# Calculus

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A ladder 15 feet long leans against a vertical wall. Supppose that when the bottom of the ladder is x feet from the wall, the bottom is being pushed towards the wall at the rate of 1/2x feet per second. How fast is the top of the ladder rising at the moment the top is 5 feet from the floor?

• Calculus -

let the ladder be y ft above the ground

x^2 + y^2 = 15^2

when foot is x ft from wall
y^2 = 225-x^2
y = (225-x^2)^(1/2)

2x dx/dt + 2y dy/dt = 0
dy/dt = -2x dx/dt/(2y) = (-x dx/dt)/y

= -2x(1/2)x/√(225 - x^2)
= -x^2/√(225-x^2)

• Calculus -

07

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