are u going on strike?
#help-36
mortal shoal
tranquil pine
First lets close this chat.
gleaming anchor
!done, as a reminder.
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versed crater
post your question first
ocean raven
but if i post it and you dont know how to solve it the timer is gonna run out
versed crater
you can extend the timer by telling the bot your question isn't solved yet
ocean raven
wym
versed crater
there is no timer
versed crater
is it graded?
ocean raven
yea
versed crater
we cant help with graded assignments, that violates academic integrity
ocean raven
wym by graded
maiden vessel
U want us to provide you with the answers?
versed crater
it wouldn't otherwise make sense that it is timed
ocean raven
wait u guys dont help w hw
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versed crater
wait u guys dont help w hw
we dont help with cheating on assignments
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Available help channel!
tranquil pine
yoo
tranquil pine
my question is for the equation of the generating curve (the radius) how do you know which plane thats on
for example how do i know that r(z) = y and not r(z) = x
formal trail
well r(z) should only depend on z, shouldn't it
tranquil pine
well r(z) should only depend on z, shouldn't it
right
but whats the output
could be either y or x
formal trail
neither?
tranquil pine
wdym
formal trail
we aren't doing r(z) = x or r(z) = y
tranquil pine
wait what
formal trail
we are doing x^2 + y^2 = [r(z)]^2
formal trail
it's the radius of the surface at a given z
tranquil pine
yes but that radius is represented by an output value of the radius function
formal trail
yeah and we aren't graphing that output value, we're graphing an equation related to the output value
tranquil pine
wait
its squared
so even when from the other direction
itll be the same
is that why
formal trail
i'm not sure what you mean
tranquil pine
i'm not sure what you mean
but even then
the generating curve has to be on a particular plane
if my generating curve was in the yz plane then my radius would be z
if it was on the xy plane my radius would be x
so idk
formal trail
the intersection of the surface of revolution with any plane containing the axis of revolution gives a generating curve. it doesn't matter which plane because they all give the same curve, just rotated
tranquil pine
the intersection of the surface of revolution with any plane containing the axis...
look
formal trail
it just says "an" equation of "a" generating curve
you can pick any of them
also you should take the square root to find r(z)
tranquil pine
it just says "an" equation of "a" generating curve
true
tranquil pine
also you should take the square root to find r(z)
that would just be what i had right?
formal trail
well its what you have in the bottom right
tranquil pine
yea
formal trail
although it should say r(z) =
tranquil pine
although it should say r(z) =
i have a question, howd you get good at math
tranquil pine
practice
would you say someone needs to practice since they were a kid to get to that level or you could manage that within a couple years later along the line? No
formal trail
not really, you can get there eventually
we should also note that this is math that i learned years ago and have been continuing to practice since then by helping people out with it. so i'm much better at it now then i was when i was learning it, and i'm better at it than the stuff i'm learning currently
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chrome hemlock
induced emf = rate of change of flux linkage
final saddleBOT
induced emf = rate of change of flux linkage
chrome hemlock
how do they know its like the yellow one
and not the blue one
oh
its negative derivative
dusky gull
rain sentinel
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rain sentinel
im abit confused about part 3b
shouldnt tha area for A1 be [....]-2 and -4
not -2 and 4
willow tiger
You need to figure out when is y positive
then substract the integral of the part between -4 and 4 where y is positive with the integral of the part between -4 and 4 where y is negative
you understand?
rain sentinel
You need to figure out when is y positive
cant i just add all 3 areas
willow tiger
no because when x is negative, the integral is negative
rain sentinel
no because when x is negative, the integral is negative
using abolute values
so changing it to positive
willow tiger
yea but thats just = to what i said
rain sentinel
yea but thats just = to what i said
so is area one correct?
willow tiger
huh
rain sentinel
im trying to figure out all 3 areas
rain sentinel
it should be (-4,-2)-(-2,3)+(3,4)
ah okay
so
Is this how I calculate area 1 then
willow tiger
yea
rain sentinel
so the answer to the question is 36.333
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gleaming anchor
you seem to consider that 6 is the only outcome of your d20
sure, but then if you know in advance that you're gonna keep rolling 6s, then I guess your strategy works.
but that's if you are 100% certain you are going to roll nothing but 6s
oh hm
that's fair. I think that this strat works with high remaining roll count
but I remember seeing this exact problem from you and a couple of helpers have given you a good strat as to when to cash out.
I think you can use the general solution to find your specific case, is that not?
I see
scarlet sequoia
if you cash out do you have to reroll on the next round?
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@vital kelp Has your question been resolved?
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@vital kelp Has your question been resolved?
rain sentinel
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severe canyon
First of all, the dx is missing everywhere
And that's the first mistake 😬
Second, yes how did the x² turn into just x?
scenic walrus
yep
rain sentinel
scenic walrus
$x^2\left(\frac{1}{x}\right)dx=xdx$
soft zealotBOT
Allen
rain sentinel
so its not like differentiation where the chain rule is used for composite functions?
and that is like IBS
scenic walrus
DI method by bprp
scenic walrus
and +c
scenic walrus
!done
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rain sentinel
so its not like differentiation where the chain rule is used for composite funct...
.
not done
rain sentinel
also how do i know whether to use IBP or IBS?
