help-28

[deft zodiac]

its just partial fractions

[merry atlas]

Yes, that

[deft zodiac]

yea just

factor the bottom first

u shld be able to easily find all 4 factors

[merry atlas]

I only find the factor I have there, can't find the rest

[deft zodiac]

well

x^4 = -1

then use polar form to find all roots

[merry atlas]

I'm not even sure I shoudl use compelx numbers here

Oh, polar form.. right. Another thing I just learned and can barely do xD.. alright I'll try that then

[vast fossil]

i isn't a solution to x^4 + 1 = 0 though

[merry atlas]

I got confused with the higher powers of i. What is i cubed and so forth?

Never gone beyond i square

[vast fossil]

i^3 = -i and i^4 = 1

[deft zodiac]

oh ye lol

[merry atlas]

so -i^4+1=0 then

[vast fossil]

You need to find 4th roots of -1, aka square roots of i and -i

[deft zodiac]

um

i guess?

but that isnt a root

[merry atlas]

Okay, so I'm probably thinking of i as similar to one too much. sqrt of i is a root then, but if -i^4+1=0, how is that not a root?

[deft zodiac]

well

its like saying

1 is a root of x^2 + 1 = 0

like

• 1^2 + 1 = 0

but like

1 is not a root

u just added a - out of nowhere

[merry atlas]

-1^2 + 1 isn't 0 though?
-(1^2)+1=0.
Are you saying I can't use -i? I'm so confused

[deft zodiac]

-1^2 + 1

is zero

,w -1^2 + 1

[glossy valve]

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[deft zodiac]

-(1^2)+1=0.

this is implicit

when no () are used

[merry atlas]

Okay, so what I meant was the opposite then

[deft zodiac]

implied

yea well

then it isnt = 0

[merry atlas]

(-i)^4 +1 =0

[deft zodiac]

,w (-i)^4

[glossy valve]

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[merry atlas]

Alright, I think I'm following now.. So polar form and go from there..

[deft zodiac]

yes

[merry atlas]

I just had complex numbers, this partitioning, polar form and a bunch of stuff dumped on me the last few days and I understand hardly any of it.. thanks for clarifying

[deft zodiac]

yes

do uve any

game recommendations

or novel

or shows

or easy to cook foods

LOL

[merry atlas]

I thought i^4 would be -1 because it seems to defeat the purpouse of i otherwise honestly. Guess not

Haha

Yeah, you should play The Bnaner saga, old Bioware folks doing their own thing. Amazing

Banner saga

[deft zodiac]

oh my

a turn based

ill check it out

[merry atlas]

You should read the slime isekai light novel. Super cheesy, loads of city building. Was a blast to read.

[deft zodiac]

eh

[merry atlas]

"That time I reincarnated as a slime"

[deft zodiac]

i

i heard of that

well

nice to trade info with u

[merry atlas]

Not for everyone, but I like it

[deft zodiac]

[merry atlas]

❤️

Thanks again

[deft zodiac]

np

u too

💕

[merry atlas]

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[shrewd hamlet]

a few months back in math class, we were learning about the area between polar curves. the formula is provided below. I remember that when we learned this, i made the observation that in order for this formula to hold true, the rate at which the slope of polar functions change must be the same for all polar curves. my math teacher agreed with me, but she said it had to do with a change to rectangular coords. for the last few days, ive been thinking as to why i thought such a thing, because looking at the formula, im not sure how i drew that conclusion. pls let me know if u know why. lol, ik this is kinda weird

[ripe hatch]

secret

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[livid peak]

https://media.discordapp.net/attachments/726421062392217721/1025839589547573328/IMG_20221002_001009.jpg

[livid peak]

My friend needs help solving this

[woven snow]

uh

[rich vessel]

what do you need?
the S of it?

[livid peak]

the x maybe

[rich vessel]

yea yea i got it

[livid peak]

Yeah he's finding x

idk what in the world he's doing

[rich vessel]

very nice

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[tribal gust]

How do i go about calculating the intersection of the two curves x^2+y^2 = 5/2 and y = 1/x?

