help-49

[chrome swift]

this is LU decomposition btw

[civic lynx]

when you reduce $[U|\vec{y}]$, you end up with four equations:
$$1\cdot x_1 = 6$$
$$1\cdot x_2 = 10$$
$$1\cdot x_3 = 4$$
$$0\cdot x_4 = 0$$
what is the possible value, or values, that $x_4$ could be?

[grand pond]

ηασιβ ♥

[midnight plank]

@chrome swift Has your question been resolved?

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[foggy badger]

I'm kind of struggling with comprehending this question. There are two parts to this question, it seems. I tried to write down as much as I comprehended. If anyone can help out, that would be appreciated.

(Also, to anyone who has seen me before: I mostly ask for help here when I'm about to complete a Khan Academy course, so that's why I'm more active here at the moment)

[bold peak]

Okay let's take this step by step

They both have 80 to begin with

Anna invests 20 and Hannah invests 80

They get back r times what they invested

How much do they have after they get it back

[foggy badger]

Anna has 20r + 60, and Hannah has 80r.

[bold peak]

Good

Now they both invest all of their money again

How much do they have after getting back

[foggy badger]

r(20r+60) for Anna and r(80r) for Hannah?

[bold peak]

Yup

[foggy badger]

But wait, hold on.

Hannah has twice the amount Anna has.

[bold peak]

In the end yes

So what's the equation we get

[foggy badger]

20r^2+60r=160r^2?

[bold peak]

No

Firstly, don't expand

You'll only confuse yourself by expanding this early

Secondly you want H to have double A

H = 2A

[foggy badger]

Let me do it without simplifying it.

r(20r+60) = 2(r(80r))?

[bold peak]

Again

You want H = 2A

[foggy badger]

Oh, right.

2(r(20r+60)) = r(80r).

[bold peak]

Yup

Now you can cancel an r

And solve

[foggy badger]

Oh, because we can divide r to both sides!

That would give us 2(20r+60) = 80r.

Thank you so much!

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[bright plinth]

Struggling on part b

[tall lintel]

Hi! Here's a hint:

The height of the design is 4m, that should be important...

[bright plinth]

makes two triangles one above and one below the rectangle right?

i thought of that but i wasnt too sure were to go from there

[tall lintel]

Welllll

If you form the triangles, you get something like this, right?

[bright plinth]

yeah?

[tall lintel]

Well, let me ask you this - why do you need these triangles?

(You do need them, I would just like to know why :)

[bright plinth]

sinx * hyp = opp

right

and cosx*hyp = adj

4cosx = 4

and 2sinx = 4

wait no

[tall lintel]

Wait

[bright plinth]

it isnt the full side

[tall lintel]

Right.

[tall lintel]

But these two are good, you just need to figure out how to use them.

[bright plinth]

find the adj and then pythag to find red line length

and vice versa for yellow line?

[tall lintel]

Ahh well you don't need Pythagoras'

[bright plinth]

uhh i cant see it

[tall lintel]

I mean, seems like you have the right idea:
Red + Yellow = 4
Right?

[bright plinth]

yeah

OHHHHH

[tall lintel]

So you just need to figure out what the red and yellow ones are

[bright plinth]

i think i got it

[tall lintel]

o

[bright plinth]

so i just find red lines and yellow line and they equal 4

[tall lintel]

When added together :)

[bright plinth]

and divide whole thing by two

also could you help on part d

this is my part a and c

[tall lintel]

Here's a hint: I am going to draw this triangle here

The reason being is because, we want to figure out a triangle that touches the length of h somehowm

[tall lintel]

What do you know about this triangle?

[bright plinth]

right angled

[tall lintel]

Good, anything else?

[bright plinth]

same angle

theta

[tall lintel]

Good! The question is, where would theta be?

[tall lintel]

(Try and draw it :)

[tall lintel]

Perfect.

Now, given this triangle,

How do we figure out the value of h?

[bright plinth]

4 - adj ?

[tall lintel]

Perfecto.

[bright plinth]

okay okay thanks alot!

[tall lintel]

I'll leave it up to you to continue from here.

[bright plinth]

yep thanks for the help

much appreciated!

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[calm stirrup]

#3

[calm stirrup]

I have a final tomorrow and this is the first time the whole semester I haven’t understood ts

[fallow scarab]

Did you read any Stokes theorem examples

[fallow scarab]

Read these two examples
https://tutorial.math.lamar.edu/classes/calcIII/stokestheorem.aspx

[calm stirrup]

Ok

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[last slate]

helo

[last slate]

What is their problem man

[lavish venture]

they told you

[blissful pier]

From here:

A connected component is a maximal connected subgraph of an undirected graph.

[midnight plank]

@last slate Has your question been resolved?

[last slate]

because 9 isnt added?

but their wording is weird

”9 can be added and it can still be connected”

[lavish venture]

is a maximal connected subgraph of an undirected graph

[livid merlin]

There is no direct connection to it.

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[twilit field]

I don't get how the double summation was simplified here

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

<@&286206848099549185>

[small jasper]

By definition,
$$(x_i, x_j)=\begin{cases} 0, & i \neq j \ 1, & i=j \end{cases}$$

[grand pond]

Civil Service Pigeon

[small jasper]

so, all of the terms vanish except for those where $i=j$

[grand pond]

Civil Service Pigeon

[small jasper]

which gives $$\sum_i \alpha_i \overline{\alpha_i} (x_i, x_i)=\sum_i \left|\alpha_i \right|^2$$

[grand pond]

Civil Service Pigeon

[twilit field]

ooh

right

thanks

got it

tysm

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[small jasper]

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[inland patio]

Stupid question maybe, but let X,Y be two random variables and f,g nonnegative measurable functions. Suppose f(X)g(Y) = f(X) g(Y) holds a.s. What can we conclude about X,Y?

