A firework rocket consists of a cone stacked on top of a cylinder where the radius of the cone and the cylinder are equal the diameter of the cylindrical base of the rocket is 8 in and the height of the cylinder is 5 in while the height of the cone is 3 in

Surface area of the rocket = 76π

Step-by-step explanation:

Given:

Diameter = 8 in

Radius of cylinder = 4 in

Radius of cone = 4 in

Height of the cylinder = 5 in

Height of the cone = 3 in

Find:

Surface area of the rocket.

Computation:

Slant hight =

Slant hight = 5 in

Surface area of the rocket = Surface area of cylinder + Surface area of cone + Area of circle

Surface area of the rocket = 2πrh + πrl + πr²

Surface area of the rocket = 2π(4)(5) + (π)(4)(5) + (π)(4)²

Surface area of the rocket = 40π + 20π + 16π

Surface area of the rocket = 76π

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1