help-49

[twilit field]

yup

so that proves that they are susets of one another right?

[visual tiger]

that will prove they are subsets of one another once you prove it

so

you pick x from Ai
and you show it's in both

how do we write the math proof for that

[twilit field]

$x\in A_i \implies x \in A_j$

[grand pond]

(why am i here )= idk

[visual tiger]

yes that's the mathematical statement we gotta show

[twilit field]

as $x\in A_i \cap A_j$

[grand pond]

(why am i here )= idk

[twilit field]

$x \in A_j$

[grand pond]

(why am i here )= idk

[visual tiger]

why

[twilit field]

Because of this

[visual tiger]

so I ask you why "X" is true

and you tell me "because of this"

this being "X"

[twilit field]

That's true as it's given

[visual tiger]

where?

it's given x in Ai

that's how we chose x

and how do we proceed?

[twilit field]

we have to show it's in $A_j$

[grand pond]

(why am i here )= idk

[visual tiger]

sure

how do we do that

[twilit field]

We know that $x \in \bigcup$

[grand pond]

(why am i here )= idk

[visual tiger]

yep

[twilit field]

and that $\bigcup = \bigcap$

[grand pond]

(why am i here )= idk

[twilit field]

so $x \in A_j$

[grand pond]

(why am i here )= idk

[visual tiger]

Because x in bigcap

[twilit field]

yeah

[visual tiger]

we can't miss any step

so recapping the steps
x in Ai
so x in bigcup
so x in bigcap
so x in Aj

[twilit field]

and now we select an arbitrary member form $A_j$ and repeat the same process

[grand pond]

(why am i here )= idk

[visual tiger]

great

[twilit field]

That is sufficient to prove that they are equal , I think

[visual tiger]

can you see why if any of those steps are missing there's no "continuity" in your argument

[twilit field]

yeah

I can now

[visual tiger]

yes, you have shown Ai = Aj

for arbitrary i,j

so it's the case for all i,j

oh and by the way

Ai = ?

[twilit field]

An arbitrary indexed set?

[visual tiger]

yeah but I was going for

Ai = S

[twilit field]

S?

[visual tiger]

the bigcap = bigcup you defined

you wrote it as S

well each Ai is equal to bigcap = bigcup

[twilit field]

Got it

Thanks!

[visual tiger]

since

bigcap <= Ai <= Bigcup

[twilit field]

Got it

Can I close this now?

[midnight plank]

@twilit field Has your question been resolved?

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[zealous schooner]

Since x was arbitrary here its true for all x in Ai, hence Ai subseteq Aj

[zealous schooner]

Wow it really sent this message just now

.close

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[dusky cradle]

I tried to solve it with cauchy schwarz

(a+b+c)^2>=0
ab+bc+ca>=-1/2

[zealous schooner]

I mean, yes, but you didn't use the condition that a^2+b^2+c^2 at all here

[dusky cradle]

But we need maximum

It is minima

@zealous schooner

ab+bc+ca<= (a^2+b^2+c^2)(a^2+b^2+c^2)

So it will be 1?

[visual tiger]

you forgot square root

ab+bc+ca <= sqrt(a^2+b^2+c^2)sqrt(a^2+b^2+c^2)

[dusky cradle]

Which gives same value no?

Yes missed it sry

[visual tiger]

yeah it gives 1

and we don't forget equality case

[dusky cradle]

I see

What is that?

[zealous schooner]

When do you have equality in catchy Schwarz inequality?

[dusky cradle]

All are same?

[zealous schooner]

Well for this case that's what it comes out to be, but no that's not the equality condition in general

You actually need $\frac{a}{b}=\frac{b}{c}=\frac{c}{a}$

[grand pond]

kheerii

[zealous schooner]

The ratio of the terms has to be the same

[dusky cradle]

I didn't get it

[zealous schooner]

Also there should be a modulus in this one on the left

[dusky cradle]

Please explain if something missed

[dusky cradle]

Never saw it but thanks sir

So how should i use?

ab=bc=ca?

[zealous schooner]

The Cauchy Schwarz inequality states that $$\left(\sum_{i=1}^nu_iv_i\right)^2\le\left(\sum_{i=1}^nu_i^2\right)\left(\sum_{i=1}^nv_i^2\right)$$ with equality iff. $$\frac{u_1}{v_1}=\frac{u_2}{v_2}=...=\frac{u_n}{v_n}$$

[dusky cradle]

3ab<=1
ab<=1/3?

[grand pond]

kheerii

[zealous schooner]

well

You have a/b = b/c = c/a

[dusky cradle]

ac=b^2, ab=c^2,bc=a^2

[zealous schooner]

Sure

[visual tiger]

sure but ab+bc+ca <= modulus(...)

[zealous schooner]

So see what abc comes out to be from each of the equalities

[dusky cradle]

not getting clearly

Both left and right

We have same thing no?

[zealous schooner]

multiply the first one with b, second with c and third with a

[dusky cradle]

abc=a^2=b^2==c^2

[zealous schooner]

cubed, but yeah

Which means a=b=c

[dusky cradle]

Cube?

You meant geometric mean?

[zealous schooner]

abc=a^3=b^3=c^3

[dusky cradle]

Ohh i see

[zealous schooner]

You essentially just want to prove that ab+bc+ca=1 is actually attainable for some value of a, b and c

We have proved using cauchy Schwarz that ab+bc+ca <= 1 is an upper bound

[dusky cradle]

Bro i am asking you the upper bound is wrong or not?

