help-36

[candid pulsar]

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[tired walrus]

resistivity is a property of the material, isn't it

[forest cargo]

oh !!

why do i keep forgetting

yes

thnx

so option 4 right

thnx

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[forest cargo]

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✅ Original question: #help-36 message

[forest cargo]

wait ik my teacher told me that 2

but rho = RA/L

here resistivity seems to be dependent on area and length

[shell condor]

it's like saying density varies if you cut a material in half

[candid pulsar]

R varies too

[shell condor]

there are two kinds of properties, intrinsic and extrinsic properties

intrinsic properties are always (ideally) constant for a material (I mean there are factors, but we usually ignore them at elementary level)

[tired walrus]

if it is a copper wire and you do that to it, it won't transmute alchemy-style into an iron wire

it'll remain a copper wire and have the resistivity of copper

[shell condor]

and things like density, resistivity are intrinsic

[rugged merlin]

do keep in mind, this is not the be-all and end-all formula for resistance. The resistivity, cross-sectional area, and current density are all assumed to be perfectly uniform throughout the material

[forest cargo]

ok

why is it so?

like

ok they dont change bcz of their behaviour

there is ntg more to it right?

[rugged merlin]

The actual formulation would be [
R = \4{\int \vv E\vd \dd\vv\ell}{\iint \vv J \vd \dd\vv A}
]
generally

but i reckon you dont have to worry about that

[forest cargo]

why is give integration twice in the denominator?

wait this isnot school lvl right?

[rugged merlin]

because its an area

its not

[tired walrus]

it's extremely NOT school level

[forest cargo]

ok then I will stop here I shouldn't go any further yet with this

thnx everyone here for helping

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[wicked zealot]

Hi! I am trying to figure out how I would solve this! The question asks “What interval of amounts of cheese represent the middle 60% of amounts dispensed?” The mean is 3 ounces and it has a standard deviation of 0.2. I am just confused on how to get middle percentage.

[wicked zealot]

I think I might have found the solution could anyone let me know if it is off?

[worldly spruce]

I am still mastering telepathy

[wicked zealot]

Sorry I thought it sent😭

but using the top and bottom how would you calculate to get the middle percentage

[shell condor]

can you send the entire question please

[wicked zealot]

yes one sec

I just need help with the 3d part though thank you:)

[fathom holly]

stats

[shell condor]

!status

[final saddle]

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

[wicked zealot]

2

[fathom holly]

mari is that the answer key

[wicked zealot]

No

Thats my work

[fathom holly]

oh

[wicked zealot]

Im confused on how to continue 3D

It says to get the middle 60 percent

So i assumed I should get the top percent and bottom

[fathom holly]

it's correct

[shell condor]

I think it means between 20% and 80%

[fathom holly]

oh

yeah

did she not calculate that

though

[wicked zealot]

Oh so just put it as an interval?

[fathom holly]

yes

[wicked zealot]

its kinda clicking now

[shell condor]

IG middle usually means equal parts above and below the centre

[wicked zealot]

okay thank you guys :))

[fathom holly]

no worries sending u love

[wicked zealot]

lol thanjs

[fathom holly]

u got this quen

queen

[wicked zealot]

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[tough crystal]

Is my work right

[shell condor]

I assume ms is milliseconds?

[tough crystal]

Yeah

[shell condor]

one way I saw someone do it is

imagine if it's 5 seconds to millisecond

we know that 1 second = 10^3 ms

so just replace the second with 10^3ms

so it goes from 5 seconds to 5 (10^3 ms), and then just get 5*10^3

[tough crystal]

But my work is right, right? I wasn't sure how we got the exponent of 6 because one of the 3's were negative so I just flipped it

[shell condor]

yeah yeah it's fine, you could just write it a bit more systematically though

[tough crystal]

Alright thank you, imean I didn't make anything up right

[shell condor]

yes yes, solving wise it's fine

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[dreamy tartan]

i don't understand this proof of cantor's theorem

[dreamy tartan]

like ok, a € X, ergo a !€ f(a)... so what?

i don't see how we get from a € X to a !€ X

where do we get that second part from

[scarlet sequoia]

If f is a bijection

[dreamy tartan]

in this case f is surjective

[scarlet sequoia]

Ok, if f is surjective, then X = f(a) for some a

So

[dreamy tartan]

hold on

[scarlet sequoia]

Is a in X or not in X?

[dreamy tartan]

why is X = f(a)?

[scarlet sequoia]

f: A->P(A) is surjective

[dreamy tartan]

didnt we define it differently

so X € P(A)

[scarlet sequoia]

X is in the codomain of f

But f is surjective

[dreamy tartan]

it's an element of the codomain

[scarlet sequoia]

So X must be the image of something

[dreamy tartan]

right?

[dreamy tartan]

right

[scarlet sequoia]

So, X = f(a) for some a

[dreamy tartan]

ok following

[scarlet sequoia]

So, fix some a in A such that f(a) = X

We now wonder whether a is in X or not

[dreamy tartan]

well didnt we just say it isnt?

[scarlet sequoia]

Well, if a is not in X

Then a is in f(a)

Because that's what it means not to be in X

[scarlet sequoia]

But this is "a is in X"

So, "a not in X" implies "a in X"

That's not possible

So does that means a is in X?

Well, the other way around

If a is in X

Then a is not in f(a) (definition of X)

Then a is not in X (f(a) = X)

[dreamy tartan]

goooot it

ok ok i see now thanks

and that's russel's paradox right?

at least it feels like it

[scarlet sequoia]

Well it's close

Russel's paradox is that there isn't a set of all sets

Otherwise you can create the set of sets that don't contain themselves as an element

[dreamy tartan]

well it's the same kind of short-circuit where a -> !a -> a -> !a ...

