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[devout snow]

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[dim horizon]

I want to know if I got the grammar into Chomsky normal form correctly, to be honest it’s an unintuitive process for me

The only part I didn’t really know if it makes sense is the EE representing 00

[robust dust]

it looks like you still have a D -> BAC and a A -> BAC production

so it can't be in CNF

oh wait I missed step 5 above

[robust dust]

yes, that is the correct way of eliminating multiple terminals

I have another worked example here if that's helpful

but it's the same procedure for removing any terminals yeah

[dim horizon]

Ok interesting

So it should be good then?

[robust dust]

yeah

I haven't checked the other rules in detail, but looks good on first glance

[dim horizon]

Yeah the main thing that trips me up is multiple terminals (but you said having multiple variables is fine)

And also removing lambdas that part is tricky

[robust dust]

the only restriction in CNF is that you don't have 3+ variables in the same production

if you had a rule like A -> 000, then you'd have to do more work

[dim horizon]

Right, but same overall process?

I guess I just need more practice doing them until it feels automatic

[robust dust]

yes, introduce new variables X -> 0, Y -> XX , then replace A -> 000 with A -> XY

and so on for even more terminals

[dim horizon]

Gotcha, ok thanks, I’ll shelve this problem for later if it looks fine. I might ask a question a bit later about making a grammar for a language once I take a crack it

.close

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[wispy warren]

hey

[wispy warren]

determine the vertical asymptote for this function

[untold ravine]

what do you think it is

[wispy warren]

this is my work

[mystic scarab]

Vertical asymptotes occur (at least for this case) when the denominator is 0

[wispy warren]

oh sorry

[mystic scarab]

Then you have to check properly with limits (from the left and from the right)

[wispy warren]

I meant the horizontal asymptote

[mystic scarab]

Ahnnn

This function has no horizontal asymptote, because the degree of num is higher than that of the denom

[untold ravine]

what does the limt being x-6 even mean

[wispy warren]

woah woah woah

that is impossible

according to the key

the answer is y = x - 11

[mystic scarab]

That can't be a horizontal asymptote!

Did you want to ask for a slanted asymptote?

[wispy warren]

yes

that would be correct

the slanted asymptote

[mystic scarab]

What have you been taught about the slanted asymptotes?

[wispy warren]

actually not much

the original question was to find all asymptotes

so I thought setting the limit to infinity would help me find one

[mystic scarab]

Well you can't compute limits randomly 😅

There are two specific formulas for the slanted asymptotes

[wispy warren]

f(x) / x

and then

f(x) - kx

[mystic scarab]

Awesome

Then use them

[wispy warren]

but by the way

why is x - 6 not a valid answer

[mystic scarab]

Because if you use those formulas you get another thing 🤷‍♂️

[wispy warren]

well

if a question asks me to find all asymptotes

how to know which method to use

[mystic scarab]

Wdym?

[wispy warren]

let's say I'm given a function

and the question is to find all asymptotes of the function

what would be the first thing to do

[devout snow]

@wispy warren Has your question been resolved?

[devout snow]

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[flat ember]

I need to simplify it.

[flat ember]

But I can’t do like x^4 : y

[jaunty mantle]

I mean the order doesn’t matter

(xy)z = x(yz)

And xy = yx

[flat ember]

So you’re telling me to just do x^4 : x^2

[jaunty mantle]

Why do you put a colon in between

[flat ember]

What colon?

[jaunty mantle]

: is a colon

[short hare]

i think that's his way to say "divided by"

[jaunty mantle]

It’s not quite the right way to think about it

[flat ember]

It means divided!

[short hare]

altho he shouldnt! : is usually used for ratios

ratios are not quite the division.

[flat ember]

It’s generally taught like that!

[jaunty mantle]

You shouldn’t split up the expression like that, and also : is used for ratios yeah

[flat ember]

• is multiplied and : is division

[short hare]

i'd say use / for division

[jaunty mantle]

Anyhow

[flat ember]

Okay anyways

[jaunty mantle]

You know how last time I said subtraction doesn’t exist

[flat ember]

I can make that like this?

[short hare]

yes you can.

[flat ember]

Strange because division is suprier to adding

[jaunty mantle]

.

[short hare]

@flat ember

[flat ember]

Which subtraction

[jaunty mantle]

Just in general

I said there’s no subtraction, you’re only ever adding negative numbers

Do you remember that

[flat ember]

I’m off guard

Now

Cause in the meantime I solved it

[jaunty mantle]

Well…you’re not really answering me

[flat ember]

But how does that matter to this?

[jaunty mantle]

Well I’m about to tell you

But first you have to remember that I said subtraction is really just adding negative versions of the numbers

[flat ember]

Sure

But like

5 - (-5)

It’s 10 right?

According to yall

[jaunty mantle]

That’s 5 + -(-5)

The - is always attached to what’s on the right of it

Knowing this, I will now say, division is also fake

You can’t divide numbers

But what you can do is multiply by “negative” versions of numbers

Here negative means a different thing

Remember how I said -a is the number that when you add it to a you get 0?

[flat ember]

I’m kinda confused what you’re doing here

For what is this

[short hare]

it doesn't have to be releated to your question, it's just general useful information

[jaunty mantle]

Just follow along for a bit

[short hare]

you best know!

[jaunty mantle]

.