[nova island]

Take the second expression you have for y, plug it in as y for the first expression and solve for x, then plug in that value of x in either of the two equations and solve for y

[tribal gust]

How would i solve x^2+1/x^2=5/2 tho

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[tribal gust]

<@&286206848099549185>

its pretty basic but my brain is just not workign

[tiny fox]

multiply both sides by x^2... it should be a quadratic equation in x^2 afterward

[tribal gust]

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[thick mountain]

I’ve tried making this into a telescoping series, but I don’t know where to go from there

[twilit leaf]

Partial fraction decomposition

[thick mountain]

Partial fractions gave me $\frac{1}{Nn} - \frac{1}{N(n+N)}$

[glossy valve]

Larry the Cucumber

[twilit leaf]

What

Where did the Ns come from

[thick mountain]

it’s the positive integer

[twilit leaf]

I know that but why do you have extra Ns is the denominator

[thick mountain]

oh

that’s how it turned out after partial fraction decomp

lemme show steps

[twilit leaf]

It shouldnt

[thick mountain]

$\frac{1}{n(n+N)} = \frac{A}{n} + \frac{B}{n+N}$

[glossy valve]

Larry the Cucumber

[thick mountain]

$1 = A(n+N) + B(n)$

[glossy valve]

Larry the Cucumber

[thick mountain]

$1 = An + AN + Bn$

[glossy valve]

Larry the Cucumber

[thick mountain]

$1 = n(A+B) + AN$

[glossy valve]

Larry the Cucumber

[thick mountain]

$AN = 1 \implies A = \frac{1}{N}$

[glossy valve]

Larry the Cucumber

[thick mountain]

$A + B = 0 \implies \frac{1}{N} + B = 0 \implies B = -\frac{1}{N}$

[glossy valve]

Larry the Cucumber

[twilit leaf]

Oh fair enough

[thick mountain]

$\frac{1}{n(n+N)} = \frac{\frac{1}{N}}{n} + \frac{-\frac{1}{N}}{n+N}$

[glossy valve]

Larry the Cucumber

[thick mountain]

the problem with it is that the terms don’t seem to cancel out

or I can’t get them to cancel out

[twilit leaf]

The first part of the nth term cancels with something N terms down the line

[thick mountain]

yeah it seems like the $-\frac{1}{N(n+N)}$ cancels n+1 terms down

[glossy valve]

Larry the Cucumber

[thick mountain]

i don’t know if I wrote that right

but if N = 2 then when n = 3, the second term from n = 1 cancels with the first term for n = 3

$(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{4} - \frac{1}{8}) + (\frac{1}{6} - \frac{1}{10})$

[glossy valve]

Larry the Cucumber

[thick mountain]

actually I think I found the pattern

the left term remains n = N times

[thick mountain]

is this right?

like if N = 2, then for n = 1 , 1/2 is left and for n = 2, 1/4 is left

[twilit leaf]

No they still increment by 1

Hold on lemme latex

Wait no youre right

Sorry for the confusion im in two help channels so im not fully focused

[thick mountain]

nah bro you’re all good

math server seems busy today

[thick mountain]

thanks for all the help!

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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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[gray nacelle]

Hi can someone tell me why this is wrong?
Correct answer is 151200

[deft zodiac]

🥣

have some soup

[gray nacelle]

help pls

[deft zodiac]

drink some soup first

[gray nacelle]

slurps

[torn jolt]

gang i dont even know what the question is

[gray nacelle]

its right above

[deft zodiac]

LOL

🥣

[torn jolt]

oh

[gray nacelle]

[deft zodiac]

💕

[gray nacelle]

why is my answer wrong

idgi

[deft zodiac]

LOL

i thought

alex wld help

[gray nacelle]

same

[deft zodiac]

just a

[gray nacelle]

;-;

[deft zodiac]

🧌

[torn jolt]

im thinking bruh

[gray nacelle]

maybe hes looking at the qn

[deft zodiac]

looking up the question

[gray nacelle]

wowowo

we could do the slotting method

6! (put all the non 1s balls down) * 7C3 * 3!

but i dont get why my approach doesnt work

[gray nacelle]

this wld be correct

[pallid hedge]

is it jsut like this

[gray nacelle]

dont think so

[pallid hedge]

312

[gray nacelle]

i mean i think that would be right

but the 1s need to be slotted in more arbitrarily

wait

nvm those arent the ones

lmao

i wanna know why my approach aint wokring th

tho

[pallid hedge]

oh i didn't read the quesiton fully, it's the num of ways you can arrange them

[gray nacelle]

lol

[gray nacelle]

hi u ther?

