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Math Help - story problem implicit differentiation

  1. #1
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    story problem implicit differentiation

    please someone smart help to get me going, i dont know how to start these

    "A 20 foot ladder is leaning against a building. The bottom of the ladder is sliding along the pavement directly away from the building at 1 foot per second. How fast is the top of the ladder moving down when the foot of the ladder is 5 feet away from the wall?"

    i know this uses the pythagorean theorem somehow... i dont know what to do though
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Pythagoras Theorem


     <br />
\frac{dx}{dt}= 1<br />

    x^2+y^2 = 400

    Differentiate both sides with respect to t

    Hence

     <br />
2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0<br />

    Put  \frac{dx}{dt} =1

    So

     <br />
\frac{dy}{dt}  = \frac{- 2x}{2y} <br />

     <br />
\frac{dy}{dt} = \frac{-x}{y}<br /> <br />
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