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Answer:
The rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.
Step-by-step explanation:
Given information:
A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station.
We need to find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.
According to Pythagoras
.... (1)
Put z=1 and y=2, to find the value of x.
Taking square root both sides.
Differentiate equation (1) with respect to t.
Divide both sides by 2.
Put , y=2,
in the above equation.
Divide both sides by 2.
Therefore the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.
