Pressure, flow, and resistance in the human body

WEBVTT
Kind: captions
Language: en

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I'm going to talk to you about
pressure, resistance and flow.

00:00:04.940 --> 00:00:06.940
We're going to try to make sure you feel

00:00:06.940 --> 00:00:09.040
real comfortable with all three of these things

00:00:10.620 --> 00:00:12.040
by the time we're done.

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So we start with the heart, and

00:00:13.860 --> 00:00:17.060
off of the heart is the aorta.

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This is the largest artery in the body.

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And, this is one branch of the aorta.

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I didn't draw a lot of the other ones.

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This is the brachial artery.

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And the blood is flowing from the aorta

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into the brachial artery.

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And let's say that the blood
is trying to make its way out to

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our finger tips,

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for example.

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So on its way out there it makes its way

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to an arterial

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and the blood continues flowing

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and it goes into a capillary bed

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and the vessels are too small

00:00:49.640 --> 00:00:52.100
to draw so I just kind of do that thing

00:00:52.620 --> 00:00:55.640
and it then goes into

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the other half of the capillary bed

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where now the blood is deoxygenated.

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So I'm going to draw that as blue.

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That's the part where

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now the blood is without oxygen

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and then it continues to

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go and get collected

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into a venule which

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sounds a little bit like the arterial

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on the other side, right?

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We've got a vein over here

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and then finally the blood gets

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collected in a large vein

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called the vena cava.

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And there are actually

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two vena cavas, so this will be the

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superior vena cava.

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There is also an inferior vena cava.

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And the blood flow

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through this half

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is, as you would guess, kind of

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continues to go around.

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And if I was to try to figure out

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the pressures, the blood pressures,

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at different points along this system

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I'm going to choose some points

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that I think would be interesting ones to check.

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So it would be good probably to check

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what the pressure is right at the beginning

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and then maybe at all the branch points

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so what the pressure is

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as the blood goes from the aorta to the

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brachial artery.

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Maybe as it ends the brachial artery
and enters the arterial,

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maybe the beginning and the end
of the capillaries

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also from the venule

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to a vein and

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also, wrapping it up,

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what the pressure is at the end.

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Now these numbers

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or these pressures can be

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represented as numbers, right?
Like, what is the millimeters

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of mercury

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that the blood is exerting on the wall

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at that particular point.

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in the system.

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And earlier we talked about

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systolic versus diastolic pressure.

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And there we wanted to use two numbers

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because that's kind of the range.

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The upper and the lower range of a pressure.

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But now I'm going to do it
with one number.

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And the reason I'm using
one number instead of two

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is that this is the
average pressure over time.

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So the average pressure
over time, for me,

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keep in mind my blood pressure's
pretty normal

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somewhere around
120 over 80 in my arm.

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So, the average pressure

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in the aorta kind of coming out

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would be somewhere around 95.

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And in the artery, in the arm,

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probably somewhere around 90.

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Again that's what you would expect,

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somewhere between 80 and 120.

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So 90 is the average because

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it's going to be not exactly 100.

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Because, remember,
it's spending more time

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in diastole and relaxation

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than in systole.

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So it's going to be closer to 80
for that reason.

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And then if you check the pressure

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over here by this X,

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probably be something
like, let's say, 80.

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And then as you
cross the arterial

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the pressure falls dramatically.

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So it's somewhere closer to 30.

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And there here it's about 20.

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Here it's about 15.

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Let's say 10 over here.

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And then, at the very end,

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it's going to be close to a 5 or so.

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Here, let me try that
again.  10 and 5.

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And the units here
are millimeters of mercury.

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So I should just write that:
pressure in millimeters of mercury.

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That's the units that we're talking about.

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So, the pressure falls dramatically

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from 95 all the way to 5.

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And the heart is
a pump, so it's going to

00:04:07.340 --> 00:04:10.460
instill a lot of pressure
in that blood again

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and pump it around and around

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and that's what keeps
the blood flowing in one direction

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So now let me ask you a question
and let's see if we can figure this out.

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Let's see if we can figure out
what the resistance is

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in all of the vessels
in our body, combined.

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So we talked about resistance before

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but now I wanted to pose this question.

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See if we can figure it out.
So what is

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total body resistance.

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And that's really

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the key question I wanted
to try to figure out with you.

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We know that there is some relationship
between radius and resistance

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and we talked about vessels
and tubes and things like that,

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but let's really figure this out

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and make this a little bit
more intuitive for us.

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So to do that

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let's start with an equation.

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And this equation's really going to
walk us through this puzzle.

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So we've got pressure P
equals Q times R.

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Really easy to remember because

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the letters follow each other
in the alphabet.

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And, here actually instead of P
let me put delta P

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which is really "change in pressure".

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So this is change in pressure.

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And a little doodle that
I always keep in my mind

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to remember what
the heck that means is

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if you have a little tube,
the pressure at the beginning --

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Let me say "start".  The s is for start.

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-- and the pressure at the end

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can be subtracted from one another.

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And that gives you Ps minus Pe
equals delta P.

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The change in pressure is really

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the change from one part of the tube
to the end of the tube.

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And that's the first part
of the equation.

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So next we've got Q.

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So what is Q?  This is flow.

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And more specifically
it's blood flow.

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And this can be thought of
in terms of a volume.

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of blood over time.

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So let's say minutes.

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So how many liters of blood

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are flowing in a minute.
Or two minutes,

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or whatever number
of minutes you decide.

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And that's kind of a hard thing
to figure out actually.

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But what we can figure out

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is that Q, the flow, will equal
the stroke volume.

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And I'll tell you what this is
just after I write it.

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The stroke volume times the heart rate.

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So what that means is that
basically if you can know

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how much blood is in each heartbeat--

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so if you know the volume per heartbeat

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and if you know how many
beats there are per minute,

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then you can actually figure out
the volume per minute, right?

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Because the beats would just
cancel each other out.

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And it just turns out,
it happens to be

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that I'm about 70 kilos.

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That's me.

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I'm 70 kilos.

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And for a 70 kilogram person

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the stroke volume is about
70 milliliters.

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So, for a 70 kilo person
you can expect

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about 70 milliliters per beat

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And, as I write this, let's say

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my heart rate is about
70 beats per minute.

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I feel pretty calm

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and so it's not too fast.

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So the beats cancel, as we said,

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and I'm left with 70 milliliters

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times 70 per minute.

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So that's about 4900
milliliters per minute.

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Or, if I was to simplify that's
a 5.  Let's say, about.

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So the flow is about 5 liters per minute.

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OK.  So I figured out the blood flow

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and that was simply because
I happened to know my weight.

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And my weight tells me
the stroke volume.

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And I know that there's
a change in pressure.

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We've got to figure that out soon.

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And lastly, this last thing
over here is resistance.

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And I'm just going to--
I know I've said it before.

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I just want to point out
to you again

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that resistance is going to be
proportional to 1/r to the fourth.

00:08:28.040 --> 00:08:33.080
And so just remember that
this is an important issue.

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r is radius, and that's the
radius of the vessel.

00:08:37.180 --> 00:08:39.660
So let's figure out this equation,
and how--

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Let's figure out the
variables in this equation.

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and how it's going to help us solve

00:08:44.020 --> 00:08:45.520
the question I asked you.

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What is the total body resistance?

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OK.  So if I have to figure out
total body resistance--

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Let me clear out the board.

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I've got, let's say,
the heart over here.

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I like to do the heart in red.

00:08:59.200 --> 00:09:02.040
And it's pumping blood
out my aorta.

00:09:02.040 --> 00:09:05.260
Right?  So blood is going out.
Out of the aorta.

00:09:05.440 --> 00:09:08.300
And then it's going and branching,

00:09:08.300 --> 00:09:12.340
branching here,
branching here, let's say.

00:09:12.340 --> 00:09:14.980
And then it's going to
branch some more

00:09:14.980 --> 00:09:16.640
and it's going to branch some more,

00:09:16.640 --> 00:09:18.660
and you can see
where this is going.

00:09:18.660 --> 00:09:20.240
It's going to keep branching.

00:09:20.240 --> 00:09:21.940
And eventually every branch

00:09:21.940 --> 00:09:24.700
kind of collects on the venous side.

00:09:24.840 --> 00:09:27.740
All the blood is
kind of filtering back in,

00:09:27.900 --> 00:09:30.620
solely into venules and veins.

00:09:30.940 --> 00:09:33.140
and finally into a vena cava.

00:09:33.140 --> 00:09:36.600
And I should really draw this going like that.

00:09:37.620 --> 00:09:40.160
The blood is going to go back
into the vena cava.

00:09:40.160 --> 00:09:41.760
So that's my system,

00:09:41.760 --> 00:09:43.300
and I've got to figure out

00:09:43.300 --> 00:09:46.820
what the total body resistance is here.

00:09:48.860 --> 00:09:51.680
So, if I have a system
drawn out for myself

00:09:51.680 --> 00:09:54.340
and I happen to know that--

00:09:54.640 --> 00:09:58.540
here I said 95 and here I said
the pressure was 5--

00:09:58.540 --> 00:10:03.380
then delta P equals 95 minus 5

00:10:03.380 --> 00:10:05.380
which is 90.

00:10:05.680 --> 00:10:09.300
And I know that there are 5 liters

00:10:09.300 --> 00:10:12.380
of blood flowing through per minute,

00:10:12.920 --> 00:10:14.920
and that was my Q.

00:10:15.680 --> 00:10:17.680
So I could say 90

00:10:19.800 --> 00:10:22.660
equals 5 liters per minute.

00:10:23.740 --> 00:10:26.080
Actually let me take
a step back from that.

00:10:26.500 --> 00:10:28.280
Instead of 90 let me write the units.

00:10:28.280 --> 00:10:31.620
90 millimeters of mercury

00:10:32.920 --> 00:10:35.360
equals 5 liters per minute.
That was my flow.

00:10:37.040 --> 00:10:39.040
That's my Q.

00:10:39.860 --> 00:10:43.700
And I've got delta P here.

00:10:44.400 --> 00:10:46.300
and my resistance is the unknown

00:10:46.300 --> 00:10:47.940
so I'll just leave that as R.

00:10:48.700 --> 00:10:50.700
So let's just solve for R.

00:10:50.700 --> 00:10:53.580
So I'll move my flow
to the other side.

00:10:53.600 --> 00:10:56.440
So R equals--
I'll put it here--

00:10:57.020 --> 00:11:01.180
90 divided by 5 which is 18.

00:11:01.580 --> 00:11:03.520
And the units are a little funky

00:11:03.520 --> 00:11:05.580
but I'll just write them out anyway.

00:11:05.580 --> 00:11:12.680
Millimeters of mercury times minutes
divided by liters.

00:11:12.680 --> 00:11:15.780
So this is the answer to my question.

00:11:16.220 --> 00:11:18.000
What is the total body resistance?

00:11:18.000 --> 00:11:19.660
Well we know what the pressures are

00:11:19.660 --> 00:11:22.220
at the beginning and end of our system.

00:11:22.220 --> 00:11:26.560
And we know that the flow
has to be around 5 liters per minute

00:11:26.560 --> 00:11:30.100
because that's based on
my weight and my heart rate.

00:11:30.100 --> 00:11:32.460
Therefore the resistance must be

00:11:32.460 --> 00:11:36.180
18 millimeters of mercury
times minutes over liters.

00:11:36.220 --> 00:11:38.720
Whatever that set of units means to you.

00:11:38.720 --> 00:11:40.160
It's kind of an abstract thing.

00:11:40.160 --> 00:11:42.280
But basically I want to demonstrate to you

00:11:42.300 --> 00:11:45.280
that this powerful equation
helps us solve

00:11:45.280 --> 00:11:49.120
for what would otherwise be kind of
a tricky problem to figure out.


11 major muscle groups

WEBVTT
Kind: captions
Language: en

00:00:02.260 --> 00:00:06.580
There are eleven major muscle groups of the body and I'm just going to go through them really quickly

00:00:06.580 --> 00:00:08.960
I'm not going to talk too much about the names of the muscles,

00:00:08.960 --> 00:00:12.300
but I want you to get a sense for where they're located on the body.

00:00:12.580 --> 00:00:14.820
So:  the arm, the leg, and the core.

00:00:16.800 --> 00:00:19.160
And I'll write that over here.  So...

00:00:19.160 --> 00:00:23.000
The eleven groups:  there are three...

