[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.66,0:00:04.33,Default,,0000,0000,0000,,We're now on problem\Nnumber seven.
Dialogue: 0,0:00:04.33,0:00:08.10,Default,,0000,0000,0000,,Problem number seven says x\Nequals 1/2, or if x equals
Dialogue: 0,0:00:08.10,0:00:15.78,Default,,0000,0000,0000,,1/2, what is the value of 1 over\Nz plus 1 over x minus 1?
Dialogue: 0,0:00:15.78,0:00:21.62,Default,,0000,0000,0000,,So 1 over x, well that's just\N1 over 1/2 plus 1 over--
Dialogue: 0,0:00:21.62,0:00:22.58,Default,,0000,0000,0000,,what's x minus 1?
Dialogue: 0,0:00:22.58,0:00:24.74,Default,,0000,0000,0000,,What's 1/2 minus 1?
Dialogue: 0,0:00:24.74,0:00:27.05,Default,,0000,0000,0000,,What's minus 1/2, right?
Dialogue: 0,0:00:27.05,0:00:31.18,Default,,0000,0000,0000,,So this is x minus\N1 is minus 1/2.
Dialogue: 0,0:00:31.18,0:00:33.96,Default,,0000,0000,0000,,And you could evaluate it.
Dialogue: 0,0:00:33.96,0:00:36.28,Default,,0000,0000,0000,,Or you could immediately see\Nthat these would cancel out,
Dialogue: 0,0:00:36.28,0:00:38.15,Default,,0000,0000,0000,,because you could take this\Nminus and put it right here
Dialogue: 0,0:00:38.15,0:00:40.13,Default,,0000,0000,0000,,and make this a plus.
Dialogue: 0,0:00:40.13,0:00:42.74,Default,,0000,0000,0000,,Or you could evaluate it and say\Nwell, this is equal to 2
Dialogue: 0,0:00:42.74,0:00:45.53,Default,,0000,0000,0000,,minus 2 and that equals 0.
Dialogue: 0,0:00:45.53,0:00:47.88,Default,,0000,0000,0000,,So this is just kind of a speed\Nquestion to see how fast
Dialogue: 0,0:00:47.88,0:00:48.84,Default,,0000,0000,0000,,you can do it.
Dialogue: 0,0:00:48.84,0:00:50.83,Default,,0000,0000,0000,,How much time do you\Nwaste on this?
Dialogue: 0,0:00:50.83,0:00:52.33,Default,,0000,0000,0000,,OK, problem number eight.
Dialogue: 0,0:00:56.29,0:00:57.37,Default,,0000,0000,0000,,I'll do it in green.
Dialogue: 0,0:00:57.37,0:00:59.40,Default,,0000,0000,0000,,Let's see, let me draw that.
Dialogue: 0,0:00:59.40,0:01:02.94,Default,,0000,0000,0000,,So we've got a coordinate\Naxis.
Dialogue: 0,0:01:02.94,0:01:05.39,Default,,0000,0000,0000,,Oh, my god.
Dialogue: 0,0:01:05.39,0:01:07.91,Default,,0000,0000,0000,,Edit, undo.
Dialogue: 0,0:01:07.91,0:01:09.30,Default,,0000,0000,0000,,It's a coordinate axis.
Dialogue: 0,0:01:09.30,0:01:11.63,Default,,0000,0000,0000,,I didn't have my line tool on.
Dialogue: 0,0:01:11.63,0:01:14.55,Default,,0000,0000,0000,,And then that's the x-axis.
Dialogue: 0,0:01:14.55,0:01:15.80,Default,,0000,0000,0000,,This is the y-axis.
Dialogue: 0,0:01:18.74,0:01:21.56,Default,,0000,0000,0000,,Then let me draw some\Npoints here.
Dialogue: 0,0:01:21.56,0:01:23.96,Default,,0000,0000,0000,,I have the point right here.
