or is this the first time?
#help-17
willow pike
fervent wasp
willow pike
why are we doing a parallel bisector
uh actually
i think it's best if you try figuring out the equation with z = x + iy first
willow pike
yes
modest wharf
can i make one side 0
modest wharf
willow pike
-3 and +3 cancel out
modest wharf
-3 and +3 cancel out
hi.. 😦
modest wharf
yes now wat?
willow pike
now if you replace the = with ≤ or ≥
modest wharf
hi sorry u kind of take a long time to answer we still on this question and it’s been 30 min ):
willow pike
it will be the region above or below the line
modest wharf
now if you replace the = with ≤ or ≥
okok
ohhh i think i rmb this from 2 year ago
i think we sub a point now
willow pike
yes
modest wharf
you can determine by picking a random point
i picked 0,5 and it didn’t satisfy
but it should’ve
because I’m the answer that part is shaded
i divided everything by a negative does that mean that the sign changes?
modest wharf
ok thanks :d
real bridge
Hi, I was working with laplace transforms and came across this summation. I’m asking for pointers on how to calculate the values of these summations. I suck at this, so any help is appreciated. Thx
vocal sleetBOT
Hi, I was working with laplace transforms and came across this summation. I’m as...
real bridge
log is the natural log. (base e)
topaz eagle
log is the natural log. (base e)
that's a univ (or above) level question, so please ask in other #math-discussion channels, say #advanced-analysis
real bridge
Oh ok, have sent a message in #advanced-analysis . But thinking its better i keep this channel incase its here i need to get assistance from
vocal sleetBOT
@real bridge Has your question been resolved?
vocal sleetBOT
@real bridge Has your question been resolved?
vocal sleetBOT
@real bridge Has your question been resolved?
flat whale
Hi, I was working with laplace transforms and came across this summation. I’m as...
show the full context
vocal sleetBOT
@real bridge Has your question been resolved?
stable relic
can somebody explain to me where the 1/2 came from in this? its not explained
stable relic
im sure it has something to do with power rules or whatever but i was never told anything about this
heady quest
Welcome
stable relic
.close
half rose
I think this is really easy, but I have no idea where to start.
vocal sleetBOT
I think this is really easy, but I have no idea where to start.
half rose
I mean, 0=m_j2 and 0=m_t1.5
but no idea where to go from there since dividing on both sides results in a rate of zero
I guess I forgot to add an intercept there but still don't think I can do anything else after adding that in
so $0=m_j(2)+b=m_t(1.5)+b$
twin meteorBOT
UCYT5040
half rose
where b is the amount of grass in the lawn and m is the rate at which we remove the grass
vocal sleetBOT
@half rose Has your question been resolved?
gritty sage
The trick is to add the speeds together.
How many lawns per hour does Javier mow?
How many lawns per hour does Tonya mow?
Add that together.
That's how many lawns per hour they can do working together.
@half rose
half rose
Ahh good point
Sorry for a late reply
So it would be a rate of 1/2+1/1.5 lawns per hour
Thank you for pointing that out
.close
alpine flame
Hi all i have several pattern recognition tests/maths puzzles that a friend sent me from their old retired tests but I'm boggled by them would anyone mind having a look and discussing theories with me / bouncing ideas ? ( the patterns rely on 3 solid repeated rules that are incredibly difficlut to uncover )
vocal sleetBOT
Hi all i have several pattern recognition tests/maths puzzles that a friend sent...
zinc quail
Hi all i have several pattern recognition tests/maths puzzles that a friend sent...
send them and wanderers will guide thee
and where are you stuck on them
alpine flame
option C was chosen by elimination through rules (number stars to shape number and ration of stars external to internal A and B❌ ) option D and E have issues with shape pattern either not increasing in shape value by enough or decreasing too much
alpine flame
i also tried representing the pattern numerically with step 6 being the predictions however this didn't help that much
zinc quail
sounds like a bit too much guesswork for me
alpine flame
if you want to jump in a channel to voice chat about it i'm happy too
zinc quail
if they're without context and you have just 5 answers you can probably arrive at a solution with a complex pattern that may be wrong
zinc quail
if you want to jump in a channel to voice chat about it i'm happy too
hm so far I'm seeing nothing
alpine flame
they're really big brain teasers but no answers online i think it's from an old L,Q test
the previous questions had straightforward answers like ( the image rotates 90 drg each time clockwise while the sides of a shape increases per sequence step) but no rules i can see
vocal sleetBOT
@alpine flame Has your question been resolved?
vocal sleetBOT
@alpine flame Has your question been resolved?
edgy sapphire
Hi all i have several pattern recognition tests/maths puzzles that a friend sent...
what's the 3 rules thing about? if it's across all puzzles then you'd need loads of examples and if it's per puzzle they're probably not that unique
alpine flame
it's not across all questions treat each question separately (each puzzle has 3 set rules to their respective sequence and changes the image as they are applied each time through each sequence per step )
alpine flame
for example, there is a rule that means the total number of stars must be 3 x the amount of total amount of internal stars this means you can eliminate A and B for not following the rule
cunning token
Help
cunning token
vocal sleetBOT
@cunning token Has your question been resolved?
cunning plaza
How does acceleration and displacement relate to velocity?
vocal sleetBOT
@cunning token Has your question been resolved?
cunning token
How does acceleration and displacement relate to velocity?
