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#help-0
azure needle
summer dirge
if this isn't a joke, but a real cry for help, I would recommend seeking help. your country probably has mental health support hotlines, so I suggest looking them up and dialing them if you're in dire straits rn. mental health is not something to be taken lightly, and I genuinely hope you can get the help you need if it's serious
regardless though, I have to close this channel because it's not exactly a mathematics question 
I wish you all the best
alpine sable
if this isn't a joke, but a real cry for help, I would recommend seeking help. y...
thanks really much
summer dirge
thanks really much
have a virtual hug, from one stranger to another 🫂
I hope you have a wonderful week 
I'll set this channel to rest now
.close
lone heartBOT
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Available help channel!
soft pagoda
Hi does anyone know how to input a range into stats on a to84
soft pagoda
Ti84
Like
0-2 is the interval
With a frequency of 3
How do I put that 0-2 in the list on my ti84
broken pivot
The interval [0, 2] with a frequency of 3?
soft pagoda
Yeah basically
broken pivot
Or the set {0, 1, 2} with a frequency of 3
soft pagoda
Uhhh
I’m not sure which one it’d be
It’s like
It’s between 0-2
There is a frequency of 3 between the numbers 0-2 for example
And a frequency of 10 between 3-5
Like gpa for example 5 kids got a gpa between 0.0-1.0
broken pivot
Do you only care about 1, 2, and 3
Or do you care about 1, 1.1, 1.2, ..., 2, 2.1, 2.2, ..., 3
broken pivot
2nd option I sippose
Oh then idk
lone heartBOT
@soft pagoda Has your question been resolved?
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@soft pagoda Has your question been resolved?
outer steppe
why does the rrange go from (-1 to 1) to (1 to 5) after u sub?
marsh hamlet
why does the rrange go from (-1 to 1) to (1 to 5) after u sub?
1+4(0)^2=1, 1+4(1)^2=5
woven bramble
Transformations: Okay, so imagine starting with a regular sin(x) wave. That '1/3' inside stretches it horizontally, like pulling it wider. That '-π/6' slides the whole thing to the right a bit. Then, the '-2' flips it upside down and stretches it vertically. Finally, the '-1' at the end just moves the whole graph down.
Key Features: The middle of the wave is at y = -1. It goes up and down 2 units from there. The highest point is at 1, and the lowest is at -3. The wave is shifted to the right. And because of the horizontal stretch, it takes longer to complete one cycle.
Next up, that triangle.
Finding x: We have those similar triangles there because of the parallel line. So, we can set up a proportion: 6 is to (x + 13) as x is to (x + 5). Cross-multiply and you get a quadratic equation. Factor that, and you get two possible values for x, but since it is a length, we need the positive value.
Finally, the surface area problem.
Surface Area: Remember that surface area formula. So you do a u-substitution where u = 1 + 4x². Now, here's the tricky part: You're not integrating with respect to x anymore, now you're integrating u. So, we need to convert the x limits to u limits. What you do is consider one side, the curve is symetrical and it's easier. The answer should be (π/6)(5√5 − 1)
lime bobcat
Transformations: Okay, so imagine starting with a regular sin(x) wave. That '1/3...
Tell me you're stupid without telling me you are stupid
marsh hamlet
Transformations: Okay, so imagine starting with a regular sin(x) wave. That '1/3...
Haha bozo
Get rekt
woven bramble
it is ai but i coded it myself to be accurate and there is no mistake i can tell you that
not chat gpt
i went to ap state and shit so yeah
marsh hamlet
Bro lagged so hard he sent an entire answer bank
marsh hamlet
it is ai but i coded it myself to be accurate and there is no mistake i can tell...
Lol
Get out
!nogpt
lone heartBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
woven bramble
nah
naive valley
like any human would write something like:
"Next up, that triangle."
woven bramble
i know my shit bro
lime bobcat
it is ai but i coded it myself to be accurate and there is no mistake i can tell...
Humans were faster and more correct
woven bramble
nah
lone heartBOT
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stark turtle
how would i do this. i've done this equation before but it didnt have a horizontal asymptote so just C * a^x.
lone heartBOT
@stark turtle Has your question been resolved?
lavish cave
you have $\frac{C}{a} = \frac{2}{3}$, that's correct
now what happens if you sub C = 6/a into this?
and yes you are on the right track
ocean sealBOT
south
stark turtle
i got 6/a^2 = 2/3
and then that gave me the a value which i got was 3
and then put 3 in c * a = 6
which gives me c = 2
i ended up with 2 * 3^x + 1
lavish cave
and then that gave me the a value which i got was 3
yeah just one comment on your working, cause you get a^2 = 9
that actually means a = -3, 3
stark turtle
that actually means a = -3, 3
oh right right
lavish cave
but you know an exponential function must have a > 0 by definition
I just feel it's worth mentioning small things like that
stark turtle
I just feel it's worth mentioning small things like that
oh yeah that's really helpful i forgot my teacher told me that a few days ago thanks for reminding me
lavish cave
so maybe just write $(\text{exponential function} \implies a > 0)$ on the side yeah
ocean sealBOT
south
lavish cave
oh yeah that's really helpful i forgot my teacher told me that a few days ago th...
alright no worries!
alpine sable
lone heartBOT
alpine sable
my work is here
im not sure where to go from there tried quite alot of stuff i can say
any important observation if anyone can provide
im pretty sure that i need to get rid of that x in there and manage to put delta inm there somehow but that -2 there is bugging it as the x is squared
then i thought hm lets do -4 + 2
then triangle inequality
| x^2 - 4 | - 2
now the issue is -2 so thats where im at
lone heartBOT
@alpine sable Has your question been resolved?
