so how
#help-42
remote mural
final parrot
Look at the second hint again
What's the characteristic of this(quadratic) function?
final parrot
Is there anything useful for us to find max min value via some concept of a quadratic value?
final parrot
wdym by characteristic exactly
What would you come up with when it comes to quadratic function?
remote mural
What would you come up with when it comes to quadratic function?
quadratic formular?
final parrot
quadratic formular?
anything else?
remote mural
i dont think i know
final parrot
that's about finding roots
final parrot
i dont think i know
Alright, do you know a quadratic function has a vertex?
remote mural
Alright, do you know a quadratic function has a vertex?
like the peak point?
final parrot
Yes
and that's our protagonist
That's the weapon to combat this heinous monster
quick question
$ax^2 + bx + c$ If a>0 does the function have maxmium value or minimum value?
potent lotusBOT
This is sad 😢
final parrot
yo, still alive?
remote mural
yes
im just thinking of the stuff inside the square root
im just gonna think out loud
final parrot
yeah for sure
remote mural
so 38 + 13t^2 - 24t comes from arbitrary distances between arbitrary lines
between the 2 lines of each ant
final parrot
sqrt(38 + 13t^2 - 24t)
remote mural
yea
and apparently
each line between each two random points forms a parabola?
when put together
final parrot
each line between each two random points forms a parabola?
no, don't think that way
well, I'd like to share more details but I get to sleep
,ti skyandnight
potent lotusBOT
The current time for skyandnight is 02:50 AM (CST) on Fri, 26/09/2025, the same as huntiebounty!
final parrot
I'm dying 💀
Let's jump to the last step, if you'd like more details then wait for the next helper
You wanna find the min of this function
So when this function has min value, the stuff inside of the sqrt must be also at its min value
For every $ax^2 + bx + c$ quadratic function\
When a > 0, the function have min value. Reversely has the max
potent lotusBOT
This is sad 😢
remote mural
oh
final parrot
This function, while a is greater than 0, it has min value
Last but not least, how do we find the min or max value of a quadratic function?????
final parrot
find its derivative
yes, that's a way
the conventional way is to convert it into vertex form
All roads lead to Rome anyways, let's try diff first
remote mural
okay
remote mural
final parrot
yes, and that indicates when t = 12/13, the distance has its min value
plug that in and you'll get what you want
final parrot
So before you leave, I'll leave something that I haven't given you.
You might just post these questions to the next helper in the future
- How do I find the min value of this function by converting it into vertex form??
- Why does derivative works on this question?
And that's it, sorry I can't stay with you longer
remote mural
And that's it, sorry I can't stay with you longer
its all good its getting late for you anyway
final parrot
Thanks for the understandings
remote mural
yeah for sure
final parrot
anymore small questions before I leave?
remote mural
anymore small questions before I leave?
ahh not really thanks
final parrot
Alright, have a good one 
@short salmon janitor come and clean up the pins, Imma go 寢
short salmon
pinger ponger
short salmon
<@693216533614166042> janitor come and clean up the pins, Imma go 寢
IT'S 3 AM はよ寝ろ
winter elbow
.solved
calm coralBOT
remote mural
Alright, have a good one <:catthumbsup:614540188747563008>
you as well
remote mural
now sleep u 坚韧不拔的纪录片
i remember u
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Available help channel!
spice venture
calm coralBOT
spice venture
i got the function as y=x^2+x
and so f(2) = 6
which is the correct answer
but for some reason it was given as bonus
can anyone explain to me why?
spice venture
yes
jade fractal
i don’t understand how that is a math problem
spice venture
what do u mean
it was given as bonus means that the question is wrong in some way
and that is a math problem..
nvm i got it the value of f(1)= 2 doesnt satisfy original equation
.close
calm coralBOT
spice venture
@jade fractal ^ (incase u want to know)
simple musk
nvm
rustic osprey
let $x=1$ and you get $0=3f(1)-1$
potent lotusBOT
Civil Service Pigeon
rustic osprey
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simple musk
,, \lim_{(x,y) \to (1,0)} \frac{\sqrt{|y|}(x-1)(x+4)}{(x-1)^2 + y}
potent lotusBOT
Renato
simple musk
this is going to 0, right?
,w lim (x,y) to (1,0) of (sqrt(|y|)(x-1)(x+4))/((x-1)^2 + y)
potent lotusBOT
quick talon
test with y = t^m and x = t^n+1 . You can play with m and n to find 2 different limits after simpliftying this thing
simple musk
wdym?
quick talon
Try to do the variable change. And once you do. If you change m and n it’s like changing the path approach
simple musk
care to elaborate
quick talon
Do the variable change and simplify first; you’ll see what I mean
simple musk
Do the variable change and simplify first; you’ll see what I mean
care to elaborate?
sour monolith
the point is that x,y change approach 1, 0 at different rates
changing the value of the limit
simple musk
dude lets just do a change of variables
sour monolith
then what do you get?
