help-17

[viscid ore]

oof 😭

[cobalt crypt]

i care about topology

[viscid ore]

that's true but i like it :(

TOPOLOGY IS LIFE

some Algebraist just got offended probably somewhere in the world

[maiden iron]

In industry, you will never talk about a compact set

[cobalt crypt]

topological groups be like

[viscid ore]

"Analysis on Locally Compact Groups"

Me: well what the fuck

[maiden iron]

To do this day, I don't understand the term "locally"

[viscid ore]

i kind of get you

it's confusing sometimes

[cobalt crypt]

locally is like you go to your neighbours to borrow some milk

[maiden iron]

😭😭

that was fun talking with u guys

[viscid ore]

you're welcome

[maiden iron]

ill go prepare myself for signal processing course

[viscid ore]

oof

[maiden iron]

the fun thing is, we never did a course on distributions and convolution

[viscid ore]

Fourier Transforms? 🥲

[maiden iron]

it will be hell

yeah

[viscid ore]

i like those but yeah

it's hell sometimes

[cobalt crypt]

tempered distributions

[maiden iron]

the hell is this lol

[cobalt crypt]

schwartz space

[maiden iron]

I only know Dirac distribution thats it

<T,φ> =T(φ)

[cobalt crypt]

[viscid ore]

damn

for a second I saw a group generated by T and phi

forgive me

😭

[maiden iron]

Loooool

[cobalt crypt]

[maiden iron]

thats ok

[viscid ore]

ok lemme keep this open so that I can ask questions if I get stuck

gotta finish through artin and Gallian before I do other questions

[maiden iron]

cya guys o/

[viscid ore]

I have exams 😭

[maiden iron]

gl

[viscid ore]

bye 🥰

[cobalt crypt]

[cobalt crypt]

$\mathfrak {gl}_n$

[cobalt crypt]

[viscid ore]

HELP

[maiden anvil]

WHAT

[viscid ore]

uhm

nothing my bad

oh also

let's say I'm determining all homomorphisms from Z to itself, we need to care only about how 1 is mapped right?

[maiden anvil]

Uh-
I'm not in (that topic)
I'm in integrations

I understood no shit what you just sai d

[viscid ore]

oh okay

[maiden anvil]

😭

Wait

@viscid ore

[viscid ore]

It's something in Group Theory

[maiden anvil]

oh

Dm?

[viscid ore]

uh okay

[viscid ore]

anyone? 🥲

Nevermind actually I just got it

[cobalt crypt]

[viscid ore]

2 isomorphisms, rest of them are injective with images mZ

[cobalt crypt]

ye

Z cyclic

[viscid ore]

it was easy I'm just too dramatic sometimes

🥲

this is actually surprising to me, lemme try proving this

[cobalt crypt]

determining the group homomorphisms Z/nZ -> Z/mZ is fun little exercise

[viscid ore]

That's what there was in our midterms and I made mistakes in that one 🥲

[cobalt crypt]

[viscid ore]

n = 12, m = 4

[cobalt crypt]

gcd(m,n)

[viscid ore]

yes

4

[cobalt crypt]

$\env{bsmallmatrix}{0 & 1 \ 1 & 0}$ $\env{bsmallmatrix}{1 & -1 \ 1 & 0}$

[cobalt crypt]

[viscid ore]

wait.

wait I see that

f^2 = g^3 = e

in my question

[vocal sleet]

@viscid ore Has your question been resolved?

[cobalt crypt]

[viscid ore]

I'm actually confused... after thta part I mean

how do I show that

for some isomorphism

phi((1 2)) = f and phi((1 2 3)) = g

[cobalt crypt]

you also have to check that fg = g^2f ig

[viscid ore]

ultimately that's going to happen as the transposition and the 3 cycle are the generators

[viscid ore]

OH BRUH

S3 ISOMORPHIC TO D6

[cobalt crypt]

[viscid ore]

i'm a complete idiot

[cobalt crypt]

i mean

you can interpret it like uh

f and g are acting on the elements 0, 1, infinity

then the functions
x, 1 - x, 1/x, 1 - 1/x, 1/(1 - x), 1 - 1/(1 - x)
correspond to the permutations
(0, 1, inf), (1, 0, inf), (inf, 0, 1), (1, inf, 0), (0, inf, 1)

[viscid ore]

I mean we have

<f , g | f^2 = g^3 = e, fg = g^2f> isomorphic to D_(2x3) = D_6

and D6 isomorphic to S3

[cobalt crypt]

yeah

i just meant like if you want to know where those functions are even coming from

[viscid ore]

Ohh

Yeah

Actually true

Damn

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[next kestrel]

I didn't really know how to do this question, and I thought I was close, but I got the sign wrong. Could someone please explain how to approach inverse trigonometry questions like this? (the question is in pink at the top - I had to find the exact value)

[astral pilot]

arccos is defined for the range [0,π]

[next kestrel]

yes

how do i know whether i need to be basing the solution off the domain or arccos or the range

[astral pilot]

you should check both domain and range

[next kestrel]

okay so the value has to be within both restrictions for it to work

[astral pilot]

yes

[next kestrel]

okay cool

so what do I do once I know that

[astral pilot]

wdym?

[next kestrel]

if it has to be between the range 0 and pi, doesn't that mean it is outside the range if it is -pi/4

so I have to find the value in the quadrants or smth

idrk

[astral pilot]

so you know the period of cos?

[vast shale]

if 2+2 is 10 then life+me is 0 why

[next kestrel]

yeah...?

help please

[vocal sleet]

@next kestrel Has your question been resolved?

