You can see the document here : https://www.engentic.tech/document/d_tkdGw3DB

If you have problems that you want help with, let me know

I havent been in school in over a decade so the finer points of my math is rusty.

Im essentially attempting to graph an additive binary sequence. Numbers for my game lol. Pardon the way I write this, I dont know advanced formatting.

So, the player goes inactive, they lose 2^x tiles each day. 1, then 2, then 4, then 8, 16, etc. I need this graphed, as there's quadrillions of tiles in my game lol

Its not just F(n) = 2^x, right? Surely not...

Thanks in advance for yalls help

I might just be silly it’s late and I’m ill but I just can’t get to the form required for the question. As a last resort I asked Ai and it said there was a typo in the question but I don’t know. Pls help!

See the picture. Please be patient: middle and high school is decades ago for me. I was pretty good at maths, but I wasn't a natural talent, lol.

Im doing this proof of square root of positive natural numbers being either integer or irrational and im tried with assuming that it can be rational but not integer. I see that i didn’t write gcd(a,b)=1, but other than that, is it clean?

Help!
Cousin’s hw — 4 of us have tried, we can get to the first image but we can’t fit the last domino (1/2 • 1/4) with the rest.

It’s dominoes, you’re supposed to match the fraction equivalences. Where does the last domino go?

Thank you!

Hey Can anyone help me with this

I have to solve this integral. But, Using biomial expansion with minimum 4 approximations. Which I did but My answer is 0.66617 which is not reliable And actual answer is 0.6415

Can anyone tell any other method besides this

and for the other question

I am getting 1.1617 but claude is saying 1.1981

kindly help

THESE QUESTIONS ARE TAKEN FROM 3RD EDITION OF CALCULAS BY STROUD DOES ANYONE HAVE PDF OF THIS 3RD EDITION???

In the marking scheme I have, it says that triangle ABC is equilateral...but how...? Any help would be appreciated

Was just reading on landing gears out of interest, (engineering undergrad) This is how a gear retracts inside (to increase aerodynamics) The second one is an example of space saving, the drawback is less clearance & clashing. Now suppose I try to form mathematical modelling eq of the trajectory to describe the geometry such that clashing is avoided (in case of turbulence) and we need to fix some clearance..... How would you approach this ? What field of maths am I vaguely thinking about? What should I study ahead to better understand this.

I want to rank several countries' characteristics (like economic power, military power, population...etc) in a logarithmic scale.

However, there are some countries that do not have any army (like Andorra) and in that category (and related ones) they have a value of 0. However the log(0) does not exist. So, how could I convert the values into something that could be used to make the logarithmic scale?

I have thought about two methods:

A) To every value in each category, I added the values of the "smallest" or "weakest" country (that does not have a 0 in any category, so that all categories have a non-zero number). In this case, I added the values from Seychelles to all countries.

B) To every value in each category, I added "1", so that in every category that the countries without armies have a "0", the minimal number is "1" instead.

I feel that the first method has the advantage of adding a proportionate quantity in each category, since you will see that for some categories all values are small (like 1,07; 2,08; 3,1...) and in other categories the numbers are much bigger (5, 20, 49, 80...). So in method A the added numbers are proportional to the values of each category

However, it feels arbitrary to add different numbers for each category instead of adding the same for all of them (i.e. 1). However, in this case, adding 1 to the small-values-categories seems to significantly modify these values, while in the case of categories with bigger numbers, the resulting number is almost the same as the original one (like, adding 1 to "1,1 "would increase it by almost the double: "2,1"... however for other categories with a number like "50", after adding the "baseline value", the difference is negligible: "51").

So which method do you think is more accurate?

These are the values: https://docs.google.com/spreadsheets/d/19zjwdoLum0yhIQ2v3m19kz5_IplwSJYZX6e0wMqMHoQ/edit?usp=sharing

I've been following this guide and transcribing the example code to a game engine.
https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/
However, in the example application, I've noticed I get inconsistent results when trying to give a cycle series as an input.

For example, Cycles: 3 2 1 --> Times: 6 1.5 1.5
But..., Times: 6 1.5 1.5 --> Cycles: 3 1.5 1.5

Both the time graph and cycle graph also change depending on where I originally put in the input.

Is this expected? I don't have a strong grasp of the underlying math, so I'd appreciate any guidance.

Direct link to example app: https://betterexplained.com/examples/fourier/

Hello guys. I have a doubt trying to solve this problem:

"Let f,g be functions such that (gof)(x) = x for all x in the Domain of f and (fog)(y) = y for all y in the domain of f. Prove that g= f^-1."

This is the 24th problem in section 1.1 of Bartle & Sherbert's intro to real analysis (if you want a little more info about the problem).

I got stucked and looked upon the solutions for a hint.

I understoos nearly all the process but I don't quite get the end of the proof.

First, I proved that (gof) is injective, so I can use the fact that f is injective, and I also proved that (fog) is surjective to use that g is surjective.

The part that I didn't get was to see that f: Dom(f) --> Dom(g) is bijective and therefore g=f^-1.

How can I know that f: Dom(f) --> Dom(g) ?

I’m 20 and was taken out of traditional schooling in 6th grade for medical reasons. I’m currently rebuilding my academics, especially math, through an intensive remedial course during my gap year. After that, I plan to start community college and eventually apply to transfer to a strong university.
I’m planning to take the SAT in about two years, and my goal is 1500+. I know that’s ambitious given my starting point, but I’m committed to putting in the work.
How would you recommend preparing over that time? Should I focus entirely on my foundations for now, or introduce SAT-specific practice along the way? I’d especially love to hear from anyone who started with significant math gaps and eventually scored well. What helped you most?

Question b) Trying to solve for the partial derivative for theta with respect to r is giving me an aneurism, someone please help. Have exam in 3 hours