try applying that logic to the question
#help-0
noble sinew
hazy knoll
so -150/52?
noble sinew
yes
noble sinew
yes
noble sinew
what?
noble sinew
Seeing how its close to the definition of variance, yes
hazy knoll
if I divide the 2nd equation by n, in this case 52
that would be the forumla for variance right?
so Σ(m - 150)^2 / 52 = 34
.close
lone heartBOT
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Available help channel!
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indigo blade
.help
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alpine sable
what 6⁶
alpine sable
i did
wary stream
Someone took this channel, you need to open your own
indigo blade
how i dont know
glass lichen
wary stream
how i dont know
Just post in it
wary stream
how i dont know
You don't need the .help or .open stuff
alpine sable
so whats 6⁶
wary stream
A big number
indigo blade
You don't need the ```.help``` or ```.open``` stuff
k i opend my own
now do i just @ the helpers
wary stream
now do i just @ the helpers
No, you wait in your channel until someone comes
indigo blade
kk
wary stream
You typed it wrong then
smoky adder
see coding
like suppose m-150=d
the mean would be then for d
sumof(m-150)/52
that mean is equal to
the real mean (x)+a
and that a=150
since d=x+a
mean of (d)=mean of (x) + a
and then the variance u just get by the formula
square this formula to get the variance
and note that if u use sum of d^2/n and mean of d in this formula
you’ll get the same variance and standard deviation as if u used the sum of x^2/n and x
lone heartBOT
@hazy knoll Has your question been resolved?
hazy knoll
@smoky adder
lone heartBOT
@hazy knoll Has your question been resolved?
lone heartBOT
@hazy knoll Has your question been resolved?
tacit arch
this channel's occupied. read #❓how-to-get-help
gaunt eagle
I dont get how the numerator is equal to zero because the denominator is
oops
sorry
lone heartBOT
@hazy knoll Has your question been resolved?
slate prawn
the triangles a similar, you have to find x and y
lone heartBOT
the triangles a similar, you have to find x and y
slate prawn
if you rotate the smaller one so the angles match up
oh crap
i just realized
im dumb
.close
ornate heath
I don't understand how the explanation proves anything about what passes in front here
ornate heath
I found the same thing by using the equation $t_B\mathbf{v}_b=t_U\mathbf{v}_u+\mathbf{d}_i$ to find the point where their paths intersect and see how long it would take each to get there, but this method looks much neater
ocean sealBOT
person2709505
ornate heath
(Where t_B, t_U are the time it takes the boat and ship to reach the crossing point, v_B and v_u are the velocities, and d_i is the initial displacement between the two)
lone heartBOT
@ornate heath Has your question been resolved?
ornate heath
<@&286206848099549185>
lone heartBOT
@ornate heath Has your question been resolved?
ornate heath
.close
short plank
hi, anyone know if this is the right solution on this tricky question?
naive valley
hi, anyone know if this is the right solution on this tricky question?
Looks 100% correct to me
bold panther
I’m taking a diagnostic for statistics and computer science tomorrow and I really don’t know wut to study for it so could someone give me an overview of what is usually on diagnostics for these subjects (high school level not college)
tacit arch
you're only starting now?
might as well just sleep early and coast to an easy A in a less difficult class
lone heartBOT
@bold panther Has your question been resolved?
jagged imp
isn't a diagnostic something you take to test your own ability/give the teacher an idea of your ability before you begin taking a subject?
opaque inlet
How did they get the answer for ii.
lone heartBOT
How did they get the answer for ii.
tacit arch
,calc sqrt(29) / 4
ocean sealBOT
Result:
1.3462912017836
hmm should be 1.3
tacit arch
maybe your x is wrong?
opaque inlet
This is the teachers working out
opaque inlet
maybe your x is wrong?
