there are reasons why some deductions are totally worthless and some aren't
#help-27
vast rain
I've also listened to people intentionally self-sabotage so they "don't get pushed into a higher tax bracket" despite that being absolutely the wrong thing to do
so I'm really skeptical in general of people who don't understand math well, but complain that it's not useful in life
taxes are just one example
mild basin
I've also listened to people intentionally self-sabotage so they "don't get push...
morally, or economically?
vast rain
morally, or economically?
economically
nova idol
economically
mild basin
they are holding themselves back thinking they will get more tax return by doing so?
vast rain
they are holding themselves back thinking they'll end up with more money
nova idol
donate the extra money
That’s not sabotaging then
vast rain
That’s not sabotaging then
donate the money except a dollar which you keep for yourself lol
nova idol
Lol
Avid do you understand why donating to save money is dumb
Like where they are messing up because they don’t understand piecewise
vast rain
donating in general doesn't save you anything on your taxes until you get above a certain point in deductions
mild basin
ya, so they wanna stay under a certain threshold, to stay under a bracket in order to be taxed less on their income. you are saying that its morally and economically wrong to do so? maybe they will go on vacation with their family for a month instead of work and go over that month, i dunno if it's so cut and clear
vast rain
because your total deductions are also ... piecewise
in the sense that donations are itemized deductions
nova idol
ya, so they wanna stay under a certain threshold, to stay under a bracket in ord...
If the tax bracket are in 10k and you make 15k
vast rain
ya, so they wanna stay under a certain threshold, to stay under a bracket in ord...
lol and I guess you're one of those people who can't visualize a tax bracket
nova idol
Say you donate 5k because you want to be in only the 10k bracket
vast rain
if you understood piecewise functions, you'd understand that you end up with LESS MONEY if you donate to go into a lower tax bracket lmfao
nova idol
So you have 10k taxed at 10k bracket
mild basin
lol and I guess you're one of those people who can't visualize a tax bracket
you're saying they would actually make more by going over the bracket?
nova idol
Or if you didn’t donate you would have 10k at 10k and 5k at 20k bracket
vast rain
yes that's obvious to someone who understands piecewise functions
nova idol
Money that is taxed is more than nothing at all
vast rain
the only case when you'd end up with less money is if your effective marginal tax rate is greater than 100%
mild basin
oh donation, ya but maybe they just wants to take time off, nothing wrong with that either. who are we to judge what their business is, from a moral standpoint
vast rain
this sometimes happens with rapid phase-outs of certain credits/deductions, but it's a very narrow thing
mild basin
to not go over and make too much
instead of donating, it's giving to travel resorts lol
vast rain
@mild basin can you calculate the tax liability of a single filer with $30,000 of taxable income?
nova idol
it’s not usually a vacation
mild basin
<@313298495417221121> can you calculate the tax liability of a single filer with...
12% according to that chart
mild basin
looks like it
vast rain
the government thanks you for your donation in excess of what you are legally required to pay
nova idol
you still don’t get it avid
vast rain
see why understanding piecewise functions is important????
vast rain
lmfao the chart isn't missing anything
nova idol
you don’t understand piecewise functions
vast rain
you're missing the understanding
mild basin
well then, it looks like donation is taking place after all. just to the government
vast rain
well technically this is describing a piecewise constant function, which then gets integrated into the function which represents tax liabilities
which is piecewise linear
vast rain
well then, it looks like donation is taking place after all. just to the govern...
not tax deductible, though the government is nice and will actually tell you that you calculated it incorrectly and give you your money back
what you won't get back is all of the poor decisions that made your tax liability higher than it should've been
mild basin
alright, so you need to show me the full chart(s) rather than expect me to guess the right answer
nova idol
The cropped chart has all the info you need
mild basin
this is exactly why i would take it to the tax professionals, as i stated originally. silly mistakes like this, not filling out proper forms, paying too much, getting too little back
nova idol
it’s not compclisted
vast rain
the tax professionals won't tell you the stuff you should do BEFORE the tax filing season is there
nova idol
You just don’t understand piecewise
mild basin
The cropped chart has all the info you need
lol
vast rain
there are things you can do BEFORE the year is up to reduce the amount that the tax professionals calculate
nova idol
it does
mild basin
thanks for sharing that after the fact you cropped it
nova idol
??
