yes ok but asymptics we us ein absolutely diffeertn situations
#help-0
teal violet
ok
foggy pecan
and it takes around 1 hour or more
to evaluate it
but you must be very very precise
teal violet
for other sort fo fucntions
but isnt fraction one of them ?
foggy pecan
but isnt fraction one of them ?
here we, have just irrational functions =radicals, they are normal
teal violet
here we, have just irrational functions =radicals, they are normal
doesnt count as polynom
foggy pecan
doesnt count as polynom
it's not any advanced mathematics, it's just a time-consuming problem as a punishment :)) do you understand?
foggy pecan
doesnt count as polynom
polynomials are inside of radical symbols
teal violet
ah ok
wispy ibex
Bro wtf
proper tangle
you can use ,align to align expressions with &, and \\ to start new lines, like
,align
1 + 1 &= 2 \
2 &< 2023 - 123
ocean sealBOT
vin100
\begin{align*}
1 + 1 &= 2 \\
2 &< 2023 - 123
\end{align*}
proper tangle
\\ is a quick dirty way to a long line into multiple lines
silk jewel
2 = 2
plucky ice
How would you approach this question?
You are given a right circular cone and an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and the bases of both cones are parallel. If you choose the upside-down cone to have the largest possible volume, what fraction of the volume of the larger cone does it occupy? Use similar triangles to relate the height and radius of the small cone
lone heartBOT
How would you approach this question?
You are given a right circular cone and an...
@plucky ice Has your question been resolved?
lone heartBOT
@plucky ice Has your question been resolved?
autumn loom
hey can somebody help me out on this? I just started this in uni and im stuck idk how to get the answer. I need to find the sum of this row
subtle birch
hey can somebody help me out on this? I just started this in uni and im stuck id...
Open a new help channel #❓how-to-get-help
cinder sundial
yeee
cinder sundial
ayy
yo
ay
This is a question for math term
so lets say i got number like 2
2
=> 2^n
emmm
from x to x^n
what does the manipulation called?
echo socket
I think the word that you are looking for is exponentiation
vale wigeon
"raising to the n'th power"?
alpine sable
what does the manipulation called?
are you saying something like [
x = 2 \implies x^n = 2^n
]
ocean sealBOT
alpine sable
anyways this is just the definition of a function
alpine sable
all algebraic manipulations are just mappings
vale wigeon
"raise both sides to the n'th power"
serene junco
I'd say something like "raising both sides to the nth power" or "taking the nth power of both sides"
cinder sundial
"mapping" i have never heard that term
cinder sundial
"raise both sides to the n'th power"
that sounds terrific, and if i have only a expression
i could say "raise it to the n'th power"
alpine sable
"mapping" i have never heard that term
[
a = b \implies \m fa = \m fb
]
ocean sealBOT
cinder sundial
it seems like you just put them into a function
alpine sable
a and b are getting mapped to f(a) and f(b) respectively. This enables you to perform all kinds of algebraic manipulations as long as you are being consistent
cinder sundial
I see, I think mapping can be considered as "transformation" then
I have a mickey in real life then I transform it into a 3D space
that is called mapping
I map my real-lifef mickey into the 3D space
serene junco
I see, I think mapping can be considered as "transformation" then
yes, "function", "mapping", and "transformation" all mean basically the same thing
although I think "transformation" may have other definitions as well in certain contexts
serene junco
does "restrict x to the realm of integer" sounds awkward
I think you would be understood if you say this, but there might be better ways. Can you give an example of how you would use this?
cinder sundial
I think you would be understood if you say this, but there might be better ways....
So it is about complex number specifially
the textbook wrote that z^n
where n has to be integer
and im trying to explain it
deliberate why it has to be integer
so blah blah blah, due to some reason, "n has to be restricted in the realm of integer"
I wonder if that claim sounds awkward
serene junco
so blah blah blah, due to some reason, "n has to be restricted in the realm of i...
I would say either
"Let n be an integer. Then, blah blah blah"
or
"Blah blah blah, where n is an integer"
cinder sundial
I would say either
"Let n be an integer. Then, blah blah blah"
or
"Blah blah ...
no, there's some causes and effects in my context
we cannot just let n be an integer, otherwise the context will be different
serene junco
Oh, so you want to specify that under certain circumstances, n must be an ingeter?
cinder sundial
yes, it is due to some reasons that n has to be limited to integers
serene junco
Okay. Then I think "the integers" sounds better than "the realm of integer"
n must be restricted to the integers
not
n must be restricted to the realm of integer
serene junco
sure thing 👍
cinder sundial
.close
torn isle
lone heartBOT
torn isle
Can anyone guide me how to get (9)?
lone heartBOT
@torn isle Has your question been resolved?
torn isle
<@&286206848099549185>
torn isle
I want to know how to integrate and get (9)
Since this paper just show the result directly
full grotto
yeah but i need the question tag it or smth
torn isle
what is your question
Also, can python help me to integrate this? I actually tried the code, but it fails.
