So, this is obviously telling us that mu of x is equal to x.

So if you, if you, the 3 would replace the x. So, f (3), so f (3) is equal to 3 plus 2, which equals 5, right?

And then that is equal to the right hand side of the equation.

like things are going to work out. So we could select a is equal to positive 5 and b is equal to 3. Those would work out to ab equal 15.

Now 1 plus 9 is 10, plus 8.

That's just x.

Because zero times negative four three.

Well let's take the partial of psi with respect to y.

So if you subtract the big part minus the little part

So this distance right here, the length of the rope, is equal to 25 feet.

That was my definition of vector addition.

No remainder.

And it's going to be all of that over the old denominator.

And there we have it.

So if we take the partial, with respect to x, of both of these, we know from this that these should be equal, if psi and its partials are continuous over that domain.

Notice it's at negative 4, right above A.

And let me just draw some points here, so it's 1, 2, 3

So I have 1, 2, 3, 4, 5.

Well, 2 is even so we do this top one.

Approximately.

Non zero number.

Then this is going to be equal to zero.

Which is going to be a positive.

So this is 3 times 0.

So the decimal will end up right over here.

7 plus 44 would be 51, so this is going to be 61.

Well the next one is easy, it's already in decimal form.

If we go down here, 8 plus 5 is 13.

So this is going to be equal to the scalar quantity times itself.

If x is equal to negative 1 3, this or this denominator would be equal to zero.

You could just swap these two the partial of P with respect to y minus the partial of Q with respect to x da.

We have a while loop, where the test is not equal to ten

That's 5P 3, and we want to set that equal to 3 4 P.

We want to find a times b that is equal to 1 times 6, which is equal to 6.

One times zero.

And the partial derivative of psi, with respect to y, is equal to N.

Let's have 3 groups of 3.

Divide both sides by 2.

I think you get it now

So we have r is equal to 8 plus or minus the square root of 16, over 8, is equal to 8 plus or minus 4 over 8.

I could just do it right over here on the right hand side.

Negative one times negative one is equal to positive one.

Now, you might be tempted to say What about the probability of X given not Y?

Now you don't have to know that fancy word alternate interior angles you really just have to deduce what we just saw over here, that vertical angles are gonna be equal and corresponding angles are gonna be equal.

So this angle is vertical with that one, so it's going to be equal to that angle right over there.