nova idol
Sacc isn’t trying to trick you
vast rain
why do you need to know about married people
why do you need to know about net investment income tax
why do you need to know about long term capital gains lmfao
nova idol
learn piecewise functions
mild basin
if thats where 30K is
i'm just looking at this chart, what does piecewise have to do with it
nova idol
sacc you want to just explain it or nah
mild basin
i don't know how this would help me to see other numbers not visible on the cropped image, or understand tax laws as per certain countries
vast rain
sacc you want to just explain it or nah
honestly I'm feeling a little lazy writing out the latex
nova idol
me too
vast rain
i don't know how this would help me to see other numbers not visible on the crop...
almost every country that has an income tax computes taxes this way with marginal rates
mild basin
<@313298495417221121> can you calculate the tax liability of a single filer with...
so to answer your question, no, I cannot. there are other factors in play
vast rain
I'll basically tell you how piecewise relates to this
nova idol
no there aren’t
mild basin
lol i gave the answer from the picture provided, it was wrong, so clearly there is other math involved here
nova idol
other math yes
vast rain
the taxes are computed as a piecewise linear function, where it's defined to be continuous, and the slope at every interval is given by the percentage in the chart
nova idol
Not other factors
mild basin
Not other factors
are you referring to factors as in the multiplication of factors equaling a product?
i'm using the term loosely, other "things" at play
vast rain
basically, what the chart says is that you pay 10% on your first $22,000 of income, and then you pay 12% on the next $67250
nova idol
For married filers
mild basin
basically, what the chart says is that you pay 10% on your first $22,000 of inco...
Ohhh, of course. Alright, that makes sense. I definitely misread this, my bad... All countries do this the same way?
vast rain
it's $11,000 and $33625 for single filers
nova idol
Ohhh, of course. Alright, that makes sense. I definitely misread this, my bad....
It’s not obvious though
mild basin
For sure
vast rain
Ohhh, of course. Alright, that makes sense. I definitely misread this, my bad....
I don't know the tax laws of all 196+ countries in the world, but the vast majority do it
nova idol
You need to know the intuition behind piecewise functions
Which is what we have been trying to explain
acoustic vault
something like this no
mild basin
It’s not obvious though
Intentionally unobvious? lol, like I wonder why they don't make it more clear
nova idol
Is this nordic
mild basin
bottom is real top is the fake
`
but taxes in Denmark are too high
Køter — Today at 12:50 AM
yes
[12:50 AM]
for me, you guys don't have jobs
[12:51 AM]
get money from studies`
mild basin
I gotta get some sleep haha, it's late here..
acoustic vault
i just use verbal language
mild basin
sounds like i insulted you
nah
vast rain
lol yeah that's not exactly what he meant
acoustic vault
so translation is weird haha
vast rain
he meant for me it's meaningless, because I have no job
nova idol
Are you getting a phd?
vast rain
a phd to call yourself doctor
acoustic vault
masters atm. in denmark they pay you throughout though
nova idol
so that’s a job
acoustic vault
I gotta get some sleep haha, it's late here..
its 5:54am here 💀
mild basin
still haven't slept or having morning coffee?
nova idol
Did you wake up or stay up
acoustic vault
stay up
nova idol
Jeez bro
nova idol
mild basin
stay up
I'm not sure if this is fake, it seems like it would be impossible.. https://www.youtube.com/watch?v=EDx1JvPEtxs
nova idol
fake
mild basin
they interviewed him and he's napping in the video hahaha
mild basin
maybe no deep sleep or something, i dunno, they say it's PTSD after Vietnam War
can't be good for the body
mild basin
fake
`Its possible that he might do something similar to dolphins. IIRC dolphins sleep with one hemisphere of their brain at a time, and then swap to the other. They are never totally asleep but often 'half asleep'.
Parts of his brain may be sleeping independently of the other parts. Definitely not normal, but with 7 billion humans on the planet, someone with weird biology is bound to crop up every now and then.`
mild basin
found that on Reddit, apparently it's still an unsolved mystery.. sounds fake for sure, but ...
nova idol
when you got class tmrw
nova idol
gn
nova idol
oh thats so late
manic timber
how do u do this
devout snowBOT
how do u do this
devout snowBOT
@manic timber Has your question been resolved?
round canyon
Use spherical coordinates. Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 4, above the xyplane, and below the cone z=sqrt(x^2+y^2)
Bit confsed on how to find phi on this problem
devout snowBOT
Use spherical coordinates. Find the volume of the solid that lies within the sph...
