Square over y
#help-19
vivid wyvern
strange aspen
uhhhh 4xy^2 - 4xy^2 = ?
spare crater
uhhhh 4xy^2 - 4xy^2 = ?
I don't know...
vivid wyvern
strange aspen
I don't know...
oh wait my bas looked at the wrong term
spare crater
I have to change it to -
vivid wyvern
I have to change it to -
Yes
Cuz in the previous line one was negative nd the other was positive
spare crater
Cuz in the previous line one was negative nd the other was positive
Ahhh
I absolutely forgot that
Worked
Tysm
Just changed the "x³ -" to "x³ +"
strange aspen
!done
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
spare crater
.close
odd edgeBOT
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next roost
Hello, may I ask what's the difference between domain and range, they seems to be similar thing to me
summer wave
domain is the set of possible "inputs" for your function
range is the set of possible "outputs" for your function
next roost
OK, but I don't really understand why the domain is divided by 3 of idk what it is and Range is divided by 2 of something idk
slender jetty
OK, but I don't really understand why the domain is divided by 3 of idk what it ...
\ doesnt mean divide
it means excluding the set
R \ {3} means the set of all real numbers R, excluding the set with only 3 in it
so "all real numbers except 3"
this is true because in f^-1(x), if u put x = 3, u get a division by 0
which is not allowed
the range is the set of all real numbers excluding -2
this is because taking the inverse function interchanges the range and domain of functions
so the range of f^-1 is the domain of f, and the domain of f^-1 is the range of f (assuming f is invertible)
the domain of f is the set of all real numbers except -2 (because again, putting x = -2 into f(x) gives a division by 0)
so the range of f^-1 is the set of all real numbers except -2
symbolically written R \ {-2}
odd edgeBOT
@next roost Has your question been resolved?
next roost
So I can understand it as range of f(x) inverse equal to the domain of f(x)?
next roost
If the question asked us to find the range of f(x) it's the domain of f(x) inverse then right?
slender jetty
If the question asked us to find the range of f(x) it's the domain of f(x) inver...
yes
next roost
Thanks for answering my question, now I understand it!
odd edgeBOT
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fallen marlin
Know a > b. Prove a² > b²
odd edgeBOT
Know a > b. Prove a² > b²
amber schooner
Know a > b. Prove a² > b²
false
fallen marlin
why false
amber schooner
0 > -1 but 0^2 = 0 < 1 = (-1)^2
outer hinge
amber schooner
consider difference of squares
fallen marlin
if it's true if a >= b, prove a² >= b²?
amber schooner
i mean yea
assuming you still have positive a and b
the equality case is trivial
low locust
compare with ab
odd edgeBOT
@fallen marlin Has your question been resolved?
odd edgeBOT
@fallen marlin Has your question been resolved?
glossy basin
a>b
a-b>0
(a-b)(a+b)>0
amber slate
how can i calculate common stock and retained earnings while only being given my total assets, total liabilities, and total stockholders equity
odd edgeBOT
how can i calculate common stock and retained earnings while only being given my...
@amber slate Has your question been resolved?
odd edgeBOT
@amber slate Has your question been resolved?
amber slate
.close
odd edgeBOT
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outer wadi
The answer was no, can someone let me know what invalid steps I made in proof
latent scaffold
What if b = 0 ? (in the transitivity bit)
outer wadi
oh I see, is that the only place where i went wrong?
latent scaffold
Pretty much. The relation is indeed reflexive and symmetric, just not transitive.
odd edgeBOT
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hot oar
hey yall, more of a physics question but i don’t know where to start here. how do i operate on an acceleration equation if its with respect to position ?
forest sky
similar problem
odd edgeBOT
@hot oar Has your question been resolved?
sudden vale
can anyone help me with my homework its so confusing
nimble blaze
which part confuses you?
nimble blaze
which specific part about divisibility
divisibility is everywhere
which line/phrase
sudden vale
the divisible by 16 and divisible by 121-(-4)=125
nimble blaze
do you know the factorisation for difference of two powers?
sudden vale
yeah
nimble blaze
a^n - b^n = (a-n)(...)
they focus on the bolded part
sudden vale
ok
nimble blaze
applying that the first way give
96p + 1904q = 16(6p+119q)
which is a multiple of 16
same idea for the multiple of 125 the second way
nimble blaze
try applying the same reasoning as i've done above
nimble blaze
yeh
odd edgeBOT
@sudden vale Has your question been resolved?
mighty locust
Why does plugging the vector a or b into the result of the cross product a and b give 0?
mental lotus
what do you mean by plugging in?
like you substitute the i,j,k with the values of the coefficients?
liks -1*2 + 1*0 + 2*1?
mighty locust
Yes
mental lotus
Thats just the same as $\vec{a} \cdot (\vec{a} \times \vec{b})$
clever fjordBOT
Bacter14Fr0g
odd edgeBOT
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peak garden
I'm trying to find the equation for the surface distance along a vertical great arc of a sphere. See the image. When theta==0, the arc is PI/2. When theta=-pi/3, the arc is PI/3. I'm having trouble figuring out the right formula.
peak garden
The red lines can be thought of as planes intersecting the sphere
Alternatively: Given a plane at x=0.5, cast a ray towards the center of the sphere (0,0,0) and find the point that intersects x=0.5.
