Ok I see this but when we try to actually so that it hits a value again we can't
#help-49
sand flume
crystal rivet
Wouldn’t g(2) be zero? Or is that not an assumption i should be making
sand flume
how would we get that? I can't see how we can do it from part a
crystal rivet
I might be over generalizing, but I’m just assuming that f is a sinusoidal function of some sort, so the integral over the period would be 0
sand flume
if we don't make that assumption how can we proceed?
solid iris
what was your answer to (b)?
sand flume
what was your answer to (b)?
g(2) = 2A and g(5) = 5A
and in general given g(2n) = we have 2nA
sand flume
I don't see it from a I just see it from g(0) = 0 and we need g(x+2) = g(x). if x = 0 then g(2) must also equal 0
solid iris
g having period 2 is equivalent to g(x+2)=g(x) for all x, which is equivalent to g(x+2)-g(x)=0 for all x
sand flume
yes
solid iris
and using (a) this is equivalent to g(2)=0
solid iris
as you said g(2)=2A
sand flume
oh
everything makes sense now. Could we not say that you can make g have any period?
oh wait nvm
f always has to have the same period as g
ok thx
.solved
midnight plankBOT
solid iris
np
solid iris
f always has to have the same period as g
the right wording is g has the same period as f if and only if A=0
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Available help channel!
woeful turret
midnight plankBOT
woeful turret
a+b+c not a+b+x
i did integration by parts
(1)(1-x^10)^20 = x(1-x^10)^20 +integral 200 x^10 (1-x^10)^19
and x(1-x^10)^20 with limits = 0
so my a = 200
b=11
c=20
but this gives a huge answer which is wrong
midnight plankBOT
@woeful turret Has your question been resolved?
woeful turret
<@&286206848099549185>
tawdry kraken
IBP seems like a good approach
woeful turret
i did integration by parts
^
tawdry kraken
I know I'm saying I agree with your idea
tawdry kraken
But I'm not sure about your process here
woeful turret
o what is wrong
tawdry kraken
So you have this: $$\int_0^1(1)(1-x^{10})^{20}dx = x(1-x^{10})^{20} + \int_0^1 200 x^{10} (1-x^{10})^{19}dx$$
grand pondBOT
Coolempire93
tawdry kraken
Verify that that's what you meant before I critique it
woeful turret
yeah thats what i meant
tawdry kraken
Ah this is after simplification, okay I agree so far
Unfortunately this integral is not the form of $\beta$
grand pondBOT
Coolempire93
woeful turret
oh
grand pondBOT
Coolempire93
woeful turret
the inside is 1-x not 1-x^10
shit broooooooo
i can get it now
thank u idk what i was thinking
.close
midnight plankBOT
midnight plankBOT
Available help channel!
maiden bridge
I’ve been trying to learn for 10 minutes now, how is this possible?
midnight plankBOT
I’ve been trying to learn for 10 minutes now, how is this possible?
grand canopy
I’ve been trying to learn for 10 minutes now, how is this possible?
how would you factorise ac - bc
maiden bridge
c(a-bc)?
grand canopy
c(a-bc)?
you have the right idea by taking out a common factor, but just re check that
when you factorised the c out, notice how the a no longer has a c term? this is correct, so it should be the same with the b term
grand canopy
what is your revised factorisation?
grand canopy
What is the proper way to facrorise
your idea is absolutely correct, we do take the c as a common factor out
grand canopy
how would you factorise ac - bc
the factorisation should be ||c(a - b)||, now how can we apply that to your question
grand canopy
I’ve been trying to learn for 10 minutes now, how is this possible?
is there a common factor you can take out?
midnight plankBOT
@maiden bridge Has your question been resolved?
twilit field
midnight plankBOT
twilit field
Couple of questions
firstly , this is the term I'm looking for , right
spamming is against server rules
sharp coral
@astral hare this is a channel to help with wai's question, do not spam here.
twilit field
firstly , this is the term I'm looking for , right
My question here is , cosh(x) isn't bounded, so how do I bound the max term
twilit field
My question here is , cosh(x) isn't bounded, so how do I bound the max term
.
like given an interval I could bound it( as it's increasing on (0,infty) and decreasing on (-infty ,0)
<@&268886789983436800>
formal blade
This is not appropriate for the help channels
It distracts people from getting help
Because it is in the way of the help channel
Ah wait you were already warned for this earlier even
unkempt sluice
This guy is also in channel 25,23,44
formal blade
They are now muted for misusing the help channels
twilit field
They are now muted for misusing the help channels
doot( can I call you that?) their earlier message is spam, pls delete that too
viral dagger
This is not appropriate for the help channels
huh what did they do?
twilit field
huh what did they do?
that clash royale message
viral dagger
that clash royale message
yea what about it?
unkempt sluice
My question here is , cosh(x) isn't bounded, so how do I bound the max term
It’s not the bound on whole R, but the bound on [x_0, x]
[a,b] means [b,a] when a>b in my message
twilit field
so if $x_0 >0$the error term is this where $\zeta=x_0$
grand pondBOT
wai
unkempt sluice
When n is odd, sinh monotonical, so yeah max(|sinh(x_0)|, |sinh(x)|}
twilit field
so if $x_0 >0$the error term is this where $\zeta=x_0$
I ofcourse have to find th 44th derivative , but that's doable
unkempt sluice
Np
twilit field
.close
midnight plankBOT
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Available help channel!
gusty sky
Can anyone please help with this
midnight plankBOT
Can anyone please help with this
livid python
Can anyone please help with this
,rccw
grand pondBOT
olive matrix
what have you tried so far
gusty sky
..
twilit field
midnight plankBOT
twilit field
!status
midnight plankBOT
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
wai
brazen onyx
**wai**
Hii I don’t think that’s right
mu is the true population mean (which is a fixed constant).
