[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.82,0:00:06.90,Default,,0000,0000,0000,,Let's consider the formula\Nfor the period of a simple
Dialogue: 0,0:00:06.90,0:00:11.47,Default,,0000,0000,0000,,pendulum of length L is\Nformula is T period.
Dialogue: 0,0:00:12.56,0:00:14.08,Default,,0000,0000,0000,,Is equal to 2π?
Dialogue: 0,0:00:15.18,0:00:21.07,Default,,0000,0000,0000,,Times the square root of L\Nover G&L is the length of
Dialogue: 0,0:00:21.07,0:00:22.05,Default,,0000,0000,0000,,the pendulum.
Dialogue: 0,0:00:23.22,0:00:27.11,Default,,0000,0000,0000,,Now on Earth, we tend to\Nregard G's being fixed it.
Dialogue: 0,0:00:27.11,0:00:30.65,Default,,0000,0000,0000,,There is a little with\Naltitude, but we tend to
Dialogue: 0,0:00:30.65,0:00:32.78,Default,,0000,0000,0000,,think of it as being fixed.
Dialogue: 0,0:00:33.81,0:00:39.100,Default,,0000,0000,0000,,Just supposing we had a pendulum\Nof a fixed length L, and we took
Dialogue: 0,0:00:39.100,0:00:43.98,Default,,0000,0000,0000,,it somewhere else. Let's say the\Nmoon or Mars.
Dialogue: 0,0:00:44.67,0:00:45.97,Default,,0000,0000,0000,,Somewhere out of the solar
Dialogue: 0,0:00:45.97,0:00:50.81,Default,,0000,0000,0000,,system. Gravity there would not\Nbe the same and we might want to
Dialogue: 0,0:00:50.81,0:00:54.53,Default,,0000,0000,0000,,measure gravity, so one of the\Nways will be to take our
Dialogue: 0,0:00:54.53,0:00:55.77,Default,,0000,0000,0000,,pendulum, set it swinging.
Dialogue: 0,0:00:56.78,0:00:58.10,Default,,0000,0000,0000,,And measure the time.
Dialogue: 0,0:00:59.06,0:01:03.54,Default,,0000,0000,0000,,Once we measured the time, we\Ncould then use that to Calculate
Dialogue: 0,0:01:03.54,0:01:09.50,Default,,0000,0000,0000,,G, but before we could do it, we\Nwould need to know what G was in
Dialogue: 0,0:01:09.50,0:01:14.73,Default,,0000,0000,0000,,terms of the rest of the symbols\Nin this formula. So we need to
Dialogue: 0,0:01:14.73,0:01:17.71,Default,,0000,0000,0000,,rearrange this formula so that\Nit said G.
Dialogue: 0,0:01:19.23,0:01:20.21,Default,,0000,0000,0000,,Equals.
Dialogue: 0,0:01:22.20,0:01:23.56,Default,,0000,0000,0000,,Now it's what?
Dialogue: 0,0:01:24.27,0:01:28.52,Default,,0000,0000,0000,,Goes instead of this question\Nmark that we're going to have a
Dialogue: 0,0:01:28.52,0:01:33.12,Default,,0000,0000,0000,,look at in this video. We're\Ngoing to be looking at how we
Dialogue: 0,0:01:33.12,0:01:36.66,Default,,0000,0000,0000,,transform formally, how we move\Nfrom an expression like this.
Dialogue: 0,0:01:37.70,0:01:39.22,Default,,0000,0000,0000,,To another expression.
Dialogue: 0,0:01:40.08,0:01:44.78,Default,,0000,0000,0000,,Involving exactly the same\Nvariables, but one that helps us
Dialogue: 0,0:01:44.78,0:01:49.95,Default,,0000,0000,0000,,answer the questions that were\Nafter in terms of a different
Dialogue: 0,0:01:49.95,0:01:52.51,Default,,0000,0000,0000,,variable. To do this?
Dialogue: 0,0:01:53.41,0:01:57.84,Default,,0000,0000,0000,,Transformation of formula will\Nneed all the techniques that we
Dialogue: 0,0:01:57.84,0:02:02.27,Default,,0000,0000,0000,,had in terms of solving\Nequations, so the video solving
Dialogue: 0,0:02:02.27,0:02:07.59,Default,,0000,0000,0000,,linear equations in one variable\Nmight be very useful to have a
Dialogue: 0,0:02:07.59,0:02:12.02,Default,,0000,0000,0000,,look at, but let's just recap by\Nhaving a look.
Dialogue: 0,0:02:13.57,0:02:15.99,Default,,0000,0000,0000,,A simple linear equation.
Dialogue: 0,0:02:16.71,0:02:21.34,Default,,0000,0000,0000,,So the one going to take\Nthree X +5.
Dialogue: 0,0:02:22.86,0:02:28.41,Default,,0000,0000,0000,,Equals 6\N- 3 * 5
Dialogue: 0,0:02:28.41,0:02:31.18,Default,,0000,0000,0000,,- 2 X.
Dialogue: 0,0:02:32.74,0:02:37.21,Default,,0000,0000,0000,,Now we've got this equation we\Nwant to solve it for X, so our
Dialogue: 0,0:02:37.21,0:02:39.76,Default,,0000,0000,0000,,aim is to end up with X equals.
Dialogue: 0,0:02:40.91,0:02:45.21,Default,,0000,0000,0000,,So one of the first things\Nwe would do is multiply out
Dialogue: 0,0:02:45.21,0:02:45.92,Default,,0000,0000,0000,,the bracket.
Dialogue: 0,0:02:48.11,0:02:53.26,Default,,0000,0000,0000,,So we have minus three times by\N5 is minus 15.
Dialogue: 0,0:02:54.13,0:03:00.44,Default,,0000,0000,0000,,Minus three times by minus\N2X is plus 6X.
Dialogue: 0,0:03:01.65,0:03:09.03,Default,,0000,0000,0000,,Next, we can simplify this\Nbit. Here three X +5
Dialogue: 0,0:03:09.03,0:03:16.41,Default,,0000,0000,0000,,equals 6X, and now six\Ntakeaway 15 is minus 9.
Dialogue: 0,0:03:17.76,0:03:24.37,Default,,0000,0000,0000,,Now, one of the things we would\Nwant to do is to try and get all
Dialogue: 0,0:03:24.37,0:03:30.15,Default,,0000,0000,0000,,the ex is together. So we were\Nthree X here under 6X there, so
Dialogue: 0,0:03:30.15,0:03:34.69,Default,,0000,0000,0000,,will take 3X away from each\Nside, so that's three X
Dialogue: 0,0:03:34.69,0:03:38.82,Default,,0000,0000,0000,,takeaway. Three X +5 equals 6X\Ntakeaway, 3X minus 9.
Dialogue: 0,0:03:39.63,0:03:46.01,Default,,0000,0000,0000,,3X takeaway 3X the X is go.\NWe've known left and then we've
Dialogue: 0,0:03:46.01,0:03:52.40,Default,,0000,0000,0000,,got this. Five is equal to six X\Ntakeaway 3X. That's three X
Dialogue: 0,0:03:52.40,0:03:53.87,Default,,0000,0000,0000,,again takeaway 9.
Dialogue: 0,0:03:55.40,0:04:00.52,Default,,0000,0000,0000,,Now we need to get the constant\Nterms, the numbers together. So
Dialogue: 0,0:04:00.52,0:04:07.78,Default,,0000,0000,0000,,to do that we would add 9 to\Neach side. So we 5 + 9 is equal
Dialogue: 0,0:04:07.78,0:04:10.77,Default,,0000,0000,0000,,to three X minus 9 + 9.
Dialogue: 0,0:04:11.57,0:04:17.08,Default,,0000,0000,0000,,So again, we're doing to the\Nsame thing to both sides. Here
Dialogue: 0,0:04:17.08,0:04:23.04,Default,,0000,0000,0000,,we took three X away from each\Nside. Here we're adding nine to
Dialogue: 0,0:04:23.04,0:04:29.93,Default,,0000,0000,0000,,each side, so five and nine is\N14 equals 3X, and we minus 9 +
Dialogue: 0,0:04:29.93,0:04:34.52,Default,,0000,0000,0000,,9.0. Now we need to divide both\Nsides by three.
