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#help-27
shrewd kettle
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plush grail
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plush grail
why is the parametrizaiton multiplied by 4
peak crest
the cone is given by z=Vx2+y2 and the plane z=4 so the intersection is Vx2+y2=4
now we go to the power of 2 on each side
x2+y2 =16
this is a circle in 2d plane
and the cercle can be parameterized as (rsint,rcost)
where r is the radius and r in this case is 4
so its (4sint,4cost)
and we know that for the last one z =4
so (4sint,4cost,4)
which is
4(sint,cost,1)
short basin
Helo
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lean glade
variance of a binomial experiment is npq, then shouldnt it be 1/4th of N?
devout snowBOT
variance of a binomial experiment is npq, then shouldnt it be 1/4th of N?
@lean glade Has your question been resolved?
tall knoll
The variance of H conditioned on N is a quarter of N's variance, but perhaps the unconditional variance of H is a little higher
devout snowBOT
@lean glade Has your question been resolved?
lean glade
The variance of H conditioned on N is a quarter of N's variance, but perhaps the...
i was also thinking that it should be a quarter of N for Hs variance
But the answer key says that it should be half of Ns variance
tall knoll
Your assumption that H is binomial is only true once you fix N
Have you encountered the formula Var(X) = E(Var(X|Y)) + Var(E(X|Y))
tall knoll
Well you need that to compute the unconditional variance of H so I'm not sure what else they expect you to use
lean glade
Can you give me a resource link from which i can learn what you're talking about?
tall knoll
Look up law of total variance
lean glade
Okay
cerulean sage
Let $f:(0,1)\to \mathbb{R}$ have the property that for all Cauchy sequences $x:\mathbb{N}\to (0,1)$ have that $f\circ x$ is also Cauchy. Then we are asked if $f$ is continuous. Here's how I tried to show that it is: Let $(x_n)$ be a sequence such that $x_n\to x_0$, $x_0\in (0,1)$. Then $(x_n)$ is also cauchy and with that $(f(x_n))$ as well, so it is convergent to a limit $L$. Let $f(x_0)\neq L$. Then $\varepsilon:=|f(x_0)-L|/2>0$. With that $\exists n_1:\forall n$,$m\geq n_1:|f(x_n)-f(x_m)|<\varepsilon$ and $\exists n_2:\forall n\geq n_2:|f(x_n)-L|<\varepsilon$. Then by the triangle inequality for a choice of $N=\max(n_1,n_2)$: $\forall n\geq N: 2\varepsilon\leq |f(x_n)-f(x_0)|+|f(x_n)-L|<2\varepsilon$. A contradiction
devout snowBOT
Let $f:(0,1)\to \mathbb{R}$ have the property that for all Cauchy sequences $x:\...
cerulean sage
And sorry for occupying two rooms, I wanted to change something, didn't know it'd close the room
sand dove
Let $f:(0,1)\to \mathbb{R}$ have the property that for all Cauchy sequences $x:\...
Unfortunately you can't argue that
but here's the trick
instead of considering x_n
consider the sequence $(y_n)$ such that $y_{2n} = x_n$ and $y_{2n+1} = x_0$
woven radishBOT
rafilou is not not born in 2003
sand dove
convince yourself that it's a cauchy sequence
cerulean sage
done
sand dove
and apply your reasoning to sequence y_n
woven radishBOT
sotiris
cerulean sage
I'm not sure if that's a general sequence
sand dove
and would showing that $f(y_n)\to f(x_0)$ imply that $f$ is continuous?
isn't f(x_n) a subsequence of f(y_n)?
sand dove
**sotiris**
if you manage to show this, wouldn't the result you wanted to prove be shown?
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echo sentinel
can someone help me get thru part d and e?
devout snowBOT
can someone help me get thru part d and e?
sand quarry
can someone help me get thru part d and e?
what are the axioms?
echo sentinel
sand quarry
Alright do you have some idea on axiom 7?
echo sentinel
its scalar multiplication
sand quarry
uh huh
So u + v = (u_1 + v_1, u_2 + v_2) as was given to you
what is k(u+v) under the same notation?
echo sentinel
k(0, u2+v2)
echo sentinel
yeahhh right
echo sentinel
what we just discussed, how am i supposed to write it mathematically?
sand quarry
So those are axioms, they cant be "proven", but you are just expected to show that they hold
so from what we have done
sand quarry
k(u_2+v_2) all of those are scalars
you can show that you have (0, ku_2 + kv_2) from what i replied to because the distributivity of scalars
ku + kv = (0,ku_2) + (0,kv_2)
apply the addition rule they described
what do you get?
echo sentinel
(0+0) , (k.u2 + k.v2)
sand quarry
(0+0) , (k.u2 + k.v2)
yeah!