simple musk
sour monolith
yes
sour monolith
consider different paths to (0,0)
v=w is natural
you already know the limit doesn't exists
simple musk
mine is better because gets rid of nasty sqrt dude
otherwise when lhopitaling
we get a nightmare-ish situation
quick talon
I forgot how to write this rigourously but here are the paths that lead to 3 different limits
simple musk
like, we should be getting $\lim_{v \to 0} \frac{|v| + \frac{5|v|}{v}}{2}$
potent lotusBOT
Renato
simple musk
last step is wrong
the issue is dude, this absolute value thing is making it hard
sour monolith
now you can consider the right limit
which is when v > 0
there its easy to find the value of this limit
but the left limit will have a different value if you look at it too
simple musk
you are checking continuity?
sour monolith
checking if the limit exists
sour monolith
yeah but continuity and existence of the limit is not the same thing
sour monolith
both lateral limits need to coincide
yes, but here they sadly don't
simple musk
,w lim x to 0 of (|x| + 5|x|/x)/(2)
potent lotusBOT
simple musk
sour monolith
on the left sided limit v stays v, but its negative
simple musk
on the left sided limit v stays v, but its negative
do I need to check other paths ?
is this enough shit?
sour monolith
if you found two paths that are not matchning then you are done
you still have a small error in the left limit
simple musk
in this case one path is undefined
sour monolith
its (v + (-5v)/v) / 2
simple musk
excuse me?
sour monolith
oh yeah xD
sorry
I looked at the one above it instead of two about it
anyway you are done with this question
sour monolith
no
simple musk
or one undefined path is enough
sour monolith
two paths that don't match --> limit undefined
you have two paths (the two directions of w=v^2)
simple musk
care to elaborate?
sour monolith
first path: w=v^2 where v approaches 0 from the right (v > 0)
second path: w=v^2 where v approaches 0 from the left (v < 0)
simple musk
wdym?
sour monolith
a path is a continuous function connecting two points
thats what this definition says
sour monolith
first path: w=v^2 where v approaches 0 from the right (v > 0)
second path: w=v^2...
now, these are two different function, so two different paths
but along these paths the limit is different
simple musk
a path is function f:[0,1] --> R^2 which is continuous
what if v < 0
sour monolith
v is not the input
here if we translate these into functions,
then the first would be
t --> (t, t^2)
and the second would be
t --> (-t, t^2)
sour monolith
the first coordinate is v, the second is w
t is mapped to (v, w)
I parameterize the path
simple musk
I parameterize the path
how?
sour monolith
here if we translate these into functions,
then the first would be
t --> (t, t^...
.
like this
sour monolith
we are trying both direction, which give two different paths
paths with different direction are different
heck even you go along the path at different speed its different
as I said a path is a function
any change to the function will give a different path
simple musk
I see
simple musk
as I said a path is a function
I didnt know
potent lotusBOT
simple musk
,w cos(2pi)
potent lotusBOT
simple musk
.close
calm coralBOT
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wide cedar
I'm struggling with understanding how to complete the square
So I'm attempting to find the inverse of the attached equation, I've gotten as far as the second screenshot
After talking with ai i'm still not understanding how to continue
jade fractal
$r = {-b \pm \sqrt{b^2 - 4ac} \over 2a}$ where r is a root
potent lotusBOT
Médicis
jade fractal
you then get $ax^2 + bx + c = (x-r_1)(x-r_2)$
potent lotusBOT
Médicis
wide cedar
I've been instructed to solve it without the quadratic formula, could you explain how to do it without?
jade fractal
there’s no direct root so idk
wide cedar
like I just genuinly don't understand how this works
wide cedar
sorry if I caused some confusion there
jade fractal
you’re searching for some solution in the form $2x^2 -6x -13 = (Ax + B)^2 +C$
potent lotusBOT
Médicis
wide cedar
yes!
jade fractal
develop the right part and try deducing what A, B and C are
wide cedar
well I know what they are I just don't understand how to get there
jade fractal
$(Ax + B)^2 + C = A^2 x^2 + 2ABx + B^2 + C$
therefore you have to search A, B and C such that:
$A^2 = 2 \2AB = -6 \ B^2 + C = -13$
potent lotusBOT
Médicis
wide cedar
.close
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halcyon ore
calm coralBOT
halcyon ore
,rotate
potent lotusBOT
halcyon ore
what my prof did was define a function $f(m,n)$ such that $$f(m,n) = g(m,n,k)$$ then you can fix $f(m,n)$ to a contant and then you are basically done
potent lotusBOT
Bubbles
halcyon ore
what i dont get is how you can define that function like that??
the function just gives the relation between the points
sleek vessel
What's the infinite ramsay theorem
halcyon ore
ramsay therom but for inf number of points
sleek vessel
That tells me very little lmao
halcyon ore
1 sec still typign
it says their exists an infinite complete subgraph that is monochromatic given a finite amount of colors
lemme find the defintino from the book
halcyon ore
sleek vessel
Oh hm okay then I have no idea how this would go
halcyon ore
lmao
sleek vessel
Hopefully someone else can help you lol
calm coralBOT
@halcyon ore Has your question been resolved?
halcyon ore
<@&286206848099549185>
calm coralBOT
@halcyon ore Has your question been resolved?