X bar is the sample mean which is a random variable
twilit field
X bar is the sample mean which is a random variable
hmm
right
Then Idk what to do
brazen onyx
soo we are told that $X_{n+1} \sim N(\mu,1)$. You should think about rewriting the pieces as squares standard normals!
grand pondBOT
Irene
twilit field
i see
grand pondBOT
wai
subtle zinc
the sum ur given should remind of u that
twilit field
this?
subtle zinc
this?
there should be something in your notes about the distribution of S^2
@twilit field what's up
subtle zinc
alright
twilit field
just this?
twilit field
normal
grand pondBOT
wai
twilit field
or is that the square of this
twilit field
Sorry
subtle zinc
not a problem.
midnight plankBOT
midnight plankBOT
Available help channel!
inland patio
Suppose we have a map $f:\mathbb{R}^n\to\mathbb{R}^m$, the total derivative of $f$ at $x$ is denoted $f'(x)$. In other words, the map $x\mapsto f'(x)$. This is not to be confused with the linear transformation $h\mapsto f'(x)h$. \
Is there something analogous as a differential in $g:\mathbb{R}\to\mathbb{R}$ in this setting, i.e. in $1$-dimension I sometimes see people write $dg=\frac{dg}{dt}dt$ and they call $dg$ the differential of $g$. So is there such a thing also for $f$?
midnight plankBOT
Suppose we have a map $f:\mathbb{R}^n\to\mathbb{R}^m$, the total derivative of $...
grand pondBOT
psie
main current
What comes to mind is the Jacobian. If X is a vector of "small input errors", then JX = Y is a vector of "small output errors"
But maybe that's the linear transformation you're telling me not to be confused with?
inland patio
But maybe that's the linear transformation you're telling me not to be confused ...
I'm not sure either. I think f'(x) is the Jacobian, so what you're saying is perhaps correct, i.e. that what I call the linear transformation is the differential ...?
main current
So to bring that to the 1-D case, we have dg = Jdt
Where the Jacobian J = dg/dt
inland patio
Makes sense. 👍
inland patio
So to bring that to the 1-D case, we have dg = Jdt
Where the Jacobian J = dg/dt
Can I ask about something related, which was the reason why I asked my question in the first place? It has to do with the derivative of a determinant.
main current
Yeah what's up?
inland patio
Yeah what's up?
On Wikipedia (see link below), we have the following identity $$\operatorname{det} '(A)(T)=\det A\operatorname{tr}(A^{-1}T).$$I'm wondering how to go from this equality to $$d\det A = \det A\operatorname{tr}(A^{-1} \cdot d A)?$$
grand pondBOT
psie
inland patio
Here's the link.
Do we simply "plug in" T = dA in the first equation, where dA is a small vector?
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Available help channel!
woeful turret
midnight plankBOT
woeful turret
i tried making denom into a perfect square
(a-cos x)^2 + 1 - cos^2 x
= (a-cos x)^2 + sin^2 x
and then i thought ill multiply and divide by sec^2 x
but that didnt help
soft stone
isn’t this just the fourier series identity
woeful turret
what is that lol
tough basin
Hi guys im a student of class 10 and my boards are from feb 17 and im starting syllabus from tommorow like fresh do u have any idea that how i can complete all my topics and memorize them thouroughly and get 90 percent plus
in maths and other subjects
soft stone
what is that lol
poisson kernel?
soft stone
Hi guys im a student of class 10 and my boards are from feb 17 and im starting s...
please refer another channel
tough basin
sure my bad
soft stone
oh mb 😭
plucky lark
im in high school
calc in hs is p good lol
woeful turret
btw i got the answer by putting a=1/2 but i still wanna know how to do it properly
plucky lark
Hi guys im a student of class 10 and my boards are from feb 17 and im starting s...
just open another channel
soft stone
uhh you can try rewriting the denominator in terms of sin²(x/2) then use the substitution t = tan(x/2)
woeful turret
uhh you can try rewriting the denominator in terms of sin²(x/2) then use the sub...
but if i come across this again ill use this ty
.close
midnight plankBOT
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Available help channel!
twilit field
Usually won't alpha be 0
midnight plankBOT
Usually won't alpha be 0
twilit field
well, whenever it converges
runic hamlet
no
twilit field
hmm., okay, why not
twilit field
I'm confused becauses doesn't p_{n+k} tend to p
lyric charm
try writing out what it would mean for alpha to be 0
twilit field
try writing out what it would mean for alpha to be 0
ln[(p_{n+1}-p)/(p_n-p)] is non zero
zealous schooner
don't use the approximation
twilit field
well, now that I read it again, we've literally defined it for alpha >1
lyric charm
=1
midnight plankBOT
native pagoda
hi guys 🤓👋🏾
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Available help channel!
royal vigil
kill me now
midnight plankBOT
kill me now
prime hornet
what’ve you tried? 
royal vigil
ok so
late rover
kill me now
-# Okay, using what
royal vigil
desmos on the other hand
so im literally getting like 10 different answers
none of which seem correct
prime hornet
you’re missing a minus sign in front of all your factors, I believe 
royal vigil
basically for x > 0
x(1+2x-x^2) > 2 (no sign flip)
(x+1)(x-1)(x-2) > 0
and i got
-1 < x < 1 , x>2
for x < 0
same thing
(x+1)(x-1)(x-2) < 0 (sign flip)
so
x < -1, 1 < x < 2
prime hornet
oh sorry, you flipped the inequality
prime hornet
basically for x > 0
x(1+2x-x^2) > 2 (no sign flip)
(x+1)(x-1)(x-2) > 0
and i got...
