#help-39 | Mathematics | Page 4

faint onyx Sep 28, 2022, 7:46 AM

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it was still

grim patrol Sep 28, 2022, 7:46 AM

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LOL

faint onyx Sep 28, 2022, 7:46 AM

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slimy

grim patrol Sep 28, 2022, 7:46 AM

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...

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well

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its ok

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thats just

faint onyx Sep 28, 2022, 7:46 AM

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😦

grim patrol Sep 28, 2022, 7:46 AM

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undercooked

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u can just

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take that

faint onyx Sep 28, 2022, 7:46 AM

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yes

grim patrol Sep 28, 2022, 7:46 AM

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n throw it on the frying pan

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LOL

faint onyx Sep 28, 2022, 7:46 AM

#

o

grim patrol Sep 28, 2022, 7:46 AM

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i rmb

faint onyx Sep 28, 2022, 7:46 AM

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true

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ANYWAY

grim patrol Sep 28, 2022, 7:46 AM

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back in the day

faint onyx Sep 28, 2022, 7:46 AM

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carbonara sauce

grim patrol Sep 28, 2022, 7:46 AM

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when i didnt think of that

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i just

faint onyx Sep 28, 2022, 7:46 AM

#

grim patrol Sep 28, 2022, 7:46 AM

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threw away so many eggs

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then

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i realised ltr

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i coulda

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cooked em

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T.T

faint onyx Sep 28, 2022, 7:47 AM

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wow

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i actually

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just ate the egg

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lmao

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the undercooked

grim patrol Sep 28, 2022, 7:47 AM

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ummm

faint onyx Sep 28, 2022, 7:47 AM

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one

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ez

grim patrol Sep 28, 2022, 7:47 AM

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LOL

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i think

faint onyx Sep 28, 2022, 7:47 AM

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built different

grim patrol Sep 28, 2022, 7:47 AM

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its jsut some chance of salmonala

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not 2 bad

faint onyx Sep 28, 2022, 7:47 AM

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wtf

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OASKSDJOADS

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anyway

grim patrol Sep 28, 2022, 7:47 AM

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ok wahts ur q

faint onyx Sep 28, 2022, 7:47 AM

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PROBLEM AT HAND

#

#

so

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here

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im tryna show the implicit form of a line

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in R^3

grim patrol Sep 28, 2022, 7:48 AM

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so

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u wanna combine that

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into some

faint onyx Sep 28, 2022, 7:48 AM

#

wait so

grim patrol Sep 28, 2022, 7:48 AM

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this?

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faint onyx Sep 28, 2022, 7:48 AM

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this is just the

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linear combination right

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wait no

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eudrlicina sapce

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space

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then now

grim patrol Sep 28, 2022, 7:49 AM

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isnt it the same

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lol

faint onyx Sep 28, 2022, 7:49 AM

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o

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wait how

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lik wheres the

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= d

grim patrol Sep 28, 2022, 7:49 AM

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eh

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idk

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just

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cross product

faint onyx Sep 28, 2022, 7:49 AM

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wow

grim patrol Sep 28, 2022, 7:49 AM

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find the

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a b c

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the sub in a val to get d

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ez

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mayb thrs another way

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shrugs

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LOL

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what works works

faint onyx Sep 28, 2022, 7:50 AM

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WO

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wait

grim patrol Sep 28, 2022, 7:50 AM

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nyani

faint onyx Sep 28, 2022, 7:51 AM

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man

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im like

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so confused

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the explicit form

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implicit form

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so confusing

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;=;

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sad

grim patrol Sep 28, 2022, 7:52 AM

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maybe

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u shld

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not do so much math

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just

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chill

faint onyx Sep 28, 2022, 7:52 AM

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wat

grim patrol Sep 28, 2022, 7:53 AM

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like

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ok actually

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u were doin some

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weird advanced math

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but actually

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now u arent

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nvm

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ignore what i justs aid

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hahahha

faint onyx Sep 28, 2022, 7:53 AM

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but theyre from the

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same thing

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tho

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linear algebra i

grim patrol Sep 28, 2022, 7:53 AM

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wait what

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actually

faint onyx Sep 28, 2022, 7:53 AM

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ye

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lmao

grim patrol Sep 28, 2022, 7:53 AM

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isnt this like

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sec sch or smt

faint onyx Sep 28, 2022, 7:53 AM

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no

grim patrol Sep 28, 2022, 7:53 AM

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i mean

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LOL

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anw

faint onyx Sep 28, 2022, 7:53 AM

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i mean

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i think

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yes

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but im not there yet

grim patrol Sep 28, 2022, 7:53 AM

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LOL

faint onyx Sep 28, 2022, 7:54 AM

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so

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im just studying

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stuff

grim patrol Sep 28, 2022, 7:54 AM

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ok lets go back

faint onyx Sep 28, 2022, 7:54 AM

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other than this

grim patrol Sep 28, 2022, 7:54 AM

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to

faint onyx Sep 28, 2022, 7:54 AM

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lal

grim patrol Sep 28, 2022, 7:54 AM

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weierstrass

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LOL

faint onyx Sep 28, 2022, 7:54 AM

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this pls

#

grim patrol Sep 28, 2022, 7:54 AM

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ye i dont get it

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whats the issue

faint onyx Sep 28, 2022, 7:54 AM

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like

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wai

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t

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i understand

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now

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magic

grim patrol Sep 28, 2022, 7:55 AM

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t hanks

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is

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cyno

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or candace

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any good

faint onyx Sep 28, 2022, 7:55 AM

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btw

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wait wat

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oh

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genshin?

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i have no idea

grim patrol Sep 28, 2022, 7:56 AM

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yes

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LOL

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sad

faint onyx Sep 28, 2022, 7:56 AM

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cyno looks dope

grim patrol Sep 28, 2022, 7:56 AM

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he looks like

faint onyx Sep 28, 2022, 7:56 AM

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btw whats linear transformation vs euclidian space n

grim patrol Sep 28, 2022, 7:56 AM

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ahem

faint onyx Sep 28, 2022, 7:56 AM

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wats the difference

faint onyx Sep 28, 2022, 7:56 AM

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grim patrol he looks like

wot

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razor ripoff

grim patrol Sep 28, 2022, 7:56 AM

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faint onyx btw whats linear transformation vs euclidian space n

NO

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IDK

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STAPH THAT

faint onyx Sep 28, 2022, 7:56 AM

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help pls

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I DONT UNDERSTAND

grim patrol Sep 28, 2022, 7:56 AM

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same

faint onyx Sep 28, 2022, 7:56 AM

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WHY DO U KNOW SO MUCH AND SO LITTLE AT THE SAME TIME

grim patrol Sep 28, 2022, 7:57 AM

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wow

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i got a sayu dupe

faint onyx Sep 28, 2022, 7:57 AM

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wow

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i want zhongli

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i lost to diluc

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fml

grim patrol Sep 28, 2022, 7:57 AM

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ive zl

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i want

faint onyx Sep 28, 2022, 7:57 AM

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give me pls

grim patrol Sep 28, 2022, 7:57 AM

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kusanali

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n

faint onyx Sep 28, 2022, 7:57 AM

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who that

grim patrol Sep 28, 2022, 7:57 AM

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c1 hutao

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the

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loli archon

faint onyx Sep 28, 2022, 7:57 AM

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hutao noob

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how is hutao gud

grim patrol Sep 28, 2022, 7:57 AM

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im a

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tier list slave

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shes pretty hot

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ngl

faint onyx Sep 28, 2022, 7:58 AM

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wot

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she is?

grim patrol Sep 28, 2022, 7:58 AM

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yea

faint onyx Sep 28, 2022, 7:58 AM

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isnt she like

grim patrol Sep 28, 2022, 7:58 AM

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so is

faint onyx Sep 28, 2022, 7:58 AM

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4

grim patrol Sep 28, 2022, 7:58 AM

#

bennett

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cl

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xq

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kokomi

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mona

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LOL

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why am i sayig this

faint onyx Sep 28, 2022, 7:59 AM

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how is

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bennett hot

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how is

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kokomi

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how is mona

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i donut understand

grim patrol Sep 28, 2022, 8:00 AM

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the

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tier list

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it says they are hot

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af

faint onyx Sep 28, 2022, 8:01 AM

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show pls

grim patrol Sep 28, 2022, 8:03 AM

#

#

#

https://genshin.gg/tier-list/

GENSHIN.GG

Genshin Impact Tier List (Best Characters) - Genshin.gg

Discover the best characters and builds ranked for all content in Genshin Impact.

