help-17

[vocal pagoda]

I bring 2 suggestions:

[twin meteor]

Wild123

[vocal sleet]

@sterile hazel Has your question been resolved?

[vocal sleet]

Channel closed

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Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dense blaze]

Hey everyone, I’m in 11th grade, or as some of you might call it, "junior year" in high school. My math skills haven’t been great- honestly, they’re pretty bad. But I’ve decided to turn things around because I’m really fascinated by math and admire people who can solve hard problems.

When I see other people’s questions in th e server, I feel completely overwhelmed because I don’t understand any of it. I’m really lost and don’t know where to start. Should I begin with trigonometry, functions, or geometry? Should I focus on solving questions or watching videos? I can’t even do my homework because I don’t know how to approach the problems.

There are so many math geniuses on this server, and if anyone could help me figure out a clear path to improve, I’d be super grateful!

[hexed needle]

imo, the most important thing to master first and foremost is your algebra skills

[dense blaze]

so you think i should start from algebra

well that sounds like a fun start

[hexed needle]

yep, I'd just do a ton of problems until you're confident with any algebra problem that's thrown at you

[dense blaze]

so first i should master algebra then i should go to trigonometry and stuff?

[hexed needle]

I would do that, yes

most of people's issues with math are rooted in a misunderstanding of algebra

[dense blaze]

how long will it take ? i know you cant give an exact amount but any estimates

well im getting close to a exam

mastering would take me a very long time

but i want to learn it on a level where i can solve basic trigonometry

i will try to master if after the exams end

because my gpa hasnt been the best

these past 2 years

[winter bloom]

Hey buddy 😄
Kudos to you for acknowledging this and taking the initiative to try and improve! That in itself is incredible! I'm proud of you 😄 I agree - Improve your algebra. Beside that, I just want to wish you luck 😄

[hexed needle]

I find math most fun when you aren't under pressure lol

but if you wanna learn and understand trigonometry, I'd focus on making sure you understand it geometrically (e g. what sin(x) has to do with the unit circle and why that relates to triangles)

[dense blaze]

thank you so much i will get a algebra book as soon as i can and start from there without you guys i would never think of starting from algebra i would just study the topic we are currently doing and school and end up being lost 😅

[winter bloom]

What is the current topic?

[dense blaze]

oh thats smart so understanding the reason behind it instead of just jumping to the questions

[winter bloom]

Yup - always.

[dense blaze]

we just did the arcsin stuff

the opposite of a function

idk what to call it in english lol

[winter bloom]

Arcus sinus yh

[dense blaze]

the questions we are doing right now arent that hard

but i find the previous topics more challenging

[hushed pewter]

Let me say a few things first.

1. I'm sorry you didn't have a good start with your maths journey, but I'm happy for you that you want to change that. I hope you find success in your journey
2. It is okay to feel overwhelmed with everything you see on this server, and it may feel impossible to learn it all. And that's because it is. There is so much math. Really it is infinite. You cannot know all of it. But you can learn about things that interest you or that help your education/career interests.
3. Knowing where to start really comes down to you and what you think you might like about math. For example, i like the geometric aspects of math, so i study topics that are near that. Others might like things more theoretical like number theory or abstract algebra. So where to start will come down to whatever you want to do
4. If you want to sharpen skills that you feel you are not proficient in, there are many ways to do that, but it helps to know what your weakness are. This can be hard to pinpoint though, especially if you feel extremely lost. It's hard to know your own weaknesses because you are so close to the problem. But you can find out your weaknesses simply by trying and asking for feedback. Most helpers here are kind and want to help you learn, so i hope you encounter people like that while you are here.
5. If you want to get really good at math, that is a large time commitment. You can be "good" with a decent amount of effort and work ethic, but if you want to be "really good" and able to solve hard problems, that is a true time commitment. That's not for everyone, and do not feel bad if you learn that it is not for you. However, that doesn't mean that you still can't enjoy math and want to be good at it to help your personal growth. In short, find joy in math, and value in what you learn. Do not try to be really good just for the sake of it (unless that is what truly brings you joy)

Altogether, it's a big personal journey, but a lot of people here will be happy to help if they see you asking questions here and are capable to offer such help

[winter bloom]

Such as?

[dense blaze]

since they leave me confused lol

[dense blaze]

basically the rest of trigonometry

im trying to do homework and i dont know where to start

or what to do

[winter bloom]

Oh well... trig sucks for most people in the beginning. Once you crack the code, you might end up enjoying it. But as doaby recommended - start with algebra. I personally think Khan Academy can help loads. I've used that a lot. (It's free)

[lament linden]

You can always ask a question to see which information you're lacking

[winter bloom]

I'd be happy to help, chillguy 😄

[hushed pewter]

This is generally true with a lot of things. When i go back to review my old math stuff, i always feel like i understand it better and i start enjoying it so much

[winter bloom]

Not only math tbh but yeah 😍

[hushed pewter]

Btw what will really help you, not just in your math class, but every class, most students start their homework and (sometimes) read the book after their teacher has covered the material. You should be reading the chapter and attempting the homework before your teacher goes over it. This lets you get an idea of what topics you are struggling with, and you can come to class prepared to ask questions and more focused on your teachers lesson for that specific part where you are struggling

[winter bloom]

+1

[dense blaze]

Wow, that was really helpful—thank you so much! I actually enjoy doing math. Being able to solve questions and the feeling of getting something right genuinely makes me happy. I used to be pretty good for my age, but then COVID happened, and I stopped studying. Since then, all the topics have just piled up on top of each other, and now I feel so behind.

I’ve decided to start with algebra, but my current knowledge is very basic. The questions I struggle with seem so easy to others that I feel embarrassed asking for help sometimes. Still, starting tomorrow, I’m going to dedicate a good amount of time to improving my math skills. I know it’s tough to get really good at math, but if I can see a clear path to follow, I’ll give it my best. Math has always been the subject I’ve been most interested in, and finding such a supportive and kind community feels like a blessing. I’m really grateful to be here—thank you all so much!

I’ll start with algebra, but I also really struggle with geometry. I don’t have the "vision" that others seem to have, like imagining lines to use a formula. I can’t see those connections at all, and I don’t know many formulas, either. Do you think this "vision" is something innate, or is it just about learning the formulas first so you can figure out where and how to apply them? Of course, knowing the formulas is essential, but I wonder if I’ll eventually be able to see those patterns once I’ve learned them.

[dense blaze]

thanks

[dense blaze]

thank you so much 😄

[dense blaze]

thats really smart i hope i dont get too overwhelmed and hate my life looking at those questions lol

[lament linden]

Its not some "vision", its the experience that comes from applying knowledge to questions

You can compare it to a good video game experience

[dense blaze]

oh that makes sense but i know people that dont solve much geometry that are able to see those imaginary lines and solve questions easily

so i thought it was a innate thing lol

so its just practice until you can easily do it

that sounds fun

well not my current situation since im totally clueless and just stare at the questions lol

but after ive got a little hang of it

it will be fun

[lament linden]

you mean constructions?

[dense blaze]

well i dont know what they call it wait lemme look up what constructions is

well its kinda hard to explain but like when people draw a line on the triangle to imply a formula

its basically every geometry question we are solving right now

can i post links here

i found a video

https://www.youtube.com/shorts/erNpAKV713Y

[hushed pewter]

The questions I struggle with seem so easy to others that I feel embarrassed asking for help sometimes.
I get this. It can be very hard to ask a question and admit you do not something, especially something so simple. And yes, sometimes people can be cruel in their reactions to your ignorance. Even here, on rare occasion, you might find someone who can be rude if you do not seem to understand something.

Sadly, it will impossible for you to avoid people like this entirely. If it ever happens, I hope you can summon the strength to not let it discourage you forever. If I see your questions here, I will do my best to offer my assistance and patience when I have the time, and most other helpers will do the same. Just try not to be discouraged because you are behind. Believe you can make it and remember that this will be worth it.

