just converting to uh
#help-13
slender atlas
do you have a picture of the exact way this question is worded?
spring forum
can you show a screenshot of your problem?
chilly warren
!original
cedar kilnBOT
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.
median sparrow
im one of yal now
median sparrow
do you have a picture of the exact way this question is worded?
nah actually ditch that
lavish vine
,tex $\log_2 \frac{x^2}{y}$
wraith daggerBOT
Triaengle
lavish vine
?
median sparrow
anyone have a file forexponential eqalities, inequalities, functiob
sudden cairn
Photo of question please
uneven dome
if you're asking for resources, consider #book-recommendations maybe
sudden cairn
This is a help channel for specific questions
median sparrow
Photo of question please
oh i taught this was like a tutor server đ
spring forum
anyone have a file forexponential eqalities, inequalities, functiob
you should have a textbook, no? and also, what CĂ©line said
median sparrow
alrr thanks ill sort it out
median sparrow
This is a help channel for specific questions
okay thanks
ember jasper
cedar kilnBOT
ember jasper
we wish to study the real roots of a fourth degree polynomial with real coefficients, thus means a polynomial P defined on C by P(z)= az^4+bz^3+cz^2+bx+d where a, b and c are all reals so that aâ 0
- Show that there is a complex number u which is a root of the equation (E) of form z^4+Ωz^3+Πz^2+Ωz+1 where Ω and Πare two reals expressed in terms of a, b and c
- a. Show that 0 is not a solution of (E)
b. given Q(z)= z^4+Ωz^3+Πz^2+Ωz+1, evaluate for all z part of C*, Q(z)/z^2
c. we assume, for z part of C*, Z=z+1/z. Express z^2+1/z^2 relative to Z then show Q(z)=0, if and only if, Z is solution of a binomial witg real coefficients - We suppose that Z is a real number k and is solution of the binomial obtained at question 2.c.
Find for which values of k the equation z+1/z = k has two distinct real solutions - Resokve in C the equation z^4+2z^3+3z^2+2z+1=0 no
so my issue here lies in question 1
im very unsure how to express Ω and Πin terms of a b and c
i got to the end of question 2.b but i can do 2.c. and thus 3 without an expression of Ω and Î
dawn junco
C'est vraiment un truc tout con qu'ils te demandent en fait
t'as un polynome en az^4 + ....
ember jasper
donc j'ai traduit tout ça manuellement pour rien mdr đ
dawn junco
C'est quoi le truc le plus simple que tu peux faire Ă ce polynome pour arriver Ă un truc en z^4 + ...
dawn junco
donc j'ai traduit tout ça manuellement pour rien mdr đ
Tu pouvais pas savoir aussi
C'est tjs mieux de traduire
twilit escarp
RĂ©el
ember jasper
C'est quoi le truc le plus simple que tu peux faire Ă ce polynome pour arriver Ă ...
j'ai aucune idée, on parle de P oui?
dawn junco
oui
twilit escarp
Tu as az⎠+ ... et tu veux un truc qui commence par z⎠+ ...
ember jasper
a = 1 mais aprĂšs pour b et c
twilit escarp
Pas forcément
Tu as une condition sur a dans l'énoncé qui est crucial pour répondre à la question
ember jasper
- a est un réel
- a â 0
twilit escarp
Si a est non nul tu peux faire quoi ducoup ?
twilit escarp
Normalement tu trouves les deux comme ça
cedar kilnBOT
@ember jasper Has your question been resolved?
ember jasper
ok donc je tombe sur Q(z)/z^2= Z^2+ΩZ+Π-2
aprÚs je sais pas trop comment on passe de ça a Q(z)=0 ssi Z est solution d'une équation du second degré
dawn junco
Z^2+ΩZ+Π-2
et ça c'est pas un polynÎme du second degré par tout hasard
ember jasper
c'est la formulation de Z Ă©tant solution qui me trouble
dawn junco
on a déjà exclu que z = 0 était solution
donc Q(z) = 0 <=> Q(z)/z^2 = 0, t'as le droit de diviser par z^2
dawn junco
ok donc je tombe sur Q(z)/z^2= Z^2+ΩZ+Π-2
et puis t'as montrĂ© cette Ă©galitĂ© lĂ
Q(z) = 0 <=> Q(z)/z^2 = 0 <=> Z^2+ΩZ+Π-2 = 0
ember jasper
donc Q(z) = 0 <=> Q(z)/z^2 = 0, t'as le droit de diviser par z^2
ah oui
dawn junco
c'est exactement ça qu'on te demande de faire
de montrer des equivalences entre différentes équations
dawn junco
Q(z) = 0 <=> Q(z)/z^2 = 0 <=> Z^2+ΩZ+Π-2 = 0
donc oui Q(z) = 0, c'est Ă©quivalent Ă dire que Z est racine d'un polynome de degre 2
ember jasper
ok merci
ember jasper
donc oui Q(z) = 0, c'est Ă©quivalent Ă dire que Z est racine d'un polynome de deg...
par contre en quoi Z^2+ΩZ+Π-2 implique que Z est une racine dudit polynome?
pardon pour ma connerie
dawn junco
Q(z) = 0 <=> Q(z)/z^2 = 0 <=> Z^2+ΩZ+Π-2 = 0
=0
faut pas oublier qu'on parle d'une Ă©quation
ember jasper
je ne crois pas avoir compris ce que "Z est solution d'une equation" veut vraiment dire mathématiquement
dawn junco
je ne crois pas avoir compris ce que "Z est solution d'une equation" veut vraime...
bha en soi si tu trouves une fonction f telle que f(Z) = 0 [le cĂŽtĂ© droit a pas trop d'importance mĂȘme si tu prends =149 au lieu de =0, en changeant le f tu peux adapter], oui Z est solution d'une Ă©quation
maintenant on te dit que Z doit ĂȘtre solution d'une Ă©quation de degrĂ© 2 Ă coefficients rĂ©els, faut que ton f soit un polynĂŽme de degrĂ© 2 Ă coefficients rĂ©els
cedar kilnBOT
@ember jasper Has your question been resolved?
ember jasper
@dawn junco je peux juste te mp plus tard la je dois faire d'autres trucs
dawn junco
<@177516015033384960> je peux juste te mp plus tard la je dois faire d'autres tr...