craggy heron
Hello
halcyon ore
hello
are you here to save me
@craggy heron any idea on how to solve 😭
or is it just wraps
manic oracle
yeah so you want to find another coloring
halcyon ore
Yes
manic oracle
so f(m, n) kinda should use information about g(m, n, k)... well, we can aggregate it for all the distinct k and just pick a color that appears infinitely often
and use that to color f(m, n)
manic oracle
but that doesn't work yet
halcyon ore
oh
manic oracle
another idea
define graph with vertices {a, b} of unordered pairs of naturals
{a, b} {a, c} has color g(a, b, c) obviously
{a, b} {c, d} ?
halcyon ore
but that doesn't work yet
alos why does this not work
manic oracle
alos why does this not work
say you grab the ascending sequence from pairs, can you reconstruct the triples in the original graph?
hmm... maybe color it with {g(a, b, c), g(a, c, d), g(a, b, d), g(b, c, d)}?
manic oracle
oh yeah we can
halcyon ore
say you grab the ascending sequence from pairs, can you reconstruct the triples ...
yes
why not
manic oracle
just take any vertex that is included? nothing about that forces the triples to share that colour
manic oracle
or are we fixing a particular k
halcyon ore
thats waht i dont get he just "erased" the k
manic oracle
we fix a k, and then we colour g(m, n) by the triple color f(m, n, k)
halcyon ore
yeah. then we can create a sequence k1, k2, etc
manic oracle
okay that's probably it
halcyon ore
and by ramseys we can create a inf sub sequence that is all the same color
not ramseys
pigeon hole
he might have messed up the proof idk
ill ask him abt it
would u mind if i sent another q?
manic oracle
usually recommend to start another channel, or #1021175428326633542 if you want it to last quite a while
calm coralBOT
halcyon ore
thank you for the help
manic oracle
oh yeah for each k we can see if it forms color 0 triples or color 1 triples
something following the classic ramsey proof where we try to construct both cliques at the same time
if it's color 0 triple, add it to the 0 sequence
if it's color 1 triple, add it to the 1 sequence
we never run out of vertices
so at least one sequence goes infinite
halcyon ore
yeah
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Available help channel!
foggy heron
calm coralBOT
final parrot
What have you tried in advance?
foggy heron
what do you mean
final parrot
these are the notes, im trying to understand them
I thought you were going to share your notes
foggy heron
no as in thats one of the excercises in the notes and i dont know how to do it and i want to know how to do the excercise so i can understand the ntoes
old plume
Let's try it.
How many total ways of selecting 5 balls from collection of 15 balls?
leaden lion
can it be solved with combinations?
foggy heron
Let's try it.
How many total ways of selecting 5 balls from collection of 15 ba...
binomial coefficient 15,5
safe lynx
can it be solved with combinations?
Yes
foggy heron
Let's try it.
How many total ways of selecting 5 balls from collection of 15 ba...
oh well order matters right
safe lynx
First find the no of ways to select 5 balls from total no of balls i.e 15
foggy heron
then 15!/(15-5)!?
leaden lion
then do 15C5 for the denominator fraction
safe lynx
then 15!/(15-5)!?
n!/k!*(n-k)!
final parrot
Can we not have so many helpers lol
leaden lion
then 15!/(15-5)!?
15!/(15-5)!5!
safe lynx
Can we *not* have so many helpers lol
Aight
leaden lion
Can we *not* have so many helpers lol
sorry
foggy heron
15!/(15-5)!5!
but thats when order doesnt matter
i thought it mattered for this
well not this problem?
old plume
Now, there are 5 red balls and 10 blue balls, you're selecting 5 such that 2 are red and 3 are blue. In how many ways you can do that?
foggy heron
Now, there are 5 red balls and 10 blue balls, you're selecting 5 such that 2 are...
i dont know
old plume
(5C2)*(10C3)
old plume
18c2 instead
(You can't select 18 out of 2)
blazing coyote
Just have time to talk about the iden tity for now
calm coralBOT
Just have time to talk about the iden tity for now
blazing coyote
$a \ in S \implies \exists s ' \in S : as'=a (S=aS)$ and $a \in S \implies \exists s'' \in S " s''a =a$ ( as S=Sa).
this isnt enough to say the set has an identity is it
I have to show that the left and right identity are the same, right
potent lotusBOT
wai
blazing coyote
though tbh this doesn't guarentee that every element will have the same identity does it
I'll have to show that too
sour monolith
$aS=S=Sa$ tell you that maps $x \mapsto ax$ and $x \mapsto xa$ from S to S are surjective.
potent lotusBOT
ExpertEsquieESQUIE
sour monolith
you good ?
calm coralBOT
@blazing coyote Has your question been resolved?
blazing coyote
you good ?
Sorry, in a class
low lodge
hey, i proved T(x) is differentiable and cont so it has MIN and MAX in the interval [-3,-1] but idk how to attack it since T'(x) is unworkable to find critical points
low lodge
any hint (no full answer) will be nice
low lodge
find critical points
מה המצב 🙂
sour monolith
אחלה
low lodge
it shouldn't be hard
אנסה עוד פעם פשוט קיבלתי משוואה של 2x + 1/(1+x^2)
jade fractal
hey, i proved T(x) is differentiable and cont so it has MIN and MAX in the inter...
do you know arctan differentiation?
low lodge
do you know arctan differentiation?
