Finding probability example 2

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:03.600
Let's do a couple of exercises
from our probability one

00:00:03.600 --> 00:00:04.200
module.

00:00:04.200 --> 00:00:08.630
So we have a bag with 9 red
marbles, 2 blue marbles,

00:00:08.630 --> 00:00:10.880
and 3 green marbles in it.

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What is the probability
of randomly selecting

00:00:13.490 --> 00:00:17.350
a non-blue marble
from of the bag?

00:00:17.350 --> 00:00:20.080
So let's draw this bag here.

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So that's my bag,
and we're going

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to assume that it's a
transparent bag, so it looks

00:00:24.730 --> 00:00:26.110
like a vase.

00:00:26.110 --> 00:00:31.020
But we have 9 red marbles,
so let me draw 9 red marbles.

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1, 2, 3, 4, 5, 6,
7, 8, 9 red marbles.

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They're kind of orange-ish,
but it does the job.

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2 blue marbles, so we have 1
blue marble, 2 blue marbles.

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And then we have 3 green
marbles, let me draw those

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3, so 1, 2, 3.

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What is the probability
of randomly selecting

00:00:59.240 --> 00:01:00.870
a non-blue marble from the bag?

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So maybe we mix them all up,
and we have an equal probability

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of selecting any one of these.

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And the way you
just think about it

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is what fraction of all
of the possible events

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meet our constraint?

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So let's just think about all
of the possible events first.

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How many different possible
marbles can we take out?

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Well that's just the total
number of marbles there are.

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So are 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, 13,

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14 possible marbles.

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So this is the number
of possibilities.

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And then we just have
to think what fraction

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of those possibilities
meet our constraints.

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And the other way you
could have gotten 14

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is just taking 9 plus 2 plus 3.

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So what number of
those possibilities

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meet our constraints?

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And remember, our constraint
is selecting a non-blue marble

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from the bag.

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Another way to think about
it is a red or green marble,

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because the only
other two colors

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we have are red and green.

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So how many non-blue
marbles are there?

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Well, there's a couple
ways to think about it.

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You could say there's
14 total marbles.

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2 are blue.

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So there are going
to be 14 minus 2,

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which is 12 non-blue marbles.

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Or you could just count them.

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1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12.

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So there are 12
non-blue marbles.

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So these are the possibilities
that meet our constraints

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over all of the possibilities.

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And then if we want to--
this isn't in simplified form

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right here, since both 12
and 14 are divisible by 2.

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So let's divide both the
numerator and the denominator

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by 2, and you get 6 over 7.

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So we have a 6/7 chance of
selecting a non-blue marble

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from the bag.

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Let's do another one.

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If a number is randomly chosen
from the following list,

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what is the probability that
the number is a multiple of 5?

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So once again, we want
to find the fraction

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of the total possibilities
that meet our constraint,

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and our constraint is
being a multiple of 5.

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So how many total
possibilities are there?

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Let's think about that.

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How many do we have?

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Well that's just
the total number

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of numbers we have to pick from,
so 1, 2, 3, 4, 5, 6, 7, 8, 9,

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10, 11, 12.

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So there are 12 possibilities.

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We have an equal chance of
picking any one of these 12.

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Now which of these 12
are a multiple of 5?

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So let's do this in
a different color.

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So let me pick out
the multiples of 5.

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32 is not a multiple of 5,
49 is not a multiple of 5.

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55 is a multiple of 5.

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Really, we're just
looking for the numbers

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that in the ones place you
either have a 5 or a 0.

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55 is a multiple of
5, 30 is a multiple

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of 5, that's 6 times 5.

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55 is 11 times 5.

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Not 56, not 28.

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This is clearly 5 times
10, this is 8 times 5,

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this is the same number
again, also 8 times 5.

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So all of these
are multiples of 5.

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45, that's 9 times 5.

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3 is not a multiple of 5.

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25, clearly 5 times 5.

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So I've circled all
the multiples of 5.

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So of all the
possibilities, the ones that

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meet our constraint of
being a multiple of 5,

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there are 1, 2, 3, 4,
5, 6, 7 possibilities.

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So 7 meet our constraint.

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So in this example,
the probability

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of a selecting a number that
is a multiple of 5 is 7/12.

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Let's do another one.

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the circumference of
a circle is 36 pi.

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Let's draw this circle.

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The circumference of
a circle is 36 pi,

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so let's say the
circle looks-- I

00:05:07.970 --> 00:05:10.080
can draw a neater
circle than that.

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So let's say the circle
looks something like that.

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And its circumference--
we have to be careful

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here, they're giving
us interesting--

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the circumference is 36 pi.

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Then they tell us that
contained in that circle

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is a smaller circle
with area 16 pi.

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So inside the bigger circle,
we have a smaller circle

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that has an area of 16 pi.

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A point is selected at random
from inside the larger circle,

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so we're going to
randomly select

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some point in this
larger circle.

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What is the probability
that the point also

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lies in this smaller circle?

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So here's a little
bit interesting,

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because you actually have
an infinite number of points

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in both of these
circles, because it's not

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kind of a separate
balls or marbles,

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like we saw in the first
example, or separate numbers.

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There's actually
an infinite number

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of points you could pick here.

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And so, when we talk
about the probability

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that the point also lies
in the smaller circle,

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we're really thinking about
the percentage of the points

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in the larger circle that are
also in the smaller circle.

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Or another way to think
about it is the probability

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that if we pick a point
from this larger circle,

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the probably that it's
also in the smaller circle

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is really just going to be
the percentage of the larger

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circle that is the
smaller circle.

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I know that might
sound confusing,

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but we're really just
have to figure out

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the areas for both of them,
and it's really just going

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to be the ratios so
let's think about that.

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So there's a temptation to
just use this 36 pi up here,

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but we have to remember,
this was the circumference,

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and we need to figure out the
area of both of these circles.

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And so for area, we
need to know the radius,

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because area is pi r squared.

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So we can figure
out the radius from

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the circumference by saying,
well, circumference is equal

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to 2 times pi times the
radius of the circle.

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Or if you say 36 pi, which we
were told is the circumference,

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is equal to 2 times
pi times the radius,

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we can divide both sides by 2
pi, and on the left hand side,

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36 divided by 2 is 18
the pi's cancel out,

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we get our radius as being equal
to 18 for this larger circle.

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So if we want to know
its area, its area

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is going to be pi
r squared, which

00:07:31.810 --> 00:07:36.075
is equal to pi times 18 squared.

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And let's figure out
what 18 squared is.

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18 times 18, 8 times
8 is 64, eight times 1

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is 8 plus 6 is 14,
and then we put

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that 0 there because we're now
in the tens place, 1 times 8

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is 8, 1 times 1 is 1.

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And really, this is
a 10 times the 10,

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and that's why it gives us 100.

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Anyway, 4 plus 0 is a
4, 4 plus 8 is a 12,

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and then 1 plus 1 plus
1 is a 3, so it's 324.

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So the area here is
equal to pi times 324,

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or we could say 324 pi.

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So the area of the entire
larger circle, the part

00:08:21.870 --> 00:08:23.830
that I shaded in
yellow, including

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what's kind of under
this orange circle,

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if you want to view it that
way, this area right over here

00:08:29.090 --> 00:08:33.230
is equal to 324 pi.

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So the probability that a point
that we select from this larger

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circle is also in
the smaller circle

00:08:40.530 --> 00:08:42.669
is really just a
percentage of the larger

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circle that is the
smaller circle.

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So our probability--
I'll just write it

00:08:47.140 --> 00:08:51.940
like this-- the probability
that the point also

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lies in the smaller circle--
so all of that stuff

00:08:54.146 --> 00:08:54.770
I'll put in it.

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The probability of
that is going to be

00:08:56.810 --> 00:08:59.840
equal to the percentage
of this larger circle that

00:08:59.840 --> 00:09:02.197
is this smaller one,
and that's going to be--

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or we could say the fraction
of the larger circle's area

00:09:04.530 --> 00:09:06.620
that is the smaller
circle's area.

00:09:06.620 --> 00:09:11.990
So it's going to be
16 pi over 324 pi.

00:09:15.580 --> 00:09:19.760
And the pi's cancel out, and
it looks like both of them

00:09:19.760 --> 00:09:21.360
are divisible by 4.

00:09:21.360 --> 00:09:24.000
If we divide the
numerator by 4, we get 4,

00:09:24.000 --> 00:09:27.220
if we divide the denominator
by 4, what do we get?

00:09:27.220 --> 00:09:31.250
4 goes into 320 80 times,
it goes into 4 once,

00:09:31.250 --> 00:09:32.900
so we get an 81.

00:09:32.900 --> 00:09:35.450
So a probability--
I didn't even draw

00:09:35.450 --> 00:09:37.910
this to scale, this area is
actually much smaller when you

00:09:37.910 --> 00:09:42.127
do it to scale-- the probability
that if you were to randomly

00:09:42.127 --> 00:09:43.710
select a point from
the larger circle,

00:09:43.710 --> 00:09:45.750
that it also lies
in the smaller one

00:09:45.750 --> 00:09:48.400
is the ratio of their areas,
the ratio of the smaller

00:09:48.400 --> 00:09:50.130
circle to the larger one.

00:09:50.130 --> 00:09:56.080
And that is 4/81, I guess
is the best way to say it.


Acute right and obtuse angles

WEBVTT
Kind: captions
Language: en

00:00:00.285 --> 00:00:01.660
In this video, I
really just want

00:00:01.660 --> 00:00:03.280
to introduce you
to some terminology

00:00:03.280 --> 00:00:06.380
for some basic angle types.

00:00:06.380 --> 00:00:09.010
And the terminology I
want to introduce you to

00:00:09.010 --> 00:00:20.410
are acute angles, right
angles, and obtuse angles.

00:00:20.410 --> 00:00:22.190
And I think when we
just go through these,

00:00:22.190 --> 00:00:24.660
they'll be pretty
self-explanatory.

00:00:24.660 --> 00:00:28.380
An acute angle is an
angle-- well, let me just

00:00:28.380 --> 00:00:29.210
draw them first.

00:00:29.210 --> 00:00:32.229
Then it might start
to make sense.

00:00:32.229 --> 00:00:34.510
So an acute angle will
look something like that.

00:00:34.510 --> 00:00:38.850
I draw two rays that are
coming from a common point.

00:00:38.850 --> 00:00:42.070
So the acute angle will be
this angle right over here.

00:00:42.070 --> 00:00:44.590
I could also draw an
acute angle, maybe

00:00:44.590 --> 00:00:48.160
an angle that's formed from
the intersection of two lines.

00:00:48.160 --> 00:00:51.200
This angle will be acute,
and so will this angle.

00:00:51.200 --> 00:00:52.894
They're both acute angles.

00:00:52.894 --> 00:00:55.060
And we're going to see is
acute angles are ones that

00:00:55.060 --> 00:00:58.120
are-- since I haven't defined
right angles yet-- they're

00:00:58.120 --> 00:00:58.620
narrower.

00:00:58.620 --> 00:01:00.411
And what we're going
to see is that they're

00:01:00.411 --> 00:01:01.760
smaller than right angles.

00:01:01.760 --> 00:01:07.770
Right angles are when the
rays or the lines are going,

00:01:07.770 --> 00:01:11.520
I guess, in the-- I don't
want to use the word, right,

00:01:11.520 --> 00:01:15.650
in my definition-- but if
one is going horizontal,

00:01:15.650 --> 00:01:17.457
the other one will
be going vertical.

00:01:17.457 --> 00:01:19.040
So let me draw it
with the rays first.

00:01:19.040 --> 00:01:21.410
So the right angle, this
one's going from the left

00:01:21.410 --> 00:01:22.220
to the right.

00:01:22.220 --> 00:01:25.570
Then the other ray is going
from the bottom to the top.

00:01:25.570 --> 00:01:28.330
This angle right over
here is a right angle.

00:01:28.330 --> 00:01:31.670
And I could label it like
that, as a traditional angle.

00:01:31.670 --> 00:01:35.560
But the general convention
for labeling right angles

00:01:35.560 --> 00:01:38.940
is to put a little, kind of a
half of a box right over there.

00:01:38.940 --> 00:01:45.080
And that means that
is a right angle.

00:01:45.080 --> 00:01:47.770
Or that if this is
going left to right,

00:01:47.770 --> 00:01:49.910
this is going perfectly
top to bottom,

00:01:49.910 --> 00:01:54.360
that this is in no way kind of--
I guess the best way to think

00:01:54.360 --> 00:01:56.150
about it and why
it's called right

00:01:56.150 --> 00:02:00.140
is that this ray is
completely upright, compared

00:02:00.140 --> 00:02:02.130
to this ray over here.

00:02:02.130 --> 00:02:03.860
And let me draw it
with some lines.

00:02:03.860 --> 00:02:07.090
So if I have one line
like this and then I

00:02:07.090 --> 00:02:10.500
have another line like
that, a right angle

00:02:10.500 --> 00:02:12.230
over here-- actually
all of these

00:02:12.230 --> 00:02:15.090
would have to be right angles--
it would mean that this line is

00:02:15.090 --> 00:02:16.860
completely-- if
this was the ground,

00:02:16.860 --> 00:02:20.590
this line is completely
upright, relative to this line

00:02:20.590 --> 00:02:21.090
over here.

