[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.94,0:00:01.57,Default,,0000,0000,0000,,Welcome back.
Dialogue: 0,0:00:01.57,0:00:06.68,Default,,0000,0000,0000,,I'm on problem number 10.
Dialogue: 0,0:00:06.68,0:00:10.98,Default,,0000,0000,0000,,Phillip used 4 pieces of masking\Ntape, each 6 inches
Dialogue: 0,0:00:10.98,0:00:25.02,Default,,0000,0000,0000,,long, to put up each\Nof his posters.
Dialogue: 0,0:00:27.65,0:00:30.15,Default,,0000,0000,0000,,So this is per poster.
Dialogue: 0,0:00:33.08,0:00:34.06,Default,,0000,0000,0000,,Good enough.
Dialogue: 0,0:00:34.06,0:00:37.61,Default,,0000,0000,0000,,Phillip had a 300-foot roll of\Nmasking tape when he started.
Dialogue: 0,0:00:37.61,0:00:40.13,Default,,0000,0000,0000,,So he starts at 300 feet.
Dialogue: 0,0:00:40.13,0:00:42.76,Default,,0000,0000,0000,,I can already tell you that\Nsome unit conversion will
Dialogue: 0,0:00:42.76,0:00:45.18,Default,,0000,0000,0000,,happen, because they're talking\Nabout 6 inches here
Dialogue: 0,0:00:45.18,0:00:47.94,Default,,0000,0000,0000,,and they're talking about\N300 feet here.
Dialogue: 0,0:00:47.94,0:00:51.85,Default,,0000,0000,0000,,If no tape was wasted, which\Nof the following represents
Dialogue: 0,0:00:51.85,0:00:55.33,Default,,0000,0000,0000,,the number of feet--and they\Nunderline it-- of masking tape
Dialogue: 0,0:00:55.33,0:00:59.08,Default,,0000,0000,0000,,that was left on the roll after\Nhe put up the n posters?
Dialogue: 0,0:00:59.08,0:01:02.33,Default,,0000,0000,0000,,And they actually tell us that\N12 inches are equal to a foot
Dialogue: 0,0:01:02.33,0:01:06.14,Default,,0000,0000,0000,,in case you aren't\Nfrom this planet.
Dialogue: 0,0:01:06.14,0:01:07.72,Default,,0000,0000,0000,,So how do we do this?
Dialogue: 0,0:01:12.52,0:01:15.46,Default,,0000,0000,0000,,So he's going to put\Nup n posters.
Dialogue: 0,0:01:15.46,0:01:17.63,Default,,0000,0000,0000,,So he's going to start\Noff-- well, how much
Dialogue: 0,0:01:17.63,0:01:18.83,Default,,0000,0000,0000,,tape will he use?
Dialogue: 0,0:01:18.83,0:01:21.39,Default,,0000,0000,0000,,So for each of those n posters,\Nhow much will he use?
Dialogue: 0,0:01:21.39,0:01:26.98,Default,,0000,0000,0000,,He uses 4 pieces\Ntimes 6 inches.
Dialogue: 0,0:01:26.98,0:01:28.30,Default,,0000,0000,0000,,But we want to go into feet.
Dialogue: 0,0:01:28.30,0:01:29.23,Default,,0000,0000,0000,,We want to know how many\Nfeet are left.
Dialogue: 0,0:01:29.23,0:01:31.17,Default,,0000,0000,0000,,So let's just convert\Nimmediately to feet.
Dialogue: 0,0:01:31.17,0:01:36.07,Default,,0000,0000,0000,,6 inches is equal to\Nhow many feet?
Dialogue: 0,0:01:36.07,0:01:37.98,Default,,0000,0000,0000,,Well, it's half a foot.
Dialogue: 0,0:01:37.98,0:01:39.16,Default,,0000,0000,0000,,6/12 inches.
Dialogue: 0,0:01:39.16,0:01:42.00,Default,,0000,0000,0000,,So it equals 1/2 foot.
