43__
_43_
__43
4343
43_
_43
43 itself
#help-43
kind viper
grim adder
noble sorrel
what about 3 digit numbera?
tired bear
you can
tired bear
what about 3 digit numbera?
both your questions would cancel each other
clever stratus
it does, but the point is you've counted 4343 twice
so its literally js 300 - 1
tired bear
including 0 includes smaller numbers
noble sorrel
both your questions would cancel each other
lmao just understood thyr
clever stratus
what about 3 digit numbera?
huh uhhhh idk js numbers with 43 in it
tired bear
na i think only 4343 being common is the problem
kind viper
so its literally js 300 - 1
yes
correcting for an overcount is quite a common thing to do in combinatorics
tired bear
you can include 0 here because of any number of digits
for larger number of digits
you might have to use inclusion-exclusion
compact pewterBOT
compact pewterBOT
Available help channel!
boreal girderBOT
raw dawn
The trig sub?
thorny kestrel
You need to split the second fraction into something of the form $\alpha \frac{2ax+b}{(ax+b)^2 + c}$ and $\frac{\beta}{(ax+b)^2 + c}$ where $\alpha, \beta, a, b, c$ are all constants
boreal girderBOT
bloubbloub
thorny kestrel
Both of which have nice antiderivatives
Also there are tricks you can use for partial fraction decomposition
raw dawn
Should I split up the -x and +2 and bring the negative to the front
raw dawn
Also there are tricks you can use for partial fraction decomposition
This isn’t homework it’s js stuff I do in my free time so I generally just do everything out
Unless if it’s like
Literally arctanx
Or something
spiral matrix
Also there are tricks you can use for partial fraction decomposition
HAHA was js typing this
thorny kestrel
Sure but solving systems is wayyyy more time consuming than just doing it the "simple" way
thorny kestrel
I think it's right
raw dawn
I think it's right
Do you know where I could check besides here, I tried asking all the math teachers at my school but there’s only 2 calc teachers and one is too busy and the other doesn’t have free periods the same as me
thorny kestrel
Well there are websites that can calculate integrals
raw dawn
Any suggestions for any specific ones
rapid crescent
compact pewterBOT
https://vm.tiktok.com/ZNdW3pV21/
rapid crescent
How to solve this ?
kind crane
verbal kiln
kind crane
use screenshots if you have an actual question
verbal kiln
What exactly are you stuck on about this?
It looks like he already answered the question?
rapid crescent
If you just have a question like "hey I saw this integral in a video and I was curious ..." then it would be fine, but if you're just grabbing questions to try and trick people or waste people's times that's not particularly nice.
verbal kiln
kind crane
wut
verbal kiln
If you just have a question like "hey I saw this integral in a video and I was c...
Are you taking to yourself my guy?
kind crane
who says you can't send screenshot actual problems
rapid crescent
Go ask the moderators
kind crane
If you just have a question like "hey I saw this integral in a video and I was c...
<@&268886789983436800> they strike again
brazen quiver
Are you taking to yourself my guy?
This was the reasoning given last time he posted.
to be fair, he is doing what we asked of him.
verbal kiln
This was the reasoning given last time he posted.
Oohhh I was confused. It looked like he was moderating himself 
rapid crescent
Can i use inducution here?
kind crane
use screenshots if you have an actual question
.
no one's gonna open a tiktok to help you
brazen quiver
isolated as a screenshot
brazen quiver
to be honest, this problem looks gross, and I doubt you'll find anyone willing to help you with it.
kind crane
Can i use inducution here?
then no
forest token
isolated as a screenshot
@rapid crescent write out each term and summation it to infinity by hand
brazen quiver
the most likely thing that will happen is you factor the numerator and denominator, some things cancel, and you're left with something that is a variation on the basel problem and something that is a variation of some other well known sum
rapid crescent
Mmm
@HenryWhitmore
@brazen quiver A user wrote to me yesterday in DM because he was kicked out of the discord, what should I reply?
I don't know what to write
verbal kiln
<@173636598150332416> A user wrote to me yesterday in DM because he was kicked o...
If they were kicked, there was a reason. Honestly, don’t reply.
Move on.
rapid crescent
He told me where the reason is written
Anyway lets focus on the question
<@&286206848099549185>
.close
compact pewterBOT
Available help channel!
quartz yoke
yo
quartz yoke
can someone help me understand induction proof on recursive algorithms
i dont quite understand
compact pewterBOT
@quartz yoke Has your question been resolved?
quartz yoke
im only asking because i thought inductive proof was intended for positive integers
near jay
It’s induction on the number of characters
Those are integers
And the base case for induction can be any integer, 1, 20, 0, -15
quartz yoke
It’s induction on the number of characters
i see
near jay
Induction can also go downwards, and doing both directions gives all integers
quartz yoke
Induction can also go downwards, and doing both directions gives all integers
so this reads "character 1 of length 1" "character 2 of length 2"?
weak cobalt
No, that's "character 1" followed by "character 2" and so on until "character k+1"
s has length k+1
near jay
Depending on how it’s defined characters won’t have a length or if they do it’s length 1
quartz yoke
No, that's "character 1" followed by "character 2" and so on until "character k+...
oh what i meant is up until C_k thats length k
thats k long
like c_2 is 2 long
weak cobalt
... no, c_1c_2 is 2 long
If you want to talk about a substring, you can introduce a new notation, but c_2 is a character, not a substring
As such, it has no "length" property
compact pewterBOT
@quartz yoke Has your question been resolved?
compact pewterBOT
compact pewterBOT
Available help channel!
blazing owl
Hello
blazing owl
I need help giving some 8th grade probability independent and dependent problems solving and determineg if they are
I have a test tommorw
Ping me whoever can help
upper bane
you need help giving problems or solving problems?
