help-33

[queen sun]

The numerator should say 2

You got rid of 2 x’s so you should remove x^2 from numerator

Like if you multiplied the X’s before cancelling them out you’d end up with $\frac{2x^{2}}{x^{2}(x+2)(x-2)}$

[elfin berry]

BBMaths

[molten quiver]

i think i messed somthing up bv

bc

for me there wasent an extra x^2

[queen sun]

The top line of this is correct

When you cancel out both X’s the numerator should lose 2 powers of x

[noble geyser]

why is there x^2

[molten quiver]

yeah im confused on what that too

[noble geyser]

you only need x to the 1st power

[molten quiver]

also guys im supposed to use conditions of existence

[molten quiver]

like its obligatory

[noble geyser]

whats that xD

[molten quiver]

i think we might have been doing everything wrong if we haven't used that guys 😭

[queen sun]

No one knows what it is

[molten quiver]

hold on lemme see

[noble geyser]

if you can explain it better that wikipedia i might help

[molten quiver]

yk =/0

like not zero

the not zero thing

[noble geyser]

yea ik that

i now know that

its easy look

wait lemme write it down on a paper

[noble geyser]

ye ye ik

[queen sun]

Oh I see

Since for x=0 in the original question, we divided by x so we are dividing by 0, we have to exclude that, even though we don’t have that division by x anymore

[molten quiver]

like this isnt optional btw

[molten quiver]

so we gotta start over right

[queen sun]

No

Everything else we said was fine

[molten quiver]

ohh

[queen sun]

This works for every other x than 0

Because the only time we cancelled stuff out was right at the end

[molten quiver]

btw im confused about this passage

[noble geyser]

This is the answer

I've learned this 3 years ago by myself and my teacher taught this last year

[queen sun]

In the top line of this you had 2 terms which were x, so I would combine them together to say x^2

[molten quiver]

ohhh

[noble geyser]

if you have questions just ask

[queen sun]

Even though I said fully factored was the best, in actuality, we like to group up identical terms into x^2

[queen sun]

This is why I said to factorise first because now the numerator is linear but you’d already started by that point

[molten quiver]

if there wasent a -2

would it be

+4

instead

[noble geyser]

wdym

there are many -2s

[molten quiver]

like x^2+4 instead

[queen sun]

If they were +2 instead of -2 the denominators would already be the same

[molten quiver]

if there wasent x-2

[molten quiver]

of

ohhh

[noble geyser]

yea

[molten quiver]

so there wouldn't be the exercise lol

[queen sun]

$(x+2)^{2}$ does not equal $x^{2}+4$

[elfin berry]

BBMaths

[molten quiver]

root 22 is diabolical

[noble geyser]

yea

[molten quiver]

not root i meant

[queen sun]

You can’t multiply together to get x^2+4

[molten quiver]

uhh

power

[noble geyser]

$(x+2)^{2}$ = $x^{2}+4x+4$

[elfin berry]

Roy

[molten quiver]

if im seeing that im closing the matchbook

[queen sun]

So this is impossible

[molten quiver]

i see

[queen sun]

Well that’s a lie

[molten quiver]

Huh

[queen sun]

But it’s kinda true

[noble geyser]

so do you understand now?

both

[queen sun]

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

[elfin berry]

BBMaths

[molten quiver]

i think so il need a bit of practice but i think this is enough for today

[noble geyser]

well okay

[molten quiver]

thanks you guys were right i should have done the first passage differently

[noble geyser]

its 9th grade math

[queen sun]

In order to multiply to get x^2+4 you need to use complex numbers

[molten quiver]

complex number

[noble geyser]

can some mods pls mute this guy

[molten quiver]

s?

[queen sun]

If you square something you will get a positive number right

[noble geyser]

she's not ready for 12th grade stuff

[molten quiver]

im really bad at math 😭

[queen sun]

Just for fun :P

[noble geyser]

stopppp

[molten quiver]

im actually not

[noble geyser]

shes not ready

[queen sun]

Okay alright

[molten quiver]

i am ready

[noble geyser]

let her live for 3 years at least

[molten quiver]

im not in 9th grade guys

[noble geyser]

huh

[molten quiver]

im just really bad at math

[queen sun]

Ima leave this here… $i^2=-1$

[elfin berry]

BBMaths

[noble geyser]

what grade then

[molten quiver]

well so i was born in 2007 but I'm an immigrant so when i arrived in the country im living in now

i didnt know the language

also i was 16 at the time

that would mean

they would have to put me

directly

into the grafe

grade*

that was already

[noble geyser]

well it takes a bit of time for ppl

[molten quiver]

not the obligatory school thing

so i got set back

like 2 years

[noble geyser]

my classmates struggled for 3 months

to understand it so

[molten quiver]

bc i had to finish the Italian obligatory school first

before going to

the 3rd year

[molten quiver]

yeah im pretty weak at math

[noble geyser]

nah i think you're pretty good

at least compared to my classmates

[molten quiver]

dosent help that my brain deletes my math knowledge during summer break

[noble geyser]

they are in the best school in hungary and the best class they could've gotten and took them 3 months

[molten quiver]

well the teacher must have explained badly or smth

[queen sun]

Do you want to know about complex numbers? Might be a cool thing to know about 🤔

[noble geyser]

nope

it was totally understandable

[molten quiver]

you seem so eager to explain that yes i would like to even though I really dont like math 😭

i appreciate your enthusiasm go ahead

[queen sun]

Sorry I really like them :P

[molten quiver]

no no go ahead

[noble geyser]

well you need some practice because you are in 11th grade i think so you should know this really well

[molten quiver]

il listen

[noble geyser]

dont

[queen sun]

Basically when you square something the answer is positive

[noble geyser]

ill listen send me in dms

[molten quiver]

Italian school works differently

[queen sun]

Basically i is a “number” which when squared gives -1

[molten quiver]

in Georgia we also have 12 grades

but in Italy

[noble geyser]

send me in dms if you want to talk

[molten quiver]

its preschool middle school highschool

[noble geyser]

i can give you some integrals to calculate

[queen sun]

A complex number is like 5+3i and that’s basically it for knowing what a complex number is

[molten quiver]

im in year 3 of highschool

[noble geyser]

yea how many is max year

in highschool

[molten quiver]

5 I think?

[noble geyser]

oh

then you need to practice

[molten quiver]

wait i?

[noble geyser]

not too much tho

[molten quiver]

is i like x

[noble geyser]

its like pi

[queen sun]

It’s a special number that isn’t like the numbers you know

[noble geyser]

its like pi

[molten quiver]

Italian school is very strict with grades

the first time i got graded i got scared

[molten quiver]

ohh

[noble geyser]

dont worry ill help

[molten quiver]

whats different

[queen sun]

Unlike x it is known but represented with a letter

[calm kettle]

what do complex numbers have to do with this

[noble geyser]

its an another dimension

[molten quiver]

nothing bbmath just wanted to talk about it

[noble geyser]

right @queen sun ?

[calm kettle]

🥀

[queen sun]

We were talking about multiplying to get x^2+4

[molten quiver]

like the dimension of time?

[noble geyser]

no

[molten quiver]

why

[noble geyser]

you know the number line

[molten quiver]

bc its long?

[molten quiver]

yeah

[noble geyser]

like from -infinity to infinity

[queen sun]

Because unlike other numbers when squared it gives -1

It’s just defined that way

[molten quiver]

...-1,0,1...

[molten quiver]

ye

[molten quiver]

WAIT WHATTR

[noble geyser]

yea well thats the real dimension

[molten quiver]

WHATT

[queen sun]

It’s like above the number line

[molten quiver]

Hold up

but

[noble geyser]

the imaginary is the vertical dimension

[molten quiver]

they said

[molten quiver]

number ^2 is always positive

thats crazy

[noble geyser]

yea yea thats hard to believe

told you shes not ready @queen sun

[molten quiver]

is there an anti vertical dimension

[noble geyser]

nope

[molten quiver]

wait i wanna know now

[noble geyser]

there are 2 right now

ok ill tell you

[molten quiver]

na we are in too deep now guts

[noble geyser]

but then you need to learn more things

[molten quiver]

guys

[calm kettle]

did you actually solve her original problem atleast

[noble geyser]

yea

[calm kettle]

ok good 💀

[molten quiver]

you cant just say some numbers ^2=-

thats crazyy

[molten quiver]

lol

[noble geyser]

so first you need to learn about coordinate systems

[molten quiver]

and then disappear into the night

[queen sun]

i is above the number line

[molten quiver]

oh i know that

[noble geyser]

no

[molten quiver]

the cartisan plane!

x and y

[noble geyser]

its not "the" number line cause theres 2

[molten quiver]

oh

[noble geyser]

the real line and the imaginary line

now coordinate systems

[molten quiver]

the magical line

[noble geyser]

so right now theres x and y

[queen sun]

Imaginary numbers are on a imagery number line perpendicular to the number line you know, the real number line

[noble geyser]

now turn that into r and theta

[molten quiver]

wait who invented that though

and why

[noble geyser]

good question

maybe euler

he invented everything in math

so back to coodinates

[elfin cairn]

You can think of i not as a number but a symbol satisfiying i * i = -1. It turns out this is consistent with the regular real numbers if we extend them by adding i and keeping our "numbers" closed under addition and multiplication.

