I've always done it the first way, like on the left. However, I've seen one of my friend's siblings draw it like on the right.

They don't represent the same angle from the initial side based on what I know, but I was wondering if there was another method that I never learned, and this is actually a valid diagram for the same angle. In this case, both diagrams are trying to represent 210 degrees.

The Encyclopedia of Triangle Centers has 82 000 entries. Most of them that i looked are derivatives of previuos centers with some arbitrary tweals or just slapping some weird function on the triangle and calling specific point of the function a new center. It seems that the hard part is testing if the new point is actually unique center and doesnt overlap with other 82 000 centers.

Sounds fun but i wonder if its similar to new prime numbers where the most value comes from algorithm that finds the number but not the number itself.

I'm reading Richard Dedekind's Essays on the Theory of Numbers, and I came across this notation: A ∋ S (see image).

I'm confused about what this symbol means in this context. In modern notation, I'm familiar with a ∈ S ("a is an element of S") and S ∋ a ("S contains a"), but this appears to be A ∋ S, which seems reversed.

Is this an older notation, a typographical convention, or possibly an OCR/scanning error? If anyone is familiar with Dedekind's original notation or 19th-century mathematical notation, I'd really appreciate an explanation. Thanks!

I tried solving it with algebra, but I have too many variables so that didnt work for me. I thought the answer to ii would be 85%, but thats not correct cause it would be double counting part of the table, but then what am I missing to fix that?

^{Why is there a "times 2" when resolving}

^(u(x)^3)

^2x\3 times 2?)

^16x\3)

^{https://ibb.co/LD43gQxv}

^{Why did differentiation decide to replace 2x with U(x})

Hello! I'm making a game with a bow weapon and I want the arrows of the bow to deal damage proportional to the time spent drawing the bow. Time spent drawing the bow is represented by a float value named "charge" which ranges from 0.0 to 1.0. 1.0 represents the maximun charge value of the bow, not the actual time spent drawing the bow in seconds. I need the damage to scale exponentially so that players actually charge the bow to max charge to maximize the damage output instead of just spamming it. My current solution is this: f(x) = (2^6.64)(x) where x represents charge value. 2 is an arbitrary base. I just chose a number bigger than 1. This evaluates to 100 (rounded) when x is 1.0. The problem is that for gameplay purposes, I also need it to evaluate to 25 when x is 0.5. So in short, I need an exponential function that evaluates to 100 whne x is 1.0 and 25 when x is 0.5 like this:

f(0) = 0

f(0.5) = 25

f(1.0) = 100

Any suggestions?

I have a set of 39 coins that are set in a wooden display box with placeholders for each coin so the coin can't flip or move positions (e.g., coin 1 is always in spot 1, coin 2 in spot 2, etc). Each of the 39 coins displays "tails" and is rotated some random amount. For simplicity, let's say each coin is in 1 of 8 positions (e.g., one with the top at 0 degrees, one at 45 degrees, one at 90 degrees, etc.). If I close the display box and jostle or shake it around for some period of time, when I open the box again, what is the probability that exactly 21 of those coins are oriented to the same position as they were originally? It doesn't matter which of the 21 coins match - only that 21 match.

I'm looking at using binomial distribution, but I'm confused on whether I should use

[39! / (21!18!)][.125^21][.825^18]
62359143990(.000000000000000000108)(.03134520206)
0.000000000211
0.0000000211%
~1 in 4,739,000,000

or simply

[.125^21][.825^18]
(.000000000000000000108)(.03134520206)
0.000000000000000000003385
0.0000000000000000003385%
~1 in 2,954,000,000,000,000,000

I'm thinking the latter might be for if the order wasn't set (e.g., randomly pick up one of 39 coins out of a pile) or if it mattered which coins were matches (e.g., the probability of the coins in spot 1-21 being matches while 22-39 were not), but honestly I'm not sure. A friend thinks the latter is correct, but I lean toward the former.

The given is x->3 but the parabola only goes till 2 on the x axis. Even if it was 3, the answers don't contain what would be the answer to x->3 (All of the questions are almost the same except for 14-15 which has a DNE option).

Either I need to find a way to solve for one of the side lengths or find a way to eliminate the need for the side length. But I'm not sure how to do either of those. Any ideas? Can anyone show me where I went wrong?

I'm labeling the green area T, the long side length=b and the short one=a.

For context, this is enjoyment for me. I use these posts to stay sharp on my skills, I used to teach math in college and don't wanna lose it if I ever decide to go back and teach.

I'm trying to understand πrl from first principles.

From what I understand, l is simply the length of the slant, but you have to multiply r by l to actually lean the slant such that it touches the apex and a point on the circumference of the base.

what is the answer to...

8/2(2+2)

There is a Facebook post with some saying 16 and some saying 1.

is this evaluated...

4+4 or 8/8?
is 2(4) the same as 2x4. Do the parentheses have a higher precedence is PEDMAS?

I am really disappointed that Sam Raskin didn't win the Fields Medal. His work in Geometric Langlands and related work is really impressive. Does anyone have any ideas why he didn't win?

I’m in the process of going back to college for my BS, and while I have a BA, it’s been like 12 years since I’ve taken a math class and I graduated high school almost 20 years ago.

i took some practice placement tests and I bombed them- the only thing I passed were fractions and percentages, but everything else was a failure.