I did not want to be prove actually

Did I apply cauchy Schwarz correctely?

[zealous schooner]

The upper bound is correct, but you technically can't state that the maximum value of ab+bc+ca is 1 until you show that ab+bc+ca actually TAKES the value 1 at suitable values of a, b and c

[zealous schooner]

Yes

I can say that 2 <= 3, but this doesn't mean that the maximum value of 2 is 3

If that makes sense

[dusky cradle]

Ohh i see

[zealous schooner]

Or a better example, -x^2 <= 1 is true for all real x, but the maximum value of -x^2 is not 1

[dusky cradle]

but i use cauchy blindly

[zealous schooner]

Using cauchy isn't wrong

And 1 does end up being the maximum value of that sum

But you need to show that that equality condition for the cauchy Schwarz inequality actually applies

[midnight plank]

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[last slate]

having trouble with finding the invertible matrix

i'm pretty sure the two diagonal matrices are the same because the eigenvalues are the same

but when i find the eigenvectors of A and combine them to get P matrix to find the invertible matrice, when I test it by doing AP = PB, I don't get the same matrix

The invertible matrix I currently found I got through combining the eigenvectors of the matrix A

i'm going to do a different problem for now so i might not respond quickly, any help is appreciated

@fish you ok bro?

[tired vapor]

i'm thinking

$A=P_1DP_1^{-1}$, $B=P_2DP_2^{-1}$, $D=P_2^{-1}BP_2$, $A=P_1P_2^{-1}BP_2P_1^{-1}$, $(P_1P_2^{-1})^{-1}=P_2P_1^{-1}$ i guess find $P_1$, the eigenvector matrix for A and $P_2^{-1}$, then inverse of the eigenvector matrix of B ) and $P_1P_2^{-1}$ is the matrix

i think this will work?

[grand pond]

fish

[last slate]

I changed it a little bit to D = P_1^(-1)AP_1 because thats what the problem statement is asking

so then P_1P_2^(-1) would be the matrix

so the same thing

[tired vapor]

i forgot how to do diagonalization, but i verified that this works

so yeah, P_1P_2^{-1} is the matrix

but make sure the eigenvalues are in the correct order, so $A=\begin{pmatrix}v_1&v_2&v_3\end{pmatrix}\begin{pmatrix}\lambda_1& 0& 0\0 & \lambda_2 &0 \ 0& 0& \lambda_3 \end{pmatrix}\begin{pmatrix}v_1&v_2&v_3\end{pmatrix}^{-1}$ and similarly for B

[grand pond]

fish

[last slate]

yeah i tried to match the order of the eigenvalues when finding the eigenvectors

like i matched the vectors for 3, -3, 1 to 3, -3, 1

the matrix test works out AP = PB

i think i have the diagonal matrices correct

I just found the eigenvalues for the second matrix and just rearranged them in the same order as the eigenvalues for first matrix

I hope the grader likes this 🙏

cool! thanks for your help!

.clspe

.close

[midnight plank]

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[last slate]

[midnight plank]

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[pure wraith]

If B was a proper subset of A, would it mean P(B) < P(A)?

[pure wraith]

I think it does but I don't know how I'd write it down mathily

Do I say A = B u C where C = A \ B

[dreamy lichen]

What do you mean by P(B) < P(A)?

[pure wraith]

probability sorry

not power set

Interesting

[dreamy lichen]

wait no

B is a proper subset of A in what sense?

[pure wraith]

in the regular sense 😅

i don't know what to answer sorry

[dawn dagger]

I think that's correct

[pure wraith]

How would I write it down

In probabilitese

[dawn dagger]

P(B) < P(A)

the way you did or what do you mean?

[pure wraith]

A sort of proof?

[dawn dagger]

Try to write P(B) in terms of A

[dreamy lichen]

What if A is some event that can happen and has 0 probability? Then there could be some subset B, whose probability is not strictly smaller than the one of A.
(In case that what i said is complete bullshit, just tell me it's wrong. I know almost nothing about this field)

[pure wraith]

I could just do it by listing out the elements right

[dawn dagger]

I think if that was the case then you already disregarded B ⊂ A

[pure wraith]

$B = {b_1, b_2 \cdots c_1, c_2, \cdots }$ and $C = {c_1, c_2, \cdots }$

[grand pond]

jewels!

[pure wraith]

So P(C) = n/|S| and P(B) = (m + n)/|S|

Well, thank you both for your help :P

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[exotic pelican]

true

take [0, 1] as a sample space with a lebesque measure and you have that P({0}) = 0

[dreamy lichen]

P({0,1/2,1}) would be also 0, right?

[exotic pelican]

yeah every finite set

[dreamy lichen]

okay

that would mean that

if B = {0} A = {0,1/2,1}
then B is a subset of A and P(A) = P(B)

which clearly violates it

[exotic pelican]

this whole thing only works with subset/equal and less/equal

[dreamy lichen]

That's what i thought, or limited to finite sample space possibly

if thats the right word

[exotic pelican]

i think not even finite always works

[dreamy lichen]

that sounds strange actually

can you give an example?

[exotic pelican]

if we take omega = {a, b} with P({a}) = 0 and P({b}) = 1

[dreamy lichen]

oh, right

[exotic pelican]

if every point has a positive probability then yeah

@pure wraith if you want to take that into consideration

[pure wraith]

Can you elaborate on this

Forget about the continuous case, this is purely discrete

[dreamy lichen]

A = {a, b}
B = {b} maybe

wait no

[exotic pelican]

in general if an element exists such that {x} has 0 probability, then this is wrong

as P({x}) = P({})

[dreamy lichen]

is this right?

