help-36

[plucky breach]

oh wait

[next wraith]

wait also i found the side lengths

[plucky breach]

its a quadrilateral

it doesnt work

umm gimmie a sec

[next wraith]

from AB to DA its 24, 30, 18, 12

[plucky breach]

ook so

find where the point is the same distance from all sides

[next wraith]

but what for

[plucky breach]

its like an incenter

but for quadrilaterals

i forgot its name

or

there is an angle bisector that divides d

[next wraith]

i mean ok tbf i think i know how to do this? but i need someone to make sure

so basically i need to find how much 5x is

then from there im gonna find the radius of a circle thats inside

and then find the larger circle

is this right?

<@&286206848099549185>

[final saddle]

@next wraith Has your question been resolved?

[next wraith]

if anyone here checks it, please dm me and let me know if I'm making any mistakes

[final saddle]

@next wraith Has your question been resolved?

[loud sundial]

$ABCD$ is a quadrilateral with $AD=a$ and $AB=2a$. The line through $D$ that splits $\triangle ADC$ into two regions of equal area intersects $AC$ at $E$. It is given that $AE/CE=2/3$, the perimeter of $ABCD$ is $84$, and $\cos \left(\angle ADC \right)=1/16$. Compute the circumradii of $\triangle ACD$ and $\triangle ABC$.

[soft zealot]

Civil Service Pigeon

[loud sundial]

$ABCD$ is a quadrilateral with an inscribed circle that has side lengths $AD=a$ and $AB=2a$. The line through $D$ that splits $\triangle ADC$ into two regions of equal area intersects $AC$ at $E$. It is given that $AE/CE=2/3$, the perimeter of $ABCD$ is $84$, and $\cos \left(\angle ADC \right)=1/16$. Compute the circumradii of $\triangle ACD$ and $\triangle ABC$.

[soft zealot]

Civil Service Pigeon

[loud sundial]

is this what your question is supposed to say

b/c I can't entirely tell

also, if this is what your question is supposed to say, then DE splitting the area of ADC in half contradicts AE/CE=2/3

@next wraith

[loud sundial]

ignore the top texit from me - just worry about this

[final saddle]

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[formal lynx]

!claim

.claim

@raven marsh

[raven marsh]

?

!noping

[final saddle]

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@formal lynx Has your question been resolved?

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[terse folio]

Hi, im having trouble understanding how this part is resulted

[dreamy warren]

is the confusion with taking dξ or the step where it becomes div F?

[terse folio]

just the part where its equal to the highlighted section

[dreamy warren]

that term appears because stokes theorem when written in vector language, is the divergence theorem

[final saddle]

@terse folio Has your question been resolved?

[terse folio]

but what is dsigma

can i have more sources on this thankss

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[calm cloud]

guys,how can i find the length of EF, with EF//DM, E ∈ AB, F ∈ CN

[calm cloud]

all sides have the same length of 1

M, N are the midpoints of BC, AD

[fickle mortar]

let me try to do that

one sec

[calm cloud]

we dont use vectors or coordinates by the way

[fickle mortar]

oh

shit

😭 😭

auxiliary planes?

@calm cloud

can i get more details

[calm cloud]

the quesstion only provides that much info

that's all, like just look at the shape

and somehow find it

[fickle mortar]

k

send full quesiton rq

[calm cloud]

it's in Vietnamese btw

20

[fickle mortar]

can i translate it 🥀 ?

oh

its square root of 3/3

in .20

[calm cloud]

yo

[fickle mortar]

😭

lemme get pen paper

u can go offline ill work ts oujt

yeqh its sqrt of 3/3

do u want the full explanation on why or everything else?

[calm cloud]

yea

i really need explanation

[fickle mortar]

alr

[final saddle]

@calm cloud Has your question been resolved?

[tiny kraken]

What have you tried?

[calm cloud]

i havent thought about anything, like im so stuck, cant think of anything

[tiny kraken]

Hang on, letmme call the guy

[calm cloud]

[thin cloud]

VN đk:D

[calm cloud]

ýe

[leaden moon]

kek

[leaden moon]

,rccw

[soft zealot]

Couldn't find an attached image in the last 10 messages.

Dec 16, 2025, 2:14 PM

[thin cloud]

kẻ AM đi

[soft zealot]

Couldn't find an attached image in the last 10 messages.

Dec 16, 2025, 2:15 PM

[thin cloud]

Alright, vì EF song song vs MD đk, nên ta đi kiếm 1 điểm trên AM gọi là H sao cho HN song song vs MP rồi đối chiếu độ dài MP vs HN rồi HN vs EF

vì MP vs HN thuộc cùng 1 mp và HN vs EF thuộc cùng 1 mp nên chỉ cần dùng hình học phẳng

[calm cloud]

MD chỉ nhỉ, ah my handwriting

=)))

tại sao HN EF đồng phẳng vậy

lấy H là trung điểm AM thì HN//MD

[thin cloud]

Mà MD || EF suy ra EF||HN

[calm cloud]

o

🤯

lemme solve this

ơ sao x tính ra EF=MD nhỉ mă

[thin cloud]

Tính sai rr

[calm cloud]

dùng talet

[thin cloud]

Bt tỉ lệ CG/CE là mấy ms sài Thales đc

[calm cloud]

MD=2GN

[calm cloud]

oh yea

this is hard

really need assist, nghĩ nãy giờ không ra luôn, chả dùng nổi dữ kiện gì 😞

[thin cloud]

[calm cloud]

[thin cloud]

Tìm đc tỉ lệ AE/EB bằng Menelaus ko

[calm cloud]

ôi menelaus hả, không nhìn ra đường nào cắt 3 cạnh tam giác hết á

oh wait

i might get it

[thin cloud]

đường EGC cắt tam giác AMB

[calm cloud]

yea yea vừa nhìn ra luôn

AE/EB=1/2

[thin cloud]

k

[thin cloud]

H menelaus tiếp, tam giác CEB vs cắt bởi đường AGM

[calm cloud]

CG/EG=3

[thin cloud]

xong rr đs

[calm cloud]

ôi ra 3/√3 finally

appreciate you a lot for thời gian

.close

[final saddle]

Channel closed

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[tiny kraken]

seems like he get the job done

[final saddle]

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[woven ledge]

,rccw

[sage stirrup]

Explain what this means

Like ehhh where did ma man derive that formula

[woven ledge]

which one

[sage stirrup]

413

[tired walrus]

that's kinda as unspecific as possible

but: this whole proof hinges on the number of divisors of N

[sage stirrup]

Well I don't even understand the first

Soo.....

