# Math

A 15 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec.

Find the velocity of the top of the ladder at time t=3.

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1. Let the foot of the ladder be x feet from the wall
let the height of the ladder be y feet

then x^2 + y^2 = 225

differentiate with respect to t, this is a "related rate problem"

2x dx/dt + 2y dy/dt = 0 (1)

when t=3 sec,
x = 9 feet (you knew the rate)
then 81+y^2=225
y=12 feet

sub x=9, y=12, dx/dt = 3 into (1) and solve for dy/dt

I got dy/dt = -9/4 ft/sec

(the negative value shows that y was decreasing at 9/4 ft/sec at that instant)

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2. a building is 3ft. from a 8ft. fence that surround propert a worker wants to wash a window in the building 13ft. from the ground. he will need what size ft. ladder

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