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Math Help - Sliding Ladder (Related Rates)

  1. #1
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    Sliding Ladder (Related Rates)

    I'm taking Calculus in College, and im doing a problem with related rates, involving a ladder. I took Calculus in High School, and I was never good at the triangular related rates problems, I don't know why. Anyway:

    A 13ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at a rate of 5ft/sec

    A. how fast is the top of the ladder sliding down the wall then?
    B. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
    C At what rate is the angle theta between the ladder and the ground moving then?

    maybe if you could just help on the first part of that problem, then maybe I can get the rest, but I need to get started on it, cause im not quite sure. Thanks!
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  2. #2
    Eater of Worlds
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    Part a:

    We have x^{2}+y^{2}=169

    Differentiate:

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

    Sub in your knowns and solve for dy/dt.

    part b:

    A=\frac{1}{2}xy

    \frac{dA}{dt}=\frac{1}{2}(x\frac{dy}{dt}+y\frac{dx  }{dt})

    Plug in your knowns from before.

    part c:

    Can you get this one by using tan?.
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