help-36

[trail mango]

but if there are no 1s, restart and don't count this experiment

yea that's how it should be

[zealous storm]

so bad wording? cuz the way it is written

the probability is like 0?

Lol or am i being dumb

[trail mango]

loll it could be clearer but like

if that meant exactly one

they would have (or should have) said that

because they say exactly two when they mean exactly two

[zealous storm]

to me "if one of the numbers is a 1" implies exactly one of the number is a 1 😭

but i can't english

so idk

[zealous storm]

oh

[trail mango]

it's unclear

[zealous storm]

[trail mango]

among 1, 2, 1, is one of the numbers a 1?

[zealous storm]

yes, otherwise the question makes no sense lol

[trail mango]

i would say yea, especially if "exactly" was used elsewhere

[zealous storm]

fair enough

lemme try again but i think the answer is D

everyone said the teacher was wrong and the answer is not D

😔 i'm the only other person to have D

[trail mango]

loll you didn't post the answer choices

[zealous storm]

oh

there was a bunch of working out (irrelevant to the problem)

but hmm wait

that's not mine

but uhm let me use conditional really quick

[trail mango]

here are all the possibilities

(just for reference in case we wanna check it like that)

[zealous storm]

loll i used that too to get the 6/19 answer 😭

[trail mango]

yea i agree with 6/19

8 of them don't have a 1 because that's just removing the triples where everything is a 0 or 1

and there are 6 that have exactly two 1s (and you don't need to worry about what was removed to count those)

you can choose 2 places for 1s, then there is one empty space to put either a 0 or 2

[zealous storm]

okay so P(at least one 1) = 1 - P(no 1's) = 1 - 8/27 = 19/27

P(exactly two 1's) = 2/27 * 3 = 6/27

P(exactly two 1's)/ P(at least one 1) = 6/19, right?

[trail mango]

so (3 choose 2)*2 is the number of triples with exactly two 1s

which is 6

and there are 19 total triples (once you remove the ones with no 1s)

[zealous storm]

😭wait sryyy brb

[trail mango]

😭

[mild dock]

this is correct

[final saddle]

@zealous storm Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[zealous storm]

.reopen

[final saddle]

✅

[zealous storm]

😭 nooo

oh

[trail mango]

😭

[zealous storm]

sry i had to feed my cat and tend to some 😭 chores

uhm okay wait

[zealous storm]

mhm that's right

so what i did is correct, right?

[trail mango]

yep

<@&268886789983436800>

bye zombie

[blissful condor]

come back tomorrow

[sturdy ocean]

come back never

[blissful condor]

or don’t

thx

[zealous storm]

zombie? :V

[zealous storm]

thanks, wait i also have another question i need confirmation for

https://math.stackexchange.com/questions/607070/a-family-has-two-children-one-child-is-a-girl-what-is-the-probability-that-the

[trail mango]

it was the username of the person who got banned

[zealous storm]

😭 i see

[zealous storm]

okay so here the answer is 1/3 right

https://math.stackexchange.com/questions/15055/in-a-family-with-two-children-what-are-the-chances-if-one-of-the-children-is-a

but now in the general case

they say this is the closed form

but that gives.... 1/2?

here's the general case

https://math.stackexchange.com/questions/1893041/conditional-probability-what-is-the-prob-that-all-are-girls-given-that-there

are the questions different?

[trail mango]

this is a lot of text to trudge through

[zealous storm]

sorry

i think you can just look at the question itself

not the answer

first question:

second question:

[trail mango]

yes they are different questions

[zealous storm]

why?

[trail mango]

well this one is different

[zealous storm]

yeah those questions are the 2 pictures

[trail mango]

that's the same thing right

[zealous storm]

yes it's just those 2 questions

i was wondering if they're different questions

like the clsoed form answer in 2)

doesn't work for the first question

why?

[trail mango]

because it's like

in question 2, the family could have a boy and girl but just not have the girl be the one picked

[zealous storm]

i see 😭 makes sense yeah

[trail mango]

so for n = 2 the space is more like
bb -> pick b
bb -> pick b
bg -> pick b
bg -> pick g
gb -> pick g
gb -> pick b
gg -> pick g
gg -> pick g

there are 4 'pick g'

and in half of them, both children are girls

so the condition is that you're in a 'pick g' case

[zealous storm]

Okay fair enough :sob

i think i partly get it

[trail mango]

[zealous storm]

and for this question, the given solution was like

"we’re looking for the probability that exactly 1 out of the 2 remaining draws is a one. By independence, this is the product of the probabilities that 1 of the draws is a one (probability 1/3) and the other draw is not a one (probability 1 - 1/3 = 2/3). Answer: 1/3 * 2/3 = 2/9."

I trust that we're right but what does this even mean

[trail mango]

[zealous storm]

Did my teacher just use chatgpt or something 😭

[trail mango]

LOL i was thinking it reads like gpt

[zealous storm]

😭 😭

[trail mango]

😭

[zealous storm]

wait aren't the draws mutually exclusive?

