[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.09,0:00:02.69,Default,,0000,0000,0000,,I promised you that I'd give\Nyou some more Pythagorean
Dialogue: 0,0:00:02.69,0:00:05.72,Default,,0000,0000,0000,,theorem problems, so I will\Nnow give you more Pythagorean
Dialogue: 0,0:00:05.72,0:00:06.78,Default,,0000,0000,0000,,theorem problems.
Dialogue: 0,0:00:06.78,0:00:09.79,Default,,0000,0000,0000,,
Dialogue: 0,0:00:09.79,0:00:12.38,Default,,0000,0000,0000,,And once again, this is\Nall about practice.
Dialogue: 0,0:00:12.38,0:00:28.02,Default,,0000,0000,0000,,Let's say I had a triangle--\Nthat's an ugly looking right
Dialogue: 0,0:00:28.02,0:00:35.03,Default,,0000,0000,0000,,triangle, let me draw another\None --and if I were to tell
Dialogue: 0,0:00:35.03,0:00:40.75,Default,,0000,0000,0000,,you that that side is 7, the\Nside is 6, and I want to
Dialogue: 0,0:00:40.75,0:00:42.25,Default,,0000,0000,0000,,figure out this side.
Dialogue: 0,0:00:42.25,0:00:45.51,Default,,0000,0000,0000,,Well, we learned in the last\Npresentation: which of these
Dialogue: 0,0:00:45.51,0:00:46.99,Default,,0000,0000,0000,,sides is the hypotenuse?
Dialogue: 0,0:00:46.99,0:00:49.47,Default,,0000,0000,0000,,Well, here's the right angle,\Nso the side opposite the right
Dialogue: 0,0:00:49.47,0:00:51.60,Default,,0000,0000,0000,,angle is the hypotenuse.
Dialogue: 0,0:00:51.60,0:00:53.12,Default,,0000,0000,0000,,So what we want to do\Nis actually figure
Dialogue: 0,0:00:53.12,0:00:54.73,Default,,0000,0000,0000,,out the hypotenuse.
Dialogue: 0,0:00:54.73,0:01:00.73,Default,,0000,0000,0000,,So we know that 6 squared\Nplus 7 squared is equal to
Dialogue: 0,0:01:00.73,0:01:01.70,Default,,0000,0000,0000,,the hypotenuse squared.
Dialogue: 0,0:01:01.70,0:01:03.80,Default,,0000,0000,0000,,And in the Pythagorean theorem\Nthey use C to represent the
Dialogue: 0,0:01:03.80,0:01:05.47,Default,,0000,0000,0000,,hypotenuse, so we'll\Nuse C here as well.
Dialogue: 0,0:01:05.47,0:01:10.93,Default,,0000,0000,0000,,
Dialogue: 0,0:01:10.93,0:01:16.03,Default,,0000,0000,0000,,And 36 plus 49 is\Nequal to C squared.
Dialogue: 0,0:01:16.03,0:01:21.15,Default,,0000,0000,0000,,
Dialogue: 0,0:01:21.15,0:01:25.51,Default,,0000,0000,0000,,85 is equal to C squared.
Dialogue: 0,0:01:25.51,0:01:30.76,Default,,0000,0000,0000,,Or C is equal to the\Nsquare root of 85.
Dialogue: 0,0:01:30.76,0:01:32.49,Default,,0000,0000,0000,,And this is the part that most\Npeople have trouble with, is
Dialogue: 0,0:01:32.49,0:01:34.65,Default,,0000,0000,0000,,actually simplifying\Nthe radical.
Dialogue: 0,0:01:34.65,0:01:40.29,Default,,0000,0000,0000,,So the square root of 85: can I\Nfactor 85 so it's a product of
Dialogue: 0,0:01:40.29,0:01:42.82,Default,,0000,0000,0000,,a perfect square and\Nanother number?
Dialogue: 0,0:01:42.82,0:01:45.92,Default,,0000,0000,0000,,85 isn't divisible by 4.
Dialogue: 0,0:01:45.92,0:01:48.35,Default,,0000,0000,0000,,So it won't be divisible by 16\Nor any of the multiples of 4.
Dialogue: 0,0:01:48.35,0:01:52.40,Default,,0000,0000,0000,,
Dialogue: 0,0:01:52.40,0:01:55.94,Default,,0000,0000,0000,,5 goes into 85 how many times?