I used to be pretty good for my age, but then COVID happened, and I stopped studying. Since then, all the topics have just piled up on top of each other, and now I feel so behind.
Yeah covid really did this to a lot of people My nephews are going through the same thing. It's a hard problem and I am sorry you have to endure it.

I know it’s tough to get really good at math, but if I can see a clear path to follow, I’ll give it my best.
That is success in my eyes. I wish you well

I also really struggle with geometry. I don’t have the "vision" that others seem to have, like imagining lines to use a formula. I can’t see those connections at all, and I don’t know many formulas, either. Do you think this "vision" is something innate, or is it just about learning the formulas first so you can figure out where and how to apply them?
This "vision" is experience. It's hard at first. Yes, it can be very hard. For some people, it comes naturally. Some people will just be very naturally talented at this, and other will not. But remember, talent is cheap, and will only get you so far. Work and dedication are the true path to success.

Of course, knowing the formulas is essential, but I wonder if I’ll eventually be able to see those patterns once I’ve learned them.
Yes. Math is like a giant puzzle. The more pieces you fit together, the clearer the whole picture gets, and the easier it becomes for you to connect even more

[dense blaze]

well basically the line the guy pulls

[hushed pewter]

You might. But remember, you are looking at them while self-learning. What you know at that point is entirely what you were capable of learning entirely on your own. It's not easy to self-teach. That's why teachers exist. Learning even one thing on your own should make you proud.

Also, you don't have to wait for your teacher, you can always ask for clarification here.

[hushed pewter]

Inverse function. There are other names, but this is the most common English name

[dense blaze]

wow thank you so much this is a very big motivation for me but unfortunately motivation is not enough i should be disciplined not giving up on questions but the thing i love about math when im discouraged if i find a way to solve the question it gives me the required motivation to keep going on so its just a chain of motivations that create discipline

[hushed pewter]

1. Try the problem on your own, do as much as you can.
2. If you are stuck, attempt to identify what you are not understanding. This step can be hard. It is hard to know what you do not know.
3. If you have some idea on what you are not understanding, re-read that part in your book. If you are completely lost, you may need to start reading over the whole chapter (this decision can be obvious to you if you feel like none of it made sense to you)
4. If it's not making sense at all, then you should begin reaching out. At least now, you know you made the effort, and hopefully you can at least know what specifically is confusing so much

This is just one approach at least. Some people like to ask for help right away, and that has its own advantages and disadvantages. Personally, I like to work things out on my own as much as possible. I do this to be sure that I truly understand the material. But it is okay for you to ask for help right away. Just be sure that your intentions are to understand the material, and not simply know how to answer that specific problem

Know the why, not just the "how"

[dense blaze]

I go to a school-like place after regular school, where I have three 30-minute private lessons every week for any subject i choose. I was thinking about using all my lessons for math, but the problem is that many people go there, and they can take the private lesson slots before me, so I might not be able to use all of my three lessons.

So, let's say I only have 30 minutes a week with a math teacher. How should I make the most of that time?

[hushed pewter]

Let me give you some advice on "mastering algebra". Algebra is huge. You will not master it. Mastering it comes from using it for years.

You can get very good at it. And good enough to easily get you through your other math classes. And you should make an effort to get very good. But "mastery" is ever-evolving. Even well-past graduating college am I seeing new things in something as simple as algebra. You will never be able to say "okay, I have now learned all of algebra"

[dense blaze]

Oh yeah, because if you reach out for help before giving your best effort, you're just copying what others say. It might help you finish the homework temporarily, but it won’t help you learn as much. What you said is really valuable, and I’m going to give my best on every question from now on. Honestly, until now, I wasn’t able to understand some questions and would just ask ChatGPT for answers and paste them into my work. I know ChatGPT isn’t always 100% accurate, but I was just doing it to get the homework done and focus on grades. Now, I want to actually learn, so I’ll put in my best effort.

[hushed pewter]

Trust me this is okay. I graduated high school with like a 2.3 gpa. It won't be the end of the world, and you can still turn your life around if you decide you want to.

I used to think having a bad gpa would close me off forever from getting a good education and a good job. But it doesn't. It becomes harder, but it's not impossible. You can overcome if you try.

[dense blaze]

Yeah, that really impresses me. Also, my bad for using the word "master" — that’s not what I meant. I meant reaching a point where I can move on to other topics.

[hushed pewter]

Yeah trig can be tricky. It starts to merge the topics of algebra and geometry, so you need to be pretty good in both of those.

[dense blaze]

so i need to be good in 2 topics to be good at trig i thought it was easier than both those topics from what i've seen 😭

by "from what i've seen" i mean the questions we solve in class

[hushed pewter]

This comes back to my "talent is cheap" remark. They are talented yes, but work and discipline are worth more, I promise you.

[dense blaze]

Yes, I just want to reach a point where I can at least have an idea of how to approach the questions. Even if my answer isn’t 100% correct, the thought process will keep me motivated.

i want to solve questions left and right but i dont have an idea on what to do

im just staring at the questions without a clue and that really breaks me down

[hushed pewter]

unfortunately motivation is not enough i should be disciplined
You are absolutely right. You will need more than "wanting" to be good at math. It does require discipline, as do many things in life.

But like everything else so far, let me give you some advice on discipline. There's a difference between healthy discipline and unhealthy discipline. Yes, you should make a real effort to concentrate on your studies and do as much as you can to succeed. However, no, you should not let it consume your life. It can become easy to forget, but don't let your whole life be just working and studying without joy. You will not last. No one could. Maintain discipline in your life, but with balance. Find joy in your life and it can make discipline easier, as it helps you remember why you want to be successful.

the thing i love about math when im discouraged if i find a way to solve the question it gives me the required motivation to keep going on so its just a chain of motivations that create discipline
This is also very true. But it can be dangerous. Sometimes you will simply not understand things. I've had math problems which I just never understood. Even with help. So yeah, find joy in your successes, but do not let failures deter you too much. You can still learn a lot from your own failures if you are brave enough to face them honestly. You are here seeking to get better, so I think you are able to do this, and I hope you keep that in mind.

[hushed pewter]

That is very respectable, and it is a good goal to have. It is possible. Problem solving is a skill, and you grow skills through practice, trying, failing, and learning. Motivation and discipline will let you keep doing that cycle of practice, trying, failing, and learning.

[hushed pewter]

Trust me this isn't so easy to do. Pace yourself. Do not think of every problem at once and about trying to do them all very quickly. Be mindful of just what you are working on. Take the time you need to understand it. Then, "solving questions left and right" will come.

[dense blaze]

Thank you so much! Yeah, I might get discouraged if I don’t understand math problems at all, even with help. But if I’m at that level already, I wouldn’t mind it as much, haha. I just feel like an idiot not understanding these simple questions that im currently at.

[hushed pewter]

I think what is breaking you down here is an inability to make progress once you do not know something. The art of problem solving is more than "read the problem, write the answer". If you understand the problem perfectly, then that is all you need to do. But this is rarely the case. Problem solving is about trying what you know, identifying where you are struggling, and seeking outside help (either reading, videos, your teachers and tutors, or here), and then trying again with your new knowledge.

If you stare at a problem and do not know what to do, your next step should be to seek help in any one of those ways that I mentioned

[hushed pewter]

It's a feeling I understand too well. There is a saying (at least for us English speakers, I do not know if it is commonly said everywhere):
The master has failed more times than the beginner has even tried

[dense blaze]

I know there needs to be a balance, but I feel like I don’t have enough time to create that balance, especially since the university system in my country is entirely focused on one exam. People study for years without sleep, and those are the people I’m up against. I feel like if I go out and focus on building a hobby, it will set me back compared to others. Even if I’m just ahead of one person, it could affect my chances of getting into the university I want. I’m already in my junior year, and I’m very behind. This exam covers all of high school, and I don’t know any of the previous topics. I want to make studying my hobby, so I can feel at peace while learning. If that makes sense, I genuinely enjoy the feeling of getting questions right, and I’m really happy to have that ability since i wont go mentally insane.

[hushed pewter]

If you want to get good, then you are going to have to fail a lot. And then fail a lot more. And you are going to have to really feel like an idiot as you struggle and struggle to understand that one thing (or perhaps many) that you just. cannot. understand.

