what abt rotations
#help-36
golden cave
wind orbit
and the problem only mentians rotations
sturdy cypress
5 pizzas are AAAA and 10 pizzas are ABAB
so i would do 610/4 + 5 + 10 so that's wrong
it doesn't divide
wind orbit
ya but im wrong too i think cuz im not accoutning for repetitions
bye imma try working it out
sturdy cypress
so there's AABB too and stuff
wind orbit
ya
bitter hamlet
hello i need help with math notes
wind orbit
this ones alr taken
bitter hamlet
okat
wind orbit
16^4
16 AAAA
240 ABAB
||16456||
same
so my first solution did work
are you still here
@golden cave
golden cave
16^4
16 AAAA
240 ABAB
||16456||
btw seems to high
wind orbit
ya but im explaining and i cant think of a differet answe
so then each of the possibilites without the rotations has four rotations
except for 256
golden cave
ye
wind orbit
which are abab or aaaa like he said
golden cave
mhmm
sturdy cypress
it's not too high, you can make 16^4 pizzas after rotations, you divide it by 4 and you get 16 thousand
wind orbit
so we take that out and divide it by four
opal plinth
(I agree with 16456)
wind orbit
and then we add 256
golden cave
(I agree with 16456)
i'm not sure about it becuase it might have rotations
oh wait
i have an idea
opal plinth
They are accounted for
wind orbit
and if we account for the fact that abab and baba are both possible then we subtract 16*15/2 for the baba case
golden cave
They are accounted for
oh yea
wind orbit
and we get (16^4-256)/4+256-15*16/2 which gives 16456
wind orbit
do you know if you got it right
golden cave
yea lol
wind orbit
yay
golden cave
i have one more
There are $8$ identical chairs around a circular table. In how many ways can $5$ people be seated in $5$ of these chairs if Richard wants to sit next to either Surya or Tamas (or both Surya and Tamas)?
(Consider two seating arrangements to be the same if one seating arrangement can be rotated to obtain the other.)
soft zealotBOT
✪~nano-rōnin~✪
golden cave
this is confusing
wind orbit
i feel like you can do a similar thing here with the rotations
winter lava
maybe you can do inclusion-exclusion
golden cave
i feel like you can do a similar thing here with the rotations
yea
golden cave
maybe you can do inclusion-exclusion
?
wind orbit
maybe you can do inclusion-exclusion
definitely
winter lava
next to surya, next to to tamas, and then subtract the times he's next to both
wind orbit
wait do we count the other two people in order
golden cave
wait do we count the other two people in order
?
winter lava
i think you can assume any time a person is in a different chair, it's different
then divide by 8 at the end
golden cave
yea
wind orbit
so it doesnt matter if they switch
winter lava
it does
golden cave
well waht abt yk
winter lava
hmm
wind orbit
14*5! for him to sit next to one person
opal plinth
You don't need to divide by 8 at the end if you just place Richard first btw
wind orbit
so 2 times that for adding both
wind orbit
You don't need to divide by 8 at the end if you just place Richard first btw
oh ya thanks
opal plinth
||2*6*5*4*2 - 2*5*4||
winter lava
yeah that's what i got
golden cave
not sure how u got it
wind orbit
same
winter lava
2*6*5*4 ways richard can sit next to surya
wind orbit
wait i dont get 2*5*4
winter lava
2 because surya can sit either to his left or his right
wind orbit
oh ya
winter lava
then there are 6 choices for where the third person sits, 5 for the fourth, and 4 for the last
golden cave
<@1410748284791689278> are you still here
my moms side quest im still in it
should've told u
5 mins
wind orbit
oh ok
golden cave
back
golden cave
then there are 6 choices for where the third person sits, 5 for the fourth, and ...
oh
i understand
ima read the solution
ty everyone for helping me
.close
final saddleBOT
final saddleBOT
Available help channel!
snow ore
I have this i am doing rewiew and i just want to make sure i have the right a k ,c and d values
final saddleBOT
I have this i am doing rewiew and i just want to make sure i have the right a k ...
snow ore
i got a=1 k=2 c=2 and d=1 this is right
cause my freind got the c vaule is -2
i not sure how he got that
loud sundial
I have this i am doing rewiew and i just want to make sure i have the right a k ...
