#help-42
wintry echo
ebon pagoda
well yes that's integration by parts, written in another way
I'd see what happens if you do this
wintry echo
well yes that's integration by parts, written in another way
Yes i applied this
$e^x*x^3/3-\int e^x x^3/3$
potent lotusBOT
Scruffy
wintry echo
So this is the right result?
ebon pagoda
nope you integrated x^2, when what you want to do by setting u=x^2 is take the derivative
generally with things like x^n it's best to set "u" to that
to lower the grade of the exponent when you take derivative
ebon pagoda
taking the integral makes the exponent higher instead and you're left with yet another integral to solve
wintry echo
I used this formula
ebon pagoda
**Scruffy**
I'm not saying this is incorrect -- it's logically sound, but this isn't the final result so to say
ebon pagoda
you still have to solve $\int e^x \frac{x^3}{3} , \dd x$
potent lotusBOT
derivada.schwarziana
wintry echo
But even in the formula there is the integral like for me
Look
$e^x*x^3/3-\int e^x x^3/3$
ebon pagoda
yes I get that this is what the formula says
potent lotusBOT
Scruffy
ebon pagoda
So i have to stop here
what you want is to know what $\int_0^1 x^2 e^x , \dd x$ is right, so writing it in terms of another integral doesn't help you much
potent lotusBOT
derivada.schwarziana
ebon pagoda
ofc not, it's just a formula, something you can apply in one step of your solution
perhaps even multiple times right
the thing is, if we do this we get a slightly different result, and one that will actually let you solve the integral eventually
potent lotusBOT
Scruffy
ebon pagoda
if you set $u=x^2$ and $\dd v=e^x dx$, then $\dd u=2x, \dd x$ and $v=e^x$, so [\int x^2 e^x , \dd x = \int u, \dd v = uv-\int v, \dd u = x^2e^x - \int 2xe^x , \dd x ]
potent lotusBOT
derivada.schwarziana
ebon pagoda
so now you'd have to solve $\int 2xe^x , \dd x$
potent lotusBOT
derivada.schwarziana
ebon pagoda
which again can be done by integration by parts right
wintry echo
But I just want to apply the formulas, not like you are doing
ebon pagoda
okay, then set $f'(x)=e^x$ and $g(x)=x^2$, same thing
potent lotusBOT
derivada.schwarziana
wintry echo
Why do you put $f'(x) = e^x$ ? What formula are you using
potent lotusBOT
Scruffy
wintry echo
And not g(x) = e^x
ebon pagoda
because in here eventually you'll want the derivative g'(x), so it's usually good to put polynomials or powers as g(x) since it makes the exponent lower
wintry echo
Oh okay
ebon pagoda
that's the best explanation I can think of, it's a "trust the process" thing at this point
wintry echo
So for example
ebon pagoda
it's just an usual thing that works
wintry echo
$$
\int_{0}^{1} x^2 e^x , dx
$$
potent lotusBOT
Scruffy
wintry echo
So I could already use it right away
ebon pagoda
yes
wintry echo
From what I understand, the integrals e^x * function must be put e^x=g'(x)
ebon pagoda
when you write $\int f'(x)g(x) , \dd x$ the implicit assumption is that we want to integrate $f'(x)$ and take the derivative of $g(x)$
potent lotusBOT
derivada.schwarziana
wintry echo
No wait
ebon pagoda
so we use whichever function gives a simpler derivative as $g(x)$ and the one that gives a simpler integral as $f'(x)$
potent lotusBOT
derivada.schwarziana
ebon pagoda
what does this have to do with the integral of x^2 e^x
ebon pagoda
Then I have to rewrite x^2 as e^x
sorry this isn't making sense
wintry echo
: (
ebon pagoda
**derivada.schwarziana**
like trust me, your integral looks 100% like something you do using integration by parts, like I already did here
wintry echo
Yes
ebon pagoda
if you want you want think of it in terms of this too, it's functionally the same thing
you have [\int_0^1 f'(x)g(x) , \dd x = f(x)g(x) - \int_0^1 f(x)g'(x) , \dd x]
potent lotusBOT
derivada.schwarziana
ebon pagoda
so now the question becomes, what should f(x) and g(x) (and hence, f'(x), g'(x)) be
we want $f'(x)g(x)=x^2 e^x$ and like I said, we usually want the function $g(x)$ to have an easy derivative. I claim $f(x)=f'(x)=e^x$ and $g(x)=x^2$, $g'(x)=2x$ works
potent lotusBOT
derivada.schwarziana
ebon pagoda
**derivada.schwarziana**
so if we replace here,[\int_0^1 x^2e^x , \dd x = x^2e^x - \int_0^1 2xe^x , \dd x]
potent lotusBOT
derivada.schwarziana
ebon pagoda
now you're left to solve the integral in the right hand side
does this make more sense
ebon pagoda
you have \[\int_0^1 f'(x)g(x) \, \dd x = f(x)g(x) - \int_0^1 f(x)g'(x) \, \dd x\...
