Unbalanced forces and motion

WEBVTT
Kind: captions
Language: en

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I have four statements here and I want you to think about which of

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of these statements are true and the first statement is an object in motion will slow down

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unless it is acted on by an unbalanced force in the direction of motion - interesting

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second statment, an object in motion will maintain it's speed and direction

00:00:18.821 --> 00:00:24.810
forever, unless acted on by an unbalanced force- also very interesting.

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Third statement, an object at rest will stay at rest, unless acted on by an unbalanced

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force. And then the fourth statement, an object acted on an by a unbalanced force will always

00:00:36.917 --> 00:00:41.426
acclerate in the direction of the unbalanced force

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So, i'll leave you to think about those statements, and figure out

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which of those statements are actually true.

00:00:46.392 --> 00:00:50.471
It might be none of them, it might be all of them, or some combination of them.

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Now that's try to think about each of these statements.

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So first of all an object in motion will slow down, unless it is acted on

00:00:58.955 --> 00:01:03.407
by an unbalanced force in the direction of motion. Well this, at least, on a first cut

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kind of seems consistant with our everyday experience. If i'm pushing some furniture

00:01:07.598 --> 00:01:12.122
across the room, so let's say that this is, that this is the carpet of my house,

00:01:12.122 --> 00:01:17.274
and i'm pushing a television set -let's say it's one of those old school heavy television set-

00:01:17.274 --> 00:01:21.661
(so i'm pushing a television set), the only way that I can keep it in motion is that I keep

00:01:21.661 --> 00:01:26.120
pushing on it. So let me draw my force of pushing (my force of pushing). So let's call

00:01:26.120 --> 00:01:33.402
that right there the force of Sal pushing the television set. So the only way that

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I can keep (the only way that I can keep) my television set moving seems like if I keep applying

00:01:38.784 --> 00:01:44.221
this pushing force on it. And I were to stop doing that, it seems like it will slow down.

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So on a first cut everday experience, this seems like it would actually maybe be true.

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It only seems that way, because i'm actually not accounting all of the forces in this situation.

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There is not just the force of me pushing. There is also the force of friction.

00:02:00.096 --> 00:02:02.597
(There is also the force of friction.)

00:02:02.597 --> 00:02:08.098
So i'll call that, there is also the force of friction. And if I want to keep this

00:02:08.098 --> 00:02:14.090
TV moving at a constant veloctiy, my force of pushing (that make that the vectors look

00:02:14.090 --> 00:02:17.772
about the same magnitude, becuase they need to be the same magnitude)

00:02:17.772 --> 00:02:22.285
If I want to keep my television set at a constant velocity in the direction that i'm

00:02:22.285 --> 00:02:27.744
pushing, I have to exactly offset the force of (the force of) friction.

00:02:27.744 --> 00:02:34.173
If my force of pushing is less than the force of friction, then the TV set will to decelerate.

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If my force of pushing is larger than the force of friction, then my TV set will accelerate.

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But in the scenario right now, I have an object in motion, but there's actually a

00:02:44.210 --> 00:02:48.279
balanced force. My pushing is completely balanced by the force of friction.

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Another scenario, if we were to go to deep space (i'm not even thinking about air resistance

00:02:52.603 --> 00:02:58.173
right here), but if we were to go into space, where, especailly deep space, no planets around, complete

00:02:58.173 --> 00:03:04.077
vacuum, if an object is in motion (if an object is in motion), and there is absolutely

00:03:04.077 --> 00:03:09.146
no forces balanced or otherwise, there are absolutely no forces acting on it,

00:03:09.146 --> 00:03:13.996
then that object is going to stay in motion. The only way it might change its direction

00:03:14.873 --> 00:03:18.281
or decelerate or accelerate is if there is a net force on it.

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And just by going back to this example, the only reason why it will slow down, if I

00:03:22.594 --> 00:03:27.567
were to stop pushing, is becuase there is a net force on it, the force of friction.

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And if you want to think about it, there would probably be very minor amount of

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air resistance. So this actually isn't true. An object in motion does not have to slow down

00:03:36.295 --> 00:03:39.237
,unless it is acted on by an unbalanced force.

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An object in motion can stay in motion, as long it is being acted on either by a balanced force, or (i guess)

00:03:47.448 --> 00:03:50.446
a set of forces that balance each other, or no forces at all.

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So this is not (that is not) true. An object in motion will maintain it's speed and direction forever

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unless acted on by an unbalanced force.

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This is true! This is exactly what's happening right over here in the case of a (I guess) a block

00:04:06.939 --> 00:04:13.323
moving through space in a vacuum. If there are no forces acting on it (no net forces acting on it)

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it is not going to change its velocity. Similarly, you could have this situation,

00:04:18.247 --> 00:04:21.951
where you actually have forces acting on it, but they balance each other out.

00:04:21.951 --> 00:04:27.896
In this situation, as long as I can keep pushing forever, and the floor doesn't change, and so the

00:04:27.896 --> 00:04:34.030
friction doesn't change, this thing will keep moving in that direction, theoretically forever.

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The only way to change its direction or accelerate in one direction or another direction, would

00:04:38.416 --> 00:04:43.187
be to have an unbalanced force. Maybe if my force of pushing were larger than the force

00:04:43.187 --> 00:04:46.869
of friction, or the force of friction were larger than my force of pushing.

00:04:46.869 --> 00:04:51.091
So this right over here is absoluely true.

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Third statement, an object at rest will stay at rest unless acted on by an unbalanced

00:04:56.668 --> 00:05:01.425
force. And this is actually pretty intuative, I think, for people. If you just leave

00:05:01.425 --> 00:05:05.100
something alone (if you just leave something alone) it's just going to stay alone.

00:05:05.100 --> 00:05:07.447
It's not going to start spontaneously moving.

00:05:07.447 --> 00:05:13.075
And so, this is true. It's not just the situation where there is no forces; it could also be

00:05:13.075 --> 00:05:17.696
the situation that's it's going to stay at rest, if there are balanced forces acting on it.

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And so the only way you can actually get this thing to come out of that rest position

00:05:22.290 --> 00:05:25.223
is if you have a net force, an unbalanced force.

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If, let's say, this force right here is (is) any amount larger than this force

00:05:30.875 --> 00:05:35.961
right over here, if they don't completely balance out. So this, once again, is true.

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Last statement, an object acted on by an unbalanced force will always accelerate in the direction

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of the unbalanced force. So if I have an object, and there's an unbalanced force, and if we

00:05:49.841 --> 00:05:55.446
net out all the forces, let's say, the direction is in the force's net out and we get a force

00:05:55.446 --> 00:06:00.214
acting in this direction. This is actually true! The object will always accelerate

00:06:00.214 --> 00:06:05.565
if it has an unbalanced force acting on it in that direction, it will accelerate if there's

00:06:05.565 --> 00:06:09.542
a net force in that direction. And there's another way of thinking about it.

00:06:09.542 --> 00:06:15.417
If you see an object that is not accelerating, like my TV that's moving at a constant velocity or this thing

00:06:15.417 --> 00:06:19.822
that's just traveling through space, if you see something that is not accelerating, that

00:06:19.822 --> 00:06:25.361
means that there must not be an unbalanced force acting on it.

00:06:25.361 --> 00:06:29.159
So could have balanced forces acting on it, or you could have no forces on it at all,

00:06:29.159 --> 00:06:32.385
but you can't have an unbalanced force. So if you have an unbalanced force, the thing will

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be accelerating.


Balanced and unbalanced forces

WEBVTT
Kind: captions
Language: en

00:00:00.577 --> 00:00:05.165
You'll hear the terms , Balanced Forces and Unbalanced Forces a lot when you're dealing with Physics

00:00:05.165 --> 00:00:10.870
and what I wanna do in this video is give you a bunch of scenarios and have you think about whether the forces in these scenarios

00:00:10.870 --> 00:00:12.955
are balanced or unbalanced.

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So let's start with the scenario where we have the ground.

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And then sitting on the ground we have a rock.

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Now the force of gravity is going to be pulling the rock downwards towards the center of the earth

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and it's going to be pulling it, as essentially the weight of the rock,

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it's going to be pulling it downwards , let's say with a force of 5 N downwards.

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But then the rock is being supported by the ground,

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the ground is keeping it from being plummeted downward.

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So the ground is providing an upwards force or normal force in this situation.

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The ground is providing a normal force, I'll do it in green.

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The ground is providing a normal force in this situation .

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So these forces have the same magnitudes but they're going in opposite directions.

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So that is the first scenario.

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Now let's think about another scenario.

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So I'll draw the rock again.

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We'll assume it's the same rock.
The force of gravity is still downwards.

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5 N downwards.

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And there's still a normal force , the ground supporting the rock of 5 N upwards.

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5 N upwards.

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And now there's some character who's trying to push the rock.

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So we have some character here and he's trying to push the rock and he's applying a force of 2 N to the right.

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But then there's a force of friction between the rock and the ground that is going 2...

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I'll do friction in orange

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2 N to the left

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So that right over there is the force of friction. It's going against that guy's pushing.

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Now let's do another scenario. Once again a very similar scenario.

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Let's draw another scenario where I have a rock now. Maybe the same rock.

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And here I have a 5 N force downwards.

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Force of gravity, like the rest of the scenarios.

00:02:29.459 --> 00:02:37.339
And I have the normal force. The rock is being supported by the ground 5 N upwards.

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And this guy over here has been able to push a little bit harder.

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He's pushing a little bit harder. He really put his back into it.

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And now he's pushing with a force of 3 N to the right

00:02:52.479 --> 00:03:03.909
and the force of friction is still 2 N to the left. So that right over there is the force of friction.

00:03:03.909 --> 00:03:05.689
Now let's do a couple of more scenarios.

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Now let's imagine that this is the ground . And I have the rock. The rock is not resting on the ground.

00:03:15.048 --> 00:03:18.475
So the only force I have acting on the rock right now

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is the force of gravity, acting downward.

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We're assuming we're not going to think too much about--

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Actually let's think about it a little bit, let's also

00:03:25.928 --> 00:03:29.809
put, so let's put it...so I have the force of gravity.

00:03:29.809 --> 00:03:34.710
That's 5 N down. But I have some air resistance here. You can view it as the

00:03:34.710 --> 00:03:40.582
force of friction of the air, and let's say that is 1 N up.

00:03:42.197 --> 00:03:48.299
This is the force of friction or you can call it air resistance.

00:03:48.299 --> 00:03:52.144
As if this thing bumps into all of the air particles as it

00:03:52.144 --> 00:03:54.974
is falling to the ground.

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The last scenario I'll draw with the rock again as that seems to be the

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theme of the video.

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The last scenario, that's the ground.

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The rock is resting on the ground.

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The rock is resting on the ground.

00:04:11.796 --> 00:04:19.569
So I have the force of gravity, 5 N downwards.

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The rock is being supported by the ground, 5 N upwards.

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And now this guy is pushing really hard.

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So now he's applying 4 N

00:04:40.087 --> 00:04:41.739
in that direction.

00:04:41.739 --> 00:04:47.398
You have 2 N from the force of friction, I won't that draw just yet; and you also have

00:04:47.398 --> 00:04:51.093
another character right over here, who is trying to keep this guy from pushing the

00:04:51.093 --> 00:04:57.000
rock. So he's pushing in the other direction at 1 N.

00:04:57.000 --> 00:05:01.803
So you have 2 N of the force of friction. You have this guy pushing 1 N against

00:05:01.803 --> 00:05:12.688
this guy's motion to the left, so between this guy and the force of friction, you have 3 N going left.

00:05:12.688 --> 00:05:19.773
So now I'll let you think about which of these have an unbalanced force in them, or another way to think about it,

00:05:19.773 --> 00:05:24.304
which of these have a Net Force going on?

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So let's look at the first scenario, we have a 5 N force of gravity acting towards the centre of the earth.

00:05:30.176 --> 00:05:33.802
5 N normal force of the ground supporting the rock.

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These have the same magnitude in the exact opposite directions

00:05:37.185 --> 00:05:41.603
so they cancel out. These forces completely balance each other out.

00:05:41.603 --> 00:05:48.274
There is zero net force going on, there are no forces the way I've drawn it, going on in the horizontal direction.

00:05:48.274 --> 00:05:51.453
So you have zero net force, these right here are balanced.

