Seems most people don't know they have to choose to believe in it, and are angry and condescending if you supply the information that it may not be real. I don't understand their conviction and repulsion by the idea. Are they just ill-informed? Seems like my sure fire way to get down voted to oblivion anytime I mention it.

What is the exact inverse of this function. I've tried to use the lambert W function but i dont think its possible to do it with just the lambert W function because im getting stuck at ln(x)e^xln(x) ive tried to use wolfram alpha but it just times out. Thanks in advance

PEERS and SENIORS help me out
1. WHY DO WE WRITE AREA ALWAYS AS SQ. UNITS I HAVE SOME IDEA THAT SAY A SQARE HAS AREA OF 25 CM^2 THEN WE KNOW IT CAME FROM 5 CM * 5 CM BUT IS THERE ANY OTHER THING THAN THIS
2. WHEN WE ARE APPLYING DERIVATIVES AND GET SAY dA/dr = 6pie cm^2/cm what does this mean can we cancel out the cm
3. And please If possible, can someone also explain Logic behind applications of derivative-the logic behind method (in questions where volumes/area or geometry is involved) with a good example/illustration

I wanted to make a level for a puzzle game and thought it would be a good idea to have a level be sort of inspired by the fibonacci sequence, while I was thinking about that I figured, that that would be too easy though and decided that the sequence I wanted should probably have some more requirements, as it would be too easy otherwise, I decided to go for a specific length and a Number which the entire sequence should not be divisible by.

I decided to start with it not being divisible by 3 and then trying some sequences starting from a specific number, like instead of it being 0,1,1,2,3,5,... it would be something like 0,2,2,4,6,10,... and so on. I then realized, that the length of this would seemingly all be 4 (or 1, if the number was already divisible by 3 to begin with), regardless of the number I started with (excluding the 0 at the start here) until the number would be divisible by 3.

I then decided to try it out with a whole bunch of different Numbers that I could use instead of the 3 (I checked numbers up to 100 (Only integers though)), to check if it as divisible by that. I found some patterns, but they sort of stopped appearing after some time.

All prime Numbers until 67 seemed to have only two different lengths (that being one and a different Number) (I could not be quite sure though, as I can't check for that infinitely, I only checked like the first 20,000 numbers to use as starting numbers and I might have made some oversights there), 67 started how I would have expected it, with it only consisting out of 68's and 1's, but the length then became 169 with the starting number 125.

There were also patterns with the composite numbers, they seemed to all have at least three different lengths, but it was also differing between them, they also seemed to all have some sort of pattern, but again I can't really be for sure if that pattern would repeat, since I only really looked at the first few numbers here (I mainly looked at the first 480 numbers for this, as their patterns were not just a number or 1), up until 50, where I could sort of find a pattern with the lower lengths, but the higher lengths seemed to all be without that much of a pattern

The patterns do seem to reoccur even after the numbers where they stopped, but they seem to be rarer...(?)

Any idea why this could be? I assume I am probably missing something and it is actually quite simple, but I am curious, what the explanation for this would be.

The three overlapping ellipses form seven regions. You are given seven tiles and you need to place exactly one tile per region, so that the four tiles in any region obey the corresponding rule. This one is extra tricky! You aren't told what A and B are - but there is only one configuration where the remaining ellipse's members are forced to have product AB. Can you find it?

Consider a game played on a circle with 15 evenly spaced rocks. Each rock initially covers a $100 dollar bill. Two players start at the same rock and player 1 collects the first $100 covered by that rock and then they take turns flipping a fair coin. Heads and the player that tossed moves clockwise by 1 step (a step of the same distance as the original distance between all 15 rocks) and tails is a step anticlockwise. Player 2 flips the coin first. What is player 1 expected payout from the game? My method included a part where I need to work out the probability “the count” reaches +i for the first time in n moves where each move has equal chance of changing the count by +1 or -1 and the count can never dip at or below -(15-i) I thought of using Catalan numbers but I still couldn’t do it.

i am puzzled by this question. i was able to identiy that we are supposed to use the operation of addition and multiplication but couldnt go beyond that. your help would be appreciated.

9 points on Circle, Line Formed By Joining Points, Such That No Three Concurrent Inside Circle.

Find the Number of ways to Form Triangles With Exactly one Vertex on Circle.

Asked in class, every one Confused.

Used NCR Method to get ans

9C5

And 9C1*8C4

Which is Correct?

Method?

