You're welcome
#help-27
muted mural
somber mulch
i will try and see if i can fix it now
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rocky marlin
I need help with b
devout snowBOT
I need help with b
rocky marlin
<@&286206848099549185>
<@&286206848099549185>
Bro can someone help ive been sitting here for so long wasting time that could be spent doing something fun in my life
cinder nova
I need help with b
do you know how to do it if A and B are just numbers?
like 3/4 of the way from 2 to 12
pure kelp
<@&286206848099549185>
do you know the section formula?
rocky marlin
Ik which is 7.5 but it need to be coordinate form
rocky marlin
k
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lapis mirage
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lapis mirage
I don’t get number 5
?
(Sorry I don’t mean to rush I just texted the ? To show am still here and didn’t leave)
lunar eagle
I don’t get number 5
what u did is correct tho u just have to use a calculator for sin 40
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zenith fable
if $||x||^{2}_{c^-1} = x^t C^{-1} x$ then would the square root of this would be the similar but then would be $\sqrt(||x||^2{c^-1}) =\sqrt(x^t C^{-1} x)$ right?
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if $||x||^{2}_{c^-1} = x^t C^{-1} x$ then would the square root of this would be...
woven radishBOT
RealTek
stone stump
well the latex is fucked up
but if two things are equal then you can take the root on both sides, sure
modulo dealing with positive/negative but thats not a problem here
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zenith fable
well the latex is fucked up
Yeah i see its messed up. im just making sure my heads screwed on tight
because im able to make a simpflicatin in my code that cuts down run time from like 5 minutes to seconds
zenith fable
well the latex is fucked up
Thank you very much
stone stump
just taking roots should not speed up your code that much
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zenith fable
just taking roots should not speed up your code that much
no, i seperated two steps
and i am writing up my thesis right now, and i saw a way to take it further
from scipy.sparse import identity
#e_j = identity(66049, format="csr")
result = (C_op @ fwd.T) @ (np.linalg.solve((fwd @ (C_op @ fwd.T)) ,fwd @ U))
this was a lagranian process i ran.
Then i took the norm of this
w = np.zeros(result.shape[1])
for j in tqdm(range(len(w)), desc="Processing columns"):
w[j] = np.sqrt(result[:, j] @ (C_inv_op @ result[:, j].T))
however, i had an idea and it reduced the code to this here
w = np.sqrt(np.diag(U.T @ fwd.T @ np.linalg.solve(fwd @ (C_op @ fwd.T), fwd @ U)))
so its much much faster'
but im asking about this because i want to make sure i got my head screwed on before coming to my supervisor with this idea '
im more of a comp sci guy, and i fail with the math so i just wanted to make sure
thank you 🙂
.close
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halcyon solar
Let F(t) be a parametric curve whose domain is an interval I ,
such that F′(t) = 0 for every t ∈ I . Show that F(t) is
constant.
this is very intuitive, yes but how am i supposed to write the proof?
devout snowBOT
Let F(t) be a parametric curve whose domain is an interval I ,
such that F′(t) =...
pseudo basin
show each of its coordinates is constant
gentle flume
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gentle flume
Hi I need help with Integrals
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gentle flume
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weary arch
If i may ask a math related coding question: in python, given two numpy arrays of shapes (a, b, c, ..., 2) and (x, y, z, ..., 2), is there a way to add them along the last axis to give something like (a,b,c,...,x,y,z,...,2)? e.g. a.shape == (4,3,2) and b.shape == (8,6,2), then i want a+b to be (4,3,8,6,2) if that makes sense. If there is a builtin way of doing something like this it'd be great! Doing b[:, None, None, :] works but only for a specific case
devout snowBOT
If i may ask a math related coding question: in python, given two numpy arrays o...
wispy oyster
so merging two arrays with last index being 2?
wispy oyster
remind me, is python 0-indexed again
weary arch
yes
wispy oyster
okay you could loop from 0 to (number of elements of the array two -1) and access each element of array 2. I dont use python much but i think theres an append function which you can use it to add it to array one on index after the first n-1 elements
weary arch
both arrays are higher dimension arrays (from 1 to 4 in practise), i dont think this is it...
wispy oyster
oh its not a 1 dimensional array?
weary arch
like a = [[[2,3], [4,5], [6,7]], [[1,2], [3,4], [5,6]]] for example
wispy oyster
ah i see
weary arch
then a.shape == (2,3,2) i believe
wispy oyster
what does the shape function do
weary arch
shape returns the dimensions of the array
wispy oyster
ahh
weary arch
Like (M, N) would be your usual M by N matrix
wispy oyster
im not too equipped with python to figure this out, hope someone else can help here
weary arch
nw, thanks anyways!
sullen island
well einsums are super powerful for stuff like that, tho the notation is pretty esoteric & I'm not sure how well they work with variable number of axes https://numpy.org/doc/stable/reference/generated/numpy.einsum.html
Doing b[:, None, None, :] works but only for a specific case
wdym by specific case here ?
@weary arch
weary arch
> Doing b[:, None, None, :] works but only for a specific case
wdym by specific ...