00:02:21.090 --> 00:02:24.010
So either of these, that's
what a right angle means.

00:02:24.010 --> 00:02:25.860
And now that we've
defined right angle,

00:02:25.860 --> 00:02:28.400
I can give you another
definition for an acute angle.

00:02:28.400 --> 00:02:32.250
An acute angle has a
measure, or it's smaller,

00:02:32.250 --> 00:02:34.080
than a right angle.

00:02:34.080 --> 00:02:36.710
When you learn about
radians and degrees, which

00:02:36.710 --> 00:02:38.510
are different ways
to measure angles,

00:02:38.510 --> 00:02:42.950
you'll see that a right angle
can be measured as 90 degrees.

00:02:42.950 --> 00:02:46.070
This over here is
less than 90 degrees.

00:02:46.070 --> 00:02:49.180
So this is less than 90 degrees.

00:02:49.180 --> 00:02:50.690
And one way to
conceptualize this

00:02:50.690 --> 00:02:57.570
is that this angle, its opening
is smaller, it's more narrow,

00:02:57.570 --> 00:03:01.520
the lines are-- you would
have to rotate one line less

00:03:01.520 --> 00:03:03.650
to get to the other line
than you would over here.

00:03:03.650 --> 00:03:06.130
Here, you'd have to move
it all the way over there.

00:03:06.130 --> 00:03:08.180
Here, you'd only have
to move it a little bit.

00:03:08.180 --> 00:03:10.950
So the acute angle is
less than a right angle.

00:03:10.950 --> 00:03:14.180
And so you might imagine
already what an obtuse angle is.

00:03:14.180 --> 00:03:16.370
It is greater than
a right angle.

00:03:16.370 --> 00:03:19.500
So let me draw a couple of
examples of obtuse angles.

00:03:19.500 --> 00:03:24.440
So an obtuse angle
might look like-- let

00:03:24.440 --> 00:03:25.930
me make it a little bit clearer.

00:03:25.930 --> 00:03:28.850
It might look like that.

00:03:28.850 --> 00:03:31.730
If this was a right
angle, this line over here

00:03:31.730 --> 00:03:33.550
would look something like that.

00:03:33.550 --> 00:03:35.940
It would be completely
upright relative to this

00:03:35.940 --> 00:03:37.120
if this were the ground.

00:03:37.120 --> 00:03:38.680
But we don't see that.

00:03:38.680 --> 00:03:43.130
This orange ray over here is
actually opened out wider.

00:03:43.130 --> 00:03:44.930
It's opened up wider.

00:03:44.930 --> 00:03:48.910
So it is obtuse.

00:03:48.910 --> 00:03:51.860
And this kind of comes from
the actual everyday meaning.

00:03:51.860 --> 00:03:54.910
Acute means very sharp
or very sensitive.

00:03:54.910 --> 00:03:57.940
Obtuse means not very sharp
or not very sensitive.

00:03:57.940 --> 00:04:01.800
So you could imagine this looks
like a sharp point or it's not

00:04:01.800 --> 00:04:05.510
opening up much, so maybe
it's more sensitive relative

00:04:05.510 --> 00:04:06.960
to other things,
or I don't know.

00:04:06.960 --> 00:04:08.590
I'm just trying to
make connections.

00:04:08.590 --> 00:04:10.040
This is less sensitive.

00:04:10.040 --> 00:04:11.380
It's all big and open.

00:04:11.380 --> 00:04:12.960
It won't be able
to notice things

00:04:12.960 --> 00:04:15.070
that are small
because I don't know.

00:04:15.070 --> 00:04:17.930
Maybe that's not an
appropriate analogy.

00:04:17.930 --> 00:04:21.019
But one way to think about it,
it's kind of open up wider,

00:04:21.019 --> 00:04:23.260
or it's bigger
than a right angle.

00:04:23.260 --> 00:04:27.820
It's larger than 90
degrees if you measure it.

00:04:27.820 --> 00:04:30.000
You would have to
rotate this ray more

00:04:30.000 --> 00:04:34.220
to get to this other ray
than you would if they were

00:04:34.220 --> 00:04:36.280
right angles, and
definitely a lot more than

00:04:36.280 --> 00:04:37.860
if they were acute angles.

00:04:37.860 --> 00:04:43.580
If I were to draw this with
lines, which of the angles

00:04:43.580 --> 00:04:45.250
are obtuse and which are acute?

00:04:45.250 --> 00:04:47.400
Well, the way I've drawn
them right over here,

00:04:47.400 --> 00:04:53.720
these two over here are acute,
and then these over here

00:04:53.720 --> 00:04:54.760
are going to be obtuse.

00:04:54.760 --> 00:05:00.860
This one and this one, these
are both obtuse angles.

00:05:00.860 --> 00:05:02.980
And I actually drew
it up here, as well.

00:05:02.980 --> 00:05:08.160
This one and this one
are going to be obtuse.

00:05:08.160 --> 00:05:11.460
So very simple idea.

00:05:11.460 --> 00:05:14.250
If one line or one ray
relative to the other one

00:05:14.250 --> 00:05:16.540
is straight up and down,
versus to left and right,

00:05:16.540 --> 00:05:18.560
or is completely
upright, then we're

00:05:18.560 --> 00:05:20.146
talking about a right angle.

00:05:20.146 --> 00:05:21.770
If they're closer to
each other, if you

00:05:21.770 --> 00:05:24.353
have to rotate them less, you're
talking about an acute angle.

00:05:24.353 --> 00:05:26.001
If you have to rotate
them more, you're

00:05:26.001 --> 00:05:27.250
talking about an obtuse angle.

00:05:27.250 --> 00:05:29.249
And I think when you just
look at them visually,

00:05:29.249 --> 00:05:32.330
it's pretty easy to pick out.


Cylinder volume and surface area

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.670
Let's find the volume of
a few more solid figures

00:00:02.670 --> 00:00:04.370
and then if we
have time, we might

00:00:04.370 --> 00:00:06.520
be able to do some
surface area problems.

00:00:06.520 --> 00:00:08.940
So let me draw a
cylinder over here.

00:00:08.940 --> 00:00:11.310
So that is the top
of my cylinder.

00:00:11.310 --> 00:00:14.910
And then this is the
height of my cylinder.

00:00:14.910 --> 00:00:16.710
This is the bottom
right over here.

00:00:16.710 --> 00:00:18.250
If this was
transparent, maybe you

00:00:18.250 --> 00:00:20.960
could see the back
side of the cylinder.

00:00:20.960 --> 00:00:23.490
So you could imagine this
kind of looks like a soda can.

00:00:23.490 --> 00:00:30.220
And let's say that the height of
my cylinder, h, is equal to 8.

00:00:30.220 --> 00:00:31.450
I'll give it some units.

00:00:31.450 --> 00:00:34.750
8 centimeters,
that is my height.

00:00:34.750 --> 00:00:37.370
And then let's say
that the radius of one

00:00:37.370 --> 00:00:40.930
of the top of my
cylinder of my soda can,

00:00:40.930 --> 00:00:45.030
let's say that this radius over
here is equal to 4 centimeters.

00:00:45.030 --> 00:00:47.620
So what is the volume here?

00:00:47.620 --> 00:00:51.100
What is the volume going to be?

00:00:51.100 --> 00:00:54.046
And the idea here is
really the exact same thing

00:00:54.046 --> 00:00:55.920
that we saw in some of
the previous problems.

00:00:55.920 --> 00:00:58.550
If you can find the
surface area of one side

00:00:58.550 --> 00:01:00.860
and then figure out
how deep it goes,

00:01:00.860 --> 00:01:02.630
you'll be able to
figure out the volume.

00:01:02.630 --> 00:01:04.463
So what we're going to
do here is figure out

00:01:04.463 --> 00:01:08.120
the surface area of the
top of this cylinder,

00:01:08.120 --> 00:01:10.510
or the top of the soda can.

00:01:10.510 --> 00:01:12.720
And then we're going to
multiply it by its height.

00:01:12.720 --> 00:01:13.970
And that'll give us a volume.

00:01:13.970 --> 00:01:15.594
This will tell us
essentially, how many

00:01:15.594 --> 00:01:17.640
square centimeters
fit in this top.

00:01:17.640 --> 00:01:20.950
And then if we multiply
that by how many centimeters

00:01:20.950 --> 00:01:23.190
we go down, then that'll
give us the number

00:01:23.190 --> 00:01:27.790
of cubic centimeters in
this cylinder or soda can.

00:01:27.790 --> 00:01:30.477
So how do we figure
out this area up here?

00:01:30.477 --> 00:01:32.060
Well the area at the
top, this is just

00:01:32.060 --> 00:01:33.570
finding the area of a circle.

00:01:33.570 --> 00:01:36.820
You could imagine
drawing it like this.

00:01:36.820 --> 00:01:38.570
If we were to just
look at it straight on,

00:01:38.570 --> 00:01:42.460
that's a circle with a
radius of 4 centimeters.

00:01:42.460 --> 00:01:45.810
The area of a circle with a
radius 4 centimeters, area

00:01:45.810 --> 00:01:48.070
is equal to pi r squared.

00:01:48.070 --> 00:01:51.580
So it's going to be pi
times the radius squared,

00:01:51.580 --> 00:01:55.940
times 4 centimeters squared,
which is equal to 4 squared,

00:01:55.940 --> 00:01:58.970
is 16, times pi.

00:01:58.970 --> 00:02:03.690
And our units now are going
to be centimeters squared.

00:02:03.690 --> 00:02:06.390
Or another way to think of
these are square centimeters.

00:02:06.390 --> 00:02:07.630
So that's the area.

00:02:07.630 --> 00:02:11.460
The volume is going to be
this area times the height.

00:02:11.460 --> 00:02:16.480
So the volume is going
to be equal to 16 pi

00:02:16.480 --> 00:02:24.486
centimeters squared, times the
height, times 8 centimeters.

00:02:29.900 --> 00:02:32.540
And so, when you
do multiplication,

00:02:32.540 --> 00:02:34.420
the associative
property, you can kind of

00:02:34.420 --> 00:02:36.700
rearrange these things, and
the commutative property.

00:02:36.700 --> 00:02:38.716
It doesn't matter
what order you do it

00:02:38.716 --> 00:02:39.840
if it's all multiplication.

00:02:39.840 --> 00:02:42.690
So this is the same
thing as 16 times 8.

00:02:42.690 --> 00:02:43.190
Let's see.

00:02:43.190 --> 00:02:44.400
8 times 8 is 64.

00:02:44.400 --> 00:02:45.860
16 times 8 is twice that.

00:02:45.860 --> 00:02:50.360
So it's going to be 128 pi.

00:02:50.360 --> 00:02:53.060
Now you have centimeter
squared times centimeters.

00:02:53.060 --> 00:02:56.430
So that gives us
centimeters cubed.

00:02:56.430 --> 00:02:59.130
Or 128 pi cubic centimeters.

00:02:59.130 --> 00:03:01.220
Remember, pi is just a number.

00:03:01.220 --> 00:03:03.130
We write it as pi,
because it's kind

00:03:03.130 --> 00:03:06.770
of a crazy, irrational number,
that if you were to write it,

00:03:06.770 --> 00:03:08.490
you could never
completely write pi.

00:03:08.490 --> 00:03:13.010
3.14159 keeps going
on, never a repeat.

00:03:13.010 --> 00:03:14.550
So we just leave it as pi.

00:03:14.550 --> 00:03:17.091
But if you wanted to figure it
out, you can get a calculator.

00:03:17.091 --> 00:03:20.020
And this would be 3.14
roughly, times 128.

00:03:20.020 --> 00:03:25.230
So it would be close to
400 cubic centimeters.

00:03:25.230 --> 00:03:28.390
Now, how would we
find the surface area?

00:03:28.390 --> 00:03:32.350
How would we find the surface
area of this figure over here?

00:03:32.350 --> 00:03:34.890
Well, part of the surface area
of the two surfaces, the top

00:03:34.890 --> 00:03:35.540
and the bottom.

00:03:35.540 --> 00:03:39.430
So that would be part
of the surface area.

00:03:39.430 --> 00:03:41.600
And then the bottom
over here would also

00:03:41.600 --> 00:03:44.650
be part of the surface area.

00:03:44.650 --> 00:03:51.490
So if we're trying to
find the surface area,

00:03:51.490 --> 00:03:54.520
it's definitely going to have
both of these areas here.

00:03:54.520 --> 00:03:57.990
So it's going to have the 16
pi centimeters squared twice.

00:03:57.990 --> 00:03:59.470
This is 16 pi.

00:03:59.470 --> 00:04:01.920
This is 16 pi
square centimeters.

00:04:01.920 --> 00:04:06.670
So it's going to have 2 times
16 pi centimeters squared.

00:04:06.670 --> 00:04:08.520
I'll keep the units still.

00:04:08.520 --> 00:04:11.432
So that covers the top and
the bottom of our soda can.

00:04:11.432 --> 00:04:13.140
And now we have to
figure out the surface

00:04:13.140 --> 00:04:15.050
area of this thing
that goes around.

00:04:15.050 --> 00:04:16.820
And the way I imagine
it is, imagine

00:04:16.820 --> 00:04:19.170
if you're trying to wrap this
thing with wrapping paper.