[midnight plank]

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[twilit field]

Q11

[twilit field]

would this be right?

Y/N please

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

<@&286206848099549185>

[pearl idol]

N, do you want me to elaborate on that or no?

[twilit field]

No.

I'll think of something

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

OK. Could I have a hint , please?

I think de-constructing the defn might help me

A is an element of the set wherein X is an element of the powerset of naturals, wherein the cardinality of X^c is finite

I don't suppose it is simpy P

where P means $A \in {X \in \mathcal{P}(N) | |x^C| < \infty}$

[grand pond]

(why am i here )= idk

[twilit field]

<@&286206848099549185>

[prime hornet]

you need to write 11) as the connection between 2 statements?

[twilit field]

I mean I think just symbolic form

I'll ask my prof today

[prime hornet]

so we need to write it as P (something) Q?

[twilit field]

Maybe

[prime hornet]

where we define P and Q to be some statements?

[twilit field]

yup

[prime hornet]

okay.

[prime hornet]

well, there's two things going on here

[twilit field]

I was thinking P could mean x\in {X \in P(N)}

[prime hornet]

A is an element of this set, and every element in that set satisfies some condition

that's all 11 is saying, really

[twilit field]

and Q could be the condition

am I right?

[prime hornet]

x \in ?

what is x

[twilit field]

$A \in {X\in P(\N)}$

[grand pond]

(why am i here )= idk

[prime hornet]

right, that's better

[prime hornet]

pretty much, in my eyes

or rather, hmm

this isn't quite it

[twilit field]

so $P \land Q$

[grand pond]

(why am i here )= idk

[prime hornet]

this is right, but quite redundant

saying that "A is an element of the set of all elements in the power set of N" can be shortened to "A is an element of the power set of N", if I am not mistaken

the "set of all elements in the power set of N" is just the power set of N, is it not?

[twilit field]

Yes

[prime hornet]

right, so you can simplify this

[pearl idol]

(this is kinda a dumb exercise in my opinion considering it's already in formal notation)

[prime hornet]

I agree

I actually hate these kinds of exercises

at least I am getting review through wai

[twilit field]

Hmm, I think I'll have a problem set on these today.

[prime hornet]

good luck!

[twilit field]

Thanks

only one maths class today though 😭

We have an hour of EVS before that

.close

[midnight plank]

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[twilit field]

thanks again!

[prime hornet]

EVS?

[pearl idol]

ohh this is homework?

[twilit field]

No!

[prime hornet]

it looks like Hammack to me

[twilit field]

I'm self studying before class starts

[pearl idol]

oh

[twilit field]

Environmental science

[prime hornet]

ahh

[twilit field]

I would NEVER ask for help with HW

I have standards

[prime hornet]

I did an ENV course in my 1st semester

[twilit field]

It's compulsory here

[prime hornet]

you can, and should, ask for help when it is needed

[twilit field]

Not if its graded

[prime hornet]

you should not learn math by yourself

[prime hornet]

you are not allowed to discuss with peers?

[twilit field]

I mean we'll be doing our HW in teams here anyway

[prime hornet]

I see

[twilit field]

so idt I'll ask for help much here

[prime hornet]

I was allowed to talk to my peers for hmw

[prime hornet]

ahh

[twilit field]

.reopen

[midnight plank]

✅

[twilit field]

could I have the last two lines formalluy explained

or is it just a defn?

[prime hornet]

this is the concept of a "vacuous truth"

I'm trying to think of an intuitive way to explain it, because this is smth I struggled with myself for a while

[twilit field]

I mean 3 sort of makes sense

ooooh

[prime hornet]

okay, let's make it more colourful

[twilit field]

yeah, it all makes sense now

if F->F

[prime hornet]

[twilit field]

then the implication is TRUE

[prime hornet]

well, do you want me to give my colourful example anyways?

or are you good?

[twilit field]

Sure! :D

Hi, Charbit!

[prime hornet]

hmm, cloud is here so I don't know if I should do this rn

okay let's just do it anyways

"if I get banned from mathcord, then the world will explode"

P -> Q

I want you to consider the situations where I am lying to you

if I get banned from mathcord, and the world blows up, then you would agree that my statement was true

P implied Q, and all is well

[twilit field]

yes

[prime hornet]

if I get banned from mathcord, and the world doesn't explode, I am a liar

so the implication is false

[twilit field]

Yeah, I understand it using an example

[prime hornet]

now, what if I don't get banned?

[pearl idol]

It is just a definition btw, this convention is called "material implication". There are other ones, but this one is the most useful for math.

[twilit field]

But formally, how would i justify it

[twilit field]

Aah,okie!

[prime hornet]

Eric is correct

[twilit field]

Thanks!

[prime hornet]

but I like exploding the world

:kanna_Fire:

[twilit field]

Why don't books mention that?

[prime hornet]

[twilit field]

Not very canadian of you/j

[pearl idol]

Depends on which book

[prime hornet]

anyways, if I don't get banned, and the world exploded anyways, I am not a liar still

[twilit field]

This is book of proofs by hammack

[pearl idol]

Getting into a philosophical discussion into the correct nature of implication is a bit of a digression from doing math tho

[prime hornet]

because I didn't say anything about what would happen if I wasn't banned

[twilit field]

Math is just applied philiosophy though /j

[prime hornet]

likewise, if I didn't get banned and the world didn't explode, then I wasn't a liar either

[twilit field]

Yeah, got it!

