Ping me if helpers are not available
#help-23
stoic torrent
stoic torrent
Oh yeah
low drift
What
low drift
i mean the angle is in the same place 99% of the time for qs like this
unless theta isnt there originally
crude light
i mean the angle is in the same place 99% of the time for qs like this
where would it be tho
its like idk how to visualise it
low drift
crude light
so it's always there? lol
crude light
no 😭
stoic torrent
stoic torrent
oh no i know that
Ah thats nice!
crude light
axioms
stoic torrent
But that word is crazy
ikr😭
crude light
Ok wait let me deep it rq
Okayyy
No yeah i get that
LAST ONE GUYS IM SO SORRY
JUST TO CONSOLIDATE WHAT I'VE LEARNT
just the angle part
so thats alpha?
low drift
ye
crude light
Yayyyyy
You guys are amazing, thank you so much for the help 🥰 Feeling much more confident
Have a lovely day!
low drift
np
twin cairn
they're not
sorry, call of the nature
crude light
sorry, call of the nature
🤣 you're good
stoic torrent
Well anymore?
stoic torrent
I mean I would, but im not trying to waste your time
No not at all
crude light
Really?
stoic torrent
if i feel like it ill let uk
stoic torrent
Okay let me try like a hard question
okey
stoic torrent
And i'm most likely going to get stuck so I'll send it to you
yeah np
stoic torrent
Oh you could hv had pinged me
crude light
Oh you could hv had pinged me
oh i thought it was you who put the thumbs up 🤣 but it was nox
thanks nox lol
stoic torrent
oh i thought it was you who put the thumbs up 🤣 but it was nox
lol
crude light
so when you're finding moments at a
twin cairn
XD np
crude light
do you have to resolve the F
for it to be Fcostheta?
Why is that so? , so when finding moments at A does it have to always be vertical
twin cairn
I can't help unless u want other method my method is about newton laws and projections @stoic torrent help
I don't know how u come up with the your first line there
and what is m(A)
stoic torrent
I can't help unless u want other method my method is about newton laws and proje...
you should state your method i feel like you have the same method
crude light
I can't help unless u want other method my method is about newton laws and proje...
Yeah sorryyyy i dont do physics
crude light
so like moment about A
yea exactly
crude light
you should state your method i feel like you have the same method
I mean yeah sure why not
crude light
I can't help unless u want other method my method is about newton laws and proje...
Nox could you try help me then?
stoic torrent
welp seems like hes busy
stoic torrent
do you have to resolve the F
Nope not reqd here
as sicne ur applying about A along the rod,
stoic torrent
wait i will right it
okay sure
stoic torrent
do you have to resolve the F
you need the forces that you take into consideration to be perpendicular to the the rod and not the surface,as thats what the moment of force means
stoic torrent
Well thats the answer to the q u had, lets see NoXs method
crude light
Yess ok let me write this all down because i'll forget
So for finding moments it has to always be perpendicular to the rod
twin cairn
never mind that just make it very complicated dealing with that much of unknows is not ideal and surely not what they want
your's is best using moments
study that at year 12 thoght not 13 that is why didn't come to mind first
crude light
never mind that just make it very complicated dealing with that much of unknows ...
Niceeee what was the first image tho
the 2nd one is what i'd do
so smart you guys wow
twin cairn
never mind that just make it very complicated dealing with that much of unknows ...
do you have a more beatiful continue to it @stoic torrent
twin cairn
the 2nd one is what i'd do
yeah that is the expected answer too
crude light
yeah that is the expected answer too
Nicee okay let me carry on the question guys, sorry i wont take up too much of your time
for part b are these the correct equations
twin cairn
the vertical yes, look again to your horizontal
always keep in mind that all weights are always and always perfectly vertical by definition. therfore the moment is ...
crude light
trueee
thank you but
im not findin moments this time
im just resolving left and right
so why wouldnt it be Fr = 3mgsintheta + Fsintheta + mgsintheta
twin cairn
I am trying to tell u that it is not
crude light
what would it be instead though sorry?
twin cairn
because the weights are vertical they are just zeros
Fr = Fsin(theta)
stoic torrent
why the cross @thin bridge
twin cairn
and that is it, they should not be in the equation
twin cairn
Sorry, I studied mechanics in physics not maths but i think still remains the same logic, it is just they way i think based on the situations i were in
crude light
because the weights are vertical they are just zeros
Fr = Fsin(theta)
So you dont add the weights in the equation?
crude light
This is mathematics
yea this is mechanics tho
twin cairn
I think so @stoic torrent can u check
dim grotto
I see
stoic torrent
I think so <@1143796624393502721> can u check
which part
dim grotto
Physics is hard
crude light
Since i resolved mg and 3mg, it should be in the equation
dim grotto
I’m currently a senior taking ap physics c
stoic torrent
Physics is hard
i mean its okayish
twin cairn
so why wouldnt it be Fr = 3mgsintheta + Fsintheta + mgsintheta
this one
dim grotto
I have a 78 in the class
stoic torrent
I’m currently a senior taking ap physics c
Ah i see gl hv fun
crude light
Physics is hard
Yea thank God i didnt pick that
stoic torrent
I have a B average
right now then lets stick to to Qsn for now getting spammed a lil
dim grotto
Sorry
crude light
Yeah lol 🤣
stoic torrent
so why wouldnt it be Fr = 3mgsintheta + Fsintheta + mgsintheta
Yeah saw that!
wieghts are always vertically down right?
twin cairn
yes
stoic torrent
Well then would they have a horizontal component then?
stoic torrent
But im resolving left and right
I know i got your point, put they dont exert force left or right
crude light
They don't?
twin cairn
same logic
crude light
So what would Fr equal then
stoic torrent
They exert vertically downwards
crude light
Fr = Fsintheta
stoic torrent
So what would Fr equal then
Just Fsin(theta)
stoic torrent
Fr = Fsintheta
yup
stoic torrent
Fr = Fsintheta
two Fr?
crude light
What a lifesaver
stoic torrent
yeah
stoic torrent
Okay so i never resolve weights then?
