the height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be…

the height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation (h = 3sinleft(\frac{4pi}{5}left(t-\frac{1}{2}\right)\right)+12). what is the minimum height of the flag?\no 3 feet\no 9 feet\no 12 feet\no 15 feet

the height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation (h = 3sinleft(\frac{4pi}{5}left(t-\frac{1}{2}\right)\right)+12). what is the minimum height of the flag?\no 3 feet\no 9 feet\no 12 feet\no 15 feet

Answer

Explanation:

Step1: Recall sine - function range

The range of the sine function $y = \sin(x)$ is $[- 1,1]$.

Step2: Find the minimum value of the given function

We have the function $h = 3\sin\left(\frac{4\pi}{5}(t-\frac{1}{2})\right)+12$. To find the minimum value of $h$, we consider the minimum value of the sine - part. The minimum value of $\sin\left(\frac{4\pi}{5}(t - \frac{1}{2})\right)$ is $-1$. Substitute $\sin\left(\frac{4\pi}{5}(t-\frac{1}{2})\right)=-1$ into the function $h$: [ \begin{align*} h&=3\times(-1)+12\ &=-3 + 12\ &=9 \end{align*} ]

Answer:

9 feet