Context; the identity is the result of conditional independence when the sub-sigma-algebra is the whole sigma-algebra, i.e. E[f(X)g(Y) | B] = E[f(X) | B]E[g(Y) | B] and B is a sub-sigma-algebra of A.

[runic hamlet]

if f,g=0 then we can say nothing

so you need stronger conditions on f and g at least

(or f,g constant)

I dont know what kind of conditions those could be

also presumably you meant f(X)g(Y)=f(Y)g(X)?

[inland patio]

Hmm, yes. I mean f(X)g(Y) = f(X)g(Y), which to be honest doesn't make much sense to me to say "they agree on a null set". The left-hand side and right-hand side are literally the same function.

[inland patio]

You see, if f(X) is in L^1(Ω, A,P) and is B-measurable, then E[f(X) | B] = f(X). So here in the second case, I interpret f(X) and g(Y) to be A-measurable, and so the formula reduces to f(X)g(Y) = f(X)g(Y).

[runic hamlet]

well then it just means that the result is boring

[inland patio]

Ok. And there's nothing we can say about X,Y when f(X)g(Y) = f(X)g(Y) (a.s.?)?

[runic hamlet]

like you said, its the same function on both sides

so of course thats just always true

so it means nothing

[inland patio]

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[placid ridge]

And what have you tried?

[lusty python]

dang

so it's this small region

[lusty python]

i can help you

[lusty python]

big hint: $y = x$ and $y = -x + 2$ is perpendicular to each other

[grand pond]

1 divided by 0 equals Infinity

[lyric charm]

are you expected to do it with integration?

[distant jetty]

yes

its from my calc class

[lyric charm]

oh that is going to be so ass

[distant jetty]

wym isnt this method correct

[lyric charm]

i am not saying that it's incorrect

i implied that it's overkill

[distant jetty]

its not ass i figured it out (if my integral is correct)

[lusty python]

looking at this question i even thought it's a non-calc question

😭

[distant jetty]

lmao

[clever sedge]

Compared to other ways of solving it excluding integrals

[distant jetty]

just tell me if the integration i set up is correct

[lusty python]

even if there's no right angle, i can just use heron's formula

[distant jetty]

.close

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[lusty python]

@austere gull

[lusty python]

Send your questions in here

And we'll try our best to answer them

[lyric charm]

when you say x^1 do you actually mean x_1

[foggy ferry]

i think we should start all again

[lyric charm]

also wait what is even happening here

[lusty python]

Let's start by letting @austere gull send his questions hers

[lusty python]

You can check #math-discussion for that

[lyric charm]

he apparently just did, or something?

urgh.

i mean the thing is @lusty python the channel is opened in your name

so it's gonna get confusing

[lusty python]

The user i pinged is confused on how to factorize a trinomial

[lyric charm]

but whatever

[lusty python]

Someone did the same thing for me in the past tho

[lyric charm]

https://www.youtube.com/watch?v=9MUDAr1PnlE

this is very much not how you type that.

4/x + 8/(x+2) = 4
and you are multiplying by x(x+2) on both sides

we are in discord and you will put proper brackets when writing fractions

you got balls saying that

but i mean ok

[foggy ferry]

@austere gull i think that if you are really intellectually gifted as you said we should restart from the basis of math. i can teach it to you if you want

[lusty python]

She is the best helper in here already

Don't just diss her like that

[lyric charm]

nah, let him shoot himself in the foot

[lusty python]

Aight then

[foggy ferry]

ok

[lyric charm]

play stupid games win stupid prizes

[lusty python]

you can go help others tho, if he annoys you then just ignore him

[foggy ferry]

from the private chat

[lusty python]

.close

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[lilac finch]

https://tenor.com/view/rage-gif-18338667365126853250

[lusty python]

Hm?

[lilac finch]

the guy

[lusty python]

He really got the balls to say that to Ann

[lilac finch]

No one teacher

(probably or not)

Thet helpers

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[fading marten]

How would i solve this?

[blissful pier]

if f(x)<=g(x) then f(x)-g(x)<=0

factor f(x)-g(x) and find where it is less than zero thus conclude where f(x)<=g(x)

[fading marten]

Graphing it gives me that x<1.172...

I think i was supposed to graph it but also it doesnt state it explicitely and i dont know if i shouldve

[small jasper]

hi

[fading marten]

That part i do get

But the point is completely arbitrary to the point where it isnt in character with this textbook

[blissful pier]

what exactly do you mean?

[gaunt mantle]

you can find it algebraically using the quadratic formula

nvm its deg 3

[fading marten]

.w 2x^3+3x^2-2x-5

[blissful pier]

,w

[fading marten]

Thank you

,w 2x^3+3x^2-2x-5

[grand pond]

Results provided by WolframAlpha

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

Requested by the_gopher_god

[fading marten]

The exact form of the real root is a long equation but i have literally no clue how i am supposed to get to this value

[blissful pier]

it is obviously algebraic but yeah it might be a nasty number

[fading marten]

I think im just gonna pester my teacher to explain this tomorrow

[junior flower]

[fading marten]

Because wtf is this

Before this, all of our polynomials had nice and elegant factorizations with integers, maybe a fraction or two

[junior flower]

,w 2x^3+3x^2-2x-5

[blissful pier]

[junior flower]

,w roots of 2x^3+3x^2-2x-5

[grand pond]

Results provided by WolframAlpha

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

Requested by slayyla

[junior flower]

lol

probably typo

[blissful pier]

wait why did it factor under one cbrt but not the other, what? lmao

[fading marten]

Wait! Nope! Its in the answers section of the book!

