and flight 2 flies 100 miles due north
#help-28
torn jolt
gilded apex
yea
torn jolt
so draw a two line with same length from the point
but flight 2 goes upward
and flight 1 goes to the left
gilded apex
ok done
torn jolt
ok done
ok and apply the angle. and draw a straight line with 50 miles length
not actual 50 miles,
prob about 5cm
gilded apex
ok
gilded apex
got t
gilded apex
no
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cobalt spruce
im struggling to understand the communication behind cofunction indetities
cobalt spruce
if i have cos tetha and they want me to turn it into sin
and i use a trig cofunction
is it my X that becmoes my sin tetha
or my pi/2 + or - my xthat because my sin tetha
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cobalt spruce
<@&286206848099549185>
im struggling with understanding solving cofunction identities that dont include a variable
i know this is french but it says suppose that sin = 0.5 use a equivelante trig expression to showcase cos = 0.5
i dont exactly know what the question is demanding
but i know how to use the functions properly
what is my final answer supposed to be
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zinc berry
i dont exactly know what the question is demanding
T’as essayé quelles formules?
cobalt spruce
Ouu un français
cobalt spruce
T’as essayé quelles formules?
Ceux en rouge
C’est la communication que je ne comprends pas
Je sais comment y arriver et quelle formule utiliser
Mais je ne comprend pas comment qu’ils veulent que je le présent sur papier
zinc berry
Mais je ne comprend pas comment qu’ils veulent que je le présent sur papier
À mon avis tu prends juste une formule qui te semble marcher et tu montre l’équivalence entre le sinus et le cosinus
cobalt spruce
Donc
zinc berry
cosx = sin(pi/2 -x) ici semble bien marcher par exemple
cobalt spruce
Une fois que je sépare mon angle original en (pi/2 +- x)
zinc berry
Oui
cobalt spruce
Et je le mets égale au fonction opposer
zinc berry
Puis tu dis juste que les deux sont égaux à 1/2 (je pense!?)
Je vois pas comment faire autrement…
Oui
cobalt spruce
Essaye je continue a le développer jusqu’à tant que j’arrive a 0.5
zinc berry
Oui j’aurais fait ça
cobalt spruce
Qu’elle devra être ma phrase de conclusion ou ma dèfniere ligne d’égalité
Sa ici sa marche
zinc berry
Oui ça m’a l’air cohérent
zinc berry
Quel dernier?
cobalt spruce
donc
tu sais comment des fois on decompose avant de remaplcer pour x
comme si c'est 13pi/18
zinc berry
Oui
cobalt spruce
et donc -sin = 4pi/18
zinc berry
Tu prends le plus petit facteur commun avec 2pi
cobalt spruce
pourquoi eseque je ne peut pas just faire
si c'est cos 13pi/18
pourquoi eseque je ne peut pas just faire
cos ( pi/2 + 13pi/18)
pourque eseque j;ai besoin de le decomposer
zinc berry
C’est une autre énoncé là?
On est d’accord ça a rien à voir avec ta question initiale?😅 que je dise pas de connerie
cobalt spruce
hm?
une seconde
l
pourquoi esequ'ls veulent que je decompose en premier
pourquoi eseque je ne peut pas simplement faire cos (pi/2 + 13pi/18)
pourquoi eseque la parenthese c'est une decomposotion
de 13pi/18 = pi/2 + x
zinc berry
Ahhh
cobalt spruce
et pas cos (pi/2 { 13pi/18)
zinc berry
Pour mieux comprendre ca je pense que faut jouer un peu avec les graphs sur Desmos
cobalt spruce
j'y jouera
zinc berry
Tu verras que en faite comme c’est des fonctions un peu bizarres, il y a pleins de manières d’avoir le meme resultat
cobalt spruce
tu sais comment on est arriver a la conclsuion que la derniere ligne etait = 1/2
le corrigé pense que c'est
zinc berry
C’est exactement ce que t’as marqué
Si tu mets ça dans la calculatrice ca te donne 1/2
C’est équivalent
zinc berry
Non pas besoin
cobalt spruce
si j'ai cos (pi/3)
ma parenthse quand jai (pi/2 + x)
elle doit etre egale a pi/3
right
zinc berry
Pourquoi pi/3
zinc berry
Mais du coup tu suis plus la formule?
