Explanation Definition used: The derivative of the logarithmic functions of the form ln u is given by the formula d ( ln u ) d x = 1 u d u d x . Calculation: The given equation is V = k ln a 2 + x 2 + a a 2 + x 2 − a where E = − d V d x . Rewrite the given equation as, V = k ln a 2 + x 2 + a a 2 + x 2 − a V = k [ ln ( a 2 + x 2 + a ) − ln ( a 2 + x 2 − a ) ] ( ∵ ln ( u v ) = ln u − ln v ) Using the above definition, differentiate both sides of the above equation and obtain the first derivative as shown below: V = k [ ln ( a 2 + x 2 + a ) − ln ( a 2 + x 2 − a ) ] d V d x = k x a 2 + x 2 ( a 2 + x 2 + a ) − k x a 2 + x 2 ( a 2 + x 2 − a ) d V d x = k x [ a 2 + x 2 − a a 2 + x 2 − ( a 2 + x 2 + a a 2 + x 2 ) ] ( a 2 + x 2 ) ( a 2 + x 2 + a 2 ) d V

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 27.5, Problem 56E

To determine

The expression for the variable E from the equation V=klna2+x2+aa2+x2−a.

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Chapter 27.5, Problem 55E

Chapter 27.6, Problem 1PE

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Page < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.

13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of the following sets and the cardinal number of each set. a) W° and n(W) b) (VUW) and n((V U W)') c) VUWUX and n(V U W UX) d) vnWnX and n(V WnX)

9) Use the Venn Diagram given below to determine the number elements in each of the following sets. a) n(A). b) n(A° UBC). U B oh a k gy ท W z r e t ་ C

Chapter 27 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 27.1 - Prob. 1PE Ch. 27.1 - Prob. 2PE Ch. 27.1 - Prob. 1E Ch. 27.1 - Prob. 2E Ch. 27.1 - Prob. 3E Ch. 27.1 - Prob. 4E Ch. 27.1 - Prob. 5E Ch. 27.1 - Prob. 6E Ch. 27.1 - Prob. 7E Ch. 27.1 - Prob. 8E

Ch. 27.1 - Prob. 9E Ch. 27.1 - Prob. 10E Ch. 27.1 - Prob. 11E Ch. 27.1 - Prob. 12E Ch. 27.1 - Prob. 13E Ch. 27.1 - Prob. 14E Ch. 27.1 - Prob. 15E Ch. 27.1 - Prob. 16E Ch. 27.1 - Prob. 17E Ch. 27.1 - Prob. 18E Ch. 27.1 - Prob. 19E Ch. 27.1 - Prob. 20E Ch. 27.1 - Prob. 21E Ch. 27.1 - Prob. 22E Ch. 27.1 - Prob. 23E Ch. 27.1 - Prob. 24E Ch. 27.1 - Prob. 25E Ch. 27.1 - In Exercises 3–34, find the derivatives of the...Ch. 27.1 - Prob. 27E Ch. 27.1 - Prob. 28E Ch. 27.1 - Prob. 29E Ch. 27.1 - Prob. 30E Ch. 27.1 - Prob. 31E Ch. 27.1 - Prob. 32E Ch. 27.1 - Prob. 33E Ch. 27.1 - Prob. 34E Ch. 27.1 - Prob. 35E Ch. 27.1 - Prob. 36E Ch. 27.1 - Prob. 37E Ch. 27.1 - Prob. 38E Ch. 27.1 - Prob. 39E Ch. 27.1 - Prob. 40E Ch. 27.1 - Prob. 41E Ch. 27.1 - Prob. 42E Ch. 27.1 - Prob. 43E Ch. 27.1 - Prob. 44E Ch. 27.1 - Prob. 45E Ch. 27.1 - Prob. 46E Ch. 27.1 - Prob. 47E Ch. 27.1 - Prob. 48E Ch. 27.1 - Prob. 49E Ch. 27.1 - Prob. 50E Ch. 27.1 - Prob. 51E Ch. 27.1 - Prob. 52E Ch. 27.1 - Prob. 53E Ch. 27.1 - Prob. 54E Ch. 27.1 - 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In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 4E Ch. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 6E Ch. 27.8 - Prob. 7E Ch. 27.8 - Prob. 8E Ch. 27.8 - Prob. 9E Ch. 27.8 - Prob. 10E Ch. 27.8 - Prob. 11E Ch. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 13E Ch. 27.8 - Prob. 14E Ch. 27.8 - Prob. 15E Ch. 27.8 - Prob. 16E Ch. 27.8 - Prob. 17E Ch. 27.8 - Prob. 18E Ch. 27.8 - Prob. 19E Ch. 27.8 - Prob. 20E Ch. 27.8 - Prob. 21E Ch. 27.8 - Prob. 22E Ch. 27.8 - Prob. 23E Ch. 27.8 - Prob. 25E Ch. 27.8 - Prob. 26E Ch. 27.8 - Prob. 27E Ch. 27.8 - Prob. 28E Ch. 27.8 - Prob. 29E Ch. 27.8 - Prob. 30E Ch. 27.8 - Prob. 31E Ch. 27.8 - Prob. 32E Ch. 27.8 - Prob. 33E Ch. 27.8 - Prob. 34E Ch. 27.8 - The energy E (in J) dissipated by a certain...Ch. 27.8 - Prob. 36E Ch. 27.8 - Prob. 37E Ch. 27.8 - Prob. 39E Ch. 27.8 - A package of weather instruments is propelled into...Ch. 27.8 - Prob. 41E Ch. 27.8 - Prob. 42E Ch. 27.8 - Prob. 43E Ch. 27.8 - 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The expression for the variable E from the equation V = k ln a 2 + x 2 + a a 2 + x 2 − a .

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The expression for the variable E from the equation V=klna2+x2+aa2+x2−a.

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Chapter 27 Solutions