How in the world is this intentional

[blissful pier]

damn gotta memorize that cubic formula, it's an important one

[junior flower]

it expected you to find this root?

[fading marten]

Literally all of our tasks before and this one

[brave gorge]

She obviously wanted you to get the nested radical expression using the Galois correspondence

[junior flower]

lol

so it was expecting you to find a numerical approximation for the root somehow probably

weird

i’m guessing with technology

[blissful pier]

Newton's in an algebra class

[junior flower]

but still weird

[fading marten]

Im so foolish! Why didnt i study undergrad mathematics in middle school?

[fallow scarab]

you're supposed to use graphing calculators ?

[fading marten]

Maybe?

But every other time i am, it is explicitly stated

[brave gorge]

Well thatd make it a bit easier wouldnt it

[fading marten]

“Use graphing to solve this”

“Use your GDC to solve this”

[fading marten]

Even the next task explicitly states to use simple polynomial graphs

[brave gorge]

Probably a typo somewhere

[fading marten]

Anyway, thank you for the shared moment of confusion everyone

[blissful pier]

Patrick Pearse mentioned

[brave gorge]

Where??

[fading marten]

.close

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[blissful pier]

your name lol

[brave gorge]

https://tenor.com/view/ultrasad-gif-23310565

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[stray drum]

anyone can spot my mistake ? I've been searching for too long and dont really want to restart but cant find the issue

[stray drum]

it should be a stupid mistake somewhere but i cant find

[abstract dust]

please why am i seeing a plane😭

[dawn dagger]

I dont understand ur 3rd line

[dawn dagger]

!help

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[stray drum]

emh

[dawn dagger]

u r saying R_1 - 4/3 * R_2

for R_1

[stray drum]

wait give me a sec to make sense of this Im having a couple brainfarts

[dawn dagger]

one step at the time should be the goal with these

[stray drum]

did I just divide everything by 5 for no reason?

that may be it

[dawn dagger]

well you divided R_2 by 5 to normalize the element in the center, i suppose

[stray drum]

yes

[dawn dagger]

ok i see how you got -16/15 brain fart from me

[stray drum]

can i not do more than one like thing at the same time though?

cause im adding and minusing the R2 from both which doesnt change

[dawn dagger]

you can do but then it's harder to do a traceback when a mistake happens

ok I see your structure, you wrote the operation next to the matrix, that were applied to, not are going to apply to

[stray drum]

yeh idk why I did it like this

or well i dont remember doing too much row operations so this is what i went with

[dawn dagger]

ok the last matrix seems sus

[stray drum]

I've done it some different way to double check without the row operations and its wrong thats why I know it should be different

[dawn dagger]

when u multiply R_3 by 16/15

we have a 20 but the -1/3 remained unchanged

or the 4/15

[stray drum]

ah

im just gonna redo the right side at the end

i think I may have compleatly fell apart there

[dawn dagger]

yeah seems u forgot the right side

somehow where only focused on the unit matrix

[small jasper]

hi

[dawn dagger]

hii

[stray drum]

emh

oh ok no

i got it now

is this way good because its easier for finding inverses past 3x3?

cause I usually use some different method for 3x3 which takes so much less for this one for example

[dawn dagger]

sure

whatever you are comfortable with

if u r good generally with row operations then sure continue

[stray drum]

I just had to go with row operations cause it told me to do it that way but i hate them tbh

gets so confusing especially since i got mid handwriting

aight anyways thanks

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[river robin]

(a^c)^b

[river robin]

Is it

a^c*b or a^c^b

and give example

[junior flower]

avoid writing a^c^b

[lyric charm]

a^(cb)

for example (2^4)^3 = 2^12

[orchid latch]

Why not just pick up the calculator, assign values, and just check

[compact copper]

Maybe he thought this is a bot

[river robin]

i thought it was square..

[slate ferry]

wdym "square"

[river robin]

like you square the power

not multiply

by the other power

[slate ferry]

oh no, you multiply.

I can prove this with you

but first, do yk that x^n * x^m = x^(n+m)?

(and- if you dont want a proof... that's fine too

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[fossil ember]

Okay, I went through like 20 linear programming books skimming to see if they have methods for solving sets of inequalities, most nothing close and some close but not, is this even linear programming or does it go by another name? Most were like optimization like max or min, I want the full 4d+ polytope solution, do I have to make my own everything? Is there even a Fourier Motzkin elimination example out now? What math area is this?

[fossil ember]

I just want a solution, it can be like n^n^n time. X E.

Note 4+ variables. X E.

[dawn dagger]

I only know simplex

[fossil ember]

Okay, what teaches that?

Preferably free. X E.

You should see the list of things I went through, haha. X E.

[silent dock]

Convex Polytopes and or Polyhedral Theory

[fossil ember]

Thanks for talking people. X E.

[silent dock]

Possibly

[fossil ember]

Anything else?

These might not be convex. X E.

[runic hamlet]

what do you mean by

I want the full 4d+ polytope solution

in what form do you expect to get that solution

[fossil ember]

Okay, I should explain, left side is P+(O-P)z+(X-O)x+(Y-O)y, basically in the form of these three variables from projection. X E.

[silent dock]

I don’t think one should used Fourier-Motzhkin in practice because the number of inequalities blows up exponentially.

[fossil ember]

Not in practice, to know what I am dealing with. X E.

[fossil ember]

x,y,z I mean, those are scalars, the rest are points. X E.

All valid points will be able to be represented in that, 3 floats only. X E.

This is 4d+. X E.

