Aplane flying horizontally at an altitude of 2 mi and a speed of 510 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 3 mi away from the station. (round your answer to the nearest whole number.)

P is the plane's position

 R is the radar station's position

 V is the point located vertically of the radar station at the plane's height

 h is the plane's height

 d is the distance between the plane and the radar station

 x is the distance between the plane and the V point

 Since the plane flies horizontally, we can conclude that PVR is a right triangle. Therefore, the pythagorean theorem allows us to know that d is calculated:

 d=(h^2+x^2)^(1/2)

 We are interested in the situation when d=2mi, and, since the plane flies horizontally, we know that h=1mi regardless of the situation.

 We are looking for 

 (dd/dt)=d'.

 d^2=h^2+x^2

 d'=(x*x')/d

 We can calculate that, when d=3mi

 x=(d^2−h^2)^(1/2)=(3^2−2^2)^(1/2)=(5)^(1/2) m

 Knowing that the plane flies at a constant speed of 510mi/h, we can calculate:

 d'=(x*x')/d=(((5)^(1/2))*(510))/3= 380.13 mi/h.

 the rate at which the distance from the plane to the station is increasing when it is 3 mi away from the station is 380 mi/h

hey seth! : )

i’m not 100% sure, but i think it’s b

hope this ya : p

miss u!

- nicole

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right