help-27

[restive river]

no problem

mr

rakeja

[humble dirge]

LOL

ok so now i have this

i'd imagine it uses the same principle

[restive river]

errm

[humble dirge]

ok minus the cubed root

it uses the same idea

[restive river]

precisely

the little i forgot the name , the numebr next to the square root

is the denominator

sqrt is 2 cube root is 3 etc etc

so sqrt of x is x^(1/2)

cube root of x is x^(1/3)

so on and so forth

[humble dirge]

so x^8 would become 8/3 and then 4/3

the coefficient isnt immune from the square and cube roots either right?

[restive river]

yup ur right sir

distribute it all

[humble dirge]

gotcha

if im correct.. 5^1/3 and then 5^1/6

[restive river]

it's going to be whateverr umm

5^(1/3*1/6)x^(8*1/3*1/6)

whatever that comes out to

[restive river]

preciseely

u got the gist of it

[humble dirge]

ok sounds good

i'm gonna check the answer sheet quickly to see if i got it

ok yeah i did

thank you so much

i'm gonna depart now lol

.close

[devout snow]

Channel closed

Closed by @humble dirge

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[restive river]

.close

[devout snow]

Channel closed

Closed by @polar wagon

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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Remember:
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[silver hollow]

$\sum\frac{k^{2}}{2^{k}(k+1)!}}$

So I had to find the convergence radius normally I do ratio test but this will give me 1/2 |x| * 0 <1 ?

[woven radish]

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

[silver hollow]

lowkey proud of that latex

[iron kindle]

still has an error though

[silver hollow]

shit happens ;-;

sadly dont got time to learn latex right now

[iron kindle]

also, you can just do $k^2$

[woven radish]

Bonk

[silver hollow]

aaah okay

alright bonk save my day

[iron kindle]

and $2^k$

[woven radish]

Bonk

[silver hollow]

okay but

[iron kindle]

anyway

[silver hollow]

help me please ;-;

[iron kindle]

is there no x?

$\sum\frac{k^2}{2^k(k+1)!}$ is just a sum that diverges or converges

[woven radish]

Bonk

[silver hollow]

eh

there should be

wait

$\sum\frac{k^{2}}{2^{k}(k+1)!}x^k}$

[woven radish]

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

[iron kindle]

from k=0 to inf?

[silver hollow]

yes

didnt know how to do that

[iron kindle]

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

[woven radish]

Bonk

[silver hollow]

aaah okay

yup

thats the one

[iron kindle]

okay so $a_k=\frac{k^2}{2^k(k+1)!}$ right?

[woven radish]

Bonk

[silver hollow]

• $x^k$

[woven radish]

BrettASUS

[silver hollow]

that is cn what you are showing right?

c_k mb

[iron kindle]

we want to turn it into $\sum a_kx^k$, no?

[woven radish]

Bonk

Bonk

[silver hollow]

I thought just ratio test < 1

then we will find the convergence radius ?

[iron kindle]

ah wait

im messing smth up

[silver hollow]

no worries

[iron kindle]

so yeah, a_k+1/a_k<1

write that down

[silver hollow]

sure!

got it

oh huh

now I get something else than first time

[iron kindle]

$\left|\frac{x^{k+1}(k+1)^22^k(k+1)!}{x^kk^22^{k+1}(k+2)!}\right|$

[silver hollow]

$ \frac{1}{2} \abs{x} \lim{\abs{\frac{2k+1}{k+2}}}$

[woven radish]

Bonk

[silver hollow]

i simplified some stuff

wait ill show u

cuz latex is not my friend yet

[iron kindle]

yup, i figured

[silver hollow]

now we must do limit of the 2k+1 k+2

which will just be 2

|x| < 1?

but if I remember correctly the answer was infinite

[iron kindle]

how did you get (2k+1)/(k+2)?

[silver hollow]

omg

dont want to tell u

[iron kindle]

$\frac{(k+1)^2}{k^2(k+2)}$

[silver hollow]

;-;

[woven radish]

Bonk

[silver hollow]

ye

that is better

[iron kindle]

🙂

i already saw what you did

dw

[silver hollow]

sssh

[iron kindle]

as k->inf, what happens?

[silver hollow]

i was trying to do it fast alright

this will go to zero

[iron kindle]

im not in a rush

[iron kindle]

and what does that mean for the ROC?

[silver hollow]

aaaaah

for any x it will always be smaller than <1

for the convergence radius is R

(-inf,inf)

[iron kindle]

yup

[silver hollow]

easy

[iron kindle]

😄

[silver hollow]

and uhm

I had a sum

and we had to calculate |s-s9| <= ?

s= s1 + s2 + s3 + ... + sn ,
so s-s9 , is s10+s11+s12+s13+...+sn

or is that not quite right?

