help-0

[weary rose]

I’m doing a a test on radical operations, I just wanna make sure if this is correct

For dividing radicals we subtract?

[analog falcon]

lemme see whats radical operations lmao

[weary rose]

Oh like

Multiplying radicals

Dividing radicals

[analog falcon]

Hmm

Depends

[weary rose]

Adding and subtracting radicals

[analog falcon]

there's laws

$a\sqrt m ± b\sqrt m = (a±b) \sqrt m\a\sqrt m \cdot b\sqrt m = ab \sqrt m\a\sqrt m \cdot a \sqrt n = a \sqrt{mn}$ etc

[ocean seal]

n11

[analog falcon]

a little oopsie. in the second one it'll be sqrt m²

[weary rose]

Thanks

Btw for the last one

U didn’t multiply a because the radicals are different?

[analog falcon]

oh fuck

it'll be a²

sorry lmao

[analog falcon]

this was confusing but my bad

[weary rose]

Nah it’s all good lol

Ima close they channel for now I gotta catch a bus ride to school

Thanks for the help 🙏

[analog falcon]

npp

[lone heart]

@weary rose Has your question been resolved?

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[thorn patio]

how do i go about solving this?

im sure itll be obvious but just cant see how

i was thinking to try and make c = 1 and make it the identity 1 + sin^2(x) = cos^2(x)? but other than that im not sure

.close

[lone heart]

Channel closed

Closed by @thorn patio

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unique salmon]

Okay, I thought I already knew how to do stuff, guess not...

I guess we start with ³√3²

[kindred anchor]

Hm

[unique salmon]

Am I correct

[kindred anchor]

Yes, go on, show what you have tried

[unique salmon]

I'll write it on a paper

Sorry for the bad quality

[kindred anchor]

Wrong.

[unique salmon]

Bottom half right

^ the wrong one

Top one seems fine to me or is it wrong too?

[alpine sable]

$\sqrt[a]{b} = b^{\frac{1}{a}} \implies \sqrt[a]{b^c} = b^\frac{c}{a}$

[ocean seal]

trololol !

[alpine sable]

use this to simplify the denominator

because that is where you are wrong

[kindred anchor]

Yes ^

[unique salmon]

Uh

I see

[alpine sable]

same mistake

[unique salmon]

Where

⁴√2³?

[alpine sable]

$\sqrt[4]{2^3} = (2^2)^{\frac{1}{4}} = 2^{\frac{2}{4}} = 2^{\frac{1}{2}} = \sqrt{2}$

[ocean seal]

trololol !

[alpine sable]

it won't help to write it as $\sqrt{2}$, but i put it there in case it helps you understand

[ocean seal]

trololol !

[alpine sable]

OOPS

forget it

$\sqrt[4]{2^3} = (2^3)^{\frac{1}{4}} = 2^{\frac{3}{4}}$

[ocean seal]

trololol !

[alpine sable]

this is correct

sorry i've mistaken the three with two

[unique salmon]

I thought so

Now

To get rid of the big ones

2¼ • 3 ⅔•¼

9⅓ • 2¾•⅓

Should I write it down?

Hellooooo

[kindred anchor]

Right.

[unique salmon]

Then I would assume

Wait let me write it

[green folio]

You keep sending the same image

[kindred anchor]

Lol, why did you do that?

[green folio]

?

[kindred anchor]

I guess he mis-clicked the image to be sent.

[green folio]

3 times? 💀

[unique salmon]

Wait

I didn't even realize I sent that again

[green folio]

💀

[unique salmon]

Ight what to do now

I wouls

Wouls

Would

Turn them to

⁶√3

³√9

Although it won't help much

The top already seems so wrong

[green folio]

Lemne check

@unique salmon keep doing

You're on the right track

[unique salmon]

Then I would magically

⁶√3 - ³√9
----- • -----
³√9 -³√9

But why would I do that

[green folio]

Why tf?

Nah don't do that

[unique salmon]

That's a good question

Let's take a step back

[green folio]

Ye ye back to this

Stare at the denominator for a bit

[unique salmon]

Okay

[green folio]

Any thoughts?

[unique salmon]

Nothing pops up for the top half

[green folio]

3²=9

Something pops now?

[unique salmon]

Yeah I had that in my mind for the bottom

[green folio]

Ye do that

[unique salmon]

⁶√3

³√3²

[green folio]

Hmm

[unique salmon]

Wouldn't it be possible to get rid of the top one

[green folio]

Why don't u remove the root overs and get fraction powers?