00:04:19.170 --> 00:04:22.019
So let me just draw a
little dotted line here.

00:04:22.019 --> 00:04:24.130
So imagine if you were
to cut it just like that.

00:04:24.130 --> 00:04:25.730
Cut the side of the soda can.

00:04:25.730 --> 00:04:30.540
And if you were to
unwind this thing that

00:04:30.540 --> 00:04:32.830
goes around it,
what would you have.

00:04:32.830 --> 00:04:34.890
Well, you would have something.

00:04:34.890 --> 00:04:36.850
You would end up
with a sheet of paper

00:04:36.850 --> 00:04:40.170
where this length
right over here

00:04:40.170 --> 00:04:42.560
is the same thing as
this length over here.

00:04:42.560 --> 00:04:45.430
And then it would be
completely unwound.

00:04:45.430 --> 00:04:47.710
And then these two
ends-- let me do it

00:04:47.710 --> 00:04:52.040
in magenta-- these two ends
used to touch each other.

00:04:52.040 --> 00:04:54.680
And-- I'm going to do it in a
color that I haven't used yet,

00:04:54.680 --> 00:04:57.380
I'll do it in pink--
these two ends used

00:04:57.380 --> 00:04:59.940
to touch each other when
it was all rolled together.

00:04:59.940 --> 00:05:02.780
And they used to touch each
other right over there.

00:05:02.780 --> 00:05:05.100
So the length of this
side and that side

00:05:05.100 --> 00:05:09.320
is going to be the same thing
as the height of my cylinder.

00:05:09.320 --> 00:05:11.660
So this is going to
be 8 centimeters.

00:05:11.660 --> 00:05:14.850
And then this over here is
also going to be 8 centimeters.

00:05:14.850 --> 00:05:16.290
And so the question
we need to ask

00:05:16.290 --> 00:05:21.430
ourselves is, what is
going to be this dimension

00:05:21.430 --> 00:05:23.027
right over here.

00:05:23.027 --> 00:05:24.860
And remember, that
dimension is essentially,

00:05:24.860 --> 00:05:28.382
how far did we go
around the cylinder.

00:05:28.382 --> 00:05:29.840
Well, if you think
about it, that's

00:05:29.840 --> 00:05:32.980
going to be the exact same
thing as the circumference

00:05:32.980 --> 00:05:36.240
of either the top or the
bottom of the cylinder.

00:05:36.240 --> 00:05:37.950
So what is the circumference?

00:05:37.950 --> 00:05:39.689
The circumference
of this circle right

00:05:39.689 --> 00:05:41.980
over here, which is the same
thing as the circumference

00:05:41.980 --> 00:05:47.110
of that circle over there, it
is 2 times the radius times pi.

00:05:47.110 --> 00:05:49.890
Or 2 pi times the radius.

00:05:49.890 --> 00:05:57.460
2 pi times 4 centimeters, which
is equal to 8 pi centimeters.

00:05:57.460 --> 00:06:00.230
So this distance right over
here is the circumference

00:06:00.230 --> 00:06:02.780
of either the top or the
bottom of the cylinder.

00:06:02.780 --> 00:06:06.440
It's going to be
8 pi centimeters.

00:06:06.440 --> 00:06:07.890
So if you want to
find the surface

00:06:07.890 --> 00:06:09.780
area of just the wrapping,
just the part that

00:06:09.780 --> 00:06:13.380
goes around the cylinder,
not the top or the bottom,

00:06:13.380 --> 00:06:16.580
when you unwind it, it's going
to look like this rectangle.

00:06:16.580 --> 00:06:19.790
And so its area, the
area of just that part,

00:06:19.790 --> 00:06:22.300
is going to be equal to
8 centimeters times 8 pi

00:06:22.300 --> 00:06:23.389
centimeters.

00:06:23.389 --> 00:06:24.430
So let me do it this way.

00:06:24.430 --> 00:06:31.880
It's going to be 8 centimeters
times 8 pi centimeters.

00:06:31.880 --> 00:06:35.190
And that's equal to 64 pi.

00:06:35.190 --> 00:06:36.260
8 times 8 is 64.

00:06:36.260 --> 00:06:40.472
You have your pi
centimeters squared.

00:06:40.472 --> 00:06:42.680
So when you want the surface
area of the whole thing,

00:06:42.680 --> 00:06:44.610
you have the top,
you have the bottom,

00:06:44.610 --> 00:06:45.950
we already threw those there.

00:06:45.950 --> 00:06:47.510
And then you want to find
the area of the thing around.

00:06:47.510 --> 00:06:48.551
We just figured that out.

00:06:48.551 --> 00:06:54.470
So it's going to be plus
64 pi centimeters squared.

00:06:54.470 --> 00:06:56.770
And now we just have
to calculate it.

00:06:56.770 --> 00:07:02.580
So this gives us 2 times 16
pi, is going to be equal to 32.

00:07:02.580 --> 00:07:09.480
That is 32 pi centimeters
squared, plus 64 pi.

00:07:09.480 --> 00:07:12.400
Let me scroll over to
the right a little bit.

00:07:12.400 --> 00:07:15.240
Plus 64 pi centimeters squared.

00:07:15.240 --> 00:07:23.330
And then 32 plus 64 is 96
pi centimeters squared.

00:07:23.330 --> 00:07:26.760
So it's equal to 96 pi
square centimeters, which

00:07:26.760 --> 00:07:30.830
is going to be a little bit
over 300 square centimeters.

00:07:30.830 --> 00:07:32.890
And notice, when we
did surface area,

00:07:32.890 --> 00:07:35.920
we got our answer in terms
of square centimeters.

00:07:35.920 --> 00:07:38.610
That makes sense,
because surface area,

00:07:38.610 --> 00:07:40.430
it's a two-dimensional
measurement.

00:07:40.430 --> 00:07:42.550
Think about how many
square centimeters can we

00:07:42.550 --> 00:07:45.080
fit on the surface
of the cylinder.

00:07:45.080 --> 00:07:48.680
When we did the volume,
we got centimeters cubed,

00:07:48.680 --> 00:07:49.907
or cubic centimeters.

00:07:49.907 --> 00:07:51.740
And that's because we're
trying to calculate

00:07:51.740 --> 00:07:58.170
how many one by one
by one centimeter

00:07:58.170 --> 00:08:01.010
cubes can we fit inside
of this structure.

00:08:01.010 --> 00:08:03.210
And so that's why it's
cubic centimeters.

00:08:03.210 --> 00:08:07.180
Anyway, hopefully that clarifies
things up a little bit.


Find the volume of a triangular prism and cube

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:03.580
Let's do some solid
geometry volume problems.

00:00:03.580 --> 00:00:06.290
So they tell us, shown
is a triangular prism.

00:00:06.290 --> 00:00:08.879
And so there's a couple of types
of three-dimensional figures

00:00:08.879 --> 00:00:09.920
that deal with triangles.

00:00:09.920 --> 00:00:11.810
This is what a
triangular prism looks

00:00:11.810 --> 00:00:14.630
like, where it has a
triangle on one, two faces,

00:00:14.630 --> 00:00:15.880
and they're kind of separated.

00:00:15.880 --> 00:00:18.449
They kind of have
rectangles in between.

00:00:18.449 --> 00:00:20.740
The other types of triangular
three-dimensional figures

00:00:20.740 --> 00:00:22.600
is you might see pyramids.

00:00:22.600 --> 00:00:24.100
This would be a
rectangular pyramid,

00:00:24.100 --> 00:00:28.340
because it has a rectangular--
or it has a square base,

00:00:28.340 --> 00:00:29.470
just like that.

00:00:29.470 --> 00:00:33.410
You could also have
a triangular pyramid,

00:00:33.410 --> 00:00:37.350
which it's just literally
every side is a triangle.

00:00:37.350 --> 00:00:38.150
So stuff like that.

00:00:38.150 --> 00:00:39.858
But this over here is
a triangular prism.

00:00:39.858 --> 00:00:42.970
I don't want to get too much
into the shape classification.

00:00:42.970 --> 00:00:46.820
If the base of the
triangle b is equal to 7,

00:00:46.820 --> 00:00:50.110
the height of the
triangle h is equal to 3,

00:00:50.110 --> 00:00:53.230
and the length of the
prism l is equal to 4,

00:00:53.230 --> 00:00:56.384
what is the total
volume of the prism?

00:00:56.384 --> 00:00:58.300
So they're saying that
the base is equal to 7.

00:00:58.300 --> 00:01:03.960
So this base, this right
over here is equal to 7.

00:01:03.960 --> 00:01:05.800
The height of the
triangle is equal to 3.

00:01:05.800 --> 00:01:09.730
So this right over here, this
distance right over here,

00:01:09.730 --> 00:01:12.540
h, is equal to 3.

00:01:12.540 --> 00:01:15.300
And the length of the
prism is equal to 4.

00:01:15.300 --> 00:01:17.680
So I'm assuming it's
this dimension over here

00:01:17.680 --> 00:01:19.210
is equal to 4.

00:01:19.210 --> 00:01:22.070
So length is equal to 4.

00:01:22.070 --> 00:01:24.350
So in this situation, what
you really just have to do

00:01:24.350 --> 00:01:27.610
is figure out the area of
this triangle right over here.

00:01:27.610 --> 00:01:29.830
We could figure out the
area of this triangle

00:01:29.830 --> 00:01:32.490
and then multiply it by
how much you go deep,

00:01:32.490 --> 00:01:34.790
so multiply it by this length.

00:01:34.790 --> 00:01:37.416
So the volume is going to be
the area of this triangle-- let

00:01:37.416 --> 00:01:39.290
me do it in pink-- the
area of this triangle.

00:01:39.290 --> 00:01:41.180
We know that the
area of a triangle

00:01:41.180 --> 00:01:44.590
is 1/2 times the base
times the height.

00:01:44.590 --> 00:01:47.530
So this area right
over here is going

00:01:47.530 --> 00:01:52.172
to be 1/2 times the
base times the height.

00:01:52.172 --> 00:01:53.630
And then we're
going to multiply it

00:01:53.630 --> 00:01:56.590
by our depth of this
triangular prism.

00:01:56.590 --> 00:01:58.500
So we have a depth of 4.

00:01:58.500 --> 00:02:01.890
So then we're going to
multiply that times the 4,

00:02:01.890 --> 00:02:02.970
times this depth.

00:02:05.680 --> 00:02:08.919
And we get-- let's
see, 1/2 times 4 is 2.

00:02:08.919 --> 00:02:10.580
So these guys cancel out.

00:02:10.580 --> 00:02:11.780
You'll just have a 2.

00:02:11.780 --> 00:02:13.835
And then 2 times 3 is 6.

00:02:13.835 --> 00:02:18.450
6 times 7 is 42.

00:02:18.450 --> 00:02:20.459
And it would be in some
type of cubic units.

00:02:20.459 --> 00:02:22.500
So if these were in-- I
don't know-- centimeters,

00:02:22.500 --> 00:02:23.750
it would be centimeters cubed.

00:02:23.750 --> 00:02:26.610
But they're not making us focus
on the units in this problem.

00:02:26.610 --> 00:02:28.580
Let's do another one.

00:02:28.580 --> 00:02:30.440
Shown is a cube.

00:02:30.440 --> 00:02:37.090
If each side is of
equal length x equals 3,

00:02:37.090 --> 00:02:38.890
what is the total
volume of the cube?

00:02:38.890 --> 00:02:42.680
So each side is equal length
x, which happens to equal 3.

00:02:42.680 --> 00:02:44.540
So this side is 3.

00:02:44.540 --> 00:02:46.910
This side over here,
x is equal to 3.

00:02:46.910 --> 00:02:48.900
Every side, x is equal to 3.

00:02:48.900 --> 00:02:50.400
So it's actually
the same exercise

00:02:50.400 --> 00:02:51.465
as the triangular prism.

00:02:51.465 --> 00:02:52.840
It's actually a
little bit easier

00:02:52.840 --> 00:02:54.965
when you're dealing with
the cube, where you really

00:02:54.965 --> 00:02:58.500
just want to find the area of
this surface right over here.

00:02:58.500 --> 00:03:00.250
Now, this is pretty
straightforward.

00:03:00.250 --> 00:03:02.350
This is just a
square, or it would

00:03:02.350 --> 00:03:03.930
be the base times the height.

00:03:03.930 --> 00:03:06.630
Or essentially the same,
it's just 3 times 3.

00:03:06.630 --> 00:03:10.180
So the volume is going to be the
area of this surface, 3 times

00:03:10.180 --> 00:03:12.575
3, times the depth.

00:03:15.980 --> 00:03:21.060
And so we go 3 deep, so times 3.

00:03:21.060 --> 00:03:24.430
And so we get 3 times
3 times 3, which is 27.

00:03:24.430 --> 00:03:26.840
Or you might recognize
this from exponents.

00:03:26.840 --> 00:03:29.270
This is the same thing
as 3 to the third power.

00:03:29.270 --> 00:03:31.300
And that's why sometimes,
if you have something

00:03:31.300 --> 00:03:34.490
to the third power,
they'll say you cubed it.

