A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter x,* as x₁.) lim n→∞ i=1 Ax Express the work as an integral. Evaluate the integral. ft-lb
A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter x,* as x₁.) lim n→∞ i=1 Ax Express the work as an integral. Evaluate the integral. ft-lb
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:A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the
bucket at a rate of 0.25 lb/s. Find the work done in pulling the bucket to the top of the well.
Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter x.* as x₁.)
n
2([
=1
Express the work as an integral.
lim
n→∞
Evaluate the integral.
ft-lb
Ax
dx
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