help-43

[dusky nymph]

is that integrable near zero?

[subtle helm]

Yup

[dusky nymph]

good

see if you can show that your fraction is smaller

[subtle helm]

Sinx > 0 over that interval

Thank u

.close

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[muted galleon]

I have a question that asks the number of observation units in a case that involves plants. Would the number of the observation units be the number of plants or all the observations actually done on the plants based on different variables? Like there is 6 types of plants but 42 observations done in total

[compact pewter]

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@muted galleon Has your question been resolved?

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[sage sphinx]

can someone please explain the difference between dot product and vector projection in words? i thought they both refer to how much 1 vector points in the directiion of the other

[kind viper]

vector projection outputs a vector and has two non-interchangeable roles, dot product outputs a number and is symmetric

[sick shard]

Is dot product × unit vector = vector projection?

Where there are 2 unit vectors for the two given vectors so there are 2 vector projections, am I right?

[kind viper]

mmmm

imprecise.

proj_b(a) = (a•b)/(b•b) * b

ok yeah no augh.

my motivation to say anything else was sapped with that pouting react.

sorry.

[sick shard]

Yo i removed the react

Don't go

Explain

[kind viper]

projection of a vector a onto a vector b means splitting a into the sum of two vectors, one of which is parallel to b and the other perpendicular to b

and then taking the parallel component

[sick shard]

Ohh

I understand

[kind viper]

you're not even OP...

@sage sphinx you still here or what

[sage sphinx]

6es

lemme see

[sage sphinx]

i dont understand

so you're saying they're the same thing except that 1 is a vector 1 is the magnitude? 😭

[kind viper]

no

idrk how to deliver a fully verbal explanation here for what each one is

[compact pewter]

@sage sphinx Has your question been resolved?

[sage sphinx]

😭

can you draw it out or smgth

[boreal girder]

Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

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[cloud ridge]

help

[cloud ridge]

how to differentiate

-2dy/dx x e^x-2y

?

[craggy sluice]

um

is there an equal sign?, or is that just it

[cloud ridge]

err

wait

[wheat pasture]

(Do you know how to differentiate x - 2y [with respect to x]?)

[cloud ridge]

yeah

1 - 2dy/dx

[wheat pasture]

Then chain rule it isn’t quite this here(!)

[cloud ridge]

wait

[cloud ridge]

i get this yeah then what

[cloud ridge]

11e^allat into this ??

[wheat pasture]

More that you know e^u differentiates with respect to u to e^u, so a matter of putting that together

[wheat pasture]

So then you’d multiply this by the derivative of x - 2y, which…

[wheat pasture]

…you just found (and of course all the other constants and stuff)

[cloud ridge]

https://tenor.com/view/243-gif-16468897745036284280

i get this

then

what

what to do

[wheat pasture]

,rccw

[wheat pasture]

You’re pretty much done in terms of differentiating both sides, just a matter of then rearranging for dy/dx

Then whatever they ask you to do with it and all

[cloud ridge]

SO

okayyyyyyyyyyyyyy

got it

thanks

[chilly parcel]

Would be quicker to use dy/dx = - partial x / partial y

But don't worry about that

[chilly parcel]

also need to rearrange the equation all onto one side first

[compact pewter]

@cloud ridge Has your question been resolved?

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[low pulsar]

!help

[compact pewter]

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

[low pulsar]

Not sure how i can start this

[olive field]

Qui penses-tu a raison

[low pulsar]

nothing for now

[low pulsar]

yanic i thin

[olive field]

I think so too yeah

Draw a diagram

[low pulsar]

what type of diagram

[olive field]

Draw a parallelogram

with two diagonals

[low pulsar]

oh ight

i did

[olive field]

and see if you notice anything that could show that the triangles are congruent

[low pulsar]

u want me to check if their congruent just by looking at the drawing?

[olive field]

well are there any congruent sides/angles you see that could help you show they're congruent?

[low pulsar]

oh ys

since theres 4 lines

and 2 lines share the same triangle

these lines have are isometric

same with this

[olive field]

Yes, but that's not inherently obvious

i.e that fact is kind of based on the fact that the diagonals form congruent triangles

I would look at the angles instead

[low pulsar]

these angles?

[olive field]

Yes

those are reflexive angles, and therefore congruent

What else

[low pulsar]

wait so the triangle on top is congruent with the one on the bottom

and the 2 on the sides r congruent aswel?

[olive field]

Yes

but remember you need two angles and a side to prove congruence

[low pulsar]

oh ight

okay so

[olive field]

It would be better to use the sides of the parallelogram

[low pulsar]

theyre isometric

cause in a parallelogram the diagonals intercept the middle or whatever

.close

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[hazy obsidian]

Find all pairs of real numbers (a,b) which satisfies the quadratic $x^2 + ax + b = 0$, and that if $\alpha$ is a root of this equation, then so must $\alpha^2 - 2$

[boreal girder]

Copter

[hazy obsidian]

i.. dont understand the problem😭

well i know that it always has 2 solutions so D > 0?

[solemn wasp]

you're effectively looking for all monic quadratics with roots $\alpha$ and $\alpha^2-2$ for a given $\alpha$

[foggy mortar]

alpha^2 - 2

[solemn wasp]

so true

[boreal girder]

Flip

[foggy mortar]

(Hint: Try applying the statement again but with the root alpha^2 - 2)

[hazy obsidian]

hm...