[prime hornet]

I lied to you if and only if I was banned and the world stayed intact

[prime hornet]

on the flip side, I propose banning @tribal temple to see if the world will explode upon their expulsion

[twilit field]

.moose

.close

[midnight plank]

Channel closed

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[prime hornet]

I was told that chartbit keeps the world together through their emotes

I wonder if their ban results in the world's destruction

[midnight plank]

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[twilit field]

. huh, that was quick

[prime hornet]

. it was, yeah

oh whatever, let me just open this

[prime hornet]

@tribal temple I demand an answer

[tribal temple]

It would

[prime hornet]

:kanna_Fire:

.close

[midnight plank]

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[prime hornet]

[prime hornet]

https://tenor.com/view/hug-warm-hug-depressed-hug-gif-4585064738068342394

[delicate helm]

isn't that when you make a statement about elements of an empty set?

[prime hornet]

no, but it is often applied to the empty set

still one of the best things I've ever seen on MSE

[junior flower]

nice to see you have a question higher

[delicate helm]

makes sense

lol

[prime hornet]

yes, I wondered if chartbit's explusion would result in the destruction of the world

far more exciting of a question than most, I know

[junior flower]

:kanna_fire:

[prime hornet]

:kanna_Fire:

[tribal temple]

[delicate helm]

this is the question i guess?

[prime hornet]

yes

[midnight plank]

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[wanton shore]

Can anyone tell me the logic behind limit as a sum

[wanton shore]

How they convert limit to integration?

[sage helm]

https://en.wikipedia.org/wiki/Riemann_integral

[midnight plank]

@wanton shore Has your question been resolved?

[midnight plank]

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[rose cobalt]

[a,b] is an interval
D is the operation of differentiation:
D:C^{k+1}[a,b] -> C^k[a,b], Df(x)=f'(x)

J is the integration:
J:C^k[a,b] -> C^{k+1}[a,b], Jf(x)=\int^x_a f(y) dy

I see that DJf(x)=f(x) and JDf(x)=f(x)-f(a) but no idea on how to find the range of D and J

[rose cobalt]

Also I found the null space of D and I: the set of all constant functions and set containing only zero function respectively, im not too sure if these are correct

[midnight plank]

@rose cobalt Has your question been resolved?

[midnight plank]

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[last slate]

are the equivalence class of mod 10 the same as the equivalence class of mod 7?

[last slate]

idk this seems like a stupid question?

but they clearly are not right?

[last slate]

which one?

[last slate]

this

@tribal temple could you give me a "lower level" reasoning to this? other than mod 7 and mod 10 of a number clearly can be different?

[tribal temple]

Well, if you think about any of the equivalence classes, the ones mod 10 are basically multiples of 10 (maybe "shifted" a bit)

Whereas those mod 7 are multiples of 7, perhaps shifted

Not all multiples of 10 are multiples of 7, and vice versa, if that helps?

[last slate]

mmmmm i guess so, maybe my question was just stupid

thanks

[tribal temple]

It happens, we all have those questions sometimes

[last slate]

what do you call mod 10?

is that an equivalence class?

is my wording correct?

[midnight plank]

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[midnight plank]

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[ripe oasis]

I have the value of an asin function outputting 0, π/2, 0, -π/2. I want to offset this value so that the starting value is 0 at π/4. How exactly do I do this? I’ve tried adding and subtracting the π/4 from the entire asin function but I get weird values further into the function like 3π/4 which isn’t what I want exactly

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@ripe oasis Has your question been resolved?

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[gilded rapids]

Hi

[gilded rapids]

I need helpp

how to find x?

[full marlin]

do you know what a cyclic quadrilateral is?

[gilded rapids]

i dont think so

[full marlin]

it's a quadrilateral with all 4 vertices lying on the circle

[gilded rapids]

oh

[full marlin]

PQRS in this diagram is cyclic too

try to apply the property of opposite angles summing to 180 to find x

[gilded rapids]

is angle Q and S = to 180?

[full marlin]

it is but neither directly involves x

you need to use the other pair

[gilded rapids]

angle P and R

[full marlin]

yes

[gilded rapids]

but i get 85 which is not in the options

[full marlin]

how did you get 85?

[gilded rapids]

180 - 10 = 2x

x = 85

[full marlin]

did you add just 2x and 10?

this angle is x+ angle ORS

just x is angle QRO in quad OPQR not PQRS

[gilded rapids]

oh 🫠

[midnight plank]

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[rain sonnet]

mb this is the updated one

[midnight plank]

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[rain sonnet]

.close

.close

.open

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[subtle torrent]

how to solve (c)?

[carmine sigil]

@subtle torrent You plug in x = 0.5, y = 0, and see if you get an equation in z which has a single solution.

Then, if so, you take the partial derivative in the usual way, and plug in the proper value for x and y (remembering to use the chain rule for z(x, y) where applicable.

!show

[midnight plank]

Show your work, and if possible, explain where you are stuck.

[carmine sigil]

Ok, so what is the value(s) of z here?

[subtle torrent]

there're two possible values of z

[carmine sigil]

Then is it a function?

[subtle torrent]

yes..?

[carmine sigil]

Vertical line test says?

