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Calculus

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at noon A is 150 km west of a ship B .Ship A is sailling east at 35 km/h , and ship B is sailling north at 25 km/h. How fast is the distance between the ships changing at 4 pm ?

  • Calculus - ,

    the distance between the ships at time t is

    d^2 = (150-35t)^2 + (25t)^2
    at t=4,
    d^2 = (150-140)^2 + (100)^2 = 100 + 10000 = 10100, so d=100.5

    2d dd/dt = 2(150-35t)(-35) + 2(25t)(25)
    at t=4,

    201 dd/dt = -700 + 5000
    dd/dt = 21.39km/h

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