@dire violet Has your question been resolved?
#help-10
obtuse pebbleBOT
obtuse pebbleBOT
@dire violet Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
ok im not sure why.. i got a different answer
the other root is. 2+5i
so
i did
- 2+5i + 2-5i + a + b = 4
and
- ab(9) = -29/4
- 4 + a + b = 4
a + b = 0
a = -b
- ab = -29/36
a^2 = 29/36
a = +/- sqrt 29 / 6
what went wrong?!
the answer was 1/2
HELP
<@&286206848099549185>
supple coral
You can divide the quartic by the root expressions you know to get a quadratic, then just solve that. Not sure what b is trying to say. As in don't use the insane radical solution?
normal cairn
i think what dapro did is he found 2 solutions and tried to find the other two by creating a system with vietta
wary meadow
2) ab(9) = -29/4
should be ab(29)=-29/4
wary meadow
(2+5i)(2-5i)=29
timid silo
You can divide the quartic by the root expressions you know to get a quadratic, ...
good idea
wary meadow
maybe thatll clear thingd up
wary meadow
You can divide the quartic by the root expressions you know to get a quadratic, ...
but the qn asks not to solve tho?
timid silo
maybe thatll clear thingd up
thanks 서정
wary meadow
nwws
timid silo
.close
old hollow
Can someone explain how to get the horizontal asymptote?
obtuse pebbleBOT
Can someone explain how to get the horizontal asymptote?
supple coral
Take a limit as x -> infinity.
obtuse pebbleBOT
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obtuse pebbleBOT
obtuse pebbleBOT
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sharp sequoia
i need help with chromatic polynomial
obtuse pebbleBOT
i need help with chromatic polynomial
sharp sequoia
i know you can divide the below graph to two small graph like you can seen above
y(y-1)(y-2) function above. But i do not know how to continue
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heavy bramble
Try to simplify
lusty tide
Hello, I need help with this problem. I understand the meaning behind it all is, that if ∂(a,b,c,d) = ad - dc = 0 the line vectors or column vectors are collinear. Which is why the three conditions are equivalent. However, I do not understand how to prove it. I was told to prove equivalency by showing 1 => 2 => 3 => 1, but nothing else about how to prove something like this and have been trying for several hours at this point.
obtuse pebbleBOT
Hello, I need help with this problem. I understand the meaning behind it all is,...
lusty tide
This was one of my attempts for showing 1 => 2.
obtuse pebbleBOT
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lusty tide
<@&286206848099549185>
obtuse pebbleBOT
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timid silo
This is one of the questions on my math hw and we weren't taught how to do this so i'm completely lost
obtuse pebbleBOT
This is one of the questions on my math hw and we weren't taught how to do this ...
timid silo
Like
I got that the perimeter is 8w + 4h
but i don't know how to write all of that in terms of only L
I can get h = (1/4)(L-8w) and the reverse with w =
but how do i write the whole thing in terms of only h i don't get it
Am I supposed to write it like this so that it's technically still about L?
Also I just have no clue what the first derivative test has to do with this
oh wait
obtuse pebbleBOT
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round stratus
Hi guys ! I need some help making sure of something
obtuse pebbleBOT
Hi guys ! I need some help making sure of something
round stratus
So if E is a vector space of finite dimension
And f is a linear application on E
We’ve got kerf^k+1 included in kerf^k+2
Where k in an integer
But do we have that
Alright I’ll design the first ker as N and the second as M to make writing things easier
So do we have f^k(N) included in f^(k+1)(M)
vale pelican
yes, because f^k(N) = {0}
vale pelican
word
round stratus
Word?
vale pelican
my bad lol
round stratus
Oh alright
I’ve been stuck on it for a while now and I know it’s true because of another inequality of dimensions I have but can’t use that cause I have to use this to prove it so I am stuck there
round stratus
It is included in it
Don’t know about the other way tho lemme check
Doesn’t seem like it’ll work
Is there anything we can use based on knowing that kerf^k is an increasing sequence while imf^k is a decreasing one
Switched to trying to prove that f^k(N) is included in Imf^k+1
If I prove this I’ll be able to use it to prove an inequality I have and then use it to prove the first problem
obtuse pebbleBOT
@round stratus Has your question been resolved?
round stratus
That doesn’t seem to be correct
So back to the first step
I’m gonna stop here
And try later
!close
.close
obtuse pebbleBOT
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patent mortar
In how many ways can four men and eight women be seated at a round table if
there are to be two women between consecutive men around the table?
For this problem, why is my solution of 4! * 8! / 12 wrong?
obtuse pebbleBOT
In how many ways can four men and eight women be seated at a round table if
the...
drifting wraith
hmm
oh ok
like, if you don't divide by 12 you have 4! × 8!, but how is that a seating arrangement
usually the part before / 12 would already count something
idk, i'm confused
patent mortar
My logic going in was to consider the positions for men
and then consider the possible sequences of the women in between the men afterr
and then divide by 12 since you can start from any of them to get an equivalent permutation as this is circular
drifting wraith
yeah so like you count arrangements that start with a man
patent mortar
yeah
patent mortar
so there would be 4 repeats of each one
I am not sure what you mean exactly
drifting wraith
like if there's 3 people
you would count 3!