C’est pas au hasard les nombres
Les nombres sont prédéfinis
zinc berry
Là tu cherches aussi une fonction sur ta feuille où ça marche
Il se trouve que la 3eme dans le rouge marche
cobalt spruce
si j"ai sa
donc je suis un peut confus de pourquoi ici ils ne demande pas de exprimé en tant de somme ou difference
et qu'il me laisse just utilisé l'equivalance trigonometrique
eseque c'est car c'est un angle remeraquableÉ
zinc berry
Ils te demandent pas de calculer quoi que ce soit mais plutôt une équivalence entre les deux fonctions trigonométriques
zinc berry
Cette équivalence est connectée dans tes formules que t’as envoyé
cobalt spruce
mon x dans mes equivalances
il est jamais egale a mon tetha de l'angle originale
par example: sin pi/6
si je veut utiliser sin (pi/2 - x) = cos x
mon x n'est pas pi/ 6
zinc berry
Ahhh
cobalt spruce
mon x est pi/6 = pi/2 - x right
zinc berry
Mais pour éviter ça, tu peux tout simplement utiliser l’autre formule, regarde
cobalt spruce
ma parenthese doit toujours etre egale a mon pi/6 (ou n<importe qu'elle angle qui est la)
zinc berry
cobalt spruce
mais
zinc berry
Choisis celle qui est le plus facile à utiliser entre les 2
cobalt spruce
oui
zinc berry
Les deux marchent toutes aussi bien
cobalt spruce
premier quadrant souvant les -
2ieme souvant les +
dernier question
ma démarche est elle bonne ici
ici eseque je commence avec le sec ou le cosec
mon prof mas dit le sec mais les autres on dit cosec
cobalt spruce
secest plus facile
attent
ici
je develope mon cosec
cosec (pi/2 -x) =sec
mon x il nest pas pi/4
mon x doit etre egale a pi/4 - pi/2
donc
jai eu sec pi/4
c'est la version positive de 3pi/4
j'ai ajouter un pi pour quelle devienne negative est elle est maintenat 5pi/4 pas 3pi/4
nvm je l'ai eu
merci
.close
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buoyant ivy
How do I do the deduce part?
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buoyant ivy
I have gotten
-1/(8N+3) + 1/(4N+6) < 1/(8N)
,, \sum_{r=N+1}^{2N} \frac{1}{(2r+1)(2r+3)} = \frac{-1}{8N+3} + \frac{1}{4N+6} < \frac{1}{8N}
cosmic pewter
¨ÅØÆ-.,
glossy valveBOT
Léon
cosmic pewter
Typo
buoyant ivy
ooh
tired smelt
Let ( n ) be a fixed integer greater than or equal to ( 2 ).
A matrix ( A = (a_{i,j}){1 \leq i,j \leq n} ) from ( M_n(\mathbb{R}) ) is called centro-symmetric if, for all ( (i,j) \in [1,n]^2 ):
[
a{i,j} = a_{n+1-i, n+1-j}.
]
Let ( S = (s_{i,j}){1 \leq i,j \leq n} ) be the matrix in ( M_n(\mathbb{R}) ) defined by:
[
s{i,j} =
\begin{cases}
1 & \text{if } i = n+1-j, \
0 & \text{otherwise}.
\end{cases}
]
-
Prove that a centro-symmetric matrix is also symmetric.
-
Let ( A = (a_{i,j}){1 \leq i,j \leq n} ). Show that ( A ) is a centro-symmetric matrix if and only if, for all ( (i,j) \in [1,n]^2 ), we have:
[
a{n+1-i,j} = a_{i, n+1-j}.
]
(a) Prove that a matrix ( A ) is centro-symmetric if and only if ( AS = SA ).
(b) Deduce that if ( A ) and ( B ) are both centro-symmetric, and if ( A ) is invertible, then ( AB ) and ( A^{-1} ) are also centro-symmetric.
- A column vector ( Z = \begin{pmatrix} z_1 \ \vdots \ z_n \end{pmatrix} \in M_{n,1}(\mathbb{R}) ) is said to be symmetric if, for all ( i \in [1,n] ), ( z_i = z_{n+1-i} ).
A column vector ( Z = \begin{pmatrix} z_1 \ \vdots \ z_n \end{pmatrix} \in M_{n,1}(\mathbb{R}) ) is said to be anti-symmetric if, for all ( i \in [1,n] ), ( z_i = -z_{n+1-i} ).
Let ( \lambda \in \mathbb{R} ) and let ( A ) be a centro-symmetric matrix in ( M_n(\mathbb{R}) ). Define:
[
E_\lambda(A) = {X \in M_{n,1}(\mathbb{R}), AX = \lambda X}.