[topaz valley]

oh

hi

[gray nacelle]

HELLO MY SAVIOUR

HELP PLS

[topaz valley]

ugh

this question is

[gray nacelle]

too trivial for u

[torn jolt]

i was thinking something having to do with using the wrong combination/permutation in the wrong spot but i forgot everything about that shit

[pallid hedge]

this is like programming level question

[gray nacelle]

hmm

[pallid hedge]

lmao

[gray nacelle]

no not really lol

[torn jolt]

like when you do 9! youre implying that order doesnt matter

even tho it clearly does

[gray nacelle]

"implying that order doesnt matter" wait wut

[topaz valley]

i think you can just PIE this

[gray nacelle]

pie?

wait but like i did
6! * 7C3 & 3! = 151200 which is correct

but then when i try to take the complement

it didnt work

[deft zodiac]

nani

[gray nacelle]

(cases where theres no restrictions : 9!) - (cases where two "1" balls are adjacent: 3P2 * 6P2 * 5! = 21600) - (cases when all three "1" balls are adjacent: 3! * 6! = 4320) = 336960

[topaz valley]

,w 9! - (2! * 8! * 3 + 3! * 7! * 2)

[gray nacelle]

wut

[topaz valley]

wait theres 9

LOL

[gray nacelle]

nice

,w 9! - (2! * 5! * 3 + 3! * 4! * 2)

[glossy valve]

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[topaz valley]

too many

[gray nacelle]

ded

ok lets just do another qn

lemme get the ans key for this

lmao

total number of ways w/o restrictions: 11c5 * 4! * 6c6 * 5! = 1330560 yes?

[topaz valley]

oh wait shit

[gray nacelle]

wat

wats happening

[topaz valley]

ugh

[gray nacelle]

no angri

[topaz valley]

PIE is annoying is whats happening

[gray nacelle]

[topaz valley]

,w 9! - ((2! * 8! - 2 * 2! * 7!) * 3 + 3! * 7!)

[empty sapphire]

man was not meant to solve such problems. You're trifling with the Lord's design. Cast away this devilish problem

[glossy valve]

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[gray nacelle]

[gray nacelle]

yes

[topaz valley]

finally

[gray nacelle]

wait so

[topaz valley]

PIE is yucky

[gray nacelle]

i did 6! * 7c3 * 3!

which is like

the slotting method

but i dont get

why my complement method

aint workin

,w rotate ccw

[glossy valve]

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[gray nacelle]

wat

[topaz valley]

LOL

[gray nacelle]

,rotate ccw

[topaz valley]

HAHAH

[gray nacelle]

wow

,w rotate cw

[glossy valve]

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[gray nacelle]

bruh

i need to stop

[topaz valley]

no bruh

[gray nacelle]

typing ,w

[topaz valley]

https://cdn.discordapp.com/attachments/903486480985489478/1025953620899926086/unknown.png

[gray nacelle]

,rotate cw

[gray nacelle]

,rotate ccw

[gray nacelle]

,rotate ccw

[gray nacelle]

ok

finally

[topaz valley]

bruh

[gray nacelle]

[topaz valley]

wait so

did you

get the answer?

or no

[gray nacelle]

yes

i used

6! * 7c3 * 3!

[gray nacelle]

but i dont get why this not working

[topaz valley]

,w 6! * 7c3 * 3!

[glossy valve]

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[gray nacelle]

nice

[empty sapphire]

did you believe hard enough?

[topaz valley]

,w 6! * (7 choose 3) * 3!

[glossy valve]

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[gray nacelle]

maybe not enuf

[topaz valley]

nice

[gray nacelle]

yes

[empty sapphire]

wow nicely done

[gray nacelle]

but i dont get

why my method

no work

[gray nacelle]

this

[topaz valley]

three 1s being adjacent is 3! 7!

pretty sure

and then 2 balls adjacent is like

[gray nacelle]

why tho

oh

lmao

OHHHHHHHHHHHHHHHHHHHHHHHHHHHH

[topaz valley]

i think you got it right

[gray nacelle]

I NEED TO PERMUTE THE 3 "1" GROUP

cant take it anymore

aaaa

ah

but the answer

kinda weird

[topaz valley]

,w 9! - (21600 + 3! * 7!)

[glossy valve]

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[topaz valley]

lol

[gray nacelle]

ah yes

i srsly dont get why

[topaz valley]

ded

[gray nacelle]

is there like more cases

or smth

[topaz valley]

wait im dumb LOL

[gray nacelle]

wot

[topaz valley]

you need all the 1s to be not next to each other

yeah okay

but

[gray nacelle]

wait wut

[topaz valley]

your 21600 might be the problem

[gray nacelle]

why tho

[topaz valley]

,w 3 * (2! * 8! - 2 * 2! * 7!)

