help-23

[wild bobcat]

Limit instances of A and B as much as possible

My algebra muscles can only stretch so far, so if you think it's as simplified as possible that's all good

Just good to have someone check my work

[grim kraken]

You want me to get back to what you found from that or do you want me to try to simplify the expression you found ?

[wild bobcat]

mmm I guess try to simplify either and see if it can go further. Both are equal, I know that much. But I don't know if that's as far as it goes

[grim kraken]

I am getting there slowly but surely

[wild bobcat]

I appreciate it

[grim kraken]

Well I arrive to something as abject as what you gave me

[grim kraken]

I was truly hoping the fraction would cancel itself when doing the weird thing but no

[wild bobcat]

holy God that's crazy. Well I'm glad I reached out, now I know it has been fully investigated.

My head hurts. Thanks for looking into it haha

/close

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[grim kraken]

I am sorry I made it hurts TwT
It was my pleasure. If you see me some time around and you have the intended simplification feel free to share it

[wild bobcat]

It's part of a math research paper I'm writing, so there unfortunately is not a neat solution I'll be recieving. You helped a lot by drawing it out, I'll keep it on file in case I need to reference it. Thank chu

[grim kraken]

Oh wow my honor I could think about it. Good luck on everything. Here is the full (messy) pdf if you want

[safe radish]

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[vagrant ice]

oooh what topic is it about?

[vagrant ice]

I can't ping you anywhere else

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[celest compass]

Im supposed to prove this with epsilon N definition.
I have given epsilon > 0, Choose N = blank
suppose n>N
check |function-0| = function < function but substitute n for N

[celest compass]

after that though idk how to get epsilon

it doesnt seem like you can solve for N if you set the function equal to epsilon and I can't think of a simple way to find another function which is strictly greater than it

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[celest compass]

<@&286206848099549185>

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@celest compass Has your question been resolved?

[zinc stirrup]

So you need to get that $|\frac{e^{\frac{1}{n}}+3}{n^2} - 0| < \epsilon$ for some n>N. you can simplify the equation down to $frac{1/n} < ln(\epsilon n^2-3)$ or $1 < ln(\epsilon n^2 - 3)^n$. We know that for $n>1, x>1: ln(x) < ln(x)^n$ so proving that $1 < ln(\epsilon n^2 - 3)$ is sufficient. From there we get that $e < \epsilon n^2 - 3$ or $N > \sqrt{\frac{e+3}{\epsilon}}$ for the final solution

[flat frigate]

Goran

[zinc stirrup]

If you need the exact formula you can say that $N=ceil(\sqrt{\frac{e+3}{\epsilon}})$

[flat frigate]

Goran

[celest compass]

alr thx

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[olive raven]

hello, i need help

[olive raven]

What am I doing wrong?

[quiet plume]

You're missing a point

[olive raven]

there’s one more point?

[quiet plume]

If you look at the feedback, it says non-differentiable point can happen at corners or discontinuities

[olive raven]

ahh i see a discontinuity

at x = 1

So it’s -2, 1 and 3

[quiet plume]

That should be it, yes.

[olive raven]

correct. Thank you😊

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[mortal thicket]

How many different ways are there of seating four married couples at a circular table with men and women in alternate position and no wife next to her husband?

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[mortal thicket]

.reopen

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[primal gazelle]

so it will be

3(1/3x+2/3)-2

x+2-2

x

am i right or wrong?

i used f(g(x))

pleade give me step by step if im wrong

im kinda laggy

[tough briar]

yep, that's exactly right

you showed f(g(x)) = x

you also have to show g(f(x)) = x

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[primal gazelle]

.reopen

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✅

[primal gazelle]

am i right?

also i dont know to solve fraction in function at letter b also the letter c has cube root

@help

<@&286206848099549185>

[tough briar]

(3x - 2) + 2 is not 6x - 4

[primal gazelle]

ohh

can you do step by step how will you gonna solve it so i can understand

[primal gazelle]

i dont know how cuz i do the parenthesis first

[tough briar]

there's nothing to do in the parentheses

(3 x - 2) + 2 is just 3 x - 2 + 2

[safe radish]

@primal gazelle Has your question been resolved?

[primal gazelle]

how about the letter b and c

can you teach me

[tough briar]

try them and see if you run into trouble

it's just what you did for the first one

[primal gazelle]

look

my first step

idk if its right

also im stuck

[tough briar]

the x in the denominator should be (2 x / (x - 1))

also you need to use parentheses, because it looks like the numerator is (2 x / x) - 1 when you meant to write 2 x / (x - 1)

[primal gazelle]

kinda confust a lil bit

confuse

oh

so same?

numerator and denominator are same to x like what i did

in the numerator?

[wispy monolith]

Wherever there is x in f(x) , replace it with 2x/(x-1)

F(x) = x/(2-x)
X comes 2 times in f(x)

[wispy monolith]

Both need to be replaced with this

[primal gazelle]

so 2x/(x-1) / 2-(2x/(x-1))

[wispy monolith]

Excellent

[primal gazelle]

like this?

so cancel x-1

bith

both

[wispy monolith]

Denominator is
2 - (2x/(x-1)) so you need to modify this a bit before cancelling x-1

[primal gazelle]

howw

[wispy monolith]

Well your question is

(a/b)/(cb-d)/b```
Then b will be cancelled from numerator and denominator

[wispy monolith]

Solve the denominator separately first
2 - 2x/(x-1)
Change this to a/b term currently it is in a - b/c form

[primal gazelle]

where did b come from why did u duplicate it?

do i cant multiple 2-(2x)?

multiply

[wispy monolith]

a - b/c , do you know how to simplify this?