1/(1+x^2)
low lodge
right
low lodge
yes, so arctan is always growing on R
ig R is real nums
jade fractal
ig R is real nums
Yes
low lodge
Yes
but i have this 2x
+1/(1+x^2)
so i get 2x+2x^3+1=0
finding critcal points with that equation not so simple
low lodge
in [-3, -1]
intuitively <0
since 2x is larger
i suppose i need to prove that on [-3, -1] T'(x)<0
sour monolith
this should be easy by continuity
low lodge
this should be easy by continuity
it has to do smth with T''(x)?
since T''(x) actually easier to work with lol
sour monolith
you can do it
low lodge
you can do it
is there a better way?
sour monolith
this is probably the easiest way
low lodge
T''(x)>0 on the interval we mentioned so T'(x) is an increasing function on that interval so i can do T'(-3) and see if its >0. if it is then T is increasing on that interval
sour monolith
you would want T'(-1)
because if its increasing before it, and its negative at -1, it must be negative before -1
low lodge
you would want T'(-1)
why? T''(x)<0 for every x<0 then T' increasing for every x<0 . if T'(-3)>0 then ofc T'(-1)>0 since its increasing..
sour monolith
because if its increasing before it, and its negative at -1, it must be negative...
.
low lodge
because if its increasing before it, and its negative at -1, it must be negative...
whys that matter its the same thing..
i think
sour monolith
Read closly
low lodge
tryin
sour monolith
You say T'(-3) > 0 which it isn't
low lodge
You say T'(-3) > 0 which it isn't
iam not sure thats y i have to check
low lodge
because if its increasing before it, and its negative at -1, it must be negative...
youre right
i mean i get what you say
low lodge
You say T'(-3) > 0 which it isn't
but theoretically if T'(3) was positive T'(-1) was also positive i think
sour monolith
Yes
calm coralBOT
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tardy kayak
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sharp narwhal
rigid jewel
ah recurring function
stupid jee
just solve upto 2 or 3 recursions and see how the pattern goes
it will probabily converge into something
sharp narwhal
u differentiated both sides wrt theta?
i think that's a decent approach
u can also integrate both sides wrt theta from 0 to pi/2
sharp narwhal
just think about what terms are constant wrt the integral
i don't think u need to know extra theory
eg. if ur interating wrt t, you can pull out sin(theta)
rigid jewel
integeral of sine term should be 0 since it is odd function
tardy kayak
eg. if ur interating wrt t, you can pull out sin(theta)
What about the f(t) and t now?
sharp narwhal
wdym
sly brook
apply kings rule here by replacing the angle theta by negative theta (as pi/2+(-pi/2)-theta=theta)
try by it
and then add the integral obtained after this transformation to the original one
tardy kayak
potent lotusBOT
sly brook
you might be thinking of `,rccw` (rotate counterclockwise)
oh
i dont know much about it
rigid jewel
is answer 1/2 ?
tardy kayak
Yes
tardy kayak
How
rigid jewel
ahem
u need to check wether terms in the exapansion are odd or even
if its odd the term vanishes if its even then the integral becomes half of 0 to 2pi
calm coralBOT
@tardy kayak Has your question been resolved?
tribal copper
is answer 1/2 ?
i keep getting 1 can you elaborate further
rigid jewel
i keep getting 1 can you elaborate further
all the odd terms keeps on vanishing in the reccuring function and only tsin(t)dt term remained
sly brook
all the odd terms keeps on vanishing in the reccuring function and only tsin(t)d...
ig you did it by king's rule?
rigid jewel
ig you did it by king's rule?
idk what is king's rule
sly brook
rigid jewel
no, i didnt do that
calm coralBOT
no, i didnt do that
rigid jewel
what i did was integral -a to a of odd function = 0
integral -a to a of even function = 1/2 of integral 0 to a
sly brook
ok ok
yes that works too
rest ill figure out
@rigid jewel close this channel mistakenly opeaned by you by typing .close
rigid jewel
.close
calm coralBOT
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frail light
is there a need to get the present year ratio first?
also tell me what it means of last two lines
fickle steeple
can you tell me the source of this question? like for what exam are you preparing with this?
frail light
SSC
fickle steeple
ok 👍
calm coralBOT
@frail light Has your question been resolved?
old plume
Since, P and S are twins.
P=S
Also, P+S = M
And 3 years ago, the ratio was (P-3)/(M-3) = 2/7
You got three equations, three unknowns.
calm coralBOT
@frail light Has your question been resolved?
calm coralBOT
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civic roost
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
1
civic roost
IS THAT A tokamak reactor on the bots pfp?
let me ask you something
how is that
in anyway
related to the problem i need help in?
<@&286206848099549185> heyy anybody free?
violet vector
@calm coral 1
violet vector
let me ask you something
the bot is broken man
rustic osprey
This is just knowing your basic facts. Reflections are rigid motions, so triangle A’B’C’ is congruent to triangle ABC.
