help-13

[wary elbow]

I didn't mean to istg 😭

[winter falcon]

i want to know why f(alpha) = f(beta) = -9

[wary elbow]

question 27?

alright

[winter falcon]

yes

i got f(x) = -9

[wary elbow]

gimme a minute

[wary elbow]

so you found out that for any value of x, f(x) remains to be -9

so whether you substitute alpha or beta instead of x

[winter falcon]

OHH

yeaaa

[wary elbow]

you'd still get -9

[winter falcon]

i did not think of that

[wary elbow]

there we go

happens to the best of us

dw

[winter falcon]

thank youu ❤️

[wary elbow]

are you good with Q26?

you mentioned you needed help with that too

[winter falcon]

i think i can do it now that i understood the concept

[wary elbow]

you can try the quadratic formula approach I mentioned eariler and see if it works for you

glad I could help 😄

[winter falcon]

the prev one is none of these right

[wary elbow]

yes

[winter falcon]

thank you

[wary elbow]

Welcome

[winter falcon]

.close

[cedar kiln]

Channel closed

Closed by @winter falcon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[cedar kiln]

@winter falcon Has your question been resolved?

[lofty sand]

Ok thinking out loud

Exp(f(0)) = 1

[winter falcon]

huh

[lofty sand]

I’m sorry, is f defined on the point 10 ?

Because It doesn’t see like It Is

[winter falcon]

No

[lofty sand]

On the right use x = 5, what do you get

@winter falcon

[cedar kiln]

@winter falcon Has your question been resolved?

[green coral]

!nosols , but yeah the push is cool

[cedar kiln]

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.

[lofty sand]

Sorry I didn’t want to leave It answerless

[green coral]

thats fine i get it

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[rich moss]

suppose vectors u and v are linearly independent. if {u,v,w} is dependent, then w must be a combination of u and v. However, I don't get why this must be the case. Why can't u be a combination of v and w? imagine u to be v+w, this does not contradict u and v being independent

[lofty sand]

Both work

If u = v+w then w = u -v

Both statements work

[rich moss]

oh yes, you are correct. I misread the explanation on our textbook

.close

[cedar kiln]

Channel closed

Closed by @rich moss

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[noble dock]

For question 3 part a, in a bit unsure how to even prove such statements. I think this is a proof by construction but I’m not sure if induction works

[noble dock]

My main idea is to first show that every generated sigma algebra from a finite collection of sets is finite

Hence we can always find more from M

[crimson sedge]

yes, construction and iterate

if M -> inf. then M has infinitely many distinct sets in it
if all sets differ finitely, the algebra will be finite -> false (contradicts)

then comes construction

A e M, M is inf -> we split A in two disjoint noempty sets A1, A2 e M

iterate: keep on splitting A1

we get infinite B's

a -> true

[cedar kiln]

@noble dock Has your question been resolved?

[crimson sedge]

because a has been proven we can prove b
we have inf. sequence of disjoint sets as seen in a {Cn} for example
M is sig.-algebra, all the countable unions of {Cn} are in M ( U_neA Cn, A C_ N) hope this is understandable lol
the number of subsets of N is 2^a0 =c ->
-> M has contin. many distinct elements
b-> true

[noble dock]

Yeah so ig I’m a bit confused on the construction part. Like why does the “iteration” method work?

Because don’t we need to create an inf sequence? But like depending on how the sequence is indexed, if the indexing set is the reals then this wouldn’t work right?

Or idk

[noble dock]

I understand up to the subset of N part

[crimson sedge]

you only need to show that there exists a countably infinite family of disjoint sets inside M

[noble dock]

Yes, but ig am confused as to why constructing recursively works here. Is it because we define a set inside of M that is disjoint from all the others for all n in N, hence countable since we can form bijection between N and the constructed collection of sets

[crimson sedge]

the infinite sequence is indexed by N

[crimson sedge]

let me find some symbols so that i don't improvise

p.s. yes

Bi ∩ Bj = {} (empty seT) wherever i =/= j
that's a countably infinite sequence of disjoint sets indexed by N

what are you showing?
∃{Bn}^inf. where n=1 ⊆ M

so we start with any set

[noble dock]

So B_n is fixed?

[crimson sedge]

A e M, A e/ {{}, X}

[noble dock]

Yes

[noble dock]

Yes

[crimson sedge]

M is sig-algebra A^c eM and A,A^c are disjoint

[noble dock]

Yes

[crimson sedge]

because M is infinite at least one of these must contain more structure

in other words

you can split it

[noble dock]

Yes, yeah ig I understand that part

But more so just why a recursive approach/formal reasoning as to why a recursive approach works

[crimson sedge]

so you can define: B1 = nonempty measurable subset

[noble dock]

Like it seems kinda like “just let it go on”

[crimson sedge]

B2 = A \ B1

[noble dock]

Yes

And then we repeat that

[crimson sedge]

yes

[noble dock]

But then that requires us to define the previous sets before it right

Before we can define the later sets

[crimson sedge]

it's recursion:
so you've constructed B1,B2 ... Bn pariwise disjoint
M is inf. the sig alegebra generated by {B1....Bn} is finite at max 2^n sets

so because M is infinite there must be/exist a set C e M not in that finite subalgebra

good until now?

[noble dock]

Yes

And so then we can do this for all n in N

[crimson sedge]

the recurse never stops because of this

[noble dock]

Is what we are showing

Ok

[crimson sedge]

because M is infinite and {B1...Bn} is finite

so there is always new set outside this

[noble dock]

Yeah ig this part is what’s kinda tripping me up. Cuz it seems like “magic”.

I was looking for more of a way to prove that this works, kinda like why induction works due to well ordering principle

[noble dock]

Yes

[crimson sedge]

well induction works because the subalgebra generated by the split is finite

and M is infinite

so there is always new, just like magic lol

[noble dock]

Oh wait we are showing all this by induction?

[crimson sedge]

you basically define new disjoint sets

[noble dock]

Yes

[crimson sedge]

Iteration*

sorry

[noble dock]

Oh okay yeah, ig is there formal proof as to why iteration works/where I can look for this?

But maybe that’s for another time

But continuing to part B

We show that card(M) = card(P(N))?

[crimson sedge]

https://en.wikipedia.org/wiki/Measure_(mathematics)

[crimson sedge]

.