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@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
charred flint
then i thought hm lets do -4 + 2
think you just keep it as x^2-2 and do triangle inequality
you can just choose delta small enough that x^2 is small to
<1 should deal with everything
alpine sable
think you just keep it as x^2-2 and do triangle inequality
like reverse triangle inequality?
= |x^2 - 2| >= | |x|^2 - 2 |
charred flint
oh whatever keeps the direction I guess
alpine sable
i see
= | f(x1) - f(x2) | = |x^2 - 2| >= | |x|^2 - 2|
min of that would be 2 i suppose because thats when x is
charred flint
you're trying to do the >0 thing ok
alpine sable
minimum ( x = 0 as x1 < 1)
WAIT
that can actually work
= | f(x1) - f(x2) | = |x^2 - 2| >= | |x|^2 - 2| >= 2
nah im
stopid
charred flint
you get to choose how close x gets to 2
charred flint
so like if you really had to you'd do 1.9999 but 1 should work
alpine sable
if we go closeeee to 2 that would be like 1.9999999999999 smth
but what i don't like about this argument is that its very vague
don't feel right
charred flint
the big idea is x^2 goes to 4 so you have to show the gap between 4 and 2 with inequalities
by getting delta small enough
alpine sable
the big idea is x^2 goes to 4 so you have to show the gap between 4 and 2 with i...
ohhh wait so we try to get bound which is greater than 0 but very close to the 0
that can be any numbers between -2 < x < 2
as -2 < x <= 0 would be same as
0 <= x < 2
charred flint
er wait you need something bigger than sqrt(2)
alpine sable
= | f(x1) - f(x2) | = |x1^2 - 2| = |x1 - sqrt(2)||x1 + sqrt(2)|
charred flint
cause if x^2 can be 2 then the limit matches and that's bad
x^2>3 basically
so the gap is like 1
alpine sable
= | f(x1) - f(x2) | = |x1^2 - 2| = |x1 - sqrt(2)||x1 + sqrt(2)| > |x1 - sqrt(2)|
is that
where u getting to
charred flint
nah I don't think you'd ever factor here
think like all these proofs do triangle inequality
and if you get a delta where x1^2>3 you just get >= 3-2 = 1
lone heartBOT
@alpine sable Has your question been resolved?
slim belfry
Could I ask?
!occupied
lone heartBOT
Could I ask?
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brittle hamlet
lone heartBOT
mental python
brittle hamlet
ive tried finding wgat the missing numbers
like finding a common pattern
idk we havent leartned tis before
mental python
do you know pythagoras
vale wigeon
and also do you know basic trig
brittle hamlet
then what is it
a2 b2 = c2 right?
brittle hamlet
and also do you know basic trig
im not sure
brittle hamlet
what is a, b and c here?
would 9 be a and 10 be B
mental python
no
fervent steeple
what is a, b and c here?
hypotnuse, perpendicular and base
mental python
hypotnuse, perpendicular and base
didnt ask you
royal trout
in the trenches atm
mental python
!occupied
lone heartBOT
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).
brittle hamlet
i dont think im familiar wit that
fervent steeple
didnt ask you
k mb
mental python
i dont think im familiar wit that
c is always the diagonal
also called the hypotenuse
mental python
yes
now which one the 9 is doesnt matter, can be a or b
lets just say 9 is a
then what is b?
brittle hamlet
then what is b?
would it be 1
since it adds uo to 10
or is it something in the trainglw
ocean sealBOT
Bonk
mental python
solve for b
brittle hamlet
$9^2+b^2=10^2$
how do i solve for b?
sorry if this is fustraiting im a little new
ocean sealBOT
Bonk
brittle hamlet
$9^2+b^2=10^2\\b^2=10^2-9^2$
do i calvulate the squares>
brittle hamlet
do you know what a square root is?
yes
mental python
okay
brittle hamlet
9 2 =81, 10 2=100
mental python
use ^ as powers
brittle hamlet
use ^ as powers
9^2 =81 10^2=100
vale wigeon
good
lone heartBOT
@brittle hamlet Has your question been resolved?
gaunt shard
hey
lone heartBOT
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full kettle
I'm stuck on this problem. I'm supposed to prove this, and I believe the representation theorem is Bezout's identity, but I can't figure it out from there once I have these represented
crisp grail
The easiest way I see is using prime factorizations of numbers
gcd is just all the prime factors of both numbers with "the maximal exponent"
full kettle
Hmm alright, I'll try that
north hemlock
Expanding from #math-discussion message
dire gazelle
if $|x+1|<1/2$ you should be able to get $|x-1|<5/2$
ocean sealBOT
Axe
dire gazelle
do you want more details?
lone heartBOT
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Available help channel!
runic obsidian
curious as to why this is 1/(x^3 +5x) and not 7/(x^3 +5x)
lone heartBOT
curious as to why this is 1/(x^3 +5x) and not 7/(x^3 +5x)
kindred atlas
curious as to why this is 1/(x^3 +5x) and not 7/(x^3 +5x)
7 is constant and can be taken outside of the integral
$\int \frac 7 x dx = 7 \int \frac 1 x dx$
runic obsidian
oh
ocean sealBOT
smeagol
runic obsidian
just making sure we're on the same wavelength im talking about the initial thing
because i dont think you should be integrating that?