huh, wait no
royal vigil
wat am i doing wrong
prime hornet
you are indeed missing the minus-
prime hornet
basically for x > 0
x(1+2x-x^2) > 2 (no sign flip)
(x+1)(x-1)(x-2) > 0
and i got...
the factored form is -(x+1)(x-1)(x-2)
prime hornet
then you should consider the roots of the expression, divide R up into intervals, and check the sign of the function on each interval
royal vigil
where is desmos getting this from..................
prime hornet
what’s the issue in the photo?
royal vigil
y is it from -1 to 0 and not -1 to 1 like that seems more intuitive no? its an entier gap under 0 not
idk i dont really get it either way
prime hornet
well, on the interval (-1, 0), both (x-1) and (x-2) are negative
combine that with your minus sign at front, and you have three negatives
meanwhile (x+1) is positive on that interval
so all in all, you’ve got a negative sign on your function, so it’s below zero
royal vigil
but isnt the entier line from -1 to 1 below 0 anyways
why does it matter which factors are below 0 and which arent
prime hornet
why does it matter which factors are below 0 and which arent
because that determines the sign of the whole function
and hence if it’s negative or positive somewhere
royal vigil
help
ive gone from dying to laughing because this is getting to a point where its like
wtf
what is going on here
this is apparently for x > 0
where is it getting those intervals from
where are those intervals coming from
the 0 < x < 1
1 < x < 2
x > 2
prime hornet
those are the roots of the polynomial
prime hornet
then you should consider the roots of the expression, divide R up into intervals...
.
native pagoda
Is there a way to calculate this quickly?
prime hornet
Is there a way to calculate this quickly?
this channel’s occupied 
royal vigil
Is there a way to calculate this quickly?
leave me alone im dying!!!!!
royal vigil
those are the roots of the polynomial
since when is 0 a root
theres only (x+1)(x-1)(x-2)
royal vigil
and why is the answer still right..
even desmos is treating it like 0 is a root
even though its not
prime hornet
ah wait, zero is excluded since it’s an asymptote
royal vigil
So why r we considering it
prime hornet
we need to consider the intervals to the left and right of it
we’re not considering the function at 0 itself
prime hornet
I’m starting to think it might be easier to not multiply by x and then subtract 2 initially
try subtracting both sides by 2/x and forming a common denominator
then you’ll have the roots of the numerator and the denominator as your partition
and you can make the sign chart off of the roots plus the asymptote
that should work better I think
royal vigil
Okok idek what a sign chart is but let me try that
prime hornet
just a table to keep track of the sign of a function across intervals
royal vigil
ok like
its working
but i dont understand WHY its working
like..
i dont understand why my way didnt work
dude why did this work but not my other way
prime hornet
dude why did this work but not my other way
sorry, I was walking back home from the bus stop in freezing temps 
prime hornet
basically for x > 0
x(1+2x-x^2) > 2 (no sign flip)
(x+1)(x-1)(x-2) > 0
and i got...
I'm pretty sure this works btw
you just missed the sign
prime hornet
nice 
royal vigil
yes i did in fact miss the sign
so
i missed the sign and graphed incorrectly and then i also didnt consider the asymptote at 0
otherwise would have been fine...
okay
thanks for helpinggggggggg
prime hornet
midnight plankBOT
midnight plankBOT
Available help channel!
balmy cypress
midnight plankBOT
$L[t^{-\frac{3}{2}}](s)$
grand pondBOT
Professor Edward C. Hawthorne
grand pondBOT
Professor Edward C. Hawthorne
snow niche
$\mathcal{L}{f(t)}(s)=F(s)=\int_{0}^{+\infty} e^{-st}f(t)dt$
grand pondBOT
alee
grand pondBOT
alee
tawdry kraken
They gave the entry from the table for t^n already
balmy cypress
But I don't think it works
tawdry kraken
I'm not sure if the gamma function extension works or not (I am betting it does, but was verifying by hand)
snow niche
For t close to 0 diverges
balmy cypress
So the Laplace transform doesn't exist?
grand pondBOT
alee
snow niche
When does it converge?
balmy cypress
p>1
grand pondBOT
alee
balmy cypress
p>1
dusky vessel
$\frac{1}{\sqrt(t^3)}$
grand pondBOT
elijah
balmy cypress
-p+1
snow niche
p<1
snow niche
👍
balmy cypress
👍
grand pondBOT
alee
balmy cypress
1-p<0
p>1
midnight plankBOT
@balmy cypress Has your question been resolved?
maiden bridge
How to factor this?
midnight plankBOT
How to factor this?
maiden bridge
x(x+5-6)?
dawn dagger
midnight plankBOT
@maiden bridge Has your question been resolved?
clear lion
How to factor this?
do you know how to search for its solutions?
clear lion
x(x+5-6)?
x(x+5-6/x) since the 6 is one degree lower than the 5 they cant be the same degree after factorisation
wanton vault
How to factorise using two brackets
you gotta divide the integer part (-6 in this case) so that the summations of the terms will create the coefficient of the middle term (aka term with the smallest order of variable, in this case its the x to the power of 1)
maiden bridge
Idk how to do that
wanton vault
you cant find 2 numbers that when multiplied makes -6?
inner barn
Idk how to do that
do you know how to expand something like (x+1)(x+2)
maiden bridge
no
maiden bridge
you cant find 2 numbers that when multiplied makes -6?
-3 and 3
grand pondBOT
The following error occured while calculating:
Error: Unexpected operator , (char 2)
maiden bridge
,w 2,449*2,449
grand pondBOT
brazen onyx
😭 where did you get that number from
maiden bridge
Anyways How to expand it?
brazen onyx
Anyways How to expand it?
