cool
#help-39
sonic patrol
stoic imp
this part it gets fuzzy
sonic patrol
if A is defined using some inequalities, you can break it up by setting 1 of them to an equality
but yeah in general this is probably the hardest step
jolly parrotBOT
Renato
sonic patrol
mhm
for the interior of A, you need these both to be strict
so $y > 0$ and $2y + x^2 < 9$
jolly parrotBOT
Pseudo (Cat theory #1 Fan)
stoic imp
2y < 9 - x^2
0 < y < (9-x^2)/2
stoic imp
for the interior of A, you need these both to be strict
but
So, if we say $B = {(x, y) \mid y = 0 \land 2y + x^2 \leq 9}$, then $B = {(x, 0) \mid -3 \leq x \leq 3$
jolly parrotBOT
Renato
sonic patrol
this is the interior
no this is the boundary
stoic imp
the boundary of $A$ is $C = {(x, \frac{9 - x^2}{2}) \mid -3 \leq x \leq 3}$
jolly parrotBOT
Renato
jolly parrotBOT
Pseudo (Cat theory #1 Fan)
stoic imp
stoic imp
well the boundary of A is B u C actually
what is B and C then
stoic imp
$\partial A = B \cup C$
B is the interior
stoic imp
$\partial A = B \cup C$
oh wait, you are saying the boundary of the region A is the union of the interior of the region A with what?
its like, B and C are partitions of A
like disjoint subsets of A
stoic imp
$\partial A = B \cup C$
what about the interior of A?
stoic imp
$\partial A = B \cup C$
no wait, A is a region, and B and C are partitions of this region (pairwise disjoint subsets of A, called B and C)
then, one of B or C is the interior of A, and the other is the boundary of A
sonic patrol
no wait, A is a region, and B and C are partitions of this region (pairwise disj...
You can break up $A = \text{Int}(A) \cup B \cup C$
jolly parrotBOT
Pseudo (Cat theory #1 Fan)
sonic patrol
Both B and C are part of the boundary of A
Neither is the interior
If you sketch what B and C look like you’ll see what I mean
stoic imp
You can break up $A = \text{Int}(A) \cup B \cup C$
so B ∪ C is the boundary of A
stoic imp
$\partial A = B \cup C$
ah, here you said it
stoic imp
You can break up $A = \text{Int}(A) \cup B \cup C$
one second, miss
the interior of A here is the system
- y = 0
- 2y+x^2 = 9
correct?
that is, x^2 = 9
so from that we get that either x = 3 or x = -3 are the interior points
stoic imp
If you sketch what B and C look like you’ll see what I mean
I am trying to understand what the interior of the region A is first
to me it looks like a curve but
sonic patrol
I am trying to understand what the interior of the region A is first
The interior of region A should be 2D
It might help if you use desmos
stoic imp
It might help if you use desmos
wait, I will pull up my calculator
sonic patrol
@stoic imp https://www.desmos.com/calculator/emvaw6evyv
Check this out
B is the flat part of the boundary of A
C is the curved part
stoic imp
stoic imp
<@1187916384341078070> https://www.desmos.com/calculator/emvaw6evyv
what am i looking at
sonic patrol
what am i looking at
You want the intersection of those shaded regions
That’s what I sent you
sonic patrol
Yes
stoic imp
B is the flat part of the boundary of A
how
sonic patrol
So, if we say $B = \{(x, y) \mid y = 0 \land 2y + x^2 \leq 9\}$, then $B = \{(x,...
.
stoic imp
sonic patrol
It’s the curved part of the boundary of A
sonic patrol
.
stoic imp
yeah so B is y = 0, x^2 <= 9
no wait
no, that's correct
B = {y = 0, x^2 <= 9}
2y + x^2 <= 9
2y <= 9 - x^2
y <= (9-x^2)/2
y >= 0
0 <= y <= (9-x^2)/2
pearl pondBOT
Available help channel!
exotic gale
I don't see how the answer is not 2
pearl pondBOT
I don't see how the answer is not 2
exotic gale
i only see triangle ABC and triangle DEC as isosceles
and there is obvi no equil triangles too so yeah
can someone please tell me what im doing wrong?
i already checked all the 7 triangles, unless im missing one idk
kindred plank
lemme think,what's awnser 2?
boreal marlin
what are the isoceles triangles you've found?
I can tell you're missing a few
you might've missed ∆ABD being isoceles
exotic gale
how
boreal marlin
find all the individual angles
vast berry
what does C^infinity(R) mean?
pearl pondBOT
what does C^infinity(R) mean?
summer imp
It's the set of smooth functions from R to R.
So it's telling you that d/dx maps smooth functions to smooth functions.
plush bramble
smooth being differentiable, infinitely many times
polynomials, exponentials, logarithms, trig functions for example
vast berry
wait C^n means differentiable n times right
summer imp
It means differentiable n times with continuous derivatives
summer imp
Well if any nth derivative exists implicitly the nth derivative is differentiable, so continuous.