Idk
vocal sleetBOT
@cunning token Has your question been resolved?
copper axle
through derivates and integral, through tangents and area under the curve like $accelaration=\frac{d v}{dx}\velocity=\frac{d s}{dx}$ where s is displacement
twin meteorBOT
nico
vocal sleetBOT
vocal sleetBOT
Available help channel!
tropic brook
vocal sleetBOT
tropic brook
could someone please help and explain why C is the answer
so i did long division
and got -2x+6/x^2+4
as remainder
but its really -2x+6
sso i plug in 80 and get b
is that not possible(as in i'm not allowed to do it that way)?
dang bro
.close
real bridge
show the full context
Here is the original prompt
vocal sleetBOT
Here is the original prompt
real bridge
And here is wolfram’s output.
All I want to do is to compute any f(t) for t>1
Theta is the Heaviside function
flat whale
Yea that's far from full context
vocal sleetBOT
@real bridge Has your question been resolved?
real bridge
Yea that's far from full context
Could you elaborate sorry
vocal sleetBOT
Could you elaborate sorry
flat whale
Could you elaborate sorry
How are you defining log(-1). And why aren't you calculating the integral explicitly if h(x) just equals -1
vocal sleetBOT
@real bridge Has your question been resolved?
flat whale
Here is the original prompt
And where did the original equation come from
So yea, context
real bridge
log(-1) is kinda from Euler's identity. However from my original problem, "a" and "h" are kinda free variables as seen in the prompt. So these specific values were more of the simplest ones i could test.
flat whale
real bridge
This came from trying to work with the problem:
f(x) = k*f(x-1)
I applied the laplace transform, and the first derivative identity. Solved for L(f(x)), and substituted that with RHS.
So L(f(x)) = k, for k is the above substitution.
Then i transformed RHS into the integral versions, and split the integrals into two. Turns out one of these splits is equal to LHS. So i just manipulated and carried over. Then did an inverse to just reverse the Laplace on LHS, which left this equation
Lemme send images
twin meteorBOT
real bridge
There might be issues with my calculation so feel free to point them out if found. Thx
twin meteorBOT
real bridge
This is first, other is second
However the above are more of different approaches as you see. First one is applying the foretold identity. Second one is more of a direct integral substitution
Just realized my initial variables aren't really valid in a sense
Clearly a=-1, h=-1 doesn't satisfy the original equation. One that does is a=h=e. So apologies
However am still interested in a pointer of how i would by finding the value of the summations. Or even if the sum exists thx
vocal sleetBOT
@real bridge Has your question been resolved?
vocal sleetBOT
@real bridge Has your question been resolved?
vocal sleetBOT
@real bridge Has your question been resolved?
upbeat locust
question about this, to find a horizontal asymptote, i state that
x -> ∞+ and x->∞-, however, these both leave me with something a bit unsolvable i think
x -> ∞+ gives: ∞^2 / root(∞)
x -> ∞- gives: ∞^2 / root(-∞) (so this one is definitely invalid)
viral copper
as x --> infinity your curve will behave like x^(3/2), if thats what you mean
there are otherwise no horizontal asymptotes
vocal sleetBOT
@upbeat locust Has your question been resolved?
upbeat locust
there are otherwise no horizontal asymptotes
so i have no horizontal asymptotes
but how can i tell if i don't have any horizontal asymptote?
viral copper
the limits to infinity and -infinity need to be finite for you to have them
upbeat locust
∞^2 / root(∞) is not finite?
upbeat locust
but if we have for example
3x+1 over x-2,
(3(∞) + 1) / (∞) - 2 => 3(∞)/(∞) = 3, so y=3 is a horizontal asymptote
viral copper
yes
viral copper
you need to have degree of the top =< the degree at the bottom
if its less than its always 0
viral copper
if its equal then leading coefficients
viral copper
yeah
upbeat locust
and it makes sense too
viral copper
but you can still check the behavious of the function
for large x you can make the graph like x^(3/2)
in your example
upbeat locust
ahhh i see
right
but what does that tell me
because doesn't that just tell me that it approaches infinity at that rate?
viral copper
yeah
for example though if you were graphing x/sqrt(x + 1) instead of x^2/sqrt(x + 1)
the graph as it goes to infinity would become flatter
but in the latter case it curves upwards
(see concavity)
ocean falcon
yo guys i need help please
vocal sleetBOT
yo guys i need help please
sweet birch
don't ask to ask, just ask
ocean falcon
would i need to do partial fractions first before i can integrate?
outer warren
technically i'd be considered partial fractions
but here its just splitting the sum
outer warren
yeh
ocean falcon
alr ty
lethal salmon
lethal salmon
please
vocal sleetBOT
@lethal salmon Has your question been resolved?