[scarlet sequoia]

so "x not in x", a bit different from "x not in f(x)"

[dreamy tartan]

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[frozen thicket]

huh?

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[left trail]

For number 10 if f has a derivative everywhere on [a,b] isn't f' defined everywhere and thus continuous and then you can just apply the intermediate value theorem directly?

[tiny gorge]

"defined everywhere and thus continuous"

why thus?

derivatives don't have to be continuous

they can't have step discontinuities but they can have the "oscillate to death" kind

[scarlet sequoia]

f(x) = x²sin(1/x) prime counterexample (with f(0) = 0)

[left trail]

I see. Thank you.

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[fallen zephyr]

I have a quick question with math that should be fast to solve. It regards problems such as

0.000000000001 = 1.00 x 10^-11 = 1.00e-11

That is an example problem and I have a few more I tried to solve but the system keeps saying I’m getting it wrong so if someone could look over it for me please 🙏

[fallen zephyr]

I don’t know what I’m doing wrong here

[languid yoke]

try e-12 instead of e-11

[whole halo]

you counted wrong

[fallen zephyr]

The first one is an example

[whole halo]

its not -14

[languid yoke]

lmao oops

[whole halo]

but ngl if its not that, the rest seem correct

now that Im looking at it again, -14 looks correct...

thats no good

oh right

4.74 not 4.70

[fallen zephyr]

Ohhh let me try that

Ok I got the rounding wrong for the last one but almost there

[whole halo]

also, 4.98149 does not round to 5.00

keep in mind you have three significant digits

that means 4.98, not 5.0

[fallen zephyr]

I got it!!

Thank you

This problem was killing me and I couldn’t figure out why despite being close 😭

[whole halo]

np

[fallen zephyr]

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[tough crystal]

Did I convert everything right?

Ignore the random letters, that was me marking that I wanted to check it lol

[loud sundial]

good

[loud sundial]

the exponent is -3, not 3

[tough crystal]

Ohhhh right I understand

It should be

[loud sundial]

good

[loud sundial]

probably fine ... depends on rounding rules ig?

also you can check this in #bots

ex:

,w (810^3)(2.3785*10^4) scientific notation

[soft zealot]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[tough crystal]

0.00763

Is this right now

[tough crystal]

She didn't state what it was so Im not sure I just left it at what my calculator ended at

[loud sundial]

yes

[tough crystal]

Okay thank you so much and thank you about the bot, that's good to know

[loud sundial]

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[tough crystal]

.close

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[restive sinew]

i did not understand the part z=n

how did they find residue

[final saddle]

@restive sinew Has your question been resolved?

[tired walrus]

do you know GENERAL solution of sin(x)=0 for all real x? @restive sinew

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@restive sinew Has your question been resolved?

[restive sinew]

i am not curious about that

i am thinking what formula they used for z=n case

sinx=0 when x=n pi

and it is obviously written there

i am asking what did they use it here

okay i got it by simply google search

thanks

they used this formula

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[lilac moat]

It's just the residue at a simple pole

You can get that form with g'(z0) in the denominator by performing L'hopitals

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[keen vector]

can someone please explain this binomial problem?

[gleaming shore]

ok

[keen vector]

thanks btw this is the model solution

[gleaming shore]

nvm but uh, i'll alert helpers in the discussion cause this is not within what I know

[keen vector]

oh ok thanks though!

[gleaming shore]

another thing cos i forget binomial lol

ok

seems like everyone's busy

if there's no one after 15 mins just ping helpers]

or what I like to do is ask chatgpt to teach me through, although I don't recommend it to tell you sols.

[keen vector]

oh ok, i might try to leave this thingy and go on another help forum

thx

[gleaming shore]

alright i think thats better

cos most helpers are on the american side, so its kinda night time for them now

theres a handful of us in the asian continent but not a lot

i can refer you to another one...

[keen vector]

Oh ok thanks

[gleaming shore]

ok someone's answering!

its the chinese guy

[craggy plank]

Could you briefly explain where you are stuck at?

[keen vector]

the whole thing i understand whats happening with the dice but not how they get each binomial

[craggy plank]

Because there are only 2 results

Success or not

It does fulfill the requirement of being a binomial situation

[keen vector]

i see but why is there p(x=0)?

i get that throw the dice four times but whats the 0 for

[craggy plank]

You get no success in the 4 attempts

[keen vector]

ohhh okok

thanks i think i understood

[craggy plank]

No worries, anything else?

[keen vector]

nope 🙂

[craggy plank]

Alright, have a good one

[keen vector]

Bye

sorry how do i leave this forum

[craggy plank]

.solved ✅

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[craggy plank]

dw

[keen vector]

ty

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[spring basin]

Hey! I'm trying to find a reliable way to compute the normal direction of a 3d plane given the positions of it's four points/corners. Let's say we have a random point generator that spawns points on an irregular ground surface, forming a 3d plane at any of these points would cause the plane to intersect with the surrounding ground surface since the individual spawn point up vector (which is used by the plane) does not account for the 4 corner points of the plane. So my solution is to get the 4 corner points of my plane (p1, p2, p3, p4) and snap them to the surface right below them and then calculate the plane normal direction from these points instead.