I don't get your question. please be more specific
blazing owl
you need help giving problems or solving problems?
Giving problems and going over them
kind crane
Giving problems and going over them
then not what help channels are for
blazing owl
then not what help channels are for
Huh
Then what is it
Cause I’ve done this before
kind crane
kind crane
no
kind crane
read
kind crane
do your own homework then
blazing owl
I finished all of it
upper bane
why not search for some problems online, try them, and then show us where you're stuck on them
compact pewterBOT
@blazing owl Has your question been resolved?
gilded lodge
Can anyone please tell me if I did this correctly?
compact pewterBOT
Can anyone please tell me if I did this correctly?
bleak dock
Can anyone please tell me if I did this correctly?
that's correct
I have these small improvements for you though
- it's not 3x^3 - 5x^3 ofc, it's 3x^3 - 5x^2
luckily that didn't affect the rest of your working
- align your work! -5x^2 should be directly above 4x^2
the way you're aligning your work right now, it's very easy for you to make arithmetic mistakes
bleak dock
also you forgot the bracket, so it's -(6x - 18)
that's not too important though, as it's clear you're subtracting correctly
bleak dock
Tysm for the tips
no worries!
,w (x^4 - 5x^2 - 6x - 10) / (x - 3) quotient and remainder
boreal girderBOT
gilded lodge
What's this
bleak dock
What's this
do you see it now?
go on https://wolframalpha.com
type this in and you can check your answers
gilded lodge
Ok thank you
bleak dock
oh yeah you needed to write (x^3 + 3x^2 + 4x + 6)(x - 3) + 8 out, as per the question instructions
but I suppose quotient = ... and remainder = .... is also pretty clear
bleak dock
Ok thank you
no worries!
gilded lodge
oh yeah you needed to write (x^3 + 3x^2 + 4x + 6)(x - 3) + 8 out, as per the que...
Ok
bleak dock
Ok thank you
if you're done type .close
ripe path
spiral plume
Who can help me?
spiral plume
No, it hasn’t.
tall pike
Hello! @spiral plume
tall pike
<@1401191714474950737> Has your question been resolved?
First you can choose ❌ so that the channel won't close
2nd, have you tried expanding lower powers first?
E.g. (x+y+z)² and (x+y+z)³
spiral plume
2nd, have you tried expanding lower powers first?
E.g. (x+y+z)² and (x+y+z)³
Yeah, I tried expanding (x+y+z)² and (x+y+z)³, but I’m still stuck.
Could you explain a bit more how that helps with the fifth powers?
tall pike
Yeah, I tried expanding (x+y+z)² and (x+y+z)³, but I’m still stuck.
The next step would multiplying those 2 so that we can get x⁵+y⁵+z⁵
tall pike
The next step would multiplying those 2 so that we can get x⁵+y⁵+z⁵
Oh wait
I mean
Aaaa, it's hard to type
tall pike
(x²+y²+z²)(x³+y³+z³)
So we will have x⁵+y⁵+z⁵ among the terms
As you may have done with this:
x²+y²+z²=-2(xy+yz+zx)
and
x³+y³+z²=3xyz
spiral plume
Ah okay, I get it now! So we end up with B=0, yeah?
tall pike
Ah okay, I get it now! So we end up with B=0, yeah?
Oh, i didn't calculate the answer, sorry
rotund sphinx
It has to be zero if there’s a unique answer b/c scaling
spiral plume
Thanks a ton, bros
compact pewterBOT
@spiral plume Has your question been resolved?
carmine garden
compact pewterBOT
carmine garden
Is this fine
I think the last part requires some justification thoug
if there were only finitely many numbers making up the sequence, we could construct subseqeunces converging to each of those points fixes it
compact pewterBOT
@carmine garden Has your question been resolved?
carmine garden
<@&286206848099549185>
mellow kernel
<@&286206848099549185>
yes
mild sky
.close
compact pewterBOT
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Available help channel!
hexed ferry
ok so
hexed ferry
we have a bounded sequeunce x(n)
into the real numbers
then we define the seqeunce y by y(n)=sup{x_i : i>=n}
prove y(n) converges
I think it's easy to show y is monotone decreasing
and then y should also be bounded
hushed magnet
yes
hexed ferry
but thats all i thought of so far
tranquil mist
I think we will started by x is bounded
hushed magnet
well thats it
monotone + bounded implies convergent
monotone convergence theorem
tranquil mist
monotone convergence theorem
There are another method
By using ε
hushed magnet
sure if you hate yourself
hexed ferry
monotone convergence theorem
so ima just say that
hushed magnet
they mean that you are supposed to use mct
hexed ferry
ok
i didnt know cuz
we didnt have lectures on it yet
just we were supposed to read rudin
and figure it out
compact pewterBOT
compact pewterBOT
Available help channel!
