help-27

[jagged harbor]

that's the only reason why I was a little hesitant earlier, since (iii) addresses all open covers, whereas our open cover O is fixed

[sand pumice]

hold on how do you know there does exist such an A

[jagged harbor]

define A this way

I_0 is a closed interval with finite bounds because K is (ii)

and I_0 cap K = K is not finitely covered by O

we are assuming inductively that, at step n, things are going well: I_n is a subset of I_{n-1} is a subset of ... I_0, and I_n is itself closed, so I_n = [a, b] for some real a,b

also that I_n cap K is not finitely covered by O

we are momentarily defining A to be, formally, the left half of I_n

if you find any gaps in my half-argument, I trust you to fill them lol

[sand pumice]

can't take that as an assumption, im supposed to prove that

[jagged harbor]

it's an inductive argument

you already have the base case established, so just assume it

[sand pumice]

oh right

i suppose for the remainder of the problem, i'll use the nested compact property for (b)
and show that there exists an I_n which in fact can be finitely covered for (c)?

[jagged harbor]

it sounds like it's at least close

[jagged harbor]

so I think your idea of splitting intervals in half was viable in the end

[sand pumice]

okay thank you

.close

[devout snow]

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[calm sentinel]

could i get some help on this question? the answer key says it's E but I don't really understand how to do this at all

[devout snow]

@calm sentinel Has your question been resolved?

[devout snow]

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[mortal escarp]

I have a question

[mortal escarp]

according to Google, f(x) = x^2 is only injective

[tender cobalt]

where did you get this image from

🤔

[mortal escarp]

google

[misty crest]

gemini?

[tender cobalt]

call the AI by its name

[mortal escarp]

AI generated Google response

[misty crest]

it’s gemini

[sand olive]

Is this not ai overview

[tender cobalt]

back in my day

when you googled something, it just meant the websites that google pulls up

instead of google's AI response

no, f(x) = x^2 is not injective

because 2 and -2 both map to 4

[mortal escarp]

its wrong right, AI can't do math 😉

[misty crest]

gemini is the worst ai for math

[tender cobalt]

call the AI by its name

[radiant python]

crazy ai

[misty crest]

at least from just doing a google search

[mortal escarp]

"complex system"

lol

[tender cobalt]

.close ok

[devout snow]

Channel closed

Closed by @tender cobalt

Use .reopen if this was a mistake.

[misty crest]

i mean it isn’t supposed to do math

[tender cobalt]

it is supposed to do math, its just never designed to do it

[misty crest]

if it’s not designed to do math then it’s not supposed to do math

[tender cobalt]

then you should be saying "it shouldnt be doing math" instead

[misty crest]

no i think saying supposed to is pretty clear

[devout snow]

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[terse bear]

struggling between pointwise and not converge

so it´s continuious at (0,1) , but discontinuous at the endpoints, the Fourier series converges pointwise on but does not converge uniformly on
because of the jump discontinuities at the endpoints

[terse bear]

how to close this

[eager cobalt]

type .close @terse bear

[terse bear]

.close

[devout snow]

Channel closed

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[devout snow]

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[vast tinsel]

<@&286206848099549185>

[winter patrol]

Please don't ping 15m before have elapsed.
Especially not before you've actually asked your question.

[vast tinsel]

arl

[upbeat forge]

aren't you supposed to be in class anyway?

[vast tinsel]

i am in class she says to wok on it

[vast tinsel]

she say to work on it before it goes missing

[upbeat forge]

why not ask her then? she's your teacher, a person quite literally paid to teach you. if you don't get it after her explanation, you can come ask us after school. how about that?

[vast tinsel]

she says to work on it by ourselves because were older

[upbeat forge]

tell her you don't understand what's going on, perhaps. while helpers don't mind helping you, it's absurd that you wouldn't trust your own school teacher to do the same.

[vast tinsel]

arl

back she only told me one question

[vast tinsel]

she only told me one question

[upbeat forge]

sounds like you need a more serious talk with your teacher. plus, I don't advise that you talk here during class.

[vast tinsel]

nah shes okay

[river rune]

maybe she is. but if she's your math teacher, you're in her class, and you're here talking despite your perceived lack of knowledge, how much respect are you giving the teacher of a subject you're weak in?

[tacit reef]

Could u take a quick look at mine after this? Its been up for forty minutes. Sorry for interruption

[vast tinsel]

i listen to her

...

[upbeat forge]

!noads, please, and I will reply if I do get how to work that problem out.

[devout snow]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[river rune]

in that case, I advise that you close the help channel and come back later. don't divide your attention between this server and your own teacher. please show her some respect.

[tacit reef]

Got it, sorry didnt know its forbidden. Wont repeat

[devout snow]

@vast tinsel Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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[potent delta]

Hello , i want to start learning math and i have only med school experience , from where i can start and with what .
Thanks.

[potent delta]

I have only middle school experience (8th grade)

[hard ocean]

You can start with khan academy

[potent delta]

Ok

[potent delta]

How please

<@&286206848099549185>

Hello

Hello

[soft umbra]

Khan academy

Just Google it

https://www.khanacademy.org/

[potent delta]

Ok , thanks

I know basics

[potent delta]

I need math olympiad problems

[turbid bane]

Which syllabus?

