ok sweet
#help-0
pine kettle
covert agate
this is as close as i could give away
alpine sable
Hello.
silk fulcrum
@pine kettle hmm and ?
silk fulcrum
Yep
Hot ACD but CAD
That makes AC = CD
@pine kettle I've also gone up till that not I'm a bit confused
Hmm?
@pine kettle you still there man?
.close
lone heartBOT
silk fulcrum
.reopen
lone heartBOT
✅
little drum
Angle subtended by a chord at center = double angle subtended at the corresponding arc
silk fulcrum
Yes
little drum
=> BD = diameter
silk fulcrum
Ok
silk fulcrum
Gotcha
little drum
@covert agate Here's a question
silk fulcrum
So all the other stuff was useless?
covert agate
little drum
Prove that C is the center of the circumcircle of triangle ABD
covert agate
Prove that C is the center of the circumcircle of triangle ABD
screw geometry 
silk fulcrum
Hmm but if we take the triangle inscribed in a circle it's useless
silk fulcrum
screw geometry <:bleak:877093280905592842>
I agree 💯
covert agate
=> x = 70°
i got 30°
silk fulcrum
Ahh
covert agate
silk fulcrum
Man so what would the answer be
covert agate
construct AE, find a bunch of angles
little drum
$$\frac{BC}{\sin(x + 40)} = \frac{AC}{\sin x}$$ and $$\frac{AD}{\sin 40} = \frac{AC}{\sin 20}$$
ocean sealBOT
ocean sealBOT
little drum
pretty easy to solve now 
silk fulcrum
Indeed 😊
covert agate
pretty easy to solve now <:uwucat:606547033691521057>
solve for cot x and you get a huge ass mess
little drum
solve for cot x and you get a huge ass mess
welp, that's a disappointment tbh
figure an elegant way through this
there is one
covert agate
figure an elegant way through this
through tan x = (sin 40)/(2 cos 20 - cos 40)?
little drum
Yes
covert agate
cos 20 + cos 20 - cos 40
cos 20 + 2 sin 30 sin 10
cos 20 + sin 10
cos 20 + cos 80
2 cos 50 cos 30
√3 cos 50
(sin 40)/(√3 cos 50)
1/√3
x = 30°
(yey my solution was right)
little drum
cos 20 + cos 20 - cos 40
cos 20 + 2 sin 30 sin 10
cos 20 + sin 10
cos 20 + cos 8...
not elegant enough
ocean sealBOT
covert agate
the hell
little drum
There's a very nice identity that applies here, at this step
covert agate
how ;-;
little drum
what I did was basic algebra tbh, combined with trig identities
covert agate
what I did was basic algebra tbh, combined with trig identities
can’t see it directly
little drum
$$\frac{\sin(40+x) + \sin(x)}{\sin(40+x) - \sin(x)} = \frac{\sin 40 + \sin 20}{\sin 40 - \sin 20}$$
ocean sealBOT
covert agate
can’t see this either
little drum
oml
this is literally the first step derived from the previous equation
$$\frac{a}{b} = \frac{c}{d} \qty(= \frac{a+c}{b+d} = \frac{a-c}{b-d}) \implies \frac{a+b}{a-b} = \frac{c+d}{c-d}$$
ocean sealBOT
lone heartBOT
@silk fulcrum Has your question been resolved?
covert agate
never knew this
potent jolt
Model fraction multiplication or division using something physical what should i use?
potent jolt
rly easy math wise, just finding problems figuring out what to use
mossy pagoda
marbles
potent jolt
hmmm
so like
3/5 x 5/9 or smt really simple
alr
ill probably do that
thanks
.close
ocean sluice
okay so im a lil confused here which one is the formula to find the slope is it this
or (y2-y1)/(x2-x1)
waxen basin
molten plank
lone heartBOT
pine kettle
@molten plank is this a quiz
molten plank
no it’s a practice forum
wary stream
<@&286206848099549185>
Also, you have to wait at least 15 minutes before pinging helpers
molten plank
oh i’m so sorry omg
molten plank
oh my god i’m so sorry i should’ve waited i totally understand
pine kettle
its fine!!!! lol
sudden hinge
usually a good idea is to split into polygons you know the area of
sudden hinge
try splitting it into triangles
molten plank
okay
sudden hinge
you know how to calculate the area of a triangle right?
sudden hinge
try it
ocean sluice
can i get help here
lone heartBOT
can i get help here
ocean sluice
so my what my teacher did is
he found the slope for the line in the equation and then divided the -1 to that slop
which i dont understand why is he using two slopes and how is dividing -1 gives the slope
wary stream
so my what my teacher did is
he found the slope for the line in the equation an...