The only advice I can offer you is to pratcice mindfulness. You will learn better if you are not so frustrated. If you are getting upset (which is natural), take some time to relax yourself and come back to the problem when your mood has stabled.

[dense blaze]

Yeah, that’s a great quote. I’ve heard other versions of it explained differently, but they all mean the same thing, and it really keeps me motivated to not give up when I fail and to keep learning from my mistakes until I get really good at it.

[dense blaze]

thank you so much

you helped me more than you think i really owe you alot

i will try to do my best on solving questions

well the last question

[hushed pewter]

That is a fair (and unfortunate) point. Education systems in other countries are extremely competitive. Yes, you may have to work and study very hard, much harder than is fair. And it sucks, it's not fair. Everyone capable should be able to have access to an education.

All I can say is just keep trying your best. Know why you want to do this and do not lose that perspective. Understand what is important to you and maintain the best balance you can to keep that going.

My educational track was not the best. I was never really a "good" student. But I never gave up. I hope that can work out for you. I cannot say with certainty whether or not it will, but I hope you can find worth and meaning in your efforts, regardless of success or failure.

[dense blaze]

what would you do if you were in my situation and had a math exam about trigonometry in a month

like study algebra for 10 days then move to geometry and stuff

im not expecting to be good at trigonometry in a month

but just so i can solve some questions and increase my exam score

[dense blaze]

Thanks! I have a little hobby of going to the gym, which helps keep me sane. It’s like a short break between study sessions.

not short

but it kinda clears off my mind

[hushed pewter]

How should I make the most of that time?
Make this lesson your last resort in learning something. Use any other resource you can before coming here. Ask your teacher, read the book, watch a video, ask on this server. Make this private lesson your very last chance to understand this. That way, you will not need to rely on it as much.

[dense blaze]

oh that makes sense or since its one on one if i really dont know a topic i can use the lesson to learn the basics of it so i can start to look at questions

[hushed pewter]

I've had situations like this before. I've had situations where the exam was in two days, and I knew nothing. Cramming does not work. Trying to absorb everything in the last few days simply does not work. Human beings cannot retain and embed such a large amount of complex information is little time.

Control what you can, endure what you cant.

I probably wasn't going to pass, and I accepted that cramming would not work. After acceptance, I just endure and move. I study at a healthy pace, maintain a decent sleep schedule and try to eat right. Take the exam and try my best. If I fail (which I usually did), I accept it, retake the class, and try to understand why I fell behind. If I pass, then that is just a happy outcome, and hopefully I would learn to be more diligent in the future.

You have a whole month though. It may be possible to succeed, but it will require serious effort on your end. I recommend you start using this server right away. Find out what material could be on your exam, and begin studying as much as you can. Just be sure to eat and sleep right. It does more for you than studying non-stop. Trust me, a healthy mindset is much more valuable.

[hushed pewter]

This is good. A healthy body gives you a healthy mind. I recommend you keep doing this.

[dense blaze]

Yeah, I’ll try to use my time as best as I can, and you’re right—it’s not the end of the world. Keeping a healthy pace is the best option, but I think I should study a bit more than the healthy pace. Achieving a decent score is still possible from where I’m at right now, so I’ll give it my best effort.

[hushed pewter]

In my experience, reviewing your fundamentals can be helpful, but if you don't have much time, fully committing to it can also be wasteful. I would say jump straight into trig. Try what you can, if you are lost, ask here. Be mindful that you struggle with algebra as well, and ask questions about the algebra related to your trig problem. This can help you not only to just learn both, but to also learn how they work together.

[hushed pewter]

Yeah you may need to study a bit more. It simply can't be avoided sometimes

[dense blaze]

Okay, thanks so much! I’ll try to solve some problems tomorrow and give my best on each one. I’ll also look for any common mistakes I’m making and focus on improving them. I’ll work on eliminating my weaknesses one by one—or at least I hope I can.

okay thank you so much

this conversation definitely changed my perspective on maths

you helped me alot

i cant wait to wake up and try to solve questions 😄

really thank you so much for taking your time to help me

[hushed pewter]

I'm glad. You can ping me if you need help (just please don't overdo it, and I may not respond if I am busy), but I'd like to help you if possible, I respect that you are trying so hard to better yourself. I identify strongly with that, it's why I want to help people if I can

btw, if you ping me, someone might give you this bot message:

!noping

[vocal sleet]

Please do not ping individual helpers unprompted.

[hushed pewter]

Just let them know I said it was okay to ping me

[dense blaze]

thanks so much

[dense blaze]

Yeah, I’ll make sure you're online and available. I really don’t like interrupting people, and don’t worry, over-pinging someone is the last thing I’d do.😄

[dense blaze]

thanks alot

well i guess i should close to channel

i think i holded it long enough 😄

and again

thank you so much

you really helped me alot

.close

[vocal sleet]

Channel closed

Closed by @dense blaze

Use .reopen if this was a mistake.

[hushed pewter]

if you reach out for help before giving your best effort, you're just copying what others say.
This is usually true, but it doesn't have to be always true. You are right though, it is a common trap to ask for help right away, and then just be given the answer (some helpers here are also too lax on handing out answers). You can ask for help right away, but it is up to you to actually try to learn from it and understand the question, not just receive the answer. I still do recommend at least first trying a little bit before asking though.

What you said is really valuable, and I’m going to give my best on every question from now on.
This is a good attitude, just be sure not to become obsessed with a single problem. If you have thirty minutes to understand three problems, it may be better to understand the last two problems in 15 minutes each, than to understand just that first problem in thirty minutes.

Honestly, until now, I wasn’t able to understand some questions and would just ask ChatGPT for answers and paste them into my work. I know ChatGPT isn’t always 100% accurate
Yeah, this is a huge problem for students. It's an "easy out" and I fear it will lead to a large-scale negative impact as so many students are cheating themselves out of their own educations.

Now, I want to actually learn, so I’ll put in my best effort.
That is good. Starting late is always better than never starting.

[hushed pewter]

Longest I've ever seen a channel open was two months.

Anyway, take care and I hope to see you soon, eager to learn.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[winged yacht]

I need help about exponential, can i use the property lim when x-->-infinity xe^x = 0

[winged yacht]

it works when I have (x+2)e^(x-1) ?

[raven owl]

Yes but if you want to be rigorous u cannot apply it immediately and you will need other facts.

For example one way to start would be doing a substitution like u=x-1

[winged yacht]

yes in our class we use X

but

if i do X=x-1

will the other one have to change?

bc there is an x+2 too

how can i put 2 variables

[raven owl]

Yes you will need to change the x+2 to now be written with respect to X and also change the limit variable from x to X

[winged yacht]

um

[winged yacht]

i didnt understand sorry

[raven owl]

If you want to apply this property you need to have only 1 variable

Can’t have two

[winged yacht]

okay

[winged yacht]

so what would x+2 be knowing x-1=X?

its X+3?

[raven owl]

Yes

[winged yacht]

okkk got it thank you very much

.close

[vocal sleet]

Channel closed

Closed by @winged yacht

Use .reopen if this was a mistake.

[winged yacht]

.reopen

[vocal sleet]

✅

[winged yacht]

oh wait so now i got (X+3)e^X can i apply the property i mentioned above now even if there is the +3?

[raven owl]

Nah not yet. Also the x in e^x should be capitalized.

You will need to distribute the e^X over (X+3), and use the sum rule for limits

Along with the property you said and the fact that lim x-> -inf e^x = 0

And also constant multiplication rule

A lot of rules need to be used

[winged yacht]

okk got it thanks

.close

[vocal sleet]

Channel closed

Closed by @winged yacht

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cold falcon]

uhhhhhhhh

[hushed pewter]

Did you have a question?

[vocal sleet]

@cold falcon Has your question been resolved?

[vocal sleet]

Channel closed

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[vast relic]

this is more physics than math but thought id ask here anyway

[hushed pewter]

yikes. That should be fun

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[hushed pewter]

what you got so far?

