Napoleon's Peninsular Campaigns

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:03.400
In the video on the Fourth
Coalition, I forgot to add to

00:00:03.400 --> 00:00:06.810
one super important
consequence of

00:00:06.810 --> 00:00:07.810
the Treaties of Tilsit.

00:00:07.810 --> 00:00:11.240
And especially the Treaty
of Tilsit with Prussia.

00:00:11.240 --> 00:00:13.560
I already talked about that it
was all about carving up

00:00:13.560 --> 00:00:15.260
Prussia, and humiliating
Prussia.

00:00:15.260 --> 00:00:19.440
And really removing it from
the status of one the

00:00:19.440 --> 00:00:20.940
preeminent powers.

00:00:20.940 --> 00:00:26.320
And all I talked about was the
loss of the territories of

00:00:26.320 --> 00:00:27.710
Prussia west of the Elbe.

00:00:27.710 --> 00:00:29.800
And that's about that
area right there.

00:00:29.800 --> 00:00:32.850
But just as important
as that, the

00:00:32.850 --> 00:00:35.050
Polish holdings of Prussia.

00:00:35.050 --> 00:00:45.340
So all of this area right over
here, this also was removed

00:00:45.340 --> 00:00:49.500
from Prussia and became a
French satellite state.

00:00:49.500 --> 00:00:52.760
It became the Duchy of Warsaw.

00:00:52.760 --> 00:00:54.160
So I just really want
to emphasize.

00:00:54.160 --> 00:00:56.300
The Treaty of Tilsit, I only
emphasized kind of what

00:00:56.300 --> 00:00:58.240
happened on the western side
of Prussia, but the eastern

00:00:58.240 --> 00:01:00.020
side of Prussia also
got carved up.

00:01:00.020 --> 00:01:03.730
And Prussia essentially
lost half of its size.

00:01:03.730 --> 00:01:06.150
So it's very dramatic
humiliation for Prussia at the

00:01:06.150 --> 00:01:08.250
end of the Treaty of Tilsit.

00:01:08.250 --> 00:01:10.740
Or the Treaties of Tilsit.

00:01:10.740 --> 00:01:12.780
Now with that out of the way,
we talked about in the last

00:01:12.780 --> 00:01:15.510
video, that at the end of the
Fourth Coalition, Napoleon was

00:01:15.510 --> 00:01:17.740
kind of near the peak
of his power.

00:01:17.740 --> 00:01:19.360
He'd kind of done everything
right.

00:01:19.360 --> 00:01:24.370
He had this kind of steady
upward momentum, or France had

00:01:24.370 --> 00:01:26.900
a steady upward momentum
in its power.

00:01:26.900 --> 00:01:29.200
But what we're going to see in
this video, at least the

00:01:29.200 --> 00:01:32.400
beginnings of the downfall
of Napoleon.

00:01:32.400 --> 00:01:33.670
And it's not going to
be obvious when

00:01:33.670 --> 00:01:34.570
you look at the territory.

00:01:34.570 --> 00:01:36.390
Because from a territorial point
of view, you're going to

00:01:36.390 --> 00:01:39.040
see in this video that he's
actually gaining territory.

00:01:39.040 --> 00:01:42.430
But he is going to start doing
some of the actions that end

00:01:42.430 --> 00:01:44.190
up undermining him.

00:01:44.190 --> 00:01:46.500
So we talked about in the last
video, we talked about this

00:01:46.500 --> 00:01:53.950
whole notion of the Continental
System, where

00:01:53.950 --> 00:01:58.800
Napoleon was obsessed with
people on the continent of

00:01:58.800 --> 00:02:02.580
Europe boycotting England,
not trading with England.

00:02:02.580 --> 00:02:04.900
And he figured this is the only
way that he could really

00:02:04.900 --> 00:02:08.800
undermine England's dominance
on the ocean.

00:02:08.800 --> 00:02:12.480
Or eventually maybe even
undermine England generally.

00:02:12.480 --> 00:02:16.390
So as we said, in the Treaties
of Tilsit he got Russia to

00:02:16.390 --> 00:02:17.850
participate in the Continental
System.

00:02:17.850 --> 00:02:20.100
So he wanted everyone
to buy into it.

00:02:20.100 --> 00:02:24.110
And one party that, at this
point, we're talking about--

00:02:24.110 --> 00:02:31.390
we're in 1807 now-- one party
that wasn't all that keen in

00:02:31.390 --> 00:02:32.240
participating in the

00:02:32.240 --> 00:02:35.420
Continental System was Portugal.

00:02:35.420 --> 00:02:37.600
That's Portugal right there.

00:02:37.600 --> 00:02:41.050
So Napoleon goes and chats--
well they didn't chat

00:02:41.050 --> 00:02:43.280
directly-- but he gets
the agreement

00:02:43.280 --> 00:02:44.590
of the King of Spain.

00:02:44.590 --> 00:02:46.790
This is Charles IV, and he's
going to look like a bit of a

00:02:46.790 --> 00:02:48.040
fool and this video.

00:02:54.480 --> 00:02:57.320
And Napoleon says, hey Charles,
let's go in there,

00:02:57.320 --> 00:02:59.740
let's go into Portugal, that
little upstart country that

00:02:59.740 --> 00:03:01.980
doesn't want to participate
in the Continental System.

00:03:01.980 --> 00:03:03.970
You and me, we'll
invade together.

00:03:03.970 --> 00:03:07.870
We'll bring them into kind of
our realm of influence.

00:03:07.870 --> 00:03:10.960
And we can both kind of pillage
the lands and get the

00:03:10.960 --> 00:03:11.910
wealth of Portugal.

00:03:11.910 --> 00:03:13.840
Charles IV, he's all
up for this.

00:03:13.840 --> 00:03:19.870
So a combined French and Spanish
force invade Portugal.

00:03:19.870 --> 00:03:22.690
So in 1807, this is
the end of 1807,

00:03:22.690 --> 00:03:24.700
it's actually in October.

00:03:24.700 --> 00:03:33.980
In October, you have a combined
French and Spanish

00:03:33.980 --> 00:03:39.060
invasion of Portugal.

00:03:39.060 --> 00:03:41.570
And they are able to take
Portugal, but we're going to

00:03:41.570 --> 00:03:44.570
see that it's reasonably
temporary.

00:03:44.570 --> 00:03:47.290
Now I just mentioned that this
guy is going to look like the

00:03:47.290 --> 00:03:48.760
fool of this video.

00:03:48.760 --> 00:03:51.400
And the reason is, because
with the excuse of

00:03:51.400 --> 00:03:56.100
reinforcements, obviously to get
to Portugal, you have to

00:03:56.100 --> 00:03:57.820
go through Spain.

00:03:57.820 --> 00:04:01.700
So with the excuse of sending in
reinforcements, Napoleon in

00:04:01.700 --> 00:04:06.410
1808-- and now we're talking
about early 1808, in

00:04:06.410 --> 00:04:08.480
particular in March.

00:04:08.480 --> 00:04:10.980
So with the excuse of sending
in reinforcements to support

00:04:10.980 --> 00:04:13.610
the Portugal campaign, and Spain
is like your my ally,

00:04:13.610 --> 00:04:16.440
sure, send those hundreds of
thousands of troops right

00:04:16.440 --> 00:04:17.250
through our territory.

00:04:17.250 --> 00:04:19.220
We're not going to
worry about it.

00:04:19.220 --> 00:04:22.250
And with that excuse, Napoleon
was able to send 100,000

00:04:22.250 --> 00:04:23.950
troops and occupy Madrid.

00:04:27.220 --> 00:04:28.570
So this is one of
those lessons of

00:04:28.570 --> 00:04:29.490
never get too greedy.

00:04:29.490 --> 00:04:31.620
This guy got greedy, wanted
to help Napoleon.

00:04:31.620 --> 00:04:33.710
Or I guess the other lesson
is be careful who

00:04:33.710 --> 00:04:34.960
your friends are.

00:04:34.960 --> 00:04:38.020
This guy wanted to invade
Portugal, but the side effect

00:04:38.020 --> 00:04:40.960
of it is that Madrid
gets occupied.

00:04:40.960 --> 00:04:43.080
And that actually he
gets dethrowned.

00:04:43.080 --> 00:04:48.650
And so you have this situation
here, the French are now in

00:04:48.650 --> 00:04:51.010
control of Spain.

00:04:51.010 --> 00:04:59.440
In May of 1808-- and this is
really going to be the first

00:04:59.440 --> 00:05:03.010
little spark that is kind of
the downfall of Napoleon.

00:05:03.010 --> 00:05:12.510
In May 2, 1808, a popular
uprising starts in Madrid.

00:05:12.510 --> 00:05:13.990
Dos de Mayo.

00:05:13.990 --> 00:05:16.136
So a popular uprising
in Madrid.

00:05:20.900 --> 00:05:22.860
And at the same time, a little
bit after that--

00:05:22.860 --> 00:05:26.350
So you can imagine, this is
a hugely tumultuous time.

00:05:26.350 --> 00:05:31.030
You have this occupation of
Portugal with the excuse of

00:05:31.030 --> 00:05:33.640
reinforcements in March.

00:05:33.640 --> 00:05:35.725
The French troops
occupy Madrid.

00:05:39.780 --> 00:05:42.860
Then in May-- so a couple of
months later-- a popular

00:05:42.860 --> 00:05:44.600
uprising starts in Madrid.

00:05:44.600 --> 00:05:47.880
This leads to popular uprisings
throughout Spain.

00:05:47.880 --> 00:05:50.490
But at the very same time as
this-- this is a little bit

00:05:50.490 --> 00:05:54.890
after the uprising in May--
Napoleon says, oh, this is

00:05:54.890 --> 00:05:59.250
just a little uprising, I'm
still in control of Spain.

00:05:59.250 --> 00:06:02.630
He appoints his other brother--
remember, there's

00:06:02.630 --> 00:06:04.650
this whole business he's putting
his brothers in charge

00:06:04.650 --> 00:06:06.860
of different parts
of the Empire.

00:06:06.860 --> 00:06:13.290
He puts his brother Joseph, he
appoints his brother Joseph--

00:06:13.290 --> 00:06:17.890
or you could kind of say-- he
inserts his brother Joseph as

00:06:17.890 --> 00:06:19.140
the King of Spain.

00:06:26.410 --> 00:06:30.410
So this is all in kind
of early, mid-1808.

00:06:30.410 --> 00:06:34.110
Spain is in all of
this turmoil.

00:06:34.110 --> 00:06:36.710
A new king has been appointed,
who is Napoleon's brother.

00:06:36.710 --> 00:06:39.350
The old king is no
longer in charge.

00:06:39.350 --> 00:06:44.060
You have this ongoing
battle in Portugal.

00:06:44.060 --> 00:06:47.960
They don't have a firm hold
on Portugal just yet.

00:06:47.960 --> 00:06:52.680
And in the rest of 1808, the
uprising that occurs

00:06:52.680 --> 00:06:56.770
throughout Spain is actually
pretty successful in enforcing

00:06:56.770 --> 00:06:58.810
the French troops to retreat.

00:07:07.490 --> 00:07:11.770
And a major, I guess, aspect of
this uprising is it's one

00:07:11.770 --> 00:07:15.780
of the first real national
uprisings in history.

00:07:15.780 --> 00:07:19.000
It's people saying we are
Spanish, we do not like being

00:07:19.000 --> 00:07:20.940
controlled by the French.

00:07:20.940 --> 00:07:23.240
We do not like how they have
treated our royalty.

00:07:23.240 --> 00:07:26.870
We as a nation are
going to rise up.

00:07:26.870 --> 00:07:30.040
And the other interesting aspect
of this whole uprising

00:07:30.040 --> 00:07:33.770
that starts in Madrid with Dos
de Mayo, but then it starts

00:07:33.770 --> 00:07:37.120
continuing throughout the whole
nation, is the idea of

00:07:37.120 --> 00:07:38.370
guerrilla warfare.

00:07:40.480 --> 00:07:41.730
Not gorilla warfare.

00:07:47.810 --> 00:07:51.360
And this comes from the Spanish
for little war.

00:07:51.360 --> 00:07:55.220
Not from the large ape.

00:07:55.220 --> 00:07:58.280
And what it implies, you
probably heard the word on the

00:07:58.280 --> 00:08:01.330
news before, is kind of a
non-conventional style of

00:08:01.330 --> 00:08:05.800
fighting, where small little
groups kind of engage their

00:08:05.800 --> 00:08:07.740
enemy in very nontraditional
styles.

00:08:07.740 --> 00:08:11.200
So it becomes a very painful--
at least for it Napoleon's

00:08:11.200 --> 00:08:13.800
forces-- it became very
difficult fighting these

00:08:13.800 --> 00:08:16.360
non-conventional battles
all over Spain.

00:08:16.360 --> 00:08:18.930
So they were able to force
the French to retreat.

00:08:18.930 --> 00:08:20.530
Napoleon says, gee,
you know what?

00:08:20.530 --> 00:08:24.630
If you want a job well done,
you've got to do it yourself.

00:08:24.630 --> 00:08:27.910
So Napoleon comes in at the end
of the year, and then he

00:08:27.910 --> 00:08:29.530
retakes Madrid.

00:08:29.530 --> 00:08:39.340
So December of 1808, Napoleon
back in Madrid.

00:08:44.700 --> 00:08:46.670
Now, you might say all
is fine and well.

00:08:46.670 --> 00:08:48.220
Now Napoleon is back here.

00:08:48.220 --> 00:08:50.470
He has firm control of Spain.

00:08:50.470 --> 00:08:52.130
But not everything is good.

00:08:52.130 --> 00:08:54.170
Because as you could imagine,
there's all these other

00:08:54.170 --> 00:08:58.050
characters here that keep
forming coalitions for and

00:08:58.050 --> 00:08:59.460
against Napoleon.

00:08:59.460 --> 00:09:01.300
Even when they say that they're
allied, you know that

00:09:01.300 --> 00:09:03.630
in the back of their minds they
can't wait until they can

00:09:03.630 --> 00:09:08.770
declare the next war
on Napoleon.

00:09:08.770 --> 00:09:19.990
So in 1809-- let me write this
down-- Austria declares war.

