Explanation Procedure used: “Solving a Quadratic Equation using quadratic formula: The solution of a quadratic equation of the form a x 2 + b x + c = 0 is found using the formula, x = − b ± b 2 − 4 a c 2 a .” Calculation: The given quadratic equation is 3 y 2 = 3 y + 2 . The quadratic equation can be rewritten as 3 y 2 − 3 y − 2 = 0 . Here a = 3 , b = − 3 and c = − 2 . Substitute the values for a , b , and c in the quadratic formula

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 7.3, Problem 13E

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The solution of the given quadratic equation using quadratic formula.

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Chapter 7.3, Problem 12E

Chapter 7.3, Problem 14E

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Matrix MЄ R4×4, as specified below, is an orthogonal matrix - thus, it fulfills MTM = I. M (ELES),- m2,1. We know also that all the six unknowns mr,c are non-negative with the exception of Your first task is to find the values of all the six unknowns. Think first, which of the mr,c you should find first. Next, consider a vector v = (-6, 0, 0, 8) T. What's the length of v, i.e., |v|? Using M as transformation matrix, map v onto w by w = Mv provide w with its numeric values. What's the length of w, especially when comparing it to the length of v? Finally, consider another vector p = ( 0, 0, 8, 6) T. What's the angle between v (from above) and p? Using M as transformation matrix, map p onto q by q = Mp - provide q with its numeric values. What's the angle between w and q, especially when comparing it to the angle between v and p?

(c) Find the harmonic function on the annular region Q = {1 < r < 2} satisfying the boundary conditions given by U (1, 0) = 1, U(2, 0) 1+15 sin (20). =

Question 3 (a) Find the principal part of the PDE AU + UÃ + U₁ + x + y = 0 and determine whether it's hyperbolic, elliptic or parabolic. (b) Prove that if U(r, 0) solves the Laplace equation in R², then so is V(r, 0) = U (², −0). (c) Find the harmonic function on the annular region = {1 < r < 2} satisfying the boundary conditions given by U(1, 0) = 1, U(2, 0) = 1 + 15 sin(20). [5] [7] [8]

Chapter 7 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 7.1 - Solve for x: x2 + 4x − 21 = 0 Ch. 7.1 - Prob. 2PE Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E

Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - In Exercises 11–48, solve the given quadratic...Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.2 - Prob. 1PE Ch. 7.2 - Prob. 1E Ch. 7.2 - Prob. 2E Ch. 7.2 - Prob. 3E Ch. 7.2 - Prob. 4E Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - Prob. 9E Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - Prob. 18E Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - Prob. 23E Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - Prob. 26E Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.3 - Prob. 1PE Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Prob. 30E Ch. 7.3 - Prob. 31E Ch. 7.3 - Prob. 32E Ch. 7.3 - Prob. 33E Ch. 7.3 - Prob. 34E Ch. 7.3 - Prob. 35E Ch. 7.3 - Prob. 36E Ch. 7.3 - In Exercises 35–38, without solving the given...Ch. 7.3 - Prob. 38E Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - In Exercises 39–62, solve the given problems. All...Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Prob. 45E Ch. 7.3 - Prob. 46E Ch. 7.3 - Prob. 47E Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - In Exercises 39–62, solve the given problems. All...Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.3 - Prob. 53E Ch. 7.3 - Prob. 54E Ch. 7.3 - Prob. 55E Ch. 7.3 - Prob. 56E Ch. 7.3 - Prob. 57E Ch. 7.3 - Prob. 58E Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Prob. 61E Ch. 7.3 - Prob. 62E Ch. 7.4 - Prob. 1PE Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - In Exercises 25–30, use a calculator to graph all...Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - In Exercises 31–50, solve the given applied...Ch. 7.4 - Prob. 36E Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Prob. 40E Ch. 7.4 - Prob. 41E Ch. 7.4 - Prob. 42E Ch. 7.4 - Prob. 43E Ch. 7.4 - Prob. 44E Ch. 7.4 - Prob. 45E Ch. 7.4 - Prob. 46E Ch. 7.4 - Prob. 47E Ch. 7.4 - Prob. 48E Ch. 7.4 - Prob. 49E Ch. 7.4 - Prob. 50E 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 - Prob. 60RE 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 - In Exercises 77–90, set up the necessary equation...Ch. 7 - In Exercises 77–90, set up the necessary equation...Ch. 7 - Prob. 91RE Ch. 7 - Prob. 1PT Ch. 7 - Prob. 2PT Ch. 7 - Prob. 3PT Ch. 7 - Prob. 4PT Ch. 7 - Prob. 5PT Ch. 7 - Prob. 6PT Ch. 7 - Prob. 7PT Ch. 7 - Prob. 8PT Ch. 7 - Prob. 9PT Ch. 7 - Prob. 10PT

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