I mean for what do you want to learn

[turbid bane]

Like puzzles? or actual math

[potent delta]

Actual math olympiad problems

[turbid bane]

Gotta go bye

[potent delta]

Bye

Please could anyone help me i want to learn actual math to solve olympiad problems

Please 🙏

Please

Hello

[junior grove]

Me too

I’m in 6th grade

I’m trying to learn ratios

And rated

Rates*

[chrome gulch]

U can try igcse

It contains all the basics and most normal and useful chapters , and contains a small peak abt calculus

[devout snow]

@potent delta Has your question been resolved?

[devout snow]

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[devout snow]

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[unique badge]

Hello! I am not sure if I am making a mistake or if the answer in the book to this problem is wrong.
So the problem is to transform this complex number $(-\sqrt3 - i)^3$ into rectangular form.
What I did is I transformed it into polar form using de Moivre theorem and then calculated the values of sin and cos.
It can also be easily solved with cube of difference formula.
I calculated that this number is equal to: -8i, however the answer in my exercise book is 8i. I pasted this problem into wolfram, and symbolab, and they both gave the same output of -8i.
Is there something I am missing or is the book wrong?

[woven radish]

beegee

[cinder bobcat]

should be -8i

[topaz beacon]

i get -8i too

[unique badge]

Thanks a lot, it must be book that is wrong then.

.close

[devout snow]

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[devout snow]

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[neon wagon]

Calculate the probability that the values of the random variable Y lie within half of the standard deviation around the corresponding expected value.

[neon wagon]

can anyone explain me how he came to 0,3 at the end

like what did he do that he didnt note

[cinder bobcat]

Since x is discrete, saying

2.31 < x < 3.49

is the same as saying x = 3. and P(x = 3) = 0.3 from the table

[neon wagon]

oh

why didnt he just stick to P(x=2)

[eager nova]

Y is discrete.

[neon wagon]

uhh

so from what i understand

[eager nova]

Because x = 2 is not inside the interval

[neon wagon]

x is inbetween 2,31 and 3,49

[eager nova]

Yes

[neon wagon]

oh

oh so as soon as its above 2

then its gone

like

[eager nova]

Y takes only integer values

[neon wagon]

oh

[neon wagon]

also, in a linear equation system in which i have 2 variables and 2 equations

is it better to multiply one and put it into the other

or for example

if you have 5a+5b= 7 and 3a+4b=10

is it better to solve for a and use that equation in the other one

so a = 10/3+4/3b

and put this into the 5a+5b=7

or is it better to multiply and subtract

[fallow fractal]

Both work fine

[neon wagon]

okay thanks

[devout snow]

@neon wagon Has your question been resolved?

[devout snow]

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[wicked jacinth]

I need help with this problem, and I honestly have no clue where to start or how to get to the end. Any help would be greatly appreciated

[solar goblet]

do you know the formula the remaining mass given initial mass and half-life?

[wicked jacinth]

No?

Sorry is that important

oh wait it is mb but still no i dont

[solar goblet]

pretty important yeah

you can easily derive it yourself using the definition of half-life

[wicked jacinth]

its making sense now

I take it back

Im not sure how I am supposed to get weight based off of the given information

because half life is for radiation

.close

[devout snow]

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[devout snow]

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[opal hamlet]

i need help with integrals

[jade oak]

What part you need help with?

[opal hamlet]

so im in calc ab and were learning derivatives and i wanna get ahead and learn integrals, where should i go?

[jade oak]

Does your class have a textbook? That would be the best place to the start. There are also many popular choices for textbooks to learn from. There are also some good websites like https://tutorial.math.lamar.edu/classes/calci/calci.aspx

[opal hamlet]

thank you, i may have a text book but i can see some online

ones

[devout snow]

@opal hamlet Has your question been resolved?

[devout snow]

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[oak sage]

can someone explain this bullshit

[oak sage]

algebra 2 sucks

yeah

i don’t understand the end behavior

and the rest

i know that

but like

idk how to actually figure it out

i lowkey lost my notes

bro

i didn’t join this server so someone could tell me to go to a website

[restive river]

whos good at precalc

[pseudo vine]

hmm

[restive river]

y=4 is one horizontal asymptote

but as x approaches -infinity, y=4

?

.

yea got it

the issue is

I cant differentiate

between how x approaches -infinity to infinity

between

[oak sage]

dude jus ttook over my channel

[restive river]

obv

no one is gonna respond to mine

and plus

I respond wayyyy

faster

[pseudo vine]

y=-1

[restive river]

as x approaches -infinity?

or infinity?

[pseudo vine]

-infinity

[restive river]

thx g

yes

.

theres 2 asymptotes here right?

y=5 and y=-2?

[pseudo vine]

Yep

[restive river]

whats the limit

no it has to like

touch the line thingy

[pseudo vine]

It wouldn’t be an arrow

If it wasn’t

An asymptote

[restive river]

so for y=5

y=-5

as x approaches -infinity

and for 5

uhhh

idk

[pseudo vine]

wait for y=5, as x approaches infinity, and for y=-2 and x approaches negative infinity

negative infinity*

[restive river]

so both positive infinity?

[pseudo vine]

no, y=-2 is negative infinity

[restive river]

o

11

i js took the sat

and

uhh

ye

[pseudo vine]

what you get

[restive river]

i js took the november one

it comes out on the 21st

its my first one

[pseudo vine]

oh ok

[restive river]

seems right

[pseudo vine]

Delta math?

