00:01
All right, guys, so we have got a circular piece of sheet metal that has a diameter of 20.
00:08
So let's just express that visually to start.
00:14
I'm just going to put the diameter, which means all the way across as 20 inches.
00:20
All right, so now all of a sudden we are going to cut a rectangle out.
00:28
Forgive me, i'm not an artist.
00:33
And when we do this, we've got two triangles built.
00:39
And what do we know about triangles? pythagorean theorem.
00:44
Smaller side plus square the taller side is the diameter square.
00:51
But this is a rectangle, and they have specified there is a smaller side and a larger side.
00:56
So i cannot assume this is is isosceles.
00:59
And i've got two unknowns.
01:01
But there is another fact i know about this triangle, which we, would be, or this rectangle, excuse me, that base times height is an area of 150 inches squared.
01:12
That's what they specified in the problem.
01:14
Okay.
01:15
So let's do a little substitution.
01:18
I'm going to solve for y.
01:20
You could solve for x as well, but i'm choosing y.
01:24
Y will be equal to 150x.
01:28
I'm going to plug it in up here.
01:31
So i will have x squared.
01:34
Oops, not times.
01:36
No, no, no, no, no.
01:40
There we go.
01:42
X squared plus 150 over x squared is equal to 400.
01:51
All right, let's clean this up a little bit.
01:54
Let's expand this guy.
02:02
Don't forget your exponent applies to both the numerator and the denominator.
02:09
All right.
02:10
Now, remember in math, whatever i do to one side, i can do to the other.
02:14
So i'm going to multiply both sides by x squared.
02:18
X to the fourth.
02:21
Let's get rid of that binomial denominator.
02:30
Okay.
02:31
Now, once i start rearranging this, i think it's going to look familiar to you.
02:40
Oh.
02:41
Kind of looks like the quadratic equation, doesn't it? except that usually with a quadratic equation, you've got a binomial, monomial, and the number.
02:50
What do i do with this? well, i can use the substitution method, and i'm going to make x squared equal to let's say t so now i can rearrange it as such okay now i am going to plug and chug in the notoriously long quadratic equation i'm writing it down just in case you have forgotten so i will have to do this plug and chug twice because i need both a plus and a minus version so let me cleaned up a little bit over here.
03:40
Hope y 'all are having a good day.
03:42
It can only be so good if you're doing math, unless you're a math buff.
03:46
Very ready.
03:49
From here, i will save you the pain of having to do the calculation.
03:55
I'm going to have 400 plus.
03:59
I do the plus version first.
04:04
400 squared...