• anonymous
A plane flying with a constant speed of 180 km/h passes over a ground radar station at an altitude of 2 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)
  • Stacey Warren - Expert
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  • chestercat
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  • phi
Here is an outline on how to do this, using calculus |dw:1332284822147:dw| all units in km. d is how far the plane moved in 1 minute (180 km/hour * 1/60 hour) r is the distance between the plane and the station using the law of cosines: \[ r^2= d^2 + 2^2 - 2dcos(120º) \] solve for r when d= 3 km (one min of flying) take the derivative wrt time: \[2 r \frac{dr}{dt}= 2 d \frac{dd}{dt} + \frac{dd}{dt}\] the plane is moving at dd/dt (sorry about choosing d!) = 3 km/min plug r, dd/dt, d into the equation and solve for dr/dt

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