sure
c'est ouvert
cedar kilnBOT
cedar kilnBOT
Available help channel!
vestal jacinth
cedar kilnBOT
wraith daggerBOT
ancient lodge
mean value theorem should suffice
If $f(x)=x^{3/2}$, then there is some $y_i \in \left(\frac{i-1}{n}, \frac{i}{n} \right)$ such that $$f \left(\frac{i}{n} \right)-f \left(\frac{i-1}{n} \right)=\frac{f'(y_i)}{n}=\frac{3}{2n} \sqrt{y_i}$$
wraith daggerBOT
Civil Service Pigeon
vestal jacinth
Uhh
vestal jacinth
.close
cedar kilnBOT
edgy spade
Eh?
cedar kilnBOT
Available help channel!
stone geyser
Hey Guys who knows about FDMs I need help in them and 2D please
hard thistle
truly math of all time
lusty pumice
truly math of all time
YES BRO
cedar kilnBOT
@stone geyser Has your question been resolved?
vast wing
Hello, quick question in function ax**2+bx+c, if a < 0 and beta < 0; the function never get higher than 0 ?
indigo lagoon
Hello, quick question in function $ax^2+bx+c$, if $a < 0$ and $\beta < 0$; the function never get higher than 0 ?
mental trail
Hello, quick question in function ax**2+bx+c, if a < 0 and beta < 0; the functio...
beta being?
wraith daggerBOT
This is sad đą
mental trail
the discriminant?
mental trail
beta = -discriminant/4a then
vast wing
beta = -discriminant/4a then
Yes
opal hinge
You mean like the vertex form?
iron wren
if you plug a and b being less than 0 in the discriminant you get a positive number every time, which means there are 2 real, distinct roots
that means it can go above and below zero
not every time actually
floral arrow
No like a(x-alpha) + beta
You're missing a square
vast wing
You're missing a square
Yes sorry
floral arrow
If you have a(x-alpha)^2 + beta and both a and beta are negative then the whole thing is negative, yes
floral arrow
(since a square is always positive or zero)
gray hamlet
If you have a(x-alpha)^2 + beta and both a and beta are negative then the whole ...
Thats not always true
mental trail
Thats not always true
....
vast wing
Yes so to solve this, I just solve Beta < 0 and a < 0; I want the function always negative
gray hamlet
In fact, there is always going to be a solution bigger than 0
gray hamlet
Because of quadratic formula
vast wing
So I canât solve this ?
mental trail
Because of quadratic formula
.... if a and beta are both < 0
then discriminant < 0
how do you plan to use quadratic formula
gray hamlet
Oh wait forgot that c should be bigger than 0 for it to be always true
vast wing
Sorry IDK what is quadratic formula
mental trail
Sorry IDK what is quadratic formula
don't worry about it if you haven't seen it yet
vast wing
So how can I sold my problem
floral arrow
,rccw
wraith daggerBOT
mental trail
just like you said you would
if you want to solve "quadratic always < 0"
then "a < 0 and beta < 0" works
you can also do "a < 0 and discriminant < 0"
vast wing
Ok thanks you very much
obsidian pelican
yoyve never seen this?
vast wing
Not for the moment, Iâm 16 and itâs what I learn at school
obsidian pelican
oh ok ok
vast wing
.close
modern quest
cedar kilnBOT
<:catglasses:1037770587235434567>
indigo lagoon
Hello, do you have any specific question to ask?
modern quest
Probably not at the moment
honest field
thua
indigo lagoon
Alright
modern quest
gĂŹ z:)
indigo lagoon
Imma green abuse since you don't have any question :))
wicked mantle
.solved
cedar kilnBOT
cedar kilnBOT
â
honest field
lol
indigo lagoon
yeah sure
honest field
.close
cedar kilnBOT
modern quest
what
modern quest
ohh
gray hamlet
lol
cedar kilnBOT
Available help channel!
noble dock
how do we know that the set ${x \in X : P(x) }$ is measurable though?
wraith daggerBOT
LXDL
noble dock
like ive been thinking about this and am just stuck
last apex
yeah you need this set to be measurable
when they say the measure is 0 they implictly mean its also measurable
cedar kilnBOT
@noble dock Has your question been resolved?
cedar kilnBOT
noble dock
.reopen
cedar kilnBOT
â
noble dock
yeah you need this set to be measurable
andit has nothing to do with being "complete" right?
since completeness only guarntees if we know m(N) = 0 then any subset of N, say E subseteq N, m(E) = 0
last apex
you are right
mu is a general measure here after all
but the point of this definition is to say P(x) holds everywhere except a negligable set
cedar kilnBOT
@noble dock Has your question been resolved?
tight steeple
.
gloomy steppe
i know the answer is x = 116 because i used chatgpt but dont ban me guys i tried 10 minutes i cant figure out i know youre meant to just use algebra and then solve but i could only find one angle for the triangle EDA which was "69" I assume there's some angle in a straight line logic at EBA, but its rly late at night and i dont see anything lmao also this is only highschool/gcse depending on location
cedar kilnBOT
i know the answer is x = 116 because i used chatgpt but dont ban me guys i tried...
@gloomy steppe Has your question been resolved?
ancient lodge
i know the answer is x = 116 because i used chatgpt but dont ban me guys i tried...
Using the result for the angle between two secants yields $$17 \cdot 2=b-d$$ $$69 \cdot 2=a-c$$
wraith daggerBOT
Civil Service Pigeon
ancient lodge
Also, because the circumference of a circle is $360^{\circ}$, $a+b+c+d=360$.
wraith daggerBOT
Civil Service Pigeon
ancient lodge
the rest is bashing
cedar kilnBOT
@gloomy steppe Has your question been resolved?
modest stream
I'm trying to understand the logic behind difference and sum of cubes.
I understand how it's proven through multiplication (from the factored form)
My issue is that I don't understand how it's proven through factoring from a^3 - b^3
My current idea is that
(a-b)(a^2 .... something)
I think I don't understand the logic behind factoring itself because I just dont understand why/how there needs to be a a^2 +ab + b^2) for difference of squares as an example.