and divide by 3 because clearly there's 2 aragnements that repeat 3 times
amd if you imagine what 4! × 8! looks like, it wouldn't have all 12 versions, only those that start with a man
so that's why, i can't explain any better
patent mortar
That makes sense
So you are saying that the order depends on the man that we hold fixed?
drifting wraith
you're not holdng anyone fixed
if you did, there wouldn't be an issue in the first place
with 3 people you would get 2! immediately, because there 2 unfixed people
and here you would get 3! × 8! because there's 3 unfixed men and 8 women
it's because you allow all people to move, division appears
drifting wraith
if you do 3(4! × 8!) you would count all arrangements
times 3 because there's 3 ways it could look like
then / 12 works
patent mortar
.reopen
obtuse pebbleBOT
✅
patent mortar
if you do 3(4! × 8!) you would count all arrangements
Are the balls supposed to represent blocks of a man and two women?
like the smaller ones?
drifting wraith
they are men
hazy flicker
indeed
drifting wraith
could be blocks too
obtuse pebbleBOT
@patent mortar Has your question been resolved?
light drift
Consider the transformation L : V → R3 give by
L(x ) = (x1, x2, x4 + x3).
where
V = {⃗x = (x1, x2, x3, x4) ∈ R4 | x4 = x3 − x2}.
- Prove that V is a vector subspace of R4 and determine its dimension
I've proven it is a vector subspace as it is closed under addition + scalar multiplication, but I don't understand how to determine V's dimension
obtuse pebbleBOT
Consider the transformation L : V → R3 give by
L(x ) = (x1, x2, x4 + x3).
where
...
brave bramble
Basically:
It's 3. R4 has dimension 4, and putting one restriction on it reduces the dimension by 1.
However, you should want to prove it:
You can find a span for V. Typically done by putting this into a matrix
x1 = x1
x2 = x2
x3 = x3
x4 = x3 - x2
And reducing
quaint radish
I hate to ask this vague of a question as my first question here, but I’m genuinely so lost on Inverse trig functions. I pretty much get sin^-1(wtv) means what angle gives you a sin of wtv. I got number 13, inverse sin of 0 is 0, but I’m already lost on 15.
obtuse pebbleBOT
I hate to ask this vague of a question as my first question here, but I’m genuin...
orchid wind
here
it helps to draw a reference drawing
what this tells us
is arccos is from [0,pi]
and arcsin is from [-pi/2,pi2]
so for your example
15
we draw this
not what angle is at that x
orchid wind
yes
it is
3pi/2 = -pi/2 essentially
but remember
the range of arcsin
[-pi/2,pi/2]
quaint radish
ah ok
quaint radish
is it easier &/or better to remember the points on the unit circle >pi as negative fractions or improper ones?
Like is -pi/2 easier to remember than 3pi/2
quaint radish
ah ok
orchid wind
7pi/6 is q3
quaint radish
ok
I’ll try the problems & come back if I need help w the third section
Cus it looks like an extra concept
ok I thing I got the first kind
the second kind I think you’d Js cancel cos & inverse cos out but I remember teacher saying theres situations you can’t do that. & i don’t know what I’d do w 4pi/5 after I cancelled anyway
dapper wing
how do I find the equation for this summation?
obtuse pebbleBOT
how do I find the equation for this summation?
worn yoke
can you classify the type of sum this is?
dapper wing
im not sure
wary badger
ggggggg
dapper wing
can you classify the type of sum this is?
the only one I know of is natural numbers
the exponent ones I can't seem to identify
wary badger
what class do you usually take after algebra 1?
worn yoke
well what classifications of sums have you learned?
dapper wing
well what classifications of sums have you learned?
honestly, I've been going over the notes and the textbook, and while we are given examples of summations, we arent given the classifications of them
so like for the natural numbers manipulation, I could base that off of n(n+1) / 2
but I cant find the one for exponents
and I don't know how to google it
worn yoke
two classifications of sums you may have encountered are arithmetic and geometric sums
worn yoke
no, they are both types of sums
an arithmetic sum is the sum of an arithmetic sequence, where the difference between each term and the next term is constant
a geometric sum is the sum of a geometric sequence, where the ratio of each term and the next term is constant
dapper wing
oh
i found the sum of geometric sequences, but my teacher used it for an induction process instead of defining what it even is to begin with
worn yoke
well if we apply that here, are the terms we're adding part of an arithmetic or geometric sequence?
dapper wing
geometric
worn yoke
so we can apply the formula for that
dapper wing
so we can apply the formula for that
is it sosmething like 1/3^(n-1)
actually thats not the summation
dapper wing
so we can apply the formula for that
i think its this but idk what r is
worn yoke
well it should be a formula like [ \sum_{k = 0}^n r^k = \frac{r^{n+1} - 1}{r-1}]
warm shaleBOT
cloud
dapper wing
well it should be a formula like \[ \sum_{k = 0}^n r^k = \frac{r^{n+1} - 1}{r-1}...
ya but I don't know what the "r" is
worn yoke
note that [ \frac{a^n}{b^n} = \ab(\frac ab)^n ]
warm shaleBOT
cloud
dapper wing
note that \[ \frac{a^n}{b^n} = \ab(\frac ab)^n \]
apparently this worked, not sure why
obtuse pebbleBOT
@dapper wing Has your question been resolved?