In the future, you should define what $a,k,c,d$ represent in general because this is not standard notation. \ \
Assuming you're working with a form of $a\sqrt{k(x-c)}+d$, then the correct answer is $a=1, k=2, c=-2, d=1$. If you're working with $a\sqrt{k(x+c)}+d$, then the correct answer is $a=1, k=2, c=2, d=1$.
soft zealotBOT
Civil Service Pigeon
snow ore
Ok however I dont know what i am working with cause the questions is asking me decribe the transfomrations
in this case it would be vertical comprsss by 1/2 then 2 units left 1 uniit down right?
loud sundial
in this case it would be vertical comprsss by 1/2 then 2 units left 1 uniit dow...
why is there a vertical compression
loud sundial
i think its horizontal compression
mhm
horizontal compression with a factor of 1/2
shift 2 units left
recheck your vertical translation
loud sundial
whichever form you pick is irrelevant
snow ore
um
but what if you do the one with minus would you have a differnt answer
i get that it might be like (x-(-2))
loud sundial
but what if you do the one with minus would you have a differnt answer
no
I mean picking the x-c form is probably more intuitive since a positive c means a shift to the right and a negative c means a shift to the left
but it doesn't really matter
x+c would mean a positive c is a shift to the left and vice versa
but whatever form you pick, the function that you're given doesn't change
so ofc there's no way that the transformations can change either
final saddleBOT
final saddleBOT
Available help channel!
radiant walrus
final saddleBOT
radiant walrus
EA and CD are perpendicular to the ground.
The angle EFA = 50 deg and the angle EHA = 30 deg
If AD = 1.5 metres, find the value of GC.
final saddleBOT
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
@radiant walrus Has your question been resolved?
radiant walrus
loud sundial
I'd let $AF=x$ and $HF=y$. See what side lengths you can fill in based on this and trig.
soft zealotBOT
Civil Service Pigeon
loud sundial
Spoiler alert: ||Some side(s) will have more than one way to label them. This is because of similar triangles.||
final saddleBOT
@radiant walrus Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
umbral fable
Only need help with the last part about distance, how do I find the time to reach that distance? do i need to convert into cartesian and operate like that somehow?
final saddleBOT
Only need help with the last part about distance, how do I find the time to reac...
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
honest carbon
Oops sorry. Didn't read about your question.
You know A(t) and B(t), right?
take the difference and take the magnitude of it.
umbral fable
okay so
the position of A is
10t
well
broken into components i suppose
so i should find the cartesian form of both position functions
and then subtract em
is that right?
umbral fable
okay
honest carbon
Like $A(t) = (a\overrightarrow{x} + b\overrightarrow{y})t$
soft zealotBOT
Xwtek
honest carbon
Or even employ a complex number, though that might be too advanced.
final saddleBOT
final saddleBOT
Available help channel!
radiant walrus
final saddleBOT
radiant walrus
EA and CD are perpendicular to the ground.
The angle EFA = 50 deg and the angle EHA = 30 deg
If AD = 1.5 metres, find the value of GC.
i asked this ques before but I did not, due to unavoidable circumstances, reply
lunar gust
what have you tried?
radiant walrus
i have try to find af, fh, ae, gc, cd, but no success.
lunar gust
hmm you may not need those
try constructing line JE, such that J is a point on CD, and JE is perpendicular to CD
and solve the angles within the resulting figure
from there, you should be able to find CG
lunar gust
yep!
lunar gust
welcome+
radiant walrus
.close
sand escarp
help
plucky rover
radiant walrus
bearing?
plucky rover
It's like some angle thing
pliant shore
You've confused that with CBA right
pliant shore
But sure, CBA = 66
pliant shore
Oh bruh
sand escarp
ac = bc
radiant walrus
damn
pliant shore
Yeah how is the diagram wrong lmao
sand escarp
idk my teacher
brave shore
CBA=CAB=66
pliant shore
Okay so the bearing from B: that's going to start from the north arrow above B
And that angle is going to go clockwise until it ends at segment BA
sand escarp
yes
pliant shore
Yeah, so can you figure out what to do to get the bearing?
brave shore
please answer correctly. which one is right?
sand escarp
no
sand escarp
CBA=CAB=66
this
pliant shore
thats why im asking
Well, you could take 90 minus angle BAC
And then that would be co-interior to the bearing
pliant shore
so the ansswer is 156?