[solemn wasp]

it could be the case that alpha is complex, yet the resulting polynomial is still real

[hazy obsidian]

i have no idea what to do with this sigh

ohh

so like

(alpha^2 - 2)^2 - 2 = alpha since theres only two possible roots

[foggy mortar]

you'll need to do some casework here

one of the cases is what you just said

another case can be that alpha^2 - 2 = alpha

[hazy obsidian]

wait, why..?

[foggy mortar]

if this is the case then a second root beta must also satisy beta^2 - 2 = beta

[hazy obsidian]

wouldnt that mean there'd be one root? or am i dumb

[hazy obsidian]

ohh

goated??

.close

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[balmy hornet]

lcm(1,2,3,4)=12

(1+x^12 + x^24 + x^36 + ..) * (1+x^12 + x^24 + x^36 + ..) * (1+x^12 + x^24 + x^36 + ..)
multiply m times..

is this approach correct ?

[celest sierra]

sure

[kind viper]

yeah that is correct

you can write this more elegantly as (1 + x^12 + x^24 + ...)^m

and even more elegantly if you recognize it as a geometric series

[balmy hornet]

(1/(1- x^12))^m ?

[celest sierra]

yes

[kind viper]

yup

[balmy hornet]

alr thx Andd and kizzyy

Ann*

.close

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[pure coral]

hello

Hello, can I be in your wonderful group?

[balmy hornet]

.close

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[granite panther]

can someone please explain where I am going wrong?

[celest lintel]

Show full Q

[inner spoke]

n look like fours

[granite panther]

a lot of bs in the first section

cuz im just learning this

but i think i got part a and b right

[celest lintel]

Is this FP2?

[granite panther]

wdym

im preparing for fp2 yes

i got destroyed by fp1

[celest lintel]

Wait how have u done fp1

R u international

[granite panther]

edexcel

regional yes

[celest lintel]

My FP1 is in like 2 weeks

[granite panther]

did u do fp1 asw?

how ru undergraduate math then

fp1 is for high school students

[celest lintel]

Cos im going undergraduate maths

[granite panther]

oh

[celest lintel]

Like once a levels r done

[granite panther]

ru doing edexcel?

[celest lintel]

Manifesting it fr

Yh

[granite panther]

no this is not a levels

this is igcse

[celest lintel]

Oh bruh u do ts in igcse?

[granite panther]

further maths

[celest lintel]

Gotcha gov eme a sec and I’ll helpu

[granite panther]

thanks boss

[worn loom]

hmm <@&268886789983436800>

[steep veldt]

Ugh barely missed

[celest lintel]

Alright I’m back lemme have a look

R u gonna do fm at a level

@granite panther

[granite panther]

im not taking a levels

im taking ib

[celest lintel]

Gotcha

[granite panther]

but at this rate

idk im kind of screwed

im taking aa hl next year

[celest lintel]

For what

[granite panther]

ib

maths

[celest lintel]

A year early?

[granite panther]

cuz its way harder

im in y11 right now

my fp2 exam is on tuesday

https://www.physicsandmathstutor.com/past-papers/gcse-maths/edexcel-igcse-further-paper-1/

these are what the papers look like typically

[celest lintel]

Yeah for a year 11 that seems pretty difficult

[worn loom]

Damn it looks like an alevel maths paper but easier

yeah

[celest lintel]

Looks like AS level

First year a level maths

[worn loom]

Anyway, to the question at hand

[granite panther]

so tragic and we spedran through the entire syllabus in 5 months

[celest lintel]

Where did this second negative come from

Oh wait u didn’t divide forget me

[granite panther]

the way i do math is so scuffed i dont know how to properly do it

like efficiently so i just do the first thing i think of

/intuition

[worn loom]

I think I see the error

[celest lintel]

Why did u flip the inequality

[worn loom]

negative 15/4

[granite panther]

because i multiplied it by a negative number

[worn loom]

nvm

yep I see it

(622/625) - 1 = -3/625

you dropped a minus

[granite panther]

https://tenor.com/view/rage-gif-24341837

[granite panther]

thank you so much

[worn loom]

valid crashout

[worn loom]

no problem

[granite panther]

i bombed my first paper so bad i think i got 50-60%

[celest lintel]

What do u need

[granite panther]

nothing

ive done 25 papers

between my first and second paper

[celest lintel]

No like percent

[granite panther]

oh im just aiming for a 7

i think a 7 is like 65% or like 70%

[celest lintel]

Best of luck

[granite panther]

im also taking the regional paper so boundaries are higher

if you don't mind taking a look at another question

its a vectors area question but its not covered in my textbook

[worn loom]

is further pure a required subject for IB so just for your school in particular?

[celest lintel]

I need 90% in further maths to meet my firm offer

[worn loom]

What board is that?

[celest lintel]

Probably just an optional thing his school does

[celest lintel]

Edexcel

FM1 FP1 modules

[granite panther]

for higher level ib maths yes

[worn loom]

Ohhh, further pure

[granite panther]

not a prerequisite but highly recommended

[worn loom]

I did further mech and stats

[celest lintel]

Dude FP1 grade boundaries are just insane

[worn loom]

I see

[celest lintel]

What uni u go to now

[worn loom]

Southampton

[celest lintel]

Gotcha

[worn loom]

what's the firm

[celest lintel]

Warwick maths

[worn loom]

Ahh nice

[celest lintel]

I don’t think I’m gonna meet the offer cos I just flopped the first 2 papers

Forgot to bracket all my trig so lost a lot of marks on calculator errors

[granite panther]

i hate trig

especially trig identities

the greediest questions ever

[worn loom]