sand quarry
you can show that you have (0, ku_2 + kv_2) from what i replied to because the d...
is that equivalent to this?
echo sentinel
yess
echo sentinel
in axiom 8, do i, instead of using k m u, i should use k u v?
sand quarry
in axiom 8, do i, instead of using k m u, i should use k u v?
hmm? could you be more clear?
echo sentinel
hmm? could you be more clear?
is that a compliment ππ
delicate fossil
π
sand quarry
no π i dont understand what you said
echo sentinel
i should stop embarrassing myself
yeah um.. the variables used in theory are "k m u" but in the question, it's "k v u" so are they the same thing or?
sand quarry
oh you're talking about ix)?
echo sentinel
number 8
sand quarry
yeah um.. the variables used in theory are "k m u" but in the question, it's "k ...
Ok so no. v is a vector, m is a scalar
its meant to be (k+m)u
echo sentinel
yeah, but m is not defined
sand quarry
well, seems like thats a problem the question-maker forgot to account for
either keep it as a variable, or choose an arbitrary scalar to represent it
echo sentinel
lets keep it as a variable
echo sentinel
as
km+(0,ku2)
sand quarry
as
km+(0,ku2)
i think you typo'd there or something haha
sand quarry
ok so the issue with what you wrote is that you're adding a vector to a scalar
that's an undefined operation
sand quarry
so lets take it a step at a time shall we
you have (k+m)u, what is this in vector notation?
sand quarry
not quite
echo sentinel
was a typo
echo sentinel
waitttt its supposed to be
(0,k.u2)+mu
still no?
sand quarry
nope
echo sentinel
ehhh
sand quarry
well actually
echo sentinel
you have (k+m)u, what is this in vector notation?
addition of scalars multiplied to a vector?
echo sentinel
m(u1+u2)
sand quarry
no
remember m is a scalar
evem though you dont know its value
it should function the same as k
echo sentinel
(mu1,mu2)
sand quarry
hint: this
echo sentinel
i shouldn't be putting zero in the first value for m right?
sand quarry
i believe you should. Presumably this operation works on any scalar
echo sentinel
wouldn't that mean m is equal to k? we just decided that m is a variable
so like (0, mu2) ?
sand quarry
well, they gave you what k is, but they didn't give you what m is. Like, if they had given you neither of those two, then[
k\mathbf u = (0, ku_2), \quad m\mathbf v = (0,mu_2)
]
still holds
woven radishBOT
Aero
sand quarry
wouldn't that mean m is equal to k? we just decided that m is a variable
ok maybe that was a misnomer on my part, but what I had meant by "variable" is that it is an unknown number
sand quarry
wdym leave
sand quarry
well yeah you haven't shown it holds yet
echo sentinel
ikrr
echo sentinel
addition of two scalars multiplied to a vector
sand quarry
hint: this
try to remember this
echo sentinel
= ku + mu
=(0,ku2) + (0,mu2)
sand quarry
yeah that's the other one
sand quarry
yes!!
sand quarry
(0, ku2+mu2)
so is this
echo sentinel
π
sand quarry
= ku + mu
=(0,ku2) + (0,mu2)
equivalent to this
echo sentinel
and so axiom 8 holds
sand quarry
yes
echo sentinel
so we move on to axiom 9?
echo sentinel
do i solve it as ku and mu?
sand quarry
no
sand quarry
hint: this
apply this
echo sentinel
[(0, ku2)(0,mu2)] u
sand quarry
no
like
(km)u is not equal to ku * mu
so like
think of km as like a simple scalar just like k in the picture
echo sentinel
we just leave km as it is?
echo sentinel
think of km as like a simple scalar just like k in the picture
that's the only conclusion i havw
echo sentinel
ohhhhh how do you even get to that point π
sand quarry
hint: this
it's like applying this
ku = (0, ku_2)
mu = (0, mu_2)
(k+4d+c)u = (0, (k+4d+c)u_2)
it always applies
no matter the scalars
sand quarry
no you haven't actually
so like
you need to set up the other equation
rhe other one is k(mu)
you need to expand
k(mu) = ...(... , ...)
fill in the blanks
sand quarry
well it should be k(0, mu_2) but the idea is to show that
k(0, mu_2) = (0, (km)u_2)
so if you treat (0, mu_2) as its own vector (which it is), say z, then you have
k(0, mu_2) = kz then you can apply the same rule again
echo sentinel
so if you treat (0, mu_2) as its own vector (which it is), say z, then you have
...