Dialogue: 0,0:01:23.96,0:01:25.87,Default,,0000,0000,0000,,They say this is 1, 0.
Dialogue: 0,0:01:28.79,0:01:31.30,Default,,0000,0000,0000,,Let's see, x-axis.
Dialogue: 0,0:01:31.30,0:01:33.53,Default,,0000,0000,0000,,That's the y-axis.
Dialogue: 0,0:01:33.53,0:01:36.21,Default,,0000,0000,0000,,So then I still use\Nthe line tool.
Dialogue: 0,0:01:39.52,0:01:43.20,Default,,0000,0000,0000,,They have this going straight\Nup like this.
Dialogue: 0,0:01:43.20,0:01:44.45,Default,,0000,0000,0000,,It goes like that.
Dialogue: 0,0:01:50.20,0:01:52.68,Default,,0000,0000,0000,,Right angle there.
Dialogue: 0,0:01:52.68,0:01:54.80,Default,,0000,0000,0000,,Right angle there.
Dialogue: 0,0:01:54.80,0:01:57.30,Default,,0000,0000,0000,,This is point s.
Dialogue: 0,0:01:57.30,0:02:00.33,Default,,0000,0000,0000,,This is point t.
Dialogue: 0,0:02:00.33,0:02:04.53,Default,,0000,0000,0000,,This is point r.
Dialogue: 0,0:02:04.53,0:02:12.34,Default,,0000,0000,0000,,They say in the figure above\Nr, s is equal to s, t.
Dialogue: 0,0:02:12.34,0:02:14.96,Default,,0000,0000,0000,,That's just saying that their\Nlengths are equal.
Dialogue: 0,0:02:14.96,0:02:20.18,Default,,0000,0000,0000,,And the coordinate of s,\Nright here, is k, 3.
Dialogue: 0,0:02:23.79,0:02:24.46,Default,,0000,0000,0000,,So what does that tell us?
Dialogue: 0,0:02:24.46,0:02:27.14,Default,,0000,0000,0000,,That means that the x value,\Nright here, this point
Dialogue: 0,0:02:27.14,0:02:29.79,Default,,0000,0000,0000,,right here is k.
Dialogue: 0,0:02:29.79,0:02:33.57,Default,,0000,0000,0000,,And that this y value, right\Nhere, is 3, right? k, 3.
Dialogue: 0,0:02:33.57,0:02:34.56,Default,,0000,0000,0000,,That's not t, 3.
Dialogue: 0,0:02:34.56,0:02:38.41,Default,,0000,0000,0000,,I'm just saying the y value\Nright here is 3.
Dialogue: 0,0:02:38.41,0:02:41.72,Default,,0000,0000,0000,,What is the value of k?
Dialogue: 0,0:02:41.72,0:02:46.30,Default,,0000,0000,0000,,Well we know that this length\Nand this length
Dialogue: 0,0:02:46.30,0:02:48.85,Default,,0000,0000,0000,,are the same, right?
Dialogue: 0,0:02:48.85,0:02:50.10,Default,,0000,0000,0000,,What is this length?
Dialogue: 0,0:02:53.67,0:02:55.77,Default,,0000,0000,0000,,Actually, that was a very\Nugly curly bracket.
Dialogue: 0,0:02:55.77,0:02:58.85,Default,,0000,0000,0000,,But we know the y value\Nhere is 3, right?
Dialogue: 0,0:02:58.85,0:03:01.56,Default,,0000,0000,0000,,This intersects the y,\Nintercepts at 3 right here, so
Dialogue: 0,0:03:01.56,0:03:03.55,Default,,0000,0000,0000,,we know that distance is 3.
Dialogue: 0,0:03:03.55,0:03:05.95,Default,,0000,0000,0000,,We know that this\Ndistance is 3.
Dialogue: 0,0:03:05.95,0:03:07.53,Default,,0000,0000,0000,,That's also 3.