For horizontal, no
stoic torrent
unless im finding moments
yup
twin cairn
when u solve for horizontal ignore vertical, nad when u solve for vertical ignore horizontal
stoic torrent
Okay so i never resolve weights then?
but, if you are resolving vertical, then obv you will
stoic torrent
when u solve for horizontal ignore vertical, nad when u solve for vertical ignor...
exaclty this
crude light
when u solve for horizontal ignore vertical, nad when u solve for vertical ignor...
Okayyyyy
I get it now
Guys you've been such a help, i'm fr done this time 🤣
Do you mind if I add you guys?
stoic torrent
Add as in?
crude light
Thank you so much, currently 11pm so im gonna sleep but thanks for helping me
As in friend request
stoic torrent
Thank you so much, currently 11pm so im gonna sleep but thanks for helping me
Oh lol
twin cairn
where are you from?
stoic torrent
its 345am here😭
crude light
england
stoic torrent
where are you from?
Uk
twin cairn
your origins from uk?
crude light
Yeah im british and arab
stoic torrent
Oh dude I love the hustle, 3am doing maths
Oh i was doing chem😭
twin cairn
that is what i thought I am from Morocco
twin cairn
oui khoya
twin cairn
nice to meet you
twin cairn
Oh i was doing chem😭
remind me of memorizing all sugars peptid ...
crude light
remind me of memorizing all sugars peptid ...
trauma 💀
twin cairn
lol
safe radishBOT
If you are done with this channel, please mark your problem as solved by typing .close
safe radishBOT
@crude light Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
safe radishBOT
tardy mango
<@&268886789983436800>
safe radishBOT
safe radishBOT
Available help channel!
fallen orchid
Hi! I am currently in Geometry with Stats in highschool.
I'm struggling with trig, inverse trig, and special right triangles.
thorn dragon
Hi! I am currently in Geometry with Stats in highschool.
I'm struggling with t...
do you have any worksheets?
fallen orchid
With me right now, i do. But they are completed.
I think i could do better if i wan't in the current situation that i am, but that unfourtunatey cant be helped.
clever tinsel
do you have any questions that you struggle with, then? we can look at those.
fallen orchid
I've always struggled with math, but nothing specifically.
Thats my main problem
So no specific things- its jsut everything, honestly.
Im not entirely sure how to get my grade up, or what to do at all.
thorn dragon
Im not entirely sure how to get my grade up, or what to do at all.
have you clarified any doubts with your teacher?
clever tinsel
mm, the way help channels work is that we work through questions you're struggling with together with you and guide you through them.
general study questions are usually better in #study-discussion.
fallen orchid
mm, the way help channels work is that we work through questions you're struggli...
Oh! I didn't see that im sorry
clever tinsel
no worries!
fallen orchid
have you clarified any doubts with your teacher?
Yes. I have.
He is not the greatest and his exact words to me when i met with him were
" That's your problem. I'm teaching perfectly "
clever tinsel
as a teacher myself, what is that attitude.
fallen orchid
I can move there if need be
fallen orchid
as a teacher myself, what is that attitude.
He is not the greatest person.
thorn dragon
Yes. I have.
He is not the greatest and his exact words to me when i met with h...
no way
clever tinsel
I think the community there might be better, though there are no restrictions on asking this sort of questions here. it's just that it may be a little hard to walk you through everything in one help session.
thorn dragon
so he's letting you suffer
clever tinsel
He is not the greatest person.
though if I may say, this is the understatement of the century.
fallen orchid
so he's letting you suffer
yep.
also, we arent allowed to sit down or ask eachother questions. We must ask the teacher.
We get new seating every day. Its randomized ( except its useless because we arent allowed to talk to eachother)
the highest grade on our recent trig was a 32%
thorn dragon
yep.
also, we arent allowed to sit down or ask eachother questions. We must ask...
WHAT
a 32%???
fallen orchid
I think the community there might be better, though there are no restrictions on...
Ok. so i'll close this and move over there.
clever tinsel
if you have more specific questions down the line though, feel free to ask it here!
safe radishBOT
safe radishBOT
Available help channel!
vapid cypress
if A is a 3X3 matrix and B is a 3X2 matrix and its given that AB = 0, can we say that either A is 0 B is 0?
safe radishBOT
if A is a 3X3 matrix and B is a 3X2 matrix and its given that AB = 0, can we say...
vapid cypress
or under what condition is it true that A = 0?
vague phoenix
What have you tried
vapid cypress
What have you tried
idk where to start tbh
peak estuary
when can it happen that Ax=0 for some vector x?
vague phoenix
if A is a 3X3 matrix and B is a 3X2 matrix and its given that AB = 0, can we say...
Are you sure AB=0 then either A=O or B=0? Do you sure this holds every time?
vapid cypress
Are you sure AB=0 then either A=O or B=0? Do you sure this holds every time?
i dont think it holds true everytime
but under what condition does A=0 hold true
vapid cypress
when can it happen that Ax=0 for some vector x?
is this smtg related eigenvectors
peak estuary
no
vapid cypress
i dont know much abt them tbh
peak estuary
well, technically you could phrase it like that. but no
do you know null space/kernel ?
vapid cypress
when can it happen that Ax=0 for some vector x?
wait A is a transformation matrix so it has to be null for the resultant vwctor to be null
nno i havent dont linal
peak estuary
wait A is a transformation matrix so it has to be null for the resultant vwctor ...
no
peak estuary
why are you doing linear algebra if you havent done linear algebra
vapid cypress
why are you doing linear algebra if you havent done linear algebra
this came up as part of a basic problem on matrices
vapid cypress
ok what i meant by i havent done linal is, i have done high school level linal
i havent taken a UG level course on linal
peak estuary
well I have no clue whats covered in a hs level la course. but the possibility that matrix*vector=0 should have come up
vapid cypress
well I have no clue whats covered in a hs level la course. but the possibility t...