[next kestrel]

<@&286206848099549185>

[next kestrel]

^

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[stuck holly]

Hi I'm not sure how to convert units into this formula I'm a bit stuck

[hasty pulsar]

1 m/s is 3.6 km/h

[stuck holly]

i need to make braking distance the subject (d) but converted into metres, the initial and final velocity in km/h and deceleration in m/s^2

im losing my mind

[fluid obsidian]

Please don't lose it

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[hushed mesa]

extremely quicky question, just not sure where to ask otherwise and this relates to a problem

[hushed mesa]

if you find cos to be like -4/5, can you transfer that into a cos^2 as (-4/5) ^ 2

imagine i wrote the thetas there

[viral copper]

Sure

[echo badger]

Yes

[hushed mesa]

gotcha, thanks

[split wind]

yea

[hushed mesa]

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[stuck raptor]

I need help

[stuck raptor]

What is 26 mod 7?

[tiny obsidian]

The remainder that's left behind by long dividing 26 by 7

[stuck raptor]

So 6?

[tiny obsidian]

Are you sure that's the remainder?

[gilded ice]

Yeah

[stuck raptor]

Yes

[tiny obsidian]

It's 5 🤦‍♂️

[stuck raptor]

How?

It's 6?

7, 14, 21

[tiny obsidian]

26 - 21 is 6?

[stuck raptor]

26-21 = 5

Oh

Nvm

Thanks

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[thin root]

what does traced in the clockwise direction imply

[rugged vortex]

The direction of the parameterization

[heavy socket]

Means that the ellipse is being "traced" in clockwise direction

[rugged vortex]

Parameterization always has a direction

[thin root]

ummm

[midnight rapids]

I guess clockwise would mean taking minus theta instead of just theta

[thin root]

im gonna try you guys tell me if im doing this right

[rugged vortex]

Eh not necessarily

Not minus theta

I mean that could work

Sonce it's an ellipse

[loud walrus]

it works

[rugged vortex]

But there's an easier way without using negative parameters

[heavy socket]

Yeah, it works but it's not necessarily always true

[loud walrus]

reverse the order of the parametric equations looks a better approach

[thin root]

giv me a second

[thin root]

t epsilon (0, -2pi)

what do ya'll think?

dont judge pls im a noob at this

🙏

[thin root]

bro what do you think of this ^

is it wrong

.close

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[thin root]

is this wrong

t epsilon (0,-2pi)

?

hello

😦

bro pls

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[half yew]

The question asks to create all possible 2x3 matrices in row echelon form

Am I missing any?

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[river minnow]

Tried anything so far?

Even rewriting sec as 1/cos and cosec as 1/sin?

[vocal sleet]

@vast shale Has your question been resolved?

[quick fjord]

sin^2 + cos^2 = 1

that would be a big hint

you just have to get the hang of this

once you have the intuition, it gets easier

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[vocal sleet]

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[spring apex]

am I taking crazy pills? MPa * area (in mm) yields N correct? I turned in a project and my professor is telling me my displacement is too low for 5000psi the resulting output of force however is 7.2532e5 Newtons and the area I calculated using radius is 75mm= Pi*75^2 = 17671mm2. Taking that and dividing by the force output by area I get a MPa of 41 ish which is nearly 6000psi. Did I miss something?

[spring apex]

,close

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[nova sluice]

is (mod (x) )is the same as (mod (-x))?

[vast shale]

it depends on how careful you are with definitions

but yes, x and -x differ by an invertible element (in Z*), so the quotients are the same

[nova sluice]

I have a HW in CS and I have to use algebra mod instead of the C compiler mod , does this function calc everything right?

int mod(int a, int b)
{
    if (b==0)/* mod 0 is undefined */
        return -1;
    int result = a % b;
    if (result < 0)
    {
        if(b<0)
        result -= b;
        else
        result += b;
    }
    return result;
}

[vast shale]

idk C, sorry

maybe ask in #computing-software or the cs server in #old-network

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[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[candid salmon]

<@&286206848099549185>

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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.

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@candid salmon Has your question been resolved?

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[vast shale]

How is the distance between these two points not 0?

[flat whale]

is t1 = t2?

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@vast shale Has your question been resolved?

[vast shale]

Probably, I haven't been provided any more information

[ornate seal]

What is the original question?

[vast shale]

Literally that

They're asking us to find the distance between those two points

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[plush roost]

Anyone know why this happening

[plush roost]

or what settings to change

[flat whale]

google your calculator model and error message

[urban edge]

can it do imaginary numbers?

[flat whale]

,w e^(i * 0.5)

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[eager walrus]

I know it can do a+bi

@plush roost did you find the setting

[plush roost]

oh i see what i was doing wrong. I had the documentation settings set up correct, but some settings don't apply for the scratch pad

[plush roost]

that's weird, yes I figured it out, thank you!

[eager walrus]

ok byee

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[blissful timber]

How do i factor this?

[soft walrus]

what do you mean factor, like factor $\frac{1}{2}y+\frac{1}{2}+\frac{1}{4y}$?

[twin meteor]

XxMrFancyu2xX

[blissful timber]

Yes

In order to get rid of sqrt

[soft walrus]

I don't think you can factor that...

[blissful timber]

Teach said to “now factor”

[soft walrus]

idk how one would factor, most you can simplify is: $\frac{1}{2}\left(\frac{1}{y}+1+\frac{1}{2y}\right)$

[twin meteor]

XxMrFancyu2xX

[blissful timber]

Welp

Dunno how to do that one then

[soft walrus]

I see a u-substitution

did your teacher do a u-sub then factorize from there?