oop sorry I mean you have [\int_0^1 f'(x)g(x) , \dd x = \left. f(x)g(x)\right\rvert_0^1 - \int_0^1 f(x)g'(x) , \dd x]
potent lotusBOT
derivada.schwarziana
wintry echo
So the integral must be solved
ebon pagoda
so we actually get [\int_0^1 x^2e^x , \dd x = 1^2\cdot e^1 - 0^2\cdot e^0 - \int_0^1 2xe^x , \dd x]
potent lotusBOT
derivada.schwarziana
ebon pagoda
So the integral must be solved
yes
you can solve that integral by using integration by parts again
ebon pagoda
well, it also holds when you have a definite integral
ebon pagoda
you can use the indefinite integral version I guess
ebon pagoda
**derivada.schwarziana**
again by doing so you get something like this
like, [\int f'(x)g(x) , \dd x = f(x)g(x) - \int f(x)g'(x) , \dd x,]and if $f(x)=e^x$ and $g(x)=x^2$ then [\int x^2e^x , \dd x = x^2e^x - \int 2xe^x , \dd x]
potent lotusBOT
derivada.schwarziana
ebon pagoda
does that make sense now
wintry echo
Yes
ebon pagoda
cool
so we "know" the indefinite integral of x^2 e^x but it's in terms of another integral
so naturally one would try to solve that integral as well, so we can find the antiderivative of x^2 e^x without unknown integrals
wintry echo
Yes
ebon pagoda
so, do you see how this formula can be used to solve $\int 2x e^x , \dd x$?
potent lotusBOT
derivada.schwarziana
wintry echo
why can I still use it?
ebon pagoda
well how else would you find the integral of 2xe^x
wintry echo
idk
calm coralBOT
@wintry echo Has your question been resolved?
calm coralBOT
@wintry echo Has your question been resolved?
old plume
well how else would you find the integral of 2xe^x
You could use LIATE
ebon pagoda
that's literally integration by parts as well
old plume
Yea
ebon pagoda
with "LIATE" just being a mnemotechnic to remember which functions to derivate or integrate
old plume
oh it was your answer.
I thought it was a question mb.
Sorry
leaden thunder
with "LIATE" just being a mnemotechnic to remember which functions to derivate o...
Differentiate 🙂
ebon pagoda
yeah that 
ebon pagoda
oh it was your answer.
I thought it was a question mb.
Sorry
yeah it's no problem
ebon pagoda
well how else would you find the integral of 2xe^x
anyway @wintry echo if you're still around, try writing f'(x)g(x)=2xe^x where f'(x)=e^x and g(x)=2x
sturdy crest
ii think i kind of know where to go with this, but not entirely
sturdy crest
the equality does hold because |E| = 16 and |V| = 8
but the equality holding doesn't necessarily make it planar, right?
wait
yeah i dunno
calm coralBOT
@sturdy crest Has your question been resolved?
calm coralBOT
Available help channel!
remote mural
I have
$\frac{k_2 k_1 [A][B]}{k_{-1}+ k_2 [B]}$
calm coralBOT
I have
$\frac{k_2 k_1 [A][B]}{k_{-1}+ k_2 [B]}$
potent lotusBOT
potent lotusBOT
remote mural
how to simplify this with the above approximation ?
fleet verge
Just delete k_-1 or am i not getting it?
potent lotusBOT
remote mural
but then
remote mural
no
fleet verge
I saw different
pseudo wedge
!XY
calm coralBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
remote mural
i didn't put a $ at the end so i edited it
its chemistry
im just having trouble with the approximations
quaint sphinx
I have
$\frac{k_2 k_1 [A][B]}{k_{-1}+ k_2 [B]}$
is this denominator written correctly
pseudo wedge
how did you get this?
pseudo wedge
k_1/k_{-1}=[HAH+]/[H+][HA], and k_2=[P]/[B][HAH+]
remote mural
OH!
remote mural
is this denominator written correctly
I DIDN'T
quaint sphinx
correct
fleet verge
pseudo wedge
what are you isolating here?
potent lotusBOT
pseudo wedge
[P]?
remote mural
i can just ignore k_-1 here
remote mural
what are you isolating here?
isolate?
remote mural
hehe sorry
pseudo wedge
what is this term equal to
fleet verge
pseudo wedge
how?
remote mural
we have two equations
first
rate of formation of Intermediate = rate of disappearance
formation is k[A][B]= k_{-1}[I]+k_2[I]
pseudo wedge
ah yeah ok
pseudo wedge
formation is k[A][B]= k_{-1}[I]+k_2[I]
I is HAH+
remote mural
thank you
pseudo wedge
?
regal remnant
Hello, I need help with performing DFT on my dataset
calm coralBOT
Hello, I need help with performing DFT on my dataset
regal remnant
this is my dataset, it is the average monthly Air quality index across 2 years. i have never done it before so need some help.
i have some questions regarding the process and the formula
what exactly is my k value?
dense estuary
Is that some sort of fourier series?
k should be frequency I think
& Xk is a complex number with the same phase & magnitude of that given frequency
regal remnant
how would I find k in the case of my graph?
dense estuary
Unless I'm wrong, you can only use fourier series up to a frequency of N/2
regal remnant
do you think fourier is even applicable in my case 😭
dense estuary
What is the formula supposed to be? It looks like a fourier series
regal remnant
the formula is for dft
dense estuary
cool
Yeah, k is frequency then.
