Question

Would the answer to this question be A?

Answer 1

the link is broken, i can;t view it

Answer 2

Jordi: I was able to view your attachment just fine.

Answer 3

We want to find a cosine function that models the height of the tide.
To do this, we'll need to find the vertical offset of the cosine function. Think: If the water level is 1 ft. at low tide and 9 feet at high tide, what's the average? That average is the vertical offset we wanted.

Next, we know that one complete cycle (high tide to low tide to high tide again) requires 12 hours. The formula for the period of a cosine function is simply 2pi/b, where b is "frequency," in y = a(bt) + c.

Think about this situation. What's an appropriate value for the amplitude, a?
for the frequency, b?
What would the whole equation look like?

Answer 4

Excuse me, I meant to type y = a*cos(bt) + c.
Again, a is the amplitude of the cosine function, b is the frequency, and c is the vertical offiset.

Answer 5

@mathmale the other option, which i believe is correct thanks to you, is the exact same thing as the equation but instead of 2pi/2 it is 2pi/6

Answer 6

Jordi: Not sure how to respond. What do your 2pi/2 and 2pi/6 signify?

Answer 7

Were I trying to calculate the frequency, b, I would use the equation Period=2pi/b.
Since we want to solve for b, we re-write this as b=2pi/12 (since the period of this cosine function is 12). That would reduce to pi/6.

Answer 8

So, Jordi, I believe your equation should come out to \[y=4\cos(\frac{ \pi }{ 6 }t)+5,\]
Don't just take my word for it. Try calculating the period of this function using the formula period=2pi/b.

Answer 9

ohh I just realized what I did, my bad @mathmale. Thank you for your help

Answer 10

My great pleasure, Jordi!