#help-39
low matrix
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pearl pondBOT
pearl pondBOT
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tacit bough
Where am I going wrong here?
pearl pondBOT
Where am I going wrong here?
light helm
your stuffed up the conversion of the division to multiplication and negative exponents for the second fraction
you tried doing too many things at once
id recommend doing each in a separate step
formal stratus
guys how would u subtract root 3 x- x ??
light helm
guys how would u subtract root 3 x- x ??
!occupied
pearl pondBOT
guys how would u subtract root 3 x- x ??
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tacit bough
your stuffed up the conversion of the division to multiplication and negative ex...
but when I flip the fractions, the exponents become positive?
light helm
as mentioned, do these steps one at a time
converting the division to multiplication,
ONLY flip the fraction
do nothing else to it yet,
Convert those negative exponents in another step
light helm
that works
tacit bough
Find three consecutive even numbers knowing that the first number plus 3 times the third number is 40 more than the second number*
tacit bough
How would I approach this problem?
An even number is (2n + 2)
The third even number, (2n + 6)
but then the second one, (2n+2) + 3(2n+6) - 40?
or is it
(2n + 2) + 3(2n+4) = (2n+4)-40?
snow sail
an even number 2n
so theyre 2n, 2n+2, and 2n+4
first number plus 3 times the third numbe is 40 more than the second number
(2n) + 3(2n+4) = (2n+2) + 40
tacit bough
ahhh
tacit bough
ok, I had tried + 40, but did 2n + 2 not 2n as the first number
snow sail
just seemed like you were pretty close already
yea in general even is 2n
and odd is 2n+1
although an even number is also 2n+2, sure
not the most convenient definition!
tacit bough
Odd is 2n + 1, so in my head I quickly did 2n + 2
The answer I get is n = 5, so the three numbers are 10, 12, & 14
snow sail
,w 10 + 3 * 14 = 40 + 12
jolly parrotBOT
snow sail
pearl pondBOT
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bold elbow
what does "at most" mean in Standard distribution curves?
pearl pondBOT
what does "at most" mean in Standard distribution curves?
fathom oasis
Have you tried replacing "at most" with "less than or equal to" ?
bold elbow
Have you tried replacing "at most" with "less than or equal to" ?
does "less than" also consider everything on the other half of the curve?
If the instructions were to shade the area of the normal curve distribution with the z score being lets say 3.00 at most, do I also shade everything in the negative side of the curve?
fathom oasis
If I want it to be at most 3 degrees outside so that we can build a snowman together then can we build a snowman if it's -2 degrees?
bold elbow
If I want it to be at most 3 degrees outside so that we can build a snowman toge...
yeah but it'd be cold
fathom oasis
does this help answer your question?
fathom oasis
i'm glad to hear it ^^
pearl pondBOT
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fading ledge
pearl pondBOT
fading ledge
Why not option D?
dense jasper
Because whoever wrote this is a crackhead: either the person writing the solution forgot to account for x being negative, or the person who wrote the question made the implicit (and incorrect) assuption that the terms of a geometric progression must be positive.
fading ledge
So i am right
ancient knoll
yes u are
daring charm
yh
pastel sentinel
can someone please help me with this? I feel like I’m losing my mind because I wasn’t trained on how to do this :(
pearl pondBOT
can someone please help me with this? I feel like I’m losing my mind because I w...
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
this is essentially just pattern matching
They give you x, find y
and they also give you an equation that approximates y given x
so
yeah
pastel sentinel
would I just plug 30 into the equation?
omg bro is that just it
I was confused by the percentages and it had me thinking it was 30% or greater
I’m sorry for panicking I feel kinda dumb now, thank you though :)
pearl pondBOT
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pastel sentinel
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severe latch
how do i do this
pearl pondBOT
how do i do this
cinder flower
well you can consider the 13c3 ways to pick which of the 3 ranks you have for pairs
also 57c2?
cinder flower
it's ok 
severe latch
well you can consider the 13c3 ways to pick which of the 3 ranks you have for pa...
i see
cinder flower
well you can consider the 13c3 ways to pick which of the 3 ranks you have for pa...
then there are 4c2 ways to choose suit for each rank
solar lily
is the number they have assigned
cinder flower
there are 13 ranks. you could just imagine them as 1,2...,13
in an actual deck they are A,2,3,...,10,J,Q,K
but the names don't matter
you have 4 cards labelled 1, 4 cards labelled 2, and so on
severe latch
ohhh i see
cinder flower
the cards labelled 1 are all distinguishable from each other (they are all a different suit, hearts, spades, diamonds, clubs)
pearl pondBOT
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Available help channel!
pearl pondBOT
<#490557019623915520>
spiral nexus
alr
pearl pondBOT
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
pearl pondBOT
@spiral nexus Has your question been resolved?
spiral nexus
no
ebon bay
please guys solve with desmos
How would you try to solve this problem?
ebon bay
yes, forget about your question
spiral nexus
How would you try to solve this problem?
I need to solve with desmos if u can please
ebon bay
ok umm
look how you would approach with/without desmos would be that you substitute x^2 as t
spiral nexus
Yeah
ebon bay
everything in your problem becomes 8t^2 +50t + 63 and at+b
spiral nexus
Yes
ebon bay
which as you can see is way more simpler than considering a degree 4 polynomial!
its basically a parabola now
spiral nexus
Can i equal the 2 expression
ebon bay
Umm could me a method
but whats more easy is to use the roots of the parabola
have you ever seen this theorem:
ax^2 + bx + c = a(x-q)(x-p)
spiral nexus
Bro can u please write at desmos at ss send me?
spiral nexus
have you ever seen this theorem:
ax^2 + bx + c = a(x-q)(x-p)
Yess
ebon bay
Where q and p are the roots of the parabola
spiral nexus
Yes
ebon bay
everything in your problem becomes 8t^2 +50t + 63 and at+b
Now do you also agree that 8t^2 +50t + 63 = 8(t-q)(t-p)
spiral nexus
Yh
ebon bay
awesome, well what are the values of q and p?
