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Math Help - about rates

  1. #1
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    about rates

    Suppose a particle is moving along a path described by g(x)=x^2/((x-4)^2). At the point (3,9), the X-coordinate of the particle is decreasing at a rate of 2.4cm/s. At what rate is the y-coordinate of the particle changing?

    Please help! Thank you!
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  2. #2
    Eater of Worlds
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    You have y=x^2/(x-4)^2

    Rewrite as y(x-4)^2=x^2

    Now, differentiate implicitly wrt time.

    2y(x-4)x'+[(x-4)^2]y'=2xx'

    Solve for y' and we get:

    y'=[(2x-2xy+8y)/(x-4)^2]*x'

    Now, enter in x, y, and x' and find y'

    Remember, x' is decreasing so it is -2.4
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