help-41

[spring kayak]

Yeah, i thing this is the right value

[bronze locust]

if the image was dilated , wouldnt U'T'/UT be the scale factor?

[amber wasp]

@bronze locust Has your question been resolved?

[amber wasp]

@bronze locust Has your question been resolved?

[bronze locust]

<@&286206848099549185>

[amber wasp]

@bronze locust Has your question been resolved?

[obsidian walrus]

wouldnt you just count the units? then be able to use that?

[bronze locust]

I cant , the lines are not following that path

[bronze locust]

But somehow, i still cant get the scale factor

I hope i didnt do a xy problem

[bronze locust]

(Not math)

[amber wasp]

@bronze locust Has your question been resolved?

[quiet osprey]

Use tge distance formula

[bronze locust]

??

[quiet osprey]

Google distance between two points it will give you a firmuala

[bronze locust]

uh k?

[quiet osprey]

For this qu3stion

[bronze locust]

k i gotta do later its 1 am

[quiet osprey]

K bye

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[mossy eagle]

Someone pls explain to me how the reverse factor formula works

[mossy eagle]

Especially the angle changes confuse me when making the products the subject of the formula

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[mossy eagle]

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[swift spoke]

can someone helpe me with these questions

i cant find some video on youtube about the same topic

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[pseudo pasture]

Hi need help with a few Questions of Topology
can someone explain this question to me

[frail lintel]

Yes it's a space of lines parallel to the line x+y=0
Note that this basically means the quotient vector space R^2/{x+y=0} subspace

[pseudo pasture]

so it is a subspace topology?
that is intersection of arbitrary open sets in R^2 with the {x+y = 0} subset?

[frail lintel]

Oh from the perspective of topology is a quotient topology

[frail lintel]

So think of this like you are identify the points on each of these lines as a single point

So in terms of finding the open sets of this here's a small excerise, what kind of open sets on this set of equivalence classes would make the map R^2 to R^2/~ where (x,y) gets sent to it's equivalence class continous

And this topology is not the indiscrete topology

[pseudo pasture]

OHK

got it

I was confusing my self

thanks

.close

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[knotty burrow]

I have trouble getting my grasp of quotient groups. I have gotten so far as to it being related to congruency and normality - actually I am quite sure, I accept the concept and is familiar with the words involved. But my intuitive powers are somehow not getting there. Can anyone help?

[amber wasp]

@knotty burrow Has your question been resolved?

[knotty burrow]

I have not heard from anyone. Maybe my question is not well-formed?

[fading crypt]

I have 0 abstract algebra knowledge so the best you have is me, a rubber duck
What is congruency and normality?

[knotty burrow]

Well, congruence modulo K is a relation on a group G with subgroup K. It has some properties:

"The congruence class of a modulo K is the right coset Ka = {ka | with k \in K}."

[fading crypt]

So it's the set of all things that satisfy that equation

[knotty burrow]

So there are a multitude of questions: What is the idea driving these right cosets? How can I form a more intuitive approach, that would enable me to get behind the definitions?

[fading crypt]

I think you can try asking #advanced-algebra

or #groups-rings-fields

[knotty burrow]

Yes. So elements of k on the right, all elements of G on the left

Opposite, of course.

[fading crypt]

Actually better to ask #groups-rings-fields

[knotty burrow]

Yes, ok. I am going to formulate my question a little better and go there. Thanks!

[amber wasp]

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[river brook]

Hi!! Can every x in (0,1) be expressed exactly in the form a/2^n where a is an integer from 1 to (2^n)-1

[prime knoll]

nah

1/pi

[river brook]

o

right

[ripe cipher]

you don't even need to go that far

even 1/3 doesn't have any such expression

[river brook]

irrationals, forgot them

[ripe cipher]

your question amounts to "does every real number between 0 and 1 have a terminating binary expansion"

[river brook]

mmm yes

None of this came to mind cause this question came up during a proof of minkowksi

Minkowsli

Minkowski

but thanks guys!

[ripe cipher]

[river brook]

.u wanna know how it came up?

[ripe cipher]

yes

[river brook]

.close

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[ember ether]

Perfect answer

[river brook]

so

[ember ether]

.reopen

[amber wasp]

✅

[river brook]

We had a lecture where we had to prove minkowski in R²

And we started w defining convexity

( oh its a summer program btw, the lecturer likes and wants us to be annoyingly precise w definitions and everything else )

And somebody asked whether x,y in S => (x+y)/2 in S is enough to state that S is concave

Initially I thought no, then yes, then finally no

but since the program just ended I thought it's fine to seek external help now

[cold vortex]

You can think of what happens if S is closed and has that property, just for fun

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[native anvil]

the dynamic frictional constant between two surfaces is 0.4 if the object slides freely what is the maximum vertical displacment it can achive in second inclined plain

[amber wasp]

@native anvil Has your question been resolved?

[native anvil]

nah bro

it was a busy day

[native anvil]

.close

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[pliant quarry]

Hello

[tropic jolt]

How to find value of arccosz

[uncut nexus]

!occupied

[amber wasp]

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).

[pliant quarry]

I am a beginner in mathematics. I am here to ask where I should begin.

[uncut nexus]

What do you want to learn

[tropic jolt]

WTF

[pliant quarry]

mathematics?

i am just asking, what are some resources and where should i begin

i am kind of clueless

[stuck flint]

Where should you begin?