[tired walrus]

do you know how to count divisors of N based on prime factorization of N yes or no

[sage stirrup]

Yes I do

[tired walrus]

ok

then this entire text sums up as follows

the number of ways to write N as a product of 2 factors:

• if N is not a perfect square, it is τ(N)/2
• if N is a perfect square, it is (τ(N)+1)/2

where τ(N) denotes the count of divisors of N (which i just confirmed from you that you know how to find)

[sage stirrup]

Okkkkkie thank you

You so nice

.close

[final saddle]

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[tranquil pine]

.reopen

.open

[tired walrus]

nope

go open your own channel

.open isnt a command btw

[tranquil pine]

BRO I AM SORRY I NEED GEKP

like

I need to show him sm

I don’t know how to use it

[tired walrus]

do not call me "bro"

[tranquil pine]

Sorry

[tired walrus]

but also, can't you DM Erode if that's the case

[sage stirrup]

Hello there

[tired walrus]

or #discussion ...

[sage stirrup]

I was just noting smth down

Ya what happened

[tranquil pine]

I wanted to chat w the bot to help
Me w sm that’s it

[tired walrus]

the bot is not chatGPT so nope.

. again if you want help then open your own help channel

[tranquil pine]

I didn’t knew it’s was ur channel sorry bye

[final saddle]

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[proud crescent]

Im not sure how to do it

Hello can someone help me work through this identity

[proud crescent]

This, but idk if it's right

[bleak granite]

uhh yes just check the first denominators

1+cos+sin? or (1+cos)sin?

[proud crescent]

Wdym

Oh like this?

[severe canyon]

No, why are you adding sinx?

[half raptor]

Bro is back again

[proud crescent]

Im adding the fractions so I add the denominator, no?

[severe canyon]

Not at all

[proud crescent]

Oh

[bleak granite]

1/2+1/3 is NOT equal to (1+1)/(2+3)=2/5

[severe canyon]

And you should already know this, way before studying trigonometry

[proud crescent]

So like this then?

[severe canyon]

Yes

[drowsy epoch]

,rccw

[proud crescent]

I factored the big one

So i could reduce into this?

And now I'm stuck

Pls help

[night raft]

,rccw

[night raft]

use the trig formula $\sin^2(x) + \cos^2(x) = 1$

[soft zealot]

MxRgD

[proud crescent]

Where would I use it

[night raft]

for sin^2(x) specifically

[proud crescent]

OHHHH

?

Is that what i do?

Hello?

<@&286206848099549185>

[shell condor]

Sorry but what did you do with the (1 + cosx) in the denominator?

[proud crescent]

Oml, I wasn't suppose to cancel it out was i

[shell condor]

no no wait

you have sin^2x + cos^2x + 1 + 2cosx in the numerator

it becomes 2 + 2cosx

2(1 + cosx)

cancel it out

what in the world

[proud crescent]

Yea i messed up

[shell condor]

Dude

Bloody hell

It was $2*cscx$

[soft zealot]

doctorstrangejr

[shell condor]

why did you write it as $\frac{1}{2*sinx}$

[soft zealot]

doctorstrangejr

[shell condor]

😭

[proud crescent]

Wdym is that not right

[shell condor]

shouldn't it be $\frac{2}{sinx}$

[soft zealot]

doctorstrangejr

[shell condor]

Even I was confused there, as to why my answer here was wrong

[proud crescent]

Oh it is 2/sinx

Ok I'm here

[night raft]

so the numerator would be 2cosx + 2, do you notice anything?

also sorry if i was gone for a bit, had to do something

[proud crescent]

I do

[night raft]

what would that be?

[proud crescent]

The 2 factors

[night raft]

yep

there we go

[proud crescent]

And that proves the identity

Omlllll

[night raft]

yeah trig identities can be a bit messy

[proud crescent]

Yeaa

Thx

[zenith prawn]

big factorisation

[night raft]

you can type .close if you have no further questions :p

[zenith prawn]

attempt fr

[proud crescent]

Do you mind if we do one more idenity

[night raft]

sure

[proud crescent]

Ok this is the identity

[night raft]

,rccw

[proud crescent]

Ok so I converted it into sin and cos

[night raft]

there's an easier way

using the $\cos^2(x) + \sin^2(x) = 1$ identity

[soft zealot]

MxRgD

[proud crescent]

Hold up I see how to prove the idenity

That should proveit

[night raft]

that works and is basically the same as dividing cos^2(x) to this identity

[proud crescent]

Kk

Mind if we do one more

[night raft]

sorry no, maybe someone else can help tho

[proud crescent]

<@&286206848099549185> could someone help with one morw

[shell condor]

sure

[proud crescent]

Alr this is the new one

[shell condor]

Alright, cross multiply the LHS

[proud crescent]

I got here

[shell condor]

yeah okay, what's (a + b)(a - b)

[proud crescent]

Wait the top equals 0

[shell condor]

Also wait, -(1 - sinx) would be -1 + sinx

[proud crescent]

Oh that's why

[shell condor]

not the place, would be better at #discussion or #serious-discussion mate

[proud crescent]

K I'm here

[shell condor]

why is it sin^2x in the numerator?

