Explanation The given rational expression is 3 h + 2 h 3 + 5 h 2 + 4 h . Factor the denominator of the expression as follows. 3 h + 2 h 3 + 5 h 2 + 4 h = 3 h + 2 h ( h 3 + 5 h 2 + 4 h ) = 3 h + 2 h ( h + 4 ) ( h + 1 ) The rational expression is undefined when the denominator is 0. Set the denominator of the function equal to zero that is h + 4 = 0 , h + 1 = 0 , h = 0 and solve for h . h + 4 = 0 h = − 4 h + 1 = 0 h = − 1 Substitute h = − 4 in the rational expression 3 h + 2 h 3 + 5 h 2 + 4 h . 3 h + 2 h 3 + 5 h 2 + 4 h = 3 h + 2 h ( h + 4 ) ( h + 1 ) = 3 ( − 4 ) + 2 − 4 ( − 4 + 4 ) ( − 4 + 1 ) = − 10 0 = − ∞ Hence, the rational expression becomes undefined for h = − 4

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Question

Chapter 7.1, Problem 40E

To determine

To find: The values of h in the rational expression 3h+2h3+5h2+4h for which it is undefined.

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Chapter 7.1, Problem 39E

Chapter 7.1, Problem 41E

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R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

Question 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]

part b please

Chapter 7 Solutions

Elementary & Intermediate Algebra

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Prob. 9E Ch. 7.8 - Prob. 10E Ch. 7.8 - Prob. 11E Ch. 7.8 - Prob. 12E Ch. 7.8 - Prob. 13E Ch. 7.8 - To prepare for a marathon run. Sue ran 18 miles...Ch. 7.8 - Prob. 15E Ch. 7.8 - Prob. 16E Ch. 7.8 - Prob. 17E Ch. 7.8 - Prob. 18E Ch. 7.8 - Prob. 19E Ch. 7.8 - Prob. 20E Ch. 7.8 - Prob. 21E Ch. 7.8 - Prob. 22E Ch. 7.8 - In Problems 15-34, solve the proportion. See...Ch. 7.8 - Prob. 24E Ch. 7.8 - Prob. 25E Ch. 7.8 - Prob. 26E Ch. 7.8 - Prob. 27E Ch. 7.8 - Prob. 28E Ch. 7.8 - Prob. 29E Ch. 7.8 - Prob. 30E Ch. 7.8 - Prob. 31E Ch. 7.8 - Prob. 32E Ch. 7.8 - Prob. 33E Ch. 7.8 - Prob. 34E Ch. 7.8 - Prob. 35E Ch. 7.8 - Prob. 36E Ch. 7.8 - Prob. 37E Ch. 7.8 - Prob. 38E Ch. 7.8 - Prob. 39E Ch. 7.8 - Prob. 40E Ch. 7.8 - In Problems 41-44, write an algebraic expression...Ch. 7.8 - Prob. 42E Ch. 7.8 - Prob. 43E Ch. 7.8 - Prob. 44E Ch. 7.8 - Prob. 45E Ch. 7.8 - Prob. 46E Ch. 7.8 - Prob. 47E Ch. 7.8 - Prob. 48E Ch. 7.8 - Prob. 49E Ch. 7.8 - Prob. 50E Ch. 7.8 - Prob. 51E Ch. 7.8 - Prob. 52E Ch. 7.8 - Prob. 53E Ch. 7.8 - Prob. 54E Ch. 