That's always pretty rough but maybe the grade boundaries will pull through

[celest lintel]

the papers have been pretty easy tho

Yesterday was fm1

[worn loom]

At least they did for aqa phys last year

[celest lintel]

Extremely easy paper

I have some extra circumstances so might get a few % of marks from edexcel which will probably help me pull through

Just got FP1 left

[worn loom]

Good luck dude

[celest lintel]

Thank you!! Warwick is such a great course and will be a huge bummer to miss couldn’t have asked for a better uni

[worn loom]

Huh weird, my year got pretty easy papers as well. Probably the easiest ones yet imo

[celest lintel]

Wait till u see our papers 😭

In fact for our year

Edexcel just redid the 2022 papers

Copied them almost exactly

[worn loom]

I'm gonna have a look actually. Probably did that for revision

[celest lintel]

Man I’ve got trauma from cp1 I sometimes wake up at night thinking abt the questions

And how stupid I was

[granite panther]

how mnay questions are you allowed to ask in this server

[celest lintel]

Unlimited

[worn loom]

In single channel, I think it's one but Idk if that's really enforced

[granite panther]

ok

.close

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[granite panther]

.close

[compact pewter]

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[austere meteor]

;

[forest token]

can u see that its a gp

[stone jackal]

This looks like a Geometric Series.

[austere meteor]

nvm i got it

i got it

[stone jackal]

!done

[austere meteor]

nvm

[compact pewter]

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

[austere meteor]

.close

[compact pewter]

Channel closed

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[austere meteor]

.reopen

[compact pewter]

✅

[austere meteor]

@stone jackal what is wavvy curve

@forest token

[stone jackal]

!original

[compact pewter]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[austere meteor]

no like explain what is it

[stone jackal]

Idk

Do you mean sinusoidal curve?

[austere meteor]

nope wavvy curve method

[forest token]

its used to find the solution set for inequalities

eg
(x-1)(x-2)/(x-3)<0

watch a video on it

[austere meteor]

ok

[civic quartz]

hes refering to the method of intervals

[austere meteor]

and also kindly provide the proof of crt

chinese remainder theorem

[civic quartz]

modular method?

[austere meteor]

yes

[civic quartz]

https://brilliant.org/wiki/chinese-remainder-theorem/

[austere meteor]

is it important for exams like ioqm in india

[celest sierra]

~~@stone jackal ~~

[stone jackal]

The racism never ended huh

[austere meteor]

why

[stone jackal]

I only lived in India until I was 8, so I don’t know.

[civic quartz]

no direct qeustion will be there

[austere meteor]

i am from india and just first time giving the exam so just asking

[civic quartz]

obv

[austere meteor]

ok thx

[civic quartz]

any concept is your tool

so more the merier

[stone jackal]

@celest sierra you should know this

[celest sierra]

😭 sorry

i just see india

[civic quartz]

cause of the name?

[celest sierra]

and associate it with you

[civic quartz]

lmfao

valid

[celest sierra]

wow

[austere meteor]

and what the sum of 1/3 + 1/2 + 5/6 + 8/6 + 13/6 + 21/6 etc

[civic quartz]

is that supposes to be an infinite series?

[austere meteor]

yep

[civic quartz]

any first thoughts?

[austere meteor]

fibonacci

[celest sierra]

yes

[austere meteor]

how to proceed further

?

[forest token]

how do u sum it to infinity 💀

[austere meteor]

have u not studied am gm etc?

[forest token]

...

[civic quartz]

dawg this isnt am gm

etc

[storm lichen]

do you know this result

[civic quartz]

i cant see it converging

[austere meteor]

um

[forest token]

exactly

[austere meteor]

yup i got it

[civic quartz]

!orignal

[austere meteor]

its fibonacci is there a certain formula that we can apply

[civic quartz]

!xy

[compact pewter]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[storm lichen]

$$\sum_{i = 0}^{\infty} ar^{i} = \frac{a}{1-r}$$

[boreal girder]

fluX

[storm lichen]

if |r| < 1

[civic quartz]

`flux i think he got that one, now he refering to a new question

[forest token]

🤔?

[civic quartz]

there are diff type of series
converging , and whatnot

do you know why flux mentioned if |r|<1

[austere meteor]

yup

[storm lichen]

taking 1/6 common, the series becomes (2 + 3 + 5 + 8 + 13 + 21 + ...)/6

[civic quartz]

can you explain it to me

[storm lichen]

which diverges

[austere meteor]

sum of gp and if its more than 1 diagram would not be possible imo

[civic quartz]

right yeah sure , but why ?
think of it intutively

[austere meteor]

hm

[civic quartz]

https://www.youtube.com/watch?v=zg9N2gAf6a4
try this

[austere meteor]

bet

[civic quartz]

11th?

[austere meteor]

8th

[civic quartz]

bet

just a tip, you can start by developing a intutive sense , like try quitioning everything presented to you

[austere meteor]

hm thx

[wind spindle]

u can probably use some generating function to find a formula for the nth partial sum of this, but it wouldn't converge if u sum to infinity

[austere meteor]

ok

@civic quartz

reply

anyone

now don

dont

i got it

[compact pewter]

@austere meteor Has your question been resolved?

[subtle shoal]

remember how you would solve for a repeating digit like x=3.333… its a similar technique here i think

[compact pewter]

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[queen basin]

Help

[queen basin]

What is the rule of law

[boreal dawn]

<@&268886789983436800> trolling

[brazen quiver]

Did you have an actual question @queen basin ?

[zealous rune]

I see your other messages are trolling in help channels

Take a day off.