I don’t think the working out is wrong
It looks correct to me
Maybe he made a mistake or something
tacit arch
sure, very possible
opaque inlet
Yeah because I got everything correct except I got 1.3km for that question and I was so fucking lost on how he got that
Thanks man
.close
lone heartBOT
sleek osprey
Id say it looks right.
lone heartBOT
@short plank Has your question been resolved?
terse oak
So i have found the value of k that is 1/8 now how do i proceed?
terse oak
little drum
P(0, Y < 0.5 | X = 1) = P(0 < Y < 0.5 && X = 1) / P(X = 1)
and you can integrate for the numerator and denom.
$$=\frac{\int_0^{0.5} k(1 + y) \dd y}{\int_0^2 k(1+y) \dd y}$$
ocean sealBOT
Ansh
lone heartBOT
@terse oak Has your question been resolved?
terse oak
thanks @little drum
lone heartBOT
terse oak
.reopen
lone heartBOT
✅
terse oak
@little drum
tacit arch
the answer comes out to be `0.15` whereas i think correct answer is `0.08`
Show your work?
little drum
,calc (0.5 + 0.5^2 * 0.5) / (2 + 2)
ocean sealBOT
Result:
0.15625
hmmm, are you certain that the correct answer is 0.08?
tacit arch
the answer comes out to be `0.15` whereas i think correct answer is `0.08`
Show the answer
terse oak
hmmm, are you certain that the correct answer is 0.08?
not perfectly sure
little drum
Pffttt
tacit arch
not perfectly sure
Don't lie. Kthx
terse oak
are u certain this is the correct way? I mean does the denominator needs to be integeated from 0 to 2?
terse oak
Don't lie. Kthx
not lying i'm just confused
little drum
my bad for being incompetent. Let me rephrase myself a bit
tacit arch
You said the answer was 0.08, why
little drum
hmmm, are you certain that the correct answer is 0.08?
Are you certain your working, nice pair of eyes saw the answer as 0.08 from the answer key given on the book/wherever you got this question from? If yes, then change the answer because it's incorrect
terse oak
am sorry
little drum
basically
the P(X = 1)
is the probability when your event rep. X is fixed, but your Y can vary in it's entirety
terse oak
You said the answer was 0.08, why
my classmate solved the que he said his answer is coming out to be 0.08, sorry for troubling u
little drum
so Y from 0 to 2 works
ocean sealBOT
Result:
0.625
i see i understand, if there is nothing given bout y then we integrate it to its full extent
little drum
Also your partner should probably revisit integration
terse oak
huh, it came out to be 0.08
little drum
$\int (1 + y) = y + \frac{y^2}{2} \neq y + y^2$
ocean sealBOT
Ansh
terse oak
huh, it came out to be 0.08
can u send the deleted message again i want to see something, your result also came out to be 0.07 something, how come? was there an error in that?
little drum
okay: $$\frac{\int_0^0.5 (1+y)\dd y}{\int_0^2 (1 + y) \dd y} = \frac{0.5 + 0.5^2 \cdot 0.5}{2 + 2^2 \cdot 0.5}$$
ocean sealBOT
Ansh
little drum
=
terse oak
comes out to be 5/32
little drum
,calc (0.5 + 0.5^3)/4
ocean sealBOT
Result:
0.15625
Result:
0.078125
but why are we dividing it by 2?
terse oak
oops, i thought it was a part of the solution my bad
little drum
I'm just tryna guess here what they could've done
terse oak
ok i got it thank you
tacit arch
HOW TF DO I KNOW
Ansh going the extra mile of not only solving the problem but also explaining why other people's answers are wrong
terse oak
.close
lone heartBOT
little drum
terse oak
<:devastation:898725325335298088>
very sorry for troubling u
lone heartBOT
Available help channel!
pliant estuary
Hey, can somebody tell me, what does this notation mean?
$$\mathbb{Z} ^+$$
I was thinking, that it means whole numbers + zero, so 0,1,2,3,4,...
ocean sealBOT
marejak023
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tacit arch
Excludes zero
pliant estuary
Excludes zero
1,2,3,4,... ? so same as $\mathbb{N}$?
ocean sealBOT
marejak023
prime badge
yes
pliant estuary
same as why you would say continue instead of go on
lmao, thanks for help
ive used this notation in my thesis and im not sure if i should chnage it or if i should i leave it
alpine sable
standard deviation
lone heartBOT
standard deviation
alpine sable
this is from udacity free course
Descriptive statistics lesson 17, not an exam or cheating
little drum
check for $$\mbb{P}(Z \leq \theta) \approx 0.14$$
ocean sealBOT
Ansh
alpine sable
I will try it, I remember I try it yesterday but nothing work
little drum
,w P(Z < -1.08)
alpine sable
0.14 = (120-122) / std, would that work ?
zscore = (observe value - mean) / std
why the picture changing so fast ?
ocean sealBOT
alpine sable
Here's a hint: using the z-table, you can find that the z-score for a height of 120 cm. Find the box with the value closest to 0.14, and you should see that occurs at the z-score -1.08.
