help-49

[autumn canopy]

(-1)^(2n) + 2(-1)^n + 1

You need to check if this is 0

[sour hull]

ok, that works, but there was this "if it is odd" part of the exercise that ticked me off. That's why I was asking, nothing to fear tho

[autumn canopy]

That part becomes important when you are trying to simplify it

[autumn canopy]

You need to show this is 0

And that's where it's helpful that n is odd

Do you see what (-1)^(2n) is equivalent to?

[sour hull]

no

I really do not

[autumn canopy]

We can say $(-1)^{2n} = \l((-1)^2\r)^n$, right?

[grand pond]

Kepe

[sour hull]

oh

yeah

[autumn canopy]

By exponent laws

[sour hull]

wwe can say that

[autumn canopy]

So this is $1^n$

[grand pond]

Kepe

[autumn canopy]

and that is..?

[sour hull]

correct, and that is 1

[autumn canopy]

Ok, so we got 1 + 2(-1)^n + 1

Now what about (-1)^n

Can you see what that is

[sour hull]

ohhh

if n is odd, it's -1

[autumn canopy]

yes

[sour hull]

ok

[autumn canopy]

So 1 + (-1)2 + 1 = 1 - 2 + 1 = 0

[sour hull]

It's too late,

[autumn canopy]

and thus x - (-1) = x + 1 divides p

[sour hull]

I'm going to sleep,

but thanks for the help

@autumn canopy

[autumn canopy]

Well we just got done so that's a good time lol

np

[autumn canopy]

(we really are done after this by the theorem we proved)

[sour hull]

yea

I'm gonna let it time out so that I get tagged when I wake up and can come back up to take notes

[midnight plank]

@sour hull Has your question been resolved?

[midnight plank]

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[atomic notch]

Hi this is a practice question how do i answer it

[fallen sparrow]

What have you tried

[atomic notch]

honestly bro im so stuck

idk if this will help me solve it

huh

<@&268886789983436800>

ty

@fallen sparrow

u there

[fallen sparrow]

Yea

[atomic notch]

what should i do

[fallen sparrow]

For starters i dont think you'll be requiring so advanced statistics

[atomic notch]

ok

[fallen sparrow]

If the coin is fair what is the probability that it lands on tails when it is flipped once?

[atomic notch]

0.50

0.50/5

[fallen sparrow]

....

[atomic notch]

bruhhh

so 0.1%?

[fallen sparrow]

Have patience

[fallen sparrow]

No.

[atomic notch]

ok mb

[fallen sparrow]

Explain why u did 0.5/5

[atomic notch]

cuz each flip is 50% chance to be tails

then i divided it 5 times

cuz 5 chances

[fallen sparrow]

For what

[atomic notch]

then got 0.1% for it to be tails 5 times in a row

[fallen sparrow]

???

[atomic notch]

Suppose you flip a coin five times. What is the probability of obtaining five tails in a row assuming the coin is​ fair?

[fallen sparrow]

Erm do you think you are making sense with the logic youve just said

[atomic notch]

not rlly

ok 5 tails in a row

what is the probability

the question is how do we get the probability

we know if we flip it once it has a 50% chance to get tails

but 5 times idk

[fallen sparrow]

So for every flip theres 2 possibikities right

[atomic notch]

yes

[fallen sparrow]

How many total possibilities are there?

[atomic notch]

2

[fallen sparrow]

No i mean in 5 flips

[atomic notch]

10

[fallen sparrow]

...

Have you been taught permutations and combinations

[atomic notch]

no

[fallen sparrow]

Ok then I would like you to count the total number of possibilities just for this question

[atomic notch]

ok look

[fallen sparrow]

Like HHTTH is one possibility

HTTTH is another

Etc

[atomic notch]

ohhh

theres inf possibilitys

[fallen sparrow]

.. think carefully

[atomic notch]

theres a large number of possibilits

but i dont. know it

[fallen sparrow]

I want u to count it

Its not that large

Do it for 3 flips

[atomic notch]

bro it is

[fallen sparrow]

Not 5

[atomic notch]

ok

HTTHT

THTTH

TTTHH

[fallen sparrow]

That is 5 flips...

Im asking for 3 flips

[atomic notch]

HTH

THH

[fallen sparrow]

Continue

[atomic notch]

HTT

TTH

THT

HTH

[fallen sparrow]

Already counted.

[atomic notch]

Hht

wait redo mb

[fallen sparrow]

Start from HHH

Will be easier

[atomic notch]

HTT HTH HHT TTH THT TTT HHH

there?

THH

[fallen sparrow]

Nice

Total?

[atomic notch]

8

[fallen sparrow]

Now do it for 2 flips

[atomic notch]

HT HH TH TT

4

[fallen sparrow]

Are you seeing a pattern?

[atomic notch]

O

OH

OH

wait

wait

dont

say it

so

if

2 is 4

3 is 8

4 would be 12

and 5 would be 16

[fallen sparrow]

Noo

[atomic notch]

16?