using desmos it is ofc possible to find the values
ebon bay
u sure?
spiral nexus
Yh
thorny rock
hi
ebon bay
thorny rock
can i join?
ebon bay
Ofc
thorny rock
alrr
spiral nexus
but bro there was 8x^4+50x^2+63 too
ebon bay
Now do you also agree that 8t^2 +50t + 63 = 8(t-q)(t-p)
Ok now finish this:
ebon bay
but bro there was 8x^4+50x^2+63 too
Yes now using the substitution x^2 = t
spiral nexus
alr
ebon bay
we analyzed it based on the parameter t
ebon bay
Instead of the actual x(the reason why i wrote x in desmos is because desmos ONLY accpets x as input for a function)
spiral nexus
ebon bay
Now you have factored the expression!
bring back the substitution we made t=x^2
8x^4 + 50x^2 + 63 = 8(x^2+4.5)(x^2+1.75)
spiral nexus
alr
ebon bay
from now on its just try and error to see which ax^2+b the problem was asking
dont forget that 8 can be multiplied inside!
spiral nexus
ebon bay
yes the app you are using is powerful enough to do it but we have to calculate those with hands
Not computers
ebon bay
look there are different combinations of ab
you might be asking why? This is:
x^2+4.5 is a factor therefore a=1, b=4.5 then ab = 4.5
x^2 + 1.75 is a factor therefore a=1, b=1.75 then ab = 1.75
Since it was 8(x^2+4.5)(x^2+1.75) we can multiply 8 inside one of them to have (8x^2 + 36)(x^2 + 1.75) or (x^2 + 4.5)(8x^2+14)
u can find other factors
those two two which have gotten multiplied by 8
ebon bay
you are writing it where?
spiral nexus
desmos
ebon bay
Yes but you cant finish the whole question with desmos
This is the factored form
And these are the different forms of written
I gotta go right now, if anyone else here please answer further question
Will cya 👀
I will try to come back asap but ye
spiral nexus
Alr ty
spiral nexus
Alright did u generally understand what we did
Yes but
With demos
It says only 63
ebon bay
Yes remember that the expression 8x^4 + 50x^2 + 63 is never zero
Why? Because x^4 is positive and x^2 is positive everything is possible therefore it is never zero
spiral nexus
Yea so
ebon bay
Therefore you can not be looking for x-intercept in the given expression
but seeing that we have the potential to substitute x^2 as t
even though if course we restrict t>=0 because x^2>=0 but here things are different
ebon bay
How would you try to solve this problem?
Why do you think i sent this at the very beginning?
spiral nexus
Idk
ebon bay
Idk
Take a deep breath because we are going to dive into the world of factorization using roots!
Give me some time to create some images and i will explain you the method..
spiral nexus
Alr
pearl pondBOT
@spiral nexus Has your question been resolved?
ebon bay
Alr
First of all i should tell you how useful factorizing is in mathematics! It’s important in alot of algebraic ways of solving problems and one of them is simplifying expressions. For example this huge looking fraction can be simplified to x-4!(meaning that instead of calculating the whole enormous expressions on the numerator and denominator, we simply evaluate x-4 to find the final value for for example x= 6)
spiral nexus
Tysm
ebon bay
Alright now lets start to see how we can factor out these terms? Obviously one method is just straight up algebraic method, which needs alot of practice (its a good skill but for now we wanna have simple methods 😆)
Lets take a precise look at this expression 🤔
what we know is that both sides are equal meaning that whatever value we give for the left side, we should get on the right side. Hmmm what if we plug in the roots of the left side? (By root we mean a x-value where the expression becomes zero!)
Hmm interesting, plugging the value of the roots we actually do get both sides equal, so lets do something, whenever we see any expression like x^2 -2x - 8 lets rewrite it based on its roots!(why?, we might need to prove this but lets just accept that for now they are equal)
So lets see if we can do the same on this one 🤔
Lets immediately find its roots 👀(i assume you know the formula for a quadratic equation)
ebon bay
Lets take a precise look at this expression 🤔
what we know is that both sides ...
Now we know the roots so lets use the thing we just concluded here:
Therefore this is the factored form!
Alright now i want you to do this one! Send me the factored form 👀
pearl pondBOT
@spiral nexus Has your question been resolved?
red sphinx
pearl pondBOT
red sphinx
Did anyone know what could have gone wrong with my working out here?
q is meant to = 2
clever hull
pearl pondBOT
@red sphinx Has your question been resolved?
pearl pondBOT
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latent glen
Given a boys and b girls. Find the number of ways that can they can be arranged in a line without having 2 girls next to each other.
jaunty lintel
@latent glen you mean a distinct boys and b distinct girls right
so firstly there are a! ways to arrange the boys in a line
worldly jewel
people are assumed to be distinct
jaunty lintel
that leaves us with a+1 gaps for the girls
frank violet
people are assumed to be distinct
-# clones
jaunty lintel
so from this we can find out that b <= a+1
latent glen
so from this we can find out that b <= a+1
so what now?
jaunty lintel
so what now?
since there are b! ways to arrange girls so you have a final formulae
a!(a+1)! / (a+1-b)! If b <= a+1
otherwise if b > a+1 then the ans is 0
i see ur on codeblocks maybe this is a programming question
maybe c++
latent glen
a, b is <= 10^8 tho 
jaunty lintel
a, b is <= 10^8 tho <:blobcry:971797574916907028>
do u know big num related algorithms
latent glen
yea but my factorial for big num only goes up to 1e5 without TLE
jaunty lintel
yea but my factorial for big num only goes up to 1e5 without TLE
are u sure the problem doesnt give you smth like
result = ans mod a prime number
latent glen
it does tell to mod by 1e9+7
jaunty lintel
oh so its okay
latent glen
oh so its okay
how?
jaunty lintel
how?