00:00:23.220 --> 00:00:27.660
actually, four in the arm, three in the leg, and four in the core.

00:00:28.480 --> 00:00:31.360
And just being familiar with where these muscles are

00:00:31.360 --> 00:00:33.980
is actually really, really helpful and powerful,

00:00:33.980 --> 00:00:37.080
because when you go to the gym or you're working out somewhere else,

00:00:37.080 --> 00:00:40.320
it's important to stretch these muscle groups out.

00:00:40.320 --> 00:00:44.560
It's important to also focus on each one and try to figure out which one is weak or strong

00:00:44.560 --> 00:00:47.340
and develop whichever one is imbalanced

00:00:47.360 --> 00:00:50.720
--that's if the left and the right side are not equal in their strength.

00:00:51.020 --> 00:00:55.740
So, it's important to be aware of where they are located and we're going to go through that really quickly right now.

00:00:55.740 --> 00:00:57.820
So, let's do the arm first.

00:00:57.820 --> 00:01:03.480
You have first the forearm.  You can see that one the best from the front.

00:01:03.480 --> 00:01:07.740
And above that you have the biceps,

00:01:07.740 --> 00:01:11.440
that's about right there.  This is your biceps.

00:01:11.440 --> 00:01:16.300
And behind the biceps --actually on the other side-- is the triceps.  That's right there.

00:01:17.120 --> 00:01:21.060
And above both the biceps and the triceps is the shoulder.

00:01:21.060 --> 00:01:23.380
And actually, I'm going to draw that right there.

00:01:23.460 --> 00:01:28.300
You actually see it from the front and the back.  I'm just going to draw it right there, just for simplicity.

00:01:28.300 --> 00:01:32.640
So those are the four arm muscles and now let's just jump down to the leg

00:01:32.640 --> 00:01:37.040
and put in the quads.  This is your quadriceps.

00:01:37.960 --> 00:01:42.700
And this is actually called the quadriceps because that's just four different muscles working together.

00:01:42.700 --> 00:01:47.040
And below the quads, or actually on the other side of the quads, rather,

00:01:47.040 --> 00:01:49.980
is your hamstring.  And right here is your hamstring.

00:01:50.860 --> 00:01:54.940
And I want to get a special kind of shout-out to the hamstring because

00:01:55.000 --> 00:01:57.600
it does a lot of work and a lot of people forget to stretch it out;

00:01:57.600 --> 00:02:02.900
and you can often get in a lot of pain for not having a good, stretched-out hamstring.

00:02:03.500 --> 00:02:06.640
Below it is the calf.

00:02:07.160 --> 00:02:09.160
There's the calf...

00:02:09.920 --> 00:02:13.700
and the calf is actually

00:02:13.700 --> 00:02:19.100
sitting on the opposite side of the bones in the lower leg --the tibia and the fibula--

00:02:19.100 --> 00:02:22.200
which is why it's so bony on the front part of your lower leg,

00:02:22.240 --> 00:02:25.120
but on the back it's very meaty and "muscle-y."

00:02:25.520 --> 00:02:28.180
So you have three leg muscles there.

00:02:28.220 --> 00:02:30.120
Now lets put in the core muscles.

00:02:30.120 --> 00:02:33.240
So you have, let's do the front first.

00:02:33.240 --> 00:02:38.300
So right here is where people talk about getting a six-pack --your abs.

00:02:38.840 --> 00:02:42.580
That's an important muscle group.  It helps you do sit-ups.

00:02:43.300 --> 00:02:49.320
And above it is your chest, so right here is your chest.

00:02:51.820 --> 00:02:54.920
And...there are two in the front...

00:02:54.920 --> 00:02:58.320
and, similarly, there are two in the back.

00:02:58.320 --> 00:03:03.900
And so the back ones --let me do in yellow--

00:03:03.900 --> 00:03:09.060
are your trapezius.  And trapezius I think  comes down like a diamond, almost...

00:03:09.740 --> 00:03:11.740
kind of like that.

00:03:11.740 --> 00:03:16.940
And it helps with the neck and upper back.

00:03:17.300 --> 00:03:20.440
And then, almost like you have wings in a way,

00:03:20.440 --> 00:03:24.480
you have two other muscles --or actually, another muscle with two sides on it--

00:03:24.480 --> 00:03:26.560
called latissimus dorsi.

00:03:26.560 --> 00:03:31.560
It's actually kind of a large, spread-out muscle --and I'm not drawing all of it--

00:03:31.560 --> 00:03:34.800
but basically it kind of spreads all the way to your back

00:03:34.880 --> 00:03:36.980
and it is

00:03:37.420 --> 00:03:39.060
the major muscle of your back.

00:03:39.060 --> 00:03:41.360
So when people say, you know, "I threw out my back."

00:03:41.360 --> 00:03:44.820
Often times, if it's the lower back, they're talking about their latissimus dorsi.

00:03:45.280 --> 00:03:50.500
And that means that we have now our four core muscles showing up here as well.

00:03:50.500 --> 00:03:53.720
So counting them out we've got our eleven muscle groups.

00:03:53.720 --> 00:03:56.960
And so just to, again, go over it very quickly.

00:03:56.960 --> 00:04:02.340
We've got one shoulder, biceps, forearm, and triceps.

00:04:02.440 --> 00:04:06.580
In our leg we have our quad, our hamstring, and our calf.

00:04:06.860 --> 00:04:09.500
And then in the core of our body we have our abs,

00:04:09.500 --> 00:04:13.420
our chest, our upper back --which would be the trapezius--

00:04:13.420 --> 00:04:18.360
and the lower back --which is the latissimus dorsi--and there are eleven groups.


How to simplify an expression by combining like terms and the distributive property

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:02.910
I've gotten feedback
that all the Chuck Norris

00:00:02.910 --> 00:00:05.326
imagery in the last video might
have been a little bit too

00:00:05.326 --> 00:00:06.140
overwhelming.

00:00:06.140 --> 00:00:08.640
So for this video, I've included
something a little bit more

00:00:08.640 --> 00:00:10.000
soothing.

00:00:10.000 --> 00:00:12.140
Let's try to simplify
some more expressions.

00:00:12.140 --> 00:00:13.860
And we'll see we're
just applying ideas

00:00:13.860 --> 00:00:15.730
that we already knew about.

00:00:15.730 --> 00:00:21.250
Let's say I want to simplify the
expression 2 times 3x plus 5.

00:00:21.250 --> 00:00:24.020
Well, this literally
means two 3x plus 5's.

00:00:24.020 --> 00:00:25.930
So this is the exact same thing.

00:00:25.930 --> 00:00:28.750
This is one 3x plus
5, and then to that,

00:00:28.750 --> 00:00:30.610
I'm going to add
another 3x plus 5.

00:00:30.610 --> 00:00:33.960
This is literally what
2 times 3x plus 5 means.

00:00:33.960 --> 00:00:37.330
Well, this is the same thing
as, if we just look at it right

00:00:37.330 --> 00:00:40.160
over here, we have now two 3x's.

00:00:40.160 --> 00:00:43.000
So we could write
it as 2 times 3x.

00:00:43.000 --> 00:00:52.490
Plus, we have two 5's,
so plus 2 times 5.

00:00:52.490 --> 00:00:55.360
You might say, hey, Sal, isn't
this just the distributive

00:00:55.360 --> 00:00:57.220
property that I know
from arithmetic?

00:00:57.220 --> 00:00:59.255
I've essentially just
distributed the 2?

00:00:59.255 --> 00:01:05.690
2 times 3x plus 2 times 5?

00:01:05.690 --> 00:01:08.102
And I would tell
you, yes, it is.

00:01:08.102 --> 00:01:10.560
And the whole reason why I'm
doing this is just to show you

00:01:10.560 --> 00:01:13.250
that it is exactly
what you already know.

00:01:13.250 --> 00:01:16.320
But with that out of the way,
let's continue to simplify it.

00:01:16.320 --> 00:01:21.430
When you multiply the 2
times the 3x, you get 6x.

00:01:21.430 --> 00:01:25.030
When you multiply the 2
times the 5, you get 10.

00:01:25.030 --> 00:01:28.364
So this simplified
to 6x plus 10.

00:01:28.364 --> 00:01:30.780
Now let's try something that's
a little bit more involved.

00:01:30.780 --> 00:01:34.710
Once again, really just
things that you already know.

00:01:34.710 --> 00:01:54.720
Let's say I had 7 times 3y minus
5 minus 2 times 10 plus 4y.

00:01:54.720 --> 00:01:57.410
Let's see if we
can simplify this.

00:01:57.410 --> 00:01:59.030
Well, let's work on
the left-hand side

00:01:59.030 --> 00:02:02.080
of the expression, the
7 times 3y minus 5.

00:02:02.080 --> 00:02:03.560
We just have to
distribute the 7.

00:02:03.560 --> 00:02:08.740
This is going to be 7 times 3y,
which is going to give us 21y.

00:02:08.740 --> 00:02:10.800
Or if I had 3 y's
7 times, that's

00:02:10.800 --> 00:02:13.770
going to be 21 y's, either way
you want to think about it.

00:02:13.770 --> 00:02:15.300
And then I have 7
times-- we've got

00:02:15.300 --> 00:02:19.100
to be careful with
the sign-- negative 5.

00:02:19.100 --> 00:02:22.640
7 times negative
5 is negative 35.

00:02:22.640 --> 00:02:24.180
So we've simplified
this part of it.

00:02:24.180 --> 00:02:26.610
Let's simplify the
right-hand side.

00:02:26.610 --> 00:02:29.690
You might be tempted to say,
oh, 2 times 10 and 2 times 4y

00:02:29.690 --> 00:02:30.990
and then subtract them.

00:02:30.990 --> 00:02:34.080
And if you do that right and
you distribute the subtraction,

00:02:34.080 --> 00:02:35.190
it would work out.

00:02:35.190 --> 00:02:39.357
But I like think of
this as negative 2,

00:02:39.357 --> 00:02:41.190
and we're going to
distribute the negative 2

00:02:41.190 --> 00:02:47.790
times 10 and the
negative 2 times 4y.

00:02:47.790 --> 00:02:53.870
So negative 2 times
10 is negative 20,

00:02:53.870 --> 00:02:56.660
so it's minus 20
right over here.

00:02:56.660 --> 00:03:00.130
And then negative 2 times
4, negative 2 times 4

00:03:00.130 --> 00:03:03.860
is negative 8, so it's
going to be negative 8y.

00:03:03.860 --> 00:03:06.760
Let's write a minus
8y right over here.

00:03:06.760 --> 00:03:08.586
And are we done simplifying?

00:03:08.586 --> 00:03:10.710
Well, no, there's a little
bit more that we can do.

00:03:10.710 --> 00:03:14.160
We can't add the 21y to the
negative 35 or the negative 20

00:03:14.160 --> 00:03:16.420
because these are
adding different things

00:03:16.420 --> 00:03:17.970
or subtracting different things.

00:03:17.970 --> 00:03:22.660
But we do have two things
that are multiplying y.

00:03:22.660 --> 00:03:24.620
Let me do all in
this green color.

00:03:24.620 --> 00:03:26.720
You have 21 y's right over here.

00:03:26.720 --> 00:03:33.730
And then we can view it as from
that we are subtracting 8 y's.

00:03:33.730 --> 00:03:37.540
So if I have 21 of something
and I take 8 of them away,

00:03:37.540 --> 00:03:39.270
I'm left with 13
of that something.

00:03:39.270 --> 00:03:42.190
So those are going to
simplify to 13 y's.

00:03:46.195 --> 00:03:48.310
I'll do this in a new color.

00:03:48.310 --> 00:03:52.270
And then I have
negative 35 minus 20.

00:03:52.270 --> 00:03:56.597
That's just going to
simplify to negative 55.

00:03:56.597 --> 00:03:58.680
So this whole thing
simplified, using a little bit

00:03:58.680 --> 00:04:00.810
of the distributive
property and combining

00:04:00.810 --> 00:04:06.072
similar or like terms,
we got to 13y minus 55.


Combining like terms introduction

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:04.580
Let's say that I've
got 2 Chuck Norrises,

00:00:04.580 --> 00:00:06.640
or maybe it's Chuck Norri.

00:00:06.640 --> 00:00:13.090
And to that I am going to
add another 3 Chuck Norrises.

00:00:13.090 --> 00:00:15.130
So I'm going to add
another 3 Chuck Norrises.

