Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 44, Problem 4A
To determine
To simplify the expression
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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
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,∞).
Chapter 44 Solutions
Mathematics for Machine Technology
Ch. 44 - Solve x3=15.Express the answer as both a common...Ch. 44 - Solve the equation 75.4=5.2C for the unknown value...Ch. 44 - Find the unknown value of b in the equation...Ch. 44 - Prob. 4ACh. 44 - Prob. 5ACh. 44 - Prob. 6ACh. 44 - Prob. 7ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 9ACh. 44 - Solve for the unknown and check each of the...
Ch. 44 - Prob. 11ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 13ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 15ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 17ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 25ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 27ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 29ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 33ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - Prob. 35ACh. 44 - Solve for the unknown and check each of the...Ch. 44 - The following formulas are used in the machine...Ch. 44 - The following formulas are used in the machine...Ch. 44 - Prob. 39ACh. 44 - The following formulas are used in the machine...Ch. 44 - Prob. 41ACh. 44 - The following formulas are used in the machine...Ch. 44 - Prob. 43ACh. 44 - The following formulas are used in the machine...Ch. 44 - Prob. 45ACh. 44 - The following formulas are used in the machine...Ch. 44 - Prob. 47ACh. 44 - The following formulas are used in the machine...Ch. 44 - Prob. 49ACh. 44 - The following formulas are used in the machine...Ch. 44 - Prob. 51ACh. 44 - The following formulas are used in machine trade...Ch. 44 - Prob. 53ACh. 44 - The following formulas are used in machine trade...Ch. 44 - Prob. 55ACh. 44 - Prob. 56ACh. 44 - Prob. 57ACh. 44 - The following formulas are used in machine trade...Ch. 44 - Prob. 59ACh. 44 - For applications 60 and 61, rearrange each formula...Ch. 44 - Prob. 61ACh. 44 - Solve for the unknown value in each of the...Ch. 44 - Prob. 63ACh. 44 - Solve for the unknown value in each of the...Ch. 44 - Prob. 65ACh. 44 - Solve for the unknown value in each of the...Ch. 44 - Prob. 67ACh. 44 - Prob. 68ACh. 44 - Prob. 69ACh. 44 - Solve for the unknown value in each of the...Ch. 44 - Prob. 71ACh. 44 - Solve for the unknown value in each of the...Ch. 44 - Prob. 73ACh. 44 - Solve for the unknown value in each of the...Ch. 44 - Prob. 75A
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- 7) 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_forward6) 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_forward
- 5) 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_forward7) Compute the Wronskian of the pair of functions sin(5t) and cos(5t). A) -5 B) 4 C) 1 D) -4 E) 5arrow_forward
- 5) 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_forwardLESSON 19 SESSION 3 3 Angel jumps rope. He does 38, 50, 22, and 29 jumps. How many jumps does Angel do in all? Do the on ⒶA 94 139 B 114 any two n make a te ℗ 179 Jess chose. How did Jess get her answer 4 Complete each equation using a number from the What a box at the right. and or numb a. 26 + 174 = 100 39 b. 39 +61= 100 48 74 c. 52+ 1481 = 100 5 Kelvin's garden has 31 daisies, 16 roses, 25 tulips, and 34 sunflowers. How many flowers are in Kelvin's garden? Show your work. 31 Ho all?arrow_forward
- = Use Qin's method to solve the pure cubic equation x³: 12,812,904. Compare this method with the old cube root algorithm discussed in the text. In each case, show wherearrow_forwardCollaborative Work (Ch4) MA244-02_Collaborative_Work_Chapter4.pdf uah.instructure.com zm Rich LTI b Answered: HW_#6 HW_06.pdf EE 213-01 Assignments zm Rich LTI uah.instruct... ✓ Download → Info × Close 0 - ZOOM + 1) a) Determine which functions are solutions of the following linear differential equation: y"- 6y' + 9y=0 i) e³x isė зх 23x ii) xe ³x iii) x² ³x iv) (x+3) e³x 3× хе b) Find the Wronskion хе the set of functions that you fand for as the solution of the differential equation above from a) c) What does the result that you found from b) imply? conici 2) Perform a rotation of axes to eliminate the xy-term, identify and sketch the graph of the following a 5x²-2xy + Sy²=24=0arrow_forwardUse the Chinese cube root algorithm to find the cube root of 12,812,904.arrow_forward
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