Because that's how you find the slope for a line perpendicular
sudden hinge
if m is the slope of a line, the slope of a line perpendicular to it (normal line) is -1/m
wary stream
Parallel lines have the same slope, perpendicular is the negative reciprocal
ocean sluice
Parallel lines have the same slope, perpendicular is the negative reciprocal
oh now i get it
so -1 is a not because of of the point (2,-1)?
wary stream
No
swift oriole
How to construct a rectangle when sum of two adjacent sides and one diagonal are given?
Anyone?
fluid eagle
(the sum of (two adjacent sides)) and (one diagonal) or
(the sum of (two adjacent sides) and (one diagonal))?
so do you know two values or one
swift oriole
(the sum of (two adjacent sides)) and (one diagonal) or
(the sum of (two adjace...
second option
swift oriole
the thing is that there is no value, i could choose the values myself
swift oriole
well, you only have the perimeter of a right triangle then
yea
fluid eagle
and the perimeter is given in the form of a length segment?
(because you told us to 'construct')
swift oriole
yea
fluid eagle
hmm
one way is to 12-sect the segment
then make a 3-4-5 triangle
there are many sufficing triangles but i think this is the easiest
fluid eagle
a and b are the side lengths of adjacent sides of the rectangle?
swift oriole
yes
fluid eagle
then it's infinitely easier right
just pick a point on the line segment
then make a rectangle
swift oriole
first I should draw a line which length represents the sum of a and b, than I should draw a line which represents the diagonal, so using these 2 lines I should construct
a rectangle
fluid eagle
wait, you're now given the sum of a and b, and the diagonal?
swift oriole
yea technically
fluid eagle
(the sum of (two adjacent sides)) and (one diagonal) or
(the sum of (two adjace...
bruh that's the first option then
swift oriole
you have any ideas?
fluid eagle
AC = diagonal, AB = sum of adjacent sides
swift oriole
ok
fluid eagle
basically you want to find the point P on segment AB such that when we draw the circle with midpoint P through B and intersect with the perpendicular line through P to AB in Q to get right triangle APQ with AP+PQ = AB for which Q lies on the circle with midpoint A and radius AC
if that makes sense to you
you want to find P such that Q lies on the big circle
right
because then AQ = AC so the diagonal is AC
swift oriole
yes
fluid eagle
notice that PB = PQ and QPB = 90deg so PBQ = 45deg
so we can intersect the line that makes a 45deg intersection with AB with the big circle
and find Q
then it's easy from there to construct P
and so the rectangle
swift oriole
I see
swift oriole
yea only the position would be different
fluid eagle
APQR is your rectangle
notice that we can all do this with compass and straightedge
(e.g. 45deg angle is a right angle + angle bisector)
fluid eagle
you can try it on paper even :)
swift oriole
I will
lone heartBOT
@swift oriole Has your question been resolved?
alpine sable
Can anyone explain me through these questions? These are word problems and my teacher hadn't explained on how to solve word problems regarding money.
alpine sable
Question 4 for the second image is what I need explaining on
a b c or d?
or all?
Let me check
Question 4 all
use the variables given
and write statement likee x+y
to answe
does it go for b and c?
oh wait nvm
.close
lone heartBOT
alpine sable
nah it ain't
lone heartBOT
Available help channel!
alpine sable
there are supposed to be 4 answers to this
lone heartBOT
there are supposed to be 4 answers to this
alpine sable
my attempt is two spread the power to-> [2^(1/2)]*[-1^(1/8)]
but that doesnt work
or does it
idk
cum, answer
answer, cum
ping
cum
cursive badger
so first we do this for formatting
[(-4)^{\frac{1}{4}}=\sqrt{2}(-1)^\frac{1}{4}]
now we solve for [(-1)^{0.25}]
[\sqrt{2}(-1)^\frac{1}{4}=\sqrt{2}(\cos(π+2πk)+i\sin(π+2πk))]
ocean sealBOT
Scythe
cursive badger
via de moivre's theorem,
actually, nvm, since this is how you get factors
and you want the root. Very sorry abotu this.