[unique salmon]

Well no

We can't

[unique salmon]

Wish I knew what that meant

[green folio]

Let's take an example

[unique salmon]

Wait do you possibly mean

[green folio]

³√4=4^⅓

Do u agree?

[unique salmon]

Yes

Oh so you want me to go to that state

[green folio]

Ye ye

[unique salmon]

3⅙

3⅔

[green folio]

Hmm

Doesn't this feel familiar?

[unique salmon]

It somehow does

[green folio]

If bases are same(multiplication) powers get added if bases are same(division) powers get Subtracted

I feel I can connect this exponent law somehow

Don't u think the same?

[unique salmon]

Hmm

To sum it up...

[green folio]

Ye

[unique salmon]

I'm actually not sure

[green folio]

2³

2¹

[unique salmon]

Continue

[green folio]

=2(³-¹)

Forgot?

[unique salmon]

OH

I SEE NOW

[green folio]

Now this feels awfully similar

[unique salmon]

3⅙-⅔

[green folio]

Yes

Simplify

[unique salmon]

3 -½ = 1/3

NO WAIT

1/√3

[green folio]

Ye

Gottit

[unique salmon]

I'm so goated

[green folio]

Ofc

[unique salmon]

So basically

[green folio]

Was that ur hw or a fun question?

[unique salmon]

Stop trying before learning the laws

[green folio]

Ye

Wait didn't learn the laws? 💀

[unique salmon]

I'm studying for my semester uni exam, this is supposed to be the 1st part of 20 different parts, basically highschool recap, but I don't remember highschool math being so difficult

[unique salmon]

I was going off pure thoughts sometimes, but I tried to remember some from highschool

[green folio]

Just go through it I'm sure ya Will recall everything easily

[unique salmon]

It's just so long and tiring to get one damn question right

[green folio]

Ya want a question?

[unique salmon]

No, I had enough of this first part

Time to move to the next one

I've already done about 10, but with this one, I'm sure I can do this

[green folio]

Sure

@unique salmon slide the question so that i can access it if in case ya get stuck

[unique salmon]

Hmm

I'm moving to the next part

A little similiar

[green folio]

I see

[unique salmon]

Can I keep this open

I'll keep studying for at least 3 hours

Been doing it for 3 hours already oof

[green folio]

I think you can if u keep asking questions in atleast an interval of half an hour

[unique salmon]

Okay

I thought that I was a math genius for a second, but then I saw that none of the optional answers matched mine

@green folio

[green folio]

💀

@unique salmon ya forgot to take lcm?

[unique salmon]

I don't know what that is

[green folio]

Hmmm

Which one is correct here?

[unique salmon]

The 2nd one obviously

[green folio]

Ye ye

[unique salmon]

I think I skipped something

[green folio]

So why ya forget to do the same?

💀

[unique salmon]

THATS A GOOD QUESTION

[green folio]

What are the mcq options?

[unique salmon]

Redoing it rn

[green folio]

Oki

[unique salmon]

Something is not right

[green folio]

Bro ya just sending one step I won't understand anything lol

[unique salmon]

I basically did all and got here

But I assume that if there is nothing

You should write 1

Instead of 0

Right

[green folio]

How tf ya got 0?

In the first place lol

[hard patio]

also theres no way you are getting a 0 in the denom

[unique salmon]

Idk

[hard patio]

(x+2)(x+2)-(x-2)(x-2)=?

[green folio]

Everything won't cancel out tohhh

[hard patio]

thats your numerator

[green folio]

Now where did 4 come from?

I mean come istg

[unique salmon]

I won't question it

[hard patio]

mmy hands arent typing well today idek wth is up

i editd it

[hard patio]

now? what is it?

[green folio]

Now time to meow

[hard patio]

meow

that was random

bro

[hard patio]

yes

now simplify the numerator

[green folio]

Bro stole my customer

[hard patio]

LMAO

how about you confront that 2x7 is not 7x2 guy till then

[hard patio]

wrong one again?

[green folio]

Nope was showing ya the time 💀

[hard patio]

nope

wheer did thte +8 come from

[unique salmon]

I feel offended after using most of my brain

[hard patio]

bhoot

[unique salmon]

There is literally minus

[green folio]

Bhootnaath

[unique salmon]

Infront of (x-2)

Wait

Don't tell me it doesn't apply

[green folio]

How did ya get 4x+8?

