Two ships leave port at the same time. One sails south at 24 mi/h, and the other sails east at 32 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.

c(t)= 40t

Explanation:

As it forms the right angle triangle. see attachment for the figure.

We will use Pythagoras theorem i.e

a² + b² = c²

where,

'a' is perpendicular

'b' is base

'c' is hypotenuse i.e the distance D between the ships in terms of the time 't'

the distance 'a' from the starting point is 24t

the distance 'b' from the starting point is 32t

therefore,  

(24t)²+ (32t)² = c(t)²

c(t)= √(24t)²+ (32t)²

c(t)= √576t² + 1024t²

c(t)=√ 1600t²

c(t)= 40t

Thus,  function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure is 40t

resonant frequency