uhm i honestly don't remember anytg of that sort
can u tell how u think abt it tho
peak estuary
wont mean anything to you
obsidian oracle
Do you know how to solve equations like Ax = b? under certain hypotheses
peak estuary
if you dont know kernels
vapid cypress
Do you know how to solve equations like Ax = b? under certain hypotheses
yea find inverse and shit
peak estuary
without inverse
obsidian oracle
So, when you have an inverse for A
then Ax = b (and thus Ax = 0) has a unique solution
and so Ax = 0 will mean automatically x = 0
When Ax isn't invertible
then Ax = 0 has multiple solutions
vapid cypress
then Ax = b (and thus Ax = 0) has a unique solution
so if A is invertible then x has to be 0
ok wait so A is invertible does that mean a matrix of the form (A^3 +aA^2 + bA +cI) is also invertible??
peak estuary
not in general
vapid cypress
basically its characteristic eqn
obsidian oracle
invertibility depends on the determinant
peak estuary
if thats the char poly then this matrix equals the zero matrix
which is famously not invertible
obsidian oracle
still you can't know whether this is invertible or not
peak estuary
ok wait so A is invertible does that mean a matrix of the form (A^3 +aA^2 + bA +...
without eigenvalues its hard to say when this is invertible
without actually computing it
vapid cypress
see so all this comes from the original problem in which i have a sq matrix AB with A(3X2) and B(2x3) , i know matrix AB, now i need to find BA
i found a way to get a characteristic eqn of BA
*the characteristic eqn of BA
safe radishBOT
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.
vapid cypress
no no
vapid cypress
ok so your original problem was completely irrelevant
it wasnt irrelevant
i needed these in the process
peak estuary
you think that you needed it. its called an xy problem. look it up. always ask the question that you were asked to do
flat frigateBOT
vapid cypress
the first line is the known eqn
we know AB matrix
so multiplying B on the LHS of the eqn
we get the 3rd line
and |AB| = 0 is a convenient fact here to get an eqn in the form of the characteristic eqn of BA
@peak estuary
it is given that |BA| is not equal to zero
peak estuary
what size does BA have
vapid cypress
what size does BA have
2X2
i mean u can factor out BA and throw it out as its det is non zero
so u'll get a "quadratic" in BA
peak estuary
which would be good given that you are looking for a quadratic after all
what is the general form of a char poly of a 2x2 matrix
vapid cypress
what is the general form of a char poly of a 2x2 matrix
yes yes
but as i asked earlier
i need to be certain that its equal to zero
coz that entire quadratic in BA is multiplied by B
and that is only equal to zero
peak estuary
if A is a 3X3 matrix and B is a 3X2 matrix and its given that AB = 0, can we say...
you flipped the sizes here which means you cant say shit here
for XY=0 with X 3x2 and Y 2x3 you can actually say something
vapid cypress
you flipped the sizes here which means you cant say shit here
ohh shit
peak estuary
namely that Y should have full rank
tho that presumably doesnt mean anything to you
vapid cypress
namely that Y should have full rank
whatr does full rank mean
peak estuary
as I guessed
vapid cypress
for XY=0 with X 3x2 and Y 2x3 you can actually say something
no in this case XY =0, where X is a 2X2 and Y is 2X3
peak estuary
another problem is that even if you find some polynomial which gives you the zero matrix, that does still not imply that it is the char poly
vapid cypress
another problem is that even if you find some polynomial which gives you the zer...
whattt
peak estuary
no in this case XY =0, where X is a 2X2 and Y is 2X3
yes but still same result
vapid cypress
for XY=0 with X 3x2 and Y 2x3 you can actually say something
what can u say though
and how can u say it
peak estuary
coz its either the characteristic polynomial or a multiple of it right?
its a multiple of the min poly but presumably you dont know what that is either
vapid cypress
its a multiple of the min poly but presumably you dont know what that is either
min poly of a 2X2 matrix is of degree 2
peak estuary
min poly of a 2X2 matrix is of degree 2
no
peak estuary
let X be the 2x2 identity matrix. what is the char poly? what do you get when you compute X^2-8X+7I ?
vapid cypress
ok so is there a way to solve my original question without having to do any of this
vapid cypress
let X be the 2x2 identity matrix. what is the char poly? what do you get when yo...
oh u get null matrix
peak estuary
there is but I am less and less interested in finding even lower tech solutions
vapid cypress
but this is a speical case
vapid cypress
there is but I am less and less interested in finding even lower tech solutions
just give me a direction
peak estuary
but this is a speical case
so? who says BA isnt the identity matrix
peak estuary
what is the general form of a char poly of a 2x2 matrix
you havent answered this yet
then you can compare with the poly you got with your attempt
vapid cypress
you havent answered this yet
A^2 - tr(A)A + |A|I
u can get the trace and determinant of the matrix BA using this
but isnt it assuming that the quadratic i got there is the characteristic poly of the matrix
simple galleon
hey whats up
vapid cypress
what are you trying to do?
the first line is what we have
the characteristic eqn of AB
in fact we have the whole matrix AB 3x3
A is 3x2 and B is 2x3
we need to find BA
and that was my work
in that pic
simple galleon
umm
vapid cypress
and is it possible to find the matrix itself
simple galleon
what is ab equal to
vapid cypress
its some 3x3 matrix with all the values given but it shud be irrelevant rn
right?
liike its not some standard matrix
vapid cypress
but its determinant is zero
simple galleon
oh ok
vapid cypress
im reading [this](https://math.stackexchange.com/questions/2898303/given-the-mat...
its not relevant here as A and B both are square matrices there
not h ere]
simple galleon
what is x here?
vapid cypress
what is x here?
its a scalar value
the sum of cofactors of the diagonal elements of AB
its from the characteristic eqn
vapid cypress
how would that equal the determinant exactly?
that is equal to the determinant of BA
from the work i've shown below
simple galleon
wait what is
i was saying BA+XI, what part of that is det BA?
oh wait nvm det ab = det ba
vapid cypress
.close
safe radishBOT
safe radishBOT
Available help channel!
upper cobalt
.reopen
brave wolf
.reopen
do you have a question to ask?
If so, go to e.g. #help-39 , write your question as the first message (DON'T use any .reopen commands) and DON'T delete the question
you can use any of these available channels
safe radishBOT
Available help channel!
cobalt saddle
This
agile scaffold
have you taken the derivative of it yet?
cobalt saddle
have you taken the derivative of it yet?