kindred atlas
You are finding area under a curve --> integrating a curve right?
runic obsidian
yeah
kindred atlas
To make the partial fraction easier they factored out the 7, they probably could have made it more clear
runic obsidian
yeah webassign fucking BLOWS when it comes to explanations
kindred atlas
does it include a video/watch button?
kindred atlas
it might be on similar questions, those are really helpful
runic obsidian
i might just look it up on youtube or something
kindred atlas
i might just look it up on youtube or something
What part is confusing now?
runic obsidian
trying to find one that gives a full explanation, I think i got everything else but I just want to double check
kindred atlas
The steps are
- Make partial fractions
- Split into different integrals
- Integrate the separate parts
light bridge
lone heartBOT
light bridge
can someone help me with this question
sly mantle
exactly which part
lone heartBOT
@light bridge Has your question been resolved?
light bridge
exactly which part
how to use the projection of the solid on xy plane to find the integration bounds
it just doesnt make sense for me
how they got the answer
sly mantle
thats how they cut up the region
an inner lump and an outer ring
what are the bounds of the lump?
@light bridge
light bridge
has r bounds of sqrt(3) to sqrt(4) for the outter?
but why would they cut it like that
light bridge
thats how they cut up the region
because its in cylindrical coordinates why do we need to cut like that, shouldnt we make 2 xy planes projections like the cap and the body.
sly mantle
in general if one of the coordinates changes bounds you need to cut up the region
heres an example in 2d
if we integrate dxdy the y bound changes so we need to cut the region along the red line
light bridge
light bridge
what does this represent
its so much easier to just substract of the smaller half ball from the bigger ball
why are they doing this
sly mantle
its so much easier to just substract of the smaller half ball from the bigger ba...
yes its way easier to integrate in spherical coords but this is good practice
lone heartBOT
@light bridge Has your question been resolved?
outer steppe
why in the first quadrant?
lone heartBOT
why in the first quadrant?
outer steppe
as well as under y = 1 and not between y = -1 and 1?
worn ivy
mental python
huh?
waxen flame
The tangent function is an odd function and secant is an even function.
outer steppe
The tangent function is an odd function and secant is an even function.
how does this affect the answer?
lone heartBOT
@outer steppe Has your question been resolved?
waxen flame
how does this affect the answer?
sec(t) is positive on the domain from t=-pi/4 to t=pi/4. tan^2(t) will always be positive as well because it is squared.
outer steppe
sec(t) is positive on the domain from t=-pi/4 to t=pi/4. tan^2(t) will always b...
ah i see, thanks
and do you know why it's under y = 1?
i havent done much of these
waxen flame
For that, you only need to look at y = tan^2(t). What is its range on the domain -pi/4 to pi/4?
outer steppe
For that, you only need to look at **y = tan^2(t)**. What is its range on the d...
thanks for the help
.close
lone heartBOT
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Available help channel!
prisma night
please explain the highlighted part
lone heartBOT
please explain the highlighted part
tacit arch
find the minimum of $x \log(x)$ on the interval $[k, k+1], \ k \ge 1$
ocean sealBOT
riemann
tacit arch
Use the information that $f(x)$ is strictly increasing
ocean sealBOT
riemann
prisma night
**riemann**
I understood the (2) but what about the lower rieman sum?
is it 1log1 + 2log2 + (n-1)log(n-1) or is it like 1log1 + 2log2 + ........................ + (n-1)log(n-1), as then it would be <= I
lone heartBOT
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lapis jetty
i want to evauate this limite
lone heartBOT
i want to evauate this limite
marsh hamlet
i want to evauate this limite
Use L'Hopital's rule
livid sage
expand using sin3x and cos3x
lapis jetty
how
marsh hamlet
$\sin(3x)=3\sin(x)-4\sin^3(x)$
ocean sealBOT
mathisfun
lapis jetty
okk thanks
hoary cypress
can anyone help with my homework
lone heartBOT
can anyone help with my homework
marsh hamlet
can anyone help with my homework
!da2a
lone heartBOT
can anyone help with my homework
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
marsh hamlet
Want me to start here?
marsh hamlet
are you down for a vc or no?
No.
Okay, I'm gonna start with number 6.
Do you know what it means to be conditionally convergent, absolutely convergent, and divergent?
hoary cypress
conditional means it is converging in wihtin an interval
absolute is converging at all values
marsh hamlet
conditional means it is converging in wihtin an interval
Which is?
marsh hamlet
wdym
Conditional means that the alternating series converges, but the absolute series does not.
hoary cypress
oh ok
so for 6 im saying it diverges
since its n to the 1/3 in the bottom
so p is less than 1
hoary cypress
ok so i wrote the sum compares to 1/n^1/3 which diverges, which eliminates it from being an absolute convergent series, but converges as an alternating series, but doesn't for the absolute value of the sum/series, which makes it conditionally convergent
is this statement good enough to explain the conditional part of it tho?
marsh hamlet
ok so i wrote the sum compares to 1/n^1/3 which diverges, which eliminates it fr...