$u=\frac{1}{y}$?

[twin meteor]

XxMrFancyu2xX

[blissful timber]

Nah thats my work

[soft walrus]

ah

[blissful timber]

How would that makes sense with the +1/2

u=1/y+1/2?

[soft walrus]

$+\frac{1}{2}$ is constant with respect to both $y$ and $u$ no need to do any conversion as doing so anyways would result in $+\frac{1}{2}$ anyways

[twin meteor]

XxMrFancyu2xX

[soft walrus]

so idk what you mean by factoring was that the exact word (s)he used?

[blissful timber]

Yes, its in red pen in the picture i sent

[soft walrus]

sorry man idk then looks like someone else is typing and can help you more, I'm sorry

[blissful timber]

Np np

[frozen bobcat]

if you factor out the 1/4 you have $y+2+\frac1y$ which factors into $(\sqrt y +\frac{1}{\sqrt y})^2

[twin meteor]

Zybikron
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[blissful timber]

Hm hm hm

That might be it?

Ima work it out, ty

.close

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[thin root]

why swapping cos and sin in parametrization of an ellipse make it go clockwise?

[lyric fossil]

what kind of justification are you looking for

[thin root]

i just wanna see how

[lyric fossil]

have you tried plotting a few points after changing the parametrization

[thin root]

nope

[lyric fossil]

click play on the value of t

https://www.desmos.com/calculator/ke8cx6k42g

[thin root]

ok thanks

that helped

.closed

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[icy spear]

let's say we have the matrix equation:
AX^2 + BX + C = 0
how can we solve for X?

[hushed pewter]

are you familiar with quadratic equation or completing the square?

[icy spear]

matrix equation

A, B, and C are all square matrices with the same dimensions

[lyric fossil]

this equation doesn't make sense

what does X^2 mean?

maybe a better question to start with is, what is X?

@icy spear

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[hazy hound]

I'm not sure how to find this area

[hazy hound]

Which region is it even talking about?

[vocal sleet]

@hazy hound Has your question been resolved?

[weary sentinel]

the lowest one

bordered on the bottom by green (by the first curve, outside) and on the top (on the inside) by the r=6

[hazy hound]

I tried to set up this integral

so for this part of the intersection

[weary sentinel]

looks right to me

[hazy hound]

yea I realized I actually made a calculation mistake at the end of evaluating the integral

thank you

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[olive spire]

hopefully this doesn't look too crazy.. but i am trying to convert that summation into closed form. https://www.desmos.com/calculator/8mznpmbggi

[olive spire]

is it even possible?

[vocal sleet]

@olive spire Has your question been resolved?

[floral pike]

I believe it is.

Since these are finite geometric series

$S_n = \sum_{k=0}^{n} r^{k-1} = \frac{1-r^n}{1-r}$

[twin meteor]

Disorganized

[floral pike]

Where r is some constant not equal to 1 (and also the ratio of consecutive terms). I didnt bother putting a constant coefficient in front b.c. you already know how that works with sums and it's not a unique feature of geometric series

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[floral pike]

In your equation @olive spire

(Rude, discordbots!)

.reopen

[vocal sleet]

✅

[floral pike]

The geometric term in your formula is (1+R)^x. A constant to the x power.

Use this property:

$\sum f(x) + g(x) = \sum f(x) + \sum g(x)$

[twin meteor]

Disorganized

[olive spire]

ok, i need some time to digest and understand what you're saying. i'm a complete math pleb.

[vocal sleet]

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[ashen fiber]

hello

the interval for this is 1<x<3

i understand why 3 is not convergent

but why is 1 not part of it

wouldnt it become an alternating series sequence

and since lim n > infinity for 1/nlnn

becomes 0

wouldnt 1 be a convergent

component

[eager walrus]

let's see

(-1)^n+1

/n *ln n

[eager walrus]

1 isn't included?

[ashen fiber]

its part c

[eager walrus]

well theres the work

what part doesnt make sense to you?

AST

1. alternating
2. lim n->inf = 0
3. decreasing

[heavy yoke]

that sheet indicates that 1 is part of it though?

[ashen fiber]

then it converges right

but the answer key

doesnt include that 1 is a converging component

[heavy yoke]

the answer key does include 1

[ashen fiber]

O SHIT

[eager walrus]

goofy butt

[ashen fiber]

IOM SORRY

ty

!close

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[eager walrus]

.coose

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[vapid robin]

i am only a few questions away from being able to get dual credit from my high school’s college algebra class. could someone help me get the answer?

[paper depot]

do you know how to go from roots to factors?

and the special treatment that complex roots get given that our polynomial has real coefficients?

[vapid robin]

like (x-2-2i)(x-2+2i)?

[paper depot]

not quite, that'll get you 2 ± 2i as roots while you want -2 ± 2i

[vapid robin]

ohhh wait it needs to be a positive

(x+2-2i)(x+2+2i)(x+4)

but whats the fourth degree

(x+4) again?

[paper depot]

-4 is a root with multiplicity 2.

so you need to multiply by (x+4) again yes

but not for the reason you stated

[vapid robin]

so i have (x+2-2i)(x+2+2i)(x+4)(x+4)

how do i turn into ax^3+bx^2+cx+d

[paper depot]

as stated just now? you cannot

you cannot transmogrify a quartic into a cubic

but what you want to do from here is expand this out

starting with (x+2-2i)(x+2+2i), on which i recommend applying the difference of squares identity

[vapid robin]

im sorry my brain is fried its almost midnight

can u explain what you mean?

