geno3141

1 L  =  1000 ml     --->     8 L  =  8000 ml

                                       8 L - 4300 ml  =  8000 ml - 4300 ml  =  3700 ml

h(x)  =  -2(x - 2)² + 2

h(x)  =  -2(x - 2)(x - 2) + 2

h(x)  =  -2(x² - 2x - 2x + 4) + 2                   [Use FOIL]

h(x)  =  -2(x² - 4x + 4) + 2                          [Simplify]

h(x)  =  -2x² + 8x - 8 + 2                             [Distribute the -2] 

h(x)  =  -2x² + 8x - 6                                   [Simplify]

If there are 12 persons and each person produces 725 BTUs, the total number of BTUs is  12 x 725  =  8700.

Assuming that the box is approximately a rectangular solid, its volume will be  39 x 7.25 x 6.5  =  1837.875 cu ft.

The number of BTUs per cubic foot is  8700 / 1837.875  =  4.73 BTU/cu ft.

An  n by n  square will have n edges on the top row, n edges on the bottom row, n - 2 edges on the left side and n - 2 edges on the right side for a total of  n + n + (n - 2) + (n - 2)  =  4n - 4 edges.

For a 20 x 20 square, there will be 4(20) - 4  =  80 - 4  =  76 edges.

The border number will be 76.

0.50

Some background:  i² = -1     i⁴ = 1     i⁸ = (i⁴) · (i⁴)  = 1 · 1 = 1

8 · (i^-6) 

Multiply by  i⁸  (which is just 1):  8 · (i^-6) · i⁸  =  8 · i²  =  8 · -1  =  -8

The formula is:  y = 2^x

First night:         y = 2¹  =  2

Second night:    y = 2²  =  4

Ninth night:        y = 2⁹  =  512

2ⁿ - 1  =  118 000

--->     2ⁿ  =  118 001

--->     log( 2ⁿ )  =  log( 118 001 )

--->     n·log( 2 )  =  log( 118  001 )

--->     n  =  log( 118 001 ) / log ( 2 )

--->     n  =  16.848 ...   

--->     n  =  17

Since  2⁵ - 1  =  31     and     2¹¹ - 1  =  2047, the size are between  31  and  2047.

It takes at most  n  checks to find an item in a field of  2ⁿ - 1  items.

When  n = 6,  2⁶ - 1  =  63

When  n = 7,  2⁷ - 1  =  127

So, if you have 106 words, it will take a binary search at most 7 checks.