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A plane flying with a constant speed of 19 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 25 degrees. At what rate is the distance from the plane to the radar station increasing 3 minutes later?
The distance is increasing at

  • calculas -

    The plane's x- and y- speed is

    dx/dt = 19 cos 25°
    dy/dt = 19 sin 25°

    At time t, the distance z is

    z^2 = x^2 + (y+4)^2
    2z dz/dt 2x dx/dt + 2(y+4) dy/dt.

    Now just figure x,y,z at t=3, and plug in the values.

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