help-42

[calm coral]

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[calm coral]

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[topaz raft]

the algebraic multiplicity of lambda = 2 is 1 and its geom multi is also 1 is it not because it has one parameter

[topaz raft]

but algebraic multi for lambda = 1 is 2

does each algebraic multiplicity for both eigenvalues have to match?

[sharp cargo]

okay uhh

im pretty dumb

what is algebraic or geometric multiplicity

[kind axle]

Brother

[unkempt drift]

something from linear algebra at uni

[sharp cargo]

yes i know

i just dont remember any algebra

if u give me something it might jog my memory

[unkempt drift]

oh it's not the algebra you learn in school

[topaz raft]

algebraic is the integer k for (b - lambda)^k where b is an eigenvalue

[sharp cargo]

why would it have to match

you can see that the algebraic multiplicity is different for both

[unkempt drift]

no, the correct result is that algebraic multiplicity geq geometric multiplicity

[topaz raft]

but the algebraic multi and geo multi for eigenvalue 2 are both 1 arent they

[unkempt drift]

that's not a problem

it's ≥

,w {{1,0,1},{0,2,0},{0,1,1}} char poly

[potent lotus]

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[unkempt drift]

oh wait for the eigenvalue 2? ah

[topaz raft]

yea

for lambda = 1 then its alg multi is 2

[glass heart]

no...

[unreal stream]

@topaz raft he is asking you politely to accept his freind request

[glass heart]

tho you probably at least mean the correct thing

[topaz raft]

what do you mean?

[glass heart]

that sentence is wrong

[topaz raft]

well im saying like the number of repeated roots ig if u call it that is the algebraic multiplicity

[sharp cargo]

algebraic multiplicity is number of times the root is repeated in a characteristic poly

[topaz raft]

which is the number k here which we already found for E1 and E2

[sharp cargo]

wait im confused whats ur question now

[topaz raft]

im asking why its not diagonalisable

for eigenvalue 2 its algebraic and geom multi are both 1

[sharp cargo]

what says its not diagonalisable?

[sharp cargo]

if the algebraic and geom multiplicity is the same it should be no?

[topaz raft]

right here

[sharp cargo]

oh wait

it has to match

[topaz raft]

thats my question

[sharp cargo]

why does it have to match?

[topaz raft]

what?

[sharp cargo]

are you asking why gm == am for it to be diagonalisable

[topaz raft]

well look

[unkempt drift]

that comes from the fact that the dimension of the eigenspace for v1 and v2 is 1

[sharp cargo]

i believe the eigenvectors form the diagonal matrix

[topaz raft]

if we look at eigenvalue lambda = 1 it has AM = 2 right

[unkempt drift]

so 2 dimensions in total, 2 < 3

for the 3x3 matrix

[topaz raft]

are we using this fact here?

or are we talking about something different

[unkempt drift]

different

[topaz raft]

this theorem

a matrix A of n x n size is diagonalisable if each eigenvalue has AM = GM

[unkempt drift]

ah I see okay

[topaz raft]

so each eigenvalue in this case 1 and 2

[unkempt drift]

yes I see now, so that's just another rephrasing

no, the geometric multiplicity is 1 for lambda = 1

[topaz raft]

how?

[unkempt drift]

but the algebraic multiplicity is 2

[topaz raft]

ye algebraic multi is 2

[unkempt drift]

,w {{1,0,1},{0,2,0},{0,1,1}} eigenvectors

[sharp cargo]

how many eigenvectors did u find for each value

[unkempt drift]

,w {{1,0,1},{0,2,0},{0,1,1}} eigenvalues and eigenvectors

[potent lotus]

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[topaz raft]

so if for eigenvalue 1 if it had geo multi = 2 as well then it would be diagonlisable?

[unkempt drift]

yes

that's not the case here however

[sharp cargo]

yes

thats just by definition

[unkempt drift]

,w eigensystem {{2, 0}, {0, 2}}

[potent lotus]

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[sharp cargo]

am must = gm

[unkempt drift]

you can look at this also

,w char poly {{2, 0}, {0, 2}}

[potent lotus]

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[unkempt drift]

this is a case where AM = GM = 2

[topaz raft]

they didnt write the working out for lambda = 1 eigenvalue so they only showed the geo multi for eigenvalue of 2

but ig if u do the working out then

youll get one parameter as well?

