# math

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A 16-ft ladder is sliding down a wall as shown in the figures below. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. Suppose that the top is sliding down the wall at a rate 5 ft/s. Calculate dx/dt when h = 10. Give your answer correct to two decimal places.

dx/dt = ? ft/s

• math -

The ladder forms a rt. triangle with the wall and ground. The wall is the
height.When the height is 10ft,
X^2+10^2=16^2, X=12.49ft. When h goes to zero(ladder flat on ground),
X^2+0^2=16^2, X=16, t=10ft/5ft/s=2sec.

dx/dt=(16-12.49)ft/2s=1.75ft/s

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