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https://game8.co/games/Genshin-Impact/archives/297465

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look at them

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xq xl

#

bennett

#

kokomi

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hutao

#

mona

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zl also p hot

faint onyx Sep 28, 2022, 8:04 AM

#

dud

#

thats not hot

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thats like

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gameplay

grim patrol Sep 28, 2022, 8:04 AM

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WOWWW

faint onyx Sep 28, 2022, 8:04 AM

#

WATTTT

grim patrol Sep 28, 2022, 8:05 AM

#

ARE U CALLING ME A META SLAVE

faint onyx Sep 28, 2022, 8:05 AM

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WHAT IS THAT

grim patrol Sep 28, 2022, 8:05 AM

#

no

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ignore that

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anyway

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wao

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genshin

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new update has a huge new region

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:O

faint onyx Sep 28, 2022, 8:05 AM

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im not even at sumeru yet

grim patrol Sep 28, 2022, 8:05 AM

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eh

faint onyx Sep 28, 2022, 8:05 AM

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i just finished inaazuma

grim patrol Sep 28, 2022, 8:05 AM

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i think u can just run there

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without completing ina

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oh man

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in sumeru

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the worst quest is the

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plants quests

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so bad

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so long

faint onyx Sep 28, 2022, 8:07 AM

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i just want

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raiden

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is she good

grim patrol Sep 28, 2022, 8:07 AM

#

grim patrol

ye

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shes

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p gd

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pretty hot

#

ngl

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HAHHAHA

faint onyx Sep 28, 2022, 8:07 AM

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kazuha is good?

grim patrol Sep 28, 2022, 8:07 AM

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yes too

faint onyx Sep 28, 2022, 8:07 AM

#

grim patrol pretty hot

this i agree

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raiden hot asf

grim patrol Sep 28, 2022, 8:08 AM

#

kazuha

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is also

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hot

faint onyx Sep 28, 2022, 8:09 AM

#

he looks good

#

zhongli is hotter than

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kazhua

grim patrol Sep 28, 2022, 8:09 AM

#

woah woah

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dont be like that

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they are both

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top tier

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hotties

faint onyx Sep 28, 2022, 8:10 AM

#

nono

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i gtg

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help me in genshin pls

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LATER

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DM ME

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bybeybe

#

.close

pearl pondBOT Sep 28, 2022, 8:10 AM

#

Channel closed

Closed by @faint onyx

Use .reopen if this was a mistake.

grim patrol Sep 28, 2022, 8:10 AM

#

LOL

pearl pondBOT Sep 28, 2022, 8:11 AM

#

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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rancid pumice Sep 28, 2022, 9:48 AM

#

pearl pondBOT Sep 28, 2022, 9:48 AM

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rancid pumice

rancid pumice Sep 28, 2022, 9:48 AM

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How do I solve these types of questions?

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I know but I don’t remember how I did it

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What do you mean by move up 1/x^2?

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Up as in to the numerator?

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Ohh makes sense

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What about something like 3

grim spoke Sep 28, 2022, 9:52 AM

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there is no 3

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that's wrong

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for c, at elast

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3 * (1/x) is what yuo're differentiating

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so its derivative will be 3 times the derivative of 1/x

rancid pumice Sep 28, 2022, 9:55 AM

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What’s the rule here? In f’(x) if you have something like 5x^2 you multiply the power and coefficient while minimising 1 from the power

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To become 10x

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Is there an explanation like that for these questions?

grim spoke Sep 28, 2022, 9:56 AM

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1/x is x^-1, so the derivative is -x^-2, and so for 3/x it's 3*(-x^-2)

rancid pumice Sep 28, 2022, 9:56 AM

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Lol e.)

grim spoke Sep 28, 2022, 9:56 AM

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smudgy e

shell oxide Sep 28, 2022, 9:57 AM

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Rewrite it as $4 *x^{-3}$ and you will see that u can use the power rule like this

jolly parrotBOT Sep 28, 2022, 9:58 AM

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❤Pauli Excluder❤

rancid pumice Sep 28, 2022, 9:58 AM

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Ohh I get it

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Alright that makes sense, thanks

grim spoke Sep 28, 2022, 9:59 AM

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rancid pumice Is there an explanation like that for these questions?

$\frac{1}{x^n} = x^{-n}$

jolly parrotBOT Sep 28, 2022, 9:59 AM

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rome of oxtrot

grim spoke Sep 28, 2022, 9:59 AM

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and then you just use the power rule as usual

shell oxide Sep 28, 2022, 9:59 AM

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If x^n counts how many times you multiply, x^-n counts how many times you divide

grim spoke Sep 28, 2022, 10:00 AM

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i'm assuming you don't want me to prove the power rule, it's not hard but it's likely in your textbook

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or else it's just given to you without proof, depends on what sort of class you're taking tbh

rancid pumice Sep 28, 2022, 10:01 AM

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I’m doing pre math methods

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I think I understand it now though

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Thanks

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.close

grim spoke Sep 28, 2022, 10:01 AM

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np

pearl pondBOT Sep 28, 2022, 10:01 AM

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Channel closed

Closed by @rancid pumice

Use .reopen if this was a mistake.

pearl pondBOT Sep 28, 2022, 1:36 PM

#

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.

surreal sky Sep 28, 2022, 1:37 PM

#

pearl pondBOT Sep 28, 2022, 1:37 PM

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surreal sky

surreal sky Sep 28, 2022, 1:38 PM

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is it just expanded with the ^2 added to it

cinder reef Sep 28, 2022, 1:38 PM

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yes it’s just expansion

surreal sky Sep 28, 2022, 1:39 PM

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why is the 3 on the outside affected by it then

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which makes the 6sina cosa

cinder reef Sep 28, 2022, 1:42 PM

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it’s not though

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you multiply with 3 after expanding

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that’s what gives the 6

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,w expand (Sinα+cosα)^2

jolly parrotBOT Sep 28, 2022, 1:42 PM

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Results provided by WolframAlpha

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

cinder reef Sep 28, 2022, 1:44 PM

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don’t mind wolframs thing hahahah

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after you expand you’ll get $3(sin^{2}α + 2sinαcosα + cos^{2}α)$

jolly parrotBOT Sep 28, 2022, 1:45 PM

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duckiescute!

surreal sky Sep 28, 2022, 1:45 PM

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i thought it would be just sin^2a+cos^2a

cinder reef Sep 28, 2022, 1:45 PM

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oh take note that

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$(sinx + cosx)^{2} ≠ sin^{2}x + cos^{2}x$

jolly parrotBOT Sep 28, 2022, 1:46 PM

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duckiescute!

cinder reef Sep 28, 2022, 1:46 PM

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expand it using foil method to not make the mistake

#

you can write it as

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$(sinx + cosx)^{2} = (sinx + cosx)(sinx + cosx)$

jolly parrotBOT Sep 28, 2022, 1:47 PM

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duckiescute!

pearl pondBOT Sep 28, 2022, 2:00 PM

#

@surreal sky Has your question been resolved?

surreal sky Sep 28, 2022, 2:01 PM

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like this is correct right?

