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an air plane is flying at a height of 6 miles on a flight path that will take it directly over a radar tracking station. the distance d between them is decreasing at a rate of 400 miles per hour when the distance between them is 10 miles. what is the speed of the plane?

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500 mph is the speed of the plane.

This creates a right triangle, with the distance between the plane and the radar station serving as the hypotenuse (s). Let y represent the plane's height and x represent its flight route.

s2 = y2 + x2

Given: the constant value of y = 6

negative since decreasing, ds/dt = -400

Trying to locate dx/dt

Taking the implicit derivative of the above equation's two sides

0 + 2xdx/dt = 2sds/dt

(S/X) ds/dt = dx/dt

When x = 8

s = √(62+82) = √100 = 10

dx/dt = (10/8)(-400) = -500 mph, or 500 mph traveling toward the radar station at a distance of 6 miles.

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