torn isle
yeah but i need the question tag it or smth
What do you mean?
full grotto
look i can help you in math or physics not in coding
full grotto
What do you mean?
mb sorry sorry i understood
torn isle
look i can help you in math or physics not in coding
Yea, I need solve by math integration
full grotto
ok
torn isle
May I know how to integrate?
full grotto
this right
full grotto
May I know how to integrate?
let me first do it bro
full grotto
this right
..
full grotto
ok no just confrimiing
torn isle
Just in case you need info from the above
full grotto
nah nah i am close to 9 will tell you in a minute
Now, we can simplify the equation by multiplying the sine terms:
wo = Flsin(wit)sin(w7t) / (mw)
wo = Flsin(wit)sin(w7t) / mw
Next, we can use the trigonometric identity, sin(a)sin(b) = (1/2)(cos(a-b)-cos(a+b)), to further simplify the equation:
wo = Flsin(wit)sin(w7t) / mw
wo = (Fl/2)(cos(wit-w7t)-cos(wit+w7t)) / (m*w)
torn isle
You are referring to (8)?
full grotto
wo = (Fl/2)(cos(wit-w7t)-cos(wit+w7t)) / (m*w) in the end you get this
this is to find the expression for displacemnt wo
full grotto
You are referring to (8)?
yes
full grotto
ok yeah wait
torn isle
wo = (F*l/2)*(cos(wi*t-w7*t)-cos(wi*t+w7*t)) / (m*w) in the end you get this
Also, actually I can’t get this
full grotto
Also, actually I can’t get this
why ?
full grotto
ok wait rn even i am not actually my lapotop is a bit old and weird so the pixels make the symbols go brr
just give me 5 min i am so sorry
torn isle
just give me 5 min i am so sorry
No problem, just take your time
Anyway, may I know is this math undergraduate level? Because I don’t think I learn before, just really curious is it an undergraduate level
full grotto
∫[0, 2π] e^(-t) [1 - s(1 + e^-sin(θt))] dt
where θ = 2π.
Let's begin by simplifying the integral:
∫[0, 2π] e^(-t) [1 - s(1 + e^-sin(θt))] dt
= ∫[0, 2π] e^(-t) [1 - s - s e^(-sin(θt))] dt
= ∫[0, 2π] e^(-t) - s e^(-t) + s e^(-t) e^(-sin(θt)) dt
= ∫[0, 2π] e^(-t) - s e^(-t) + s e^(-t-sin(θt)) dt
i think this is more clear
∫[0, 2π] e^(-t) dt = [-e^(-t)] [0, 2π]
= -e^(-2π) + e^0 this is for sperate terms
= 1 - e^(-2π)
∫[0, 2π] -s e^(-t) dt = -s ∫[0, 2π] e^(-t) dt
= -s(1 - e^(-2π))
torn isle
∫[0, 2π] e^(-t) [1 - s(1 + e^-sin(θt))] dt
where θ = 2π.
Let's begin by simpli...
Wait, which part are you referring to?
I don’t see any integration with the first line
full grotto
there is a integral in the eq 8
To evaluate the last term, we need to use the substitution u = -sin(θt), which gives us du = -θ cos(θt) dt. Rearranging, we have dt = -du/(θ cos(θt)).
∫[0, 2π] s e^(-t-sin(θt)) dt = ∫[0, 2π] s e^(-t
full grotto
oh mb
torn isle
And get (9)
torn isle
Divided by hbar
full grotto
and what is -r divided by what ?
torn isle
and what is -r divided by what ?
a_0
torn isle
that i is imaginary number right
Yea
lone heartBOT
@torn isle Has your question been resolved?
full grotto
sorry @torn isle i had a lecture sorry
torn isle
sorry <@909451723515523102> i had a lecture sorry
Nvm, I’m not in a hurry for that
So, you’re also undergraduate?
full grotto
yeah pursuing a phd in physics
alpine sable
hwta the fuck
lone heartBOT
@torn isle Has your question been resolved?
torn isle
yeah pursuing a phd in physics
Oh, I’m studying undergraduate physics 🤣
lone heartBOT
@torn isle Has your question been resolved?
lone heartBOT
@torn isle Has your question been resolved?
olive sundial
any hints?
lone heartBOT
any hints?
olive sundial
<@&286206848099549185>
olive sundial
using similar ideas to the previous exercise ?
yeah i found that
if x is a root
then so is x^2
ans so is
(x+1)^2
which would make the roots go on for infinity right
which means there are like
marsh rapids
unless
olive sundial
yeah i dont know what the unless part is
olive sundial
ye
marsh rapids
if R is stable under x -> x² and x -> (x+1)²
olive sundial
yeah hmm
0 and 1?