[proud crescent]

Cuz the 1 was subtracted and it was sinx + sin x

Oh wait

Shit it's suppose to be 2sinx right?

[shell condor]

yes

[proud crescent]

And that proves the identity

[shell condor]

yes, and 1 - sin^2x is just cos^2x, so the denominator is equal too

[proud crescent]

Yea

@shell condor could we do one more?

[shell condor]

sure, how many do you have in total?

[proud crescent]

This will be the last one

Im just practicing for my test

[shell condor]

Alright then

[shell condor]

alright, break cotx and cscx into sinx and cosx

[proud crescent]

K I did this

[shell condor]

but $cotx$ = $\frac{cosx}{sinx}$, not $\frac{sinx}{cosx}$

[soft zealot]

doctorstrangejr

[proud crescent]

Crap mb

Think I solved it

[shell condor]

Yes nice

[proud crescent]

Yay

Alr thx for all the help

.close

[final saddle]

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[brazen stump]

for this question when do we do x/90

[white jay]

@gaunt ibex get your own help channel please

[brazen stump]

?

[white jay]

don't worry about it, they were just mistaken
so I presume you got the solution but don't understand how it came to be?

[brazen stump]

yh

i got lucky with 90/x

when do i do x/90

[white jay]

the x represents the number of bees in the hive, which you do not know yet, and since she caught 90, its 90/x
it cant be the opposite because its part/whole

[brazen stump]

how will they state when it is whole

[small vale]

If you know the whole number of bees? Perhaps
Shirley has 540 bees in her hive. She marks some number of bees on Monday. On Tuesday, she catches 120 bees and 20 of them are marked. How many bees did she mark on Monday?

Exercise: write an equation describing this word problem and solve it. Explain why this agrees with the result of the previous word problem.

We could actually obscure any of the four values.

Shirley has 540 bees in her hive. She marks 90 bees on Monday. On Tuesday, she catches some bees and 20 of them are marked. How many bees did she catch on Tuesday?

Exercise: write the fourth possible variation.

[brazen stump]

number of bees catched does not equal shirley has bees

?

[small vale]

I'm not sure what you mean.

[brazen stump]

the wording is diffrent

one is shirley has 540 bees and the other states it catches

i think thats wht gives it away if its the total or not

[small vale]

Yes precisely. Which number you want to know determines what equation describes the problem. The wording tells you which number you want to know.

[brazen stump]

alr i see thanks

.close

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[sage stirrup]

Prove that if N is odd , And there are 3 numbers N+1 , N-1 and N , then N has to be 3k

[cerulean igloo]

I dont think the problem makes sense

The second condition is incomplete ig

[sage stirrup]

Well this is sub part

[cerulean igloo]

What about N+1, N-1 and N

[sage stirrup]

of another problem so....

Like.

eh wait

The probem is show that n(n^2-1) Congruent to 0 mod 24 if n is odd

[rocky tusk]

why not?

they said N was odd

[cerulean igloo]

What is the meaning of the second part of the question

[sage stirrup]

Sol^n includes proving this

[tired walrus]

this is the real question right

[sage stirrup]

yea

[tired walrus]

can you share the solution where it says that

[sage stirrup]

I think

[tired walrus]

cause im curious exactly what you mangled

[rocky tusk]

yea maybe its incomplete wording

[sage stirrup]

Well this is the question

you may solve however you like

It's just ma version

Like ehh N+1 has to be 2k

b-1 4p

cuz successive even

or vice versa ofc

idk what to do with N

Oh nvm I am dumbass

I forgot multiples of 3 occur in gaps of 2

Smh

.close

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[novel dirge]

Im studying Random Variables and Expected Values and get to Bernoulli random variable. I can solve for any given p value within E[X] = 1(p) + 0(1-p)

But I dont get why we treat it "linear" by having constants a and b in: E[aX + b] = aE[X] + b

[obtuse hedge]

It's not that they treat it as such, but it's provably so based on the explanation provided below the equation

[tired walrus]

afraid i don't understand what you're asking

[novel dirge]

Im afraid I dont understand enough to properly ask

is it fine if I send the whole page?

[tired walrus]

sure

[novel dirge]

example 1.3c

[tired walrus]

$E[aX+b] = aE[X]+b$ is a property satisfied by \textbf{any} random variable; it isn't exclusive to Bernoulli ones. what they seem to be doing is \textbf{verifying} this property in the case where $X$ is discrete (and then its expectation is some summation that they mess with)

[soft zealot]

Ann

[tired walrus]

in fact this verification doesn't have anything specifically to do with example 1.3c

it just comes directly after

[novel dirge]

oh alright so it's a way to verify our expectation of... the average random number we're settling on after running it many times?

if that's so then I get it!

[tired walrus]

not really, no.

[novel dirge]

is it the average I predict before observing anything?

[novel dirge]

I'll read this over again

[final saddle]

@novel dirge Has your question been resolved?

[novel dirge]

.close

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[marsh onyx]

could someone explain this to me, im looking online and im getting a variety of answers, the answer key my teacher gave us says it D?

[formal trail]

what qualifies as a logarithmic function to you?

[marsh onyx]

i was trying to use y=log base 3 to find its end behaviors but im kinda lost, i thought that as x goes to infinity, f(x) would go to infinity no?

[silver dew]

Yes

[rugged merlin]

Indeed

Do a process of elimination, I suggest

Start with (A). What can you say to validate it or disprove it

[marsh onyx]

could this question be talking about a decreasing log function? if so i see why its D because if it was a decreasing log function

[rugged merlin]

Yeah

[marsh onyx]

oh i think i got it now

thanks

.close

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[vestal citrus]

Hello! 🙂

[craggy plank]

Hi

Do you have any question to ask?

@vestal citrus

[civic terrace]

Questions?

This is a help channel.

So being straight to the point would be more helpful.

[wild horizon]

Hi can anyone help with trigonometry 11th and 12th grade

[final saddle]

@vestal citrus Has your question been resolved?