00:00:15.130 --> 00:00:16.990
And this might seem
a little bit obvious,

00:00:16.990 --> 00:00:20.160
but how many Chuck
Norrises do I now have?

00:00:20.160 --> 00:00:22.940
Well, 2 Chuck Norrises,
we can represent this

00:00:22.940 --> 00:00:26.610
as literally a Chuck
Norris plus a Chuck Norris.

00:00:26.610 --> 00:00:28.280
So let me do that,
a Chuck Norris

00:00:28.280 --> 00:00:31.600
plus another Chuck
Norris, 2 Chuck Norrises.

00:00:31.600 --> 00:00:33.610
You could also do this
2 times Chuck Norris,

00:00:33.610 --> 00:00:35.770
and this is just another
way of representing it.

00:00:35.770 --> 00:00:40.900
And 3 Chuck Norrises-- you
could do that as a Chuck Norris

00:00:40.900 --> 00:00:45.290
plus a Chuck Norris plus
another Chuck Norris.

00:00:45.290 --> 00:00:47.300
And so we would
have a grand total--

00:00:47.300 --> 00:00:50.000
and this might be
very simple for you.

00:00:50.000 --> 00:00:52.660
But you would have a
grand total of 1, 2, 3, 4,

00:00:52.660 --> 00:00:54.450
5 Chuck Norrises.

00:00:54.450 --> 00:01:00.582
So this would be equal
to 5 Chuck Norrises.

00:01:00.582 --> 00:01:02.540
Now, let's get a little
bit more abstract here.

00:01:02.540 --> 00:01:05.209
Chuck Norris is a
very tangible thing.

00:01:05.209 --> 00:01:07.330
So let's go to a
little bit more of

00:01:07.330 --> 00:01:09.380
traditional algebraic notation.

00:01:09.380 --> 00:01:13.720
If I have 2x's and
remember, you could

00:01:13.720 --> 00:01:16.260
do this as 2x's or 2 times x.

00:01:19.370 --> 00:01:23.220
And to that, I would add
3x's How many x's do I have?

00:01:23.220 --> 00:01:25.450
Well, once again,
2x's, that's 2 times x.

00:01:25.450 --> 00:01:27.410
You could do that
as an x plus an x.

00:01:27.410 --> 00:01:29.270
We don't know what
the value of x is.

00:01:29.270 --> 00:01:32.460
But whatever that value is,
we can add it to itself.

00:01:32.460 --> 00:01:34.780
And then 3x's are they're
going to be that value.

00:01:34.780 --> 00:01:37.590
Let me do that in
that same green color.

00:01:37.590 --> 00:01:41.640
3x's are going to be that
value plus that value plus

00:01:41.640 --> 00:01:43.460
whatever that value is.

00:01:43.460 --> 00:01:46.300
And so how many
x's do I now have?

00:01:46.300 --> 00:01:50.810
Well, I'm going to
have 1, 2, 3, 4, 5 x's.

00:01:50.810 --> 00:01:57.119
So 2x plus 3x is equal to 5x.

00:01:57.119 --> 00:01:59.660
And if you think about it, all
we really did-- and hopefully,

00:01:59.660 --> 00:02:01.160
you conceptually
get it-- is we just

00:02:01.160 --> 00:02:03.950
added the 2 numbers that
were multiplying the x.

00:02:03.950 --> 00:02:07.350
And these numbers, the 2 or the
3, they're called coefficients.

00:02:07.350 --> 00:02:09.860
Very fancy word, but it's
just this constant number,

00:02:09.860 --> 00:02:12.980
this regular number that's
multiplied by the variable.

00:02:12.980 --> 00:02:16.814
You just added the 2 and
the 3, to get your 5x.

00:02:16.814 --> 00:02:18.730
Now, let's think about
this a little bit more.

00:02:18.730 --> 00:02:21.400
Let's go back to this original
expression, the 2 Chuck

00:02:21.400 --> 00:02:23.400
Norrises plus 3 Chuck Norrises.

00:02:23.400 --> 00:02:27.380
Let's say, to that,
we were to add

00:02:27.380 --> 00:02:31.680
to some type of a-- let's we
were to add 7 plums over here.

00:02:31.680 --> 00:02:34.050
So this is my drawing of a plum.

00:02:34.050 --> 00:02:38.410
So we have 7 plums plus 2 Chuck
Norrises plus 3 Chuck Norrises.

00:02:38.410 --> 00:02:41.040
And let's say that I
add another 2 plums.

00:02:41.040 --> 00:02:42.950
I add another 2 plums here.

00:02:42.950 --> 00:02:44.990
So what this whole thing be?

00:02:44.990 --> 00:02:48.170
Well, I wouldn't add the 7
to the 2 to the 3 plus the 2.

00:02:48.170 --> 00:02:49.750
We're adding
different things here.

00:02:49.750 --> 00:02:51.950
You have 2 Chuck Norrises
and 3 Chuck Norrises,

00:02:51.950 --> 00:02:54.895
so they're still going to
simplify to 5 Chuck Norrises. .

00:02:54.895 --> 00:02:57.020
And then we would separately
think about the plums.

00:02:57.020 --> 00:02:59.700
We have 7 plums, and we're
adding another 2 plums.

00:02:59.700 --> 00:03:01.820
We're going to have 9 plums.

00:03:01.820 --> 00:03:06.920
Plus 9 plums, so this simplifies
to five Chuck Norrises and 9

00:03:06.920 --> 00:03:07.810
plums.

00:03:07.810 --> 00:03:12.360
Similarly, over here,
instead of just 2x plus 3x,

00:03:12.360 --> 00:03:21.970
if I had 7y plus 2x plus 3x
plus 2y, what do I now have?

00:03:21.970 --> 00:03:24.050
Well, I can't add the
x's and the y's.

00:03:24.050 --> 00:03:26.420
They could very well
represent a different number.

00:03:26.420 --> 00:03:28.590
So all I can do is
really add the x's.

00:03:28.590 --> 00:03:30.022
And then I get the 5x.

00:03:30.022 --> 00:03:31.480
And then, I'd
separately add the y.

00:03:31.480 --> 00:03:35.800
If I have 7y's and to that I add
2y's, I'm going to have 9y's.

00:03:35.800 --> 00:03:38.170
If I have 7 of something
and I add 2 of something,

00:03:38.170 --> 00:03:40.440
I now have 9 of that something.

00:03:40.440 --> 00:03:42.710
So I'm going to have 9y's.

00:03:42.710 --> 00:03:44.235
So you add that.

00:03:44.235 --> 00:03:45.740
Do that in a different color.

00:03:45.740 --> 00:03:48.700
You add this and this.

00:03:48.700 --> 00:03:50.140
You get that.

00:03:50.140 --> 00:03:54.070
You add the x's.

00:03:54.070 --> 00:03:56.064
You get that right over there.

00:03:56.064 --> 00:03:57.730
So hopefully, that
makes a little sense.

00:03:57.730 --> 00:03:59.313
Actually I'll throw
out one more idea.

00:03:59.313 --> 00:04:04.530
So given this, what would happen
if I were to have 2x plus 1

00:04:04.530 --> 00:04:08.407
plus 7x plus 5?

00:04:08.407 --> 00:04:09.990
Well, once again,
you might be tempted

00:04:09.990 --> 00:04:11.350
to add the 2 plus
the 1, but they're

00:04:11.350 --> 00:04:12.220
adding different things.

00:04:12.220 --> 00:04:12.970
These are 2x's.

00:04:12.970 --> 00:04:14.910
This is just the number 1.

00:04:14.910 --> 00:04:17.490
So you really just have
to add the x's together.

00:04:17.490 --> 00:04:19.430
So you're going to
say, well, I got 2x's.

00:04:19.430 --> 00:04:21.550
And I'm going to
add 7x's to that.

00:04:21.550 --> 00:04:23.507
Well, that means
I now have 9x's.

00:04:23.507 --> 00:04:25.090
And then, separately,
you'd say, well,

00:04:25.090 --> 00:04:27.130
I've got just the
abstract number 1.

00:04:27.130 --> 00:04:28.460
And then I've got another 5.

00:04:28.460 --> 00:04:32.280
1 plus 5 is going
to be equal to 6.


Expressions with two variables

WEBVTT
Kind: captions
Language: en

00:00:00.568 --> 00:00:02.323
Now, let's think about expressions

00:00:02.323 --> 00:00:04.079
with more than one variable.

00:00:04.125 --> 00:00:06.009
So, let's say I had the expression

00:00:06.040 --> 00:00:09.325
"a + b"

00:00:09.325 --> 00:00:11.222
and I were to ask you

00:00:11.222 --> 00:00:13.042
what is this expression equal to

00:00:13.042 --> 00:00:16.000
when "a" is equal to 5

00:00:16.000 --> 00:00:19.574
and "b" is equal to 7

00:00:19.574 --> 00:00:23.789
Well, in this situation, this expression would be...

00:00:23.789 --> 00:00:25.635
instead of an "a" we would have a 5

00:00:25.635 --> 00:00:28.004
it would be 5 plus...

00:00:28.004 --> 00:00:31.821
instead of a "b", we would have a 7.

00:00:31.821 --> 00:00:36.169
So it would be 5 + 7 is equal to 12.

00:00:36.214 --> 00:00:38.111
Now let's try another expression.

00:00:38.111 --> 00:00:39.751
Let's say we had the expression

00:00:39.751 --> 00:00:54.102
"10x - 3y"

00:00:54.102 --> 00:00:55.401
And, let's think about

00:00:55.401 --> 00:00:57.594
what would this expression evaluate to

00:00:57.641 --> 00:01:01.187
when "x" is equal to - 1

00:01:01.187 --> 00:01:06.244
and when "y" is equal to 5.

00:01:06.291 --> 00:01:07.849
Well, let's just evaluate it.

00:01:07.849 --> 00:01:09.998
We have 10 times...

00:01:09.998 --> 00:01:10.825
instead of an "x",

00:01:10.825 --> 00:01:13.471
we know now that "x" is equal to -1,

00:01:13.471 --> 00:01:21.877
it would be 10 (-1) - 3 (5).

00:01:21.877 --> 00:01:23.338
So three times...

00:01:23.338 --> 00:01:25.630
instead of a "y", we will put a 5 there.

00:01:25.630 --> 00:01:28.268
- 3 (5).

00:01:28.268 --> 00:01:32.503
And so 10 (-1), that is -10

00:01:32.503 --> 00:01:35.727
and we're going to subtract from that 3 (5).

00:01:35.727 --> 00:01:37.010
You want to do the multiplication first

00:01:37.010 --> 00:01:38.091
by order of operations

00:01:38.091 --> 00:01:38.910
that's the convention.

00:01:38.910 --> 00:01:43.149
3 times 5 is 15.

00:01:43.149 --> 00:01:46.656
So, it is -10 - 15,

00:01:46.656 --> 00:01:52.256
which is equal to -25.

00:01:52.256 --> 00:01:54.807
And now, you have the next exercise

00:01:54.807 --> 00:01:57.992
to practice some of these a little bit more.


Why aren't we using the multiplication sign?

WEBVTT
Kind: captions
Language: en

00:00:00.770 --> 00:00:03.280
We now hopefully know a little about variables

00:00:03.280 --> 00:00:05.436
and as we covered in the last video, a variable can be

00:00:05.436 --> 00:00:08.834
really any symbol, although we typically use letters

00:00:08.834 --> 00:00:11.510
because we're used to writing and typing letters.

00:00:11.510 --> 00:00:17.193
But it can be anything from an x, to a y, a z, an a, a b,

00:00:17.193 --> 00:00:20.833
and oftentimes we start using greek letters like theta.

00:00:20.833 --> 00:00:22.826
But you can really use any symbol to say

00:00:22.826 --> 00:00:24.090
Hey, this is going to vary

00:00:24.090 --> 00:00:26.300
You can take on multiple values

00:00:26.300 --> 00:00:27.767
But out of all of all of these

00:00:27.767 --> 00:00:29.759
The one that is most typically used in algebra

00:00:29.759 --> 00:00:31.754
Or really in all of mathematics

00:00:31.754 --> 00:00:33.703
is the variable "x"

00:00:33.703 --> 00:00:36.471
Although all of these are used to some degree

00:00:36.471 --> 00:00:39.168
But given that x is used so heavily

00:00:39.168 --> 00:00:42.757
it does introduce a slight problem.