00:09:23.630 --> 00:09:28.410
And since Great Britain was in--
at this point in time--

00:09:28.410 --> 00:09:30.790
perpetual war with France, this

00:09:30.790 --> 00:09:32.076
becomes the Fifth Coalition.

00:09:38.070 --> 00:09:40.920
But this one is fairly
short-lived.

00:09:40.920 --> 00:09:45.980
Napoleon says gee, I got these
guys on my eastern front.

00:09:45.980 --> 00:09:49.980
Austria is re-declaring
war on me.

00:09:49.980 --> 00:09:53.330
So he leaves Spain to
go lead that fight.

00:09:53.330 --> 00:09:56.210
And he leaves 300,000 of
his best troops in

00:09:56.210 --> 00:09:57.860
Spain to hold Spain.

00:09:57.860 --> 00:10:00.690
And frankly, this is the most
important side effect of the

00:10:00.690 --> 00:10:04.750
Fifth Coalition, is that it
makes Napoleon go to fight

00:10:04.750 --> 00:10:07.150
Austria, to lead that effort,
as opposed to

00:10:07.150 --> 00:10:08.680
worrying about Spain.

00:10:08.680 --> 00:10:12.790
And essentially by doing that--
and I don't know if

00:10:12.790 --> 00:10:15.300
it's necessarily the fact that
Napoleon wasn't there.

00:10:15.300 --> 00:10:18.250
But it could be because Napoleon
wasn't there-- is

00:10:18.250 --> 00:10:20.510
that Spain just becomes
a major thorn

00:10:20.510 --> 00:10:21.390
in Napoleon's side.

00:10:21.390 --> 00:10:25.480
This guerrilla warfare just
continues on and on and on.

00:10:25.480 --> 00:10:26.990
And it just goes
back and forth.

00:10:26.990 --> 00:10:28.550
And the French will
win a battle and

00:10:28.550 --> 00:10:29.360
they'll win another battle.

00:10:29.360 --> 00:10:30.470
But they still don't
have control.

00:10:30.470 --> 00:10:33.240
And these guerrillas will kind
of peck at them and continue

00:10:33.240 --> 00:10:34.680
the uprising.

00:10:34.680 --> 00:10:38.190
And this really just drains
the French army.

00:10:38.190 --> 00:10:41.060
And really just gets at them
little bit by little bit,

00:10:41.060 --> 00:10:44.340
really over the remainder
of Napoleon's reign.

00:10:44.340 --> 00:10:46.540
So all the way until 1814.

00:10:46.540 --> 00:10:47.800
We haven't gone over that yet.

00:10:47.800 --> 00:10:50.870
But this occurs all
the way to 1814.

00:10:50.870 --> 00:10:54.140
So I said at the beginning the
video, this is one of the

00:10:54.140 --> 00:10:55.950
starting points of Napoleon's
downfall.

00:10:55.950 --> 00:11:01.490
That's just because he was just
stuck in Spain from 1808

00:11:01.490 --> 00:11:05.260
on, just continuing to have to
send troops and supplies and

00:11:05.260 --> 00:11:08.730
reinforcements and wealth to
support what they called the

00:11:08.730 --> 00:11:09.980
Peninsular Campaign.

00:11:15.300 --> 00:11:16.420
And it just drains him.

00:11:16.420 --> 00:11:18.710
It drains his resources,
it drains his energy.

00:11:18.710 --> 00:11:22.200
And it really hurts his ability
to fight wars with all

00:11:22.200 --> 00:11:25.800
of the other people who he
needs to fight wars with.

00:11:25.800 --> 00:11:27.660
This is one of the
major downfalls.

00:11:27.660 --> 00:11:29.720
The other one, which we'll
probably talk about in the

00:11:29.720 --> 00:11:31.830
next video or video
after that, is

00:11:31.830 --> 00:11:33.060
his invasion of Russia.

00:11:33.060 --> 00:11:38.140
Which he does in 1812.

00:11:38.140 --> 00:11:40.340
One could debate which
one drains

00:11:40.340 --> 00:11:42.280
France's resources more.

00:11:42.280 --> 00:11:43.950
But the invasion of
Russia really

00:11:43.950 --> 00:11:46.040
decimates Napoleon's forces.

00:11:46.040 --> 00:11:49.950
And really makes him susceptible
to really conquest

00:11:49.950 --> 00:11:52.160
by England and all of
the other allies.

00:11:52.160 --> 00:11:54.590
And we're going to see that
in a couple of videos.

00:11:54.590 --> 00:11:56.810
So you have this been Peninsular
Campaign continuing

00:11:56.810 --> 00:11:58.920
to drain Napoleon.

00:11:58.920 --> 00:12:01.880
It all started because he
wanted to enforce the

00:12:01.880 --> 00:12:03.570
Continental System
on Portugal.

00:12:03.570 --> 00:12:04.580
And he got a little
bit greedy.

00:12:04.580 --> 00:12:06.480
And he also wanted
to conquer Spain.

00:12:06.480 --> 00:12:08.480
And just to highlight
why it's called

00:12:08.480 --> 00:12:09.490
the Peninsular Campaign.

00:12:09.490 --> 00:12:12.050
This right here, a little bit
of geography, this is called

00:12:12.050 --> 00:12:15.120
the Iberian Peninsula right
there that I'm circling.

00:12:15.120 --> 00:12:17.580
So you could call it the Iberian
Peninsular Campaign,

00:12:17.580 --> 00:12:19.895
because it's everything that's
going on in this Peninsula in

00:12:19.895 --> 00:12:21.145
Spain and Portugal.

00:12:33.220 --> 00:12:36.290
Now if we back up a little bit
back to 1808, where we had

00:12:36.290 --> 00:12:39.380
this uprising in Spain, and
they were able to push the

00:12:39.380 --> 00:12:40.380
French back.

00:12:40.380 --> 00:12:45.320
At the same time, you also had a
popular uprising in Portugal

00:12:45.320 --> 00:12:49.330
roughly in the fall, late
summer or fall of 1808.

00:12:49.330 --> 00:12:50.440
The British got excited.

00:12:50.440 --> 00:12:54.570
They saw it as their chance to
push Napoleon out of Portugal.

00:12:54.570 --> 00:12:56.880
So you have this
gentleman right

00:12:56.880 --> 00:12:58.830
here, Sir Arthur Wellesley.

00:12:58.830 --> 00:13:00.600
He's a future Duke
of Wellington.

00:13:00.600 --> 00:13:03.590
And he's eventually going to
be responsible for pushing

00:13:03.590 --> 00:13:06.720
Napoleon out of Spain
entirely.

00:13:06.720 --> 00:13:07.970
Or at least out of Madrid.

00:13:19.270 --> 00:13:22.670
Him and along with the British
and along with the Portuguese

00:13:22.670 --> 00:13:26.240
are able to push the French
out in August of 1808.

00:13:26.240 --> 00:13:30.510
So let me put this in my not so
neatly drawn timeline here.

00:13:30.510 --> 00:13:33.280
So in December, Napoleon is
back, so right before that in

00:13:33.280 --> 00:13:36.836
August, out of Portugal.

00:13:39.970 --> 00:13:41.900
And this is another motivation
for Napoleon to say,

00:13:41.900 --> 00:13:42.570
gee, you know what?

00:13:42.570 --> 00:13:45.340
Things aren't going well on the
Iberian Peninsula, I have

00:13:45.340 --> 00:13:48.810
to take charge of
things myself.

00:13:48.810 --> 00:13:52.000
Now, at the very same time as
all of this is happening, and

00:13:52.000 --> 00:13:57.200
this is really just kind of
out of interest. Well it's

00:13:57.200 --> 00:13:59.510
more than out of interest,
because actually it has huge

00:13:59.510 --> 00:14:00.460
global repercussions.

00:14:00.460 --> 00:14:02.680
You might say, OK, well you have
this Iberian Peninsula.

00:14:02.680 --> 00:14:04.510
Spain is going back and
forth between the

00:14:04.510 --> 00:14:05.690
French and the guerillas.

00:14:05.690 --> 00:14:09.590
And Portugal has this whole
situation where their king was

00:14:09.590 --> 00:14:12.180
dethrowned, but then the British
help and take it back.

00:14:12.180 --> 00:14:14.720
But you could imagine, these
nations are in just a super

00:14:14.720 --> 00:14:15.970
state of flux.

00:14:17.950 --> 00:14:22.440
Now you could also imagine, the
King of Spain wasn't just

00:14:22.440 --> 00:14:25.640
the King of Spain, he was King
of the Spanish Empire.

00:14:25.640 --> 00:14:29.670
And the Spanish Empire, the main
land mass of the Spanish

00:14:29.670 --> 00:14:32.180
Empire was in the Americas.

00:14:32.180 --> 00:14:33.170
So this right here.

00:14:33.170 --> 00:14:34.830
That was the Spanish
Empire at the time.

00:14:34.830 --> 00:14:37.900
This was a 400 year old
Spanish Empire.

00:14:37.900 --> 00:14:42.970
Starting with Columbus sailing
the ocean blue in 1492.

00:14:42.970 --> 00:14:45.490
You had this huge
Spanish Empire.

00:14:45.490 --> 00:14:48.680
And one of the really important
side effects of

00:14:48.680 --> 00:14:53.180
Napoleon invading Spain and
having this long protracted

00:14:53.180 --> 00:14:58.380
engagement in Spain, is it
catalyzed the ability of these

00:14:58.380 --> 00:15:01.040
colonies at the time to start
looking for their

00:15:01.040 --> 00:15:01.500
independence.

00:15:01.500 --> 00:15:03.260
And we're going to do whole
videos on that in the future.

00:15:03.260 --> 00:15:06.890
But this really is one of the
things that allowed them to

00:15:06.890 --> 00:15:08.350
get independence.

00:15:08.350 --> 00:15:10.860
Obviously, if the empire is in
flux, these guys can say hey,

00:15:10.860 --> 00:15:14.860
gee, why do we have to listen
to that nation anymore?

00:15:14.860 --> 00:15:16.950
We don't even know who's
in charge there.

00:15:16.950 --> 00:15:18.580
At the same time, same
thing in Portugal.

00:15:18.580 --> 00:15:21.540
Brazilian independence didn't
come until a little bit later

00:15:21.540 --> 00:15:24.860
after this period, but
Napoleon's invasion is what

00:15:24.860 --> 00:15:27.320
really sparked the beginning
of a lot

00:15:27.320 --> 00:15:28.500
of turmoil in Portugal.

00:15:28.500 --> 00:15:32.300
And that eventually is one of
the causes that leads to the

00:15:32.300 --> 00:15:34.510
eventual independence
of Brazil.

00:15:34.510 --> 00:15:36.790
That doesn't happen for another
10 or 15 years.

00:15:36.790 --> 00:15:40.240
But you could imagine, this is
where a lot of that action can

00:15:40.240 --> 00:15:41.550
be traced back.

00:15:41.550 --> 00:15:44.510
Now, another interesting
point that

00:15:44.510 --> 00:15:47.900
occurred around this time.

00:15:47.900 --> 00:15:49.580
And actually, I didn't tell
you what happened

00:15:49.580 --> 00:15:50.710
on the Fifth Coalition.

00:15:50.710 --> 00:15:52.500
I said Austria declared war.

00:15:52.500 --> 00:15:54.730
Obviously Britain was
already at war.

00:15:54.730 --> 00:15:56.130
So it was the Fifth Coalition.

00:15:56.130 --> 00:15:59.200
Napoleon had to leave, that
maybe made Spain a little bit

00:15:59.200 --> 00:16:00.860
harder to hold for France.

00:16:00.860 --> 00:16:03.550
And that's why it kind of
bled France slowly.

00:16:03.550 --> 00:16:06.580
But Napoleon was able to
take care of Austria.

00:16:06.580 --> 00:16:07.930
And then he was able to
take a little bit

00:16:07.930 --> 00:16:09.140
more land from them.

00:16:09.140 --> 00:16:12.890
Actually Galicia, this area of
Austria was given to the Duchy

00:16:12.890 --> 00:16:15.880
of Warsaw, which was a French
satellite state.

00:16:15.880 --> 00:16:19.330
And then Austria once again, had
to say oh Napoleon, we're

00:16:19.330 --> 00:16:22.460
your friend, we're going to
do whatever you ask us to.

00:16:22.460 --> 00:16:26.020
So you can imagine at this time
landwise, the empire of

00:16:26.020 --> 00:16:28.530
Napoleon seemed pretty
dramatic.

00:16:28.530 --> 00:16:30.480
You could include Spain here.

00:16:30.480 --> 00:16:33.500
Although he had to spend a lot
of resources to keep Spain.

00:16:33.500 --> 00:16:36.510
And then now we had Austria, at
least it was in the fold.

00:16:36.510 --> 00:16:38.770
You know Prussia was not
really happy about it.

00:16:38.770 --> 00:16:44.230
But this whole area here, the
western half of Poland was

00:16:44.230 --> 00:16:45.300
under French control.

00:16:45.300 --> 00:16:48.310
Germany-- the Confederacy
of the Rhine--

00:16:48.310 --> 00:16:49.600
which is now Germany.

00:16:49.600 --> 00:16:54.070
And then a good bit of Italy,
the Kingdom of Italy was also

00:16:54.070 --> 00:16:56.900
a French satellite state.

00:16:56.900 --> 00:16:59.950
But Napoleon, of course, he
wanted everyone to participate

00:16:59.950 --> 00:17:00.870
in the Continental System.

00:17:00.870 --> 00:17:03.440
That's the only way to really
strangle England.

00:17:03.440 --> 00:17:05.940
And the Papal States were
not participating in the

00:17:05.940 --> 00:17:07.190
Continental System.

00:17:11.500 --> 00:17:15.270
So he sent some people over
to kind of try to

00:17:15.270 --> 00:17:16.339
convince them to.

00:17:16.339 --> 00:17:20.470
And when they didn't, they
occupied the Papal States.

00:17:20.470 --> 00:17:22.630
So French troops occupied
the Papal States.

00:17:22.630 --> 00:17:26.920
And then once again, this
was still back in 1808.

00:17:26.920 --> 00:17:28.620
This is actually early
1808, it's just

00:17:28.620 --> 00:17:30.120
on a different front.

00:17:30.120 --> 00:17:32.040
So in February, up
here, in 1808.