This video might prove helpful!
https://youtu.be/xMeI1S6VfNU?si=u1nW5STfqCyBn2hK
maiden bridge
I’ll see.
midnight plankBOT
@maiden bridge Has your question been resolved?
outer portal
Yes?
maiden bridge
How to factor this?
Fkung this
opaque rose
How to factor this?
Hm..
celest jacinth
Fkung this
There’s something called the “AC method” that might help.
But also learning how FOIL multiplies out two binomials may help.
outer portal
Just do the quadratic formula no better way exists
celest jacinth
There’s something called the “AC method” that might help.
Essentially, you multiply an and c, compare the product to b (in the polynomial ax^2+bx+c), and think of what factors of ac can sum to b.
celest jacinth
Just do the quadratic formula no better way exists
There is, but you likely aren’t aware of it yet.
celest jacinth
There’s something called the “AC method” that might help.
@maiden bridge please look this up and get back to me on your understanding of it.
If you don’t understand, I’d be willing to go deeper into an example.
outer portal
There is, but you likely aren’t aware of it yet.
I mean at a high school level dont get me wrong
cloud moth
How to factor this?
You need to find two numbers that add to 5 and multiply to -6
celest jacinth
I mean at a high school level dont get me wrong
Yes.. I learned this in Algebra…
outer portal
You need to find two numbers that add to 5 and multiply to -6
Just 6 no need the -
celest jacinth
Essentially, you multiply an and c, compare the product to b (in the polynomial ...
@maiden bridge This is the same method as referred to by @cloud moth.
outer portal
You can say subtract to 5 and multiply to 6
celest jacinth
Just 6 no need the -
Yes… you do need the negative in the 6…
outer portal
You can say subtract to 5 and multiply to 6
.
maiden bridge
Just do the quadratic formula no better way exists
I want to be a pro
celest jacinth
You can say subtract to 5 and multiply to 6
No, because the polynomial is not “x^2-5x+6”
celest jacinth
You need to find two numbers that add to 5 and multiply to -6
@maiden bridge think of this
maiden bridge
You need to find two numbers that add to 5 and multiply to -6
But not ALWAYS this works… it’s a quadric equation
celest jacinth
But not ALWAYS this works… it’s a quadric equation
Yes, not always, but in this one, it does.
maiden bridge
Yes, not always, but in this one, it does.
Cause it’s a fokking quadric equation
celest jacinth
The quadratic formula, however, is this
maiden bridge
The quadratic formula, however, is this
OMG I DONT WANT TO DO THIS WAY
I want to learn FACTORISE
TO SAVE TIME
…
celest jacinth
I want to learn FACTORISE
okay that’s what we were saying before
what two numbers add to get 5 and multiply to -6
maiden bridge
You need to find two numbers that add to 5 and multiply to -6
6 and -1?
celest jacinth
Now what
since there is no coefficient in front of the x^2, those two numbers can be put into two binomials (two parentheses)
celest jacinth
(x[+/- first number]) (x[+/-second number])
the positive negative is just to reaffirm what sign it is
celest jacinth
i.e. “3” is positive 3
cloud moth
(x+6)(x-1)
celest jacinth
so (x+6)(x-1)
cloud moth
then if you wanna solve it you have to do the null factor law
celest jacinth
then if you wanna solve it you have to do the null factor law
don’t overcomplicate it
celest jacinth
How do you know that it’s not the other way around?
works both ways
cloud moth
How do you know that it’s not the other way around?
it doesnt matter
celest jacinth
in this scenario
cloud moth
youre multiplying them
cloud moth
u can do (x-1)(x+6) or (x+6)(x-1) both r right
maiden bridge
Cassie is being bossy rn…
cloud moth
bro what
maiden bridge
Okay so
x = 1
x = -6
celest jacinth
another example is “x^2+2x-3”, where -3 is the product of 3 and -1, which also, when added, is positive 2 (middle term); the factored form would be (x+3)(x-1)
cloud moth
Okay so
x = 1
x = -6
ya u gotta set them equal to 0
maiden bridge
Without calculating with use of formula
maiden bridge
ya u gotta set them equal to 0
I know that.. Cassie..
celest jacinth
I know that.. Cassie..
So all done?
maiden bridge
I don’t know
celest jacinth
I don’t know
Are you done with the question? If so, you can close this one and create a new one at a later time when you have a new question.
midnight plankBOT
@maiden bridge Has your question been resolved?
near geyser
Mod 10?
near geyser
You seem very active helper
small jasper
grand pondBOT
Ann
near geyser
2^100+3^84-3^37
tawdry kraken
You seem very active helper
Yes but I'm not helpful yet 🙂
lyric charm
sure, that also works.
near geyser
What should I do next?
tawdry kraken
2^100+3^84-3^37
Oh this is nicer than the method I envisioned
I was using phi(10) = 4 to reduce the exponents 😆
near geyser
Should I apply it?
tawdry kraken
I think that would be easiest now that you have primes
lyric charm
hold on a bit
near geyser
As remainder
lyric charm
how did 0 come
near geyser
3^84 exponent fully divided by 4
lyric charm
that means 3^84 ends in a one not zero!
near geyser
,w 3^84 mod 10
grand pondBOT
lyric charm
see
tawdry kraken
anything^0 = 1
near geyser
Let's check our answer
It's correct
tawdry kraken
,w 8^100 + 7^84 - 3^37 mod 10
grand pondBOT
near geyser
lyric charm
Can I ask one more tricky?
!1q
near geyser
midnight plankBOT
Can I ask one more tricky?
