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krek1111 [17]
2 years ago
11

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 ca

n be modeled by the equation h = 15 cosine (StartFraction pi Over 20 EndFraction t). How long does it take for the waterwheel to complete one turn? 5 seconds 10 seconds 20 seconds 40 seconds.
Mathematics
1 answer:
adelina 88 [10]2 years ago
8 0

Solving the trigonometric equation, it is found that it takes 40 seconds to complete one turn.

The height is modeled by:

h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}

The initial height is h(0) = 15, hence, one turn is completed when h(t) = 15.

h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}

15 = 15\cos{\left(\frac{\pi}{20}t\right)}

\cos{\left(\frac{\pi}{20}t\right)} = \frac{15}{15}

\cos{\left(\frac{\pi}{20}t\right)} = 1

The length of one turn is of 2\pi, and \cos{(2\pi)} = 1, hence, the solution is found according to:

\frac{\pi}{20}t = 2\pi

t = \frac{40\pi}{\pi}

t = 40

It takes 40 seconds to complete one turn.

You can learn more about trigonometric equations at brainly.com/question/24680641

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