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 29, Problem 7PT
To determine
To find: The volume with the help of double
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10) Which of the following is the general solution of the homogeneous second-order differential
equation y + 8y + 52y=0? Here, C, C₁, and C2 are arbitrary real constants.
A) y = C₁ecos(61) + C₂e*sin(61) + C
B) y = et (sin(4t) + cos(6t)) + C
C) y = C₁esin(6) + C₂e+ cos(6t) + C
D) y = C₁esin(6) + C₂e+cos(6)
E) y=e(C₁sin(61) + C₂cos(61))
3) Consider the initial value problem
'
y' + 8y = 0, y(0) = -4, y (0) = 16
What is the solution of this initial value problem?
A) y = -4t - 2e8t
D) y = -4 + 2e-8t
B) y = -2 + 2e8t
C) y = -2 -2e-8t
E) y = -4+ 2e8t
F) y = -2t-2e-8t
Chapter 29 Solutions
Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)
Ch. 29.1 - Practice Exercise
If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1ECh. 29.1 - Prob. 2ECh. 29.1 - Prob. 3ECh. 29.1 - Prob. 4ECh. 29.1 - Prob. 5ECh. 29.1 - Prob. 6ECh. 29.1 - Prob. 7ECh. 29.1 - Prob. 8ECh. 29.1 - Prob. 9E
Ch. 29.1 - Prob. 10ECh. 29.1 - Prob. 11ECh. 29.1 - Prob. 12ECh. 29.1 - Prob. 13ECh. 29.1 - Prob. 14ECh. 29.1 - Prob. 15ECh. 29.1 - Prob. 16ECh. 29.1 - Prob. 17ECh. 29.1 - Prob. 18ECh. 29.1 - Prob. 19ECh. 29.1 - Prob. 20ECh. 29.1 - Prob. 21ECh. 29.1 - Prob. 22ECh. 29.1 - Prob. 23ECh. 29.1 - Prob. 24ECh. 29.1 - Prob. 25ECh. 29.1 - Prob. 26ECh. 29.1 - Prob. 27ECh. 29.1 - Prob. 28ECh. 29.1 - Prob. 29ECh. 29.1 - Prob. 30ECh. 29.1 - Prob. 31ECh. 29.1 - Prob. 32ECh. 29.1 - Prob. 33ECh. 29.1 - Prob. 34ECh. 29.1 - Prob. 35ECh. 29.1 - Prob. 36ECh. 29.1 - Prob. 37ECh. 29.1 - Prob. 38ECh. 29.1 - Prob. 39ECh. 29.1 - Prob. 40ECh. 29.1 - Prob. 41ECh. 29.1 - Prob. 42ECh. 29.1 - Prob. 43ECh. 29.1 - Prob. 44ECh. 29.2 - Prob. 1PECh. 29.2 - Prob. 2PECh. 29.2 - Prob. 1ECh. 29.2 - Prob. 2ECh. 29.2 - Prob. 3ECh. 29.2 - Prob. 4ECh. 29.2 - Prob. 5ECh. 29.2 - Prob. 6ECh. 29.2 - Prob. 7ECh. 29.2 - Prob. 8ECh. 29.2 - Prob. 9ECh. 29.2 - Prob. 10ECh. 29.2 - Prob. 11ECh. 29.2 - Prob. 12ECh. 29.2 - Prob. 13ECh. 29.2 - Prob. 14ECh. 29.2 - Prob. 15ECh. 29.2 - Prob. 16ECh. 29.2 - Prob. 17ECh. 29.2 - Prob. 18ECh. 29.2 - Prob. 19ECh. 29.2 - Prob. 20ECh. 29.2 - Prob. 21ECh. 29.2 - Prob. 22ECh. 29.2 - Prob. 23ECh. 29.2 - Prob. 24ECh. 29.2 - Prob. 25ECh. 29.2 - Prob. 26ECh. 29.2 - Prob. 27ECh. 29.2 - Prob. 28ECh. 29.2 - Prob. 29ECh. 29.2 - Prob. 30ECh. 29.2 - Prob. 31ECh. 29.2 - Prob. 32ECh. 29.2 - Prob. 33ECh. 29.2 - Prob. 34ECh. 29.2 - Prob. 35ECh. 29.2 - Prob. 36ECh. 29.2 - Prob. 37ECh. 29.2 - Prob. 38ECh. 29.2 - Prob. 39ECh. 29.2 - Prob. 40ECh. 29.2 - Prob. 41ECh. 29.2 - Prob. 42ECh. 29.2 - Prob. 43ECh. 29.2 - Prob. 44ECh. 29.2 - Prob. 45ECh. 29.2 - Prob. 46ECh. 29.3 - If z = 4x2 + x sin y, find ∂z/∂x and ∂z/∂y.