[subtle torrent]

vertical line test? here?

[carmine sigil]

Yes

z(x, y) so your vertical line is parallel to the z axis (rather than the y axis, as you might be used to)

Alternatively and equivalently, a function needs to have a single output

Is there a single output to z(0.5, 1)?

(or is there two?)

[subtle torrent]

2

[carmine sigil]

Therefore...

[subtle torrent]

the function doesnt exist

[carmine sigil]

It's not a function. Yeah

It's so convenient when you don't have to do a bunch of extra work!

[subtle torrent]

so no need to calculate the partial derivatives?

Thank you !

.close

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[pearl hull]

What does that dot stand for?

[late palm]

Multiply

[pearl hull]

Alr, what have you tried?

[pearl hull]

Have you tried simplifying this?

[late palm]

Don't know where to start

[modern shore]

factorize the 2 powers

take 2^192 as a common factor

[late palm]

Ok

[modern shore]

done ?

[late palm]

Yup

[modern shore]

what u got

[late palm]

$2^192(2^8 -1)*31+2^n$

[grand pond]

sun.flour

[late palm]

2^(192)**

[modern shore]

itd okay u can write on papaer if u have

[late palm]

Ok

[modern shore]

simplify 2^8 -1

[pearl hull]

It doesn’t look like the case

[late palm]

Using a²-b² identity??

[modern shore]

u can just calculate it

2^8 aint a big number

[late palm]

Ok

256

[pearl hull]

It’s incorrect

[modern shore]

2^192 x 255 x 31

[late palm]

Ohh ya

[modern shore]

255= 3517

[late palm]

How?

[modern shore]

255 = 3 x 5 x 17

so 2^192 x 3 x 5 x 17 x31

[pearl hull]

Look at the original question closely

[modern shore]

the number that hould be multiplied with this to make it a perfect square is

3 x 5 x 17 x31

so the number becomes

2^192 x 3 x 3 x 17x17 x31 x 31

[late palm]

Where do +2^n goes??

[modern shore]

let a = 3 x 5 x 17 x 31

so new number = 2^192 x a^2

[pearl hull]

……

[modern shore]

subtract old No. from new number

[late palm]

Didn't get it

[modern shore]

(2^192 x a^2 ) - (2^192 x a)

2^192a(a-1)

thats ur difference

idk how to evaluate further

[pearl hull]

Looks concise

Is it my time to talk?

[late palm]

Yes pls

[modern shore]

SHUT UP PEASENT

(jk continue)

[late palm]

You both are free

[pearl hull]

….

First of all, you’re result is incorrect

[modern shore]

ok

[pearl hull]

No, I’m referring to her result lol

[modern shore]

oh shit

[pearl hull]

That’s all I wanted to say lol

[late palm]

Where did 2^192 goes??

[pearl hull]

But both of you just ignored me 😭

[late palm]

Pls explain

[modern shore]

2^192a(a-1) , how do we evaluate this further

[late palm]

I was waiting for you to correct

[modern shore]

WHY DINT U CORRECT URSELF

SMART AHH MOFO

[late palm]

Idk

He was saying that I was incorrect

[pearl hull]

Stop…. You could get banned for this

[late palm]

Ofc I didn't knew what was wrong

[modern shore]

damm i can

sorry bruh

[pearl hull]

It’s ok

[modern shore]

i just talk to the homies like that

[pearl hull]

Anyways, proceed

[late palm]

...

[pearl hull]

What did you get from this?

[late palm]

Like this

I took common

Is it wrong??

[pearl hull]

That’s not the original question

[late palm]

We can multiply the whole wig 31+2^n

Can't we??

[pearl hull]

Why??

Why can we

[late palm]

Opps

I thought the whole is multiplying with that

Got it

Nvm

Sorry

[pearl hull]

No, it’s not XD

Proceed

[late palm]

$2^(192) *225 +2^n$

This is what I got

[grand pond]

sun.flour

[pearl hull]

Looks good

Do you have any idea from here?

It’s better that you come up with the final solution yourself

[late palm]

Ok

Thanks for helping

[pearl hull]

Have you gotten the solution?

It’s only one step far from the answer

🤔️

It shouldn’t take that long

@late palm Have you solved it?

[midnight plank]

@late palm Has your question been resolved?

[midnight plank]

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[iron gulch]

l

[iron gulch]

.close

[midnight plank]

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[iron gulch]

that was by mistake

[midnight plank]

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[dusky cradle]

any hints for this trick?

[pearl hull]

Damn, looks like an advanced question

[dusky cradle]

Ohh

[onyx locust]

in what chapter is this ?

[dusky cradle]

quadratic equations?

What level are you studying if you don't mind?

is this really a hard problem?

[onyx locust]

first degree engineering

[onyx locust]

i dont know just im from belgium and i dont remember seen this in calss

or this type of excercices

[midnight plank]

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[dusky cradle]

.close

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[fossil ember]

So I have a set of points and another set of points. All numbers are real and finite. This is in 3d. Trying to sort so that intersect parts of shapes in a 2d view plane by a view point are z then distance sorted. Z buffer does not handle transparency well and I was thinking just if overall intersect was closer like whole shape closer. Yes partly inaccurate. If I am doing all wrong tell me. How to do this? If you can recommend a reusable or small resource usage solution would be great. All shapes are planar and not self intersecting. I can find whole centroid of shapes. X E.

[fossil ember]

Feel free to ask if I should clarify. X E.