When both a and b are three dimensional, doing a[None, None, :, :, :] + b[:, :, None, None, :] works. But then if the dimensions are not the same it kinda breaks
and thanks for the tip, though not sure how to apply it here
sullen island
well I ain't exactly sure what you're trying to do here
weary arch
For now i think I'll just add the maximum number of newaxis everytime and reduce from there
sullen island
could you try and give a simple example of what you want ?
weary arch
well I ain't exactly sure what you're trying to do here
Trying to vectorise my code😭
sullen island
say (n, 2) and (m, 2) to (n,m,2)
weary arch
yes!
sullen island
Trying to vectorise my code😭
I meant what the operation is
weary arch
say (n, 2) and (m, 2) to (n,m,2)
a[:, None, :] + b[None, :, :] would give what i want
weary arch
I meant what the operation is
I guess just a simple sum along the last dimension (which is always equal so that works), the rest is just dealing with all the other non-matching axes
weary arch
Trying to vectorise my code😭
Incomprehensibility is at an all time high😔
(the context here is a simple integral along a straight line segment in 2d, but i want to vectorise the code to take in multiple positions (two or three dimensional r) at once as well as integrate over multiple line segments at once (two dimensional a and b, but then theres a linspace in there), anyways this is getting annoying...)
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faint zinc
sorry, retracted.
I saw you already answered the question a little bit higher, my bad
weary arch
nw!
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weary arch
Actually I think something like b[..., *(None,)*len(a.shape), :] works, although a bit ugly..
Enjoy some beautiful point sources together
.close
tulip pendant
How do I get the upper bound for the integral
devout snowBOT
How do I get the upper bound for the integral
tulip pendant
Lower bound solved to be one using basels
tulip pendant
Cosine looks like
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sonic hill
can anyone explain why the set {1, 1/2, 1/3,...} is Jordan Mesurable
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can anyone explain why the set {1, 1/2, 1/3,...} is Jordan Mesurable
@sonic hill Has your question been resolved?
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@sonic hill Has your question been resolved?
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sonic wadi
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sonic wadi
<@&286206848099549185>
pseudo basin
@sonic wadi stick to one channel. i have closed your other two.
sonic wadi
alright
pseudo basin
so... you just want somebody to tell you how much you scored on this test?
sonic wadi
<@1162794583990747307> stick to one channel. i have closed your other two.
i didn't know
tranquil bloom
You got them all wrong
pseudo basin
You got them all wrong
wait are you for real
tranquil bloom
Because you ticked every answer, which is diabolical
pseudo basin
i can see at least question 38 seems to be right? on the first pic?
pseudo basin
Because you ticked every answer, which is diabolical
are you just saying "this is the wrong way to select answers" or what
tranquil bloom
Seems you got most right though
sonic wadi
in india it is allowed to write on the test
tranquil bloom
are you just saying "this is the wrong way to select answers" or what
Yeah I mean it shouldn’t matter but I couldn’t tell at first since it wasn’t circled
tranquil bloom
All though I guess an answer sheet was there
pseudo basin
let me go through it all, i guess...
sonic wadi
Seems you got most right though
i need to get atleast 75+/80 or i am dead to my family
tranquil bloom
And this was just the paper which doesn’t matter
tranquil bloom
What test is this even
sonic wadi
if you will be kept in the family or not
tranquil bloom
That seems more of a socio-cultural issue
sonic wadi
That seems more of a socio-cultural issue
yes yes
mystic scarab
if you will be kept in the family or not
What? Really? It's the first time I hear this kind of bad things
sonic wadi
it is reality
for us
that is why many people after getting marks which doesn't meet there parnets requirements
take their own life
tranquil bloom
A grade 5 level test determining your life sounds harsh
pseudo basin
@sonic wadi do the questions in sections B, C and D carry any partial marks
or is it just get full marks on right answers and 0 otherwise
sonic wadi
they carry
sonic wadi
<@1162794583990747307> do the questions in sections B, C and D carry any partial...
yes
pseudo basin
(im still going through section A, mind you)
sonic wadi
ok
pseudo basin
where did you write your answers to questions 19 and 20?
sonic wadi
i wrote
19 is b
and 20 is a
a
Q21. K=-3, Q23 and Q24 are right (i was able to prove)
Q27,Q28,Q29 i was able to do
pseudo basin
should i just take your word for 23 and 24
sonic wadi
yes
Q33 and Q34 (a) part i was able to do
Q35. slant height=26
Q36. C answer is 10
tranquil bloom
Someone check 26
From headsolving, I get a different answer but it’s a high chance my mental maths is wrong
sonic wadi
Q26 was a bit challenging at first
but if you use (x+y+z)^2 identity
you can get the answer
pseudo basin
ok
i think i have calculated all of it
and the total comes to 72 marks
90%
but i had to take your word for 23 of these marks so be careful
@sonic wadi
tranquil bloom
i need to get atleast 75+/80 or i am dead to my family
.
pseudo basin
where have you gone <@183668144404037632>
i have my own stuff to go in real life lmao
18, 36bc, 37c is where you lost marks
pseudo basin
unfortunately i cannot do anything about the family who are about to commit literal murder on you or even worse abandon you to suffer forever
pseudo basin
hey 18 is right
let me see again
i see you ticked 7
the correct answer for the UPPER boundary is 13
so nope
sonic wadi
ok
pseudo basin
how old are you and why is your family putting you through such harsh testing
it's very fucked up of them
sonic wadi
how old are you and why is your family putting you through such harsh testing
don't know
.close
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kind flame
these are my notes from lecture, I understand that everything up until 5/9N < 1/N but i'm not sure why we can just equate 1/N to epsilon
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these are my notes from lecture, I understand that everything up until 5/9N < 1/...