Ch. 29.3 - Prob. 2PECh. 29.3 - Prob. 1ECh. 29.3 - Prob. 2ECh. 29.3 - Prob. 3ECh. 29.3 - Prob. 4ECh. 29.3 - Prob. 5ECh. 29.3 - Prob. 6ECh. 29.3 - Prob. 7ECh. 29.3 - Prob. 8ECh. 29.3 - Prob. 9ECh. 29.3 - Prob. 10ECh. 29.3 - Prob. 11ECh. 29.3 - Prob. 12ECh. 29.3 - Prob. 13ECh. 29.3 - Prob. 14ECh. 29.3 - Prob. 15ECh. 29.3 - Prob. 16ECh. 29.3 - Prob. 17ECh. 29.3 - Prob. 18ECh. 29.3 - Prob. 19ECh. 29.3 - Prob. 20ECh. 29.3 - Prob. 21ECh. 29.3 - Prob. 22ECh. 29.3 - Prob. 23ECh. 29.3 - Prob. 24ECh. 29.3 - Prob. 25ECh. 29.3 - Prob. 26ECh. 29.3 - Prob. 27ECh. 29.3 - Prob. 28ECh. 29.3 - Prob. 29ECh. 29.3 - Prob. 30ECh. 29.3 - Prob. 31ECh. 29.3 - Prob. 32ECh. 29.3 - Prob. 33ECh. 29.3 - Prob. 34ECh. 29.3 - Prob. 35ECh. 29.3 - Prob. 36ECh. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - Prob. 39ECh. 29.3 - Prob. 40ECh. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - Prob. 42ECh. 29.3 - Prob. 43ECh. 29.3 - Prob. 44ECh. 29.3 - Prob. 45ECh. 29.3 - Prob. 46ECh. 29.3 - Prob. 47ECh. 29.3 - Prob. 48ECh. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.4 - Prob. 1PECh. 29.4 - Prob. 1ECh. 29.4 - Prob. 2ECh. 29.4 - Prob. 3ECh. 29.4 - Prob. 4ECh. 29.4 - Prob. 5ECh. 29.4 - In Exercises 5–18, evaluate the given double...Ch. 29.4 - Prob. 7ECh. 29.4 - Prob. 8ECh. 29.4 - Prob. 9ECh. 29.4 - Prob. 10ECh. 29.4 - Prob. 11ECh. 29.4 - Prob. 12ECh. 29.4 - Prob. 13ECh. 29.4 - Prob. 14ECh. 29.4 - Prob. 15ECh. 29.4 - Prob. 16ECh. 29.4 - Prob. 17ECh. 29.4 - Prob. 18ECh. 29.4 - Prob. 19ECh. 29.4 - Prob. 20ECh. 29.4 - Prob. 21ECh. 29.4 - Prob. 22ECh. 29.4 - Prob. 23ECh. 29.4 - Prob. 24ECh. 29.4 - Prob. 25ECh. 29.4 - Prob. 26ECh. 29.4 - Prob. 27ECh. 29.4 - Prob. 28ECh. 29.4 - Prob. 29ECh. 29.4 - Prob. 30ECh. 29.4 - Prob. 31ECh. 29.4 - Prob. 32ECh. 29.4 - Prob. 33ECh. 29.4 - Prob. 34ECh. 29 - Prob. 1RECh. 29 - Prob. 2RECh. 29 - Prob. 3RECh. 29 - Prob. 4RECh. 29 - Prob. 5RECh. 29 - Prob. 6RECh. 29 - Prob. 7RECh. 29 - Prob. 8RECh. 29 - Prob. 9RECh. 29 - Prob. 10RECh. 29 - Prob. 11RECh. 29 - Prob. 12RECh. 29 - Prob. 13RECh. 29 - Prob. 14RECh. 29 - Prob. 15RECh. 29 - Prob. 16RECh. 29 - Prob. 17RECh. 29 - Prob. 18RECh. 29 - Prob. 19RECh. 29 - Prob. 20RECh. 29 - Prob. 21RECh. 29 - Prob. 22RECh. 29 - Prob. 23RECh. 29 - Prob. 24RECh. 29 - Prob. 25RECh. 29 - Prob. 26RECh. 29 - Prob. 27RECh. 29 - Prob. 28RECh. 