What is the area of Angular Land below sea level?

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Discussion Overview

The discussion revolves around determining the area of a region referred to as Angular Land, defined by specific inequalities and a formula for altitude above sea level. Participants explore the mathematical implications of the provided inequalities and the altitude formula, with a focus on calculating the area below sea level. The conversation includes elements of calculus, graphing, and potential typographical errors in the altitude formula.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant presents inequalities that define the region of Angular Land and a formula for altitude above sea level.
  • Another participant questions the clarity and correctness of the altitude formula, suggesting it may contain errors.
  • Several participants express confusion regarding the interpretation of the altitude formula, particularly concerning potential typographical errors.
  • There is a discussion about the mathematical tools needed to approach the problem, including coordinate transformations and Jacobians.
  • Some participants indicate a lack of familiarity with the necessary mathematical concepts to solve the problem, expressing uncertainty about their course background.
  • A participant mentions that the exercise is from a contest, implying a context for the problem but not providing further details.

Areas of Agreement / Disagreement

Participants generally express uncertainty about the altitude formula and its implications for solving the problem. There is no consensus on the correctness of the formula or the approach to calculating the area below sea level.

Contextual Notes

Participants highlight potential typographical errors in the altitude formula, which may affect the interpretation and solution of the problem. The discussion also reflects varying levels of familiarity with the mathematical concepts involved.

Who May Find This Useful

This discussion may be of interest to individuals studying calculus, particularly those exploring applications involving inequalities and altitude calculations in mathematical contexts.

ghostfirefox
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The area of ​​Angular Land is described by inequalities | x + 5y − 28 | ≤30 and | 3x + 5y −34 | ≤30, where the point with coordinates (x, y) is the point distant x kilometers east of a certain reference point (in the case of x negative, this is a point | x | kilometers west) and y kilometers north (or | y | kilometers south in the case of negative y) from this reference point. The altitude of the point of the Angular Land with coordinates (x, y) expressed in meters above sea level is given by the formula h = 2 || x + 5y − 28 | + | 3x + 5y − 34 | −15 | −3− | x + 5y -28 | - | 3x + 5y-34 |. Calculate the area of ​​Angular Land lying in depression (i.e. below sea level). Enter the integer part of this number.
 
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Have you graphed what the xy region looks like? Have you had calculus and change of variables in integrals?
Your formula for h doesn't make any sense. Please check that and type it correctly. Also, where did this problem come from?
 
Unfortunately there seem to be several "typos" in this. You say you are given that the height above sea level at point (x, y) is given by
h = 2 || x + 5y − 28 | + | 3x + 5y − 34 | −15 | −3− | x + 5y -28 | - | 3x + 5y-34 |.
I will assume that the first "||" is a typo and it should be just "|" but then I have no idea how to interpret "-15|- 3- |x+ 5y- 28|".
​
 
HallsofIvy said:
Unfortunately there seem to be several "typos" in this. You say you are given that the height above sea level at point (x, y) is given by
h = 2 || x + 5y − 28 | + | 3x + 5y − 34 | −15 | −3− | x + 5y -28 | - | 3x + 5y-34 |.
I will assume that the first "||" is a typo and it should be just "|" but then I have no idea how to interpret "-15|- 3- |x+ 5y- 28|".
​


Looks like it is not a typo.
It is:
$$h = 2 \Big|| x + 5y − 28 | + | 3x + 5y − 34 | −15 \Big| −3− | x + 5y -28 | - | 3x + 5y-34 |$$

Hi ghostfirefox, welcome to MHB!

What are the mathematical tools that you are supposed to use?
Are you for instance familiar with coordinate transformations and the Jacobian to make them work?
Or should we limit ourselves to multiple integrals with variable boundaries?
 
Hi, I don't know how to do this exercise. I have only content from the first post. H is probably
Klaas van Aarsen said:
$$h = 2 \Big|| x + 5y − 28 | + | 3x + 5y − 34 | −15 \Big| −3− | x + 5y -28 | - | 3x + 5y-34 |$$

as Klass said
 
ghostfirefox said:
Hi, I don't know how to do this exercise. I have only content from the first post. H is probably

as Klass said

At least two of us have asked you about what your course background is. You haven't answered any of my questions in post #2.
 
I did nothing with this exercise, because I couldn't. It is from contest, on which I was.
 

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