00:03:34.490 --> 00:03:36.740
Because, literally, to
find the volume of a cube,

00:03:36.740 --> 00:03:40.050
you take the length of one side,
and you multiply that number

00:03:40.050 --> 00:03:43.680
by itself three times, one
for each dimension-- one

00:03:43.680 --> 00:03:46.850
for the length, the
width, and-- or I

00:03:46.850 --> 00:03:49.172
guess the height, the
length, and the depth,

00:03:49.172 --> 00:03:50.880
depending on how you
want to define them.

00:03:50.880 --> 00:03:55.344
So it's literally just
3 times 3 times 3.


Alternative minimum tax

WEBVTT
Kind: captions
Language: en

00:00:00.204 --> 00:00:02.094
Let's see if we can shed some light on the

00:00:02.094 --> 00:00:06.603
Alternative Minimum Tax,
which is also one of the most

00:00:06.603 --> 00:00:10.137
confusing aspects of taxation in the U.S.,

00:00:10.137 --> 00:00:13.563
but hopefully this video will
clarify things a little bit.

00:00:13.563 --> 00:00:15.735
So let's go back to that
example from the first video

00:00:15.735 --> 00:00:18.005
of the person making $100,000

00:00:18.005 --> 00:00:20.395
and what I'm going to do
is I'm going to calculate

00:00:20.395 --> 00:00:24.337
the AMT, the Alternative
Minimum Tax for that person

00:00:24.337 --> 00:00:26.813
then we're going to see
what happens from there.

00:00:26.813 --> 00:00:30.270
So Alternative Minium Tax
for someone making $100,000,

00:00:30.270 --> 00:00:32.403
so what I've drawn right over here,

00:00:32.403 --> 00:00:36.145
this applies if you
make less than $300,000.

00:00:36.145 --> 00:00:39.403
The first 47,000 or so is exempt

00:00:39.403 --> 00:00:42.069
when you're calculating the
Alternative Minimum Tax.

00:00:42.069 --> 00:00:45.003
So for this person making $100,000,

00:00:45.003 --> 00:00:46.315
we're just going to have to consider

00:00:46.315 --> 00:00:49.603
the balance above 47,450.

00:00:49.603 --> 00:00:55.070
So 100,000 - 47,450, would be what?

00:00:55.070 --> 00:01:00.070
It would be 50 ... It would
be 52,000 ... Let's see,

00:01:00.070 --> 00:01:02.937
this would be ... So this amount
right over here is going to be

00:01:02.937 --> 00:01:13.671
52,000 and then 6 or 550 ...
52,550, if I did my math correct.

00:01:13.671 --> 00:01:18.205
That's 100,000 - 47,450

00:01:18.205 --> 00:01:20.403
and what the Alternative
Minimum Tax says is

00:01:20.403 --> 00:01:22.603
whatever you are above this exemption,

00:01:22.603 --> 00:01:25.603
above this 47,450 exemption,

00:01:25.603 --> 00:01:30.069
you're just going to pay
a flat 26% on that amount

00:01:30.069 --> 00:01:33.470
and if this person had made over 175,000,

00:01:33.470 --> 00:01:35.269
it would have been a flat 28%,

00:01:35.269 --> 00:01:36.737
but let's not go there,
just complicates things

00:01:36.737 --> 00:01:39.647
and these things can get
arbitrarily complicated.

00:01:39.647 --> 00:01:42.005
And if the person made over 300,000,

00:01:42.005 --> 00:01:43.812
they would have to use the 28%

00:01:43.812 --> 00:01:46.736
and this 0, this
exemption would disappear,

00:01:46.736 --> 00:01:48.270
but once again, let's
not over complicate it.

00:01:48.270 --> 00:01:49.980
Let's just focus on this person.

00:01:49.980 --> 00:01:54.146
So this person has to pay 26% of 52,550

00:01:54.146 --> 00:02:06.563
which would be ... So it is
.26 x 52,550 gives 13,663.

00:02:06.563 --> 00:02:16.561
So 13,663. That is equal to 52,550 x 26%.

00:02:16.561 --> 00:02:18.752
So this would be the
Alternative ... Alternative

00:02:18.752 --> 00:02:21.204
Minimum Tax calculation, this 13,000.

00:02:21.204 --> 00:02:23.136
You're like, "Okay, that's not so bad."

00:02:23.136 --> 00:02:25.716
"Do I pay this above
and beyond the 21,000"

00:02:25.716 --> 00:02:27.559
"that we calculated in the first video?"

00:02:27.559 --> 00:02:30.628
"You know, how does this work
out?", and the answer is no.

00:02:30.628 --> 00:02:33.506
You ... The IRS or your
accountant would look at

00:02:33.506 --> 00:02:35.270
both of these numbers and you would pay

00:02:35.270 --> 00:02:37.269
the higher of the two.

00:02:37.269 --> 00:02:39.842
So in this situation, your
regular taxes are higher

00:02:39.842 --> 00:02:41.645
than your Alerternative Minimum Tax,

00:02:41.645 --> 00:02:44.008
so you would just pay your regular taxes.

00:02:44.008 --> 00:02:47.646
Now this does come into
play in situations where

00:02:47.646 --> 00:02:50.197
1) if someone is making
a ton of money, the AMT

00:02:50.197 --> 00:02:51.936
is probably going to be the larger number,

00:02:51.936 --> 00:02:54.337
but in general it would
be the larger number

00:02:54.337 --> 00:02:56.284
if this person has a lot of deductions.

00:02:56.284 --> 00:02:59.270
So let's say they made $100,000,
but they're able to take

00:02:59.270 --> 00:03:03.028
ten grand off because they
have ... They have mortgage

00:03:03.028 --> 00:03:04.319
interest that they can deduct,

00:03:04.319 --> 00:03:06.736
so maybe they have all sorts
of other crazy deductions.

00:03:06.736 --> 00:03:10.480
So that their actual reported
income to the IRS becomes,

00:03:10.480 --> 00:03:12.870
I don't know, well maybe
it becomes nothing.

00:03:12.870 --> 00:03:14.339
Maybe they're able to deduct everything.

00:03:14.339 --> 00:03:17.205
So that with the regular
taxations, it goes down ...

00:03:17.205 --> 00:03:18.736
the reported income.

00:03:18.736 --> 00:03:20.737
When I say deductions, remember,
I'm not deducting taxes,

00:03:20.737 --> 00:03:22.896
I'm reporting income. So
they're able to keep taking

00:03:22.896 --> 00:03:25.649
things off of this until eventually
... Well, I won't say nothing,

00:03:25.649 --> 00:03:29.812
maybe their reported
income becomes $8,350.

00:03:29.812 --> 00:03:34.480
In which case, the regular
taxes would only be $835.

00:03:34.480 --> 00:03:39.146
And in this situation, they
would have to pay the 13,663

00:03:39.146 --> 00:03:41.039
and that's the whole point of the AMT

00:03:41.039 --> 00:03:42.671
is because you had the
situation where people

00:03:42.671 --> 00:03:45.042
had all these deductions
and were able to get out of

00:03:45.042 --> 00:03:47.736
paying taxes even though
their income was pretty high,

00:03:47.736 --> 00:03:50.472
so they had this alternate
calculation to just make sure that

00:03:50.472 --> 00:03:54.267
people do pay some taxes.


Tax deductions introduction

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:02.670
In this video, I
now want to cover

00:00:02.670 --> 00:00:06.140
one of the other most
misunderstood ideas

00:00:06.140 --> 00:00:08.850
when people think
about taxes, and that's

00:00:08.850 --> 00:00:11.850
the idea of deductions.

00:00:11.850 --> 00:00:14.350
So, one of the most
common tax deductions

00:00:14.350 --> 00:00:18.310
is the deduction you get on
interest on your mortgage.

00:00:18.310 --> 00:00:22.020
So let's say that this year
on my mortgage-- of the part

00:00:22.020 --> 00:00:26.070
of my mortgage that is interest,
let's say it's $10,000.

00:00:26.070 --> 00:00:36.030
It is $10,000 on my
interest on my mortgage.

00:00:36.030 --> 00:00:39.640
And you'll either already
know or someone might tell you

00:00:39.640 --> 00:00:42.200
that this is tax deductible.

00:00:42.200 --> 00:00:46.050
And the misconception that
I've seen many, many times

00:00:46.050 --> 00:00:49.230
is that people think that
since this is a tax deduction,

00:00:49.230 --> 00:00:54.020
that this $10,000 should be
deducted from their taxes.

00:00:54.020 --> 00:00:56.790
So in the previous example,
we showed the scenario

00:00:56.790 --> 00:00:58.730
where this person
making $100,000

00:00:58.730 --> 00:01:02.042
would have to pay
$21,720 in taxes.

00:01:02.042 --> 00:01:03.500
And so based on
that misconception,

00:01:03.500 --> 00:01:07.310
they would say, OK, I get
a $10,000 tax deduction,

00:01:07.310 --> 00:01:10.240
now I would pay $11,720.

00:01:10.240 --> 00:01:12.470
And that is wrong.

00:01:12.470 --> 00:01:15.810
The deduction doesn't happen
from the taxes you pay.

00:01:15.810 --> 00:01:20.060
The deduction happens
from your stated income.

00:01:20.060 --> 00:01:24.060
So if this person right here
had a $10,000 tax deduction,

00:01:24.060 --> 00:01:28.180
instead of saying that they
made $100,000 that year,

00:01:28.180 --> 00:01:35.520
they would say that
they made $90,000.

00:01:35.520 --> 00:01:37.620
So once again, the
deduction does not

00:01:37.620 --> 00:01:40.280
come directly from the taxes.

00:01:40.280 --> 00:01:42.830
That would be a tax credit.

00:01:42.830 --> 00:01:46.370
The deduction comes from
the reported income.

00:01:46.370 --> 00:01:49.330
So what would be the
actual effect on the taxes?

00:01:49.330 --> 00:01:52.110
Well, we just have to
look at this $90,000.

00:01:52.110 --> 00:01:55.120
It still kind of shows
up in that top bracket.

00:01:55.120 --> 00:01:57.190
So the real difference
is just going

00:01:57.190 --> 00:01:59.170
to be this $10,000 difference.

00:01:59.170 --> 00:02:04.460
Before, he was paying
28% on this $10,000.

00:02:04.460 --> 00:02:10.560
Now he won't have to pay 28%
on that incremental $10,000.

00:02:10.560 --> 00:02:15.830
Another way to think about it,
instead of this being 17,750

00:02:15.830 --> 00:02:20.460
times 28%, it
would now be 7,750.

00:02:20.460 --> 00:02:24.830
Because the reported
income is now only $90,000.

00:02:24.830 --> 00:02:27.200
So the actual number-- we
can get our calculator out

00:02:27.200 --> 00:02:28.685
and just calculate it.

00:02:28.685 --> 00:02:30.060
There's two ways
you could do it.

00:02:30.060 --> 00:02:32.850
You could just say, look, if
I'm going to have spent 10,000--

00:02:32.850 --> 00:02:35.840
if my income is
deducted by 10,000,

00:02:35.840 --> 00:02:37.980
and I'm going to save
28% on that 10,000,

00:02:37.980 --> 00:02:40.680
you could just subtract
2,800 from this.

00:02:40.680 --> 00:02:42.360
But just to show you
how it'll all work,

00:02:42.360 --> 00:02:44.026
that it all works out
to the same thing,

00:02:44.026 --> 00:02:46.110
let's just go through the
same calculation again.

00:02:46.110 --> 00:02:55.150
We have 7,750 times
0.28 plus 48,300 times

00:02:55.150 --> 00:03:05.370
0.25 plus 25,600
times 0.15 plus $835.

00:03:05.370 --> 00:03:09.260
And it's $18,920.

00:03:09.260 --> 00:03:13.574
So now the taxes
will be $18,920.

00:03:13.574 --> 00:03:14.990
And as you can
see, the difference

00:03:14.990 --> 00:03:16.900
between the old and
the new is exactly

00:03:16.900 --> 00:03:21.510
$2,800 because that's
essentially what the amount

00:03:21.510 --> 00:03:23.790
that we would be
taxed on that $10,000

00:03:23.790 --> 00:03:26.730
if we had made that much money.

00:03:26.730 --> 00:03:29.830
Anyway, hopefully that
doesn't confuse you too much.


Fair value accounting

WEBVTT
Kind: captions
Language: en

00:00:00.650 --> 00:00:03.390
Let's say I run some type of
sheep farm, maybe some type

00:00:03.390 --> 00:00:06.240
of wool producing business.

00:00:06.240 --> 00:00:09.440
And in year one, I go out
there, I buy a bunch of sheep,

00:00:09.440 --> 00:00:10.890
and I put them on some land.

00:00:10.890 --> 00:00:14.090
And I go and I buy the
sheep for $1 million.

00:00:14.090 --> 00:00:17.020
And I buy the land
for $1.2 million.

00:00:17.020 --> 00:00:19.870
So I have $2.2
million in assets.

00:00:19.870 --> 00:00:21.520
Nothing confusing there.

00:00:21.520 --> 00:00:23.580
Now, let's go to
year two, and think

00:00:23.580 --> 00:00:27.950
about how we want to account
for the sheep and the land.

00:00:27.950 --> 00:00:29.450
So one way we could
say is, oh look,

00:00:29.450 --> 00:00:30.560
the sheep are still there.

00:00:30.560 --> 00:00:31.850
The land is still there.