[unkempt drift]

ah okay so it's a problem with the working

[topaz raft]

for eigen 1

[sharp cargo]

find the eigenvectors for lambda = 1

[sharp cargo]

yes

[topaz raft]

i see

[sharp cargo]

sorry i didnt realise what you were asking ahaha

[topaz raft]

allg

ok thanks guys

[sharp cargo]

if you sub in 1, try and find the eigenvectors

[topaz raft]

.solved

[calm coral]

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[unkempt drift]

yeah cause you get
(0 0 1)
(0 1 0)
(0 1 0)

and when multiplied by (x, y, z)^t, you get (z, y, y) so that forces y = 0 and z = anything, which is 1 dimensional

[sharp cargo]

wait is the blue writing ur notes

u wrote it wrong

[topaz raft]

nah its my lecturerer's notes lmao

.reopen

[calm coral]

✅

[sharp cargo]

\ = 2 has geometric of 1 and algebraic = 2

okay ur lecturer wrote it wrong lol

the underlined part is wrong

it should be "geometric multiplicity of lambda = 1 is 1"

[topaz raft]

ok yeah i was confused, cuz i checked the working it said GM = 1 but the AM should also be 1 for eigenvalue of 2

[sharp cargo]

ur lecturer is silly

thats very unfortunate

also funny no one in ur class picked it up

is this unsw?

[topaz raft]

nah lmao

usyd

[sharp cargo]

ah yep

engineering or maths or what

[topaz raft]

js maths

like what this class is?

unsw would be more rigorous lol

in their working out a tleast

[unkempt drift]

lmao

I wonder how it's like studying maths at USyd

[topaz raft]

[sharp cargo]

i study engg and cs at uq

queensland

it sucks here

[topaz raft]

ohhhh

[unkempt drift]

nice, UQ is a nice uni but I think that combination is miserable

CS in particular has a shortage of good lecturers

[sharp cargo]

no honestly uq is terrible

[unkempt drift]

cause they could make 2x the pay working in industry

[sharp cargo]

its actually embarrasing how bad some of the stuff is run here

[topaz raft]

maths is aight, unsw has a much better math dept but physics and chem is goated for usyd

[sharp cargo]

lowkey makes me regret leaving adl

[unkempt drift]

that's why I ask

cause you get compared to UNSW all the time

[topaz raft]

ye

[unkempt drift]

hopefully the maths department is decent

doesn't need to be world-beating

like do you have decent course options, especially for 3rd year

[topaz raft]

yea theres plenty of stuff, unsw has a lot more but let me check

[unkempt drift]

do lecturers and teachers give good explanations when questioned

[topaz raft]

yea the lecturers are pretty good at explaining things and the students pick up on it if theres a mistake so they can correct it

[topaz raft]

engi at unsw is worlds better tho^^

[unkempt drift]

ah it's like my uni then, we're definitely very mediocre for pure maths course selection

[unkempt drift]

same everyone's just so warm here

[unkempt drift]

ofc ANU is the best

UNSW is probably on their level

and everyone else is below

[unkempt drift]

BAHAHA JUST LIKE MINE

why do even 2nd year maths electives only get offered once a year

if you start midyear you're screwed

[sharp cargo]

adl uni?

[sharp cargo]

i dont think anu is the best

[topaz raft]

uni melb is number 1 isnt it

for aus

[sharp cargo]

these rankings

i realise now

are complete poo poo

the only thing they tell u about is research output

[unkempt drift]

yes

[sharp cargo]

not actually about how good the uni is

[unkempt drift]

exactly

even for research yk you've got to find a fricking supervisor

[sharp cargo]

i didnt go to anu for cs because their cs program is outdated as hell

[unkempt drift]

Adelaide only offers geometry-related topics for pure maths research

if you want to do number theory they'd make you do geometry with some application to that

[sharp cargo]

yea ive seen

[unkempt drift]

really? wow

[sharp cargo]

adl maths department is a bit lacking i think

[sharp cargo]

yea imo, i did a tiny bit of research

[unkempt drift]

students have gone to Cambridge and shit

but yeah that's not cause of the uni I feel

[sharp cargo]

yea i think its not the uni, its just people are cracked

[unkempt drift]

I switched out of majoring in maths

[sharp cargo]

tons of ppl in adl got into the quant firms tho

they may have something good going on in cs

[unkempt drift]

that's also true

Jane Street came last year

[sharp cargo]

ah yea same at uq

[unkempt drift]

my friend told me they don't teach well

[sharp cargo]

yea possibly

i think they have a summer program

which is very very good

for something

[unkempt drift]

but yeah I think the societies are quite supportive regarding work opportunities

[sharp cargo]

my friend just got an atlassian internship

[unkempt drift]

have no direct experience but that's my general impression

[sharp cargo]

at least smth is going good

[unkempt drift]

maths society's fairly dead at ours

[sharp cargo]

oop

[unkempt drift]

if you look at the UNSW maths society, not to compare, they're really really active with what like 5000 members

[sharp cargo]

ive seen their reels

last year

cs reels go crazy too

[unkempt drift]

mhm

[sharp cargo]

are you a first year?