Yes
hoary cypress
ok can we move to 7 now?
lone heartBOT
@hoary cypress Has your question been resolved?
tepid ravine
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@tepid ravine Has your question been resolved?
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@tepid ravine Has your question been resolved?
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@tepid ravine Has your question been resolved?
golden trench
lone heartBOT
golden trench
so im solving using lagrange multipliers
outer swift
I need help
golden trench
I dont understand why f(x,y,z) is the square of the distance formula.
and not the distance formula with root
outer swift
Can I ask question here about diffrantian equation?
golden trench
Can I ask question here about diffrantian equation?
use one of the free channels, go to #help-4
outer swift
Ok thanks
rancid trail
so im solving using lagrange multipliers
i dont know how to solve this question via this method, but i do know how to solve this question
broken pivot
Dont you just use the basic formula for distance from a point to a plane
golden trench
Dont you just use the basic formula for distance from a point to a plane
yea but we're learning lagrange multipliers, so i guess we're supposed to use that
ik its easier to do it directly
broken pivot
yea but we're learning lagrange multipliers, so i guess we're supposed to use th...
Oh then good luck
golden trench
anyways i figured out the answer to my doubt
lone heartBOT
If you are done with this channel, please mark your problem as solved by typing .close
golden trench
.close
lone heartBOT
pseudo ice
anyways i figured out the answer to my doubt
.(just in case you hadn’t, minimising the square of the distance will get you the same thing as minimising the distance itself, so may as well work with the easier squared distance 
)
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Available help channel!
charred jewel
how do i find a basis for b
lone heartBOT
how do i find a basis for b
vale wigeon
try to find one polynomial of every possible degree
there will be one degree for which no such p exists
charred jewel
there will be one degree for which no such p exists
by p you mean the polynomial
i still dont follow
vale wigeon
yes i do mean the polynomial
ok so let's start simple, like dead simple.
so simple you should not overthink it.
name me a polynomial p of degree 0 which satisfies p(0) = p(1).
vale wigeon
any nonzero number would've worked, yes.
now let's try a higher one
name me a polynomial p of degree 2 which satisfies p(0) = p(1).
charred jewel
btw i know that the all of the coefficients, excluding the constant term should add to 0
vale wigeon
overthinking
charred jewel
so degree 2 would be 1-4x+4x^2
vale wigeon
that sounds like (2x-1)^2
i was actually gonna suggest x(x-1)
and this is gonna be easier to extend to even higher degrees
anyway give it a think.
vale wigeon
sure. that's just adding a constant to your previous thing.
vale wigeon
good
btw, try to figure out what degree is IMPOSSIBLE for a polynomial to have while satisfying p(0)=p(1).
charred jewel
so far n = 1, 2, 3 works
vale wigeon
can you give me one of degree 1?
vale wigeon
ok thats good enough
so now can you come up, for n ≥ 2, with a polynomial of degree n s.t. p(0)=p(1)?
charred jewel
3rd degree could be x²(x-1)
couldnt i just extend this
vale wigeon
perhaps you could. how do you figure?
charred jewel
perhaps you could. how do you figure?
x^n - x^(n-1) could be one
if we extend that
vale wigeon
yeah good
charred jewel
k then what
vale wigeon
well you basically have your basis in front of you already
x^(k-1) (x-1) for 2 ≤ k ≤ n, and the constant 1.
charred jewel
heres the answer that was provided btw
charred jewel
x^(k-1) (x-1) for 2 ≤ k ≤ n, and the constant 1.
does the sign flip not matter then
since i guess its some sort of linear combination between the two?
deep grail
Hello. Anyone free to help out on how to calculate percent difference?
vale wigeon
Hello. Anyone free to help out on how to calculate percent difference?
!occupied
lone heartBOT
Hello. Anyone free to help out on how to calculate percent difference?
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).
vale wigeon
open your own channel and post your question there directly
vale wigeon
does the sign flip not matter then
it doesn't. the choice of a basis is never unique anyway
(except in like 1 edge case)
deep grail
open your own channel and post your question there directly
Oh sorry. I didn't know I need to open another text channel. When I joined the server it popped me here.
charred jewel
aha ok
vale wigeon
see #❓how-to-get-help for instructions.
deep grail
Thank you
charred jewel
.close
sterile walrus
I have a question about proving that sqrt(3) is irrational. The standard proof by contradiction seems to be to assume n = a/b in Q and then show that a and b have a common divisor. Now my confusion is that in the assumption there seems be an implicit assumption that a/b is in its lowest-terms form, so does the contradiction only apply to rational numbers in their lowest-term form? I understand that we can always reduce a number to its lowest-term form, but I think my confusion is why we are allowed to assume that n=a/b is in that state to begin with?
vale wigeon
there seems be an implicit assumption that a/b is in its lowest-terms form
why implicit? it's very much explicit, that's what you contradict with!
so does the contradiction only apply to rational numbers in their lowest-term form
"lowest-term form" is a property of notation, NOT of the number itself.
after all, just because i write 1/2 as, say, 2/4 or 0.5 doesn't make it a different number, any more than i would be referring to different numbers with "three", "trois", "san" or "три"
sterile walrus
That makes sense, but lets say we find common factors of 3, what rules out the possibility of sqrt(3) being 3/3=1 which is still a rational number. Its obviously not true, but I don't see how the proof contradicts it.
vale wigeon
i mean, sqrt(3) isn't 1...