It's more of a parameter
You choose a value k, and the sum returns the amplitude & phase of that specific frequency
When k is zero, you should get a value proportional to the average value of your dataset (or equal)
regal remnant
okay tysmm
dense estuary
yw! <:)
regal remnant
my main goal is to make a mathematical model for the AQI. so far i have a basic sinosudial model (using desmos) and I need something more complex, so was reccomendde dft. do you have any other suggestions?
I'm in higschool btw
regal remnant
And you're doing advanced things like this?
unfortunately 😭
dense estuary
I can't give a great recomendation for a good model
I'll give it a go though
Is it periodic?
regal remnant
the usual trend is that there is a peak, in the 12th month (the winter months)
dense estuary
Any other peaks?
dense estuary
the usual trend is that there is a peak, in the 12th month (the winter months)
Sinusoidal will cover that quite well
If the peaks are very regular, then sinusoidal is perfect
regal remnant
Any other peaks?
not really
regal remnant
If the peaks are very regular, then sinusoidal is perfect
tyyy
dense estuary
yw
Just in case, you could look for a second opinion.
Not exactly the most qualified person here (not by a LONG shot)
regal remnant
😭 lol ty still!
dense estuary
Glad I could help <:D
calm coralBOT
@regal remnant Has your question been resolved?
leaden sandal
Proving
leaden sandal
Let a be a positive natural number, then there exist exactly one natural number b such that b++ = a
I've tried searching an answer for this one and I'm getting different results, so here's what I'm thinking
midnight oasis
Let a be a positive natural number, then there exist exactly one natural number ...
what is b ++ ?
leaden sandal
Let b = 0, then a is a positive number since it's a != 0 (definition)
leaden sandal
what is b ++ ?
just b + 1
midnight oasis
hmm
alpine stone
Let b = 0, then a is a positive number since it's a != 0 (definition)
Can't induct on b
The statement is about a
leaden sandal
hmmm but i'm not sure how to induct though
midnight oasis
Let b = 0, then a is a positive number since it's a != 0 (definition)
if a = 0 then b=-1 ?
alpine stone
Also, consider whether the proposition is true for a = 0
midnight oasis
I think i saw that if a++ = b++, then a = b
damnnnn
that aint an axiom
that is true
alpine stone
Also, consider whether the proposition is true for a = 0
.
midnight oasis
a=0 b=-1
leaden sandal
oh i'm only talking about natural numbers here btw
midnight oasis
oh i'm only talking about natural numbers here btw
ohh
alpine stone
that aint an axiom
It's one of the Peano axioms iirc
midnight oasis
It's one of the Peano axioms iirc
what ?
basic equation rules ?
they are axioms ?
alpine stone
Also, consider whether the proposition is true for a = 0
Can you answer this? @leaden sandal
leaden sandal
if a = 0, then b doesn't exist no?
leaden sandal
since 0 can't be a positive successor
alpine stone
Induct on a then
leaden sandal
so base case would be 1 instead of 0?
alpine stone
Yeah
leaden sandal
let me try
alpine stone
Hmm no doesn't seem to work
leaden sandal
yeah, the hint on the exercise is to induct base case
then won't use induction
so I think we just have to use that axiom where a++ = b++ -> a = b
alpine stone
The induction axiom says 0 in A and (n in A => S(n) in A) implies A to be the set of all natural numbers, so define A to be the set of all natural numbers that have a predecessor and use the induction axiom
Formulating it this way makes the inductive step trivial
If n in A, then S(n) in A because n is its predecessor
alpine stone
so I think we just have to use that axiom where a++ = b++ -> a = b
This shows existence, for uniqueness you just state what you said here
calm coralBOT
calm coralBOT
Available help channel!
primal abyss
need help please im in grade 9
calm coralBOT
need help please im in grade 9
primal abyss
okay thanks let me try
till here is correct maybe?
hallo?
<@&286206848099549185>
@winter elbow
i gotta sleep now
anyone?
<@&286206848099549185>
😦
dusky flax
x^3 + y^3 = (x+y)(x^2 - xy + y^2)
i think thats the wrong formula
dusky flax
need help please im in grade 9
do you know this identity?\
If $a + b + c = 0$, then $a^3 +b^3 + c^3 = 3abc$
potent lotusBOT
dusky flax
the what
dusky flax
that is not a thing
glad parrot
?
dusky flax
that is the sum of a progression
this is not a progression
you are talking about 1^3 + 2^3 + 3^3 ... n^3
this is x^3 + y^3 + 2^3
glad parrot
right mb
dusky flax
and it does not apply for arbitary variables
primal abyss
guys im in grade 9 chill
dusky flax
i think its this one 🤷♂️
primal abyss
no we didnt learn that
primal abyss
so a=x and b=y and c=2?
dusky flax
yes
dusky flax
ok im confused what do we do after that?
youll get the answer as 3abc
thats it
try writing a^3 + b^3 + c^3
primal abyss
it will be 6ab?
dusky flax
6xy
primal abyss
thats what i meant
dusky flax
ya
primal abyss
since if we subtitute 3abc with x,y and 2 $3xy*2 = 6xy$
potent lotusBOT
im8tvelve
calm coralBOT
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Available help channel!
