aight
#help-36
silent meadow
It's garbage and boring
Switzerland is much better I got family there
But yea anyways back to the question
violet echo
aihgt
rlly doesn't look good
but
every 20 seconds it does an "half turn"
meaning
it goes either all the way to the top
or all the way to the bottom
final saddleBOT
violet echo
U gotta be trolling..
why?
final saddleBOT
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unkempt seal
can someone tell me why this system of equations doesn't work
final saddleBOT
can someone tell me why this system of equations doesn't work
unkempt seal
my graphing calculator outputted values
and wolfram outputted t, x and y expressed in terms of a for some reason
the first problem should be -a+x=0.5 but same result
shut gazelle
can someone tell me why this system of equations doesn't work
That's because you have 4 equations that uses 4 variables but on the right side, you listed only 2 of them
unkempt seal
That's because you have 4 equations that uses 4 variables but on the right side,...
so it's not supposed to be solvable?
cause my graphing calculator somehow got t=0.5, x and y =0, and a=-0.5
some of the online calculators like symbolab also gave this result
shut gazelle
can someone tell me why this system of equations doesn't work
Do you see this box? Add in a and t
And see what it results in
unkempt seal
OH
oh so it is
huh that's weird, x and y shouldnt be 0...
so it's not an unsolvable system of equation?
i have no idea how to check, i have not learned linear algebra...
shut gazelle
,w Solve[{-a+x=5,t+y=0.146,-7t-0.4645a=-0.7954,13.4641t-10.4645x+20.4635y=1.96},{a,t,x,y}]
soft zealotBOT
shut gazelle
Idk if I typed it in correctly @unkempt seal
unkempt seal
weird, last time wolfram expressed x and t in terms of a
alright thanks so it's solvable
shut gazelle
weird, last time wolfram expressed x and t in terms of a
Because you didn't tell what variables it has
unkempt seal
oh i need to tell wolfram that too?
shut gazelle
Do you see this box? Add in a and t
Like this, you didn't include a or t so it didn't solve it, same with wolfram
unkempt seal
alright thanks
i feel like i shouldnt be getting x and y to be 0 but if it's determinate then i guess i cant argue with that
final saddleBOT
@unkempt seal Has your question been resolved?
woven estuary
[X'(t) = \begin{pmatrix}
2 & 4 \ 1 & -1
\end{pmatrix}X(t) + \begin{pmatrix}
1 \ 0
\end{pmatrix}e^{-t} + \begin{pmatrix}
0 \ 1
\end{pmatrix}t]
[X(0) = \begin{pmatrix}
0 \ 0
\end{pmatrix}]
soft zealotBOT
syecko
woven estuary
[\mathcal{L}{x'} = \mathcal{L}{2x + 4y + e^{-t}}]
[\mathcal{L}{y'} = \mathcal{L}{x - y + t}]
soft zealotBOT
syecko
woven estuary
[\implies sX(s) = 2X(s) + 4Y(s) + \frac{1}{s+1}]
[sY(s) = X(s) - Y(s) + \frac{1}{s^2}]
soft zealotBOT
syecko
woven estuary
from here i take it i will need to solve this system and use partial fraction decomposition
$X = \frac{4Y + \frac{1}{s+1}}{s-2}$
soft zealotBOT
syecko
soft zealotBOT
syecko
woven estuary
so then substituting gives
$Y = \frac{\frac{4Y + \frac{1}{s+1}}{s-2} + \frac{1}{s^2}}{s+1}$
soft zealotBOT
syecko
woven estuary
common denominator up top
$Y = \frac{\frac{4Ys^2 + \frac{s^2}{s+1} + s -2}{(s-2)s^2}}{s+1}$
soft zealotBOT
syecko
woven estuary
$Y = \frac{4Ys^2 + \frac{s^2}{s+1} + s -2}{(s-2)(s^2)(s+1)}$
soft zealotBOT
syecko
woven estuary
fuck i shouldve separated Y first
$(s+1)Y = \frac{4Y}{s-2} + \frac{1}{(s+1)(s-2)} + \frac{1}{s^2}$
soft zealotBOT
syecko
woven estuary
$(s+1 - \frac{4}{s-2})Y = \frac{1}{(s+1)(s-2)} + \frac{1}{s^2}$
soft zealotBOT
syecko
woven estuary
$\frac{(s-3)(s+2)}{s-2}Y = \frac{s^2 + (s+1)(s-2)}{(s+1)(s-2)(s^2)}$
soft zealotBOT
syecko
soft zealotBOT
syecko
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fallen crest
When I plug -1^2/3 into calculator it gives not a number, how did my teacher get its positive?
final saddleBOT
When I plug -1^2/3 into calculator it gives not a number, how did my teacher get...
fallen crest
Why would it be 2 not 2/3?
thorny fox
upbeat magnet
Why would it be 2 not 2/3?
Basically it's (-1)^2 = 1 and then sqrt_^3(1) = 1
so it's a positive number = 1
fallen crest
It that makes sense, still weird that the calculator gives error
upbeat magnet
It that makes sense, still weird that the calculator gives error
you didn't put the bracket
(-1)^(2/3)
fallen crest
I did
upbeat magnet
what calculator are you using?
fallen crest
Even did 2/3 separately
fallen crest
what calculator are you using?