@kind flame Has your question been resolved?
kind flame
someone pelase help 
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supple trench
these are my notes from lecture, I understand that everything up until 5/9N < 1/...
because logically we can
note that in the (ε-N) definition, N appears after ε, so N = N(ε) (in other words, N can be a function of ε)
we equate 1 / N to ε cuz we want ε on the RHS of the inequality, so that it matches the (RHS of the) inequality
|f(x) − L| < ε
in the definition
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dusty sigil
hi
dusty sigil
iron kindle
whats your question
dusty sigil
how do i solve this?
supple trench
how do i solve this?
!showwork
devout snowBOT
how do i solve this?
Show your work, and if possible, explain where you are stuck.
iron kindle
!xy
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
faint gorge
Doesn't seem doable that way, I suggest to change the order of integration.
dusty sigil
dusty sigil
Doesn't seem doable that way, I suggest to change the order of integration.
is this flip ok?
faint gorge
your y bounds are wrong
ln(1) and ln(2) are the y bounds
and your x bounds should be from e^y to 2
dusty sigil
faint gorge
this precisely
you are now integrating along the y-axis so you need to look at it vertically
so in order to capture still the same region (the red one)
it is bounded by the line x = 2 and curve x = e^y
dusty sigil
this is the original ya?
faint gorge
ye
dusty sigil
ln(1) and ln(2) are the y bounds
hmm why are ln 1 and ln 2 the y bounds
isnt it 0 to ln2?
faint gorge
and what is ln(1)?
dusty sigil
and what is ln(1)?
you sir are a legend
faint gorge
you sir are a legend
no i am not 😭 i am literally a student of @arctic field
dusty sigil
okay wait im back to square
its looks like integrating the thing originally
before flip
faint gorge
it should been from e^y to 2 but tbh it doesnt look very promising
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faint gorge
are u sure you are not missing something
dusty sigil
are u sure you are not missing something
my friend sent me the answer its like this
just a simple u sub xD
faint gorge
i am so dumb
dusty sigil
nah its my fault
i messed up the upper and lower bound
so its harder to see the
pattern
but thansk so much i learn much from the flip (which is the the main point)
🙏
.close
mellow willow
I am confused what my teacher met by “ opposite inputs produce the same outputs” and opposite inputs have opposite outputs “
devout snowBOT
I am confused what my teacher met by “ opposite inputs produce the same outputs”...
mystic scarab
Do you know what opposite means?
lament plover
on the upper one whether u give +x or -x u get +y
but in the lower if u give +x u get +y, if -x u get -y
fierce matrix
on the upper one whether u give +x or -x u get +y
but in the lower if u give +x ...
So is opposite to the y axis is meant by opposite for the parabola?
If y axis is a road, and (1,4) is a shop, opposite the shop there is a laundrette, at (-1,4)?
lament plover
well i can see the teacher clearly cooked with the wording
it only makes sense 4 the second one
fierce matrix
If you fold the first graph along the y axis, you get the same graph, the graph is symmetric to the y axis, in other words even. x values on opposite sides of the x axis, where the origin is the middle, are mapped to the same y values, or outputs.
For the second one if you fold the along the y axis and then along the x the curves match, I think.
A value and its additive inverse as inputs are both mapped to the same output, that's the even function, the parabola.
fierce matrix
it only makes sense 4 the second one
Oh the second one is tricky to understand, at least for me it is.
mellow willow
on the upper one whether u give +x or -x u get +y
but in the lower if u give +x ...
Ok thank you the wording is so confusing to me.
lament plover
Oh the second one is tricky to understand, at least for me it is.
i told u bro u overthinking
little totem
a simpler way to say this, since it looks like you know functions already from the worksheet
even functions: f(x) = f(-x)
odd functions: -f(x) = f(-x)
fierce matrix
i told u bro u overthinking
What maybe was meant by the teacher is for an odd function
x ⟼ f(x)
-x ⟼ -f(x)
so the opposite of x, -x is mapped to the opposite of f(x), which is -f(x).
I didn't know the names odd and even came from the powers of x.
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thick schooner
I didn't know the names odd and even came from the powers of x.
is this thomas?
i vaguely remember lol!
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toxic kernel
The final project involves examining and analyzing statistical data. The project can be completed in pairs or individually.
Those working in pairs must document their work and submit a brief text along with the project, describing how the collaboration went and what each person contributed.
Distance learners must also keep track of their work on the project and submit it with the final deliverables. This can be done through short journal entries or a brief report (no more than one page).