Yeah
sand escarp
oh
bruh
i got that but then i asked chatgpt
and chatgpt said its wrong
bruh chatgpt scam
umbral steppe
!nogpt is here for a reason.
final saddleBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
pliant shore
yep, law of cosines is the right appraoch
pliant shore
,w 10^2 = 10^2 + (6 sqrt 2)^2 - 2 * 10 * 6 sqrt(2) cos(x)
soft zealotBOT
pliant shore
,w arccos(3/(5 sqrt2)) in degrees
soft zealotBOT
pliant shore
<@1151031274413228043>did i input something wrong
you should try typing it out on your calculator again
if you rearrange it, you get $\cos x = \frac{10^2 + (6 \sqrt 2)^2 - 10^2}{2 \cdot 10 \cdot 6 \sqrt2}$
soft zealotBOT
south
pliant shore
is your calculator in degrees (not radians)?
pliant shore
indeed, well don't round too early though
soft heart
how??
I did this in the past..but don't remember why the answer is 3
tired walrus
a : b = c : d
looks like "sum of means is 5" means b+c=5
"ratio of two terms" is obscure and confusing though
soft heart
a : b = c : d
looks like "sum of means is 5" means b+c=5
why b+c =5
tired walrus
the middle numbers in a proportion are called the "means" and the two others are called the "extremes".
that's how i read it.
soft heart
oh right
is there any use of
The sum of the squares of the four no. is 50
two terms .
a+b+c+d = 1+3
no?
tired walrus
is there any use of
> The sum of the squares of the four no. is 50
a^2+b^2+c^2+d^2 = 50
tired walrus
two terms .
a+b+c+d = 1+3
no?
i will be honest i have no idea what "ratio of two terms" means here.
soft heart
ok
final saddleBOT
@soft heart Has your question been resolved?
prisma cave
Hello great math fellows. I need some help regarding a question I have in inner products in linear algebra.
So we know that:
<a,b> = |a| |b| cos(t), and also:
<a,b> = (a_1)(b_1)+(a_2)(b_2) + ... + (a_n)(b_n)
My question is regarding the definition of the cos. From above we can find cos(t) as:
cos(t) = (<a,b>)/(|a| |b|)
Now what if we use another inner product? then the above statement still holds true?
And by defining/using the new inner product, did we just define a new geometry? Or this statement works only for standard inner product?
Thanks.
final saddleBOT
Hello great math fellows. I need some help regarding a question I have in inner ...
desert mantle
yes every inner product defines a new geometry
a different way to measure angles etc
different lengths
different things that are orthogonal
formal trail
the cos(t) formula is a theorem using the euclidean inner product and a definition using other inner products
(we know that it is possible to define angles with that formula due to cauchy-schwarz)
final saddleBOT
@prisma cave Has your question been resolved?
prisma cave
Thanks you very much @desert mantle and @formal trail . Understoon. Much appreciated.
So generally for any two non-zero vectors a, and b, if <a,b>=0, then then angle between them will be pi/2 (by geometry of the inner product).
desert mantle
or -pi/2, yes
lavish crescent
can someone confirm my working
final saddleBOT
can someone confirm my working
timber plume
can someone confirm my working
It would be better to write in one column
stone wagon
,w integral (sqrt(x) - 1/sqrt(x)) from 1 to 4
soft zealotBOT
stone wagon
can someone confirm my working
yup
timber plume
where the steps follow this structure:
step 1:
step 2:
step 3:
lavish crescent
It would be better to write in one column
sure but besides that is everything good
timber plume
sure but besides that is everything good
let me check
I think they are looking good for now, unless if im missing something
final saddleBOT
final saddleBOT
Available help channel!
proud igloo
maybe im just silly
final saddleBOT
maybe im just silly
junior token
maybe im just silly
what have you done so far?
I think you’re supposed to assume C_{12} is horizontal
final saddleBOT
final saddleBOT
Available help channel!
round kraken
How do I know which angle is opposite to equal sides? I mean i actually in most casesis not able to identify which one angle will be considered oposite to the line?
final saddleBOT
How do I know which angle is opposite to equal sides? I mean i actually in most ...
ivory bear
How do I know which angle is opposite to equal sides? I mean i actually in most ...
!xy
final saddleBOT
How do I know which angle is opposite to equal sides? I mean i actually in most ...
