An Open Box Is to Be Made from a Square $x ^ { 2 }$

question 31

Multiple Choice

An open box is to be made from a square piece of cardboard having dimensions 32 inches by 32 inches by cutting out squares of area $x ^ { 2 }$ from each corner as shown in the figure below. Express the volume V of the box as a function of x. $$32 - 2 x$$ $$32 - 2 x$$

• A) \(V ( x ) = 32 x ^ { 2 } - 2 x ^ { 3 }\)
• B) \(V ( x ) = 32 x - 64 x ^ { 2 } + 4 x ^ { 3 }\)
• C) \(V ( x ) = 1024 - 128 x + 4 x ^ { 2 }\)
• D) \(V ( x ) = 1024 x - 128 x ^ { 2 } + 4 x ^ { 3 }\)
• E) \(V ( x ) = 1024 x - 64 x ^ { 2 } + 4 x ^ { 3 }\)

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Definitions:

Withdrawal

The process of retracting or turning inward, often used to describe the physiological and psychological symptoms experienced when discontinuing a substance upon which one has become dependent.

Sodium Pentothal

A barbiturate drug historically used as a sedative and famously referred to as a "truth serum" in the context of interrogation.

Barbiturate

A class of drugs that are used as sedatives and hypnotics, which can depress the central nervous system, leading to effects ranging from mild sedation to total anesthesia.

Barbiturates

A class of drugs that are used as sedatives and hypnotics. They can depress the central nervous system, leading to effects ranging from mild sedation to total anesthesia.