CPhill

Think about this, Mathman :

If it sold for 100% above the minumum bid.....100% of $125 = $125

So......$125  plus 100% of $125   =  $125 + $125  =  2* $125 =  $250

Thus.... 100%  above the minimum bid  means that the price was doubled

And 200% more means   200% of $125  = $250

So $125 plus 200% of $125  = $125 + $250 = $375

Thus.....200% above the minimum bid = 3 times $125 = $375

So....by this logic.......288%  =  3.88 times $125 = $485

Notice that if  it was sold for 100%  more than the minimum bid, it would be sold for 2 times as much....thus......

100%  = 1.00 + 1  = 2 times as much   .....so.....

288%  =  2.88 + 1  = 3.88 times as much

And we have

3.88($125)   = $485

"Guest" did a pretty good job, but when he gets to this:

7v+5=5+7v  

We have an identity.......both sides are exactly the same...so......any value of v will  make this equation true....!!!

d/dx (x^2/x-1)  =   2x(x - 1)^-1  - x^2(x -1)^-2  =  [2x^2 - 2x - x^2] / [x-1]^2   =  [x^2 - 2x] / [x - 1]^2 =

[x^2 -2x + 1  - 1] /[x -1]^2  =  [x -1]^2/ [x -1]^2 -  1/[x - 1]^2  =   1 - 1/[x -1]^2  = 2 g(x)

So

g(x)  = 1/2  - 1/ [2(x -1)^2]

And  (1/3)g(x)  =  1/6 - 1/[6(x -1)^2]  ......... . so we have

3                               3

∫  1/6 dx        -   (1/6) ∫  1/ (x - 1)^2  dx   

2                               2

The first integral evaluates to 1/6

For the second  integral    let x - 1 = u  .....so......     du = dx

So we have

       3

(1/6)∫   [1/ 1/u^2 ] du   =

       2

                3

-(1/6)u^-1 ]  =  -(1/6)[ 1/ (3-1)  - 1/(2-1)]  =  (1/6)[1 - 1/2]   = 1/12

                2

So   1/6  - 1/12   = 1/12

0 / 0   is known as an "indeterminate" form.......we can't say WHAT it might be

sqrt(144)  = 12

4n^2-16n-14=6  add 14 to both sides

4n^2 - 16n   = 20    divide through by 4

n^2 - 4n  =  5          take (1/2)  of  (-4)  = (-2)....square it = 4 and add to both sides

n^2 - 4n + 4 = 5 + 4      factor the left side, simplify the right

(n - 2) (n -2)  = 9

(n - 2)^2   = 9        take the positive and negative roots of both sides

n - 2   = (plus/minus)( 3)

So

n - 2 = 3     and n = 5     or

n - 2 = -3     and n = -1

-3^2  = -9     but

(-3)^2  = 9

(What's Equivalent to 3x squared minus 5x plus 4) plus (2x squared minus 7)

3x^2 - 5x + 4 + 2x^2 - 7  =   [combine like terms ]

5x^2 - 5x - 3

Here's a good resource for this :  http://www.purplemath.com/modules/ratio4.htm