bronze osprey
if one of the kids takes any number of candies, cookies, and chocolates
then you know for sure that the other child must have everything that is left
you can just count the number of ways for the first child to choose
hopefully you know of the multiplication principle
so the first kid can take either 0, 1, 2, 3 candies
can you extend this logic to the cookies and the chocolates?
great, now multiply the number of possibilities for each one all together
lethal salmon
4x5x6 - 2
grim oasis
not sure if you read my messages from the other channel you opened, but this is a good opportunity to practice that method
label what each of these numbers mean and draw out how you made your choices
for instance, the first 4 must mean that you have 4 choices you can make. what are these 4 choices and once you've made one of 4, one of 5, and one of 6 choices each, how does that produce one way of distributing the items
show an explicit example
bronze osprey
ah wait that's correct
yeah the first kid can't get everything (2nd kid gets nothing), and the first kid can't get nothing
nice work
I was on some other people's question so yeah coming back to your one was a bit confusing
vocal sleetBOT
@lethal salmon Has your question been resolved?
lethal salmon
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
lean iris
$f' \times e^{f} = [e^f]$ or $[\frac{e^{f+1}}{f+1}]$
vocal sleetBOT
$f' \times e^{f} = [e^f]$ or $[\frac{e^{f+1}}{f+1}]$
twin meteorBOT
SELVATOR
hard atlas
$\int f'(x) e^{f(x)} dx = e^{f(x)}$
twin meteorBOT
Denascite
hard atlas
I assume thats what you mean
vocal sleetBOT
@lean iris Has your question been resolved?
lean iris
**Denascite**
Example: $e^{x+ 4}$
twin meteorBOT
SELVATOR
lean iris
<@&286206848099549185>
lean iris
<@&286206848099549185>
lean iris
$f' \times e^{f} = [e^f]$ or $[\frac{e^{f+1}}{f+1}]$
...
flat whale
$f' \times e^{f} = [e^f]$ or $[\frac{e^{f+1}}{f+1}]$
!xy
vocal sleetBOT
$f' \times e^{f} = [e^f]$ or $[\frac{e^{f+1}}{f+1}]$
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.
vocal sleetBOT
@lean iris Has your question been resolved?
twin meteorBOT
SELVATOR
lean iris
Befause: $\int f' \times f^n = [\frac{f^{n+1}}{n+1}]$
twin meteorBOT
SELVATOR
lean iris
<@&286206848099549185>
flat whale
Im just asking about the rule
Rule about what
autumn palm
lean iris
Rule about what
Integral, primitives
lean iris
What does [] mean
Something like from a to b
lean iris
A function?
Yes, example, f = 5x² + 3 or f = -4x
flat whale
$\int e^{f(x)}dx$ doesn't have a general rule no
twin meteorBOT
riemann
jolly lava
**Denascite**
So this is not enough for answering the question?
vocal sleetBOT
@lean iris Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
heavy palm
vocal sleetBOT
ancient skiff
When u substituted root x with u, your differentiation was wrong
dull bear
(It wasn't)
dull bear
Awwww 
it happens 
atomic jasper
,ti loki..._.
twin meteorBOT
This user hasn't set their timezone! Ask them to set it using ,ti --set.
heavy palm
(What did I do wrong)?
atomic jasper
damn wtf
ancient skiff
(What did I do wrong)?
Idt I can help u sorry
dull bear
This doesn't look like uv to me though 
heavy palm
It's 1.34 am
atomic jasper
go sleep bruv
heavy palm
This doesn't look like uv to me though <a:nyaNana:586338925983957009>
Ah okay
atomic jasper
thats why u go to sleep now
heavy palm
If I replace it with sin is everything correct
ancient skiff
Js stressin out abt it
atomic jasper
to vibe and study tmrw early on
heavy palm
Everything else
ancient skiff
to vibe and study tmrw early on
Good idea
dull bear
I've got a phyiscs exam on Friday
Awww, good luck with the exam 
heavy palm
I've got a phyiscs exam on Friday
heavy palm
dull bear
If I replace it with sin is everything correct
And yep 
heavy palm
I hope you enjoy the cats
ancient skiff
Oh def do
They keep me going fr
This help channel has turned into real help
Canon event fr
dull bear
Awwwww 
heavy palm
Isn’t canon event where someone dies
atomic jasper
Y'all are too nice for strangers on the internet 😭
❤️
heavy palm
In that one movie
ancient skiff
Isn’t canon event where someone dies
Well yes. But.
atomic jasper
canon event is important story point, no?
ancient skiff
Ykwim 🤠
ancient skiff
canon event is important story point, no?
Yep
heavy palm
Yes I know
atomic jasper
cannon is smth different
ancient skiff
But in the movie it was about an imp charecters death
atomic jasper
atomic jasper
Imma go put that timezone thing
ancient skiff
Yep done
ancient skiff
<#488104216678760469>
U can try now lol
atomic jasper
@heavy palm is your question answered btw
atomic jasper
U can try now lol
,ti @ancient skiff
twin meteorBOT
The current time for loki..._. is 01:40 AM (IST) on Thu, 20/02/2025.