[fallen sparrow]

Do it for one flip

[fallen sparrow]

Yess

[atomic notch]

4 would be 16?

SO

32 WOULD BE 5

[fallen sparrow]

Yes

[atomic notch]

OMG

IM SO SMART

[fallen sparrow]

But I want you to understand the logic behind it

[atomic notch]

each addition flip is multiplyed by 2

MHMMHMHMMH

[fallen sparrow]

Can you explain why

[atomic notch]

bruh

hm

cuz

there

are mor epossibliltys when we add a cflip

[fallen sparrow]

Yeah but why only 2? And why multiplication? Why not addition?

[atomic notch]

dudeee cuzzzz

wait lemme think

[fallen sparrow]

Yes think!

[atomic notch]

multiplication because were adding flips

2 because the number of flips we have

[fallen sparrow]

I'll give another hint: for 3 flips its 2^3
For 4 flips its 2^4
For 5 flips its 2^5

[atomic notch]

the amount of flips is the amount we multiply 2 by

[fallen sparrow]

And why is that

[atomic notch]

because the possbilitys are increasint

[fallen sparrow]

No but why 2?

[atomic notch]

bro

cuz

2

is

what

w

e

started

with

[fallen sparrow]

i swear im not ragebaiting you im just trying to help

[atomic notch]

OH

BECAUSE

BRO

NO

CUZ

THERES

ONLY

TWO

THINGS

HEAD

AND

TAIL

SO ITS 2

[fallen sparrow]

Yes.

[atomic notch]

BVRO IM FKING SMART

[fallen sparrow]

Now you understand?

For every flip theres 2 possibilities

For 5 flips we will multiply those possibilities

[atomic notch]

the possiblities are heads or tails

[fallen sparrow]

So 2 times 2 times 2 times 2 times 2

[fallen sparrow]

Yes

[atomic notch]

4

8

16

32

[fallen sparrow]

So for 5 flips, total number of possibilities is 32 correct?

[atomic notch]

yes

and

1/32 is

ANSWER ISSS

0.03125

YES

TYSM

[fallen sparrow]

And among them, how many do you think will have all 5 tails

[atomic notch]

i got it already right

[fallen sparrow]

Yes but answer my question still

[atomic notch]

ok

[atomic notch]

1

possibility

only

[fallen sparrow]

Nice

[atomic notch]

and there is 32 in total

so we have a 1/32 possibility

[fallen sparrow]

Good job

[atomic notch]

we do the calculations

then get the answer

0.03215

damn

D

none the above

hypothesis isnt a living thing it doesnt have a heart

[fallen sparrow]

......

[atomic notch]

?

[fallen sparrow]

Im genuinely curious are you being fr

[atomic notch]

i mean thats my best guess

education guess

[fallen sparrow]

Dude its a metaphor

[atomic notch]

it sounds stupid but it was all i could make

[fallen sparrow]

Its personalisation

[atomic notch]

yea ik

but i dont know the answer

so i just did that

[fallen sparrow]

What is a hypothesis

This is legit an english question

[atomic notch]

hypothesis

simple

basically

making a desicison based on data

it allows us to test an assumption called a hypothesis

[fallen sparrow]

So what is option C then?

[atomic notch]

oh

wow

so basically what hypothesis is

JUST ASK WHAT HYPOTHESIS IS NOT THE HEART OF IT

ok it makes sense

c is correct

[fallen sparrow]

Yeah

!done

[midnight plank]

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

[atomic notch]

wait

ur busy

u cant help me anymore

🙁

[fallen sparrow]

No nk im not busy

[atomic notch]

can u helpme

🙂

[fallen sparrow]

I can entertain more doubts

[atomic notch]

ok

this is

the answer it

null

[fallen sparrow]

Is this a test?

[atomic notch]

because its stays the same

no

i swear it isnt

i could shar emy screen

if u want

[fallen sparrow]

Then why does it say only one attempt at this question

[atomic notch]

cuz

[fallen sparrow]

Also stop spamming

[atomic notch]

my teacher wants us not to get any of the questions wrong

[fallen sparrow]

Write your sentences properly

[atomic notch]

cuz he siad its rlly important chapter

Ok i will start wirting my sentences more properly.

Writing*

But i know the answer for this it is very simple it would be null.

But this is more confusing.

[fallen sparrow]

I'm sorry I cant help with this

[atomic notch]

How is someone supose to know if a hypothesis test is left tailed right tailed or two tailed

[fallen sparrow]

I would say if I knew : )

[atomic notch]

Oh you just wont help because you dont know it

[fallen sparrow]

Ping helpers after 15m

[atomic notch]

ok thanks rudy

[fallen sparrow]

Yes.