[vast relic]

ill send

give me one sec

ok its drawn weird since i did it w a mouse

but amplitude is highest at U_0

like the dotted line

on the right side

since its spends the most time there

more like this

@hushed pewter

[hushed pewter]

Why is the wave function increasing as it enters the potential boundary on the left?

[vast relic]

should be decaying right

i think its drawn weird

[hushed pewter]

If my understand of finite wells is correct, yeah, it should be decaying

[vast relic]

the magnitude of the amplitude must decay right

i think for some reason i was just decreasing it

but thats incorrect

?

[hushed pewter]

The triangle potential is weird. I'd rather solve it than intuitively guess the wave function. Intuition hurts in QM

[vast relic]

😭

[hushed pewter]

Yeah I'm pretty sure

[vast relic]

im not sure how id solve it tbh

is the problem

[hushed pewter]

it may not be solvable. But regardless, we are not being asked to solve it, we are being asked to intuitively give a sketch. So this requires more understanding of QM than basic differential equations.

[vast relic]

yeah

[hushed pewter]

let me bust out my old QM book

[vast relic]

😭 thanks

[hushed pewter]

sorry got side-tracked. But I'm still here

[vast relic]

nw

i kinda jujst moved to the next problem

i know the general shape of the graph but im not sure how frequency would changgge

[hushed pewter]

Okay, consider what the time-independent schrodinger equation is saying about the relation of a particle's energy, and the potential energy of its surroundings. What conservations do they obey? What does this imply as the potential energy increases? Total energy must be conserved in a closed system (classical idea, but you need the QM equivalent idea here), so if the potential energy increases, what else change to maintain conservation?

[vast relic]

kinetic must decrease?

[hushed pewter]

Yes

We see this in the infinite-potential-well example, where the particle has zero wave function inside the potential barrier

[vast relic]

but thats only the right side rtight

ok yeah

[hushed pewter]

So if the kinetic energy of the particle decreases, what does that say about the frequency of the wave function?

[vast relic]

it goes down

so frequency increases at the left end

or as you approach the left end

[hushed pewter]

This is a little trickier. We now need to care about reflections and transmissions, which I forgot so much of

[vast relic]

i see

.close

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[dire lynx]

How do I solve these kinds of problems?

[vocal sleet]

Please don't occupy multiple help channels.

[half imp]

Factor each side and cancel out common factors

[vocal sleet]

@dire lynx Has your question been resolved?

[dire lynx]

So I just get the greatest common factor right

For each side

[half imp]

well you're looking for the greatest common factor of both sides

one side can't have a "greatest common factor" by itself

[vocal sleet]

@dire lynx Has your question been resolved?

[dire lynx]

Oh okay

[vocal sleet]

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[normal haven]

This is wrong right? I think x should be raised to the n + 1 power initially.

[vocal sleet]

@normal haven Has your question been resolved?

[normal haven]

<@&286206848099549185>

[novel wedge]

1/1+x
Series (-x)^n
Series (-1)^n (x^n)

((-1)^n (x^n+1))/n+1

[novel wedge]

Yea

[normal haven]

Thanks!

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[hexed umbra]

im confused

[hexed umbra]

does closed interval mean including >=< or ><

oh wait

i skipped over a sentence

.close

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[hexed umbra]

.reopen

[vocal sleet]

✅

[hexed umbra]

wait

if [] exlucdes the number (ex. x <= 10)

[open sage]

this includes

the number

] includes ) does not include

[hexed umbra]

oh

[open sage]

closed interval is ]

[hexed umbra]

how does a closed interval of infinity work

[open sage]

you can’t

enclose infinity

[hexed umbra]

wait

oh my god i keep getting them confused

[open sage]

but it basically means negative infinite nunbers

look at it this way

[] looks like a box

something you want to keep

in the box

() is more loose

i guess?

[hasty kindle]

Can u guys help me please

with a math problem

[open sage]

#hola

[hexed umbra]

oh thats a good way to remember it

[open sage]

uh

#❓how-to-get-help

go there

[open sage]

yeah inifinity is always an open interval

basically the interval (-inf,10] tells you all numbers from minus infinity up to, and including, 10

[hexed umbra]

does [] mean > and < and () mean <= >=

[open sage]

dawg

[hexed umbra]

😭

[open sage]

[] means <= =>

[hexed umbra]

but what if you have 10)

[open sage]

<10

[hexed umbra]

ok

[open sage]

[2,8] means 2 <= x =< 8

[jagged cargo]

interesting notation

[hexed umbra]

[] sideways is =

[open sage]

wait no

wait

[hexed umbra]

bro 😭

[jagged cargo]

$\rotatebox{90}{$[]$}$

[jagged cargo]

doesnt seem = to me

[open sage]

it’s similar i guess is what they mean

[jagged cargo]

ok house

[open sage]

sorry i mixed it up

there you go

[hexed umbra]

why the hell is non-included intervals open

why not closed since theyre closed off

[open sage]

[2,8]
means
any number greater or equal 2 up to, and including, 8

[open sage]

i don’t know what to tell ya man

it’s the way it is

[hexed umbra]

it makes it so much more confusing 💀

[open sage]

i’m sure some mathematician came up with some clever reason for it

i’m in engineering

i don’t care

[hexed umbra]

and (2,8) is any number from 2-8 excluding 2 and 8

[open sage]

yes

so 2.00000…001 (assuming we’re in R)

would be included

but 2 would be excluded

[hexed umbra]

im not gonna remember this bro 😭

ima try to imagine the () slapping the numbers to exclude them

[open sage]

dawg

you’re making this harder than it is

[ ] includes

( ) excludes

that’s all you have to remember

[hexed umbra]

oh wait if you look at the exclude and include, exclude looks curvy because of the e and includes look straight because of the i

okay maybe ill remember

thanks

.close

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[hexed umbra]

.reopen

[vocal sleet]

✅

[hexed umbra]

WAITTT

() does NOT mean exclude cuz the infinity

but wait

oh my god

how do you "exclude" infinity

oh nvm i get it

[open sage]

you can’t include all of infinity

[open sage]

() means exclude

simple as

there is the exception for infinity

[hexed umbra]

okay i need to reread this whole chapter

.close

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[vocal sleet]

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[sly basin]

Can sum1 explain stokes theorem to me

[sly basin]

Do the 2 formulas five same answer

[vocal sleet]

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[frosty thorn]

is this correct?

[frosty thorn]

oh sheeee i should factor out the e

[uncut holly]

yes

[frosty thorn]

ty

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[jagged cargo]

i have a question regarding vector space dimension. it is defined that dimS = length of S basis. but what about {0}? one of its basis is 0, but that has a length 1, so why is dim{0} = 0, not 1?

[heavy yoke]

{0} is not a basis for {0} as it is linearly dependent

for that reason we define {} as the basis of {0}

[jagged cargo]

but how does that span {0}?

i mean, theres nothing

[heavy yoke]

define the empty sum as 0

[jagged cargo]

hm, i see

and its vacuously true that {} is LI

right, thanks

.close

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[indigo rose]

Can someone tell me what I did wrong here (Law of sines)

[solar cape]

Uh I think you might have made some misinputs on your calculator

[indigo rose]

Have i? which ones?

[solar cape]

10/sin 34

Is not equal to 0.05

[solar cape]

Oh

You flipped your fraction

[indigo rose]

the mode is set to degree

[solar cape]

sin 81/a to a/sin 81

Why

[indigo rose]

because i’m calculating in degrees not radians

[solar cape]

That's probably your error

Wait gimme a sec

[indigo rose]

i don’t flip?

[solar cape]

If you flip on one side

You should flip on the other

[indigo rose]

ohhhhh shit

u right

[indigo rose]

GOAT

[solar cape]

Yey

[vocal sleet]

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[golden parrot]

Clearer pic

[vocal sleet]

@golden parrot Has your question been resolved?