]
(a) Prove that any column vector ( X ) in ( E_\lambda(A) ) belongs to ( E_\lambda(A) ). \
(b) Prove that if ( X \in E_\lambda(A) ), then ( S X \in E_\lambda(A) ). \
(c) Deduce that if ( E_\lambda(A) ) does not contain only the zero column vector, then it contains at least one nonzero symmetric column vector or one nonzero anti-symmetric column vector.
glossy valveBOT
Akti
tired smelt
I'm looking for help for the last question
I noticed that $X = \dfrac{X+SX}{2}+\dfrac{X-SX}{2}$ with $X+SX$ a nonzero symetric colomn matrice and $X-SX$ a nonzero antisymetric column matrix but I don't see how I can go any further
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Akti
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pulsar kiln
eigenspace
A is centro symmetric, you know the eigenspace relation to the eigenvalue
${X \in M_{n,1}(\mathbb{R}) \mid AX = \lambda X}$
glossy valveBOT
Quantie
glossy valveBOT
Quantie
pulsar kiln
AX = lambdaX
insert the symmetric form
and substitute or apply A to X
(X = X_S + X_A)
glossy valveBOT
Quantie
pulsar kiln
if X,A are nonzero, then E_lambda contains at least one nonzero column vector or an anti symmetric column vector
and thats it really
forest flint
Ok
pulsar kiln
@tired smelt let me know if you have any questions
tired smelt
eigenspace
Never heard any of that that’s why
pulsar kiln
Never heard any of that that’s why
is this part of your course plan, or are you supposed to use other techniques?
tired smelt
I’ll learn it in some months I guess, yet we’ve just done the first chapter on matrices
But I can’t use any property about eigenspace
Only what I proved in the previous questions
tired smelt
if X,A are nonzero, then E_lambda contains at least one nonzero column vector or...
I mean I don’t see why X=X_s + X_a implies it contains at least one nonzero column vector OR an anti-sym column vector
tired smelt
**Quantie**
Did u mean SX not X_s ?
pulsar kiln
**Quantie**
do you know this equation
tired smelt
do you know this equation
Nah, is that famous or something ?
pulsar kiln
Did u mean SX not X_s ?
its the same thing, just the reversed of X
pulsar kiln
Nah, is that famous or something ?
its whats needed to prove this kind of problem, wouldnt call it famous
i cant recall another way to prove it right now
tired smelt
its whats needed to prove this kind of problem, wouldnt call it famous
i cant ...
Yes please
pulsar kiln
if you want ill try 
gimme some time
do you know how a nonzero vector implies that symmetries and anti symmetries are also nonzero?
tired smelt
do you know how a nonzero vector implies that symmetries and anti symmetries are...
Yes I think
pulsar kiln
its a short proof but imma skip it for now, imma do it in my notes so gimme a min to figure this out
it can be applied
tired smelt
If X=(x1,…,xn) was zero then X+SX=(x1+xn…,xn+x1) would be also zero
tired smelt
its a short proof but imma skip it for now, imma do it in my notes so gimme a mi...
Sure
I think I understand the previous proof btw
By contrapositive if X_a=0 and X_S=0 then X=0
kindred grove
By contrapositive if X_a=0 and X_S=0 then X=0
yeah
so if you can show both of X+SX/2 and X-SX/2 are in E_l(A), you'll have shown what you gotta show
tired smelt
This is the question 4)b)
kindred grove
not exactly
tired smelt
When we divide by two it’s still symetric or anti-sym ?
kindred grove
you know X+SX/2 and X-SX/2 are sym/anti-sym already, no need to show it again
pulsar kiln
kindred grove
nice yap
pulsar kiln
ikr
kindred grove
what does that have to do with the question 4c tho
pulsar kiln
they dont know S + SX / 2 and S - SX / 2 so you gotta use other proofs
pulsar kiln
what does that have to do with the question 4c tho
d)
kindred grove
**Akti**
didn't they say that just at the beginning tho
I assume they're aware of it from that
pulsar kiln
Nah, is that famous or something ?
i proved it by projection first but they werent familiar
then they asked me to use other methods
i just provide
tired smelt
didn't they say that just at the beginning tho
They introduced the set E_l(A) but I’m seeing it for first time
But by contrapositive, can’t I just say that if X is a sum of a nonzero sym vect X_a = … and X_s = … then X=0 ?
kindred grove
say that in order to show what though ?
pulsar kiln
you need x + sx / 2 and x - sx / 2 to be able to do that, since you cant show that
kindred grove
like ok you managed to show that if X isn't 0 then either X_a or X_s isn't 0
pulsar kiln
(AX_S = \lambda X_S), (AX_A = \lambda X_A).
glossy valveBOT
Quantie
pulsar kiln
is true otherwise
kindred grove
I know we're talking about 4c lol
pulsar kiln
thought it was d not c, if anyone cares 
tired smelt
you need x + sx / 2 and x - sx / 2 to be able to do that, since you cant show th...
