00:01
Okay, we want to find the volume under this plane, and that's going to make a tetrahedron.
00:09
So let's figure out what it looks like when x and y are zero, zero is five.
00:19
When x and z are zero, y is five.
00:25
And when y and z are zero, x is five halves.
00:29
I think i said that wrong, but i drew it right.
00:33
All right.
00:34
So it looks like this.
00:38
And then we're using the coordinate planes also.
00:41
So let's go ahead and do dz first.
00:47
Okay, so z is going from the x, y plane, so zero, up to the plane that we just drew, which will be 5 minus 2x minus y.
01:06
All right, then let's look in the x.
01:09
Y, plain.
01:13
Okay, remember it went through five on y, but just five halves on x.
01:20
So i'm going to do y first.
01:22
So y is going to go from the bottom, which is zero, up to this line.
01:28
So i'm going to have to write the equation of this line, but the equation of this line is just plug in z equals zero here.
01:38
So you get y equals minus 2x plus 5...