00:03
All right.
00:04
So we are looking at a problem about pollution, concentration of pollution, and based on the height of a smoke stack.
00:14
And the formula that's given is pretty complicated.
00:18
We've got a variable, variables, z, h, and y.
00:24
And based on the diagram, z is a height from the point of release of the smoke.
00:33
Is the height of the smoke stack and then y is a perpendicular distance in the horizontal direction so we've got a lot going on in here problem part a says well if both z equals zero and y equals zero what happens to the concentration as the height of the smoke stack increases so we can simplify this big expression a little bit by subbing in for z equals 0 and y equals 0.
01:06
And so the first term, the first factor remains the same.
01:09
When i go to my second factor of e to the minus y over 2a square, if y equals 0, this is just e to the 0, which is 1.
01:18
So that term, that factor is just 1.
01:22
Now in the second, in the two terms inside the brackets, the if z equals 0, then what we get is e to the minus, and then we have minus h squared.
01:33
Over 2b squared.
01:37
And then similarly, we have minus, let's see, h squared over 2b squared.
01:46
And then now i can simplify that even a little bit more because those two terms inside the bracket are the same because when negative h times negative h is h squared, and then i multiply that by negative 1.
02:00
So i have an exact same term twice.
02:02
So i have 2e to the minus h squared over 2b squared.
02:11
All right.
02:12
Now q, v, a, and b are all constants.
02:16
So the only thing that's changing, the only variable that's changing is the h...