help-17

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[harsh canopy]

i might be very stupid but can someone tell me how these two series are the same

[harsh canopy]

or at least how did they go from one to the other

[frozen bobcat]

multiply it out and simplify

the top line gives you $$\sum_{j=0}^\infty \frac{(z-1)^2}{(z-1)^{j+1}} + \sum_{j=0}^\infty \frac{2}{(z-1)^{j+1}}$$
and expanding the first term you have
$$\frac{(z-1)^2}{z-1} + \frac{(z-1)^2}{(z-1)^2} + \sum_{j=2}^\infty\frac{(z-1)^2}{(z-1)^{j+1}}+\sum_{j=0}^\infty \frac{2}{(z-1)^{j+1}}$$

[twin meteor]

Zybikron

[vocal sleet]

@harsh canopy Has your question been resolved?

[harsh canopy]

oh i see, so you just take out the first 2 terms and then see that the thing you have left can be rewritten to add on to the 2nd term

[frozen bobcat]

yep

[harsh canopy]

i eventually realised just by expanding the series of $\frac{(z-1)^2 - 1}{(z-1)^{j+1}}$ but the other way seems a bit quicker if you can realise

[twin meteor]

eugene_krabs_has_cake

[harsh canopy]

thx

.close

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[broken orchid]

how do you do exp(A) exp(B)

[broken orchid]

i know you have to do taylor expansion but like what else do you do

do you express this in jordan canonical form?

<@&286206848099549185>

[dull bear]

Have you worked out exp(A) or exp(B) yet?

(have you tried to work out any poweres of A or B?)

[broken orchid]

not sure how we would do that

this is what i got

not sure if its right

[dull bear]

Left as exp(A) and right as exp(B)?

[broken orchid]

yep

i realised that A = A^2 = A^3

so i used that

similarly with B

so i have that Exp(A) = I + A + A^2/2! + ...

so i got that

but like its wrong

actually there should be an 1

[dull bear]

Hmmm, the idea of how to get it is fine, but I'm not so sure about the entries you found in the end

[broken orchid]

its suppose to be this

this is the solution

but like when multiplying it i'm really close

[dull bear]

Hmmmm

,w matrix exponential [[1, 1], [0,0]]

[twin meteor]

Results provided by WolframAlpha

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

Requested by chartbit

[broken orchid]

i think i'm missing a 1

in the right

[dull bear]

(in particular, for all terms but the first, you can factor that and get that to be A(e - 1), so you have I + (e - 1)A, which simplifies to the below)

[broken orchid]

i think i got it now thanks

yeah i' missing the right entry

thank you so much

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[dense cedar]

Any more details?

Like P odd function or even?

[vocal sleet]

@vast shale Has your question been resolved?

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[devout pine]

Find maximum and minimum values in e^x (cos (x) + sen(x))

I got the derivative but I just cant continue because ive never practiced something like this

[dawn talon]

equate the derivative to 0

find the critical points

use first derivative test to verify if its maxima or minima

[hybrid flicker]

well you got the critical points

[devout pine]

Do i use 40° for the line?

[hybrid flicker]

local or global tho?

[devout pine]

Like to determine if its pos or neg

[devout pine]

Dont know what that is, but i suppose global. I speak spanish so I dont really know much about math terms in english. But im pretty sure it wasnt mentioned in the instructions

[hybrid flicker]

ok

well now that you got the critical points (all of them)

can you write f(x) at those critical points

(might be useful to write each critical point as pi/2 + n*pi

and then write f(x) in terms of n)

[devout pine]

Ok so like what I do is put a line and the result of x in it and thats how I find the points and if theyre max or min

But idk if its any different in this one because its trig

[vocal sleet]

@devout pine Has your question been resolved?

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[golden vine]

Can someone help me please

[granite flicker]

which one

[vocal sleet]

@golden vine Has your question been resolved?

[golden vine]

2a and 2b

[granite flicker]

okay so for 2a you know the linearity condition right ? 👀

[golden vine]

No

[granite flicker]

A system $L$ is linear if for any inputs $u(t),v(t)$ and a constant c, we have $L(cv) = cL(v)$ and $L(u+v) = L(u) + L(v)$

[twin meteor]

Mohamed Mohsen

[granite flicker]

your system here is the absolute value function

you gotta check if satisfies these two conditions

if it fails just one of them for one example then it's non-linear

[vocal sleet]

@golden vine Has your question been resolved?

[blissful sentinel]

(Fun question! I remember having to do similar stuff for my digital signal processing class)

[granite flicker]

yea I love that stuff, DSP is one of my fav subjects

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[bronze marten]

any intuitive explanation for why the 3rd line is true?