we start with the assumption that sqrt(3) = a/b for integers a and b with b not zero. if you want to pretend you had some a and b handed down from above, then define a' = a/gcd(a,b) and b' = b/gcd(a,b) and apply the same argument to the now coprime a' and b'.
sterile walrus
Is the fact that sqrt(3) is not 1 relevant to the proof at all? If so then that makes more sense, but I think my confusion is more of a logical one, I don't see how the proof rules out that case.
vale wigeon
i don't really understand your confusion i admit
sterile walrus
Me neither probably, I'll move along maybe later it'll dawn on me, thanks though 😅
Oh I see now, my confusion has to do with notation like you initially said. 3/3 would be the same as 1/1 which would be the lowest terms not some "different number". Thanks :)
.close
lone heartBOT
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Available help channel!
mighty thunder
Should i try White monster
lone heartBOT
Should i try White monster
zinc haven
what is white monster
gray isle
Please don't use these channels for non-math questions.
zinc haven
yes, it's good to try something new
gray isle
take it to the social channels #chill #discussion
mighty thunder
Please don't use these channels for non-math questions.
I need Energy for maths
But thx
.Close
/close
vale wigeon
it's .close, lowercase
mighty thunder
.close
lone heartBOT
mighty thunder
Thx
lone heartBOT
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undone ermine
Guys
alpine sable
What is it?
vale wigeon
@undone ermine do you have a math question to ask?
undone ermine
Yes
Alright lemme bring the doubt
Im tensed about my math exam on tommorows tommorow, and ive not prepared the half of the syllabus still , is there any way to prepare it quickly? I wanna ace it
That's it
undone ermine
Oh yeah
vale wigeon
how big is the exam
it might not be feasible to study for it in the 2 days you have left before it
so you might be cooked
undone ermine
It's annual like 20 questions
vale wigeon
annual? so it covers topics throughout the entire year?
undone ermine
annual? so it covers topics throughout the entire year?
Not really just has more chapters
vale wigeon
what chapters
vale wigeon
and you only got through half of that?
undone ermine
Im basically cooked
vale wigeon
yes you are.
you are definitely cooked. no way you are acing it except by divine intervention, sorry!
undone ermine
Ive prepared 12,16,19,15
undone ermine
you are definitely cooked. no way you are acing it except by divine intervention...
😭😭
What if I focus on important and frequent chapters
I might not ace but get impressive marks
lone heartBOT
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undone ermine
<@1345285575787413617> Has your question been resolved?
Yo bot
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novel carbon
How to find f'(x)=0 🙏😭
lone heartBOT
How to find f'(x)=0 🙏😭
patent vale
broo just it to 0
spring summit
How to find f'(x)=0 🙏😭
If a fraction equals 0 then its numerator must equal zero
so really youre just solving (x-4)(x^2+x+4) = 0
and since if ab=0 either a=0 and/or b=0 that means youre acutally just solving
x-4 = 0
and
x^2+x+4 = 0
novel carbon
broo just it to 0
You cannot devise by 0 💀
novel carbon
If a fraction equals 0 then its numerator must equal zero
so really youre just s...
Oh okie
It's just that I got confused about how to solve the /x part
spring summit
You cannot devise by 0 💀
He meant set it equal to 0, he didnt reailze your problem was solving the equation he thought you didnt know what equation to set up
novel carbon
Oh lol
spring summit
It's just that I got confused about how to solve the /x part
btw if you wanna understand why think about it this way:
if numerator/denominator = 0
then you multiply both sides by denominator
numerator = 0 x denominator
numerator = 0
so the numerator has to be 0
so yeah when a fraction equals 0 forget the denominator
vale wigeon
broo just it to 0
you accidentally the verb!
vale wigeon
btw if you wanna understand why think about it this way:
if numerator/denominato...
don't use the letter x for multiplication
spring summit
Mb
novel carbon
btw if you wanna understand why think about it this way:
if numerator/denominato...
Well it's not 0 because that would result to -16/0
spring summit
What are you referring to by "it"?
novel carbon
X
novel carbon
Idk thought you did mb
spring summit
and since if ab=0 either a=0 and/or b=0 that means youre acutally just solving
x...
.
novel carbon
Uh still confused
spring summit
About which part?
novel carbon
and since if ab=0 either a=0 and/or b=0 that means youre acutally just solving
x...
Why ab=0 and what even is ab here
spring summit
a and b just represent any 2 numbers
so what im saying is
if 2 numbers multiplied by each other equal 0
one or the other has to be 0 (or both are 0)
since you cant have like 2 * 3 = 0
So in our case its (x-4)(x^2 + x + 4) = 0
so either x-4 is 0 or x^2 +x + 4 is 0 because they cant both be non-zero yet multiply to give 0
so thats how we get
x-4=0
or
x^2+x+4=0
novel carbon
Now what about the /x² part?
spring summit
btw if you wanna understand why think about it this way:
if numerator/denominato...
Its insignificant like i mentioned here
glacial shell
How to find f'(x)=0 🙏😭
i think at this point you just have to think about the top line like (x-2)(x+2)(x2+x+4), and just think like
spring summit
i think at this point you just have to think about the top line like (x-2)(x+2)(...
its (x-4)(x^2+x+4) not (x^2 - 4)(x^2+x+4)
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wet magnet
Hello quick question. Im doing a so called Extended Essay for Math in the IB programme. I was thinking of covering the topic of laplace transform, are there any simple experiments that could be done for this topic?
lone heartBOT
Hello quick question. Im doing a so called Extended Essay for Math in the IB pro...
