00:01
Okay, so we have this problem here where there is a house and it's two miles off of the main road.
00:09
And then it's five miles from that point to a box if they need to connect something to.
00:18
So we're going to go x amount down the road, which will cost us $500 when it's on the road.
00:27
And then we're going to jet off and go at a diagonal to the house.
00:34
So we need to find a function for this.
00:39
So first i want to find this distance right here.
00:43
So we're going to use the distance formula.
00:45
This side here is two.
00:47
So i'm going to do two squared plus.
00:52
This distance right here is not the five, right? because the five goes all the way to the box.
00:58
But it is 5 subtract x squared.
01:05
Okay, i'm going to simplify this a little more.
01:11
2 squared is 4.
01:14
And then remember this is like taking 5 subtract x times itself.
01:23
So 5 times 5 is 25.
01:25
5 times negative x, negative 5x.
01:29
Another negative 5x.
01:34
Things not writing, sorry about this.
01:41
And then negative x times negative x is the positive x squared.
01:48
Again, i'm going to simplify it a little better.
01:50
I'm also going to rearrange the order because i prefer the x squared to be first.
01:58
And then the negative 5x and the negative 5x is going to give me negative 10x.
02:02
And then the 25 and the 4 are going to give me 29.
02:06
So that is the distance, the slanted distance.
02:09
And it costs $700 to go along that off of the road.
02:19
And then to finish to the box, we still have this x.
02:24
Remember i told you it's going to cost $500 along the road.
02:29
So this is my cost for going from the box to the house.
02:39
The next thing they wanted me to do is evaluate this twice.
02:48
The first one they needed to evaluate it with x equals 1.
02:54
This distance right here being 1 squared.
03:00
All right, so we're going to use this formula.
03:05
1 squared minus 10 times 1 plus 29, all that times 700 plus 500 times 1.
03:21
Sorry i have to go on to the next line.
03:26
1 squared is 1.
03:31
Negative 10 times 1 is negative 10 and plus 29.
03:35
So i'm going to do 29, subtract 10.
03:38
I'm going to go backwards.
03:40
That's 19 add 1.
03:42
That is 30.
03:44
Square root of 30...