CPhill

Let the midpoint of the base  of  the triangle  =  (0,0)

Let the bottom left vertex of the triangle =  (0, -1)

Let  the top left vertex o f the hexagon be   ( -1/2 , sqrt (3)  / 2)

A =  [   (-1 + -1/2)  /2   ,  (sqrt (3)/2 + 0)/ 2 ] =  [ -3/4  , sqrt (3) / 4) ] 

So   the  base of the triangle =  2    and the height = y coord of A  =   sqrt (3) / 4

Its area =   (1/2) (2) ( sqrt (3) / 4)  =    sqrt (3)  /4

Area of  the hexagon =   (6) ( 1)^2  * sin (60°)  =   3 sqrt (3)  / 2 =     6sqrt (3) / 4 

Fraction that is  gray =       sqrt (3) / 4                 1

                                      ____________  =        ____

                                        6 sqrt (3) / 4                 6

(x^2 + 2x + 1)^4   =

[ ( x + 1)^2 ] ^4   =

(x + 1)^8 =   1 x^8  +  8x^7  +  28x^6 + 56x^5 + 70x^4 + 56x^3 + 28x^2 + 8x +  1

a1 =  8

a3 = 56

a5 = 56

a7 = 8 

Sum =   64 * 2  =   128

Volume of   of original cylinder  =  pi ^r^2 * h

When the  diameter is  increased by 150%  (1.5 times) so is the radius

New volume =    pi * ( 1.5 r)^2 * h =   (2.25) * pi ^r^2 * h

% increase   =    ( 2.25  -1)  / ( 1)  x  100%  =   1.25 x 100%   =   125 %

Nice, Builderboi  !!!

{ I might have tried to make this one more difficult....LOL!!!!   }

ab^2   = 27/5

ab =   135                divide the first by the second and we  get

b =  27 / ( 135 * 5)  =   27 /  675  = 1/25

a ( 1/25)  =  135

a =   25 (135)    =   3375

a + 5b  = 

3375 + 5 (1/25)  =  

3375  + 1/5  =

3375. 20

Why stop at 1000 ????

You need to  stick around  !!!!

We have a total of    (9) (8)   =  72 outcomes =  72 sets   (the order of sets matter)

(1,8)  (8,1)  (2,4) (4, 2)

P(8)  =   4 /  72   =    1/18

120 -  120(1/4)  - 25  - 120 (.20)  = 

120 -  30   - 25   -  24  =

41  have no spread

3n   where n is the row  number

So

3 (100) =    300

To find the height of the triangle, let x = 0

Then  y = 2  = the height

To find the width of the base, let y = 0

Then x = 3  = the base width

Area =  (3)(2) / 2   =    3 units^2