Sorry this is complex math stuff. X E.

I can get rectangle common to both polygons in 2d. I just can't find parts of polygons in them. X E.

Anyone know what this is called so I can look it up?

Oh and sorry about this, <@&286206848099549185>, anyone?

Should I give out like my email? I feel like a partner might help at this point. X E.

Making a 3d math programming library. X E.

P.S. X E is in like my bio. X E.

And hey, if I have centroid XYZ, is that centroid distance if I get distance from view point?

And again no one answers, <@&286206848099549185> should I stop?

[carmine sigil]

only ping helpers once please

[fossil ember]

Okay, I am new, sorry. X E.

Anyway z buffer I am finding won't work entirely, I need like my transparency. X E.

[carmine sigil]

https://www.sjbaker.org/steve/omniv/alpha_sorting.html

[fossil ember]

If that is your opinion of a z buffer almost what do I got to lose with like my inside polygon area algorithm?

[carmine sigil]

but if you search for alpha-blending, you should be able to come up with some workable tutorials that walk you through it

[fossil ember]

"Alpha compositing" is like my first result and not seeing much tutorials. X E.

[carmine sigil]

http://learnwebgl.brown37.net/11_advanced_rendering/alpha_blending.html

but this also requires sorting. And there's just no perfect way to do sorting.

[fossil ember]

Great, another thing I can't do without direct access to screen. X E.

[fossil ember]

There is a mathematical way to do it, it would take longer than gamers are willing to wait though. X E.

Good tip to only ping once. X E.

[carmine sigil]

It's the rule

!15min

[midnight plank]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[fossil ember]

Oops, did not see that. Sorry everyone else. X E.

Just so I am not missing anything, where is that rule?

[carmine sigil]

I've never implemented one of these before

but perhaps https://en.wikipedia.org/wiki/A-buffer

#❓how-to-get-help message

[fossil ember]

Okay, I guess I forgot that one, I just read other stuff, why I never did this before I guess. X E.

[carmine sigil]

https://dl.acm.org/doi/pdf/10.1145/964965.808585 <- pdf warning, description of the A-buffer algorithm

opengl supports it natively

[fossil ember]

Okay saw all that, if you ever find code to study/use would be good, I understand almost all. X E.

[carmine sigil]

https://registry.khronos.org/OpenGL-Refpages/gl2.1/xhtml/glAccum.xml

[fossil ember]

I guess really how to measure all parts of polygon in that rectangle and I should be good. Like min and max x at min and max y and how to determine whether between a part of a polygon too? I have that implemented except that between parts of polygon outside rectangle part and I think I can do that. Based on what I know this might actually be a good algorithm. X E.

I guess find x and y intercepts for other side once I have those mins and maxes at mins and maxes? I guess I really should just implement like my own algorithm but I don't think current stuff allows good testing. I just have triangles, quads, and lines. X E.

Well this and a cutter, I should be good with that. X E.

.solved

[midnight plank]

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[dense arch]

lowkey lost

[dense arch]

tried power rule but that failed

thought of using quotient rule but i don' think that would work

just saw that 3^x is 3^x * ln(3)

.close

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[iron whale]

6+2i/5

Ive been tasked to "Rationalize the denominator or numerator", but I don't see what this question wants me to do. Any ideas?

[iron whale]

It's written exactly like this with the terrible formatting

[worthy wing]

Can you take a picture of the question?

[iron whale]

i need to get my camera hang on

[worthy wing]

The only thing you can do there is add up into a single fraction and factor (unless i am missing something)

[dawn dagger]

They managed to use for 62 and 63 normal lines

but at 64 this is where they drew the line

[iron whale]

64 is actually where they didnt draw the line

[dawn dagger]

you didnt get the joke lol

[iron whale]

https://tenor.com/view/foiled-again-foil-again-cat-kitten-gif-24575588

[worthy wing]

There is nothing to do in that exercise

[dawn dagger]

Write this as answer

There is nothing to do in that exercise

[midnight plank]

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[pearl hull]

Firstly, note that this simply can't have positive roots. So we are trying to find the smallest root essentially. As a gets larger, we are adding a non-negative number to the polynomial, which (because of the shape of the graph) implies that the smallest root gets smaller. So we want a to be the largest possible, which is 1. So now we have x^3 + x^2 + bx + c. Observe that by setting b = c, we get a root -1. For a fixed b, c = b is also the largest value of c we can possibly get. And the smaller value of c gets, the larger the root gets. (Again, imagine the graph shifting down). This means that x^3 + x^2 + bx + c where b = c is the optimal solution

From, helpers lounge

Credit to methisalwaysright

Well, I still don’t get it

[dusky cradle]

Same

[pearl hull]

Does it help?

[dusky cradle]

Is there hidden channels too?

[pearl hull]

yes, it’s for those with helpful role

[dusky cradle]

Where extraordinary people helpes?

[dusky cradle]

Wow nice

I wish normal students can see/ask also

[pearl hull]

When you obtain helpful, you can join the secret club

Anyways, I hope meth’s message would do you a favor

I’m too bad for this

[dusky cradle]

I didn't understand it completely actually

Should we not use derivative of function?

[pearl hull]

Not really

It appears that it can be solved without derivatives

[dusky cradle]

Yeah i didn't understand it

Could you make it more easy please?

[pearl hull]

Let me try, but don’t expect that I can provide you a satisfying explanation

[pearl hull]

I understand most of it

Where are you getting stuck at?

