help-23

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[stone birch]

can someone help

[safe radish]

Please don't occupy multiple help channels.

[plucky elk]

!noclopen

[safe radish]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

[stone birch]

but u r not helping

🙁

[plucky elk]

.

[stone birch]

what do i do then

riemann:(

[glass carbon]

Use standard parametrization for a circle

x = h + rcos(t)
y = k + rsin(t)

Are you able to determine the center and radius of the circle?

[plucky elk]

#help-20 message

[safe radish]

@stone birch Has your question been resolved?

[stone birch]

i got part a and b

but stuck in c now

[safe radish]

@stone birch Has your question been resolved?

[loud cedar]

Can someone help with no.2

How to illustrate in Venn diagram

<@&286206848099549185>

[safe radish]

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).

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[safe radish]

Channel closed

Closed due to timeout

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[thick mauve]

Hey uh

[thick mauve]

Trig question

Answer is not same

As the back answer

Question

Here

3rd one

[median vigil]

,rotate 180

[thick mauve]

Good this exists

Idk what mistake i made

[plucky elk]

Your work looks incomplete

[thick mauve]

Hmm

Tell

Where did I do wrong

At squaring ?

I feel there

[plucky elk]

How do you get sqrt(3) = cos(45 deg)

[median vigil]

how did you distribute the square in the second picture

[naive dragon]

freshman dream kek

[thick mauve]

I ain't but I haven't revised a lil about trig

[thick mauve]

.

[median vigil]

freshman's dream is the false statement (a+b)^2 = a^2 + b^2

which you appear to have done in the second picture

[thick mauve]

Yeah

[median vigil]

what would be better is if you instead multiplied on top and bottom in such a way that you would have the difference of squares
a^2 - b^2 = (a+b)(a-b)
which we call multiplying by the conjugate

[thick mauve]

Identities done wrong

[thick mauve]

But I see plus tho

[median vigil]

so if you have a term of the form a + b, you would want to multiply top and bottom by a term of the form a - b

so that you can use that identity

[thick mauve]

This

[median vigil]

you must multiply by the same thing on numerator and denominator

in order to not change the value

[thick mauve]

Ok minus on top as well

Another mistake i guess top not right

'

'

'

'

[median vigil]

you can simplify sqrt(18)

[thick mauve]

THANKS

🙏

Arigato

It's done

I found the pattern and it's solved

.close

[safe radish]

Channel closed

Closed by @thick mauve

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[silent fractal]

I know how to do the induction part, I just cant get the algebra to work

[silent fractal]

F is the fibonnaci sequence

[astral glacier]

What have you done so far

[silent fractal]

wait i might have misread one of the identities

nvm. start with $f_{2}f-f_{1}^{2}=(-1)^n$

[flat frigate]

sodium fluoride

[silent fractal]

the inductive step $f_{3}f_{1}-f_{2}^{2}=(-1)^{n+1}$

[flat frigate]

sodium fluoride

[silent fractal]

simplify to $\left(f_{1}^{2}+f_{2}f_{1}\right)-f_{2}^{2}$

[flat frigate]

sodium fluoride

[silent fractal]

rewrite as $f_{2}f_{1}-\left(f_{2}^{2}-f_{1}^{2}\right)$

[flat frigate]

sodium fluoride

[silent fractal]

use this identity (it was a previous question)

to get $f_{2}f_{1}-\left(ff_{2}\right)$

[flat frigate]

sodium fluoride

[silent fractal]

whic is obviously not equal to $(-1)^{n+1}$

[flat frigate]

sodium fluoride

[silent fractal]

ive tried other algebras and used the inductive step to get a -1^n but it got canceled it

nothing ive tried reduces to -1^n+1

<@&286206848099549185>

[astral glacier]

The inductive step should involve n in some way

[silent fractal]

yeah that was just a shortcut to make writing it in desmos easier

f_2 just means f_2+n, f is f_n, f_1 is f_n+1

[naive dragon]

Factor out F_{n+2}, and express F_{n+2} as F_{n+1}+F_n

[naive dragon]

We haven't used our hypothesis

So yeah it should be involved somewhere

[silent fractal]

$f_{n+1}-f_{n} would be f_{n-1}$ which doesnt work because im proving for n>0=0

[flat frigate]

sodium fluoride

[naive dragon]

No we won't express F_{n+1} as F_n+F_{n-1}

[silent fractal]

i dont know where

the times i did get it involved and got a -1^n it got canceled out

[naive dragon]

$F_2(F_1-F)=(F_1+F)(F_1-F)$

[flat frigate]

Alexis_Fx

[naive dragon]

What should this be

[naive dragon]

Why don't you show it work for n>1 and then show it also work for n=0 by compute it

[silent fractal]

$f_1^2-f^2$?

[flat frigate]

sodium fluoride

[silent fractal]

true

[naive dragon]

Hmm I was think of smth but I forgot it, gimme a min

$2F_1^2-(F_1^2+2F_1 F + F^2)+2F_1 F$

[flat frigate]

Alexis_Fx

[naive dragon]

$2F_1^2-F_2^2+ 2F_1 F$

[flat frigate]

Alexis_Fx

[naive dragon]

Hmmm

[safe radish]

@silent fractal Has your question been resolved?

[naive dragon]

Okay nvm your work is wrong here

Damn it

@silent fractal you should have got F_-1F2 in this step

[naive dragon]

You should have just factor out F_2 F_1-F_2^2=F_2(F_1-F_2)=-F_2 F

[silent fractal]

but thats not -1^n+1

[naive dragon]

$F_{n+1}^2+F_{n+2} F_{n+1}-F_{n+2}^2= F_{n+1}^2-F_{n+2} F_n$

[flat frigate]

Alexis_Fx

[naive dragon]

(-1)^{n+1} is just reverse sign of (-1)^{n}

[silent fractal]

yes, it is not that either

[naive dragon]

This's our hypothesis, kinda

[silent fractal]

i am sure i am misunderstanding

oooh

right

thank you!

