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The altitude of a triangle is increasing at a rate of 1500 centimeters/minute while the area of the triangle is increasing at a rate of 1000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 99000 square centimeters?

  • math - ,

    This is a calculus problem.
    When the altitude H is 1000 and the area A is 99000, the base width is
    B = 2A/B =2*99,000/ 10,000 = 198 cm

    A = (1/2)*altitude*base = H*B/2

    dA/dt = (1/2)[H*dB/dt + B*dH/dt]
    1000 = (1/2)[1000*dB/dt + 198*1500]
    solve for dB/dt in cm per minute

    1000 = (1/2)[10,000dB/dt + 198*dH/dt]

  • math - ,

    for dB/dt, i got -295 is that correct?
    so i just plug it in to find dH/dt?

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