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#help-27
devout snowBOT
devout snowBOT
Available help channel!
devout snowBOT
loud urchin
i forgot how to do this
loud urchin
isn't 0 to 3 zero?
loud urchin
im confused
fickle magnet
a min pls
loud urchin
alr ty for helping me at least
fickle magnet
fickle magnet
fickle magnet
so im assuming its 18
dont assume, it is for certqain
fickle magnet
no problem, to err is human, to help is divine
loud urchin
.close
devout snowBOT
loud urchin
thank you so much
devout snowBOT
Available help channel!
tribal goblet
why are these different?
devout snowBOT
why are these different?
tribal goblet
acoustic leaf
mean and median will not be equal if the distribution is skewed
the mean will be father in the direction of skew
tribal goblet
i thought the expected value was both the mean and the median for continuous pdfs
pulsar sand
No. The most famous example is the Cauchy distribution which doesn't have a mean and has a median
tribal goblet
i see
I got the first question right, what is E(X) then if not the midpoint in X's pdf?
pulsar sand
E[X] is a weighted sum of x's in the support of X where the weights are f(x). The midpoint just doesn't make sense in general for a pdf.
It is baked right into the definition, $E[X] = \int_{-\infty}^{\infty} xf(x) dx$. The weights are $f(x)$.
woven radishBOT
JessicaK
simple willow
find the centroid of the bounded shape
devout snowBOT
find the centroid of the bounded shape
simple willow
i found it out to be this point but it doesnt look like i did the correct calculations
simple willow
yeah
pseudo basin
if so i would expect it to be left of the y axis cause there is more stuff there
simple willow
wait why u laughin š
willow helm
sorry
simple willow
aight bro
now how do i do this
i used my professors formulas
lemme pull up that
aight i used dis
with the limits being -3 to 2
,w integrate 6-x-x^2 from -3 to 2
woven radishBOT
simple willow
,w integrate x(6-x-x^2) from -3 to 2
woven radishBOT
simple willow
,w 10.417/20.833
woven radishBOT
simple willow
do i have to take the absolute value of this?
cobalt cloak
hmm
simple willow
what did u get for ur area
125/6
well i think i have to take absolute value of the area but not for the moments of x and y
cobalt cloak
everything else is fine
silver breach
Okay so i know i didnt get the question right on the exam but i just wanted to know how to do it. It was something like assume theres a equivalence relation ~ on set S. Show that there is a partition related to the equivalence relations on set S and prove that it is a partition.
devout snowBOT
Okay so i know i didnt get the question right on the exam but i just wanted to k...
uncut crow
Okay so i know i didnt get the question right on the exam but i just wanted to k...
so something like prove the equivalence classes form a partition?
you just want to show each element in S lies in exactly one class
do you know what all the relevant words mean?
silver breach
ooohh... i said blocks instead of class
....
like blocks within a partition
like each elements in S corrsponds to exactly 1 block in a partition and a block is an element of the partition
uncut crow
that sounds like approximately the right idea
silver breach
and like cant have less or more
wait i mightve gotton that right yayy or atleast half points yeyy
Okay and then part c is like the other way around
uncut crow
you just want to show each element in S lies in exactly one class
this requires a little bit of proof though
silver breach
like assume theres a partition P on set S? show there is a equivanence relation on S?
uncut crow
yea, a partition also prescribes an equivalence relation
silver breach
like i dont understand how these two are related
cause like i know the definition of a partition and the definition of an equivalence relation but how do they relate
uncut crow
well do you have an image of a partition of a set in mind
like a set with each element put into a box
do you see how those boxes are like equivalence classes?
silver breach
do you see how those boxes are like equivalence classes?
no...
uncut crow
ok maybe letās look from the other direction
silver breach
I know it has something to do with reflexive, symmetric, transitive and shows it lol
uncut crow
letās say you have an equivalence relation on a set S
and you write out all the equivalence classes
ok with that?
silver breach
yes i think
uncut crow
the equivalence classes form a partition
silver breach
see this is what i dont get lol
uncut crow
ok letās try an example maybe
silver breach
how is like a~a, a~b b~a, a~b, b~c then a~c make a partition? like it doesnt even look close
uncut crow
let's take S = {-3,-2,-1,0,1,2,3,4} and a~b iff |a| = |b|
the equivalence classes are {-3,3}, {-2,2}, {-1,1}, {0}, {4}, right?
and notice that's a partition of S
uncut crow
it defines whether two elements a and b are related to each under the relation
which is the same as defining the equivalence classes i guess
silver breach
yeah this made sense to me
ohh so the equivalence classes is a partition?
cause that looks like it
uncut crow
yes
the problem wants you to explain why that happens in general
why the classes form a partition
silver breach
i honestly dont know i said they must satisify reflexive (a~a), symmetric (a~b then b~a) and transitive (a~b, b~c, then a~c)
uncut crow
which will consist of proving each element in S belongs to exactly one class (so, each element belongs to a class, and not two different classes)
each element belonging to a class is easy. take an element s in S. since ~ is reflexive, s is in [s]
[s] is the class of elements related to s
silver breach
[s] is part of the partition?
