#help-42
mossy wigeon
ouii
opal sinew
donc ca ca repond a question 1?
opal sinew
ahh
mossy wigeon
tu vois
opal sinew
c toutT
?
parce que le prof a dit quon peut utiliser un maximum de 1 page et demi dont il s'attent a une longue preuve
mossy wigeon
aahhh okay genre montrer en preuve mdr
estce que tas besoin de genre
rules of inference
et chose comme ca
mossy wigeon
je dis ca comme ca, mais si je dois le prouver je peux dire genre.. 1. AxO1 = r = Ax O2 et BxO1 = r = BxO2
donc juste ca tu peux savoir quils sont equidistance a O1 et O2
att enft
tas juste besoin de ca
mossy wigeon
il dis que si un point M est equidistant de A et B il est sur la droite perpendicu a AB passant par milieu I oui? et si un point est sur cette mediatrice il est equidistant a A et a B
donc la on a prouve que A et B
sont equidistant a o1 O2
donc A B sont tous 2 la mediatrice de O1O2
et droite = ligne entre 2 points A B est la mediatrice
jsp si mon explication fait du sense mdr francais cest genere ma troisieme langue š
opal sinew
damn troisieme langue is crazy cest quoi les autres
mossy wigeon
mais oui cest literalement ca ce que tas besoin
opal sinew
je relis pour comprendre
mossy wigeon
bah mandarin anglais aha
mossy wigeon
haha nice
opal sinew
donc si M est a la meme distance de A et B il est obligatoirement sur une droite perpendiculaire a A et B car sinon cest impossible?
mossy wigeon
ca cest dans les notes de cours
ce que tas ici
opal sinew
mais comme on dirait que cest trop simpleš
mossy wigeon
bah tas tout lexplication ici sur ton pdf š
ca depend de la profondeur
de ce que ton prof demande
parce que moi il suffit de montrer que il y a deja une preuve connu pour le prouver
opal sinew
bah aupire jvais ecrire juste ca et voir lautre monde si ils ont mis plus
mais la jai tu prouver le 1
mossy wigeon
si ton preuve tas le droit dutilizer une preuve qui a deja ete prouve avant oui
sinon ca va te prendre des heures
opal sinew
cest ca que je me dit haha
mossy wigeon
estce que tes premiere annee?
opal sinew
donc pour le 2 je fais juste "copier" l'image que jai send des note de cours?
opal sinew
estce que tes premiere annee?
premiere session d'universitƩ
oui
it is not looking goodš
mossy wigeon
donc pour le 2 je fais juste "copier" l'image que jai send des note de cours?
bah tse tas prouve que AB est mediatrice de O1O2, donc CD et EF sont aussi des mediatrices donc la par ta theoreme de mediatrice les mediatrices qui forment le triangle sont concourants
opal sinew
toi aussi premiere annƩe?
opal sinew
wow je me fais intellect gap
mossy wigeon
š its ok jai tryhard pendant lete pour ca
opal sinew
lespreuves sont trop chiants honnetemenet
en plus le prof est tlm mid
mossy wigeon
le mien est un vieux mr que personne entend mdr
cest meme pas la peine dallee
avec le strike de stm en plus
opal sinew
att tes mtl aussi??
mossy wigeon
oui mdr
opal sinew
what uni
mossy wigeon
haha bah deja francais et anglais
opal sinew
avec le strike de stm en plus
currently a la biblio en train dattendre
mossy wigeon
cest un big giveaway
opal sinew
cest un big giveaway
mm pour toi jetais pas sur
opal sinew
a cause de ca
nah moi je rate pas mais genre vendredi je fini a 10h30 et les metro repartes a 2h45
...
mossy wigeon
š
non moi jsuis dans
genie logicielle
donc premier session je me fais niquer en math aussi
opal sinew
Whaatt ta geometrie en genie logicielle??
mossy wigeon
pas necessairement geometrie
mais on a genre
des millions de preuves a faire
cest pour ca que je savais pas a quelle niveau faut que tu demontres tes preuves
normallement pour moi il suffit de prouver par une autre preuve qui existe
opal sinew
des millions de preuves a faire
Algebre lineaireš
opal sinew
Je sais pas comment je vais faire
Calc 1 et proba c free
Mais geo et alg lineaire c cooked
opal sinew
Oui
opal sinew
......
mossy wigeon
preuve on the other hand š
opal sinew
Ca cetait le premier devoire de alg lin
mossy wigeon
genre les dimensions etc
opal sinew
Moi aussi
mossy wigeon
ca cest plus discreet math
opal sinew
š
Chui tlm lost
C wild
Mais exam c apres la semain de lecture so we dont think about itš
mossy wigeon
all flower and rainbows until then š
opal sinew
Merci merci mais je vais etre de retour dans le serv soon
opal sinew
bonnne chance!
Btw je peut te add? Pcq jvais finir le devoir quand jarr chez moi
mossy wigeon
yeah sure but im not that good either lmao if its anything harder than that im dead
calm coralBOT
@opal sinew Has your question been resolved?
calm coralBOT
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clear sapphire
I reasoned that max static friction for m_1 = 4 N and max static friction for m_2 = 8N.
Until F = 4N, there is no spring force, and after that any increase in F results in a similar increase in spring force. The minimum Spring force we need to make the m_2 block move is the maximum of static friction value for m_2 (8N) . For minimum force scenario, m_1 doesnt have to have any acceleration. so F = 12N
It is incorrect, but i cant find the flaw in my reasoning.
I know we can use Work-Energy Theorem (it gives F = 8N)
fathom shuttle
im surprised they dont distinguish between static and kinetic friction
safe lynx
I reasoned that max static friction for m_1 = 4 N and max static friction for m_...
