help-19

[warped cargo]

( Tu voulais dire P(S) )

[near spoke]

J’ai fais ça 😅

ah bah longuement c’est 0.12

[warped cargo]

Oui, les valeurs numériques sont justes, mais la notation n'est pas tout à fait exacte ahah

[near spoke]

oh my god ma prof va me tuer si c’est mal écrit🤣

[warped cargo]

Tu dois utiliser les événements fournis par l'énoncé

[near spoke]

ah euh donc c’est sensé être 0,3 car il y a 10% et 20% de pesticides dans la boîte A et B ?

[warped cargo]

Non, comme je te dis, les valeurs numériques sont justes

Pour le #3, tu fais le ratio de ce que tu as trouvé en 2a) par ce que tu as trouvé en 2b)

[near spoke]

0.04/0.12= 0,33 my bad 😭

donc 4x10^-2/12x10^-2..?

[warped cargo]

T'as fait une multiplication là

[near spoke]

oops

je veux dire diviser ahaha

c’est 0.33 xd

[warped cargo]

1/3 plutôt, mais oui lorsque arrondi 🙂

[near spoke]

je peux écrire 1/3 alors!

[warped cargo]

L'énoncé te demande d'arrondir à 2 chiffres, non?

[near spoke]

On arrondira à 10^-2 oui haha

okay donc pour la 4, je dois j’imagine encore utiliser la formule proba conditionnelle ?

[warped cargo]

En gros, tu dois calculer $P_{\bar{S}}(A)$

[clever fjord]

all matrices are invertible

[near spoke]

$P_{\bar{S}}(A) = \frac{P(A \cap \bar{S})}{P(\bar{S})}$

[clever fjord]

𝐷𝑖𝑛𝑎 🇪🇺 - دينا الزاهر

[warped cargo]

Exactement!

[near spoke]

$P(A \cap \bar{S}) = 0{,}8 \times 0{,}9 = 0{,}72
P(B \cap \bar{S}) = 0{,}2 \times 0{,}8 = 0{,}16
P(\bar{S}) = 0{,}72 + 0{,}16 = 0{,}88
Donc
P_{\bar{S}}(A) = \frac{0{,}72}{0{,}88} = 0{,}818≈0{,}82$

[clever fjord]

𝐷𝑖𝑛𝑎 🇪🇺 - دينا الزاهر
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[near spoke]

ahhh je veux dire que j’arrondis à 0,82 XD

[warped cargo]

Ok, oui, et donc est-ce que l'affirmation du grossiste est juste?

[near spoke]

on peut dire que oui car les valeurs sont rapprochées!

[warped cargo]

(En passant, pour calculer P(S barre), tu aurais pu faire plus facilement en passant par le complémentaire) (en faisant 1 - P(S))

[near spoke]

« Plus de 80% » on a trouvé 82

[warped cargo]

Oui exact

[near spoke]

OH MAIS OUI!! J’avais complètement oublié cette formule, devrais-je utiliser celle là?

[warped cargo]

C'est toi qui vois! Les deux sont justes ici

Mais celle avec le complémentaire permet une réponse un peu plus rapide

[near spoke]

logiquement c’est 1-P(S) donc 0,88

[warped cargo]

Tu trouves la même réponse oui

[near spoke]

1-0,12 purée je me suis compliqué ahah

merci beaucoup en tout cas!!, j’ai un deuxième problème sur le 2nd degré. Je vais essayer de le faire et ça vous dérangerait pas si je vous montre?

[warped cargo]

Tu peux me tutoyer et oui tu peux me contacter si tu veux

[near spoke]

Ahaha merciiiiii!!!

[topaz jewel]

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[waxen talon]

Given triangle ABC, with B and C are fixed while A can move freely, heights AD, BE, CF. The line that parallels with EF and goes through D intersects AB, AC at Q and R. EF intersects BC at P. Prove that the circle that goes through P, Q, R is always going through one fixed point

[waxen talon]

!status

[odd edge]

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

[waxen talon]

1

here is the diagram for reference

[wary fox]

What did you think of so far

[odd edge]

@waxen talon Has your question been resolved?

[waxen talon]

im thinking that P was fixed, until I moved A elsewhere and P was not fixed anymore

I thought it was just as simple as proving P was fixed

[brittle plinth]

gang

@waxen talon notice 2 things:

1. C, B, D, P is a harmonic set of points
2. DBQ and DRC are similar

[odd edge]

@waxen talon Has your question been resolved?

[odd edge]

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[south plume]

need stats assistance

[south plume]

how do i do q1

is F_n a discrete or random variable

i am confused whether i need to do\
$E(F_{n}(x)) = \int_{-\infty}^{\infty} x \cdot\left( \frac{1}{n} \sum_{i=1}^{n} \mathbf{1}{{X{i}\leq x}} \right) dx$\
or\
$E(F_{n}(x)) = \sum_{n=1}^{\infty??} n \cdot\left( \frac{1}{n}\sum_{i=1}^{n} \mathbf{1}{{ X{i} \leq x }}\right)$

[clever fjord]

artemetra

[odd edge]

@south plume Has your question been resolved?

