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Calculus Practice Problems

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The height of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 square cm/min. At what rate is the base of the triangle changing when the height is 7 centimeters and the area is 91 square centimeters?

  • Calculus Practice Problems -

    A = (1/2) b h

    dA/dt = (1/2)(b dh/dt + h db/dt)

    given: dA/dt = 2 , dh/dt = 1 , A = 91 , h = 7 ,

    we need the base b,
    from A = 1/2)bh
    91 = (1/2)(7b)
    182 = 7b
    b = 26

    2 = (1/2)(26(1) + 7db/dt)
    4 = 23 + 7db/dt
    db/dt = -19/7 cm/min

    At that moment, the base is decreasing at 19/7 cm/min

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