1)
The first step is to find a dataset or research topic (in consultation with the teacher) that you are interested in analyzing based on what you have learned in the course. You can search for data online, such as on the Statistics Iceland website or the Eurostat website. Both sites offer a variety of datasets that can be downloaded in Excel format for analysis. Once you have found a dataset(s) of interest, you must contact the teacher to confirm that the data is suitable for the project.
2)
Next, you will conduct a simple study by analyzing your data using the statistical knowledge gained in the course. The analysis will vary depending on the topic and datasets, so use creativity and focus on what best suits your research goals. Use descriptive statistics to present numerical information and graphs. Interpret the results in your own words and relate them to the data.
(Concepts covered in the course that you might explore include: descriptive statistics, measures of central tendency (mean, median, mode), distribution (range, mean deviation, standard deviation), correlation, significance, normal distribution, binomial formula, etc.)
devout snowBOT
The final project involves examining and analyzing statistical data. The project...
toxic kernel
3)
You will present your findings to the teacher and classmates on the assessment days at the end of the term. The presentation format can vary (e.g., slideshow, video, brochure, or poster).
The presentation should include:
- Introduction: Overview of the topic and objectives.
- Methodology: Description of methods and statistical processing.
- Results: Explanation of findings with tables and graphs.
- Conclusions: Summary of results and interpretation of their significance.
Presentations will take place on Teams on Monday, March 3rd, between 10:00-12:00. Both distance and on-campus students are expected to attend. Note that the presentation accounts for 30% of the project grade.
4)
In this submission area, you must submit:
- Your presentation materials.
- The Excel files used for the project (work documents).
- If the project was done in pairs, each student must submit a short text discussing the collaboration and their individual contributions.
- Distance learners must also submit their report on their work for the project.
I chose unemployment rate.
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restive river
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restive river
for the part b
is that gonna be like i make a secant from p to q1
then p to q2 then q3 q4
getting closer to the p
that would be the tangent
i suppose?
.close
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icy acorn
Determine all extremum points of this function and classify them!
so normally I would take the 1. derivation of the function, set equals 0, 2. derivation, form the Hesse matrix and the determinant and then classify. Is there a quicker way to find the solution cause this is lowkey time consuming
sonic wolf
hello im not rly sure how to use this discord server but i need help with any tips on factorizing and simplifying in grade 9 maths
icy acorn
icy acorn
hello im not rly sure how to use this discord server but i need help with any ti...
u can use one of the available help
this is occupied
by me
hi hi
sonic wolf
oh sorry i dont rly know how to use this server
supple knot
Determine all extremum points of this function and classify them!
so normally I...
nope. just get better at partial derivatives
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finite briar
HELLO
iron kindle
!da2a
devout snowBOT
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finite briar
integration time (source: mqnic)
$-\frac{1}{4}\int_{0}^{\infty}\frac{1}{te^{t}}\sum_{n=1}^{\infty}\frac{1}{n\left(-t\right)^{n}}\left(\int_{0}^{t}x^{\frac{n-1}{2}}e^{-x}dx\right)^{2}dt$
woven radishBOT
rak³en
finite briar
alrighty
iron kindle
yuck
finite briar
right off the bat, the squared term is the lower incomplete gamma function
iirc theres a recurrence relation between the s+1 and s terms
sturdy mango
iirc theres a recurrence relation between the s+1 and s terms
yess
finite briar
found it
from here I should be able to get a result in terms of the error function (gamma(1/2, t)) and a e(-x)(finite GP)
or something like that
but the square term scares me :\
finite briar
**rak³en**
I'd like if I could just..you know whoop everything into a double integral
but I have to check convergence before hand
which reminds me does this converge as written at all?
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finite briar
<@&286206848099549185>
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raw bear
oh sorry i dont rly know how to use this server
Pick any channel that has the word "help" in its name WITHOUT the "|" and the name of someone behind (the person who occupied the channel).
But your question is too broad,
so i think the math-discussion channel should be fine,
the help channels are for specific problems
@sonic wolf
dense lynx
this probably is not solvable
dense lynx
**rak³en**
i derived it from
$\int_0^1 \int_0^1 \frac{\ln(1 + xy)}{1 + x^2 + y^2}, \mathrm{d}x, \mathrm{d}y$
woven radishBOT
Mqnic_
finite briar
thank you for giving me the original integral
finite briar
this probably is not solvable
u tried complex stuff?
dense lynx
it does
finite briar
How did you test a double integral?
dense lynx
to about 0.1111415849
you check it numerically using like matlab or wolfram
well ig that’s not necessary here
finite briar
I see
dense lynx
this function has no poles where integrated and it’s integrated over a finite region so it’s not like it’s going to diverge anyway
finite briar
oh right good point
finite briar
.close
devout snowBOT
empty flame
still obsessed with integrals as usual 
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long panther
can someone explain the derivative of a^x to me without any circular reasoning
crude spruce
can someone explain the derivative of a^x to me without any circular reasoning
,, a^x = e^{\ln \qty(a^x)} = e^{x \ln (a)}
woven radishBOT
kizzyyy
long panther
yea
i swear to god if you use the derivative of e^x or logarithms im actually gonna jump out my window
iron kindle
i swear to god if you use the derivative of e^x or logarithms im actually gonna ...