[pliant quarry]

yes

i am confused

[stuck flint]

I hope you know substraction addition multiplication and division

[pliant quarry]

i know those

but

what are some resources to learn mathematics

[stuck flint]

Book

Youtube

[pliant quarry]

i have tried, but can you give a more detailed answer?

[stuck flint]

Well start from algebra 1 maybe

@worn geyser can I ask something?

[pliant quarry]

I was recommended pre-algebra, and told to figure out my level of mathematics by my family

but i am still confused as to where should i learn

what are some popular resources?

<@&286206848099549185> I am an absolute beginner in maths. What are some places to start learning mathematics?

[stuck flint]

It depends on what do you want to start

In which grade you are ?

[jaunty remnant]

Do you wanna self learn math? @pliant quarry

[pliant quarry]

yes

[jaunty remnant]

and not for your school

for now

[pliant quarry]

i did not really pay attention to mathematics, so i just need to catch up

[stuck flint]

?

[jaunty remnant]

then it is for school lol

[stuck flint]

Then it's for school

[pliant quarry]

4th grade

[stuck flint]

Bro

[pliant quarry]

what

[jaunty remnant]

what's your age bro?

[stuck flint]

Just ask your teacher what he have taught and cover it

[pliant quarry]

but my teacher can't help me, i am too far behind

[stuck flint]

You can't be far behind in grade 4 tbh

[pliant quarry]

i definitely do, because i meant my level of mathematics is 4th grade

sorry for not being clear

[jaunty remnant]

what is your age bro?

[pliant quarry]

ban ):

[stuck flint]

What are the topics you need to do?

[uncut nexus]

Lower than 13??

[jaunty remnant]

Don't say it aloud

[jolly shell]

well probably, since gra&de 4

[uncut nexus]

My advice is that don’t worry about it tbh

[jaunty remnant]

you have to worry

[craggy spear]

Use gpt

[uncut nexus]

About math?

[jaunty remnant]

!nogpt

[amber wasp]

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).

[queen dragon]

Help the guy out and then ban him

[jaunty remnant]

about age here? lol

[craggy spear]

Atleast for grade 4th math cant go wrong with that

[jaunty remnant]

it can

[uncut nexus]

I meant “dont worry about math and being behind if you’re 10 and 4th grade”

[craggy spear]

Breh

[uncut nexus]

Not like “dont worry about their age guys”

[stuck flint]

Guys let's just help him and close the channel 😭

[jaunty remnant]

How bro??

[pliant quarry]

just tell me about some websites, books or something

[craggy spear]

Watch yt videos thst allign with ur topic

[pliant quarry]

what yt channel

[queen dragon]

Try khan academy

[jaunty remnant]

Use KA bro

[craggy spear]

Khan academy is good too

[pliant quarry]

i do use khan academy, helpful

[queen dragon]

Professor leonard comes to mind

[pliant quarry]

but not enough, some videos feel vague

[pliant quarry]

link

[queen dragon]

Search it on yt

[pliant quarry]

okay.

[jaunty remnant]

You don't have to worry if it 10th and 8th

[queen dragon]

Its a famous channel

[stuck flint]

Bro you don't need to research and shit for grade 4 😭

[uncut nexus]

Age 10 bro

[jaunty remnant]

but you should worry for this much gap lol

[stuck flint]

Just remember all the multiple upto 20 😭

[queen dragon]

He just said that his skill level is 4th grade

[stuck flint]

Tell me what's 17 times 7

[uncut nexus]

That’s what I’m saying when you look back few years later you’ll notice you were worrying for no reason

[stuck flint]

Without calculator

[queen dragon]

Hes not a 4th grader

[stuck flint]

Yeah fr

[pliant quarry]

am i not stating this clearly? i am 13, but my level of mathematics is comparable to fourth grade.

[uncut nexus]

Oh okay

[pliant quarry]

and now i am forced to learn maths

[stuck flint]

Bro then what's your orginal grade ?

[uncut nexus]

Why you say “ban:(“ when we ask your age then bro 13 is enough to use discord 😭

[stuck flint]

Bro's definitely 13-

[pliant quarry]

i thought 13 is young for discord

[queen dragon]

The fire went down quick

[jaunty remnant]

oh

i too dk

[uncut nexus]

I think we should help instead of investigating tho lol

[pliant quarry]

i agree ):

[stuck flint]

He's just saying he needs resources

[queen dragon]

I assume you are a sixth grader

[stuck flint]

Resources for exactly what level

[queen dragon]

So you gotta learn basic algebra

[rain arch]

if u need help can't u go to discussion instead

[pliant quarry]

i just searched professor leonard

[rain arch]

this is for help with math questions

[pliant quarry]

his videos are like, mostly around algebra and calculus

[queen dragon]

He covers algebra

[pliant quarry]

Pre-algebra?

[queen dragon]

I assume you just need to learn factorisation and whatnot

[stuck flint]

You already know all the resources

Now you need to study

[queen dragon]

I think he covers that too, KA is better for that though

[pliant quarry]

@asm recommended professor leonard to me just now in this chat.

[queen dragon]

I was not sure what grade you were in

[pliant quarry]

it's okay

but any advice for a beginner

not calculus

[queen dragon]

Do problems, thats all

[pliant quarry]

where

any websites or books?

[jaunty remnant]

ka

[queen dragon]

Are you looking for problem sets?

[pliant quarry]

i am looking for: tutorials, courses, books and more

[uncut nexus]

You can buy a book with math problems suitable for your grade and your country’s curriculum. Just ask your teacher for a book to recommend and start solving it

[pliant quarry]

okay

but that wouldn't be enough

[uncut nexus]

What topics are needed in 6th grade changes a bit depending on where you are

[pliant quarry]

what?