uncut crow
well we don't know that yet
it's what we're trying to show
right now we just have an equivalence relation ~
and we want to show the equivalence classes for ~ form a partition
uncut crow
now we wanna show s is only in one equivalence class
because we're trying to show the classes are a partition of S and in a partition, elements need to lie in exactly one block
uncut crow
let's take S = {-3,-2,-1,0,1,2,3,4} and a~b iff |a| = |b|
also going back to this example to demonstrate something, the equivalence classes are [-3], [-2], [-1], [0], [1], [2], [3], [4]
but e.g. [-3] and [3] are the same thing, the set {-3,3}
silver breach
i thought those were blocks lol
like P={{-3},{-2},{-1},{0},{1},{2},{3},{4}} is a partition on S
and like each elements of P is a block
uncut crow
that is a partition yes
uncut crow
sure
are we ready to move on
well i'll continue on i guess
let's say s is in classes [a] and [b]. then a~s and s~b, so a~b. hence a and b are in the same class and [a] = [b]
maybe a~b implies [a] = [b] requires a little more proof
devout snowBOT
@silver breach Has your question been resolved?
opal saffron
Hello guys
devout snowBOT
Hello guys
frigid shale
Hello guys
!original
devout snowBOT
Hello guys
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.
supple knot
Hello guys
Did you have a question
devout snowBOT
@opal saffron Has your question been resolved?
turbid spoke
Can someone please help me with this
devout snowBOT
Can someone please help me with this
turbid spoke
Whatever expression I make to evaluate the number of ways always comes out as too big or too small
Because the median can only be 4, 5, or 6 and the number of cases in those values should be relatively the same
Iām pretty sure in one row itās 5, a number greater than 5, a number less than 5, and in the other rows the layout of the numbers remaining is unrestricted
Because no matter what the medians of the other rows, one of them will be less than 5 and one of them will be greater than 5
Never mind I got it
.close
molten spindle
I need to find lagrange basis function but I am not sure what /0 means.
devout snowBOT
I need to find lagrange basis function but I am not sure what ``/0`` means.
@molten spindle Has your question been resolved?
Available help channel!
burnt drift
e is proving harder than I thought
devout snowBOT
e is proving harder than I thought
burnt drift
so I have calculated the following information: the matrix A has two eigenvalues, 2 and 1, with 2 having algebraic multiplicity 1 and 1 having algebraic multiplicity 3
the eigenvector for eigenvalue 2 is (1, 0, 0, 0)
the eigenvectors for eigenvalue 1 are (1, 0, 1, 0) and (0, 1, 0, 1)
because 1 has algebraic multiplicity 3 and geometric multiplicity 2 we know it has one generalized eigenvector
the Jordan chain is where I'm stuck
because E(1) = A-I is
burnt drift
the eigenvectors for eigenvalue 1 are (1, 0, 1, 0) and (0, 1, 0, 1)
so solving for either eigenvector here leads to 0 row equalling 1 error
I already know the Jordan matrix is
(1, 0, 0, 0)
(0, 1, 1, 0)
(0, 0, 1, 0)
(0, 0, 0, 2)
but finding that final generalized eigenvector is tough
cobalt cloak
the eigenvectors for eigenvalue 1 are (1, 0, 1, 0) and (0, 1, 0, 1)
wait how did u get (0,1,01) for eigenvalue 1
burnt drift
wait how did u get (0,1,01) for eigenvalue 1
it checks out
dot product of 1st row of A with (0, 1, 0, 1) is 0
dot product of 2nd row of A with (0, 1, 0, 1) is 1
dot product of 3rd row of A with (0, 1, 0, 1) is 0
dot product of 4th row of A with (0, 1, 0, 1) is 1
cobalt cloak
that second row
maybe iām slow
nvm u get 2-1
i came to try help and now iām suffering too
i have the same eigenvectors
i put the matrix into wolfram alpha, but the method is behind a paywall
we can try work backwards if u want but i wont share the matrix P if u dont want me to
burnt drift
we can try work backwards if u want but i wont share the matrix P if u dont want...
I tried it myself, the question is how to get there
cobalt cloak
it looks like they have multiplicity 2 for eigenvalue 1
burnt drift
it looks like they have multiplicity 2 for eigenvalue 1
geometric or algebraic?
cobalt cloak
algebraic
burnt drift
same
devout snowBOT
@burnt drift Has your question been resolved?
devout snowBOT
@burnt drift Has your question been resolved?
devout snowBOT
@burnt drift Has your question been resolved?
timber mortar
can anyone help me w this
devout snowBOT
can anyone help me w this
jaunty bane
what have you tried so far?
timber mortar
I tried the (i) one
but i cannot understand (ii)
a is umberella, b is shirt and c is caps
jaunty bane
good
so you are told that 25 people bought umbrellas and 22 people brought shirts.
however, you are not told that these people brought only umbrellas or only shirts.
timber mortar
uhuhh
jaunty bane
so now your job is, from this information and whatever else already there on the Venn diagram, to find the number of people who bought only umbrellas.
(so no shirt, no cap)
jaunty bane
have you heard of the principle of inclusion-exclusion?
timber mortar
like shud i substract 22 from 25 to find how many ppl bought umberella AND shirt? so then, i cud be able to find only umberellas
timber mortar
have you heard of the principle of inclusion-exclusion?
no..
jaunty bane
right, okay
timber mortar
My tutor has never taught me smtg like that
jaunty bane
technically the way to go here is to use inclusion-exclusion, but let me see if I can give you the same intuition without it
jaunty bane
like shud i substract 22 from 25 to find how many ppl bought umberella AND shirt...
ok I see what you're trying but that's not the way to do it
instead, first, consider how many people bought an item at all.
hint: the number of people who bought an item at all isn't 40.
sand quarry
My tutor has never taught me smtg like that
Do you know how to find, say, $\abs{A\cup B}$ or $\abs{A\cup B\cup C}$?
woven radishBOT
timber mortar
Do you know how to find, say, $\abs{A\cup B}$ or $\abs{A\cup B\cup C}$?
huh š no
timber mortar
yess this i doo
sand quarry
Ok carry on with what Koyuki is saying
jaunty bane
I guess I'll let Lex take over then
timber mortar
sand quarry
So, i haven't totally read the chat earlier so I am going to try to explain it from what I already said above
Could you tell me three parameters:
1- the number of buyers
2- the number of shirt buyers
3- the number of umbrella buyers
timber mortar
Could you tell me three parameters:
1- the number of buyers
2- the number of sh...