.close

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[tropic agate]

Consider a linear system of differential equations $x'=Ax$, where $A$ is a $n\times n$ diagonalizable matrix. I know already that a solution $x$ is a solution to the system if and only if it is of the form $$x(t)=e^{\lambda_1 t}z_1+e^{\lambda_2 t}z_2+\cdots+e^{\lambda_k t}z_k$$where $\lambda_1,\lambda_2,\ldots,\lambda_k$ are the distinct eigenvalues of $A$ and $z_1,z_2,\ldots,z_k$ are eigenvectors in the corresponding eigenspaces. Now I'm asked to show that the solution space to $x'=Ax$ is $n$-dimensional using what I already know. How do I do this?

[boreal girder]

psie

[compact pewter]

@tropic agate Has your question been resolved?

[compact pewter]

@tropic agate Has your question been resolved?

[compact pewter]

@tropic agate Has your question been resolved?

[jagged blade]

If we have n eigenvalues and n eigenvectors, then we have n terms in the solution

Right?

In order for that to be considered n-dimensional, each term would need to be linearly independent of the others

[tropic agate]

well, the eigenvalues could be non-distinct, right?

[jagged blade]

Sure, but I think that's fine

I think showing linear independence is sufficient

[tropic agate]

Ok, I'm thinking, suppose there are k distinct eigenvalues, We know the exponentials are linearly independent (there will be k of them), and there will be n linearly independent eigenvectors as well (as A is diagonalizable). Now, if we set x = 0 in the above equation I posted several hours ago ( ), then we obtain a system of n equations in n unknowns. If we group together the terms with the common exponentials, their linear independence immediately reduces the system of equations to p separate system of homogenous equations in just the components of the eigenvectors. This is where I'm getting stuck ...

[tropic agate]

.close

[compact pewter]

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[stone jackal]

Officially, the course is not an AP course, but it is worth 2 credits (as opposed to most non-math classes being worth 1).

[stone jackal]

I am also studying it in 11th grade, so would Accelerated be an acceptable level to input?

[spark folio]

You should match the syllabus of the courses, like is your course teaching the same concepts as the course recognised as one of these

pretty much everything we needed to know for the AP Calculus BC exam
I would say AP Calculus BC is what you choose

[stone jackal]

I don't understand. My school is unique in that we study Calculus BC only in the first semester, then move on to Mulivariable Calculus.

[spark folio]

and mention equivalent to AP Calculus BC if you have an option to say that

[stone jackal]

Most other high schools (in my area) offer just AP Calculus BC.

[stone jackal]

Sadly, I don't.

[spark folio]

Oh

then its tough to say

[compact pewter]

@stone jackal Has your question been resolved?

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@stone jackal Has your question been resolved?

[celest sierra]

It's certainly between advanced/accelerated, no?

[compact pewter]

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[kindred shell]

Heya everybody please help with this problem
///
How Far Can You See? The conning tower of the U.S.S.
Silversides, a World War II submarine now permanently
stationed in Muskegon, Michigan, is approximately 20 feet
above sea level. How far can you see from the conning tower?

[kindred shell]

I have no idea to solve this problem

[compact pewter]

@kindred shell Has your question been resolved?

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[kindred shell]

https://www.reddit.com/r/askmath/s/XA9jlmIMzS

[kindred shell]

Heya everybody please help with this problem
///
How Far Can You See? The conning tower of the U.S.S.
Silversides, a World War II submarine now permanently
stationed in Muskegon, Michigan, is approximately 20 feet
above sea level. How far can you see from the conning tower?

In reddit one guy sent me a picture to help me

...

[unkempt sail]

What's the problem

What have you tried

[kindred shell]

I tried to get some help

It is not your business to know what I have tried

If you do not want to help just ignore it шалава

[unkempt sail]

If that's the case then nobody here will help you

There's a reason it's called a help channel and not a solution channel

[kindred shell]

If I know how to calculate it I won't ask for help

[unkempt sail]

Sigh

!status

[compact pewter]

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

[kind viper]

ok what the fuck was that about

you do NOT get to throw that kind of word around

[kindred shell]

1step х

[kind viper]

why the fuck did you call him the russian equivalent of "whore" but worse

[unkempt sail]

There's some basic facts you would want to know before like radius of earth and the assumption that it's a sphere

[unkempt sail]

Is that what he did

[kind viper]

yeah this is an extremely rude and offensive word in russian

[kindred shell]

@kind viper because he/she started throwing wise words where I just need guide to do some calculations

[unkempt sail]

Bruh

[kind viper]

<@&268886789983436800>

[foggy mortar]

jesus

[unkempt sail]

What wise words? I politely asked for what you have tried
Is that offensive in your dictionary?

[kindred shell]

Yes it is offensive

[unkempt sail]

Interesting

[kind viper]

if you find being asked about progress offensive,

then this server isn't for you.

[spark cedar]

yeah

bye bye

.close

[compact pewter]

Channel closed

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[kind viper]

was that a bye bye or was it a stfu

[spark cedar]

it was a stfu but I may upgrade it to a bye bye on the fence rn

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[velvet lagoon]

Okay I plug for 0 but nto getting the exact result

[velvet lagoon]

2^0=1?

0,2

1,1.6

What would the in() be?

[patent wolf]

well what’s the out()

[thorny urchin]

for the ln curves, you don't really need the exact values
you could consider stuff like
increasing/decreasing
signs
and/or asymptotes to deduce it

consider the value at x=1
2.5 - x and x+0.5 are both 1.5
is ln(1.5) positive or negative?

