A heavy rope, 30 ft long, weighs 0.4 lb/ft and hangs over the edge of a building 80 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it. How much work W is done in pulling half the rope to the top of the building

180 fb*lb

45 ft*lb

Step-by-step explanation:

We have that the work is equal to:

W = F * d

but when the force is constant and in this case, it is changing.

 therefore it would be:

Where a = 0 and b = 30.

F (x) = 0.4 * x

Therefore, we replace and we would be left with:

We integrate and we have:

W = 0.4 / 2 * x ^ 2

W = 0.2 * (x ^ 2) from 0 to 30, we replace:

W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)

W = 180 ft * lb

Now in the second part it is the same, but the integral would be from 0 to 15.

we replace:

W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)

W = 45 ft * lb

answer: 230 miles ( vote ! )

step-by-step explanation:

180.39 minus 17.99 equals 162.4

then divide 162.4 by .80 to get 230