A dilation with scale factor k multiplies all of the side lengths by k. So, the side lengths of A’’B’’C’’ are twice the corresponding side lengths in A’B’C’.
civic roost
This is just knowing your basic facts. Reflections are rigid motions, so triangl...
I figured it out
It's A
calm coralBOT
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narrow folio
can proofs have "subproofs"
calm coralBOT
can proofs have "subproofs"
narrow folio
i.e. if im proving smth can i posit something then prove the thing i posited inside the proof 
swift laurel
yeah that's called a lemma
narrow folio
thanks
pallid halo
you could factor it out as a lemma yea
narrow folio
.close
red breach
So I am having trouble conceptually understanding what the problem wants me to do
red breach
(currently am on a)
the column space would just be composed of columns, right? [3, 6, -9] and [-1, -2, 3]
I'm just not sure how constraint equations come into play and I'm not sure why there is a linear combination of rows of A summing to 0
So this is listed in the answers- same as what I got myself
but I just don't get how it leads back to the column vector, I'm getting confused
leaden thunder
did you try to row reduce A
b is in the column space of A does not mean what you think it is
red breach
wdym
red breach
did you try to row reduce A
I could divide the top row by 3 which would be the last step but I don't see how it would help
red breach
b is in the column space of A does not mean what you think it is
my work so far comes from trying to reverse engineer the solution provided
leaden thunder
yea that looks right
red breach
leaden thunder
the column space would just be composed of columns, right? [3, 6, -9] and [-1, -...
column space does not just equal the columns
red breach
column space does not just equal the columns
I mean, you know, after you remove the reduncancies
So just [-1, -2, 3]
yeah guys I got it
thanks
.close
calm coralBOT
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median cloak
https://www.youtube.com/watch?v=iv-5mZ_9CPY 5:00 to 5:20
calm coralBOT
https://www.youtube.com/watch?v=iv-5mZ_9CPY 5:00 to 5:20
median cloak
can someone explain what the presenter trying to convey.
hexed grove
ive seen this video lol
we use physical diffusion processes in reverse to generate images from text
and hence diffusion models
median cloak
specifically, why the diagonal is matching and others is not? also matching to what
median cloak
he says the diagonal is "matching" and other entries are not
"the diagonal" correspond to matching image and caption
this is what he said, while others are not
hexed grove
i think this is called the co-occurance matrix, idrk
the diagonal is where the text represents the image
median cloak
the diagonal is where the text represents the image
what do you mean.
hexed grove
so we need each diagonal entry to dominate the non-diagonal entries
median cloak
the diagonal is where the text represents the image
text represent the image what do you mean
hexed grove
text represent the image what do you mean
the text "photo of a cat" should be assigned to the actual photo of a cat, and nothing else
median cloak
the text "photo of a cat" should be assigned to the actual photo of a cat, and n...
yes
hexed grove
so, the entries in the matrix are probabilities that the text matches the pictures
rather, they encode the probabilities with vectors
median cloak
I totally agree. But why others do not match but only the diagonal
hexed grove
training
before training its totally random
but after (assuming we trained it properly) it should match
median cloak
I mean if you look at the entry_21, it has a caption of cat as well as a picture of cat
it is matching, no?
hexed grove
i honestly have no idea
hexed grove
but the point is to make this matrix totally randomly, and then through training, the model will "learn" to match text to images
median cloak
How
hexed grove
thats a much more technical question lol
the general idea is to evaluate the error, and backpropagate it through gradient descent
we need to start with a training batch of correctly assigned images to do this
median cloak
no
hexed grove
i suppose these channels can be used to help you learn actual math as well (i might be wrong), but you shouldnt leave it open if youre done
median cloak
I'm not done. someone has not answered my question yet.
hexed grove
everything starts out randomly, and then through the training process, the model learns to make the diagonal match and nothing else match
using this idea https://en.wikipedia.org/wiki/Backpropagation
calm coralBOT
@median cloak Has your question been resolved?
scenic briar
lets say we wanna use an identity on (-4x-1)^2
calm coralBOT
lets say we wanna use an identity on (-4x-1)^2
amber bay
For this to be less complicated
velvet osprey
lets say we wanna use an identity on (-4x-1)^2
what identity
name which identity you wish to use
(you can use either one)
amber bay
u can write (-4x-1)^2 = (-1(4x+1))^2 = -1^2 * (4x+1)^2 = 1*(4x+1)^2
velvet osprey
ok and you want to use that AS IS?
scenic briar
yup
velvet osprey
then a=-4x and b=+1.
but @amber bay's suggestion is good otherwise bc it cuts down on minus signs
somber swift
Calculate the three quartiles for a random variable
𝑋 with the probability density function
somber swift
dont know how i should go about this problem
I'm not sure which function should be used when calculating each quartile
this didnt help either
kind light
67
calm coralBOT
@somber swift Has your question been resolved?
somber swift
.close
spice venture
calm coralBOT
spice venture
i dont understand what that 'D' is for in the differential eqn
i differentiated y=mx + c wrt x to get dy/dx = m
and thats it
void frost
Df sometimes refers to the first derivative of f
spice venture
oh
void frost
D(Df) might be written as D^2f, the second derivative
harsh night
Dy = differential of y w.r.t any variable if im not wrong
so lets take it with respect to x
spice venture
oh wrt any variable?
spice venture
so lets take it with respect to x
okay
harsh night
ur eqn would be y'' - 3y' - 4y = -4x
spice venture
ye
void frost
so how do i solve this?