29 - Prob. 29RECh. 29 - Prob. 30RECh. 29 - Prob. 31RECh. 29 - Prob. 32RECh. 29 - Prob. 33RECh. 29 - Prob. 34RECh. 29 - Prob. 35RECh. 29 - Prob. 36RECh. 29 - Prob. 37RECh. 29 - Prob. 38RECh. 29 - Prob. 39RECh. 29 - Prob. 40RECh. 29 - Prob. 41RECh. 29 - Prob. 42RECh. 29 - Prob. 43RECh. 29 - Prob. 44RECh. 29 - Prob. 45RECh. 29 - Prob. 46RECh. 29 - Prob. 47RECh. 29 - Prob. 48RECh. 29 - Prob. 49RECh. 29 - Prob. 50RECh. 29 - Prob. 51RECh. 29 - Prob. 52RECh. 29 - Prob. 53RECh. 29 - Prob. 54RECh. 29 - Prob. 55RECh. 29 - Prob. 1PTCh. 29 - Prob. 2PTCh. 29 - Prob. 3PTCh. 29 - Prob. 4PTCh. 29 - Prob. 5PTCh. 29 - Prob. 6PTCh. 29 - Prob. 7PTCh. 29 - Prob. 8PT
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- 6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).arrow_forward7) Compute the Wronskian of the pair of functions sin(5t) and cos(5t). A) -5 B) 4 C) 1 D) -4 E) 5arrow_forward8) The pair of functions y₁ = eбt and y₁ = teбt forms a fundamental set of solutions for the differential equation y'' - 12y' + 36y= 0.arrow_forward
- 6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).arrow_forward5) Consider the initial value problem 9 (8² 9t+ 1)y' - 8ty = sin(2πt), ) = -4, y = -3.5 16 16 On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. A) (-∞, ∞) B) (0, 1) 25 C) (-4, -3.5) D) E) 32'32 明arrow_forward1) Which of the following are solutions to the homogeneous second-order differential equation 4y 7y -2y=0? Select all that apply. A) YA = Ce2t, where C is any real constant B) y = 2e-21 6 2t C) y = C (e- 21 + e21), where C is any real constant D) 1/3 = 8 (221 + €21) E) y2 = Ce 2t, where C is any real constant 2t F) y₁ = 8e +2e2t G) y5 = (C₁ e²) · (C₂e-21), where C₁ and C₂ are any real constants 1arrow_forward
- 7) Compute the Wronskian of the pair of functions sin(5t) and cos(5t). A) -5 B) 4 C) 1 D) -4 E) 5arrow_forward5) Consider the initial value problem 9 (8² 9t+ 1)y' - 8ty = sin(2πt), ) = -4, y = -3.5 16 16 On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. A) (-∞, ∞) B) (0, 1) 25 C) (-4, -3.5) D) E) 32'32 明arrow_forward2) For which of these differential equations is the characteristic equation given by r(10r + 1) = 0? A) y (10y + 1) = 0 B) 10y'' + 1 = 0 C) 10y+1y=0 D) y (10y + 1y) = 0 E) 10y'' + 1y=0arrow_forward
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