An incoming airplane is x miles due north from the control tower at an airport. A second incoming airplane is y miles due east of the same control tower. The shortest distance between the two airplanes is z miles.

Which of the following functions would best model the situation above?

A.

cube root

B.

square root

C.

piecewise

D.

step

B. Square root

Step-by-step explanation:

using distance formula:

x = √z^2 - y^2

y = √z^2 - x^2

=> z = √x^2 + y^2

Option B. square root

Step-by-step explanation:

An incoming airplane is x miles due North at A from the control tower and a second airplane is y miles East at B of the same control tower.

The shortest distance between the two airplanes is z miles.

By Pythagoras Theorem

z² = x² + y²

z = √ (x² + y²)

So function which models the situation best is "square root".

Therefore, option B. square root is the answer.