.
scenic walrus
there’s no chain rule for integration
severe canyon
Substitution (usually) works well if you have the derivative of some part of the integrand multiplied with the integrand itself
scenic walrus
Substitution (usually) works well if you have the derivative of some part of the...
yep this is the inverse (kinda) of chain rule
final saddleBOT
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tawny bridge
Ok theres some stuff here I need clarified
final saddleBOT
Ok theres some stuff here I need clarified
tawny bridge
honest carbon
Where is the question?
tawny bridge
Im Just trying to understand this concept
Well
This concept
In that idk what they mean by the word "concept" here
All I've understood so far is that under PAC, we only need the learner be such that it chooses a hypothesis which with high probability gets a low enough loss
As opposed to exact framework where the loss is expected to be 0, and hypothesis is chosen with a 100% probability
Also is this class of algos
Something which is tunable with epsilon and delta params?
(i.e., the accuracy and confidence parameters)
<@&286206848099549185>
hot hornet
In that idk what they mean by the word "concept" here
it doesn't seem different from "subset", as far as i can tell
hot hornet
i'm not actually sure..
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@tawny bridge Has your question been resolved?
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@tawny bridge Has your question been resolved?
tawny bridge
tranquil pine
can someone solve 11 where the limit is in the form of x^m - a^m / x^n - a^n ?
opal plinth
You can factorize the numerator and the denominator
It's a little difficult but the limit gives you a big hint
tranquil pine
It's a little difficult but the limit gives you a big hint
I tried to solve it myself and i got 20/27 instead of 20/3
Im not sure whats wrong
tranquil pine
If you have it available, you can L'Hopital it
I still haven’t taken that yet unfortunately
faint locust
Do you know polynomial long division?
/synthetic division for polynomials
/Horner's method
tranquil pine
not that one either
tranquil pine
I tried to solve it myself and i got 20/27 instead of 20/3
my teacher solved it by turning it from x-> -2/3 to 3x = -2 then at the end substituted a for -2 instead of -2/3 but im not sure how that’s right
opal plinth
I'm not sure about your teacher's method, and I might be overcomplicating this, but if you know a root r of a polynomial P(x), you can rewrite it as (x - r)(Q(x)) where Q(x) is one degree lower than P(x)
floral bronze
hi
tranquil pine
I'm not sure about your teacher's method, and I might be overcomplicating this, ...
hmm i’ll try to figure it out, thank youuu
.close
rain sentinel
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rain sentinel
how do i know there are vertical and horzontal forces at A?
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@rain sentinel Has your question been resolved?
formal trail
pins always have horizontal and vertical reactions
rain sentinel
pins always have horizontal and vertical reactions
thanks
glossy zephyr
You good with calculating torque/moment?
rain sentinel
You good with calculating torque/moment?
yes CWM-ACM
glossy zephyr
Well, theres a neat rule about torque, its that its the same everywhere, for this case, considering that the piece is static and not rotating, its 0
It makes it pretty easy to find the perpendicular components of most parts
Suppose we use the point C as reference, we know that the torque caused by vertical component of reaction A is equal and opposite to the force in B.
You can do the same from A, considereding the vertical component of the strut force
From there, you can find both the horizontal of the strut, and the horizontal of the reaction
rain sentinel
From there, you can find both the horizontal of the strut, and the horizontal of...
how?
glossy zephyr
Do you know how projections of forces using cosine and sine works?
rain sentinel
Do you know how projections of forces using cosine and sine works?
can you expand
glossy zephyr
On a different but similar example.
Lets say I apply a force at an angle you know of, would you be able to tell me the vertical and horizontal components?
rain sentinel
On a different but similar example.
Lets say I apply a force at an angle you kn...
yes the x and y axis
glossy zephyr
Well, yeah, but theres a formula for it
For this situation, imagine i gave you the Value of "F" and the angle "α"
You could find the vertical components anyways.
Fx = F . cos(α)
Fy = F . sin(α)
rain sentinel
yes ik this
glossy zephyr
Well, you can also do it the other way around
Fy / sin α = F
So, if you know the vertical, and also the angle it comes from, you can know the real force
and by extension, also the horizontal.
On our problem, you can probably see that the only real force we know is purely vertical
But there is a horizontal reaction, and its because the stunt is pushing against the wall too, so the reaction has to be keeping the bar attached to the wall by tugging on the opposite side
Thats how you get the true reaction
rain sentinel
because every action has a reaction
so because its pushing on the wall the wall pushes back leads to horizontal force
glossy zephyr
For example, we wouldnt get no horizontal reaction if the stunt was purely vertical too
On a really "stupid" sense, the horizontal reaction comes from the fact that we have to do extra work to keep the bar static, because some is wasted in pushing the bar away.
glossy zephyr
The vertical blue force coming from the bar is the one mantainind the bar from not falling
But because it comes at an angle, theres some part of the real force that is "wasted" pushing the bar away.
So the reaction at the left side must be keeping it from just flying away
rain sentinel
normal force is the blue force?
rain sentinel
and is a consequence of gravity
glossy zephyr
We are not considering gravity here, just the force at the right side
rain sentinel
But because it comes at an angle, theres some part of the real force that is "wa...
this is the horizontal force
and the purple force?
is a result of fv and fh?
glossy zephyr
its the combination of the two
aka, the real force which is coming at an angle and we decomposed into the horizontal and vertical
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dusty schooner
How can i find the derivatives of sin cos and tan?
final saddleBOT
How can i find the derivatives of sin cos and tan?
tiny gorge
well for sin and cos it depends on how you have defined them
(assuming you're asking how to prove that sin' = cos, for example)
dusty schooner
Yeah
tiny gorge
there are a couple of standard approaches
one defines sin and cos as the solutions to certain differential equations
another defines sin and cos as certain power series
and in both cases you can rigorously show that sin' = cos and cos' = -sin
for tan, it's easy, just write tan = sin/cos and use the quotient rule
ember ether
😂
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craggy plank
Claim your own channel
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exotic shale
why is u+ υ = M?
