CPhill

See if this  helps  : https://web2.0calc.com/questions/help-with-algebra_96

minor arc CB =  180  - minor arc AC  =  180 -  40 =  140

(1/2) (minor arc AD + minor arc CB)  = angle AED

(1/2) (100 + 140)  =  120° = angle AED

angle AED + angle DEB =  180

120  + angle DEB =  180

angle DEB  = 180 - 120   =   60°

Simplify  as

x^2  +  14x  +  31

Discriminant  =   14^2  - 4 (1)(31)  =  196 - 124   =   72

Simplify  as

-7x^2 - kx + 95   =  0

If this  has no real  solutions,  the discriminant  <  0

k^2 - 4(-7) (95)  <  0

k^2  + 2660 <  0

No integer  k  makes this  true

Circumference of  cone base =   ( 2 pi ) (36) (150 / 360)  =   30 pi

Radius of cone =    30 pi  / ( 2 pi )  =  15  =   r

Height of cone =  sqrt [ 36^2 - 15^2 ]  =  sqrt [ 1071 ]  =   3sqrt (119)

Volume of  cone =   (1/3) pi  r^2 * h   =   (1/3) pi * (15 )^2 *  3 sqrt (119)  = 

225 sqrt (119)  pi ≈   7710.9

Call the radius of the  sphere   = r  = the radius of the cylinder

Call the height of the  cylinder  =  2r  =  h

Volume of  cylinder  =   (4/3) pi r^3

144 pi  = (4/3) pi r^3

(3/4) 144 =  r^3

108   = r^3

(27 * 4)  = r^3

3(4)^(!/3)   =    r

Surface area of  cylinder  =  2 pi r^2  + 2pi r * h  =

2 pi [ 3(4)^(1/3)]^2  +  2 pi [( 3 )(4)^(1/3)] * [(2)  (3)(4)^(1/3) ]   ≈  427.48

Lateral surface area of the cone  =  pi * r * L      r = 7    L = 18

So   A =   pi * 7 * 18    =   126 pi   = 

Lateral surface area of the cylinder  =  2pi r *h  =  2 pi * 8 * 15 =  240 pi    = B

A /  B =       [126 pi ]   ) /  [ 240 pi]  =  .525

No rectangle  shown

We need to know the side lenght of the  triangle

-7 sqrt ( x - 1)  < -14                  divide both sides by -7 ,  reverse the inequality sign

sqrt (x - 1) >  2                          square both sides

x - 1  >  4

x >  5

Open circle at x = 5 with an arrow pointing to the right   ( to indicate that the the solution does  not stop at  x =10 )