So it's enough to just say smooth implies any order derivative exists.
stoic imp
pearl pondBOT
warm current
!status
pearl pondBOT
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
well 2
I did started using cylindrical coordinates
(x,y,z) = (rcos(♡), y, rsin(♡))
and simplified the inequalities of the region D
1 <= r^2(cos^2(♡) + sin^2(♡)) <= 16
1<= r^2 <= 16
rsin(♡)<=rcos(♡)
and
0<=y<=sqrt(r^2(cos^2(♡)+sin^2(♡)))
0 <= y <= sqrt(r^2)
stoic imp
!status
I got stuck
I get
1<= r^2 <= 16
rsin(♡)<=rcos(♡)
0 <= y <= sqrt(r^2)
everything good so far? @warm current
I have a cheat sheet of the common quadric surfaces
warm current
everything good so far? <@374795910032523266>
Yeah so far you are doing fine
stoic imp
what am I missing here?
I might need some more help with this one
if possible handholding
is that okay?
warm current
What are your definite bounds for r and y?
stoic imp
I am assuming r is in between [1,4]
warm current
Why 1?
stoic imp
1<= r^2 <= 16
rsin(♡)<=rcos(♡)
0 <= y <= sqrt(r^2)
.
stoic imp
is r positive then
warm current
Try graphing $\sin\theta$ and $\cos\theta$ to figure out your bounds
jolly parrotBOT
SWR
warm current
Using this plot, where is sin<=cos?
stoic imp
Using this plot, where is sin<=cos?
stoic imp
Using this plot, where is sin<=cos?
first I need you to tell me when does sin and cos intersect
warm current
first I need you to tell me when does sin and cos intersect
You need to figure this out
stoic imp
help
warm current
You can either use the unit circle, or you can use $\sin=1-\cos^2$
jolly parrotBOT
SWR
stoic imp
at 45 deg
stoic imp
You can either use the unit circle, or you can use $\sin=1-\cos^2$
ok great
sin = 1 - cos^2?
that's too advanced for me
warm current
Oops i meant sin^2
stoic imp
Oops i meant sin^2
how does that
stoic imp
Radians btw
pi/4
warm current
Good. That's one. You just need the other
Where else on the unit circle is sin=cos?
stoic imp
let me use soh cah toa
warm current
You just need to know for which $\theta$ in $[0,2\pi)$ is $\sin\theta\le\cos\theta$
stoic imp
3pi/4
jolly parrotBOT
SWR
stoic imp
I think this will be the hard part
knowing the graphs of sin and cos
also quick question dude
warm current
You only care within 0 to 2pi
stoic imp
You only care within 0 to 2pi
but
stoic imp
You only care within 0 to 2pi
am I missing something here?
stoic imp
You only care within 0 to 2pi
I know but I don't get why this doesnt include the intervals when cosine is on top
It feels like I am missing something here
warm current
Think of what polar coordinates are doing. Normally you are within the bounds of 0 to 2pi
stoic imp
Think of what polar coordinates are doing. Normally you are within the bounds of...
yes
theta or ♡ is in between [0,2pi)
stoic imp
Think of what polar coordinates are doing. Normally you are within the bounds of...
but how do you know
which one is above or below
idk if I am explaining myself
warm current
which one is above or below
Using the graph you did
The graph tells you which one is less than the other
stoic imp
The graph tells you which one is less than the other
yes but for example
in between the intersections, in first case sine is above cosine
in second case cosine is above sine
and in third case sine is above cosine
stoic imp
You want just section 2
sir
you here?
basically all of this 3 sections are in between 0 and 2pi, correct?
@warm current
pearl pondBOT
@stoic imp Has your question been resolved?
stoic imp
.close
stoic imp
pearl pondBOT
jolly parrotBOT
Renato
lilac quartz
Can you rewrite the integtal in terms of limit?
stoic imp
this?
lilac quartz
now can you compute inner integral?
quiet tendon
is hard
try splitting up the numerator, doing a u-sub for the first integral, and maybe doing a comparison for the second integral
quiet tendon
what's the first integral you get?
quiet tendon
@stoic imp when you split up the numerator, you'll get two different integrals. the first one could be evaluated with a u-sub, the numerator looks similar to the derivative of the denominator
stoic imp
now can you compute inner integral?
i just need to use comparison test for improper integrals
stoic imp
<@1187916384341078070> when you split up the numerator, you'll get two differen...
comparison test approach please
quiet tendon
okay, try comparing to something like x^3 / (x^4 + 4)
lilac quartz
Do you know this?
stoic imp
okay, try comparing to something like x^3 / (x^4 + 4)
this is smoller
quiet tendon
mmhm so does it converge or diverge
quiet tendon
do you know how to integrate that smaller one?
quiet tendon
i mean the point is to compare to something that you know how to integrate (or at least something you know converges/diverges)
lilac quartz
$\frac{x^3}{x^4 + x^4} = \frac{1}{2x} \leq \frac{x^3 +5}{x^4 +4}, x \geq 2$
stoic imp
i mean the point is to compare to something that you know how to integrate (or a...