[bronze marten]

nvm figured it out

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[vast trout]

hi, i have this equation in red, for which i have a limited y because i just want to have the x and z axis for now, but what i want to do is rotate it around the z axis so it will be like a pen shape. i thought of using the rotation matrix and then letting the angle be between 0 and pi, but for that i would need to parametrize the function, which i can't figure out how to do. so my question is if there is a way to parametrize it, and if not how else would i be able to make a revolution around the z axis?

[vast trout]

please ping me if you know anything

[vocal sleet]

@vast trout Has your question been resolved?

[vocal sleet]

@vast trout Has your question been resolved?

[viral shell]

since when did desmos have a 3d version 😮

[vast trout]

i dunno i also didn't know since yesterday

but it's really cool

[viral shell]

i didn't exactly understand what way you want to rotate it around the z-axis, is it like this?

[vast trout]

yes

and the y-width would have to be infinitely thin so if you rotate it, it would be round

like i said, like a pen

[viral shell]

https://www.desmos.com/3d/arzzb4tjgz

like this?

[tawny hollow]

A neat trick to keep in mind is that z = x^2+y^2 is rotational symmetric

so subbing x = x^2 + y^2 in your first line should do the trick

[viral shell]

oh i understood it wrong

[tawny hollow]

here's an example

https://www.desmos.com/3d/15lmacitmn

[vast trout]

thanks so much, but i still don't really understand why it works, could you try to explain?

[tawny hollow]

oh and i should of used z = sqrt(x^2+y^2) btw and not the square of it

but basically this is due to how sqrt(x^2+y^2) has rotational symmetry, say if you let r = sqrt(x^2+y^2)

then z = r can be thought of as a slice in any rotation about the z-axis

it's always gonna look the same

if you look above for a fixed r=1

it's a circle

[vast trout]

yeah

ohh

i think

i get it now

[tawny hollow]

so varying r is like varying the distance in all direction from the origin as a circle

neat!

[vast trout]

yeah

thanks so much

.close

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[finite hatch]

can i have some help

[lyric hamlet]

u can use auxiliary

[fervent wasp]

Of course you can

A diligent and courteous student

[lyric hamlet]

where u can expand Rsin(x+β) (for example) then equate coefficients to find beta and R, and then afterwards u can use for whatever R and beta is and make it equal to 1 for now

[finite hatch]

how do they know which

cos2A formula to use

<@&286206848099549185>

[steady ridge]

is this your question?

[steady ridge]

or this?

[steady ridge]

The other option could be to simplify this using half angle formulae

That's a better alternative imo

[finite hatch]

DAT ONE

[steady ridge]

we have to prove cosec2A-cot2A = tanA right?

It is preferred to convert it into sines and cosines

[finite hatch]

why dont they change it to cos

how is 1-cos2a = 2sin^2a

[steady ridge]

Do you know $cos(A+B) = cosAcosB-sinAsinB$

[twin meteor]

Bagchi234

[finite hatch]

yes

[steady ridge]

Just replace B with A in this equation

What does that yield?
$\cos2A = \cos^{2}A-\sin^{2}A$

[finite hatch]

1-cos2a = 2sin^2x?

[twin meteor]

Bagchi234

[steady ridge]

Now, we know $\cos^2{A} = 1-\sin^{2}A$

[twin meteor]

Bagchi234

[finite hatch]

oh yeh

ohhh okok

and one more q if its ok ):

[steady ridge]

alright

[finite hatch]

for the first one im stumped

what do i do

[steady ridge]

The approach is absolutely correct

[finite hatch]

how do i factor in +1

[steady ridge]

Use the fact that cos^2x-sin^2x = 1-2sin^2x

You get a quadratic in sinx

That is $2\sin^{2}x+\sin x-1 = 0$

[twin meteor]

Bagchi234

[steady ridge]

Solving this will give us $\sin x = 1/2$ and $\sin x = -1$

[twin meteor]

Bagchi234

[steady ridge]

So this gives us $x = \frac{\pi}{6}, \frac{5\pi}{6}$ and $x = \frac{3\pi}{2}$

[finite hatch]

i think i did that

[finite hatch]

idk how to factor this

is it sinx(2sinx+1)

but then the -1

theres no common factor

[hallow crescent]

quadratic formula

[steady ridge]

Do you know the Quadratic Formula?

[finite hatch]

yes

=b+/- root of b squared minus 4 ac over 2a

how come rhere they didnt use quadratic formula tho

[steady ridge]

oof my bad I mistook pi/3 with pi/6-

[twin meteor]

Bagchi234

[hallow crescent]

there are different ways to factor a quadratic, the formula is the easiest as its general and works almost always (disregarding complex numbers)

[finite hatch]

how did they factor it

cus i think my teachers tend to avoid quadratic formula in tests

cuz we only get 30 mins

and its non calc 😢

[steady ridge]

I mean this is an easy quad that can be factorised, like the product of roots are -1 and the sum is -1/2, so choose just two numbers that can satisfy this

[hallow crescent]

just intuitevly (2u-1)(u+1) = 1u^2 + u - 1

[finite hatch]

):

[hallow crescent]

yea

[finite hatch]

ok thx i ask my teachs tmr

thank u guys :D

[hallow crescent]

thats what i hate with quadratics is that without the formula u just gotta guess

yw i didnt rly do anything tho lol

[finite hatch]

yeh and when im rushing its

kiinda easy

to get things wrong in quadratic formula

[hallow crescent]

ah i get you

teachers really be making you take tests without calculators lol

thats kinda fcked tbh

[finite hatch]

noo we have a calculator section

and a non calculator section

in calc section we get notes + graphic calculator

[hallow crescent]

ah, they just dont allow us to have programmable calculators or graphic calculators

[finite hatch]

• normal scientific calculator

we need them loll

[hallow crescent]

yea we can only use this one

[finite hatch]

for qs like dis

[hallow crescent]

but like the school bans graphic calculators in general lol

[hallow crescent]

ah makes sense

ig our teachers just avoid q's like those or if they do then we get laptops with geogebra

[finite hatch]

ohhh yehhh

i wish we did that

[hallow crescent]

much easier and more comfortable ahaah

[finite hatch]

i was bummed when i had to fork out 200 bucks for a calculator

[hallow crescent]

SHIII

i mean

where i live its hella expensive

we pay like 500 for the books alone

switzerland prices 🥲

[finite hatch]

omg

dw its expensive where i live too

i live in australia 😭

my books were like 800 aud idk how much that is in swiss francs

[hallow crescent]

damn yea like same price

[bronze osprey]

ozzie ozzie ozzie

[hallow crescent]

yea its crazy how much they make us pay for these stuff like we didnt even use the math book this year and next year they make us buy a new one

[finite hatch]

i couldve justr got the online textbook

we just use online

[bronze osprey]

I go to uni in Australia and we don't have textbooks

we just use the professor's course notes for everything

[hallow crescent]

i know some unis that just post the lectures on yt lol my brother barely attends classes anymore

just watches the lectures

[bronze osprey]

damn specialist maths has sum-to-product? that's insane

other states don't have that in their specialist maths

[finite hatch]

really lol

[bronze osprey]

yeah

[finite hatch]

i thought WA was easiest

[hallow crescent]

yooo thats cool we have smthing similar but for english (its a third language here)

[finite hatch]

THIRD!??!!?

[hallow crescent]

and like only the teacher actually has access so its useless

[finite hatch]

nahh i failed japanese

i ended with 18%

[hallow crescent]

1st is italian, 2nd german or french (or both if ur crazy), 3rd english or spanish (or both if ur crazy)

[finite hatch]

wat do u study

[hallow crescent]

oh and 4th: latin and greek

[finite hatch]

omd

[bronze osprey]

maths!

https://senior-secondary.scsa.wa.edu.au/__data/assets/pdf_file/0005/1121279/Mathematics-Specialist-ATAR-Year-11-Syllabus-for-teaching-from-January-2025_pdf.PDF

[finite hatch]

here they force u to learn a second language only until 9th grade

and then after its optional

[bronze osprey]

I have your state's syllabus and yeah I can't see sum-to-product

[finite hatch]

!??!?!!??!?!?!!?

wth

[bronze osprey]

maybe your textbook just has some extra info

[finite hatch]

its in my test too

[bronze osprey]

I have the syllabus from 2025 onwards

[bronze osprey]

so maybe it was removed

[finite hatch]

this is the 2023 test

but i got taught it

[bronze osprey]

nvm

I'm blind

otherwise your syllabus looks super normal for specialist

even the unit 3 and 4 stuff

[hallow crescent]

whats specialist

[finite hatch]

umm

idk wait

[bronze osprey]

maths for high-achieving students

[hallow crescent]

ooo cool

[bronze osprey]

it's not that impossible

[hallow crescent]

damn i wish we had that

[bronze osprey]

IB has very similar content

I did IB

AAHL to be precise

[finite hatch]

it is for me i am accelerated 😢

im in year 10

[bronze osprey]

oh that's nice

you're just accelerated in maths right?