By plugging in
spice venture
By plugging in
i got
3m+4mx+4c=4x
harsh night
i think now u have to differentiate y=mx + c and put values of y' and y'' in the differential eqn
void frost
I don't think that's helpful
You can right away follow something out of this
On both sides, you have a parametrization of a line
spice venture
4y=4x-3m
y=mx+c
now we can compare?
void frost
And well, when are two such things equal?
void frost
4y=4x-3m
y=mx+c
now we can compare?
You compare the left side to the right
You will get two equations out of this
spice venture
You compare the left side to the right
no we can just match the coefficients right
harsh night
no we can just match the coefficients right
yup
calm coralBOT
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low lodge
hey i would like a hint with 2.
calm coralBOT
hey i would like a hint with 2.
low lodge
thats what ive tried so far:
the problem is with the red. if it was <0 then ofc it was an increasing function on the interval [1,+inf) so then f(1) was the min in that interval
ornate thunder
Differentiate the function
low lodge
Differentiate the function
i did
low lodge
here @ornate thunder
low lodge
where is your differentiated function?
purple brackets
tranquil sundial
ah, didnt see
mb
when x is very big, sinx->x, cosx->1
meaning that f'(x)~=pi/x^2>0
f(x) is increasing
so if absolute minimum exists, it would be closer to 0
low lodge
meaning that f'(x)~=pi/x^2>0
thing is i cant use ~.. anyways the answer in the book says that since for every x>1 f itself is >0 and f(1)=0 so ofc x=1 is the min in the interval [1,inf]
anyways thx for trying < 3
.close
calm coralBOT
tranquil sundial
thing is i cant use ~.. anyways the answer in the book says that since for every...
o, didnt see it start from 1. Obviously when x>=1, 0<=pi/x<=pi, meaning that sin(pi/x)>0. In addition, (x-1)>=0 when x>=1. As explained earlier, that it is increasing, so the f(x)'s absolute minimum exists. For a absolute minimum to not exist, the f(x) has to decreasing to -infinity at some values. Furthermore, abs minimum exists at x=1
low lodge
.reopen
calm coralBOT
✅
low lodge
o, didnt see it start from 1. Obviously when x>=1, 0<=pi/x<=pi, meaning that sin...
thx !
.close
tardy kayak
calm coralBOT
tardy kayak
how do I solve this??
odd fulcrum
tardy kayak
I have tried integrating the whole function
wrt theta
but then I got stuck
is there any other way of solving this?
tardy kayak
So it might help to isolate it
I didn't understand it
tardy kayak
yea i did
tribal copper
what did you get
tardy kayak
after integrating wrt theta i got $\int_0 ^{\frac{\pi}{2}}f(\theta)d(\theta) = 1 + \int f(t)dt + \int tf(t)dt$
oops
upbeat coral
Put d outside of \dtheta
potent lotusBOT
Prathmesh
tardy kayak
yup this is what i got
upbeat coral
$\int f(\theta) d\theta = \int f(t) dt$
potent lotusBOT
Miyagi
tribal copper
i got 1 but i didnt integrate wrt theta
i did simultaneous equations instead
do you have the correct answer
calm coralBOT
@tardy kayak Has your question been resolved?
calm coralBOT
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Available help channel!
sleek vessel
Can someone explain what a regular language is? And what a context-free language is?
I'm doing a course on program analysis, and I was promised I wouldn't need any automata theory stuff but they just threw this at me in an assignment.
sleek vessel
The assignment problem, if that helps
I don't want help with answering this. I just wanna know what exactly a regular language and a context-free language is. Preferably a description that doesn't use automata
(please tag me if anyone answers)
thorny stump
Can someone explain what a regular language is? And what a context-free language...
I might not be the best to answer this but:
- a regular language is a set of strings that can be produced by a regular expression (a finite state machine)
- a context-free language is a set of strings that can be produced by a pushdown automaton (it's like a FSM but with a stack)
sleek vessel
I'm gonna need to learn automata theory huh
thorny stump
Well, you probably don't need to if that's the only problem you want to answer; one is a strict subset of the other
sleek vessel
I mean I imagine regular is a subset of context-free
Cuz an FSM with a stack should be able to capture anything an FSM without a stack captures
thorny stump
It's not clear to me what IVP means? Interprocedurally Valid Paths? Did they really write IVPaths paths?