Why is there supposed to be an ab, how is that ab gotten? How is this thing even factored
floral arrow
Are you asking why a^3+b^3 = (a+b)(a^2-ab+b^2) ?
modest stream
Yeah or for difference of cubes why it's (a-b)(a^2 + ab + b^2)
I just don't understand the ab part
Like sure as far as I understand it's like this:
Like sure the a^2 + b^2 have to be there because we're trying to get a^3 - b^3
But what's the logic behind +ab as an example
or -ab if we're speaking about sum of cubes
I just don't understand that part
floral arrow
Do you think a^3+b^3 should equal (a+b)(a^2+b^2) ? I'm honestly not sure what the issue is
modest stream
No I don't I just don't understand how someone gets -ab though
Ik this is kind of a stupid question I just can't get my mind around it
I don't make sense do I?
floral arrow
Yeah I'm not sure how to answer
modest stream
Sorry then
You think I should ping math help or like just try to make more sense because idk how to rephrase
floral arrow
If you know that (a+b) divides (a^3+b^3), then you can do:
a^3+b^3 = (a+b)(x)
and find x
modest stream
Well x needs to include a^2 and b^2 obviously
but the one in between idk how I'm supposed to solve for
Hmmm okay I'll think about it more
floral arrow
Well x needs to include a^2 and b^2 obviously
Right, and (a+b)(a^2+b^2) = a^3 + a^2b + ab^2 + b^3 which has extra terms
modest stream
Wait
Then can I not do
OHHHH
Because then ab is able to become a^2(b) and a(b^2)
So it's able to subtract those stuff out
Which is why it has to be -ab
floral arrow
Yeah
modest stream
Damn
I feel stupid now, but thank you
I guess I'll close the ticket
Thanks once again makes more sense
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
jagged stag
AP calc BC question and stuck on this homework problem, at the point where we've gone over singular shapes but not multiple. Was wondering where I should start, either separating the "pool" into 3 shapes or doing it altogether. Any help would be nice
cedar kilnBOT
AP calc BC question and stuck on this homework problem, at the point where we've...
@jagged stag Has your question been resolved?
cedar kilnBOT
@jagged stag Has your question been resolved?
jagged stag
<@&286206848099549185>
whole nexus
Yeah IG, break it down into 3 shapes, find their volume and add them
In terms of h
Like get the cuboid 20,25,h
Also the 4 ft is honestly bugging me
cedar kilnBOT
@jagged stag Has your question been resolved?
jagged stag
AP calc BC question and stuck on this homework problem, at the point where we've gone over singular shapes but not multiple. Was wondering where I should start, either separating the "pool" into 3 shapes or doing it altogether. Any help would be nice
whole nexus
Yeah IG, break it down into 3 shapes, find their volume and add them
this
jagged stag
Also the 4 ft is honestly bugging me
.
also I can't wrap my head around the triangle in the middle
when the volume changes the area it changes by isn't a constant amount so how would I represent that
cuz I don't think 1/2 b h * the 20 ft depth of the pool works
so im stuck here lol
whole nexus
Insane stuff dude, gotta think about this
whole nexus
Well for starters let's find dV/dt for the ones that don't pose this problem
We can then add all the dV/dt together
jagged stag
then the right bit is also that, but it comes in only after h=16
so (h-16) somewhere?
whole nexus
Ahhhh yeah
jagged stag
idk
jagged stag
well if I break it down into 4 shapes it's the rectangle on the left, right, one on the top of the triangle, and the triangle
whole nexus
well if I break it down into 4 shapes it's the rectangle on the left, right, one...
Yeah missed the extra space over the triangle
whole nexus
Do you have the answer?
This please
jagged stag
it wouldn't make sense adding that on unless im wrong
jagged stag
Do you have the answer?
uh no
whole nexus
well 500(h-16) just gets the same 500 dh/dt cuz that constant cancels out
Yeah once we differentiate it
jagged stag
Yeah once we differentiate it
mhm
well at least I can do the rectangles, but would you know how to get dv/dt just for the triangle at the bottom?
jagged stag
AP calc BC question and stuck on this homework problem, at the point where we've...
minus the 4ft bit, it's 16 ft tall and 25 ft wide
whole nexus
well at least I can do the rectangles, but would you know how to get dv/dt just ...
I feel like go for it
jagged stag
but the area at which it fills up by isn't a constant amount so I can't just use the area formula I don't think
or the rate of the height if that makes sense
whole nexus
Don't worry about the changing rate, because I'm not sure how else we'd do it
jagged stag
so it'd just be 1/2 * 25 * 16 * the 20ft depth?
I dunno if that sounds right
to differentiate from there
whole nexus
And the h?
whole nexus
Exactly my concern too
whole nexus
Alright, maybe ask this question again after closing this channel
Someone better might help
whole nexus
Alright, maybe ask this question again after closing this channel
in a new channel
jagged stag
Alright, maybe ask this question again after closing this channel
no stress thanks for the insight đ
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
tacit aurora
Are there any closed analytical formulas/approximations for projectile motion with linear drag?
wintry monolith
Linear drag
Meaning? Like air resis?
if air resis is proportional to velo u will get the time period and range will come as expo function i think
And i mean the whole velo vector
cedar kilnBOT
@tacit aurora Has your question been resolved?
tacit aurora
if air resis is proportional to velo u will get the time period and range will c...
So no closed formula like without drag?
tacit aurora
Meaning? Like air resis?
Yeah
wintry monolith
So no closed formula like without drag?
Depends on the question
Like air drag can be given as a function of anything
Mostly they give as a function on velo vector
Meaning
it will have both vertical and horizontal components
So u will have to integrate
by writing velo at some point
tacit aurora
Yeah thats what im trying to avoid
wintry monolith
And we know dv/dt is a
tacit aurora
Alr ty
cedar kilnBOT
cedar kilnBOT
Available help channel!
robust pulsar
Hello is there a way to prove this
cedar kilnBOT
Hello is there a way to prove this
normal cipher
Hello is there a way to prove this
What is R and r?
chilly warren
Is there any constraint in A B and C?
normal cipher
This seems like some ugly length bash maybe with extended sine rule
robust pulsar
What is R and r?
radius of outer circle and inner circle
robust pulsar
Is there any constraint in A B and C?
uh what is a constraint
i dont speak english very well
sorry
normal cipher
uh what is a constraint
what are the conditions on A, B and C?
please send the original question
robust pulsar
what are the conditions on A, B and C?