[finite hatch]

and chemistry

and previouslyt physics

but i dropped it

to take next year

[bronze osprey]

oh damn

[hallow crescent]

whats accelerated? is it like specialist

[finite hatch]

umm i skip a year

[bronze osprey]

taking subjects a year early

[finite hatch]

i skipped in year 7

[hallow crescent]

ohhh thats cool

[finite hatch]

so it wasnt that bad

[bronze osprey]

year 7 doesn't teach shit man

[finite hatch]

ik

actuallyt

it taught algebra

[bronze osprey]

fair

[finite hatch]

and when i satrted yr 8 maths

i didnt know algebra

😢

[bronze osprey]

ah I was wondering if you were always advanced in maths

that's interesting then

you caught up by a lot

[finite hatch]

thx :D

[finite hatch]

noo i asnt

my parents thought i was dumb in primary

but then they made us take a test on orientationa

and i tested really high

[hallow crescent]

isnt it kinda stressful tho

like being put with ppl older

[finite hatch]

nooo

im friends wit hthem

they chill

[hallow crescent]

thats cool then

[bronze osprey]

like socially lmao that's good

I was going to say that who you interact with in your classes and who you have as friends are two separate things

[hallow crescent]

i mean yea ig but like dont ur parents or ppl around you expect a lot

[finite hatch]

no

bc i do average

😭

[hallow crescent]

ah thats good then atleast ahahaha

[finite hatch]

im finishing subjects early

so i dont have to stress a lot later

[hallow crescent]

i get a 90% on tests and get shit for it 😭

[finite hatch]

omd

90% is my dream

[bronze osprey]

lol someone got 12

dw you're doing pretty fine

[hallow crescent]

lmfao

heyy thats good tho

i mean u are accelerated so in ur actual grade u would ace them probs

[bronze osprey]

I've always wondered how some private schools and selective schools place so much pressure on students to go to a good uni

Australian unis are created mostly equal

in fact I've been talking to international students and they're surprised the academic requirements are that low

and no personal statement needed

[finite hatch]

yeh i only need 88 to get into my course lol

[hallow crescent]

here you get immediate access to uni from hs, but 50% drop out rate after 1st year in the UNI is crazy

[finite hatch]

88 atar

[finite hatch]

omg.

[bronze osprey]

oof sounds like Europe

[hallow crescent]

yea

[finite hatch]

is it free

[hallow crescent]

basically

like very cheap

for switzerland atleast

[bronze osprey]

yeah I heard the student fee is only a couple hundred euros

[hallow crescent]

but like u only get access to other UNIS in switzerland

[bronze osprey]

ETH is a good uni lol but must be hard to stay in

[hallow crescent]

so like ETH and stuff (but idk german and the ba courses are only german)

[hallow crescent]

yea

anyways you end up paying in rent

cause like rent in zurich can be 800 a month for a student single room lmfao

[finite hatch]

take me back 😢

[hallow crescent]

damnnn

who scored a 0 tho 😭

[finite hatch]

probably cheated

[bronze osprey]

loool

[hallow crescent]

lmfao

its funny how they show it tho

[finite hatch]

yeah hahaha

everytime after a maths test everyone wants to find who got the minimum

[bronze osprey]

they even have the standard deviation

[finite hatch]

actually every test

[bronze osprey]

honestly this isn't healthy in terms of competition

even without these stats we would just go up to each other and try to look at each other's scores after class tests

[hallow crescent]

yea...

[bronze osprey]

adding these stats only intensifies rivalries that's why I don't like it

[finite hatch]

only average is needed

anwyays i have to sleep now

its 11:51

thx guys :DDDDDD

[hallow crescent]

average is needed to be able to hold teachers accountable cause i swear sometimes the exams get an average of like 50% yet somehow its our fault

[hallow crescent]

byeee

goodnight

[finite hatch]

yes

one of our tests avg

was 40%

[finite hatch]

erjewjfgew

[hallow crescent]

wtf..

damn yea

[finite hatch]

the average is getting higher

every test

cause people are getting kicked out of the course

not lol.

ok its my bed time bye

.close

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[weary vault]

Help

[weary vault]

Im rlly confused about getting the domain and range

[fervent wasp]

[weary vault]

Of functions

How do i determine the domain?

[fervent wasp]

It depends

Domain means the interval which x is exist

[weary vault]

{x|x¢r}

[weary vault]

Its something like this

[fervent wasp]

Yes

[weary vault]

So how

[fervent wasp]

For example, function: sqrt x

[weary vault]

Wut

Squirt x?

[weary vault]

Oh

[fervent wasp]

In this function, x must be greater or equal to zero, do you agree?

[weary vault]

I just don't understand how they get it

[weary vault]

Hmm

So it should only be greater or 0?

No inbetween?

[fervent wasp]

The way they show looks confusing

[weary vault]

Thats the way they taught it

[fervent wasp]

No, anything that yields a real number follow the rule

[fervent wasp]

Extremely confusing

[weary vault]

What is even real number

🥹

[fervent wasp]

Ig I’ve mentioned too far

[fervent wasp]

Based on what you have learnt so far, x shouldn’t be negative, right?

[weary vault]

Why number csnt just be all real

[weary vault]

It can be negative

[fervent wasp]

For what reason?

[weary vault]

Oh wait nvm

[fervent wasp]

I’m referring to this

[weary vault]

It is a different formula

Yes

I cant be -x

[fervent wasp]

Correct

[maiden blade]

What's the problem

[weary vault]

It has to be tranfered into. Positivr

[fervent wasp]

That’s how domain works. Domain tells you what you can put and what you can’t

[weary vault]

I need help on hownto translate it into a real number

This stuff

I already understand how the formula works

But doesnt understand how I get this

[fervent wasp]

For this function, the domain would be {x|x€R, x>=0}

[weary vault]

Ohh ok

[fervent wasp]

Ignore the process, they look freaking confusing

Tell me, when you have a line, you can plug in any x to yield relative y value, correct?

[weary vault]

We can't use other formula?

We have to show solution 😄

😄

[weary vault]

Wdym

Yes

[fervent wasp]

yeah, that’s all

What you have to explain is, you can put any x value

[weary vault]

But its not always like this tho

Sometimes its

[fervent wasp]

Of course

What you have to do is discover the conditions that won’t work

[weary vault]

{X|X Not equal sign -2}

[weary vault]

Pls give example

[fervent wasp]

Alr, I’ll provide you with another example

What can’t you put at x?

[weary vault]

Idk?

[fervent wasp]

Have you learnt log so far?

[weary vault]

What that

[fervent wasp]

Alr..

[weary vault]

We dont have log

Only this

[weary vault]

Hmm

[fervent wasp]

Same question

What can’t you put at x?

[weary vault]

1?

[fervent wasp]

No, think of definition

[weary vault]

Wdym

[fervent wasp]

What cannot be placed in the denominator

[weary vault]

2?

Ohh

0

[fervent wasp]

Correct

Can you try writing its domain?

[weary vault]

So denominator cant be higher than i forgot it uppernator

[fervent wasp]

That’s not the case

[weary vault]

{x|x not equal 0}

[fervent wasp]

It can be greater than the numerator

[weary vault]

?

[fervent wasp]

Yes, you’ve gotten it

[weary vault]

Ohh ok

Wait i though x is always 0?

[fervent wasp]

Make sure you put x€R

[weary vault]

1

I mean

[fervent wasp]

No

[weary vault]

Why not equal to 0 if x is always 1?

[fervent wasp]

x is not always 1

[weary vault]

Oh

[fervent wasp]

x can be anything aside from zero in that equation

[weary vault]

Ohhh ok

Hmm how about

[fervent wasp]

That’s the whole point of domain

[weary vault]

2/x-5

🤔

[fervent wasp]

Apply what we discussed to this function

[weary vault]

So 3?

[fervent wasp]

Incorrect

Try again

[weary vault]

0?

[fervent wasp]

5

Because the denominator cannot be zero

[weary vault]

What why

Ohh ok

Soo

How do i know if its real number

[fervent wasp]

They’re all real number

[weary vault]

{x|x¢r}

[weary vault]

Wdym

[fervent wasp]

Forget real number XD

[weary vault]

Why

[fervent wasp]

It’s too advanced for this question atm

Not necessary

[weary vault]

Some of our example have real number

[fervent wasp]

Everything we’ve mentioned so far are real numbers

[weary vault]

Im confused?

Why they add {x|x¢r} then as a final answer?

If everything is real number

[oak magnet]

Saying $\mathbb{R}$ is set of real numbers

[twin meteor]

YakuBros

[oak magnet]

It is the math form to say all x taken in real numbers set

[weary vault]

Im confused

On why my teacher added it on example

If everything is real number

😵‍💫

[weary vault]

So in short if x is not the thing on denominator its {x|x¢r}

?

[fervent wasp]

Consider real number as any number you can think of currently

It’ll be a tremendous task to introduce the difference between real number or imaginary number rn

[weary vault]

Oh ok

[fervent wasp]

Temporarily, just see them as normal numbers

[weary vault]

I'm just confused on why example like this

[oak magnet]

Stay real for now

[weary vault]

Why is it {x|x¢r}

[fervent wasp]

It means you can put any numbers you can imagine

[oak magnet]

Litteraly can be readen like : x, such that x is a real number

[weary vault]

Instead of doing {x|x not equal -2}

[weary vault]

But in short it will never be the answer?

[oak magnet]

What is the function ?

[weary vault]

This

[fervent wasp]

Domain is a concept which tells you everything you can put into.