[unkempt drift]

3rd year lol

[sharp cargo]

oh what

[unkempt drift]

yeah

[sharp cargo]

ohhh sorry

i forgot u werent asking the question whoops

[unkempt drift]

that's very true

[topaz raft]

i have unsw math notes for first year and the pdf they use and its so much more rigorous and detailed compared to usyd even comparing with advanced and regular stream

[sharp cargo]

i thought u were asking eigen questions as a third year ahhaha

[unkempt drift]

I've forgotten a lot of 1B so I might need to actually lol

[sharp cargo]

nah who needs eigen info

just use laplace

[unkempt drift]

if there's some algebra application idk

[sharp cargo]

❤️‍🔥

[warm warren]

Yo Sydney uni discussion and no one pinged me

[topaz raft]

u know before i think 2 years ago linear algebra and calculus were separate credit point courses

but they combined them

[unkempt drift]

that's not necessarily a good thing

[topaz raft]

so linear alg and calc is one whole course

[sharp cargo]

oh no

[unkempt drift]

yeah it's an Aus-wide trend

[topaz raft]

and next semester

they mixed stats and multi var

😭

[unkempt drift]

so that means that IB students can't get any maths credit

[sharp cargo]

we have lin alg and calc separately

[unkempt drift]

since they obviously don't learn LA, no one does in high school

[unkempt drift]

oh that's nice

actually Adl doesn't do discrete maths

[sharp cargo]

we do sequences, series and lin alg etc sem 1

[unkempt drift]

the prof left one year and the course just died

[sharp cargo]

then odes and multi var sem 2

[topaz raft]

lmao lustri the goat

[warm warren]

They learn matrices

[sharp cargo]

yes this is one of the big sillies at adl imo

[unkempt drift]

different

[warm warren]

Goat fr

[sharp cargo]

not same

[unkempt drift]

I think they cram some of it into 2nd year algebra

[warm warren]

I know but it is kinda LA

In a way

[unkempt drift]

shut up you go to Macquarie

[warm warren]

Fuck me dead why am I here

[topaz raft]

lmfaooo

bro macq uni has me dead cuz the slander is too funny

[warm warren]

Why am I here…just to suffer

[topaz raft]

after i saw that law video

[sharp cargo]

red is not the best album wth

1989

is her best album

[warm warren]

Ur just wrong tho

[sharp cargo]

hell no

[warm warren]

You are objectively wrong in this subjective competition

I’m sorry to tell you that

I know it’s hard to face reality

[warm warren]

unsw notes are pretty good

From what I can tell you can actually learn from them

Not so much the usyd notes

[topaz raft]

ya they cover a lot of things in lot more detail

[warm warren]

Those always seem to be a mess

[sharp cargo]

tell me why tho

[topaz raft]

does unsw mix calc and lin alg

idk if they do

[unkempt drift]

they have trimesters so they suck

[unkempt drift]

no one uses our notes lol

simply cause no one has ever heard of them

[topaz raft]

theyre getting rid of it!

[unkempt drift]

I believe ours are good

[unkempt drift]

in what, like 2027

2029

[topaz raft]

and @gritty copper is a big fan of the trimesters hes a unsw boy

[unkempt drift]

oh, 2028

[topaz raft]

he says he likes it cuz hecan overload on credit or some bs

[unkempt drift]

wait did you go to a private or public school?

just curious

[topaz raft]

public

[unkempt drift]

selective?

[topaz raft]

na

[unkempt drift]

interesting

[topaz raft]

our school is pretty good at specific hsc subjects tho

[topaz raft]

we'll all be drowing in hecs debt at the end

does it matter which uni we go to

[unkempt drift]

at least we all get 20% off

thanks Labor!

[topaz raft]

trueeeee

W albanese

[unkempt drift]

wait so are you actually doing a maths degree?

[topaz raft]

physics major

just minor in maths

[unkempt drift]

nice

well physics is like half maths tbh

[topaz raft]

for 2nd year physics and beyond ya

[topaz raft]

@unkempt drift oh yeah they banned calculators this year for maths

🤣

someone asked on our forums this

[gritty copper]

...

[topaz raft]

lmaooo

[unkempt drift]

hey man

[gritty copper]

wsg

[topaz raft]

hows it going bro

[gritty copper]

im back at uni already

fucks sake

my usyd friend isnt even done exams ye

yet

[topaz raft]

LMAOOOO

HAHAHA

bro unsw core 💔

[topaz raft]

ours start next week

[gritty copper]

die

[topaz raft]

is it really worth the overload bro

🥀

[gritty copper]

i dont like you

[topaz raft]

take me to poker night some time

[gritty copper]

bruh come

june 20

[topaz raft]

june 20 my last exam i think or its 21st ill have to check

[gritty copper]

Guten Abend <@&1345378535463718943>

Just here to let everyone know that we have a poker tournament week 3 Friday with collaboration with Elsoc, Quantsoc, Ramsoc

Details:
DATE: 20th June (Week 3 Friday)
LOCATION: Tyree G16
ENTRY: $5 for UNSW students, $10 for non-UNSW
TIME: 3:30pm Start, 5pm Rego closes. 5:30 - 6pm food break. Finishes late
PRIZES: $500 in prizes to be given out!
CAPPED at 100 players!!!