If 120 is 1.08 standard deviations below the mean of 122, then what is the standard deviation?
this is a hint message
he got 1.08 from the zscore table
little drum
Yes I figured all of those without the hint. As you just saw
ocean sealBOT
Result:
1.8518518518519
should be the deviation
alpine sable
this is True, but I need more time to think about it
I will copy this "Z = (120 - 122)/sd
ds = -2/-1.08
,calc 2/1.08"
and try to think about it alone
Thanks for help me
alpine sable
Thanks for helping me, you are amazing
little drum
alpine sable
an amazing I guess
little drum
*amazing works just fine
alpine sable
such a difficult language
alpine sable
hahahahaha
alpine sable
lone heartBOT
alpine sable
Anyone can help me do this..pls
oak perch
He means x^2=x+30
alpine sable
Why did we take X + 30
I guess I know what to do after that.. but I don't understand the starting
oak perch
There are infinitely many sqrt(30+) if you let that thing to be x, x^2-30 is just x with 1 sqrt(30+) deleted, which is still x
alpine sable
So if I get some other no. For eg like ✓15 + ✓15 + ✓15.. then x^2 = X+ 15 right?
oak perch
Yeah
gray isle
you really need parentheses there
alpine sable
After this we will get a quadratic equation.. then solve it right?
lone heartBOT
lone heartBOT
Available help channel!
sullen pine
good day <@&286206848099549185> I need help about this 3x3 inverse matix
fluid eagle
hint: you want a diagonal matrix multiplied by an unknown matrix giving a diagonal matrix, so the unknown matrix is probably a diagonal matrix as well
lone heartBOT
@sullen pine Has your question been resolved?
sullen pine
.close
little drum
When I'm supposed to show that a polynomial, say x² + 1, is irreducible over Q, I'm assuming the definitive way is to show that there does not exist two linear factors (ax + b)(cx + d) of that polynomial.
little drum
I'm looking for an abstract algebra way of doing this ._.
little drum
wha
pale kestrel
(If it splits in Q, that means it splits in 2 different ways in C)
x² + 1 = (x + i)(x - i)
Factorisation is unique in C.
Or because its degree is 3 or less, if it has factors, at least one factor must be linear.
Then you can use the factor theorem - the linear factor must be (x+-1) (if it exists)
pale kestrel
K[x] is a euclidean domain if K is a field
Eucliean domain -> Unique Factorisation Domain
pale kestrel
K[x] is a euclidean domain if K is a field
(Note I take this as a fact, I have no idea how to prove it)
little drum
wait I do not understand.. (x - 1)(x - 3) can be split in 2 different ways in C?
pale kestrel
what?
x² + 1 = (x + i)(x - i)
how
(x - 1)(x - 3) is written as a product of irreducible factors
little drum
"if it splits in Q, it splits in 2 different ways in C" were you talking about the x² + 1 in specific?
pale kestrel
K[x] is a euclidean domain if K is a field
Using this, C[x] is a UFD so no thats important
vale sapphire
(Note I take this as a fact, I have no idea how to prove it)
To prove this you try to build the algorithm of euclidian division and it only works if you can invert every nonzero element
pale kestrel
"if it splits in Q, it splits in 2 different ways in C" were you talking about t...
Well not quite
If it splits in Q, x² + 1 can be written as (x+a)(x-b) for a, b in Q
But we already know one way it factorises in C
(x+i)(x-i) which does not have a, b in Q
So yes I was talking about this specific example
vale sapphire
but like, what did you mean by "two different ways in ℂ" ?
pale kestrel
Suppose, for contradiction we have
x² + 1 = (x+a)(x-b) for a, b in Q
We already know
x² + 1 = (x+i)(x-i) if we consider this polynomial in C[x]
little drum
then we have the contradiction argument on T_T
pale kestrel
C[x] is ED hence it is UFD. This is impossible.
little drum
Anyways, this one's kinda being convenient for Shuri with the +i , -i roots
pale kestrel
Well yh pick a better example lul
little drum
What about $$x^3 + 9x + 6$$
ocean sealBOT
Ansh
pale kestrel
This is eisenstein.
little drum
:o
pale kestrel
You're just gonna have to remember it
pale kestrel
The proof isn't v. hard but I can't remember it.