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maybe little overcomplicated but works

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i used this rule

cinder reef Sep 28, 2022, 2:04 PM

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surreal sky maybe little overcomplicated but works

I mean yes but it’s kind of over complicating hahaha

surreal sky Sep 28, 2022, 2:04 PM

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well

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its still correct

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nothing else matters to me

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: )

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need to pass an exam

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.close

pearl pondBOT Sep 28, 2022, 2:05 PM

#

Channel closed

Closed by @surreal sky

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Available help channel!

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

midnight haven Sep 28, 2022, 2:10 PM

#

Venn-Diagramm

pearl pondBOT Sep 28, 2022, 2:10 PM

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midnight haven Venn-Diagramm

midnight haven Sep 28, 2022, 2:10 PM

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#

6 Players can play midfield and striker
1 Player can only play defence
4 Players can play every position
5 Players can play midfield and defence
4 Players can play striker and defence
14 Players can play defence or striker
3 Players can't play striker or defence

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Question: How many Players can only play midfield?

#

pearl pondBOT Sep 28, 2022, 2:26 PM

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@midnight haven Has your question been resolved?

midnight haven Sep 28, 2022, 2:29 PM

#

#

@cyan oracle

#

#

how to fill the last 2 in the venn diagramm?

#

red is striker
blue is midfield
yellow is defence

#

#

right?

pearl pondBOT Sep 28, 2022, 3:06 PM

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@midnight haven Has your question been resolved?

pearl pondBOT Sep 28, 2022, 4:06 PM

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@midnight haven Has your question been resolved?

midnight haven Sep 28, 2022, 4:56 PM

#

.close

pearl pondBOT Sep 28, 2022, 4:56 PM

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Channel closed

Closed by @halcyon ridge

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pearl pondBOT Sep 28, 2022, 6:21 PM

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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>.
• 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.

golden kraken Sep 28, 2022, 6:22 PM

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anyone good at micro

pearl pondBOT Sep 28, 2022, 6:22 PM

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golden kraken anyone good at micro

grim patrol Sep 28, 2022, 6:23 PM

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no

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sad

slate thicket Sep 28, 2022, 6:23 PM

#

grim patrol Sep 28, 2022, 6:24 PM

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just ask ur

#

Q

golden kraken Sep 28, 2022, 6:24 PM

#

pearl pondBOT Sep 28, 2022, 6:39 PM

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@golden kraken Has your question been resolved?

pearl pondBOT Sep 28, 2022, 6:54 PM

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Channel closed

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pearl pondBOT Sep 28, 2022, 9:24 PM

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Available help channel!

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

pine lantern Sep 28, 2022, 10:21 PM

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Full disclosure, I am pretty sure I know how to do this. But I would like someone to show me how my answer is wrong here

pearl pondBOT Sep 28, 2022, 10:21 PM

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pine lantern Full disclosure, I am pretty sure I know how to do this. But I would like someon...

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@pine lantern Has your question been resolved?

pearl pondBOT Sep 28, 2022, 10:51 PM

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Channel closed

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pearl pondBOT Sep 29, 2022, 1:45 AM

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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.

pearl pondBOT Sep 29, 2022, 2:23 AM

#

jade kite Sep 29, 2022, 2:23 AM

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3.70

pearl pondBOT Sep 29, 2022, 2:24 AM

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Channel closed

Closed by @hot raven

Use .reopen if this was a mistake.

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

frail summit Sep 29, 2022, 2:38 AM

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Need immediate answers! Thank you! Evaluate the Following functions grade11

pearl pondBOT Sep 29, 2022, 2:38 AM

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frail summit Need immediate answers! Thank you! Evaluate the Following functions grade11

light helm Sep 29, 2022, 2:39 AM

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why immediate?

frail summit Sep 29, 2022, 2:40 AM

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I'm at school ☠️

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Please NervousSweat

green verge Sep 29, 2022, 2:43 AM

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plug in for x

frail summit Sep 29, 2022, 2:45 AM

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dn

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<@&286206848099549185>

pearl pondBOT Sep 29, 2022, 3:12 AM

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@frail summit Has your question been resolved?

pearl pondBOT Sep 29, 2022, 3:27 AM

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Channel closed

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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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• 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.

kindred ruin Sep 29, 2022, 3:32 AM

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pearl pondBOT Sep 29, 2022, 3:32 AM

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kindred ruin

kindred ruin Sep 29, 2022, 3:33 AM

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Hey, so I'm almost positive that E is right, but I don't see how any of the others could be correct

#

especially because the bounds from 4 to 2 are incorrect

#

desmod graph i used to help me

#

.close

pearl pondBOT Sep 29, 2022, 3:35 AM

#

Channel closed

Closed by @kindred ruin

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pearl pondBOT Sep 29, 2022, 2:53 PM

#

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hallow basalt Sep 29, 2022, 2:59 PM

#

is this correct?

pearl pondBOT Sep 29, 2022, 2:59 PM

#

hallow basalt is this correct?

hallow basalt Sep 29, 2022, 3:08 PM

#

.close

pearl pondBOT Sep 29, 2022, 3:08 PM

#

Channel closed

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warped bear Sep 29, 2022, 3:19 PM

#

6x²-10x+7-√45

pearl pondBOT Sep 29, 2022, 3:19 PM

#

warped bear 6x²-10x+7-√45

warped bear Sep 29, 2022, 3:19 PM

#

Is this a polynomial?

pearl pondBOT Sep 29, 2022, 3:34 PM

#

@warped bear Has your question been resolved?

deep bane Sep 29, 2022, 3:49 PM

#

warped bear Is this a polynomial?

yes

pearl pondBOT Sep 29, 2022, 3:49 PM

#

Channel closed

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pearl pondBOT Sep 29, 2022, 6:49 PM

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• Be polite and have a nice day!

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proper widget Sep 29, 2022, 6:56 PM

#

Hello, does anyone know where I made the mistake here ?

pearl pondBOT Sep 29, 2022, 6:56 PM

#

proper widget Hello, does anyone know where I made the mistake here ?

proper widget Sep 29, 2022, 6:57 PM

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I need to find a fraction without any unknown value

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Is there even a mistake here ?

#

Where ?

grim patrol Sep 29, 2022, 7:00 PM

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whats the full Q

proper widget Sep 29, 2022, 7:01 PM

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U(n+1) = (2/5)Un + 3
And V(n) = Un - 5

proper widget Sep 29, 2022, 7:01 PM

#

grim patrol whats the full Q

It is in french

grim patrol Sep 29, 2022, 7:01 PM

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at least tell us the Q context then

proper widget Sep 29, 2022, 7:01 PM

#

I have to find the coefficient of the sequence V(n)

#

To Make

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,,V(n) = v(0) × q^n

jolly parrotBOT Sep 29, 2022, 7:02 PM

#

Sama様

proper widget Sep 29, 2022, 7:03 PM

#

This is why i did

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,,V(n+1)/V(n)

jolly parrotBOT Sep 29, 2022, 7:03 PM

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Sama様

proper widget Sep 29, 2022, 7:05 PM

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I am gonna rephrase it to Make it more clear

#

I have :

jolly parrotBOT Sep 29, 2022, 7:06 PM

#

Sama様

#

Sama様

#

Sama様

proper widget Sep 29, 2022, 7:08 PM

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,,(Vn)=(V0) × q^n

jolly parrotBOT Sep 29, 2022, 7:08 PM

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Sama様

proper widget Sep 29, 2022, 7:09 PM

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Here i need to find the value of q by using :