[iron kindle]

depends

[silver hollow]

owh

ill just show the sum

[iron kindle]

i think it should be
s-s9=s1+s2+...+s8+s10+s11+...+sn

[silver hollow]

$\sum_{n=1}^\infty (-1)^{n-1}\frac{n+2}{n^4}$

[iron kindle]

$\sum$

[woven radish]

Bonk

[silver hollow]

ye forgot it

[iron kindle]

just edit your message

\frac, not /frac

[silver hollow]

it was this one

[iron kindle]

one } too many

at the end

perfect, no more errors

so, what about this Q?

[silver hollow]

they said first show that it converges

that was easy

but then

|s-s9| <= ?

[iron kindle]

what?

[silver hollow]

ill try to find the question

but this is what our TA put on the bord

[iron kindle]

$s_n=(-1)^{n-1}\frac{n+2}{n^4}$?

[woven radish]

Bonk

[silver hollow]

aaah we had to give an upperbound on that error

[iron kindle]

having the original is nice 🙂

[silver hollow]

What?

[woven radish]

BrettASUS

[iron kindle]

is there anything above that?

[silver hollow]

this is it

[iron kindle]

hmm

and nothing is said about what s or s9 are?

[silver hollow]

nope

this is the entire question

[iron kindle]

hmm

okay, then im gonna assume $s_k=\sum_{n=1}^\infty (-1)^{n-1}\frac{n+2}{n^4}$

[woven radish]

Bonk

[iron kindle]

btw, this starts at n=1, not n=0 like you said before

[silver hollow]

true!

[iron kindle]

anyway

then |s-s9|=|s10+s11+s12+..|

[silver hollow]

alright

so they just said |s-s9|<=b10

i have no idea why

[iron kindle]

whats b? 😭

[silver hollow]

;-;

i think this is bn

so b10

dont ask me ;-;

thats the entire reason I came here

[iron kindle]

where is this from

[silver hollow]

my TA

[iron kindle]

ah

i think i know

[silver hollow]

W

[iron kindle]

actually, nvm

[silver hollow]

Rip

[iron kindle]

im confused too

[silver hollow]

alright

skip that then

can u help with something else?

[iron kindle]

ill try

[silver hollow]

great

convergence radius again

with maclaurin series

i thought maybe

ln(4(1-(x/4)) = ln(4) + ln(1-(x/4)) ?

then do maclaurin series for the second one?

[iron kindle]

why not just on ln(4-x)?

maclaurin series is a taylor series around x=0, right?

[silver hollow]

cuz the form is only for ln(1+x)?

yes

[iron kindle]

Taylor series: $\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n$

[woven radish]

Bonk

[iron kindle]

Maclaurin series: $\sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!}x^n$

[woven radish]

Bonk

[iron kindle]

so just find f^(n) (0)

[silver hollow]

Okay i dont understand this way at all ;-;

is this correct tho:

[iron kindle]

you know the definition of the taylor and maclaurin series?

[silver hollow]

$\ln{4} + \sum_{n=1}^\infty (-1)^{n-1}\frac{x^n}{n}$

[woven radish]

BrettASUS

[silver hollow]

sadly not

[iron kindle]

.

[iron kindle]

.

i just gave them 🙂

[silver hollow]

hmmm

[silver hollow]

is this correct tho?

[iron kindle]

/n?

[silver hollow]

yes?

[iron kindle]

no

[silver hollow]

omh

i forgot the -4/x

[iron kindle]

why cant you just find it of ln(4-x)?

[iron kindle]

need me to explain the general form?

[silver hollow]

if it is not too complicated

[iron kindle]

so, the maclaurin series is defined as the taylor series around x=0

for a function f

as you can see from my definitions earlier

here, f(x)=ln(4-x)

and we need to find its derivatives

f'(x)=-1/(4-x)

f''(x)=1/(4-x)^2

f'''(x)=-2/(4-x)^3

f''''(x)=6/(4-x)^4

and we need to evaluate these at x=0

f'(0)=-1/4

f''(0)=1/4^2

f'''(0)=-2/4^3

f''''(0)=6/4^4

so, what pattern do we see?

what can we say about $f^{(n)}$?

[woven radish]

Bonk

[silver hollow]

well i see that we divide by x^n ?

and uhm

[iron kindle]

*4^n

and the numerator?

[silver hollow]

true and uhm

(-1)^n and uhm

n!

(-1)^n * n! ?

[iron kindle]

yup

[silver hollow]

alright

[iron kindle]

$f^{(n)}=\frac{(-1)^n(n-1)!}{4^n}$

[woven radish]

Bonk

[silver hollow]

why not n!?

[iron kindle]

look at the 4th derivative

its coefficient is 6

which is 3!

[silver hollow]

aah true

alright

[iron kindle]

so, now we fill this into our series

[silver hollow]

this is so wonderful

[iron kindle]

$\sum_{n=0}^\infty\frac{f^{(n)}(0)}{n!}x^n$

[woven radish]

Bonk

[silver hollow]

i see

and the (n-1)! and n! will just give 1/n

[iron kindle]

remember that f^(0) is just our function

[iron kindle]

yup!

