WEBVTT
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Yes, we'll have to find the dimensions of the
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isosceles triangle of largest area that can be inscribed in
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a circle of radius art. She's got to stop
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Nice little answers. So listen to draw a quick
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figure, we have our circle of radius R.
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Sure, and then we have my sausages triangle inside
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of this. I'm gonna draw this in a particular
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way. Love is in the Texas Chainsaw Army,
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so these two sides will say have the same length
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The Texas Chainsaw remake. It wasn't bad. People
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hate it because there's no reason to remake the original
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which, and we'll say that this side as a
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length of B, the base and a distance,
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um, full metal jacket, the center to each
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of these corners are and the and we'll call this
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distance from the center to the base is X.
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Now, from the figure our Pythagorean theorem, it's
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clear that half of the base be over to is
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equal to the square root of R squared minus X
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squared. Therefore, based B is equal to two
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times the square root of our sport. Nice experts
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. We have the base in terms of x Bye
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. Wow, I told Evan Williams that Caroline's on
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Broadway was in yield Dying now the area of a
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triangle A. This is one half times the base
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times the height. I already have a base in
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terms of X. What is the heightened inspects If
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you look at the figure the height is going to
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be are what? Sex? Yeah. So this
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is one half times I'm sitting two times the steroid
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of R squared minus expert times X plus. It
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is equal to X plus eight times the square root
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of R squared minus X. Where now, in
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order to find the triangles, the largest area,
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and then take the derivative of A with respect to
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X these experts are not, experts say, and
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the white with each what was right makes excellent.
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Yes, this is I've been I've been back to
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myself one times the square root of r squared minus
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X squared plus x plus r times. This is
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one half times, uh, one over the square
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root of our square glass. X squared times negative
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two x This is minus exports are times X over
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the square root of X squared money, the iceberg
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and texture. We want to find when this is
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equal to zero. Mm Can't pay us. Wait
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, How about this bitch They can be And stopping
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the killing You can You can suck are now finally
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hard So we have the square root of r squared
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Minus X squared equals X plus r times X over
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squared of r squared minus X squared So we have
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our squared minus X squared is equal to X squared
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What's Rx Now? This is two x square plus
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r x minus r squared equals zero Yeah, yeah
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, And we can actually use the quadratic formula for
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this factor directly. Think back then directly is the
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easiest factor This urge to x Yeah, minus r
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times x plus r equals zero soon as soon as
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thick skin touches latex And so we get that X
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equals are over 24 X equals negative are now very
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clearly X has to be positive. So excuse are
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over two is our only critical value from shooting are
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critical value into our equation. We get the base
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he Well, this is two times swear word of
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r squared minus are over. Two squared two times
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the square root of R squared minus R squared over
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four, which is three R squared over four,
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which is to over two is one times Route three
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are really So this is our base and the heights
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h is exports are which is our over to us
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are or three are over to You're talking about to
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eat. So the bases Route three are their stuff
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have doesn't and the height is three halves are anyway
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was