What Function Determines the Height of a Rectangle with Variable Base Length?

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Homework Help Overview

The discussion revolves around determining a function that relates to the height of a rectangle based on its variable base length. Participants are exploring the mathematical relationships involved in defining the dimensions of a rectangle, particularly in the context of its area.

Discussion Character

  • Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the original problem's phrasing, particularly the request for "the equation of the shaded box." There are discussions about the area of the rectangle and the inequalities that might define its boundaries. Some are also inquiring about the restrictions on the rectangle's dimensions and the function that describes its height based on the base length.

Discussion Status

The discussion is active, with participants providing guidance on how to interpret the problem and suggesting that more information is needed to clarify the original question. There is no explicit consensus on the interpretation of the problem, but various lines of reasoning are being explored.

Contextual Notes

Participants note the ambiguity in the original problem statement and the need for additional context, such as a visual representation or further details about the constraints on the rectangle's dimensions.

Liquidice_69
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No, it doesn't have anything to do with a circle, it has to do with the area of a rectangle. Could please give us the entire problem. There are an infinite number of rectangles that could be positioned as you show it.
 
What level math are you in?
That picture wouldn't hurt.
 
Not a lot. First you ask for the "equation of the shaded box". A box does not have "an equation". You might want the four inequalities that are satisfied by points in the box or you might want the area of the box. I don't know what you original problem asked for- "the equation of the shaded box" just doesn't mean anything! One problem I think you could answer is "what is the area of the largest box of this form".
 
What restrictions give the length of each side of the rectangle?
The base goes from -x to x, whos length is (2x). What function gives the height of the sides of the rectangle for [itex]x = x_i [/tex][/itex]
 

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