we know 1/x^p integral diverges
when p >=1
jolly parrotBOT
dotdoc
lilac quartz
you could also use this,
compute the improper integral of 1/2x
stoic imp
what
lilac quartz
you can always find an “a” above such that the inequality holds for all values larger than a
stoic imp
**dotdoc**
1/x diverges
lilac quartz
oops sorry
stoic imp
lilac quartz
you have to take care of the integral from 1 to 2
but it doesn’t matter since they diverge
lilac quartz
**dotdoc**
using this you might estimate the impropert integral from 2 to infty
and add little part (don’t compute but it exists)
stoic imp
x^3 / 5x^4 works
stoic imp
**dotdoc**
we need to prove this is lesser
stoic imp
**dotdoc**
great idea but help me
with the inequality proof
x^3 <= x^3 + 5 true always
lilac quartz
for all x >=1 yes
stoic imp
$\frac{x^3}{x^4 + x^4} = \frac{1}{2x} \leq \frac{x^3 +5}{x^4 +4}, x \geq 2$
would be better if we can find something like this that works for x>=1
but we are close
lilac quartz
x^3 / 5x^4 works
this works
stoic imp
let me think
stoic imp
this works
then we get 1/5 , int from 1 to infinity of 1/x
lilac quartz
5x^4 >= x^4 + 4 for all x>= 1
stoic imp
yes
lilac quartz
then we get 1/5 , int from 1 to infinity of 1/x
yep
lilac quartz
5x^4 >= x^4 + 4 for all x>= 1
you might want to prove this
stoic imp
4x^4 - 4 >= 0
x^4 - 1 >= 0
x^4 >= 1
x >= 1 <=> x^2 >= x >= 1
@lilac quartz
we can use transitivity
x >= 1 <=> x^4 >= x^3
x>= 1 <=> x^3 >= x^2
x >= 1 <=> x^4 >= x^3 >= x^2 >= x >= 1 <=> x^4 >= 1
lilac quartz
for all x>1, (we can apply
montonicity of powers in this range)
x^4 >= 1 iff 4x^4 >= 4 iff 5x^4 >= x^4 + 4
lilac quartz
basically adding to an inequality is always safe
the key step is montonicity in [1,inft)
for any a,b in [1,infy)
a < b implies a^n <= b^n
for any n in N
stoic imp
for all x>1, (we can apply
montonicity of powers in this range)
x^4 >= 1 iff 4...
is proven
now wat
lilac quartz
Do you know this?
you are done, use this
stoic imp
help
lilac quartz
$\frac{1}{5x} = \frac{x^3}{5x^4} \leq \frac{x^3 +5}{x^4 +4}, x \geq 1 \implies \frac{1}{5x} <= \frac{x^3 +5}{x^4 +4}$
stoic imp
you are done, use this
the issue is that the 1/x^p idk how it works because for integrals with an infinity as bound diverges but for regular definite improper integrals it converges
p>=1
jolly parrotBOT
dotdoc
lilac quartz
apply improper integral to last inequality
or what’s the improper integral from 1 to infy of 1/5x?
does it converge or diverge?
stoic imp
does it converge or diverge?
who the fuck knows at this point
lilac quartz
“harmonic series”
stoic imp
this is a nice little summary i just found
is confusing because sometimes they do sometimes they dont depending on the bounds
lilac quartz
or what’s the improper integral from 1 to infy of 1/5x?
just write out the limit definition of this
and compute the integral push the limit and see
stoic imp
alright let's see
lilac quartz
the whole point of this exercise is computing smaller integrals
you can’t avoid that
you would be pushing something like log to infy
stoic imp
lilac quartz
what what?
stoic imp
unsure what the range of ln is
lilac quartz
check you evaluation of limits again
stoic imp
what?
stoic imp
its just
lilac quartz
just?
stoic imp
1/5 × ln|t) - 1/5 × ln1
lilac quartz
what’s ln(1)?
stoic imp
who knows what the domain of ln is
stoic imp
what’s ln(1)?
0 ig
lilac quartz
what’s your domain of integration?
jolly parrotBOT
The following error occured while calculating:
Error: Undefined function ln
lilac quartz
bruh
stoic imp
what’s your domain of integration?
1 to t
stoic imp
yes
lilac quartz
what do you get?
stoic imp
i don't know the range of ln
lilac quartz
you should check then
stoic imp
but i presume the supremum of the range
stoic imp
lilac quartz
or you should know at this point that it shoots to infy
stoic imp
,w lim n to infty of ln(n)
jolly parrotBOT
stoic imp
what u studying
lilac quartz
psychology
stoic imp
oh sht, gl
stoic imp
finding upper bounds proving etc
lilac quartz
find bounds of?
rough forge
i have lecture in 15 mins
doing side quests atp
lilac quartz
**dotdoc**
set f:= 1/5x, g:= x^3+ 5/(x^4 +4)
a := 1
lilac quartz
gl
pearl pondBOT
pearl pondBOT
Available help channel!
kind forum
I don't understand the derivation
pearl pondBOT
I don't understand the derivation
kind forum
Why is there w_0 all of a sudden
The Eq 9.18e mentioned by the book is the reciprocal rule of complex number
Ohhh w_0 is 1/RC
Nvm
.close
pearl pondBOT
pearl pondBOT
Available help channel!
