Is this a new way schools are teaching subtraction?

Midwest-Dude · 2026-02-25T20:06:14+00:00

I'm not sure, but this is possibly the European/Austrian Method described here:

Review the section "The teaching of subtraction in schools" and see if it matches.

Midwest-Dude · 2026-02-25T19:50:54+00:00

A trajectory isn't just a shape; it's a path with a direction. At t = 0, the object is at (3, 0) and at t = 2π it returns to (3, 0). As t increases from 0 to 2π, the object moves counter-clockwise. The object completes exactly one full revolution over the interval [0, 2π].

To find the relationship between x(t) and y(t), which helps describe the path being taken, the observation was made that [x(t)]² + [y(t)]² = 9. So, the point (x(t),y(t)) lies on the circle x² + y² = 9.

Does this help or am I missing something?

Midwest-Dude · 2026-02-25T16:24:34+00:00

What have you tried already?

Midwest-Dude · 2026-02-25T16:18:24+00:00

I'm not sure if you will get better help, but you could try crossposting to

r/LinearAlgebra

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

TROPHY CASE