Calculus

Two ships leave the same port at noon. Ship A sails north at 22 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

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  1. after t hours, the distance d is given in terms of the distances x east and y north,

    d^2 = x^2 + y^2
    2d dd/dt = 2x dx/dt + 2y dy/dt

    at 1:00, x=12 and y=22, so
    d^2 = 12^2 + 22^2
    d = 25

    so,

    2*25 dd/dt = 2(12)(12) + 2(22)(22)
    dd/dt = 25.12 mi/hr

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  2. QUESTION 3

    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

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