Yeah
cobalt saddle
what did you get
The second picture
agile scaffold
theres a mistake in your first line already
chain rule for both arctan 3x and arcsin(...)
cobalt saddle
theres a mistake in your first line already
For arctan i get but why arcsine
agile scaffold
For arctan i get but why arcsine
im pretty sure this part is incorrect
cobalt saddle
im pretty sure this part is incorrect
Do you not use quotient rule then chain rule?
tall sierra
agile scaffold
this is what i got
here v is the 3x/sqrt(9x^2 + 1)
wait no
oh wait dude the qs is wrong you cant do that
it only works if arcsin(v) is v = 3x/sqrt(9x^2 + 1) not v = 1/sqrt(9x^2 + 1)
safe radishBOT
safe radishBOT
Available help channel!
gentle summit
Im so confused. There's no other context besides the one in the screenshot. I don't know how to start with ii), iii)
safe radishBOT
Im so confused. There's no other context besides the one in the screenshot. I do...
vague phoenix
For question 2, assume we fix the seat X
then since Y cant sit next to X, then how many options left?
broken stream
it only works if arcsin(v) is v = 3x/sqrt(9x^2 + 1) not v = 1/sqrt(9x^2 + 1)
Bro what the hell am i reading i just started my cert 3 for maths and this makes me scared
agile scaffold
Bro what the hell am i reading i just started my cert 3 for maths and this makes...
LOL its okayy
gentle summit
then since Y cant sit next to X, then how many options left?
I assume 6... Where should we go from there?
vague phoenix
So you got the total is 7! ways to rearrange 8 people
how many ways can X sit next to Y?
gentle summit
how many ways can X sit next to Y?
Ahhh i'm a bit confused. Is it two?
I looked at the answer scheme and they counted the number of ways to arrange them both by multiplying 6 x 5. I'm assuming that 6 is the number of seats that Ben has left so is 5 the number of seats that Dorty has?
My bad, I'm really bad at english if it's math related stuff so it's hard for me to understand 😭
What's with questions that look like riddles 😔
safe radishBOT
@gentle summit Has your question been resolved?
clever tinsel
is this still unsolved, or are you done? and if it is still unsolved, would you prefer I speak in English or Malay?
lavish magnet
When I divide x^9/2 by x^1/2 I get 9? So how are they taking x^1/2 in common? What's tripping me out is when I distribute and expand the bracket I get the same equation so I know its correct I don't understand why I'm getting a different answer myself.
safe radishBOT
When I divide x^9/2 by x^1/2 I get 9? So how are they taking x^1/2 in common? Wh...
lavish magnet
nvm im dumb
when powers are divided tehy get substracted
i've been dividing the powers not substracting them.
.close
safe radishBOT
safe radishBOT
Available help channel!
atomic bloom
If the eqn of the circle is x^2 + y^2 = 4, other than calculating semi perimeter what other ways are there to find the area?
safe radishBOT
If the eqn of the circle is x^2 + y^2 = 4, other than calculating semi perimeter...
opaque fern
,rccw
flat frigateBOT
opaque fern
If the eqn of the circle is x^2 + y^2 = 4, other than calculating semi perimeter...
do note that CD is the perp bisector of AB
atomic bloom
yes
opaque fern
if a quadrilateral ahs its diagonals intersect at 90 degrees, what is its area
atomic bloom
1/2(product of diagonal)(h1+h2)
opaque fern
why (h1+h2)
atomic bloom
perpendicular from the sides ig
safe radishBOT
@atomic bloom Has your question been resolved?
jade charm
the correct formula is 1/2 product of diagonals when they are perpendicular
also, are you sure the information provided is complete?
something seems to be missing
safe radishBOT
@atomic bloom Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
primal gazelle
how many subets of size k from {1,2,...,2n} are there such that no two consecutive numbers are in the subset? Answer is (2n-k+1) C k, why?
safe radishBOT
how many subets of size k from {1,2,...,2n} are there such that no two consecuti...
safe radishBOT
pliant perch
ye
safe radishBOT
Available help channel!
vale onyx
help with understanding mark scheme
safe radishBOT
help with understanding mark scheme
vale onyx
I got stuck here
like what exactly are they doing, i dont really understand the concept of the question
like is it some graphical thing or just regular proof
uhh guys pls elp
bump
ok fawk it
.close
safe radishBOT
safe radishBOT
Available help channel!
coarse tulip
i need a channel
safe radishBOT
i need a channel
raven heart
& you got it, gg
coarse tulip
thank you
Can anyone help me out with finding its formula, so that i can follow the formula and solve it, please
safe radishBOT
@coarse tulip Has your question been resolved?
cedar snow
Can anyone help me out with finding its formula, so that i can follow the formul...
-
you first need to find the mean using the formula for finding the mean, in this case it should be:
$\bar{X} = \frac{\sum (X \cdot f)}{N}$ -
formula for variance (since you can't get stdev without variance), which is:
$\sigma^2 = \frac{\sum f (X - \mu)^2}{N}$
finally for c.) standard deviation, just get the square root of the variance:
$\sigma = \sqrt{\sigma^2}$
d. and e.) use the formula for finding the z-score:
$z = \frac{X - \mu}{\sigma}$
flat frigateBOT
undermaster
1. you first need to find the mean using the formula for finding the mean, in this case it should be:
$\bar{X} = \frac{\sum (X \cdot f)}{N}$
2. formula for variance (since you can't get stdev without variance), which is:
$\sigma^2 = \frac{\sum f (X - \mu)^2}{N}$
finally for c.) standard deviation, just get the square root of the variance:
$\sigma = \sqrt{\sigma^2}$
d. and e.) use the formula for finding the z-score:
$z = \frac{X - \mu}{\sigma}$
cedar snow
for the ones with summations i recommend you setup a table to avoid complications further when adding
safe radishBOT
safe radishBOT
Available help channel!
opaque fern
Just more of a conceptual question: I am simulating the construction of a pulse wave/function by means of a Fourier transform (i.e., the sum of complex exponentials) and it seems like no matter how much you increase the accuracy of the transform you are never able to rid of those ripples at the transitions. Why is that?
