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calculus

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A boat sails 30 miles to the east from a point P, then it changes direction and sails to the south. If this boat is sailing at a constant speed of 10 miles/hr, at what rate is its distance from the point P increasing
a) 2 hours after it leaves the point P
b) 7 hours after it leaves the point p

  • calculus -

    at 10 mph, it is still going east at t=2
    so, distance is increasing at 10 mph

    at t=3, it turns south. After that, the distance d from P is

    d^2 = 30^2 + (10(t-3))^2
    since it has only been sailing south for (t-3) hours.

    2d dd/dt = 200(t-3)
    at t=7, d=50
    2*50 dd/dt = 200(4)
    dd/dt = 8 mph

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