[iron kindle]

$\rightarrow \ln(4)+\sum_{n=1}^\infty\frac{(-1)^n}{4^nn}x^n$

[woven radish]

Bonk

[iron kindle]

f(0)=ln(4)

[silver hollow]

aah isee

alright

thanks 🙂

[iron kindle]

(i knew you were gonna ask it)

[iron kindle]

for n=0, we get f(0)

[silver hollow]

gotta love studying in library at 19:00 ;-;

[iron kindle]

fr

[silver hollow]

i wanna go home

I miss wiskunde B

bro this year so far I have been studying more than in my entire high school years

[iron kindle]

hahaha

it goes so fast doesnt it

[silver hollow]

fr ;-;

[iron kindle]

when icompare the speed at uni to HS im kinda disappointed HS didnt go faster

[silver hollow]

FR

one lecture is like an entire chapter

we have 3 a week 😦

[iron kindle]

so fun 😄

/s

[silver hollow]

yes ;-;

[iron kindle]

HS wouldve beens omuch more itneresting if its went just a bit faster

and it would better preparey ou for uni

[silver hollow]

true

but that wouldnt be fair for people that are not good at math for example

[iron kindle]

but math is a choice subject anyway

wis B can go faster

wis D even more so

[silver hollow]

true

Wiskunde B almost went backwards

I remember when I was going to uni I thought I already knew everything about math

;-;

I was so cocky

[iron kindle]

+1

first year hit hard lol

[silver hollow]

true 😦

[iron kindle]

but youll be fine 😄

[silver hollow]

Next year wont be easier tho

you know what master you want to do ?

I think u said u didnt know yet right?

[iron kindle]

just dont give up, and youll make it through

bro i dont even know if i can finish the bachelor

🤣

[silver hollow]

You definitely can

[silver hollow]

I want to go cum laude tho ;-;

now i am at a 7,6

;/

[iron kindle]

oh damn

i gave up on that quite quikcly lol

but for some its doable

like yourself

[silver hollow]

i guess we will see

alright gotta finish my last few questions then i am going home

thank you bonk 🙂

have a good night

.close

[devout snow]

Channel closed

Closed by @silver hollow

Use .reopen if this was a mistake.

[iron kindle]

u at erasmus library rn?

[silver hollow]

yup

it is beautifulllll

[iron kindle]

ah nice

[silver hollow]

bro at the start of the year

[iron kindle]

i should to the tu library sometime aswlel ngl

[silver hollow]

I thought i would be the only one

[iron kindle]

packed?

oh, empty?

[silver hollow]

i thought so

cuz I was still a rookie universitaity student

[iron kindle]

ig its only packed during exam week

[silver hollow]

true

it is crazy now

[iron kindle]

ye i can imagine

anyway, i gtg

and youre going aswell

have a safe trip home 🙂

[silver hollow]

thank you!

[devout snow]

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[ember solstice]

how do i go about this?

[ember solstice]

I have to subtract the first term from the second

[mystic scarab]

A minus sign before parentheses changes all the signs inside

So A - (B + C) = A **-**B - C

[ember solstice]

Id rather keep the signs as they are while i solve it so i dont get them mixed up as i already have trouble with that

[mystic scarab]

Similarly A - (-B + C) = A **+**B - C

[mystic scarab]

Do what you want, but sooner or later you can't escape from changing the signs ...

[ember solstice]

I know

Thats what im saying, ill end up switching them around so much i wont know what ive done and have to start over again

is is 9a^3 b+6ab-10a^2 b+6a^2 b^2+4?

[mystic scarab]

Yes

[ember solstice]

Ayyyyy!!
i guess it was really confusing bc there was only one uhh common term i could combine

thank you!

.close

[devout snow]

Channel closed

Closed by @ember solstice

Use .reopen if this was a mistake.

[devout snow]

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.

[tropic skiff]

!15min

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[tropic skiff]

$\qty(8 \times 4 \times \frac 92)^2$

[woven radish]

King Leo

[tropic skiff]

is that the problem?

[desert arch]

Hi

[olive snow]

You can use a calc for this tbh

[desert arch]

What are u strugling with

[tropic skiff]

ok, so according to PEMDAS, we evaluate the parentheses first

$8 \times 4 \times \frac 92$

[woven radish]

King Leo

[ripe grove]

chat - calc is short for calculator

[tropic skiff]

we only have multiplication/division here, so try to just evaluate from left to right @keen needle

[desert arch]

Chat is this true?

[tropic skiff]

can you evaluate 32 * 4.5

hint: ||i recommend evaluating (32 / 2) * 9||

[desert arch]

Bruh

[tropic skiff]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[olive snow]

The same as 16*10 - 16

[vital dagger]

16x9 is just 16x10-16

[desert arch]

Just hand us a friggin packet yo

On the real

Jus use a calculator

[mystic scarab]

Or 4²×3², hence 12²

[pseudo basin]

what grade are you in?