Dialogue: 0,0:04:35.34,0:04:41.72,Default,,0000,0000,0000,,So we have 3X over three an 14\Nover 3, dividing both sides by
Dialogue: 0,0:04:41.72,0:04:46.74,Default,,0000,0000,0000,,three, and so those three\Ncanceled and we're left with X
Dialogue: 0,0:04:46.74,0:04:51.76,Default,,0000,0000,0000,,equals 14 over 3. Now I've\Nwritten this out very fully.
Dialogue: 0,0:04:51.76,0:04:56.77,Default,,0000,0000,0000,,I've written out every step that\NI've said, but we wouldn't
Dialogue: 0,0:04:56.77,0:05:00.88,Default,,0000,0000,0000,,normally expect to see all of\Nthat written down.
Dialogue: 0,0:05:02.10,0:05:03.72,Default,,0000,0000,0000,,Starting from here.
Dialogue: 0,0:05:07.75,0:05:11.97,Default,,0000,0000,0000,,The next line we'd expect\Nto see is this one because
Dialogue: 0,0:05:11.97,0:05:16.20,Default,,0000,0000,0000,,we say Take 3X away from\Nboth sides and we'd expect
Dialogue: 0,0:05:16.20,0:05:18.50,Default,,0000,0000,0000,,to see that as the result.
Dialogue: 0,0:05:19.54,0:05:24.71,Default,,0000,0000,0000,,Then we'd say add 9 to both\Nsides, and So what we would
Dialogue: 0,0:05:24.71,0:05:28.30,Default,,0000,0000,0000,,expect to see having done that\Nwould be that.
Dialogue: 0,0:05:28.93,0:05:31.99,Default,,0000,0000,0000,,And then we, say, divide both\Nsides by three.
Dialogue: 0,0:05:34.03,0:05:38.40,Default,,0000,0000,0000,,And so we see that So what we\Nwould see written down in our
Dialogue: 0,0:05:38.40,0:05:41.83,Default,,0000,0000,0000,,exercise book or on a piece of\Npaper that carried the
Dialogue: 0,0:05:41.83,0:05:44.64,Default,,0000,0000,0000,,solution to this equation will\Nbe something like this.
Dialogue: 0,0:05:45.83,0:05:49.81,Default,,0000,0000,0000,,OK, we've been through the\Nsteps now of solving an
Dialogue: 0,0:05:49.81,0:05:52.99,Default,,0000,0000,0000,,equation. These techniques,\Nparticularly idea of a balance
Dialogue: 0,0:05:52.99,0:05:57.77,Default,,0000,0000,0000,,of keeping the same on both\Nsides by doing the same thing
Dialogue: 0,0:05:57.77,0:06:02.94,Default,,0000,0000,0000,,to both sides is what we're\Ngoing to do when we look at
Dialogue: 0,0:06:02.94,0:06:04.54,Default,,0000,0000,0000,,the transformation of\Nformally.
Dialogue: 0,0:06:07.06,0:06:14.46,Default,,0000,0000,0000,,So let's begin with our\Nfirst formula V equals U
Dialogue: 0,0:06:14.46,0:06:20.16,Default,,0000,0000,0000,,plus AT. And the variable\Nthat we're going to try and
Dialogue: 0,0:06:20.16,0:06:21.31,Default,,0000,0000,0000,,find is TI.
Dialogue: 0,0:06:22.32,0:06:28.46,Default,,0000,0000,0000,,T is the variable we're going to\Nfind what is T expressed?
Dialogue: 0,0:06:29.13,0:06:33.49,Default,,0000,0000,0000,,In terms of the rest of the\Nletters or symbols that there
Dialogue: 0,0:06:33.49,0:06:37.84,Default,,0000,0000,0000,,are in this formula well, in\Norder to model this, what I'm
Dialogue: 0,0:06:37.84,0:06:42.20,Default,,0000,0000,0000,,going to do is I'm going to\Nwrite down an equation which
Dialogue: 0,0:06:42.20,0:06:44.74,Default,,0000,0000,0000,,looks like this, but it just got
Dialogue: 0,0:06:44.74,0:06:51.60,Default,,0000,0000,0000,,numbers in. With a T there as\Nthe unknown. So what we might
Dialogue: 0,0:06:51.60,0:06:56.44,Default,,0000,0000,0000,,have is something like this.\NSeven for V5 for you.
Dialogue: 0,0:06:57.04,0:07:02.03,Default,,0000,0000,0000,,Let's say a tool\Nfor A and then T.
Dialogue: 0,0:07:03.44,0:07:08.43,Default,,0000,0000,0000,,Now what would we do to solve\Nthis equation? The first thing
Dialogue: 0,0:07:08.43,0:07:15.09,Default,,0000,0000,0000,,we try and do is get the TS on\Ntheir own and so to do that,
Dialogue: 0,0:07:15.09,0:07:20.91,Default,,0000,0000,0000,,we take 5 away from each side.\NSo this would be 2. Over here
Dialogue: 0,0:07:20.91,0:07:25.90,Default,,0000,0000,0000,,equals 2 T, so having done\Nthat there, let's do it here.
Dialogue: 0,0:07:25.90,0:07:29.65,Default,,0000,0000,0000,,V minus U taking you away from\Neach side.
Dialogue: 0,0:07:31.28,0:07:36.19,Default,,0000,0000,0000,,Now we would divide both sides\Nby two over here.
Dialogue: 0,0:07:39.40,0:07:46.60,Default,,0000,0000,0000,,In order to end up with just T\Non its own, so let's do the
Dialogue: 0,0:07:46.60,0:07:52.84,Default,,0000,0000,0000,,same. Here. A is what multiplies\Nby T, so we need to divide
Dialogue: 0,0:07:52.84,0:07:59.08,Default,,0000,0000,0000,,everything on this side V minus\NU over a equals T. That's it.
Dialogue: 0,0:07:59.08,0:08:05.32,Default,,0000,0000,0000,,Notice everything here is over\Na, not just one part of it, but
Dialogue: 0,0:08:05.32,0:08:07.24,Default,,0000,0000,0000,,both the whole expression.
Dialogue: 0,0:08:07.47,0:08:10.07,Default,,0000,0000,0000,,The minus U over a.
Dialogue: 0,0:08:11.80,0:08:16.66,Default,,0000,0000,0000,,Let's take another\None. V squared equals
Dialogue: 0,0:08:16.66,0:08:20.14,Default,,0000,0000,0000,,U squared plus 2A S.
Dialogue: 0,0:08:21.19,0:08:24.78,Default,,0000,0000,0000,,And this time, let's say the\Nsymbol that I'm going to try and
Dialogue: 0,0:08:24.78,0:08:28.37,Default,,0000,0000,0000,,find all the variables that I'm\Ngoing to try and find in terms
Dialogue: 0,0:08:28.37,0:08:30.02,Default,,0000,0000,0000,,of all the others, is you.
Dialogue: 0,0:08:31.99,0:08:36.58,Default,,0000,0000,0000,,So that's the case. Again,\NI'm going to write down an
Dialogue: 0,0:08:36.58,0:08:39.91,Default,,0000,0000,0000,,equation over here which\Nlooks like this one.
Dialogue: 0,0:08:41.09,0:08:42.21,Default,,0000,0000,0000,,So let's have.
Dialogue: 0,0:08:43.45,0:08:44.62,Default,,0000,0000,0000,,25
Dialogue: 0,0:08:46.06,0:08:48.37,Default,,0000,0000,0000,,equals U squared.
Dialogue: 0,0:08:49.36,0:08:51.66,Default,,0000,0000,0000,,+9.
Dialogue: 0,0:08:53.18,0:08:58.26,Default,,0000,0000,0000,,Weather 9 is in place of this\Nlump here of algebra.