safe radishBOT
Just more of a conceptual question: I am simulating the construction of a pulse ...
agile scaffold
Just more of a conceptual question: I am simulating the construction of a pulse ...
i think you might be better off in #math-discussion
opaque fern
i think you might be better off in <#359052581022203914>
My messages usually get drowned out in there so I would rather not
median vigil
,w gibbs phenomenon
opaque fern
Oh there is a term for it
Let me read
so the fourier series converges pointwise to the square wave but not uniformly?
so there will always be an 8.95% overshoot
.close
safe radishBOT
safe radishBOT
Available help channel!
vale onyx
safe radishBOT
vale onyx
i was doing this question and i went wrong somewhere
instead of putting 2(n+2) i expanded those
quiet plume
Just show your work
thin bridge
dropped the - sign
nothing inherently wrong with expanding 2(n+2) to 2n + 4
as those are equivalent, though its a little inefficient
safe radishBOT
safe radishBOT
Available help channel!
agile moss
how do i do a specific question which may be like: the average of a, b, c, d and e is 48. What is the product of a and e?
safe radishBOT
how do i do a specific question which may be like: the average of a, b, c, d and...
peak estuary
well you cant solve that
peak estuary
the numbers could be 1, 200, 30, 8, 1 or 5, 100, 100, 30, 5 or lots of other options
you cannot find the product of a and e with just this information
agile moss
should i try ai?
agile moss
ai cant suddenly do impossible things
ill try?
peak estuary
or were you given this problem
agile moss
or were you given this problem
given
peak estuary
!original
safe radishBOT
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.
agile moss
ok here
The average of five consecutive numbers A. B, C, D and E is 48. What is the product of A and E?
quiet plume
The fact that they're consecutive is very important.
peak estuary
consecutive is a very strong extra property
agile moss
oh
peak estuary
observe that both examples I gave do not satisfy it
agile moss
I contacted my teacher and he hinted that the middle number is the average
and everthing before it u havesubtract and after you have to add or smthn like that
peak estuary
yes
peak estuary
yes
jade charm
yes
agile moss
so it is 46X50=2300?
peak estuary
yes
safe radishBOT
safe radishBOT
Available help channel!
twin prawn
hello !
twin prawn
i genuinely dont know where to go next TT the problem is is thats theres a fraction in a fraction
quiet plume
Well first write $\frac{1}{x+3} - 1$ on a common denominator
flat frigateBOT
Azyrashacorki
twin prawn
Well first write $\frac{1}{x+3} - 1$ on a common denominator
the original was
$\frac{\frac{1}{x+3} - 1}{x + 2}$
flat frigateBOT
Maladroit
twin prawn
i separated it thinking i could do something about it
quiet plume
Yes, I'm just saying you should treat the numerator first by writing it on a common denominator
twin prawn
**Azyrashacorki**
Oh i get it
quiet plume
This is just $\frac{1}{x+2} \left( \frac{1}{x+3} - 1\right)$, so focus on the parentheses first.
flat frigateBOT
Azyrashacorki
flat frigateBOT
Maladroit
quiet plume
Indeed
twin prawn
the overall goal here is to get rid of the x + 2 because x is approaching -2
quiet plume
Yes
flat frigateBOT
Maladroit
quiet plume
Before doing that, try rewriting 1-(x+3).
twin prawn
oh wair
OH
i got it
$\frac{\frac{x+2}{x+3}}{x+2} = \frac{x+2}{x+3} * \frac{1}{x+2}$
flat frigateBOT
Maladroit
wind lodge
safe radishBOT
wind lodge
Im sitting with question d) and there is something im missing, because i keep getting that its 0
First of all, is it true that $\nabla \times \mathbf{u} = \mathbf{e}_i \times \frac{\partial}{\partial x_i}(\mathbf{u)}$
flat frigateBOT
Alrik
wind lodge
This is the solution to the problem but i dont follow.
I cant find this definition of curl and it doesn't make sense to me that it's defined like this
.close
safe radishBOT
wind lodge
.reopen
safe radishBOT
✅ Original question: #help-23 message
wind lodge
Nope i dont understand the first step
celest ember
do you know what curl is?
wind lodge
Yes
I have this and this makes sense to me, i dont see how it is the same thing as above. i will be the index of the direction of the curl i suppose, j will be the index of the derivative and k will be the index of the thing that we are taking the curl of
cause then i would be the same as j?
or am i misunderstanding? Are they different definitions? Am i just tupid?
Maybe its the sums that are messing with me
celest ember
**Alrik**
ei is the direction of del/del(x_i)
its just separating the direction and operator in the cross product
you can separate everytin and just cross the directions
wind lodge
cause then i would be the same as j?
I think this is my issue
because of this which i suppose isnt the same thing
in my mind we get $\varepsilon_{iik}$
flat frigateBOT
Alrik
wind lodge
which is always zero
celest ember
cause then i would be the same as j?
no j x k = i, so your final direction will be i
wind lodge
so what is my epsilon
celest ember
epsilon is just a magnitude after crossing the basis vectors i think
celest ember
o then idk
wind lodge
Thats alright
its supposed to take care of my issues in a nice way
its a nice way to write the cross product
but its causing me headaches
safe radishBOT
@wind lodge Has your question been resolved?
safe radishBOT
@wind lodge Has your question been resolved?
slender anchor
in order to choose epsilon dont you need a unique limit why was the epsilon chosen arbitrarily here while proving that the limit doesnt exist for this function (by the epsilon-delta definition)
safe radishBOT
in order to choose epsilon dont you need a unique limit why was the epsilon chos...
quiet plume
The point is that if you can find one epsilon that doesn't work, then the limit doesn't exist.
slender anchor
isnt an epsilon always "around" a limit like how delta is around a limiting input
quiet plume
This particular shot illustrates that the limit isn't 1.5
But in the video he moves it around and no matter the position you pick it still does the same thing.
