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pearl pondBOT
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north talon
A prism with width 1 and length 2 is cut by a plane, creating a quadrilateral with an area of 6. which of the following is the longest possible perimeter of the plane?
north talon
my ideas right now are
the intersecting plane is a parallelogram(?) and id use some inequality to get the answer but im not sure
why am i like the only person to not get help every single time😭
<@&286206848099549185>
cinder thistle
perimeter of the plane right?
north talon
yeah
cinder thistle
so the 4 points of the plane will be
(0,0,0)
(0,2,2x)
(1,0,x)
(1,2,3x) right?
dapper kraken
cant the plane have more than 4 points
cinder thistle
cant the plane have more than 4 points
points as in intersection with the edges of cuboid
dapper kraken
i mean yea this is a cube but im sure it extends to the rectangular prism
wait is the prism even rectangular
cinder thistle
i mean yea this is a cube but im sure it extends to the rectangular prism
those are possible, but i am assuming that it is a prraleogram by looking at the diagram
north talon
i mean yea this is a cube but im sure it extends to the rectangular prism
whoops i lost this bit in translation
"creating a quadrilateral"
dapper kraken
ah
cinder thistle
so the 4 points of the plane will be
(0,0,0)
(0,2,2x)
(1,0,x)
(1,2,3x) right?
so the area of the plane will be ||[0,2,2x] X [1,0,x]||
north talon
so the 4 points of the plane will be
(0,0,0)
(0,2,2x)
(1,0,x)
(1,2,3x) right?
huh..?
whys (0,0,0) a part of that
cinder thistle
so the area of the plane will be \|\|[0,2,2x] X [1,0,x]\|\|
=||[2x,2x,-2]||
=root(8x^2+4)
so 6 = root(8x^2+4)
so x = + or - 2
i reflect coordinate system wlog so that it is 2
north talon
so the area of the plane will be \|\|[0,2,2x] X [1,0,x]\|\|
ive never learnt this before... what is this
cinder thistle
ignor that then
north talon
oh
north talon
bh
north talon
no
north talon
this question is supposed to use like middle school knowledge😭
cinder thistle
oh
north talon
dyk dot product of vectors?
ive studied vectors but not to that level yet
north talon
probably
idk this is a test for middle schoolers
you could probably include some grade 10-11 knowledge
cinder thistle
ok
so you do know how to calulate [erpenidcular distance between two parralel lines?
north talon
yeah
cinder thistle
so write the area of the parrelogram interms of x
solve for x
and then find the perimeter
because interms of x you can find out the 2 lines
north talon
wait im so dumb what
cinder thistle
we have the 4 points as
(0,0,0)
(0,1,x)
(2,0,y)
(2,1,x+y)
now do the area interms of x and y thing
pearl pondBOT
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north talon
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pearl pondBOT
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fast heron
hii can someone help me prove that int(A) times int(B) = int(A times B)
fast heron
for the first direction: int(A) times int(B) in int(A times B)?
(x,y) is an element of int(A) times int(B) --> x in int(A) and y in int(B)
rustic gate
the direction $\Int(A) \times \Int(B) \subsete \Int(A \times B)$ should be easy
jolly parrotBOT
rustic gate
since both $\Int(A)$ and $\Int(B)$ are open, and certainly $\Int(A) \times \Int(B) \subsete A \times B$
jolly parrotBOT
fast heron
ok so int(A) times int(B) is open therefore there is an open set int(A) times int(B) containing (x,y) such that int(A) times int(B) in A times B
so (x,y) in int(A times B)
rustic gate
sure that works
alternatively one knows that Int(A × B) is the largest open subset of A × B, so must contain Int(A) × Int(B)
fast heron
alternatively one knows that Int(A × B) is the largest open subset of A × B, so ...
does it mean that int(A x B) contains all other open subsets of (A x B)?
rustic gate
for the converse direction, you want to consider the basic open sets of the product
fast heron
i dont understand, (x,y) in int(A x B); and then?
rustic gate
actually hmm
lets try this instead
so Int(A × B) is open, and (x, y) ∈ Int(A × B)
this means theres an open neighbourhood of (x, y) in Int(A × B) right?
you can write this open neighbourhood as U × V ∋ (x, y) for example
fast heron
yes, so i have to show that U in int(A) and V in int(B)?
fast heron
it's because int(A) is the largest open of A and since U is an open of A, int(A) contains U and same for V and B?
rustic gate
yes
fast heron
ok thank youuu
rustic gate
fast heron
rustic gate
fast heron
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pearl pondBOT
pearl pondBOT
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unborn abyss
that is not true
rustic gate
because an open neighbourhood of the product is covered by U × V where U and V are both open
fast heron
ok but U x V open ---> U open and V open is generally not true?
rustic gate
also if $U \times V$ is open, then
[ U \times V = \Union_\alpha U_\alpha \times V_\alpha ]
whence we get that
[ U = \Union_\alpha U_\alpha, \quad V = \Union_\alpha V_\alpha ]
jolly parrotBOT
rustic gate
so both U and V are open
fast heron
ok so she was wrong?
rustic gate
that is not true
do you have a counterexample?