[gray nacelle]

wut

[glossy valve]

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[topaz valley]

this is exactly two 1s next to each other

[gray nacelle]

nani

what did u do

[topaz valley]

wait am i just being dumb

[gray nacelle]

but its right tho

[gray nacelle]

ths

[topaz valley]

this is some kind of

weird trickery going on

[gray nacelle]

ifkr

[topaz valley]

anyway

so

[gray nacelle]

lets continue

ill just

not use

complement

[topaz valley]

like

[gray nacelle]

ever

actually thats probably bad

[topaz valley]

3 * 2! * 8!

wait no just

2! * 8!

is like

putting 2 specific colours of 1s together

[gray nacelle]

but we cant put the

like

theres a chance the third "1" gets chosen

[topaz valley]

yeah

[gray nacelle]

and put beside the two other ones

[topaz valley]

so you just subtract it off

and thats 2 * 2! * 7!

since you choose the two 1s

then you can put the last 1 on either side

so thats 2 *

and then you permute the whole group

so 7!

thats why its 2! * 8! - 2 * 2! * 7!

[gray nacelle]

heh

erm

i get the idea i guess

but

i think

in the future

if i can avoid using permutations

i mean

avoid using comlpement

i should

[topaz valley]

you gotta do what you gotta do

[gray nacelle]

yesmam

can u help me

with the

next one

pls

[topaz valley]

https://cdn.discordapp.com/attachments/903486480985489478/1025952379314651136/unknown.png

[gray nacelle]

im dying even more

[topaz valley]

cant stay for too long

[gray nacelle]

o

yesmam

[topaz valley]

oh my

yuck

[gray nacelle]

ways w/o restrictions: 11c5 * 4! * 6c6 * 5!

is that correcto

[topaz valley]

like

is that

saying the round tables dont matter

as in rotation

[gray nacelle]

i took that into

account

[topaz valley]

not sure if the question means that but i think probably

so yeah i think thats fine

[gray nacelle]

yay

okay then

[topaz valley]

6c6 is 1 tho lol

[gray nacelle]

cases when two friends sit next to each other at table for 5

[topaz valley]

once you choose one group

[gray nacelle]

would be

[topaz valley]

the other group is determined

you dont need to 6c6

[gray nacelle]

11c2 * 2 * 9c3 * 2! * 5!

[gray nacelle]

yesmam

[topaz valley]

bruh

trying to figure out what you did through the product

[gray nacelle]

ah

lemme

type

[topaz valley]

i think that works

wait or does it

[gray nacelle]

11c2 (choose the two friends) * 2 (permute them) * 9c3 (choose table 5's people) * 2! (permute the 3 of them but -1) * 5! (permute the 6 table)

THING IS

ITS MORE THAN THE TOTAL NUMBER OF CASES

[topaz valley]

,w (11 choose 5) * 4! * 5!

[glossy valve]

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[topaz valley]

,w (11 choose 2) * 2 * (9 choose 3) * (4! / 5) * 5!

[glossy valve]

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[topaz valley]

LOL

[gray nacelle]

ah

just a slight difference

[gray nacelle]

wait

where did u get

4!

[topaz valley]

im doing them in a line

and then dividing out the symmetries

might not actually work

[gray nacelle]

wait cant we do like

(5-1)!

for the round table

thingy

[topaz valley]

thats the 4!

[gray nacelle]

nani

[gray nacelle]

wait then whats the 5!

[topaz valley]

thats the other table

[gray nacelle]

11c2 (choose the two friends) * 2 (permute them) * 9c3 (choose table 5's people) * 2! (permute the 3 of them but -1) * 5! (permute the 6 table)

ok wait

but its the same as this yes

[topaz valley]

is it

im not sure

[gray nacelle]

um

its not

nvm

rip

[topaz valley]

,w (11 choose 2) * 2 * (9 choose 3) * (2!) * 5!

[glossy valve]

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[gray nacelle]

this is sad

[topaz valley]

wait

im dumb

[gray nacelle]

if ur dumb im ret0rded

[topaz valley]

,w 2! * (9 choose 3) * 4! / 5 * 5!

[glossy valve]

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[gray nacelle]

wat

[topaz valley]

,w 2! * (9 choose 4) * 5! / 6 * 4!

[glossy valve]

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[topaz valley]

,w (11 choose 5) * 4! * 5! - 2! * (9 choose 3) * 4! / 5 * 5! - 2! * (9 choose 4) * 5! / 6 * 4!

[glossy valve]

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[topaz valley]

making a wild guess here

[gray nacelle]

lemme check the answer

1064448

[topaz valley]

bruh

[gray nacelle]

sorry

[topaz valley]

im so bad at combi

[gray nacelle]

or maybe

this question

is wrong

cuz if u cant do it then theres a problem yes

[topaz valley]

,w (11 choose 5) * 5! * 6! - 2! * (9 choose 3) * 4! * 6! - 2! * (9 choose 4) * 5! * 5!

[glossy valve]

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[gray nacelle]

MLMAO

[topaz valley]

LOL okay thats definitely not it

[gray nacelle]

ah yes

[topaz valley]

,w (11 choose 5) * 4! * 5! - (2! * (9 choose 3) * (4! + 3!)) / 5 * 5! - (2! * (9 choose 4) * (5! + 4!)) / 6 * 4!