i don't get your point here
sand quarry
well a vector is defined as u = (u_1, u_2) for example
similarly, (0, mu_2) is a vector
so if we say z = (0, mu_2)
then we have k(0, mu_2) = kz
echo sentinel
yeah
sand quarry
isn't that right?
echo sentinel
yess!
sand quarry
hint: this
so this says that kz = (0, kz_2)
sand quarry
then we have k(0, mu_2) = kz
and z_2 = mu_2 in here
so kz = (0, kz_2) = (0, kmu_2)
im sorry if this is still unclear π
echo sentinel
it isπ₯²
sand quarry
hmm
yeah sorry idk how to explain that better then. I feel like it's the type of thing where you just need to like think about it for a few minutes until it clicks
echo sentinel
lets move on
echo sentinel
yeah sorry idk how to explain that better then. I feel like it's the type of thi...
i get what you're saying lol
sand quarry
lets move on
ok
echo sentinel
part e asks me to prove axiom 10 does not hold
echo sentinel
okayyy
sand quarry
so the thing is
1 is a scalar
what did i say earlier about the form of a scalar multiplied by a vector
sand quarry
ku = (0, ku_2)
mu = (0, mu_2)
(k+4d+c)u = (0, (k+4d+c)u_2)
this again
echo sentinel
and it is not equal to u
sand quarry
yesss good job :D
echo sentinel
u is (u1 + u2)
sand quarry
u is (u1 + u2)
(u1, u_2) but i think u typo'd that haha
sand quarry
thank you aero
no worries lily
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sand quarry
π
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Available help channel!
tranquil cairn
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royal radish
yea gl with that one
tranquil cairn
I am trying to understand how this author derives that there is zero electric field inside a hollow shell at any point P inside the shell. One of the claims he makes is that since the cones (in the image above) have the same opening angle, the infinitesimally small areas that they intersect the spheres at have the same number of electric field lines going through them if the point P has a unit test charge isotropically emittting a field.
I don't believe the claim because even though the cones may have the same opening angle the areas dS2 and dS1 don't cover the same area (one could be larger than the other). Thus, isn't it possible they don't have the same field lines going through the area? Can someone prove his claim?
vital mango
i wouldnt worry about the size of dS2 and dS1, honestly i dont even find this visualization to be that helpful
its also been a while since ive worked with physics so i might be rusty here and not provide satisfactory explanations but
the way i see it is, if you focus on the point P itself, first do you believe that the point P generates field lines in a uniformly distributed way? i.e. all field lines are equally distant apart from any other field line
then as you expand out, the angle theta of the cone is all that really matters, because the when you hit the shell with different dS1 dS2 sizes, the number of field lines dont change because the density of the field lines will be inversely correlated with the area of the dS
maybe a more intuitive example would be heat: we know that if we move our hand away from a fire the heat drops off at a inverse squared rate: 1/x^2
and the reason is because the fire generates some fixed amount of heat that is spread evenly across the surface area of a sphere (4 pi r^2) and as you get further from the fire the surface area increases at a rate of r^2, so the fixed heat must also distribute itself thinner and thinner at a rate of 1/r^2
same logical reasoning is happening here
the claim this author is trying to make is that if you integrate over all directions from point P to the shell, the forces will cancel to 0. this point is very close to the left side of the shell and the E field will be larger because the electron forces are higher due to proximity, but this is balanced out by the fact that the right side of the shell has weaker forces, but just a lot more charges (due to area) to pull with
tranquil cairn
the claim this author is trying to make is that if you integrate over all direct...
Actually he is trying to prove the other view; "Instead of showing that (the charges on) the caps exert equal and opposite
forces on a unit test charge at P, we will show the unit test charge exerts
equal and opposite forces on the (charges on) the two caps."
vital mango
oh ok, those are basically the same thing but sure
tranquil cairn
then as you expand out, the angle theta of the cone is all that really matters, ...
Since the density of field lines is correlated with the area of dS doesn't that mean that one of the areas will cover more field lines?
vital mango
if i told you that area was A, and the density of field lines was K/A, wouldn't you agree that no matter what the area A was, the amount of field lines for any area would just be K?
tranquil cairn
if i told you that area was A, and the density of field lines was K/A, wouldn't ...
Oooh right, because (K/A * A) would be irrespective of the area.
vital mango
π
maybe now the question to ask is, why is the density K/A?
or is that part intuitive
tranquil cairn
maybe now the question to ask is, why is the density K/A?
That would fall from the fact that from a test charge the lines are isotropic and uniform?
vital mango
thats part of it, yes
personally i think its easier to think about it like, if i wrapped a shell around a unit charge at radius 1, and then another at radius 2
the field lines coming out of the unit charge is the same going through shell 1 as it is going through shell 2
and there are no other field lines because we are not considering any other charges in this problem
so the density of field lines for shell 2 has to be less than the density for shell 1 since shell 2 has 4x more area but the same amount of field lines going through
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chilly anchor
Consider a homogeneous system of m linear equations in R^3. For p, q as real numbers, determine which of the following are possible solution spaces.
