Question

20 POINTS!

Answer 1

Answer:

Period =  $\frac{2}{3}$

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,

$h=82.5 \sin 3\pi(t+0.5)+97.5$, 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 $\frac{P}{|b|}$.

Since, the function $\sin x$ has period $2\pi$, so the function h will have period $\frac{2\pi}{3\pi}$ i.e. $\frac{2}{3}$.

Thus, the period of the given function is $\frac{2}{3}$.

Now, as the period is $\frac{2}{3}$ minutes i.e 40 seconds.

Hence, we get that the Ferris wheel will complete one round in 40 seconds.