[weary vault]

Just an example

[fervent wasp]

It doesn’t specify a number or two

[oak magnet]

So you have y = -2x + 5 ?

[weary vault]

I choose a computer focused strand so not that much math 😄

And yet so much math

[weary vault]

Nah

3x + xy= -10

I have to answer

[weary vault]

There is 5 of them this is one of it

[fervent wasp]

For domain and range?

[weary vault]

Yep

[fervent wasp]

Well, for domain, it’s kinda easy. Because you can put anything into x

[weary vault]

How bout range

[oak magnet]

Isolate y

[weary vault]

Hm what

😵‍💫

I hate math

[fervent wasp]

Do you know how to separate y from other figures?

[oak magnet]

3x + xy = -10
xy = -3x - 10
y = -3 -10/x

[weary vault]

Yes

[fervent wasp]

Like this

[weary vault]

Then doman is

{x|x not equal 0}

Correct?

[fervent wasp]

Don’t forget to mention x€R

[weary vault]

Wdym

There is none

[oak magnet]

Meh

[fervent wasp]

….

Is it written by your school teacher?

[weary vault]

Yes

[oak magnet]

Id have my paper in the bin for writting it like this xd

[weary vault]

Why

[oak magnet]

Maybe depends

[weary vault]

Im confused

[weary vault]

So my answer is correct?

Is my teacher just confusing to teach?

[fervent wasp]

Because it’s just garbage ngl.
Your teacher wrote it unprofessionally. Worse still, they didn’t explain the fundamental concept.

[weary vault]

Oh

[oak magnet]

Well, since your teacher write it like this, you wont lose points

[weary vault]

No wonder why barely of us manage to answer question

It was explained poorly

So my answer correct

🤔

[fervent wasp]

Your answer is correct

[weary vault]

Ok noice

[fervent wasp]

x€R tells you that you can put anything to the spot of x

[weary vault]

So it will always be not equal to?

[fervent wasp]

That’s crucial and it shouldn’t be omitted

[weary vault]

And if not what are the instances it will result into equal to

🤔

When will it be

{x|x=0}

[fervent wasp]

Let me state it again

Domain tells you what you can put in the spot

They only serve as this purpose

[oak magnet]

When the only possible value of x is 0

[weary vault]

Ahhh

I get it

So

2/x-8

Means

{x|x not equal 8}

[oak magnet]

Be careful of parentheses

Is it 2/(x-8)

[weary vault]

They look the same xD

[oak magnet]

Or 2/x -8

[weary vault]

🤔

[weary vault]

2/ x -8

I meant minus

Not negative

[weary vault]

But correct?

[fervent wasp]

They are quite different

[oak magnet]

This ?

[weary vault]

What

Why is there ()

[oak magnet]

The denominator is x-8 ?

[weary vault]

Yes

[oak magnet]

So with parentheses

[weary vault]

The one on bottom

[oak magnet]

The one you firstly wrote was the first as interpretation

[weary vault]

So u add parenthesis so u can make sure they are not seperated?

Ahh ok

[oak magnet]

To make a "package"

[weary vault]

So am i right

[weary vault]

.

I just have to find a number that will result the denominator into 0

[fervent wasp]

Correct, according to your teacher

[weary vault]

Ohh ok

[weary vault]

I feel like there is more to this

But either i understand

[fervent wasp]

That’s everything tho

pretty easy

[weary vault]

True

XD

[fervent wasp]

Step1. Find the exception
Step2. Done

[weary vault]

Just confusing cuz of the {x|x¢r}

As final answer

-_-

Hmm

[fervent wasp]

You’re supposed to include that in formal circumstances

[weary vault]

Oh wait btw

If its

3/2

There is no x

What will be the domain

[oak magnet]

?

[fervent wasp]

x can be anything

[weary vault]

Or not possible

[weary vault]

But there is none

[fervent wasp]

y= 3/2

[weary vault]

3/2 i mean

[oak magnet]

Whatever you take as a value of x will give 3/2

Graph it and see

Its a parralel line to x axis

[weary vault]

What will be the { } then

[fervent wasp]

€R

[weary vault]

Ohhh ok

Make sense

So {x|x¢r} will only be used if there no y or x in denominator?

[fervent wasp]

They should always be used lol

[weary vault]

But u cant change anything?

So how will u find exception

[oak magnet]

You just need to get out the forbidden value

Of the answer set

R \ {forbidden value} like R \ {8} for last example

[weary vault]

Huh

So is the reason the final answer {y|y¢r} is because nothing could be changed?

Since there is nothing to change in denominator

🤔

[oak magnet]

Y can be anything since it dont destroy mathematical rule of dividing by 0

[weary vault]

And if the

Denominator is negative it gets erased?

