A cable that weighs 6 lb/ft is used to lift 800 lb of coal up a mine shaft 450 ft deep. Find the work done.A.) Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)B.) Express the work as an integral.C.)Evaluate the integral.

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Asked Dec 2, 2019
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A cable that weighs 6 lb/ft is used to lift 800 lb of coal up a mine shaft 450 ft deep. Find the work done.

A.) Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)

B.) Express the work as an integral.

C.)Evaluate the integral.

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Expert Answer

Step 1

Given that a cable that weighs 6 lb/ft is used to lift 800 lb of coal up a mine shaft 450 ft deep

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To find: a) To show the required work done using Riemann sum

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Step 2

To begin with we consider the following assumption.

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Let work done on the cable be Weable We'll divide the cable into segments. Let x be the distance from top of the shaft to the segment. Let Ax be the length of the segment Work done on a segment = Weight of the segment X Vertical distance travelled Work Done бДх хх — бхДх

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Step 3

b) Now, express the work...

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450 Therefore, Weable = 6xdx cab

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Math

Calculus