ElectricPavlov

Yes.....that is correct....

(6.9 x 10^36)  /  [ 4 pi *( 5.68 x 10^16)^2 ]    =  170.19    or     1.70 x 10^2  watts/ m²         ... when I use my calculator.....  (NOTE: it is w/m²    NOT   w/m )  

(6.9 x 10^36 ) / [4pi ( 3.22624 x 10^33) ]  = 170.19 

CPhill made just a slight error :

Re-write as  ax^2 + 2x + 46  = 0      Should be    ax^2 + 2x + 44   

Then following through with his calculations will show a = 4/ 176 =   1/44 

If she deposits at the beginning of the month, this becomes and ANNUITY DUE calculation...here is the formula :

Pluggin' in the numbers    FV = $ 10 000   

                                           i = decimal interest per period  = .0125/ 12 months   

                                          n = number of periods = 3 x 12 = 36 months  ( when she is 24)

    then solving for "C"       results in   C = $ 272.46  per month

Calculate side length as 5 sqrt(3) / 3

the two ends contribute 10 side lengths to the perimeter 

    each hexagon squished in the middle contribute 4 side lengths 

      (10 + x ) ( 5 sqrt (3)/3)  < 100

              shows x < 24.64  sides =====>        6 hexagons in the middle would supply 24 sides 

 6 in the middle + 2 ends = 8 hexagons would be less than 100cm 

975   

4 add'l pails would be 1/2 more of the 8 already in the tank then the tank will be      7/12  +  7/12 * 1/2   =  7/8  full 

   then 1/8 th more of the tank requires 3 jugs  to completely fill it.....       wellll then   8 / 8 of the tank will require   8 * 3 = 24 jugs 

1 + 3 +5 + 7 + 9 + 11  = 36         SIX cosecutive odd POSITIVE integers before the sum exceeds 40 

Re-arrange to 

x^2 -x -35 > 0      this is a  BOWL SHAPED parabola .....the values of x on either side of the roots are > 0 

Use quadratic formula to find   the roots as x = 1/2 + sqrt(141) /2     and   1/2 - sqrt(141)/2 

so the answer would be 

(- inf ,1/2 - sqrt(141)/2 )   U   (1/2 + sqrt(141) /2  ,  + inf) 

Here is a graph: