The answer seems to be 39 when I look it up tho
#help-42
solid marten
The answer seems to be 39 when I look it up tho
yeah i feel the same way. I dont think we have enough information to be sure.
scarlet magnet
yeah i feel the same way. I dont think we have enough information to be sure.
I think we do..... not too sure tho
Can I ask smth tho
solid marten
yeah
calm coralBOT
@solid marten Has your question been resolved?
solid marten
nah im 21 in an access course bro but i covered a level pure on my own a while ago
I just have some areas where i lack and some where i dont 😂 i didnt like maths before i was 19 and i left school at 16 so
scarlet magnet
nah im 21 in an access course bro but i covered a level pure on my own a while a...
ohh alr
doing my AS rn lol
solid marten
ah i never covered stats or mechanics just worked my way through pure year 1 and 2. Bicen maths was great. looking back after starting stewarts calc though I can say the edexcel a level maths textbooks (and most other a level maths textbooks) are horribly written
scarlet magnet
ah i never covered stats or mechanics just worked my way through pure year 1 and...
yea i agree, the a level books are rlly confusing
even on easy topics
solid marten
yeah 100%,
people accuse stewart of excessive handwaving, but all a level maths textbook authors are worse, they make stewart look like a king 😭
scarlet magnet
yeah 100%,
people accuse stewart of excessive handwaving, but all a level maths ...
lmao fr
calm coralBOT
@solid marten Has your question been resolved?
fading grotto
ok broo so basically we gotta find the gap between the middle of these two circles. it looks a bit extra but it's actually just some clean trig.
large circle: diameter is 30m, so the radius is 15m.small circle: diameter is 18m, so the radius is 9m.the angle from that point on the small circle to the big one is 60°.
imagine drawing a line from the center of the big circle to the point where the tangent hits it. that creates a right-angled triangle.since the whole angle is 60°, we split it in half to get 30° for our triangle.we use sine because we have the opposite side (the radius) and we want the hypotenuse (the distance from the center of the big circle to that point on the small circle)
alpine cobalt
i think maybe its better if you draw it
fading grotto
alr
$$\sin(30^\circ) = \frac{\text{opposite}}{\text{hypotenuse}}$$$$\frac{1}{2} = \frac{15}{d_1}$$$$d_1 = 30\text{ metres}$$
potent lotusBOT
Innocent Zero
solid marten
so its this one? @fading grotto
fading grotto
fading grotto
so its this one? <@1225769778338070562>
ye that one is correct
so, the distance from the center of the large circle to that point on the small circle is 30m.
now, that point is on the edge of the small circle. to get to the center of the small circle, we just need to add its radius
($r = 9\text{m}$).$$\text{total distance} = 30 + 9 = 39\text{ metres}$$
potent lotusBOT
Innocent Zero
solid marten
ahh yeah thanks man. Hate circles. cheers bro
alpine cobalt
i believe this is a better picture
fading grotto
ahh yeah thanks man. Hate circles. cheers bro
this is basic circle question
solid marten
cheers guys for telling me these questions are basic and im stupid? 😂 😂 😂 get fucked? not much need to be rude really fellas
.close
calm coralBOT
fading grotto
cheers guys for telling me these questions are basic and im stupid? 😂 😂 😂 ge...
well i am not tellin u are stupid
solid marten
well i am not tellin u are stupid
what need was there to tell me it was a "basic" question mate.
fading grotto
what need was there to tell me it was a "basic" question mate.
well i just like was confused with the long debate on this problem
solid marten
if you scroll up its like really obvious
spice venture
Alr guys don't fight the channel is closing
fading grotto
what need was there to tell me it was a "basic" question mate.
btw just remember this rule for circle radius and tangent are perpendicular thats a theorm
solid marten
btw just remember this rule for circle radius and tangent are perpendicular that...
okay ill forgive you for what i percieved as rudeness ngl i was looking for a statement like this
that clears up the confusion
cheers bro much love
fading grotto
okay ill forgive you for what i percieved as rudeness ngl i was looking for a st...
well sorry if it sounded rude lmao
alpine cobalt
it is a basic question tho
solid marten
nah its chill bro no stress ♥️
solid marten
it is a basic question tho
mate give it a rest now seriously
alpine cobalt
not like im saying you're stupid
fading grotto
it is a basic question tho
well, everyone has their weaknesses in maths
alpine cobalt
i hate geometry but its still a basic one
solid marten
not like im saying you're stupid
yeah idc its insulting and youre fucking me off because thats how youve come off and ive already stated this
solid marten
i hate geometry but its still a basic one
telling me serves no purpose other than to make yourself seem better than the people youre helping
fading grotto
well u understood now ryt?
solid marten
i never acted like it was an extremely high level question lol
solid marten
btw just remember this rule for circle radius and tangent are perpendicular that...
yeah cos this
alpine cobalt
okok guys, chill, im sorry too if i insulted
solid marten
thats why i had two different methods with two answers because i didnt understand this in a way not intuitively
okay we are all chill then
thank you all
been a pleasure lads may we meet again under better circumstances lol
fading grotto
thats why i had two different methods with two answers because i didnt understan...
