a positive integer Y(>1) in an electronic calculator and then goes on pressing the square . root key repeatedly. Then

Question 14

What is the sum of the following series: $$\frac{1}{1 \times 2} + \frac{1}{2 \times 3}+\frac {1}{3 \times 4}$$ ....... $$+ \frac{1}{100 \times 101}$$?

Question 15

The value of $$\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}$$

Question 16

Let a, b be any positive integers and x = 0 or 1, then

Question 17

There are six boxes numbered 1, 2, 3, 4, 5, 6. Each box is to be filled up either with a white ball or a black ball in such a manner that at least one box contains a black ball and all the boxes containing black balls are consecutively numbered. The total number of ways in which this can be done equals.

Question 18

Consider the following steps :
1. Put x = 1, y = 2
2. Replace x by xy
3. Replace y by y +1
4. If y = 5 then go to step 6 otherwise go to step 5.
5. Go to step 2
6. Stop Then the final value of x equals

Question 19

In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?

Question 20

From any two numbers $$x$$ and $$y$$, we define $$x* y = x + 0.5y - xy$$ . Suppose that both $$x$$ and $$y$$ are greater than 0.5. Then
$$x* x < y* y$$ if

OR