khan academy!!
#help-42
hexed grove
supple siren
khan academy!!
Oh
hexed grove
he used to run the courses on khan, but as since started 3b1b on youtube
queen fog
im taking 17 credits which is the max credits at my uni so this is been a bit stressful
i have 4-5 days of free time to actually put into math
short pumice
what book are u following?
just follow stewart calculus book, it isnt that long and is quite complete
queen fog
Calculus: Early Transcendentals
queen fog
just follow stewart calculus book, it isnt that long and is quite complete
is it expensive
queen fog
alright
queen fog
just use paul's online math notes then
could u send a link to this pls
hexed grove
khan is completely free
hexed grove
just use paul's online math notes then
these are also really good
queen fog
is it a youtuber?
calm coralBOT
calm coralBOT
Available help channel!
tough shadow
calm coralBOT
tough shadow
Hello I'm stuck on this question. I'm used to it being just tanx= not tan2x , do i get rid of the 2 and if so how ?
leaden thunder
can you solve tan(z) = -sqrt(3) ?
leaden thunder
right so z = -pi/3 is one solution
now if z = 2x because tan(z) = tan(2x), can you solve for x?
tough shadow
now if z = 2x because tan(z) = tan(2x), can you solve for x?
that would be -2/3pi
I think I understand now
leaden thunder
that would be -2/3pi
are you saying x = -2/3 * pi?
tough shadow
yes
leaden thunder
can you explain how you got that from z = 2x
tough shadow
can you explain how you got that from z = 2x
ah i think it should be -pi/6 ? since its z=2x not 2z=x my bad I read it wrong
checked and it's correct thank you for the help
.close
patent phoenix
can someone explain why number 2 is true
calm coralBOT
can someone explain why number 2 is true
patent phoenix
i dont rlly get it
short pumice
the solutions of the homogeneous case are translated by some vector to give you the solution in the nonhomogeneous case
we have that dim(nullsplace) = 1 via rank nullity and u can visualize this as a line passing through the origin. the nonhomogeneous solution is given by shifting that line by any solution of Ax = b
dusky flax
ohh kk ty
calm coralBOT
@patent phoenix Has your question been resolved?
simple musk
also, when you try to find a solution to Ax = b, you will get that the solution is depending on a free variable, that free variable is the lambda that is multiplied by the direction vector of the line that passes through the origin, where the direction vector is one of the vectors from the nullspace of A, where lambda times that vector represent the whole span of that nullspace of A, no? they are parallel because both lines have same direction vector
also since the matrix is non square, the dimension of the nullspace will be not 0
it is given rank 2, because from there you can figure out the nullspace is exactly dim 1, as dj said
tough shadow
calm coralBOT
tough shadow
Hello I need some help with this question. I don't understand why the answer is (-1 0) not (-1 1) like I wrote
the answer
dusky flax
stretching by 2 increases all the y-coordinates by 2x
so the flat line in the graph (at y = 2) ends up at y = 4 when you stretch 2x
because the x-axis is your reference line for the stretch
not y = 1 (1 unit above x-axis) as you have assumed to be
tough shadow
stretching by 2 increases all the y-coordinates by 2x
I'm still a little confused
oh wait no I should have drawn it 1 lower
okay thank you for explaining
.close
calm coralBOT
tough shadow
.reopen
calm coralBOT
✅ Original question: #help-42 message
tough shadow
It seems I also got the order of it wrong I don't really understand how it matters though
dusky flax
It seems I also got the order of it wrong I don't really understand how it matte...
yeah i think they are indedpendent of each other
tough shadow
I can see how it also works in that order but I don't understand why mine would be wrong 🥲
calm coralBOT
@tough shadow Has your question been resolved?
lament sorrel
is there any reason to choose one or the other here for matrices? they're both just notation for matrices right?
manic oracle
is there any reason to choose one or the other here for matrices? they're both j...
you mean, square vs round brackets?
lament sorrel
you mean, square vs round brackets?
yes
manic oracle
if it's that, it doesn't really matter, just pick what you are more comfortable with
calm coralBOT
calm coralBOT
Available help channel!
molten knoll
calm coralBOT
molten knoll
I need help with finding the sum of perimeter formula of this fractal.
What I know:
- every nth term theres 4(2^n-1) new triangles added.
- every nth term the new triangles are half the size?
- the triangles are 30-60-90 so the sides in n=1 is 1, 2, √3
molten knoll
also I've attached 2 images because I'm supposed to ignore the white triangles and only focus on brown ones so I edited for better visualization
oak elm
The triangles are 30-60-90 so the sides in n=1 is 1, 2, √3
This doesnt match the fractal you showed in the pic
jade fractal
I need help with finding the sum of perimeter formula of this fractal.