twilit patrol
Can someone please explain why $\sum_{k=2}^ \infty \frac{1}{\ln(k)}$ diverges? A series converges if $\lim_{k\to\infty] a_k = 0$ and the limit $\frac{1}{\ln(k)$ as k goes to infinity is 0
compact pewterBOT
Can someone please explain why $\sum_{k=2}^ \infty \frac{1}{\ln(k)}$ diverges? A...
boreal girderBOT
Denascite
Pen
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
hushed magnet
$\lim a_k=0$ does NOT imply $\sum a_k$ converges
boreal girderBOT
Denascite
twilit patrol
So uhh, if the series converges, that implies that the limit of the series is 0?
hushed magnet
the limit of the terms of the series is 0, yes
twilit patrol
You just also explained another question that I had for a while
why the harmonic series are divergent...
oh my god, I always thought that if the limit of the terms of the series is 0, then the series is convergent
ohh this clears up so many issues ive had
I will revisit the subchapter again
thank you so so so much Denascite
.close
compact pewterBOT
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Available help channel!
rich pollen
compact pewterBOT
strong ivy
What have you tried?>
rich pollen
I did The area of the circle / The area of the rectangle
strong ivy
And you got..?
strong ivy
a fraction sounds right
rich pollen
I have a question: What if the diagonals of the faces of the die are equal to the diameter of the circle?
kind viper
I have a question: What if the diagonals of the faces of the die are equal to th...
you're supposed to treat the die as a point, i think.
strong ivy
Then the math gets a lot harder
Here you treat the die like a single point, yes, like ann said
ripe ether
I have a question: What if the diagonals of the faces of the die are equal to th...
very good question, valid concern, but the thing is they just assume its a point
kind viper
also since when has a die been 1 meter across
kind viper
very good question, valid concern, but the thing is they just assume its a point...
ok and Where Do They Say This Assumption Is Justified
ripe ether
ok and Where Do They Say This Assumption Is Justified
im not justifying it but they should at least specify it in the problem
as well they might also be making the assumption that the die landing at each position of the square is "equal" (uniform or something i forgot the word for it)
all of these should be specified
strong ivy
go for it
rich pollen
I think the second argument is wrong even though the conclusion happens to be correct.
strong ivy
What makes you think that?
rich pollen
The argument is that since there are only two possible outcomes, the probability of each outcome is the same - 1/2 - but we must check if the number of odd numbers = the number of even numbers on the die
strong ivy
Yeah, you're exactly right
It's not about the number of outcomes, but the actual chance of reaching each outcome
rich pollen
Yes, thank you.
ripe ether
I think the second argument is wrong even though the conclusion happens to be co...
btw the die could be unfair: that is it might be possible it rolls more of one number
rich pollen
Is a cubical die fair?
ripe ether
Is a cubical die fair?
i mean they drill holes for the sides to indicate what number u get so there is mass difference on each side. also this is more physics than math
compact pewterBOT
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Available help channel!
carmine garden
Does this work for the forward direction
compact pewterBOT
Does this work for the forward direction
hushed magnet
notation is messed up
all kinds of nonsense
(\exists (x_n)\to x)\subseteq A
using epsilon that wasnt defined
stating (x_n) != x which is a type error
x_n != x wasnt established earlier
carmine garden
Okay, i'll get off discord after thsi
hushed magnet
get off discord now
compact pewterBOT
compact pewterBOT
Available help channel!
eager plinth
i wanna know how i can prove y is -2
compact pewterBOT
i wanna know how i can prove y is -2
eager plinth
do i get x in terms of y
then substitute in
but then i’m still left with 2 unknowns
bleak dock
but then i’m still left with 2 unknowns
elimination is the easiest
bleak dock
but they’re different symbols?
what do you mean by this?
eager plinth
if the equations have the same sign (- or +) then you can subtract one from the other
bleak dock
if the equations have the same sign (- or +) then you can subtract one from the ...
indeed, so 4kx and 2kx have the same sign
eager plinth
eh idk
i feel like we learnt this a different way
i found this from my class resources
bleak dock
do you understand why they turned x - 2ky = 5 into 3x - 6ky = 15?
eager plinth
they multiplied by 3
bleak dock
yes, but why?
bleak dock
so what do you have to do to 2kx - y = 4 to make that happen?
flint wing
south w the clutch
bleak dock
so if i multiply the first equation by 3 i can cancel out the y?
algebraically correct, but yes you don't want to do that
you don't want to eliminate y
my point is that if you eliminate x, you only have y
eager plinth
okay so i have 4kx - 2y = 8
bleak dock
okay so i have 4kx - 2y = 8
correct
keep going
eager plinth
so now i subtract one from the other
bleak dock
yep
eager plinth
awesome thanks
i started teaching myself integration yesterday
i got up to area under a curve
bleak dock
i got up to area under a curve
interesting
you'll find that a lot of integration exercises require a ton of algebra
you'll see yourself in your book or whatever
eager plinth
you'll see yourself in your book or whatever
yeah that’s what i was learning using
just sat down for 3 hours and did it over and over
bleak dock
oh yeah it's not that hard to learn the reverse power rule
$\int x^n \ dx = \frac{x^{n + 1}}{n + 1} + c$
boreal girderBOT
south
eager plinth
i was doing the x^n+1 / n+1
bleak dock
and then with definite integration you do (upper value - lower value)
eager plinth
what does in respect to x actually mean?