[trail mango]

wdym

[zealous storm]

i mean like he wrote "independence" right?

isn't each case kinda mutually exclusive?

not independent

[trail mango]

wdym case

[zealous storm]

sorry i'm probably AI myself

ignore me

lol

[trail mango]

loll

[royal grove]

That is what independent means

[zealous storm]

what

no

[trail mango]

[zealous storm]

wait

"we’re looking for the probability that exactly 1 out of the 2 remaining draws is a one"

from the sample space consisting of all 3-element tuples with exactly 2 copies of 2

u can't choose a tuple such that there's exactly 1 copies of 2 right?

so it's 0

if we parse the question that way

[trail mango]

that answer doesn't make any sense

it's like

no i can't even think of what question it could possibly be trying to answer

it reads like they thought the problem was the condition is that the first number is a 1

but then even then it's not correct

because you have 12, 10, 01, or 21 as the final 2

so it would be 4/9

[zealous storm]

isn't it trying to answer something like:

P( exactly two copies of 1 | exactly one copy of 1 )

[trail mango]

that would just be 0 so no idts

we’re looking for the probability that exactly 1 out of the 2 remaining draws is a one.
this reads like "first draw was 1"

[zealous storm]

yeah i think

😭 i'm not spending more time

[trail mango]

😭

[zealous storm]

on this AI solution

loll

[trail mango]

haha

[zealous storm]

thanks for the help :3

oh yeah wait i had one more question

whoops i'm asking

way too many today

[trail mango]

[zealous storm]

the answer choices were mean, median, and mode

u can select multiple answers

i chose all 3

because in the case where mean = median = mode

all work, no?

[trail mango]

weird question

[keen lotus]

Mean = median = mode?

Weird

Weird question

[zealous storm]

i mean it says "can"

so you can consider this edge case

[zealous storm]

every single question is not phrased well

[keen lotus]

Hmm

[zealous storm]

smh

[keen lotus]

Hrmm

[trail mango]

idek what to say about that question

[zealous storm]

😭

i guess nobody is wrong here

[keen lotus]

I might try to rephrase it but idk if it will make sense

[zealous storm]

the teacher selected median

but i selected all (cuz of the edge case)

by transitivity, if mean = mode = median then it can also describe central tendency & position

[twilit arrow]

whats the question here

[dense coral]

what is a measure of position

[zealous storm]

😭 don't ask me

i googled it

LOL

[dense coral]

all three can be a measure of central tendency

[zealous storm]

it says percentiles are measure of position

[dense coral]

but idk what measure of position means

[zealous storm]

so median

[trail mango]

then i would just say median and nothing else

[dense coral]

I suppose all three can still be correct under this definition

but median is likely most accurate?

idk

this question is so weird

[zealous storm]

a website says only medians work

[dense coral]

ambiguous question means I wouldn't know

[zealous storm]

but the mean = median = mode edge case 😭 is why i thought all works

cuz if i tell you this and then give u the mode

u can describe bla bla

bla bla cuz idk what that is either lol

[zealous storm]

okok

thanks @trail mango

and thanks higher too

[trail mango]

[zealous storm]

buh bye

[trail mango]

bye

[zealous storm]

i might be back but 😔 with geo probably

lol

[trail mango]

nooooooooooooooo

[zealous storm]

geo sucks!!

are the other geo's any better?

like non-euclidean

[keen lotus]

Fuck geo

[zealous storm]

projective

differential

all those?

[zealous storm]

[dense coral]

I did nothing but thank you

Layla did 99.999942234242% of the work

[dense coral]

maybe hs geometry I can agree

[dense coral]

pretty much all geometry is more interesting than whatever hs has you do, imo

[zealous storm]

mhm layla has been helping for hours 😭

i feel bad

[zealous storm]

ohh

[dense coral]

I'm sure she enjoyed it

[zealous storm]

hopefully

[dense coral]

@trail mango what says you

[trail mango]

i say

i love generating functions

[zealous storm]

[dense coral]

unfortunately combinatorics scary

so I do not know

[zealous storm]

at least if u use generating functions to solve combinatorics

you aren’t guessing

LOL

[dense coral]

I cannot count to save my life idk

it's too hard for me

[trail mango]

it's so fun

[zealous storm]

same

[dense coral]

you gotta be at least somewhat clever to go into combinatorics

and I just lack cleverness

literal skill issue, but I can't help it

[zealous storm]

or be a fast brute forcer

[dense coral]

I don't think that'll get you far

[zealous storm]

higher the machine!

[dense coral]

Layla, you need to teach me how to appreciate combinatorics one day

I see any question about seating people in a certain way and I just run away

[trail mango]

those can be tough

[dense coral]

every discrete math esque problem is hard for me haha

[zealous storm]

oh yeah the one me and layla did was super nice

on the surface its combinatorics

[trail mango]

which one was that?