im seeing u should compute each factorial iteratively
a! Then a+1 then a+1-b
then inverse modulo
latent glen
a! Then a+1 then a+1-b
yeah but even a! has a problem when a <= 1e8
jaunty lintel
yeah but even a! has a problem when a <= 1e8
youre only printing out the answer after the modulo operation right
wait i dont get why youre seeing a problem here
latent glen
ohhh i thought that we'll have to calculate (a+1)! and (a+1-b)! seperately
pearl pondBOT
@latent glen Has your question been resolved?
latent glen
but still i don't know how to get a/b mod m tho
jaunty lintel
but still i don't know how to get a/b mod m tho
ehh
i assumed you know inverse modulo
maybe read some documentation about it
assuming m is the prime then a/b mod m then its essentially a*b^(-1) mod m
i remember then this had something to do with fermats little theorem
but you juust need to rem
a/b 三 a*b^(m-2) mod m
so thats essentially it
latent glen
but running b^(m-2) is time-consuming tho, isn't it?
jaunty lintel
but running b^(m-2) is time-consuming tho, isn't it?
true but if u use binary exp it only takes O(log(m))
log 1e9 + 7 is extremely small
the thing is python they have this built in
c++ you just have to write it out by hand
so its just memorization and apply atp
latent glen
#include <bits/stdc++.h>
using namespace std;
int mod = 1e9+7;
long long binpow(long long a, long long b){
long long kq = 1;
while (b > 0) {
if (b & 1)
kq = (kq % mod * a % mod) % mod;
a = (a % mod * a % mod) % mod;
b >>= 1;
}
return kq % mod;
}
int main(){
ios::sync_with_stdio(false); cin.tie(nullptr);
//freopen("TH05.INP", "r", stdin);
//freopen("TH05.OUT", "w", stdout);
long long a, b;
cin>>a>>b;
int af = 1;
for(int i = 2; i <= a; i++) af = (af * i%mod)%mod;
int af1 = (af * (a + 1) % mod) % mod;
cout << ((af % mod) % (af1 % mod) % mod *(binpow(a+1-b, mod-2) % mod)) % mod;
return 0;
}
where's this wrong? (ignore the freopen, the question says so)
jaunty lintel
alr
ok so
The output looks pretty weird
and looks like you forgot to compute (a+1)!
latent glen
i saw it
jaunty lintel
im having a hard time looking at the code on my phone
ok so
Suggestion
The output is basically
latent glen
#include <bits/stdc++.h>
using namespace std;
int mod = 1e9+7;
long long binpow(long long a, long long b){
long long kq = 1;
while (b > 0) {
if (b & 1)
kq = (kq % mod * a % mod) % mod;
a = (a % mod * a % mod) % mod;
b >>= 1;
}
return kq % mod;
}
int main(){
ios::sync_with_stdio(false); cin.tie(nullptr);
//freopen("TH05.INP", "r", stdin);
//freopen("TH05.OUT", "w", stdout);
long long a, b;
cin>>a>>b;
int af = 1;
for(int i = 2; i <= a; i++) af = (af * i%mod)%mod;
int af1 = (af * (a + 1) % mod) % mod;
cout << (((af % mod)* (af1 % mod)) % mod *(binpow(a+1-b, mod-2) % mod)) % mod;
return 0;
}
fixed the output having the wrong symbol
jaunty lintel
ok so your output is still wrong
ok basically
Youre trying to output this
a! × (a+1) × a ... × (a+2-b)
or like i said above
a!(a+1)! / (a+1-b)!
but your output basically missed the (a+1)! part
latent glen
af1 is (a+1)!
jaunty lintel
maybe you should put af1 as long long
oh
the a+1-b part
you forgot the factorial
you inversed the a+1-b instead of (a+1-b)!
and if you dont want to risk overflow just put long long on af and af1
latent glen
so we need b! also?
jaunty lintel
so we need b! also?
no
i cant actually fix your code and send it here
because im on my phone
but you see the problem
latent glen
isn't (a+1-b)! = af1/b! tho?
latent glen
wait no my brain was lagging
latent glen
bro nói tiếng việt à
jaunty lintel
ừ
latent glen
mà sao bt ng việt hay v
jaunty lintel
kq
th05
t học chuyên tin nên thấy quen th
nói chung
bài này ko phức tạp đâu
Xóa từ int main viết lại đi
lấy nháp ra suy nghĩ lain
lại
latent glen
v là vẫn dùng binpow đko?
latent glen
mà cho hỏi là lớp mấy v
jaunty lintel
lớp 11
latent glen
v gọi bằng e cx đc mà th gọi bro đi cho chung
latent glen
là (a+1-b)! là af1 nhg lùi lại b bước đko
latent glen
có test mẫu:
a = 6, b = 2
output: 30240
jaunty lintel
vậy cũng đc r đó
chắc tự sinh test đc
có ct toán r
cho số a và b thỏa BĐT b <= a+1 th
latent glen
mà chx bt tính (a+1-b)! sao cho khỏi TLE
jaunty lintel
a!(a+1)! / (a+1-b)!
cái ct này chia ra 2 phần
a!
với khúc còn lại sẽ = (a+1)×a×...(a+2-b)
tính dòng lặp for 2 phần đó
latent glen
xét if trg for lúc đầu đko
jaunty lintel
ừ
latent glen
khi nào i = a+1-b thì lấy a hiện tại
jaunty lintel
if để loại edge case
kiểu
khúc đầu sài if loại trường hợp b > a+1 th
khúc sau đâu cần sài
latent glen
kiểu do mình bt a+1-b >= a r thì mình lấy a+1-b luôn cho nhanh mà
jaunty lintel
kiểu do mình bt a+1-b >= a r thì mình lấy a+1-b luôn cho nhanh mà
:)))
ko chắc
mà chắc sai
Lũy thừa nó khác
Mà cái a+1-b >= a thì nó cho b = 0 với b = 1 thôi chứ
thôi xin lỗi bro nha
phải gtg
có j cứ bình tĩnh làm 1 chút là cũng xong th
pearl pondBOT
@latent glen Has your question been resolved?
frank violet
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pearl pondBOT
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mild spoke
I am doing a simple analysis of a time series but I have a few different steps and I want to know if there is a comprehensive name for this technique:
- Perform quadratic regression
- "Correct" the data by applying the inverse of the quadratic function produced in step 1
- Perform Fourier synthesis on what is hopefully now a simple cyclical series
- Combine the quadratic function from step 1 & synthetic function from step 3
Are the assumptions I'm making about the data and process here sound? Is there any light literature I can read to see if someone has done this before?
pearl pondBOT
I am doing a simple analysis of a time series but I have a few different steps a...