[compact pewter]

@velvet lagoon Has your question been resolved?

[velvet lagoon]

Okay so instead 0 it would be 1

[thorny urchin]

wdym

[celest sierra]

<@&268886789983436800>

[compact pewter]

@velvet lagoon Has your question been resolved?

[velvet lagoon]

.close

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[halcyon flame]

I have to prove that ${ 2a+\sqrt{2}b : a,b \in \mathbb{Z}}$ is an ideal in $\mathbb{Z}[\sqrt{2}]$

[boreal girder]

Lambda

[halcyon flame]

But isn't $\mathbb{Z}[\sqrt{2}]$ of this form anyways?

[boreal girder]

Lambda

[halcyon flame]

I mean that $\mathbb{Z}[\sqrt{2}]={ 2a+\sqrt{2}b : a,b \in \mathbb{Z}}$

[boreal girder]

Lambda

[young kestrel]

that's not all of Z[sqrt2] no

3 is in Z[sqrt2] for example

it's not in the set you got there

[halcyon flame]

you're right, thanks

but that's it, it's only odd integers?

[young kestrel]

that's the only things out yes

integer part has to be even, sqrt2 part can be any integer

[halcyon flame]

alright thank you!

.close

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[velvet lagoon]

How do I solve this type of problem?

[lost jackal]

By knowing the identities of logarithms

These are some of them

You can search for the proof of each Identity up the internet if you wanted

This is a better image

@velvet lagoon anything else?

[velvet lagoon]

No I think thats it

thx man

[lost jackal]

Np

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[cerulean tartan]

Solve this

[forest token]

u want us to solve it for u?

[cerulean tartan]

Yes

[forest token]

we dont do that

[cerulean tartan]

Then why is this channel called "help"

[forest token]

#❓how-to-get-help

read.

[cerulean tartan]

I mean if I posted my solution (which is obviously wrong) you folks won't understand my handwriting

And I have tried mathematics and failed at finding the solution. That seems like enough detail for a question

[compact pewter]

@cerulean tartan Has your question been resolved?

Channel closed

Closed by @cerulean tartan

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[cerulean tartan]

What

No

It isn't resolved

.reopen

[compact pewter]

✅

[civic quartz]

!status

[compact pewter]

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

[cerulean tartan]

3 i guess

[civic quartz]

solution is available online, or not , but this is a help server not a solution serrver, we are here to help you get to the answer

!nosols

[compact pewter]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[civic quartz]

share your attempt

if not your thought

[cerulean tartan]

How high are you

[civic quartz]

morally? i say pretty high

also thats a bot

[rigid sedge]

If u want a straight answer just google it bro

[cerulean tartan]

You wouldn't really understand anything as it is written all over the place

[storm lichen]

rewrite it neatly then

[rigid sedge]

But thx for posting this looks like a cool problem I’m finna save it 🙂

[cerulean tartan]

I did and the answer was like hell

[rigid sedge]

Did it give u an answer

[civic quartz]

^

[cerulean tartan]

The website tried to derive the answer multiple time and somehow they magically appeared the right answer

[civic quartz]

oh sorry , mistakenly i think i forgot to turn the ping off

[cerulean tartan]

Yes

[rigid sedge]

Ok so you wanna know how to solve it then

[civic quartz]

is it doubt nut lmfao

[rigid sedge]

So what’s the problem

[cerulean tartan]

Yeah lol

[civic quartz]

lowkey trash , try sharing your problem tho , we will try to see what you did , if not you can share your steps or as flux said rewrite the solution

[civic quartz]

^

[soft bobcat]

I just stopped trusting websites so long ago lol i try to do it myself if i cant then i ask others if they cant i ditch it and put it into my massive sheaf of unsolved ones

Better than searching online every single time atleast u remember when u messed up

[cerulean tartan]

I am preparing for a engineering entrance exam but my writing is more akin to a doctor

[civic quartz]

we get it bro

^

[cerulean tartan]

Lol

[rigid sedge]

No I mean what’s the issue

[rigid sedge]

I would kill for that handwriting

[soft bobcat]

Venn diagram = ez clutch

[cerulean tartan]

The issue is i am not getting the right answer

[rigid sedge]

Let’s see what u did

[civic quartz]

share us your thought process bro , so we can see what went wrong 😭

[cerulean tartan]

God bless whoever invented venn diagrams

[soft bobcat]

Just start rewriting your work already lol stop chatting were just delaying till you finish

Doesnt work if u delay as well

[cerulean tartan]

As I have previously explained,I didn't write my answer neatly. It's all over the place

[civic quartz]

redo it bro

[soft bobcat]

The essential anime girl to aid you in answering that question

[civic quartz]

yuh

with a deep voice

[rigid sedge]

Just word it out and some typeset genius can put it into typeset

[civic quartz]

im sorry

[soft bobcat]

[storm lichen]

it was venn

[civic quartz]

framing him up

[cerulean tartan]

All my life was a lie

[soft bobcat]

Bro

[civic quartz]

dawg question

[soft bobcat]

Stop chatting

[forest token]

no its - hi how are you

[civic quartz]

just type your thought process from start

what was your first step

[cerulean tartan]

Ahh man leave it, arguing with you guys is the same as arguing with chatgpt

I can never win

[cerulean tartan]

I put a formula

I think it is called the inclusion exclusion formula

[civic quartz]

try drawing the venn diagram first

slowly read through the question and start forming it

if there is a tad bit difficulty in formulating the diagram , try doing ncert first

[cerulean tartan]

Tried it but the venn diagram doesn't work on this question

[soft bobcat]

Who is even arguing

[soft bobcat]

Based

Venn diagram not working on a question with the names of subjects in it

Is highly improbable

[cerulean tartan]

Lol you are indian too

[soft bobcat]

Yes me too

We are the world

[cerulean tartan]

It also could be that I am dumb

[civic quartz]

na dont say that

[cerulean tartan]

Wait we are surrounded...