@round canyon Has your question been resolved?
meager steppe
B. Reduce
meager steppe
i need help
rotund heron
See if something factors out and then cancels
Also by reduce you mean simplify, right?
meager steppe
yeah translating isnt really my strong point
so like i know i can turn the top into 2x(x + 2)
but idk what to do with the bottom one
meager steppe
a^2 - b^2 = ?
isnt that (a+b)(a-b) thing
meager steppe
(x+2)(x-2)
restive river
yep
proper rampart
yessir
proper rampart
👍
meager steppe
.close
restive river
Over reals, cauchy implies convergent and convergent implies cauchy right?
But under the rationals
it only goes convergent -> caughy right?
ALSO
Differentiality -> Continuity
& also
Continuity -> Integrabilty
all arrows imply one way implications
correct?
devout snowBOT
Over reals, cauchy implies convergent and convergent implies cauchy right?
But u...
devout snowBOT
@restive river Has your question been resolved?
pseudo basin
yes
restive river
yes
Differentiality -> Continuity
Continuity -> Integrabilty
correct?
from f:S -> Reals
id doesnt go both way for those right?
pseudo basin
yes as i said before
devout snowBOT
devout snowBOT
Available help channel!
light mica
Hi
stuck field
@light mica read #❓how-to-get-help
And you already have #help-18
light mica
one sec
stuck field
,rccw
woven radishBOT
stuck field
Which question/part?
stuck field
Are you familiar with" long division method"
light mica
Yeah thats the method we are supposed to do
stuck field
Then what's stopping you?
light mica
Idk how to
stuck field
light mica
Ive seen that video already
stuck field
yes write it in that long division format.
Then n times what equals n^2?
light mica
Idk-
stuck field
Do you realise what ^2 means?
light mica
yeh
stuck field
What's 2^2?
light mica
n x n?
light mica
n
stuck field
yes!
So now you'd subtract n(n-1) from your dividend
Like he does in the video.
I hope you realise how to do that.
stuck field
Yes, the only thing is that you also multiply that -1 by n.
You don't only multiply n by n but entire (n-1) by n
light mica
That is 1 n
stuck field
-1n
light mica
Oh -1 x n is -1n
stuck field
Yes.
Now subtract.
-2n - (-n) = -n
And there's 1 remaining.
So you have - n + 1
Do you get this?
light mica
Oh ok
stuck field
Is this correct?
it is correct.
light mica
Thanks
stuck field
You're welcome, can you similarly do the other parts?
You're free to seek assistance once you get stuck...
light mica
Ill try
shut inlet
light mica
😢
stuck field
You're late.
shut inlet
You're late.
hmm k why do you have iota as your pfp (like complex numbers?)
stuck field
Irrelevant.
light mica
This correct?
stuck field
And that's not the purpose of this help channel, so yes. Don't.
In the quotient it should be m - n
light mica
I get mixedup with signs
restive river
This correct?
Quotient is m-n
light mica
How to know which sign comes in the quotient
shut inlet
This correct?
If you look at the term inside the division(dividend or wahtever not sure) you see that it is just (m-n)^2 then you can cancel this with the denominator
shut inlet
shut inlet
I dont understand
m^2 -2mn+n^2 = (m-n)^2
light mica
I still dont have clue
restive river
I dont understand
Quotient X Divisor + Remainder = Dividend
restive river
like quotient is m-n, divisor is m-n and remainder is 0... Hope u understand
light mica
Yeh i do
Thanks
This?
How about this?
This one has numbers
And idk how to do it with numbers
Hello?
4a^2+4a+1 by 2a-1
How to do that
.close
restive river
For any sets A and B, show that
P ( A ∩ B ) = P ( A ) ∩ P ( B ).
Really having trouble grasping what the first step might be
hollow pollen
this isnt true
and the expression "P ( A ) ∩ P ( B )" doesnt make sense
did you mean P ( A ) x P ( B )?
or is this power set?
restive river
power set, maybe
hollow pollen
if its powerset then you can just the definition and get the proof directly
restive river
i dont follow
could you please elaborate a bit
a powerset is the set of all the subsets
wind vale
and the expression "P ( A ) ∩ P ( B )" doesnt make sense
intersection of 2 sets
hollow pollen
could you please elaborate a bit
prove double set inclusion
hollow pollen
if x is in P ( A ∩ B ) then ... therefore x in P ( A ) ∩ P ( B )
and other way around
hollow pollen
P(A) should be power set yes
yes
wind vale
mb
restive river
if x is in P ( A ∩ B ) then ... therefore x in P ( A ) ∩ P ( B )
oooh i think i get it
restive river
and other way around
why is that necessary to prove?
hollow pollen
to prove A = B one must prove that A is subset of B and B is subset of A
if you just prove one way, you dont know that every element of P ( A ) ∩ P ( B ) is in P ( A ∩ B )
restive river
i understand now
thank you so much
have a good day:)
i'll close this channel now
.close
trail stratus
devout snowBOT
trail stratus
WHere did the sqrt 3 come from?
wind vale
height of an equilateral triangle whose given side is a is equal to sqrt(3)a/2
trail stratus
height of an equilateral triangle whose given side is a is equal to sqrt(3)a/2
I dont understand
how do you find the height?
wind vale
im sorry
trail stratus
of course I can do basic Pythagoras theorem
trail stratus
the height is on the z axis, right?
comes out of the page
right, I get it now.