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,,(Vn+1)/(Vn)

jolly parrotBOT Sep 29, 2022, 7:09 PM

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Sama様

pearl pondBOT Sep 29, 2022, 7:24 PM

#

@proper widget Has your question been resolved?

proper widget Sep 29, 2022, 7:28 PM

#

<@&286206848099549185> please

pearl pondBOT Sep 29, 2022, 7:58 PM

#

@proper widget Has your question been resolved?

pearl pondBOT Sep 29, 2022, 8:58 PM

#

@proper widget Has your question been resolved?

proper widget Sep 29, 2022, 9:00 PM

#

.close

pearl pondBOT Sep 29, 2022, 9:00 PM

#

Channel closed

Closed by @proper widget

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serene orchid Sep 29, 2022, 9:10 PM

#

hey, so I've been stuck on this problem for a while. I've tried solving by using the property F(a) - F(b) = F(x), but it just cancels out

pearl pondBOT Sep 29, 2022, 9:10 PM

#

serene orchid hey, so I've been stuck on this problem for a while. I've tried solving by using...

midnight haven Sep 29, 2022, 9:10 PM

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i need to find the are of abc

serene orchid Sep 29, 2022, 9:13 PM

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find AC and use tan

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@midnight haven

midnight haven Sep 29, 2022, 9:14 PM

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how can i find ac

#

@serene orchid

serene orchid Sep 29, 2022, 9:15 PM

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AD is 20 man

midnight haven Sep 29, 2022, 9:15 PM

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yeah so ac is 20-x

wind wigeon Sep 29, 2022, 9:16 PM

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its not necessarily symmetric

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so yes 20-x

serene orchid Sep 29, 2022, 9:16 PM

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yea I'm stupid

wind wigeon Sep 29, 2022, 9:17 PM

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you can make a drawing i think

#

#

that might make it easier

midnight haven Sep 29, 2022, 9:18 PM

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mhm and after i create 90 degree triangle

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what should i go for nxt

wind wigeon Sep 29, 2022, 9:18 PM

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just the usual

midnight haven Sep 29, 2022, 9:18 PM

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d cant be 90

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D cant be 90?

wind wigeon Sep 29, 2022, 9:19 PM

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im not saying D is 90 degrees

midnight haven Sep 29, 2022, 9:19 PM

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mb i thought you meant by the

wind wigeon Sep 29, 2022, 9:19 PM

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maybe it doesnt make it easier lol

midnight haven Sep 29, 2022, 9:19 PM

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or maybe it

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does

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yeah ill try

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with a drawing

wind wigeon Sep 29, 2022, 9:20 PM

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you can use the sin identity

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i would that tbh

midnight haven Sep 29, 2022, 9:20 PM

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a:sin=b:sin

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that one?

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ant than the usuals

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find the missing x

wind wigeon Sep 29, 2022, 9:20 PM

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yes

midnight haven Sep 29, 2022, 9:20 PM

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but where should i apply it

wind wigeon Sep 29, 2022, 9:21 PM

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16 and 20 degrees

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ad = 20 and corner abc

midnight haven Sep 29, 2022, 9:22 PM

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wait

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w8 can you fit in the numbers in the equation

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because i am not sure

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how you use the sin here

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with this triangle

wind wigeon Sep 29, 2022, 9:24 PM

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did you not learn the identity?

midnight haven Sep 29, 2022, 9:24 PM

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yeah i learned it

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a:sina=b:sinb=c:sinc

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that one

wind wigeon Sep 29, 2022, 9:24 PM

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yes

midnight haven Sep 29, 2022, 9:24 PM

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so you want me to find first

wind wigeon Sep 29, 2022, 9:24 PM

#

midnight haven Sep 29, 2022, 9:24 PM

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cd

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So you want me to find cd

wind wigeon Sep 29, 2022, 9:25 PM

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you dont need cd

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well to answer the question you do

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but this is an intermediate step

wind wigeon Sep 29, 2022, 9:25 PM

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serene orchid hey, so I've been stuck on this problem for a while. I've tried solving by using...

it looks like you didnt integrate 1/xlnx sienna

midnight haven Sep 29, 2022, 9:26 PM

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16:sin90=cb=sin20?

wind wigeon Sep 29, 2022, 9:27 PM

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how did you get that

midnight haven Sep 29, 2022, 9:27 PM

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i meant

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16:sin90=cb:sin20?

wind wigeon Sep 29, 2022, 9:27 PM

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no thats not right

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forget about cb for a second

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wait sorry dont do that

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theres a way easier way

midnight haven Sep 29, 2022, 9:29 PM

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mhm listening

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^_^

wind wigeon Sep 29, 2022, 9:29 PM

#

#

you know the green angle

midnight haven Sep 29, 2022, 9:29 PM

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its 180-90

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the other two sides of it

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as i remember or no>?

wind wigeon Sep 29, 2022, 9:30 PM

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well no but almost

midnight haven Sep 29, 2022, 9:30 PM

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.>>>>>

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...

wind wigeon Sep 29, 2022, 9:30 PM

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180 - 90 -20

midnight haven Sep 29, 2022, 9:31 PM

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why minus 20?

wind wigeon Sep 29, 2022, 9:31 PM

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because corner cab

midnight haven Sep 29, 2022, 9:32 PM

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so its 70

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than

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then

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"""

wind wigeon Sep 29, 2022, 9:32 PM

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yes

midnight haven Sep 29, 2022, 9:32 PM

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then you find acb

wind wigeon Sep 29, 2022, 9:33 PM

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you already know acb

midnight haven Sep 29, 2022, 9:33 PM

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i am talkin about the

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the c one but on thel eft

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oh

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fuck

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it is 90 degree i am idiot

wind wigeon Sep 29, 2022, 9:34 PM

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no worries lol

midnight haven Sep 29, 2022, 9:34 PM

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what should i do next

#

?

wind wigeon Sep 29, 2022, 9:35 PM

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but yeah youre gonna need sine

#

or something else

solid prairie Sep 29, 2022, 9:35 PM

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Im trying to find the contrapositive for this statement

pearl pondBOT Sep 29, 2022, 9:41 PM

#

@serene orchid Has your question been resolved?

#

Channel closed

Closed by @serene orchid

Use .reopen if this was a mistake.

solid prairie Sep 29, 2022, 9:47 PM

#

.reopen

pearl pondBOT Sep 29, 2022, 9:47 PM

#

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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.

solid prairie Sep 29, 2022, 9:47 PM

#

pearl pondBOT Sep 29, 2022, 9:47 PM

#

solid prairie

solid prairie Sep 29, 2022, 9:48 PM

#

Can someone help me with the contrapositive

cursive wraith Sep 29, 2022, 9:49 PM

#

recall : the contrapositive of "If A, then B" is "if NOT B, then NOT A" where A and B are both statements

solid prairie Sep 29, 2022, 9:51 PM

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i need help on the 2nd statement

cursive wraith Sep 29, 2022, 9:51 PM

#

Your statement is : If a = b (mod n), then a^3 = b^3 (mod n)

solid prairie Sep 29, 2022, 9:52 PM

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for contrapositive i got the first statement

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wait nvm'

#

go head

cursive wraith Sep 29, 2022, 9:53 PM

#

cursive wraith recall : the contrapositive of "If A, then B" is "if NOT B, then NOT A" where A ...

identify in your statement what "A" and "B" corresponds, find what are the statements "NOT A" and "NOT B", then you got the contrapositive

solid prairie Sep 29, 2022, 9:53 PM

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the B is the part after then