[queen dragon]

You could practice these

[pliant quarry]

math changes depending by country?

[queen dragon]

Kind of

[uncut nexus]

What they teach to 6th graders*

[astral ruin]

yeah, it could help us if you stated clearly or gave us example of exactly the type of problem you are trying to solve/deal with

[uncut nexus]

These look disgusting wow

[queen dragon]

True

[astral ruin]

because you saying pre-algebra

[trim wraith]

Facts

[astral ruin]

all i can do is add https://www.youtube.com/watch?v=vhm8ri0XNBM&list=PL0o_zxa4K1BVoTlaXWFcFZ7fU3RvmFMMG

[pliant quarry]

then why did you give them to me if you find them disgusting?

[uncut nexus]

The organic chemistry tutor mentioned

[pliant quarry]

another tutor?

let me check

[astral ruin]

he has a nice playlist

[queen dragon]

Hey its not that bad

[astral ruin]

on pre-algebra

[pliant quarry]

forget about it.

[pliant quarry]

thank you

i think the tutorial is enough help for now

I will search more websites and resources myself

[queen dragon]

I dont think you need more than organic chem tutor

[pliant quarry]

for now, the tutorial, and other things like (KA for example) are enough

[queen dragon]

Gotta start practicing

[astral ruin]

what would be a more productive way of using these channel is that once you have a question you are stuck on post it here then we can concretely help tbh

[pliant quarry]

you are right

[worn geyser]

you could also try going through your old math workbooks like last years

[pliant quarry]

i should practice, and actually ask questions

that would be more productive

[pliant quarry]

yeah, now that i am using the internet that would work

okay

thanks to everyone for helping me

[queen dragon]

Good luck

[pliant quarry]

i will close the channel now

[astral ruin]

i would also say’s, like others, that you need to clarify what you need with your teacher

[pliant quarry]

Goodbye!

.close

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Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[modern frost]

i need someone to verify my answer

[modern frost]

i split it into two integrals

actually ill split into 3 first then merge two

$$\int_{C_1} 6x , ds$$
$$\textbf{r}(t) = \langle t, 3 + t^2 \rangle \implies || \textbf{r}'(t) || = \sqrt{1 + 4t^2}$$
$$\implies \int_{-2}^{0} 6t\sqrt{1 + 4t^2} , dt$$

[grizzled pagoda]

MARETU

[modern frost]

$$\int_{C_2} 6x , ds$$
$$\textbf{r}(t) = \langle t, 3 - t^2 \rangle \implies || \textbf{r}'(t) || = \sqrt{1 + 4t^2}$$
$$\implies \int_{0}^{2} 6t\sqrt{1 + 4t^2} , dt$$

[grizzled pagoda]

MARETU

[modern frost]

so $\int_{C_1} 6x , ds + \int_{C_2} 6x , ds = \int_{-2}^{2} 6t\sqrt{1 + 4t^2}$, which after a quick u-sub resolves to 0

[grizzled pagoda]

MARETU

[modern frost]

$$\int_{C_3} 6x , ds$$
$$\textbf{r}(t) = \langle 2 - 3t, -1 - t \rangle \implies || \textbf{r}'(t) || = \sqrt{10}$$
$$\implies \sqrt{10} \int_0^1 12 - 18t , dt = \boxed{3\sqrt{10}}$$

[grizzled pagoda]

MARETU

[modern frost]

so $\int_C 6x , ds = \boxed{3\sqrt{10}}$

[grizzled pagoda]

MARETU

[modern frost]

is this correct?

[elder harbor]

,w int from 0 to 1 6(2-3t)sqrt{10} dt

[grizzled pagoda]

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[elder harbor]

seems

good?

[pallid canopy]

Looks right

[modern frost]

thanks

.close

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Channel closed

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

https://youtu.be/AQkDEYIsCS8?feature=shared

[orchid patrol]

So I don't get how his proof at the end works

[elder harbor]

how so

[rich elm]

Write the number of paths to a node inside the node
And represent it as combinations with n being the length of the path and r being the number of right turns
That's how I think about Pascal's triangle

[elder harbor]

to pick 4 things from 6 things

let's say 1 of the 6 balls is pink aka unique

[rich elm]

For pascals identity you just add up the number of paths to each parent node

[orchid patrol]

So he says 6 choose 4 can be made of 5 choose 3 and 5 choose 4. So he says this is possible because if he has has 6 beads and he highlights one that he wants to use and says that he then has 5 left so he can choose 3 and that's 5 choose 3 but if he doesn't choose that bead he needs to choose 4 from 5

[orchid patrol]

Yes I understand this but I don't get how choose things out of 5 can be 6

[elder harbor]

so

there are two cases of choosing the 6 thing

1. i get the pink one first and then i pick the rest

2. i dont get the pink one (cuz ill ignore it) and ill get the remaining

[orchid patrol]

Yes but we are always choosing out of 5

[elder harbor]

yes

cuz the first step is actually to pick the pink one

for 1.

in its full form

[ \binom{1}{1} \cdot \binom{5}{3}]

[grizzled pagoda]

k

[orchid patrol]

Yes I understand you either choose pink or don't so then you get 5 choose 3 or 5 choose 4

[elder harbor]

yes

[orchid patrol]

What does this equal ?

