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
Answer
Answer:
B. 9 feet
Explanation:
Step1: Recall sine - function range
The range of the sine function $y = \sin(x)$ is $[- 1,1]$.
Step2: Analyze the given function
We have the function $h = 3\sin\left(\frac{4\pi}{5}(t-\frac{1}{2})\right)+12$. Let $x=\frac{4\pi}{5}(t - \frac{1}{2})$. Then $y = \sin(x)$ and $h = 3y+12$.
Step3: Find the minimum value of $y$
The minimum value of $\sin(x)$ is $y=-1$.
Step4: Calculate the minimum value of $h$
Substitute $y = - 1$ into the equation $h = 3y+12$. $h=3\times(-1)+12$. $h=-3 + 12=9$. So the minimum height of the flag is 9 feet.