Signup at https://shorturl.at/Ax2Ph

More details regarding weekly poker nights will be announced soon. We are all excited for term 2!
(There is no week 1 event.)

[topaz raft]

shiii i gotta photoshop my ID card to pretend like im unsw

[gritty copper]

"$10 for non-UNSW"

[topaz raft]

im a broke uni student i need those 5 dollars

[topaz raft]

u ever win a game yet

[gritty copper]

bruh

[topaz raft]

have u

i js realised

ive never been to unsw campus'

so far away

[gritty copper]

not missing much

pay a pilgrimage visit to anita b lawrence east

[topaz raft]

is it nice

[gritty copper]

its the math department

the other wing is school of built environment

[topaz raft]

oh hell nah

i only know of the famous rainbow staircase

or is that uts

[gritty copper]

thats us

[topaz raft]

ohh bet bro

how big is ur campus compared to usyd

[gritty copper]

smaller afaik?

[topaz raft]

u gotta give me a tour one day bro

if our schedules align

[unreal isle]

waterrbeam

[topaz raft]

tbnd boy

[unreal isle]

come hold me accountable in vc 🐑

[topaz raft]

.close

[calm coral]

Channel closed

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[warm warren]

You mean the red centre

Goated building btw

[calm coral]

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[gritty copper]

yeah but that doesnt help him navigate a map

[calm coral]

@gritty copper Has your question been resolved?

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[dull token]

please help fast i need to complete my dpp

[calm coral]

@dull token Has your question been resolved?

[dull token]

nah

@trail epoch

[leaden thunder]

did you try plugging in alpha = x + iy and 1/alpha_bar into both circles

[dull token]

yeah

i made 4 equations

but answers was'nt right though

[dull token]

?

[leaden thunder]

!show

[calm coral]

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

[dull token]

i am on pc btw

[leaden thunder]

and?

[dull token]

?

[leaden thunder]

type your work here like everyone else does

[dull token]

ok

2 min

alpha lies on (x - x_{0}) ^ 2 + (y - y_{0}) ^ 2 = r ^ 2 ) eq 1
(1/aplha) = (aplha/mode(alpha^2) lies on (x - x_{0}) ^ 2 + (y - y_{0}) ^ 2 = 4r ^ 2 eq 2

these two are first two eq ?

do u want 3 and 4rth also ?

[kind axle]

Uh i recommend u use `

like this

[leaden thunder]

don't see where you did this yet

[dull token]

ummmmmmmmm

Lad i am here to get my problem solved

😔

[leaden thunder]

[kind axle]

There's gotta be a better way than to just solve 4 equations

[leaden thunder]

!noans

[calm coral]

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.

[leaden thunder]

great you think of it then

[dull token]

ok

the question is hard that the reason i am here

coz i usually have no problem solving locus questions...

[calm coral]

@dull token Has your question been resolved?

[calm coral]

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[calm coral]

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[stark jetty]

How do i answer this question?

Question 6.) If p,q are primitive statements, use duality theorem to prove that
(p →q)∧(q∧p∨True) ≡ (p∧q)

I started but idk where to go from here:

[fierce snow]

I think (p →q)∧(q∧p∨True) ≡ (p∧q) is not correct?
take p=False, q=True

[stark jetty]

Oh that’s what’s given to us

[stark jetty]

But that’s also what I thought

[fierce snow]

left side evaluates to true but right side evaluates to false

[stark jetty]

So you’d just write that it’s not valid?

[fierce snow]

yeah the question is not correct...

[stark jetty]

Hmm alright 😭

.close

[calm coral]

Channel closed

Closed by @stark jetty

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[calm coral]

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[raven crest]

Please help I'm very close to solving this problem

[raven crest]

I think the denominator of the probability is 64 choose 2

and I also that there are 4 cubes that have exactly two painted faces

but i dont know how to write it in a way so that the numerator shows that only 1 of the 2 unit cubes chosen have 2 painted faces exactly

oh wait 36 choose 1 * 4?

so is the answer 1/14

can someone please confirm before i submit it

<@&286206848099549185>

[pulsar knot]

How many cubes have exactly 2 painted faces?

[raven crest]

yeah i did my explaining above

[pulsar knot]

Correct

How many cubes have no painted faces?

[raven crest]

36?

[pulsar knot]

Correct I think

So it would be 4.36/(64choose2)

[raven crest]

what how is it 4.36?

[pulsar knot]

4 choices for the one with 2 painted faces

[raven crest]

oh wait that is times

i thought it was a decimal point

[pulsar knot]

36 choices for the one with no faces

[raven crest]

yay i got it right

thanks

.close

[calm coral]

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[frosty leaf]

if I know a number is 1 mod 5^n and 0 mod 2^n, how can I find the value mod 10^n ?