[unique salmon]

For the 2nd bracket

The minus

Oh my god it doesn't

[green folio]

My man is more confused then we are frfr

[hard patio]

$$(x+2)(x+2)-(x-2)(x-2)$$
$$(x^2+4x+4)-(x^2- 4x+4)$$

[ocean seal]

Deol

[unique salmon]

Okay

8x only

[green folio]

Latex pro here

[unique salmon]

Right

[green folio]

Affirmative

[unique salmon]

Okay

[hard patio]

i just added $$ 💀

[green folio]

💀

[green folio]

Add "a" Before those dollar signs for extra luck yk 💀

[unique salmon]

Today

I became a legend

It's

[green folio]

How?

@hard patio what class ya in?

[unique salmon]

4

x - 2

HAHAHAHA

[green folio]

Ye

Correct

[unique salmon]

I had it in me all along

[green folio]

Next question yayyyy

[hard patio]

looks good

[hard patio]

e

[unique salmon]

Flirting with Math

On a date with Math

[green folio]

Bro doesn't feel secure enough to expose

[green folio]

Dating with shinobu

[hard patio]

lol 10th

[green folio]

Lemme throw some trigonometry at u

Frfr

[unique salmon]

If only she was real

[green folio]

[unique salmon]

Cosplayers look bad ASF after putting 2 tons of makeup and getting a hairwig, eye contacts to look like a character

[green folio]

What to do?

[unique salmon]

I'll start first

First

I would replace the 1s

I feel like they don't belong here

My personal opinion

[green folio]

Bro what does the question want tho?

Bro go fix ur phones keyboard

[unique salmon]

Fr, I Aim for both 2D and 3D it doesn't matter

[green folio]

I aim for 1d

[unique salmon]

How am I supposed to do

To know*

[hard patio]

my hands are cold

[hard patio]

you are gonna have to provide context

[unique salmon]

Determine the difference of the sum and product of the expressions

[green folio]

And mine are black

[unique salmon]

Based of Google translate

[green folio]

💀

Bro what's the origin language of ur question paper?

[unique salmon]

Czech Language

I'm not Czech tho

[green folio]

OHH you live in c-

Nvm.

[hard patio]

also wheres that trig questiom?

[unique salmon]

Trig what

Trigonometry?

[green folio]

I forgot what kinda trig y'all used to do in 10

I can give u few class 12 ones

[green folio]

Ya focus on ur paper ☠️

[unique salmon]

Ok

[green folio]

I don't even understand what the question wants

[unique salmon]

Like I said

I would replace the 1s

[unique salmon]

@green folio

I don't even know what it means in Czech

I only understand math with examples

[green folio]

Bro i don't know what the question wants 💀

[hard patio]

i think its {(1+a/a+1)+(1-a+1/a)}-{(1+ a/a+1)(1-a+1/a)}

like that?

ig?

[unique salmon]

SO WHAT DO YOU WANT ME TO DO, THATS THE DAMN QUESTION

[green folio]

I'll go search few czech vids in Incognito mode yk

[unique salmon]

(•_•)

[green folio]

LOL. JK.

[unique salmon]

Wish I knew what that says

Anyways

Let me find what the whole thing is called

[hard patio]

find the sum and the product and subtract the prodct from the sum

ig

[unique salmon]

modifying an algebraic expression

[green folio]

Oh ig the question wants you to

1. Find the sum
2. Find the product
3. Get their difference

[unique salmon]

This is what the whole thing is called

[green folio]

Am I ryt deol?

[hard patio]

i think so unless the translation messed up

[unique salmon]

(•_•)

[green folio]

Ye true

I think some monke is stalking this chat

[hard patio]

i read that scrunchy or whatver that was

[green folio]

Should probably call 911 and send the monke to the zoo

[unique salmon]

Monkeypox

[green folio]

Yeah spreading monke pox

[hard patio]

guys trollig

[unique salmon]

Okay so

[green folio]

Waiting for -

Ur response

[unique salmon]

Optional answers

For what I sent

[green folio]

WTF? 💀

Determine the difference of the sum and product of the expressions

[unique salmon]

Basically get rid of a

[unique salmon]

Or get a =

[green folio]

OH YE

[unique salmon]

Something

Idk

Wait

Aren't we supposed to put something instead of a

Like to assign a number

Chat died

[green folio]

Nah me trynna calculate

[unique salmon]

@ me

[green folio]

Wait

Demn my plan failed

💀

[unique salmon]

Rip

[hard patio]

ye

it check out

to an option

[green folio]

Oki

[hard patio]

start brute forcing heh

[green folio]

Always works

[hard patio]

i swear to god if my answer is wrong though 💀

did you get it?