barren sand
Can we cancel the common denominators of complex fractions?
calm coralBOT
Can we cancel the common denominators of complex fractions?
glacial nacelle
yes
barren sand
Why
dull wagon
multiply numerator and denomiminator of main fraction by (x+1)
solid pollen
short answer: complex set is a field.
glacial nacelle
what
barren sand
multiply numerator and denomiminator of main fraction by (x+1)
Too lazy frl
I'll take your word for it tho
dull wagon
or view division as multiplication of the reciprocal and cancel it that way
barren sand
or view division as multiplication of the reciprocal and cancel it that way
Yeah that's what I usually do, but I just found this shortcut
thanks guys
.solved
calm coralBOT
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delicate oriole
calm coralBOT
delicate oriole
i got this integral from the problem $\int \frac{1}{-x^2 - 4x + 21} , dx$
potent lotusBOT
probromomgamermaster123
sweet zodiac
uh
primal bear
isn't there a standard formula
primal bear
i know i need to make 25 turn into a 1
force it?
delicate oriole
yeah but how
idk what to multiply outside and inside the integral to mkae it a 1
wait
multiply the inside by 1/sqrt(1/25) ?
sweet zodiac
**probromomgamermaster123**
you can solve this integral with partial fraction
delicate oriole
i havent gotten up to pfd
sweet zodiac
oh
delicate oriole
multiply the inside by 1/sqrt(1/25) ?
but wait lemme gtry this
i think that works
sweet zodiac
have you done trig substitution?
delicate oriole
no
well i know this can be reduced to sin^-1
but if you mean like converting the integrand into a function of theta then no
sweet zodiac
ok
sweet zodiac
have you tried u sub?
delicate oriole
yeah i think it becomes $\frac{1}{5} \int \frac{1}{\sqrt{1 - (\frac{x - 2}{5})^2}} , dx$
potent lotusBOT
probromomgamermaster123
delicate oriole
now i can do usub
sweet zodiac
you could do u sub before though couldn't you?
delicate oriole
yeah
sweet zodiac
this one
sweet zodiac
therefore your left with 1/sqrt(1-u^2)
potent lotusBOT
probromomgamermaster123
eager forge
Trig sub
delicate oriole
no i solved it
sweet zodiac
yea
delicate oriole
**probromomgamermaster123**
!
sweet zodiac
your right
delicate oriole
okay thanks guys
sweet zodiac
i forgot it was a 25 lmfao
calm coralBOT
calm coralBOT
Available help channel!
solar oasis
calm coralBOT
solar oasis
in this question we need to test the hypothesis
but my question is'
Xbar= the number on these machines/divided by how many numbers are there
right?
.close
calm coralBOT
solar oasis
.reopen
calm coralBOT
✅
solar oasis
okay so this is the question
im tryna get Z between two populations
and the equation is
but it says in the question that the means are equal so does that mean they cancel each other out?
calm coralBOT
@solar oasis Has your question been resolved?
solar oasis
.close
still zodiac
im trying to understand how those numbers were found to get the discriminant
calm coralBOT
im trying to understand how those numbers were found to get the discriminant
@still zodiac Has your question been resolved?
still zodiac
<@&286206848099549185>
swift laurel
this appears to be the hessian determinant
the hessian determinant of a function of two variabes $f(x,y)$ is [ f_{xx} f_{yy} - f_{xy}^2 ]
potent lotusBOT
cloud
swift laurel
except instead of x and y we have Pa and Pb
for further reference, you can look up the "second partial derivative test"
calm coralBOT
@still zodiac Has your question been resolved?
leaden thunder
<@&286206848099549185>
You need to write your R equation in terms of just P_A and P_B
and then find the hessian
restive escarp
hi, how to find the rank of that matrix
calm coralBOT
hi, how to find the rank of that matrix
restive escarp
for A and then A | b
calm coralBOT
@restive escarp Has your question been resolved?
restive escarp
.close
red locust
am i right with B here
calm coralBOT
am i right with B here
red locust
<@&286206848099549185>
oak elm
am i right with B here
Nope it's c
(x-a)²+(y-b)²=r²
In other words, a is the x value of the centre of the circle, while b is the value for y
red locust
thank you so much man
red locust
Nope it's c
wait why couldn't it be B i just wanted a short reason
oak elm
C is (-1,3)
barren sand
Why no square bracket in the domain when that is where we cannot equal the number?
swift laurel
the round parenthesis ) means the endpoint is not included
whereas the square bracket ] means that the endpoint is included
calm coralBOT
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Available help channel!
covert horizon
helloo I just wanted to check if my solution was right
calm coralBOT
helloo I just wanted to check if my solution was right
covert horizon
A field hockey player starts from rest and accelerates uniformly to a speed of 4.0 m/s in 2.5s
a) Determine the distance she travelled.
b) What is her acceleration?
this is my solution
broken adder
no that's not right
she's knly travelling @ 2.5 at the end
she starts at rest
u need to multiply time by the average velocity
broken adder
The formula for the distance is average velocity×∆t, not ∆v×∆t
don't u mean ×, not /?
covert horizon
ohhh I see so it's 5m?
broken adder
ohhh I see so it's 5m?
ye
oak elm
don't u mean ×, not /?