.bonk__ is 4 hours and 30 minutes behind, at 09:10 PM (CET) on Wed, 19/02/2025.
atomic jasper
ah, india
ancient skiff
Yay
atomic jasper
JEE victim?
atomic jasper
we have a few more victims around here
ancient skiff
Anyway time to sleep. Can't even differtiate root x anymore
atomic jasper
perhaps we should make a JEE support group
atomic jasper
Anyway time to sleep. Can't even differtiate root x anymore
gn
ancient skiff
we have a few more victims around here
Yep I met most of em already
ancient skiff
perhaps we should make a JEE support group
Lol that's a great idea
vocal sleetBOT
vocal sleetBOT
Available help channel!
dull cairn
How can I prove that the 2 triangles with blue dots in them are equal in area, it's not drawn perfectly, and the givens are on the drawing
vocal sleetBOT
How can I prove that the 2 triangles with blue dots in them are equal in area, i...
dull cairn
oops
hushed pewter
,rccw
twin meteorBOT
dull cairn
been trying at it for hours rn
hushed pewter
For triangle FEC, the base is FE, and the height is CD
For triangle AXB, consider breaking it into two triangles.
- From X, draw a line parallel to DB. Mark Y where this line intersects AB. Consider now the two triangles AXY and BXY. Their base is XY.
stray sonnet
did I solve this right?
vocal sleetBOT
atomic jasper
did I solve this right?
!msgdel
vocal sleetBOT
did I solve this right?
The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.
Available help channel!
stray sonnet
vocal sleetBOT
reef agate
✅
vocal sleetBOT
Available help channel!
tidal dock
my acquaint is arguing that you need axiom of choice in order for cantor's diagonalization argument to work
vocal sleetBOT
my acquaint is arguing that you need axiom of choice in order for cantor's diago...
tidal dock
i have read that this is false and i agree with that but i don't seem to be able to communicate that
this is where it started btw
paper depot
where does bro see a need for choice
you need to fix a function on the set of digits without fixed points
tidal dock
"Arbitrary binary sequences are arbitrary choices. The set is not ordered is it? So it's got arbitrary numbers one after another. Where does this random order come from? By a choice of random sequences one after another"
paper depot
"Arbitrary binary sequences are arbitrary choices. The set is not ordered is it?...
no the order comes from a supposed bijection between it and N
lmao
tidal dock
YES EXACTLY
paper depot
like that's our input data
tidal dock
oml
paper depot
we suppose such a thing exists
in order to explicitly contradict that
there's no choice lol
tidal dock
i wrote:
"we assume that there exists a mapping from N to R that makes some kind of assignment from naturals to reals. this does not invoke AC since we simply assume existence of a function."
he writes:
"And in what order did you get the reals? If it is a map, either there is a way to construct it, or its existence is a self reference"
paper depot
fym what order?
what
why does it matter what ordering the reals come with
is bro like, a constructivist or sth
tidal dock
yep
that's the diagnosis (it seems)
"Take all finite mathematical statement. The set is countable; so a majority of real numbers are never going to be reasoned on; why bring them in to existence?"
paper depot
ok well the constructive viewpoint is that we suppose a map N -> R exists in the constructive sense, then the proof gives a way to CONSTRUCT a real not in its image
paper depot
"Take all finite mathematical statement. The set is countable; so a majority of ...
oh so bro rejects non constructible reals.
tidal dock
"Take all finite mathematical statement. The set is countable; so a majority of ...
i would to order one HOLELESS number line please
paper depot
boneless pizza
tidal dock
yes that's what i was referencing lol
ok whatever i don't even know whether he is pro or against real numbers at this point
vocal sleetBOT
winter hawk
if this guy hates cantor he probably doesnt accept |P(A)| > |A|
oak magnet
I agree
winter hawk
but |P(A)| > |A| is just the general version of R being uncountable
both their proofs use a diagonal argument
the usual protocol here is to dismiss this guy as a crank and go back to watching anime
vocal sleetBOT
Available help channel!
bleak prawn
vocal sleetBOT
bleak prawn
I know how to get the answer but I dont really get what im doing 😅
paper depot
in order for the function to lack a vertical asymptote, that fraction must be able to simplify until there's no denominator left
bleak prawn
So we want the denominator to be 1?
The denominator (2x - a) can be written as 2(x - a/2)
Which means x = a/2
The numerator factorizes to (x - 1)(x + 1)
Set both equal to 0 and sub in x = a/2
bleak prawn
(a/2) - 1 = 0
a = 2
(a/2) + 1 = 0
a = -2
Thats how I got my 2 answers
But I dont really get why I do this step?
paper depot
you match the factor (x - a/2) to either (x - 1) or (x + 1) for both possibilities of what it cancels with
what you just did is the same thing but... kinda overengineered
bleak prawn
you match the factor (x - a/2) to either (x - 1) or (x + 1) for both possibiliti...
Why do we want it to cancel
Why do we want the denominator to be = 1?