Dialogue: 0,0:01:42.00,0:01:46.79,Default,,0000,0000,0000,,So he does 4 pieces for each\Nposter, and each of those
Dialogue: 0,0:01:46.79,0:01:48.64,Default,,0000,0000,0000,,pieces is 1/2 foot.
Dialogue: 0,0:01:48.64,0:01:50.80,Default,,0000,0000,0000,,And now we're immediately\Nin feet length.
Dialogue: 0,0:01:50.80,0:01:52.29,Default,,0000,0000,0000,,So this is how much he uses.
Dialogue: 0,0:01:52.29,0:01:55.79,Default,,0000,0000,0000,,So he will use-- so 4\Ntimes 1/2 is just 2.
Dialogue: 0,0:01:55.79,0:01:57.64,Default,,0000,0000,0000,,So he uses 2n feet.
Dialogue: 0,0:02:00.40,0:02:06.21,Default,,0000,0000,0000,,So if he starts with 300, the\Namount that he has left is
Dialogue: 0,0:02:06.21,0:02:08.48,Default,,0000,0000,0000,,what he started with\Nminus what he used.
Dialogue: 0,0:02:08.48,0:02:10.90,Default,,0000,0000,0000,,He used 2n.
Dialogue: 0,0:02:10.90,0:02:14.36,Default,,0000,0000,0000,,So he starts with 300 feet minus\N2n feet, so that's the
Dialogue: 0,0:02:14.36,0:02:15.35,Default,,0000,0000,0000,,expression.
Dialogue: 0,0:02:15.35,0:02:18.60,Default,,0000,0000,0000,,That's choice B.
Dialogue: 0,0:02:18.60,0:02:20.68,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:02:20.68,0:02:24.99,Default,,0000,0000,0000,,Problem 11.
Dialogue: 0,0:02:24.99,0:02:28.87,Default,,0000,0000,0000,,I'll switch to magenta.
Dialogue: 0,0:02:28.87,0:02:32.45,Default,,0000,0000,0000,,In the x, y coordinate plane,\Nline m is the reflection of
Dialogue: 0,0:02:32.45,0:02:35.32,Default,,0000,0000,0000,,line l about the x-axis.
Dialogue: 0,0:02:35.32,0:02:42.65,Default,,0000,0000,0000,,If the slope of m-- so m slope--\Nis equal to minus 4/5,
Dialogue: 0,0:02:42.65,0:02:45.30,Default,,0000,0000,0000,,what is the slope of l?
Dialogue: 0,0:02:45.30,0:02:48.00,Default,,0000,0000,0000,,So you should hopefully be able\Nto do this on the real
Dialogue: 0,0:02:48.00,0:02:50.98,Default,,0000,0000,0000,,exam without having\Nto draw it.
Dialogue: 0,0:02:50.98,0:02:53.33,Default,,0000,0000,0000,,Or you could actually just draw\Na really quick and dirty
Dialogue: 0,0:02:53.33,0:02:55.74,Default,,0000,0000,0000,,one, and that actually\Nprobably would
Dialogue: 0,0:02:55.74,0:02:56.99,Default,,0000,0000,0000,,do the job for you.
Dialogue: 0,0:03:00.02,0:03:01.45,Default,,0000,0000,0000,,So minus 4/5.
Dialogue: 0,0:03:01.45,0:03:05.46,Default,,0000,0000,0000,,That means for every\N5-- and it's a
Dialogue: 0,0:03:05.46,0:03:06.51,Default,,0000,0000,0000,,reflection about the x-axis.
Dialogue: 0,0:03:06.51,0:03:08.80,Default,,0000,0000,0000,,So let's draw a line m.
Dialogue: 0,0:03:12.87,0:03:14.51,Default,,0000,0000,0000,,Now let's just assume that\Nthe origin's here.
Dialogue: 0,0:03:14.51,0:03:16.35,Default,,0000,0000,0000,,They don't tell us that,\Nbut they don't
Dialogue: 0,0:03:16.35,0:03:17.15,Default,,0000,0000,0000,,tell us it's not that.
Dialogue: 0,0:03:17.15,0:03:21.86,Default,,0000,0000,0000,,So that's zero, one, two,\Nthree, four, five.
