Answer:
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