[nocturne heron]

use the chinese remainder theorem

[frosty leaf]

can I use p-adic numbers?

[nocturne heron]

yes using Hensel’s lemma

[manic lily]

But I think crt should be easier? Depends on what you rather use

[frosty leaf]

ok

is this correct btw

[nocturne heron]

no

[frosty leaf]

oof

[nocturne heron]

how did you factorize that

[frosty leaf]

2^k*5^k = 10^k ?

[nocturne heron]

yes this step is correct

the next one is incorrect

[frosty leaf]

and 2^(k-2)*4 = 2^k

i am interested in this btw

i wanted to try it myself

[frosty leaf]

so did i make a silly mistake

[manic lily]

Seems cool although would try this as an alternative as soon as I got it right the “conventional” way because teachers can be strict on solutions not made the way they were in class

[frosty leaf]

ok

[nocturne heron]

2^(4*5^k) ≠ 1 mod 5^k+1

[frosty leaf]

so the normal way is crt?

[frosty leaf]

i thought the totient of 5^(k+1) is 4*5^k

[manic lily]

For me, it is, idk what you were taught?

[frosty leaf]

i am self taught

idk how to use crt lowkey

this is what I have, ig I need to find m or n?

[nocturne heron]

ok im dumb

2^(4*5^k) = 1 mod 5^k+1

[frosty leaf]

or figure out which m/n make this equal

[nocturne heron]

but you can’t raise to the power of 2^k-1 while preserving 1 mod 5^k+1

[manic lily]

I recommend either https://www.math.cmu.edu/~mradclif/teaching/127S19/Notes/ChineseRemainderTheorem.pdf
or YouTube

[frosty leaf]

1 thought 1 mod anything powered is still 1

because 1^x = 1

[nocturne heron]

if u write $2^{10^k} = (2^{4 \cdot 5^k})^{2^{k-2}} \equiv 1^{2^{k-2}} \equiv 1 \pmod{5^{k+1}}$ it mean that $10^k \mid 4 \cdot 5^k$

[potent lotus]

tm

[nocturne heron]

or maybe im saying full shit 😭

[frosty leaf]

4*5^k | 10^k right

not the other way around

[manic lily]

Think so yup

Gtg, if you can’t resolve it tonight dm me, I’ll be answering in 8-10 hrs

[calm coral]

@frosty leaf Has your question been resolved?

[calm coral]

@frosty leaf Has your question been resolved?

[calm coral]

@frosty leaf Has your question been resolved?

[frosty leaf]

.close

[calm coral]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[covert orchid]

Any ideas what to do niw

[covert orchid]

,rccw

[nocturne heron]

polar coordinates ?

||i think this limit don’t exist||

[covert orchid]

Is there ab identity here or sum

,rccw

[covert orchid]

Why

How did u know

It 's possible

[nocturne heron]

let $f(x, y) = x^3 (x^2 + y^2)^{-3/2} - x (x^2 + y^2)^{-1/2}$ and check lim f(x,0), lim f(0,x) and lim f(x,x) when x->0

[potent lotus]

tm

[nocturne heron]

there is a problem with lim f(x,x)

[covert orchid]

?

,rccw

[covert orchid]

Am i just trolling right now

Also how did u know to look at those curves

So fast

<@&268886789983436800>

[nocturne heron]

i have -1/2^(3/2)

[nocturne heron]

if we want to calculate the limit just make sure it has no problem about existence lol

[covert orchid]

Yes i get that but how did u know it has a problem specifically at f(x,x) so fast

[covert orchid]

Where exactly

[nocturne heron]

because this is frequently where the problem of the limit arises

when we take y=x

[nocturne heron]

for f(x,x)

[covert orchid]

Oki

[nocturne heron]

u need details ?

[covert orchid]

Let me try again ok

[nocturne heron]

[covert orchid]

Yes

Idk i got something wrong again i think

,rccw

[nocturne heron]

(x^2)^(-3/2)=x^-3

[covert orchid]

Omg

[nocturne heron]

and (x^2)^-1/2=x^-1 and then everything simplify there is no more x

[covert orchid]

True

[nocturne heron]

its ok its 3 am for me idk what’s ur time zone 😭

[covert orchid]

4am😭🙏

Like 3:52

[nocturne heron]

you’re forgiven🙏🏼

[covert orchid]

Ok i get it now

Thx so limit doesn't exist

[nocturne heron]

yep

[covert orchid]

.solved

[calm coral]

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[calm coral]

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[heavy sundial]

Wassup bakas

[heavy sundial]

I need a chronically online tutor

[elder pawn]

@heavy sundial we're not a tutoring service. we're volunteers who can help with specific problems or topics

[calm coral]

@heavy sundial Has your question been resolved?