Anyways, I’ll try slowing down my pace

First of all, you have to notice that the real root is negative

[midnight plank]

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[midnight plank]

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[drifting root]

Q19

[drifting root]

my working out so far

whats an easy way to say the ab=1 branch is rejected

<@&286206848099549185>

[midnight plank]

@drifting root Has your question been resolved?

[summer terrace]

you did the identification of only the x³ terms and the constant terms, right?

[drifting root]

yep

do i need the x^2 for the simplest way to prove?

[summer terrace]

the x term!

give it a try

[drifting root]

okok

[summer terrace]

its important to gather/use all the possible information

they are there for a reason

[summer terrace]

exactly

[drifting root]

so do i even need to do the constant term one or can i just do this straight away

[summer terrace]

haha, you see, after all the best selection would have been the x³ and the x terms 😛

[drifting root]

fr

thx for the help

.close

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[quaint field]

What interest rate would you need to double your money in 10 years?

I just did 2^0.1 = 1.07177 = 7.177% yearly interest rate but I didn't use logarithms so I feel like there is something wrong.

[soft token]

No, that's correct.

[quaint field]

oh ok

then why do people use the rule of 72 to solve it, and I think rule of 72 requires logarithms to derive?

[soft token]

That's just an estimation but it's the exact same thing as what is generally done.

[next bramble]

You'll want 7 percent interest.
$$ 1 * (1+x)^{10} = 2 \implies x = 1 - \sqrt[10]{2} = 0.07177... $$

[soft token]

You have this:

$$ A/P = \left( 1 + \frac{r}{100}\right)^{t}$$
Since you want it to be doubled, A/P = 2

then you take logarithm to get an estimation for t in terms of r.
So, taking logarithm on both sides,

$$\ln(2) = t \cdot \ln\left[ \left( 1 + \frac{r}{100}\right)\right] $$
Which gives,
$$ t = \frac{\ln(2)}{\ln\left[ \left( 1 + \frac{r}{100}\right)\right]} \approx \frac{72}{r}$$

I hope that works. Lol.

[grand pond]

Shuba

[soft token]

To understand approximation at the end, you will need to know expansion of ln(1+x).

Perfection. Nice.

[grand pond]

Anonymous

Anonymous

[midnight plank]

@quaint field Has your question been resolved?

[quaint field]

I think I am confused about what interest rate actually is

does a 7% yearly interest rate mean that if I invest $100, I will get $107 after a year?

or is it slightly higher because my money is growing continuously instead of jumping by 7% at the end of the year

[next rover]

could be either

[midnight plank]

@quaint field Has your question been resolved?

[midnight plank]

@quaint field Has your question been resolved?

[midnight plank]

@quaint field Has your question been resolved?

[pure shore]

I think the interest rate is usually calculated with a specific period in mind. a yearly interest rate would get you interest over your money in a year while a monthly one would be over a month. your money wouldn't be increasing continuously it would be increasing every month for example.

[quaint field]

so you wouldn’t use e^(kt) for interest right?

in the real world

[next rover]

in the real world you can ask what to use

[pure shore]

i think that would be too generous xD

[delicate helm]

it really wouldn't if you choose k carefully

you can even choose negative k for lulz

[pure shore]

Negative k would be a nice model for getting scammed

[quaint field]

ok I think I understand now

you don't use e

[delicate helm]

idk if you use exponentials tbh, you probably just do one month/year at a time

[quaint field]

you use the (1+r)^t formula, where r is the yearly interest rate instead of the continuous interest rate

and to solve for t, you need to take the ln of both sides

so that's how you get the rule of 72 thing

but you can also solve for r in terms of t by using an exponential equation

but using 2 as the base

[quaint field]

like what I did here

[delicate helm]

sure

[quaint field]

and this is the other way to do it, which solves for t in terms of r

but for rule of 72, it's a recipricol relationship, so it doesn't matter which way you go about it

that's why it's so effective

the only issue is it's an approximation instead of exact

.close

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[last slate]

i got l =3

actual answer is 5

[midnight plank]

@last slate Has your question been resolved?

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[placid dragon]

bro can yall help with this

[placid dragon]

like hows this done bro

seems easy but im missing smth

[drifting root]

cause diameter, you know b = 90

you can find the other angle from cyclic quad

then triangle sum

[kindred wraith]

Was bout to say same thing but u beat me to it

:/

[drifting root]

lmao

[placid dragon]

hoe do i know?

how*

[drifting root]

its a circle geometry proof

[placid dragon]

else id have solved it

oh ok

[drifting root]

angles in a semicircle are 90degrees

[placid dragon]

but it should be mentioned

[pearl hull]

[placid dragon]

bro its not given its a semicircle, the questions vague af

[drifting root]

?

O is the centre

[pearl hull]

AB passes O

[kindred wraith]

Bro wait if AB diameter then how it equal DC

[placid dragon]

bro AB can be any chord

[kindred wraith]

Any chord passing through center is diameter

[drifting root]

i think its just saying that point is O, the lines too short

[placid dragon]

obviously assuming AB as the diameter is correct in this case but technically the stuff should be mentioned

[placid dragon]

bro you DONT know whether o is centre lmao

[kindred wraith]

O i see

Wait a sec

[drifting root]

its criminal if its not the centre

[placid dragon]

fr

[kindred wraith]

a+b=180-50

[placid dragon]

ye

[kindred wraith]

Is AB =DC given?

