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Part B

Suppose that there is space between the inner and outer cylinders and the
radius of the inner cylinder must be an integer greater than or equal to 3.
What is the domain of V?
A. all integers greater than or equal to 3
B. 3, 4, 5, 6, 7, 8, 9, or 10
C. 3, 4, 5, 6, 7, 8, or 9
D. 3 ≤ r ≤ 9

1 Answer

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Answer:

Explanation:

To find the domain of V, we need to consider the restrictions on the radius of the inner cylinder. The problem states that the radius of the inner cylinder must be an integer greater than or equal to 3.

Let r be the radius of the inner cylinder. Then the volume of the space between the cylinders is given by:

V = πh(r_o^2 - r^2)

where h and r_o are fixed constants.

Since r must be an integer greater than or equal to 3, the domain of V is the set of possible volumes for all such values of r. We can find the minimum and maximum values of r by considering the endpoints of this interval:

When r = 3: V = πh(r_o^2 - 3^2)

When r = 9: V = πh(r_o^2 - 9^2)

Therefore, the domain of V is given by option B, which lists all the possible integer values of r between 3 and 9 inclusive.

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