vale sapphire
Eisenstein's criterion is a tad tricky to prove actually
The cleanest way I remember it is using some modular arithmetic
pale kestrel
vale sapphire
It's nothing too bad once you have the tools, but the tools are convenient
pale kestrel
Statement.
little drum
Eisenstein's criterion is a tad tricky to prove actually
I'm 2nd yr into my math course lmfao 
and yet shameless enough to ask for its proof
Ik the statement
pale kestrel
I gave you the list before, just learn it lul
It will take a long time to understand why the inclusions work
so for now just learn it imo
pale kestrel
R is a Ring
polynomials in x with things in R as coefficients
Rings
Integral Domains (ID) - no zero-divisors (ab = 0 implies a or b = 0)
Unique Factorisation Domains (UFD) - all factorisations are unique
Principal Ideal Domains (PID) - all ideals can be generated by one element
Euclidean Domains (ED) - euclidean algorithm exists
Fields
little drum
nu ;-;
if I learn those, I'd definitely most certainly not understand my already skipped lessons
pale kestrel
Well you need to learn the definitions regardless
As for the set inclusions, I cannot remember for most.
But you don't really need it for Galois stuff (the why, I mean. You just need to know the inclusions sometimes)
vale wigeon
Q extended by sqrt(2)
frozen stump
pale kestrel
vale wigeon
you can think of it as Q[x] quotiented by the ideal (x^2 - 2)
pale kestrel
This is a really important theorem to know. Using it, you know it is just
little drum
Yeah I kinda know Q(√2) is extension of Q, and that Q[x]/(x² - 2)
pale kestrel
{a + b√2}
Because the theorem holds
little drum
but
it's really hard to understand how to arrive at {a + b√2}
or what exactly is meant by Q[x]/(x² - 2)
pale kestrel
One thing at a time then
Your 2nd question, think of it as polynomials in Q
1 + 0.5x + 3.5x^2 +... -2x^n
pale kestrel
But you now need to mod them out by (x^2 - 2). You treat this as 0 (equivalence relation).
So basically, anything degree 2 or above can be reduced to degree 0 or 1
because euclidean algorithm. (K[x] polynomial ring where K is a field -> K[x] is an ED where you can apply the eucliean algorithm)
oak perch
Maybe Eisenstein. x^2+1 is reducible in Q iff it is reducible in Z. Replace x with (x+1), it’s equivalent to whether (x+1)^2+1=x^2+2x+2 being reducible in Z. This can be applied with Eisenstein
Where p=2
little drum
But you now need to mod them out by (x^2 - 2). You treat this as 0 (equivalence ...
hmmm
the remainder would always be of the form (ax + b)
pale kestrel
indeed.
little drum
pale kestrel
Because x^2 - 2 is irreducible, the quotient gives you a field.
little drum
how to continue to show this is {a√2 + b}
pale kestrel
This comes up a lot in Galois so like...... prove it again if you want to
But remember it
Oh wait this is not the one you proved (but were important)
It is proven using the fact K[x] is a euclidean domain though. For the basis part
The first part of the proof is similar to the other theorem you proved ig.
So you need to convince yourself this is an isomorphism.
Q[x]/(x² - 2) === Q(√2)
pale kestrel
This is how you form the equivalence classes
oak perch
The quotient ring of Q[x] respect to the ideal generated by p(x)
little drum
ohh
pale kestrel
Also I would recommend this notation
Q[x]/(p)
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
little drum
Yeah K[x]/(f) I understand
pale kestrel
Do you understand this quotient is a field if and only if.................
little drum
If (f) is a maximal ideal?
pale kestrel
maximal ideal
little drum
🤔 or smth like that
pale kestrel
f minimal polynomial <-> (f) maximal ideal <-> K[x]/(f) is a field
Otherwise the quotient will just be a ring.
pale kestrel
the divide sign
ocean sealBOT
little drum
so like, pick any (2x^2 + 5x + 2) from Q[x] say, and f = x^2 + 1
so the quotient would be \frac{2x^2 + 5x + 2}{x^2 + 1} ???
pale kestrel
ill call your left thing f
it is f mod x^2+1
It is a different kind of quotient from normal division
x/y <-- x and y numbers
X/Y <-- X and Y algebraic structures
========
Z/2Z is a quotient ring (or group if you like)
It is all of the integers mod 2
You can draw a lot of analogies between quotients of numbers and quotients of abstract structures
little drum
So quotient is basically modular division?