@unique salmon

[green folio]

My brain ded

[hard patio]

what class you in?

[unique salmon]

Me?

Lol I didn't even start

💀

[green folio]

💀💀💀💀

[hard patio]

try it bruh

[green folio]

This mf

💀💀💀

[hard patio]

making us slave

[unique salmon]

Let me check some videos my teacher made

[green folio]

Frfr

💀💀💀

Ye fr

[hard patio]

anand? you dont have to tell me

[green folio]

Bro wtf I got 0

[green folio]

12 commerce

[hard patio]

with math?

[green folio]

Ye

[unique salmon]

This is what my teacher did

An example^

[green folio]

Commerce without math is a dumb choice frfr

Isn't difference subtracting?

Or is it dividing?

[hard patio]

cool, is it good? i cant decide what to choose tbh

[green folio]

Ya confused between sci and com?

[unique salmon]

Why didn't I just check these

[green folio]

Do u have the question go this soln?

[unique salmon]

For the one you're asking

[green folio]

Man this is direct question

Ya gave such an indirect question

Ur professor is bullying us

[unique salmon]

Why

He bullies everyone so it doesn't matter

Actually

[hard patio]

ist it simple though?

[unique salmon]

A she

My bad

[green folio]

WAUF

[unique salmon]

I'm not aure

[green folio]

WAITTT

[unique salmon]

I'm going to try

[green folio]

LEMME GET SOMETHING CLEAR

[hard patio]

what values can you have for

[green folio]

Is sum addition or multiplication

?

[hard patio]

you can have everything except

a is neq 0 and -3

[green folio]

BRO I DESERVE TO DIE FR

Answer quick

Oh addition

Nvm me not gae

[hard patio]

lol what?

[green folio]

The question gae tho

[hard patio]

ffff

simplify it

as much as you can

[green folio]

@unique salmon this question on u fr

💀

[hard patio]

why?

am i looking at the wring question or somthing?

[green folio]

Idk I just am unable to understand what the question wants me to do

[hard patio]

this one

?

[green folio]

Not this

Dis

[unique salmon]

Hmm I got lost again

[green folio]

What happene

Ned?

[unique salmon]

Can something be

[green folio]

@unique salmon is this exam test?

[unique salmon]

a² + 1

[green folio]

Nope

[unique salmon]

Nah, just a random question

[green folio]

a becomes imaginary

[unique salmon]

My test is in 5 days

I got to

[green folio]

a²+1=0
a²=-1
a=±√-1
Which makes a an imaginary number

[green folio]

Let's do the next questions then and ask this question tmr as doubt

[unique salmon]

a² + 1 1
------ | ------
a+1 a

I got this

[green folio]

What's that line in between?

[unique salmon]

You can see

That

There is a ,

So I put |

Cause it looks better

[green folio]

💀

[green folio]

Yeah you simplified em

Now what?

[green folio]

It will be 2a+1 not a²+1

There's difference between a+a and a*a

[unique salmon]

Oh yea

My bad

[green folio]

But now what to do

Determine the difference of the sum and product of the expressions

Hmm

[unique salmon]

Wait so you're in the same spot?

[green folio]

Kinda

I can't figure out what the question demands

[hard patio]

i wrote my answer down

should i send pic

[green folio]

What is it?

[green folio]

Ye

[hard patio]

2?

idek

[green folio]

Slide lemme see

[unique salmon]

Can't we just remove the a+1

And put both of them onto the other side

[green folio]

Wdym?

[unique salmon]

Like

2 |. a+1
-----
a (a + 1)

Then we would get rid of a + 1

Then there will be 2 and a

Although idk why

[hard patio]

i swear to god if its wrong i am gonna crawl under some rock somewhere

[unique salmon]

a = 2?!

I also think 2 is the answer

Or -2

[hard patio]

yo are talkinh about this oen?

[unique salmon]

One of them

[green folio]

Ye

[hard patio]

Goodbye

[unique salmon]

I'm not sure how you got that - between them

[hard patio]

"difference''

[green folio]

I too feel this is it

[hard patio]

thats what it is

then

[green folio]

Ye

[hard patio]

so i dont have to dissapear off the face of the surface of our planet?

yay

[green folio]

Btw

Ya said you're confused between sci and com ryt?