[calm coral]

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[half trench]

!status

[calm coral]

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

[primal bear]

uhhh

what do you wanna do

[sour yoke]

ok

i calculated the total angle of c to be 90

because semi circle

but

then i calculated 180-98 getting 82

but now what do i do

[half trench]

That doesnt work

Oh wait

You mean to find f + the third angle in the left triangle?

Yeah so use algebra to find the angles

[sour yoke]

no i mean 90 as the angle of C

point c

since its a semi circle right

[half trench]

No the 180-98 is 82

[sour yoke]

yes

But angle of C

is 90

[open atlas]

have you learnt angle at center = 2 times angle at circumference?

that might be applicable here

[sour yoke]

yeah

[half trench]

No thats just the semicircle bit

I dont think you can use it from there

[open atlas]

for angle e

is that not just 98 / 2

[half trench]

Oh your right

I would have just used algebra but thats better

[sour yoke]

could you explain

my goat

??

[open atlas]

for angle f: OA = OC. An isosceles triangle can be formed.

[open atlas]

Angle AOC is the angle at center.

Angle ABC = e is the angle at circumference

[half trench]

If you take 2 points on the circle and connect them each to the center and some other point on the circumference, the angle at the center is twice the angle at the other point

[sour yoke]

yeah

the angle at he center is 180

i got that

but why is it an isocles

if there is not 2 radiuses

[oblique birch]

the angle at the center is not 180

[sour yoke]

but the angle at the circumfrience is 90?

[oblique birch]

look at it from point b

[sour yoke]

since its a semi circle

[open atlas]

okay yeah for that one the angle at center is 180

[sour yoke]

yeaah

[open atlas]

but for ABC the angle at center is different

[open atlas]

angle ABC is the one we're interested in

[sour yoke]

yeah

ohh

Wait

i get that

so 98 is its angle at the center ur saying?

[open atlas]

yup

[sour yoke]

oh

e is 41

41+82=123

other one is 57?

[open atlas]

are you sure you calculated this right?

[sour yoke]

oh

sorry

49

[open atlas]

yeah'

[sour yoke]

49+82

=131

59

31 is f?

@open atlas

[open atlas]

where are you getting 82

[oblique birch]

no

[sour yoke]

180-98

??

[oblique birch]

180 - 131 is not 59

[sour yoke]

sorry 49

[oblique birch]

and then you also mess up your f

[sour yoke]

so 41

is f

ok

so center is 84

360-180-84

[open atlas]

what angle?

[sour yoke]

=96

[open atlas]

specifically?

[sour yoke]

AOB

[open atlas]

yup

[sour yoke]

96+42

128

so 180-128

=52

90-52

38

84+38

122-180

58

X IS 58

👏

[open atlas]

wrong

there are two easy methods i can think of

one doesnt need the angle at center = 2 times angle at circumference property at all

[sour yoke]

what

where'd i go wrong

[oblique birch]

where did you get 96

also as 0 said ther is a much easier method

[open atlas]

96 + 42 = 138

[sour yoke]

bro

i'll have a calc tom

its good

[unreal rose]

138

[sour yoke]

ok

[open atlas]

anyways

[sour yoke]

otherwise fine

[open atlas]

there are two easier methods

[oblique birch]

no

[sour yoke]

yh?

[oblique birch]

listen there is a way easier method

[open atlas]

First method, using angle at center = 2 * angle at circumference, angle AOB = 84. OA = OB so angle OAB = angle OBA. Hence x = (180 - 84)/2

Second, use your right angle in semicircle property. CBA = 90. x = 180 - 90 - 42..

[sour yoke]

oh shoot

yeah

x=48

nice bro

[open atlas]

y'know about the properties of angles in cyclic quadrilaterals?

[sour yoke]

yeah

[open atlas]

name them

[sour yoke]

would i do 180-101

d=96

[open atlas]

no...

[sour yoke]

opposite angles equal 180

d is 96

[open atlas]

yeah

[sour yoke]

idk abt c

[open atlas]

what angle is opposite to d?

[sour yoke]

96

[open atlas]

so 96 + d = 180...?

[sour yoke]

wait

mb gng

84

is d

[open atlas]

okay

now try to find e

[sour yoke]

is C 101

[open atlas]

c*

[sour yoke]

??

[open atlas]

why?

[sour yoke]

because c is opposite to 180-101

wtv u get for that answer

u subtrnce anyways

so u get 101

[open atlas]

okay that's great

all correct

[sour yoke]

is 101 a tangent

??

[open atlas]

no

[oblique birch]

juist some friendly advice man don't rush it

[sour yoke]

k

yeh

[sour yoke]

yeah

exam in 6 hours

[open atlas]

@sour yoke if at any point you feel these questions are too easy i got some harder ones if you need more practice

[sour yoke]

alright thanks

is it fine if i leave this open till im done

[open atlas]

you can open a post in #1021175428326633542

wait actually

yea it's fine

[calm coral]

@sour yoke Has your question been resolved?