00:00:31.850 --> 00:00:34.534
I paid a $1 million
for the sheep

00:00:34.534 --> 00:00:35.700
and they're all still there.

00:00:35.700 --> 00:00:40.060
So I'll put on my books that
the sheep are still $1 million.

00:00:40.060 --> 00:00:43.020
And I paid $1.2
million for the land.

00:00:43.020 --> 00:00:47.950
So I'll put on my books that
the land is $1.2 million.

00:00:47.950 --> 00:00:50.620
So in this situation,
I've accounted

00:00:50.620 --> 00:00:55.080
for the sheep and the land
based on their historical cost.

00:00:55.080 --> 00:00:56.540
So let me write this down.

00:00:56.540 --> 00:00:58.820
This is based on
historical cost.

00:01:03.260 --> 00:01:06.756
Now, this is a legitimate way to
account for things, especially

00:01:06.756 --> 00:01:08.380
if there's no other
way to really think

00:01:08.380 --> 00:01:10.660
about what my sheep
or my land are worth.

00:01:10.660 --> 00:01:12.860
I'd say, look, this is
what I paid for them.

00:01:12.860 --> 00:01:15.650
Now let's say that there is
an active market in sheep,

00:01:15.650 --> 00:01:17.930
and you can get
a sheep appraiser

00:01:17.930 --> 00:01:20.100
to come over to your
farm and tell you

00:01:20.100 --> 00:01:21.520
what your sheep are worth.

00:01:21.520 --> 00:01:23.190
And your sheep appraiser
comes and says,

00:01:23.190 --> 00:01:24.950
wow, your sheep
are looking good.

00:01:24.950 --> 00:01:27.469
There's been a big-- I
don't know-- sheep epidemic

00:01:27.469 --> 00:01:28.760
in another part of the country.

00:01:28.760 --> 00:01:30.620
So there's a sheep shortage.

00:01:30.620 --> 00:01:32.960
So your sheep are
actually worth a lot more

00:01:32.960 --> 00:01:34.670
than they were last year.

00:01:34.670 --> 00:01:38.040
And they say, I think your
sheep are now worth $2 million.

00:01:38.040 --> 00:01:40.390
So you say, hey, wow, the
market value of my sheep

00:01:40.390 --> 00:01:41.380
is $2 million.

00:01:41.380 --> 00:01:43.880
So you could say, well, instead
of putting $1 million there,

00:01:43.880 --> 00:01:44.900
let me put $2 million.

00:01:44.900 --> 00:01:47.440
Let me put $2
million for my sheep.

00:01:47.440 --> 00:01:49.500
And let's say that the
land is also appreciated.

00:01:49.500 --> 00:01:52.820
A highway's gone by
and someone wants

00:01:52.820 --> 00:01:55.160
to build a development nearby.

00:01:55.160 --> 00:01:57.900
So the fair value of your
land has also gone up,

00:01:57.900 --> 00:02:00.690
maybe it's also $2 million.

00:02:00.690 --> 00:02:01.740
So both of these.

00:02:01.740 --> 00:02:03.290
So this is $2 million.

00:02:03.290 --> 00:02:04.370
And this is $2 million.

00:02:04.370 --> 00:02:05.786
So this right over
here, you could

00:02:05.786 --> 00:02:13.300
view as the market value or
the fair value of your sheep.

00:02:13.300 --> 00:02:16.529
Now, either one of these are
legitimate ways of accounting,

00:02:16.529 --> 00:02:18.070
but it's good to
know the difference.

00:02:18.070 --> 00:02:20.120
This is historical
cost accounting.

00:02:20.120 --> 00:02:21.910
This is fair value accounting.

00:02:21.910 --> 00:02:24.530
In general, most
accounting standards boards

00:02:24.530 --> 00:02:27.070
want people to
report the fair value

00:02:27.070 --> 00:02:30.580
or to market value as
frequently as possible.

00:02:30.580 --> 00:02:32.500
And it's very easy
to do if there

00:02:32.500 --> 00:02:33.894
is kind of a market in that.

00:02:33.894 --> 00:02:36.060
Or you can get an appraiser
in and they can give you

00:02:36.060 --> 00:02:39.010
a pretty good estimate of
what these things are worth.

00:02:39.010 --> 00:02:41.970
If that isn't around, or if
it's just inefficient to do it,

00:02:41.970 --> 00:02:44.610
then you'd probably want to
do the historical cost method.

00:02:44.610 --> 00:02:45.870
So that's all the difference.

00:02:45.870 --> 00:02:48.250
Historical cost, how
much you paid for it.

00:02:48.250 --> 00:02:52.020
Fair value, what's the
current market value today.

00:02:52.020 --> 00:02:53.830
So they sound like
very fancy words,

00:02:53.830 --> 00:02:56.560
but it's a pretty simple idea.


LIBOR

WEBVTT
Kind: captions
Language: en

00:00:00.987 --> 00:00:05.968
You might have heard the term LIBOR when people are quoting interest rates.

00:00:05.968 --> 00:00:11.076
Or they're saying "Hey I'm gonna lend you money a few percentage points above LIBOR"

00:00:11.076 --> 00:00:14.267
You will hear...LIBOR quoted on some of the financial news channels.

00:00:14.267 --> 00:00:21.533
And what it is, is just an average of the interest rates that banks are lending to each other.

00:00:21.533 --> 00:00:27.533
And it is calculated by the British Bank Association.

00:00:27.533 --> 00:00:30.350
It's actually calcuated by Thomson Reuters for the British Bank Association.

00:00:30.350 --> 00:00:35.944
But it's there to kind of provide a benchmark for other types of securities and financial transactions.

00:00:35.944 --> 00:00:40.267
And it literally stands for the London Interbank Offered Rate.

00:00:40.267 --> 00:00:45.733
So...it's the..... in London...it's the rate..the offered rate between banks.

00:00:45.733 --> 00:00:48.667
The London Interbank Offered Rate.

00:00:48.667 --> 00:00:52.667
To understand that a little bit better we have set up two banks over here

00:00:52.667 --> 00:00:56.359
Bank A and Bank B. And you might have already known that

00:00:56.359 --> 00:00:59.095
when you go and deposit your money in banks,

00:00:59.095 --> 00:01:01.791
the bank won't leave all that money around.

00:01:01.791 --> 00:01:08.267
The way it makes money is lend a good bit of money to other people as loans.

00:01:08.267 --> 00:01:10.283
And it keeps just enough cash on hand

00:01:10.283 --> 00:01:14.467
That things well you know, people would actually come and ask for money from their checking account.

00:01:14.467 --> 00:01:15.933
We have enough on hand

00:01:15.933 --> 00:01:19.636
You could imagine....every now and then that bank might get low on cash.

00:01:19.636 --> 00:01:22.875
or it might get close to kind of a reserve requirement

00:01:22.875 --> 00:01:26.867
that the central bank in that country requires a bank to have on it.

00:01:26.867 --> 00:01:32.231
So in those situations ...say bank A is getting to that...that situation.

00:01:32.231 --> 00:01:34.200
They said "let me go borrow some money"

00:01:34.200 --> 00:01:37.067
Let me go borrow money from another bank.

00:01:37.067 --> 00:01:39.056
So this is interbank borrowing.

00:01:39.056 --> 00:01:41.000
Bank B over here they are flushed with cash

00:01:41.000 --> 00:01:43.067
So they say we don't like to keep so much cash around.

00:01:43.067 --> 00:01:46.754
We want to lend it. So we can actually get interest. We get no interest on cash

00:01:46.754 --> 00:01:49.933
So maybe bank B lends money to Bank A

00:01:49.933 --> 00:01:53.067
So maybe they lend this much cash

00:01:53.067 --> 00:01:55.548
So that's the new cash that bank A got.

00:01:55.548 --> 00:01:58.338
Right over there ...the new cash

00:01:58.338 --> 00:02:01.671
And of course it is a loan

00:02:01.671 --> 00:02:05.079
So this is a new loan. To offset it, remember

00:02:05.079 --> 00:02:07.570
assets are equal to liabilities plus equity.

00:02:07.570 --> 00:02:09.985
So liabilities is this whole thing over here.

00:02:09.985 --> 00:02:15.187
So this is loan from B for this cash.

00:02:15.187 --> 00:02:18.530
They have a little bit better of a cushion.

00:02:18.530 --> 00:02:23.035
And now B, their loan has increased and their cash has decreased.

00:02:23.035 --> 00:02:26.053
So this is a loan, loan to A.

00:02:26.153 --> 00:02:29.444
Right now, they took this cash and they gave to bank A

00:02:29.444 --> 00:02:32.694
And that rate that they lent it at,

00:02:32.694 --> 00:02:36.038
maybe it was that 1% annual rate.

00:02:36.038 --> 00:02:41.656
And of course it is to be renewed everyday, it is overnight rate.

00:02:41.656 --> 00:02:44.119
This rate is an interbank rate.

00:02:44.119 --> 00:02:48.856
So what they do is on behalf of the British Bank Association

00:02:48.856 --> 00:02:51.456
They go survey a bunch of banks in London

00:02:51.456 --> 00:02:54.333
eight, twelve, sixteen banks in London.

00:02:54.333 --> 00:02:57.122
So they said "Hey what was the rate in which you all transacted"

00:02:57.122 --> 00:03:00.373
and they will quote that

00:03:00.373 --> 00:03:03.205
They quote that as the overnight LIBOR

00:03:03.205 --> 00:03:08.830
So they quoted it, say hey 1.2% across all of the banks that we surveyed

00:03:08.830 --> 00:03:12.726
But what's interesting about the LIBOR, it is done in ten currencies

00:03:12.726 --> 00:03:14.723
It is not just in the sterling, the dollar

00:03:14.723 --> 00:03:18.733
or the yen...It is in ten currencies

00:03:18.733 --> 00:03:21.642
That's what really differentiate it amongst other things

00:03:21.642 --> 00:03:28.605
But really differentiate it from the effective Federal Funds Rate which is another interbank borrowing rate

00:03:28.605 --> 00:03:30.867
But that's in the United States

00:03:30.867 --> 00:03:34.390
And that's more revolving around policy concerns.

00:03:34.390 --> 99:59:59.999
The Federal Bank actually tries to change it.


Strokes

WEBVTT
Kind: captions
Language: en

00:00:01.108 --> 00:00:02.577
You've probably heard of

00:00:02.577 --> 00:00:04.481
people having a stroke,

00:00:04.481 --> 00:00:07.750
and you're probably familiar with the notion

00:00:07.750 --> 00:00:09.049
that it has something to do

00:00:09.049 --> 00:00:10.985
with the brain, and you'd be right.

00:00:10.985 --> 00:00:14.453
In particular, it's a rapid loss of

00:00:14.453 --> 00:00:15.922
brain function because of

00:00:15.922 --> 00:00:17.903
something strange happening

00:00:17.903 --> 00:00:20.938
with the blood flow to the brain.

00:00:20.938 --> 00:00:21.960
And let me show you that

00:00:21.960 --> 00:00:23.446
in a little bit more detail.

00:00:23.446 --> 00:00:24.359
And to do that,

00:00:24.359 --> 00:00:24.859
let's think about

00:00:24.859 --> 00:00:26.604
the 2 major types of strokes.

00:00:26.604 --> 00:00:32.708
There's the ischemic strokes,

00:00:34.215 --> 00:00:35.377
and the other type of stroke

00:00:35.377 --> 00:00:36.605
is hemorrhagic,

00:00:36.605 --> 00:00:38.933
and these can kind of be sub-categorized,

00:00:38.933 --> 00:00:44.159
but I won't go into all of the details there.

00:00:44.159 --> 00:00:46.046
And if I really just define

00:00:46.046 --> 00:00:48.399
ischemia and hemorrhaging to you,

00:00:48.399 --> 00:00:49.390
I think you'll have an idea

00:00:49.390 --> 00:00:50.921
of how these strokes are different

00:00:50.921 --> 00:00:53.197
and how they interrupt the blood flow

00:00:53.197 --> 00:00:55.751
to different parts of the brain.

00:00:55.751 --> 00:00:57.192
You know from the videos on

00:00:57.192 --> 00:00:59.141
stenosis and ischemia

00:00:59.141 --> 00:01:00.613
and the videos on heart attacks

00:01:00.613 --> 00:01:01.743
that ischemia is

00:01:01.743 --> 00:01:03.087
a lack of blood flow

00:01:03.087 --> 00:01:05.968
to certain body tissues.

00:01:05.968 --> 00:01:07.918
So an ischemic stroke is actually

00:01:07.918 --> 00:01:09.637
very, very similar to what we saw

00:01:09.637 --> 00:01:10.844
in a heart attack,

00:01:10.844 --> 00:01:11.502
except it's not occurring

00:01:11.502 --> 00:01:12.858
in a coronary blood vessel,

00:01:12.858 --> 00:01:14.792
it's occurring in a blood vessel

00:01:14.792 --> 00:01:16.140
in the brain.

00:01:16.140 --> 00:01:18.399
So let me draw that right over here.

00:01:18.399 --> 00:01:19.482
Let's say that this is

00:01:19.482 --> 00:01:24.123
a blood vessel in the brain.

00:01:25.877 --> 00:01:27.562
And let's say that blood is flowing

00:01:27.562 --> 00:01:29.689
in that direction (this is an artery).