[naive dragon]

Np

[silent fractal]

.close

[safe radish]

Channel closed

Closed by @silent fractal

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lusty spear]

I would appreciate help with the following:

[lusty spear]

I wanted to prove if f : [a,b] -> R is a continous function then f is evenly continous on [a,b]
And [a,b] is an interval in R the real numbers

Now my idea was to approach it from the observation that whenever a function is uniformly continous then for each e > 0 there exists a d > 0 which is "good" for all x,y in the domain D.
Meaning, whenever |x-y| < d then |f(x) - f(y)| < e

I concluded that therefore for each e > 0 there must exists an infimum d* > 0 in R of the set of all "good" d(x0) for all x0 in D, meaning the d(x0) which certifies us that f is continous in x0

For all x in D : |x-x0| < d(x0) => |f(x)-f(x0)| < e

I figured this infimum must exist because otherwise we would always find some x0 in D where the d-environment has to be smaller than the d-environment we assumed sufficient for f being uniformly continous, hence its not.

Then I wanted to use the knowledge we have about f being continous on a closed interval to argue that there exists an infimum on those d(x0) for on this interval.

But somehow I dont find a way to proceed
Also I feel like the "infimum" argument is kind of unclean

Would appreciate any help

this is sort of also my intution for continous vs unfiormly continous that I came up with.

That for continous functions we only have one good d(x0) per x0 per e>0 but these good d(x0) can differ a lot

But for uniformly continous functions we have sort of a "globally" good d > 0 for each e > 0

Does that even make sense?

[peak estuary]

(just noting that evenly continuous is usually called uniformly continuous)

[lusty spear]

ah thanks a lot! :)

[safe radish]

@lusty spear Has your question been resolved?

Channel closed

Closed by @lusty spear

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[austere spade]

hi what does this notation mean for I? ive only seen it for <A> where A is a subset

[manic patrol]

an ideal of Z[X], generated by n and X.

[austere spade]

so like $I={\sum_i nX\cdot P_i(X): P_i(X)\in\mathbb{Z}[X]}$?

[flat frigate]

lyric

[obsidian oracle]

Not generated by nX, generated by the subset {n,X}

$I = {\sum_i (nP_i + XQ_i)}$

[flat frigate]

Rafilouyear2026

[austere spade]

ahh okay

i think i still need help w this problem, i need a ring homomorphism from Z[X] to Z/nZ that has I in its kernel and preserves equivalence classes

this subject is so new its so weirdddd i just cant think of how to find that

[austere spade]

bc im tyring to use this theorem

[manic patrol]

I think you are very much on the right track, barring finding the actual homomorphism here. but your attack plan looks absolutely correct.

sorry if that was not what you needed confirmation on.

[austere spade]

naw its ok thats good to hear

[manic patrol]

well, one thing the new map has to consider is that you are quotienting by (n, X).

in that case, what happens to n and X in the quotient?

[austere spade]

sorry but what does it mean, quotienting by (n,X)?

up until this semester the closest ive been to this subject of algebra was like learning about like fields so forgive my cluelessness 😭

[severe valley]

Nice to meet you.

I want to understand the current situation, so I want TL;DR

[astral glacier]

Have you done groups

[manic patrol]

nono, it's fine! I am just trying to find a way to hint at what quotients are. not to much luck at the moment, sorry.

[astral glacier]

What book are you following, what topics have you done so far

[astral glacier]

Not your fault, they might not have done quotients yet

[manic patrol]

you can check the pinned message and read your way down, not much have gone by.

[austere spade]

its an honours algebra class, if it helps here's the contents of what we've done so far

[astral glacier]

That's.. weird

[austere spade]

but yeah i did groups and stuff last semester

[astral glacier]

Oh okay

[severe valley]

Thank

[austere spade]

not much though

[astral glacier]

Do you remember doing quotients in groups

[austere spade]

honestly not really, i just remember the definition

that being the set of cosets of a normal subgroup

nothing beyond applying lagranges theorem tbh

[astral glacier]

God what uni is this just so I can tell everyone I know to avoid it

Anyway

[austere spade]

😭 😭

[astral glacier]

When you quotient by something, it is the same as mapping the ideal generated by that to zero

In this case, we want to quotient by (x, n)

Well, we want (x, n) to be among the things we quotient by

Easier to just use them directly

[astral glacier]

Now based on this, what can you say

[austere spade]

uhh well thats what i wanted, to have the ideal generated by (x,n) to be in the kernel of the map

does that tell anything about how to construct such a map?

like i cant tell whether the map should evaluate it at a point, or do something with the degree, irdk

[astral glacier]

^^

[manic patrol]

if an ideal generated by some elements is mapped to zero, what do you think the generating elements are mapped to?

[austere spade]

well zero

[manic patrol]

yes!

now, what kind of ring is Z[X]?

consider a general function of the kind of ring Z[X] is.
then, using what you've answered me with, identify what would happen once you start quotienting by X first.

[austere spade]

only way i could imagine that happening is by evaluating at 0

[manic patrol]

yes! but evaluate what at 0 exactly? and what does that result in?

it is at this point you will find it helpful to start writing things out.

[austere spade]

alr just did, i assume evaluating X at 0? like the map should be $f:P(X)\to P(0)$, but given an arbitrary $\sum_i (nP_i + XQ_i)$, we get $$f(\sum_i (nP_i + XQ_i))=nf(P_i(X))+f(X\cdot Q_i(X))=n\cdot P_i(0)$$ which isnt necessarily zero

[flat frigate]

lyric

[manic patrol]

but you have noted that such a polynomial must reduce to its constant term.

[austere spade]

OHH

AND THAT MOD N IS 0

so f should evaluate X at 0 modulo n which gives an image in Z/nZ

[manic patrol]

yes!

actually a slight caution to your wording

oh wait, never mind, ignore what I said.

you may proceed.

[austere spade]

YAYY

THANKS QUEEN ❤️ ❤️

[manic patrol]

please thank Xavier. he's really the one who made that most important point clear. I practically did nothing.
anyway, is there anything else you would like to ask?

[austere spade]

u were both a great help in my understanding of factor rings but yes @astral glacier tysm <333

[astral glacier]

Oyi give yourself some credit too

[manic patrol]

I can't give myself undue credit, sorry.

[austere spade]

https://cdn.discordapp.com/attachments/439187946885611521/1262114271207362711/cometiny.gif

[astral glacier]

[austere spade]

i think i can continue with this problem sheet fine now, thankuuuu

[astral glacier]

Good luck!

[manic patrol]

good luck, OP!
if you have no other problems, I think you may close the channel with .close, and see you around!

[austere spade]

i hope so! ^w^

.close

[safe radish]

Channel closed

Closed by @austere spade

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[frosty leaf]

not sure about statement 1 alone

can i get some hlep

I know that i need both x and y, but the way i arrived at 36/y = 9x/y i am starting to second guess wether i really need y

y could be 0 .. maybe thats the issue ?