rustic gate
thats empty 
unborn abyss
and open!
unborn abyss
i'm a pretty silly girl
unborn abyss
otherwise yeah it's true
fast heron
oh okkk 😅
rustic gate
and we have that because its a neighbourhood of a point
pearl pondBOT
rustic gate
pearl pondBOT
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midnight haven
how do I express vector AE in terms of p and
pearl pondBOT
how do I express vector AE in terms of p and
@midnight haven Has your question been resolved?
midnight haven
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summer hearth
I am stuck on this question
pearl pondBOT
I am stuck on this question
midnight haven
I am stuck on this question
b?
summer hearth
yeah
I was able to get to the point where you plugged in the values into the dot angle formula
$$\theta=\cos^{-1}{\frac{56}{680}$$
versed mica
I was able to get to the point where you plugged in the values into the dot angl...
what were your norms
summer hearth
$$\theta=\cos^{-1}{\frac{56}{680}}$$
jolly parrotBOT
KXLI
summer hearth
to find the inverse, what do i do on a calculator?
midnight haven
magnitude of a vector = $\sqrt{x^2+y^2}$
jolly parrotBOT
summer hearth
yeah im done with that part
midnight haven
for the vector u=xihat+yjhat
versed mica
yeah im done with that part
how’d you get 680
versed mica
,calc (8)(sqrt(49+36))
jolly parrotBOT
Result:
73.756355658343
yep
jolly parrotBOT
KXLI
versed mica
yep
summer hearth
would i find the inverse using rads or deg mode on a calc?
versed mica
radians
we’re grown ups now
we don’t use degrees
oh wait
they want degrees
lol
summer hearth
ok so I got 0.709 as the answer
how would I turn that into degrees?
do you just multiply it by 180/pi?
versed mica
yea
pearl pondBOT
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summer hearth
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pearl pondBOT
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flint musk
pearl pondBOT
flint musk
Am I doing something wrong here? This would be the third time I'm doing integration by parts
sharp vigil
at this point you can make an equation relating the integral you just got to your original integral
flint musk
at this point you can make an equation relating the integral you just got to you...
How would you do this?
Or is there a topic I can search up on YT in order to get a better grasp of this
sharp vigil
you would set your original integral equal to the expression you have now (since they are equivalent)
then you will notice that you have the same integral (up to constant multiple) on both sides of the equation
flint musk
flint musk
then you will notice that you have the same integral (up to constant multiple) o...
Like this?
sharp vigil
yes
flint musk
but what can i do with this
sharp vigil
if you factor out all of the constants from the integral on the right you'll note that the same integral is on both sides of the equation
flint musk
Yeah but I don't quite get how that helps me solve the integral
I just factored it out and they are the same, but how does that help me solve it?
sharp vigil
well if we call that integral "I" we can solve for I like we would any other variable given an equation
e.g. if you had
[ \int f(x)\ dx = 5x^2 - 3\int f(x)\ dx ] then you could solve for $\int f(x)\ dx$ by adding to both sides:
\begin{gather*}
4 \int f(x)\ dx = 5x^2 \
\int f(x)\ dx = \frac 54 x^2
\end{gather*}
jolly parrotBOT
cloud
sharp vigil
like adding $3 \int f(x)\ dx$ to both sides, to solve for it like you would any other variable
jolly parrotBOT
cloud
flint musk
so youre treating the integral as if it's a variable?
flint musk
So just like this and then solve for I, right?
And thats the final answer?
@sharp vigil
sharp vigil
yes
flint musk
Thank you
I didnt know that you could integrate like that
i appreciate it !!!
.close
pearl pondBOT
pearl pondBOT
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exotic gale
Can someone help me on this question:
pearl pondBOT
Can someone help me on this question:
exotic gale
<@&286206848099549185>
ocean hornet
Can someone help me on this question:
do you know how the rsa cryptosystem works?
exotic gale
yes but i don't know how to calculate for d in this case
ocean hornet
yes but i don't know how to calculate for d in this case
well you know that e and d are integers so that M^{ed} = M, hence, ed|varphi(M) by euler's theorem
do you know how to compute varphi(M)?
exotic gale
no, i wasn't taught that yet
ocean hornet
do you know what varphi(M) represents?
exotic gale
unfortunately, no
ocean hornet
can you give some more context as to where this question came from?
if you are not familiar with any of this, im a bit confused where this question came from
exotic gale
can you give some more context as to where this question came from?