Actually, reframing it as a projection problem simplifies it a lot I think. Looks like I was able to get it scaled correctly
.close
odd edgeBOT
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prime ferry
Just making sure I can do this when doing row operations
viscid flint
yep thats allowed
odd edgeBOT
cedar geyser
Just making sure I can do this when doing row operations
Multiplication, addition, subtraction, division row swap are valid elementary row operations
odd edgeBOT
Available help channel!
fleet lake
odd edgeBOT
fleet lake
First one pls
wooden python
,rccw
clever fjordBOT
wooden python
#2 ? the one asking for number of distinct roots of a quartic?
fleet lake
Yes
wooden python
any progress so far?
wooden python
RRT says that the only candidates for rational roots here would be x = ±1
have you checked both of these y/n
fleet lake
No
fleet lake
RRT says that the only candidates for rational roots here would be x = ±1
I don't think if they are roots
wooden python
that sentence doesn't make sense
but ok then you should check them both before doing anything else.
you said you "tried a bit of hit-and-trial"
your hit-and-trial didn't include both x=1 and x=-1? or did it include only one but not the other?
fleet lake
you said you "tried a bit of hit-and-trial"
Actually I did that but by ur sentence I felt like i would have made some silly mistakes
So i tried again but they aren't the roots
wooden python
ok, so we have no luck with RRT.
since we don't care about what the roots are but instead want to know only how many exist, let's try looking at the turning points.
fleet lake
Oh actually we can make a graph
wooden python
let f(x) = (your quartic). calculate f'(x) and then attempt to solve f'(x) = 0 to find the stationary points. then evaluate f(x) at each of those.
fleet lake
f''(x)=12(x-1)^2
wooden python
why did you go straight to the second derivative...
i only asked about the first
@fleet lake
fleet lake
Hmm ohk
wooden python
it would be nice if you could follow instructions as they are written instead of trying to think up your own shit
if you do something on your own initiative then at least first do what i ask and then yap about your own idea.
fleet lake
Ohk pls calm down lady
granite bridge
it would be nice if you could follow instructions as they are written instead of...
that's rude.
fleet lake
that's rude.
Naah pls
granite bridge
im sorry he ain't no postgraduate. Neither am I
wooden python
he* ?
potent nexus
I think the idea is to show that the maximas have different signs so thus it must’ve passed the x axis
wooden python
mathemystic is a he
wooden python
im sorry he ain't no postgraduate. Neither am I
it doesn't take being a postgrad to understand that when someone asks for f'(x) (the first derivative) they don't want f''(x) (the second derivative)
fleet lake
I think the idea is to show that the maximas have different signs so thus it mus...
Answer is 2
wooden python
i am being rather blunt here, yes.
fleet lake
Please guys
Have some peace
granite bridge
it doesn't take being a postgrad to understand that when someone asks for **f'(x...
im not denying that. Im asking you to calm down.
fleet lake
Her frustration was worthy
wooden python
im not denying that. Im asking you to calm down.
i am perfectly calm.
potent nexus
Answer is 2
Which we would expect for 3 stationary points
wooden python
do you want to see me go bitch mode?
potent nexus
with different signs
wooden python
i think you don't.
fleet lake
🫣
potent nexus
lol
granite bridge
regardless, again, i am jumping in again, right? i won't
descartes shortcut wont give, so then use use smth else, as she says differentiating once will give the answer. It's almost a standard for JEE
potent nexus
What’s that?
granite bridge
do you want to see me go bitch mode?
Do you want to?
fleet lake
One more useless message and I'm closing it if anyone of u didn't quit
wooden python
again, tell us what f'(x) is
fleet lake
4x^3 - 12x^2 + 24x +1 =0
wooden python
f'(x) = 4x^3 - 12x^2 + 24x + 1, yes
wooden python
4x^3 - 12x^2 + 24x +1 =0
so what do you get when solving this
fleet lake
Still thinking
More probably I would say that the first 3 terms give even and +1 at last is odd so no natural roots
wooden python
hang on i think your f''(x) was wrong before
wooden python
More probably I would say that the first 3 terms give even and +1 at last is odd...
so the roots (if any) are not natural numbers. that is correct but it is only part of the story.
fleet lake
hey
f(0)=-1
at x= +- infinity = is at infinite
so minimum 2 roots
wooden python
that was typed in a very slightly bad way
but yes f does have at least two roots
can we prove it has no more than that
fleet lake
u know that im a big typo'd
wooden python
anyway it looks like the roots of f'(x) are not easily findable so then we move on to f''(x), which works out to 12x^2 - 24x + 24, or 12(x^2 - 2x + 2), and this is always positive.
which means that f'(x) is strictly-increasing, and so has exactly one root.
wooden python
did you mean "no" like "none", or "no" like short for "number"
fleet lake
none real roots it was
fleet lake
it can be clearly called no real roots for f''(x)
wooden python
well that is correct, f'' doesn't have any real roots
however your previous (wrong) value for it would have one real root
fleet lake
😅
fleet lake
however your previous (wrong) value for it would have one real root
so what can we do further
wooden python
which means that f'(x) is strictly-increasing, and so has exactly one root.
do you understand up to and including here
fleet lake
not truly
wooden python
ok let me copy the full chain of reasoning
- We want to know how many roots f(x) = x^4 - 4x^3 + 12x^2 + x - 1 has.
- Rational root theorem doesn't give anything (x = ±1 are not roots).
- In hopes of getting more info, we find the derivative of our polynomial: f'(x) = 4x^3 - 12x^2 + 24x + 1.
- The derivative does not have easily findable roots either.