[desert arch]

Type shi

Yes

[tropic skiff]

@keen needle if youre on discord, youre supposed to be above 13. but i dont think [this problem](#help-27 message) is given to 13-year-olds

[desert arch]

Lmao

Let him be mate

[mossy rapids]

just study for ur test lil bro

[pseudo basin]

<@&268886789983436800> pointless troll is pointless.

[tropic skiff]

bro's speedrunning getting banned

[tropic skiff]

emphasis on lil

[desert arch]

It is for sure

[pseudo basin]

also not everybody is american @keen needle

[mossy rapids]

bruh what

[pseudo basin]

<@&268886789983436800> this is sounding a little too racist.

[tropic skiff]

i only know a few words in hindi lol

.close waste of time

[devout snow]

Channel closed

Closed by @tropic skiff

Use .reopen if this was a mistake.

[crisp trench]

In reality most people arent

[desert arch]

Let the mods sleep bru

😭

On a math server is crazy

[sour osprey]

interesting thread to randomly open

[vital dagger]

Statistics from the NYU states that 100% of people are American.

[desert arch]

Real

[winter torrent]

now to decide mute vs ban

[mossy rapids]

phew, got timed out, thanks mods

[desert arch]

Defo not albanian

[pseudo basin]

ban already

[mossy rapids]

ban

racist

[sour osprey]

ban

[pseudo basin]

bro spewed politics in here and was vaguely transphobic to me personally

[mossy rapids]

n immature

[pseudo basin]

and also racist elsewhere

[olive snow]

• trolling

[tropic skiff]

lmao

[desert arch]

😭😭

Bro got hit with everything at once

24 hour mute is enough trust

[mossy rapids]

we deciding his public execution

[pseudo basin]

what's it to you lol

[desert arch]

Fun

[mossy rapids]

hes too immature to realise anytg in 24 hrs

[olive snow]

Could be one rock two hits

[tropic skiff]

your role says "undergraduate"

[desert arch]

Whats that mean

[mossy rapids]

.close

already closed i see

[tropic skiff]

#help-27 message

[mossy rapids]

yeah yeah mb

[vital dagger]

Nah trust me. I'm undergrad and I only just started learning my times table.

[devout snow]

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.

[tropic skiff]

oh man

[tropic skiff]

.close

[devout snow]

Channel closed

Closed by @tropic skiff

Use .reopen if this was a mistake.

[tropic skiff]

what is the point of the picture 👀

[vital dagger]

[vital dagger]

To tell you that the original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.)

[tropic skiff]

i meant the bottom half

[olive snow]

A frenchman in New-York (joke/ref to sting song)

[crisp trench]

Looks like a sad frog

[mossy rapids]

frog. sad.

[olive snow]

@vital dagger im french in case

[crisp trench]

Came back for the statue of liberty?

[olive snow]

Nah its a gift we won't take it back

[dense sparrow]

<@&286206848099549185>

i need help

🙂

.open

[desert arch]

Wheres the problem

[dense sparrow]

8x4x9/2

[desert arch]

Lmao

[mystic scarab]

Are you trolling?

[dense sparrow]

i need help

[stable flare]

!15m

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[desert arch]

Is it all square by chance

[olive snow]

Thats the second account lmao

[dense sparrow]

js a coincidence

[desert arch]

🤯

You right you right

[dense sparrow]

i need help

[desert arch]

Might jus be

[dense sparrow]

https://tenor.com/view/e-e-ei-i'm-on-vacation-echo-you-are-going-to-be-the-death-of-me-my-little-sibling-is-obsessed-it's-okay-though-ily-gif-15149604940529451161

[devout snow]

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.

[dense sparrow]

help meeeee

[mystic scarab]

<@&268886789983436800>

[dense sparrow]

<@&268886789983436800>

these helpers arent helping me much

i feel violated

[tropic skiff]

tbf @mystic scarab what did they do

[tropic skiff]

!da2a

[devout snow]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[stable flare]

Please do not abuse Moderator ping

[mystic scarab]

Look above in the chat 😅

[tropic skiff]

oh nvm

[dense sparrow]

i aint do nun bru

[autumn fjord]

you don’t have to discourage mod pings

[tropic skiff]

ok yk what?

[desert arch]

Not the same person 🗣️🗣️

[tropic skiff]

ill help you withy your question

[autumn fjord]

are you going to ask a question?