i understood that cause i was confused at how 60 came when radius and tangent meant
that's why u didnt get the ans
alpine cobalt
been a pleasure lads may we meet again under better circumstances lol
xD
fading grotto
thats why i had two different methods with two answers because i didnt understan...
alr peace off i have to do trignometry or else am cooked
solid marten
alr peace off i have to do trignometry or else am cooked
love bro have fun
alpine cobalt
alr peace off i have to do trignometry or else am cooked
need help?
fading grotto
need help?
well not now so far all correct
calm coralBOT
Available help channel!
drowsy spruce
hello
drowsy spruce
quick matrix question
i have the solution that my teacher gave me
from the a we know that A^3 = -I
but i dont know why did she do all these unnesesary ways and have it worth the grade
cant i just
A^2025 = (A^3)^675 = (-I)^675 = -I
glass heart
yes seems weird to give extra points for computing A^4 and A^5
drowsy spruce
hmm
drowsy spruce
A^2025 = (A^3)^675 = (-I)^675 = -I
but i can freerly do that right?
no like strange things about (-I)^n?
glass heart
yes that works
drowsy spruce
ok thx, since i didnt see the grade but i remember not doing A^4,5,6 and going straight
will see tmorrow
thx man
.close
calm coralBOT
calm coralBOT
Available help channel!
frozen mantle
help
frozen mantle
@icy skiff
leaden thunder
close your other channel 
potent lotusBOT
Ezra
leaden thunder
alright i closed it
icy skiff
period $$3\Rightarrow \omega=\frac{2\pi}{3}$$
potent lotusBOT
Ezra
icy skiff
highest point at $$t=0\Rightarrow (0,2)$$
potent lotusBOT
Ezra
icy skiff
ok?
icy skiff
yes and yes
sullen grove
$$how do i use texit$$
potent lotusBOT
Voltic Slick
icy skiff
and yes
icy skiff
ok
frozen mantle
with this info
icy skiff
think of it this way
sullen grove
i get everything except 2pi/3
0.66~pi?
sullen grove
https://tenor.com/view/ilgbtenha-stantwt-stan-twt-dude-nobody-invited-funny-gif-...
yo im just tryina procrastinate ok?
icy skiff
think of it this way
think of the angle as what fraction of a full turn you’ve completed
sullen grove
dont judge 😔
icy skiff
a full turn is $$2\pi$$ radians
you finish that full turn in 3 seconds
potent lotusBOT
Ezra
icy skiff
so after t seconds, the angle must be
$$\theta(t)=\frac{2\pi}{3},t$$
potent lotusBOT
Ezra
icy skiff
literally all the $$2\pi/3$$ is
potent lotusBOT
Ezra
icy skiff
radians per second so the motion closes after 3 seconds
frozen mantle
bruh
sullen grove
hehehehe
frozen mantle
am i dumb
icy skiff
no
sullen grove
no?
frozen mantle
for still being confused
icy skiff
not dumb
frozen mantle
i know 2pi/3 formula
sullen grove
for still being confused
i lied i dont understand it either
sullen grove
yo lowkey stop typing
lowkey ts is a public server so i can type all i want 
icy skiff
lowkey ts is a public server so i can type all i want <:catblush:563818370550595...
highkey zip it
you’re disturbing
sullen grove
highkey zip it
highkey im offended
icy skiff
highkey keep it in
sullen grove
highkey i dont get the joke
icy skiff
but why we using omega here
weuse $$\omega$$ here for one reason only
potent lotusBOT
Ezra
icy skiff
to make sure the motion repeats after 3 seconds
ok?
sine and cosine repeat every $$ 2\pi$$
potent lotusBOT
Ezra
frozen mantle
oh so for repetitive motion
icy skiff
so whatever is inside $$ \sin(,\cdot,) and \cos(,\cdot,)$$ must increase by $$2\pi$$ in 3 seconds
potent lotusBOT
Ezra
icy skiff
that forces
$$(\text{inside}) = \frac{2\pi}{3}t$$
potent lotusBOT
Ezra
frozen mantle
yeah that makes sm sense
icy skiff
calling $$\frac{2\pi}{3}$$ $$ “\omega”$$ is just shorthand
potent lotusBOT
Ezra
icy skiff
ellipse centered at origin with intercepts $$(\pm5,0),(0,\pm2)$$
potent lotusBOT
Ezra
icy skiff
now build the parametric equations
icy skiff
swap
frozen mantle
what
icy skiff
use sine/cosine, and start at the top
start at the top
(0,2)
at t = 0
your answer would start at (5,0)
mb im typing with one hand
frozen mantle
i dont get 🙁
potent lotusBOT
Ezra
icy skiff
ok?