Right side is, =Q+sum((V_i)s_i). All lower case scalars, upper case vectors here, all scalars unknown bounded except no z upper bound and all points and vectors known. X E.

Man I kind of wish someone could just look for me, contacted a librarian. X E.

I can gaussian eliminate this first, then solve, but still need something to study, sorry. X E.

Should I just let that librarian handle it?

Yeah, the library database is turning up almost nothing useful. X E.

I am on it now. X E.

Should the equation I just gave with s_i bounded and x/z and y/z bounded all with known numbers and z>=1, all with >=, be convex always when cut to be inside the equation space?

[coral belfry]

X E.*

[dawn dagger]

MLK

[fossil ember]

Hello people, I am screwed. X E.

[dawn dagger]

hi screwed

[silent dock]

All as per one might be maybe or might not be maybe, maybe or maybe not, maybe
I have no clue what this means.

[fossil ember]

Lots of linear programming, nothing for my problem. X E.

[dawn dagger]

Maybe u r not meant to know

[fossil ember]

It is a not lying thing. Suffice it to say I am weird. X E.

[dawn dagger]

I would recommend looking up Simplex if you wanna do linear programming

[fossil ember]

It is about the problem, not necessarily linear programming. X E.

[dawn dagger]

oh mb X E.

[fossil ember]

mb?

[silent dock]

my bad

[dawn dagger]

my bad* X E.

[fossil ember]

Well, looking up simplex. X E.

[silent dock]

Can one perhaps use use z >= 1 to linearise the ratio constraints

[fossil ember]

Probably. X E.

I am uneducated though. X E.

x increases linearly with z and same for y. X E.

[fallow scarab]

then read more books and stop opening channels every day saying the same thing

[fossil ember]

Hi riemann, looking for a book, I skimmed like 20 that don't include what I need. X E.

[fallow scarab]

"skimming"

[fossil ember]

Yes. X E.

[fallow scarab]

i skimmed moby dick. i know how to do whale surgery now

[fossil ember]

The table of contents is useful. X E.

I have found like one that might help but anyway, just don't know, always check contents before committing to read. You could gain nothing for years otherwise. X E.

Kind of sorry that this is so annoying, should I leave it to that librarian?

The one I contacted. X E.

[runic hamlet]

I still dont know what you are even looking for. you are trying to solve for x,y,z, yes? and you already know some bounds on x,y,z? what result on x,y,z are you expecting as a solution?

[fallow scarab]

this is just pure laziness.

no one said to read for years

[fossil ember]

Yes, the solution will be planar figures that satisfy everything. X E.

[fossil ember]

Read one book well, like a month, read 12, a year, if they contain nothing useful to you, why?

[runic hamlet]

the set of solutions (x,y,z) will be some polytope. sure

[fallow scarab]

no one said to read 12 books

[runic hamlet]

in what form are you expecting to get that polytope

[fossil ember]

True but if I just blindly read books, that is where I end up. X E.

[fallow scarab]

your excuses to not do any reading are also just lazy

[fossil ember]

I have now found two possibly useful books. X E.

[dawn dagger]

Which ones? X E.

[fossil ember]

Boundaries, like x,y,z of the planar figures. X E.

[runic hamlet]

but these boundaries will just be other inequalities involving several variables

[fossil ember]

Orthogonal Sets and Polar Methods in Linear Algebra
Enrique Castillo, Angel Cobo, Francisco Jubete, Rosa Eva Pruneda. X E.

[runic hamlet]

you wont get something simple like 2<=x<=4 or something

[fossil ember]

True, what I am looking for is all the planes on the outside and the 3 coordinates each point that define them. X E.

https://www.open.edu/openlearn/science-maths-technology/linear-programming-the-basic-ideas/content-section-0?intro=1
This was the other book thing. X E.

[fossil ember]

This is one book. X E.

I know, I will always be dumb and uneducated at this rate. X E.

Thanks for talking. X E.

[coral belfry]

youre not dumb

[fossil ember]

At this point I just want possibilities of solutions, I can think how to optimize later. X E.

[fossil ember]

Thanks. X E.

By the way, page 200 if you have free online access to the first mentioned book is good. X E.

[runic hamlet]

look, all these kinds of calculations are easy. sagemath can do them for you in seconds

the problem is that I dont get what you are looking for

[fossil ember]

Can SageMath do inequalities?

[runic hamlet]

yes you can just enter that polytope

and then you can find its vertices or facets or whatever

[chrome swift]

hi

[dawn dagger]

!help

[midnight plank]

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

[surreal moon]

!occupied

[chrome swift]

oops

[midnight plank]

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).

[fossil ember]

What I am looking for is what shapes can a ND cube (calling it cube as in extruded every way), can be cut projected. X E.

Basically like where the ends of the plane are, at least three points per each, and how to define them, unsure, can this be concave?

Anyway, I guess SageMath might be able to but I will need to know how to do this some. X E.

I think it can only be convex. X E.

But need a solution to know and not going down the AI trash dump. X E.

That first book, I think I may just read it, then report back. X E.

[runic hamlet]

polytopes are convex

thats just known

[frail carbon]

the hypercube is convex, i.e. for any two points, the line between them is also in the cube; in particular two points in a slice of the cube will have the line between them is also in the slice and so the slice will also be convex

[fossil ember]

True, but are their projected forms?

[runic hamlet]

yes

[fossil ember]

Great, thanks. X E.

Okay, good progress from the math nerds. X E.

Okay, I downloaded the useful book, I will have to read it soon. X E.

Thanks for all the work you put in for nothing in return. X E.