$\dv{x}e^{x\ln(a)}=\ln(a)e^{x\ln(a)}=\ln(a)a^x$
woven radishBOT
Bonk
misty crest
then we use lhoptial
no
feral agate
$\dv{}{x} \left(a^x\right)=\lim_{h\to 0}\frac{a^{x+h}-a^x}{h}=a^x\cdot\lim_{h\to 0}\frac{a^h-1}{h}$
e is defined as the value of a for which that second limit is 1
wtf
woven radishBOT
kheerii
long panther
let me guess then that limit is equal to lna
misty crest
and?
long panther
thanks for 0 circular reasoning
feral agate
dude...
misty crest
you’re insufferable
he derives the derivative of e^x using this
using the definition of e^x
feral agate
define $e^x$ as the taylor series $1+x+\frac{x^2}{2!}+...$ and prove everything from there
woven radishBOT
kheerii
long panther
you’re insufferable
bla bla bla without circular reasoning
circular reasoning
i wanted it without circular reasoning
youre insufferable
misty crest
nothing is circular smart guy
long panther
watch this
so its basically just really advanced stuff?
misty crest
so its basically just really advanced stuff?
no
feral agate
you have to start from some definition of an exponential
it could be the limit or the series
misty crest
**kheerii**
you’re the type of guy to say e^x = this is circular lmao
it’s literally just a definition
long panther
it’s literally just a definition
dude thats why its circular
iron kindle
dude thats why its circular
huh
long panther
im talking about how youd show the derivbbative of ax^b
misty crest
🤔
misty crest
obviously not
misty crest
has to be
spring salmon
np
long panther
.close
deft scaffold
(ignore that some of the numbers are different between the two images, but im struggling to understand why in the first image the (12-y) is not squared?
devout snowBOT
(ignore that some of the numbers are different between the two images, but im st...
pseudo basin
they are doing it with the shell method
neither the 12-y nor the y^2 are supposed to be raised to the second power here
it's just that their shells enclose the x-axis rather than the y as is usual
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mystic bloom
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mystic bloom
Idk how to do binomials
devout snowBOT
@mystic bloom Has your question been resolved?
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@mystic bloom Has your question been resolved?
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@mystic bloom Has your question been resolved?
tawny pewter
Idk how to do binomials
!show
devout snowBOT
Idk how to do binomials
Show your work, and if possible, explain where you are stuck.
mystic bloom
Idk how to do it
mystic bloom
Idek wat a binomial is
tawny pewter
if you pick one american what's the probability he lives in a city with 100k+ people in it?
tawny pewter
Idek wat a binomial is
it's a random variable representing the number of success after n trials, in your cases the "successes" are people living in a city with 100k+ population and the number of trials is 30.
tawny pewter
Idek wat a binomial is
ok let's make this simpler, if you pick one person, he has 7/10 chances/probability to be in a city with 100k+ pop (and 3/10 chance not to) it's a binomial n = 1, p=7/10, if you pick 2 person, both can be in such a city, none of the 2 and 1 of the 2 so the number of people in a city with 100k+ pop in your sample of 2 people (let's call it X) is a binomial with n=2 and p = 7/10 with the probabilities P(X=0) = (3/10)^2 P(X=1)=2 * (3/10) * 7/10 and P(X=2) = (7/10)^2
does this make any sense?
mystic bloom
if you pick one american what's the probability he lives in a city with 100k+ pe...
1/100000
mystic bloom
ok let's make this simpler, if you pick one person, he has 7/10 chances/probabil...
Idk the end
tawny pewter
1/100000
I doubt it your question says he has 70% chance to be in a city with 100k+ pop.
tawny pewter
that's the p parameter in the binomial distribution
ok now for a) let's make it simpler, if you had 3 American instead of 30 what's the chances that exactly 2 of them are in a city with 100k+ pop in it?
mystic bloom
ok let's make this simpler, if you pick one person, he has 7/10 chances/probabil...
I don't get the ending at all
idrk wat p() means in stats
tawny pewter
It's a shorthand for the probability the chance that a random variable takes a certain value
so for one people the probability that exactly 1 guy lives in a city with 100k+pop is P(X=1) = 7/10
tawny pewter
idrk wat p() means in stats
for example
tawny pewter
ok now for a) let's make it simpler, if you had 3 American instead of 30 what's ...
now back to this
mystic bloom
so for one people the probability that exactly 1 guy lives in a city with 100k+p...
Y is it P(x=1) instead of p(1)
mystic bloom
ok now for a) let's make it simpler, if you had 3 American instead of 30 what's ...
Idk
tawny pewter
Y is it P(x=1) instead of p(1)
it can be p(1) if you have seen it written this way before, I learned it as P(X=1)
tawny pewter
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mystic bloom
ill try tmrrw idk
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@mystic bloom Has your question been resolved?
inner ibex
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lost laurel
huh, domain of 1/(9-x), right
inner ibex
how do i know the domain for that..
wispy oyster
domain of the inverse function is the range of the original function
wispy oyster
the denominator is always negative for x>9
so from -inf to 0
0 not included since that is the horizontal asymptote
inner ibex
wow this is hard 😢
inner ibex
the denominator is always negative for x>9
ok lemmet ry antoerh one
wait that ones easy
ok so the range of the inverse function is
(1,infinity)
and the domain is
idk..
is it
2^2 - 1 bcoz x is greater than 1 but not 1... so u sub in 2 to find the smallest value..