[unique salmon]

I'll check if it's 2

Let's move on

[green folio]

Oki

[green folio]

I won't recommend ya any particular stream but lemme clear some basic shit up before ya choose

[green folio]

(In ur dms later)

[green folio]

Try ur self first

[hard patio]

^^

[unique salmon]

Already doing

[green folio]

With whom?

[unique salmon]

With my pen and paper

[green folio]

DAMN

[unique salmon]

Sometimes, one has to be different

[hard patio]

okay yes

[unique salmon]

is rs-r² different from r²-rs

[hard patio]

factor out r

[unique salmon]

r (s-r) or r (r-s)

That's my question oof

[hard patio]

facyor -1 from one

of those expressions

[unique salmon]

WOAH

Wait how do I do that

[hard patio]

say you had to factor -1 from s-r

[green folio]

Send me ur location I'll fk ya bro

💀

[unique salmon]

I don't think this was a math equation

[hard patio]

-1(-s+r)

[hard patio]

language.

[unique salmon]

Wait so am I allowed to add +1

-1

[hard patio]

NOT ADD

[unique salmon]

then what

[green folio]

💀

[unique salmon]

Bro

So what do I put

For the bottom half

For the 3rd one

[hard patio]

(x-y)

that is just

[unique salmon]

I know

R (r-s)

But I can't do that

I'm asking how to do the -1 thing first

So I can get r (r-s)

[hard patio]

r{(1)r+ (-1)s} = -r(-r+s)

-r(s-r)

you will get this

[unique salmon]

But i don't want that

I want

R (r-s)

Or should I just keep

[hard patio]

Then shift the minus to the numerator

[unique salmon]

-r (s-r)

What is a numerator

[hard patio]

The number on the top of a frac

Or variable

Or expression

[unique salmon]

So from minus to plus

Yeah i got this

Easy

Okay I'm back

Took a break

Lol

My progress

What to do now

Like

Can I remove the r

So I don't have to write r(r+s ) • (r+s) (r-s) • r(r-s)

But

(r+s)(r-s)

Only

Actually

I get it

[green folio]

I/x(x-1)?

Is there in option?

Damn I took a 5min nap lol

[unique salmon]

B

This is what I got so far

[hard patio]

That’s not a nap. That’s forcing yourself to stay up. No offence

[unique salmon]

So...

Am i in the right direction?

Don't think this is correct

Helpp

[hard patio]

Hard to read honestly

[unique salmon]

I started the next one

This is how far I got

Isn't this too complicated tho

[hard patio]

So far so good

[normal sky]

Hi

I need an help

[hard patio]

Hi

#❓how-to-get-help

[normal sky]

I can't access

[hard patio]

Click on it

[normal sky]

Idk why

[hard patio]

Click on it and read it

[normal sky]

I don't have that

What is showed there

[unique salmon]

Idk how to approach no matter how i think

What about

x+2

[hard patio]

Expand that and the denom(the expression on the bottom)

You’ll see stuff cancelling out

[unique salmon]

Expand the (x+2)²?

[normal sky]

Can you help me too here?

[unique salmon]

Type in #help-12

[hard patio]

(x+2)^2 - 2x = x^2 + 2x + 4

And the bottom

Apple

Apply*

[unique salmon]

Wait so

[hard patio]

a^3 - b^3

[unique salmon]

Oh tht

Okay

Okay

Done that

Now

I guess I should go back to what is in the bracket

But how do I approach that

[hard patio]

Many ways

To do that

Take common denominator for one

[unique salmon]

(x+2)

[hard patio]

No

[unique salmon]

Wait

I misunderstood

No idk

[hard patio]

Add them up

The whole thing

In the brackets

[unique salmon]

The top half?

Inside the brackets

X (x-2)

2 (x²-4)

[hard patio]

No the whole thing inside the brackets

[unique salmon]

Well exactly, Idk what should be in the bottom half

Just (x+2)?

[hard patio]

Add the fractions?

[unique salmon]

Can you write it down

[hard patio]

$$\frac{x(x-2)}{(x+2)^2} + \frac{2(x^2 -4)}{(x+2)^3}$$
$$\frac{x(x-2)(x+2)}{(x+2)^3} + \frac{2(x^2-4)}{(x+2)^3}$$

[ocean seal]

Deol

[hard patio]

That is what I meant

[unique salmon]

I get it

Now

K think

No

I actually don't

Well basically

Here are my thoughts

What if

(x²-4) = (x-2) (x+2)

I would be able to get rid of the ²

[hard patio]

Yes

[unique salmon]

I'm still not sure what you did there, I know it went from ² to ³ and that you added a new bracket

But why

That I don't know

[hard patio]

Write (x-2)(x+2) as (x^2-4) for now

[unique salmon]

It's already there as (x²-4)

[hard patio]

Do you know how to add fractions?