[primal gazelle]

a/c -b/c

[wispy monolith]

Nooo /c is under b

Not under (a-b)

a-(b/c)

[primal gazelle]

it should be the same of a right

like a/a -b/c

[wispy monolith]

No

It will be
ac/c - b/c
(ac-b)/c

This is how you simplify these

[primal gazelle]

hmmm

[wispy monolith]

You need to solve in same way

Your original question

[primal gazelle]

2(x-1)-2x/(x-1)

[wispy monolith]

Yes

[primal gazelle]

like this?

[wispy monolith]

Yep

Now you can cancel the (x-1) from numerator and denominator

[primal gazelle]

so cancel x-q

x-1

[wispy monolith]

Yep

[primal gazelle]

2x / 2-2x/(x-1)

or the other sidee of x-1

[wispy monolith]

Whattt, why did you have a (x-1) after cancelling

[primal gazelle]

cuz i only remove one of x-1 in numerator and denominator

[wispy monolith]

Write the complete equation after doing this

[primal gazelle]

waitttt

(2x/x-1) / (2(x-1)-2x/(x-1))

hmm

[wispy monolith]

Yep

[primal gazelle]

(2x/x-1) / (2-2x)

like this

[wispy monolith]

Nooo

Solve the numerator part of denominator

That is
2(x-1)-2x

[primal gazelle]

(2x) / (2(x-1)-2x)

so numerator to denomitor of denominator?

[wispy monolith]

Yeah this is correct, that's what I was saying (x-1) will be gone from numerator and denominator both

[wispy monolith]

Solve the denominator

[primal gazelle]

(2x) / (2(x-1)-2x)

(2x) / (2x-2-2x)

(2x) / (-2)

[wispy monolith]

A little bit more

[primal gazelle]

hmm

is there more?

[wispy monolith]

Yeah 2 is there in numerator and denominator

[primal gazelle]

ohh

its an x

[primal gazelle]

-x

[wispy monolith]

Yep

[primal gazelle]

i see

how about the letter c

[wispy monolith]

What letter c

[primal gazelle]

this one

im going to be confuse with cube root

[wispy monolith]

Do you know formula for
(a+b)³

[primal gazelle]

(a+b) (a+b) (a+b)

[wispy monolith]

a³+b³+3a²b+3ab²

[primal gazelle]

oh my bad

kinda confuse

[wispy monolith]

f(x) is in this form

[primal gazelle]

hmm

[wispy monolith]

Then change f(x) first to this form

[primal gazelle]

x^3-1^3+3x^2-1+3x(1)^2

[flat frigate]

Shîro

[primal gazelle]

[wispy monolith]

No (a-b)³ = a³-b³-3a²b+3ab²

x³-1-3x²+3x

[primal gazelle]

so u simplified it

[wispy monolith]

Yeah also your answer was wrong

[primal gazelle]

whyy

[wispy monolith]

You did +3x² , it will be -3x²

But it's ok now we have
f(x) = x³-1-3x²+3x
Put g(x) value in f(x)

[primal gazelle]

cuz its that the sign how it possible?

to be a negative

[wispy monolith]

This is the formula for (a-b)³

Look at this carefully and put a=x, b=1

[primal gazelle]

u said 3a^2b

[wispy monolith]

That was for (a+b)³

Not (a-b)³

[primal gazelle]

oh

got it

[wispy monolith]

Now do this

Remember ³√x meaning x⅓

³√(x-1) means (x-1)⅓

[primal gazelle]

f(x) = x³-1-3x²+3x
Put g(x) value in f(x)

$f(g(x)) = ((x-2)1/3 +1)^3 -1 -3(x-2)1/3 +1)^2 +3(x-2)1/3 +1)$

[flat frigate]

Shîro

[primal gazelle]

am i wrong?

[wispy monolith]

Seems fine

[wispy monolith]

Do one thing for your simplification, assume x-2 = y and simplify this equation, at last change y with (x-2) again

[primal gazelle]

f(x) = x³-1-3x²+3x
Put g(x) value in f(x)

$f(g(x)) = ((y)1/3 +1)^3 -1 -3(y)1/3 +1)^2 +3(y)1/3 +1)$

[flat frigate]

Shîro

[primal gazelle]

like this?

$= ((y) 1 1/3)^3 -1 -3(y)1 1/3)^2 +3(y)1 1/3$

[flat frigate]

Shîro

[primal gazelle]

$= ((y) 1 & 1/3)^3 -1 -3(y)1 & 1/3)^2 +3(y)1 & 1/3$

my bad i dont know if i am doing right

[steep solstice]

you want me to just give you the answer lol? you can think about how to do it after if you want. If you want it just dm me since i cant do it here. If not thats fine too

[primal gazelle]

check dms

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[narrow pine]

This problem is for our homework, I tried to compute it but I can't seem to fully solve the equation. We were given the answer and only provide the solution. Is there something wrong with my solution and how can I improve it?

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[random hazel]

First of all

it should be

f( x + delta(x)) - f(x)

then the first three steps are ok

but on the second line

How did you get that expression??