frozen mantle
yes
frozen mantle
wait
potent lotusBOT
Ezra
icy skiff
so plug t = 0 into what you write
icy skiff
so
$$x(0) = 0$$ means x uses sine
$$y(0) = 2$$ means y uses cosine with coefficient 2
potent lotusBOT
Ezra
frozen mantle
the ellipse
icy skiff
wont it start at like x axis though
no because check $$t = 0$$
potent lotusBOT
Ezra
icy skiff
the ellipse crosses the x axis at $$(5,0)$$ and $$(-5,0)$$ but the particle is not starting there
potent lotusBOT
Ezra
icy skiff
it starts at the highest point so at $$t=0$$ it is at $$(0,2)$$
potent lotusBOT
Ezra
icy skiff
sin(0) = 0 so how is it 2
because y does not use sin
we have
$$y(t)=2\cos!\left(\tfrac{2\pi}{3}t\right)$$
potent lotusBOT
Ezra
icy skiff
so at $$t=0$$
$$y(0)=2\cos 0=2$$
sin being zero only affects x
not y
potent lotusBOT
Ezra
frozen mantle
wait the question asks us to assume the ellipse starts at
0,2
but
i am unable to understand the logic behind this assumption
icy skiff
easy
its not deep
the ellipse itself does not start anywhere
only the particle has a starting position
the phrase assume that at $$t=0$$ the particle is at the highest point is not a consequence
it is an initial condition they give you
potent lotusBOT
Ezra
icy skiff
it is like saying
assume $$x(0)=0$$ and $$y(0)=2$$
potent lotusBOT
Ezra
icy skiff
once that is imposed
you choose sine and cosine to satisfy it
since
$$\sin 0 = 0$$
$$\cos 0 = 1$$
potent lotusBOT
Ezra
icy skiff
the only way to hit $$(0,2)$$ at $$t=0$$ is
potent lotusBOT
Ezra
icy skiff
$$x(t)=5\sin(\cdot)$$
$$y(t)=2\cos(\cdot)$$
potent lotusBOT
Ezra
frozen mantle
yes because x corresponds to a and y corresponds to b as this is a horizontal ellipse
frozen mantle
whats next
icy skiff
b
frozen mantle
b?
icy skiff
so we did a
icy skiff
we did
parametric just means x and y are written in terms of t
$$x(t)=5\sin!\left(\frac{2\pi}{3}t\right)$$
$$y(t)=2\cos!\left(\frac{2\pi}{3}t\right)$$
potent lotusBOT
Ezra
icy skiff
here boss
icy skiff
because of the starting point condition
icy skiff
because of the starting point condition
at $$t=0$$ the particle must be at the top $$(0,2)$$
now check the trig values at $$t=0$$
$$\sin 0 = 0$$
$$\cos 0 = 1$$
potent lotusBOT
Ezra
frozen mantle
i m annoying u alot
icy skiff
i m so sorry ezra
it’s okay don’t be sorry
icy skiff
i m annoying u alot
no I am happy to help
frozen mantle
oh so we need 2cos(0) = 2
icy skiff
**Ezra**
so:
if x uses sin, then $$x(0)=5\sin 0=0$$
if y uses cos, then $$y(0)=2\cos 0=2$$
potent lotusBOT
Ezra
icy skiff
yeah so sin for x and cos for y is forced by where the motion starts, nothing else
there’s no deep theorem in this lowkey
just trash teachers that force you to hit your head on the wall
until you can see a system
anyway what the hell is this math
frozen mantle
so x = rcostheta and y = rsintheta is wrongly taught?
icy skiff
not wrong
frozen mantle
just forced
icy skiff
it’s misleading lowkey
frozen mantle
part b wth is part b
icy skiff
$$x=r\cos\theta,\ y=r\sin\theta$$ is polar coordinates
that assumes
potent lotusBOT
Ezra
icy skiff
a circle
an angle measured from the positive x axis
starting at the rightmost point
not your problem
icy skiff
its so weird
try something
say something and we go from there
or what you find weird
frozen mantle
wait
ellipse moves straight up at a rate of 4 units per second. up so dy/dt = 4
in a second
icy skiff
frozen mantle
center starts at origin meaning (0,0)
so both sin and cos need to be 0
what the hell
frozen mantle
"assume it starts at origin"
icy skiff
yess
icy skiff
yes
icy skiff
i wanna lowkey cry
no crying
graceful dust
i wanna lowkey cry
icy skiff
so what do we do
the motion around the center is the same as part a
ok?
the center itself moves up at 4 units per second
frozen mantle
yes yes
frozen mantle
isnt the wording weirrd
icy skiff
yeah
they mix particle motion and center motion in one sentence
what they mean is
the center of the ellipse moves upward at 4 units per second
& the particle keeps moving on the ellipse relative to the center
are you able to separate these mentally
frozen mantle
so we add 4 to our y(t)
icy skiff
4t
not 4
since center moves up at 4 units per second, its vertical position after time t is 4t
frozen mantle
oh at t seconds
so our x stays same but we add +4t to y
and give two parametric eq like part a
frozen mantle
hopefully
frozen mantle
i hated calculus
icy skiff
i’m a doctor
frozen mantle
omg
icy skiff
i do no math
icy skiff
literally md
frozen mantle
in maths
icy skiff
lmao
graceful dust
what kind of doctor?
frozen mantle
do u miss undergrad
frozen mantle
did u grind in ug
frozen mantle
u r smart
frozen mantle
no lol i m the dumbest in my class
icy skiff
yo fuck your class
i’ll nuke them all
you the smartest
so we are done with b
$$x(t)=5\sin!\left(\frac{2\pi}{3}t\right)$$
$$y(t)=2\cos!\left(\frac{2\pi}{3}t\right)+4t$$
potent lotusBOT
Ezra
icy skiff
gemini said its -ve sin though
that would just flip
gemini tripping
not tripping rly
icy skiff
ezra my goat
said the goat himself
calm coralBOT
@frozen mantle Has your question been resolved?