For each case, specify the values of m that make it possible. If it is not possible, state "none." If it is possible, provide an equation (e.g., m=2) or inequality (e.g., mβ₯10).
The solution space is given by:
x = p [18 12 24] + [12 8 16]
i have no idea how to do this π¦
all i notice is [12 8 16] is constant multiple of [18 12 24]
devout snowBOT
Consider a homogeneous system of m linear equations in R^3. For p, q as real num...
@chilly anchor Has your question been resolved?
rain delta
I can't understand how this was solved
devout snowBOT
I can't understand how this was solved
rain delta
I've spent at least 30 minutes on this
supple knot
which line first do you get lost
rain delta
which line first do you get lost
the 2nd picture
supple knot
the 2nd picture
which line exactly
rain delta
first
like why and where did he get the 1/y^3 from what is he doing there
then how did he change from the u integral to the -1/2 where the arrow is pointing
and in the first picture why is he saying that F(y) = integrat f)y) dy, that's so random
rain delta
yes
we divided the integral into two
solved them separately
and added them together
supple knot
like why and where did he get the 1/y^3 from what is he doing there
this?
rain delta
mhm
rain delta
what about this
supple knot
power rule for integrals.
tranquil cairn
I think the way this was solved is incorrect.
The derivative of tan^3(x) is tan^2(x) sec^2(x) so there is no u-substitution.
rain delta
we cant use sec^2 though cause havent learned it
hexed berry
devout snowBOT
hexed berry
tg = tan
hexed berry
rewrite the cos^2 in the denominator as sec^2
ah
well the thing is
they have not teached us about the cos^2 = sec^2
how is that?
I would like to learn
misty crest
1/cos^2 = sec^2
i mean maybe you just learn the derivative of tan is 1/cos^2
doesnβt matter
same thing
misty crest
just a notational difference
hexed berry
thank yah buddy
hexed berry
i mean maybe you just learn the derivative of tan is 1/cos^2
no
I didn't learn that
=(
btw
@misty crest
U = cos
misty crest
whet
misty crest
nope
hexed berry
not in this exercise
I'm talking in general
suppose I pick Cos as my u
and I express tan as sin/cos
would that become sin/u?
even if I used a different cos?
misty crest
a different cos?
misty crest
would that become sin/u?
it would be sinx/u and in some instances the sinx might cancel
misty crest
u = tan
devout snowBOT
@hexed berry Has your question been resolved?
hexed berry
yeah
misty crest
$\int \frac{-1}{u^3} du$
woven radishBOT
knief
hexed berry
is it wront
misty crest
and probably was the intention
hexed berry
but tangent is much easier imo
teach me that tangent method
misty crest
u = tanx -> du = 1/cos^2(x) dx -> dx = cos^2(x) du
$\int \frac{u}{\cos^2 x} \cdot \cos^2 x , du$
woven radishBOT
knief
woven radishBOT
knief
misty crest
$\frac{1}{2} u^2 + c = \frac{1}{2} \tan^2 x + c$
woven radishBOT
knief
misty crest
you should have the derivative of the basic trig functions memorized
derivative of tan is 1/cos^2
hexed berry
you should have the derivative of the basic trig functions memorized
I do, I do
cos is -sin
sin is cos
tan is sec^2
I don't know the other ones
xD
winter dome
You reminded me that I need to remember these stuffβ¦.
misty crest
You reminded me that I need to remember these stuffβ¦.
yep
misty crest
no pattern
there is
winter dome
Is there any tips?
misty crest
sec and csc are very similar
hexed berry
yeah
misty crest
likewise tan cot are very similar
hexed berry
but like
hexed berry
sec is sectan
does that mean I gotta do the products rule?
ah wait wait
there's a pattern fuck
misty crest
does that mean I gotta do the products rule?
wdym
hexed berry
sec is sectan
misty crest
$\frac{d}{dx} \sec x = \sec x \cdot \tan x$
woven radishBOT
knief
hexed berry
sec' * tan + sec * tan'?
misty crest
so wouldn't it be
we arenβt taking the second derivatives
hexed berry
I know
misty crest
iβve listed the first derivatives
hexed berry
but what if we gotta do that
winter dome
Would it be helpful if we turned like csc into 1/sine and then derive it?
misty crest
Would it be helpful if we turned like csc into 1/sine and then derive it?
