given:
x^2 + y^2 = 25^2
dx/dt = 2
when x=7, y=25
x dx/dt + y dy/dt = 0
plug in your numbers to find dy/dt
a = 1/2 xy
da/dt = 1/2 (y dx/dt + x dy/dt)
tanθ = y/x
sec^2θ dθ/dt = (x dy/dt - y dx/dt)/y^2
A ladder 25 feet is leaning against the wall of the house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.
how fast is the top of the ladder moving down the wall when the base is the ladder is 7 feet away from the wall?
Consider the triangle formed by the side of the house the ladder and the ground. Find the rate at which the area is changing when the base of the ladder is 7 feet from the wall.
Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.
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