You tried finding energy stored in the spring?
fathom shuttle
not necessary
personally i agree that 12N should be right
possible reasons why not:
- kinetic friction factor is 0 (porrly clarified)
- sig figs (gross)
clear sapphire
Did I maybe messed up at my assumption that a_net for m_1 = 0
fathom shuttle
oh it does say shift
so you can pull on the first block until it builds up enough tension in the spring to jerk the second block forward
it wont be constant acceleration and/or velocity, but it will shift
clear sapphire
it wont be constant acceleration and/or velocity, but it will shift
which one?
calm coralBOT
@clear sapphire Has your question been resolved?
swift laurel
if you have an 8N force then block 1 would move forward until the spring force is 4N at which point there is no net force on m1, but then m1 would continue moving at constant velocity (and then decelerating once the spring force exceeds 4N), and the entire time the spring would continue stretching and causing more force on m2
clear sapphire
okay let me process that
clear sapphire
if you have an 8N force then block 1 would move forward until the spring force i...
I now do understand the root cause of my mistake, I had seen a similar question with string intsead of spring and I didnt account of the fact that spring force never changes instantly. I am still having a little trouble generalising it for Force F. Can I still salvage this approach by making some modifications?
F_net on 2nd block = F-4-Kx.
a_net = 1/m * (F-4-kx) = v dv/dx
and then I integrate, is that correct?
but what would be my limits?
kx = 8 at that instant
x = 8/k
and initially x = 0
so 0 to 8/k
but what do i do with velocity?
calm coralBOT
@clear sapphire Has your question been resolved?
calm coralBOT
@clear sapphire Has your question been resolved?
pure breach
kx = 8 at that instant
x = 8/k
and initially x = 0
so 0 to 8/k
but what do ...
dont think u can do this because
ur effectively finding the velocity at the end of 8/k displacement
fallow haven
I reasoned that max static friction for m_1 = 4 N and max static friction for m_...
the answer would be 12 if there was a string instead of a spring
pure breach
I wonder if there's a way to use COM frame here 
clear sapphire
if you have an 8N force then block 1 would move forward until the spring force i...
But Iām still having trouble wrapping my head around this
pure breach
well you could just use WE theorem? honestly bad advice but I usually just try to remember some of these things, ie 'i cant use this here, dunno why'
clear sapphire
Yes, thatās how I know the correct answer is 8N.
But my mechanics is weak, and assumptions like this are the reason why. Iām trying to improve my reasoning. If I donāt correct the fallacies now, whatās even the point?
pure breach
Yes, thatās how I know the correct answer is 8N.
But my mechanics is weak, and...
true
okay well do agree that for m_2 to start shifting min(spring force) = 8
correct?
pure breach
and when F=4N, spring force will start acting on m_1
flat orchid
im surprised they dont distinguish between static and kinetic friction
its assumed both are same
pure breach
lol
but because spring force is dependent on x, it will not increase enough to stop m_1 from moving
clear sapphire
Yes fair
pure breach
so m_1 will start moving with some acceleration a
clear sapphire
Yes
pure breach
err
clear sapphire
What happens next?
pure breach
okay wtf this doesnt make sense
i thought i cracked it but i hadnt so thats the 'err'
i then decided to try and use the formula for a_com
and that disagrees with the answer
clear sapphire
Ohh
pure breach
kx = 8 at that instant
x = 8/k
and initially x = 0
so 0 to 8/k
but what do ...
wait okay got it
clear sapphire
Okay
pure breach
i then decided to try and use the formula for a_com
will deal with this later
clear sapphire
wait okay got it
Can you please explain?
pure breach
wait okay got it
when we apply F to m_1 as i said it will move with some acceleration a, but eventually spring force will stop it
when it does stop it, it will be at the maximum extension
do you see why?
clear sapphire
Yes
fallow haven
when it does stop it, it will be at the maximum extension
yeah
and then you can apply work energy theorem
for that moment
pure breach
and this maximum extension = 8/k because we f_s max = 8
pure breach
kx = 8 at that instant
x = 8/k
and initially x = 0
so 0 to 8/k
but what do ...
since our intial = final =0, just integrate from 0 to 0
u'll have the same equation as from WE theorem
infact technically this is WE theorem, just written out step by step
clear sapphire
when we apply F to m_1 as i said it will move with some acceleration a, but even...
But we donāt know at what stage the scenario weāre concerned with happens
pure breach
But we donāt know at what stage the scenario weāre concerned with happens
its the stage of maximum compression...
do you see why? or should I explain it
clear sapphire
No I donāt think I follow
pure breach
well think of it this way
initially a for m_1 = F - f_1 - f_s
and initially a is positive because f_s is too small to prevent motion
but as it moves, f_s will increase
so a will decrease and eventually become negative
then at some extension x' the velocity of m_1 will be 0 and m_1 will then start moving backwards because a is negative
so x' will start decreasing
thus the spring doesnt get extended more than x' and so it must the maximum elongation
clear sapphire
then at some extension x' the velocity of m_1 will be 0 and m_1 will then start ...
No but we donāt know when m_1 moves with respect to that moment?
pure breach
wdym.?
clear sapphire
What if m_2 moves before it reaches maximum xā or velocity = 0?
pure breach
well thats literally what we will build our equation on
fallow haven
What if m_2 moves before it reaches maximum xā or velocity = 0?
yeah in general the maximum extension in the spring will be when both blocks have a common velocity
but in the limiting case we can say that the common velocity will be zero
pure breach
What if m_2 moves before it reaches maximum xā or velocity = 0?
we will restrict m_2's motion to move exactly at x'
pure breach
kx = 8 at that instant
x = 8/k
and initially x = 0
so 0 to 8/k
but what do ...
1 equation from here, 2nd by setting F_s>=f_2
the 1st equation will be identical to what you get from WE
clear sapphire
yeah in general the maximum extension in the spring will be when both blocks hav...
