Question

Eastport, Maine, has among the highest tides in the United States. Write a cosine function that models the oscillation of Eastport’s tides if their amplitude is 9 feet 8 inches, the equilibrium point is 12 feet 3 inches, the phase shift is
-2.68 hours, and the period is 12.34 hours.
Possible Answers:
y=9.67sin[t/6.17π - 6.17π/4.68] + 6.125
y=12.25sin[t/6.17π - 2.34π/4.68] + 9.67
y=9.67sin[t/12.34π - 2.34π/6.17] +12.25
y=9.67sin[t/6.17π + 2.68π/6.17] +12.25

Answer 1

It strikes me as odd that you have to write a cosine function, where the answer options only has sine functions...

In itself this is not a problem, because you can desctibe any such situation both with a sine or a cosine.

Hint: amplitude 9 ft 8 in converts to 9.67. Amplitude is a in asint, so the second option is wrong.
Equilibrium point (12.25) is number added to sine function, so first one is also wrong.

Now you have to interpret the other numbers to get the right answer...

Answer 2

How does 9ft 8in convert to 9.67?

Answer 3

1 ft = 12 in, so 8 in = 8/12 ft = 2/3 ft or about 0.67 ft

Answer 4

Funny you ask me: I'm from Holland.
We only use the metric system...(easier conversions - only factors of 10).

Answer 5

oh wow I'm dumb cx and yeah I'm from America where we use the other system of conversion >_<

Answer 6

But I believe the answer is c?

Answer 7

Let me help you with the other numbers: the period of sin(bt) is 2pi/b = 12.34
To get b, you have to solve:\[\frac{ 2 \pi }{ b }=12.34 \Leftrightarrow b=\frac{ 2 \pi }{ 12.34 }=\frac{ \pi }{ 6.17 }\]Now in the answer options it seems like t is divided by 6.17pi, but this is wrong, it has to be:\[t \frac{ \pi }{ 6.17 }\]So the whole formula is:\[y=9.67\sin[t\frac{ \pi }{ 6.17 } + \frac{2.68π}{6.17}] +12.25\]

So option D

Answer 8

Ohhh okai I get it c:

Answer 9

Thank you c:

Answer 10

yw!