Calculus (related rates)

A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.4 m/sec. How fast is the top sliding down the wall when the foot of the ladder is 5 m from the wall?

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  1. If the base of the ladder is x feet from the wall, and the ladder reaches up y feet, then we have

    x^2 + y^2 = 13^2

    taking derivatives wrt t,

    x dx/dt + y dy/dt = 0

    Now just plug in your numbers and solve for dy/dt

    (note that at the moment in question, you conveniently have a 5-12-13 right triangle.)

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