[kind light]

i found a solution but i got cd to be irrational which is slightly concirning

oh nvm

basically you draw line BD and AC and use ptolemy to get a quadratic

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[vast shale]

Hi, could anybody help me with this question please

[vast shale]

Question 2

[gaunt sparrow]

Think of the second term on the left, $2^{k+1}$ as $2 \cdot 2^{k}$.

[twin meteor]

Azyrashacorki

[gaunt sparrow]

Can you factor something out of both terms?

[vast shale]

how did it become 2x2^k?

[distant pike]

property of exponents

[vast shale]

ohh that makes sense, thank you i will try the problem again

Thank you everyone i managed to solve it, is it intended for me to mark it as resolved? Im sorry im unsure how

[jagged cargo]

.close

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[true gale]

hi, i need to show that not every 4 regular Euler graph also a Hamiltonian graph is, but I cant seem to draw it. Some help would be greatly appreciated

[spiral turtle]

@true gale a complete graph with 5 members is a 4 regular Euler graph, yes? What if you had two disconnected copies of this?

[true gale]

then is not Euler anymore?

[spiral turtle]

I might be misremembering the exact definition of Euler, but I thought it was just that every edge had an even degree

Not that it was connected

[true gale]

yes, also connected

because you need a path that traverses every edge

[spiral turtle]

Looking it up, there are different definitions, but ok, we are going with connected as well

I'm not certain from here, but I'll ponder a bit

[true gale]

btw i think that i mean Eulerian graph (my course is in Dutch)

[vocal sleet]

@true gale Has your question been resolved?

[spiral turtle]

The Petersen Graph is an example of a 3-regular graph with no Hamilton cycle. Perhaps this can help you find a 4-regular graph without a Hamilton cycle?

Actually, if you're allowed to use edges that connect from a node to itself, you can use the Petersen Graph with each edge connected to itself.

That will be a 4-regular Eulerian graph, but not Hamiltonian

[true gale]

no we cant, it has to be a "simple graph", so it needs to be connected, no loops and it cant be a multigraph

[spiral turtle]

Oh

[spiral turtle]

This except connect them with a single node connected to 2 nodes on each half by deleting the edges connecting those pairs of nodes.

@true gale ^

Gross drawing

[true gale]

this is also a hamilton graph no?

[spiral turtle]

No

No way to make a closed circuit without passing through the central point twice

(the center point is a node, but the rest of the intersections are not)

@true gale courtesy ping

[true gale]

if the center poit is a node, then is not a 4 regualr graph

[spiral turtle]

Yes it is

Each node has 4 neighbors

@true gale

[true gale]

ah yes srry i was mistaken

u are correct

[spiral turtle]

So there is an example!

🎉

[true gale]

thank you very much

[vocal sleet]

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[white acorn]

Optimizing volume of triangular prism in a sphere using differenciation

[white acorn]

i got to a disgusting equation that i need to solve for maxima and minima (so i dont think i got it right)

heres my work as of now

let A be base area of triangle, let $r_{1}$ be radius of circumcircle of triangle, let $r_{2}$ be radius of sphere

[twin meteor]

Kai The Cat

[white acorn]

$r_{2}^2=r_{1}^2+\left(\frac{h}{2}\right)^2$

[twin meteor]

Kai The Cat

[white acorn]

$V=A\sqrt{4(r_{2}^2-r_{1}^2)}$

[twin meteor]

Kai The Cat

[white acorn]

then i let $\alpha$ be one angle in the triangle, $\beta$ another angle, and b be the side between them

[twin meteor]

Kai The Cat

[white acorn]

the area of the triangle is then $\frac{b^2tan(\beta)tan(\alpha)}{2(tan(\alpha)+tan(\beta))}$

[twin meteor]

Kai The Cat

[white acorn]

$r_{1}$ is also $\sqrt{\left(\frac{b}{2}\right)^2+\left(\frac{b}{2}(-cot(\alpha)+csc(\alpha)sin(\beta)csc(\alpha+\beta))\right)^2}$

[twin meteor]

Kai The Cat

[white acorn]

after substituting it back in

i get the function\ $V[\alpha,\beta,b]=b^2sin(\alpha)sin(\beta)csc(\alpha+\beta)\sqrt{r_{2}^2-\frac{b^2}{4}+\left(\frac{b}{2}(-cot(\alpha)+csc(\alpha)sin(\beta)csc(\alpha+\beta))\right)^2}$

[twin meteor]

Kai The Cat

[white acorn]

and i have to differenciate this and solve but i dont think its right?

also im allowed to use wolfram or anything that may help, including papers or the internet but i cant find anything

<@&286206848099549185> sorry but kinda need help

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[errant sigil]

where did i go wrong

[errant sigil]

exam is rlly soon i need help asap

4a(i)

[vast shale]

,rcw

[errant sigil]

sooo…

@vast shale

[vast shale]

i didnt get your working so.......

do you have to prove that the differential equation is exact ?

if not

then

[errant sigil]

yes and then find the parent function which i’m yet to do

[errant sigil]

mine doesn’t match

did i do it right?

[vast shale]

the first differential equation is not exact

see how we have sin(xy) in the first part and os(xy^2) in the second

you can directly say the D.E is not exact

idk how to prove though 🤷‍♂️

there cant be a function which gives sin(xy) when differentiated wrt x and cos(xy^2) when differentited wrt y

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[abstract palm]

I am asked to find matrix $A:\mathbb{R}^3\rightarrow\mathbb{R}^2$, such that its kernel is $\left\langle\begin{pmatrix}
1\0\0
\end{pmatrix}, \begin{pmatrix}
1\1\0
\end{pmatrix}\right\rangle$.\
To find it i need to solve [\left(
\begin{array}{ccc|c}
1&0&0&0 \
1 & 1&0&0
\end{array}
\right)] which is equal to $\left\langle\begin{pmatrix}
0\0\1
\end{pmatrix}\right\rangle$.
so my matrix is $\begin{pmatrix}
0&0&1
\end{pmatrix}$, but its kernel is $\left\langle\begin{pmatrix}
1\0\0
\end{pmatrix}, \begin{pmatrix}
0\1\0
\end{pmatrix}\right\rangle$. What am i doing wrong?

[twin meteor]

Slowaq

[abstract palm]

or are those two kernels the same?

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[abstract palm]

.reopen

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[viscid thicket]

A is a matrix 2x3

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[torpid merlin]

Assume i is true and prove ii

[vocal sleet]

@torpid merlin Has your question been resolved?

[torpid merlin]

<@&286206848099549185>

[vocal pagoda]

Are you sure it's written correctly? L seems to appear out of nowhere...

[torpid merlin]

It’s different version of the definition of series convergence

[vocal sleet]

@torpid merlin Has your question been resolved?

[torpid merlin]

@help

<@&286206848099549185>

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[open sage]

b) If B3 is another basis for V such that C(B1,B3) is (in the image) find C(B2,B3)

B2 is given above

so is B1

I was thinking we could go

B2 -> B1 -> B3

B1 -> B3 is given
I'm having trouble finding B2 -> B1

it's the inverse of B1 -> B2 i think

but it's got alphas in it so

[vocal sleet]

@open sage Has your question been resolved?

[vocal sleet]

@open sage Has your question been resolved?

[vocal sleet]

@open sage Has your question been resolved?

[vocal sleet]

@open sage Has your question been resolved?

[tender lotus]

yeah so what you’re doing differently is

[open sage]

differently to what, sorry?

[hushed pewter]

@open sage close this if done

[open sage]

not done

[hushed pewter]

Then please do not open multiple channels. Stay either here or in #help-7｜zen1thxyz, but please do not use both

[open sage]

Right but it's different problems

[hushed pewter]

irrelevant

[open sage]

I won't get an answer on this one if I flood another channel with a different question

[hushed pewter]

There's a reason for this rule

There's a lot of people to help

Allowing people to clog with as many channels as they like makes it that much worse

Please, choose the one question you need answered and focus on just that for now

you can ask both eventually, we just ask that you not use more resources than is allowed

[open sage]

I am aware of the message which pops up when you open a second help channel, but I don't think by any means i was "spamming" or "flooding" the help channels

at any rate i understand what it is you are getting at

but i'm sure if something is wrong a moderator or a staff member will let me know about it

thanks for your advice

i'd also appreciate it if you kept my help channel limited to helping me. if you're not able to help me that's alright but now this entire channel is flooded with unrelated conversation. I understand you are not trying to annoy me or anything it's just with the channel already being buried it only makes it harder with getting help

next time feel free to message me or let a staff member know

[autumn trail]

The server rules do specifically say not to do what you are being asked not to do here.