@narrow pine

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[grim trail]

how do i get the lowest common multiple of 216 and 188 using prime foactors

[thin bridge]

take the highest power for each prime factor

[grim trail]

what do u mean by that

because im doing a factor tree but i dont know how to get the prime factors because itis confusing

[thin bridge]

$2^{\red{3}} \cdot 3^{2}\
2^{1} \cdot 3^{\blue{5}}$
$$2^{\red{3}} \cdot 3^{\blue{5}}$$

[flat frigate]

ℝαμOmeganato5

[thin bridge]

show your factor tree

[grim trail]

i did for 288

2 108

2 56

2 28

2 14

2 7

[pine horizon]

what 288

[grim trail]

oh i meant 216 not 288

[pine horizon]

its 188

still wrong

$216 = 2^3\times 3^3 \ 188 = 2^2\times 47^1$

[flat frigate]

Astar777

[mossy lotus]

108/2 =/= 56

[grim trail]

i know that but how do i get the 3 cubed

[mossy lotus]

If you do this correctly, youd get that

[grim trail]

but i di halding but i dont really know how i get the prime factor

[pine horizon]

216/2 = 108
108/2 = 54
54/2 = 27
27/3 = 9
9/3 = 3
3/3 = 1

$2 \times 2 \times 2 \times 3 \times 3 \times 3$

[flat frigate]

Astar777

[pine horizon]

= $2^3 \times 3^3$

[flat frigate]

Astar777

[grim trail]

thanks but how to i get the answer for lcm

lowest common multiple

[pine horizon]

u have factors now

for lcm

u pick the highest powers of factors

so the highest power of 2 is 2^3

for 3 its 3^3

and 47^1

now multiply all these

$\text{LCM} = 2^3\times 3^3\times 47^1$

[flat frigate]

Astar777

[grim trail]

how would i get the prime factors for 121 280 and 550 then get the lowest common multiple

[pine horizon]

the same way i did for the question above

[grim trail]

ok thanks u really helped me

close

[pine horizon]

[pine horizon]

its .close

[grim trail]

oh thenks

.close

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[fleet sentinel]

If 3x−y=12, what is the value of 8x2y??????????

[fleet sentinel]

nvm

wrong question

.close

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[vapid inlet]

.

[vapid inlet]

.

How do I solve sin(- (sq of 2)/2)?

[vapid inlet]

It wants a pi on the answer..

[digital vine]

Use a Taylor series

[midnight plume]

denom will simplify as -sin(1/root2)

[vapid inlet]

Wait, it doesnt. Only if it needs to

[vapid inlet]

Oh lemme search that

[vapid inlet]

Wait, Ill write this guy in the denominator?

[midnight plume]

or you could take it as -cosec(1/root2)

[digital vine]

wouldn't the sins just cancel out?

[vapid inlet]

Wait.. it was root2/2, why did it become 1/root2?

[vapid inlet]

Oop, Im not sure

Ill check the value

[midnight plume]

bcz 2=root2 x root2
cancel out one from the numerator and denominator
you are left with 1/root 2

[digital vine]

but shouldn't you want the denominator to be rationalised anyway?

[digital vine]

like how does this help the person find what sin is?

[midnight plume]

idk
just simplified the angle a bit
if you are gonna use the taylor series it will be easier to calculate with 1/root 2 instead of root2/2

[digital vine]

to be honest, if this person doesn't know how to simplify a surd then they're probably not on the level to use taylor series

[vapid inlet]

sorry for the wait. Says here when I calculated it, It's -1.53932, which is not equal to 7pi/4

[digital vine]

@vapid inlet does the question ask you to find a decimal value for sin?

[vapid inlet]

no

it wants me to write theradian in terms of pi

[digital vine]

waitrr

are these two pictures part of the same question?

[vapid inlet]

yeah, the picture of my laptop is the question

while the paper is what I solved

Ill try checking the taylor series if I can do it

oop nope

[digital vine]

can you show the rest of your working out?

[vapid inlet]

I just converted sin(7pi/4) to -root2/2

that was all on my notes

[midnight plume]

oh
just re write the sin 7pi/4 as sin(2pi - pi/4)
which makes it -sin(pi/4)
which will give arcsine(-sin (pi/4)) as equal to -pi/4

sin pi/4 lies in the principle domain of sin inverse x
sin and arc sin can be cancelled out

[vapid inlet]

zam, wait lemme try processing that

[digital vine]

you should know what sin(pi/4) is

[vapid inlet]

yeah

roo2/2

[vapid inlet]

so the answer is -pi/4?

[midnight plume]

ye

[vapid inlet]

IGHT IGHT, thanks for the time! Im gonna try solving this through your method by my own so Ill learn it

thank youu

.close

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[digital vine]

wait

@vapid inlet you need to understand something

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[vapid inlet]

what is it?

[digital vine]

sin^-1 is not 1/sin

[midnight plume]

probably that sin inverse does not mean 1/sin x

[frozen marlin]

^

sin^-1 is arcsin

bad notation we know

[vapid inlet]

OH DAM

[digital vine]

that's why i didn't understand your answer for a while

[vapid inlet]

Oh right, I remember failing one question in my physics test cause of that

[midnight plume]

sin inverse is a function that gives the angle for which x is equal to sin of that angle
arcsin x = angle
x=sin(angle)

[vapid inlet]

zam, alright alright

thank you for the clarification

I really love this server

thank youu

.close

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[lime ocean]

is the answer 25

[neon reef]

i got that answer as well

[lime ocean]

so is it correct?

[pine horizon]

yes

1ml of wallpaper remover for 30ml of water

so for 750ml of water 25ml of wallpaper remover

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[timber karma]

the question is "find K_n such that I_n = K_n I_n-2"

[smoky nacelle]

I don't read *uhh whatever this is *

[timber karma]

ill translate it chill vro😭

[smoky nacelle]

fair enough lmao

find $K_n$ such that $I_n = K_n I_n-2$

[flat frigate]

Percy

[timber karma]

and I_n is given

[smoky nacelle]

now i can read

[timber karma]

its I_(n-2)

yeah

should i solve it like an equation?

[smoky nacelle]

what's $I_n$?

[flat frigate]

Percy

[timber karma]

integral from 0 to pi/2 of sin^n x

what should i do?

[safe radish]

@timber karma Has your question been resolved?