[tropic skiff]

just dont start bullying ppl for no reason

[dense sparrow]

yes sir

[autumn fjord]

let’s not be antagonistic please

[dense sparrow]

ye thats mean

hurts my feeling

[autumn fjord]

you too

[desert arch]

The answer is 20 736

[tropic skiff]

$8 \times 4 \times \frac 92$

[woven radish]

King Leo

[desert arch]

All squared

[dense sparrow]

ye

i forgot that

[tropic skiff]

@dense sparrow can you evaluate this

[dense sparrow]

no

[desert arch]

Bro its just 20 736

[tropic skiff]

yes, but we're working inside the parentheses before we apply the exponent

[dense sparrow]

yea that

https://tenor.com/view/grater-happy-gif-21739362

[desert arch]

Theres no way to explain basic multiplication brev

Jus put it in a calculator

[dense sparrow]

im special

[dense sparrow]

NO

[tropic skiff]

#help-27 message

[desert arch]

I can tell

[dense sparrow]

❤️

[dense sparrow]

idk whay that is lowk

who is backyard freak

idk him

[tropic skiff]

i never said anything about backyard freak

[dense sparrow]

sound:0:7

[tropic skiff]

.close no point

[crisp trench]

Is this a movie

[devout snow]

Channel closed

Closed by @tropic skiff

Use .reopen if this was a mistake.

[dense sparrow]

yes

[dense sparrow]

i need help bru

[tropic skiff]

.reopen

[devout snow]

✅

[dense sparrow]

helpers aint helping

[desert arch]

Bro

[tropic skiff]

#help-27 message helpees aint accepting help

[desert arch]

It gets to a point

[devout snow]

Helpers are just people volunteering their time to help you. Be polite and patient.

[dense sparrow]

les do a vote

[tropic skiff]

starting from left to right, how do you evaluate $8 \times 4 \times \frac 92$

[woven radish]

King Leo

[desert arch]

Why are you # the channel

[autumn fjord]

keep it on topic please

[dense sparrow]

yes mam

[restive river]

Calculator ahh question

[tropic skiff]

its a link to your message ._.

[desert arch]

@dense sparrow it aint funny nonore gang hate to break it to you

[tropic skiff]

_ _

[restive river]

Why starting from left to right

It's multiplication

Personally starting from right to left is easier

[desert arch]

Its always left to right

[dense sparrow]

type sh

[restive river]

It doesn't matter if it's all multiplication

[desert arch]

Cuz if it was 4x2:3 you wouldnt start from the right would u

[desert arch]

Its just a learning habit

[tropic skiff]

$9 \div 2$

[woven radish]

King Leo

[dense sparrow]

js give me the friggin asnwer yo

[desert arch]

20 736

[dense sparrow]

4.5

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[restive river]

?

[tropic skiff]

$9\div 2$ evaluates differently based on how you read it

[desert arch]

Its a division 🥲

[woven radish]

King Leo

[restive river]

It's a fraction

[dense sparrow]

https://tenor.com/view/wrizz-monkey-monkey-sigma-gif-14012962261800188400

[tropic skiff]

@dense sparrow

[autumn fjord]

they’ve been timed out.

[wicked rover]

.close

[devout snow]

Channel closed

Closed by @wicked rover

Use .reopen if this was a mistake.

[autumn fjord]

not meant as a reply

thanks

[tropic skiff]

lol

[desert arch]

Yh

[autumn fjord]

sorry about that. the channel is going to lock soon so please take the conversation elsewhere

[tropic skiff]

suggestion: mute noobhassan while youre at it

[desert arch]

Tbh i dont mind a lil trollin but it gets to a point

[desert arch]

Lmao

[restive river]

?

[desert arch]

Why

[restive river]

What i said is correct...

It doesn't matter how it's read

If its all multiplication and division here

[wicked rover]

OP has been muted and the channel is closed, everyone pls move on from here

[tropic skiff]

have you heard of cos(x)?

[tropic skiff]

😭

[restive river]

Come dms if you want to argue

[desert arch]

What does cosx have to do with this

[restive river]

He's not the brightest

[desert arch]

Math beef

Love it

[wicked rover]

@restive river @desert arch pls stop using this channel

[desert arch]

But its fun tho 🥲

[pseudo basin]

#chill

[devout snow]

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[muted orchid]

Need help with this exercise, (complex numbers)

[faint gorge]

\bar z ought to be a-bi

[placid rover]

u substituted in z bar wrong

[muted orchid]

oh shit, you're right

What's next?

<@&286206848099549185>

[crisp trench]

Solve it

Imaginary part and real part are all 0

[placid rover]

yes equate real and imaginary parts on both sides of the equation

[muted orchid]

so

a^2 - b^2 + 2a = 1
2ab -2b = 0
?

[devout snow]

@muted orchid Has your question been resolved?

[devout snow]

@muted orchid Has your question been resolved?

[devout snow]

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[remote elbow]

how to do 33

[iron kindle]

,rccw

[runic prawn]

did you do 32

[remote elbow]

no

[runic prawn]

just add the vectors

find the x and y component of each vector then add

[versed garnet]

is

this bearings ?

[remote elbow]

is the components for the second one along the x axis is that just negative 300

or is it positive

idek

is the answer -120i + 173.2j

how tf do u find the angle it makes

with x axis

[remote elbow]

vectors

[lethal pollen]

Me when trigonometry

[remote elbow]

idk how to do it

[devout snow]

@remote elbow Has your question been resolved?