How does that mean theres no VA?
paper depot
we want the denominator to lack any factors post-simplification that could be zero at some value of x
cause those factors are why VAs happen
bleak prawn
cause those factors are why VAs happen
So if the denominator has an x or x^2 term then theres a VA?
paper depot
i do not see any good way to rephrase the thing i said, and your rephrase is frustratingly imprecise.
bleak prawn
i do not see any good way to rephrase the thing i said, and your rephrase is fru...
Sorry for frustrating you
Im just trying to learn
atomic jasper
you want to remove any division by x
paper depot
no see the thing is
if the denominator had x^2 + 1
this factor would be safe to keep
but odie's restatement of my thing would have us get rid of that one as well
atomic jasper
ah, right
bleak prawn
but odie's restatement of my thing would have us get rid of that one as well
I was just trying to understand what you said im not the best at understanding complicated mathematical language like that
Tbh I still dont get what it means
paper depot
curse my inability to communicate in a way that is immediately 100% clear to everyone 100% of the time, then.
ok look
VAs happen when your function involves division by something that, for some value of x, is 0
do you understand this yes or no
bleak prawn
curse my inability to communicate in a way that is immediately 100% clear to eve...
Please do not take this as a personal attack......
bleak prawn
VAs happen when your function involves division by something that, for some valu...
I think so
paper depot
ok
in the denominator we have the factor (x - a/2)
which is a source of one VA in this way
EXCEPT if it cancels out with something
do you understand this yes or no
bleak prawn
Yes im with you so far
paper depot
this factor is the only thing that could possibly cause VAs to happen
if we find which values of a make it cancel out with something from the numerator, then we are done
do you understand this yes or no
vocal sleetBOT
bitter pilot
vocal sleetBOT
Available help channel!
half rose
how is
half rose
$25\frac{yz}{c}=4\frac{ak}{x}$ equiv to $25\frac{x}{c}=4\frac{ak}{yz}$??
twin meteorBOT
UCYT5040
tawny nacelle
$25\frac{yz}{c}=4\frac{ak}{x}$ equiv to $25\frac{x}{c}=4\frac{ak}{yz}$??
multiply both sides by x, and divide both sides by yz
vocal sleetBOT
tawny nacelle
bleak prawn
oooeeeeooo
tawny nacelle
oooeeeeooo
vocal sleetBOT
Available help channel!
gusty sun
Im a bit stuck on proving a2 > b2 and the induction process of n + 1
vocal sleetBOT
Im a bit stuck on proving a2 > b2 and the induction process of n + 1
@gusty sun Has your question been resolved?
vocal sleetBOT
@gusty sun Has your question been resolved?
vocal sleetBOT
@gusty sun Has your question been resolved?
dull bear
Proving that an > bn in general (from their definitions) should not be too difficult to do 
woven talon
need help on this, thank you
vocal sleetBOT
need help on this, thank you
woven talon
my answer is $1.00,$1.20,$1.25 least to most price per battery
elfin arrow
vocal sleetBOT
vocal sleetBOT
Available help channel!
fallow sphinx
Just choose an option other than the second
vocal sleetBOT
Just choose an option other than the second
flat whale
Just choose an option other than the second
Why other than the second
fallow sphinx
Cuz it’s wrong
tranquil trellis
lmfao
fallow sphinx
🥲🙂
flat whale
You know you picked the third one?
fallow sphinx
I picked that after
tranquil trellis
Well let's go through each answer choice
fallow sphinx
Okay
tranquil trellis
what do you think about the first one
tranquil trellis
right
fallow sphinx
Yesir
fallow sphinx
I got it wrong
tranquil trellis
why would it be a midsegment
fallow sphinx
why would it be a midsegment
Come back
tranquil trellis
oops
midsegment means exactly in the middle
which it is not
you can tell because it divides the side on the left into 4 and 5
which aren't the same
fallow sphinx
So nahhh???
tranquil trellis
not 3rd option
fallow sphinx
No wait
It still could be tho couldn’t it???
Cuz all it says is since 6 is the midsegment
Value of x is doubled
tranquil trellis
but 6 is not the midsegment...
fallow sphinx
I see
fallow sphinx
but 6 is not the midsegment...
Are you sure
tranquil trellis
if u don't believe me pick the 3rd one then 😵
tranquil trellis
it's the 2nd one
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
vast shale
what am i suppose to do here like graph those functions? how do one go about doing that do i have to do it manually with adding up the values and stuff
shell crest
what am i suppose to do here like graph those functions? how do one go about doi...
sin inverse x + cos inverse x = pi/2
so y = pi/2?
vast shale
makes sense
why its like that
its at 1.57
which is pi/2
oh now i see why it is like that cuz sin and cos has same values at pi/2 apart
because thats where there values flip
vast shale
yess
and arcsin range is -pi/2 to pi/2 and for arccos its 0 to pi which means ahhh also that the every value cos has in case of arc the sin will have it opposite to the cos when the cos in the second quadrants sin will be in 4th which is negative so it will go to pi/2 again but what if cos is in the first quadrant if it is then in that case say cos is 1/2 which in arc will be pi/3 and for the sin that will be pi/6
which is on addition gives pi/2
but i need to do smth to make it more general for any x
atleast from examples it seems to be working
shell crest
and arcsin range is -pi/2 to pi/2 and for arccos its 0 to pi which means ahhh al...