final saddleBOT
why is u+ υ = M?
exotic shale
isnt it u + υ = t
i dont understand how we went from the first region to the second with the substitution
exotic shale
?
exotic shale
i dont understand how we went from the first region to the second with the subst...
can someone explain
drowsy epoch
isnt it u + υ = t
You would have three variables, obv you wanna rid t
exotic shale
You would have three variables, obv you wanna rid t
and how would ido that
like on the graph u and υ how do i find the new region
drowsy epoch
t runs from 0 to M
exotic shale
t runs from 0 to M
thats what i dont understand since t = u + υ
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frank folio
Im having trouble understanding the surjectivity of this proof:
final saddleBOT
Im having trouble understanding the surjectivity of this proof:
frank folio
The existance of T should not have such importance unless its a basis right?]
thats the lemma they are talking about
neither of these are the basis so im lost as to how they made the connection
formal trail
the linear map lemma guarantees that for every matrix, there is a linear map corresponding to it
so let's say we have a fixed matrix $A$, and pick fixed bases $v_1,\ldots ,v_n$ and $w_1,\ldots,w_m$. then we define a second list of vectors in $W$, $w_1',\ldots w_n'$ by
[ w_k' = \sum_{j = 1}^m A_{j,k} w_j ]
then we are saying there exists a linear map $T$ such that
[ T v_k = w_k' ]
by the linear map lemma, and by definition $A = \mathcal M(T)$
soft zealotBOT
κλαουντ ☁ (cloud)
frank folio
the linear map lemma guarantees that for every matrix, there is a linear map cor...
is this not only for the basis
or are we going through the linear combinations
ok nvm that makes sense
so it garenttes that for any matrix there is a lienar map corresponding to it
through linear combinations of the basis?
formal trail
yes
frank folio
ok we just took A to be arbrtraty here
and showed that there is a linear map to every T
from A
@formal trail
formal trail
well we are saying that the map which rakes in a linear map and spits out its matrix is bijective. in this phase we are saying it is surjective because every output (matrix) has an input (linear map)
frank folio
oh because the elements of the matrix are just coefients, and legit all elements and combinations in R are included here
?
formal trail
well we are saying that if we use the entries of the matrix in a particular way that gives us a list of outputs w_k which, when paired with the basis v as inputs, uniquely specify a linear map (by 3.4)
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frank folio
.close
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winged ember
i cant seem to figure out how to evaluate this
frank folio
plucky rover
i cant seem to figure out how to evaluate this
I tagged you in an available channel. Please post there
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rustic narwhal
hi, teachers, do you know where i can find a proper proof about this equility
rustic narwhal
1
severe verge
use set builder
desert mantle
double inclusion
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@rustic narwhal Has your question been resolved?
cloud zephyr
I tried it in two ways and I got different answers. I am off by one (-) sign and I can't figure out from where its seeping in into my answer.
final saddleBOT
I tried it in two ways and I got different answers. I am off by one (-) sign and...
final saddleBOT
robust mulch
@cloud zephyr did you figure it out?
cloud zephyr
<@733585715673432135> did you figure it out?
no still trying
robust mulch
why close then
cloud zephyr
but i dont know how to send in my solution because i cant send a picture of my work rn and its hard to explain what i did via text
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violet junco
I tried it in two ways and I got different answers. I am off by one (-) sign and...
sorry isnt it physics?
robust mulch
physics is fine
violet junco
oh mb
thin cloud
sorry isnt it physics?
-# even Bio and Chem are fine
violet junco
so what you want to do here is take force perunit length as lamda times g
you want to assume a pully system with mass
assum,e the pulley si the sphere with a mass
robust mulch
the sphere is practically irrelevant except for it being a smooth round surface
cloud zephyr
ok where you at so far?
I got (λg) (1/2 - 2/pi)
violet junco
-# even Bio and Chem are fine
ahh mb
craggy plank
-# even Bio and Chem are fine
-# So are English essay proofreads
robust mulch
-# So are English essay proofreads
-# we do all sciences, even political science
violet junco
-# we do all sciences, even political science
Ok ty
robust mulch
-# /j in case you couldnt tell
thin cloud
-# we do all sciences, even political science
-# awww, I thought I can send my SAT reading here
cloud zephyr
I think its plus
Yes thats my issue
robust mulch
im curious where the minus came from
cloud zephyr
me too 
robust mulch
can you explain your thought process a little more?
cloud zephyr
Okay I assume a small element of length dl, mass dm, subtending a small angle dθ at an angle (θ) from the vertical .
dl = Rd(θ), dm = (λ)dl. so dm = Rλd(θ).
small gravitational force on this is dF = g* dm. The component of that force we're concerning with here is gsin(θ)dm. so basically gsin(θ)Rλd(θ). Then i integrated it
robust mulch
ah there it is
check your triangles
oh angle from the vertical
i need to be better at reading physics
cloud zephyr
i took my angles from the vertical
F_net - λg/2 = integration of gsin(θ)Rλd(θ) (limits pi/2 o 0)
robust mulch
so its just a sign thing
but the weird thing is if you integrate backwards, the idea is the same, but the sign flips
cloud zephyr
wait wait
robust mulch
and i cant tell you whats making the difference
cloud zephyr
but the weird thing is if you integrate backwards, the idea is the same, but the...
if we take the angle from the horizontal right?