Dialogue: 0,0:01:55.94,0:01:58.34,Default,,0000,0000,0000,,No, that's not perfect\Nsquare, either.
Dialogue: 0,0:01:58.34,0:02:02.03,Default,,0000,0000,0000,,I don't think 85 can be\Nfactored further as a
Dialogue: 0,0:02:02.03,0:02:04.23,Default,,0000,0000,0000,,product of a perfect\Nsquare and another number.
Dialogue: 0,0:02:04.23,0:02:06.98,Default,,0000,0000,0000,,So you might correct\Nme; I might be wrong.
Dialogue: 0,0:02:06.98,0:02:09.57,Default,,0000,0000,0000,,This might be good exercise for\Nyou to do later, but as far as
Dialogue: 0,0:02:09.57,0:02:12.67,Default,,0000,0000,0000,,I can tell we have\Ngotten our answer.
Dialogue: 0,0:02:12.67,0:02:15.07,Default,,0000,0000,0000,,The answer here is the\Nsquare root of 85.
Dialogue: 0,0:02:15.07,0:02:17.25,Default,,0000,0000,0000,,And if we actually wanted to\Nestimate what that is, let's
Dialogue: 0,0:02:17.25,0:02:21.81,Default,,0000,0000,0000,,think about it: the square root\Nof 81 is 9, and the square root
Dialogue: 0,0:02:21.81,0:02:25.01,Default,,0000,0000,0000,,of 100 is 10 , so it's some\Nplace in between 9 and 10, and
Dialogue: 0,0:02:25.01,0:02:26.44,Default,,0000,0000,0000,,it's probably a little\Nbit closer to 9.
Dialogue: 0,0:02:26.44,0:02:28.24,Default,,0000,0000,0000,,So it's 9 point something,\Nsomething, something.
Dialogue: 0,0:02:28.24,0:02:30.26,Default,,0000,0000,0000,,And that's a good reality\Ncheck; that makes sense.
Dialogue: 0,0:02:30.26,0:02:33.08,Default,,0000,0000,0000,,If this side is 6, this side\Nis 7, 9 point something,
Dialogue: 0,0:02:33.08,0:02:36.27,Default,,0000,0000,0000,,something, something makes\Nsense for that length.
Dialogue: 0,0:02:36.27,0:02:37.26,Default,,0000,0000,0000,,Let me give you\Nanother problem.
Dialogue: 0,0:02:37.26,0:02:44.79,Default,,0000,0000,0000,,[DRAWING]
Dialogue: 0,0:02:44.79,0:02:49.25,Default,,0000,0000,0000,,Let's say that this is 10 .
Dialogue: 0,0:02:49.25,0:02:51.30,Default,,0000,0000,0000,,This is 3.
Dialogue: 0,0:02:51.30,0:02:53.09,Default,,0000,0000,0000,,What is this side?
Dialogue: 0,0:02:53.09,0:02:55.06,Default,,0000,0000,0000,,First, let's identify\Nour hypotenuse.
Dialogue: 0,0:02:55.06,0:02:57.68,Default,,0000,0000,0000,,We have our right angle here,\Nso the side opposite the right
Dialogue: 0,0:02:57.68,0:03:00.23,Default,,0000,0000,0000,,angle is the hypotenuse and\Nit's also the longest side.
Dialogue: 0,0:03:00.23,0:03:01.12,Default,,0000,0000,0000,,So it's 10.
Dialogue: 0,0:03:01.12,0:03:05.39,Default,,0000,0000,0000,,So 10 squared is equal to\Nthe sum of the squares
Dialogue: 0,0:03:05.39,0:03:06.64,Default,,0000,0000,0000,,of the other two sides.
Dialogue: 0,0:03:06.64,0:03:10.26,Default,,0000,0000,0000,,This is equal to 3 squared--\Nlet's call this A.
Dialogue: 0,0:03:10.26,0:03:11.89,Default,,0000,0000,0000,,Pick it arbitrarily.
Dialogue: 0,0:03:11.89,0:03:14.38,Default,,0000,0000,0000,,--plus A squared.
Dialogue: 0,0:03:14.38,0:03:23.86,Default,,0000,0000,0000,,Well, this is 100, is equal to\N9 plus A squared, or A squared
Dialogue: 0,0:03:23.86,0:03:29.72,Default,,0000,0000,0000,,is equal to 100 minus 9.
