# What is the area of Angular Land below sea level?

• MHB
• ghostfirefox
In summary, This exercise involves finding the area of Angular Land, which is described by two inequalities. The altitude of a point in Angular Land is given by a formula involving absolute values. The exercise also involves calculating the area of Angular Land that is below sea level.
ghostfirefox
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.

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.

## 1. What is the definition of "area" in this context?

In this context, "area" refers to the total surface area of Angular Land that is located below sea level.

## 2. How is the area of Angular Land below sea level calculated?

The area of Angular Land below sea level can be calculated by subtracting the total area of the land above sea level from the total area of the country.

## 3. What is the significance of knowing the area of Angular Land below sea level?

Knowing the area of Angular Land below sea level can help scientists understand the topography and geography of the country. It can also provide valuable information for predicting the impact of sea level rise on the land and its inhabitants.

## 4. Is the area of Angular Land below sea level constant or does it change over time?

The area of Angular Land below sea level can change over time due to natural processes such as erosion and sedimentation, as well as human activities such as land reclamation and coastal development.

## 5. How does the area of Angular Land below sea level compare to other countries?

The area of Angular Land below sea level is relatively small compared to other countries. However, its low-lying geography makes it particularly vulnerable to the effects of climate change and sea level rise.

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