By friends

[civic quartz]

we all had our fair share of problems when introduced with something new

[soft bobcat]

See some examples then

Youll become smart

[cerulean tartan]

This question came in jee advanced

[civic quartz]

yeah i know

i had a familarity to this type

[cerulean tartan]

To slove kar do na please 🥺

[civic quartz]

dawg we here to help in developing your mindset

simply seeing the solution

wont help you in the prep

[cerulean tartan]

Bro I am preparing for JEE,you think anybody preparing for jee has time to devolp mathematical intuition?

[soft bobcat]

Yes

[civic quartz]

bro has 2 years

[soft bobcat]

Chhapega toh katega tera

[cerulean tartan]

Yeah but I also have physics and chemistry (unfortunately)

[cerulean tartan]

Lol

[civic quartz]

24 months

[soft bobcat]

So did we

[cerulean tartan]

Vese koi ISI ki tyaari kar raha hai kya

[soft bobcat]

Mains and ISI polar opposites

Ek choose kar

Jack of all trades master of none ho jayega yato

[cerulean tartan]

I want to go to ISI but papa IIT se hai toh smjh jao...

[soft bobcat]

I just met one similar case today afternoon

Like literally today afternoon

Itne log hai kya ese

[cerulean tartan]

Yeah their are many people in india whose mathematics dreams were cut by boards, physics and chemistry lol

[soft bobcat]

bhai maths mein physics toh zaruri hai

Chem theeke samajh sakta hoon

And boards is closer to research than mains

[cerulean tartan]

Bro ab nahi smjh me aata physics to kya karu

[soft bobcat]

Anyway ye baat karne keliye nahi hai channel lol,
.close karke examples padh venn ke

[cerulean tartan]

Okay

.close

[compact pewter]

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Remember:
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[fallen frost]

I'm taking some notes regarding modular arithmetic. Based on the definition shown, do those examples look correct?

[copper sierra]

the grammar is very off

for instance 3mod7 is not a statement so it doesnt make sense to say ‘if 3mod7 then ..’

and the forall part of ex 22 doesnt make sense

[fallen frost]

For your first point, what about "If (3 mod 7) is a congruence class, then ..." ?

What is it about the forall that's confusing?

[copper sierra]

if i say $\forall x\in S$ then $S$ must be a clearly defined set

[boreal girder]

ロケットジャンプ

[copper sierra]

in 22 ur set is very unclearly defined

[lime juniper]

"and may be denoted (a mod m)" the syntax should be
and may be denoted "a (mod n)"

[fallen frost]

hmm, I got that notation from here: https://en.wikipedia.org/wiki/Modular_arithmetic#Congruence_classes

[lime juniper]

ah, it does say it there

[fallen frost]

Is the set in .23 clear to you?

[lime juniper]

I've never seen it before, but you copied wikipedia correctly\

[copper sierra]

yes

how i interpret 22 and the best way to write it is

[fallen frost]

The set in .22 and .23 are kind of same thing, so I'm not understanding. .23 is {3, 10, 17, 703}

[copper sierra]

if $x=3\pmod7$ then $x\in[3]$

[boreal girder]

ロケットジャンプ

[copper sierra]

then follow with a separate statement

$x\in[3],\forall x\in\cbr{3,10,17,703}$

[boreal girder]

ロケットジャンプ

[fallen frost]

But that's what I have.

[lime juniper]

better to use triple equals for this

[copper sierra]

yes but mobile typing hurts so meh

[copper sierra]

yes its what u mean to say but how u did it butchers grammar

[fallen frost]

You mean because the ints have equalities on them?

[lime juniper]

I would add, that you can add as a subscript the modulus to the brackets if you want to

and the double brackets is prettier than single brackets but means the same thing

[fallen frost]

Oh, I like that modulus subscript.

the double brackets, too.

I wasn't too crazy about using [a], because I do vector stuff as [1,2,3], and didn't like that notation reuse.

So, thanks for the double bracket suggestion.

[copper sierra]

yes. u should write the set like in 23

[copper sierra]

23 should be just what i boxed

[fallen frost]

oh, I see. You mean that you don't like the way it looks, not that it's mathematically incorrect.

[lime juniper]

sure. and (a mod b) = (c mod b) I've never seen, despite it being on wikipedia, so I wouldnt use it

it strikes me as obscure

usually:

a mod b <- this is a NUMBER, where a convention is chosen to give a unique remainder

[copper sierra]

its incorrect due to the incorrect grammar, but i did my best to understand the content. but not everyone is guaranteed to understand

[lime juniper]

a ≡ b (mod c) is a statement about an equivalence relation

and [[a]] = [[b]] is an equality of sets

[fallen frost]

I don't agree that it's incorrect grammar. Unusual, yes.

Since these notes are for myself, I wrote it like that so break it down for myself how those numbers mean a group.