What I kn...
every nth term the new triangles are a quarter the size
take 1 the length of the side of the 1st square
which you can decompose into 4 squares
you get 8 new squares on n=2
which side's size is 1/4
molten knoll
> The triangles are 30-60-90 so the sides in n=1 is 1, 2, √3
This doesnt match t...
how does it not? look at the first pic. if you see it it looks like a right triangle and if we consider the white triangle its 60-60-60
I might be wrong idk but thats how I see it
molten knoll
every nth term the new triangles are a *quarter* the size
how's it quarter? I'm sorry I dont get it
jade fractal
the side's size of the new squares for n is 1/4^(2n)
jade fractal
how's it quarter? I'm sorry I dont get it
oak elm
how does it not? look at the first pic. if you see it it looks like a right tria...
if we consider the white triangle its 60-60-60
uhhh are we seeing the same image 😭
calm coralBOT
@molten knoll Has your question been resolved?
vale flower
4×2^(n-1) = 2²×2^(n-1) = 2^(n+1)
(1+2+sqrt(3))×4
+½(1+2+sqrt(3))×8
+¼(1+2+sqrt(3))×16
- ...
= (1+2+sqrt(3))×4
+(1+2+sqrt(3))×4
+(1+2+sqrt(3))×4- ...
when n=1 the perimeter is (1+2+sqrt(3))×4
everytime the number of triangles added doubles from 4 but their sizes are also half
so like ×2 then ÷2 which doesn't change
molten knoll
everytime the number of triangles added doubles from 4 but their sizes are also ...
you say that the sizes are half so it means 1/2 but why are people saying its quarter?
I dont get it
oak elm
from your diagram, "half the size" implies that its base and height are halved
half the base, half the height and its 1/2*1/2=1/4
vale flower
you say that the sizes are half so it means 1/2 but why are people saying its qu...
you are asked to find the perimeter right?
molten knoll
you are asked to find the perimeter right?
yeah
vale flower
perimeter is halved
molten knoll
half the base, half the height and its 1/2*1/2=1/4
I see
vale flower
if area then yes 1/4
molten knoll
oh ok
molten knoll
if area then yes 1/4
so for n=2,3,4... its 1/2, 1/4, 1/8... respectively right?
not the final perimeter
just the size
vale flower
so for n=2,3,4... its 1/2, 1/4, 1/8... respectively right?
yes
simple musk
calm coralBOT
simple musk
how does this three work?
simple musk
simple musk
Btw are the : division?
gcd dude
honest crypt
Ooh
simple musk
you from America?
honest crypt
nop
French system
We note it a v b instead of a : b
So anyways we know that to prove the equivalence we must prove the two implications
First implication goes like this we know that $a:b | a $ and $a:b | b $( because if a : b = r the r = ka and r= k’b )
Now just use the properties
a:b|b so a:b|t’b
a:b|a so a:b|s’a
a:b | t’b and a:b|s’a so a:b|t’b+ s’a
honest crypt
Okey ask anything if there is a step you dont understand
honest crypt
also can you make a drawing
You mean latex?
simple musk
First implication goes like this we know that $a:b | a $ and $a:b | b $( because...
this is for the left direction <== I presume
correct?
honest crypt
honest crypt
this is for the left direction <== I presume
No —->
simple musk
honest crypt
we can't start from the right side and get to the left side then
We start from both sides because its equivalent
simple musk
you are assuming a : b = r
honest crypt
you are assuming a : b = r
Yes so what
simple musk
this is left direction
honest crypt
Yes
simple musk
then a and b is divisible by r
honest crypt
So r = kb and r= ak’
simple musk
you could add a few lines of wording
honest crypt
then a and b is divisible by r
Yes
simple musk
like otherwise i need to overthink
honest crypt
you could add a few lines of wording
Math symbols are enough
honest crypt
like otherwise i need to overthink
If you overthink youll learn to not overthink much
simple musk
idk how you get to second line
balmy bane
that's directly from the definition of gcd
simple musk
if a is divisible by r and b is divisible by r, then r can be expressed as an integer times a
balmy bane
a:b, which is r, has to be a divisor of a and of b
So r divides a and r divides b
unless this notation is supposed to mean lcm
honest crypt
unless this notation is supposed to mean lcm
Nop its not
simple musk
if a is divisible by r and b is divisible by r, then r can be expressed as an in...
then, since r can be expressed as a certain amount of times a, you use this transitive argument to say gcd a,b is divisible by a
honest crypt
then, since r can be expressed as a certain amount of times a, you use this tra...
I didnt wrote a:b| r
I dont know where did u see it
simple musk
? i edited
balmy bane
First implication goes like this we know that $a:b | a $ and $a:b | b $( because...
Then this line is slightly wrong - it should be that a = kr and b = k'r for some integers k, k'
honest crypt
then, since r can be expressed as a certain amount of times a, you use this tra...
Yes just replaced the r with a:b
balmy bane
But you can remove that line and the argument still works
honest crypt
Then this line is slightly wrong - it should be that a = kr and b = k'r for some...