well it's a idenity, do you want proof?
like if you want to add proof in your answer?
vast shale
well
-pi/2 <= arcsin(x) <= pi/2
0 <= arccos(x) <= pi
-pi/2 <= arcsin(x) + arccos(x) <= 3pi/2
vast shale
like if you want to add proof in your answer?
yeah and the identity u talking about yet to be proved
shell crest
well
-pi/2 <= arcsin(x) <= pi/2
0 <= arccos(x) <= pi
-pi/2 <= arcsin(x) + arcco...
no no, you are ignoring the fact that value of x will be same
the final value stands if x for sin x and cos x aren't equal
shell crest
yeah and the identity u talking about yet to be proved
wait
lemme just send you proof?
shell crest
do you want a headstart
vast shale
thats like chatgpt type shit
shell crest
no that's from my edu site
vast shale
oh
vast shale
no no, you are ignoring the fact that value of x will be same
can we first talk about this
shell crest
yea say
shell crest
well you have to
if for sin, you take x as 0 and for cos it has to be 0
it is bounded
in fact you are bounded
vast shale
but like that inequality was taking same x for both or am i getting smth wrong here
shell crest
i am asian, don't doubt my maths, lmao just kidding, i can be wrong
shell crest
but like that inequality was taking same x for both or am i getting smth wrong h...
it's not really inequality it's a identity
listen like
x - x = y
it's identity
x belongs to (-inf, inf)
but y = 0
vast shale
well
-pi/2 <= arcsin(x) <= pi/2
0 <= arccos(x) <= pi
-pi/2 <= arcsin(x) + arcco...
i was talking about this
shell crest
no matter what
vast shale
thats inequality
shell crest
i was talking about this
for final line the equation suggests, sin inv q + cos inv p , where q is not equal to p
so if you mean that then yes your answer is correct, elsewise the answer stays as pi/2
check up
vast shale
omg
REMOVE TI
QUICK
i think i get the idea
let me try now
u can remov eit
lmao
QUCK
vast shale
i was thinking of what i can do with i know and from that i came up with some ideas like
arcsin x + arccos x
arcosx = y
cosy = x
x = sin(pi/2 + y)
but that won't really give pi/2 to in the end
shell crest
wha
boyyy
see
why dont we
just make x the king?
instead of sin inverse x
= something
we can do x = sin something
and same goes for x = cos something
we get x = sin smtg = cos smthg
now
sin smthg = cos smthg
cos smtg = sin(90 - smhtg)
we get
smthg = pi/2 - smtg
smthg + smthg = pi/2
vast shale
smthg = pi/2 - smtg
how did u came up to this
vast shale
canada
shell crest
ohh
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lunar pecan
I don’t want the answer
I wanna know how to do it
<@&268886789983436800> Can u get this delinquent out of here?
Is pinging everyone unnecessarily even allowed ?
tidal salmon
I wanna know how to do it
wheres the q?
lunar pecan
I made a new help channel
tidal salmon
kk
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@sharp ridge Has your question been resolved?
sonic grove
I was given a task to do a comparative report on whether a semi-elliptic or parabolic arch is better, and the situation is:
"Your construction firm was contacted by a client who wants to construct a passage tunnel
which is either in the shape of a parabola or semi-ellipse. Given that the passage is to be
constructed for one-way or two-way traffic and with a height of 16-24 feet and width of 34-58
feet along the ground, help the client decide on what shape to use [Each group will be given
specific values]. For this project, we assume that the dimensions of the cross section of the bus
is 8 feet by 10 feet. There is a 2 feet space between the buses if they are entering the tunnel in
the same direction. For the two-way tunnel, there will be a 4 feet space in between the buses
that are in opposite directions and 2 feet space for every additional lane." But let's assume that the height is 24 feet and the width is 58 feet. I have no problem getting the equation and the graph, but in this situation, how will I know how much vehicles, specifically the bus, can enter the arch at given times? Any help is much appreciated 🙂
vocal sleetBOT
I was given a task to do a comparative report on whether a semi-elliptic or para...