@mild spoke Has your question been resolved?
mild spoke
have I done something wrong
modern talon
I am doing a simple analysis of a time series but I have a few different steps a...
what i can potentially think of is trend cycle decomposition
but unsure
mild spoke
what i can potentially think of is trend cycle decomposition
that sort of sounds right, there is the basic assumption here of both a trend and cycle
modern talon
that sort of sounds right, there is the basic assumption here of both a trend an...
im unsure if theres a specific name in literature for this though
mild spoke
im unsure if theres a specific name in literature for this though
can you at least say if my processing steps make sense?
modern talon
can you at least say if my processing steps make sense?
what do you mean by the inverse of the quadratic func?
mild spoke
what do you mean by the inverse of the quadratic func?
as in i take the half of the parabola to the right of the vertex and create an inverse function from that
modern talon
are you detrending?
dont think i've seen detrending of data through an inverse function, i always thought it was just through residuals to preserve linearity
mild spoke
are you detrending?
I think so if I understand what that means
modern talon
I think so if I understand what that means
to see cyclicity right?
mild spoke
dont think i've seen detrending of data through an inverse function, i always th...
I want to remove linearity so the fourier analysis is more accurate
modern talon
im assuming since from step 3
modern talon
I want to remove linearity so the fourier analysis is more accurate
linearity in the superposition of the components? or
mild spoke
linearity in the superposition of the components? or
I'm not sure how to explain but I want the sample data to more closely resemble a simple oscillation (superposition of sinusoids) so I take the parabolic curve out of it first
modern talon
I'm not sure how to explain but I want the sample data to more closely resemble ...
couldnt you just do this with simple residuals? i dont see inversion being incredibly necessary here, and if you believe your data to be sinusoidal in nature, then wouldnt subtracting the quadratic component leave you with the sinusoidal comps
mild spoke
couldnt you just do this with simple residuals? i dont see inversion being incre...
maybe I should have you explain what you mean by residuals
modern talon
maybe I should have you explain what you mean by residuals
just your typical r = obs - expec
mild spoke
couldnt you just do this with simple residuals? i dont see inversion being incre...
there's another question I have here which is that I'm not sure whether it's necessary to subtract (linear transform) a quadratic from the series or to apply the inverse of the quadratic to it and then perform the fourier analysis
My goal is to make this curve more horizontal for lack of a better word
make it more sidways and only then determine the frequency components
modern talon
there's another question I have here which is that I'm not sure whether it's nec...
what im more worried about is the fact that taking the quadratic inverse (by limiting time >= 0, im assuming) removes the linearity
modern talon
also, i think its known that XLE is cyclical
if you're talking about the energy sector
mild spoke
also, i think its known that XLE is cyclical
this is XLE/XLP and there are other ratios between various index funds I want to analyze
modern talon
oh interesting
mild spoke
some of these tickers are on their own don't show much of a pattern
if you're curious, look into XLK/XLP
also these are really short periods, like 5-10 days
modern talon
yeah, i dont think ive done a personal look into relationships myself but i do know about ratios between the sectors
interesting
mild spoke
so instead should I treat these as the sum of a quadratic and a superposition of components?
modern talon
so instead should I treat these as the sum of a quadratic and a superposition of...
that is my take, yes
mild spoke
that was my original model but the gradient descent for that seems daunting
mild spoke
that is my take, yes
ok I'll just do this then, thanks!
looks like I'll be spending the rest of the day writing out partial derivatives for the GD algorithm
you can mark this thread as closed, you were a big help
modern talon
looks like I'll be spending the rest of the day writing out partial derivatives ...
it definitely will be an annoying issue, but at least there's linearity
so differentiation shouldnt be too big of an issue, just tedious
mild spoke
yeah tedious is acceptable
modern talon
you can mark this thread as closed, you were a big help
if you ever want to discuss some stock math in the future, feel free to @ me again or dms
mild spoke
if you ever want to discuss some stock math in the future, feel free to @ me aga...
okay for sure!
modern talon
im personally a day trader and dont really look at long term stuff all that much, but i know my way around the math
good luck!
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wise cipher
wait is this trade market
pearl pondBOT
wait is this trade market
wise cipher
.close
pearl pondBOT
pearl pondBOT
Available help channel!
daring bay
how do i change it to U = ...?
pearl pondBOT
how do i change it to U = ...?
daring charm
how do i change it to U = ...?
square both sides
then rearrange to isolate u
then solve for u
verbal whale
like square the lamda first?
And consequently the other side as well, of course, right? 😉
daring bay
And consequently the other side as well, of course, right? 😉
what
okay
wait
why both sides we havent done it like this
atleast i havent learned that
verbal whale
Impossible
daring bay
oh wait so
you just do to both sides righ
but when u multpily something u dont do that on both sides
verbal whale
You indeed do
verbal whale
Where did you read/hear you don't?
daring bay
we just dont do that tho right
wait
let me find an example
actually yes ur right but
so lets say we have
3x/5x = 10
you do times 5x but you dont do that on both sides?
jolly parrotBOT
riemann
verbal whale
you do times 5x but you dont do that on both sides?
Do you have some written notes about this? If so, please send them
daring bay
**riemann**
yeah
daring bay
Do you have some written notes about this? If so, please send them
no but it was so loong ago
verbal whale
Forget everything about that, then
You misremembered a lot of very very wrong things
daring bay
we just learned it in middle school
once
and for all
ever since then i havent really concerned myself with it
verbal whale
First of all, $\frac{3x}{5x} = \frac{3}{5}$.