[crimson sedge]

we shown that a is true, we have an infinite sequence of disjoint sets right ? we called them {Bn} now

so we consider all unions of subsets of {Bn}

Union of Bn n e A , A C _ N

because M is sig. algebra all these countable unions are in M

[noble dock]

Yes.

[noble dock]

Or wait how are these subsets part of M?

[noble dock]

Ohh wait I’m sorry these B_n are all in M

[crimson sedge]

the number of subsets of N is 2^a0 = c
ok i don't have aleph wait:
so N is the set of natural numbers
a0 aleph0 is the cardinality of N (the smallest inf.) countable infinity
2^a0 = the cardinality of the power set of N

in other words the set of all subsets of N

c is the continuum

[noble dock]

What is a0 here?

Yes

[crimson sedge]

c is the cardinality of the real numbers R

[crimson sedge]

aleph 0

the cardinality of the power set of N

the smallest infinity

it's like saying |P(N)| = |R|

[noble dock]

I thought smallest infinity was countable N?

[noble dock]

Ah ok

[crimson sedge]

yes that's a0

[noble dock]

Oh ok

[crimson sedge]

|P(N)| = 2^a0

does this make more sense?

{0,1)}^N

[noble dock]

So essentially what we have is since the collection of B_n all in M, and M is a sigma algebra

[noble dock]

Yeah I’m still a bit confused on the subsets part

Like is it subset of the collection?

[crimson sedge]

so you either include or exclude natural numbers

0,1

cardinally it's 2^a0

2 choices

any subset of N can be included or excluded n (natural number)

so : (b0,b1,b2,....) bi e {0,1} for excluded included

2 choices

cardinally 2^a0

or aleph0

its 2 choices for each of countably infinitely many positions

so why is this c?

real numbers in [0,1] can be written binary:
b0,b1,b2 with bi e {0,1}

|P(N)| = |{0,1}^N| = |[0,1}| = |R| = c

aleph0 is countable infinity just like N

it's smallest

2^aleph0 is much bigger infinity in other words uncountable

and it's the same size as c

in english: the whole/collection of all subsets of the naural itself is uncountable

[noble dock]

Ah ok

[noble dock]

Yes that makes sense

[noble dock]

Yeah ig I’m more confused as to we show that there is infinite sequence of disjoint sets in M. But then where is the subset of N coming from?

Lie are the subsets actually a collectioj of sets

[crimson sedge]

we are kinda coding subsets of N by unions of the disjoint family

we want to show that |M| has at least continuum (c) many distinct elements

se we have a sequence of disjoint sets {Bn}n e N

for every A C _ N from the union of those Bn whose indices are in A
Fa:= union n eA Bn

each Fa e M because sig. alegras are closed under countable unions

different subsets give different unions because Bn are dijoint

index matters

P(N) -> M

which -> |M| > _ |P(N)|

[crimson sedge]

so in english: the subsets of N aren't already inside M, it's indexing set N for the dijoint family: B1, B2 and so on

any subset of N will tell us which Bn to include in a union

that's how N gets inside M

since |P(N)| = 2^aleph0 (which is uncountable and strictly bigger than aleph0) and is the same size as c

-> |M| > _ c

your original question:
a) gives us disjoined sets Bn
b) uses those to code every subset of N as a union

[noble dock]

ah so essentialy here we are mapping the subsets to the unions?

[crimson sedge]

yes

injective map

[noble dock]

and there is a bijection here, hence they have the same cardinality?

[noble dock]

or wait oh ok

[crimson sedge]

injective

[noble dock]

ah so this implies the cardinality of the collection of subsets is greater than the cardinality of the collection of unions

but then the cardinlaity of the collection of unions is ..., im trying to connect this part

[crimson sedge]

the opposite direction, every subset of N corresponds to a unique union of the Bn so the set of unions has AT LEAST as many elements as P(N)

it shoows that M must contain AT LEAST c many sets

it doesn't show equal

M can be larger

but it guarantees that |M| > _ c

so bigger or equal than c

[noble dock]

I thought we show that $f: \mathcal{P}(\mathbb{N}) \to A$ where $A$ is the set of unions of $B_n$ is injective?

[crimson sedge]

function is injective

[wraith dagger]

LXDL

[noble dock]

yes

[crimson sedge]

P(N) -> M

f: P(N) -> M

f(A) = FA

FA := union n e A Bn

[noble dock]

so then M has cardinality greater than P(N)

[crimson sedge]

injective it's one to one

[noble dock]

yes

[crimson sedge]

|M| > _ |P(N)| = 2^aleph0 = c

therefor |M| > _ c

[crimson sedge]

could be

but it's AT LEAST same size

which is the proof you need

[noble dock]

oh yeah i see okay, because we know that A is a subset of M?

hence it has cardianlity less thna or equal to M as well

[crimson sedge]

yes, gonna go rest 5:40 am 👍

hope all this helps

[noble dock]

so basically the order is:
use part a, that is there eixsts sequnece of disjoint sets (non-empty) that is in M.

Then becuase of this, we are somehow able to form an injective funtion f: P(N) -> A where A is colllection of all unions

And since A susbeteq M we are done

[noble dock]

alr tysm i apprecitae it

[noble dock]

have a gn

thanks again

[crimson sedge]

bingo

[cedar kiln]

@noble dock Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[vestal fable]

Assume you are communicating with another mathematician, but all you can use to communicate are small metal plates that you can add 1 to 20 dots on top of, which he will count. The procedure is that you give him an amount of plates, and he gives you one back. This is the only communication you have.

For example, you could give him a plate with 1, a plate with 1, a plate with 2, a plate with 3, a plate with 5, and he gives back a plate with 8. He has smart problem-solving skills and recognizes mathematical theories, and can infer things. For instance, if you give 5 and 4, then 9, and then you give 3 and 8, he will understand that you are adding and give back 11.

Assume you wanted to mess with him and give him a sequence of numbers that he understood what it meant and it was a famous (ish) pattern or equation, but it hadn't been discovered what the next set in the numbers is.

[vestal fable]

no this isnt a random question, yes i do need a answer.

[split ice]

so, a sequence where (currently) some point isn't known?

