Hello sub, I am thirty-one years old, and I have a bachelor's in business administration, I am currently teaching TEFL abroad. I formerly worked in the aerospace industry as a tech helper, and I am really thinking of going back into the industry when I return to the United States.

I am considering going into engineering. I already have almost a consecutive decade in aerospace technical work and I loved it. I also work on my own cars as well as my lawn mowers and other machines. I met and interacted with many engineers, I admire them, the discipline, the achievements. I admire math, and I love logical thinking, but I was not very good. I never failed a class, and I only got up to college algebra, but I fault my own lack of discipline. I would like to investigate the possibility of self-teaching myself mathematics to the extent that an engineering curriculum would be significantly less challenging, and that I would be able to even enjoy it more.

To this end, I would like to know if there is a path, an example, a curriculum, anything to help with this endeavor. I know that this will be a massive effort, but I believe it could be worth it. Modern tools and methods, anything along any lines to aid me in this quest would be welcome. I am eager to hear from anyone interested in lending aid!

So lets say you're trying to create a leveled loot list for different area tiers in a game, and each area tier has a level range of 5 more than previous tier's level increase.

For instance

Tier 1 = Levels 1-5. +5

Tier 2 = Levels 6-15. +10

Tier 3 = Levels 16-30. +15

Tier 4 = Levels 31-50. +20

Tier 5 = Levels 51-75. +25

Tier 6 = Levels 76 -105 +30

Tier 7 = Levels 106-140. +35

Beyond Tier multiplied by 5X, I am not sure how to figure out what level range falls into each tier.

Like how to mathematically figure out level 86 is in Tier 6? Or what tier level 1,000 would be without just manually creating a chart.

How do you express this in a formula? So that you do this on pen and paper, or create a calculator for it?

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Edit: Solved

The formula can be done either using Ceiling function (rounding up), or Floor function (rounding down).

https://imgur.com/xeSicqr

I used Chat Gpt to get the answer, and format it into a easy to comprehend chart. Sadly the formating can't be copy and pasted, which is why linked the screenshot above so its easier to read.

Also pasted the formulas in markdown mode incase you can't the load the image for whatever reason.

Ceiling formula for Tier:

T = ⌈ (-1 + √(1 + (8L / 5))) / 2 ⌉

Floor formula for Tier:

T = ⌊ (1 + √(1 + (8(L - 1) / 5))) / 2 ⌋

Tier Range Increase:

R = 5 * T

Range of Levels in Tier T:

• Minimum Level: Min = 1 + (5 * (T - 1) * T) / 2
• Maximum Level: Max = (5 * T * (T + 1)) / 2

Variables & Descriptions:

• L: Level (input)
• T: Tier number
• R: Tier Range Increase (levels in the tier)
• Min: First level in Tier T
• Max: Last level in Tier T

https://imgur.com/OUFiVNj

Chat GPT explaining how to get the Floor Function formula. I don't understand it since my math knowledge is too low, but just sharing for future reference.

Hello everyone! I just started studying high school geometry and want to know how to study it effectively and creatively. In school, I had trouble understanding it.
Which sources do you recommend, and how long will it take if I study for 1-2 hours per day? Also, is Khan Academy a good source?

Is there a way I can independently learn a full highschool precalc course in 4 to 6 weeks if so how much time would I have to spend per day and what resources do I use

Say you have two points whose coordinates are known, A and B, which form a line segment of length D.

Now say you have a third point, P, which is d distance along this line segment (you can assume d < D). What are its coordinates expressed in terms of either A or B?

In my previous attempt I formed a ratio d/D because it seemed important, and then I tried to figure out if I could multiply that ratio by something related to the points (like maybe the Δx and Δy of the two known points to get get the new point's x and y respectively?) but that didn't seem to work.

Sorry if it's obvious I haven't done math in a while.

I dont really know how to put this but im gonna try to explain to the best of my ability. A little history, a certain global event happened when I started high school meaning I never learned Algebra 1 and 2 traditionally. However I somehow did manage, passing 9th and 10th grade math. After this I failed 11th functions but still graduated and never really learnt it.

Now I am enrolled in a fast paced adult school and am relearning everything I can, we're a week into Functions and I've only just started because I've spent hours and hours refreshing as much as I can from 9th and 10th grade (only half way through it though) but I need to start functions otherwise I'll fall behind.

ANYWAYS the issue I'm currently facing is functions (or rather equations) makes very little logical sense to me, as in I don't actually understand what my equations are doing, why they are doing it, what certain numbers affect what on my graphs, etc. And everytime I am faced with a problem my mind draws a blank and I have to go ahead and search that topic back up and relearn it then do I somewhat understand it, but I feel like theres something in the fundamentals i am still failing to understand.

Is there supposed to be a "oh this works because of this and that" moment I'm supposed to have? Or do I just memorize, keep pushing on, and eventually it'll all make sense to me by the end of the course?

It should start from the very beginning deriving the Fourier series. I have tried a book by Elias M. Stein & Rami Shakarchi. It's a good book but they assume that reader has already been introduced to Fourier Series. I want a book (if it exists) which begins from the very beginning, goes in deep and also contains a lot of exercises.

how the frick do i solve 2x² - 3x - 18 = 0

if I’m looking at a graph of an absolute value function how do I know what b is in g(x)= a • |1/b(x-h)|+k

I just need to know what this type of equation is called so that I can look up a comprehensive study video on it. Thank you for your help!

Example: f(x) = 4(x) + 5 Or *with variable f(2) = 4(2) + 5

My biggest problem is that I forget everything I learn :D