[zealous storm]

well i guess bijection is kinda combinatorics too

[zealous storm]

the 1/3 one

[trail mango]

loll yea i like that one

[dense coral]

what problem are we talking about?

[trail mango]

#help-45 message

[dense coral]

ah, an impossible question for me

[zealous storm]

oh you beat me to it

[dense coral]

I recall Layla was quite impressed by your solution

[trail mango]

i was!

[dense coral]

that's definitely smth worth commending

she doesn't say that often

[zealous storm]

wow, i didn’t know it was that special!

also it wasn’t fleshed out at all

also she said “since the answer is nice there might be an easier way”

so i trusted her 😭

[dense coral]

good choice

[trail mango]

it was actually so good

i bet i could make a problem that's super annoying without your idea

[trail mango]

and yea i don't say that often

[dense coral]

when was the last time you said smth like that

[zealous storm]

[dense coral]

it's probably been so many months that I don't even remember

[zealous storm]

if u ever do, i look forward to it 😭

[trail mango]

last time i was impressed in a help channel was probably mqnic on the palaeeudyptes problem

[dense coral]

agh, why did that channel get closed

[trail mango]

it was such a good problem 😭

[dense coral]

Existentialistic's channel was closed too, recently

I thought that was a bit of a shame

[trail mango]

i love giving the impossible version that sounds totally doable to unsuspecting overconfident people

[dense coral]

what is it?

[trail mango]

just palaeeudyptes problem on anything bigger than 25 x 25

anyone who can do it will immediately steal my heart

[dense coral]

is it actually impossible?

[trail mango]

well it has an answer

[zealous storm]

i guess that’s above my pay grade

[dense coral]

I literally don't even know how I would start that problem ngl

[trail mango]

but i would be very impressed if someone can compute it for 50 x 50

25 x 25 with a supercomputer could be done

[zealous storm]

are the answers nice? LOL 😭

[dense coral]

when have answers to counting problems ever been nice

[trail mango]

i would not call it nice, no

[dense coral]

the only thing I know how to do is expand definitions and spam theorems

[zealous storm]

i don’t even know that

[dense coral]

yes you do wdym

[zealous storm]

😭i’ve never had any theorems to begin with

at least formalized

no corollaries either

okay maybe some

and i only how to do basic geo proofs

[dense coral]

and I don't

[trail mango]

i don't either

[dense coral]

[zealous storm]

okay i don’t either then

[trail mango]

[dense coral]

[zealous storm]

i’m the unsuspecting overconfident person layla was referring to

[dense coral]

I don't think so

[trail mango]

noooooo

i'm talking like

"hello i am an expert in math i can solve any problem for you"

[dense coral]

who the heck claims that in this day and age

[zealous storm]

😭WHATTT i’ve never seen anyone like that before

unless they’re trolls and/or “paid tutors”

[trail mango]

yea it's not rare for people trying to make money to advertise themselves like that

outside of that and trolls though yes it is very rare

[dense coral]

I feel like the only people who could claim that and not feel anything are the people who have never seen math beyond... perhaps calculus? idk

[zealous storm]

i mean if 😭they’ve done calculus they at least some random integrals should’ve phased them

maybe lower

[dense coral]

@neon

[trail mango]

yea it probably feels gross for some of them

[zealous storm]

[trail mango]

unless they are like, really proud of themselves and ignore all the math they can't do or something lmao

[zealous storm]

do you guys have one of those “easiest hard” problems you couldn’t solve?

[trail mango]

this is why i don't like being a salesman

[zealous storm]

idk if that even makes sense

[dense coral]

wdym

[trail mango]

or saleswoman

[dense coral]

I absolutely cannot sell myself

I don't know how to

[zealous storm]

you’d make a great saleswoman!

[zealous storm]

uhhhh like easiest question u couldn’t solve

[dense coral]

not to employers, professors, commitees, etc

[zealous storm]

the hard bit comes in cuz it’s hard for u

idk nvm this makes no sense

[dense coral]

makes applying for things hard when I have no idea how to tell ppl that I'm fit for whatever

[trail mango]

yep

[dense coral]

easiest problem I couldn't solve?

[zealous storm]

oh yeah 😭others market themselves

[dense coral]

there's probably a few hundred

[zealous storm]

way better than i do myself

[dense coral]

yeah it makes me really sad and/or anxious sometimes when I see others talk about applying to this or that or making their CV/resumes, etc

because I've been unable to do that

Layla how does your CV/resume look, if you're willing to share?

[zealous storm]

me: “i got a 5 on ap calc”

others: “scored in the top 1 percentile among 5 million test takers”

[dense coral]

or is this too personal?