The fact that there's even this "epsilon-gap" there means that no matter the value you pick for the limit you'll fail to get a corresponding delta.
slender anchor
The fact that there's even this "epsilon-gap" there means that no matter the val...
what does he mean by everything
quiet plume
There is no value for the limit you can choose where the function remains within a distance epsilon of that output.
slender anchor
There is no value for the limit you can choose where the function remains within...
its obvious that the range of outputs is big when the limit is assumed to be 1.5 but how did we deduce that limit =2 and limit =1
quiet plume
What do you mean by lim = 2 and 1?
If you set the limit to 2, then no matter what delta you choose you'll have some part of f that's outside of the range delimited by epsilon.
Similarly for 1
slender anchor
What do you mean by lim = 2 and 1?
If you set the limit to 2, then no matter wha...
no like for limit 1.5 even when delta approached zero epsilon stopped at 0.5 which means that both dont form a limit how did we show this for lim to 2 and lim to 1
quiet plume
no like for limit 1.5 even when delta approached zero epsilon stopped at 0.5 whi...
I'm not sure what you're asking. The argument is the same. If you try to set the limit to 2, then no matter delta there's stuff outside of the epsilon region around 2.
Just like when you set it to 1.5 no matter delta there's stuff outside the epsilon region around 1.5
safe radishBOT
@slender anchor Has your question been resolved?
zenith maple
its obvious that the range of outputs is big when the limit is assumed to be 1.5...
See if you are taking delta on either side of 0 then if you take epsilon at say 2 then for the delta on the left side the functions value falls out of the range of epsilon similarly if you take 1 the right side will be out of range
So the function's value on either side must fall with the limiting range of epsilon
slender anchor
See if you are taking delta on either side of 0 then if you take epsilon at say ...
why is the epsilon assumed to be less than 1
zenith maple
why is the epsilon assumed to be less than 1
We are just trying to see if the limit is satisfied for all values of epsilon so you can start with however a big epsilon you want but you want to see if that limit is valid as to continuously make epsilon smaller (make it approach zero)
slender anchor
isnt that unrigorous as the epsilon be any value
zenith maple
isnt that unrigorous as the epsilon be any value
Don't think any it is 'for all'
slender anchor
Don't think any it is 'for all'
ohh
zenith maple
it is intentionally made 0.4 so that epsilon stays out of the functions range
It is just one of many cases if you look at any epsilon< 1
slender anchor
Don't think any it is 'for all'
so as long as you can fix a epsilon value and it works out with the deltas then we have a limit?
zenith maple
so as long as you can fix a epsilon value and it works out with the deltas then ...
No you should see the trend as epsilon moves closer to 0
Not any one value
But one example that falls out of range is enough to prove that the limit DNE
Because all the ranges in that range also imply the same
This is the epsilon delta definition
No extra caveats
safe radishBOT
@slender anchor Has your question been resolved?
turbid rivet
One message removed from a suspended account.
safe radishBOT
One message removed from a suspended account.
brave wolf
One message removed from a suspended account.
do you know what limits are in general?
turbid rivet
do you know what limits are in general?
One message removed from a suspended account.
brave wolf
so your only issue is with the 1^+ I suppose?
turbid rivet
One message removed from a suspended account.
brave wolf
oh alright
so the first limit says x -> 1^+
let's just ignore the + for now and find x = 1
it's right here
so we're gonna look at what happens as x approaches that
brave wolf
so the first limit says x -> 1^+
now we have to deal with the +
turbid rivet
One message removed from a suspended account.
brave wolf
the + basically means that we're approaching it from right
turbid rivet
One message removed from a suspended account.
brave wolf
and where does it go if you're approaching it from right?
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
prolly a typo
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
One message removed from a suspended account.
the both directional limit doesnt exist, but the limit from + side does
brave wolf
One message removed from a suspended account.
*because it's not continuous
turbid rivet
One message removed from a suspended account.
brave wolf
but that only works for both-sided limits
turbid rivet
One message removed from a suspended account.
brave wolf
One message removed from a suspended account.
yep
turbid rivet
One message removed from a suspended account.
brave wolf
and what would the 1^- limit be?
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
One message removed from a suspended account.
if we're talking about the limit, you dont really care about what happens exactly at the point
you just care about what happens around it
the x -> 1^- limit is 1
turbid rivet
One message removed from a suspended account.
brave wolf
and the hole doesnt really matter
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
yeah
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
so what do you think?
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
indeed
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
what about 9?
turbid rivet
One message removed from a suspended account.
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
either the limits from - and + match - and then the limit exists and is the common limit
turbid rivet
One message removed from a suspended account.
brave wolf
One message removed from a suspended account.
still not
brave wolf
either the limits from - and + match - and then the limit exists and is the comm...
or the limits from - and + don't match and then the limit doesnt exist
turbid rivet
One message removed from a suspended account.
brave wolf
you dont take the average or anything like that, which seems like what you tried to do
it just doesnt exist if it doesnt match
turbid rivet
One message removed from a suspended account.
One message removed from a suspended account.
One message removed from a suspended account.
One message removed from a suspended account.
brave wolf
One message removed from a suspended account.
np
turbid rivet
One message removed from a suspended account.
safe radishBOT
safe radishBOT
Available help channel!
atomic python
how do i label the dual of a graph?
safe radishBOT
how do i label the dual of a graph?
@atomic python Has your question been resolved?
Available help channel!
cobalt lake
hey, looking for some general advice (not a specific problem). I’ve got important college entrance exams coming up and I can choose between a national informatics test or a uni-specific math exam. I’ll take both and see which score is better.
problem is the math one: I’m really solid at algebra and calculus, but I get like 70% on geometry and around ~60% on probability tests. I know people say “just do more problems” but the questions change a lot every year, and since these are my weaker areas, I struggle with them.
I tried private lessons but they didn’t help much, mostly stuff I know or could’ve read from my textbooks.
How would you suggest I improve in geometry and probability and how should I prepare for those problems on the exam?
safe radishBOT
hey, looking for some general advice (not a specific problem). I’ve got importan...
primal gazelle
hey, looking for some general advice (not a specific problem). I’ve got importan...
do problems
cobalt lake
.close
safe radishBOT
safe radishBOT
Available help channel!
safe radishBOT
honest idol
quiet plume
So we keep (3,1) to the side for now.
Now we want to investigate the boundary.