cosmic raven
Why does my teacher multiply the perimeter and area together here?
obtuse pebbleBOT
Why does my teacher multiply the perimeter and area together here?
safe haven
Why does my teacher multiply the perimeter and area together here?
where
safe haven
you want A as a function of r
A = something something r
but your A function has a h in it, we dont want it
so you get h in terms of r from the perimeter, then replace it with that
cosmic raven
so you get h in terms of r from the perimeter, then replace it with that
ohh alright, if the question was just to write an equation for the area, you wouldn’t need to do that?
cosmic raven
ok I see
safe haven
so you gotta remove any other variables that is not r
obtuse pebbleBOT
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silk monolith
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hasty lily
Let $A \subset 2^\mathbb{R}$ be a countable collection of sets of real numbers such that every finite subset of $\mathbb{R}$ is a subset of some set in A.
Show that there exists a chain $S_1 \subset S_2 \subset S_3 ...$ of subsets of $\mathbb{R}$ such that $\bigcup_{i \in \mathbb{N}} S_i = \mathbb{R}$ and $\forall i \in \mathbb{N}, \exists a \in A | S_i \subset a$.
obtuse pebbleBOT
Let $A \subset 2^\mathbb{R}$ be a countable collection of sets of real numbers s...
warm shaleBOT
chloe
patent osprey
what have you done so far?
hasty lily
well pretty much nothing. i dont have any ideas
obtuse pebbleBOT
@hasty lily Has your question been resolved?
obtuse pebbleBOT
@hasty lily Has your question been resolved?
hasty lily
yep
obtuse pebbleBOT
@hasty lily Has your question been resolved?
obtuse pebbleBOT
@hasty lily Has your question been resolved?
hasty lily
R represents real numbers here i assume?
I just realized why i havent been able to prove this
its not true
.close
obtuse pebbleBOT
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frosty fractal
obtuse pebbleBOT
frosty fractal
What exactly do they mean by A* is a polynomial in A?
I think I am having a brain dead moment
kind hawk
A* = p(A) for some polynomial p
frosty fractal
so like it can be written as a function of A?
kind hawk
yes
but just as a function of A is not interesting
the interesting part is that this function is a polynomial
kind hawk
trivially A* is a function of A, namely take A, transpose it and conjugate each entry
but now it could be for example that A* = 13A^2-7A+3I
frosty fractal
Okay that makes some more sense on why it's relevant, thank you. That's actually pretty cool
.close
obtuse pebbleBOT
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signal yacht
Please help
obtuse pebbleBOT
Please help
signal yacht
ill be honest I dont relly know how to go about this
alpine bison
$\log_2(2^{-n})=-n$
warm shaleBOT
everg
old lily
u wanna split the integral into parts where u know the value of the floor(log_2(x))
alpine bison
$(0,2]=\bigcup_{n\ge -1} (2^{-n-1},2^{-n}]$
warm shaleBOT
everg
signal yacht
oh my
old lily
floor(log_2(x)) = -n iff -n <= log_2(x) < -n+1
signal yacht
i dont think Ive learnt this integration technique
old lily
it's ok
can u solve -n <= log_2(x) < -n+1 for x
i'm using -n cuz on (0,2) log_2(x) is negative
signal yacht
yes
old lily
it goes from -inf to 0 if u think about it
signal yacht
okay
signal yacht
can u solve -n <= log_2(x) < -n+1 for x
could you explain a little how you made this equation?
alpine bison
you have to use $\log_b(b^n)=n$
warm shaleBOT
everg
alpine bison
in this case b=2
old lily
floor(log_2(x)) = -n iff -n <= log_2(x) < -n+1
it's from here
do you understand the floor function
like floor(x) = 2 iff 2 <= x < 3
alpine bison
it's from here
what sheaf would you put on the klein bottle ?
signal yacht
do you understand the floor function
i think i understand it, but ive never really worked with it in class
alpine bison
i think i understand it, but ive never really worked with it in class
your integral just turn out to be an infinite summation...actually your function is not continous so you cannot apply the foundamental theorem
of calc.
signal yacht
oh wow
old lily
what sheaf would you put on the klein bottle ?
structure sheaf
signal yacht
i think I might be doomed for this test lmao
alpine bison
structure sheaf
of continous functions? differential functions ? or some other type ?
old lily
C^2 functions ig
alpine bison
oo I see
old lily
i think i understand it, but ive never really worked with it in class
umm maybe try sketching its graph
signal yacht
i
old lily
huh
signal yacht
i think this might be too advanced, sorry i didnt realise when I asked the question
old lily
like the complex number?
signal yacht
like the complex number?
Accidentally hit enter lol
old lily
ohh haha
signal yacht
while I have your attention, woudl you mind if I asked a different question instead?
old lily
okay
signal yacht
am I right in saying that the discriminant should be 0 if I factor out an x?
nevermind
.close
obtuse pebbleBOT
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rain yoke
How do i calculate what percent an amount is from a total? Like 256 out of 280. I did read you do 256/280x100 but i don't understand why x100
obtuse pebbleBOT
How do i calculate what percent an amount is from a total? Like 256 out of 280. ...
tardy epoch
just definition of percentage
last pilot
rain yoke
Okay, thanks i'll read that it's so long since i studied so i've forgotten some
.close
obtuse pebbleBOT
heavy anvil
clear cosmos
You might get a better support in the early uni.
