sheeeeeeesh
#help-42
mint verge
good
woeful basin
how ddi you do it
woeful basin
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blazing coyote
trying to find the number of solns $arcsin(sin(x))=x$ has in $(0,2\pi)$
potent lotusBOT
Why am. I here
blazing coyote
so between(0,pi/2), x=sin(x) only happens at x=0
which we neglect
now for x belonging to 0,π
sin(π-x) =sin(x)
so π-x=x
or x=π/2
for x belonging to (π,2π) I pressume I use (sin(2π-x))=-sin(x)
clever ruin
Hate to break it to you but this has infinite solutions
blazing coyote
in 0,,2π?
clever ruin
Yea
blazing coyote
oh
clever ruin
Every value is a solution
clever ruin
$\arcsin(\sin(x))=x$ is an identity
potent lotusBOT
Max
clever ruin
Ah okay
potent lotusBOT
Why am. I here
blazing coyote
so when x is between 0 and π/2, the only sol is at 0, which isn't in the domain
hmm, I'm guessing I graph it to solve it
doesn't look like it can be solved algebrically
clever ruin
Yeah it can't
$\arcsin(\sin(x))=\sin(x)\Rightarrow \sin(x)=\sin(\sin(x))$. Set ,$u=\sin(x)$ and we get $u=\sin(u)$ which doesn't have exact solutions
calm coralBOT
potent lotusBOT
Max
clever ruin
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blazing coyote
Maybe it has just 1 solution?
it has 5 according to my book
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quartz breach
hi
quartz breach
lets say we have a function called f(x)
how do i find h(x) such that h and f are symmetrical based on a line like -5x + 2
(sorry for the bad english i did not know the correct verb)
as an example f(x) = sqrt(x) and h(x) would be x^2. in this case the line is y=x but what if it was y=-5x+2
(I just came up with moving the coordinates so it would be something similar to -5x but idk how to the rest)
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quartz breach
<@&286206848099549185>
rigid cedar
so you want it be f(x) = h(x) such that h and f both follow line y=x ? or on line -5x+2=y?
rigid cedar
<@&286206848099549185>
yeah
quartz breach
but what should i do if its anything else than just x
rigid cedar
the 2nd one you can try by getting value for x in the eqn given
quartz breach
oh no you got my question wroung I guess
f and h are not equal
they are symmetrical
based on a line
like -5x + 2
quartz breach
for example f and f^{-1} are symmetrical and the line is y=x
but what if the line was something else
rigid cedar
i can only think of hit and trial for that
by finding points on the line -5x+2=y
or whatever line is given
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olive wigeon
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olive wigeon
how do i solve this question
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olive wigeon
then find tan of the angles in botht the triangles
how do i use tab tho cuz idk what opposite is
tan
ocean jacinth
you can split the length 60m in two (not halves but in two)
tan(angle) = one part / x
where x is the length you are trying to find
my working could be wrong but if you want to know my thinking process open the spoiler
||tan18 = (60 - y)/x
tan14 = y/x
xtan18 = 60 - y
xtan14 = y
xtan18 + xtan14 = 60
solve for x||
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steep nest
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glass heart
what are gamma(2), gamma(3), gamma(4) ?
steep nest
why do those matter?? aren't we only looking at gamma(1) coz it says specified
glass heart
how should the other ones not matter
specified by gamma(1) means that you can compute them from knowing gamma(1)
steep nest
could you explain why they matter pls?
steep nest
what are gamma(2), gamma(3), gamma(4) ?
haven't been told
glass heart
what does it mean if gamma is a group homomorphism
steep nest
if gamma is a group homomorphism from G to H, where G and H are groups with not necessarily the same operations then with any a,b from G and and any c,d from H you get gamma(a [G's operation] b) = gamma(c) [H's operation] gamma(d)
right?
glass heart
ok so then what is gamma(2) = gamma(1+1)
steep nest
why did you choose 2?
glass heart
because its 1+1
glass heart
I wrote gamma(2) in the form gamma(1+1) to get you to see what you can do
to find out what value it has
steep nest
ok so getting past the you don't only have to put 1 into gamma
gamma would make 0 from Z_4 equal to ("mapping") 1 from U_5 for injectivity
glass heart
ok so getting past the you don't only have to put 1 into gamma
gamma would make ...