@wet magnet Has your question been resolved?
keen idol
its a tool used to solve differential equations primarly, what do you mean by "experiment"?
lucid cargo
hi
lucid cargo
how do i find the image of a point
(0,0) about the line x - 2y + 5 = 0
my first thought was to just get the distance and change the sign of it so its on the opposite side of the line but obviously that didn't work
not sure how to proceed
small lance
First, find the distance between the line and the origin
Find the line that is parallel to x-2y+5 = 0 and passes through the origin
Find the relative line passes through the reflection point by using line distance formula
Next, find the line that is orthodox to x-2y+5 and passes through the origin
The found line should also passes through the reflection point
Two non-parallel line => intersect at the point
lucid cargo
Find the relative line passes through the reflection point by using line distanc...
ok im lost
like
perpendicular line that passes through 0,0?
small lance
At which part
lucid cargo
the one i replied to
small lance
perpendicular line that passes through 0,0?
Yeah
Perpendicular >> the multiple of slope(gradient) should be -1
lucid cargo
Ohhhhhh
i see
thanks for the help wow wtf i didnt know it was acc this simple
.close
native brook
im trying to show is zero
lone heartBOT
im trying to show is zero
native brook
as you can see im getting a singularity here and i don't know why or what i have done wrong?
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native brook
<@&286206848099549185>
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@native brook Has your question been resolved?
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@native brook Has your question been resolved?
native brook
<@&286206848099549185>
lone heartBOT
@native brook Has your question been resolved?
celest swift
what the heck is this
left grotto
what the heck is this
i think it's hieroglyphics
lyric gale
as you can see im getting a singularity here and i don't know why or what i have...
May I ask what exact mathematics is being studied?
I might be able to help.
oblique lichen
Looks like an accident language
topaz mortar
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@native brook Has your question been resolved?
alpine sable
(0,0) about the line x - 2y + 5 = 0
is the answer for this (-2,-2) ?
round burrow
I was watching this video about Bertrand's Paradox https://www.youtube.com/watch?v=mZBwsm6B280 and a logic came to mind, if I do a linear sweep of all the possible cords along one direction, that should be enough to check the ratio between the cords that are greater or lesser than square root of 3. If that's so, than the initial question probability is 0.5.
round burrow
So here's a linear sweep of cords along the X axis
Red is greater than sqrt(3)
Cyan is lesser than sqrt(3)
No matter how I would rotate these, the ratio would be the same
so I don't need "All the Angles"
one linear sweep is fine I guess there could be some bias on the lengths..
But given the about that would be 50% probability, no?
If I have a sine distribution though. not linear, so that I have a more uniform sampling of the possible cord lengths...
I get a probably of 33% instead of 50%, for the cord to be longer than sqrt(3) so I guess I'm back into the paradox, never mind, lol
vocal verge
please help
raw jetty
please help
!occupied
lone heartBOT
please 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).
round burrow
ok, I'm gonna go with the 1/2 linear distribution for this one...
the 1/3 would be more fitting for "possible" lengths of a cut of a circle, but I'm also making the thing more bias by fitting to it.
So, 1/2 is the correct answer, no paradox exists 😄
Alright, I don't have a question anymore
shadow monolith
what the heck is this
i think it is electrodynamics
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dusty crest
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dusty crest
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marsh hamlet
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$-x^2-4x=-(x^2+4x)$
ocean sealBOT
mathisfun
marsh hamlet
Can you complete the square
dusty crest
Can you complete the square
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marsh hamlet
One message removed from a suspended account.
Oh
How did you do it for other questions
dusty crest
How did you do it for other questions
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marsh hamlet
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AAA
Ok
Basically, for $x^2+ax+b$ it equals $\qty(x+\frac{a}{2})^2-\frac{a^2}{4}+b$
ocean sealBOT
mathisfun
marsh hamlet
See why?
marsh hamlet
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Ok
$x^2+ax=x^2+ax+\frac{a^2}{4}-\frac{a^2}{4}$
ocean sealBOT
mathisfun
marsh hamlet
Agree?
dusty crest
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marsh hamlet
Ok
dusty crest
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ocean sealBOT
mathisfun
dusty crest
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marsh hamlet
It's fine
dusty crest
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marsh hamlet
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What do you mean
dusty crest
What do you mean
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lone heartBOT
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Available help channel!
plush valve
quick question do i add the + 2πn then multiply by 5 or multiply by 5 then add 2πn
plush valve
to solve for x
im guessing add 2πn first then multiply cuz thats what u do with division
actually yeah
.cloes
.close
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Available help channel!
twin bridge
super basic but how did we know we have to find theta here?
lone heartBOT
super basic but how did we know we have to find theta here?
brisk ruin
you know trigonometry?
twin bridge
yeah
brisk ruin
alright easier then
so I see you have calculated the value of theta to be 30 deg
it is obvious that the line is linear right?
so therefore y=mx+b
answer this question: what is the m in this equation?
lone heartBOT
@twin bridge Has your question been resolved?
trail oasis
Hello everyone who see this problem
Im sillybacon just call me silly
Im currently doing lots of problem and preparing for an exam in a future
In this problem i got stuck at a point
The problem as follows:
How many Positives integers are there satisfy this 3 conditions
- Can be divided by 2020
- Has at most 2020 unit digit
3.The decimal digit of it are string of consecutive ones followed by a string of consecutive 0s
Im currently stuck at the last conditions, if you help me or giving me advice thanks alot for that. If you don't. You still deserve a thanks for watching this.
vale wigeon
Has at most 2020 unit digit
... what does this mean?
did you translate from another language?
marble hamlet
Hello everyone who see this problem
Im sillybacon just call me silly
Im currentl...