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and A is the If part

cursive wraith Sep 29, 2022, 9:53 PM

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yes

#

in your case, A is "a = b (mod n)" and B is "a^3 = b^3 (mod n)"

solid prairie Sep 29, 2022, 9:54 PM

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yeah

cursive wraith Sep 29, 2022, 9:54 PM

#

so, "not A" is ... and "not B" is ...

cursive wraith Sep 29, 2022, 9:54 PM

#

cursive wraith recall : the contrapositive of "If A, then B" is "if NOT B, then NOT A" where A ...

then, with this, you got your contrapositive

solid prairie Sep 29, 2022, 9:55 PM

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So If a^3 not cvongruent b^3(modn), then A is not congruent B

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(modn)

cursive wraith Sep 29, 2022, 9:57 PM

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yes

#

do you need the proof that goes along or you got it ?

solid prairie Sep 29, 2022, 9:58 PM

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yea i need the proof

cursive wraith Sep 29, 2022, 9:59 PM

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ok

#

what is a^3 - b^3 ?

solid prairie Sep 29, 2022, 10:05 PM

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cursive wraith ok

it is n

cursive wraith Sep 29, 2022, 10:05 PM

#

ok, I'll tell you how to do it, it is not "n"

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Suppose a = b (mod n)

#

then n divides (a-b)

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but a^3 - b^3 = ?

solid prairie Sep 29, 2022, 10:06 PM

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it qould euqal n^3

cursive wraith Sep 29, 2022, 10:07 PM

#

do you know this binomial identity ?

#

a^3 - b^3 = (a-b) * ...

solid prairie Sep 29, 2022, 10:08 PM

#

(a – b)(a2 + ab + b2)

cursive wraith Sep 29, 2022, 10:12 PM

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yes

#

but n divides a-b

#

so, what can we say about a^3 - b^3 ?

solid prairie Sep 29, 2022, 10:14 PM

#

it that would be variable k

#

like k*n

cursive wraith Sep 29, 2022, 10:15 PM

#

no need to introduce k, unless you really want to get into the calculations

#

so, since n divides (a-b), we have a-b = k*n for some integer k

cursive wraith Sep 29, 2022, 10:16 PM

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solid prairie (a – b)(a2 + ab + b2)

so a^3-b^3 = ... (using that formula)

solid prairie Sep 29, 2022, 10:17 PM

#

(a-b)

cursive wraith Sep 29, 2022, 10:20 PM

#

well

cursive wraith Sep 29, 2022, 10:21 PM

#

solid prairie (a – b)(a2 + ab + b2)

you just told me it was (a-b) times (a^2 + ab + b^2)

#

but ok

#

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

solid prairie Sep 29, 2022, 10:22 PM

#

yeah

cursive wraith Sep 29, 2022, 10:22 PM

#

cursive wraith so, since n divides (a-b), we have a-b = k*n for some integer k

and now, using this, a^3 - b^3 = ?

solid prairie Sep 29, 2022, 10:25 PM

#

im not sure tbh

cursive wraith Sep 29, 2022, 10:26 PM

#

well, a-b = k*n

#

so (a-b)(a^2 + ab + b^2) = k*n x (a^2 + ab + b^2)

cursive wraith Sep 29, 2022, 10:27 PM

#

cursive wraith a^3 - b^3 = (a-b)(a^2 + ab + b^2)

so with this, a^3 - b^3 = ...

solid prairie Sep 29, 2022, 10:27 PM

#

oh so it be k^3

cursive wraith Sep 29, 2022, 10:29 PM

#

nonono

#

a^3 - b^3 = k*n x (a^2 + ab + b^2)

#

you just have to replace

cursive wraith Sep 29, 2022, 10:30 PM

#

cursive wraith a^3 - b^3 = k*n x (a^2 + ab + b^2)

now, if you note M = k * (a^2 + ab + b^2)

#

you get a^3 - b^3 = M*n

#

and M is indeed an integer...

solid prairie Sep 29, 2022, 10:31 PM

#

so it is m*n

cursive wraith Sep 29, 2022, 10:42 PM

#

yes, so what can you say about a^3 - b^3 (mod n) ?

solid prairie Sep 29, 2022, 10:44 PM

#

we can say it is m

#

wait are we using contra positive proof or direct proof

cursive wraith Sep 29, 2022, 10:47 PM

#

solid prairie we can say it is m

a^3 - b^3 = m*n = ? (mod n)

cursive wraith Sep 29, 2022, 10:47 PM

#

solid prairie wait are we using contra positive proof or direct proof

direct

solid prairie Sep 29, 2022, 10:49 PM

#

cursive wraith a^3 - b^3 = m*n = ? (mod n)

a^3-b^3=(a-b)(mod n)

cursive wraith Sep 29, 2022, 10:52 PM

#

do we agree that n divides m*n ? so m x n = ? (mod n)

solid prairie Sep 29, 2022, 10:55 PM

#

b (mod n)

cursive wraith Sep 29, 2022, 10:55 PM

#

ok, let's get out of this exercice 2 seconds to get our heads cleared up

#

take n a natural integer. then n = ? (mod n)

solid prairie Sep 29, 2022, 11:01 PM

#

b

cursive wraith Sep 29, 2022, 11:02 PM

#

where did b come from ? let's look at a more concrete example.

#

6 = ? (mod 6)

solid prairie Sep 29, 2022, 11:02 PM

#

\

#

1

cursive wraith Sep 29, 2022, 11:02 PM

#

6 = 1 mod 6 ?

solid prairie Sep 29, 2022, 11:02 PM

#

sorry ignore the slash

cursive wraith Sep 29, 2022, 11:03 PM

#

that would mean that 6 divides 6-1 = 5

#

which is not the case...

solid prairie Sep 29, 2022, 11:03 PM

#

oh i mean 12

cursive wraith Sep 29, 2022, 11:05 PM

#

12 is a correct answer

#

to be honest there are an infinity of correct answers

#

but the simplest one is : 6 = 0 (mod 6)

#

when x is divisible by 6, automatically x = 0 (mod 6)

#

so, new question : 12 = ? (mod 6)

solid prairie Sep 29, 2022, 11:07 PM

#

18

cursive wraith Sep 29, 2022, 11:07 PM

#

yes, correct again, but even simpler ?

cursive wraith Sep 29, 2022, 11:07 PM

#

cursive wraith when x is divisible by 6, automatically x = 0 (mod 6)

(remember this)

solid prairie Sep 29, 2022, 11:08 PM

#

6

cursive wraith Sep 29, 2022, 11:08 PM

#

yes, but simpler ?

solid prairie Sep 29, 2022, 11:09 PM

#

0

cursive wraith Sep 29, 2022, 11:09 PM

#

Yes !

#

alright, one last time before a bit more general : 18 = ? (mod 6)

solid prairie Sep 29, 2022, 11:09 PM

#

0

cursive wraith Sep 29, 2022, 11:10 PM

#

yes !

#

More general : if k is any integer, 6*k = ? (mod 6)

solid prairie Sep 29, 2022, 11:12 PM

#

brb let me get dinner

#

m

cursive wraith Sep 29, 2022, 11:21 PM

#

let's recap

#

we said that 6*1 = 6 = 0 (mod 6)

cursive wraith Sep 29, 2022, 11:22 PM

#

solid prairie 0

6*2 = 12 = 0 (mod 6)

cursive wraith Sep 29, 2022, 11:22 PM

#

solid prairie 0

and 6*3 = 18 = 0 (mod 6)

#

can you sense that 6*4 = 0 (mod 6) and so on ?

solid prairie Sep 29, 2022, 11:24 PM

#

yes it the multple

cursive wraith Sep 29, 2022, 11:24 PM

#

so 6*k = 0 (mod 6) for ANY integer k, right ?

solid prairie Sep 29, 2022, 11:24 PM

#

yes

cursive wraith Sep 29, 2022, 11:25 PM

#

Now, I could have chosen any number other than 6, let's say 251, and the argument would still be the same :
251*k = 0 (mod 251) for ANY integer k

solid prairie Sep 29, 2022, 11:26 PM

#

yeah

cursive wraith Sep 29, 2022, 11:31 PM

#

so...