7.8 - Prob. 55E Ch. 7.8 - Prob. 56E Ch. 7.8 - Prob. 57E Ch. 7.8 - Prob. 58E Ch. 7.8 - Prob. 59E Ch. 7.8 - Prob. 60E Ch. 7.8 - Prob. 61E Ch. 7.8 - Prob. 62E Ch. 7.8 - Prob. 63E Ch. 7.8 - Prob. 64E Ch. 7.8 - Prob. 65E Ch. 7.8 - Prob. 66E Ch. 7.8 - Prob. 67E Ch. 7.8 - Prob. 68E Ch. 7.8 - Prob. 69E Ch. 7.8 - Prob. 70E Ch. 7.8 - Prob. 71E Ch. 7.8 - Prob. 72E Ch. 7.8 - Prob. 73E Ch. 7.8 - Prob. 74E Ch. 7.8 - Prob. 75E Ch. 7.8 - Prob. 76E Ch. 7.8 - Prob. 77E Ch. 7.8 - Prob. 78E Ch. 7.8 - Prob. 79E Ch. 7.8 - Prob. 80E Ch. 7.8 - Prob. 81E Ch. 7.8 - Prob. 82E Ch. 7.8 - Prob. 83E Ch. 7.8 - Prob. 84E Ch. 7.8 - Prob. 85E Ch. 7.8 - Prob. 86E Ch. 7.8 - Prob. 87E Ch. 7.8 - Prob. 88E Ch. 7.8 - A student reads the following sentence from a word...Ch. 7.8 - When modeling work problems, we assume that...Ch. 7.8 - Prob. 91E Ch. 7.8 - Explain why the following proportions all yield...Ch. 7 - Evaluate a3b3a+b when a = 2 and b = 3.Ch. 7 - Prob. 2PCT Ch. 7 - Prob. 3PCT Ch. 7 - Prob. 4PCT Ch. 7 - Prob. 5PCT Ch. 7 - Prob. 6PCT Ch. 7 - Prob. 7PCT Ch. 7 - Prob. 8PCT Ch. 7 - Prob. 9PCT Ch. 7 - Prob. 10PCT Ch. 7 - Prob. 11PCT Ch. 7 - Prob. 12PCT Ch. 7 - Prob. 13PCT Ch. 7 - Prob. 14PCT Ch. 7 - Prob. 15PCT Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Prob. 46RE Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Prob. 53RE Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Prob. 57RE Ch. 7 - Prob. 58RE Ch. 7 - Prob. 59RE Ch. 7 - In Problems 5972, perform the indicated...Ch. 7 - Prob. 61RE Ch. 7 - Prob. 62RE Ch. 7 - Prob. 63RE Ch. 7 - Prob. 64RE Ch. 7 - Prob. 65RE Ch. 7 - Prob. 66RE Ch. 7 - Prob. 67RE Ch. 7 - Prob. 68RE Ch. 7 - Prob. 69RE Ch. 7 - Prob. 70RE Ch. 7 - Prob. 71RE Ch. 7 - Prob. 72RE Ch. 7 - Prob. 73RE Ch. 7 - Prob. 74RE Ch. 7 - Prob. 75RE Ch. 7 - Prob. 76RE Ch. 7 - Prob. 77RE Ch. 7 - Prob. 78RE Ch. 7 - Prob. 79RE Ch. 7 - Prob. 80RE Ch. 7 - Prob. 81RE Ch. 7 - Prob. 82RE Ch. 7 - Prob. 83RE Ch. 7 - Prob. 84RE Ch. 7 - Prob. 85RE Ch. 7 - Prob. 86RE Ch. 7 - Prob. 87RE Ch. 7 - Prob. 88RE Ch. 7 - Prob. 89RE Ch. 7 - Prob. 90RE Ch. 7 - Prob. 91RE Ch. 7 - Prob. 92RE Ch. 7 - Prob. 93RE Ch. 7 - Prob. 94RE Ch. 7 - Prob. 95RE Ch. 7 - Prob. 96RE Ch. 7 - Prob. 97RE Ch. 7 - Prob. 98RE Ch. 7 - Prob. 99RE Ch. 7 - Prob. 100RE Ch. 7 - Prob. 101RE Ch. 7 - Prob. 102RE Ch. 7 - Prob. 103RE Ch. 7 - Prob. 