[flat ember]

No

[jaunty mantle]

Okay well, yesterday you asked why 0 and 1 are special in maths

[jaunty mantle]

0 is special because of this

0 is the unique number where a + 0 = 0 + a = a

When you do addition with 0 it stays the same

Now if we want negative numbers, then -a is the unique number such that adding it to a yields 0

[jaunty mantle]

(We already discussed that 0 is special because of this property)

So “-5” is the symbol we use for the number where if you add it to 5, you get 0

[flat ember]

Okay

But like if I had 5 - (-5) then what?

Frost

[jaunty mantle]

You can’t do that

As I said here, you can have 5 + -(-5)

[jaunty mantle]

.

[jaunty mantle]

We’re going to do this exact same thing to multiplication now

[jaunty mantle]

1 is the unique number where a * 1 = 1 * a = a

[jaunty mantle]

When you do multiplication with 1 it stays the same

[jaunty mantle]

Now if we want division, then a^-1 is the unique number such that multiplying it with a yields 1

[jaunty mantle]

So “5^-1” is the symbol we use for the number where if you multiply it with 5, you get 1

But all this 5^-1 is annoying to write so instead we say 1/5

This concludes why 0 and 1 specifically are special

[flat ember]

I understand

Frosst

[jaunty mantle]

What this means for you is that $\frac{x^5\cdot y^3}{y^5\cdot x^2} = x^5 \cdot y^3\cdot y^{-5} \cdot x^{-2}$

[woven radish]

frosst

[jaunty mantle]

So no, there’s no addition happening here

The adding of powers is just a notational shortcut for us

[flat ember]

Multiplication instead!

Actually

I found the answer

[jaunty mantle]

$x\cdot x\cdot x\cdot x\cdot x\cdot y \cdot y \cdot y \cdot y^{-1} \cdot y^{-1} \cdot y^{-1} \cdot y^{-1} \cdot y^{-1}\cdot x^{-1} \cdot x^{-1}$

[woven radish]

frosst

[jaunty mantle]

I think you can agree that this is far more troublesome to write out

[flat ember]

Ikr

But I know how to minus it

[jaunty mantle]

That’s why we use the powers

It just happens to work out that you can instead add the powers together

[jaunty mantle]

And it does the same thing and doing this and then cancelling them one by one

(Really we pick the notation that allows us to do shortcuts like adding powers cos it’s convenient)

[flat ember]

Mym

Mhm

Yes

.close

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[errant hinge]

is this correct? online forums are giving me different answers

[errant hinge]

wait, this question doesn't make any sense to me. how can the center of mass be in the middle if each half is different mass but same volume

center of mass should be closer to the denser object's center no ?

wtf am i missing

[acoustic leaf]

it doesn't say the center of mass is in the middle

[errant hinge]

it says it is cut through its center of mass

and the cut is in the middle

each are 12cm

am i misreading

[acoustic leaf]

it says it cuts through the center of mass, it doesn't say it cuts through the middle

[errant hinge]

but the image shows the cut is on the border of a and b

wait

the image is before cutting it

OHH

im calculating mass of left and right

after cut

i thought left and right was just a and b

im cooked

[devout snow]

@errant hinge Has your question been resolved?

[errant hinge]

4/5 got it jeeeeeeeeez bro bad question

.close

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[peak rock]

Not sure what i did wrong here

[wicked turtle]

is this correct when i+3 is less than 9?

in that case the inner loop doesn't get executed at all

[peak rock]

hm

well

that was done so i could use the other formula

where

and im basically getting ride of the start 1 - 8 numbers and keeping the 9 - i + 3 numbers in the sigmas

[peak rock]

so the new statement where i minus is equal

[wicked turtle]

yea i understand what you were trying to do

but i think you have to handle as a separate case the first few values of i, where i+3 < 9

[peak rock]

so

what would be a better

approach

or statement

than the one i put

[wicked turtle]

something like $\sum_{i=1}^6 (blahblah) + \sum_{i=7}^n (blahblah)$

[woven radish]

Bungo

[wicked turtle]

where in the first sum there's no inner sum over k

and then you also have to worry about what if n < 6

unless you're given that it is bigger

[peak rock]

i see

so its seperate

[wicked turtle]

yes then in the second sum you can safely do what you were doing

[peak rock]

but

how are we

taking the

outter loop? into count

with the

inner one

[wicked turtle]

wdym?

in which sum?

[devout snow]

@peak rock Has your question been resolved?

[peak rock]

Could you maybe 🤔 solve it on paper for me?

[long pasture]

hello! @peak rock
consider for i=1 to 5
what happens to the inner loop?

[peak rock]

It won’t run after like I=3

[long pasture]

oh well, for all i from 1 to 5, it wouldn't meet the condition k=9; k≤i+3
so it will bypass the inner loop

therefore we can write it as
500 + sum i=1 to 5 (10)

• sum i=6 to n (10+18(inner loop))

[peak rock]

Ohhhh

I see

So it properly works

[peak rock]

Thank you very much 🙏

[long pasture]

hope that helps!

[vague crag]

confusing

[peak rock]

Wait

[peak rock]

Yo

🤔 wait

1 to 5

Wouldn’t it meet the condition

[long pasture]

yes?

