help-13

[wraith dagger]

Goëtia

[proper prism]

i might be wrong but idk let me know

[crimson sedge]

Hello If any help needed msg!

[proper prism]

help here though?

[crimson sedge]

Okay np

[viscid dust]

Wdym at equilibrum ? At t=0 ?

[viscid dust]

What is c ?

[proper prism]

have a look at lyapunov equation

[proper prism]

the sum of sigma_ii & sigma_jj

[viscid dust]

and why it's constant ?

[proper prism]

one must exist

[viscid dust]

I don't have that in my course, I think there's just an error in the statement, I think I'll see that with my teacher at the start of the school year, thank you for your help (how do we close the channel?)

[proper prism]

.close

[viscid dust]

.close

[cedar kiln]

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[upper laurel]

shouldnt this be squared with a negative constant added to it?

oh nvm presumably i isnt the same as j

[upper laurel]

.reopen

[cedar kiln]

✅

[upper laurel]

.close reset timer

[cedar kiln]

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[tired mural]

i want to ask why am I this bad at math? i had an exam yesterday like I mentioned and i froze and started shaking in the middle of the exam, i couldn't answer anything

[tired mural]

I can answer small questions where i plug in values and just done

But i cannot solve anything that requires brainstorming

or whatever

Am I dumb?? i feel so stupid

[edgy spade]

hi

[edgy spade]

you probably need more practice in solving questions

[tropic oxide]

are the exam questions published?

[edgy spade]

this skill requires tons of practice to understand concepts

[tropic oxide]

it might be worthwhile to print out a copy of the exam and try to do it at home, no time limit

to see which questions you can solve without exam stress in the picture

[edgy spade]

yes exam environment is very different from when you are solving at home or at a library

[tired mural]

Yes

after exams I can find them

[tired mural]

i cannot understand maths

and i cannot remember anything

[tired mural]

okay friend I'll try one day

i just cannot understand maths and how each steps happens after one another

neither know how to derive things

[tired mural]

each math is different I'm going crazy

[vocal wyvern]

I just wanted to reach out and say that you are absolutely NOT dumb or stupid. What you’re describing (freezing up during a math exam, feeling physically shaken, and being unable to think clearly) sounds a lot like test anxiety, which is far more common than people realize. It’s not a reflection of your intelligence or potential, but rather how your body and mind are responding to a high-pressure situation.

There are so many different factors that can affect someone’s experience with math (or any subject, for that matter), such as how it’s taught, how your brain processes information, past experiences with failure or stress, or even just what kind of day you’re having. Everyone learns and thinks differently, and struggling with certain types of problems (especially ones that require brainstorming under stress) doesn’t mean you lack ability. It just means you might need different strategies, more support, or maybe just more time and practice in a lower-pressure setting (e.g., homework, study guides).

You mentioned being able to do plug-in type questions. That’s still math! It shows you can follow the procedure and understand the concepts. The fact that you want to understand the material and feel frustrated by your performance also says a lot about your motivation and self-awareness. That also matters.

That said, it might be really helpful to talk to someone with professional training, like a counselor, psychologist, or academic coach, who can help you explore what’s going on with the anxiety and problem-solving blocks. I am by no means a medical or mental health professional, and this isn’t a diagnosis or clinical advice, but seeking help is a strong and smart move, not a weakness.

You’re not alone in this, and things can get better with the right tools and support. You deserve that support. You’ve got more strength and potential than you probably realize! 🫶

[royal finch]

There are really not that many techniques you need to be successful at a large amount of mathematics. It is really a matter of identifying the most useful techniques and understanding their limitations. It is helpful to look at old exams and look for which tricks are being used to solve those problems rather than memorizing the whole problem from start to finish.

[dusty wren]

Having adhd might worsen you being able to remember these formulae and performing well under pressure, but you might still be able to do it if you work hard enough

[royal finch]

For example, a huge number of problems involve using a 1 or 2 tricks and now the problem is linear or quadratic and there are only so many zany tricks they can throw at you before the problems are not that solvable.

If you know exactly how to deal with linear or quadratic equations, you really just need to recognize that the crux of a problem may be a change of variables that turned something scary into a quadratic, or it involved multiplying by 1.

[rapid mauve]

also, i hope your teachers aren't the kind to just tell you stuff like
"this is formula, remember it, kthxbye"

[cedar kiln]

@tired mural Has your question been resolved?

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[strong jacinth]

can someone pls explain them both

[atomic forum]

I will answer first question

You remember what the definition of an even function right?

[strong jacinth]

yeah

i thougth it was 0 becausae

f2 = 2

f-2=2

[tropic oxide]

don't drop the brackets

[atomic forum]

So f is odd and g(-2)=g(2)=-2

[tropic oxide]

you need to write f(2) and not f2

[strong jacinth]

yuh

[atomic forum]

And since f is off itself it admits negative value such that f(-2)=-f(2)

[tropic oxide]

off itself

[strong jacinth]

huh

isnt f(-2)=2

[atomic forum]

It is -2

[slender ginkgo]

F(-2) = -f(2)=-2

[atomic forum]

f(-x)=-f(x)

[strong jacinth]

isnt that for odd functions

oh omg

i read it wrong

yeah

[atomic forum]

You still don’t understand what odd even function is.. so revise on that and second

To find this derivative do you know the formula of changing it to natural log?

If no then search up and try

If yes then try again

[strong jacinth]

i do i read the question wrong

[atomic forum]

If try again failed then search up how to change the log into natural log

You need to practice this, if it’s more a different question I might hint you the answer but basic arithmetic is helpful for your overall school experience

[strong jacinth]

ok ty

.close

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[pure thorn]

Hi! Does anybody have a link to Markov's proof of the fact that the nth lagrange number can be written in terms of the nth markov number

[pure thorn]

I've been searching for half an hour but I can't find the actual proof

[crimson delta]

equal to itself?