X+SX/2 + … is a property that need to be proved in class or can’t I just pose X=X+SX/2 + X-SX/2
tired smelt
**Quantie**
what does that mean ?
pulsar kiln
X+SX/2 + … is a property that need to be proved in class or can’t I just pose X=...
uuuuuhhhhh
it needs a proof to be able to use, just like any math. but from X you can quickly show that its true
but unless taught, its not something youd come up with
pulsar kiln
(X = \frac{2X}{2} = \frac{(X+SX) + (X-SX)}{2} = \frac{X+SX}{2} + \frac{X-SX}{2})
glossy valveBOT
Quantie
tired smelt
it’s a theorem isn’t it
tired smelt
**Quantie**
Yes I understood that
pulsar kiln
does this method have a name ?
the projection formula for symmetries
tired smelt
I remember in a exo we showed to any matrice can decomposed as a sum of a symetric and a non symetric matrice such as X=Y+Z with Y=1/2(X+ tX) and Z=1/2(X-tX) and here tX is SX
tX is the transposed of X
pulsar kiln
exactly!
tired smelt
So here is my proof
Let X in E_l(A). We put X=Y+Z with Y=(X+SX)/2 and Z=(X-SX)/2 (which is a unique decomposition that can be shown by synthesis analysis). Both Y and Z are in E(A).
If Y=0 and Z = 0, then X=-X ie X=0
By contrapositive, if X is non zero then at least Y or Z is non zero
pulsar kiln
well
its the same proof that i wrote
but if you got there yourself its amazing, really
mine just explains more stuff in further detail 
yeah but you got it
im going to someone else now, this has been fun!
kindred grove
there's some questions in there that are weird really
like 1 is straight up false for example
where did you find all of this ? @tired smelt
tired smelt
there's some questions in there that are weird really
I mislatexed it was a question
« is a centro-symm matrix also symmetric ? »
obviously false
kindred grove
ah okok
pulsar kiln
i want to help others, but the fun unsolved ones OPs are sleeping or just gone
also akti you might wanna close this channel now
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craggy tapir
!xy
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
brittle steeple
numb. ?
craggy tapir
number i assume
brittle steeple
was writing out the whole word too hard?
usually when you multiply numbers by negative numbers they don't increase
the exception is when you start with a negative number
but divide what?
that's not negative
you always get a higher number when you divide a positive number by something less than one
because it's convenient for a number system to be closed under subtraction
it's not increasing
it's a number
it doesn't change over time
no
increasing would be if it was smaller first and then became 85938
but it was 85938 the whole time
so it's constant
not increasing
brittle steeple
57192*1.5 = 57192 + 57192*0.5
reef moss
because 0.5 < 1. If you multiply by less than 1, then the result will be less than the original number
brittle steeple
1/10
how old are you?
i was guessing around 12
well the comma is in the wrong place for that to be one number
so five hundred twenty six
and nineteen
like this
are you ready
,
ornate eagle
If you want someone to talk to go to a female entertainment server
brittle steeple
fr fr
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indigo gyro
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indigo gyro
I dont know how to draw the diagram
rocky vale
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mild verge
.close
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static verge
these 2 have me genuinley tweaking 🥲
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these 2 have me genuinley tweaking 🥲
static verge
<@&286206848099549185>
bruh
<@&286206848099549185> help me outt
@final juniper ainno way
ur laughij
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@static verge Has your question been resolved?
jade dome
That's for 1 try 2 for yourself
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static verge
That's for 1 try 2 for yourself
k wait
man
@jade dome
the answer
contains
log values
i truly dont know
static verge
Wym? 2π comes from the fact that a complete circle is 2π radians
oh
oops
im stupid
seinaka
do you do
a level further maths?
i dont need these logorithmic questions atm but id like to have someone who i can asks questions to
bc
further mech
is so hard bro
how do i calculate
nmber of revolutions
jade dome
time t, just divide it by π√(a/g)
jade dome
nmber of revolutions
.
jade dome
Ok
jade dome
And what's your question
static verge
Tension is 20
jade dome
What can you calculate with that
jade dome
Why do you need F m a?
jade dome
You can do f m a
jade dome
Show me your approach
Why? It's given
The tension in the string is 20
Do it with F m a
But what do you use for a then?
jade dome
Because we have a circular motion
static verge
wdym
jade dome
I mean
In circular motion centripetal acceleration a = rω^2 because Centripetal acceleration points to center of circleIt's related to both
jade dome
Yep
Then I would use v to get T
But that would be seconds per revolution
So I would get it to minute's
And then done
jade dome
T = 2πr/v
static verge
and why is that
jade dome
It asks it in minutes
static verge
whats the 60?
jade dome
1 min has 60 seconds
You need to study more my friend
I can tell you that right away
If you study more problem's like this will be easy for you
static verge
1 min has 60 seconds
why is
it in seconds
o wait
the T is the time
im stupid ash
@jade dome answer my question tho
are u doing CIE or whaat
could u sketch this for example
jade dome
I study in Germany
static verge
University?
jade dome
Yes
static verge
oh nice
im going to study applied maths
mechanics is js hard ashh
well
sometimes
static verge
😂
jade dome
could u sketch this for example
That?
static verge
yh
jade dome
Sure but I don't have much time besides on weekend's
static verge
np
jade dome
Mon to Friday I have almost no time
jade dome
And you got the drawing done?
jade dome
static verge
cheers
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marble fable
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marble fable
Answer key says 8 so I am a little confused
keen vector
,rotate ccw
glossy valveBOT
marble fable
🐢
hoary ember
4(n-4)=4n-16
marble fable
How come?
marble fable
No like how did you arrive to that
hoary ember
arrive to what
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marble fable
4(n-4)=4n-16
This
hoary ember
it would be 3^4×a^-4 and since we only want the variable just get rid of the constant, so a^4=a^4(n-4)×a^-4
4=4(n-4)-4
marble fable
Guys how do we arrive to that spot
hoary ember
what do you not understand?
marble fable
I am using the following formula
hoary ember
<@711340488946483323> Has your question been resolved?
also you should react the x so the channel doeseny close
spice widget
So, I'm struggling to think through problems like this. We are going to use either the disk method, washer method, or shell method. I'm struggling to determine what's happening, however. The height is 10cm. The depth is 20cm.
spice widget
I think I get a bit shook up by the total amount of information and I'm not processing things correctly.
nimble current
what are you trying to find here?
spice widget
Sorry, I should have made that clear. The volume of the wok.
I assume we'll leverage the fact that it's part of a sphere.
We have a sphere, so, the radius will be just the x-axis of whatever the radius happens to be.
So, would step one be solving for x?
woeful pasture
Integrate from one y value to another
Using washer method
$\pi \int_{y_1}^{y_2} (\sqrt{a^2 - y^2})^2 \dd y$
glossy valveBOT
k
woeful pasture
@spice widget
spice widget
Thank you, I'm thinking about it using the washer method.
I think I'm being a bit slow. Why the washer method and not the disk method here? I'm failing to see where the hole would be.
Also, I believe you wrote the disk method, no?
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dry arch
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dry arch
whjy are these two wrong
nimble current
i think your estimates are not price enough
the first one is 6.85 i believe so you probably did intermediate estimates that made your final answer wrong
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dry arch
lol i also got 6.83 for the first one
idk i was thinking may it wants some other form but what
and also
can someone help me with this problem. chat gpt gives two dif answer
an angle of 150 degrees with an area of 12
How many units is the arch lenght
i got 3.02
150 degrees
5pie/6
sqrt(2a/(5pie/6))
is 3.0277
but its a review sheet and we were not given answers
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torn jolt
arch length?
i mean you can use a = 1/2 r θ^2 to find r, and then use it with θ to find arc length using s = rθ
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dry arch
i mean you can use a = 1/2 r θ^2 to find r, and then use it with θ to find arc ...
so would that be correct in that case
also would side c be 25.56 in this case
torn jolt
show steps pls
slow sleet
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slow sleet
am i right with B here?
robust slate
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fierce quest
Help with my algebra plz
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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
spiral spindle
which one
fierce quest
2
fierce quest
We are doing “systems of equations and inequalities”
fierce quest
what are you suppose to do just graph them
Both
spiral spindle
so how do you think you do it
fierce quest
Convert them to y=mx+b?
spiral spindle
ima guess u didnt learn this in class
you should probably watch a quick video on solving basic systems of equations
and see if you still need help
fierce quest
I did but it was only on the ones with y=mx+b
spiral spindle
I did but it was only on the ones with y=mx+b
fierce quest
Ohhh I’m watch this
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lusty tartan
my friend and i rly need some help on our math homework we rly dont get any of it at all 🙏 pls help
spiral spindle
my friend and i rly need some help on our math homework we rly dont get any of i...
u should prob watch a video on trig
than come back here if you still have no idea
what your doing
lusty tartan
okayy ty
lusty tartan
u should prob watch a video on trig
trig stands for trigonometry right or is it something else
spiral spindle
trig stands for trigonometry right or is it something else
yea
thats right
just look up
lusty tartan
okayyyy
spiral spindle
basic trig problems
and u will find like exact problems
like those
organic tutor prob has a good video on it
if ur struggling to find one
lusty tartan
okk ty :3
errant saffron
how to do using law of sines?
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how to do using law of sines?
ornate eagle
Label them that should help
errant saffron
uhh
thorn hornet
draw the horizontal from the vertex where the angles are indicated
then you can construct two right triangles
thorn hornet
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daring cairn
I feel silly asking but how would I solve a quartic in the form ax^4+bx+c=0?
gritty rose
I feel silly asking but how would I solve a quartic in the form ax^4+bx+c=0?
it's not trivial
daring cairn
ah
daring cairn
https://math.stackexchange.com/questions/3658305/is-there-formula-that-solves-qu...
thanks
woven sand
There's tricks for specific cases but overall it's generally based on identifying a specific case
There's no general closed-form formula like there is for quadratic and 3rd degree polynomials
daring cairn
There's no general closed-form formula like there is for quadratic and 3rd degre...
ah
woven sand
Actually that's a lie
I'm thinking of 5th degree
There is a quartic formula but it's not nice
daring cairn
I somehow had desmos plot my equation but not properly solved but I think it did it wrong and I want to solve it properly now
woven sand
That is a good method to doing it if you're allowed a graphing calculator or desmos
They can just spit out the answer
daring cairn
They can just spit out the answer
this is what I wanted to plot
and if I try to solve for y properly I get a quartic
woven sand
Some forms have cool tricks, my favorite being ones of the form $ax^4 + bx^2 + c = 0$ which can be rewritten as $au^2 + bu + c = 0$ if you let u equal x^2
glossy valveBOT
al-jebruh
Compile Error! Click the 
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woven sand
Then it can be solved like a quadratic
daring cairn
this is what I wanted to plot
and it somehow plots it even though not y the subject, but I dont think it is plotting it correctly
daring cairn
**al\-jebruh**
Compile Error! Click the <:errors:504266556054962196> reaction fo...
it only it was in this form lol, my equation ends up in the form ax^4+bx+c
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brazen terrace
hi would i just multiply everything by 3? solving for x
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hi would i just multiply everything by 3? solving for x
left summit
hi would i just multiply everything by 3? solving for x
Do you have an idea of the first step to take?
brazen terrace
well make the absolute value equal to >5 and <-5
left summit
Yes, so you have two cases
brazen terrace
but im not sure what to do with the fraction
brazen terrace
-2/3x>2 and -2/3x<-8
left summit
$\frac{-2}{3} x > 2$,
$\frac{-2}{3} x < -8$
What happens when I multiply a negative number, let's say -3 to both sides?
brazen terrace
the 3s cancel?
glossy valveBOT
leoh
left summit
the 3s cancel?
and the inequality sign?
brazen terrace
ohh they switch?
because youre multiplying by a - number
the same works for division too right
glossy valveBOT
leoh
left summit
Hope this clears everything, it's easy peazy now
brazen terrace
because youre multiplying by a - number
oops ya thats what i meant by the negative symbol lol sorry
Thank you
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tall spindle
How
glossy valveBOT
Roy
tall spindle
Whats that
whole lily
you rotate from the positive x-axis anti-clockwise till you reach (-2, 0)
tall spindle
180
brave wind
can someone help me
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@tall spindle Has your question been resolved?