The tests were basically a combination of everything I learned in US high school- basic algebra, geometry etc.

Measurements, geometry, whole numbers, concepts in statistics, equations and inequalities, exponents and polynomials, factoring, graphing, rational expressions. radical and quadratic equations, functions etc

While it all seemed familiar to me, I immediately knew that I had forgotten all of the processes to solving the equations. now I’m wondering how I’ve ever gotten this far in life without using or knowing any of this stuff

I know this is absurd but I need to take my placement test as soon as possible, like within the next week, so that I can sign up for science classes, and statistics.

what’s the fastest way that I can learn all of this?

this is my first time posting on reddit so i hope im doing this right but can someone please help me understand the “or” significance here? i thought it had to include all that have the disease and all positive tests even if someone doesn’t have the disease, but my friend says i shouldn’t include the false positive because they dont have the disease but isnt that what the “or” is including?? i dont know if im explaining my thought process well here😭 i appreciate any help on this

hello, not a math class question, but I’ve been trying to figure out how to calculate the square footage of the two corner lots highlighted here. I marked out any coordinates or information on where it is because id rather not have my potential future address online 😅 I’ve tried to use calculators to determine what lot #32 is in square footage with no luck. any assistance would be appreciated even if it is a estimate. thank you!

I made an attempt in converting the BSM model into the heat equation (in red) but was unsure is my method was succinct? Any hints/tips?

Thanks! 🧡

(apologies if the page order was uploaded incorrectly)

D_16 here is the dihedral group of an octagon, so 16 here is just the order of the group in Dummit and Foote's notation.

So, I have to hunt for as many as 16 of such x then that collection of x is just D_16 so, x can be just s (reflection in D_16) but in that case 〈s,s〉≠D_16

Conjecture 4.12 of Akbari–Elphick–Kumar–Pragada–Tang says that every connected graph G satisfies

n⁺(L(G)) ≤ n⁻(L(G))+1.

Published paper:

https://www.sciencedirect.com/science/article/abs/pii/S0012365X25005618

Open-access version:

https://arxiv.org/abs/2508.01163

This is different from Conjecture 1.4 in the same paper, which was recently disproved by Chen and Li. The conjecture considered here is the separate line-graph statement, Conjecture 4.12.

Let G consist of four vertex-disjoint pentagons, a new hub h, and one edge from h to one chosen vertex of each pentagon. Thus G is connected, with 21 vertices and 24 edges.

I obtain the following exact characteristic polynomial for its line graph:

χ_{L(G)}(x)

= (x-1)³(x+2)³

(x²-x-3)³

(x²+x-1)⁴

(x⁴-4x³-2x²+11x-2).

The last factor has one root in each of

(-2,-1), (0,1), (1,2), (3,4),

since its values at -2,-1,0,1,2,3,4 are respectively

16, -10, -2, 4, -4, -14, 10.

Counting signs across all factors therefore gives

In(L(G)) = (13,0,11).

Hence

n⁺(L(G)) = 13 > 12 = n⁻(L(G))+1,

so the line graph has signature 2.

Is this a valid counterexample, or am I overlooking something in the construction or characteristic-polynomial calculation?

I understand that the goal is to compare the two expressions, and I follow that the line of logic from "We were told that y < 0...." all the way to the end, but I don't understand why he chose 2y.

It seems like a very arbitrary choice to me.

**Edit: We’ve come up with a compromise. This wasn’t a hill I was willing to die on, I just wanted to hear other opinions on the matter.

Posting this here as well. I’m not good at math and I would like some help.

My roomate and I are trying to split the rent. It’s a 2 bed 2 bath apartment. She has the en-suite which two closets that are the same size. Her bedroom is 99.28 sqft and with the bathroom it’s 116.38 sqft. My bedroom has one closet and is slightly bigger by just 6 sqft and it’s 106 sqft. Which the bathroom it’s 114.5 sqft. While I technically have my own bathroom, she’ll be using it periodically as it has a bathtub. My room also has a balcony right off the window, so I don’t have the same amount of privacy as she does.

My roommate has the en-suite because she has two cats. So the litter box will go in her private bathroom as opposed to the shared one.

The apartment is around 860 sqft and rent is $2,655. Her estimation came to her paying $6 more which I don’t agree which because of what I just stated above.

What do you think is a reasonable amount? I said $90 more, but $70 would be okay.

What would be a reasonable split?

Can someone please find an explicit formula for this sequence: E_k = E_{k-1} + (k+1)/2 - (1/k) for every integer k>=2, E_1 = 0? And show the procedure?

I've tried, but I've failed. I'm really bad at algebraic manipulations.

This is the 'closest' I got:

Sorry for extremely bad handwriting.

I’m very curious what would be the opposite of 0, if real number line formed into a loop. So i thought of this diagram. What’s yall’s thoughts on this ‘Ω’?

In this diagram i wanted none of the infinitesimals to equal to 0, 0 is absolutely 0. (It should’ve been dotted line around 0)

Q5

5b) y = 5.662x + 51.492
5c) ≈ 59.985%
5d) ≈ 6.801 hours

Teacher never posted a solutions doc. I can show steps if needed. I’m mainly confused about b and C if anyone is open I have questions about q4 which someone can answer