Since velocity of m_1 will be 0 when it just moves, we can say that also be the case for m_2?
But velocity for m_2 will be 0 at every moment before it actually moves?
clear sapphire
we will restrict m_2's motion to move exactly at x'
We can?
How?
pure breach
We can?
How?
we will set f_2)max=F_s at x'
thats how
because after this point F_s will again decrease and f_2 will start adjusting
clear sapphire
8 = kxā ?
Is that what you mean?
pure breach
yes
pure breach
kx = 8 at that instant
x = 8/k
and initially x = 0
so 0 to 8/k
but what do ...
so essentially you need to be able to wrap your head around this
clear sapphire
Okay thatās fair
Why v = 0 to v=0 is my only question
Initial I understand
Final v=0, I donāt
pure breach
Final v=0, I donāt
we just discussed why v=0 at x' š
x' is maximum elongation remember??
clear sapphire
Let me rephrase, Why is it xā at that instant?
pure breach
Let me rephrase, Why is it xā at that instant?
because after that it moves backwards as a is negative and if it moves backwards the elongation of spring will start decreasing
first elongation increases then attains some maximum then decreases
clear sapphire
Why can m_2 not move at any instant before maximum elongation is attained?
pure breach
Why can m_2 not move at any instant **before** maximum elongation is attained?
it can, we are simply constraining it to move that way ...
there will exist some value of F
fallow haven
we will set f_2)max=F_s at x'
.
pure breach
where it will move that way
remember integration gives u a relation between f_1, F and F_s
and the constraint of f_2 = F_s gives us a relation between F_s and f_2
clear sapphire
When I said my mechanics was shit, I really wasnāt kidding
clear sapphire
it can, we are simply constraining it to move that way ...
Wouldnāt assuming that alter important parameters in the question?
pure breach
and when f_1,f_2 are known, you can simply eliminate F_s to derive a relation between F,f_1 and f_2
pure breach
Wouldnāt assuming that alter important parameters in the question?
no? Even when you're doing WE you are still solving for some value of F
and you are still assuming v=0 at x'
this is literally that, just in a derivation form
pure breach
When I said my mechanics was shit, I really wasnāt kidding
in all:
m_2 can move at any instant before maximum elongation is attained, but we constraint m_2's motion such that it moves exactly at the maximum elongation i.e. we choose that (F_s)max = 8
m_2 will move at any instant before maximum elongation if F_s reaches the value of 8N BEFORE maximum elongation
which in case would gives us a larger value of F
fallow haven
WE on m1:
Fx - (1/2)*0.4*m1*g*x - (1/2)*k*x^2 = KE of m1
also kx = 8
from here you can see that the value of F will be minimum when KE is minimum = 0
pure breach
WE on m1:
Fx - (1/2)\*0.4\*m1\*g\*x - (1/2)\*k\*x^2 = KE of m1
also kx = 8
fro...
u dont have to do the integration shenanigans but writing this still needs you to understand this motion
does it make sense now @clear sapphire?
pure breach
Wouldnāt assuming that alter important parameters in the question?
also in case this still isnt answered - tell me what you think assuming something like this will change in the question parameters?
clear sapphire
Wait is this reasoning good: we are trying to essentially the minimum value of F that can move the block m_2. If that F is minimum, if it moves block m_2 at the spring force that arises from maximum elongation, thatās what we want.
pure breach
yes
theres lots of ways to conclude this - doing what dread did, thinking about the motion way i did etc.
pure breach
np
this was a learning experience for me as well lol
never thought of this way before
clear sapphire
I appreciate it
clear sapphire
never thought of this way before
Oh what way? The analysis of the motion?
clear sapphire
Oh
Thank you so much again
pure breach
np
clear sapphire
.close
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tall moon
calm coralBOT
tall moon
so im smelling inversion on P? cause the other points kinda depend on P right?
although the favourable center point is supposed to be a point that goes trough any circles? so idk for sure
ok so just to clarify, im asking for how to continue the inversion here (or even if its the right point to invert), and also for the solution in general
calm coralBOT
@tall moon Has your question been resolved?
calm coralBOT
@tall moon Has your question been resolved?
calm coralBOT
@tall moon Has your question been resolved?
calm coralBOT
@tall moon Has your question been resolved?
steel ember
calm coralBOT
desert relic
dude the 1/2 theta is lowkey forced
desert relic
Like just keep it theta/2
steel ember
Like just keep it theta/2
lol
yeah alright
doesnt rly matter thop
its js in the mark scheme like that
i js dont get how on earth im meant to integrate this
desert relic
Integrate!?
desert relic
Ahhh thank god
desert relic
Well just go product rule and chain rule
desert relic
its killing me i have 69/75 on this paper
Nice man
steel ember
the diff of arctan is weird as is
steel ember
Apply the power rule, bring it down
like the 2/3?
steel ember
omds
desert relic
So do the same for your base function
steel ember
i messed up with integration
ok so first thing i do
is power rule right?
i domnt have to touch anything else
desert relic
For the whole question or just the root part?
desert relic
Alright see
Let's differentiate just the root part for now
It's (arctan(theta/2))^1/2
So for now, our primary focus is the root
Hence everything inside the root is just absolute for now, we don't touch anything there yet, we keep it as it is
Now, give me the derivative of x^(1/2)
steel ember
1/2x^-.5
desert relic
Alright, replace x with arctan(theta/2)
That's our first part
Now we apply the chain rule
Once we've tackled the outside, finally now we move inside the root
Okay, so what's the derivative of arctan(theta/2)
desert relic
No what
steel ember
like i said the wrong thing
steel ember
1/(4+theta^2)
desert relic
2/ innit?
steel ember
?
desert relic
Also wait, multiply the root part you had achieved to this
steel ember
what?
desert relic
Okay see
First we had differentiated the root part
And we had 1/2 (arctan(theta/2))^(-1/2)
Right?
desert relic
Okay
desert relic
1/2 / 1+ theta^2/4
And now you've got this
steel ember
yes
and you ahve a 1/2 outside already
and that 1/2 at the top turns into 1/4
could you write it out please im really confused
desert relic
One minute please
steel ember
alr tyty
desert relic
You got these two yeah?
steel ember
ok
desert relic
Alright, now multiply them
desert relic
so ur xing the original by the differeniation insidde the bracket
In a way, basically to derivate f(g(x)), I am multiplying f'(g(x)) with g'(x)
See how in f'(g(x)), g(x) remains the same, so g(x) was your arctan(theta/2), and f was the root function
steel ember
desert relic
Yup that's correct
Now just apply this into product rule for the original problem, and you'll have your answer
You got it?
calm coralBOT
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ivory crow
calm coralBOT
ivory crow
Does someone have a source for this integral? My professor cited it as an identity.
calm coralBOT
@ivory crow Has your question been resolved?
leaden thunder
the right side almost looks like the beta function. try manipulating the integrand on the left to utilize the definition of beta function
lost arch
for this is it fine if i find surface area of 1 cylinder thn times it by 3 then devide it by 5 to find out the number of tins
lost arch
i got 7.86 doing that meaning not enough paint
velvet osprey
why are you asking if it's "fine"? it sounds as if you're asking for permission to do those calculations.
as if somebody would forbid multiplication by 3, or division by 5, or the two in combination when both the month and date are even numbers or whatever
scenic plaza
for this is it fine if i find surface area of 1 cylinder thn times it by 3 then ...
Yeah makes sense
velvet osprey
you should not be trying to ask whether a process (with just the numbers, ripped out of context) is "fine" or not,
but instead, try to reason through it:
(SA of one cylinder) * 3 = total area to be painted
(total area to be painted) / (5 m^2) = number of tins of paint required
"I find the area of one cylinder.
I _multiply_ it by 3, that's how much area we need to paint.
I _divide_ that by 5, that's how many tins we need."
@lost arch do you catch what im saying
calm coralBOT
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steel ember
yo
unkempt drift
1/2 integral of sec2x
do you know the integral of sec x?
unkempt drift
i dont think im supposed to use this cuz its not on my formula book
really?
winter elbow
1/2 integral of sec2x
sleek vessel
Could you show the original question
sleek vessel
Are you 100% sure you didn't mess up smth along the way
steel ember
ye
sleek vessel
Well show the full question anyway
sleek vessel
...do they expect you to use product rule
unkempt drift
the easiest way is that
steel ember
but
unkempt drift
that should be on your formula booklet somewhere
steel ember
what is 'that'
unkempt drift
do you know the integral of sec x?
ln(|sec x + tan x|) + c
steel ember
and then
sleek vessel
I said Lemme think
steel ember
mb
sleek vessel
Lolol nw
sleek vessel
ln(|sec x + tan x|) + c
Okay so working backwards from this
We wanna use the last thing on that formula sheet
sleek vessel
So we want (sec x tan x + secĀ² x)/(sec x + tan x)
steel ember
ON THE FORMULA SHEEt
sleek vessel
...
sleek vessel
You almost made me derive it manually
void umbra
Vro
sleek vessel
You will feel my wrath
steel ember
its fun for u lot aint it
sleek vessel
void umbra
Anti climatic
sleek vessel
sleek vessel
Good luck for your exam
steel ember
did u study math
steel ember
Good luck for your exam
ty
sleek vessel
what u study
Currently doing logic, and program verification
primal bear
did u study math
has a postgraduate role
steel ember
LOL
unkempt drift
yes and then reverse chain rule, so you need to divide by 2 because it's sec(2 theta)
so $\frac{1}{2}a \cdot \frac{1}{2} = \frac{1}{4} a$ in front
potent lotusBOT
south
sleek vessel
Currently doing logic, and program verification
Prolly gonna explore some TCS in the next semester
steel ember
i rly wana go UCL but the scholarships r competetive
do u guys have any recs in europe or smth
sleek vessel
i dont think ill get into a top uni
You don't need to get into a top uni to study maths
steel ember
You don't need to get into a top uni to study maths
im not a us citizen so i kinda do for a scholarship
sleek vessel
ETH Zurich is up there
sleek vessel
im not a us citizen so i kinda do for a scholarship
Where are you from if I may ask
You don't necessarily need to go out of your country for an undergrad
unkempt drift
i really want to study maths
nothing wrong with Australia mate
sleek vessel
Australia is amazing for maths lmao
I'm looking to come there for my PhD if possible
unkempt drift
like, you probably don't want to go to Europe where they teach you introductory real analysis in 1st semester
steel ember
You don't necessarily need to go out of your country for an undergrad
im from georiga
i am NOT staying here
unkempt drift
if you thought that UWA (in Perth) teaching multivariable calculus in 1st sem was bad, that's twice as worse
steel ember
like, you probably don't want to go to Europe where they teach you introductory ...
is that hard?
or bad>
unkempt drift
but yeah if affording uni is an issue, Australia isn't the best option
primal bear
is that hard?
yes
sleek vessel
That's the spirit
unkempt drift
it's just a system where 50% of students fail 1st year and have to repeat
unfortunately you're not an EU citizen so you don't get the cheap EU fees
if you were an EU citizen it's worth it
unkempt drift
I guess
steel ember
and cheaper then uk and us
steel ember
u from there?
unkempt drift
nah
unkempt drift
I have family there but I don't have any direct experience
steel ember
thats urt real name?
primal bear
hes from antarctica
unkempt drift
thats urt real name?
ofc not dummy
steel ember
Lol
primal bear
south southerland
steel ember
i wanted to apply to brown
unkempt drift
that's like one of the unis that favours rich applicants the most
steel ember
.close
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river knoll
Hi guys, Iām trying to do this question by finding intersection but whenever I grab the points onto desmos it doesnāt give me the fraction form but the decimal form, and then it isnāt exact and doesnāt show me the simplest fraction form, how would I get the simplest fraction form on desmos?
calm coralBOT
Hi guys, Iām trying to do this question by finding intersection but whenever I g...
river knoll
Actually this equation doesnāt have intersections but for other ones I had the same problem
winter elbow
Do you have a question that "has such problem" and "have intersection point(s)"?
river knoll
Do you have a question that "has such problem" and "have intersection point(s)"?