For my usecase, I've determined that computing the normal direction using only the 3 points of my plane isn't sufficient enough for getting the least "interesectable" orientation for the plane if that makes sense. Imagine the top right point (p3) as the final third point used for computing the plane normal direction, if you rotate that plane 45 deg around itself such that that the top left corner (p4) is facing a steep ramp, and you move that plane towards that ramp, the plane normal direction wouldn't get updated at all and you would get an intersecting plane, unlike if you rotate the plane -45 deg such that the third point (top right) is facing that ramp, which then it would update the normal direction correctly.

My first solution was to get the halfway point between the top two as my third point:

vector p3 = p3-(p3-p4)/2;
vector N  = cross((p1-p2), (p2-p3));

but idk if that would be a good way to do that.

My other solution was to flip the plane direction horizontally to use the fourth point as the third point and get the median vector between the two:

vector N1  = -cross( ( p1-p2 ), ( p4-p2 ) );
vector N2  =  cross( ( p2-p1 ), ( p3-p1 ) );

vector N = ( N1 * 0.5 )+( N2 * 0.5 );

Seems to work a bit better than my first method but I'm still wondering if there's a correct way to do this (:

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[spring basin]

.reopen

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✅ Original question: #help-36 message

@spring basin Has your question been resolved?

[opal plinth]

I did not understand any of that and I suspect I'm not the only one who tried. You probably should post a detailed picture of a problematic situation and then describe precisely why it's problematic and what you would want instead, ideally with another picture or drawing.

@spring basin

[spring basin]

ahh I see, well that makes sense why no one was replaying haha, I'll try to demonstrate the problem a bit better

[opal plinth]

<@&268886789983436800>

[magic flare]

?

[magic flare]

<@&268886789983436800>

[steep hatch]

what

you're not owed an explanation for someone modpinging

don't post inappropriate gifs in help channels

shitposting goes in #chill

[tulip coyote]

Yeah, not particularly a smart idea to send annoying .gifs in a help channel and then try and ping us have a day off

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[spring haven]

So far this is what I have:

If $W$ is not full rank, then $\operatorname{det}W = 0$ and also $\operatorname{detA} = 0$ as $A$ is also not full rank.

If $W$ is full rank, the rows of $V$ are linear combinations of the rows of $W$, so by subtracting multiples of the rows of $W$ we get that [ \operatorname{det}A = \operatorname{det}\begin{pmatrix}U&0 \ 0&W\end{pmatrix}. ]

[soft zealot]

kheer257

[spring haven]

How do I show that that last determinant is detU * detW?

I know I can just induct on the size of U but I'm looking for a better way

[worldly mesa]

if you know the formula for determinant using permutations you can use that

[tired walrus]

^

it feels kinda obvious though

[spring haven]

mm

[tired walrus]

well, that or you can do some kinda geometric volume-scaling-factor argument on R^(m+n)

[spring haven]

😭

I think I'll just do the induction lol

well actually

is it true that without swaps, any non-singular matrix can be reduced to a diagonal matrix?

[final saddle]

@spring haven Has your question been resolved?

[tired walrus]

row swaps are redundant bc you can accomplish the same via row additions and scalings i think

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[tranquil pine]

<@&268886789983436800>

[leaden moon]

<@&268886789983436800> user id: 919239993686368336

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[proper reef]

hi guys im new into this server

[final tangle]

as mentioned ask your question if you need help
or close the channel
use a social channel like #discussion if you just want to chat.

[leaden moon]

!redir

[final saddle]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

@proper reef Has your question been resolved?

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[brisk lion]

<@&268886789983436800> um...

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[cyan kayak]

one moment

thanks for the ping

[tranquil pine]

🤔 what was the matter

[brisk lion]

I'm not sure how that helped, but I'm glad to have helped!

[cyan kayak]

they deleted their own post, then attempted to dodge consequences by leaving the server.

[tired walrus]

... what happened

[brisk lion]

I see.

the user posted a rather inappropriate message and then deleted it.

[tranquil pine]

they think they can dodge by leaving

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

Why is the set of points [−3,+∞) ? It looks like it's only going till 7.

[brisk lion]

there is no indication the graph stops there.

[floral patio]

Zoom out. Other than that this looks like parabole

[tiny gorge]

i assume you mean the range/image?

[brisk lion]

so it's assumed that the graph continues forever upwards.

[opal plinth]

It's just poorly drawn tbh

[mossy monolith]

it stops right before 7, and the drawn graph still continues tho

so how can I assume

[glossy inlet]

круто

[tranquil pine]

Cuz when u give it any number positive it can give u answee

[tranquil pine]

Russian

[glossy inlet]

yep

[glossy zephyr]

Its a poorly drawn graph, usually its more consistent to guide yourself using the formula for the function

[brisk lion]

normally, such a graph should have arrows at its endpoints.

but you can convince yourself using the domain of the function.

[tiny gorge]

when problems are badly stated like this one, you go with what is the most likely intent

[glossy inlet]

Russian speaking*

[tiny gorge]

we are talking about the y values here surely?

[mossy monolith]

yeah

[glossy zephyr]

yea mb

lmao.

[tranquil pine]

What

[brisk lion]

um, why is there another conversation ongoing here?

[tranquil pine]

The function u can said it's completely finished when u put number and can't get an answer

[mossy monolith]

whatg does that mean

[tranquil pine]

Like for example

[mossy monolith]

uhh

[tranquil pine]

When I said 1/x

I can't put zero

Right?

[mossy monolith]

.close

[final saddle]

Channel closed

Closed by @mossy monolith

Use .reopen if this was a mistake.