[restive river]

yea

ts my last one

and im done

so asymptote at 5 and -4

as x approaches infinity, y=5

[pseudo vine]

negative

infinity

[restive river]

why

oh it goes down

like the curvy thing

[pseudo vine]

f(x) is 5 as x approaches negative infinity

no no

It goes to the left

[restive river]

OH

so for -4?

its positive

because it goes to the right?

[pseudo vine]

f(x) = -4, as x approaches infinity

Yep

[restive river]

DAMN BRO

couldve soloed this

[pseudo vine]

If it goes left, it’s negative

If it goes right, it’s positive

[restive river]

thx g

also u took the sat before right?

[pseudo vine]

Lmao

[restive river]

who

[pseudo vine]

ignore my friend

[restive river]

functions r ez

[pseudo vine]

he’s being sarcastic

[restive river]

I was doing it js now

lol

what u got

if 1600

need a masterclass

asap

.

[pseudo vine]

Lmaooo

[pseudo vine]

i can solve IMO problems btw

yeh

Right @limber bough

[restive river]

wow

[pseudo vine]

Aight bro that never happened

[restive river]

thats ez

[devout snow]

@oak sage Has your question been resolved?

[oak sage]

how do i get the table values

don’t look at the graph

[oak sage]

<@&286206848099549185>

[cunning valley]

Hi

table values is just

one side you put x, one side you put y

[turbid bane]

Make a table of thd values of x and y

[cunning valley]

then put like -2, -1, 0, 1, 2

for x

then solve for the according y value

[turbid bane]

How many though?

[cunning valley]

as many as makes sense

[oak sage]

howw do i get the y

[untold ravine]

use the function f(x)

[cunning valley]

you plug in the x value

into the initial equation

[oak sage]

ok thanks

i’m so done for on this test bois 🥺

[cunning valley]

so for -x^4 + 3x^3 + x^2 - 3x

[cunning valley]

when is your test

[oak sage]

tommorow

first hour

ima wake up extra early tho

study a lil

how do i know what to put on the x side of the table values

[cunning valley]

^

generally I think you usually put -2, -1, 0, 1, 2?

but like

[oak sage]

nah

well

idk if ur right or not

but my teacher does it another way sadly

[cunning valley]

I mean like

not necessarily that

but that's super common

but like if it changes direction at -2

how does your teacher do it?

[oak sage]

i’m looking at my notes and she seems to do it different everytime
like one of my equations the table was
-3
-1.5
1.5
3
and another was
-3
-1
1
2.5
4

so idrk what to do

[cunning valley]

Just make sure

your points

cover all of the turning points

so for example if the "action" of the graph happens from -3 to 3

try to do points from -3.5 to 3.5 that make sense

[oak sage]

what do you mean by action of the graph

[cunning valley]

like where it turns

turning points

[oak sage]

so the real zeros?

[cunning valley]

ig so

😭

[devout snow]

@oak sage Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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.
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[languid jungle]

I'm not sure how to tell when to use V or the ^

[misty crest]

i mean why do you think it would be ^

look at the middle two rows

[languid jungle]

I don't think I'm just asking how to differeniate cus I dont get the concept sorry for not clarifyingg

[cunning valley]

^ v -. and or not?

v is or, so P or Q is true

^ is and, so P AND Q is true

[languid jungle]

oh that actually helps a lot I kind of been thinking of it differently

[cunning valley]

(i've never learned this before wait for someone else to clarify)

just kinda googled it

😔

[languid jungle]

nah you got it right

[cunning valley]

I'm not sure about not though

-.

[languid jungle]

I just read your message in my head applied so its easy this way. I've just been lost how to do it

it's V

[cunning valley]

what would not(1, 1) return?

oh

[languid jungle]

true

so 1

[misty crest]

P not Q is nonsensical

[cunning valley]

P not Q

[misty crest]

it has no truth value

[cunning valley]

so it would be false then?

1 is not 1

wait what

1 is 1

wait what

[misty crest]

!help

[devout snow]

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

[calm blade]

Ts means neither of them 1

[cunning valley]

oh its

is 1 not equal to 1

so its false

sorry ill stop

[misty crest]

🤔

[calm blade]

Wdym

[misty crest]

1 means true

0 means false

they should be using T and F but they are choosing to use 1 and 0

[languid jungle]

yeah my math just like that but we know the meaning of it as T and F

[misty crest]

are you a CS major

[languid jungle]

yeah

[misty crest]

makes sense

anyways do you need any help still

[languid jungle]

nope sorry I just had a confusion but It clicked to me now

Ill close

.close

[devout snow]

Channel closed

Closed by @languid jungle

Use .reopen if this was a mistake.

[devout snow]

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

Can I hop in a call with someone and share my screen with them I need help with trigonometry

[fossil locust]

sorry, we don't do calls on this server

[knotty yacht]

Okay I’ll send a photo

[fossil locust]

which questions do you need help with?

the main thing is to use the conversion (pi radians) = (180 degrees)

[knotty yacht]

We can start with 2

How do I convert it to find the solution

[fossil locust]

yep, so for 2a, theta = -5 * (180 degrees)/6 right?

[knotty yacht]

Yes

[fossil locust]

and you should realise that's negative

but that's okay

you can just add 360 degrees and it won't change the angle

[smoky gyro]

south w the clutch

[knotty yacht]

Yes I see that it is negative

I just don’t understand how I’m supposed to know which way the angel is supposed to go. Is there an equation I need to write to get the degree?

It wants me to label it on the xy plane

[fossil locust]

if you follow the steps I told you, you should know which angle it is

it's one of the angles on your unit circle

[knotty yacht]

Would it look like this? And that is the unit circles flipped because it’s a negative right?