Phone
upbeat magnet
(-1)^(2/3)
you tried that?
upbeat magnet
Phone
send a scrn
yeah the google calculator says undefined
but it's defined š
fallen crest
fallen crest
but it's defined š
Yeah itās weird
fallen crest
Not allowed
upbeat magnet
(-1)^2 and then answer^(1/3)
upbeat magnet
Not allowed
what?
fallen crest
I was just checking my work and got the error
upbeat magnet
I was just checking my work and got the error
ooh
upbeat magnet
(-1)^2 and then answer^(1/3)
you can always do that...
upbeat magnet
np
fallen crest
.close
final saddleBOT
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mortal berry
$V=-\nabla W$
final saddleBOT
$V=-\nabla W$
soft zealotBOT
Bob Pancakebutter
soft zealotBOT
Bob Pancakebutter
mortal berry
I know they are the partial derivatives of W
but if V is a vector in 3 dimensions, should I write that it is equal to $V=-dW/dx -dW/dy -dW/dz?$
soft zealotBOT
Bob Pancakebutter
final saddleBOT
@mortal berry Has your question been resolved?
pliant bridge
Yes
final saddleBOT
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dry tide
Would someone be able to check this if itās right
final saddleBOT
Would someone be able to check this if itās right
cursive bough
looks correct to me
dry tide
thanks
plush merlin
question 12 last part the one asking to prove that l is irrational
final saddleBOT
question 12 last part the one asking to prove that l is irrational
plush merlin
i tried reaching a contradiction using archimedean property using the fact that {u_n} converges to l but i didnt reach anything
final saddleBOT
@plush merlin Has your question been resolved?
plush merlin
<@&286206848099549185>
verbal pendant
question 12 last part the one asking to prove that l is irrational
not super knowledgeable but looks like taylor series for e^x when x = 1? So then prove e is irrational?
plush merlin
i cant use any series rn
verbal pendant
ah alright
plush merlin
taking real analysis and didnt reach this topic yet
plush merlin
ah alright
any other ideas ?
verbal pendant
tryna think of stuff
plush merlin
tysm take your time
verbal pendant
havenāt done much real analysis so my ideas donāt really seem useful past that
plush merlin
i am trying too
plush merlin
havenāt done much real analysis so my ideas donāt really seem useful past that
np when you have an idea you can tell me regardless if it gives a way to prove this or no
i mean i am also trying stuff that are not working too
i got something but i am not sure if it works or no
verbal pendant
i got something but i am not sure if it works or no
welp iāll try and see if it makes sense if you want
found an interesting proof on wikipedia as well if you want
plush merlin
ahh nvm after writing for a long time I reached a place where I found it wrong XD
verbal pendant
rip
final saddleBOT
@plush merlin Has your question been resolved?
plush merlin
<@&286206848099549185>
final saddleBOT
@plush merlin Has your question been resolved?
copper roost
when you derive (3-5x)e^-x
does the whole term turn negative because of the (-1)
final saddleBOT
when you derive (3-5x)e^-x
does the whole term turn negative because of the (-1...
abstract bramble
when you derive (3-5x)e^-x
does the whole term turn negative because of the (-1...
"whole term"? theres 2 terms when u distribute or use product rule
copper roost
"whole term"? theres 2 terms when u distribute or use product rule
so u got 5* e^-x + (3-5x) * e^-x * (-1)
i dont understand what gets -
come on tenshi dont leave me bro
abstract bramble
so u got 5* e^-x + (3-5x) * e^-x * (-1)
-5*e^-x + (3 - 5x) * e^-x * (-1)
abstract bramble
it's (3 **-**5x)
abstract bramble
the -1 only applies to the 2nd term with (3 - 5x) * e^-x
copper roost
the -1 only applies to the 2nd term with (3 - 5x) * e^-x
yeah so when you simplify
you just get (-8-5x)?
abstract bramble
wuh
final saddleBOT
@copper roost Has your question been resolved?
urban field
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urban field
What
warm ether
What
warm ether
what do you want me to say to that, i dont know what troubles you
its a triangle
gotta give me more to work with
urban field
Oh youāre helping me out?
Alrighty then
Uh
Yeah everything in that picture is what I see and what I know
warm ether
id normally say go use soh cah toa
but the ratio is there for you to use, so you just need to think what x is in this case
warm ether
which of the 3 parts of the ratio do you think the hypotenuse is?
urban field
My educated guess would be the corners of the triangle
urban field
Sqrt is square root?
warm ether
yeah
urban field
Probably 2x
warm ether
probably?
urban field
No?