[unique salmon]

Yes

[hard patio]

That’s what we did

We tried to make the denom same

[unique salmon]

So you added the 2nd one to change the ² to ³?

Is that allowed?

[hard patio]

2nd one?

[unique salmon]

Look

From x(x-2) to x(x-2)(x+2)

[hard patio]

Yes

[unique salmon]

Hmm

Okay

I'll just keep in mind that I can do that

[hard patio]

As long as you multiply both the numerator and the denomerator by the same number

[unique salmon]

I understand now why you did that

But it feels so illogical

Like illegal

All of sudden to change it to make it multiply

[hard patio]

Cancel things out in the frac outside the frac

Why did you now?

Not*?

[unique salmon]

Weong

[hard patio]

First do this one

[unique salmon]

Thoughts?

[hard patio]

And I need to go in like 10 minutes

[hard patio]

Bro

[unique salmon]

Trying my best to finish already

[hard patio]

Don’t start calculating

Cancel stuff out

Take (x-2)(x+2) common in the brackets

[unique salmon]

How

Like remove them?

Let's stop I don't think I'll get anywhere

I'll try to watch more videos

Thank you for the time

.close

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[steady basin]

bit confused by the final part
it says its not a pdf since fz doesnt integrate to 1
but what about fy
thats e^t-1
that doesnt integrate to 1

[worn fox]

,w int from -inf to 1 e^(t-1) dt

[ocean seal]

Results provided by WolframAlpha

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Requested by iCaird#6258

[worn fox]

[steady basin]

why r u using limits 1 to - inf

i thought it was just the integral wihout taking any limits

[worn fox]

How would you ever possibly get the result to be 1 if you had no limits?

The whole "integrates to 1" thing means "the probability of anything at all happening is 1", something has to happen

[steady basin]

.close

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[rocky summit]

Hey, quick question

[rocky summit]

What is a "functional equation" for a generating function?

[vale wigeon]

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

these things

[rocky summit]

Ahhh! Perfecrt

I swear, I looked

But nothing came up. I'll check this out

.close

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[median siren]

In what different ways can you graph the expression for "a quarter of y"?

[median siren]

I need help with this question it's an algebra question.

you don't ask here lol

#❓how-to-get-help

Can you help me tho

:D.

no? oki.

[amber roost]

y = 4x

cause technically your x would be x = y/4

x = (1/4)y

x = quarter of y

[median siren]

thanks!

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[dusty flare]

i don't know where i went wrong in this proof but the expansion is not looking too good rn

[dusty flare]

(for complex numbers z and w)

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[drowsy sedge]

when solving for eigenvalues why do we set the determinant of it equal to 0?

[plain flame]

well you start by writing $A\bf{v} = \lambda \bf{v}$

[ocean seal]

Gijs

[plain flame]

then you can manipulate that

[drowsy sedge]

right

[plain flame]

namely $A\bf{v} - \lambda \bf{v} = 0$

[ocean seal]

Gijs

[drowsy sedge]

ye

[plain flame]

$(A - \lambda I)\bf{v} = 0$

[ocean seal]

Gijs

[drowsy sedge]

yup

[plain flame]

which is only true if $A-\lambda I$ has determinant 0

[ocean seal]

Gijs

[drowsy sedge]

ohhh okay ye I get that but here is a maybe stupid quesiton

wait what happened to the v

when u take the det

cus its just det(a - lambaI) = 0

the v dissapears

[plain flame]

well this only has a solution for v nonzero if determinant $A-\lambda I$ is 0

[ocean seal]

Gijs

[plain flame]

#❓how-to-get-help

[drowsy sedge]

bruv #❓how-to-get-help

[plain flame]

its okay

[drowsy sedge]

sorry do u mind repeating that

[plain flame]

we use that a property of full rank matrices (determinant not 0) dont map non zero vectors to zero vectors

[drowsy sedge]

so (A-lambaI) det must be 0

why not v's det = 0

wait

[plain flame]

v is a vector it has no determinant

[drowsy sedge]

cus v is not a transformation?

right

[plain flame]

matrix multiplication is a linear transformation yes

v is a vector not much more

[drowsy sedge]

okay so wait

when I calculate the det

I find

v?