00:00:42.757 --> 00:00:46.247
And that problem is that it looks a lot like the multiplication symbol

00:00:46.247 --> 00:00:48.501
Or the one that we use in arithmetic

00:00:48.501 --> 00:00:49.924
So in arithmetic

00:00:49.924 --> 00:00:51.209
if I want to write 2 x 3

00:00:51.209 --> 00:00:53.635
I literally write "2 x 3"

00:00:53.635 --> 00:00:55.481
But now that we are starting to use variables,

00:00:55.481 --> 00:00:57.489
if I want to write "2 times x"

00:00:57.489 --> 00:00:59.916
Well if I use this as the multiplication symbol

00:00:59.916 --> 00:01:01.533
it would be 2 times x

00:01:01.750 --> 00:01:03.491
And the times symbol and the X

00:01:03.598 --> 00:01:05.593
look awfully similar

00:01:05.593 --> 00:01:08.747
and if I'm not really careful with my penmanship

00:01:08.747 --> 00:01:10.248
it can get very confusing.

00:01:10.248 --> 00:01:11.348
Is this "Two x x"?

00:01:11.348 --> 00:01:13.301
Is this "two times times something"?

00:01:13.301 --> 00:01:15.689
What exactly is going on here?

00:01:15.689 --> 00:01:18.023
And because this is confusing,

00:01:18.023 --> 00:01:21.729
This, right over here, is extremely confusing

00:01:21.729 --> 00:01:23.967
And it can be misinterpreted,

00:01:23.967 --> 00:01:28.636
We tend not to use this multiplication symbol

00:01:28.636 --> 00:01:31.101
When we are doing algebra

00:01:31.101 --> 00:01:33.683
Instead of that, to represent multiplication,

00:01:33.683 --> 00:01:35.971
We have several options.

00:01:35.971 --> 00:01:38.692
Instead of writing two times x this way,

00:01:38.692 --> 00:01:45.831
we could write 2 dot x.

00:01:45.831 --> 00:01:48.434
And this dot, I want to be very clear,

00:01:48.434 --> 00:01:50.683
This is not a decimal

00:01:50.683 --> 00:01:52.903
This is just written a little bit higher

00:01:52.903 --> 00:01:54.911
And we write this so we don't get confusion

00:01:54.911 --> 00:01:57.700
in between this and one of these variables right here.

00:01:57.700 --> 00:02:00.324
But this can really be interpreted as "2 times x"

00:02:00.324 --> 00:02:02.748
So for example, if someone says

00:02:02.748 --> 00:02:06.995
2 dot x, when x is equal to 3,

00:02:06.995 --> 00:02:09.762
well this would be the same thing

00:02:09.762 --> 00:02:12.409
as two times three, when x is equal to three.

00:02:12.409 --> 00:02:13.825
Another way you could write it is

00:02:13.825 --> 00:02:16.574
You could write "2" and then you could write the x in parentheses

00:02:16.574 --> 00:02:18.494
right next to it.

00:02:18.494 --> 00:02:22.221
This is also interpreted as 2 times x

00:02:22.221 --> 00:02:23.285
Once again, so in this situation

00:02:23.285 --> 00:02:24.504
If "x" were seven, this would be

00:02:24.504 --> 00:02:27.294
two times seven, or fourteen

00:02:27.294 --> 00:02:29.671
And the most traditional way of doing it

00:02:29.671 --> 00:02:32.302
is to just write the x right after the 2.

00:02:32.302 --> 00:02:35.669
And sometimes this will be read as "2x"

00:02:35.669 --> 00:02:39.568
But this literally does mean "Two times x"

00:02:39.568 --> 00:02:41.633
And you might say, how come we didn't always do that?

00:02:41.633 --> 00:02:44.247
Well it would be literally confusing if we did it over here.

00:02:44.247 --> 00:02:46.501
Instead of writing "2 times 3"

00:02:46.501 --> 00:02:48.272
And wrote "2 3"

00:02:48.272 --> 00:02:49.894
Well, that looks like "23".

00:02:49.894 --> 00:02:51.253
This doesn't look like two times three

00:02:51.253 --> 00:02:52.633
And this is why we never did it.

00:02:52.633 --> 00:02:54.365
But here, since we're using a letter now,

00:02:54.365 --> 00:02:57.579
It's clear that this isn't a part of that number.

00:02:57.579 --> 00:02:59.354
This isn't "twenty something"

00:02:59.354 --> 00:03:02.838
This is two times this variable x.

00:03:02.838 --> 00:03:05.900
So all of these are really the same expression.

00:03:05.900 --> 00:03:09.070
Two times x, two times x, and two times x.

00:03:09.070 --> 00:03:10.163
And so with that out of the way

00:03:10.163 --> 00:03:13.554
Let's try some few worked examples, a few practice problems

00:03:13.554 --> 00:03:14.895
And this will hopefully prepare you for the

00:03:14.895 --> 00:03:16.215
next exercise

00:03:16.215 --> 00:03:18.034
Where you'll get a lot of chances to practice this.

00:03:18.034 --> 00:03:24.702
So if I where to say "what is 10 minus three y"

00:03:24.702 --> 00:03:29.636
And what does this equal when "y" is equal to two

00:03:29.636 --> 00:03:31.821
Well, every time you see the "y"

00:03:31.821 --> 00:03:32.833
You'd want that 2 there

00:03:32.833 --> 00:03:35.636
So this is y is equal to 2.

00:03:35.636 --> 00:03:37.298
Let's set that y equal to two

00:03:37.298 --> 00:03:41.368
This is the same thing as 10 minus three times two

00:03:41.368 --> 00:03:43.503
You do the multiplication first.

00:03:43.503 --> 00:03:46.369
Multiplication takes precedence in order of operations

00:03:46.369 --> 00:03:48.829
So three times two is six,

00:03:48.829 --> 00:03:53.215
Ten minus six is equal to four.

00:03:53.215 --> 00:03:54.414
Let's do another one.

00:03:54.414 --> 00:04:08.073
Let's say we had "7x minus 4"

00:04:08.073 --> 00:04:14.970
And we want to evaluate that when

00:04:14.970 --> 00:04:19.861
when x is equal to three.

00:04:19.861 --> 00:04:22.169
Where we see the x, we want to put the 3 there

00:04:22.169 --> 00:04:29.221
So this is the same thing as "7 times 3"

00:04:29.221 --> 00:04:34.168
And I'll actually use this notation, so seven times three minus four.

00:04:34.168 --> 00:04:37.250
And once again, multiplication takes precedence

00:04:37.250 --> 00:04:40.104
by order of operations, over addition or subtraction

00:04:40.104 --> 00:04:41.701
So we want to do the multiplying first

00:04:41.701 --> 00:04:43.970
7 times 3 is 21

00:04:43.970 --> 00:04:48.233
21 minus 4 is equal to 17.

00:04:48.233 --> 00:04:50.263
So hopefully that gives you a little bit of background,

00:04:50.263 --> 00:04:52.763
and I really encourage you to try the next exercise,

00:04:52.763 --> 00:04:54.367
It will give you a lot of practice

00:04:54.367 --> 00:04:56.357
on being to evaluate expressions like this.


What is a variable?

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:02.640
Let's say that I'm
working in a restaurant,

00:00:02.640 --> 00:00:04.870
and I'm making $10 per hour.

00:00:04.870 --> 00:00:09.670
But on top of my hourly wage,
I also get tips each hour.

00:00:09.670 --> 00:00:12.120
So this entire expression,
you can view this

00:00:12.120 --> 00:00:15.630
as how much I might
make in a given hour.

00:00:15.630 --> 00:00:18.580
Now, you might also realize
that the number of tips

00:00:18.580 --> 00:00:20.470
or the amount of tips
I might make in an hour

00:00:20.470 --> 00:00:23.040
can change dramatically
from hour to hour.

00:00:23.040 --> 00:00:26.120
It can vary-- one hour it
might be lunchtime, get

00:00:26.120 --> 00:00:28.530
a lot of tips, people might
get some big-ticket items.

00:00:28.530 --> 00:00:30.480
The next hour, I might
not have any customers.

00:00:30.480 --> 00:00:32.740
And then my tips
might be really low.

00:00:32.740 --> 00:00:35.010
So the tips part
right over here,

00:00:35.010 --> 00:00:37.730
we consider that--
the entire word,

00:00:37.730 --> 00:00:40.370
we consider that
to be a variable.

00:00:40.370 --> 00:00:43.100
From scenario to
scenario, it can change.

00:00:43.100 --> 00:00:47.340
So for example, in one
scenario, maybe it's lunchtime.

00:00:47.340 --> 00:00:49.130
I'm getting really big tips.

00:00:49.130 --> 00:00:53.350
So tips is-- let's
say it's equal to $30.

00:00:53.350 --> 00:00:56.470
And so the total amount I
might make in that hour--

00:00:56.470 --> 00:00:58.730
we can go back to this
expression right over here--

00:00:58.730 --> 00:01:02.360
it's going to be 10 plus--
instead of writing tips here,

00:01:02.360 --> 00:01:06.730
I'll write 30 because that's
what my tips are in that hour.

00:01:06.730 --> 00:01:10.590
And so that is going
to be equal to 40.

00:01:10.590 --> 00:01:12.810
Let me do it in
that yellow color.

00:01:12.810 --> 00:01:15.820
It's going to be equal to $40.

00:01:15.820 --> 00:01:18.860
But let's say right after that,
the restaurant slows down.

00:01:18.860 --> 00:01:20.860
We're out of the lunch
hour for whatever reason.

00:01:20.860 --> 00:01:23.970
Maybe the restaurant next door
has a big sale or something.

00:01:23.970 --> 00:01:26.910
And so the next hour, my
tips go down dramatically.

00:01:26.910 --> 00:01:30.640
My tips go down to
$5 for that hour.

00:01:30.640 --> 00:01:32.870
Now I go back to
this expression.

00:01:32.870 --> 00:01:35.190
The total I make
is my hourly wage

00:01:35.190 --> 00:01:42.720
plus the $5 in tips,
which is equal to $15.

00:01:42.720 --> 00:01:45.920
As you see, this entire
expression-- the 10 plus tips--

00:01:45.920 --> 00:01:51.170
it changed depending on what the
value of the variable tips is.

00:01:51.170 --> 00:01:54.180
Now, you won't see whole
words typically used

00:01:54.180 --> 00:01:56.020
in algebra as variables.

00:01:56.020 --> 00:01:56.900
We get lazy.

00:01:56.900 --> 00:02:00.040
And so instead, we tend to use
just easier-to-write symbols.

00:02:00.040 --> 00:02:02.520
And so in this context,
instead of writing tips,

00:02:02.520 --> 00:02:08.009
maybe we could have
just written 10 plus t,

00:02:08.009 --> 00:02:10.424
where t represents the tips
that we get in an hour.

00:02:10.424 --> 00:02:11.840
And so then we
would say, OK, what

00:02:11.840 --> 00:02:13.310
happens when t is equal to 30?

00:02:19.040 --> 00:02:20.500
Well, then, we have a situation.

00:02:20.500 --> 00:02:21.950
t is equal to 30.

00:02:21.950 --> 00:02:25.830
This evaluates to 10 plus
30, which would be 40.

00:02:25.830 --> 00:02:28.500
What would happen
if t is equal to 5?

00:02:28.500 --> 00:02:31.660
Well, then, this would
evaluate to 10 plus 5,

00:02:31.660 --> 00:02:34.810
which is equal to 15.

00:02:34.810 --> 00:02:35.840
Now, I want to be clear.

00:02:35.840 --> 00:02:37.090
We didn't even have to use t.

00:02:37.090 --> 00:02:38.881
We didn't even really
have to use a letter,

00:02:38.881 --> 00:02:41.420
although in traditional algebra,
you almost do use a letter.

00:02:41.420 --> 00:02:46.220
We could have written
it as 10 plus x, where

00:02:46.220 --> 00:02:49.590
x is your tips per hour.
x might not be as natural.

00:02:49.590 --> 00:02:51.670
It's not the first
letter in the word tips.

00:02:51.670 --> 00:02:57.200
Or you could have even
written 10 plus star,

00:02:57.200 --> 00:02:58.960
where you could
say star represents

00:02:58.960 --> 00:03:00.270
the number of tips in an hour.

00:03:00.270 --> 00:03:02.609
But it just might have not
made as much intuitive sense.