frozen mantle
@icy skiff do you think its worth it learning the x and y intercept formulas cant i just put x = 0 or y = 0
frozen mantle
also isnt the x and y intercept like a and b
why this long complicated formula for that
icy skiff
also isnt the x and y intercept like a and b
yeah only sometimes
frozen mantle
like when origin is center
but what about when origin is not the center
we can just lowkey plug in x =0 and y = 0
to check intercepts right
icy skiff
but what about when origin is not the center
then you can’t use ±a or ±b at all
calm coralBOT
@frozen mantle Has your question been resolved?
solar jackal
Hello can someone help me answer number 2... I get what sohcahtoa is but I don't really get what the question is asking
thorny stump
Did you draw CP? Can you show?
solar jackal
like this?
thorny stump
Cool, so now you just need to express the length of CP in terms of the length of AC and the angle BAC
calm coralBOT
@solar jackal Has your question been resolved?
solar jackal
Cool, so now you just need to express the length of CP in terms of the length of...
I don’t get it, english is not my first language
🥲
thorny stump
Express the purple length (h) using the green length (b) and the green angle (A)
remote mural
Show that no group of order 108 is a simple
calm coralBOT
Show that no group of order 108 is a simple
remote mural
I have calculated that the N3 being the number of sylow 3 SUBGROUP is either 1 or 4
I don't know how to go ahead after thais
This
quasi tundra
Fist resolve N3=1
quasi tundra
Create a homomorphism and compare it with G
remote mural
How
quasi tundra
Just define something like this $\phi: G \to S_4$
potent lotusBOT
Ajay
remote mural
How will that help with proving that g is not simple
quasi tundra
You're letting G act on the set of 4 sylow subgroups by conjugation
remote mural
Ohh it's not symmetric group
quasi tundra
How will that help with proving that g is not simple
The idea is to show that when comparing the orders, we show that the map cannot be injective and hence a non-trivial kernel must exist.
quasi tundra
Ohh it's not symmetric group
Actually it is a symmetric group
remote mural
Ok i will try it
quasi tundra
We're trying to show that because we can't map G into S_4 injectively, the group cannot be simple.. Because if G were simple we could map all the elements to S_4 (i.e. the map would be injective) and the group would be normal.
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
olive folio
guys
pallid halo
calm coralBOT
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
elder pawn
@olive folio do u need math help? pls post ur problem, show what u tried and where ur stuck
velvet osprey
stuck on which one of these?
sleek vessel
velvet osprey
@olive folio are you able to do #4?
elder pawn
@olive folio pls answer these questions or it will be hard for ppl to help u: which problem do u need help on? what did u try? where r u stuck?
calm coralBOT
@olive folio Has your question been resolved?
olive folio
sry im back
calm coralBOT
sry im back
olive folio
had to do homework
velvet osprey
olive folio
im stuck on all but 7
velvet osprey
i mean how can i explain this
do you know how percentages work generally?
specifically as regards the first blank in the orange box:
if we remove 13% of something, what percentage will be left?
@olive folio ?
i guess he's off to do homework again
calm coralBOT
@olive folio Has your question been resolved?
olive folio
i guess he's off to do homework again
you're right abt that
calm coralBOT
you're right abt that
olive folio
btw the way, i js finished the problem
velvet osprey
when you come here you should expect not to disappear for 20+ min at a time to do homework or whatever
if you think you will get interrupted a lot then open a forum thread instead
olive folio
ok sry abt that
velvet osprey
do you have any more questions you need help with rn?
calm coralBOT
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Available help channel!
golden prairie
if i got 3 w's how can i solve the same equation ? will it be, w.x+w.x+w.x+b ? / i learned the equation from the other photo but i only know how to solve it if its 1 w. help please
calm coralBOT
if i got 3 w's how can i solve the same equation ? will it be, w.x+w.x+w.x+b ? ...
@golden prairie Has your question been resolved?
calm coralBOT
@golden prairie Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
errant python
A survey was conducted on 100 developers regarding Python (P), JavaScript (J), and C++ (C). The results are as follows:
45 use Python.
40 use JavaScript.
25 use Python but not JavaScript.
20 use JavaScript but not Python.
10 use both Python and C++.
10 use only JavaScript.
15 use only C++.
5 use all three languages.
clear delta
45 total use python but you've drawn 45 using only python
errant python
its initial for now i guess
25 use Python but not JavaScript.
20 use JavaScript but not Python.
they're related but i cant make the connection
clear delta
you might assign variables to the unknown quantities and make equations
errant python
A survey was conducted on 100 developers regarding Python (P), JavaScript (J), a...
OH okay i see it
20 people use both python and js
no wait im kidding, i need to see how much exclusively use python first
void umbra
A survey was conducted on 100 developers regarding Python (P), JavaScript (J), a...