[tranquil pine]

Wdym

[brisk lion]

see #❓how-to-get-help for how help channels work.

[opal plinth]

I think it's pretty clear what she means

[final saddle]

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[zenith cedar]

Given the vertex of the parabola, a point P on the parabola and the angle between line VP and axis, how do we construct the focus using straight edge and compass

[zenith cedar]

@opal plinth I was unable to see your message due to a network issue

How would I construct the tangent at point P

[opal plinth]

The tangent to x^2 at x=p goes through (p/2,0)

[zenith cedar]

But why are we choosing x² as the paraboal

[opal plinth]

All parabolas are the same

[zenith cedar]

I guess it will

[opal plinth]

green = red

[zenith cedar]

Now that I have this tangent

[austere cobalt]

Vertex of the parabola is the lowest point

[zenith cedar]

I guess I can construct the normal

Then I will get my focus

Thanks for the help @opal plinth

.solved

[final saddle]

Channel closed

Closed by @zenith cedar

Use .reopen if this was a mistake.

[final saddle]

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Send your question here to claim the channel.

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

[narrow ingot]

Exercise 2 1st request

[narrow ingot]

Foundations

How can I prove that the power set of the cartesian product AxB on the lhs is included in the cartesian product of the 2 power sets on the rhs

[scarlet sequoia]

Prove or disprove

[narrow ingot]

Ofc yeah

But what do I use

A power set is a set of sets

[scarlet sequoia]

Do you think it's true or false?

[narrow ingot]

I think it's true

[scarlet sequoia]

Then if you take an element of P(A x B), call it X

That's a subset of A x B

[narrow ingot]

So I can only
Let X (a set) belong to P(AxB)

[narrow ingot]

But AxB is a cartesian product so it should be 2 subsets

[scarlet sequoia]

So you would need to write

X = X1 × X2

[narrow ingot]

X E A, Y E B

[narrow ingot]

Or that

Yeah

[narrow ingot]

But not cartesian product

X={X1,X2}

[scarlet sequoia]

So you already see a problem

[narrow ingot]

What is it

I don't

[scarlet sequoia]

Rather (X1, X2)

X is a set

[narrow ingot]

Oh yeah

[scarlet sequoia]

And at the same it needs to be a couple of sets

[narrow ingot]

Powerset is all the possible sets that can be found from all the elements in a set

How can I use that

[scarlet sequoia]

Powerset is just the set of all subsets

Subsets are sets

[scarlet sequoia]

So at the same time, X is a set

And a couple of sets (X1,X2)

They're not the same kind of object...

So it's hard to say they're equal

[narrow ingot]

So... Is it a contradiction?

[scarlet sequoia]

The way the exercise asks, yes

[narrow ingot]

But that's not what my professor told me

Wait lemme show u my attempt

[scarlet sequoia]

Multiple things wrong

[narrow ingot]

Ok

Where

[scarlet sequoia]

First, $X \subseteq A \times B$ implies $X \subseteq A$ and $X\subseteq B$??

[soft zealot]

Rafilouyear2026

[narrow ingot]

Oh it doesn't

[scarlet sequoia]

Did you mix up cartesian product with intersection?

[narrow ingot]

I know it was wrong but I had to turn up with something on google classroom

Can't I say

{X,Y} belongs to P(AxB)?

[scarlet sequoia]

Is {X,Y} a subset of A×B?

[narrow ingot]

No🥲

[scarlet sequoia]

Right

[narrow ingot]

But why

[scarlet sequoia]

(X,Y) btw again

[narrow ingot]

Yeah because AxB elements are points

Right?

[scarlet sequoia]

Yes

In any case

[narrow ingot]

So you can't have a point of two sets

Is why

[scarlet sequoia]

Asking if (X,Y) is a subset of something is wrong to begin with

A point is not a set

[narrow ingot]

Exactly

[scarlet sequoia]

It's the other way around tho

[narrow ingot]

Ts too hard and our proff didn't teach us

[scarlet sequoia]

You start with X a subset of A×B

[narrow ingot]

I really doubt it's gonna be in the exam

[scarlet sequoia]

And you have to prove/disprove that it's = (X1,X2)

[narrow ingot]

Yeah?

[scarlet sequoia]

That's false

Because a set is not a point

[narrow ingot]

Again because points not sets

[narrow ingot]

Exactly

[scarlet sequoia]

Though, I believe maybe the professor was looking for something else

Instead of P(A) × P(B)

[narrow ingot]

No she told me because it's cartesian I should start with a point?

I know it's worng

[scarlet sequoia]

Maybe they meant ${X_1\times X_2:: X_1\in P(A), X_2\in P(B)}$

[soft zealot]

Rafilouyear2026

[narrow ingot]

No

They meant the same question

[scarlet sequoia]

Ok, then point ≠ set

Or, and this is based on you mixing up cartesian product and intersection

$P(A\cap B) = P(A)\cap P(B)$

[soft zealot]

Rafilouyear2026

[narrow ingot]

I don't have them mixed up I was just trying😭

I'm the best student in foundations in my college

However out professor gave us the assignment without giving us an example before it

[final saddle]

@narrow ingot Has your question been resolved?

Channel closed

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Channel closed

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

[vital crag]

!msgdel

[final saddle]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

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Remember:
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[gentle zephyr]

\textbf{Exercise 1.} Define on $\mathbb{Z}$ the relation $R$ given by
[
n , R , m \iff 10 \mid \left(n^2 + 4m^2 + m - 6n\right).
]

\begin{enumerate}[label=\alph*)]
\item Prove that
[
n , R , m \iff 5 \mid \left(n^2 - m^2 + m - n\right)
\quad \text{and} \quad
n \equiv m \pmod{2}.
]

\item Prove that $R$ is an equivalence relation.
\end{enumerate}

[soft zealot]

Renato

[final saddle]

@gentle zephyr Has your question been resolved?