[trail mango]

i never made a cv

[zealous storm]

[trail mango]

i begrudgingly made resume to apply to grad school (i did not have a choice) and i don't even wanna think about it

[dense coral]

yeah I feel like this kind of thing makes me seem full of myself if I say it

[trail mango]

nor do i remember what i put on it

[dense coral]

and I disdain that so much

[dense coral]

at least it got you accepted, I suppose

[trail mango]

i don't mean to brag but i scored in the top 99 percentile among 5 million test takers

[dense coral]

I scored in the top 100% (I didn't take the test)

[trail mango]

i repeat this joke or similar sometimes but i actually just stole it from a twitter post one time

[zealous storm]

😭😭

[trail mango]

like 5 years ago

[dense coral]

[zealous storm]

i think someone i know unironically said that too

and i just smiled

[dense coral]

I steal all my jokes from other people

[zealous storm]

let’s go to the same uni! although id be applying for undergrad

[trail mango]

i am not in school

[dense coral]

Layla return to grad school arc

what were your main interests, while you were there?

was it also combinatorics?

[trail mango]

i had none

[dense coral]

what did you feel strongest in?

[trail mango]

i dunno, i felt pretty weak in every class i took

[zealous storm]

do people have something they’re the best in? i feel weak in everything

[zealous storm]

[dense coral]

no I feel bad at everything too

there's definitely some things I'm more interested in than others

[zealous storm]

there’s combinatorics on finite sets and what about if it isn’t finite?

[dense coral]

but I don't feel good about anything

[dense coral]

https://en.wikipedia.org/wiki/Infinitary_combinatorics

[trail mango]

other than combinatorics and probability and some bits of other stuff i'm not really into much

though i do need to learn some algebra which i'm VERY bad at for combinatorics

[dense coral]

how was your UG background, if I may ask?

[zealous storm]

you know it’s wayyyyy above my league 😭if the description looks easy cuz 0 symbol spam

[trail mango]

wdym?

[dense coral]

it was a math major, I presume?

[trail mango]

yea

[dense coral]

did you go breadth or depth?

[zealous storm]

[trail mango]

neither? LOL

mmmm7 is blue

[dense coral]

what did you do then

congrats on Active mmm7

[trail mango]

uhh ig closer to breadth

[zealous storm]

I’m verified to be actively dumb

[dense coral]

not true

[dense coral]

wait, can I ask smth about your calculus class in particular

[trail mango]

sure

[dense coral]

cause I've seen you complain about calculus classes lmfao

[trail mango]

the ones i took?

[dense coral]

yeah

were they computational or more rigourous?

[trail mango]

computational

[dense coral]

then did your professors never use the words "concave up" in those classes?

[zealous storm]

oh, isn’t real analysis the first course in university for math majors?

[dense coral]

sometimes

[zealous storm]

convex and concave sound so much cooler

[trail mango]

we used that. but with regards to my other question idr if it meant convex or strictly convex

i LOVE the word convex

[zealous storm]

it’s so sexyyy

[trail mango]

yesss

[zealous storm]

[dense coral]

what did your class define it to be

[trail mango]

'convex hull' and 'cluster point'

my favorites

[dense coral]

convex is a very cool word yes

[keen lotus]

Sexy in pronouciation too

[dense coral]

cluster point, as in accumulation/limit point?

[trail mango]

i don't remember haha

[trail mango]

yea

[dense coral]

icic

what is my favourite math word

[trail mango]

i wonder if i have any other than those 2 that i'm forgetting

[dense coral]

idk if I know enough math to have one yet

[trail mango]

i love the word convex and i love closure operators

so convex hulls are awesome

[dense coral]

unfortunately I know nearly nothing about convex hulls

convex optimization scary

[trail mango]

my favorite project euler problem was about convex hulls and that was the first time i really worked with it

[dense coral]

are you still doing PE every day?

[trail mango]

nope, haven't done any recently

[dense coral]

[zealous storm]

hoschild cohomology

[dense coral]

[zealous storm]

don’t ask me what that is

sounds fancy though

[dense coral]

why Hoschild out of every possible name :kekehands:

I find even de Rham cooler sounding

[trail mango]

[dense coral]

oh cobordism is a cool word

I like it

unfortunately I have yet to get there

how much diff geo/topo do you know, Layla?

[trail mango]

none

[dense coral]

maybe you can help me a bit when I get there

[dense coral]

oh

wait what the heck

it's 3:33am

[zealous storm]

good night guys

i mean morning

[dense coral]

is it also 3:33am for you

wait maybe don't answer that

[trail mango]

it is for me

[dense coral]

[zealous storm]

no

12:34 am for me

[dense coral]

ah, pacific time

[zealous storm]

LOL why?