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.
tired walrus
How do I know which angle is opposite to equal sides? I mean i actually in most ...
do you mean angles in a triangle, or what
round kraken
do you mean angles in a triangle, or what
Yeah trinagles. Let me show you a example
In example 6 -
tired walrus
,rccw
soft zealotBOT
round kraken
You can see that <B and <C are two angles opposite to two equal sides as written in the solution
tired walrus
yeah, they are.
you should look at only triangle ABC and temporarily ignore everything else in the diagram.
angle B is opposite to side AC
and angle C is opposite to side AB
final saddleBOT
final saddleBOT
Available help channel!
feral knoll
Hi
feral knoll
Can anyone help me study a few PDFs if they are free
thin cloud
feral knoll
Can I put PDFs herr
final tangle
post snapshots
don't post files that could potentially be corrupted and cause a world of hurt
thin cloud
yeah I don't want my pc to mine bitcoin
feral knoll
How to check if they are corrupted
onyx peak
just post pics
feral knoll
Ok
final tangle
antivirus, but people are wary of downloading random files online
vague anchor
How do I know which angle is opposite to equal sides? I mean i actually in most ...
Can we just most of time draw a bisector of angle
The side it will meet first should be opposite to it
round kraken
Can we just most of time draw a bisector of angle
The side it will meet first s...
Didn't understand
vague anchor
Didn't understand
I mean u know the line drawn to bisect(divide angles into 2 equal parts) angles
round kraken
Yeah, I know
vague anchor
U mean u want help with all these
thin cloud
damn talent search, what question that you need help
thin cloud
U mean u want help with all these
guys stop
feral knoll
I can only do one question?
thin cloud
1 at the time
vague anchor
Yeah, I know
Then extend that line it will meet a line of the polygon it will be opposite to it most probably tho I'm not sure
vague anchor
So 5 right? Do u know AM GM
plucky rover
Then extend that line it will meet a line of the polygon it will be opposite to ...
Gonna ask you and Yuto to move to another channel since this is occupied by another user now
vague anchor
It guarantees that no y + 1/y be less that 2
feral knoll
x²+x+1= 0 what is x²+1/x
vague anchor
Gonna ask you and Yuto to move to another channel since this is occupied by anot...
Huh I'm quitting that conversation
plucky rover
Cool cool
vague anchor
x²+x+1= 0 what is x²+1/x
Ya I'm talking the same rn
umbral steppe
Arena master grand master?
the arithmetic mean-geometric mean inequality.
feral knoll
I don't know what that is
vague anchor
Which grade/standard?
feral knoll
9th
vague anchor
Oh that it was obvious i guess
feral knoll
Pls tell me
vague anchor
So it guarantees that
a+b/2 >/= sqrt(ab)
slim kraken
since when do they teach am gm in grade 9
i mean geometric progression itself comes during 11th grade
vague anchor
So now can be put x^2 and 1/x^2 in the variable a and b
This we'll get 1/x^2 + x^2 >/= 2
It means that it will be always greater or equal to 2
feral knoll
Where is 2 frm
vague anchor
Bro show ur work what have I told have u implemented
Bro in sqrt 1 will remain
From a+b /2. 2 will come to RHS
feral knoll
Oh ok
vague anchor
Bye going to have supper
vague anchor
Indian friend pls come to help me if you can
I'm Indian btw
feral knoll
So there is no option greater than 2
Minimum value is 2
Ok 2 theb
feral knoll
Wtf is vieta
vague anchor
Wtf is vieta
Sum and product of roots
candid pulsar
Wtf is vieta
sum and product of roots
ivory bear
I'm Indian btw
hello there. i dint attempt your ques that you gave me, mb. will do it in a few upcoming days...
lunar olive
Never seen a paper with other language like that
ivory bear
Sum and prdocst of rort
$\alpha+\beta= \frac{-b}{a}$
soft zealotBOT
Dhairya
ivory bear
$\alpha \beta=\frac{c}{a}$
soft zealotBOT
Dhairya
feral knoll
Idk that
candid pulsar
is that malayalam
feral knoll
Yess
candid pulsar
damn almost didnt notice
ivory bear
the roots of a quadatic equation $ax^{2}+bx+c=0$
soft zealotBOT
Dhairya
thin cloud
the answer is -1
ivory bear
maybe you dont know it and might overdose you but ig it was necessary
lunar olive
What is the question btw
candid pulsar
x²+x+1= 0 what is x²+1/x
this?
candid pulsar
theres a funny way to solve problems like this
candid pulsar
if you have x^2 + 1/x^2 then you almost always need x + 1/x
thin cloud
if you have x^2 + 1/x^2 then you almost always need x + 1/x
yeah
ivory bear
theres a funny way to solve problems like this
😔 yes fr
thin cloud
x^2 is not even positive xD
feral knoll
x^2+1=-x => x+1/x=-1
How did it go to that
lunar olive
(x- 1/x)^2 +2
candid pulsar
How did it go to that
divide by x
feral knoll
What.