thatβs how you derive it yes
winter dome
Ok
misty crest
but itβs useful to keep them in this form when memorizing
winter dome
Yea
hexed berry
I'm gonna be
misty crest
you're amazing
thank you sir
misty crest
a good physicist one day
best of luck sir
hexed berry
knief
misty crest
what physics book are you reading rn
hexed berry
xD
hexed berry
Okay so
I did found a patern
sec and csc
they both multiply themselves with tan
and the second one with cotan
and cotan is just -csc^2
I think that's easy to memorize
winter dome
but don't be mean
I apologise if I am
misty crest
I better leave before I lose more brain cells
yo what town hall are you rn
winter dome
Take a guess
misty crest
17?
winter dome
Nah
misty crest
15?
winter dome
Yup
misty crest
π₯π₯
winter dome
Halfway maxed
misty crest
nice
winter dome
U?
hexed berry
are we talking about CoC
misty crest
are we talking about CoC
yep
winter dome
Yup
winter dome
do you play CR
Nope
misty crest
nah iβm not maxed
hexed berry
Knief do you play cr
misty crest
i was like halfway done with th16
misty crest
Knief do you play cr
nope
misty crest
that game is terrible
hexed berry
I know
misty crest
used to play
hexed berry
ptw crap
misty crest
but theyβre so greedy
winter dome
Can I join your CoC clan anyway?
What th?
winter dome
You an active player?
hexed berry
I can be. <.<
winter dome
Do you mind a quiet clan ?
hexed berry
Do you mind a quiet clan ?
Sure.
winter dome
I can add you if u want
hexed berry
weβre also masters 2 in cwl
Expected from the math genius.
misty crest
nah im that not great at clash
winter dome
Missed global chat
hexed berry
wait
misty crest
2013-2014 ish
hexed berry
how old are you
misty crest
global chat was elite
misty crest
how old are you
18
winter dome
how old are you
17
hexed berry
oh
hexed berry
If I was 24 or 32 I wouldn't be in this app xD
misty crest
you just keep going older
misty crest
If I was 24 or 32 I wouldn't be in this app xD
there are some 40 year olds on this server
winter dome
I have 2 in mine that are round that age
winter dome
I have 2 in mine that are round that age
Thatβs my assumption anyways
What are your tips on vectors in further mathematics ?
winter dome
Point product?
hexed berry
and cross product
misty crest
What are your tips on vectors in further mathematics ?
watch 3b1b linear algebra
hexed berry
I don't know how it's called in english
winter dome
Iβm not in uni yet
winter dome
I don't know how it's called in english
Letβs hear it in your lang
hexed berry
but that thingy of x1x2 + y1y2
misty crest
Iβm not in uni yet
donβt need to be
what math are you in
or what math do you know rather
winter dome
Final year sixth form ( high school final year)
misty crest
i recommend watching dr trefor on youtube as well, he has some good videos on vectors
devout snowBOT
@hexed berry Has your question been resolved?
devout snowBOT
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carmine orbit
lim x->infinity of 8-x^3)/x^4)-4x^2
devout snowBOT
lim x->infinity of 8-x^3)/x^4)-4x^2
frank crag
locate absolute extrema on the closed interval:
f(x)= 2(3-x), [-1,2]
f'(x)=-2
f(-1)=8
f(2)=2
max = (-1,8)
min = (2,2)
i did this right (probably) but why do we have to find the critical numbers?
devout snowBOT
locate absolute extrema on the closed interval:
f(x)= 2(3-x), [-1,2]
f'(x)=-2
f...
@frank crag Has your question been resolved?
frank crag
<@&286206848099549185>
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frank crag
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jade sierra
Can someone explain to me how i find the limit D here, Ive tried sketching the region and its just not sticking
devout snowBOT
Can someone explain to me how i find the limit D here, Ive tried sketching the r...
jade sierra
Am I just fundamentally misunderstanding?
ohhhhhhhhhhhhhhhhh
Yeah we werent big on polar coordinates in high school
ok so i just need to in a way remember the points on a unit circle for the major angles
Ok ty ty
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jade sierra
.reopen
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β
jade sierra
rq tho @sudden grail
does it like
not matter if its a multiple or like?
oh wait
does it have something to do with the radius being 3
wait y= r sintheta
so thats why it is how it is but theta would still be 45 degrees?
its like ive had an epiphany thank you good sir
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jaunty bane
Would I just need to bring up the 5x^2 to the top ad make it 5x^-2?
fossil locust
Would I just need to bring up the 5x^2 to the top ad make it 5x^-2?
exactly, do not use the quotient rule
be careful though, you are multiplying each term in the numerator by $\frac{x^{-2}}{5}$
woven radishBOT
southlander!
