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haleyelizabeth2017

  • one year ago

In Buenos Aires, Argentina, the average monthly temperature is highest in January and lowest in July, ranging from 83 degrees Fahrenheit to 57 degrees Fahrenheit. Write a cosine function that models the change in temperature according to the month of the year. -How can you find the amplitude? -What part of the problem describes the length of the cycles?

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  1. haleyelizabeth2017
    • one year ago
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    I got the amplitude....it's 13, but I'm not sure about the rest. Is it 70+13 cos ____ because 70 is where the middle of the graph is....

  2. jim_thompson5910
    • one year ago
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    13 is definitely the amplitude and y = 70 is the midline

  3. jim_thompson5910
    • one year ago
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    what is the period or length of each cycle?

  4. haleyelizabeth2017
    • one year ago
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    erm...not sure in this case....uno momento

  5. haleyelizabeth2017
    • one year ago
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    \(\pi/6\) because there are 6 months in between January and July, which are the min and max values.

  6. jim_thompson5910
    • one year ago
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    well the period is actually 12 months since things repeat themselves each season (more or less) so B = 2pi/T B = 2pi/12 B = pi/6 so you have the pi/6 correct but pi/6 isn't the period. It's the coefficient for the t value

  7. haleyelizabeth2017
    • one year ago
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    Oh!

  8. jim_thompson5910
    • one year ago
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    So the function is \[\Large y = 70+13\cos\left(\frac{\pi}{6}t\right)\] y = average temperature at month t

  9. haleyelizabeth2017
    • one year ago
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    Ah...I think we missed something...in the back of the book, it says that \(\frac{\pi}{6}\) is the coefficient for (x-1), where x is the month of the year. I have to explain everything I do and it's my last question...any idea how they got that?

  10. jim_thompson5910
    • one year ago
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    the (x-1), instead of just x, is to allow x to start at 1 instead of 0 notice how x-1 = 0 when x = 1

  11. jim_thompson5910
    • one year ago
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    \[\Large y = 70+13\cos\left(\frac{\pi}{6}x\right) ... \text{ x starts at x = 0}\] \[\Large y = 70+13\cos\left(\frac{\pi}{6}(x-1)\right) ... \text{ x starts at x = 1}\] x = month number y = avg temp

  12. haleyelizabeth2017
    • one year ago
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    Oh! Duh! *face palm*

  13. haleyelizabeth2017
    • one year ago
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    Again, thank you very much. You're a lot of help lol

  14. jim_thompson5910
    • one year ago
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    you're welcome

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