00:17:32.040 --> 00:17:34.460
Actually, that's before they
even occupied Madrid.

00:17:34.460 --> 00:17:42.070
So in 1808, February, French
troops occupy Papal States.

00:17:47.720 --> 00:17:51.300
They essentially give them over
to the Kingdom of Italy,

00:17:51.300 --> 00:17:55.180
which at that time was a
French satellite state.

00:17:55.180 --> 00:17:57.090
So it's almost like annexing
it to France.

00:17:57.090 --> 00:18:00.020
And then once the Fifth
Coalition was done with,

00:18:00.020 --> 00:18:02.880
Napoleon felt so good about
himself, that he formally

00:18:02.880 --> 00:18:05.530
annexed the Papal States.

00:18:05.530 --> 00:18:06.900
Now we're in 1809.

00:18:06.900 --> 00:18:19.030
In 1809, he formally-- The
Papal States are actually

00:18:19.030 --> 00:18:20.940
annexed into the
French Empire.

00:18:26.360 --> 00:18:28.410
Now you can imagine that
the Pope wasn't

00:18:28.410 --> 00:18:29.530
that happy about this.

00:18:29.530 --> 00:18:31.660
This is the Pope at the time,
this is Pius VII.

00:18:36.960 --> 00:18:38.590
He wasn't so happy about it.

00:18:38.590 --> 00:18:40.660
So he excommunicates Napoleon.

00:18:40.660 --> 00:18:43.230
And I'll do a whole video
on excommunication.

00:18:43.230 --> 00:18:46.210
But it's really about as bad as
something you could do to

00:18:46.210 --> 00:18:48.990
someone within the powers
of the Catholic Church.

00:18:48.990 --> 00:18:51.700
And by implication, you're no
longer part of the church, and

00:18:51.700 --> 00:18:54.430
you'll probably go to hell now,
at least if the Pope has

00:18:54.430 --> 00:18:55.610
anything to do with it.

00:18:55.610 --> 00:18:58.560
So Napoleon wasn't
happy about this.

00:18:58.560 --> 00:19:01.110
He sent some people, some
officers, once again to talk

00:19:01.110 --> 00:19:02.180
to the Pope about it.

00:19:02.180 --> 00:19:03.410
To say hey, gee, why
do you want to

00:19:03.410 --> 00:19:04.700
excommunicate Napoleon?

00:19:04.700 --> 00:19:05.920
Why don't you just play nice?

00:19:05.920 --> 00:19:09.470
Why don't you just agree to
whatever Napoleon says?

00:19:09.470 --> 00:19:13.060
The Pope doesn't agree, and
so he gets abducted.

00:19:13.060 --> 00:19:14.310
This is why it's interesting.

00:19:14.310 --> 00:19:18.710
Napoleon, he's not afraid to
take some serious action.

00:19:18.710 --> 00:19:22.370
So he gets abducted in 1809
by French officers.

00:19:32.450 --> 00:19:37.120
And it's not clear, it's not
obvious that Napoleon told

00:19:37.120 --> 00:19:37.930
them to do it.

00:19:37.930 --> 00:19:39.990
But once he was abducted, and
they actually started

00:19:39.990 --> 00:19:43.430
shuttling him all around France
depending on who needed

00:19:43.430 --> 00:19:44.200
to talk to him.

00:19:44.200 --> 00:19:47.800
Or if they were afraid that the
British might try to free

00:19:47.800 --> 00:19:50.560
him from one port, they would
send them some place else.

00:19:50.560 --> 00:19:52.810
But it wasn't clear that
Napoleon ordered this.

00:19:52.810 --> 00:19:55.020
But he never ordered
his release.

00:19:55.020 --> 00:19:57.180
So in some ways, you got
to say that it was

00:19:57.180 --> 00:19:59.240
sanctioned by Napoleon.

00:19:59.240 --> 00:20:01.790
So all of this mess starts, you
know, Napoleon is messing

00:20:01.790 --> 00:20:02.520
with the Pope.

00:20:02.520 --> 00:20:06.730
He has this ongoing bleeding
going on in Spain.

00:20:06.730 --> 00:20:09.620
And that ends actually in 1812
where Sir Arthur Wellesley

00:20:09.620 --> 00:20:11.240
finally retakes Madrid.

00:20:11.240 --> 00:20:13.590
But during this whole period,
you can imagine it's really

00:20:13.590 --> 00:20:20.830
draining into the resources
of the French Empire.


Napoleon and the War of the Fourth Coalition

WEBVTT
Kind: captions
Language: en

00:00:00.420 --> 00:00:02.900
Where we left off in the last
video, Napoleon was doing

00:00:02.900 --> 00:00:03.860
pretty well.

00:00:03.860 --> 00:00:09.410
In 1804, just as a bit of
review, he declared himself

00:00:09.410 --> 00:00:14.750
Emperor Napoleon I.

00:00:14.750 --> 00:00:17.810
And then, the whole last video
was about the Third Coalition

00:00:17.810 --> 00:00:19.160
that formed in 1805.

00:00:19.160 --> 00:00:23.030
And we saw that at the end of
1805, after the Battle of

00:00:23.030 --> 00:00:31.880
Austerlitz, Napoleon was able to
crush the Third Coalition,

00:00:31.880 --> 00:00:34.880
which was mainly made up
of Russia and Austria.

00:00:34.880 --> 00:00:35.580
And this is all review.

00:00:35.580 --> 00:00:36.920
We saw this in the last video.

00:00:41.380 --> 00:00:44.660
And the big by-product of that,
other than the fact that

00:00:44.660 --> 00:00:47.800
it just made everyone think gee,
this Napoleon guy, he's

00:00:47.800 --> 00:00:51.880
pretty formidable, is that it
ended the Holy Roman Empire.

00:00:51.880 --> 00:00:53.860
Which you remember was
neither holy, nor

00:00:53.860 --> 00:00:55.290
Roman, nor an empire.

00:00:55.290 --> 00:00:57.360
It was really just
a collection of

00:00:57.360 --> 00:00:58.880
German speaking states.

00:00:58.880 --> 00:01:04.050
But it ended the official
Holy Roman Empire.

00:01:10.630 --> 00:01:13.360
And Napoleon felt so good about
himself at this point,

00:01:13.360 --> 00:01:17.890
especially after crushing the
Austrian and Russian forces at

00:01:17.890 --> 00:01:21.330
Austerlitz, that he had the Arc
de Triomphe, which if you

00:01:21.330 --> 00:01:23.950
go to Paris right now,
it's one of the

00:01:23.950 --> 00:01:25.230
things you should see.

00:01:25.230 --> 00:01:26.490
He had this built.

00:01:26.490 --> 00:01:29.240
And now it's to commemorate all
of the soldiers who have

00:01:29.240 --> 00:01:30.040
died for France.

00:01:30.040 --> 00:01:34.720
But it was originally built
by Napoleon, or it was

00:01:34.720 --> 00:01:37.640
commissioned by Napoleon, to
celebrate his victory at

00:01:37.640 --> 00:01:38.210
Austerlitz.

00:01:38.210 --> 00:01:41.030
So this is the Arc
de Triomphe.

00:01:41.030 --> 00:01:42.750
My spelling is always
a little weak.

00:01:42.750 --> 00:01:44.280
But it's especially weak
when I'm spelling

00:01:44.280 --> 00:01:45.530
something in French.

00:01:48.490 --> 00:01:50.210
And that's right there.

00:01:50.210 --> 00:01:53.630
So Napoleon was doing
pretty well.

00:01:53.630 --> 00:01:56.010
Now, on the other side of the
equation, you could imagine

00:01:56.010 --> 00:02:00.130
that the other major powers of
Europe were kind of licking

00:02:00.130 --> 00:02:00.780
their wounds.

00:02:00.780 --> 00:02:03.820
They weren't sure what was
going on and they were

00:02:03.820 --> 00:02:05.310
starting to feel threatened.

00:02:05.310 --> 00:02:09.800
And in particular, this guy
started to feel especially

00:02:09.800 --> 00:02:12.540
threatened.

00:02:12.540 --> 00:02:18.300
This is Frederick-- once again
my spelling is not the

00:02:18.300 --> 00:02:21.160
strongest, especially when I'm
doing something in German--

00:02:21.160 --> 00:02:22.540
Frederick Wilhelm III.

00:02:25.445 --> 00:02:28.040
It actually took me a long time
to realize that Wilhelm

00:02:28.040 --> 00:02:29.550
and William are the
same names.

00:02:29.550 --> 00:02:31.350
And William is just the
English version of it.

00:02:31.350 --> 00:02:34.060
But this is Frederick
Wilhelm III and he

00:02:34.060 --> 00:02:35.310
is the King of Prussia.

00:02:38.810 --> 00:02:40.570
And he stayed out of the action

00:02:40.570 --> 00:02:42.080
during the Third Coalition.

00:02:42.080 --> 00:02:46.220
And even now, Prussia is
a major European power.

00:02:46.220 --> 00:02:50.250
And he gets threatened by this
rising power of Napoleon, who

00:02:50.250 --> 00:02:53.880
was able to break up, or almost
take away Austria's

00:02:53.880 --> 00:02:55.590
influence from the Holy
Roman Empire.

00:02:55.590 --> 00:02:57.510
And now it kind of becomes this

00:02:57.510 --> 00:02:58.820
Confederation of the Rhine.

00:02:58.820 --> 00:03:01.850
Let me show you the map.

00:03:01.850 --> 00:03:03.515
So this whole area over here.

00:03:10.290 --> 00:03:15.770
All of this right over here,
which is now mainly modern day

00:03:15.770 --> 00:03:20.090
Germany, that used to be the
Holy Roman Empire, it's

00:03:20.090 --> 00:03:23.840
emperor was the King of
Austria, who wasn't

00:03:23.840 --> 00:03:26.790
necessarily in it, but it kind
of implies some type of

00:03:26.790 --> 00:03:29.030
allegiance.

00:03:29.030 --> 00:03:30.370
This is France right here.

00:03:30.370 --> 00:03:35.170
Once he was able to trounce
Austria in Austerlitz--

00:03:35.170 --> 00:03:37.240
Austria and Russia-- then
this becomes the

00:03:37.240 --> 00:03:40.630
Confederation of the Rhine.

00:03:40.630 --> 00:03:43.290
Let me highlight this
a little bit better.

00:03:43.290 --> 00:03:44.850
So this general area.

00:03:44.850 --> 00:03:46.720
Holy Roman Empire no
longer exists.

00:03:46.720 --> 00:03:49.730
And it now becomes kind of a
satellite region of France.

00:03:49.730 --> 00:03:52.120
France has a huge amount
of control.

00:03:52.120 --> 00:03:54.670
So you could imagine that the
King of Prussia starts getting

00:03:54.670 --> 00:03:55.350
a little bit threatened.

00:03:55.350 --> 00:03:59.740
France is on its borders, it has
shown itself to be able to

00:03:59.740 --> 00:04:01.890
defeat other great
powers with ease.

00:04:01.890 --> 00:04:04.880
So this guy gets a little
paranoid whether he feels that

00:04:04.880 --> 00:04:08.630
France might kind of threaten
Prussia's power.

00:04:08.630 --> 00:04:10.440
Or maybe on the other side of
the equation, that he just

00:04:10.440 --> 00:04:12.910
didn't like this upstart who was
not related to all of the

00:04:12.910 --> 00:04:15.870
other royalty of Europe.

00:04:15.870 --> 00:04:17.790
He maybe wanted to put
him in his place.

00:04:17.790 --> 00:04:23.250
So Frederick Wilhelm
III declares war.

00:04:23.250 --> 00:04:28.430
We're now in 1806.

00:04:28.430 --> 00:04:41.320
We have Prussia declares
war on France.

00:04:41.320 --> 00:04:43.420
And you're going to see this
pattern multiple times.

00:04:43.420 --> 00:04:45.430
And the one thing to kind of
remember, if you just want to

00:04:45.430 --> 00:04:47.340
remember kind of major themes.

00:04:47.340 --> 00:04:49.210
We're always talking about the
First Coalition, Second

00:04:49.210 --> 00:04:50.430
Coalition, Third Coalition,
Fourth

00:04:50.430 --> 00:04:51.190
Coalition, all of these.

00:04:51.190 --> 00:04:54.310
And it's always some combination
of Britain.

00:04:54.310 --> 00:04:56.780
And Britain has kind of already
dominated the ocean.

00:04:56.780 --> 00:04:59.480
So when we talk about these
battles on land, we're not

00:04:59.480 --> 00:05:00.250
talking about Britain much.

00:05:00.250 --> 00:05:02.700
But this whole time, Britain is
in the background trying to

00:05:02.700 --> 00:05:04.990
be a pain in France's neck.

00:05:04.990 --> 00:05:06.560
And then all the other
coalitions are some

00:05:06.560 --> 00:05:09.900
combination of Prussia,
Austria, and Russia.

00:05:09.900 --> 00:05:11.390
And some other countries
here and there.

00:05:11.390 --> 00:05:13.550
But you see one after another
that they keep challenging

00:05:13.550 --> 00:05:14.750
Napoleon up to this point.

00:05:14.750 --> 00:05:17.930
And Napoleon keeps trouncing
them, takes more and more land

00:05:17.930 --> 00:05:19.340
and territory and
power from them.

00:05:19.340 --> 00:05:21.550
And they get even more insecure
and then they want to

00:05:21.550 --> 00:05:23.080
form other coalitions.

00:05:23.080 --> 00:05:24.690
So this happens again.

00:05:24.690 --> 00:05:26.770
And this is the start of
the Fourth Coalition.

00:05:26.770 --> 00:05:28.370
In the last video,
it was the third.

00:05:28.370 --> 00:05:32.650
This is now the formation
of the fourth.

00:05:32.650 --> 00:05:35.890
And essentially, the coalition
forms as soon as someone else

00:05:35.890 --> 00:05:37.520
other than Great Britain
joins the fight.

00:05:37.520 --> 00:05:40.290
Because Great Britain is kind
of in a continuous war with

00:05:40.290 --> 00:05:43.370
Napoleon over this entire
time period.