[lime juniper]

if a and b are positive integers then: a mod b means, the unique remainder given by the division theorem n=pd+r , 0 le r < d
if the numbers are negative some convention is chosen

"if (3 mod 7) " doesnt make sense because (3 mod 7) isn't a statement that's true or false

[fallen frost]

(3 mod 7) is defined defined, though

one sec,

I'll look it up

[lime juniper]

the whole senstence ios a mess for 22

[sturdy forge]

1 is a defined value. It doesn't make the sentence "if 1, then x+y=5" sensible

[fallen frost]

oh, this is what I was going to look up:

I though they were meaning the first part. b mod m

What about said like this: "If 3 (mod 7) is a congruence class, then ..." ?

[sturdy forge]

uhhh

is that necessary? it seems to be pretty clear what [3] means in your notation

[fallen frost]

Basically, I'm trying to write down an example and a non-example. I understand that I'm fumbling the language, but that's basically what I'm asking about.

Is the way that I'm saying that correct. If not, what would be a good way to state that.

Basically, there is some "congruence class" blahblahbha, and this is an example of the set: ...

This is jist of this post

Alright, I'm going with this and calling it a day:

Thanks

.close

[compact pewter]

Channel closed

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[compact pewter]

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Send your question here to claim the channel.

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

[dawn palm]

hello

[dawn palm]

can someone help me to decompose this function

like for example cos(2x) => x->2x->cosx the same

[acoustic yarrow]

factor out 3 and see what u get

[lime juniper]

so i thought i knew what you were asking

but idk what that line means

[acoustic yarrow]

cos(x) = g(x)
2x = f(x)
g(f(x)) = cos(2x)

they mean compositions

[dawn palm]

decompose a compound function

[lime juniper]

if you mean partial fraction decomposition

that doesn't have to do with trig

do you have an example of a problem worked through that you can show us

[keen granite]

ohh finding functions that when composed, form the function f?

[lime juniper]

oh is that what you mean?

[acoustic yarrow]

thats what i would think

[dawn palm]

no

[acoustic yarrow]

lol

[lime juniper]

[keen granite]

😔

[lime juniper]

please show an example of a solved problem

that is similar to this one

[keen granite]

can you provide a more thorough example to demonstrate what you mean?

[dawn palm]

i need to decompose all the function to find the domain of the function

ok wait

this is an example

[lime juniper]

ah I see

you're expected to find the domain and image of the function based on the building blocks of the function and repeated compositions

[dawn palm]

yes

[lime juniper]

well first of all I would write -3x+3=(x+3)-4x, do you see why?

[dawn palm]

yes i see but why we need to do this

[lime juniper]

I dunno, I just think it will be easier. you dont have to

[dawn palm]

oh ok

[lime juniper]

okay let's keep it the way it is then

domain and image of -3x+3 is ?

[dawn palm]

R and R

[lime juniper]

great

... do you NEED to solve it the way you solved the other one? iterated composition?

[dawn palm]

idk but i want do to like the other one

[lime juniper]

did you learn about functions of two variables yet

it will be easier with that

[dawn palm]

wdym by two variables

[lime juniper]

$$f(x,y) = 2x+y$$

[boreal girder]

gfauxpas

[dawn palm]

no i didnt

[lime juniper]

well, it works exactly the same as regular functions, except, for the domain, you have two domains multiplied by easy other

so the domain for this would be $\mathbb R \times \mathbb R$, which means x is in R, and y is in R

[boreal girder]

gfauxpas

[lime juniper]

make sense?

[dawn palm]

y means the image ? or still the domain

[lime juniper]

it's a double domain

[dawn palm]

Ok

[lime juniper]

this question will be easier for it

$$f(x) = \dfrac{-3x+3}{(x+3)^3}$$
$$y=-3x+3$$
$$f(x,y)=\dfrac{y}{(x+3)^3}$$

[boreal girder]

gfauxpas

[lime juniper]

follow?

[dawn palm]

wait 2 sec

[lime juniper]

[dawn palm]

why did you put y=-3x+3

[lime juniper]

because it gives me more freedom to do compositions, i can do compositions in x or compositions in y

[dawn palm]

ok

[lime juniper]

so we have: dom(y) = R, image(y)=R

[dawn palm]

yes

[lime juniper]

the domain of f is RxR that's the notation

except

not all x are allowed

[dawn palm]

yes

[lime juniper]

so you want to make this a composition? it would be something like

y/x^3 o (x+3, -3x+3)

this means you're composing the x part with the first part and the y part with the second part

does that make sense or am i making it too complicated

[dawn palm]

i can do this with arrow like that ? or no

[lime juniper]

yes you can

it would be

$(x,y) \to (x+3,-3x+3)$

[boreal girder]

gfauxpas

[lime juniper]

you "replace" x with x+3, and "replace" y with -3x+3

I can try a different way if this is too confusing

[dawn palm]

no its ok

not exactly like my method but its fine

[lime juniper]

$\frac {y}{x^3}$

[boreal girder]

gfauxpas

[lime juniper]

y has domain: R, image: R

x has domain: ... , image: .... ?

