7.
a. a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution. find volume of the solid.
b. a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. describe the solid.
c. a 3-4-5 right triangle is revolved about its legs to create two solids. find the volume of each solid

a. 45 π

b. 12 π

c. 16 π

Step-by-step explanation:

a.

If a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution, we can see a cilinder with:

Radius: 3

Height: 5

Then the volume of the cylinder is:

V=π*r^{2} *h= π*(3)^{2} *(5) = π*(9)*(5)=45 π

b. If a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. We can see a cone with:

Radius: 3

Height: 4

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(3)^{2} *(4) = (1/3)*π*(9)*(4)=12 π

c. We can answer this item using the past (b. item) and solving for the other leg revolution (3):

Then we will have:

Radius: 4

Height: 3

Then the volume of the cone is:

V=(1/3)*π*r^{2} *h= (1/3)*π*(4)^{2} *(3) = (1/3)*π*(16)*(3)=16 π

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

57.09 minus 7.0435 equals

step-by-step explanation:

just subtrach them both and u get the answer of 50.0465