[quasi bison]

how exactly do you envision y being 0

anyway, regardless of which data you're working with, y is an input to the problem. the answer will be in terms of y.

[frosty leaf]

makes sense, there are no workers if y is 0

[safe radish]

@frosty leaf Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[pearl ravine]

Can sm1 help ?

[stiff magnet]

Is it parallel to the line AC

?

[quasi bison]

,rccw

[stiff magnet]

How are m and n defined

[quasi bison]

yeah what are these points M and N?

also if you wanna refer to the line going through them that's just called MN. no comma in between.

[pearl ravine]

No they are not

[quasi bison]

?????

what do you mean, "No they are not"

wtf are they? we're given no data here at all

[pearl ravine]

Yes

They want the slope of mn

X1+ x2

2,

?

Then y1+y2

---

2

?

[quasi bison]

......

you're making zero sense right now

[pearl ravine]

Ik thats why i need help

[quasi bison]

right now you have not even told us what the question tells you about points M and N

so we don't know on what info we could even find either of them

[pearl ravine]

Mid point

[quasi bison]

so, it tells you that M and N are the midpoints of AC and BC respectively?

[pearl ravine]

Yes

[quasi bison]

you need to mention that sort of info upfront next time, jsyk

ok

[pearl ravine]

Okk

Mb

[quasi bison]

ok then like... this mess, i guess is your attempt to write out ( (x1 + x2)/2 , (y1 + y2)/2 ) i.e. the midpoint formula?

yes, you can use this formula to find the coordinates of M and N. yes you will need those ||(though there's a shortcut actually)||

[pearl ravine]

This

[pearl ravine]

What is it if u dont mind ?

[quasi bison]

MN has the same slope as AB, so you don't even need to bother finding M or N individually.

[pearl ravine]

If i found

Ab

Is 1/2

Mn?

Or mn is 1/2 ab?

[quasi bison]

i have no idea what you just asked

[pearl ravine]

So like

This

[quasi bison]

i am not asking you to find any segment's length

so this is completely irrelevant to the question

[pearl ravine]

Ohhh

U wanted mr to to tge first thing i did twice

[quasi bison]

no

[pearl ravine]

Firstly is a and c then b and c

[quasi bison]

no

MN has the same slope as AB
did you see this

[pearl ravine]

But how

[quasi bison]

"how is this true?" or "how do i use this?"

[pearl ravine]

Hoa is this true

[quasi bison]

geometrically, triangle CAB is an enlargement of triangle CMN with center C and scale factor 2

[pearl ravine]

Ohh

Larger on smaller ?

[quasi bison]

i again don't understand your question.

[pearl ravine]

Pls say this is right

[quasi bison]

the notation is wonky, it doesn't make use of my shortcut (even though you explicitly asked for it), and the final answer -4/2.5 is unsimplified.

despite all this, -4/2.5 is the correct value.

(but i would want you to put it into simplest fraction form)

[pearl ravine]

How would i use it ?

Into the simplest fraction form

[quasi bison]

well, can you write 2.5 as a fraction, and do you also know how to divide fractions?

[pearl ravine]

Yes

But this is right ?

The solving i did

[quasi bison]

despite all this, -4/2.5 is the correct value.
i already said it

i can repeat it more times if you need

i do not know how else to tell you what i think about your work

[pearl ravine]

-1.6

This is how it ended

When i did divide

[quasi bison]

ok, you made it as a decimal. that's fine.

[pearl ravine]

Oh so thats for this ?

I get it

Now

M is the center point of a and c

[safe radish]

@pearl ravine Has your question been resolved?

Channel closed

Closed by @pearl ravine

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[indigo thistle]

i was doing some programming in rust and used the default hasher to generate a u64
i then flipped a single bit (from a 0 to a 1) and the hash stayed the same

what are the odds of this? i reached about 1 in 4 quintillion but my math is literally half of the odds of generating the same u64 twice
i have no idea of how to compute this to a higher level of accuracy

(a u64 is 64 bits aka. 64 ones and zeros (ordered))
(i asked the rust nerds, but we then reached the conclusion to ask the math nerds)

[honest perch]

what are you hashing

[indigo thistle]

technically numbers???

i dunno the full code definition has abt 600 lines so...

its big

but it shouldnt result on the same hash either way

[honest perch]

are you just generating 64 bits randomly

[indigo thistle]

nope

[honest perch]

idk how hashing works mb

[indigo thistle]

me neither ngl

i just know that it shouldnt happen

[honest perch]

i know that encryption is something where you have a string or something and convert it a sequence of bits or something

and the same string always gives you the same bits

[indigo thistle]

yeah, then this sequence of bits goes trough an algorithim that returns another fixed lenght string of bits (the u64)
this sequence should vary wildly based on the input string

i also checked, its not a bug, just a coincidence

[honest perch]

i think hashing is the same as encryption

[indigo thistle]

the algorithim i used to generate such hash is SipHash 1-3

[honest perch]

ok and what was your input string?

[honest perch]

^

[indigo thistle]

its very gigantic, about 500 bits in length
in theory the input shouldnt matter

[honest perch]

like what data are u encrypting

[honest perch]

ok

[indigo thistle]

um

this

#[derive(Debug, Serialize, Deserialize, Hash)]
pub struct Pipeline {
    pub name: String,

    pub system: System,
    pub target: Action,

    pub dependencies: Vec<Dependency>,
    pub dependents: Vec<PlChild>,

    pub logger_options: Option<LoggerOptions>,
    pub store_options: Option<StoreOptions>,
}

the full definition abt 600 lines long

[honest perch]

so you changed 1 bit in the input and your output was still the same?

[indigo thistle]

yep

also

it only happens if its engulfed inside Pipeline

the bit itself is a part of Action

¯_(ツ)_/¯

[honest perch]

no idea what that means

anyways

from what i've found online, it is possible for hashing function to give the same output for 2 different inputs

[indigo thistle]

yep

[honest perch]

this is known as collision

[indigo thistle]

but the odds are ridiculously low

expecially for close inputs

[honest perch]

well the function itself is not random so idk how you would find odds

[indigo thistle]

buahh

[honest perch]

but ok let's say we know nothing about this function and want to pretend that its output is random (but fixed)

[indigo thistle]

its supposed to work like a random function tho

[honest perch]

then the prob they are equal is 1/2^(64)

[indigo thistle]

just that the same input gives the same output

[honest perch]

then our approximation is pretty good

[indigo thistle]

nice

okidoki then

thanks!!!!