Wait rlly?
balmy bane
(well, r is a factor of a and of b
balmy bane
So if r is a factor of a, then r times something, say, k, is a; etc)
honest crypt
@simple musk second line is wrong
balmy bane
But you can remove that line and the argument still works
But otherwise - a:b = r => r|a is basically from the definition of "greatest common divisor"
simple musk
i understand that bit
simple musk
<@1187916384341078070> second line is wrong
what is second line exactly
balmy bane
This line - you can safely remove it
simple musk
this is why i hate skipping info like r | a => a = kr, because then it's easier to mess up
even if it's obvious, i didn't noticed the mistake neither
honest crypt
Nah i just forgot the gcd thing
simple musk
no, what i mean gcd(a,b) = r => r |a is clear
that's from the definition of gcd
now, it was skipped this implication r|a => a = k.r
there exists some k in Z, etc etc
from the definition of divisibility
what i mean is, skipping directly from gcd(a,b) = r => a = kr
instead of doing gcd(a,b)=r => r | a => a = k.r
honest crypt
i wanted to make sure u get it
simple musk
what i mean is like we shouldn't skip any info
otherwise filling the gaps in between is like, prone to errors, i missed that what you said was wrong for example
simple musk
no
gcd(a,b) = gcd(kr, k'r) = r.gcd(k,k')
i don't get the transitive argument you are saying
honest crypt
Its just a proof to why gcd(a,b) |a and b
simple musk
you are saying something like
r | a, and a | r so gcd(a,b) | a
balmy bane
no
honest crypt
Nop forget the a| r thats wrong
simple musk
but again, i cant manage to fill the gaps
balmy bane
There's literally no gap
honest crypt
a doesnt divide r
balmy bane
This is a definition
simple musk
a doesnt divide r
why do you write second line
honest crypt
why do you write second line
I gave you the correct proof
simple musk
you could've done,
gcd(a,b)=r
-> r | a and r | b
-> gcd(a,b) | a etc
honest crypt
I just wrote it in case you didnt know the def
But if u understand it u can read the rest
simple musk
yeah i think it tracks
calm coralBOT
@simple musk Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
regal crystal
calm coralBOT
potent lotusBOT
regal crystal
Guys why does infinite gp start from 2r I got confused
Is my solution going right?
velvet osprey
where do you think it should start from
regal crystal
I mean in all questions I was using the first term (a) as start here I just wrote soltuion and got confused in between also im sorry for my handwriting
I mean a part of me says (stupid ass it starts from 2r) but then again
like mid part I got confused
velvet osprey
i mean it does start from 2r
youve just got that 3 left over at the start
but you just keep it as is
regal crystal
oh yea I just understood thanks I just got confused im sorry it was stupid 😭
thanks @velvet osprey
do I close?
velvet osprey
if you got nothing else to ask about this question then yes
tall moon
$ABCD$ is a trapezium such that $AD\parallel BC$. $M$ is the midpoint of $AD$, and $C$ is reflected across $BD$ to get $C'$. $BM$ and $AC$ intersect at $N$, and $O$ is the intersection of $BD$ and ray $C'N$. Prove that $AO\perp BD$
potent lotusBOT
ihave<skissue>
tall moon
ive been staring at this and i have no idea what to do
angle chasing somehow? length bash cause we can get AON simm CC'N maybe (but i kinda doubt), or smth else??
either way i couldnt get progress
dusty crescent
Before reading the text I thought that C' is up in height from the picture lol
tall moon
what?
dusty crescent
anyway, this should be rather easy if you just follow along the angles, like, every division write out how you can express the new angles
tall moon
huh?? 😭
dusty crescent
Let's start with our trapezoid thingly
ABCD
We know <ABC + <BAD = 180°
and <BCD + <CDA = 180°
So let's just set <ABC = a, and <BCD = b
the upper angles are then 180° - a and 180° - b
mortal wren
geometry is so scary damn
tall moon
what are upper angles
dusty crescent
and you go from there until you get to <AOD = 90°
tall moon
??
quasi delta
and you go from there until you get to <AOD = 90°
CN has no property
dusty crescent
CN has no property
What?
mortal wren
So let's just set <ABC = a, and <BCD = b
nah dude i dont think this has variable game
i searched and ot showed menlaus theorem
did u apply that op
dusty crescent
One thing to note is that O is on the circle of A to D, so knowind that and knowin AMD is 180° you could prove from the circle angle theorem thingy that AOD is 90°, but you gotta prove that O is really on the circle
angle chasing could still work
What I mean wth the circle angle theorem thingy is like the central angle being twice of peripheral angle or something, idk ain't nobody got time to remember theorem name fr
tall moon
i searched and ot showed menlaus theorem
terrible at length bashing soo i couldnt really see the vision wih this
calm coralBOT
@tall moon Has your question been resolved?
tall moon
sorry gtg sleep!
rough walrus
Hello need help doing this I’ve been trying for the past 2 hours even using chat gpt but can’t get it
rough walrus
bleak rain
calm coralBOT
@rough walrus Has your question been resolved?
rustic osprey
Also what is j
engineer's version of i
rustic osprey
What is De Moivre's theorem
$(\cos \theta+i \sin \theta)^n=\cos n\theta+i \sin n\theta$
potent lotusBOT
Civil Service Pigeon
rustic osprey
duck 
blissful carbon
heloo
wise ore
Note that the circle is divided up into 24 sectors. A circle is also made of 2pi radians. This means that each sector is 2pi/24 radians or pi/12 radians. z is made of 8 sectors from the positive x axis meaning it has the angle 8pi/12 or 2pi/3
blissful carbon
Note that the circle is divided up into 24 sectors. A circle is also made of 2pi...
is that the only way
calm coralBOT
@blissful carbon Has your question been resolved?