-# i saw what you said about the professor 0-0

[vestal fable]

yhea

[split ice]

OEIS 40

[vestal fable]

i deleted it cuase i didnt want to get incorectly flaged by whatever mods there may be on this server

[split ice]

eh. as long as it's a physics professor no one will mind

[vestal fable]

what is this?

[split ice]

the sequence of prime numbers :)

[vestal fable]

but dosent it go super high before the next number becomes unknown?

[split ice]

sure, but the person will identify the sequence, and just not know past a certain point

regardless of communicability

[vestal fable]

yhea but it has to be phisicly doable

where you give first 1-5 numbers and then they give next

and none of the numbers go over 20 or so (60 as a uper limit)

[split ice]

the only way i see that happening is if you gave 5 numbers that corresponded to a similar sequence

[vestal fable]

dose reyman work?

[split ice]

then the 6th number could be one of two and theres no way to work

[crimson sedge]

how do you even recognise a sequence

from finitely many terms

[vestal fable]

3 3 6 4 4 18 5 5 _ is reymand right? and the blank isnt known

[vestal fable]

idk it might not be posible

[vestal fable]

?

[split ice]

what is "reymand", sorry?

[vestal fable]

*Ramsey

Ramsey numbers

[crimson sedge]

next term is -1/117 🙏

[vestal fable]

i thought it hasent been found?

thats what the wiki said

[split ice]

Take the Baum-Sweet sequence:
1, 1, 0, 1, 1, 0, 0, 1, 0, 1, ...
and the Regular paperfolding sequence:
1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ...

If i gave you the first 8 terms, it would be impossible to say which sequence - and therefore which number - it is, without any additional info.

this is what i mean by "similar sequence"

[vestal fable]

ahh

yhea i think i just have to change plans

[split ice]

yeah, ramsey(3,n) is only known up to 9, and there are probably shorter ones that i cant find atm

[split ice]

bro just ask him to recall the cross product in R^7 from memory, he'll combust

[vestal fable]

(this is for hard sifi wrighting asighnment about communicateing with aliens with just a on and off light.)

[split ice]

ah

you should look into the voyager golden records - they used the spin of hydrogen to create a number system before laying out their message

perhaps you can do something similar

[vestal fable]

.close

[cedar kiln]

Channel closed

Closed by @vestal fable

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[amber elk]

I dont get what its asking me to do. how is this any different

[amber elk]

to this

[dire geode]

n may be different from 4

if you did it for n, then just plug in n=4 to your resulting formula

[amber elk]

so the order of the questions were first the R4 and then the next question is Rn

so is it just a redundant question?

surely I cannot just slap the answer from R4 to the Rn question

right?

[dire geode]

correct. the problem with n instead of 4 is a generalization

do 4 for practice. then re-do with nearly identical steps to get the general n case

[cedar kiln]

@amber elk Has your question been resolved?

[amber elk]

what

[dire geode]

what part of that was confusing

[amber elk]

what do you mean by "re-do with nearly identical steps"

do I just not have a defined variable for n and develop the equation?

[dire geode]

sure if you want to skip doing 4

[amber elk]

I mean, ive done 4 already but are you telling me I have to do it again?

[dire geode]

right because you pointed out this already

[dire geode]

which i also stated here

[amber elk]

so in short, I have to define n

[dire geode]

i don't know what you mean by "define n"

just try some steps and show it here

[amber elk]

this is for R4

[dire geode]

what does "define n" mean?

[amber elk]

give it a value

because I can put whatever since its just the number of end points, right?

[dire geode]

n is a variable

your answer will have n in it

[amber elk]

right

I think I got it

thanks

.close

[cedar kiln]

Channel closed

Closed by @amber elk

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[novel sphinx]

integration by parts twice, not sure if i messed up a previous step but rn i’m stuck on balancing the original equation with the last line (if thats even the right step next)

[sullen cipher]

U need to integrate v here

Not u

[novel sphinx]

i'm a bit confused, i chose u=8^(8x), dv=sin(9x)

integral of dv came out to v=-cos(9x)/9

u was not integrated where you outlined

uv - ∫v du

is what i followed

[sullen cipher]

Ur u states e^8theta

[novel sphinx]

yeah, i didn't integrate it

just said x because i didnt feel like finding the theta symbol

[sullen cipher]

Right sorry

What was the mistake is u and v

Uk LIATE

[novel sphinx]

yeah, i heard the T & E is interchangable

should i swap the u & dv terms?

[sullen cipher]

Following this u is sintheta function and v is e^theta function

[sullen cipher]

Exchange u and v

[sullen cipher]

I m not sure abt this but i dont think it works in every case ,there r some cases maybe

[novel sphinx]

how do we know v?

i thought the integration of parts formula is: ∫u dv = ∫e^8theta * sin(9theta)

unless you meant dv

[sullen cipher]

U r using this one right

[novel sphinx]

i'm using this

looks a bit different

[sullen cipher]

Oh

Yes then set u to -cos(9theta)/9
And dv to 8e^8theta

[novel sphinx]

like this?

[sullen cipher]

U took du . dv here

It's supposed to u . dv

[cedar kiln]

@novel sphinx Has your question been resolved?

Channel closed

Closed by @novel sphinx

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[sturdy escarp]

confused with the drawing

this was my attempt

why does 1/2 PQ start at origin?

[upper laurel]

thats the default location for a vector

you can see all they did was just sketch the vector

the position of your vector shouldnt affect the results

[sturdy escarp]

but isn't my black vector more correct?