[timber karma]

<@&286206848099549185>

okay i got k_n = (n-1)/n

.close

[safe radish]

Channel closed

Closed by @timber karma

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[safe radish]

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[buoyant sandal]

really need help with this question, went through many different methods and still cant get the answer, the question asks for sqrt(u) - sqrt(v). the answer is 1

[buoyant sandal]

it is also given that v > 1

the question must be solved by manipulating the given equation until it's sqrt(u) - sqrt(v), but i think it's impossible. my teacher wont allow us to find the values of them separately

[safe radish]

@buoyant sandal Has your question been resolved?

[grim kraken]

Okay so you got no other information other than this relation ?

In those type of problem I would look for a neat simplification. Like we have already what we want in the left side

Let me look into it

[buoyant sandal]

alright thanks

[buoyant sandal]

nothing else, i really feel that theres an issue with the question, or it has to be solved by individually finding the values of u and v separately, because ive been racking my head over this for quite a while 😭

[grim kraken]

You can't really find the value of v and u separately cuz you only have a single relation, you would get an elliptic curve equation at most and you ain't solving that

[buoyant sandal]

ohh there's a reason for it

thats interesting

[grim kraken]

You would get an equation like $au^n + bu^{n-1} + \cdots + cv^n + dv^{n-1} + \cdots = e$

[flat frigate]

Lilly (NasaExploration)

[grim kraken]

With a,b,c,d,e some numbers

[buoyant sandal]

that seems really complex

i've never heard of an eliptic curve

[grim kraken]

It tends to be czu the possible value are actually infinite

[buoyant sandal]

i cant wait to learn higher level mathematics, im just entering college, so we're reviewing high school maths rn

[grim kraken]

Yippee I am glad you have passion it's important

[buoyant sandal]

that's insane, and im not even sure why it's equal to eulers number

[grim kraken]

No no no it's not e the constant it's just a random varialbe

[buoyant sandal]

i rlly love maths, its the one of the only subjects without memorisation

[grim kraken]

I would agree and disagree with that but yeah absolutely

[buoyant sandal]

ohhh, i can't wrap my head around that equation

as for my question, is there no way to simplify it??

[grim kraken]

Here is an interesting read if you want to enrich your personal knowledge

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

[grim kraken]

I am getting there slowly but surely ^^

[buoyant sandal]

tysm!! i was actually just googling more info about it when you mentioned eliptical curve lol

[grim kraken]

And okay the exercise was actually beautiful @buoyant sandal

I found a solution

[buoyant sandal]

yayy!!

[buoyant sandal]

after 15 minutes i started getting stressed lol

😭

[grim kraken]

Yeah sorry it was quite tedious

[buoyant sandal]

how did you approach it??

[grim kraken]

So how do you want to proceed

Do you want me to give you leads and you look for yourself

[buoyant sandal]

sure that'd be great!!

[buoyant sandal]

no not your fault at all

[grim kraken]

Okay very well then, if you have trouble I will give you the steps. Keep in mind the solution isn't unique and multiple ways could lead to the same result

[buoyant sandal]

more so when i was doing it

[buoyant sandal]

alright

[grim kraken]

Okay so firstly what can you say of $v-4$ ?

[flat frigate]

Lilly (NasaExploration)

[buoyant sandal]

uhm....i'm already lost, sorry 😭

[grim kraken]

It's fine don't worry

So this is our starting point

Do you see some cool factoring you could do to have something better than v-4

[buoyant sandal]

let me try to mess around

[grim kraken]

Something that would use $\sqrt{v} + 2$ for example

[flat frigate]

Lilly (NasaExploration)

[grim kraken]

It's like a simple factorization tool. You just have to think about it

[buoyant sandal]

is it conjugation a factorisation tool??

[grim kraken]

What do you call conjugaison ?

[buoyant sandal]

multilying the upper one and the bottom with (v+4)

[grim kraken]

Okay no that's not what we will be doing

[buoyant sandal]

tu parlez francais??

[grim kraken]

Yes I do

[buoyant sandal]

omgg thats cooll i noticed the way you spelled conjugaison

i did my one year exchange there

[grim kraken]

Ohhhh taht's awesome

[buoyant sandal]

anwyays

[grim kraken]

France is great

[buoyant sandal]

i have no idea what to do

[buoyant sandal]

i really loved the place, i was in toulouse

WHA-

uhmm...okay

i dont have a degree yet lol

😭

[grim kraken]

What if you think about $(\sqrt{v})^2 - 2^2$

[flat frigate]

Lilly (NasaExploration)

[grim kraken]

Lovely

How do we report people here already

[buoyant sandal]

ohhh-

[buoyant sandal]

im not sure 😭

we can talk in dms if its easier

[grim kraken]

<@&268886789983436800> I am sorry for the ping but I am pretty sure this isn't good behavior

[buoyant sandal]

ill try to mess around with this now!! ty

[hard crest]

plz don't be afraid to ping mods if you have any concern like this

[grim kraken]

THank you I truly appreciate ! Thanks for the quick answer

[grim kraken]

Okay so I am not sure you saw the rule before, does something like this comes to mind :

[buoyant sandal]

wait i was jsut doing that

[grim kraken]

Perfect

There is a neat simplification that comes right after doesn't it ?

[buoyant sandal]

yess!! let me try to finish it

[grim kraken]

Oki doki

[buoyant sandal]

i am unable to avoid getting sqrt(uv) is this inevitable??

[grim kraken]

No you can do without it

Don't try to factor with either u or v

[buoyant sandal]

AHHH im so lost 😭

what i did was cancel the den on the left side with the sqrt(v) + 2

is that no tlogical?

[grim kraken]

Yeah that's what I did too

I just put the right side on the left with a minus a factorized by sqrt(v) + 2

Then got right of it by multiplication by sqrt(v) + 2

[buoyant sandal]

ohh, so after wards you equal the bracketed part to 0??

