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Math Help - Related Rates - Check my work please

  1. #1
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    Related Rates - Check my work please

    A point moves on the hyperbola x^2-4y^2=36 in such a way that the x-coordinate increases at a constant rate of 20 units per second. How fast is the y-coordinate changing at the point (10,4)?

    4y^2=x^2-36

    8y*\frac{dy}{dt}=2x*\frac{dx}{dt}-0

    \frac{dy}{dt}=\frac{2x*\frac{dx}{dt}}{8y}

    \frac{dy}{dt}=\frac{(2)(10)(20)}{(8)(4)}

    \frac{dy}{dt}=\frac{400}{32}=\frac{25}{2} units per second is what I come up with.

    The book, however, provides an answer of 50 units/sec

    Did I mess this one up?
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  2. #2
    A Plied Mathematician
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    I don't see any errors in your derivation. I would say the book is wrong.
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  3. #3
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    Makes me feel good when I win one of these every now and then
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  4. #4
    A Plied Mathematician
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    Makes me feel good when I win one of these every now and then.
    Naturally. Have a good one!
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