the height of a seat on a ferris wheel can be modeled as h(t)=47 sin((π/30)t + (3π/2)) + 52, where t is time…

the height of a seat on a ferris wheel can be modeled as h(t)=47 sin((π/30)t + (3π/2)) + 52, where t is time in seconds and h(t) is height in feet. how far off the ground is a seat when it is at the top of the ferris wheel? a. 52 feet b. 99 feet c. 94 feet d. 104 feet

the height of a seat on a ferris wheel can be modeled as h(t)=47 sin((π/30)t + (3π/2)) + 52, where t is time in seconds and h(t) is height in feet. how far off the ground is a seat when it is at the top of the ferris wheel? a. 52 feet b. 99 feet c. 94 feet d. 104 feet

Answer

Explanation:

Step1: Recall the range of sine function

The range of $y = \sin(x)$ is $[- 1,1]$. The maximum value of $\sin(x)$ is $1$.

Step2: Find the maximum of $H(t)$

We have $H(t)=47\sin(\frac{\pi}{30}t+\frac{3\pi}{2}) + 52$. When $\sin(\frac{\pi}{30}t+\frac{3\pi}{2}) = 1$, we calculate $H(t)$. Substitute $\sin(\frac{\pi}{30}t+\frac{3\pi}{2}) = 1$ into $H(t)$: $H(t)=47\times1 + 52$. $H(t)=47 + 52=99$.

Answer:

B. 99 feet