no
i cant seee any x which make R not infinitely
expanding
marsh rapids
I hope you're familiar with complex numbers, otherwise that one isn't easy to visualize
marsh rapids
geometric intuition
olive sundial
does the (1+x)^2 transformation
ok i dont know what that does
i know what the
x^2 does hto
marsh rapids
squaring squares the module
olive sundial
it just makes the square of the magnitude and twice degree
olive sundial
squaring squares the module
what?
marsh rapids
you just said it
olive sundial
oh ok
marsh rapids
module = magnitude
marsh rapids
let's see about x² first
marsh rapids
we can look at the set of points stable under squaring
And then what subset of it is stable under x -> (x+1)²
marsh rapids
the degree measure is prolly 0 and magnitude is 1?
that's just z=1
marsh rapids
that's still just 1
marsh rapids
squaring squares the module
I voluntarily made you forget about the argument for the a second
olive sundial
isnt that z^n -1 = 0
marsh rapids
also known as "the nth roots of unity"
olive sundial
yeah
marsh rapids
we can look at the set of points stable under squaring
And then what subset of i...
is that the set of points stable under squaring ?
marsh rapids
where did 4 come from
olive sundial
where did 4 come from
like any power of 2
marsh rapids
also known as "the nth roots of unity"
does it have to be ?
marsh rapids
squaring squares the module
letting r be the module
we know r must be 1 (or 0, but we know we'll discard it)
olive sundial
yep
marsh rapids
the argument set must be stable under doubling
olive sundial
yeb
olive sundial
wait but dont we want the whol set of those?
marsh rapids
because we're saying:
theta in R -> theta 2^n in R as well
but what are the possible starting thetas ?
marsh rapids
is that an interval ?
olive sundial
theta?
olive sundial
is that an interval ?
yeah
marsh rapids
then please write it as an interval
olive sundial
[0,360)
marsh rapids
so my candidate set is all of them
olive sundial
ye
marsh rapids
all angles possible
Surely that's stable under doubling
so it's a solution
and there's no bigger one
olive sundial
ye
marsh rapids
so we know that must be right
olive sundial
no isnt that
marsh rapids
we can look at the set of points stable under squaring
And then what subset of i...
so that's part 1 done
olive sundial
like infiity roots?
marsh rapids
it's the unit circle
olive sundial
oh wait thats just one part
marsh rapids
like infiity roots?
try to make sense of that, and notice it doesn't make sense
marsh rapids
that's why we call it unit circle
it contains all the nth roots of unity, for all n, and things that aren't roots of unity
olive sundial
ye
olive sundial
yeah
marsh rapids
so now, we can move on to part 2
which of those only generate a finite set when we add the second action
marsh rapids
yes
so that's 2 candidates, they're the only ones that don't leave the circle immediately
olive sundial
yes
marsh rapids
is it a stable set ?
olive sundial
where does it fail ?
like when it is squared
like the degree measure doubles
so it would go to another point rather than be reflected across x axis
wait
marsh rapids
btw, these points are, along with 1, the 3rd roots of unity
We call them 1, j, j²
j = -1/2 + i/2
marsh rapids
btw, these points are, along with 1, the 3rd roots of unity
We call them 1, j, j...
you can verify that j^3 = 1
olive sundial
but also how did u figure that out?
marsh rapids
but also how did u figure that out?
x = -1/2 you said
on the circle, that's only 2 points
j, j²
olive sundial
oh so
wait but i could have like -1/4
and those wouldnt be 3rd roots of unity
yknow what i mean
marsh rapids
wait but i could have like -1/4
let f(x) = (x+1)²
will its image by f be on the circle ?
olive sundial
let f(x) = (x+1)²
will its image by f be on the circle ?
no
unless its those specific points
olive sundial
o ok...?
marsh rapids
and I ask you, whether that set is stable under f
olive sundial
yeh if there roots of unity then like they are just reflected across the x axis
olive sundial
is it clear ?
i mean im still kinda confused how just because
they are on the circle
and clear a certain
constraint
we can figure out its a root of unity like
marsh rapids
we can look at the set of points stable under squaring
And then what subset of i...
this is the idea leading us
olive sundial
what does (x+1)² have to do with roots of unity?
marsh rapids
we want points on the circle it maps somewhere on the circle
olive sundial
it could have been like part of the 7th root of unity or smth
olive sundial
we want points on the circle it maps somewhere on the circle
ye
marsh rapids
and squaring only sends to the circle if the input is in the circle
olive sundial
ye
marsh rapids
so we need x+1 to be in the circle
but a²+b² = 1 and (a+1)² + b² = 1 can only happen together when a² = (a+1)²
olive sundial
yes
so just because the points satisy that they are
on the unity circle
i dont see how that leads to it being specifically 3rd root of unity
marsh rapids
it turns out to be extremely restrictive when we add the 2nd constraint
marsh rapids
but a²+b² = 1 and (a+1)² + b² = 1 can only happen together when a² = (a+1)²
this forces the value of a
Which then forces the value of b
olive sundial
yes
ok so if i said
(a+1/2)² + b² = 1
how would you know those werent part of 3rd root of unity?