[plain flame]

no

[drowsy sedge]

I am sorry I am just so confused on what the purpose of v is

[plain flame]

well v is an eigenvector

[drowsy sedge]

wut I thought (A-lambdaI) was

[plain flame]

uhm okay lets go to the basics

[drowsy sedge]

okie

[plain flame]

an eigenvector of a matrix "does not change direction" when you multiply that matrix by that vector

i can send a visualisation

[drowsy sedge]

yes

plox

nvm ignore that

[plain flame]

https://youtu.be/PFDu9oVAE-g?t=193

its linked with the correct timestamp

you can see what a matrix does when multiplied by certain vectors

and eigenvectors are only ever stretched out or shortened

they dont "change direction"

[drowsy sedge]

lul

im watching that vid rn

but yes please continue the basics

[plain flame]

alright so a matrix of full rank never maps a nonzero vector to the zero vector

[drowsy sedge]

i have to go for a min but feel free to dump all the info u think is important

[plain flame]

that might be tough to understand at first but its very important

so since a matrix of full rank never maps a nonzero vector to the zero vector, $A-\lambda I$ must not be a matrix of full rank as it does map v (a nonzero vector) to the zero vector

[ocean seal]

Gijs

[plain flame]

hence $det(A-\lambda I) = 0$

[ocean seal]

Gijs

[lone heart]

@drowsy sedge Has your question been resolved?

[drowsy sedge]

Thanks!

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[keen orbit]

this is going to require trig sub innit

😬

I forgot trig sub already

[tacit arch]

https://xaktly.com/IntegrationByTrigSubstitution.html

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@keen orbit Has your question been resolved?

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[spice frigate]

hi can someon e help me with this?? is for a friedn

[spice frigate]

21519 ÷ 36,2

[raven rover]

You can put that into a calculator

[spice frigate]

ye but with a process

[sour dove]

You can multiply the numerator and denominator by 10 to get 215190 / 362. Then do the standard division algorithm

[raven rover]

You can do long division, but that’ll be awful

[raven rover]

^^

[spice frigate]

thx

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[gaunt dirge]

lets say you have a grid of squares in a random path-connected shape like this
(question continued below)

[gaunt dirge]

like, for instance, maybe you are building a platform in a game engine and the top of the platform is a seemingly-random shape like this

and lets say you want to add grass to the top of this shape by adding rectangles that align with the grid

and in this problem, the grass above is separated by rectangles like this:

and notice that the grass hangs beyond the platform by exactly 1 unit (and the overhang does include diagonally adjacent grid squares)

with this in mind, how would one determine the minimum number of grass rectangles and their locations on any given connected grid of squares?

[worn fox]

For what purpose are you trying to minimise grass rectangles?

[gaunt dirge]

optimization

less rectangles = less polygons that the computer needs to render

[worn fox]

Just run some kind of greedy algorithm

Find the biggest rectangle, place grass, do the same for all new ungrassed sections

[gaunt dirge]

well this question is sort of a theoretical one, im just using its application as a method to help people understand what the question is asking

[worn fox]

I don't think this is going to have any kind of simple theoretical answer that isn't just running an algorithm

[gaunt dirge]

think about this

heres a valid answer for that diagram

it may or may not be the best answer, but it is one

[gaunt dirge]

it won't have an answer?

i mean its easy to just write an algorithm that spams rectangles until satisfied

but i find the problem itself interesting

[worn fox]

Well there's not gonna be some magic formula that tells you "yes you can do it in 7 rectangles", the constructions will be algorithmic and proving whether they are or are not minimal it quite likely not so easy

[gaunt dirge]

what field of mathematics would problems like these be under then?

because i want to study further

[worn fox]

Honestly no idea

There will probably be more compsci literature on jt

[gaunt dirge]

i'll keep my question open for a little while longer to see if there's anyone around with a second opinion

[manic wind]

Are you strict about your definition of overhang?

[gaunt dirge]

well, i don't really know how to word it

but uh

take an island with only 1 grid square

a grass overhang for only 1 grid square would be a 3x3 square of grass

because we include diagonally adjacent squares for the edge

[manic wind]

“exactly” one overhang or minimum

[gaunt dirge]

hmmmm

[manic wind]

because this diagram fails that test

[gaunt dirge]

where does it fail?