karmic sage
Hi !!! I need help with "arithmetic sequence" because I have a math test tuesday...
grim nexus
Hi !!! I need help with "arithmetic sequence" because I have a math test tuesday...
arithmetic progressions?
karmic sage
yes
grim nexus
alright so the sequence of numbers with a common difference is an AP
like if you subtract any 2 consecutive terms of that sequence, you will find 1 common term which is the common difference
often noted as 'd'
and now comes all the formulas for AP lol
karmic sage
uhm.. I dont understand😭
marble pendant
can you share the ques you have a doubt in?
karmic sage
what even is AP?
grim nexus
can you share the ques you have a doubt in?
its a concept
grim nexus
what even is AP?
arithmetic progression
karmic sage
can you share the ques you have a doubt in?
wait.
marble pendant
its easier to explain with a ques
grim nexus
alright so the sequence of numbers with a common difference is an AP
^
ah wait it was a question all along?
damn
marble pendant
you have much to learn
grim nexus
honestly you have to memorizr this stuff ngl 😭
karmic sage
Exercise 1
Let the sequence (un) be an arithmetic sequence with common ratio r.
-
Given: u5 = 8, r = 3. Calculate u1, u20, and u101.
-
Given: u3 = 23, u8 = 7. Calculate r, u5, and u10.
-
Given: u7 = 4/3, u13 = 17/9. Calculate u0.
Exercise 2
Let the sequence (un) be defined by un = 7 − 3n.
-
Calculate u0, u1, and u2.
-
Prove that (un) is an arithmetic sequence and determine the common ratio of the sequence.
-
What is the value of the 51st term?
-
Calculate the sum of the first 51 terms.
here.
marble pendant
Exercise 1
Let the sequence (un) be an arithmetic sequence with common ratio r.
...
common ratio? arithmatic progression?
grim nexus
Exercise 1
Let the sequence (un) be an arithmetic sequence with common ratio r.
...
common ratio is in a geometric progression
karmic sage
common ratio? arithmatic progression?
uh yes arithmetic progression..
grim nexus
common difference is in an arithmetic progression
marble pendant
send a pic of the ques
grim nexus
either the q is wrong or thats a typo
karmic sage
karmic sage
raison is the number you add each time
grim nexus
alr so what have you tried?
^?
karmic sage
I dont understand Exercice 2
marble pendant
- or 2) or 3) or 4)?
karmic sage
1
marble pendant
to find u_0 you just need to put n=0 in u_n
karmic sage
No I dont understand n
grim nexus
No I dont understand n
substitute the value of n
karmic sage
oh okay
marble pendant
lets take the ap: 1, 4, 7, 11, ...
karmic sage
sorry if I sound stupid but what is U0
it could be anything tbh
grim nexus
it could be anything tbh
its only 1 value
firstly before you solve that, do you know what a general term is and how you can use it?
karmic sage
what do you mean anything?
I dont know how im supposed to guess what u0 is....
math is tiring
grim nexus
I dont know how im supposed to guess what u0 is....
the general term is given tho
you just have to substitute 0 in place of n
marble pendant
lets take the ap: 1, 4, 7, 11, ...
lets return to this example
can you write the general term for it?
karmic sage
uhm. u mean ..,exemple = u0 = 1 then u add 3 each time.??
so the general term
Is
un+3
I guess
Un+1 = un + 3
marble pendant
that is correct
karmic sage
thank u
marble pendant
but then if we want to know u_2 we need to know u_1
so we need to replace the u_n with something else
marble pendant
$u_2, u_1$
potent lotusBOT
Duck Man
marble pendant
represents subscripts
karmic sage
oh okay
karmic sage
bye
marble pendant
a_0 = 1
a_1 = 4
a_2 = 7
...
anyways it will be u_n = 3n - 2
karmic sage
so we need to replace the u_n with something else
u2 = un+1 + Uo * R?
karmic sage
anyways it will be u_n = 3n - 2
ohh okayy
grim nexus
do u have any video u could recommend to me?
id recommend you ask your teacher
cuz he/she would know better about what exactly to explain
karmic sage
id recommend you ask your teacher
The next time I see my teacher is tuesday. And I have a math test on tuesday...
remote mural
Organic chemistry tutor
karmic sage
what.
remote mural
karmic sage
okayy thank u!!
marble pendant
im sorry i have to go
calm coralBOT
@karmic sage Has your question been resolved?
flat flare
hiii
flat flare
<@&286206848099549185>
i found the pattern
but idk how to state it
its a triangular patter
the next term is gonna be
m = 0
and n = 2
and after that we'lll have
m = 3
and n = 0
and then so on and so forth
flat flare
so ummm state this pattern in some notation
flat flare
thanl u
bright tree
$\forall k \in \mathbb{N}$ there is $m, n \in \mathbb{N}$ such that$2 k=(m+n)(m+n+1)+2 n$.
potent lotusBOT
ben
bright tree
now the induction step
Assume there exist $m, n \in \mathbb{N}$ such that ^^ holds for some $k$.