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We would not consider this one of the scenarios we see an

00:05:54.589 --> 00:05:56.210
unbalanced force.

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Let's go to scenario 2.

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Once again, 5 N up and 5 N down, they are balancing each other.

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Then in the horizontal direction, this guy is pushing of 2 N to the right

00:06:06.244 --> 00:06:10.994
is being completely balanced by the force of friction of 2 N to the left.

00:06:10.994 --> 00:06:15.808
Because they're balanced there is no net force and this rock isn't going to accelerate.

00:06:15.808 --> 00:06:22.744
So once again these are all balanced forces or there's no net force going on right over here.

00:06:22.744 --> 00:06:25.888
In scenario 3. Once again, in the vertical direction.

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The force of gravity is being balanced by the normal force of the ground.

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Keeping the rock from plummeting or accelerating towards the centre of the earth.

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And you do have two forces that are counteracting on the horizontal direction.

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This guy's pushing harder with 3 N, but the force of friction is now 2 N to the left.

00:06:43.188 --> 00:06:47.872
So you do have a net force to the right. 3 N to the right, 2 N to the left.

00:06:47.872 --> 00:06:56.898
You have a net force of 1 N to the right.

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Or you see it's right based on how I drew the vector.

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So you do have a net force or in another way of thinking about it, that this is

00:07:03.911 --> 00:07:10.372
a scenario where you have unbalanced forces, in particular, in the right left direction.

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Now let's look at scenario 4.

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We only have forces acting in this vertical direction.

00:07:17.401 --> 00:07:20.463
You have the force of gravity 5 N downwards.

00:07:20.463 --> 00:07:25.277
You have a counteracting force, the force of air resistance, I N upward.

00:07:25.277 --> 00:07:27.332
But they don't completely balance out.

00:07:27.332 --> 00:07:33.729
There is still a net force of 4 N downwards.

00:07:33.729 --> 00:07:37.583
Therefore this is an unbalanced situation.

00:07:37.583 --> 00:07:38.969
And finally in the last scenario.

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We're sitting on the ground in the vertical direction, normal force counteracting the force of gravity.

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Those are balanced.

00:07:45.111 --> 00:07:46.534
But in the horizontal direction.

00:07:46.534 --> 00:07:50.870
To the right we have more force, 4 N, than what we have going to the left.

00:07:50.870 --> 00:07:53.244
3 N is the guy on the right plus the force of friction.

00:07:53.244 --> 00:07:57.719
So in this situation there is a net force in the rightward direction.

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A 1 N force to the right or 1 N net force.

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This is a scenario where we have unbalanced forces.


Normal forces on Lubricon VI

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:04.730
Let's continue with our study
of the planet Lubricon VI.

00:00:04.730 --> 00:00:07.470
Now the one thing I did not
tell you in the last video

00:00:07.470 --> 00:00:14.250
is that Lubricon VI is
not rotating at all.

00:00:14.250 --> 00:00:15.900
And because it's
not rotating, it

00:00:15.900 --> 00:00:18.190
can really not have an equator.

00:00:18.190 --> 00:00:21.110
So when we talked about in
the path of this frozen sock,

00:00:21.110 --> 00:00:23.310
instead of saying it's
traveling across an equator,

00:00:23.310 --> 00:00:25.990
I should say it's traveling
along a great circle.

00:00:25.990 --> 00:00:27.730
If you assume that
earth is a sphere--

00:00:27.730 --> 00:00:29.771
and it's not a perfect
sphere-- but if you assume

00:00:29.771 --> 00:00:32.340
it's a sphere, our equator
would be a perfect sphere.

00:00:32.340 --> 00:00:35.431
But in order to have an equator,
you need to have some rotation.

00:00:35.431 --> 00:00:36.930
This right over
here, we'll just say

00:00:36.930 --> 00:00:40.040
it's traveling along the
largest possible circle

00:00:40.040 --> 00:00:41.230
that it can travel along.

00:00:41.230 --> 00:00:44.480
It's traveling along one of the
great circles of this sphere,

00:00:44.480 --> 00:00:46.740
this block of sock
right over there.

00:00:46.740 --> 00:00:48.590
And now that we know
it's not rotating,

00:00:48.590 --> 00:00:50.430
I want to enter another
thought experiment.

00:00:50.430 --> 00:00:54.850
Because this little frozen block
of sock is not the only thing

00:00:54.850 --> 00:00:58.230
that's on the surface
of Lubricon VI.

00:00:58.230 --> 00:01:01.010
Over here-- we were
viewing it at a distance--

00:01:01.010 --> 00:01:03.220
but right over there,
if we were to zoom in,

00:01:03.220 --> 00:01:08.870
you would see sitting on
the surface of Lubricon VI--

00:01:08.870 --> 00:01:12.390
so once again, that's the
surface-- is a frozen banana.

00:01:12.390 --> 00:01:16.750
So this right over
here is a block of ice.

00:01:16.750 --> 00:01:19.710
And in that block of
ice we have a banana.

00:01:19.710 --> 00:01:21.750
It's a frozen banana.

00:01:21.750 --> 00:01:25.600
So that's my best attempt
at drawing our banana.

00:01:25.600 --> 00:01:29.370
And this relative to the
surface of Lubricon VI

00:01:29.370 --> 00:01:32.030
is absolutely stationary.

00:01:32.030 --> 00:01:36.800
It has absolutely no tangential
velocity like this block had

00:01:36.800 --> 00:01:39.500
and will continue to
have for all eternity.

00:01:39.500 --> 00:01:42.900
This has absolutely no
tangential velocity.

00:01:42.900 --> 00:01:44.650
And so my question
for you, if we

00:01:44.650 --> 00:01:48.680
think about what are the
forces acting on this?

00:01:48.680 --> 00:01:51.020
Well, we have the
force of gravity

00:01:51.020 --> 00:01:53.590
towards the center
of Lubricon VI.

00:01:53.590 --> 00:01:55.350
So we have the force of gravity.

00:01:55.350 --> 00:01:57.270
And I'm drawing all the
forces from the center

00:01:57.270 --> 00:01:59.570
of mass of this block of banana.

00:01:59.570 --> 00:02:01.940
So once again, let me
draw that same color.

00:02:01.940 --> 00:02:04.910
We have the force of gravity
acting radially inward.

00:02:10.080 --> 00:02:12.650
And then we know that
this banana is not

00:02:12.650 --> 00:02:14.900
plummeting straight into
the center of the Earth.

00:02:14.900 --> 00:02:19.830
There must be some other force
that is keeping it stationary.

00:02:19.830 --> 00:02:21.940
And that force is the
force of the surface

00:02:21.940 --> 00:02:26.480
of Lubricon VI on the banana or
on this block that's keeping it

00:02:26.480 --> 00:02:29.410
from plunging towards
the center of the planet.

00:02:29.410 --> 00:02:31.540
So that, in this case,
is the normal force.

00:02:37.880 --> 00:02:42.110
And my question to you
is, are these two things

00:02:42.110 --> 00:02:44.595
equal in the case of the banana?

00:02:47.320 --> 00:02:49.450
Well, as far as we
can tell, this banana

00:02:49.450 --> 00:02:50.880
is completely at rest.

00:02:50.880 --> 00:02:54.220
This planet right over here, at
least relative to the planet,

00:02:54.220 --> 00:02:57.270
this planet right here has
absolutely no rotation.

00:02:57.270 --> 00:03:01.020
And this banana has no relative
motion towards the planet.

00:03:01.020 --> 00:03:04.990
It is not accelerating in
absolutely any direction.

00:03:04.990 --> 00:03:07.730
And if it's not accelerating
in any direction,

00:03:07.730 --> 00:03:10.030
the net forces on
it in any dimension

00:03:10.030 --> 00:03:13.320
must all or must be 0,
or all of the forces

00:03:13.320 --> 00:03:15.400
must cancel out with each other.

00:03:15.400 --> 00:03:20.230
So in the case of this banana,
the normal force exactly

00:03:20.230 --> 00:03:22.510
cancels out the
force of gravity.

00:03:22.510 --> 00:03:26.520
These two things,
the normal force

00:03:26.520 --> 00:03:30.830
is exactly equal to the
inward force of gravity.

00:03:30.830 --> 00:03:32.730
Or I guess we should
say that they add to 0.

00:03:32.730 --> 00:03:34.320
They're going in
opposite directions.

00:03:34.320 --> 00:03:40.190
So I should say the normal
force plus the force of gravity

00:03:40.190 --> 00:03:41.490
are going to be equal 0.

00:03:41.490 --> 00:03:43.400
They have the same
exact magnitude.

00:03:43.400 --> 00:03:45.240
They're going in
opposite directions.

00:03:45.240 --> 00:03:49.090
So when you add them together,
they are going to cancel out.

00:03:49.090 --> 00:03:52.160
Now, with that little thought
experiment out of the way,

00:03:52.160 --> 00:03:55.210
let's return to the frozen sock.

00:03:55.210 --> 00:03:57.790
The frozen sock, as
we already learned,

00:03:57.790 --> 00:04:02.330
is orbiting around this
planet at a altitude of 0

00:04:02.330 --> 00:04:05.660
for all eternity at
1 kilometer per hour.

00:04:05.660 --> 00:04:07.520
And we know that
the force of gravity

00:04:07.520 --> 00:04:09.780
is acting on it towards
the center of the planet

00:04:09.780 --> 00:04:11.740
and there is a
normal force that's

00:04:11.740 --> 00:04:14.400
keeping it from
plummeting, from spiraling

00:04:14.400 --> 00:04:15.950
towards the center
of the planet.

00:04:15.950 --> 00:04:19.899
But my question to you is, in
the case of the frozen sock

00:04:19.899 --> 00:04:22.940
right over here,
are these two forces

00:04:22.940 --> 00:04:25.790
equal like they
are for the banana?

00:04:29.050 --> 00:04:32.090
So in the case of the
frozen sock, the traveling,

00:04:32.090 --> 00:04:39.280
orbiting sock, if these two
forces had the same magnitude,

00:04:39.280 --> 00:04:41.200
but just going in opposite
directions the way

00:04:41.200 --> 00:04:44.690
we've drawn it right over here,
it would completely cancel out.

00:04:44.690 --> 00:04:47.270
And then we would
have no net force.

00:04:47.270 --> 00:04:48.460
So let me make it clear.

00:04:48.460 --> 00:04:55.210
If the normal force plus
the force of gravity

00:04:55.210 --> 00:04:58.490
canceled out with each
other, if this equalled 0,

00:04:58.490 --> 00:05:03.270
then we would have
absolutely no net force

00:05:03.270 --> 00:05:06.630
and the object would not
accelerate in any direction.

00:05:06.630 --> 00:05:09.114
An object in motion
will stay in motion.

00:05:09.114 --> 00:05:10.530
So this one right
over here, if it

00:05:10.530 --> 00:05:13.740
had no net force
acting on it, it

00:05:13.740 --> 00:05:16.360
would not stay on the
surface of the planet.

00:05:16.360 --> 00:05:18.265
It would just travel
in a straight line,

00:05:18.265 --> 00:05:20.890
in a tangential line from where
it happens to be at this moment

00:05:20.890 --> 00:05:21.660
forever.

00:05:21.660 --> 00:05:24.900
So if it was right over here--
I know this isn't the path,

00:05:24.900 --> 00:05:26.960
it would just keep
traveling forever

00:05:26.960 --> 00:05:30.150
off the surface of the planet.

00:05:30.150 --> 00:05:32.820
We know that clearly is
not what's happening.

00:05:32.820 --> 00:05:34.740
It is orbiting
around the planet.

00:05:34.740 --> 00:05:36.860
It has a circular path.

00:05:36.860 --> 00:05:39.156
And since it has
a circular path--

00:05:39.156 --> 00:05:41.030
so if I were to draw a
cross-section of its--

00:05:41.030 --> 00:05:43.430
if I were to look at
its path from the side,

00:05:43.430 --> 00:05:45.730
it has a circular
path like that.

00:05:45.730 --> 00:05:46.880
It is going like that.

00:05:46.880 --> 00:05:52.330
It is constantly being
accelerated inward.

00:05:52.330 --> 00:05:55.910
There is some
centripetal acceleration

00:05:55.910 --> 00:05:58.330
going on, inward acceleration.