[sinful grove]

why not directly use the linearity of expection for this?

[south plume]

oh

right.

[south plume]

yeah that makes sense

i'll ask again later

.close

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[lone steppe]

Need help finding the angle so that I can find the surface area of a trapezoidal prism

[lone steppe]

I have the surface area of the other two "sides" but can't figure out the length this one would be

[proper maple]

think this should be fine?

[lone steppe]

wow that's way easier than what I thought I'd have to do

thanks

[proper maple]

no worries. just make sure it's correct

[lone steppe]

those numbers look right

[proper maple]

this can be broken down into 4 equal triangles + a rectangle btw

you dont need to remember the formula for a trapezoid

[lone steppe]

this is for a personal project, and I haven't had to do math like this in about 7 years so I'm not used to thinking smart anymore

thanks for all the help though

[proper maple]

interesting

are you "relearning" some math?

[lone steppe]

a little but mostly just relearning how to think about this topic

my end goal is figuring out the mass of a shell that's in this shape

I have the density, but I need the volume/surface area figured out first
I think

[proper maple]

well if its like

if its that shape but "extruded" if that makes sense

just multiply it by the length

[lone steppe]

my vocab isn't entirely sure on that so I'll just explain.
This is for a scifi thing I'm working on, I like to have numbers be somewhat "realisitic" so I get a couple at the beginning and scale from there.
This is for a starship and I want to find the mass of the hull/hull plating

is there an easier way to figure this all out or did I go about it in a way that is somewhat sensical

[proper maple]

this is what i mean by extruded

the same shape just "lengthened" in 3D

[lone steppe]

then yes

[proper maple]

yeah your volume will be the area multiplied by the height

think in terms of units

[lone steppe]

my numbers aren't seeming right

[proper maple]

length is in meters
area is in meters squared (m * m)
volume is in meters cubed (m * m * m)

[proper maple]

give me your full data

density and height

[lone steppe]

To explain a little more
Length: 2000m
Width: 1250m
Height: 750m
in the shape I sent initially

The hull plating is on average 15m thick.
Material Mass is 3 metric tons/m^3

at this point I just want to know where I'm messing up

need anything else?

[proper maple]

give me a sec

@lone steppe

[lone steppe]

is that icluding the 15m thick hull plating? I don't see a 15

[proper maple]

oh

i thought

[lone steppe]

thanks for writing this out though, I think I got pretty similar stuff

[proper maple]

750 was

give me a sec

so wheres the 750 come from

[proper maple]

i dont see it here

i used these dimensions

[lone steppe]

oh I put it here
#help-19 message

when you asked

sorry

[proper maple]

yeah but height of what

[lone steppe]

it's a space ship

[proper maple]

i need you to draw out the shape with accurate dimensions

[lone steppe]

so it's a 3d object
the 3d object is a shell in the shape I posted above, in the first two photos
the thickness of the shell is 15m

does that help? I'm not sure what/how to draw it more clearly

[proper maple]

you wrote 420 in the shape

i don't see any 750

that's my confusion

i get the 15m thickness

[lone steppe]

420 is the width of the front rectangle

1250 is the total width across
750 is the heigh shown in the 2nd pic

I'm really sorry this has been so much trouble

[proper maple]

no its fine im just

really having a hard time understanding this

lets do the following

its a hexagon right

[lone steppe]

Yeah

[proper maple]

so go ahead and confirm each of these lenghts for me

and then tell me what h is

[lone steppe]

well the sides "a" aren't all the same length though?

[proper maple]

thats fine the shape is just a placeholder

give me these

[proper maple]

THEN give me this h

[lone steppe]

w= 1250

l=2000

h=750

[proper maple]

so where's the 15 come from then?

[lone steppe]

it's the thickness of the empty shell

[proper maple]

oH

its hollow????

[lone steppe]

yeah that's why I needed the surface area

right

[proper maple]

dude 😭

[lone steppe]

I thought I said that

[proper maple]

alright thats fine

we just need to calculate the volume for the solid

then subtract.. uhh

every length minus 15?

[lone steppe]

out of curiosity what did you think I meant by shell when I said that previously?

[proper maple]

like the shell of a ship

the outer shell

like it was plating

[lone steppe]

yeah that is what I mean

I'm trying to find the mass of that outer shell

[proper maple]

the plating is hollow?

like each panel

its a hollow panel

[lone steppe]

no it's 15m thick
the inner volume hasn't been built yet for this I guess

Imagine the filling isn’t there but the shape is the same

I’m trying to determine the mass of the shell

I worry I've ran you off

thanks for what you've done if so

[proper maple]

its fine

im just trying to figure another way to solve this

frankly i dont feel like doing numbers

i may have an idea though

[proper maple]

is that a fucking newton

[lone steppe]

I mean, I had one nearby…

[proper maple]

i love those lol

@lone steppe

your shape is not possible

with the dimensions you've given me

[lone steppe]

How? The drawing is clearly not eldritch or something

[proper maple]

this is not a regular polygon

your drawings showed a regular polygon

when taken to reality (what i did)

it is not possinle

[lone steppe]

Well I’m thoroughly confused then. What part makes it impossible? The 420 length at the front and back?