fossil locust
the 5 up
no, you are still dividing by 5
but when you are dividing by x^2, that's the same as multiplying by x^(-2)
jaunty bane
okay thank you so much
jaunty bane
but when you are dividing by x^2, that's the same as multiplying by x^(-2)
Would this be correct then?
fossil locust
Would this be correct then?
nearly
don't bring the 3/2 inside the bracket
$-\frac{3}{2} \frac{3}{5} \cdot x^{-5/2}$
jaunty bane
okay so just leave it at -3/2 on the otuside?
woven radishBOT
southlander!
fossil locust
okay so just leave it at -3/2 on the otuside?
yes and then that fraction is just -9/10
on the outside
jaunty bane
ohhhhh
fossil locust
okay so just leave it at -3/2 on the otuside?
you do realise that say, $(2x)^2 = 4x^2$
woven radishBOT
southlander!
fossil locust
which is not the same as 2x^2
fossil locust
yes so hopefully you realise how that is relevant to what you wrote now
devout snowBOT
devout snowBOT
Available help channel!
unreal stone
Hey guys quick question when multiplying a power in a complex number, without using Euler notation but rather mod arg form if itβs cis(pi/2)^4 would it be 4cis(4pi/2) or just cis(4pi/2), and would this change if there was a constant at the front
devout snowBOT
Hey guys quick question when multiplying a power in a complex number, without us...
unreal stone
Iβd assume not since itβs not affected by the bracket but I wanted to double check
devout snowBOT
@unreal stone Has your question been resolved?
viscid lagoon
(cosx-4)(cscx+1) = 0 is the factor right?
devout snowBOT
(cosx-4)(cscx+1) = 0 is the factor right?
rare merlin
shouldn't it be (2csc+1)(csc-2)
viscid lagoon
shouldn't it be (2csc+1)(csc-2)
have I forgotten how to factor
rare merlin
probably
soft umbra
have I forgotten how to factor
Show your work
viscid lagoon
Show your work
i'll do it with this
soft umbra
Sure
viscid lagoon
Sure
so you can find a factor by just finding two numbers that multiply to 2 and add up to 3
so (secx+2)(secx+1)
viscid lagoon
my original thought process was
two numbers that multiplied to 2 and that add up to 3
soft umbra
That is correct, ig you just made a mistake during the calculation
viscid lagoon
That is correct, ig you just made a mistake during the calculation
answers to solutions are 2pi/3, 4pi/3, pi?
devout snowBOT
@viscid lagoon Has your question been resolved?
warped wave
So i just started learning statistics and i would love some explanation on how to analyze these questions. Preferably, helping me with some steps
devout snowBOT
So i just started learning statistics and i would love some explanation on how t...
@warped wave Has your question been resolved?
devout snowBOT
@warped wave Has your question been resolved?
devout snowBOT
@warped wave Has your question been resolved?
high obsidian
Let the time ken spent be denoted by K, and the time gigi spent denoted by G. These are random variables. Then the total time is T = K + G.
The expected value of T, I'll denote <T> = <K+G>, but the expectation value is linear, so <T> = <K> + <G>
Where <K> and <G> are just the means of their respective distributions
Finally Var(T) is given by the variance of a sum formula, i.e. Var(T) = Var(G) + Var(K) + 2Cov(G, K)
Where Var(G) and Var(K) are the squares of their standard deviations and the covariance is 0 since the times gigi and ken spend are independent of each other
For the second part you need to perform an integral, I'm a bit rusty on my stats so I'm not sure if there's a recommended way to tackle that one
@warped wave is that helpful?
high obsidian
Ah it seems that for the second part you should assume T is approximately normally distributed, then use the expectation value as the mean and Var(T) as the square of its standard deviation, then proceed as usual
devout snowBOT
@warped wave Has your question been resolved?
fallen hinge
I need help with formaziling my answer
devout snowBOT
I need help with formaziling my answer
fallen hinge
So i have to find f-1(B) which means original for B elements
So i wrote f^-1(B) = {(m,3)|m=<3)} U {(1,11), (11, 1)} U {m, 11 | m<0}
is it correct to write so?
long sundial
Do you mean $f^{-1}(B)$ ? surely the domain of $f^{-1} $ is incompatible with B
woven radishBOT
Max
fallen hinge
Whys that
long sundial
The original functions range is the inverses domain, B would not be in that range
fallen hinge
But yea i mean finding originals for B, so thats what im finding yes
Oh is it because B is in N^2
And i can find F(B) but not F^-1(B)?
frozen aurora
The original functions range is the inverses domain, B would not be in that rang...
he is trying to get the preimage of B
fallen hinge
Oh yeah preimage, its just in estonian we call it originals
But uhm is it correct way to formalize preimage like this?