[dense coral]

I've seen some people apprehensive about revealing their time zones before

sometimes they can say a lot

[zealous storm]

oh, fair enough

ANYWAY TYYYY GUYS

and good night

i won’t keep you guys up

[dense coral]

okay tbf there was one time where I found somebody's country via their time zone :kekehands:

[zealous storm]

[dense coral]

no, not at all! I'm having fun here

Layla has an insane sleep schedule most of the time, and it's not like mine is good either

[trail mango]

i got up at like 6 pm

[dense coral]

how do you manage that

I woke up at 12pm today and thought it was wayyy too late

on the bright side, that means I finally slept well for the first time in 2 weeks

I was running on 3-5hrs of sleep per day for the entire last week

[random forge]

it is currently 3:39am for me, where am i

using am is definitely not a massive hint

(but i know what you mean, esp with those 15 minute-off timezone things and whatnot)

[dense coral]

I mean, I couldn't precisely say

okay I think I shall go to sleep

[trail mango]

i could take a guess

[dense coral]

you might be wrong though

there's more than just 2 countries in this time zone, after all

[trail mango]

no i just remember a specific message from one time

[dense coral]

ic

[random forge]

you would have a pretty good chance of being right, since theres only 2 likely candidiates. That being said I used to hide my timezone until i realized theres like hundred million+ people in my timezone and all my other information was more identifying anyways

i could be in some random carribean island in which case you would be wrong though

[dense coral]

you could also be in South America

Peru and Venezeula are candidates there

[random forge]

i think most of south america by population is in one timezone east of me iirc?

but that is true

[dense coral]

yeah I meant like

the western side of SA

why is this channel still open :kekehands:

[trail mango]

discussion 3 help channels are the best

[dense coral]

they are!

[dense coral]

I wonder if the mods approve

okay well, it's nearing 4am

so I'll take my leave

[random forge]

location located

good night!

[dense coral]

I already said my time earlier!

@trail mango @zealous storm @random forge have a good night, and thanks for the conversation!

[random forge]

ohi dont think anyone ever closed the channel

[dense coral]

I really enjoyed this one ❤️

[trail mango]

bye

[random forge]

.close

[final saddle]

Channel closed

Closed by @random forge

Use .reopen if this was a mistake.

[dense coral]

hope you all have a wonderful night!

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[delicate fiber]

can someone verify my solutions

i got 80 and 120

[unkempt wigeon]

you

you're right

for the first one there's 5 ways to choose a male, 4 ways to choose someone else's wife. There are 4 ways to choose the opponent male and only 1 match for that male which is 5.4.4=80

same for the next one 5.4.3.2

[final saddle]

@delicate fiber Has your question been resolved?

[delicate fiber]

Ok ty bro

[final saddle]

@delicate fiber Has your question been resolved?

Channel closed

Closed by @delicate fiber

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[dreamy spire]

A 2×3 frame can be divided into 1×1 squares by placing 7 matches as
in the picture. Which a × b frames, where a b, can be divided in this way by
exactly 110 matches? Determine all possibilities.

[dreamy spire]

How do I do this?

If it was a 2 by to I have to use 4 matches right

3x3 that wouldn need 12 matches

cuz its n= the number of matches that makes up the whole side, n-1 x 2 x n

2n^2-2n

=110

Therefore n^2-n=55

So its gonna be close to 8x8 table?

8x7 maybe

But whats the mathematical solution to get an exact answer?

[plush scarab]

im not completely sure if im on the right track but i got a formula like
$$y(x-1)+x(y-1)$$

[soft zealot]

sunsick

[plush scarab]

which you can turn into $$2xy-x-y=110$$

[soft zealot]

sunsick

[final saddle]

@dreamy spire Has your question been resolved?

[dreamy spire]

So x is the lenght of side a and y of the side b?

[dreamy spire]

How did you come up with that?

[plush scarab]

yeah or you can switch them around, the order doesn't matter

[plush scarab]

if you look at the diagram, the number of matches going horizontally is equal to the width times 1 less than its height

and the same thing happens for the number of matches going vertically

[dreamy spire]

oh yeah i see

but how can you find the numbers noiw

now

out of that equation

[plush scarab]

ok so i don't know how you would really find them other than just guessing and checking tbh

they would be ||111x1 and 9x7 though||

[dreamy spire]

nothing else?

[plush scarab]

other than the inverses (1x111 and 7x9) i dont think so, but i might be missing some

[dreamy spire]

2xy-x-y=110 can you rewrite this somehow?

Idk I still think we are missing something

it cant be just trial and error

no you are right

it can be only those two possibilites

but how can we know

<@&286206848099549185> ??

[twin meteor]

hi

where is the question

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[dreamy spire]

A 2×3 frame can be divided into 1×1 squares by placing 7 matches as
in the picture. Which a × b frames, where a b, can be divided in this way by
exactly 110 matches? Determine all possibilities.

[dreamy spire]

right here

[barren hound]

it might be good to try a few cases

how many matches does it take to divide a 3x3 grid?

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@dreamy spire Has your question been resolved?

[dreamy spire]

12

already tried that

if you look a few messages back, we already got the fitting numbers actualy

Those grids are only 9x7 or 1x111

But I dont know the math solution for it so im asking here

[dreamy spire]

Somebody?