[fossil locust]

nearly

should look like this

oh and you also need to label that angle as $210^{\circ}$

[woven radish]

south

[knotty yacht]

Okay I’m gonna try B

[fossil locust]

or actually you might be correct

I think for q2 you're not using reference angles, so yeah -150 degrees is just -150 degrees

yep

so if you do 2b you should find that it's nearly 2 times around the unit circle

[knotty yacht]

Where does does the 8pie/4 come from

[fossil locust]

you can think of 15pi/4 = 8pi/4 + 7pi/4

so 8pi/4 = 2pi

2pi is a very important angle, cause that's one full turn around the unit circle

[fossil locust]

with this conversion, it's 2 * (180 degrees) = 360 degrees

[knotty yacht]

Okay thank you

[fossil locust]

no worries!

I'll just give you 1 more idea that will help you for the other parts and I'll let you go

pi radians = 180 degrees

divide both sides by pi, and you get 1 radian = 180/pi degrees

so 2 radians? that's 2 * 180/pi degrees
3 radians? 3 * 180/pi degrees

[fossil locust]

if you're done for now type .close

[knotty yacht]

Okay sorry I was looking at some more equations and finishing the last 2

If I close the chat can I open it later if I need more help

[crystal dawn]

you are always welcome to open a new channel, even if your current one is locked or occupied.

[knotty yacht]

I am lost on C and need help with D please

.close

[devout snow]

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[hard ocean]

How do I prove that given a symmetric and PD matrix, the diagonal elements are positive

[glass canopy]

What are the conditions required for a matrix being PD?

[stone stump]

do your previous proof backwards. assume a diagonal entry is <=0. construct a counterexample

[devout snow]

@hard ocean Has your question been resolved?

[hard ocean]

.solved

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[potent delta]

Hello , i nned help please
I want to learn how to solve olympiad problems and puzzles, but i have only middle school experience 8th grade (3th Year in middle school in Algeria)
Can u give me some advices and books and i will be very happy.
Thanks.

[solar goblet]

personally i don't do olympiad, but i assume you just practice olympiad problems to get a feel for them

you should try asking this in discord.gg/mods

[potent delta]

Ok

[lunar parcel]

u can study geometry on art of problem solving

( and not only geometry)

https://artofproblemsolving.com/wiki/index.php/Olympiad_books?srsltid=AfmBOopFgtB2C1q2RTXVIlFF3BDuwY2ygg9DqzN4vnVuyZAvVatKq5pF

[devout snow]

@potent delta Has your question been resolved?

[potent delta]

Ok ,

[devout snow]

@potent delta Has your question been resolved?

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[ocean thicket]

How is it called when you need to find a function of a specific point and you use :
X^n = nx^n-1
And you mark it using y’ instead of y

[ocean thicket]

What’s the method name is what I’m asking

[late scaffold]

power rule of derivatives, I suppose?

[ocean thicket]

oh yeah a derivative

Thank you

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[verbal knot]

why cant i just take the lawn of both sides?

they made it a quadratic

[eager cobalt]

take take

send yr working too

[verbal knot]

ok

[stone stump]

ln or log

not lawn

[verbal knot]

lawn

[stone stump]

but well, ln doesnt simplify it really all that much

[eager cobalt]

lawn is log x base e

[stone stump]

you probably have made some simplification thats false

[stone stump]

ln(4+7e^(-3x)) is not the same as ln(4)+ln(7e^(-3x))

you have to take ln of the entire left side

[verbal knot]

ok

how do you simplify that lawn than

is it not possiblus?

[eager cobalt]

sending 4 to other side helps?

[stone stump]

no

then you have ln(3e^(2x)-4) on the other side

not helpful either

dont take ln

turn it into a quadratic

[verbal knot]

can you simplify the lawn?

[stone stump]

no

[verbal knot]

ok

[eager cobalt]

first take e to power 2x terms on one side then simplify em first

then try with lawn

[verbal knot]

how am i supposed to spot this first try?

my first instinct was to take lawn

[eager cobalt]

uh idk much of these type of qns

[stone stump]

well you see e^(-2x) and e^(2x) so its not a stretch to think "hmm maybe I should substitute that"

then you get u and 1/u and from there its automatic

[verbal knot]

also is it lawn or lin or lan?

[stone stump]

ln

[verbal knot]

ln?

lin?

[eager cobalt]

log base e is aka lawn

[soft umbra]

$\ln x = \log_e x$

[woven radish]

🌙 ЅκψΑиdΝιɡħτ

[stone stump]

if you want to pronounce it as lawn, thats one thing

but do not write lawn

its nonsense

do not do it

[verbal knot]

why do they write it lawn (x) than?

[eager cobalt]

fr

[stone stump]

its ln

[eager cobalt]

not written

[verbal knot]

why is ln(x)=loge(x)

[stone stump]

ln stands for logarithmus naturalis

it has a special name cause history

[verbal knot]

oh ok

[eager cobalt]

log x base e is aka natural logarithm so that can be a reason

[verbal knot]

did they just do to make it look cool 😆

[eager cobalt]

betr representation and method of identifying log base 10 and base e in a moment fs

[verbal knot]

does log10(x) have a fansi name?