[fallen sparrow]

Np

[sacred folio]

through the inequalities

[atomic notch]

Hm

[sacred folio]

if we have a < it's left tailed if we have a > it's right tailed

[atomic notch]

im guessing

its two tailed?

because its +

[sacred folio]

ye

[atomic notch]

😗

BRUH

= *

[sacred folio]

bcs it's not equals to yes

[atomic notch]

What parameter is being​ tested?
Population standard deviation
Population mean
Population proportion

wait

it has a second part

lemme give it a try

the prameter?

the proportion?

6?

[sacred folio]

are you attempting a test rn

[atomic notch]

nope

i have infinite try

ill get it wrong and tell u th answer

[sacred folio]

mb my internet bugging i cant see the images

[atomic notch]

bruh i mis clicked the answer

but look

i could choose

similar question

but how was the answer standard deviation

i wanna understand it

@sacred folio u there

[sacred folio]

assuming ts is the complete question

that symbol is the general symbol for a pop. standard deviation

[atomic notch]

huh

[atomic notch]

ooooo

so the thing like the o

ok

[sacred folio]

sigma

[atomic notch]

hmmm what abt this

sigma

yea

[sacred folio]

hmm

[atomic notch]

ima try it

one second

ehhh

[sacred folio]

the first one's definatly =

[atomic notch]

yea

second

is prolly gonna rise

but idk which one to choose for rise

[sacred folio]

nah

[atomic notch]

and idk if it actually risen

[sacred folio]

probably not equals to

since we dont know if it rose or fell

just that it changed

[sacred folio]

do you have an option for that ??

[sacred folio]

ye

[atomic notch]

oh

[sacred folio]

what course is ts

[atomic notch]

what does the sign mean

[sacred folio]

[atomic notch]

statistics

[sacred folio]

thats sigma is not 5.64

could be higher or lower

just not 5.64

[atomic notch]

mu?

[sacred folio]

[atomic notch]

p?

[sacred folio]

what....

[atomic notch]

dude

im cofnused

[sacred folio]

i have no clue either

[atomic notch]

im gonna cry

😭

[sacred folio]

what are you asking ??

btw my internet kinda buns rn so i might have to leave soon

[atomic notch]

ok

this

im asking somone to help me understand this so i can answe ir

i5

it

[sacred folio]

basically H0 case where the deviation is the initial deviation and H1 is the new one

[atomic notch]

aka nul and alternative?

[sacred folio]

and the question is just asking you to convert the english into mathematical terms

[atomic notch]

so basically first on

is

nothing changed

so =

[sacred folio]

ye

[atomic notch]

and sigma

?

then h1

/=

EH?

[sacred folio]

what all options does it have

the second part

[atomic notch]

< =

<

=

oH

ITS

GONNA

BE

GREATER

THEN

[sacred folio]

no no

[atomic notch]

SO

oh

[sacred folio]

the first part

i mean

the first blank of the second part does it have a s symbol in it

[sacred folio]

if no then sigma is correct and ts should be the answer

[atomic notch]

ok

dude

my answer is correct

[sacred folio]

if yes then choose s for it instead as the weekly analysis would be a sample

[atomic notch]

i just entered it in lol

[sacred folio]

gn then

bye bye

[atomic notch]

<@&268886789983436800>

[midnight plank]

@atomic notch Has your question been resolved?

[midnight plank]

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[midnight plank]

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[stable dragon]

PLEASE HOW DO I DO THIS PLEASE HELP ME

[midnight plank]

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

[brave gorge]

Do you know any value that p cant be

[stable dragon]

what i have so far

so p < -1???

[brave gorge]

Yeah

[midnight plank]

@stable dragon Has your question been resolved?

[midnight plank]

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[sleek lagoon]

Vẽ ra ngoài tam giác ABC 3 tam giác đều có cạnh lần lượt là 3 cạnh của tam giác đó. Chứng minh tâm của 3 tam giác đều đó là 3 đỉnh của một tam giác đều

[civic gazelle]

are you required to prove this thing?

what have you learnt so far?

[sleek lagoon]

yes

e học lớp toán 8 chuyên (clb ánh sáng)

nên phải làm

thầy em bảo làm thế

thầy bảo bài này*

thầy ko cho hình lên lấy trên mạng

[civic gazelle]

dịch để mấy thg khác còn giúp

[sleek lagoon]

Draw outside triangle ABC 3 equilateral triangles whose sides are the 3 sides of that triangle. Prove that the centers of the 3 equilateral triangles are the 3 vertices of an equilateral triangle.

why fire

[lusty python]

🙏

có mỗi cái reaction thôi mà cũng hỏi

[civic gazelle]

bất lịch sự

@sleek lagoon anh nghĩ ra rồi

bài khá hay

[civic gazelle]

Chắc chắn lớp 7 lớp 8 e đã làm cái bài chứng minh ∆AFC = ∆ABE nhiều rồi đúng ko

[sleek lagoon]

dạ

[civic gazelle]

có ngay BE = CF

[sleek lagoon]

vâng

[civic gazelle]

giờ ta gọi G là trọng tâm ∆ABC

thấy có một đống đường song song chưa e

từ đó chứng minh GO2 = GO3 và O3GO2 = 120°

[sleek lagoon]

dạ

[civic gazelle]

chứng minh tương tự thì sẽ có GO1 = GO2 = GO3 và góc giữa chúng là 120°

thế là coi như xong

[sleek lagoon]

vâng ạ

em cảm ơn

[civic gazelle]

đến đây chắc e tự làm đc

[wicked mauve]

what language is this

[sleek lagoon]

vietnamese

[wicked mauve]

oh baller

[sleek lagoon]

e cảm ơn @civic gazelle

.close

[midnight plank]

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[last slate]

bro i need help please

[lusty python]

?