its just a triangle
robust pulsar
please send the original question
its in another language
normal cipher
its in another language
send anyway
robust pulsar
Can I send text instead
robust pulsar
and add the image to the text
robust pulsar
no
normal cipher
ok
this might be sin rule man
can you think of an easier way to express cos^2 (a/2)
i kinda gtg
cedar kilnBOT
@robust pulsar Has your question been resolved?
queen stirrup
s is the semi-perimeter
perhaps you can use 1/cos^2(A/2) = 1 + tan^2(A/2)
= 1 + (r/s-a)^2
queen stirrup
i dont know how helpful it is tho
yeah lol i was pretty active
but i left due to studies...
robust pulsar
Same
queen stirrup
like s(s-a)/bc
so what do you get when you try this formula?
robust pulsar
Uh I dont get much
queen stirrup
hm
how would you write R/r
do you know the relation between them? @robust pulsar
robust pulsar
Like uh (abc/4S)/(S/s) maybe
cedar kilnBOT
@robust pulsar Has your question been resolved?
vapid forge
hey
if you still need help then the RHS=2R(4R+r)/s^2
the proof for this is, peculiar, but its the best thing i came up with
robust pulsar
if you still need help then the RHS=2R(4R+r)/s^2
:O
In that case im done
Just need proof
queen stirrup
if you still need help then the RHS=2R(4R+r)/s^2
wait how
ancient lodge
,w (sec^2 (1/2 arccos(3/5))+sec^2 (1/2 arccos(4/5))+sec^2 (pi/4), 2(5/2)(4*5/2+1)/6^2)
wraith daggerBOT
ancient lodge
idt that holds for a 3-4-5
robust pulsar
no way đ
opal hinge
no way đ
I'm checking my work lol
I meant wth
oh waittttt
4R/r * 1
not +1
yeah yeah
yeahhhh
opal hinge
no way đ
Aww man this took long
robust pulsar
Wdym
tardy patio
Use the half-angle identity sec^2 t=1+tan^2 t
vapid forge
i want to hear
robust pulsar
Do you want to hear the proof
yeah
vapid forge
i feel like the problem is probably very simple but i cant devote alot of brain power for this for some reason
robust pulsar
ive been trying to multiply everything lol
vapid forge
tbh thats my proof
opal hinge
$\cos(\frac{A}{2})^2=\frac{s(s-a)}{bc}$
wraith daggerBOT
Alexis_Fx
opal hinge
this's what we gonna do first
robust pulsar
yes
opal hinge
Prove this
robust pulsar
i already did it
opal hinge
Alright
robust pulsar
like s(s-a)/bc
.
opal hinge
Then $\frac{1}{\cos(\frac{A}{2})^2}=\frac{bc}{s(s-a)}$
wraith daggerBOT
Alexis_Fx
robust pulsar
yes
tardy patio
Alexis\_Fx
There is better
opal hinge
$\frac{bc}{s(s-a)}=\frac{abc(s-b)(s-c)}{a\cdot s(s-a)(s-b)(s-c)}$
wraith daggerBOT
Alexis_Fx
robust pulsar
ok
tardy patio
$\tan\frac{A}{2}=\frac{r}{s-a},\qquad
\tan\frac{B}{2}=\frac{r}{s-b},\qquad$
\tan\frac{C}{2}=\frac{r}{s-c},
wraith daggerBOT
Adam
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
opal hinge
$\frac{abc(s-b)(s-c)}{a\cdot s(s-a)(s-b)(s-c)}=\frac{4R\cdot A (s-b)(s-c)}{a\cdot A^2}$
wraith daggerBOT
Alexis_Fx
robust pulsar
ok
opal hinge
$\frac{4R\cdot A (s-b)(s-c)}{a\cdot A^2}=\frac{4R (s-b)(s-c)}{a\cdot A}=\frac{4R(s-b)(s-c)}{a\cdot s\cdot r}$
wraith daggerBOT
Alexis_Fx
robust pulsar
â
opal hinge
$\frac{4R(s-b)(s-c)}{a\cdot s\cdot r}=\frac{2R}{r}\cdot\frac{2(s-b)(s-c)}{a\cdot s}$
wraith daggerBOT
Alexis_Fx
robust pulsar
yes
opal hinge
now this part is interesting
$a+b \geq 2\sqrt{ab} \Rightarrow \frac{(a+b)^2}{4} \geq ab$
wraith daggerBOT
Alexis_Fx
robust pulsar
yes
opal hinge
$\frac{2R}{r}\cdot\frac{2(s-b)(s-c)}{a\cdot s} \leq \frac{2R}{r}\cdot\frac{2(s-b+s-c)^2}{4a\cdot s}$
wraith daggerBOT
Alexis_Fx
opal hinge
$=\frac{2R}{r}\cdot\frac{2a^2}{4a\cdot s}$
wraith daggerBOT
Alexis_Fx
vapid forge
this solution is more neat definitely
robust pulsar
đ
opal hinge
$=\frac{2R}{r}\cdot\frac{a}{2\cdot s}$
wraith daggerBOT
Alexis_Fx
opal hinge
so RHS=$\frac{2R}{r}\cdot\frac{a}{2\cdot s}+ \frac{2R}{r}\cdot\frac{b}{2\cdot s}+\frac{2R}{r}\cdot\frac{c}{2\cdot s}$
wraith daggerBOT
Alexis_Fx
vapid forge
i dont think its an "equal" sign but
robust pulsar
its fine
vapid forge
ik
opal hinge
i dont think its an "equal" sign but
sorry mb
robust pulsar
i just needed the cauchy
vapid forge
i just wanted to point it out
robust pulsar
forgot
opal hinge
$=\frac{2R}{r}\left( \cdot\frac{a+b+c}{2\cdot s}\right)$
wraith daggerBOT
Alexis_Fx
opal hinge
$=\frac{2R}{r}$
wraith daggerBOT
Alexis_Fx
opal hinge
done
robust pulsar
thank you :)
opal hinge
holy crab this took me long lol
robust pulsar
lol
vapid forge
i can tell
opal hinge
I guessed it hold when a=b=c at the start
robust pulsar
yes
opal hinge
But it took a bit to prove
vapid forge
my lazy ass seen this in a tighter inequality and thought its applicable here
opal hinge
holy crab what exam/class is this
vapid forge
its like 11th grade math olympiad
opal hinge
Man I already hate trig, but here trig + inequality
opal hinge
its like 11th grade math olympiad
bruhh what
vapid forge
its insane ik, or like 12nd grade math if we're being generous
so im guessing like 11-12 grade level problem
ive see 9th graders when i was their age solves things like this though
so idk
opal hinge
ive see 9th graders when i was their age solves things like this though
Bro wtf.....