alpine sable
its okay 🙂
pale kestrel
If you have seen both euler and cis
i think i would recommend euler
less writing
$$re^{i\theta} = r(\cos\theta+i\sin\theta)$$
ocean sealBOT
Shuri2060
raven rover
I want to say standard form had the terms in decreasing power
Higher power terms on the left going down to the lower power terms on the right
pine kettle
yup
open folio
somber hare
Given a group A with an associative operation <>, an identity element id, and a function inv : A -> A s.t. ∀a : A. a <> inv a = id && inv a <> a = id, can it be shown that ∀a : A. inv (inv a) = a?
pale kestrel
why must you word it this way?
is that how the original question is given?
Could you not just ask:
For a group $G$, can it be shown for all $g\in G$, $(g^{-1})^{-1}=g$?
ocean sealBOT
Shuri2060
somber hare
Could you not just ask:
For a group $G$, can it be shown for all $g\in G$, $(g^...
That works too
pale kestrel
The way you wrote it was such pain to comprehend 
And yes, you can prove it.
Try.
Any ideas how to start
somber hare
I think the existence of inv does imply that that λx -> a <> x is injective
somber hare
So we have that inv a <> inv (inv a) = id and inv a <> a = id, so then you can extract that inv (inv a) = a
somber hare
What course are you doing
None. Just piddling around with groups. I'm writing my own Prelude for Haskell
somber hare
Well yh this gives me CS vibes
From the multi-character names?
ocean sealBOT
Shuri2060
pale kestrel
Would this be comprehendible to you
somber hare
Yes
pale kestrel
this is usually how the inverse law might be written
Ok, you can get what you want immediately from this
I will write it a bit more formally, though
If the below statement holds for some $g\in G$,
$$(\exists h\in G)(gh = hg = e)$$
we say this $h$ is the inverse of $g$, and denote $g^{-1} = h$
ocean sealBOT
Shuri2060
pale kestrel
(You usually start with the group axioms and then prove all inverses are unique, so the notation g^-1 is well defined)
So if h satisfies the above criteria
we call h: g^-1
Now using this exact definition
We are able to justify (g^-1)^-1 = g
We have the above holds for any g
Hence g is also the inverse of g^-1
Therefore (g^-1)^-1 = g
somber hare
The uniqueness of the inverse is what I wasn't sure about at first. It's weird, because even though I feel like I did prove the uniqueness, it hasn't really sunk in
pale kestrel
Right
So the first 2 things you usually prove
Are unique identity
and then unique inverses
Suppose we have identities a and b
then a*b = a and a*b = b
Hence a = b
Suppose for some g in G, we have inverses a and b
pale kestrel
Then ga = e
Then b(ga) = be
Then (bg)a = b
Then ea = b
Then a = b
We generally omit the group operation * and write it like multiplication
And now you have proven inverses are unique
You can assume the notation g^-1 for the inverse of g
If you like, you can consider the ^-1 operation to be a bijective function
inv : G -> G, denoted by ^-1
The group axiom shows surjectivity. The uniqueness shows it is a well defined function. To show injectivity you need a little more.
somber hare
This is a little harder to parse. Is this right:
Given inverses a and b of g:
By right-inverse
ga = e
Left multiplication by b:
b(ga) = be
(Added) by identity:
b(ga) = b
By Assoc.
(bg)a = b
By left-inverse
ea = b
By left-identity
a = b
pale kestrel
yes if i were to write out my reasoning
Then ga = e (a is inverse)
Then b(ga) = be (left * by b)
Then (bg)a = be (associativity)
Then (bg)a = b (e is identity)
Then ea = b (b is inverse)
Then a = b (e is identity)
Yes
left-inverse/identity is more precise
opaque hinge
How would I solve a question like this?
lone heartBOT
How would I solve a question like this?
pine kettle
How would I solve a question like this?