Write $\mathcal{T}:=m+n$.
$$
2 k=\mathcal{T}(\mathcal{T}+1)+2 n
$$
We construct ( $m^{\prime}, n^{\prime}$ ) for $k+1$ by two simple cases.
Case 1: $m>0$.
Set
$$
m^{\prime}=m-1, \quad n^{\prime}=n+1
$$
Then $m^{\prime}+n^{\prime}=s$. so,
$$
\left(m^{\prime}+n^{\prime}\right)\left(m^{\prime}+n^{\prime}+1\right)+2 n^{\prime}=\mathcal{T}(\mathcal{T}+1)+2(n+1)=\underbrace{[\mathcal{T}(\mathcal{T}+1)+2 n]}_{=2 k \text { by }(\mathrm{H})}+2=2(k+1) \text {. }
$$
Thus $\left(m^{\prime}, n^{\prime}\right)$ works.
potent lotusBOT
ben
bright tree
this should suffice fr ya to complete the proof
flat flare
whats m and n prime supposed to be
bright tree
sorry i was supposed to label 2k=s(s+1)+2n H but did not
s id \mathcal{T}
jeez sorry i am typesetting too fast and making mistakes]
bright tree
hope this helped
bright tree
i'll be arounf here, its a drear eveny in ny here lol
flat flare
damn
calm coralBOT
Hello there
errant python
i get the explanation as to why for range... but i've encountered discontinuities a while and their ranges did not need to be unionized.. why is that?
like just recently, this one
rough arrow
What is your question? How to define the range?
thorny stump
[-4,3) U [2,4] = [-4,4]
errant python
i get the explanation as to why for range... but i've encountered discontinuitie...
why is the range union here
errant python
like just recently, this one
but the range here isnt?
errant python
yeah
errant python
like just recently, this one
but why is this not a union
errant python
[-4,3) U [2,4] = [-4,4]
why isnt this the answer
thorny stump
... what don't you understand about this equality
If the answer to a question is 7 you wouldn't say that it's 3+4, would you?
errant python
yes...
errant python
i get the explanation as to why for range... but i've encountered discontinuitie...
then why isnt the answer (-3, 5) here tho?
thorny stump
Because [-2,0] is not in the range
errant python
Because [-2,0] is not in the range
is it because they're hollow circles?
thorny stump
No
It's because there is no input to h that gives an output between -2 and 0 (included)
If the range was (-3, -2] U [0, 5) (solid circles at -2 and 0), then (-2,0) would not be in the range
errant python
wait, gnna think about how i understand this
errant python
If the range was (-3, -2] U [0, 5) (solid circles at -2 and 0), then (-2,0) woul...
is it a different story if its (-3, -2] U (0, 5) for instance (the 0 is a curly)
then therefore, it can be (-3, 5)?
thorny stump
... no, there's still a big hole, this time it's (-2,0]
errant python
It's because there is no input to h that gives an output between -2 and 0 (inclu...
why included when the illustration shows that the point in y = -2 and 0 are open?
really sorry if im dumb af here hjwqdjawbd
thorny stump
I'm saying there is no input that gives those points
errant python
I'm saying there is *no* input that gives those points
and to add to this
compared to something like this
this latter is within range?
because its between -5, and positive 1 correct?
thorny stump
What is
thorny stump
this latter is within range?
What is
thorny stump
I don't know what you mean 
errant python
and is the non existence of inputs shown by the fact that they're not overlapping?
rough arrow
Domain is all possible x-values, range is all possible y-values. Your solution explanations notes that with the red interval.
calm coralBOT
calm coralBOT
Available help channel!
calm coralBOT
pure kayak
seems okay at a glance
calm coralBOT
@delicate rune Has your question been resolved?
dusk iris
how do I solve this without l'hôpital
calm coralBOT
how do I solve this without l'hôpital
swift laurel
you could use the binomial series
dusk iris
https://tutorial.math.lamar.edu/Classes/CalcII/BinomialSeries.aspx
can you try and do it pls my memory got totally wiped after summer 😭😭
dark obsidian
https://tutorial.math.lamar.edu/Classes/CalcII/BinomialSeries.aspx
I left for an entire year and I come back to see you still helping people
What an absolute legend
🐐
calm coralBOT
@dusk iris Has your question been resolved?
dusk iris
bruh this is past midnight I'm dying
trail glacier
you probably won't get far like that. better off trying to explain your thought process and how you are thinking of approaching this question so people can point you in the right direction
dusk iris
you probably won't get far like that. better off trying to explain your thought...
at this point I just need someone to solve it for me so that I can see how to approach a problem like this in the future
trail glacier
at this point I just need someone to solve it for me so that I can see how to ap...
unfortunately that does not align with the intentions of the server. no one is asking you to solve it completely alone but your engagement and involvement is expected
dusk iris
unfortunately that does not align with the intentions of the server. no one is ...
