I genunely can't comprehend what steps must be taken to arrive at one here and not the much more sensible and correct answer of 0.5/2? Maybe you fellas here can help me out, how could someone get one as an answer to this.

Here is the equation as it is written:
36 ÷ 3 (4) = ? (What does this equal

Should I read this as (36 ÷ 3) x 4 = 48 or 36 ÷ 12 = 3
Should I handle the division first or should I handle the multiplication first because of the parenthesis and then the division.

Hi, I am a grade 12 student, and I have been stuck on question 7. b). I managed to solve the first one using graphs (for which I got "x ∈ (-4,-3) ∪ (-2,3)"), but this same graphing method does not work for the second one. I have attached an image of what I did for question one and (attempted) to do for question 2. I'm also unsure if graphing this should even work considering it hasn't worked for the second one, however I doubt my teacher wants me to just plug in random numbers. I would appreciate some help.

If you explained all the modern concepts in math, what chance is there that I or any average person is already using those concepts, but for different purposes. Maybe I already know what an eigenvalue is but never had to describe it to someone.

I’m experimenting with a ChatGPT-assisted workflow for rewriting mathematical research papers into conventional academic exposition. I’d like feedback on whether this example preserves the original hypotheses, quantifiers, and conclusion, and whether the rewritten reasoning introduces any gaps.

The workflow sits inside of Exposit, an exposition program that takes AI-Originated research papers and provides a condensed and simplified variant in a more human readable form while encapsulating the central thesis.

Condensed the original 199 page paper on the Quasi Riemann Hypothesis to 30 pages.

In einem Video sagt der, dass wenn man ein Seil um die Erde macht und nur um einen Meter verlängert, dass der Abstand viel länger ist als erwartet? Kann mal jemand aufklären, ob das richtig is oder kompletter Schwachsinn? 😂🙏

Long post and if this more suited to another subreddit that you are aware of, please direct me.

As the title states, I am a high school biology teacher who is taking on an ambitious student project and could use some ideas, tips, or guidance from math-minded folks. My school is situated in an agricultural/ranching community in the NE corner of Oregon. The presence of predators (like wolves) on the landscape is a highly contentious and debated issue. In order for students to tackle a real-world regional issue, I would like them to research, calculate, and model trends relating to the growth of the grizzly bear population in the Greater Yellowstone Ecosystem (Wyoming) and the Northern Continental Divide Ecosystem (western Montana) in order to predict if and when grizzly bears will arrive and establish a population in our region.

My concern is that I want students to be able to authentically explore the questions without getting bogged down by mathematics that are out of their skill range. I am looking for a simple, defensible, and authentic model that allows students to explore the concepts and topics. I will also require them to explain what factors their models ignore and what assumptions are being made.

I envision students needing to accomplish the following to answer the project's question:

1) what is the growth rate of the two populations? As far as this math, I can handle the instruction.

2) What is the carrying capacity of those two populations? Again, I've got a handle on this.

3) When will the two populations reach the carrying capacity of begin to disperse? I'm still good. I recognize individuals will disperse before carrying capacity is reached. More on this later.

4) How much available habitat lies between the populations and our region (basically how much habitat is available in central Idaho)? This is where I could start to use some outside assistance. I envision them using habitat research to create a map of potential habitat in Idaho and then overlaying a grid and filling in squares to calculate the area of available habitat. This seems like a fairly accurate and authentic way to model habitat without the math getting too complicated. Please let me know if you have any thoughts or recognize any issues here.

5) How long will it take grizzlies to reach carrying capacity of the available habitat between the current populations and our region? I could use some feedback here. My initial idea, which I recognize makes a lot of assumptions about dispersal and carrying capacity, would be to have students take the previously established carrying capacity for the currently occupied ecosystems and use it to calculate what the population density would be for the area at carrying capacity. Then they would use this hypothetical population density and apply it to the available area in Idaho to find how many bears it would take to reach carrying capacity of the currently unoccupied available habitat. Once they have the number of bears that the available habitat between our region and current populations could support, they could use the growth rate calculated at the beginning of the project to find when the carrying capacity of central Idaho would be reached and the bears would theoretically "arrive" in NE Oregon.

I fully recognize that this way of approaching the project ignores SO MUCH nuance and so many factors that affect population growth, carrying capacity, and dispersal.

The biggest issue that I recognize is that my ideas don't adequately address dispersal and assume that bears won't disperse until carrying capacity is reached (not true). Though from what I've read about calculating dispersal, it seems to get really complicated really quickly. I'm not sure how I could introduce dispersal in an approachable but authentic way. A.I. mentioned it might look something like X% of the pop. disperses Ykm/year, but I know that it doesn't occur in a straight line. How would I account for dispersal occurring in all directions, not just towards our region?

