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?\n5 seconds\n10 seconds\n20 seconds\n40 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?\n5 seconds\n10 seconds\n20 seconds\n40 seconds

Answer

Explanation:

Step1: Identify the formula for period

The general form of a cosine - function is $y = A\cos(Bx - C)+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$. In the given function $h = 15\cos(\frac{\pi}{20}t)$, we have $B=\frac{\pi}{20}$.

Step2: Calculate the period

Using the period formula $T=\frac{2\pi}{|B|}$, substitute $B = \frac{\pi}{20}$ into it. Then $T=\frac{2\pi}{\frac{\pi}{20}}$. When dividing by a fraction, we multiply by its reciprocal, so $T = 2\pi\times\frac{20}{\pi}$. The $\pi$ terms cancel out, and $2\times20=40$.

Answer:

40 seconds