lunar olive
How did it go to that
Dividing the LHS and RHS by x
vague anchor
AM-GM won't work here
My knowledge 🗑️
feral knoll
Ok let's do another
thin cloud
ngl my first look I crossed out the answer -1 cuz I thought it can't be negative
thin cloud
Ok let's do another
So you solved the question?
vague anchor
What if we divide the equation by x
candid pulsar
What if we divide the equation by x
yeah thats it
thin cloud
What if we divide the equation by x
yeah that's what i did
leaden moon
i assume that's the question?
feral knoll
No the question continues with another question
leaden moon
No the question continues with another question
what's the question?
thin cloud
okay which one
leaden moon
i just joined in this channel
feral knoll
It doesn't I just mean I needa study more
vague anchor
Then why isn't c the answer
leaden moon
is this the qeustion or what?
thin cloud
Then why isn't c the answer
it's the answet
vague anchor
is this the qeustion or what?
Yes
leaden moon
because im confused out here
vague anchor
it's the answet
Ohk let's go then
leaden moon
realize that $x^2 + x + 1 = 0$ has no solutions in reals
vague anchor
It doesn't I just mean I needa study more
Ig u should open another channel for new question
soft zealotBOT
1 divided by 0 equals Infinity
vague anchor
It's been a long
feral knoll
Star how do you do it
candid pulsar
Star how do you do it
can you find an obtuse triangle in there
leaden moon
wait wait
feral knoll
Idk
leaden moon
so look at this
thin cloud
Star how do you do it
feral knoll
Yeah
leaden moon
first off
what's the total angle of a pentagon?
there's this formula you can use: $180(n - 2)$ in degrees
soft zealotBOT
1 divided by 0 equals Infinity
feral knoll
360
leaden moon
where $n$ is the total of sides
feral knoll
I know that
soft zealotBOT
1 divided by 0 equals Infinity
leaden moon
well a pentagon has 5, not 4
leaden moon
it does not matter about the names
feral knoll
Alright pls continue
leaden moon
but you still needs to count the sides
it's kinda easy to consider what's the total angles in a triangle
vague anchor
but you still needs to count the sides
Bro he is in 9th standard/grade
leaden moon
Bro he is in 9th standard/grade
well uhm
leaden moon
Star how do you do it
you see, the angles in a star basically are created from the angles from a pentagon and 5 triangles
so add the measurements you got and you got your answer
feral knoll
But
feral knoll
Only need the pointy angles sum
candid pulsar
theres a really clever method
feral knoll
Pls share
feral knoll
Blurple W colour
candid pulsar
ok i think i can put it this way
sullen gale
you can just angle chase, no?
candid pulsar
well yeah that too
feral knoll
What's angle chase 😢😢🔥
vague anchor
Blurple W colour
Hey there
We came to have SMTH like hit and trial
Assume angle to be 60° and add all of em is 300°
sullen gale
you know the red angle, so you can find the green angle, and hence the black angle 
and then you multiply everything by 5 
feral knoll
But I don't know the red angle
signal adder
you know the red angle, so you can find the green angle, and hence the black ang...
Well it's not a regular Pentagon though
vague anchor
The star is random here
leaden moon
you know the red angle, so you can find the green angle, and hence the black ang...
no, i don't think he knows what those angles measured to
signal adder
just a Pentagon
leaden moon
you know the red angle, so you can find the green angle, and hence the black ang...
i can notice the 5 triangles are similar
vague anchor
It means it also includes symmetric star
candid pulsar
you can notice the symmetry and try finding the angles in the pentagon
leaden moon
and there are vertically opposite angles
vague anchor
i can notice the 5 triangles are similar
Note: they can be congruent in special case
sullen gale
the sum of the external angles is 360º
candid pulsar
you'll get the sum
loud sundial
the sum of the external angles is 360º
feral knoll
you can notice the symmetry and try finding the angles in the pentagon
You wrote on paper for me? 🥹
candid pulsar
i cant draw on texit you know
sullen gale
the sum of the external angles is 360º
this means the sum of all the green angles is 360º
can you take it from here?
yes, very
candid pulsar
you know the red angle, so you can find the green angle, and hence the black ang...
i dont think we know the red angle...
leaden moon
sum of all external angles of a polygon always sum up to 360
thin cloud
you can notice the symmetry and try finding the angles in the pentagon
yes that's also what i did
leaden moon
you know the red angle, so you can find the green angle, and hence the black ang...