pale kestrel
yes
If you care for an analogy, I thought of an ok-ish one
Take $600 = 2^3\cdot3\cdot5^2$.\
If we divide by the maximal power of $5$, which is $5^2$, we can make the new number coprime with $5$.\
$\gcd(5, 2^3\cdot3) = 1$\
If we divide by $5$ only, this doesn't happen.\
Can I say $24=2^3\cdot3$ somehow 'behaves' like a field for a full analogy?\\
We can say something like 'after we take our quotient, we want all of the factors to have inverses mod $5$'.\\
So the 'full analogy', we take $n\in\bZ$. We want to quotient $n$ by a number so that all the factors of the new thing have multiplicative inverses mod $p$. For that to happen, we need $\gcd(\frac nk, d) = 1$. So in this sense $k$ needs to be the 'maximal' power of $p$.
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
oak perch
Quotient groups, quotient rings, they are all, first , are quotient sets. You know equivalence relation equivalence class right
Like R=Q[x], I=(p) . R/I first is a quotient set R/~ ignoring algebraic structure , where f~g iff f-g belongs to I.
little drum
now
I just need to build up the facts with the modular division definition in mind
smh
little drum
x + 2
oak perch
Yeah
pale kestrel
yep
pale kestrel
god i wrote that sht
little drum
hmm
pale kestrel
Let $f = x^2+1$\
So $x^4 + 2x^2 + x + 3\equiv x+2 \pmod f$\
Or\
$x^4 + 2x^2 + x + 3 + (f) = x+2 + (f)$
Either notation works
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
pale kestrel
Its like 15 === 3 mod 4
15 + 4k = 3 + 4j
15 + (4) = 3 + (4) is alternate notation
little drum
so if f has a root \alpha (say), then ofc F/(f) would have a root (\alpha) if f is an irreducible poly.
oak perch
Any f actually. This case x+(f) is actually a root of f(T) in R/(f)
little drum
Let $\mbb{F}$ be a field and let $f(x) \in \mbb{F}[x]$. Let $f$ be irreducible over $\mbb{F}$.
Q) Does $\exists$ an extension K over F such that f has a root in K?
ocean sealBOT
Ansh
little drum
Ans. yes : K = F/(f)
pale kestrel
Do you see what the root is, though.
pale kestrel
right
oak perch
Yeah x+(f) is one of the roots
oak perch
Oh
little drum
**𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎**
I mean, now that I've internalized this.. it's kinda feeling like within reach
pale kestrel
The elements of the quotient are polynomials mod f
Now we claim f has a root in K
What does this mean though......
it doesnt make sense unless we consider the polynomial ring of K
K[y]
so we are saying f(y) in K[y] has a root in K
little drum
no absolutely not
bruh
(2x^2 + 2x + 1) = 2x - 1 mod (x² + 1) does not have the root I
._. t
f
pale kestrel
listen
We want to construct a field
So that f has a root in that new field
Call this field K
This means there exists a in K such that f(y) in K[y] and f(a) = 0 in K
Does this make sense?
Take the polynomial in R[x] x^2 + 1. We want to construct a field so this has roots.
We are then considering x^2 + 1 as a polynomial in C[x] and saying +-i is its roots
little drum
uhh 😂 yeah and also, I'm wondering if all this time F/(f) just meant stuff like polynomials under modular division with f
oof
pale kestrel
This means there exists `a` in `K` such that `f(y) in K[y]` and `f(a) = 0` in `K...
Unravel what this means
little drum
can not :| f(y) in K[y] does not sink in
pale kestrel
Write down K[y] for the example
pale kestrel
can not :| `f(y) in K[y]` does not sink in
Or did you mean for what I said originally
Does the x^2+1 make sense
little drum
what you said originally
pale kestrel
We say x^2 + 1 has a root in C
For this to happen we must be taking this polynomial as a complex polynomial
in C[x]
(are you familiar with the evaluation map?)