00:01:30.458 --> 00:01:31.510
And so you could imagine

00:01:31.510 --> 00:01:33.835
that maybe there is a big blood clot

00:01:33.835 --> 00:01:35.598
that forms in some part of the brain.

00:01:35.598 --> 00:01:37.270
Let me do the blood clot in magenta.

00:01:37.270 --> 00:01:38.755
This blood clot might form because --

00:01:38.755 --> 00:01:40.566
no, that's not magenta --

00:01:40.566 --> 00:01:41.867
the blood clot might form

00:01:41.867 --> 00:01:43.621
because maybe there's a plaque there,

00:01:43.621 --> 00:01:45.581
maybe the plaque got ruptured,

00:01:45.581 --> 00:01:48.460
either way, this clot is restricting

00:01:48.460 --> 00:01:49.314
the flow of blood.

00:01:49.314 --> 00:01:50.706
And we know that this blood clot --

00:01:50.706 --> 00:01:54.284
we can call this a thrombus,

00:01:55.760 --> 00:01:57.363
or we could say that thrombosis

00:01:57.363 --> 00:01:58.667
has occurred over here--

00:01:58.667 --> 00:02:01.667
either way, the blood flow is restricted,

00:02:01.667 --> 00:02:05.491
and the brain tissue that's further downstream

00:02:05.491 --> 00:02:07.269
is not going to get its oxygen,

00:02:07.269 --> 00:02:11.135
and it might die; it might experience infarction.

00:02:11.135 --> 00:02:13.250
And that's why ischemic strokes are also

00:02:13.250 --> 00:02:19.471
sometimes called cerebral infarctions.

00:02:19.533 --> 00:02:20.898
These are all very fancy words,

00:02:20.898 --> 00:02:22.595
but I think, hopefully, they're becoming

00:02:22.595 --> 00:02:24.561
a little bit more common in our vocabulary,

00:02:24.561 --> 00:02:27.378
they keep showing up over and over again.

00:02:27.378 --> 00:02:29.015
And I also want to be clear:

00:02:29.015 --> 00:02:30.933
most strokes are actually

00:02:30.933 --> 00:02:32.801
ischemic strokes.

00:02:32.801 --> 00:02:34.318
The numbers I looked up, they say,

00:02:34.318 --> 00:02:39.887
87% of strokes are ischemic.

00:02:39.887 --> 00:02:41.558
Now, the other type of way

00:02:41.558 --> 00:02:42.982
that you could have ischemia

00:02:42.982 --> 00:02:44.004
in one of these blood vessels,

00:02:44.004 --> 00:02:45.159
and this is completely analogous

00:02:45.159 --> 00:02:47.578
to what we saw in the heart,

00:02:47.578 --> 00:02:49.400
when we had heart attacks, is:

00:02:49.400 --> 00:02:50.737
you could have thrombosis,

00:02:50.737 --> 00:02:52.919
or you could also have an embolism.

00:02:52.919 --> 00:02:55.891
Whenever someone says thrombosis,

00:02:55.891 --> 00:02:57.609
or a thrombus, or thrombi,

00:02:57.609 --> 00:02:59.205
they're talking about blood clots.

00:02:59.205 --> 00:03:00.257
Whenever someone talks about

00:03:00.257 --> 00:03:03.540
an embolus, or emboli, or embolism,

00:03:03.540 --> 00:03:04.575
they're talking about something

00:03:04.575 --> 00:03:05.933
moving through the blood

00:03:05.933 --> 00:03:08.569
that eventually blocks a blood vessel.

00:03:08.569 --> 00:03:09.298
So you can actually have

00:03:09.298 --> 00:03:10.647
a thromboembolism,

00:03:10.647 --> 00:03:14.096
you can actually have a blood clot

00:03:14.096 --> 00:03:15.442
that gets broken off --

00:03:17.734 --> 00:03:19.933
so let me ignore this for now--

00:03:19.933 --> 00:03:22.116
let me paint over it a little bit

00:03:22.116 --> 00:03:24.547
so that this isn't the main cause of blockage--

00:03:24.547 --> 00:03:26.421
but you could actually have a blood clot

00:03:26.421 --> 00:03:33.530
that breaks off, becomes an embolus,

00:03:33.530 --> 00:03:35.753
and since it's an embolus due to a blood clot,

00:03:35.753 --> 00:03:37.921
you call it a thrombembolus --

00:03:37.921 --> 00:03:39.823
I always have trouble saying all of these words--

00:03:39.823 --> 00:03:46.498
and eventually it blocks an artery over here.

00:03:46.498 --> 00:03:51.713
So this right here is an embolism,

00:03:51.713 --> 00:03:53.933
but either way, you're blocking the blood flow

00:03:53.933 --> 00:03:55.600
further down the brain,

00:03:55.600 --> 00:03:56.559
[which] could cause infarction,

00:03:56.559 --> 00:03:57.937
that brain tissue will die,

00:03:57.937 --> 00:04:00.118
and whatever that brain tissue did

00:04:00.118 --> 00:04:03.183
for mental function, or whatever,

00:04:03.183 --> 00:04:04.529
is going to make it very hard

00:04:04.529 --> 00:04:06.248
for this person who is experiencing this stroke

00:04:06.248 --> 00:04:08.245
to do those things.

00:04:08.245 --> 00:04:08.895
Now, it's not always noticeable,

00:04:08.895 --> 00:04:11.913
that's called a silent stroke,

00:04:11.913 --> 00:04:13.771
but damage is occurring.

00:04:13.771 --> 00:04:15.072
The person experiencing the stroke--

00:04:15.072 --> 00:04:16.110
and I'm not a doctor,

00:04:16.110 --> 00:04:17.720
so take all of this with a grain of salt--

00:04:18.520 --> 00:04:20.272
the person experiencing the stroke

00:04:20.272 --> 00:04:21.358
could be anywhere from -

00:04:21.358 --> 00:04:22.751
well, one, they may not even notice

00:04:22.751 --> 00:04:24.391
that damage is occurring,

00:04:24.391 --> 00:04:25.784
they might have a headache,

00:04:25.784 --> 00:04:26.838
or it might be more severe,

00:04:26.838 --> 00:04:28.074
they might actually

00:04:28.074 --> 00:04:29.667
not be able to properly move

00:04:29.667 --> 00:04:30.954
a side of their body,

00:04:30.954 --> 00:04:32.116
or a side of their face,

00:04:32.116 --> 00:04:33.294
or properly be able to speak,

00:04:33.294 --> 00:04:34.471
so it really depends on what

00:04:34.471 --> 00:04:37.100
part of the brain is being damaged.

00:04:37.100 --> 00:04:39.000
But in either of these situations,

00:04:39.000 --> 00:04:40.723
an ischemic stroke is caused by

00:04:40.723 --> 00:04:43.400
some type of restriction or blockage

00:04:43.400 --> 00:04:45.667
that causes things downstream to not

00:04:45.667 --> 00:04:47.364
get proper oxygen, and then,

00:04:47.364 --> 00:04:48.170
so you can imagine,

00:04:48.170 --> 00:04:49.365
cells over here aren't going

00:04:49.365 --> 00:04:50.313
to get their oxygen,

00:04:50.313 --> 00:04:53.045
and then they might actually die.

00:04:53.045 --> 00:04:54.330
A hemorrhagic stroke -

00:04:54.330 --> 00:04:56.063
to hemorrhage means to bleed,

00:04:56.063 --> 00:04:58.267
it's literally just a fancy word for bleeding-

00:04:58.267 --> 00:05:00.197
and so in a hemorrhagic stroke

00:05:00.197 --> 00:05:02.441
you have a situation where a blood vessel

00:05:02.441 --> 00:05:06.369
can actually break, where you have a blood vessel-

00:05:06.369 --> 00:05:07.271
I'm actually trying to draw

00:05:07.271 --> 00:05:09.917
the same blood vessel- where it actually breaks.

00:05:09.917 --> 00:05:10.894
We'll talk more in the future

00:05:10.894 --> 00:05:12.610
of why a blood vessel might break -

00:05:12.610 --> 00:05:14.236
strongly related to high blood pressure

00:05:14.236 --> 00:05:15.369
and other risk factors,

00:05:15.369 --> 00:05:17.053
but I don't want to get into that right now -

00:05:17.546 --> 00:05:19.738
but you could imagine if a blood vessel breaks,

00:05:20.000 --> 00:05:22.667
you have all this blood spewing into the brain

00:05:22.667 --> 00:05:24.593
in, kind of, an uncontrolled way.

00:05:24.593 --> 00:05:26.281
So let's say this little diagram

00:05:26.281 --> 00:05:27.610
[that] I drew right here,

00:05:28.087 --> 00:05:29.129
that part of the brain,

00:05:29.129 --> 00:05:30.152
if you have a hemorrhagic stroke,

00:05:30.152 --> 00:05:31.296
you have all of this blood

00:05:31.296 --> 00:05:32.733
that's flowing into the brain,

00:05:32.733 --> 00:05:35.147
and all of that uncontrolled blood

00:05:35.147 --> 00:05:37.667
will mess up that part of the brain,

00:05:37.667 --> 00:05:39.625
that causes those neurons

00:05:39.625 --> 00:05:40.972
and brain tissue to malfunction

00:05:40.972 --> 00:05:43.000
and maybe causes some of them to die,

00:05:43.000 --> 00:05:44.189
and it would also cause

00:05:44.189 --> 00:05:46.343
the blood flow further dowstream

00:05:46.343 --> 00:05:47.905
to be impaired, so the stuff

00:05:47.905 --> 00:05:49.901
downstream aren't going to get

00:05:49.901 --> 00:05:50.911
the blood they need

00:05:50.911 --> 00:05:51.715
because all the blood

00:05:51.715 --> 00:05:54.795
is being released everywhere else.

00:05:54.795 --> 00:05:57.718
And since 87% of strokes are ischemic strokes,

00:05:57.718 --> 00:05:59.594
the remainder are hemorrhagic,

00:05:59.594 --> 99:59:59.999
so this is the remaining 13% of strokes.


Common divisibility examples

WEBVTT
Kind: captions
Language: en

00:00:00.465 --> 00:00:01.044
- [Voiceover] In this video

00:00:01.044 --> 00:00:02.740
I wanna do a bunch of example problems

00:00:02.740 --> 00:00:04.679
that show up on standardized exams

00:00:04.679 --> 00:00:07.710
and definitely will help you
with our divisibility module

00:00:07.710 --> 00:00:10.363
because it's asking you
questions like this.

00:00:10.363 --> 00:00:12.243
And this is just one of the examples.

00:00:12.243 --> 00:00:14.802
All numbers divisible by both 12 and 20

00:00:14.802 --> 00:00:17.509
are also divisible by:

00:00:17.509 --> 00:00:19.366
And the trick here is to realize

00:00:19.366 --> 00:00:21.967
that if a number is
divisible by both 12 and 20,

00:00:21.967 --> 00:00:26.505
it has to be divisible by each
of these guy's prime factors.

00:00:26.505 --> 00:00:28.573
So let's take the prime factorization,

00:00:28.573 --> 00:00:30.674
the prime factorization of 12,

00:00:30.674 --> 00:00:32.635
let's see, 12 is 2 times 6.

00:00:32.635 --> 00:00:35.677
6 isn't prime yet so 6 is 2 times 3.

00:00:35.677 --> 00:00:37.407
So that is prime.

00:00:37.407 --> 00:00:39.527
So any number divisible by 12

00:00:39.527 --> 00:00:41.972
needs to be divisible
by 2 times 2 times 3.

00:00:41.972 --> 00:00:43.969
So its prime factorization needs

00:00:43.969 --> 00:00:46.513
to have a 2 times a 2 times a 3 in it,

00:00:46.513 --> 00:00:48.580
any number that's divisible by 12.

00:00:48.580 --> 00:00:51.353
Now any number that's divisible by 20

00:00:51.353 --> 00:00:53.200
needs to be divisible by,

00:00:53.200 --> 00:00:55.325
let's take it's prime factorization.

00:00:55.325 --> 00:00:57.181
2 times 10

00:00:57.181 --> 00:00:59.503
10 is 2 times 5.

00:00:59.503 --> 00:01:01.662
So any number divisible by 20

00:01:01.662 --> 00:01:04.785
needs to also be divisible by

00:01:04.785 --> 00:01:06.445
2 times 2 times 5.

00:01:06.445 --> 00:01:07.618
Or another way of thinking about it,

00:01:07.618 --> 00:01:12.006
it needs to have two 2's and a
5 in its prime factorization.

00:01:12.006 --> 00:01:13.644
If you're divisible by both,

00:01:13.644 --> 00:01:17.021
you have to have two 2's, a 3, and a 5,

00:01:17.021 --> 00:01:19.204
two 2's and a 3 for 12,

00:01:19.204 --> 00:01:22.745
and then two 2's and a 5 for 20,

00:01:22.745 --> 00:01:24.445
and you can verify this for yourself

00:01:24.445 --> 00:01:26.042
that this is divisible by both.

00:01:26.042 --> 00:01:29.487
Obviously if you divide it by 20,

00:01:29.487 --> 00:01:30.695
let me do it this way.