Dialogue: 0,0:03:07.53,0:03:09.80,Default,,0000,0000,0000,,And we also know that this is\Nequal to this, so we also know
Dialogue: 0,0:03:09.80,0:03:11.94,Default,,0000,0000,0000,,that this distance is 3.
Dialogue: 0,0:03:11.94,0:03:15.04,Default,,0000,0000,0000,,And if that distance is 3, we\Nknow that this distance is 3.
Dialogue: 0,0:03:15.04,0:03:20.90,Default,,0000,0000,0000,,But we're 3 to the left\Nof the y-axis, right?
Dialogue: 0,0:03:20.90,0:03:23.35,Default,,0000,0000,0000,,We've gone 3 units in the\Nnegative direction.
Dialogue: 0,0:03:23.35,0:03:26.09,Default,,0000,0000,0000,,So the value of k, or the\Nx-coordinate here would be
Dialogue: 0,0:03:26.09,0:03:27.97,Default,,0000,0000,0000,,negative 3 because we\Nwent 3 to the left.
Dialogue: 0,0:03:27.97,0:03:29.91,Default,,0000,0000,0000,,If it was out here it'd be\Npositive 3, but since it's
Dialogue: 0,0:03:29.91,0:03:34.76,Default,,0000,0000,0000,,here it's negative 3,\Nand that's choice A.
Dialogue: 0,0:03:34.76,0:03:36.97,Default,,0000,0000,0000,,Next question, number nine.
Dialogue: 0,0:03:41.15,0:03:43.76,Default,,0000,0000,0000,,OK, let's see.
Dialogue: 0,0:03:43.76,0:03:48.36,Default,,0000,0000,0000,,So they drew a table and\NI'll just write it the
Dialogue: 0,0:03:48.36,0:03:48.88,Default,,0000,0000,0000,,way they did it.
Dialogue: 0,0:03:48.88,0:03:53.69,Default,,0000,0000,0000,,So they did x and f of x.
Dialogue: 0,0:03:53.69,0:04:02.39,Default,,0000,0000,0000,,And then they say 0, 1,\N2, 3, 1, 2, 5, 10.
Dialogue: 0,0:04:02.39,0:04:05.68,Default,,0000,0000,0000,,The table above gives the\Nvalues of the quadratic
Dialogue: 0,0:04:05.68,0:04:08.32,Default,,0000,0000,0000,,function f for the selected\Nvalues of x.
Dialogue: 0,0:04:08.32,0:04:10.98,Default,,0000,0000,0000,,Which of the following\Ndefines f?
Dialogue: 0,0:04:10.98,0:04:13.73,Default,,0000,0000,0000,,So it's a quadratic function, so\Nwe know it's going to have
Dialogue: 0,0:04:13.73,0:04:18.34,Default,,0000,0000,0000,,the form-- f of x is going to be\Nsomething like x squared--
Dialogue: 0,0:04:18.34,0:04:23.81,Default,,0000,0000,0000,,well it could be ax squared\Nplus bx plus c.
Dialogue: 0,0:04:23.81,0:04:26.24,Default,,0000,0000,0000,,My suspicion though is it's\Ngoing to be something fairly
Dialogue: 0,0:04:26.24,0:04:27.90,Default,,0000,0000,0000,,you-- simple.
Dialogue: 0,0:04:27.90,0:04:29.58,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:04:29.58,0:04:31.73,Default,,0000,0000,0000,,The way I would do it is I would\Nplay around with it.
Dialogue: 0,0:04:31.73,0:04:37.91,Default,,0000,0000,0000,,So if I squared this x value and\NI still end up with a 1--
Dialogue: 0,0:04:37.91,0:04:39.94,Default,,0000,0000,0000,,and this is actually the biggest\Nclue right here,
Dialogue: 0,0:04:39.94,0:04:43.14,Default,,0000,0000,0000,,because when x is\N0, f of x is 1.