[proper maple]

actually

hold on

could be my cad

[proper maple]

my bad. ignore what i said

[lone steppe]

Okay I was like what?

that makes more sense

[proper maple]

@lone steppe

this is your shape then

[lone steppe]

yes

[proper maple]

ignore the density and mass

i have not changed them

but area and volume should be accurate

there's your mass

@lone steppe

[lone steppe]

gotcha

thank you so much

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[odd edge]

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[jaunty hollow]

!status

[odd edge]

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

[night nimbus]

hi everybody, i am new here

[jaunty hollow]

have yoou come to help?

[night nimbus]

no just seeing the maths around

[tropic yew]

Radius=X:Y
Area=X²:Y²
Volume=X³:Y³

[pearl lava]

So far i thought that i have to do 350/110

[night nimbus]

do anyone here have any idea about this topic- projective geometry

[tropic yew]

T-T

[pearl lava]

Then with that answer I thought i had to do 75 × what the answer was before but cubed it

[odd edge]

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[tepid pelican]

since they are similar, one is just a larger version of the other

[tepid pelican]

if you have some object, and you scale its dimensions by 2 (height, length and width), by what factor does the surface area change?

[pearl lava]

Its multiplied by 2 right?

[tepid pelican]

not quite

try it with a simple cube

whats the surface area of unit cube? (side 1)

[wind turret]

heyyy

[pearl lava]

Im confused on what ur asking me

[wind turret]

do anyone have studypool pro account ?

[pearl lava]

Isnt surface area just length x width x height?

[tepid pelican]

nope

that'd be volume for cube

[eager wraith]

that's volume (for a cuboid)

yeah

[tepid pelican]

surface area is how big is the boundary of the object

or how much paint you'd need to paint it from the outside

[pearl lava]

Ok

[tepid pelican]

notice that if we have a cylinder and we focus only one one little small part of its surface, when we make the cylinder 2 times larger, the area of the small piece gets 4 times larger

does this make sense? We will thus need 4 times more paint to paint the 2x larger cylinder

(the width got 2x larger and the height got 2x larger, so in total that results in 4x larger surface area)

[pearl lava]

Yes

[tepid pelican]

okay cool

now lets focus on the volume

we could divide the cylinder into great many tiny cubes to approximate its volume

[pearl lava]

Oķ

[tepid pelican]

then if we made it 2 times larger, the side length of each cube would get 2 times larger as well

what would happen to its area?

[pearl lava]

4x?

Larger

[tepid pelican]

nope, not quite

how many little "unit cubes" are in this rubiks cube?

[pearl lava]

In total or the ones that I can see

[tepid pelican]

in total

[pearl lava]

24

[tepid pelican]

thats too much

[tepid pelican]

we can see 7

oh you were counting squares

i was asking about cubes

[pearl lava]

Ye

[tepid pelican]

like the 3D thing

this is one cube

how many cubes are there in total

[pearl lava]

7 then

[tepid pelican]

almost

you missed the one you cant see

[pearl lava]

8

[tepid pelican]

yep

[pearl lava]

🤦‍♂️

[tepid pelican]

so when we made the side length 2 times larger, (so that the cube had 2 little cubes on side) its volume got 8 times larger

so surface area got 2^2 times larger and volume got 2^3 time larger

so lets now say that the side length got x times larger here

that would mean that the surface area would get x^2 times larger and volume would get x^3 times larger

but you can calculate how many times the surface area got larger

can u do that?

[pearl lava]

Ye i would do 350/ 110

[tepid pelican]

if the later one is 350 and the prior one is 110

exactly

so 350 / 110 = x^2

[pearl lava]

Yes

[tepid pelican]

from this, we can get that x = sqrt(350 / 110)

and what would x^3 be?

simply sqrt(350 / 110)^3

[pearl lava]

Yes

[tepid pelican]

,calc sqrt(350 / 110)^3

[clever fjord]

Result:

5.6756164501008

[tepid pelican]

so the volume will be this many times larger

[pearl lava]

Then I would multiply it by 75

[tepid pelican]

exactly

i gtg now, can u finish it from here?