Dialogue: 0,0:08:58.85,0:09:04.75,Default,,0000,0000,0000,,So what would we do here? Our\Nfirst step would be to take
Dialogue: 0,0:09:04.75,0:09:10.65,Default,,0000,0000,0000,,nine away from both sides. So\Nlet's do that. 25 - 9 equals
Dialogue: 0,0:09:10.65,0:09:16.56,Default,,0000,0000,0000,,U squared and that gets us EU\Nsquared on its own. So let's
Dialogue: 0,0:09:16.56,0:09:21.55,Default,,0000,0000,0000,,do that over here. Let's take\Nthis lump away from both
Dialogue: 0,0:09:21.55,0:09:26.54,Default,,0000,0000,0000,,sides. 20 squared minus 2A S\Nis equal to U squared.
Dialogue: 0,0:09:28.15,0:09:33.54,Default,,0000,0000,0000,,Now what I would want to do now\Nis to take the square root of
Dialogue: 0,0:09:33.54,0:09:37.84,Default,,0000,0000,0000,,both sides 'cause I want just\Nyou and here I've got you
Dialogue: 0,0:09:37.84,0:09:43.23,Default,,0000,0000,0000,,squared. So I need the square\Nroot of 25 - 9 and I want the
Dialogue: 0,0:09:43.23,0:09:47.90,Default,,0000,0000,0000,,square root of all of that not\Nsquare root of 25 minus the
Dialogue: 0,0:09:47.90,0:09:53.28,Default,,0000,0000,0000,,square root of 9. I want the\Nsquare root of 25 - 9, so again
Dialogue: 0,0:09:53.28,0:09:58.31,Default,,0000,0000,0000,,I've got to do the same over\Nhere I want the square root of.
Dialogue: 0,0:09:58.43,0:10:00.62,Default,,0000,0000,0000,,All. Love it.
Dialogue: 0,0:10:05.40,0:10:10.85,Default,,0000,0000,0000,,Let's just check why I need the\Nsquare root of all of this.
Dialogue: 0,0:10:12.03,0:10:18.68,Default,,0000,0000,0000,,25 - 9 is 16, so that 16 equals\NU squared. Take the square root
Dialogue: 0,0:10:18.68,0:10:24.43,Default,,0000,0000,0000,,of both sides. Four is equal to\Nyou and we're happy. That's the
Dialogue: 0,0:10:24.43,0:10:30.57,Default,,0000,0000,0000,,answer. But what if I do the\Nsquare root of 25 minus the
Dialogue: 0,0:10:30.57,0:10:36.49,Default,,0000,0000,0000,,square root of nine? Well,\Nthat's 5 - 3 is 2, which is not
Dialogue: 0,0:10:36.49,0:10:41.56,Default,,0000,0000,0000,,the answer very definitely not\Nthe answer, so we need to take
Dialogue: 0,0:10:41.56,0:10:46.22,Default,,0000,0000,0000,,the square root of everything,\Nnot just each little piece. And
Dialogue: 0,0:10:46.22,0:10:52.14,Default,,0000,0000,0000,,so this over here has to be the\Nsquare root of all of that.
Dialogue: 0,0:10:55.72,0:11:01.46,Default,,0000,0000,0000,,I've been working so far with\Nthe formula that are for uniform
Dialogue: 0,0:11:01.46,0:11:05.28,Default,,0000,0000,0000,,acceleration, so let's continue\Nwith that and take.
Dialogue: 0,0:11:05.89,0:11:13.53,Default,,0000,0000,0000,,Another one of them S equals\NUT plus 1/2 AT squared, and
Dialogue: 0,0:11:13.53,0:11:16.08,Default,,0000,0000,0000,,this time it's a.
Dialogue: 0,0:11:17.63,0:11:21.91,Default,,0000,0000,0000,,Then I'm going to be looking for\Ncan I rearrange this formula?
Dialogue: 0,0:11:21.91,0:11:24.77,Default,,0000,0000,0000,,Can I transform it so it says a
Dialogue: 0,0:11:24.77,0:11:32.06,Default,,0000,0000,0000,,equals? Again, let me model it\Nwith an equation. Let's say that
Dialogue: 0,0:11:32.06,0:11:39.94,Default,,0000,0000,0000,,S is 21, but U times by\NT is 15 + 1/2 of a
Dialogue: 0,0:11:39.94,0:11:41.63,Default,,0000,0000,0000,,Times by 9.
Dialogue: 0,0:11:42.87,0:11:49.24,Default,,0000,0000,0000,,And it's this a the time after\Nfirst of all. Let's isolate the
Dialogue: 0,0:11:49.24,0:11:55.61,Default,,0000,0000,0000,,term with the unknown in it. So\Nthat's the ater. So let's take
Dialogue: 0,0:11:55.61,0:12:02.96,Default,,0000,0000,0000,,15 away from both sides. So I'm\N21 - 15 is equal to 1/2 of
Dialogue: 0,0:12:02.96,0:12:09.82,Default,,0000,0000,0000,,a times by 9. So again, let's do\Nthat here. Let's take this lump
Dialogue: 0,0:12:09.82,0:12:12.76,Default,,0000,0000,0000,,away. S minus Utah equals 1/2.
Dialogue: 0,0:12:12.87,0:12:18.52,Default,,0000,0000,0000,,AT squared, so again, my first\Nsteps are to try and isolate the
Dialogue: 0,0:12:18.52,0:12:20.70,Default,,0000,0000,0000,,variable. The term that I'm
Dialogue: 0,0:12:20.70,0:12:25.92,Default,,0000,0000,0000,,looking for. Now this one\Nlooks a bit complicated. We
Dialogue: 0,0:12:25.92,0:12:31.43,Default,,0000,0000,0000,,got a half. There would be\Nnice to get rid of the half,
Dialogue: 0,0:12:31.43,0:12:36.95,Default,,0000,0000,0000,,so let's multiply both sides\Nby two. If we do it at this
Dialogue: 0,0:12:36.95,0:12:43.31,Default,,0000,0000,0000,,side, that's just a times by\N9. We do it this side 2 * 21
Dialogue: 0,0:12:43.31,0:12:48.82,Default,,0000,0000,0000,,- 15 and it multiplies all\Nof it. So let's do the same
Dialogue: 0,0:12:48.82,0:12:53.48,Default,,0000,0000,0000,,here. Multiply both sides by\N2, two times S minus UT.
Dialogue: 0,0:12:54.78,0:12:58.34,Default,,0000,0000,0000,,Equals AT squared.
Dialogue: 0,0:13:00.00,0:13:06.10,Default,,0000,0000,0000,,Going back to the equation we\Ngot equals a Times by 9. I just
Dialogue: 0,0:13:06.10,0:13:12.21,Default,,0000,0000,0000,,want a on its own and so I must\Ndivide both sides by 9.
Dialogue: 0,0:13:15.47,0:13:18.94,Default,,0000,0000,0000,,Here the thing that's doing\Nthe multiplying it's T
Dialogue: 0,0:13:18.94,0:13:23.56,Default,,0000,0000,0000,,squared. So let's divide both\Nsides by T squared and in the
Dialogue: 0,0:13:23.56,0:13:27.79,Default,,0000,0000,0000,,same way as I divided\Neverything by 9, I've got to
Dialogue: 0,0:13:27.79,0:13:30.10,Default,,0000,0000,0000,,divide everything here by T\Nsquared.
Dialogue: 0,0:13:37.74,0:13:40.40,Default,,0000,0000,0000,,And that gives me a.
Dialogue: 0,0:13:42.54,0:13:47.30,Default,,0000,0000,0000,,Notice I haven't made any\Neffort to cancel because T
Dialogue: 0,0:13:47.30,0:13:52.54,Default,,0000,0000,0000,,is not a common factor. It\Nis not a common factor.