thorny stump
Ok well I'm not familiar with these terms (initial IVP, program points, call-strings, call points)
sleek vessel
Ah that's fine, I really just wanted to know what regular language means
thorny stump
I imagine, since (2) says "of call-strings along initial IVPs" while (1) just says "of initial IVPs", that (1) is the context free
sleek vessel
I can describe the terms to you but that isn't really relevant to my question
Fair enough
I just don't know if that's enough justification
And it just feels unsatisfying to use the containment
thorny stump
Me neither, maybe ask in https://discord.com/channels/268882317391429632/1313711459385081876 though
sleek vessel
Fair maybe I will closer to the deadline
Gonna keep this open in case anyone else wants to comment
thorny stump
To give a little more context, combinatorial logic circuits are contained by finite-state machines which are contained by pushdown automata which are contained by Turing machines
sleek vessel
Interesting. Somehow the only thing on that list that I've done are turing machines lol
And even that was very limited
thorny stump
You start with "instant output given current inputs", then add a graph of states and transitions, then add a stack (which you can only read and write to at the top), then you switch from stack to tape (which you can access anywhere without losing data)
(that's my understanding anyway, I'm no automata theory expert)
sleek vessel
Well you certainly understand it better than me lol
But yea thanks. Ig I'll ask my prof tomorrow and then ask #theoretical-cs
.close
coarse karma
hello,
So I have an exam in a few hours and I was running through practice problems online. My brain might be fogging right now because I couldn't figure out what went wrong and how I got the boxed answer a^2-a-3 instead of -19/8
The topic is about rational equations and I'd appreciate it if someone would point out the thing(s) I did wrong
coarse karma
this was the problem for referenc
what I did was eliminate the lcds by multiplying the whole expression with the denominmators
coarse karma
wher
coarse karma
sory bad handwriting
upbeat coral
Your approach is correct
coarse karma
I was rushing through
coarse karma
Your approach is correct
That's good to hear
do you think it was a problem with the answer key
coarse karma
ooh I see
coarse karma
That equals zero
Do you have any tips regarding rational equations? or is there not much to say about the topic
upbeat coral
Not much to say
novel raven
Do you have any tips regarding rational equations? or is there not much to say a...
on the second line shouldnt it be (a-2)(a+2)?
coarse karma
on the second line shouldnt it be (a-2)(a+2)?
wait lemme double check
coarse karma
on the second line shouldnt it be (a-2)(a+2)?
o I merged them
fringe reef
$\int_0^1 \frac{\ln(x)}{x^2 - x+1} dx$
calm coralBOT
$\int_0^1 \frac{\ln(x)}{x^2 - x+1} dx$
potent lotusBOT
artemetra
potent lotusBOT
fringe reef
bruh
pseudo wedge
You can multiply the numerator and denominator by 1+x and then series expand the denominator
That’ll lead to some series which are hopefully simplifiable
rustic osprey
,w integrate (ln x)/(x^2-x-1) dx from 0 to 1
potent lotusBOT
rustic osprey
,w \frac{pi^2}{5sqrt5}
potent lotusBOT
rustic osprey
Typo?
fringe reef
possibly..
pseudo wedge
This is a pretty famous integral
fringe reef
You can multiply the numerator and denominator by 1+x and then series expand the...
do you mean with the x^2-x+1 or the x^2-x-1 version?
pseudo wedge
You can multiply the numerator and denominator by 1+x and then series expand the...
[ \sum_{n\ge 0} (-1)^n \int_0^1 (1+x)x^{3n}\log x\dd{x} ]
potent lotusBOT
kheer257
pseudo wedge
do you mean with the x^2-x+1 or the x^2-x-1 version?
The latter
fringe reef
True..
fringe reef
The latter
you mean the former lol
(x^2-x+1)(1+x) = (x^2-x+1+x^3-x^2+x) = x^3+1
(x^2-x-1)(1+x) = (x^2-x-1+x^3-x^2-x) = x^3-2x-1
pseudo wedge
you mean the former lol
(x^2-x+1)(1+x) = (x^2-x+1+x^3-x^2+x) = x^3+1
(x^2-x-1)(1...
No, the latter is famous
My method was for the former
fringe reef
ah alr
pseudo wedge
The latter is solved in a different way
pseudo wedge
I take it back - this does reduce quite nicely
Does it
It’ll still be nonelementary I think
fringe reef
at least the integral inside the sum does
rustic osprey
It’ll still be nonelementary I think
Yeah but it’s concise
fringe reef
$\int_0^1 x^k \log(x) dx = -\frac{1}{(k+1)^2}$
potent lotusBOT
artemetra
fringe reef
if I'm not mistaken
pseudo wedge
Yes
calm coralBOT
@fringe reef Has your question been resolved?
rustic osprey
@fringe reef You good?
calm coralBOT
@fringe reef Has your question been resolved?
torpid anvil
calm coralBOT
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remote mural
i found the equation for the parabola at the y = 5 plane , i just dont know how to continue from there
nimble harbor
send
nimble harbor
i found the equation for the parabola at the y = 5 plane , i just dont know how ...
js imagine z as the dependent variable and x as the independent variable
like what u normally do for when y is the dependent one instead of z
calm coralBOT
@remote mural Has your question been resolved?
tawny mesa
is xy+2y=1 a function
calm coralBOT
calm coralBOT
Available help channel!
shut harness
Need help
desert relic
odd fulcrum
shut harness
Ok ignore what question 9 asks. But for 11. ive encountered many questions like it on tests and always get it wrong.. im pre calc grade 12 level i understand the first answer which is 3 but not the 2 second one and i understand the 3rd one and 4th
anyone pls
@desert relic @odd fulcrum 😄
desert relic
Okay
odd fulcrum
<@938824014313426965> <@1311394031640776716> 😄
im sorry bro I cannot help 
desert relic
Also @shut harness please don't ping individual helpers, like me and Infinium are chill but some of the helpers are very particular about this :)
shut harness
Also <@1376024914338910289> please don't ping individual helpers, like me and In...
