A plane flying horizontally at an altitude of 2 miles 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 5 miles away from the station. (Round your answer to the nearest whole number.)

The rate at which the distance from the plane to the station is increasing when it is 5 miles away from the station is 421 mi/hr

Step-by-step explanation:

Assume a plane flying horizontally at an altitude of 2miles

h= 2

Considering speed 460mi/hr

Let

Let the distance from the plane to the station be 'c'

c= 5miles

= ?

h is constant , so

The plane diagram is attached below ,

now,

Using pythagorean theorem ,

Now, differentiate with respect to 't'

divide by  2,

        =     421.36 mi/hr

        = 421 mi/hr

Hence , the answer is 421 mi/hr

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.