AoPS
ocean hornet
ok, can you tell me how they explained rsa to you?
exotic gale
i can send you an image of the transcript of the lesson if you want me to
ocean hornet
could you tell me in your own words?
exotic gale
they basically explained about the brief history of RSA encryption, the properties it relies on, and how to encode and decode RSA encyption (if you were to know the modulus and exponent)
ocean hornet
can you explain the key generation, encryption, and decryption steps in more detail
exotic gale
Well you can encrypt it by raising x (an integer) to the exponent published in the public key and taking the modulus (also published in the public key) to find the residue
They also explained that "d" is a "secret" decryption exponent for the private key that uses the same modulus published in the public key
I don't have that much time in my hands, please hint towards the answer or smth
ocean hornet
well there's a lot that you are missing
i would suggest re-reading your lecture notes, or looking on the wikipage
the idea is that you must have e*d = (p-1)(q-1)
exotic gale
well there's a lot that you are missing
could you specify what im missing
ocean hornet
could you specify what im missing
how exactly d depends on e, how they are chosen
in the beginning, you choose two primes p, q, then take M=pq, then you take e,d so that e*d = varphi(M)=(p-1)(q-1)
then e is a public key and d is a private key
then, if x is your message, you can encrypt by g=x^e
then to decrypt, you do g^d = x^{ed}=x^{varphi(M)} = x by euler's theorem
exotic gale
the idea is that you must have e*d = (p-1)(q-1)
i was taught this a little
but everything else, not really
thanks for the help nevertheless
.close
pearl pondBOT
midnight haven
I also got 0.038.
P(> 5 defective) is about 0.037777
P(>= 3 boxes) is then roughly 0.038
I notice that 1 - 0.038 = 0.962, incidentally
pearl pondBOT
@spice anvil Has your question been resolved?
midnight haven
I think your teacher accidentally calculated the probability of "**5 or more **defective hooks" per box, rather than "more than 5 defective hooks"
split bridge
When do you use angle angle angel, angle side angle and side angle side?
sick adder
It depends on what information you're given in the problem
split bridge
It depends on what information you're given in the problem
But for what do you use itv
??
midnight haven
Angle-Angle can prove similarity between two triangles.
Angle-SIde-Angle and Side-Angle-Side can prove congruence between two triangles.
sick adder
If you have something like this, you're given an angle, side, and angle in order (which is why they're named that way)
So whichever technique you end up using depends on what you're given and what you want to do, be it show similarity or congruence like josh mentioned
split bridge
What’s congruence?
sick adder
If you're not given any side lengths, you're not going to be able to use anything with side in it
When two triangles have the same side lengths
split bridge
If you're not given any side lengths, you're not going to be able to use anythin...
And do the values need to be equal?
On both triangles?
sick adder
To be congruent you need equal angle and side lengths
To be similar you just need equal angles, or in other words equal ratio of side lengths to each other
split bridge
Whats difference between congruent and similarity?
So AAA - similarity
ASA or SAS congruence
midnight haven
In basic terms...
congruence = same size and same shape
Similarity = same shape, but not necessarily same size
split bridge
In basic terms...
congruence = same size and same shape
Similarity = same shap...
Ohhhh Similarity is if you took a triangle and dragged it with mouse to resize it
Congruence is 1:1
Same but different rotation
midnight haven
You can prove triangle congruence with SAS, ASA, or AAS, or SSS.
But note that you cannot prove triangle congruence with SSA.
midnight haven
Ohhhh Similarity is if you took a triangle and dragged it with mouse to resize i...
Yes thats a good analogy
split bridge
So to prove similarity , what do I need?
midnight haven
You only need two angles (AA) to show similarity, or any of the congruence conditions.
Congruent triangles are similar triangles, but similar triangles aren't always congruent triangles.
split bridge
Ok, and if any criteria let’s say angle doesn’t match, those aren’t congruence?
midnight haven
You could still show congruence with SSS, without any given angles. But otherwise, yes
warm current
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solar jungle
If I take a shape like this, I can draw an even arc between the two mid points of the outer edges of the shape.
solar jungle
2 more arcs swing between the inner and outer edges of the shape, so that all 3 arcs are evenly spaced
The smallest arc falls outside of the shape though
somewhere on the dotted diagonal line is a new centre point where 3 evenly spaced arcs can be redrawn, all landing within the shape, with the radius of the middle arc still being the same as it was originally
obviously the length of the inner and outer arcs will change, as will the spacings between the three arcs
How do i find this new centre point?
Its possible to brute force it, i can find it by trial and error when drawing it. I dont know how to work it out though
pearl pondBOT
@solar jungle Has your question been resolved?
pearl pondBOT
@solar jungle Has your question been resolved?
pearl pondBOT
@solar jungle Has your question been resolved?
kindred hill
-x^2+6x-12
complete the square
pearl pondBOT
-x^2+6x-12
complete the square
summer imp
kindred hill
could u show me with those numbers 😅
supple knoll
is this gpt
summer imp
No.
supple knoll
other ai?
summer imp
No.
supple knoll
no
summer imp
could u show me with those numbers 😅
That would be me doing the problem for you. Where do you struggle following what I sent?
pearl pondBOT
Available help channel!
midnight haven
help me out
pearl pondBOT
help me out
midnight haven
in triangle XYZ, the perimeter is 40 units. XY = 12, YZ = 14 and XZ is the unknown length. what is the length of XZ?
the answer is supposed to be 10 units but how is it 10
buoyant sandal
the answer is supposed to be 10 units but how is it 10
well
from what you're saying it's not 10
main oxide
sounds like your teacher is wrong 
buoyant sandal
^
supple knoll
^
prime pier
^
midnight haven
supple knoll
buoyant sandal
no
midnight haven
14
surreal relic
Yes
midnight haven
dang
pearl pondBOT
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junior vapor
hello how do you do part a using complex numbers/theorems
pearl pondBOT
hello how do you do part a using complex numbers/theorems
@junior vapor Has your question been resolved?