#

replace 6 and 251 with any natural number n

#

so... for any integer k, n*k = ? (mod n)

solid prairie Sep 29, 2022, 11:33 PM

#

ok that is essentially the proof

cursive wraith Sep 29, 2022, 11:34 PM

#

basically you gotta use that n*k = 0 (mod n) for ANY integer k

solid prairie Sep 29, 2022, 11:36 PM

#

ok

#

i think i kind of get it thanks

cursive wraith Sep 29, 2022, 11:39 PM

#

np

solid prairie Sep 29, 2022, 11:48 PM

#

.close

pearl pondBOT Sep 29, 2022, 11:48 PM

#

Channel closed

Closed by @solid prairie

Use .reopen if this was a mistake.

#

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

primal skiff Sep 29, 2022, 11:59 PM

#

How do I solve this?
I know the identities, but I'm not sure how cos(theta) corelates to cos^2(theta). I'm not sure where and how to plug the 11/61 in.

pearl pondBOT Sep 29, 2022, 11:59 PM

#

primal skiff How do I solve this? I know the identities, but I'm not sure how cos(*theta*) co...

hallow citrus Sep 30, 2022, 12:03 AM

#

pearl pondBOT Sep 30, 2022, 12:14 AM

#

@primal skiff Has your question been resolved?

primal skiff Sep 30, 2022, 12:15 AM

#

hallow citrus

I said I know the identity, but im not sure where to plug in 11/61. do i square it when plugging it into cos^2 (x)?

dense jasper Sep 30, 2022, 12:16 AM

#

$\cos^2 x=(\cos x)^2$

jolly parrotBOT Sep 30, 2022, 12:16 AM

#

Civil Service Exam is good

primal skiff Sep 30, 2022, 12:28 AM

#

dense jasper $\cos^2 x=(\cos x)^2$

thank you! just lost my grasp on some basics 😄

#

.close

pearl pondBOT Sep 30, 2022, 12:28 AM

#

Channel closed

Closed by @primal skiff

Use .reopen if this was a mistake.

pearl pondBOT Sep 30, 2022, 1:24 AM

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• 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.

teal hazel Sep 30, 2022, 1:38 AM

#

pearl pondBOT Sep 30, 2022, 1:38 AM

#

teal hazel

teal hazel Sep 30, 2022, 1:38 AM

#

Yo can anyone help me with question 8?

real scarab Sep 30, 2022, 1:39 AM

#

ok what did you try?

teal hazel Sep 30, 2022, 1:39 AM

#

I tried substituting those values into the Geometric Sum formula

#

but since first term

#

and ratio

#

are unknown

#

Im stuck

#

In a geometric sequence T5 = 625 and T7 = 3906.25. Find the first 3 terms?

real scarab Sep 30, 2022, 1:42 AM

#

so whats the general form of a geometric sequence?

teal hazel Sep 30, 2022, 1:44 AM

#

oh wait nvm I think I got it

#

Thanks

#

.close

pearl pondBOT Sep 30, 2022, 1:44 AM

#

Channel closed

Closed by @teal hazel

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naive musk Sep 30, 2022, 2:16 AM

#

is -14+1/8x the same as 1/8x-14?

pearl pondBOT Sep 30, 2022, 2:16 AM

#

naive musk is -14+1/8x the same as 1/8x-14?

wind wigeon Sep 30, 2022, 2:17 AM

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yes

naive musk Sep 30, 2022, 2:17 AM

#

ty

#

.close

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viral kayak Sep 30, 2022, 2:58 AM

#

So for this question you have to determine the weight of the large container. I forgot the formula in class to firgure it out and i cant find it in class but the question is

3 large containers and 5 small containers weigh a total of 45 tons when the containers are full of materials.
2 large containers and 10 small containers weigh a total of 70 tons when the containers are full of materials.

pearl pondBOT Sep 30, 2022, 2:58 AM

#

viral kayak So for this question you have to determine the weight of the large container. I ...

viral kayak Sep 30, 2022, 3:01 AM

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I dont im having a complete brain fart on it. I tried figuring out one of the questions and then checking it on the other one but then it was always off im in algebra 2 if that helps

#

2L + 10S = 70 I believe

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I'm sorry I still seem to not understand can you show what you mean?

#

I apologize if I seem like an idiot ive been studying all day and its all not making complete sense

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oh my goodness. that makes so much more sense. Thank you!

#

.close

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viral kayak Sep 30, 2022, 3:24 AM

#

I am always really bad at these and get caught up on the words, can someone help walk me through this question? The function f(t)=345(1.03)^t/4 represents the total amount, in dollars, in an investment account that earns 12% annual interest, compounded quarterly, where t is the number of years since the initial deposit was made. If no additional deposits or withdrawals are made, which statement is true about the function when graphed on a coordinate plane?
Possible answers:

The function has a y -intercept at ( 345 , 0 ) .

The function has a y-intercept at (0,345).

As t increases, f ( t ) decreases without bound.

As t increases, f(t) decreases, eventually approaching 0.

pearl pondBOT Sep 30, 2022, 3:24 AM

#

viral kayak I am always really bad at these and get caught up on the words, can someone help...

old geyser Sep 30, 2022, 3:27 AM

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In the last channel I said x; I meant t

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Set t = 0

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That'll find your y intercept

viral kayak Sep 30, 2022, 3:27 AM

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oh, I though t was equal to y

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sorry

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thank you

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.close

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fiery peak Sep 30, 2022, 3:35 AM

#

pearl pondBOT Sep 30, 2022, 3:35 AM

#

fiery peak

fiery peak Sep 30, 2022, 3:35 AM

#

#

28 and 18

pearl pondBOT Sep 30, 2022, 3:50 AM

#

@fiery peak Has your question been resolved?

fiery peak Sep 30, 2022, 3:51 AM

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for 28 i get <10/sqrt5,-5/sqrt5>

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.close

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midnight haven Sep 30, 2022, 4:04 AM

#

If one US dollar equals $.85 in foreign currency, then what would $10.71 in foreign currency equal in US currency?

pearl pondBOT Sep 30, 2022, 4:04 AM

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midnight haven If one US dollar equals $.85 in foreign currency, then what would $10.71 in fore...

midnight haven Sep 30, 2022, 4:04 AM

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its ratios

small spruce Sep 30, 2022, 4:06 AM

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10.71/0.85 * 1

quartz rune Sep 30, 2022, 4:09 AM

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midnight haven If one US dollar equals $.85 in foreign currency, then what would $10.71 in fore...

1 US dollar = .85 foreign currency

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x US dollars = 10.71 foreign currency

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you can write two ratios

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1/x = 0.85/10.71

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then you can cross multiply to get 10.71 = 0.85x

midnight haven Sep 30, 2022, 4:11 AM

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thank you

#

.close

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viral kayak Sep 30, 2022, 4:23 AM

#

I'm confused by this question. can someone help? A company makes an area rug with a border that is x feet around each side of the interior of the area rug. The interior of the area rug is 6 feet by 4 feet. Which function, r(x), represents the area of the entire rug including the border, in square feet, based on the value of x? Answers r(x)=2x^2+10x+24 r(x)=2x^2+24 r(x)=4x^2+20x+24 r(x)=4x^2+24

pearl pondBOT Sep 30, 2022, 4:23 AM

#

viral kayak I'm confused by this question. can someone help? A company makes an area rug wit...

viral kayak Sep 30, 2022, 4:23 AM

#

Screen_Shot_2022-09-29_at_11.23.24_PM.png

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length is 4ft and width is 6ft

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thats what im supposed to calculate for but im not sure. I have to figure out the written equation to calculate it.