1- 40
2- 22
3- 25
timber mortar
whhy nawtt
jaunty bane
hint: the number of people who bought an item at all isn't 40.
^^
timber mortar
but isnt that whats said in the question š idkk
jaunty bane
sand quarry
Well, the question boils down to what $|A\cup B|$ is hence why I asked
woven radishBOT
timber mortar
uhm uhuh
sand quarry
So the total amount of people in our universe is 40. 6 are explicitly said not to be buyers at all. In that case the amount of buyers is...
timber mortar
ohh 34?
sand quarry
yeah
timber mortar
okey then, how does that help me with the (ii) 
sand quarry
If 5 people went to a restaurantāand you know they ordered either shawarma or kebabā3 people ordered shawarma. How many ordered only kebab
sand quarry
Go for it
timber mortar
people who only bought umberella - 12
people who bought umberella AND shirts- 13
people who only bought shirts/ shirts and caps- 9
cz i added 25 and 22 (47) and substracted them from 34, which is how i got the asnwer
timber mortar
people who only bought umberella - 12
people who bought umberella AND shirts- 13...
if i add all these up, im getting 34
jaunty bane
congratulations. you have (re)discovered the formula for inclusion-exclusion
timber mortar
congratulations. you have (re)discovered the formula for inclusion-exclusion
what is that anywayy, I wana knoww
sand quarry
,, \abs A + \abs B - \abs{A\cap B} = \abs{A\cup B}
jaunty bane
given two subsets of a sample space A and B, \
$|A \cup B| = |A| + |B| - |A \cap B|$
woven radishBOT
Koyuki
jaunty bane
A + B - (A \cap B), right?
woven radishBOT
jaunty bane
ah
sand quarry
Yeah 
jaunty bane
given the following subsets, say which one to include or exclude based on the description in iv):
- people who bought only umbrellas
- people who bought umbrellas and shirts
- people who bought only shirts
- people who bought shirts and caps
then you can form your set notation based on that
timber mortar
given the following subsets, say which one to include or exclude based on the de...
2 and 3rd
wait 4thh i mean
2nd and 4th
jaunty bane
you want the people who bought only shirts
on top of that, please also say whether you're including or excluding your choices
timber mortar
but they're mentioning that ''who bought only 2 types of items is 19'' so 2nd + 4th = 19
jaunty bane
oh shit that's iv) LMAO
timber mortar
i already know who bought both umberella and shirt, so if i substract that from 19
jaunty bane
I read the wrong question
timber mortar
I read the wrong question
its okeyy
jaunty bane
6 is right
timber mortar
i already know who bought both umberella and shirt, so if i substract that from ...
im getting 6, which im guessin is the ans
jaunty bane
I've already given a hint for iv)
timber mortar
I've already given a hint for iv)
ohh waitt
sand quarry
I think describe what it means to have only bought shirts in words first before using any set notation
timber mortar
including 2nd, 3rd and 4th
jaunty bane
given the following subsets, say which one to include or exclude based on the de...
you may base your choices on this
only shirts, remember?
sand quarry
If someone has only bought shirts that means they are in __ but not in __
sand quarry
I mean ignore the numbers
timber mortar
only shirts=3
sand quarry
It wants you to find an expression for that in set notation
timber mortar
exclude 1, 2, and 4
jaunty bane
now take a shot at forming the expression
if I'm not being high, your expression should have two intersections and two complements
but if you can find an equivalent, that would work as well
sand quarry
You're in fact not high
timber mortar
(A' U B U C')?
sand quarry
no
sand quarry
If someone has only bought shirts that means they are in \_\_ but not in \_\_
You should do this first imo
timber mortar
exclude 1, 2, and 4
am i correct w this
jaunty bane
you are right
timber mortar
If someone has only bought shirts that means they are in \_\_ but not in \_\_
i swear i dont get it
sand quarry
Im asking you to fill the blanks
Basically
With "A", "B", "C", "not", or "and" and whichever valid combination of the above
timber mortar
i swear i dont get it
in B but not in A or C?
sand quarry
Yeah actually
Start inside out
How do you represent "not in A or C" in set notation
timber mortar
(A U B)'
sand quarry
Yeah
sand quarry
Hol up
timber mortar
Where did the B come from in here lol
sorry i js had everything messed up ugh
timber mortar
We're talking about only A and C
uhm so A' and C'? š
sand quarry
Actually both of these expressions are equivalent
,, \comp A \cap \comp B = \comp{(A\cup B)}
woven radishBOT
sand quarry
uhm so A' and C'? š
That's true
timber mortar
That's true
then how do i connect em both in an expression
sand quarry
I kinda just typed it above for you
timber mortar
I dont quite understand the notation, but tysmm!! u guys cleared up the above questionsss
tyy
jaunty bane
(fun fact: this is called de morgan's law)
!occupied, please use another available channel like #help-49
devout snowBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
jaunty bane
?
jaunty bane
to avoid ambiguity, please show the answer as a diagram
jaunty bane
where is C?
timber mortar
the small circle in blue
jaunty bane
then incorrect
timber mortar
why 
jaunty bane
you are told that essay writers selected at least one of the other two types
your subset is firmly within the intersection, meaning that you imply that essay writers must select both other types
jaunty bane
so C now contains people outside the sample space?