[pure thorn]

wait mb

markov number**

[crimson delta]

hmm wikipedia says it might be in the book of cassels

[atomic forum]

https://arxiv.org/pdf/1612.05782

[crimson delta]

and I would expect that you can probably find that book somewhere on the net

[cedar kiln]

@pure thorn Has your question been resolved?

[pure thorn]

oh wait it's free to download online, just realized

ty!!

.close

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[desert atlas]

Number six

[desert atlas]

Pls ping

[slender ginkgo]

,rccw

[sullen cipher]

What did u try

[blazing zephyr]

you can see at some point all powers below a certain number will always have nonzero coefficients

like, say the number is 5 or smth, thenthere will be a term with ^5, ^4, ^3,...,^-9,^-10

[desert atlas]

Why is this info important?

Oh wait

[desert atlas]

Why all the way to -10?

[blazing zephyr]

well if you can get that certain number you can know all the terms below it, and you can manually count the things larger than the number

[blazing zephyr]

cause thats the minimum

[blazing zephyr]

*the number should be close to the maximum, aka ^30

[desert atlas]

Why not -5

[blazing zephyr]

why would the minimum be ^-5

[desert atlas]

(x^(-1))^5

For your example that expression raised to 5

<@&286206848099549185>

Also maximum would be ^15

[desert atlas]

^

[blazing zephyr]

what

[blazing zephyr]

yeah but its ^10??

[desert atlas]

I was talking about this example

[blazing zephyr]

say the number is 5, not the exponent

[desert atlas]

?

Sorry my English not good

The constant inside the expression?

[cedar kiln]

@desert atlas Has your question been resolved?

[blazing zephyr]

this "number"

[cedar kiln]

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[dusk goblet]

thank you

[cedar kiln]

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[tribal siren]

Can someone solve this question and explain it to me

[tribal siren]

It is from arithmetic progression

[dusty wren]

What part of the provided solution confuses you

[tribal siren]

We know that the ap ends with odd number

But when we apply the formula to get the sum of all odd number . We need to first subtract all the even terms

Can you explain how to subtract even terms and get a particular term to put in formula to get sum

[edgy spire]

If you consider all the even terms, they too will be in an AP with common difference 2d and first term as a+d. Same goes for the odd terms except their first term is just a.

[dusty wren]

There is one thing though

[tribal siren]

What

[dusty wren]

It's not given whether the first term is odd or even

[lavish vine]

Hmmm

[dusty wren]

But that doesn't really matter, since the equations will just switch around

[lavish vine]

That doesn't matter though

[edgy spire]

Don't they mean odd terms as in a_1, a_3, a_5?

[tribal siren]

Yeah

Got it

[dusty wren]

Ah

oops

[tribal siren]

Thanks buddies

I got it

[lavish vine]

Since that would mean the d and a have to be of opposite parity

[tribal siren]

.close

[cedar kiln]

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[dusty wren]

welcome to the server btw @tribal siren and @edgy spire

[tribal siren]

Thanks for your help

[cedar kiln]

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[cobalt grotto]

I'm trying to find the maximum height (at x=3) for this probability distribution

[tropic oxide]

is the curve shaped like a triangle?

[cobalt grotto]

The curve of the actual dataset?

[tropic oxide]

the curve in the picture

[cobalt grotto]

Oh

Yes

[tropic oxide]

ok

ok then remember that its area has to be 1

[cobalt grotto]

Yeah I know that

[tropic oxide]

treat it as an actual geometric triangle

you know its base is 5 and its area is 1

so what's the height gotta be

you know the area formula for a triangle, right? the most basic one

[cobalt grotto]

If its base was in the middle I'd know I just had to divide the area in half and solve for the height

[tropic oxide]

overthinking!

[cobalt grotto]

yes

[tropic oxide]

A = bh/2

[cobalt grotto]

hw/2

[tropic oxide]

just apply this

you know A and w and you want h

[cedar kiln]

@cobalt grotto Has your question been resolved?

[cobalt grotto]

I HATE doing anything at work it's so infuriating

But I have no real choice because I work constantly

.close

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[cedar kiln]

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[white rover]

for 4c I am trying to prove for n+1 by divding the n+1 polygon into two simpler polygons. But the question I have is if I divide it with a diagnol wouldn't I be adding an edge?

[tropic oxide]

you would in fact be adding an edge

two edges, really -- one for each side of the cut

so the two polygons into which your (n+1)-sided polygon is split will have a combined total of n+3 edges between them

[white rover]

I am not seeing how it wouldl be 2 edges?

say I have a trapezoid

oh

are you saying its the same edge but if you broke the shape up that same edge would now be on two shapes

show the thing is I know that both shapes have less than n+1 edges but is having n+3 edges allowed?

[tropic oxide]

they'd have a total of n+3 edges.

one would have k edges and the other would have n+3-k edges

with k and n+3-k both ≥ 3 of course

and thus each is at most n

[white rover]

Im looking at something like this if we look at the two shapes separately and we have n= 3 and n= 4

[tropic oxide]

i do not understand this picture

is the black line meant to be your cut?

[white rover]

yes

[tropic oxide]

then it is not a diagonal

it does not connect a vertex to a vertex

it connects a vertex to something else that isn't

[white rover]

so if our n+1 = 5. now both shapes have n = 3

[tropic oxide]

our n+1 is 4 here, not 5.

the red shape has 4 sides.

you made it a bit confusing for yourself by referring to the big shape's side count as n+1

[white rover]

sorry was thinking vertices

[tropic oxide]

sides and vertices are equal in number

there's n+1 of each

only, in your notation, n+1 is 4

n is not 4

[white rover]

How do we get the n+3-k part?

