Sculpture is in the shape of a cone. the sum of its radius and height is 30 in. use a graphing calculator to find the radius, to the nearest inch, that gives the largest possible volume for the sculpture.
a 10 in.

b 15 in.

c 20 in.

d 30 in.

Option C.  

Step-by-step explanation:

we know that

The volume of a cone is equal to

------> equation A

In this problem we have

-----> equation B

substitute equation B in equation A

using a graphing tool

the largest possible volume for the sculpture is for

see the attached figure

7

step-by-step explanation:

the answer would be 7

{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