prime pier
hello how do you do part a using complex numbers/theorems
let x = cos(theta) + isin(theta)
$2\cos\theta = x + \frac{1}{x}, \quad \sin\theta = \frac{1}{2i} \left(x - \frac{1}{x}\right)$
jolly parrotBOT
DW1
junior vapor
yep
prime pier
$\sin^5\theta = \left[\frac{1}{2i} \left(x - \frac{1}{x}\right)\right]^5$
jolly parrotBOT
DW1
prime pier
expand using combinatorics
prime pier
4U?
pearl pondBOT
prime pier
nice
junior vapor
;-;
prime pier
good luck
junior vapor
thanks i'll need it
pearl pondBOT
Available help channel!
midnight haven
pearl pondBOT
rough forge
the y-coordinate just changes
(1,t)
-1 to 1
y = 1
(1-t,1) 0 to 2 from right to left
rough forge
oh yea
rough forge
basically 4 line segments with counter clockwise orientation
midnight haven
oh wait
why can't it be 1 to -1 ?
they didnt mention wihch orientation right
gives the same result >?
rough forge
i thought it was convention
midnight haven
oh okay
rough forge
oh okay
Line integrals of vector fields are independent of the parametrization r in absolute value, but they do depend on its orientation. Specifically, a reversal in the orientation of the parametrization changes the sign of the line integral.
midnight haven
this change is because of the direction of the vectors ?
for opposite direction we have to give a negative sign
?
rough forge
i would say so
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
going backwards
pearl pondBOT
rough forge
vector fields ate my brain
it's just a bunch of vectors distributed on a field
like sticks on the lawn, pointing into an arbitrary direction
maybe in roblox there are vectors
that will haunt you
oak quiver
pearl pondBOT
Available help channel!
plain ridge
pearl pondBOT
vestal tapir
,rccw
jolly parrotBOT
vestal tapir
why does it have blank lines
pearl pondBOT
@plain ridge Has your question been resolved?
west vault
$\iiint_R \abs{xyz}, dxdydz$ where $R$ is the region $\left {(x, y, z) : \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{b^2} < 1 \right }$
jolly parrotBOT
jewels!
west vault
I thought converting it to spherical coordinates would be a good idea
But the limits for rho are really weird
pine jay
Probably elliptical coordinates in that case
pine jay
Yeah it’s just spherical coordinates but scaled and squished via a linear map
midnight haven
Okau hello what can i help
west vault
Ah yeah okay let me try that
west vault
Yeah it’s just spherical coordinates but scaled and squished via a linear map
Just to be clear can I show you my sub before computing the determinant
pine jay
Yeah
west vault
alright that should be simple then
pine jay
And of course a, b, c are by assumption non zero
west vault
yeah
Okay so It's just $a^2b^2c^2\iiint_R \abs{xyz} , dxdydz$ where $R$ is the unit sphere
jolly parrotBOT
jewels!
west vault
$a^2b^2c^2\int_0^{\pi}\int_0^{2\pi}\int_0^1 \abs{\rho^5\cos \theta \sin \theta \sin^3 \phi \cos \phi} , d\rho d\theta d\phi$
jolly parrotBOT
jewels!
west vault
Is that right?
pine jay
The spherical substitution or just so far?
west vault
So far I guess
pine jay
Because yes that’s correct if you’ve also done the spherical substitution correct, it’s just that I don’t recall the exact formula but I’m assuming you know it, so should be right then
west vault
The jacobian is just rho^2sin phi
pine jay
Right
pine jay
Np
west vault
.close
pearl pondBOT
pearl pondBOT
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cunning galleon
Need another help guyzz
pearl pondBOT
Need another help guyzz
pearl pondBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
cunning galleon
<@&286206848099549185>
pearl pondBOT
@cunning galleon Has your question been resolved?
pearl pondBOT
@cunning galleon Has your question been resolved?
midnight haven
Use this equation:
You're essentially being asked to calcuate PV with monthly payments of 10000 Php at an interest rate of 12% for 48 periods
midnight haven
What did you get for #5?
cunning galleon
I haven't really solved it since I was unsure
My math teacher of a cousin said it was multiplication
I had to ask here too as well
midnight haven
For #3, you can use the same equation, but instead you're only solving for the quarterly payment (P).
Use r = 0.11, PV = 250000, and n = 10
cunning galleon
But isn't it finding the months?
midnight haven
It says 11% compounded quarterly and that's also how often Francis is making the payments
cunning galleon
Is it considered basic algebra? Our teacher told us that it's just basic algebra
I don't know what shit he meant with that
I mean how to do basic algebra
midnight haven
Yes, all you have to do is rearrange that equation I posted depending on what variable you're solving for
cunning galleon
So for months, it's n?
