00:02
So for this problem, we are given that the function that models this is that the length of in terms of the time is equal to 12 plus 2 .8 times the sign of, okay, let me put in here, okay, the sign of 2 times pi divided by 360.
00:32
5, this times the time minus 80.
00:38
Now, we need to use this model to compare the number of hours of daylight is increased in philadelphia of march 21 and may 21.
00:49
So the first thing that we need to do is to take the derivative of this because we are asked about the increasing.
00:57
The number of hours is increasing.
00:59
So with that said, we need to take the derivative of this expression.
01:04
Jet is the derivative of l with respect to time.
01:08
So the derivative of this, as you can see, we have two expressions in here, but first we have a number, so that is a constant.
01:20
Its derivative is a constant.
01:23
Later, we have a product between 2 .8 and the sign of something that is in terms of the time.
01:31
So we will have the derivative of that.
01:35
So remember that we can take out a constant out of the integral, out of the derivative, so that will be 2 .8.
01:44
These times the derivative of the sine function, which is the cosine function.
01:50
So we have the cosine function of just simply two times pi, divided by 365, this times the time minus 80.
02:04
And then we just multiplied this, by the internal derivative, which is the derivative of this expression right here.
02:15
So that will be just simply 2 times pi divided by 365.
02:23
So with that set, we can just simply and simplify this further.
02:31
So that will be 28 times pi this divided by 1 .5, this divided by 1.
02:39
1 ,825, this times the cosine of 2 times pi divided by 365, this times the time minus 80...