[peak rock]

For inner loop 😭

Since

It has to be less than 9

So

1+3 =4
2+3=5
3+3=6

Etccc

Until 9

[long pasture]

9≤1+3 will return FALSE
up til
9≤5+3 will return FALSE

until when i=6
9≤6+3 will return TRUE

[peak rock]

Wait I’m dumb 🤦‍♂️ it’s saying k is less than or equal to blah blah blah

Well that was kinda dumb to ask but thanks for answering

[long pasture]

no worries!

[devout snow]

@peak rock Has your question been resolved?

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[peak rock]

@long pasture you still awake??

[peak rock]

ima die im like 500 ish off 💀

[pseudo basin]

is this about a math question

[peak rock]

yes

[pseudo basin]

can you perhaps show the original for reference

[peak rock]

Prof gave an annoying quesiton

[peak rock]

Sure

[peak rock]

^

[peak rock]

Let me know if you can help after inspecting the question

[pseudo basin]

no i think im gonna tap out

[peak rock]

alrighty LOL

I’m going to crsshout been on this question for 3hrs+ 😐

[versed juniper]

so this is wrong?

[peak rock]

Yes

[peak rock]

Si

[frozen light]

I don't think you can turn the sum from 9 to i+3 of k into the sum from 1 to i+3 minus the sum from 1 to 8

If i+3 is less than 8 you get a negative number

[peak rock]

Why not 🤔

[frozen light]

even though it was originally a sum of positive numbers

[peak rock]

I did that so

The number 1-8 get removed

And only the

9 and on numbers stay

What other way

Would I simplify?

[versed juniper]

i stops at 6 tho

[frozen light]

sorry I didn't understand

[versed juniper]

i + 3 <= 9

[peak rock]

How would I simplify? Then

If that’s wrong

You tell me

[peak rock]

Um it’s the other way around?

[versed juniper]

im fried

[peak rock]

9 <= i + 3

[frozen light]

good question

[frozen light]

ah I see

[peak rock]

So um what would i do instead?

[frozen light]

right or else the loop wouldn't run

but then the sum of 18k shouldnt be included in the outer sum of 1 to n

from i=1 to 5 you only add 10, then from i=6 to n you add 10 + sum of 18k

[peak rock]

Hm

Would u be able to solve on paper?

[frozen light]

no

hold on

[peak rock]

Oh 🤨

[frozen light]

,tex $500+\sum_{i=1}^{5}10+\sum_{i=6}^{n}(10+\sum_{k=9}^{i+3}(18k))$

[woven radish]

Discusser

[frozen light]

should be something like this

[peak rock]

I did that tho?

[frozen light]

oh that's not what you had sent earlier

[peak rock]

Oh

That’s cause

The other person wanted to see initial version

I guess you saw the wrong one lol

[peak rock]

I want to know what i did wrong

Ik it’s wrong

[frozen light]

no clue honestly

sorry

[peak rock]

😔

All good

[devout snow]

@peak rock Has your question been resolved?

[peak rock]

😢

[devout snow]

@peak rock Has your question been resolved?

[peak rock]

No

😢

[lost tide]

Im stuck on it too

[worthy canopy]

Hello

[devout snow]

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[spark aurora]

hello can someone actually help me with combining these two functions to be just one function but still gives out the same graph

[spark aurora]

(red and orange graph)

btw this was my old blue graph

but when i somehow dont know how to combine the other two.....

do you guys get me

[modern lance]

what're these two functions I see 3

[faint gorge]

you mean like piece-wise function?

[spark aurora]

no no just the red and orange ones

[spark aurora]

what's that........

[faint gorge]

for example

[modern lance]

It can't be a function lmao cuz it will fail vertical line test

[faint gorge]

,tex .abs def

[faint gorge]

like that

i have two functions f(x)=x and g(x)=-x which i combine

[spark aurora]

and btw because its our project to like have a graph that can represent a rollercaoster thing, but only 2 functions can be made, but i dont know how to make those two in just one function (red n orange)

[faint gorge]

only way i can think by doing that is by using nested if conditions in geogebra

[spark aurora]

how do i use that.....

[spark aurora]

what do you put in condition and then???

help im sorry i dont use geogebra often

[faint gorge]

for example
If(x>0,x²,If(x<0,x))

You are saying for positive x, we have x^2

else for negative, we have x

and so you can continue this nested (nasty) if

else i dont know how to combine these functions

So the condition refers to the domain

then refers to what should happen on that domain (well your function)

[spark aurora]

what language is this.....

how do i know what my domain is

[devout snow]

@spark aurora Has your question been resolved?

[devout snow]

@spark aurora Has your question been resolved?

[devout snow]

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[potent compass]

can someone help me, i keep getting it wrong

[pseudo basin]

i see one typo

[late scaffold]

are those dots supposed to mean multiplication 😐

[pseudo basin]

anyway what you should have now is $\frac{2 + \frac{1}{9}}{5 \cdot 3 - \frac{7}{3}}$.

[woven radish]

Ann

[potent compass]

yuh

[potent compass]

tysm

[pseudo basin]

also make your fraction bars proper length.

bits and pieces of the denominator should NOT be exposed to the elements just because your fraction bar is shrivelled up into a point

[crystal dawn]

not everyone knows what \cdot is I suppose

[fossil locust]

you're just being nitpicky Ann

[pseudo basin]

https://tenor.com/view/no-bugs-bunny-gif-18219884

[fossil locust]

it's the same principle as "yes you made some noun in French the wrong gender, but it doesn't impact on communication"

[pseudo basin]

op was lucky it didnt impact communication here specifically

[fossil locust]

oh wait I see

ohno

[potent compass]

tysm guys

.close

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[dusky belfry]

how do I analytically figure out the "monotomy" I think that's the name, like, when it's growing or shrinking and where maximums and minimums are?

