A plane flying horizontally at an altitude of 1 mile and a speed of 460 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 2 miles away from the station. (Round your answer to the nearest whole number.)

The rate increases at 398mi/h

Step-by-step explanation:

Given

--- rate when --- distance

The given parameters is represented with the attached figure

Using Pythagoras theorem [take the attached image as a point of reference]

Differentiate with respect to time (t):

Divide both sides by 2

--- (1)

When y = 2:

--- Pythagoras Theorem

Collect like terms

Solve for x

So:

Substitute: , and

Divide by 2

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)