Dialogue: 0,0:03:21.86,0:03:24.90,Default,,0000,0000,0000,,And this is one, two,\Nthree, four.
Dialogue: 0,0:03:24.90,0:03:25.85,Default,,0000,0000,0000,,Let me do it here.
Dialogue: 0,0:03:25.85,0:03:28.33,Default,,0000,0000,0000,,One, two, three, four.
Dialogue: 0,0:03:28.33,0:03:30.49,Default,,0000,0000,0000,,I just want to draw it\Nso you understand.
Dialogue: 0,0:03:30.49,0:03:34.41,Default,,0000,0000,0000,,So 4, minus 4, this is 5.
Dialogue: 0,0:03:34.41,0:03:36.12,Default,,0000,0000,0000,,So we know line m.
Dialogue: 0,0:03:36.12,0:03:42.53,Default,,0000,0000,0000,,For every line m, for every\N5 it goes to the right,
Dialogue: 0,0:03:42.53,0:03:43.45,Default,,0000,0000,0000,,it goes down 4.
Dialogue: 0,0:03:43.45,0:03:46.59,Default,,0000,0000,0000,,So this could be a legitimate\Nline m right here.
Dialogue: 0,0:03:46.59,0:03:48.67,Default,,0000,0000,0000,,It could be like this.
Dialogue: 0,0:03:48.67,0:03:50.84,Default,,0000,0000,0000,,Line m could look like that.
Dialogue: 0,0:03:54.17,0:03:57.37,Default,,0000,0000,0000,,So a reflection about the\Nx-axis, if I were to reflect
Dialogue: 0,0:03:57.37,0:04:00.52,Default,,0000,0000,0000,,it about the x-axis.
Dialogue: 0,0:04:00.52,0:04:04.16,Default,,0000,0000,0000,,This is the x-axis right here,\Nso I just want to take its
Dialogue: 0,0:04:04.16,0:04:06.19,Default,,0000,0000,0000,,mirror image, or flip\Nit over the x-axis.
Dialogue: 0,0:04:06.19,0:04:07.44,Default,,0000,0000,0000,,It would look like this.
Dialogue: 0,0:04:11.90,0:04:14.96,Default,,0000,0000,0000,,Oh, I thought I was using\Nthe line tool.
Dialogue: 0,0:04:14.96,0:04:16.21,Default,,0000,0000,0000,,It would look like this.
Dialogue: 0,0:04:18.83,0:04:20.95,Default,,0000,0000,0000,,I'm still not using\Nthe line tool.
Dialogue: 0,0:04:20.95,0:04:23.43,Default,,0000,0000,0000,,Now, I'm using the line tool.
Dialogue: 0,0:04:23.43,0:04:25.44,Default,,0000,0000,0000,,It would look like\Nthat, right?
Dialogue: 0,0:04:25.44,0:04:27.27,Default,,0000,0000,0000,,So what's the slope here?
Dialogue: 0,0:04:27.27,0:04:35.23,Default,,0000,0000,0000,,Well, for every 5 I go to\Nthe right, I move up 4.
Dialogue: 0,0:04:35.23,0:04:37.94,Default,,0000,0000,0000,,So change in y.
Dialogue: 0,0:04:37.94,0:04:40.79,Default,,0000,0000,0000,,Let me make sure this is\Nline m, this is line l.
Dialogue: 0,0:04:40.79,0:04:47.35,Default,,0000,0000,0000,,Change in y over change in\Nx for line l is equal to
Dialogue: 0,0:04:47.35,0:04:48.60,Default,,0000,0000,0000,,positive 4/5.
Dialogue: 0,0:04:52.26,0:04:55.00,Default,,0000,0000,0000,,It shouldn't take you\Nthat long to do it.
Dialogue: 0,0:04:55.00,0:04:57.72,Default,,0000,0000,0000,,One thing that you could just\Ndo as well, you could just
Dialogue: 0,0:04:57.72,0:04:58.53,Default,,0000,0000,0000,,draw a quick and dirty one.