It would be better in general for you to stick to one question at a time for these help channels.

Since you are doing linear algebra you might actually have better luck in #linear-algebra

Though sometimes it happens where a person has a question and it gets buried or they don't want to intrude on a question being discussed in those channels I guess.

[open sage]

I suppose you specifically refer to this:

● Do not spam your questions in the wrong channel or across multiple channels. Be patient and wait for someone to answer.

I'm not trying to bend or misinterpret the rules, to be clear

I just interpreted this to cover the case of those who are annoyed by not getting a response and then posting the same question over multiple channels

I figured since I had one buried question it would be counterproductive to erase the channel figuring someone might come back to it later

[autumn trail]

Yeah this is not how you should read the rules.

[hushed pewter]

That is fair. The rule should be a little more direct, like

• Please do not open multiple channels for your questions. Stay in one channel. If you have a new question, either close your current channel, or wait for your current question to be answered before opening a new channel
  but maybe that's just my own opinion.

[autumn trail]

The issue is mainly that the rules are already meant to address users being annoyed rather than as things you can bend at your leisure due to annoyance.

We get a lot of users much more annoyed and worse than you and as a result the rules ended up this way.

[open sage]

Oh I don't think I'm annoyed

I'm sorry if I came across as such

[autumn trail]

Sorry this is kinda hijacking your channel fwiw

[open sage]

I like the free help this server provides and i've helped others many times

no it's fine at this point i'll just post it in the linear alg channel

I just felt i was being reasonable with the use of the channels. But I suppose "reasonable" doesn't hold up against the rules

which is fair you know

it's just not what I interpreted

[hushed pewter]

I respect your willingness to embrace and accept change or regulations

I would help you on your problem if I could

[open sage]

it's fine. there's not much sense in arguing over a small interpretation issue, when it also doesn't change much for me. if staff prefers the channels to be managed a certain way that's fine

[open sage]

no worries. i'll be asking in the linear algebra channel, thanks

.close

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[lusty mesa]

Is this integral set up correctly?

I am not sure if my second half is correct because the upper and lower bounds are both +x and -x

[vocal sleet]

@lusty mesa Has your question been resolved?

[lusty mesa]

<@&286206848099549185>

[silk osprey]

wdym

also

!done

[vocal sleet]

If you are done with this channel, please mark your problem as solved by typing .close

[silk osprey]

not .end

looks good to me though

[hexed umbra]

diddy party

[lusty mesa]

I am trying this approach

[silk osprey]

what was wrong with this?

are you trying to change the order

to see if they evaluate to the same thing?

oh

[lusty mesa]

I just thought this might mean the same thing

[silk osprey]

i see

[lusty mesa]

But i tried to evaluate this but i got 1/10,

[silk osprey]

i’m not sure what’s going on in your integrals on the botttom here

[lusty mesa]

I got this

It’s weird cause 4/10 is less than I expect the answer to be…

Did i get it wrong?

[silk osprey]

yea i’m just not sure what’s you’re doing tbh like where is 0^x^2 coming from

[silk osprey]

this looks correct to me

[vocal sleet]

@lusty mesa Has your question been resolved?

[vocal sleet]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[scenic ravine]

I;m not sure how to proceed

My inital thoughts are $a \leq \sup(A) ; \forall a \in A$ and $b \leq \sup(B) ;\forall b \in B$. Adding them gives us $a+b \leq \sup(A)+ \sup(B)$ but that feels sus

[twin meteor]

ƒ(Why am. I here)=I don't Know

[zinc quail]

so far right c:

[high maple]

What is wrong with that, why sus. It feels right to me

[zinc quail]

you have an upper bound, now just show it's the lowest

[vocal sleet]

@scenic ravine Has your question been resolved?

[scenic ravine]

mhm

[scenic ravine]

idk, just feels off

[zinc quail]

a+b <= sup(A)+b <= sup(A)+sup(B)

[high maple]

Hmmmm. Anyway yeah surely it is right

[frail violet]

Then u do the thug shaker

[scenic ravine]

anyway, I'll try the second part then

[high maple]

The second will be a bit more technical

[scenic ravine]

yeah, feels like it will

This is where I'm currently at

[high maple]

You can use the fact to give a bound >.>

[scenic ravine]

wdym

ooh

$t- a \geq b$ too

[twin meteor]

ƒ(Why am. I here)=I don't Know

[scenic ravine]

well, that doesn't help much

[high maple]

Did you get what I mean by this part, or should I specify more?

[scenic ravine]

didn't really get what you mean

well, one thing I know is that $t \geq b$

[twin meteor]

ƒ(Why am. I here)=I don't Know

[high maple]

u - a is larger than any element of B

What do you call this, you have a word for this

[scenic ravine]

supremum

well, upper bound to be more precise

but t is the least upper bound

so $u-a \geq t

[high maple]

Yeah u - a is upper bound of B

I think you need more to prove that it is a supremum

[scenic ravine]

welll, it isn't

t is the least upper bound

Now to show that $s+t$ is the supremum of $A+B$

[twin meteor]

ƒ(Why am. I here)=I don't Know

[scenic ravine]

Let $u$ be the supremum of $A+B$, then $ \sup(A) + \sup(B) \geq u \geqa+b$. From this it follows $\sup(A) + \sup(B) -a \geq u-a \geq b$

[twin meteor]

ƒ(Why am. I here)=I don't Know
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[scenic ravine]

I kind of lost here

[high maple]

You want to show u = sup(A) + sup(B), right?
You might want to use the previously shown fact, u - a >= sup(B) for all a.

Key is "for all a"

Maybe it is easier to see in the form of
u - sup(B) >= a

[scenic ravine]

I get that

hmm

[scenic ravine]

<@&286206848099549185>

[lone pike]

Hello guyss

I'm new here

[scenic ravine]

Hi

[lone pike]

Hii btw where do I need help?

[scenic ravine]

If you need help look at #❓how-to-get-help

[lone pike]

Actually I just need help in getting x- intercepts of cubic functions

I think that's it

[scenic ravine]

yeah, even then

open your own channel

that way it will be easy to keep track of what you do

[scenic ravine]

so I was thinking $\sup(A) + \sup(B) \geq u \geq a+b$, where $u$ is the supremum of $A+B$

[twin meteor]

ƒ(Why am. I here)=I don't Know

[scenic ravine]

Now what

.close

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[mild trench]

.done

.solved

.close

[vocal sleet]

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[bold jetty]

may someone teach me dis

[scenic ravine]

,rotate

[vocal sleet]

@bold jetty Has your question been resolved?

[bold jetty]

hi

[spice whale]

Is the solution to a (13/4,19/4)?

[bold jetty]

Huh?

[spice whale]

what's the answer for part a

[bold jetty]

(3.25, 4.75)

C coordinate

[spice whale]

13/4=3.25, 19/4=4.75

[bold jetty]

really

[spice whale]

here's how to solve it. calculate change in x direction first. that comes out to be 7-2=5. now multiply that 1/4 as we need one fourth of the distance of 5
That comes out to be 5/4=1.25 now we have calculated how much we have to walk starting from point A in x direction. 2+1.25=3.25

now calculate change in y direction. 7+2=9. 9/4=2.25 is the distance you have to walk starting from point A in y direction. 7-2.25=4.75

same method can be used for part b, c and d.

[bold jetty]

ohh interesting

what about a+f(b-a)? can u inspect this formula to see if it works?

[spice whale]

what's f here?