[empty frigate]

this is a quartic, if you expand it it's going to look like ax^4 + bx^3 + cx^2 + dx + e
unless you're asking about what the difference of squares is

[vapid robin]

im pretty sure thats what the final answer is supposed to look like

[paper depot]

i mean exactly what i said

expand out the product

i recommend starting with expanding (x+2-2i)(x+2+2i), and in particular i recommend applying the difference of squares identity rather than blindly expanding into a sum of nine terms

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[fiery egret]

how to solve?

[fiery egret]

ans= 6

[empty frigate]

(i'm assuming by "units digit" they mean in base ten?)

[fiery egret]

no as in ones tens units

ex:150 here 0 is units digit

[night bane]

yeah, the units digit in base ten.

[empty frigate]

does "150" represent one hundred and fifty

if it does then that is base ten

[night bane]

you use a cyclic property of units for this

[empty frigate]

anyway
modular arithmetic
the unit digit of N is the remainder of N when divided by 10, which is the same as N mod 10

[fiery egret]

oh so this works for every number

?

[empty frigate]

yes

[fiery egret]

what is that property

what i was doing till now was i memorised unit digits patters say 3^n = it will have 3,9,7,1 as units digits

[night bane]

exactly

[empty frigate]

yep
1, 3, 9, 7, and then it repeats
it cycles => it's cyclic

[fiery egret]

is there any else easier way go around it'

[night bane]

I mean, Im going here by grade 6th math, and def not provide the correct notation, but the unit digits repeats

[fiery egret]

ohh ok

[night bane]

and then you just need to subtract 2 from whatever you end up on, because its 32 <- 2 is the units digit here

[fiery egret]

but if here it was 32^19 it would be easy for me to get patterms of 2^n

[night bane]

so 2 repeats with every 4th power -> 2, 4, 8, 6 and then 2 again

[fiery egret]

but 32 is subtracted from it

[empty frigate]

find the answer for 32^19 mod 10, then subtract 2 from it

[night bane]

for the units digit, the unit digit of what we subtracted will be the only thing that matters. The tens digit won't do anything.

[fiery egret]

ohh gotcha

is it 4 ?

unit dig 4

[night bane]

if its only the units digit, we could also do 19 mod 4 and then use that to find out which of the 4 (2,4,8,6) do we need to use.

[empty frigate]

yep

because the cycle is 4 long

[fiery egret]

19 mod 4 represents what

what is the process going behind this term

are you saying multiples of 4?

[night bane]

19 is our power, and 4 is the number of times (dont remember the exact word) that 2 repeats

[fiery egret]

so 20th power will have 8 as unit dig right?

32^20

[night bane]

so for something like 6, it has a repetition of 2 (6,4) so we would do 19 mod 2

[fiery egret]

ohh ok i say that going in a pattern of two

but here 32^19 's unit dig iam geting is 6

[empty frigate]

...how did you get 6?

[fiery egret]

2^20 = has unit dig 8

[empty frigate]

how did you get that?

also wait even if it did, wouldn't that mean 2^19's unit digit is 4

[night bane]

why'd you do 2^20?

[fiery egret]

i did cos 20 is multiple of 4 and powers are following that pattern

[night bane]

but its not 32^20, its 32^19, right?

[fiery egret]

so 2, 4, 8, 6 this way 20th powers unit dig will be 6 and 19th powers has 8

[night bane]

yes, that is correct

[fiery egret]

yes right

[night bane]

so now we know 32^19 has the power of 8

[fiery egret]

i tried finding nearest multiple of 4 power

[night bane]

and we subtract 2 from 8 (because -32)

[fiery egret]

right

[night bane]

so we end up on?

[fiery egret]

yes 6!'

got it

thanks a lot!

.close

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[fiery egret]

.reopen

[vocal sleet]

✅

[fiery egret]

how can i go about this one

0.51=ans

[floral pike]

conditional probability?

[fiery egret]

ya can you pls explain

[floral pike]

Idunno, if I can swing this, they should let me into grad school

[fiery egret]

i dont know whether on 6th run x has occured or not

[floral pike]

show me your working so far

[fiery egret]

lol

[fiery egret]

no i haven't worked on it

[fiery egret]

because of this ambiguity

[floral pike]

well it seems we have
P(X|X) = 0.3 and
P(Y|Y) = 0.4

generally

$P(A|B) = \frac{P(A\cap B)}{P(B)}$

[fiery egret]

right

[twin meteor]

Disorganized

[floral pike]

I don't know how to leverage this though

[fiery egret]

prob of a and b / p (b) is this you want to say

[floral pike]

or if we can

[fiery egret]

i'am not understanding it

[floral pike]

I would like to figure out P(X) and P(Y), maybe using total probability and conditional probability definition

[floral pike]

me neither

<@&286206848099549185>

P(X) + P(Y) = 1 for each run

[fiery egret]

ya

but if x has ocuured then on next turn p(x)= 0.3 and will p(y)=0.7?

[floral pike]

I'm stuck and I can't find my stats textbook, which I don't think goes deep into this anyway

[fiery egret]

same with y occuered then next turn p(y)=0.4 and p(x)=0.6

[floral pike]

yeah

maybe we can work a tree backwards

sounds computer-y

[fiery egret]

means?

