the height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of…

the height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation $h = 15cos(\frac{pi}{20}t)$. how long does it take for the waterwheel to complete one turn?\no 5 seconds\no 10 seconds\no 20 seconds\no 40 seconds

the height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation $h = 15cos(\frac{pi}{20}t)$. how long does it take for the waterwheel to complete one turn?\no 5 seconds\no 10 seconds\no 20 seconds\no 40 seconds

Answer

Answer:

D. 40 seconds

Explanation:

Step1: Recall cosine - function period formula

The general form of a cosine function is $y = A\cos(Bx - C)+D$, and its period $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B in the given function

The given function is $h = 15\cos(\frac{\pi}{20}t)$, where $B=\frac{\pi}{20}$.

Step3: Calculate the period

Using the period formula $T=\frac{2\pi}{|B|}$, substitute $B = \frac{\pi}{20}$ into it. Then $T=\frac{2\pi}{\frac{\pi}{20}}$.

Step4: Simplify the expression

$T = 2\pi\times\frac{20}{\pi}=40$ seconds. So it takes 40 seconds for the water - wheel to complete one turn.