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calculus

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1. A rectangle has a constant area of 200 square meters and its length L is increasing at the rate of 4 meters per second.

a. Find the width W at the instant the width is decreasing at the rate of .4 meters per second.
b. At what rate is the diagonal D of the rectangle changing at the instant when the width W is 10 meters?

  • calculus - ,

    lw=200
    l dw/dt+ W dl/dt=0
    given dl/dt=4
    a) find w then dw/dt=-.4
    -.4*L+W*4=0
    but remember LW=200 or L=200/W
    -.4*200/W+4W=0
    solve for W

    b. diagonal D.

    D= sqrt(L^2+W^2
    dD/dt= 1/2 *1/sqrt( ) * (2L dl/dt+ 2W dw/dt)

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