tender egret
I want to find the average(expected?) cost of random restart hill climbing
tender egret
My confusion begins with how we can even define cost
languid plover
please provide question
tender egret
And secondly how it extends to n dimensions
languid plover
do it... do it now!!!
tender egret
That is the question
tender egret
And thirdly to find cost for having some x% confidence interval
languid plover
It's more helpful if you give me an actual framed question with a scenario and values instead of a general question about a generic procedure
I'll give it a shot but trust me it'll be more difficult
tender egret
But it is in fact a general question about a generic procedure
languid plover
I want to find the average(expected?) cost of random restart hill climbing
what is random restart hill climbing
tender egret
Simplifying it will kill it's essence
languid plover
But it is in fact a general question about a generic procedure
okay ill help u now
understood
tender egret
what is random restart hill climbing
If you don't know this im not sure you can help me.
tender egret
Reiterating:
I want to find the average(expected?) cost of random restart hill climbing
My confusion begins with how we can even define cost
And secondly how it extends to n dimensions
And thirdly to find cost for having some x% confidence interval
<@&286206848099549185>
tardy reef
Reiterating:
I want to find the average(expected?) cost of random restart hill ...
I am not sure you can even define an associated cost with the restarts
like the reason you actually restart is to check whether you got stuck at a local maxima
tender egret
After each restarts there will be a cost required to reach the local minima righ
Right
tardy reef
After each restarts there will be a cost required to reach the local minima righ
like how many iterations you take to stably achieve the extreme?
sure
but thats not relevant to the reason you restart
tardy reef
and also, the initial steps are too quick, the time taken to converge depends on the behaviour in the small neighbourhood
tender egret
That's why I'm talking about finding an average cost
tender egret
and also, the initial steps are too quick, the time taken to converge depends on...
Could you elaborate
tardy reef
wait, I might have been a bit confused. Am i correct assuming that the direction of movement is influenced by how much improvement is there? like would you be moving in the direction of climb by a fixed amount or would that be influenced by how much the improvement is?
would my $\vec{x}n - \vec{x}{n-1}$ be same as my $\vec{x}k - \vec{x}{k-1}$
jolly parrotBOT
βαχτϵρ10Φρ4γ
pearl pondBOT
@tender egret Has your question been resolved?
tender egret
wait, I might have been a bit confused. Am i correct assuming that the direction...
I don't know myself 
tardy reef
I don't know myself <:blobcry:971797574916907028>
well, no matter, what you are looking for is to cover a reasonably large subset of your domain over which you randomly start. so, I dont think there is any point in looking at a cost to random restarts. the aim is to be exhaustive, so you should not look at ways to reduce efforts here. The only reason you restart is that you dont end up missing the maximum of this unknown function.
pearl pondBOT
@tender egret Has your question been resolved?
tardy reef
<@&268886789983436800>
pearl pondBOT
zinc pewter
pastel umbra
tardy reef
lol I thought you did the work and lance just lanced
pastel umbra
(oh shit that's actual cinema here lol)
pearl pondBOT
Available help channel!
hollow oxide
Is this channel available?
pearl pondBOT
Is this channel available?
rotund ferry
Is this channel available?
Yeah, you just claimed it
hollow oxide
Oh okay
rotund ferry
You can read this @hollow oxide
hollow oxide
Got it
Multiplication/Division in Different Bases in this problem I need to multiply the following but I'm stuck on problem d. Which is B12twelve×83twelve?
cedar sentinel
are you stuck on all the digits?
toxic lichen
are you expected to do it in dozenal?
or do they expect you to convert to base ten first
kinda unclear from this question in isolation how you would be meant to proceed
aside from this, do you know the algorithm for multiplication in base ten?
hollow oxide
They're expecting us to do it in Bases from base 2-12 this one is just base 12
hollow oxide
From what I've known base 10 numbers are broken down to ones, tens, hundreds, thousands, and so on.
toxic lichen
so they are
do you know how to do multiplication if both numbers are in base ten?
yes or no
hollow oxide
No
toxic lichen
so uhh. hm.
if i asked you to work out
731
* 43
-----
and these are just regular base ten numbers
would you know how to do it?
toxic lichen
so you can't do multiplication of multi digit numbers even in base ten?
hollow oxide
yes?
toxic lichen
wait a minute
how were you able to do letters a-c
can you show me the entire worksheet
warm dagger
Multiplication/Division in Different Bases in this problem I need to multiply th...
Wait does b stand for 11?
toxic lichen
sure does
but op is having a bigger issue
she seems unable, by her own account, to do long multiplication at all
warm dagger
;-;
toxic lichen
@hollow oxide can you take a photo of the whole worksheet please
warm dagger
Welp good luck on this one Ann
toxic lichen
mmmm not what i was looking for.
cedar sentinel
with your answers to a) to c), please.
toxic lichen
Multiplication/Division in Different Bases in this problem I need to multiply th...
i was looking for this but uncropped to show the entire page!
cedar sentinel
aka the actual paper itself
hollow oxide
I’ve done a to c but not d unfortunately
toxic lichen
I’ve done a to c but not d unfortunately
show us HOW you did a-c
pastel umbra
!show is a wonderful blessing in this server; it says the following:
pearl pondBOT
Show your work, and if possible, explain where you are stuck.
toxic lichen
brb
hollow oxide
toxic lichen
ok look at part b
you do know the algorithm for multiplication
you know that you need to multiply each digit of the first number with each digit of the second
yes?
hollow oxide
Yes
toxic lichen
yes so
same idea here
now you just need to write down all the single digit dozenal multiplications that you will need
then proceed in the exact same way
void glen
she is having problem with the letters it seems?
toxic lichen
she is having problem with the letters it seems?
let her say it
void glen
ok
hollow oxide
I think I have to multiply by 3 in the ones place for problem d.
3 × 2 = is 6
3 × 1 = 3
3 × B = 3 × 11 = 33¹⁰ = 2(12) + 9 = 29¹² but I have to write 9 and carry the 2.
Next I need to multiply times 8 which is the twelve place
8×2=16¹⁰ =14¹² I need write 4 and carry 1
8×1=8, plus carry 1 = 9
Shoot
I'm stuck
I don't know what to do next..
cedar sentinel
never do this kind of math without writing it down
you risk confusion and chunking too big of an operation
hollow oxide
Okay
cedar sentinel
your first round of multiplication looks correct though. write that down first, then do the second round separately
hollow oxide
I think 8 × B = 8 × 11 = 88¹⁰ = 74¹²
So 8 × B12 = 7494¹² (shifted one place left) = 74940¹²
I get 2936¹²+74940¹²=
hollow oxide
You had to?
hollow oxide
No the problem is Identifying the place values in base 6
cedar sentinel
base 6?
hollow oxide
And base 12
cedar sentinel
ok, this algorithm works on any base
and no, multiplication of the two intermediate results here is not what should be done
let's just take a simple example to show why
suppose you're asked to multiply 123 with 13
in base 10*
cedar sentinel
that does not justify the multiplication of the two intermediate results.
again, I'm about to show you why
cedar sentinel
sure then
what's your final answer then?
wait a sec
you added the intermediate results in this problem.
hollow oxide
Yes
cedar sentinel
so why are you switching to multiplication now? adding is the correct step here
cedar sentinel
I get 2936¹²+74940¹²=
unless you mistakenly put the multiplication sign when you meant an addition sign?
hollow oxide
Oh wait I think I mistakenly added a multiplication sign by mistake
hollow oxide
Sorry
cedar sentinel
yes, that would be the correct step to proceed
cedar sentinel
I'm more surprised that you didn't double check when I pointed it out the first time, but it worked out in the end
cedar sentinel
The answer is 77876¹²
hm. I got a slightly different answer
check.
specifically, your third digit seems to be wrong
every other digit is correct
hollow oxide
Wait no it's
cedar sentinel
(also pedantic note, but don't indicate bases with superscripts. those are reserved for exponents)
hollow oxide
77676¹²
jolly parrotBOT
Tairin
cedar sentinel
but yes, well done
hollow oxide
Does any know numeration systems unit. That is Egyptian, Roman, Babylonian, and Mayan numerals. It will also include converting between different bases and adding, subtracting, multiplying, and dividing in other bases as well.
So I'm hoping if anyone is aware of these kinds of subjects in math and helping me out?
hollow oxide
A review on these math subjects
I just want to go over the numeration systems and numerals and I do want to go over different basses also
I desperately need the help I can get
glass meadow
These channels aren't for reviewing an entire topic
Feel free to ask specific questions
hollow oxide
Oh...
glass meadow
Or I guess you can ask in https://discord.com/channels/268882317391429632/326138737606262786... not really sure what the appropriate channel would be
hollow oxide
Nevermind then
glass meadow
I mean you can also keep this channel and wait for someone who would be willing to go through an entire topic
I'm not
Still, I'm happy to answer specific questions
pearl pondBOT
@hollow oxide Has your question been resolved?
bronze warren
hi im having some trouble with ODEs and the Lipchitz condition. Whilst i get that its essentially sets a 'speed limit' as to how a function grows im not understanding why we let y vary and not x in a multivariate function.
So say f(x,y)
then lipchitz condition says that
|f(x,y2) - f(x,y1)| <= K|y2 - y1| y2,y1 E D
I'm also having trouble seeing how this links with ODEs
if someone could clear this up for me that would be amazing!
pearl pondBOT
hi im having some trouble with ODEs and the Lipchitz condition. Whilst i get tha...