00:05:58.330 --> 00:06:01.340
So in order for that inward
acceleration to be going on,

00:06:01.340 --> 00:06:04.680
there must be some
net inward force.

00:06:04.680 --> 00:06:07.950
So in this situation, in the
situation for the stationary

00:06:07.950 --> 00:06:11.020
banana, these two guys
cancelled each other out.

00:06:11.020 --> 00:06:15.020
But for the case of the moving
frozen sock, the sock that

00:06:15.020 --> 00:06:18.850
is orbiting for all of
eternity, it is in orbit.

00:06:18.850 --> 00:06:20.600
It has a circular path.

00:06:20.600 --> 00:06:22.110
So there are centripetal motion.

00:06:22.110 --> 00:06:25.480
There is some net inward
force going on here.

00:06:25.480 --> 00:06:25.980
So

00:06:25.980 --> 00:06:32.570
In this situation, the magnitude
of the force of gravity

00:06:32.570 --> 00:06:40.030
is going to be greater than the
magnitude of the normal force.

00:06:40.030 --> 00:06:41.700
So we don't have this situation.

00:06:41.700 --> 00:06:43.360
In that situation,
you wouldn't orbit.

00:06:43.360 --> 00:06:45.100
We have the situation
where you do

00:06:45.100 --> 00:06:47.690
have some net centripetal force.

00:06:47.690 --> 00:06:49.890
The force of gravity,
the magnitude of it,

00:06:49.890 --> 00:06:53.834
is slightly larger than the
magnitude of the normal force.

00:06:53.834 --> 00:06:55.500
And an interesting
thing to think about,

00:06:55.500 --> 00:06:57.950
and we might address it
in a future tutorial,

00:06:57.950 --> 00:07:01.320
is what would happen if this
started going faster and faster

00:07:01.320 --> 00:07:04.600
and faster, if the frozen
sock were to accelerate.

00:07:04.600 --> 00:07:05.520
What then?

00:07:05.520 --> 00:07:08.370
How would the relationship
between these two things

00:07:08.370 --> 00:07:11.930
potentially change,
if they change at all?


Slow sock on Lubricon VI

WEBVTT
Kind: captions
Language: en

00:00:01.310 --> 00:00:04.540
This is a picture of
the planet Lubricon-VI.

00:00:04.540 --> 00:00:07.890
And Lubricon-VI is a
very special planet

00:00:07.890 --> 00:00:10.220
because it's made up of
a yet to be discovered

00:00:10.220 --> 00:00:12.420
element called Lubrica.

00:00:12.420 --> 00:00:15.460
And Lubrica is special
because if anything glides

00:00:15.460 --> 00:00:18.470
across the surface
of Lubrica, it

00:00:18.470 --> 00:00:20.677
will experience
absolutely no friction.

00:00:20.677 --> 00:00:22.760
So if this right over here
is a sheet of Lubrica--

00:00:22.760 --> 00:00:24.340
we're looking at
it from the side.

00:00:24.340 --> 00:00:29.010
And if we have a brick on top of
it, maybe gliding on top of it

00:00:29.010 --> 00:00:36.050
like that, it experiences
absolutely no friction.

00:00:36.050 --> 00:00:38.700
Now, the other things we
know about Lubricon-VI

00:00:38.700 --> 00:00:41.830
is it's drifting in deep
space and it does not

00:00:41.830 --> 00:00:43.190
have an atmosphere.

00:00:43.190 --> 00:00:45.720
In fact, it is a complete
vacuum outside of it.

00:00:45.720 --> 00:00:48.620
It's in such deep space,
such a remote part of space,

00:00:48.620 --> 00:00:51.820
that there aren't even a few
hydrogen atoms right over here.

00:00:51.820 --> 00:00:54.750
It is a complete,
absolute vacuum.

00:00:54.750 --> 00:00:56.490
And it's also an ancient planet.

00:00:56.490 --> 00:00:58.840
The star that it
used to orbit around

00:00:58.840 --> 00:01:00.990
has long since died away.

00:01:00.990 --> 00:01:04.099
So it's just this lonely
planet drifting in deep space

00:01:04.099 --> 00:01:06.030
without an atmosphere.

00:01:06.030 --> 00:01:08.610
The other thing we
know about Lubricon-VI

00:01:08.610 --> 00:01:10.950
is that it is a perfect sphere.

00:01:10.950 --> 00:01:15.090
It is a perfect, perfect sphere.

00:01:15.090 --> 00:01:16.420
Now, my question to you.

00:01:16.420 --> 00:01:19.420
For some bizarre
reason there happens

00:01:19.420 --> 00:01:21.990
to be, on the surface
of Lubricon-VI--

00:01:21.990 --> 00:01:25.100
so this right over here is
the surface of Lubricon-VI.

00:01:25.100 --> 00:01:28.890
There happens to be a sock that
is frozen in a block of ice.

00:01:28.890 --> 00:01:35.190
So this is my sock and its
frozen in this block of ice.

00:01:35.190 --> 00:01:41.430
And it happens to be traveling
at 1 kilometer per hour

00:01:41.430 --> 00:01:42.750
in that direction.

00:01:42.750 --> 00:01:45.080
If we were to look at it
from this kind of macro scale

00:01:45.080 --> 00:01:46.660
when we're looking
at the planet,

00:01:46.660 --> 00:01:49.000
let's say then that
is the frozen sock,

00:01:49.000 --> 00:01:52.940
and it is traveling
along the equator.

00:01:52.940 --> 00:01:56.580
It is traveling along the
equator of Lubricon-VI.

00:01:59.860 --> 00:02:02.960
So my question to you,
given all of the assumptions

00:02:02.960 --> 00:02:05.610
we made that it has
absolutely no atmosphere,

00:02:05.610 --> 00:02:08.639
it's a perfect
sphere, and Lubrica

00:02:08.639 --> 00:02:10.660
has absolutely no
friction regardless

00:02:10.660 --> 00:02:13.020
of what's traveling
on top of it-- what

00:02:13.020 --> 00:02:19.190
will happen to this
frozen sock over time?

00:02:23.780 --> 00:02:26.330
To answer that question,
we need to think about all

00:02:26.330 --> 00:02:30.630
of the forces that
are acting on this,

00:02:30.630 --> 00:02:33.700
I guess, frozen block
of ice and sock.

00:02:33.700 --> 00:02:36.310
And first of all, let's
think about these forces that

00:02:36.310 --> 00:02:39.990
are acting in the radial
direction, inward or outward,

00:02:39.990 --> 00:02:41.880
of the center of the planet.

00:02:41.880 --> 00:02:44.160
Well, this planet has a mass.

00:02:44.160 --> 00:02:47.700
And so you have an inward force
towards the planet's center

00:02:47.700 --> 00:02:48.670
of mass.

00:02:48.670 --> 00:02:50.990
And so you have the
force of gravity

00:02:50.990 --> 00:02:54.290
acting on this
block going radially

00:02:54.290 --> 00:02:56.440
inward to the center
of the planet.

00:02:56.440 --> 00:02:58.250
So I'll draw it like this.

00:02:58.250 --> 00:03:00.850
So we have our force of gravity.

00:03:00.850 --> 00:03:04.520
We have our force of gravity
going radially inward,

00:03:04.520 --> 00:03:05.830
just like that.

00:03:05.830 --> 00:03:07.730
But then we know that
the block is not just

00:03:07.730 --> 00:03:10.520
spiraling towards the
center of the earth.

00:03:10.520 --> 00:03:11.620
We have the surface here.

00:03:11.620 --> 00:03:14.250
It's not going to go through
the surface of Lubrica.

00:03:14.250 --> 00:03:16.840
We can also assume that
Lubrica is a very, very, very

00:03:16.840 --> 00:03:18.460
strong material.

00:03:18.460 --> 00:03:21.160
And so you also
have a normal force.

00:03:21.160 --> 00:03:22.840
You also have a
normal force that

00:03:22.840 --> 00:03:26.860
is keeping the
block from spiraling

00:03:26.860 --> 00:03:29.120
towards the center of the earth.

00:03:29.120 --> 00:03:31.870
So this is a normal force.

00:03:31.870 --> 00:03:33.880
And one thing we'll
think about now,

00:03:33.880 --> 00:03:37.590
and we'll address it
directly in another tutorial,

00:03:37.590 --> 00:03:44.100
is whether this normal force is
equal to the force of gravity.

00:03:44.100 --> 00:03:46.216
We'll think about that
in a future video.

00:03:46.216 --> 00:03:47.590
But these are all
the forces that

00:03:47.590 --> 00:03:49.460
are acting in the
radial direction,

00:03:49.460 --> 00:03:53.320
either inward towards the
center of the planet or outward.

00:03:53.320 --> 00:03:55.440
But if we think about in
the tangential direction,

00:03:55.440 --> 00:03:59.930
along the surface of the
planet, there are no net forces.

00:03:59.930 --> 00:04:02.630
And because there
are no net forces

00:04:02.630 --> 00:04:06.010
in this tangential
direction right over here,

00:04:06.010 --> 00:04:09.870
this block will not either
accelerate nor decelerate.

00:04:09.870 --> 00:04:13.132
There is no air friction.

00:04:13.132 --> 00:04:15.090
Or I should say air
resistance, which is really

00:04:15.090 --> 00:04:17.990
just friction with the particles
if you had an atmosphere.

00:04:17.990 --> 00:04:20.130
It's a complete vacuum,
so there's nothing there.

00:04:20.130 --> 00:04:22.760
There is no friction with
the surface of the planet.

00:04:22.760 --> 00:04:25.030
So there's no
friction there, which

00:04:25.030 --> 00:04:29.500
could have been a force in
the tangential direction.

00:04:29.500 --> 00:04:33.050
So there's absolutely no forces
in the tangential direction.

00:04:33.050 --> 00:04:35.120
So this block of
ice will actually

00:04:35.120 --> 00:04:38.090
continue to travel at
one kilometer per hour

00:04:38.090 --> 00:04:40.830
for all of eternity.

00:04:40.830 --> 00:04:42.680
So it'll just continue
to do it given

00:04:42.680 --> 00:04:46.010
the assumptions that
we've just made.


Whether a special quadrilateral can exist

WEBVTT
Kind: captions
Language: en

00:00:00.499 --> 00:00:02.990
An interesting question has
come from some of the engineers

00:00:02.990 --> 00:00:05.580
here at the Khan Academy while
they were working on the code.

00:00:05.580 --> 00:00:07.340
Are there any
quadrilaterals-- And I've

00:00:07.340 --> 00:00:09.740
drawn an arbitrary
quadrilateral right over here.

00:00:09.740 --> 00:00:12.000
Quadrilateral ABCD.

00:00:12.000 --> 00:00:14.350
But is there any
quadrilateral that if I

00:00:14.350 --> 00:00:17.580
were to draw the diagonals,
so let me draw the diagonals.

00:00:17.580 --> 00:00:19.370
So one diagonal is BD.

00:00:19.370 --> 00:00:23.712
And then the other diagonal,
I'll draw it right here, is AC.

00:00:23.712 --> 00:00:26.900
And the point of intersection
of these two diagonals

00:00:26.900 --> 00:00:30.840
is, let's call that point E.

00:00:30.840 --> 00:00:46.350
Is there any quadrilateral where
angle AEB is congruent to angle

00:00:46.350 --> 00:00:50.562
ECB is congruent to this
angle right over here?

00:00:50.562 --> 00:00:51.062
ECB.

00:00:53.660 --> 00:00:55.650
So I'll let you think
about that for a second.

00:00:55.650 --> 00:00:59.370
Is there any quadrilateral
where these two angles

00:00:59.370 --> 00:01:03.620
are going to be
congruent to each other?

00:01:03.620 --> 00:01:05.570
Now to think about
whether this is possible,

00:01:05.570 --> 00:01:07.550
let's assume that it is.

00:01:07.550 --> 00:01:13.120
So let's assume that we do
have a quadrilateral where

00:01:13.120 --> 00:01:14.780
this is indeed the case.

00:01:14.780 --> 00:01:21.764
Where AEB, this angle right
over here, is congruent to angle

00:01:21.764 --> 00:01:22.263
ECB.

00:01:25.790 --> 00:01:28.910
We're just going to assume
that right from the get-go.

00:01:28.910 --> 00:01:31.790
Now let's try to visualize
this whole thing a little bit

00:01:31.790 --> 00:01:32.950
differently.