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@dreamy spire Has your question been resolved?

[languid scroll]

hey

can someone help me solve

pls i rly need help

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[proud steppe]

Start with the right side of the implication. a+2 > ...
Square both sides and subtract 3, simplify. Square again and you get an equation similar to the left side of the implication.

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[livid ice]

I feel like you could make up a bunch of rules for this

I think it's D but this is a stupid question, imo

I'm guessing that "+" does the following:

1. Concatenates the string

2. Reverses the order of the string

It would be like

323 + 2 = 2323

As an intermediate step, you first concatenate to get 3232 then reverse for the final answer

I am more curious as to the context of the exercise

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[gritty solar]

Draw a diagram for your integration region

That should make it more apparent

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[drifting cliff]

i need help with problems 1 and 2

how do u get c, e, and f?

[fluid sky]

ucan see it in the picture right

[drifting cliff]

oops my bad

e and f

maximum height for problem 2

oh wait.

[fluid sky]

have u graphed it?

if u have u can look at the graph and give the answer

[drifting cliff]

wait

do u just estimate in problem 1?

[fluid sky]

yes

there is no other way of doing it

[drifting cliff]

how do u determine without graphing?

is it h or k

the maximum height

[fluid sky]

what are h and k?

[drifting cliff]

vertex

[fluid sky]

the height is a y coordinate

[drifting cliff]

oh, so k?

[fluid sky]

yes

[drifting cliff]

okay thanks

i just solved it

WAIT

how do u solve c in problem 2?

[fluid sky]

look at the x coordinate when the y coordinate is the max

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[cinder sierra]

Prove that If we have 12 distinct 2-digit numbers, we can always find two of them whose difference is a two digit number of the form n = AA (a two-digit number with both digits the same)

i get that i'm supposed to use the pigeonhole principle here but i'm not really sure how. so far, i have that there are 9 distince differences that we are looking for, 11, 22, ..., 99 and of the 12 numbers, there are 66 pair options (12 choose 2) but how does the pigeonhole principle apply?

[cinder sierra]

wait actually 99 doesn't could right?

*count

[loud pilot]

think about using modulo

[cinder sierra]

like mod 10 or something?

[runic chasm]

i don't know if this would work, just throwing things in the air. Maybe trying to choose numbers in a way they dont fall into this prohibition will show something. I'm thinking, if you choose 1, 2, 3, 4... up to 10, then you will not be able to write any numbers like 1+11, 1+22, 1+33..., neither 2+11, 2+22... and like that.

[loud pilot]

think about it more

what's a good mod base we can use for this problem

[cinder sierra]

11?

[loud pilot]

yea

[cinder sierra]

OHHH i see i see

[loud pilot]

👍

[cinder sierra]

thank you so much!

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[trail mango]

this is also a good idea

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[soft zealot]

Rin

[gritty solar]

I guess take $a_n = (-1)^{n+1}/n$ and $b_n = (-1)^{n+1}/n^2$

[soft zealot]

neon

[gritty solar]

nah

Oh wait just take -1/n^2 and 1/n^2

both converge conditionally

and the max also converges conditionally

[timber rivet]

this..?

[timber rivet]

This converges absolutely

[gritty solar]

wait nvm I got the definitions mixed

I thought absolute => conditional

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[pearl wraith]

cosx >0.6
If I do inverse of both sides will the inequality flip or nah?
(i dont know how to prove or check)

[pearl wraith]

dont know if it will be arccos(0.6) < x or what

also can u @ me if u know thanks

[rigid sonnet]

0.6 a little lesser than pi/4

see the graph at that area

[pearl wraith]

i am asking if doing this
arcos[cos(x)] and arcos[0.6] will flip the inequality sign

sorry not good at english

like when we multiply negative 1 we flip the inequality sign

[rigid sonnet]

apologies, i gave you the wrong idea there
if cos(x) > 0.6, then x has a fixed range in the principal branch

you cant just flip or unflip the sign here

there are x values above and below 0.6 which satisfy your equation

[pearl wraith]

hmm

[rigid sonnet]

approximately your eqn satisfies for x values between -0.927 to 0.927

[pearl wraith]

okay wait let me just type the original quesiton

[pearl wraith]

there is this equation
zeta = cos(B)
we want to shade the region where zeta>0.6
but we start counting the angle here

am i making sense

sorry

so basically i am triyng to look for an inequality for Beta

for B

for |B| i mean

[rigid sonnet]

should i consider the symbol B as beta here?

[pearl wraith]

yea

sorry i forgot how to type latex in discord

$|\beta|$

[soft zealot]

ahtrader

[rigid sonnet]

is the image you uploaded also given in the question or did you draw it yourself

[pearl wraith]

i draw it

the expected result is like this

the blue region is where zeta>0.6

[rigid sonnet]

cos (B) will be the values on the x axis and so will be zeta

so all x values above 0.6 should be considered

[pearl wraith]

nah nah

i forgot to mention that this is the s-plane

the horizontal line is for s

and the vertical line is jw

[rigid sonnet]

and the vertical?