I'd label all the regions on the diagram that don't contain any sub regions
Like the intersection between the 3 sets and the regions of each sets J and C that do not intersect the other sets
errant python
I'd label all the regions on the diagram that don't contain any sub regions
Lik...
but isnt the intersection of the 3 sets basically sub-regions already
eg. people that use python an C
and C
void umbra
but isnt the intersection of the 3 sets basically sub-regions already
Yea I kinda missaw your diagram somehow sorry
calm coralBOT
@errant python Has your question been resolved?
calm coralBOT
crisp sphinx
<@&268886789983436800> hello btw :>
calm coralBOT
stark sparrow
crisp sphinx
robust sedge
calm coralBOT
Available help channel!
glossy agate
z^4-2z^3+3z^2 -8z -4 =0 has a purely imaginary rot of the type z=ib
glossy agate
How do I solve it
I can solve them when they have a real root
But this I new to me
leaden thunder
are you given that z = ib is a root?
glossy agate
It says that the root is of the type ib I’m not sure what that means
leaden thunder
It says that the root is of the type ib I’m not sure what that means
!original
calm coralBOT
It says that the root is of the type ib I’m not sure what that means
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.
glass heart
plug ib in
calm coralBOT
@glossy agate Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
crisp minnow
calm coralBOT
crisp minnow
im not sure why when I put these values into the calculator i don't get the correct answer
rough arrow
You forgot the minus sign of the first part.
calm coralBOT
@crisp minnow Has your question been resolved?
calm coralBOT
crisp minnow
.reopen
calm coralBOT
✅ Original question: #help-42 message
rough arrow
eVen when I minus them
Look at the top right corner, the expression, when you turn it into $]_{-1}^{5}$, you didn't include the minus sign of the first part $$5x \cdot \frac{-1}{4} e^{-4x}$$
potent lotusBOT
Good
rough arrow
$$
5x \cdot \frac{-1}{4} e^{-4x}-\int-\frac{1}{4}e^{-4x};5 ;dx=5x \cdot \frac{-1}{4} e^{-4x}+\frac{5}{4} \cdot -\frac{1}{4}e^{-4x}=-\frac{5}{4}e^{-4x}\left( x+\frac{1}{4} \right)
$$
potent lotusBOT
Good
rough arrow
Yeah, and you also forgot to integrate $\int e^{-4x};dx$
potent lotusBOT
Good
calm coralBOT
@crisp minnow Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
topaz raft
for part b) is it just sufficient enough to say that arctan cannot be a potential function for F because the closed integral of F is not 0
velvet osprey
sufficient enough
nice pleonasm
anyway no i think they would've gone for an answer of that shit ain't continuous
topaz raft
anyway no i think they would've gone for an answer of **that shit ain't continuo...
not continuous on where? (0,0)?
velvet osprey
the entire line x=0 i believe
topaz raft
the entire line x=0 i believe
i thought it was the domain of the vector field that we are only interested in and if so x=0 is allowed in this domain (excluding 0,0)
unique jackal
i thought it was the domain of the vector field that we are only interested in a...
the potential function isn’t defined wherever x = 0 though
unique jackal
while the vector field is defined everywhere but the origin
topaz raft
the potential function isn’t defined wherever x = 0 though
but is that the only reason why it cant be a potential function?
i thought maybe its because our domain for the potential function must be D->R
which must be single valued
unique jackal
but is that the only reason why it cant be a potential function?
the other problem as Ann said is that it’s not continuous
unique jackal
which must be single valued
why’s that a problem? 
every potential function is real valued
topaz raft
why’s that a problem? <:catthink:526983414226747393>
because for a function to be a potential function we have g: D -> R and iirc a vector field F is conservative on D if there exists a scalar function g such that grad g = F on D
and a scalar field is as D -> R
but arctan is not single valued
so it cannot work by that definition of a potential function?
unique jackal
er, arctan is single valued, is it not? 
topaz raft
wait
arctan itself is but the angle
something goes wrong with the angle
like if i pick (1,0) and say its angle is 0 degrees
i can walk counter clockwise around the origin back to (1,0)
now the angle might be 2pi right
but we are still at (1,0)
unique jackal
that might have to do with the issue that it’s not defined on the y-axis 
walking counterclockwise makes you fall into a ravine on that line 
topaz raft
that might have to do with the issue that it’s not defined on the y-axis <:pikat...
i guess what i am getting at is because of the hole at (0,0) the potential function works only locally not globally
and then we get this angle problem because of (0,0) where we can walk around in a loop
unique jackal
sure, that’s a reasonable way to say it
topaz raft
sure, that’s a reasonable way to say it
right so if i just said that for x=0 for arctan(y/x) that alone would not be sufficient?
topaz raft
like if my answer was arctan(y/x) cannot be a potential function because it is discontinuous at x=0
that wouldnt be enough as an answer
because its not necessarily x=0 is the problem but the hole in the domain of F and the problem it brings with the angle
unique jackal
well I mean, if F is defined on R^2 \ 0, then this arctan function clearly can’t be its potential function simply because its domain is different, so taking its gradient yields a vector field that is like F, but undefined on the y-axis; I personally feel like that’s enough 
but your argument isn’t wrong by any means
I just see it as overkill :p
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pseudo wedge
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pseudo wedge
I don't get the very last bit of the question
To minimise the mean squared error of T_N, why are we finding E(T_N) - E(S_N) at all?