lethal mica
either way the value of the hypotenuse is already given, no need to find it again
warm ether
well, yeah i know that, but its how we find x
urban field
So 2x is the hypotenuse
warm ether
yup, so what must x be
urban field
10
warm ether
you now have everything you need
urban field
Huh
copper abyss
you now have everything you need
Yes
He just need to substitute 10 as x in the ratios to solve for the short and longer legs
And the hypotenuse is already given, so no need to solve for the hypotenuse
urban field
Oh that easy huh
Alright for this one
Can you correct me when Iām wrong
So
Oh nvm that wasnāt really a question
The this one
knotty night
Side A to C is already given
For everything else, just use SOH CAH TOA
Or SIne law
Whichever you like nmore
knotty night
Soh Cah Toa are trig ratios used to help find missing sides or angles of a triangle. You would need to use one of the 45 degree angles, and label the side opposit from it as opposite. Side below it as Adjaced. The Hypothenus as Hpyothenus. Then, you look at what sides you need to find. For example, you're missing X. You could do tan45 = x over 9sqrt2. Then, rearrange to solve for X.
urban field
I learn that soon but I havenāt yet
knotty night
I kinda dumped it
that's the main idea
You substitute the the corresponding sides and angles of the triangle to find the missing values
copper abyss
the first 3 questions are asking you for the labels of the 2 sides (AC and AB) and the Hypotenuse
You just need to look at the diagram given and determine which is which šš¼
An example is 9 square root of 2.
9 square root of 2 is side AC , as labelled in the diagram
knotty night
On the second Side AB and hypo CB
Do you know what the trig ratios are?
urban field
Nope
knotty night
By the way, if you don't know what you're doing, you could watch tutorials or go to https://www.jensenmath.ca/
urban field
Havenāt learned jack about trig yet
knotty night
Nope
SinĪø = Opposite / Hypotenuse
CosĪø = Adjacent / Hypotenuse
TanĪø = Opposite / Adjacent
I don't suggest tackling the question without understanding it first
urban field
It looks like theyāre the same distance to me
knotty night
Or, you could just always figure out everything knowing some sides are the same
b and X should be the same
Can find Y with Pythagorean theorem too
I don't know. I prefer some methods over others
urban field
I genuinely like
Iām sorry but I havenāt been able to gather anything yet
At all
urban field
From the start of the chatroom besides maybe this question
copper abyss
@urban field hello! I recorded a math video tutorial (with explanations) for this question
I can send it to you thru dms if you want šš¼
final saddleBOT
@urban field Has your question been resolved?
urban field
<@921184729347264532> hello! I recorded a math video tutorial (with explanations...
Please
dusky dock
final saddleBOT
jagged flare
!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
that works for finding the first equation, using that what dis you get?
dusky dock
that works for finding the first equation, using that what dis you get?
6x-10=6y+4 and 4x+8=3y+2
jagged flare
soo your saying the red angles and yellow angles are equal?
dusky dock
soo your saying the red angles and yellow angles are equal?
wait i think only 6y+4=6x-10
jagged flare
why do you think so? how do you arrive to that?
dusky dock
bc alt int angles
jagged flare
what does alt int say?
dusky dock
what does alt int say?
Alternate interior angles are formed when a transversal intersects two parallel or non-parallel lines they are located on the inner side of the lines but on the opposite sides of the transversal. If the alternate interior angles are equal, the two lines intersected by the transversal are parallel to each othe
jagged flare
a transversal is a single line correct?
dusky dock
yea
jagged flare
soo your saying the red angles and yellow angles are equal?
but here the red one is 2 parallels trough 2 diffrent lines
dusky dock
yea
jagged flare
so can we still use alternate interior angles?
dusky dock
for for the other equation, any ideas?
na
jagged flare
heres a lil hint: what angles have you not used yet?
jagged flare
yeah
final saddleBOT
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woven estuary
given a joint cdf F(x,y) can i find the joint pdf by finding $\frac{\partial F^2}{\partial y \partial x}$
final saddleBOT
given a joint cdf F(x,y) can i find the joint pdf by finding $\frac{\partial F^2...
soft zealotBOT
syecko
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@woven estuary Has your question been resolved?
final saddleBOT
@woven estuary Has your question been resolved?
final saddleBOT
final saddleBOT
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frosty cargo
why is the ans this
final saddleBOT
why is the ans this
opal osprey
It's a theoretical question
You do know how to define an inverse right
Inverses only exist for bijective functions
And for sin and cos to be bijections...
We have to define a certain domain and codomain
I hope this clears your doubt
You can dm me or ping me here if it doesn't
final saddleBOT
@frosty cargo Has your question been resolved?
untold kiln
Is my formulation of the general case correct?
final saddleBOT
Is my formulation of the general case correct?
prime oriole
Is my formulation of the general case correct?
What does delta i denote? the distance is only between two points right
untold kiln
n is the dimension. ie, 2d vs 3d
prime oriole
yup, then it should be valid. but why are you trying to generalise it wont n just take 3 values ie 1,2 and 3?
untold kiln
Maybe said like this:
I'm trying to get confortable with notation; trying to formulate my own generalities.
thanks for confirming
.close
final saddleBOT
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tranquil pine
help me out
final saddleBOT
help me out
final saddleBOT
@tranquil pine Has your question been resolved?
stable dew
final saddleBOT
stable dew
How do you do this
severe canyon
,rccw
soft zealotBOT
severe canyon
!original
final saddleBOT
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.
stable dew
Teacher wrote this on the white board and left
Said solve it I will tell ans in next class
severe canyon
The teacher just wrote this
Better if you ask him/her to check what you have to do
stable dew
Better if you ask him/her to check what you have to do
Ok I think I gonna have to wait for next class
severe canyon
It could be a simplification task, but there isn't much to simplify actually
stable dew
It could be a simplification task, but there isn't much to simplify actually
Can we simplify further than what I did?
