So let me give you one very easy problem, a second very easy problem and then a third, hard, problem.

K3b detected a problem with the medium.

I'll come back to that in more detail again when I talk about the bonus problem.

Don't complicate the problem by raising new issues.

Look at that.

Welcome to homework assignment number 3.

Clearly the test has a strong correlation to whether I have cancer.

Hometown security means creating wealth here at home, instead of destroying it overseas.

Our teacher will give us difficult problems.

So, how do you render authenticity, is the question.

So I would argue A is preferable.

So, let's start doing some problems.

So.

I'm going to try and explain why it is that perhaps we don't understand as much as we think we do.

I thought she went back home, but she is working in that restaurant.

I got into trouble with the police by driving too fast.

I got into trouble with the police for driving too fast.

Our teacher will give us difficult problems.

It challenges the norms.

When I asked this question, were you excited?

Well, it's going to give us what a minus 1 times b is, which is a times b minus b.

You're damn right. You're right in the middle.

And once we had the answer to that, we need to multiply that by 2 to get the answer to the original problem.

So we have these anatomical categories that persist, that are in many ways problematic and questionable.

Probably better than I do.

Congratulations for doing this. So this is the last, and final, class.

I think you might see the pattern if we do a couple of more problems.

Let's do some problems with plotting points and graphical representations of functions.

Now what do you want us to do?

I can't afford any traps.

Let's say I had the situation let me give me a couple of problems if I said three over x is equal to, let's just say five.

We can move things out of the stratosphere into the mesosphere, in principle solving the ozone problem.

I'll reconsider the matter.

It's not like its relation to some abstract form.

Oh, Shaun, do we have to go through all that again?

So I'll make a video an algebraic long division.

So we can also generate instructions on how to operate the controls of the vehicle.

(Laughter)

Wanted to make sure you got off all right.

But we are done.

As a rule of thumb, as soon as you do have a test case that reproduces the problem, the test case makes the problem report obsolete.

After that, we're clear here, too.

Then we run an algorithm for solving problem X to get solutions to those and maybe that generates more instances but after polynomial number of calls to this algorithm, what comes spitting out is a solution to the original instance of problem Y.

Let's see if we could do a couple more of these conic section identification problems.

Let's say we have the absolute value of 2x let me do another one over here.