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=3sin(4pi/5(t-1/2))+12. What is the minimum height of the flag?
Answer:
The minimum height of the flag is 9 feet.
Step-by-step explanation:
The function representing the height of the flag is given by,
\(h(t)=3\sin (\frac{4pi}{5}(t-\frac{1}{2}))+12\)
It is required to find the minimum height of the flag.
As, we know,
The function \(\sin t\) have values between [-1,1] for all values of t.
So, \(\sin (\frac{4pi}{5}(t-\frac{1}{2}))\) have values between [-1,1] for all values of t.
Then, \(3\sin (\frac{4pi}{5}(t-\frac{1}{2}))\) have values between [-3,3] for all values of t.
Thus, \(h(t)=3\sin (\frac{4pi}{5}(t-\frac{1}{2}))+12\) have values between [-3+12,3+12] for all values of t.
That is, \(h(t)=3\sin (\frac{4pi}{5}(t-\frac{1}{2}))+12\) have values between [9,15] for all values of t.
Hence, the minimum height of the flag is 9 feet.