I don't really rearrange, I solve them as is and save the last missing variable for the last
midnight haven
n represents the number of payments that will be made
Sometimes, that's months (like in #5) but other times, it could be quarters (like in #3)
midnight haven
Do you have an example problem where that happened ?
midnight haven
Ok, then just pay attention to how often the compounding is occurring (monthly, quarterly, annually?) and how often the payments are being made
The problem should tell you
cunning galleon
Compounding occurs monthly here
midnight haven
Which problem are you referring to?
midnight haven
Ok, I thought you were still working on 3. I'll take a look at 2
cunning galleon
Isn't it FV?
midnight haven
Right, you'll need this one. P is the periodic payment of 2500, FV is 100000, and r = 1.06. Solving for n
Solved for n:
pearl pondBOT
@cunning galleon Has your question been resolved?
flint wyvern
so this is my question and answer
pearl pondBOT
so this is my question and answer
hallow remnant
so this is my question and answer
not related but i would highly recommend using overleaf or a different latex software rather than typing it out that way
inverse seems to be calculated correctly in end
and graph seems to be correct
flint wyvern
not related but i would highly recommend using overleaf or a different latex sof...
yeah lol this is notepad i need something else
flint wyvern
not related but i would highly recommend using overleaf or a different latex sof...
ill check it out
flint wyvern
inverse seems to be calculated correctly in end
thank you
main oriole
not related but you are based for using desmos
flint wyvern
not related but you are based for using desmos
😭 nah fr
rough python
This might be a very simple question, but I want to understand the theory correctly.
When you have something like this:
$$\lambda \sim \gamma_{(\kappa_{1}, \tau_{1})}(l)$$
Is it always true that:
$$\lambda = \frac{\kappa}{\tau}$$?
rough python
This is from statistics btw. Poisson Process. Gamma Distribution
jolly parrotBOT
HqppyFeet
plush bramble
what is ~ and what does gamma(kappa, tau) mean
rough python
what is ~ and what does gamma(kappa, tau) mean
I know that "~" is the same thing as "is distributed as", but honestly I haven't gotten to comprehend that 
I just treated it like an equals sign. And the gamma(kappa, tau) is a gamma distribution involving kappa and tau as (hyper?) parameters. Am I wrong in some parts here?
plush bramble
I know that "~" is the same thing as "is distributed as", but honestly I haven't...
should be $\Gamma$ then, not $\gamma$
jolly parrotBOT
riemann
plush bramble
You're claiming $\lambda$ is a random variable distributed as Gamma(kappa, tau), so it's not equal to a constant.
jolly parrotBOT
riemann
plush bramble
Read the properties
https://en.wikipedia.org/wiki/Gamma_distribution
rough python
Read the properties
https://en.wikipedia.org/wiki/Gamma_distribution
Perhaps the context might be totally different in this page? The expression I written above was a posterior probability distribution for lambda.
plush bramble
Perhaps the context might be totally different in this page? The expression I wr...
show the definition of $\gamma(\kappa, \tau)$
jolly parrotBOT
riemann
plush bramble
either its density or distribution formula
pearl pondBOT
@rough python Has your question been resolved?
rough python
either its density or distribution formula
Sorry for late response. From what I am seeing in this formula booklet, it looks to me like it’s a distribution, no?
plush bramble
Yes they use $\gamma$ to refer to the density and $\Gamma$ to refer to the distrbution.
jolly parrotBOT
riemann
plush bramble
**HqppyFeet**
Your question still doesn't make sense. $\lambda$ is a random variable, certainly not a constant. Is your question about something else besides the random variable?
jolly parrotBOT
riemann
rough python
lambda is a random variable, not a constant... That's what I needed. oof
silent bramble
Im a little bit confused, is holomorphic functions not the same as analytic?
silent bramble
this is refering to complex variables
because if the function satisfies the cauchy riemann equations, we know its analytic
but another site is saying if the function satisfies cauchy riemann its holomorphic
merry carbon
pearl pondBOT
@silent bramble Has your question been resolved?
silent bramble
just gonna stay in case of more questions
pearl pondBOT
@silent bramble Has your question been resolved?
outer oak
Hi
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@outer oak Has your question been resolved?
pearl pondBOT
@outer oak Has your question been resolved?
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@outer oak Has your question been resolved?
silk forge
I figured out triangle ITE But how do I find angle AIK
pearl pondBOT
I figured out triangle ITE But how do I find angle AIK
dapper zephyr
Read the properties
https://en.wikipedia.org/wiki/Gamma_distribution
corrupted governments do not wanna you learn this
i do not think they steal mathematically
pearl pondBOT
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silk forge
.close
midnight haven
pearl pondBOT
midnight haven
F = $\nabla f$
jolly parrotBOT
jolly parrotBOT
midnight haven
what do they mean by "natural domain" here?
feral sedge
R^2\{(0,0)}
midnight haven
that took wayyy to long lol
sharp vigil
"natural domain" generally means the largest domain where the definition makes sense to apply
feral sedge
this has a smaller domain than F
sharp vigil
not really necessary for path integration
feral sedge
this has a smaller domain than F
This is a fundamental problem which cannot be resolved
There is no f which actually works
If there was then the vector field would be conservative
midnight haven
im lost
midnight haven
why
feral sedge
this has a smaller domain than F
^
sharp vigil
it does work if we restrict the domain of F (which is why the question is about its natural/unrestricted domain)
we can verify that F is not conservative by taking a suitable path integral
midnight haven
midnight haven
it does work if we restrict the domain of F (which is why the question is about ...