[severe canyon]

!occupied

[final saddle]

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).

[civic terrace]

Hi bro.

Ask your question in another help channel.

[wild horizon]

oh ok

[wild horizon]

which other help channel

[civic terrace]

Dude there are so many there...

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[warm python]

part(a)

.close

[final saddle]

Channel closed

Closed by @warm python

Use .reopen if this was a mistake.

[plucky rover]

Fastest closure in history

[hasty mist]

You're welcome.

[sonic crystal]

what is blud talking about

[hasty mist]

You're welcome, too

[rugged merlin]

bro had to say something so he gets closer to helpful

[leaden moon]

[rugged merlin]

<@&268886789983436800> random ass link

[cyan kayak]

What is this?

[leaden moon]

i even needed permission to enter this lol

[obtuse hedge]

!filetype

[final saddle]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[leaden moon]

i think once he has my request, he can have my data

[faint edge]

They joined today and their only msg history is them spamming this link

[cyan kayak]

ooooh, yeah good point.

[barren hound]

it will have sent your email address to them if you requested access yes

[leaden moon]

probably ban him for spam

probably bot account

idk

[faint edge]

They are already ded

[plucky rover]

Rip

[leaden moon]

meta commitee

mmm

[final saddle]

Available help channel!

Send your question here to claim the channel.

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[long forum]

Hello I need help with this question please

800 people were supposed to vote on a resolution, but 1/3rd of the people who had decided to vote for the motion were abducted. However, the opponents of the motion, through some means managed to increase their strength by 100%. The motion was then rejected by a majority, which was 50% of that by which it would have been passed if none of these changes would have occurred. How many people finally voted for the motion and against the motion.

please explain the steps

[long forum]

the Highlighted is the question

it is Percentage question

[fossil kiln]

!noai

[final saddle]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[long forum]

it is just my conversation with Gemini for what it meant

either way please help me with the question

[fossil kiln]

Yep just dont trust ai fully yk

[long forum]

Answer please

[obtuse hedge]

!noans

[final saddle]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[long forum]

how am I supposed to learn if I have no answer(with steps)?

like I said I want to know how to solve this type of question

not just the answer

steps is what I am looking for

[main mirage]

Hi! Suppose x people are voting for the resolution and y people are voting against the resolution. Can you make some equations in terms of x and y based on the question?

[long forum]

For > x and Against > 800 -x ,
then double the A > 800 - x - (800 - x) > 1600 - 2x

For > x - 1/3

I am confused after this

[main mirage]

The last sentence is kind of the trickiest part to interpret.
"The motion was then rejected by a majority which was 50% of that by which it would have been passed if none of these changes occured"

This is how I interpret: Let me ask you this.

[main mirage]

Which one is the majority here?

[long forum]

expected was F and actual is A

[main mirage]

actual is F?

[long forum]

sorry

A

[main mirage]

There you go! Nice

[main mirage]

So, based on this,

How might you write an equation representing the scenario?

Hint: Remember the number of voters voting against is 1600 - 2x

[long forum]

1600 - 2x - (5/3x -800) = 1/2 of 800 - x ?

[main mirage]

Hm, that's a little different to what I had in mind

You might be overcomplicating this a little bit:

[long forum]

ohh

[main mirage]

Think about which one is the majority before and after the changes.

[long forum]

I got this as Majority of reject = 50% of how much should have passed

the majority is A after change

[main mirage]

Don't think it should be how much should have passed, the wording of the statement just implies to me that it is talking about the old majority.

The old vertict is passing I agree, but I believe the subject of the question on the right side is the actual old majority.

[long forum]

Sorry my handwriting is bad 🥲

[main mirage]

Your handwriting is pretty good compared to some I've seen lol

[long forum]

ty 😇

[main mirage]

So heres the deal

As I mentioned above, I have a problem with this equation.

It doesn't exactly match up with what the question is saying.

[long forum]

what should I do there?

[main mirage]

What you have here is right, but let me ask you this.

What is the majority?

What is the majority of rejection?

[long forum]

1600 - 2x

[main mirage]

Good.

What is the majority of passing without changes?

[long forum]

x?

[main mirage]

Yep

Hmm

[main mirage]

So how would you put these two in an equation?

[main mirage]

Hmm it is interesting. The method I have gives a nonsensical answer

It might be that I am having the wrong interpretation, so I'll clarify. How'd you get the equation in yellow?

[long forum]

It is actually what my teacher from video wrote

[main mirage]

Hmm

[long forum]

this is also where I am a bit confused plus back there in x - 1/3x - (800 - X)

here (800 - x) is confusing

wouldnt it be be just 1/3 x?

i dont understand how (800 - x) came since only the abducted is mentioned

[long forum]

since the ones who converted are not mentioned so that adds up to the confusion

[main mirage]

I know the right hand side of your equation is the difference in the x and the y, which is fair enough.

But I have no idea whats going on in the left hand side

If you want to find a difference in majority again, it should just me Against - For.

[long forum]

yes but wouldnt that be 1600 - 2x - (2/3x)

[main mirage]

Yeah

[long forum]

thats where I am confused as well

[main mirage]

Idk the wording of the last statement seems a little unclear to me

I thought initially it was just

[long forum]

the 5/3x -800 is not siting well with what question is saying

[main mirage]

1600 - 2x = 0.5(x)

Since the new majority is half of the old majority

[long forum]

yes

[main mirage]

But this gives a value of x that can't be divided by 3, so that cannot be the answer

[main mirage]

Pretty sure that is New Against - New For, but it seems very random

I.e

Wair

Nvm

Yeah I have no idea where that expression comes in

[main mirage]

I am sure nothing changes but, is this the exact question?

Any background context?

