Bounding Region Inequalities for Solid Rectangular Box in First Octant

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Homework Help Overview

The discussion revolves around formulating inequalities to describe the bounding region of a solid rectangular box located in the first octant, specifically defined by the planes x=1, y=2, and z=3.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore various ways to express the constraints of the box, including attempts to define the volume and the relationships between the variables x, y, and z. Questions arise regarding the validity of specific points in relation to the defined box.

Discussion Status

The conversation is ongoing, with participants questioning the inclusion of certain points within the box and discussing the necessity of constraints for each variable. Some guidance has been offered regarding the reasonableness of creating individual constraints.

Contextual Notes

There are discussions about specific points that may or may not lie within the defined region, indicating a need for clarity on the boundaries set by the inequalities.

Winzer
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Homework Statement


Ok I just wanted to make sure of this one.
Write inequalities to describe the region:
The solid rectangular box in the first octant bounded by the pane x=1 y=2 z=3.

The Attempt at a Solution


I thought of it as the volume of the box bounded boy the planes so:
0\leq xyz\leq 6
 
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So, you are claiming that the point
(1000, -1/100, -1/10)​
lies in the box?
 
ok so how about

0\leq x+y+z \leq 6
 
What about the point (100, 200, -300)?

(Oh, and why do you think (1000, -1/100, -1/10) isn't in the box?)
 
Hurkyl said:
What about the point (100, 200, -300)?

(Oh, and why do you think (1000, -1/100, -1/10) isn't in the box?)

They are all in the box. Should I just make a contraint for each varible?
 
Winzer said:
Should I just make a contraint for each varible?
That's certainly a reasonable thing to do.
 

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