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?\n3 feet\n9 feet\n12 feet\n15 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?\n3 feet\n9 feet\n12 feet\n15 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

For the function $h = 3\sin\left(\frac{4\pi}{5}(t-\frac{1}{2})\right)+12$, when $\sin\left(\frac{4\pi}{5}(t - \frac{1}{2})\right)=-1$, we get the minimum value of $h$. Substitute $\sin\left(\frac{4\pi}{5}(t-\frac{1}{2})\right)=-1$ into the equation: $h = 3\times(-1)+12$.

Step3: Calculate the minimum height

$h=-3 + 12=9$.

Answer:

9 feet