[upper laurel]

looks like you want someone to back you up on a question that has no other meaning to it

yes, your black vector makes me happy

its not more or less correct than the other one though

[sturdy escarp]

okay cool

makes sense

tysm

[upper laurel]

np

[sturdy escarp]

.close

[cedar kiln]

Channel closed

Closed by @sturdy escarp

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[delicate temple]

i need the amplitude, period, and equation of this graph

[buoyant latch]

What have you tried

[delicate temple]

literally everything

[buoyant latch]

No but how did you get there

Like what steps did you take

[delicate temple]

i just used the general equations for sin and cos and plugged in values lmfao idk

half of those were given to me by like 10 different people and nobody can figure it out

[chrome quail]

Start by writing the general structure of a sine function out

[wicked mantle]

I assume they have the same y value

[buoyant latch]

Don’t just guess, there’s a systematic approach to this

[delicate temple]

i used the y=Asin(B(x-C)+D and plugged in the values i thought were right but apparently were wrong which are in the list of answers i tried

im at a complete loss for ideas like idek what else to try

i have 1 attempt left 💀

[chrome quail]

What does A represent? Start with that

[scenic heron]

sometimes the approach is to just take a guestimate ngl

a lot of the time thats what they want

[wicked mantle]

Not this one

[chrome quail]

Not in this problem though

[wicked mantle]

You’re not going to find an exact equation by pure guesswork

[scenic heron]

shi you never know

[buoyant latch]

You should only do that if you can do it “properly”

[delicate temple]

are you guys like not allowed to just help solve it i feel like ur just telling me to do what i already tried lmaoo

[lofty sand]

Thanks for the grammar correction ! Much apprécié

[delicate temple]

like i know how to calculate amplitude its just not right for whatever reason

[chrome quail]

If you mean give you the answer, no we're not allowed. If you follow our instructions you'll solve it correctly

[delicate temple]

you asked me what a means i feel like thats not gonna get me to an answer lmaoo

[wicked mantle]

It does

You need to know what does those alphabet represent to move on

[delicate temple]

i know what they represent i just cant find them 😭

[chrome quail]

It's up to you if you want to work with us. There's a reason I'm asking you this.

Then what did you get for Amplitude?

[delicate temple]

^

[wicked mantle]

Right, could you briefly explain your approach?

[delicate temple]

this is the format of the question all of the answers ive tried are in those other screenshots

[chrome quail]

There's some 3s and some 2s. Which is it and why?

[delicate temple]

i thought it was 3 then it was wrong so i asked people for help and they said 2 and that didnt work either

[chrome quail]

Why did you think it was 3?

[delicate temple]

cause you do the max - min and divide by 2 or at least i thought

[chrome quail]

Yeah that's right, so the amplitude is 3

So A = 3.

Now do D

[delicate temple]

yes i knew that

i dont think there is one

[wicked mantle]

So it’s zero

[chrome quail]

yes, it's 0

So now we have y = 3sin(B(x-C))

What about C?

[delicate temple]

i have no idea

[wicked mantle]

Notice the function passes through (-3, 0)

[delicate temple]

yeah

[wicked mantle]

What’s the value of sin0?

[delicate temple]

0??

[wicked mantle]

Ye, so what’s the value of C?

[delicate temple]

i dont understand the point of what you just asked😭

im confused altogether

[wicked mantle]

Imagine you move 3 unit from the origin

[delicate temple]

so 3?

[chrome quail]

The function also passes through (0,0)

That means at x = 0, y = 0

[delicate temple]

huh

how does that relate to C

[chrome quail]

Cause C is the horizontal shift of the function from the origin.

Given that we know y = 3sin(B(x-C)), we want 0 = 3sin(B(0-C))

Does that make sense?

[delicate temple]

i understand how you plugged in the 0s yeah

[chrome quail]

Alright, so what argument (ie. what do you need to put into sin) of sin results in 0?

We want the output (y) to be 0 when the input (x) is 0, as we can see from the graph

[delicate temple]

i dont understand

[chrome quail]

0 = 3sin(B(0-C)), that part you understand right?

[delicate temple]

yes you took the (0, 0) and plugged it in bc the function passes through it

thats all i understand about it

[chrome quail]

We want to choose a value of C, so this equation holds

What value of C must you choose?

[delicate temple]

0?

[chrome quail]

Yes, but why?

[delicate temple]

sin0 = 0 and 0 - 0 = 0 so i put the 0 there

[chrome quail]

yeah exactly

now we have y = 3sin(Bx), right?

[delicate temple]

yes

[chrome quail]

Now the period of a regular sine function (for it to complete 1 loop) is 2 pi. What is the period of this sine function?

[delicate temple]

i dont know

i thought period was 2pi divided by B but i dont know what B is

[chrome quail]

yeah it is, but we can find out the period by looking at the graph, allowing us to calculate B

Look at this graph, can you point at the start and end of one period?

[delicate temple]

(0, 0) to (3,0) ?

[chrome quail]

yup, so what's the period (as a single number)?

[delicate temple]

would it just be 3?

[chrome quail]

yeah, it's just the horizontal length of one "cycle"

So now that the period = 3, and as you said 2pi/period = B, what is B?

[delicate temple]

2pi/3

[chrome quail]

Yes

So what's the complete function

[delicate temple]

3sin(2pi/3x) ?

[chrome quail]

Yes

[delicate temple]

so this?

i have one left so this like has to be right

just to make sure i typed it correctly

[chrome quail]

I'll check it one sec

[delicate temple]

thank you

[chrome quail]

lgtm

[delicate temple]

omg it was right thank you so much

[chrome quail]

See? Asking for A gets you the answer

[delicate temple]

im sorry i doubted you LMAO

that was frustrating af

tysm have a good night

[chrome quail]

15 tries over 5 days is hilarious

[delicate temple]

i asked my friends in calc 3 and they gave me those bro

i was tweaking out

[chrome quail]

Happens, just need to approach it step-by-step

you can close the channel with .close

[delicate temple]

.close

[cedar kiln]

Channel closed

Closed by @delicate temple

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[long swan]

1.4.2:
By the Archimedean Property, for every eps > 0, there exists n in N s.t 1/n < eps.
So s + eps is an upper bound for A, and s - eps is not an upper bound for A.
Then s - eps < sup A < s + eps, and since this holds for every eps > 0, s = sup A by squeeze theorem or some shit?

[dull oxide]

You're kinda doing it backwards. Start by choosing any $\varepsilon>0$

[wraith dagger]

SWR

[long swan]

ngl bro i'm getting filtered hard rn

so i choose eps > 0, then by Archimedean, for large enough n, 1/n < eps, then?