Thanks
gloomy ingot
devout snowBOT
gloomy ingot
how do i differentiate this
sonic smelt
$\dv{y}{x}=\frac{\dv{y}{t}}{\dv{x}{t}}$
woven radishBOT
A Lonely Bean
weak cove
sonic smelt
Chain rule, basically
devout snowBOT
@gloomy ingot Has your question been resolved?
devout snowBOT
gloomy ingot
.reopen
devout snowBOT
✅
gloomy ingot
im not struggling with the chain rule, its the actual differentiation of dx/dt
gloomy ingot
no
gloomy ingot
Do you know how to differentiate e^t?
ive nevee been taught it
sonic smelt
Hm, I see
Then using chain rule is not the way
Instead we need to express y in terms of x
From x = 4 * 2^-t + 3 we have 2^t = 4/(x - 3)
Now you simply plug this into y = 3 * 2^t - 5 and differentiate
gloomy ingot
ive done chain rukle but not a^x
sonic smelt
Forget about the chain rule
upper schooner
ive done chain rukle but not a^x
Have you done for e^x though?
sonic smelt
Have you done for e^x though?
No, they haven't been taught about e^x
upper schooner
No, they haven't been taught about e^x
Hmmm real weird then, but anyways, I shall leave it to you 
sonic smelt
ive done chain rukle but not a^x
Just express y in terms of x like I showed
gloomy ingot
ok
devout snowBOT
@gloomy ingot Has your question been resolved?
pseudo basin
where in this picture does it say to let guess = 25?
obsidian mortar
i told me that its right
when i hit show solutio
but it didnt give an explanation
it just said 25
and im not sure why
upper schooner
Did you do this?
obsidian mortar
yea
i did
2(1) + 2(3) + 2(5) + 2(7) + 2(9)
and it gave me a bigger number
but it said to add 5 numbers
so
winged lynx
I think you are supposed to replace the 25 with your own guess
upper schooner
2(1) + 2(3) + 2(5) + 2(7) + 2(9)
obsidian mortar
but it said its wrong
upper schooner
The odd numbers are like in a form 2i-1
obsidian mortar
2(1) + 2(3) + 2(5) + 2(7) + 2(9)
i did that because it said to do the stuff with odd numbers
oh
wot
upper schooner
Either you can do it like 1 + 3 + 5 etc
upper schooner
Or something like (2(1) -1) + (2(2)-1) + (2(3)-1) etc
upper schooner
did i misread the question somehow?
I think you might have
winged lynx
did you compute 1, 1+3, 1+3+5 and 1+3+5+7 like they said to
obsidian mortar
oh
upper schooner
Note that the first bit where they do this is for the even integers
obsidian mortar
where did it ask me to
upper schooner
Note however inside that the numbers there can be odd, they’re taking the general form of even integers to be 2k for some integer k
upper schooner
Did you do this?
Here btw is where they asked you to
obsidian mortar
how do u know what positive numbers they r talking abotu
upper schooner
“…try adding the odd positive integers together…”
obsidian mortar
1+3+5+7+9 =
wait
oh shit
its 25
bruhh
i thought the problem was more complicated than it seems
because of the weird symbols
💀
that were in the text
thx
.close
manic sedge
devout snowBOT
wooden veldt
From the sec tan pythagoras identity
manic sedge
Um actually I was not getting any identities like this in my book or nor even in internet
quaint citrus
$\sec^2 x - \tan^2 x = 1 \therefore (\sec x - \tan x)(\sec x + \tan x) = 1$
see if u can go from there
devout snowBOT
feral agate
-1?
wooden veldt
Should be 1
manic sedge
sec²x=1+tan²x
quaint citrus
oops mb
manic sedge
No problem
woven radishBOT
Stephen
wooden veldt
I can barely ever remember the signs on that identity lol dw
devout snowBOT
Available help channel!
copper hatch
devout snowBOT
copper hatch
Im really having some trouble understanding the wording of probability questions
From my understanding
Total = 25
16 study either art or music?