I dont know what that sentence is supposed to mean
glass heart
gamma(0)=1 because gamma is a homomorphism
do you mean that?
I am still asking what gamma(2) is
glass heart
yes. gamma(2) = 3
no
gamma(2)=gamma(1+1)=gamma(1)*gamma(1)
because gamma is a homomorphism
steep nest
so the "1+1" you just look for elements in H that make up 2 under multiplication?
what
it's confusing me coz gamma is only taking in one element instead of two
glass heart
so the "1+1" you just look for elements in H that make up 2 under multiplication...
why in H
glass heart
it's confusing me coz gamma is only taking in one element instead of two
and I never give it two elements. I dont know what you mean
gamma is a group homomorphism
like you said, that means gamma(a+b)=gamma(a)*gamma(b)
now I choose a=b=1
then gamma(1+1)=gamma(1)*gamma(1)
so gamma(2)=3*3
steep nest
like you said, that means gamma(a+b)=gamma(a)*gamma(b)
yh, it always takes 2 elements
steep nest
now I choose a=b=1
why are both a and b 1, did you decide that?
glass heart
"I choose"
glass heart
yh, it always takes 2 elements
thats not what it means to take two elements
steep nest
what does it mean to take two elements?
glass heart
if it was something like gamma(x,y)
steep nest
oh right. so what's the right term? though "a+b" is one thing, its result, a and b can be two different elements from the group
but sure a=b=1 for now
glass heart
a+b is just one thing
steep nest
yh
glass heart
it cant be two different elements
steep nest
ik
glass heart
ok I misread
but yes, a=b=1 for now
and from that we can find out what gamma(2) is
steep nest
idk what you mean when you ask me that
for homomorphism here, gamma(a+b)=gamma(a)*gamma(b). yh, we agree
but i'm checking for isomorphism, we needa know it's both injective (that gamma(a) = gamma(b) ) and surjective (that gamma(x) = y, where y is any element in the codomain)
glass heart
before we can check that, how we find out what gamma actually does as a function
how should we be able to check whether a function is injective when we dont even know what gamma(2) is
steep nest
ok, so we're checking gamma is a homomorphism even tho it already tells us?
steep nest
alr, given gamma(a+b)=gamma(a)*gamma(b)
left hand side -> gamma(a+b)
right hand side -> gamma(a)*gamma(b)
LHS
gamma(2) = gamma(1+1) where 1,2 are in Z_4
RHS
gamma(2) = gamma(1) * gamma(2) where 1,2 are in U_5
glass heart
no
the things inside of gamma are always in Z_4
gamma(something) is then as a result always in U_5
steep nest
😫
oh ok
LHS
gamma(2) = gamma(1+1) results in 2 where 2 is in U_5
RHS
gamma(2) = gamma(1) * gamma(2) results in 2 where 2 is in U_5
glass heart
how do you know it results in 2
from where is that coming from
and the second line should say gamma(2)=gamma(1)*gamma(1)
steep nest
coz gamma(1) * gamma(2) = 1*2
steep nest
and the second line should say gamma(2)=gamma(1)*gamma(1)
why
glass heart
coz gamma(1) * gamma(2) = 1*2
from where
gamma(1)=3
and gamma(2) you dont know yet
steep nest
ok 🤨
forgor about the a=b=1
lemme try again
LHS
gamma(2) = gamma(1+1) results in 2 where 2 is in U_5
RHS
gamma(2) = gamma(1) * gamma(1) results in 1 where 2 is in U_5
but then 2 != 1 UGHHH
glass heart
you are trying to guess what the things result in
instead of using that you know that gamma(1)=3
glass heart
gamma(1)=3 is given
steep nest
ok
the frustration is not helping, i'm not thinking clearly :c
uhh
lemme drink water
back
wait is it 4?
gamma(2) = 4?
idk i'm iterating through
steep nest
ok, using this
lemme take a new pic
we've been told gamma(1) = 3. that's a starting point
so just iterate through and map the rest ?