So that can't be equal to 10
jolly parrotBOT
Alberto Z.
plush bramble
then ud have 3x = 10 * 5x
don't make up problems. do real ones
verbal whale
Especially considering you're a newbie
daring bay
First of all, $\frac{3x}{5x} = \frac{3}{5}$.
So that can't be equal to 10
okay but like lets say it is
then mathematically
verbal whale
okay but like lets say it is
No!?
daring bay
okay nvm
verbal whale
don't make up problems. do real ones
@daring bay please really consider this
daring bay
<@419857529032409088> please really consider this
yeah
plush bramble
plush bramble
daring bay
i just forgot some things
plush bramble
then only watch videos on those "some things"
verbal whale
i just forgot some things
Well then you have to revise them
plush bramble
nobody knows what you remember or don't remember
daring bay
Well then you have to revise them
Yes, you dont actually see the multiplication happening because it eliminates each other
i get it now
pearl pondBOT
@daring bay Has your question been resolved?
mild spoke
wait is this trade market
what
modern talon
cinder flower
i think i did ts once. let me check
rustic gate
the quotient is cyclic
modern talon
the quotient is cyclic
if P is a sylow 3 subgroup, G/P is cyclic, and aut(P) = 2 so that G/C_G(P) is trivial, P \leq Z(G)
|G/Z(G)| \leq |G/P| = 35, and any group of order that divides 35 is cyclic?
rustic gate
you can just directly argue with P
if you have a central subgroup whose quotient is cyclic the group is abelian
modern talon
if you have a central subgroup whose quotient is cyclic the group is abelian
so if H is a subgroup of Z(G), then G/H cyclic implies G is abelian as well?
rustic gate
yeah it's the same argument
modern talon
oh interesting
rustic gate
the only thing you need in the proof is being able to commute the part in H with the representatives
pearl pondBOT
cinder flower
i think i did ts once. let me check
omg i got distracted right after and totally forgot i sent this message
lol
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haughty storm
Hello! I am curious as to how I could develop a quadratic or exponential regression scenario project. https://www.kaggle.com/code/itzpekay/student-analysis this is the link to my linear regression project and model
haughty storm
I also want to make sure my interpretation of the data is correct
there is no linear relationship between attendance and final grade in this data right? since it shows that attendance lowers a grade, which isn't possible
pearl pondBOT
@haughty storm Has your question been resolved?
outer crystal
help
outer crystal
anyone?
outer crystal
i couldnt find
daring charm
daring charm
you hate me
daring charm
you weren't annoying me
pearl pondBOT
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fading ledge
If a line equation in parametric form is
(x-2)/1=(y-0)/0=z/1
Then it will pass through (2,0,0,) and direction ratio are (1,0,1)
fading ledge
how can we write y/0 is this not infinity?
I didn't understand the direction ratio or I can't see the line in desmos 3d
solar ember
It jsut means you ar ein the xz-plane
If you have (y-0)/0 it just means that y - 0= 0, so y=0
pearl pondBOT
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fading ledge
The line is passing through origin?
unborn abyss
is it? try plugging in (0, 0, 0) to that eqn and see if it's true
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latent glen
Given a = 3n^2 + 3n + 1 with positive n.
a) Prove that 2a and a^2 are each sums of three squares.
b) Prove that if a is a factor of b and b is also a sum of 3 squares then b^x would also be the sum of three squares with every positive whole x.
pearl pondBOT
Given a = 3n^2 + 3n + 1 with positive n.
a) Prove that 2a and a^2 are each sums ...
@latent glen Has your question been resolved?
latent glen
<@&286206848099549185>
hazy bear
Idk if there's a proper way but I tried expressing 2a as sum of three squares and I got it by hit and trial.
latent glen
for 2a i got (2n+1)^2 + (n+1)^2 + n^2
hazy bear
yea same, did you get anything for a²
latent glen
sadly no
ionic merlin
Given a = 3n^2 + 3n + 1 with positive n.
a) Prove that 2a and a^2 are each sums ...
Well
Try 2a
Convert the eqt
latent glen
for 2a i got (2n+1)^2 + (n+1)^2 + n^2
.
ionic merlin
Into 3 perfect squares
ionic merlin
.
Good
Now for a²
a² =
9n⁴+9n²+1+18n³+6n+6n²
Clear till now
How I got this
@latent glen
untold lichen
<@&286206848099549185>
?
ionic merlin
yeah still understood
Okk
Now
I don't think we can write it as different squares
Sum
But .. u can write it as
3 (3n²+3n+1)²/(√3)²
Js write it as sum of same terms
Or u can write it as:
(3n²+3n+1/3)² +(6n²+6n+2/3)²+(6n²+6n+2/3)²
Gives the same thingy
latent glen
,w simplify (3n^2+3n+1)^2 - ((3n^2+3n+1)^2 + (6n^2+6n+2)^2 + (6n^2+6n+2)^2)/3
latent glen
(3n²+3n+1/3)² +(6n²+6n+2/3)²+(6n²+6n+2/3)²
uhh...it doesn't?
