An Open Box Is to Be Made from a Square $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$

question 8

Multiple Choice

An open box is to be made from a square piece of cardboard,24 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below) .If the volume of the box is represented by $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$ ,determine the domain of $V ( x )$ .

• A) \(D = \{ x \mid x > 0 \}\)
• B) \[D = \{ x \mid 0 < x < 12 \}\]
• C) \(D = \{ x \mid 48 < x < 96 \}\)
• D) \(D = \{ x \mid 0 < x < 24 \}\)
• E) \(D = \{ x \mid 12 < x < 24 \}\)

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Definitions:

Transaction

An instance of buying or selling, or the exchange of goods, services, or funds.

Range

The difference between the highest and lowest values in a set of numbers.

Domain

In mathematics, it is the set of all possible input values for a function; in computing, it refers to a distinct subset of the Internet under the control of a specific organization or individual.

Staff Allocation

The process of assigning employees to various projects, duties, or departments based on their skills, availability, and the operational needs of the organization.