Can you clarify hint 2
trail oasis
2020 unit digit is uh the total of number in that is 2020 number
Like 111(k number)..000(n numer) and k+n = 2020
lilac dome
did you translate from another language?
i asked this exact question yesterday to someone asking help and i got scolded by another member... why is this server like this???💔
vale wigeon
??
trail oasis
i asked this exact question yesterday to someone asking help and i got scolded b...
Wha
vale wigeon
who scolded you, where and when?
vale wigeon
2020 unit digit is uh the total of number in that is 2020 number
ok, so the number's LENGTH is at most 2020 digits.
vale wigeon
2020 = 10 * 2 * 101
trail oasis
I just dont know what the last ine do
lilac dome
i don't remember but they were like "idk why u didn't understand..
it was pretty clear english" but it was really not...
it happened yesterday
some very tense people here :*(
vale wigeon
seems relevant
trail oasis
I just need the last part
silent snow
who scolded you, where and when?
i have been trying to explain some 8th grader some basics for almost and hour and people here cant even wait for a minute before scolding others
thats sad
marble hamlet
I just need the last part
Probably something to do with modular arith
silent snow
i don't remember but they were like "idk why u didn't understand..
it was prett...
dont mind man wrong person wrong time
trail oasis
i have been trying to explain some 8th grader some basics for almost and hour an...
I was grade 8 ;-; and im forcefully to solve this problem :(
marble hamlet
Oh
trail oasis
marble hamlet
I guess there should be an easier way to solve it
trail oasis
What is mod tho
marble hamlet
Uh, a bit complicated shouldnt need it to solve this
I'll think of a better solution
vale wigeon
i asked this exact question yesterday to someone asking help and i got scolded b...
for the record, asking if a question has been translated is completely kosher
marble hamlet
Ok, lets have a shot at it then
Lets call our positive integer that satisfies all 3 conditions be N
trail oasis
Sure
marble hamlet
Wait let me refine this
give me 2 mins
wait are you sure you need to do this question?
It seems awfully complex
trail oasis
sure
marble hamlet
and also k + n <= 2020
trail oasis
n > 1
marble hamlet
Ok, nvm completely scrap that idea, I have an easier method
Ok, so the question says that N has at most 2020 digits
So k + n <= 2020
trail oasis
Hm!
marble hamlet
But instead of using the inequality, we can kind of strech out the number until it reaches 2020
to do that you can add filler numbers
trail oasis
But instead of using the inequality, we can kind of strech out the number until ...
Limits?
trail oasis
Hmm
marble hamlet
And in total, there are 2020 digits
trail oasis
Yes
marble hamlet
leave that idea for a second, but we will come back to that
trail oasis
Sure
marble hamlet
For N to be divisible by 2020, it must be divisible by both 20 and 101
A number is divisible by 20 if it ends in at least two zeros (because 20 = 2×10 and having two zeros ensures divisibility by both of them)
With me so far?
@trail oasis
So far so good?
Our number is just made up of all ones followed by zeros. If we take away the zeros, we re left with a number made up of just ones, which we’ll call L
For example, if our number is 111110, then L=11111
lone heartBOT
@trail oasis Has your question been resolved?
unique flower
lone heartBOT
unique flower
I'm using u=1+x^3 substitution to solve the integral
everything was going fine until I had to integrate:
(1/3) * integral(sqrt(u) du)
when integrating that you add 1 to the power of u, and multiply the integral by the new power
so it would become (1/3) * u^(0.5+1) * (0.5+1) = 0.5*u^(3/2)
however in the answer it says to multiply by the reciprocal of the new power, why is that?
in what cases do we multiply by reciprocal of new power, and in what cases do we just multiply by the new power
multiplying by 2/3 instead of 3/2
charred jewel
when integrating that you add 1 to the power of u, and multiply the integral by ...
thats just wrong
you divide the new power not multiply
lone heartBOT
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Available help channel!
livid sage
@spring elm
lone heartBOT
<@1087983523421507644>
livid sage
i have what i believe is the ans to ur q, but the process to get it is very not nice
zinc haven
what's your question?
livid sage
so u know for k = 5 you have 10^6 as the max
as an aside u probably also know, to minimize P(1000) you must have the constant quadratic term to be non-negative and the linear quadratic term to be non-positive
spring elm
<@1087983523421507644>
mhm?
livid sage
by fixing the linear + constant terms of the quadratic you can sort of optimize values of x and y where the inequality fails to hold
spring elm
so u know for k = 5 you have 10^6 as the max
ye
livid sage
by optimizing for the linear term, and then optimizing for the constant term
so this is very messy as you get like 12 terms and you have to differentiate these long expressions multiple times
spring elm
so this is very messy as you get like 12 terms and you have to differentiate the...
wth
livid sage
but it gives a result i think is correct
also if u don’t mind where did this q come from?
