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March 29, 2017

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A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? Evaluate your answer numerically. (Round the answer to three decimal places.)

  • Math - ,

    Use the Pyth theorem:

    10^2=base^2 + height^2 You know the base, find the height.

    Now, to work the rates...
    take the derivative of the pyth theorem
    0=2b db/dt + 2h dh/dt
    so dh/dt=-b/h db/dt
    Now you know b, h, and db/dt solve for dh/dt.

  • Math - ,

    1.6

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