If this is linear algebra in uni then #linear-algebra or #elementary-number-theory if not then I’m Sorry
obtuse pebbleBOT
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obtuse pebbleBOT
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obtuse pebbleBOT
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dense schooner
can you help me in 2b
obtuse pebbleBOT
can you help me in 2b
obtuse pebbleBOT
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dense schooner
<@&286206848099549185>
velvet spoke
can you help me in 2b
if √x = tan
can you find √(x+1)
obtuse pebbleBOT
@dense schooner Has your question been resolved?
dense schooner
if √x = tan
can you find √(x+1)
What does that mean
velvet spoke
find √(x+1)
velvet spoke
now f becomes 4/pi arctan(sec - tan)
im sure you can take it from there
using this
obtuse pebbleBOT
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dark orchid
Is this right?
obtuse pebbleBOT
Is this right?
restive acorn
Looks ok
The exact answer would be in terms of logarithms
x = log(3)/log(8) - 11
red ice
warm shaleBOT
south's secret twin brother
dark orchid
yeah
obtuse pebbleBOT
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timid silo
Are here any ways to prove that A, C, and D Is 0 in the partial fraction of 1=a/x+b/x^2+c/(4-x)+d/(4-x)^2+e/(4-x)^3
obtuse pebbleBOT
Are here any ways to prove that A, C, and D Is 0 in the partial fraction of 1=a/...
@timid silo Has your question been resolved?
obtuse pebbleBOT
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boreal pier
can anyone help me setting up this integral please
obtuse pebbleBOT
can anyone help me setting up this integral please
boreal pier
<@&286206848099549185>
obtuse pebbleBOT
@boreal pier Has your question been resolved?
worn coyote
can anyone help me setting up this integral please
$$vol=\int_{-1}^1\int_{-3\sqrt{1-x^2}}^{3\sqrt{1-x^2}}\int_0^{x+3} dz dy dx$$
warm shaleBOT
EQUENOS
boreal pier
$$vol=\int_{-1}^1\int_{-3\sqrt{1-x^2}}^{3\sqrt{1-x^2}}\int_0^{x+3} dz dy dx$$
no need to convert to cylindrical?
worn coyote
no need to convert to cylindrical?
It's up to you
Tbh this particular volume can be calculated without any integrals
boreal pier
Tbh this particular volume can be calculated without any integrals
how so?
worn coyote
how so?
S = (area of the ellipse with axis 1 and 3) = 3 pi
h1 = 2
h2 = 2
V = 2 * 3pi + 3 pi = 9 pi
boreal pier
I really appreciate the help, God bless 🙏
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strange wraith
How do I know if something is exponential growth or decay when a is negative
strange wraith
Videos and sources states rules only about b
So I’m confused on questions like these
toxic oyster
i need help finding critical numbers
merry stratus
i need help finding critical numbers
please use other chat, i was using this one
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drowsy pollen
obtuse pebbleBOT
drowsy pollen
This is the original question
I understand why we have -3 and 5x^2, but I don't understand how the middle term is 2x
orchid wind
remember
worn yoke
2x^(1/2) = 2x^(1 - 1/2) = 2x * x^(-1/2)
timid silo
when does this not work?
obtuse pebbleBOT
when does this not work?
thorny idol
obtuse pebbleBOT
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obtuse pebbleBOT
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stable yew
i need help
obtuse pebbleBOT
i need help
meager mural
hi
stable yew
hiiiiiiiiiiiiiiiiiiiiiiii
meager mural
type ur qn
stable yew
How many 4-digit numbers can be formed from the digits 0 through 9 if no digit can be
repeated and the number should contain digits 2 and 6?
meager mural
for the purpose of this question, is 0123 a 4-digit number?
stable yew
yes
meager mural
The hard naive way: ((ways to choose 1 digit from 2-6) x (ways to choose 3 digits from 0,1,7,8,9)x(ways to interleave 1 digit with 3 digits)) + ((ways to choose 2 digits from 2-6) x(ways to choose 2 digits from 0,1,7,8,9) x (ways to interleave 2 digits with 2 digits)) + ((ways to choose 3 digit from 2-6) x (ways to choose 1 digits from 0,1,7,8,9) x (ways to interleave 3 digits with 1 digits)) + (ways to choose 4 digits from 2-6)
The trick:
(ways to choose 4 digits from 0-9) - (ways to choose 4 digits from 0,1,7,8,9)
meager mural
how would I find those?
check your textbook, course materials, or chatgpt for "permutations", or "ordered choosing without replacement". What is the formula that they give you?
obtuse pebbleBOT
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obtuse pebbleBOT
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vestal forge
what does mathematically tractable mean
obtuse pebbleBOT
what does mathematically tractable mean
vestal forge
what makes a range not tractable mathematically?
gilded needle
wdym by range in this context
vestal forge
statistics, highest minus lowest value in data set
this a bit confusing, i tried scouring the internet but all i see is mathematically tractable being used in more complex situations
timid silo
what does mathematically tractable mean
Pretty sure it refers to a problem that can be solved easily with simple math methods
worn yoke
can you show a picture of the full context?