I don't really understand the significance of S_N at all actually
Are we saying E(T_N) >= E(S_N) for any arbitrary T_N, so S_N is the best possible approximation?
glass heart
yes
that is a very classic tactic
show that (error of random object) >= (error of specific object) which implies that your specific object is your optimum
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blazing coyote
I want to find the MLE here
so I start by finding the Likelihood function
so I need to minimise $\frac{2^n}{ \theta^n}(x_1 \dots x_n) e^{-\left(\sum_{i=1}^{n} \frac{x_i^2}{\theta} \right)}$
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🦆
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frank jungle
what have you tried?
blazing coyote
Would I be wrong to say the likelihood function is simply $\frac{1}{\theta^n}$?
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wai
blazing coyote
so there is no MLE
frank jungle
yes you would be wrong
blazing coyote
blazing coyote
yes you would be wrong
what's wrong with it
frank jungle
Because of the support
The probability density function is only nonzero for $-\theta \leq x_i \leq \theta$, so if you choose a theta that is smaller than any of your data points, the probability of observing it goes to 0
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blazing coyote
mhm
frank jungle
If you write out the full likelihood function with the domain, you'll see that this works fine
blazing coyote
So I instead want the nth order statistic of this
blazing coyote
If you write out the full likelihood function with the domain, you'll see that t...
so $L( \theta) = \begin{cases} 0 & x_i \in \R \setminus [ -\theta,\theta] \ \frac{1}{2^n\theta^n} & \text{ otherwise } \end{cases}$
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blazing coyote
Make theta the subject in your domain
wdym
Like I get what you mean
but I'm confused
frank jungle
yeah I was gonna ask you about that
basically theta here is the variable
its your x_i's that are fixed
blazing coyote
yeah
frank jungle
so what is the largest and smallest a certain theta can be?
if you need to ensure that every x_i is in [-theta, theta]
blazing coyote
so what is the largest and smallest a certain theta can be?
$max{\left(x_i \right)_{i=1}^{n}}$
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wai
frank jungle
in standard noration, the condition goes under \max but yeah
you need to put an absolute value around x_i
to account for -theta
frank jungle
Can you write the full function out for me just to be sure?
blazing coyote
$L(\theta) = \begin{cases} \frac{1}{2^n \theta^n} & \theta \in {x_1,x_2,\dots ,x_n} \ 0 & \text{ otherwise} \end{cases}$
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blazing coyote
I'll be sleeping now, so gn
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hasty fiber
<@&268886789983436800>
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shrewd wolf
im having serious trouble with this problem
ok so we know that we're trying to find the petals in this odd function so we set up an equation to find theta as
4sin2theta = 2
we get theta = pi/12, 5pi/12
im stuck as to how i find the other intersection points because pi/12 and 5pi/12 are very limited bounds
hollow totem
It'll probably help to graph them both
mellow crater
from 0 to pi/12 you are limited by 4sin(2θ) (petal), from pi/12 to 5pi/12 you have a circle r = 2, and from 5pi/12 to pi/2 again by 4sin(2θ) (petal)
The 1st and the 2nd part are equal (symmetry)
shrewd wolf
It'll probably help to graph them both
this is pretty much it
mellow crater
im having serious trouble with this problem
ok so we know that we're trying to f...
you don't have to find them, you count one quarter and then multiply the result by 4
shrewd wolf
you don't have to find them, you count one quarter and then multiply the result ...
i understand this part but im looking at the answers right now and i don't understand why we have to find 3 areas to calculate this
mellow crater
hollow totem
it's before the petal intersects but it's just under the petal
mellow crater
Your three parts
hollow totem
There's still a symmetry argument you can use here to be a little lazy but
shrewd wolf
mm got it
wow ok this makes things a lot more tedious but i understand it
thank you sorry for not getting it the first time 😭
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celest jolt
I'm having trouble understanding this problem on the webwork (problem 12). I literally have no clue what question I got wrong with.
What I understand is that when we check for fx/fy -> we check for if were going downhill or up, for fxx/fyy -> we check for concave (up/down) and that's positive of negative.
The point (A) is in the middle, so I put zero because it's flat in the middle.
For part B, that's where I'm not so sure about. For the first part, I thought it would be no change in sign because there isn't an increase or decrease in the X when we go up from A to B. For the second one I thought it would be from 0 to positive because it's an increasing Y axis.
leaden thunder
This is very difficult to answer without being able to rotate the image
lime quarry
I agree
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pulsar wing
can Someone help me with Picard Method and DL?
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can Someone help me with Picard Method and DL?
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
pulsar wing
I am doing DL and x_n+1=a+tsin(x_n) why is x_3 is not the DL_3 but instead it is DL_2?
glass heart
I am not sure what you mean with DL_3 and DL_2?
pulsar wing
developpement limitée AKA Taylor expansion/approximation ig
glass heart
so are you asking why they only computed the taylor poly up to t^2 for sin(a+tsina+t^2sinacosa+o(t^2)) ?
otherwise I am not sure what you are asking
pulsar wing
well they did calculate x_4 in order to find the Taylor poly of order 3
my question is why though x_3 got o(t^3) the coefficient is missing terms and it is not the right poly
apparently it is linked to picard method which is used with integrals and differential equations
glass heart
well computing more terms for x_3 would have been unnecessary if you only want up to t^3 for x_4
pulsar wing
well that's what I thought until I saw the correction and asked AI/watched yt videos about the Picard method, all of them concluded it is necessary to go up to x_4 to get the right coefficient in Taylor Poly
which I didn't understand well
glass heart
and they did go up to x_4
pulsar wing
and they did go up to x_4
why?