steep nest
sadge
steep nest
yh
steep nest
yh
steep nest
oh
ok using that. for a=1, b=2, gamma(3) = gamma(1) * gamma(2) => gamma(3) = 3*4 mod 5 ?
so 2
glass heart
yes
steep nest
ok, chilling
now isomorphism
we needa know it's both injective (that gamma(a) = gamma(b) ) and surjective (that gamma(x) = y, where y is any element in the codomain)
glass heart
those arent really the definitions of injective and surjective. but you might mean the correct thing
steep nest
ik, more monomorphism and epimorphism
glass heart
not what I meant
glass heart
injective means that gamma(a)=gamma(b) implies a=b
surjective means that for all y you can find an x with gamma(x)=y
steep nest
mhm, ik
i said that, just didn't include the "implies a=b"
glass heart
"I just didnt incldue the actually important bit"
steep nest
ok using that. for a=1, b=2, gamma(3) = gamma(1) `*` gamma(2) => gamma(3) = 3`*`...
is this commutative btw, generally? if a was 2 and b was 1, would gamma(3) still be 2?
glass heart
try it out
steep nest
true, but what about generally
glass heart
if gamma is a homomorphism, then no matter how you write 3=a+b, you will always get the same thing for gamma(3)
steep nest
asking coz if we were working with a matrix group under multiplication, we wouldn't have the luxury of commutativity
glass heart
indeed we wouldnt have
steep nest
🙌
injective means that gamma(a)=gamma(b) implies a=b
surjective means that for all y you can find an x with gamma(x)=y
injective?
a= 0, b = 0, gamma(0) = gamma(0) => 0=0
how is it 'implying' when i'm the one having to make sure a=b, huh
surjective?
this time, do the elements gamma takes in have to be in the codomain?
glass heart
lets be more precise: surjective means: for all elements y in the codomain there is an element x in the domain with gamma(x)=y
for injective, can you find different a,b with gamma(a)=gamma(b) ?
if not, then gamma is injective
steep nest
injective
a = 1, b = 2
gamma(1) = 3, gamma(2) = 4 (using gamma(a+b)=gamma(a)*gamma(b) from the homomorphism part). 3 != 4 so it's injective?
glass heart
well you need to check all pairs of a,b
glass heart
wdym backwards
glass heart
https://lh3.googleusercontent.com/pw/AP1GczPzqowdtzJSEeYAwgjn7AQBQhX_p3NHAL-I9xb...
I hope you have this picture fully filled out by now, yes?
injective means: no arrows point to the same thing
surjective means: every element on the right has (at least) one arrow pointing to it
steep nest
gamma(x) = 1
gamma(x) = 2
gamma(x) = 3
gamma(x) = 4
that doesn't help me find x
steep nest
I hope you have this picture fully filled out by now, yes?
correctly? no
steep nest
a=0,b=0, gamma(0) = gamma(0)*gamma(0) ??
glass heart
0=1+3
steep nest
ugh, modulo arithmetic 😫
a=1,b=3, gamma(0) = gamma(1)*gamma(3) => 3*2 = 1
okay cool. diagram filled
want a pic?
what would it look like if it wasn't surjective. would-- ohh, nvm
thank you!!
gonna reexplain this to myself later on notes. but gonna move on to next question. will prolly be back asking for help again 😅
byee
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quasi bane
can someone help?
calm coralBOT
can someone help?
quasi bane
I've assigned a 2x2 matrix B = (a b c d) and solved the inner product to get that 5a+3d=b+4c, but I don't know how to continue from here or even if I'm right
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untold compass
looks like it'd be 5a+3d+b=4c instead, but yea after that you can just pick numbers that work, there's a bunch of freedom. it comes from M2 being a 4-dimensional space so the stuff orthogonal to a vector would span 3 dimensions
remote mural
heyy im not sure like what to do there im sooo cnfussed, the answer choices are 'must be congruent' or 'are not necessarily congruent' 😭
swift laurel
think about what needs to be the same between two triangles for them to be congruent
swift laurel
think about how many sides and angles you need to know two triangles are congruent(see https://www.mathsisfun.com/geometry/triangles-congruent-finding.html if you need a refresher)
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inland pawn
im having trouble knowing what equations to use to find a
i keep getting alpha r but the answer is B and i dont know why its not alpha r
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chilly oak
am i messing up something?
calm coralBOT
am i messing up something?
chilly oak
for 1c
stray tundra
am i messing up something?
