ElectricPavlov

The sum of the angles of the quadrilateral = 360 degrees ....

so 

 q   +    4q+17     +   8q+21     +    15q+148 = 360 

28q + 186 = 360 

q = 6.214               Then the largest angle is  15 (6.214) + 148 = 241.2 degrees 

First , simplify the equations :

s/2   + 5t = 3 - 7t + 8s 

   =    S + 10T = 6 - 14T + 16S

     =  24T = 15S + 6 

3T - 6S = 9 - 2T

= 5T = 6S + 9         Multiply this equation by -2.5 to get 

  -12.5 t = -15s - 22.5      And add this to the first equation

   11.5 t =  - 16.5

        T = - 16.5/11.5  = - 33/23       Use this value in one of the equations to solve for s :      S =  - 62/23 

Re-arrange by simplifying to :  

x^2 +12x       +y^2   +2y    =   10        Now complete the squares for x and y 

x^2 + 12x +36    +   Y^2  +2y +1    = 10  +36 + 1 

(x+6)^2       + ( y+1)^2  =   47             47 is r^2   For this circle 

         Area of a circle = pi r^2   = pi * 47 = 47*pi = 147.65  units^2 

Arrange into standard circle equation form by completing the squares for x and y 

x^2 - 10x    + 25       + y^2 + 10y    + 25   = 25 +25 -c

(x-5)^2                   + ( y+5)^2     = 50 - c            50 - c = radius ^2 

                                                                             50 - c = 1^2

                                                                                -c = -49      So    C = 49  

Interior angles of an   n-gon sum to   ( n-2) 180

exterior angles sum to 360 

so

(n-2)(180) / n  = 2 *  360 / n     solve for 'n'

180 - 360/n = 720 / n 

180 = 1080 / n 

180 n = 1080 

n = 6   sides 

See image 

Find sqrt (72 ) using Pythag theorem 

then using Pythag theorem again:

 ( r+ sqrt(72) ^2  = r^2 + r^2 

r^2 - 2 sqrt(72) - 72 = 0                        Now use Quadratic Formula   with a = 1     b = -2 sqrt (72)    and   c = - 72

               to find r = 20.4853 units 

(d-7)  = (g-7) * 9        Given     this can be re-arranged to   (d+56) / 9 = g 

(d-4)  = ( g-4) * 6       Given       Solve this system for   g       sub in the underlined equation (above) for g  

d-4 = ( d+56)/9  -4 ) * 6 

d-4 = (6d + 336 ) /9 -24 

d-4 = 2/3 d  + 13 1/3 

1/3 d = 17 1/3 

d = 52    y/o                              (and g = 12 y/o) 

This does not have an answer   using  28/9   or    2  8/9    

10 p * 10 min  /  1000 ft^2 =  1 p m / 100 ft^2     <====  it takes   1 people min to paint 100 ft^2 

Now with 5 people 

    1000 ft^2 *  ( 1 p m  / 100 ft^2 )   =  100  p m   

                then   100 p m / 5 p  = 20 min 

( if you halve the number of people ....you double the amount of time required)