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A leaky 10-kg bucket is lifted from the ground to a height of 10 m at a constant speed with a rope that weighs 0.5 kg/m. Initially the bucket contains 30 kg of water, but th water leaks at a constant rate and finishes draining just as the bucket reaches the 10-m level. Find the work done. (Use 9.8 m/s? for g.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter x;* as xj.) ) ax lim i= 1 Express the work as an integral. dx Evaluate the integral. (Round your answer to the nearest integer.)

A leaky 10-kg bucket is lifted from the ground to a height of 10 m at a constant speed with a rope that weighs 0.5 kg/m. Initially the bucket contains 30 kg of water, but th water leaks at a constant rate and finishes draining just as the bucket reaches the 10-m level. Find the work done. (Use 9.8 m/s? for g.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter x;* as xj.) ) ax lim i= 1 Express the work as an integral. dx Evaluate the integral. (Round your answer to the nearest integer.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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A leaky 10-kg bucket is lifted from the ground to a height of 10 m at a constant speed with a rope that weighs 0.5 kg/m. Initially the bucket contains 30 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 10-m level. Find the work done. (Use 9.8 m/s? for g.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter x;* as xj.) n ). lim Ax i = 1 Express the work as an integral. dx Evaluate the integral. (Round your answer to the nearest integer.)
Transcribed Image Text:A leaky 10-kg bucket is lifted from the ground to a height of 10 m at a constant speed with a rope that weighs 0.5 kg/m. Initially the bucket contains 30 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 10-m level. Find the work done. (Use 9.8 m/s? for g.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter x;* as xj.) n ). lim Ax i = 1 Express the work as an integral. dx Evaluate the integral. (Round your answer to the nearest integer.)
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