Dialogue: 0,0:04:58.53,0:05:00.16,Default,,0000,0000,0000,,It's like, well, if I have\Nsomething with a negative
Dialogue: 0,0:05:00.16,0:05:02.64,Default,,0000,0000,0000,,slope-- let's say I have\Na negative, really
Dialogue: 0,0:05:02.64,0:05:04.59,Default,,0000,0000,0000,,shallow slope like that.
Dialogue: 0,0:05:04.59,0:05:07.04,Default,,0000,0000,0000,,If I flip it, it's going to have\Nthe same slope, but it's
Dialogue: 0,0:05:07.04,0:05:08.62,Default,,0000,0000,0000,,going to be a positive slope,\Nbut it's still going to be
Dialogue: 0,0:05:08.62,0:05:12.26,Default,,0000,0000,0000,,shallow, so it's going to\Nbe the same magnitude.
Dialogue: 0,0:05:12.26,0:05:14.29,Default,,0000,0000,0000,,You'll flip the sign.
Dialogue: 0,0:05:14.29,0:05:16.10,Default,,0000,0000,0000,,So the answer is B, 4/5.
Dialogue: 0,0:05:16.10,0:05:18.92,Default,,0000,0000,0000,,But I did this just to give\Nyou the intuition.
Dialogue: 0,0:05:18.92,0:05:21.94,Default,,0000,0000,0000,,The next problem.
Dialogue: 0,0:05:21.94,0:05:24.55,Default,,0000,0000,0000,,Or to let you know why you got\Nit wrong, if you got it wrong.
Dialogue: 0,0:05:24.55,0:05:24.96,Default,,0000,0000,0000,,Anyway.
Dialogue: 0,0:05:24.96,0:05:28.09,Default,,0000,0000,0000,,Problem number 12.
Dialogue: 0,0:05:28.09,0:05:37.90,Default,,0000,0000,0000,,If n is equal to 3p, for what\Nvalue of p is n equal to p?
Dialogue: 0,0:05:51.63,0:05:53.38,Default,,0000,0000,0000,,This is kind of crazy.
Dialogue: 0,0:05:53.38,0:05:56.24,Default,,0000,0000,0000,,And at first, I was like,\Nwhat are they saying?
Dialogue: 0,0:05:56.24,0:05:57.89,Default,,0000,0000,0000,,And then I read one\Nof the choices.
Dialogue: 0,0:05:57.89,0:06:02.81,Default,,0000,0000,0000,,Because no matter what,\Nn is equal to 3p.
Dialogue: 0,0:06:02.81,0:06:08.10,Default,,0000,0000,0000,,There's no circumstance--\Nwell, oh, sorry.
Dialogue: 0,0:06:08.10,0:06:09.82,Default,,0000,0000,0000,,I was incorrect.
Dialogue: 0,0:06:09.82,0:06:12.35,Default,,0000,0000,0000,,There is a circumstance in\Nwhich n is equal to 3p.
Dialogue: 0,0:06:15.85,0:06:19.07,Default,,0000,0000,0000,,Well, what's the circumstance?
Dialogue: 0,0:06:19.07,0:06:25.29,Default,,0000,0000,0000,,Well, you might initially say,\Nwell, as long as p is not 0, n
Dialogue: 0,0:06:25.29,0:06:28.58,Default,,0000,0000,0000,,is going to be exactly\N3 times p.
Dialogue: 0,0:06:28.58,0:06:31.89,Default,,0000,0000,0000,,But then in our statement, I\Njust told you the answer.
Dialogue: 0,0:06:31.89,0:06:33.75,Default,,0000,0000,0000,,They both can be 0.
Dialogue: 0,0:06:33.75,0:06:37.68,Default,,0000,0000,0000,,If p is 0, then 3\Ntimes 0 is 0.
Dialogue: 0,0:06:37.68,0:06:39.54,Default,,0000,0000,0000,,So there's no real\Nalgebra there.
Dialogue: 0,0:06:39.54,0:06:42.31,Default,,0000,0000,0000,,It's just kind of to realize\Nthat 0 is a choice.