[last slate]

someone help me understand why that in a set of vectors, when

c1v1 + c2v2 + c3v3 + … ckvk = 0

If ∀ck-n ∃ck-n such that ck-n ≠ 0 then theres redundancy in the vector set

Help me understand why this implies redundency

fixed

[sharp coral]

if one of the $c$'s is not zero, let's say $c_i \ne 0$, then that means you can solve the equation for $v_i$. that means $v_i$ can be written as a linear combination of the others and is redundant

[grand pond]

cloud ☁

[last slate]

i see but why does doing algebra like this work. Like how can this help us also see redundancy geometrically

like without solving for one of the vectors

idk how to explain it in a better way

[sharp coral]

i mean you can have a geometric picture but that only works in R^n. whereas the algebra is true for all vector spaces

the entire definition of a vector space is basically a set of objects where this sort of algebra works

[last slate]

like say you have a set of polynomials.. those are different from vectors in R^n.

Having a non zero scalar .. the outcome of that on the combination of polynomials isnt the same as the one on vectors in R^n

yet both outcomes imply redundancy

how does that work?

same thing with matrices

Whats the common thing here that makes a non zero scalar of their combination imply redundancy I don’t get it

like if in R^n we dont want vectors expressed in terms of other vectors

what do we want in P_n?

a polynomial not expressed in terms of other polynomials?

[sharp coral]

so iv we have a set of vectors $v_1, \ldots, v_k$ then every vector $v$ in their span can be written as a linear combination of them:
[ v = \sum_{i = 1}^k a_i v_i ]
If they are linearly independent, then the choice of $a_i$'s is unique, and if they are dependend then it isn't

[grand pond]

cloud ☁

[sharp coral]

since if there are not all zero $c_i$'s such that $\sum_{i = 0}^k c_i v_i = 0$, that would imply that
[ v = \sum_{i = 1}^k a_i v_i = \sum_{i = 1}^k (a_i + c_i) v_i ]
which are two different linear combinations!

[grand pond]

cloud ☁

[last slate]

its not making sense to me tbh

[last slate]

by “in their span” you mean what exactly? That every vector in the parent space can be written as a linear combination of the vectors?

like for example in R^n every vector (x,y,z) is a linear combination of all vectors in the set?

or any vector in R^n can be written as a linear combination of all vectors in the set

[sharp coral]

$\vspan{v_1,\ldots,v_k}$ is by definition the set of all linear combinations of $v_1,\ldots,v_k$

[grand pond]

cloud ☁

[last slate]

right

okay so

”if they are linearly independent then the choice of a_i is unique”

true you want vectors that are unique

and?

[last slate]

okay I don’t get this one

[sharp coral]

,align v &= v + 0 \
&= \sum_{i = 1}^k a_i v_i + \sum_{i = 1}^k c_i v_i \
&= \sum_{i = 1}^k (a_i + c_i) v_i

[grand pond]

cloud ☁

[sharp coral]

that's two distinct linear combinations (at least some of the a_i + c_i are different since not all of the c_i are zero!)

[last slate]

can u explain how you set up the sums

and youre expressing v = (the non zero scalar were talking about)*v + other vectors with 0 scalar?

[sharp coral]

all it's saying is that if $v$ can be expressed as a linear combination of $v_1,\ldots v_k$ (i.e. there are scalars $a_1,\ldots a_k$ such that$\sum_{i = 1}^k a_i v_i = v)$), and $v_1, \ldots v_k$ is linearly independent ($\sum_{i = 1}^k c_i v_i = 0$ with not all scalars zero) then it can be written as a different linear combination as well

[grand pond]

cloud ☁

[last slate]

the sum notation is a little confusing tbh

[sharp coral]

what about it is confusing you?

try writing it out more explicitly if it makes it more intuitive

[last slate]

lemme ask something, does the fundamental thing about linear independence revolves around the scalars themselves?

like 1 vector cant be expressed in terms of another

doesn’t matter the vector space

brooooo

[fallow scarab]

Your questions are all over the place and you're missing a lot of basics. I recommend reading a linear algebra book to catch up on basics

[last slate]

wait but when you solve for v_i everythin else is already 0

[last slate]

im not missing any basics bro

linear algebra just tends to get abstract

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[lusty python]

I needed help with this question: Given triangle ABC only has acute angles. Draw a circle with diameter of BC, such that this circle intersects AB at F and intersects AC at E. Let H be the intersection of BE and CF, AH intersects BC at D. We also let M be the reflection of F through BC, prove that M, D, E both lies on the same line.

[lusty python]

The diagram above simplifies to this

How can I use Menelaus theorem for this?

[gilded bison]

hello

[lusty python]

hello

<@&286206848099549185>

[civic gazelle]

You don't even need Melenaus for this

MDB = FDB = EDC is sufficient enough

Mê với chả Lê cho nó mệt người

[runic pebble]

Equate their gradients?

[civic gazelle]

In fact, this is true if H is any point on the altitude AD

you can use Ceva to prove this

[lusty python]

alr

[civic gazelle]

The fact that FDB = EDC is used quite a lot in olympiads

@lusty python any more questions?

[midnight plank]

@lusty python Has your question been resolved?

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[midnight plank]

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[dapper nacelle]

how is 2 an explanation of 1?

[lyric charm]

(n+1)^7 - n^7 - 1 = [(n+1)^7 - (n+1)] - [n^7 - n]

[dapper nacelle]

i see

the way i did it was expand it, 1st term is n^7 last term is 1 and they are subtracted out and the all the remaning binomial coeeficents are multiples of 7

2nd one is fermat's litttle theorem

isnt it too ambigious cuz there are many ways to do it?

[lyric charm]

i mean it says "stmt 2 is a correct explanation for stmt 1"

no claim is made of "this is the ONLY correct way to explain it"

[dapper nacelle]

that does work out

thanks

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[twilit field]

$\langle T(x^2), 3x \rangle = \langle x^2, 3x \rangle$ would be true if it were self adjoint

[grand pond]

wai

[twilit field]

but $\int_{0}^{1} 3x^3dx ≠0$

[grand pond]

wai

[twilit field]

is that enough

[lyric charm]

do you think it is enough or do you think it isnt

[twilit field]

I think it is

it's a counter example

[lyric charm]

then why ask here

[twilit field]

just wanted to be sure

thanks

.close

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[shut canyon]

numerator: (1+x+x^2)^½ - 1
denominator: x

x⟶0, f⟶…

factor x?

[umbral timber]

rationalize the numerator

[shut canyon]

x•g(x)

[umbral timber]

to remove the 0/0 form

[shut canyon]

(√(1+x+x²)−1)(√(1+x+x²)+1)=1+x+x²−1=x+x²

[umbral timber]

yes

dont forget to multiply the conjugate in the denominator as well

[shut canyon]

(√a − 1)(√a + 1) = a − 1

x(√(1+x+x²)+1)

[umbral timber]

(√(1+x+x²)+1) is your conjugate. u multiplied it at the numerator to rationalize it but now u must multiply it with the denominator too to keep the fraction unchanged

[shut canyon]

x+x² / x(√(1+x+x²)+1)

[umbral timber]

yes

[shut canyon]

x(1 + x) / x(√(1+x+x²)+1)

(1 + x) / (√(1+x+x²)+1)

[umbral timber]

yes

now try subbing x=0

[shut canyon]

Thanks lots @umbral timber

[umbral timber]

no worries

[shut canyon]

x⟶0, terms in (1 + x) / (√(1+x+x²)+1)
x⟶0,
x²⟶0

1+0 / √(1+0+0)+1

[umbral timber]

yup, and you arent getting an undefined form either now

[shut canyon]

1 / 2

[umbral timber]

yess

[shut canyon]

Danke

[umbral timber]

any more doubts?

[shut canyon]

It's smooth sailing now maybe, I'll try to formalise it

⛵️

[umbral timber]

okie

[shut canyon]

xₙ⟶0,
∀ε>0 ∃N>0 ∀n>N ⇒ |f(xₙ)−½|<ε
f(xₙ) = (√(1 + xₙ + xₙ²) − 1)/xₙ,
f(xₙ) = (1 + xₙ)/(√(1 + xₙ + xₙ²) + 1) (retionalise),
xₙ → 0 ⇒ 1+xₙ → 1, √(1+xₙ+xₙ²) → 1.
∴ f(xₙ) → 1/(1+1) = ½.
∀ suite (xₙ)→0 ⇒ f(xₙ)→½ ⇒ limₓ→0 f(x)=½

[umbral timber]

i dont understand x_n notation but everything else looks legit

[shut canyon]

xₙ is sequence converges to 0 I think

Thank you for your help @umbral timber

[umbral timber]

ohh i see

[shut canyon]

∀ε>0 ∃N>0 ∀n>N ⇒ |f(xₙ)−½|<ε

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[grand stratus]

Prove that in any party the number of people who have made an odd number of handshakes is even.

[grand stratus]

It is not necessary that everyone does a handshake.

[spiral rock]

Try to translate it into the language of graphs

[last slate]

read the question wrong mb 👍

[jade sparrow]

sum the number of handshakes made by one person, for all the people.

One handshake is counted twice in the sum.

So the sum is always even.

