ElectricPavlov

(1) sqrt2  + 1/2 sqrt2      +  (1) sqrt3  + 1/3 sqrt3 =

3/2 * sqrt2      + 4/3 * sqrt 3 =

9 sqrt2  + 8 sqrt 3

             6

Bob rate   1 table /4hr  = 1/4

Sue rate   = 1/6

Jim rate  = 1/12

Build 1 table          1  /  (1/4 + 1/6 +1/12 )   hr   = 2 hours 

Line equation    y = mx + b     m = slope  =   (y1-y2) / (x1-x2)

    then you will have    y = m x + b 

                                            plug in one of the given points to calculate 'b' and complete your equation

From an online listing:

9  12  15

15  20 25

15  36  39

8 15 17            That is all I saw....

....and the one the guest listed below...that I missed...     15  112   113

Area of triangle = 1/2 b h  =   1/2  2r * 2r  = 2r^2  

           2r^2 = 20

            r^2 = 10

Area of rectangle   3r x 2r = 6 r^2      = 60

Area of semicircle  1/2   pi r^2 =         = 5pi

Add the REDs for the total area  

The first candle burns at rate   1 candle / 4 hrs

    multiply rate * time   to get amount burned    1/4 t

       the amount REMAINING  is    1 candle - 1/4 t    = 1- 1/4t

 Similarly for the SECOND candle, the amount remaining is   1 - 1/3 t

We want the time for the length of first to be 2 times length of second:

1-1/4t   =  2   *   (1 - 1/3t)     solve for   t = ........ hrs

Two numbers    x     and   x-21    sum to 63

x     +      x-21     = 63

2x = 84       x = 42      x-21 = 21  

9 (x^2 + 8/3 )       complete the square

9 ( x+ 8/6)^2        now put '9' back into the parentheses  expand to find 'a'

   (3x+4)²                expand to see what 'a' is

9x^2 +24x + (16)            a = 16

-5x -49 >= 113      add 49 to both sides of the equation

-5x >= 162             multiply both sides by -1     >>>>>>>> this reverses the > sign !!!!

5x <= -162           divide by 5

x <= - 162/5

x = 4y-3     from second equation    sub this in for 'x' in the first equation

5 (4y-3) + 2y = -15

20y - 15 + 2y  = -15

y = 0      then     x = -3