00:01:30.695 --> 00:01:31.636
Dividing it by 20 is the same thing

00:01:31.636 --> 00:01:34.460
as dividing by 2 times 2 times 5,

00:01:34.460 --> 00:01:35.493
so you're going to have

00:01:35.493 --> 00:01:37.037
the 2's are going to cancel out,

00:01:37.037 --> 00:01:38.476
the 5's are going to cancel out.

00:01:38.476 --> 00:01:40.404
You're just going to have a 3 left over.

00:01:42.818 --> 00:01:44.026
So it's clearly divisible by 20,

00:01:44.026 --> 00:01:47.357
and if you were to divide it by 12,

00:01:47.357 --> 00:01:49.938
you'd divide it by 2 times 2 times 3.

00:01:49.938 --> 00:01:51.517
This is the same thing as 12.

00:01:51.517 --> 00:01:53.282
And so these guys would cancel out

00:01:53.282 --> 00:01:54.884
and you would just have a 5 left over

00:01:54.884 --> 00:01:56.022
so it's clearly divisible by both,

00:01:56.022 --> 00:01:57.624
and this number right here is 60.

00:01:57.624 --> 00:01:59.761
It's 4 times 3, which is 12,

00:01:59.761 --> 00:02:01.653
times 5, it's 60.

00:02:01.653 --> 00:02:04.497
This right here is actually
the least common multiple

00:02:04.497 --> 00:02:06.564
of 12 and 20.

00:02:06.564 --> 00:02:08.178
Now this isn't the only number

00:02:08.178 --> 00:02:10.801
that's divisible by both 12 and 20.

00:02:10.801 --> 00:02:12.961
You could multiply this number right here

00:02:12.961 --> 00:02:15.979
by a whole bunch of other factors.

00:02:15.979 --> 00:02:18.661
I could call them a, b, and c,

00:02:18.661 --> 00:02:20.879
but this is kind of the smallest number

00:02:20.879 --> 00:02:22.864
that's divisible by 12 and 20.

00:02:22.864 --> 00:02:25.024
Any larger number will also be divisible

00:02:25.024 --> 00:02:27.775
by the same things as this smaller number.

00:02:28.843 --> 00:02:31.000
Now with that said, let's
answer the questions.

00:02:31.000 --> 00:02:33.763
All numbers divisible by both 12 and 20

00:02:33.763 --> 00:02:35.446
are also divisible by:

00:02:35.446 --> 00:02:37.246
Well we don't know what these numbers are

00:02:37.246 --> 00:02:39.429
so we can't really address it.

00:02:39.429 --> 00:02:41.530
They might just be 1's
or they might not exist

00:02:41.530 --> 00:02:43.132
because the number might be 60.

00:02:43.132 --> 00:02:44.305
It might be 120.

00:02:44.305 --> 00:02:46.012
Who knows what this number is?

00:02:46.012 --> 00:02:49.309
So the only numbers that
we know can be divided

00:02:49.309 --> 00:02:50.133
into this number,

00:02:50.133 --> 00:02:51.506
well we know 2 can be,

00:02:52.346 --> 00:02:53.593
we know that 2 is a legitimate answer.

00:02:53.593 --> 00:02:54.951
2 is obviously divisible into

00:02:54.951 --> 00:02:56.925
2 times 2 times 3 times 5.

00:02:56.925 --> 00:03:00.407
We know that 2 times 2
is divisible into it,

00:03:00.407 --> 00:03:02.974
cuz we have the 2 times 2 over there.

00:03:02.974 --> 00:03:05.284
We know that 3 is divisible into it.

00:03:05.284 --> 00:03:08.808
We know that 2 times 3
is divisible into it.

00:03:08.808 --> 00:03:09.870
So that's 6.

00:03:09.870 --> 00:03:10.764
Let me write these.

00:03:10.764 --> 00:03:11.646
This is 4.

00:03:11.646 --> 00:03:12.935
This is 6.

00:03:12.935 --> 00:03:14.851
We know that 2 times 2 times 3

00:03:14.851 --> 00:03:15.675
is divisible into it.

00:03:15.675 --> 00:03:17.672
I could go through every combination

00:03:17.672 --> 00:03:19.030
of these numbers right here.

00:03:19.030 --> 00:03:22.687
We know that 3 times 5
is divisible into it.

00:03:22.687 --> 00:03:24.592
We know that 2 times 3 times 5

00:03:24.592 --> 00:03:25.567
is divisible into it.

00:03:25.567 --> 00:03:27.691
So in general you can look
at these prime factors

00:03:27.691 --> 00:03:30.013
and any combination of these prime factors

00:03:30.013 --> 00:03:34.147
is divisible into any
number that's divisible by

00:03:34.147 --> 00:03:35.795
both 12 and 20,

00:03:35.795 --> 00:03:37.270
so if this was a multiple choice question,

00:03:37.270 --> 00:03:38.959
and the choices were

00:03:38.959 --> 00:03:41.427
7 and 9

00:03:44.381 --> 00:03:45.681
and 12

00:03:47.388 --> 00:03:48.851
and 8.

00:03:48.851 --> 00:03:49.809
You would say, well let's see,

00:03:49.809 --> 00:03:52.851
7 is not one of these
prime factors over here.

00:03:52.851 --> 00:03:55.811
9 is 3 times 3

00:03:55.811 --> 00:03:57.413
so I need to have two 3's here.

00:03:57.413 --> 00:03:58.910
I only have one 3 here

00:03:58.910 --> 00:04:00.130
so 9 doesn't work.

00:04:00.130 --> 00:04:01.338
7 doesn't work, 9 doesn't work.

00:04:01.338 --> 00:04:03.392
12 is 4 times 3

00:04:03.392 --> 00:04:04.751
or another way to think about it,

00:04:04.751 --> 00:04:07.619
12 is 2 times 2 times 3.

00:04:07.619 --> 00:04:09.975
Well there is a 2 times 2 times 3

00:04:09.975 --> 00:04:11.820
in the prime factorization,

00:04:11.820 --> 00:04:16.082
of this least common multiple
of these two numbers,

00:04:16.082 --> 00:04:18.798
so this is a 12 so 12 would work.

00:04:18.798 --> 00:04:20.761
8 is 2 times 2 times 2.

00:04:20.761 --> 00:04:23.269
You would need three 2's
in the prime factorization.

00:04:23.269 --> 00:04:24.823
We don't have three 2's,

00:04:24.823 --> 00:04:27.761
so this doesn't work.

00:04:27.761 --> 00:04:29.805
Let's try another example

00:04:29.805 --> 00:04:31.523
just so that we make sure

00:04:31.523 --> 00:04:33.741
that we understand this fairly well.

00:04:33.741 --> 00:04:35.098
So let's say we wanna know,

00:04:35.098 --> 00:04:36.979
we ask the same question.

00:04:38.811 --> 00:04:43.287
All numbers divisible by

00:04:43.287 --> 00:04:45.340
and let me think of two
interesting numbers,

00:04:45.340 --> 00:04:49.188
all numbers divisible by 12

00:04:49.188 --> 00:04:51.829
and let's say 9,

00:04:54.394 --> 00:04:55.964
and I don't know, let's
make it more interesting,

00:04:55.964 --> 00:04:58.926
9 and 24

00:04:58.926 --> 00:05:03.866
are also divisible by

00:05:03.866 --> 00:05:06.396
are also divisible by

00:05:06.396 --> 00:05:09.620
And once again we just do
the prime factorization.

00:05:09.620 --> 00:05:11.582
We essentially think about
the least common multiple

00:05:11.582 --> 00:05:13.010
of 9 and 24.

00:05:13.010 --> 00:05:14.763
You take the prime factorization of 9,

00:05:14.763 --> 00:05:16.829
it's 3 times 3 and we're done.

00:05:17.699 --> 00:05:19.384
Prime factorization of 24

00:05:20.524 --> 00:05:24.023
is 2 times 12.

00:05:24.023 --> 00:05:26.195
12 is 2 times 6,

00:05:26.195 --> 00:05:29.402
6 is 2 times 3.

00:05:29.402 --> 00:05:30.947
So anything that's divisible by 9

00:05:30.947 --> 00:05:33.525
has to have a 9 in it's factorization

00:05:33.525 --> 00:05:35.243
or if you did its prime factorization

00:05:35.243 --> 00:05:37.251
would have to be a 3 times 3,

00:05:37.251 --> 00:05:39.515
anything divisible by 24

00:05:39.515 --> 00:05:41.373
has got to have three 2's in it,

00:05:41.373 --> 00:05:45.042
so it's gotta have a
2 times a 2 times a 2,

00:05:45.042 --> 00:05:46.737
and it's got to have at lease one 3 here.

00:05:46.737 --> 00:05:49.419
And we already have at
least one 3 from the 9,

00:05:49.419 --> 00:05:50.405
so we have that.

00:05:50.405 --> 00:05:52.507
So this number right here is divisible

00:05:52.507 --> 00:05:55.398
by both 9 and 24.

00:05:55.398 --> 00:05:57.245
And this number right here is actually 72.

00:05:57.245 --> 00:06:01.726
This is 8 times 9, which is 72.

00:06:01.726 --> 00:06:03.502
So if the choices for this question,

00:06:03.502 --> 00:06:05.127
let's assume that it was multiple choice.

00:06:05.127 --> 00:06:07.046
Let's say the choices here were

00:06:07.046 --> 00:06:08.050
16

00:06:09.240 --> 00:06:10.343
27

00:06:12.694 --> 00:06:14.076
5

00:06:14.076 --> 00:06:15.128
11

00:06:16.084 --> 00:06:18.962
and 9.

00:06:18.962 --> 00:06:21.643
So 16, if you were to do
its prime factorization,

00:06:21.643 --> 00:06:25.876
is 2 times 2 times 2 times 2.

00:06:25.876 --> 00:06:27.159
It's 2 to the 4th power.

00:06:27.159 --> 00:06:29.422
So you would need four 2's here.

00:06:29.422 --> 00:06:31.581
We don't have four 2's over here.

00:06:31.581 --> 00:06:33.485
I mean there could be
some other numbers here

00:06:33.485 --> 00:06:34.685
but we don't know what they are.

00:06:34.685 --> 00:06:35.864
These are the only numbers

00:06:35.864 --> 00:06:37.630
that we can assume are in
the prime factorization

00:06:37.630 --> 00:06:39.569
of something divisible

00:06:39.569 --> 00:06:41.718
by both 9 and 24.

00:06:41.718 --> 00:06:43.377
So we can rule out 16.

00:06:43.377 --> 00:06:44.677
We don't have four 2's here.

00:06:44.677 --> 00:06:49.578
27 is equal to 3 times 3 times 3,

00:06:49.578 --> 00:06:51.736
so you need three 3's in
the prime factorization.

00:06:51.736 --> 00:06:53.037
We don't have three 3's.

00:06:53.037 --> 00:06:53.850
We only have two of them.

00:06:53.850 --> 00:06:56.531
So once again, cancel that out.

00:06:58.031 --> 00:06:59.091
5's a prime number.

00:06:59.091 --> 00:07:00.113
There are no 5's here.

00:07:00.113 --> 00:07:01.112
Rule that out.

00:07:01.112 --> 00:07:02.993
11, once again, prime number.

00:07:02.993 --> 00:07:04.153
No 11's here.

00:07:04.153 --> 00:07:05.593
Rule that out.

00:07:05.593 --> 00:07:08.752
9 is equal to 3 times 3.

00:07:08.752 --> 00:07:10.853
And actually I just realized
that this is a silly answer

00:07:10.853 --> 00:07:12.547
because obviously all numbers divisible

00:07:12.547 --> 00:07:14.499
by 9 and 24 are also divisible by 9.

00:07:14.499 --> 00:07:16.007
So obviously 9 is going to work

00:07:16.007 --> 00:07:17.274
but I shouldn't have made that a choice

00:07:17.274 --> 00:07:20.187
cuz that's in the
problem, but 9 would work,

00:07:20.187 --> 00:07:22.474
and what also would work if we had a,

00:07:22.474 --> 00:07:25.017
if 8 was one of the choices,

00:07:25.017 --> 00:07:28.453
because 8 is equal to 2 times 2 times 2,

00:07:28.453 --> 00:07:31.437
and we have a 2 times 2 times 2 here.

00:07:31.437 --> 00:07:33.074
4 would also work.

00:07:34.614 --> 00:07:35.651
That's 2 times 2.

00:07:35.651 --> 00:07:37.063
That's 2 times 2.

00:07:37.063 --> 00:07:38.623
6 would work since that's 2 times 3.

00:07:38.623 --> 00:07:39.658
18 would work

00:07:39.658 --> 00:07:42.398
cuz that's 2 times 3 times 3.

00:07:42.398 --> 00:07:44.302
So anything that's made
up of a combination

00:07:44.302 --> 00:07:47.784
of these prime factors will be divisible

00:07:47.784 --> 00:07:51.221
into something divisible by both 9 and 24.

00:07:51.221 --> 00:07:53.484
Hopefully that doesn't
confuse you too much.