(3, infinity)
wispy oyster
finding range can be tough by just looking at the function
advice:
find inverse, look at the domain of the inverse
that is the range of the original function
wispy oyster
yes that is correct but notice how they have the x>1 requirement
wispy oyster
f(x) = x^2 - 1
range are all possible outputs, if x>1 then the minimum value would be something around x~1, plugging that in yields
f(1.000000001) = 0. So the range is from 0 to inf
for quadratics, u can find the range by finding the max or min
inner ibex
f(x) = x^2 - 1
range are all possible outputs, if x>1 then the minimum value wou...
doesnt it give u the range alr
in the thing
x>1
im havign trouble finding da domain
wispy oyster
thats the domain, x>1
wispy oyster
thats 0 to inf
wispy oyster
look at this graph
inner ibex
yes
wispy oyster
since we restrict domain to x>1
we start at around x=1
notice how it is 0 at x = 1
but 0 is not included since the initial condition was x>1 so it is (0, inf)
inner ibex
if we restrict the domain to x>1 dont we have to start at x=2
wispy oyster
is 1.0000001 not a number?
inner ibex
oh
1.0000000000000000000000000001
wow thats cheating because then wont the range thing be off by a few 0.00000000000000120121391293
wispy oyster
u have infinite real numbers between any two points a and b no matter how close a and b are as long as |a-b| ≠ 0
there are infinite real numbers between 0.0000000000001 and 0.0000000000000000001
inner ibex
oh
ok
what is it was x>=1
would the range be da same
wait ok let me try again with my new found knowledge
inner ibex
u have infinite real numbers between any two points a and b no matter how close ...
also for the inverse do u guys use the same method as my teacher
he makes the subject x
wispy oyster
yes
inner ibex
ohhh okok
inner ibex
u have infinite real numbers between any two points a and b no matter how close ...
whats the point of <= >= if u can just cheat like this
wispy oyster
but 0 is not included since the initial condition was x>1 so it is (0, inf)
if it was x≥1
the range would be [0, inf)
notice the square bracket
it means 0 is a possible value that the output can take
wispy oyster
,w quadratic equation
woven radishBOT
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@inner ibex Has your question been resolved?
inner ibex
use the quadratic equation to isolate x
oh
cant u jus tcomplet ethe square much easier
stone juniper
$$In the arithmetic progression (a_n): a_{1} = - 4 , a_{5} = a_{4} + 3; Determine the (a_1_0) of this progression.$$
devout snowBOT
$$In the arithmetic progression (a_n): a_{1} = - 4 , a_{5} = a_{4} + 3; Determin...
woven radishBOT
www.
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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@stone juniper Has your question been resolved?
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www.
wide ember
no
bro
ur given
a5 = a4 + 3
right?
then how will you find common diff from this info?
think about it
stone juniper
i can express $a_5$
woven radishBOT
www.
stone juniper
$a_5 = -4 +3d +3$
woven radishBOT
www.
woven radishBOT
lizzie250
stone juniper
yes
wide ember
and this is equal to?
stone juniper
-4
wide ember
bro what?
stone juniper
$a_5 - a_4 = a_1 = -4$
woven radishBOT
www.
stone juniper
$d = a_2 -a_1$
woven radishBOT
www.
stone juniper
oH ITS DIFF
wide ember
yessss
stone juniper
we got diff 3
wide ember
yes
stone juniper
craftily task
wide ember
lol
stone juniper
thank you
wide ember
np
stone juniper
.close
finite briar
time to open a help channel
devout snowBOT
time to open a help channel
olive snow
Never a bad time to
finite briar
how to convert this into polar coordinates
and more generally any rectangular polygon into polar coordinates
jaunty mantle
That looks hard
lost laurel
and more generally any rectangular polygon into polar coordinates
do you have the points
jaunty mantle
That doesn’t look very nice to polar coordinates
finite briar
from here https://math.stackexchange.com/questions/1248630/converting-unit-square-domain-in-x-y-to-polar-coordinates i know what it is for a square but I have 0 idea why this is true
jaunty mantle
Especially ones that aren’t centred
finite briar
Especially ones that aren’t centred
😐
finite briar
The thing is that how do you manage r in your mind ?
that is precisely the problem i can figure out theta easily
jaunty mantle
Like your r both the top and bottom limit needs to change wrt θ i
finite briar
i think of r like the minute hand of a clock
finite briar
Like your r both the top and bottom limit needs to change wrt θ i
because it isnt centred?
jaunty mantle
Yeah
Cos you need to cut out the bottom
Your r isn’t starting from the origin
Or any nice circular line
finite briar
ur photo btw
it had two regions
was it because i also had the bounds flipped
for the 2 variables
finite briar
And your question had 2 integrals added together
ahh okay okay so since my integrand is symmetric they're effectively the same thing right?