[tropic oxide]

ok look

you said your red polygon has n+1 edges

by making the cut along the black line you've added 2 edges to the total

do you agree or disagree

i dont want to come back to this for the 40th time

[white rover]

Agree

[tropic oxide]

ok

so the total number of edges among the two smaller polygons is n+1+2, or n+3

do you agree or disagree

[white rover]

Agree

[tropic oxide]

ok

i used k for the edge count of the first of your two pieces

since the total number of edges is n+3

the number of edges that remains for the other piece is n+3 - k

does this make sense to you yes or no

[white rover]

Yes

[tropic oxide]

have i answered your question of "how do we get the n+3-k part?"

[white rover]

Yes

Inductive step makes sense thanks

[dire geode]

<@&268886789983436800> spam

[white rover]

.close

[cedar kiln]

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[versed coral]

hi id like to how i messed up, thought i was doing well until i saw my answer wasnt getting close to the form

[versed coral]

markscheme is a bit vague too so im not sure whats happening here

oh

let me post the wuestion sorry

[dusty wren]

Your A and B are in the wrong order

Should be flipped

[versed coral]

does it matter?

bc B was + and A was - so i switched

[dusty wren]

It does matter

[versed coral]

i see

[dusty wren]

Put the A and B into the equality and find out

[split ice]

i thought the same thing but they did sub correctly, check where the (u+1) goes

[versed coral]

perhaps its not clesr in the image

1/2(u-1) is first

-1/2(u+1) is second

[dusty wren]

Oof my fault

[versed coral]

yh no worries

[dusty wren]

I thought the - was a + lol

[versed coral]

haha yeha my handwiritngs terrible

that aside, what else did i mess up on?

[dusty wren]

Nothing, your working is correct

They just did it a different way

[split ice]

yeah, you're on the right track, just need to do some more log property stuff to get the desired answer

[versed coral]

ohhi js did it

[dusty wren]

You can take the 2u-2 inside the mod as 2(u-1)

[versed coral]

holdon ill show

[dusty wren]

Same with the 2u+2

[versed coral]

something like this?

its supposed to be modulus

i think i did it wrong still

[dusty wren]

No

When you take 2 common

You take it from both the numerator and the denominator

So they chancel

Cancel*

[versed coral]

omg

theres no way

i acc made this mistake at my bug age

😂😂😂😂

[dusty wren]

🫂 us

[split ice]

we've all been there

i finished a complex contour integration by cancelling a term instead of a factor... it keeps me up at night

[versed coral]

im not getting the A in sight

😦

is the A 1 or have i done something else

[dusty wren]

Substitute u back in

[versed coral]

i did

[dusty wren]

O

[split ice]

remember, C is an arbitrary constant, so you can redefine it a bit

[versed coral]

lnk?

and then it multiplies?

within the Ln yeah?

i see

lnA

ahhh i see

yep got it now

[dusty wren]

Yh

[versed coral]

thank you for that

sometimes u forget the +cheese and it all goes wrong

[split ice]

so true

[versed coral]

thanks guys

ull see me here often

pls help next time if u can too haha 🥲🥲

[split ice]

im not so sure, you hit every single mark on your scheme

so i think you'll get it soon, if not already :)

[versed coral]

🙏🙏🙏

.close

[cedar kiln]

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[queen juniper]

how come ur doing usub alr

u learning ahead or what?

[versed coral]

wdym

[queen juniper]

you're sitting alevel maths right

[versed coral]

oh bc im

yeah

im y12

[queen juniper]

yes

[versed coral]

im leaenign ahead

[queen juniper]

yes

ic

[versed coral]

i js finished y13 content 4 days ago

👍👍

[queen juniper]

nice bro

[versed coral]

gonna self learn fm soon

[dusty wren]

[queen juniper]

just make sure ur good on ur 3rd/4th subject too

entrance exams asw

[versed coral]

chem im good with

Biology...

[queen juniper]

no point of being good at maths and then not doing well on restr

[versed coral]

😰😰😰

[queen juniper]

yeah haha

[dusty wren]

Welcome to the server Hello!

[queen juniper]

ur skl doesnt offer fm?

[versed coral]

nah im fine for all

it does

i didnt take it bc

[queen juniper]

hi

[versed coral]

originally i was going for medicine

but now ive decided not to

and its kinda too late to switch alevels

[queen juniper]

yeah

but then why self learn fm?

[versed coral]

but ive recently js discovered a passion for maths

and i wanna do enginerring now

[queen juniper]

ahhh

i see

[versed coral]

so i dont find it a chore either

its quite fun

[queen juniper]

i would recommend doing the mat then

or if engineering

only chemical i think would be possible

[versed coral]

yeah i wanna do chemical anyways

[queen juniper]

or possible architecture

[versed coral]

i think im goikg w chemEng rn

[queen juniper]

sure

[versed coral]

i feel more sure ab it

[queen juniper]

where u triyng to apply to

[versed coral]

than medicine or anyt else

[versed coral]

UoB is my top choice

[queen juniper]

is that bristol or brum

[versed coral]

brum

[queen juniper]

ahh nice bro

[versed coral]

wbu

[queen juniper]

london ones

like

uh

[versed coral]

ucl kcl

[queen juniper]

kcl imp ucl so on

qmul

[versed coral]

niceee

fancy shmancy

[queen juniper]

yh not tryna leave london icl haha

[versed coral]

if u can get into any of thise ur set

if i cud, i wudda went for one of them too

[queen juniper]

yeah hopefully

[versed coral]

engineering ?

[queen juniper]

yes

eee

[versed coral]

nice

maybe one day well end up at the same place

😂😂

[queen juniper]

yh haha

[cedar kiln]

Available help channel!