Some people made odd number handshakes, and they are part of the sum.

[grand stratus]

Let there be 2k odd handshakers and f even handshakers.
Let us describe the next handshake.

1. An odd handshaker and an even handshaker handshake.
   Result: The numbers of people in each groups remain equal, i.e., 2k and f.

2. Two odd handshakers handshake.
   Result: Odd handshakers = 2k - 2 = even and even handshakers = f + 2

3. Two even handshakers handshake.
   Result: Odd handshakers = 2k + 2 = even and even handshakers = f - 2

Now at the start of every party there is an even number of odd handshakes, which is 0. Hence by the principal of mathematical induction the statement is true.

[midnight plank]

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[last slate]

hello

[last slate]

i showed 1 2

and an implication of 3

but i can't show the other sens

$$$ \ker \varphi = {e}$ $\implies$ $\varphi$ injective

[grand pond]

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

[last slate]

you have a morphism of groups Phi from (G, . ) to (H, * ) e is the neutral element of G and f is the neutral element of G

[robust isle]

donc c'est bien cette direction que t'arrive pas à faire ?

[last slate]

ouii

[robust isle]

qu'est-ce que t'as essayé alors ?

@last slate

[last slate]

j'ai essayé de prendre 2 élément arbitraires de G et possé l'égalité des image par phi et faire une manipulation avec les éléments neutre (somehow?) mais j'arrive pas a trouvé la méthode

[robust isle]

c'est une bonne idée de preuve déjà

[last slate]

$\varphi (a)=\varphi (b) (\forall (a,b) \in G)$

[robust isle]

maintenant oui faut trouver le somehow

[grand pond]

Drk

[last slate]

oui

je pense a faire

[robust isle]

donc ok ker phi c'est phi^-1({f})

[last slate]

oui

je pense a faire $ \varphi(a)*varphi(e) ...ect$

mais je trouve rien

$ \varphi(a)* \varphi(e) = \varphi(b)* \varphi(e) $

et apres \varphi(a.e)...

[robust isle]

donc si tu prends x dans ker phi, ça veut dire que phi(x) = f

[last slate]

ouii

[robust isle]

essaie de réécrire ton équation d'injectivité sous cette forme

[last slate]

f= phi(e)

hm

[last slate]

ok

$Soit (a,b)\in \Ker \varphi , On pose \varphi(a) = \varphi(b)$

[robust isle]

non tes a, b doivent être arbitraires

[last slate]

mais ca donne rien?

[last slate]

i'll sont arbitraires?

[robust isle]

oui

si tu veux montrer que phi est injective

faut que ça marche pour tous les éléments de ton groups

[last slate]

ici i'll sont un couple arbitraire ? ou non?

[robust isle]

(a,b) dans ker phi ils sont pas arbitraires non

c'est (a,b) dans G qu'il faut

[last slate]

ah oui

[robust isle]

$\varphi(a) = \varphi(b)$ essaie de réécrire ça sous la forme $\varphi(\text{quelquechose}) = f$

[grand pond]

aPlatypus

[robust isle]

en faisant passer phi(b) de l'autre côté de l'équation

[last slate]

OH

$\varphi(a) * \varphi(b^{-1}) = \varphi (b . b^{-1} ) = \varphi(e) = f$

[grand pond]

Drk

[robust isle]

typo

c'est phi(ab^-1)

[last slate]

same thing

car le morphism

donc

[robust isle]

ah oui fine

ok

[last slate]

ca donne

$a . b^{-1} \in \ker \varphi$

[grand pond]

Drk

[last slate]

comment passer a l'injectivité hmm

[robust isle]

et ker phi il y a quoi dedans

[last slate]

$a.b^{-1} \in \varphi^{-1} ({f})$

[grand pond]

Drk

[robust isle]

faut pas oublier ce que tu veux prouver

[robust isle]

il y a une hypothèse importante là dedans

[last slate]

oh

$a.b^{-1}= e$

[grand pond]

Drk

[robust isle]

oui

[last slate]

et

donc

a=b

damn

merci bcp

d'ou l injectivité

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[buoyant grove]

!occupied

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[buoyant grove]

<@&286206848099549185> Explain Graham's Number to me/

[oak kelp]

!15m, please.

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

[obtuse mason]

It’s the G function applied 64 times

All I know really

[buoyant grove]

So can u tell me onw more quest?

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[bright shoal]

Can my site be reviewed
I need someone with collatz conjecture knowledge and interest in trying out tools

[spiral rock]

Explain

[bright shoal]

Ok so like collatz scribbles is a site where you can see how collatz conjecture works to like take a number to 1

sequence visualisation in form of a graph

this is my site collatz scribbles

[grim vector]

By reviewed you want ppl to try the site or read the code ?