I tried to solve the problem I've been on it for an hour now. How do I develop the expression using the binomial series
trail glacier
I tried to solve the problem I've been on it for an hour now. How do I develop t...
that's great! can you share what avenues you've explored? what have you tried so far? what ideas have come to mind?
dusk iris
that's great! can you share what avenues you've explored? what have you tried so...
well I've tried using l'hôpital, only to be told that I shouldn't use it, I tried solving it in a normal way, that didn't lead me anywhere, and now I'm trying the binomial series but I totally forgot about it so now I'm struggling
trail glacier
well I've tried using l'hôpital, only to be told that I shouldn't use it, I trie...
okay thank you
trail glacier
did you read the page linked above? Particularly the part under binomial series?
dusk iris
or even if it's correct
dusk iris
did you read the page linked above? Particularly the part under binomial series?
yup of course
trail glacier
great, can you find a way to express the root in the form (1 + f(x))^k
dusk iris
great, can you find a way to express the root in the form (1 + f(x))^k
well that's what I did and then it became what's in the last attachment I sent...
trail glacier
well that's what I did and then it became what's in the last attachment I sent.....
seems like you did some substitution there, i would recommend writing out the first few terms of the series and leaving it in terms of x
dusk iris
seems like you did some substitution there, i would recommend writing out the fi...
without changing the variable? it's just gonna be messier I can always keep the y and then substitute back
the problem is the 1/n
trail glacier
why is it a problem?
I think you will find it works out quite easily if you keep it in terms of x, try writing the first three terms in the expansion
dusk iris
I think you will find it works out quite easily if you keep it in terms of x, tr...
well that's the main reason I'm here, how do I write the first 3 terms
trail glacier
great, can you find a way to express the root in the form (1 + f(x))^k
first show me the root expressed in this form @dusk iris
trail glacier
okay great, now use the binomial series formula to get the first three terms
dusk iris
okay great, now use the binomial series formula to get the first three terms
I don't know how to use it when k=1/n 😭😭
trail glacier
which part trips you up
dusk iris
the development
trail glacier
the combinatorics?
dusk iris
I just need to know how to write the first term and I'll be able to do the rest
trail glacier
the page that was linked actually shows you the first four terms in terms of k and x
dusk iris
the page that was linked actually shows you the first four terms in terms of k a...
will it be the same with 1/n ?
trail glacier
yeah just substitute
dusk iris
alright imma try
trail glacier
k is any number
dusk iris
k is any number
I'm honestly not sure if what I did is right
trail glacier
I'm honestly not sure if what I did is right
looks somewhat correct
if you use this expression in place of the root, can you simplify it? cancel anything out?
dusk iris
oh and then now the 1s cancel out and I simplify by x leaving everything equal 0 except the -1/n
wait wait I think it's finally solved
trail glacier
my handwriting is awful but I think it's correct thanks so much
No problem, glad you were able to work it out
btw you can close the channel with .close if you dont need anything else
calm coralBOT
@dusk iris Has your question been resolved?
dusk iris
.close
calm coralBOT
calm coralBOT
Available help channel!
earnest dove
Can anyone help with stoichiometry math
calm coralBOT
Can anyone help with stoichiometry math
old plume
Question?
earnest dove
Did I do this right
steep zinc
,rccw
potent lotusBOT
jolly pilot
32.07 is for S, and your moles are for S_8
earnest dove
So id do 32.07 times 8
jolly pilot
yea
Afterall, the reaction consumes equal moles of atomic zinc and sulfur
Number of Zn atoms must match the number of S atoms
jolly pilot
your reaction utilizes 8 Zn atoms and 8 S atoms
S_8 is just 8 separate sulfur atoms
and 8 Zn is obv 8 separate zinc atoms
and one of each combine together to form a single ZnS
jolly pilot
so number of Zn atoms involved in this needs to be same as number of S atoms (not S_8 molecules) to balance the reaction
jolly pilot
With converting mol to gram of s
yea
earnest dove
Okay thank u
calm coralBOT
@earnest dove Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
arctic dirge
@mossy furnace sorry for the ping but I wanted to ask when you said “It's not just analogous, it's the same thing. The topology induced by a metric is the topology generated by the basis of open balls, by definition.”
arctic dirge
Is that topology induced known as a standard topology?
This is the video that defined a standard topology for R^d
mossy furnace
I've mainly heard the term "standard topology" in reference to R^d
arctic dirge
Ah so it’s the topology induced by the Euclidean metric
mossy furnace
Yes
arctic dirge
.close
calm coralBOT
calm coralBOT
Available help channel!
latent gulch
calm coralBOT
jolly pilot
why is my answer different from mark scheme
explain this
latent gulch
oops
i just realized that
😭
thankyou thankyou so much
i will try to fix
wait so how to integrate sin^3x
jolly pilot
substitute the relation in part 1
then you get integral of sinx and sin3x
literally what you did here
lmao
jolly pilot
you got the idea right
but you substitiuted the wrong thing so the answer you got is wrong
latent gulch
wait i dont get it
latent gulch
but you substitiuted the wrong thing so the answer you got is wrong
is the "-4" supposed to stay in place?
like only substitute the sin^3(x)
jolly pilot
no, that -4 is the consequence of your previous mistake
you are only suppposed to integrate sin^3(x)
you took that as sin(3x) and applied the result of part 1
thats why you messed up
latent gulch
ohh
ok i will try to redo
thankyou so much
im still getting the same answer
wait what is wrong
jolly pilot
literally what you did here
girl you literally got the correct answer before
just divide this whole thing by -4
jolly pilot
why do you still have this? 😭
latent gulch
OHHH
jolly pilot
just read it once? for me? please? 🥺
jolly pilot
no, thank you 😭
jolly pilot
np
latent gulch
.close
foggy storm
i need some help with this limit, it has to be done with the ratio test
unkempt drift
i need some help with this limit, it has to be done with the ratio test
are you sure you need to do it with the ratio test?