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[quaint valve]

just solved the integral with di method does anyone know what to do about the infinity part

[twilit escarp]

Its the same way to do when its real numbers but you have to write it as a limit

[quaint valve]

?

honestly idk how to solve this limit

[twilit escarp]

Yes

[dire geode]

$e^{-x} = \frac{1}{e^x}$

[wraith dagger]

riemann

[dire geode]

in general

,tex .exp rules

[twilit escarp]

use growth comparison

[wraith dagger]

riemann

[quaint valve]

idk what this is honestly

i might just ask chat gbt to explain

[twilit escarp]

Exp is winning the limit race

[twilit escarp]

So if you have x/e^x where x goes to infinity, you have that e^x is bigger than x

[dire geode]

the bottom row is all you need once you identify the general type of function

[quaint valve]

alright

also chat gbt is talking abt some l'hopital rule which i havent been taught yet

[dire geode]

yea don't use gpt then

[twilit escarp]

I was sure it would recommand l'hôpital lmao

L'hôpital is bazooka here also

[quaint valve]

do u guys learn that in ap

[twilit escarp]

I learn that in math

[quaint valve]

in the uk we really dont look at limits for some reason outside of differentiation by first principles

[quaint valve]

cool

[quaint valve]

i mean in high school

[twilit escarp]

Oh then yes

I just don't know what ap is

[quaint valve]

in the US advanced placement classes

[twilit escarp]

Anyway you don't need gpt, and you don't need l'hôpital just pure observation about the speed of divergence/convergence

[twilit escarp]

So you are doing improper integrals before limits ? Or its self taught ?

[cedar kiln]

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[quaint valve]

not self taught idk why the uk education system works like this

[quaint valve]

im just doing a course online for differential equations

and it requires knowledge of limits

[atomic forum]

So you want help with differential equation?

You can either do integrating factor or use Euler formula

[quaint valve]

no not at the moment

i just need to learn how to use limits to answer these questions

[atomic forum]

What do you think the second

[quaint valve]

i havent answered the first yet

[atomic forum]

I mean we don’t have to think of lhopital

[quaint valve]

i got here then got stuck

e.g idk what this is

[atomic forum]

For first question

[quaint valve]

yeah

[atomic forum]

So first we see this convergence you agree

Becasue e^{-x} converges

And we adapt the integration by parts

How to do it?

[quaint valve]

uhm

i might just look at the graph to understand it

[atomic forum]

So you don’t know how to do the integral?

I will show you

Basically we take u and v

[quaint valve]

no the intergral is fine

[atomic forum]

So which part isn’t?

[quaint valve]

my working out is here

the limit

[quaint valve]

i dont know why this is equal to 1

[atomic forum]

…

That’s not a mathematical expression as far as I know

[atomic forum]

This

Limit is NOT a number

[quaint valve]

i know i cant just put infinity in

but that was just me trying to imagine it

i guess

[atomic forum]

I quite wanted to do a more abstract way but here I I’ll do lohoputal

[stiff brook]

I think you should learn limits (including l'hospital) first.

[atomic forum]

Basically after differentiating x and e^{-x}

[stiff brook]

go in order

[quaint valve]

wdym

[atomic forum]

E^{-x} dominates x

[atomic forum]

Strictly speaking you don’t need lhopital

[stiff brook]

self learn what limits are if the course doesn't teach you. it is perhaps the most crucial part of calculus

[stiff brook]

yes, you can use taylor expansions

[atomic forum]

Actually no

I mean I can simply argue e^x dominates x

[quaint valve]

i honestly dont know what that means

[quaint valve]

could i have a study source

[stiff brook]

this is not sufficiently rigorous but anyways, self learn limits. i can send u sources

[quaint valve]

yeah that would be good

[stiff brook]

start here:
https://youtu.be/YNstP0ESndU?si=BzB5U0sdgYF2Bh--

[atomic forum]

Still why would you do those very hard questions

[quaint valve]

wdym

[atomic forum]

Khan is actually better only for calculus

I was studying there as high schooler

[stiff brook]

khan academy works as well

[atomic forum]

Only for calculus though

[quaint valve]

its for a taster for differential equations which im currently learning for my personal statement (college essay in the uk) for chemical engineering

[atomic forum]

Can we stop thinking about differential equations first?

You need relax your mind

[quaint valve]

ive already started learning them at school

[atomic forum]

And actually it’s quite far from your current progress to odes

Nice

[quaint valve]

but not limits

😭

[atomic forum]

Okay

[quaint valve]

actually if i can ask one more thing

[atomic forum]

Basically calculus is the study of limit

Differentiation is process of taking limit

You at least need basic for differential equations

[quaint valve]

ik how to differentiate

its the only time where we use limits in uk high school

even then we arent really taught them

[atomic forum]

Yes tell me how differentiate f(x)

[quaint valve]

its just differentiation from first princible

[atomic forum]

F(x) is arbitrary

Yes

You can’t just write down the expression also

You need to show it’s actually that

[quaint valve]

do u want me to write the formula?

[atomic forum]

Condition f is differentiable… I just want you to study step by step

So you can actually reach your goal realistically

[remote nacelle]

tbh odes are not too far from calculus, basic odes are often covered in a first computational course on calculus.

[atomic forum]

Yes

That’s true but you need basic knowledge of calculus

[stiff brook]

high school does a thing where they dont emphasize the importance of limits

[quaint valve]

i can see that atm

[atomic forum]

Calculus is the study of limit

[quaint valve]

the course says im missing two topics

[stiff brook]

which ones?

[quaint valve]

that i havent learnt in school

[atomic forum]

What’s the difference between analysis and algebra? Analsysis is developed by the study of limits developed by newton

[quaint valve]

eigenvalues and the complex exponential function

[atomic forum]

Any study involving limit is a branch of analysis aka calculus

[quaint valve]

everything else mentioned we have covered

[atomic forum]

Then study

[stiff brook]

okay so this is actually a full course on ODEs

[quaint valve]

yeah

[stiff brook]

you need to finish computational linear algebra and single variable calculus

[quaint valve]

can anyone suggest a source

[atomic forum]

To be honest, without limit you literally tell me that you want to study calculus but not wanting to study calculus

[quaint valve]

you dont understand that i want to learn limits

[atomic forum]

Any reasonable source includes limits unfortunately

[quaint valve]

im not trying to avoid them

[atomic forum]

I don’t know actually

[stiff brook]

MIT opencourseware, gilbert strang (linear algebra), and stewart calculus (or paul's online math notes) all work

look into them

[quaint valve]

i never said that

i asked for sources earlier to learn them

[atomic forum]

Yes then khan academy

It’s not even hard limit compared to ode

You don’t even know how hard it can get

[quaint valve]

?

from MIT opencourseware

[remote nacelle]

ok that sounds more advanced, i agree with dj linear algebra again at a computational level could be useful. It gives a lot of insight into what’s going on later on imo.

