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Math Help - Related Rates

  1. #1
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    Related Rates

    Equation; y = 2(x^2 - 3x)

    Find;
    a) dy/dt
    b) dx/dt

    Given;
    a) x = 3, dx/dt = 2
    b) x = 1, dy/dt = 5

    How do I go about solving this? I'm confused as to the procedure I need to use. A step-by-step solution would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by Archduke01 View Post
    Equation; y = 2(x^2 - 3x)

    Find;
    a) dy/dt
    b) dx/dt

    Given;
    a) x = 3, dx/dt = 2
    b) x = 1, dy/dt = 5

    How do I go about solving this? I'm confused as to the procedure I need to use. A step-by-step solution would be greatly appreciated.
    y = 2(x^2 - 3x)
    and we are assuming that the functions x = x(t) and y = y(t). So we do this implicitly:

    \frac{dy}{dt} = 4x \frac{dx}{dt} - 6 \frac{dx}{dt}

    Thus for part a you have x = 3 and dx/dt = 2 so
    \frac{dy}{dt} = 4(3)(2) - 6(2) = 12

    You try the second one.

    -Dan
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    Quote Originally Posted by topsquark View Post
    y = 2(x^2 - 3x)
    and we are assuming that the functions x = x(t) and y = y(t). So we do this implicitly:

    \frac{dy}{dt} = 4x \frac{dx}{dt} - 6 \frac{dx}{dt}

    Thus for part a you have x = 3 and dx/dt = 2 so
    \frac{dy}{dt} = 4(3)(2) - 6(2) = 12

    You try the second one.

    -Dan
    Thank you. I just have one last question; how would you implicitly derive this function; xy = 4? It is of the same topic.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Archduke01 View Post
    Thank you. I just have one last question; how would you implicitly derive this function; xy = 4? It is of the same topic.
    xy is a product. Thus:
    \frac{dx}{dt}y + x \frac{dy}{dt} = 0

    -Dan
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  5. #5
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    I'm having trouble with something. The topic question was fine because it only had 3 variables, 2 of which were given, so you just had to isolate the 3rd one and solve for it. But for this one, there's 4 variables; xy' + x'y = 0. You're asked to find the value for y' while given x and x'. How could I solve that? I have 2 unknown variables. (y' and y)

    BTW; x = 8, x' = 10.
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