00:03:02.609 --> 00:03:04.400
But hopefully this
gives you a general idea

00:03:04.400 --> 00:03:07.790
of just what a variable is.

00:03:07.790 --> 00:03:13.610
All it is is a symbol that
represents varying values.

00:03:13.610 --> 00:03:16.410
And that's why we
call it a variable.


LeBron asks about comparing Earth's history to a basketball game

WEBVTT
Kind: captions
Language: en

00:00:00.963 --> 00:00:03.765
LeBron: If the history of the
earth was a basketball game,

00:00:03.765 --> 00:00:07.607
at what point in the game
will the humans show up?

00:00:09.084 --> 00:00:12.518
Voiceover: Let's first think about how
long a basketball game is in the NBA.

00:00:12.518 --> 00:00:16.099
We have 4 quarters that
each lasts 12 minutes,

00:00:16.099 --> 00:00:19.110
so we're talking about 48 minutes.

00:00:19.110 --> 00:00:22.629
48 minutes of regulation play.

00:00:22.629 --> 00:00:25.057
I'm not considering half
time and the time outs

00:00:25.057 --> 00:00:27.333
and the commercial breaks
and potential overtime.

00:00:27.333 --> 00:00:29.002
I am just taking about regulation play.

00:00:29.002 --> 00:00:31.297
We could think about how the numbers
might change if you think about

00:00:31.297 --> 00:00:34.338
the total duration of the game,
including time outs and commercial breaks

00:00:34.338 --> 00:00:38.090
and everything that might get
you closer to 2 or 2 1/2 hours.

00:00:38.090 --> 00:00:40.584
But 48 minutes we can
actually convert to seconds

00:00:40.584 --> 00:00:44.503
because we know that there
are 60 seconds per minute,

00:00:44.503 --> 00:00:49.690
times 60 seconds, 60 seconds per minute

00:00:49.690 --> 00:00:51.552
and this is pretty straight
forward multiplication.

00:00:51.552 --> 00:00:58.421
We can just say 48 times 60
gives us, so we got this 0 here

00:00:58.421 --> 00:01:02.293
and then 6 times 48, 6 times 8 is 48

00:01:02.293 --> 00:01:07.137
and then 6 times 4 is 24 plus 4 is 28.

00:01:07.137 --> 00:01:15.520
So there's 2,880 seconds
during regulation play.

00:01:15.520 --> 00:01:21.421
Now let's think about
the actual age of earth.

00:01:21.421 --> 00:01:24.417
We estimate that the earth, and
actually the entire solar system,

00:01:24.417 --> 00:01:30.073
which was all formed roughly at the
same time, is 4.54 billion years old.

00:01:30.073 --> 00:01:32.083
So let me draw that here.

00:01:32.083 --> 00:01:32.965
We're going to make a comparison,

00:01:32.965 --> 00:01:34.852
so I am going to draw
it as the same length.

00:01:34.852 --> 00:01:40.996
So 4.54 billion years old
and just to give a sense

00:01:40.996 --> 00:01:45.497
of how large of a number that
is, a billion is a 1,000 million.

00:01:45.497 --> 00:01:52.474
So we could also write this
as 4,540 million years.

00:01:52.474 --> 00:02:01.080
or we could write it as 4,540,000
thousand years, or millennia,

00:02:01.080 --> 00:02:11.964
or we could just write out the
number as 4,540,000,000 years

00:02:11.964 --> 00:02:16.447
which seems kind of old but let's
think about how long anatomically,

00:02:16.447 --> 00:02:19.608
modern humans have been roaming
the surface of the earth

00:02:19.608 --> 00:02:23.587
and here we estimate that
anatomically modern humans have been

00:02:23.587 --> 00:02:30.251
on the surface of the earth
for about 200,000 years,

00:02:30.251 --> 00:02:32.691
which seems like a
reasonable amount of time

00:02:32.691 --> 00:02:34.998
but we'll see it's a very small fraction

00:02:34.998 --> 00:02:38.496
when you compare it to 4.54 billion years.

00:02:38.496 --> 00:02:40.526
So let's say that that's that little there

00:02:40.526 --> 00:02:42.895
and I am actually overdoing it
when I'm drawing the diagram.

00:02:42.895 --> 00:02:46.469
So that right over there is the amount
of time humans have been 200,000 years

00:02:46.469 --> 00:02:48.661
and I am actually
drawing this way too big.

00:02:48.661 --> 00:02:53.596
But what we want to figure out
is what is that equivalent length

00:02:53.596 --> 00:02:55.748
in seconds on a basketball game

00:02:55.748 --> 00:03:02.712
or another way to think
about it, 200,000 years is

00:03:02.712 --> 00:03:15.691
to 4.54 billion years as
the number of seconds.

00:03:15.691 --> 00:03:22.306
Let's call this thing
right over here x as x is

00:03:22.306 --> 00:03:24.482
to the total number of seconds in a game.

00:03:24.482 --> 00:03:27.726
So 2,880 seconds,

00:03:27.726 --> 00:03:33.633
2,880 seconds just like that.

00:03:33.633 --> 00:03:36.524
And one way that we can
do this, to solve for x

00:03:36.524 --> 00:03:39.750
and this is kind of a more basic algebra,

00:03:39.750 --> 00:03:41.260
but just as a reminder if
we want to solve for x here,

00:03:41.260 --> 00:03:44.508
the easiest way is to multiply by 2,880

00:03:44.508 --> 00:03:47.127
and that will cancel with
this right over here.

00:03:47.127 --> 00:03:49.673
but we can't just do it to the right
hand side, we also have to do it

00:03:49.673 --> 00:03:55.625
to the left hand side and so if
you multiply both sides by 2,880,

00:03:55.625 --> 00:04:01.959
so multiply both sides
by 2,880, you get that x,

00:04:01.959 --> 00:04:05.010
the number of the equivalent number
of seconds in a basketball game.

00:04:05.010 --> 00:04:06.820
If the history of the earth
was a basketball game,

00:04:06.820 --> 00:04:11.014
when the humans would show up is equal
to the fraction of earth's history

00:04:11.014 --> 00:04:12.655
that humans have been around.

00:04:12.655 --> 00:04:16.786
That's this part right over here,
times the number of seconds in a game.

00:04:16.786 --> 00:04:19.990
So let's think about what we get there.

00:04:19.990 --> 00:04:22.337
We are going to have the
fraction of earth's history,

00:04:22.337 --> 00:04:28.907
so 200,000 divided by 4.45 billion.

00:04:28.907 --> 00:04:30.412
There's a couple of ways I could write it.

00:04:30.412 --> 00:04:37.545
I could write it 4.54e9, which
literally means 4.54 times 10

00:04:37.545 --> 00:04:42.208
to the 9th or 4.54 times
1 followed with 9 zeros

00:04:42.208 --> 00:04:47.496
or 4.54 times a billion,
which is exactly 4.54 billion.

00:04:47.496 --> 00:04:48.881
So I could write it like that

00:04:48.881 --> 00:04:50.920
or I could just write it out.

00:04:50.920 --> 00:04:56.877
I could write 4, 5 so 4
billion, we'll be careful,

00:04:56.877 --> 00:05:04.606
4, 540,000,000 and now
I am doing the thousands

00:05:04.606 --> 00:05:09.346
2, 3 and now I am just doing the 1, 2, 3.

00:05:09.346 --> 00:05:13.319
So this is 4 billion and then I
should have 9 places after that

00:05:13.319 --> 00:05:18.710
1,2,3,4,5,6,7,8,9.

00:05:18.710 --> 00:05:21.586
So this expression right here
is a fraction of earth's history

00:05:21.586 --> 00:05:24.372
that anatomically modern
humans have been around

00:05:24.372 --> 00:05:26.574
and then I am going to multiply that,

00:05:26.574 --> 00:05:30.936
I am going to multiply that, times

00:05:30.936 --> 00:05:32.729
I am going to multiply that
times the number of seconds

00:05:32.729 --> 00:05:39.004
of regulation play,
2,880 and now drum roll,

00:05:39.004 --> 00:05:45.183
we get .12, we could round up .13 seconds.

00:05:45.183 --> 00:05:50.424
So we get x is equal to, or I could
say maybe approximately equal to

00:05:50.424 --> 00:05:57.150
0.13 seconds and so, just to imagine

00:05:57.150 --> 00:06:01.656
if the history of earth were
regulation play of an NBA game

00:06:01.656 --> 00:06:03.605
and let's say this game is kind of,

00:06:04.742 --> 00:06:08.729
at the end of this game there is a
buzzer beater shot that wins the game,

00:06:08.729 --> 00:06:12.980
the humans don't show up in the
game until the ball has left

00:06:12.980 --> 00:06:18.820
that final shot taker's hands and it
has just about to enter the basket

00:06:18.820 --> 00:06:23.513
that's when the first humans,
200,000 years ago will show up.

00:06:23.513 --> 00:06:27.407
A little over a tenth of a
second before the end of the game

00:06:27.407 --> 00:06:30.597
and since we already have
our brains in this mindset,

00:06:30.597 --> 00:06:32.433
I will throw out another
interesting question.

00:06:32.433 --> 00:06:34.566
Okay, humans are you know, just a flash

00:06:34.566 --> 00:06:35.820
that they've actually shown up.

00:06:35.820 --> 00:06:37.429
Just as the ball is about
to go into the basket,

00:06:37.429 --> 00:06:41.135
we have a little over a tenth
of a second left in the game.

00:06:41.135 --> 00:06:44.420
Think about when the
dinosaurs went extinct.

00:06:45.574 --> 00:06:46.539
I will give you a hint here.

00:06:46.539 --> 00:06:48.237
The dinosaurs went extinct.

00:06:48.237 --> 00:06:50.520
So we believe an asteroid hit the earth.

00:06:50.520 --> 00:06:52.235
So, this kind of a meteorite.

00:06:52.742 --> 00:06:55.611
This is a current theory,
meteorite hit the earth,

00:06:55.611 --> 00:06:59.986
mass extinction event
65.5 million years ago.

00:07:00.878 --> 00:07:04.321
So if we think of that 65.5
million years ago relative

00:07:04.321 --> 00:07:05.766
to the history of the earth

00:07:05.766 --> 00:07:08.792
and if the history of the earth were just
regulation play of a basketball game,

00:07:08.792 --> 00:07:10.813
when did that happen?

00:07:11.351 --> 00:07:13.794
Well, once again let's
get our calculator out.

00:07:13.794 --> 00:07:16.510
What fraction of the earth's
history ago was this?

00:07:16.510 --> 00:07:23.563
65.5 million, I could write this
as 65.5 times 10 to the 6th,

00:07:23.563 --> 00:07:29.784
which is that and then I'll just
divide that by 4.54 billion years.

00:07:29.784 --> 00:07:33.886
So times 10 to the 9th and so this
is the fraction of earth's history

00:07:33.886 --> 00:07:38.487
that has happened since the
extinction of the dinosaurs.

00:07:38.487 --> 00:07:41.898
So a little more, about a percent and
a half of earth's history has happened

00:07:41.898 --> 00:07:47.778
since the extinction of the
dinosaurs 65.5 million years ago

00:07:47.778 --> 00:07:49.445
and if we are talking
about a basketball game,

00:07:49.445 --> 00:07:52.868
let's just multiply that times the
number of seconds in a basketball game,

00:07:52.868 --> 00:07:57.711
2,880 and we get about 41 seconds.

00:07:57.711 --> 00:08:00.646
So with less than a minute
left in the 4th quarter

00:08:00.646 --> 00:08:03.568
is when the meteorite hits the earth


LeBron asks about Newton's 3rd Law

WEBVTT
Kind: captions
Language: en

00:00:03.020 --> 00:00:06.160
LEBRON JAMES: Newton's third law
tells us that to every action,

00:00:06.160 --> 00:00:08.780
there's always an equal
and opposite reaction.

00:00:08.780 --> 00:00:11.744
When I'm shooting the ball, I am
clearly applying a force to it.

00:00:11.744 --> 00:00:13.410
Where's the equal and
opposite reaction?

00:00:16.757 --> 00:00:18.840
SALMAN KHAN: That's an
excellent question, LeBron.

00:00:18.840 --> 00:00:20.980
So as you mentioned, if
someone's shooting a ball,

00:00:20.980 --> 00:00:23.272
they're clearly applying
a force to that ball.

00:00:23.272 --> 00:00:24.980
And let me see if I
can draw that for us.