Dialogue: 0,0:13:54.77,0:14:00.59,Default,,0000,0000,0000,,No, we've been working with the\Nequations that are to do with
Dialogue: 0,0:14:00.59,0:14:05.04,Default,,0000,0000,0000,,uniform acceleration. But there\Nare some other kinds of
Dialogue: 0,0:14:05.04,0:14:09.43,Default,,0000,0000,0000,,equations that we need to gain\Npractice at and in order to
Dialogue: 0,0:14:09.43,0:14:13.46,Default,,0000,0000,0000,,develop these skills, I'm going\Nto start with some made up
Dialogue: 0,0:14:13.46,0:14:16.39,Default,,0000,0000,0000,,equations that don't have\Nphysical applications in the
Dialogue: 0,0:14:16.39,0:14:20.41,Default,,0000,0000,0000,,real world, but we will come\Nback once we've developed those
Dialogue: 0,0:14:20.41,0:14:24.07,Default,,0000,0000,0000,,skills to looking at some real\Nequations that do contain
Dialogue: 0,0:14:24.07,0:14:27.73,Default,,0000,0000,0000,,physical applications that we\Nwill be able to transform, but
Dialogue: 0,0:14:27.73,0:14:32.49,Default,,0000,0000,0000,,we need to develop some skills\Nto begin with. So first of all.
Dialogue: 0,0:14:32.67,0:14:38.44,Default,,0000,0000,0000,,Let's take this expression,\Nlet's call it rather than a
Dialogue: 0,0:14:38.44,0:14:39.02,Default,,0000,0000,0000,,formula.
Dialogue: 0,0:14:40.84,0:14:46.99,Default,,0000,0000,0000,,So then we have Y times 2X plus\None equals X Plus One and the
Dialogue: 0,0:14:46.99,0:14:52.32,Default,,0000,0000,0000,,thing that we're going to be\Nafter is X. Can we rearrange it
Dialogue: 0,0:14:52.32,0:14:54.37,Default,,0000,0000,0000,,so it says X equals?
Dialogue: 0,0:14:55.03,0:14:58.100,Default,,0000,0000,0000,,Well gain, let me\Ntry and model this.
Dialogue: 0,0:15:00.60,0:15:05.50,Default,,0000,0000,0000,,With an equation. So all\NI need to do to model
Dialogue: 0,0:15:05.50,0:15:09.94,Default,,0000,0000,0000,,this as an equation is\Nreplaced the Y by three.
Dialogue: 0,0:15:11.47,0:15:16.03,Default,,0000,0000,0000,,And if I was to solve this\Ninequation, my first step would
Dialogue: 0,0:15:16.03,0:15:20.97,Default,,0000,0000,0000,,be to multiply out the bracket.\NSo let's do that. 6X plus three
Dialogue: 0,0:15:20.97,0:15:23.25,Default,,0000,0000,0000,,is equal to X plus one.
Dialogue: 0,0:15:23.97,0:15:30.27,Default,,0000,0000,0000,,So let's do that over here.\NMultiply out this bracket. So
Dialogue: 0,0:15:30.27,0:15:33.14,Default,,0000,0000,0000,,that's two XY Plus Y.
Dialogue: 0,0:15:33.85,0:15:37.22,Default,,0000,0000,0000,,Is equal to X plus one.
Dialogue: 0,0:15:38.73,0:15:44.75,Default,,0000,0000,0000,,Our next step with the equation\Nwill be to get all the excess
Dialogue: 0,0:15:44.75,0:15:50.77,Default,,0000,0000,0000,,together. So I would take X away\Nfrom both sides, so that would
Dialogue: 0,0:15:50.77,0:15:57.25,Default,,0000,0000,0000,,be 6X takeaway X +3, and taking\Nthe X away from this side just
Dialogue: 0,0:15:57.25,0:16:03.27,Default,,0000,0000,0000,,leaves me with one. So let's do\Nthat here. Let's take this X
Dialogue: 0,0:16:03.27,0:16:08.82,Default,,0000,0000,0000,,away from both sides, so have\Ntwo XY minus X Plus Y.
Dialogue: 0,0:16:09.06,0:16:10.65,Default,,0000,0000,0000,,Is equal to 1.
Dialogue: 0,0:16:12.03,0:16:18.39,Default,,0000,0000,0000,,Now I would naturally want to\Ncombine these two in some way.
Dialogue: 0,0:16:18.39,0:16:21.57,Default,,0000,0000,0000,,6X minus X is just 5X.
Dialogue: 0,0:16:22.79,0:16:28.88,Default,,0000,0000,0000,,I can't really do that at this\Nside, but what I can do is
Dialogue: 0,0:16:28.88,0:16:34.54,Default,,0000,0000,0000,,gather together the terms in X\Nby taking out X as a common
Dialogue: 0,0:16:34.54,0:16:40.19,Default,,0000,0000,0000,,factor. So we take out X from\Nthis as a common factor. The
Dialogue: 0,0:16:40.19,0:16:42.80,Default,,0000,0000,0000,,other factor is 2 Y minus.
Dialogue: 0,0:16:44.01,0:16:46.95,Default,,0000,0000,0000,,And taking X out\Nof there is one.
Dialogue: 0,0:16:48.33,0:16:52.49,Default,,0000,0000,0000,,Plus Y equals\N1.
Dialogue: 0,0:16:54.80,0:16:59.94,Default,,0000,0000,0000,,What now? Well now I've got my\Nex is together over here. Let's
Dialogue: 0,0:16:59.94,0:17:05.86,Default,,0000,0000,0000,,write this as 5X plus 3 equals\N1. My next step will be to leave
Dialogue: 0,0:17:05.86,0:17:10.100,Default,,0000,0000,0000,,the X term on its own by taking\Nthree away from each side.
Dialogue: 0,0:17:13.19,0:17:19.54,Default,,0000,0000,0000,,So let's do that here. Lead\Nthe Exterm on its own by
Dialogue: 0,0:17:19.54,0:17:24.83,Default,,0000,0000,0000,,taking the other term. That's\Nwhy away from both sides.
Dialogue: 0,0:17:30.20,0:17:34.80,Default,,0000,0000,0000,,Now I'm just going to simplify\Nthis. Five X equals minus two,
Dialogue: 0,0:17:34.80,0:17:40.54,Default,,0000,0000,0000,,and in order to solve this to\Nget a value of XI need to divide
Dialogue: 0,0:17:40.54,0:17:45.52,Default,,0000,0000,0000,,both sides by this number 5. So\Nthat's X equals minus two over
Dialogue: 0,0:17:45.52,0:17:51.26,Default,,0000,0000,0000,,5. So if I come back to this\Nthis term in the bracket, two Y
Dialogue: 0,0:17:51.26,0:17:56.24,Default,,0000,0000,0000,,minus one is the term that's\Nmultiplying the X, and so I need
Dialogue: 0,0:17:56.24,0:18:03.50,Default,,0000,0000,0000,,to divide. Both sides by so X\Nis equal to 1 minus Y over
Dialogue: 0,0:18:03.50,0:18:09.37,Default,,0000,0000,0000,,2Y plus. Sorry made a mistake\Nthere. Two Y minus one.
Dialogue: 0,0:18:12.02,0:18:16.68,Default,,0000,0000,0000,,I just look again at what we've\Ndone here. We've mimic the
Dialogue: 0,0:18:16.68,0:18:20.56,Default,,0000,0000,0000,,solving of an equation. First,\Nwe multiplied out the brackets.
Dialogue: 0,0:18:22.30,0:18:25.61,Default,,0000,0000,0000,,Then we got the terms together
Dialogue: 0,0:18:25.61,0:18:29.20,Default,,0000,0000,0000,,in X. The variable\Nthat we were after.
Dialogue: 0,0:18:31.31,0:18:33.76,Default,,0000,0000,0000,,Having got those terms together.
Dialogue: 0,0:18:34.54,0:18:38.57,Default,,0000,0000,0000,,We then isolated them so that\Nthey were on their own.
Dialogue: 0,0:18:39.97,0:18:43.87,Default,,0000,0000,0000,,So we need to bear that in mind\Nand follow it through.
Dialogue: 0,0:18:47.19,0:18:54.16,Default,,0000,0000,0000,,Let's take another expression Y\Nover Y plus X.
Dialogue: 0,0:18:55.77,0:18:58.71,Default,,0000,0000,0000,,+5 is equal to X.
Dialogue: 0,0:18:59.44,0:19:04.48,Default,,0000,0000,0000,,This time. We're going to be\Nfinding why we're going to be
Dialogue: 0,0:19:04.48,0:19:08.56,Default,,0000,0000,0000,,getting Y equals, and we want\Nsome lump of numbers and X is
Dialogue: 0,0:19:08.56,0:19:09.50,Default,,0000,0000,0000,,over this sigh.