.close

[midnight plank]

Channel closed

Closed by @fossil ember

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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• 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.
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[marsh agate]

probability of a 5 card hand from a 52 card deck containing at least one ace

[marsh agate]

so i first thought 4/52
after that whatever happens may happen so times 1 time 1 times 1 times 1
so final answer 1/13

but does it matter when i get the ace. like is it the 1st card or the fourth.
so i though maybe its 4/50.5?

[junior flower]

it is easier to find the complement (probability of no aces)

in terms of not accidentally counting cases more than once, yes, “when” you get the ace matters

[marsh agate]

got it! sorry been so long since i touched any math 😭

and thank you

[junior flower]

but i recommend this

[marsh agate]

.close

[midnight plank]

Channel closed

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[midnight plank]

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.

[last slate]

Hi

[last slate]

I need help interpreting the set representation when it comes to identifying graph isomorphism

Like based off of the given sets how am I supposed to draw the graphs

[lavish venture]

label A, B, C, D, E with 1, 2, 3, 4, 5 then form a set {n, k} if there is an edge between the two vertices n, k and see what matches

you just need to make sure it has the same edges

[last slate]

Well we need:

Same # edges
Same # vertices
Same degree sequence
And same degree vertex for each corresponding vertex ?

Am I missing something

[lavish venture]

i didn't say same number of edges

[last slate]

Yes but I’m saying that’s a requirement tho no?

[lavish venture]

sure but i don't see how this relates to my comment

[last slate]

I thought that is what you were referring to lol

[lavish venture]

read this again

[last slate]

Yes

[last slate]

Btw how do you know in what order it goes

Like the vertices set

Like do you just assume it goes 1-5

[lavish venture]

doesn't matter

its just a labeling

what matters is what vertices are connected to what other vertices

[last slate]

Is this correct for checking for isomorphism?

Or is there anything else

[lavish venture]

i mean you seem to be listing necessary conditions but again im not sure whats confusing about what i said

[last slate]

I mean I was asking for conditions, but I guess I still dont get how to make the correlation between the vertices tbh

I drew the last one

How can I know from this drawing that they are isomorphic

[lavish venture]

ok lets work with A first

if we label A, B, C, D, E as 1, 2, 3, 4, 5 in that order then what vertices are connected to A (which is 1)

give me the answers in terms of the numbered labeling

[last slate]

3 and 5

[lavish venture]

are you sure?

[last slate]

We’re doing the first choice right ?

[lavish venture]

yes. vertex A/1

[last slate]

I see the 1 being with 3 and 5

[lavish venture]

which vertices are connected to A

is that it?

how many lines are drawn out of A

[last slate]

Oh you’re talking about the diagram ? I thought you were referring to the first option in the multiple choice

[last slate]

3

[lavish venture]

no lol

[lavish venture]

yes

so what are the three vertices that are connected to 1

give me the numbered labeling

[last slate]

2,3,4

{1,2} {1,3} {1,4}

[lavish venture]

now do that for all of the vertices

[last slate]

Ohh I see, okay but my problem is with the labeling

How do you know which vertices even correspond to which other vertices from the second graph

[lavish venture]

well for starters which ones can you rule out immediately

[last slate]

Definitely option 1

Not the same number of edges

So

[lavish venture]

yea and then you should honestly look at the degree of the vertices in each answer choice

[last slate]

Btw if you look here the final answer is correct but there is no correlation between 1 and 2

[lavish venture]

you don't actually need to find the correct labeling they want for this

yea because they labeled differently but its really the same thing

they're testing necessary conditions here

[last slate]

So yeah that’s what’s confusing me tbh

Like what are you exactly supposed to check for

[lavish venture]

can you find the degree of each vertex in our original graph?

label it as a list for me

[last slate]

Degree sequence:
3,3,3,2,1

[lavish venture]

yea

now do that for the answer choices and see if any of the answer choices dont have the numbers 3, 3, 3, 2, 1

in any order

the third option has a glaring issue too

sorry third

what do you notice about the edge set for option 3?

[last slate]

4 is disconnected

[lavish venture]

mhm

so clearly not that one

[last slate]

Yup

[lavish venture]

now look at option 2

what goes wrong

[lavish venture]

compare with this

[last slate]

4,2,2,2,1

[lavish venture]

uhh well vertex 5 has degree 4 no?

not sure where that came from

[last slate]

Yea ur right

[last slate]

So is the whim point to make sure all vertices have the same degree vertex ?

[lavish venture]

yea they are testing necessary conditions here

option 4 is the only possible answer based on the degrees

as an exercise you might want to identify what each vertex (A, B, C, D, E) maps to

start with the obvious ones

like the vertices of degree 1,2

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[last slate]

Hi can someone please help me understand graph connectivity

[last slate]

I don’t get it bro

Can someone help

[prime hornet]

the edge connectivity of a graph is the largest number k for which removing k - 1 or less edges from the graph keeps it connected

you kinda just have to imagine deleting edges until you get a disconnected graph for that exercise

[radiant scarab]

Im way to dumb for this server tbh. Im not even 10th grader 🥀

hi tho:)

[last slate]

What’s up

[last slate]

Don’t say that

[last slate]

I don’t get it bro 😂

[prime hornet]

a good place to start might be to look for the literal weakest links

[last slate]

Can you describe it in simple words

[wraith dirge]

#❓how-to-get-help

[prime hornet]

the vertices with the fewest neighbours

[radiant scarab]

im doing semi pro geometery

[last slate]

Hmm

[radiant scarab]

like basic pi 🥀

altough me love math :D

[prime hornet]

a square is 2-edge connected because removing one edge from a square doesn't leave it disconnected, while removing two does

[last slate]

Well I see the weakest links to be 3 edges

[prime hornet]

an N is 1-edge connected because removing any edge from it disconnects it

[last slate]

So a triangle is 2 edge connected ?