We'll keep the vertices in bank as well for now since they are corners and we can't deal with corners with derivatives anyways.
So we have (3,1), (0,0), (0,4) and (5,0) in the bank.
Let's pick the left side from (0,0) to (0,4) first.
honest idol
Let's pick the left side from (0,0) to (0,4) first.
test those for the inequalities?
quiet plume
No, we want to find extrema of f(x,y) on the sides.
One the line x=0, the value of f(x,y) is given by f(0,y), yes?
honest idol
No, we want to find extrema of f(x,y) on the sides.
yes
honest idol
One the line x=0, the value of f(x,y) is given by f(0,y), yes?
but i dont get this part
quiet plume
We want the value of f(x,y) along those lines.
The left leg is just the line x = 0 from y=0 to y=4.
So you should consider g(y) = f(0,y) and maximize it like you would any one-variable function.
honest idol
We want the value of f(x,y) along those lines.
yes
i keep forgetting my keybaord in arabic 😂
quiet plume
Ooops
honest idol
The left leg is just the line x = 0 from y=0 to y=4.
yea..
honest idol
The left leg is just the line x = 0 from y=0 to y=4.
wdym by the left leg
honest idol
The side (0,0) -- (0,4)
ohh
and we do the same thing for all sides right
and to be specific here we are actually considering the region under the triangle not the triangle itself correct
quiet plume
Here we're just dealing with the lines themselves.
We've already investigated inside the triangle, now we need to to the sides.
For the first side for instance, as I said, this is just the line x=0 from y=0 to y=4, so we're looking for possible critical points of
g(y) = f(0,y) within the interval (0,4).
g(y) = -3y, so g'(y) = -3. This is never 0, so no critical points. Done for this side.
honest idol
For the first side for instance, as I said, this is just the line x=0 from y=0 t...
where did -3y come from
yeah idk how you did that
also idk why we need to investigate the triangle
quiet plume
also idk why we need to investigate the triangle
Because you need to treat the boundary separately. For instance, f(x,y) = x^2 + y^2 only has one critical point : (0,0). It has no maximum.
However, if you restrict the domain to the region x^2 + y^2 <= 1, then suddenly, on the boundary, there's a maximum. In this case it's fairly simple because any point on the boundary is a maximum, but it means that considering a closed region may add some extrema that aren't there originally.
quiet plume
where did -3y come from
It's what you get for g(y) = f(0,y).
Plugging in x=0 in f(x,y).
honest idol
It's what you get for g(y) = f(0,y).
sorry i dont get it, why isnt the line on the left just y = 1
quiet plume
y=1 is a horizontal line
quiet plume
How I did what?
honest idol
express the left side
honest idol
yea
quiet plume
And the left side is a vertical line
honest idol
yes
quiet plume
Similarly, the bottom side is on the line y=0
honest idol
And the left side is a vertical line
how do you show this particular line
quiet plume
If you want to think about it some other way, we could say that points the left side are parametrized by $\gamma(t) = (0,t)$ with $t \in (0,4)$. Then you want to maximize $f(\gamma(t)) = f(0,t) = -3t$.
flat frigateBOT
Azyrashacorki
honest idol
**Azyrashacorki**
is that just a vector that you expressed
because i dont see any equations initially
okay i actually dont get how you did that ngl
quiet plume
I'm just trying to find other ways you can see that the side on the left is on the line x=0
honest idol
whats y(t) = (0,t)
quiet plume
It's a curve parametrized by t which gives the points on the line segment we're talking about
The line between (0,0) and (0,4).
But again this is the same as considering the line x=0 between y=0 and y=4.
honest idol
But again this is the same as considering the line x=0 between y=0 and y=4.
oh so you do pathagrean theorem? 💀
honest idol
This is just the region R drawn with the left side highlighted
no i mean can you find the equation of the two lines then apply pathagrean identity
quiet plume
We're not really interested in the length of the hypotenuse.
We just want to see what value f(x,y) takes on the left side of the triangle.
honest idol
We're not really interested in the length of the hypotenuse.
no were interesting in the blue side
which can be obtained via pathagrean right
then plug that into f(x,y)?
quiet plume
We're not looking for its length
honest idol
oh ok
quiet plume
This left side contains points of the form (0,y) with y between 0 and 4
honest idol
This left side contains points of the form (0,y) with y between 0 and 4
yeah but im not getting how to express it
quiet plume
It's just a vertical line between the points (0,0) and (0,4).
This line has equation x=0, that's the equation of a vertical line going through (0,0) and (0,4).
On this line, the value of f depends only on y, since x=0.
g(y) = f(0,y) is a function of y
honest idol
This line has equation x=0, that's the equation of a vertical line going through...
okay im good till this part
honest idol
On this line, the value of f depends only on y, since x=0.
g(y) = f(0,y) is a f...
but i dont get what youre saying here
quiet plume
We're just restricting f(x,y) to x=0.
This is the same thing as looking at f(0,y)
Fixing x=0.
honest idol
This is the same thing as looking at f(0,y)
ohhh i think i understand you now
but were only gonna get anything if the function touches that region. rigth
quiet plume
but were only gonna get anything if the function touches that region. rigth
What do you mean by this?
honest idol
like the points on the left side of the triangle need to be mutually inclusive with the points in f(0,y)
right
quiet plume
You mean we should ensure that y is between 0 and 4 ?
So that the line doesn't keep going
honest idol
You mean we should ensure that y is between 0 and 4 ?
no like
honest idol
So the goal is to find critical point to g(y) = f(0,y).
ohh ok ay i see what youre doing now
but how does that exactly restrict it
to that specific line
because (0,y) is more general
and could be longer obviously
quiet plume
Well we're only interested in the segment between y=0 and y=4.
So if we do find critical points, we'll only keep those in there.
honest idol
So if we do find critical points, we'll only keep those in there.
so you mean youll plug into the inequalities as well?
quiet plume
Right now the only thing that exists is this segment between (0,0) and (0,4).
There's nothing else we're considering.
We want to find critical point of f on this segment on which x=0 for y between 0 and 4.
This is the same as finding critical point of the function g(y) = f(0,y) = -3y for 0 < y < 4.