[worldly mesa]

note that n^2 - m^2 + m - n is equivalent to n^2 + 4m^2 + m - 6n modulo 5, and n^2 + 4m^2 + m - 6n is even (0 mod 2) if and only n = m (mod 2)

[winter lava]

,align
10\mid (n^2+4m^2+m-6n) &\iff 10\mid (n^2-6m^2+m-6n)\
&\iff 10\mid(n^2-m^2+m-n -5(m^2+n))\
&\implies 5\mid (n^2-m^2+m-n -5(m^2+n))\
&\iff 5\mid(n^2-m^2+m-n)

[soft zealot]

Axe

[winter lava]

Yeah I think since 2 and 5 are coprime, you can say $10\mid x\iff 5\mid x \land 2\mid x$

[soft zealot]

Axe

[final saddle]

@gentle zephyr Has your question been resolved?

[gentle zephyr]

What did you do in the second iff

[winter lava]

just algebra

[gentle zephyr]

Completed the square

[winter lava]

i wanted to make it look like n^2 - m^2 + m - n as much as possible

there's a more direct route

,align
10\mid (n^2+4m^2+m-6n) &\implies 5\mid (n^2+4m^2+m-6n)\
&\iff 5\mid (n^2-m^2+m-n)

[soft zealot]

Axe

[gentle zephyr]

The issue here is the one sided implication

[winter lava]

yeah

[winter lava]

use this

[smoky egret]

its not really an issue

this proves the first half of the implication mRn implies 5|... and m\equiv n mod 2

[gentle zephyr]

Care to elaborate?

[winter lava]

this doesn't address mod 2

[smoky egret]

now you want to prove that m\equiv n mod 2

using what axe said above

[smoky egret]

right, thats why i said it proves half of the implication

[winter lava]

not even half

[smoky egret]

the implication nRm implies 5|n^2-m^2+m-n and n\equiv m mod 2 can be split into nRm implies 5|n^2-m^2+m-n and nRm implies n\equiv m mod 2, what you have done prove the first part

which i believe is half of this implication

[winter lava]

oh, sorry i misunderstood

[hot hornet]

yep this is true

-# i go through this in a bit more detail in https://pseudonium.github.io/2026/01/18/Products_Categorically.html

[smoky egret]

np, i figured that you were talking about the equivalence not just the one sided implication

[gentle zephyr]

This is CRT or what?

[hot hornet]

in general it's true that $\text{lcm}(a, b) | x \iff a | x \text{ and } b | x$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[smoky egret]

where exactly are you stuck renato

[smoky egret]

yes

[gentle zephyr]

Don't know how to start a)

A lot of hints where given but

Don't know how to connect them

[smoky egret]

ok so you know nRm\iff 10|n^2+4m^2+m-6n

[hot hornet]

i would recommend starting with axe's hint

$10 | n^2 + 4m^2 + m - 6n \iff 5 | n^2 + 4m^2 + m - 6n \text{ and } 2 | n^2 + 4m^2 + m - 6n$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[smoky egret]

check this, is there something here that you dont follow?

btw does replying to the output of the bot ping the user?

[winter lava]

no, it doesn't

[smoky egret]

ohh ok, thanks for the info

[gentle zephyr]

Yes

Now what?

[hot hornet]

try manipulating $5 | n^2 + 4m^2 + m - 6n$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

After simplification I get 5 | n^2 - m^2 + m - n

[hot hornet]

yep, that's exactly what you want to show

[gentle zephyr]

Because 4 = -1 under mod 5

[hot hornet]

so $5 | n^2 + 4m^2 + m - 6n \iff 5 | n^2 - m^2 + m - n$, right?

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

Yes now what

[hot hornet]

do the same for $2 | n^2 + 4m^2 + m - 6n$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

2 | n^2 + m

[hot hornet]

mhm

but what you want is $n \equiv m \pmod 2$, i.e. $2 | n - m$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

N^2 + M = 0 (mod 2)

[hot hornet]

yep

[gentle zephyr]

N^2 = -M (mod 2)
N^2 = M (mod 2)

Because -1 = 1 (mod 2)

[hot hornet]

yep

[gentle zephyr]

Now what

This is where I am fucked

[hot hornet]

you may not be aware of this, but the following is true

$x^2 \equiv x \pmod 2$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[hot hornet]

this is cause $0^2 \equiv 0 \pmod 2$ and $1^2 \equiv 1 \pmod 2$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

Oh. I can use a remainder table

[hot hornet]

yep!

[gentle zephyr]

Very very nice

[hot hornet]

so that completes part a

[gentle zephyr]

You remember this in the back of your head or is it just plain obvious under mod 2

[hot hornet]

both

[gentle zephyr]

I literally didn't saw it

[hot hornet]

you can derive lots of these kinds of identities using remainder tables

here's another important one

$x^2 \equiv 0 \text{ or } 1 \pmod 3$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

Nice.

