Math Is Fun Forum

Or maybe 6 was afraid of 7 simply because 7 is bigger then him.

Or perhaps 6 was afraid of 7 because the two of them together make 13, an unlucky number.

perhaps. But can you prove 2 + 2 will always equal 4? We obvserve it happens every time we try but technically can't prove it. Does that make it less true?

I agree proofs should be done most of the time, but sometimes proving an obvious concept feels redundant.

Ah, I forgot. The graphs of an inverse function is the graph of the original function, reflected about the line y = x. So you could also draw a graph of the two functions and determine whether they appear to be relfections about the line y = x.

technically g(x) is not a function as a function only returns one value for a given input. It does not pass the vertical line test and does not qualify as a function. I just drew it that way to illustrate how the reflection works.

bery good? are you being funny?

Nah we just pretend to be.

No problem at all. I only wish high school chicks would ask for help with math in my neighborhood. ;-)

John E franklin, averaging the zero's, to find the axis of symetry. Why didn't I think of that? Just remember this is only ok to do when the parabolla is verticle. It cannot be solved for x instead and the xy coefficient must be zero. (remember the general conic equation)

Well basicly its the same problem presented in two different forms. When you graph an equation or a function on a cartesian coordinate grid, the horizontal location on the x axis represents the value of what they call the independant variable. The height on the y axis represents the value of the expression evaluated at that location.

Therefore if you have the eqaution:

L - S = 10

And

S * L = Product

We can rearrange the first equation to find L = 10 + S and subsitute this expression for L:

S * (10 + S) = Product

10S + S^2 = Product

if we graph were to replace S with x and Product with Y we would have:

x^2 + 10x = y

this is the eqaution of a parabolla. This graph represents the product of the two numbers who's difference is 10. Therefore we can look at the low point on the graph to find the minimum product, and note what value of x is required. We used x to represent S so we can use the x coordinate of the lowpoint on the graph for S, and the solve for L. The equation y = x^2 + 10x is a parabolla that opens upward, thus the vertex is the lowpoint on the graph. Using any of the various methods to find the vertex, we find the x coordinate of the vertex is x = -5. We used  x to represent S so S = -5

Now lets use this value of S in the original equation to find L.

L - S = 10

L - (-5) = 10

L + 5 = 10

L = 5

So the two numbers are 5 and -5. :-)

lol. I just saw this yesterday and learned how to do it today. Yeah I suspected you could write it in  tersm of e but wasn't sure. Very cool.

I'm not sure I've done differentiation of the form u^x yet. I think I know how to do it but I'm not sure so I'll let someone who knows tell you.

Hahaha! This is great stuff! Keep it coming!

Math = anything and everything that ever was uber!

science = math + wiseguy

Decaf = Coffee/infinity 

I find the description of the rules unclear.

He "randomly" opens all the remaining cases? Why not just open all the remaining cases at once? I'm not following.

Maybe I should just stop asking questions and watch the show.