[prime hornet]

yeah

[last slate]

A pentagon is 2 edge connected also

I see

So we are looking for how many edges we remove that disconnects the graph?

[prime hornet]

in your graph, you need to look for the maximum number of edges you can remove without disconnecting your graph, and then add one to that number

[prime hornet]

yup

the minimum number it takes to disconnect, essentially

[last slate]

Dude idk what’s wrong with me but

I know this is simple

But it isn’t clicking for me

[prime hornet]

think of it like this

how many edges do we gotta remove to disconnect the graph?

that's what we want to know

[last slate]

3?

[prime hornet]

3 definitely works, I can't tell if it's the least though

I suspect it is, but I don't know for sure

[last slate]

Oh It needs to be least

[prime hornet]

yeah

you can sever a vertex with 3 edges from all of its neighbours to disconnect for sure

I wonder if it's possible to only sever 2 edges

nah, there's no way

[last slate]

Then why is my book saying it’s 2

[prime hornet]

every vertex has at least 3 neighbours, so we can't just cut 2 edges and call it a day, right?

[prime hornet]

[last slate]

What do they mean dude

[prime hornet]

vertex connectivity

not edge connectivity

[last slate]

Ohhh oops

Oopsie

[prime hornet]

vertex connectivity is the minimum number of verticies we need to remove

[last slate]

Dude I was thinking of edges the whole time 💀

[last slate]

It can be anywhere ?

[prime hornet]

you can delete wherever you want, sure

if I delete these two nodes, then the graph is disconnected

[last slate]

I was just thinking the same exact thing 😂

I was about to say c and d

[last slate]

Yessir

[prime hornet]

MS Paint to the rescue

[last slate]

I miss paint

This is 3 right

[prime hornet]

I'm confident

it can't be more than 3 because we can kill all 3 the edges connecting G to the world to disconnect the graph

I'm about 95% sure it can't be less than 3 because all verticies have at least 3 neighbours

only reason that I'm not 100% sure is that it's been over a year since I did graph theory and I forgot almost everything

[last slate]

You are right 😁

[last slate]

I have a test tomorrow

Lowkey cooked

[prime hornet]

good luck

[last slate]

Thank you

[prime hornet]

you can close the channel if you're done here

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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• 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!

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[gusty falcon]

is there an efficient way to calculate smth like the tens digit of $21^{3^{50}}$?

[grand pond]

mmmm7

[junior flower]

omg hi

[gusty falcon]

heyy 😭 omggg

[junior flower]

euler’s theorem can be helpful

[silent dock]

omg hi

[gusty falcon]

what i do for this is crt and euler's theorem

[bold peak]

I'd try to see a pattern personally

[gusty falcon]

too slow tho

[silent dock]

I apologise for calling you temu layla

[bold peak]

,w 21^3

[grand pond]

Results provided by WolframAlpha

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

Requested by xavier_dragon

[bold peak]

Why did I w that

,calc 21^4

[grand pond]

Result:

1.94481e+5

[junior flower]

note the nesting

[gusty falcon]

oh i think i see what u mean

[bold peak]

2,4,6,8 hmmm

,w 21^5

[grand pond]

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Requested by xavier_dragon

[bold peak]

,w 21^6

[grand pond]

Results provided by WolframAlpha

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Requested by xavier_dragon

[bold peak]

Interesting

[silent dock]

I mean

number theory

mod 100

[bold peak]

I don't feel like proving whether this repeats so that's up to you to do

[silent dock]

Euler's theorem blah blah

[junior flower]

those were my thoughts exactly kuri

[gusty falcon]

,w table 21^i mod 100 for i = 1,2,3,4,5,6,7,8

[grand pond]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by mmmm70177

[gusty falcon]

mmm pattern

[gusty falcon]

yeah euler's theorem and crt

takes too long

i did it that way

[silent dock]

It only depends on 3^50 mod 40

by Euler's

Which is quite easy to compute

[gusty falcon]

apparently people do this question in 30 secs

[silent dock]

Yeah

[gusty falcon]

without a calculator

[bold peak]

People be crazy

[gusty falcon]

yeah so

surely it isn't crt and euler

[junior flower]

i’m too stupid for that

[gusty falcon]

also crt and euler is out of scope

[silent dock]

No CRT

[gusty falcon]

but i already tried it

[silent dock]

Euler took 2 secs

[gusty falcon]

crt cuz mod 100

so mod 25 and mod 4

[silent dock]

[gusty falcon]

2 seconds? 😭 wha

there's no way it takes 2 seconds

[silent dock]

how long would it take for you to compute 21^9 mod 100?

[junior flower]

more than 2 seconds

[silent dock]

But less than 30 seconds?

[gusty falcon]

well definitely not 2 seconds yep

[junior flower]

depends what the stakes are

[gusty falcon]

idk probably not less than 30 seconds either

[junior flower]

and yea same

not everyone is so smart like you kuri

[gusty falcon]

btw this is from like an elementary algebra class like usual

[silent dock]

People whoc an do this in 30 seconds have done many similar questions

[gusty falcon]

😭 would be funny to whip out carmichael, euler, and crt

[silent dock]

I don't know why you're saying CRT, but it's not relevant here.

[lyric charm]

21^n always ends in 1 lololol

[gusty falcon]

yeah but we need the tens digit

😔

[lyric charm]

oh tens

so mod 100

[gusty falcon]

is this the pattern we should go for?

[lyric charm]

binomial bs

[gusty falcon]

yep

[lyric charm]

1 + 3^50 * 20 + shit divisible by 100...