(4-lambda) at the very beginning
that needs to go in parenthesis
also on 2nd to last line: (lambda = L)
4-8L+4L^2-L+2L^2-L^3+2-2L
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hasty creek
how do i solve this?
calm coralBOT
how do i solve this?
hasty creek
im a bit confused
i know how to eliminite the parameter, but im not sure how to do this
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steep nest
can someone explain this please?
calm coralBOT
can someone explain this please?
dense pewter
You need to check if the matrix is indeed a group homomorphism
It needs to map unit to unit, and to distribute over group multiplication
dense pewter
If that's how you read the first line, then yes, I'm not familiar with that notation
steep nest
oh ok
it's not a matrix btw
it's a permutation
how do i know C_3's respective group operation?
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solemn plover
im used to shrinking a spanning set when they are vectors, how do I do it for matrices?
pallid halo
it works the same way
solemn plover
you can "stretch" the matrices into vectors
how?
pallid halo
i.e. treat them as 4-dimensional vectors
solemn plover
do I just make a 2x10 matrix?
like this?
pallid halo
no
solemn plover
i.e. treat them as 4-dimensional vectors
ah
glacial raven
I used induction on this question but the furthest I got is to 2-((1/x)^(k+1))*(3k+5), where the induction RTP is 2-((1/2)^(k+1)) (k+3). Am I missing anything? Thank you!
glacial raven
i know the process of induction, it is just that when I tried to prove for k+1, it just doesn't come back to the RTP
lol somebody helllp
thx
patent tundra
I used induction on this question but the furthest I got is to 2-((1/x)^(k+1))*(...
You should write using equations
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north plover
hi how can you tell angle CAF and angle DAB are 15 degrees?
calm coralBOT
hi how can you tell angle CAF and angle DAB are 15 degrees?
north plover
the answer sheet doesnt provide any explanation aside from "this is because ABC is equilateral"
amber wedge
well whats the measure of angle daf
north plover
90
amber wedge
yeah
calm coralBOT
amber wedge
oh congrurent
wcongruent traingles
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tidal geyser
how do ik which one will be negative ( num or deom )
calm coralBOT
how do ik which one will be negative ( num or deom )
idle marten
wdym
tidal geyser
like
idle marten
-1/3 = 1/-3
idle marten
it's the same thing
if you did positive 12 and negative 5 you would end up with the same tan
oh
tidal geyser
huh
idle marten
sin(x) is negative
surreal patio
it's the same thing
they are probably asking how do they know which quadrant it lies in , QII and QIV both have tan negative
tidal geyser
yeah
idle marten
how do ik which one will be negative ( num or deom )
for the second problem
sinx is positive which means the numerator of sin/cos is positive
tidal geyser
i'll just ask my teacher
idle marten
i'll just ask my teacher
tan(x) = sin(x)/cos(x) right
tidal geyser
never learned tht
tidal geyser
yes
idle marten
and sin(x) is opposite/hypotenuse right
tidal geyser
yesh
idle marten
hmmm
if tangent is a negative number
either the opposite side or the adjacent would have to be negative right
idle marten
the hypotenuse is always a positive number so if sin(x) is negative, opposite would have to be negative
idle marten
because a^2 + b^2 = c^2
tidal geyser
yeah
tidal geyser
pytho theorum
tidal geyser
they are always positive
yeah
idle marten
do you understand now
idle marten
how do ik which one will be negative ( num or deom )
ok walk through the 2nd problem
idle marten
yeah cuz -1/1 is -1
tidal geyser
and tan= 1/1 does that mean tan is positive?