It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.
near geyser
.close
midnight plankBOT
tawdry kraken
!1q
Oh that's interesting
They were just telling someone to stop doing that the other day
Because they backtoback opened them and had like 4 stuck open waiting to close
They said it was against the rules but !1q suggests otherwise
I'll keep that in mind
near geyser
Hey are you coming?
tawdry kraken
Yeah
I was seeing if Ann had anything to add
Since they're helpful they have more experience
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Available help channel!
tulip kiln
- The circles k1 (with centre M1 and radius 13) and k2 (with centre M2 and radius 15)
intersect each other in the points P and Q. The length of the distance PQ is 24. What
possible value could the distance M1M2 be?
A) 2 B) 5 C) 9 D) 14 E) 18
midnight plankBOT
6) The circles k1 (with centre M1 and radius 13) and k2 (with centre M2 and radi...
tulip kiln
I am unable to visualize this.
lyric charm
midnight plankBOT
@tulip kiln Has your question been resolved?
next bobcat
@tulip kiln you with me?
so firstly do you know the property about perpendiculars from the center?
willow spindle
so firstly do you know the property about perpendiculars from the center?
they bisect the chord theyre drawn to?
stone ivy
How to solve this equation?
$2^{\ln x}=-3$
midnight plankBOT
How to solve this equation?
$2^{\ln x}=-3$
grand pondBOT
fort craft 🇵🇸
lyric charm
How to solve this equation?
$2^{\ln x}=-3$
observe 2^(whatever) > 0 always
therefore no real solutions
lyric charm
nothing else to say
stone ivy
therefore no real solutions
ik. I am asking for complex solutions.
next bobcat
oh
next bobcat
I have a weird method
next bobcat
Take ln both sides, recall ln(-1) = i*pi 👌
o wow
west iron
take log_2 of both sides
tawdry kraken
Yeah but log 2 gets messy because you have to base change to get the i*pi out
So usually I prefer ln
next bobcat
isn’t $2^ln(x) = x * 2/e$?
stone ivy
Take ln both sides, recall ln(-1) = i*pi 👌
That is not something I recall AT ALL. What does logarithms of negative numbers even mean.
grand pondBOT
BKB
next bobcat
I mean it shouldn’t help here
tawdry kraken
That is not something I recall AT ALL. What does logarithms of negative numbers ...
Mmm think of it like log asks what power should I raise the base to to get what's inside
next bobcat
the basic definition of logarithms is to find the exponent such that x^y = z where y is logx(z)
tawdry kraken
So since we know $e^{i\cdot\pi} = -1$
grand pondBOT
Coolempire93
next bobcat
so here z is to take a negative value
tawdry kraken
Then $\ln(e^{i\cdot\pi}) = i\cdot\pi = \ln(-1)$, at least in the principal branch
This is a challenge on mobile
grand pondBOT
Coolempire93
stone ivy
**Coolempire93**
logarithms of negative numbers sounds like cheating but idk
tawdry kraken
Yes, but not in the complex field
stone ivy
Yes, but not in the complex field
okay I can see that working
tawdry kraken
Once raising to a power becomes rotation, now its just a question of what rotation gives us -1
Which makes a lot more sense when you are working with the unit
stone ivy
@tawdry kraken okay bro I accept that ip = ln(-1). How do we solve the initial equation given this new information?
tawdry kraken
Recall the log rule $\log(a^b) = b\cdot\log(a)$
grand pondBOT
Coolempire93
pure wraith
I don't think you should only restrict it to the principal branch in this case, the question probably expects all solutions
tawdry kraken
Take ln both sides, recall ln(-1) = i*pi 👌
Now you can follow the steps
tawdry kraken
I don't think you should only restrict it to the principal branch in this case, ...
Probably a good point
Although the raising as a power of e will collapse it back down again
pure wraith
**Coolempire93**
Also this doesn't hold in general for a specific branch cut
tawdry kraken
Ah well now we're out of my depth because I don't know about branch cuts
I saw someone talking about them the other day
But as a reference I was going to suggest
\ln(2)\ln(x) = \ln(-3)
pure wraith
It's probably better to ignore the branch cuts for now and use $\log z = \ln \abs{z} + i\arg(z)$
grand pondBOT
jewels!
tawdry kraken
Listen to jewels 
and follow her instructions
Also I just remembered the formula $a^{\log_b(c)} = c^{\log_b(a)}$ which may have made the problem easier (then x = ln(2)th root of -3) but I'm not sure if it holds for complex
grand pondBOT
Coolempire93
tawdry kraken
How many ln 2th roots of unity are there anyway xd
tawdry kraken
Listen to jewels <:this:489575168314966026> and follow her instructions
But yes
grand pondBOT
fort craft 🇵🇸
stone ivy
$(\ln x)=\frac{\ln -3}{\ln 2}$
grand pondBOT
fort craft 🇵🇸
stone ivy
$\ln x=log_2{-3}$
outer scaffold
llike this
grand pondBOT
fort craft 🇵🇸
stone ivy
$x=e^{log_2{(-3)}}$
grand pondBOT
fort craft 🇵🇸
stone ivy
Is this the correct solution?
outer scaffold
stone ivy
@outer scaffold what happened to the negative sign behind 3?
outer scaffold
if it is really this then this has no solution
we are moving into complex numbers then
stone ivy
if it is really this then this has no solution
I am speaking in the Complex world not the Real world.
outer scaffold
let me figure in complex world then.
pure wraith
**fort craft 🇵🇸**
right now split ln(-3) into its real and complex parts
outer scaffold
lyric charm
if it is really this then this has no solution
!noai
midnight plankBOT
if it is really this then this has no solution
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
pure wraith
$\log z = \ln \abs{z} + i\arg (z)$ for $z \in \mathbb C$
grand pondBOT
jewels!
outer scaffold
I just took my student thru logs.
stone ivy
!noai
bro if I wanted ai response I would go use AI. I'm here to recieve human feedback.
stone ivy
**jewels!**
what does the function arg do?
pure wraith
It's the argument of z
The angle it makes with the positive real axis, and it is multivalued
If $\theta$ is an angle, then so is $\theta + 2n\pi$ for all $n \in \mathbb Z$
grand pondBOT
jewels!
pure wraith
So what angle does -3 make (as a vector) with the positive real axis?
stone ivy
**jewels!**
ok is this the new definition of logarithms for complex numbers?
pure wraith
**jewels!**
btw do you see where this comes from
pure wraith
ok is this the new definition of logarithms for complex numbers?