@sonic grove Has your question been resolved?
sonic grove
I've already constructed the graphs on desmos but I don't know how to project the buses in the program with the given specifics... is there a way?
vocal sleetBOT
@sonic grove Has your question been resolved?
sonic grove
.
vocal sleetBOT
@sonic grove Has your question been resolved?
vocal sleetBOT
@sonic grove Has your question been resolved?
vocal sleetBOT
@sonic grove Has your question been resolved?
vocal sleetBOT
crimson jetty
what is that confidential watermark
cunning prairie
idk they added it to make it seem like a legal case
grim marsh
hello guys can anyone help me with this? i cant use graphing software
ocean falcon
normally i use desmos, and its really good!
grim marsh
normally i use desmos, and its really good!
i cant use it
i have to draw it
can anyone explain me how to draw it
grim marsh
like youve gotta think of it
how
ocean falcon
like put in whole values of x into the equation -x^2
so you can get y
like 1, 2 ,3
do you know table of values?
grim marsh
like y/x -2,-1,0,1,2
ocean falcon
yeah!!
ocean falcon
just put the numbers you gave me, into the eqation -x^2
it might be best for you to draw the table out on some paper
ocean falcon
becaues its -x^2 and not (-x)^2
unkempt plover
mb
unkempt plover
lol
grim marsh
it should look like this
okay
ocean falcon
do you understand how i got that?
grim marsh
yeah
ocean falcon
then you do that for the rest of them, and draw
unkempt plover
right right thats an reverse U shape
just
remember that x is the horisontal axis and y is the vertical
unkempt plover
i just remember it cause when i was a kid i liked that and it was easy for me
chrome steppe
I need help understanding why the correct answer to this problem has mixed units in the calculation
vocal sleetBOT
I need help understanding why the correct answer to this problem has mixed units...
chrome steppe
The original problem isn't really relevant here, but it's a Mechanics of Materials problem looking at how a bronze tube is affected by uniform heat transfer
The core of what I'm stuck on.. and this is the correct answer in the box... is why it requires mixing inches at feet? They don't cancel out anywhere that I can tell
slight mistake in labeling..
heavy yoke
can you post the original problem? just so we know what the units of each quantity are
chrome steppe
I can, but there's a lot of backstory to get you caught up on what you're looking at, which is why I just labeled things with red and green... but
The unlabeled numbers are either coefficients of thermal expansion, or they're temperatures
The 15E6 is the modulus of elasticity, in psi
17.5 is degrees F / foot
.754 is square inches.. it's the surface area along the axis
Like I said.. kinda messy, just to get to the core of where I'm confused
heavy yoke
so then the modulus of elasticity is pounds per square inch (psi), and the area is square inches, so the square inches cancel there
leaving only pounds on the denominator
chrome steppe
... and that would be where I should have been paying attention to how the units interact
Cool, thanks
.close
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onyx spade
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silk osprey
so 6(1/1-(-x))
geometric
silk osprey
did you read the hint
onyx spade
yes
silk osprey
$\frac{1}{1 - x} = \sum_{n = 0}^{\infty} x^n$
twin meteorBOT
knief
silk osprey
use this to write the power series for g
wary hull
so i integrate ths
Yes.
onyx spade
silk osprey
no
onyx spade
Theres a 6 outside yhe integral
silk osprey
oh
onyx spade
It got cut off
silk osprey
also where is the equal sign
wary hull
Theres a 6 outside yhe integral
Good, then.
silk osprey
and
silk osprey
🤔
wary hull
Wait. You should have split the (-1)^n before integrating.
wary hull
Wait. You should have split the (-1)^n before integrating.
Or, you could apply chain rule, and it would become (-x)^(n+1)*-1=(-1)^(n+1)*-1*x^n=(-1)^n*x^n regardless.
wary hull
Yeah.
onyx spade
Do i do u sub or soemthing since its like mulitplying
wary hull
Do i do u sub or soemthing since its like mulitplying
No, you simply integrate x^n.
wary hull
That is correct.
$\frac{6}{1+x}=\sum_{n=0}^{\infty}6(-x)^n$, thus $\int\frac{6}{1+x}{dx}=\int\sum_{n=0}^{\infty}6(-1)^nx^n$, and $6\ln(1+x)=\sum_{n=1}^{\infty}6(-1)^n\frac{x^{n+1}}{n+1}$.
twin meteorBOT
mathisfun
onyx spade
I thought when it starts at 1 u would do n-1?
@wary hull
For the index
Or us that for soemthing else
wary hull
I thought when it starts at 1 u would do n-1?
Yeah, you subtract one from the index if you're adding one to the lower indice.
wary hull
Yes.
wary hull
so do i subtract a 1
$\sum_{n\ge 0}a_n=\sum_{n\ge 1}a_{n-1}$
twin meteorBOT
mathisfun
wary hull
which then becomes
6(-1)n-1 *(x^n/n)
Yes.
wary hull
i see
tahnks
You're quite welcome!
vocal sleetBOT
@onyx spade Has your question been resolved?
rare radish
Is this correct?
vocal sleetBOT
Is this correct?
rare radish
which are you talking abt?
rare radish
Could it be -4
whats -4
fast heart
as -1-3 is -4
rare radish
are you talking abt the equals 3
cuz thats for the total amount of terms
not the answer to the actual questin
fast heart
i understand now. Yes -1 is the constant term.
fast heart
Yes.
rare radish
whats the differenece between classifying polys with the nymber of terms and by the degree of the polynominal
fast heart
Define clearly.
rare radish
what is the difference between classifying polynominals by the number of terms
and classifying polynominals by the degree of the polynominal
that's what it says on my packet
fast heart
P(
deg(P(x)) = N_t(P(x)) - 1
N_t = Number of terms/coefficients
deg(P(x)) = degree of function.
junior vault
im supposed to do this with first principles, can i use any number in the given interval for my x value
vocal sleetBOT
im supposed to do this with first principles, can i use any number in the given ...
minor path
im supposed to do this with first principles, can i use any number in the given ...