[pearl wraith]

i am basically just looking for a expression for $\beta$ from
$\cos(\beta) > 0.6$

[soft zealot]

ahtrader

[pearl wraith]

so i know where to shade

[rigid sonnet]

and Beta should be an angle in radians here right?

[pearl wraith]

degrees

[rigid sonnet]

okay then i would first draw a circle of radius 0.6, we need magnitude greater than that so the part inside the circle is out

[pearl wraith]

i knkow it is weird i am having a hard time with this too (control theory)

[rigid sonnet]

now we need to pick an area outside the circle

[pearl wraith]

ok

[rigid sonnet]

cos(\beta) > 0.6 but i dont think 0.6 is a standard value for cosine which you can calculate by hand

[pearl wraith]

i got calculator

arccos(0.6) \approx 53.13 degrees

[rigid sonnet]

well then we can simply do cos inverse 0.6, the principle range is from 0 to pi

[pearl wraith]

okay

[rigid sonnet]

or 0 to 180 degrees

now the sign part you asked makes sense

[pearl wraith]

okay

[rigid sonnet]

it should be \beta < 53.13 degrees, the sign does change because cosine is a decreasing function near those values

[pearl wraith]

okay

so

[rigid sonnet]

so you can shade the region outside the circle for angles between 0 and 53.13

[pearl wraith]

u are saying if i got a exprssion like this
cos(B) > A
and i use inverse

then i will get this B < arccos(A)

[rigid sonnet]

not always it depends on what A is

[pearl wraith]

A is always between 0 and 1

for my usecase

srry this is very specific

and noob question

[rigid sonnet]

well then you can reverse it, since cos (90) = 0 and cos (0) = 1

it is decreasing in the entire domain

[pearl wraith]

okay

thank u

just 1 more thing

its the same with ln right

A > B
ln(A) < ln(B)

oh nah

nvm

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[teal robin]

I have this question to do and I am having trouble with the final step

[teal robin]

I know that I need to use the principle of inclusion-exclusion to remove what does not consider the restrictions but I am unsure how to

I tried to make a venn diagram to visualize it but I am not sure that I did it correctly.

[runic needle]

can u summarise what u need to show in ur final step

[humble oriole]

Are these hand written

[teal robin]

I think I need to remove what doesn't consider the restrictions from A using

 $|B|, |C|, |D|, |B \cap C|, |B \cap D|, \text{and } |C \cap D|$ 

[humble oriole]

$\cap$

[soft zealot]

heavenly_lamb_61155

sara 🧸

[teal robin]

Yes

[runic needle]

i don't understand this sentence

[teal robin]

Which one?

[runic needle]

.

[teal robin]

Idk maybe I am saying it wrong then. What I mean is I want to find the number of non-negative integer solutions by removing the numbers that do not consider the restrictions, using these sets:

$|B|, |C|, |D|, |B \cap C|, |B \cap D|, \text{and } |C \cap D|$ 

I'm sorry idk how else to explain it

[soft zealot]

sara 🧸

[plain star]

what 😭

[teal robin]

I just mean I want to use those sets (that I used in my progress for this question) to find the number of non-negative integer solutions

Please let me know what I am saying that is too confusing lol

.close

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[minor bramble]

@fringe mulch you can ask here

[final saddle]

Please don't occupy multiple help channels.

[minor bramble]

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[pliant plover]

.open

.reopen

.close

i dont undertsand this

[torn eagle]

#❓how-to-get-help

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[glad basalt]

how is this equal to this

wouldn't the (x-1)^2 go to the numerator

[solar glade]

Yes

[glad basalt]

so this is wrong

[solar glade]

Apparently yes, it is wrong

[glad basalt]

are you telling me the king professor leonard is wrong

[solar glade]

The two expressions are not the same

You also saw that

Everybody makes mistakes

Unless

The second line is larger

[glad basalt]

it is I think

the top is a fraction

[solar glade]

Then is correct

(A/b)/c = A/(bc)

In the other hand: A/(b/c) = (Ab)/c

So that should clarify he is correct

[glad basalt]

alright ty

[solar glade]

Welcomed

!done

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[elder depot]

C) Show that there is a point P with x coord = 0 at which the line tangent to the curve at P is horizontal. Find the y coordinate of P.
D) Find the value of d^2y/d^2x at the point P found in part C

<@&286206848099549185> please

the function is y^2 - x^2y = 6

and the derivative is

2xy/(2y-x^2)

<@&286206848099549185>

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[elder depot]

<@&286206848099549185>

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[runic chasm]

Can you take another photo? I'm not really confident I can help u but having a better quality image would definitely help.