vestal forge
It's just a sentence from my book. It's under the properties of a range. "Finally, the range is not tractable mathematically." Which just felt like it came out of left field
vestal forge
Pretty sure it refers to a problem that can be solved easily with simple math me...
i saw this one too, chatgpt tells me mathematical tractability is not applicable to range because there is no "complexity involved"
timid silo
I mean if your just analyzing it wouldn't it mean that range can't be solved with simple math solutions idk
vestal forge
what does simple math methods entail? is subtraction not a simple math method? im sorry, im really too stupid for this i guess i should stop fixating on this part and move on
worn yoke
it's difficult to really comment on it without further context
vestal forge
I see. That's all the context I could give. It's an elementary statistics books for freshmen, under a chapter for measures of dispersion with range being the first example for measure of absolute dispersion. I guess the author just randomly threw the term out
worn yoke
,rccw
warm shaleBOT
vestal forge
sorry! didnt know u could do that
trail musk
it just means "it's not easy to work with"
worn yoke
even though if you are given a data set it is easy to calculate, when you are considering more abstract properties of data samples, other measures of dispersion are easier to work with
obtuse pebbleBOT
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obtuse pebbleBOT
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sinful falcon
How do I sketch a graph of f(x) if f’ = 0 and f’’ = 4?
obtuse pebbleBOT
How do I sketch a graph of f(x) if f’ = 0 and f’’ = 4?
ember onyx
can you show the entire problem
sinful falcon
Uhhh yea I’ll be back then I was trying to recollect the question from memory lemme find it
.close
obtuse pebbleBOT
merry canyon
Uhhh yea I’ll be back then I was trying to recollect the question from memory le...
Hi
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gloomy pelican
May i get a hint for this pls? Let ( f : \mathbb{R} \to \mathbb{R} ) be a non-increasing function. Let ( a_0 \in \mathbb{R} ) and define ( a_{n+1} = f(a_n) ) for ( n \geq 0 ). Prove that the sequence ( (a_n) ) has at most two distinct limit points.
obtuse pebbleBOT
May i get a hint for this pls? Let \( f : \mathbb{R} \to \mathbb{R} \) be a non-...
warm shaleBOT
ω
gloomy pelican
so I have to do probably something like this: suppose there are some three limit points $L_1 < L_2 < L_3$, we have $f(L1 ) \geq f(L2) \geq f(L3)$
warm shaleBOT
ω
gloomy pelican
aand idk how to proceed from here
I can suppose that this sequence is divergent
otherwise we wouldnt have three limit points
<@&286206848099549185>
obtuse pebbleBOT
@gloomy pelican Has your question been resolved?
obtuse pebbleBOT
@gloomy pelican Has your question been resolved?
obtuse pebbleBOT
@gloomy pelican Has your question been resolved?
obtuse pebbleBOT
@gloomy pelican Has your question been resolved?
gloomy pelican
.close
obtuse pebbleBOT
short leaf
Does it always beacome 1 if you divide when its even number and add 1 when its odd number
short leaf
Does it always beacome 1 if you divide when its even number and add 1 when its o...
<@&286206848099549185>
timid silo
Huh
marsh glen
huh
marsh glen
the question
marsh glen
🤷♂️
timid silo
Aiyayayai
short leaf
Does it always beacome 1 if you divide when its even number and add 1 when its o...
If i apply these rules to any number does it always beacome 1?
For exempel 3 is odd so 3+1=4 and 4 is even 4÷2=2 2÷2=1
short leaf
the question
.
timid silo
For exempel 3 is odd so 3+1=4 and 4 is even 4÷2=2 2÷2=1
Doesn't that just mean that if u apply the rule to even number it always ends up at 1 if it's divisible by 2
💀💀💀 idk
short leaf
Doesn't that just mean that if u apply the rule to even number it always ends up...
? Like 8 is even so you divide always and get 1
marsh glen
the way you worded the question is bad
timid silo
the way you worded the question is bad
Yeah
Okay like I don't get why ur doing this for
Like
What is it for
marsh glen
i get what ur saying now tho with the example and the answer is yes
cause by definition, an odd number is just an even number plus 1
timid silo
? Like 8 is even so you divide always and get 1
Yes
short leaf
cause by definition, an odd number is just an even number plus 1
So always 1 all numbers
marsh glen
your wording is bad but yes
short leaf
your wording is bad but yes
Wouldnt this be the same in the Collatz conjecture ?
marsh glen
by adding 1 to an odd number, you make it even.
if u keep dividing an even number by 2, you will eventually get 1
no idea what that is
short leaf
no idea what that is
Look it up
obtuse pebbleBOT
Available help channel!
timid silo
For odd number multiply by 3 and add 1??
obtuse pebbleBOT
For odd number multiply by 3 and add 1??
timid silo
That thing??
short leaf
Wouldnt this be the same in the Collatz conjecture ?
Beacuse in the collatz conjecture, when its and even number= divide by 2 and if its an odd number= multiply by 3 and add 1, multiplying a odd number by 3 always gives a odd number and then the +1 to make it even
short leaf
That thing??