,w expand (3n^2+3n+1)^2
jolly parrotBOT
hazy bear
(3n²+3n+1/3)² +(6n²+6n+2/3)²+(6n²+6n+2/3)²
fractions? is n any positive number and not natural number?
or you need not express it as sum of perfect squares?
latent glen
(3n²+3n+1/3)² +(6n²+6n+2/3)²+(6n²+6n+2/3)²
i mean this
ionic merlin
i mean this
yea
Idk how to use bot
It's not 1/3
Or 2/3
It is a complete term divided by 3
jolly parrotBOT
latent glen
<@&286206848099549185>
latent glen
the original one?
latent glen
<@&286206848099549185> still can't solve this problem
midnight haven
<@&286206848099549185> still can't solve this problem
bro this problem is little complex give me some mins
nova flare
<@&286206848099549185> still can't solve this problem
Which?
latent glen
i need to prove that a^2 is a sum of three squares
before question b
,w (3n^2+3n+1)^2 - (3n^2+3n-1)^2 - (2n)^2 - (2n+2)^2
jolly parrotBOT
latent glen
maybe we don't need to find, just prove
untold lichen
(3n^2+3n+1)^2 - (3n^2+3n-1)^2 - (2n)^2 - (2n+2)^2 = a^2
are you asking proof of this??
latent glen
i mean the question jst says to prove, not to find
shell nexus
Ill try something
One thing i noticed Is that if you add n³ both sides, right side becomes a bynomial cube
Idk if that's helpful tho
pearl pondBOT
shell nexus
I SOLVED
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shell nexus
Nvm
shell nexus
.close
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loud vortex
can someone check these over, also i had someone point out the notation where it shouldnt be velocity. is that correct?
ashen ivy
,w d/dt -t^2 + 8t + 1 at t=2
jolly parrotBOT
ashen ivy
both look good calculation wise \
technically, velocity is a vector, so writing (a vector) = (a number) isn't right, and you should write "$\mathrm{speed} = \dots$" or even "$\norm{\vec{v}} = \dots$" when doing your calculations.
whether it matters... i dont think physicists particularly care about this, especially at this stage, but it depends on your teacher
jolly parrotBOT
حسیب ♥
ashen ivy
yeah as long as you know that you're calculating the magnitude
and because you're putting a direction in your final answer, that tells me you know it's a vector you're dealing with, and you've given me all the necessary info i need
but again - your teacher is marking your work, not me
loud vortex
but again - your teacher is marking your work, not me
thats true
thank you so much \
here are the last 3 questions if youre willing to check them over aswell
im pretty sure the asnwers are correct
but idk about the notation
ashen ivy
would be happy to :)
loud vortex
signal finch
aura
ashen ivy
Q1 is correct, i personally am a little iffy on m_(sec) as notation
my reasoning is that slope of a line is the m_(tan) thing you used in the next question, and m_(sec) is technically an approximation
and also, you're implying the slope of something by m_(sec), but it's not clear what that something is
may i suggest $\Delta_{\mathrm{avg}}$, $\mathrm{ROC}_{\mathrm{avg}}$, or even $\mathrm{AROC}$?
jolly parrotBOT
حسیب ♥
ashen ivy
the most appropriate would be defining your own symbol (because you forgot what you're supposed to use) 
but i think $\Delta_{avg}$ because $\Delta$ is a discrete derivative operator which is sort of related
jolly parrotBOT
حسیب ♥
ashen ivy
(dont worry about what 'discrete derivative operator' is)
plush bramble
loud vortex
(dont worry about what 'discrete derivative operator' is)
what about 3 and 4
ashen ivy
Q3 looks good and i'm a fan of the notation there, since you're finding an actual tangent line
Q4 also looks good and again no problems with the notation!
i mean ultimately it doesnt matter, you can just insert a sentence saying "let m be the slope of the tangent line to f at x", then go crazy
loud vortex
i mean ultimately it doesnt matter, you can just insert a sentence saying "let m...
tyty
you are so helpful
im beyond greatful!
ashen ivy
np! you did all the work anyways
pearl pondBOT
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radiant frost
Hello all! I’m answering a prompt in 150 words about this box plot for my stats class. The prompt is "What does this display tell you about the data? Describe the shape of the distribution and what it tells you about the data. Describe the scale of measurement for each variable and how this impacts the display."
I know it’s right-skewed, and the median is 38, the variable is continuous/ratio level, but I’m unsure about the IQR. My answer is 13, but truthfully I am not confident in that answer/I don’t know if i answered that correctly. Thank you for any help!
unkempt yacht
the length of the box is the IQR, and the length of the whisker is the range excluding outliers
radiant frost
the length of the box is the IQR, and the length of the whisker is the range exc...
Ahhh, so, if I have this right, the IQR would be 14 then?
unkempt yacht
yes
radiant frost
Gotcha, thank you!!
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nocturne grail
<@&268886789983436800>
pearl mauve
my reasoning is that slope of a line is the m_(tan) thing you used in the next q...
m_(sec) is prob gradient of the secant line
pearl pondBOT
m_(sec) is prob gradient of the secant line
pearl pondBOT
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sharp smelt
\
sharp smelt
Really sillly, but N_1+N_2= N(334, 25^2) no?
Just confused, because 334 is huge
that's like 10 feet ☠️
tardy reef
is it weird that heights of two people sum to 334cm?
its not the height of a single person
tardy reef
and my calculatins are right I suppose
yea, looks correct
pearl pondBOT
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flint mica
Bro how r all ppl here so smart
pearl pondBOT
Bro how r all ppl here so smart
proper nova
Bro how r all ppl here so smart
!redir
pearl pondBOT
Bro how r all ppl here so smart
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
warped violet
Bro how r all ppl here so smart
Luck, work.
And also, pretty much everyone is good / smart at something. Unfortunately, many don't find what it is
pearl pondBOT
@flint mica Has your question been resolved?
eager jewel
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fathom saffron
am i stupid or shouldnt A = kB imply |A| = k^3 |B|
pearl pondBOT
am i stupid or shouldnt A = kB imply |A| = k^3 |B|
fathom saffron
we get the given answer only when we take |A| = k |B|
pearl pondBOT
@fathom saffron Has your question been resolved?
pearl pondBOT
@fathom saffron Has your question been resolved?
daring charm
we get the given answer only when we take |A| = k |B|
hey
your confusion is about the matrix size
you momentarily treated
$$|2A| = 2|A|$$
jolly parrotBOT
Ezra
jolly parrotBOT
Ezra
daring charm
if $$A = kB$$ and the matrix is $$n \times n$$, then
$$|A| = |kB| = k^n |B|$$
NOT just $$k|B|$$
jolly parrotBOT
Ezra
fathom saffron
yea thats what im confused about. We get the correct answer only iff |kB| = k|B|
im guesing thats an errata just wanted to make sure
pearl pondBOT
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sharp smelt
Show \
$f(x) = \begin{cases} \sin \left( \frac{1}{x} \right) & x \in (0,1] \ 0 & x=0 \end{cases}$ is not a function of bounded variation on $[0,1]$.