Yes, but it has a simple enough derivation
stone ivy
btw do you see where this comes from
nope
pure wraith
The polar form?
stone ivy
The polar form?
Can you derive rn it if it is as easy as you claim it is?
lyric charm
bro if I wanted ai response I would go use AI. I'm here to recieve human feedbac...
don't call me "bro".
stone ivy
don't call me "bro".
ok sis
pure wraith
Can you derive rn it if it is as easy as you claim it is?
You can write any $z \in \mathbb C$ as $re^{i\theta}$, where $r = \abs{z}$ and $\theta = \arg (z)$. So you can just take the logarithm on both sides, $\log z = \log (re^{i\theta}) = \log r + \log e^{i\theta} = \log r + i\theta = \ln \abs{z} + i\arg (z)$
grand pondBOT
jewels!
pure wraith
It is your preference if you want to use the notaton "ln" for complex inputs, but I don't
stone ivy
**jewels!**
this makes sense. okay so we plug the argument and the radius and get the answer right?
midnight plankBOT
@stone ivy Has your question been resolved?
twilit field
midnight plankBOT
grim vector
Tried anything?
grim vector
moment method right ?
twilit field
yes
pure wraith
spam calculate moments until you get it
grim vector
So first moment, second moment, empiric moment and you solve the equality between all
twilit field
what's empiric moment?
grim vector
The sum
pure wraith
I think this one is doable with the second moment alone
grim vector
so the first moment is 0
sounds good
twilit field
The second moment is $\frac{\theta^2}{3}$
grand pondBOT
wai
grim vector
I agree
twilit field
and that is equal to $\frac{1}{n} \sum_{i=1}^{n} X_i^2$?
grand pondBOT
wai
twilit field
mhm, my question is what do I do with the sum
pure wraith
what about it?
grim vector
Nothing, let it as a sum
twilit field
this is very similar to sample variance
twilit field
so $\theta^3/n = M_2 \implies \theta = \sqrt[3] {nM_2}$?
grim vector
M_2 is already a standart thing
grand pondBOT
wai
grim vector
Ja
twilit field
I mean how would I find M_2
grim vector
I mean how would I find M_2
You need the values of X_i
Given by observations of the phenomen
twilit field
I know there are n values all with idetical dist
grim vector
I know there are n values all with idetical dist
I mean
X_1 = ...
X_2 = ...
Else its not really doable
flat spire
yakuu
midnight plankBOT
midnight plankBOT
Available help channel!
woeful turret
midnight plankBOT
woeful turret
i took 3 cases
D4 shows same as D1,D2,D3
since all 3 cases are same we can multiply by 3
D1 D2 D3 D4
say D1 is the dice with same number, it can have any number
D1 = 6/6
D2 cannot have the same number as D1 so D2= 5/6
D3 cannot have same number as D1 so D3=5/6
D4 has to have same number as D1 to 1/6
so on multiplying by 3 i get 75/216 which dosent match anything
can someone help?
bold peak
Holy shit I hate this problem so much
woeful turret
oh why
bold peak
D1 D2 D3 D4
say D1 is the dice with same number, it can have any number
D1 = 6/6...
Why are you saying D2 can't have the same number as D1
Nothing in the problem restricts that
hard shard
if D1 D2 D3 roll 1 2 3 respectively, what is the probability D4 is the same as one of the other dice?
now consider D1 D2 D3 roll 1 2 2
woeful turret
Why are you saying D2 can't have the same number as D1
it says D4 shows a number appearing on ONE of D1,D2 and D3 right?
bold peak
Doesn't say exactly one
bold peak
In usual english, it would mean at least one
woeful turret
if D1 D2 D3 roll 1 2 3 respectively, what is the probability D4 is the same as o...
oh 3/6
oh alr alr i get what ur saying
woeful turret
In usual english, it would mean at least one
oh
let me try again
im getting 81/216 now
i took 3 cases
All distinct
2 same
3 same
for all distinct (6/6)(5/6)(4/6)(3/6) = 60/216
2 same (6/6)(5/6)(2/6)(2/6) = 20/216
3 same (6/6)(1/6)(1/6)(1/6) = 1/216
where have i gone wrong
@bold peak
woeful turret
do you account for a roll of 2 2 1?
yeah i did right? 2 same
woeful turret
yeah
hard shard
5/6 means second dice isnt the same as first
woeful turret
yeah
hard shard
2/6 means third dice is the same as one of the first two
woeful turret
yea
hard shard
so it will count 1 2 2 and 2 1 2, but not 2 2 1
woeful turret
so it will count 1 2 2 and 2 1 2, but not 2 2 1
arent all the dices the same? they are being rolled simultaneously right so how can we say 2 2 1 is different from 1 2 2
hard shard
thats like saying rolling a 1 2 is the same as rolling 2 1, so the probability of that happening is 1/36
obviously thats nonsense, its 2/36
maybe i shouldnt say obviously
woeful turret
oh ok its the same but we still have to count it..my bad
hard shard
yes, the case can appear in multiple scenarios
one of the hardest things to get right in probability questions is understanding what cases have equal probability/weight
woeful turret
so do i make another case inside 2 same in which 1st is same as 2nd?
