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A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 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 Express the work as an integral. Evaluate the integral. ft-lb

A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 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 Express the work as an integral. Evaluate the integral. ft-lb

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 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 x¡.) (1 Express the work as an integral. lim n→∞ i=1 Evaluate the integral. ft-lb Ax dx
Transcribed Image Text:A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 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 x¡.) (1 Express the work as an integral. lim n→∞ i=1 Evaluate the integral. ft-lb Ax dx
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