[dull oxide]

This is only the first half though

You got more to go

[long swan]

idk

feels like my reasoning is correct

i don't see how it's backwards

[dull oxide]

Because to prove sup, you need to start with an arbitrary epsilon

[cedar kiln]

@long swan Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[heady sequoia]

i started to understand how to do it with whole numbers but when it came to question d i was stumped

[wicked mantle]

Welcome back

[heady sequoia]

howdy

im not too good with the decimal points

i believe it doesnt exist but at the same time i want a second opinion since its my final chance to answer

oh i got it nevermind

.close

[cedar kiln]

Channel closed

Closed by @heady sequoia

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[azure vault]

lim
x--> 0 ( sin 3x / x)

[azure vault]

where do i start wityh this

[lone dune]

what have you tried

[pastel vault]

$\lim_{x \to 0} \frac{\sin x}{x} = 1$ is a pretty famous result

[wraith dagger]

south

[prisma pike]

Proof by fame

[jolly token]

direct subtition and then trig identities im guessing

[jolly token]

or this lol

[stiff brook]

sin(u)~u for small u

[pastel vault]

yeah, and think about which u you should choose for your problem

which u u should choose, lol

[jolly token]

ah man screw it use l'hopital

i dont get this

[prisma pike]

I mean I guess this works

[jolly token]

wait

[prisma pike]

Seems like the simplest solution

[jolly token]

you cant even use derivitives

[lone dune]

you can use l'hopitals

[jolly token]

this is sin3x/x tho

[lone dune]

but i would suggest you do it normally

[prisma pike]

Sub u=3x

[jolly token]

would make den x^2

[pastel vault]

this is the intuitive idea

[pastel vault]

like formally, you should say this

[jolly token]

what is u..

[pastel vault]

but that's the same thing as sin(u) is approximately u, when u is small

[lone dune]

placeholder variable

[lone dune]

?

d/dx x = 1

[jolly token]

the denominator would be x^2

[lone dune]

itd be 1

[jolly token]

why would it be 1

[lone dune]

because d/dx x = 1

[jolly token]

its not just x

its sin3x/x

[lone dune]

when you use l'hopitals you differentiate the numerator and denominator separately

not as a whole

you differentiate sin(3x) separately and x separately

[jolly token]

ohhh

makes so much more sense

[stiff brook]

using lhopital here would be frowned upon

[jolly token]

why

[stiff brook]

taylor expansions or invoking sinx/x as x->0 is the best

[jolly token]

bro this is a calc 1 problem 😭

who is doing taylor expansions

[stiff brook]

squeeze theorem works as well iirc

[lone dune]

there are a bunch of ways to tackle this

but the point is you should probably learn how to manually do it rather than relying on l'hopitals

its never good to rely on l'hopitals

[stiff brook]

differentiating sinx requires us to know lim x->0 sinx/x = 1

[jolly token]

why

isnt it just

chain rule

[pastel vault]

if you try from first principles, so $\lim_{x \to 0} \frac{\sin(x + h) - \sin(x)}{h}$

[wraith dagger]

south

[pastel vault]

you'll need the angle addition formula and you'll see

[jolly token]

yeah my brain stopped working

can someone close this

[pastel vault]

I could but the original poster hasn't said anything

so it would be rude to close it for them

[digital bane]

quick hint, but please don't ask to close another person's channel just because you do not wish to continue

[jolly token]

?

he hasn't said a word in

well since he posted it

[prisma pike]

Maybe bro just getting lunch rn fr

[jolly token]

weird time to get lunch but maybe

[prisma pike]

I mean timezones

[cedar kiln]

@azure vault Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[twilit stratus]

Hello, this is a more of a general question and I don't know if this is the right place to ask.
I am about to start my 10th year or school so I'm still studying pretty basic math, however the pace that everything's going seems pretty slow and I would like to go further on my own. The problem is that I have no idea what path to follow, I don't know what topics to study and in what order. Could you please help me find a clear path?

[fallen trail]

Make use of AI to make a learning checklist

Like first, you have to establish what you want to learn. Best is to pick up a textbook since it already has a structure

Otherwise you could use resources from the internet

[weak granite]

if you could somehow acquire books from higher-grade students then you can just use that. follow the path within those textbooks!

or perhaps you could dig into a specific concept thats generally interesting and useful (calculus)

[twilit stratus]

The problem is that I have a very limited budget for school itself, so buying extra books would make it too expensive

[weak granite]

do you have access to what 11th year students learn?

like just the names of the concepts

[twilit stratus]

I've tried learning a topic that I liked, but then I noticed that I'm missing so much to be able to understand it

[twilit stratus]

I don't have access to even 10th year concepts yet, the book hasn't arrived

It arrives at anytime this week

[tropic oxide]

!nogpt

[cedar kiln]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[weak granite]

I'm talking about the curriculum of 11th year students

not the books themselves.

[neon wasp]

Hello, I’m confused on a math problem. It is algebra 2 level. My teacher did this, I have no idea how. The problem we’re solving is (1, 60°) – (1, 300°). I have a test tomorrow. Also when solving polar form, am I trying to find the length of the line?

[twilit stratus]

No I have no idea

[digital bane]

!occupied

[cedar kiln]

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).

[opal hinge]

!occupied

[cedar kiln]

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).

[digital bane]

oh oops

[digital bane]

is there not a website or something that tells you what lies ahead in your school syllabus?

[twilit stratus]

I don't know, that's kind of what I'm looking for, even just a list of topics in order that I can follow without missing topics would be already a very good start

[opal hinge]

It quite depends on what you want to learn, Are you studying for a test or you just want to study math for fun?

[digital bane]

have you tried searching for something like "{your country} 11th grade syllabus"

[twilit stratus]

For fun

[weak granite]

I wouldnt really recommand focusing on- everything in your future-curriculum. how about you grind out the very fun concepts like calculus! ofcourse, start from the basics and ladder up to the good stuff!

[digital bane]

if for fun, i have a good written resource for you to start on

[opal hinge]

If so you could just pick any topic you like and learn it, as long as you have enough background for studying it

[digital bane]

https://math.libretexts.org/Bookshelves

[twilit stratus]

It doesn't really work that well, here we have categorized schools so it's really confusing to get a right result from a research like that

[loud gyro]

if you feel like you are good at school maths, you might wanna have a look at maths olympiad books

[digital bane]

from here, depending on what you choose to study, you have extra video sources like The Organic Chemistry Tutor, 3Blue1Brown, blackpenredpen, Khan Academy, etc.