.close

[safe radish]

Channel closed

Closed by @indigo thistle

Use .reopen if this was a mistake.

[honest perch]

welcome

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[radiant ice]

I was thinking 15 because that's the middle of the table

[covert yoke]

how many restaurants in total are there?

[radiant ice]

17

[covert yoke]

do you remember the definition of median?

[radiant ice]

like middle

[covert yoke]

can you be more specific?

[radiant ice]

like data set is 1 2 3 4 5

the median is 3

[covert yoke]

what if the dataset is 1 1 1 2 2 2 3 4 5?

[radiant ice]

2

[covert yoke]

alright, so if you line up the restaurants in a similar manner, because there are 17 of them, which restaurant will be the middle numbered one?

[radiant ice]

is it not 14-19(employees)

[quasi bison]

not answering OE's question

[covert yoke]

Rather than answering directly, I'm trying to lead you to figuring out the answer, maybe you're correct, maybe you're wrong, but the reasoning you used before was faulty and I'm pointing that out

[radiant ice]

do i have to like write

[covert yoke]

I didn't to figure it out, but I'm very experienced in these sorts of basic probability questions, you might need to

[radiant ice]

out the table

as like a list

[covert yoke]

you can but again you don't need to

[quasi bison]

@radiant ice OE is trying to guide you in a more general direction:

if you have a list of 17 numbers, then at what position in the list will you look for the median?

[radiant ice]

oh like 8.5

[covert yoke]

well, remember that if you have 3, the middle index will be 2, that's because indexing starts with 1.

[radiant ice]

so 8 or 9

[covert yoke]

so it's not 9.5 but 9, (17-1)/2 + 1

[radiant ice]

oops

well

[covert yoke]

it's confusing, and it's generally not well explained in the material

[radiant ice]

if you have 16 numbers middle is 8 no?

[covert yoke]

the middle one is (16-1)/2 + 1 = 8.5, in other words you would take the 2 member average of items 8 and 9

[radiant ice]

so like why 😭

[covert yoke]

what's the middle number in the list 1 2 3 4?

it's not 2 and it's not 3, it's in between them, so we take the average of 2 and 3 and we say that 2.5 is the median

[radiant ice]

oh ok

[covert yoke]

anyway

[quasi bison]

https://www.reddit.com/r/math/comments/4dbc0x/the_middle_of_7_is_4_how_would_you_explain_this/

[covert yoke]

anyway, so you have 17 restaurants

you line them up in the manner I described before,

in which bin does the 9th restaurant appear?

[radiant ice]

middle is 9

[radiant ice]

14-19

[covert yoke]

why do you think that?

ok, different question, in which bin does the 2nd restaurant appear?

[radiant ice]

2-7

[covert yoke]

what about the 3rd?

[radiant ice]

8-13

[covert yoke]

and the 6th?

[radiant ice]

8-13

[covert yoke]

and the 7th?

[radiant ice]

14-17

[covert yoke]

and the 8th?

[radiant ice]

14-17

[covert yoke]

now, where's the 9th?

[radiant ice]

14-17

wait

that’s a2

[covert yoke]

yup

so it's not in 14-17

[radiant ice]

20-25

[covert yoke]

there you go

[radiant ice]

wait w

thanks

.close

[safe radish]

Channel closed

Closed by @radiant ice

Use .reopen if this was a mistake.

[covert yoke]

no worries, it's a little counterintuitive

so I wanted to make sure that you stepped through it and really understood what was going on

[radiant ice]

i suck at data problems 😭

[covert yoke]

nah, you don't suck, you're just learning

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hybrid pier]

can someone help me find a group isomorphism between ${z\in\mathbb{C}: |z| = 1}$ and $\mathbb{C}-{0}$?

[flat frigate]

Hanno

[hybrid pier]

maybe Zorn's lemma something?

I know there is a $\mathbb{Q}$-vectorspace isomorphism between $\mathbb{R}$ and $\mathbb{C}$ if that's useful

[flat frigate]

Hanno

[plucky elk]

yea so you just need an isomorphism from the unit circle to R and then you can compose the two and you're done

[hybrid pier]

but will that respect multiplication?

[plucky elk]

try it and see

[hybrid pier]

but if we let R be additive, then 0=f(1)=f(i^4)=4*f(i) which can not really be

[queen ingot]

the complex numbers with absolute value 1 is isomorphic to the (additive) group R/Z, can it really be isomorphic to R as well?

[peak estuary]

obviously no as there is no element of order 4

[hybrid pier]

I think an isomorphism would have to fix all elements e^(2pi i r) with r rational as they are the only ones with finite order in both groups, or at least map them to each other

[peak estuary]

some other probably important isomorphic groups here are C-{0} = unit circle * R_>0^* and R_>0^* = R

[queen ingot]

this is for R and C as additive groups though, right?

[hybrid pier]

additive vector spaces

so it's homogeneous with respect to Q as a bonus if that's ever useful

[queen ingot]

oh it's on wikipedia but they didn't give an explicit isomorphism

https://en.wikipedia.org/wiki/Circle_group#Group_structure under "group structure"

[peak estuary]

giving an explicit one isnt that nice but the intuition is not that bad

both C-{0} and unit circle are some number of finite order elements and then an uncountable rest. C-{0} is just one direction more. but who cares about one direction in infinite dims

you just have to put it together properly

[peak estuary]

and this is helpful for that

[safe radish]

@hybrid pier Has your question been resolved?

[hybrid pier]

yeah then maybe let $A={e^{2\pi i r}: r\in\mathbb{Q}}$ be the elements with rational argument and then find an isomorphism between $S^1-A$ and $\mathbb{C}-{0}-A$ and fix the elements $A$ and hope that that respects multiplication properly

[flat frigate]

Hanno

[peak estuary]

you cant just subtract it, no

we have almost all the pieces. we know that unit circle = R/Z

we know that R=R^2

we know that unit circle * R = C-{0}

we just need to put it together properly

[safe radish]

@hybrid pier Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[blazing olive]

hello fellow friends i do have an exam tomorrow and wonder if someone knows how to solve this question. I have been breaking my head for hours

[safe radish]

@blazing olive Has your question been resolved?

[safe radish]

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

@blazing olive Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[open lodge]

Can someone help the question is solve for x and I know I got the right side right but the left side is making me blow up

[magic junco]

Quick question, are there ?

