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

question 59

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:

Fetal Periods

Stages of human development in the womb, from conception to birth, marked by rapid growth and organ formation.

Trimesters

The three periods of approximately three months each into which pregnancy is divided, marking different phases of fetal development.

Fetal Movements

The motions made by a developing fetus within the uterus, including kicks, rolls, and stretches, often detectable by the pregnant individual.

Gestation

The process of carrying or being carried in the womb between conception and birth, commonly referred to as the period of pregnancy.