00:05:43.370 --> 00:05:46.000
So we've got this Fourth
Coalition that forms. We've

00:05:46.000 --> 00:05:50.050
got Prussia, we've got Great
Britain, and Russia wants to

00:05:50.050 --> 00:05:50.890
join the fight again.

00:05:50.890 --> 00:05:54.240
So as you can imagine, the end
of the Third Coalition didn't

00:05:54.240 --> 00:05:56.960
keep Russia out of the
fight for long.

00:05:56.960 --> 00:05:57.850
Let me write it down.

00:05:57.850 --> 00:06:03.510
You have Prussia, Russia,
and Great Britain.

00:06:03.510 --> 00:06:05.840
There's always some other
actors, but these are the

00:06:05.840 --> 00:06:08.550
major ones.

00:06:08.550 --> 00:06:10.730
And it was kind of silly
on the part of Prussia.

00:06:10.730 --> 00:06:13.510
Because Prussia would've been in
a much better situation if

00:06:13.510 --> 00:06:15.520
it had helped the
Third Coalition.

00:06:15.520 --> 00:06:17.960
Maybe that would have
changed the outcome.

00:06:17.960 --> 00:06:21.160
But now they're kind of taking
on Napoleon, at least

00:06:21.160 --> 00:06:22.110
initially on their own.

00:06:22.110 --> 00:06:25.510
Because Russia is always kind of
behind Austria or Prussia,

00:06:25.510 --> 00:06:27.130
depending which coalition
you're talking about.

00:06:27.130 --> 00:06:28.940
So Prussia and Austria
are always the

00:06:28.940 --> 00:06:29.830
first line of offense.

00:06:29.830 --> 00:06:32.250
In this case, in the Fourth
Coalition, it's Prussia.

00:06:32.250 --> 00:06:38.550
And they get trounced
in Jena-Auerstedt.

00:06:38.550 --> 00:06:39.530
Let me show you where that is.

00:06:39.530 --> 00:06:42.600
So this is actually Napoleon
getting the troops together at

00:06:42.600 --> 00:06:44.080
Jena-Auerstedt.

00:06:44.080 --> 00:06:47.190
This right here is a charge of
the French troops there.

00:06:47.190 --> 00:06:48.440
Let me write this down.

00:06:57.140 --> 00:07:01.440
Two cities close by each
other in Germany.

00:07:01.440 --> 00:07:06.010
They are roughly around here.

00:07:06.010 --> 00:07:09.300
Let's see, this map is a little
difficult to read.

00:07:09.300 --> 00:07:13.210
But they're roughly in that
area right there.

00:07:13.210 --> 00:07:15.740
Napoleon, once again,
he trounces Prussia.

00:07:15.740 --> 00:07:17.780
So Prussia is just
out of the way.

00:07:17.780 --> 00:07:27.420
That's in October of 1806.

00:07:27.420 --> 00:07:30.890
And then Napoleon essentially
chases the Russians through

00:07:30.890 --> 00:07:32.275
most of what's now Poland.

00:07:37.580 --> 00:07:41.110
He has this hugely bloody
stalemate at Eylau.

00:07:41.110 --> 00:07:42.250
I don't even know
how to say that.

00:07:42.250 --> 00:07:44.390
It's right around there.

00:07:44.390 --> 00:07:46.265
If I read my maps correctly.

00:07:46.265 --> 00:07:47.515
So a stalemate.

00:07:51.250 --> 00:07:53.830
This is in 1807.

00:07:53.830 --> 00:07:59.780
Stalemate, February 1807
at-- let me get the

00:07:59.780 --> 00:08:03.020
spelling right, E-Y-L-A-U.

00:08:03.020 --> 00:08:03.900
Super bloody.

00:08:03.900 --> 00:08:05.000
They actually win the battle.

00:08:05.000 --> 00:08:08.130
But they aren't able to
decisively defeat the Russian

00:08:08.130 --> 00:08:10.130
troops, or the Russian army.

00:08:10.130 --> 00:08:12.220
And there are estimates that
in that one battle, there's

00:08:12.220 --> 00:08:15.520
anywhere from 15,000 to 25,000
casualties on both sides.

00:08:15.520 --> 00:08:17.490
Which was huge at that time.

00:08:17.490 --> 00:08:20.440
Even now, if you think about
even modern wars, that's a

00:08:20.440 --> 00:08:22.260
major amount of casualties
to have in

00:08:22.260 --> 00:08:24.600
just one single battle.

00:08:24.600 --> 00:08:28.730
But Napoleon persists, and
he's eventually able to

00:08:28.730 --> 00:08:34.159
decisively meet the Russians at
Friedland, which is right

00:08:34.159 --> 00:08:35.409
about there.

00:08:40.500 --> 00:08:45.500
That is in June of 1807.

00:08:45.500 --> 00:08:48.400
And then he's able
to decisively

00:08:48.400 --> 00:08:50.680
defeat the Fourth Coalition.

00:08:50.680 --> 00:09:01.150
So here we we're kind of
at the summer of 1807.

00:09:01.150 --> 00:09:03.930
We're talking about June is
when Friedland occurs,

00:09:03.930 --> 00:09:05.875
Russians decisively defeated.

00:09:05.875 --> 00:09:09.530
The Prussians were already
trounced several months ago.

00:09:09.530 --> 00:09:20.380
And then in July of '07, July
of 1807, you have France

00:09:20.380 --> 00:09:22.060
signing the Treaties
of Tilsit.

00:09:27.620 --> 00:09:30.540
And it's called the Treaties
of Tilsit, instead of the

00:09:30.540 --> 00:09:34.150
Treaty of Tilsit, because he
signed separate treaties with

00:09:34.150 --> 00:09:35.880
Russia and Prussia.

00:09:35.880 --> 00:09:37.750
At this point, Napoleon
had kind of lost

00:09:37.750 --> 00:09:39.560
all respect for Prussia.

00:09:39.560 --> 00:09:40.650
And he wanted to show it.

00:09:40.650 --> 00:09:43.040
So he had a separate treaty with
Prussia and a separate

00:09:43.040 --> 00:09:44.190
treaty with Russia.

00:09:44.190 --> 00:09:46.170
The one with Russia was a
lot more respectable.

00:09:46.170 --> 00:09:48.960
It had all this language about
how Napoleon and Tsar

00:09:48.960 --> 00:09:51.120
Alexander I are now friends.

00:09:51.120 --> 00:09:54.530
This is Tsar Alexander
I right here.

00:09:58.920 --> 00:10:01.220
And as you'll see, this
friendship is very temporary.

00:10:01.220 --> 00:10:03.620
As you could imagine, I mean
this is the guy Napoleon

00:10:03.620 --> 00:10:05.940
defeated at Austerlitz
not too long ago.

00:10:05.940 --> 00:10:09.380
So all this friendship should
probably be written in quotes.

00:10:09.380 --> 00:10:11.920
But the treaty with Russia
was very friendly.

00:10:11.920 --> 00:10:17.280
And I think Napoleon still
respected Russia's power.

00:10:17.280 --> 00:10:22.835
So friendly with Russia, it
declared them allies.

00:10:27.670 --> 00:10:33.600
But the other Treaty of Tilsit
with Prussia carved it up.

00:10:33.600 --> 00:10:38.010
Carved up Prussia.

00:10:38.010 --> 00:10:40.720
And the main thing it did, if we
look at this map here, this

00:10:40.720 --> 00:10:43.250
is a map of central Europe.

00:10:43.250 --> 00:10:47.720
Or I guess Prussia and Austria
and France at the end of the

00:10:47.720 --> 00:10:48.780
Third Coalition.

00:10:48.780 --> 00:10:51.250
The main thing it did, it took
the territory west of the

00:10:51.250 --> 00:10:53.750
river Elbe from Prussia.

00:10:53.750 --> 00:10:57.070
So this is the river
Elbe right here.

00:10:59.670 --> 00:11:02.720
The blue is Prussia after
the Third Coalition.

00:11:02.720 --> 00:11:06.150
So all of this stuff gets
taken away from Prussia.

00:11:06.150 --> 00:11:09.310
And most of it turns into a
French satellite kingdom

00:11:09.310 --> 00:11:11.600
called the Kingdom
of Westphalia.

00:11:11.600 --> 00:11:15.000
So this is part of the Prussian
Treaty of Tilsit.

00:11:15.000 --> 00:11:16.400
So you have the Kingdom
of Westphalia.

00:11:23.900 --> 00:11:26.130
And to really emphasize,
it really is a

00:11:26.130 --> 00:11:27.370
French satellite state.

00:11:27.370 --> 00:11:31.470
And to add insult to injury to
the Prussians, Napoleon puts

00:11:31.470 --> 00:11:33.140
his brother Jerome as king.

00:11:43.930 --> 00:11:47.290
So it really is a satellite
state of France.

00:11:47.290 --> 00:11:49.790
So here at the end of this,
the other powers in Europe

00:11:49.790 --> 00:11:53.790
haven't learned that this
Napoleon character with his

00:11:53.790 --> 00:11:56.490
grand army, this huge army that
he's been able to raise

00:11:56.490 --> 00:12:00.550
and his military tactics, really
is someone formidable

00:12:00.550 --> 00:12:01.270
to deal with.

00:12:01.270 --> 00:12:04.000
So they keep, Third Coalition,
and then they lose territory.

00:12:04.000 --> 00:12:05.190
Then the Fourth Coalition,
then they

00:12:05.190 --> 00:12:07.050
lose even more territory.

00:12:07.050 --> 00:12:09.790
So what happens at the end of
this Fourth Coalition, and

00:12:09.790 --> 00:12:13.360
actually during the Fourth
Coalition, after Napoleon

00:12:13.360 --> 00:12:15.460
defeated Prussia, he realized
gee, you know what?

00:12:15.460 --> 00:12:20.300
I have, I'm in either direct
control or indirect control of

00:12:20.300 --> 00:12:22.160
a significant part of Europe.

00:12:22.160 --> 00:12:24.880
And at the same time, he knew
that Britain had complete

00:12:24.880 --> 00:12:26.110
domination of the oceans.

00:12:26.110 --> 00:12:29.410
And it was this kind of rising
industrial power.

00:12:29.410 --> 00:12:33.100
It was the beginning of the
Industrial Revolution.

00:12:33.100 --> 00:12:40.950
So Napoleon's ideas, well I
can't defeat Great Britain on

00:12:40.950 --> 00:12:41.730
the waters.

00:12:41.730 --> 00:12:42.490
Did I say Russia?

00:12:42.490 --> 00:12:46.140
No I've been saying-- the whole
point is that Great

00:12:46.140 --> 00:12:48.090
Britain is dominant
on the oceans.

00:12:48.090 --> 00:12:50.580
And Napoleon realizes
that he can't invade

00:12:50.580 --> 00:12:52.050
Great Britain by sea.

00:12:52.050 --> 00:12:56.630
He can't do anything in the
water with Great Britain kind

00:12:56.630 --> 00:12:57.950
of pestering him.

00:12:57.950 --> 00:13:02.280
So what he tries to do is
declare economic warfare on

00:13:02.280 --> 00:13:02.730
Great Britain.

00:13:02.730 --> 00:13:08.740
And he institutes at
the end of 1806,

00:13:08.740 --> 00:13:09.940
the Continental System.

00:13:09.940 --> 00:13:11.180
So I'll put this right here.

00:13:11.180 --> 00:13:13.550
This is in November of 1806.

00:13:13.550 --> 00:13:16.400
So this is right after he
trounces the Prussians at

00:13:16.400 --> 00:13:19.120
Jena-Auerstedt.

00:13:19.120 --> 00:13:23.560
This is in November of 1806,
where he's feeling really good

00:13:23.560 --> 00:13:26.930
about his strength on the
actual continent.

00:13:26.930 --> 00:13:29.050
He institutes what he calls
the Continental System.

00:13:34.390 --> 00:13:37.040
And this is really just the
notion of economic warfare

00:13:37.040 --> 00:13:37.850
with Great Britain.

00:13:37.850 --> 00:13:41.770
That hey, if you are either a
part of the French Empire,

00:13:41.770 --> 00:13:45.370
controlled by the French Empire,
or aligned with the

00:13:45.370 --> 00:13:47.670
French Empire, you embargo
Great Britain.

00:13:47.670 --> 00:13:50.610
This little island, it controls
the waters, but it is

00:13:50.610 --> 00:13:51.730
dependant on trade.

00:13:51.730 --> 00:13:54.580
So Napoleon's idea through this
Continental System is to

00:13:54.580 --> 00:14:02.185
embargo the United Kingdom of
Great Britain, whatever we

00:14:02.185 --> 00:14:02.770
want to call it.

00:14:02.770 --> 00:14:04.320
Embargo Great Britain.

00:14:09.320 --> 00:14:11.150
And one thing he got out of
the Russians, this was

00:14:11.150 --> 00:14:13.990
actually a huge concession,
because Russia was a major

00:14:13.990 --> 00:14:15.510
power at the time.

00:14:15.510 --> 00:14:20.640
He got them, through the Treaty
of Tilsit, to also join

00:14:20.640 --> 00:14:21.890
the Continental System.

00:14:24.320 --> 00:14:26.380
Let me write that in a color
that'll actually show up.

00:14:33.870 --> 00:14:36.730
And in return, he also got some
land, some islands, the

00:14:36.730 --> 00:14:39.790
Ionian Islands off the western
coast of Greece.

00:14:39.790 --> 00:14:43.630
And some of the land off the
Dalmatian coast. Let me show

00:14:43.630 --> 00:14:44.450
you right there.

00:14:44.450 --> 00:14:46.760
So this area over here.

00:14:46.760 --> 00:14:49.830
And Russia in return, and it's
pretty good because Russia

00:14:49.830 --> 00:14:52.660
essentially lost the war, but in
return they were allowed to

00:14:52.660 --> 00:14:54.460
do whatever they want with
the Ottoman Empire.

00:14:54.460 --> 00:14:56.760
And we'll talk more about the
Ottoman Empire in future

00:14:56.760 --> 00:14:59.110
videos, but if you want to have
a general view of what

00:14:59.110 --> 00:15:04.040
the Ottoman Empire is, I guess
the last remnant of it is what

00:15:04.040 --> 00:15:05.550
is today modern Turkey.

00:15:05.550 --> 00:15:08.500
But obviously it was an
empire at that time.