Dialogue: 0,0:19:11.18,0:19:19.06,Default,,0000,0000,0000,,So let's model this with an\Nequation Y over Y plus 3
Dialogue: 0,0:19:19.06,0:19:23.01,Default,,0000,0000,0000,,+ 5 is equal to 3.
Dialogue: 0,0:19:24.58,0:19:28.10,Default,,0000,0000,0000,,Look at this side. Here we've\Ngot an algebraic fraction.
Dialogue: 0,0:19:28.95,0:19:33.62,Default,,0000,0000,0000,,Y over Y plus 3Y plus three is\Nthe denominator. It's in the
Dialogue: 0,0:19:33.62,0:19:35.05,Default,,0000,0000,0000,,bottom of the fraction.
Dialogue: 0,0:19:35.84,0:19:41.88,Default,,0000,0000,0000,,So in order to get rid of that,\Nwe need to multiply everything
Dialogue: 0,0:19:41.88,0:19:46.54,Default,,0000,0000,0000,,in this equation by this\Ndenominator. So I'm going to
Dialogue: 0,0:19:46.54,0:19:53.04,Default,,0000,0000,0000,,write that out in full Y over Y,\Nplus three. Put that in a
Dialogue: 0,0:19:53.04,0:19:55.37,Default,,0000,0000,0000,,bracket times Y plus 3.
Dialogue: 0,0:19:56.68,0:19:59.89,Default,,0000,0000,0000,,Plus five times Y.
Dialogue: 0,0:20:00.29,0:20:06.53,Default,,0000,0000,0000,,Three is equal to three times Y\Nplus three. Let me just
Dialogue: 0,0:20:06.53,0:20:13.29,Default,,0000,0000,0000,,emphasize we have to do the same\Nthing to both sides, so here
Dialogue: 0,0:20:13.29,0:20:19.53,Default,,0000,0000,0000,,I've had to multiply everything\Non both sides of the equation by
Dialogue: 0,0:20:19.53,0:20:22.13,Default,,0000,0000,0000,,this term Y plus 3.
Dialogue: 0,0:20:23.23,0:20:27.19,Default,,0000,0000,0000,,Here those will cancel out,\Njust leaving me with why, so
Dialogue: 0,0:20:27.19,0:20:30.79,Default,,0000,0000,0000,,let's do that at this site.\NLet's multiply everything by
Dialogue: 0,0:20:30.79,0:20:35.47,Default,,0000,0000,0000,,this term Y plus X so we know\Nthis first one. When we've
Dialogue: 0,0:20:35.47,0:20:39.79,Default,,0000,0000,0000,,multiplied it by wiper sex is\Njust going to give us Why.
Dialogue: 0,0:20:41.39,0:20:48.09,Default,,0000,0000,0000,,Plus five times by Y\Nplus X is equal to
Dialogue: 0,0:20:48.09,0:20:52.11,Default,,0000,0000,0000,,X times by Y plus\NX.
Dialogue: 0,0:20:54.00,0:20:57.34,Default,,0000,0000,0000,,Coming back to the equation\Nhere, faced with a lot of
Dialogue: 0,0:20:57.34,0:21:00.69,Default,,0000,0000,0000,,brackets, we know the first\Nthing we would do is multiply
Dialogue: 0,0:21:00.69,0:21:03.12,Default,,0000,0000,0000,,out the brackets. So let's do\Nthat, why?
Dialogue: 0,0:21:04.35,0:21:11.94,Default,,0000,0000,0000,,Plus five times by Y is 5\NY five times by three is 15
Dialogue: 0,0:21:11.94,0:21:19.53,Default,,0000,0000,0000,,is equal 2 three times by Y\Nis 3 Y and three times by
Dialogue: 0,0:21:19.53,0:21:21.15,Default,,0000,0000,0000,,three is 9.
Dialogue: 0,0:21:23.21,0:21:25.67,Default,,0000,0000,0000,,Do the same here, why?
Dialogue: 0,0:21:27.05,0:21:34.70,Default,,0000,0000,0000,,+5 Y.\NFive times by X Plus 5X is
Dialogue: 0,0:21:34.70,0:21:41.94,Default,,0000,0000,0000,,equal to X times by Y is\NXY&X times by X is X.
Dialogue: 0,0:21:42.60,0:21:43.23,Default,,0000,0000,0000,,Square.
Dialogue: 0,0:21:45.39,0:21:49.69,Default,,0000,0000,0000,,On this side now we would like\Nto get all of our wise together.
Dialogue: 0,0:21:50.68,0:21:53.94,Default,,0000,0000,0000,,So we've Y plus
Dialogue: 0,0:21:53.94,0:22:00.14,Default,,0000,0000,0000,,5Y6Y. Take away 3 Y\Nso we've six. Why
Dialogue: 0,0:22:00.14,0:22:05.37,Default,,0000,0000,0000,,already and we're going\Nto take away 3Y. Plus
Dialogue: 0,0:22:05.37,0:22:11.18,Default,,0000,0000,0000,,15 is equal to 9, so\Nlet's gather all the
Dialogue: 0,0:22:11.18,0:22:15.82,Default,,0000,0000,0000,,wise together Y +5. Y\Nis 6 Y.
Dialogue: 0,0:22:17.34,0:22:23.33,Default,,0000,0000,0000,,I need to bring this term over,\Nso I'll take XY away from both
Dialogue: 0,0:22:23.33,0:22:24.62,Default,,0000,0000,0000,,sides minus XY.
Dialogue: 0,0:22:25.41,0:22:29.10,Default,,0000,0000,0000,,And then let's just write down\Nthe other terms.
Dialogue: 0,0:22:30.94,0:22:37.00,Default,,0000,0000,0000,,Now here I simplify this. I'd\Nhave six Y takeaway 3 Y and that
Dialogue: 0,0:22:37.00,0:22:43.06,Default,,0000,0000,0000,,would just leave me with three Y\Nplus 15 equals 9. I can't do
Dialogue: 0,0:22:43.06,0:22:49.13,Default,,0000,0000,0000,,that here, but the thing that I\Ncan do is bring them much closer
Dialogue: 0,0:22:49.13,0:22:51.29,Default,,0000,0000,0000,,together by taking out why.
Dialogue: 0,0:22:52.29,0:22:58.19,Default,,0000,0000,0000,,The thing that I'm after as a\Ncommon factor. So let's take why
Dialogue: 0,0:22:58.19,0:23:04.09,Default,,0000,0000,0000,,out of these two terms. Why\Nbrackets? Why times by 6 Y means
Dialogue: 0,0:23:04.09,0:23:11.36,Default,,0000,0000,0000,,I must have a 6 in their minus\NXY means I must have a minus X
Dialogue: 0,0:23:11.36,0:23:14.08,Default,,0000,0000,0000,,there plus 5X equals X squared.
Dialogue: 0,0:23:15.38,0:23:22.34,Default,,0000,0000,0000,,Now over here I'd isolate this\Nterm in why by taking 15 away
Dialogue: 0,0:23:22.34,0:23:29.82,Default,,0000,0000,0000,,from both sides 3 Y is equal\Nto. Now this is 9 - 15,
Dialogue: 0,0:23:29.82,0:23:36.78,Default,,0000,0000,0000,,so I've got to do the same\Nhere. Take 5X away from each
Dialogue: 0,0:23:36.78,0:23:43.74,Default,,0000,0000,0000,,side, isolating this term in YY\Ntimes 6 minus X is equal to
Dialogue: 0,0:23:43.74,0:23:45.34,Default,,0000,0000,0000,,X squared minus.
Dialogue: 0,0:23:45.48,0:23:47.17,Default,,0000,0000,0000,,5X.
Dialogue: 0,0:23:48.93,0:23:54.82,Default,,0000,0000,0000,,This side now I've got 3 Yi,\Njust need Y so I would divide
Dialogue: 0,0:23:54.82,0:23:59.88,Default,,0000,0000,0000,,everything on this side by\Nthree. So I've got to do the
Dialogue: 0,0:23:59.88,0:24:04.51,Default,,0000,0000,0000,,same with this. I've got to\Ndivide everything on this side
Dialogue: 0,0:24:04.51,0:24:09.98,Default,,0000,0000,0000,,by this term 6 minus X so we\Nhave X squared minus 5X.