[sour yoke]

could angle ADC be 90 degrees since u can divide into semi circles?

@open atlas

<@&286206848099549185>

[alpine cobalt]

it is

[sly brook]

yes

it is

[alpine cobalt]

thales theorem

[sour yoke]

ok

w=45

AOC=180

Is T also not equal to 32

due to same segment theorem

<@&286206848099549185>

b=a?

ADB angle is 90 due to semi circle?

[alpine cobalt]

yea

[sour yoke]

ok

whatdo i do hen

then

[alpine cobalt]

thales theorem btw

whats the question

[sour yoke]

find the unknowns bruv

this is the question

no text given

[alpine cobalt]

you need answer or help

[sour yoke]

help

what do i do fromhere

[alpine cobalt]

start with ACB = 90

calculate c

[sour yoke]

oh yah equal

ohhh

c=40

could i do 180-50

do get 130

for this angle

[unreal rose]

wow thread still alive

[alpine cobalt]

xD

[sour yoke]

??

[alpine cobalt]

yes

then you get a from which you get b

[sour yoke]

yessir

ty gng

[alpine cobalt]

np

[unreal rose]

did he get a and b

[alpine cobalt]

prob

[unreal rose]

no
whats your answer

[alpine cobalt]

thats from before

[sour yoke]

they're not the same right?

[unreal rose]

theyre not the same

[sour yoke]

ok

here i got the angles of bot triangle as 40 70 70

now what do i do

<@&286206848099549185> 😭

[alpine cobalt]

bruhhh

calculate ABC

[rotund beacon]

dude you have someone helping you, you dont need to ping helpers

[alpine cobalt]

yea

[sour yoke]

its 70

[sour yoke]

sorry

[alpine cobalt]

i think its not calculateble under current circumstances

[sour yoke]

wdym?

[alpine cobalt]

there are too less information

[unreal rose]

triangleABC equilateral

[alpine cobalt]

unless there is more and you didnt show

[sour yoke]

quesion like this here

[alpine cobalt]

ok this is just harder

[unreal rose]

slow down dude

[open atlas]

did they give that CB or AB are tangents?

[rugged pine]

alternate segment theorem

[alpine cobalt]

yea thats a good question

[rugged pine]

For q1

[sour yoke]

there is no text in the question

[rugged pine]

alternate segment theorem

[sour yoke]

only the question

[open atlas]

then it is impossible.

[alpine cobalt]

told you

[unreal rose]

oh

[rugged pine]

Don’t move onto the next problem without finishing the previous

[alpine cobalt]

xD

[open atlas]

alt. seg. theorem only works if they have tangents

[alpine cobalt]

yea

[open atlas]

(not given)

[rugged pine]

I thought AB was a tangent

[sour yoke]

yeah

[rugged pine]

Okay these questions are weird

[sour yoke]

what ab q3

[rugged pine]

Again, it looks like we have tangents

I think we should say they are tangents if the problem is unclear

[sour yoke]

tangent is not clearly shown though

[sour yoke]

i think i'll skip these and practice the other questions

[rugged pine]

That way at least we have an idea of what the answer is if it turns out to have one

[sour yoke]

bec in my exam im getting pp which define if theres a tangent

[open atlas]

AB doesnt look like a tangent imo

[rugged pine]

It looks like we can solve it if they are tangents*

[open atlas]

look at the bottom

[rugged pine]

I know

[open atlas]

i think it's CB

[sour yoke]

what abou this

[open atlas]

one question at a time

[rugged pine]

But if there is no other way, we must assume the question is faulty, and in that case we should just make the smallest changes possible imo

[sour yoke]

im going to practice tangent from smwhere else dw

[rugged pine]

Stop going so quick

[sour yoke]

leave that question

sorry

[unreal rose]

maybe tell us that youre leaving that question beforehand

[open atlas]

once again, if AC is not given as a tangent, then we do not know.

[unreal rose]

if AC is indeed a tangent, can you solve it

[open atlas]

if AC is a tangent though, then 4a + a + 90 = 180 (angle sum of triangle)

[unreal rose]

guh

[sour yoke]

why 90

because is 2 straight lines?

[open atlas]

tangent perpendicular to radius

[sour yoke]

oh yes

okk

thnk you

[open atlas]

OB is the radius, AC is the tangent, angle OBC = 90

[sour yoke]

yhh

[open atlas]

anyways what do you get after solving this?

[alpine cobalt]

is this still that one or another one

[open atlas]

@sour yoke you still here?

[calm coral]

@sour yoke Has your question been resolved?

[calm coral]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[unreal rose]

should i check D?

