CPhill

Uh...h7....can you show the steps to this one???.....just giving the answers doesn't explain how you got there...

Well...this would cover a lot of territory.......

Hers's a basic guide to Trigonometry that includes a discussion of the unit circle....you might want to take this a little at a time....

A "Googol"  is 10^100  ....a pretty large number

A "Googolplex" is 10^(10)^100 = 10^^googol  a number that is so large, that we could not write it out in the physical universe, even if we "shrunk" each zero to an "atomic" scale

 {However, these numbers are chickenfeed compared to "Graham's" Number}

Here's another method, h7......when two fractions are equal, their cross-products are equal

This implies that

3 * x = 5 *15

3x = 75    divide by 3 on both sides

x = 25  ....  just as you found.....!!!

Here's a graph of the position function and the velocity fuction that demonstrates Alan's and Heureka's answers....

Excellent, h7....!!!!

I'm impressed.....

There is a "long division" method that used to be taught many years ago in schools, but I think that it's pretty tricky to use until you get the hang of it....

Here's a simpler way - the "bisection" method.....this website explains it pretty well

C=15+ 0.10n                      C=0.25n

n=65

15 + .10(65)  = 21.5             .25(65) = 16.25

Company "A" is the better option.....

Using x + y = 2   →  y = 2 - x      and xy = 23  ...so....

x(2- x)= 23      expand

2x - x^2 = 23    rearrange

x^2 - 2x + 23 = 0    .....which implies that...

x^2 = 2x -23

And y^2 = (2 - x)^2 = (x -2)^2 = x^2 - 4x + 4

Therefore

x^2 + y^2 =

2x - 23 + x^2 - 4x + 4 =

x^2 - 2x - 19

Ah...that's very clever, Melody.....that thought didn't strike me...!!!