timber mortar
nahh i just drew it cz i ddint have space
jaunty bane
wrong
you are along the right lines, in that you should expand the size of C
but not like this
C must still be within A and B as stated
jaunty bane
you are told that essay writers selected **at least one of the other two types**
think about this particular sentence
timber mortar
and all 3 shud intersect in a specific place too?
jaunty bane
how would you make sure there is some part of C that is still in A or B, but in a way that implies that people in C could have taken only one of the two other types?
jaunty bane
and all 3 shud intersect in a specific place too?
that would be the dead center
sand quarry
Congrats on the active, Koyuki lol
jaunty bane
I mean you got that part correct. you just need to widen C a little bit more
jaunty bane
Congrats on the active, Koyuki lol
oh didn't know that was what it is, thanks
timber mortar
that would be the dead center
but in the question, they've given a value for ''ALL three questions''
timber mortar
I mean you got that part correct. you just need to widen C a *little* bit more
oh
can u draw that for me?
jaunty bane
but in the question, they've given a value for ''ALL three questions''
I don't think that changes anything
jaunty bane
can u draw that for me?
unfortunately, no. but I can tell you that you just needed to tweak your original diagram a little bit by expanding C.
timber mortar
smtg like this
jaunty bane
expand C, not move it outside the sample space
C should never extend out of the sample space
also, C should remain within A and B
jaunty bane
also, C should remain within A and B
this is the key you must remember. don't extend C anywhere outside A or B.
jaunty bane
closer, but that implies that everyone who have answered the two other question types must also have answered the essay
don't think that's implied or stated by the question. try making the circle narrower from top to bottom
jaunty bane
I mean you are very close, I'll tell you that
but I'm not going to stop you if you choose to skip.
timber mortar
I mean you are very close, I'll tell you that
ikk but i only know this way, i cant think of anything
jaunty bane
your way does address the expansion, but now your circle is too big vertically
timber mortar
ur saying that C shud be in between ''A and B''
jaunty bane
alright fine, I'll give you this one
timber mortar
like not leave that intersection area?
jaunty bane
this is what I envisioned C to look like. your latest attempt was almost there, just needed to make the circle narrower so it doesn't cover the entirety of A \cap B
remember, you are told that all essay takers did at least one of A or B, but you're NOT told that those who did A and B also did the essay
that's why you should not cover the whole of A \cap B with the circle
devout snowBOT
Available help channel!
frank ermine
Can anyone help explain this to me plss
devout snowBOT
Can anyone help explain this to me plss
frank ermine
Its electric field
devout snowBOT
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.
steep mulch
Can anyone help explain this to me plss
What exactly do you not understand
frank ermine
What exactly do you not understand
How to use the line graph to get the distance
Cuz theres 2 distances
steep mulch
Cuz theres 2 distances
2 distances of what?
frank ermine
0 and 30
steep mulch
Electric fields are very simple
frank ermine
Q1 and q2
frank ermine
Electric fields are very simple
Yea im just confused with this part
steep mulch
Yea im just confused with this part
Oh i see
They're asking for a point where the field is zero?
frank ermine
What do they ask for
steep mulch
It's on the x axis of a graph
The distance of the first charge from the point is 0-(-0.10)
Which is 0.10
The second one is 0.40
Note that electric fields are vectors
frank ermine
Ya how to get that
steep mulch
Ya how to get that
It's like this
The distance between any 2 points will be their difference
frank ermine
Oh i get it now thank you 
devout snowBOT
@frank ermine Has your question been resolved?
lost laurel
devout snowBOT
lost laurel
so the forward direction is trivial so I'll skip that
The backwards , I'd do something like this
Let ${e_1,\dots,e_n}$ form a basis of $V$. Let $x = \sum_{i=1}^{m} a_ie_i$.
We desire $A(x)=y$ So define $A(e_i)= \sum_{i=1}^{n} \frac{y}{a_i}$. The rest of the basis are mapped to themselves
woven radishBOT
wai
lost laurel
Does this work
low parrot
Does this work
i dont think so
lost laurel
why not
woven radishBOT
ViĶ„ŃaĶ£nĶ«
steel sage
What is a positive transformation and what is this bracket <>?
lost laurel
What is a positive transformation and what is this bracket <>?
<> is inner product
steel sage
Positive transformation?
lost laurel
<Ax,x> >0 for all xā 0
steel sage
Oh, positive definite you mean
lost laurel
I think it has to be self adjoint too
yup has to be self adjoint too
so lemme redo this then
tq
.close
devout snowBOT
steel sage
I think it has to be self adjoint too
Can you reopen it?
lost laurel
.reopen
devout snowBOT
ā Original question: #help-27 message
lost laurel
yea
steel sage
I just want to add that you only need to consider the two dimensional case
lost laurel
just realised if I take the field to be complex I'm done
steel sage
The subspace generated by x and y
lost laurel
why
steel sage
Two dimension is true then any dimension is true, since you can let the n-2 dimensional complement part of A be identity
lost laurel
sure, but why is what I did wrong
steel sage
WLOG, you can let x=(1,0)^t, y=(a,b)^t, A clearly =(a,b;b,c)
Simply choose a c such that ac-b^2>0 since a>0 is given by condition <x,y>>0
So can be done on R. Positive definite is defined on R anyway I think
low parrot
so for all non zero v we have v = x so if Ax = y then <x,y> > 0
steel sage
He proved this other direction himself already
low parrot
He proved this other direction himself already
ok wait
steel sage
Anyway, both directions are done
devout snowBOT
@lost laurel Has your question been resolved?