[lethal pollen]

Use arctan

[remote elbow]

2nd

[lethal pollen]

Yes 2nd quadrant

[remote elbow]

i got it

[lethal pollen]

Nice

What'd you get

[versed garnet]

ahh

[remote elbow]

264.4 N , 139 degrees

angle with positive x axis

[lethal pollen]

Probably correct

Ggs

[devout snow]

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[remote elbow]

how to do 35

[midnight echo]

Draw the FBD, the sum of all forces on the x direction must be zero, that will help you.

[remote elbow]

fbd?

[midnight echo]

free body diagram

[midnight echo]

Disregard the text

Decompose the two tensions using trig, you should be able to solve for T1 and T2

[remote elbow]

is there any way we use the length of the two cables

like can we use the length of the two cables then use normal sin and cosine to find the components of each vector

or is that useless information that they gave us the length

[midnight echo]

I dont really see how the lengths of the two cables can be used. Force doesn't depend on the length of the cable.

[devout snow]

@remote elbow Has your question been resolved?

[remote elbow]

ok

[devout snow]

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[charred frigate]

Can I calculate this mathematically? So, i can put it in my lab report showing the work. and if so, how do i start?

[devout snow]

@charred frigate Has your question been resolved?

[charred frigate]

<@&286206848099549185>

[devout snow]

@charred frigate Has your question been resolved?

[charred frigate]

Plss

[charred frigate]

<@&286206848099549185>

[topaz vale]

I'm sorry I have no idea what this is 😭

[charred frigate]

It's Fourier Series!! I just dont remember this topic as much. I forgot it lol.

[topaz vale]

Good luck with that 😭

[charred frigate]

Tyy! I really need it lol

[devout snow]

@charred frigate Has your question been resolved?

[devout snow]

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[pure spindle]

Please and thanks ahead

[devout snow]

@pure spindle Has your question been resolved?

[pure spindle]

<@&286206848099549185>

[pure spindle]

.close

[devout snow]

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[devout snow]

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[shrewd sluice]

The sum of the first 5 members of a infinite decreasing geometric progression, what was the formula for it?

[shrewd sluice]

Is it like the normal geometric progression

[half birch]

yeah

[shrewd sluice]

Ah ok

.close

[devout snow]

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[idle rose]

Complex Number.

[idle rose]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[idle rose]

1

[devout snow]

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[restive river]

Oh, my gosh.

[restive river]

Finally.

sin(π/3x) = e_(2) - x_(2)/2 + |x|

How do I do this?

I am so confused.

[pseudo basin]

... can you post a picture of the question

it looks very odd right now

[restive river]

Oh.

I didn't notice. Hold on.

Someone told me to solve it, but did not give much information.

This is what it looks like written.

I can not tell if it is the first or the second.

[pseudo basin]

uhh

$e_2$??

[woven radish]

ann.in.a.teacup

[pseudo basin]

and $x_2$???

[woven radish]

ann.in.a.teacup

[pseudo basin]

this makes no sense at all now?

[restive river]

Er...

No, it does not...

[solid osprey]

things are definetly missing

[restive river]

Indeed.

Hold on, let me look for more information.

???

Apparently, 2 was not a subscript.

[pseudo basin]

ok well at least now it looks more obvious that this is one of those equations that must be solved by trickery rather than algebra

.....

[restive river]

.

[pseudo basin]

ok this is just awful

[restive river]

I think the person was attempting to make a heart...

[pseudo basin]

who gave you this equation

[restive river]

Some friend.

[devout snow]

@restive river Has your question been resolved?

[devout snow]

Channel closed

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[devout snow]

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[frigid wagon]

Hello everyone I can't recognize which criterion I should apply to study the character of the series.

I have verified the necessary condition but after that I don't know how to continue.

Can anyone give me a little help?

[frigid wagon]

$\sum_{n=2}^\infty \frac{1}{n \space \log_e n}$

[woven radish]

Shadow91518

[pseudo basin]

seems ripe for the integral test

[devout snow]

@frigid wagon Has your question been resolved?

[frigid wagon]

In my textbooks there is no mention of this test

[foggy ermine]

HOW?

[fossil locust]

get a better textbook if this is really the case

[pseudo basin]

what tests do they mention?

maybe they mention it by a different name?

[frigid wagon]

• criterion of comparison
• criterion of infinitesimals
• root criterion
• ratio criterion

[pseudo basin]

what's this "criterion of infinitesimals"?

[frigid wagon]

can I share a link? but is in italian language, I don't know what his name is in English

[pseudo basin]

i can probably figure it out so yes share it here

[frigid wagon]

https://www.andreaminini.org/matematica/serie/teorema-degli-infinitesimi-sulle-serie-numeriche

[pseudo basin]

hm

ok this won't help us unfortunately

[pseudo basin]

are these the only ones that we're permitted

cause i can tell you right away that root and ratio will be useless

comparison is the only hope, and that only if we can find something to compare against

[frigid wagon]

got it, thank you

[pseudo basin]

hm?

you managed to do it?