[weary vault]

Like the example on left

[fervent wasp]

wdym

[weary vault]

The denominator just disappeared

[oak magnet]

No matter sign of denominator, only zero is trouble

[weary vault]

Oh ok

[oak magnet]

And i dont see what you mean by erased

[weary vault]

Look at left

-1 gone

[oak magnet]

No

Its not gone

[weary vault]

Where it go

[oak magnet]

It just change the sign of denominator

Remember lavoisier

[weary vault]

No

But i think this good i understand how to get it now

Thanks

[fervent wasp]

You don’t fully understand

[weary vault]

Wait

[fervent wasp]

I can smell it 👃

[weary vault]

Im missing something??

What is

All i know is that if there is x or y in denominator i just make it not equal and find the exception

[fervent wasp]

No, that’s not the case

[weary vault]

And if there is no x or y I just turn it into {x|x¢r}

[weary vault]

E..

Wut

[fervent wasp]

Sighs, anyways

It looks like it’s the most efficient way for you atm

[weary vault]

Wdym

[fervent wasp]

I feel like explaining further, but looks like it’s difficult to explain it

[weary vault]

So basically my plan works?

Its wrong but it works?

[fervent wasp]

yeah, go for it

It’s not how people usually determine it

[weary vault]

Oh ok

But it works 😎

[fervent wasp]

You’ll have to go over this again when new stuff is added

For example, log

[weary vault]

Let future me handle future problem

Its already 1 am

[fervent wasp]

Same here

[weary vault]

I have class at 7 am

😄

I hate morning class

[fervent wasp]

gngn

Same, go to sleep :))

!done

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[weary vault]

.close

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[bleak prawn]

Just ignore part A im stuck on part B

Im not really sure why they say equationS, as in theres multiple?

[hushed pewter]

I believe so, yes

It probably wants both vertical and horizontal asymptotes

[bleak prawn]

Oooooooooooh

[hushed pewter]

ah this won't have a horizontal asymptote though

[bleak prawn]

I was still thinking about perforations for some reason 🤦‍♂️

[hushed pewter]

Oh. Equations for asymptotes

[bleak prawn]

So VA is gonna be x = 3

Then since theres no HA, oblique asymptote I get by just doing long division and getting rid of the remainder, right?

Like just ignore the remainder right?

Ok awesome then I think I can solve it all

Thank you!

❤️

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[waxen hawk]

V_AB=V_CD=V_EF

Agree?

[waxen hawk]

Yes or no?

[somber yew]

Why do you think the second equality holds

[waxen hawk]

I want an answer

[somber yew]

Then no

[waxen hawk]

Cool

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[olive olive]

hey could anyone help me with this plz

nvm

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[solar saffron]

@vast shale These channels under "Math Help" on the left side of your screen are channels that are available.

[solar saffron]

.close

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[lilac plaza]

.Good tip

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[quiet forum]

I know its basic

But, i dont understand how do they get 18 i3 = 8

[vast shale]

i dont follow

what is i2 and i3

[quiet forum]

Oh wait i get it

💀 wow.. i forgot how to eliminate

[quiet forum]

I am doing physics, i is for current strength

[quiet forum]

😔 omg

Sorry

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[alpine mantle]

im a bit confused

[alpine mantle]

i dont see how this is true

if for example u had n = 5 and since [0] [4] = [0] but b is not equal to 0, then isnt this a counterexample?

[a], [b] are the equivalence classes of the modular arithmetic of n btw

[vast shale]

i think change the question to "one of a, b = 0" lol

[alpine mantle]

ye that's what i thought

[vast shale]

what's modular arithmetic?

[alpine mantle]

so if $x \in [a]$ then $x \eq a $mod n

[twin meteor]

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

[alpine mantle]

im not got at latex 💀

[vast shale]

it's ok

i will google it

[tidal dock]

how exactly is J_n defined? are you sure it includes [0]?

[tidal dock]

i agree

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@alpine mantle Has your question been resolved?

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[finite hatch]

how did I do dis wrong

[river kettle]

bum chicken

[finite hatch]

PART B

[vast shale]

it seems correct to me?

[finite hatch]

this is the answer

[vast shale]

website must be being silly

[finite hatch]

if it says this

which one do i do first

is it left to right rule

[vast shale]

x-axis first

then do the one in the y-axis

(they should however be independent of each other)

[finite hatch]

so x axis multiplied by y axis?