00:00:24.980 --> 00:00:27.760
So let's say that this is
the force that your hand is

00:00:27.760 --> 00:00:30.070
applying on the ball.

00:00:30.070 --> 00:00:32.830
And this force is what
accelerates the ball upwards

00:00:32.830 --> 00:00:34.290
and towards the basket.

00:00:34.290 --> 00:00:38.150
So force is force
applied by hand,

00:00:38.150 --> 00:00:44.650
applied by hand on the ball.

00:00:44.650 --> 00:00:47.030
So where is this equal
and opposite force

00:00:47.030 --> 00:00:49.740
that Newton's third
law tells us about?

00:00:49.740 --> 00:00:51.320
Well, that's going
to be the force

00:00:51.320 --> 00:00:54.530
that the ball is
applying to your hand.

00:00:54.530 --> 00:00:56.350
And so I'll draw the
force right here.

00:00:56.350 --> 00:00:57.510
I could draw it
anywhere on the hand.

00:00:57.510 --> 00:00:58.350
But I'll draw it
here, just so you

00:00:58.350 --> 00:01:00.310
see it's going in the
exact opposite direction.

00:01:03.500 --> 00:01:05.610
And it has an equal magnitude.

00:01:05.610 --> 00:01:07.580
So it's an equal
but opposite force.

00:01:07.580 --> 00:01:09.600
Opposite is the direction.

00:01:09.600 --> 00:01:11.900
So just like that.

00:01:11.900 --> 00:01:23.020
So that is the force applied
by the ball on your hand.

00:01:26.004 --> 00:01:27.420
But then you might
say, wait, this

00:01:27.420 --> 00:01:29.030
doesn't make a lot of sense.

00:01:29.030 --> 00:01:32.330
The ball is clearly getting
accelerated in that direction.

00:01:32.330 --> 00:01:34.700
But my hand isn't
accelerating backwards

00:01:34.700 --> 00:01:37.400
in kind of that
opposite direction.

00:01:37.400 --> 00:01:40.040
And the reason why your hand
isn't accelerating backwards,

00:01:40.040 --> 00:01:42.640
isn't just flopping backwards
because of this force

00:01:42.640 --> 00:01:44.720
of the ball applying
to the hand,

00:01:44.720 --> 00:01:47.430
the reason is because
your hand or your fingers

00:01:47.430 --> 00:01:51.750
have other forces acting on
it that counteract this force.

00:01:51.750 --> 00:01:54.590
So for example, the reason
why your fingers and your hand

00:01:54.590 --> 00:01:57.700
don't flop backwards, don't
accelerate backwards because

00:01:57.700 --> 00:02:01.400
of this force, is because you
have muscles in your forearm.

00:02:01.400 --> 00:02:03.700
You have muscles in your
forearm, roughly right

00:02:03.700 --> 00:02:07.610
around there, that are
pulling on your fingers

00:02:07.610 --> 00:02:11.199
and on your hand and are
counteracting this force.

00:02:11.199 --> 00:02:12.740
So they are
counteracting that force.

00:02:12.740 --> 00:02:14.040
So you say, OK, fair enough.

00:02:14.040 --> 00:02:15.900
I see why my fingers
aren't flopping back

00:02:15.900 --> 00:02:17.440
and why my hand
isn't flopping back.

00:02:17.440 --> 00:02:20.070
It's because of these
muscles right over here.

00:02:20.070 --> 00:02:23.420
But why isn't my entire forearm
being pushed or accelerated

00:02:23.420 --> 00:02:27.230
back by this force applied
by the ball on my hand?

00:02:27.230 --> 00:02:31.650
And the reason is that
you have other muscles

00:02:31.650 --> 00:02:34.830
in the back of your upper arm,
in particular your triceps,

00:02:34.830 --> 00:02:41.510
that are keeping-- that are
tugging on your forearm.

00:02:41.510 --> 00:02:42.990
It's contracting.

00:02:42.990 --> 00:02:47.440
They're contracting-- that
more than offset any net force

00:02:47.440 --> 00:02:50.100
on your forearm that would
want to make it go that way.

00:02:50.100 --> 00:02:51.540
It's pulling on your forearm.

00:02:51.540 --> 00:02:53.664
And in fact, that's what's
contracting and allowing

00:02:53.664 --> 00:02:56.950
your forearm to go in
actually that direction.

00:02:56.950 --> 00:02:58.210
And we could keep going.

00:02:58.210 --> 00:03:00.510
I mean, the fun, or
the complicated thing,

00:03:00.510 --> 00:03:02.579
about Newton's third law
is if every force has

00:03:02.579 --> 00:03:04.870
an equal and opposite force,
will every one of these we

00:03:04.870 --> 00:03:06.453
have have an equal
and opposite force?

00:03:06.453 --> 00:03:08.330
And we can keep going
on as, OK, there's

00:03:08.330 --> 00:03:12.100
an equal and opposite
force of the tricep tugging

00:03:12.100 --> 00:03:13.132
on the forearm.

00:03:13.132 --> 00:03:15.090
Well, that's the forearm
tugging on the tricep.

00:03:15.090 --> 00:03:16.423
But why doesn't the tricep move?

00:03:16.423 --> 00:03:18.870
Well, the tricep is attached
to other parts of your body.

00:03:18.870 --> 00:03:21.140
And we could keep
going on and on and on.

00:03:21.140 --> 00:03:22.900
But just to focus
on the question,

00:03:22.900 --> 00:03:25.860
your hand is definitely
applying a force to the ball,

00:03:25.860 --> 00:03:28.470
but the equal and opposite
force is the force

00:03:28.470 --> 00:03:30.870
that the ball is
applying to the hand.

00:03:30.870 --> 00:03:33.360
But we actually-- even though
we said that your hand isn't

00:03:33.360 --> 00:03:35.740
flopping back because it's
being balanced-- you actually

00:03:35.740 --> 00:03:37.680
can sense this force.

00:03:37.680 --> 00:03:40.690
And the reason why you do sense
this force is you actually do

00:03:40.690 --> 00:03:44.950
have the ball compressing
against the palm of your hand.

00:03:44.950 --> 00:03:47.560
If it didn't do that, you
wouldn't even feel the ball.

00:03:47.560 --> 00:03:50.620
So that gives you at
least a sensory clue

00:03:50.620 --> 00:03:52.200
of Newton's third law.

00:03:52.200 --> 00:03:54.197
If Newton's third
law wasn't true,

00:03:54.197 --> 00:03:55.530
you wouldn't even feel the ball.

00:03:55.530 --> 00:03:57.196
You wouldn't even
have the ball compress

00:03:57.196 --> 00:03:59.709
against the skin of your palm.


LeBron Asks:  What muscles do we use when shooting a basket?

WEBVTT
Kind: captions
Language: en

00:00:00.764 --> 00:00:03.239
[LEBRON JAMES] What muscles do I use when I take a free throw?

00:00:04.886 --> 00:00:08.761
[SAL KHAN] Excellent question, LeBron.

00:00:08.761 --> 00:00:11.344
So you can imagine whenever you're doing anything –

00:00:11.344 --> 00:00:13.927
whenever you stand, or even run – you're using a ton of muscles

00:00:13.927 --> 00:00:16.217
just to to keep your balance – Just to keep your body rigid.

00:00:16.217 --> 00:00:17.744
But what we're going to focus on are

00:00:17.744 --> 00:00:19.271
the muscles that are directly acting on the ball

00:00:19.271 --> 00:00:20.799
to make the ball go in that direction –

00:00:20.799 --> 00:00:24.746
to make it accelerate upwards and towards the basket –

00:00:24.746 --> 00:00:28.417
which you would hopefully do

00:00:28.417 --> 00:00:32.493
when you are taking a free throw.

00:00:32.493 --> 00:00:36.250
So, the muscles that are doing that are

00:00:36.250 --> 00:00:39.243
the ones that help your fingers go in that direction,

00:00:39.243 --> 00:00:42.236
help the palm of you hand going in that direction,

00:00:42.236 --> 00:00:45.230
and help your entire forearm to go in that direction.

00:00:45.230 --> 00:00:47.672
Obviously, at the same time, there are many other muscles at work,

00:00:47.672 --> 00:00:49.300
even the muscles that keep your entire arm

00:00:49.300 --> 00:00:50.928
above your head like this –

00:00:50.928 --> 00:00:52.557
the muscles that keep you standing.

00:00:52.557 --> 00:00:55.638
But we're going to just focus on these muscles right over here.

00:00:55.638 --> 00:00:59.286
So first, the muscles that allow your fingers to go

00:00:59.286 --> 00:01:02.934
in the direction that you want the ball to go, and your palm.

00:01:02.934 --> 00:01:06.584
And you might be surprised to find that

00:01:06.584 --> 00:01:08.287
those muscles actually sit in the forearm.

00:01:08.287 --> 00:01:09.990
most of those muscles actually do not sit in the hand.

00:01:09.990 --> 00:01:11.695
Those muscles are actually here.

00:01:11.695 --> 00:01:16.369
So the muscles in the front of your forearm right here,

00:01:16.369 --> 00:01:19.485
they are actually all about flexing the fingers

00:01:19.485 --> 00:01:22.601
and the hands in that direction.

00:01:22.601 --> 00:01:25.208
There are a bunch of names for them.

00:01:25.208 --> 00:01:27.815
And I encourage folks to look them up.

00:01:27.815 --> 00:01:29.902
But it is a really interesting thing, because we are often used to

00:01:29.902 --> 00:01:31.989
muscles being directly where the motion is.

00:01:31.989 --> 00:01:34.078
But in this case, these muscles, when they're in action, they contract

00:01:34.078 --> 00:01:37.678
And muscles, when they're in action do contract.

00:01:37.678 --> 00:01:41.278
So they're going to contract and they are going to pull essentially on tendons.

00:01:41.278 --> 00:01:44.880
They're going to pull the whole hand to that way.

00:01:44.880 --> 00:01:46.616
You could view as a kind of pulley

00:01:46.616 --> 00:01:52.100
So if this was... If you view your wrist joint as kind of pulley.

00:01:52.100 --> 00:02:03.706
And if you had a rope that is attached to another block. And that block you can view as your hand and your finger

00:02:03.706 --> 00:02:10.899
So that block is your hand. These muscles right over here, they contract this way

00:02:10.899 --> 00:02:16.210
so its ..... pulling on this rope. And were to pull on this rope, what would happen to this block up here?

00:02:16.210 --> 00:02:20.187
Well, this block up here is going to go in that general direction.

00:02:20.187 --> 00:02:23.098
So that what's keep your hand and your fingers going in that way

00:02:23.098 --> 00:02:25.422
But what about the entire forearm?

00:02:25.422 --> 00:02:31.298
So once again. The muscles that get your entire forearm going in that direction aren't in your forearm.

00:02:31.298 --> 00:02:34.018
They are in the back of your upper arm.

00:02:34.018 --> 00:02:38.365
So they are right over here. Often referred to as the triceps.

00:02:38.365 --> 00:02:42.205
The official name are the triceps brachii, but they're right over here

00:02:42.205 --> 00:02:46.970
and it's called triceps because kind of three-headed muscle. There are three muscle bundles that are going on

00:02:46.970 --> 00:02:51.249
And when these muscles over here, your triceps, when they contract

00:02:51.249 --> 00:02:59.868
they allow your entire forearm to essentially straighten out on your elbow so it will go in that direction

00:02:59.868 --> 00:03:02.382
In this case, when this muscle, the triceps, contract

00:03:02.382 --> 00:03:06.196
your entire forearm is going to .... on your elbow

00:03:06.196 --> 00:03:10.196
And go like that, which will allow the basket to go in the intended direction


LeBron Asks:  Why does humidity make it feel hotter?

WEBVTT
Kind: captions
Language: en

00:00:00.880 --> 00:00:04.977
LEBRON: Some reason Miami can be hot. I'm told the humidity makes it hotter

00:00:04.977 --> 00:00:06.602
Why is this?

00:00:07.109 --> 00:00:08.999
KHAN: Excellent question LeBron.

00:00:09.014 --> 00:00:14.105
Let's first think about what people are talking about when they even say "humidity"

00:00:14.105 --> 00:00:17.833
And there's a couple of ways to think about humidity, but typically when you are the weatherman

00:00:17.833 --> 00:00:21.985
or in everyday talk people say "Hey it's really humid out there." or "It's high humidity."