00:01:32.950 --> 00:01:36.870
DB is a segment, but it's
a segment of a larger line.

00:01:36.870 --> 00:01:40.200
So we could keep extending
it off like this.

00:01:40.200 --> 00:01:43.150
And let's call that
larger line, line l.

00:01:43.150 --> 00:01:44.360
Let me draw it like this.

00:01:44.360 --> 00:01:47.070
So this right over
here is line l.

00:01:47.070 --> 00:01:50.210
DB is a subset of line l.

00:01:50.210 --> 00:01:54.511
And CB, which is a segment,
is also a subset of a line.

00:01:54.511 --> 00:01:57.010
And we could call the line, if
we were to keep extending it,

00:01:57.010 --> 00:01:59.070
let's call that line m.

00:01:59.070 --> 00:02:00.800
So I'll draw it like this.

00:02:00.800 --> 00:02:03.350
So line m.

00:02:03.350 --> 00:02:07.030
CB is a subset of line m.

00:02:07.030 --> 00:02:09.880
And then we also
have the segment AC.

00:02:09.880 --> 00:02:12.220
And AC, once again,
is a segment but we

00:02:12.220 --> 00:02:15.420
can view it as a subset
of a larger line.

00:02:15.420 --> 00:02:18.600
And we'll call that
larger line, line n.

00:02:18.600 --> 00:02:20.760
And so let me draw
a line n like this.

00:02:20.760 --> 00:02:24.590
And we see that it intersects
both line l and line m.

00:02:24.590 --> 00:02:28.540
So let me draw it like this, so
it looks something like that.

00:02:28.540 --> 00:02:31.580
That is line n.

00:02:31.580 --> 00:02:37.810
And we've assumed that angle
AEB is congruent to angle ECB.

00:02:37.810 --> 00:02:43.080
Well point E is just
where n and l intersect.

00:02:43.080 --> 00:02:46.490
So this right over
here is point E.

00:02:46.490 --> 00:02:52.350
And point C is where
lines n and m intersect.

00:02:52.350 --> 00:02:54.250
So this is point C.

00:02:54.250 --> 00:02:56.200
So this assumption
right over here,

00:02:56.200 --> 00:02:57.770
that we're assuming
from the get-go,

00:02:57.770 --> 00:03:01.600
is saying that this
angle AEB-- I'll

00:03:01.600 --> 00:03:06.300
do it in the same magenta--
AEB is congruent to this angle.

00:03:06.300 --> 00:03:09.110
ECB is congruent to that angle.

00:03:09.110 --> 00:03:12.320
These angles are these
angles right over here.

00:03:12.320 --> 00:03:18.670
Now what does that tell
us about lines m and l?

00:03:18.670 --> 00:03:23.400
Well the way we've set it up, we
have two lines, lines l and m.

00:03:23.400 --> 00:03:26.000
Line n is a transversal.

00:03:26.000 --> 00:03:28.687
And now we have two
corresponding angles

00:03:28.687 --> 00:03:29.270
are congruent.

00:03:29.270 --> 00:03:31.380
We assumed that from
the get-go that we

00:03:31.380 --> 00:03:33.900
could find two quadrilateral,
where these two

00:03:33.900 --> 00:03:36.160
corresponding angles
are congruent.

00:03:36.160 --> 00:03:38.480
But if you have two
corresponding angles congruent

00:03:38.480 --> 00:03:43.610
like this, that means that these
two lines must be parallel.

00:03:43.610 --> 00:03:49.240
So this tells us that line
l is parallel to line m.

00:03:49.240 --> 00:03:52.780
Line l is parallel to line m.

00:03:52.780 --> 00:03:55.540
Which means that they
will never intersect.

00:03:55.540 --> 00:03:58.590
But we have a
contradiction showing up.

00:03:58.590 --> 00:04:02.130
And I'll let you think about
what that is for a second.

00:04:02.130 --> 00:04:04.340
Well the contradiction
that shows up,

00:04:04.340 --> 00:04:07.580
is that if line l is
parallel to line m,

00:04:07.580 --> 00:04:09.420
then any subset
of those two lines

00:04:09.420 --> 00:04:11.230
have to be parallel
to each other.

00:04:11.230 --> 00:04:13.520
So if l is parallel
to m, then that

00:04:13.520 --> 00:04:19.990
tells us that DB,
segment DB, needs

00:04:19.990 --> 00:04:28.220
to be parallel to segment CB,
which means that they can never

00:04:28.220 --> 00:04:29.790
intersect with each other.

00:04:29.790 --> 00:04:31.320
But that's a contradiction.

00:04:31.320 --> 00:04:33.170
They do intersect
with each other.

00:04:33.170 --> 00:04:35.940
They intersect right over here.

00:04:35.940 --> 00:04:38.330
So if we assume that
there's a quadrilateral,

00:04:38.330 --> 00:04:41.510
where this is the case, you
end up with this contradiction,

00:04:41.510 --> 00:04:42.830
something that's not possible.

00:04:42.830 --> 00:04:44.780
By definition it
was a quadrilateral.

00:04:44.780 --> 00:04:46.580
This diagonal
intersects at point B,

00:04:46.580 --> 00:04:49.670
which is where this
side intersects, too.

00:04:49.670 --> 00:04:51.200
And so they have to intersect.

00:04:51.200 --> 00:04:54.310
These two cannot be parallel in
order for this to actually even

00:04:54.310 --> 00:04:56.130
be a quadrilateral.

00:04:56.130 --> 00:04:58.310
And because of that,
it is impossible

00:04:58.310 --> 00:05:02.270
for any quadrilateral
for this angle AEB

00:05:02.270 --> 00:05:05.910
to be congruent
with this angle ECB.


Interview with Jessica Yuen

WEBVTT
Kind: captions
Language: en

00:00:00.950 --> 00:00:02.780
SAL: I'm here with Jessica.

00:00:02.780 --> 00:00:04.550
What do you do here, Jessica?

00:00:04.550 --> 00:00:06.910
JESSICA: Great question, Sal.

00:00:06.910 --> 00:00:09.020
My title here is
the chief of staff,

00:00:09.020 --> 00:00:12.400
but I like to think of it as
a catch-all for any position

00:00:12.400 --> 00:00:14.460
that we haven't hired
full-time for, I pick up.

00:00:14.460 --> 00:00:17.106
So it's a lot on the business
strategy and operations

00:00:17.106 --> 00:00:18.730
side of the house
and covers everything

00:00:18.730 --> 00:00:24.660
from recruiting and prepping
our documentation for our board

00:00:24.660 --> 00:00:27.170
meetings to going to
Costco and picking up

00:00:27.170 --> 00:00:29.030
the toilet paper if we need it.

00:00:29.030 --> 00:00:29.880
SAL: When necessary.

00:00:29.880 --> 00:00:30.880
JESSICA: When necessary.

00:00:30.880 --> 00:00:33.440
SAL: From very high level
tasks to somewhat low level--

00:00:33.440 --> 00:00:36.240
but sometimes has to get done.

00:00:36.240 --> 00:00:37.570
And how did you end up here?

00:00:37.570 --> 00:00:39.350
Where did you start your career?

00:00:39.350 --> 00:00:42.430
What did you think you're
going to end up being?

00:00:42.430 --> 00:00:45.270
JESSICA: I am a
native of California,

00:00:45.270 --> 00:00:48.750
so I went through the UC
system, went to UC San Diego,

00:00:48.750 --> 00:00:50.760
and started studying
electrical engineering.

00:00:50.760 --> 00:00:53.557
SAL: And you went on some
type of super scholarship.

00:00:53.557 --> 00:00:55.640
JESSICA: I was a Jacobs
scholar while I was there.

00:00:55.640 --> 00:00:57.890
It is a full merit scholarship.

00:00:57.890 --> 00:00:59.259
SAL: Named for Irwin Jacobs.

00:00:59.259 --> 00:00:59.800
JESSICA: Yes.

00:00:59.800 --> 00:01:03.330
Dr. Irwin Jacobs and his wife,
Joan, very generous supporters

00:01:03.330 --> 00:01:06.350
of UC San Diego and had
started the scholarship program

00:01:06.350 --> 00:01:10.600
in hopes of attracting talent on
the caliber of the Ivy Leagues.

00:01:10.600 --> 00:01:13.010
He had been at MIT
before that and had

00:01:13.010 --> 00:01:15.090
wanted to create that
culture [INAUDIBLE].

00:01:15.090 --> 00:01:16.584
SAL: And this was a full ride.

00:01:16.584 --> 00:01:17.750
JESSICA: It was a full ride.

00:01:17.750 --> 00:01:21.137
SAL: And how many students
got this at UCSD every year?

00:01:21.137 --> 00:01:22.720
JESSICA: So I was
the inaugural class,

00:01:22.720 --> 00:01:23.875
and we were a class of 10.

00:01:23.875 --> 00:01:24.915
SAL: A class of 10.

00:01:24.915 --> 00:01:26.280
JESSICA: A class of 10.

00:01:26.280 --> 00:01:29.040
SAL: Probably not
too easy to get.

00:01:29.040 --> 00:01:32.050
JESSICA: I figure I was
just really, really lucky.

00:01:32.050 --> 00:01:34.370
My parents were very happy, too.

00:01:34.370 --> 00:01:35.950
SAL: And a lot less.

00:01:35.950 --> 00:01:38.075
They could go buy
a car or something.

00:01:38.075 --> 00:01:40.200
JESSICA: They were able to
retire a little earlier.

00:01:40.200 --> 00:01:41.990
SAL: Retire a
little bit earlier.

00:01:41.990 --> 00:01:43.865
And so you majored in
electrical engineering,

00:01:43.865 --> 00:01:45.239
and so you thought
you were going

00:01:45.239 --> 00:01:46.496
to be an electrical engineer?

00:01:46.496 --> 00:01:47.120
JESSICA: I did.

00:01:47.120 --> 00:01:50.610
So I did all of my internships
in electrical engineering,

00:01:50.610 --> 00:01:53.195
had worked at a number
of defense companies,

00:01:53.195 --> 00:01:54.890
worked at Qualcomm.

00:01:54.890 --> 00:01:57.670
And then I ended up
going to Stanford

00:01:57.670 --> 00:02:00.559
for a PhD in
electrical engineering.

00:02:00.559 --> 00:02:02.100
And then my first
quarter, I actually

00:02:02.100 --> 00:02:03.740
got sidetracked when
a friend took me

00:02:03.740 --> 00:02:07.270
to a management consulting
info session that was actually

00:02:07.270 --> 00:02:09.350
geared towards engineers.

00:02:09.350 --> 00:02:11.835
And I had no idea
what this field was.

00:02:11.835 --> 00:02:13.260
I'd never heard of it.

00:02:13.260 --> 00:02:14.442
SAL: Few people do.

00:02:14.442 --> 00:02:15.900
JESSICA: But they
had talked about,

00:02:15.900 --> 00:02:17.360
you can have all this impact.

00:02:17.360 --> 00:02:21.350
You get to work with amazing
companies and learn a lot

00:02:21.350 --> 00:02:23.032
and travel the world
while you're at it.

00:02:23.032 --> 00:02:25.240
And I just thought, what
could be a better education,

00:02:25.240 --> 00:02:27.990
while getting paid a little
bit at the same time.

00:02:27.990 --> 00:02:29.740
SAL: And staying
in nice hotels--

00:02:29.740 --> 00:02:30.486
JESSICA: Exactly.

00:02:30.486 --> 00:02:30.860
SAL: Nice dinners.

00:02:30.860 --> 00:02:33.068
JESSICA: It's amazing how
quickly you become obsessed

00:02:33.068 --> 00:02:33.900
with travel points.

00:02:36.500 --> 00:02:38.410
SAL: And how long
did you do that for?

00:02:38.410 --> 00:02:40.370
JESSICA: I did that for
three and a half years

00:02:40.370 --> 00:02:42.078
following my master's,
so I went directly

00:02:42.078 --> 00:02:43.470
from Stanford into McKinsey.

00:02:43.470 --> 00:02:45.990
SAL: So you are now
in your early 20s?

00:02:45.990 --> 00:02:46.930
JESSICA: Mid-20s.

00:02:46.930 --> 00:02:47.750
SAL: Mid-20s, now.

00:02:47.750 --> 00:02:52.210
And what kind of work-- how
was McKinsey what you expected,

00:02:52.210 --> 00:02:53.960
or how was it different
than you expected?

00:02:53.960 --> 00:02:55.810
And what kind of stuff
did you end up doing?

00:02:55.810 --> 00:02:59.900
JESSICA: So I ended up
focusing on consultancy jargon

00:02:59.900 --> 00:03:03.130
of operational and
organizational transformation,

00:03:03.130 --> 00:03:06.540
which looks at the operational
piece goes into organizations--

00:03:06.540 --> 00:03:09.270
oftentimes it's technology
organizations in my case--

00:03:09.270 --> 00:03:10.910
and looking at how
people did things,

00:03:10.910 --> 00:03:13.493
and thinking of ways they could
do it more effectively or more

00:03:13.493 --> 00:03:14.220
efficiently.

00:03:14.220 --> 00:03:16.760
So I worked with engineers,
data centers, executives,

00:03:16.760 --> 00:03:17.900
and the like.

00:03:17.900 --> 00:03:20.880
On the organizational side, it
was actually looking more at

00:03:20.880 --> 00:03:23.980
how company culture
was, and how you

00:03:23.980 --> 00:03:26.130
could make that thrive
in an organization

00:03:26.130 --> 00:03:27.810
and think about
development for people.

00:03:27.810 --> 00:03:30.030
SAL: Which sounds eerily similar
to some of what you do here.

00:03:30.030 --> 00:03:31.710
JESSICA: Yes, very
eerily similar.

00:03:31.710 --> 00:03:33.940
And then a third piece of
what I did at McKinsey, I

00:03:33.940 --> 00:03:37.760
had this awesome stint in
their internal learning group--

00:03:37.760 --> 00:03:41.200
so developing the
training of how

00:03:41.200 --> 00:03:42.760
to make a consultant
a consultant

00:03:42.760 --> 00:03:46.470
and looking at how to allow
people to learn how to problem

00:03:46.470 --> 00:03:49.210
solve and become better
with client relationships

00:03:49.210 --> 00:03:50.700
and interpersonal skills.

00:03:50.700 --> 00:03:52.719
So I really loved the
learning piece of it.

00:03:52.719 --> 00:03:54.760
SAL: And then, while you
were at McKinsey, that's

00:03:54.760 --> 00:03:56.970
where you first met Shantanu
who is our president.

00:03:56.970 --> 00:03:59.620
JESSICA: Yes, we worked on
several projects together.

00:03:59.620 --> 00:04:02.200
SAL: And despite that, you
still wanted to work with him.

00:04:02.200 --> 00:04:03.120
JESSICA: Despite that.

00:04:03.120 --> 00:04:06.320
For some reason, rose
colored glasses [INAUDIBLE]

00:04:06.320 --> 00:04:08.740
were really good
memories out of it.

00:04:08.740 --> 00:04:10.170
Yeah, consulting
was interesting.

00:04:10.170 --> 00:04:14.095
It was a lot of long
hours, a lot of travel.

00:04:14.095 --> 00:04:15.720
People think it's
glamorous when you're

00:04:15.720 --> 00:04:16.803
traveling to other places.

00:04:16.803 --> 00:04:19.840
Oftentimes it was like,
typing up my PowerPoint

00:04:19.840 --> 00:04:21.589
slides as I was on the
go and on my phone.

00:04:21.589 --> 00:04:22.390
SAL: It's probably a
little bit of both.

00:04:22.390 --> 00:04:24.220
It was a little bit glamorous.

00:04:24.220 --> 00:04:25.770
JESSICA: The
traveling was amazing.

00:04:25.770 --> 00:04:27.277
I don't think I ever would
have had an opportunity

00:04:27.277 --> 00:04:28.150
to [INAUDIBLE] otherwise.

00:04:28.150 --> 00:04:29.750
SAL: And you were interfacing
at a very high level

00:04:29.750 --> 00:04:31.166
with a lot of these
organizations,

00:04:31.166 --> 00:04:32.250
the senior executives.

00:04:32.250 --> 00:04:33.730
JESSICA: Best
learning experience

00:04:33.730 --> 00:04:35.180
I could have ever hope
for coming out of school.

00:04:35.180 --> 00:04:36.150
SAL: Especially
at that age, to be

00:04:36.150 --> 00:04:37.770
able to interface
with senior people

00:04:37.770 --> 00:04:39.600
at some major
organizations, I could

00:04:39.600 --> 00:04:40.620
imagine would be
very great learning.

00:04:40.620 --> 00:04:41.453
JESSICA: Absolutely.

00:04:41.453 --> 00:04:44.265
It was and incredible
training ground.

00:04:44.265 --> 00:04:46.576
SAL: And then after
that-- what was it,

00:04:46.576 --> 00:04:49.076
three and a half years-- and
then you decided to leave for--

00:04:49.076 --> 00:04:51.034
JESSICA: Yeah, so after
three and a half years,

00:04:51.034 --> 00:04:52.040
the lifestyle was tough.

00:04:52.040 --> 00:04:53.420
I found whenever
I was at home, I

00:04:53.420 --> 00:04:56.850
was just sleeping to make
up for the work week.

00:04:56.850 --> 00:05:00.770
And so I decided to leave,
and I went to Yahoo!

00:05:00.770 --> 00:05:03.730
Given my background
in transformations,

00:05:03.730 --> 00:05:06.820
this was a company that was
in the midst of a huge one.

00:05:06.820 --> 00:05:08.590
And I thought I could help.

00:05:08.590 --> 00:05:12.590
So I went there-- also was
a great actual learning

00:05:12.590 --> 00:05:13.320
ground for me.

00:05:13.320 --> 00:05:15.480
I was able to interface
with everybody

00:05:15.480 --> 00:05:18.550
from the engineers to marketing,
finance, legal, and just

00:05:18.550 --> 00:05:21.210
learned about the
entire organization

00:05:21.210 --> 00:05:24.280
and how things worked both on
the search side of the house

00:05:24.280 --> 00:05:27.420
as well as on the advertising
side of the house.

00:05:27.420 --> 00:05:31.700
SAL: And you worked with a
whole-- you ended up at Search.

00:05:31.700 --> 00:05:32.200
You were--

00:05:32.200 --> 00:05:33.420
JESSICA: I did end up in Search.

00:05:33.420 --> 00:05:34.650
SAL: --a product manager there.

00:05:34.650 --> 00:05:35.191
JESSICA: Yes.

00:05:35.191 --> 00:05:37.780
So I ended up in Search as
a senior project manager

00:05:37.780 --> 00:05:38.619
by the time I left.

00:05:38.619 --> 00:05:40.160
SAL: And so that
sounded pretty good.

00:05:40.160 --> 00:05:42.300
So how did you end up here?

00:05:42.300 --> 00:05:44.330
JESSICA: Yeah.

00:05:44.330 --> 00:05:47.060
SAL: Which now, in hindsight,
is the worst decision you ever

00:05:47.060 --> 00:05:47.560
made.

00:05:47.560 --> 00:05:48.923
JESSICA: Best decision ever.

00:05:48.923 --> 00:05:50.200
You can pay me $5 after.

00:05:50.200 --> 00:05:51.070
SAL: Yes, yes.

00:05:51.070 --> 00:05:53.250
JESSICA: Just kidding.

00:05:53.250 --> 00:05:56.730
SAL: I would have edited out
any negative remarks anyway.

00:05:56.730 --> 00:05:58.690
JESSICA: I had kept in
touch with Shantanu.

00:05:58.690 --> 00:06:02.577
And so he he had
told me, over time,

00:06:02.577 --> 00:06:04.910
about how he was interfacing
with this guy named Sal who

00:06:04.910 --> 00:06:08.456
was making these YouTube
videos, and I just

00:06:08.456 --> 00:06:09.580
thought it was really cool.

00:06:09.580 --> 00:06:12.204
I had checked out the site, seen
that we had all these practice

00:06:12.204 --> 00:06:14.090
modules and some
analytics behind it,

00:06:14.090 --> 00:06:16.770
and just thought what was
happening here was awesome.

00:06:16.770 --> 00:06:18.540
So I offered up my
free time and said,

00:06:18.540 --> 00:06:19.820
hey, I'd love to volunteer.

00:06:19.820 --> 00:06:22.500
I started doing that.

00:06:22.500 --> 00:06:24.810
And then right around
the time of the Ted talk,

00:06:24.810 --> 00:06:27.510
things kind of got really
crazy for you guys.

00:06:27.510 --> 00:06:29.900
And I had been helping
to try to find, actually,

00:06:29.900 --> 00:06:33.680
a different role that you were
thinking of hiring at the time.

00:06:33.680 --> 00:06:38.000
And then when things got crazy,
Shantanu said, hey actually,

00:06:38.000 --> 00:06:39.430
you might actually
be a great fit.

00:06:39.430 --> 00:06:40.060
SAL: Yeah, I think
we realized you

00:06:40.060 --> 00:06:41.700
were doing more
in your free time

00:06:41.700 --> 00:06:43.866
than we would have expected
from a full [INAUDIBLE].

00:06:43.866 --> 00:06:47.240
It was like, maybe Jessica's
the right person for this.

00:06:47.240 --> 00:06:50.510
And then you've come, and
that was 18 months ago.

00:06:50.510 --> 00:06:51.900
But it was at an early stage.

00:06:51.900 --> 00:06:53.930
I mean, how many
people were we then?

00:06:53.930 --> 00:06:55.980
JESSICA: Yeah, when
I joined, I think I

00:06:55.980 --> 00:06:57.900
was employee number
six, after Marsha.

00:06:57.900 --> 00:07:00.166
She was really early on.

00:07:00.166 --> 00:07:01.290
SAL: And now we're at what?

00:07:01.290 --> 00:07:02.410
We're at--

00:07:02.410 --> 00:07:05.544
JESSICA: We're now, I believe,
we're in our early 30's.

00:07:05.544 --> 00:07:06.210
SAL: Early 30's.

00:07:06.210 --> 00:07:08.830
JESSICA: Early 30's.

00:07:08.830 --> 00:07:09.830
SAL: 31, 32 people.

00:07:09.830 --> 00:07:11.560
And we have a bunch
of interns right now.

00:07:11.560 --> 00:07:13.309
JESSICA: Yeah, a bunch
of awesome interns.

00:07:13.309 --> 00:07:15.680
SAL: We're like five
times bigger than we were.

00:07:15.680 --> 00:07:17.640
JESSICA: It's incredible
how much we've grown.

00:07:17.640 --> 00:07:19.972
SAL: Yeah, it is incredible.

00:07:19.972 --> 00:07:20.775
Wow.

00:07:20.775 --> 00:07:22.670
And what's your takeaway?

00:07:22.670 --> 00:07:24.775
What's the experience been
like, and where do you

00:07:24.775 --> 00:07:25.858
think this is going to go?

00:07:25.858 --> 00:07:28.065
JESSICA: Yeah, so my
experience has been phenomenal,

00:07:28.065 --> 00:07:29.690
I think beyond what
I could have hoped.

00:07:29.690 --> 00:07:30.731
SAL: I don't believe you.

00:07:30.731 --> 00:07:32.378
I'm sure, but anyway.

00:07:32.378 --> 00:07:33.901
Continue.

00:07:33.901 --> 00:07:35.400
JESSICA: But it's
just been amazing.

00:07:35.400 --> 00:07:39.480
I think the people
here are all just

00:07:39.480 --> 00:07:43.180
so thoughtful and so
nice and just awesome.

00:07:43.180 --> 00:07:46.070
Everyone's brilliant but
just humble about it.

00:07:46.070 --> 00:07:47.870
And so I just feel
incredibly lucky to be

00:07:47.870 --> 00:07:49.414
amongst this group of folks.

00:07:49.414 --> 00:07:50.830
I think as we've
grown, we've been

00:07:50.830 --> 00:07:54.080
able to [? main ?] the
quirky, fun culture of being

00:07:54.080 --> 00:07:57.925
proactive and thinking epic
and shipping beats perfection.

00:07:57.925 --> 00:07:59.870
Some of our values,
we've been really

00:07:59.870 --> 00:08:03.260
great at keeping that going.

00:08:03.260 --> 00:08:05.280
As we grow, it's interesting.

00:08:05.280 --> 00:08:08.120
I think you once posed
the question around,

00:08:08.120 --> 00:08:11.130
where would we be
500 years from now?

00:08:11.130 --> 00:08:13.670
What would that ideal
picture be like?

00:08:13.670 --> 00:08:15.940
And I think it'd be awesome
if Khan Academy still

00:08:15.940 --> 00:08:19.160
exists in 500 years and that
we're still completely free

00:08:19.160 --> 00:08:24.210
and that we have all
the content that anybody

00:08:24.210 --> 00:08:25.170
could want to learn.

00:08:25.170 --> 00:08:27.420
SAL: And plug directly into
their brain at that point.

00:08:27.420 --> 00:08:30.760
JESSICA: Yes, by at that point,
hopefully it's just plug in,

00:08:30.760 --> 00:08:33.600
and you're done.

00:08:33.600 --> 00:08:35.710
But I think that
would be amazing,

00:08:35.710 --> 00:08:40.049
if we could leave something
for future generations

00:08:40.049 --> 00:08:43.200
to be able to use and
have a resource, that,

00:08:43.200 --> 00:08:46.600
at this point in time, seemed
unthinkable that it would be

00:08:46.600 --> 00:08:51.195
free and that anybody can access
that quality of education.

00:08:51.195 --> 00:08:54.690
SAL: You're inspiring
me, Jessica.

00:08:54.690 --> 00:08:56.910
JESSICA: The feeling
is mutual, Sal.


PPACA or "Obamacare"

WEBVTT
Kind: captions
Language: en

00:00:00.774 --> 00:00:04.427
Theres been a lot of talk about the Patient Protection and Affordable Care Act (PPACA)

00:00:04.427 --> 00:00:09.537
often referred to as "ObamaCare"; usually by those that are not a big fan of it.

00:00:09.537 --> 00:00:13.825
And my goal here is to not take any political sides, and hopefully give

00:00:13.825 --> 00:00:16.874
an overview of what all of the debate is about and what this 'Affordable Care Act' is all about.

00:00:16.874 --> 00:00:24.257
and I'm going to start with the most controversial part, and this is the 'Individual Mandate'

00:00:24.257 --> 00:00:30.931
And this is the idea that you either have to get insurance, or pay: a penalty; or a fee; or a tax.

00:00:30.931 --> 00:00:35.854
-Penalty- Which is now being referred to as a tax by many folks.

00:00:35.854 --> 00:00:43.594
And the idea here is that there are obviously many folks who are uninsured right now,

00:00:43.594 --> 00:00:48.253
and when they get sick especially when they get very sick they still get healthcare.

00:00:48.253 --> 00:00:54.430
In particular they will go to the Emergency Room. They will go to the E.R., and that is

00:00:54.430 --> 00:00:59.180
quite posiibly the most expensive part of the healthcare system to interface with.

00:00:59.180 --> 00:01:03.731
So there's kind of a moral argument here, that-

00:01:03.731 --> 00:01:09.226
1) These people are getting sicker than they need to get if they had insurance. e.g. getting preventative care and not getting that sick.

00:01:09.226 --> 00:01:14.134
Then there's a financial or, I guess you could say, a fairness argument: that these people are getting sick,

00:01:14.134 --> 00:01:20.555
going to the E.R., and they have to be given care at that E.R. The Hospitals bear those costs, and then

00:01:20.555 --> 00:01:24.672
eventually recoup those costs by charging more for all sorts of other services.

00:01:24.672 --> 00:01:30.215
[These costs] go back to the people who are paying for the healthcare.

00:01:30.215 --> 00:01:36.686
So, if you have an Individual Mandate it will clear things up a little bit. People will have to

00:01:36.686 --> 00:01:43.328
essentially pay for the healthcare they are already getting. Now, the argument against the

00:01:43.328 --> 00:01:49.766
'Individual Mandate' is that this is the Government putting into law that people *have to buy something*.

00:01:49.766 --> 00:01:56.850
In particular, that they have to buy health insurance. Now, the counterargument that many people make is that there

00:01:56.850 --> 00:02:02.304
is something similar going on with car insurance. If you want to drive in most states, you have to buy some type of

00:02:02.304 --> 00:02:08.173
car insurance or at least show that you have financial abilities to pay any liabilities you might have if you get into an accident.

00:02:08.173 --> 00:02:18.183
Now the 'Counter-Counter-Counter-Argument' to that is that, driving is something that someone chooses to do.

00:02:18.183 --> 00:02:24.314
That you do not have to drive, while in the case of health insurance, this is something that every person in

00:02:24.314 --> 00:02:30.814
the country is being forced to [purchase].
I'll leave it to you to decide where you sit on that,

00:02:30.814 --> 00:02:32.824
and what balances what other issue.

00:02:32.824 --> 00:02:37.780
Now, obviously, if you're going to decide whether you want insurance, or whether you are going

00:02:37.780 --> 00:02:42.888
to pay a penalty/tax, you have to figure out how high that penalty is going to be on you.

00:02:42.888 --> 00:02:48.183
Or if you want to figure out if this is a fair situation. You have to think about high that penalty is going to be.

00:02:48.183 --> 00:02:53.571
And the current provisions say that by 2016, which is when the full penalties take effect,

00:02:53.571 --> 00:03:04.094
you are going to have to pay the maximum of either 2.5% of your income, or $695 for an individual,

00:03:04.094 --> 00:03:10.521
or $2085 for a family.
And there are exceptions, and this whole

00:03:10.521 --> 00:03:16.401
individual mandate won't apply to you if having/getting insurance will cost you more than 8% of your total income.

00:03:16.401 --> 00:03:23.492
or if you belong to a religion that does not participate in the healthcare system, then it doesn't apply.

00:03:23.492 --> 00:03:31.571
So you will never have to pay more than 8% [of your total income] to get an insurance policy.

00:03:31.571 --> 00:03:39.824
But these are the general penalties; If you made $100,000 and chose not to get the insurance,

00:03:39.824 --> 00:03:48.229
you would pay $2,500 (2.5% of income, and is greater than the minimum penalties).

00:03:48.398 --> 00:03:56.421
If your [family] makes $50,000, then the 2.5% [$1250] would be less than the [family] minimum, so you would pay $2085.

00:03:56.421 --> 00:04:03.046
Now the other provisions of the PPACA are based around the idea that, "If we want people to get insurance,

00:04:03.046 --> 00:04:05.665
- then we need to make it easier for them to get insurance"

00:04:05.665 --> 00:04:12.196
The biggest deal, at least in my mind, is this one covering Pre-Existing Conditions.

00:04:12.196 --> 00:04:20.123
Right now, if you have a Pre-Existing Condition, e.g. Cancer, and you do not have insurance, or your employer

00:04:20.123 --> 00:04:23.653
does not cover it - or perhaps you are unemployed - and if you try to get insurance on your own,

00:04:23.653 --> 00:04:28.467
you are likely to be denied. If you are offered insurance, it will be ridiculously expensive.

00:04:28.467 --> 00:04:32.644
This is because the insurance company knows that they're going to take a huge loss on paying

00:04:32.644 --> 00:04:40.029
all of your medical expenses. The PPACA says that you can no longer base the premiums, or whether

00:04:40.029 --> 00:04:43.001
you will or not give someone insurance based on Pre-Existing Conditions.

00:04:43.001 --> 00:04:51.685
People will be charged premiums, which what you pay to receive the policy, based on age and geography.

00:04:51.685 --> 00:04:58.669
So if you have two 40-year-olds, and one of them has the misfortune of having cancer,

00:04:58.669 --> 00:05:06.748
the other not having any pre-existing conditions; and they both live in, let's say, in Virginia.

00:05:06.748 --> 00:05:13.077
Under this, they will pay the exact same amount for insurance, the same premium.

00:05:13.077 --> 00:05:18.139
These other two points are just to make it easier to get insurance. Right now, if you've

00:05:18.139 --> 00:05:21.919
ever tried to get insurance, it can be really hard to compare and contrast policies,

00:05:21.919 --> 00:05:24.390
and to really understand what you're getting and what you're not getting.

00:05:24.390 --> 00:05:29.810
So this part of the Act says that every state will set up one of these Insurance Exchanges, which will allow

00:05:29.810 --> 00:05:33.804
for more transparency in terms of buying and selling policies.

00:05:33.804 --> 00:05:38.960
And then this final part here, -though this is just an overview, I'm not covering everything, not all the details-

00:05:38.960 --> 00:05:46.170
is the idea that the Government will also subsidize people getting policies, especially if they are in lower income

00:05:46.170 --> 00:05:49.837
brackets, or in more difficult financial situations.

00:05:49.837 --> 00:05:54.193
Now on top of this, if you're deciding whether or not you support things, if you're saying,

00:05:54.193 --> 00:05:58.431
'This might be a good idea', or 'This is a bad idea' because you don't like the government forcing things

00:05:58.431 --> 00:06:06.225
like this, there is also the issue of the Cost.
Now this whole thing, even thought there might be

00:06:06.225 --> 00:06:11.325
savings in terms of lower medical care, because people would get preventative healthcare,

00:06:11.325 --> 00:06:22.595
there is still a Net Cost to this. It will primarily be paid for by an increase to the Medicare Tax for

00:06:22.595 --> 00:06:36.479
high-income brackets. So it's really going to be larger Medicare taxes on people with larger incomes.

00:06:36.479 --> 00:06:43.800
This is estimated to generate about $200 Billion a year, (or $210 Billion, there are different estimates)

00:06:43.800 --> 00:06:49.943
but that's going to bear most of the costs, and on top of that, there are some extra fees on insurers,

00:06:50.020 --> 00:06:56.555
as well as what's called an 'Excise Tax', which tends to be a large tax on a specific type of policy,

00:06:56.555 --> 00:07:04.066
which are referred to as 'Cadillac' policies. These policies are very very very generous. This will be used to make up some of the cost of all this.

00:07:04.066 --> 00:07:10.665
Once again, I'm not going to take any political sides on this, but hopefully this gives some clarity about what

00:07:10.665 --> 00:07:14.000
people are actually debating.


Divisibility tests for 2, 3, 4, 5, 6, 9, 10

WEBVTT
Kind: captions
Language: en

00:00:00.190 --> 00:00:01.690
What we're going
to do in this video

00:00:01.690 --> 00:00:05.060
are some real quick tests to see
if these three random numbers

00:00:05.060 --> 00:00:07.260
are divisible by any
of these numbers here.

00:00:07.260 --> 00:00:10.080
And I'm not going to focus a
lot on the why of why they're

00:00:10.080 --> 00:00:11.830
divisible-- we'll do that in
other videos-- but really just

00:00:11.830 --> 00:00:13.690
to give you a sense
of how do you actually

00:00:13.690 --> 00:00:18.110
test to see if this is
divisible by 2 or 5 or 9 or 10.

00:00:18.110 --> 00:00:19.570
So let's get started.

00:00:19.570 --> 00:00:22.220
So to test whether any of
these are divisible by 2,

00:00:22.220 --> 00:00:24.230
you really just have to
look at the ones place

00:00:24.230 --> 00:00:27.620
and see if the ones
place is divisible by 2.

00:00:27.620 --> 00:00:30.840
And right over here,
8 is divisible by 2,

00:00:30.840 --> 00:00:33.210
so this thing is going
to be divisible by 2.

00:00:33.210 --> 00:00:36.150
0 is considered to
be divisible by 2,

00:00:36.150 --> 00:00:38.426
so this is going to
be divisible by 2.

00:00:38.426 --> 00:00:40.050
Another way to think
about it is if you

00:00:40.050 --> 00:00:41.800
have an even number
over here-- and 0

00:00:41.800 --> 00:00:43.640
is considered to be
an even number-- then

00:00:43.640 --> 00:00:45.710
you're going to
be divisible by 2.

00:00:45.710 --> 00:00:50.110
And over here, you do not have
a number that is divisible by 2.

00:00:50.110 --> 00:00:52.110
This is not an even
number, this 5,

00:00:52.110 --> 00:00:53.720
so this is not divisible by 2.

00:00:53.720 --> 00:00:54.990
So I won't write any 2 there.

00:00:54.990 --> 00:00:56.830
So we've gone through the 2s.

00:00:56.830 --> 00:00:59.240
Now, let's work through the 3s.

00:00:59.240 --> 00:01:01.600
So to figure out if
you're divisible by 3,

00:01:01.600 --> 00:01:03.720
you really just have to
add up all the digits

00:01:03.720 --> 00:01:06.735
and figure out if the
sum is divisible by 3.

00:01:06.735 --> 00:01:07.720
So let's do that.

00:01:07.720 --> 00:01:17.185
So if I do 2 plus 7 plus 9
plus 9 plus 5 plus 8 plus 8,

00:01:17.185 --> 00:01:18.560
what's this going
to be equal to?

00:01:18.560 --> 00:01:19.870
2 plus 7 is 9.

00:01:19.870 --> 00:01:27.910
9 plus 9 is 18, plus 9 is 27,
plus 5 is 32, plus 8 is 40,

00:01:27.910 --> 00:01:31.530
plus 8 is 48.

00:01:31.530 --> 00:01:34.120
And 48 is divisible by 3.

00:01:34.120 --> 00:01:37.010
But in case you're not sure--
so this is equal to 48-- in case

00:01:37.010 --> 00:01:39.100
you're not sure whether
it's divisible by 3,

00:01:39.100 --> 00:01:40.970
you can just add
these digits up again.

00:01:40.970 --> 00:01:47.734
So 4 plus 8 is equal to 12, and
12 clearly is divisible by 3.

00:01:47.734 --> 00:01:49.150
And if you're not
even sure there,

00:01:49.150 --> 00:01:50.566
you could add those
two digits up.

00:01:50.566 --> 00:01:55.950
1 plus 2 is equal to 3, and
so this is divisible by 3.

00:01:55.950 --> 00:01:57.969
This right over here,
let's add up the digits.

00:01:57.969 --> 00:02:00.010
And we can do this one in
our head pretty easily.

00:02:00.010 --> 00:02:02.130
5 plus 6 is 11.

00:02:02.130 --> 00:02:04.774
11 plus 7 is 18.

00:02:04.774 --> 00:02:07.160
18 plus 0 is 18.

00:02:07.160 --> 00:02:11.700
And if you want to add the 1
plus 8 on the 18, you get 9.

00:02:11.700 --> 00:02:14.430
So the digits add up to 9.

00:02:14.430 --> 00:02:15.795
So these add up to 9.

00:02:18.640 --> 00:02:22.425
Well, they add to 18, which
is clearly divisible by 3

00:02:22.425 --> 00:02:25.300
and by 9, and these two
things will add to 9.

00:02:25.300 --> 00:02:27.280
So the important
thing to know is

00:02:27.280 --> 00:02:31.116
when you add up all the digits,
the sum is divisible by 3.

00:02:31.116 --> 00:02:35.987
So this is divisible by 3
as well, divisible by 3.

00:02:35.987 --> 00:02:37.820
And then finally, Let's
add up these digits.

00:02:37.820 --> 00:02:44.680
1 plus 0 plus 0 plus 7 is 8,
plus 6 is 14, plus 5 is 19.

00:02:47.300 --> 00:02:49.472
So we summed up the digits.

00:02:49.472 --> 00:02:51.912
19 is not divisible by 3.

00:02:51.912 --> 00:02:54.370
So this one, we're not going
to write a 3 right over there.

00:02:54.370 --> 00:02:56.180
It's not divisible by 3.

00:02:56.180 --> 00:02:57.540
Let's try 4.

00:02:57.540 --> 00:02:59.505
And to think about
4, you just have

00:02:59.505 --> 00:03:01.296
to look at the last
two digits and to see--

00:03:01.296 --> 00:03:03.570
are the last two
digits divisible?

00:03:03.570 --> 00:03:07.360
Are the last two
digits divisible by 4?

00:03:07.360 --> 00:03:09.610
Immediately, you can look
at this one right over here,

00:03:09.610 --> 00:03:10.640
see it's an odd number.

00:03:10.640 --> 00:03:12.020
If it's not going to
be divisible by 2,

00:03:12.020 --> 00:03:14.000
it's definitely not going
to be divisible by 4.

00:03:14.000 --> 00:03:19.010
So this one's not divisible by
any of the first few numbers

00:03:19.010 --> 00:03:19.848
right over here.

00:03:19.848 --> 00:03:21.730
But let's think about one, 88.

00:03:21.730 --> 00:03:23.130
Is that divisible by 4?

00:03:23.130 --> 00:03:24.505
And you can do
that in your head.

00:03:24.505 --> 00:03:25.860
That's 4 times 22.

00:03:25.860 --> 00:03:29.530
So this is divisible by 4.

00:03:29.530 --> 00:03:30.370
Now, let's see.

00:03:30.370 --> 00:03:33.600
4 goes into 60 15 times.

00:03:33.600 --> 00:03:36.210
And then to go from 60 to 70,
you have to get another 10,

00:03:36.210 --> 00:03:38.250
which is not divisible by 4.

00:03:38.250 --> 00:03:39.590
So that's not divisible by 4.

00:03:39.590 --> 00:03:41.780
And you can even try to
divide it out yourself.

00:03:41.780 --> 00:03:44.980
4 goes into 70,
let's see, one time.

00:03:44.980 --> 00:03:46.996
You subtract, you get a 30.

00:03:46.996 --> 00:03:49.320
4 goes into 30 seven times.

00:03:49.320 --> 00:03:51.966
You multiply, then you subtract.

00:03:51.966 --> 00:03:55.490
You get a 2 right over
here as your remainder,

00:03:55.490 --> 00:03:57.915
so it is not divisible by 4.

00:04:01.740 --> 00:04:03.990
Now, let's move on to 5.

00:04:03.990 --> 00:04:07.100
Now, you're probably already
very familiar with this.

00:04:07.100 --> 00:04:11.810
If your final digit is a 5 or
a 0, you are divisible by 5.

00:04:11.810 --> 00:04:13.280
So this one is not
divisible by 5.

00:04:13.280 --> 00:04:14.850
This one is divisible by 5.

00:04:14.850 --> 00:04:17.600
You have a 0 there, so
this is divisible by 5.

00:04:17.600 --> 00:04:20.070
And this, you have a
5 as your ones digit.

00:04:20.070 --> 00:04:22.880
So once again-- finally-- this
is divisible by something.

00:04:22.880 --> 00:04:24.910
It's divisible by 5.

00:04:24.910 --> 00:04:27.060
Now, the number 6.

00:04:27.060 --> 00:04:30.310
The simple way to think
about divisibility by 6

00:04:30.310 --> 00:04:33.070
is that you have to be
divisible by both 2 and 3

00:04:33.070 --> 00:04:36.810
in order to be divisible by 6,
because the prime factorization

00:04:36.810 --> 00:04:39.260
of 6 is 2 times 3.

00:04:39.260 --> 00:04:41.860
So here, we're
divisible by 2 and 3,

00:04:41.860 --> 00:04:43.556
so we're going to be
divisible by-- let

00:04:43.556 --> 00:04:45.055
me do that in a new
color-- so we're

00:04:45.055 --> 00:04:47.290
going to be divisible by 6.

00:04:47.290 --> 00:04:49.000
Here, we're
divisible by 2 and 3,

00:04:49.000 --> 00:04:51.000
so we're going to
be divisible by 6.

00:04:51.000 --> 00:04:53.830
And if you were just divisible
by 2 or 3, just one of them,

00:04:53.830 --> 00:04:55.371
then you wouldn't
be able to do this.

00:04:55.371 --> 00:04:57.012
You have to have
both a 2 and a 3,

00:04:57.012 --> 00:04:58.220
divisibility by both of them.

00:04:58.220 --> 00:05:01.450
And here, you're divisible
by neither 2 nor 3,

00:05:01.450 --> 00:05:03.970
so you're not going
to be divisible by 6.

00:05:03.970 --> 00:05:06.150
Now, let's do the test for 9.

00:05:06.150 --> 00:05:09.390
The test for 9 is very
similar to the test for 3.

00:05:09.390 --> 00:05:10.690
Sum up all the digits.

00:05:10.690 --> 00:05:13.565
If that sum is divisible
by 9, then you're there.

00:05:13.565 --> 00:05:17.040
Well, we already summed
up the digits here, 48.

00:05:17.040 --> 00:05:18.640
48 actually is not
divisible by 9.

00:05:18.640 --> 00:05:20.890
If you're not sure, you can
add up the digits there.

00:05:20.890 --> 00:05:21.810
You get 12.

00:05:21.810 --> 00:05:24.530
12 is definitely
not divisible by 9.

00:05:24.530 --> 00:05:27.800
So this thing right over
here is not divisible by 9.

00:05:27.800 --> 00:05:30.550
And this one over here, if
you added up all the digits,

00:05:30.550 --> 00:05:32.700
we got 18, which is divisible.

00:05:32.700 --> 00:05:35.200
It is divisible by 9.

00:05:35.200 --> 00:05:36.550
And I'm running out of colors.

00:05:36.550 --> 00:05:38.660
So this one is divisible by 9.

00:05:38.660 --> 00:05:41.352
All the digits added up to 18.

00:05:41.352 --> 00:05:43.810
And this one over here, you
don't even have to add them up,

00:05:43.810 --> 00:05:45.810
because we already know
it's not divisible by 3.

00:05:45.810 --> 00:05:48.596
If it's not divisible by 3,
it can't be divisible by 9.

00:05:48.596 --> 00:05:49.970
But if you did
add up the digits,

00:05:49.970 --> 00:05:52.950
you get 19, which is
not divisible by 9.

00:05:52.950 --> 00:05:55.730
So this also is
not divisible by 9.

00:05:55.730 --> 00:05:58.330
And then finally,
divisibility by 10.

00:05:58.330 --> 00:06:00.870
And this is the easiest one
of all, because you just

00:06:00.870 --> 00:06:04.030
have to see if you have
a 0 in the ones place.

00:06:04.030 --> 00:06:06.740
You clearly do not have a
0 in the ones place here.

00:06:06.740 --> 00:06:09.520
You do have a 0 in
the ones place there,

00:06:09.520 --> 00:06:12.330
so you are divisible by 10 here.

00:06:12.330 --> 00:06:15.150
And then finally, you don't
have a 0 in the ones place here,

00:06:15.150 --> 00:06:17.579
so you're not going
to be divisible by 10.

00:06:17.579 --> 00:06:19.120
Another way you
could think about it,

00:06:19.120 --> 00:06:22.950
you have to be divisible by both
2 and 5 to be divisible by 10.

00:06:22.950 --> 00:06:26.536
Here, you are divisible
by 5 but not by 2.

00:06:26.536 --> 00:06:27.910
But obviously,
the easiest one is

00:06:27.910 --> 00:06:31.660
to just see if you have
a 0 in the ones place.


Ordering improper fractions and mixed numbers

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:02.450
Let's order these
improper fractions

00:00:02.450 --> 00:00:04.970
and mixed numbers from
least to greatest.

00:00:04.970 --> 00:00:06.220
And there's two ways to do it.

00:00:06.220 --> 00:00:07.490
You could put them
all as mixed numbers,

00:00:07.490 --> 00:00:09.790
or you could put them all
as improper fractions.

00:00:09.790 --> 00:00:14.185
I will write them all-- let's
try it as mixed numbers first

00:00:14.185 --> 00:00:15.060
and see what happens.

00:00:15.060 --> 00:00:18.820
And then we could also
try improper fractions.

00:00:18.820 --> 00:00:20.730
So if we write them
all as mixed numbers,

00:00:20.730 --> 00:00:22.570
this expression right
here, this number.

00:00:22.570 --> 00:00:27.310
3 goes into 7 two times,
and the remainder is 1.

00:00:27.310 --> 00:00:29.610
So it's 2 and 1/3.

00:00:29.610 --> 00:00:32.159
Then we have our
4 and 1/2, which

00:00:32.159 --> 00:00:35.340
is already a mixed number.

00:00:35.340 --> 00:00:38.240
Then this one over here--
3 goes into 4 one time

00:00:38.240 --> 00:00:42.750
with a remainder of 1,
so this is 1 and 1/3.

00:00:42.750 --> 00:00:46.630
And then you have
1 and 2/5, which

00:00:46.630 --> 00:00:49.550
is already written
as a mixed number.

00:00:49.550 --> 00:00:51.960
And then finally, we
have this quantity.

00:00:51.960 --> 00:00:54.980
15 goes into 17 one time
with a remainder of 2.

00:00:54.980 --> 00:00:57.534
So this is 1 and 2/15.

