And what we calculated here is just the average slope across this change in time.

B goes straight up and down, so we can add up arbitrary multiples of b to that.

Let's say we're dealing with two dimensional vectors.

So c1 is equal to x1.

2 is just one little point in R.

This is minus 4 times our vector v.

Now my claim was that I can represent any point.

What does vector b do?

If you pay a premium of five hundred dollars every year for ten years so the term here is ten years ten years if you are to die at any point over dose ten years we will give you

This goes there. This matches that part.

PROBLEM Construct a line perpendicular to the given line.

There you go.

Looks like a reversed check mark.

So let me take another arbitrary point on this ellipse.

So let's say that you're starting at the point x1, and x2.

If you say, OK, what combination of a and b can get me to the point let's say I want to get to the point let me go back up here.

But the convention for vectors is that you can start at any point.

You can only hold me for 48 hours.

So, the first thing we realize, all of a sudden is that no matter where we go, it was easy to do it with these points.

Minus 5 comma 6 Is right there, so I draw my vector like that.

The height of this ring is f of x,1. f of x evaluated at that arbitrary point we picked up.

Any

For any given price, it's going to lower the quantity demanded.

It could be 1 2, it could be 10.

We said this could be any constant and this could be any constant.

If we want to say there's no dirt in any location, it's a little bit more complicated.

So this number right here is going to be the exact same thing as if I took a point right here and I'm picking these points arbitrarily, as long as they're on the hyperbola, and if I called these two points d3 and d4, the difference between d1 and d2 is the same thing as the difference, between d3 minus d4.

I could draw it like that as well, but let's just say this is set R.

An open ended mutual fund at any point in time or I should say at the end of trading at the end of a day, they can lose investors, or they can gain investors so it's an incentive for an open ended fund to constantly market itself because the manager wants to manage more money so that he gets more of a management fee

I mean, we don't know what they are.

Random engine

Random colors

Random Lamp Style

Any files

Any kind of value

Jeeves, Mr. Bickersteth is still up the pole.

Any raccoon.

You can turn the lock if you're like that, you know.

And this line, it essentially describes all the possible combination of cost for a given number of sessions.

But just for seeing why choice C doesn't work or figuring out the slope, think about it this way.

Now our domain is the xy plane.

So we could, say, we could add vector b to it.

Well this guy is just the dot product of this with itself.

And the way I want you to get there is through a programming exercise.

And then we can simply say that execution of this line directly is related to passing or failing.