00:15:08.500 --> 00:15:11.010
But Russia and the Ottoman
Empire were kind of that at

00:15:11.010 --> 00:15:11.960
odds with each other.

00:15:11.960 --> 00:15:14.310
So it was great for Russia to
say hey, I'm going to be able

00:15:14.310 --> 00:15:16.730
to do whatever I want with
the Ottoman Empire.

00:15:16.730 --> 00:15:20.380
Because before this, Napoleon
was nominally

00:15:20.380 --> 00:15:22.170
aligned with the Ottomans.

00:15:22.170 --> 00:15:25.360
So this was actually a big
concession for Russia.

00:15:25.360 --> 00:15:28.550
So at the end of this, we have
a situation once again, I

00:15:28.550 --> 00:15:31.100
guess the other powers
don't realize it.

00:15:31.100 --> 00:15:36.070
Over and over, Third Coalition,
Napoleon, he really

00:15:36.070 --> 00:15:39.080
takes care of the Russians
and the Austrians.

00:15:39.080 --> 00:15:41.190
Destroys the Holy Roman
Empire, makes it the

00:15:41.190 --> 00:15:44.930
Confederation of the Rhine
under Napoleon's control.

00:15:44.930 --> 00:15:48.290
Prussia wants to put
down Napoleon.

00:15:48.290 --> 00:15:50.660
Declares war again,
Fourth Coalition.

00:15:50.660 --> 00:15:55.070
The only by-product of that is
now they lose this land.

00:15:55.070 --> 00:15:57.140
Napoleon becomes
even stronger.

00:15:57.140 --> 00:16:02.380
Puts his brother as king in
the kingdom of Westphalia.

00:16:02.380 --> 00:16:06.020
And now he has Russia
as an ally to help

00:16:06.020 --> 00:16:07.780
his embargo on England.

00:16:07.780 --> 00:16:11.820
So really, after the end of the
Fourth Coalition, a lot of

00:16:11.820 --> 00:16:14.980
historians view this as kind
of the height of Napoleon's

00:16:14.980 --> 00:16:17.480
power in Europe.


Surveys and Samples

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:05.610
What we have here is six
examples of possible surveys

00:00:05.610 --> 00:00:06.700
that might be conducted.

00:00:06.700 --> 00:00:09.560
What we want to do is critique
them, see whether they're

00:00:09.560 --> 00:00:12.880
actually doing things that will
give meaningful results,

00:00:12.880 --> 00:00:14.400
or results that you can
actually make some

00:00:14.400 --> 00:00:15.370
judgment based on.

00:00:15.370 --> 00:00:16.379
So let's read the directions.

00:00:16.379 --> 00:00:19.570
It says, comment on the way
the following samples have

00:00:19.570 --> 00:00:20.730
been chosen.

00:00:20.730 --> 00:00:25.120
For the unsatisfactory cases,
suggest a way to improve the

00:00:25.120 --> 00:00:25.950
sample choice.

00:00:25.950 --> 00:00:26.890
All right.

00:00:26.890 --> 00:00:33.020
So A, you want to find whether
wealthier people have more

00:00:33.020 --> 00:00:36.200
nutritious diets by interviewing
people coming out

00:00:36.200 --> 00:00:38.970
of a five-star restaurant.

00:00:38.970 --> 00:00:42.120
So this is skewed on
two directions.

00:00:42.120 --> 00:00:46.320
One, if you're only interviewing
people out of a

00:00:46.320 --> 00:00:48.880
five-star restaurant, you're
going to have a

00:00:48.880 --> 00:00:52.210
disproportionate number
of wealthy people.

00:00:52.210 --> 00:00:55.290
And even the non-wealthy people
who are eating at the

00:00:55.290 --> 00:00:57.390
five-star restaurant, they feel
like they have enough

00:00:57.390 --> 00:01:01.350
money to eat there, so they're
probably not that not-wealthy.

00:01:01.350 --> 00:01:05.940
They're probably pretty close
to the threshold of wealthy.

00:01:05.940 --> 00:01:07.740
The other skew is that you're
interviewing people at a

00:01:07.740 --> 00:01:10.700
restaurant, so you're
disproportionately probably

00:01:10.700 --> 00:01:13.980
going to get people who eat out,
as opposed to people who

00:01:13.980 --> 00:01:15.020
cook for themselves.

00:01:15.020 --> 00:01:17.300
And depending on whether this
is a really healthy

00:01:17.300 --> 00:01:20.220
restaurant, maybe some type of
organic, vegan, who knows

00:01:20.220 --> 00:01:21.990
what, restaurant, where
you're going to get a

00:01:21.990 --> 00:01:23.390
disproportionate number
of healthy people.

00:01:23.390 --> 00:01:25.140
Or maybe it's a really
unhealthy restaurant.

00:01:25.140 --> 00:01:29.580
Maybe it's they put a lot of
butter and sugar in the food.

00:01:29.580 --> 00:01:31.420
Who knows what it's all about?

00:01:31.420 --> 00:01:34.030
But this seems skewed
on two dimensions.

00:01:34.030 --> 00:01:38.160
The best way to do it is, survey
some proportion of

00:01:38.160 --> 00:01:41.610
wealthy people in an environment
where it isn't

00:01:41.610 --> 00:01:43.990
being skewed by the type
of food they eat.

00:01:43.990 --> 00:01:46.690
So you, once again, you wouldn't
want to survey people

00:01:46.690 --> 00:01:48.870
at the organic grocery, because
once again, you'd be

00:01:48.870 --> 00:01:51.110
skewing for people who maybe
eat a little healthier.

00:01:51.110 --> 00:01:56.660
You'd want to do it maybe at
some type of wealthy type of

00:01:56.660 --> 00:01:59.050
event, or something that's
not food-oriented.

00:01:59.050 --> 00:02:02.530
I'd have to think more about
what that might be.

00:02:02.530 --> 00:02:07.720
And you'd also want to survey
people who are not wealthy, so

00:02:07.720 --> 00:02:10.240
at some other type of event
where most of the population

00:02:10.240 --> 00:02:11.710
doesn't fall under the
wealthy category.

00:02:11.710 --> 00:02:15.760
Or probably the best thing would
be sampling people at an

00:02:15.760 --> 00:02:18.410
event that doesn't discriminate
on wealth, and

00:02:18.410 --> 00:02:20.960
just surveying people and just
ask them, in a broad bucket,

00:02:20.960 --> 00:02:22.290
do you make more than x?

00:02:22.290 --> 00:02:24.120
Whatever your definition
of wealthy is.

00:02:24.120 --> 00:02:27.270
Or is your wealth, or is your
income less than x?

00:02:27.270 --> 00:02:30.370
And then ask people what do
they eat on a daily basis,

00:02:30.370 --> 00:02:31.540
something like that
might work.

00:02:31.540 --> 00:02:34.470
So in general, I'm not
a fan, not a fan.

00:02:34.470 --> 00:02:37.830
I don't think this
passes mustards.

00:02:37.830 --> 00:02:41.100
It's biased on really
two dimensions.

00:02:41.100 --> 00:02:45.850
B, you want to find out if there
is a pedestrian crossing

00:02:45.850 --> 00:02:49.240
needed at a certain intersection
by interviewing

00:02:49.240 --> 00:02:53.050
people walking by that
intersection.

00:02:53.050 --> 00:02:56.290
So this is better than the first
survey, but it still

00:02:56.290 --> 00:02:58.770
seems a little biased.

00:02:58.770 --> 00:03:02.480
And it depends how you
define needed.

00:03:02.480 --> 00:03:05.420
Is needed if the people walking
around the pedestrian

00:03:05.420 --> 00:03:08.010
crossing think it's needed,
then this is OK.

00:03:08.010 --> 00:03:11.200
But if you want to objectively
find out whether people in

00:03:11.200 --> 00:03:13.860
your community think it's
needed, you want to have a

00:03:13.860 --> 00:03:15.170
broader sample.

00:03:15.170 --> 00:03:19.320
So you might want to also
include drivers.

00:03:19.320 --> 00:03:22.050
Because obviously, the
pedestrian crossing is going

00:03:22.050 --> 00:03:23.770
to affect them.

00:03:23.770 --> 00:03:26.740
You want to interview taxpayers
in general.

00:03:26.740 --> 00:03:29.530
And obviously a lot of people
might be all of the above.

00:03:29.530 --> 00:03:32.980
And you also might be missing
pedestrians who would be

00:03:32.980 --> 00:03:35.520
walking by that intersection
if there was a pedestrian

00:03:35.520 --> 00:03:37.940
crossing, but they're avoiding
it, and so those are the

00:03:37.940 --> 00:03:40.250
people who would want it the
most, but they're not even

00:03:40.250 --> 00:03:42.740
going to be there because they
don't think that it's worth

00:03:42.740 --> 00:03:44.440
walking around there because
you can't cross the street.

00:03:44.440 --> 00:03:46.700
So you're missing a whole
sample of people.

00:03:46.700 --> 00:03:50.790
The best way I would do this
is I would look within a,

00:03:50.790 --> 00:03:54.050
maybe a three block radius, or
maybe a six block radius, of

00:03:54.050 --> 00:03:57.390
all of the homes and offices,
and I would randomly survey a

00:03:57.390 --> 00:03:59.000
sample of those people.

00:03:59.000 --> 00:04:02.080
And I think that would be a
better indication of whether

00:04:02.080 --> 00:04:04.440
the pedestrian crossing
is needed.

00:04:04.440 --> 00:04:06.170
And actually, even a better
way would be do

00:04:06.170 --> 00:04:07.020
it without a survey.

00:04:07.020 --> 00:04:09.630
You'd actually want to look at
patterns of people walking and

00:04:09.630 --> 00:04:11.860
all of that, and compared
to other things

00:04:11.860 --> 00:04:12.670
that might be needed.

00:04:12.670 --> 00:04:18.680
But this one definitely
doesn't work for me.

00:04:18.680 --> 00:04:22.890
Now C, you want to find out if
women talk more than men by

00:04:22.890 --> 00:04:26.830
interviewing an equal number
of men and women.

00:04:26.830 --> 00:04:28.450
That seems reasonable.

00:04:28.450 --> 00:04:31.760
I guess if your survey, if
you do it in a non-biased

00:04:31.760 --> 00:04:34.440
environment-- if you don't do it
at, like, a business school

00:04:34.440 --> 00:04:37.570
or a law school where people
might talk disproportionately,

00:04:37.570 --> 00:04:41.200
or it might be skewed towards
women or men more.

00:04:41.200 --> 00:04:43.190
I don't know which way
it would be skewed.

00:04:43.190 --> 00:04:45.930
But as long as you do it in a
neutral place, and I guess

00:04:45.930 --> 00:04:48.640
their survey is, maybe they'll
ask some arbitrary question.

00:04:48.640 --> 00:04:51.940
And they'll just time, or
they'll count how many words

00:04:51.940 --> 00:04:56.210
the women talk versus the number
of words the men talk.

00:04:56.210 --> 00:04:58.130
That seems like a reasonable
way to see if women

00:04:58.130 --> 00:04:58.880
talk more than men.

00:04:58.880 --> 00:05:01.670
And once again, as long as
you're not talking to some

00:05:01.670 --> 00:05:03.390
skewed sample, or biased
sample, this

00:05:03.390 --> 00:05:04.900
seems pretty good.

00:05:04.900 --> 00:05:05.990
And it's good if it's
an equal number.

00:05:05.990 --> 00:05:07.930
There's an equal number of men
and women in the world.

00:05:07.930 --> 00:05:15.880
This seems to be-- I'll give it
a smiley face right here.

00:05:15.880 --> 00:05:20.590
D, you want to find whether
students in your school get

00:05:20.590 --> 00:05:23.210
too much homework by
interviewing a stratified

00:05:23.210 --> 00:05:26.400
sample of students from
each grade level.

00:05:26.400 --> 00:05:28.600
Well the first thing I want
to do is, what is

00:05:28.600 --> 00:05:32.040
a stratified sample?

00:05:32.040 --> 00:05:34.960
And all that means is, you're
going to sample people in the

00:05:34.960 --> 00:05:37.210
same proportion that they
exist in the population.

00:05:37.210 --> 00:05:39.600
So let's say that your
population-- your school--

00:05:39.600 --> 00:05:44.610
had, say they had 100
ninth graders.

00:05:44.610 --> 00:05:48.990
It has 200 tenth graders.

00:05:48.990 --> 00:05:52.280
300 eleventh graders.

00:05:52.280 --> 00:05:55.680
And 400 twelfth graders.

00:05:55.680 --> 00:05:57.940
Actually, the school I attended
actually, it went in

00:05:57.940 --> 00:05:58.710
the reverse order.

00:05:58.710 --> 00:06:02.460
I think we had like 800 ninth
graders and 400 twelfth

00:06:02.460 --> 00:06:04.600
graders since so many
people dropped out.

00:06:04.600 --> 00:06:06.320
But anyway, we don't have
to be realistic here.

00:06:06.320 --> 00:06:08.730
So you had a total
school population

00:06:08.730 --> 00:06:14.010
of about 1,000 students.

00:06:14.010 --> 00:06:16.040
So if you want to do a
stratified sample, let's say

00:06:16.040 --> 00:06:18.720
you wanted to have
a sample size of,

00:06:18.720 --> 00:06:20.320
let's say, 50 students.

00:06:20.320 --> 00:06:23.650
So you wanted to sample 50
students, and you wanted it to

00:06:23.650 --> 00:06:25.440
be a stratified sample.

00:06:25.440 --> 00:06:28.490
What that means is, you had 100
ninth graders out of 1,000

00:06:28.490 --> 00:06:29.000
in your school.

00:06:29.000 --> 00:06:33.400
So 10% of your school's
population is ninth graders.

00:06:33.400 --> 00:06:37.070
So in your stratified
sample, 10% also

00:06:37.070 --> 00:06:37.910
need to be ninth graders.

00:06:37.910 --> 00:06:41.650
So 10% of 5-- sorry--
10% of 50 is 5.

00:06:41.650 --> 00:06:43.435
So you'd survey 5
ninth graders.

00:06:46.200 --> 00:06:55.290
In both situations, this is 10%
of the population, it's

00:06:55.290 --> 00:06:57.090
going to be 10% of
your sample.