marsh rapids
but a²+b² = 1 and (a+1)² + b² = 1 can only happen together when a² = (a+1)²
you need both conditions
olive sundial
well i mean if
(a+1/2)² + b² = 1
and a²+b² = 1
like a = -1/4
but that doesnt mean its on 3rd root of unity right?
marsh rapids
(a+1/2)² + b² = 1
and a²+b² = 1
if you don't believe, solve the system
Work it out yourself
I'm skipping over steps you may not be able to afford skipping
marsh rapids
(a+1/2)² + b² = 1
and a²+b² = 1
we have proved, these are necessary requirements for members of R
so R must be a subset of the solutions to that system of of equations
olive sundial
we have proved, these are necessary requirements for members of R
ye
marsh rapids
we have proved, these are necessary requirements for members of R
(not sufficient because we asked that f maps it to the circle, not yet that f maps it to itself)
marsh rapids
if you don't believe, solve the system
Work it out yourself
did you ?
olive sundial
oh but this was the one
i made uo
(a+1)² + b² = 1
and a²+b² = 1
is the real one
lemme
do that rq
yeah the original ones
are
roots of unity
cause like 30 60 90
the one i created isnt
@marsh rapids
marsh rapids
cause like 30 60 90
what is that argument
olive sundial
what is that argument
well -1/2 + sqrt(3)/2 has a
marsh rapids
but that doesnt mean its on 3rd root of unity right?
no, now you'd have a = -1/4
By the same reasoning
marsh rapids
so that would be 120 degree from that to root 1
which is clearly a 3rd root of unity
olive sundial
ye
olive sundial
no, now you'd have a = -1/4
By the same reasoning
yeah i know a = -1/4
but it also lies on the unit circle
just like the
a = -1/2 one
which means that the fact that its (a+1)^2 = a^2 has something to do witht he fact that its a 3rd root of unity
and not just any (a+k)^2 = a^2 argument
would mean that its a 3rd root of unity so i was jut wondering what
marsh rapids
yeah no
olive sundial
was so special about 1
marsh rapids
there are only so many 3rd roots of unity, they can't verify so many incompatible equations
olive sundial
there are only so many 3rd roots of unity, they can't verify so many incompatibl...
ye
anyways how do you proceed from here since 1 is not in our set
so like its still not closed
olive sundial
ye
so they are still in our set but
if u use both of them then ur gonna also get 1 when u do x^2
but 1 doesnt work
marsh rapids
if u use both of them then ur gonna also get 1 when u do x^2
are you ?
olive sundial
are you ?
well if u use one of them ur gonna get the others
so does that mean our polynomial has no roots?
which would mean its constant?
wait damn so answer is just 2016
???
marsh rapids
well if u use one of them ur gonna get the others
again, are you ?
olive sundial
what
marsh rapids
{j, j²} is a stable, finite set
marsh rapids
f(j) = j, f(j²) = j²
olive sundial
nvm im tripping they are
marsh rapids
it's as stable as it gets
olive sundial
i thought 240 times 2 = 360 for some reason rather than 120
marsh rapids
j² = j² (duh)
(j²)² = j j^3 = j
olive sundial
yep
marsh rapids
so it's stable
and we showed no other element can be in R
so wlog, P(z) = (z-j)^n (z-j²)^m
marsh rapids
why ?
marsh rapids
now
olive sundial
wait but still
marsh rapids
we can actually look at P(x²) = P(x)P(x-1), because P is simple enough
olive sundial
alright
yeah i think that works
for any degree does it not?
cause like they both will have m+n for each root degree
marsh rapids
I saw a solution to this 2 years ago, I think n=m somehow
olive sundial
I saw a solution to this 2 years ago, I think n=m somehow
did u do competition math
olive sundial
wtf
lol ok
yeah n = m cause its rational
like p(1)
cause otherwise how can it be rational
marsh rapids
yeah n = m cause its rational
convenient
marsh rapids
in my 1st year of undergrad
except there was no P0(1) | 2016
it was just find all P such that
olive sundial
oh
dont see a difference cause u
anyways get
(x^2 - 1)^m
no nvm
so
(x^2 + x + 1)^m
oh so
just evaluate for highest m
marsh rapids
easy
olive sundial
yep its right
marsh rapids
,w factor 2016
olive sundial
maximum
ocean sealBOT
olive sundial
dehree
marsh rapids
ok
honest gull
I'm curious as to a more elegant way of writing out a formula for this. Mostly asking about pure math.
