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Math Help - Derivatives related

  1. #1
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    Derivatives related

    If x^2 +y^2 =25 and dy/dt = 6, find dx/dt when y = 4

    When I did this, I got positive and negative three, but that can't be right. What is the right way to do this?
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  2. #2
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    The curve is the circle of radius 5, at y=4, which means x could be -3 or 3.

    Fully differentiate:

    2x x' + 2y y' = 0

    x x' + y y' = 0

    x x' + 4*6 = 0

    x' = 24/x

    so dx/dt is 8 or -8.

    Only one answer is expected here?
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  3. #3
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    Quote Originally Posted by bobsanchez View Post
    If x^2 +y^2 =25 and dy/dt = 6, find dx/dt when y = 4

    When I did this, I got positive and negative three, but that can't be right. What is the right way to do this?
    x^2+y^2=5^2
    is a circle centred at the origin (0,0) with radius=5.

    Hence, when y=4,

    x^2+16=25\ \Rightarrow\ x^2=9\ \Rightarrow\ x=\pm3

    The radius is unchanging..

    \frac{d}{dt}\left(x^2+y^2\right)=0

    \frac{dx}{dt}\frac{d}{dx}x^2+\frac{dy}{dt}\frac{d}  {dt}y^2=0

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

    Solve this at (3,4) and (-3,4).

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  4. #4
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    No, two answers were expected.
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