rare wagon
<@&286206848099549185>
devout snowBOT
<@&286206848099549185>
sharp garnet
!15min
devout snowBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
drifting mauve
<@&286206848099549185>
,lwrc
sharp garnet
,ccw
drifting mauve
uh yeah
tender wharf
<@&286206848099549185>
,rccw
woven radishBOT
rare wagon
2nd i want
sharp garnet
do you understand what an A.P is
bitter creek
ayo got a kid question
rare wagon
My ans
steel sage
How can you write a series on one paper. A series have infinitely many terms
sharp garnet
keep trolling outta help channels
drifting mauve
write the general term as well
ebon coyote
How can you write a series on one paper. A series have infinitely many terms
"1, 2, 3, ..." is already a representation of all the natural numbers above zero, so
drifting mauve
Is that right?
yes, but it would help to include the general nth term
just looks more neater that way
ebon coyote
ayo got a kid question
!occupied if you were referring to yourself; if you were referring to the question you responded to, that's discourteous
devout snowBOT
ayo got a kid question
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
bitter creek
!occupied if you were referring to yourself; if you were referring to the questi...
wait bruh am solvin
steel sage
I mean usually the homework is of the form like āwriting down the first 10 terms of ā¦ satisfyingā¦ā
Never have seen those not specifying first how many terms
abstract plover
you can then get away with putting ...
ebon coyote
(further, this is a progression, not a series; those are two different things)
rare wagon
Can you guys help me solvin it
ebon coyote
ill write it
!nosols if you're gonna attempt to help him btw
devout snowBOT
ill write it
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
rare wagon
š
tender wharf
Can you guys help me solvin it
use last sentence
sharp garnet
this server is for you to learn
ebon coyote
Have the student work through the problem themselves and guide them along the way.
bitter creek
I did first equation for you šāāļø
bitter creek
!nosols if you're gonna attempt to help him btw
Nah dude, I just got slipped from a rave
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
bitter creek
I did first equation for you šāāļø
@ebon coyote this is just a bit of salt I gave a reference dude it's not gonna help him for the h.w š«” @tender wharf
rare wagon
@bitter creek @sharp garnet @ebon coyote š is. That right? It's so fockin hard bruh tomorrow is my exam and am cooked
sharp garnet
!noping
devout snowBOT
Please do not ping individual helpers unprompted.
bitter creek
<@894790142391353445> <@832188363758370825> <@660973674870079488> š is. That ri...
ayoo
rare wagon
wtf? Well formatted algebra in Mathcord!?
š
rare wagon
š
rare wagon
Er... just check that "4" there?
6 will come there ig?
ebon coyote
ye
rare wagon
Solving this now
bitter creek
<@894790142391353445> <@832188363758370825> <@660973674870079488> š is. That ri...
ur cooked bro lol its exam right f- em ill give u a us chit ill write it down for you, that u can memo before exam
rare wagon
ur cooked bro lol its exam right f- em ill give u a us chit ill write it down fo...
š¼ wym?
rare wagon
Yes
devout grotto
Solving this now
i think you know enough to do this given the excellently formatted work above. you got this!
rare wagon
Damn
rare wagon
Are you Indianš®š³? Too?
bitter creek
yeah bro ur giving 10th exams right chill, anyways they will say you few mcq answers while at exam hall in final so chill
rare wagon
yeah bro ur giving 10th exams right chill, anyways they will say you few mcq ans...
Even at the boards exam? š±
bitter creek
yeah
tender wharf
yeah bro ur giving 10th exams right chill, anyways they will say you few mcq ans...
lmao
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
bitter creek
its not anysolution dude its a trick for him to help on exams
bitter creek
CBSE OR ICSE?
ur questions seems like mostly from cbse 10 field
sharp garnet
its not anysolution dude <:blobcry:971797574916907028> its a trick for him to h...
Okay, my bad brodie
rare wagon
ur questions seems like mostly from cbse 10 field
Yesss
bitter creek
yeah its for boards and cbse
ebon coyote
its not anysolution dude <:blobcry:971797574916907028> its a trick for him to h...
Sure, but shit like this? if you understand how an AP works, you honestly don't need this imo
These aren't even formulas
It's just algebra
bitter creek
Sure, but shit like this? if you understand how an AP works, you honestly don't ...
Yeah true, it is just algebra ā thatās the whole idea.
He struggles with the setup, so this is just a quick way for him to remember how to form the equations. Once he understands AP properly, he wonāt need these notes.
ebon coyote
Solving this now
As for this, you should have an understanding on how to use the sum part first...?
bitter creek
@rare wagon isnt this helpful?
ebon coyote
Yeah true, it is just algebra ā thatās the whole idea.
He struggles with the set...
Algebra isn't memorisation (and in practice this is something I have a personal gripe with the education system in India, at least as far as gets exposed on this server) - to this extent, most people I know here wouldn't try to solve these via things they've memorised so much as techniques and methods they've learnt
And as for "struggles"? maybe slow to set stuff up, but he can defo do the execution pretty well
bitter creek
Algebra isn't memorisation (and in practice this is something I have a personal ...
i understand bro
inner sorrel
aight
inner sorrel
Solving this now
Take the middle term as x
so the sum of three consecutive terms is (x-d)+x+(x+d)
which is 3x
now you can find the middle term
inner sorrel
similarly their product is $x^3-d^2x$
woven radishBOT
BKB
ebon coyote
(Wait for a response, jeez)
inner sorrel
[the hint specifies `a` btw, not `x`]
oh
inner sorrel
(Wait for a response, jeez)
Iām very impatient lol
Iād solve ts right here right now if nosols wasnāt a rule
bitter creek
And as for "struggles"? maybe slow to set stuff up, but he can defo do the execu...