[fiery egret]

how

[floral pike]

drawing with a pen on paper

start with X

then the previous step was either X or Y

and so on

we can annotate the branches with probabilities

[fiery egret]

so what we add?

prob of x for earlier attempt is unknown

[floral pike]

I would like to know if P(A|B) = 1 - P(B|B)?

all of our annotations will be based on conditional probabilities

boom.
https://faculty.math.illinois.edu/~hildebr/408/408general2.pdf

[fiery egret]

i don't know

[floral pike]

#5

[fiery egret]

ohh

[floral pike]

Complement Rule for Conditional Probabilities: P(A'|B) = 1 - P(A|B)

so then

P(Y|X) = 1 - P(X|X) and
P(X|Y) = 1 - P(Y|Y)

so then

P(X|X) = 0.3,
P(Y|X) = 0.7,
P(Y|Y) = 0.4,
P(X|Y) = 0.6

and that's all we need

[fiery egret]

DOES P (x')= P(y)

[floral pike]

not important

I'm drawing a new diagram

[fiery egret]

they how you deduced from the given formula

[fiery egret]

ya but how we can tell whats the 7th term prob

how to determine whether x occuered in 6th term or y occured

[floral pike]

we grow the tree again from X

the bottom X

2 more rows

...

I'm actually not sure if I have this down yet, let me see if I actually accounted for everything b.c. this still feels like there's too many choices

[fiery egret]

i'am not understanding the tree thing

shall i ask this in some other channel ?

[floral pike]

give me a second, I'm sending it

[fiery egret]

ya sure

[floral pike]

Maybe we only care about steps 5 through 7 actually

[fiery egret]

okk

[floral pike]

,rotate

[floral pike]

got it

0.3*0.3 + 0.7*0.6 = 0.51

it's just steps 5 through 7 that we care about

[fiery egret]

i try that

i haven't understood it completely

i have to go now

[floral pike]

we can also see that our intuition about total probability is satisfied while we are growing the tree but not when I was working backwards, so I am glad this worked out

I added the product of probabilities on each path that resulted in X on step 7

beginning with step 5

starting from X, left branch is P(X|X), right is P(Y|X)

etc.

[fiery egret]

ohh

[floral pike]

P(destination|previous)

reminder

P(Y|X) = 1 - P(X|X) and
P(X|Y) = 1 - P(Y|Y)
so then
P(X|X) = 0.3,
P(Y|X) = 0.7,
P(Y|Y) = 0.4,
P(X|Y) = 0.6
and that's all we need

[fiery egret]

thanks

[floral pike]

no problem

that's just how I roll

[fiery egret]

great

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[glossy blaze]

Hello, I would like to get help with finite field numbers.
Let me give some context.
All the numbers are in finite field(base field of Bn256 curve).
I have array of numbers.
sum of numbers = count of numbers * 100.
But, every number(decimal presentation) is big and I cannot use that values for real world use.
I would like to scale them so that their decimal presentation is small enough for human to easily read and compare.
How can I do that?

Example: numbers = [ 0x2f4333ef3349bb7470aeb6fa55e18d8ddbe46103b01556cb91da9028f6a8bb29, 0x00df27ddc33c04327efd9e65cb1b3f700475dddb368d42669b48ea4d10089144, 0x0041f2a5eaabe082c8a3f05660848b5f47d9a9699316d75f16be7b1de94eb4c0, ] sum = 3 * 100(0x64) = 300 (0x12c)

Thanks in advance!

[hard atlas]

what kind of real world use do you want

I'm not familiar with the Bn256 curve but can you do the same construction with just some smaller prime? sure that would be less safe but maybe ok for whatever you wanna do?

[vocal sleet]

@glossy blaze Has your question been resolved?

[glossy blaze]

I would like to compare the numbers so that which value is high, and how much(like percentage).
The number of scores(values) could be big, like 500 or 1000.

If you are not familiar with Bn256 curve, you can just assume that the p of field is very large. (0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001)

Also, I should use this large field.

[hard atlas]

if you wanna check which values are bigger then you could just check which is the last important digit to decide that and then cut off after that

[glossy blaze]

Um, I am not sure if this question is silly.
But, can I get the percentage of values?

[hard atlas]

I dont know what you mean by that

you can just divide them by another. and if x/y is like 1.5 then x is 50% bigger than y

[glossy blaze]

yes, but all the values are in finite field.
So, the division result is not float number.
x / y = x * y ^(p - 2)

[hard atlas]

well for percentages you should talk about actual integers

size makes no sense in a finite field

and given that you already care about which is "bigger" you are already talking about the integers

[glossy blaze]

okay, so the big, small, percentage are all for integers, not for finite field.
hmm

okay, thanks for help! @hard atlas
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[sudden harbor]

a cone has a height h and a base area A. it is cut by a plane beta parallel to the base. We obtain a section that has an area which is half of A. So, if d is the distance between the plane beta and the vertices of the cone, which one of the answers below is true?
d=h/2
d²=h²/2
d²=h³/2
d³=h²/2
d³=h³/2

I've been having trouble with this one for a few days..any help?

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[river kettle]

Im not sure if I drew this diagram right

[river kettle]

can anyone lmk if i did it incorrectly

[paper depot]

might benefit from an explicit right-angle marker left of the north line.

but otherwise it is correct.

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[vocal sleet]

@pulsar scroll Has your question been resolved?

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[orchid jewel]

?

nice pictures

[celest crystal]

Its a thing...

Idk is it hseful

:-;

Srry

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[karmic mural]

From points A and B, the distance is 40 kilometers, two passengers came out to meet each other at the same time. After 4 hours, they had to travel another 4 km before they would met. If the passenger had come out of point A 1 hour earlier, then he would have met the other in the middle of the road. At what speed did each passenger go?

[karmic mural]

Solved

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[tulip nebula]

Show your work

[wicked ice]

thats the thing my teacher gave us this exercise to get back into these type of problems but I don't remember where to start

so i just need like a pointer

i think i start with making x^3 even right by turning it to x and x^2??