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[timid mist]

This is basic algebra but I’m not sure what to do

((5n+5)^1/2 (2n^2+7))/(2(n+1)^2 +7)(5n)^1/2 is what I have so far

How to simplify

[verbal aurora]

Do you realize the fact you are doing Algebra 2 because that is not Algebra I..

[timid mist]

This is calc

I’ve just completely forgotten how to do it tbh

I got the answer though

[wise elbow]

i dont think you need to simplify to solve the limit

[timid mist]

Since a^2/(b)^2

Then

(A/b)^2

[timid mist]

How would you do it

[wise elbow]

do you rmbr what the ratio test is?

[timid mist]

Mhm.

Plug in n+1

For every n

Then take reciprocal of og thing

If lim>1 then it’s di

If lim<1 then con

This is all abs value

If lim=1 then inconclusive

[wise elbow]

oh wait

sorry

[timid mist]

?

[wise elbow]

i didnt see your first image

[timid mist]

What were you picturing

[wise elbow]

the parenthesis was making it impossible for me to visualize what u typed here lol

[timid mist]

My bad

Thanks for help guys

The answer was 1

And inconclusive.

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[craggy citrus]

s

[craggy citrus]

How does this guy get the 3?

like how does he add up 4, 1 and 4

to get 3?

this is for solving vertex forms

[wise elbow]

x^2 + 4x + 4 is simplified to (x+2)^2

from there 1 -4 = -3

hes completing the square

[craggy citrus]

what if the quadratic equation was: x^2 - 5 + 20

how would do i do that step by step using this method?

[wise elbow]

in f(x) = x^2 - 8x + 5 what is the coefficent of x

[craggy citrus]

not sure

[wise elbow]

wait do you only need to find the vertex?

[craggy citrus]

yea vertex form

[wise elbow]

or are you trying to put it in vertex form

[craggy citrus]

yea

[wise elbow]

well theres a difference between putting it in vertex form and finding the vertex

[craggy citrus]

i need to put in vertex form

[wise elbow]

how about i explain an easier way to find the vertex then how you can put the vertex in vertex form

[craggy citrus]

Sure

[wise elbow]

okay

so the formula for the x value of the vertex is simply -b/2a

where in standard form a quadratic is = a x^2 + bx + c

does that make sense?

[craggy citrus]

Yes

Thanks

[wise elbow]

okay so from there

you can plug your x value back into the original equation to get the y value of the vertex

[craggy citrus]

how can i do that visually

[wise elbow]

take for example the problem x^2 -4x + 10

what would your a, b, and c be?

[craggy citrus]

a=1 b=-4 c=10

[wise elbow]

okay so plugging the values into the formula, what would you get for the x-value of the vertex

[wise elbow]

i dont quite understand what you mean by this

[craggy citrus]

just like step by step

[wise elbow]

oh okay

[craggy citrus]

2

[wise elbow]

1. Put equation in standard form ax^2 + bx +c = 0
2. Determine a,b, and c values
3. Plug values into the equation -b/2a to get x value of the vertex
4. plug x value back into original equation to get y value of the vertex

those are the steps to finding the vertex

to convert from vertex to vertex standard form its: (x - {x value of vertex}) ^2 + {b value of the vertex}

[craggy citrus]

what if its negative C would i still put a + in the formula

[wise elbow]

what do you mean

[craggy citrus]

in the formula it states everything is postive but what if my orginal equation had a negative

would i follow the formula's postives or the orginal equations negatives and postives?

[wise elbow]

follow the negatives and positives

your a, b, and c values should account for the differences between (+) and (-)

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[coarse coral]

Could someone please help me with this problem?

Here’s my work^

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[rugged idol]

How do I solve this problem?

[blissful meadow]

Change of basis formula

[rugged idol]

did u mean change of base formula?

[blissful meadow]

Yes

[rugged idol]

So its just

potato chromebook

sorry for the long reply time

@rugged idol

odd this channel didnt show up on mobile

.close

[final saddle]

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[final saddle]

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[gritty solar]

wait could you restate

[final saddle]

@timber rivet Has your question been resolved?

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[amber portal]

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[graceful geyser]

Whatchu not understand

What u try

[pliant shore]

quotient rule

[amber portal]

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[pliant shore]

yes

[amber portal]

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[final saddle]

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[final saddle]

✅

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[pliant shore]

what do you have so far?

[amber portal]

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[pliant shore]

well $h'(x) = \frac{f'(x) (g(x) + 3x) - (f(x) + 1) (g'(x) + 3))}{(g(x) + 3x)^2}$ right

you should write out this step first to avoid confusing yourself

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[soft zealot]

south's secret twin brother

[amber portal]

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[pliant shore]

yes it's a different multiplication order

so you can write (g(x) + 3x)) f'(x) and so on

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[pliant shore]

yeah?

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[pliant shore]

ah it should be (3 + 1)(-2 + 3) instead