Stenosis, ischemia and heart failure

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:04.620
As someone who's married to a
doctor, in the medical field,

00:00:04.620 --> 00:00:07.430
I think it's pretty important
to have a precise understanding

00:00:07.430 --> 00:00:09.530
of what the words mean, just
so that you can understand what

00:00:09.530 --> 00:00:11.863
people are talking about if
either you are a health care

00:00:11.863 --> 00:00:15.150
professional or if some health
care professional is talking

00:00:15.150 --> 00:00:18.110
to you, as my wife does
when, well, sometimes does,

00:00:18.110 --> 00:00:19.960
when she comes home from work.

00:00:19.960 --> 00:00:22.790
So let's get a little bit more
precise with some of the words

00:00:22.790 --> 00:00:25.050
we've been talking about,
especially relative to heart

00:00:25.050 --> 00:00:27.850
disease and heart failure
and all of the rest.

00:00:27.850 --> 00:00:29.550
So let's say this is an artery.

00:00:29.550 --> 00:00:31.230
The blood is flowing
in that direction.

00:00:31.230 --> 00:00:33.060
I'll show the artery
branching off.

00:00:33.060 --> 00:00:35.940
It thins as it goes
farther and farther along.

00:00:35.940 --> 00:00:37.600
So this right here is an artery.

00:00:37.600 --> 00:00:39.870
And let me draw a
plaque in that artery.

00:00:39.870 --> 00:00:42.590
And we've been
studying these plaques

00:00:42.590 --> 00:00:46.280
in arteries since the
video on heart attacks.

00:00:46.280 --> 00:00:50.750
So let's say that this is a
bunch of white blood cells

00:00:50.750 --> 00:00:52.390
and lipid material.

00:00:52.390 --> 00:00:55.970
So it's cholesterol and
fats and all the rest.

00:00:55.970 --> 00:00:59.370
Now a word that you might hear
in kind of a medical context

00:00:59.370 --> 00:01:00.053
is stenosis.

00:01:04.800 --> 00:01:08.020
And the word "stenosis" just
refers to the narrowing,

00:01:08.020 --> 00:01:09.480
usually of a blood vessel.

00:01:09.480 --> 00:01:12.830
So this right here, this blood
vessel has been narrowed.

00:01:12.830 --> 00:01:15.040
So this right over
here is stenosis.

00:01:15.040 --> 00:01:17.060
It's been narrowed
by this plaque.

00:01:17.060 --> 00:01:18.920
It can also refer
to the narrowing

00:01:18.920 --> 00:01:21.050
of kind of any type
of tubular structure.

00:01:21.050 --> 00:01:25.000
So if you have any type of kind
of pipe in a biological system

00:01:25.000 --> 00:01:27.350
and it gets narrow, they
might refer to stenosis there.

00:01:27.350 --> 00:01:29.391
But usually they're talking
about a blood vessel.

00:01:29.391 --> 00:01:32.390
In this example that I've
drawn here it's an artery.

00:01:32.390 --> 00:01:34.260
So the stenosis is
just the narrowing.

00:01:37.800 --> 00:01:42.320
Now once the blood
vessel is narrowed,

00:01:42.320 --> 00:01:44.060
that restricts the blood supply.

00:01:44.060 --> 00:01:46.570
So you aren't able to get
as much blood through it.

00:01:49.860 --> 00:01:52.500
So the blood supply
is restricted.

00:01:52.500 --> 00:01:54.080
So restricted blood supply.

00:01:57.620 --> 00:01:58.560
Put the I there.

00:01:58.560 --> 00:02:01.000
Restricted blood supply.

00:02:01.000 --> 00:02:04.050
This restriction
of a blood supply

00:02:04.050 --> 00:02:05.980
that usually leads
to some type of loss

00:02:05.980 --> 00:02:10.380
of function, that's called-- so
this restricted blood supply--

00:02:10.380 --> 00:02:12.440
this is called ischemia.

00:02:12.440 --> 00:02:14.150
Another fancy word,
but it literally just

00:02:14.150 --> 00:02:16.720
means restricted blood supply.

00:02:16.720 --> 00:02:18.840
Ischemia.

00:02:18.840 --> 00:02:22.670
Now if you have stenosis in one
of your blood vessels, in one

00:02:22.670 --> 00:02:26.110
of your arteries, and it
restricts your blood supply.

00:02:26.110 --> 00:02:29.990
So it leads to ischemia.

00:02:29.990 --> 00:02:32.810
Let's say let me draw a
muscle cell farther over here.

00:02:32.810 --> 00:02:37.100
Let's say this is a coronary
artery that we're dealing with.

00:02:37.100 --> 00:02:41.370
The muscle cells over here
are going to get less oxygen.

00:02:41.370 --> 00:02:45.520
So this guy-- let me draw
this cell right over here.

00:02:45.520 --> 00:02:48.020
And I'm just drawing an
oversimplified diagram.

00:02:48.020 --> 00:02:50.360
I'm not going to imply
that muscle cells really

00:02:50.360 --> 00:02:51.350
look like that.

00:02:51.350 --> 00:02:52.996
And actually, they
won't be-- well,

00:02:52.996 --> 00:02:54.370
I won't go into
the details here.

00:02:54.370 --> 00:03:00.675
But this guy's not going
to get not enough oxygen.

00:03:03.810 --> 00:03:06.560
So you can imagine
that if we're really

00:03:06.560 --> 00:03:08.480
zoomed in on the
surface of the heart,

00:03:08.480 --> 00:03:11.610
we're looking at the heart
muscle tissue right here.

00:03:11.610 --> 00:03:14.300
If whoever's heart this was,
if they started to go jogging

00:03:14.300 --> 00:03:18.140
or whatever, and this
cell needed more oxygen,

00:03:18.140 --> 00:03:21.410
probably wouldn't be able
to get that oxygen because

00:03:21.410 --> 00:03:24.310
of the stenosis which
caused ischemia.

00:03:24.310 --> 00:03:26.680
And because of that, it
doesn't have enough oxygen

00:03:26.680 --> 00:03:28.669
so it won't be able to
help the heart pump.

00:03:28.669 --> 00:03:31.210
Remember, this is just one of
the muscles in the heart that's

00:03:31.210 --> 00:03:33.610
going to help it pump
the blood properly.

00:03:33.610 --> 00:03:35.505
So it's going to lead
to heart failure.

00:03:38.077 --> 00:03:39.660
And once again, the
word heart failure

00:03:39.660 --> 00:03:42.800
sounds more dramatic
than maybe it really is.

00:03:42.800 --> 00:03:45.250
It sounds like cardiac
arrest, where the heart stops.

00:03:45.250 --> 00:03:47.330
But heart failure is not saying
that the heart is completely

00:03:47.330 --> 00:03:48.000
failed.

00:03:48.000 --> 00:03:50.960
It's just saying that the
heart is failing its ability

00:03:50.960 --> 00:03:53.010
to kind of properly
do its function.

00:03:53.010 --> 00:03:55.040
So when this guy goes
jogging, because he

00:03:55.040 --> 00:03:58.720
has a restricted blood
supply, because the heart is

00:03:58.720 --> 00:04:04.830
experiencing ischemia
downstream from this stenosis,

00:04:04.830 --> 00:04:06.620
that's why there's
heart failure.

00:04:06.620 --> 00:04:08.390
So not able to deliver.

00:04:08.390 --> 00:04:12.070
Now this heart failure, which
is due to the ischemia which

00:04:12.070 --> 00:04:15.480
is due to the stenosis, you
would call this heart failure

00:04:15.480 --> 00:04:18.264
due to coronary artery disease.

00:04:18.264 --> 00:04:18.930
Let me write it.

00:04:18.930 --> 00:04:20.930
We talked about
that two videos ago.

00:04:24.940 --> 00:04:27.280
Coronary artery disease.

00:04:27.280 --> 00:04:31.560
Which is really just kind of
an impairing of the heart's

00:04:31.560 --> 00:04:34.500
function because of
reduced blood supply,

00:04:34.500 --> 00:04:37.120
because of a narrowing
in a blood vessel

00:04:37.120 --> 00:04:39.360
restricts the blood
supply ischemia,

00:04:39.360 --> 00:04:41.410
that is coronary artery disease.

00:04:41.410 --> 00:04:45.210
And because of coronary
artery disease,

00:04:45.210 --> 00:04:46.730
when this muscle
cell in the heart

00:04:46.730 --> 00:04:48.950
really needs to pump hard--
maybe because someone's

00:04:48.950 --> 00:04:50.650
going up a hill or
climbing stairs--

00:04:50.650 --> 00:04:53.500
it's not able to do it because
it's not getting enough oxygen.

00:04:53.500 --> 00:04:56.530
And that inability to
properly, for the heart,

00:04:56.530 --> 00:04:59.207
not just the cell, but for the
whole heart, this is just one

00:04:59.207 --> 00:05:01.540
of many cells that maybe won't
be able to pump properly,

00:05:01.540 --> 00:05:05.940
for the entire heart to not do
its job, that is heart failure.

00:05:05.940 --> 00:05:08.795
Now you've also probably
heard the term coronary heart

00:05:08.795 --> 00:05:09.295
disease.

00:05:14.630 --> 00:05:16.520
Or maybe just heart disease.

00:05:19.830 --> 00:05:23.600
These three things are
all the same thing.

00:05:23.600 --> 00:05:25.050
These are all the same.

00:05:25.050 --> 00:05:28.640
They all imply some type
of narrowing or stenosis

00:05:28.640 --> 00:05:32.970
of arteries that leads to
ischemia, reduced blood flow,

00:05:32.970 --> 00:05:37.290
so that the heart can't function
as well as it otherwise could.

00:05:37.290 --> 00:05:38.970
Now the last thing
I want to focus on,

00:05:38.970 --> 00:05:41.320
and I talked a little bit
about it in the last video,

00:05:41.320 --> 00:05:44.390
is the idea of an
infarct or an infarction.

00:05:44.390 --> 00:05:47.480
These are kind of
funny words to say.

00:05:47.480 --> 00:05:48.750
I'll write it over here.

00:05:48.750 --> 00:05:53.330
So infarct or infarction.

00:05:53.330 --> 00:05:57.850
So in the example I've drawn
so far, this cell, for example,

00:05:57.850 --> 00:05:59.680
maybe does not
get enough oxygen,

00:05:59.680 --> 00:06:01.690
especially once the
person is going upstairs

00:06:01.690 --> 00:06:06.200
and all of that, to properly
contract and help the heart

00:06:06.200 --> 00:06:07.390
actually pump.

00:06:07.390 --> 00:06:08.810
But it's not dead.

00:06:08.810 --> 00:06:11.280
It's still getting
some base level oxygen.

00:06:11.280 --> 00:06:14.340
Less because of the
stenosis and the ischemia,

00:06:14.340 --> 00:06:16.140
but it still gets some oxygen.

00:06:16.140 --> 00:06:19.030
And we saw in the video
on myocardial infarction

00:06:19.030 --> 00:06:21.760
or the video on heart
attacks that sometimes one

00:06:21.760 --> 00:06:25.580
of these plaques might become
unstable and they break off

00:06:25.580 --> 00:06:29.600
and then you have
a complete blocking

00:06:29.600 --> 00:06:33.699
of a vessel, a complete blocking
of an artery right here.

00:06:33.699 --> 00:06:35.240
And we saw in the
last video, we call

00:06:35.240 --> 00:06:37.330
this blocking what's
called an embolism.

00:06:37.330 --> 00:06:41.210
And an embolism is the
general term for something

00:06:41.210 --> 00:06:44.390
that floated around and then
eventually blocks a vessel.

00:06:44.390 --> 00:06:48.190
And if it was due to kind of
a released plaque that also

00:06:48.190 --> 00:06:50.530
had clotting factors around
it after it got released,

00:06:50.530 --> 00:06:52.280
then we would call
this a thromboembolism.

00:06:54.860 --> 00:07:00.011
This would reduce the
blood flow so much,

00:07:00.011 --> 00:07:02.010
maybe a little bit might
be able to leak around,

00:07:02.010 --> 00:07:05.600
but it reduces it so much that
the cells downstream from this

00:07:05.600 --> 00:07:07.360
actually die.

00:07:07.360 --> 00:07:09.250
So you actually have
the cell right over here

00:07:09.250 --> 00:07:11.360
and this cell will die.

00:07:11.360 --> 00:07:14.100
It might get very little
blood or no blood at all,

00:07:14.100 --> 00:07:17.990
so it's not getting enough
oxygen to actually survive.

00:07:17.990 --> 00:07:23.970
And when you have dead tissue
that's due to a loss of oxygen,

00:07:23.970 --> 00:07:27.550
this is an infarct, dead
tissue due to a loss of oxygen.

00:07:27.550 --> 00:07:31.970
The process of it becoming dead
tissue due a loss of oxygen

00:07:31.970 --> 00:07:34.280
is an infarction.

00:07:34.280 --> 00:07:37.200
And this infarction, this
dead tissue due to loss

00:07:37.200 --> 00:07:41.915
of oxygen, in the myocardium, in
the muscle tissue of the heart.

00:07:41.915 --> 00:07:43.790
So now all of a sudden
you have muscle tissue

00:07:43.790 --> 00:07:45.610
in the heart that's
beginning to die.

00:07:45.610 --> 00:07:46.730
This is a heart attack.

00:07:46.730 --> 00:07:49.510
This is a myocardial infarction.

00:07:49.510 --> 00:07:53.250
So hopefully that clarifies
things a little bit.