If it takes him t minutes to go and t minutes to come back, he traveled t minutes.

This is equal to x squared minus 2 times xy plus y squared.

All right, let's plot these on a graph, as they tell us to do.

It's a slightly different color, but maybe you won't notice.

And then the coefficient on the original function is just a constant, right?

So let me draw it like this.

That tells us that the inverse Laplace transform, if we take the inverse Laplace transform and

I could have my dx's let me pick a vibrant color so you can see it.

So now and I'll switch colors just avoid monotony this is equal to, actually, let me just this is y.

Square root of y squared is y, times y squared y to the third over 2.

And then 180 plus another 36 is 216.

As you can see, it is a reflection of our original f of x along the line y is equal to x.

This means 5 times itself three times, so this is equal to 5 times 5 times 5.

So this is the graph right here of 3 times x plus 5 squared plus 1

I either have a blue forehead, or I don't have a blue forehead.

Let me put this in a new color, so now he's at 1,800.

So it's almost a greater infinity of potential possibilities.

Minus threei plus fouri.

And maybe the constant in one of the cases is 0 or something.

For that x, this relation seems to have two possible f of x's. f of x could be that value or f of x could be that value.

So, we know that a to 1 over log base x of a, is equal to b to the 1 over log base x of b.

So their operating profit.

Sure. What is it?

It's going to be 15 minus You see it's going to be n minus 1 right here.

And that's the same thing as if you divide the top and bottom by three.

But we learned that the vertex of this parabola is the point x sub 1 comma y sub 1.

Because we're multiplying i times i we get a negative one, but it becomes real again.

Well this is a function, assuming that it's kind of the traditional way that you see it.

It goes into 63 one time, because 2 times 35 is 70, so that's too big.

And then what is v prime?

If x is equal to 0, then what do we have?

Its vertex, right there, its vertex is the point x1 comma y1.

And if you go the other way, 8a times 2a squared is 16a squared.

So let's work that out here. 125 times 0.75.

Let me graph y equals x. y equals x. y equals x is that line right there.

Well, we know we can add these exponents.

I moved three things by a millimeter.

So when you add them together you have b plus d i's. b plus d in the imaginary direction, you can almost imagine.

But note this

Well, shall we?

Zoom in a little bit because I think you might have trouble reading it because it kind of shrinks it when I go to YouTube. 2,117.

And governments do very well. They pat themselves on the back.

So you get g of 3 is equal to 6 plus 1.

This was just, times plus thirteen, I wrote that just to make sure that you understood that the negatives canceled out.

The diameter would equal 10 meters over pi or 10 over pi meters.