ayo bro
Man dropped a whole TED Talk just to say āitās not memorization.ā
Calm down, professor, nobody asked for your National Geographic documentary on Indiaās math curriculum.bro i understand you are trying to explain how the education system in india is i know its like messed up but due to politics all are used to it
ebon coyote
Unfortunately the purpose of this sever is to teach, not to do people's homework for them
inner sorrel
India education system is cooked
bitter creek
India education system is cooked
FR-
inner sorrel
there is too much of a jump from class 10 to class 11
thatās why Iām trying to learn some class 11 concepts rn so that I donāt get slapped in the face in class 11
devout snowBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
inner sorrel
oh oh mv
bitter creek
Unfortunately the purpose of this sever is to teach, not to do people's homework...
aight, bro i was gonna do that but am new to the server so i aint helpin anyone
tender wharf
Algebra isn't memorisation (and in practice this is something I have a personal ...
mm.. tricks sometimes help once you understand them
inner sorrel
I think OP is busy somewhere else
bitter creek
who is op
rare wagon
<@1403202324079444058> isnt this helpful?
Yess it's helpful
rare wagon
Solving this now
@bitter creek @inner sorrel @ebon coyote what'd you guys think it's right?
jaunty bane
,rcw
woven radishBOT
bitter creek
<@894790142391353445> <@962284969542164550> <@660973674870079488> what'd you guy...
bro u got that wrong
rare wagon
bro u got that wrong
How
ebon coyote
Ignore him, you're correct
bitter creek
Ignore him, you're correct
wait, isnt (9ā5)(9+5)=4ā
14=56not equal to14 this is wrong i guess
if product is 14
If product = 56 then
(9ā5)(9+5)=4ā
14=56
rare wagon
Ignore him, you're correct
š„°
ebon coyote
wait, isnt (9ā5)(9+5)=4ā
14=56not equal to14 this is wrong i guess
if product is...
And where did you see that this product be equal to 14?
jaunty bane
wait, isnt (9ā5)(9+5)=4ā
14=56not equal to14 this is wrong i guess
if product is...
what?
bitter creek
And where did you see that this product be equal to _14_?
lemme check the question,
When I first looked at the notebook, I thought the product had been miscopied because:
81-d^2=504 --> d^2-423
This looked impossible, so I thought maybe the kid wrote the product wrong.
But then I rechecked the book , and I realized:
9(9ād)(9+d)=504 not (9ād)(9+d)=504
but correct expression is (aād)(a)(a+d)=504
ebon coyote
So the actual realisation is, you can't read a question, good job
jaunty bane
but correct expression is (aād)(a)(a+d)=504
?
(substituting a = 9)
apparently you missed the memo on that line?
or something else entirely, which I don't know at this point
bitter creek
(substituting a = 9)
apparently you missed the memo on that line?
Skill issue ā temporary. Solution issue ā solved.
jaunty bane
okay? dk why you feel the need to tell me that again but sure.
ebon coyote
Yeah, you don't need to click reply on every message
bitter creek
nvm
devout snowBOT
@rare wagon Has your question been resolved?
bitter creek
@rare wagon u good?
rare wagon
Yess i am good
soft kindle
part b)
supple knot
What's V_delta
soft kindle
it represents 0 < |x - a| < delta
harsh sierra
If f(a) > 0 its the same as part a
soft kindle
oh wait, can we do a by cases proof? where we choose a different epsilon for each case (where case 1, f(a) > 0 and case 2, f(a) < 0)
harsh sierra
If f(a) < 0 then its the same as part a for the function -f
harsh sierra
oh wait, can we do a by cases proof? where we choose a different epsilon for eac...
Epsilon?
soft kindle
yeah, cuz we start with the eps-delta definition of continuity
and we get the inequality |f(x) - f(a)| < epsilon
and we just need to choose an appropriate epsilon such that this inequality matches the inequality of the problem
harsh sierra
Yeah
Because you split into cases at the start of the proof, you can solve the two different cases unrelated to each other
soft kindle
got it
woven radishBOT
SWR
soft kindle
we know that |f(a)| = f(a) if f(a) > 0
and |f(a)| = -f(a) if f(a) < 0
lusty sapphire
we know that |f(a)| = f(a) if f(a) > 0
and |f(a)| = -f(a) if f(a) < 0
You don't need to break into cases
If $f(a)\ne0$, then $|f(a)|>0$ and you can solve using part a
woven radishBOT
SWR
soft kindle
okay, the thing is
when I rewrite the inequality |f(x) - f(a)| < eps with the terms split,
I get f(x) > f(a) - eps, where none of f(x) and f(a) are under absolute values
lusty sapphire
You don't need to do any of that
Since $|f(a)|>0$, it meets the criteria for part a and thus proves part b
woven radishBOT
SWR
lusty sapphire
To make it easier to understand, let $g(x)=|f(x)|$. If $f(x)\ne0$, then $g(x)>0$, right?
woven radishBOT
SWR
soft kindle
yeah
i think I partly got it
so, if we put f(a) under absolute values, then we'll basically be back to part a), since |f(a)| > 0 just like case a), where f(a) > 0
lusty sapphire
Exactly
soft kindle
the only difference is that if we need to put |f(a)| under abs value, then |f(x)| has to be under absolute value for the inequality to hold, right?
lusty sapphire
Not sure what you mean here
Absolute value of $|f(a)|$ will just simplify to $|f(a)|$
woven radishBOT
SWR
soft kindle
part b)
like, in part a), f(x) wasn't under abs values, but in part b), f(x) was under abs values
i've figured out the question
.close
devout snowBOT
devout snowBOT
Available help channel!
