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anonymous

  • one year ago

The temperature of a chemical reaction ranges between 40 degrees Celsius and 180 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 12-hour period. What is a cosine function that models this reaction? f(t) = 70 cos 12t + 110 f(t) = 110 cos 12t + 70 f(t) = −70 cos pi over 6t + 110 f(t) = −110 cos pi over 6t + 70

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  1. anonymous
    • one year ago
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    @Jacob902 @pooja195 @Hero

  2. anonymous
    • one year ago
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    @ganeshie8

  3. anonymous
    • one year ago
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    @Michele_Laino @dan815

  4. Michele_Laino
    • one year ago
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    the amplitude A of your function is: \[\Large A = \frac{{180 - 40}}{2} = ...?\]

  5. anonymous
    • one year ago
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    140/2= 70

  6. anonymous
    • one year ago
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    So A?

  7. Michele_Laino
    • one year ago
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    no, since the period of our function is 12 hours, so the shape og our function has to be this: \[\Large \cos \left( {\frac{{2\pi }}{{12}}t} \right)\]

  8. Michele_Laino
    • one year ago
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    of*

  9. anonymous
    • one year ago
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    It's really hard so I don't really know what to plug in for the shape of function

  10. Michele_Laino
    • one year ago
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    since at t=0, the value is 40, then we have this drawing: |dw:1436896425801:dw|

  11. Michele_Laino
    • one year ago
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    now, if I set t=0 into the first option I get: f(0)= 180 so the first option is not the right option

  12. anonymous
    • one year ago
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    Oh okay so what is next? @Michele_Laino

  13. Michele_Laino
    • one year ago
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    please substitute t=0 into the third option, what do you get? f(0)=...?

  14. anonymous
    • one year ago
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    -70 cos + 110?

  15. anonymous
    • one year ago
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    @Michele_Laino

  16. Michele_Laino
    • one year ago
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    we have: \[\Large - 70\left( {\cos 0} \right) + 110 = - 70 \times 1 + 110 = 40\]

  17. Michele_Laino
    • one year ago
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    so, what can you conclude?

  18. anonymous
    • one year ago
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    I can conclude the answer is C.

  19. Michele_Laino
    • one year ago
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    that's right!

  20. anonymous
    • one year ago
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    Yay.

  21. Michele_Laino
    • one year ago
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    :)

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