Consider the partition ${0,\frac{2}{π}, \dots, \frac{2}{(2n+1)π},1}$. Let's consider the variation over the set ${\frac{2}{π}, \dots, \frac{2}{(2n+1)π} }$. Note that $\abs{ f\left( \frac{2}{(2n+1)π} \right) - f\left( \frac{2}{(2n+3)π} \right)}=2$ We thus have $2n≤V_{f}[0,1]$, and as we take a greater number of refinements, this goes to $\infty$. Thus $f$ is of unbounded variation
jolly parrotBOT
wai
plush bramble
is this your definition of BV?
sharp smelt
essentially, yeah
plush bramble
it's just slightly confusing you're using n as both the index when calculating |f(thing1) - f(thing2)| = 2 and the number of points in the partition
i'd probably also explicitly calculate f(thing1) - f(thing2) for all indices
sharp smelt
i'd probably also explicitly calculate f(thing1) - f(thing2) for all indices
fair, but the key idea is fine?
plush bramble
yea should be
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eager wedge
Heyhey, need some help with this problem, to show that the answer cant be less than 75. Any tips would help a lot 😄
So far I can prove if we only move the contents from one A bins to B bins, we can get the 75 case, and not 74. But cant strongly show that if we can move items from both A and B bins, they'll still be >=75
pearl pondBOT
Heyhey, need some help with this problem, to show that the answer cant be less t...
@eager wedge Has your question been resolved?
pearl pondBOT
@eager wedge Has your question been resolved?
eager wedge
@vast sluice
glass meadow
Might just be me but this makes no sense without context. What's a bin? What does it mean to pack items? Can items have negative size? Zero size? What is OPT? Do A and B share any item? Can they be the same set? Where do they come from?
toxic lichen
i believe it might be implied that the size of each item is a positive number strictly between 0 and 1?
but op would need to confirm
eager wedge
You can imagine a bin as a car in which we put some items who have weights 0<weight<=1. Max size of the bin is 1
Opt is the minimal number of bins that we need, for our items to be fully packed. A and be do not share any item and cant be the same. The sets A and B are random, the main problem is to show, that en every case, opt(A U B) >=75
eager wedge
i believe it _might_ be implied that the size of each item is a positive number ...
more than 0, less or equal 1
toxic lichen
well your question says all items have size <1
eager wedge
oops, in reality it does not matter
toxic lichen
well presumably you could try to start with a packing of A \cup B into 74 bins (which need not be optimal) and attempt to cook up a contradiction to OPT(A) or OPT(B) being exactly 50
though how this could be achieved i don't see yet
eager wedge
You always get to the contradiction, but I cant clearly show why that happens
toxic lichen
actually hold on
why don't we categorize the bins into 3 categories
- "A-only" bins (ones that contain only A items)
- "B-only" bins (likewise)
- "mixed" bins (ones that contain both A and B items)
isn't there some pigeonhole-ish thing you can come up with here?
eager wedge
A-only + mixed >= 50
B-only + mixed >=50
A-only + B-only + mixed >= 100
its too far from 75
eager wedge
we need it to be >=75
glass meadow
So far I can prove if we only move the contents from one A bins to B bins, we can get the 75 case
Can you show?
eager wedge
> So far I can prove if we only move the contents from one A bins to B bins, we ...
yep
toxic lichen
i mean the thing is, adding these ineqs gives is (A-only) + (B-only) + 2 * (mixed) ≥ 100
eager wedge
one second
toxic lichen
and obviously (A-only) + (B-only) + (mixed) = 74 by assumption
since we assumed that a packing of A \cup B into 74 bins exists
so this lets you say something about the number of mixed bins
eager wedge
> So far I can prove if we only move the contents from one A bins to B bins, we ...
for the 75 case
A is 50 times 0.49 and 25 times 0.52
B is 50 times 0.51
A U B gives you
50 bins with weight 1
25 bins with weight 0.52
so its 75
eager wedge
so this lets you say something about the number of mixed bins
hmm
eager wedge
and obviously (A-only) + (B-only) + (mixed) = 74 by assumption
so far I was doing the categorization as this
Bin is white if its >0.5 mass contains items from A, and B otherwise
that was giving me that
|A|+|B|/2 >= 50
and
|A|/2 + |B| >=50
eager wedge
and, its clear that we cant move contents from 26 A bins to 50 B bins, as, in every B bin, masses of A items is <0.5, so, if we divide 50 by 2, we will get that our items can be put in 25 A bins, so we come to contradiction
But, lets lets say if we have 40 A bins and 35 B bins, what is the contradiction here? When this gets an answer, the problem will be solved
pearl pondBOT
@eager wedge Has your question been resolved?
brave sluice
i need to interpret this integrand as the limit of a sequence of functions right? but isn't it kind of ambiguous what the terms in the sequence are?
plush bramble
why do you think it's ambiguous
jolly parrotBOT
Modus
brave sluice
$\frac{e^x}{e^x}, \frac{e^x}{e^x+\frac{e^x}{e^x}}, \ldots$\
$e^x, \frac{e^x}{e^x+e^x}, \frac{e^x}{e^x+\frac{e^x}{e^x+e^x}}, \ldots$
jolly parrotBOT
Axe
buoyant panther
Then you can see that y = e^x/(e^x + y)
brave sluice
aren't these both reasonable?
brave sluice
Then you can see that y = e^x/(e^x + y)
oh yeah i probably just need to use this approach
shouldn't it be y = e^x / (e^x + y) ?