Dialogue: 0,0:03:29.72,0:03:32.56,Default,,0000,0000,0000,,A squared is equal to 91.
Dialogue: 0,0:03:32.56,0:03:38.39,Default,,0000,0000,0000,,
Dialogue: 0,0:03:38.39,0:03:40.39,Default,,0000,0000,0000,,I don't think that can be\Nsimplified further, either.
Dialogue: 0,0:03:40.39,0:03:41.71,Default,,0000,0000,0000,,3 doesn't go into it.
Dialogue: 0,0:03:41.71,0:03:43.95,Default,,0000,0000,0000,,I wonder, is 91 a prime number?
Dialogue: 0,0:03:43.95,0:03:44.88,Default,,0000,0000,0000,,I'm not sure.
Dialogue: 0,0:03:44.88,0:03:49.20,Default,,0000,0000,0000,,As far as I know, we're\Ndone with this problem.
Dialogue: 0,0:03:49.20,0:03:51.89,Default,,0000,0000,0000,,Let me give you another\Nproblem, And actually, this
Dialogue: 0,0:03:51.89,0:03:56.50,Default,,0000,0000,0000,,time I'm going to include one\Nextra step just to confuse you
Dialogue: 0,0:03:56.50,0:04:00.24,Default,,0000,0000,0000,,because I think you're getting\Nthis a little bit too easily.
Dialogue: 0,0:04:00.24,0:04:01.80,Default,,0000,0000,0000,,Let's say I have a triangle.
Dialogue: 0,0:04:01.80,0:04:05.13,Default,,0000,0000,0000,,
Dialogue: 0,0:04:05.13,0:04:07.99,Default,,0000,0000,0000,,And once again, we're dealing\Nall with right triangles now.
Dialogue: 0,0:04:07.99,0:04:10.13,Default,,0000,0000,0000,,And never are you going to\Nattempt to use the Pythagorean
Dialogue: 0,0:04:10.13,0:04:12.78,Default,,0000,0000,0000,,theorem unless you know for a\Nfact that's all right triangle.
Dialogue: 0,0:04:12.78,0:04:16.13,Default,,0000,0000,0000,,
Dialogue: 0,0:04:16.13,0:04:19.81,Default,,0000,0000,0000,,But this example, we know\Nthat this is right triangle.
Dialogue: 0,0:04:19.81,0:04:25.05,Default,,0000,0000,0000,,If I would tell you the length\Nof this side is 5, and if our
Dialogue: 0,0:04:25.05,0:04:32.81,Default,,0000,0000,0000,,tell you that this angle is 45\Ndegrees, can we figure out the
Dialogue: 0,0:04:32.81,0:04:36.41,Default,,0000,0000,0000,,other two sides of\Nthis triangle?
Dialogue: 0,0:04:36.41,0:04:38.22,Default,,0000,0000,0000,,Well, we can't use the\NPythagorean theorem directly
Dialogue: 0,0:04:38.22,0:04:40.83,Default,,0000,0000,0000,,because the Pythagorean theorem\Ntells us that if have a right
Dialogue: 0,0:04:40.83,0:04:43.75,Default,,0000,0000,0000,,triangle and we know two of the\Nsides that we can figure
Dialogue: 0,0:04:43.75,0:04:45.14,Default,,0000,0000,0000,,out the third side.
Dialogue: 0,0:04:45.14,0:04:47.32,Default,,0000,0000,0000,,Here we have a right\Ntriangle and we only
Dialogue: 0,0:04:47.32,0:04:48.87,Default,,0000,0000,0000,,know one of the sides.
Dialogue: 0,0:04:48.87,0:04:51.08,Default,,0000,0000,0000,,So we can't figure out\Nthe other two just yet.
Dialogue: 0,0:04:51.08,0:04:54.33,Default,,0000,0000,0000,,But maybe we can use this extra\Ninformation right here, this 45
Dialogue: 0,0:04:54.33,0:04:57.12,Default,,0000,0000,0000,,degrees, to figure out another\Nside, and then we'd be able
Dialogue: 0,0:04:57.12,0:04:59.28,Default,,0000,0000,0000,,use the Pythagorean theorem.