[tulip nebula]

If it's a+a can you factor it?

[wicked ice]

yeah you can

[tulip nebula]

So how

[wicked ice]

wait no cause you can only factor a + b right?

[tulip nebula]

Factor is basically taking terms common

So a+a can be written a(1+1)

You took a common

Does this give pointer on how to solve this question?

[tulip nebula]

a+b can never be factored

[wicked ice]

okay somewhat let me see if I'm able to get something down and ill show you

[tulip nebula]

if it's a + ba then yes it can be factored because both terms has 'a' in common so upon factoring it will be a(1+b)

[wicked ice]

okay I got it

[tulip nebula]

Ok

Remember that if higher power is involved, for example a^3 - a^2 you can simplify a^3 into a^2*a and here you see a^2 being common in both terms so upon factoring it will be a^2(a-1)

[wicked ice]

@tulip nebula how does this look?

[tulip nebula]

Definitely correct

I had the answer in mind by one look

[wicked ice]

alright cool

i need help with another question though

[tulip nebula]

This is also another question for which I've answer in one look

But I'll ask you, what's your work

Or atleast your first impression/idea to begin

[wicked ice]

i haven't gotten to this one yet these are all just test prep questions

[tulip nebula]

Okay let's do it like this, do you know degree of f(x)=x^2-2?

[wicked ice]

yeah no lol my teacher did a horrible job tryin to explain it

[tulip nebula]

Wait, do you know the definition of degree

I mean you should first know what you're asked for before finding it

Because telling the degree of x^2-2 is the easiest if you know the meaning of degree

[wicked ice]

yeah it should be the largest exponent with the number up top

which would be x^2 but the 5 is making me confused

[tulip nebula]

It's not the number up top, I mean there could be x^2- 2^3 but degree is 2 not 3

It should be variable up top

[tulip nebula]

Where is 5 in x^2-2?

[wicked ice]

oh no the behind the 5 second bracket

but im guessing I shouldn't be even looking over there right?

[tulip nebula]

That's not what I asked though

I asked degree of x^2-2

[tulip nebula]

Well I'll come to original question after I make sure you know basic things first

So the degree of x^2-2, that's all I'm asking

[wicked ice]

okay well the degree of x^2-2 would be 2

[tulip nebula]

Yeah

What is degree x^3

[wicked ice]

it would be 3

[tulip nebula]

And what is degree of x^3 + x^2?

[wicked ice]

it would be 3 again since it the biggest one

[tulip nebula]

Yes

then what is degree of (x-2)^5?

[wicked ice]

it would be 0

[tulip nebula]

Lol no

How did you come to that conclusion

Let's do with (x-2)^2 first since power 5 may seem big to you

[wicked ice]

because since x doesn't have a degree over it and the 5 is outside of the brackets it wouldn't be considered a degree I would think

2 then?

[tulip nebula]

So you don't consider the degree 1 on x?

[tulip nebula]

Yes it's 2 for this one

[wicked ice]

i was thinking that but I wasn't sure but if so that makes sense

[tulip nebula]

You need to simplify the full expression before writting degree

And also degree of (x-2)^2 is 2 not because of 2 on top of bracket because on simplifying it's x^2+4-4x and degree is 2 here

Now can you tell tell degree of (x-2)^8868?

[wicked ice]

okay

[tulip nebula]

Tell

[wicked ice]

it would be 8868 cause simplifying it would make it a degree over x

[tulip nebula]

Yes

So can you tell degree (x^2-3)(x-2)^500?

[wicked ice]

it would have to be 500 but im not sure how we would simplify this my best guest would have to be putting it over the x in the second bracket then simplifying that even more with the x^2 since they would be common factors right?

[tulip nebula]

No it's nothing complicated as that

The degree is 502

The biggest exponent of (x-2)^500 would be x^500

And x^2 will multiply to that making it x^502 which would be biggest exponent

So degree will be 502

Do you understand?

[wicked ice]

yeah I got an understanding now

[tulip nebula]

Yeah it's simply that understanding

You have ability to solve the original question now

[wicked ice]

yeah but to show the question again

it would have to be 11

as the biggest degree

[tulip nebula]

Correct

As for explain how, the words are not part of math you can do it if you know english

[wicked ice]

sorry man me no speak english

[tulip nebula]

Lol I mean the question, explain how you know

[wicked ice]

alright cool let me write it down and I'll show you

[tulip nebula]

Ok

[wicked ice]

what you think?

[tulip nebula]

Yeah you wrote good english

You will get full marks

[wicked ice]

alright cool I got another one but I think I got it just want you to check my work afterwards

[tulip nebula]

Main thing is you understood how to find degree in these problems

That was most important, you can conceptualize your understanding into words if it asks explain how

[wicked ice]

alright here the problem ill show you my work in a second\

[tulip nebula]

Oh

You mean roots/zeros

I alr have the answers in mind

The important part of question is factorisation

[wicked ice]

i kno it look a little bad but I found x could equal -10 and +6

what you think?

[tulip nebula]

Yeah it's basically that

What did you write in right side though

-CaO, calcium oxide?

Its the correct solution

[wicked ice]

lol alright cool

yeah it not easy trying to write with a mouse

[tulip nebula]

Do you know the name of process? I call it middle term factorization

Because latter part of question is identify the process

Well that's again English thing

[wicked ice]

yeah my teacher calls it something similar i forgot the name though

[tulip nebula]

Ya it's not important

I think teacher do these English questions beside math is to check whether you cheat or not

[wicked ice]

yeah makes sense since it super easy now with things like chatgpt

[tulip nebula]

Yes

[wicked ice]

alright onto the next one!

i'm be honest I was sick for like the whole week for when she was teaching this so I have no idea how to even start this

[tulip nebula]

Basically it's odd degree polynomial function graph

How do I know?