[dusky belfry]

I know how to do it using derivatives,

but I don't know if I am doing it right

[iron sun]

Monotomy?

[dusky belfry]

yeah it's not the name is it

alright makes sense

let me show you a tavble

table

by the table you're understand

I hope

[iron sun]

Not something ive personally heard, but sounds a bit like monodromy from e.g. complex analysis

But I’m guessing you’re talking about something else

[dusky belfry]

hold it, I'll take another the image is terrible

ok not perfect

but you see more or less?

it's that table in the middle of the pic

[iron sun]

It’s too blurry for me

[dusky belfry]

ok

another one

[thin inlet]

https://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtI.aspx

[dusky belfry]

here

alright there, it's good enough

[iron sun]

Okay

[dusky belfry]

it has arrows, on the table, and it's studying the growth of the function

[iron sun]

Like the points of the graph where it in some sense changes direction?

[dusky belfry]

yeah

where the derivative is 0

[iron sun]

Do you have a concrete example you want to talk about?

[dusky belfry]

yes I do

so

this is exercise 7

this table is actually made by me

but am I not doing it the right way

I got there

but I got there with the help of a calculator,

I don't know how to do it analytically

I am given

f(x)

which equals

$\frac{4x-2}{x^2+2}$

[woven radish]

ℕ∈ℝD ALERT: Gonçalo Gonçalves

[wild grove]

find f'(x) = 0

[dusky belfry]

I did

n't

kinda

that I do understand

but the first step is to understand if before the first 0 it is increasing or decreasing

and I thought there would be a process for this, because I can't figure that out

it's zeros are -2 and 1

ma job is to "study the function f's "monotomia" (in my languange)" and extremes

that's the table

[wild grove]

So f'(x) is increasing on an interval if f'(x) > 0, x is any number inside the interval

[dusky belfry]

but that seams such a bad way to solve it

so I reached out

sorry

I didn't mean to offend you btw

it just sounds to unelegant to be on a textbook

u know what I mean

I though there would be an actual method

[dusky belfry]

didn't mean to offend

[wild grove]

Basically

If f'(x) > 0, then the slope of the tangent is also positive

Which is a line going up

If f'(x) < 0, then the slope is negative

So it's going down

I don't know how that's a bad solution

[dusky belfry]

sorry

it just sounded too simple to be true

and I wasted about an hour on it

[wild grove]

No worries it's always great to understand why something works by yourself

[dusky belfry]

100000000% AGREE @wild grove

EVERYONE HAVE A GOOD DAY!

tks

.close

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[kindred mauve]

i dont understand why 7pi/3 = pi/3

[pseudo basin]

7pi/3 and pi/3 arent equal by themselves

but they are one full turn apart

which means their cos and sin values match

[devout snow]

@kindred mauve Has your question been resolved?

[kindred mauve]

can you expand

[pseudo basin]

a full turn is 2pi radians

ie going exactly once all the way around the unit circle

and landing right back where you started

[kindred mauve]

So they're equivalent

[pseudo basin]

"equivalent" is a somewhat vague word

there's one specifically for angles that land on the same position on the unit circle: coterminal

...but essentially yeah ig

[kindred mauve]

so we can write pi/3 for this reason

I don't understand this step

[lament prawn]

S^2 + C^2 = 1 --> S^2 = 1 - C^2

[kindred mauve]

so sub it in

[lament prawn]

yes

[kindred mauve]

also do you know what your username means?

And

is binominal expansion using pascals triangle.

[dusky belfry]

there is a lot of methods to expand a polinomial

but I think that is one of them yea

i think

[devout snow]

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[wet robin]

i need help regarding this question

[wet robin]

the markscheme doesnt make sense to me

why isnt it

[olive snow]

What about it

[wet robin]

bruh i was just being dumb oops lol

.solved

[devout snow]

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[jolly oar]

Yo can yall tell me if this is correct

[pure stone]

first one is wrong because you still have 0/0

[jolly oar]

But what can be changed there

[pure stone]

second one is wrong as well because you havent factored out x+2 on the whole numerator to cancel it out

you still have -x-2 at the end

[pure stone]

factor both numerator and denominator

[jolly oar]

The language barrier will certainlly be an issue here

Numerator and denominator are above and below the line that divedes right

[pure stone]

yes

do you know what factoring means?