[vast shale]

what

[finite hatch]

reflection in x axis multiplied by reflection in y axis

[vast shale]

oh matrices

sure

[finite hatch]

but i thought i twas reflectiopn in y axis multipled by reflection in x axis

[vast shale]

oh sorry if you're doing matrices then transformation A followed by B would be multiplication by BA

but really in this case it should not matter

[finite hatch]

.closed

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[hazy sparrow]

ask

[hazy sparrow]

I know logica is not math, but I thought you guys would know:

its proposition logica

It says: Lifeless things can never be judged, but men could. (Conclusion) If men cannot be judged, then lifeless things can.

wow nevermind, I was stuck on this for more than 30 minuts, by translating I saw the construction even better

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[finite hatch]

hi

[finite hatch]

can someone explain why we use tan inverse

here

...

@fervent wasp

[fervent wasp]

I'm too bad to do trig

not me

[finite hatch]

trig is actually

my favourite topic this year :D

[fervent wasp]

but I'm bad, I don't know how to do it

[finite hatch]

did u learn it in schol

[elder scaffold]

arctan is just to find theta

[fervent wasp]

no, I live in a poverty

[finite hatch]

um...

;-;

[elder scaffold]

realistically u dont have to use arctan

[finite hatch]

but why

[fervent wasp]

(I'm watching an ongoing debates in help-27)

[elder scaffold]

because we want to solve for theta?

[finite hatch]

why is theta = arctan

[elder scaffold]

oh i see what ur saying

u see how we have cos and sin theta?

just divide the 2 equations

to get tan theta

[finite hatch]

oh

ok so im gonna remember that by making sure

that sin and cos feel included!

so we use tan inverse :D

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[hard atlas]

you are wording it as if function 2 and 3 dont have a lot to do with function 1

[rare swift]

Have u studied derivatives?

[hard atlas]

just intuitively it should not be surprising that slope of 0 means that the graph has a turning or stationary point there

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[hard atlas]

and then its just a question of whether the slope was positive before and negative afterwards or other way around or maybe both times the same

[rare swift]

Doesn't seem so

Great question

Nah not your mistake just said it was a great ques

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[fierce halo]

whats the fastest way to determine a factor using factor theorum

[fierce halo]

i might be rinsed if i dont know

whats an ideal appraoch to determining the constants etc

[vast shale]

whats factor theorem even

[fierce halo]

finidng the x value where p(x)=0

x-a

[vast shale]

p(x) being ehat

what

a polynomial

[fierce halo]

polynomial

[vast shale]

ok

example?

[velvet zephyr]

bro

who's to help

idk

[fierce halo]

i jsut need the process

[vast shale]

it depends

there isnt a process for all exercises

[velvet zephyr]

You can use this:
if the factors are of the form (ax+b), where a and b are integers,
then find factors of the constant term and check whether they are the roots.

now apply factor theorem

[fierce halo]

do i ifnd factors through trial error

[velvet zephyr]

probably

[fierce halo]

theres no alternate method?

[velvet zephyr]

iam not sure anbout that sorry

[fierce halo]

shit alr thats calm

thanks anyway

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[remote trench]

The equations in the middle

Why did 5,5 turn into 5500

[full forge]

ah

[outer warren]

result of unit conversions

[full forge]

^

[remote trench]

Oh right

[full forge]

with cubic you will have to take into account you multiply it by itself three times

[remote trench]

Makes sense thanks

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[terse fiber]

What would be the best way to distribute a fraction into here?

[upbeat chasm]

the second bracket is divisible by 4 so you can distribute the 1/4 there

multiply either bracket by 3

unless one of the brackets is divisible by the fraction, you can just pick one randomly

[terse fiber]

thanks

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[clear slate]

could someone just help me fix what i have here

[somber portal]

for a start, the period is not pi. the function does not repeat itself at points 0 and pi, for example.

[clear slate]

yes i know that was wrong, i changed my answer to 2 pi but dont know if this is correct

the range looks good to me

idk what else i should fix

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[vale ermine]

How do i convert (2,-2,1) into cylindrical coordinate?

[vale ermine]

i know i need to get sm

(r,phi,z)

is r = √x²+y²

And phi arctan (√x²+y²)/z

?

[civic otter]

Yep

[civic otter]

For the angle you have to pay attention to which quadrant you're in, because arctg gives values only between -π/2 and π/2

[vale ermine]

oh

so i am gettinf tan phi = -1

Is this

(2√2, 3pi/4 , 1)

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[stuck moss]

for which value of a is this function convergent

or is it divergent for all real a

[vast shale]

hm

[inner osprey]

wondering have you learned l'hopital yet

[stuck moss]

yes

with which function to compare

im assuming ur suggesting me to use limit comparison test

[inner osprey]

indeed

[inner osprey]

try a very simple function and see what happens

[thin vale]

I say just plug in a=600000

it might be the only value that works

[stuck moss]

lol

[red bear]

what about 600001

[thin vale]

no chance

[stuck moss]

maybe 69^420 might be the only real number that works