19 study either 1 or both art and music?
So neither art nor music would be 25-19
= 6
I am not sure how to figure out the rest of the values within the venn diagram
devout snowBOT
@copper hatch Has your question been resolved?
copper hatch
<@&286206848099549185>
frosty cradle
Is this for probability
midnight finch
16 study **either** art or music?
should be 16 study nothing or study art or study music
frosty cradle
That's not true. The question is asking for what you have as x4 and x2.
Yes, you can. And that's not the best way to do it anyway
copper hatch
Is this for probability
Yes
copper hatch
should be 16 study nothing or study art or study music
here are the answers if that makes it any clearer.
copper hatch
I kinda do, just need to get the question straight
frosty cradle
Let n be the students taking neither course.
copper hatch
That would be 6 correct?
copper hatch
So neither art nor music would be 25-19
^
As stated in my original go at the explanation
I was able to get that
then got confused with the other values
copper hatch
19 study either 1 or both art and music?
Then its the 19 studying a b and m right?
frosty cradle
Then you also have that a + m + n = 16, and since you got n = 6, then what can you do
copper hatch
When it says "16 of them study at most one of Art and Music"
Is this what you are referring to?
frosty cradle
yes
frosty cradle
ok so what equations do you have then?
copper hatch
a+b = 10
frosty cradle
why a+b?
copper hatch
sorry a + m - b = 10
copper hatch
oh right, just a + m then
frosty cradle
good
frosty cradle
what can you do w/ that now?
frosty cradle
yes
copper hatch
right okok
I get that now
I think just the wording threw me off a bit
Now, for next question relating to the venn diagram
it says this
Does this mean, when picking 2 studnets, one has to be a and one has to be m?
frosty cradle
or both from a, or both from m
frosty cradle
yes
frosty cradle
yes I believe so
copper hatch
Ok, yep that makes sense
I never feel confident with these quetsions
like, just the wording sometimes isnt clear at first glance
frosty cradle
no worries, glad you got there
copper hatch
and I end up thinking multiple possible scenarios
anyway, thanks for the help
this question is sorted now
.close
lyric folio
Using the graph below, between what values of x is the graph nonlinear and decreasing? Describe the graph of the function between x = 3 and x = 5.
devout snowBOT
Using the graph below, between what values of x is the graph nonlinear and decre...
@lyric folio Has your question been resolved?
lyric folio
.close
devout snowBOT
devout snowBOT
Available help channel!
gilded nova
what’s DE
feral furnace
what’s DE
don’t you have text version of a problem? I think DE and BC should be parallel to each other, otherwise this question is unanswerable for now
gilded nova
feral furnace
and E is bisectors of AC
okay, so you forgot about D point here
woven radishBOT
rkky
devout snowBOT
@gilded nova Has your question been resolved?
feral furnace
do you recall Tales theorem?
gilded nova
yes
warped relic
Okay now from that fact, can you tell me the ratio of AD:AB?
gilded nova
the middle point
warped relic
Okay...what does the middle point do to a line?
gilded nova
like the middle of the line?
warped relic
Yep
When you put a midpoint on a line
What does it do to the original line?
Like line AB here
We put a midpoint to it
It became AD and DB
Right?
gilded nova
i guess yes
warped relic
Okay
Now midpoints are really cool in the sense that they can divide the line into 2 equal parts
Right?
gilded nova
yes
warped relic
In our case, AB becomes AD + DB
Now since midpoints divides into 2 equal parts, can't we say that AD = DB?
gilded nova
yes
gilded nova
AD + DB?
gilded nova
is AB
gilded nova
yes
warped relic
Now this looks like a ratio
Also before we go further, are triangles ABC and ADE similar or not?
gilded nova
yea
warped relic
They're similar?
warped relic
No guessing 😁
warped relic
bc DE and BC are paraell
Yep
And AD is part of AB and AE is part of AC so triangle ADE is similar to ABC
Now since they are parallel, doesn't that mean that they have the same ratios?
gilded nova
im not sure
warped relic
Why not sure?
gilded nova
idk 
gilded nova
yes
warped relic
That means the sides are related to each other under one ratio, correct?
gilded nova
yes
warped relic
So...that means that if we take for example the ratio of AD:AB, we will get the similarity ratio of both triangles
gilded nova
ohh
vital stratus
devout snowBOT
wooden hamlet
so for those to be parallel
TS to TQ ratio is TR to TP ratio
system of equations
devout snowBOT
@vital stratus Has your question been resolved?
