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 -

    The distance from point P after t hours is
    d = sqrt[30^2 + (10 t)^2]
    = sqrt(900 + 100 t^2)
    dd/dt = [ (1/2)/( sqrt(900 + 100 t^2)]*200 t

    Plug in the t value and compute the corresponding rate of change of d

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