[grim kraken]

Nope, I try to get rid of the sqrt(v) - 2

So what you can do with that is maybe adding and removing 2 in the fraction to have something neat

[buoyant sandal]

im just going to give up, i feel this is beyond me!! ill just let you tell me how to do it...

[grim kraken]

Oki doki

The document is being exported in PDF

Here we go

[buoyant sandal]

tysm!! my brain is like in knots, but its a sign that im learning something

[grim kraken]

Yeah it's great

[grim kraken]

So try to read this and ask me if you don't understand anything

[buoyant sandal]

This is incredible, could you explain to me what you've done??

and why isnt it a + symbol inbetween it

sorry if its a dumb question, im really not sure

[grim kraken]

There are no dumb question in this world dear

[grim kraken]

It's because of the minus

[buoyant sandal]

tysm!! i can see it!!

[grim kraken]

Wonderful

[buoyant sandal]

wow i think thats it, tysm for helping me, i really appreciate it. i'd need to study on your working, it's really beautiful

[grim kraken]

No problem it was my pleasure to help ! I hope you learned something. And tahnk you for complimenting that work it was mostly the exercice that's really beautiful in the end

If you need anything don't hesitate to DMI will try to answer as fast as possible

[buoyant sandal]

i definitely learned a lot from you tysm!! goodluck on your endeavours

[grim kraken]

Thanks. Good luck on your first year of college

[safe radish]

@buoyant sandal Has your question been resolved?

Channel closed

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[safe radish]

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[long marten]

can someone just help me interpret this?

is this saying log(100)*n OR log(n)^100

[plucky elk]

The latter

[long marten]

okay thank you!

.close

[safe radish]

Channel closed

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[lean otter]

3. American football uses a field that is 100.0 yd long, whereas a soccer field is 100.0 m long. Which field is longer, and by how much (give yards, meters, and percent)?

how would i convert this

[safe radish]

Available help channel!

Send your question here to claim the channel.

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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• 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.

[fathom adder]

Your question havent been considered as one, you should open a new channel since the bot didn't reset this one yet

[fathom adder]

Frick

.close

[safe radish]

Channel closed

Closed by @fathom adder

Use .reopen if this was a mistake.

[plucky elk]

Do you have a question

We can help

Just post your question and ping helpers after 15 minutes

[fathom adder]

Can i ask help for math hw ?

xd

[obsidian oracle]

we are here to help

[lean otter]

😭

[plucky elk]

No this is a chemistry server

[fathom adder]

Ty mamen tu es le sang

[plucky elk]

Orbitals only

[obsidian oracle]

ah fréro fais gaffe les fr se font pas respecter par ici

[fathom adder]

Oh how can i get math help then?

[plucky elk]

#old-network for EE server

[obsidian oracle]

go to your math teacher

[plucky elk]

They can help you with your FFTs

[fathom adder]

Ah ok ok

[frozen marlin]

wait are you french

[frozen marlin]

also

if i'm translating that correctly

is that "thank you mother, you are the blood"

[obsidian oracle]

camarade je me suis fait démasquer, fuis pauvre fou

[fathom adder]

Not the Mother part

[obsidian oracle]

"my man"

[frozen marlin]

i thought you mistyped maman

[sharp comet]

@ivory schooner hope it helps

[fathom adder]

Ah ic xd

[obsidian oracle]

it's the meme of that guy that says MY MAN

and it sounds like this to french ppl

[frozen marlin]

but

"you are the blood"?

[fathom adder]

Yeah

[obsidian oracle]

you are blood, you're family

[frozen marlin]

...

[frozen marlin]

ohhhhhhh

[frozen marlin]

what does this mean

hang on

lemme try

myself

[obsidian oracle]

||be careful bro french people don't get respected around here|| solution to french homework

[frozen marlin]

i don't know what frero and gaffe are

[fathom adder]

Frero = bro, fais gaffe =becareful

[frozen marlin]

i see

hm

so

bro be careful, the french don't show respect here?

or something

sorry if i butchered that

[obsidian oracle]

it's the other way around

[frozen marlin]

i'm barely B1

[frozen marlin]

oh.

[fathom adder]

Youre getting it very well

[obsidian oracle]

it's pretty good attempt

[fathom adder]

I mean the sentence

[frozen marlin]

thanks

[frozen marlin]

i'mma try this too

[fathom adder]

(Was it a joke or fr ?)

[frozen marlin]

[camarade] i defame myself maybe?

i feel like that's what the first bit is

[obsidian oracle]

si on continue à parler fr c'est juste une source infinie de devoirs pour ren

[fathom adder]

Parfait

[frozen marlin]

if we continue to speak french, it's simply a source of infinite homework for ren

i know that much

yay! :D

this is fun

[obsidian oracle]

it's not defame here

[frozen marlin]

oh i guessed

[fathom adder]

"Mask are fallen"

[frozen marlin]

i don't get it

[fathom adder]

Un-masked

[frozen marlin]

also i think we should continue in #「helpers-lounge」

oh

de-mask

[fathom adder]

Mdr je sais pas le mot en anglais

[obsidian oracle]

"se faire démasquer" means you got caught/exposed or more literally unmasked

[frozen marlin]

i see

[fathom adder]

My channel my rules

.reopen

[safe radish]

✅

[frozen marlin]

AHHAHAHA

[obsidian oracle]

the beginning of the end

[frozen marlin]

i don't think the mods would approve though

[fathom adder]

Kekw

[obsidian oracle]

Poste un truc relié au maths vite!!