pale kestrel
When we write down x^2 + 1 we can consider it in Z[x], Q[x], R[x], C[x]
or whatever
pale kestrel
But if we say 'x^2 +1 has a root in C'
little drum
I give up
pale kestrel
We are saying x^2 + 1 in C[x] equals 0 when you plug in an x from C
pale kestrel
what are u doing 
little drum
Anyways forget this
Show me
$\mbb{Q} (\sqrt{2} + \sqrt[3]{3}) = \mbb{Q} (\sqrt{2}, \sqrt[3]{3})$
pale kestrel
You should really get this idea of quotient rings down 
You're almost there
ocean sealBOT
Ansh
little drum
minimal poly. for left = degree 6.
pale kestrel
thats a guess, isn't it?
ocean sealBOT
Ansh
pale kestrel
In fact if you found rational factors for it
it isn't
(3x^2-2) <-- if this factorises into it, its not irreducible.
little drum
well, since it is indeed a degree 6 poly, it is reducible in quadratic factors
little drum
🤔
pale kestrel
If you claim the minimal polynomial is of degree 6, then it cannot be reduced, of course.
The question wants you to find the minimal polynomial last
not first
First you need to show this
I would recommend via inclusion
But I can't fully remember how to do this
One way is easy, can you see?
little drum
mwahahaha
yes I do
cuz I'm smort
show that √2 and cbrt(3) are elements of Q(alpha) and therefore Q(..., ...) subset of Q(alpha)
the other way is trivially true
pale kestrel
yep
pale kestrel
Have you seen the primitive element theorem?
pale kestrel
nevermind that
little drum
do you like to play with big words
pale kestrel
I don't get how you just showed this
pale kestrel
$$\mbb{Q} (\sqrt{2} + \sqrt[3]{3}) \subseteq \mbb{Q} (\sqrt{2}, \sqrt[3]{3})$$
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
pale kestrel
this is trivially true
$$\mbb{Q} (\sqrt{2}, \sqrt[3]{3})\subseteq\mbb{Q} (\sqrt{2} + \sqrt[3]{3})$$
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
pale kestrel
This is not.
little drum
I showed that tho UwU
pale kestrel
what?
How do you know root 2 is in the right thing
$$\sqrt{2}, \sqrt[3]{3}\in\mbb{Q} (\sqrt{2} + \sqrt[3]{3})$$
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
little drum
$$\alpha = \sqrt{2} + \sqrt[3]{3}$$
$$\alpha^2 = 2 + \sqrt[3]{9} + 2\sqrt{2}\sqrt[3]{3}$$
$$\alpha^3 = 2\sqrt{2} + 3 + 6\sqrt[3]{3} + 3\cdot \sqrt{2} \cdot \sqrt[3]{9}$$
ocean sealBOT
Ansh
pale kestrel
im dumb, i dont see how
little drum
pale kestrel
oh you mean sub
little drum
Yes
pale kestrel
i shall try
pale kestrel
whats the 'or'
ocean sealBOT
Ansh
pale kestrel
yes this is the usual way iirc.
pale kestrel
yep
can i check my work with yours
$$\sqrt2 = \frac{\alpha^3+6\alpha-3}{3\alpha^2+2}$$
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
little drum
but
pale kestrel
first time i done this exercise
little drum
don't we need to show that 1/(3alpha^2 + 2) \in Q(\alpha) 🤔
pale kestrel
I am doing the first question right
little drum
Yes
little drum
**𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎**
bcuz you got \sqrt{2} = a fraction in alpha
pale kestrel
but this is a field
pale kestrel
wait how the heck did you do it then
little drum
little drum
little drum
every such questions I've seen solved so far,
had √2 or some surd like that expressed as a polynomial in alpha
pale kestrel
then wtf did i do wrong
I did elimination as you said
Either im crap at algebra
or
little drum
:| I thought it being expressible as a polynomial must be a necessary condition for
little drum
oof shuri
pale kestrel
5i)
little drum
okay
1/(3alpha^2 + 2) exists in Q(alpha)
and the other thing exists in Q(alpha)
so
√2 exists in Q(alpha)
little drum
little drum
mhm (@_@;)
little drum
x^3 = 3
pale kestrel
wat
pale kestrel
(x - \sqrt(2))^3 = 3
its quick to show/explain why its irreducible
little drum
pale kestrel
maybe
little drum
how tf
little drum
pale kestrel
$(x - \sqrt 2)^3 - 3$
little drum
x^3 = 3 minimal poly
ocean sealBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
little drum
nu
little drum
x^3 = 3 minimal poly <:sadcat:547124024585486359>
.
pale kestrel
x^3 = 3 minimal poly <:sadcat:547124024585486359>
this is not the answer
pale kestrel
aosdsdokpdsakposopkasdpksdo
little drum
fufufufu
pale kestrel
right?
little drum
I'm smort
pale kestrel
smart smart
little drum
pale kestrel
but do you know what arguments you are using formally
pale kestrel
👋
little drum
and I absolutely understood nothing lmfao
pale kestrel
I will write the argument u are using
pale kestrel
You are showing y^3 - 3 is irreducible in Z[sqrt 2] using eisenstein (p = 3).
