AP Calculus ABhardmcq1 pt
A ladder 10 ft long leans against a wall. The bottom slides away at 2 ft/s. When the bottom is 6 ft from the wall, how fast is the top sliding down?
A.1.5 ft/s
B.3 ft/s
C.2.5 ft/s
D.1 ft/s
Explanation
Core Concept
By Pythagorean theorem: x² + y² = 100. Differentiating: 2x(dx/dt) + 2y(dy/dt) = 0. When x = 6, y = 8. So 2(6)(2) + 2(8)(dy/dt) = 0, giving dy/dt = -24/16 = -1.5 ft/s (sliding down).
Correct Answer
A1.5 ft/s
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