[pearl lava]

I can finish it but when put in the answer it tells me that im wrong

Even with those steps

[pearl lava]

Ty for helping

[tepid pelican]

Np

,calc 5.675 * 75

[clever fjord]

Result:

425.625

[tepid pelican]

Try putting in 426

[pearl lava]

Its wrong 🤦‍♂️

Its telling me im wrong

[tepid pelican]

Huh

[pearl lava]

That website annoys me

Ur correct but the website is being a pain

😂

[tepid pelican]

,calc 75*(350/110)^(3/2)

[clever fjord]

Result:

425.67123375756

[tepid pelican]

Yeah, seems like it

[pearl lava]

To 1 dp is 426

[tepid pelican]

To 1dp qohld be 425.7

[pearl lava]

Its right now 😂

Ty

[tepid pelican]

Np

[pearl lava]

.close

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[uncut sand]

can anyone help me with solving this? I tried to look up how to solve stuff like this on internet and I di
dnt find any satisfying answers

[odd edge]

@uncut sand Has your question been resolved?

[wispy cliff]

what do u need to find

[uncut sand]

a, b and c

[wispy cliff]

as numbers right?

[uncut sand]

yes

the first one is geo sequence, second one is ar. sequence and the third one is geo sequence again

[mystic saffron]

I would use the value for a in the first equation and see what i go from there

[uncut sand]

alr

but wouldnt getting the c out of this be better?

like c=2a-b

and then you try

[mystic saffron]

notice that a cant be 7

or wait

can you tell me if the third equations a-7 or b -7

??

[uncut sand]

b-7)(c+3=a square

[mystic saffron]

oh then a can be 7

mb

didnt understand the writing

[uncut sand]

ye my writing isnt crazy good

[mystic saffron]

give me 5 mins i wilkl think about your question i will figure it out and i will tell you

[uncut sand]

appreciate it

[mystic saffron]

is this like all the details u have?

this system and nothing else

?

[uncut sand]

it s sequence task

if you want i can translate it and send it

[mystic saffron]

sure

please do

that might make my life easier

[uncut sand]

alr give me a sec

[mystic saffron]

thanks.

[uncut sand]

Three numbers are consecutive terms of a geometric sequence whose ratio is different from 1. If we take, in order, the second number, the first number, and the third number, we obtain three consecutive terms of an arithmetic sequence. If we then decrease the first term of this arithmetic sequence by 7, leave the second term unchanged, and increase the third term by 3, we get three consecutive terms of a geometric sequence. Find these numbers.

and that s it

I dont think there s other way around to make it

[mystic saffron]

how did you arrive at this system?

is it given?

[uncut sand]

it is not, it s based on the formula

[mystic saffron]

yeah true

its good

i will think

[uncut sand]

thanks a lot

[mystic saffron]

from second equation

get c

c = 2a-b

substitute into (1)

b^2 =a(2a-b)

continue from here

then after you did that substitute c = 2a-b into third equation

then it is solvable

[uncut sand]

what do you mean by continue from here? am I supposed to get the value of a from b^2 =a(2a-b)?

[mystic saffron]

no just open brackets

[uncut sand]

like get it in b's

alr

then you get 2asquare -ba=bsquare

[mystic saffron]

get bsquare into LHS

2a^2 -ba -b^2 = 0

now substitute c = 2a-b into (3 )

eq

[uncut sand]

okay give me a sec

(b-7)(2a-b+3)=asquare

[mystic saffron]

open brackets

actually

dont

dont open

[uncut sand]

2ab-14a-bsquare+7b+3b-21...

alr

[mystic saffron]

now your system is made of

2a^2-ab-b^2 = 0
a^2 = (b-7)(2a-b+3)

[uncut sand]

yes

I dont think you can do much about it tho

or wait

[mystic saffron]

solve the first quadratic

quadratic in b

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

[wispy cliff]

3/7

theresanotherone

[uncut sand]

or maybe a^2=(ab+b^2) x 2

[wispy cliff]

mypcislaggingbruh

[uncut sand]

hate to brake it to you my friend

the anserw is -3,6,-12

or -7/9,14/9,-28/9

[wispy cliff]

well if the question is finding numerical values

that satisfy it

there are many

[uncut sand]

no no, it s like a=-3 or -7/9

[wispy cliff]

thats another larger solution

[uncut sand]

and then b=6 or 14/9

[wispy cliff]

what b?

[uncut sand]

wdym

[wispy cliff]

that looks like a v

anyways

i foound v is 6.43 too

but theres 2 solutions in general i believe

since c can be v or -2v

[uncut sand]

"v" is either worth 6 or 14/9

or maybe my writing sucks and you made slightly diffrent task tho

[wispy cliff]

....

the system

v or b

[uncut sand]

it is b

[wispy cliff]

are variables we dont care about the letter

it has 2 solutions

[uncut sand]

yea ik

[wispy cliff]

mathematically and if the question is to find values

[uncut sand]

yes, you need to find values of a,b, c

2 anserws

oh shit

v

dude mb I forgot that "v" means "or"

mb mb

😭

[wispy cliff]

oh

....

i m wrong

i wrote times c +3 instead of times(c+3)...

mb mb

[uncut sand]

oh lol

no worries

actually there s easier way tho

since it s sequence you can get a, a1q and a2q

[wispy cliff]

yeah it is easy

[uncut sand]