[frozen marlin]

of us yk doing french in an active channel

[frozen marlin]

oh damn

that was fast

[obsidian oracle]

!status

[safe radish]

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

[frozen marlin]

LOL

[fathom adder]

7

[frozen marlin]

are we actually doing this

[obsidian oracle]

oh noes!

everything here is in english!

[frozen marlin]

we must flee

[obsidian oracle]

but YakuBros can only read french

[fathom adder]

Je suis sans indices en anglais

[obsidian oracle]

@frozen marlin please translate all of those into french for Yaku

[frozen marlin]

uhhhh

[fathom adder]

Bwawawaahahha

[frozen marlin]

*sweating profusely*

tbf that'd be a fun exercise

[fathom adder]

Je suis sûr que tu y arriveras

[frozen marlin]

but i think we should do it elsewhere

[obsidian oracle]

accidental french transgenderism

[frozen marlin]

unless ofc this is an actual problem yaku needs to solve

[obsidian oracle]

I won't forget what was edited

[frozen marlin]

i have

[fathom adder]

Take example on ren then

[frozen marlin]

btw does this mean "i am without experience in english"?

[obsidian oracle]

it's very close

[fathom adder]

"Im clueless in english "translated litteraly

[frozen marlin]

ah

[obsidian oracle]

it's like I have no clue

[frozen marlin]

i'm without a clue in english

i see

very interesting

[fathom adder]

We don't say this in fr tho

[obsidian oracle]

Les indices de bleu

[frozen marlin]

"what have you tried so far"

uh

"quel avez-vous essayer jusqu'a maintenant?"

is that correct

[obsidian oracle]

damn that's a very good attempt

[fathom adder]

Les billets en franc ça

[frozen marlin]

or is it qu'est-ce que

[obsidian oracle]

qu'avez-vous for the abbreviation

[frozen marlin]

ah okay

[obsidian oracle]

or qu'est-ce que vous avez...

[frozen marlin]

i see i see

[obsidian oracle]

essayé for "passé composé", equivalent of present perfect

[frozen marlin]

oh yeah mb i forgot

how'd i forget passe compose 😭

[fathom adder]

On a besoin d'un channel pour enseigner les langues aussi

[frozen marlin]

forgive me i know omitting the accents is a sin

[obsidian oracle]

and the last one is just "common usage"

[frozen marlin]

c'est tragique

[obsidian oracle]

you rather say "jusqu'à présent" than "jusqu'à maintenant"

[frozen marlin]

will do

[obsidian oracle]

Never thought I would help someone progress in french in a MATHS discord server

[frozen marlin]

you guys wanna go to #「helpers-lounge」

i'm getting kinda nervous

[fathom adder]

As you wanr

[obsidian oracle]

oops sorry chemistry server

[frozen marlin]

okay

[fathom adder]

.close

[safe radish]

Channel closed

Closed by @fathom adder

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[safe radish]

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>.
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• Be polite and have a nice day!

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

[teal linden]

I've been struggling with this integral for the past 2 hours...can someone help?

I've done the work out by hand, used chatGPT, etc but my HW is still saying its wrong.

[teal linden]

this is integration with decomposition

the integrating part isnt' hard, but finding the constants is where I am struggling

[pseudo flax]

what constants

[thin bridge]

I've done the work out by hand, used chatGPT
Don't use chatGPT for math.
Show your attempt

[teal linden]

@thin bridge

[teal linden]

fractional decomp, you usually break up the fraction in like A/something + B/something etc

on the bottom of the first page, I used the equation solver thing in the calculator

and plugged it into 6(A+B)-1 to get C on a calculator

[thin bridge]

expanding everything makes stuff more tedious and more chances to make mistakes

[teal linden]

oh

So I should've just left like it like?

[thin bridge]

don't even expand out those product pairs

[teal linden]

oh

so

A(x+13)(6x-2)?

and then just leave it like that?

[thin bridge]

yes

[teal linden]

ok

[thin bridge]

and doing substitutions like x=-13,
will result in mass cancellations making it much easier to determine your constants

[teal linden]

ohh alright

i see

let me do it out rq

[teal linden]

This is just one but is it like this?

[thin bridge]

not =2,

= original numerator evaluated at your chosen value of x

[teal linden]

ok, so B represents the "2" in 2x

so it would be 2(-13) so -26?

[thin bridge]

no

the idea is to find the values of A,B,C in

such that'll it'll be equivalent to
x^2 + 2x - 50

[teal linden]

yes

[thin bridge]

numerator when x is 13 for your decomp =
numerator when x is 13 of the original

[teal linden]

so I plug in -13 for that entire polynomial?

so like
(-13)^2+2(-13)-50

[thin bridge]

yes

[teal linden]

and that would be like

oh ok

so in that case, the polynomial will yield 93

so B(-11)(-80) = 93

B = (93)/(880)

[thin bridge]

yeh

[teal linden]

alright thanks!

[thin bridge]

if there are non-linear denominators for your decomp then you'd need to go through that long way

but be careful when doing that

[teal linden]

ok

so like, if the denominator was like x^2-1 or something like that?

[thin bridge]

well x^2-1 can be factorised to (x-1)(x+1)

which can be decomposed

[teal linden]

x^2+1*

[thin bridge]

yeh

[teal linden]

yea, you saved me here.

