Use a graphing utility to graph the functions of the form d = a − a cos ω t and comment on the role of the damping factor c > 0 in the equation. a. d = 6 e − 0.1 t cos π t b. d = 6 e − 0.3 t cos π t c. d = 6 − 0.5 t cos π t
Use a graphing utility to graph the functions of the form d = a − a cos ω t and comment on the role of the damping factor c > 0 in the equation. a. d = 6 e − 0.1 t cos π t b. d = 6 e − 0.3 t cos π t c. d = 6 − 0.5 t cos π t
Solution Summary: The author explains how the graph of the function, d=6e-0.1tmathrmcospi t, and the damping factor are calculated.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
University Calculus: Early Transcendentals (4th Edition)
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