Use what you know about graphs and derivatives
opaque hinge
Use what you know about graphs and derivatives
I did
but like
for april I got 4hours / 30 days?
but that doesn't make sense
<@&286206848099549185>
lone heartBOT
@opaque hinge Has your question been resolved?
opaque hinge
;-;
lone heartBOT
@opaque hinge Has your question been resolved?
opaque hinge
I'm lost still
lone heartBOT
@opaque hinge Has your question been resolved?
lone heartBOT
@opaque hinge Has your question been resolved?
opaque hinge
ah fk it, no one bothered
sick snow
lone heartBOT
sick snow
I don’t even know where to begin 😭😭
mossy lodge
placid zinc
Expectation is linear. That is:
E[Y] = E[1/k(Z - m)] = 1/k E[Z] - m
sick snow
okay i gave it another go
but idk if i m supposed to get a concrete number??
i found k as an attempt to go somewhere with this but got stuck :"))
jagged imp
the wording of the question seems to imply that you already have the mean and variance of Z
is it not somewhere in a-e?
lone heartBOT
@sick snow Has your question been resolved?
lone heartBOT
@sick snow Has your question been resolved?
tacit arch
The expectation of a constant is just the constant
Also you factored out the constant incorrectly in variance
patent tinsel
A group of 6 women and 9 men must select a four-person committee. How many committees are possible if it must consist of the following:
a. At most of 3 men?
patent tinsel
How do i do this? 15C3?
signal monolith
You can do the opposite
signal monolith
If I'm not mistaken the final answer should be 1170
Ok so do you know what is combination though?
patent tinsel
Yes
patent tinsel
1365?
signal monolith
Yeah yeah
I actually expect you to say 15C4, but is ok
Now the four can me at most 3 men
Which means we have four cases
First case is none ot them is man
Second is only one
Third only two
And fourth only three
There are two ways to solve it
One is calculate the ways of getting at most 3 men
Another way is just take all the possible way minus will the all the four people are men
patent tinsel
One is calculate the ways of getting at most 3 men
Can you show me how u will do it if this is what you use? 
Like in formula form or something @_@
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
what does x: mean?
high badger
i think it just means that highlight the range of x when x(3-x) <0 is valid
warm flame
f(x)=2/(3+e^x)
lone heartBOT
f(x)=2/(3+e^x)
warm flame
I suck at Domains and Ranges a bit, how would I solve this easily?
is a calculator necessary?
vale wigeon
no, you do not need a calculator here.
you might find it helpful to note that your function is monotone (specifically, monotone decreasing) which will help a lot with finding the range
it is also helpful to note that e^x is always positive, so 3 + e^x is also always positive and so no division by zero will ever occur
warm flame
you might find it helpful to note that your function is _monotone_ (specifically...
yeah it's decreasing but how would you write this
vale wigeon
write what
warm flame
it's monotone decreasing right? but how would you write this out in set notation or something
is it the same as the domain anyway?
vale wigeon
set notation is not appropriate to write "f is monotone decreasing"
no, the statement that f is monotone decreasing is not the same as the statements "the domain of f is ___" or "the range of f is ___"
lapis valley
Can someone explain why it can go from top to below
lone heartBOT
Can someone explain why it can go from top to below
vale wigeon
persumably you have Y = aX + b?
lapis valley
This is regarding linear transformation of a random variable
lapis valley
persumably you have Y = aX + b?
Yes
lapis valley
But i dont understand why sigma y P(Y=y) can change to sigma x P(X=x)
vale wigeon
they replaced y with ax + b
Y = y thus become Y = ax + b, which is equivalent to aX + b = ax + b, which is equivalent to X = x
vale wigeon
why would E(Y) become E(X)
vale wigeon
we're only messing with the right hand side here.
vale sapphire
The expected value of X is the sum of x*P(X=x), not (ax+b)*P(X=x) ; as Ann said, only the RHS is manipulated here
lapis valley
yea so the expected value of Y is the sum of y*P(Y=y) right?
so how come we can just plug P(X=x)
.close
lone heartBOT
vale sapphire
Did you really want to close?
lone heartBOT
Available help channel!
lapis valley
ya ill just ask my friends ltr
lone heartBOT
ya ill just ask my friends ltr
vague pumice
lone heartBOT
vague pumice
Is this still counted as a upper triangular?
high badger
as long as the entries below diagonal is 0, i think its called upper triangular, there for it probably still counts
supple tundra
lone heartBOT
supple tundra
The correct sketch is one on the left, my sketch is on one on the right
It seems in the correct sketch, there is a concavity change
How would I infer this without finding further derivatives?
vale wigeon
well you know that y'(0) = 0
but for x close to 0 you have y' > 0
so the derivative is increasing, at least locally
split cloud
lone heartBOT
vale sapphire
Channel occupied
alpine sable
oh ok
vale sapphire
Do you know how to factor a root?