Dialogue: 0,0:04:59.28,0:05:01.81,Default,,0000,0000,0000,,Well, we know that the\Nangles in a triangle
Dialogue: 0,0:05:01.81,0:05:03.86,Default,,0000,0000,0000,,add up to 180 degrees.
Dialogue: 0,0:05:03.86,0:05:05.61,Default,,0000,0000,0000,,Well, hopefully you know\Nthe angles in a triangle
Dialogue: 0,0:05:05.61,0:05:06.63,Default,,0000,0000,0000,,add up to 180 degrees.
Dialogue: 0,0:05:06.63,0:05:08.32,Default,,0000,0000,0000,,If you don't it's my fault\Nbecause I haven't taught
Dialogue: 0,0:05:08.32,0:05:09.72,Default,,0000,0000,0000,,you that already.
Dialogue: 0,0:05:09.72,0:05:14.31,Default,,0000,0000,0000,,So let's figure out what\Nthe angles of this
Dialogue: 0,0:05:14.31,0:05:15.08,Default,,0000,0000,0000,,triangle add up to.
Dialogue: 0,0:05:15.08,0:05:17.41,Default,,0000,0000,0000,,Well, I mean we know they add\Nup to 180, but using that
Dialogue: 0,0:05:17.41,0:05:20.79,Default,,0000,0000,0000,,information, we could figure\Nout what this angle is.
Dialogue: 0,0:05:20.79,0:05:23.59,Default,,0000,0000,0000,,Because we know that this angle\Nis 90, this angle is 45.
Dialogue: 0,0:05:23.59,0:05:30.34,Default,,0000,0000,0000,,So we say 45-- lets call this\Nangle x; I'm trying to make it
Dialogue: 0,0:05:30.34,0:05:35.87,Default,,0000,0000,0000,,messy --45 plus 90--\Nthis just symbolizes
Dialogue: 0,0:05:35.87,0:05:40.72,Default,,0000,0000,0000,,a 90 degree angle --plus x\Nis equal to 180 degrees.
Dialogue: 0,0:05:40.72,0:05:43.52,Default,,0000,0000,0000,,And that's because the\Nangles in a triangle always
Dialogue: 0,0:05:43.52,0:05:46.74,Default,,0000,0000,0000,,add up to 180 degrees.
Dialogue: 0,0:05:46.74,0:05:55.97,Default,,0000,0000,0000,,So if we just solve for x, we\Nget 135 plus x is equal to 180.
Dialogue: 0,0:05:55.97,0:05:57.55,Default,,0000,0000,0000,,Subtract 135 from both sides.
Dialogue: 0,0:05:57.55,0:06:01.19,Default,,0000,0000,0000,,We get x is equal\Nto 45 degrees.
Dialogue: 0,0:06:01.19,0:06:02.68,Default,,0000,0000,0000,,Interesting.
Dialogue: 0,0:06:02.68,0:06:06.80,Default,,0000,0000,0000,,x is also 45 degrees.
Dialogue: 0,0:06:06.80,0:06:11.38,Default,,0000,0000,0000,,So we have a 90 degree angle\Nand two 45 degree angles.
Dialogue: 0,0:06:11.38,0:06:13.71,Default,,0000,0000,0000,,Now I'm going to give you\Nanother theorem that's not
Dialogue: 0,0:06:13.71,0:06:16.92,Default,,0000,0000,0000,,named after the head\Nof a religion or the
Dialogue: 0,0:06:16.92,0:06:17.56,Default,,0000,0000,0000,,founder of religion.
Dialogue: 0,0:06:17.56,0:06:19.73,Default,,0000,0000,0000,,I actually don't think this\Ntheorem doesn't have a name at.
Dialogue: 0,0:06:19.73,0:06:26.92,Default,,0000,0000,0000,,All It's the fact that if I\Nhave another triangle --I'm
Dialogue: 0,0:06:26.92,0:06:31.98,Default,,0000,0000,0000,,going to draw another triangle\Nout here --where two of the
Dialogue: 0,0:06:31.98,0:06:34.84,Default,,0000,0000,0000,,base angles are the same-- and\Nwhen I say base angle, I just
Dialogue: 0,0:06:34.84,0:06:39.89,Default,,0000,0000,0000,,mean if these two angles are\Nthe same, let's call it a.