00:06:57.090 --> 00:07:00.080
Likewise, you had 20% were
tenth graders in the

00:07:00.080 --> 00:07:02.450
population, so 20%
of your sample.

00:07:02.450 --> 00:07:10.640
Or 20% times 50 is 10 tenth
graders should be surveyed.

00:07:10.640 --> 00:07:15.560
And then 30% of your school is
eleventh graders, so 30% of

00:07:15.560 --> 00:07:16.720
your survey.

00:07:16.720 --> 00:07:21.050
So that should be 15
eleventh graders.

00:07:21.050 --> 00:07:23.990
And then finally 40% were
twelfth graders.

00:07:23.990 --> 00:07:28.390
So in this situation, 40% of
your survey, which is 20,

00:07:28.390 --> 00:07:29.990
should be twelfth graders.

00:07:29.990 --> 00:07:34.150
So that's all-- that's what
a stratified sample means.

00:07:34.150 --> 00:07:35.220
Now let's talk about
whether this is

00:07:35.220 --> 00:07:36.560
actually a good survey.

00:07:36.560 --> 00:07:38.310
You want to find out whether
students in your school get

00:07:38.310 --> 00:07:39.420
too much homework, and
you're interviewing

00:07:39.420 --> 00:07:41.230
students in your school.

00:07:41.230 --> 00:07:43.440
The one thing you definitely
will find out is you will find

00:07:43.440 --> 00:07:49.860
out whether students in your
school think-- think-- they

00:07:49.860 --> 00:07:52.020
think they get too much homework
by interviewing a

00:07:52.020 --> 00:07:52.470
stratified sample.

00:07:52.470 --> 00:07:53.890
That would be true.

00:07:53.890 --> 00:07:55.450
That's what you would
find out.

00:07:55.450 --> 00:07:58.150
Now, whether you could say
that in a broader sense

00:07:58.150 --> 00:08:00.290
they're getting too much
homework, you might want to

00:08:00.290 --> 00:08:04.240
include a larger audience,
especially the other

00:08:04.240 --> 00:08:07.470
stakeholders in the whole
homework doing process,

00:08:07.470 --> 00:08:13.250
especially parents
and teachers.

00:08:13.250 --> 00:08:16.720
And actually a better way to
do it would be, probably to

00:08:16.720 --> 00:08:19.830
compare the students in your
school to a very similar

00:08:19.830 --> 00:08:23.070
school that has a different
amount of homework, and maybe

00:08:23.070 --> 00:08:24.770
see the results on standardized
tests.

00:08:24.770 --> 00:08:26.030
And you want to control.

00:08:26.030 --> 00:08:28.430
You want to make sure that there
isn't a huge difference

00:08:28.430 --> 00:08:31.150
between the income levels, or
the education levels of the

00:08:31.150 --> 00:08:32.120
kids' parents, and all that.

00:08:32.120 --> 00:08:33.679
I mean, it becomes much
more involved.

00:08:33.679 --> 00:08:35.659
But this one still seems a
little bit narrow, and all

00:08:35.659 --> 00:08:37.740
you're going to find out is
whether students think they

00:08:37.740 --> 00:08:38.880
get too much homework.

00:08:38.880 --> 00:08:41.220
And I can almost guarantee you,
they will think that they

00:08:41.220 --> 00:08:43.880
get too much homework, and so
this survey might be a little

00:08:43.880 --> 00:08:45.470
bit of a waste of time.

00:08:45.470 --> 00:08:47.780
So I will put a frowny face.

00:08:47.780 --> 00:08:50.500
E, you want to find out whether
there should be more

00:08:50.500 --> 00:08:54.150
public buses running during
rush hour by interviewing

00:08:54.150 --> 00:08:56.820
people getting off the bus.

00:08:56.820 --> 00:08:59.770
So once again, what you're going
to find out is whether

00:08:59.770 --> 00:09:02.670
people who ride, people getting
off the bus think

00:09:02.670 --> 00:09:04.560
there should be more buses.

00:09:04.560 --> 00:09:07.110
So I won't write it here, but
you're not going to find out

00:09:07.110 --> 00:09:09.370
objectively whether there
should be more buses.

00:09:09.370 --> 00:09:12.210
Frankly, the best way to
evaluate that, I think, is to

00:09:12.210 --> 00:09:15.000
just see how full, on average,
the buses are.

00:09:15.000 --> 00:09:18.060
I would actually poll the actual
buses and see how full

00:09:18.060 --> 00:09:20.970
they are during rush hour.

00:09:20.970 --> 00:09:26.860
If 90% of them are 100% full,
or people can't get on a bus

00:09:26.860 --> 00:09:29.900
because they're full and that's
happening frequently,

00:09:29.900 --> 00:09:31.900
and their total wait time is
just getting ridiculous,

00:09:31.900 --> 00:09:33.190
that's probably a better
assessment than

00:09:33.190 --> 00:09:34.210
just surveying people.

00:09:34.210 --> 00:09:37.950
But even beyond that, this is
skewed on several levels.

00:09:37.950 --> 00:09:41.550
One, you are surveying only
the people riding the bus.

00:09:41.550 --> 00:09:43.940
You're not surveying the other
people in the community who

00:09:43.940 --> 00:09:48.140
might have an opinion on this:
drivers, taxpayers who would

00:09:48.140 --> 00:09:49.560
have to pay for more buses.

00:09:49.560 --> 00:09:53.470
And then even within the
bus-riding population, you

00:09:53.470 --> 00:09:56.290
have to think about when they're
getting off the bus.

00:09:56.290 --> 00:09:59.450
If you're getting people off
the bus during rush hour, I

00:09:59.450 --> 00:10:01.090
can almost guarantee you that
they're going to say, yeah,

00:10:01.090 --> 00:10:03.280
we'd like more buses because
then they would have less wait

00:10:03.280 --> 00:10:05.030
time, and the buses would be
less crowded, and they

00:10:05.030 --> 00:10:07.240
wouldn't have to sit
next to anybody.

00:10:07.240 --> 00:10:09.860
So even if it's not needed,
they're going to say it is.

00:10:09.860 --> 00:10:12.270
But if you interview people
maybe getting off the bus

00:10:12.270 --> 00:10:14.910
during lunchtime, who don't use
the bus during rush hour,

00:10:14.910 --> 00:10:17.510
they might say no, we don't need
more buses at rush hour.

00:10:17.510 --> 00:10:18.600
We need more at lunchtime.

00:10:18.600 --> 00:10:20.740
So you're going to get different
answers depending on

00:10:20.740 --> 00:10:23.180
when the people are getting off
the bus, and obviously,

00:10:23.180 --> 00:10:25.700
you're going to get very
different answers from people

00:10:25.700 --> 00:10:26.790
not riding the bus.

00:10:26.790 --> 00:10:28.670
So if you want a broader
audience, if you're kind of

00:10:28.670 --> 00:10:31.740
the city councilman trying to
figure out what to do, I, once

00:10:31.740 --> 00:10:36.490
again, like the crosswalk, I
would survey a random sample

00:10:36.490 --> 00:10:41.080
of people within three miles
of the bus route, or

00:10:41.080 --> 00:10:41.830
something like that.

00:10:41.830 --> 00:10:44.510
I think that might be
a better result.

00:10:44.510 --> 00:10:47.450
F, F-- I'll switch colors.

00:10:47.450 --> 00:10:49.890
You want to find out whether
children should be allowed to

00:10:49.890 --> 00:10:52.080
listen to music while doing
their homework by interviewing

00:10:52.080 --> 00:10:53.930
a stratified sample
of male and female

00:10:53.930 --> 00:10:55.000
students in your school.

00:10:55.000 --> 00:10:58.320
Once again, stratified sample
just means that, OK, if my

00:10:58.320 --> 00:11:02.580
school is 60% male, then 60%
of my sample will be male.

00:11:02.580 --> 00:11:04.830
And that doesn't really
seem relevant here.

00:11:04.830 --> 00:11:08.370
F seems very similar to the, do
students think they get too

00:11:08.370 --> 00:11:09.390
much homework?

00:11:09.390 --> 00:11:11.590
Just as almost every student is
going to say they get too

00:11:11.590 --> 00:11:13.830
much homework, almost every
student should say they should

00:11:13.830 --> 00:11:16.550
be allowed to listen to
music if they want to.

00:11:16.550 --> 00:11:18.920
And that's not going to be--
that's not really going to

00:11:18.920 --> 00:11:22.630
answer the question of whether
children should be allowed.

00:11:22.630 --> 00:11:25.800
If you want a broader sample,
you might-- just like the

00:11:25.800 --> 00:11:29.270
situation with the homework--
include

00:11:29.270 --> 00:11:33.840
parents and include teachers.

00:11:33.840 --> 00:11:36.220
But really, if you wanted to
answer this question, the best

00:11:36.220 --> 00:11:40.390
way would actually be to look
at, to survey students who

00:11:40.390 --> 00:11:43.840
listen to music while doing
their homework, and students

00:11:43.840 --> 00:11:46.930
who don't listen to music while
doing their homework,

00:11:46.930 --> 00:11:50.480
and see their relative grade
performance, and that might

00:11:50.480 --> 00:11:52.180
give you a better answer.

00:11:52.180 --> 00:11:55.855
So once again, I think this
one's a little weak.

00:11:55.855 --> 00:11:58.020
And the bus one was also
a little weak.

00:11:58.020 --> 00:12:01.150
So the only good one here,
if it's done right, is C.

00:12:01.150 --> 00:12:03.840
The other ones, they all needed
a little bit of work to

00:12:03.840 --> 00:12:08.050
actually be surveys that would
give meaningful information.


Two more examples of solving rational equations

WEBVTT
Kind: captions
Language: en

00:00:00.540 --> 00:00:03.030
Let's solve some more
rational equations.

00:00:03.030 --> 00:00:11.640
So let's say I have x plus
1/x is equal to 2.

00:00:11.640 --> 00:00:14.635
Once again, we have an x in a
denominator over here, it

00:00:14.635 --> 00:00:16.100
looks kind of bizarre.

00:00:16.100 --> 00:00:18.660
But you just have to remember,
if we multiply every term in

00:00:18.660 --> 00:00:22.210
this equation by this
denominator, right here, by

00:00:22.210 --> 00:00:27.980
this x, right there, then
essentially, you'll have x

00:00:27.980 --> 00:00:31.540
times 1/x and the x will
disappear out of the

00:00:31.540 --> 00:00:32.130
denominator.

00:00:32.130 --> 00:00:32.920
So let's do that.

00:00:32.920 --> 00:00:34.860
So we have to multiply every
term by that, you can't just

00:00:34.860 --> 00:00:36.230
multiply one term.

00:00:36.230 --> 00:00:39.840
So multiply this term times
x, this term times x,

00:00:39.840 --> 00:00:41.300
and the 2 times x.

00:00:41.300 --> 00:00:44.320
We're just multiplying both
sides of this equation by this

00:00:44.320 --> 00:00:45.300
denominator.

00:00:45.300 --> 00:00:46.640
So what do we get?

00:00:46.640 --> 00:00:54.860
We get x times x is x squared
plus x times 1/x is just 1.

00:00:54.860 --> 00:00:56.890
x's cancel out.

00:00:56.890 --> 00:00:59.540
And then that's going
to be equal to 2x.

00:01:02.960 --> 00:01:05.269
And this is starting
to look like our

00:01:05.269 --> 00:01:07.400
standard quadratic equations.

00:01:07.400 --> 00:01:10.650
We just have to subtract
2x from both sides.

00:01:10.650 --> 00:01:14.650
And if we do that-- so let me
subtract 2x from there,

00:01:14.650 --> 00:01:19.060
subtract 2x from there-- the
left-hand side of our equation

00:01:19.060 --> 00:01:24.160
becomes x squared
minus 2x plus 1.

00:01:24.160 --> 00:01:27.850
And the right-hand side
is equal to 0.

00:01:27.850 --> 00:01:29.800
And we know how to solve
an equation like this.

00:01:29.800 --> 00:01:32.410
We could either factor or use
the quadratic formula.

00:01:32.410 --> 00:01:35.050
This actually seems pretty
straightforward to factor.

00:01:35.050 --> 00:01:37.120
Negative 1 times negative
1 is 1.

00:01:37.120 --> 00:01:39.580
Negative 1 plus negative
1 is negative 2.

00:01:39.580 --> 00:01:47.140
So this is x minus 1 times
x minus 1 is equal to 0.

00:01:47.140 --> 00:01:50.170
And we know, if two numbers,
when you multiply them, they

00:01:50.170 --> 00:01:53.050
equal 0, that means one or both
of those numbers have to

00:01:53.050 --> 00:01:54.310
be equal to 0.

00:01:54.310 --> 00:01:57.470
In this situation, the number
is the same, right?

00:01:57.470 --> 00:02:02.310
This is x minus 1 squared
is equal to 0, right?

00:02:02.310 --> 00:02:05.700
So we know that x minus 1
has to be equal to 0.

00:02:05.700 --> 00:02:10.243
Add 1 to both sides of this
equation and we get

00:02:10.243 --> 00:02:13.840
x is equal to 1.

00:02:13.840 --> 00:02:14.870
And you can verify it.

00:02:14.870 --> 00:02:19.080
Verify that this works.

00:02:19.080 --> 00:02:24.680
1 plus 1/1 does, indeed,
equal 2.

00:02:24.680 --> 00:02:26.340
So it definitely does work.

00:02:26.340 --> 00:02:31.470
Let's do a more involved one
now, now that we're warmed up.

00:02:31.470 --> 00:02:44.150
Let's say I have 2 over x
squared plus 4x plus 3 is

00:02:44.150 --> 00:02:54.960
equal to 2 plus x minus
2 over x minus 3.

00:02:54.960 --> 00:02:57.270
So just like we've done in the
last problem and in all of the

00:02:57.270 --> 00:02:59.880
other ones, we want to get all
of these x's out of the

00:02:59.880 --> 00:03:00.510
denominator.

00:03:00.510 --> 00:03:04.380
And the best way to do it is to
multiply every term in this

00:03:04.380 --> 00:03:07.790
equation by-- you can view it
as the least common multiple

00:03:07.790 --> 00:03:09.140
of the denominator.