Dialogue: 0,0:04:43.14,0:04:45.34,Default,,0000,0000,0000,,So we know that this constant\Nterm is going to be 1.
Dialogue: 0,0:04:45.34,0:04:49.19,Default,,0000,0000,0000,,It's going to be something plus\N1 because when x is 0,
Dialogue: 0,0:04:49.19,0:04:52.25,Default,,0000,0000,0000,,these things are equal to 0,\Nthis ax squared plus bx.
Dialogue: 0,0:04:52.25,0:04:53.60,Default,,0000,0000,0000,,And we still have\Nit equal to 1.
Dialogue: 0,0:04:53.60,0:04:54.90,Default,,0000,0000,0000,,So we know c is 1.
Dialogue: 0,0:04:54.90,0:04:57.21,Default,,0000,0000,0000,,So we know that already,\Nthat's ax squared
Dialogue: 0,0:04:57.21,0:05:00.37,Default,,0000,0000,0000,,plus bx plus 1.
Dialogue: 0,0:05:00.37,0:05:02.16,Default,,0000,0000,0000,,And then let's see.
Dialogue: 0,0:05:02.16,0:05:05.39,Default,,0000,0000,0000,,We know that we have a\Nplus 1 here, right?
Dialogue: 0,0:05:05.39,0:05:09.67,Default,,0000,0000,0000,,So we know that this whole term\Nis-- you can put it in
Dialogue: 0,0:05:09.67,0:05:13.87,Default,,0000,0000,0000,,here, but when you get a plus\N1-- well I'm explaining it in
Dialogue: 0,0:05:13.87,0:05:14.59,Default,,0000,0000,0000,,a very confusing way.
Dialogue: 0,0:05:14.59,0:05:17.95,Default,,0000,0000,0000,,But your brain might just say\Nhey, if I square this and add
Dialogue: 0,0:05:17.95,0:05:20.35,Default,,0000,0000,0000,,this plus 1, I get 2.
Dialogue: 0,0:05:20.35,0:05:22.99,Default,,0000,0000,0000,,If I square this and\NI add 1, I get 5.
Dialogue: 0,0:05:22.99,0:05:25.54,Default,,0000,0000,0000,,If I square 3 and I\Nadd 1, I get 10.
Dialogue: 0,0:05:25.54,0:05:29.96,Default,,0000,0000,0000,,And you would say well, f\Nof x must just equal x
Dialogue: 0,0:05:29.96,0:05:32.23,Default,,0000,0000,0000,,squared plus 1.
Dialogue: 0,0:05:32.23,0:05:34.05,Default,,0000,0000,0000,,If your brain doesn't\Njust stumble on
Dialogue: 0,0:05:34.05,0:05:35.05,Default,,0000,0000,0000,,that-- although it should.
Dialogue: 0,0:05:35.05,0:05:36.38,Default,,0000,0000,0000,,You should probably just say\Nwell it's probably just
Dialogue: 0,0:05:36.38,0:05:38.07,Default,,0000,0000,0000,,something simple like I\Nsquared and I add 1 or
Dialogue: 0,0:05:38.07,0:05:39.46,Default,,0000,0000,0000,,subtract one, because they're\Nnever going to give you
Dialogue: 0,0:05:39.46,0:05:41.20,Default,,0000,0000,0000,,something really complicated.
Dialogue: 0,0:05:41.20,0:05:44.71,Default,,0000,0000,0000,,But if they did, or I guess if\Nyou're not doing this on the
Dialogue: 0,0:05:44.71,0:05:47.66,Default,,0000,0000,0000,,SAT, hopefully you see how I\Nimmediately got that the y
Dialogue: 0,0:05:47.66,0:05:52.38,Default,,0000,0000,0000,,intercept is 1, because when\Nx is 0, f of x is 1.