No but for a similar question as the one above I graphed it onto desmos and found the solutions for x, but the x points were like 0.666666667, and putting that into the calculator made it into like 0.66667 so it was a different fraction when it wouldāve been 2/3 as the most simple
Doesnāt rlly have anything to do with the problem.
Just a desmos thing
alpine cobalt
maybe try using geogebra
river knoll
maybe try using geogebra
I canāt this is for sat :ā(
river knoll
I wanna do it as fast as possible
alpine cobalt
algebraically is the fastest
river knoll
Im slow with other questions so the stuff I can do with desmos id rather just do faster
alpine cobalt
would be half min for me
river knoll
Im really bad at math
alpine cobalt
oh
unkempt drift
if you can solve 8u + 15 = 6u + 13
winter elbow
It's okay, I'm bad too š§”
Jokes aside, you can try writing it into fractions with the given decimal number
unkempt drift
then you should be able to solve |x + 4| = u, for the u you got
river knoll
It's okay, I'm bad too š§”
Jokes aside, you can try writing it into fractions wi...
Idk how id do that
unkempt drift
for example, |x - (-4)| = 3
x is 3 units away from -4 on the number line, so x = -7 or x = -1
winter elbow
@unkempt drift wait south, lemme explain how to transform it into fraction first
river knoll
And for multiple choice I need the simplest right
alpine cobalt
how did you get -1
unkempt drift
algebraically is the fastest
sure I'm just jumping in to explain this
alpine cobalt
this question does not even has a solution in real numbers
winter elbow
@river knoll So I'll quickly explain how the transformation works.
alpine cobalt
or any numbers
unkempt drift
if you can solve 8u + 15 = 6u + 13
oh yeah, u is negative, so that's automatically no solution
absolute value is always non-negative
winter elbow
Can you first tell me how you get the decimal form with desmos? Do you just input the equation into it?
alpine cobalt
you just get |x+4|=-1
river knoll
Can you first tell me how you get the decimal form with desmos? Do you just inpu...
Yeah I put in the equation and I grabbed it from the graph to get the fraction form
winter elbow
Yeah I put in the equation and I grabbed it from the graph to get the fraction f...
Before I explain how you transform it, you should still learn how to do it algebraically if you have time.
alpine cobalt
yea
winter elbow
Alright, let's talk about how to do it
alpine cobalt
thats quicker
winter elbow
There are 4 types of decimal form and 4 of them results in infinite numbers of digits
river knoll
Before I explain how you transform it, you should still learn how to do it algeb...
Could you explain please but I kinda need to figure it out before my sat and itās in like 9 hours lol
winter elbow
Let's say we have a simpliest form of fraction $\frac{a}{b}$
potent lotusBOT
Swaamii
winter elbow
if b just has the factor of 2 or 5, the fraction yields a finite numbers of digits upon transformation
for example $\frac{7}{625}$
oh wait I'm an idiot, 225 has 3 as factor
potent lotusBOT
Swaamii
winter elbow
,w calc 7/625
potent lotusBOT
river knoll
is that clear for you?
Thank you so much Iām having dinner right now Iāll check later
winter elbow
I haven't finished lol
calm coralBOT
@river knoll Has your question been resolved?
spring beacon
hello, can you help me with ordinary linear differential equations?
calm coralBOT
hello, can you help me with ordinary linear differential equations?
No need to ask āCan I askā¦?ā or āDoes anyone know aboutā¦?āāitās faster for everyone if you just ask your question! See https://dontasktoask.com/
spring beacon
I need to share my screen to show the problem, is there a voice channel in this server?
violet turret
I need to share my screen to show the problem, is there a voice channel in this ...
Unfortunately no
You can share a screenshot though
spring beacon
how?
spring beacon
i know that command but then how to send on discord
violet turret
Uh you can send the image
chilly marten
then just cntrl+v
considering it will be on your clipboard
windows+ v to check your clipboard history if its enabled
spring beacon
chilly marten
now just breif your doubt
spring beacon
how would you solve this ordinary differential equations? I am really just trying to get an idea of what it would mean. Is there a solution to it?
you are trying to solve for voltage (V)... d, m and t are variables depending on V
the rest, they are constants for the most part
let me check what alpha and betha stand for, 1 sc
chilly marten
let me check what alpha and betha stand for, 1 sc
voltage dependent rate functions
crisp sphinx
how would you solve this ordinary differential equations? I am really just tryin...
what this would mean is, you need to find a family of functions (like Ce^x, something with an unknown constant(s) ) that will satisfy each DE at once. in practice, this is usually done by writing the equations in a matrix form, then analyzing that matrix and related matrices to pull a solution out
spring beacon
voltage dependent rate functions
yes, I wondery why they didn't bother to write those equations
chilly marten
btw these are non linear COUPled ode , they dont have a function solve if you are looking for it , its like a numerical solve , hence calculator
spring beacon
btw these are non linear COUPled ode , they dont have a function solve if you ar...
that's what i was thinking, can you tell me more why they can't be solved?
crisp sphinx
that's what i was thinking, can you tell me more why they can't be solved?
in a linear system, if f(x) and g(x) are solutions, so is Cf(x) + Dg(x) (the principle of superposition), but this is not always true in the non-linear case
chilly marten
yes, I wondery why they didn't bother to write those equations
they are non polynomial rate functions btw..