the root test should work
foggy storm
are you sure you need to do it with the ratio test?
yes
unkempt drift
okay, what did you get when you tried to apply the ratio test?
do you have your working on a piece of paper?
foggy storm
unkempt drift
no, that's not how you do the ratio test
$a_{n + 1} = \sqrt[n + 1] {\frac{(n + 1)\ln (n+1)}{(n+1)^{\ln (n+1)}}}$
potent lotusBOT
south
foggy storm
i mean its written Xn>0
unkempt drift
i mean its written Xn>0
fair enough
okay I checked and the ratio test gives L = 1, so it's inconclusive
we need to use another test
I think that means you should use this test
foggy storm
i havent learnt this one yet, the professor said it has to be done with the root test
unkempt drift
i havent learnt this one yet, the professor said it has to be done with the root...
ask your professor how to do it then
cause the root test clearly gives inconclusive
foggy storm
ask your professor how to do it then
would've, but i want to understand it before class
thats why i ask for help
unkempt drift
would've, but i want to understand it before class
your professor has given you a problem that cannot be done with what you have learnt in class
mortal wren
that's the root test!! (the one on the 2nd line)
thats ratio definitely
unkempt drift
thats ratio definitely
the one on the 2nd line?
mortal wren
first
unkempt drift
your professor has given you a problem that cannot be done with what you have le...
if it doesn't work with the root test, then it also can't work with the ratio test
calm coralBOT
calm coralBOT
Available help channel!
blazing coyote
calm coralBOT
blazing coyote
so I was thinking this can be re-written as
jade fractal
what is 1/2n
how is it confusing
blazing coyote
I think it's (1/2)n
last lantern
1/2 times n or 1/(2n)
jade fractal
I think it's (1/2)n
it’s 1/(2n)
last lantern
yeah probably
blazing coyote
how is it confusing
right
last lantern
or else it would say n/2
solemn steeple
n tends to what?
blazing coyote
only then will it converge to 1
blazing coyote
n tends to what?
infty
solemn steeple
1
jade fractal
use exp
last lantern
$=\sqrt[2n]{3n}$
potent lotusBOT
Allen
blazing coyote
what now
potent lotusBOT
Médicis
last lantern
ohhhh
blazing coyote
pull out the 3?
well, that's what I was thinking
last lantern
since 1/(2n) goes to 0, so it is just 1
jade fractal
since 1/(2n) goes to 0, so it is just 1
you can’t do that
mortal wren
take log?
jade fractal
since 3n goes to infinity
mortal wren
log will take that 1/2n down
glass heart
have you done the limit n^(1/n)
blazing coyote
It's more like ((3)^{1/n})^1/2->1
glass heart
if yes, try to use that one
last lantern
but why can’t you break that into 2 roots
last lantern
but why can’t you break that into 2 roots
(I’m not an expert in limits)
blazing coyote
(I’m not an expert in limits)
you can?
last lantern
but they said i can’t
blazing coyote
where
blazing coyote
1/(2n)->0 doesn't work as justification here
last lantern
i think so
calm coralBOT
calm coralBOT
Available help channel!
tardy adder
Prove that HCF(a,b,c) = [abc * LCM(a,b,c)]/[LCM(a,b) * LCM(b,c) * LCM(a,c)]
nimble harbor
holy
[ HCF(a,b,c) = \frac{[abc \cdot LCM(a,b,c)]}{[LCM(a,b) \cdot LCM(b,c) \cdot LCM(a,c)]}]
potent lotusBOT
k
tardy adder
Let (x,y) = HCF(x,y) and [x,y] = LCM(x,y)
Obsersations:
(a,b,c) = ((a,b), c) = ((a,c), (b,c)) = (a,c) * (b,c) / [(a,c), (b,c)]
Now we can write (a,c) as ac/[a, c] and (b,c) as bc/[b, c]
sleek vessel
Yeah that seems like it'll work
tardy adder
We get (a,b,c) equal to "numerator = abc^2, denominator = [a,c] * [b,c] * [(a,c), (b,c)]"
Now I am stuck
Not really stuck but I THINK I need help and therefore I came to ask for some apparent help
(Ignore this vague message)
sleek vessel
[(a,c),(b,c)] is the same as [(a,b),c] right
sleek vessel
Nvm only the same brackets can do that
I'd recommend expanding the brackets one at a time
You are familiar with this right
$HCF(a,b) \cdot LCM(a,b) = a \cdot b$
potent lotusBOT
Xavier 🌺
tardy adder
yeah
sleek vessel
And $HCF(a,b,c) = HCF(HCF(a,b),c)$
potent lotusBOT
Xavier 🌺
sleek vessel
Same with LCM
I'd start with substituting and seeing where that gets you
The end goal is to replace all the HCFs with LCMs
calm coralBOT
@tardy adder Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
junior sleet
can anyone solve
calm coralBOT
can anyone solve
spice venture
could u provide a translation if possible
spice venture
d(by/4)?