Dialogue: 0,0:05:52.38,0:05:54.67,Default,,0000,0000,0000,,And then you could have\Nsaid well, when x is
Dialogue: 0,0:05:54.67,0:05:56.36,Default,,0000,0000,0000,,1, f of x is 2.
Dialogue: 0,0:05:56.36,0:05:57.57,Default,,0000,0000,0000,,So you could have substituted\Nhere.
Dialogue: 0,0:05:57.57,0:06:04.66,Default,,0000,0000,0000,,You could have said 2 is\Nequal to ax-- sorry.
Dialogue: 0,0:06:04.66,0:06:09.92,Default,,0000,0000,0000,,You could say 2 is equal to a\Ntimes 1 squared plus b times 1
Dialogue: 0,0:06:09.92,0:06:12.87,Default,,0000,0000,0000,,plus 1, right?
Dialogue: 0,0:06:12.87,0:06:17.56,Default,,0000,0000,0000,,Because I just substituted 1 for\Nx, and then I put f of x
Dialogue: 0,0:06:17.56,0:06:18.92,Default,,0000,0000,0000,,is equal to 2.
Dialogue: 0,0:06:18.92,0:06:21.62,Default,,0000,0000,0000,,And then you would get-- if\Nyou subtract 1 from both
Dialogue: 0,0:06:21.62,0:06:27.67,Default,,0000,0000,0000,,sides, you get 1 is equal\Nto a plus d, right?
Dialogue: 0,0:06:27.67,0:06:30.82,Default,,0000,0000,0000,,And you know on the SAT they're\Nnot going to give some
Dialogue: 0,0:06:30.82,0:06:32.47,Default,,0000,0000,0000,,crazy fractional thing.
Dialogue: 0,0:06:32.47,0:06:35.46,Default,,0000,0000,0000,,And I'm actually hesitant\Nto even go in this whole
Dialogue: 0,0:06:35.46,0:06:36.66,Default,,0000,0000,0000,,direction, because\NI think it's just
Dialogue: 0,0:06:36.66,0:06:37.73,Default,,0000,0000,0000,,overcomplicating the thing.
Dialogue: 0,0:06:37.73,0:06:40.56,Default,,0000,0000,0000,,Because you could then do the\Nsame thing with 2 and 5, and
Dialogue: 0,0:06:40.56,0:06:41.41,Default,,0000,0000,0000,,then get a system of equations,
Dialogue: 0,0:06:41.41,0:06:42.02,Default,,0000,0000,0000,,et cetera, et cetera.
Dialogue: 0,0:06:42.02,0:06:44.07,Default,,0000,0000,0000,,And you would have wasted\Na lot of time.
Dialogue: 0,0:06:44.07,0:06:47.28,Default,,0000,0000,0000,,The big discovery here is that\Nmost of these on the SAT are
Dialogue: 0,0:06:47.28,0:06:48.74,Default,,0000,0000,0000,,going to be really\Nsimple equations.
Dialogue: 0,0:06:48.74,0:06:51.31,Default,,0000,0000,0000,,And frankly, more than doing\Nthis-- this is just multiple
Dialogue: 0,0:06:51.31,0:06:53.60,Default,,0000,0000,0000,,choice, I just realized-- you\Ncould just try out the
Dialogue: 0,0:06:53.60,0:06:55.21,Default,,0000,0000,0000,,equations that they give you.
Dialogue: 0,0:06:55.21,0:06:57.37,Default,,0000,0000,0000,,And it's lucky that the\Nfirst one works.
Dialogue: 0,0:06:57.37,0:06:58.65,Default,,0000,0000,0000,,Actually, you should just\Ntry out all of them and
Dialogue: 0,0:06:58.65,0:07:01.45,Default,,0000,0000,0000,,see which ones work.
Dialogue: 0,0:07:01.45,0:07:02.70,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:07:06.32,0:07:08.87,Default,,0000,0000,0000,,Write me a message if you found\Nthat last explanation a
Dialogue: 0,0:07:08.87,0:07:10.56,Default,,0000,0000,0000,,little confusing.