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@tall spindle Has your question been resolved?
main echo
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whole lily
I would factorize the denominator and test the sign at the critical points
main echo
I would factorize the denominator and test the sign at the critical points
isn't it already factorized or
whole lily
no you still have a hanging +1
main echo
no you still have a hanging +1
How would I factorize that
glossy valveBOT
Roy
whole lily
so $2x^2 - 4x + 1$ factored is $2\left(x + \frac{2+\sqrt{2}}{2}\right)\left(x-\frac{2-\sqrt{2}}{2}\right)$
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Roy
main echo
so $2x^2 - 4x + 1$ factored is $2\left(x + \frac{2+\sqrt{2}}{2}\right)\left(x-\f...
Thanks
whole lily
okay hopefully you do know where to go from there
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white vortex
In this problem we can say that the absolute value of cos(c) <= 1 because it alternates between 1 and -1 right? Or is there another reason why we are allowed to assume that?
tidal citrus
In this problem we can say that the absolute value of cos(c) <= 1 because it alt...
that statement holds regardless of the problem, yes
wet wave
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cobalt star
I'm sure this has been asked before, but what is the antiderivative of $\frac{1}{x^{4}+1}$
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aurora borealis
cobalt star
the answer I got was
glossy valveBOT
aurora borealis
$\frac{1}{4\sqrt{2}}\ln\left|\left(x-\frac{1}{\sqrt{2}}\right)^{2}+\frac{1}{2}\right|+\arctan\left(2x-\frac{2}{\sqrt{2}}\right)+\frac{1}{4\sqrt{2}}\ln\left|\left(x+\frac{1}{\sqrt{2}}\right)^{2}+\frac{1}{2}\right|+\arctan\left(2x+\frac{2}{\sqrt{2}}\right)+C$
cobalt star
i'm sure this is wrong
brisk obsidian
You can use Wolfram Alpha to find out.
scarlet pike
,w 1/(x^4 + 1)
glossy valveBOT
brisk obsidian
🤮
cobalt star
I did, but looking at this is somewhat pointless without seeing the steps
brisk obsidian
LPT : Get the WolframAlpha app on your phone. It only costs a few dollars and it's basically the same thing as Pro on their website. Best part, you only pay once.
rigid shoal
hi im new here but i just saw this and if youre in college, most colleges give you free access to wolfram alpha pro with a student ID and let you see the steps
student email i mean
cobalt star
I live in a region where the app isn't available, and I study math on my own. I'm still in highschool :p
violet bolt
I did, but looking at this is somewhat pointless without seeing the steps
there are some yt vids solving this specific integral
even from the legend bprp
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cobalt star
i just realised a stupid mistake i made 
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merry lodge
Can someone give me their method to solve this pls
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Can someone give me their method to solve this pls
slate violet
Can someone give me their method to solve this pls
well, note that the rows of (a) are linearly dependent
same as with the columns of (a)
for (b) also note that (8, -2, 1) + (0, 0, -1) * -1 = (8, -2, 0) = 2 * (-4, 1, 0)
you don't have to find the RREF necessarily
the RREF does help a lot for the null space though
merry lodge
bro ngl idk much besides how to get RREF
and even then I am struggling to understand when a matrix is in RREF
slate violet
a basis is just a linearly independent spanning set
you just need to remove all the vectors which are linearly dependent, a linear combination of the other vectors
merry lodge
and even then I am struggling to understand when a matrix is in RREF
is there a general way to know this?
for 2x3, 4x5 etc
slate violet
yes, there are some conditions
merry lodge
which are 😅
tawdry cloud
Does anyone know how to use Maple soft?
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Does anyone know how to use Maple soft?
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@tawdry cloud Has your question been resolved?
tawdry cloud
<@397060770388770847> Has your question been resolved?
No
minor crater
Does anyone know how to use Maple soft?
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devout knoll
could anyone help me in regards to the average case of a function? I'm a bit confused on it
craggy tapir
!da2a
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devout knoll
i see, to be honest i'm just a bit confused in general when doing exercises with it
little prism
Would be quite useful to provide an exercise you don't understand, or something more specific.
devout knoll
hmmm ok ok
i have one where i have to find the average case of this function
int b = 0;
for (int i = 0; i < N; i++)
if (a[i] == 1) b++;
if (b == 1) return g(a,N);
else return 0;
}```g is a function of class Θ(2^𝑁)
minor crater
oh average time complexity
devout knoll
oh average time complexity
ye it's what i was referring to
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@devout knoll Has your question been resolved?
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@devout knoll Has your question been resolved?
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@devout knoll Has your question been resolved?
narrow crypt
could someone please explain how i work this out?