[glossy valve]

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Requested by 夢雪#2250

[topaz valley]

yeah okay

[gray nacelle]

ah yes

[gray nacelle]

WOAH

[topaz valley]

so it was that weird thing i was worrying about

and i ignored it

like a fool

[gray nacelle]

wait before u go thru

ur solution

can u tell me

why my one

doesnt work pls

[topaz valley]

you mean this?

[gray nacelle]

erm

[topaz valley]

,w (11 choose 2) * 2 * (9 choose 3) * 2! * 5!

[glossy valve]

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Requested by 夢雪#2250

[topaz valley]

the 11 choose 2 is totally busted lmao

[gray nacelle]

$11C2 * 2 * \choose{9}{3} * 2! * 5!$

[glossy valve]

HellO

[gray nacelle]

wtf

[topaz valley]

LOL

[gray nacelle]

wataheck

[topaz valley]

you dont need the 11 choose 2

[gray nacelle]

wait why

[topaz valley]

because theres only 1 pair

of friends

[gray nacelle]

omg

OHHHHHHHHH

[topaz valley]

two particular friends

LOL

[gray nacelle]

that makes

sense

so

2! * 9C3 * 2! * 5!

[topaz valley]

now lemme check if im being dumb

,w (2! * (9 choose 3) * (4! + 3!)) / 5 * 5!

[glossy valve]

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Requested by 夢雪#2250

[gray nacelle]

wut

[topaz valley]

,w 2 * (9 choose 3) * 2! * 5!

[glossy valve]

Results provided by WolframAlpha

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Requested by 夢雪#2250

[topaz valley]

okay i wasnt being dumb

[gray nacelle]

ih

OH

ok

so

using my method

i would do the same thing

for table of 6

[topaz valley]

yeah

but you gotta count it properly

how many ways they can sit together at a particular table

i just did it in a line and divided out the rotations

[gray nacelle]

2 * 9C4 * 3! * 4! = 36288

nani

my answer is

very wrong

saad

[rapid laurel]

hmmm

[topaz valley]

2 frens at 5 table: (2! * (9 choose 3) * (4! + 3!)) / 5 * 5!
2 frens at 6 table: (2! * (9 choose 4) * (5! + 4!)) / 6 * 4!

[rapid laurel]

be sad

[gray nacelle]

Ok chris

[topaz valley]

you shouldve gotten 120960

not 40320

[gray nacelle]

wait wats wrong

[topaz valley]

like

the way you're arranging the people

at the 5 table

you're undercounting by a lot

just do it in a line

[gray nacelle]

but i did the 4! thou

[topaz valley]

and the divide out the rotations

its not this

its (2! * (9 choose 3) * (4! + 3!)) / 5

so the 2! * (9 choose 3) is fine

but then

(4! + 3!) / 5 is how many ways you can arrange the (group of 2) and the 3 others

[gray nacelle]

oh

that

makes sense

for me i split them tho

like the 2!

is for the remaining 3 people at the table of 5

[topaz valley]

no no like

so you just lump the 2 people together

as 1 group

so you have 4 things to permute

thats why its 4!

[gray nacelle]

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

[topaz valley]

but then right

so we're doing this in a line

the /5 is the 5 rotations we need to divide out

but

if we do it in a line

we miss the case where the group of 2 get split at the edges

like X -------- X

so thats the + 3!

cuz you put them at the edges and permute the middle 3

theres probably a better way to do this but im too lazy to think of it rn

[gray nacelle]

how about

this

[topaz valley]

yeah

[gray nacelle]

NICE

OKAY

ur probably not free alr yes

[topaz valley]

thats a better way to do it i think

yeah

[gray nacelle]

nooooo

[topaz valley]

nice

[gray nacelle]

wait so

u gtg now

[topaz valley]

yeah

im gonna

[gray nacelle]

noooo

[topaz valley]

depart

[gray nacelle]

okay

i shall

see u soon

[topaz valley]

suffer with more problems

[gray nacelle]

wow why u do dis

ok

have fun

[topaz valley]

[gray nacelle]

madam

snow

[topaz valley]

do you really believe circle

[gray nacelle]

Yes

[topaz valley]

i see

[gray nacelle]

Yes

So u r madam

Yes

Anyway

.close

[full forum]

Channel closed

Closed by @gray nacelle

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[gray nacelle]

Hah

[topaz valley]

[gray nacelle]

[full forum]

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[viral zenith]

Hello

[viral zenith]

Could anyone please explain why WA won't integrate this?

Did I type something wrong?

