Aplane flying horizontally at an altitude of 1 mi and a speed of 480 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station. (round your answer to the nearest whole number.)

465 mi/h

Step-by-step explanation:

= Velocity of plane = 480 mi/h

a = Distance plane travels when it is 4 mi away from radar

= Velocity of plane with respect to height = 0 mi/h (altitude is not changing)

b = Horizontal distance between plane and radar = 1 mi

c = Distance between plane and radar after some time = 4 mi

From Pythagoras theorem

a²+b² = c²

⇒a = √(c²-b²)

⇒a = √(4²-1²)

⇒a = √15 mi

a²+b² = c²

Now, differentiating with respect to time

∴ Rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station is 465 mi/h

25

step-by-step explanation: