The manager opened the door and identified himself.

She was anxious lest she might miss the train.

She was worried that she might miss the train.

She was worried that she might be late for the train.

No, Kelby's got nothing to worry about. I'm only here temporarily.

It's OK now. Don't worry. You can depend on me one hundred percent.

And we just distributed it along two and we just, we distributed it twox plus y along each of these numbers.

I just multiplied these two expressions or these complex numbers, really

Master, there's something strange here.

lady, you don't have to ask twice. you got yourself a rider, honest. i don't have any gas, though. we'll fix that up. you try the people here? the man's in bed.

I'll put this in yellow. We get 30 equals one half b 2 times b 4

I want him manning a radar tower in Alaska by the end of the day.

If you're not sufficiently stimulated by this investigation do us both a favor and ask for a transfer.

What we're going to do is apply gradient descent to minimize our squared error cost function.

And so we can just re associate these or actually move this around from the commutative and dissociative properties of multiplication.

Don't worry. I'll leave. First I'm gonna get you to your ship.

And a hyperbola's equation looks like this. x squared over a squared minus y squared over b squared, or it could be y squared over b squared minus x squared over a square is equal to 1.

One of these days.

Well in that situation, that literally means multiplying x squared by itself, three times.

And I'll do those two ways.

Maybe if I can factor out something here I can make it more interesting.

Uh, we have some concerns about some health exposure you may have experienced during the flight. I'm sorry, I don't...

What does that mean?

If this is the formula for the ellipse, this is where the a comes from. x squared over a squared plus y squared over b squared is equal to 1.

This is how to build the structure.

And so you see it's a pattern.

Hop on in.

Because if you were to multiply just the x terms here, when you actually do your distributive property and multiply out these binomials, you'll just get an x to the third, but we had an ax to the third.

So we could say, 60, let's call that x.

So they give us x to the negative 3 times 5 to the negative 2 times x squared.

The first step is attention training.

Action stations. Action stations.

Action stations. Launch alert, Vipers.

Express Delivery.

Those are pretty intuitive, I think.

Well, the fever's down a Little. I think he'll be all right.

Come on. Hey, hey, hey!

Get in, you dumb bastards!

Get in.

And that would be 2x plus 1, times 2x minus 1.

The other one would be if the minus sign was the other way around.

So that simplifies too.

Our area squared is equal to a squared times b squared. a squared times d squared, plus c squared times b squared, plus c squared times d squared.

We're multiplying a by itself five times, then another two times, so let me make it clear this over here is a to the fifth, this over here is a squared, when you multiply the two you're multiplying a by itself seven times!

And that equals c squared minus d squared i squared.