Question

The function f(t) = 65 sin (pi over 5t) + 35 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: 65°; minimum: 35°; period: pi over 5 hours

Maximum: 100°; minimum: −30°; period: pi over 5 hours

Maximum: 65°; minimum: 35°; period: 10 hours

Maximum: 100°; minimum: −30°; period: 10 hours

Answer 1

This i dont have a clue on. xD

Answer 2

lol which one you want to do first, max, min
or period?
both are very easy

Answer 3

Period ;o

Answer 4

Wait, dont they already give us the period? pi/5?

Answer 5

on no!!

Answer 6

i know what you are thinking, that the period of
\[\sin(bx)\] is \(b\) but it is not
the period of
\[\sin(bx)\] is \[\frac{2\pi}{b}\]

Answer 7

OH. Then the Period is 10 ;o

Answer 8

you are quicker on the algebra than i am
yes, 10
easy right?

Answer 9

now we need the range

Answer 10

So, Its either C or D c:

Answer 11

that is also easy
do you know what the biggest sine can be? just asking, if not let me know and i will tell you

Answer 12

65?

Answer 13

lets go slow

Answer 14

the largest sine can be is 1
so we can replace \[\sin(\frac{\pi}{5}t)\] by \(1\) and compute
\[65\times 1+35\] a pretty fast computation gives \(100\) as the max

Answer 15

OH. So its D :3

Answer 16

the smallest it can be is \(-1\) and
\[65\times (-1)+35=-30\]

Answer 17

right, D

Answer 18

Youre too great c: can i have your input on an answer i put?