Wait, do you understand what is odd degree polynomial function

[wicked ice]

yeahh no i don't think its a terminology im used to

[tulip nebula]

Basically something like polynomial whose degree is odd

Odd means not divisible by 2

[wicked ice]

ahh okay

like 3 and 5 right?

[tulip nebula]

Yeah

On power of x

It covers the whole y axis

And is moving up and down like parabola

That's the description of odd degree polynomial I simply memorized in brain

Also the zeros/roots can you find it from graph?

[wicked ice]

ahh okay and yeah no

is its -1 and 2?

[tulip nebula]

Where is -3

[wicked ice]

its on the x axis

which is another point where it connects to the line

[tulip nebula]

Basically x intercepts of the graphs are the roots/zeroes of any function

So whenever you're given a graph or have to make a graph remember that x intercepts will be the zeros

[wicked ice]

can you give an example?

[tulip nebula]

Yes the points on x axis where the graph intercepts are x intercepts and also the zeros of the function

[tulip nebula]

Like the graph of y=x the roots will be the x coordinates for which y=0

And when you draw y=x graph the x intercept is 0

The roots/zeros are those points of x axis for which function's value is 0

Like y=x-2, the root/zero will be 2 as then only y=0

[wicked ice]

ahh okay I think I get it now

[tulip nebula]

Because in this question youre not given function but it's graph

You have to see x intercepts to know the roots/zeros

So can you tell the roots by looking at the graph now?

[wicked ice]

okay so the x intercepts within the graph are -3 -1 and 2

[tulip nebula]

Yes

Now you have completed first part of question which is to find zeros or toots

[wicked ice]

then since those are the x intercepts they could all be equal to x which is x=0

[tulip nebula]

x=0 no, they are the points at which y=0

You should be saying since they are x intercepts so they are the zeros or roots of the function

And I alr told you definition of zeros/roots, they are x coordinates for which function's value or y coordinate is 0

[wicked ice]

alright the 0s would have to be the oppsites of the x intercepts which are 3 1 and -2

[tulip nebula]

Lol no

Zeros are exactly the same as x intercepts

Not the opposites

[wicked ice]

oh alright I though since that how we had found our x's in previous problems that would stay the same

[tulip nebula]

The zeros are often called the roots, solutions, or x-intercepts of the function. These all mean the same as the zero definition and are used throughout mathematics

Basically the roots/solutions/zeros/x intercepts are all same things

[tulip nebula]

The meaning in this and previous question is same

So you should finally be able to say the zeros from the graph of this question ,right?

[wicked ice]

oh okay yeah I'm just finding it hard to turn the points on the graph into a equation like how it was before

[tulip nebula]

We will do that turning as well after I make sure you can find zeros from the graph

I was about to go to that point as well

So can you tell zeros?

[wicked ice]

okay so the 0s are pretty much points on the y axis right since y=0

[tulip nebula]

You mean the points on x axis where the graph intercepts or strike

Zeros are always points of x axis

[wicked ice]

wait would the 0s also be -3 -1 and 2 then?

[tulip nebula]

Yes

Thanks

They are zeros

Now the second part of the question is finding factors

[wicked ice]

alright cool

[tulip nebula]

I will ask a question

[wicked ice]

and i will answer lol

[tulip nebula]

If the zero is 5, what is factor

[wicked ice]

5 then

wait no

[tulip nebula]

No

[wicked ice]

x - 5

[tulip nebula]

Yes

So can you write all the factors?

We have 3 zeros so there will be 3 factors

[wicked ice]

that would mean then (x+3) (x +1) (x-2)

[tulip nebula]

Yes

To be exact the function will be k(x+3)(x+1)(x-2) where k is non zero constant

For example here the constant 3 is there

[wicked ice]

does it have to be k or can it just be any variable like m or x?

[tulip nebula]

No it has to be non zero constant

You have to mention that k is non zero constant

Because if there is a variable like m or y it's not equation in one variable

If there is the same variable x then another zero/root=0 will be born but from the graph we see 0 is not the x intercept

[wicked ice]

ahh okay I get

[tulip nebula]

So the odd degree polynomial function possible for the graph will be

You answer

[wicked ice]

okay got it

onto the next

[tulip nebula]

Ok

[prime falcon]

Does anyone here know probability? I'm kind of in a rush

I'm gonna studying for an exam

[tulip nebula]

I don't know multiplicity

[wicked ice]

alright its cool

[tulip nebula]

But I searched Google and now I know the meaning of multiplicity

So rest assured as I have answer of this question in mind alr now

You should know how to find zeros by now, can you fill the first blank?

[wicked ice]

yup one second

wait I'm used to us figuring out 0s without x with powers does the powers change anything or finding the solution stays the same?

[tulip nebula]

Well powers doesn't change anything except a new term is introduced by the presence of power called multiplicity which is the number of times the same factor of a zero is multiplied

[wicked ice]

okay cool

[tulip nebula]

You can also think about it like this, for example function (x-2)^888789 is there and you're asked the root/zero of it, the zero will be 2

But multiplicity of the zero which is 2 will be 888789

And if it's just (x-2) then multiplicity will be 1 of zero 2

The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. For example, (x-2)^2, the zero associated with this factor, x=2, has multiplicity 2 because the factor (x−2) occurs twice

[wicked ice]

how does this look?