Dialogue: 0,0:24:10.64,0:24:14.62,Default,,0000,0000,0000,,Divided by 6 minus X.
Dialogue: 0,0:24:15.96,0:24:21.14,Default,,0000,0000,0000,,Put it all in a bracket to keep\Nit together. Notice I'm
Dialogue: 0,0:24:21.14,0:24:25.46,Default,,0000,0000,0000,,attempting no canceling 'cause\Nthere is no common factor in
Dialogue: 0,0:24:25.46,0:24:29.78,Default,,0000,0000,0000,,this numerator and this\Ndenominator. They do not share a
Dialogue: 0,0:24:29.78,0:24:34.54,Default,,0000,0000,0000,,common factor, so that's my\Nanswer and I finished. I've got
Dialogue: 0,0:24:34.54,0:24:39.29,Default,,0000,0000,0000,,Y equals a lump of algebra\Ninvolving X is and numbers.
Dialogue: 0,0:24:42.98,0:24:48.66,Default,,0000,0000,0000,,We started with a real formula.\NWe started with the formula for
Dialogue: 0,0:24:48.66,0:24:50.08,Default,,0000,0000,0000,,a simple pendulum.
Dialogue: 0,0:24:50.88,0:24:57.08,Default,,0000,0000,0000,,Of length Lt equals\N2π square root.
Dialogue: 0,0:24:57.63,0:25:04.27,Default,,0000,0000,0000,,L over G and the problem that we\Nposed was what was G in terms of
Dialogue: 0,0:25:04.27,0:25:06.90,Default,,0000,0000,0000,,T? So G.
Dialogue: 0,0:25:07.99,0:25:10.91,Default,,0000,0000,0000,,After G equals.
Dialogue: 0,0:25:13.23,0:25:17.78,Default,,0000,0000,0000,,Let's have a look at a simple\Nequation. Let's say it's 10
Dialogue: 0,0:25:17.78,0:25:22.70,Default,,0000,0000,0000,,equals 2π and I'll keep the two\NPike's. Part is just a number,
Dialogue: 0,0:25:22.70,0:25:24.98,Default,,0000,0000,0000,,so 2π is just a number.
Dialogue: 0,0:25:26.36,0:25:30.95,Default,,0000,0000,0000,,Square root\Nof 3 over G.
Dialogue: 0,0:25:32.20,0:25:37.03,Default,,0000,0000,0000,,Now as an equation, this one is\Na bit tricky because the G is
Dialogue: 0,0:25:37.03,0:25:41.17,Default,,0000,0000,0000,,trapped inside this square root\Nsign. We need to bring it out
Dialogue: 0,0:25:41.17,0:25:46.00,Default,,0000,0000,0000,,and the way to get a square root\Nsign to disappear, so to speak,
Dialogue: 0,0:25:46.00,0:25:50.14,Default,,0000,0000,0000,,is to square both sides, reverse\Nthe operation if you like, so
Dialogue: 0,0:25:50.14,0:25:56.57,Default,,0000,0000,0000,,will square. Both sides of this\Nequation so 10 multiplied by
Dialogue: 0,0:25:56.57,0:26:02.90,Default,,0000,0000,0000,,itself. I'm going to write it as\N10 squared equals 2π multiplied
Dialogue: 0,0:26:02.90,0:26:09.22,Default,,0000,0000,0000,,by itself, 'cause we're squaring\Nthe whole of both sides times by
Dialogue: 0,0:26:09.22,0:26:11.33,Default,,0000,0000,0000,,a nice square this.
Dialogue: 0,0:26:11.92,0:26:14.83,Default,,0000,0000,0000,,Three over G.
Dialogue: 0,0:26:16.45,0:26:21.55,Default,,0000,0000,0000,,Now we need to do the same here,\Nsquare the whole of both sides.
Dialogue: 0,0:26:22.42,0:26:25.31,Default,,0000,0000,0000,,So that will be T squared.
Dialogue: 0,0:26:26.89,0:26:33.21,Default,,0000,0000,0000,,2π all squared\NL over G.
Dialogue: 0,0:26:35.04,0:26:38.65,Default,,0000,0000,0000,,Coming back to the equation,\Njeez, in the denominator I don't
Dialogue: 0,0:26:38.65,0:26:43.57,Default,,0000,0000,0000,,want it there. I want it to say\NG equals I want G upstairs, so
Dialogue: 0,0:26:43.57,0:26:48.49,Default,,0000,0000,0000,,to speak, so I have to get rid\Nof it out of the denominator and
Dialogue: 0,0:26:48.49,0:26:52.10,Default,,0000,0000,0000,,so to do that I must multiply\Nboth sides by G.
Dialogue: 0,0:26:52.95,0:27:00.07,Default,,0000,0000,0000,,So I've got 10 squared times.\NG is equal to 2π squared
Dialogue: 0,0:27:00.07,0:27:07.18,Default,,0000,0000,0000,,times three, so let's do that\Nhere. Multiply both sides by G.
Dialogue: 0,0:27:07.18,0:27:14.30,Default,,0000,0000,0000,,So I have T squared times\Nby G is equal to 2π
Dialogue: 0,0:27:14.30,0:27:17.26,Default,,0000,0000,0000,,all squared times by L.
Dialogue: 0,0:27:19.50,0:27:26.70,Default,,0000,0000,0000,,Gee, I want on its own. I want\Nto say G equal, so I must divide
Dialogue: 0,0:27:26.70,0:27:33.00,Default,,0000,0000,0000,,by this thing 10 squared. So G\Nis equal to 2π all squared times
Dialogue: 0,0:27:33.00,0:27:35.25,Default,,0000,0000,0000,,3, all over 10 squared.
Dialogue: 0,0:27:36.32,0:27:43.38,Default,,0000,0000,0000,,And I can work that out. Let's\Ndo the same with this G equals
Dialogue: 0,0:27:43.38,0:27:49.93,Default,,0000,0000,0000,,2π all squared times by L, and\NI'm getting rid of this T
Dialogue: 0,0:27:49.93,0:27:53.46,Default,,0000,0000,0000,,squared by dividing everything\Nby T squared.
Dialogue: 0,0:27:55.80,0:27:58.54,Default,,0000,0000,0000,,And we can leave it like that.
Dialogue: 0,0:27:59.35,0:28:05.43,Default,,0000,0000,0000,,We can make it look a little\Nbit nicer if we want to buy
Dialogue: 0,0:28:05.43,0:28:09.33,Default,,0000,0000,0000,,spotting that we've got a\Nsquare here under Square
Dialogue: 0,0:28:09.33,0:28:13.67,Default,,0000,0000,0000,,there, and it might be nice\Nto combine those two.
Dialogue: 0,0:28:13.67,0:28:17.58,Default,,0000,0000,0000,,Squaring process is by\Nwriting 2π over T all
Dialogue: 0,0:28:17.58,0:28:19.31,Default,,0000,0000,0000,,squared times by L.
Dialogue: 0,0:28:20.41,0:28:23.78,Default,,0000,0000,0000,,Basically this is the answer\Nthat we finished with.
Dialogue: 0,0:28:24.70,0:28:27.89,Default,,0000,0000,0000,,Let's take another couple of.
Dialogue: 0,0:28:29.28,0:28:33.80,Default,,0000,0000,0000,,Examples of real formula that we\Nmight want to be able to
Dialogue: 0,0:28:33.80,0:28:38.70,Default,,0000,0000,0000,,manipulate. So let's have a look\Nat the lens Formula One over F.
Dialogue: 0,0:28:39.54,0:28:41.46,Default,,0000,0000,0000,,Is equal to one over U.
Dialogue: 0,0:28:43.03,0:28:44.10,Default,,0000,0000,0000,,This one over V.
Dialogue: 0,0:28:44.93,0:28:46.58,Default,,0000,0000,0000,,Let's say it's you.
