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AP Calculus

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Two ships sail from the same port. The first ship leaves port at 1:00a, and travels eastward at a rate of 15 knots. the second ship leave port at 2:00am and travels northward at a rate of 10 knots. Determine the rate at which the ships are separating at 3:00am

  • AP Calculus -

    the distance d between the ships is

    d^2 = x^2 + y^2
    2d dd/dt = 2x dx/dt + 2y dy/dt
    at 3:00 am, x=30 and y=10, d=10√10

    20√10 dd/dt = 2(30)(15) + 2(10)(10)
    dd/dt = 1100/10√10 = 110/√10 = 11√10

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