Then (x - sqrt2)^3 - 3 is also irreducible in Z[sqrt 2] (lemma)
Then (x - sqrt2)^3 - 3 is irreducible in Q(sqrt 2) (Gauss' lemma)
little drum
Also, can you flip through dummit n foote and gib me the topics I must read
to proceed with splitting fields, etc.
favor, do
pale kestrel
idkkkkkkkkkkkkkkkk
you need to understand F/(f)
im not sure where all your gaps are
but u need to get this for starters
and then everything kinda follows-ish
lone heartBOT
Available help channel!
sacred siren
lone heartBOT
lone heartBOT
Available help channel!
karmic rapids
what's an inscribed regular tetrahedron
lone heartBOT
what's an inscribed regular tetrahedron
karmic rapids
channel is already taken
gleaming wyvern
solar ermine
karmic rapids
a sphere is supposed to have that
karmic rapids
no idea what that is
lone heartBOT
@karmic rapids Has your question been resolved?
fallen rain
How to work out the value of x?
lone heartBOT
How to work out the value of x?
floral pawn
oak perch
Look for Inscribed angle theorem
fallen kayak
lone heartBOT
fallen kayak
tacit arch
what did you try
fallen kayak
I don't know bro
this is my last question, and I've spent 20 minutes stuck
@tacit arch
tacit arch
plug in the equation of f(x) for g(x)
do the same for f(g(x)). if you get x back both times, then the answer's yes.
fallen kayak
f(x)-3x+5 and g(x)=5x-3?
tacit arch
f(x) = -3x + 5 yes
read "Steps To Find An Inverse Function"
https://www.cuemath.com/algebra/inverse-functions/
fallen kayak
g(f(x)) means just replacing the f(x) with 'x' in g(x)
g(x) = 5x-3 f(x) = -3x+5
g(f(x)) = 5(-3x+5) - 3
tacit arch
$x \neq -15x+14$
ocean sealBOT
riemann
lone heartBOT
@fallen kayak Has your question been resolved?
smoky jungle
lone heartBOT
smoky jungle
its probably rlly easy but im dumb so can somone pls help
merry depot
Can you fill in the blanks with the correct porbabilitiies?
raven rover
@smoky jungle Start with the tiny tiny steps ^^
smoky jungle
i got it wrong so i have a new question now but is this right so far?
merry depot
yeah, that's correct so far
merry depot
you'll add the probabilities where he ends up doing his homework in the two cases of going to the park, and not going to the park
So if he goes to the park and does his homework you'd multiply those probabilities together.
Same for not going to the park and doing his homework.
smoky jungle
so 7/10x1/2?
merry depot
yep, that's one probability you'll need
smoky jungle
and 3/10x3/4
merry depot
yep.
Then add those two probabilities together
and that's the probability that he does his homework.
storm pebble
I need help
The graph shows f(x). The dashed line is a vertical asymptote.
What is the correct statement?
storm pebble
The graph shows f(x). The dashed line is a vertical asymptote.
also on the stop
it says fx
echo socket
Clearly the graph goes infinitely downwards near 1
cunning crow
the question is asking what the limit is approaching 1 from the positve side
storm pebble
yeah
storm pebble
What is the correct statement?
the first one is correct
cunning crow
asking or telling?
lone heartBOT
Available help channel!
modest yew
lone heartBOT
serene helm
why theres 10 pts behind the question
modest yew
It's hw
serene helm
k gl
raven rover
Have you ended up starting?
With the limit definition, the first steps are:
-
Finding f(x + h)
-
Finding f(x) (most of the time you're given f(x))
modest yew
Yes I have, but I don't know how it applies to this question. I think I have to use it but I don't see how
Ah, this is for question 2 I see
So then I would do the limit def for both of those right?
Nvm I see what you're saying
Ok thank you!