[open lodge]

wdym

I just put them there to help show me where the numbers were going

[magic junco]

Is it
$\frac{(\sqrt2)^x}{2} or \(\frac{\sqrt2}{2}) ^2$

[flat frigate]

雙目

[open lodge]

the top one

[magic junco]

So presumably it applies to the right one, right?

1 to the power of x-2

[open lodge]

ya

[magic junco]

Then why did you include it to the 8 in the denominator?

[open lodge]

wdym

idk what you mean by that

[magic junco]

$\frac18^{x-2} = \frac18$

[flat frigate]

雙目

[magic junco]

Look, you only applied the power x to the sqrt2 on the left side

While you applied x-2 to the entire fraction on the right side

[open lodge]

ohhhhh thank you

[magic junco]

imo they presumably want you to apply the power to the entire fraction on both sides

[open wedge]

By normal notation, each of the exponents is only applying to the numerator

[drifting terrace]

isntx = 2?

[open wedge]

!nosols

[safe radish]

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.

[magic junco]

Nevertheless it’s kinda ambiguous so you prolly should verify it with your TA

That’s everything for this question, if you’re done with this channel don’t forget to close it by typing .close

[open wedge]

!done

[safe radish]

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

[magic junco]

.solved they left the server

[safe radish]

Channel closed

Closed by @magic junco

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hybrid oyster]

OMG

[hybrid oyster]

Bro你在这里啊@magic junco

[quasi bison]

!noping

[safe radish]

Please do not ping individual helpers unprompted.

[quasi bison]

do you have a question to ask?

[hybrid oyster]

NO

Thanks

[normal moss]

[hybrid oyster]

yes

[quasi bison]

ok then .close the channel please

[hybrid oyster]

.close

[safe radish]

Channel closed

Closed by @hybrid oyster

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wind basin]

I have no idea where to even begin with this even though I've been staring at it for maybe a day now, and i feel like it's quite simple and im missing something. Any help would be appreciated

[safe radish]

@wind basin Has your question been resolved?

[wind basin]

<@&286206848099549185>

[brittle mango]

not a proper helper, although just curious (and so i might be able to help better), what field is this fromm ?? (havent seen it before)

[wind basin]

this is set theory but probably overlaps with some others for this particular question

I suspect I might have to analyse $\Phi(\gamma)$ in the supremum and relate it to 1 but im not sure how

[flat frigate]

charnixe

[brittle mango]

yeahh it might have to do with the fact that as gamma approaches alpha it nearly becomes alpha (sorta like the epsilon^2 = 0 thing) but i dont know the notation welll

[wind basin]

well this is less so to do with the function but rather the properties of limit ordinals i think, but good instincts!

<@&286206848099549185>

[brittle mango]

im not sure if this will help, but i found this on the wiki describing the lemma of fixed-point for normal functionss

[brittle mango]

and idk if this is discussed or already obvious from what you've been reading, but the second property is apparently just describing that phi is continuouss

[wind basin]

mhm

[wind basin]

oh hm ok

[sharp tangle]

Actually, i think this pretty much answers his question

[wind basin]

yeah lol

but im quite confused, where did you find this?

[brittle mango]

it was literally just wikipedia hehe lemme get the linkk

https://en.wikipedia.org/wiki/Fixed-point_lemma_for_normal_functions

includes background and formal statementt

[wind basin]

i dont think \Phi is normal

it's not necessarily strictly increasing

[brittle mango]

ohhh yeah i see now because of the <= rather than the <

[wind basin]

yeah

[sharp tangle]

Actually, it still works

[wind basin]

oh?

[sharp tangle]

Regardless

[brittle mango]

because its either increasing or staying the samee ??

[sharp tangle]

Because it is not decreasing

As long as it increases, it will still hit some fixed point

[wind basin]

yes, the proof is by necessity of the fact that that is the question

but this lemma in particular doesn't apply

[sharp tangle]

hmmm

I still think it works if you just be a little fuzzy with the technicalities

[wind basin]

perhaps

i think it's pretty much that lemma but we change it

[sharp tangle]

I wish i could help more but I don't have any pen and paper to write on

So i'm trying to eyeball everything

[wind basin]

oh shit

it's actually pretty like

[wind basin]

this just clicked

we can just pretend its strictly increasing cuz if equality ever happens its Q.E.D.

.close

[safe radish]

Channel closed

Closed by @wind basin

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[kind galleon]

Ok one more question, what is the difference between usage of translation vector and inside + outside translations?

[kind galleon]

The translation vectors work horizontally also reversed or they just manipulate the cordinates?

[rustic yoke]

hmm

[kind galleon]

I got this in conceptual knowledge

But the issues is that it seems to work the different way

So they are contradicting pretty much

Oh shit no they aren't

Im sorry

.close

[safe radish]

Channel closed

Closed by @kind galleon

Use .reopen if this was a mistake.

[delicate shore]

just a note, "inside" corresponds to horizontal translation and "outside" corresponds to vertical

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[split kelp]

i dont understand that formula why is it even true and how it even be discovered

[quasi bison]

do you know what a linear transformation is?

[split kelp]

yeah i do

[quasi bison]

right

and you know how in the single variable case for a differentiable function f of one variable you have that f(x+h) is well approximated by f(x) + hf'(x), yes?

namely that $f(x+h) = f(x) + f'(x)h + o(h)$ or some notational variation of this

[flat frigate]

Ann

[split kelp]

yes i do

[quasi bison]

yeah so that formula is the multivar equivalent of that

[split kelp]

o(h) for very little numbers that doesnt even need to be considered

[quasi bison]

f'(x) is now a matrix instead of a number

[quasi bison]

no not really

[split kelp]

oh

[quasi bison]

do you know little-o notation

[split kelp]

ye

[split kelp]

so is it like
f(x+h)-f(x)-o(h)=f'(x)h

[quasi bison]

mm not really

f(x+h) - f(x) - f'(x)*h = o(h)

thats your idea here

going into high dimension you swap out o(h) for o(|h|)

[split kelp]

oh

why are we even trying to find o(h)

or doing our operations via o(h)

[split kelp]

ye i did not understand the norm part too

[quasi bison]

we are not "finding" o(h)

f(x+h) - f(x) - f'(x)*h = o(h) is not even an equality as such

rather it is the statement that, for small h, f(x+h) - f(x) - f'(x)*h is vanishingly small COMPARED TO h

i could write down $$\lim_{h \to 0} \frac{f(x+h)-f(x)-f'(x)h}{h} = 0$$ as well

[flat frigate]