[long forum]

I asked Gemini and it had similar saying to it being wrong but since AI can be wrong thats why I wanted to clear it with someone

[long forum]

nope

cant contact the teacher as he has moved out from this Ed tech and teaching somewhere else

btw if A had 100% increase

[main mirage]

Hmmmmmmmmmm

[long forum]

then wouldnt we minus it from F

[main mirage]

Well I wouldn't think so, because 100% increase just means to double it.

[long forum]

yes but since the 800 is fixed then the once who converted were priorly supporting F?

[main mirage]

Ohhh I see what you mean

You are saying that

[long forum]

then if we if we double by adding 800 -x then wouldn't it mean that it was substracted from x - 1/3x ?

[main mirage]

The strength being doubled comes from the remaining

[long forum]

yes

since the cap was decided then external help is impossible

[main mirage]

Yes okay, I suppode that makes sense

[main mirage]

To be honest, since some people got 'abducted' I assumed that anything could happen lol

Like if people got abducted, then magically the place might get some random new people. But anyway, yeah that makes sense.

[long forum]

yea

but there is stil a problem

[long forum]

this part

[main mirage]

Wait

Hmm

We have that

Against = 1600 - 2x
Initially there was 2x/3 going for, but a portion of that amount went to against.
Specificially, 800 - x went over to the other team

So actually we have
Against = 1600 - 2x
So
For = 2x/3 - (800 - x)

[fossil kiln]

Is the ans A 400 and F 200...?

[long forum]

yes after dividing which we got new F which was 5/3x - 800

[main mirage]

That gives us For = 5x/3 - 800

[long forum]

thats what my teacher said as well

but the process has me confused

[long forum]

yes

[main mirage]

Okay so that means

They did

New Against - New For = 0.5(For - Against)

[long forum]

yes

[main mirage]

Okay so yeah

[long forum]

but why

[fossil kiln]

This is wht i did. Altho i highly doubt myself

[main mirage]

Then they solve that

[main mirage]

Yeah I have no clue

The wording is particularly off here

[fossil kiln]

A ,F being final votes. a,f being supposed to be votes

F would be 2f/3- a. Cos well a ppl were somehow convinced to reject the idea

[long forum]

but how did 2a -2/3f + a = 1/2 (f-a) come?

[fossil kiln]

"Majority by which"

[long forum]

but the majority is diff?

[fossil kiln]

F-A = 50% (f-a)

[long forum]

ohh i cee

see*

so to take the diff you subtract a and f?

[fossil kiln]

To get the majority yk

[main mirage]

Wouldn't the majority just have been A though?

Or just F?

This is difference in majority, or at least - how much more F won over A

[fossil kiln]

"Majority by which" means by how many votes X one upped Y

[main mirage]

If it had said that, then that would have made more sense in my opinion

[main mirage]

Sure but thats only for the second half

[fossil kiln]

I suppose majority by which implies js tht tbh

[long forum]

50% of of by which the F would have won

meaning half of x ?

[fossil kiln]

Yesyesyes

[main mirage]

Wait no,

[fossil kiln]

Half of by how many votes f would've one upped a

[main mirage]

Because that would contradict the equation

^

[fossil kiln]

Need a better word than one up

[long forum]

ohhh yes

[main mirage]

I think this is still a little ambiguous though but anyway

[fossil kiln]

Ok so solving tht eqn we get the relation 3a=f

Then its all a piece of cake i suppose?

[long forum]

so the question is saying 50% of the diff if that would have passed?

[fossil kiln]

Majority by which

[fossil kiln]

..

[long forum]

ohh I think I undertood

let me decode the last sentence

[fossil kiln]

Yh read it like 5 6 times you'll get it

[fossil kiln]

I was so confused as to why u hv a feedback form in ur bioTT

[long forum]

'The motion was then rejected by a majority, which was 50% of that by which it would have been passed if none of these changes would have occurred'
here 1st - The motion was then rejected by a majority > this means that the current scenario implies that A has won by majority
2nd - the majority is 50% of that by which it would have been passed if none of these changes would have occurred > which means if no abduction or conversion were to happen then the difference between them would be measured as x - (800 - x) and in the current scenario the 50% is taken from this diff thats how you get the ans like @fossil kiln mentioned

[fossil kiln]

Diff variable but yeah

[long forum]

Thank you @main mirage and @fossil kiln

[fossil kiln]

Woah u understood?

[long forum]

yes

[fossil kiln]

Phew tht was a confusing ques

[long forum]

when you mentioned this

[fossil kiln]

I should get the helpful role for this ngl

Im so proud of myself

[long forum]

me too I never thought my dumb brain could understand it

but you two helped a lot

[leaden moon]

do you have the helper role?

at least get that role

[fossil kiln]

Nopies i dont wanna get randomly pinged

[leaden moon]

psst

hop into dm

[fossil kiln]

!done

[final saddle]

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

[long forum]

just waiting for @main mirage

wanted to make it clear for him as well

[fossil kiln]

Ahh maybe u can dm or smth idk

[long forum]

okk

.close

[final saddle]

Channel closed

Closed by @long forum

Use .reopen if this was a mistake.

[main mirage]

👍

Looks fine to me.

[long forum]

Ty 😇

[main mirage]

Oh it's mainly for people if they want to give feedback whenever I answer a question. I don't really do anything outside of maths on discord lol, so I might as well put it on my bio.

[fossil kiln]

BEST OF LUCKKKKK FOR UR TEACHING CAREEERRRR. YOU'LL MAKE AN AMAZING TEACHER.

[main mirage]

Thanks :D

[final saddle]

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.
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• 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.

[worldly spruce]

Please don't occupy multiple channels

With the same exact question

It's literally one channel below this one

[rocky tusk]

i'd bet money you asked chatgpt these questions and are asking here to verify gpt is right

[worldly spruce]

a total of 7 messages were sent after your question ...