[eager cobalt]

nothing

nada

called as log x itself

[simple seal]

log x is usually ln x

log base 10 is sometimes seen as lg x

[eager cobalt]

oh

sm new info for me never heard or saw

[simple seal]

not official though i think

[eager cobalt]

yea yea

[stone stump]

in university etc no one really cares about any log except ln

sometimes log_2

in particular in those contexts log just means log_e

so its not a good idea to think that log means log_10

sadly some schools do teach that

[eager cobalt]

how can they

[verbal knot]

how do i verifify if one of the stationary points is maxima or minima?

2 derivative test?

[stone stump]

yes

[eager cobalt]

if >0 minima <0 maxima

[verbal knot]

because of the happy and sad face

i see

.close

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[devout snow]

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[potent delta]

Hello , i nned help please
I want to learn how to solve olympiad problems and puzzles, but i have only middle school experience 8th grade (3th Year in middle school in Algeria)
Can u give me some advices and books that is good to my experience and it will learn me about equations algebra geo nt ....etc and i will be very happy.
Thanks.

[nova jasper]

the aops series of books https://artofproblemsolving.com/store/list/aops-curriculum

[potent delta]

I want free books and the best book in the series

[stone stump]

should we also gift you a car?

[nova jasper]

https://artofproblemsolving.com/wiki/index.php/Resources_for_mathematics_competitions

[potent delta]

Why u say like that , i wanted to ask only.

[potent delta]

Thank you so much

[devout snow]

@potent delta Has your question been resolved?

[devout snow]

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[subtle ermine]

dont the two equations i highlighted immediately prove the proposition?

[tiny panther]

They prove that is c *lcm(a, b) is a common multiple of ca and cb, but not that it's the least common multiple

[subtle ermine]

i think i get it i guess

.close

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[shrewd phoenix]

Hello I need Help for my homework pls

[shrewd phoenix]

The 1 and the 2

In english the order is factorize and reduce the expressions

.close

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[elfin cedar]

if x³=x+2, how much is x¹⁰

[elfin cedar]

if x³=x+2, how much is x¹⁰

[austere wave]

do u want to know the value of x?

[elfin cedar]

no

the value of x¹⁰

did i do something wrong?

[supple knot]

what could you have done wrong? you haven't shown anything besides the question

[pseudo basin]

show your work

[elfin cedar]

this was a question lf the hardest math test in brazil

[pseudo basin]

show your work

[elfin cedar]

oh

okay

i cant now

im in school

the solve isnt with me

[pseudo basin]

wdym you can't. how can you expect us to know what you did or didn't do wrong

we don't even know what answer you got

[calm blade]

:sus_picious

[elfin cedar]

oh

on this channel you help us solve problems

i thought it was an ai

[austere wave]

yea but we cant solve them for you

[pseudo basin]

!noai

[devout snow]

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).

[elfin cedar]

sorry

[calm blade]

!nosols

[pseudo basin]

(also the question itself is kinda sus...)

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[elfin cedar]

its just because i saw a bot

i entered here 20 mins ago

im on 8 grade

on school

[polar chasm]

maybe wait till u get home then

[elfin cedar]

ok

like

do you know ITA

[obtuse wedge]

then long divide it for other solns and check options

[elfin cedar]

its the hardest faculty in brazil

oh

i think i got it when i solve

yeees

wait

[polar chasm]

u sure?

[elfin cedar]

i dont remenber where i stoped

[calm blade]

how is it a soln?

[obtuse wedge]

oh

wait

nvm

sign mistake

[polar chasm]

it has only one really ugly solution (irrational, can only be expressed with lots of very ugly roots)

and x^10 will also be really ugly

[elfin cedar]

yes

[polar chasm]

the best that can be really done by hand (unless you are a maso type) is reducing x^10 to some quadratic in x

[calm blade]

this is lost cause

[elfin cedar]

but this was the problem

[polar chasm]

the exact phrasing of the problem is really important. Maybe you missed some cruicial piece of info?

[elfin cedar]

no

[polar chasm]

can u send the exact pic?

[elfin cedar]

the question was saying

no

i've family link...

F

[polar chasm]

I see, can u copy it word for word then?

[elfin cedar]

okay

[polar chasm]

exactly as its stated (even if in different language)

[elfin cedar]

like in portuguese?

[polar chasm]

sure

[elfin cedar]

Considere na equação a o valor integral x³ = x +9, determine o valor de x¹⁰

wait

sorry

it was x+9

[polar chasm]

okay, now we might be able to guess a solution

do you know rational root theorem or nah?

[elfin cedar]

yes

[lyric hornet]

-# I don't think that has any integral solutions?

[polar chasm]

actually its still bad :/

yeah

[elfin cedar]

oh

[polar chasm]

so it still has ugly sol

are u sure the x^3 isnt x^2 or sth else?

[elfin cedar]

what do you mean with ugly sol?

[polar chasm]

and that all the signs are correct?

[polar chasm]

,w x^3 = x + 9

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by methisalwaysright

[elfin cedar]

im not fluently in english

not at all

[lyric hornet]

can you send a picture of the question?

[polar chasm]

this is the solution, as you can probably see, its not easy to find this by hand

[polar chasm]

family link, cant

[calm blade]

brodie you sure?

