Question

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?

Answer 1

It basically asking for the gradient so do 'change in y/change in x'
(18-12) / (6-4) = 3

Answer 2

arctan 3

Explanation:

Given that a ramp with a constant incline is made to connect a driveway to a front door.

Let x represent the distance from the driveway and y the height of ramp.

Then the two points are (4,12) and (6,18)

Thus the slope = rate of change of incline = change in y/change in x

= 6/2 =3

Slope = 3

Incline would be tan of the angle

Hence change in incline is arctan 3.