And since Discord groups them, there's 2 groups of messages

Your question is still very visible

Plus, let's not forget about the bot pinning the first message anyway

If anyone would "get lost" in the flooding that is 7 messages

Yeah I was about to say 8

My bad

[shell condor]

Bro is just sending all of the questions one after the other

[rocky tusk]

most intelligent cheater

[shell condor]

even in #help-25

[worldly spruce]

OH

LOL

I am so stupid

I thought that was the end 😂

[shell condor]

nah still it gets pinned, not like it gets lost or anything

[worldly spruce]

Yeah I still stand by my point

Though it's not 8

😂

[rocky tusk]

bro just submit it gpt is good enough at this kind of math

this isn't 2022 anymore

[pliant shore]

I think you're causing more problems than solving them with GPT

[worldly spruce]

If you want an answer

Yes, C is correct

If A were correct, the company would have roughly half a trillion employees at the end of the year

[shell condor]

True, exponentials go crazy

[worldly spruce]

I myself would happily be the owner of such a successful company

[trail mango]

!noai

[final saddle]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[shell condor]

Nah paying the salaries would go crazy

[worldly spruce]

Who said anything about paying salaries

¯_(ツ)_/¯

[night raft]

mind you, the earth has like 8.2 billion people

where would you keep them

[trail mango]

my basement

[worldly spruce]

not my problem

[trail mango]

i will expand to fit a trillion people

[final saddle]

Channel closed

Closed by @umbral shuttle

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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• 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.

[flint sundial]

can anyone tell me if im right

[timber jungle]

yep, looks good to me

[final saddle]

@flint sundial Has your question been resolved?

Channel closed

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[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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• Type the command .close to free the channel when you're done.
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Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[obtuse hedge]

<@&268886789983436800> they're back 🙁

[final saddle]

Available help channel!

Send your question here to claim the channel.

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• Type the command .close to free the channel when you're done.
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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 nest]

Given 6 variables all bounded on both sides like constant>=number>=constant and all in an equation like a+b+c+d+g+f=constant, how to solve? This comes from a solution for a space by Gaussian elimination and the bounds come after that with possibly no relation to left side, how to get the solution shell in the form of planar polygons in terms of x, y, and z which may be any one of these each noting that constants may multiply the variables in the formula? Can you ask if this is not enough? Note that max x or y has z multiplying it. X E.

[scenic nest]

There may be less than 6 variables and less than 3 of xyz or not may be a plane or less. X E.

[cyan kayak]

Are these equations linear?

[scenic nest]

They involve just numbers. X E.

[cyan kayak]

you mentioned planar forms previously, which are not necessarily linear

[scenic nest]

They could be considered linear. X E.

Oh, yeah, not linear. X E.

This is a continuation of before. X E.

[cyan kayak]

Then your answers can only be drawn from algebraic geometry, at best, and might not be solveable in the general case.

[scenic nest]

Thanks for talking. X E.

I know Fourier Motzkin elimination works. X E.

This can be done I know, but how?

[cyan kayak]

This is, unfortunately, beyond my ability of math as of right now. But I would recommend reading the book Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea. It's a introduction to Algebraic Geometry that only assumes a basic undergraduate level of mathematics. But this is still probably too advanced from where I suspect your education is.

I can craft you a sort of path to reach this book, if you're interested, but I would need to know what math you have taken and are familiar with.

[scenic nest]

Honestly, I think I can handle it enough. X E.

Is it after linear algebra?

[cyan kayak]

Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions.

It wouldn't work, because as you just confirmed, your equations are not necessarily linear.

[scenic nest]

Oh, okay. X E.

Thanks. X E.

[cyan kayak]

Yes, you'll need firm grounding in linear algebra, probably a proofs based class, perhaps a class in topology and abstract algebra as well.

I would recommend you don't try to reinvent the wheel on this.

It's OK to allow yourself to trend on the path that has been laid before. You should attempt to reimplement things that have already been implemented before trying new things.

You can't explore the ocean until you reach the shore, after all.

[scenic nest]

Can you lead me to what linear means, I think it might be linear, just numbers only, this could be formulated as a linear equation maybe. X E.

The multipliers and all variables and constants are scalars. X E.

There is no squared or powers. X E.

No functions nearly. X E.

[cyan kayak]

@scenic nest candid question, what is your actual level of educational attainment? You're kind of gesturing as if you have learned linear algebra, but it feels as if you're half faking it, and your grasp of something as basic as "linearity" makes me think that you're significantly farther behind than you're attempting to let on.

it would help me help you if I actually knew.

[scenic nest]

High school in USA, I am in Precalculus 2 now. X E.

[cyan kayak]

ok, this helps.

[scenic nest]

Completed high school. X E.

[cyan kayak]

Linearity is something you'll learn about in calculus. It's essentially the property that if you have a function f(ax + by) this is equal to a f(x) + b f(y).

where a and b are constants and x and y are variables.

this can be extended to any number of constants and variables.

and also extended beyond just functions to other things like operators, which you will learn about later (for instance, the derivative is a linear operator so d/dx(a f(x) + b g(x)) = a df/dx + b dg/dx)

[scenic nest]

I also know some Calculus. X E.

Integration mostly. X E.

So, do you say linear?

[cyan kayak]

linear algebra is called linear algebra because all of the functions we solve using linear algebra are linear functions.

[scenic nest]

Okay, then yes, this is a linear thing. X E.

[cyan kayak]

they're functions that look roughly like y = Ax + b, where y, x, and b are vectors (the first two are vectors of variables) and A is a matrix of coefficients.

[scenic nest]

Yeah, I think this can be formulated as a constant vector dot an unknown vector + constant. X E.

I can give you a solid linear form if you want, should I?

Okay, multipliers can also be vectors, similar form, but all multipliers as vectors and a constant vector equal to. X E.

[amber vector]

go ahead

[scenic nest]

Already gave it basically. X E.

Just have known parts be vectors not numbers. X E.

$P+(O-P)z+(X-O)x+(Y-O)y=Q+sum((V_i)s_i)$ where all capitals are known. X E.