[hot hornet]

cause $0^2 \equiv 0 \pmod 3, 1^2 \equiv 1 \pmod 3, 2^2 \equiv 1 \pmod 3$

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

Very interesting

[hot hornet]

i think it's case of - it's easy to verify, but hard to come up with yourself independently if you've never seen it before

[gentle zephyr]

We literally proved a) in a couple minutes

[hot hornet]

yep

[gentle zephyr]

I have seen it before, but you made me remember to keep my guard up, I literally forgot about divisibility almost as a whole

n R n <=> 10 | n^2 + 4n^2 + n - 6n
<=> 10 | 5n^2 - 5n

We might need to use the proved identity for part b)

[hot hornet]

yes that'll be helpful

in fact, you can split part b into 2 parts

i) show that $n \equiv m \pmod 2$ is an equivalence relation

[soft zealot]

Pseudo (Cat theory #1 Fan)

[hot hornet]

ii) show that $5 | n^2 - m^2 + m - n$ is an equivalence relation

[soft zealot]

Pseudo (Cat theory #1 Fan)

[gentle zephyr]

Reflexivity is shown easily because modular equivalence preserves commutativity

Is hard

[final saddle]

@gentle zephyr Has your question been resolved?

[final saddle]

@gentle zephyr Has your question been resolved?

[mossy sapphire]

bro is this even math 😭

[vagrant lichen]

It's deep math

[mossy sapphire]

how deep 🙂

[vagrant lichen]

yes

[gentle zephyr]

@hot hornet

sorry for the ping, but can you help me finish it

[hot hornet]

What are you stuck on

[karmic shard]

[final saddle]

@gentle zephyr Has your question been resolved?

[tranquil pine]

<@&268886789983436800> troll

[final saddle]

Channel closed

Closed due to timeout

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• Show your work, and if possible, explain where you are stuck.
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[brisk lion]

,rccw

you'll probably need to rotate them yourself, since the last image is not the one that needs rotating.

[brisk lion]

why not rotate them before uploading?

,rccw

[brisk lion]

you mean q3(a)?

oh what?

[tired walrus]

troll

[brisk lion]

did OP get banned?

[plucky rover]

Where's the message delete thing

[tranquil pine]

OP has left the server

[brisk lion]

and yeah that.

[plucky rover]

.close

[final saddle]

Channel closed

Closed by @plucky rover

Use .reopen if this was a mistake.

[plucky rover]

Well it is what it is

[brisk lion]

is the bot now capable of sustaining help channels without initial messages?

actually wrong place to ask, sorry.

[plucky rover]

Nah it's fine to ask lol

I don't think so

I think I'd find out if such a big change happened

[tranquil pine]

lets test

[final saddle]

Available help channel!

Send your question here to claim the channel.

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

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

[frozen sinew]

wha-

[frozen sinew]

how

[tired walrus]

consider triangle BAC and what can be said about it

[tranquil pine]

two tangents drawn from a single point to a circle are equal in length

[frozen sinew]

why am i getting 55°..

[tranquil pine]

because you should get 55 ?

[frozen sinew]

fr?

[brisk lion]

if you're doubting, why not share your steps?

then helpers can see how you got it and comment on that.

[frozen sinew]

the "steps" in question

[tired walrus]

why not simply say ABC is isosceles and AB=BC

55° is the correct answer anyway

[frozen sinew]

yea ty

[tranquil pine]

well this works as well the angle bisector is perpendicular to the chord, but yh hard way

[frozen sinew]

my way was easier tho..

anyways Ill ask more questions cs i get stuck on simple probs like this

[tired walrus]

mine doesn't require any further constructions

[frozen sinew]

maths is weird for me..cud be that

idk

[tranquil pine]

-# yeh ask questions help me get green

[narrow cradle]

Ik im a bit late but since the sum of the angles of any triangle is 180, and since we are facing an isosceles triangle, these two unknown angles will be equal, we can then say then that (x=value of the angle) : 70 + 2x = 180, so x=55

[frozen sinew]

issok...ic ic

[frozen sinew]

aite twin

im getting a diff ans from the one marked

[frozen sinew]

.

[jaunty isle]

the answer should be 2

[tranquil pine]

yh answer should be 2

[jaunty isle]

the radius of c2 is 4 so the diameter is 8 which is also equal to the radius of c3, and subtract that from 10 and u get the radius of c1 is 2

[frozen sinew]

js say "ur reasoning was correct" frfr

[tranquil pine]

ur reasoning was correct

[jaunty isle]

ur reasoning was correct

[frozen sinew]

this is so funny idk why

Lemme get more questions

[jaunty isle]

alr

[frozen sinew]

@jaunty isle @tranquil pine
am i tripping or its js the question

it ltrl says AB=4 which is named as x

[tranquil pine]

yh a typo or something

[frozen sinew]

yea

6 units then

[tranquil pine]

they probablly switched the places of x and 4 or something like that

[frozen sinew]

yep

[tranquil pine]

yh

[frozen sinew]

this is the easiest shi Ive ever done in my life

like related to mathd

maths*

wait until the test comes up tmr..

[tranquil pine]

gl

[frozen sinew]

Ill be cooked nonetheless

[tranquil pine]

,rccw

[tranquil pine]

how strecthed that image is

[frozen sinew]

idk why

[tranquil pine]

so

[tranquil pine]

,rccw

[tranquil pine]

better

[frozen sinew]

hm

[tranquil pine]

so what do you think

[frozen sinew]

2 pi

[tranquil pine]

right

[wild venture]

see 360 degrees correspond to 2pi

[tranquil pine]

1sec let me check the formula

[wild venture]

2 pi r * (thetha/2pi)

[tranquil pine]

yh R\theta is

[wild venture]

its unitary method i guess

[frozen sinew]

what i did was so shitty..

i put r as 3 and cancelled it out w the 3 in denominator

[tranquil pine]

well it matched with what was supposed to be done

[frozen sinew]

mhmm

[tranquil pine]

remember this from now

[frozen sinew]

i dont get it

[tranquil pine]

or this , where theta is in radians

[tranquil pine]

what

[frozen sinew]

😭

its complex

[tranquil pine]

the formula?