but they said "natural domain" right how can we restrict it
sharp vigil
we won't for the purposes of this question
you should try a path integral which looks easy for this function and actually verify whether it matches the formula given by the potential function
midnight haven
Okay so i have F
we know this
i found out f
problem is this f doesnt work because its domain is smaller than that of the vector field F
no f works
why though ?
feral sedge
Because the vector field isn't conservative
feral sedge
The problem tells us to prove that it's not conservative
sharp vigil
if a vector field is conservative, we expect the line integral around a closed path to be 0. what would be a closed path that seems easy to integrate on for this function?
feral sedge
And I can solve the problem myself and see why
So I am telling you you will not find a working f
midnight haven
this is hard
midnight haven
if a vector field is conservative, we expect the line integral around a closed p...
a circle?
sharp vigil
that would work
midnight haven
i dont see where we are going from here
we found a closed path and we integrate it
let me find out the result
i cant even integrate it 😭
its too hard
sharp vigil
did you parameterize it?
sharp vigil
you take the derivative by individually by components
one thing that may make it (somewhat) easier as well is the fact that you don't need to integrate every possible circle, just one counterexample is enough
midnight haven
one thing that may make it (somewhat) easier as well is the fact that you don't ...
because they said conservative on its domain ?
ohhh
we are not solving this by finding \nabla f because the domain of f is smaller than that of F
OHHH
i see it now
sharp vigil
they said it's conservative, which would imply every possible closed path integrates to 0. we just have to provide a single example of that not being true to disprove it
midnight haven
r(t) owuld be rcos(t) $\hat i$ + rsin(t) $\hat j$
jolly parrotBOT
midnight haven
?
sharp vigil
that is a path that we can use. what limits on t would we want for it to be closed?
midnight haven
that is a path that we can use. what limits on t would we want for it to be clos...
one small thing
nvm
LOL
its 1
$F \cdot dr = 1$
jolly parrotBOT
midnight haven
that gives us $\int_0^{2\pi} dt$
jolly parrotBOT
midnight haven
its 2pi
which is not equal to 0
so not conservative
:D
lets go
if we were to restrict the domainof F, we can show if its conservative or not through finding f right ?
in the restricted domain we considered
we can do that by finding the period of f ?
because we have to show f(B)-f(A) =0
sharp vigil
well for a closed curve the endpoints are the same, so it would have to be true
the problem is that our curve encircles a point that encircles a point outside of its domain (the origin)
midnight haven
Why haven't we considered the fact that the curve is encircling a point which is not in the domain of F?
sharp vigil
the integral is what it is, i'm just saying that we expect closed path integrals of this function to necessarily be 0 only if they don't encircle the origin
midnight haven
😅sorry
Not able to visualise the integral of a vector field is making it hard to grasp the concept
sharp vigil
don't worry too much about it, it's a minor complication to our rules about conservative line integrals which shows up here mostly for the sake of letting you know it exists
pearl pondBOT
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autumn heart
can someone check these please
pearl pondBOT
can someone check these please
hard kite
you could just use wolfram alpha or desmos to check your answers
dense jasper
can someone check these please
this is right
dense jasper
can someone check these please
this is fine
dense jasper
can someone check these please
,w minimize 4x^3 + 3x^2 - 6x + 1 for -2 \leq x \leq 1
jolly parrotBOT
dense jasper
can someone check these please
this is fine
dense jasper
can someone check these please
this is fine
autumn heart
👍
pearl pondBOT
👍
If you are done with this channel, please mark your problem as solved by typing .close
autumn heart
if u dont mind me sending a few more just to make sure (then im good)
i could fit D) in the screenshot for 8 but it shouldnt be right anyways
dense jasper
if u dont mind me sending a few more just to make sure (then im good)
i could f...
fine
dense jasper
if u dont mind me sending a few more just to make sure (then im good)
i could f...
,w 3x^2-4x+5=\frac{5^3-25^2+55}{5}, 0<x<5
dense jasper
if u dont mind me sending a few more just to make sure (then im good)
i could f...
this is fine
dense jasper
if u dont mind me sending a few more just to make sure (then im good)
i could f...
,w critical points (x+2)^5 (x-3)^4
jolly parrotBOT
dense jasper
if u dont mind me sending a few more just to make sure (then im good)
i could f...
,w local max 3x^5 - 4x^3 - 3x
jolly parrotBOT
silver nest
pearl pondBOT
silver nest
I tried to use bayes theorem where A = scam, B = "free money" in the mail
P(A | B) = P(B | A) * P(A) / P(B) = P(B | A) * 0.8 / 0.082
im stuck in getting P(B | A)
or should I use the P( A | B ) = P(A and B) / P(B) formula?
ocean hornet
or should I use the P( A | B ) = P(A and B) / P(B) formula?
yes this is probably more helpful
still bane
yeah
silver nest
or should I use the P( A | B ) = P(A and B) / P(B) formula?