00:00:21.985 --> 00:00:28.942
They're talking about relative humidity, and it's usually indicated by a percentage

00:00:28.942 --> 00:00:33.466
Let's just think about what the different percentages of relative humidity mean.

00:00:33.466 --> 00:00:36.365
So right over here, we have 0%.

00:00:38.009 --> 00:00:40.864
So right over here, we have 0% relative humidity.

00:00:40.864 --> 00:00:45.821
and over at the extreme other hand, you have 100% relative humidity.

00:00:45.821 --> 00:00:53.858
at any given point, the air is some place between 0% humidity and 100% relative humidity.

00:00:53.858 --> 00:00:59.778
at 0% relative humidity is essentially saying that there is no water vapor in the air

00:00:59.778 --> 00:01:03.942
or non-measurable amount of water vapor in the air.

00:01:03.942 --> 00:01:10.435
As we go to this molecular view of what it might look like little water droplet maybe on our surface of our skin

00:01:10.435 --> 00:01:15.869
So just to be clear, these are the skin molecules - not even skin cells, which will be the actual skin molecules.

00:01:15.869 --> 00:01:19.015
Let's just simplified them as brown circles.

00:01:19.335 --> 00:01:25.488
And this right over here - this is the actual water molecules.

00:01:25.488 --> 00:01:29.461
So these are water molecules

00:01:29.461 --> 00:01:33.677
And maybe is a drop of sweat, or little water that got dropped on our skin

00:01:33.677 --> 00:01:37.893
and it is in liquid state

00:01:37.893 --> 00:01:41.088
you have this hydrogen bond between the molecules that are super strong

00:01:41.088 --> 00:01:46.513
so allows these molecules to slide pass each other and that's why liquid flows the way it does.

00:01:46.513 --> 00:01:51.182
And we've already talked about why sweat makes you cooler but warm up you a little bit.

00:02:00.001 --> 00:02:00.751
Captions by Isaac@RwmOne (youtube.com/RwmOne)


LeBron Asks: Why does sweating cool you down?

WEBVTT
Kind: captions
Language: en

00:00:00.201 --> 00:00:03.704
Why does sweating cool you down?

00:00:03.704 --> 00:00:06.774
That is an excellent question LeBron,

00:00:06.774 --> 00:00:11.345
and to answer it, let's zoom in on a little droplet of sweat.

00:00:11.345 --> 00:00:15.583
And sweat is mostly water, so when we zoom in, and we've really zoomed in,

00:00:15.583 --> 00:00:16.083
even more than I've drawn over here.

00:00:16.083 --> 00:00:21.288
When we really zoom in, we'll start seeing mainly these water molecules.

00:00:21.288 --> 00:00:23.757
And the water molecules, just to be a little more accurate,

00:00:23.757 --> 00:00:29.964
I've drawn the oxygen in blue, and then the hydrogens that are bonded with that oxygen I've done in white.

00:00:29.964 --> 00:00:36.961
We all know that water is sometimes refered to as H2 -- that's for the two hydrogens -- H20.

00:00:36.961 --> 00:00:42.009
So each of these are a molecule of H2O, or a molecule of water.

00:00:42.009 --> 00:00:47.348
What I've drawn down here, and this is an oversimplification of the molecules of your skin,

00:00:47.348 --> 00:00:52.620
but just for simplification, these are molecules of your skin.

00:00:52.620 --> 00:00:55.856
really, the parts of the skin cells. These aren't even the skin cells themselves,

00:00:55.856 --> 00:00:58.692
these are the molecules that make up the skin cells.

00:00:58.692 --> 00:01:05.927
And right over here, these are molecules of sweat, or it's really just molecules of water.

00:01:05.927 --> 00:01:10.504
So the question of why does sweat cool you down could really be restated as:

00:01:10.504 --> 00:01:15.476
Why does having water on the surface of your skin actually cool you down?

00:01:15.476 --> 00:01:18.445
And to answer that, or to think about that question,

00:01:18.445 --> 00:01:22.516
we have to think about what it means to have temperature, or what temperature even really means.

00:01:22.516 --> 00:01:28.756
Temperature, what we perceive as temperature, is really just the motion of the molecules of something.

00:01:28.756 --> 00:01:32.126
So higher temperature means that they're moving around more.

00:01:32.126 --> 00:01:36.630
So high temperature they're moving around more, and low temperature they're moving around less.

00:01:36.630 --> 00:01:38.332
And they can move around in different ways,

00:01:38.332 --> 00:01:42.670
they can have translational motion, which is they're actually moving around.

00:01:42.670 --> 00:01:46.540
They could be vibrating. They could be rotating in some way.

00:01:46.540 --> 00:01:53.981
And in general, on average, the more of this motional energy, often referred to as kinetic energy,

00:01:53.981 --> 00:01:58.986
that these molecules have on average, the higher the perceived temperature would be.

00:01:58.986 --> 00:02:03.457
Now, how does having this water here cool down the skin?

00:02:03.457 --> 00:02:05.726
And well, first of all, why is the skin warming up?

00:02:05.726 --> 00:02:09.275
Because the muscles are doing all of this work. They're releasing heat.

00:02:09.275 --> 00:02:11.811
That heat is being transferred to the skin.

00:02:11.811 --> 00:02:15.336
But then how does having this water here help?

00:02:15.336 --> 00:02:19.506
Well, the skin has a certain temperature, a certain kinetic energy, or motional energy.

00:02:19.506 --> 00:02:25.579
But when we say that it doesn't mean that all of these molecules have the exact same motion.

00:02:25.579 --> 00:02:32.739
The temperature is the average motion. Some of these are bumping around at a faster speed.

00:02:32.739 --> 00:02:35.856
Or vibrating at a faster speed, or rotating at a faster speed

00:02:35.856 --> 00:02:38.025
Some are doing it at a slower speed.

00:02:38.025 --> 00:02:43.130
But as these bump around, they're going to bump into these water molecules and get them moving around.

00:02:43.130 --> 00:02:46.133
They would probably be moving around a little bit to begin with,

00:02:46.133 --> 00:02:50.037
but then the warmer this is, the more energy here, they'll bump into these molecules.

00:02:50.037 --> 00:02:53.941
So let's say this guy bumps into that, then he'll bump over there ,

00:02:53.941 --> 00:02:58.011
so that energy, this bumping energy, or this kinetic energy,

00:02:58.011 --> 00:03:00.848
well, some of it will be transferred, or you could even say some of that temperature,

00:03:00.848 --> 00:03:06.372
some of that heat will be transferred to these water molecules.

00:03:06.372 --> 00:03:11.358
But the important thing to remember is this is a really kind of crazy thing, they're all bumping into eachother

00:03:11.358 --> 00:03:14.061
and rotating in all sorts of crazy ways.

00:03:14.061 --> 00:03:18.098
They will have an average kinetic energy, which we perceive as temperature,

00:03:18.098 --> 00:03:22.970
but this one might be going really, really, really fast in that direction,

00:03:22.970 --> 00:03:25.839
while this one might be going really, really, really slow,

00:03:25.839 --> 00:03:29.276
this one might be going really really really fast in that direction

00:03:29.276 --> 00:03:33.147
this one might be going really slow in this direction

00:03:33.147 --> 00:03:41.193
So the thing to think about is, given that you have all of this variation in the energy of each of these particles,

00:03:41.193 --> 00:03:46.059
which of these are most likely to escape, to actually evaporate?

00:03:46.059 --> 00:03:49.663
And to think about evaporation, you just have to think about that most water molecules

00:03:49.663 --> 00:03:52.232
or the water molecules that are in that droplet

00:03:52.232 --> 00:03:56.640
they do have an attraction to eachother, we call those hydrogen bonds.

00:03:56.640 --> 00:04:00.274
They do have an attraction to eachother,

00:04:00.274 --> 00:04:02.543
that's why a droplet kind of sticks together.

00:04:02.543 --> 00:04:07.347
But if one of these molecules is moving fast enough and if it's moving in the right direction

00:04:07.347 --> 00:04:10.684
it has a higher probability of being able to escape,

00:04:10.684 --> 00:04:13.287
being able to actually escape that droplet.

00:04:13.287 --> 00:04:18.592
And the process of these molecules actually escaping, that's what we refer to as evaporation.

00:04:18.592 --> 00:04:24.965
If a molecule has enough energy it will escape this, escape the bonds of the other water molecules,

00:04:24.965 --> 00:04:31.538
and just evaporate into the air.

00:04:31.538 --> 00:04:34.041
But we still haven't fully answered our question.

00:04:34.041 --> 00:04:38.078
So let's say that this is one that has evaporated, it has fully escaped.

00:04:38.078 --> 00:04:42.583
Why would that actually cool down this entire system?

00:04:42.583 --> 00:04:49.556
Why would it cool down the droplet and essentially give it more capability to accept more energy from the skin?

00:04:49.556 --> 00:04:55.229
Well, we just said the ones that have the highest energy are the ones that are most likely to escape,

00:04:55.229 --> 00:04:58.098
the ones that have the highest kinetic energy.

00:04:58.098 --> 00:05:02.402
So if you have a bunch of stuff, some are fast, some are slow, some are vibrating a lot, vibrating less

00:05:02.402 --> 00:05:08.942
but the ones that have a high kinetic energy are the most likely to escape, what happens when they escape?

00:05:08.942 --> 00:05:11.879
Well then the average kinetic energy will go down.

00:05:11.879 --> 00:05:17.985
Or you could say the temperature would go down,

00:05:17.985 --> 00:05:24.024
which is really just the average amount of motion or kinetic energy that's in this droplet.

00:05:24.024 --> 00:05:28.529
If the really fast ones, the ones with a lot of energy, are leaving, then the ones are left over, on average,

00:05:28.529 --> 00:05:33.000
are going to have a lower kinetic energy, or a lower temperature.

00:05:33.000 --> 00:05:39.172
And so that is what is cooling you down at a molecular level.


Overview of KhanAcademy.org

WEBVTT
Kind: captions
Language: en

00:00:00.278 --> 00:00:02.845
Welcome to the Khan Academy

00:00:02.845 --> 00:00:05.311
we are honored that you have joined us

00:00:05.311 --> 00:00:07.546
and what I hope to do is just give you a walk through

00:00:07.546 --> 00:00:10.129
to think about how you might want to use the site.

00:00:10.129 --> 00:00:12.206
So, first of all you might know exactly what

00:00:12.206 --> 00:00:13.894
you want to learn about, you might say wait

00:00:13.894 --> 00:00:15.845
I kind of wonder what a derivative is.

99:59:59.999 --> 100:00:02.599
So you can do a search right over there

99:59:59.999 --> 100:00:02.865
and there all sorts of exercises and videos

99:59:59.999 --> 100:00:02.665
that deal with derivatives. For example,

99:59:59.999 --> 100:00:02.665
you could go to the derivative intuition

99:59:59.999 --> 100:00:02.465
exercise and you would see this thing

99:59:59.999 --> 100:00:02.865
right over here which makes you think about

99:59:59.999 --> 100:00:02.732
well what's the slope of the tangent line

99:59:59.999 --> 100:00:02.865
at any of these points? And when you do it,

99:59:59.999 --> 100:00:02.532
you're essentially plotting, plotting,

99:59:59.999 --> 100:00:02.799
the derivative. Or you might say, well no,

99:59:59.999 --> 100:00:03.132
I actually want, I actually want an explanation

99:59:59.999 --> 100:00:03.332
of what a derivative is. Maybe you've already done

99:59:59.999 --> 100:00:02.732
the derivative module. So, you might want

99:59:59.999 --> 100:00:02.865
to look at a calculus proof or look at some

99:59:59.999 --> 100:00:02.865
type of what a partial derivative might be.

99:59:59.999 --> 100:00:02.999
And you click there and you would actually go

99:59:59.999 --> 100:00:02.932
to the video. So, that's if you kind of know


Why is this art? Andy Warhol, Campbell's Soup Cans

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:04.776
(piano playing)

00:00:04.776 --> 00:00:08.780
Steven: We're looking at one of the single canvases from a series of canvases

00:00:08.780 --> 00:00:12.167
of the Campbell Soup Cans by Andy Warhol from 1962

00:00:12.167 --> 00:00:13.786
at the Museum of Modern Art.

00:00:13.786 --> 00:00:16.721
And one of the really important questions that comes up about,

00:00:16.721 --> 00:00:21.058
especially modern art, is well, why is this art?