Yeahh my bad I'm kinda hung over rn
calm coralBOT
@covert horizon Has your question been resolved?
cursive river
calm coralBOT
cursive river
can someone explain how to get b and c it just doesnt make snese
hasty fiber
it seems like you already put down answers for b
cursive river
yeah i got that one but when i plug 6 in i ge 21.16 and its incorrect
cursive river
Because I thought it would be the same type of question as question b
hasty fiber
mayhaps we should look at the question a little more carefully
in words, what is x and what is R?
cursive river
x is the concertation R is the reaction rate?
hasty fiber
concentration
question c says the reaction rate is 6 moles per cubic meter per second. What does that tell you about the numerical value of either x or R?
hasty fiber
the reaction rate is 6 units
cursive river
i know that part but im confused on how to solve for that
hasty fiber
the **reaction rate** is **6** units
which variable is being talked about, and what is its value?
cursive river
R and its value is 6
cursive river
?
hasty fiber
i would appreciate words if you have a question
calm coralBOT
@cursive river Has your question been resolved?
red locust
am i right with A here
calm coralBOT
am i right with A here
calm coralBOT
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hushed perch
Just a quick question, when applying the ratio test to number 13, since im takin the absolute value of the limit, can i omit the cos(npi/3)? Im assuming so because cos(n) as n approaches infinity fluctuates between 1 and -1 so the absolute value of it is just 1, so that would leave just the expression 1/n! To deal with appropriately right?
leaden thunder
If you just need to show convergence, then just use comparison test
hushed perch
Its specifically tellin me to use the ratio
leaden thunder
Pain
leaden thunder
Yea what you said is right
leaden thunder
No
leaden thunder
1/n!
hushed perch
Cuz i think that woulda worked too, no?
Cuz doesnt n! Grow exponentially bigger than just n?
Wait
Nvm
lucid dragon
1/n is harmonic which is divergent
leaden thunder
Factorial grows faster than exponential
lucid dragon
^
hushed perch
1/n is harmonic which is divergent
I know lol
leaden thunder
Cuz doesnt n! Grow exponentially bigger than just n?
No it isn't
hushed perch
Yes it is
U literally just agreed with me
My mistake was just saying that 1/n! Was bigger than 1/n which it isnt
lucid dragon
well yeah but ratio test tells you 13 converges, that's why I mentioned that :)
leaden thunder
Cuz doesnt n! Grow exponentially bigger than just n?
This is also incorrect
hushed perch
This is also incorrect
What
I dont literally mean exponentially like it grows how n² or n³ does
I just meant as an exaggeration
Like much bigger
Buuuttt i think i realized my mistake again
Waig
Wait
Nah i think im tweakin rn
hushed perch
This is also incorrect
Nope explain what i said was wrong
9! Is much bigger than just 9
9! Is much bigger than 9³
Therefore,
1/n! < 1/n
And using a direct comparison test is inconclusive
Limit comparison maybe but i dont feel like doin that rn
lucid dragon
I might be confused but I'm pretty sure direct comparison still works
ratio test is the way that feels rigorous yeah
hushed perch
If 1/n! Is the original expression, right? A_n (a sub n). Since 1/n is larger and divergent, its inconclusive since we dont know what the smaller expression " is doing". It could be divergent, it could be convervent
Convergent*
Now MAYBE we could do a limit comparison test, but i dont feel like doing that
And if we get a nonzero, finite limit, then yes theyd be both divergent
Since 1/n is divergent because its harmonic or p series
lucid dragon
ah well we take 1/n! to be proven to converge
hushed perch
The ratio test imo should be that simple
As cos(n) as n -> infinity fluctuates between 1 n -1
lucid dragon
yes!
hushed perch
We can omit that since the test uses absolute value
Boom
I taught myself most of these tests over the weekend
With the help of this discord and organic chem tutor
My brain is goin crazy rn
lucid dragon
ochem tutor is awesome
hushed perch
He sounds like a younger mark wahlberg with a cough drop/lozenge in his mouth
If youve ever watched the ted show (not movies)
And you listen to him, i promise u, thats what he sounds like
lucid dragon
i hope that doesnt ruin him fpr me lol
lucid dragon
yep! looks good
blazing coyote
calm coralBOT
blazing coyote
I was thinking $aRb \land bRa$( By symmetry)
\
BY transitivity $aRb \land bRa \implies aRa$.
