00:02
If a farmer wishes to enclose a rectangular region, bordering a river, so here's the river, with fencing, as shown here in this picture, i'm drawing.
00:17
Suppose that x represents the length of each side of the three parallel pieces of fencing.
00:22
There's actually a line down the middle here.
00:25
We've got x, x, and x, and they've got 600 feet of fencing available.
00:31
What is the length of the remaining piece of fencing in terms of x? so this piece right here, we're going to call it y for a moment.
00:39
And if the whole thing, we get 3x plus y, because i've got one, two, three x's, equals 600, because that's how much fencing they have available.
00:49
Subtract 3x from both sides.
00:52
And we get y equals 600 minus 3x.
00:56
I'm going to erase that and plug in the 600 minus 3x there.
01:04
Our second piece wants us to determine a function a that represents the total area of the enclosed region.
01:11
And we're going to find any restrictions.
01:13
So the area is going to be x, this length here, times this length here, 600 minus 3x.
01:23
We're going to distribute.
01:25
We get x times 600 is 600x.
01:28
X times negative 3x is negative 3x square.
01:32
I'm going to rewrite that so it's in standard form.
01:34
The area is negative 3x squared plus 600 x.
01:40
What are the restrictions? well, we said we've got that 600 and we have three x's.
01:45
So 600 divided by three is 200.
01:48
So x has to be less than or equal to or less than 200.
01:52
So my restrictions are that x is between zero and 200...