spring beacon
you mean something like this?
they got the data from squid axon voltage
And they came up with those ordinary equations
But like mathematically, how did they figure the equations from the data?
placid lion
by fitting?
spring beacon
by fitting?
placid lion
a lot of guesses i suppose
they have an idea of how it should look like roughly and then they let computer guess
spring beacon
So how do i try to understand these equations? It can only be solved numerically (i am guessing this mean you put in initial condition values and see where the equations take you).
spring beacon
in a linear system, if f(x) and g(x) are solutions, so is Cf(x) + Dg(x) (the pri...
are C and D constants?
crisp minnow
can someone explaing the limiting behaviour points because i dont undertsand
crisp minnow
using the graph
compact crest
What do you understand so far
crisp minnow
As x approaches positive infinity f(x) becomes positive infinity
but how can i see this?
calm coralBOT
@crisp minnow Has your question been resolved?
calm coralBOT
crisp minnow
.reopen
calm coralBOT
ā Original question: #help-42 message
safe lynx
Yes? @crisp minnow
safe lynx
Whats the doubt?
crisp minnow
let me think
safe lynx
i dont get this bit
Which part?
crisp minnow
soooo how do i see it on the graph
inland iris
infinity?
crisp minnow
because when x is positive infinity f(x) is also positive infinity
like how would i know this
inland iris
like how would i know this
do you know what a limit is? (This will help me give you an answer)
crisp minnow
We do it to check asymptote right? <@1190424151131955252>
checking the limiting behavious
crisp minnow
do you know what a limit is? (This will help me give you an answer)
the limit is infinity?
inland iris
in this case yes, the easiest way to know what the limiting behaviour or end behaviour of a function is is to plug in an absurdly large number like 1000000000 and see if the output of the function is about as large or larger, from this you can conclude that if you keep plugging in bigger and bigger numbers approaching infinity the function's output will approach infinity
You can tell by the slant asymptote (the dashed line) that the function must stay either above or below it forever meaning that as you move towards x = positive infinity the output of the function is positive inifinity, and going left towards negative infinity we can see the function must also reach negative infinity
calm coralBOT
Available help channel!
charred flame
I can do this question by finding the partial derivative of x and y, then froming the "basis" of the affine subset of the gradient; however, it looks like if would be really convenient to use polar coordinates. How could Ido this?
hollow totem
what function?
charred flame
The functon that takes a radius r and an angle theta that outputs z = r
hollow totem
oh, g'(r, theta)?
charred flame
Yeah
hollow totem
Ok
hollow totem
And which partial derivative is 1
charred flame
Yeah
charred flame
The partial derivative in terms of r
hollow totem
With respect to r
charred flame
Yes
hollow totem
What about with respect to theta
charred flame
Just 0
hollow totem
Right
charred flame
But the "basis" of the affine subset $B_{polar} = {(1,0,1),(0,0,1)},$ where each ordered pair is $(r,\theta,z)$ doesn't make sense in Cartesian
potent lotusBOT
CalculusDude
charred flame
Also sorry if I'm misuisng Linear Algebra terms, I'm kind struggling in that class too
hollow totem
Well polar coordinates aren't a vector space
This is more than just a change of basis
charred flame
Oh
hollow totem
All you can have really is a local basis at your point (3,4)
charred flame
Would that be helpful for finding the direction derivative?
atomic notch
yeh it would
charred flame
Okay. I hope it will be a good exercise at least
hollow totem
So we need a vector in the direction of r and one in the direction of theta
Also I g2g but I'll be back in ~15 minutes
hollow totem
So we need a vector in the direction of r and one in the direction of theta
Ok this, in Cartesian coords
also they should probably both be unit vectors to not screw things up
charred flame
CalculusDude
These vectors?
hollow totem
No
charred flame
Oh okay
hollow totem
A vector that points outwards and one that points perpendicular in the positive theta direction
At (3,4)
charred flame
$(r, \theta) = (5, \arctan(\frac 4 3))$?
potent lotusBOT
CalculusDude
hollow totem
No
That's not in Cartesian coords
And it doesn't point outwards
Also it's not in the direction of positive theta either
Also it's only one vector and not two
hollow totem
Well you should probably be looking at 2D
charred flame
This would be a cross-section at x = 0 or y = 0 depending how you label the axis
charred flame
The input space is (x,y) in cartesian which is R^2
hollow totem
Yes
And you're at (3,4)
If you want to make a local basis for polar coordinates, you need to define them in Cartesian
Because currently all your info is in Cartesian
charred flame
So it is redundant to even look at g(x,y) in terms of polar coordinates?
hollow totem
I mean you can
You avoid having to do derivatives on the square root
You're at (3,4). What direction is positive r without changing theta
charred flame
5
hollow totem
That's a number, not a direction
charred flame
Oh arctan(15/8)
hollow totem
That's also a number
charred flame
I am I supposed to say first quadrant
hollow totem
that's not specific enough
charred flame
theta = arctan(15/8)?
charred flame
I can do this question by finding the partial derivative of x and y, then fromin...
the definition of v
charred flame
you want to go in the direction of (3,4)
Oh theta = arctan(4/3)
hollow totem
sure that's the angle
but you don't need the angle
you need to know where your local polar basis is in cartesian coords so you can convert back and forth
and arctan(4/3) is not a cartesian vector
charred flame
(3,4) in cartesian coords has magnitude 5 and direction arctan(4/3). Is the local polar basis just (cos(theta), sin(theta))
charred flame
Mb (cos(theta),0), (0,sin(theta))
hollow totem
No
charred flame
Are these vectors not in R^2, or am I looking at it from a wrong coordinate
hollow totem
They can be if theta is defined but they don't really have any significance
The first vector in the basis should be a scaled version of (3,4) since that's the direction that increases r
charred flame
So (3/5, 4/5)
hollow totem
Yeah
Going in that direction directly increases r (at a "rate" of 1) while not changing theta
So that's an element of your polar basis
The r direction
charred flame
So $(r,\theta) = (\frac 3 5, \frac 4 5)$ is in my local bolar basis?