Thus it's an equivalnce relation
potent lotusBOT
A dense set(Ping when reply)
unique jackal
seems okay to me
calm coralBOT
calm coralBOT
Available help channel!
delicate tapir
hi, i forgot how to do (c) part onwards, thanks!
calm coralBOT
hi, i forgot how to do (c) part onwards, thanks!
delicate tapir
hi, i forgot how to do (c) part onwards, thanks!
odd moon
find the 1st and 2nd derivatives and analyse critical points
delicate tapir
thanks
calm coralBOT
@delicate tapir Has your question been resolved?
blazing coyote
calm coralBOT
blazing coyote
It's reflexive as $4 \mid 4x$
potent lotusBOT
A dense set(Ping when reply)
short prawn
I mean, does $xRy$ imply $yRx$
potent lotusBOT
Xwtek
short prawn
Or, even more easily, honestly, express 4|(x+3y) in modular arithmetic. Though this might be incorrect if you're actually trying to define equivalence relation on Z/nZ
potent lotusBOT
A dense set(Ping when reply)
blazing coyote
so $3x+y = 4k+2x-2y$
potent lotusBOT
A dense set(Ping when reply)
short prawn
**A dense set(Ping when reply)**
Now substitute the x on the right side of the equation with the value from this:
blazing coyote
wdym
short prawn
$4k+2x-2y = 4k+2(...)-2y$
potent lotusBOT
Xwtek
blazing coyote
nhmm
ancient thistle
graceful dust
:AA_sus:
ancient thistle
this feels like multiplying fractions but you refuse to simplify any of them
blazing coyote
so what do I do
ancient thistle
4 | x + 3y if and only if 4 | x - y
calm coralBOT
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finite oasis
What exactly is meant by "duality" here? Would be great if your answer(s) don't involve knowing about Hilbert spaces because I don't know about those, as I would just like to know it's "layman" interpretation to put it that way
calm coralBOT
What exactly is meant by "duality" here? Would be great if your answer(s) don't ...
@finite oasis Has your question been resolved?
violet solar
Is there a way to do this without vectors and pure geometry. My intution tells me to do it via similar triangles but can't find a way
calm coralBOT
Is there a way to do this without vectors and pure geometry. My intution tells m...
@violet solar Has your question been resolved?
wooden tinsel
calm coralBOT
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high hedge
Helo
high hedge
Hellooo
wet urchin
hi
high hedge
Bro im cooked
Helpp plssa
Plss
Im noob at fortnite
Brooo plssss
Brihhh
R u gone
gray smelt
wait here somebody will come and help
gray smelt
Have you tried anything
wary sequoia
Replace n with the first four natural numbers and force n to exist in said natural numbers
jolly pilot
wary sequoia
1,3,9,19
calm coralBOT
@high hedge Has your question been resolved?
potent lotusBOT
Wild123
wise bluff
calm coralBOT
wise bluff
show that they intersect is the question
i am not sure if i am doing something wrong or there is something im missing
potent lotusBOT
Wild123
solid pollen
You made a mistake there. And yes, I likely wrote "u" instead of the greek letter; too lazy to check what the code for it is.
wise bluff
You made a mistake there. And yes, I likely wrote "u" instead of the greek lette...
man
the stupidest mistake
solid pollen
No problem. It's a common mistake
calm coralBOT
@wise bluff Has your question been resolved?
calm coralBOT
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burnt crystal
help-42, haha 42 funny number
calm coralBOT
help-42, haha 42 funny number
burnt crystal
ok, let a^^b denote tetration
i.e. a^^b = a^a^…^a (b times)
then, 42^^42 = ? (mod 69)
burnt crystal
or you could say 42^^^2 = ? (mod 69)
same thing
69 = 3 * 23 so phi(69) = 2 * 22 = 44
not sure how to use it though
primal bear
according to me modular arithmetic notes, $(M \cdot N) \equiv (r_1 \cdot r_2) \pmod{\text{whatever}}$
potent lotusBOT
Percy
burnt crystal
yeah
primal bear
so that's kinda helpful
burnt crystal
no
primal bear
,wolf 42^2 mod 69
potent lotusBOT
burnt crystal
no wolframalpha
primal bear
shh
burnt crystal
wolframalpha bad
primal bear
i havent done mod in forever
consider this amateur guesswork until someoe who actually knows stuff comes around
tired kayak
hi what's going here ?
burnt crystal
then, 42^^42 = ? (mod 69)
this is the question
tired kayak
I can help may be if you have any question.
burnt crystal
yes, 42^^42 = ? (mod 69) is the question
tired kayak
or will try to help and also will learn from others
calm coralBOT
@burnt crystal Has your question been resolved?
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spice coral
i neead help
calm coralBOT
i neead help
primal bear
!da2a
calm coralBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
drifting seal
are you 12
spice coral
13
primal bear
hmmmmm
remote mural
i need help
Do you have any example questions from a textbook or something? Thatd help get an answer
spice coral
i could share my screen im on an online program
remote mural
Cant join rn, might be easier if you could just screenshot the question
Or if you could name a specific problem
spice coral
kk
remote mural
We need more to work off of lol
spice coral
spice coral
We need more to work off of lol
this is one
remote mural
So what do you think so far? Any easy eliminations or thoughts?
