Posted by Stacy on Wednesday, February 22, 2012 at 4:02pm.
a ladder is 20 feet long and its top is slidding at a constant rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground when the bottom is 16 feet from the wall?

Calculus  Reiny, Wednesday, February 22, 2012 at 5:10pm
Let the ladder be x ft from the wall, and y ft up along the wall
x^2 + y^2 = 20^2
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
when x=16 , y^2 = 400256 > y = 12
and dy/dt = 2 ft/sec
16(dx/dt) + 12(2) = 0
dx/dt = 24/16 = 3/2
the ladder is moving away from the wall at 1.5 ft/s

Calculus  Reiny, Wednesday, February 22, 2012 at 5:11pm
last two lines should have been
16(dx/dt) + 12(2) = 0
dx/dt = 24/16 = 3/2
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