orchid coral
final saddleBOT
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agile flume
Can someone help me find the inverse for this equation
final saddleBOT
Can someone help me find the inverse for this equation
agile flume
I donāt think I did it right
devout tulip
Put $y=f(x)$ and solve for x. You'll get $x = f^{-1}(y)$, so you know what $f^{-1}(x)$ is
soft zealotBOT
cristorenzo99
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potent seal
this derivative does not tell me if fx has any points it crosses 0 at, right?
rare girder
this derivative does not tell me if fx has any points it crosses 0 at, right?
yeah. because f(x) could have been an antiderivative for f'(x), shifted arbitrarily high up
rare girder
I guess there could be something said like, "if there is a root here, then there must be a root here and here (gesturing to other points)"
based on the shape of f I suppose
or antiderivatives for f' rather
glad harbor
however, if the highest power of x is even in f'
then it has to have a 0
bc the highest power of x in f will be odd
oc I'm only talking about polynomials here
rare girder
yeah that's fair
f' is of odd degree, so f is of even degree, so it could have no roots
potent seal
.reopen
final saddleBOT
ā
glad harbor
on your thing f' have an odd degree
so my statement doesn't apply
potent seal
i see
because like
if f' is x^3
then f is like 1/4x^4
right?
and an odd degree means it like is symmetrical in opposite sides so it has to touch zero?
potent seal
im not exactly sure why a odd degree means it has to cross zero
oh wait nvm
I get it
glad harbor
and an odd degree means it like is symmetrical in opposite sides so it has to to...
if f has an odd degree, then the end behavior is going to infinity on one side, and -infinity of the other side
then IVT
glad harbor
yea so this also poses another condition, that f has to be defined in all of R
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modest garnet
Can sum1 tell me the answer to the first question and if you got time please could you tell me the answers on the whole paper?
final saddleBOT
Can sum1 tell me the answer to the first question and if you got time please cou...
@modest garnet Has your question been resolved?
final saddleBOT
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proper grail
I need help with this limit pleasee
final saddleBOT
I need help with this limit pleasee
ornate spade
!show
final saddleBOT
Show your work, and if possible, explain where you are stuck.
proper grail
!show
Well I thought you could always use l'hopital's rule like whenever but I don't think you can š
ornate spade
there are times where it fails
proper grail
there are times where it fails
When can I not do it?
ornate spade
oh f'(x)/g'(x) = 0/0 here but you can take l'hopital of that again until its out of indeterminate form
proper grail
So it'll be likeee
proper grail
oh f'(x)/g'(x) = 0/0 here but you can take l'hopital of that again until its out...
Like this
And I can plug in the 2- and get - infinity rightt?
Could we go over some other methods though
Because you can't always use that rule
proper grail
Okayy
atomic moon
You can also say that 2x-4 is negative when you come from the left values of 2 so it will be a 0- and so 3xĀ² is strict positive
proper grail
You can also say that 2x-4 is negative when you come from the left values of 2 s...
Tyy
proper grail
factorize numerator
It looks hard to factorizee š
I don't really know any method because it's usually simpler to do
latent ermine
It looks hard to factorizee š
8 is cube of what?
proper grail
8 is cube of what?
2
proper grail
factorize numerator
Like this?
ornate spade
last term of second factor is wrong
hybrid heath
what's xĀ³-yĀ³
You should learn about difference of cubes, and the formula for difference of powers in general. They become handy
proper grail
last term of second factor is wrong
Isn't y^2 supposed to equal 8? Sorry I'm confused š
ornate spade
yĀ³ = 8 so
latent ermine
I need help with this limit pleasee
Is this supposed to have a finite solution?
proper grail
Is this supposed to have a finite solution?
The problem is to calculate the limit that's all it sayss
proper grail
yĀ³ = 8 so
OKAY SO THIS IS OUR LIM AFTER
We could plug in the x here too right
12/0- is - infinity
latent ermine
We could plug in the x here too right
The solution comes out to be infinity
proper grail
The solution comes out to be infinity
Negative infinity yes?
latent ermine
Negative infinity yes?
Correct.
final saddleBOT
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Available help channel!
flint solstice
Soo.
Question
Probelms are these :
(see image for more )
Problem 1
(1) Obtain a kinematic equation for Position rdā with respect to Position rbā.
(2) Obtain a kinematic equation for Position rdā with respect to Position raā.
(3) Let vbā and vdā be a time derivative rbā and rdā (linear velocity of Point B and Point D ), respectively, and assume vbā=0. Then, derive a velocity-level kinematic equation for vdā.
(4) Obtain a Jacobian matrix from the above equation.
Problem 2
Assume that thare is no external force or moment on the system.
(1) Derive the linear and angular momentum conservation equations for this system.
(2) Derive the equation of motion for this system using Ļ1ā,Ļ2ā,Īø1āĀØā and ĪøĀØ2ā.