What does ping mean?
desert relic
What does ping mean?
Like '@'ing someone
odd fulcrum
like you just did @{somebody}
shut harness
Okey sorry
odd fulcrum
nah its good, some people are adiment about it though.
desert relic
Okey sorry
Nah you're fine dude, we don't mind it much, but some of the others are just kinda serious about it
desert relic
Well I looked it up, it says to get the original function and transformed function equal to each other and then find their value
Like f(x) = y^2
So for the first one, f(x) = 3/sqrt(f(x))
y^2 = 3/y
y^3 = 3
So it has only one solution, hence only one point
Now I should say that I'm shooting shots in the dark here, I've got no clue if this is the correct approach
desert relic
Well I looked it up, it says to get the original function and transformed functi...
The only actually reliable stuff which I've looked up is this, the rest is me rambling
calm coralBOT
@shut harness Has your question been resolved?
rustic osprey
Well I looked it up, it says to get the original function and transformed functi...
backing this up ^
nimble badge
Is the space of non-parametric functions strictly larger than parametric functions? Ie are there functions that can be described non-parametrically, that cannot be described by parametrically? (This is for my own edification, and a simple counter example would suffice)
nimble badge
Ik that it is generally assumed to be true, but my intuition says that anything can be modeled parametrically
nimble badge
define non-parametrically
Good follow up, i am not sure. Citing this response to googling my question, an infinite dimensional or infinite number of parameters. Which implies that parametric (finite dimensional theta) is nested by non-parametric models, so the answer is yes. But not for reason I initially thought
Now, i need to review gaussian process regression where i saw this last
Anyway
.close
calm coralBOT
calm coralBOT
Available help channel!
weak vapor
yo i have a question, just want to confirm my work is right
calm coralBOT
yo i have a question, just want to confirm my work is right
weak vapor
acoustic wraith
please send it here
winter elbow
weak vapor
heres my answer, im sending question 1s
Georgia has 15 apps on her phone. Of these apps, 10 are connected to social media, seven are games, and five are prayer/meditation apps.
jovial bridge
Georgia has 15 apps on her phone. Of these apps, 10 are connected to social medi...
wait what are questions a)/b)?
jovial bridge
acoustic wraith
you seem to not have considered prayer/meditation apps in a)
your conclusion is correct though
weak vapor
so everything is right, just need to add the prayer/mediation apps to a?
acoustic wraith
for completeness, I would say so.
weak vapor
alright, thanks
acoustic wraith
your Venn diagram is also missing the prayer/meditation app circle
(if it was drawn as part of the question)
weak vapor
how would i draw it instead
acoustic wraith
three circles
not two
and you probably no longer need the rectangle outside, but no harm keeping it I think
acoustic wraith
3rd rectangle?
acoustic wraith
put however much you found out
I haven't fully worked it out yet, so can't confirm
acoustic wraith
you may send it, if I'm not available other helpers will come in
but either way, sure
acoustic wraith
you've got to show the original context, mate
weak vapor
oh it's basically a toy caterpillar that has a 50/50 chance of either going to red or blue
lowk forgot to send that lol
acoustic wraith
then what does it mean hitting red twice? I think the original question would still help here
weak vapor
Connect the caterpillar scenario above to a question you would ask related to probability.
basically the probability of the caterpillar not hitting red in 2 attempts
and instead going to blue both times
weak vapor
Connect the caterpillar scenario above to a question you would ask related to pr...
this was the initial question, i made that one up
acoustic wraith
so in 2 attempts, the caterpillar turns blue
weak vapor
yeah, both times
acoustic wraith
in that case, it's more straightforward to just calculate the probability it hits blue both times, right?
if you want to do inclusion-exclusion, you'd have to account for any event where at least one of them is red
weak vapor
i'm allowed to do either
weak vapor
in that case, it's more straightforward to just calculate the probability it hit...
wouldn't that be 1/4
the red text is the feedback I recieved, i'm not exactly sure what i'd change
acoustic wraith
and it'd be 1/4. try listing out the possible events (R = red, B = blue)
weak vapor
red red
red blue
blue red
blue blue
so the probability of it not being red twice is 3/4
so the answer is right? but something with P(A') is wrong?
acoustic wraith
so in 2 attempts, the caterpillar turns blue
^
when I asked, you said that both times must be blue
so is it "at least one time not red", or "neither attempt is red"?
(also, this is why i asked for the og question)
weak vapor
Connect the caterpillar scenario above to a question you would ask related to pr...
this is the og question
"what is the probability of the caterpillar never hitting red"
thats the choice i made
weak vapor
so is it "at least one time not red", or "neither attempt is red"?
neither attempt is red
acoustic wraith
then your P(A') should be 3/4, because A is the event where neither attempt is red, so A' is the event where at least one attempt was red.
weak vapor
ohh, so where i wrote P(A') should be P(A)