Make sure this isnt a graded assignment btw lol
spice coral
it isnt
spice coral
So what do you think so far? Any easy eliminations or thoughts?
im so bad with box and wisker plots idk
remote mural
im so bad with box and wisker plots idk
Thats np lol, lets focus on reading it first then
Do you know what the very middle line is?
remote mural
That ones a bit easier if you know your vocab, do you remember what each quartile represents?
remote mural
Each quartile is the next 25% or fourth of the data, notice how quartile sounds like quarter (and also has "quar" in it) so say we have values
1, 2, 3, 4, 5, 6, 7
What would the first quartile be?
remote mural
im dumb asf
I mean I wouldnt call someone dumb for not completely knowing how to read a "box and whisker plot" lmao, its just school stuff youre fine
remote mural
You only count the number that marks the 25% mark, so just 2 would be it
spice coral
oh
remote mural
Didnt clarify that mb but yeah right at 25% you get 2
And then 2nd quartile is easier cause it's right in the middle
And then 3rd quartile is just the 3rd quarter
remote mural
So knowing that, you should be able to find these
calm coralBOT
@spice coral Has your question been resolved?
wise bluff
vectors question,
when we have a rectangle ABCD formed by 3d position vectors, whats the best way to find D if we know A,B,C and D?
wise bluff
is it using the fact that D subtended between A nd C is 90 degrees? so, AD . DC = 0? or is there a more direct way
onyx berry
well I'd first confirm whether the 90 degree angle lies at A, B or C
wise bluff
its a rectangle so its all 90 degrees
onyx berry
yes but
wise bluff
do you mean like
onyx berry
if you are only given ABC
wise bluff
i get what you mena
yes
no i am given a rectangle ABCD
or not given but the question leads me there, then it tells me D is a point in which forms the rectangle ABCD
onyx berry
so D is not given
onyx berry
but like if you have them arranged this way
A B
C
then a 90 degree angle will lie at A, looking at ABC as a triangle
wise bluff
nono i start from origin
so
D C
A B
right my bad
i see what you mean now
sorry i thought this was a somewhat standard didnt account for that
onyx berry
but do you know how to check for 90 degrees?
wise bluff
yes
dot product of AD and DC will be 0
but that gets me nowhere realistically i still have 3 unkowns
onyx berry
well that depends whether A and C will really be the two neighbors of D
but if you say they are
wise bluff
not necessarily because a plane like this can be covered in multiple ways so all that matters is that i keep the same direction vectors
onyx berry
can you determine the vector from A to D, or C to D?
onyx berry
but the good thing about rectangles is that it has parallel sides of same length
wise bluff
ok i got it thoguh
i can see what i cna do
i think the best way to do it is by getting BA and naming that a or something, then finding CD
then compare those 2 since they are equal ^ as you mentioned above
onyx berry
yeah, at the end I would also check whether all angles are really 90 degree though
onyx berry
just to confirm
wise bluff
if its a rectangle why would i need to check if its 90 degrees
onyx berry
the problem I had initially is that, lets say ABC are laid out like this
A B
C
then if you determine the A->B vector and add that to C, it will all be fine and you get D
A B
C D
but now what if they are arranged like this
B C
A
then if you add the A->B vector to C, you get
D
A C
B
a parallelogram
wise bluff
i see what youre saying but to be fair you gotta read the question
that makes sense
especially since when you're given 3 coordinates ABC you should always lay them out as a triangle
onyx berry
yeah idk, me personally I would check it just to be safe, but if the ABCD really walk along the perimeter in order then it should be fine
wise bluff
well it is confirmed to be a rectangle
and my answer is correct so im assuming it does hold :P
lavish wind
ok I don't understand the solution for the laplace transform of the last term
lavish wind
I know this is a standard result
as is this
But I don't get how to combine the two
marsh valley
It's not like the product of the laplace transforms.
It's a separate result you can either compute yourself using the definition of the laplace transform and probably like 2 integrations by parts, or refer to a table.
calm coralBOT
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modern shale
calm coralBOT
frozen sierra
We can use completing the square
And because we have 2 intersections on the x axis, we would also know that a is positive I’ve hence a curve with a minimum
frozen sierra
We can use completing the square
We reverse the process by putting it back into the form a(x-b)^2. + or - c
frozen sierra
We reverse the process by putting it back into the form a(x-b)^2. + or - c
b and c is not the c and b in your question
modern shale
sorry, what you're saying is really confusing lol wdym
wanton wave
sorry, what you're saying is really confusing lol wdym
I'd actually start with the vertex form, since you're given the vertex (9,-14). The only thing you don't know is the value of a. But we can deduce at least that a is positive
If you expand it out into the form ax^2+bx+c, you can find an expression for a+b+c just in terms of a.
Are you familiar with the vertex form for a quadratic? @modern shale
calm coralBOT
@modern shale Has your question been resolved?
valid basin
I am trying to pass a reducible First Order Differential Equation to Exact.
$xdx + (y-x^2 - y^2)dy = 0$
For the equation to be exact, it must be satisfied that from the functions $M(x,y)$ and $N(x,y)$:
$$\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$$.
Let $M(x,y) = x$ and $N(x,y) = y-x^2-y^2$:
-
$$\frac{\partial M}{\partial y} = \frac{\partial}{\partial y} (x) = 0$$
-
$$\frac{\partial N}{\partial x} = \frac{\partial}{\partial x} (y-x^2 - y^2) = -2x$$
Given that $$\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}$$.
The equation is not exact.