ok yes if i do that it gives me a + 10
= 91/216
thanks a lot bro
dont feel good tho cause u gave me lots of help for this
.close
midnight plankBOT
hard shard
dont feel good tho cause u gave me lots of help for this
practice makes progress, dont feel too bad
midnight plankBOT
Available help channel!
woeful turret
midnight plankBOT
woeful turret
i took 3 cases S1={1,2} , {1,3} and {2,3} and tried to calculate each set
woeful turret
oh wait this is not the question
in my book its given Let E2-S1 and F2 = F1 U S1
let me try again then..seems like a misprint
.close
midnight plankBOT
midnight plankBOT
Available help channel!
twilit field
midnight plankBOT
hard shard
.3?
grand pondBOT
wai
hard shard
this should not be equal
hard shard
alligator eats the bigger number
hard shard
the ceiling exists later
twilit field
so $\ceil{\log_{2} ( 3000)}$
grand pondBOT
wai
twilit field
the ceiling exists later
just this, right
hard shard
which is?
twilit field
12
twilit field
wait, it's that easy 😭 ?
I was sure I had messed up somewhere
hard shard
assuming the bisection method is bascially just binary search, yes its that easy
twilit field
Thanks!
twilit field
assuming the bisection method is bascially just binary search, yes its that easy
It is yea
.close
midnight plankBOT
midnight plankBOT
Available help channel!
midnight plankBOT
near geyser
What do you want to see?
lyric charm
i want to see where in your book the notion of "coplanar pts" is introduced for the first time
near geyser
Points coolinear
Or points coplaner never saw in the book
I guess they are saying vectors are co planer not points
What next?
lyric charm
Points coolinear
Or points coplaner never saw in the book
never anywhere in the book?
can you read all of it in full?
i do not want to give you a solution only to find out that it's not how your book wants it done
near geyser
of course it says about vectors not points
lyric charm
ok well can you show me ANYTHING AT ALL that it says about coplanarity.
near geyser
Sure
midnight plankBOT
@near geyser Has your question been resolved?
soft stone
notice the coefficients sum to zero (affine relation)
basically try rearranging the given vector equation into the form of the section formula
lyric charm
i was trying to get OP to show us anything from his textbook that'd talk about a formula
like yknow i could definitely say that e.g. the vectors PQ, PR, PS are linearly-dependent but i am not sure that this would be valid for op's context.
soft stone
mhmmm go ahead that's a valid concern
midnight plankBOT
@near geyser Has your question been resolved?
near geyser
i was trying to get OP to show us anything from his textbook that'd talk about a...
And OP is not sending
inland patio
When someone says that the determinant is infinitely differentiable since it is a polynomial in the entries of the matrix, which derivative do they have in mind? Total derivative? Partial derivative with respect to one entry? I'm interested in knowing if $A\mapsto\det(A)$ is \emph{continuously} differentiable?
midnight plankBOT
When someone says that the determinant is infinitely differentiable since it is ...
grand pondBOT
psie
steady saddle
All of the partial derivatives
inland patio
All of the partial derivatives
Ok. So is A -> det(A) infinitely differentiable?
steady saddle
As you said, it's a polynomial. Are polynomials infinitely differentiable? (yes) (but convince yourself they are)
inland patio
As you said, it's a polynomial. Are polynomials infinitely differentiable? (yes)...
But A -> det(A) is a function of A. Yes, det(A) is a polynomial in the entries of A, but when considering the derivative of A -> det(A), we don't take the derivative with respect to an entry, right?
inland patio
What do you mean by "funcion of A"?
det takes as an input a matrix A, therefore it is a function of A.
inland patio
yeah (or complex)
steady saddle
Then you can really think of A simply as a vector of entries rearranged in a square
So a 2x2 matrix is just a 4-element vector
inland patio
So a 2x2 matrix is just a 4-element vector
Ah, ok. So in that sense, det becomes a real-valued multivariate function?
steady saddle
I suppose this is what the question you were given meant
steady saddle
Ah, ok. So in that sense, det becomes a real-valued multivariate function?
Yes
midnight plankBOT
midnight plankBOT
Available help channel!
sand flume
I don't see how the inequalities provide anythign for part a. For it to be cont we need the limit of sin x at 0 to exist and to equal sin(0). The only thing I could possibly see that inequality being used for is sinx<|x| and sinx>-|x| we could then see left and right limits but we can just find lim x-> of sin(x) directly
midnight plankBOT
I don't see how the inequalities provide anythign for part a. For it to be cont ...
wanton spade
I don't see how the inequalities provide anythign for part a. For it to be cont ...
you'd end up using the inequalities to prove the limit is 0
remote bone
mods
wanton spade
<@&268886789983436800>
sand flume
you'd end up using the inequalities to prove the limit is 0
Why can't we compute it directly? And was I right then for using it for one sided limits?
wanton spade
Why can't we compute it directly? And was I right then for using it for one side...
i assumed you'd have to prove the limit if you were taking it
wanton spade
Why can't we compute it directly? And was I right then for using it for one side...
i dont think you need one sided limits either way
sand flume
i assumed you'd have to prove the limit if you were taking it
I'm guessing neighborhoods then?
wanton spade
I'm guessing neighborhoods then?
not too sure what you mean
sand flume
Delta eplison
wanton spade
but itd be much easier to just use epsilon delta for continuity
wanton spade
Delta eplison
👍
wanton spade
but itd be much easier to just use epsilon delta for continuity
if you have to prove the limit because then that's just extra steps
sand flume
But don't we need to prove the limit exists for cont?
wanton spade
do you know the epsilon delta definition of continuity?
wanton spade
gl
midnight plankBOT
@sand flume Has your question been resolved?
bold hill
After factorising, I don’t really know what to do
midnight plankBOT
After factorising, I don’t really know what to do
near cliff
what do you notice about the denominators?
slate ferry
-# also do you know series? 