[placid dragon]

nah see yourself

[kindred wraith]

Well I'll give you tip

[placid dragon]

the question's kinda incorrect

[kindred wraith]

In mcq if it looks like trapezium then it trapezium

[drifting root]

yea the q is kinda stupid if you take it literally

[drifting root]

its not parallel

[kindred wraith]

It normally

Not always

[drifting root]

ye but this one isnt

[placid dragon]

nahhh bruhh

never do that

especially competitive exams

[kindred wraith]

I did and got like 47/50

[drifting root]

lmao

[kindred wraith]

Depends on your grade ig

[placid dragon]

which exam? ur school exams?

[drifting root]

honestly, theyre not gonna label a point thats not the centre O

just use that

[kindred wraith]

It was earlier some test like IMO

[placid dragon]

ive seen so many question with points o that are not the centre

[drifting root]

on a circle?

[kindred wraith]

Daym

[placid dragon]

imo is fake as shit no offense

[placid dragon]

yes

[drifting root]

damn

[hybrid thorn]

thats cursed

[drifting root]

theyre bullies

[kindred wraith]

Well I got class

I gtg

[placid dragon]

.close

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[drifting root]

sketching ths

uhhhh

[drifting root]

inv?

y=-x

[runic hamlet]

if x is for example 0, what could y be

[drifting root]

ah,

are there multiple lines

[runic hamlet]

yes

[drifting root]

but is this correct for the shape?

[runic hamlet]

thats one of the lines, yes

[drifting root]

ic

thx

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[summer ravine]

range = u^2 sin(2theta)/ g

are you stucK?

what do you need help with

Ok so confirmation

you're correct

no

Wait

oh yes you're correct

maybe try vertical range

nvm you'd still get the same r 1 = r2

The answer sheet is surely incorrec?

because 30 = 45 - 15 and 60 = 45 + 15

so same range

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[gaunt nimbus]

${\log_{10}|x| < 1}$?

[grand pond]

:D

[gaunt nimbus]

should be that, no?

[hollow kettle]

sa

[gaunt nimbus]

alright

lets try figure why

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[mental wraith]

This is gonne be stupit question propably, but im doing some math homework right now and i came across multiplying 92 with 0.5 wich apperantly equals to 46. I dont understand how that works, because shouldnt multiplying make the number bigger instead of smaller? (Pls dont make fun of me, i am currently repeating 8th grade because of math )

[surreal moon]

If you multiply by a number less than 1, you get a smaller number

[mental wraith]

What!? Why? How is that possible, you are still multiplying with something, how does that make it smaller?

[surreal moon]

Because multiplying is basically saying how many times something happened. Say 92 is how many kilometers you drive per hour. If you drive for one hour, then you've traveled 92 kilometers. But if you've driven for less than an hour, it stands to reason you've traveled less than 92 kilometers

[mental wraith]

Oohh i think i might get it, so if you multiply 92 with 1, you are essentialy repeating 1 92times or the other way around, if its less then one, you are repeating less of it

Thank you!

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[surreal moon]

Exactly

[mental wraith]

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[odd lagoon]

I did the wrong where

if it is impossible to read i can rewrite it

oh i found it

didnt multiply the -2 with 6

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[young summit]

Can someone go over my answers

Oops idk why it sent sideways

[odd lagoon]

When you say the function is multiplied by -3 and you say "which means it is decreasing"

isn't that unnecessary to point out

and maybe not entirely correct since you already determined it was decreasing because of the base being <1

[young summit]

So then how should I rephrase it?

[odd lagoon]

I just thought your first statement was fine on its own

"Since 3/4 < 1 the term (3/4)^(5x+5) decreases as x increases."

I just felt it was unnecessary to add the following sentence but maybe it adds some more info I am not picking up on

[young summit]

Alright so leave it at that?

[odd lagoon]

yeah unless you feel it is important to leave it in

*i could be wrong so dont just blindly take my word to leave it

[young summit]

that’s fine thank you

What about the rest

Does it look good

[odd lagoon]

sry let me keep reading

[young summit]

Okok

I just don’t know how to graph it

[odd lagoon]

Sorry I can't help you to graph but that seems logical to me

Since the exponential is negative like you said

and the base would otherwise be decreasing since it is less than 1

the negative sign would just mean you start dividing a division

it would effectively increase

[young summit]

Okay I’ll reword

[odd lagoon]

no no

yours were concise i just meant it is easy to follow your logic

good thing

[young summit]

Ohhhh

Sorry I got confused lol

[odd lagoon]

what was the question for this

or did you just want to practice

[young summit]

I’m just doing an practice assignment my teacher gave me

[odd lagoon]

you might want to double check with a different helper to make sure, im sure if you ping another one more well-versed with domains will respond. i still think your logic about the function increasing is sound

[young summit]

Alright

Thank you

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[vernal moon]

is this correct?

[tall tide]

can be further simplified, let me add a photo

[vernal moon]

ok

[vernal moon]

so if i understand correctly, the answer is : ln(4)+ ln (x)- (ln(x-4)+ln(x+4))/(2)

[tall tide]

yes correct

[vernal moon]

ok, i will try it

i only get 2 attempts

it was correct! Thanks

is this also right?

@tall tide

.close

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[iron escarp]

i have a suspicion there's a mistake on the far right

context, but probably not relevant:

so shouldn't it be $$P(x<4) \color{red}+1-P(x<3)$$

[grand pond]

atif

[iron escarp]

.close

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