[elder harbor]

this is equal to the first case

right?

for the first case:

1. i pick the pink ball out first so i choose that 1 thing out of the 1 option that i have
2. then i will go on to pick the remaining 5 balls whatever they may be

[orchid patrol]

Yes but like how can you compute it

[elder harbor]

well

1C1 is trivially 1, do u agree?

[elder harbor]

this is how i set up the computation

[orchid patrol]

Ok I guess because you are still technically choosing out of 6 things. But then in the second case you are just choosing out of 5

[elder harbor]

that is correct

[orchid patrol]

Ye but I don't understand why but I can't get around how this addition means there equal

[elder harbor]

in the second case, the pink ball is completely ignored

[orchid patrol]

Like sure I understand how the proof works but I don't see why it proves it

[elder harbor]

addition principle of counting

[elder harbor]

these two are disjoints, no?

[orchid patrol]

Well no right? Since both sets definitely don't have the pink element but the rest of the three can be the same

[elder harbor]

the first one has

the first set is {pink, smth, smth, smth}

the second set is {smth, smth, smth, smth}

and smth is not pink

[orchid patrol]

Also by this do you mean the computer value if 6c4 is the same as the sum of 5c3+5c4

[elder harbor]

yes

[orchid patrol]

Yes but for disjoint I thought it had to have no elements in common

[orchid patrol]

What are cardinalities?

[elder harbor]

size of set

fancy word

but do u get that these 2 cases are disjoint

[orchid patrol]

No sorry

[orchid patrol]

.

[elder harbor]

ok so for case 1

it's the set

[crystal swan]

hican someone help me with this question?

[elder harbor]

of element in this form {pink, smth, smth, smth}

[elder harbor]

open ur channel plz

[crystal swan]

how do i do that

[elder harbor]

#help-38

[crystal swan]

thanks

[elder harbor]

so in full

the sets for case is {{pink, smth, smth, smth}, {pink, smth, smth, smth}, {pink, smth, smth, smth}, ...}

it's a set of sets

[orchid patrol]

Ok oh so each element in this set is a set and those don't match with the other sets in the set of sets for case 2

Sorry I was thinking about single sets

[elder harbor]

yup

[elder harbor]

thats fine. i understand sets can be confusing 😭

[orchid patrol]

Ok so going back to your definition here. Would task mean 6c4?

[elder harbor]

yup

choosing 4 balls from 6 balls

[orchid patrol]

Ok so 6c4 can be made up of choosing from other sets that have no elements in common

But cant you make it from other sets then

[elder harbor]

could u elaborate

[elder harbor]

yes u can make it

like

pink, blue, and 2 other elements

[orchid patrol]

But even with this definition I feel like it is like the marble thing. Like I still don't get it intituivitly

[orchid patrol]

Can we not find a different combination of two things that equal 6c4?

[elder harbor]

hmm

i think there is

but this is prolly the chillest one

[orchid patrol]

So can't our marble example be disproved then

[elder harbor]

4 = 2 + 2 and 4 = 1+3

dont disprove that 2+2 = 4

[orchid patrol]

Ok i just fixed my issue which was I was stuck on the fact that your choosing from a different amount of things. But the solution is as long as the number of choosing things is the same then it should be good

[elder harbor]

its just a different way to view the same process

essentially

[orchid patrol]

Ye

Ok thank you so much for helping me

[elder harbor]

hope my explanation helps

👍

[orchid patrol]

Ye it was great

.close

[amber wasp]

Channel closed

Closed by @orchid patrol

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

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[raven mortar]

the sum of first 20 terms of series 5+11+19+29+41 is......

[elder harbor]

have u found

the explicit formula

for the sequence/series

[raven mortar]

lemme send the sol^n i did

The wrong sol^n

[ripe cipher]

some of the digits are hard to read/distinguish in this picture...

especially 4 vs. 9

[raven mortar]

im really soryy 1st line
S= 5+11+19+29+41

[ripe cipher]

anyway i see you got the 20th term as 461

which at least looks reasonable

but then you treated your original progression like an AP and applied the AP sum formula

when it's not an AP

so you can't do that

[raven mortar]

i thought that ive got last term so....... .

[ripe cipher]

first and last term are enough for AP only

(and maybe GP if you stretch a bit)

do you understand why it is wrong to apply the AP sum formula to a series that is not AP

[raven mortar]

yeah now i thought and understood
actually i did that bcoz i had no other options

[ripe cipher]

yours is a quadratic progression

[raven mortar]

my my whats that
can i solve this even without it

[ripe cipher]

it's a sequence/progression/whatever where the n'th term rule is a quadratic function of n

[raven mortar]

one like this?

[ripe cipher]

no this looks like GP

geometric

quadratic isnt the same

[raven mortar]

my teacher never told me anything like that indeed

[marble apex]

I mean cant he solve it like

Finding sum of first 20 squares

And firs 20 numbers

[ripe cipher]

sure eventually you can

but without proper terminology and notation it will be a struggle

and with the big barrier of "teacher never taught this" it will also be a struggle

so it's a struggle^2

[marble apex]

I mean sn a²

• Sn a should give the same answer

[marble apex]

True that

Cause from the pattern i see its

[ripe cipher]

i worked out the rule for the sequence

not sure if it's worth spilling the beans on that here

[marble apex]

I see

[raven mortar]

in such series we are only told to just substract as u can see there i know nothing else

is it the actual method

that teacher taught us

series having difference in AP

[marble apex]

I don't think so

Since it isnt forming AP in difference too

No it is

Mb

Its 6 8 10

[raven mortar]

??

any formula for sum of terms of quadratic progression

[ionic leaf]

what's the general term?

