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calculus

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A recatangle has constant area of 200 square meters and its lenght L is increasing at the rate of 4 meters per second
a) find the width W at the instant that the width is decreasing at the rate of .5 meters per second
b) at what rate is the diagonal d of the rectangle changing at the instant when the width is 10 meters?

  • calculus -

    A = 200 = W * L
    dL/dt = 4

    W = 200/L
    dW/dL = -200/L^2
    dW/dt = -(200/L^2)dL/dt

    if dW/dt = -.5
    then
    -.5 = -(200/L^2) * 4
    L^2 = 1600
    L = 40
    W = 200/40 = 5

    go through that again for W = 10 to get L, dW/dt
    then
    D^2 = L^2 + W^2
    2 D dD/dt = 2 L dL/dt + 2 W dW/dt

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