Dialogue: 0,0:06:39.89,0:06:44.77,Default,,0000,0000,0000,,They're both a --then the sides\Nthat they don't share-- these
Dialogue: 0,0:06:44.77,0:06:46.61,Default,,0000,0000,0000,,angles share this side, right?
Dialogue: 0,0:06:46.61,0:06:49.56,Default,,0000,0000,0000,,--but if we look at the sides\Nthat they don't share, we know
Dialogue: 0,0:06:49.56,0:06:53.24,Default,,0000,0000,0000,,that these sides are equal.
Dialogue: 0,0:06:53.24,0:06:54.81,Default,,0000,0000,0000,,I forgot what we call\Nthis in geometry class.
Dialogue: 0,0:06:54.81,0:06:57.27,Default,,0000,0000,0000,,Maybe I'll look it up in\Nanother presentation;
Dialogue: 0,0:06:57.27,0:06:57.96,Default,,0000,0000,0000,,I'll let you know.
Dialogue: 0,0:06:57.96,0:07:00.04,Default,,0000,0000,0000,,But I got this far without\Nknowing what the name
Dialogue: 0,0:07:00.04,0:07:01.37,Default,,0000,0000,0000,,of the theorem is.
Dialogue: 0,0:07:01.37,0:07:04.17,Default,,0000,0000,0000,,And it makes sense; you don't\Neven need me to tell you that.
Dialogue: 0,0:07:04.17,0:07:07.08,Default,,0000,0000,0000,,
Dialogue: 0,0:07:07.08,0:07:10.48,Default,,0000,0000,0000,,If I were to change one of\Nthese angles, the length
Dialogue: 0,0:07:10.48,0:07:11.66,Default,,0000,0000,0000,,would also change.
Dialogue: 0,0:07:11.66,0:07:14.31,Default,,0000,0000,0000,,Or another way to think about\Nit, the only way-- no, I
Dialogue: 0,0:07:14.31,0:07:15.35,Default,,0000,0000,0000,,don't confuse you too much.
Dialogue: 0,0:07:15.35,0:07:18.82,Default,,0000,0000,0000,,But you can visually see that\Nif these two sides are the
Dialogue: 0,0:07:18.82,0:07:21.67,Default,,0000,0000,0000,,same, then these two angles\Nare going to be the same.
Dialogue: 0,0:07:21.67,0:07:25.43,Default,,0000,0000,0000,,If you changed one of these\Nsides' lengths, then the angles
Dialogue: 0,0:07:25.43,0:07:28.66,Default,,0000,0000,0000,,will also change, or the angles\Nwill not be equal anymore.
Dialogue: 0,0:07:28.66,0:07:31.12,Default,,0000,0000,0000,,But I'll leave that for\Nyou to think about.
Dialogue: 0,0:07:31.12,0:07:34.32,Default,,0000,0000,0000,,But just take my word for it\Nright now that if two angles in
Dialogue: 0,0:07:34.32,0:07:39.40,Default,,0000,0000,0000,,a triangle are equivalent, then\Nthe sides that they don't share
Dialogue: 0,0:07:39.40,0:07:41.69,Default,,0000,0000,0000,,are also equal in length.
Dialogue: 0,0:07:41.69,0:07:43.82,Default,,0000,0000,0000,,Make sure you remember: not the\Nside that they share-- because
Dialogue: 0,0:07:43.82,0:07:46.92,Default,,0000,0000,0000,,that can't be equal to anything\N--it's the side that they don't
Dialogue: 0,0:07:46.92,0:07:49.41,Default,,0000,0000,0000,,share are equal in length.
Dialogue: 0,0:07:49.41,0:07:52.99,Default,,0000,0000,0000,,So here we have an example\Nwhere we have to equal angles.
Dialogue: 0,0:07:52.99,0:07:55.02,Default,,0000,0000,0000,,They're both 45 degrees.
Dialogue: 0,0:07:55.02,0:07:58.91,Default,,0000,0000,0000,,So that means that the sides\Nthat they don't share-- this is
Dialogue: 0,0:07:58.91,0:08:00.23,Default,,0000,0000,0000,,the side they share, right?
Dialogue: 0,0:08:00.23,0:08:03.21,Default,,0000,0000,0000,,Both angle share this side --so\Nthat means that the side that
Dialogue: 0,0:08:03.21,0:08:05.08,Default,,0000,0000,0000,,they don't share are equal.