Dialogue: 0,0:06:42.31,0:06:43.97,Default,,0000,0000,0000,,And if you looked at the\Nchoices, you'd immediately see
Dialogue: 0,0:06:43.97,0:06:45.16,Default,,0000,0000,0000,,choice A is 0.
Dialogue: 0,0:06:45.16,0:06:45.87,Default,,0000,0000,0000,,Try it out.
Dialogue: 0,0:06:45.87,0:06:49.18,Default,,0000,0000,0000,,You say, oh, well, if p is\N0, then n is also 0.
Dialogue: 0,0:06:49.18,0:06:51.93,Default,,0000,0000,0000,,So then n would equal p.
Dialogue: 0,0:06:51.93,0:06:53.14,Default,,0000,0000,0000,,So next problem.
Dialogue: 0,0:06:53.14,0:06:56.31,Default,,0000,0000,0000,,Problem 13.
Dialogue: 0,0:06:56.31,0:06:58.92,Default,,0000,0000,0000,,That was one of those problems\Nthat in some ways are so easy
Dialogue: 0,0:06:58.92,0:07:00.70,Default,,0000,0000,0000,,that you waste time\Non it, making sure
Dialogue: 0,0:07:00.70,0:07:03.30,Default,,0000,0000,0000,,you didn't miss something.
Dialogue: 0,0:07:03.30,0:07:07.26,Default,,0000,0000,0000,,Let's draw what they drew.
Dialogue: 0,0:07:07.26,0:07:09.35,Default,,0000,0000,0000,,So we have a line like that.
Dialogue: 0,0:07:09.35,0:07:11.38,Default,,0000,0000,0000,,I have a line like that.
Dialogue: 0,0:07:11.38,0:07:15.03,Default,,0000,0000,0000,,Then I have a line like that.
Dialogue: 0,0:07:15.03,0:07:18.25,Default,,0000,0000,0000,,And this is line l.
Dialogue: 0,0:07:18.25,0:07:20.58,Default,,0000,0000,0000,,This is y degrees.
Dialogue: 0,0:07:20.58,0:07:23.43,Default,,0000,0000,0000,,This is line m.
Dialogue: 0,0:07:23.43,0:07:29.52,Default,,0000,0000,0000,,This is x degrees, and this\Nis line n right here.
Dialogue: 0,0:07:29.52,0:07:32.44,Default,,0000,0000,0000,,In the figure above, if z--\Noh, they tell us this is z
Dialogue: 0,0:07:32.44,0:07:34.67,Default,,0000,0000,0000,,right here.
Dialogue: 0,0:07:34.67,0:07:42.16,Default,,0000,0000,0000,,In the figure above, if z is\Nequal to 30, what is the value
Dialogue: 0,0:07:42.16,0:07:44.67,Default,,0000,0000,0000,,of x plus y?
Dialogue: 0,0:07:44.67,0:07:46.72,Default,,0000,0000,0000,,x plus y is what?
Dialogue: 0,0:07:46.72,0:07:48.80,Default,,0000,0000,0000,,Well, what can we figure out?
Dialogue: 0,0:07:48.80,0:07:53.05,Default,,0000,0000,0000,,What do we know about this\Nangle right here?
Dialogue: 0,0:07:53.05,0:07:55.13,Default,,0000,0000,0000,,It's supplementary\Nto y, right?
Dialogue: 0,0:07:55.13,0:07:56.76,Default,,0000,0000,0000,,So this is kind of the angle\Ngame, but we're going to have
Dialogue: 0,0:07:56.76,0:07:59.26,Default,,0000,0000,0000,,a little bit more variables\Nthan normal.
Dialogue: 0,0:07:59.26,0:08:01.81,Default,,0000,0000,0000,,It's supplementary to y, so this\Nis going to be 180 minus
Dialogue: 0,0:08:01.81,0:08:03.88,Default,,0000,0000,0000,,y because y plus this\Nangle are going to
Dialogue: 0,0:08:03.88,0:08:05.61,Default,,0000,0000,0000,,have to equal 180.
