Question

In Bear Creek Bay in July, high tide is at 1:00 pm. The water level at high tide is 7 feet at high tide and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Bear Creek Bay's water level in July as a function of time (t).

Answer 1

f(t) = 6 cos pi over 2 t + 2

f(t) = 3 cos pi over 2 t + 4

f(t) = 6 cos pi over 6 t + 2

f(t) = 3 cos pi over 6 t + 4

Answer 2

Alright so you need an equation in the form\[f(t)=acoskt +c\]where a is the amplitude, c is the average water level and\[k =\frac{ 2\pi }{ period }\]So what are you actually having trouble with?

Answer 3

i just dont understand what i have to do

Answer 4

You have to find a, k, and c. Do you know how to do that?

Answer 5

t is the time in hours and f(t) is the depth of the water in meters.

Answer 6

\[a =\frac{ Maximum - minimum }{ 2 }\]and\[c =\frac{ Maximum + minimum }{ 2}\]

Answer 7

so a= 5.5 and c=6.5

Answer 8

No

Answer 9

Your question reads high tide is 7 feet and low tide is 1 feet. Sorry I said meters earlier. I meant feet.

Answer 10

High tide (maximum vale) and low tide (minimum value)

Answer 11

so its 7-1/2 and 7+1/2?

Answer 12

Yes. But more accurately, (7 - 1)/2 and (7 + 1) /2.

Answer 13

ohh ok and then a=3 and c= 4

Answer 14

You Got It!

Answer 15

thank you so much!

Answer 16

And now k = ?

Answer 17

um would you put 2pi over 3 and 4 but different equations?

Answer 18

No. The period is the length of time between two successive (consecutive) high tides or two successive low tides.

Answer 19

Hence what is the period and then\[k =\frac{ 2\pi }{ period }\]

Answer 20

Read the question carefully! It states the period!

Answer 21

the period would be 12?

Answer 22

Correct! Because the question reads "the next high tide occurs 12 hours later." So then what does k = ?

Answer 23

i got .523 repeating....did i do something wrong i multiplied 2 times 3.14 and divided it by 12

Answer 24

No Decimals! What is the exact value of k?

Answer 25

The exact value of k as a reduced fraction is...?

Answer 26

pi/6?

Answer 27

Yes!!!

Answer 28

Now then what is the final equation?

Answer 29

it would be D

Answer 30

Beautiful!!

Answer 31

thanks for helping me!!! i appreciate it so much :)

Answer 32

See! I knew you could do it!!! Have more faith in yourself! You're welcome.

Answer 33

Anything else while I'm still logged in?

Answer 34

For an angle Θ with the point (−20, −21) on its terminating side, what is the value of cosine?

negative 20 over 29

negative 21 over 29

−20

−21

Answer 35

There 's a bunch of stuff missing that I can't see. Could you write it out properly please?

Answer 36

-20/29
-21/29
-20
-21


the rest of it is all that they gave me

Answer 37

There's stuff missing from the question itself that I can't see. I don't care about the answer choices! I don't need them. I need the question lol

Answer 38

For an angle Θ with the point (−20, −21) on its terminating side, what is the value of cosine?

Answer 39

uhhhh what the heck...

Answer 40

Is there perhaps a diagram there that is not translating here?

Answer 41

Do you think you can type out the problem yourself, instead of simply trying to copy and paste?

Answer 42

for the angle theta with the point (-20,-21) on its terminating side, what is the value of cosine?

Answer 43

Sorry, I had to step away for a few seconds.

Answer 44

its ok

Answer 45

\[\cos \theta =\frac{ adj. side }{ hypotenuse }\]

Now what is the hypotenuse side?