We can divide an equation, or multiply an equation by a scalar.

What we can do is, we can replace any equation with that equation times some scalar multiple, plus another equation.

There's a basic equation that we can't get away from.

So because it's a parametric equation, we can draw some arrows.

So this is a straight up quadratic equation, so we could use the quadratic formula here.

We can even set up a parametric equation that goes in the other direction.

But let's see if we can get the equation for that plane.

You can make it a quartic equation. Make it kind of harder, calculating wise.

And by doing these activities and by training your brain just like we train our bodies, what we've found is we can reverse the formula for happiness and success, and in doing so, not only create ripples of positivity, but a real revolution.

What we learn is that if it can be homogeneous, if this is a homogeneous differential equation, that we can make a variable substitution.

So how do we set up an equation where if I put in one of these numbers I'm going to get 0?

So here I have an equation, a linear equation.

Now, the quadratic formula, it applies to any quadratic equation of the form we could put the 0 on the left hand side.

And this is the best that we humans can do at graphing a three variable linear equation on a piece of paper.

Formula

Well, we can take the partial derivative of this with respect to y, and we could call this function of x and y, M.

And I can put it in this simple equation.

Bernoulli's equation.

And this is an equation.

Archimedes' formula.

So we know m 3 4, and b is equal to 8, so we can write the equation of this line. in slope intercept form.

We're really just learning a lot of physics here, but this will set us up with a nice quadratic equation that we can use the quadratic formula for.

Now we can do the same exercise if we wanted to find out the line, the equation of the line, that goes between x1 and x2.

So p plus 5 cannot be equal to 0, or if we subtract both sides of this we can't call it an equation, but we could call it a not equation by negative 5, if we subtract negative 5 from both sides, you get p cannot be equal to these cancel out negative 5.

I want to share with you a little equation, okay?

It's one in which we can all gain.

And we were about to show them some pretty simple math.

Let's say we have the following second order differential equation.

If argument is war, then there's an implicit equation of learning with losing.

It's a partial differential equation.

Hendersen Hasselbalch Equation.

A very simple equation.

If I gave you an equation, an arbitrary equation now.

A no brainer.

let's say another equation.

Did I just say equation?

That's why they're called 'equations.'

But this is an equation.

We could just pack up our bags. Tonight. We could go now.

A tax on carbon should be equivalent to its damage.

One, how do I know that it's an exact equation?

So they claim that this is a solution of this differential equation.

We just, I guess we could say, simplified this set of parametric equations to this one equation, where y is a function of x.

This is the pricing equation.

Forfeiture of assets of equivalent value