- Thus we move on to the second derivative: f''(x) = 12x^2 - 24x + 24 = 12(x^2 - 2x + 2).
- We can see f''(x) has no real roots; in fact f''(x) > 0 everywhere.
- This means that f'(x) is strictly increasing.
- Since f'(x) is strictly increasing and an odd-degree (3) polynomial, it has exactly one real root.
tell me the earliest step number that confuses you.
or tell me "everything is clear" if everything is indeed clear.
fleet lake
i didnt noted 6th before but 7 is what i cant understand
wooden python
if $g'(x) > 0$ always, then $g$ is a strictly increasing function
clever fjordBOT
Ann
wooden python
agree or disagree?
fleet lake
yeah
wooden python
$f''$ is the derivative of $f'$.
clever fjordBOT
Ann
wooden python
so f''(x)>0 always (from point 6) thus f' is strictly increasing
fleet lake
change in f'(x) will be +ve so it will increase
so now how is 8th
oh yes
i got it ty
fleet lake
how does it prove that f(x) has only 2 roots
wooden python
for any continuously-differentiable function $f$ (it need not even be a polynomial, but polynomials do fit this bill), if $f$ has $k$ roots, then the equation $f(x)=0$ has at most $k+1$ solutions.
clever fjordBOT
Ann
wooden python
i.e. a function has at most 1 more root than it has turning points.
fleet lake
grest\
wooden python
i can explain the reasoning to you if you want.
fleet lake
pls sure
wooden python
call the turning points $x_1, x_2, \dots, x_k$
clever fjordBOT
Ann
wooden python
chop the real number line into the following intervals:
\begin{itemize}
\item $I_1 = (-\infty, x_1)$
\item for $2 \leq j \leq k$, $I_j = (x_{j-1}, x_j)$ [i.e. $I_2 = (x_1, x_2)$, $I_3 = (x_2, x_3)$ and so on]
\item $I_{k+1} = (x_k, +\infty)$
\end{itemize}
focusing on each one of these intervals, $f$ will be either strictly increasing or strictly decreasing and so only have 1 or 0 roots on that interval
clever fjordBOT
Ann
wooden python
(and if it happens that $f(x_j) = 0$ then $f$ is guaranteed not to have any roots in $I_j$ nor in $I_{j+1}$)
clever fjordBOT
Ann
fleet lake
oh great ty
for the second question that is the third one
can we continue in this channnel
wooden python
we've gone on for long enough, you should close this and open a new one
odd edgeBOT
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Available help channel!
wintry heart
can someone teach me how to do this 💔
odd edgeBOT
can someone teach me how to do this 💔
wintry heart
im sure its easy once i understand it
wooden python
did your username use to be perseverance4
vivid wyvern
The other h is active
wooden python
anyway w/e
wintry heart
oo thats cool
wooden python
you need to pull out a common factor from all these terms
look at how many x's you can pull out, how many y's you can pull out, and what raw number is a common factor of 2, 8 and 6
wintry heart
man i dont understand this 💔
wooden python
ok lets take a step back
do you understand the distributive law
or distributive property perhaps
wintry heart
yes
wooden python
right
a(b+c) = ab + ac
factorization means figuring out what kind of "a" you can pull out to go "backwards" in this
so let's first look at just the x's
no actually let's look at just the numbers first
i will temporarily block out the x's and y's
$2A - 8B + 6C$
clever fjordBOT
Ann
wooden python
what can you factor out of all these terms?
wooden python
well you're on track so far.
so factor out a 2 from 2x^3y^4 - 8x^2y^3 + 6xy^2.
just a 2.
so you'll be left with 2(_________________)
fill in the blank
wintry heart
2(x^3y^4 - 4x^2y^3 + 3xy^2)
wooden python
ok so far so good
let's now look at the x's
how many factors of x can we factor out from all 3 terms simultaneously?
wintry heart
i dont know 💔 💔
how do you know like this makes no sense to me
i see theres x, -4x and 3x
wooden python
ok lets see here
wintry heart
but its clumped with everything else
wooden python
those x's have some exponents on them.
wintry heart
yes
wooden python
so ok let's try to do this again
you understand that $xA + xB + xC$ factorizes as $x(A+B+C)$ yes?
clever fjordBOT
Ann
wooden python
well i am taking you through the basics of it.
let's now try $x^2 A + xB + xC$. this factors to $x(xA + B + C)$. do you understand still?
clever fjordBOT
Ann
wintry heart
yes
wooden python
ok right
if we wanted to factor out x^2 from this thing, we would need each term to contain x with an exponent of 2 or higher.
(and there's nothing sacred about 2; the same reasoning goes for factoring out x^3, x^4, or even x^69)
wintry heart
hmm okay
wooden python
so x^3y^4 - 4x^2y^3 + 3xy^2
we see one term has x^3, another has x^2, and the third has x^1. (an unwritten exponent means ^1.)
so how many x's can we pull out at most?
wintry heart
2
wooden python
how can you pull out two x's when the last term has only one
wintry heart
because each term needs to have an exponent of 2 or higher
😞
can we do something less difficult and work up to that problem
nimble blaze
factorise
$$x + x^2 + x^3$$
clever fjordBOT
ℝαμOmeganato5
wintry heart
x(x^1 + x^2) ?
wintry heart
where is the 1
signal yacht
$x(1+x+x^2)$
clever fjordBOT
Percy
signal yacht
where is the 1
$\frac{x}{x}$ is $1$ no
clever fjordBOT
Percy
wintry heart
yes
signal yacht
so
wintry heart
this is confusing
nimble blaze
refer back to this
#help-19 message
x + x^2 + x^3
after identifying x as a common factor, consider
x * What = x
x * wHat = x^2
x * whAt = x^3
nimble blaze
yes
nimble blaze
the above example I gave is easier but ok
same idea
start with identifying a common factor in all terms
odd edgeBOT
nimble blaze
careful with your signs
wintry heart
careful with your signs
thanks
odd edgeBOT
Available help channel!
wooden oar
Hi! I need help with the task below. I dont know what i have done wrong, because i am trying to show that the left-hand side (VS) and the right-hand side (HS) are equal, but i didnt get the same result, and so i believe i have made a silly mistake, but i dont know where.
The task: Prove that 1+4+9+ … + n^2 = (n(n+1)(2n+1))/6 for all natural numbers n.
wooden oar
Thanks in advance!
hollow fulcrum
sand horizon
Yeah you should just add (k+1)²
odd edgeBOT
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Available help channel!
lofty kernel
hi ive got a question does Integrability guarantee primative func
lofty kernel
?
glass vault
the very definition of an integral is its the antiderivative
vernal pilot
The very slightly more interesting question would be are all integrable functions differentiable and that is false
low locust
the very definition of an integral is its the antiderivative
it isnt. thats the fundamental theorem
lofty kernel
so not every Integrabal func has anti derv?
low locust
if $f$ is integrable, then $\int_a^x f(t) dt$ is a primitive of $f$. is that what you are asking?
clever fjordBOT
Denascite
low locust
whether thats expressible using all the normal functions is a different question
to which the answer is no in general
lofty kernel
when does a func has an primitave func only when the func is countious?
late dust
if $f$ is integrable, then $\int_a^x f(t) dt$ is a primitive of $f$. is that wha...
f needs to be continuous too
vernal pilot
f needs to be continuous too
For a function to be integrable you don't need continuity
lofty kernel
like does this func has an antiderv?
late dust
For a function to be integrable you don't need continuity
Yes, but for it to have a primitive, you do
amber schooner
Yes, but for it to have a primitive, you do
no
low locust
ok integrable isnt enough. but you dont need full continuity either
late dust
no
What's the primitive of Thomae's function?
amber schooner
low locust
take something like x sin(1/x) (or whatever the classic example is), its the primitive of its derivative which isnt continuous
tacit wasp
like does this func has an antiderv?
,w antiderivative of floor(x)abs(sin(pix))
clever fjordBOT
tacit wasp
Seems not
odd edgeBOT
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.
lofty kernel
so only when f is countious then f has prim func?
late dust
like does this func has an antiderv?
It's continuous so yeah it does
late dust
so only when f is countious then f has prim func?
No, some non-continuous functions also have primitives
lofty kernel
but its the only condition ?
lofty kernel
No, some non-continuous functions also have primitives
what the conditions for a functions to have prim function?
late dust
Honestly, not sure
low locust
it doesnt seem like a full characterisation is known
see what I linked
there are some quite cursed examples which have an antiderivative
amber schooner
being continuous guarantees it though of course
lofty kernel
there are some quite cursed examples which have an antiderivative
yeah i know there some weird func that has antiderv but i only saw the condition for antiderv was the continuity
i didnt find any other condtions
late dust
Continuity is sufficient, but not necessary, and I agree with Denascite, there doesn't seem to be a general rule for finding an antiderivative, if one exists
amber schooner
yeah i know there some weird func that has antiderv but i only saw the conditio...
it’s a sufficient condition
lofty kernel
i dont want to find it just want to know if one exist or no
late dust
Let me rephrase: there doesn't seem to be a general rule for finding if a function accepts an antiderivative
Integrability isn't sufficient
amber schooner
odd edgeBOT
@lofty kernel Has your question been resolved?
strong horizon
if α, β are the roots of the equation ax^2 + bx + c and α + k, β + k are the roots of the equation px^2 + qx + r, then what is
strong horizon
$\frac{q^2 - 4pr}{b^2 - 4ac}$
clever fjordBOT
bagelguy3
wooden python
where is r?
strong horizon
A) $\frac{a}{p}$ B) $\frac{p}{a}$ C) $\frac{p^2}{a^2}$ D) $\frac{a^2}{p^2}$
a constant
clever fjordBOT
bagelguy3
strong horizon
where is r?
constant i suppose
wooden python
also im gonna be a pedant about this but
the equation ax^2 + bx + c
did you miss a=69at the end of that?
strong horizon
the second equation
wooden python
this has no r variable anywhere
wooden python
again, did you miss a =69 or =420 at the ends of these equations?
strong horizon
let me check if i missed anything
signal yacht
im guessing its =0 actually
wooden python
im guessing its `=0` actually
im deliberately saying sth wrong in hopes of making op correct me
signal yacht
'roots of equations' gives an expression
strong horizon
since its the roots are alpha + k
i treid putting the first equation a(x-k)^2 + b(x-k) + c
and expanding that
and uh lets just say
terms started canceling each other out but i didnt get where i wanted to be
I've decided to entirely give up on getting a solution to this madness
.close
odd edgeBOT
mystic saffron
bruh
odd edgeBOT
Available help channel!
woeful rivet
odd edgeBOT
short terrace
Like why they're using those ranges?
woeful rivet
yeah
wooden python
where is your density function positive?
