ElectricPavlov

"The space between the circle and the inner square is what?"  <======= From the header of the question....implies AREA.

If you just want the length of the line, I did most of the work already:

    (circle diameter - square side)/2  =   (8 - sqrt32)/2      Nothing hard there.....anyone should be able to get that !

4/9 x  =  5/6 +2

4/9 x = 17/6

x = 17/6  * 9/4 = 153/24 =6.375

x = -y^2 -6y+12    this is a sideways parabola opening the left

    y coordinate of the vertex is   - b/2a    =     -  -6/(2(-1)) = - 3

    x coordiante will be found b plugging this y value into the equation   x = 21

Circle diameter = 8      radius = 4 cm    area = pi r^2 = 16pi   cm²

DIAGONAL of smaller square = 8 cm

   side length of smaller square    s^2 + s^2 = 8^2     s = sqrt 32

       area of square = s x s = 32 cm2

The FOUR areas inside the circle and out side the square =   16pi - 32    cm^2     

    if you want the area of ONE....divide by four

See if you can apply the method used HERE:

https://web2.0calc.com/questions/quadratic_76

Extremely similar....see if you can compute this one......

https://web2.0calc.com/questions/quadratic_76

-2x^2 - 10x - 83

factor out -2

-2 (x^2+5x)      - 83      complete the square for x

-2(x+2.5)²      + 12.5  - 83

-2(x+2.5)² -70.5 

The original surface area is still there obviously....but each new slice (twenty of them )  increases the surface area by the area of two faces

   EXCEPT for the two end faces which only increase the area by ONE face (as the other face was part of the original surface area)

       so originally  each face was 6x6 = 36  cm²          (and the surface area was 6 x 6 x 6  = 216 cm² )

               now add  18 slices with two faces    18 x 2 x 6 x 6    and two slices with one face  2 x 6 x 6

                   for a total increase of   1368 cm²

12 into 6

is    6 ÷ 12     is the same as   6/12    and this =   1/2      or    0.5

z = 2/5 x

y = 2/3 x

x + 2/3 x - 2/5 x = 95

(15+10-6)/15  x = 95

19/15 x = 95

x = 95 (15/19) =  75

z = 2/5x      y = 2/3 x