jaunty mantle
It’s 2 times 1 of the parts
Now
Have you considered
Doing the square or triangle
And subtracting the extra bits
finite briar
no
because i came here from a square
if u remember gpt integral is over a unit square
finite briar
wait 🤯
jaunty mantle
Like do the big square
The minus the small square and the medium square
Idk just a thought
They seem a bit nicerly aligned for polar coords
finite briar
maybe let me see
i think i'll worry abt this one later
thx for the idea
the reason i split it is because if $|x|,|y| < \frac{1}{\sqrt{2}}$ then i can expand $\frac{1}{1+x^2+y^2} = \sum_{n \geq 0} (x^2+y^2)^n$
woven radishBOT
rak³en
finite briar
right??
jaunty mantle
I don’t know and I’m too tired atm
finite briar
I don’t know and I’m too tired atm
devout snowBOT
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wide ember
help
wide ember
wide ember
convert to sin^2 theta?
wicked turtle
also 69-21 =48 and 57-33 = 24 = 48/2, might be useful(?)
wide ember
i converted the numerator to sin^theta
pseudo basin
do not miss the two
wide ember
yeaaa..but now i am stuck
pseudo basin
what do you have on the numerator exactly
in full
just to check that we have not both gone off track
pseudo basin
ok so i asked you for only the numerator
wide ember
sorry
pseudo basin
but if you were gonna give the entire fraction then you would have to wrap the numerator and the denominator in parentheses
anyway
it is actually better to convert only ONE of the things on top to a sine
so cos^2(33) - sin^2(33)
this is cos(2*33)
wide ember
soryyyyy
pseudo basin
the bottom is sin^2(10.5°) - sin^2(34.5°)...
wide ember
yes
pseudo basin
wait so you've learned the compound angle formulas right
pseudo basin
then you also know that sin^2(x) = (1 - cos(2x))/2 yes?
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versed ledge
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hexed fractal
what's the general equation of a circle? do you think you can work your way around convert this?
devout snowBOT
@versed ledge Has your question been resolved?
versed ledge
Yes
feral skiff
A tower stands on level ground. From a point P on the ground, the angle of elevation of the top of the tower is 26 degrees. point q is 3m vertically above p and from this point the angle of elevation of the top of the tower is 21 degrees. Find the height of the tower. This is in the sine cosine rule chapter btw.
devout snowBOT
A tower stands on level ground. From a point P on the ground, the angle of eleva...
rose rock
Start by drawing a diagram
feral skiff
this is what I thought it was trying to describe
i then tried 90-26 = 64 degrees
Is that allowed?
I then did 180 - 26 - 64 = 90
rose rock
Think that 23 should be 21 and it should be from a line parallel to the base
feral skiff
the answer is 14.1
I used the sine rule to try get this line, but it came out to 1.2 which is way off
rose rock
That 23 is not the angle there
devout snowBOT
@feral skiff Has your question been resolved?
devout snowBOT
feral skiff
.reopen
devout snowBOT
✅
wintry flare
is this right? where do I go from here?
your 23 degree is supposed to be 21 from what it says in the question
do you know which trig function would you use here
devout snowBOT
@feral skiff Has your question been resolved?
feral skiff
do you know which trig function would you use here
nope
feral skiff
.reopen
devout snowBOT
@feral skiff Has your question been resolved?
wintry flare
nope
based on the picture you drew and the value youre trying to find (height) it would be cosine
wait
lemme actually solve the problem first, im lowk talkin crazy
@feral skiff okay sorry, you'd be using tangent lol
feral skiff
can you explain what im supposed to do im completely lost
wintry flare
can you explain what im supposed to do im completely lost
yeah
so it give you two angles, 21 degrees and 26 degrees
you can make a relationship between the height using tangent for both
tangent = adjacent/opposite
so, for point q, you know tan(21)=h/x
does this make sense so far ^
feral skiff
yeea
wintry flare
now try the same for point p
wintry flare
yea i dont get it lol
which part
devout snowBOT
@feral skiff Has your question been resolved?
wintry flare
i dont see how you apply tan to this
have you learned tangent yet?
valid vector
@feral skiff Can you show the original question you need help with?
devout snowBOT
@feral skiff Has your question been resolved?
feral skiff
have you learned tangent yet?
All i know about tangent is that its equal to sin/cosine and that tan(x) = opposite/adjacent
feral skiff
<@1238576667044220979> Can you show the original question you need help with?
A tower stands on level ground. From a point P on the ground, the angle of elevation of the top of the tower is 26 degrees. point q is 3m vertically above p and from this point the angle of elevation of the top of the tower is 21 degrees. Find the height of the tower. This is in the sine cosine rule chapter btw.
valid vector
is this right? where do I go from here?