short terrace
So everywhere else has density zero, which essentially means that it cannot take values anywhere else
wooden python
the cdf will be 0 to the left of that range and 1 to its right
short terrace
Intuitively that's because it can't take any values to the left, and at the right it has taken all the values it can
odd edgeBOT
Available help channel!
sick fossil
odd edgeBOT
woeful briar
sqrt(n) and log(n)?
woeful briar
notice what happens when you take square n
in that case sqrt(n) is squared
but logn only multipled by a constant factor
sick fossil
square ( sqrt n ) = n
clever fjordBOT
ExpertSqueeSQUEE
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
woeful briar
wait I confused myself
wait a sec
what you want to show is that sqrt(n) >= log(n) eventually
woeful briar
ok... sorry for the messy answer
what you do is you let n = m^2 and then instead of comparing the growth of sqrt(n) and log(n) you compare the growth of m and 2log(m) which should be easier
Then you can convince yourself that m >= logm. (induction can work)
odd edgeBOT
Available help channel!
proud verge
How to maximize the value of cos a + cos b + cos c if a+b+c=π
stoic cloud
well obviously $a=b=c$
molten palm
Well each cos has to equal 1/3pi
clever fjordBOT
𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³
molten palm
So whats cos (a) = 1/3pi?
stoic cloud
@proud verge
odd edgeBOT
@proud verge Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
prime ferry
just seeing if i have completeld this correctly
odd edgeBOT
just seeing if i have completeld this correctly
prime ferry
prime ferry
just seeing if i have completeld this correctly
the third one on here
cold swift
can you elaborate more on what you did to get from the second matrix to the third
looks to be a missing step there
odd edgeBOT
@prime ferry Has your question been resolved?
prime ferry
looks to be a missing step there
I did mess up and I am now lost, dont see how this could become echelon form? Can't change The 1 or 0 in R3 without changing the other?
viscid flint
swap r2 and r3
prime ferry
swap r2 and r3
in order of me doing them or make another matrix?
viscid flint
actually swap rows 1 and 3
you're allowed to swap rows when reducing
or maybe I'm confused on where you're struggling
prime ferry
trying to get the bottom left of the matrix to be zeros so its an echelon
atomic void
atomic void
Ain't this wrong?
prime ferry
yea, I accidentally multplied
cold swift
might be easier if you were to get rid of the bottom left corner first instead of turning the -1 into a 0
since once the bottom left corner is a 0, you can use row 2 to turn it into ref
prime ferry
might be easier if you were to get rid of the bottom left corner first instead o...
can i change one row multiple times?
brazen hare
multiply R1 by -1, add R3 - R1 -> R3, R3 - 3R2 -> R3
might be wrong though
prime ferry
multiply R1 by -1, add R3 - R1 -> R3, R3 - 3R2 -> R3
might be wrong though
didnt work, nothing got turned to zero
brazen hare
didnt work, nothing got turned to zero
it should at least turn the bottom left into zero?
im continuing on the matrix you have in the image btw
prime ferry
it should at least turn the bottom left into zero?
could i just cancel out -x_1 in R1 and x1 in R3?
brazen hare
could i just cancel out -x_1 in R1 and x1 in R3?
yes that would work too
prime ferry
does the first column of row 1 have to be 1 for it to be considered an echelon?
brazen hare
does the first column of row 1 have to be 1 for it to be considered an echelon?
some people say yes, some people say no, that the first column of row 1 only has to be 1 for reduced row echelon form. Consult your textbook for what it says on it.
odd edgeBOT
@prime ferry Has your question been resolved?
proud verge
Well each cos has to equal 1/3pi
Sir the thing is how did you know it has to be π/3
proud verge
<@1235039991545987084>
Sorry sir I am ill I slept
odd edgeBOT
Available help channel!
sick fossil
odd edgeBOT
sick fossil
are both false?
pastel steeple
is there more context? is O like... worst case complexity of an algorithm lmao
odd edgeBOT
@sick fossil Has your question been resolved?
sick fossil
is there more context? is O like... worst case complexity of an algorithm lmao
thheres no more context
juz dis
pastel steeple
... okay i wont pretend i know what O is then 
odd edgeBOT
faint knot
np
odd edgeBOT
Available help channel!
languid verge
can someone teach me recurrence relation
odd edgeBOT
can someone teach me recurrence relation
languid verge
questions like these
Solve an = 3an−1 − 2an−2
wooden python
recurrence relations come in many shapes and sizes, do you mean specifically linear recurrence relations?
languid verge
yess
an − 3an−1 + 2an−2 = 2n How so i solve this 😭
what am i even supposed to do in this
wooden python
ok well step 0 is to write it properly or send a picture
did you mean:
$a_n - 3a_{n-1} + 2a_{n-2} = 2n$
Ann
languid verge
languid verge
did you mean:
```tex
$a_n - 3a_{n-1} + 2a_{n-2} = 2n$
```
yess
languid verge
idk
wooden python
hopefully you at least know the difference between these.
languid verge
😭
wooden python
or are you telling me you do not know the difference between multiplication and exponentiation 
wooden python
bruh what.
wooden python
$10 \times 3$ vs. $10^3$
clever fjordBOT
Ann
wooden python
are you really telling me you can't tell the difference here
languid verge
oh i knowthis
wooden python
between times and power
languid verge
lol
wooden python
then why do you say you dont know the diff between that
languid verge
i know what multiplications and power is
wooden python
sounds like you're more stressed/panicked than un-knowledgeable
languid verge
then why do you say you dont know the diff between that
you were using proffesional terms
like exponential
so i got confused
wooden python
i was using utterly standard terms in math
"exponent" is the usual name for ^
anyway:
look up other vids on youtube with "linear recurrence relations with constant coefficients"
this isnt really a topic that can be taught over a discord chat easily
languid verge
ok
odd edgeBOT
help?
