Seth has two similar ice-cream cones, cone a and cone b. the slant height of cone a is 16 inches, and the slant height of cone b is 4 inches. what is the ratio of the volume of cone a to the volume of cone b?
64 : 1
8 : 1
4 : 1
16 : 1

64:1

Step-by-step explanation:

For similar lengths, we use the relationship   where A and B are the measurements of the two figures' lengths and k is the scale factor.

For similar volumes, we use the relationship  where A and B are the measurements of the two figures' volumes and k is the scale factor.

Since lengths are given, we use the first formula to find k:

The 2nd formula also tells us that volumes are of each other. So

That means the larger cone has a volume that is 64 times the smaller. So the ratio is 64:1

{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

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