[bright shoal]

try it

so can i share the link

@grim vector @spiral rock

[grim vector]

We not the person to ask

[bright shoal]

https://collatz-scribbles.vercel.app

[grim vector]

Ask a mod or idk

[bright shoal]

okay okay

[last slate]

that wasn't a wise decision to click on the link but pretty cool website

[fallow scarab]

Can you not share your spam

[midnight plank]

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[lyric charm]

!occupied

[midnight plank]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[lyric charm]

!status

[midnight plank]

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

[near geyser]

1

Ohh Hello Ann

[lyric charm]

hello popking

[near geyser]

Sorry by my side!!

Let's back to the question

[lyric charm]

oh, so you had a moment of clarity.

ok

well call the original cost price something like x

[near geyser]

x+40 after increasing

[lyric charm]

can you tell me an expression in terms of x for the following, in this order:

1. original sale price
2. cost price after increase by 40 INR
3. sale price after reduction by 55 INR

ok that's #2 of what i'm asking

[near geyser]

149x/100 selling price

1.49x

[lyric charm]

1.49x is probably a little bit better

yes ok

that's #1

[near geyser]

3 -->1.49x-50

[lyric charm]

you've got #1 and #2 now #3 remains

ok

so increased cost price is x+40 and decreased sale price is 1.49x - 50

and new profit margin is 47.5%

do you see what to do from here

[near geyser]

Hmm yeah yeah

x+40-1.49x+50=90-1.48x

[lyric charm]

wait why are you. what

why are you doing new CP - new SP at all

[near geyser]

(90-1.48x)100/(x+40)=47.5

[lyric charm]

ok you can do that

[near geyser]

Cp-sp/cp ×100

[lyric charm]

but x - 1.49x is not -1.48x

[near geyser]

%profit?

[lyric charm]

numerator is surely SP - CP

also brackets.

[near geyser]

In profit?

cp >sp no?

[lyric charm]

CP > SP is nonsense

why sell something for 1 rupee when it cost you 1 lakh

[near geyser]

Ohh right right

[lyric charm]

also why not

CP * (1 + profit%) = SP

will make your life so much easier

[near geyser]

Never saw such formula that way

Ohh nice

[lyric charm]

you used it already

when you said original SP is 1.49x

[near geyser]

1.49x/(1+47.5)?

Ohh NO

[lyric charm]

CP * (1 + profit%) = SP
new CP = x + 40
new SP = 1.49x - 55

also yeah 55 not 50

we both misread it or sth

[near geyser]

(x+40)=(1.49x-55)/(48.5%)

[lyric charm]

loud incorrect buzzer.

[near geyser]

😭

[lyric charm]

also where is 48.5% coming from, that's nonsense

[near geyser]

1+47.5%

[lyric charm]

100% + 47.5%

you're trying to do 34 lakh things at once btw

[near geyser]

147.5%

[lyric charm]

please stop doing that

you shouldnt be trying to set up the equation AND do algebruh to it simultaneously

thats a very surefire way to fuck up and get wrong answers

[near geyser]

Hmm true

Let me do it again slowly

[lyric charm]

(x+40) * 1.475 = 1.49x - 55

that is it. like thats just put pegs in holes based on what i told you

[midnight plank]

@near geyser Has your question been resolved?

[near geyser]

7600 yoo

[midnight plank]

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[stable dragon]

how would i solve this

[plucky lark]

You can use casework

[stable dragon]

what

[plucky lark]

You know like proving each case right or wrong

I would first simplify the equation tho

I think the answer is the thrid one

we can isolate the ((ln(n))^p)/n

when the ln is raised to a negative power its undefined so p must be greater than or equal to 0

@stable dragon

wait nevermind this is wrong

[rich yew]

@stable dragon (-1)^𝑘-4 = (-1)^𝑘

so simplify that first.

We can ignore the alternating sign for a moment, in which we would have $\frac 1{n\log^p{n}}$

[grand pond]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[rich yew]

we can integrate that.

$\int_2^\infty \frac{dx}{x\log^p x}$

[grand pond]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[rich yew]

\whrule
substitute $u=\log(x)$, which would give us $$\int_{\log(2)}^\infty\frac{du}{u^p}$$

[grand pond]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[rich yew]

@stable dragon Do you understand everything thus far?
-# assuming i’m not explaining to nobody.

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[stable dragon]

.reopen

[midnight plank]

✅ Original question: #help-49 message

[stable dragon]

wait so

are we using the integral test

[rich yew]

[stable dragon]

on an alternating series

test

im gonna lose my fucking mind

[rich yew]

Well tbf my steps are not entirely necessary

you can just jump tot he alternating series test if you want

yeah it was redundant

Anyway, use the leibnitz test.

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[edgy crater]

would i have to also consider the case where i am assume root 2 > a/b, or is this sufficient

[patent goblet]

Well, you have to show the statement for arbitrary a and b, and we can pick a and b such that sqrt{2} > a/b so we also have to consider that case! I am not sure however if there is a slick argument to get it done.

