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:

Fraction

A numerical quantity that is not a whole number, representing a part of a whole.

Evaluate

To calculate the value of an expression or assess the significance of something in a given context.

Fraction

A mathematical expression representing a part of a whole, typically written with a numerator and a denominator.

Exponentiation

A mathematical action that consists of elevating a number to the exponent of another number.