i think i see how to do it now
thin cloud
that's much easier
sullen gale
i dont think we know the red angle...
yes, never mind that, I forgot it wasn't regular
feral knoll
In the exam I have 2 hours for 20 questions
candid pulsar
yes that's also what i did
also sorry its 108 * 5 here
leaden moon
yes, never mind that, I forgot it wasn't regular
wait
sullen gale
but we know the sum of the green angles
leaden moon
you know the red angle, so you can find the green angle, and hence the black ang...
let's take this diagram for example
we know the sum of the green angles are 360
signal adder
Yo this lowk getting overcomplicated
leaden moon
mark the other angle of the triangle as yellow
signal adder
Can we choose one guy to do this or something
thin cloud
I vote for blurple
signal adder
Same
sullen gale
but we know the **sum** of the **green** angles
I think this is the fastest way
feral knoll
I also vote for blurple
sullen gale
okie
signal adder
Welp you're the judge
sullen gale
I shall leave then 
leaden moon
Welp you're the judge
lel
feral knoll
Where is blurple thi
candid pulsar
im here
candid pulsar
do you get why its 180 - A - C though
candid pulsar
yeah the obtuse one
if you add all you should get the sum of angles of a pentagon
which is (5 - 2) * 180
= 540
and can you find the sum in terms of the five angles now
candid pulsar
what about each of the pentagon angles
candid pulsar
you can notice the symmetry and try finding the angles in the pentagon
two are already marked here
just say the other three
feral knoll
Ok so
Theres 180-A-C
Then there's 180-(e+b)
180-(b+d)
180-(e+c)
180-(b+d)
That's it
I think
candid pulsar
you repeated one
feral knoll
Oh
sullen gale
I really think there's an easier way without variables 
but I can show you after you finish
feral knoll
180•5-(2(a+b+c+d+e))= 540?
candid pulsar
correct
feral knoll
Oh I thought I missed
candid pulsar
now its a matter of algebra
candid pulsar
correct
feral knoll
Yaasy
candid pulsar
I really think there's an easier way without variables <:eeveethink:601029006418...
yeah go on
sullen gale
this is more or less the same idea…but you can see that the green angles sum to 360º
feral knoll
Yeah
sullen gale
the red angles too
feral knoll
Yeah
oak blade
Yo
sullen gale
so, the sum of the green and red angles is 360*2
feral knoll
Ok that's also right
sullen gale
thank you 
sullen gale
if you're done, you can .close this channel 
sullen gale
You play chess?
yes, I do! but we should move this to #chess-go-shogi
sullen gale
me too, good luck with your studying!
feral knoll
me too, good luck with your studying!
Thank you
sullen gale
if you're done, you can `.close` this channel <:happy:908558103992225822>
or I can close it for you 
.close
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feral knoll
Uhm blurple are you free
sullen gale
you can always open a new one again if you need help
feral knoll
@blurple
sullen gale
@candid pulsar
final saddleBOT
Available help channel!
candid pulsar
Uhm blurple are you free
maybe
i could try to help
final saddleBOT
maybe
i could try to help
candid pulsar
.close
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feral knoll
Dm?
candid pulsar
k
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radiant carbon
final saddleBOT
signal adder
For the first 4 and 6
signal adder
That would mean an increase of the score by 10
And so the tens digit would increase by 1
So the only possible tens digit for the initial score is 7
tired walrus
you should write out what the digits look like on a 7-segment display
signal adder
Yea
radiant carbon
yeah i did this
tired walrus
so think about the first +4
the visible part of the score, and so of the last digit, is unchanged
which digit from {2, 3, 7}, when increased by 4, gives another digit from {2, 3, 7}?
tired walrus
did you retrace all the intermediate score readings
show your work for how you got 303
tired walrus
sorry, typo on my end.
i intended to type: show your work for how you got your answer
can i see it
radiant carbon
yes, it was convoluted though so lemme try to explain it
wary siren
is b correct? 297
radiant carbon
initially the number is {2,3,7} {2,3,7} {2,3,7}. after the first 4, it didn't change, so we can deduce that the digit in the one's place is 7. after this, 6 is added, which means that {20, 30, 70} + 13 = {2, 3, 7} {8, 9, 0} {2, 3, 7} - the only possible combination for this is 70 + 13 = 83 which gives a valid number in both the tens and ones place. it didn't change until after the 3rd 6, so 83 + 4 + 6 = 93 is still {2,3,7} {8,9,0} {2,3,7}. adding the third 6 to this gives us 93 + 6 = 99 -> {2,3,7} {8,9,0} {8,9,0} which lines up. after the last 4 it goes to {200, 300, 700} + 103 = {2,3,7} {8,9,0} {2,3,7}. the only possibility of this is 200 + 103 = 303, so i just proved myself wrong nice
radiant carbon
is b correct? 297
nope
this problem hurt my brain
and took way longer than it should
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@radiant carbon Has your question been resolved?