[twilit stratus]

Yeah but like, then I have no idea what the background that I need is

[opal hinge]

Doing Olympiad math is a great way to kill free time and have absolutely no problem done

[twilit stratus]

A few months ago I thought that concepts about limits were cool, I looked into them, saw that I was missing a lot of stuff before it and stopped

[digital bane]

if that's the case, peek into the link i shared. it's more or less listed in prerequisite order

[twilit stratus]

Ok

[digital bane]

but after calculus in that link, you're really p much free to explore anything else in that page

[weak granite]

yeah imagine differential equations before calculus 🤩

[twilit stratus]

Imagine differential equations before basic algebra

[opal hinge]

Olympiad inequality or geo is a great topic to study

Especially inequality

[loud gyro]

NT would be even better tbh, coz it has no prerequisites

[weak granite]

right, what kind of math do 10th year students learn in your country? name us some of the concepts

[twilit stratus]

I don't know, I haven't started 10th year yet xD

9th year was very basic algebra, like basic equations, sets up to rational numbers and stuff like that

[weak granite]

yeah def ladder up in that list furina provided

dont... dont get near calculus. not now atleast

[twilit stratus]

Only thing that I can assume for next year is quadratic equations and irrational numbers

[digital bane]

in that case, start from Algebra in that link

then you can do Geometry and Precalc more or less together

[twilit stratus]

You're making it sound like a mini-boss

[digital bane]

then slowly ease into Calculus

[digital bane]

at your level calculus is just a straight boss

[twilit stratus]

Ah okay

[weak granite]

calculus requires a GOOOOD comprehension of algebra

[loud gyro]

it is the Big Boss of the hs curriculum

[twilit stratus]

How long is it going to take before calculus?

[digital bane]

depends on how fast you study

[twilit stratus]

Which I still don't know what is about but I guess it's complicated

[digital bane]

calculus is the study of the idea of continuous change, super generally speaking

[opal hinge]

A little bit of algebra and how functions work and you can start learning calculus

[weak granite]

I took calculus after combinatorics, logs, linear algebra

[twilit stratus]

Fair enough

[weak granite]

not like combinatorics and logs are required

it just- takes a great comprehension of algebra

[digital bane]

logs would help

combinatorics not so much

[twilit stratus]

like logarithms?

[digital bane]

yes

[weak granite]

yes

[twilit stratus]

Oh that's a topic I tapped into on my own

[weak granite]

🤩

[twilit stratus]

I honestly don't know if there's much more to it or not though, I just know how the logarithm works basically

[weak granite]

I'd say the two most required factors with calculus are algebra and trig

[opal hinge]

If you are studying math for fun, just go for anything you like lol

It's jut that we don't recommend

[twilit stratus]

Like when I put log5(25) on calculator and it says "2", I know what it did to find that

[silent ivy]

does anyo

ok wrong channel mb

[weak granite]

thats fine. but yes you do need more! algebra path should cover all that you need for calculus

[twilit stratus]

How much is there to trigonometry? I just know sin cos and tan

[loud gyro]

in fact I'd go as far as recommending you not to study the stuff in school syllabus since you would inevitably end up learning it anyways soon enough

[twilit stratus]

That's great

[digital bane]

unit circle, pythagorean identities, and all of the other good formulas in trig

[weak granite]

there is only sin cos and tan! the rest of trig is just- using them in more advanced ways and giving you new formulas and new concepts! you got the building ground :))

[twilit stratus]

I mean not really, our teacher is horrible at teaching so I end up having to study on my own anyways

[twilit stratus]

That doesn't sound too bad

[weak granite]

it isnt

geometry is great

nothing in math is "hard" to understand

unless- post-calculus 2 or smth idk

anyways nothing to worry about

[opal hinge]

I recommend studying inequality the only thing you need is algebra

And it could get extremely hard too

[twilit stratus]

Oh of course there's a calculus 2

Lol

[opal hinge]

Also you could do some calculus problems faster with inequality

[weak granite]

if we consider vector calculus as calculus then theres a calculus 4!!

[twilit stratus]

dies

[weak granite]

its okay

nobody learns that

...

unless- asylum people

(mathematicans and math majors)

[loud gyro]

isnt vector calculus part of uni syllabus for all of STEM ppl?

[weak granite]

yeah you will only reach the start of calculus 2 with hs. you'll need a math heavy collage to learn 3 and more advnaced stuff

[opal hinge]

Ykw

[weak granite]

STEM people are just asylum people for all subjects 🤩 not only math

or... sciences ig

[opal hinge]

Why not try some topology

[weak granite]

?

topology 😭 ?

[digital bane]

i'm dying it in atm

but fun

[loud gyro]

pretty sure youd need real analysis for that to be done properly, or at least set theory

[opal hinge]

-# i was kidding lol

[weak granite]

"yeah how about you climb mount everest"- directed to a toddler

[twilit stratus]

Hydrogen bomb VS Coughing baby

[weak granite]

anyways!
https://math.libretexts.org/Bookshelves

you got this acar,

focus on algebra.

[digital bane]

all the best!

[opal hinge]

Oh wait, combinatorics is quite fun and doesn't require much math background

I mean counting things

[twilit stratus]

In like two days, still got a bunch of latin stuff to study before vacations end

[weak granite]

yes, you have all the time you need

[twilit stratus]

: (

Latin is boring

[weak granite]

you should close the channel before namington person appears out of nowhere

unless you got more math concerns.

[twilit stratus]

Who is namington

[weak granite]

use .close to close a channel at any time 🤩

[weak granite]

a moderator

[twilit stratus]

Hmmm

Ok so let me just

.close

[cedar kiln]

Channel closed

Closed by @twilit stratus

Use .reopen if this was a mistake.

[weak granite]

good luck!

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[sacred tinsel]

Having shown this

Show this

[sullen cipher]

Have u tried anything?

[sacred tinsel]

well

I have a method I think, but I can’t justify it

Im confused because when you apply the inequality to the denominator, you should flip the inequality sign, but otherwise you get the wrong answer

@helper

<@&286206848099549185>

[frail citrus]

,rotate

[nova snow]

dr du moment

[cedar kiln]

@sacred tinsel Has your question been resolved?

[sacred tinsel]

can I get some help 💔

[vernal basin]

I don’t understand why

You replace c with (a+b)/2

[elder thunder]

Do not mind my ignorance please but Can't we just refer that Arithmetic Mean >= Geometric Mean for deducing portion of this problem?