covert agate
do you know factor theorem
split cloud
ye
covert agate
do you know polynomial division
split cloud
no
do i need it for this?
i found this video
the factored form he got looks like how i should get it
but i dont get how he got it
this is the answer btw
vale sapphire
You do kind of need it for this (well, it makes things simpler)
So yeah, find a good resource on long division/polynomial division (same thing, different term)
But the crux of the problem is that if you know P(k)=0, then you can write P=(X-k)Q with Q another polynomial
split cloud
.close
magic cove
lone heartBOT
magic cove
Any suggessions for this question
lone heartBOT
@magic cove Has your question been resolved?
magic cove
oh i made a different one
Oh we extended pq in the opposite directions
@high badger
magic cove
ok gimme a sec
Sure. Any help will be really helpful.
@high badger sorry for disturbing but did you get any answer yet?
high badger
yea ive redrawn the diagram and figuring it out
magic cove
oh ok thanks for helping btw.
high badger
i could not solve it but a few points i have found out, idk whether they can help you or not but maybe youve missed it (or not and were still stuck but lets see)
angle PRQ=angle PQR (tangent properties)
angle RQC=angle RBC=180-angle CBA
i also figure that if CBA+CAB=ARP+APR, then RAP=ACB (our objective), but im still stuck
its not really much more info but i hope it helps :P
lone heartBOT
@magic cove Has your question been resolved?
magic cove
If i can somehow prove thag pd is parallel to rs
Then pr = da
And /_a = /_c
@high badger
lone heartBOT
magic cove
.reopen
lone heartBOT
✅
lone heartBOT
@magic cove Has your question been resolved?
runic gorge
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
runic gorge
79.36 is 6% of n
alpine sable
runic gorge
ok
lone heartBOT
@runic gorge Has your question been resolved?
sterile idol
79.36 is 6% of n
Can you write a linear equation for this?
sour sparrow
3x=3
tame falcon
Please clarify what your question is, what exactly you have tried so far, and where you are stuck.
What you've sent so far is an equation with nothing else.
tame falcon
Okay, so you wish to solve for the unknown variable x here?
sour sparrow
yes
tame falcon
Alright.
pine kettle
If you know the ans why you asking?
Maybe they wanted clarification
@sour sparrow do you need help with anything else?
pine kettle
It's ok
lone heartBOT
@sour sparrow Has your question been resolved?
lone dagger
-helpers math
lone heartBOT
-helpers math
wide raven
,rotate
ocean sealBOT
lone dagger
This is the question
wide raven
what is this?
lone dagger
r
placid zinc
Completing the square works, but it would be much easier to instead expand the right
wide raven
ohk
placid zinc
The steps look good. Not too easy to check for no mistakes
lone dagger
Im not too sure how to do that tbh, I got this from pacing a video, could u show how to complete it with expansion?
placid zinc
You can complete the square but you can't expand a binomial? That's very, very backwards haha
Have you heard of FOIL or rainbow method or something similar?
lone dagger
never
placid zinc
Give FOIL a quick Google imo
placid zinc
Not my kind of thing. Perhaps someone else might.
versed elm
(x-r)^2 =x^2-2xr+r^2
and then u times that by q
qx^2-2qxr+qr^2
and then just add 7 at the end
versed elm
it's q(x-r)^2+7 right
so u expand (x-r)^2 first
and then times that by q
and then add 7
lone dagger
can u solve the whole thing with expansion, I want to study the steps thoroughly to understand
like with numbers
versed elm
huh?
lone dagger
like can u solve it with numbers normally
like i did, but i used square, can u use expansioon
lone dagger
thank you
versed elm
3x^2-12x+p=q(x-r)^2+7
3x^2-12x+p=q(x^2-2xr-r^2)+7
3x^2-12x+p=qx^2-2qxr-qr^2+7
qx^2=3x^2
q=3
-2*3xr=-12x
-6xr=-12x
r=2
-3*2^2+7=p
p=-5
u might wanna check ur p again
?
versed elm
u r very welcome
lone dagger
@versed elm
sorry, but could you explain with words what u did
I apologise for bothering
versed elm
it's okie
the main concept here is expanding square
so something that is in the form of (a-b)^2 can be expand as a^2-2ab-b^2
because (a-b)^2=(a-b)(a-b)
and you would have a(a-b)-b(a-b)
and so on
like the others said, check foil method and try to understand what's going on in that method
then it should be a lot easier
lone dagger
oh so its mostly based off of foil
versed elm
yeah tbh I didn't learn it with foil and I can't remember how I learned it cuz it was ages ago so I can't explain it....QwQ, but I googled foil and it's a great method , 120% recommending
lone dagger
okok bett
versed elm
okie, try to do the problem after searching up
lone heartBOT
@lone dagger Has your question been resolved?
