00:01
All right, so for this question, we're asked to solve it like we would a bernoulli equation.
00:05
So to start off, let's go ahead and divide everything by xv.
00:10
So we'll have dv -d -x equals to v.
00:15
Oh, sorry, not equals to, plus v divided by x equals to 32 divided by v.
00:26
Okay.
00:27
I'm going to go ahead and rewrite this just a little bit.
00:30
So i have dvdx plus v, 1 divided by x equals to 32 times 1 divided by v.
00:41
Okay.
00:43
So in a bernoulli equation, we generally want to use substitution, and the substitution is based on whatever term is on this side.
00:50
So our substitution, i'm going to let it be the letter y.
00:54
So i'll say y equals to v to the one minus whatever power this is right here.
01:08
And this is negative 1, so 1 plus 1, which equals to v squared.
01:15
So in this case, d .y, dx, it's going to be 2 v.
01:28
D, d, x.
01:30
All right.
01:31
So now we can go ahead and substitute these into here.
01:36
But before we do that, we want to multiply everything by v squared.
01:43
Or sorry, 2v.
01:45
So we'll have 2v, dv, dv, d, x, plus 2v squared 1 divided by x equals to 64.
01:57
For just 64.
02:03
And then we can do the substitution.
02:05
So we have d -y -d -x plus, let's see, 2y, 1 divided by x.
02:18
And this equals to 64.
02:21
Let me rewrite this a little bit...