rain sentinel
final saddleBOT
tired walrus
do it
ornate tree
yeah sure
plucky rover
Ann I need your gif stash
plucky rover
That's a very pretty calculator
Oh right I'm supposed to check your work
You've multiplied the fractions incorrectly
3* (7y/4) is not 21y/12
rain sentinel
is it 21y/4
plucky rover
Yes
rain sentinel
why?
leaden moon
you remembered how to multiply fractions?
rain sentinel
and then do i do -8*4
leaden moon
yes
rain sentinel
and then do i do -8*4
?
leaden moon
you multiply the numerator with the numerator
and multiply the denominator with the denominator
that's why it's 21y/4
leaden moon
so it should be $\frac{21y}{4} - 8y = 10$ right?
soft zealotBOT
1 divided by 0 equals Infinity
opal plinth
Either you do -8\*4/4, or you multiply *every term of the equation* by 4
I recommend the latter
leaden moon
i recommend make the denominator the same
rain sentinel
1 divided by 0 equals Infinity
yes
leaden moon
then remove the denominator
rain sentinel
so im left with 21y-32y=40?
rain sentinel
and y = 40/-11
leaden moon
now substitute that into x
opal plinth
= -40/11, but sure
leaden moon
and y = 40/-11
there are other ways to write fractions so i don't mind that
leaden moon
now substitute that into x
anyways
leaden moon
i don't think that's right
rain sentinel
?
plucky rover
x is 7y/4
leaden moon
oh im sorry
plucky rover
Now you know y
leaden moon
my bad
plucky rover
So substitute it into x
opal plinth
Yes, x = -70/11
plucky rover
Yup you're right
leaden moon
i gotta fix my calculation asap
rain sentinel
thanks guys
plucky rover
I just went along with you smh
rain sentinel
.close
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warm python
Part(b)
warm python
I'm just confused
vital crag
Did you try finding F(y) = P(Y <= y) first
warm python
Did you try finding F(y) = P(Y <= y) first
NO, I had something else in mind
Y(x)=1/X(x)
the problem is this doesn't work everywhere does it
versed crater
X doesn’t take x as in input
vital crag
Did you try finding F(y) = P(Y <= y) first
Your first step after this should be F(y) = P(1/X <= y)
versed crater
By first principles you can go through the CDF
warm python
Your first step after this should be F(y) = P(1/X <= y)
so I consider $\frac{1}{5} ≤y \frac{1}{3}$ , $\frac{1}{3}≤y≤1$, $y≥1$
soft zealotBOT
wai
versed crater
Use \geq or \leq
vital crag
Your first step after this should be F(y) = P(1/X <= y)
i guess to be more clear, i should say
$F_Y(y) \le P(1 / X \le y)$ because after some algebra, the right side will have $F_X$ in terms of some function of $y$
soft zealotBOT
riemann
vital crag
and then you'll plug in your result from a)
versed crater
Equals
versed crater
You wrote the cdf is le the probability
versed crater
@vital crag
vital crag
what ?
versed crater
You wrote cdf \le P(…)
versed crater
Yuh
warm python
Kind of stupid question, but formally how's a distbution defined
vital crag
worldly mesa
formally a distribution is a measure
warm python
also , I'm using all of statistics to self study, bad idea?
vital crag
so for the first interval and 2nd iterval it's 1/4
this was your answer?
warm python
yes
vital crag
doesn't look right. your answer should have y in it
warm python
why, f_X(x) doesn't
vital crag
i guess to be more clear, i should say
$F_Y(y) \le P(1 / X \le y)$ because aft...
