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All right, hello.
00:01
In this question, we're told that we're going to build a fence in kind of a ridiculous shape.
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We're going to have two parabolas that is going to be enclosed by.
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And we want to figure out what the area enclosed by this is.
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So to start, i'm going to go ahead and graph these very roughly.
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So i know that i have y1 is 10x squared.
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That's a very narrow parabola that passes through the origin.
00:19
So i'm going to have something that looks like that.
00:21
That's going to be y1.
00:22
And then x squared plus 6 is going to have its vertex at 6 here, but it's going to be much wider.
00:29
It's not going to be quite as narrow as the 10x squared one.
00:32
So that's going to be y2.
00:34
The area enclosed by these is just going to be this guy here.
00:36
Well, i need to figure out where they intersect.
00:39
And to do that, i'm just going to solve where y1 equals y2.
00:43
So that is where 10x squared equals x squared plus 6.
00:46
I move that over.
00:49
X squared, 9x squared equals 6.
00:52
So x squared is going to equal 6 ninths.
00:54
So x is going to be plus or minus the square root of 6 ninths, which is the square root of 2 thirds.
01:01
I can go ahead and plug that in as a number if i'd like.
01:04
But since it's going to be an inexact value, i'm going to opt to not do that until the very, very end...