@bronze warren Has your question been resolved?
snow sail
hi im having some trouble with ODEs and the Lipchitz condition. Whilst i get tha...
in case you dont get what you need here, you might try #real-complex-analysis or #odes-and-pdes
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quick venture
How do I solve the sum of moment equation to get theta?
pearl pondBOT
How do I solve the sum of moment equation to get theta?
plush bramble
you can isolate tan(t) = some number then use inverse tangent
arctan(tan(t)) = t
theta is written as $\theta$, not $\varnothing$
jolly parrotBOT
riemann
quick venture
arctan
plush bramble
and show the answer
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hard chasm
Ayo how do i do 6
pearl pondBOT
Ayo how do i do 6
hard chasm
Im familar with the idea of these questions but whats the formula
Whats the radius have to do with this
And am i basing this on the formula for volume of a cylindar, or which formula do i derive?
Oh wait
Yea i feel like sum is wrong here
Wait no dr/dt cuz the radius is constant
Wait na im lost af
.close
pearl pondBOT
velvet ruin
Wait na im lost af
Have you figured it out?
hard chasm
Yea i gpted it
velvet ruin
Ayo how do i do 6
Number 6 should be related rates if I'm not mistaken.
hard chasm
Its about the idea of once part of the equation goes to 0
Since its a constant
Like dr/dt is 0
Which confused me
velvet ruin
Which confused me
Does it still confuse you?
hard chasm
Lemme see if i can do # 7
velvet ruin
Alright 👌
hard chasm
Nah les go i got the answer right
Its basically like
At one point u have to derive using the product or quotient rule
And one part of it is 0
I think atleast
velvet ruin
Well, you have to relate things first and usually everything given should help you find out which formula to use
You have to establish first what you're looking for.
Since you're going with related rates problems, it usually involves formulas from basic geometry and it's on you to construct it in a way that the given of the problem would somehow relate to each other
hard chasm
Yea
Its mainly just these geometric shape formulas
And we did some triangle work but i didnt get to that review yet
But like 2 cars goes in directions that makes a right angle
Or a guy walking away from a light making a shadow
velvet ruin
You should be good to go as long as you know your geometry formulas and you know what you're looking for
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hard chasm
You should be good to go as long as you know your geometry formulas and you know...
Can u help with 8?
pearl pondBOT
Can u help with 8?
hard chasm
Some how i got 1/0.333 as my answer which is defo off cuz my entire r term cancelled out
Imma redo my work rq
velvet ruin
Can u help with 8?
Hello, let me solve it rq
tardy reef
did you put r in terms of h in your volume expression?
hard chasm
Wym
tardy reef
coz to me it looks like you didnt do anything to r till the very end
hard chasm
coz to me it looks like you didnt do anything to r till the very end
Like i didnt subsitute?
velvet ruin
Dang its still wrong
It should be 0.72cm/h
hard chasm
gimme the expression for volume in terms of only h
I lowkey dont know what that means
tardy reef
Like i didnt subsitute?
no, you didnt stubstitute before differentiating
velvet ruin
I lowkey dont know what that means
Like what bacter said, you should first get the volume of a cone and express it in terms of h
tardy reef
I lowkey dont know what that means
you have v = 1/3 * pi * r^2 * h
now replace r with h
like properly according to their relationship
tardy reef
no
leaden wadi
It should be 0.72cm/h
!noanswers
pearl pondBOT
It should be 0.72cm/h
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
tardy reef
you have this right?
hard chasm
Yea
tardy reef
use it
hard chasm
Oh
tardy reef
pls dont hand out answers like that
tardy reef
Right into the formula?
yes
velvet ruin
pls dont hand out answers like that
My bad, didn't know. Will reflect on this.
hard chasm
It = 0
tardy reef
Dang its still wrong
coz by some magic you seem to have put it 0
hard chasm
Derivtive of the constant i thought
tardy reef
It = 0
yea, and obv thats not the case coz the radius is also changing with time as the volume changes
hard chasm
If r = 2/3
hard chasm
yea, and obv thats not the case coz the radius is also changing with time as the...
Ohh
tardy reef
well, in that case why is your dh/dt not 0?
tardy reef
coz you got this expression here
like here you could have also subbed in h = 12r to calculate dr/dt in terms of dh/dt
but you didnt realize that
so its better if you do this substitution as soon as possible
hard chasm
like here you could have also subbed in h = 12r to calculate dr/dt in terms of d...
I lowkey got a bunch of dr/dt
Idk if im supposed to have them
leaden wadi
At this point in Calculus, you have not been taught how to evaluate multiple variables. Because there are three variables in the equation for the volume of a cone, you need to eliminate one of them. You can do that by using substitution which was provided to you by the relation h = 12r.
hard chasm
Does this look right
I remember my teacher going over cones but i passed out during that lesson
hard chasm
And thats = to dv/dt
leaden wadi
Does this look right
Not for this problem.
leaden wadi
Yes, it does ask for dh/dt.
And it gives you dV/dt.