Dialogue: 0,0:28:48.12,0:28:50.71,Default,,0000,0000,0000,,That we're after we want you
Dialogue: 0,0:28:50.71,0:28:55.66,Default,,0000,0000,0000,,equals. Well, let me write\Ndown an equation.
Dialogue: 0,0:28:58.55,0:28:59.26,Default,,0000,0000,0000,,Similar.
Dialogue: 0,0:29:00.72,0:29:05.16,Default,,0000,0000,0000,,One over 3 equals 1 over U plus\None over 5.
Dialogue: 0,0:29:06.65,0:29:12.16,Default,,0000,0000,0000,,I want to isolate this term\Nfirst in one over you.
Dialogue: 0,0:29:13.38,0:29:18.98,Default,,0000,0000,0000,,To do that, I'm going to take\Nthis away from both sides. 1/3
Dialogue: 0,0:29:18.98,0:29:21.57,Default,,0000,0000,0000,,takeaway 150 is equal to one
Dialogue: 0,0:29:21.57,0:29:26.86,Default,,0000,0000,0000,,over you. So let's do that.\NIsolate this term in you.
Dialogue: 0,0:29:29.00,0:29:33.68,Default,,0000,0000,0000,,And so to do that, we take away\None over V from both sides, so
Dialogue: 0,0:29:33.68,0:29:34.93,Default,,0000,0000,0000,,we want over F.
Dialogue: 0,0:29:35.53,0:29:39.52,Default,,0000,0000,0000,,Take away one over V is equal to\None over you.
Dialogue: 0,0:29:40.93,0:29:45.49,Default,,0000,0000,0000,,Now, faced with problems\Nlike this, it's very, very
Dialogue: 0,0:29:45.49,0:29:49.04,Default,,0000,0000,0000,,tempting to simply turn\Neverything upside down.
Dialogue: 0,0:29:50.29,0:29:56.80,Default,,0000,0000,0000,,Well, I just have a think about\Nthat. This says 1/3 - 1/5. Now a
Dialogue: 0,0:29:56.80,0:29:58.97,Default,,0000,0000,0000,,third is bigger than 1/5.
Dialogue: 0,0:30:00.81,0:30:05.22,Default,,0000,0000,0000,,So 1/3 - 1/5 is a positive\Nnumber, so you at the very least
Dialogue: 0,0:30:05.22,0:30:06.80,Default,,0000,0000,0000,,has got to be positive.
Dialogue: 0,0:30:07.86,0:30:12.08,Default,,0000,0000,0000,,Watch what happens if I just\Nturn everything upside down.
Dialogue: 0,0:30:12.71,0:30:19.67,Default,,0000,0000,0000,,3 - 5 equals U, which tells me\Nthat minus two is equal to you.
Dialogue: 0,0:30:19.67,0:30:25.70,Default,,0000,0000,0000,,But we just agreed that you had\Nto be positive and not negative.
Dialogue: 0,0:30:25.70,0:30:27.56,Default,,0000,0000,0000,,You can't do that.
Dialogue: 0,0:30:28.38,0:30:32.02,Default,,0000,0000,0000,,These are fractions, and so\Nbecause their fractions we have
Dialogue: 0,0:30:32.02,0:30:36.39,Default,,0000,0000,0000,,to combine them as fractions,\Nwhich means we have to find a
Dialogue: 0,0:30:36.39,0:30:40.03,Default,,0000,0000,0000,,common denominator and a common\Ndenominator for three and five
Dialogue: 0,0:30:40.03,0:30:44.03,Default,,0000,0000,0000,,is a number that both three and\Nfive will divide into.
Dialogue: 0,0:30:44.91,0:30:48.63,Default,,0000,0000,0000,,Easiest number is 3 times by 5.
Dialogue: 0,0:30:49.27,0:30:55.50,Default,,0000,0000,0000,,So three Zing to three times by\N5, which is 15 goes five times.
Dialogue: 0,0:30:55.50,0:31:02.18,Default,,0000,0000,0000,,So I found multiplied 3 by 5. I\Nmust multiply by this one by 5,
Dialogue: 0,0:31:02.18,0:31:03.96,Default,,0000,0000,0000,,so that's 5 minus.
Dialogue: 0,0:31:04.60,0:31:10.17,Default,,0000,0000,0000,,I've multiplied 5 by three, so I\Nmultiply this one by three
Dialogue: 0,0:31:10.17,0:31:17.13,Default,,0000,0000,0000,,equals one over. You know if I\Ndid that here, I've got to do it
Dialogue: 0,0:31:17.13,0:31:21.75,Default,,0000,0000,0000,,over here. So I want\Nto common denominator.
Dialogue: 0,0:31:23.30,0:31:27.94,Default,,0000,0000,0000,,Here the common denominator I\Ntalk was three times by 5, so
Dialogue: 0,0:31:27.94,0:31:30.27,Default,,0000,0000,0000,,let's take F times by vis.
Dialogue: 0,0:31:32.72,0:31:34.69,Default,,0000,0000,0000,,I've multiplied F.
Dialogue: 0,0:31:36.23,0:31:38.96,Default,,0000,0000,0000,,By the so I must multiply the
Dialogue: 0,0:31:38.96,0:31:40.73,Default,,0000,0000,0000,,one. By faith.
Dialogue: 0,0:31:43.89,0:31:44.73,Default,,0000,0000,0000,,Minus.
Dialogue: 0,0:31:45.83,0:31:49.44,Default,,0000,0000,0000,,I've multiplied the V by F.
Dialogue: 0,0:31:50.18,0:31:53.44,Default,,0000,0000,0000,,So I must multiply the one by F.
Dialogue: 0,0:31:58.70,0:32:04.21,Default,,0000,0000,0000,,Now if I come back over here,\Nlet me just simplify this. This
Dialogue: 0,0:32:04.21,0:32:10.15,Default,,0000,0000,0000,,is 2 over 15 is one over you,\Nand now I've got a complete
Dialogue: 0,0:32:10.15,0:32:15.24,Default,,0000,0000,0000,,fraction on both sides. I can\Nturn it upside down and say
Dialogue: 0,0:32:15.24,0:32:16.93,Default,,0000,0000,0000,,that's what you is.
Dialogue: 0,0:32:18.37,0:32:23.43,Default,,0000,0000,0000,,Now there was a lot of\Ncalculation went on here. I
Dialogue: 0,0:32:23.43,0:32:28.49,Default,,0000,0000,0000,,can't do that calculation here,\Nbut I have got a complete
Dialogue: 0,0:32:28.49,0:32:31.71,Default,,0000,0000,0000,,fraction here so I can turn it.
Dialogue: 0,0:32:34.74,0:32:35.82,Default,,0000,0000,0000,,Upside down.
Dialogue: 0,0:32:36.85,0:32:38.20,Default,,0000,0000,0000,,To give me you.
Dialogue: 0,0:32:39.67,0:32:44.93,Default,,0000,0000,0000,,So let's take as our final\Nexample the time dilation
Dialogue: 0,0:32:44.93,0:32:46.51,Default,,0000,0000,0000,,formula from relativity.
Dialogue: 0,0:32:47.48,0:32:52.71,Default,,0000,0000,0000,,The formula is T\Nequals T, not.
Dialogue: 0,0:32:53.99,0:32:55.44,Default,,0000,0000,0000,,Divided by.
Dialogue: 0,0:32:56.63,0:33:04.21,Default,,0000,0000,0000,,1. Minus. V\Nsquared over C squared to the
Dialogue: 0,0:33:04.21,0:33:07.30,Default,,0000,0000,0000,,power. 1/2 or square root.
Dialogue: 0,0:33:08.88,0:33:13.53,Default,,0000,0000,0000,,So let's take some numbers and\Nin fact what we're going to be
Dialogue: 0,0:33:13.53,0:33:17.11,Default,,0000,0000,0000,,after is we're going to be\Nlooking for this expression
Dialogue: 0,0:33:17.11,0:33:21.41,Default,,0000,0000,0000,,here, V over C. So I just\Nwrite that down there. That's
Dialogue: 0,0:33:21.41,0:33:26.42,Default,,0000,0000,0000,,what we're going to be looking\Nfor. Can we get V over C in
Dialogue: 0,0:33:26.42,0:33:27.85,Default,,0000,0000,0000,,terms of T&T Nord?