normal echo
normal echo
sorry
flat marlin
If tanx= −2 then tan(π+x)
devout snowBOT
If tanx= −2 then tan(π+x)
flat marlin
I understand the basics
like how to do it if it were tanx = -2 then tan(-x)= 2
But I'm not quite sure how to understand pi+x
pseudo basin
tan is periodic with period pi
flat marlin
Okay yeah yeah yeah
So like a circle right
add pi
That changes the quadrant its in
That's what its doing here right
ok so
a negative tan would be q2 or q4, but regardless of adding pi or not the answer stays negative
I got the right answer from that, if there's a better explanation lmk I'm still trying to figure this all out
pseudo basin
I got the right answer from that, if there's a better explanation lmk I'm still ...
yeah there is a better explanation
tan(x+pi) = tan(x)
sand peak
/image
sand peak
一直很可爱的狗
regal torrent
sand peak
I can't speak English.
devout snowBOT
narrow plank
(Make a new channel)
sonic smelt
Isn't this an international server though?
narrow plank
If it is, I was not made aware. I had assumed it was English only given that I have never seen anything else pretty much
devout snowBOT
Available help channel!
proud nimbus
$k = 0, \pm1, \pm2,.......$ \
$x = \pm \frac{\pi}{6} + k\pi$ \
Solution of what: \
a. $cot2x = 1 + cotx$ \
b. $sin2x - cosx = 0$ \
c. $cosx + 2cos2x = 0$ \
d. $tan2x = 3tanx$ \
e. $sinx + sin2x = 0$ \
devout snowBOT
$k = 0, \pm1, \pm2,.......$ \\
$x = \pm \frac{\pi}{6} + k\pi$ \\
Solution of wha...
woven radishBOT
Bunnings
proud nimbus
Is the correct ans "b" ?
pseudo basin
10 counts of 
arguably 11 if we count the first line not being $k \in \bZ$ as another one
woven radishBOT
Ann
pseudo basin
anyway, b has solutions other than x = ±pi/6 + kpi, and -pi/6 is not a solution of b either
proud nimbus
sorry i did not understand
i thought b could be ans because some of its values match the criteria
pseudo basin
incorrect
proud nimbus
i dont know how to solve cot2x = 1+cotx
pseudo basin
you need ALL values to match, otherwise you could add total garbage into the solution set and be none the wiser
proud nimbus
yeah i figured
pseudo basin
i dont know how to solve cot2x = 1+cotx
double angle identity on cot(2x), then you have a polynomial equation in cot(x)
proud nimbus
i''ll give another shot and let you know
devout snowBOT
@proud nimbus Has your question been resolved?
proud nimbus
i get 2 solutions if i solve cot2x = 1+cotx,
$(cotx-1)(3cotx+1)=0$ \
cotx = 1, satisfy the condition but $cotx = -\frac{1}{3}$ dont
@pseudo basin
woven radishBOT
Bunnings
pseudo basin
$\cot(x)$, not $cotx$ (and otherwise for other trig functions)
woven radishBOT
Ann
pseudo basin
also i am somewhat doubtful
proud nimbus
let me show my work
woven radishBOT
proud nimbus
pseudo basin
,w simplify cot(2x) - (cot^2(x)-1)/(2cot(x))
woven radishBOT
pseudo basin
ok
the identity checks out
as does the factorization
now... what is the solution set of cot(x)=1?
proud nimbus
pi/4
pseudo basin
that's far from the only solution
but even so
do you think even this falls under ±pi/6 + kpi?
proud nimbus
yeah pi/4 + pin
proud nimbus
do you think even this falls under ±pi/6 + kpi?
oh no
pseudo basin
well then don't claim it does
pseudo basin
$\cos(x)$ not $cos(x)$
woven radishBOT
Ann
pseudo basin
anyway, you have applied the double angle identity for cot earlier
i think you also know the one for cos
woven radishBOT
Bunnings
proud nimbus
i think you also know the one for cos
yes, cos has 4 double angle formula
proud nimbus
proud nimbus
i'm confused rn
pseudo basin
are you buridan's-assing yourself over formulas 1, 2 and 3?
barren loom
why does this recursive function shows this kinda pattern, I mean the values are oscillating in a certain range...
devout snowBOT
why does this recursive function shows this kinda pattern, I mean the values are...
pseudo basin
f(x) = f(x-1) - f(x-2) = [f(x-2)-f(x-3)] - f(x-2)
= -f(x-3)
so this periodicity is just a consequence of your recurrence relation applied twice
devout snowBOT
@barren loom Has your question been resolved?