That it your hint that you need to eliminate the r variable somehow.
tardy reef
Idk if im supposed to have them
if you did sub h earlier, then you shouldnt have any dr/dt's. But in case you didnt, you could still do dr/dt = d(h/12)/dt and end up with dr/dt = 1/12 * dh/dt and that would work too
hard chasm
Oh i see where i messed up
I subbed in 12r for h
But i think i should sub in h/12 for r
Would be easier
tardy reef
is it really, coz its like 1 step from here
tardy reef
just switch up r and h and from there you are back on route
tardy reef
yep, this is correct
hard chasm
Idk if ive ever seen
Quotient rule and power rule at same time
Its just 2(h/12’h
?
tardy reef
quotient rule?
tardy reef
why do you need that here?
hard chasm
Its just all big product rule
tardy reef
there is just one small chain rule, nothing else tbh
hard chasm
But idk ive never seen examples with a quotient and chain rule
Normally just like (x+q)^2
Got it
Gpt
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pearl pondBOT
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sharp smelt
I think I'm having a brainfart
pearl pondBOT
I think I'm having a brainfart
sharp smelt
What's the non-zero area of f?
I'm getting -2/3 💀
jolly parrotBOT
wai
void sorrel
So I would just begin by sketching 0 < y < x < 1
sharp smelt
So I would just begin by sketching 0 < y < x < 1
oh
got mt mistake
tq
I'll close this now
.close
pearl pondBOT
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sharp smelt
pearl pondBOT
sharp smelt
So the formula here ie E(XY)-E(X)E(Y)
$\int_{0}^{1} \int_{0}^{1-y} 2xydxdy - \int_{0}^{1}\int_{0}^{1-x} 2ydydx \int_{0}^{1} \int_{0}^{1-y} 2xdxdy$
This feesls wrong
jolly parrotBOT
wai
sharp smelt
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dapper kraken
find all $x$ such that
$$\tan(x)=\tan(x+10^\circ)\tan(x+20^\circ)\tan(x+30^\circ)$$
hollow sonnet
degrees?
dapper kraken
oh yea
jolly parrotBOT
ihave<skissue>
tropic saddle
well symmetry makes me think that you should either sub u=x+15 or u=x+20
but dunno
dapper kraken
huh
hollow sonnet
no idea how tf that happened
pearl pondBOT
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dapper kraken
gtg sleep now, sorry
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Available help channel!
sharp smelt
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sharp smelt
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prime bramble
<@&268886789983436800>
fossil drum
is there an intuitive way to think about why being prime implies irreducibility in an integral domain
fossil drum
a = bc
a = atc if a | b
thus tc = 1 by cancellation
hmmmmm
like proof makes sense but not really getting it intutively
deep coral
Why do these chats go on for so long? I'm new, and this isn't just one question right?
fossil drum
fossil drum
thats literally the same book im using for my probability class lol and I was just working on that problem not too long ago
toxic lichen
Why do these chats go on for so long? I'm new, and this isn't just one question ...
this one has just started
we have 50 channels for this sort of real-time help and they're rotated in and out
toxic lichen
when the bot posts this message it means the channel is up for grabs and whatever follows is a new question
static helm
like proof makes sense but not really getting it intutively
yk how factors of a prime are 1 and itself, kinda of just a proof of that. Assume it was the product of 2 numbers, you have now proven that one of those numbers is 1, and the other is the prime
at least that’s my take on it
mortal imp
like proof makes sense but not really getting it intutively
I think the proof mentioned is itself intuitive
fossil drum
hm what do you mean by that
mortal imp
It just seems messed up cause if all the symbols and all
fossil drum
the proof makes perfect sense but Im having trouble picturing it
mortal imp
The statement is provable by definition of prime numbers itself
static helm
the proof makes perfect sense but Im having trouble picturing it
what do you mean “picturing it”?
fossil drum
what do you mean “picturing it”?
like conceptualizing it, like the way I started to think about it was we have a = bc and that a is prime so we know a breaks up b or c into pieces, say it breaks up b into pieces evenly, then there exists some element t such that a = atc but from these elements live inside an integral domain which has a structure such that we know 1 = tc. Maybe im having trouble conceptulizing why cancellation is being held, like in some diagrams we can imagine things as having some circular path, say the cyclic ring generated by an element. I was wanting to have a pictoral view of this proof similar to that where I could maybe diagram it
let me go refresh on integral domains and cancellation
pulsar flax
integral domains are exactly the rings where you have cancellation
static helm
like conceptualizing it, like the way I started to think about it was we have a ...
if a = atc then 1 = tc and since t and c are positive integers, both t and c must equal 1
pulsar flax
they are not positive integers
fossil drum
gonna take me a while I need to review back up on rings for a better understanding of their structure thanks for the help!