I got 0.1/0.082 = 1.29 = 129%
ocean hornet
I got 0.1/0.082 = 1.29 = 129%
howd you get these
silver nest
P(A) = 0.8, P(B) = 0.8 * 0.1 + 0.2 * 0.01 = 0.082
still bane
and some non-spam emials have "free money" too
still bane
P(A) = 0.8, P(B) = 0.8 * 0.1 + 0.2 * 0.01 = 0.082
yeah you got it i think just use the formula now
silver nest
or should I use the P( A | B ) = P(A and B) / P(B) formula?
(0.8 * 0.082) / 0.082 = 0.8, which is incorrect
still bane
i just solved for probability of any "free money" emails, which you have (0.082)
here this is what i did
let $x$ denote the total number of emails \
there are $0.8x$ spam and $0.2x$ non-spam \
then, there are y "free money" emails \
$y = 0.10.8x + 0.010.2x = 0.08x + 0.002x = 0.082x$ \
then there are $0.8x$ scams so \
$0.8x/0.082x = ~0.975$ \
jolly parrotBOT
reaver
silver nest
that was very helpful, thanks 😄
still bane
np
silver nest
.close
midnight haven
pearl pondBOT
midnight haven
outward flux ?
sharp vigil
with the normal to the curve oriented outward
midnight haven
would -$\ointctrclockwise_C F\cdot nds$ be inward flux then?
sharp vigil
the opposite orientation would result in the sign flipping, yes
pearl pondBOT
jolly parrotBOT
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midnight haven
.reopen
pearl pondBOT
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midnight haven
jolly parrotBOT
sharp vigil
yes
pearl pondBOT
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Available help channel!
midnight haven
Paramatize the paraboloid
z=9-x^2-(y-3)^2
pearl pondBOT
Paramatize the paraboloid
z=9-x^2-(y-3)^2
midnight haven
In cylindrical coordinates
sharp vigil
you can directly plug in the cylindrical coordinate conversions
midnight haven
Is it too hard to do it?
But the axis of the paraboloid isn't the z axis right
Shouldn't I worry about changing r into a function of theta
sharp vigil
well we can either parameterize it based on "modified cylindrical coordinates" based on the axis of the paraboloid, or "normal cylindrical coordinates based on the z-axis
those will get you two different parameterizations
sharp vigil
what are the usual cylindrical coordinate conversions?
sharp vigil
like how would you express x = ..., y = ..., z = ...
where ... is some function of r, theta, z
jolly parrotBOT
sharp vigil
yes
midnight haven
now i have to bother myself with finding r in terms of theta
at a certain Z value
we get a circle which is x^2 + (y-3)^2 = 9-Z
r would be (9-z) sin($\theta$) ?
sharp vigil
we might try the modified coordinates
sharp vigil
ok
midnight haven
did i get this right ?
jolly parrotBOT
midnight haven
🤞 yes ?
sharp vigil
how do you get that from the equation?
now that i'm considering it, i think it may be easier to solve for z in terms of r and theta
midnight haven
i kind of solved it similar to the way we found out r for cylinder with center at 0,3,0
i.e just adding 3 to the y coordinate
?
and keeping the rest in terms of r and theta
sharp vigil
if you want to solve for r you have to plug in the coordinate conversions to the equation and solve for it from there
which turned out to be easier in the case of the cylinder than i suspect it will be here
sharp vigil
now that i'm considering it, i think it may be easier to solve for z in terms of...
if we are going the cylindrical coordinate route this is what I would recommend
sharp vigil
if we are doing the modified cylindrical coordinate route, then yes
midnight haven
we would still be having a 3 in the y coordinate for modified axis ?
sharp vigil
that's the modification. for the unmodified it would just be r sin theta
pearl pondBOT
hushed leaf
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Available help channel!
pearl pondBOT
jolly parrotBOT
lord_breadcrumb
pearl pondBOT
jolly parrotBOT
Cryolite
pearl pondBOT
@agile ridge Has your question been resolved?
limpid lily
That looks like it is recursive already.
Are you looking for a closed form or something?
@agile ridge
Like you have the integral from n - 1 to n for a_n. Then, you add it to the integral from n - 2 to n - 1 for a_(n - 1). That sums to the integral from n - 2 to n.
So, it's like the integral from -infinity to n of f(u)/u du when you add everything up.
Unless you have a base case like a_0 = 5 or something. Then a_n is five plus the integral from 0 to n of f(u)/u du.
pale skiff
since its in a different language, its asking me which statements are true.
i) the gradient for line AB = 1 1/3
ii) the gradient for line PQ = 0
iii) the gradient for line MN = -1 1/2
i know ii) is true, but i dont know how to check/solve i) and iii), i remember the formula which was y = mx + c but i dont really know how to make use of it
boreal raptor
since its in a different language, its asking me which statements are true.
i) ...
you don't know the gradient formula?
rise/run
(y1-y2)/(x1-x2)
for AB,
(4--2)/(1--4)
=6/5
pale skiff
(y1-y2)/(x1-x2)
i dont usually use this one cause i do y = mx + c, is the question applicable for the one im using or do i have to use that?
boreal raptor
i dont usually use this one cause i do y = mx + c, is the question applicable fo...
to use y=mx+c, you need the gradient
which i just gave u the formula for
and u only need the gradient to solve the question
pale skiff
ooh.. sorry if im asking stupid questions by the way i dont know anythign
boreal raptor
you do not use the y-intercept form
boreal raptor
ooh.. sorry if im asking stupid questions by the way i dont know anythign
algs bro
pale skiff
i assume y-intercept form is y = mx + c.. right...?
tacit wolf
since its in a different language, its asking me which statements are true.
i) ...