By the integral factor method:
$$\frac{M_y - N_x}{N} = \frac{0-(-2x)}{y-x^2 -y^2} = \frac{2x}{y-x^2-y^2} $$
$$f(x) = \frac{2x}{y-x^2-y^2}$$
Let $\Phi$ be the integrating factor:
$$\Phi = e^{\int \frac{2x}{y-x^2-y^2} dx} $$
$$\Phi = e^{\frac{1}{x^2+y^2-y}}$$
Multiply the entire original equation by $\Phi (x) = e^{\frac{1}{x^2+y^2-y}}$
$$e^{\frac{1}{x^2+y^2-y}}(xdx) + e^{\frac{1}{x^2+y^2-y}}(y-x^2-y^2)dy = 0$$
The above gives rise to new functions $M(x,y)$ and $N(x,y)$
$$M(x,y) = xe^{\frac{1}{x^2+y^2-y}}$$
$$N(x,y) = (y-x^2-y^2)e^{\frac{1}{x^2+y^2-y}}$$
But if I find the new partial derivatives they still don't give me the same. The same happens if I choose
$$\frac{M_y - N_x}{-M} = \frac{0-(-2x)}{-x} = \frac{2x}{-x} = -2 $$
$$\Phi = e^{\int -2 dx} = e^{-2x}$$
$$M(x,y) = xe^{2x}$$
$$N(x,y) = (y-x^2-y^2)e^{2x}$$
potent lotusBOT
Melo
valid basin
basically I am trying to make the differential equation exact.
$$xdx + (y-x^2 - y^2)dy = 0$$$.
By integral factor
potent lotusBOT
Melo
Compile Error! Click the 
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valid basin
<@&286206848099549185>
calm coralBOT
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valid basin
<@&286206848099549185>
valid basin
.close
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simple musk
can it be said that a sequence diverges or converges?
like my reader says that but I think is controversial, right?
maybe only for monotonically increasing/decreasing sequences?
whats the deal with finding the convergence of a sequence is that posible right?
marsh valley
I think it's perfectly sensible to talk about a sequence converging. That's kind of how you define limits in the first place.
In the same way that one can talk about the convergence of a series to a certain value.
In fact, infinite series are pretty much defined as the sequence of their partial sums, so they are special cases of sequences.
I guess the question is why do you think it's controversial?
calm coralBOT
@simple musk Has your question been resolved?
simple musk
can I apply RATIO TEST TO A SEQUENCE OR NO?
sorry for the caps, is just that okay taking the limit $\lim_{n \to \infty} a_n$ and seeing if it approaches a finite value should make the sequence converge
potent lotusBOT
xbz
drifting seal
can I apply RATIO TEST TO A SEQUENCE OR NO?
yea that’s a thing
simple musk
is it?
Like in my country is called d'alembert criterion
but in america is called ratio test or something?
marsh valley
D'Alembert Test, Cauchy Test, Ratio Test are all referring to the same test for convergence of series
For sequences, you can still apply it, but it's a bit strict, in the sense that sequences converge "more easily" than series.
You're essentially pretending that the terms of your sequence are the terms of a series, and so naturally if the ratio test says this series converges, then by the divergence criterion the sequence must converge to 0.
simple musk
.solved
granite spade
calm coralBOT
granite spade
Can someone please help me with this?
calm coralBOT
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
I already proved 1 and 2
That its continuous and differentiable
Right now I'm stuck on the 3rd part of rolles
rustic osprey
The f'(c)=0 part, right?
granite spade
yes
rustic osprey
Have you done anything yet (such as finding f')
rustic osprey
recall the chain rule
rustic osprey
so now we have that $-2 \sin (2c)=0$
potent lotusBOT
Civil Service Pigeon
rustic osprey
for convenience let's just work with $\sin(2c)=0$ since that's the crux of it
potent lotusBOT
Civil Service Pigeon
rustic osprey
we divide both sides by -2 since it's a constant
granite spade
kk
rustic osprey
**Civil Service Pigeon**
Are you familiar with when sin x = 0? If not, sketch a quick graph of the sine function or use the unit circle.
rustic osprey
Kind of. Any integer multiple of pi works
so ..., -5pi, -4pi, -3pi, -2pi, -pi, 0, pi, 2pi, 3pi, 4pi, 5pi, ...
granite spade
okay
rustic osprey
we can write this more concisely as $x=n \pi, n \in \mathbb{Z}$
potent lotusBOT
Civil Service Pigeon
rustic osprey
$n \in \mathbb{Z}$ is saying that $n$ is an integer
potent lotusBOT
Civil Service Pigeon
granite spade
mhm
rustic osprey
Kind of. Any integer multiple of pi works
so yeah an integer times pi, which is just this
anyway, we don't have sin(x)=0
we have sin(2c)=0
so what can we say abt 2c
quiet lagoon
What type of mathematics is this?
granite spade
calc
quiet lagoon
ok
granite spade
so what can we say abt 2c
2c would have to equal 0?
quiet lagoon
I'm still at pre-algebra I think
granite spade
oh good luck buddy
rustic osprey
2c would have to equal 0?
Kind of. [For sin x = 0] Any integer multiple of pi works
quiet lagoon
You too thx
rustic osprey
> Kind of. [For sin x = 0] Any integer multiple of pi works
except again, we have 2c instead of x
so 2c is ... ?
rustic osprey
yeah that's the only solution in the interval
I was trying to get you to get at $2c=n \pi \implies c=\frac{n \pi}{2}$
potent lotusBOT
Civil Service Pigeon
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