So you're going to get some combination of the i and j unit vectors.

3 minus nothing is 3.

And then you'd get x could be equal to negative 8, or x could be equal to negative 10.

There, we just set up a equation with one unknown and we can solve for x.

And now I evaluate this at 1 and 0.

let's just divide by a again.

So this was c plud d i, so this is its conjugate.

And so, if we just put this on the other side of the equation, what do we get?

Transform of any arbitrary function very, very quickly.

Here we go the other way.

So, so far so good.

What the point here really is is that we can do things with the social environment.

Plus 1 s that's this right there times the Laplace transform of 1.

Got it.

So you get 10 billion for them.

If I multiplied this area times a small dy, then all of a sudden I have a sliver of volume.

We're multiplying our f of t times e to the 1t.

If you distribute the negative 3, you're going to get that expression.

So, minus 2 3 x, you go down 2 for every 3 that you go out.

We'd also want to multiply the right hand side by x.

You multiply that times negative 8

Someone has to say, well, when x is 2, y is 3.

If you add 26 42, you should get 68.

And if x plus 6 is 0, then that means that x is negative 6.

13 00 00 42,55 gt 00 00 46,34 Now, all this is saying is what value does the expression x squared approach as x approaches 2?

So now we just solve for x.

Or the probability of getting heads, tails, right?

So this first term here, the upper left term, where does it get its row information from and where does it get its column information from?

In 2004, if we assume the pattern continues, let's add another 75.

Everywhere where you see an x, and you replace it this expression, you get these and that's what the question, essentially, was asking us.

So I get x squared plus b a x is equal to you have to divide both sides by a minus c a.

So if I initialize the first row in the triangle to 1.

If you were to add 2 to Diya's age, if you were to go to more, so plus 2, you would get to Imran's age.

So if I multiply 2 times my vector a minus 2 3 times my vector b, I will get to the vector 2, 2.

So the negative 1 is what provides the alternating numbers.

Now, last step, we just have to divide both sides by 4, so you divide both sides by 4, and you get x is equal to negative 1 plus or minus 2, times the square root of 2, over 4.

This is a single successor state of 100, so if we have 100 over here minus the 3 that it costs us to get there, we get 97.

You give me any x, any y, you give any x, y in the x y plane, and these are going to end up with some numbers, right?

And it contributes to about 70 samples of those thousand samples.

Imran's no dummy, so he does the same thing. He raises his price to 2.

And then we can essentially just add and subtract them from the center.

Next was this trial.

This term comes from the x times the x.

We have AC and DC, get 12 volts DC, so that could be used for certain applications.

And then we distribute again.