[frigid wagon]

unfortunately not but I'll try later, thanks for the help

one last thing but can I rewrite the series as $\sum_{n=2}^\infty \frac{1}{ (\log_e n)^n}$ ?

[woven radish]

Shadow91518

[devout snow]

@frigid wagon Has your question been resolved?

[devout snow]

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[devout snow]

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[thin geode]

so we can rewrite it as e^x/x^3 right

but i tried applying l hospitals once but it dont seem to take me anywhwere

[misty crest]

do it three times

conditions are still satisfied

[thin geode]

is that allowed, i though you only do twice

[misty crest]

but you should probably know that e^x outgrows any polynomial

[misty crest]

why wouldn’t it

it’s still inf/inf

[thin geode]

oh ok so i can do it how many times i want

[misty crest]

so long as the conditions are satisfied each time

[thin geode]

but i get e^x/6

[misty crest]

as x -> inf

what do you get

[thin geode]

oh wait it goes to negative infinity

negative infinity for exponential is 0 right

[misty crest]

oh

i didn’t even see that

[thin geode]

wait thats not right

[misty crest]

then you have 0/inf so you have to adjust actually

[thin geode]

oh yeah i could of finished the question after the first derivative

[misty crest]

wdym?

[thin geode]

like e^x/3x^2 or do i have to remove the ^2 term first?

[misty crest]

you can’t do that

[thin geode]

huh

[misty crest]

0/inf is not the proper form

[thin geode]

oh ok, so we do nothing. we just realize that 0/infinity ^3 is just 0

[misty crest]

try writing e^x as 1/e^{-x}

$x^{-3}e^x= \frac{x^{-3}}{e^{-x}}$

[woven radish]

knief

[thin geode]

its not 1/( e^-x * x^3)?

[tawny anvil]

I though 0/inf = 0

[thin geode]

Tara u think this reasoning is right?

[tawny anvil]

I think intuitively it's fine, but doing 3 derivative to make it 0/(-6) make it much clearer

so yes, the logic is sound

[thin geode]

oh yeah thayt makes sense too

[tawny anvil]

ok, I've check, 0/inf is proper, I think knief is thinking 0/0

[thin geode]

wait can you help with this one too, i havent done it with normal logs before

[tawny anvil]

is x suppose to be t?

[thin geode]

huh i think so

must been spelling error

[tawny anvil]

yeah, otherwise it's constant

lemme take a look

[thin geode]

can we rewrite log 2 (t) to ln(t)/ln 2?

[tawny anvil]

yep

[thin geode]

and then we get infinity/infiinty

so we apply l hospitals

?

[tawny anvil]

yes, but I think we can simplify before that no?

[thin geode]

how? like the bracket?

[tawny anvil]

nvm, mistook some property, do l'hos

[thin geode]

i got xln2/ (x+2)

so i must do it again?

[tawny anvil]

yep

[thin geode]

oh yess

i got correct, just ln2

thank you so much

aight have a good day

🫡

.close

[devout snow]

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[tawny anvil]

Good day too

[devout snow]

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[thorn perch]

how do you prove what the derivative of a^(x^2) is, where a is a constant? how does chain rule apply here

[iron kindle]

$a^{x^2}$?

[woven radish]

Bonk

[thorn perch]

yes

[faint gorge]

prove as in with first principles?

[thorn perch]

uhh with anything

[iron kindle]

turn it into e^stuff

then u-sub

as a hint

[thorn perch]

ohh

i think I can prove it with taking natural log

[faint gorge]

implicit differentiation works too yea

assuming a > 0

[thorn perch]

it would apply generally too tho

[faint gorge]

applying log no

[thorn perch]

no the result would

because you can just separate the negative sign

[faint gorge]

log(-1) is undefined

[iron kindle]

https://tenor.com/view/get-real-funny-math-gif-16370759773966566088

[thorn perch]

but if a < 0 it would be complex

right

[faint gorge]

you mean imaginary

[faint gorge]

yea

[iron kindle]

yeye, it was a joke 🙂

[faint gorge]

!nojokes

[thorn perch]

ok i think i only need to consider positive a

i think i got it ty

.close

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[devout snow]

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[toxic pike]

a square and equilateral triangle have a total perimeter of 10. what dimensions will maximize the total area?

[toxic pike]

So this is optimization, but im struggling to understand it ocnceptually. we can express the side length of the square as x and sidelength of the triangle as y, and say 4x+3y=10

[placid rover]

yes that's a good start

[toxic pike]

and the total area is x^2+(sqrt(3)/4)y^2

[placid rover]

yes, say A =

[toxic pike]

rewriting y in terms of x and substituting, the total area is x^2+(sqrt(3)/4)((10-4x)/3)^2

man i need to learn how to use tex

i know you take the derivative next, but i dont understand why, or what to do from there

[placid rover]

right so you have

A = f(x)

agreed?