idle marten
1/1 = 1
idle marten
how do ik which one will be negative ( num or deom )
if opposite/hypotenuse is positive
what
yes
tidal geyser
ok
idle marten
if opposite/hypotenuse is positive
what is adjacent/hypotenuse
idle marten
yeah but is it positive or negative
tidal geyser
where did u get cos from
idle marten
what do you mean
tidal geyser
in number 2 cos was never mentioned
idle marten
how do ik which one will be negative ( num or deom )
oh ok
so basically
is sin is positive
tidal geyser
only tan and sine
idle marten
the opposite side and the hypotenuse
MUST be positive right
since tan = opposite/adjacent
tidal geyser
yes
idle marten
the adjacent side MUST be negative if the opposite side is positive
and tan is negative
does that make some sense
tidal geyser
uh
idle marten
if tan is negative, either the opposite side or the adjacent side is negative
since the hypotenuse is always positive, knowing whether sin or cos is positive will tell you what side is negative
since if sin is negative, opposite is negative
or if cos is negative, adjacent is negative
tidal geyser
i cant understand this rn but ill just ask my teacher later today
ty tho
much appreciated
idle marten
👍
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empty tartan
In the last line, why do they replace w with -w, and why does it hold true also for -w
lethal sail
on the left and right hand sides of the inequality you have an absolute value of w so changing w to -w wouldnt do anything
as for why, i dont know if there is an intuitive geometric implication, but replacing the w with -w makes it the reverse triangle inequality which is useful for some proofs in real analysis
lethal sail
yeah i guess, you understand why tho right?
empty tartan
can w be a negative number here?
lethal sail
yes
empty tartan
cuz if so, i guess i understand but if not, then wouldn't the left most expression be strictly equal to the middle one
ah
wait no what i said is wrong too
lethal sail
z or w being negative wouldnt affect the left or right hand sides of both inequalities
empty tartan
but i can definitely think of cases where the left on isnt less than or equal to the middle one
for example z=-10 and w=1
oh wait
no
hmm, yeah i guess i see why it works
thanks
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sturdy sequoia
I have a somewhat stupid question I don't understand how we can go from this equation
sturdy sequoia
to this equation
brazen elbow
multiply both sides by $-\frac{x}{y^2}$
potent lotusBOT
FungusDesu MSC2020 34A05
brazen elbow
that doesnt change anything
idle marten
mb
sturdy sequoia
multiply both sides by $-\frac{x}{y^2}$
Sorry but I don't understand how you see this 😦
idle marten
the way I saw it was subtracting y^2cosx
brazen elbow
Sorry but I don't understand how you see this 😦
you can see it went from y'1/x to -y'/y^2, which is fairly obvious
sturdy sequoia
the way I saw it was subtracting y^2cosx
oooooooooo I'm so stupid thank you
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ebon narwhal
\
pure kayak
you can just say pi, if you know latex then \pi
ebon narwhal
A- Πrh =Πr^2
pure kayak
capital pi, nice
ebon narwhal
lol
pure kayak
why did you choose to move pi rh across?
ebon narwhal
because i want to make h the subject
pure kayak
i know, but why not move pi r^2
ebon narwhal
so make it A-Πr^2 = Πrh?
pure kayak
that would be a better choice yes
pure kayak
elaborate
ebon narwhal
so A-Πr^2/Πr = h?
pure kayak
brackets, but yeah that works
pure kayak
np
ebon narwhal
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remote mural
Why step 4?
calm coralBOT
Why step 4?
proper igloo
it is the condition for SHM
remote mural
I don’t understand how that came into being
proper igloo
do you need the proof for it (I remember it in the case of linear SHM but not for angular)
remote mural
I kind of understand it in linear but not angular
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pearl skiff
i think it's because the question requires 
strange schooner
umm can anyone help me with this
so for inverse proportion we use y/x=k ryt ,so instead of that can we do y=kx
pearl skiff
but seriously, for situations that are harder, using inverse to solve would be faster than solving those equations one by one
and hoping for an elimination
pearl skiff
A*A^-1 = I
as team132 have said
strange schooner
no for the constant
pearl skiff
so for inverse proportion we use y/x=k ryt ,so instead of that can we do y=kx
! occupied
calm coralBOT
so for inverse proportion we use y/x=k ryt ,so instead of that can we do y=kx
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).