That is a correct diagram. Now, let us denote h to be the height of the tower, and x to be the distance from point P to the tower. Note that $\sin(23^{\circ})=\frac{h-3}{x}$, and $\sin(26^{\circ})=\frac{h}{x}$. Do you see why?
woven radishBOT
mathisfun
coral cosmos
How do I find the area of triangle ABC
devout snowBOT
How do I find the area of triangle ABC
winter patrol
what have you tried
coral cosmos
Need help writing the equation to solve this
devout snowBOT
Need help writing the equation to solve this
winter patrol
what have you tried?
jovial current
Need help writing the equation to solve this
try and set up proportions of sides because you have similar triangles
coral cosmos
.close
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dark siren
What does this upside-down triangle notation mean?
devout snowBOT
What does this upside-down triangle notation mean?
wicked turtle
probably gradient but maybe depends on the context?
dark siren
probably gradient but maybe depends on the context?
Idk if this helps
wicked turtle
Idk if this helps
not really, i'm not familiar with linear transport theory
but if the context is physics then i would be very surprised if this means anything other than "the gradient of L at the point (x,omega)":
devout snowBOT
@dark siren Has your question been resolved?
dark siren
not really, i'm not familiar with linear transport theory
but if the context is ...
I see, thanks! Another question: what does the omega times the gradient mean?
wicked turtle
almost certainly it's the dot product of omega with the gradient of L
(since both are vectors)
geometrically speaking, it's the directional derivative of L in the direction of omega, time the magnitude of omega
dark siren
geometrically speaking, it's the directional derivative of L in the direction of...
Thanks! Really appreciated!
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frail igloo
please explain to me, like i'm a stupid idiot, why the position of C, if the square is free to roll is described by r(x,y) = <(r+b)sintheta +rthetacostheta, (r+b)costheta + rthetasintheta>
devout snowBOT
please explain to me, like i'm a stupid idiot, why the position of C, if the squ...
frail igloo
i just don't understand where the second additional costheta and sinetheta terms appear in the x and y components
i know why the product is rtheta but idk why it's opposite trig functions.
DOES THIS EVEN MAKE SENSE IN THE WAY THAT IM EXPLAINING IT
faint zinc
please explain to me, like i'm a stupid idiot, why the position of C, if the squ...
The three angles are equal
frigid mantle
Can someone help me with 21 and how the answer is 2 pie/3 and 5 pie/3 ion get it😭💔
devout snowBOT
Can someone help me with 21 and how the answer is 2 pie/3 and 5 pie/3 ion get it...
wide ember
do you know the quadrants it may lie on?
frigid mantle
wide ember
since the value is negative
where is tan theta negative
in which quadrants
it is in quad 2 and 4
wide ember
Why tho ion get quadrants
cause x in 2nd quad is negative and y in the thrid quad is negative....
since tan theta = perpendicular / base
frigid mantle
Oh okay what about QIII they both negatives 🤣🤣
wide ember
they cancel out no
wide ember
when you divide the negative perpendicukar and negative base
wide ember
Then it be the same for cot right
yes
woven radishBOT
lizzie250
wide ember
do you agree?
frigid mantle
Where I put in the quadrant thing
pseudo basin
so you can say that $y/x = -root 3/1 or root3/-1$
$\frac{y}{x} = -\frac{\sqrt{3}}{1}$
woven radishBOT
Ann
pseudo basin
if you're gonna use latex, use latex properly!
woven radishBOT
lizzie250
wide ember
yes
wide ember
Where I put in the quadrant thing
since the answer lies in the 2nd and 4th quad
pseudo basin
sorry idk the fucntions yet
#latex-help has a cheat sheet
wide ember
<#840667252793802752> has a cheat sheet
ok
pseudo basin
\frac{TOP}{BOTTOM} makes fractions and \sqrt{stuff} makes square roots
wide ember
since the answer lies in the 2nd and 4th quad
you will one mark (-root3,1) as one of the points
frigid mantle
👍
frigid mantle
Ok
wide ember
$(1, -\sqrt{3})$
winter patrol
you're mixing up the x and y coordinates
woven radishBOT
lizzie250
wide ember
for quad 2
frigid mantle
👍
woven radishBOT
lizzie250
wide ember
for quad 4
frigid mantle
👍
wide ember
now you know the angle that will be formed between the triangle
frigid mantle
👍
So cuz in quad II 2 pie/3 got like square root of 3 and it also got like -1 on top of that shi and then for quad IV there’s like a 1 and like a negative square root of 3 which is like it’s 5 pie/3?
Am I thinking right
😈😈
frigid mantle
WOW! THX! 😁
wide ember
np
frigid mantle
/done
wide ember
but in theory you won't do that
frigid mantle
Oh
wide ember
i watched a video on it once i will find and share
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remote elbow
amber mantle
idk how this works ngl u good 😭
dense lynx
Here is a reputable question for you to solve @hoary sierra :
Let X be a finite set of points. Let M be a collection of subsets of X.
We say that M is satisfactory if each of the points of X can be colored either red or blue in such a way that no set of M has all points red or all points blue.
Suppose that each set of M has exactly 5 points. What is the smallest number of sets in a collection M that is not satisfactory?
dense lynx
.close
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silver folio
help
pseudo basin
,rccw
woven radishBOT
pseudo basin
show your calculation
woven radishBOT
pseudo basin
how do you get from 12 = 4.2 * (4+R)/(4R) to R=10
silver folio
Sorry I write wrong is 4r/4+r
pseudo basin
little r or big R?
silver folio