00:03:09.140 --> 00:03:10.940
So let me show you what
I'm talking about.

00:03:10.940 --> 00:03:13.100
The first thing we might want
to do is factor this, to see

00:03:13.100 --> 00:03:16.620
if this guy and this guy have
anything in common.

00:03:16.620 --> 00:03:17.880
So let's see if we
can factor it.

00:03:17.880 --> 00:03:20.050
What two numbers when you
multiply them equal 3 and when

00:03:20.050 --> 00:03:21.240
you add them equal 4?

00:03:21.240 --> 00:03:22.710
Well, 3 and 1, right?

00:03:22.710 --> 00:03:33.710
So this right here, I can
rewrite it as x plus 3 and--

00:03:33.710 --> 00:03:35.580
and really this is a plus
over there, too.

00:03:35.580 --> 00:03:37.760
I wrote the original
problem wrong.

00:03:37.760 --> 00:03:38.820
That is a [? product. ?]

00:03:38.820 --> 00:03:46.010
So this over here on the left
is x plus 3 times x plus 1.

00:03:46.010 --> 00:03:49.420
And so, what can we multiply
both sides of this equation by

00:03:49.420 --> 00:03:53.305
to get rid of the x plus 3 and
an x plus 1 here, and an x

00:03:53.305 --> 00:03:54.990
plus 3 over there?

00:03:54.990 --> 00:03:58.830
Well, we multiply everything
by x plus 3 and

00:03:58.830 --> 00:04:00.530
then by x plus 1.

00:04:00.530 --> 00:04:04.320
So this expression right here is
actually divisible by this.

00:04:04.320 --> 00:04:07.180
So the least common multiple of
x plus 3 and x squared plus

00:04:07.180 --> 00:04:11.290
4x plus 3 is actually x squared
plus 4x plus 3,

00:04:11.290 --> 00:04:12.580
because this is a multiple
of that.

00:04:12.580 --> 00:04:14.140
It's divisible by it.

00:04:14.140 --> 00:04:17.290
So let's multiply both sides
of the equation by this

00:04:17.290 --> 00:04:19.250
expression, right here.

00:04:19.250 --> 00:04:24.550
So we're going to get-- let me
just rewrite it-- x plus 3

00:04:24.550 --> 00:04:29.050
times x plus 1-- and then we
have this term over here--

00:04:29.050 --> 00:04:40.933
times 2 over x plus 3 times x
plus 1 is going to be equal to

00:04:40.933 --> 00:04:49.470
x plus 3 times x plus 1 times
this 2 times that 2, over

00:04:49.470 --> 00:05:01.585
there, plus x plus 3 times x
plus 1 times this term-- times

00:05:01.585 --> 00:05:06.220
x minus 2 over x plus 3.

00:05:06.220 --> 00:05:09.470
Now, the whole reason why we did
that is because that will

00:05:09.470 --> 00:05:10.790
cancel with that.

00:05:10.790 --> 00:05:14.680
The left-hand side of our
equation will just be a 2.

00:05:14.680 --> 00:05:20.320
And 2 will be equal to-- well,
2 times this-- we know what

00:05:20.320 --> 00:05:25.400
this is equal to-- x plus 3
times x plus 1 is x squared

00:05:25.400 --> 00:05:27.880
plus 4x plus 3.

00:05:27.880 --> 00:05:28.310
We know that.

00:05:28.310 --> 00:05:29.310
We actually went
the other way.

00:05:29.310 --> 00:05:30.450
We factored it.

00:05:30.450 --> 00:05:35.010
So it's going to be 2 times x
squared plus 4x plus 3, which

00:05:35.010 --> 00:05:38.380
is 2 times x squared is-- I'm
going to do it in that green

00:05:38.380 --> 00:05:39.420
color so you know we're
dealing with

00:05:39.420 --> 00:05:40.390
this 2 right here.

00:05:40.390 --> 00:05:43.970
So this term right here is going
to be 2 times x squared.

00:05:43.970 --> 00:05:51.250
So it's 2x squared plus 2
times 4x plus 8x plus 2

00:05:51.250 --> 00:05:55.120
times 3 plus 6.

00:05:55.120 --> 00:05:56.320
And now this term.

00:05:56.320 --> 00:05:58.190
We have an x plus 3
in the numerator.

00:05:58.190 --> 00:06:00.260
Or it would be, if I multiplied
it times this

00:06:00.260 --> 00:06:02.440
fraction or this rational
expression.

00:06:02.440 --> 00:06:05.530
That x plus 3 will cancel
with that x plus 3.

00:06:05.530 --> 00:06:10.840
So we're just left with an x
plus 1 times an x minus 2.

00:06:10.840 --> 00:06:15.750
An x plus 1 times x minus 2--
let me just focus in on this

00:06:15.750 --> 00:06:18.070
expression right here.

00:06:18.070 --> 00:06:20.790
I'll just box the whole thing.

00:06:20.790 --> 00:06:27.420
x plus 1 times x minus 2 is,
let's just say it's x times x,

00:06:27.420 --> 00:06:29.796
which is x squared.

00:06:29.796 --> 00:06:33.960
x times negative 2, which
is negative 2x.

00:06:33.960 --> 00:06:37.800
And then you have 1 times x, so
plus x, and then you have 1

00:06:37.800 --> 00:06:40.940
times negative 2, so
you have minus 2.

00:06:40.940 --> 00:06:42.790
And now we can simplify it.

00:06:42.790 --> 00:06:44.830
So once again, the left-hand
side of this

00:06:44.830 --> 00:06:46.970
equation is still 2.

00:06:46.970 --> 00:06:49.350
Now on the right-hand side,
let's look at the x squared

00:06:49.350 --> 00:06:53.420
terms. We have a 2x squared,
and we have an x squared.

00:06:53.420 --> 00:06:57.260
Add them together, you
get 3x squared.

00:06:57.260 --> 00:07:05.930
Then we have an 8x, and we
have a minus 2x plus x.

00:07:05.930 --> 00:07:06.940
So what's that going to be?

00:07:06.940 --> 00:07:09.180
This is an 8x, and then when
you add these together, you

00:07:09.180 --> 00:07:12.260
just get a minus-- you just
get a negative x.

00:07:12.260 --> 00:07:14.020
So when you add everything
together, you're going

00:07:14.020 --> 00:07:15.926
to get a plus 7x.

00:07:18.770 --> 00:07:22.280
Those are the x terms. And then
finally, you have a-- no,

00:07:22.280 --> 00:07:26.890
I already used the orange--
you have a 6 and you

00:07:26.890 --> 00:07:29.280
have a minus 2.

00:07:29.280 --> 00:07:32.980
So that's going to be plus 4.

00:07:32.980 --> 00:07:37.470
And now let's subtract 2 from
both sides of this equation.

00:07:37.470 --> 00:07:39.920
Let's subtract 2 from
both sides.

00:07:39.920 --> 00:07:46.890
And we are left with 0 is equal
to 3x squared plus 7x.

00:07:46.890 --> 00:07:51.520
We are subtracting 2 from both
sides, so 4 minus 2 is plus 2.

00:07:51.520 --> 00:07:54.870
So we've stumbled, then we've
turned this bizarre-looking

00:07:54.870 --> 00:07:56.890
thing into kind of
a standard, plain

00:07:56.890 --> 00:07:59.010
vanilla quadratic equation.

00:07:59.010 --> 00:08:02.310
We have a non-zero coefficient
out here.

00:08:02.310 --> 00:08:03.930
We might-- well, we just
want to solve for it.

00:08:03.930 --> 00:08:05.420
We actually don't even
have to factor it.

00:08:05.420 --> 00:08:07.240
So we might as well just use
the quadratic formula.

00:08:07.240 --> 00:08:11.820
That's the easiest way to solve,
especially a quadratic

00:08:11.820 --> 00:08:15.850
equation that has a non-one
coefficient on

00:08:15.850 --> 00:08:17.390
the x squared term.

00:08:17.390 --> 00:08:20.320
So our solutions, using the
quadratic formula. x is going

00:08:20.320 --> 00:08:24.070
to be equal to negative b--
which is negative 7-- plus or

00:08:24.070 --> 00:08:29.060
minus the square root of b
squared-- that's 7 squared--

00:08:29.060 --> 00:08:34.820
which is 49 minus 4 times
a-- which is 3--

00:08:34.820 --> 00:08:38.990
times c, which is 2.

00:08:38.990 --> 00:08:44.280
All of that over 2 times
a, over 2 times 3 is 6.

00:08:44.280 --> 00:08:45.120
So what does this equal to?

00:08:45.120 --> 00:08:49.600
4 times 3 is 12 times 2 is 24.

00:08:49.600 --> 00:08:52.350
So that, right there, is 24.

00:08:52.350 --> 00:08:55.630
What's 49 minus 24?

00:08:55.630 --> 00:08:59.240
It's 25.

00:08:59.240 --> 00:09:01.190
So I don't want to make
that too messy, so

00:09:01.190 --> 00:09:01.960
let me rewrite it.

00:09:01.960 --> 00:09:11.110
So x is equal to negative 7 plus
or minus the square root

00:09:11.110 --> 00:09:20.490
of 49 minus 24 is 25 over 6,
which is equal to negative 7

00:09:20.490 --> 00:09:24.960
plus or minus 5-- the square
root of 25-- over 6.

00:09:24.960 --> 00:09:28.170
And let's see, if we were to add
5, that would be negative

00:09:28.170 --> 00:09:32.550
7 plus 5 is negative
2 over 6, which is

00:09:32.550 --> 00:09:34.530
equal to negative 1/3.

00:09:34.530 --> 00:09:36.520
That is one solution.

00:09:36.520 --> 00:09:42.170
And then if I do negative 7
minus 5, that is negative 12

00:09:42.170 --> 00:09:46.060
over 6, which is equal
to negative 2.

00:09:46.060 --> 00:09:51.620
So those are our two solutions
to this original rational

00:09:51.620 --> 00:09:55.340
equation right up here.

00:09:55.340 --> 00:09:57.510
Hopefully you enjoyed that.


Solving Rational Equations

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:02.880
Let's solve some rational
equations.

00:00:02.880 --> 00:00:10.590
Let's say I had 5 over 3x
minus 4 is equal to--

00:00:10.590 --> 00:00:11.590
actually, let me write it.

00:00:11.590 --> 00:00:13.610
Let me scoot it over
a little bit.

00:00:13.610 --> 00:00:21.240
So let's say I have 5 over
3x minus 4 is equal to

00:00:21.240 --> 00:00:24.548
2 over x plus 1.

00:00:24.548 --> 00:00:26.790
So your first reaction
might be, geez, I've

00:00:26.790 --> 00:00:28.330
never seen this before.

00:00:28.330 --> 00:00:30.520
I have x's in the denominators,
how do I

00:00:30.520 --> 00:00:32.290
actually solve this equation?

00:00:32.290 --> 00:00:34.470
And the easiest way to proceed,
and there's other

00:00:34.470 --> 00:00:38.000
ways to do this, is to try to
multiply both sides of this

00:00:38.000 --> 00:00:42.730
equation by expressions that
will get rid of it these x's

00:00:42.730 --> 00:00:43.680
in the denominator.

00:00:43.680 --> 00:00:52.360
So if we multiply both sides of
the equation by x plus 1,

00:00:52.360 --> 00:00:55.320
it's going to get rid of this
x plus 1 in the denominator.

00:00:55.320 --> 00:00:57.110
Of course, we have to
do it to both sides.

00:00:57.110 --> 00:00:58.510
We can't just do
it to one side.

00:00:58.510 --> 00:01:01.080
But we also want to get rid of
this expression right here.

00:01:01.080 --> 00:01:05.850
So let's multiply both sides of
the equation by that, by 3x

00:01:05.850 --> 00:01:10.740
minus 4, so you're multiplying
by 3x minus 4 on

00:01:10.740 --> 00:01:12.060
this side as well.

00:01:12.060 --> 00:01:15.000
So I'm just multiplying both
sides of the equation times

00:01:15.000 --> 00:01:16.510
this and times this.

00:01:16.510 --> 00:01:18.760
So whatever I multiply on
this side, I also have

00:01:18.760 --> 00:01:21.550
to do on this side.

00:01:21.550 --> 00:01:23.570
What is it going
to simplify to?

00:01:23.570 --> 00:01:28.000
Well, this 3x minus 4 is going
to cancel out with this 3x

00:01:28.000 --> 00:01:31.460
minus 4, so the left-hand side
is just going to be x plus 1

00:01:31.460 --> 00:01:36.770
times 5, or 5 times x plus 1.

00:01:36.770 --> 00:01:40.150
And my right-hand side, this x
plus 1 is going to cancel with

00:01:40.150 --> 00:01:41.390
that x plus 1.

00:01:41.390 --> 00:01:44.100
It's just going to equal
2 times 3x minus 4.

00:01:48.590 --> 00:01:50.630
And if you just look at it, if
you didn't look at what we

00:01:50.630 --> 00:01:52.310
actually did, it looks like
we did something called

00:01:52.310 --> 00:01:53.810
cross-multiplying.

00:01:53.810 --> 00:01:55.530
When you have something over
something is equal to

00:01:55.530 --> 00:01:58.930
something else over something
else, notice, the end product

00:01:58.930 --> 00:02:02.220
when we multiplied both sides
by both of these expressions

00:02:02.220 --> 00:02:09.050
was 2 times 3x minus 4 is equal
to 5 times x plus 1.

00:02:09.050 --> 00:02:10.680
So it looks like we
cross-multiplied.

00:02:10.680 --> 00:02:14.870
5 times x plus 1 is equal
to 2 times 3x minus 4.

00:02:14.870 --> 00:02:16.360
But the reality is we didn't
do anything new.

00:02:16.360 --> 00:02:19.830
We just multiplied both sides
by this expression and that

00:02:19.830 --> 00:02:20.750
expression.

00:02:20.750 --> 00:02:22.690
But now we just have a
straight-up linear equation.

00:02:22.690 --> 00:02:24.810
We can just simplify
and solve.

00:02:24.810 --> 00:02:29.360
So the left-hand side becomes 5x
plus 5, just distribute the

00:02:29.360 --> 00:02:34.620
5, is equal to 6x minus 8.