Nomenclatures
Point O: Origine of the inertia coordinate frame
Point A: Mass center of Link 0
Point B: Joint 1
Point C : Joint 2
Point D: Endpoint of the manipulator arm
raā=[xaāyaāā] : Position vector from O to A
rbā=[xbāybāā]: Position vector from O to B
rdā=[xdāydāā]: Position vector from O to D
MY QUESTION now is .
For problem 1 - questions 3 and 4. for the l1 part. is it theta 0 + theta 1 or just theta 1 ? I understand that vb = 0 therefore manipulator is not moving. but does that mean that now we assume it is like a ground base manipulator and point B is the origin now ( even if its joint moves ) and therefore only theta 1 and 2 matter now ?
final saddleBOT
Soo.
Question
Probelms are these :
(see image for more )
Problem 1
(1) Obt...
@flint solstice Has your question been resolved?
final saddleBOT
@flint solstice Has your question been resolved?
flint solstice
<@&286206848099549185> please š I need this to then solve problem 2 haha
flint solstice
prof called it linear algebra calculations of robotics xD
flint solstice
license ?
spiral patrol
Undergraduate*
flint solstice
Master's student. but very very bad a math. and very very good at other things haha
spiral patrol
So you going to be doc huh? š
spiral patrol
Master's student. but very very bad a math. and very very good at other things h...
Thats what i call as an intellectual
flint solstice
hahaha do you know how to help me tho ? x)
spiral patrol
I wish i can š¦
I really dont know about linear algebra . Excuse that i cant help
hybrid heath
Master's student. but very very bad a math. and very very good at other things h...
Everything is math. So being good at other things technically makes you good at math 
flint solstice
hahahah I'm good with hands on stuff. I guess I'm good a intuitively visualising what other need maths for understanding. and that is why I'm bad a exercizing math. because I usually don't need it so exercise it less.
no help tho ? š¦
flint solstice
<@&286206848099549185>
hybrid heath
no help tho ? š¦
I would if I knew the material.
@flint solstice, maybe you can try in #linear-algebra, but your question has a high chance of getting buried in there. While we have some talented lin-alg folks, I think yours is the first robotics question I've seen. I don't want to clog this channel with endless questions to try to understand what is going on here. (But perhaps that would be best since no one has come to help yet)
final saddleBOT
@flint solstice Has your question been resolved?
bronze mica
Hello i need some help understanding this kind of second order EDOs
i know how to do sums but not products, any help to guide me?
final saddleBOT
Hello i need some help understanding this kind of second order EDOs
i know how t...
@bronze mica Has your question been resolved?
candid hull
have you tried anything ? @bronze mica
bronze mica
well, my initial thought was finding 2 particular solutions then mulplaing them together to finally add it to the homo solution, but i have tried and i got stuck on the y=A e to the x
candid hull
you just need 1 particular solution
i have tried
tried what ? what kind of method are you planning to use for the particular solution ?
@bronze mica
bronze mica
we only learnt indeterminate coefficients, i dont know if thats the name in english tho
bronze mica
3Ae^x=3xe^x
candid hull
yeah there's no constant A that fits here you're right
well ok that guess didn't work
it's time to guess better then
bronze mica
this is the answer given buy i haven no idea how they get there
candid hull
what about y=B x e^x, something that looks a bit more like the right hand side
yeah I mean indeterminate coefficients is just glorified guessing
you gotta try multiple times sometimes
& when it doesn't work you update a bit your guess
candid hull
yeah you're left with some e^x you can't cancel probably
bronze mica
yeah 3B e to ex
candid hull
well let's try and add also some e^x in our guess to counter that
which is essentially what the answer did
y = Axe^x + Be^x
this should work out fine if we are to believe the answer
bronze mica
oh i didnt know that trick, i only multplied x to get them to be independant
didnt know you can add too
lets see
candid hull
yup it's mostly a matter of experience, not a nice systematic way of solving that's the main drawback
but it's super fast if you can guess well
big IF there
bronze mica
well i didnt get the answer
A=3 and B=-3 is that right?
candid hull
there's not one unique answer
bronze mica
wdym isnt this part of the general solution?
like the homo solution + this solution = GS?
bronze mica
so, y=C1 +C2 e^(-2x)+3xe^x-3e^x ?
candid hull
I haven't checked your answer yet tho
it was just a warning that even if your answer didn't match the answer key, it still might be correct
yeah with that guess I get what the answer key has
candid hull
show your non-mathing math then
bronze mica
1 sec fixing it
yesss i got it
damn man this is hard too see
got A=1 and B=-4/3
and they match with the answer
now i know you can add em up, thanks
final saddleBOT
@bronze mica Has your question been resolved?
keen vector
@bronze mica .close
heavy grove
can someone explain the idea behind adding the "negative" frequencies to the sum of the fourier transform to cancel out the imaginary terms?
final saddleBOT
can someone explain the idea behind adding the "negative" frequencies to the sum...
heavy grove
I get that it works but I dont know what a negative frequency is supposed to be and how this doesn't alter the actual fourier transform
slender rampart
final saddleBOT
@slender rampart Has your question been resolved?
digital steeple
!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
I believe this is all about barycentric coordinates
frozen rain
how do i prove this is bounded and monoteric ( im doing calculus in a different language not sure these are the terms)
final saddleBOT
how do i prove this is bounded and monoteric ( im doing calculus in a different ...
hybrid heath
how do i prove this is bounded and monoteric ( im doing calculus in a different ...
