angle is 60 to save you the working
#help-0
safe tartan
chilly crag
we got a+b+c=2b
so in total we get
a * 2b = 2 a * b
using the definition of the scalar product:
2 |a| * |b| * cos(60)
= 2 * 4 * 4 * 0.5 = 16
ok nvm its correct
👍
pretty sure the answer is 3
safe tartan
.close
alpine sable
can anyone give me a roamap to study maths from algebra1
lone heartBOT
can anyone give me a roamap to study maths from algebra1
severe tangle
Hello
alpine sable
thx
ocean hawk
and close the channel if you don't have a specific question
agile grove
I disagree
alpine sable
me too
alpine sable
I disagree
y is there <= if < can do the whole job
y is this channel named after me ?
pale kestrel
I disagree
the epsilon delta definition is equivalent with =< and <
you can prove this.
for the epsilon part, that is.
|?| < e
or
|?| =< e
alpine sable
for the epsilon part, that is.
tru
anybody here who is 13 yrs old
?
@alpine sable
lone heartBOT
@alpine sable Has your question been resolved?
polar zephyr
alpine sable
solution
agile grove
the epsilon delta definition is equivalent with =< and <
no u cannot renato.cus ur only considering two particular values which is false as the proof # consider all neighbourhood values
must*
alpine sable
notice that in this case median is 58
average is mean not median
u mean the average of odd numbers is the middle number ?
that is the median
minor needle
the set is as follows
pale kestrel
no u cannot renato.cus ur only considering two particular values which is false ...
open a new channel if you wish to discuss
minor needle
..., ..., ..., ..., ..., ..., 58, ..., ..., ..., ..., ..., ...
so...
what is the amount of the numebrs higher than 58
alpine sable
..., ..., ..., ..., ..., ..., 58, ..., ..., ..., ..., ..., ...
6
minor needle
yes
fresh coral
hey, im trying to show this expression.
I am able to get to $\vec{n} \bullet (c_1\vec{v}) + \vec{n} \bullet (c_2\vec{w}) + \vec{n} \bullet (c_3 \vec{n})$ but im not really sure what to do next
ocean sealBOT
hhhapz
visual cloak
what question is that
fresh coral
hmm?
worn fox
You should know what n ● v and n ● w are
fresh coral
like based on the information in the question above, or something else?
worn fox
Based on what n is and propteries of dot and cross product
fresh coral
hmm, so the first 2 arguments are both 0
and $n \bullet n$ is nonzero, since $v \times w$ is nonzero, but that would imply we have to make that expression equal zero, but why would that have to be the case?
ocean sealBOT
hhhapz
worn fox
What you are doing in this question is dotting both sides of the equation with n = v x w
daring totem
Find a vector that forms an angle of 30° with (2,2,-1) and 45° with (0,1,-1)
lone heartBOT
Find a vector that forms an angle of 30° with (2,2,-1) and 45° with (0,1,-1)
@daring totem Has your question been resolved?
lone heartBOT
@daring totem Has your question been resolved?
daring totem
<@&286206848099549185>
daring totem
<@&286206848099549185>
daring totem
<@&286206848099549185>
can someone help me find a vector from this family of vectors?
someone in the linear algebra channel suggested to use length of u = 1
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
foggy current
someone in the linear algebra channel suggested to use length of u = 1
That's a good suggestion because from that we know sqrt(x^2+y^2+z^2)=1 which simplifies the equations
daring totem
That's a good suggestion because from that we know sqrt(x^2+y^2+z^2)=1 which sim...
yes but I still cant manage to simplify the equation after that
foggy current
Remember that sqrt(x^2+y^2+z^2)=1 itself is an equation that you can use
lone heartBOT
@daring totem Has your question been resolved?
daring totem
<@&286206848099549185>
foggy current
First solve y-z=(sqrt(2)sqrt(x^2+y^2+z^2))cos(45) for y
Then substitute into 2x+2y-z=3sqrt(x^2+y^2+z^2)cos(30)
Also substitute it into sqrt(x^2+y^2+z^2)=1 to solve for x
Then substitute the previous step into the result you got from step 2
Simplifying should yield a quadratic equation which you can solve
daring totem
==> 2x+2y-z=3sqrt(x^2+y^2+z^2)cos(30)
but: sqrt(x^2+y^2+z^2)=1
==> 2x+2y-z=3*cos(30)
how do I clear y
foggy current
how do I clear **y**
By substituting step one into step two
Note that cos(45)=sqrt(2)/2
There is a problem though
And that's that assuming the norm of the vector is 1 will result in a very complicated answer
daring totem
can we use a simpler one? for the norm assumption
foggy current
can we use a simpler one? for the norm assumption
By using a computer, assuming the norm is 1/sqrt(2sqrt(3)-2) will yield the simplest result
daring totem
alright, let me try this, one sec
tacit bobcat
By using a computer, assuming the norm is 1/sqrt(2sqrt(3)-2) will yield the simp...