bleak dock
so +c - (+c) cancels out
eager plinth
and then with definite integration you do (upper value - lower value)
yeah limits
bleak dock
what does in respect to x actually mean?
do you know the rectangle sum definition of integration?
eager plinth
no i do not
bleak dock
each rectangle has a tiny, tiny width
bleak dock
no i do not
learn that first
they're called Riemann sums to find the picture online
eager plinth
oh i’ve done that before
bleak dock
each rectangle has a tiny, tiny width
that width is along the x-axis
and d() means a small change in, so a small change in x
eager plinth
splitting up the area under curves into 3 parts then finding the area
bleak dock
cool and then the heights of the rectangles are f(x)
eager plinth
did it in biology
bleak dock
splitting up the area under curves into 3 parts then finding the area
damn
okay so that's actually a rule called the trapezoid rule
that's a legit calculus thing, yes
eager plinth
seriously?
like splitting up the area under curves into rectangles
to find an estimate for the area
bleak dock
like splitting up the area under curves into rectangles
this is with trapezoids though
but rectangles also work for the approximation
eager plinth
isn’t calculus itself like splitting the area under curves into infinitely small rectangles to find the exact area
ornate garnet
Can't you use like any polygon for approximation
Although it affects the accuracy ofc
eager plinth
this is with trapezoids though
yeah we did something like this. but with triangles on top of rectangles
bleak dock
Can't you use like any polygon for approximation
it's not actually about polygons
bleak dock
yeah we did something like this. but with triangles on top of rectangles
which are just trapezoids, so yep
ornate garnet
it's not actually about polygons
Wdym
bleak dock
can anyone spot what i’ve done wrong here
it's a good idea to close this channel and open a new one
so that other people see this new question
eager plinth
.close
wintry root
Hello! I made these three limits, and I don’t know if they’re correct. Can someone correct them?
compact pewterBOT
Hello! I made these three limits, and I don’t know if they’re correct. Can someo...
verbal kiln
Can you send the limits?
wintry root
verbal kiln
yes.
short violet
wintry root
yes.
Thanks!!!! My mates where telling me that was the last one was undefined
And I was like no?
verbal kiln
Thanks!!!! My mates where telling me that was the last one was undefined
which one? The 1^𝑥 one or the (1/2)^x one?
wintry root
Lim x->infinite 1^x
It’s not indefinite, right?
Also, are you sure? I love your bioxd
verbal kiln
It’s not indefinite, right?
Only if you plug in ∞ directly
If you even put a giant number it’s still 1.
1^𝑥 = 1, 𝑥 ∈ C
wintry root
Thanks!!!
verbal kiln
❤️
late fox
It’s not indefinite, right?
Bro that's not indefinite obviously
late fox
If you even put a giant number it’s still 1.
No bro infinity isn't a number
verbal kiln
No bro infinity isn't a number
I get that?
I never said it was.
also @wintry root has your questionn been answered?
late fox
Even if you tend it to inf, it's still gonna be 1
verbal kiln
Even if you tend it to inf, it's still gonna be 1
Exactly — which is what i already have stated.
late fox
Exactly — which is what i already have stated.
Anyway what question are Y'all discussing
verbal kiln
Anyway what question are Y'all discussing
it’s been answered, and you can check the pinned messages.
late fox
it’s been answered, and you can check the pinned messages.
There's no pinned question ig
bleak steppe
hi– i found this on a practice for a math olympiad in my country and i don't understand it fully
compact pewterBOT
hi– i found this on a practice for a math olympiad in my country and i don't und...
compact pewterBOT
@bleak steppe Has your question been resolved?
mortal sentinel
Hartshorne example 6.5.2 : On $Spec(k[x,y,z]/ (xy-z^2))$, let $D$ be the divisor $(y, z)$. Why is $div(y) = 2D$? The textbook says $y = 0 \rightarrow z^2 = 0$, but I'm not sure what that has to do with $div(y) = 2D$. Don't we need to localize at $(y, z)$, find a uniformizing parameter, etc. ?
compact pewterBOT
Hartshorne example 6.5.2 : On $Spec(k[x,y,z]/ (xy-z^2))$, let $D$ be the divisor...
boreal girderBOT
bvghfgjfg
hushed magnet
to the advanced channels with you
compact pewterBOT
@mortal sentinel Has your question been resolved?
haughty trout
“y=0\—> z^2=0” is shorthand for the same
local observation: at points of the divisor (y,z) the equation
xy=z^2 forces y to look like a square of z up to a unit, hence
the vanishing multiplicity is 2. The rigorous way is exactly the
localization argument above (find the uniformizer z in A_p
and compute the valuation of y).
limpid narwhal
f(x) = 1/3, 0 ≤ x ≤ 3, the variance is 0.75.
I am confused, why the variance wouldn't be equal to 0? When are we deviating from the mean in a constant function?
compact pewterBOT
f(x) = 1/3, 0 ≤ x ≤ 3, the variance is 0.75.