[whole harness]

$x^2+(\frac{\sqrt(3)}{4})(\frac{10-4x}{3})^2$

[placid rover]

and you want to find x such that A is maximized

[toxic pike]

yea

[woven radish]

ASda

[placid rover]

Assuming f is smooth (you can), then does that answer your question?

You want to find the maximum of f

[toxic pike]

so you take the derivative, find the critical points within x<=10, and test if its a min or max?

[placid rover]

yes

and also test the extremes

in case they are also min/max

[toxic pike]

yea so in this case its a minimum, so test x=0 and x=10

[placid rover]

x = 2.5 i think

[toxic pike]

what is x=2.5?

[placid rover]

4x+3y=10

x = 2.5 at most?

[toxic pike]

ohh

makes sense, ty

.close

[devout snow]

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[hexed sparrow]

answer is like so different from what i got im probably universes away from solving it
3 E

2x^2 - 4x + 1
2(x^2 - 2x) = -1
2(x^2 - 2x - 1^2) = -1 + 2
2 (x-1)^2 = 1
2(x-1)^2 / 2 = 1 / 2
(x-1)^2 = surd 1/2
x-1 = surd 1/2
x-1 = + - surd 1/2

[ripe scroll]

you can't subtract 2 from one side and add to the other

[devout snow]

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[compact hawk]

Does anyone know how to solve this

I got the anwser and it's 6384

But I'm confused on how that's the awnser

[wind mason]

,rccw

[wind mason]

Which number? 27?

[grizzled yew]

u probably want to use picks theorem on 7x+11y<=1001 and subtract 7x+11y=1001 cases

[devout snow]

@compact hawk Has your question been resolved?

[steel tinsel]

Do you have to do it on paper?

Positive including 0?

[compact hawk]

Wdym

[compact hawk]

1001?

[solid osprey]

honestly i would try to find a pattern with diffrent y's, so like
y=91 <=> x=0
y=90 <=> x=1
y=89 <=> x=3
y=88 <=> x=4
but theres prolly a brtter method

[steel tinsel]

Pick's theorem?

[solid osprey]

you would have yo only check 7 cases with y as it would repeat

[grizzled yew]

yes because 1001 is divisible by 7 and 11. this is required for picks theorem to work, look it up if u haven’t seen it before

[solid osprey]

(<=> x=1 means there is only 1 x that holds)

[steel tinsel]

The area of a polygon?

[solid osprey]

isnt picks theorem polygons?

[solid osprey]

basically you should find a pattern with how as y decreases x increases, and you want to sum the ammount of x's

[devout snow]

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[solid osprey]

bro 😭

[grizzled yew]

yes, it works perfectly here

[devout snow]

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[spice forum]

I have no idea where to start, stuck right at the beginning. Could someone walk me through this please?

[lethal pollen]

@spice forum

[valid vector]

$f(x)$ transformed should be $f(x-4)+1$

[woven radish]

mathisfun

[lethal pollen]

I mean I think he could probably have figured it out from the table

But yea

[devout snow]

@spice forum Has your question been resolved?

[devout snow]

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[unique wyvern]

is there a difference between "R" and "r"

im assuming there is

[trail eagle]

Yes

[unique wyvern]

what is the difference

[foggy vault]

what’s the context

[unique wyvern]

im assuming one is real numbers?

[trail eagle]

They’re two different variables

[unique wyvern]

why are they the same letter

like does that mean something

[trail eagle]

The point is they aren’t the same symbol

[foggy vault]

sometimes in physics they use them to denote inner and outer radius

[unique wyvern]

or is it the same as just having x and y

[foggy vault]

it’s just two different variables

[trail eagle]

It doesn’t mean anything they could’ve been a and b

[foggy vault]

X would be different from x

Y is different from y

it’s just a diff variable

[unique wyvern]

okay cool beans

thank you

[trail eagle]

Although as potatomonke pointed out sometimes it’s used in a way that makes sense, like big radius R and small radius r (say for an annulus shape)

So that you’re able to keep up with their meanings easier

[unique wyvern]

okay right

in this context though

the context of "transposing formulas" its just two different variables

like theres no relation between the two

anyway thanks guys

.close

[devout snow]

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[hardy flower]

How do I convert quadratic standard form to vertex form

[hardy flower]

This can solve me 4-5

[valid vector]

,rccw

[valid vector]

Complete the square

[hardy flower]

Yeah but whats the process

[valid vector]

$y=x^2-6x+5$, $y=x^2-6x+9-4$, $y=(x-3)^2-4$

[woven radish]

mathisfun

[hardy flower]

Alr so we factor out a

divide by 2 and square it

[valid vector]

Yes

[hardy flower]

then add and subtract it from the equation

[valid vector]

Mhm

[hardy flower]

What from there

Oh you just factor

[valid vector]

Ye

[hardy flower]

Is number 5

3(x-2)^2-3

no the k is wrong