[tulip nebula]

Correct

[wicked ice]

cool

[tulip nebula]

I'm sure you can answer all remaining blanks now as well

[wicked ice]

alright yeah give me a second

how does this look?

[tulip nebula]

You did a mistake in multiplicity of the zero 5/2

The number of times the factor 2x-5 is multiplied not 0 but 1

[wicked ice]

ohh yeah you're right

[tulip nebula]

Because (2x-5)^0=1 and (2x-5)^1= 2x-5

[wicked ice]

cause if we don't se a power over x we should assume there's a 1

good now?

[tulip nebula]

Degree is also wrong

It's like you missed the x from third factor again

[wicked ice]

yeah you're right should be 16

[tulip nebula]

Yeah 16 is correct

Also as a extra information not related to this question but I think you should be knowing for future reference..the graphical meaning of multiplicity..The multiplicity of a zero determines how the graph behaves at the x-intercepts. The graph of a polynomial will cross the horizontal axis at a zero with odd multiplicity. The graph of a polynomial will touch the horizontal axis at a zero with even multiplicity

[wicked ice]

okay appreciate it

here the next problem Im pretty sure i got it just want to you to check my answer

[tulip nebula]

I think it should be x-intercepts/zeros/roots

I already told you didn't i

Zeros are known by synonyms such as roots, solutions, x intercepts etc

[wicked ice]

okay alright cool that what I wrote

[tulip nebula]

Ok

[wicked ice]

it seems like I'm have to be working backwards to start

[tulip nebula]

Ohh

Wdym by that

Backwards to start

[wicked ice]

since we got the multiplicity and not the original function i though we would have to work backwards to start this problem right?

[tulip nebula]

Wdym the original function

[wicked ice]

no like the function we gotta find

[tulip nebula]

the original function q(x) was given in previous question when we were asked to find multiplicity

Oh you mean the current question

[wicked ice]

yeah

[tulip nebula]

I understand now!!

The funny thing about this question is that when it says have zero at 6/7 for example

It simply means the zero is 6/7

[wicked ice]

okay and the same goes for the -7 right?

[tulip nebula]

You're given 3 zeros

Yes

So make 3 factors

And then use multiplicity to write exponent on those factors

Easy

[wicked ice]

so basically the opposite of what we did for the graphing problem??

[tulip nebula]

Yes

Opposite?

No the same thing!

We found zeros from graph by finding x intercepts then turned them into factors

[wicked ice]

oh okay got it

[tulip nebula]

Also to answer first question, remember to multiply a non zero constant k

It's more like general form of solution

In fact even if you don't multiply the non zero constant k or even if you multiply 3 or 4, the answer would be right since it asks for possible function and this kind of function is possible but by writting k it makes solution more general and neat imo

After doing the first question, the second question is totally dependent on first and you have ability to do that as well!

[wicked ice]

i got the other two down I'm not sure how to go about doing 6/7 since its a fraction

[tulip nebula]

Hey I understand you short formed zero into 0 but you can't do that in subjective exams

[wicked ice]

alr i got it i'll show the work

[tulip nebula]

Btw the first one will be x-6/7 then multiply 7 since it's non zero constant which will make it 7x-6

Now you understand that multiplying non zero constant doesn't change zeros, multiplicity and even factors remains same

So it technically comes into the possible function

And possible function can be infinitely many in this way but we chose the general one, atleast that's how I used to do when I was in your grade ig

So even if you write x-6/7 as the factor, it doesn't change anything and your answer will be correct then also. However if I was in your place, I would write the factor as 7x-6 just coz it looks neat imo so it's opinionated and youre free to write any possible solution

[wicked ice]

how does this look?

[tulip nebula]

7x^2-6? Not (7x-6)^2 💀

Lol you forgot the multiplicity meaning

[wicked ice]

ohhh yeah you're right one sec

[tulip nebula]

It's the numbers of times a factor is multiplied to itself

[wicked ice]

good now right??

[tulip nebula]

Yeah

Just mention that k is non zero constant

Because it can't be 0 as then the function becomes 0 as well

[wicked ice]

okay got it

then the degree should just be 8 then

for part b

[tulip nebula]

Yes

[wicked ice]

what you think?

[tulip nebula]

Well there was no need to write we get 8 not 7

You could just mimic the previous English one

[wicked ice]

alright got you

[tulip nebula]

I mean this is not any assumption but fact

[wicked ice]

alright onto the last question

[tulip nebula]

H is the height

When rock lands on ground h will be 0

H is also the function

So basically find value of t's for which the function value is 0

You're being asked the zeros in another word

[wicked ice]

alright cool so pretty much -2t^2 + 7t +4 = 0 right?

[tulip nebula]

Yes

For convenience sake you can multiply (-1) on both sides of equation and then proceed to factoring

I mean in that process of middle term factorization it's more convenient if the leading coefficient (coefficient of highest power variable which is t^2 here) is positive

[wicked ice]

alright so pretty much factor 2t^2 + 7t -4= 0 then??

[tulip nebula]

-7t should be there though?

[wicked ice]

oh i thought you just wanted me to multiply that only yo -2t^2 and 4

so 2t^2 -7t -4=0

[tulip nebula]

Nah I said multiply (-1) both sides of equation to get rid of negative sign on the leading coefficient

[tulip nebula]

Just factor it like you normally do

[wicked ice]

alright got you

im be honest I'm stuck I don't think there is factors for these that can make both of these

[tulip nebula]

There surely is factors

Because you know Discriminant?

D>=0

You can calculate it

Also if you have problem finding factors, just directly fine zero using Quadratic formula also known by shree dharacharya formula