So we said that this is equal to e to the r, so p times this is equal to p.

The P initial is equal to 0.

Does a to the power of p minus 1 mod p equal 1?

The discount is equal to p times x.

Well, if you just look here, I just showed you that that's also equal to p squared. p squared is equal to 9 .

So let me write p is equal to mass

Look, if y is equal to p times x .

I'll say p, just so it makes sense, p is equal to the percentage off.

We could have let y is equal to force and m is equal to... or mass is equal to p.

for which we are going to use the symbol p which is equal to p times acceleration.

And if you want to factor a p out of this, this is going to be equal to p times, if you take p divided p you get a 1, p square divided by p is p.

So we could say that p is equal to 15 divided into 5 equal groups.

Let's say that p is equal to I don't know.

So this is going to be equal to 1 minus p.

Well, if 5 times p is equal to 15 if I want to figure out what p is,

So if you were to borrow, let's say, p is equal to,

So this right here becomes, you have this p right over here, so this is equal to p.

So we get p plus q has to be equal to 100 , or I could just write equal to 1.

Divide both sides by 4. p cannot be equal to negative 5.

So, for example, if p is the frequency of blue eyes, so let me say p is equal to the frequency of blue eyes, and q is equal to the frequency of brown eyes, what's p plus q going to be?

In the equation, P is constructed to equal 1.00 in the base year.

I is equal to P times A times T population, affluence and technology.

let's say we know that y is equal to p times x what if you want to have them both be equal.

Well y was equal to p times x so y divided by x is gonna be the same as p times x divided by x

But we were able to manipulate the abstraction here, and get y over x is equal to p

The partial of Q with respect to x is equal to the partial of P with respect to y.

Of course, this whole time, we have to add the caveat that p cannot equal negative 5.

121 to 128 p. 121, p. 122, p. 123, p. 124, p. 125, p. 126, p. 127, p. 128.

7 P 4 to P 5 1 P 4 to P 3

5 P 4 to P 5 1 P 4 to P 3

Over here, we could do the same exercise for p plus 20 also cannot be equal to 0.

So in both situations, p being equal to negative 5 would make either of these rational expressions undefined.

That's going to be equal to sorry we're going to have to add these two plus the integral from x is equal to b to x is equal to a of do it in that same color of p of x.

So the domain here is the set of all reals such or p is equal to the set of all reals such that p does not equal negative 5, or essentially all numbers except for negative 5, all real numbers.

If you take 15 miles and divide it into 5 equal groups, you're going to end up with p.

P 2 to P 3

P 3 to P 4

P 4 to P 5

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5 P 3 to P 4

10 P 2 to P 3

10 P 2 to P 3

a P 4 to P 2.

And then p times p squared is p to the third.

So then you could say, partial of Q with respect to x, minus the partial of P with respect to y, has to be equal to 0, or these two things have to equal each other.