Ann

[split kelp]

i get that we use o(h) but still didnt understand why do we even use it

[glacial pumice]

https://courses.maths.ox.ac.uk/mod/resource/view.php?id=7804

I liked the exposition given in this set of notes

You can look at pages 8–12 to motivate the definition of the total derivative in higher dimensions

[split kelp]

oke

.close

[safe radish]

Channel closed

Closed by @split kelp

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[cobalt raft]

How does one go about solving this? I know it's in quadrant 2

[plucky elk]

do you know that sin(-t) = -sin(t)

[cobalt raft]

hmm im guessing its odd

csc (-t) = - csc (t)

am i correct to say that

like i know how to solve this

[glass carbon]

Yes

[cobalt raft]

but im clueless as what to do with the theta

[glass carbon]

in csc(-θ)?

[cobalt raft]

mhm

i have no idea what to with that info

i only know that were dealing with quadrant 2

[glass carbon]

if csc(-θ) = -csc(θ), then it's enough to determine whether csc(θ) is positive or negative in the 2nd quadrant

(in fact whether sin(θ) is positive or negative)

[cobalt raft]

The answer would be negative

[glass carbon]

Yes, because sinθ is positive in the 2nd quadrant

[cobalt raft]

mhm

but i still understand why we have to change it

[glass carbon]

and hence csc(θ) is also positive there

right?

[cobalt raft]

why do we have to change csc(-θ) = -csc(θ)

cant we just leave it as csc(-θ) and either way in quadrant 2 they are negative

OH IM WRONG

wait im lowk confused 😵‍💫

csc --> 1/sec

[glass carbon]

cscθ = 1/sinθ

[cobalt raft]

mhm

yes

[cobalt raft]

im still confused on this part though

[glass carbon]

theoretically you don't have to convert it, but if you consider -θ, then -90 > -θ > -180 so it's as if it was in the 3rd quadrant

then sin(-θ) < 0 and obviusly csc(-θ) < 0

which is excatly the same thing

I think it's "less intuitive" way to do this

[cobalt raft]

ohh ok ok

yeah tysm for clarifying

.close

[safe radish]

Channel closed

Closed by @cobalt raft

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[quick valley]

A plane is steering at N450E at an air speed of 525 km/h. The wind is
from N600W at 98km/h. Find the groundspeed and track (or course) of
the plane

[quick valley]

I really need help im trying to understand it

[safe radish]

@quick valley Has your question been resolved?

[safe radish]

@quick valley Has your question been resolved?

[fickle jacinth]

<@&286206848099549185>

[main matrix]

do you mean 45 degrees east and 60 degrees west?

so to rewrite, the plane vector has speed 525 km/h and heading 45 degrees between north (up) and east (right). the wind vector has speed 98 km/h and is blowing towards the south east (right + down) an angle of 60 degrees

are you familiar with breaking up vectors into components along the x and y axes?

[safe radish]

@quick valley Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[stone birch]

help

[safe radish]

Channel closed

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

[mighty mango]

@stone birch

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[sharp crag]

Guys I have a question about statistics:

Imagine you do some repetitions of a lab test with measurement equipment with their own uncertainty. You repeat the whole process three times, and now you have to calculate the total uncertainty.
The thing is, there are two types of way you can do this, statistically with standard dispersion and with propagation of errors. My question here is: is it statistically correct to calculate both type A and B uncertainty and then combine both with the formula u_c = sqrt(u_A^2 + u_B^2)? Or just pick one and expand and show that one as the total uncertainty? I've tried to seek the GUM for answers but I am really confused...

[safe radish]

@sharp crag Has your question been resolved?

[sharp crag]

I am now realizing that maybe this isn't a very mathematical question...

Oh well

[safe radish]

@sharp crag Has your question been resolved?

[blazing swallow]

it's a little statistical, so i think you have a good chance of getting an answer on this :) but the americans haven't woken up yet, so it might be a few hours
otherwise, you can check out #old-network for some other science-centric servers and ask questions there ^^

[safe radish]

@sharp crag Has your question been resolved?

[sharp crag]

I'll give it a look, thank you!

[safe radish]

@sharp crag Has your question been resolved?

[safe radish]

@sharp crag Has your question been resolved?

[stoic dune]

@sharp crag
Take me with a grain of salt, I am not an expert in this field. I hope anyone will correct me if needed.

Uncertainty isn't statistical. A ruler with ±1 cm uncertainty can't become more precise through multiple checks. That ±1 cm will always affect any calculation you do.

Like, if the actual measurement is 3.9 cm, you aren't going to measure 4 cm most of the time, you're going to measure 4 cm every time.

[glass carbon]

In fact, it all depends on how precisely you want to determine the uncertainty. In simple measurements (e.g. workshop measurements), it is enough to take into account the uncertainty of the measuring device, but if the measurements are more precise (e.g. mass measurement on precise scales), both components are often taken into account (and sometimes even other factors, such as air buoyancy or temperature influence)

What you are talking about is combined uncertainty (u_c) and yes, you are right, that is how it is done in practice

to calculate the expanded uncertainty U, an additional so-called confidence interval (k, usually 95%) is assumed

[safe radish]

@sharp crag Has your question been resolved?

[safe radish]

Channel closed

Closed by @sharp crag

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[frosty hinge]

can you give me any kind of a hint or something to start this proof because i don't know where to start from

[delicate shore]

where is the problem

[frosty hinge]

like this is quite letterly just the question

am currently applying to PROMYS program

i believe that they just want a mathematical proof of the concept not a numirical proof if you know what i mean

[shut hound]

If this is an ongoing questionaire and not a mock exam then I don't think we can help regardless because this server doesn't endorse cheating

[frosty hinge]

i just want a hint i can continue after it

i feel quite lost

[shut hound]

Then just put NS and move on

[frosty hinge]

meh

.close

[safe radish]

Channel closed

Closed by @frosty hinge

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[severe pebble]

I know this looks obvious, but how do I show this is true for any arbitrary metric? Like for the standard norms (L_1 ...) but since they haven't mentioned that or anything i am guessing they mean this is true in general?

[severe pebble]

or to begin with, is this even true for any arbitrary metrics?