[topaz valley]

remove dot

[slate compass]

Yh

[native flicker]

Ibp with u = 2x+2 , dv = e^iwx

Waow pro premium

[viral zenith]

I need every resource I can get my hands on to pass my maths degree

It's all tax deductible for me anyway because my course relates to my work

Also guys, is there any way of integrating both of these fast or efficiently? Are they equal or almost equal?

The area under the red and green lines are the same?

[full forum]

@viral zenith Has your question been resolved?

[full forum]

@viral zenith Has your question been resolved?

[brittle steeple]

yes

[brittle steeple]

probably not

I think the e^-iwx screws up any symmetry you'd have otherwise

[viral zenith]

.close

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[torn jolt]

Hmm can someone explain how this is conjugated

[rapid laurel]

somebody help out the poor fairylog

[brittle steeple]

oh this is cursed

[rapid laurel]

ikr it's not even a^2-b^2 cause it's 2 sqrt n+1

in the denominator

[brittle steeple]

but my approach if I had to conjugate a denominator like that would be precisely to multiply both sides by the thing on the left that the fraction is equal to

$\frac1{\sqrt a+\sqrt b+\sqrt c}=\frac{\sqrt a+\sqrt b-\sqrt c}{a+b-c+2\sqrt{ab}}$

[glossy valve]

monikanicity

[brittle steeple]

which you can then conjugate the normal way

[rapid laurel]

why does the LHS denominator equal that??/

ahh ill just accept it

[brittle steeple]

difference of squares

Oh lhs

[rapid laurel]

rhs

i meant

also like from the pic, the C is different

[brittle steeple]

ah difference of squares or u can do super foiling

you can conjugate pretty much any denominator it's actually sick

like

$\frac1{2+3^{1/3}}$

[rapid laurel]

bro i wrote the notes wrong

f

[glossy valve]

monikanicity

[rapid laurel]

nvm nvm i got it

[rapid laurel]

this is cool tho

actually just continue

[brittle steeple]

just multiply both sides by $2^2-2*3^{1/3}+3^{2/3}$

[glossy valve]

monikanicity

[rapid laurel]

why this unworldly thing😭

[brittle steeple]

the big part of the difference of cubes factorization lol

[rapid laurel]

wtf

[brittle steeple]

or sum of cubes rather

that's actually the final value of the expression too I believe

,w $\frac1{2+3^{1/3}}$

[glossy valve]

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Requested by monikanicity#0205

[brittle steeple]

,w 2^2-2*3^{1/3}+3^{2/3} to 10 digits

[rapid laurel]

ok?

[brittle steeple]

THANKS WOLFRAM

[glossy valve]

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Requested by monikanicity#0205

[rapid laurel]

bro wut are u

doing

[brittle steeple]

oh I see

[rapid laurel]

😭

[brittle steeple]

,w (2^2-2*3^{1/3}+3^{2/3})/11 to 10 digits

[glossy valve]

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Requested by monikanicity#0205

[brittle steeple]

THERE

Finally

[rapid laurel]

?????

im passing out

[brittle steeple]

it's the same

as 1/(2+cbrt(3))

[rapid laurel]

haha nice, i dont get it but i got my own question

its fine

is this thing u typed ever useful

[brittle steeple]

Doubt it

Unless you really want to prove 2 complicated algebraic expressions are equal

[rapid laurel]

anyway, the conjugate

was used to solve this question

like if u just keep on conjugating it, the denominator goes to infinity

and then the numerator becomes very simplified

and the limit becomes 0

neat technique

[topaz valley]

kinda dumb tbh

[rapid laurel]

how

seems smart to me

[brittle steeple]

ah I see

[rapid laurel]

is there a better way>?

and why is it a bad method

[brittle steeple]

Could just multiply through by sqrt(1/n)

and then multiply the whole expression by sqrt(n) at the end

[brittle steeple]

or nah

that probably doesn't work

[topaz valley]

thats all too much work

this is just difference of two limits

which are the same limit

i guess you need to show the limit exists for one of them

but otherwise its just 0

[brittle steeple]

wait this is fine actually

Or you get 0*inf

ah well yeah that's easier

[rapid laurel]

snow's way works?/,

[brittle steeple]

yeah

[rapid laurel]

u can do limit operation like that? why is it subtracting sqrt n

at the end

[brittle steeple]

cause the whole second limit is subtracted

[rapid laurel]

wut isnt it + sqrt n

on the LHS

[brittle steeple]

double subtraction here

[rapid laurel]

oh

just like

algebra

[brittle steeple]

yeah

[topaz valley]

limit exists because (sqrt(x+1) - sqrt(x)) (sqrt(x+1) + sqrt(x)) is bounded by 1

so sqrt(x+1) - sqrt(x) is bounded by 1

[brittle steeple]

ok see now that's just conjugation

[topaz valley]

well yes but not on 3 terms

and you dont need work out any of the limits

[rapid laurel]

moni, explain snow's first line😭

[brittle steeple]