[dawn palm]

R/0

[lime juniper]

great. same domain and image

now compose

$\frac y {x^3} \circ (-3x+3, x+3)$

[boreal girder]

gfauxpas

[lime juniper]

or in yournotation

$x \to -3x+3; y \to x+3$

[boreal girder]

gfauxpas

[lime juniper]

so before we had x goes from R to R

now -3x+3 is still x from R to R

before we had $x \ne 0$, now we have $x + 3 \ne 0$

[boreal girder]

gfauxpas

[dawn palm]

so x=/=-3

[lime juniper]

yes. and y disappears, which makes sense, because the original problem didn't have y anyway

do y ou need to find the image of the whole function as well? or just the domain

[dawn palm]

yeah image also

[lime juniper]

$\frac y {x^3}$

[boreal girder]

gfauxpas

[lime juniper]

so we have y can be any number, and x can be any non-zero number

[dawn palm]

yeah

[lime juniper]

any limitations you can see here?

you have numerator/denominator

which real numbers can be written as (something)/(something)

[dawn palm]

i dont understand ur question

[lime juniper]

I'm looking for what numbers can come out of this expression y/x^3 and I notice the function is of the form (some number)/(some number other than 0)

I'm asking you, what limitations does that give us? what numbers can or cannot be written as (some number)/(some nonzero number)

[dawn palm]

i need to find a number other than 0 ?

[lime juniper]

0 can be written as a fraction, 0 = 0/1

pi can be written as 2pi/2

-sqrt(2) can be written as -2/(sqrt 2)

[dawn palm]

sqrt(-1)

[lime juniper]

not a real number

to find the image, you have to find what real numbers can be expressed as numerator/denominator

i assume youre only looking for real numbers

[dawn palm]

y =/=0

[lime juniper]

nope, that works too

0 = 0 /1

let y=0, x = 1

[dawn palm]

there is no limitations then

[lime juniper]

correct

the image is, all real numbers. (or all complex numbers if youre supposed to use complex numbers)

[dawn palm]

i know from the start there is no but i though there were one with that question

[lime juniper]

so domain: all numbers except x=-3; image: all numbers

is the answer!

[dawn palm]

Ok

[lime juniper]

🎉

gonna playh skyrim now

gl

[dawn palm]

xd

ty

[lime juniper]

anyway, jsut to recap

whenyou have a function with 2 inputs

the domain is connected using a multiplication symbol

$\mathbb R \times [0,1)$

[boreal girder]

gfauxpas

[lime juniper]

like that

and if both the sets are the SAME set, you can abbreviate it with a superscript 2

$\mathbb R \times \mathbb R = \mathbb R^2$

[boreal girder]

gfauxpas

[lime juniper]

make sense?

[dawn palm]

yeah

[lime juniper]

!close

.close

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[near swan]

Hello! I want to prove via induction

[near swan]

I thought base case was n=1, cuz it holds

but I see n-2, so my brain is like oh base case should be n=2 since we can't have deg less than 0

Can someone confirm my thoughts?

[old mica]

I agree with you

[near swan]

n=2 will be done then

thank u

[old mica]

[compact pewter]

@near swan Has your question been resolved?

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[molten coral]

Got a question.

[boreal girder]

jan Niku

[molten coral]

So the coefficient functions have singularities at x=0

but we can find two LI solutions that are not singular there

[boreal girder]

jan Niku

[molten coral]

I'm curious how we go about finding such a system

because the one that they mention, y'=y+xz and z'=0 seems to come a bit out of nowhere

[chilly parcel]

are you trying to solve it

[molten coral]

no I already know the solution

I'm curious how we find systems that lack the singularities of the original diff eq

and if they are unique, I guess

[sage oxide]

y1=e^x and y2=-(x+1) then y=c1y1 + c2y2 form

[molten coral]

yea, i know the solution, thats not what im curious about

[compact pewter]

@molten coral Has your question been resolved?

[compact pewter]

@molten coral Has your question been resolved?

[lime juniper]

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

the usual uniqueness theorem fails , so you turn to this one

if it applies, which I think it does here

then if you're lucky, the solution you find analytically continues through the problem point

[molten coral]

ill have to look at it

thanks!

[lime juniper]

but it's exactly what youre looking for

np

[molten coral]

[compact pewter]

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[lime juniper]

.reopen

[compact pewter]

✅

[lime juniper]

@molten coral hey

So according to AI, you get solutions that are different for the Frobenius method!
I haent checked the math by hand, but, its interesting

your solution set was

$\operatorname{span}{e^x, x+1}$ and this is valid on $(0,+\infty)$ or on $(-\infty,0)$

[boreal girder]

gfauxpas

[lime juniper]

but the Frobenius solution gives

[molten coral]

sory im in bed

[lime juniper]

so look at it tomorrow

[molten coral]

[molten coral]

i will

i gotta track out frobenius here

[lime juniper]

$\operatorname{span}\left{ { x+1, \frac{I_2(2\sqrt{x})}{x} }\right}$

[boreal girder]

gfauxpas

[lime juniper]

is the family of Frobenius solutions, where:

$$I_2(x) = \sum_{k=0}^\infty \frac{1}{k!(k+2)!} \left({\frac x 2}\right)^{2k +2}$$

[boreal girder]

gfauxpas

[lime juniper]

this is a modified Bessel fucntion of the first kind.

These solutions are LOCALLY analytic around x=0

So you have a choice:
analytic on (0,infty) or (-infty,0) <- the solutions you found

the Frobenius solution family is analytic locally at 0

!close

.close

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[trail crater]

Can someone pls provide me with some guidance on this question thanks

[kind viper]

Assure tre fur n=4

[trail crater]

thats a k

mb

(bad handwriitng)

assume true for n = k

[kind viper]

it's extraordinarily bad handwriting lol you should really rewrite the entire thing in better handwriting later on

[trail crater]

yeah bet

[kind viper]

actually no yknow what rewrite it now cause i for sure dont wanna have to decipher every single line

[trail crater]

ok one sec

[trail crater]

Better?

[kind viper]

yes but could use some improvement still cause your k ends up looking like h a lot

anyway ok time to read