.close
pearl pondBOT
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rustic atlas
Let $E$ be the space of bounded real sequences with the infinite norm, $F \subset E$ be the set of convergent sequences and $G \subset E$ the set of sequence which converge to $0$.
$$\begin{enumerate}
\item Does there exist a linear bijective continuous map $F \rightarrow G$ which has a continuous inverse (homeomorphism)
\item Does there exist a linear bijective isometry $F \rightarrow G $
\end{enumerate}$$
jolly parrotBOT
bloubbloub
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rustic atlas
stuck on the first one
I tried to express each element of G as the limit of linear conbinations of $(\delta_k)_n$ ($=1$ if $k=n$ and $0$ otherwise)
jolly parrotBOT
bloubbloub
rustic atlas
I'm not even sure if it exists
pearl pondBOT
@rustic atlas Has your question been resolved?
thin remnant
I'm not even sure if it exists
A homeomorphism preserves metric properties of the two spaces
Think about a few general key properties of metric spaces and see if they coincide for F and G
I think that can help get u started in a direction
rustic atlas
A homeomorphism preserves metric properties of the two spaces
Think about a few ...
would it work if I did something like this:
define $\phi: u \in F \mapsto \lim_{n \rightarrow \infty} u_n \in \mathbb{R}$. $\phi$ is continuous for the infinite norm. Then $G = \phi^{-1} ({0})$ so $G$ is not open in $F$ whereas $F$ is open in itself so they can't be homeomorphic?
jolly parrotBOT
bloubbloub
rustic atlas
wait
F is connected so if G was open and closed it would either be F or the empty set, which it isn't
so the argument I gave should work right?
<@&286206848099549185>
pearl pondBOT
@rustic atlas Has your question been resolved?
pearl pondBOT
@rustic atlas Has your question been resolved?
plucky python
F is connected so if G was open and closed it would either be F or the empty set...
but i mean our topology is in G right?
G is closed in F, but G is open in G
plucky python
Let $E$ be the space of bounded real sequences with the infinite norm, $F \subse...
anyway for the first part you have some good ideas
plucky python
**bloubbloub**
||hint: ^ limit map is cts as you said||
futher hint: ||what's a very crude way to take a sequence that converges to l and make it converge to 0?||
plucky python
**bloubbloub**
Compile Error! Click the <:errors:504266556054962196> reaction fo...
(also btw the existence of part ii strongly suggests ||the answer to the first part is yes, cus otherwise if the answer to the first part is no that immediately implies the answer to the second part is no||)
pearl pondBOT
@rustic atlas Has your question been resolved?
minor tapir
hi can someone tell me if I did this correctly please?
pearl pondBOT
hi can someone tell me if I did this correctly please?
@minor tapir Has your question been resolved?
brittle tinsel
minor tapir
is my approach erong
pearl pondBOT
is my approach erong
minor tapir
I think im tripping so hard
median swan
I think im tripping so hard
The limits of integration in basically all of the steps are wrong, but the calculations seem right. For the limits in the first line what are the allowed values for x in the original function?
pearl pondBOT
@minor tapir Has your question been resolved?
rustic atlas
futher hint: ||what's a very crude way to take a sequence that converges to l an...
I mean I could substract the limit from the sequence but that wouldn't be bijective
pearl pondBOT
I mean I could substract the limit from the sequence but that wouldn't be biject...
@rustic atlas Has your question been resolved?
hearty fiber
Can anyone please help solve this
pearl pondBOT
Can anyone please help solve this
hearty fiber
Wont this be correct instead?
proper nova
Can anyone please help solve this
what do they mean by area of 4 lines when these 4 lines only make a triangle (y = 0 makes no sense of role)
🙏
hearty fiber
I used the area identity to solve this but im getting two values of m but there is only 1 correct answer
acoustic latch
Hi guys I need help in math
pearl pondBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
hearty fiber
what do they mean by `area of 4 lines` when these 4 lines only make a triangle (...
the language is kinda ambiguous took me some time to understand it too 😅
proper nova
the language is kinda ambiguous took me some time to understand it too 😅
how do you understand it?
hearty fiber
Wont this be correct instead?
Look at this graph i drew
Area of shaded region is given i believe
hearty fiber
I used the area identity to solve this but im getting two values of m but there ...
I used the area Identity and im getting 2 values of m can you help me understand how do I eliminate 1
As answer is x+y=2 in answer key so m=-1 only
pearl pondBOT
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eager jewel
pearl pondBOT
hollow sonnet
where are you stuck at?
hollow sonnet
first, let's find the probability of P(A) and P(C)
is it stated how many sides are in this die
if not, we assume the numbers are from 1-6
eager jewel
yes 1-6
hollow sonnet
1 2 3 4 5 6
which of these are prime?
eager jewel
235
hollow sonnet
so, what's the probability that rolling a dice gives a prime number?
eager jewel
1/2
eager jewel
only 1 right
hollow sonnet
(hint, there are only 2 numbers which satisfy this property. one of them is not on the dice, the other is 1)
eager jewel
uh no
eager jewel
yes
hollow sonnet
whats the ans then
eager jewel
9
golden bramble
whats the ans then
Have to consider turn order
eager jewel
i had put 3 only in the exam tho
hollow sonnet
Have to consider turn order
damn
eager jewel
Have to consider turn order
yes this is what i need help with
golden bramble
Maybe it can help to consider it on a per-turn basis
eager jewel
P(A) = 1/2 + (1-1/3)(1-1/6)(1/2) + ....?
hot timber
Maybe it can help to consider it on a per-turn basis
Yeah that’s what I was thinking as well
eager jewel
cause 1/2 probability of getting A in first roll
then for 2nd role we shouldnt get B on first roll and shouldnt get C in first roll
so (1-1/3)(1-1/6)
golden bramble
but also A can't get it