00:01
So i'm reading this problem that you have an island.
00:02
Let's call it i over here.
00:04
That's four kilometers.
00:06
And then we're going to lay some pipe under the water.
00:10
And then the distance from that is eight kilometers to, what are we trying to get it to? a power station.
00:20
And so how far, how should the power line be laid so it has a minimum cost? well, i've seen problems where they call this distance x.
00:28
And then from here to here is where they write eight minus x.
00:34
And so as far as a cost equation goes, you need the distance times the rate that it goes.
00:41
And they don't give you specific numbers, but they tell you that whatever this rate is, the rate over here is three times that.
00:48
So what i need to apply is with this right angle in here, the pythagorean theorem, that this distance, whatever it is underwater, is the square root of x squared plus four squared.
00:59
It's the pythagorean theorem.
01:01
So the minimum cost equation, well, let's first come up with a cost equation, is we're going to triple the rate.
01:13
So i'm actually just going to drop the r because it doesn't matter if it's one or if r is two, then over here, six is just tripled.
01:23
And i would write it as x squared plus 16...