I'm not asking for any practical purpose. I needed to do something like this in game development, where I can just use if statements, and there's no issues regarding breaking it up like shown in the image. Just curious regarding pure math, and if these three lines shown in my image can be combined into one single formula.
twin nimbus
you can probably do it using abs
tidal lichen
Have you heard of a piecewise function
twin nimbus
Yes, you can also use a piecewise function, but he's already doing that.
tidal lichen
Ok yea just checking
honest gull
you can probably do it using abs
wouldn't this just make the values less than 4 and greater than 8 go upward? Where would I put an absolute value?
tidal lichen
Sorry
honest gull
I assume not just around the whole formula then
foggy oxide
i assume yes
twin nimbus
@honest gull the idea is to use separate terms with abs that cancel each other out under certain circumstances
honest gull
ah ok, in theory I understand, I just need to think about that
twin nimbus
so it's easiest to build up functions. Like, let's make the ramp function out of abs. The ramp function is 0 for x < 0 and x for x > 0
we can do x/2 + x/2 to make x when x is positive and x/2 - x/2 to make 0 when x is negative
so we can so x/2 + abs(x/2)
honest gull
@twin nimbus I got this before reading your thing, hold on i still need to read what you said
honest gull
haha im seeing that now, thank you! Can this be simplified any further, or is this about as clean as it gets without using piecewise functions?
twin nimbus
You can factor a 1/2 out of both terms
And notationally, you can assign the inside of the abs to a function to reuse it, like f(x) = 1 - sqrt((x-6)^2)/2, y = 1/2 (|f(x)| + f(x))
honest gull
ah I see, that's nice and elegant.
twin nimbus
one other thing you can think about doing is using abs internally to do an x-reflection
I think that's possible
honest gull
That's something I don't know about
honest gull
Could you explain that? I don't know anything about reflections as functions
twin nimbus
same thing
twin nimbus
in fact, if you don't want to use abs, and prefer to use only sqrt of squares, then the identity |x| = sqrt(x^2) should be useful
honest gull
ok I'll be honest, it's not computing in my brain how that worked out
like how the sqrt of a square is removed and it's still giving that shape
twin nimbus
because |x| = sqrt(x^2)
honest gull
oh yeah, sorry my brain is lagging a little
ok yes i see now
I'm guessing without further context, it makes no difference whether I use abs or sqrt(x^2)
twin nimbus
yup
honest gull
ok thank you this was useful. I wanted to do this same thing but with another formula, and I don't think I can just plug in the exact same concept without any alterations
Basically, a bell curve that actually goes to zero and stays at zero. Let me plot it out
twin nimbus
Sorry
No need to be sorry. I wasn't snapping at your or anything. Just figured based on the way that the OP was talking that they already knew about piecewise functions. Thanks for trying to help, earnestly 🙂
honest gull
@twin nimbus The cosine is definitely messier than it needs to be, but just to give you an idea:
and then y=0 on either end
cancelling it out with abs won't work because cosine doesn't work like that
and the formula for a bell curve doesn't actually reach 0
twin nimbus
ah, so this time it's cosine, so because it's periodic it's not going to stay negative.
yeah
well, you can do something like a bell curve except it's dragged down by like 0.1 or 0.01
honest gull
But that's no fun :) I want it to actually reach zero and stay at zero
twin nimbus
as in
then you can apply the 1/2 (|f| + f) trick in that case
because it goes and stays negative.
one other thing you can do is use a beta distribution function
honest gull
I see what you mean, that does work for a practical purpose. But if theoretically I want the S curve to perfectly go down to zero with a flat tangent line (don't know the technical terms for what I'm trying to say), that wouldn't work because it would ever so slightly snap at an angle
honest gull
one other thing you can do is use a beta distribution function
I don't know about this concept, let me look it up
twin nimbus
I chose alpha = beta = 3 to give a moderately sharp curve, higher values give sharper curves
honest gull
well that is what I'm looking for, now to understand it.
And if I want the apex to be one, I'm guessing I need to add a pi somewhere in there, like with the normal distribution graph
honest gull
oh interesting, that makes sense
how would the graph be shifted to the right? Like in the other functions, I'd replace x with (x-6) to shift it to the right by 6 units along the x axis, but I'm not figuring out how that would fit in here
honest gull
right that makes sense
twin nimbus
you can also motify the xs in the f(x) function of course
honest gull
Oh yeah that worked, I thought I tried that and it was funky, but I must have mistyped something
Well that answers all of my questions! I'll probably just read more about beta distributions and get a better understanding of them, but I have no specific questions about it. Thanks!
.close
lone heartBOT
twin nimbus
you're welcome!
lone heartBOT
Available help channel!
tardy bison
Hi, I am stuck on a division, I know it sounds stupid but I didn't do any division by hand for I guess 6 years (I'm 18). The division is 311493/3 and I always find 13831 but it's 103831 while checking on the calculator and I can't figure out why
gray isle
show work
deep moon
You start out with 3
tardy bison
Yeah ?
deep moon
Why do you bring them down in pairs?
tardy bison
Because 1 is less than 3
deep moon
My bad
tardy bison
So I take 11
tardy bison
Yeah
tardy bison
Hm
tardy bison
Yeah
deep moon
Now you're allowed to bring down an extra digit only on the first time
Does that make any sense?