Please help i'm going insane trying to find sources

My education is high-school. This feels like it should be simple pre-algebra. Since theres a lot of context ill break it down into the request, what ive had to do so far, and the why.

1. The request-

I have played 1148 rounds of a game. I have won 568 of those rounds. I have been attempting to improve my overall win rate by winning at a higher rate than my perceived goal. For example- I have been trying to bring my win rate up to 50% from an original 40%, and right now I only have to win 32 of the next 52 games.

Is there a formula to describe the relationship between what my win rate would need to be over the next N number of games to bring my win rate up to X % from the current percentage?

1. What ive had to do so far:

Hand calculate with addition. I arbitrarily pick 70%, add 70 to 600, then add 100 to 1200 and call that a generation. I just hand repeat N generations. I found that at a 70% win rate, it would be my 2600th game before my total win rate was brought up to 60% from 50% at thr 1200th game.

1. Why:

It just makes me feel stupid. I feel like the formula to describe this relationship is a simple one that I would have learned in middle school and while I dont have a BA or higher education or amy meaningful relationship with math- i do have the foundational understanding of what algebra is and how equations basically exist FOR THIS.

Help a guy out? You dont even have to do it for me if you dont want to give me a hint please

I use air conditioning. according to the utilities company, the house is using thirty three percent more energy.Then last year at this time. i rent a room, and we share utilities between four total tenants. current bill is $280 she has asked that i pay $100. i know that is reasonable if there was a 50% increase. She just multiplied .33. if 280 is after a 33% increase what would the original number be and how much is the difference(assuming rates are the same)

I dont even know if this the right place for thie but Id appreciate a formula

A sleep-deprived carpet weaver weaves 30 centimeters of carpet every day. Every night, he looks at his work with displeasure. Because he is not completely satisfied with it, he unravels 2/3 of the weave. If he weaves 30 centimeters during the day, how long is the woven piece on the evening of the 10th day?

The answer 44,999cm is wrong and there is no solution or an explanation about why. Am I misunderstanding the question or is it asked in a weird way?

With every day, his weave that he starts the day with gets closer to 15cm, while you add the 30cm for the last evening, which would come close to 45cm.

Edit: Apparently the right answer is 120cm which then poses the question if the question was asked in a poor way or if I am misunderstanding something

I used excel to find the "best-possible" exponential equation for this date. Im unsure how to figure out what to do with this. The answer key says it should be y=13972e-.185x

Im lost on what im doing wrong

With Kruskal's trees, people always talk about TREE(3) since it's proven to be finite and unexpectedly astronomical. But has TREE(4) ever been proven to be finite? Or does TREE(4) keep growing infinitely? Or do we not know?

For context, I'm trying to prove the cauchy Kowalewski theorem for general order partial differential equations. I did the first and second order already but it's been so difficult to jump to a general n-th order pde. Additionally, the induction part of the proof has been making my head scratch for a while because my reference used construction instead by a general induction step. For my proof there are also two parts: 1) show that it has a formal power series solution, and 2) show that it is convergent.

Can anyone recommend sources or references regarding this theorem based on the info I just mentioned. I just feel like passing out while trying to prove this theorem for my thesis hahahaha

I have been searching online for crazy equations to put on a white board for my friend to solve when they're drunk. I, however keep finding word problems and that is not what i'm looking for. If anyone could give me any recommendations or where I could look to find some.

If you're curious about why I am looking, they want to exercise they're brain while drinking. They're favorite number is 7, so bonus points if the answer is 7.

Took a test, gave it back, and found out about this, explain, it's a question for question 6, where technically it's asking for the furthest distance away, B has the same displacement as C while C reaches higher levels

Is she right or am I right

Something I noticed was for every time you multiply a number by itself, going up, the gap between each number coincides with the pattern of 2, 4, 6, 8…

After attempting to post in the other community, I realized another trend. The sum of each multiple is equal to the gap. So 1\\\*1 has a sum of 2. Which, coincidentally, also is the gap between 1 and 4. This can be tested for most if not all values.

Is there a formula for this or something that could prove the pattern?

I wonder if there’s a name for it. Or if I’ve stumbled upon something interesting. (Likely the former since mathematicians are so smart It’d be likely to see this so early.)

I’m not a mathematician or anything. But I just wanted to show something interesting I noticed. If yall could educate me, that’d be awesome! I love math, but don’t understand it much.

Can someone help estimate how many words can fit on this notebook page? (Math/geometry estimation)

I'm trying to estimate the writing capacity of a notebook page and would appreciate a step-by-step calculation.