patent tundra
so for inverse proportion we use y/x=k ryt ,so instead of that can we do y=kx
!occupied
calm coralBOT
so for inverse proportion we use y/x=k ryt ,so instead of that can we do y=kx
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).
pearl skiff
we have A•A^(-1) = I where I is the identity matrix
so, if we multiply both sides by A^(-1) from the left
we have
A^(-1) A (x,y) = A^(-1) (11,-4)
therefore we have
I (x,y) = A^(-1) (11,-4)
recall:
so we have
( x ) = A^(-1) (11)
( y ) (-4)
i think that's where you didnt understand
x means the vector x
(x)
(y)
we usually write these equations in such form
Ax=b
where A is a matrix
x and the vector with all unknows
and b is a vector of the number on the right hand side
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light iron
Hey, I want to calculate specific chances. Here is an example:
You have a bag full of pearls. One of the 20 pearls is black and the other 19 are white. Now you draw one after another each random pearl out until you reach the black pearl. So it would be first pearl 1/20, second 1/19 and so on.
How would I calculate the whole chance of the black pearl being the last one as example? It would ofc be 100% for the last one, but unlikely to be the last one if you calculate the chance of the entire event happening.
light iron
it's equal everywhere
But the chances are increasing for it being the black pearl, so it would be more unlikely to draw the black pearl as first one with 5% or as second one with a chance of 5.2% and before already having the 5% chance.
amber bolt
yes
that happens too
both are true
,calc (19/20)(18/19)(17/18)(16/17)(15/16)(14/15)(13/14)(12/13)(11/12)(10/11)(9/10)(8/9)(7/8)(6/7)(5/6)(4/5)(3/4)(2/3)(1/2)
potent lotusBOT
Result:
0.05
Oh, that makes sense. Thank you!
amber bolt
the chance is larger if you know it's not at the start, which you realize after looking
the chance is equal everywhere before you start looking
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steep apex
How to workout volume of a cylinder with already with cross sectional area
steep apex
How do I workout volume of a cylinder with the cross sectional area already given to me
onyx bloom
you multiply it by the depth of the cylinder
potent lotusBOT
frgo
potent lotusBOT
frgo
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frigid gate
what are the total number of ways of rolling an 11 from 5 dice?
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frigid gate
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torpid vine
What about Permutations
I remember somebody had a similar question to this and they said Generating Functions
frigid gate
yeah it was me but no one helped unfortunately
torpid vine
So do you need to create a generating function for the scenario and then use a partial sum equation
frigid gate
yeah
torpid vine
Hmmm
Okay
Well I guess you need to look at the number of possibilities for 5 dice
Well each one has 6 sides
5*6=30
So the number of possibilities is 30!
Oof
That's big
Well how can you get it equal to 11
Hmmm
frigid gate
thanks tho - maybe ill ask later hopefully ill get more help
appreciate it tho
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halcyon shore
i need help with laurent series
calm coralBOT
i need help with laurent series
halcyon shore
f(z)=1/(z+1) when z = 0, then z=-1
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@halcyon shore Has your question been resolved?
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@halcyon shore Has your question been resolved?
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unkempt kite
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civic dirge
Yeah that's good
unkempt kite
Yeah that's good
Thanks!
I tried proving it using induction as well
does it look right? my inductive step stumped me sorta 😭
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terse saddle
i need help
calm coralBOT
i need help
still marlin
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terse saddle
I integrated it and got this:
which is correct
I just dont know how to find the geometric sequence
still marlin
Hmm dividing the (k + 1)th area by the kth area should work
terse saddle
in the answers appears this:
so the ratio would be e^(4kpi)
i dont know how they got it tho
still marlin
oh i just assumed k would be the k-th spiral
Woops lol
Ok just pretend I said n-th area
Looks like you got the right area for A
still marlin
so I'd imagine you just integrate similarly for B and C, except the bounds are different
terse saddle
I just solved it
like the spiral does a second turn for getting to B
u have to use angle 5pi/4
instead of pi/4 for A
still marlin
bet
still marlin
yeah
terse saddle
so 9pi/4
still marlin
And 2pi
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lucid knot
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visual halo
whats the full question
lucid knot
is this a good graph for the function
visual halo
yes
lucid knot
it gave me a few options but this was the closest to the graph i was able to produce
my graph touches the x axis between 1 and 2 which is why i was a little skeeved
visual halo
wait
onyx bloom
nope
visual halo
nono
onyx bloom
consider the +2 at the end
queen pollen
onyx bloom
desmos is an incredible tool btw
visual halo
yes
they even have 3d graphs (in the works)
onyx bloom
just use geogebra for 3d graphs, or avoid 3d graphs all together because they always look hella messy :p
visual halo
just use geogebra for 3d graphs, or avoid 3d graphs all together because they al...