[bold jetty]

fraction

aka 1/4 , 1/6 etc

[spice whale]

I don't think this is correct. It's probably for specific types of questions. here the line segment is situated away from origin and is neither completely horizontal nor completely vertical

so using that here won't get correct solution

[bold jetty]

Oh wut

my friend says it works for finding any fraction of a segment

Which was proven here:
a +f(b-a)
2 + 1/4(7 - 2)
2 + 0.25(5)
2 + 1.25
3.25 (x)
a + f(b-a)
7 + 1/4(-2 - 7)
7 + 0.25(-9)
7 + -2.25
4.75 (y)

@spice whale

Idk though am not saying ur wrong but i thought it would work

[spice whale]

Yeah my bad. I plugged in the values for change in x and change in y in the formula. It seems to work yeah. But I prefer the traditional method of observation if you get good at it you can solve these questions in matter of seconds by just looking

remembering formulas where you don't have to also complicates stuff

[bold jetty]

Hmmmm

Can you solve this then

[bold jetty]

Find point C, which is 1/4 of distance A to B

Point A(-2,-1)
Point B(6,3)

[spice whale]

I have told you the method. And you also have the formula so why don't you try to solve this one yourself?

I can help you if you have problem with a specific step.

[bold jetty]

Hmm

Okay

I just wanted to compare my answer

from using the formula my friend gave

a +f(b-a)
-2 + 0.25(-1-(-2)
-2 + 0.25(-1)
-2 + 0.25
-1.75 (x)?

[spice whale]

Try to visualise the question and you'll be able to do that yourself. Plot the line segment on a graph, plot the coordinates you calculated over the line segment and see if they seem to divide the line in 1/4

[spice whale]

change in x is 8
change in y is 4
8/4=2
4/4=1
answer should (0,0)

[bold jetty]

So why's the A+F(B-A) formula isnt working? :(

[spice whale]

I honestly don't know maybe the formula is a generalized version and cannot be applied to all questions

[bold jetty]

I had a mini quiz yesterday and it folded me 😭

I guess ill use yours method now

how do u get change in x and change in y

[empty frigate]

i'm pretty sure the formula does work

you just computed it wrong

[empty frigate]

yeah you put in the wrong numbers here

[bold jetty]

huh!!

[empty frigate]

if you want the x coordinate of the result, then a = -2 (the x coordinate of point A) and b = 6 (the x coordinate of point B)

[bold jetty]

why would it be that way if..

[empty frigate]

and then for the y coordinate, a = -1 (the y coordinate of point A) and b = 3 (the y coordinate of point B)

[bold jetty]

huh

why is it arranged that why

[empty frigate]

well the x coordinate of "the point 1/4 of the way from A to B" is 1/4 of the way from the x coordinate of A to the x coordinate of B

and it makes sense that A + (B-A)/4 expresses that, you start at A and then move 1/4 of the distance (which is B-A)

...the thing you did would imply that the x coordinate of the result only depends on where A is, which is kind of obviously ridiculous if you think about it

[bold jetty]

but how i arranged this

[bold jetty]

is the same how i arranged this

if i switch it around then how am i supposed to make sense of the formula?? 😢

[empty frigate]

well that time the numbers happened to be the same so it ended up working anyway

[spice whale]

It's honestly the best method. If you get the grasp of it you won't forget it.

[bold jetty]

huh!

[empty frigate]

well B-A is the distance from A to B
so you start at A, and then go F of the distance from A to B

(as sanity checks: if you put in F=0, you go none of the distance from A to B and so you're still at A. if you put in F=1, you go all of the distance and you get A + (B-A) = B)

and like. the distance from, for example, (2,3) to (14,36), is "12 to the right (14 - 2) and 33 up (36 - 3)", right?

[empty frigate]

not "1 to the right (3 - 2) and 22 up (36 - 14)", which is the kind of thing you were doing here

so basically the way you make sense of the formula, is that the variable A is about point A, and the variable B is about point B

not "the variable B is the y coordinate of point A" which seems like it should be more confusing?

[bold jetty]

i.. i see 😭

what do u think is the most efficient method

[bold jetty]

this by mr great real rex15

[bold jetty]

or this by i forgot who ig ot it from

[empty frigate]

...i mean those are two different ways to express the exact same computation

so i think probably the important thing is more like, which one makes more sense to you

especially in terms of like, which method are you more likely to actually remember how to do correctly instead of putting the variables in the wrong order or something

[bold jetty]

😭

which do u think is less confusing then @empty frigate

i cant really find what makes more sense to me cause i dont understand the both of them

[bold jetty]

wait how did u get change in x or chainge in y?

[spice whale]

For x direction
-2-6=-8 sign does not matter here as it's basically the distance between -2 and 6
Similarly for y direction
-1-3=-4 or 4

[bold jetty]

what do u mean sign does not matter here as it's basically the distance between -2 and t6?

do u mean when doing changes in x and y's in those specific questions/problems, i have to make them all positive for changes in x and y's?

[bold jetty]

after dividing 8/4 and 4/4 how is it immediately (0,0)?

[spice whale]

we calculated that we have to walk 2 units in x direction by doing 8/4. so start from x=-2 and walk till x=0

for y you start from y=-1 and walk in y direction till y=0 i.e. 1 unit

[spice whale]

the blue point here is point A for reference and point B is the green point

[bold jetty]

oh so

after calculating x/x and y/y i just use the result of the number and walk them till the number i just found, is the distance of C?

cause tahts the kind of kindergarden imagination i am having

[spice whale]

Yeah for example if you were asked to calculate the point C that divides the line segment in ratio 3/4 from B to A instead of A to B you'd do it like this.

Units we have to walk in x direction=8×3/4=6
Units we have to walk in y direction=4×3/4=3

Coordinates of B are (6,3) now you have to walk in negative x and y direction

6 - change in x direction=6-6=0
3 - change in y direction=3-3=0

we reach same result by doing it from either side so we have basically verified the method, this I think helps in getting a clear understanding of the method

[vocal sleet]

@bold jetty Has your question been resolved?

[bold jetty]

wait why negative x and negative y direction

i dont get dis

i get 4x3/4 = 6 and 4x3/4 = 3 but what do i do next?

[bold jetty]

😭

<@&286206848099549185>

[spice whale]

you're starting from point B this time. You cannot go towards positive x and y direction, as the line segment with respect to B extends towards negative x and y direction

[bold jetty]

I was constantly thinking about this

I wondered

i understand change in x and change in y

[bold jetty]

the distance betweem xyA to xyB

and the need to divide them cause of 1/4

but why do u do -2 - 2 and - 1 - 1 afterwards?

[spice whale]

I don't get you

[bold jetty]

Dis

You did got (0,0) because u did -2 - 2 and - 1 -1 right?

Oops

my math..

Uhm

2 - - 2
1 - -1 right?

i understand u got it from A (-2 , -1 ) but why speciically A(-2,-1) ?

[spice whale]

okay think about it logically I was just trying to express it in forms of number.

You're at x=-2 coordinate you move by 2 units in positive direction where will you end up at?

Similarly for y direction you're at -1 you move 1 unit in positive y direction where you'll end up at?

[bold jetty]

Oh

Why do we move at a positive direction?

[spice whale]

Find point C, which is 1/4 of distance A to B

Point A(-2,-1)
Point B(6,3)

question states that we have to calculate the distance FROM A to B

[bold jetty]

Oh.

[spice whale]

the line segment with respect to point A extends towards +X, +Y direction. And we have to find a point on the line segment.

[bold jetty]

So its basicaly A and B extending on the right side which is a positive direction, made it to be positive?

[spice whale]

For example if you move in negative x direction by 2 units from A x will be=-4
and 1 unit in negative y direction, y will be =-2

(-4,-2) Point does not lie on the line segment

[spice whale]

Yes

[bold jetty]

oh..

so if it was a formula it would be (x1 - x1, y1 - y1)/4 - (a to b/b - a)? would it work ?

[spice whale]

whenever you're given these kind of questions try to plot a rough graph. once you've got a good understanding of graphs you'll be able to solve them without having the need to lift up the pen

[bold jetty]

I see..