[quaint valve]

im in a weird situation where the course im doing at my school has a weird range of advanced topics but struggles to teach properly more simple ones

and it leaves me unsure of what i can and cannot learn

[remote nacelle]

this could work also for calculus it depends how you want to learn books, online courses, etc.

[split ice]

that is on them and not you, but yeah unfortunately ODEs require a good grasp of linear algebra and calculus, which is quite a bit of work

if this is a requirement, are there any other options?

[quaint valve]

im just not sure what linear algebra im missing

[quaint valve]

or what calculus im missing because at the moment it seems like mainly these topics

we sort of just stopped after techniques of integration

but i have much more learnt outside of these topics

[split ice]

you'd need eigenvalues => determinants & transformations => matrices => vectors, which any introductory linear algebra course will cover

(uni-level introductory, anyways)

[quaint valve]

ive done all of those except eigenvalues

which was one of the two topics i said i needed to learn

il find a relevant resource to learn them from

[quaint valve]

im just going into my last year of high school to be fair

[quaint valve]

is there a link between eigenvalues and lines of invarient points and invarient lines

[split ice]

i will recommend one of Linear Algebra Done Right or Linear Algebra Done Wrong. You can supplement these books with 3blue1brown's linear algebra series, it has some pretty pictures

[quaint valve]

thank you

[split ice]

eigenvectors are "sort-of-invariant" vectors under a transformation, so that's a good intuitive explanation :) you will need more though

as for your calculus, this is a bit of a weird order, but chapter 5 seems to have what you need

[quaint valve]

the other topic was the complex exponential function

[quaint valve]

yeah and my calculus so 3 topics

eigenvalues in linear algebra touch up on chapter 5 for my calculus and then the complex exponential function which im confused about

my friend doing the same course said something abt the last one being a transformation in complex space but idk

[split ice]

im gonna guess they would want you to understand euler's formula, at the least, and the idea that a complex exponential describes a rotation in C. i'd lowkey read the wikipedia page on Euler's Formula, im not sure what to recommend for the rotation part

[quaint valve]

k

[split ice]

it just crops up everywhere to the point that idk how i learned it ;-;

[remote nacelle]

https://www.youtube.com/watch?v=OAahmA7lr8Q i like 1-4 from this guy

[quaint valve]

we have covered argand diagrams thankfully and complex numbers

[quaint valve]

1-2 looks normal

3 looks weird il watch the video

yeah 3 is what i need to learn from

then 4 i guess

cheers

[split ice]

best of luck 🫡

[quaint valve]

actually i take that back 2 isnt fine

il get to it though

[split ice]

2 should give you good intuition for 4, though

[quaint valve]

kk

im so glad i got this plotted out honestly

thanks pola and haseeb

[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
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[modern fable]

has anyone ever been so bad at math to where you cant understand algebra like me? and if so how did you get over that mental obstacle anything helps. ive been trying for so long

[silk gust]

do you need help with a certain question?

[modern fable]

no im just really lost right now. i cant even pass my algebra one class im very dissapointed in myself

im a senior

[crimson sedge]

meh, when word problems were hard i read lots of books

[silk gust]

i see

[austere hull]

I used sources like khan academy but yeah show a problem that u struggle with

[modern fable]

yea sorry its not alot of information

[crimson sedge]

what are u losing questions on

[modern fable]

thanks

[crimson sedge]

like topic

[silk gust]

the only advice i can give is do lots of problems

[modern fable]

well the most i know is that when soemthing is in a parentheses you add it first

and then i forgot eeverything else

and ive really tried to learn

[silk gust]

what are you learnign in class right now

[modern fable]

im not lazy

[austere hull]

try reviewing them

[modern fable]

well i remember trying to learn some stuff but its summer and i already forgot them

let me try to remember

[modern fable]

its not a certain problem i just dont remember anything after studying it and then i study again and im like in a loop

[waxen mica]

Hi

[austere hull]

that happened to me a lot actually

[modern fable]

how did you get over it

[austere hull]

im literally reviewing some stuff when i help ppl on this server

thats how

[modern fable]

the only jobs im interested in are space jobs and i really need to know math for them

olay maybe i can try that or soemthing

[austere hull]

and yea i google thing if i forgor something

things*

[silk gust]

just do a lot of practice problems, that way youre kinda forcing yourself to be comfortable with the topic

[modern fable]

i cant even remember what i was studying in class i didnt understand it at all

[modern fable]

yea that makes sense

[austere hull]

do u have ur notes?

[modern fable]

ill try thanks

[modern fable]

yes

[austere hull]

read them

[modern fable]

okay

[silk gust]

do you have problem sets from your teacher? those help a lot

[coral pond]

Oh uh

[modern fable]

but most of the notes i took were in these pieces of paper that were loose they might be lost

no its all online

indont really have a teacher

[austere hull]

ah

[modern fable]

its just a classroom with soemone surpervising you

[austere hull]

maybe the thing u dont understand try reading it though online

[coral pond]

You're just asking for like, tips on how to remember stuff more concretely?

[austere hull]

such as integrals when i cant read it

just an example

[crimson sedge]

.

[modern fable]

yea but i can remember stuff i just like cant seem to do it with math

[coral pond]

I like to uhm

As a general guideline

[modern fable]

like you search it up if you cant read it?