[soft zealot]

maybeJosiah

[scenic nest]

All but 6 or less will be known. X E.

That is the original equation. X E.

[final saddle]

@scenic nest Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[scenic nest]

.reopen

[final saddle]

✅ Original question: #help-36 message

[scenic nest]

I think this can be considered a 1d linear problem. Linear programming and Polyhedral Geometry. X E.

<@&286206848099549185> hi?

By the way, this will be parallel on the GPU. X E.

Good hi?

Wow, unbusy today. X E.

[final saddle]

@scenic nest Has your question been resolved?

[scenic nest]

Can I at least get a scammer to report?

[scenic nest]

Joke. X E.

[leaden moon]

hm

probably start with the smaller cases

3 variables for instance

[scenic nest]

Yeah, I know a basic case. That would not work for my use case. X E.

[leaden moon]

you only need the domain of 2 variables in order to figure out the domain of the other variable

[scenic nest]

In 3 vars. X E.

[leaden moon]

so following the logic, you only need the domain of 5 variables in order to figure out the domain of the other variable

[scenic nest]

I have basically all domains. X E.

Yeah, z upper bound can be found. X E.

To start what we know 0<=x<=z(constant) and same for y and z>=1 is the start for x, y, and z, but I can bound them with the others which are entirely of original form. X E.

The range of this function is 1 number. X E.

[scenic nest]

By the way, good luck on the language. X E.

[leaden moon]

eh?

[scenic nest]

Your bio, you making a language, good luck. X E.

[scenic nest]

Well, anyone want to talk?

What theory should I study?

Bounds tightening?

[crimson bronze]

Study linear algebra

[scenic nest]

All of it?

I want a something to work toward understanding, like a theory, does that not exist yet?

Well thanks. X E.

[crimson bronze]

Take any intro linear algebra book and read at least half of it

[scenic nest]

I did look at most of the 3b1b linear algebra stuff, not enough. X E.

Is this linear algebra or linear programming?

Which should I study more?

[crimson bronze]

3b1b is great, but you can't get a good enough understanding just from watching videos

[scenic nest]

True enough. X E.

[crimson bronze]

Start with linear algebra, it's a prerequisite for learning linear programming

[scenic nest]

Are there any polyhedral geometry books I might need to study or things including them?

Or whatever the term I am supposed to look for for this problem. X E.

[crimson bronze]

I would focus on linear algebra to begin with

It's not clear whether you need polyhedral geometry, and if you learn linear algebra you'll be able to figure that out yourself

[scenic nest]

Any other remarks, I have a basic understanding of linear algebra from 3b1b. X E.

Basic, not advanced. X E.

I also took some Khan Academy stuff. X E.

I feel like using AI at this point might almost but not be a good idea from the lack of people helping. X E.

[scenic nest]

.close

[final saddle]

Channel closed

Closed by @scenic nest

Use .reopen if this was a mistake.

[final saddle]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[calm cloud]

guys, i need some assist on question 63, find m (m ∈ Z) so that (m²-5m+4)x⁵+x²+4=0 has solutions

[calm cloud]

m ∈ [-2,9] as well

[silver dew]

ax^5+x^2+4 has a real root if and only if a is not 0

Since real polynomial of odd degree always has a real root

So just solve a doesn’t equal 0 for your a=m^2-5m+4

[calm cloud]

it doesnt have to be real root

[silver dew]

If complex then the question itself has very little meaning

complex roots always exist

All m satisfying your range, [-2, 9] works. I doubt it’s the purpose of this question. So assume it means real roots

[onyx peak]

it asks for how many m work

[silver dew]

This gives you version 1: solution in question means real solution

[onyx peak]

and i'd guess it only wants real

[calm cloud]

oh real root, i misunderstood

[silver dew]

This gives you version 2, solution means complex roots

[calm cloud]

my bad, no complex

[silver dew]

Choose whichever you prefer

[calm cloud]

[silver dew]

Okay, {-2,-1,…,8,9}-{roots of m^2-5m+4}, solved

[calm cloud]

ohhhh, mind you explain more to me please, kinda lost and confused

[silver dew]

Real polynomial of odd degree always has a real root

ax^5+x^2+4 is of odd degree of and only if a is not 0, on the other hand x^2+4 has no real root

So solve a doesn’t equal 0

[calm cloud]

this is NEW

havent learnt that at school

[silver dew]

Because f(x) a real coefficients polynomial

f(z)=0 for some complex z

Taking conjugation both sides

f(conjugate of z)=0

Thus complex but not real roots always come in pairs

Odd degree, then there has to be at least one real root

complex but not real roots come in pairs

[quartz coyote]

Hellow I'm new here btw I'm studying in 10th standard. I just need strict helps with geometry especially focusing on trigonometry. Thanks.

[silver dew]

Ask your question in a vacent help channel

[calm cloud]

definitely have to delve into this new knowledge

[quartz coyote]

Wdym I just saw this channel and joined it mb I'll just get some knowledge?

[chilly pollen]

!help

[final saddle]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[silver dew]

Fundamental theorem of algebra (a complex polynomial has its degree many complex roots (can be duplicated)))

Or any algebraically closed field

[quartz coyote]

Ow you meant the bot alrighty thx!

[silver dew]

It’s funny. Of algebra, but rarely one sees a pure algebraic proof

Usually proved using topology or complex analysis

[calm cloud]

aw man

[quartz coyote]

I understood thx man 😭

[calm cloud]

thanks for your help

appreciate it a lot

.close

[final saddle]

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[final saddle]

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[crisp haven]

Can someone help me part 3

It is very hard for me😭

[dreamy warren]

can you tell me exactly which part of part 3 is confusing you

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[lethal thistle]

WAHT IS THIS MADNESS?

[loud sundial]

Hint: factor of 11 -> remainder is zero

[lethal thistle]

I have never done such a problem That hisnt dosent help at all

[tacit dust]

k! = 1x 2 x ... x k, so when is k! divisible by 11?

