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anonymous

  • one year ago

MEDAL!!!!! The temperature of a chemical reaction ranges between 20 degrees Celsius and 160 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during an 8-hour period. What is a cosine function that models this reaction?

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  1. anonymous
    • one year ago
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    answer choices f(t) = -90 cos pi/4t +70 f(t) = -70 cos pi/4t +90 f(t) = 70 cos 8t +90 f(t)= 90 cos 8t +70

  2. anonymous
    • one year ago
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    Let's figure out the amplitude of the cosine function first. Given that the min is 20 degrees and max is 160 degrees, what is the amplitude?

  3. anonymous
    • one year ago
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    90

  4. anonymous
    • one year ago
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    Amplitude should be calculated as \[A = \frac{ Max - Min }{ 2 }\]

  5. anonymous
    • one year ago
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    70

  6. anonymous
    • one year ago
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    Correct, so A and D are gone.

  7. anonymous
    • one year ago
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    answer is c

  8. anonymous
    • one year ago
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    So now calculate omega such that \[70 \cos(\omega t) + shift\]

  9. anonymous
    • one year ago
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    We are given the period 8.

  10. anonymous
    • one year ago
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    \[\omega = \frac{ 2 \pi}{ k }\]

  11. anonymous
    • one year ago
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    Where k = 8 (period)

  12. anonymous
    • one year ago
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    What is omega in this case?

  13. anonymous
    • one year ago
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    idk

  14. anonymous
    • one year ago
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    \[\omega = \frac{ 2\pi }{ 8 } = \frac{ \pi }{ 4 }\]

  15. anonymous
    • one year ago
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    oh

  16. anonymous
    • one year ago
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    answer is b

  17. anonymous
    • one year ago
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    Correct

  18. anonymous
    • one year ago
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    can i ask another question

  19. anonymous
    • one year ago
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    Compare the functions below: f(x) = −3 sin(x − π) + 2 g(x) x y 0 8 1 3 2 0 3 −1 4 0 5 3 6 8 h(x) = (x + 7)^2 − 1

  20. anonymous
    • one year ago
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    which function has the smallest minimum

  21. anonymous
    • one year ago
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    Let's look at the f(x). We can quickly determine the minimum of the function by looking at its amplitude.

  22. anonymous
    • one year ago
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    Without the shift, it would be -3 right? Combining the vertical shift of 2, the minimum is -3+2=-1.

  23. anonymous
    • one year ago
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    i believe that h(x) has the smallest minimum value

  24. anonymous
    • one year ago
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    The minimum of g(x) is clearly shown in the table as -1.

  25. anonymous
    • one year ago
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    h(x) minimum is also -1

  26. anonymous
    • one year ago
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    Now, h(x) is a parabola. A parabola is normally centered at the origin, but it has been shifted downwards by -1.

  27. anonymous
    • one year ago
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    Correct, all of them have the same minimum.

  28. anonymous
    • one year ago
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    thanks

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