[austere hull]

I search up for similar examples and yea sometimes reading

e.g proofs

[coral pond]

Learn something, however you learn it best (whether that's visually, reading, taking notes, try yo summarize it in your own words. And then the vital last component: teach it

[modern fable]

ohhh okay ill tey that

[coral pond]

Let's take order of operations (PEMDAS) for example

[modern fable]

teach it to who

but ill try

[silk gust]

anyone

[modern fable]

lol thats what i know about algebra and thats it

[modern fable]

okay ill try

[silk gust]

you can even pretend to walk yourself through it

thats what i do

[modern fable]

ohhhh okay okay

so what do you guys recommend i start with because all i know is pemdas

[austere hull]

feel free to use #study-discussion for general advice on studying or anything related to math strategies study methods im sure a lot ppl could help u with this too

help channels are meant for math problems

[coral pond]

Imagine this: Your teacher is explaining PEMDAS. You take notes on what each letter means. You take a 5 minute break to distract yourself and try to recall everything from memory. Congrats, you're able to remember the acronym, however a few days later...you struggle.

[modern fable]

thanks alot man that means alot

[coral pond]

So what do you do? You teach PEMDAS to yourself.

[modern fable]

yea and then what

[modern fable]

ohhhhhh

and then i can remember it

[coral pond]

You get a pen and paper, or whatever

[modern fable]

interesting

yea

[coral pond]

And you think about HOW you would explain it to someone else

That way, you're thinking about it in a way that makes sense to you

I found that I remember things much better like that

[modern fable]

okay ill give it a shot thanks sm bro

[coral pond]

ha okay

[modern fable]

so what do i do after learning pemdas im lost lol

[coral pond]

good luck man you got it

[modern fable]

thanks alot man im trying and you too on whatever your doing

[coral pond]

Think about how you would explain it to someone else

[silk gust]

do you have a list of topics from the whole year?

[coral pond]

Thats my biggest tip

[silk gust]

or even part of the year

[modern fable]

no my school only wants you to get your diploma and leave they dont really help you out on stuff like that

i gotta do it independently pver the summer

no😢

[silk gust]

ok uh

do any of these sound familiar:
Arithmetic/geometric sequences
Arithmetic/geometric series
Trigonometry (sin, cos, tan)
Polynomials (quadratic formula)
Systems of equations

theres a lot more im forgetting but that should be a start

[modern fable]

pnly arithmetic because i think thats about adding and subtracting and everything simple like that

[gentle echo]

focus on the basics, how are you going to build a bridge if you don't even know how to hammer a nail :3

[modern fable]

yea that makes sense

[gentle echo]

just see what level you are

and build up on it

[modern fable]

should i take an assesment

to see

[gentle echo]

i'm not entieely sure what resources but khan academy is okay for begineer stuff

[modern fable]

okay ill use that

[gentle echo]

good luck

[modern fable]

thanks!

[silk gust]

good luck! you got this

[modern fable]

thansk you too frances !

[silk gust]

(dont forget to type .close)

[cedar kiln]

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[cedar kiln]

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[dim magnet]

how to graph r = 2sectheta

[dim magnet]

on polar graph

[slender ginkgo]

Plug in angle as u move around

[dim magnet]

so if i plug in pi/6

[slender ginkgo]

Or convert it back to Cartesian

[slender ginkgo]

(This is easier)

[dim magnet]

r = 2sec(pi/6) whichi is sqrt(3) so its 2/sqrt(3) = r?

[slender ginkgo]

4/sqrt(3)?

Nevertheless

I suggest ur convert it back to cartesian

[dim magnet]

nah i cant do that

i have to keep it in polar

but arent i supposed to do something like change it to cos

so it becomes r = 2/cos(theta)

[scarlet plinth]

me when i do 4+4

oh srry

not that chat

[dim magnet]

then i have to do one of the normal points like pi/6, pi/3, pi/4

multiplied by 2

and then that will be my theta for the points

[slender ginkgo]

Good

So rcos(theta) = 2

[dim magnet]

so x = 32

2

wait how does that help

[slender ginkgo]

So it forms a vertical line

[dim magnet]

yea but im graphing in polar

so would that point just be at (2, pi/2)

or nah

i got it

[slender ginkgo]

(Pi/2, 2sqrt(2))?

[dim magnet]

yea i got a line

at r = 2

vertical

thanks

.close

[cedar kiln]

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[teal tangle]

Hi

[teal tangle]

uh

Currently trying to do this

[teal tangle]

That’s how hard I’m failing

I don’t even know where to start

[dire geode]

Did you expand the square of the sum

[cedar kiln]

@teal tangle Has your question been resolved?

[hallow pelican]

hi riemann your integral sucks

[hallow pelican]

yeah do this

[split ice]

you must be lebesgue

[cedar kiln]

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[dire geode]

Blocked

[dire geode]

.close

[cedar kiln]

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[void sand]

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[whole violet]

If 5x+1=5y-2

If we solve for y by Algebra, we get y=3/5+x .

Why is that y=3/5+x specifically into 5y-2 will give 5x+1?

Because in my mind, it's just something algebraic that he did in order to reach to y=3/5+x. Why is it that it holds the sole key to make 5y-2 equal to 5x+1 ?

Thanks guys ^_^

[whole violet]

Its not 2nd nature logic that pops in my mind like 2+2=4 😂😅😔

If someone can explain it step by step. I would be thankful. Maybe there is a simple idea that I'm missing and would make it clear :))

[idle tusk]

Why is that y=3/5+x specifically into 5y-2 will give 5x+1?
the unsatisfying answer is because 5(3/5 + x) - 2 = 3 + 5x - 2 = 5x+1

[twilit escarp]

You probably using an equivalence reasonning to solve the algebra, thats why when you put back (the same as just going back from the end to the start) you get the same result

[idle tusk]

but tbh unless you are very algebraically skilled, you would not arrive at that answer in your head right away

at least i won't

i'd have to either use paper or do the algebra i'd do on paper in my head

[cedar kiln]

@whole violet Has your question been resolved?