[frozen sinew]

yea

i havent heard of it

ever

[tranquil pine]

what is the circumference of a circle

[frozen sinew]

2 pi r

[tranquil pine]

right

hm.. do you know radians?

[frozen sinew]

lowk..

(i kind of skipped that lecture)

(and didnt bother myself learning em on my own)

[tranquil pine]

hm.. nw radians is just another unit to measure angle,
360degree = 2pi radians

[tranquil pine]

you should know them tbf

[frozen sinew]

kk

[frozen sinew]

mhm ic

[tranquil pine]

mb typo 360 degree

[frozen sinew]

😪

[tranquil pine]

so you can see, a circle is 360 degrees

[frozen sinew]

so pi=180 radians?

[frozen sinew]

hmm

[tranquil pine]

mm. not quite pi radians = 180 degrees

[frozen sinew]

mm?

[tranquil pine]

,, \pi radians = 180^\circ

[frozen sinew]

cuz like

[soft zealot]

firestepper

[frozen sinew]

360/2 🤷🏻‍♀️

[tranquil pine]

ok nvm that

so in 2pir you can see that we do nothing but simply multiply r by 2pi, which is the angle subtended by the arc, a whole circle here 360 degrees
so basically what we are doing to find the arc length is multiply the give angle in radians by radius

moreover why this, is 1 radian is defined as the length of arc which is equal to its radius

[frozen sinew]

hmmm

I seeee.....

my fam is excluding me wait a sec brb

[tranquil pine]

diagram not to scale but image this sector, a partition of a circle of radius r, what we have in a circle are 2pi,(360) such sectors so basically by unitary method you can arrive at the result, lenght of arc = r\theta

[tranquil pine]

aight gtg as well

[final saddle]

@frozen sinew Has your question been resolved?

[frozen sinew]

okie and also

TYSM

[tranquil pine]

i'm back

[tranquil pine]

np

[frozen sinew]

ohk

I think Ill get back to studying asw

[final saddle]

@frozen sinew Has your question been resolved?

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[soft pewter]

how can i find the domaine

[winter lava]

it should be the same as the domain of log x

[flat hare]

guys can i hop to calculus after trig

[subtle path]

you can rewrite that log as ln(x)/ ln(1,25)

[winter lava]

!occupied

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[subtle path]

and the domain of ln(x) is R+*

[subtle path]

?

[soft pewter]

ln (1,25) > 0

[winter lava]

for leibniz

[subtle path]

oh ok

[subtle path]

huh

wdym

do you know what the domain of definition of a function is

[soft pewter]

wait the domaine is xer?

[subtle path]

xer ?

I thought the question was in which domaine the function g is defined

[soft pewter]

like ]-infinite,+infinite[?

[soft pewter]

thats the question

[subtle path]

oh

well no cause x I --> ln(x) is defined in R+*

like all positive non 0 real numbers

[soft pewter]

oh so everything after 0

xer?

[subtle path]

yes everything after 0 without 0 included

[subtle path]

idk wtf that is but i call it R+*

[soft pewter]

cause x cant be negative

what about the variation

[soft pewter]

so it decreases

because the a is negative

-3

[subtle path]

derivate the function to find the variations

[soft pewter]

how

[soft pewter]

-3/(xln(1,25))

[subtle path]

yessir

-3<0 and ln(1,25)x >0 in R+*

so g ...creases

[soft pewter]

decreases

[subtle path]

yep

[soft pewter]

but decreases from what to what

]-3,-infinite[

@subtle path

[subtle path]

it decreases in the whole interval

[soft pewter]

oh

[subtle path]

why ]-3 ; -infinite[ ??

[soft pewter]

]infinite,-infinite[

[subtle path]

i think you made a big confusion

[soft pewter]

what did the derivative do

[subtle path]

g is not defined in all of R

[soft pewter]

so its decreasing in ]0,infinite[

[subtle path]

yes

dont get confused

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@soft pewter Has your question been resolved?

[soft pewter]

.close

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[median sable]

. Reopen

[soft pewter]

for g(x) = ln(-5(x+1)) how can ifind the domaine

[old quarry]

if g(x) = ln(x) could u tell the domain

[soft pewter]

log_e (-5x-5)?

[old quarry]

yes that is what ur function is expanded but could u answer what i asked u first

[soft pewter]

i cant because i need the argument

[tired walrus]

what numbers are legal inputs for ln

[soft pewter]

log_e

[tired walrus]

not answering my question

[soft pewter]

any number above 0

[tired walrus]

ok

so your function is ln(-5(x+1))

what expression is passed as input to ln here?

[soft pewter]

(x+1)

[tired walrus]

no

[soft pewter]

(-5(x+1))

[tired walrus]

there.

now, THIS shit has to be >0. as you yourself just said.

[soft pewter]

-5x+5 > 0

-5x > -5

x <1

[tired walrus]

why equals

[soft pewter]

oh

[tired walrus]

no, not >

[soft pewter]

oh because it swapped

right

[tired walrus]

yes

[soft pewter]

because negative number is divided

[tired walrus]

x < 1

[soft pewter]

x < 1

so its ]-infinite,1[

the domain

[tranquil lake]

Does infinity use ( or [ ? ⁨@soft pewter⁩

[tired walrus]

in french-style bracketing it uses a prongs-outward bracket

so it is correct but french-accented

also "domain" has no final e in english

[tranquil lake]

I didn't know French math had it different thanks

[soft pewter]

the variation is decreasing ]-infinite,1[

[brave pivot]

Wait, in french they use [] for infinity??

[wild venture]

la variables

[soft pewter]

yeah but its not included

[brave pivot]

So, definition is interchanged?

[soft pewter]

]-infinite is the same as (-infinite

[brave pivot]

Oh, it's a different system

Sorry for the confusion

[soft pewter]

is this good

[tired walrus]

no

in french they say ]a, b[ for open intervals and [a, b] for closed ones

[tired walrus]

@soft pewter i already approved your answer here

[wild venture]

lmao

[tired walrus]

i can repeat it 17 more times if you need me to

[brave pivot]

This makes more sense than english ones tbh

[tranquil lake]

so ] = (
and [ = )

[soft pewter]

no but the variation

[tired walrus]

yes it's decreasing all throughout

[soft pewter]

alright thanks

.close

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[grave crater]

I am having trouble with this one:

[grave crater]

And i dont have any "Correct answer" for it.

[twin shuttle]

Not only france

[twin shuttle]

Where did you get this from?

[wild venture]

hlo

[grave crater]

a video

why?

and sorry i sent the wrong one

i meant this one

[twin shuttle]

How did u solve this

[grave crater]

just addition if they are on same side and subtraction if not

[wild venture]

dot + dot make box

and dot + box cancel

add 1 st 2 columns

dot + nothing is nothing

[sour bane]

whats box + box finna do

[wild venture]

box+nothing is noting

[sour bane]

i think it might make dot based of the dot pattern

[wild venture]

box+box is dot

going by that logic

[sour bane]

yea

[twin shuttle]

I tought It was some kind of pattern 😭

[grave crater]

i dont see how box+bow is dot

[sour bane]

for each row the first 2 combined make the third

is usually the pattern for these

[wild venture]

u gotta observe

[sour bane]

its just a guess based off how dot + dot works

[twin shuttle]

Box + box Is a dot

Look second COLOUMN, not row

[grave crater]

i was just thinging like the 2 and 3 element in the first row have box+box which dispears

[wild venture]

is this the ans?

[grave crater]

but thats backwards, so maybe yeah its dot

[grave crater]

ye that is my guess

[wild venture]

nice

[twin shuttle]

This

[sour bane]

bro gave the mathcord an i q test

why is that filtered lmao

[wild venture]

precisely my question

i thoght i was banned or sum shi

[grave crater]

I have to study these for my job interviews, so its prep

[wild venture]

best of luck

[sour bane]

are u training for quant or sum

[grave crater]

idk what quant is, its just CS stuff

[sour bane]

ah

we usually do leetcode

but both are useless for actual engineering imo

[urban sky]

j*b

[wild venture]

how can you say that offensive word?

[sour bane]

idk why companies do i q stuff for coding jobs just test the actual skill

i remember reading a study and the leet correlation with development was pretty ass

[urban sky]

All this for a job where you'd spend your time either sitting on a desk and doing stuff with no mental stimulation or doing something unrelated to your work

[grave crater]

another here, if someone can help

oh nvm

i got it

you can try tho

options

[tranquil pine]

this is it

you can close it now

[grave crater]

ty

.close

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[lapis wedge]

So I found the joint pdf of U, V but the problem now is that I dont know how to solve this integral
$$ \int_0^\infty f_{U,V}(u,v) dv = \tfrac18 \int_0^\infty v^2 e^{\frac{-v(1+ u)}{2}}dv$$

[lapis wedge]

anyone got any ideas

u is a constant

[soft zealot]

Branshi (Hints only plz)

[lapis wedge]

been so long since ive solved integrals

forgot most of the techniques

mm this might be an integration by parts

if I let $s = \frac{-(1+u)}{2}$ then I get
$$ \tfrac18 \int_0^\infty v^2 e^{sv}dv$$

[soft zealot]

Branshi (Hints only plz)

[lapis wedge]

ok I think thats just integrtation by parts

will come back if it fails

.solved

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[peak tapir]

Is this right i dont have answers

[loud sundial]

,w 2cot^3 (x)+3csc^2 x-8cot x=0, 0 \leq x \leq pi

[soft zealot]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[peak tapir]

What

[loud sundial]

Yes

[peak tapir]

O ok

Is my working fine

[loud sundial]

Your answers are rounded to the nearest tenth

[peak tapir]

Yea u have to for the exam

[loud sundial]

Also wolfram alpha usually just does tangent half angle sub because polynomials

Hence why there’s factors of 2 on the arctan

You can cut these bits out

You end up only testing one root anyway so it’s not like you’re exhaustively checking all rational roots

And the spurious = after “quadratic”

Idk what that does tbh

[silent shore]

Wow I love rational root theorem

[peak tapir]

o ok

[peak tapir]

the book taught me that idk either

alr thanks

.close

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[tranquil pine]

Let's say I have a digit number 1-9. and I have 3x3 matrix. I want to map the each digit to an element in that matrix. like number 3 points to third element of first row in 3x3 matrix. Is their way I can convert the number 1-9 into the number that gives me the position in matrix like i,j ?

[trail mango]

sure

let the number be a

ceil(a/3) will give you the row

the column will be a mod 3 (with 0 = 3)

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