An Open Box with Square Ends Is to Be Constructed

question 85

Short Answer

An open box with square ends is to be constructed with a volume of 125 cubic inches. The bottom is to be made of a material that weighs twice as much per square inch as the material used for the sides. What should the dimensions of the box be in order to minimize its weight? (Note: the actual weights of the materials do not matter.)Enter your answer exactly as a, b, c where these integers represent length, width, and height (no units or × symbols)

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Definitions:

Cognitive Appraisal

The process of interpreting and evaluating an event or situation which significantly influences one's emotional and psychological response.

James-Lange Theory

A theory of emotion proposing that emotions occur as a result of physiological reactions to events.

Sympathetic Nervous System

Part of the autonomic nervous system that prepares the body for fight or flight responses by increasing heart rate, blood flow, and adrenaline release.

Intense Anxiety

A heightened state of fear or apprehension that can interfere with daily activities, often accompanied by physical symptoms such as rapid heartbeat and sweating.