My professor dosen't permit the use of calculators in his exams, so its helpful to learn this shortcut methods

[teal linden]

oh wait btw...would it -C or +C

because the C = -50

[thin bridge]

its a different C

[teal linden]

like when writing out A(x+13)(6x-2)...+C(x+13)(x+2)

[thin bridge]

the capital C is the constant in your decomp
is not directly linked to the constant term of the original numerator

[teal linden]

oh ok

[thin bridge]

just C,

[teal linden]

so just keep it all +

[thin bridge]

and in your calculations it may end up positive or negative

[teal linden]

C is equal to -449/280 in my calculations

[thin bridge]

you could start with -C, but the sign will just end up being the opposite as what you'd have if you started with C
either way, the end result will be teh same

yeh, that seems alright

[teal linden]

i will just say this:

don't play with the signs, just write it like:

A/(something) + B/something + C/something

[thin bridge]

yeh

[teal linden]

alr cool

thanks

[thin bridge]

(different somethings)

[teal linden]

yea you know what i meant

[safe radish]

@teal linden Has your question been resolved?

Channel closed

Closed by @teal linden

Use .reopen if this was a mistake.

[teal linden]

.repon

.reopen

[safe radish]

✅

[teal linden]

What did I do wrong?

nvm

.close

[safe radish]

Channel closed

Closed by @teal linden

Use .reopen if this was a mistake.

[safe radish]

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.

[empty laurel]

(1.00-0.001^2)^0.5

[empty laurel]

is the answer not 1E0?

when considering sig figs

[plucky elk]

Answer to what question

[empty laurel]

this

[plucky elk]

How many sig figs

[frozen marlin]

,w (1 - 0.001^2)^0.5

[flat frigate]

Results provided by WolframAlpha

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

Requested by justarenegade

[frozen marlin]

there

[empty laurel]

smallest is 1

right?

[plucky elk]

Smallest what?

[empty laurel]

amount of sig figs

[plucky elk]

You can't have fewer than 1 sig figs yes

[empty laurel]

for this question specifically

I thought the answer should be 1 sig fig

[thin bridge]

which value are you basing that off?

[empty laurel]

1.00

or is that 3 sig figs

[thin bridge]

trailing 0s after the decimal point are significant

[plucky elk]

You didn't give the full instructions

[empty laurel]

I need to solve the problem

fallowing all sig fig rules

thats the instructions

[plucky elk]

!original

[safe radish]

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

[empty laurel]

.close

[safe radish]

Channel closed

Closed by @empty laurel

Use .reopen if this was a mistake.

[safe radish]

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 axle]

In calc 2 I never learned what hyperbolic means, so when someone told me that the integral of 1/1-u^2 is just hyperbolic tangent, I was completely lost and my brain almost committed seppuku when I saw a hyperbolic function, can anyone explain what that is and why this hyperbolic tan is the integral of 1/cos(x)

[safe radish]

Please don't occupy multiple help channels.

[eternal carbon]

tbh this is probably not something you will truly need to understand the meaning of, rather just a definition

hyperbolic functions are analogues of the trigonometric functions you are familiar with

these are the two main definitions from which all other hyperbolic functions can be derived

for example, the hyperbolic tangent tanh(x) is sinh(x)/cosh(x)

[eternal carbon]

the reason hyperbolic functions appear in integrals sometimes is because they satisfty similar identities to trig functions

you may be familiar with (sinx)^2 + (cosx)^2 = 1
the following is also true: (coshx)^2 - (sinhx)^2 = 1

so if you've ever done a trigonometric substitution in integration before (i.e. u = tanx) then you can note that substitutions like (u = sinhx) may also give valid results

[eternal carbon]

in the case of integral of 1/(1 - u^2), the substitution u = tanh(x) is what allows for the immediate result of artanh(x) + C

(these are very general explanations and i'm skipping a few steps here but i just want to give you a basic idea of what is going on)

[eternal carbon]

to see the connection, write this out in terms of exponential functions, you have that this is true:

[desert swallow]

(Should be noted that the derivative of sinh x is cosh x and vice versa)

[eternal carbon]

just like arctan(x) is defined as an inverse of tan(x), you can define artanh(x) as an inverse of tanh(x)

[delicate axle]

(I was looking at the e's and all I could think of was series and then I was like, do we factor out the e^x to get e^2x? where's that coming from)

[eternal carbon]

oh yeah multiply numerator and denominator by e^x

[eternal carbon]

and you can algebraically show this to be true

[eternal carbon]

going back to the integral of 1/(1 - u^2), normally when you integrate this you use partial fraction decomposition and split it into 1/2 (1/(u + 1) - 1/(u - 1))

and as you can see integrating that partial fraction decomposed result gives you the same thing as artanh(u)

@junior smelt

[delicate axle]

I got it

(partial fractions was the only way I knew how to do this problem 😭 )

(Someone showed me that you can just change 1/cosx into secx and then multiply it by sec+tanx making life easy as anything if you know the derivative of secx+tanx)

[eternal carbon]

oh ye this is interesting

[eternal carbon]

(btw if ur interested in reading more on properties of hyperbolic functions you can see here https://en.wikipedia.org/wiki/Hyperbolic_functions)

[eternal carbon]

(the integral of 1/(cosx) is a very interesting problem that has many solutions and has been studied extensively
though when it is first introduced in calculus classes it comes off as an unintuitive result and is usually memorized by students
https://en.wikipedia.org/wiki/Integral_of_the_secant_function)

[delicate axle]

0_0

wow

those aren't triangles

[desert swallow]

You could also use t-subsitution

[delicate axle]

ye but I definitely forgor how to do that

😭

wow this is so cool

[eternal carbon]

yep they're all the same thing

[delicate axle]

yo the trig sub is here

but what the heck is this dude doing here

no one invited him to the party

😭

[eternal carbon]

lol

[delicate axle]

it blows my mind how we can actually use the half angle theorem

we never use it

like never

[eternal carbon]

that is true

(for context, tangent half-angle substitution is another well-used integration trick, though falls outside the scope of introductory calculus classes)

[delicate axle]

math majors must be so happy when they see something like this

cause everything just feels nice

cause it all connects

math is so cool

for no reason

[eternal carbon]

[delicate axle]

hey I was wondering if I could learn some calc 3 in here

I've been procrastinating my calc 3 homework until the last minute cause I just can't do it

(the teacher has no lectures or anything, only a textbook that doesn't like anything)

(A lot of calc 3 for me rn is just figuring it out, doing it for the homework, and just moving onto something else without understanding anything about it so it's all just so disconnected...)