I meant I had to look up every single trig formula cuz I don't remember exactly any of them
I just like, oh there's a trig formula that look like that then I look it up on google
Man I feel so stoopid
vapid forge
Nah its fine
They are like hyper geniuses though
These questions can be hard even for college students
But who am I to speak im a math major anyways
opal hinge
@robust pulsar Ummm.... do you still need this channel?
opal hinge
But who am I to speak im a math major anyways
I don't even like Math lol
vapid forge
Wait it doesnt auto close?
opal hinge
Wait it doesnt auto close?
Not that we keep texting here
vapid forge
Isnt there like a 15 minutes time
opal hinge
bye
cedar kilnBOT
hi
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #âhow-to-get-help for instructions).
cedar kilnBOT
@robust pulsar Has your question been resolved?
ancient lodge
are all of your questions bashing
đ
anyway here is my stream of conciousness
opal hinge
3 pages long 
, at least that look really cool
ancient lodge
3 pages long <a:AAAAAAAA:584760367293399058> , at least that look really cool
definitely could've been shorter
but I didn't have planning time
I was writing the proof as I was solving cause I was killing time before recitation
so there's definitely places where it's longer than necessary
speaking of which time to go
opal hinge
My dead brain can't remember smth that's more than a page long so I could never do smth like this, that's so cool
ancient lodge
cedar kilnBOT
cedar kilnBOT
Available help channel!
wheat widget
Trig Question: how do I find cosine manually without a calculator? In the lecture I'm watching, my teacher writes down that cos(pi/6) = sqrt3/2 but I'm not understanding where the square root came from. I'm missing something.
wheat widget
ah I see. so he is just pulling from that. thank you
velvet matrix
Yep, it's a good idea to have at least the first quadrant memorized
cedar kilnBOT
twilit escarp
Yes max element is unique
twilit escarp
As long as you are on an ordered set yes
twilit escarp
(2,2) has two maximal elements
Which are ?
oak anchor
Which are ?
a tuple
twilit escarp
As long as you are on an ordered set yes
.
cedar kilnBOT
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Available help channel!
flint dome
I have 3x 6-sided dices. And I throw them once. The probability of triplets is 6/216. Now I have the problem with the twins. These can be arranged on 3 different ways * 6 = 18 so theoretically 18/216. My question is, but do I have to exclude the twins from the triplets? Because I have programmed a small dice game and I want to reward people for it, but I donât want to overlap the rules, so I have a priority list where the rarer is what the player gets then. I hope you understand my problem, thank you đ
digital cliff
normally it would include the triplet case
but in the context of what youre doing I'm fairly sure you would exclude those as they offer different rewards
otherwise when you get a triple youd be rewarded twice
flint dome
Exactly, but do I have to subtract something from the probability of the twin then?
chrome wolf
Btw, the probabilty of the twins is not 18/216. It is 90/216 in total.
chrome wolf
3 x 6 x 5
flint dome
Why *5?
chrome wolf
You can arrange 3 dice AAB, ABA and BAA, but you still have 6 choices for A and 5 choices for B.
chrome wolf
No, just 90/216. By takeing only 5 possibilities for the B above, we do not include triplets in the 90.
chrome wolf
AAA : 6/216 AAB: 90/216 ABC: (6x5x4)/216 = 120/216
chrome wolf
Asc and desc. are the same, you throw the dice at the same time, I sassume.
flint dome
4+4
chrome wolf
YOu can rearrange them, don't you?
flint dome
No the order is important and no Permutation
flint dome
Here this is a sneak peak
chrome wolf
If you have a fixed order of them, then it is only 8/216, correct.
flint dome
Ok
Perfect
Do u have a idea of a add rule cause for my Taste there are too much lose
I would like to give the player more coins
chrome wolf
square number, or second power of a number is the same
flint dome
This is a fantastic idea
May I note in my documentation that the idea comes from you?
chrome wolf
No, that is not necessary, thanks.
flint dome
Okkkkk thx :3 Iâll see how many coins the players collect then thank you đ
.close
cedar kilnBOT
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spiral iris
whats this rule called i wanna search up a proof but searching up lim f(un) doesnt give anything
split ice
en anglais c'est "sequential characterization of the limit"
en français... "la caractérisation séquentielle de la limite" travaille à mon propos
split ice
honnĂȘtement, la façon plus façile que j'ai trouvĂ© et d'utiliser epsilon-delta
commencez avec $$\lim_{x \to a} f(x) = L$$ avec la definition. Puis ajoutez la definition de $$\lim_{n \to \infty} u_n = a$$ dedans pour obtenir que $$|f(u_n) - L| < \epsilon$$ pour une choix de $(\delta, N)$ (vous devez choisir les deux)
wraith daggerBOT
ÏαÏÎčÎČ â„
split ice
finalement... ._.
cedar kilnBOT
@spiral iris Has your question been resolved?
spiral iris
jÂČai cherchĂ© tous mes livres masi je ne trouverais pas une defintion au
quand x tend vers inf
split ice
normalement pour une suite, c'est défini
mais la definition formal est: $\forall \epsilon > 0,$ il existe une choix de $N \in \mathbb{N},$ que si $n \geq N$ (pour tout les termes apres N), puis $|x_n - L| < \epsilon$
vous voyez mon problĂšme avec texit maintenant, j'espĂšre ;-;
wraith daggerBOT
ÏαÏÎčÎČ â„
spiral iris
je trouvais cette question trop similaire a lim x=> de gofx
split ice
oui, mais c'est une suite et une fonctionne, alors c'est un delta et un N qu'on doit choisir
spiral iris
ÏαÏÎčÎČ â„
cette defintion est de la suite non? il n'y a pas une differente defintion pour x => + inf?
split ice
oh je vois ce que te dis
spiral iris
je la trouver
x>b => |fx - l|< epsilon
la on prend x = n
si on prend N=B cest resolue non?
