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Math Help - Calc related rates

  1. #1
    Junior Member
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    Calc related rates

    Hello, can someone please help me to set this problem up. Let theta(in radians) be an acute angle in a rt triangle, and let x and y respectively be the lengths of the sides adj and opp to theta. Suppose x and y vary with time.

    At a certain instant, x =2 units and is increasing at 1 unit/s, while y = 2 units and is decreasing at 1/4 unit/s. How fast is theta chaning at that instant?

    I know the answer is d0/dt = cos^0/x^O(x(dy/dt) - y(dx/dt) where I am representing 0 as theta.

    Thanks,
    Pantera
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  2. #2
    MHF Contributor Calculus26's Avatar
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    tan(q) = y/x

    sec^2(q)dq/dt = [xdy/dt - ydx/dt]/x^2


    when x = 2 = y q = pi/4 seq(q) = sqrt(2)

    2dq/dt = [-1/2-2]/4

    dq/dt = -5/16 rad/s
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