00:00:57.534 --> 00:00:59.450
So we already know the
largest number is, just

00:00:59.450 --> 00:01:01.825
looking at the whole number
parts of these mixed numbers.

00:01:01.825 --> 00:01:05.209
It's 4 and 1/2, so let
me write it out here.

00:01:05.209 --> 00:01:07.750
The second largest
number is the 2 and 1/3.

00:01:11.230 --> 00:01:13.647
And now the whole number part
of all of these last three--

00:01:13.647 --> 00:01:15.146
they're all the
same, so we now have

00:01:15.146 --> 00:01:16.440
to look at the fractional part.

00:01:16.440 --> 00:01:18.540
And they all have
different denominators.

00:01:18.540 --> 00:01:21.150
So to simplify things, or so
that we can compare apples

00:01:21.150 --> 00:01:23.690
to apples, let's all give
these the same denominator.

00:01:23.690 --> 00:01:26.370
And the best common
denominator will

00:01:26.370 --> 00:01:31.830
be the least common multiple
of 3, 5, and 15, which is 15.

00:01:31.830 --> 00:01:33.230
So we can rewrite it.

00:01:33.230 --> 00:01:36.430
So this is going to be
1 and something over 15.

00:01:36.430 --> 00:01:40.180
To go from 3 to 15, you have to
multiply the denominator by 5.

00:01:40.180 --> 00:01:42.200
So let's also multiply
the numerator by 5.

00:01:42.200 --> 00:01:44.900
So this is 1 and 5/15.

00:01:44.900 --> 00:01:45.780
Let's do this one.

00:01:45.780 --> 00:01:48.520
This is 1 and something over 15.

00:01:48.520 --> 00:01:51.230
We multiply the
denominator by 3,

00:01:51.230 --> 00:01:53.490
so we also have to multiply
the numerator by 3.

00:01:53.490 --> 00:01:54.630
So let's put a 6 there.

00:01:54.630 --> 00:01:56.420
2 times 3 is 6.

00:01:56.420 --> 00:01:59.070
And then finally,
this one already

00:01:59.070 --> 00:02:00.180
has 15 as the denominator.

00:02:00.180 --> 00:02:02.190
This is 1 and 2/15.

00:02:02.190 --> 00:02:03.720
So now this is
easier to compare.

00:02:03.720 --> 00:02:05.370
They all have 15
as the denominator

00:02:05.370 --> 00:02:07.410
in the fractional part
of the mixed number.

00:02:07.410 --> 00:02:09.313
The smallest of
these is 2/15, so I'm

00:02:09.313 --> 00:02:10.479
going to write it out front.

00:02:13.310 --> 00:02:14.500
That's the smallest.

00:02:14.500 --> 00:02:16.656
Then the next smallest
is 1 and 5/15,

00:02:16.656 --> 00:02:18.530
which is this quantity
right over here, which

00:02:18.530 --> 00:02:23.140
is-- I could write
it as 1 and 1/3.

00:02:23.140 --> 00:02:26.820
And then the next smallest,
or I guess the larger one

00:02:26.820 --> 00:02:29.320
after that, is the
1 and 6/15, which

00:02:29.320 --> 00:02:31.220
is the same thing as 1 and 2/5.

00:02:34.015 --> 00:02:34.640
And we're done.

00:02:34.640 --> 00:02:36.264
And we can then
rewrite them in the way

00:02:36.264 --> 00:02:37.940
that they were
originally written.

00:02:37.940 --> 00:02:40.000
So this one right
over here in pink

00:02:40.000 --> 00:02:44.680
was originally written as 17/15,
so I'll write it as 17/15.

00:02:44.680 --> 00:02:47.470
This 1 and 1/3 was
originally written as 4/3.

00:02:47.470 --> 00:02:49.590
So I can write it as 4/3.

00:02:49.590 --> 00:02:54.710
The 1 and 2/5 was already
written as 1 and 2/5.

00:02:54.710 --> 00:02:59.420
And then the 2 and 1/3
was written as 7/3.

00:02:59.420 --> 00:03:01.560
And the 4 and 1/2 was
already 4 and 1/2.

00:03:04.081 --> 00:03:06.330
Now, the other way to do it
is to convert all of these

00:03:06.330 --> 00:03:08.455
into improper fractions.

00:03:08.455 --> 00:03:12.040
If we do it that way,
the 7/3 is still a 7/3.

00:03:12.040 --> 00:03:16.600
4 and 1/2-- to turn that into
an improper fraction, 2 times 4

00:03:16.600 --> 00:03:18.480
is-- well, one way
to think about it--

00:03:18.480 --> 00:03:20.790
4 is the same thing as 8/2.

00:03:20.790 --> 00:03:24.390
8/2 plus 1/2 is 9/2.

00:03:24.390 --> 00:03:27.600
Or a simple way, 2 times
4 is 8, plus 1 is 9.

00:03:27.600 --> 00:03:29.210
9/2.

00:03:29.210 --> 00:03:32.370
And then 4/3 is already written
as an improper fraction.

00:03:32.370 --> 00:03:33.660
1 and 2/5?

00:03:33.660 --> 00:03:37.220
Well, 1 is the
same thing as 5/5.

00:03:37.220 --> 00:03:40.820
And 5/5 plus 2/5 is 7/5.

00:03:40.820 --> 00:03:43.940
Or you could say 5
times 1 plus 2 is 7.

00:03:43.940 --> 00:03:45.496
And then finally,
we have the 17/15.

00:03:49.880 --> 00:03:52.150
Now, in order to really
compare apples to apples,

00:03:52.150 --> 00:03:54.180
we have to have a
common denominator here.

00:03:54.180 --> 00:03:58.840
And the least common multiple
of 3, 2, 3, 5 and 15--

00:03:58.840 --> 00:04:02.170
it looks like, if we just
had 3, 5's, and 15's here,

00:04:02.170 --> 00:04:03.330
it would be 15.

00:04:03.330 --> 00:04:05.364
But that's not
divisible by 2, so we're

00:04:05.364 --> 00:04:06.530
going to have to go with 30.

00:04:06.530 --> 00:04:09.290
So we're going to have 30 as
the common denominator for all

00:04:09.290 --> 00:04:11.330
of these.

00:04:11.330 --> 00:04:14.930
So 7/3-- to get the
denominator from 3 to 30,

00:04:14.930 --> 00:04:17.079
we multiplied by 10.

00:04:17.079 --> 00:04:18.790
So we multiply the
numerator by 10.

00:04:18.790 --> 00:04:21.690
So we have 70/30.

00:04:21.690 --> 00:04:23.856
Then we have 9/2,
but now we're going

00:04:23.856 --> 00:04:25.450
to make the denominator 30.

00:04:25.450 --> 00:04:29.680
To go from 2 to 30, we had to
multiply the denominator by 15.

00:04:29.680 --> 00:04:33.410
So we're going to have to
multiply the numerator by 15.

00:04:33.410 --> 00:04:36.490
So 9 times 15 is 90, plus 45.

00:04:36.490 --> 00:04:40.100
So that's 135.

00:04:40.100 --> 00:04:41.380
Now we have 4/3.

00:04:41.380 --> 00:04:45.050
We're going to rewrite
the denominator as 30.

00:04:45.050 --> 00:04:47.050
We're multiplying the
denominator by 10,

00:04:47.050 --> 00:04:49.320
so we want to multiply
the numerator by 10.

00:04:49.320 --> 00:04:51.100
So it's 40/30.

00:04:51.100 --> 00:04:54.720
And then 7/5, we're going to
write with a denominator of 30.

00:04:54.720 --> 00:04:56.760
We're multiplying
the denominator by 6,

00:04:56.760 --> 00:04:58.710
so we have to multiply
the numerator by 6.

00:04:58.710 --> 00:05:01.370
7 times 6 is 42.

00:05:01.370 --> 00:05:04.660
And then finally, 17/15.

00:05:04.660 --> 00:05:07.310
If the denominator's 30, we're
multiplying the denominator

00:05:07.310 --> 00:05:08.310
by 2.

00:05:08.310 --> 00:05:10.435
So we also have to multiply
the numerator by 2.

00:05:10.435 --> 00:05:12.660
17 times 2 is 34.

00:05:12.660 --> 00:05:15.214
And now we can compare
apples to apples.

00:05:15.214 --> 00:05:16.630
All the denominators
are the same,

00:05:16.630 --> 00:05:18.213
so we can just compare
the numerators.

00:05:18.213 --> 00:05:23.950
The smallest numerator here is
34, so 34/30 is the smallest.

00:05:23.950 --> 00:05:26.850
Then the next smallest--
it looks like 40/30.

00:05:31.480 --> 00:05:33.385
And then the next
smallest is 42/30.

00:05:38.150 --> 00:05:43.920
And then the next
smallest is 70/30.

00:05:46.750 --> 00:05:49.643
And then the next smallest or
the largest, now, is 135/30.

00:05:53.394 --> 00:05:55.810
And you convert these back
down to what they're originally

00:05:55.810 --> 00:05:56.680
represented at.

00:05:56.680 --> 00:05:59.594
You get this exact
same ordering.


New operator definitions 2

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:03.900
If x-- and the operator here is
this x with a circle around it,

00:00:03.900 --> 00:00:05.280
so maybe we'll call it circle-x.

00:00:05.280 --> 00:00:10.510
If x circle-x y is equal
to x plus 3y, and x--

00:00:10.510 --> 00:00:11.707
I'll call that circle-plus.

00:00:11.707 --> 00:00:13.540
So it's not plus, it's
a different operator.

00:00:13.540 --> 00:00:15.581
It's a new operation, and
we're defining it here.

00:00:15.581 --> 00:00:20.350
And x circle-plus y is equal
to 4x squared minus y squared,

00:00:20.350 --> 00:00:25.245
find negative 2 circle-plus the
quantity three circle-cross,

00:00:25.245 --> 00:00:28.371
or circle-x minus 1.

00:00:28.371 --> 00:00:30.620
So if we just break it down,
we use these definitions,

00:00:30.620 --> 00:00:32.536
it should hopefully be
pretty straightforward.

00:00:32.536 --> 00:00:36.710
So let's evaluate 3
circle-x negative 1.

00:00:36.710 --> 00:00:40.530
So 3 circle-x negative 1.

00:00:40.530 --> 00:00:43.790
Well, they define
that as whatever

00:00:43.790 --> 00:00:46.730
is x plus 3 times whatever is y.

00:00:46.730 --> 00:00:48.650
So this is going
to be whatever is

00:00:48.650 --> 00:00:53.440
x, so that is our 3, plus
3 times whatever is y.

00:00:53.440 --> 00:00:56.830
Well, that's going
to be negative 1.

00:00:56.830 --> 00:01:03.560
So this is 3 plus negative
3, which is equal to 0.

00:01:03.560 --> 00:01:08.150
So this whole part right
over here is equal to 0.

00:01:08.150 --> 00:01:10.270
So our entire
expression simplifies

00:01:10.270 --> 00:01:15.620
down to negative
2 circle-plus 0.

00:01:19.150 --> 00:01:21.170
And now we can use this
definition right here. x

00:01:21.170 --> 00:01:24.850
circle-plus y is equal to
4x squared minus y squared.

00:01:24.850 --> 00:01:29.160
So in this situation, our x--
let me circle it over here.

00:01:29.160 --> 00:01:37.270
Our x is negative
2 , and our y is 0.

00:01:37.270 --> 00:01:40.240
So this is going to be
equal to-- it's going

00:01:40.240 --> 00:01:43.650
to be equal to 4
times x squared.

00:01:43.650 --> 00:01:45.610
So that's negative 2 squared.

00:01:45.610 --> 00:01:51.050
4 times negative 2
squared minus y squared.

00:01:51.050 --> 00:01:53.500
Well, y is just 0.

00:01:53.500 --> 00:01:56.070
Minus 0 squared.

00:01:56.070 --> 00:01:59.240
And 0 squared is
obviously just 0.

00:01:59.240 --> 00:02:02.880
And so this simplifies to
4 times negative 2 squared.

00:02:02.880 --> 00:02:04.950
Negative 2 squared
is positive 4.

00:02:04.950 --> 00:02:06.740
So it's 4 times 4.

00:02:06.740 --> 00:02:10.990
So it simplifies to 4 times
4, which is equal to 16.

00:02:10.990 --> 00:02:12.860
And we're done.