Show how to approximate the required work by a Riemannsum. Then express the work as an integral and evaluate it. A bucket that weighs 4 lb and a rope of negligible weightare used to draw water from a well that is 80 ft deep. Thebucket is filled with 40 lb of water and is pulled up at a rateof  2ft/s , but water leaks out of a hole in the bucket at a rateof 0.2lb/s . Find the work done in pulling the bucket to thetop of the well.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 54AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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Show how to approximate the required work by a Riemann
sum. Then express the work as an integral and evaluate it.

A bucket that weighs 4 lb and a rope of negligible weight
are used to draw water from a well that is 80 ft deep. The
bucket is filled with 40 lb of water and is pulled up at a rate
of  2ft/s , but water leaks out of a hole in the bucket at a rate
of 0.2lb/s . Find the work done in pulling the bucket to the
top of the well.

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