robust mulch
yeah that works
but it still doesnt fix the issue that the direction of integration flipping will change your answer
cloud zephyr
and i cant tell you whats making the difference
I KNOW, i cant figue it out 
I've been going crazy
robust mulch
wait i might just be silly
integral of sin is -cos
-cos(pi/2)-(-cos(0))=0-(-1)
which is 1
violet junco
isnt the limit 0 to pi.2?
cloud zephyr
-cos(pi/2)-(-cos(0))=0-(-1)
but its pi/2 (LL) to 0 (UL), which is -1
violet junco
t1 is 0 adn t2 is pi/2
violet junco
but its pi/2 (LL) to 0 (UL), which is -1
I think it si the reverse
robust mulch
right
im being extra silly
just use magnitude
you know the sphere isnt removing any forces
cloud zephyr
This is still bothering me though. I would've gone : (4) None of the above, in a high stakes situation. How would I know to take the magnitude?
violet junco
is it a olympiad?
cloud zephyr
No
cloud zephyr
No no, i am prepping for some medical school entrance tests and came across this question
and couldnt resist
violet junco
( T + dT = T + (dm)g \cos\theta ), ( N = (dm)g \sin\theta )
soft zealotBOT
qfalcon_
violet junco
is this right
$$
\int_{T_1}^{T_2} dT = R \lambda \int_0^{\pi/2} \cos \theta , d\theta
$$
soft zealotBOT
qfalcon_
violet junco
ok yay the converter is working
cloud zephyr
do you mind explaining a little bit?
final saddleBOT
@cloud zephyr Has your question been resolved?
robust mulch
the chain links pull on the rope, adding to the tension still
they dont relax the tension
thus, take magnitude
worldly pendant
🍆
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@cloud zephyr Has your question been resolved?
rain sentinel
ou will need to create a plot that:
• has Temperature along the X-axis and Impact Energy along the Y-axis
• Y-axis crosses X-axis at -120 deg C
Impact Energy (J)
Temperature, T (°C)
• includes three series of data – representing the lowest, mid and highest
results for Impact Energy at each temperature
• uses different styles of marker for each series, and includes a legend
final saddleBOT
ou will need to create a plot that:
• has Temperature along the X-axis and Impac...
rain sentinel
however when ive tried plotting this in excel the axis looks like this
im not sure how to change it to look like this
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@rain sentinel Has your question been resolved?
bold zenith
In the excel data put rows below for the minimum using MIN and maximum using MAX and the one in between (which tbh I can’t think of how to get easily)
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cloud zephyr
Assuming the pulleys are massless, find the time at which the 2kg Block will lift from the ground.
final saddleBOT
Assuming the pulleys are massless, find the time at which the 2kg Block will lif...
cloud zephyr
I had too many variables and I looked at the solution, they didnt consider net accelerations for either block. Why is that?
Like I was made the equation:
For the 2kg block:
N + 2T - 20 = 2a
And then N = 0 (condition for leaving contact)
2T - 20 = 2a
I know that T = 5t/3. and even if I make equations for the 8 kg block as well, I would have too many variables and too few equations
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@cloud zephyr Has your question been resolved?
crisp mason
Like I was made the equation:
For the 2kg block:
N + 2T - 20 = 2a
And then N =...
i hated physics
and now im making myself learn classical dynamics in a month and a half 😃
swift bone
Maybe u forgot that for the block to just lift off, the forces have to be balanced?
runic tulip
Did you use string constraint?
Using that you can find the relation between the acc of the blocks
@cloud zephyr
cloud zephyr
Maybe u forgot that for the block to just lift off, the forces have to be balanc...
oh hell, i confused it with a prior question
runic tulip
Using that you can find the relation between the acc of the blocks
We don't need this here
Mb
cloud zephyr
Did you use string constraint?
No, I am reviewing that approach next. I learnt mechanics a while ago, so I've forgotten a lot of it
cloud zephyr
okay so if i want it to just lift, I just need to consider the bare minimum scenario with net force = 0 ?
runic tulip
Yes
You need to do a > 0
Which means Fnet > 0
So solve for Fnet = 0 to get the limiting case
swift bone
yep
cloud zephyr
okay what if the Force was like 1000N (constant and huge). Wouldnt that cause a sudden acceleration when liftoff?
runic tulip
It would
swift bone
Yeah. The second it leaves the ground, the normal force is gone, so u get a sudden net upward force.
cloud zephyr
but then wouldnt i need to give at an initial acceleration the moment the N = 0?
runic tulip
?
swift bone
nah, a=0 is the condition for it to just start moving. If the upward force is bigger than the weight, there's a net force, and that's what causes the acceleration.
cloud zephyr
I am just a little confused that the Normal reaction if 0 the moment it leaves the ground, and it experiences an upward acceleration the moment it leaves the ground, why do i not include acceleration in my equations?
swift bone
It's cuz you're solving for the tipping point. The exact moment the upward force equals its weight. At that single instant, a=0. The acceleration kicks in right after.
cloud zephyr
okay, that makes a little more sense to me
i'll try to process that
thank you so much:)
.close
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cloud zephyr
I am getting an answer different from the options, and would like to find my mistake.
