The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?

57 in³

Step-by-step explanation:

1. You know that the volume (V) of gas a balloon can hold varies directly as the cube of its radius (r). Then, you can write the following expression:

Where k is the constant of proportionality.

2. You can calculate k as following:

3. Then, to calculate the cubic inches that must be released to reduce the radius down to 2 inches:

- Solve for the volume as following:

- Make the subtraction of the two volumes shown above. Then, the result is:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

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