[jolly oar]

Like 2² is factoring

[pure stone]

no that's prime factorization

factoring is breaking down an expression into a product

for example, x^2 + 5x can be factored as x(x+5)

[jolly oar]

Ok i know what that is

But is the last question right

[pure stone]

hmm

the way you write the last one is confusing

[jolly oar]

The handwriting or general way i wrote it

[pure stone]

and then you confused yourself leading to the wrong answer

the right answer is e^8

[jolly oar]

I see so that x on top was suposed to be infinite

[jolly oar]

Wait so it is correct

[pure stone]

you should write lim 2x/3 * 12/(x-9) seperately

[jolly oar]

I did that but i divided 3 with 3 and 12 with 3

[pure stone]

this step is ehhh

I'll let it slide

[jolly oar]

Here is this some cardinal flaw

Will they execute me if i do this on a test

[pure stone]

Anyways fix the other 2 problems above

[pure stone]

very likely

the cancellation should only be done on a draft

writing that on a test/exam is usually not accepted

[jolly oar]

Ight ive done it the other way its 8

[pure stone]

fix no.4 and 5 I mean

[jolly oar]

Got to here and got stuck

Maybe if instead of x i factor with an 8

[pure stone]

do you know the (x-y)^2 formula

[jolly oar]

Is it (x-y)*(x²-2xy-y²)

[pure stone]

no

[jolly oar]

(x-y)*(x+y) maybe

[pure stone]

I mean (x-y)^2 = x^2 - 2xy + y^2

and then you notice 8x is 2.x.4 and 16 is 4^2

[jolly oar]

Ok give me second to see how far ill get now

Can i do this

[pure stone]

yep

[jolly oar]

Ok then the anwser should be 4 no

[pure stone]

why do you think it is 4?

[jolly oar]

When i change Xs to 4s it becomes 4/4-4 and

And its lowkey 0

So what now

[pure stone]

4/(4-4) is 4/0 right?

[jolly oar]

Yea but can the anwser be 0

[pure stone]

is 4/0 = 0?

[jolly oar]

Yes?

What else could it be

[pure stone]

what is 0/4 then

[jolly oar]

0 too

Youre really making me doubt my basic knowlage rn

[pure stone]

because there is indeed a problem with your basic knowledge

try putting 4/0 into your calculator and tell me what it equals to

[jolly oar]

Then what else is 0/4 and 4/0

It says error

Sick

[pure stone]

if 4/0 is 0...

then 0*0 = 4???

[jolly oar]

But then what here

[crystal dawn]

,rccw

[pure stone]

Division by 0 is undefined

[jolly oar]

Ok but what can even be done here

[pure stone]

And since you have 4/0 here and the limit doesnt specify the direction of x, the limit does not exist

[crystal dawn]

a quick reminder that when dealing with limits, we don't care about what happens at the point itself, only about what happens nearby as you approach the point

[jolly oar]

This sounds strangelly philosophical

So i just write down that there is no anwser

[crystal dawn]

more accurately, the limit DNE, as mentioned

[crystal dawn]

I mean you could look it up I suppose

keyword: deleted neighbourhood

[jolly oar]

Ok can i cut these 2 up

[crystal dawn]

,rccw

[crystal dawn]

no

in fact the first cancellation you did is wrong too

[pure stone]

you take care of this I'm gonna go to sleep

[crystal dawn]

nah it's 3 mate

I also need to sleep LOL

[pure stone]

(and forget 4/0 = 0)

[jolly oar]

Dw i need to sleep too

But the tests will never sleep

[jolly oar]

So what can be done here exept cancelation

It look so canclablle

[modern lance]

It is canclable but ain't doin it right

[jolly oar]

Wait a moment

What about this

[modern lance]

Okay now you just multiply it with 1

Do you know how to cancel out the num and denom

[jolly oar]

Fuckass app

Smt like this

[devout snow]

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[devout snow]

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[clear bobcat]

how do i find the area of this
this exercise was about cosine and sine rule and blah blah but idk how to find the area ive tried multiple times but always get it wrong

[thorn cypress]

Could you find the area of ABD?

[clear bobcat]

uh

wait lemme try

[short hare]

does it say its cyclic by any chance

[clear bobcat]

no

[clear bobcat]

wiat so i just find the smaller triangle ad minus it from the bigger one?

[fierce viper]

yes

finding the area of the smaller triangle may be slightly difficult

[clear bobcat]

how would i find it

[fierce viper]

do you want to think about this more before i tell you?

[clear bobcat]

uhm ive got like no idea

[fierce viper]

first find BD, then reverse the cosine rule to get Angle BCD, then use the 1/2 ab sin C to get the area of the smaller triangle... there may an easier method i dont see though

[crude crest]

What is this channel guys

[clear bobcat]

its maths help

[crude crest]

Oh ok

Can i ask questions for my math class here?

[clear bobcat]

wait how would i find BD

[short hare]

you got two lengths and an angle, what do you think?

[clear bobcat]

oh shoot ya

[fierce viper]

#❓how-to-get-help

[clear bobcat]

omggg tysm guys

finally got it

[short hare]

https://tenor.com/view/have-a-great-day-gif-13578415868193855261

[clear bobcat]

.close

[devout snow]

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[devout snow]

@uncut nebula Has your question been resolved?

[devout snow]

@uncut nebula Has your question been resolved?

[drifting sierra]

The centralizer is $C_{S_{20}}(\sigma) = {\pi \in S_{20} \mid \pi\sigma\pi^{-1} = \sigma}$

[woven radish]

Nel

[drifting sierra]

\pi can permute the cycles of the same length, and can "rotate" each cycle

I don't quite remember some of the terminology

@uncut nebula do you agree with this?