Dialogue: 0,0:08:05.08,0:08:08.46,Default,,0000,0000,0000,,So this side is\Nequal to this side.
Dialogue: 0,0:08:08.46,0:08:10.52,Default,,0000,0000,0000,,And I think you might be\Nexperiencing an ah-hah
Dialogue: 0,0:08:10.52,0:08:12.02,Default,,0000,0000,0000,,moment that right now.
Dialogue: 0,0:08:12.02,0:08:15.38,Default,,0000,0000,0000,,Well this side is equal to this\Nside-- I gave you at the
Dialogue: 0,0:08:15.38,0:08:18.05,Default,,0000,0000,0000,,beginning of this problem that\Nthis side is equal to 5 --so
Dialogue: 0,0:08:18.05,0:08:20.32,Default,,0000,0000,0000,,then we know that this\Nside is equal to 5.
Dialogue: 0,0:08:20.32,0:08:23.92,Default,,0000,0000,0000,,And now we can do the\NPythagorean theorem.
Dialogue: 0,0:08:23.92,0:08:25.75,Default,,0000,0000,0000,,We know this is the\Nhypotenuse, right?
Dialogue: 0,0:08:25.75,0:08:28.94,Default,,0000,0000,0000,,
Dialogue: 0,0:08:28.94,0:08:35.18,Default,,0000,0000,0000,,So we can say 5 squared plus 5\Nsquared is equal to-- let's say
Dialogue: 0,0:08:35.18,0:08:38.95,Default,,0000,0000,0000,,C squared, where C is the\Nlength of the hypotenuse --5
Dialogue: 0,0:08:38.95,0:08:42.01,Default,,0000,0000,0000,,squared plus 5 squared-- that's\Njust 50 --is equal
Dialogue: 0,0:08:42.01,0:08:44.11,Default,,0000,0000,0000,,to C squared.
Dialogue: 0,0:08:44.11,0:08:48.37,Default,,0000,0000,0000,,And then we get C is equal\Nto the square root of 50.
Dialogue: 0,0:08:48.37,0:08:56.25,Default,,0000,0000,0000,,And 50 is 2 times 25, so C is\Nequal to 5 square roots of 2.
Dialogue: 0,0:08:56.25,0:08:57.22,Default,,0000,0000,0000,,Interesting.
Dialogue: 0,0:08:57.22,0:09:00.11,Default,,0000,0000,0000,,So I think I might have given\Nyou a lot of information there.
Dialogue: 0,0:09:00.11,0:09:02.84,Default,,0000,0000,0000,,If you get confused, maybe you\Nwant to re-watch this video.
Dialogue: 0,0:09:02.84,0:09:05.63,Default,,0000,0000,0000,,But on the next video I'm\Nactually going to give you more
Dialogue: 0,0:09:05.63,0:09:08.10,Default,,0000,0000,0000,,information about this type of\Ntriangle, which is actually a
Dialogue: 0,0:09:08.10,0:09:11.55,Default,,0000,0000,0000,,very common type of triangle\Nyou'll see in geometry and
Dialogue: 0,0:09:11.55,0:09:14.47,Default,,0000,0000,0000,,trigonometry 45,\N45, 90 triangle.
Dialogue: 0,0:09:14.47,0:09:15.93,Default,,0000,0000,0000,,And it makes sense why it's\Ncalled that because it has
Dialogue: 0,0:09:15.93,0:09:19.93,Default,,0000,0000,0000,,45 degrees, 45 degrees,\Nand a 90 degree angle.
Dialogue: 0,0:09:19.93,0:09:22.46,Default,,0000,0000,0000,,And I'll actually show you\Na quick way of using that
Dialogue: 0,0:09:22.46,0:09:25.92,Default,,0000,0000,0000,,information that it is a 45,\N45, 90 degree triangle to
Dialogue: 0,0:09:25.92,0:09:29.52,Default,,0000,0000,0000,,figure out the size if you're\Ngiven even one of the sides.
Dialogue: 0,0:09:29.52,0:09:31.87,Default,,0000,0000,0000,,I hope I haven't confused you\Ntoo much, and I look forward
Dialogue: 0,0:09:31.87,0:09:33.20,Default,,0000,0000,0000,,to seeing you in the\Nnext presentation.
Dialogue: 0,0:09:33.20,0:09:35.12,Default,,0000,0000,0000,,See you later.