oh yeah
(thats why i said in the works)
lucid knot
i used desmos but i messed it up a bit you guys are righ
t
phew
i totally avoid 3d graphs lmao
thanks!
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dawn basalt
how do i solve this
calm coralBOT
how do i solve this
wraith robin
Product rule and sub in x =3
Product rule on f(x)g(x), and you just differentiate 2x normally as differentiation is a linear operation
dawn basalt
Product rule on f(x)g(x), and you just differentiate 2x normally as differentiat...
ohh I understand now, ty
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glacial lily
$f(x) = \frac{x^2}{2}$\
$g(x) =
\begin{cases}
f(x) & \text{if } f(x) \in \mathbb{Z} \
g(f(x)) & \text{if } f(x) \not \in \mathbb{Z}
\end{cases}$\
Is g(x) defined at points that converge to a point like x=1?
potent lotusBOT
Oğuzhan
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agile loom
ive got a is 48/x but idk how to work it into b
calm coralBOT
ive got a is 48/x but idk how to work it into b
lyric ravine
ive got a is 48/x but idk how to work it into b
If the number of books Gaya has is G and the number of books Mayra has is M, how would you related G and M?
agile loom
G+4=B?
lyric ravine
No, Gaya has 4 more books than Mayra
agile loom
B+4=G?
lyric ravine
Your wish however you want to simplify
agile loom
i moved it across
lyric ravine
You can divide through by four
potent lotusBOT
smidgin
potent lotusBOT
smidgin
agile loom
yea
lyric ravine
That does nothing though
You're dividing the numerator and denominator by 4 when you do that
We are dividing both sides of the equation by 4 here
agile loom
oops i meant +
lyric ravine
Yes
agile loom
then like this?
lyric ravine
Yes
agile loom
then this?
lyric ravine
Yes
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verbal stag
how does it get from this to the step after
calm coralBOT
how does it get from this to the step after
tidal grotto
see this article about u-sub. https://tutorial.math.lamar.edu/classes/calci/substitutionruleindefinite.aspx
there are plenty of videos about u-sub as well
assuming you aren't confused about the u=(3x^2-7) part, they get the 1/6 from du=6xdx => 1/6 du=x dx
so they replace x dx with 1/6 du
@verbal stag
verbal stag
see this article about u-sub. https://tutorial.math.lamar.edu/classes/calci/subs...
cant open it
verbal stag
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-9/a/revi...
thank you
tidal grotto
np
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green night
sorry I'm blanking where do I start here?
calm coralBOT
sorry I'm blanking where do I start here?
blazing coyote
how's the numerator 0?
green night
I wasn't sure it was
but because I thought if the power of e is -x then it would become like 1/inf
blazing coyote
what's e^{-x} as x tends to infty
brisk pelican
but because I thought if the power of e is -x then it would become like 1/inf
It’s 1+ tho
blazing coyote
but because I thought if the power of e is -x then it would become like 1/inf
yes, but there's a 1
blazing coyote
it's $1+e^{-x}$
potent lotusBOT
Why am. I here
brisk pelican
Either way the limit is the same
brisk pelican
Yea
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icy mulch
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icy mulch
I think i did everything right, i cant find anything in the table on 1.54 with 24 degrees of freedom
So there’s something wrong with my solution
I just dont know what
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modern peak
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blazing coyote
A thin nonconducting ring of radius R has a linear charge density $\lambda= \lambda_0 cos(\phi)$ where phi is the azimuthal angle
potent lotusBOT
Why am. I here
blazing coyote
what does that even mean?