If by quadratic progression you mean sum of squares then yeah there is a formula

[ripe cipher]

you want something to mug up?

[raven mortar]

lets try

[ionic leaf]

hmm

[grizzled pagoda]

dyxn

[raven mortar]

ik this

[gleaming forge]

something like this i m getting this pattern 5, 11, 19 where difference is in ap with a = 6 and d = 2 and then

[raven mortar]

a lot ppl gathered just to solve a JEE Question

[marble apex]

You will have to make sure to subtract 1 from result though

If u use formula

Cause u are starting from 2²

[ionic leaf]

you must know sigma notation

[raven mortar]

quadratic progression isnt like that
i can substract excess no out of formula

[raven mortar]

c'mon im no that naive i do know

[ionic leaf]

yeah

so

did you find the general term

[raven mortar]

nope whats that

[gleaming forge]

is this this question only??

[raven mortar]

yeah

[gleaming forge]

ok

[raven mortar]

hmm

[ionic leaf]

If you have $a_1 + a_2 + \cdots + a_n + \cdots + a_{20}$, have you found $a_n$

[grizzled pagoda]

dyxn

[raven mortar]

and what an here

[marble apex]

The general term is like what follows after sigma

[raven mortar]

a10?

[ionic leaf]

Basically we wanna rewrite your sum as $\displaystyle \sum_{k = 1}^{20} a_k$

[grizzled pagoda]

dyxn

[ionic leaf]

the general term

[raven mortar]

yeah

[marble apex]

Here the term is a²+b

[ionic leaf]

Is English hard for you to work in @raven mortar ?

[raven mortar]

not at all

[ionic leaf]

Well okay

[ionic leaf]

Does this make sense

[raven mortar]

how

[raven mortar]

nope it doesnt it Ap

[marble apex]

A is like ur square series ranging from 2 -21 since u need to find 20 terms

And b starts from 1

[gleaming forge]

i have something wait

[marble apex]

Cus its 4+1 then 9+2 then 16+3 and so on

[raven mortar]

oh well did

now i can solve my self

[gleaming forge]

wow

noice

[gleaming forge]

smart af

[marble apex]

The term which forms the base of AP is general term

[raven mortar]

truly good

[gleaming forge]

what about this @marble apex

[raven mortar]

whats the answer u got

[marble apex]

Ngl i cant seem to get what you hv done here

[gleaming forge]

i didnt solve the squares method is better

[raven mortar]

true indeed but answer?

[gleaming forge]

leave it behind smh

[raven mortar]

what anser u are getting im stil getting wrong

[marble apex]

Should be around 3000 i think

[raven mortar]

yeah its above that

[marble apex]

3520

Did you add the rest?

Like 1 + 2 + 3 terms?

[raven mortar]

yes

[gleaming forge]

im getting 3079

[raven mortar]

nachti is right

[gleaming forge]

how

[marble apex]

Are your calc correct?

[gleaming forge]

yes

[raven mortar]

ur approach would have issue

[marble apex]

Yeah i think

But it should work

[raven mortar]

ty natch i had underestimated u very before but u r so good which country?

i cant understand his method

[gleaming forge]

no i did the same method as nachti

\the square one

im still getting wrong tho

[marble apex]

No i am getting correct answer

[raven mortar]

send me a proper image portrait not landscape

u do natch

[raven mortar]

which country?

[marble apex]

U need to find sum of all square till 21

[ember ether]

Chaos

[marble apex]

Ind

[raven mortar]

same my my

[marble apex]

Then add sum of first 20 digits

[raven mortar]

really sorry sir i apologies im new i wont repeat it

[marble apex]

I mean i legit used a calc to see if i did wrong but i am getting correct anwer smh

[gleaming forge]

isnt it 1+4+9+16..... + 2+3+4...+20

[marble apex]

Yeah

[marble apex]

No

U cant take 1

[gleaming forge]

why

[marble apex]

Its not there

[raven mortar]

use formulas

[marble apex]

It starts from 2

[marble apex]

Yeah

[gleaming forge]

5=1+4

[raven mortar]

and -1 from it coz it start from 2

[marble apex]

U said 1+4+9 thats what i am talking about

[marble apex]

Exactly you need n=21

[gleaming forge]

ohhh

okkkk

i get it

[raven mortar]

it was a good question

[gleaming forge]

shit

[marble apex]

And then -1

And add 1-20

[gleaming forge]

whyyy

ok

[marble apex]

Because then ull get 3521

As 1 isnt a term in question

[raven mortar]

n(n+1)/2 sum of n positive no.

[marble apex]

Yeah

[raven mortar]

its 10th grade maths formula

[marble apex]

So ([{n(n+1)(2n+1)}/6]-1)+n(n+1)/2 should give the answer

Where n in first bracket is 21

And n after term 1 is 20

[raven mortar]

close

[marble apex]

Did u get the answer?

[raven mortar]

obviously a lot before

just with u as soon as u told method

[marble apex]

Its . close

[raven mortar]

yeah i was just asking if i should close iy

it*

.close

[amber wasp]

Channel closed

Closed by @raven mortar

Use .reopen if this was a mistake.

[raven mortar]

.reopen

[amber wasp]

✅

[marble apex]

I mean u got the answer

[raven mortar]

yeah

[gleaming forge]

am getting 3443

help me plij

plij dont laph

halp

[marble apex]

Calc mistake atp

Just use a calculator

[gleaming forge]

i did

[raven mortar]

.close

[amber wasp]

Channel closed

Closed by @raven mortar

Use .reopen if this was a mistake.

