$\text { An open box of maximum volume is to be made from a square piece of material } 30$

question 77

Multiple Choice

$\text { An open box of maximum volume is to be made from a square piece of material } 30$ centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure) . What is the domain of the function $V = x ( 30 - 2 x ) ^ { 2 }$ .

• A) domain: \(0 < x < \infty\)
• B) domain: 30
• C) domain: \(0 < x < 15\)
• D) domain: \(0 < x < 30\)
• E) domain: 15

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Definitions:

Standard Form

A structured format for presenting arguments or equations in a universally understood manner.

Proposition

A declarative sentence that can be either true or false but not both.

Hypothetical Syllogism

A logical argument form where two conditional statements lead to a conclusion, essentially connecting the antecedent of one to the consequent of the other.

Modus Ponens

A form of deductive reasoning that allows one to conclude a certain proposition if a conditional statement (if-then) is true and its antecedent is true.