et on a que un appartient a I (xEI)
donc on peut poser Un=x?
split ice
si on prend N=B cest resolue non?
ouais exactement
split ice
donc on peut poser Un=x?
on peut pas conclure ca, seulement u_n -> a, alors |u_n - a| < (epsilon_0)
cvd une epsilon spécifique
spiral iris
on peut pas conclure ca, seulement u_n -> a, alors |u_n - a| < (epsilon_0)
prq
un existe sur I le meme pour x?
cala cest logique non?
split ice
oui mais une suite ne peut pas Ă©galer une valeur comme x
spiral iris
mais attends on peut just remplacer x dans 0<|x-a|<alpha par un?
split ice
normalement on dit aussi que u_n =/= x n'importe quelle terme u_n
oui tu peut le remplacer
mais j'hesite de le dire "Ă©galite" si tu me comprends
spiral iris
oui je vous comprends
donc jai resolue
ohh
je vraiment deteste les defintions des limites
merci beaucoup @split ice
.close
cedar kilnBOT
split ice
je vraiment deteste les defintions des limites
c'est juste, mais c'est la seul façon pour le preuver que j'ai vu malhereusement
bref bien resolué !
cedar kilnBOT
Available help channel!
neon kernel
J'ai du mal a comprendre les parties d'etude de signe et variations. La premiere question a ete facile mais apres je suis totalement bloqué.
oak anchor
faut que tu Ă©tudies quand fâ(x) est inferieur ou supĂ©rieur Ă 0
neon kernel
Avec une inequation?
neon kernel
Parce que je sais que quand e^x est soit egale a -4 ou a 1 elle s'annule
oak anchor
$e^x > 0 \Longrightarrow e^x + 4 > 0$
wraith daggerBOT
MĂ©dicis
oak anchor
$2(e^x-1)(e^x+4) = 0 \Longrightarrow 2(e^x-1) = 0$
wraith daggerBOT
MĂ©dicis
oak anchor
tu divises des deux cotés par 2, tu retrouves e^x - 1 = 0
donc e^x = 1
la fonction exponentielle Ă©tant croissante stricte, il nây a quâune seule valeur qui annule fâ(x)
cedar kilnBOT
cedar kilnBOT
Available help channel!
dry sage
cedar kilnBOT
frail citrus
is this right
correct
frail citrus
fine ask
frail citrus
im goated
everyone should be
idts that its a great achievement if u hv been good with algebra but if not it can be counted
dry sage
idts that its a great achievement if u hv been good with algebra but if not it c...
lol i wanna learn caclulus but im struggling with basic algebra
just need to figure a few things out
is this good
oh i can simplify wait
wait no nvm
lol
dry sage
@frail citrus
frail citrus
yea its fine
junior idol
cedar kilnBOT
junior idol
Guys I need a place to start here
tropic oxide
got a diagram?
opal hinge
Guys I need a place to start here
start by making a diagram
gritty galleon
heres an idea
construct OF and BO, then find EF and BF in terms of something common (diagonal. square side, circle radius) using the two triangles formed
gritty galleon
okay wit that is a completely different approach to what i was thinking
opal hinge
||EB is known, so using pytagore BH^2-BF^2=FH^2 and EH^2-EF^2=FH^2 and EF+FB=EB||
||That's enough to find exactly both EF and FB||
gritty galleon
damn
cedar kilnBOT
@junior idol Has your question been resolved?
junior idol
okay wit that is a completely different approach to what i was thinking
What was your approach
Iâm trying to use PoP
gritty galleon
What was your approach
i wrote it above (just above the diagram alexis sent)
gritty galleon
Iâm trying to use PoP
not too familiar with power of a point, sorry
opal hinge
Well I said WLOG itâs 2
oh okay
so BF*BE=1
and this BE^2=BO^2+EO^2
so basically that is it
yeah that's much shorter than mine
gritty galleon
wait the pa *pb = pt^2 comes under PoP?
junior idol
Where did we get p and t
opal hinge
AoPS said so
gritty galleon
Where did we get p and t
thats how we learnt the theorem u applied, atleast i think so
gritty galleon
o i was seeing wikipedia :\
gritty galleon
Where did we get p and t
damn but yes much better approach
opal hinge
So please elaborate
I did, just below that message
junior idol
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
zenith sedge
cedar kilnBOT
zenith sedge
is this a valid proof?
solemn stump
It works, the logic for the bound is solid.
But maybe you forgot to check if there's a simpler bound for the denominator? You don't always have to use the tightest one possible.
zenith sedge
It works, the logic for the bound is solid.
But maybe you forgot to check if th...
for the denominator can't you have anything less then sqrt3 + 2
solemn stump
Maybe u forgot that sqrt(x) has a minimum value? what does that tell u about the whole denominator?
zenith sedge
Maybe u forgot that sqrt(x) has a minimum value? what does that tell u about the...
oh right
so the denominator can be 2 which occurs when sqrtx is0
cedar kilnBOT
@zenith sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
dreamy sleet
Yes, you let N and M be arbitrary, then you have the equivalence
Big hint: ||use the five lemma||
crimson sedge
what fraction of the cube does the cone fill??
cedar kilnBOT
what fraction of the cube does the cone fill??
tropic oxide
you know the ratios of cone/pyramid and pyramid/cube
how can you combine these to get cone/cube
crimson sedge
.close
normal sage
cedar kilnBOT
proven summit
<@&268886789983436800>
cerulean sail
Please don't spam pictures in help channels, this isn't the place for it 
cedar kilnBOT
sacred iron
looks like op left?
Or booted. 
cedar kilnBOT
Available help channel!
cedar kilnBOT
wicked mantle
.solved
cedar kilnBOT
crimson delta
<@&268886789983436800>
wicked mantle
autopiloted đ
cedar kilnBOT
Available help channel!
fleet lava
Hello, I need some help with mathematics, particularly with functions. I can send you the exercises I need to work on. Iâm from the Czech Republic, but I speak English quite well i am having test tomorrow so i would like some helpp
past wave
Yes send the question
fleet lava
dont you mind its in czech tho? or you want me to translate it
swift moth
fleet lava
okay i will gimme a minute
tropic oxide
dont you mind its in czech tho? or you want me to translate it
post the original first, then translate
fleet lava
- determine the domain.