Your terms are correct
First, determine if the sequence would be monotonic increasing or decreasing
frozen rain
This is what Ive done so far not sure how to continue
im saying that a2 is > than a1 so an+1 - an has to be larger than 0 and then ive got to a polinomic equation of x^2
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hard egret
Everything in brackets is a number?
For example
(7*1) is a singular number?
tranquil pine
Everything in brackets is a number?
For example
(7*1) is a singular number?
yeah?
hard egret
.close
final saddleBOT
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exotic cape
ok so like i have a test tomorrow. in algebra 2 and i have no idea how to do this shit
final saddleBOT
ok so like i have a test tomorrow. in algebra 2 and i have no idea how to do thi...
exotic cape
its like quadratic equations or something but idk what fr
my friend gave me the asnwers to this but i have 0 clue how he did it
had to get a couple wrong cus ik how to cheat properly
idk how to make the image clearerā¦ :(
ivory vessel
exotic cape
<:ugh:1315243934544429097>
i have a C in this class, pls help š
ivory vessel
can you like, do one at a time please
stone wagon
there's SO MUCH going on in this picture lmao
exotic cape
there's SO MUCH going on in this picture lmao
just screenshotted the pdf and did markup cuz i didnt kno ho else to do it š
16 for now ig?
im gonna fail this testā¦
my dadās gonna beat my ass and take my ps4
how am i gonna grind camos š¢
the dude ho gave me the answers is in lik college
āi did it with a special method i learned from many teachers and professors over the yearsā
so he cant explain how he did it
exotic cape
And
https://www.cuemath.com/geometry/parabola/
english please?
tulip gyro
I suspect you should take a general quadratic ax^2+bx+c=0; and check those points to be on the graph, although it's probably not enough.
exotic cape
I suspect you should take a general quadratic ax^2+bx+c=0; and check those point...
tf are a b and c
vital crag
english please?
Read until you don't understand something
exotic cape
ššš
tulip gyro
tf are a b and c
they're the things you'll have to calculate
vital crag
a, b, c are numbers
tulip gyro
if you want to solve the exercise...
exotic cape
they're the things you'll have to calculate
but oike what are they
tulip gyro
numbers; numbers we don't yet know.
tulip gyro
the curve, the blue curved line, is the graph of a quadratic
that is, an equation looking like ax^2+bx+c.
where, a, b, and c are numbers.
tulip gyro
a point (x, y) is on the graph of the quadratic (the blue line), if ax^2+bx+c=y..
tulip gyro
looks like in both exercises, 15 and 16, you have a special point (the vertex), and an arbitrary (random) point.
these 2 points need to fill the equation too.
that is, for 15, points (1, 86) and (3, 150) need to be on the graph.
which one of these is the vertex?
exotic cape
which one of these is the vertex?
erm
tulip gyro
what's a vertex?
tulip gyro
I don't think I am skilled enough to help; sorry.
exotic cape
I don't think I am skilled enough to help; sorry.
bro plsssss
exotic cape
Read until you don't understand something
come back
the other dude gave up on me before it even started
im too dum š
charred knoll
guys need help with anything?
final saddleBOT
@exotic cape Has your question been resolved?
final saddleBOT
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raven spruce
How would I be able to do this?
final saddleBOT
How would I be able to do this?
languid yoke
similar triangles will be helpful
raven spruce
would I set up the equation as ST=RU+16 ?
raven spruce
alright what would I do next?
upper prism
alright what would I do next?
two equations, two unknowns. its a system of equations, there are various ways to solve them
upper prism
yep
and then solve it how you like, substitution, elimination, gaussian row reduction...
lol
somber belfry
and then solve it how you like, substitution, elimination, gaussian row reductio...
gaussian row reduction would be the easiest
languid yoke
š
raven spruce
v=(vā16)+16 ???
somber belfry
ST = RU + RU
ST = RU + 16
As they both equal ST, you can say they are both equal
so
RU + RU = RU + 16
so if we subtract RU from both sides we get RU = 16
somber belfry
Oh i'm sorry lol i read the instruction wrong š
i thought difference between st and ru was v
willow ember
soft zealotBOT
Wild123
willow ember
.close
mortal berry
but should that red part of the circle be integrated from 0 to Ļ/2 or from Ļ to 3Ļ/2?
final saddleBOT
but should that red part of the circle be integrated from 0 to Ļ/2 or from Ļ to ...
mortal berry
In d$\theta$
soft zealotBOT
Bob Pancakebutter
mortal berry
If I set the origin O(0,0) as reference
golden slate
It depends how your integral is parametrised, but the typical convention is that theta=0 corresponds to the point (1,0) and theta increasing corresponds to going anticlockwise around the unit circle
mortal berry
I didn't parameterize anything
golden slate
What is the context of the question? Do you have a specific integral?
mortal berry
Do you know the electrostatic field?