I thank you so much for being so patient with my idiocy

I understand how to do these now

[spice whale]

yeah but it will only work for questions where you've to calculate 1/4 the distance. tbh instead of remembering it as formula remember it as method that formula already looks very ugly to me so I doubt you'll retain it for more than a few days

[bold jetty]

yeah, its being able to recognize the pattern for solving fractions of a distance right?

[spice whale]

It's all good. We all start at some point!

[bold jetty]

Thank you ^^

Also quick question

.rotate

.rotate

!!! how do u use rotate

,rotate

[bold jetty]

Mmm i wanted to study this too but i wonder if it'll also take a while

But this is basically the reverse of the last part right?

Still not sure how you do this though

[spice whale]

Correct. First start off by plotting the line segment on the graph

[bold jetty]

how do i put lines in the graph lol

[spice whale]

I was talking about plotting it on the paper you sent above. It has a graph for that purpose I assume

[bold jetty]

Oh, isnt' this the same thing though?

[spice whale]

Yeah, but I don't think you can put lines on graphing calculators like these without the equation of line

[bold jetty]

Graphing calculators? wut is that i thought desmos was used to just visualize our lines Whoops

Well the paper isn't with me right now thats why i took screenshots

[spice whale]

since the question you sent above is also asking for an explanation how you calculated it, I assume you're required to use a formula? as the same question can also be done using distance formula

[bold jetty]

Hmmmm

[spice whale]

I will take that as a yes. First start off by calculating the distance between AB and AC

[bold jetty]

AHHHH

the distance is (8, 12)

am i right

change in x and change in y

[spice whale]

correct! now can you also plot point C on the graph. once you've done that think about how it divides the line and in what ratio

[bold jetty]

Huhh

Right

8, 12 is point C?

[spice whale]

Point C is given to you in question. You've to calculate the ratio in which point C divides the line segment AB. Actually I'd recommend you to use the distance formula. This method will get you the answer but I doubt your teachers will accept it

[bold jetty]

I see

Thank you

What do i do after i plot 8, 12 on point C

[spice whale]

It is not point C. Point C is given to you in question -2,-7/2. What you've calculated is change in x and change in y direction

[spice whale]

But let's forget this for now. Use this formula and calculate the distance between point A and B, and point A and C

[bold jetty]

agaein?

okay

d = root of (-3 - 5)^2 + (-5 - 7)^2
d = root of -8^2 + -12^2
d = root of -16 + -24
d = root of -40
d = -6.32

i think

[spice whale]

-12 squared is 144. -8 squared is 64

[bold jetty]

oops

am bad at distance formula

144 + 64
208
14.42 (rooted)

[spice whale]

Correct. I assume you got 4×sqrt(13) as the length of line segment AB so let's keep it like that. now calculate the length of line segment AC using distance formula

[bold jetty]

Hold on

Ill brb in 15 mins i have eto do smt

[bold jetty]

I'm back

@spice whale

@spice whale

Oop

Sorry. For double ping

I'm on mobile

[bold jetty]

Root of (5-8)^2 + (7-12)^2
Root -3^2 + -5^2
Root 9 + 25
Root 34
5.83

[spice whale]

You seem to have plugged in the values of point C wrong.

[vocal sleet]

@bold jetty Has your question been resolved?

[vocal sleet]

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[sleek flame]

just wanna clarify somethings

[sleek flame]

geometric series works if |r|<1 and it converges to a/(1-r)

but if its |r|>1, its a/(1-(1/r))

what is this talking about then?

[dull bear]

That’s slightly different to what I thought you meant

[dull bear]

It’s the same thing but if |r| > 1, while the “original” geometric series (that’s your a + ar + …) doesn’t converge, you could instead deal with 1/r as your common ratio, and you’d have that having absolute value less than 1, for which the series a + a/r + a/r^2 + … does converge (replace r with 1/r in the geometric series formula)

[sleek flame]

ok

yes, so |r| doesnt converge its |1/r|

ok thank you

im still a bit confused, how do you determine what to factor out for the geometric series?

I guess you always want the r value to be a fraction, (value<1)?

[dull bear]

They’re also trying to get it into the forms in the corner I think

[sleek flame]

im not going to be able to remember this😭 i'll do a few more questions

see if theres a pattern

[dull bear]

Awwww

[sleek flame]

I think I'll just derive everything on the spot on the exam

cause the formula for geometric series is same

I just have to treat r as a fraction and r by itself seperately

nooo its over

[vocal sleet]

@sleek flame Has your question been resolved?

[sleek flame]

i need a drink

[sleek flame]

also whoever made this amazing laurent series video on youtube deserves all the love❤️

[vocal sleet]

@sleek flame Has your question been resolved?

[sleek flame]

alright, took forever but I think I understand how to find laurent series given function and it’s region

how do you determine the singularity and residue for ((z-1)/(z+1))^3?

yup i got it

[sleek flame]

what should you do if the angle is -pi/2

because angle has to fall in range (-pi/2, pi/2)

oh wait, sorry, z is sippose to have arctan(-1) = 3pi/4

but even then, when I multiply by 2, i get 3pi/2 which I have to subtract by 2pi to get it within the range

but its (-pi/2) which doesnt work

oh no its arctan(a) that has to be within (-pi/2, and pi/2), but -pi/2 falls within the principal value

[dull bear]

What I was about to write

[sleek flame]

thank you! @dull bear literally dont know what I would do without your help

also everyone else in this channel 🙂

[dull bear]

Awwwww

[sleek flame]

lot more honourable mentions lol but the helpers know who they are! Thanks to everyone

[sleek flame]

omg im so brain dead rn

[vocal sleet]

@sleek flame Has your question been resolved?

[sleek flame]

am i stupid

im a bit tired rn ngl

[sleek flame]

is the residue theorem just 2pi i times the sum of residues at each singularity?

yes, but you have to note that the singularity must be in the curve

so if a singularity is outside, just ignore it

ok

and to calculate the residues, you can use partial fractions (it will be the numerator) if the pole is simple, otherwise you gotta use the order m residue theorem (formula)

[sleek flame]

i’m making an error somewhere for this residue

is this actually the only way for non simple poles

[sleek flame]

I think this expansion is missing an i?

<@&286206848099549185>

yea it is

i hope im not trippin

[small marsh]

The second term should have an i.

[sleek flame]

ok

thank you

[vocal sleet]

@sleek flame Has your question been resolved?

[sleek flame]

its over

sleepy time

i think I know everything now its just a matter of whether I can solve quickly enough

[sleek flame]

.close

[vocal sleet]

Channel closed

Closed by @sleek flame

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[soft timber]

Can someone say if theres anything wrong with this? The original queston was: (12+2×sqRoot(3x+1))÷sqRoot(3x+1)=4+sqRoot(5) and i got it down to 12= 2a + sqRoot(5) × a
Which is what you see from the first page. If its wrong pls give the answer with step by step

[soft timber]

not upside down anymore

[cunning plaza]

!original

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[cunning plaza]

Or say what you're trying to do at least, where did 3x+1 come from?

[soft timber]

I got the answer

Thanks for ur time

.close

[vocal sleet]

Channel closed

Closed by @soft timber

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[misty wave]

how do u start solving this? do i need to know a formula for it

[vocal pagoda]

did you calculate the sides of the big right triangle? The one with the black corner rectangle.

[misty wave]

noo i havent

1/2 x b x h

so 1/2 x 4 x 7?

[vocal pagoda]

this is the formula for area...

but as far as I know, in the big right triangle, you only have a side = 7.

find the other 2.

[strong grove]

dont u just need 1 more? the diagonal of square and then 1/2 * b * h

[vocal pagoda]

true; I thought maybe the hypotenuse might help with finding the sides of the black rectangle... but I guess it wont

[strong grove]

why u want to find sides of black rectangle D:

[bronze osprey]

yes the area is 1/2 * 4 sqrt(2) * 7

4 sqrt(2) is the hypotenuse of the square from Pythagoras

[vocal pagoda]

oh wtf I didn't realize what we're supposed to calculate 😄. Since it's marked differently than the 90 deg angle, I thought we're trying to find the area of black rectangle.