Dialogue: 0,0:33:29.16,0:33:34.55,Default,,0000,0000,0000,,So let's have 6\Nequals 5 over 1
Dialogue: 0,0:33:34.55,0:33:36.57,Default,,0000,0000,0000,,minus X squared.
Dialogue: 0,0:33:39.17,0:33:42.80,Default,,0000,0000,0000,,To the half. Now solving this.
Dialogue: 0,0:33:43.41,0:33:48.28,Default,,0000,0000,0000,,What would we do? Well, we've\Ngot a square root. Let's Square
Dialogue: 0,0:33:48.28,0:33:53.56,Default,,0000,0000,0000,,both sides in order to get rid\Nof that square root. So that
Dialogue: 0,0:33:53.56,0:33:58.43,Default,,0000,0000,0000,,would be 6 squared equals 5\Nsquared all over 1 minus X
Dialogue: 0,0:33:58.43,0:34:03.67,Default,,0000,0000,0000,,squared. So let's do that here.\NSquare both sides.
Dialogue: 0,0:34:04.32,0:34:11.07,Default,,0000,0000,0000,,T squared. Equals TN\Nsquared all over 1
Dialogue: 0,0:34:11.07,0:34:15.90,Default,,0000,0000,0000,,minus V squared over\NC squared.
Dialogue: 0,0:34:17.59,0:34:24.39,Default,,0000,0000,0000,,Now, well here the term I want\Nin X is in the denominator. I
Dialogue: 0,0:34:24.39,0:34:29.25,Default,,0000,0000,0000,,need it upstairs, so let's\Nmultiply both sides of this
Dialogue: 0,0:34:29.25,0:34:34.11,Default,,0000,0000,0000,,equation by one minus X\Nsquared. That would be 6
Dialogue: 0,0:34:34.11,0:34:39.46,Default,,0000,0000,0000,,squared times 1 minus X\Nsquared is equal to 5 squared.
Dialogue: 0,0:34:40.74,0:34:42.75,Default,,0000,0000,0000,,So let's do that here.
Dialogue: 0,0:34:43.99,0:34:49.44,Default,,0000,0000,0000,,T squared times, 1\Nminus V squared over
Dialogue: 0,0:34:49.44,0:34:54.89,Default,,0000,0000,0000,,C squared is equal\Nto T Nord squared.
Dialogue: 0,0:34:57.15,0:35:00.57,Default,,0000,0000,0000,,Now I want the X squared bit.
Dialogue: 0,0:35:01.72,0:35:06.65,Default,,0000,0000,0000,,And it would be nice perhaps to\Nmultiply out the bracket, but
Dialogue: 0,0:35:06.65,0:35:11.58,Default,,0000,0000,0000,,there's a slightly quicker way.\NI can divide both sides by 6
Dialogue: 0,0:35:11.58,0:35:15.69,Default,,0000,0000,0000,,squared, and that's nice. 'cause\Nit keeps the square bits
Dialogue: 0,0:35:15.69,0:35:21.45,Default,,0000,0000,0000,,together, so to speak. So let me\Ndo that one minus X squared is
Dialogue: 0,0:35:21.45,0:35:26.79,Default,,0000,0000,0000,,equal to 5 squared over 6\Nsquared. So I'm going to do that
Dialogue: 0,0:35:26.79,0:35:31.72,Default,,0000,0000,0000,,here. Divide both sides by T\Nsquared, 1 minus V squared over
Dialogue: 0,0:35:31.72,0:35:38.81,Default,,0000,0000,0000,,C squared. Is equal to\NTN squared over T squared?
Dialogue: 0,0:35:40.74,0:35:41.19,Default,,0000,0000,0000,,Now.
Dialogue: 0,0:35:42.43,0:35:45.43,Default,,0000,0000,0000,,Running out of paper here.\NSo what I'm going to do is
Dialogue: 0,0:35:45.43,0:35:48.68,Default,,0000,0000,0000,,turn over and write this one\Ndown at the top of the next
Dialogue: 0,0:35:48.68,0:35:50.18,Default,,0000,0000,0000,,page, and this one as well.
Dialogue: 0,0:35:52.98,0:36:00.04,Default,,0000,0000,0000,,So we've got 1 minus V\Nsquared over. C squared is
Dialogue: 0,0:36:00.04,0:36:05.18,Default,,0000,0000,0000,,equal to T not squared over\NT squared.
Dialogue: 0,0:36:07.34,0:36:13.68,Default,,0000,0000,0000,,And here, with one minus X\Nsquared is equal to 5 squared
Dialogue: 0,0:36:13.68,0:36:15.26,Default,,0000,0000,0000,,over 6 squared.
Dialogue: 0,0:36:17.05,0:36:23.84,Default,,0000,0000,0000,,It's The X squared that we're\Nafter so I can add X squared
Dialogue: 0,0:36:23.84,0:36:30.10,Default,,0000,0000,0000,,both sides, so this is one\Nequals 5 squared over 6 squared
Dialogue: 0,0:36:30.10,0:36:37.41,Default,,0000,0000,0000,,plus X squared. So let me add\NV squared over C squared to each
Dialogue: 0,0:36:37.41,0:36:44.19,Default,,0000,0000,0000,,side. One is equal to T not\Nsquared over T squared plus B
Dialogue: 0,0:36:44.19,0:36:46.28,Default,,0000,0000,0000,,squared over C squared.
Dialogue: 0,0:36:47.84,0:36:50.21,Default,,0000,0000,0000,,Now I want the X\Nsquared on it so.
Dialogue: 0,0:36:51.44,0:36:58.56,Default,,0000,0000,0000,,So take this away from both\Nsides. 1 - 5 squared over
Dialogue: 0,0:36:58.56,0:37:05.67,Default,,0000,0000,0000,,6 squared is equal to X\Nsquared, so 1 minus T, not
Dialogue: 0,0:37:05.67,0:37:12.79,Default,,0000,0000,0000,,squared over T squared is equal\Nto V squared over C squared.
Dialogue: 0,0:37:12.79,0:37:15.75,Default,,0000,0000,0000,,Taking this away from both
Dialogue: 0,0:37:15.75,0:37:23.51,Default,,0000,0000,0000,,sides. Almost there now it's\NX that I want not X squared
Dialogue: 0,0:37:23.51,0:37:26.91,Default,,0000,0000,0000,,selects. Take the square root of
Dialogue: 0,0:37:26.91,0:37:33.92,Default,,0000,0000,0000,,both sides. So do the\Nsame here. The oversee that I
Dialogue: 0,0:37:33.92,0:37:39.59,Default,,0000,0000,0000,,want, so let's take the square\Nroot of both sides.
Dialogue: 0,0:37:43.54,0:37:47.97,Default,,0000,0000,0000,,And that's it. We have found\Nthe ratio of the velocity to
Dialogue: 0,0:37:47.97,0:37:51.66,Default,,0000,0000,0000,,the speed of light in terms\Nof the two times.
Dialogue: 0,0:37:52.68,0:37:57.10,Default,,0000,0000,0000,,So. That concludes this video on\Ntransformation of formula thing
Dialogue: 0,0:37:57.10,0:38:02.06,Default,,0000,0000,0000,,to do is to treat it always as\Nthough it was an equation that
Dialogue: 0,0:38:02.06,0:38:03.84,Default,,0000,0000,0000,,you were trying to solve.
Dialogue: 0,0:38:05.00,0:38:10.60,Default,,0000,0000,0000,,In terms of the variable that\Nyou want, X equals G equals and
Dialogue: 0,0:38:10.60,0:38:15.34,Default,,0000,0000,0000,,you just perform the steps as\Nthough you were solving an
Dialogue: 0,0:38:15.34,0:38:20.52,Default,,0000,0000,0000,,equation. If you keep that in\Nmind, then most of your problems
Dialogue: 0,0:38:20.52,0:38:22.67,Default,,0000,0000,0000,,should be taken care of.