glass heart
well presumably your sources said why
pulsar wing
well presumably your sources said why
I didn't understand them 🥲 that's why I am asking
and even yt videos are talking about integrals and not Taylor poly in relation with this method
apparently this is the translation
glass heart
from what we have seen
pulsar wing
> from what we have seen
apparently they were meaning that x have a taylor approximation that's it
glass heart
look I'm not sure what to answer you
pulsar wing
because the first part was about proving that x got a taylor appoximation
glass heart
you know that when we are using some numerical algorithm to compute eg pi, then we need some number of iterations until we get e.g. 10 digits
afterwards, only higher digits change, the low digits dont change anymore
glass heart
same thing here, the start of the taylor series eventually doesnt change anymore
pulsar wing
you know that when we are using some numerical algorithm to compute eg pi, then ...
yessss exactlyyy, why did we need to do 4 iterations
to get order 3 of taylor approximation
that's my question
why not 3 iterations, then order 3 of taylor approximation
glass heart
well order 3 means 4 coefficients you need to determine
x_1 also only did the 0th coefficient
you could just aswell be start counting at x0
but I dont know if thats a general rule. presumably the book proved a theorem about it
pulsar wing
apparently it is a known method in engineering curriculum when dealing with integrals
But I didn't why x_0 is "a random guess" a x_1 is actually the starting point of the count 🥲
why can't x_0 can be the start of the count?
glass heart
it can
the book just started at x_1
so what
mathematicians are not in agreement of whether counting starts at 0 or 1
pulsar wing
mathematicians are not in agreement of whether counting starts at 0 or 1
no no what I meant is books and youtube videos said that you MUST start from 1 and not 0 😅
I didn't understand this part, because since it is kinda of recursive algorithm then I hoped to understand the point of starting from 1 and not 0
because here for example
x_0=0, x_1=a and x_2= a+tsin(a) and x_n+1=a+tsin(x_n)
according to them x_0 is a random guess and the true Taylor poly starts from x_1
so is it a rule? no explanation ? just accept it and move on?
glass heart
x_0=a might aswell be a random guess
I dont care how people count
at some point the early taylor terms wont change anymore
you need to compute up to that point
one coefficient per iteration seems reasonable but I dont know if its true in general
pulsar wing
one coefficient per iteration seems reasonable but I dont know if its true in ge...
hmmmm interesting interesting
got it thank youuu
gonna wait for a bit before closing this convo maybe someone from MPSI come and help me they are used to this stuff 😅
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old epoch
why is the case where e < 0 (i,e, limit approahces from the left) not considered?
leaden thunder
The definition of continuous says for every positive eps > 0
old epoch
The definition of continuous says for every positive eps > 0
sorry i meant for \lim_{eps to 0}, it seems they are only consdiering eps > 0
however we have |eps| > 0
so eps could be negative
leaden thunder
|eps| = eps for eps > 0
old epoch
yes, I mean the definiton of a $\lim_{\epsilon \to 0} f(\epsilon)$ means for all $\epsilon_1 > 0$ there exists delta > 0: for alll $|\epsilon| < \delta$ we have $|h(\epsilon) - L| < \epsilon_1$, where L is the limit. Here it is okay for e to be less than 0, and when defining $\gamma_\epsilon = z_0 + \epsilon \cdot e^{it}$ it seems okay to have eps < 0
thorny stump
epsilon is a distance
gentle olive
E_0 is the radius of the circle where the function is continuous. A radius can't be negative
leaden thunder
yes, I mean the definiton of a $\lim_{\epsilon \to 0} f(\epsilon)$ means for all...
This is an incomplete thought/question
thorny stump
yes, I mean the definiton of a $\lim_{\epsilon \to 0} f(\epsilon)$ means for all...
Why are you using e as the function's input
I think you need to review the actual definition because that's not it
old epoch
Why are you using e as the function's input
here i am mean a differnet function f
old epoch
why is the case where e < 0 (i,e, limit approahces from the left) not considered...
here $f$, i dont mean $f$ in the original question
old epoch
This is an incomplete thought/question
sorry i reforomulated
old epoch
I think you need to review the actual definition because that's not it
I am consdeirng $h(\epsilon) = \frac{1}{2 \pi i} \int_{\gamma_\epsilon} \frac{f(z)}{z-z_0} dz$
potent lotusBOT
LXDL
thorny stump
Smells like an XY tbh
leaden thunder
What definition are you pulling out
old epoch
Smells like an XY tbh
what is an XY
thorny stump
!xy
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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.
old epoch
What definition are you pulling out
for limit?
leaden thunder
Show a book source that considers a radius of negative length
old epoch
why is the case where e < 0 (i,e, limit approahces from the left) not considered...