.close
lone heartBOT
lone heartBOT
Available help channel!
white ivy
I forgot how to do 3.1.2
lone heartBOT
I forgot how to do 3.1.2
knotty spire
When are the values of f(x) larger than g(x)
white ivy
I think around -120 to 0?
knotty spire
yep
white ivy
Do i
white ivy
will I get the mark from just writing that down or do I have to do more
vernal agate
anyone know this?
lone heartBOT
anyone know this?
cunning crow
you need to find the function
you can map it to decide if it's linear or exponential
lone heartBOT
@vernal agate Has your question been resolved?
white ivy
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@white ivy Has your question been resolved?
junior condor
Show that if f is a continuous function on the real line such that for all x and y, $$f(\frac{(x+y)}{2})=\frac{f(x)+f(y)}{2}$$ then f(x)=ax+b for some real a and b. Then, show that this holds for any borel function f, but not for a non-measurable f?
fluid eagle
seems like the cauchy functional eq? unless the tex is scuffed
ocean sealBOT
DeathlyKnights
junior condor
sure I get the first part, but how do I show that it holds for any borel function f
but not for a non-measurable f
A second question is:
Show that for every distribution function F there exists a probability measure $\mu$ on $(\mathbb{R},\mathcal{B})$ such that F(x)=$\mu {(-\infty, x}$
ocean sealBOT
DeathlyKnights
lone heartBOT
@junior condor Has your question been resolved?
plain plank
yo
junior condor
hello lil murda
plain plank
yo
lapis saffron
hi, can someone help me with this?
junior condor
no
lapis saffron
junior condor
This is out of my paygrade
please take this to #get-advanced-access for better help
lapis saffron
oh okok
tacit arch
this channel's occupied #❓how-to-get-help
plain plank
how about me
lone heartBOT
@junior condor Has your question been resolved?
junior condor
.close
lone heartBOT
lone heartBOT
Available help channel!
potent plank
I was trying out this problem and I got average revenue per passenger as 15.7 $ and SD as 19.95 $ which is correct. In the second part, revenue expected of 120 passengers, I did 15.7 * 120 = 1884 which is also correct.
In the case of SD in b part, should I multiply 120 with the Standard deviation (19.95)?
In a) part I am finding SD per person right? so in b) part, for 120 people, It must be multiplied right?
lone heartBOT
I was trying out this problem and I got average revenue per passenger as 15.7 $ ...
@potent plank Has your question been resolved?
potent plank
<@&286206848099549185>
lone heartBOT
@potent plank Has your question been resolved?
viscid wren
can someone help me factor this lol?
lone heartBOT
can someone help me factor this lol?
buoyant kayak
let u = x^2
buoyant kayak
cool
torn forge
uh
viscid wren
completing the square right?>
torn forge
ye
viscid wren
its been literally forever
buoyant kayak
what
buoyant kayak
this is not what you need
torn forge
After that use the difference of two squares
torn forge
this is not what you need
??
viscid wren
this doesnt really help lol
torn forge
a
placid zinc
Basically, you just want to factor
u² - 40u + 144
buoyant kayak
uhh
placid zinc
I wouldn't say there's anything to learn, haha
placid zinc
Unless you have forgotten how to factor, which a lot of people do, haha
torn forge
buoyant kayak
you've done substitution before
if you've taken an algebra class
it's just like that
placid zinc
So it's an algebraic substitution, not a u-sub. We're just looking at the denominator in a new way:
u² - 40u + 144
If you can factor that, you can factor the original
viscid wren
Lol I don’t remember and if it was algebra two that was like 7 years ago
Looks easy enough tho so I’ll just go do that now
buoyant kayak
i assume you've covered u subs in calc tho?
viscid wren
Yeah of course
buoyant kayak
it's just like that except no du
viscid wren
Applying it to algebra shouldn’t be hard at all
buoyant kayak
it's u sub but easier lol
viscid wren
It’s just new or something I don’t remember so I’ll have to do it a few times to get it
But yeah I see
buoyant kayak
👍
wary stream
if so could you close it
Why do you want it closed?
proven oriole
@wary stream i wanna ask a q lol
wary stream
If you read #❓how-to-get-help
proven oriole
you right
wary stream
you right
You would know there is a section named MATH HELP (AVAILABLE) with open channels to use
proven oriole
yes
lone heartBOT
@viscid wren Has your question been resolved?