devout snowBOT
wooden wraith
<@&268886789983436800>
celest dock
.close
valid gale
Why ∫_{0}^{r}\sqrt{r - x}dx = a○
devout snowBOT
Why ∫_{0}^{r}\sqrt{r - x}dx = a○
sonic smelt
$\int_0^r\sqrt{r-x}\dd{x} = a$?
woven radishBOT
A Lonely Bean
polar chasm
whats a?
valid gale
a? = \prod_{k = 1}^{a} k \neq a○
sonic smelt
Oh god, already implying a =/= a?
polar chasm
valid gale
a○ = ±\pir^2
sonic smelt
Can you screenshot the problem or?
sonic smelt
a○ = ±\pir^2
I assume you mean $a = \pi r^2$ because a can't be negative here
woven radishBOT
A Lonely Bean
sonic smelt
Also, $\int_0^r\sqrt{r-x}\dd{x}=\pi r^2$ is false
woven radishBOT
A Lonely Bean
sonic smelt
What you posted doesn't contain x^2 
valid gale
It isnt circle, its square
sonic smelt
So, were you curious about why $\int_0^r\sqrt{r^2-x^2}\dd{x}=\pi r^2$
woven radishBOT
A Lonely Bean
sonic smelt
Which is also false btw, it's pir^2/2
sonic smelt
What squares are you talking about?
valid gale
And it will be cancelled by square root so it is just ∫_{0}^{r}r - x dx
woven radishBOT
A Lonely Bean
valid gale
Also because of \sqrt{x ^2 ± y ^ 2} = x ±y because square root cancels ^2 for every formula
sonic smelt
I am sorry to tell you but that is misinformation
sonic smelt
Don't do calculus without being able to handle basics
I recommend you to revise algebra
polar chasm
valid gale
I dont think it would find reason of reason why ∫_{0}^{r}\sqrt{r - x}dx = a○
sonic smelt
I believe you can find that in khan academy as well
polar chasm
I dont think it would find reason of reason why ∫_{0}^{r}\sqrt{r - x}dx = a○
It wouldnt. But it would find reason why sqrt(a^2+b^2)=/=a+b
you gotta have a decent background in algebra to do calculus
apparently you dont. Sorry
Starting from pre-algebra, I learned calculus in 2 months with khan academy. With your current background you could be able to do it in a single month
dull otter
what is her question exactly?
sonic smelt
what is her question exactly?
My closest guess is "Why $\int_0^r\sqrt{r^2-x^2}\dd{x}=\frac{\pi r^2}2$"
woven radishBOT
A Lonely Bean
sonic smelt
But she keeps rewriting $\sqrt{r^2 - x^2}$ as $r - x$
woven radishBOT
A Lonely Bean
sonic smelt
And puts it under another root for some reason
devout snowBOT
@valid gale Has your question been resolved?
valid gale
아니요
dull otter
**A Lonely Bean**
@valid gale 질문입니까?
devout snowBOT
@valid gale Has your question been resolved?
devout snowBOT
@valid gale Has your question been resolved?
devout snowBOT
@valid gale Has your question been resolved?
hybrid snow
Are you wondering why $\int_{-r}^r\sqrt{r^2-x^2}\dd{x}=\frac{\pi r^2}2$?
Or you just gonna do the same old bs where you just click the X multiple times
woven radishBOT
Umbraleviathan
hybrid snow
My closest guess is "Why $\int_0^r\sqrt{r^2-x^2}\dd{x}=\frac{\pi r^2}2$"
Shouldn't it be -r to r
frank mortar
I am sorry to tell you but that is misinformation
fake
sonic smelt
Why do you read old messages?
devout snowBOT
devout snowBOT
Available help channel!
untold vector
How the term in green evaluated?
devout snowBOT
How the term in green evaluated?
craggy dagger
multiply numerator and denominator by e^x
warm sun
How the term in green evaluated?
(e^x)/(e^x - 3/e^x + 2) = (e^x)/(((e^x)^2 + 2e^x - 3)/e^x) = (e^2x)/(e^2x + 2e^x -3)
untold vector
@craggy dagger @warm sun Okay, One more thing, they assumed e^x =t then the second last term should be t^2.
untold vector
remember substitution for integrals
yeah, but didn't understand what exactly happened here.