So i wrote f^-1(B) = {(m,3)|m=<3)} U {(1,11), (11, 1)} U {m, 11 | m<0}
got the answer.
.close
dry lotus
devout snowBOT
dry lotus
What am I doing wrong?
sand dove
you just went back on your feet
dry lotus
you just went back on your feet
Yep π and it's all 0=0
sand dove
what's the point of differentiating u, integrating v' if you're going to integrate u' and differentiate v afterwards?
when you do IBP, if you have to go backwards it means you didn't need the IBP
dry lotus
what's the point of differentiating u, integrating v' if you're going to integra...
Yeah true
sand dove
in this case you do need the IBP
dry lotus
when you do IBP, if you have to go backwards it means you didn't need the IBP
Yeah it makes sense now
sand dove
so no going backwards
dry lotus
Yes
dry lotus
Partial fractions ?
sand dove
so you'll be integrating constant + constant/(1+4x^2)
violet rampart
devout snowBOT
violet rampart
AM i correct?
winter patrol
how are you getting the second last line?
restive river
what is this
violet rampart
how are you getting the second last line?
I put everything in n^2 because n(n)=n^2
winter patrol
also, actually why are you doing in the third line
winter patrol
why did you insert that in
i don't understand the meaning of the arrow
or where that is coming from
violet rampart
i don't understand the meaning of the arrow
It is just a reminder
violet rampart
or where that is coming from
winter patrol
,rotate
woven radishBOT
winter patrol
i still don't udnerstand'
restive river
i still don't udnerstand'
wheres the x coming from
winter patrol
what's the blue part? and where's the red part coming from?
violet rampart
@stable cloak
violet rampart
wheres the x coming from
Bro
stable cloak
alr lemme see
stable cloak
<@703813252013883444>
i cant really understand what you have done but i can find the range of values of m if you want
violet rampart
what's the blue part? and where's the red part coming from?
stable cloak
m should be >= ( -16/3)
winter patrol
if i'm not mistaken you seem to be doing something like:\
going from
$$\frac{2m^2}{3m+16} + 1 \geq 1$$
to
$$\frac{2m^2}{3m+16} - 1 \geq -1$$
then combine the left side into a single fraction and then also convert that $\geq$ to an $=$ sign
woven radishBOT
βΞ±ΞΌOmeganato5
violet rampart
**βΞ±ΞΌOmeganato5**
I need to go but can i DM you later about that?
@stable cloak
stable cloak
I need to go but can i DM you later about that?
sure
devout snowBOT
winter patrol
m should be >= ( -16/3)
no equality
stable cloak
no equality
oh yea my bad
devout snowBOT
Available help channel!
untold pivot
devout snowBOT
untold pivot
For part(a), wouldn't the answer be yes? Since in either case Y is still just a standard normal distribution?
I.e. $P(Y\le y\cap X=i)=P(Y\le y)P(X=i)$
woven radishBOT
somethingwrong
devout snowBOT
@untold pivot Has your question been resolved?
hexed berry
Why ln(A-b) β Ln(a)/ln(b)
devout snowBOT
Why ln(A-b) β Ln(a)/ln(b)
olive snow
a = 3 and b = 2
acoustic leaf
why should that be true?
olive snow
ln(3) = 0 ?
winter patrol
raising e to each side gives different results
devout snowBOT
@hexed berry Has your question been resolved?
devout snowBOT
@hexed berry Has your question been resolved?
devout snowBOT
@hexed berry Has your question been resolved?
marsh mortar
heya
normal merlin
devout snowBOT
supple knot
set t = x-8. then (n+1) |t| is always positive except for what values of t?
supple knot
typo. fixed
normal merlin
8
supple knot
I dont know what to do next since it goes to infinity for both
one will be infinity, but the other will not be infinity
normal merlin
but arent both being multiplyed so anyting multiplied by infinity is infinity
supple knot
anyting multiplied by infinity is infinity
that's wrong
devout snowBOT
devout snowBOT
Available help channel!
vocal narwhal
need help solving this 1ΒΊ order diferentian equation in homogeneous
vocal narwhal
i am having trouble putting the new variabled in
i am tired of trying to understand homogeneous
I got here
sick valley
@vocal narwhal hi
vocal narwhal
hi
sick valley
What do you have to compute?
vocal narwhal
compute?
sick valley
Ok, do you have to start here?
vocal narwhal
yeah
sick valley
Or have you already done something?
vocal narwhal
i did
sick valley
Can you show
vocal narwhal
up there is my photo of what i did on tablet
vocal narwhal
I got here
.
