ElectricPavlov

ab = -40     a = -40/b

a+b=-3

-40/b + b = -3

-40 + b^2 = -3b

b^2 +3b-40 = 0            Quadratic Formula  show   b =  -5   or  -8

                                                                   then    a  =    2   or   5           The red numbers work

2 + 2(n+1)   =    (via distributive property)

2 + 2n + 2 =

4 + 2n                   exactly the same as Ther's          (Not sure this is what you wanted.....)

Knowing that the angles of an octgon are 135^o  , here a is a handscrawled solution  (h is the side length of the sign)

2 pi radians per revolution

2 pi x 18 =  113 Radians      in 43 seconds

113 R / 43 seconds  x  60 seconds/min  = 157.8 Radians/min

3/7  x  =  15     multiply both sides of the equation by  7/3

7/3  *   3/7  *x   =  15  *  7/3

x=35

Start at R      x   goes from  -6   to  15     = 21      add 2/3 of this to -6 =  8

                     y goes from     19 to -5     = -24       add 2/3 of this to 19 =  3

x,y    =    8,3

I think integral   1/(sqrt(1-x^2)     is a standard     arcsin (x)

4 arcsin x   + c        f(0) = 2   means   c = 2

4 arcsin (sqrt3 /2) + 2 = 242  ^o

rectangle is    a x b = 6 x 9 = 54 cm²

triangle is 1/ 2  b_ase h_eight    but there ere TWO of them so area =  bh  = c x a = 18 cm²

Add the two areas to find the total area

20 bottles per minute is a unit rate

20 b/m  /  1 min/60sec = .333333 bottles per second would be another unit rate   

1 minute / 20 bottles = .05  minutes per bottle   could   be another  

                                       3 seconds per bottle    could   be another

Y= mx + b   is the form of a line where m = slope

y = 1/3 x   +0     is of this form    slope = 1/3

y=  13/9  x  + 0                            slope = 13/9

we need the angle between these two       [arctan (1/3) + arctan (13/9)]/2 = 36.8699^o   

tan ( 36.8688) = slope of line bisecting other two = .75   = 3/4        

so y = 3/4 x   will bisect the angle of the other two ~ 

Here is a verification graph:

https://www.desmos.com/calculator/7gf4hgooic