{ 2a = aq+ aq2 2 2 a = (aq− 7)(aq + 3).

damn what is that

it s not readable

mb

[wispy cliff]

i cant read it

[uncut sand]

pasting this was not a good idea

if you want I can give you a link

[wispy cliff]

nah np i gotta finish my work first i just take a break to solve different things from time to time

[uncut sand]

https://zadania.info/d722/5887660

[wispy cliff]

what language is that

[uncut sand]

alright

[uncut sand]

polish

[wispy cliff]

alr

[uncut sand]

yea but it doesnt matter tho

[wispy cliff]

maths

[uncut sand]

number and letters didnt change

anyways, thanks for help

.close

[odd edge]

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[fierce ore]

need help w all 3

honestly dont know where to start

[odd edge]

@fierce ore Has your question been resolved?

[odd edge]

@fierce ore Has your question been resolved?

[hollow stump]

need help all

[wary fox]

Create your own help channel

[odd edge]

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[outer wadi]

how is U,V union (a,b)

[outer wadi]

I see how were getting almost all values of (a,b) since were giving the pre image almost all of R

but hmm what about that 0

oh we assumed there existed no x such that f(x) = 0

so removing 0 from the f^-1 doesnt affect (a,b)

what do they mean by since f is continuos the sets are nonempty

doesnt seem like the same definition of seperation is used here

since there are positive y values and negative y values I see how condition (ii) is satisfied

I see why condition 1 is satisfied

ok I see now

.solved

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[north spoke]

hello i need help heres the question, i sthe image good enough, do u want another proper one

[north spoke]

we use k-method right ?

um

nobody there

[fair forum]

it's literally been less than a minute lol

[north spoke]

sry

mb

last time i had responses within a min

mb

oh it was u last time

lol

see i got a proper ss this time

[wary fox]

Well what have you tried so far

[north spoke]

so i tried doing it using k method

and i tried simplifying it

i got like rly long list of exponents of k which was rly hard to correlate on both sides

then i gave up

and sent it here

so for the second method i didnt convert it to d and k values immediately

and tried simplifying the equation itself

soo

no working

[brittle plinth]

try simplifying (a-b)/c + (a-c)/b

[north spoke]

howand to what

[brittle plinth]

expand it

[north spoke]

ic

so like

[brittle plinth]

by that i mean separate the fractions

[north spoke]

(a-b) b + (a-c)c / bc

oh

[north spoke]

ohk

so

(a/b) - 1 like that

or am i not following..

[brittle plinth]

not what i meant

[north spoke]

ic

[brittle plinth]

actually lemme do an example

[north spoke]

could u elaborate

ya

k

[brittle plinth]

rewrite (a-b)/c as a/c - b/c

and same for the other one

[north spoke]

oh k

um

so what does taht do

[brittle plinth]

rewrite this whole thing and you'll see

[north spoke]

like the enitre thing or that portion

[brittle plinth]

that portion

[north spoke]

that ortion specifically i got(ab + ac -b^2 - c^2)/bc

do i take b+c common

??

wait

[brittle plinth]

no that's not what i meant

[north spoke]

what am i yapping

mb

[brittle plinth]

alr lemme do an example

[north spoke]

okie

[brittle plinth]

(a-b)/c + (a-c)/b = a/c - b/c + a/b - c/b

this is what i meant

[north spoke]

ok

ya

so i dont do anything further

oh wait

sht

k leeme try something from herre

[brittle plinth]

since a, b, c and d are in continued proportion you might notice you can simplify some things here

[north spoke]

k^4 - 1/K^2??

like that

[brittle plinth]

dont use k here

[north spoke]

then what do i use instead

[brittle plinth]

it'll make things worse

[north spoke]

oh

shit

im stupid

a/b = b/c

like that right

[brittle plinth]

exactly

use that

[north spoke]

thanks

k lemme try like that for the rest

[brittle plinth]

actually

[north spoke]

but

a/c and c/b

dont go that way do they

ill have tto use k to simplify them

so do i leave them as is

[brittle plinth]

you get a/c - c/b right?

[north spoke]

up

yup

[brittle plinth]

it can be simplified further

notice that d/c = c/b

[north spoke]

yes

[brittle plinth]

so this whole thing equals to (a-d)/c

[north spoke]

a/c - d/c

oooooh

nice

then that become a-d whle square by cr

c^2

cuz of the whole square brackets

[brittle plinth]

this is great because we have found a way to get (a-d)^2/c^2 on the right hand side

[north spoke]

thats smart

and we aso have the second portion right

the d-b/c

[brittle plinth]

yes

[north spoke]

thingyu

ok i got the idea

ill try it on my own

thanks

[brittle plinth]

!done

[odd edge]

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

[north spoke]

.close

[odd edge]

Channel closed

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Use .reopen if this was a mistake.