Ok do you know how to derive that
You can't use any number for x
minor path
Do you still need help?
vocal sleetBOT
minor path
Okay you're welcome
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dusky scaffold
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twilit jewel
$\sqrt{1-x}=2x^2-1-2x\sqrt{1-x^2}$
vocal sleetBOT
$\sqrt{1-x}=2x^2-1-2x\sqrt{1-x^2}$
twin meteorBOT
nayuzz
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
4
wet halo
post it
twilit jewel
$\sqrt{1-x}=2x^2-1-2x\sqrt{1-x^2} x\in[-1;1].\medskip$
I made a variable change cos(t)= x with t \in[0;pi]
twin meteorBOT
nayuzz
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
twilit jewel
until this $sin(\frac{t}{2})=cos(2t+\frac{\pi}{4})$
twin meteorBOT
nayuzz
twin meteorBOT
nayuzz
twilit jewel
$t= \frac{\pi}{10}+\frac{4k\pi}{5}$
twin meteorBOT
nayuzz
twilit jewel
theses values are in the interval $\frac{\pi}{10}; \frac{9\pi}{10}: \frac{5\pi}{6}$
twin meteorBOT
nayuzz
twilit jewel
But it seems incorrect to me
vocal sleetBOT
@twilit jewel Has your question been resolved?
twilit jewel
well
an intermediate step on which I can easily test the values are
$sin(\frac{t}{2})=cos(2t)-sin(2t)$
twin meteorBOT
nayuzz
twilit jewel
I just tested it and it works yes
Now I have to go back to my x = cos(t)
is that right <@&286206848099549185>
vocal sleetBOT
@twilit jewel Has your question been resolved?
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@twilit jewel Has your question been resolved?
rancid cosmos
ive been messing around with shapes recently, and then i realised that if you make a bunch of circles intersect, you can draw lines between the intersections and make some cool shapes, which led the question, given any polygon, can you generate these circles, so that each circle intersects each other circle, and the outside edge, or "perimeter" of the lines drawn between each intersection (green in this image matches?
idk if this is a solved question or something, but the more i try to solve it the more my brain disolves in the process
vocal sleetBOT
ive been messing around with shapes recently, and then i realised that if you ma...
rancid cosmos
for example, given a regular octagon, you could create something like this?
inner osprey
maybe i am dumb. i have read over this paragraph a few times and i do not quite seem to understand what the goal is
rancid cosmos
maybe i am dumb. i have read over this paragraph a few times and i do not quite ...
ok, so you have a bunch of circles, and you draw lines at where they intersect (every circle intersects with each other circle)
rancid cosmos
ive been messing around with shapes recently, and then i realised that if you ma...
like what i did here
the "green" is the polygon that those circles would create
inner osprey
how do you determine which lines to draw?
rancid cosmos
how do you determine which lines to draw?
im saying, what if you reverse that, and draw a polygon, and make the circles so that this is true still
iykwim
inner osprey
the "green" is the polygon that those circles would create
is the green construction well-defined?
rancid cosmos
is the green construction well-defined?
?
inner osprey
take here for example
why is a single green segment drawn here instead of at that vertex where those 4 red segments intersect?
rancid cosmos
right that would be helpful to be able to define
i just did it intuitively but
seems to occur when more than 2 circles intersect
if that helps
nvm
i lied
i have... no clue how to define this
well i guess thats the question now :p
rancid cosmos
take here for example
after a bit of research, it seems like a concave hull
so the concave hull of the points located at the intersections of the circles forms a polygon
you can draw circles, and easily draw points at the intersections, then draw the concave hull
inner osprey
to my knowledge the "concave hull" is an ill-defined concept
rancid cosmos
but what im asking is, given a polygon, can you reverse that and get the circles?
rancid cosmos
to my knowledge the "concave hull" is an ill-defined concept
i see
i'm not sure what to do then :p
inner osprey
there's multiple ways you can sort of parameterize concavity that make it less straightforward to define than the much more prominent term "convex hull"
rancid cosmos
there's multiple ways you can sort of parameterize concavity that make it less s...
i mean i guess that just seperates the question into 2 then
inner osprey
maybe you (or someone) can make progress on this question but as i'm not sure if how to phrase it in a way that makes sense 🤷♂️
rancid cosmos
maybe you (or someone) can make progress on this question but as i'm not sure if...
is there a term to seperate polygons from ones that a concave hull can generate vs what it cant
like if it has "spikes"
oh its just concave and convex polygon
lmfao
(i may be not smart)
vocal sleetBOT
@rancid cosmos Has your question been resolved?
rancid cosmos
.close
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steady musk
What makes polynomial of integer coefficients countable but sequence not?