brave sluice
but, this is quadratic and has two solutions, so i think you still need to refer to the idea of a sequence of functions to choose a solution
plush bramble
yes show your two solutions
brave sluice
plush bramble
try to reason why only one of those makes sense.
brave sluice
i guess it should take positive values for positive x
plush bramble
y is positive yes
brave sluice
oh yeah for negative x too
plush bramble
yes
brave sluice
so it should be + rather than -
buoyant panther
2nd seems incorrect to me because you substituted the denominator by e^x + e^x, while it should be e^x + e^x/...
split berry
pearl pondBOT
split berry
im doing this practice problem
my logic was let x = 8
3y^2 >= 27 >= 19 >= 3y+10, therefore 3y^2 >= 3y+10 for all y >= 3. I notice that this only holds true for the example of y being at itsa minimum value of 3 so the proof probably would't hold since its for all y not just the minimum value. how could i fix this inequality chian to account for that
limber pivot
how did you conclude that 19>=3y+10?
buoyant panther
notice that x >= (3y + 10)/y^2 = 3/y + 10/y^2
What can we say about 3/y and 10/y^2 when y >= 3 (or even y > 0)
split berry
how did you conclude that 19>=3y+10?
"I notice that this only holds true for the example of y being at its a minimum value of 3 so the proof probably would't hold since its for all y not just the minimum value. "
buoyant panther
nvm not at 3 though
Mhm, you're close, but talking about the behaviour, these fractions increase or decrease when y increases?
split berry
decrease as y increases
buoyant panther
Yes, so if y >= 3, then when the max value of them occurs?
If they decrease as y increases
split berry
y>=3 is the max
buoyant panther
For what value of y is that max?
split berry
3
pearl pondBOT
@split berry Has your question been resolved?
vast folio
Can anyone make it easy to understand?
pearl pondBOT
Can anyone make it easy to understand?
still hamlet
Can anyone make it easy to understand?
if a list of vectors is linearly independent, and a linear combination of those vectors equals zero, then what should the coefficients be?
toxic lichen
Can anyone make it easy to understand?
do you know/understand the concept of linear combination
cinder flower
ts proof is so ick
pearl pondBOT
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vast folio
limit --> x^3/(x^2+y^4) where x,y=\0
glacial bluff
,rccw
jolly parrotBOT
patent acorn
Hello!
patent acorn
They want me to find the m for which the system is simply undeterminate
And I found that m = 1 is a double solution since the determinant with m is (m-1)^2 * (m+2)
I guess if m was 1 then the rank of A was 1 and that wouldn't be simply undeterminate?
As in double undeterminate
candid mauve
.
patent acorn
?
pearl pondBOT
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exotic mango
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umbral briar
pearl pondBOT
oak notch
do you mind taking a better photo of the page
umbral briar
Sorry that’s the only photo I have but I can crop it?
Or I can write it out for you
oak notch
yeah that would help
umbral briar
A bag contains red green and white counters only the table shows the proportion of each colour of counter that else believes to be in the bag
Red = p
Green = 0.2
White = 4p
Elsa selects at random 40 counters from the bag, one at a time, with replacement
Assuming Elsa’s belief is true
A) find the distribution of the number of red counters else selects
Jayda believes that the true proportion of green counters is greater than 0.2
She takes a random sample of 40 counters from the bag, one at a time, with replacement
There are 11 green counters in her sample
b) i) use a suitable test to assess Jaydas belief
You should
- state your hypothesis clearly
- use a 5% level of significance
- state the p value for the test
ii) find the acceptance region for the test in part (i)
@oak notch
rough stream
Part a) is a you-know-it-or-you-don't kind of question. It's a hypergeometric distribution. Take a bit of time to read up if you're new to that one
pastel umbra
A) find the distribution of the number of red counters else selects
Your working out for a is almost there, but you're being asked for the distribut-
umbral briar
I think I worked a out
pastel umbra
Part a) is a you-know-it-or-you-don't kind of question. It's a hypergeometric di...
It's not, not for this context
umbral briar
I think it is X - B(40, 0.16)
rough stream
with replacement I see it now. Ignore me!
umbral briar
But i dont have any clue for b apart from the hypothesis
pastel umbra
It's not, not for this context
It's A Level maths, year 1, statistics (so hypergeo. dist. isn't on the syllabus)
pastel umbra
Assume H0
rough stream
I know the null hypothesis is H0: p=0.2 and H1 > 0.2
Your H0 should be directly opposite your H1. We're missing cases where p < 0.2
umbral briar
Oh
pastel umbra
It's A Level maths, year 1, statistics (so hypergeo. dist. isn't on the syllabus...
@umbral briar This is correct, right?
rough stream
This matters as we're assuming H0
umbral briar
<@734118801330667561> This is correct, right?
Yes!
pastel umbra
Then @rough stream no, the syllabus states to take H0 as a fixed probability
So p = 0.2 in the H0 test
rough stream
I don't see how you're following "the hypergeometric doesn't exist in this course" with "we only do very specific tests" but I'll give you the reigns
pastel umbra
I don't see how you're following "the hypergeometric doesn't exist in this cours...
I literally teach this syllabus
It's hypothesis testing, which comes straight after teaching the binomial distribution
pastel umbra
How do i assume H0
Assuming just means when we do some calculations for e.g. distribution results, we use that p-value
pastel umbra
Is it bpd?
bcd; lemme see if I can pull something up on this
Because a lot of the calculations are very similar
umbral briar
ok thank you so much
We were given lots of questions to do by our maths teacher but then she got hospitalised and my test is tomorrow and I am so so confused
pastel umbra
well that's a shock to the system
umbral briar
Yeah I know
She gave us 5 questions to do as similar ones will come up in our test. I have spent 3 hours and only managed to do 1 and a half
Im so utterly screwed
random ermine
the p ur using in part b btw is different from the p in part a
umbral briar
Ohhh ty
pastel umbra
I know the null hypothesis is H0: p=0.2 and H1 > 0.2
@random ermine She did say that, yes
umbral briar
Wait what