[edgy crater]

okok ty

.close

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[rigid turret]

I have found that T1 = Fg

T2sin45 = T3sin60

T2cos45 + T3cos60 = T1

are those true?

and where do i go from there

[blazing nacelle]

They are^ They resolve the forces to 0
The second one shows an inequality between T2 and T3, so what is that inequality?

[rigid turret]

T2/T3 = sin60/sin45 = 1.225
so numerator is greater? T2 > T3

[blazing nacelle]

Yep - and which option does that mean your answer is?

[rigid turret]

but how is T1 greater than each of those

T1 has a greater y component than each of them

i see that

but how to prove that overall it has a bigger magnitude

[blazing nacelle]

If T1 > T2 then T1 > T3, so you can plug your ratio into the other equation you have, and see if this is the case

[rigid turret]

?

what do you mean

plug in my ratio

[blazing nacelle]

$T3 = T2 \times \frac{\sin(45)}{\sin(60)}$

[grand pond]

Varixiuqlhfbgraijbzjnqghppxnqmvw

[rigid turret]

wait

[blazing nacelle]

Probably best that way around

[rigid turret]

i got it

i think

[blazing nacelle]

Good :)

[rigid turret]

T1 ~ 1.36 T3

?

is that good

oh

i should probably try to find t1 in terms of t2

hold

[blazing nacelle]

Okie dokie :)

[blazing nacelle]

Probably, but there's still only one option that it could be if $T2 \neq T3, \And T1 > T3$

[grand pond]

Varixiuqlhfbgraijbzjnqghppxnqmvw

[rigid turret]

1.52 T2 = T1

1.36 T3 = T1

wait does that seem right

whatever

its T1 > T2 > T3?

[blazing nacelle]

Think so - it's what I get

[rigid turret]

ok

thx

[blazing nacelle]

No worries :)

[rigid turret]

i got 9/9

thx bro

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[alpine gyro]

How do you simplify this to A'C'+AB'+AC? I always get A'C' + B'C'+AC

[gleaming latch]

can you show your steps

[alpine gyro]

A'B'C'+A'BC'=A'C',
A'B'C'+AB'C'=B'C',
AB'C+ABC=AC

[midnight plank]

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[alpine gyro]

.close

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[small warren]

Can I please get help with this question? Here is my work so far, I'm not really sure what to do.

[last slate]

do you get what it means to solve for an unknown?

[small warren]

If I had to think, you have to find the value that makes the equation valid?

[last slate]

Yes

[small warren]

How do you do that?

[gaunt jetty]

Do you know how to factor

[small warren]

Yes

[outer copper]

is there something you could factor from $2x^2 - 4x$

[grand pond]

joseph

[small warren]

2x

[gaunt jetty]

Do so then

[small warren]

$2x(x-2)$?

[grand pond]

🩷Aurora💜

[outer copper]

yep

[gaunt jetty]

Yeah

[outer copper]

so what values can x be to satisfy the equation?

[gaunt jetty]

Now you have a product of two numbers and you want to see when that product is zero

When is a product of two numbers zero?

[small warren]

Either x=2 or x=0? Because 2x=0 is the same as x=0/2 which equals x=0 and x-2=0 is the same as x=2

[gaunt jetty]

Ye

U r done

[small warren]

Yayyy tysm!! ❤️ i saw in my mind that it could be something to do with something common between them but i didn't see that you'd have to factor out a GCF because i haven't done that when trying to solve stuff in this form

.close

[midnight plank]

Channel closed

Closed by @small warren

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

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[last slate]

Yoyoyo

[last slate]

when we talk about row and vector spaces of matrices

Are the subspaces formed from the row and column vectors, exactly 1 dimension less? Or could be less than that?

[rain wasp]

less than what?

consider I_3, the matrix lives in R^3 and its row and column spaces are also R^3

[last slate]

i think it can be less

[last slate]

like R^n

[rain wasp]

like the space that the matrix lives in?

[rain wasp]

then no, by this

where did you get this thought from?

[last slate]

say you have a 3x5 matrix

This means the row space is the subspace of R^5 formed by the row vectors of the matrix. Our row vectors can span some shape in R^3 in this case but if we had 4 rows instead of 3 then our row vectors would span something in R^3

(a plane)

[last slate]

row spaces and column spaces

[rain wasp]

i'm not sure i follow here

the added row vector may or may not change the span of the matrix row space

[last slate]

I worded that wrong lemme retry

[last slate]

Random matrix

also im assuming the row vectors are a basis

which the book didn’t do a great job at explaining

wait must i put it in RREF first

then use the non zero vectors in the reduced one

REF*

<@&286206848099549185>

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[dim quest]

please help

[midnight plank]

Available help channel!

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Remember:
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[peak ridge]

Do u still need help?

[dim quest]

yess

please

[bold peak]

They have already claimed a channel

[peak ridge]

Oh

[bold peak]

.close #help-21｜아리스킨충1

[midnight plank]

Channel closed

Closed by @bold peak

Use .reopen if this was a mistake.

Available help channel!

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Remember:
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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.

[last slate]

can someone help me