Holdon
tardy bison
Yeah so if i have a small number I put a zero right ?
tardy bison
Lemme think a bit because that's not how I write it in my country (France)
Lemme understand it
tardy bison
Lmao yeah but in any case that's not how I write things
deep moon
Notice how I brought both the numbers down on the second case?
That's allowed only on the first time
Another example should help
tardy bison
Maybe yes
tardy bison
It says 909/3 right ?
(not saying you write horribly just I don't know this way of writing division)
deep moon
2727/3=909
fallow siren
ends in 2
deep moon
You bring the first 3 down, okay fine you get 1
deep moon
1 is less than 3, so you bring the next digit , but you have put a 0
tardy bison
toa how do you vizualize numbers?
Wdym ?
fallow siren
when you see 9/3 what do you see?
tardy bison
Write or think ?
fallow siren
picture
deep moon
When you divide say 31124/3
Try
tardy bison
Try
I have a question first, why didn't you put a zero at the end then because you took 27 two times. But wrote 90 then only 9
deep moon
First I got 9 no problem?
fallow siren
why dint you extend it to the product of multiplication using this model?
tardy bison
First I got 9 no problem?
You said you add a zero because you took 27 not 2 so I understand but after that you take 27 again but don't put a zero
tardy bison
why dint you extend it to the product of multiplication using this model?
I did but there are zeros missing and I don't know when I am supposed to put them
deep moon
First I got 9 no problem?
Then I dropped the next digit, 2 which is less than 3, now I'm forced to drop the next digit. I put a 0 then I proceed. So now I dropped the next digit, I got 27 which is greater than 3. 9×3 = 27 therefore 9 joins the answer
tardy bison
Okay I think I kinda see where I failed
But I think I have a counter exemple
Lemme go check
deep moon
Yessir
tardy bison
Ok on this one I know I am wrong
But I added a zero because I took 24 and not 2
But I shouldn't have because when I dropped the 2, I will not use that column a second time
(that's the worst way I could've explain that)
I said 2*3 is 6 so 8-6=2 and than I go on column on the right so the 4 but because there is a 2 before it's 24. And in this case I don't add a zero
Am I right ? Or am I gonna go crazy
deep moon
You have divided it already
You need not add a 0 for that
2 is just left over
Now divide 24
Then proceed
tardy bison
So basically for each number I have a result
Don't know the exact terms
But 100 has 3, 1000 has 4 etc
And so my result also does
If I divide 6729 (which contains 4 numbers) my result has 4 numbers too even if the first is 0
deep moon
You're dividing what by what?
tardy bison
On the picture above ? 846720/3
ocean whale
If you are having trouble, here's a video https://www.youtube.com/watch?v=GiiuZ8sfw00&ab_channel=TheOrganicChemistryTutor
tardy bison
Thanks, I'll watch it tomorrow it's 3:00 am rn
lone heartBOT
@tardy bison Has your question been resolved?
deep moon
Organic chemistry tutor is the goat
atomic bobcat
#38
atomic bobcat
Find k's time for distance in terms of x 😭 how tf am I supposed to know whether its a trick question or not bruh
crystal berry
That's really long but I love your handwriting.
crystal berry
Show if you want to ask questions about the solution
Oh hello my twin.
summer dirge
can a linear transformation have a finite number of eigenvectors?
lone heartBOT
can a linear transformation have a finite number of eigenvectors?
@summer dirge Has your question been resolved?
foggy oxide
!15mins
lone heartBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
summer dirge
.close
warped topaz
lone heartBOT
tacit arch
Or is 2 not a solution
Why would you think 2 is a solution
eager summit
can anyone help with this question?
lone heartBOT
can anyone help with this question?
lone heartBOT
@eager summit Has your question been resolved?
mellow grail
!status
lone heartBOT
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
@eager summit Has your question been resolved?
whole otter
Hi
whole otter
What is the integral of x^2cosx sin^2x
I had an integral calculator do it for me
And it gave me a completely different looking answer
And I went over my process multiple times
And I didn’t see any error
storm ridge
$\int x^2 cosx sin^2 x dx$
ocean sealBOT
Lorentz
storm ridge
This eh?
whole otter
Yes
storm ridge
I see
storm ridge
I see
whole otter
So can I just tell you what I did
storm ridge
Sure
storm ridge
Right...
whole otter
Then I did integration by parts
I chose u for (arcsin u) squared
And dv for u^2
Then I got u^3(arcsin u)^2/3 - 2/3 integral(u^3 arcsinu / sqrt(1 - u^2)
I did trig sub
u = sin theta
And I got theta * sin ^3 theta
Integratuib by parts
Wait a sec
Oh I saw my mistake
storm ridge
Then I got u^3(arcsin u)^2/3 - 2/3 integral(u^3 arcsinu / sqrt(1 - u^2)
Where did the 2/3 come from?
Or is 2 in the exponent?
whole otter
Where did the 2/3 come from?
Or is 2 in the exponent?