[north spoke]

.reopen

[odd edge]

✅ Original question: #help-19 message

[north spoke]

soo

im gtting ) as my lhs

cuz ((a-d)^2 )/c^2 - ((d-a)^2 )b^2 gives me 0

so help pls

um

anybody there

soo

[cobalt umbra]

.

bruh just use k method

[north spoke]

@cobalt umbra ru able to solve

ru dum

it so much simpler

the otherway

[cobalt umbra]

k method is simple

[north spoke]

scroll and see msgs

up

its literaly 4 steps to get nearly full simplifiction on lhs

[cobalt umbra]

u got the answer nice

[north spoke]

this y u got lower than me in math

[cobalt umbra]

so.... what u call me for

[north spoke]

no i didnt

i didnt

what

[cobalt umbra]

he told you the method

are you dyslexic?

[north spoke]

oh

oopsy

mb

i got the answer

lol

[cobalt umbra]

istg

[north spoke]

how fat ru

ong

[cobalt umbra]

🙁 uncalled for

[north spoke]

sowwy

pls dont hurt me

k

imma close ts

[cobalt umbra]

ye

[north spoke]

.close

[odd edge]

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[sharp abyss]

Is there a convenient way to answer this except for writing down all the possibilities with 11 conflicts and showing its fine?

Or at least an elegant way?

[fair forum]

,rcw

[sharp abyss]

TeXit, the bot, is a girl?

Bet

[distant flax]

@sharp abyss hi

[sharp abyss]

ty

[distant flax]

how familiar are you w graph theory @sharp abyss

consider what must be true for it to be impossible

[sharp abyss]

uh

not at all

[distant flax]

try this

[sharp abyss]

isnt that just trying all possible methods till you find one thats wrong

[distant flax]

think about it in terms of no. pairs

i think you can show both parts in the same proof

[sharp abyss]

alr

but isnt that basically a given with this question

[distant flax]

you want to remove 5 of 8 such that there are no pairs in the remaining 3

[sharp abyss]

the conflicts show links and make relationship pairs

[sharp abyss]

but there can be pairs in the remaining 3, they just dont have to be in the same rooms as their pairs

[distant flax]

within the remaining 3*

[sharp abyss]

shouldnt it be within the remaining 5

since the remaining 3 are closed off

[distant flax]

no pairs within the remaining 3

between each other

[sharp abyss]

but the remainig 3 are closed of

NVM

i cant read

[distant flax]

it's okieee

[sharp abyss]

i got confused and thought there were only 3 rooms

yuh, that checks out

[distant flax]

ah okie

now consider the inverse relationship: two knights are not feuding

[sharp abyss]

alr

[distant flax]

let's call this relation the unpaired relation, what can you say about the 3 remaining knights

[sharp abyss]

they all possess relationship 2 within one another

[distant flax]

yesh

it's hard to prove for every case <=11, so what you can do is prove what happens when an arrangement is not possible

what does an arrangement not being possible imply, with respect to unpaired knights

[sharp abyss]

you only need to prove for when n=11 cause anything less is in n=11 but with one taken away

[sharp abyss]

wdym?

it implies that relationship 1 exists between the 3 knights

[distant flax]

which means you cannot find any arrangement where 3 knights are unpaired with each other

[sharp abyss]

wdyn with unpaired?

[distant flax]

not feuding

or relationship 2

[sharp abyss]

yuh

[distant flax]

obviously, this is true when all knights are feuding

[distant flax]

you want a minimum bound for relationship 1 pairs, such that this is true

aka no triangle of unpaired (R2) knights exists

[sharp abyss]

alr

[distant flax]

therefore you want maximum number of R2 such that no triangle of unpaired (R2) knights exists

how would you do this

[sharp abyss]

uh huh

[distant flax]

because it minimises R1, and that will be your lower bound for impossibility

[sharp abyss]

make the fewests possible amount of knights have all the r1 relationships

[distant flax]

yeppp, it's equivalent to making the most knights have r2 relationships

(you know the total: 8(8-1)/2=28)

[sharp abyss]

doesnt amount of r1 stay the same

[distant flax]

because the total is fixed r1+r2 has to be all pairs

[sharp abyss]

what

where does this come from

[distant flax]

the total number of pairs between every knight

if they didn't teach this idk what the intended solution is

[distant flax]

n(n-1)/2 is the number of pairs between n points

[sharp abyss]

its a comp

they dont teach shit

its a homework round so its fine if i get help

[distant flax]

have you seen this before

[sharp abyss]

in any way related to this?

no

[distant flax]

for every point in n, you can join it to n-1 other points, and because you double-count by doing that, divide by 2

that's the reason for why you can count all pairs like this

[sharp abyss]

ic

makes sense

[distant flax]

so number of r1 + number of r2 = 8(8-1)/2=28

[sharp abyss]

yuh

[distant flax]

yay

hence minimising r1 is equiv to maximising r2

[sharp abyss]

yuh

[distant flax]

how would you maximise r2 in a set of 8 knights

such that no triangle is formed

[sharp abyss]

shouldnt r2 stay the same though

since r1=11

[distant flax]

as in you want to find the max number of r2 such that this is possible

[sharp abyss]

by minimising r1

[distant flax]

i think it's easier to find the minimum for impossibility, rather than maximising r1 for what is possible

also i suspect the question is wrong in the bounds, i think it should be <= and >=

