Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Chapter 7.2, Problem 38P
To determine
To prove:
The
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3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum
was at its resting position. The pendulum then moved right (positive displacement) and left (negative
displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its
resting position. The pendulum's furthest distance to either side was 6 in. Graph the function that represents
the pendulum's displacement as a function of time.
Answer:
f(t)
(a) Write an equation to represent the displacement of the pendulum as a function of time.
(b) Graph the function.
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A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually
cranked into the lowest position in order to exit the ride. Sine function model: h = −82.5 cos (3πt) + 97.5
where h is the height of the last passenger above the ground measured in feet and t is the time of operation of
the ride in minutes.
(a) What is the height of the last passenger at the moment of the power outage? Verify your answer by
evaluating the sine function model.
(b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
The Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers
board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the
ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board
over the course of the 15 min ride.
Height of Passenger in Ferris Wheel
180
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€120
Height, h (ft)
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Time of operation, t (min)
Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the passenger above the ground
measured in feet and t is the time of operation of the ride in minutes.
What is the period of the sine function model? Interpret the period you found in the context of the operation of
the Ferris wheel.
Answer:
Chapter 7 Solutions
Differential Equations and Linear Algebra (4th Edition)
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Prob. 5PCh. 7.1 - Given that v1=(2,1) and v2=(1,1) are eigenvectors...Ch. 7.1 - Prob. 7PCh. 7.1 - Prob. 8PCh. 7.1 - Prob. 9PCh. 7.1 - Prob. 11P
Ch. 7.1 - Prob. 12PCh. 7.1 - Prob. 13PCh. 7.1 - Prob. 14PCh. 7.1 - Prob. 15PCh. 7.1 - Prob. 16PCh. 7.1 - Prob. 17PCh. 7.1 - Prob. 18PCh. 7.1 - Prob. 19PCh. 7.1 - Prob. 20PCh. 7.1 - Prob. 21PCh. 7.1 - Prob. 22PCh. 7.1 - Prob. 23PCh. 7.1 - Prob. 24PCh. 7.1 - Prob. 25PCh. 7.1 - Prob. 26PCh. 7.1 - Prob. 27PCh. 7.1 - Prob. 28PCh. 7.1 - Prob. 29PCh. 7.1 - Prob. 30PCh. 7.1 - Prob. 31PCh. 7.1 - Prob. 32PCh. 7.1 - Find all eigenvalues and corresponding...Ch. 7.1 - If v1=(1,1), and v2=(2,1) are eigenvectors of the...Ch. 7.1 - Let v1=(1,1,1), v2=(2,1,3) and v3=(1,1,2) be...Ch. 7.1 - If v1,v2,v3 are linearly independent eigenvectors...Ch. 7.1 - Prove that the eigenvalues of an upper or lower...Ch. 7.1 - Prove Proposition 7.1.4.Ch. 7.1 - Let A be an nn invertible matrix. Prove that if ...Ch. 7.1 - Let A and B be nn matrix, and assume that v in n...Ch. 7.1 - Prob. 43PCh. 7.1 - Prob. 44PCh. 7.1 - Prob. 45PCh. 7.1 - Prob. 46PCh. 7.1 - Prob. 47PCh. 7.1 - Prob. 48PCh. 7.1 - Prob. 49PCh. 7.1 - Prob. 50PCh. 7.1 - Prob. 51PCh. 7.1 - Prob. 52PCh. 7.1 - Prob. 53PCh. 7.1 - Prob. 54PCh. 7.1 - Prob. 55PCh. 7.1 - Prob. 56PCh. 7.2 - Prob. 1PCh. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Problems For Problems 1-16, determine the...Ch. 7.2 - Prob. 10PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13PCh. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.2 - For problems 17-22, determine whether the given...Ch. 7.2 - Problems For Problems 17-22, determine whether the...Ch. 7.2 - Prob. 21PCh. 7.2 - Problems For Problems 17-22, determine whether the...Ch. 7.2 - Prob. 23PCh. 7.2 - Prob. 24PCh. 7.2 - For problems 23-28, determine a basis for each...Ch. 7.2 - The matrix A=[223113124] has eigenvalues 1=1 and...Ch. 7.2 - Repeat the previous question for A=[111111111]...Ch. 7.2 - The matrix A=[abcabcabc] has eigenvalues 0,0, and...Ch. 7.2 - Consider the characteristic polynomial of an nn...Ch. 7.2 - Prob. 33PCh. 7.2 - Prob. 34PCh. 7.2 - Prob. 35PCh. 7.2 - In problems 33-36, use the result of Problem 32 to...Ch. 7.2 - Prob. 37PCh. 7.2 - Prob. 38PCh. 7.2 - Let Ei denotes the eigenspace of A corresponding...Ch. 7.3 - Prob. 1PCh. 7.3 - Prob. 2PCh. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - Prob. 5PCh. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - Prob. 10PCh. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - For Problems 1822, use the ideas introduced in...Ch. 7.3 - For Problems 1822, use the ideas introduced in...Ch. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - For Problems 1822, use the ideas introduced in...Ch. 7.3 - For Problems 2324, first write the given system of...Ch. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - We call a matrix B a square root of A if B2=A. a...Ch. 7.3 - Prob. 29PCh. 7.3 - Prob. 30PCh. 7.3 - Prob. 31PCh. 7.3 - Let A be a nondefective matrix and let S be a...Ch. 7.3 - Prob. 34PCh. 7.3 - Prob. 35PCh. 7.3 - Show that A=[2114] is defective and use the...Ch. 7.3 - Prob. 37PCh. 7.4 - Prob. 1PCh. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Problems If A=[3005], determine eAt and eAt.Ch. 7.4 - Prob. 10PCh. 7.4 - Consider the matrix A=[ab0a]. We can write A=B+C,...Ch. 7.4 - Prob. 12PCh. 7.4 - Prob. 13PCh. 7.4 - Problems An nn matrix A that satisfies Ak=0 for...Ch. 7.4 - Prob. 15PCh. 7.4 - Prob. 16PCh. 7.4 - Prob. 17PCh. 7.4 - Problems Let A be the nn matrix whose only nonzero...Ch. 7.4 - Prob. 19PCh. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - True-False Review For Questions a-h, decide if the...Ch. 7.5 - Prob. 1PCh. 7.5 - Prob. 2PCh. 7.5 - Prob. 3PCh. 7.5 - Prob. 4PCh. 7.5 - Prob. 5PCh. 7.5 - Prob. 6PCh. 7.5 - Prob. 7PCh. 7.5 - Prob. 8PCh. 7.5 - Prob. 9PCh. 7.5 - Prob. 10PCh. 7.5 - Prob. 11PCh. 7.5 - Prob. 12PCh. 7.5 - Prob. 13PCh. 7.5 - Prob. 14PCh. 7.5 - Prob. 15PCh. 7.5 - Prob. 16PCh. 7.5 - Prob. 17PCh. 7.5 - Prob. 18PCh. 7.5 - Prob. 19PCh. 7.5 - Prob. 20PCh. 7.5 - The 22 real symmetric matrix A has two eigenvalues...Ch. 7.5 - Prob. 22PCh. 7.5 - Prob. 23PCh. 7.5 - Problems Problems 23-26 deal with the...Ch. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.6 - True-False Review For Questions a-l, decide if the...Ch. 7.6 - True-False Review For Questions a-l, decide if the...Ch. 7.6 - Prob. 3TFRCh. 7.6 - True-False Review For Questions a-l, decide if the...Ch. 7.6 - Prob. 5TFRCh. 7.6 - True-False Review For Questions a-l, decide if the...Ch. 7.6 - Prob. 7TFRCh. 7.6 - True-False Review For Questions a-l, decide if the...Ch. 7.6 - Prob. 9TFRCh. 7.6 - Prob. 10TFRCh. 7.6 - True-False Review For Questions a-l, decide if the...Ch. 7.6 - Prob. 12TFRCh. 7.6 - Prob. 1PCh. 7.6 - Prob. 2PCh. 7.6 - Prob. 3PCh. 7.6 - Prob. 4PCh. 7.6 - Prob. 5PCh. 7.6 - Prob. 6PCh. 7.6 - Prob. 7PCh. 7.6 - Prob. 8PCh. 7.6 - Prob. 9PCh. 7.6 - Prob. 10PCh. 7.6 - Prob. 11PCh. 7.6 - Prob. 12PCh. 7.6 - Prob. 13PCh. 7.6 - Prob. 14PCh. 7.6 - Prob. 15PCh. 7.6 - Problems Give an example of a 22 matrix A that has...Ch. 7.6 - Problems Give an example of a 33 matrix A that has...Ch. 7.6 - Prob. 18PCh. 7.6 - Prob. 19PCh. 7.6 - Prob. 20PCh. 7.6 - Prob. 21PCh. 7.6 - Problems For Problem 18-29, find the Jordan...Ch. 7.6 - Problems For Problem 18-29, find the Jordan...Ch. 7.6 - Prob. 26PCh. 7.6 - Problems For Problem 18-29, find the Jordan...Ch. 7.6 - Prob. 30PCh. 7.6 - Problems For Problem 30-32, find the Jordan...Ch. 7.6 - Problems For Problem 30-32, find the Jordan...Ch. 7.6 - Prob. 33PCh. 7.6 - Problems For Problem 33-35, use the Jordan...Ch. 7.6 - Problems For Problem 33-35, use the Jordan...Ch. 7.6 - Prob. 36PCh. 7.6 - Prob. 37PCh. 7.6 - Prob. 38PCh. 7.6 - Prob. 39PCh. 7.6 - Prob. 40PCh. 7.6 - Prob. 41PCh. 7.6 - Prob. 42PCh. 7.6 - Prob. 43PCh. 7.6 - Prob. 44PCh. 7.6 - Prob. 45PCh. 7.7 - Prob. 1APCh. 7.7 - Prob. 2APCh. 7.7 - Additional Problems In Problems 16, decide whether...Ch. 7.7 - Additional Problems In Problems 16, decide whether...Ch. 7.7 - Additional Problems In Problems 16, decide whether...Ch. 7.7 - Additional Problems In Problems 16, decide whether...Ch. 7.7 - Additional Problems In Problems 710, use some form...Ch. 7.7 - Additional Problems In Problems 710, use some form...Ch. 7.7 - Additional Problems In Problems 710, use some form...Ch. 7.7 - Prob. 10APCh. 7.7 - Prob. 11APCh. 7.7 - Prob. 12APCh. 7.7 - Prob. 13APCh. 7.7 - In Problems 13-16, write down all of the possible...Ch. 7.7 - In Problems 13-16, write down all of the possible...Ch. 7.7 - In Problems 13-16, write down all of the possible...Ch. 7.7 - Prob. 17APCh. 7.7 - Prob. 18APCh. 7.7 - Assume that A1,A2,,Ak are nn matrices and, for...Ch. 7.7 - Prob. 20AP
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