00:02:34.620 --> 00:02:38.730
Now, let's say we subtract
5x from both sides.

00:02:38.730 --> 00:02:44.800
If we subtract 5x from both
sides, the left-hand side just

00:02:44.800 --> 00:02:46.130
becomes a 5.

00:02:46.130 --> 00:02:50.880
The right-hand side, we are left
with x minus 8, and now

00:02:50.880 --> 00:02:52.800
we could add 8 to both sides.

00:02:56.690 --> 00:03:01.970
The left-hand side becomes 13,
the right-hand side is just an

00:03:01.970 --> 00:03:02.902
x, and we're done.

00:03:02.902 --> 00:03:06.640
x is equal to 13 solves
this equation.

00:03:06.640 --> 00:03:07.700
You could even try it out.

00:03:07.700 --> 00:03:12.260
5 over-- 3 times 13 is 39.

00:03:12.260 --> 00:03:20.680
39 minus 4 is 35, and this
should be equal to 2 over 13

00:03:20.680 --> 00:03:23.030
plus 1, or 14.

00:03:23.030 --> 00:03:25.370
And they both equal 1/7.

00:03:25.370 --> 00:03:27.410
So it checks out.

00:03:27.410 --> 00:03:29.640
Let's do a more involved one.

00:03:29.640 --> 00:03:32.060
Let's do a more involved
problem.

00:03:32.060 --> 00:03:33.730
So let's say I had--
this one's pretty

00:03:33.730 --> 00:03:35.200
involved right here.

00:03:35.200 --> 00:03:47.230
Let's say I have negative x
over x minus 2 plus-- I'm

00:03:47.230 --> 00:03:52.580
going to give it some space
here-- 3x minus 1 over x plus

00:03:52.580 --> 00:04:03.390
4 is equal to 1 over x squared
plus 2x minus 8.

00:04:03.390 --> 00:04:06.490
So once again, if we want to
get rid of all of these x

00:04:06.490 --> 00:04:10.500
terms in the denominator, we
want to multiply essentially

00:04:10.500 --> 00:04:15.720
by the least common multiple
of this expression, this

00:04:15.720 --> 00:04:18.240
expression, and this
expression.

00:04:18.240 --> 00:04:20.070
So this one looks like
it can be factored.

00:04:20.070 --> 00:04:22.185
So maybe it already has some
of these guys in it.

00:04:22.185 --> 00:04:24.700
So let's try to figure
that out.

00:04:24.700 --> 00:04:26.820
So this right here,
this is what?

00:04:26.820 --> 00:04:35.240
This is x plus 4 times x minus
2, so it does, indeed, have

00:04:35.240 --> 00:04:37.330
both of these in it.

00:04:37.330 --> 00:04:41.920
So lets them multiply both sides
of this equation by this

00:04:41.920 --> 00:04:45.400
thing or by x plus
4 and x minus 2.

00:04:45.400 --> 00:04:47.700
So if we multiplied-- so this
thing, it could just be

00:04:47.700 --> 00:04:50.100
rewritten as that, so
I just did that.

00:04:50.100 --> 00:04:52.450
Now let's multiply both sides
of the equation by that.

00:04:52.450 --> 00:04:56.520
So let's see, we're going
to multiply by x plus 4

00:04:56.520 --> 00:04:58.690
times x minus 2.

00:04:58.690 --> 00:05:00.910
If we do it on the right-hand
side, we have to do it on the

00:05:00.910 --> 00:05:02.770
left-hand side.

00:05:02.770 --> 00:05:03.650
Scoot over a little bit.

00:05:03.650 --> 00:05:07.400
So this term, I'm going to have
to multiply by x plus 4

00:05:07.400 --> 00:05:09.500
times x minus 2.

00:05:09.500 --> 00:05:10.700
Same thing for this term.

00:05:10.700 --> 00:05:11.925
That's why I left some space.

00:05:11.925 --> 00:05:15.890
X plus 4 times x minus 2.

00:05:15.890 --> 00:05:19.120
I'm just multiplying every term
in this equation by this

00:05:19.120 --> 00:05:20.420
right there.

00:05:20.420 --> 00:05:22.540
Now, on the left-hand side,
what do we get?

00:05:22.540 --> 00:05:26.070
This x minus 2 cancels
with this x minus 2.

00:05:26.070 --> 00:05:28.070
We have nothing left
in the denominator.

00:05:28.070 --> 00:05:33.760
This term right here will
become negative x

00:05:33.760 --> 00:05:36.440
times x plus 4.

00:05:36.440 --> 00:05:38.570
That's that term right there.

00:05:38.570 --> 00:05:42.420
Now, this term and this term
right here, this x plus 4 will

00:05:42.420 --> 00:05:44.670
cancel with that x plus 4.

00:05:44.670 --> 00:05:53.090
So we're a left with plus 3x
minus 1 times x minus 2.

00:05:53.090 --> 00:05:57.610
And then the right-hand side,
that cancels with that, that

00:05:57.610 --> 00:05:58.740
cancels with that.

00:05:58.740 --> 00:06:00.820
And we've essentially multiplied
both sides by this

00:06:00.820 --> 00:06:02.875
denominator or by the inverse
of this whole expression.

00:06:02.875 --> 00:06:05.910
So we're just left
with this 1.

00:06:05.910 --> 00:06:08.720
And now, we have to simplify
it, or we have to multiply

00:06:08.720 --> 00:06:09.160
things out.

00:06:09.160 --> 00:06:12.510
So negative x times negative
x is negative x squared.

00:06:12.510 --> 00:06:16.030
Negative x times
4 is minus 4x.

00:06:16.030 --> 00:06:21.790
And then we have 3x times
x is plus 3x squared.

00:06:21.790 --> 00:06:25.740
3x times negative
2 is minus 6x.

00:06:25.740 --> 00:06:29.740
Negative 1 times x is minus
x or negative x.

00:06:29.740 --> 00:06:33.790
Negative 1 times negative
2 is plus 2.

00:06:33.790 --> 00:06:36.660
All of that's going
to be equal to 1.

00:06:36.660 --> 00:06:41.530
Now let's add the same degree
terms. So we have a second

00:06:41.530 --> 00:06:43.040
degree term and a second
degree term.

00:06:43.040 --> 00:06:45.290
3x squared minus x squared.

00:06:45.290 --> 00:06:50.420
That gives us 2x squared, and
you have a negative 4x, a

00:06:50.420 --> 00:06:53.110
negative 6x and a negative x.

00:06:53.110 --> 00:06:54.410
So what is that going
to be equal to?

00:06:54.410 --> 00:06:57.930
Negative 4 and a negative
6 is negative 10.

00:06:57.930 --> 00:07:03.380
Minus another 1 is
a negative 11x.

00:07:03.380 --> 00:07:06.900
And then finally, we just have
that constant term out here,

00:07:06.900 --> 00:07:11.670
plus 2 is equal to 1.

00:07:11.670 --> 00:07:13.070
Let me make sure I got all the
terms. Yeah, I got all the

00:07:13.070 --> 00:07:19.030
terms. Now we could subtract
1 from both sides and the

00:07:19.030 --> 00:07:25.610
equation becomes 2x squared
minus 11x plus

00:07:25.610 --> 00:07:27.690
1 is equal to 0.

00:07:27.690 --> 00:07:30.510
So it just becomes a
straight-up, traditional

00:07:30.510 --> 00:07:31.630
quadratic equation.

00:07:31.630 --> 00:07:34.320
And if we're just looking for
the roots, we set it equal to

00:07:34.320 --> 00:07:37.290
zero, we're just looking for the
x's that satisfy this, we

00:07:37.290 --> 00:07:39.640
can use the quadratic formula.

00:07:39.640 --> 00:07:43.510
So the solutions are x is going
to be equal to negative

00:07:43.510 --> 00:07:45.100
b. b is negative 11.

00:07:45.100 --> 00:07:49.990
So negative negative 11 is
positive 11 plus or minus the

00:07:49.990 --> 00:07:53.320
square root of b squared.

00:07:53.320 --> 00:07:59.960
Negative 11 squared is 121 minus
4 times a, which is 2,

00:07:59.960 --> 00:08:05.840
times c, which is 1, all of that
over 2 times a, all of

00:08:05.840 --> 00:08:07.760
that over 4.

00:08:07.760 --> 00:08:13.450
So x is equal to 11, plus or
minus the square root of-- 4

00:08:13.450 --> 00:08:16.460
times 2 times 1 is 8.

00:08:16.460 --> 00:08:20.190
So 121 minus 8.

00:08:20.190 --> 00:08:20.750
So what is that?

00:08:20.750 --> 00:08:23.180
That's 113; is that right?

00:08:23.180 --> 00:08:30.890
The square root of 113,
all of that over 4.

00:08:30.890 --> 00:08:33.400
Can I factor 113 at all?

00:08:33.400 --> 00:08:34.340
Did I get that right?

00:08:34.340 --> 00:08:37.220
4 times 2 times 1.

00:08:37.220 --> 00:08:38.120
Yeah, that looks right.

00:08:38.120 --> 00:08:39.860
Let's get our calculator out
to actually figure out what

00:08:39.860 --> 00:08:41.929
these values are.

00:08:41.929 --> 00:08:49.360
Let me see, so we want to
turn the calculator on.

00:08:49.360 --> 00:08:55.140
Go to my main screen, and
we want the square root

00:08:55.140 --> 00:09:00.680
of 121 minus 8.

00:09:00.680 --> 00:09:03.370
10.63.

00:09:03.370 --> 00:09:11.490
So this is equal to 11 plus
or minus 10.63 over 4.

00:09:11.490 --> 00:09:12.750
Those are two answers.

00:09:12.750 --> 00:09:15.430
And if we want to find the
particular answers, it would

00:09:15.430 --> 00:09:20.350
be 11 plus 10.63 over 4,
which would be what?

00:09:20.350 --> 00:09:24.460
That would be 21.63/4.

00:09:24.460 --> 00:09:26.480
We could try to calculate
that in a second.

00:09:26.480 --> 00:09:32.670
And then if you subtract it,
11 minus 10.63 is-- so 11

00:09:32.670 --> 00:09:36.980
minus 10.63 over 4, this
is equal to what?

00:09:36.980 --> 00:09:44.460
Like 0.37, 0.37/4, if I'm
doing my math correctly.

00:09:44.460 --> 00:09:46.940
So what do we get?

00:09:46.940 --> 00:09:55.710
So let's see, 21.63 divided
by 4 is 5.51, so

00:09:55.710 --> 00:09:58.990
this is equal to 5.41.

00:09:58.990 --> 00:10:03.556
And then the other solution,
0.37 divided by 4 is going to

00:10:03.556 --> 00:10:06.370
be like 0.09 something.

00:10:06.370 --> 00:10:17.930
So then we have the other
solution is 11 minus 10.63.

00:10:17.930 --> 00:10:25.960
Yep, we got our 0.37 divided
by 4 is equal to 0.0925 So

00:10:25.960 --> 00:10:37.500
this is equal to 0.0925.

00:10:37.500 --> 00:10:39.140
So I lost some precision.

00:10:39.140 --> 00:10:40.950
This isn't the exact, because
this wasn't 10.63.

00:10:40.950 --> 00:10:41.980
It was 6301.

00:10:41.980 --> 00:10:43.060
It just kept going.

00:10:43.060 --> 00:10:45.750
It's an irrational number, but
this should get close.

00:10:45.750 --> 00:10:46.550
So let's check.

00:10:46.550 --> 00:10:48.570
Let's verify that these
actually work.

00:10:48.570 --> 00:10:55.480
So let's try the 5.41 solution
first. So if this is true, if

00:10:55.480 --> 00:11:01.070
we take-- so let me put 5.4--
let me just do it.

00:11:01.070 --> 00:11:04.490
So if we do-- so we're going
to start off with 5.41.

00:11:04.490 --> 00:11:10.340
So our original equation was
negative x, so negative 5.41

00:11:10.340 --> 00:11:13.580
divided by x minus 2.

00:11:13.580 --> 00:11:18.280
So 5.41 minus 2 is 3.41.

00:11:18.280 --> 00:11:19.760
So that's that term.

00:11:19.760 --> 00:11:36.130
And then we have plus 3 times
5.41 minus 1 divided by-- 5.41

00:11:36.130 --> 00:11:41.320
plus 4 is 9.41-- 9.41.

00:11:41.320 --> 00:11:49.190
So the left-hand side
gives us 0.0319.

00:11:49.190 --> 00:11:51.320
So that's what the left-hand
side equals.

00:11:51.320 --> 00:11:54.510
Now let's see what the
right-hand side equals when we

00:11:54.510 --> 00:11:56.430
substitute x equals 5.41.

00:11:56.430 --> 00:11:58.540
And of course, we've lost
some precision here.

00:11:58.540 --> 00:11:59.680
We've lost some of the
zeroes, but we

00:11:59.680 --> 00:12:01.140
should get pretty close.

00:12:01.140 --> 00:12:10.870
So the right-hand side, if we
take 1 divided by 5.41 squared

00:12:10.870 --> 00:12:19.340
plus 2 times 5.41 plus-- this
is a minus 8, I think.

00:12:19.340 --> 00:12:19.920
I lost that.

00:12:19.920 --> 00:12:22.760
That's a negative 8 right
there, so minus 8.

00:12:25.840 --> 00:12:30.670
That is that, and they are very,
very, very close, at

00:12:30.670 --> 00:12:33.740
least up to three
digits, 0.31.

00:12:33.740 --> 00:12:35.030
So it does work out.

00:12:35.030 --> 00:12:38.060
And these other things, they
don't equal past that because

00:12:38.060 --> 00:12:39.200
we weren't precise enough.

00:12:39.200 --> 00:12:42.010
If we added the trailing zeroes
here when we took the

00:12:42.010 --> 00:12:44.940
square root of 113, we would
have gotten the right answer.

00:12:44.940 --> 00:12:46.740
If you actually kept it in
this form you would have

00:12:46.740 --> 00:12:48.490
gotten the exact right answer.

00:12:48.490 --> 00:12:51.140
So I'll leave it up to you to
verify that this is also

00:12:51.140 --> 00:12:52.650
another solution.

00:12:52.650 --> 00:12:56.590
But, hopefully, you found that
slightly instructive.