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well 6+2x?

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I think so, let me try to work it out

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its 4x^2+20x+24 right?

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YES! thank you!

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/close

#

oh whoops

#

.close

pearl pondBOT Sep 30, 2022, 4:34 AM

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Channel closed

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pearl pondBOT Sep 30, 2022, 5:05 AM

#

grim patrol Sep 30, 2022, 5:06 AM

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ok

#

i see what happened to ur prev chat

#

HAHHAHA

cinder reef Sep 30, 2022, 5:07 AM

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what happened hahaha

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also what are you asked to do

rustic gate Sep 30, 2022, 5:07 AM

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rip

grim patrol Sep 30, 2022, 5:08 AM

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yea um

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let y=4

pearl pondBOT Sep 30, 2022, 5:38 AM

#

@midnight haven Has your question been resolved?

pearl pondBOT Sep 30, 2022, 6:09 AM

#

@midnight haven Has your question been resolved?

pearl pondBOT Sep 30, 2022, 6:39 AM

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Channel closed

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slate thicket Sep 30, 2022, 6:46 AM

#

hola

pearl pondBOT Sep 30, 2022, 6:46 AM

#

slate thicket hola

midnight haven Sep 30, 2022, 6:46 AM

#

catThink

slate thicket Sep 30, 2022, 6:46 AM

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reference: #help-54 message

#

okay so as @rustic gate suggested i multiplied it by n! to get n! a_1 + n!/2! a_2 + n!/3! a_3 +…. a_n = n!*p/q and maybe proved existence

#

umm btw

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p/q is the rational number

midnight haven Sep 30, 2022, 6:49 AM

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slate thicket okay so as <@118663865264242688> suggested i multiplied it by n! to get n! a\_1 ...

existence of?

slate thicket Sep 30, 2022, 6:50 AM

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midnight haven existence of?

of the sum

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for every rational number

midnight haven Sep 30, 2022, 6:50 AM

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I mean u aren't done with the question definitely?

slate thicket Sep 30, 2022, 6:50 AM

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hm?

grim patrol Sep 30, 2022, 6:51 AM

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ITS U HIHI

slate thicket Sep 30, 2022, 6:51 AM

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hihi

slate thicket Sep 30, 2022, 6:51 AM

#

grim patrol ITS U HIHI

bless me wit the answer goddess

#

SCpray

grim patrol Sep 30, 2022, 6:52 AM

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this feels like a weird question

rustic gate Sep 30, 2022, 6:52 AM

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oh hi

grim patrol Sep 30, 2022, 6:52 AM

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sad

rustic gate Sep 30, 2022, 6:52 AM

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deep you're back

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have you used my hint wisely?

slate thicket Sep 30, 2022, 6:52 AM

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not sure sad

rustic gate Sep 30, 2022, 6:52 AM

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whats your proof for existence

grim patrol Sep 30, 2022, 6:53 AM

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lol what

slate thicket Sep 30, 2022, 6:53 AM

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lhs is integer

rustic gate Sep 30, 2022, 6:53 AM

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indeed

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i think its easier to kill the a1 term and assume p/q < 1

slate thicket Sep 30, 2022, 6:53 AM

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hmm okay

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so a_1 + p/q

rustic gate Sep 30, 2022, 6:54 AM

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ye but more like just say p/q < 1

grim patrol Sep 30, 2022, 6:54 AM

#

rustic gate i think its easier to kill the a1 term and assume p/q < 1

yea i was thinking of that

rustic gate Sep 30, 2022, 6:54 AM

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and you want n!/2! a_2 + n!/3! a_3 +…. a_n = n!*p/q

grim patrol Sep 30, 2022, 6:54 AM

#

then cant we just repeat this iteratively until we get a rational number thats 0

rustic gate Sep 30, 2022, 6:54 AM

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lol

#

good luck guaranteeing that you hit 0

slate thicket Sep 30, 2022, 6:54 AM

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hmm thonk

grim patrol Sep 30, 2022, 6:54 AM

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ull defn hit 0 after some n no?

rustic gate Sep 30, 2022, 6:55 AM

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the "finite" part is what makes that attempt not good

grim patrol Sep 30, 2022, 6:55 AM

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well its a finite numb of rational numbers too

rustic gate Sep 30, 2022, 6:55 AM

#

you have to prove that eventually your difference is exactly a fraction that is attainable

grim patrol Sep 30, 2022, 6:55 AM

#

just pick a decently large n

slate thicket Sep 30, 2022, 6:55 AM

#

sad_think

rustic gate Sep 30, 2022, 6:55 AM

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how do you prove that the difference between your current sum and p/q is a fraction of the form a_n/n!

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thats the hard part

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anyway thats not a good proof

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i like my method

grim patrol Sep 30, 2022, 6:56 AM

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ok

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always liking ur own methods

#

sad

rustic gate Sep 30, 2022, 6:56 AM

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we're looking for n!/2! a_2 + n!/3! a_3 +…. + a_n = n!*p/q

slate thicket Sep 30, 2022, 6:56 AM

#

catGiggle

grim patrol Sep 30, 2022, 6:56 AM

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dun laugh

#

sad

rustic gate Sep 30, 2022, 6:56 AM

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LHS is integer

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and we can guarantee RHS integer too

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just by picking large enough n

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so the question is

slate thicket Sep 30, 2022, 6:56 AM

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not really

rustic gate Sep 30, 2022, 6:56 AM

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we definitely can lol

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just pick a really large n so that all the factors of q appear in n!

slate thicket Sep 30, 2022, 6:57 AM

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hm wait so n>q

grim patrol Sep 30, 2022, 6:57 AM

#

oh

rustic gate Sep 30, 2022, 6:57 AM

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yeah

grim patrol Sep 30, 2022, 6:57 AM

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i guess ur method is trivial

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hais

#

gg

slate thicket Sep 30, 2022, 6:57 AM

#

@midnight haven

rustic gate Sep 30, 2022, 6:58 AM

#

just pick n so that q | n!

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itll be fine

#

all thats left to prove is if you can make LHS = RHS

slate thicket Sep 30, 2022, 6:58 AM

#

wait but we can pick any arbitrary n

rustic gate Sep 30, 2022, 6:58 AM

#

yeah

slate thicket Sep 30, 2022, 6:58 AM

#

because it is unique to p/q

rustic gate Sep 30, 2022, 6:59 AM

#

well

#

prove existence first

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then prove uniqueness

grim patrol Sep 30, 2022, 6:59 AM

#

oh wait

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its expressed uniquely

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ok

rustic gate Sep 30, 2022, 6:59 AM

#

uniqueness is easy after existence proof is sorted

grim patrol Sep 30, 2022, 6:59 AM

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ur method will also be a long journey

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hf

rustic gate Sep 30, 2022, 6:59 AM

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its the same idea

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nah nah

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its easy

grim patrol Sep 30, 2022, 6:59 AM

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no i mean

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i thought

#

u can just use a

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an = the left side

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n ignore the rest

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LOL

rustic gate Sep 30, 2022, 7:00 AM

#

??

slate thicket Sep 30, 2022, 7:00 AM

#

catThink

grim patrol Sep 30, 2022, 7:00 AM

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i forgot the cond on the an

midnight haven Sep 30, 2022, 7:00 AM

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rustic gate just pick a really large n so that all the factors of q appear in n!

no

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at least not n>q

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3!=3 *2 *1

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prime decomposition of 6 is 3*2

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well appears in 3!

slate thicket Sep 30, 2022, 7:00 AM

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321 sotrue

rustic gate Sep 30, 2022, 7:01 AM

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the point is it doesnt matter lol

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we're just trying to show existence

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any n will do

midnight haven Sep 30, 2022, 7:01 AM

#

ok

slate thicket Sep 30, 2022, 7:01 AM

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yes existence QED

rustic gate Sep 30, 2022, 7:02 AM

#

so we want n!/2! a_2 + n!/3! a_3 +…. + a_n = n!*p/q

#

this should be relatively straightforward

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the RHS is some integer < n!