[median vigil]

linking this in case you haven't seen it: https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

it all comes together at the end with the integral theorems

[delicate axle]

for example when i see this it's just something to TRY to rememebr 😭

[delicate axle]

👀

[safe radish]

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[lean otter]

Hi

[lean otter]

I have this problem

I don't know how to solve it

I already reach the hypotesis part

But I don't understand the Thesis

I will sent a picture of my work

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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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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[proud zealot]

Im stuck on this problem, I dont quite remember the steps for how to solve it.

[icy lance]

did you try do what i said?

[proud zealot]

I've been looking at the notes, and just

[icy lance]

always good to reference but its asking a different thing

[proud zealot]

right

[icy lance]

,w graph y=96+64x-16x^2, y=16

[flat frigate]

Results provided by WolframAlpha

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

Requested by aldrnari_

[icy lance]

youre trying to find when that blue line is above the yellow one

ie h>16

to do that though you need to know when h=16

[proud zealot]

So how to do that, what formula to use?

[icy lance]

you have the formula for h

[proud zealot]

plug in 16 for 96?

[icy lance]

youre just solving for t in the case that h=16

no

plug in 16 for h

[proud zealot]

ok

16 = -16t^2 +64t+96

ok...

So now whats next?

[icy lance]

solve for t

you may have a nicer time if you divide by -16

[proud zealot]

Using this?

Or solving for t by this?

[icy lance]

no

[icy lance]

well this yes

[proud zealot]

ok so

[icy lance]

but this is just routine solving a quadratic

[proud zealot]

t^2 -4t -6

[proud zealot]

Im assuming divide every term by -16

After that, what do I do with the equation now?

Use this formula?

[icy lance]

you need to stop obsessing over that

it just tells you the x value of the vertex

which you dont need right now

[icy lance]

solve the quadratic

and find t

[proud zealot]

i wish i could remember, but I forgot the step to do after getting 10240

[icy lance]

that looks like youre solving h=0

lets back up

[flat frigate]

AℤØ

[icy lance]

division by -16

[flat frigate]

AℤØ

AℤØ

[proud zealot]

oh. forgot that -1

[proud zealot]

time to factor it ig?

[icy lance]

you were solving h=0, not h=16 here

yes

[proud zealot]

(t-5)(t+1)

and then set to zero, so t-5=0

+5 +5

t=5

and t+1=0

is -1

[icy lance]

so thats when h=16
when is h>16

[proud zealot]

Ah. I understand it now.

[proud zealot]

thank you.

[proud zealot]

wait, interval notation?

[proud zealot]

so probably this,

hm

( ♾️ , 5) ?

[icy lance]

can t be negative?

[proud zealot]

-5 secs would be odd.

[icy lance]

thats not an interval

[proud zealot]

but i think im starting to remember now,

[proud zealot]

the interval is probably something to do with this,

[icy lance]

you have everything you need
mathematically you have the interval to be (-1,5)

but think of the context

[proud zealot]

oh

[proud zealot]

So to say, -1 would just be 0?

[icy lance]

the bound type would also change

[proud zealot]

hmm

(1,5) ?

[icy lance]

nope

when i say bound type im referring to ( and [

[proud zealot]

ahh

(-1,5]

[icy lance]

no

[proud zealot]

oh

[icy lance]

when t=5 youre at 16, not above it

and t cant be negative

[proud zealot]

(16,5) ?

[proud zealot]

Im not rlly getting this part,

[icy lance]

youve gone wildly off course with that one

read the hint

its simpler than youre making it in your mind

[proud zealot]

(5,5) ?

Probably not

[icy lance]

no

how do you take (-1,5) and exclude the negative values

[icy lance]

?

[proud zealot]

exclude by +1 to get rid of the neg?

[icy lance]

thats not how sets work

youre overcomplicating this

imagine the number line

if i want to cut off the negative parts, what am i left with

[proud zealot]

the positive parts, and zero

[icy lance]

exactly

so what set do we have?

[proud zealot]

(0,5)

[icy lance]

that doesnt have 0 in it

[proud zealot]

just (5) ?

[icy lance]

no, we're back to this

(0,5)

but we want to include 0

[icy lance]

the first image

[proud zealot]

[0,5]

[icy lance]

we dont want 5

[proud zealot]

[0,5)

[icy lance]

we got there

[proud zealot]

oh well. Thanks for the help thro. :)

[icy lance]

no worries

eh why did they include 5

oh im silly

'at least'

[proud zealot]

.close

[safe radish]

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Use .reopen if this was a mistake.

[safe radish]

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>.
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• Be polite and have a nice day!

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

[rustic goblet]

okay, I'm having a hard time reading this statement and figuring out what I need to do

[rustic goblet]

For which $n$ is there a graph $G$ with $|G| = n$ such that $G$ is isomorphic to $\overline{G}$?

[flat frigate]

higher!

[rustic goblet]

is this asking me to show that $G$ is isomorphic to $\overline{G}$ if and only if $\text{[insert condition here]}$, or only one of the implications?

and if the latter, which implication is it?

[alpine igloo]

unrelated but, which book are you using?

[rustic goblet]

this isn't from a book haha

[alpine igloo]

ah ok thank you

[flat frigate]

higher!

[safe radish]

@rustic goblet Has your question been resolved?

[rustic goblet]

<@&286206848099549185>