Yes
timid silo
Okay
timid silo
Isn't this like an unsolved problem
timid silo
Wtf was Lothar collz thinking when he introduced this 😭
short leaf
Wtf was Lothar collz thinking when he introduced this 😭
Why?
short leaf
Wtf was Lothar collz thinking when he introduced this 😭
Sorry if im talking in a way you dont understand, i would say that my english isnt that good
obtuse pebbleBOT
marsh glen
Sorry if im talking in a way you dont understand, i would say that my english is...
nw
ill look into the conjecture in a bit cause im helping someone else in another chat
obtuse pebbleBOT
✅
short leaf
Bc it's under my name idk why 💀
If the one i said, even= divide 2, odd= +1, always makes to 1 and the colletz thing is that when its an odd number you just multiply by 3 which always gives you an odd number and then add 1 to make it even so this would too always be 1?
obtuse pebbleBOT
@timid silo Has your question been resolved?
marsh glen
just saw a vid on it
collatz conjecture is slightly different to the first problem you stated
and the answer is idk
for the new question
there is a video you might be interested in that goes over the things in mathematics that are logically impossible to be proven or disproven https://www.youtube.com/watch?v=HeQX2HjkcNo
short leaf
and the answer is idk
To which question
obtuse pebbleBOT
To which question
short leaf
collatz conjecture is slightly different to the first problem you stated
Could you elaborate?
marsh glen
in the first one u said
get a number n
if even /2
if odd add 1
in this case. yes, it will always reach 1
short leaf
in the first one u said
get a number n
if even /2
if odd add 1
in this case. yes...
And what the diffirence between this and the collatz
marsh glen
because u dont scale it by a large factor like 3
or maybe i might be wrong, idk
ill have to check in depth but rn im not up for thta
its almost 11
short leaf
@tardy epoch
tardy epoch
What
short leaf
What
Does it always beacome 1 if you divide by 2 when its even number and add 1 when its odd number
short leaf
Does it always beacome 1 if you divide by 2 when its even number and add 1 when ...
If i apply these rules to any number does it always beacome 1?
tardy epoch
Alright just stop pinging me if you can't ask a coherent question
short leaf
Alright just stop pinging me if you can't ask a coherent question
No im serious
tardy epoch
So am i
short leaf
Maybe my english is bad
tardy epoch
Definitely stop pinging me
short leaf
.
When i apply theses rules, rules: even number= ÷2, odd number=+1, and if i do it with any number will it be 1, for example 3 is odd so 3+1=4 4÷2=2 2÷2=1
short leaf
When i apply theses rules, rules: even number= ÷2, odd number=+1, and if i do it...
<@&286206848099549185>
obtuse pebbleBOT
@short leaf Has your question been resolved?
obtuse pebbleBOT
@short leaf Has your question been resolved?
timid silo
@dusk widget sorry I took so long wanna continue?
obtuse pebbleBOT
<@456913063300431934> sorry I took so long wanna continue?
dusk widget
well uhh.. a couple things
- you really shouldn't ping individual users for help, and that goes for me too
- I can try to keep it going, but I also have to be off to bed sometimes soon
let's go for now, shall we?
ionic oar
hi
timid silo
1. you really shouldn't ping individual users for help, and that goes for me too...
You told me to pin you incase you forget-
dusk widget
well yes, but I thought you were coming back before the channel closed 
timid silo
I was just following orders from you 
dusk widget
you shouldn't open a new channel by pinging me 
timid silo
Oh okeh
dusk widget
it should be a channel where I've already helped you
timid silo
Okeh
Uhh let's continue with a new thing shall we?
It's the same thing but just the function of the formula
dusk widget
@thorny idol my apologies, but may you please stop 
reacting every message 😭
dusk widget
Uhh let's continue with a new thing shall we?
okay sure
timid silo
For now I kinda understand most parts of this
dusk widget
sure
timid silo
Sure
dusk widget
it'll be easier to explain triangle and square later
timid silo
Okk
dusk widget
the area of a rectangle is given by A = lw, where l is its length and w is its width
do you want me to explain where this comes from? 
timid silo
2 × 3?
dusk widget
yeah
timid silo
dusk widget
yes, though I should've added units to this problem
say that it's 2m x 3m
then the area is ...
fathom flicker
timid silo
6m
dusk widget
Austin, not now please
timid silo
^2
dusk widget
not +, *
timid silo
Multiply sorry
dusk widget
you're fine
dusk widget
do you want me to explain where this comes from? <:eeveethink:601029006418116608...
.
do you just want to accept it, or do I need to explain where this comes from? 
timid silo
Eh accept it
dusk widget
sure...
we can do that
I'll just drop this picture here though 
do you want to move onto the square or the triangle now
which one?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
dusk widget
@timid silo I have to go to bed now, so if you have further questions, please open a new help channel and wait for somebody else to respond
obtuse pebbleBOT
Available help channel!
rare sail
if a system of linear equations has the matrix
a b c
a b c
a b c
if they're the exact system of 3 linear equations, what would the eigenvector be and why?
obtuse pebbleBOT
if a system of linear equations has the matrix
a b c
a b c
a b c
if they're th...
gilded needle
well you know (1,1,1) is one eigenvector, right?
rare sail
well you know (1,1,1) is one eigenvector, right?
yea
gilded needle
are you asking for others? probably depends on a,b,c
you do know something about the eigenvalues though
rare sail
eigenvalue is 0 here is it not?
gilded needle
yea, because?