Wdym

It can change the cycles independently, not elements between cycles

Well, it's the whole point of $\pi \sigma \pi^{-1} = \sigma$

[woven radish]

Nel

[drifting sierra]

I'm not really confident enough to tell you exactly why but intuitively it should make sense: if pi inverse takes an element from cycle A and puts it into cycle B, then sigma takes that element somewhere else in cycle B, and then pi won't return it from cycle B to cycle A, instead it will return another element from cycle B

Try taking an example:

sigma:
0 1 2 3 4
1 2 0 4 3

pi:
0 1 2 3 4
3 0 1 2 4

pi inverse, then sigma, then pi:
0 1 2 3 4
1 2 3 0 4
2 0 4 1 3
1 3 4 0 2 <- not the same as sigma

Yes, specifically rotate inside cycles

I'm not exactly sure how to show why to be honest

True, that's the intuition, but that doesn't quite show why there are no exceptions

Hm perhaps it's more obvious to you because you've been working on permutations

I mean it does make sense to me, but not enough to prove it

Anyway, given these facts, the order is quite easy to compute

No

You can only reorder cycles of the same length

Well you need the cycles of pi to act on cycles of sigma of the same length, otherwise you're slicing within cycles

Yeah sorry it's kinda hard for me to convey this

You might be thinking of permuting every cycle because you can write the permutation cycles in any order, but that doesn't matter

sigma:
0 1 2 3 4 5
1 2 0 4 5 3

pi:
0 1 2 3 4 5
3 4 5 0 1 2

pi inverse, then sigma, then pi:
0 1 2 3 4 5
3 4 5 0 1 2
4 5 3 1 2 0
1 2 0 4 5 3 <- same as sigma

See how the (0 1 2) and (3 4 5) cycles got swapped by pi inverse, then sigma did its thing, and then they got swapped back by pi?

I should have chosen (3 5 4) instead

Yes, but it only works because both cycles have the same length

Uh.. try it

[sick sinew]

I think this property may be helpful for you to understand: If
$$
\sigma = (a_{1,1}, \ldots, a_{1,n_1})(a_{2,1}, \ldots, a_{2,n_2}) \cdots (a_{s,1}, \ldots, a_{s,n_s}),
$$
then we have, for any $\tau \in S_n$,
$$
\tau\sigma\tau^{-1} = (\tau(a_{1,1}), \ldots, \tau(a_{1,n_1}))(\tau(a_{2,1}), \ldots, \tau(a_{2,n_2})) \cdots (\tau(a_{s,1}), \ldots, \tau(a_{s,n_s})).
$$

[woven radish]

andywho

[sick sinew]

Then I think this should be clear

You mean you dont know why this property holds or how to use it here?

[drifting sierra]

sigma:
0 1 2 3 4 5
1 2 0 4 3 5

pi:
0 1 2 3 4 5
5 3 4 0 1 2

pi inverse, then sigma, then pi:
0 1 2 3 4 5
3 4 5 1 2 0
4 3 5 2 0 1
1 0 2 4 5 3 <- not sigma

[sick sinew]

ok, then let's take (12)(34) as an example

after conjugation by \tau, we want it to remain exactly the same permutation

the $\tau(12)(34)\tau^{-1}$ we get can be of the equivalent form (12)(34), (21)(34), (21)(43), (12)(43)

[woven radish]

andywho

[sick sinew]

Also, we can switch the order of the (12) and (34) cycles

which doubles the number of possibilities

[sick sinew]

if, in the original decomposition, the lengths of cycles are 1, 2, 2

i.e., $s = 3, n_1 = 1, n_2 = 2, n_3 = 2$

[woven radish]

andywho

[sick sinew]

then, by the above property, after conjugation by \tau, the lengths' order still remains the same

we can only switch order for the two 2-cycle in this example without violating the property

[sick sinew]

just think of the forms i gave here as how $(\tau(a_{1,1}), \ldots) \cdots$ exactly looks like

[woven radish]

andywho

[drifting sierra]

I think I can agree with that

[sick sinew]

i can agree with that too

[drifting sierra]

If you'd like a more formal answer, check this: https://math.stackexchange.com/questions/208790/centralizer-of-a-given-element-in-s-n

I don't fully understand it myself, so good luck

[devout snow]

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[barren orchid]

this is my attemp (yes all of this is just one question)
can someone help me out with finding out why im getting the wrong ans

fundamentally im doing it correct right?

just some substituions

and then using the linear differential equation solution

[devout snow]

@barren orchid Has your question been resolved?

[olive plank]

Factorise and take x+y=t

[devout snow]

@barren orchid Has your question been resolved?

[barren orchid]

already did that

but after like 2 ore subtituion it ends up being ruined cuz of the e^ term

[olive plank]

Is the answer 1?

[devout snow]

@barren orchid Has your question been resolved?

[grave mantle]

Mate that is unreadable

[devout snow]

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[barren orchid]

no

[barren orchid]

.reopen

[craggy dagger]

it's already closed, so this is a new channel

[devout snow]

@barren orchid Has your question been resolved?

[barren orchid]

oh so do i need to post the ques again?

[craggy dagger]

it has been pinged, so you don't have to worry about that

[barren orchid]

: D thnx

[craggy dagger]

what I notice here is that x+y comes together a lot

so maybe setting z=x+y is the first obvious step

though you already written something too

[barren orchid]

yes i thought so the same
after substituing u have to again substitute the value of 1/z^2 as U to get a linear differntial eqn

im pretty sure ive solved it right up until that point

after the lde substitution it all went downhill

[devout snow]

@barren orchid Has your question been resolved?