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).
languid verge
https://www.youtube.com/watch?v=d5jTxBNK6OU
is this question have mentioned that
a0 = 1
a1 = 0
but the questions i have dont do that
wooden python
you don't have any initial conditions, yeah
best you can do in that case is to give the general solution
& skip the step of figuring out the coefficients to match the first 2 terms
languid verge
ok ill try to solve one question on my own
languid verge
https://www.youtube.com/watch?v=d5jTxBNK6OU
why did he take 2, 3 for x^2 - 5x + 6 = 0
wooden python
solving a quadratic equation...?
languid verge
yea
languid verge
i used to
wooden python
well go review that
languid verge
dont remember now
red perch
As a Calculus 1 student, I've got a question that is for integrals
red perch
Is Indefinite Integral same as Integral from Positive infinity to negative infinity
jolly halo
no
red perch
How so?
jolly halo
why so?
red perch
Because indefinite wasn't it just Positive infinity to negative infinity
wooden python
Is Indefinite Integral same as Integral from Positive infinity to negative infi...
an integral involving infinity of any kind is called an improper integral.
red perch
Since you got no boundaries
wooden python
indefinite vs. definite is a different thing
indefinite just means antiderivative
definite means area under the curve between specific bounds
red perch
So Indefinite Integral was just trying to find the original function right?
On the other hand, That integral from Positive to negative infinity was just trying to find its value?
wooden python
So Indefinite Integral was just trying to find the original function right?
"original function" is bad phrasing
actually no all of this is bad phrasing
jolly halo
So Indefinite Integral was just trying to find the original function right?
On t...
function doesnt have a value , definate was just trying to find area under curve
wooden python
you're doing calculus 1? i think it'll be a while before you even see integrals from or to infinity.
red perch
definite means area under the curve between specific bounds
Oh alr I get it now... So there is no other way to explain it rather than this
Which is its definition are DIFFERENT
wooden python
i mean yeah the defns are different by a long shot.
rapid echo
Could someone be able to explain to me how to interpret this diagram (https://en.wikipedia.org/wiki/Type_I_and_type_II_errors)
rapid echo
odd edgeBOT
@rapid echo Has your question been resolved?
odd edgeBOT
@rapid echo Has your question been resolved?
odd edgeBOT
@rapid echo Has your question been resolved?
odd edgeBOT
@rapid echo Has your question been resolved?
west elbow
Which part is confusing to you, and also are you refering to the diagram top left or the bottom one (ROC curve)?
Furthermore, if nobody is available or don't see this thread, you might want to post in #probability-statistics
mystic nova
-# I wonder how long this channel will last considering the last one....
prime ferry
I think I've finally finished this but I just wanna make sure. Thoughts?
odd edgeBOT
I think I've finally finished this but I just wanna make sure. Thoughts?
@prime ferry Has your question been resolved?
glossy basin
Shouldn't this be +1
Shouldn't this be -6
what about you put your x1,x2,x3 values in original equations and verify your solution
odd edgeBOT
@prime ferry Has your question been resolved?
prime ferry
I am pretty confident that I have solved it this time
prime ferry
Just checking if I have made any errors
odd edgeBOT
@prime ferry Has your question been resolved?
old quail
I am pretty confident that I have solved it this time
1st transformation should be wrote "R3=R3+R1"
Also somewhere the one disappeared while evaluating x1
And you should describe variables using only free variables so it would be something like x1=x3+..., without x2
prime ferry
And you should describe variables using only free variables so it would be somet...
a bit confused by this part
old quail
Just substitute x2 for what you have already calculated
prime ferry
oh
old quail
Something like x1=3x2+...= 3(3+3x3)+...
prime ferry
prime ferry
It should be x1**+**3x2+...
row 2 is 0,1,-3 = 3 tho?
prime ferry
The first row has a negative x1 tho?
prime ferry
Yes, but positive x2
old quail
Somehow x3 changed into x2 in 1st equation
prime ferry
Somehow x3 changed into x2 in 1st equation
(Just noticed I accidentally made the last 3x_3 3x_2, ignore that i just fixed it)
old quail
If you small mistake in last transformation, everything will be fine
prime ferry
are you saying i made a small mistake in the last transformation or that i fixed a small mistake in the last transformation?
old quail
There' still a small mistake
prime ferry
There' still a small mistake
is it the x3 i accidentally left on the -3?
old quail
Yeah, it's this
old quail
Not sure if I you send wrong photo or I understood you wrong
I meant the last expression should be x1=8+3x3
old quail
Now everything is good
old quail
No problemo
Next time if you're not sure about solutions, you can check if they work for original equations
odd edgeBOT
odd edgeBOT
Available help channel!
errant pine
can anyone please explain why only these are the rational functions?
safe vapor
A rational function is one that can be written as the ratio of two polynomial functions. a polynomial function is $p(x) = a + bx + cx^2 + dx^3 + ...$
clever fjordBOT
Stitches
safe vapor
$5-6x^{-5}$ is not polynomial, since a polynomial does not have a "-5" coefficient
clever fjordBOT
Stitches
errant pine
$5-6x^{-5}$ is not polynomial, since a polynomial does not have a "-5" coefficie...