It's like you're given a new problem saying "Find critical point of the function f(x,y) restricted to the line x=0 with -4 < y < 4."
safe radishBOT
@honest idol Has your question been resolved?
honest idol
This is the same as finding critical point of the function g(y) = f(0,y) = -3y f...
yes
well
hm
quiet plume
So do you agree that on this segment we have g(y) = f(0,y) = -3y?
honest idol
So do you agree that on this segment we have g(y) = f(0,y) = -3y?
yes
i do
but we are still considering some bound right
the length of the triangle specifically
so the inequality 0<= y <=4
right
honest idol
So does g(y) have any critical points?
gotta check it right now
honest idol
So does g(y) have any critical points?
i took both partials and i got -3 and 0
quiet plume
First off g(y) = -3y is a function of one variable. You don't need to take the partial with respect to x.
That being said, g'(y) = -3, so there are no critical points on this line.
honest idol
First off g(y) = -3y is a function of one variable. You don't need to take the p...
how do we know theres no critical points from getting -3
quiet plume
Can the derivative be 0 if it’s constant -3?
honest idol
Can the derivative be 0 if it’s constant -3?
no
quiet plume
So there aren’t any critical points on the line
quiet plume
Okay. So this is for the left side of the triangle.
We can also check the bottom side similarly since it’s on the line y=0, so you can check whether there are critical points for the function g(x) =f(x,0)
honest idol
Okay. So this is for the left side of the triangle.
We can also check the botto...
im just wondering
honest idol
so like i wanna summarize the objections here:
(i dont know if this applies for all optimization problems or not)
we find the critical points on the funciton itself then see if its inside the bounds of the shape bounding it or not
then we wanna check the bounds intersecting the shape thats bounding itself , then plug into whichever expression that expresses that particular bound
@quiet plume
quiet plume
so like i wanna summarize the objections here:
(i dont know if this applies for...
First we have a region.
The gradient of f can only inform us about possible extrema on the interior of the region.
This means we need to check the boundary of the region for extrema manually.
The way you do this, in a way, is to parameterize the boundary (maybe piece by piece) and you find critical point of f evaluated along this parameterization.
For the left side of the triangle, we parameterize this piece of the boundary by the points (0,y) for y between 0 and 4.
For the bottom side, you can parameterize it with the points (x,0) where x is between 0 and 4.
For the hypotenuse, we know that y=-4/5x +4, so we may parameterize is as the points (x, 4-4x/5) for x between 0 and 5.
All of those parameterizations, once plugged into f, yield one-variable functions which you find critical points for as usual.
Once you’ve singled out the points which are : critical in the interior and critical on the boundary, then you test them one by one. The largest is your maximum and the smallest is the minimum.
The same holds for pretty much all optimization problems in R^n where you have a constraint which is a closed, bounded set.
The main difference encountered is with the method used to find extrema on the boundary.
When the boundary is simple like in this case, considering functions of one variable works. It may be that the constraint is complicated though, and then it may call for a method called Lagrange multipliers, which help deal with smooth but complicated boundaries.
honest idol
The main difference encountered is with the method used to find extrema on the b...
hm yeah this is the next topic lol
safe radishBOT
@honest idol Has your question been resolved?
safe radishBOT
@honest idol Has your question been resolved?
honest idol
@quiet plume thanks alot for the help btw
agile scaffold
when u sub -4/5x 5 into ur function an expand it ur last term distribution is wrong
you wrote -12/5x - 12 when its + 12/5x - 12
the next line u took the derivative of +4x and got x which is also wrong
(also to find the absolute extrema you have to check all three boundaries of the triangle, u did not check the bottom side)
honest idol
when u sub -4/5x 5 into ur function an expand it ur last term distribution is wr...
oh thanks, i just wanted to make sure that i didnt get anything conceptual wrong
safe radishBOT
@honest idol Has your question been resolved?
stuck cedar
How am i supposed to solve this lol. i fell for an obvious trap with the options but i dont even know how to begin solving this, the solution is just a total mess too
safe radishBOT
How am i supposed to solve this lol. i fell for an obvious trap with the options...
spring bison
Start by defining a function where g(k) = P(k) - k/k+1 for k = 0, 1,2...k
Then we know that g(k) = k(k-1)(k-2)..(k-n) since k = 1,2,3..n are roots for g(k)
vague phoenix
Or assume a Q(x)
spring bison
finally plug in n+1 for k and rearrange to get P(n+1)
spring bison
Or assume a Q(x)
of corse we could define any function
vague phoenix
Ye ye
obsidian oracle
Start by defining a function where g(k) = P(k) - k/k+1 for k = 0, 1,2...k
sorry, how exactly do you define that function
vague phoenix
A side function
spring bison
kind of like auxillary diagrams in geometry(The purpose of the function)
stuck cedar
oooh i see
think i'm getting the hang of it now, the solution also says to define a new function
obsidian oracle
Then we know that g(k) = k(k-1)(k-2)..(k-n) since k = 1,2,3..n are roots for g(k...
for which k? just k = 0,..., n or all k? It seems I'm getting lost in this one
isn't it just lagrange interpolation
obsidian oracle
so, g(x) = P(x) - x/(x+1)? which is not a polynomial
stuck cedar
Solution says to define a function Q(x) = (x+1)P(x) - x
stuck cedar
i dont understand the why part of it
i'm not exactly good at this kinda math so... gotta teach me step by step
vague phoenix
You see P have k degree
obsidian oracle
i dont understand the why part of it
Q(x) = (x+1)P(x) - x is a polynomial of degree n+1
and you'll find it has n+1 easy to find roots
(because of what the exercise gives you)
vague phoenix
And since x=0,1,....n then Q0=Q1=Q2=0
stuck cedar
hm... okay, think i understand, so this is kinda like a pattern based question where i'm supposed to use a secondary function to solve it, correct?
nvm got it
proven smelt
safe radishBOT
proven smelt
idk how to ocntinue, not sure if i did it right
primal gazelle
idk how to ocntinue, not sure if i did it right
so far so good
now we need to show 3k + 3 divides this expression
proven smelt
ive tried factorising but im not getting anywhere lol