Question

can't figure this out...thought I would use the antiderivative but it's not working

Answer 1

In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function
\[T(t) = 50 + 16 \sin \left(\frac{\pi t}{12} \right)\]

Determine the temperature at 9 am and 3pm

Answer 2

also Find the average temperature during the period from 9 am to 9 pm.

The formula for that I know is \[\frac{ 1 }{ b-a } \int\limits_{a}^{b} f(x) dx\]

Answer 3

hmm since it t hour after 9am
at 9am the temp should be T(t=0)=50
initial temp

Answer 4

oh hold on mis understand the question

Answer 5

how many hours are there btw 9am to 3pm?

Answer 6

which part do you need help with
the calculus or the algebra ?

Answer 7

or both ?

Answer 8

ohh ok that makes since and then how would i get 3...would be like t=6

Answer 9

I figured it out thanks!

Answer 10

no i got it! That made it clear. I just had to interchange the numbers..So like 9am is the initial so that means my first number is 0 (which is equivalent to 9am to some extent).

Answer 11

hmm i thought i saw something else into your question lol
did you do the calc part

Answer 12

yup! i figured it out. for 9am it's gonna be 50 F and for 3pm it's gonna be 66 F. Then the average is 60.186 using the equation I provided

Answer 13

the average temp is using derivative

Answer 14

taking derivative

Answer 15

yes i got that part too! Haha It clicked when u set t=0 for the initial temp

Answer 16

hmmm integral of what did you do?

Answer 17

\[\frac{ 1 }{ 12-0 } \int\limits\limits_{0}^{12} 50 + 16 \sin \left(\frac{\pi t}{12} \right) dt\]

Answer 18

hmm i was thinking about derivative somehow
you are correct :)