potent lotusBOT
CalculusDude
hollow totem
No
charred flame
Cause (3/5, 4/5) is cartesian, right
hollow totem
yes
(1,0) is the polar equivalent of that vector
$(1,0)\text{pol}=(\f35,\f45)\text{cart}$
potent lotusBOT
Dreyuk
charred flame
Are we defining theta = 0 to be in that direction, because traditionally theta = arctan(4/3)
charred flame
So what is the 0 in (1,0)_pol
hollow totem
The component in the direction of theta
charred flame
Oh so even though that = arctan(4/3), relative to that theta, the difference between this angle and the traditional theta is 0
hollow totem
I can't understand, so I'm going to assume the answer is no
charred flame
Oh so even though that = arctan(4/3), relative to that theta, the difference bet...
For example, would
$(1,\frac {\pi} 2)\text{pol}=(\frac 45,-\frac 35)\text{cart}$
potent lotusBOT
CalculusDude
charred flame
I don't quite understand that
hollow totem
Ok, so, polar coordinates don't form a vector space, right
hollow totem
no it's like
I mean they can form a vector space if you "add" them by converting into Cartesian, adding those the normal way, and then converting back
But otherwise
well it's like
charred flame
Wouldn't even (r_1, theta_1) + (r_2, theta_2) = (r_1 + r_2, theta_1, theta_2) work?
That's kust cartesian with extra steps
oh
hollow totem
I mean you could but now you're no longer adding them in a way that makes sense
Probably saying they don't form a vector space is the wrong way to say it but like
hollow totem
Wouldn't even (r_1, theta_1) + (r_2, theta_2) = (r_1 + r_2, theta_1, theta_2) wo...
Graphically, this form of addition is just a random meaningless operation
charred flame
Yeah, cause we could rename r to x and theta to y and it's suddenly just cartesian
charred flame
So it's not important?
How would we show that polar coords don't form a vector space then
hollow totem
That was the wrong way to phrase it
But like
Adding them coordinatewise is meaningless
Adding them by converting to Cartesian is just a strictly worse version of using Cartesian coordinates
But there's no global r direction in terms of Cartesian coords
It changes depending on where you are
charred flame
I thought r was a scalar/magnitude and theta was the angle/direction
hollow totem
Eh sort of
calm coralBOT
calm coralBOT
Available help channel!
turbid thicket
how do i do this?
ive tried to take two paths to show the limit doesnt exist but nothings working like y= 0 or y = x
stoic epoch
how do i do this?
ive tried to take two paths to show the limit doesnt exist but...
Have you tried with x=0?
stoic epoch
that's a well known limit it should be -1/2
and for y=0 you get (e^x-1)/(2x) that gives 1/2 and there is no limit
you could use l'hƓpital to get it
calm coralBOT
@turbid thicket Has your question been resolved?
nocturne rose
Starting with integral from
0 to pi of Li_2(sin^2(x)), and after reflection formula getting to pi^3/24+ two times the integral from 0 to pi/2 of lnsinxcosx. Then you make a new function like I(a,b)= integral from 0 to pi/2 of sin^a(x)cos^b(x). Then you take both partials, and get the original integral. So how do you use all that to get the answer to the dilogarithm integral?
nocturne rose
Starting with integral from
0 to pi of Li_2(sin^2(x)), and after reflection form...
my terrible messy work on the problem
calm coralBOT
@nocturne rose Has your question been resolved?
calm coralBOT
@nocturne rose Has your question been resolved?
nocturne rose
<@&286206848099549185> š„ŗ
safe lynx
Starting with integral from
0 to pi of Li_2(sin^2(x)), and after reflection form...
!original
calm coralBOT
Starting with integral from
0 to pi of Li_2(sin^2(x)), and after reflection form...
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.
nocturne rose
int[0,pi/2]{Li_2(sin^2(x))}
calm coralBOT
@nocturne rose Has your question been resolved?
calm coralBOT
@nocturne rose Has your question been resolved?
crisp minnow
im not sure what to do for the bit in red
calm coralBOT
im not sure what to do for the bit in red
@crisp minnow Has your question been resolved?
dusky flax
Let $M = [a_{ij}]{3 \times 2}$ and $N = [b{ij}]{2 \times 3}$ be two matrices such that $(MN)^2 = 3MN$ and $det(NM) \neq 0$, then choose the correct option(s): (P is a 2x2 matrix)\\
(A) $det(NM) = 9$\
(B) If $P(NM) = I$, then $lim{n \to \infty} det(P + P^2 + P^3 + ... + P^n) = 9$\
(C) $det(NM) = 27$\
(D) If $P(NM) = I$, then $lim_{n \to \infty} det(P + P^2 + P^3 + ... + P^n) = 0.25$
velvet osprey
texfail
potent lotusBOT
calm coralBOT
@dusky flax Has your question been resolved?
sharp narwhal
sharp narwhal
take det on both sides
sharp narwhal
no det(MN) is non-zero
sharp narwhal
^
dusky flax
oh noo i forgot the subscript
one min
Let $M = [a_{ij}]{3 \times 2}$ and $N = [b{ij}]{2 \times 3}$ be two matrices such that $(MN)^2 = 3MN$ and $det(NM) \neq 0$, then choose the correct option(s): (P is a 2x2 matrix)\\
(A) $det(NM) = 9$\
(B) If $P(NM) = I$, then $lim{n \to \infty} det(P + P^2 + P^3 + ... + P^n) = 9$\
(C) $det(NM) = 27$\
(D) If $P(NM) = I$, then $lim_{n \to \infty} det(P + P^2 + P^3 + ... + P^n) = 0.25$
potent lotusBOT
dusky flax
better
sharp narwhal
umm ok
sharp narwhal
we already know det(MN) = 0
how do you know that
dusky flax
how do you know that
glad parrot
Its not working
Apart from the 0's, it says that detNM is not 0 which means that its invertible but you would have proved that its only invertible on one side and not the other
i.e not an inverse
dusky flax
uh yeah NM gives a 2x2 matrix and MN gives a 3x3 matrix
glad parrot
Wait nvm my explain is wierd
unkempt drift
its more like what i should try
hints:
- given MN is 3 by 3, what is det(3 MN) in terms of det(MN)?