I am confused, why the variance w...
limpid narwhal
I understand how to calculate it but intuitively I would think it would be 0
I would like an intuitive understanding of it
hushed magnet
the density might be constant, sure
but that doesnt mean the random variable is
like if we have a fair coin we also have a "constant" density p(head)=p(tails)=1/2 but clearly we can get different results
same idea here
the density is constant but the random variable could be any number from 0 to 3
compact pewterBOT
@limpid narwhal Has your question been resolved?
trail cave
just want to check my answer since the key doesnt have it
i drew a circle with radius 3 around the origin, with dotted lines to show it doesnt include the border
then dotted lines along x=2 and x=-1 to show those arent included either
compact pewterBOT
just want to check my answer since the key doesnt have it
i drew a circle with r...
trail cave
compact pewterBOT
@trail cave Has your question been resolved?
rotund sphinx
could use some labels, but it's fine otherwise
compact pewterBOT
compact pewterBOT
Available help channel!
flint cliff
can someone help me put this into REF form
compact pewterBOT
can someone help me put this into REF form
wind urchin
That seems like a pretty difficult way to start this
Back to the beggining note that if you perform R2>R2 + R3, R2 looks quite similar to R1
So I’d start there
You could also do R3>R3 + R2
Instead of the other
compact pewterBOT
@flint cliff Has your question been resolved?
flint cliff
So you're trying to get R1 and R2 to be simular
strange ermine
That's a possible way, sure
compact pewterBOT
@flint cliff Has your question been resolved?
honest nest
Is this true?:
If a characteristic function is Riemann-Integrable, such function must be piecewise constant
compact pewterBOT
Is this true?:
If a characteristic function is Riemann-Integrable, such functio...
mild sky
what do you mean by a characteristic function?
mild sky
also what do you consider piecewise constant
honest nest
from my book
mild sky
one last thing, is the domain of the characteristic function all of the real numbers or just some interval?
mild sky
well look at 1_Z where Z are the integers
its reimann integrable with integral 0
but its not constant on each of a finite number of intervals
honest nest
Sorry, the set must be bounded, that's my oversight
I mean in the case I'm trying to apply this to that is
also Q is not bounded or am I missing something
maybe u meant Q intersection [0,1]?
honest nest
makes sense. But yeah, not Riemann Integrable
mild sky
take the set $A = \left {\frac{1}{2^n} \mid n \in \bN \right }$
boreal girderBOT
ExpertEsquieESQUIE
mild sky
its closure is itself with 0, and that set has measure 0, and thus 1_A is Reimann integrable
but you have infinitely many discontinuities, so the function 1_A cannot be piecewise constant
honest nest
so you have infinitely many discontinuities but not so many that the measure of the set of discontinuities will be greater than 0?
mild sky
yeah
you just have countable amount of discontinuities
and countable sets have measure 0
honest nest
so it cannot be piecewise constant clearly
mild sky
yes
honest nest
ahh that complicates things
well thank you v much for your help
I'll close the channel now
mild sky
bye
honest nest
.close
wanton hazel
hi
hexed ferry
sup
wanton hazel
do you have a question
yeah
south minnow
compact pewterBOT
@wanton hazel Has your question been resolved?
wanton hazel
<@1392510542702448792> Has your question been resolved?
❌
I can't take a photo of my problem 😢
compact pewterBOT
If you are done with this channel, please mark your problem as solved by typing .close
wanton hazel
so tomorrow i'm going to sleep
untold echo
compact pewterBOT
untold echo
Can anyone check if my answers are correct
also if my meanings are correct for part a
anyone??
<@&286206848099549185>
untold echo
it was 15 minutes
untold echo
Yes, all its correct, also, generally be patient
the meanings too?
i didnt know if i worded the meaning for -0.13 properly
tranquil prawn
yes, usually consider that "a" is usually just called the rate of change
But you got the idea right
Is by how much the water level changes per unit of time
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low pulsar
how do i solve 0 = -0.6 |x-3| + 6.5
lost jackal
You assume first that what's inside the absolute value is greater than or equal zero and solve it
Then assume that what's inside the absolute value is smaller than zero then solve for it again
@low pulsar understandable?
boreal dawn
-6.5 = -0.6 |x-3|
First, divide both sides by -0.6
low pulsar
<@723362224717955123> understandable?
sorry dont get it
lost jackal
to be able to solve these problem
They might have multiple answers or just one answer or none
So to make sure
We first check if a solution exist if what's inside the absolute value is greater than 0
In your example
X-3
Because we assume that it is greater than 0 we can remove the absolute value brackets and solve it normally
If the final value of X matches our initial assumption, then the answer is a solution to the problem.
low pulsar
wait dude im so sorry i did a mistake
the 0 is in the wrong placr
f(x) = -0.6 |0-3| + 6.5
-0.6(-3)
+6.5
?
lost jackal
Umm
So what is exactly the question
lost jackal
Like a point on the graph ?