golden slate
I suppose, but not precisely
frank ginkgo
rotate the pic
mortal berry
,rotate
soft zealotBOT
golden slate
What I was referring to before is that the function you are integrating along that quarter circle will depend on the angle theta. It may in this case be irrelevant as everything looks radially symmetric, in which case either of your two options would result in the same answer
mortal berry
But is -Ļ/4 Ļ/4 also okay?
golden slate
This is something you can try and check. Notice that there is nothing inside your d theta integral. Try changing the limits
mortal berry
In theory the cosine varies with theta in the first quadrant, while d\theta is in the third quadrant
Because a sector of a circle is L=theta Ć radius, so dL=dthetaĆradius
One thing varies in the first quadrant, while another in the third
golden slate
I'm not sure I'm following, when we introduce theta we will probably have to choose where theta = 0, right?
mortal berry
Isn't it at (1.0)?
golden slate
Yes that is the usual convention, in which case the integral would be from pi to 3*pi/2. Does it make sense why this would be reasonable to assume?
mortal berry
Yes
But cos(theta) doesn't vary with the thetas of the first quadrant?
Is it always okay to do Ļ to 3Ļ/2?
golden slate
No, I believe you should be doing pi to 3pi/2. The actual function cos(theta) is not what is important when integrating, it is the actual values theta is taking that you should be focusing on. In this case if we are saying theta = 0 corresponds to (1,0), then what I have said are the correct limits of integration for that reason
mortal berry
Yes, but if I set theta=0 for example Ļ, wouldn't the value of the integral change then?
golden slate
Yes, but then cos(theta) would become cos(theta+pi). This is what I mean about it depending on the parametrisation
mortal berry
So the result Is -$k\lambda/R$?
soft zealotBOT
Bob Pancakebutter
golden slate
I haven't done the integral, but if your theta integral evaluates to -1 then I suppose this is the answer yes
mortal berry
But if I go from -Ļ/4 to Ļ/4 it comes out different
golden slate
Yeah, so this is saying that it really depends where our theta = 0 is. I am not familiar with the actual maths you are doing as a disclaimer, but there should be some standard "convention" if you will for doing these calculations
final saddleBOT
@mortal berry Has your question been resolved?
final saddleBOT
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Available help channel!
gentle zephyr
,, \lim_{x \to \infty} \sin(x) = \lim_{y + \pi \to \infty} \sin(y + \pi) = \lim_{y \to \infty} (-\sin(y)) = -\lim_{y \to \infty} \sin(y)
final saddleBOT
,, \lim_{x \to \infty} \sin(x) = \lim_{y + \pi \to \infty} \sin(y + \pi) = \lim_...
soft zealotBOT
938c2cc0dcc05f2b68c4287040cfcf71
gentle zephyr
can someone explain what happened here
final saddleBOT
@gentle zephyr Has your question been resolved?
blissful meadow
Substitution for x = y + pi, both go to infinity.
Then sin(y + pi) = -sin(y) is a property of sin.
gentle zephyr
I understand the change of variable now if x approahces infinity x = y + pi aswell
but im confused with the sum of sine step
wdym property of sin}
blissful meadow
sin(x+pi) is a sine wave shifted half a period to the left, so that's equivalent to it starting on the bottom half of the unit circle.
The addition formulas work too. a = y and b = pi in the first equation yields -sin(x)
gentle zephyr
wait but sin(x) function never ends
why does it changes of sign if we shift it half a period to the left
blissful meadow
Whether it ends or not has little to do with it
tranquil pine
use the addition formula
blissful meadow
You can also convince yourself that x+pi and -x represent the same angle.
And then sin(-x) = -sin(x) since it's odd
tranquil pine
yes it's shifted half a period
gentle zephyr
how so?
tranquil pine
the roots also shift
gentle zephyr
roots being [-1, 1]?
tranquil pine
The root of sin is at kĻ
tranquil pine
and then they will overlap
gentle zephyr
yes, can the same be said with sin(x+pi) = sin(x-pi)
tranquil pine
yeah
gentle zephyr
wdym extrema, absolute maxima, absolute minima?
tranquil pine
yes or 3/2Ļ in [0,2Ļ]
tranquil pine
not for sin(x+Ļ)
gentle zephyr
yeah
gentle zephyr
I dont think I understand
tranquil pine
use the addition formula then
gentle zephyr
oh you talking about sin(y+pi) = -sin(y)
tranquil pine
yeah
gentle zephyr
yeah I see it now, but I was worrying about the maxima and minima
tranquil pine
don't worry about that it was just an observation
final saddleBOT
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jagged flare
let there be $a_1<a_2<a_3<\dots<a_{2023}$ such that $a_1+a_2+a_3+\dots+a_{2023}=1234^{5678}$, find
$$a_1^9+a_2^9+\dots+a_{2023}^9 \mod 15$$
final saddleBOT
let there be $a_1<a_2<a_3<\dots<a_{2023}$ such that $a_1+a_2+a_3+\dots+a_{2023}=...
soft zealotBOT
Skissue ping4response
jagged flare
i dont have any ideas for this
actually.. nvm a^9 mod 15=a
so 1234^5678 mod 15=4^5678=16^2839=1
.close
final saddleBOT
jagged flare
.reopen
final saddleBOT
ā
young bobcat
um your reasoning seems right
jagged flare
wait is there an easy way to prove a^9 mod 15=a cause i used a calculator
young bobcat
do you know euler's totient?