What did you get?
tacit bobcat
By using a computer, assuming the norm is 1/sqrt(2sqrt(3)-2) will yield the simp...
I did not get somethinig simple with this.
lone heartBOT
@daring totem Has your question been resolved?
daring totem
<@&286206848099549185>
daring totem
.close
barren portal
What are the different behaviour of sequences? montonically increasing/decreasing, alternating
barren portal
is it all that?
gray isle
quadratic/polynomial/random/other
lone heartBOT
@barren portal Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
granite rapids
Someone pls pls pls help me
lone heartBOT
@granite rapids Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
fickle wasp
How can I simplify x^2 * sqrt(x) to be able to use the power rule to find the derivative
fallen verge
sqrt(x)=x^(1/2)
fickle wasp
I did do that then did 1/2(x^2 * x)^ -1/2 but don't know where to go from there
fickle sandal
$\frac12(x^2\times x)^{-\frac12}$
ocean sealBOT
chlamydia
fickle sandal
bro what
fickle wasp
lmao, that's where I am at right now but don't know where to go from there
fickle sandal
I did do that then did 1/2(x^2 * x)^ -1/2 but don't know where to go from there
what did you do
glacial patrol
fickle wasp
I don't know what to do..
fickle wasp
wdym
glacial patrol
how u get to Calc w/o being able to add up powers
fickle wasp
so.. ((1/2) + (4/2) ) (x * x)^((-1/2)+(4/2))
bruh dont ask me
that what im tryna figure out
frank merlin
idk, helping other people rn so my question gets answered 😭
fickle wasp
so yes?
fickle sandal
yeah that's your derivative, just simplify the fractions lol
fickle wasp
(5/2)(x * x)^3/2
glacial patrol
Wait why $x*x$
ocean sealBOT
992qqoloy
glacial patrol
Ur tryna derive $x^2 \cdot \sqrt{x}$ right?
ocean sealBOT
992qqoloy
fickle wasp
yes
glacial patrol
yeah idk where ur getting $x*x$ inside the parentheses then
ocean sealBOT
992qqoloy
glacial patrol
Yeah so u end up with $x^{\frac{5}{2}}$
ocean sealBOT
992qqoloy
fickle wasp
WHAT
glacial patrol
(5/2)(x * x)^3/2
No this would simplify to $(5/2)x^3$
ocean sealBOT
992qqoloy
glacial patrol
U did most of the derivative right
frank merlin
you can multiply x and x together bc they are the same base and its the derivative with respect to x
glacial patrol
$x^{a+b} = x^ax^b$
ocean sealBOT
992qqoloy
fickle wasp
ooo
glacial patrol
That's why from the original expression one x disappears
Bruh this is algebra 1 shizz tho
fickle wasp
so x^5/2 and now I use power rule
glacial patrol
ye
glacial patrol
aight
frank merlin
That's why from the original expression one x disappears
you seem like you are pretty advanced in calc 😘 come to my room
glacial patrol
you seem like you are pretty advanced in calc 😘 come to my room
uwu
stark path
fickle wasp
I can't simplify 5/2 x ^3/2 anymore correct?
frank merlin
yes you are done
fickle wasp
ok just wanted to make sure
ty all
will prolly be back here in a little
I wanna check my next answer with yall
$[d/x] x^8 + 3x^4 + 2x^3 + x +1 = 8x^7 + 12x^3 + 6x^2 + 1$
ocean sealBOT
aggieian
$[d/x] x^8 + 3x^4 + 2x^3 + x +1 = 8x^7 + 12x^3 + 6x^2 + 1$
glacial patrol
Yup
lone heartBOT
@fickle wasp Has your question been resolved?
glacial patrol
Oh that one looks painful
fickle wasp
yeah....
trying to work it out
not going great
especially since idk how to work with the ln and ik that will be in the answer
tall crag
how can i tell if a parabola is concave up or down just based on its general form equation
tall crag
so does the third term (not a coefficient, just a constant) matter?
like c in ax^2+bx+c
sour verge
No. The constant term is effectively just a vertical shift of the parabola, so it doesn't affect the concavity
b neither
tall crag
so just the sign on b?
tall crag
how about in ax+by+c=0
sour verge
No problem
tall crag
.close
shut vessel
i dont know how to express circle radius in term of quadrant radius
ionic sedge
sorry i interfered with ur question,
lone heartBOT
@shut vessel Has your question been resolved?
shut vessel
<@&286206848099549185>
lone heartBOT
@shut vessel Has your question been resolved?
shut vessel
lemme draw something more
Ok
nimble fern
wanton socket
lone heartBOT
wanton socket
hi so im stuck on this problem and i have some work but i think i went wrong somewhere
worn fox
your very first matrix does not represent the system of equations
you cant switch columns like you did
barren portal
Help with counting subgroups of Zn
lone heartBOT
Help with counting subgroups of Zn
barren portal
I encountered number of subgroups are number of divisors of n.
