Answer:
Period = [tex]\frac{2}{3}[/tex]
The Ferris wheel will complete one round in 40 seconds.
Step-by-step explanation:
We have the function representing the height of the passenger by,
[tex]h=82.5 \sin 3\pi(t+0.5)+97.5[/tex], where t = time in minutes.
It is known that when a function f(x) has period P, then the function a×f(bx+c)+d will have the period [tex]\frac{P}{|b|}[/tex].
Since, the function [tex]\sin x[/tex] has period [tex]2\pi[/tex], so the function h will have period [tex]\frac{2\pi}{3\pi}[/tex] i.e. [tex]\frac{2}{3}[/tex].
Thus, the period of the given function is [tex]\frac{2}{3}[/tex].
Now, as the period is [tex]\frac{2}{3}[/tex] minutes i.e 40 seconds.
Hence, we get that the Ferris wheel will complete one round in 40 seconds.