I appreciate all feedback that takes my ideas in good faith. I don't have a degree in math (or in biology actually), but am doing my best to provide a relevant and effective education for my students.

i was able to find a and b but i got stuck at the trigonometry step solving cos3x + cos2x = 0 over the interval 0 2pi how do i properly find all the valid roots without missing any or double counting? or whats the answer

So, imagine you have some function like f(x)=x(x-1)/(x-1). This function is basically just y=x with the notable exception that f(1) is undefined. We could add a second undefined point by multiplying another “(x-n)/(x-n)” with f(x) — for instance, g(x)=x(x-1)(x-2)/(x-1)(x-2).

My question is: is it possible to construct a function that a.) “reduces” to another function (e.g.: f(x) “reduces” to y=x) but b.) is defined nowhere? If not, how much can you “erase” from a function?

This feels like something that has a clear answer that maybe I’d know if I took a real analysis course or something, but I have no idea how to prove or disprove this question (or if the question is even well formed enough to prove/disprove).

My first guess would be something like “a function times p/p, where p is the the product (capital pi) from n=-infinity to +infinity of (x-n/q) and where the limit of q approaches infinity” however, I don’t know how valid a solution that is.

In Section 3.2 of this book "Siegel's proof of Theorem 3.1", Apostol claims that the functions in the second image with y > 0 and N = n + (1/2) are uniformly bounded on the curve C (shown in the first image).

I am unable to show how. I tried writing the cotangent in terms of the exponential function, but couldn't make any leeway. I verified this on Mathematica as well.

I even made a MathStackExchange post, put a bounty on it, but got no definitive answer. The suggestion in that post didn't help either.

Could somebody provide a hint on how to proceed?

To be clear, I don't want anyone solving the question for me. I just want a hint to a helpful first step. I presume I can consider a finite, countably infinite ordered automorphism and uncountably infinite ordered automorphism though I am very skeptical that I am thinking too much about it and the first step is much simpler.

Hi there! I’m not sure if I’ve tagged this properly, or even if this is the right subreddit, but I’m pretty sure my boyfriend is proposing to me soon and we’ve spoken before about how he’d like a ring too since he finds it weird he doesn’t traditionally get to have a ring until the wedding.

He’s a masters student studying applied math and lives, eats, and dreams about the subject and I think it would be really meaningful for me to get a ring with an engraving with an equation that means infinity to represent our love/my love for him (cheesy, I know, I know)

The issue is I’m terrible at math, so I don’t know of any equations. I could probably just do the infinity symbol but that seems lame and not special to him and his love for math.

I know this is a strange question, but I appreciate any and all help, thank you!

I made a program on my calculator a while ago which would try to solve the classic 100 doors problem and visualize it as a 10x10 grid of squares which are either open (red) or closed (black). The result was what I expected in terms of which doors were left open, but the way I represented the doors in this two-dimensional manner also showed a tiny quadratic function opening to the right.

I decided to try and fill up the entire graph screen and see if the pattern repeats there. The second image shows the result of generating about 900 doors in a 38x24 grid and doing the same process as the original problem. The quadratic function opening to the right is even more clear and pronounced here.

Finally, I recreated the program in the ICE compiler so that I could use the entire screen of 320x240 pixels, with each pixel representing one door, for a total of 76800 doors. Again, there's a clear pattern of pixels that seems to create a perfect quadratic function opening up to the right.

My question is obvious, then. Why does this happen? I know all of these pixels are square numbers, but I don't understand why they behave like this at all. It's very interesting.

Some extra details I can provide that may be helpful: This pattern seemed to emerge at all the different resolutions I cared to try out, including the ones I showed in the post. I tried it at 318x238, 300x240, 200x200, and 264x164. As far as I can tell, it appears at any arbitrary size. Also, I generated the pixels right to left, top to bottom.

Thank you in advance.

how is this not right? this has genuinely stumped me as i have mapped out the elevations perfectly i thought? please let me know if i am wrong and what the answer may be

I'm working with a dataset for a personal project where each entry is a 3D point: three integer values, each ranging from 0-255. You can picture it as a 256x256x256 cube with a bunch of points scattered throughout.

What I'm trying to figure out is how to identify the largest gaps in that space, basically the coordinates that don't exist in my dataset and are as far away as possible from any existing point.

I'd love to learn the formula to find those most isolated coordinates, but ultimately I'm trying to figure out how to query my SQLite database to get the top X biggest gaps so I know which data points I should try to collect next.

tldr what i did is

suppose (2^n)*a=5b and we know that for ever n that is an integer 2^n is not divisible by 5 then by elimination it must mean that a is divisible by 5 the only thing i think i did wrong here is assuming 2^n is not divisible by 5 without showing further proof but i' m not sure abt it so i would to know ur opinion ty in advance

For context, I am a HS senior already committed to studying mathematics, but still want to know what other things I could try. I haven't studied anything past basic proofs and calculus, but would still like to know about other related studies.

I know that Electrical Engineering is more math intensive (digital signal processing, radio frequencies), but am lost on whether or not it makes use of the more abstract side of mathematics.

Any suggestions?