[elfin cedar]

im on school

And i have family link

[calm blade]

was it x^3=x+6

[elfin cedar]

almost

[calm blade]

:mammamia

[elfin cedar]

guys

i promisse when i get gome i'll send the pic

[polar chasm]

not much can be done with the current question, so there are 2 options:

1. you misremember it / misread it, in that case, once you correct it you can come back and ask the correct question

2. you are only supposed to simplify x^10 to something a bit nicer in x. The process of that would be writing x^10 as (x^3)^3 * x = (x+2)^3 * x, then expand it and repeat similarly, until you get a quadratic in x. (Gonna be sth like 13x^2 + 16x + 12)

[calm blade]

ig close it for now

[rustic bluff]

@polar chasm

[polar chasm]

Ye?

[supple knot]

!noping

[devout snow]

Please do not ping individual helpers unprompted.

[rustic bluff]

What do you do in coding?

[polar chasm]

depends ig, and please move this to #chill or #discussion

[devout snow]

@elfin cedar Has your question been resolved?

[devout snow]

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[oblique rover]

Given the linear fractional transformation
[
f(z) = \frac{z + i}{z - i},
]
find ( f(M) ) if ( M = { z \in \mathbb{C} \mid |z| = 1 }; )

[woven radish]

Slowaq

[oblique rover]

how should i do this i have no clue

in school we were using diagrams like this but as im looking at them one month later i im completely lost

[supple knot]

plug z = e^(i t) for any real t into f(z)

[oblique rover]

alright and what then?

[supple knot]

what do you get

[oblique rover]

[
f(e^{it}) = \frac{e^{it} + i}{e^{it} - i} = \frac{e^{it} + e^{\frac{i\pi}{2}}}{e^{it} - e^{\frac{i\pi}{2}}}.
]

[woven radish]

Slowaq

[supple knot]

yea you can find split that into real and imaginary parts and vary t from [0, 2pi] and see what the shape is

[devout snow]

@oblique rover Has your question been resolved?

[devout snow]

@oblique rover Has your question been resolved?

[devout snow]

@oblique rover Has your question been resolved?

[inland carbon]

I would multiply top & bottom by i then use a "half angle formula"

[devout snow]

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[hazy plover]

can someone help me with this

[hazy plover]

This is what I have rn

(Not a lot) lol

Im working on B)the line y=2

On second thought its y=2 so it should be like 2-y not x

Oops

[devout snow]

@hazy plover Has your question been resolved?

[hazy plover]

.close

[devout snow]

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[mortal escarp]

I have a question

[mortal escarp]

is 1 correct?

i. prove injectivity ii. prove surjectivity

[hardy trail]

Yep, reasoning for Q1 looks good.

[mortal escarp]

ok thanks

What about 2 and 3?

[hardy trail]

At least, f : R -> R where f(x) = |x| is not surjective,

But f : R -> R^+ is

[mortal escarp]

what is R -> R^?

[hardy trail]

Set of reals to set of positive reals

$\mathbb{R} \to \mathbb{R}^+$

[woven radish]

Redfern Station

[mortal escarp]

right

but the question states R -> R

[hardy trail]

Yeah, I'm just adding that fact :)

[mortal escarp]

ok thanks, yea that helps build more intuition for a newbie like me

[hardy trail]

If a function is not surjective, it might be possible to restrict the codomain so that it is surjective.

[mortal escarp]

nice

good to know

regarding 2i. what is the issue there, sorry can't read some of that writing

[hardy trail]

Oh there's no issue

I'm just saying that

a^3 = b^3 only implies a = b if both a, b are real numbers

Because by the fundamental theorem of algebra, every polynomial has three complex solutions

It's just a little extra but yeah, the fact that we have real numbers means theres only one solution

Like

If you solved x^3 = 1, the only real solution is x = 1

[mortal escarp]

oh, I see, so it is right since we are going from R -> R, but if the domain / codomain included complex numbers, there would be more solutions>

[hardy trail]

Yep exactly

Its definitely not injective is the domain was complex

[mortal escarp]

is this true only if we are dealing with polynomials of degree 3?

[hardy trail]

Yeah, polynomials degree 2 or more as well

I mean fundamental theorem of algebra applies to all polynomials

[mortal escarp]

so n number of complex solutions = polynomials of degree n

[hardy trail]

Yep

[mortal escarp]

ok awesome

[ionic heron]

!reopen

[mortal escarp]

what about B1 and B2

same thing, prove i. injectivity and ii. surjectivity

forgot to add that B2. ii is not surjective

[mortal escarp]

?

[devout snow]

@mortal escarp Has your question been resolved?

[mortal escarp]

not sure if this channel got closed

[devout snow]

@mortal escarp Has your question been resolved?

[mortal escarp]

Is B1 and B2 correct?

[ebon coyote]

Both seem fine to me

Wait actually, for B2, I'm not quite sure

Isn't your function's domain there from 0 to 1?

If f is restricted to that domain, then it's bijective (check a graph of this)

[devout snow]

@mortal escarp Has your question been resolved?

[devout snow]

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[keen sundial]

@upbeat forge I did press the SD button

and the context is general

[soft umbra]

what's the original question?

[keen sundial]

its giving me

decimal approx

on the calc

[winter patrol]

been a while since i used a casio,
but might be due to the number of fractions you put into it

try doing it in parts

like simplify the numerator first

[devout snow]

@keen sundial Has your question been resolved?

[keen sundial]

the numerator has brackets

I do that first

Im not sure but I am getting this now

which doesnt match the answer key

[winter patrol]

your fraction is unsimplfied

[devout snow]

@keen sundial Has your question been resolved?