00:00:21.058 --> 00:00:24.963
Sal: When you ask me that a bunch of things kind of surface in my brain.

00:00:24.963 --> 00:00:28.365
It does evoke something in me so I'm inclined to say yes,

00:00:28.365 --> 00:00:30.418
but then there's a bunch of other things that say well,

00:00:30.418 --> 00:00:32.750
if I didn't see this in a museum and if I just saw this

00:00:32.750 --> 00:00:35.168
in the marketing department of Campbell's Soup,

00:00:35.168 --> 00:00:37.074
would you be viewing it differently?

00:00:37.074 --> 00:00:38.976
Steven: Because it's advertising then.
Sal: Yes.

00:00:38.976 --> 00:00:41.418
Steven: But in the context of the museum or in the context

00:00:41.418 --> 00:00:44.881
of Andy Warhol's studio, it's not quite advertising, right?

00:00:44.881 --> 00:00:47.552
Sal: Even if it's the exact same thing.
Steven: Yeah.

00:00:47.552 --> 00:00:50.335
Sal: And the idea here is by putting it in the museum

00:00:50.335 --> 00:00:52.290
it's saying look at this in a different way.

00:00:52.290 --> 00:00:54.752
Steven: Well that's right, it really does relocate it,

00:00:54.752 --> 00:00:57.835
it does change the meaning, it does transform it,

00:00:57.835 --> 00:01:00.399
and that's really one of the central ideas of modern art

00:01:00.399 --> 00:01:03.133
is that you can take something that's not necessarily based

00:01:03.133 --> 00:01:05.870
in technical skill, because I don't think you would say

00:01:05.870 --> 00:01:08.085
that this is beautifully rendered.
Sal: Right.

00:01:08.085 --> 00:01:11.419
Steven: But it relocates it and makes us think about it in a different way.

00:01:11.419 --> 00:01:14.611
Sal: And so, I guess he would get credit for taking something

00:01:14.611 --> 00:01:19.116
that was very, almost mundane, something you see in everyone's cupboard,

00:01:19.116 --> 00:01:23.620
and making it a focal point like you should pay attention to this thing.

00:01:23.620 --> 00:01:26.690
Steven: I think that's exactly right and I think that he's doing it

00:01:26.690 --> 00:01:31.028
about a subject that was about as low a subject as one could go.

00:01:31.028 --> 00:01:34.365
I mean cheap advertising art was something that was so far away

00:01:34.365 --> 00:01:38.870
from fine art from the great masters and then to focus on something

00:01:38.870 --> 00:01:44.309
as lowly as a can of soup, and cream of chicken no less, right? (laughs)

00:01:44.309 --> 00:01:47.893
Sal: A lot of it is, if he did it 50 years earlier,

00:01:47.893 --> 00:01:49.780
people would have thought this guy's a quack

00:01:49.780 --> 00:01:52.613
and if he did it now they'd think he was just derivative and...

00:01:52.613 --> 00:01:57.411
It was really just that time where people happened to think this was art.

00:01:57.411 --> 00:01:59.021
Steven: I think that that's right.

00:01:59.021 --> 00:02:02.161
In 1962, what Warhol is doing is he's saying

00:02:02.161 --> 00:02:06.661
what is it about our culture that is really authentic and important?

00:02:06.661 --> 00:02:09.494
And it was about mass production, it was about factories.

00:02:09.494 --> 00:02:13.079
He in a sense said let's not be looking at nature

00:02:13.079 --> 00:02:16.949
as if we were still an agrarian culture, we're now an industrial culture.

00:02:16.949 --> 00:02:19.866
What is the stuff of our visual world now?

00:02:19.866 --> 00:02:21.434
Sal: I think I'm 80 percent there.

00:02:21.434 --> 00:02:24.899
I remember in college there was a student run art exhibit

00:02:24.899 --> 00:02:28.675
and as a prank a student actually put a little podium there

00:02:28.675 --> 00:02:30.482
and put his lunch tray.

00:02:30.482 --> 00:02:33.380
He put a little placard next to it, you know, lunch tray on Saturday

00:02:33.380 --> 00:02:34.948
or something is what he called it.

00:02:34.948 --> 00:02:37.065
So he did it as a prank and everyone thought it was really funny

00:02:37.065 --> 00:02:40.553
but to some degree it's kind of a sign that maybe what he did was art.

00:02:40.553 --> 00:02:42.232
Steven: Well I think that's why it was funny

00:02:42.232 --> 00:02:43.493
because it was so close, right?

00:02:43.493 --> 00:02:45.635
Sal: And to some degree when someone took a lunch tray

00:02:45.635 --> 00:02:49.037
and gave it the proper lighting and gave it a podium to look at it

00:02:49.037 --> 00:02:51.743
and wrote a whole description about it, I did view the lunch tray

00:02:51.743 --> 00:02:52.872
in a different way.

00:02:52.872 --> 00:02:54.374
That's kind of the same idea, that something

00:02:54.374 --> 00:02:56.709
that's such a mundane thing but you use it everyday.

00:02:56.709 --> 00:02:58.779
I mean, what would you say to that?

00:02:58.779 --> 00:03:00.492
Was that a prank or was that art?

00:03:00.492 --> 00:03:02.171
Steven: I think it is a prank but it's also very close

00:03:02.171 --> 00:03:04.884
to some important art that had been made earlier in the century.

00:03:04.884 --> 00:03:08.222
He had license to do that because of somebody named Marcel Duchamp.

00:03:08.222 --> 00:03:11.692
In fact, Warhol had in a sense the same kind of license

00:03:11.692 --> 00:03:15.743
to not focus on the making of something, not focus on the brushwork,

00:03:15.743 --> 00:03:18.565
not focus on the composition, not focus on the color,

00:03:18.565 --> 00:03:21.825
but focus on the refocusing of ideas.

00:03:21.825 --> 00:03:25.410
Sal: And the reason why we talk about Warhol or Duchamp

00:03:25.410 --> 00:03:27.707
or any of these people is that, as you said,

00:03:27.707 --> 00:03:29.642
it's not that they did something technically profound.

00:03:29.642 --> 00:03:32.243
Obviously Campbell Soup's marketing department had already done

00:03:32.243 --> 00:03:37.450
something as equally as profound, it's more that they were the people

00:03:37.450 --> 00:03:41.161
who looked at the world in a slightly different way and highlighted that.

00:03:41.161 --> 00:03:42.493
Steven: Well I think that that's right.

00:03:42.493 --> 00:03:46.659
Warhol is also very consciously working towards

00:03:46.659 --> 00:03:49.695
asking the same questions that the prankster at your school was asking.

00:03:49.695 --> 00:03:52.599
He's saying can this be art?

00:03:52.599 --> 00:03:54.201
And in fact he's really pushing it.

00:03:54.201 --> 00:03:55.909
Look at the painting closely for a moment.

00:03:55.909 --> 00:03:58.513
This is one of the last paintings that he's actually painted.

00:03:58.513 --> 00:04:01.846
He's really defined the calligraphy of this Campbell's,

00:04:01.846 --> 00:04:05.743
he's really sort of rendered the reflection of the tin at the top.

00:04:05.743 --> 00:04:08.832
But then he stopped and he said, I don't want to paint the fleur de lis.

00:04:08.832 --> 00:04:11.541
You see those little fleur de lis down at the bottom.

00:04:11.541 --> 00:04:12.809
I don't want to paint those.

00:04:12.809 --> 00:04:14.545
So he actually had a little rubber stamp made of them

00:04:14.545 --> 00:04:17.666
and actually sort of placed them down mechanically.

00:04:17.666 --> 00:04:19.551
What does that mean for an artist then,

00:04:19.551 --> 00:04:21.625
to say I don't even want to bother to paint these?

00:04:21.625 --> 00:04:24.813
I'm just going to find a mechanical process to make this easier.

00:04:24.813 --> 00:04:26.863
Warhol is doing something I think which is important

00:04:26.863 --> 00:04:29.433
which is reflecting the way that we manufacture,

00:04:29.433 --> 00:04:31.731
the way that we construct our world.

00:04:31.731 --> 00:04:35.338
Think about the things that we surround ourselves with,

00:04:35.338 --> 00:04:37.776
almost everything was made in a factory.

00:04:37.776 --> 00:04:40.211
Almost nothing is singular in the world anymore.

00:04:40.211 --> 00:04:43.230
It's not a world that we would normally find beautiful.

00:04:43.230 --> 00:04:45.564
Sal: I don't know, sometimes I feel and correct me if I'm wrong,

00:04:45.564 --> 00:04:49.585
that a decision was made that Warhol was interesting or great

00:04:49.585 --> 00:04:53.958
and then people will interpret his stuff to justify his greatness.

00:04:53.958 --> 00:04:58.262
That oh look, he used a printer instead of drawing it

00:04:58.262 --> 00:05:01.847
which shows that he was reflecting the industrial or whatever,

00:05:01.847 --> 00:05:04.265
but if he had done it the other way, if he had hand drawn it

00:05:04.265 --> 00:05:08.003
or hand drawn it with his elbow you know, or finger painted it or something

00:05:08.003 --> 00:05:10.220
people would say oh isn't this tremendous because we normally

00:05:10.220 --> 00:05:13.001
would see this thing printed by a machine and now he did it with his hands.

00:05:13.001 --> 00:05:16.557
How much do you think that is the case or am I just being cynical?

00:05:16.557 --> 00:05:20.725
Steven: Well no, I think that there's value in a certain degree of cynicism

00:05:20.725 --> 00:05:24.515
and I think that in some ways what we're really talking about here

00:05:24.515 --> 00:05:26.559
is what does it mean to be an avant-garde artist?

00:05:26.559 --> 00:05:29.307
What does it mean to sort of change the language of art

00:05:29.307 --> 00:05:33.888
and to try to find ways that art relates to our historical moment

00:05:33.888 --> 00:05:36.292
in some really direct and authentic way?

00:05:36.292 --> 00:05:38.427
Sal: And maybe it's easy for me to say this because

00:05:38.427 --> 00:05:43.057
I remember looking at this when I took 5th grade art class,

00:05:43.057 --> 00:05:47.893
Andy Warhol and all of that, so now it seems almost not that unique

00:05:47.893 --> 00:05:51.105
but in '62 what I'm hearing is that Warhol was really noteworthy

00:05:51.105 --> 00:05:53.393
because he really did push people's thinking.

00:05:53.393 --> 00:05:58.114
Steven: I think that Warhol was looking for, in 1962, a kind of subject matter

00:05:58.114 --> 00:06:02.552
that was completely outside of the scope of that we could consider fine art.

00:06:02.552 --> 00:06:04.484
One of his contemporaries, Roy Lichtenstein,

00:06:04.484 --> 00:06:06.544
was asked what pop art was and he said,

00:06:06.544 --> 00:06:10.092
"Well we were looking for subject matter that was so despicable,

00:06:10.092 --> 00:06:14.097
"that was so low, that nobody could possibly believe that it was really art."

00:06:14.097 --> 00:06:16.124
And I think you're right, I think now we look at it

00:06:16.124 --> 00:06:20.248
and it's so much a part of our visual culture that we immediately accept it.

00:06:20.248 --> 00:06:22.950
But I think that it's really interesting to retrieve

00:06:22.950 --> 00:06:25.617
just how shocking and radical that was.

00:06:25.617 --> 00:06:26.868
Sal: This is fascinating.

00:06:26.868 --> 00:06:29.311
It seems like there's a lot of potential there,

00:06:29.311 --> 00:06:32.363
that stuff that's pseudo-art made for other purposes,

00:06:32.363 --> 00:06:35.822
for commercial purposes but if you kind of shine a light on it,

00:06:35.822 --> 00:06:39.430
in the way that a light has been shone on this, that it does...

00:06:39.430 --> 00:06:43.181
In your mind would that cross the barrier into being art?

00:06:43.181 --> 00:06:45.371
Steven: Well I think that, you mentioned before,

00:06:45.371 --> 00:06:48.430
that if somebody was doing this now it would feel really derivative.

00:06:48.430 --> 00:06:49.740
And I think that that's right.

00:06:49.740 --> 00:06:54.380
I think it underscores just how hard it is to find in our culture now,

00:06:54.380 --> 00:06:57.316
ways of making us see the world in new ways.

00:06:57.316 --> 00:06:59.015
Sal: Fascinating.

00:06:59.015 --> 00:07:06.230
(piano playing)