- calculate f (6)
decide if the function can take the value y = 2
and like this its repeating all along
just with different numbers
cobalt iron
red text are ans?
fleet lava
yeah
stoic crystal
yeah
whole nexus
Alright, for Domain, the numerator and denominator are fairly simple, so just check for denominator = 0 and remove the value of x that does that
cobalt iron
well x cannot be -3 because if it become -3 then the function become not defined
therefore domain is R-{-3}
whole nexus
For f(6), just place the value of x as 6 in your original function
fleet lava
Would you mind calling? Itâs easier for me to understand math when I can see how someone does it but if no then its alr
whole nexus
Also to check whether y=2 is possible, you could take the long route and find the Range of the function and check whether 2 is in the Range or not, or just put f(x) = 2 and then check the value of x
whole nexus
Would you mind calling? Itâs easier for me to understand math when I can see how...
Well there's no VC in this server
fleet lava
we can do like i can add you
whole nexus
Ahhhh maybe later, also my accent might be a problem, let's try here only
whole nexus
But it's root, it cannot be negative too
frosty creek
But it's root, it cannot be negative too
Sorry? Which one?
whole nexus
Sorry? Which one?
Whoops, I didn't check and thought you meant the second one among the ones we can see (i.e. the 3rd one)
fleet lava
The domain for 2) is easy no?
i mean it is easy, but for me idk i just need to see how you do it idk how to explain that tbh and i just dont get it
frosty creek
Whoops, I didn't check and thought you meant the second one among the ones we ca...
All good mate
frosty creek
i mean it is easy, but for me idk i just need to see how you do it idk how to ex...
Its easy, just clear your concepts and observe the questions, the idea of what to use will come to your mind
fleet lava
yeah, thanks
frosty creek
yeah, thanks
What help do you actually need tho, cuz every problem seems a bit easy
Also back tracking helps
fleet lava
it is easy ik that, i just dont know how you get all of the answers to it i have no idea how to do it
whole nexus
Like you understand the problems but you don't know how to do it?
fleet lava
math is hard for me in general and i am just trying to look for some help
fleet lava
Like you understand the problems but you don't know how to do it?
yeah
whole nexus
yeah
Do you have problem in knowing what to do, or do you know what you have to do still you don't know how to start
?
frosty creek
math is hard for me in general and i am just trying to look for some help
Ik how it feels, just needs a lot and lot of practice
fleet lava
Do you have problem in knowing what to do, or do you know what you have to do st...
i dont know how to start
fleet lava
Ik how it feels, just needs a lot and lot of practice
i am trying to get this for a week every day but it never came into my mind so
whole nexus
i dont know how to start
Yeah that comes with practise
Have you tried getting a tutor?
They could help you with the issue you have, someone in your area
frosty creek
i dont know how to start
Cover different concepts and practice questions based on that concept
fleet lava
Have you tried getting a tutor?
yeah i tried
whole nexus
yeah i tried
You just need someone to guide you with the hesitation you feel whilst approaching a problem, and then a lot of practise
A tutor could help with that, see if you could find someone good in your area
fleet lava
yeah, thanks for help
frosty creek
yeah, thanks for help
Also if you have any queries related to questions or anything you could always open a ticket
You can count on helpers
whole nexus
Well all you need is confidence, and that comes with clarity
frosty creek
this is making me feel like idk i cannot do anything so xd
Believe me, everyone feels like that once in a whileđ€Ł
whole nexus
Once you get clarity on how to approach questions, then you'd no longer feel like that
fleet lava
oh
whole nexus
And for clarity, you need guidance, try to pay attention in class and practise a lot, maybe get a good tutor for your other issues
fleet lava
i am not doing anything than paying attention in class especially in math i am asking her why is that there or whateber i dont know but she never answeres me shes saying that i should be quiet cuz afterall i will get a bad grade so i tried to look for some help here but didnt worked out too
whole nexus
i am not doing anything than paying attention in class especially in math i am a...
Well I'm really sorry for the teacher you've got, she seems like a piece of work but we can't really do anything about her
fleet lava
yeah i know you cannot, but i just had hope that here maybe i will get help here but by words or something i cannot understand it but all good dw
whole nexus
You need someone supportive, there are online tutors too yk, you could ask if someone tutors in #math-discussion
weak granite
i am not doing anything than paying attention in class especially in math i am a...
got the same bitch here too- writes down the formula then starts solving??? hello đ ???
fleet lava
got the same bitch here too- writes down the formula then starts solving??? hell...
yeah well she does that too then shes walking around the class helps everyone but me and my friend no so
frosty creek
yeah i know you cannot, but i just had hope that here maybe i will get help here...
You can get help from here mate
fleet lava
You can get help from here mate
yeah i tried but by words i dont understand it
weak granite
yeah well she does that too then shes walking around the class helps everyone bu...
you can def report her- girly got some issues with you and your friend đ
frosty creek
yeah i tried but by words i dont understand it
So what do you want?
whole nexus
We can help with any question you're stuck in after you have clarity, but to get clarity you need someone to teach you
weak granite
yeah i tried but by words i dont understand it
well people here are very patient. just post, wait, and you'll eventually get it.
fleet lava
you can def report her- girly got some issues with you and your friend đ
i tried. our teacher said we will have different teacher but then she said that principle and the math teacher said no cuz she wants to teach us
whole nexus
So what do you want?
She wants to get on a call where one could explain how to do a question properly
weak granite
She wants to get on a call where one could explain how to do a question properly
I could try that, depending on the subject and the level of math (if its math)
@fleet lava can you describe your issue?
whole nexus
I've got no problem with personally helping, but I am hesitant about getting on vc
frosty creek
well people here are very patient. just post, wait, and you'll eventually get it...
Yeah from my observations, some people here are better teachers than the actual onesđ€Ł
weak granite
all the helpers here are better than teachers.
whole nexus
@weak granite she shared this
frosty creek
I've got no problem with personally helping, but I am hesitant about getting on ...
You can do it mate, why hesitating to go on vc?
fleet lava
I could try that, depending on the subject and the level of math (if its math)
...
i need to help especially with functions we are at the beginning but i just dont get it
whole nexus
You can do it mate, why hesitating to go on vc?