lost jackal
You are trying to find y intersection
So you substituted x = 0
That is correct by far
low pulsar
yeah
lost jackal
The absolute value turns negative values to positive values so |-3| = 3
lost jackal
,calc -0.6 * 3 + 6.5
boreal girderBOT
Result:
4.7
nice
lost jackal
Yes correct
low pulsar
alright thanks for ur help
but
0 = -0.6 |x-3| + 6.5
what if it was this
this one i dont know how to solve
lost jackal
Here you want the x intersection
As I said you first assume that what's inside the absolute value is greater than 0
So |x-3| = x-3
Then solve it normally
If the final value of x atchieves the first assumption then it is a solution
lost jackal
I assumed that x - 3 > 0
So |x - 3| = x - 3
low pulsar
what do i replace the x with
low pulsar
alright how
lost jackal
By solving for a single unknown variable in a linear equation
You can search that up in YouTube if you don't know what is it
Here X is an unknown variable I want to find its value
So by solving for it we want to try find its value
We usually do that by trying to isolate x on its own
low pulsar
ok but what happend to the initial equation with 0 = -0.6 |x-3| + 6.5
lost jackal
So first let's assume that what's in inside the absolute value is bigger than 0
Meaning x - 3 > 0
This makes
|x -3| = (x - 3)
lost jackal
We substitute it in the original question and solve for x
0 = -0.6(x - 3) + 6.5
0 = -0.6x + (-0.6)(-3) + 6.5
And then you can complete
low pulsar
ah
low pulsar
And then you can complete
so what if it was now it was x - 3 < 0
lost jackal
After we solve for the previous case we can find that
,wolf 0 = -0.6x + (-0.6)(-3) + 6.5
boreal girderBOT
lost jackal
Here as we can see x is 13.8333
Checking the first assumption
13.8333 - 3 = 10.8333 > 0
Assumption is true
Then this x is a solution
After that we want to find if there would be a solution for x - 3 < 0
So we assume that x - 3 < 0
This will make
|x - 3| = -(x-3) = (3-x)
Then we will do as we did earlier
@low pulsar understandable?
low pulsar
i see yes
@lost jackal last question
what form is tis
like i need o find the surface of this
lost jackal
The surface area?
lost jackal
I think it's easier if you took the area of the whole shape and subtracted the area of the smaller shape from it
low pulsar
how do i get the area of the whole shape
like its not a pentagon
i need to like divide it into shapes
lost jackal
Dividing it like this will make it easy to calculate the area
After that we want the area of the unwanted shape
Calculate them then subtract
low pulsar
how do i find the height of the triangle
ohhh
nvm
i know how
aalright ill do that thank you
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hexed ferry
basically i made some adjustments to what i found on wikipedia but this is what I have
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basically i made some adjustments to what i found on wikipedia but this is what ...
hexed ferry
oops
\text{Let $R$ be a binary relation over $A$ and $B$. Then we have the following definitions:}
$R$ is called left-unique iff $\forall x \in A, \forall y \in A, \forall z \in B, ((x,z) \in R \land (y,z) \in R \implies x=y).$\\
$R$ is called right-unique iff $\forall x \in A, \forall y \in B, \forall z \in B, ((x,y) \in R \land (x,z) \in R \implies y=z).$\\
$R$ is called left-total with respect to B iff $\forall x \in A, \exists y \in B, (x,y) \in R$.\\
$R$ is called right-total with respect to A iff $\forall x \in B, \exists y \in A, (y,x) \in R$.\
$R^{-1}$ is the binary relation ${(y,x) \mid \exists x \in A, \exists y \in B, (x,y) \in R}$.\
$R$ is called a function from $A$ onto $B$ iff $R$ is right-unique and left-total with respect to $B$.\
$R$ is called an injection (injective) iff $R$ is a left-unique function.\
$R$ is called a surjection with respect to $A$ (surjective) iff $R$ is right-total with respect to $A$ and is function.\
$R$ is called a bijection (bijective) iff $R$ is an injection and a surjection with respect to $A$.\
Let $T$ be a binary relation over $B$ and $C$. The composition of $T$ and $R$, denoted $T \circ R$, is the set ${(x,z) \mid \exists y, (x,y) \in R \land (y,z) \in T }$.
boreal girderBOT
Julian
hexed ferry
i felt like it was necessary to say with respect to for the totality ones
but wiki didnt
does respect make sense or is there a better way to word it
or should i say over domain R / range R
or over its domain
/ over its range
oh shoot i messed up hella stuff
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Julian
hexed ferry
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✅ Original question: #help-43 message
hexed ferry
so for left and right total it is necessary to give some indication we mean on B and A respectively of course
it feels awkward saying with respect to, especially for the bijection
is there a better phrasing
maybe from A and onto B?
i feel like onto is reserved for functions maybe
for the unique ones there might be an issue too cuz
if A' is a superset of A and B' is a superset of B
R is a binary relation over A' and B'
but
the definition could be contradictory
oh shoot i could just say over A and B in every case
hexed ferry
oh shoot i could just say over A and B in every case
is this correct?
does all of this make sense
compact pewterBOT
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twin anchor
are those from a reference?
hexed ferry
edit from wikipedia
twin anchor
what do you mean
hexed ferry
what do you mean
for example in this definition
Let R be a binary relation over X' and Y' as wwell
where X' and Y' are supersets of X and Y respectively
twin anchor
so those bullets are your summaries of statements from Wikipedia?
hexed ferry
could be injective with respect to X and Y
yes
but could not be injective with respect to X' and Y'
im assuming its implied
?
hexed ferry
so those bullets are your summaries of statements from Wikipedia?