I am denoting vector quantities in bold here. i and j are unit vectors along x axis and y axis respectively.
ds is the small displacement.
ds = dx i + dy j
small work $$dW = ydx-xdy$$
$$y^2 + x^2 = a^2 $$
$$y = \sqrt{a^2 - x^2} $$ and $$ x= \sqrt{a^2 - y^2} $$
$$dW = \sqrt(a^2 - x^2) dx - \sqrt(a^2-y^2)dy $$
$$W = \int_{\a}^{\0} \sqrt{a^2 - x^2} dx - \int_{\0}^{\a}\sqrt{a^2-y^2}dy$$
$$W = (\frac{a^2}{2} - \frac{a^2 \times pi}{4}) - (\frac{a^2 \times pi }{4} - \frac{a^2}{2})$$
final saddleBOT
I am getting an answer different from the options, and would like to find my mis...
soft zealotBOT
Adrien-Marie Legendre
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cloud zephyr
Adrien\-Marie Legendre
Compile Error! Click the <:errors:504266556054962196> rea...
Oof
okay this is it, this is about the best i can do lmao
formal trail
I am getting an answer different from the options, and would like to find my mistake.
I am denoting vector quantities in bold here. $\vb i$ and $\vb j$ are unit vectors along $x$ axis and $y$ axis respectively.
$d\vb s$ is the small displacement.
$$ d\vb s = dx \vb i + dy \vb j $$
small work $dW = ydx-xdy$
\begin{gather*}
y^2 + x^2 = a^2 \
y = \sqrt{a^2 - x^2} \quad \text{and} \quad x= \sqrt{a^2 - y^2} \
dW = \sqrt{a^2 - x^2} dx - \sqrt{a^2-y^2}dy \
W = \int_{a}^{0} \sqrt{a^2 - x^2} dx - \int_{0}^{a}\sqrt{a^2-y^2}dy \
W = \left(\frac{a^2}{2} - \frac{a^2 \times \pi}{4}\right) - \left(\frac{a^2 \times \pi }{4} - \frac{a^2}{2}\right)
\end{gather*}
soft zealotBOT
κλαουντ ☁ (cloud)
formal trail
since both of those essentially integrating the area under the circle for 1 quadrant they should each contribute a quarter circle area (negative)
cloud zephyr
magnitude understood, negative why?
OHHHH
I couldve gotten the -ve by analysing the direction of force and displacement
is that right?
formal trail
well just noting that [ \int_0^a \sqrt{a^2 - x^2} \dd{x} ] is the area of the quarter circle; the first one has the bounds reversed and the second one is being subtracted so they both contribute negatively
soft zealotBOT
κλαουντ ☁ (cloud)
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warm python
So $x'=x^{-1}$ for convention's sake.
\
$xx' =e \implies xx'(x'') = x'' \implies x(x'x'')=x'' \implies x''=x$.
\
Then $xx'=e=x'x''=x'x$
soft zealotBOT
wai
onyx peak
So $x'=x^{-1}$ for convention's sake.
\\
$xx' =e \implies xx'(x'') = x'' \implie...
what are axioms (ii) and (iii)?
warm python
what are axioms (ii) and (iii)?
warm python
what are axioms (ii) and (iii)?
It's fine, I just have to sort out part of the problem now
If I can show the left identity is the right identity then I'm done
onyx peak
wai
Yeah, this looks fine. I'd just write (xx')x'', parens around a single element are a bit pointless
warm python
Yeah, this looks fine. I'd just write (xx')x'', parens around a single element a...
well, subject to showing ex''=x''
I suppose I use the hint to prove that
onyx peak
yeah, that's a good idea
that hint actually gives u sth slightly different, but you can get ex = x from that
warm python
$ee=e\implies e(xx')=xx' \implies (ex)x'=xx' \implies ex=x$
soft zealotBOT
wai
warm python
This works too I think
onyx peak
yep, that looks fine
warm python
cool :D. I know this is an easy problem, but kind of proud of myself for doing it
onyx peak
||x'xx'x'' = x'(xx')x'' = x'ex'' = x'x'' = e
x'xx'x'' = (x'x)(x'x'') = x'xe = x'x
so e = x'x||
This is what they intended to do with the hint btw
onyx peak
cool :D. I know this is an easy problem, but kind of proud of myself for doing i...
its actually not that trivial to come up with
took me like an hour when i first tried it
warm python
I had first seen this long ago
onyx peak
so u can be rightly proud of urself
warm python
never got it then
warm python
so u can be rightly proud of urself
Cool!
I'll eat lunch now, thanks for the help again!
,ti
soft zealotBOT
The current time for math_rocks is 12:21 PM (IST) on Wed, 01/10/2025.
warm python
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plain rain
I have a math uni- related question if thats okay. I am first semester and I wanna take a course that is available a few years later normally. Is it okay to take it from now? And can I also take the exams if I wanna?
final saddleBOT
I have a math uni- related question if thats okay. I am first semester and I wan...
plain rain
Whoever answers answer in terms of experience, because I know it prolly depends
worldly mesa
you can take the course if:
1 - your uni lets you
2 - you are ready in terms of mathematical maturity and prerequisites
plain rain
it is set theory, but its for 6th semester for sum reason
odd seal
Some courses require knowledge taught in previous courses, so unless you are good with these prerequisites, you would find it difficult to keep up with the pace of the course
worldly mesa
it is set theory, but its for 6th semester for sum reason
this might mean its a grudute level course
you should check online to see if this is the case
plain rain
Some courses require knowledge taught in previous courses, so unless you are goo...
true, but if I try and I can follow, is it possible to allow me to take the exams?
plain rain
this might mean its a grudute level course
nono I checked it
worldly mesa
true, but if I try and I can follow, is it possible to allow me to take the exam...
this is up to your university
plain rain
its a choice subject thats why its so later on
odd seal
those prerequisites need not be the courses, but might also come in the form of mental juggling that gets taught during the lectures, like some specific way to handle a specific type of problem, and that comes with the practice which you might lack right now
odd seal
true, but if I try and I can follow, is it possible to allow me to take the exam...
if you are able to keep up with the pace, I dont see a reason why not?
might help you later on, if you do good in the course and if you are interested to pursue it further, in terms of finding undergrad research opportunities or thesis or any such thing
plain rain
might help you later on, if you do good in the course and if you are interested ...