sick valley
It doesn't read very well
vocal narwhal
then lets start over
because i did all the info the slides show that is to replace (y/u) with U
sick valley
Ok
vocal narwhal
and that y= u*x
and yΒ΄= uΒ΄*x +u
and then i am having trouble placing it and simplify it
small urchin
Hi
sick valley
@vocal narwhal ah ok
small urchin
but isn't it enough that you bring dy to the right and integrate?
vocal narwhal
hi sombody save me XD im cooked my exam is tomorrow
vocal narwhal
but isn't it enough that you bring dy to the right and integrate?
suposedbly DY is replaced with yΒ΄= uΒ΄*x +u right?
small urchin
Wolfram alpha
sick valley
,w x^2y dx - (x^3+y^3)dy = 0
vocal narwhal
its calculater?
woven radishBOT
vocal narwhal
w??
sick valley
It's to start wolfram from here
small urchin
Wronkian I think
small urchin
No wait but I don't know if I made the right command
What do the slides say?
Can I see?
sick valley
@vocal narwhal can we do the exercise ?
woven radishBOT
mohammed
sick valley
Right ?
woven radishBOT
mohammed
vocal narwhal
its both dx? isnt one du?
sick valley
Where ?
vocal narwhal
on dy
sick valley
**mohammed**
You mean here?
small urchin
Do you have an example where the mohammed substitution is used?
vocal narwhal
vocal narwhal
didnt notice first
sick valley
some say its udx +xdu
How does du come out if we wrote dy = u'x dx + u dx
small urchin
Look here
sick valley
vocal narwhal
yeah?
sick valley
No
small urchin
@vocal narwhal If you do the same things as in the example but in this exercise, where do you get stuck?
vocal narwhal
i was trying to understand where dy goes in the equation
small urchin
What was the original question?
sick valley
woven radishBOT
mohammed
sick valley
woven radishBOT
mohammed
sick valley
After a little algebra
woven radishBOT
mohammed
sick valley
Guys hello?
sick valley
Is it clear?
sick valley
?
vocal narwhal
sick valley
Can you take It from here ?
vocal narwhal
yes thank you
sick valley
vocal narwhal
.close
devout snowBOT
devout snowBOT
Available help channel!
digital zephyr
devout snowBOT
devout snowBOT
@digital zephyr Has your question been resolved?
devout snowBOT
Available help channel!
feral rain
What happens to the y-intecept of a line y=-1/3x+4 when rotated 90 degrees about its bottom right vertex?
devout snowBOT
What happens to the y-intecept of a line y=-1/3x+4 when rotated 90 degrees about...
feral rain
I only learned what happens to it's slope
devout snowBOT
@feral rain Has your question been resolved?
worthy hornet
Iβm watching a YouTube video where the questions are all trick questions and the trick for this one is that itβs impossible and there is no solution but canβt you take the decimal result of them added to together and then convert it to a logarithm that is equal to the same thing
devout snowBOT
Iβm watching a YouTube video where the questions are all trick questions and the...
fair mantle
Iβm watching a YouTube video where the questions are all trick questions and the...
Technically you can write it as a log in any base
Let's say log_a(x)=log_5(4)+log25
Then x=a^(log_5(4)+log25)
So it can be written as log_a(a^(log_5(4)+log25))
worthy hornet
So Iβm right and the video is wrong lol
fair mantle
Yes
worthy hornet
.close
alpine python
$\text{How can I show:}\lim_{x\to\infty}\left(x-\sqrt{x^2-1}\right)=0$
woven radishBOT
Axe
solar goblet
$\text{How can I show:}\lim_{x\to\infty}\left(x-\sqrt{x^2-1}\right)=0$
multiply and divide by the conjugate
lament schooner
lets say i throw an object away and it makes a parabolic curve down, it explodes midway. are the pieces of the debris follow the parabolic curve?
devout snowBOT
lets say i throw an object away and it makes a parabolic curve down, it explodes...
lament schooner
assume that the explosion is not tooooo big
heavy current
lets say i throw an object away and it makes a parabolic curve down, it explodes...
the same parabolic curve?
lament schooner
yeahhhhhhh
somewhat
i feel like if the explosion doesnt have a huge force it will still somewhat follow the curve
not exactly
ofc
heavy current
I mean, each piece will go on its own trajectory after the explosion
if the explosion is small, then the change in momentum for any given piece is tiny
so the path it follows will still be roughly the original
heavy current
but that's only because the explosion was small
lament schooner
thats all i wanted to confirm
heavy current
okie dokie
devout snowBOT
heavy current
upper schooner
devout snowBOT
Available help channel!
halcyon yew
help plz
halcyon yew
for this question my teacher was writing possible equations for the same graph and for the 4th one, can u do the exact same thing but instead do horizontal reflection instead of vertical? Thas my question