[raven mortar]

.reopen

[amber wasp]

✅

[gleaming forge]

thanku

colse it out probably a calc error

[raven mortar]

it would be like with formula and values
21(22)(43)/6 - 1 + (20)(21)/2

3311-1+210

[gleaming forge]

i get it now

[raven mortar]

3520

oh my finally

[gleaming forge]

i wrote 2n+1 as 42 insted 43

[solar gust]

<@&268886789983436800>

[gleaming forge]

idk why im having a really hard time today

[ripe cipher]

oh fuck i was sniped

was about to report the macbook guy

[solar gust]

Me too actually

[sterile nymph]

I was already in the process of banning them

But someone else got them before me

[solar gust]

Lucky luke

[raven mortar]

whatll u get by that

[gleaming forge]

is it not allowed?

[vernal bobcat]

Man I really wanted that mbp too it was free

[sterile nymph]

Spamming a scam? Of course it's not allowed

[solar gust]

Even if its not a scam, its a math server, not ebay

[ripe cipher]

huh?

[raven mortar]

sry

by the fact, we solved the question

.close ty everyone bye good night

[amber wasp]

Channel closed

Closed by @raven mortar

Use .reopen if this was a mistake.

[turbid pebble]

I had a question, can anyone solve??

[gleaming forge]

create a new help channel this one bout to close

[sterile nymph]

^

[turbid pebble]

Ahh okok I see

[elder harbor]

GOJO SATORU???

[turbid pebble]

haha yess !!

[sterile nymph]

!help if you need help with figuring out how to open a channel

[amber wasp]

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

[turbid pebble]

But I don't have the permission to create

!help

[amber wasp]

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

[elder harbor]

#help-6

[fluid wren]

Post your question in one of the available help channels

[solar gust]

You do, talk in the above channel

[turbid pebble]

Ahhh okkk

[turbid pebble]

Yeahh got it now

Thanks everyone ❤️

[amber wasp]

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[turbid pebble]

This is a question I am having problem with...

[sterile nymph]

Ok, so how can these two expressions be equal? There are two ways.

[late birch]

actually i think there are 4 cases

[sterile nymph]

There are likely more than 4 solutions, but broadly two different ways you get them

[late birch]

oh i think i see what you meant

[turbid pebble]

hmm I was thinking the same

[late birch]

!nosols

[amber wasp]

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.

[split sail]

right

Thing about the terms in terms of a,b,c and imagine the different cases

[sterile nymph]

@turbid pebble first I'd like to draw your attention to the fact that the two bases for the exponents are the same

[turbid pebble]

hmm so powers will be equal

[sterile nymph]

That is one way!

But there's another

Leading question, are there any values for which the base makes it so that the exponent is irrelevant?

Values a such that a^x = c for all x, where c is a constant

[turbid pebble]

Can we take log on both sides??

[sterile nymph]

You're jumping ahead a little bit

[turbid pebble]

nah, I don't think so

[turbid pebble]

ohh

[sterile nymph]

Well, what if the base is 1?

[turbid pebble]

hmm right I never thought that

[sterile nymph]

Is there another case?

[turbid pebble]

Then we will have to find the domain too

[split sail]

Did someone just say domain?

[turbid pebble]

Ahhh not that one !!!

[split sail]

:]

[turbid pebble]

It's the possible values of x which satisfies the equation

[split sail]

Yup you should think of the whole quadratic as a,b,c and then try to fit different cases

For example the one you already did a^b =a^c when b=c

[turbid pebble]

hmm I understand

[sterile nymph]

Well, a^b = a^c only implies b=c when a isn't a special sort of value

Like if we have a = -5 and b and c are not whole numbers, then it doesn't work

Unless you introduce complex numbers

[split sail]

0^0 is not defined but b can't be 0

[sterile nymph]

0^0 is typically defined to be 1

[turbid pebble]

What I get is that if we divide both sides by a^c, and make RHS = 1... we get a^(b-c) = 1, which is ultimately a^(b-c) = a^0, and then we can make the powers equal and calculate roots of quadratic.... then we will take it's intersection with domain of x

[split sail]

No that's not true

[turbid pebble]

But it should be undefined ig

[sterile nymph]

Depends on context. But we can allow it to be undefined for this problem

It won't affect the result

[turbid pebble]

hmm okok

[split sail]

I mean if it's a limiting value them only its 1

[split sail]

But yea

a^b = a^c

b = c

What else do we have mr satorou

[sterile nymph]

Take the log base a of both sides, which is only possible if a is a nice number

[split sail]

Then a can't be 0 in that case

[sterile nymph]

If a is not a nice number then we have to handle that case separately

[turbid pebble]

okk

[turbid pebble]

done

[sterile nymph]

So what numbers don't play nice at the bottom of log?

[split sail]

Taking log won't do any good

[sterile nymph]

a^b = a^c => b = c is exactly the process of taking the log

You just hid the step

[split sail]

You'd still be cases then

[sterile nymph]

Yes, you need to work the cases separately

[split sail]

for a =!0

Yea so conclusion

a^b=a^c when mr gojo?

I think he's gone

[turbid pebble]

Nahh just trying by own

[sterile nymph]

!nosols

[amber wasp]

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.