runic gate
lone heartBOT
oak perch
d(x^4)=4x^3dx
runic gate
d(x^4)=4x^3dx
oh okok
oak perch
So (1/4) dt/sqrt(1+t) where t=x^4 and (2(sqrt(1+t))’=1/sqrt(1+t) that’s why you have 1/2, (1/4)*2
runic gate
what about 41
runic gate
So (1/4) dt/sqrt(1+t) where t=x^4 and (2(sqrt(1+t))’=1/sqrt(1+t) that’s why you ...
okok thx
oak perch
41 is not hard better you figure it out yourself, using 3=e^(In3)
oak perch
And (t^a)^b=t^(ab)
runic gate
thankyou!
oak perch
Np
runic gate
.close
lone heartBOT
runic gate
question
oak perch
41 or still 40?
runic gate
then will be 1/3
oak perch
What?
d(rx)/dx=r
How the hell you got 1/3….
The derivative of constant function is 0
oak perch
Np
lone heartBOT
Available help channel!
misty bobcat
lone heartBOT
misty bobcat
any ideas how to solve this liimit
?
probably is meant to Lhospital rule
type is like 1^(does not exist), i dont know how to move further
ocean sealBOT
Ansh
ocean sealBOT
Ansh
little drum
e^bracket ?
Yes.
And I hope you can now solve the limit within the bracket pretty conveniently
misty bobcat
still I dont get it, how did you come up with this form
i ended up with e^( (1/x) ln((1+x)^1/x/e))
ocean sealBOT
Ansh
tacit arch
Do you know the definition of the remainders?
what's the earliest thing you don't understand?
$e^x$ ?
ocean sealBOT
riemann
tacit arch
I can't see what you're looking at. either take a picture or screenshot
what in the convoluted taylor remainder formula is this
do you have a name or textbook source for this result
oh ok maybe it's this one
https://en.wikipedia.org/wiki/Taylor's_theorem#Explicit_formulas_for_the_remainder
"Lagrange and Cauchy forms of the remainder"
Show the other two
I really doubt it's the one in your picture
Probably peano
or lagrange actually
Do you have one that looks like this?
Alright I think you can start calculating pieces of it then
Every term in the remainder has the nth derivative. Take the derivative of your function and evaluate at your specified c
lone heartBOT
@hasty bramble Has your question been resolved?
tacit arch
Do you have one that looks like this?
if you can find in your notes a remainder that looks like this, you're basically done. or maybe if you find what your $\varepsilon(x^{n+1})$ equals we can help. You just need to show your $R_3$ is nonnegative for all $x$, which is pretty easy.
ocean sealBOT
riemann
versed crater
can anyone think of a fucntion that goes from a curve to a straight line
pine kettle
,w plot e^-x
ocean sealBOT
versed crater
is there nothig for example that would go from 1,4,7 to 9-infinty
like whe x is 1 y=1 etc
tacit arch
can anyone think of a fucntion that goes from a curve to a straight line
these are usually done piecewise
grave matrix
$S = M_n(\mathbb{R}$ where $n \geq 2$ and $A \star B = \frac{1}{2} (AB + BA)$
tacit arch
$S = M_n(\mathbb{R}$ where $n \geq 2$ and $A \star B = \frac{1}{2} (AB + BA)$
what are you trying to show? this is a group?
tacit arch
Right but you specified a relation $\star$ and want to compute its inverse
ocean sealBOT
riemann
tacit arch
so you're just trying to find the inverse?
grave matrix
No, I'm trying to determine whether the inverse exists
I've just defined a set and a binary operation
If S were a group, then by definition an inverse would exist
grave matrix
Right
If an inverse exists, I'd imagine I want to find some way to find a way of expressing it
If it doesn't, I'd want to find some matrix A that has no inverse, I suspect
I'm a little stuck on moving past $AA^{-1} + A^{-1}A = 2Id_n$
ocean sealBOT
Waes (Wires)
tacit arch
Plenty of matrices don't even have inverses
so is that enough?
