Question

The function f(t) = 20 sin (pi over 5t) + 12 models the temperature of a periodic chemical reaction where t represents time in hours. What are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take?

Maximum: 20°; minimum: 8°; period: 12 hours

Maximum: 32°; minimum: −8°; period: 10 hours

Maximum: 20°; minimum: 12°; period: pi over 5 hours

Maximum: 32°; minimum: 8°; period: pi over 5 hours
@mathmale

Answer 1

is it c?

Answer 2

I will always ask you to explain / show how you arrived at any particular answer. What clues have you found that seem to indicate that the answer is c?

Answer 3

i just looked at what was give.
@mathmale

Answer 4

Important: Your f(t) = 20 sin (pi over 5t) + 12
should be written as f(t) = 20 sin (pi over 5)t + 12, I believe. Agree or disagree?

Answer 5

ik the period would be pi over 5.

Answer 6

So, what is your argument that the answer is c?

Answer 7

Look at your f(t) = 20 sin (pi over 5)t + 12.
Compare this to
f(t) = a sin bt + d

The value of b here is pi over 5.
The period is 2pi/b.

Knowing b,
find the period now, please.

Answer 8

that the a is the max and that is 20 and the 12 is the min and the min is d

Answer 9

is the max and min right?

Answer 10

'a' is the AMPLITUDE of your sine function.
What is the maximum value that the given sine function will attain? The minimum? Explain how you got these figures.
'd' is not the minimum. 'd' represents your VERTICAL OFFSET.

Answer 11

If any of these terms are not familiar to you, either look them up or ask me specific questions.

Answer 12

i am so confused!! how do i find the max and the min in this problem?

Answer 13

Suppose that t=0. What would the value of your sine function be?

Just substitute 0 for t in f(t) = 20 sin (pi over 5)t + 12.

Answer 14

12

Answer 15

Right. 12 = 'd' = your vertical offset. Good.
Now add 20 to 12. What do you get?
Now subtract 20 from 12. What do you get?
What do these two results represent?

Answer 16

20+12=32 and 20-12=8

Answer 17

ohhh wow so the answer is a

Answer 18

Add 20 to 12: you get 20+12=32. Yes.
Subtract 20 from 12. Instead, you have subtracted 12 from 20. No.
Try again: Subtract 20 from 12.

Answer 19

my b i meant d

Answer 20

ohh 12-20=-8

Answer 21

OK. In summary, adding the amplitude, 'a,' or 20, to the vertical offset, 'd,' or 12, results in 32. What does 32 represent?
subtracting the amplitude, 'a,' or 20, from the vertical offset, 'd,' or 12, results in -8. what does -32 represent?

Answer 22

32 is the maximum

Answer 23

Yes, and ... ?

Answer 24

-8 is the minimum

Answer 25

Nice work. Please review our conversation (above) and determine what 'b' is in f(t) = 20 sin (pi over 5)t + 12 .

Answer 26

so the period is 10

Answer 27

Yes. Don't mind me... but please explain how you got 10.

Answer 28

5 times 2 and the pies cancel

Answer 29

Good.
So, which of the four possible answers is the correct one? Is it c?

Answer 30

no its not c, it is b

Answer 31

Right. Now you see why I rejected your "Is it c?" question. Wanted to be absolutely sure that you knew how to find a, b and d and what to do with them to find the min, the max and the period. Nice work.

Answer 32

thank you so much! :-) can you help me with a couple more?

Answer 33

Perhaps one more. Have to get off the Internet soon. Always please post a problem with which you want help before asking for help. Thanks.

Answer 34

You're welcome; happy to help you!

Answer 35

ok and thanks again.

Answer 36

(cos Θ − cos Θ)2 + (cos Θ + cos Θ)2