[silent dock]

They know, for instance, that the last two digits are 21,41,61,81,01,… so we only need 3^50 mod 5

[gusty falcon]

u decompose mod 100 to mod 25 and mod 4

hmm i could try the binomial thing too

let me see

[silent dock]

,w 3^50 mod 5

[grand pond]

Results provided by WolframAlpha

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Requested by caelum.intra

[silent dock]

Why would you need to do this???

[bold peak]

3^50 mod 5 is easy to do as well cuz 3^x has a pattern in its last digit

3,9,7,1,...

[junior flower]

i should go to sleep but @gusty falcon

[silent dock]

Goodnight slayla

[junior flower]

goodnight

[gusty falcon]

goodnight

okay i guess i'll indeed just do what u guys suggested

😭

3^50 (mod 20) then 21^9 mod 100

[silent dock]

I suggested 3^50 mod 5

[gusty falcon]

how did you get here?

3^50 (mod 40) if you want to strictly euler

phi(40) = 16

and bla bla

why is it mod 5?

[silent dock]

The last two digits of 21^n are 21,41,61,81,01,… so the cycle length is 5.

So it only depends on n mod 5

[gusty falcon]

😭 okay if you know that then the problem is trivial

wouldn't you take time to figure that out

[gusty falcon]

that's the pattern thing i wrote out here

[silent dock]

When a base ends in 1, powers tend to cycle very quickly modulo 100.

That ought to mean you should always try the first few terms as the cycle is expected to be very short.

[gusty falcon]

is that smth you're expected to know?

seems like a random fact

like consider an entirely different example

2^99 mod 99

this one has a much longer cycle

[silent dock]

Well, if you think about it...multiplying by something ending in 1 changes only the last two digits in a simple way.

[gusty falcon]

yes it doesn't end with 1

[gusty falcon]

hmm i guess

[silent dock]

I mean this is just a completely different type of problem

[gusty falcon]

i mean in terms of cyclicity

[untold basin]

simon

[gusty falcon]

how can we know for sure if a cycle is long or short

maybe there's merit trying

a few numbers regardless (?)

i just randomly 😭 typed out mmmm7

that wasn't the inspiration

[silent dock]

Well, for general moduli, cycles can be long and unpredictable.. The right method is to use prime factorisation and multiplicative orders, not trial cycles.

[untold basin]

sure

[silent dock]

You can typically expect to have short cycles when 1. modulus = 10, 100, 1000, etc. 2. modulus is prime. 3. modulus is a power of prime 4. (weak expectation) base ends in 1, 3, 7, or 9 5. base and modulus share strong structure.

For this instance, the cycle length of 2^k mod 99 is the order of 2 modulo 99, and that order is ord_{99}(2) = lcm(ord_9(2), ord_{11}(2)); that is to say, it's not easily predicable.

[gusty falcon]

yeah okay thanks

i guess since this isn't an elem number theory question

it might just always be either 1), 2), or 3)

[silent dock]

I suppose

[hard shard]

whats the question?

[gusty falcon]

21^{3^{50}} mod 100

smth faster than euler/carmichael/crt bash

[hard shard]

(20+1)^(3^50) congruent to 20*3^50+1 using binom thm

[gusty falcon]

yes

[hard shard]

then eulers thm

or flt

whatever the fuck

[silent dock]

Yeah, that's not faster than 3^50 mod 5

[gusty falcon]

3^50 mod 5 😭 requires you to find the cycle length of 5 too

so it's not just 3^50 mod 5

is it

[silent dock]

Come on

21 x 21 = 441 etc

[hard shard]

you cant really escape calculatinglike 4 numbers

[gusty falcon]

41 * 21

[hard shard]

nbd at all

[silent dock]

Yes

[gusty falcon]

61 * 21

[silent dock]

Go on

yes..

[gusty falcon]

81 * 21

😭

yeah that's not fast...

[silent dock]

1701

[gusty falcon]

but yeah i guess it's okay

[silent dock]

(80+1)(20+1) = 1600 + 100 + 1

That should take like 1.5 seconds

[hard shard]

i still think my method is the coolest with the binom thm

[hard shard]

once you get here, just find 3^50 mod 5 and then you do 20*4+1 to get 81

[gusty falcon]

your method

is the same as his yeah

but without needing cycle

well i mean you get to 3^50 mod 5 yeah

[hard shard]

no implicit bash

implicit as in implied

[gusty falcon]

yeah okay

thanks everyone

[gusty falcon]

.close

[midnight plank]

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[arctic bronze]

I've done the basic stuff

[arctic bronze]

i pulled that 16 outta nowhere so please correct me

and ignore the 16

I think there might not be enough info but can anyone confirm that

[unkempt sluice]

I don’t have a pen. I am doing it here:

[arctic bronze]

Alright thanks

[unkempt sluice]

86-(180-x)+140+70+27+80=360

I got x=223

[arctic bronze]

That wouldn't be the answer though

I think the question might be wrong?

[unkempt sluice]

Something wrong I need to check again

[arctic bronze]

AAlright

[sullen bolt]

don't forget to find angle LJH

[unkempt sluice]

86+a+140+70+27+80=360

(a represent how many angle I turned clockwise when I travel past point x)

a=-43

180-x=43, x=137

answer is C

Clearly I miscalculated first time

This time should be alright

[sullen bolt]

got C as well

[arctic bronze]

I don't even remember learning this ...

I guess maybe this question might be out of my capability

[unkempt sluice]

Imaging you are walking along the closed path one cycle

You eventually turned 360 degrees

This is the idea

[sullen bolt]

an alternate method is to recognize the shape as a hexagon

hexagons have 720 degrees

the rest of your job is just finding all the angles

[unkempt sluice]

You keep record how many angles you turned at each vertex, add up, being 360

[arctic bronze]

Okay thank you so much

Ah

I understand it now

[arctic bronze]

How do I get the A though?

