7. Consider the curve given by y = f(x) = 2xe-1.25x + (30-x)e-0.25(30-x) b. Let x and y be measured in inches. Find the total volume of the baseball bat generated by revolving the given curve about the x-axis. Include units on your answer. c. Suppose that the baseball bat has constant weight density, and that the weight density is 0.6 ounces per cubic inch. Find the total weight of the bat whose volume you found in (b). d. Because the baseball bat does not have constant cross-sectional area, we see that the amount of weight concentrated at a location x along the bat is determined by the volume of a slice at location x. Explain why we can think about the function p(x) = 0.67f(x)² (where f is the function given at the start of the problem) as being the weight density function for how the weight of the baseball bat is dis- tributed from x = 0 to x = 30.
7. Consider the curve given by y = f(x) = 2xe-1.25x + (30-x)e-0.25(30-x) b. Let x and y be measured in inches. Find the total volume of the baseball bat generated by revolving the given curve about the x-axis. Include units on your answer. c. Suppose that the baseball bat has constant weight density, and that the weight density is 0.6 ounces per cubic inch. Find the total weight of the bat whose volume you found in (b). d. Because the baseball bat does not have constant cross-sectional area, we see that the amount of weight concentrated at a location x along the bat is determined by the volume of a slice at location x. Explain why we can think about the function p(x) = 0.67f(x)² (where f is the function given at the start of the problem) as being the weight density function for how the weight of the baseball bat is dis- tributed from x = 0 to x = 30.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7.
Consider the curve given by y = f(x) = 2xe-1.25x + (30-x)e-0.25(30-x)
b. Let x and y be measured in inches. Find the total volume of the baseball bat
generated by revolving the given curve about the x-axis. Include units on your
answer.
c. Suppose that the baseball bat has constant weight density, and that the weight
density is 0.6 ounces per cubic inch. Find the total weight of the bat whose volume
you found in (b).
d. Because the baseball bat does not have constant cross-sectional area, we see that
the amount of weight concentrated at a location x along the bat is determined by
the volume of a slice at location x. Explain why we can think about the function
p(x) = 0.67f(x)² (where f is the function given at the start of the problem) as
being the weight density function for how the weight of the baseball bat is dis-
tributed from x = 0 to x = 30.
e. Compute the center of mass of the baseball bat.
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