[sharp abyss]

why

[distant flax]

$\leq$ and $\geq$

[clever fjord]

Estelle

[sharp abyss]

it ia

is

mb

translation didnt pick that up

[distant flax]

that's very hard to do directly

[sharp abyss]

how can i increase r2 if i cant decrease r1, which its proportional to

[distant flax]

you find either of them and you automatically get the other

[sharp abyss]

ye

ok im lost

how do i increase r2

[distant flax]

any ideas?

[distant flax]

when there is no triangle you can always do something with the points

[distant flax]

number of r1 and r2 sum to 28

[sharp abyss]

i got that

[sharp abyss]

replace them?

idk

[distant flax]

you can arrange them in a certain way

you can separate them into two groups, with paired points on different sides

from this you can get the maximum number of r2

[sharp abyss]

and they stay a triangle?

im ngl, this makes no sense

[distant flax]

i'm trying to think of an explanation

[distant flax]

consider what happens when there isn't a triangle in r2:
you can place points on the left and right, such that every r2 goes between the left and right side

you can try drawing out smaller number of points to see why

[sharp abyss]

i get what you mean with a triangle to r2 but wdym with left abd right sides

or points

[distant flax]

knights

you can place the knights on the left and right such that no r2 happens in the same group, if there is no triangle

[sharp abyss]

so replacing the points?

[distant flax]

arranging them

you can divide them

[sharp abyss]

i dont get it

ill give up on this question

.close

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[half lance]

In the context of these problems, would I find the arc lenght the same way I'd find the centroid?

[odd edge]

@half lance Has your question been resolved?

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[steel yew]

pretty sure this qualifies as maths, how do i word my answer?

[mystic saffron]

Nope, this qualifies as physics, hence, you have an special server destinated for physics in #old-network

[steel yew]

oops sorry

[odd edge]

@steel yew Has your question been resolved?

[brazen hare]

i think you just need to state the direction

up, down, left, right, into page, out of page

into page meaning when you are staring down the tip of the arrow, and out of the page when you are for the tail of the arrow of force

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[coarse barn]

the way ive been taught was that you always check for critical values, then make a sign chart

but obiviously x^2+4 = 0, you would get imaginary numbers, meaning there are no critical values

so then how would i know if its always increasing or decreasing

[amber schooner]

it’s always increasing if f’(x) > 0 for all x

it has nothing to do with critical values

[coarse barn]

wait what

i get what your saying im just confused then as to why my teacher always says to check for critical values

[amber schooner]

well in this instance it’s irrelevant

[coarse barn]

so lets say i had to show my work for a question like this on a test, what would i show?

that for any x value, f(x) is always positive?

[amber schooner]

f’(x) = 3x^2 + 12 = 3(x^2 + 4) > 0

hence f is always increasing

[amber schooner]

f’(x) always positive, not f(x)

[coarse barn]

sorry, thats what i meant

alright then, thank you

.close

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[unreal pasture]

hello directions are express each rational expression as a sum or difference of partial fractions. I dont know where to start

[short terrace]

Do you know what partial fractions are

[unreal pasture]

is it the broken up form

[short terrace]

I'm going to guess you mean what I think you mean

...dude way to jump the gun

[lapis compass]

oop

[short terrace]

Either way

[unreal pasture]

i know how to do it when its a trinomial but ik its different when theres a sqaure right

[short terrace]

Ehhh the idea is more or less the same

Step 1, factorize the denominator

[unreal pasture]

so is it juse a over x^2 b over - x

[short terrace]

No

[unreal pasture]

ok yueah then idk

[short terrace]

You can't break up the denominator this way

You want to factorize it

[clever fjord]

Xavier 🌺

Factorize $x^2-x$

[unreal pasture]

x (x-1)

[short terrace]

Good

Now the partial fraction is obtained by solving this expression:

[clever fjord]

Xavier 🌺

$\frac{4x+1}{x^2-x} = \frac{a}{x} + \frac{b}{x-1}$

[short terrace]

Do you know how to solve such expressions

[unreal pasture]

ok for this one i cant use the domain can i

[short terrace]

It won't help much

[unreal pasture]

ok so im not sure how i would solve it

[short terrace]

Well let's start by adding up the RHS

You know how to add fractions right

[unreal pasture]

common denominator

[short terrace]

Yes

Do that

[unreal pasture]

so 4x+1 = A(x-1) + B (x)

[short terrace]

Yes

[unreal pasture]

ok i know how to get to this part and usually i would use the domain but i know i cant in this one

[short terrace]

What do you mean by "using the domain"

[unreal pasture]

like for example if the denominator was (x-2) (x+3) i would plug in for the x 2 and -3

[short terrace]

Interesting

I'm confused at what that achieves

[unreal pasture]

in the next promblem i did it

it is x + 1 / x^2 - x - 6

so i factored the denominator and then i did x + 1 = a x-3 + b x + 2 then i plugged both numbers in

[short terrace]

Oh that

[unreal pasture]

yea

i think i said it worng lmao mb

[short terrace]

You can do that here too

[unreal pasture]

would i do it with 1

-1

no js 1

[short terrace]

What did you do for x-3 and x+2

You plugged in 3 and -2 right?