Yeah ik

[rapid laurel]

how did u get this

[topaz valley]

anyway im leaving bye

[rapid laurel]

moni, moni

how did snow get that line

[brittle steeple]

difference of squares

[rapid laurel]

ahh

[brittle steeple]

(a-b)(a+b)

[rapid laurel]

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

is bounded by 1？？？

oh

it is

nvm

[brittle steeple]

ah yeah

[rapid laurel]

whats the next line

then

[brittle steeple]

It would have been better described as just conjugation

[rapid laurel]

why does snow's first line imply the second line

[brittle steeple]

requires the assumption that sqrt(x+1)+sqrt(x)≥1

what should be done is the limit just written as 1/(sqrt(x)+sqrt(x+1)) really

[topaz valley]

this is better

limit is 0

[rapid laurel]

i understood till here

can u explain

moni

[brittle steeple]

sqrt(x+1)-sqrt(x)=1/(sqrt(x+1)+sqrt(x))

[rapid laurel]

yes

and thats just 0

[brittle steeple]

it goes to 0 yeah

but for any nonnegative x it's 1 or smaller

yeah its easier to just say it goes to 0

[rapid laurel]

wait so isnt what u did only saying the second limit is 0?

do you still have to do the first limit??/

[brittle steeple]

first limit is pretty much the same limit

[rapid laurel]

oh

ok

ok

[brittle steeple]

if you replace x with x-1 you get the same

[rapid laurel]

okokok nice

nice

[brittle steeple]

and x-1 goes to inf as x does yeah

[torn jolt]

Ok

Moni

U should check out

Help 26

[rapid laurel]

^

[brittle steeple]

ah ok I can

[torn jolt]

[topaz valley]

actually hilarious

[brittle steeple]

ah right

[rapid laurel]

snow im going to meet fairy in person

this christmas

[brittle steeple]

I looked at that one and was just like 😨

[topaz valley]

using two accounts to evade the bot from saying not to open multiple channels

[rapid laurel]

more hilarious

[topaz valley]

[brittle steeple]

Ah lmao

[torn jolt]

Maybe u should check out 26

Too

Like Chris is suffering

[brittle steeple]

Somehow I didn't catch on even

[full forum]

@torn jolt Has your question been resolved?

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[misty sundial]

For this question imagine a typical deck of cards with an additional 5 suit(s). Each new suit is unique and distinct from any original or new suit and still has the normal 13 denominations as the original suits. Your new expanded deck then has 117 total cards and a total of 9 unique suits.

[misty sundial]

Selecting 4 cards without replacement, how many different ways, regardless of order, can you get three "Aces" and one "Heart"?

[full forum]

@misty sundial Has your question been resolved?

[ivory cairn]

How many ways can you pick 3 aces?

[misty sundial]

9C3

[ivory cairn]

Great!

How many ways can you pick one heart (that isn’t an ace)

[misty sundial]

should be 13C1

oh not an ace

12C1

[ivory cairn]

Now multiply those together

[misty sundial]

So is that one of the 2 cases?

would you want to remove the aces that can be hearts from that?

why or why not?

[ivory cairn]

The problem is vague.

I’m not sure if it wants exactly 3 aces and one heart.
Or if 4 aces or 2 hearts is ok.

[misty sundial]

I’m assuming you can’t have more or less than 3 aces

and can’t have more of less than 1 heart

[misty sundial]

pretty sure 4 aces or 2 hearts isnt okay

[ivory cairn]

Ok then, yeah. Two cases. One without the ace of hearts, one with the ace of hearts.

[misty sundial]

okay let me see if i can try

case without the ace of hearts is

8C3 x 12C1

i think

[ivory cairn]

Yep, so no ace of hearts is good

[misty sundial]

and then i think the one with ace of hearts could be

1 x 8C2 x 102

[ivory cairn]

Yeah, ace of hearts, 2 other aces, any other non-ace or non-heart

[misty sundial]

ohhh

i dont think i got rid of the aces

just got rid of the 2 i selected

let me fix it

i think its 96

instead

[ivory cairn]

Yep!

[misty sundial]

awesomeeee

so i just add the two

and then i divide by

130 C 4 ?

actually it just asks for the total number

not a probability

so i just add those 2 and im done i think

thank youuuu

[misty sundial]

sorry to bother you I got another question also. if cards are selected with replacement what is the probability of drawing a face card before an ace?