[dusky stratus]

cannot assume anything above 2 term AM/GM w/in Australian syllabus

[elder thunder]

Oh well.

[sacred tinsel]

since from the previous part a + b /2 is the minimum value

[sacred tinsel]

I assumed it in line 4, however should I not flip the inequality because it is used on the denominator ?

[elder thunder]

We flip the inequality when we're multiplying or dividing both sides with something that is certainly negative

[sacred tinsel]

yes but we also do so with fractions

[elder thunder]

Like taking reciprocals you mean?

[sacred tinsel]

Like so

in Line 4 i use the AM GM inequality on the denominator yet do not flip the sign as above, however I arrive at the correct answer. How can this be

[elder thunder]

True that

[sacred tinsel]

Actually they just have to be positive

but yeah

Do u see what I mean

[elder thunder]

You see that this is true when we're taking reciprocal of things

[sacred tinsel]

What is true

[elder thunder]

How did we change the inequality to equality

[sacred tinsel]

It simply means it is equal to the line above, NOT to the LHS

[elder thunder]

|| Oh, my bad, but then again, I do not think we can substitute (a²b + ab²)/2 = (ab)^3/2 in from Line 3 to 4 ||

|| Equality in AM-GM exists only at a specific condition, otherwise it's an inequality, and here, we are not given any data to conclude that whether this equality exists or not I guess ||

Oh wait

@sacred tinsel I think I got this, are you clear with whats f(x) and what's the minimum value of f(x) ?

The problem is basically asking us for range of f(x) or to say range of f(c)

[sacred tinsel]

That’s why I changed to an inequality sign…

[sacred tinsel]

It is asking to prove f(c) >= (a+b/2sqrtab)^2

[elder thunder]

On RHS, we have f³(c)

And on LHS

[sacred tinsel]

Yes

[elder thunder]

We have

[sacred tinsel]

The first part I am fine with

[elder thunder]

(Min f(x))²

[sacred tinsel]

Yeah I know lol

Im wondering why I can use the am gm on the denominator without flipping the inequality

[nova snow]

GL on ur 4u hsc 🥀

[elder thunder]

Isn't it all solve now then

[sacred tinsel]

ty🙏🙏 cooked

[elder thunder]

f³(x) >= ( min. f(x) )²

[sacred tinsel]

Im unsure why I can use the amgm on the denominator in line 4 and say it is less than LHS, not more than

[sacred tinsel]

because of this

[sacred tinsel]

Furthermore, we cannot assume this if f(x) is between 0 and 1

[dusky stratus]

This is wrong

[elder thunder]

How did we come to 0.5 and stuff?

[dusky stratus]

I’m just saying that if the function is below 1 at some point

Your postulated fact dissolves

[elder thunder]

I didn't think of that, but instead like,

f(x) belongs to [ min. f, inf )
f²(x) belongs to [ square of min. f, inf )

Min. f is positive and is greater or equals to 1

f³(x) belongs to [ cube of min. f, inf )

[elder thunder]

F(x) is AM/ GM of three positive numbers, it is always equals to greater than 1

[elder thunder]

@dusky stratus

[sacred tinsel]

I see

Well then, I’m still unsure why we can apply the am gm in line 4 and maintain the inequality direction

[elder thunder]

We can, for here only I guess, because LHS is f((a + b)/2)

And for x = (a + b)/2 , f((a + b)/2) = min. f

Not sure tho

[cedar kiln]

@sacred tinsel Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[void stag]

We all know that 0.999... = 1 but how is this logic in the picture wrong?

[tropic oxide]

$1.999\ldots\infty\ldots98$ is not a real number

[wraith dagger]

Ann

[opal hinge]

there won't be ...98

[void stag]

But why? It clearly follows the pattern

[opal hinge]

just 1.99999999999....

[digital bane]

you can't think of infinite decimals the same way you do finite decimals

[opal hinge]

it goes on to forever so there won't be last digit

[magic solar]

P-adic numbers 67?

[tropic oxide]

in decimal representations of real numbers there is no such thing as any decimal places "after infinity".

[void stag]

Ohh

Okay

.close

[cedar kiln]

Channel closed

Closed by @void stag

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[timid plover]

if $z_{r} : r = {1,2,3,\ldots,50}$ are the roots of the equation $\sum_{r=0}^{50} z^r = 0$, then find the value of $\sum_{r=0}^{50} \frac{1}{z_{r} - 1}$

[wraith dagger]

Sypse

[timid plover]

I dont really know how to do this one

[cedar kiln]

@timid plover Has your question been resolved?

[lofty sand]

Do you have the final answer ? Is it 0 ?

You need to see it as a geométric series

[last apex]

It diverges as a geometric series

[lofty sand]

That is not the point since we stop at 50 ?

[last apex]

I meant that you cannot expand 1/zr-1 as a geometric series

[daring linden]

zr for r=0 is not defined

did you mean to start the summation at r=1?

[timid plover]

its ||-25||

[lofty sand]

My bad

[daring linden]

but yeah zr are just the 51st root of unity excluding 1

[timid plover]

I think that z_r are the complex roots while z0 would be the real one which is 1?

[daring linden]

put z0 = 1

first term goes to inf

I think they meant to start at 1

[timid plover]

yea mb

[daring linden]

ok so

you know there are 50 roots

complex roots

there will be 25 conjugate pairs

try solving for one pair of conjugates

and see

[timid plover]

hm I dont really get it can you explain a little more?

wdym by solve on pair of conjugates?

[daring linden]

there are 50 complex roots right?

[timid plover]

yea I do get that part

[daring linden]

so the summation would look smth like

e^pi/25.5 + e^2pi/25.5 + ............ + e^49pi/25.5 + e^50pi/25.5

right?

[timid plover]

yes

[daring linden]

now e^51pi/25.5 can be written as e^(-pi/25.5) which is a conjugate to e^pi/25.5

right?

[timid plover]

yes

[daring linden]

so e^pi/25.5 + e^50pi/25.5 will be a conjugate pair

same you can do with e^2pi/25.5 and e^48pi/25.5 and so on

in total we'll have 25 pairs

[timid plover]

ok

[daring linden]

wait a min

fuck

there will be 25.5 in the denominator

not 25

[timid plover]

ah yeah 2/51

can we not use transformation of roots?

