# Calculus

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A 20' ladder leans against a building. The bottom of the ladder is sliding away horizontally at a rate of 2 feet per second. How fast is the top of the ladder sliding down the building when it is 12' above the ground?

• Calculus -

If you draw a diagram, let x be the distance of the base of the ladder from the wall, and h the height of the ladder against the wall:

x^2 + h^2 = 400

When h = 12,
x^2 = 400 - 144 = 256
x = 16

2x dx/dt + 2h dh/dt = 0
32 * 2 + 24 dh/dt = 0
dh/dt = -64/24 = -8/3

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