fossil crag
(bc,ac,-2ab) should be another
gilded needle
and what's the eigenvalue that goes with (1,1,1) eigenvector?
gilded needle
(bc,ac,-2ab) should be another
nice
fossil crag
and (-2bc,ac,ab)
rare sail
(bc,ac,-2ab) should be another
but how do you get that kinda eigenvector from this
fossil crag
but how do you get that kinda eigenvector from this
abc abc -2abc
or -2abc + abc + abc
gilded needle
(usual caveat that eigenvectors have to be nonzero, so depending on a,b,c these may or may not qualify)
rare sail
(usual caveat that eigenvectors have to be nonzero, so depending on a,b,c these ...
oh ok
fossil crag
anyways if all of a,b,c are non zero, there are at least two LI eigenvectors among (bc,ac,-2ab), (-2bc,ac,ab) and (bc,-2ac,ab)
otherwise if exactly one is zero, suppose it's c for example
then (b,-a,0) and (0,0,1) work
fossil crag
if exactly two are zero (for example b and c), then (0,1,0) and (0,0,1)
if all three are zero... pretty easy
rare sail
if all three are zero... pretty easy
eigenvector is undefined
fossil crag
eigenvector is undefined
no eigenvectors are defined
rare sail
oh uh 0 0 0
gilded needle
for the zero matrix, everything is an eigenvector (except (0,0,0))
fossil crag
since Ox = 0
rare sail
hm
ok so what if the matrix is
2 -1 1
-1 2 -1
1 -1 2
and i had to find its eigenvector given that an eigenvalue is 1?
cuz when i tried to solve (A-lambdaI)v=0
i ended up getting
x -y + z = 0
x -y + z = 0
x - y + z = 0
fossil crag
anyways the challenge is if a+b+c = 0, how to find the non zero eigenvalue
rare sail
ok so what if the matrix is
2 -1 1
-1 2 -1
1 -1 2
and i had to find its eigen...
im struggling with this because theres more than one free variable here
fossil crag
im struggling with this because theres more than one free variable here
if there are more than one free variable then no problem
x-y+z = 0
z = y-x
(x,y,z) = (x,y,y-x) = x(1,0,-1) + y(0,1,1)
rare sail
wait so its fine if i get more than one eigenvector from this eigenvalue?
fossil crag
it's never not been fine
rare sail
damnnn ok i got it then
fossil crag
there are eigenvalues with geometric dimension > 1
meaning eigenspace bigger than just a line
rare sail
whats an eigenspace
fossil crag
whats an eigenspace
the set of all eigenvectors of an eigenvalue + (0 vector)
it's a subspace
fossil crag
(x,y,z) = (x,y,y-x) = x(1,0,-1) + y(0,1,1)
so for example here
rare sail
ok nvm
fossil crag
the set of all eigenvectors of eigenvalue 1
is {x(1,0,-1) + y(0,1,1)} = span((1,0,-1),(0,1,1))
rare sail
wait that makes so much sense
cuz the eigenvectors of that eigenvalue would ultimately span in R3
ok i got it ty
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
patent socket
In here I thought it didn't had a vertical asymptote. I refactored it was 2(x+1)/(x+1)(x+1) = 2/(x+1). Here it would have a vertical asymptote if i would say that x = -1 (which is the correct answer). But when setting in x in the original function that would return 0/0. After refactoring the function, do we still look at what the original function looks like or not?
obtuse pebbleBOT
In here I thought it didn't had a vertical asymptote. I refactored it was 2(x+1)...
@patent socket Has your question been resolved?
warm shaleBOT
bruhmoment
patent socket
Yeah because it's basically the same, right? Does that mean that it wouldnt really matter?
Because before refactoring if we set in -1 it becomes 0/0, but after it would become 2/0
warm shaleBOT
bruhmoment
patent socket
So what really is the difference between a asymptote and discontinuity? Looks like they're quite the same
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
runic arrow
obtuse pebbleBOT
runic arrow
Shouldn’t it be C+lna?
tardy epoch
ln(a) = constant
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
restive ginkgo
Hello I need help with building a circuit - I am still an amateur when it comes to programming and etc
obtuse pebbleBOT
Hello I need help with building a circuit - I am still an amateur when it comes ...
restive ginkgo
Here is the table and the question, I was wondering how to get it an answer and what to do first and how to solve
Here it is in English, sorry
digital yew
Hey
restive ginkgo
Hello
digital yew
If I post 5 questions will you guys answer em?
digital yew
Ok
zenith raft
I’m asking for help too lol
omg hi
restive ginkgo
Hey
zenith raft
@patent crag look
restive ginkgo
Look where
zenith raft
sorry i will stop griefing this channel
restive ginkgo
Ah can someone please help
<@&286206848099549185>
What do I do here?
I know I am supposed to build a circuit but I don’t know how to get to the outcome, how to set it up and what to do and etc
<@&286206848099549185>
What do I do when I get no response?
<@&286206848099549185>
obtuse pebbleBOT
@restive ginkgo Has your question been resolved?
restive ginkgo
<@832966124224118794> Has your question been resolved?