yeah understood
i dont get how G is a rational function
safe vapor
Why wouldn't it be
errant pine
Why wouldn't it be
it has sqrt 5
doesnt that go against the rules of being a polynomial?
safe vapor
you're confusing the coefficient with the variable. $1 + \sqrt(2)x+ \pi x^2$ is a polynomial. The number beside the x can be anything you want, the important part is that the power of x is a positive whole number
clever fjordBOT
Stitches
errant pine
you're confusing the coefficient with the variable. $1 + \sqrt(2)x+ \pi x^2$ is ...
ahh okay
west elbow
you're confusing the coefficient with the variable. $1 + \sqrt(2)x+ \pi x^2$ is ...
use \sqrt{2} for nicer formatting. Also a question to you, original poster please ignore this so I don't further confuse you; how do we feel about B. if we multiply top and bottom with x^5
safe vapor
use `\sqrt{2}` for nicer formatting. Also a question to you, original poster ple...
Abstract algebra isn't really my thing, but technically I think it can be classified as a rational.
odd edgeBOT
Available help channel!
shrewd trellis
I’m not sure if I’m on the right track
odd edgeBOT
I’m not sure if I’m on the right track
simple zealot
looks right to me
shrewd trellis
I’m not sure if I’m on the right track
what about this
simple zealot
I’m not sure if I’m on the right track
looks right as well, it's just double checking the multiplications
unkempt lichen
wrong works
shrewd trellis
how?
unkempt lichen
oh wait that's a multiplication
shrewd trellis
ya
shrewd trellis
I’m not sure if I’m on the right track
im a bit stuck on the next step
unkempt lichen
looks ok
outer wadi
notation question: f(A) isn't the ordered pairs from A to Y but just the set of y values in it's range right?
rough birch
yeah f(A) is just "all points y in Y such that for some x in A, f(x) = y"
odd edgeBOT
odd edgeBOT
Available help channel!
grim cliff
Hey
grim cliff
4 if
mystic saffron
bro just posted his name on a public discord server
grim cliff
Yo please help
final nexus
draw the line f(x)=-8 and then rub out everything except between -10 and -6
and then do the same for the rest is what I am assuming you have to do
golden sonnet
@grim cliff maybe this is correct for the 1st one
grim cliff
Ok thanks
grim cliff
Yea it’s correct
odd edgeBOT
<@692142981116985364> maybe this is correct for the 1st one
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
golden sonnet
As a helper, please do not give out answers that could be copied as a homework s...
wtf?
i just cross verified my answer
well this server in itself is weird
odd edgeBOT
@grim cliff Has your question been resolved?
honest hull
odd edgeBOT
amber veldt
real part and imaginary part
if a complex number is x+iy, where i^2 = -1 and x and y are real
then Re(x+iy)=x, Im(x+iy)=y
honest hull
Also I wanna study maths in depth, like i wanna know these concepts graphically and connect it to trigo etc. So any yt channel suggestion?
honest hull
real part and imaginary part
Ty
lean yew
organic chemistry tutor, 3b1b
amber veldt
#book-recommendations check there
lean yew
khan academy too
amber veldt
for a BOOK about complex numbers, I highly recommend Churchill and Brown
it has like 8 editions so it's cheap
honest hull
I saw a vid for complex numbers from organic chemistry but cant understand anything
honest hull
for a BOOK about complex numbers, I highly recommend Churchill and Brown
Idk i can't understand from books😭
amber veldt
well, ask in #book-recommendations , despite the name you can ask about videos there too
odd edgeBOT
honest hull
.reopen
odd edgeBOT
✅
honest hull
In my class, we have completed domain, range functions, etc., complex numbers and going to finish trigonometric equations now. I haven't done anything! What do I do? Should I do complex numbers or trigo? I'm just introduced to these angles pi/4, pi/3 and these are just blowing my mind! I can't make any graph in my brain, i don't understand relations, plus I can't find anything good on yt either! What should I do????? I'm cooked🥀🥀
golden sonnet
In my class, we have completed domain, range functions, etc., complex numbers an...
is the whole batch of your classmates suffering or is it you only?
honest hull
is the whole batch of your classmates suffering or is it you only?
They've got some sorta coaching afterclass so they're pretty fine with it
golden sonnet
contact them and get yr doubts cleared or if theyre not helping dm me
honest hull
They'll not help me🥀
golden sonnet
ill try to fix yr trigo
honest hull
ill try to fix yr trigo
Really?
honest hull
Tysmm❤️
Hope you don't ask ask for money after that😭
Btw can you tell me in what sequence should i study now?
Complex no.s first or trigo?
golden sonnet
Complex no.s first or trigo?
trigo
golden sonnet
Hope you don't ask ask for money after that😭
im a 12th grader why would i ask money for concepts😔 already im broke asf
no cash on me🥀
golden sonnet
Then why did the teacher teach complex no. First?
course restrictions prolly
lean yew
Then why did the teacher teach complex no. First?
we aren't your teacher lmao
but yeah probably syllabus related issues
honest hull
I'll obv trust yall than my teacher
lean yew
i'd rather you take our word, compare it against your teacher's, then judge for yourself
golden sonnet
i'd rather you take our word, compare it against your teacher's, then judge for ...
thats the ✅ mentality
honest hull
Trigo is so intimidating🥶🥶
honest hull
There's still 20 days left for the tests to start
golden sonnet
Trigo is so intimidating🥶🥶
how?
lean yew
Trigo is so intimidating🥶🥶
for trig
honest hull
That's a lot of time ig😭
lean yew
you just need to learn one thing
honest hull
The formulas?
golden sonnet
send a random qn from the exercise once
lean yew
and that one thing is (fortunately or not) somehow known from me
the unit circle
from there, you can derive a lot of useful formulas
honest hull
from there, you can derive a lot of useful formulas
Ya inorder to have that elite power you gotta need a good lecture
Which i unfortunately unable to find on yt
honest hull
are you a uni student?