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could someone please explain how i work this out?
alpine flower
I would first try to remove the denominators of the fractions. Notice that if you multiply by 10 on both sides, it will cancel out the denominators
After that, you will simply have a linear equation
narrow crypt
I would first try to remove the denominators of the fractions. Notice that if yo...
👍 ty that completely solves it because i did *2 and *5 first
x2 and x5
which made the x cancel out
thanks
alpine flower
yeah np!
narrow crypt
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tepid glen
PadeApproximant[erfc(x)*exp(x^2), {x, 0.5, {3, 3}}]
how can I generate Pade Approximants on my own computer? I want to generate Pade Approximations with a relative accuracy of 2^-105 or 10^-32
fast peak
wikipedia has a section on how to compute it
implement it
presumably you looked if there is already an implementation for whatever language you are using?
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magic knot
H
magic knot
LMAO
glossy valveBOT
fiery trench
Bro has become TeXit
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magic knot
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magic knot
How does one find the regression line from a graph?
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patent plinth
How does the log4(x) become 1?
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How does the log4(x) become 1?
narrow ermine
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random needle
how to estimate g(35)
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how to estimate g(35)
lime ether
how to estimate g(35)
they told you to use the midpoint rule
random needle
i dont know how to do it
lime ether
you don’t know the midpoint rule?
lime ether
it’s an approximation technique where you consider the value of the function at the midpoint of each of the sub intervals and use that as the height of your rectangle
lime ether
but how would i use it
i just told you
random needle
i know what hte midpoint is bro but i dont know how to apply to problem
lime ether
apparently you don’t
can you tell me what the subintervals are
or at least the width of each interval
random needle
it doesnt say what the sub intervals are
lime ether
🤔
random needle
i got it dw
lime ether
it gives you x = 0, 5, 10, 15, 20 etc
random needle
its 150
lime ether
i got it dw
do you
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its 150
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
random needle
lfmao i didnt use gpt
lime ether
sure
random needle
im being serious
idle umbra
How would you solve this?
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How would you solve this?
gritty rose
idle umbra
I dont really understand these type of questions and how to go around it to solve it
I tried looking at the mclaurin series of e^x and using that
gritty rose
Do you know how to find the maclaurin series of e^(2x)
idle umbra
im given the mclaurin for e^x and i know to just put 2x instead of x into the thing
gritty rose
plug that series into the integrand
idle umbra
I have done that now
this is what I have left
wait nvm
thats for e^x not 2x
I got it now ty
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zealous hill
how do u do this
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how do u do this
zealous hill
ignore everything i wrote
i dont know what i was writing
for a i got g(-1)=11, g'(-1)=-2, and g''(x)=2
i checked with a friend apparently that's wrong?
so im so confused
clever sequoia
For g(-1) that's basically the area
For g`(-1), if the integral of f(t) = g(x), what would be the derivative of g(x)?
zealous hill
what
clever sequoia
For g''(-1), first see is the function differentiable at that point?
zealous hill
no???
royal holly
Do you know how to differentiate g(x)?
zealous hill
uhhh
i learned this a different way sry
i learned that g(x)=integral of f(x) and g'(x)=f(x) and g''(x)=f'(x)
royal holly
yeah thats correct
so for the first part its just the area under the curve from -4 to -1 do you agree?
zealous hill
yea mhmm
royal holly
okay, for the second part g'(x) = f(x) so g'(-1) will be?
zealous hill
f(-1)
zealous hill
is it the slope?
royal holly
they are asking for the derivative of f'(-1) which may or may not exist
royal holly
so you basically have to check whether you can differenaite the function at -1
royal holly
so does g''(x) not exist cause its pointy
yeah
zealous hill
oh
royal holly
so f'(-1) does not exist!
royal holly
for a function to be differentiable at a point the left hand derivate should be equal to the right hand derivative provided the function is continuous
the function is continuous over here but the left hand derivative is not equal to the right hand derivative
left hand derivative is basically the slope just left of the point
royal holly
so thats where the "pointy" thing comes from
royal holly
x=0?
zealous hill
uhh
royal holly
yeah they are asking for the x- coordinate
zealous hill
oh yea sry i misread
royal holly
whts the asnwer for it
zealous hill
so when it's changing signs right
royal holly
how have you been taught inflection points?
royal holly
but g''(1) is undefined
royal holly
the condition is f'' can be 0 or undefined and f' changes signs
zealous hill
Mhmm
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dry arch