[honest perch]

you mean the inclusion?

inclusions are always isometries

[thin wraith]

wuts this ginny

[honest perch]

if you use the same metric on both spaces

[thin wraith]

ginny potter?

harry potter's wife?

[severe pebble]

bruh

[thin wraith]

then?

how is harry?

[severe pebble]

how do you do that? they are different spaces

[severe pebble]

we are in the middle of something?

[thin wraith]

who? you and harry? (srry nvm bye)

[honest perch]

Let (M, d) be a metric space and N a subset of M

then d restricted to NxN is a metric on N

[honest perch]

this is what i meant by same metric

technically of course, they are not the same

[severe pebble]

but R^2 is not a subset of R

[honest perch]

inclusion maps are from subsets

[honest perch]

yes R is not a subset of R^2 technically but you can identify it with Rx{0} which is what they've done

[severe pebble]

but R or R^2 neither is the subset of the oter

hmm

[honest perch]

yes

the map x -> (x,0) is technically not an inclusion

[severe pebble]

makes sense

[honest perch]

basically you just view R as the x-axis in R^2

[severe pebble]

yeah i got it

since they used the word inclusion they want to use the same metric

[honest perch]

mhm

[severe pebble]

i thought since nothing of the sort is mentioned it should be true for arbitrary metrics

<@&268886789983436800>

[honest perch]

what are u doing

[severe pebble]

I already told them to stop

[honest perch]

is he banned

[severe pebble]

doubt it

.close

[safe radish]

Channel closed

Closed by @severe pebble

Use .reopen if this was a mistake.

[severe pebble]

thanks @honest perch

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[runic basin]

Hello, I have a doubt

[runic basin]

Which of this is correct

if the same identical dice is rolled or two identical dice are rolled then if the order will not matter then only 21 will be the sample space because 1,2 is same as 2,1

if two different are rolled then order will matter and sample space will be 36

if same dices are rolled or identical dice is rolled order will still matter since no two dice can actually be identical.
and same for the distinct dice

for both case 36 will be sample space.

I used ncr with repetition and the answer is 21 ofc, but then logically what will be the answer?

[quasi bison]

using "sample space" to actually mean "cardinality of the sample space" is not good

[runic basin]

ive a exam soon, and I don't think they consider the combinatorics part

[runic basin]

okay, can u help?

[quasi bison]

anyway, if you want 21 outcomes, then they won't be equiprobable anymore -- any doubles roll will be only half as likely as a non-doubles roll

[runic basin]

can you help me understand

ifwe have two similar dices

will the order matter

in a hypothetical world, their dropping at once.

Please ma'am.

[shut hound]

That depends entirely on you doesn't it

If you want it to, it will, if you don't want it to it won't

[runic basin]

ive an exam soon sir, I need what maths thinks of this

[quasi bison]

(2,1) is by default not the same outcome as (1,2). but you can treat them as the same. then their combined probability will be 1/18 instead of 1/36 each

[runic basin]

Yeah, exactly.

see if u use ncr with repetition

the outcomes turn out to be only 21

but traditionally we all know 2 dice roles have 36 outcomes.

[quasi bison]

and i will repeat then they will not be equiprobable any more

[shut hound]

It doesn't think of it at all. It tells you to decide and gives you tools to work with your decision.

[quasi bison]

if you want i can say this 20 more times

[runic basin]

im sorry.

you're being a little mean

but thats alright, thankyou for help.

all the best for ur future endeavours

.close

[safe radish]

Channel closed

Closed by @runic basin

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[surreal kayak]

any1 help me

[earnest nacelle]

have you learnt about the inscribed angle theorem?
if you have, you can find what angle ACB is immediately.

on top of that, considering the nature of triangle OAB will help you get a few more angles

[surreal kayak]

no i havent

[earnest nacelle]

then what have you learnt and/or are allowed to use?

[surreal kayak]

im in 9 class

[winged flare]

angle subtended on circumference is half of that of angle subtended at center?

[surreal kayak]

ye ik this

[winged flare]

that is this

[earnest nacelle]

that is what I meant by the inscribed angle theorem

[surreal kayak]

oh k

[earnest nacelle]

but anyway, use that information to get angle ACB

[surreal kayak]

then

[earnest nacelle]

then consider the nature of triangle OAB. this gives you the value of angle OAB

[fathom pasture]

cursed 90 deg angle

[earnest nacelle]

from there, you have angles ACB, CBA and OAB (which forms part of angle CAB together with angle CAO).
you know that CAB is a triangle, so from there it should be rather straightforward

give it a shot

[surreal kayak]

ok 8

i get 60 as my answer

[earnest nacelle]

correct

[surreal kayak]

ty

[earnest nacelle]

!done?

[safe radish]

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

[surreal kayak]

.close

[safe radish]

Channel closed

Closed by @surreal kayak

Use .reopen if this was a mistake.

[mighty mango]

you might want to reopen the channel for this question.

[winged flare]

.reopen

[safe radish]

✅ Original question: #help-23 message

[earnest nacelle]

you don't need to repost the question I believe

[surreal kayak]

im new idk how to use

[quasi bison]

ok, any progress on this one so far?

[surreal kayak]

i have no idea to start

[quasi bison]

draw segments AC, CB, BD and DA. also give a name to the intersection pt of the chords, say P

you will need to apply the inscribed angle theorem at some point

[surreal kayak]

k leg me do

done

done

[quasi bison]

do you know the inscribed angle theorem btw

[surreal kayak]

ye

[quasi bison]

ok

consider triangle PCB

what can you say about its angles at C and B

[surreal kayak]

ok

u mean abc

?

[faint whale]

Just draw the chords and use the angles to prove the sum of the chords to be equal. That way the sum of the corresponding arcs would be equal

[quasi bison]

no

i mean PCB

[faint whale]

This looks like ncert tho? Which one,exemplar?

[surreal kayak]

class 9

[surreal kayak]

u got it rigjt

[faint whale]

Oh.....then it shouldn't be that hard....I'm in 9 too

[surreal kayak]

ok

help me out

[quasi bison]

i am trying to help you

what can you say about angles PCB and PBC

[surreal kayak]

ok btw i cant find p in the fig

[quasi bison]

draw segments AC, CB, BD and DA. also give a name to the intersection pt of the chords, say P

[faint whale]

Wait....ig u don't need to draw anything!

[surreal kayak]

ok

mb

[faint whale]

Just the original figure is enough

[surreal kayak]

done

[faint whale]

No need to draw chords

The hint is written in the last line of the question, "semicircle"

Think about it,how can you use angles here?

