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Problem 4 - Entrance Test

A ladder 10 ft long leans against a wall. The foot of the ladder slides away at 1 ft/s. How fast is the top sliding down when the foot is 6 ft from the wall (in ft/s)?

Correct: B

x² + y² = 10². Given dx/dt = 1, x = 6 → y = 8. Differentiate: 2x dx/dt + 2y dy/dt = 0 → dy/dt = –x/y = –6/8 = –0.75 ft/s (downward).