I had a lesson in something similar and was able to follow almost the whole of it, thats why Im thinking of taking set theory. it is even easier than what I attended
anyways ill ask the people here too
thank you
.solved
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plain rain
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✅ Original question: #help-36 message
odd seal
talk to your seniors who have taken the course, if you know any (might be tough since you are just starting uni) it might help you more if you are able to find videos of lectures from the prof (might give you an idea of what the prof expects and how the stuff is going to be paced)
candid hull
do you have a syllabus for that 3rd year class ? I'd assume it's much different than what you've seen about now, starting from ZFC and all that
plain rain
talk to your seniors who have taken the course, if you know any (might be tough ...
He let me attend a similar class he had, but idk if its okay to ask to actually join it ya know? i dont wanna piss him off lol
plain rain
do you have a syllabus for that 3rd year class ? I'd assume it's much different ...
what does syllabus mean? second language oops
worldly mesa
and homework/exam format
plain rain
the content of the course
Ive read a quarter of a book abt set theory but I have no idea what he will do in there
worldly mesa
Ive read a quarter of a book abt set theory but I have no idea what he will do i...
it should appear online
thats our point
plain rain
it should appear online
I have to request online in order to see the contents of his class
its weird
the system
odd seal
He let me attend a similar class he had, but idk if its okay to ask to actually ...
oh, so you know the prof? Then you might as well ask him for a meeting and talk this directly. Profs are very forthcoming when you express an interest in their topics. He would be able to help you better in that regard
plain rain
oh, so you know the prof? Then you might as well ask him for a meeting and talk ...
okeoke, will do that then
thank you chat
.solved
final saddleBOT
worldly mesa
thank you chat
chat
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Available help channel!
warm python
I don't get how ths is differnt from a partial order
final saddleBOT
I don't get how ths is differnt from a partial order
faint edge
Not sure how you defined partial order but the usual difference is that two elts of a poset need not be comparable
Ur case (i) ensures this never happens.
warm python
plucky rover
I don't get how ths is differnt from a partial order
Think of power set of a set (with more than 2 elements) under set inclusion. That's a partial order, but not a total order
faint edge
If you've ever seen a tree describing a tournament that's a partial order which is not total for ex
Oh the powerset is a good one too.
warm python
so this is a partial order
plucky rover
A total order is just a partial order where all elements are comparable
faint edge
Yah so in this case if I give u a and b, nothing tells you a<=b or b<=a
warm python
so in a partial order a can be NOT related to b
faint edge
Yah!
final saddleBOT
warm python
(I'm using a variety of other books to study)
plucky rover
I wish my courses covered all this
It's very interesting that they didn't cover this
warm python
It's very interesting that they didn't cover this
Tbf we did do this in RA
Total order in class and partial order in the notes
faint edge
It's hit or miss whether you do this.
plucky rover
Yeah same
faint edge
Often you just start with a linear order or something that has one because delving into order theory stuff is kinda niche and unproductive if you're focused on other stuff
faint edge
Order theory is cool in general. I think the first time I saw these things was set theory or discrete math.
warm python
I've to eat and then head to a class , see y'all !
warm python
It's 7 pm what fucking class lol
Extra classes
plucky rover
Yeah figures
warm python
Taken by students
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vague anchor
26
tired walrus
!status
final saddleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Ofc😭
tired walrus
do you know what trace is
vague anchor
Yes
tired walrus
i don't think there's any fancy theory here
or at least i don't see anything
maybe there is some stupid bs trick but i would just bash
write sth like $A=\bmqty{a_1&a_2\a_3&-a_1}$ and similar for $B$
soft zealotBOT
Ann
tired walrus
you want to check AB vs BA for if they are equal
tired walrus
But why diagonally, opposite of a_1 i.e. -a_1
trace zero.
vague anchor
trace zero.
Oh fr
vague anchor
30
Assuming A to be I_4
Or all elements to be zero except 1 elements (which is one)
It can be known
But proving in a proper way I need help
final saddleBOT
30
Assuming A to be I_4
Or all elements to be zero except 1 elements (which is o...
vague anchor
,rccw
soft zealotBOT
tired walrus
let u = [1; 1; 1; 1]
(ie u is the vector of size 4 with all coordinates 1)
then your condition is equivalent to saying Au = u
think about why that is based on what you know about multiplying matrices
$\bd{u}=\bmqty{1\1\1\1}$
vague anchor
let **u** = [1; 1; 1; 1]
(ie u is the vector of size 4 with all coordinates 1)
Just using
Matrices
I haven't learnt vectors yet
Except vector in physics
soft zealotBOT
Ann
tired walrus
then pretend i said 4×1 matrix.
vague anchor
then pretend i said 4×1 matrix.