So if you do the work
You get v being u^3/3
And du being 2arcsin u / sqrt(1-u^2)
So I pulled out the 2/3
Cuz it’s a constant
storm ridge
You get v being u^3/3
Wait x² becomes x³/3 right?
storm ridge
Oh ok
whole otter
Cuz of u sub
whole otter
I just saw my mistake lol
storm ridge
Lol
whole otter
I did integration by parts
But the thing I was supposed to turn dv to v
I integrated it and forgot it was supposed to be integrated again cuz
Yonow integration by parts just like that
storm ridge
Yes
whole otter
Ty for helping though
storm ridge
Cya
hollow jetty
Hi! So I posted this to math stack exchange couple weeks ago (see attatched image), but it got closed due to "the website is not a proof verification site". I can re-edit it to make it more focused on a question, but I believe someone here can just verify the proof out of the kindness of their heart 😁 . BTW, the product $ST$ of linear maps $S$ and $T$ is just the composition $S \circ T$.
ocean sealBOT
pash
lone heartBOT
@hollow jetty Has your question been resolved?
golden canyon
I dont think TE(v) = T(v) implies TE = T
hollow jetty
I dont think TE(v) = T(v) implies TE = T
Yep...that was my concern. But they have the same domain, codomain, and for every $v$, they have the same output. So wouldn't that make them equal?
ocean sealBOT
pash
golden canyon
Is your definition of T supposed to hold for all a_i?
smoky zephyr
hi
hollow jetty
It should because I defined it on the basis of $V$, which means $T$ is uniquely defined for every $v \in V$.
ocean sealBOT
pash
golden canyon
but since T is linear, it can't be true that T(v) = v1 for all v, right?
because T is non-zero as well
hollow jetty
but since T is linear, it can't be true that T(v) = v1 for all v, right?
OH RIGHT. Thank you, so my definition of $T$ is garbage. I'll fix this tomorrow. Thanks again
.close
lone heartBOT
ocean sealBOT
pash
lone heartBOT
Available help channel!
outer grotto
lone heartBOT
outer grotto
Help me with number 8
I did not really understand
What is “the minimum value”, please can you give an example?
nimble fern
like for just x²-6x+13
there is a minimum value for it
which you can find it by completing square
and for a>1, the larger the exponent is, the larger the "value" is
which in this case "the value" means the value of f(x)
lone heartBOT
@outer grotto Has your question been resolved?
upbeat eagle
lone heartBOT
upbeat eagle
Part A,
Is it wrong to start with v=u +at
5= 3 + at
8=4 + a(t-1)
And since acc = constant just sub in 1
So
2= t
4= t-1
languid bolt
Constant acceleration ≠ 1 though…
languid bolt
Bc it has the same acceleration
Why?
The question didn’t say that…
The time is the thing that is the same….
upbeat eagle
I thought you can assume they are accelerating at the same speed
languid bolt
Since they arrived at the same time… (edit misresd the ques)
upbeat eagle
Ah ok
upbeat eagle
Yeah hmmm
languid bolt
And t for particle one
languid bolt
What is U here?
upbeat eagle
initial veloicity
But then I dont know how to rearange to make t
t/2 4/(t-1)
and I dont think you can put them equal?
languid bolt
I think you can just use the distance formula, since they hve the same distance
languid bolt
Just… do substitution
languid bolt
Okayy
cinder breach
hi guys how do you solve this using notable limits?
lone heartBOT
hi guys how do you solve this using notable limits?
cinder breach
i know that lim x--> +inf (1 + 1/x)^x = e
golden canyon
remember that a * ln(b) = ln(a ^ b)
thorn monolith
A shorter alternative is by knowing the following limit
$$\lim_{x \to 0} \frac{ \ln { \left ( 1 +x \right) }{x}$$
golden canyon
$$\lim_{x \to 0} \frac{ \ln { \left ( 1 +x \right) }}{x}$$
ocean sealBOT
Jelle
cinder breach
I copied your message
but that is for x-->0, not for x-->+inf ?
golden canyon
whoops I meant a * ln(b) = ln(b ^ a)
golden canyon
but that is for x-->0, not for x-->+inf ?
yes but as x tends to infinity 1/x^2 goes to 0
cinder breach
i'm so confused
thorn monolith
Do the sub 1/x² = u then you will see
thorn monolith
for x--->+inf you get 0
You mean u approaches 0?
cinder breach
yes
thorn monolith
u doesnt only approach 0, it approaches 0 from the right side
cinder breach
Then you apply this limit
sorry if i am slow but can you show it step by step please
cinder breach
**Jelle**
i get that this is 1/x^2
but that's if x approached 0
i dont understand how we can just change lim x--> +inf to lim x-->0
i solved it the other way
thorn monolith
$\frac{1}{x^2} = u$
\$ \implies u \to 0^+$
$$ \frac{1}{3} \lim_{x \to \infty} \frac{ \ln ( 1 + \frac{1}{x^2} ) }{ \frac{1}{x^2}} =
\frac{1}{3} \lim_{u \to 0^+} \frac{ \ln (1+u) }{u}$$
opal jolt
i solved it the other way
arent you missing a parenthesis there? it should be:
$ln[(1+\frac{1}{x^2})^{x^2}]$
thorn monolith
@cinder breach
lone heartBOT
@cinder breach Has your question been resolved?
cinder breach
arent you missing a parenthesis there? it should be:
$ln[(1+\frac{1}{x^2})^{x^2}...
