a ferris wheel is designed in such a way that the height (h), in feet, of the seat above the ground at any…

a ferris wheel is designed in such a way that the height (h), in feet, of the seat above the ground at any time, t, is modeled by the function h(t)=60 - 55 sin(π/10 t+π/2). what is the minimum height a seat reaches? o 5 feet o 60 feet o 110 feet o 115 feet

a ferris wheel is designed in such a way that the height (h), in feet, of the seat above the ground at any time, t, is modeled by the function h(t)=60 - 55 sin(π/10 t+π/2). what is the minimum height a seat reaches? o 5 feet o 60 feet o 110 feet o 115 feet

Answer

Explanation:

Step1: Recall the range of sine function

The range of the sine - function $y = \sin(u)$ is $[- 1,1]$, i.e., $-1\leqslant\sin(u)\leqslant1$. In the function $h(t)=60 - 55\sin(\frac{\pi}{10}t+\frac{\pi}{2})$, let $u=\frac{\pi}{10}t+\frac{\pi}{2}$.

Step2: Find the maximum value of $\sin(u)$ for minimum $h(t)$

To find the minimum value of $h(t)$, we need to find the maximum value of $\sin(\frac{\pi}{10}t+\frac{\pi}{2})$. Since the maximum value of $\sin(u)$ is $1$.

Step3: Calculate the minimum value of $h(t)$

Substitute $\sin(\frac{\pi}{10}t+\frac{\pi}{2}) = 1$ into the function $h(t)=60 - 55\sin(\frac{\pi}{10}t+\frac{\pi}{2})$. Then $h(t)=60-55\times1$. $h(t)=60 - 55=5$.

Answer:

A. 5 feet