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AP Calculus AB· difficulty 4/5

A 13-ft ladder leans against a wall. The bottom slides away at 2 ft/s. When the bottom is 5 ft from the wall, how fast (in ft/s) is the top sliding down?

  • A

    213\frac{2}{13}

  • B

    125\frac{12}{5}

  • C

    22

  • D

    56\frac{5}{6}

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Explanation

x2+y2=169x^2+y^2=169. At x=5x=5: y=12y=12. Differentiate: 2xx+2yy=02x\,x'+2y\,y'=0. 5(2)+12y=0y=10/12=5/65(2)+12 y'=0 \Rightarrow y' = -10/12 = -5/6. Speed downward = 5/6 ft/s.

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