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) \(D = \{ x \mid 12 < x < 24 \}\)

---

Definitions:

Spanish Empire

A historical empire that, at its height in the 16th and 17th centuries, included territories in Europe, the Americas, Asia, and Africa, known for its extensive conquests and colonial rule.

Peace of Paris

The term commonly refers to the 1783 set of treaties that ended the American Revolutionary War, recognizing American independence.

Economic Centers

Key urban or regional areas that serve as hubs of financial and commercial activity, influencing local and global economies.

French Immigrants

Individuals from France who relocate to another country.