I’m trying to see why
I’m aware every subgroup should divide the order of G,
This where i am at, you can help me from here hopefully
vale wigeon
all subgroups of Z_n, a cyclic group, are themselves cyclic
and for every d | n there is exactly one subgroup of Z_n of order d
... i am like 90% sure of this
glacial patrol
Ur right
barren portal
Suppose 2 | n
the subgroup generated by 2 and subgroup generated by any multiple of 2 are the same?
ie subgroup generated by 4 and 2 will be same? If 2 divides n
fluid basin
if 2 divides n and 4 does not divide n, then 4 genreates the same group as 2. if both 2 and 4 divide n, then 4 generates a proper subgroup of the group generated by 2
fluid basin
in Z_8, 2 generates a group that is iso to Z_4, but 4 generates a group that is iso to Z_2
barren portal
if 2 divides n and 4 does not divide n, then 4 genreates the same group as 2. if...
How do I see why?
fluid basin
<2> = {2,4,6,0} <4> = {4,0}
barren portal
I mean how do I prove if d divides n, but k doesn’t divides n but d divides k, then subgroup generated by d and k are same
vale wigeon
if d divides n, but k doesn’t divides n but divides d,
are you sure you stated that correctly?
fluid basin
that feels awkward if not actually wrong
vale wigeon
"d divides n, and k divides d, but k does not divide n" is IMPOSSIBLE.
fluid basin
this is a theorem the name of which i cannot remember right now
barren portal
2 divides 10, but 4 doesn’t divide 10 but 2 divides 4
vale wigeon
this is backwards from what you said originally...
barren portal
did i got that incorrect?
barren portal
I mean how do I prove if d divides n, but k doesn’t divides n but d divides k, t...
^^
Is it correct now?
barren portal
this is a theorem the name of which i cannot remember right now
lagrange theorem?
fluid basin
that sounds familiar
vale wigeon
so you're asking: if d divides both k and n, but k doesn't divide n, then do k and d generate the same subgroup?
barren portal
exactly
barren portal
^^
barren portal
if 2 divides n and 4 does not divide n, then 4 genreates the same group as 2. if...
^^
fluid basin
lol
vale wigeon
you expect me to address 3 things at the same time => im out
fluid basin
mostly the issue for me is what are you allowed to use here
lone heartBOT
@barren portal Has your question been resolved?
rich quail
lone heartBOT
lone heartBOT
@rich quail Has your question been resolved?
long axle
I gotchu Gomez
@rich quail
R u still here
Or u got it
Tag me
Ok I prolly won’t be here when u get back but
Here
Find what m+s is
From there, set up two Pythagoras relations
Then it’s a system
Then just do a mental graph then find distance formula between D and B
Idk there’s prolly a more efficient way
But that’s just what I’m thinking
Let A be (0,0)
lone heartBOT
@rich quail Has your question been resolved?
full garnet
I will like to show that, assuming $\sum_{h=-\infty}^{\infty} \left|\gamma\left(h\right)\right| < \infty$,
$$
\lim_{n \to \infty}=\sum_{h=-(n-1)}^{n-1}\left(1-\frac{|h|}{n}\right) \gamma(h) = \sum_{h=-\infty}^{\infty} \gamma(h).
$$
The hint says that one should do an epsilon-delta proof. Note $\gamma(h)$ is the autocovariance function, so it's an even function, for this reason I'm hoping it is sufficient to show
$$
\lim_{n \to \infty} \sum_{h=1}^{n-1} \left(1-\frac{h}{n}\right) \gamma\left(h\right) = \sum_{h=1}^{\infty}\gamma\left(h\right).
$$
Then use the symmetry of $\gamma\left(h\right)$ to conclude
$$
\lim_{n \to \infty}=\sum_{h=-(n-1)}^{n-1}\left(1-\frac{|h|}{n}\right) \gamma(h) = \sum_{h=-\infty}^{\infty} \gamma(h).
$$
Also, I'm not sure if the following consideration is correct:
$n \to \infty \implies \frac{h}{n} \to 0 \implies 1-\frac{h}{n} \to 1 \implies \sum_{h=1}^{n-1} \left(1-\frac{h}{n}\right) \gamma\left(h\right) \to \sum_{h=1}^{\infty} \gamma\left(h\right)$
lone heartBOT
I will like to show that, assuming $\sum_{h=-\infty}^{\infty} \left|\gamma\left(...
ocean sealBOT
baan
unique orchid
waht is 4032-33-4
full garnet
What is up?
vale wigeon
with all due respect this is not really the place for such comments.
alpine sable
myb gang
vale wigeon
I will like to show that, assuming $\sum_{h=-\infty}^{\infty} \left|\gamma\left(...
you should drop the equals signs that immdiately follow the limit symbols btw it's a little distracting to read this way
anyway i think this might be fine since the sum of gamma(h) converges absolutely? intuition tells me you're fine, but i am not 100% on it.
full garnet
anyway i _think_ this might be fine since the sum of gamma(h) converges absolute...
