Here we have terminal values. We have chance nodes where the two options are equiprobable.

The chance nodes have two results heads or tails.

So we're going to take a to the zero and divide it by a. a to the zero is one, so what's one divided by a?

So let's see if we can figure out this time.

And what do we get?

It's one of the shortest paths from a to g, but it's by no means the only path from a to g.

So a over x plus 5 plus b over x minus 8 is equal to well, let's get the common denominator it's equal to x plus 5 times x minus 8.

C is more difficult.

Well, phi is equal to A over B, which is equal to A plus B over A we know that A plus B over A is the same thing as

So let's divide by a again, so one over a.

left with an a in the numerator, and a divided by a is just 1.

We know in regular mathematics, if I have 1 times a, I get a.

On the day she is late, the train passes or at time is equal to 5 6 plus a minus 1 hours, where a is the amount of time it normally takes her to travel her entire route to the crossing.

So if we go from a to the first, which is just a, and divide by a, right, so we're just going to go we're just going to divide it by a.

let's think about it.

Nothing going on.

So this term now if we substitute r3 with that, this will just turn into a this will just turn into a plus 1.

180 plus 36 is 216.

Plus this a times that a.

Or the other way, you could imagine, is when you decrease the exponent, what are we doing?

It takes 1 parameter to specify P of A from which we can derive P of not A.

So to go from a to the minus one to a to the minus two,

Well, in order for this to be a finite path, this is true before t is greater than or equal to a, and less than or equal to b.

So this is equal to s a times the Laplace transform of sine of a t.

A over A plus B over A

b squared is 9, so this is going to be the same thing as

And then, 54 minus 5 that is 49, and we're done.

So that gets us to this. x to the 1 power, right?

So that means that f of x has to be less than positive a or greater than negative a.

I'm telling you that I can take let's say I want to represent, you know, I have some let me rewrite my a's and b's again.

Somebody passing?

Like when you found a route that went from X to Y

I mean, if I just wrote this right here, you would just cancel these two terms out and you would get a over x plus 5.

This is the Laplace transform of e to the and what's a? a is what we shifted by.

So when x is equal to 1, we get let me pick another color A times, 1 minus 2 is minus 1, squared is just 1.

We multiplied by a, right? a squared is just a times a.

We're essentially dealing with the same number, the negatives of each other.

So this'll be a because I just distribute the a, right? a times a to the zero, plus a times a to the 1, plus a times a squared, plus all the way a times a to the n minus one, plus a times a to the n.

So this is a to the seventh power. (A to the five plus two power.)

And we show why this works in a previous video.

So let's do that.

Let me do it here.

So, it's a normal looking syringe.

So, just say the semicolon thing usually means, you know, go to the next line.

A to the fifth literally means a times a times a times a times a.