Nope
honest hull
I need a good conceptual knowledge of the things right
lean yew
Ya inorder to have that elite power you gotta need a good lecture
tbh i have a good teacher and a good book, not sure about yt but i use yt now merely to brush up
lean yew
I need a good conceptual knowledge of the things right
if you seek understanding, yes
if you seek to pass tests, eh....? i don't encourage this mentality but if you only want to pass tests you can technically scrape by without much
from concepts you can get a lot of stuff though
honest hull
I want understandingggg
honest hull
from concepts you can get a lot of stuff though
Right you can easily get over the tests with concepts
golden sonnet
just checking - are you above 15?
wbu
lean yew
I want understandingggg
that's the spirit
honest hull
just checking - are you above 15?
Yup I'm not a prodigy kid😭
honest hull
turning 15 in three months
Woah but you are
golden sonnet
myself 17
lean yew
for trig, the most basic thing you should start from is the unit circle
honest hull
Ok
lean yew
a help channel's probably not the best place to start a crash course in trig
but let me dig up an old drawing i did for a helpee two months ago
golden sonnet
for trig, the most basic thing you should start from is the unit circle
wb the extreme basic definition of sine and cosine etc? that it is a ratio of any 2 given sides of a triangle?
lean yew
wb the extreme basic definition of sine and cosine etc? that it is a ratio of an...
oh we can define it with the unit circle as a visual aid
this is the diagram
golden sonnet
after that comes unit circle then formulas and then solns to trignometric eqns
lean yew
yes, i know, it's a shitty diagram, i drew this in like 30 seconds
honest hull
wb the extreme basic definition of sine and cosine etc? that it is a ratio of an...
I've some basic knowledge of trigo
lean yew
i would prefer OP learn ASTC as a consequence of the unit circle
but if OP wants to memorize ASTC directly, sure
golden sonnet
isnt unit circle and astc same?
golden sonnet
but if OP wants to memorize ASTC directly, sure
op?
lean yew
original poster
lean yew
isnt unit circle and astc same?
not exactly. ASTC is a simplification of the unit circle and only shows the signs
the unit circle is the visual diagram itself
lean yew
ASTC provides no motivation as to how the formulas came about
golden sonnet
not exactly. ASTC is a simplification of the unit circle and only shows the sign...
unit circle has unit triangle in it right
lean yew
How to derive formulas?
the definitions of the main formulas are fixed
honest hull
How to apply the unit circle to each concept like in complex numbers
lean yew
ok hold up too many questions in one go
honest hull
Kk
golden sonnet
How to apply the unit circle to each concept like in complex numbers
roots of unity?
lean yew
how to visualize stuff: i draw
i mean, literally
this diagram i drew in paint in like half a minute
honest hull
You won't know what to draw😭
lean yew
the unit circle is the easiest thing to draw
just draw a + sign (make the arms longer)
then draw a circle whose center is the center of the + sign
done!
honest hull
Like I've seen people using graphs, unit circles and coordinate geometry to solve the deadliest looking algebra qs super easily
lean yew
unit circles can't really solve algebra unless there's like a sine or smth in there
but as for how to get intuition as to what to draw
practice
honest hull
Thankyou
odd edgeBOT
@honest hull Has your question been resolved?
golden sonnet
I'll obv trust yall than my teacher
mate u from the west? america?
atomic lotus
is there anyone willing to sit in a call with me and help me with ap calc
pastel steeple
is there anyone willing to sit in a call with me and help me with ap calc
you can just send it here as text. voice doesnt have any advantages
atomic lotus
i dont know where to even start here
i only know how to find continuous graphs by checking left and right limits
proven harbor
try to identify points of discontinuity
atomic lotus
holes?
proven harbor
yes
atomic lotus
so would I ignore the (x+0.5)
proven harbor
nope
atomic lotus
do I plug in the x intercepts of the options??
proven harbor
as the num and denom both has x+0.5, your first instint would be to cancel them
but you have to also be careful about if it can be of the form 0/0
atomic lotus
wdym 0/0
proven harbor
the indeterminant form
atomic lotus
okay
proven harbor
ok, tell me the value of f(-0.5)
atomic lotus
0/0?
proven harbor
yes
so its not defined
hence this is a point of disconti
do you see why i specifically chose -0.5?
atomic lotus
yes
atomic lotus
by plugging in the x values of the options?
proven harbor
by trying to make a 0/0 form
atomic lotus
I understand what an indeterminant form is but I'm confused on how to relate the points they gave me to the function
because when I plug the x values into the function they dont give me holes
proven harbor
ok so at x=-0.5, f(x) is not continnuous
so any interval which has x=-0.5 cant be continuous
atomic lotus
yes
pastel steeple
I understand what an indeterminant form is but I'm confused on how to relate the...
the answer choices arent holes dear, they're open intervals