A cable that weighs 6 lb/ft is used to lift 500 lb of coal up a mine shaft 400 ft deep. Find the work done. 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.)

8.2 *10^5 ft lb

Step-by-step explanation:

Wcoal = 800*500  = 400000 = 4*10^5 ft lb

Using a right Riemann sum

The width of the entire region to be estimated = 400 - 0 = 400

Considering 8 equal subdivisions, then the width of each rectangular division is 400/8 = 50

F(x) = 6(400-y)

Wrope = 50(2100) + 50(1800) + 50(1500) + 50(1200) + 50(900) + 50(600)

+ 50(300) + 50(0) = 420000 = 4.2 * 10^5 ft lb

Note: Riemann sum is an approximation, so may not give a accurate value

work done =  Wcoal + Wrope= 4*10^5+ 4.2 * 10^5 = 8.2 *10^5 ft lb

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step-by-step explanation:

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