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Sagot :
Answer:
20 seconds
Step-by-step explanation:
I assume you mean [tex]h(t)=8\cos(\frac{\pi}{10}t)[/tex] for your function.
As the given function is in the form of [tex]f(t)=a\cos(bt+c)+d[/tex] (some textbooks may write this formula differently), the period is equal to [tex]\frac{2\pi}{|b|}[/tex]. Hence, the period of the given function is [tex]\frac{2\pi}{|\frac{\pi}{10}|}=\frac{2\pi}{1}*\frac{10}{\pi}=\frac{20\pi}{\pi}=20[/tex], or 20 seconds.
The period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.
What are some properties of a cosine function?
Suppose that we've got: [tex]f(x) = a\cos\left(\dfrac{2\pi x}{b}\right)[/tex]
Then, this function has:
- Amplitude (the maximum distance of the graph from the middle line) = a
- Period = b
For this case, we're given that:
[tex]h = 8\cos\left(\dfrac{\pi x}{10}\right)[/tex]
We can rewrite it as:
[tex]h = 8\cos\left(\dfrac{2\pi x}{20}\right)[/tex]
Thus, we get a = amplitude = 8 units(distance), and b = period = 20 units(time in seconds).
Thus, the period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.
Learn more about amplitude and period of a cosine function here:
https://brainly.com/question/4104379
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