anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
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?
anonymous
  • anonymous
90

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anonymous
  • anonymous
Amplitude should be calculated as \[A = \frac{ Max - Min }{ 2 }\]
anonymous
  • anonymous
70
anonymous
  • anonymous
Correct, so A and D are gone.
anonymous
  • anonymous
answer is c
anonymous
  • anonymous
So now calculate omega such that \[70 \cos(\omega t) + shift\]
anonymous
  • anonymous
We are given the period 8.
anonymous
  • anonymous
\[\omega = \frac{ 2 \pi}{ k }\]
anonymous
  • anonymous
Where k = 8 (period)
anonymous
  • anonymous
What is omega in this case?
anonymous
  • anonymous
idk
anonymous
  • anonymous
\[\omega = \frac{ 2\pi }{ 8 } = \frac{ \pi }{ 4 }\]
anonymous
  • anonymous
oh
anonymous
  • anonymous
answer is b
anonymous
  • anonymous
Correct
anonymous
  • anonymous
can i ask another question
anonymous
  • anonymous
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
anonymous
  • anonymous
which function has the smallest minimum
anonymous
  • anonymous
Let's look at the f(x). We can quickly determine the minimum of the function by looking at its amplitude.
anonymous
  • anonymous
Without the shift, it would be -3 right? Combining the vertical shift of 2, the minimum is -3+2=-1.
anonymous
  • anonymous
i believe that h(x) has the smallest minimum value
anonymous
  • anonymous
The minimum of g(x) is clearly shown in the table as -1.
anonymous
  • anonymous
h(x) minimum is also -1
anonymous
  • anonymous
Now, h(x) is a parabola. A parabola is normally centered at the origin, but it has been shifted downwards by -1.
anonymous
  • anonymous
Correct, all of them have the same minimum.
anonymous
  • anonymous
thanks

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