Aplane flying horizontally at an altitude of 1 mile and a speed of of 500mih passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it is 2mi away from the station.

447.2 mph

Explanation:

The vertical distance from the plane to the station is 1 mile.

The horizontal distance from the plane to the station is x miles.

The distance between the plane and station is therefore:

d² = 1² + x²

Taking derivative with respect to time:

2d dd/dt = 0 + 2x dx/dt

d dd/dt = x dx/dt

We know that x = 2 miles and dx/dt = 500 mi/hr.  We need to find d when x=2.

d² = 1² + 2²

d² = 5

d = √5

Therefore:

√5 dd/dt = (2) (500)

dd/dt = 1000/√5

dd/dt = 200√5

dd/dt ≈ 447.2 mph

a high pressure system is a dense air mass that is usually cooler and drier than the surrounding air. a low pressure system is a less dense air mass that is usually wetter and warmer than the surrounding air.

in general, areas that experience high atmospheric pressure also experience fair weather. low pressure systems can cause the formation of clouds and storms. air usually flows from areas of high pressure to areas of low pressure..

explanation:

newton's third law, for every action there is an equal and opposite reaction.