wispy forge
no idea how to proceed with this question, please help
just did sin(2arctan(sqrt(x)-(pi/2))) = (x-1)/(x+1) but nothing beyond it
devout snowBOT
no idea how to proceed with this question, please help
just did sin(2arctan(sqrt...
supple knot
Use difference formula for sine
wispy forge
Use difference formula for sine
sin(a-b) = sin(a)cos(b) - cos(a)sin(b)?
wispy forge
Use difference formula for sine
I got this done, idk what to do afterwards
wispy forge
I got this done, idk what to do afterwards
got the last step wrong, supposed to be +cos(2A) = (x-1)/(x+1)
fast garden
suppose that is correct, consider just cos(A) for example
how can you rewrite cos(arctan sqrt x) in a nicer way
wispy forge
suppose that is correct, consider just cos(A) for example
how can you rewrite c...
since arctan(sqrt(x)) = A
cos(arctan(sqrt(x))) = cos(A)
fast garden
that is not quite what i mean
draw a triangle
there is a way to simplify this nicely
fast garden
yes
fast garden
one sec
wispy forge
okay
fast garden
so how can we extract cos(A) from this
wispy forge
so how can we extract cos(A) from this
cos(A) = 1/sqrt(x+1)
fast garden
right, and how does this help us with the rest of the problem
do you think you can finish from here
wispy forge
do you think you can finish from here
wait i'm kinda confused
i'm just tired that's why
i can't rly seem to proceed š
fast garden
there is an identity
wispy forge
sorry if i'm not being cooperative i'm just sleep deprived okay š
wispy forge
have you seen that before
yeah what about it
fast garden
can you rewrite cos(2A) in terms of just cos(A)
^
fast garden
cos(A) = 1/sqrt(x+1)
^
wispy forge
oooookay
fast garden
@wispy forge you manage to finish it?
wispy forge
<@561834995413549057> you manage to finish it?
I got till here
fast garden
slightly wrong approach
you already have cos A in terms of x right
so you can just plug it in
and you have x on both sides already
no need for more trig
wispy forge
you already have cos A in terms of x right
okay so cos^2(A) = (x)/(x+1)
so therefore cos(A) = sqrt(x)/(x+1)
do I just put the value of A in the LHS
A = arctan(sqrt(x)) that is
fast garden
no
you have this
you put your value of cos A in
and hopefully your left hand side will be the same as right
wispy forge
you put your value of cos A in
uh huh
fast garden
and that is it
you were trying to show the left hand side is the same as the right the entire time, and plugging in your value of cos A, you are finished
wispy forge
i'm getting x^2 - x + 1 = 0 ššš
fast garden
....
wispy forge
okay lemme do it again
fast garden
what
fast garden
cos^2(A) = (x-1/x+1)^2
?
wispy forge
wait lemme just show my procedure
fast garden
ok
fast garden
you have this
but cos A = sqrt x / sqrt(x+1) from your diagram
and then you are finished
nothing more is needed
devout snowBOT
fast garden
nw
devout snowBOT
Available help channel!
old seal
devout snowBOT
old seal
my understanding is, that if b_n converges, and a_n is smaller than b_n, then a_n converges also
is that the correct understanding? and to solve this I would test I, II, and III to see if they converge then check if I, II, and III are larger than a_n?
old seal
dont tell me please I want to explain my thought process and you correct any mistakes for each one
I take the limit of each one as n approaches infinity. for I, the limit = 1/2[lim]1/(n^2)
here is 1/2 times a p series where p = 2
if p is greater than 1, the series converges to 0, which means I is convergent. Now i have to test if I is larger than a_n
(1/(n^2+1)) <? 1/(2n^2)
i multiply both sides
and get 2n^2 < n^2+1
fast garden
if p is greater than 1, the series converges to 0, which means I is convergent. ...
what are you testing, b_(n+1)/b_n?
old seal
and get 2n^2 < n^2+1
which is false, so I isnt larger than a_n
old seal
what are you testing, b\_(n+1)/b\_n?
what do you mean here
old seal
so am i correct that I is convergent but I isnt larger than a_n, so it cannot be used to prove a_n converges?
and my math is correct?
fast garden
yes
but
it should be sum of
not just hte limit directly
the limit directly is 0
woven radishBOT
Miyamoto
old seal
which p = 2, so the series converges to 0
because p is greater than 1
i dont know what you mean by sum of
fast garden
you are not looking at whether b_n converges at all
that is not the problem
since, b_n can converge but the sum may not
you are trying to see whether the sum converges instead
1/n^2 is not a p-series, but sum of 1/n^2 is
does that make sense
old seal
yes
fast garden
so, in your first one, you are saying that \sum b_n = 1/2 \sum 1/n^2, which converges and that is correct
then, you are testing whether 1/(n^2 + 1) < 1/(2n^2) and it is not, so you are correct
the only issue was that
while you had the right idea, you said a completely different thing
fast garden
which p = 2, so the series converges to 0
also, the series does not converge to 0
but this doesn't matter
old seal
where does it converge to
fast garden
\sum 1/n^2 converges to pi^2/6 but it's not important
old seal
oh ok
so this same process i repeat for II and III to get the answer?
our answer for I applies to II i think because its just 1/n^2 still
and 1/2n i see as a harmonic series that diverges
fast garden
yes
old seal
for II, I think i would test if 1/(n^2+1) is smaller than 1/n^2
and this is true
so the answer is II only
fast garden
correct
old seal
fast garden
:)
old seal
you are like a math pro
fast garden
all you, i just gave you small guidance
old seal
what are you strongest subjects
fast garden
algebraic number theory, elliptic curves etc
old seal
i need to master algebraic number theory, how did you study it?