[sterile nymph]

@jovial field ^

Also there are other ways this can be true

[jovial field]

Yes like that's why I told some

👍

Ok ok I get it

Sorry mb

Oh wait right

[sterile nymph]

There are many ways this can be true and I'm trying to get gojo to think it through

[ember ether]

Oh the powers in the brackets are the same, phew- almost started when i saw quad^quad

[turbid pebble]

Yess I got it now 👍

[sterile nymph]

Ok, so what cases do you have?

[split sail]

Think about what a can be so that the b=c case does not take into account

[sterile nymph]

Did he disappear?

[late birch]

he's helping in another channel lol

[jovial field]

What

[turbid pebble]

Sorry, but I got that ans'

[jovial field]

Noice

Good work

[sterile nymph]

@turbid pebble as in you've finished the problem, and your answer checks correctly with the autograder?

[turbid pebble]

It's really a big answer

[turbid pebble]

hmm yess

[jovial field]

Noice you can close the channel by .close

[turbid pebble]

ahh okk

.close

[amber wasp]

Channel closed

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Use .reopen if this was a mistake.

[jovial field]

Noice

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[last mango]

For 2

I know the phase shift is pi/3

Isn't the amplitude 2 in this case though?

[true jackal]

No

Amplitude is the number in front of the function sin (or cos)

In general, A•sin(ω(x - φ)) + k

A is the amplitude

[last mango]

Sorry I meant period

[true jackal]

Nope

2 is the angular frequency, which is 2π/T

So the period T is 2π/ω. Hence, 2π/2 in this case

Therefore the period is π

[last mango]

I said that

😭

None of the answers have a 2 in em. tho

[true jackal]

Because indeed the amplitude is 3

[last mango]

It says "phase shift, period, and amplitude"

[true jackal]

Yeah

[last mango]

So pi/3, 2, 3

I tbgount

[true jackal]

So π/3, π, 3

[true jackal]

Why 2?

[last mango]

Oh nvm

Can you explain in simpler where that pi comes from

[true jackal]

I wrote it above...

[last mango]

simpler

So you just take that number and do 2pi/that number

Allways?

Like if there was a 5 instead of a 2 it would be 2pi/5

[opaque idol]

T= 2pi/omega

do you agree with this formula

are you aware of its origin

[last mango]

I just wanna know if my question is correct

Instead of confusing me

[opaque idol]

sure it would work concerning the function if type of
f(x) = sin(ax+-kt) +c
period = 2pi/a

[last mango]

The textbook says it's A)

Not D

Anyone know why

.close

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[ionic bison]

what was wrong with this answer?

[ionic bison]

I got 4.3 but there was no closer option

[autumn jungle]

Are you allowed to use calculator?

[ionic bison]

well this isnt graded, but even if it was yes

it's a practice thing to prep for the final but i submitted my answers and it doesn't tell me what the right answer is for the ones I got wrong

[autumn jungle]

Oh then don't you just need to plug that into a calculator?

[ionic bison]

I did, i got 4.3

rounded to nearest tenth

[autumn jungle]

My calculator tells a different story

Double check if you made any typos

[ionic bison]

now I'm getting 6.4??

[autumn jungle]

Typo again

Okay I wonder what on earth u typed onto ur calc

Take a screen shot

[ionic bison]

oh nvmd that one was bc of a typo ur right

[autumn jungle]

Yeah js be careful with ques like these

[ionic bison]

im being lazy and using google instead of my handheld calculator and it did this

dont laugh at me

[autumn jungle]

I couldn't help but laugh 💀

Well you should close the channel now

[ionic bison]

oh

yeeah

i need glasses

thank you!

.close

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Channel closed

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wanton harbor]

For question 3, I did 10x^4 + 1

[lusty pine]

d/dx of a constant is 0

[wanton harbor]

How

What’s the power of that 1?

Is it 0 or 1

[lusty pine]

the power of a constant is 0

9 is 9x^0

[wanton harbor]

And u know that that a power of a constant is 0 which equals to 1

[wind osprey]

And the devirative of a any constant is 0

Basically think of it as that number ×x^0

When u differentiate you get that exponent out right?

Well a 0 multiplied by anything is 0

Just

Make every constant disappear when u differentiate it

2x^5 +1 is like

2x^5 +x^0 right?

Now we do the usual stuff

2×5x^4 + 0×x^-1 and yeah. It disappears

Same goes for the other one

2x^5 -7 is like

2x^5 -7x^0

And

2×5x^4 -7×0×x^-1 and yeah. It disappears again

All constants disappear

@wanton harbor

[wanton harbor]

@wind osprey Wait so that 1 has a power of 0 which makes it 0x1

Which equals to 0

Is that how it is seen

[wind osprey]

Exactly

Yes

So now always erase them constants 🔥🔥

Fuck em

[wanton harbor]

Lmao

I forgot my power rules for

Exponents of 0 and 1

I can’t find the difference

[wind osprey]

Power of 1 is just yeah. The x disappears and u only have the constant

(5x)'=5×1×x^0 wich is 5

When its a constant its 0

Think of it like that

[wanton harbor]

Wait wait it would make the constant 1 as such —-> 0x1^-1

Right

[wind osprey]

Hmm?

Wich one

[wind osprey]

This?

[wanton harbor]

The constant we were talking about

[wind osprey]

Any constant is already multiplied by x^0

Its 1

Everything is multiplied by 1

So constants always go to 0

[wanton harbor]

So this happens before it even becoming an exponent as -1

Which doesn’t exist

Correct?