Denominator is just factorization
craggy dagger
$\frac{dt}{dx}=?$
woven radishBOT
Element118
untold vector
$\frac{dt}{dx}=?$
craggy dagger
do you remember how that relates to integration by substitution
untold vector
do you remember how that relates to integration by substitution
Don't know if I'm missing something here.
craggy dagger
,w integration by substitution
woven radishBOT
Requested by Element118#2437
craggy dagger
,w u-substitution
untold vector
,w u-substitution
okay I'll see.
Thank you so much @craggy dagger @warm sun
.close
devout snowBOT
warm sun
Thank you so much <@104219409991626752> <@324537744208429066>
you're welcome
devout snowBOT
Available help channel!
lyric warren
hey, in the following image
devout snowBOT
hey, in the following image
lyric warren
lets imagine that the circle is a perfect circle
and i have the angle of the green triangle, and the radius of the circle
how should i solve the area of the green triangle?
is it possible?
i mean, its not a triangle per say, but you get the point
devout snowBOT
@lyric warren Has your question been resolved?
lyric warren
Is the triangle equilateral
so
yes, but only with it extend
to the rest, like
this triangle is equilateral
i have the answer from the internet
but i didnt understand
it says that 2r = (10\sqrt{3})/2
why is that?
here (its in portuguese)
the fact that that angle is 120 i get it
devout snowBOT
@lyric warren Has your question been resolved?
lyric warren
.close
devout snowBOT
devout snowBOT
Available help channel!
left imp
devout snowBOT
left imp
I am on the last part of ther question
and am struggling to solve the improper integral
this is answer for the parts before the last one because it is much neater than my working XD
from my knowledge the volume around the y axis should be:
could you ping me if u respond because I wont be tabbed in
devout snowBOT
@left imp Has your question been resolved?
left imp
<@&286206848099549185>
restive river
from my knowledge the volume around the y axis should be:
a volume of revolution around the y-axis?
left imp
no
i havent seen that one before
thats for rotation about the y axis?
if its about the y axis how does using x work?
cos your limits would be y coords no?
restive river
no, 0 and 1
left imp
if it is 'about the y axis' that means it is going around the y axis right?
restive river
if it is 'about the y axis' that means it is going around the y axis right?
yeah
i was able to show ln(2) > 2/3 with this method
left imp
hmmm
if your limits are y coordinates how can you put them in a function of x
i still dont get that
restive river
no, the limits are x-coordinates
well the formula is derived differently
look up disk method and washer* method if you want to learn
restive river
yep. let me know if it works out
restive river
you have to use this property to prove ln(2) is larger than 2/3
left imp
hmm ok
restive river
but how come the other doesnt work then
the limits of integration should be converted to y
one sec, i'll give it a try
left imp
it has to be between 1 and 0 again because the curve has a range of 0 < y <= 1
restive river
ah ok. yeah so because of the "dy" your limits of integration should be:
y(0) = 1/1 = 1
and
y(1) = 1/2
restive river
a better formula would be:
$V = \pi \int_{y(a)}^{y(b)}[x(y)]^2dy$
woven radishBOT
hannibal
left imp
ah ok. yeah so because of the "dy" your limits of integration should be:
y(0) = ...
wait but how can we integrate between 2 and 1 of the curve
if it doesnt even go above 1
restive river
so it should have worked?
it should be:
$x^2 = \frac{1}{y} - 1$
woven radishBOT
hannibal
left imp
okok
restive river
... which you got
left imp
nah i read your thing wrong
restive river
long day, let me try
left imp
i read it as y(1) = 2
restive river
oh ok
restive river
wait but how can we integrate between 2 and 1 of the curve
well, you integrate along the y-axis instead of the x-axis
yeah
what you're doing with that formula is integrating along the y-axis
so you flip the axis, in a way
so you need to use the corresponding y-coordinates as limits
restive river
alr
left imp
would it be alright if i swapped the limits
cos it is 1 0
so wuld it have to be 1/2 1
or is 1 1/2 still fine
restive river
yeah, so if you flipped the limits, you would have to put a negative sign in front of the integral
restive river
you want to write it as:
$\int_{\frac{1}{2}}^{1}$ right?
woven radishBOT
hannibal
restive river
can you show me your work?
restive river
i tried using the same method as before but by changing the limits
hmm yeah i also didn't get the right answer
one sec
restive river
did you get $\pi ln(2) - \frac{1}{2}\pi$ ?
woven radishBOT
hannibal
devout snowBOT
@left imp Has your question been resolved?
light quail
devout snowBOT
light quail
is the first part cos(u), sin(x) ?
weak cove
don't close and reopen channels for the same question
light quail
oh
weak cove
what do you think the inner function u= ?