#

since by assumption p/q < 1

#

can you make the LHS be an arbitrary integer < n! ?

slate thicket Sep 30, 2022, 7:03 AM

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🤔

rustic gate Sep 30, 2022, 7:03 AM

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if you cant then my proof is gone lol

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i only sketched it out so idk

slate thicket Sep 30, 2022, 7:03 AM

#

pandaOhNo

rustic gate Sep 30, 2022, 7:03 AM

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well

#

lets write out what the n!/j! are

#

starting from the right

#

we have

slate thicket Sep 30, 2022, 7:04 AM

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nPi ?

rustic gate Sep 30, 2022, 7:04 AM

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1, n, n(n-1), n(n-1)(n-2), ...

#

yeah

slate thicket Sep 30, 2022, 7:04 AM

#

hmm

rustic gate Sep 30, 2022, 7:04 AM

#

and the corresponding coefficients are

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a_n, a_n-1, a_n-2 ...

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which are each < n, < n-1, < n-2

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doesnt look a lot like

#

base k expansion

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except not really

slate thicket Sep 30, 2022, 7:05 AM

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a_n < n-1

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might be helpful here no?

rustic gate Sep 30, 2022, 7:05 AM

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nah its an < n

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basically my idea is right

slate thicket Sep 30, 2022, 7:06 AM

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hmm okay

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yes

rustic gate Sep 30, 2022, 7:06 AM

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for all the integers from 1 to n-1

#

you can just use a_n

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then after you hit the limit

#

you switch to a_n-1

#

and then increase a_n to cover the rest

#

etc

#

its just like expanding a number in base k

#

but its not regular powers of k

#

you have the falling product instead

slate thicket Sep 30, 2022, 7:07 AM

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hmm

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i still don’t get how we proved uniqueness tho

rustic gate Sep 30, 2022, 7:08 AM

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we havent lol

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this is existence

slate thicket Sep 30, 2022, 7:08 AM

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hmmCat

rustic gate Sep 30, 2022, 7:08 AM

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uniqueness follows i think

#

suppose that p/q can be written using a_i coefficients and also b_i coefficients

#

then by our construction

#

(a_n - b_n) + (a_n-1 - b_n-1) n + (a_n-2 - b_n-2) n(n-1) + ... = 0

#

consider the first time from the right (a_n-j - b_n-j) is nonzero

#

but because the sum of the lower terms is bounded by n(n-1)(n-2) ... (n-j+1)

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its not possible for the sum to equal 0

slate thicket Sep 30, 2022, 7:11 AM

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hmm 🤔 i’m not following

rustic gate Sep 30, 2022, 7:11 AM

#

so like

#

from our previous construction

#

its just like base k expansion right?

slate thicket Sep 30, 2022, 7:11 AM

#

yes

rustic gate Sep 30, 2022, 7:11 AM

#

so we need to switch on the a_n-j coefficient

#

the moment the integer we need to represent is larger than n(n-1)(n-2) ... (n-j+1)

#

which means that the terms before the a_n-j term are too small

rustic gate Sep 30, 2022, 7:12 AM

#

rustic gate (a_n - b_n) + (a_n-1 - b_n-1) n + (a_n-2 - b_n-2) n(n-1) + ... = 0

but that means if we have this sum here

#

and any term to the right is nonzero

#

all the terms to the left cant balance it out

#

probably

dense owl Sep 30, 2022, 7:12 AM

#

hey can someone hep with trignometry ?

rustic gate Sep 30, 2022, 7:12 AM

#

i havent written it out formally yet so maybe its all a dream

slate thicket Sep 30, 2022, 7:12 AM

#

no

rustic gate Sep 30, 2022, 7:12 AM

#

LOL

slate thicket Sep 30, 2022, 7:12 AM

#

oh okay i get it now

#

it’s similar to base k

rustic gate Sep 30, 2022, 7:13 AM

#

yep

slate thicket Sep 30, 2022, 7:13 AM

#

like really similar

rustic gate Sep 30, 2022, 7:13 AM

#

way too similar hmmCat

slate thicket Sep 30, 2022, 7:13 AM

#

oh my snowie you are smart happy

rustic gate Sep 30, 2022, 7:13 AM

#

hmmCat

slate thicket Sep 30, 2022, 7:13 AM

#

kawaiiCat

#

anyways thanks happy flonshed

rustic gate Sep 30, 2022, 7:14 AM

#

❄️

slate thicket Sep 30, 2022, 7:14 AM

#

.close

pearl pondBOT Sep 30, 2022, 7:14 AM

#

Channel closed

Closed by @slate thicket

Use .reopen if this was a mistake.

slate thicket Sep 30, 2022, 7:14 AM

#

thonk_cool

pearl pondBOT Sep 30, 2022, 7:46 PM

#

Available help channel!

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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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cedar falcon Sep 30, 2022, 8:38 PM

#

What is this formula [n * (n - 1)] / 2 used for?

pearl pondBOT Sep 30, 2022, 8:38 PM

#

cedar falcon What is this formula `[n * (n - 1)] / 2` used for?

bronze pivot Sep 30, 2022, 8:38 PM

#

What

cinder flower Sep 30, 2022, 8:39 PM

#

it is equal to the sum of the first n positive integers

cedar falcon Sep 30, 2022, 8:39 PM

#

cinder flower it is equal to the sum of the first n positive integers

thats

[n * (n + 1)] / 2

cinder flower Sep 30, 2022, 8:40 PM

#

oh yea it's actually equal to the sum of the first n-1 positive integers, sorry

cedar falcon Sep 30, 2022, 8:40 PM

#

thanks

#

.close

pearl pondBOT Sep 30, 2022, 8:40 PM

#

Channel closed

Closed by @cedar falcon

Use .reopen if this was a mistake.

rustic gate Sep 30, 2022, 8:44 PM

#

cinder flower oh yea it's actually equal to the sum of the first n-1 positive integers, sorry

first n non-negative integers thonk

pearl pondBOT Sep 30, 2022, 8:48 PM

#

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thorny stream Sep 30, 2022, 8:57 PM

#

could someone please help me out on 7b?

pearl pondBOT Sep 30, 2022, 8:57 PM

#

thorny stream could someone please help me out on 7b?

thorny stream Sep 30, 2022, 8:57 PM

#

i got 7a

#

i just have no idea what the hint has to do with the variance, though i do understand the intersection probability.

#

.close

pearl pondBOT Sep 30, 2022, 9:06 PM

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Channel closed

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thick ridge Sep 30, 2022, 9:10 PM

#

help

pearl pondBOT Sep 30, 2022, 9:10 PM

#

thick ridge help

thick ridge Sep 30, 2022, 9:11 PM

#

#

someone help with B

mighty marten Sep 30, 2022, 9:15 PM

#

I think you can just plug in 5 and 6, and then you can find an equation of a line with 2 points

thick ridge Sep 30, 2022, 9:16 PM

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so like 6=5(5)^2-6(5)

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?

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@mighty marten

mighty marten Sep 30, 2022, 9:17 PM

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thick ridge so like 6=5(5)^2-6(5)

Idrk where you got that. If h(x) = x^2 - 6x, and you are to find h(5), you can just plug in 5 for x

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Same goes for 6