Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Textbook Question
Chapter 7.1, Problem 2E
Show that the solutions to the BVPs in Exercise 1 are
(a)
(b)
(c)
(d)
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(b)
t+1)dt
2. The Batmobile travels in a straight line such that t seconds after passing through Arkham, its
velocity v(t) in meters per second is given by
v(t) = 5t3 + (20 – 30k)t² – 100kt + 200k + 50
where k is constant.
(a) Find an expression for the acceleration of the Batmobile in terms of k and t.
(b) Suppose that the acceleration of the Batmobile five seconds after passing through Arkham
is 175 m/s?. Determine the value of k five seconds after passing through Arkham.
(c) Using the value of k from item (b), find the range of values of t for which the Batmobile
is accelerating positively.
(d) Using the value of k from item (b), determine the values of t when the Batmobile is
accelerating at its fastest and slowest within six seconds of passing through Arkham.
Write the equation
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dt
dr
in the form of
+p(t)x=q(t). Then identify p(t) and q(t).
dt
Select one:
O a. da
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9(t)=e
1
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dt
p(t)=-
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Chapter 7 Solutions
Numerical Analysis
Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Apply the Shooting Method to the linear BVPs....
Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CPCh. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SACh. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SACh. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CPCh. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...
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- An object is moving along a horizontal path with its position modeled by the equation x (t) = t³ – 2t? 3t , where position is measured in meters and time in seconds. What is its position x(t), velocity v(t) and acceleration a(t) at time t = 1? O x(1) = 4, v(1) = -2, and a(1) = 2. O x(1) = 4, v(1) = -4, and a(1) = -2 O x(1) = -4, v(1) = 4, and a(1) = 2. O x(1) = -4, v(1) = -4, and a(1) = 2.arrow_forwardI ALMOST know how to do this one, but I need help, please.arrow_forwardPlease help me to understand how to solve step-by-step.arrow_forward
- Let V(t) = t – 6t + 8 represent the velocity after t seconds of an object in meters per second. (a) What is the object's initial velocity? The object's initial velocity is i meters per second.arrow_forwardg(x) gʻ(5) = 2 x 13 1+t² dtarrow_forwardIf s (t) = 4t3 – 3t describes the position of a particle moving along a straight path where s (t) is measured in meters and t is measured in seconds. The acceleration of the particle at 10 seconds is 1197 meters per second squared. True Falsearrow_forward
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