fast garden
ummm i took a course on it when i was in my 3rd year of university and then carried on studying it using marcus and just kept going from there
old seal
ummm i took a course on it when i was in my 3rd year of university and then carr...
what is marcus and were you a math major?
old seal
did you compete in the putnam exam
fast garden
i'm not american
devout snowBOT
old seal
.reopen
devout snowBOT
ā Original question: #help-27 message
old seal
i'm not american
what are good resources for oxbridge math and currently ive been memorizing formulas i find important to free up my mind during calculations
sometimes i see randomly people say memorization of formulas is a bad approach
fast garden
for.... what exactly
old seal
i want your input pls
old seal
sorry, I am asking how best to prepare a student that wants to do well in the Mathematical Tripos
to free up my brain to think better during problem solving I have been memorizing formulas so i dont waste energy/effort on deriving the formulas during a question
fast garden
are you pre uni
old seal
yes
fast garden
so maybe, the question should not be "how do you do well in tripos" but "how do i improve at math"
and the answer is simple, i think
just do math that you find challenging and do lots of it
willow helm
to free up my brain to think better during problem solving I have been memorizin...
You also have to find ways of learning that work for you
In my opinion, simply memorizing formulas does more bad than good
Because after all, math is all about understanding
And then your entire success relies on the fact whether you remembered that one formula or not
fast garden
In my opinion, simply memorizing formulas does more bad than good
agree... save this for your first differential geometry course for when they give you 1298338912398 definitions and then the course suddenly ends without getting to anything
willow helm
And if that fails, everything else falls like dominoes
old seal
how would you approach remembering that formula for a question
fast garden
also this should probably be in #study-discussion
i dont want to get shouted at by a random for not helping with a problem in this channel
old seal
okay sorry
willow helm
I mean yeah probably, but I don't see the benefit of losing this chat flow
willow helm
how would you approach remembering that formula for a question
Uhh, difficult question
I personally haven't had problems remembering formulas
It's kind of like I get them
And either way, I've never really had to memorize them
Because the two times I need them: not in school, I can look them up, and in school during an exam, I can always have an A4 cheat sheet
So I can't really give proper tips about that unfortunately
old seal
Because the two times I need them: not in school, I can look them up, and in sch...
do they offer the a4 cheat sheet in math tripos
fast garden
it's just cam math undergrad
devout snowBOT
willow helm
thank you guys, you guys rock.
I'm really sorry, I just don't believe I can give any meaningful advice.
old seal
you gave good advice to me i didnt mean it negatively, sorry
willow helm
you gave good advice to me i didnt mean it negatively, sorry
Oh I see. Well look, you'll figure it out. Everyone does. And best of luck with everything
devout snowBOT
Available help channel!
inner garden
I don't really know the answer to this question. may you help me step by step on how to do it?
devout snowBOT
I don't really know the answer to this question. may you help me step by step on...
sand dove
I don't really know the answer to this question. may you help me step by step on...
Do you remember the formula for inverse derivative
inner garden
Not really...
sand dove
Well without it it'll be hard to answer this question
sand dove
So, use that if $g(a) = b$, then $(g^{-1})'(b) = \frac{1}{g'(a)}$
woven radishBOT
Raphaelisius Maximus MMIII
inner garden
ok
thank you
so if $h(x) = 5 - x - x^{3}$ and $f(x)$ is the inverse of $h(x)$, then $h'(7) = -7 - 3(7)^{2} = 7 - 147 = -140$, then $(h^{-1})'(7) = \frac{1}{-140}$
woven radishBOT
š/āšš ššš & ıĒM ā„ĪŌ/É
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
modest steppe
seeing this makes me scared of future math
inner garden
right?
modest steppe
if you are talking to me, yes fr im in 9th grade and ts makes me scared
inner garden
oh yeah im 9th gr too
sorry for responding late
im just learning this for fun
edit: so if $h(x) = 5 - x - x^{3}$ and $f(x)$ is the inverse of $h(x)$, then $h'(7) = -7 - 3(7)^{2} = 7 - 147 = -140$, then $(h^{-1})'(7) = \frac{1}{-140}$
woven radishBOT
š/āšš ššš & ıĒM ā„ĪŌ/É
inner garden
nvm actually... if $h(-1) = 7$, then $(h^{-1})(7) = -1$, and so therefore $f(7) = -1$
woven radishBOT
š/āšš ššš & ıĒM ā„ĪŌ/É
inner garden
and if $f(7) = -1$, then $f'(7) = \frac{1}{-1}$, which is equal to $-1$.
woven radishBOT
š/āšš ššš & ıĒM ā„ĪŌ/É
open sun
How would I find the area of these questions? If thereās any videos explaining how to you can send them as well!
devout snowBOT
How would I find the area of these questions? If thereās any videos explaining h...
open sun
supple knot
,tex .plane geom
woven radishBOT
riemann
supple knot
top right and middle right. and middle middle
devout snowBOT
devout snowBOT
Available help channel!
kindred mauve
devout snowBOT
kindred mauve
how is this derived? from the previous answer
pastel rose
They expanded the bracket
And see how itās symmetrical
From -3 to 3
Same as going from 0 to 3 and multiply by 2
kindred mauve
Same as going from 0 to 3 and multiply by 2
?
pastel rose
Given u see itās an odd function
kindred mauve
why is it multiplied by 2
pastel rose
Can u draw that function?