[still marlin]

no, the minimum could be very local

[unreal rose]

what a trap

[balmy bane]

If it were a global minimum, it'd be true

But "local" just means there's some "circle" around this point I could draw where that point itself is the minimum

The circle could be tiny af

[unreal rose]

alr then

ty

.close

[calm coral]

Channel closed

Closed by @unreal rose

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[royal cape]

The numbers 1, 2, ....., 9
are randomly placed into the
9 squares of a 3 x 3
grid. Each square gets one number, and each of the numbers is used once. What is the probability that the sum of the numbers in each row and each column is odd?

[final parrot]

What have you tried in advance?

[royal cape]

uh

9 choose 3

jk'

[final parrot]

lol

[royal cape]

i lowkey dont know

thats why i need help

[final parrot]

Alright

[royal cape]

9! on the bottom?

[final parrot]

Can you draw me a 3x3 grid first?

[royal cape]

oh shoot

ok done

[final parrot]

okay, in what condition will you get an odd number after adding up three numbers?

[royal cape]

odd odd odd

[final parrot]

decent

anything else?

[royal cape]

uh

nah

[final parrot]

nope, there's one more :))

[royal cape]

even even odd

bruh i thought i sent htat

[final parrot]

correct

Alright, now we can work on it

Take out the paper with your grid on it, and try to fill it out with any of the solution

[royal cape]

uh

wait the middle has to be odd

and the corners are even

yooo

wait

is that right

yoooo

bro

[final parrot]

Can you take a pic of it?

[royal cape]

uh nah im on pc

wait

so 9 choopse 4

times

9 choose 5

wait

nah

its just

9 choose 4

time

5!

/9!

[final parrot]

uhhh....Do you have canva or smth

draw it on canva and take a screenshot of it

[royal cape]

wait

i understnad it now

uh

ys

lemme draw

cuz 1 through 9

is 5 odds

and 4 evens

so it has to be like this

[final parrot]

good start, but you over looks smth

[royal cape]

oh shoot

[final parrot]

This shit also works

[royal cape]

oh shi

that means 4 e in every crner

works

shi

[final parrot]

YES!!

You got it

[royal cape]

ok lemme lock in now

wait

we missed another one

[final parrot]

mhm

yes

[royal cape]

there can be 4 evens in edge

oh

[final parrot]

you've already calcualted it

[royal cape]

so 9 choose 4 time 5! / 9! = 1/24

1/24 times 6

since there are 4

6

[final parrot]

no wait, let's not calcualte anything for now

[royal cape]

ways

1/4

trust

[final parrot]

just discuss the possibility

bruh

[royal cape]

ok

[final parrot]

lemme talk

plz

[final parrot]

Do you find any pattern here?

[royal cape]

uh

wdym it all add up to odd

idk

isnt it justg 1/4

[final parrot]

yes, that's the whole point

[royal cape]

yeah there are 6 ways

it does

[final parrot]

We want either OOO or 1 O in a row or column, right?

[royal cape]

yes

[final parrot]

And we don't want two O in a column or a row, right?

[royal cape]

yes

[final parrot]

There are five O on the board, right?

[royal cape]

yes

[final parrot]

Right, so we want all the Os to stay together, or else there must be two isolated O staying together

[royal cape]

yes

[final parrot]

Lemme show you what I mean

[royal cape]

wtj

[final parrot]

look, if we banish that guy to the marginal of the grid, there would be three rows/column that does not fit our requirement

2*

[royal cape]

oh

[final parrot]

That's why we want all Os to stay together, while maintaining a T / cross / L shape simultaneously

[royal cape]

yes

[final parrot]

Alright, how many cross and T are there?

[royal cape]

wdym T

[final parrot]

This is what I'm talking about

[royal cape]

oh shoot

[rugged pine]

I saw this problem yesterday but with 4x4, they did it by showing the 3x3 area decides the letters for the rest of the grid, and counting how many ways that can be filled in (2^9)

[royal cape]

so

4! times 5!

OH

i see

4 Ls

4 Ts

1 cross

9 total

9 times 5! times 4!

[final parrot]

yes

[royal cape]

9!

over

lol i got kinda confused

[final parrot]

no, wtf

[royal cape]

9 times 5! times 4! all over 9!

because 9 ! total chance

[final parrot]

OH

but still, nah

[royal cape]

what

[final parrot]

nvm, you're correct, I've verified it with a senior helpful

[royal cape]

oh alr

im a freshman

[final parrot]

Anything else you wanna ask?

[royal cape]

wait

i just suck and combinations

[rugged pine]

Oh wait it’s numbers 1…9 nvm sorry (about my method)

[royal cape]

wait we could do

9/ 9 choose 5 right?

because 9 choose 5

[final parrot]

what does 9/ 9 mean?

[royal cape]

9 / (9 5)

[final parrot]

I'm not sure about your method

can you elaborate it?

[royal cape]

so

there are 9