[surreal kayak]

ok

le me

[faint whale]

Just know: Angles and length of arc are directly related......and the chords are perpendicular here

[quasi bison]

not even i am sure what you're cooking with this

[faint whale]

I'm not telling the entire solution rn.....let him think

[quasi bison]

don't call me "brother"!

[faint whale]

Oh sorry my fault

[quasi bison]

P isn't the center of the circle btw

[faint whale]

I'm new here,so my bad

[earnest nacelle]

well I will say that if you're directly applying the inscribed angle theorem, these chords might not intersect at the center of the circle

[faint whale]

Oh wait yeah

They aren't at the center.....then yes we might need to do that

[earnest nacelle]

otherwise this would have been killed easily by two applications of the inscribed angle theorem

hence why Ann is doing what she's doing

and we should probably let her continue

[faint whale]

Yup my bad

[quasi bison]

im gonna ask op the same question for the third time

[earnest nacelle]

(sorry to have intruded myself Ann, I'll back off)

[quasi bison]

im still gonna insist on considering triangle PCB, which btw is right angled

[surreal kayak]

im confused

now

[winged flare]

diagram

[quasi bison]

you don't really need the center here

[winged flare]

yes you do

[earnest nacelle]

unnecessary because I think Ann is going to use the other form of the inscribed angle theorem

the intercepted arc definition

[surreal kayak]

bro can only 1 guy help me out?

[earnest nacelle]

sure. I'll step out then

[faint whale]

Yup ann was doing a great job now I get what her solution meant

[winged flare]

just came for the diagram

im out

[quasi bison]

i am not a guy

[faint whale]

Im out too

[mighty mango]

wasn't even here, I'm out.

[safe radish]

@surreal kayak Has your question been resolved?

[winged flare]

.. anyone there?

@surreal kayak there?

maybe ill continue

[surreal kayak]

ok

do

[winged flare]

alright

[winged flare]

can you see that angle DOB is twice that of angle 1 (angle DCB)

[surreal kayak]

y

[winged flare]

did you mean y(es)?

or why?

[safe radish]

Channel closed

Closed due to timeout

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[kind galleon]

Can someone help me with 7.b and 7.c?

[kind galleon]

It seems like the answers are either wrong for the worksheet or I am doing something wrong and repeating this mistake

Answer for this

[quasi bison]

can you show your answers for comparison

[kind galleon]

My first 2 points are (1, -3), (2, -3)

It's a vertical stretch by 3 and reflection over x axis

[quasi bison]

reflection over y axis though

reflection over the x-axis would give you y=-3f(x)

[kind galleon]

What would be the point of x =1

I thought x stays normal, and the input is negative, thus the function gets evaluated for x = -1

So it will make it reflected and then stretched by 3

[quasi bison]

(1, 3) gets sent to (-1, 3)

again you reflect across the vertical axis not the horizontal

[kind galleon]

But x as the input, and x as what the function will evaluate aren't 2 different things?

[quasi bison]

ok i am once again not sure about my ability to explain this to you

[kind galleon]

Are my questions clear for any answer or I am messing something up?

Because we have 2 different perspectives

[earnest nacelle]

but the original function isn't defined at x = -1, is it? might not make sense to talk about that.
however, I am also in the same position as Ann because I have heard about you and have tried to cook up several examples in preparation, none of which I think would work

[kind galleon]

What

[kind galleon]

The original is only defined for 0 1 2 3 4

[earnest nacelle]

yes, exactly so. so when your intuition says that the function gets evaluated at x = -1, it should ring some alarm bells already

can't exactly be evaluating f at a point outside its domain

[kind galleon]

Ok so I have another breaking point, how does y = f(qx) for q < 0 reflect the function over y axis?

[kind galleon]

I am saying it is evaluated for the same x's as the original function

But I don't understand how transformation y = f(qx) reflects the function over y axis

[earnest nacelle]

well how do I put this

[kind galleon]

Since x is the input, and it the graph is drawn always in respect to it

[earnest nacelle]

suppose you have f(-x) here

[kind galleon]

Yes

[earnest nacelle]

do you think x = 1 works?

[kind galleon]

yes?

[earnest nacelle]

remember, f is only defined for inputs in the range 0 to 4

but substituting x = 1 makes the input to f -1

[kind galleon]

Yes

[earnest nacelle]

so how would f be defined at x = 1

[kind galleon]

so F will be evaluated for input -1

[earnest nacelle]

eh sorry

[kind galleon]

(1, -1)

[earnest nacelle]

how would f(-x) be defined at x = 1? f would be evaluated at input -1... which is outside of the domain of f

[kind galleon]

Isn't domain what we put into function, and what happens in the parentheses is no related to domain?

[earnest nacelle]

um

the domain of a function is where it's defined

[kind galleon]

Yes

[earnest nacelle]

anything outside the domain of a function is nonsense

[kind galleon]

Yes

[earnest nacelle]

well any input outside its domain is nonsense

-1 is outside the domain of f

so -1 as an input is nonsense

[kind galleon]

I don't think so it works like this

The original input for it was 1

The operation in parentheses evaluated this value to -1

Because f(-x)

[earnest nacelle]

yes, so the input to f is made to be -1 for x = 1

[kind galleon]

Yes

[earnest nacelle]

which is nonsense as it's outside the domain of f

[kind galleon]

So domain is not what we input but for what value f is evaluated?

[earnest nacelle]

well yes, x can be modified before it's used as the input for f

here x would have its sign flipped before it's used as the input

[kind galleon]

So domain is the thing that actually is fed into a function

Not what we can put as x

[earnest nacelle]

the domain of a function is the set of all input values over which the function is defined

that's the proper way to say it

in short, it's the range of inputs for which f makes sense

[kind galleon]

Why they ask me to evaluate it outside of it' domain 😭

[earnest nacelle]

aha

though x = 1 makes the input to f(-x) outside its domain

have you tried x = -1?

[kind galleon]

Oh shit no I didn't

Wait

Oh you mf's

Tricky

type shit

Why I didn't see this before?

[earnest nacelle]

see why now a negative q flips the graph over the y-axis?

[kind galleon]

Yeah

Makes sense

But in this example

what about this

[earnest nacelle]

about what

[kind galleon]

for y = f(qx)

[earnest nacelle]

uhuh

[kind galleon]

Uh, it's just the sam ething

ok

[earnest nacelle]

yes