i changed the wording
to be more specific
the wikipedia definitions allows for contradictions I believe
alr i think its fine
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upper bane
Hi
hi, welcome to the server! for chatting, please head to #discussion
dense dagger
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kindred hemlock
hey guys just checking, if we were to calculate something say P(X=1)*P(Y=2), thats probaiblity 2 out of 10 drivers are drunk AND 1 out of the 10 drivers are not wearing seatbelt, it also include case where 2 of the drunk drivers may be the one that is also not wearing a seatbelt so we have cases where there is only total 2 people committing all the offences
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hey guys just checking, if we were to calculate something say P(X=1)*P(Y=2), tha...
unkempt flower
sounds like it, yes.
kindred hemlock
oh haha i see, thanks for the extra calrification
i was thinking about it and i thought i might have gotten crazy
but ive asked the math teacher, ill do some revision on other topics while i wait for the reply
kindred hemlock
sounds like it, yes.
thanks man, u have a nice day
unkempt flower
you too!
dense dagger
hey guys just checking, if we were to calculate something say P(X=1)*P(Y=2), tha...
Careful, you can only multiply probabilities if the events are independent
If they are not, you would need to apply inclusion-exclusion
kindred hemlock
ah i see, thank you for teling me
thats a very tricky things that i should consider everytime i consider AND probabilities
kindred hemlock
If they are not, you would need to apply inclusion-exclusion
but im supposed to multiply them in my question in this case right? when they say the two infractions are independent of each other
dense dagger
Yep, weird setup but yeah theyre independent so you just multiply them
kindred hemlock
ye i know right its weird
kindred hemlock
Yep, weird setup but yeah theyre independent so you just multiply them
how would u solve the question
dense dagger
Need inclusion-exclsuion since they're not disjoint
P(drunk OR no belt) + P(drunk) + P(no belt) - P(drunk AND no belt)
Since independent, P(drunk AND no belt) + P(drunk) * P(no belt)
Once you find P(drunk OR no belt), call it "p"
You then just do Binomial(10, p) and plug in 3 for the parameter to find the probability that exactly 3 are drunk or not wearing a belt
kindred hemlock
You then just do Binomial(10, p) and plug in 3 for the parameter to find the pro...
have a great day man
dense dagger
np, you too
kindred hemlock
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molten grotto
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gaunt lynx
!original
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
molten grotto
Is this result valid for checking convergent?
gaunt lynx
Is this result valid for checking convergent?
Limit comparison can be done ig
To see if it matches the corollary
gaunt lynx
But it has finite value no?
Yeah ig
What we have to do tho?
Check if its divergent?
compact pewterBOT
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dry night
kinda stuck on this
compact pewterBOT
kinda stuck on this
dry night
not even sure where to start
well
I notice that the first group has an highest order element of 8
and the second group highest is 4
but thats about it
hm so if f is an homomorphism from G to G'
we have |f(G)| divides |G| and |G'|
so if we have a homorphism for this
nvm that wont be useful here
maybe I can use f(g^n) = f(g)^n
and find an element where this is false
young raft
kinda stuck on this
also notice that it says onto
like the trivial homomorphism exists but isn't onto
dry night
whats the trivial homomorphism, f(g) = g?
young raft
also notice that it says **onto**
so what you are looking for is some element that, no matter the homomorphism, is "unreachable"
also notice that $\forall g\in \bZ_8 \oplus \bZ_2$, we have that the second component of $g^2$ is 0
boreal girderBOT
artemetra
dry night
there are no generators right
dry night
of Z4 Z4?
I thought external product of Zm and Zn is only cyclic if m n are relatively prime
young raft
that's true
dry night
I think I got the solution
rought draft solution srry for poor handwriting and grammar
does this seem right?
got that mixed up a bit
there exists an element of order 4 ot lower in Gbar that is mapped to by an element of order 8
wait hmm
that makes this wrong then
yeah this proof is wrong idk what I was writing
I need some sleep 😭
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sinful willow
Hello Im new and I needed help with this question
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rotund wave
i think this step is wrong
you can't take the limit of part of the expression like that
otherwise you could say $\lim_{x\to 0} \frac{\sin x}{x} = \lim_{x\to 0} \frac{0}{x} = 0$
clear swan
if x = 0, sine of x gives you 0. In the second to last line, you divide 0 by 0. It gives you undefined. i believe in that case you must use l'hopitals rule
boreal girderBOT
69th-order logician
rotund wave
if x = 0, sine of x gives you 0. In the second to last line, you divide 0 by 0. ...
lim of sin^2x/x^2 = 1
by l'hopital, if u like
strange ermine
Why not simply by squaring sinx/x ? 🤔
rotund wave
yes also that
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eager plinth
how do i find a variable in the terms of a constant
compact pewterBOT
how do i find a variable in the terms of a constant
eager plinth
do i make the equation equal the variable?
eager plinth
something like
x = 2k
where k is the constant
i can give an example
find y in terms of k
what do i need to do?
eager plinth
plug x=-2 into the first equation
would it be - -2 or just -2
hushed magnet
2ky-(-2)=4
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kind hollow
when we have a sum that goes from 0 to n, and we wanna do n-->n+1, do we only change the upper limit of the sum? im talking abt the case in which n is also inside the sum
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when we have a sum that goes from 0 to n, and we wanna do n-->n+1, do we only ch...
viscid shard
so something like $\sum_{k = 0}^n 2k$?
boreal girderBOT
Mikya
kind hollow
nono lemme write my example actually
viscid shard
sure
kind hollow
,tex
$\sum_{i= 0}^{n} n $
boreal girderBOT
fijokazż
kind hollow
just this
viscid shard
uh
verbal kiln
What do you mean by 𝑛 —> 𝑛 + 1?
mild sky
Its i-->i+1
kind hollow
u=n+1
viscid shard
this will just end up as n^2, no?
kind hollow
its not abt the sum's result
verbal kiln
this will just end up as n^2, no?
