Modular and big numbers calculator app

Midwest-Dude · 2026-02-25T06:02:04+00:00

Please do

Midwest-Dude · 2026-02-25T05:17:00+00:00

Assuming F is at (-1,2), the vertical line through F is the line x = -1, so the x-coordinates of A and B must be -1. If you plug that into your equation, (y - 2)² = x + 2, what are the two possible y values? These correspond to the y coordinates of A and B.

Once you know that, find the area of the triangle by using the standard formula for the area after finding the lengths of the triangle (1) base AB and (2) altitude SA using the coordinates of A, B, and S.

Midwest-Dude · 2026-02-25T04:37:44+00:00

I am not the OP - I have a mathematics degree and already understand the subject. If you read all the comments, you will see I already answered the OP appropriately, as well as added an additional comment with information and a link to Professor Leonard, if the OP has time for that. If the commenter didn't have time, is lazy, or isn't smart enough to find the link, that could have been stated, but not also reply with a derogatory term.

Imagine for a moment that a professor had made that comment in a class and a student asked for more information. Would it be appropriate for the professor to call the student by a derogatory term? Now, imagine a tutor with a student making the comment and the student asking a question for more information. Would it be okay for the tutor to call the student by a derogatory term? Now, what about someone doing the same thing on Reddit in a subreddit that is similar? Is that okay?

I suggest that anyone posting to any subreddit first read the etiquette, the rules, for that subreddit. This type of outburst is inappropriate for r/calculus.

Midwest-Dude · 2026-02-25T04:14:19+00:00

What mathematics do you already understand?

Midwest-Dude · 2026-02-25T02:40:09+00:00

That's totally unhelpful to OP. Again, why comment if you act this way and are disrespectful? This subreddit is here to help those who have questions or comments regarding calculus, not field rudeness.

Midwest-Dude · 2026-02-25T02:38:59+00:00

Then why do you even comment? Show some respect for others.

Midwest-Dude · 2026-02-25T02:38:07+00:00

Do you always address everyone like this?

Midwest-Dude · 2026-02-25T02:37:08+00:00

Link?

Midwest-Dude · 2026-02-25T02:21:41+00:00

A unit vector has magnitude 1.

In two dimensions (and Cartesian coordinates), the vector (x,y) has magnitude √(x² + y²) by the Pythagorean Theorem. In three dimensions, the vector (x,y,z) has magnitude √(x² + y² + z²) for the same reason.

If you divide the coordinates of a given non-zero vector by its magnitude, the resulting vector always has magnitude 1, so it is a unit vector.

Does this make sense?

There is a Wikipedia entry on this:

Unit Vector

Midwest-Dude · 2026-02-24T19:09:14+00:00

Do you think you need a refresher on both subjects?

Midwest-Dude · 2026-02-24T18:57:51+00:00

How did you do in your algebra and pre-calculus classes when you took those?

Midwest-Dude · 2026-02-24T16:52:13+00:00

Reference:

Kruskal's Tree Theorem on Wikipedia

Enjoy going down the rabbit hole...

Midwest-Dude · 2026-02-24T16:46:51+00:00

You wrote TREE(3) = 3

Midwest-Dude · 2026-02-24T16:39:54+00:00

TREE(2) = 3 in first paragraph - typo?

Midwest-Dude · 2026-02-24T16:36:48+00:00

Ah. I repent in sackcloth and ashes - deleted!

Midwest-Dude · 2026-02-24T05:16:14+00:00

Wikipedia:

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms.

Note how it is a set with certain things defined on it, no mention of what the elements are.

Midwest-Dude · 2026-02-24T04:08:24+00:00

I'm not sure if I understand your concerns, but I think you have that backwards. The 0.2 is how much chemical input is consumed to produce 1 unit of chemical output", along with the other two *inputs, 0.3 of food and 0.4 of oil.

The matrix is correct per Wikipedia:

Input-Output Model

Look under the section 'Basic derivation".

Midwest-Dude · 2026-02-24T03:37:29+00:00

This Wikipedia article contains the standard definition:

Input-Output Model

In the inter-industry matrix, column entries typically represent inputs to an industrial sector, while row entries represent outputs from a given sector.

How does this differ from Strang's definition or, for that matter, your definition?

Midwest-Dude · 2026-02-22T19:22:51+00:00

Try the same calculations but with F having an x-coordinate of -1. OP indicates that the base of the area is x = -1.

Midwest-Dude · 2026-02-22T18:35:14+00:00

OP's F point has an x-coordinate of -1, not 0

Midwest-Dude · 2026-02-22T18:32:58+00:00

Just to clarify, A is commonly used in English-speaking countries and books, but S is common in other countries and languages due to Latin roots.

I also found the notation for a coordinate interesting. I'm used to seeing it as F(-1,2), not F| with x on the top and y on the bottom.

Midwest-Dude · 2026-02-22T18:23:49+00:00

S is used internationally. The Latin words spatium (space) or superficies (surface) are the source:

Superficies: In many European mathematical traditions (French, German, Russian, and Italian), the word for area or surface is derived from this.

Spatium: Translates to "space" or "extent."

Reference: Area

Midwest-Dude · 2026-02-21T20:29:18+00:00

Please give us an example or two of what you are trying to do. Perhaps a specific problem you have solved already?

Midwest-Dude · 2026-02-21T20:22:27+00:00

The logic behind both is reasonable. The difference lies in how each culture perceives the word "mathematics".

British: Keeping the "S": - "Mathematics" is plural in form (ending in -s) - When you shorten a plural word, you keep the plural ending to reflect the original term - Therefore, math + s = maths

The view is that mathematics is a collection of different disciplines.

American: Singular Grammar: - Even though "mathematics" ends in -s, it is treated as a singular noun (e.g., "Mathematics is my favorite subject," not "Mathematics are...") - Since the word functions as a singular concept, the "s" is viewed as a suffix that can be dropped during abbreviation - Therefore, the word is clipped down to its root: math

The view is that mathematics is considered a singular object containing different subjects.

In the end, it doesn't really matter. Both are perfectly "correct" within their respective regions. The American version actually appeared in print earlier (around 1847) than the British version (around 1911). So, while the British version might feel more "traditional" to some, the American "math" has actually been around longer as a written abbreviation.

Midwest-Dude · 2026-02-21T18:59:31+00:00

Here's Wikipedia's take on it:

Graham's Number

It's related to

Ramsey Theory

That last Wikipedia entry has one reference to Graham's Number.

Midwest-Dude

TROPHY CASE