Dialogue: 0,0:07:10.56,0:07:12.81,Default,,0000,0000,0000,,I just didn't want to show you\Nthe correct way to do it,
Dialogue: 0,0:07:12.81,0:07:14.66,Default,,0000,0000,0000,,because that would take you\Nforever and it's not really
Dialogue: 0,0:07:14.66,0:07:16.67,Default,,0000,0000,0000,,the correct way to\Ndo it on the SAT.
Dialogue: 0,0:07:16.67,0:07:17.96,Default,,0000,0000,0000,,Problem number ten.
Dialogue: 0,0:07:17.96,0:07:21.84,Default,,0000,0000,0000,,How old was a person exactly\None year ago if, exactly x
Dialogue: 0,0:07:21.84,0:07:24.12,Default,,0000,0000,0000,,years ago, the person\Nwas y years old.
Dialogue: 0,0:07:24.12,0:07:26.77,Default,,0000,0000,0000,,So this is just something\Nto confuse you.
Dialogue: 0,0:07:30.19,0:07:35.02,Default,,0000,0000,0000,,So x years ago the person\Nwas y years old.
Dialogue: 0,0:07:35.02,0:07:36.84,Default,,0000,0000,0000,,So let's put it this way.
Dialogue: 0,0:07:50.86,0:07:53.74,Default,,0000,0000,0000,,Let me think of the best\Nway to write this.
Dialogue: 0,0:07:53.74,0:07:55.54,Default,,0000,0000,0000,,So let's write their\Ncurrent age.
Dialogue: 0,0:08:00.69,0:08:02.67,Default,,0000,0000,0000,,Well let's just write\Nit as equal to a.
Dialogue: 0,0:08:02.67,0:08:05.38,Default,,0000,0000,0000,,So we know a couple of things.
Dialogue: 0,0:08:05.38,0:08:11.32,Default,,0000,0000,0000,,We know that a minus x is equal\Nto y, or we know that
Dialogue: 0,0:08:11.32,0:08:15.80,Default,,0000,0000,0000,,their current age is equal\Nto x plus y, right?
Dialogue: 0,0:08:15.80,0:08:18.28,Default,,0000,0000,0000,,This is their current age.
Dialogue: 0,0:08:18.28,0:08:19.57,Default,,0000,0000,0000,,And what do we want\Nto figure out?
Dialogue: 0,0:08:19.57,0:08:22.94,Default,,0000,0000,0000,,We want to figure out their\Nage 1 year ago.
Dialogue: 0,0:08:22.94,0:08:26.81,Default,,0000,0000,0000,,So we want to figure out their\Ncurrent age minus 1.
Dialogue: 0,0:08:26.81,0:08:28.29,Default,,0000,0000,0000,,So the current age minus 1?
Dialogue: 0,0:08:28.29,0:08:30.78,Default,,0000,0000,0000,,Well their current\Nage is x plus y.
Dialogue: 0,0:08:30.78,0:08:34.56,Default,,0000,0000,0000,,So you just substitute that back\Nin, and you get x plus y
Dialogue: 0,0:08:34.56,0:08:40.61,Default,,0000,0000,0000,,minus 1 is how old they\Nwere 1 year ago.
Dialogue: 0,0:08:40.61,0:08:45.52,Default,,0000,0000,0000,,So x plus y minus 1,\Nthat's choice E.
Dialogue: 0,0:08:45.52,0:08:47.14,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:08:47.14,0:08:49.89,Default,,0000,0000,0000,,Actually I only have a minute\Nleft, so I'll do the next
Dialogue: 0,0:08:49.89,0:08:51.73,Default,,0000,0000,0000,,problem in the next video.
Dialogue: 0,0:08:51.73,0:08:53.13,Default,,0000,0000,0000,,I'll see