Indonesia?
tacit wolf
since its in a different language, its asking me which statements are true.
i) ...
I reccomend to identify all the cordinates
the basic concept of PLSV is
$y = mx+c$
jolly parrotBOT
Newt
tacit wolf
where is c is constant
y = the height or vertical,
x = the length or the horizontal
m = is gradient / Kemiringan (in Indonesia)
pale skiff
M IS THE LINE??
tacit wolf
to find gradient u need 2 point of coordinate
tacit wolf
$m = \frac{y_1 - y_2}{x_1-x_2}$
jolly parrotBOT
Newt
tacit wolf
oh my god i didnt know m is the line
what do you meant by that
boreal raptor
the basic concept of PLSV is
$y = mx+c$
wth is plsv
pale skiff
are you indonesian
pale skiff
persamaan linear satu variabel
tacit wolf
wth is plsv
is how the Indonesian translation
pale skiff
wait ill translate it like directly
boreal raptor
is how the Indonesian translation
ah
pale skiff
equivalent linear one variable
tacit wolf
oh my god i didnt know m is the line
what do you meant by this
pale skiff
oh is this not PGL?
pale skiff
what do you meant by this
i didnt know youre supposed to get the gradient from the line
pale skiff
oh is this not PGL?
i dont know the english for it but isnt this supposed to be gradients?
boreal raptor
u should play around on desmos.com just to figure out what m and b do in y=mx+b
tacit wolf
u should play around on [desmos.com](https://www.desmos.com/calculator) just to ...
other country use b?
pale skiff
okk
boreal raptor
different curriculum
tacit wolf
i dont know the english for it but isnt this supposed to be gradients?
wdym
PGL stands for "Persamaan Garis Lurus"? yeah to make it it works as sames as PLSV but usually PLSV is the algebra calculation thingy and PGL for the graphic drawing
pale skiff
wdym
PGL stands for "Persamaan Garis Lurus"? yeah to make it it works as sames...
im kinda lost i dont know what to say 😭
but yes i get the plsv thing
i know how to do plsv and spldv
but i cant do pgl
tacit wolf
but yes i get the plsv thing
nyeh ignore it
pale skiff
okok so i have to find the coordinates to check the statements right?
pale skiff
since its in a different language, its asking me which statements are true.
i) ...
but for AB the ?x-intercept? goes through the middle of -3 and -2
im really stupid how do i get x2?
tacit wolf
but for AB the ?x-intercept? goes through the middle of -3 and -2
use the coordinate that is "bulat" or round so it get easier the equation
use the coordinate of letter A and B to make it easier
also with N and M find the coordinate
it doesn't has to use the x or y intercept
just atleast 2 cords
pale skiff
it doesn't has to use the x or y intercept
huhh if we dont use x or y intercept what are we using? or is it 2 random coordinates??
im so lost
tacit wolf
huhh if we dont use x or y intercept what are we using? or is it 2 random coordi...
use 2 random coordinates at the line
i will help for the AB k
pale skiff
use 2 random coordinates at the line
so i just pick 2 random numbers for x and y? like (3, 4)?
tacit wolf
tacit wolf
so i just pick 2 random numbers for x and y? like (3, 4)?
random numbers of coordinate that was in the line
so the cords of A is (-4,-2) and cord of B is (1,4)
pale skiff
so the cords of A is (-4,-2) and cord of B is (1,4)
huhh where did 1 and 4 come from..
tacit wolf
$(x_1,y_1) = (-4,-2) $ and $ (x_2, y_2) = (1,4)$
so $x_1 = -4$ and then $y_1 = -2$ etc.
jolly parrotBOT
Newt
boreal raptor
wha
boreal raptor
bro
pale skiff
ohh i jsut had to look down
boreal raptor
what 😭
boreal raptor
ohh i jsut had to look down
btw y do u have ur pronouns as he/him but also as she/her
pale skiff
wait its like this then right
pale skiff
btw y do u have ur pronouns as he/him but also as she/her
oh i just copied my friend's bio
im a girl
boreal raptor
wait its like this then right
no
pale skiff
yes
pale skiff
4
boreal raptor
so therefore x = 1, y = 4
boreal raptor
for A, it is 2 down and 4 left
tacit wolf
are we allowed to use some other languange to ease this up
boreal raptor
so x = -4, y = -2
tacit wolf
pale skiff
i thought we were looking at where the line intercepts
boreal raptor
i thought we were looking at where the line intercepts
no.. we're looking for A and B
the coordinates
tacit wolf
i thought we were looking at where the line intercepts
no use the A and B coords
pale skiff
ok i get (1, 4) now, so we just use the same method for a?
tacit wolf
ok i get (1, 4) now, so we just use the same method for a?
yes
pale skiff
for A, it is 2 down and 4 left
where does the line start..
sorry this is so dumb im SO SO SO SORRY