Well I have an accent
Also it's pretty new for me
frosty creek
Well I have an accent
Doesnt matter
frosty creek
Also it's pretty new for me
Believe me, when i first joined discord, i felt the same
But what comes above hesitation is help
whole nexus
True dude
I mean I can take the step but there's also no private place here where I'd be able to talk properly
frosty creek
@fleet lava if i get some time, iâll help, dw
frosty creek
I mean I can take the step but there's also no private place here where I'd be a...
We can give suggestions i guess
For creating a vc and a new role for thet
That*
whole nexus
Well @fleet lava you can add us
whole nexus
For creating a vc and a new role for thet
I agree, the only problems would be the trolls, if they find a way to tackle that then we'd be fine
weak granite
this might be a lagnuage barrier but- idk what the numbers with the one on the left are supposed to represent but... yeah I can explain how domains-ranges work
frosty creek
I agree, the only problems would be the trolls, if they find a way to tackle tha...
Idts, just an addition in couple of moderators would do the work
whole nexus
Idts, just an addition in couple of moderators would do the work
Let's see, we can add it in suggestions
fleet lava
so should i wait a little?
frosty creek
Let's see, we can add it in suggestions
I cant, you can
weak granite
I can try to explain domain/range in vc. if you dont understand, then yeah you shall.
whole nexus
I cant, you can
Alright then, I will
frosty creek
Alright then, I will
Im a new member so i cant suggest anything as of now
frosty creek
I can try to explain domain/range in vc. if you dont understand, then yeah you s...
Wavy curve method is great for domains
whole nexus
so should i wait a little?
Well @weak granite can get on a vc with you, you guys can handle things out among you both
fleet lava
I can try to explain domain/range in vc. if you dont understand, then yeah you s...
we can try i dont mind, if you want i can even translate the text there for you
weak granite
we can try i dont mind, if you want i can even translate the text there for you
then off we go.
you can close this now and if things dont work out properly
you may reclaim another channel
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
frosty creek
Glhf
fleet lava
.close
warped spire
Hello, can I express this sequence as
cedar kilnBOT
Hello, can I express this sequence as
warped spire
this?
night wedge
No
night wedge
Since you are square rooting you halve the power each time so it would be 1/2^n not 1/n
night wedge
Hello, can I express this sequence as
If you are trying to find the limit of this then yes
You can easily create a formula for a_n in terms of n
warped spire
Do I have to give constraints like n is element of integers?
night wedge
When you use the letter n you imply it should be an integer
last apex
When you use the letter n you imply it should be an integer
Especially in the context of sequences
night wedge
Usually variables can be represented with anything but there are some letters people give specific meanings to like n, x or z
cedar kilnBOT
cedar kilnBOT
Available help channel!
storm jewel
Hello
I'm struggling to start solving this. Where do I begin?
hollow trail
do you know the definitions of those three things?
chilly warren
No help for this one. Just use the formula and plug that in.
storm jewel
one moment lemme get a screenshot of the formula in my notes
wait
so do i just take the integral between x=0 and x=10?
or
storm jewel
for the mean, i have this. would that mean in the question i just take the sum of 0(0.562) + 7(0.109), and so on?
tropic oxide
yes
the sum will have 4 terms only
3 if you're OK throwing out the 0*0.562 term immediately
storm jewel
i managed to solve the question
thank you for your time 
i think it was just about finding the formulas themselves
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
cedar kilnBOT
night wedge
.close
cedar kilnBOT
Available help channel!
zenith sedge
cedar kilnBOT
zenith sedge
why are we taking delta as the min of 1 and epsilon/6?
why wouldn't picking delta as epsilon/6 simply satisfy ?
hollow trail
we need delta to be at most 1 so that we can put a bound on x + 4
(we didn't have to choose 1 specifically but we did need to put some constant bound on delta)
zenith sedge
we need delta to be at most 1 so that we can put a bound on x + 4
i get that part
but when we state detla = min{1, epsilon/6}, why do we do that?
why wouldn't picking delta = epsilon/6 satisfy any epsilon > 0?
dire geode
why wouldn't picking delta = epsilon/6 satisfy any epsilon > 0?
try it for x = 3
cedar kilnBOT
@zenith sedge Has your question been resolved?
hollow trail
if epsilon > 6 then our claim that delta < 1 would fail
dusky linden
cedar kilnBOT
dusky linden
im a little confused
digital cliff
in what way
dusky linden
in what way
i know there will be 2 functions
dusky linden
I would say theres only one
well she gets an extra 5% of her sales **over **1k
that would be the second function
digital cliff
it would be a part of the function, not a separate thing necessarily
dusky linden
it would be a part of the function, not a separate thing necessarily
how so
digital cliff
if i have x^2+2x, i wouldnt count x^2 and 2x as separate functions, just separate terms
dusky linden
if i have x^2+2x, i wouldnt count x^2 and 2x as separate functions, just separat...
well thats different
in this scenario
she doesnt earn the extra if she doesnt make more than 1k
digital cliff
ah, alright i see what you mean now, a piecewise function
my apologies
so whats your idea?
digital cliff
lets call the value of sales as x
for x<=1000, what does the function look like
dusky linden
lets call the value of sales as x
for x<=1000, what does the function look like
wdym by the value of sales
units sold?
digital cliff
total amount of money she made through sales (for the company)
dusky linden
lets call the value of sales as x
for x<=1000, what does the function look like
it would look like a straight line?
digital cliff
bit more specific?
dusky linden
bit more specific?
ti will always be smaller or equals to 1k?
digital cliff
x will be yeah, thats the upper bound on this section
but what is the straight line like? Is it at a slope? A constant value? If so, what is that value?
dusky linden
x will be yeah, thats the upper bound on this section
but what is the straight ...
a constant value
digital cliff
what value would that be
dusky linden
what value would that be
8.05x40?
digital cliff
nice
now what do you think for x>1000
dusky linden
nice
now what do you think for x>1000
im not sure
well i know the c value will be 322 using the previous constant value for the first function
how can i find the scaling?
digital cliff
the c value?
and by scaling do you mean the slope/gradient?
lets say x>1000
then whats the value that the 5% is applying to
dusky linden
lets say x>1000
then whats the value that the 5% is applying to
to the x?
so 0.05(x-1000)?
dusky linden
the 322