or did you mean $GL_n(\R)$ instead of just all square matrices?
ocean sealBOT
riemann
grave matrix
Nah I did mean $M_n(\mathbb{R})$
ocean sealBOT
Waes (Wires)
grave matrix
ik GL(n, C) is a group under matrix mult.
tacit arch
Then how do you know $A^{-1}$ exists?
ocean sealBOT
riemann
grave matrix
This might be a notation thing
tacit arch
So you don't mean inverse matrix?
grave matrix
No
I mean the inverse under the star function I defined
i.e. A*B = 1/2 (AB + BA)
Although maybe that should extend?
tacit arch
Probably don't want to use that notation then
grave matrix
Unfortunately it's exactly the notation my course uses
tacit arch
dafuq
grave matrix
Most of the group theory work done so far has not involved matrices tho so interpreting a^(-1) as the inverse of a under some given operator is not too difficult to grasp
But obvs this is confusing for matrices
tacit arch
can you take a picture of what the original question is asking for
tacit arch
I guess the inverse element under $*$ is the inverse of the matrix itself.
tacit arch
**Waes (Wires)**
by this calculation
ocean sealBOT
riemann
grave matrix
Yh I might have to go with that
And then ofc that means the inverse can't always exist (say if det A = 0)
.close
dim carbon
Hello, I have a question about calculus. Using calculus of variations, how can you find the shortest path between two points, where the line cannot cross a specific region?
dim carbon
.close
south totem
lone heartBOT
knotty spire
what have you tried so far?
south totem
Idk I've never come across this kind of question
I've found point of intersection but applying it to solve for A is something I have no clue about
south totem
Wait let me try substituting it in
wtf
youre a wizard
thank you
bye
🤣
.close
astral breach
I have a Poisson distribution task and managed to answer other questions but I have to give a probability of P(X>=3) (X takes a value of atleast 3). The lambda (or E(X)) is 2. I figured I have to calculate the sum 2^k / k! * e^-2 for all k values from 3 to infinity. As the k grows, this 2^k/k! gets smaller and smaller so it should be some kind of geometric progression and concentrate (idk the correct term) to some certain value? If so, how can I get the value, if not, how is it calculated?
finite flax
I have a Poisson distribution task and managed to answer other questions but I h...
$P(T \ge t)=e^{-\lambda t}$
ocean sealBOT
Disorganized
astral breach
In my case then it should be e^-6?
finite flax
0.002478752176666... 🤔
this feels too easy
I did nastier shit than this in my undergrad
when this came up
I have a book at home but it isn't on me
<@&286206848099549185>
finite flax
In my case then it should be e^-6?
that's what I used
astral breach
The answer doesn't match tho :/
finite flax
what is the answer
astral breach
0.323
tacit arch
I have a Poisson distribution task and managed to answer other questions but I h...
P(T >= t) = 1 - P(T < t)
astral breach
I am dumb 😦 I thought it like it and I had already calculated P(x<=3)
finite flax
?
you already calculated the answer?
how.
I am expecting an integral
so we can sum-up the values from 0 to 3
tacit arch
Poisson distributions are discrete
finite flax
^ yup
tacit arch
so it's just a sum of 3 terms or something small
finite flax
but I remember doing something funky with the e 😛
tacit arch
P(T >= t) = 1 - P(T < t)
did you get the right answer using this @astral breach ?
finite flax
you reliably divide by the lagrangian or something
astral breach
did you get the right answer using this <@!193024276515913729> ?
sec, jumped behind the desk
It should be correct yes. I just used previous answers probability (which was that X upmost value is 3 so P(X<=3) instead of P(X<3) and gave up as this seemed too easy anyways. Brain doesn't function correctly after 8 hours of studying >D
finite flax
It should be correct yes. I just used previous answers probability (which was th...
so you just did 1-previous answer?
astral breach
yeah but I lost focust and didn't see it was <=3 not < 3
astral breach
P(X>=3) = 1 - P(X<3) yes. Strictly smaller
astral breach
did you get the right answer using this <@!193024276515913729> ?
