# calculus

A cable hangs between two poles of equal height and 40 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x) = 10+(0.1)*(x^1.5). The cable weighs 19.2 pounds per linear foot. Find the weight of the cable.

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1. h' = 3/20 √x

the length of cable is

s = 2∫[0,20] √(1+h'^2) dx
= 2∫[0,20] √(1+9x/400) dx
= 44.2 ft

Now figure the weight.

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