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Math Help - Related rates problem -- Am I right??

  1. #1
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    Related rates problem -- Am I right??

    Q: Point A moves along the x-axis at the constant rate of 8ft/sec while point B moves along the y-axis at the constant rate of 10ft/sec. Find how fast the distance between them is changing when A is at the point (10,0) and B is at the point (0,8).

    z^2 = x^2 + y^2
    x = 10
    y = 8
    z = sqrt(10^2 + 8^2) --> sqrt(164)
    x' = 8
    y' = 10
    want to find z'

    2z*dz/dt = 2x*dx/dt + 2y^dy/dt
    dz/dt = [2x(dx/dt) + 2y(dy/dt)] / 2z
    dz/dt = [2*8*10 + 2*8*10] / 2z
    dz/dt = 320 / 2z
    dz/dt = 160 / sqrt(164) --> FINAL ANSWER!
    Last edited by golfman44; December 4th 2009 at 01:11 AM.
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  2. #2
    Senior Member
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    hope this'll help you

    z^2 = x^2 + y^2 then

    2z \frac{dz}{dt} = 2x \frac{dx}{dt} + 2y\frac{dy}{dt}
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  3. #3
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    Joined
    Oct 2009
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    OK, using that i redid the problem and got:

    z^2 = x^2 + y^2
    x = 10
    y = 8
    z = sqrt(10^2 + 8^2) --> sqrt(164)
    x' = 8
    y' = 10
    want to find z'

    2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)
    dz/dt = [2x(dx/dt) + 2y(dy/dt)] / 2z
    dz/dt = [2*8*10 + 2*8*10] / 2z
    dz/dt = 320 / 2z
    dz/dt = 160 / sqrt(164) --> FINAL ANSWER!
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