00:01
All right, so we have two functions, a function for the points of a circumference of earth, x squared plus y squared equals 41, and the trajectory of a meteor, y squared equals 20x plus 140.
00:13
And what you will see here on the right is what that would look graphically.
00:23
You could just put a chart on and put x values of interest, y values.
00:27
And you'll get this and you'll see that the trajectory of earth of the meteor does not hit earth.
00:35
But if you wanted to do that analytically, what you could do is you could look at our earth equation and rewrite it as y squared equals negative x squared plus 41.
00:53
I hope that is obvious, just moving the x squared to the right side.
00:57
And what you'll see is that there's y squared on one side of both the trajectory of the meteor and earth.
01:08
So we can imagine a situation in which our earth equation is set equal to our meteor equation.
01:26
And that would just be negative x squared plus 41 equal to 20x plus 140.
01:39
And this would be the supposed condition if the meteor does in fact hit earth.
01:46
And we'll put everything on one side so we can get zero equal to x squared plus 20x minus 99.
02:00
And this is pretty ugly.
02:03
We want to figure out what x is allow this solution to be correct.
02:07
And that means x is equal to.
02:12
Going to do the the quadratic formula where 1 is our a, 20 is our b, negative 99 is our c.
02:23
So x equals negative b plus or minus a square, x equal x or minus b squared.
02:46
Sorry, i had to remember that for a second b squared minus four ac all over two a it's been a while since i've had to do that and once you fill up this negative 20 plus or minus square root 20 squared minus four times one times negative 99 all over two times one what you'll get close negative 20 plus or minus square root 400 minus and so this is 99 times four is 396 plus three 96 all over two and we get simplified this even more and that is 796 over two and it keeps.
04:16
And that actually equates to nothing nice, which is equal to negative 24 .107 and 4 .107.
04:36
That is the exact numbers that that gives us.
04:41
Probably not that exists.
04:42
It might be around about...