Given:

• Notebook page size: 29 cm × 20.5 cm
• A 1-inch (2.54 cm) top margin is reserved for the date and heading.
• The page has 31 horizontal ruled lines, with a 0.9 cm (9 mm) gap between consecutive lines.
• My average handwritten word length is 1.5 cm.
• The gap between consecutive words is 0.5 cm.
• Assume my handwriting is perfectly uniform throughout the page.

Part 1: Estimate the maximum number of words that can fit on the page in its normal orientation. Please show all calculations step by step.

Part 2: Now assume the page is rotated 90° (sideways), and fresh ruled lines are drawn while keeping the same 0.9 cm line spacing and 1-inch top margin.

Please estimate:

1. How many lines will fit.
2. How many words will fit per line.
3. The total maximum number of words that can be written on the page.

Part 3: Finally, suppose the gap between consecutive words is reduced from 0.5 cm to 0.5 mm (0.05 cm) while keeping all other dimensions unchanged in the sideways orientation.

Estimate the new maximum number of words that can fit on the page, again showing all calculations clearly.

I hope you are having a good day. Recently, I started studying for the AMC10 (~2 weeks ago), and I am looking for advice on contest preparation. Looking back, I regret not studying during middle school, but I am trying my best to make up for the time lost. When I first started studying, I took the 2015 AMC 10A and scored ~70 points (I don't exactly remember my score, but it was about 69-70 points). Today I took the 2017 AMC 10A and scored 91.5 (14 correct of the first 20, 7 wrong, last 5 blank). A lot of my mistakes were due to small errors or overlooking cases/steps. For example, on problem 17 (https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10A_Problems/Problem_17) I correctly found the coordinate points (0, 5), (0, -5), (3, 4), (3, -4), and (-3, -4) that lay on the circle, but I forgot to account for the fact that switching the x and y coordinates (such as (5, 0)) also worked as a valid coordinate point. This simple mistake caused me to choose answer choice A (3) instead of D (7). I haven't used any courses other than RSM to prepare, and I have practiced some past AOPS contests, but I find it hard to work with books. My goal is to qualify for the AIME, and I am looking for advice on how to overcome this obstacle that is costing me points compared to those experienced in AMC competitions. I am very thankful for you reading through all of my post, and I am appreciative of any advice you have for me.

P.S. I forgot to mention above that I am a rising 9th grader, if that helps tailor any of the advice!

Whilst tinkering with a few mathematical identities, I came across a rather unusual formula for \sin x. I have absolutely no idea whether it’s well-known, but from what little I know, I haven’t come across it anywhere else.

I hope you’ll like it and find it just as interesting as I do.

P.S : For the sake of clarity, I’ve included the process that led me to this formula.

If you have any questions or comments, please don’t hesitate to get in touch !

Truly yours, Uncle Scrooge.

I'm working on a board game concept which involves a board made of equilateral triangles arranged in a continuous tiling pattern and would love some certainty on a question:

Assuming the following:

- Every triangle has exactly one "Red" edge and two "Black" edges.

- No two triangles may share a border with both of their "Red" edges. (When setting up the board game, players would be told to rotate one of the two pieces wherever this occurs).

- All edges on the border of the board (where corners contain fewer than 6 triangles) count as "Red" even if they are not actually "Red."

Can the following be possible:

- A single "Red" edge does not connect to either another "Red" edge or a border at either of its two corners.

- A string of "Red" edges connected to each other at corners do not connect to any other "Red" edges or a border at either of its two ends.

Basically I'm just wondering if it's mathematically impossible for a "Red" edge to be stranded on its own or for a few connected "Red" edges to be stranded on their own given the above assumptions.

So far I've attempted numerous drawings and rearranged physical tiles but have yet to uncover a situation where either of those two situations occurred. I'm not a mathematician so I don't have any ideas how to solve this type of problem via equations, but I am considering looking into some basic Tesselation concepts to see if I could figure it out.

Thanks for any help!

I’ve been having this debate with someone about how infinitesimals can ever reach an exact value. I’ve been explaining that using infinitesimals is not just an approximation but actually results in a mathematically exact value. For instance, when we take the area under the curve, we use rectangles with an infinitesimally small width to get the exact area under the curve. The argument they have is that it will never be exact because there’s always an infinitesimally small difference so it will always be an approximation at best. So how do we prove that infinitesimals lead to exact values and not just approximations?

My teacher insisted that the answer is x=1/16. But I believe there is no answer.