[keen sundial]

It’s giving me a decimal

Also

I need help with this

18

Im not sure if my working out is correct

[winter patrol]

what happens when you press the SD button on that screen

[keen sundial]

and I dont even know what the question is actually asking

[keen sundial]

nothing happens

its pretty unusual

[winter patrol]

try the $\boxed{\qed '"}$

[woven radish]

ραμOmeganato5

[keen sundial]

degree box?

[winter patrol]

argh, wrong one,
i mean the fraction button again

$\frac{\boxed{\ }}{\boxed{\ }}$

[woven radish]

ραμOmeganato5

[keen sundial]

instead of SD

I press fraction button?

[winter patrol]

try and see what happens

[winter patrol]

after you get the output

[keen sundial]

Yeqh after the decimal

I pressed fraction button

[winter patrol]

hmmm,

[keen sundial]

but Its alright

I think

[winter patrol]

S to D should be working

[keen sundial]

the question didnt specify

[winter patrol]

might need to set it up

shift mode/setup

for 18, looking up infinite geometric series
should give you the info you need
and then using that, solve an inequality

[keen sundial]

Im confused

wdym?

[winter patrol]

which part

[keen sundial]

for 18, looking up infinite geometric series
should give you the info you need
and then using that, solve an inequality

[winter patrol]

ok, so look up

infinite geometric series

[keen sundial]

on yt?

[winter patrol]

no

just google

[keen sundial]

ohh

[winter patrol]

watch a vid if you want more depth
but just the basic properties is enough

[winter patrol]

so

when do geometric series have a limiting sum (converge)

[keen sundial]

when r is less than 1

but greater than -1

so it cant be -2

[winter patrol]

i mean yes, but how did you jump to that single value?

[keen sundial]

is my working out incorrect/

[keen sundial]

used -2 as an example

[winter patrol]

the working is incorrect

[keen sundial]

which part?

[winter patrol]

why did you set S_inf equal to 1

you were able to identify
r = 2x
now apply

when r is less than 1
but greater than -1

[keen sundial]

I cant see where I set S_inf equal to 1

[winter patrol]

how did you get

[keen sundial]

i multiplied it by

(1-2x)

both sides

But Im pretty sure

we arent allowed to do that

[winter patrol]

yeh but what was the left side before it became 1-2x

your work implies that you had 1 = 2/(1-2x)
if you started with 1 = 2/(1-2x)
you'd be allowed to multiply both sides by 1-2x
to get 1 - 2x = 2
but the issue is how you got 1 = 2/(1-2x) in the first place

[keen sundial]

S_inf

[winter patrol]

S_inf is S_inf

multiplying S_inf by (1-2x)
gives S_inf * (1-2x)

[keen sundial]

I see

still incorrect?

[junior grove]

Hey can you help me with my homework

[keen sundial]

!help

[devout snow]

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

[winter patrol]

you were able to identify
r = 2x
now apply
when r is less than 1
but greater than -1

[devout snow]

@keen sundial Has your question been resolved?

[devout snow]

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[gloomy kernel]

y=-3(1/2)^x solve this

[sand olive]

Hi, what is asked to be solved?

[gloomy kernel]

y=-3(1/2)^x To plot the graph of a function

[pseudo basin]

do you know how exponential functions look in general

[gloomy kernel]

No😭

[haughty hull]

Try using desmos it is really good for visualising different functions. There u can add parameters to the function and by changing them see how it reacts

https://www.desmos.com/calculator?lang=en

[pseudo basin]

ok then review that

you can't really do much otherwise

[haughty hull]

Also the general way of plotting a function is just knowing general view of it and finding important points: where graph intersects OX and OY, extremums (minimums and maximums of the function). Also, depending on the function u can find some other convenient points which will help to build the function more accurately

[devout snow]

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[mortal escarp]

Is this correct? Proving injectivity in i. and surjectivity in ii.

[mortal escarp]

For both B1 and B2

[harsh sierra]

You need to explain more why
e^a = e^b --> a = b

Same thing with tan

Hmm.... I guess you could say it has an inverse

[harsh sierra]

But I think its a good exercise to prove that

[devout snow]

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[lapis wolf]

What is the Fourier transform?

[grand warren]

$\hat{f}(t)=\int_{-\infty}^\infty f(x) \exp(-i2\pi tx) dx$

[woven radish]

tm

[tender cobalt]

since I dont know enough about this to really tell you, I can say 3blue1brown made a good video that explains what this is for

[lapis wolf]

i watched before

but I'm struggling to understand the intuition behind this. Why does this process of multiplying and integrating actually isolate just that one frequency component? What's the underlying mathematical principle that makes this work?

[grand warren]

the orthogonal projection

[lapis wolf]

Am I right to link this to a higher-dimensional vector space analogy?

[grand warren]

if we define for each $\xi\in\mathbb{R}$ the family
$e_\xi(x)=e^{-2\pi i\xi x}$, she is orthonormal in the distributions sense and
we define the Fourier transform of $f$ as the orthogonal projection coefficient of $f$ onto $Span(e_\xi)$:
$$\widehat{f}(\xi)=\langle f,e_\xi\rangle=\int_{\mathbb{R}}f(x)e^{-2\pi i\xi x},dx.$$

[woven radish]

tm

[grand warren]

yeah as i said for example the family e_xi isn’t orthonormal in the usual sense but in the distributions sense

[lapis wolf]

Then how does the orthogonal projection (inner product) actually separate the individual frequency components from the complex signal?