- how can you simplify det((MN)^2)?
that should give you det(NM)
dusky flax
hints:
1) given MN is 3 by 3, what is det(3 MN) in terms of det(MN)?
2) how can ...
- 27 det(MN)
- (det(MN))^2
- invalid (det(M) and det(N) not defined)
unkempt drift
1) 27 det(MN)
2) (det(MN))^2
3) invalid (det(M) and det(N) not defined)
oh wait I messed up with 3
but yes, 1) and 2) are correct
but yeah, okay so you get the idea that det(NM) = 0
dusky flax
ok i saw something related to this question
and i got the property that the eigenvalues of MN and NM coincide
is that true?
calm coralBOT
@dusky flax Has your question been resolved?
calm coralBOT
@dusky flax Has your question been resolved?
dusky flax
[https://www.wolframalpha.com/input?i2d=true&i=%7B%7Bsqrt+3%2C0%2C0%7D%2C%7B0%2C...
i mean its just the trivial solution thats missing
and its obvious why 0 is not common
so mayyyyyyyyyyybe?
rustic osprey
i mean its just the trivial solution thats missing
Eh it depends on what you mean by "coincide"
if you mean that they are identical including algebraic multiplicity, then no
but if you mean that the nonzero eigenvalues coincide (counting algebraic multiplicity), then yes
I'm assuming you're taking "trivial" to be "zero"
,texsp ||The eigenvalues of $P$ are $\frac{1}{3}$ and $\frac{1}{3}$||
potent lotusBOT
Civil Service Pigeon
dusky flax
yaaaaaayyyyyyy
and how would you prove this
is it something like symmetrical transformations
rustic osprey
and how would you prove this
Suppose that the invertible matrix $A$ has eigenvalue $\lambda$. Then, $$A\vec{v}=\lambda \vec{v} \implies A^{-1} A \vec{v}=\lambda A^{-1} \vec{v} \implies \vec{v}=\lambda A^{-1} \vec{v} \implies A^{-1} \vec{v}=\frac{1}{\lambda} \vec{v}.$$
potent lotusBOT
Civil Service Pigeon
rustic osprey
@dusky flax Hello?
dusky flax
oh hm
dusky flax
Suppose that the invertible matrix $A$ has eigenvalue $\lambda$. Then, $$A\vec{v...
but how would this say AB and BA have the same eigenvalues
rustic osprey
and i got the property that the eigenvalues of MN and NM coincide
didn't you say that yourself up here
dusky flax
didn't you say that yourself up here
that was supposed to mean 'i got it from a query in google'
they barely went over eigenvalues in school
and this was the only problem which heavily involved it
rustic osprey
If $NM \vec{v}=\lambda \vec{v}$ with $\lambda \neq 0$, then $M \vec{v} \neq \vec{0}$ (since $MN\vec{v}$ would be $\vec{0}$ otherwise). \ \
We then have that
$$MN(M\vec{v})=M(NM)\vec{v}=M \lambda \vec{v}=\lambda M\vec{v}$$
meaning that $M\vec{v}$ is a nonzero eigenvector of $MN$ with eigenvalue $\lambda$. Thus, the map $\vec{v} \mapsto M\vec{v}$ sends the $\lambda$-eigenspace of $NM$ injectively to the $\lambda$-eigenspace of $MN$. \ \
The other direction (mapping the $\lambda$-eigenspace of $MN$ injectively to that of $NM$ is the same logic). \ \
So the two injections are inverses on the respective eigenspaces, the $\lambda$-eigenspaces (and thus algebraic multiplicities) agree for every $\lambda \neq 0$. \ \ \ \
Alternatively, you can cite $\det(I+tMN)=\det(I+tNM)$ for all $t$.
potent lotusBOT
Civil Service Pigeon
dusky flax
If $NM \vec{v}=\lambda \vec{v}$ with $\lambda \neq 0$, then $M \vec{v} \neq \vec...
okayyyyyyy got it
clevr
and so from here we form the characteristic equations and then find the trace and determinant of the 2x2 matrix from there
alrightt
let me try one min
dusky flax
ok so we get MN(MN - 3I) = 0 (matrix)
det(MN) = 0 or det(MN - 3I) = 0
so lambda = 0, 3, 3?
or 0, 0, 3?
rustic osprey
or 0, 0, 3?
the eigenvalues of MN and NM coincide
the determinant of NM being zero implies none of the eigenvalues of NM are zero (product of eigenvalues = determinant)
calm coralBOT
@dusky flax Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
queen fog
help
queen fog
whats the best way to learn 11 topics of calc 2 in 4-5 days
hexed grove
what 11 topics do you want to learn?
queen fog
is there any good calc 2 youtubers?
hexed grove
im willing to teach
hexed grove
do it here
queen fog
like in this channel tmrow?
is there any youtubers you know
that are good for calc 2?
supple siren
whats the best way to learn 11 topics of calc 2 in 4-5 days
Why do you need to do this lmao
queen fog
exam
queen fog
grant is a wonderful teacher
grant?
queen fog
okay ty