[tranquil oracle]

Well maybe study each step when you solve for y

At each step, you are performing some operation that maintains the set of (x, y) pairs which make the equation true

5x - 1 = 5y + 2
"Subtract 2 from both sides"
5x - 3 = 5y

Okay so say (x, y) made the upper equation true, equal to some value k, then the left side of the modified equation is k-2, so is the right side, so the lower equation is true.

The other steps and reasoning are left as exercises

[whole violet]

I asked a friend and he said that the reason why it y=... holds in the original equation is that the both express the same relation.

Like if we had:

1. y +2 =5

2. y=3

3. and 2) are basically expressing the same relation and thay why 2) and can be inputted into 1) correctly.

[tranquil oracle]

This can be generalised further:

Let h be a function with an inverse. For variables x1, ... xn:
f(x1, ... xn) = g(x1, ... xn)
if and only if
h(f(x1, ... xn)) = h(g(x1, ... xn))

and it is also how you can spot transformations which remove information: if h is not invertible (for instance, squaring both sides), you may introduce more solutions

[whole violet]

I asked another friend and he said that:

When equating two equations that have different variables, you come up with a condition, you solve for one of them to find this condition, which is y=3/5 + x in this case
This implies that : in order for these equations to be equal, then y has to be 3/5 more than x
This is a condition that we derive to make a conclusion

[tranquil oracle]

Yeah both of them are pretty much stating an aspect of the general philosophy on why we have algebraic manipulations in the first place

[whole violet]

This example of:

y +2 =5
y= 3

is clear and obvious.

But 5y-2=5x+1
to y=x+3/5 is the same analogous speaking but not as intuitive as the one above. But I guess one must "extend" the idea.

The 2nd one is obvious in that they are the same relation because it is reversible and one came from the original. But it's not so obvious that y= x +3/5 into 5y-2 gives 5x+1. Not as obvious as y=3 into y+2=5

=p

But it's the same of ofcourse I guess

In school, I was just taught algebraic manipulations but not what they signify and I guess that's why it's confusing :))

[cedar kiln]

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[gritty galleon]

boo

[slender ginkgo]

scared

[gritty galleon]

if $(1+x+x^2)^n = a_0 + a_1x + \dots + a_{2n}x^{2n}$, find $a_0 + a_2 + \dots + a_{2n}$

[wraith dagger]

rak³en

[gritty galleon]

standard way would be to plug in x=1, and x=-1 and then add those expressions

is there a way to solve this by multiplying the expansion of (1-x)^n and comparing it to expansion of (1-x^3)^n

[muted bear]

i wonder if theres a convenient way to pick out the odd numbered powers

lets start with this: how can you find a0+a1+a2+...

[crimson delta]

well he already said, x=1 and x=-1. aka roots of unity filter

I doubt that you get nice things from comparing (1-x^3)^n = (1+x+^2)^n(1-x)^n

[muted bear]

oh

[crimson delta]

except for funny identities for binomial coefficients

[muted bear]

i can read

[opal hinge]

When i do this type of question I just do $$\sum_{k=0}^{n}{^nC_k \cdot a^k \cdot b^{n-k}} = (a+b)^n$$ two times

[wraith dagger]

Alexis_Fx

[gritty galleon]

sadge

.close

[cedar kiln]

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[cunning plover]

For this question, why is the answer for y=tan(4x) the last one? Im confused between the correct answer and the one to the very left of it. Don't you divide 2pi by 4x to get the period?

[slender ginkgo]

period of tanx is pi

generally

also the thing on the very very left is -tan(4x)

[cunning plover]

how is the 4th one different from the third?

[rapid mauve]

third vs fourth

[cunning plover]

so you dont divide 2pi/4?

[civic pumice]

it repeats every pi/4 instea of every pi/2

[civic pumice]

you divide pi by 4

not 2pi

[coral estuary]

yo

[civic pumice]

because tan is pi periodical, not 2pi periodical

[coral estuary]

can someone pls help im about to die

[rapid mauve]

!occupied

[civic pumice]

unlike cos and sin

[cedar kiln]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[coral estuary]

wha

[civic pumice]

create your own help channel

[rapid mauve]

someone else is using this help channel

[dire geode]

Read #help-13 message

[rapid mauve]

please open another one

[coral estuary]

o mb

[cunning plover]

Ohhhh, so is it only cos and sin that you divide by 2pi?

[civic pumice]

if it were cos or sin, you would divide 2pi by whatever yes

[slender ginkgo]

Period of cos and sin is 2pi yes

[civic pumice]

since here its tan, its pi

[rapid mauve]

if you mean the period, yes

[cunning plover]

ok, thank you so much

.close

[cedar kiln]

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[cedar kiln]

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[gentle lintel]

.close

[cedar kiln]

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[gentle lintel]

.reopen

[cedar kiln]

✅

[gentle lintel]

I have no idea what I've done wrong; the answer to the integral is artanh(2x) rather than 2 artanh (2x)

Sorry I forgot to include the original integral which was $\int \frac{4}{(1-4x^2)^2} dx$, and we're intended to use differentiation under the integral sign to solve it

[dusty wren]

your d/dalpha is incorrect in the last step

[gentle lintel]

is the first term incorrect

d/da (-1/a^2) = d/da (-a^(-2)) = 2a^(-3) should make sense no?

[gentle lintel]

That did not impact the main calculation though

but yes that would be wrong as well

[cedar kiln]

@warm crow Has your question been resolved?

[gentle lintel]

<@&286206848099549185>

[reef ether]

wot

wolframalpha.com

good luck.

[gentle lintel]

I've used that to check every step

[slender ginkgo]

,w d/da [4/(a^2 - 4x^2)^2]

[wraith dagger]

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[reef ether]

so whats your problem here?

