ElectricPavlov

If they sit around the table ....can they not be seated   

3    2                          2      3

   1              and             1            I don't think  these can be rotated to produce the other...so there would be   288 * 2   ways to be seated around the table.    

Not sure what the answer is....but it has to be more than 8 doesn't it?:

10   0    0

9     1    0

8      2   0

7       3  0

6       4   0

5       5   0

8     1     1

7     2     1

6     2     2

6      3    1

5       4   1

5     3     2

4     3    3

4     4    2

                         fourteen ways?

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This describes an upside down parabola (opens downward...looks like a dome)

so    a^2 = 49   means  a = -7

so you have   -7x^2+bx-6 =0        Using quadratic formula

\(0> {-b \pm \sqrt{b^2-4(7)(-6)} \over -14}\)   yields   b <12.96   and b  > -12.96  

                                                        so b<12.96 is the greatest value

In     Out

5        1

4        2

3        3

2        4

1        5           Five ways  

Total would be   98.25 x 3

Average PER DAY would be   98.25/10

The STARTING midpoint of BG  is at   3, 1   then it is translated 5 to the left

  so the 'x' coordinate becomes   3-5 = -2  

    and translated UP 2 units

       so the 'y' coordinate becomes 1+2 = 3

(-2,3)

Let's write the beginning of the parabola in vertex form

y= a(x-h)^2 +k   (h,k) is the vertex  ...substitute

y= a(x-3)^2 + 2                expand

 y = a (x^2 - 6x +9) + 2         now substitute the point (1,0) in to the equation

0 = a (1^2 -6 +9) + 2

 0 = 4a + 2

so a = -1/2 in THIS equation and it looks like this

y = -1/2 (x^2-6x+9) +2     Simplify

y = -1/2x^2 +3x -4.5 + 2

 y= -1/2 x^2 + 3x - 2.5 

Here is a graph:

1    4    x 3

      2 x 2   x 3

2.

       2 x 13

1      22/55   vs   20/55

2   -18/78     vs   -18/78