ElectricPavlov

Volume of 1 'batch' =   9 * 13 * 1 = 117 in³

   volume of 1.5 batch   =   1.5 * 117 = 175.5  in³

12 * 15  * d   = 175.5

d = depth = .975 inch ~~  .98 inches

(2z+4)*2       +       16z+12 = 180       (inscribed angles intercept arcs twice their measure)

z =  8

Arc BA = 16z+12 = 140 degrees

l x w x h = 8

l = w = h = 2

side length = 2 ft

2x2 = 4 ft²   = surface area of 1 side    there are 6 sides     = 24 ft2

Vertex 1,-3

Parabola vertex form     y = a (x-1)^2 - 3      sub in one of the points (3,2) to calculate 'a'

                                       2 = a (3-1)^2 - 3

                                       2 = 4a - 3

                                         a = 5/4

y = 5/4 (x-1)^2 -3     is your parabola    expand it to get the 'quadratic'

f(x) = 5/4 x^2 - 5/2 x + 5/ 4  - 3

      = 5/4 x^2 - 5/2 x - 7/4      

https://web2.0calc.com/questions/help_1108#r1

v = vo +   a t

0 = 188 - 32.2 t          t = thud! = 5.84 seconds

12 * 19 = 228 in²

(12 +x ) * (19+x) = 3 * 228   + 6

x^2 +31x + 228 = 690

x ^2 + 31x - 462 = 0    Quadratic formula shows x = 11   in            new width = 12 + 11 = 23 inches

The dotted line triangle + Visible black area + visible white area = 16 cm^2        so each is 16/3 cm^2

Square with area 16/3

has sides    x^2 = 16/3

                      x = 4 /sqrt3

     diagonal =   sqrt ( (4 /sqrt3)^2 + (4/ sqrt3)^2 )

                   = sqrt (32/3)

               A has moved 4 sqrt (2/3)      =4/3 *  sqrt 6     

3/ 8   = 9/24       5/6 = 20/24         so 3/8 IS smaller

It says to fill the glasses up to 2 cm from the top..... which is 6cm height       6/8 * 226.2 = 169.65