Sorry that's all I don't understand rn

I understand everything else

[unkempt sluice]

Can’t help, running

[arctic bronze]

Ah alright

[midnight plank]

@arctic bronze Has your question been resolved?

[unkempt sluice]

What do you mean A?

[arctic bronze]

the a u got here

[arctic bronze]

i know you said this but

idk how you got 43

[unkempt sluice]

The angle I turned when I pass vertex x. I don’t know its value, I set it a. In the end it turns out to be -43, meaning at vertex x I actually turned left 43 degrees

[unkempt sluice]

By this, adding all angles I have turned (positive for clockwise (right), negative for anti clockwise (left)) will be 360

[arctic bronze]

Ohhh

so basically a is just an unknown? and we get it after adding everything then minusing it with 360

alright tysm

[unkempt sluice]

Yes

Np

You can type .close to close this dialogue, in order to make it vacant.

[arctic bronze]

.close

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[half quail]

guys are these tricks useful ? for mental math ?

[lusty python]

$(a - b)^2 = a^2 - 2ab + b^2$

[grand pond]

1 divided by 0 equals Infinity

[lusty python]

so basically

plug a = 20 and b = 1

then you got $19^2$

[gaunt jetty]

Well they made a pretty bad typo here so I'd advance with caution

[grand pond]

1 divided by 0 equals Infinity

[half quail]

would this method work for all numbers from 1 to 99 ?

[half quail]

can you explain what's wrong with that please

[gaunt jetty]

52 ≠ 52 - 2

[half quail]

so how to correct it ?

[gaunt jetty]

,, \def\mm{\mulsymbol}
52\mm9 = (50+2)\mm9

[gaunt jetty]

They meant to say this

[half quail]

oh

alright tysm ❤️

[lusty python]

2 digit works the best

but you can customize your methods

for example, for 3 digits:

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$

[grand pond]

1 divided by 0 equals Infinity

[midnight plank]

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[full grail]

Hi can someone explain if my logic is correct

[full grail]

I just don’t get why I needed to transpose it for the multiplication to work

[prime rampart]

sure ill not give ans but help

go on

whats ur problem ur facing

i see ur struggles with chords

its easy

When you build a basis matrix, the rule is: S=[v1​v2​v3​]

If you accidentally write them like the image i gave

then your coordinates won’t multiply correctly.
So you transpose the vectors to put them back into column form, which fixes the multiplication.

@full grail

[full grail]

What

Cords?

what is that

[full grail]

No but is my answer correct in the first place

Cuz like

THATS what chat gave

And

If it’s correct then the only way to get to that answer is if I transpose the c in standard basis coordinate

<@&286206848099549185>

Can someone help me with this too pls

[gaunt jetty]

I feel like the whole multiplication is unnecessary. You know that a a matrix times a vector is a linear combination of the columns, so you can just directly scale the [1, 1, 1] vector with 2, the first element of the [2; 0; 0] vector

[gaunt jetty]

The dimensions don't work if you multiply a 3x1 vector with a 3x1 vector

The column dimension of the first matrix (1) needs to be equal with the row dimension of the second matrix (3), which isn't the case

[midnight plank]

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[edgy crater]

is this how u do it? feel like smths wrong

[visual elk]

Physics problem btw

[midnight plank]

@edgy crater Has your question been resolved?

[fallen sparrow]

Its fine

[slow thorn]

i feel like you assumed that the masses rebound away from each other with equal speed after collision

which is surely not right

[fallen sparrow]

Your assumption that v is same for both masses after collision is false

[slow thorn]

you need to use energy conservation and linear momentum conservation together

[fallen sparrow]

I would just like to say that, try to draw certain instants of the motion

First the instant the mass M collides to the ground

Next i want you to visualise what happens after this very instant

[midnight plank]

@edgy crater Has your question been resolved?

[edgy crater]

so small mass up and bigger mass down?

[edgy crater]

okok, but if v is different then i would have to find another question involving both vs? then simultanous equations?

[shy rampart]

yah

there are two equations

(or, you should get an intuition for what happens when something really big and something really small collides
i mistook the problem for a similar problem where M >> m, but my responses above (there are two equations) still holds

[midnight plank]

@edgy crater Has your question been resolved?

[fallen sparrow]

Possibly the best hint you could receive

Another would be to approximate terms

[midnight plank]

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[leaden seal]

can some one explain how we get the bt in the question mark

is it t/sqrt(t) =

[dawn dagger]

they split the fraction i guess

[leaden seal]

and then 1/sqrt(t)

yh okay

[dawn dagger]

ye

[leaden seal]

so

[dawn dagger]

t=sqrt(t)^2 basically

[leaden seal]

t/sqrt(t)=sqrt(t)

[dawn dagger]

ye

[leaden seal]

ok

[dawn dagger]

ty

[leaden seal]

yh

[dawn dagger]

then can apply exponent rules

,tex .exp rules

[leaden seal]

t^1 - t^1/2

[leaden seal]

what about on this part

[dawn dagger]

they integrated each term

do u know how to integrate?

[leaden seal]

yh

[dawn dagger]

u add 1 to the exponent, and then divide by the exponent

[leaden seal]

isnt that what i just showed you

[dawn dagger]

you mean the 4^3/2?

that is a factor which remains untouched

[leaden seal]

oh

[dawn dagger]

yea there is a different between having something like ...+4^(3/2)+... only or having a scalar as a factor

also 4^(3/2) simplifies to 8 first since 4^3 is 64 and the sqrt is 8

[leaden seal]

oh

yh i see