Would that simply be

(3x9)/117 x (9)/117

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[valid saddle]

I just wanted to know if i did the division and composition correctly. f(x)= 3/x g(x)= x/x+3

[frozen spade]

here should be g(x)

$f(g(x)) = \frac{3}{g(x)}$

[glossy valve]

秋水

[valid saddle]

Oh right

I changed the x into the value of g(x)

Is the rest correct?

[frozen spade]

the rest is correct

[valid saddle]

Alright thankss

The division is also correct?

[frozen spade]

yes, a/(b/c) = a*(c/b)

[valid saddle]

Alright thankss

.close

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[frosty mural]

is this solvable?

[oak basin]

yes

any system of equations is solvable

tho i guess that statement depends on how you define "solvable"

[frosty mural]

wolfram came up with no solution exists

[oak basin]

that does not make a system of equation unsolvable

but anyway, there is a solution to this system

you probably entered sth wrong in there

[frosty mural]

I did XD and I did it twice it seems to symbolab aswell

thankyou and apologies

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[signal beacon]

Could someone please tell me where I am going wrong with this question on RSA encryption in my exercise book?

The question:
encode the message "TELL ME WHY" using three-digit blocks and the RSA public key (3071,3)
Use the digit 0 as padding in the last block, if needed.
The resulting cipher text should be written in 4-digit blocks.

I tried the first part of the message just to test it. So, "TELL"
T = 19
E = 4
L = 11
L = 11
Are the correct groupings:
190 400 110 110 ?

If not, how do I group the digits?
Also, what does it mean by "Use the digit 0 as padding in the last block, if needed."?

Here is my attempt encode it

e = 3
n = 3017

C = P^e mod n

190^3 mod 3071 = 1457 - this one is the correct answer in the book
400^3 mod 3071 = 360 - These last three are incorrect.
110^3 mod 3071 = 1275
110^3 mod 3071 = 1275

So I am going wrong somewhere. Any help is appreciated.

Also, the answer from my exercise book for the whole message is:
1457 0434 1036 1420 0843 1528

[signal beacon]

pls

[full forum]

@signal beacon Has your question been resolved?

[signal beacon]

Alright I figured out the correct groupings were

190 411 111 204 220 724

.close

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[errant abyss]

e^ipi=-1
what will happen if you replace e with some other number?

[fast peak]

You will end up somewhere else on the unit circle

Use a=e^ln(a)

[errant abyss]

ohhh yes i ddnt think of that

Thanks

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[dim kernel]

i did this question by finding the distance between the 2 vectors, then minimising it, but the solution had a alternative method which i dont understnad

can someone help me understand this alternate method?

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[dim kernel]

Image
Image
i did this question by finding the distance between the 2 vectors, then minimising it, but the solution had a alternative method which i dont understnad
Image
can someone help me understand this alternate method?

[dim kernel]

did this question by finding the distance between the 2 vectors, then minimising it, but the solution had a alternative method which i dont understnad

can someone help me understand this alternate method?

<@&286206848099549185>

[deep flint]

!15m

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[deep flint]

sorry, the channel header shows 5:00 my time

[dim kernel]

nvm sorry

[deep flint]

i'm wondering how the aircraft proposes to drop its cargo backwards

oh. i see, it's not dropping it at that poisition, yhou're just asked to figure out how clos eit gets for some incomprehensible reason

[dim kernel]

ye

so i found the distacne and minimissed it

it wroked, but the solu had alternative mthod

[deep flint]

the aircraft's path is a straight line, so the minimum distance will be when the vector is normal

[dim kernel]

whick i dont underdtnad

ye

o

[deep flint]

so you end up with a right triangle, pythagoras does the rest

[dim kernel]

but

how to u know the time

when its closest to 1800

[deep flint]

you don't need to

[dim kernel]

dont u need t to find the distance

then use pythagoras

since its a position vector

[deep flint]

i'm pretty sure this is using the fact that the position vector plots out a line

and then uses a trig identity with repsect to the dot product

[dim kernel]

im not understadning

.close

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[ionic terrace]

guys simple question

[hearty lynx]

What question

[tired quarry]

answer is trival

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@ionic terrace Has your question been resolved?

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[limpid pollen]

hi, I'm doing my parabolas homework and I'm stuck on the extended response questions as usual. The question follows. A 100m steel cable is threshed through a series of posts in order to construct a fence around a paddock with four straight sides as shown (a rectangle). Write an equation which links l and w, (length and width)

[limpid pollen]

oh and m means meters

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[willow bloom]

Hi, I have No idea How to solve this this.

[warm abyss]

Try to bring the 1+1/n to a common denominator