(I have a feeling that you dont... and you're supposed to magically do this...)
bold hill
they are decreasing by 3 inside the roots
assuming that you can write it as a series, what would the common difference be?
<@&286206848099549185>
.closer
.close
midnight plankBOT
slate ferry
assuming that you can write it as a series, what would the common difference be?
I dont really know but I thought of (n-3) , (n-9) for the two square roots
ending with n=30 but I dont think that's very solvable nor is a good idea.
It's been a while since I've done series.
midnight plankBOT
Available help channel!
maiden bridge
The table shows the prices of raisins and dried plums.
Price per 1 kg
raisins – 20.00 PLN
dried plums – 32.00 PLN
Zosia bought half a kilogram of dried plums. Ala bought only raisins and paid the same amount as Zosia paid for the plums.
Calculate the mass of raisins bought by Ala.
Write down all calculations.
midnight plankBOT
The table shows the prices of raisins and dried plums.
Price per 1 kg
raisins –...
grand pondBOT
grand pondBOT
inner barn
also this is 6th grade exam
how old are you?
maiden bridge
what does that have to do with anything?
scenic wyvern
that has to do with the fact that ToS and this server's rules do not allow users under 13.
inner barn
because I swear 6th grade in Poland is 11-12
scenic wyvern
I'm tempted to preping mods just in case
maiden bridge
XD I’m testing if I’m stupider than 6th grader relax
scenic wyvern
ToS violations are not exactly things to relax about in a partnered server, so do be careful about casually mentioning something that may imply you're under 13, regardless of whether you are.
now, are you done with your question?
inner barn
holy aura…
candid gull
!done
midnight plankBOT
If you are done with this channel, please mark your problem as solved by typing .close
@maiden bridge Has your question been resolved?
scenic wyvern
@maiden bridge if you have another question, don't just ❌ the bot. do send your next question here or state what you still have left with your current one
and yes, we can tell you ❌'d the bot.
maiden bridge
I didn’t actually
maiden bridge
For what are logarithms used for? They’re just pointless and easy enough… basically the opposite of doing numbers under powers.
midnight plankBOT
For what are logarithms used for? They’re just pointless and easy enough… basica...
pearl hull
more like inverse of power
olive matrix
I don't think this question is well-formed, but for an early application of logarithms you can look at a slide rule, which was a pre-calculator method of multiplying two large numbers together very quickly
lusty python
So useless
if $2^x = 5$, what's $x$
grand pondBOT
1 divided by 0 equals Infinity
lusty python
tell me
grand pondBOT
mystic condor
Logs are often used for certain scales and are also big parts of calculus and differential equations, as well as other things but they are also just handy in general algebra and arithmetic
cerulean oyster
this guy/girl is surely trolling anyways
white moss
logarithms famously have zero applications
cerulean oyster
tbh reminds me of someone else that recently was doing something similar, wouldnt be surprised if its an alt.
mystic condor
Well you convert it to a log equation
mystic condor
It’s difficult to calculate that
Yeah its probably irrational
keen wigeon
It’s difficult to calculate that
you can leave it as is
maiden bridge
Exactly you guys can’t even calculate it
keen wigeon
Exactly you guys can’t even calculate it
i mean calculators can do that
bold peak
,w log_2(5)
grand pondBOT
mystic condor
"Stupid mathematicians cant calculate a log with an irrational result which is practically impossible to do on paper! What losers!"
keen wigeon
"Stupid mathematicians cant calculate a log with an irrational result which is p...
tbh, we can, it just takes a horribly long amount of time
mystic condor
tbh, we can, it just takes a horribly long amount of time
Exactly
olive matrix
For what are logarithms used for? They’re just pointless and easy enough… basica...
help channels are for help with specific mathematical problems, not with general questions like these. While those are sometimes allowed, in this case it does not seem like you are asking in earnest, and so I will be closing this channel and forbidding you from opening another until you have an actual homework-type question to ask for help with.
.close
near geyser
midnight plankBOT
near geyser
How do I solve it?
midnight plankBOT
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
1
unkempt sluice
Say four points a,b,c,d. As vectors a,b,c not dependent. Then as vectors d=ua+vb+wc for some u,v,w
d is on the plane containing a,b,c if and only if u+v+w=1
(w on the affine space generated by v_1,…,v_m if and only if expressing w as linear combination of these v_j, sum of coefficients being 1)
olive matrix
You already sent this problem last night, and did not respond to requests for elaboration at the time. Have you made any progress since then?
#help-49 message
near geyser
You already sent this problem last night, and did not respond to requests for el...
No progress since then as the helper was not ready to help properly
olive matrix
No progress since then as the helper was not ready to help properly
Yes, I mean have you made any progress since then using your brain and pencils
near geyser
i googled and found solutions and read out
unkempt sluice
Say four points a,b,c,d. As vectors a,b,c not dependent. Then as vectors d=ua+vb...
You need to know this result. If you don’t, it probably is somewhere in your textbook or something.
unkempt sluice
I prove the more general thing I said in the bottom of my message: w is in the affine space generated by those v_j is the same thing as those v_j-w are linear dependent , there exists Σc_j (v_j-w)=0 thus w=Σ(c_j/ (Σc_k)) v_j. (Σc_k won’t be 0, since those v_j are linear independent) Sum of coefficients being 1
(v_j being dependent cases can be derived from this)
The special case being three dimensional space and plane case
5p-2q+6r-9s you will notice negation of one coefficient is the sum of other three coefficients
Second part same idea, xp+(1-x)r=yq+(1-y)s
midnight plankBOT
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near geyser
Tq so much cog
midnight plankBOT
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