104RE Ch. 7 - Prob. 105RE Ch. 7 - Prob. 106RE Ch. 7 - Prob. 107RE Ch. 7 - Prob. 108RE Ch. 7 - Prob. 109RE Ch. 7 - Prob. 110RE Ch. 7 - Prob. 111RE Ch. 7 - Prob. 112RE Ch. 7 - Prob. 1T Ch. 7 - Prob. 2T Ch. 7 - Prob. 3T Ch. 7 - Prob. 4T Ch. 7 - Prob. 5T Ch. 7 - Prob. 6T Ch. 7 - Prob. 7T Ch. 7 - Prob. 8T Ch. 7 - Prob. 9T Ch. 7 - Prob. 10T Ch. 7 - Prob. 11T Ch. 7 - Prob. 12T Ch. 7 - Prob. 13T Ch. 7 - Prob. 14T Ch. 7 - Prob. 15T Ch. 7 - Prob. 16T Ch. 7 - Prob. 17T Ch. 7 - Prob. 18T Ch. 7 - Prob. 19T Ch. 7 - Prob. 20T Ch. 7 - Prob. 1CUR Ch. 7 - Prob. 2CUR Ch. 7 - Prob. 3CUR Ch. 7 - Prob. 4CUR Ch. 7 - Prob. 5CUR Ch. 7 - Prob. 6CUR Ch. 7 - Prob. 7CUR Ch. 7 - Prob. 8CUR Ch. 7 - Prob. 9CUR Ch. 7 - Prob. 10CUR Ch. 7 - Prob. 11CUR Ch. 7 - Prob. 12CUR Ch. 7 - Solve the equation using the Zero-Product...Ch. 7 - Prob. 14CUR Ch. 7 - Prob. 15CUR Ch. 7 - Prob. 16CUR Ch. 7 - Prob. 17CUR Ch. 7 - Prob. 18CUR Ch. 7 - Prob. 19CUR Ch. 7 - Prob. 20CUR Ch. 7 - Prob. 21CUR Ch. 7 - Prob. 22CUR Ch. 7 - Prob. 23CUR Ch. 7 - Prob. 24CUR Ch. 7 - Prob. 25CUR Ch. 7 - Prob. 26CUR Ch. 7 - Prob. 27CUR Ch. 7 - Prob. 28CUR Ch. 7 - Prob. 29CUR Ch. 7 - Prob. 30CUR Ch. 7 - Prob. 1IA Ch. 7 - Prob. 2IA Ch. 7 - Prob. 3IA Ch. 7 - Prob. 4IA Ch. 7 - Prob. 5IA Ch. 7 - Prob. 6IA Ch. 7 - Prob. 7IA Ch. 7 - Prob. 8IA Ch. 7 - Prob. 9IA Ch. 7 - Prob. 10IA Ch. 7 - Prob. 11IA Ch. 7 - Prob. 12IA Ch. 7 - Prob. 13IA Ch. 7 - Prob. 14IA Ch. 7 - Prob. 15IA Ch. 7 - Prob. 16IA Ch. 7 - Prob. 17IA Ch. 7 - Prob. 18IA Ch. 7 - Prob. 19IA Ch. 7 - Prob. 20IA Ch. 7 - Prob. 21IA Ch. 7 - Prob. 22IA Ch. 7 - Prob. 23IA Ch. 7 - Prob. 24IA Ch. 7 - Prob. 25IA Ch. 7 - Prob. 26IA Ch. 7 - Prob. 27IA Ch. 7 - Prob. 28IA Ch. 7 - Prob. 29IA Ch. 7 - Prob. 30IA Ch. 7 - Prob. 31IA Ch. 7 - Prob. 32IA Ch. 7 - Prob. 33IA Ch. 7 - Prob. 34IA Ch. 7 - Prob. 35IA Ch. 7 - Solve: 7y2+y124yy2+7y+12=6y29

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The values of h in the rational expression 3 h + 2 h 3 + 5 h 2 + 4 h for which it is undefined.

Solution Summary: The author explains how to find the values of h in the rational expression 3h+2h3.

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To find: The values of h in the rational expression 3h+2h3+5h2+4h for which it is undefined.

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Chapter 7 Solutions