## 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 requ

Question

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.)

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2021-11-23T17:37:09+00:00
2021-11-23T17:37:09+00:00 1 Answer
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## Answers ( )

Answer:8.2 *10^5 ft lbStep-by-step explanation:Wcoal = 800*500 = 400000 = 4*10^5 ft lbUsing a right Riemann sumThe width of the entireregion to be estimated

=400 – 0 = 400Considering 8 equal subdivisions, then the width of each rectangular division is 400/8

=50F(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 lbNote: Riemann sum is an approximation, so may not give a accurate valuework done = Wcoal +Wrope= 4*10^5+ 4.2 * 10^5 = 8.2 *10^5 ft lb