[daring linden]

yes we can

prolly will require some binomial tho

if you know some basic binomial we can

[timid plover]

yea

I do

[daring linden]

ohk so

for ease of communication

JEE?

[timid plover]

yea

[daring linden]

ohk

hindi?

[timid plover]

👍

[daring linden]

theek

so dekh

hume basically sum of roots nikalna hai

of a polynomial which has the roots 1/zr - 1

so we can let

1/(zr - 1) = kr

zr ko isolate kardo

zr = 1 + 1/kr

[timid plover]

ha

[daring linden]

and substitute the 1 + 1/kr in the polynomial

pen and paper nikalna padega

wait a min

[timid plover]

ok

[daring linden]

try to find coefficient of x^49

@timid plover

sorry coefficient of x^50 would be 50

last line is incomplete

[timid plover]

ohk

so we would get -1250/50 right?

[daring linden]

yeah ig so

[timid plover]

yea its correct thanks

[daring linden]

ohk

[timid plover]

.close

[cedar kiln]

Channel closed

Closed by @timid plover

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[sturdy escarp]

can someone check my work please

also how would I do direction?

[cedar kiln]

@sturdy escarp Has your question been resolved?

Channel closed

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

Available help channel!

Send your question here to claim the channel.

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

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

[hardy sequoia]

I need help studying for Data Classification and Visualisation, Probability and also Volume

[hardy sequoia]

.close

[cedar kiln]

Channel closed

Closed by @hardy sequoia

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[long swan]

How do you show that R\Q is uncountable? Can I just say that uncountable - countable = uncountable? Or do I have to justify that somehow

[stiff totem]

$\mathbb{R}=\mathbb{Q}\cup\mathbb{R}\setminus\mathbb{Q}$

[wraith dagger]

Desync

[stiff totem]

would be the countable union of two countable sets and hence countable

[floral arrow]

Did you forget parentheses?

[stiff totem]

around the right two

I'm used to setminus binding tighter than union

but Q U (R\Q), yes

[long swan]

Oh that makes sense. It's a contradiction argument. But what I don't understand is the "countable union" part

What does that mean exactly

[stiff totem]

union of countably-many sets

countability is preserved under countable union

you can show this by induction on the Cantor pairing function

or more simply just enumerate two countable sets, remove duplicates, and induct on the number of sets

[long swan]

Ok thanks

How I originally tried to do this was so complicated haha

I tried assuming R\Q countable and then taking different enumerations to make a new sequence but I couldn't find a new element

[stiff totem]

that approach will be tricky because rationals can either terminate or have periodic decimal expansions

and your diagonalisation step will have to deal with a bunch of edge cases

it might be cleaner to diagonalise on continued fraction expansions

since they're effectively just lists of naturals

[cedar kiln]

@long swan Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[last apex]

x^2 - 2 is irreducible over Q by the rational root theorem

[cedar kiln]

Channel closed

Closed by @austere garnet

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[strong prairie]

Hi, I'm trying to solve this quadratic equation and I'm pretty lost I have seen it done a couple times but I need help

[strong prairie]

so far i know that x^2=A and 11x=B and -26 = c , to plug into this formula, x=-B+-sqrt(b-4AC)

[upper ruin]

No no no no

A, B C are numbers

A: coefficient of x²
B: coefficient of x
C: coefficient of x⁰ (in other words, the remaining term, the one without any x)

[strong prairie]

how do i include that into the formula?

[upper ruin]

You just... replace the values 😅

[strong prairie]

ok il try

[floral arrow]

$\textcolor{red}{a} x^2 + \textcolor{green}{b} x + \textcolor{orange}{c} \rightarrow \textcolor{red}{1} x^2 + \textcolor{green}{11} x + \textcolor{orange}{-26}$

[wraith dagger]

Nel

[floral arrow]

That's the quadratic you have

$x = \frac{- \textcolor{green}{b} \pm \sqrt{\textcolor{green}{b}^2 - 4\textcolor{red}{a}\textcolor{orange}{c}}}{2\textcolor{red}{a}}$

[wraith dagger]

Nel

[floral arrow]

This is the formula

[strong prairie]

but where did the -26 and the 11x go?

[upper ruin]

Huh?

A = 1
B = 11
C = -26

[upper ruin]

I don't understand what your doubt is, honestly

[upper ruin]

From here it should be (really) clear what a, b, c are.

[strong prairie]

mb i thougt he was giving me the answer for a second

[upper ruin]

That "color code" should help you, too

[strong prairie]

Like this?

[upper ruin]

A is 1

Why did you write a²?

And also, inside the square root it's b²

Not just b

And also c is NEGATIVE 26

[strong prairie]

well i thought there should be something becuase the ^2 cant be by itself

[upper ruin]

Wasn't this enough clear? 😭

[upper ruin]

Wdym?

[strong prairie]

answering your first question, "Why did you write a²?"

[upper ruin]

Yeah but this makes zero sense

[strong prairie]

what makes it 11^2?

[upper ruin]

Why 11²??

11 is b, not a!!

A is 1

[regal marlin]

why does it say to factor this equation when no factor pairs add up to 11

[upper ruin]

I'm using both upper and lower case with the same meaning because I don't know which ones you're used to

[strong prairie]

dude im tryna figure it out, i really appreciate the help but i dont need the " this makes 0 sense" this is my first time doing this equation

ok so instead of a ^2 i will use 1^2

[upper ruin]

Of course, because a is 1

[strong prairie]

and i will put in -26

[upper ruin]

But this shouldn't be a surprise

[upper ruin]

Instead of c, yep

[regal marlin]

Becauses x's multiplicative identity is 1

[strong prairie]

bruh

Like this?

[regal marlin]

x = -(11) +- sqrt(11^2 - 4(1)(-26)/2(1^2)

[upper ruin]

A is 1, why have you written 1²?

[young flume]

a = 1 , b = 11, c = -26

the variables are the coefficients

u dont include exponents

only the constant

(the number that doesnt change)

[upper ruin]

And also this #help-13 message @strong prairie

[young flume]

that sounded confusing

x^2 is the same thing as 1x^2 so the coefficient is just 1