A plane flies 240 miles due north, then 320 miles due west. How many miles must it fly to return to its starting point by the shortest
route? (Enter your answer without units.)

The distance of the shortest route of return is 400

Step-by-step explanation:

The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

BC² = 320² + 240²

BC² = 160000

BC = √160000

BC = 400

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50