No
<@&286206848099549185>
.close
torpid maple
how do i swap the double integral from dydx to dxdy? ive drawn the graph but Im not sure whats the upper bound for x. For now my lower bound for x is 0 but not sure if thats right
obtuse pebbleBOT
how do i swap the double integral from dydx to dxdy? ive drawn the graph but Im ...
torpid maple
So far this is what I got, not sure if I’m on the right track though
deft ginkgo
Doing it with the dydx approach would be the way since it's simpler to compute, and that integral is properly set-up, you're on the right track
torpid maple
ah i cant do it with dydx approach cause the question specifically asked to reverse the order of integration ;-;
im just stuck on how to get the upper bound for x
deft ginkgo
MB I didn't see the question XD
torpid maple
MB I didn't see the question XD
naw nw, i didnt put the question in so thats mb
deft ginkgo
I'd say u would have to do 2 integrals
One for the upper triangle
And one for the lower one
torpid maple
oohh
deft ginkgo
That would make it easier
torpid maple
then add them up?
deft ginkgo
Yee
torpid maple
oooohhh.... that makes more sense
deft ginkgo
The game is to make the bounds easier to swallow, if it looks painful it's probably wrong XD
torpid maple
ahhh... thats fair enough, thanks alot!
torpid maple
I'd say u would have to do 2 integrals
o thanks! it worked, got the right answer
deft ginkgo
You're welcome 😁
white gull
obtuse pebbleBOT
spark monolith
is it parallel
white gull
It doesnt say
timid silo
sieht so aus
spark monolith
did it mention what shape
timid silo
looks like it
white gull
Nope
white gull
it just says geometry: write an expression for the area of each figure
spark monolith
looks like straightup a^2b*b^3 to me
timid silo
if it is then the area is just
A = $$\text{base} \cdot \text{height}$$
warm shaleBOT
Edmund Cloudsley
white gull
Wait what
spark monolith
$A=b\cdot h$
warm shaleBOT
Pop
white gull
its b times h and not side times side
timid silo
the area of a parallelogram is just base times its height
white gull
the area of a parallelogram is just base times its height
Oh
timid silo
so effectively you need to evaluate
$$b^3 \times a^2b$$
warm shaleBOT
Edmund Cloudsley
timid silo
I thought its side times side
That is for square
white gull
Yeah i got it thanks.
white gull
That is for square
I thought its for like
Everything with 4 sides that has parallel sides
😭
timid silo
cheers goood day
white gull
u too
What ab this one
Do we use pythagorean
Or smt
Cuz right angle
And we need height
obtuse pebbleBOT
@white gull Has your question been resolved?
timid silo
how do i do this
obtuse pebbleBOT
how do i do this
timid silo
<@&286206848099549185>
past valve
what have you tried?
obtuse pebbleBOT
@timid silo Has your question been resolved?
past valve
Like if the radius of the circles is r the side of the square is 2r right, then just calculate the area of the 4 circles and the of the square to determine the area of the grey area
timid silo
Like if the radius of the circles is r the side of the square is 2r right, then ...
but i dont have the radius
timid silo
how do i do this
Assume the radius of rhe circle is x cm
So one side of the square is 4x cm
The area of the square is 4x•4x= 16x²
And rhe area of the circle is
4 • pi • x²= 4pix²
well like take side of square to be r then circle radius is r/4 then total area of all the circles will be 4 * pi * r^2/16
right?
total area of square is r^2
that works
oh shit i said radius
for diameter
😅
timid silo
well like take side of square to be r then circle radius is r/4 then total area ...
*r^2 - pir^2/4 = 40
side is comin 13.65
answer in the end
so yeah
obtuse pebbleBOT
timid silo
obtuse pebbleBOT
Available help channel!
winter crescent
What's ab+b/b
obtuse pebbleBOT
What's ab+b/b
ember onyx
show the entire problem pls
timid silo
ab+b/b = ab/b + b/b = a + 1
winter crescent
ab+b/b
b(a+1)/b
(a+1)×b/b
(a+1)×1
(a+1)
So I'm correct
Wait till that sucker knows
tardy epoch
,w simplify (ab+b) / b
warm shaleBOT
trim portal
Here it is
Lmao
warm shaleBOT
tardy epoch
tardy epoch
I'm in a hurry
https://cdn.discordapp.com/emojis/1045999194390933644.webp?size=4...
why
tardy epoch
why does he have little time left
winter crescent
Because the exam is in the next hour
winter crescent
just tell your friend to join discord then
too busy
winter crescent
oh it's not even your own work
Mhm
tardy epoch
obtuse pebbleBOT
@winter crescent Has your question been resolved?
obtuse pebbleBOT
@winter crescent Has your question been resolved?
queen dragon
Hey, I want to find a reference to a method for solving nonlinear PDEs literally 10 years ago, and forgot how it is even called. I used it for the non-linear heat equation with both heat capacity and conductivity dependant on temperature.
After going into dimensionless variables you would end up with dimensionless temperature \theta(t,x), and equation for it. Next I specifically seem to remember taking a transform of the equation with the dependant function (I don't remember steps before or after) to produce a number of algebraic equations which when solved gave an approximate solution dependant only on how many sin (n\theta) transforms you calculated.
I might be just remembering wrong, but if I am not crazy, could you help me remember the method name, or even better some reference books and articles?
obtuse pebbleBOT
Hey, I want to find a reference to a method for solving nonlinear PDEs literally...
@queen dragon Has your question been resolved?