Then?
tired walrus
then your condition is equivalent to saying Au = u
in fact it is a general fact that Au, with my u here, is a 4×1 matrix containing the row sums of A as entries
so you will want to look at A^10 u
think about what that must be
don't try to descend back into what'stheformulaism
vague anchor
so you will want to look at A^10 u
A^10 should be A only, shouldn't it?
u as it is
vague anchor
A^10 should be A only, shouldn't it?
u as it is
I mean should it or not?
tired walrus
do you mean "be" or "become"
vague anchor
*question asks for total element sum in A^10*
What difference does it make
My weak English
tired walrus
well i don't speak Hindi so we are a bit stuck here
& can't figure out how to say same thing again but in simpler form
vague anchor
Thats not a big difference
If it becomes A
It will be equal to A
gray yacht
well i don't speak Hindi so we are a bit stuck here
What do you want to translate, lmk if i can help
gray yacht
<@&286206848099549185>
Yes bro?
vague anchor
Pls Help me solve question no. 30
tired walrus
I just want to prove A=A^10
impossible because not true!
vague anchor
Oh there she comes
vague anchor
impossible because not true!
Then what's the approach then?😵
jovial grotto
one way to solve is to take advantage of the generality of the problem
and consider an identity matrix
vague anchor
It's not a way to solve it that's completely hit n trial like
ivory bear
which one?
vague anchor
30
tranquil pine
I have a question, can someone help me with absolute value functions? I don't understand and have tried many things
vague anchor
occupied!
ivory bear
I have a question, can someone help me with absolute value functions? I don't un...
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I have a question, can someone help me with absolute value functions? I don't un...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
tranquil pine
Sorry new!
tired walrus
where e is the [1 1 1 1] matrix from before
i called it u
not e
just to be clear on that
vague anchor
<@1184081012381204507> but then this implies that A^ke = e
That that thing I can't understand man
jovial grotto
oh sorry
jovial grotto
That that thing I can't understand man
see Ae=e
multiply A by both sides
then A^2e=Ae
but Ae =e
so A^2e = e
jovial grotto
do you see how this can be continued
vague anchor
Freakingly hell
jovial grotto
now, remember that multiplying by e is effectively summing the rows
now how do you sum the columns?
do you have any idea?
try to find a vector similar to e
vague anchor
Now further I can do it myself
jovial grotto
nice
vague anchor
Thank you🙇♂️🙂↕️
jovial grotto
👍
vague anchor
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ember escarp
log2(x-1)+log2(x-1)=3
How to solve this?
final saddleBOT
log2(x-1)+log2(x-1)=3
How to solve this?
tired walrus
log2(x-1)+log2(x-1)=3
How to solve this?
just to clarify, your equation is $$\log_2(x-1) + \log_2(x-1) = 3$$ yes?
soft zealotBOT
Ann
ember escarp
yep
tired walrus
ok then yes as @tall cape said the first step is definitely to add them as $$2 \log_2(x-1) = 3$$
soft zealotBOT
Ann
tall cape
chomp are you okay from here or you need hint for next step
ember escarp
i really do need guidance in solving it
tall cape
okok
so
think about the end goal
we want
x = ???????
so look at what we have, our x is trapped in log right?
is it possible to take it out?
ember escarp
yes?
tired walrus
do you know how to solve logarithmic eqs in general
ember escarp
yes
tired walrus
ok right
so if you had something that looked like $\log_b(x) = k$ how would you rewrite it
soft zealotBOT
Ann
tired walrus
(dont worry about your original eq yet; we will tie back to it shortly)
(i wanna see whether you know the key step)
ember escarp
(b)(k) = x correct me if im wrong
ember escarp
oh just remove the ()
soft zealotBOT
Progameyen
ember escarp
yes
tired walrus
you should use ^ for exponents btw
tired walrus
$2 \log_2 (x-1) = 3$
backslash \ not forward slash /
soft zealotBOT
Progameyen
tall cape
okok tq
tired walrus
yeah so how can we get the log term on its own here
(just basic algebra, no log-law manipulation yet)
past cairn
!helpm on maths
final saddleBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
past cairn
new here
tall cape
?
ember escarp
wait, how did we get the 2log₂?
tired walrus
!helpm on maths
hello and welcome to the server. this channel is currently occupied
tall cape
so like
past cairn
annn need help for yr8 hw
soft zealotBOT
Progameyen
tired walrus
annn need help for yr8 hw
go to your channel #help-29 and post your thing there.
tall cape
Progameyen
realise that both are exact same thing
so we can just add them together
as if $a + a = 2a$, where a = $\log_2 (x - 1)$
soft zealotBOT
Progameyen
tall cape
@ember escarp Do i need to clarify anything more?
ember escarp
nonee
soft zealotBOT
Progameyen
tall cape
And you know that if your expression is in the form of
$$\log_a b = c$$
Then you can rewrite it as:
$$a^c = b$$
soft zealotBOT
Progameyen
tall cape
Where a, b, c can be constant (just number) or any variable (any expression that as x)
So far so good?
ember escarp
yupp
tall cape
Now
tall cape
$2 \log_2 (x - 1) = 3$
If we can get our expression to...
tall cape
And you know that if your expression is in the form of
$$\log_a b = c$$
Then you...