jagged flare
no
young bobcat
ok so euler's totient is the number of integers from 1 to n which are relatively prime to n
so, the totient of 15 is 8, as 1,2,4,5,7,8,11,13,14 are all relatively prime to 15
and Euler's Theorem
states that if you raise any number to the totient of n, you will get something 1 modulo n
so this means, that whenever a isn't 0, then a^8=1(mod 15)
Therefore, a^9=a(mod 15)
jagged flare
oooo
young bobcat
final saddleBOT
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Available help channel!
proven lion
I got -1tan(b)^-2*sec^2(b), but calculators are saying that this isn't equivalent to the derivative of tan^-1. We're supposed to be using chain rule. What did I do wrong? š§
final saddleBOT
I got -1tan(b)^-2*sec^2(b), but calculators are saying that this isn't equivalen...
rocky tusk
$\tan^{-1} x \neq (\tan x)^{-1}$
soft zealotBOT
knief
proven lion
a h. Yeah Ig that wouldn't work, huh. I got mixed up around here I think xD
how would I apply the chain rule here then?
rocky tusk
this isnāt the same question
proven lion
no I know, that's the example where I got mixed up
rocky tusk
do you know what an inverse function is
rocky tusk
its best to write arctan(x) to not get confused
proven lion
fair. Might hafta redo 5 then, woops
rocky tusk
no
proven lion
Oh
soft zealotBOT
knief
proven lion
... ah
rocky tusk
itās strange i know
proven lion
welp xD
rocky tusk
just only use it for positive integers
proven lion
wait so how DO I do chain rule w/ arcsine then?
proven lion
just only use it for positive integers
ahhh oki, I can do that
rocky tusk
you use a nice trick
so
we have $y = \arctan x$
can you solve for beta
for simplicity letās just use y and x actually so i donāt have to write out beta and P
proven lion
honestly so fair
soft zealotBOT
knief
rocky tusk
solve for x in terms of y
proven lion
uuuuh 
rocky tusk
use inverse function properties
proven lion
ew, I shall attempt
rocky tusk
do you know what it means for a function to be an inverse of another
hidden pasture
$y = \tan^{-1} x$ might be easier to show it as??
soft zealotBOT
TH_0214
proven lion
š
proven lion
in my defense, I knew arcsine was in there somewhere xD
hidden pasture
oh lol sryyyyy
proven lion
do you know what it means for a function to be an inverse of another
kiiinda?
I used to know it better but T~T
I left precalc and then immediately forgot everything from those two terms lmao
soft zealotBOT
knief
proven lion
oooh I've done this before, kinda
I need to stop doing all my calc last minute cause I am so lightheaded, I'm sorry :')
rocky tusk
with that in mind, what is $\tan(\arctan x)$
soft zealotBOT
knief
proven lion
oknowI'mdoubting
uH
my brain is processing like nothing suddenly I'm so sorry, lemme stare at this xD
proven lion
si
proven lion
am I dealing with the inside or outside rn :')
rocky tusk
maybe i should give you another example
rocky tusk
are you aware that sqrt(x) is the inverse of x^2
proven lion
yeh :D
rocky tusk
so whatās (sqrt(x))^2
proven lion
just x
rocky tusk
and btw for all of these we are just ignoring any domain restrictions because itās besides the point iām trying to make
proven lion
ye that'
rocky tusk
whatās sqrt(x^2)
proven lion
not- entirely sure. Like if I wanted to get rid of the sqrt I'd do x^(2/2) but that is just x so like. Aaaaa? T~T
rocky tusk
whatās the sqrt of 3^2
proven lion
@~@ I'm really dizzy lmao
proven lion
I take it back, yes xD
lmaooo no
look at this omg
I have all of this AND
all of this
rocky tusk
this looks like fun
proven lion
I MCFUDGED UP OK
rocky tusk
how much time did you have for this
proven lion
I PROCRASTINATEDDDDD T~T
welllll
the textbook work is just due on the day of the final so like
whenever you know all the material Ig
the oldest thing would be lab 6, so probs like 5 weeks :')
rocky tusk
anyways
proven lion
anywho's
rocky tusk
as i was saying
soft zealotBOT
knief
rocky tusk
inverse functions undo each other so to speak
you can think of arctan as the function which takes in a ratio and tells you the angle such that the tan of that angle is the ratio
$\arctan(\tan x) = x$
soft zealotBOT
knief
proven lion
and is that the outter formula ?
rocky tusk
so we will use this fact
proven lion
outer*
rocky tusk
we had $y = \arctan x$
soft zealotBOT
knief
rocky tusk
so by definition $\tan y = x$
soft zealotBOT
knief
proven lion
ok, I can work w/ that š¤
proven lion
sec^2(y) ???
rocky tusk
close
so because weāre differentiating with respect to x, the derivative of y with respect to x is not just 1, itās dy/dx so we need to multiply by dy/dx
have you ever heard of implicit differentiation
or just chain rule is fine
proven lion
sadly yes, but I don't think we're supposed to use it here since that technically comes next