[unreal pasture]

yes

[short terrace]

Cuz you wanna make one of the A or B terms zero

[unreal pasture]

yes

[short terrace]

So in this case what would you use

[unreal pasture]

so rthe A would be 0 then it would be 1B

1

[short terrace]

0 and 1 yes

This doesn't work if your denominator is a higher power however

I mean it works but isn't as easy

[unreal pasture]

so b = 5/1 which is 5

[unreal pasture]

what do you mean

[elder elbow]

Hello

[short terrace]

If the denominator is a cubic

You'd have three terms

[elder elbow]

I need help

[short terrace]

You already have a channel

[elder elbow]

No I closed that

[short terrace]

Stick to it

Then open another

[elder elbow]

No thanks

[short terrace]

This is someone else's channel

[unreal pasture]

oh yeah i think theres another question like that on here

[elder elbow]

I like this one

[unreal pasture]

lmaooo

[short terrace]

<@&268886789983436800> don't wanna deal with this myself get in here

Oh my guy also said a racial slur

[proud cradle]

Deleted?

[short terrace]

Yeah

Automodded ig

[proud cradle]

For now get out of this channel and go elsewhere or you can go to another server

[short terrace]

Either way

[unreal pasture]

so would it be 5B and -1 A

[short terrace]

Yeah so in that case you gotta solve it "properly"

[short terrace]

Write it properly lol

[unreal pasture]

yes the proper way confuses it me

[short terrace]

B = 5, A = -1

[unreal pasture]

yes

[short terrace]

Let's do this one the proper way

[unreal pasture]

ok

but would the asnwer be correct

[short terrace]

We have this

[short terrace]

Should be

[unreal pasture]

ok lets do the proper way

[short terrace]

Now let's expand this

Open up the brackets essentially

[unreal pasture]

ok

so what would we do

[short terrace]

Do you know how to open up the brackets

[unreal pasture]

no

[short terrace]

By multiplying

[unreal pasture]

i think my etacher did it but i zoned out

[short terrace]

What's A(x-1)

[unreal pasture]

ax - a1

-a

[short terrace]

Yes

So you have Ax - A

[unreal pasture]

so distributing?

[short terrace]

Yes

So now what's the expression

After distributing

[unreal pasture]

4x+1 = Ax-A + BX

[short terrace]

Good

Now "collect" the terms with the same power of x

Does that make sense

[unreal pasture]

4x ax and bx

[short terrace]

No just on the right

[unreal pasture]

so Ax and BX

[short terrace]

Yes

Now take the x out

[unreal pasture]

ok yea she was highlighting them in class

[short terrace]

Makes sense

[unreal pasture]

ok so a + b

[short terrace]

So what does your equation look like now

[unreal pasture]

4x-1 = A - A + B

[short terrace]

No

The x won't just disappear

You have 4x + 1 = A(x-1) + Bx

Distribution gives you 4x + 1 = Ax - A + Bx

What do you get from here

[unreal pasture]

ohh ok

hmm im not sure

[short terrace]

Well let's write it as 4x + 1 = Ax + Bx - A

Now do you see what to do

[unreal pasture]

im sorry im stuck

[short terrace]

Well how can you write Ax + Bx

[short terrace]

It's okay

[short terrace]

Like can you factorize it somehow

[unreal pasture]

sorry im back my wifi cut

x ( a +b)

[short terrace]

Nice

[short terrace]

So what happens when you do that here

[unreal pasture]

4x + 1 = x( A + B) - A

[short terrace]

Nice

Gimme a minute doing laundry

[unreal pasture]

alr dw

[short terrace]

Okay now

You wanna equate coefficients

Does that make sense to you, if not I'll explain what I mean

[unreal pasture]

please do

[short terrace]

So essentially

4x + 1 = (A+B)x - A

What is the coefficient of x on the left side

[unreal pasture]

4

[short terrace]

And on the left?

Right

Sorry

[unreal pasture]

a+b

[short terrace]

So we set them to be equal

[unreal pasture]

so 4 = a+b

[short terrace]

Yes

And now what's the constant term on the left

[unreal pasture]

1?

[short terrace]

Yes

And on the right?

[unreal pasture]

-A

[short terrace]

So we set those equal too

[unreal pasture]

ok so 1 = -A

[short terrace]

Yes

And now we solve for A and B