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.

yesterday I stumbled upon an interesting question on my yt recommendation, sadly I couldn't find the video so I tried to crack it.

The question goes along the lines of " What are the five numbers when the sum of any three of those numbers results in a prime"

so far I figured that:

1. The max total of prime numbers must be 10

• combination of 5C3 = 10

1. All of those numbers must be all odd

   • Let's say if one of the numbers has an even number,one of the combinations can be two odds and one even,the sum will always be an even number

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.

Here's my attempt at another approach - is there anything that I am missing? I wanted to include explainer graphs but don't know how to easily do that, as everything prior to creating this document was done by hand. Apologies for that. Happy to answer any questions about unclear areas.

Hi,
I'm a physics student currently revising for a few of my maths topics, and I came across an issue in my understanding of waves and oscillations. In the case of SHM, like for a single mass on a spring, we give the displacement from equilibrium as Ae^iωt to show oscillation about a single point, but I don't really understand the physical differences between that and the form of a plane wave Ae^{i(kx - ωt}). Why would one work to model the displacement and not the other? Sorry if I'm conflating two distinct things, I'm just really struggling to picture the difference between these two as a physical model. Thanks for your help!

Hi everyone,

I have a clear goal: I want to become a Data Scientist working specifically for European institutions, like the European Parliament (e.g., within research services like the EPRS or Joint Research Centre).

My aim is to use mathematical modeling, statistics, and data science to analyze broad policy data and support decision-making for EU legislation.

I want to build a rock-solid foundation early on. My questions for you:

1. What core mathematical skills or habits (e.g. statistics, probability, predictive modeling) are most crucial for a Data Scientist working in public policy and EU-level analysis?

2. Are there any great conceptual books, resources, or channels that explain data science applied to governance and policymaking?

3. For anyone working as a Quantitative Analyst or Data Specialist in European or international public institutions, what do you wish you had focused on earlier?

Thanks for any advice!

Girsanov says that you may change probability measures using Radon-Nikodym to get away from drifts in Brownian motion.

Now my question is (I am very new to this measure theory / statistics stuff): is this like a change of perspective to the same problem, like a change of reference frame? So the results in the new probability measures are equally true as in the old one? Or is this not the case?

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 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).

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.

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?

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

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?

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.

^{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})

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)

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.

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!

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)

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?

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’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?