[gentle lintel]

for some reason it still led to the wrong answer

[slender ginkgo]

what was op trying to do?

were they using feynman tehcnique or.?

[gentle lintel]

Yeah

[slender ginkgo]

feynman technique is applicable to indefinite integrals?

[flint cape]

The integral at the top here?

[gentle lintel]

Yeah

[flint cape]

yes, the strict technically is that your integral is pseudo-definite from 0 to another variable, so that it makes some sense

[so here from 0 to a variable alpha]

[cedar kiln]

Channel closed

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[gentle lintel]

.reopen

[cedar kiln]

✅

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[gentle lintel]

tagged photo

[cedar kiln]

@gentle lintel Has your question been resolved?

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[obsidian marsh]

Hello.

27048 × 27044 - 27047 × 27043
Can someone tell me the shortcuts to solve this please

[slender ginkgo]

let u be smth

prolly u = 27044

[dusk finch]

or a = 27047 and b = 27043

then it simplifies to (a+1)(b+1) - ab

[crimson delta]

well the relationship between a and b is interesting

that is better captured by only using one variable

imo

[dusk finch]

this one?

im prolly missing sth then

[ember heath]

i would say take u=27045

expression simplifies to 2u+1

[crimson delta]

well no matter what u you take, it always simplifies to 2u +- something small

[ember heath]

ohk mb then

i thought taking that would make the second expression in a^2-b^2 form

[dusk finch]

oh ic what you mean

[slender ginkgo]

,w (u+4)(u) - (u+3)(u-1)

[wraith dagger]

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[obsidian marsh]

Thanks everyone

I got it

I appreciate the help

[cedar kiln]

@obsidian marsh Has your question been resolved?

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[cobalt plover]

Let k>0 be a real number. On the sides (AB), (BC), (CD), (DA) of the convex quadrilateral ABCD, consider points M,N,P,Q such that AM/MB = BN/NC = CP/PD = DQ/QA = k. Find the condition that MNPQ is a parallelogram.

[cobalt plover]

Im fairly new to vectors, can you give me a hint for the solve?

I have to prove that MN = PQ (vectors)

No wait

[tough finch]

i dont think this is vectors, this just seems like geometry

[cobalt plover]

may O be a random point, i have to prove that OM+OP = ON+OQ

Its at the vectors chapter tho

and id like to solve with vectors so i learn these better

[tough finch]

wait is ABCD just any quadrilateral?

[cobalt plover]

yes

[tough finch]

oo

look idk how to do this with vectors but i can give you a hint for geometry

[cobalt plover]

sure

it looks like menelaus

or ceva

at first glance

[tough finch]

actually sorry i was thinking about it wrong

[cobalt plover]

its fine

[tough finch]

i mean you can always take k=1

but that wont get a general solution

ping helpers someone will help you out

[cobalt plover]

sure

<@&286206848099549185>

[edgy spade]

Could you translate this perhaps

[cobalt plover]

i did

[dusty wren]

.

[cobalt plover]

Let k>0 be a real number. On the sides (AB), (BC), (CD), (DA) of the convex quadrilateral ABCD, consider points M,N,P,Q such that AM/MB = BN/NC = CP/PD = DQ/QA = k. Find the condition that MNPQ is a parallelogram.

[edgy spade]

Ok

Thanks

[cobalt plover]

np

[cedar kiln]

@cobalt plover Has your question been resolved?

[gentle lintel]

that's quite daunting for a vectors starter question icl

is it olympiad vectors?

[cobalt plover]

im trying to hit olympaid next year

yes

[gentle lintel]

where's this question from?

[cobalt plover]

Gazeta Matematica, romanian math book

[honest field]

@cobalt plover I figured it out

[cobalt plover]

With vectors or

[honest field]

Vectors

[cobalt plover]

Nice

[honest field]

I used this formula over and over basically

[cobalt plover]

D is midpoint or random

becuase in the provlem its random

[honest field]

D is random

[cobalt plover]

kk

[honest field]

This is just an example

I think the problem asked you to solve for k

[cobalt plover]

yeah

[honest field]

your idea of breaking down the parallel vectors works

then k/k+1 has to be equal to 1/1+k

because those vectors in the other brackets add up to 0

sorry it took this long, I made a dumb mistake along the way

[cobalt plover]

its fine

I dont know how to write it down tho

I have to look into notations, I taught all of this myself lol

[honest field]

basically

in triangle AMD you break vector MQ into components of MA and MD

then you break down vector DM into vectors DA and DB

you do get a nice theorem about mid-segments in a quadrilateral

@cobalt plover btw have you solved the really difficult inequality you posted like a week ago?

the sth<=4 and x+y+z=2 one

[cobalt plover]

yeah

ill send you the solve

after i try to write this one down

[honest field]

alr

[cedar kiln]

@cobalt plover Has your question been resolved?

[honest field]

@cobalt plover any problems you're having?

[cobalt plover]

its late and i cant link what you sent

like i dont know how to write the solve down

i think im tired

[honest field]

alr

[cobalt plover]

ill try again tmr

i think

[gentle lintel]

yeah that's super useful

I've always found it hard to incorporate side/side quantities in vector questions

where does that formula come from?

[honest field]

oh I learnt it while trying to solve a problem preparing for an exam

[gentle lintel]

are you able to find this theorem online? would love to read the proof

[honest field]

the idea is vectors DB and DC are opposing each other

multiply vector DB by DC/BC and vector DC by DB/BC and their sum is 0

then just rewrite vector DB as the sum of vector DA and AB, likewise for vector DC

pretty sure it has a name but I don't study in an English-speaking environment so...

[gentle lintel]

I would think it's used in some english written math problems though?

it seems very highly useful

[honest field]

yea it's super useful

[gentle lintel]

man I want to read more examples of this theorem

[honest field]

it's sorta like Stewart's theorem idk

[gentle lintel]

but I don't know how to describe it

I asked GPT and it seems to be a result of the section formula