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haleyelizabeth2017

  • one year ago

The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:30 p.m. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m. I have the first part of it, I just need helping finding the last bit of the function. So far I have 44 + 32 cos ______

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  1. anonymous
    • one year ago
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    I don't think the 44 and 32 are right.

  2. haleyelizabeth2017
    • one year ago
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    Wait...20 is midline actually I think

  3. anonymous
    • one year ago
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    20 is amplitude

  4. haleyelizabeth2017
    • one year ago
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    Whoops...wasn't thinking lol 32 + 20 cos :P

  5. anonymous
    • one year ago
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    ok yeah

  6. haleyelizabeth2017
    • one year ago
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    :) how do I figure out the second part?

  7. anonymous
    • one year ago
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    the period is going to be twice the time between 9:15 am and 3:30 pm

  8. haleyelizabeth2017
    • one year ago
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    Which is 6.25 hours...so 13.5?

  9. haleyelizabeth2017
    • one year ago
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    And then I divide 2pi by that?

  10. anonymous
    • one year ago
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    12.5 hrs. and then yes divide 2π by that

  11. haleyelizabeth2017
    • one year ago
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    Ah! Sorry...brain's not wanting to work today :( did that earlier too haha so I got: \[32 + 20 cos \frac{\pi}{6.25}\] we didn't really even need to multiply it by 2 :P

  12. haleyelizabeth2017
    • one year ago
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    Wait! forgot x

  13. haleyelizabeth2017
    • one year ago
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    ...or theta.

  14. anonymous
    • one year ago
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    yes. and I think there's a shift

  15. haleyelizabeth2017
    • one year ago
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    Ah. wouldn't that be x +/- something?

  16. haleyelizabeth2017
    • one year ago
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    Like it depends which way I thought...

  17. haleyelizabeth2017
    • one year ago
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    so \[32 + 20 cos \frac{\pi}{6.25}(x+9.25) \] maybe?

  18. anonymous
    • one year ago
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    yes. but since you shifted by half you could just switch the sign

  19. anonymous
    • one year ago
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    \[32-20\cos \frac{ \pi x}{ 6.25 }\]

  20. haleyelizabeth2017
    • one year ago
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    instead of adding 9.25? O.o

  21. anonymous
    • one year ago
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    yest

  22. haleyelizabeth2017
    • one year ago
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    Ah...is that all?

  23. anonymous
    • one year ago
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    yes

  24. haleyelizabeth2017
    • one year ago
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    Awesome! Thank you!

  25. anonymous
    • one year ago
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    you're welcome

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