00:01
Alright, hello, in this question we're told that the certain temperature in a city is given by this equation, and this is where t is hours after 9 a .m.
00:09
And from this we're asked in part a, determine the temperature at 9 a .m.
00:12
So if t is an hour since 9 a .m., the temperature at 9 a .m.
00:17
Will be at time equals 0.
00:18
So we'll go ahead and just plug this into this equation.
00:20
Wherever we see t, we're going to plug it in at 0.
00:23
So we're going to get this term here is going to be the sine of 0, and we know that the sine of 0 is 0, and so our time, our temperature at time 0 is going to be 50 degrees, and that's in degrees fahrenheit, that's given in the question there, so don't forget units.
00:40
Part b says determine the temperature at 3 p .m.
00:43
So how many hours is 3 p .m.
00:45
Past 9 a .m.? that's 6 hours.
00:47
So we'll go ahead and plug in a 6 wherever we see a t.
00:51
And so this here is going to reduce down to pi over 2, and we know that the sine of pi over 2 is equal to 1, so we're going to have 50 plus 11, which is 61 degrees fahrenheit.
01:04
That is going to be our maximum temperature.
01:06
And part 3 says find the average temperature during the day from the period of 9 a .m.
01:11
To 9 p .m...