Question

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?

Answer 1

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

Answer 2

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?

Answer 3

90

Answer 4

Amplitude should be calculated as \[A = \frac{ Max - Min }{ 2 }\]

Answer 5

70

Answer 6

Correct, so A and D are gone.

Answer 7

answer is c

Answer 8

So now calculate omega such that \[70 \cos(\omega t) + shift\]

Answer 9

We are given the period 8.

Answer 10

\[\omega = \frac{ 2 \pi}{ k }\]

Answer 11

Where k = 8 (period)

Answer 12

What is omega in this case?

Answer 13

idk

Answer 14

\[\omega = \frac{ 2\pi }{ 8 } = \frac{ \pi }{ 4 }\]

Answer 15

oh

Answer 16

answer is b

Answer 17

Correct

Answer 18

can i ask another question

Answer 19

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

Answer 20

which function has the smallest minimum

Answer 21

Let's look at the f(x). We can quickly determine the minimum of the function by looking at its amplitude.

Answer 22

Without the shift, it would be -3 right? Combining the vertical shift of 2, the minimum is -3+2=-1.

Answer 23

i believe that h(x) has the smallest minimum value

Answer 24

The minimum of g(x) is clearly shown in the table as -1.

Answer 25

h(x) minimum is also -1

Answer 26

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

Answer 27

Correct, all of them have the same minimum.

Answer 28

thanks