Calculus

the side of an equilateral triangle decreases at a rate of 3cm/s. at what rate is the area decreasing when the area is 150cm squared?

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  1. altitude = (s/2)sqrt3
    A = (s/2) (s/2) sqrt 3 = (s^2/4) sqrt3
    dA/dt = (2 s/4) sqrt3 ds/dt
    = (s/2) sqrt 3 * (-3)
    = (-3s/2) sqrt 3
    now what is s when A = 150?
    (s^2/4) sqrt 3 = 150
    s^2 = 600/sqrt3
    so
    dA/dt = (-3/2) sqrt3 (sqrt 600)/3^.25
    = (-3/2)(sqrt600)(3^.25)

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