00:01
In a certain city, the temperature in degrees fahrenheit or at t hours after 9 a .m.
00:06
Was modeled by the function t, little t, is equal to 40 plus 13, sine, pi of x, excuse me, pi of t over 12.
00:29
So we need to find the average temperature between 9 a .m.
00:39
And 9 p .m.
00:40
And then we round to the nearest whole number.
00:46
So since t is hours after 9 a .m., we need to find where t, little t, is equal to 0 and 12.
01:04
So we're going to use the equation 1 over b minus a integrated from a to b, and then we have to find the derivative of f of x.
01:17
In this case, a is going to equal zero, and b is going to equal 12.
01:24
So we have to find 1 over 12 minus 0 over the course of 0 to 12.
01:33
And then we're going to have 40 plus 13, 9, i over t over t over x.
01:50
So let's simplify this to 1 over 12.
01:53
And then we're going to have from 0 to 12, 4d, d, sorry, this should be t, not x, plus 13, 0 to 12, sine of pi over t divided by 12.
02:22
We're going to have 1 over 12, times 40, that's 12, plus 13.
02:32
And then we've integrated, so this will be cosine over t.
02:37
Over 12 divided by pi over 12 from 0 to 12 and we'll draw a little line there.
02:50
Let's simplify this even further.
02:55
So we'll have 1 over 12, 480 plus 13 12 over 5 times the cosine and times the cosine and pi.
03:12
And then we're going to put 12 over 12 minus cosine of zero.
03:23
So let's simplify this a bit more.
03:30
We'll have one over 12.
03:35
Swiggle.
03:37
480 plus 13 times 12 is equal to 156 over pi...