What does the linear charge density vary as
,w azimuthal angle
potent lotusBOT
blazing coyote
that helps a lot, thanks wolfram
modern peak
LMAO
The azimuth is the angle between the north vector and the star's vector on the horizontal plane. Azimuth is usually measured in degrees (°), in the positive range 0° to 360° or in the signed range -180° to +180°.
blazing coyote
How's that related to this though
modern peak
idk
topaz raft
blazing coyote
assuming it means at phi tha electric field is precisely that
wait, does this require vector calculus
Idts
blazing coyote
A thin nonconducting ring of radius R has a linear charge density $\lambda= \lam...
Find the electric field at the centre of the ring
ok , starting with the first quadrant\
The x component would be
$dE=\frac{\lambda_0\cos\left(\phi\right)dr}{r^2}\cos\left(\phi\right)$
potent lotusBOT
Why am. I here
blazing coyote
$dE=\frac{\lambda_0R\cos\left(\phi\right)d\phi}{r^2}\cos\left(\phi\right)$
potent lotusBOT
Why am. I here
blazing coyote
my bad
this
is this right?
and is there any way to streamline this or do I have to repeat this for all 4 quadrants
modern peak
tf is bro doing
blazing coyote
Irodov rn
blazing coyote
IE Irodov, a physics book
the name is problems in general physics
he's the author
ok, so this is giving me a crazy result
$dE=\frac{\lambda_0\pi}{R4}$
potent lotusBOT
Why am. I here
potent lotusBOT
Why am. I here
modern peak
is this channel just ur rough notebook now
blazing coyote
is this channel just ur rough notebook now
rough notebook, I work better when I'm on discord, funnily enough
modern peak
xd
blazing coyote
eh
the answer is idnetical to that for a uniformly charged ring
WTH
according to my book
blazing coyote
The azimuth is the angle between the north vector and the star's vector on the h...
what this means, I just assumed it meant the angle the pos vector makes
modern peak
ohk
modern peak
the answer is idnetical to that for a uniformly charged ring
uniformly charged legit means same charge distribution
blazing coyote
yeah
modern peak
so...?
blazing coyote
but does this problem statement mean the same thing
blazing coyote
A thin nonconducting ring of radius R has a linear charge density $\lambda= \lam...
is the description of charge density here
ok, gtg, i'll get back to this soon
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blazing coyote
A thin nonconducting ring of radius R has a linear charge density $\lambda= \lambda_0 cos(\phi)$ where phi is the azimuthal angle,Find the electric field at the centre of the ring
potent lotusBOT
Why am. I here
blazing coyote
what does this even mean
winter loom
Well
In short it's non uniform charge density.
So variable magnitude for electric field.
Basically, if you have a ring with centre (0,0)
potent lotusBOT
Why am. I here
winter loom
If you're considering Q1 then the direction is going to be negative X for this one, yes.
If you're only looking at x.
blazing coyote
wait, what?
winter loom
Electric field?
winter loom
Are you going to find quadrant wise separately and then add them all?
blazing coyote
is there any other way?
winter loom
Yes.
You can consider two symmetrically placed elements so that when tou add the electric field of because of these elements, you get just one component while the other cancels out. And then simply integrate this
winter loom
Do you atleast picture what I'm trying to say?
Just ensuring you're thinking about it correctly.
blazing coyote
below the x-axis , won't the charge be negative?
winter loom
below the x-axis , won't the charge be negative?
It's cos(x)
Not sin(x)
Fourth quadrant is positive.
winter loom
Cool.
blazing coyote
$E_x=\frac{2dQ}{r^2}\cos\left(\theta\right)$
potent lotusBOT
Why am. I here
blazing coyote
where $dQ=r\lambda _0 cos(\theta)d\theta$
blazing coyote
which expression is wrong
winter loom
The elementary charge.
potent lotusBOT
Why am. I here
winter loom
Correct.
blazing coyote
so this would this be right?
potent lotusBOT
! What the hell am I doing here?