...this form
Then we can 'take out' the x right?
cause the x is sitting inside log()
we have to take it out
Now the question is
Is it possible to arrange our expression $2 \log_2 (x - 1) = 3$ to the form of $\log_a b = c$?
soft zealotBOT
Progameyen
tall cape
Note: There are multiple ways to do so, we could just choose one
ember escarp
i think yes
tall cape
Hm how would you do so then?
ember escarp
combining like terms?
ember escarp
the (x-1)
tall cape
When we talk about like term__s__, we need at least two of them tho 🤔
So for your information, I cannot see where is the like terms hm
Unless you do think there are like terms, you can point it out to me
Otherwise we try other method
ember escarp
what is the other method?
tall cape
Lets go to our goals in case we forgot
Is it possible to arrange our expression $2 \log_2 (x - 1) = 3$ to the form of $\log_a b = c$?
soft zealotBOT
Progameyen
tall cape
First subquestion:
Is this expression $2 \log_2 (x - 1) = 3$ already in the form of $\log_a b = c$?
soft zealotBOT
Progameyen
tall cape
Do tell me if you dont understand what im saying
ember escarp
not yet
tall cape
and a = 2 right?
ember escarp
yea
tall cape
But dont forget the 2 that is sitting outside
it is extra
so both of them isnt the same thing yet
cause the 2 sitting outside of log
So if we want to make both same thing, we have to eliminate the extra 2 (or move it somewhere)
So any idea?
ember escarp
noopee
ember escarp
yea
tall cape
So is it possible to somehow make the 2 no longer stay there?
ember escarp
hmmm, yea?
tall cape
do tell me how
ember escarp
by dividing?
ember escarp
2
ember escarp
log₂ (x-1) = 3/2 ?
tall cape
yup
now
Is our expression $\log_2 (x - 1) = \frac{3}{2}$ in the form of $\log_a b = c$?
soft zealotBOT
Progameyen
ember escarp
yes
tall cape
yup
a = 2
b = x - 1
c = 3/2
So we can finally apply the rules that we are waiting for!
So after apply the formula, what we will get?
ember escarp
2^2 = 3/2 ?
tall cape
ermmmm not really tho...
ember escarp
do we have to add x-1?
tall cape
And you know that if your expression is in the form of
$$\log_a b = c$$
Then you can rewrite it as:
$$a^c = b$$
soft zealotBOT
Progameyen
tall cape
In case you forgot
ember escarp
2^3/2 = x+1?
ember escarp
oh i thought we done
tall cape
Almost
but not done
cause our goal is to solve it
We have to get it to x = ???
@ember escarp
ember escarp
hello
tall cape
Have you got the answer?
soft zealotBOT
Progameyen
tall cape
2^3/2 = x+1?
btw its x - 1, not x + 1
tall cape
Progameyen
we are at final step!
ember escarp
oh right, srry
ember escarp
uhm
soft zealotBOT
Progameyen
tall cape
how to get the expression x = ???
ember escarp
square root?
tall cape
no need
x is at left side right?
so to get form of x = ???
we can just move that -1 to right side
$$x= 2^\frac{3}{2} + 1$$
soft zealotBOT
Progameyen
ember escarp
oh so transpose?
tall cape
errrr you just +1 from both sides
ember escarp
oh
tall cape
$$x - 1 + 1 = 2^\frac{3}{2} + 1$$
soft zealotBOT
Progameyen
ember escarp
so thats the answer?
soft zealotBOT
Progameyen
ember escarp
im still kinda confused but I understand the point
ember escarp
Progameyen
here
tall cape
It is a formula for logarithm
And it is basically how logarithm is defined
Wait are you asking how this formula work?
Or you are asking how to apply it?
ember escarp
both, bcuz this was given to us without prior knowledge huhu
I only know the basics
tall cape
hmmm...
Cause like, the logarithm itself is an inverse of exponent
Like its existance is basically the "reverse" of exponent
late rose
I only know the basics
do you know the logarithm rules?
ember escarp
nop
tall cape
Hm...someone has to teach you about log again tho...
I wish i can do that but im about to sleep ;-;
late rose
oh alright
youll probably be taught it later in your class ig
you dont need it for this problem though
ember escarp
log2(x-1)+log2(x-1)=3
How to solve this?
can I have the summary steps on how to solve this?
tall cape
$$\log_2 (x - 1) + \log_2 (x - 1) = 3$$
$$2 \log_2 (x - 1) = 3$$
$$\log_2 (x - 1) = \frac{3}{2}$$
$$2^{\frac{3}{2}} = x - 1$$
$$x = 2^{\frac{3}{2}} + 1$$
soft zealotBOT
Progameyen
ember escarp
- add the same term
- divide both sides by 2
- Convert logarithm form to exponential form
- put +1 both sides
is that all or did I miss any?
soft zealotBOT
Progameyen
ember escarp
what step is that
tall cape
After you divide both side by 2
ember escarp
anything else?
tall cape
nope
ember escarp
is there anything else I should remember or take note of?
tall cape
for now try to understand what log do
tall cape
Progameyen
and this thing
ember escarp
.close
tulip panther
I don't even know how to start this, can someone break it down for me into manageable chunks?
final saddleBOT
I don't even know how to start this, can someone break it down for me into manag...
solid notch
draw a visual representation while reading the question out
use different shapes to represent a group type and write a number ( frequency ) for the group type in thoese shapes
tulip panther
okay, i got the total amount of combinations possible, how do i restrict it to only 3 substitutes possible?
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eager shore
final saddleBOT
eager shore
@blissful condor @sick roost right I'd like to formulate a thought process for this now
I'll try proving that bounded continuous functions are UC
worldly mesa
<@316739634405048331> <@330098469597347840> right I'd like to formulate a though...
!noping
final saddleBOT
<@316739634405048331> <@330098469597347840> right I'd like to formulate a though...
Please do not ping individual helpers unprompted.
sick roost
hold on!
you have a continuous periodic function
consider your compact period interval
show UC and bounded on that first
then, since its UC and bounded on that interval, periodicity implies UC and bounded everywhere
onyx peak
I'll try proving that bounded continuous functions are UC
this is not even true btw