[digital sable]

fwiw, you can remove discord formatting by putting a \ before it

eg * hello *

[tacit dust]

thanks

[spark swan]

well after 11! every term has 11 in it right?

[lethal thistle]

what is k suppose to do in solving for the division

[spark swan]

nothing they're using it to define the expression k!

[spark swan]

@lethal thistle

[lethal thistle]

yes what do we need k! for?

[spark swan]

^

[onyx peak]

This is just asking you to think about what factorials are divisible by 11 (factorial is the ! thing)

if we wanna know the remainder of a sum of many factorials, then it's certainly beneficial to know something about remainder of single factorials

so think for example about the following:
Is 3! divisible by 11?
Is 9! divisible by 11?
Is 13! divisible by 11?
Why?

[lethal thistle]

yok but at point wont this get too big

[onyx peak]

it's not about calculating them all. it's about finding a pattern

just do few examples and see which are divisible by 11 and which are not

Can you write 9! as a product?

[lethal thistle]

yes

[onyx peak]

Is it divisible by 11?

1. yes (explain why)
2. no (explain why)
3. maybe (I'd need to calculate it to know for sure)

[lethal thistle]

mabey let me check

[onyx peak]

okay, in that case dont use a calculator yet

there is a simpler way

how would you know if e.g. 15 * 12 * 11 * 7 is divisible by 11 without calculating it?

[lethal thistle]

I actually woudnt know😅

[onyx peak]

15 * 12 * 11 * 7

what about now

[lethal thistle]

ohhhh

but can this help us

do we just see if there if a multiple of 11

in the fatorial

[onyx peak]

well, try writing e.g. 15! as a product

[lethal thistle]

yeah there is 11 in the multiplication ohh so anything above 11! is just divisible by 11

[onyx peak]

exactly

so you only need to consider 3! + 5! + 7! + 9!

which is probably simple enough to calculate already

if u wanted to, you could use some modular arithmetic tricks to do it by hand

but if you can use a calculator, its easiest to just plug it in

[lethal thistle]

yeah but i dont that will allowed

[onyx peak]

And do you know some modular arithemtic? Do you know what a modulo is?

[lethal thistle]

I am oblivious

[onyx peak]

the basics is that if we are only concerned about the remainder after dividing by 11, we can apply the "remainder" operation whenever our number gets inconveniently large

for example lets try to calculate remainder of 9! when divided by 11

we start by 9 * 8

that's 72

now whats the remainder of 72 when divided by 11?

its 6 more than 66, so the remainder is 6

so 9*8 is same thing as 6 if we only care about the remainder

so next, instead of doing 72 * 7, we just do 6 * 7

thats 42

we can simplify this again to 9

and then we do 9 * 6...

etc

[lethal thistle]

ok ok i see

[onyx peak]

if u wanted to be even quicker, 9 is basically the same thing as -2

if we are working "modulo 11"

9 + 22 is the same thing as 9 + 11 is the same thing as 9 is the same thing as 9 - 11 = -2

similarly, 8 would be -3

7 would be -4 and 6 would be -5

so it's just (-2) * (-3) * (-4) * (-5) * 5 * 4 * 3 * 2

there is even number of -, so they cancel out

and you are left with 2^2 * 3^2 * 4^2 * 5^2 = 4 * 9 * 16 * 25

this is the same thing as 4 * (-2) * 5 * 3

which is -8 * 5 * 3 = 3 * 5 * 3 = 15 * 3 = 4 * 3 = 12 = 1

im kind of abusing = here, but i really mean that they have the same remainder

[lethal thistle]

ok ok I understand

dont worry i can do the rest thanks !

[onyx peak]

np

[final saddle]

@lethal thistle Has your question been resolved?

[final saddle]

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[next wraith]

there's a right triangular pyramid (not necessarily a regular tetrahedron though). its height is h (given). the angle between 2 sides (I'll show a drawing) is a.

[next wraith]

1. prove the following

2. find a

and well I got stuck here:

my idea was to do a⁴=4l²x² but it's a mess

ik I went in the right direction with sin(a/2) because it's in the equation I'm supposed to prove but idk where to go with it now

[final saddle]

@next wraith Has your question been resolved?

[finite crow]

I’m not sure how to solve this but I’m sure someone does. The rules say you are allowed to ping the Helper role if your question hasn’t been answered within 15 minutes

[finite crow]

See the 3rd bullet point under “Remember”

Just so you know

[final saddle]

@next wraith Has your question been resolved?

[next wraith]

yeah I know but thank you

<@&286206848099549185>

[finite crow]

ok just making sure

sorry i couldnt help!

[heady moon]

Pyramid?

[next wraith]

yeah

[next wraith]

no worries

[heady moon]

do you have original diagram?

Kinda can't understand yours

[next wraith]

there's no drawing

I had to draw it myself

[heady moon]

from question?

[next wraith]

yeah

[heady moon]

send question

[next wraith]

i did

[next wraith]

^

[next wraith]

^

[next wraith]

^

[worldly spruce]

I assume oppenheimer meant the original question

From the book

[worldly spruce]

What is $\alpha$?

[soft zealot]

USS-Enterprise

[worldly spruce]

dihedral angle?

[next wraith]

well it's not like that'd help bc its not in english

[next wraith]

yes sorry that's what I meant

[proud dock]

This is so ugly im sorry .

I'll try helping. From what I understand:

• you have a pyramid.
• I assume all edges have the same length.
• Angle between two edges is a.

Simply asked, find the expression for volume. Right?

Googled, volume of pyramid, assuming width=length=l, $V = \frac{h\cdot l^{2}}{3}$

[soft zealot]

HqppyFeet

[next wraith]

again, no

it's not necessarily a regular tetrahedron

[proud dock]

ah

[next wraith]

nowhere does it say that all sides are of equal length

[proud dock]

got it, my bad, im bad at reading