[wind osprey]

Dont overthink it

I gave u an example just to understand why they disappear

Its actually like this deviratives are the speed of growth of a function

Constant functions never increase neither decrease

So their state of change is always 0

They're called constants because they dont change wether we mess with x or not

Thats why they disappear when we differentiate them

[wanton harbor]

Ahh makes sense

Thanks 🙏

.close

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[split sail]

i dont how to use the 12 to get AD

[grizzled plume]

Greetings

[split sail]

hello

[grizzled plume]

What have you tried?

[split sail]

i tried to use the square

to get GD

but i figured that wont work

[grizzled plume]

Can you find a way to relate the area of the square to that of the rectangle?

[split sail]

ok

[grizzled plume]

what

[grizzled plume]

see my previous message

[split sail]

sure

[grizzled plume]

there is a nice way to finish this question by using an area argument

[solemn escarp]

yeah rhat might be more complicated, nvm

[split sail]

not rlly sure about what you mean

[grizzled plume]

Alright ill tell you

Connect GC

Do you see something?

[split sail]

GC

wait is GC = AD

[split sail]

im not too sure

@grizzled plume wat else can i try?

[grizzled plume]

What can you conclude about the area of GBC

[split sail]

its half of BEFG?

[grizzled plume]

Yes

And?

[split sail]

And since the square BEFG is adjacent to b

[split sail]

the area of triangle gbc helps realate dimensions of height of saquare of ad

[grizzled plume]

what

The thing i was going for was

[split sail]

?

[grizzled plume]

GBC is half GBEF

And is also half ABCD

Can you see how?

[split sail]

um

yea

[split sail]

yea

[grizzled plume]

Were done

So ABCD is GBEF

(area)

[split sail]

yea

[grizzled plume]

can you do from here?

[split sail]

yea its 13.5?

wait

[grizzled plume]

,w 18^2/12

[grizzled pagoda]

Results provided by WolframAlpha

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Requested by craze.cv

[split sail]

ok

[grizzled plume]

Do you understand?

[split sail]

yes, thank you

[grizzled plume]

Yay

[grizzled plume]

np

!done

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

[split sail]

.close

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[covert mountain]

my idea is i could find the taylor polynomial of f and g and prove f and g are analytic

[covert mountain]

wait i need to try smth rq

so i have the taylor polynomial of $f$ about $x=a$ is $f(a) \cdot \sum_{n=0}^{\infty} \frac{(x-a)^n}{n!}$

not that

[grizzled pagoda]

Julian

[covert mountain]

so i have the taylor polynomial of $g$ about $x=a$ is $g(a) \cdot \sum_{n=0}^{\infty} \frac{(x-a)^n}{n!}$

[grizzled pagoda]

Julian

[covert mountain]

im unfamiliar with the theory of taylor polynomial but how do i go about proving it converges to the function?

well the reason im tryna do it this way is

it eliminates a few of the later questions in 1

alright ill try that

.close

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[covert mountain]

thanks

[covert mountain]

.reopen

[amber wasp]

✅ Original question: #help-41 message

[covert mountain]

for the taylor of f i have remainder
$R_k(x)=f(x)- f(a) \cdot \sum_{n=0}^{k-1} \frac{(x-a)^n}{n!}$

[grizzled pagoda]

Julian

[covert mountain]

kind of stuck

showing it goes to 0

i feel like maybe theres a trick

maybe some linearity trick

.close i gtg

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[serene basin]

how to solve h(i(x))

h(x) = 6 squareroot x+11 - 19

i(x) = (4x - 1)/(8x + 3)

[serene basin]

h(4x-1/8x+3) = 6 squareroot 4x-1/8x+3 + 11 - 19

h(4x-1/8x+3) = 6 squareroot (4x-1)/(8x+3) + (88x + 33)/(8x+3) - 19 ?

.close

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[turbid pulsar]

How do i verify that 8 is the only case where this happens? I verified that 8 is a case where the list is dependent as 2v_1 + 3v_2 = v_3

[pallid canopy]

write equations from the definition of linear dependence

[turbid pulsar]

2a+b+7z = 0
3a-b+3z = 0
a+2b+zc=0?

[pallid canopy]

sure

[turbid pulsar]

ok then, we know c=8 has a soltuion

how do i show that c!=8 does not have a solution?

rref?

[pallid canopy]

only c=8 makes it so that eqn 3 are a linear combination of 1 and 2

[turbid pulsar]

yeah how do i varify that tho

[pallid canopy]

if c!= 8 then the coefficients must be 0

find a, b, z

[turbid pulsar]

in terms of c?

[pallid canopy]

yea try it

there are some theorems that make this easier, so if you've learned some recently, go review them

[turbid pulsar]

ok

[covert mountain]

.reopen

mb

[wide perch]

too late for that, if you have a follow up open a new channel

[turbid pulsar]

.close

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[zinc warren]

bit confused on why they stated by the cancellation law

[zinc warren]

oh wait hmm

I was going to say do we need cancellation law to multiply both sides by the inverse of a^j

but we dont know if that inverse exists

so they are using the cancellation law to do something that I dont quite see yet

m I think I see

$(a^{i-0}) = a^j \implies (a^{i-j+j}) = a^j \implies (a^{i-j})a^j = a^j$

[grizzled pagoda]

Branshi

[zinc warren]

and by cancellation a^{i-j} = 1

[shrewd elm]

yes

and the reason you can cancel is because a^j is nonzero and this is a domain

[zinc warren]

I see ok thank you

.solved

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[brisk jungle]

Is my work have something that need to be corrected??

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@brisk jungle Has your question been resolved?

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