What did you do after P(1 / X <= y)
worldly mesa
the probability density function is the derivative of the the cumulative density function
warm python
yes, and f_X(x) is a PDF
vital crag
i think you're underestimating how much calculation you need to do in this problem
After P(1 / X <= y) there's a few lines of algebra to arrive at F_X(1/y), especially with the three cases
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Available help channel!
old quarry
final saddleBOT
old quarry
yes this is what i got
willow tiger
you sure?
willow tiger
somehow i got $y=\int xe^{\beta x} dx$
soft zealotBOT
Roy
ivory bear
speak in human pls
❌
old quarry
u dont know what integrating factor is?
old quarry
then i dont think u can help much with this question
willow tiger
i mean ik everything until uni year 1
old quarry
oh ur in uni
willow tiger
lemme search it up
willow tiger
oh ur in uni
no im 10th grade
old quarry
bro
umbral hamlet
what was your integrating factor
willow tiger
yes
old quarry
what was your integrating factor
e^(ax)
umbral hamlet
okay that seems right, your integral seems fine too i think
now just multiply both sides by e^(-ax)
to isolate y
old quarry
yeah okay and then?
umbral hamlet
then thats your f(x)
willow tiger
lemme read this article 2 min you guys talk until then
umbral hamlet
you have a +C right
old quarry
yes
umbral hamlet
hm okay ill look
umbral hamlet
they dont all have an x^2?
are you sure the first and last options dont work
i havent really checked your work thoroughly or done this out
but i think its plausible those ones work
umbral hamlet
does it tell you how many should be correct
umbral hamlet
there's a special case when a+b=0
compute that one separately and you'll get a diff solution
umbral hamlet
did the problem say a+b cant be 0?
old quarry
uh no
umbral hamlet
and a and b are arbitrary real numbers
so this case will absolutely correspond to functions in our set
old quarry
ohh
ok that makes sense
yes i can see the x^2 term appearing now
thank u
.close
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still drum
final saddleBOT
still drum
$f_n$ is a sequence of functions that uniformly converge to $f$
soft zealotBOT
lifelong dumbass
still drum
im stuck on d
ive been trying to construct counterexamples but no dice
oh wait
hang on
ok i think i figured out that if f_n has discontinuities at some point then f also has discontinuities at the same point (i think)
i dont really know how to move forward
hot thunder
im stuck on d
My d
still drum
?
final saddleBOT
@still drum Has your question been resolved?
final saddleBOT
@still drum Has your question been resolved?
final saddleBOT
@still drum Has your question been resolved?
opaque ember
i dont really know how to move forward
try to prove the contrapositive
still drum
which is like
if f has at least uncountable discontinuities, then some f_n has at least uncountable discontinuities
opaque ember
arent you doing d?
still drum
oh wait
sorry i misread
uh yes (i moved on after a while and forgot which one i asked help for sorry)
so
if f has more than M discontinuities, then some f_n has more than M discontinuities
opaque ember
=M but yes
still drum
ok
ok
oh this is a lot more straightforward
so like
ok
so like
for the discontinuities of f
they must necessarily be discontinuous for f_n forall n> N
opaque ember
continuity doesnt include 0<|x-x0|
still drum
oh right
ok
wait
hmm
oh right cause $x'$ cannot be equal to $x_ \lambda$ by definition
ok
soft zealotBOT
lifelong dumbass
opaque ember
ur argument might be sus bc what im thinking of uses the normal triangle ineq
it should look very similar to the proof of fn cont => f cont
still drum
surely i can make epsilon arbitrarily small enough for it to work tho
because you know that f is discontinuous at $x_\lambda$
soft zealotBOT
lifelong dumbass
still drum
so then there is some $\epsilon_0$ and $x'$ such that $x'$ is in every delta neighborhood of $x_\lambda$ and $|f(x_\lambda)-f(x')|>\epsilon_0$
soft zealotBOT
lifelong dumbass
opaque ember
using normal triangle ineq the gist of the argument is $$\e<|f(x)-f(x')|\le|\dots|+|\dots|+|\dots|$$
soft zealotBOT
ロケット・ジャンプ
still drum
im doing reverse triangle inequality
opaque ember
reverse might work but normal seems cleanest to me. itd take me a lot of energy to figure out and explain why, so ig a bit of faith is needed
still drum
mmm ok
opaque ember
i gave the gist above, so try fleshing it out
still drum
ill give it a shot
uhhh
yea i dont really see it
cause then how do you prove discontinuity at those pointws
still drum
oh wait
i misread what you put
wait
uhh
almost the same stuff basically i think
still drum
which basically means
f_n(x_lambda) and f_n(x') cannot get arbitrarily close
because its bounded below by ($\epsilon_\lambda$)
soft zealotBOT
lifelong dumbass
still drum
thatt was much cleaner then whatever the fuck i came up with