this is the entire proof/problem
I understnad radius is postiive length. But here they denote the limit where $\epsilon \to 0$, not $0+$ hence my confusion
potent lotusBOT
LXDL
leaden thunder
eps is already > 0 so it's redundant to say 0^+ instead of 0
old epoch
eps is already > 0 so it's redundant to say 0^+ instead of 0
so they technically only consdier positive
leaden thunder
The definition of continuous says for every positive eps > 0
Yes because of the definition
old epoch
The definition of continuous says for every positive eps > 0
the eps used in continuous is not the same eps used here
its a bit overloaded here, but the one in continuous is different
thorny stump
It feels like there's a statement missing here
leaden thunder
Then I suggest you ask your question without repeating variables that already have meaning
thorny stump
epsilon_0 is defined ("for some epsilon_0 > 0"), but not epsilon
Unless I'm reading your thing wrong, I can barely read this handwriting
old epoch
Unless I'm reading your thing wrong, I can barely read this handwriting
this is not my hand writing either. This is my teacher's lecture notes and I am revieiwng them.
old epoch
It feels like there's a statement missing here
I feel that too whcih si why I am confused
old epoch
Then I suggest you ask your question without repeating variables that already ha...
how would i go about doing this? then I woudl be completley different/possibly even more confusing since it wontn align with the screenshot
thorny stump
What are those symbols?
old epoch
What are those symbols?
I think the left most circle is "i" (imaginary) and other circlle is gamma_eps, the path which is specified by eps
thorny stump
And so this is the path? A circle around z_0?
thorny stump
Well then it doesn't matter whether epsilon is positive or negative
It's still going to give you a circle around z_0
Later on they say this:
because they think of epsilon as a distance, thus positive
thorny stump
But still, it doesn't really matter
old epoch
But still, it doesn't really matter
yeah cuz we can just repacle with |eps| and they all cancel out in the end
thorny stump
At the end here, I would assume epsilon is defined to be |z-z_0|
But at the beginning (second line), the sign of epsilon doesn't matter because gamma_epsilon is a circle anyway
old epoch
At the end here, I would assume epsilon is defined to be |z-z_0|
okay hmm, yeah i think at the end it can be positive or negative but ok
yeah woudlnt matter for the proof tho anyways i realie now
since can just sub in |e|
thanks
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grim island
Is there anyone who can help me with a question?
They ask if the function b) is continu in (0,0) and to explain it with epsilon delta definition
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boreal river
hello i could use some help on a problem with getting the derivative
boreal river
if someone is available
antiderivatie*
this is what i have so far
pls ping me if someone comes
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boreal river
ohh youre syaing do u sub?
rustic osprey
yes
rustic osprey
alright lemme give it a shot
boreal river
ohhh
i see where ur going with this
i got it now
thank you so much for your help bro
i appreciate it
rustic osprey
thank you so much for your help bro
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still terrace
hello can anyone help here? whats meant by a horizontal tangent
leaden thunder
hello can anyone help here? whats meant by a horizontal tangent
A tangent line that's horizontal. Horizontal lines have slope 0
plush stream
hello can anyone help here? whats meant by a horizontal tangent
differentiate this, set it equal to zero. find value of a.
fleet stone
I presume you know what- oh ok that was direct
still terrace
but what do they mean number of points
rustic osprey
I presume you know what- oh ok that was direct
hi
plush stream
f(a) for the differnt a
u get a = smth then u put a=smth in the function and find the f(x) values
fleet stone
but what do they mean number of points
depending on the value of a, there can be a different number of points at which there is a horizontal tangent
plush stream
YOU OFC DO
fleet stone
you do
still terrace
no we need 2
plush stream
otherwise how will u find tangent?
fleet stone
well I think my presence here is not productive, I'll step back
plush stream
no why 2nd?
leaden thunder
the 1st derivative isnt a line
All tangent lines are lines
plush stream
no the first derivative is the tangent.
the second derivative is the rate of change of tangent
plush stream
well I think my presence here is not productive, I'll step back
wanna be friends?
leaden thunder
All differentiable functions have tangent lines, in particular polynomials which you have
fleet stone
wanna be friends?
not a productive question to be asking in a help channel!
still terrace
OHHHHH hold on
still terrace
i feel like you got it?
no
still terrace
a horizontal tangent says the slope is 0 right
plush stream
so first derivative is zero
or you could take first derivative and use discriminants
still terrace
yeah so
horizontal tangent basically means extreme points
minimums and maximums
right
crisp sphinx
horizontal tangent means f'(a) = 0, so a possible extreme point
but yeah, you examine the horizontal tangents of a curve, among other things, when you are looking for mins and maxes
fleet stone
eh I mean it kinda is phrased properly, it's just that the nature of the question is such that it will need some deciphering
crisp sphinx
why couldnt they just phrase it properly then
because, mathematicians and physicists and economists and actuaries all use math, but they use it in different ways
part of learning math is learning all the little stupid names for the same thing
still terrace
😭
so basically im just doing a locus of extremepoints here
so i can just solve it like how ik
crisp sphinx
yeah try your method and see what you get
leaden thunder
looks right
still terrace
omg
wait
divided by 0,5
actually nvm
now i have to do the discriminant stuff?
leaden thunder
oh there's a missing factor of 2 in the denom of the root
leaden thunder
,tex .quadratic formula
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riemann
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@still terrace Has your question been resolved?
crisp sphinx
,w solve x^2 - 8x + a^2 = 0
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