[smoky gyro]

oh tm

[grand warren]

take 2 pure frenquencies :$e^{2\pi i \xi x}$ $e^{2\pi i \eta x}$

if $\xi\neq\eta$, then
$$\int_{\mathbb{R}} e^{2\pi i \xi x} \overline{e^{2\pi i \eta x}} dx
= \int_{\mathbb{R}} e^{2\pi i (\xi-\eta)x} dx
=\delta(\xi-\eta)$$

which means that \
-when the frequencies are different, the inner product is zero -> they are orthogonal.
\
-when the frequencies match, the integral gives something nonzero -> they align

[woven radish]

tm

[grand warren]

yogurt

[grand warren]

idk if that’s what you were talking about

[smoky gyro]

oh tm what is this math

[lapis wolf]

yeah i wanna know about the process of it

[lapis wolf]

How does the inner product (multiplying and integrating) mathematically enforce orthogonality to isolate one frequency and eliminate all the others

[grand warren]

if u have $f(x)=A e^{2\pi i\xi_0 x} + B e^{2\pi i\eta x},
\ \xi_0\neq\eta,$ its Fourier coefficient at frequency $\xi_0$ is

$$\langle f, e_{\xi_0}\rangle
= \int f(x) e^{-2\pi i \xi_0 x} , dx.
= \int A e^{2\pi i\xi_0 x} e^{-2\pi i\xi_0 x}, dx
\int B e^{2\pi i\eta x} e^{-2\pi i\xi_0 x}, dx.
$$ $$= A \int 1 , dx
B \int e^{2\pi i(\eta - \xi_0)x}, dx.$$

the first term is constant -> it integrates to something significant and the second term is highly oscillatory -> integrates to zero in the limit

[woven radish]

tm

[grand warren]

we return to the dirac delta

[lapis wolf]

well I'm developing an algorithm to recover the original waveform of a cosmic signal, aiming to minimize attenuation. What is the fundamental principle of the Fourier Transform that allows it to suppress signal degradation or attenuation?

[grand warren]

let $r(t)$ be the original waveform of a cosmic signal and $h(t)$ a linear invariant filter

1. convolution :
   $$s(t)=(r*h)(t)=\int_{\mathbb{R}} r(\tau),h(t-\tau),d\tau.$$

2. frequency domain transformation:
   $$R(f)=\mathcal{F}(r)(f),\ H(f)=\mathcal{F}(h)(f).$$

3. use
   $$\mathcal{F}(r*h)=\mathcal{F}(r),\mathcal{F}(h).$$

4. frequency filtering :
   $$S(f)=R(f),H(f).$$

5. back to the temporal realm :
   $$s(t)=\mathcal{F}^{-1}(S)(t)=\mathcal{F}^{-1}(R(f)H(f))(t).$$

[woven radish]

tm

[grand warren]

if i remember right 🥀

idk if you know the convolution *

[kind bloom]

Uh can someone help me 😭

[slate peak]

!help

[devout snow]

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

[devout snow]

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).

[kind bloom]

Owh thanks

So I can just write it

So, I have a big ahh digit (several millions of digits long 2^10000000 of something like that)

I wanna be able to find the smallest expression that it can be expressed in, for example (8**11)+1 = 8589934593

[lapis wolf]

I don't fully get the whole convolution thing yet, but I totally get the gist. I'm gonna hit the books and really grind to figure it out. Seriously, thanks a ton for all the info—that was super helpful!

[grand warren]

vro use another channel 🥀

[kind bloom]

Oh which one 😭

[grand warren]

u welcome🫂

[grand warren]

one of these

[kind bloom]

Okie thank you 😭

[grand warren]

np

[lapis wolf]

I sent you a friend request! Can you accept it?

I'd love to be your friend.

.close

[devout snow]

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[grand warren]

ye i didn’t see lol

[lapis wolf]

It's all good, lol.

[devout snow]

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[spring oasis]

Hi, I need some help with this one

they give me the third order taylor poly of f centered at (1,-2) and I need to calculate the limit as (x,y) tends to (1,-2)

[woven radish]

Renato

[pseudo basin]

try replacing f with its taylor poly and see if you can cook anything with that

alternatively substitute u := x-1, v := y+2 and see if anything shakes out

[spring oasis]

polar coords

[spring oasis]

kinda gets messy if I do change of variable, no?

[pseudo basin]

i think some dust should settle

but it's going to be somewhat of a mess

[spring oasis]

in a non figurative language what does it mean

im new to english

[pseudo basin]

things should eventually simplify

[spring oasis]

im doing it

got stuck at this step a lil

[sharp zinc]

im new

[spring oasis]

I think this could have went other way, if we used $$\lim_{(x,y) \to (a,b)} \frac{f(x,y) - P_3(x,y)}{\norm{(x,y) - (a.b)}^2} = 0$$

[woven radish]

Renato

[spring oasis]

things are getting out of hand in here

[devout snow]

@spring oasis Has your question been resolved?

[devout snow]

@spring oasis Has your question been resolved?

[devout snow]

@spring oasis Has your question been resolved?

[spring oasis]

For Christ sake dude

Someone help me

[faint gorge]

why didnt you continue?

[spring oasis]

Don't know how

[spring oasis]

Also the second alternative I suggested might be simpler

We can do both paths tho

[faint gorge]

well u didnt write it out did you?

[faint gorge]

I dont quiet get that tbh

[spring oasis]

It's like

The condition for the Taylor polynomial to exist

One second

[faint gorge]

Oh ofc