Yes, it worked, thanks
.close
gilded vessel
Is this the correct negation:
y != 0 AND (y+1)/y is greater than or equal to 1
tacit arch
what's the original statement you're negating?
gilded vessel
the image
y != 0 AND (y+1)/y is greater than or equal to 1
is the negation of the statement in the image
pale kestrel
not(P => Q)
is
not((not P) or Q)
is
(not(not P)) and (not Q)
is
P and (not Q)
pale kestrel
read what I said and deduce ...
gilded vessel
well what you said is the exact process which i used to work it out myself
but if thats fine then alright
pale kestrel
I'm saying that's how I would approach as well.
keen mulch
lone heartBOT
keen mulch
Q8
lone heartBOT
@keen mulch Has your question been resolved?
alpine sable
alpine sable
NfA for non ants
alpine sable
<@&286206848099549185>
frosty eagle
whats the volume of
a cylinder with
height 8cm
and radius 4cm
alpine sable
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
🥲
lone heartBOT
lone heartBOT
Available help channel!
zenith compass
lone heartBOT
zenith compass
Lol I take statistics as my free electives in my college
zenith compass
An exam coming up?
Yes few days later
zenith compass
I take cal II, modern math logic and intro to stat this semester
little drum
15/52 is when you select one and he's determined to be a burglar
and the probability of catching the other is (16 - 1)/(53 - 1)
coz both sample space and the number of possibilities shrink by 1
zenith compass
Ok
Oh I think I misunderstood the question
I think it is “given that the criminal do bad bad things in 2004, what is the prob of the criminal do bad bad things again”
Lol thank you I get it
.close
wheat oar
I don't know if you are able to help, but if you can, what is the time complexity of this code?
vale wigeon
the code does nothing
doing nothing is a constant-time endeavor
unless you're a human in which case there's something known as fucking around
wheat oar
I think its more of a how many times does the code run type of thing
vale wigeon
however, if the "Do Nothing" were replaced with something more meaningful
that'd be a different story
wheat oar
where the do nothing signifies O(1)
vale wigeon
outer loop runs n/2 times, inner loop runs log(log(i)) times for each i
wheat oar
what would the overall complexity be though? thats where i'm stuck on
bright hedge
Use what Ann said
If the inner loop runs bank many times and that loop is ran blank many times, what would the time complexity be? (Think product)
wheat oar
do you mean that it is O(n)*O(log(log(n))?
which is O(n(log(log(n))))
I am confused as to what to put for i in log(log(i)) since i changes
swift shore
how many values does i take on?
wheat oar
n/2 right?
swift shore
If the inner loop runs bank many times and that loop is ran blank many times, wh...
the problem is, the inner loop depends on the current index of the outer loop
it doesn't seem as simple as multiplying outer * inner
wheat oar
yep
swift shore
lmao
lone heartBOT
@wheat oar Has your question been resolved?
wheat oar
<@&286206848099549185> maybe you can help me with this question?
tacit arch
I don't know if you are able to help, but if you can, what is the time complexit...
if you can write code, you can implement this with a counter and figure this out in <5 minutes
wheat oar
but I am trying to find the time complexity as n approaches infinity
the time complexity of the upper limit
tacit arch
then evaluate the counter for 10^3, 10^4, 10^5 and you'll find a pattern
tacit arch
you'll know because you did it for homework
quasi tangle
A baker famous for his golden snails is planning to build a new bakery. He therefore needs a loan of 5,000,000 to finance the construction. The loan is repaid with DKK 250,000 per year. The loan interest rate for the entire period is 3%.
Set up a recursion equation whose solution describes the repayment of the baker's loan.
Set up a formula for calculating the debt at any time, n, where n = 1, 2, 3, ...
How many years must it take before the baker has repaid the loan
Use Binets formula to solve this:
lone heartBOT
A baker famous for his golden snails is planning to build a new bakery. He there...
@quasi tangle Has your question been resolved?
tacit arch
A baker famous for his golden snails is planning to build a new bakery. He there...
these problems are all over the place
pick one and show what you've done so far
quasi tangle
Set up a recursion equation whose solution describes the repayment of the baker's loan.
yn = y0 * 0,03 + 250.000
y0 is the first 0,03 * 250000
but idk if im right or wrong:/
tacit arch
no
tacit arch
> loan interest rate for the entire period is 3%.
read this again
tacit arch
A baker famous for his golden snails is planning to build a new bakery. He there...
although it seems stupid to set up a recursion formula as a question for my interpretation.
quasi tangle
although it seems stupid to set up a recursion formula as a question for my inte...
Couldnt I just use the interest formula instead?
anyways
quasi tangle
read this again
oh wait