Yea
plucky phoenix
wow
iron river
So i have this exercise could someone explain it to me?
To prove that there are no non-zero integers a and b such that a^2=2b^2, use the fundamental theorem of arithmetic regarding the unique prime factorization of a number into prime factors.
lone heartBOT
So i have this exercise could someone explain it to me?
To prove that there are ...
@iron river Has your question been resolved?
mortal trellis
iron river
Like how many times i see 2? I have the 2 outside the seocnd parenthesis so when i put it inside it gives me 2^2 times bk
i am still very new to this so i dont know much about the theory it;s hard to understand
like i have gotten to this point
but have no clue how t compare them
lone heartBOT
@iron river Has your question been resolved?
lone heartBOT
@iron river Has your question been resolved?
lone heartBOT
@iron river Has your question been resolved?
raven night
@iron river i'm confused
are you forced to use the fundemental theorem of arithmetic?
Cause otherwise you can just prove it using the irrationality of sqrt(2)
frail grove
$\int_{a}^{b} |f(t)| \dd t$ converge $\implies \int_{a}^{b} f(t) \dd t$ converge
ocean sealBOT
Adam Chebil
frail grove
why ?
unkempt mica
for the riemann integral or the lebesgue integral?
but in general if $f \leq g$ then $\int f \leq \int g$
ocean sealBOT
LF
frail grove
for the riemann integral or the lebesgue integral?
f can be any single variable function (not necessarily continuous)
frail grove
how is that relevant to the question ?
unkempt mica
$-|f| \leq f \leq |f|$
ocean sealBOT
LF
ebon torrent
lone heartBOT
feral hemlock
okay
ebon torrent
so can I just do this
feral hemlock
yes, but no
ebon torrent
how otherwise do I find x
feral hemlock
kepe master of Latex is here
thick lynx
so can I just do this
More formally, that's multiplying by (x^2 - 4)^2
ebon torrent
but what if I look it as this
thick lynx
And you can only do that when $(x^2 - 4)^2 \neq 0$, namely $x \neq \pm 2$. So just say [\frac{-50x}{(x^2 - 4)^2} = 0] [\iff -50x = 0 \qquad (\text{for }x \neq \pm 2).]
ebon torrent
multiplying diagonally
feral hemlock
multiplying diagonally
nah
thick lynx
feral hemlock
multiplying diagonally
it won't work if it's zero
ebon torrent
then what is the solution?
feral hemlock
solve -50x=0
ebon torrent
isn't just x=o?
feral hemlock
yes
ebon torrent
but what if I look it as this
then this worked
thick lynx
then this worked
Yes, but see my last part
feral hemlock
then this worked
Only in this particular situation:(
thick lynx
You need to check if it really lies in the domain of your expression
thick lynx
but what if I look it as this
Take $\frac{x - 2}{x^2 - 4} = 0$ now.
ebon torrent
so only if x is not equal to 0 in the denominator it will work
thick lynx
ebon torrent
so this has no solution
ebon torrent
yea I'm a bit confused with algebra still I haven't practiced it enough for it all make sense to me
thick lynx
thick lynx
yea I'm a bit confused with algebra still I haven't practiced it enough for it a...
Especially for 4. there you have to pay some attention
ebon torrent
4 is ok?
thick lynx
What do you mean?
thick lynx
you can have 0 in a square root but not in the denominator
Yes, but there is a different problem you have for number 4.
ebon torrent
2 has a solution
ebon torrent
i dont know what the trick is to finding which ones are fine quick
1 doesnt have a solution because its a negative number inside a square root in the numerator
thick lynx
1 doesnt have a solution because its a negative number inside a square root in t...
Actually, it does have a solution
ebon torrent
and 3 should be fine
oh 1 has one solution and another option which can't be a solution
thick lynx
$\frac{\sqrt{x^2 - 5}}{x + 1} = 0$. First, check when $\sqrt{x^2 - 5} = 0$.
ebon torrent
I dunno I'm just using my head .. but I dont know a good method
feral hemlock
I dunno I'm just using my head .. but I dont know a good method
just to know
Maybe you will understand better...
thick lynx
ebon torrent
thanks
cloud kiln
Ok so
cloud kiln
How did he replace cosx with e^ix, shouldn't it be e^(ix) - isinx
this is diff equation btw
in case you're wondering what D is
can anyone clear up how he ignored isinx
tacit arch
How did he replace cosx with e^ix, shouldn't it be e^(ix) - isinx
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