Dialogue: 0,0:08:05.61,0:08:07.98,Default,,0000,0000,0000,,And for the exact same reason,\Nthis angle right here
Dialogue: 0,0:08:07.98,0:08:12.87,Default,,0000,0000,0000,,is 180 minus x.
Dialogue: 0,0:08:12.87,0:08:13.53,Default,,0000,0000,0000,,And what do we know?
Dialogue: 0,0:08:13.53,0:08:17.12,Default,,0000,0000,0000,,We know this angle plus this\Nangle plus z is equal to 180.
Dialogue: 0,0:08:17.12,0:08:18.73,Default,,0000,0000,0000,,So let's write that down.
Dialogue: 0,0:08:18.73,0:08:29.23,Default,,0000,0000,0000,,This angle, 180 minus y, plus\Nthis angle, plus 180 minus x,
Dialogue: 0,0:08:29.23,0:08:33.42,Default,,0000,0000,0000,,plus z is equal to 180\Nbecause they're
Dialogue: 0,0:08:33.42,0:08:35.39,Default,,0000,0000,0000,,all in the same triangle.
Dialogue: 0,0:08:35.39,0:08:37.38,Default,,0000,0000,0000,,So let's try our best\Nto simplify this.
Dialogue: 0,0:08:37.38,0:08:44.54,Default,,0000,0000,0000,,Well, we could immediately get\Nrid of one of the 180's on
Dialogue: 0,0:08:44.54,0:08:47.61,Default,,0000,0000,0000,,that side, and that becomes 0.
Dialogue: 0,0:08:47.61,0:08:50.10,Default,,0000,0000,0000,,z is 30, right?
Dialogue: 0,0:08:50.10,0:08:51.49,Default,,0000,0000,0000,,So let's simplify it.
Dialogue: 0,0:08:51.49,0:08:58.99,Default,,0000,0000,0000,,We get minus y minus x, and\Nthen you have 180 plus 30,
Dialogue: 0,0:08:58.99,0:09:02.66,Default,,0000,0000,0000,,plus 210, is equal to 0.
Dialogue: 0,0:09:02.66,0:09:05.16,Default,,0000,0000,0000,,Now let's add x and\Ny to both sides.
Dialogue: 0,0:09:05.16,0:09:06.10,Default,,0000,0000,0000,,I'm kind of skipping a step.
Dialogue: 0,0:09:06.10,0:09:08.44,Default,,0000,0000,0000,,You could add x to both sides\Nand then add y to both sides.
Dialogue: 0,0:09:08.44,0:09:12.41,Default,,0000,0000,0000,,But if you add x and y to both\Nsides, you get 210 is
Dialogue: 0,0:09:12.41,0:09:14.19,Default,,0000,0000,0000,,equal to x plus y.
Dialogue: 0,0:09:14.19,0:09:15.68,Default,,0000,0000,0000,,And that's the answer.
Dialogue: 0,0:09:15.68,0:09:17.71,Default,,0000,0000,0000,,They want to know what\Nx plus y is.
Dialogue: 0,0:09:17.71,0:09:20.44,Default,,0000,0000,0000,,And that is choice D.
Dialogue: 0,0:09:20.44,0:09:22.06,Default,,0000,0000,0000,,And so the trick here is really\Nsaying, well, they
Dialogue: 0,0:09:22.06,0:09:23.37,Default,,0000,0000,0000,,only give us z.
Dialogue: 0,0:09:23.37,0:09:26.44,Default,,0000,0000,0000,,The only thing I know is that\Nz is in a triangle with this
Dialogue: 0,0:09:26.44,0:09:28.22,Default,,0000,0000,0000,,angle and this angle.
Dialogue: 0,0:09:28.22,0:09:30.80,Default,,0000,0000,0000,,And let me express those two\Nangles in terms of x and y,
Dialogue: 0,0:09:30.80,0:09:34.80,Default,,0000,0000,0000,,because they are supplementary\Nto x and y.
Dialogue: 0,0:09:34.80,0:09:36.61,Default,,0000,0000,0000,,See you in the next video.