No, there’s no indice of 𝑖 in the summand here so it’s really undefined, unless 𝑛 is constant?
kind hollow
,tex
$ \sum_{i=0}^{n} in $
boreal girderBOT
fijokazż
kind hollow
this. what if we sub u=n+1
mild sky
Then n=u-1
mild sky
No its still the same number
kind hollow
then the summation has one extra term
yes, but what would the inside be? n×i or n×(i+1)?
mild sky
n×i
kind hollow
sorry meant (n+1)i
viscid shard
you defined it as in, so it would remain in
mild sky
Because only n changes
viscid shard
only the upper bound changes
kind hollow
Because only n changes
yea but n is also in the sum
viscid shard
n itself still remains the same
mild sky
yea but n is also in the sum
And? Its a constant
viscid shard
yea but n is also in the sum
doesn't matter, n's value is practically unchanged
kind hollow
n itself still remains the same
yeah thats what confuses me
viscid shard
ok do you understand pseudocode?
kind hollow
And? Its a constant
i didnt think of it like that
kind hollow
ok do you understand pseudocode?
idk what it is
mild sky
I is the variable that is bound to the sum
viscid shard
let me write down in a sort of code-like manner what happens
kind hollow
I is the variable that is bound to the sum
interesting
mild sky
idk what it is
Describing algorthims without a programming language
viscid shard
your original summation is this.
var result = 0
var n = {some value}
for(i = 0, i <= n, i++) {
result = result + (i * n);
}
what your modification does is simply this.
var result = 0
var n = {some value}
for(i = 0, i <= n + 1, i++) { // one more term is added because of the upper bound + 1
result = result + (i * n); // nothing changes here
}
the loop runs n times in the first summation, n+1 times in the second
but both times, notice that (i*n) is getting added to the result
that's because the summand didn't change, only the upper bound
you can test this with some small values of i and n
kind hollow
coding doesnt work for me lol
viscid shard
you can test this with some small values of i and n
raw testing should
kind hollow
but thanks for trying
viscid shard
try i = 5, n = 3
kind hollow
try i = 5, n = 3
wdym by "i=5"?
weak cobalt
If $f(n) = \sum_{i=0}^n in$ then $f(n+1) = \sum_{i=0}^{n+1} i(n+1)$
boreal girderBOT
Nel
viscid shard
**fijokazż**
in here
weak cobalt
It's kind of unclear what exactly you're asking
viscid shard
I thought OP said to increase only the upper bound 
but I suppose it's worth a clarification
kind hollow
I thought OP said to increase *only* the upper bound <:eeveethink:60102900641811...
waitttt noooo
Sorry sorry
i meant what Nel wrote
viscid shard
ahhh
kind hollow
my question was if we just sub in everywhere
weak cobalt
Also, $\sum_{i=0}^n in = n \cdot \sum_{i=0}^n i$, n is a constant
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Nel
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rich pollen
Find (p-1)^(p-1) mod p, with p = prime
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Find (p-1)^(p-1) mod p, with p = prime
strange bolt
Do you know Fermats little theorem?
rich pollen
Ah, yes.
strange bolt
So?
rich pollen
I think it says that if p is a prime then (p-1)! + 1 is divisible by p
rich pollen
Fermat's Little Theorem states that for any prime number (p) and any integer (a), the number (a^{p}-a) is an integer multiple of (p).
boreal girderBOT
Yogest Kumar Verma
rich pollen
(Hope this didn’t sound harsh…)
nope, it didn't
rich pollen
**Yogest Kumar Verma**
the power of p-1, not p
strange bolt
$a^p - a=a^{p-1}$
boreal girderBOT
Icephoenix
strange bolt
Wait
No
Sry
But you can formulate it to $a^{p-1}$ is congruent to 1 mod p if the common largest factor of a and p is 1
boreal girderBOT
Icephoenix
rich pollen
Oh, a^p - a = a(a^(p-1) - 1)
Hence a^(p-1) - 1 = 0 (mod p)
a^(p-1) = 1 (mod p)
Putting a = p - 1
we get (p-1)^(p-1) = 1 (mod p)
is this corect?
rich pollen
but p - 1 = -1 (mod p)
Hence (p-1)^(p-1) = -1 ^ (p-1) (mod p)
p = odd => p-1 = even
=> (p-1)^(p-1) = -1 ^ even = 1 (mod p)
wanton hazel
hi
wanton hazel
Hello. What is your question?
Wait i'm going wash me pls
verbal kiln
Wait i'm going wash me pls
What?
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