fickle musk
d(π/4)?
junior sleet
yes
spice venture
what problem are u facing
fickle musk
this i mean
Okay
junior sleet
i want to slove it
calm coralBOT
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 are you familiar with the chain rule
junior sleet
1
fickle musk
Well are you familiar with the chain rule
@junior sleet
junior sleet
no
pale blade
time to read then: https://tutorial.math.lamar.edu/classes/calci/chainrule.aspx
empty quail
,tex .diff rules
potent lotusBOT
Aκιρɑ
pale blade
<@&268886789983436800>
calm coralBOT
@junior sleet Has your question been resolved?
hexed nebula
can anyone solve
ذا سؤال تحصيلي؟
blazing coyote
A deck numberd 1 though is throughly shuffled so that all possible n! orderings can be assumed to be equally likely. Suppose you are to make $n$ guesses sequentially where the ith one is a guess of the card in position $i$, Let $N$ denote the number of correct guesses.. If you are not hoben any information about your earlier guesses, Show that for any stategy $E[N]=1$
potent lotusBOT
wai
blazing coyote
uh, so I take an infinite sum
sleek vessel
Why
Again use linearity of expectation
What are the chances of you guessing one card right
blazing coyote
What are the chances of you guessing one card right
1/N
calm coralBOT
calm coralBOT
Available help channel!
royal flame
how can i tell if it diverges or converges, i only studied partial series and geometric
royal flame
is it divergency test
ocean cypress
Try the limit comparison test with the harmonic series
pale blade
just use the divergence test
calm coralBOT
@royal flame Has your question been resolved?
hardy spindle
calm coralBOT
hardy spindle
to find a can i replace any coordinate with x and y?
does it matter if i choose (-77,0) or (0,14)
remote mural
whats a
hardy spindle
its increasing
hardy spindle
sorry
spiral crow
What is a?
hardy spindle
-2
spiral crow
Ah
calm coralBOT
@hardy spindle Has your question been resolved?
hardy spindle
.close
reef solar
hey any movie recommendations ?
calm coralBOT
hey any movie recommendations ?
untold flint
!noping
calm coralBOT
Please do not ping individual helpers unprompted.
untold flint
what about not pinging do you not understand?
elfin dragon
alright bro youre getting banned...
reef solar
euh what
untold flint
also, now, I'm going to give you a chance to tell us what your original math question is
reef solar
you know how a triangle
elfin dragon
you know how a triangle
🤦
ocean cypress
!da2a
calm coralBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
untold flint
i know my triangles. what about them
reef solar
what about not pinging do you not understand?
i didn't know sorry it won't happen again
ocean cypress
!xy
calm coralBOT
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.
reef solar
i know my triangles. what about them
you euh the big one what's it called
oh fuck sorry
i didn't know that counted as a ping
elfin dragon
fox this kid is clearly trolling
reef solar
woops
elfin dragon
time for a timeout
elfin dragon
he joined TODAY
reef solar
my mathematical companions please do turn against me !
untold flint
I'm no mod, but if you don't keep this help channel on topic, I'll modping anyway
reef solar
please nooooo pleaseeee
untold flint
now, state your original question in full, without pinging.
reef solar
There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
that is my math question
untold flint
and you need a movie for this, why?
reef solar
figure this one out
untold flint
figure this one out
!noans
calm coralBOT
figure this one out
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.
elfin dragon
There are 49 dogs signed up for a dog show. There are 36 more small dogs than la...
impossible.
reef solar
the movie is to entertain me while i do mathematics
sleek vessel
hey any movie recommendations ?
<@&268886789983436800> troll
elfin dragon
fox surely its time to ban
untold flint
untold flint
and yeah the modping
untold flint
fox surely its time to ban
I'm not a mod
reef solar
i DID ask a math question tho ! please
reef solar
is love math just as much as the next guy i swear on pythagora !
stark sparrow
Please don’t troll, only math questions go here
reef solar
i DID ask one tho
elfin dragon
ive told him that lance
stark sparrow
If you want movie recommendations we have great social channels
elfin dragon
he wont listen
reef solar
im so listening !
stark sparrow
If you do this again you will get the opportunity to have a a few hours off mathcord
elfin dragon
im so listening !
SHUT UP
reef solar
got my listening cap on
stark sparrow
.close
calm coralBOT
reef solar
.reopen
calm coralBOT
✅ Original question: #help-42 message
stark sparrow
<@514542702013186049> surely WE have seen enough
You don’t need to minimod.
elfin dragon
heh...im just doing my job
reef solar
if julie has 7 apples and mark has 4 oranges and james takes two apples from julie and three oranges from mark how many apples does julie have ?
elfin dragon
if julie has 7 apples and mark has 4 oranges and james takes two apples from jul...
5
.close
reef solar
that was an easy one
reef solar
you just got lucky
untold flint
but
reef solar
is my channel being closed
elfin dragon
elfin dragon
untold flint
.close (irrelevant conversation)
<@&268886789983436800>
calm coralBOT
reef solar
guys