An Open Box Is to Be Made from a Square $V ( x ) = x ( 22 - 2 x ) ^ { 2 }$

question 185

Multiple Choice

An open box is to be made from a square piece of cardboard, 22 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 $V ( x ) = x ( 22 - 2 x ) ^ { 2 }$ , determine the domain of $$V ( x )$$ .

• A) \(D = \{ x \mid 0 < x < 22 \}\)
• B) \(D = \{ x \mid 0 < x < 11 \}\)
• C) \(D = \{ x \mid x > 0 \}\)
• D) \(D = \{ x \mid 44 < x < 88 \}\)
• E) \(D = \{ x \mid 11 < x < 22 \}\)

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Definitions:

NaCN

Sodium cyanide, a white solid highly soluble in water, used in organic synthesis and metal processing.

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A strong oxidizing agent in concentrated form, potassium permanganate (KMnO4) is used in various chemical reactions, particularly in organic chemistry for oxidation reactions.

Oxalyl Chloride

A colorless liquid organic compound with the formula (COCl)2, used as a reagent in organic synthesis, notably for the introduction of the acyl chloride group.

Phenylacetic Acid

A white, crystalline organic compound with a honey-like odor, used in perfumes and as a precursor in the synthesis of penicillin.