Oh, those are typos.
Do you think that my last consideration is OK? If so, then that will be the "intutive proof"—it's definitly not formal, that's for sure 🙃
vale wigeon
yeah it looks fine to me
full garnet
Thanks. How about an epsilon-delta proof?
cursive garnet
lone heartBOT
cursive garnet
how to solve this
cursive garnet
huh
fickle sandal
is the entire angle 41
frail minnow
then
cursive garnet
little sliver
but the whole half circle is 180
the middle angle is 41
the side angles are unknown
cursive garnet
ok
frail minnow
only and only iff they are parallel
cursive garnet
okay ty
lone heartBOT
@cursive garnet Has your question been resolved?
civic spindle
u,v different vectors in vector space V over R
S={u+v,u-v,u+3v}
does Sp(S) != Sp{u,v} ?
round geyser
u,v different vectors in vector space V over R
S={u+v,u-v,u+3v}
**does Sp(S) != ...
there is a math stack exchange post for this exact problem:
https://math.stackexchange.com/questions/4378540/let-u-v-be-different-vectors-in-linear-space-v-in-bbb-r-and-let-s-uv
strong wedge
lone heartBOT
strong wedge
is this always true?
alpine sable
no
alpine sable
what are u and v
alpine sable
it's false for $V_{induced}=(B×v).l$
ocean sealBOT
deltaG
strong wedge
are there two ways to solve for this, one where i distrubute the u so itl be (u . u) x (v . u) and the 2nd way to just solve (u x v) first and dot product
alpine sable
I hate latex on phone
I have not reached vectors in mathematics yet, I did question on this formula in physics so I just know that this is false
strong wedge
yea so its the magnitude
strong wedge
okay but say there was actual values for u and v
strong wedge
are there two ways to solve for this, one where i distrubute the u so itl be (u ...
can i do this
alpine sable
u and u are linearly dependet
dependent
but they're the same vectors
That means (u×u)=0
Yes u=1u
strong wedge
lets say its three different vectors, (u x v) . y or smth
alpine sable
lets say its three different vectors, (u x v) . y or smth
if none of them are parallel, it's not zero
strong wedge
yea but are there different ways to solve it
like (u . y) x (v . y) or do (u x v) and get the vector, and then multiply by y
strong wedge
yea i got my question answered, this is just another hypothetical for a different question
strong wedge
That means (u×u)=0
back to this, u arent doing (u x u) tho. first ur doing (u x v), which gives another vector. and then dot product of two vectors give a scalar value
how is it always 0
doesnt it depend on the values given for u and v
alpine sable
$(u \times v) \cdot u= u \cdot (u \times v)= v \cdot (u \times u)$
ocean sealBOT
Plazzi
alpine sable
**Plazzi**
This is Always true
alpine sable
First equation is the use of the commutivity of the scalar product
strong wedge
only (u x u) . vgives 0
strong wedge
so both give 0?
strong wedge
no matter the values for u and v?
i need to try an example
ur right
i made up numbers and its 0
thats crazy
wtf
alpine sable
$(u \times v) \cdot u=(u_2v_3-u_3v_2)u_1+(u_3v_1-u_1v_3)u_2+(u_1v_2-u_2v_1)u_3=0$
@strong wedge
ocean sealBOT
Plazzi
alpine sable
np
lone heartBOT
@strong wedge Has your question been resolved?
calm kiln
hi
calm kiln
I need help with this question
I need to differentiate
For this question im supposed to use product rule right?
thick lynx
Yes
calm kiln
so i got
(2theta)(theta^2sin theta) * (theta^2)(cos theta)
is that right?
because when I click show answer its different
thick lynx
so i got
(2theta)(theta^2sin theta) * (theta^2)(cos theta)
The first part isn't
calm kiln
wdym
thick lynx
Also it's +, not *
calm kiln
oh yea
thick lynx
$(u(\theta)v(\theta))' = u'(\theta)v(\theta) + u(\theta)v'(\theta)$. \ In your case, $u(\theta) = \theta^2$ and $v(\theta) = \sin \theta$.
thick lynx
so i got
(2theta)(theta^2sin theta) * (theta^2)(cos theta)
what's u'(theta)?
calm kiln
2theta
calm kiln
sin theta
calm kiln
oh right
calm kiln
so (2theta)(sin theta) + (theta^2)(cos theta)
thick lynx
Yes
calm kiln
oh ok
so for this should I do product rule first
for x^2 cos x
and then after getting the result just add 3 to it?
or is there a better way to do it without doing it in parts?
thick lynx
and then after getting the result just add 3 to it?
Yes, using the sum rule. [(3x + x^2\cos x)' = (3x)' + (x^2\cos x)'.]
calm kiln
how did u get that?
thick lynx
so would
((2x)(cosx) + (x^2)(-sinx)) + 3
-sin(x)
calm kiln
by multiplying it out?
calm kiln
ok ty
thick lynx
and rewrite a bit like I said, pulling out the -
calm kiln
yea i see
calm kiln
You can remove the brackets
i wouldnt need the extra ()?
(2x)(cosx) + (x^2)(-sinx) + 3
so that would be good
thick lynx
so that would be good
Yes
(a + b) + c = a + b + c
After the associative property, since (a + b) + c = a + (b + c)
calm kiln
yep
for this would it be
(sec theta)(tan theta)(tan theta) + (sec theta)(sec^2theta)
thick lynx
(Factoring out sec theta)
calm kiln
for this I got
(cos theta)(cos theta) + (sin theta)(-sin theta)
thick lynx
Yes, you can pull out the -
calm kiln
(Factoring out sec theta)
we dont have to simply so im just focusing on getting the correct answer
ok ty
ty for the help b ro
bro
.close
lone heartBOT
nimble fern
<@&268886789983436800>
median dirge
nimble fern
ty.
real gazelle
.close
lone heartBOT
lone heartBOT
Available help channel!
kind notch
what is x?
lone heartBOT
what is x?
unkempt robin
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
idk how doe
lethal belfry
Have you considered multiplying both sides by 4
kind notch
but why is it square root of 507?
unkempt robin
We'll get there
kind notch
12x^2 /16
ocean sealBOT
USS-Enterprise
covert tundra
1
lone heartBOT
@kind notch Has your question been resolved?
kind notch
nvm got the answer
unkempt robin
ok
lone heartBOT
@kind notch Has your question been resolved?
stiff seal
lone heartBOT
stiff seal
For number 3. I just want to know if my answer is correct
lone heartBOT
@stiff seal Has your question been resolved?
fathom dragon
a1=1-1/1, a2=1-1/2, a3=1-1/3, a4=1-1/4, a5=1-1/5, a6=1-1/6
to simplify, a1=0, a2=1/2, a3=2/3, a4=3/4, a5=4/5, a6=5/6
I think
Does that sound about right?
lone heartBOT
@stiff seal Has your question been resolved?
olive urchin
I can't figure out what u sub to use, so please dont recommend "try u sub". Idrk where to go with it though, I've tried u = e^t and u = e^2t
olive urchin
That came off as kind of mean but I get it every time I ask for help with an integral
olive urchin
right, and should the second sub be 16/9 tan theta?
olive urchin
ok got it
so the integrand is (64/27(tan^3(theta))(4/3sec^2(theta)))/(1/3(4/3)(sec^2(theta)))?
which simplifies to (64/81)tan^3(theta)d(theta) right?
mortal trellis
wolframalpha has something else
mortal trellis
what did you have after the first sub
olive urchin
3(u^3)du/(sqrt(16/9+u^2))
olive urchin
oml
no way
and that meets my formula
damn ok
ok i got iot
thank you!
.closer
.close
lone heartBOT
lone heartBOT
Available help channel!
mild ice
can this n - (nmod4 - 1) be simplified?
lone heartBOT
can this n - (nmod4 - 1) be simplified?
mild ice
i am trying to simplify it to the form of 4k - 3, where k is an integer
wondering if that is possible
mortal trellis
n-nmod4 is always of the form 4m
that's precisely what mod does
so then 4m+1.
or 4k-3 for k=m+1
mild ice
?
sorry I am a bit lost, I havent really learnt moduluo operations, but I need to be able to simplify this for a way broader proofs questions, that isnt really contingent on my knowledge of modolou operations
so can you walk me step by step how i can do this?
my class is a proofs class, but i found a rule that is in this form n-nmod4
which i need to show can be simplified to 4k-3
if u want me to give more context i can, but the main mathematical component of this question is induction and proving something else
which i have already done
i just need to simplify n-(nmod4 - 1) to 4k-3
mortal trellis
n mod 4 is the remainder
so if you subtract it from n, the result will be divisible by 4
aka it will be of the form 4m where m is an integer
mild ice
makes sense
ok lemme try this and can you verify if this works?
wait never mind
right ok
so ur saying that
n - n mod 4 = 4m where m is an integer
however, since it is n - (n mod 4 - 1), it will simplify to 4m + 1
if we let k = m + 1, we will get 4k-3?
mortal trellis
yes
lone heartBOT
@mild ice Has your question been resolved?
silk terrace
lone heartBOT
silk terrace
Any ideas?
I am guessing it is wrong as:
actually im not sure
Wouldnt the lebesgue measure on R count as a counter example? with the set (a,b) a,b in R which is a subset of the borel sigma algebra with measure b-a?
mortal trellis
yes
fossil slate
lone heartBOT
@fossil slate Has your question been resolved?
shell narwhal
A is a matrix, if A is inversible, is A^-1 also inversible ?
patent topaz
$A^{-1}$ is the inverse of A.
ocean sealBOT
WayneTundra
patent topaz
that's the definition.
shell narwhal
okay ?
patent topaz
dude, 1/a is invertible to a/1 all day every day
ocean sealBOT
WayneTundra
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
shell narwhal
what do i do ?
A^-1 * A^-1
we know that A^-1 *A=I
A^-1=A^-1
lol idk im clueless
patent topaz
as a rule, the product of two invertible matrices is also invertible
if you need to walk through the steps that's ok, but i'd say that should be enough
shell narwhal
as a rule, the product of two invertible matrices is also invertible
isnt this the proof ?
A^2 = A*A
there u go
patent topaz
^
shell narwhal
?
fluid basin
try proving that $(A^2)^{-1} = (A^{-1})^2$
ocean sealBOT
rome of oxtrot
patent topaz
ok, sure
fluid basin
hint: multiply both sides by $A^2$
ocean sealBOT
rome of oxtrot
shell narwhal
(A * A )^-1 = A^-1 * A^-1 = (A^-1) ^2
fluid basin
alternative;y start with (A)(A^-1 ) = I. left multiply by A and right multiply by A^-1; this gives you (A)(A)(A^-1)(A^-1) = (A)(I)(A^-1). but the lhs is (A^2)(A^-1)^2 and the rhs is I, which proves that (A^-1)^2 is the inverse of A^2
fluid basin
left hand side and right hand side
shell narwhal
oh kk
i see, thanks for the proof, this was very educational
thank you too @patent topaz
.close
limpid needle
Why is the answer D in this question?
lone heartBOT
Why is the answer D in this question?
@limpid needle Has your question been resolved?
lone heartBOT
@limpid needle Has your question been resolved?
limpid needle
<@&286206848099549185> 🙏
winged lava
Why is the answer D in this question?
if x0,y0 is on Q(x) a and Q(x) = y0,
Q(x0) = y0 = P(2x0)/2
therefore:
P(2x0) = 2y0
so if the input 2x0 gives 2y0 then (2x0, 2y0) is a point on P(x)
cinder sundial
Given there’s 9 balls in a bag, in which 2 of these 9 balls are named number 2, 3 of them are number 3, and 4 of them are number 4. Now we pick 3 balls from the bag, what is the expected value of the number sum?
cinder sundial
This question is nothing hard but time-consuming.
If you list out all of the possibilities for the numbers of these 3 chosen balls
However
My textbook mentiond that the EV would equal to the EV with just one pick from the bag multiplied by 3
And that’s sounds like a cap to me
We only have 2 of number 2, tf can we compute the answer like that
lone heartBOT
@cinder sundial Has your question been resolved?
cinder sundial
<@&286206848099549185>
winged lava
oh wait no this is tedious
bro i cant be asked thats so annoying
or maybe im forgetting an easier way to do it
winged lava
Given there’s 9 balls in a bag, in which 2 of these 9 balls are named number 2, ...
okay so all possibilities are:
2 2 3 (7)
2 3 3 (8)
3 3 3 (9)
2 3 4 (9)
3 3 4 (10)
3 4 4 (11)
4 4 4 (12)
is that all?
yeah now calculate the probability for each and use
∑ x P to find the expected value
glacial patrol
I think OP's question is if the book's method is right or not 
cinder sundial
I think OP's question is if the book's method is right or not <:hmmCat:831508801...
Yes
plucky sluice
I think the book method makes sense but it's a clever trick imo
The average value per ball is 9/9
If each ball is equally likely to be chosen, the average value of each picked ball should be the same
Not sure I have the energy to prove that right now
cinder sundial
If each ball is equally likely to be chosen, the average value of each picked ba...
The problem is after we pick a ball, we don’t put it back the bag
cinder sundial
Not sure I have the energy to prove that right now
You have, be confident to yourself
cinder sundial
Not sure I have the energy to prove that right now
You’re the smartest person
We all depend on you
glacial patrol
save him like u saved my wife xenaphon
plucky sluice
I'm thinking
2 2 3 (7)
2 3 3 (8)
3 3 3 (9)
2 3 4 (9)
3 3 4 (10)
3 4 4 (11)
4 4 4 (12)
Using Adi's work, each of these values is equally likely, right
cinder sundial
Using Adi's work, each of these values is equally likely, right
“Value”??
cinder sundial
But 8 is bigger than 7
cinder sundial
Yes, the value is bigger, but only 1 set of draws can produce that value
But (3,2,2)also equals to 7
plucky sluice
Yeah, it's missing the permutations
cinder sundial
Using Adi's work, each of these values is equally likely, right
Then I can’t seem to understand what the “value”means in your sentence
cinder sundial
2 2 3 (7)
2 3 3 (8)
3 3 3 (9)
2 3 4 (9)
3 3 4 (10)
3 4 4 (11)
4 4 4 (12)
But they are not the same, from top to the bottom
plucky sluice
The values are different, yes, but each set of three is equally likely
cinder sundial
The sum of them aren’t the same
plucky sluice
My argument is not that each draw will have the same value
My argument is that the average value of each draw will be the same
But I don't think it's super convincing
Maybe your book as more detail
cinder sundial
Maybe your book as more detail
No, it do not
cinder sundial
My argument is that the average value of each draw will be the same
That’s obscure
plucky sluice
Thanks
I try
Last attempt. What's the expected value of the first ball?
the first ball that you pick
Okay, I guess I will do the calculation and drain my energy even further....
E(b1)=(22+33+4*4)/9=3.22
lol, 2*2, etc
cinder sundial
Okay, I guess I will do the calculation and drain my energy even further....
We can assume it as P, the EV of the first ball
Then we can avoid the calculation
The question is would the EV of second be equivalent as the first pick
As well as the third pick, We have to prove it
plucky sluice
Yes, now, try to calculate E(b2 given b1)
plucky sluice
If b1 was low, the E(b2 given b1) will be higher than E(b1)
Because there's more value per ball left in the bag
Vice versa, the next ball would be expected to have a lower value if we draw high
cinder sundial
Vice versa, the next ball would be expected to have a lower value if we draw hig...
God you’re so smart
You figure out the inside-mechanism used in the clever trick
plucky sluice
I am sure now that it can be proved using conditonal probabilites
But the margin of this discord channel is too small to contain the proof
cinder sundial
I am sure now that it can be proved using conditonal probabilites
Yes, I suppose
But it gotta be tiresome
cinder sundial
If b1 was low, the E(b2 given b1) will be higher than E(b1)
That’s one good way to think about it tho
plucky sluice
HA, thought of an easier proof
What's the expected value of 9 draws?
The total value of the bag!
http://web.mit.edu/14.380/www/practiceproblems/handouts/hypergeometric.pdf, see also this pdf where they do a good derivation in the general hypergeometric distribution case
cinder sundial
terrific
plucky sluice
In particular, they use the conditional probability of the previous draw
You will need to replace the 1 or 0 with the numerical values, but you'll get the same answer
plucky sluice
lone heartBOT
@cinder sundial Has your question been resolved?
icy herald
PLS
icy herald
Amount of red increase by one for every layer (From layer 3 (Including))
Lag = Layer
icy herald
Amount of red increase by one for every layer (From layer 3 (Including))
How tf is this true?
vale wigeon
can this be a translation issue?
icy herald
vale wigeon
!original
lone heartBOT
Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.
If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.
icy herald
Im not english
vale wigeon
If the original problem is not in English, then post it anyway!
and post the whole problem as one picture please
icy herald
prime olive
i am a student of 9th grade and ig maths is not my cup of tea
help please
icy herald
icy herald
i am a student of 9th grade and ig maths is not my cup of tea
help please
go here and tpe
type
and it make channel for you
icy herald
> **If the original problem is not in English, then post it anyway!**
and post t...
No one speak my langauge
icy herald
Answer
vale wigeon
i am a student of 9th grade and ig maths is not my cup of tea
help please
!occupied
lone heartBOT
i am a student of 9th grade and ig maths is not my cup of tea
help please
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
icy herald
I'm just confused why it say red increase by 1 for every layer from layer 3
vale wigeon
the book might not be conveying it properly
icy herald
ye that book sucks, i dont understand and there isnt any explenation
vale wigeon
from layer 3 to layer 4 the difference is 1
from layer 4 to layer 5 the difference is 2
from layer 5 to layer 6 the difference is 3
and it is these differences that go up by 1
icy herald
Oh its just diffrebces
vale wigeon
but idk enough Danish to say whether the book told you that
icy herald
it says that nowhere in book lol
vale wigeon
fifty fifty chance
vale wigeon
Danish and Norwegian both have that ÆØÅ
icy herald
ye
@vale wigeon ty i understand now (in book it said explain how it changes so you are right)
.close
undone hornet
Would this negation be correct?
lone heartBOT
Would this negation be correct?
tropic bane
💀 I don't know what negotiation and all is but the Claim is true
idts there exists an irrational number and a rational number such that the sum results in a rational number
lone heartBOT
@undone hornet Has your question been resolved?
prime badge
frozen sand
How do I describe the solutions to the equation $sin(ax)=sin(bx)$ for some generic a and b?
ocean sealBOT
Methylfluorophosphonylcholine
frozen sand
Is there a general solution
near apex
Is there a general solution
Yes. Try using sin(A) - sin(B) formula.
past knot
lone heartBOT
past knot
can i solve this , using this?
lone heartBOT
@past knot Has your question been resolved?
past knot
<@&286206848099549185>
lone heartBOT
@past knot Has your question been resolved?
tacit arch
can i solve this , using this?
Yes
If a function is continuous on a compact set, then it is also integrable on that compact set
tacit arch
well what are the sets A and B in the exercise?
A and B are sets where you integrate over. A x B is the Cartesian product of those two sets
past knot
yes but what are precisely their values in my example
tacit arch
...
tacit arch
Just read and compare
tacit arch
can i solve this , using this?
f: A x B
past knot
and which "theorem " should i use? the one in the second picture or the one in the third?
past knot
ok so my A is [a,b] and my B is [a.x]?
past knot
AxB ={ (x,y): x from [a,b] and y is from [a,x]}
tacit arch
No that's not B
tacit arch
Read the description of f again and compare to the theorem
past knot
well if i apply the theorem to f i obtain two integrals that have the limits a and b
what do i do next
tacit arch
If a function is continuous on a compact set, then it is also integrable on that...
Read this again
You should have proven that previously or you'd have to prove it for this exercise
past knot
yes
well how do i solve the exercise then? because i cannot simply apply the theorem to f
tacit arch
... why do you say you can't apply the theorem
I'm explicitly telling to apply the theorem
past knot
but the theorem doesent have the x as the integral limit
tacit arch
What are you referring to
past knot
.
tacit arch
x as in the variable?
past knot
no
tacit arch
...
That's just double integrals
Review this if you haven't taken multivariate calculus
https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/15%3A_Multiple_Integrals/15.01%3A_Double_Integrals_over_Rectangles
past knot
should i use one of the above theorem to solve the exercise ?
past knot
but how do i apply it? the theorem DOESEN T have x and y as integral limits
tacit arch
Review this if you haven't taken multivariate calculus
https://math.libretexts....
Did you do this yet
Should only take 5-10 minutes to review
past knot
.close
molten frigate
anyone into french math?
lone heartBOT
anyone into french math?
tacit arch
Just ask if you have one and follow the these instructions
molten frigate
Just ask if you have one and follow the these instructions
where can i ask?
tacit arch
Here
tacit arch
Read this for instructions
molten frigate
Read this for instructions
yeah that i get but where can i ask my question
real topaz
how can I create my own channel for help?
tacit arch
i just asked my question
That's not a question
molten frigate
how can I create my own channel for help?
same
molten frigate
That's not a question
Does anyone speak french? because i need help with math in french
tacit arch
A math question is like "what's the inverse function of 2x+5?"
molten frigate
A math question is like "what's the inverse function of 2x+5?"
but where can i ask my question
unkempt robin
how can I create my own channel for help?
Go into the category "MATH help (available)" and send your question in one of the avaliable channels
tacit arch
...
unkempt robin
but where can i ask my question
🤦♂️
molten frigate
Ok wait
gray isle
post an image of the original question
translate if possible
molten frigate
ok
neat mango
Does anyone speak french? because i need help with math in french
I speak a little French. I'll try to help as best I can
gray isle
people that may know french may drop by and/or the image has sufficient mathematical symbols for context clues to infer what's being asked
real topaz
how can I create my own channel for help?
?
gray isle
!help
lone heartBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
unkempt robin
Go into the category "MATH help (available)" and send your question in one of th...
I mean seriously, literally mentioned you in that reply
molten frigate
f(x) = 2(x-6)(x-2) show for all reels x, f(x)>= -8
molten frigate
I speak a little French. I'll try to help as best I can
great its fine i managed without
bitter marten
ok so you're finding the minimum of this function, this can occur at either +- infinity or at a local minimum
gray isle
there are many ways to go about this,
which are pretty much all related to the vertex of a parabola
molten frigate
another one: maybe this will help, f(x) = 2x^2 -16x + 24, find the canonique function of f
gray isle
what does
canonique function
refer to
do you have an image of that form?
other places use different words
molten frigate
canonical function with delta and alpha
gray isle
image please