[gaunt dirge]

one minimum

like if you have some weird stuff like this

then you'd need a piece there to cover for the diagonals of the corners

[manic wind]

Anyways, there are algorithms to find least rects in a grid. I don’t know it off the top of my head but I’m sure a google search will yield some results

[gaunt dirge]

if there's an algorithm like that, then the answer would be to take the original grid and outline it with more grid squares

[manic wind]

Yes

[gaunt dirge]

and then to run that algorithm on the new grid

[carmine reef]

The overhang doesn't really factor into this problem does it?

It's just about finding the smallest number of rectangles needed to cover some mino

[gaunt dirge]

perhaps it doesnt

[carmine reef]

i suppose not every mino will correspond to an overhang situation but I don't think that will help

[manic wind]

I’d start by trying some “naive” solutions and seeing where they fail, if at all

[carmine reef]

Could start from the left

[manic wind]

It should be logical to start with the largest possible bounding box

[carmine reef]

Like look at the leftmost (nonempty) column

Cover it with rectangles, extend those right as far as they will go

then repeat

fails in some situations tho

[manic wind]

Fails in the example diagram

[ripe elk]

she does want to hang off, so what if we just extend it, and then maybe a greedy algorithm?

[carmine reef]

does the example in 7 right

Displayed is in 8

[manic wind]

Yeah

[carmine reef]

so unless you have one in 6

[manic wind]

Max is 6 I believe

I’ve gotten 6 several ways

[carmine reef]

ah ok

fails for t mino pointing left

. O
OO
O

[manic wind]

I’d say start with finding the largest bounding box

[carmine reef]

smallest bounding box?

[ripe elk]

this feels like a converse on the bin packing problem

[carmine reef]

ah I see

[manic wind]

Trying to think of a case where it would fail

[gaunt dirge]

heres the og grid

[manic wind]

It is more computationally complex tho

[carmine reef]

Largest area?

largest area bounding box fails here

[manic wind]

Yeah it would fail

Hmm

This would be terribly inefficient but maybe all possible rectangles could be generated

Where I was going with this doesn’t work prolly

[ripe elk]

it would work, but i would presume it would be at an O = x!

as its every permutation

[manic wind]

Yeah

I mean not every case

Just generating rectangles, and using that to determine the “best” rectangles

[carmine reef]

Well all possible rectangles would be like O(n^4)

[manic wind]

Generating all cases would run Marianna trench deep in recursion

Other thought is having some smart parameters to label "stray" rectangles, and seeing the largest areas that incorporate the most strays (without subdividing anything etc. to create more "strays")

In an actual application though, the cheapest, although slightly suboptimal, option would probably be the best

[ripe elk]

so searching it up gives this article http://library.utia.cas.cz/separaty/2012/ZOI/suk-rectangular decomposition of binary images.pdf

something about fast fourier transform

with it being able to do at O(MN log MN), with M and N being image dimensions

which is, as far i could tell, better than O(x^3), supposing a X by X grid

[manic wind]

yeah I found some other "dissection" algorithms following O(n log n)

[ripe elk]

so if you need a fast, optimized algorithm, id go with the GDM, basically a fill in row by row with rectangle

but if the start and end points are the same, combine the rectangles

[manic wind]

here is a js impl I found https://github.com/mikolalysenko/rectangle-decomposition

[gaunt dirge]

What with QTD?

[ripe elk]

?

[gaunt dirge]

Quadtree decomposition

Oh wait

For larger grids it has more rectangles

[ripe elk]

i dont think thats a good one for you

[gaunt dirge]

nevermind

[ripe elk]

that one is if you wnat a low res basicly

[gaunt dirge]

Well in my game engine I'm trying to go for a like

lego look

which means low res basically

[manic wind]

is this theoretical or not?

[gaunt dirge]

idk

from what he says here, apparently its applied

but on a theoretical level then yeah gdm is better

[ripe elk]

what i mean for low res is like, it gets a general shape first, then the details

[gaunt dirge]

oh ok

[manic wind]

yeah gdm seems like the best bet

[ripe elk]

for GDM, this would be 7 rectangles i think

[manic wind]

yep

[gaunt dirge]

interesting

thats a decent algorithm, but apparently it's beatable

[gaunt dirge]

as shown earlier

[manic wind]

but GDM is way computationally cheaper

[ripe elk]

and its generalized for any map

[manic wind]

worth it over minimal optimizations

[manic wind]

although it will struggle against structures like this

[ripe elk]

i wonder if it would be also better that like if your height is bigger, you do vertical rectangles