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[frank cloud]

Hi, I've got a problem with question 6 here, I tried solving it and my answer comes to 12.75 approx but apparently the correct answer is approx 8.81 km, can someone explain what im doing wrong??

[tall linden]

,rccw

[pseudo basin]

apparently you read the ambiguous expression of "55° northeast" in the wrong way

[tall linden]

🤦

[pseudo basin]

and the 55 angle you marked is actually 90-55

[frank cloud]

BRUH😭

My brain lacking

Thanmyou so much

Waiit wait

[frank cloud]

Wdym?

[pseudo basin]

so the problem said, and i quote, that hiker #2 went in the direction of

55° north-east

and i think this could mean two different things and so should not be said

[frank cloud]

Yea

[pseudo basin]

if they meant N55E then they should have said that

or better yet give a three digit bearing as 055°

either way that's 35° off from east, not 55°

[frank cloud]

Its a book error?

[pseudo basin]

basically yes

[frank cloud]

Thanks I get it now

.close

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[fathom viper]

Hello, I would need help for the (b). "borné" means "bounded" (sorry I'm french).
I don't know at all if my reasoning is good because I've never used the integral bounds in that way

[devout snow]

@fathom viper Has your question been resolved?

[craggy dagger]

I'm thinking that some sort of holder inequality might be used but I'm not very sure

[fathom viper]

yes i used that a few times

[devout snow]

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[devout snow]

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[restive river]

how do i show this

[restive river]

A is a finite subset of G stable by *

Show that Phi isn't injective

i think it has to do with A being finite but i'm not sure

[still zephyr]

My bad french 😭

[craggy dagger]

is the group G assumed to be finite?

[restive river]

it doesn't mention anything about G being finite or not

just that G is a group

and A is a finite subset of G

[harsh sierra]

What is known about A

[restive river]

subset of G and finite

and not empty

[harsh sierra]

If G is finite this is very not injective

And even if G is infinite, x can still have finite order

[restive river]

what do we mean exactly by finite order

[harsh sierra]

x^n = 1 for some n

[craggy dagger]

what's "Soit"

[restive river]

oh yeah if G is finite injectivity will br contradiction with the pigeon hole principle

[restive river]

let

let x in A

[craggy dagger]

let x in a and phi be defined as the following

hmm

oh wait

but the problem is that A has to be finite and closed under *

ah so what you have to show is that $\varphi$ maps into $A$

[woven radish]

Element118

[restive river]

is that even possible to show?

with our limited info

maybe the exo is missing an info i think i'll just assume that G is finite

[devout snow]

@restive river Has your question been resolved?

[craggy dagger]

yes, A is closed under *

i'm assuming N excludes 0, but if N includes 0, just do A union {id}

[restive river]

i'll look into this further at a later time i need to deepen my understanding further

they were right when they said the first 3 months of uni are rough 😔

thanks guys

[devout snow]

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[sweet steppe]

Are lines 12 & 13 invalid here?

[copper kindle]

no

bcs we have plental expanation from integral e^X

[sand dove]

There's a problem of using the same name for the x in "forall" and "exists"

[sweet steppe]

wat

[copper kindle]

d

[sweet steppe]

right but existential elimination requires this clause

that

[sand dove]

it's no problem renaming it x in lines 14,15

but calling both instances of variables x in lines 12, 13 is not valid

[sweet steppe]

hmm

ahhh i see okay

[sand dove]

if you want to say that x itself verifies the claim X.P

[copper kindle]

ez question

[sweet steppe]

Because that name of x will be omitted once I use the rule

[sand dove]

If you're not here to help, please stop intervening

[sweet steppe]

its not even a question

[sweet steppe]

I see okay

so its a trivial issue if anything

I can do for all introduction and instead introduce something like y:X ?

does that make sense?

wait no that won't work either

I'm a bit lost here

[sweet steppe]

The variable of the first & second condition need to be the same, no?

[sand dove]

you don't need to say "exists x" then

[sweet steppe]

Oh 🤔

I can omit that part and include it later

[sand dove]

$\forall x: (P\wedge Q\implies X\cdot P)$

[woven radish]

Raphaelisius Maximus MMIII

[sweet steppe]

Exactly so what you're saying instead is I get from
P ^ Q => P
P ^ Q => Q

Then add the exists at the end before I use ^I

Am I understanding you right?

[sand dove]

well it's basically this

you just need to add "exists x such that Q" at the conclusion

[sweet steppe]

I get it ok

So instead I show for P, Q individually and then just do exists introduction

and then concluding conjunction introduction

but i dont understand whats wrong exactly with lines 12 & 13

is it because x is not free?

[sand dove]

x is already the variable used at "forall"

so indeed it's not free for naming another variable

[sweet steppe]

ahhhh ok that makes sense

so to get around that issue i just prove it without any quantifier

then add the exists quantifier at the end

ok yeah i can see it like that

[sand dove]

that's what I requested here

[sweet steppe]

yeah exactly

Do I need to denote that X.P ?