spring elm
also if u don’t mind where did this q come from?
||i made it
but since i have no idea if my answer is correct (since i just have the answer, not the process to get it) i needed a bit of help||
livid sage
oh that is kind of awesome
spring elm
ty
livid sage
this is the answer i get, if it means anything
$P(1000) \geq 10^6\left(1 - \frac{(k - 5)(2k - 1)}{(k - 1)(2k - 5)}\right)$
ocean sealBOT
Mqnic_
spring elm
**Mqnic\_**
yups same with me
livid sage
👍 cool
spring elm
can i have your sol?
livid sage
by fixing the linear + constant terms of the quadratic you can sort of optimize ...
i delete my work as i go but the rough idea is here
i.e. set quadratic P(x) = x^2 + cx + d, your first goal is find (a, b) such that k(P(a) + P(b)) - P(a + 2b) is as close to 0 as possible without going negative
(i replace (x, y) with (a, b) to avoid overloading notation)
you will notice if you view k(P(a) + P(b)) - P(a + 2b) as an expression in a, or b, you have a quadratic, which has a clear min point
you can minimize this using any method you wish
you find the point to be
$(a, b) = \left(\frac{c(k - 3)}{2(5 - k)}, \frac{c(k - 1)}{2(5 - k)}\right)$
ocean sealBOT
Mqnic_
livid sage
plugging this into the expression you minimized and simplifying gives
$(2k - 1)d - \frac{c^2(k - 1)(2k - 5)}{4(k - 5)}$
ocean sealBOT
Mqnic_
livid sage
d is non-negative so no issues here, you can solve for d
$d = \frac{c^2(k - 1)(2k - 5)}{4(k - 5)(2k - 1)}$
ocean sealBOT
Mqnic_
livid sage
to solve for c i again optimized the original P(x) by differentiating with respect to c
this gives
$c = -2000 \frac{(k - 5)(2k - 1)}{(k - 1)(2k - 5)}$
ocean sealBOT
Mqnic_
livid sage
so knowing c, d, you have the full quadratic P(x)
and evaluating P(x) at x = 1000 gives the result
$P(1000) \geq 10^6\left(1 - \frac{(k - 5)(2k - 1)}{(k - 1)(2k - 5)}\right)$
ocean sealBOT
Mqnic_
livid sage
glad you liked 👍
lone heartBOT
@livid sage Has your question been resolved?
livid sage
sure, why not
valid whale
hello is anyone know about irrational function i was confused the difference between rational and irrational function
vale wigeon
in what context?
valid whale
polinomial? i guees
vale wigeon
most likely "irrational function" refers to an expression that has square/cube/etc roots (of non-constants) in it
!xy
lone heartBOT
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.
valid whale
hmm i think it was more like this
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prime nebula
Show that this number is perfect square
lone heartBOT
Show that this number is perfect square
prime nebula
dusk oxide
$4^{2025}8^{2024}3^2 = 2^{4050 + 6072}3^2 = 2^{10122}3^2 = (2^{5061}3)^2$.
ocean sealBOT
richard feynman
vale wigeon
$4^{2025}8^{2024}3^2 = 2^{4050 + 6072}3^2 = 2^{10122}3^2 = (2^{5061}3)^2$.
uhhhhh i dont think OP's thing is a product
@prime nebula do you mean that you're looking at a number whose decimal representation consists of 2025 fours followed by 2024 eights followed by a single nine?
and you want to show that is a perfect square?
dusk oxide
Oh woops, that's definitely what they meant
lament wyvern
this is 44...488..8 + 1where each half is 2025 digits long
and 44...4400..00/88..88 (with 2025 0s) is 5x10^2024
so the whole number is ((5 x 10^2024) + 1) * 88 .. 88 + 1
idk maybe there's something there
prime nebula
<@1321468886956380193> do you mean that you're looking at a number whose decimal...
Yes
<@&286206848099549185>
karmic breach
?
karmic breach
ok
prime nebula
So i wrote it as 4 *10^4049+4 *10^4048+....
karmic breach
this is not even a perfect square
karmic breach
44…488…89
prime nebula
Yes
karmic breach
wait it is
7
2
49
7
2
=49
6
7
2
4489
67
2
=4489
66
7
2
444889
667
2
=444889
Since the pattern holds for smaller cases and can be generalized, so
N
N is indeed a perfect square.
@prime nebula
prime nebula
8k?
karmic breach
ye
prime nebula
And why is this perfect square
prime nebula
Cause k isn t the same here at 4 and 8
I mean at 4 k has 10^n
And at 8 k has 10^(n-1)
@karmic breach
rancid trail
Cause k isn t the same here at 4 and 8
im pretty sure that part is wrong
prime nebula
I still don t understand how should I write
rancid trail
because if you sub n=1 in this result, 49 is not obtained
prime nebula
Ok and how s that perfect square
rancid trail
well, thats the proof
this is only the starting point
@prime nebula i found it
adding the top parts, we will get $N=\frac{4\cdot(10^{2n}-4\cdot10^n+8\cdot10^n-80)}{9}+9$
further simplyfying, you will get
rancid trail
$N=\frac{4\cdot10^{2n}+4\cdot10^n+1}{9}$
prime nebula
now, this is a perfect square
Why?
rancid trail
$(\frac{2\cdot10^n+1}{3})^2$
prime nebula
**therealtdp**
It doesn t give the thing that s up