I havent seen that before

[sand dove]

because look, if P ^ Q is true for some x, then it's X . P that's true for the same x

[sweet steppe]

Exactly

Okay that makes sense

I need to pay more attention with names

thank you

we can close this somehow

[sand dove]

command is .close

for when your question is solved

[sweet steppe]

oh right

thank you

.close

[devout snow]

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[nimble mirage]

Hi

[nimble mirage]

What is trigonometry

[fierce viper]

https://en.wikipedia.org/wiki/Trigonometry just read this

[nimble mirage]

Can you explain in basic pls

[thick knoll]

Which grade are you in rn

[nimble mirage]

In 9th

Trigonometry is in our syllabus I don't understand

[thick knoll]

9th where

[nimble mirage]

I m 14

[cold haven]

What don’t you understand?

[nimble mirage]

It deals with circles also and makes waves and how to spot in triangles also

[thick knoll]

Well if you're from Asia then you need a lot more than if you were in the Uas

[nimble mirage]

Yes I m asian 🙁

[thick knoll]

*US

[thick knoll]

I see

[nimble mirage]

You?

[thick knoll]

Same

But in uni

[nimble mirage]

Uae?

[thick knoll]

Asia

Well to start off

[nimble mirage]

Oh

Let's study?

[fierce viper]

for 9th grade trigo it's literally just this

[nimble mirage]

Yes

[thick knoll]

Trigonometry is the study of triangles

[nimble mirage]

@fierce viper thanks

[thick knoll]

Now do you know the types of triangles

You'll use them a lot

[nimble mirage]

@thick knoll add me as friend we will study ok bro

[thick knoll]

K

[nimble mirage]

I m new on discord but I mostly you ig

Use*

@thick knoll can you make me understand these formulas

[thick knoll]

Do you know the types of triangles

[glad mountain]

in 9th grade you'd mostly wanna memorize those trignometry formulae

[thick knoll]

Mostly

[glad mountain]

youll get the hang of it once you start solving problems

[thick knoll]

But for us it was also subjective

[thick knoll]

.

[nimble mirage]

@thick knoll your syllabus can you tell

[thick knoll]

Trig

Or overall

[fierce viper]

just to gauge where you are, can you answer the following questions?

1. What are tan, sin, and cos in terms of ratios of sides of a right-angled triangle
2. What does the pythagorean theorem tell us?
3. For what quadrants are each of sine, cosine, and tangent positive?
4. What is the angle opposite of a side a called?
5. What is the area of a triangle ABC, given sides a, b, and the included angle of the two sides, C?
6. What is the length of the third side of a triangle c, given two sides a and b and an included angle of the two sides, C?

[glad mountain]

math wasnt subjective for us honestly just solving problems

[thick knoll]

That would be so much better

[glad mountain]

9th is easy peasy

lmao

[nimble mirage]

I can solve 6th question

[nimble mirage]

6. Whole Square root of a² + b² - 2abcos (c )

[thick knoll]

What about the others

[nimble mirage]

Let me try

[thick knoll]

Correct!

[nimble mirage]

2. In Quadrant 1. sin cos tan are all postive
3. sin + cos and tan -
4. tan + sin and cos -
5. cos + sin and tan -

[thick knoll]

Start with Q1 if you can

[fierce viper]

okay great so you know ASTC

[nimble mirage]

K

[nimble mirage]

Maybe

[thick knoll]

It is what you just typed out

[nimble mirage]

sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent

Answer of q1

This is ig,

Hypotenuse Is longest side

[fierce viper]

okay so you know what SOH CAH TOA is

[thick knoll]

Yes

[nimble mirage]

Yes

[thick knoll]

Go on

[nimble mirage]

Sine = Opposite/ Hypotenuse?

...

Like that ig

[thick knoll]

Yea

[nimble mirage]

Yeah I know

[thick knoll]

Now what about the other 3

Cot, Sec and Cosec

[nimble mirage]

Yes

Its

CHO ,SHA,CAO

For other three they are reciprocals

[thick knoll]

Yes

[nimble mirage]

K

Can you help me with medium trig

[thick knoll]

Now these are the fundamentals of trigonometry

[nimble mirage]

That is hard fr

Yes I know

[thick knoll]

Like

[nimble mirage]

The trig functions

They are hard

What is yr age pls if you don't mind?

[thick knoll]

These are the trig functions

[thick knoll]

19

[nimble mirage]

Ohh Can you help me pls

[fierce viper]

certified unc /j

[thick knoll]

Nooooo....

[thick knoll]

Yes I can

For now, these are the trigonometric functions

We will build on this

Starting with the identities

@nimble mirage Hello

[nimble mirage]

Thank You So Much

Yes go on

[thick knoll]

Do you know the trig identities

[nimble mirage]

Yes

[thick knoll]

What are they

[nimble mirage]

sin²0 + cos²0 = 1

Proof is

[thick knoll]

Using pythogoreas

[nimble mirage]

sin0 = a / c c is hypotenuse
cos0 = b / c

a²/c² + b²/c² = c² / c²

= 1

[thick knoll]

Yes

[nimble mirage]

2 is

1 + tan²0 = sec²0

Proof is

[thick knoll]

No need to do it

If you know it

[nimble mirage]

K

[thick knoll]

And 3 is the same way right

[nimble mirage]

3. 1 + cot²0 = csc²0

[thick knoll]

Yea

If you're good with them then that is very good

Now can you work with them

[nimble mirage]

4. sin( 90° - ∅ ) = cos∅

And same with cos also