[queen sun]

https://en.m.wikipedia.org/wiki/Imaginary_number

It solves the equation x^2+1=0

Because i^2=-1

[molten quiver]

so with the power of a magical i

[noble geyser]

oh i still remember the most beautiful math equation

[molten quiver]

i can rebel against

[queen sun]

It’s like the square root of -1

[noble geyser]

@queen sun

[molten quiver]

x^2

[molten quiver]

the forbidden tool!

[queen sun]

Do you know e and pi

[calm kettle]

e^ipi = -1

👍

[molten quiver]

i know pi is 3.14

but idk about e

i didnt even know so many things existed

[noble geyser]

e is around 2.7

[calm kettle]

(it isnt)

[queen sun]

e=2.7182818284590… is a special number which is really important for lots of higher mathematics and accounting

[molten quiver]

it seems really random why

also why is pi important

[calm kettle]

if you differentiate e its still e

[queen sun]

https://en.m.wikipedia.org/wiki/E_(mathematical_constant)

[calm kettle]

forgot the ^x

Yep

[queen sun]

Pi is the ratio between the circumference and diameter of a circle

It’s used in everything to do with circles even spheres

[noble geyser]

$e^{i\pi}+1=0$

bruh

[queen sun]

You can edit

[molten quiver]

what's a ratio

[noble geyser]

oh yea

[queen sun]

Like division

[molten quiver]

sounds like something greek philosophers would dig

[elfin berry]

Roy

[molten quiver]

since they like circles so much

[queen sun]

Circumference/diameter = pi

[noble geyser]

the most beautiful equation of all time

[molten quiver]

your telling me

you somehow took

[queen sun]

https://en.m.wikipedia.org/wiki/Pi#Fundamentals

[molten quiver]

3 crazy letters

and got a 0

with the power of 1

how

[noble geyser]

the 5 fundamental numbers and the basic operation alltogether in 1 equation

[queen sun]

These numbers are all seemingly unrelated when you learn about them

[noble geyser]

crazy right?

you will learn that probably never

[molten quiver]

they aren't even 3rd cousins 😭

[molten quiver]

maybe thats why i dont like math BC they never talk about stuff like this

[noble geyser]

but its so beutiful i couldnt not show them

[calm kettle]

they do at higher levels

[noble geyser]

you would learn this in university

[molten quiver]

i hate math and even my brain has been scratched

[noble geyser]

if you choose the math path

[molten quiver]

definitely not for me but its cool

[queen sun]

Some university mathematics is very fun other bits not so much depends on your taste

Like game theory is about trying to win at games

[noble geyser]

ok now lets not bother her with these things its quarter passed 10

[molten quiver]

its the weekend

im not bothered

if you want we can do more of my math homework

[queen sun]

Okay UTC+2

[noble geyser]

ok well bbmaths you keep explaining

[molten quiver]

its 10:15 for me too

[molten quiver]

bai roy

gn

[noble geyser]

ik were in same timezone

[queen sun]

I’m in BST UTC+1

[noble geyser]

im prob going to shower then maybe ill come back

@molten quiver if you want to talk or do the remaining homework i can help tomorrow

[molten quiver]

okay Ty

[noble geyser]

you can dm me ot open a help thingy here

bye

[queen sun]

Do you want to know what e is

[molten quiver]

tbh i like watching play troughs more than playing

[molten quiver]

yes

[noble geyser]

If you still have homework tomorrow dm me

[molten quiver]

yes

[noble geyser]

Bye gn

@queen sun if you want to talk about maths dm me as well

[queen sun]

I have a finance example of e do you want to use euros for it

Doesn’t really matter which currency really

[molten quiver]

euros is fine you can use lari too if you want

[queen sun]

I only have euro/dollar/pound currency on keyboard
Imagine you have €1 and you want to put it in a bank for 1 year (365 days) and then get it back. There are 2 banks which gives loads of interest:
Bank 1: Every year you get 100% compound interest
Bank 2: Every day you get (100/365)% compound interest
Which bank do you put it in or does it matter

[molten quiver]

hmm

lemme see

i choose

bank 1

[queen sun]

You will get €2

[molten quiver]

yay

so what next?

[queen sun]

Bank 2 gives €2.71 though

[molten quiver]

dang

[queen sun]

They look like they would give the same though right

[molten quiver]

i should have chosen bank 2

[molten quiver]

i even thought bank 2 would give less

[queen sun]

If they gave less interest but more often then it eventually reaches a limit of 2.71828…=e

Bank 2 gives 1/365th the interest but for 365 more often

It gives more because you get interest in what’s already in there

[molten quiver]

always?

[queen sun]

No bank would end up giving that much but they can’t get over that number

[molten quiver]

the magical number

what is it rounded though?

[queen sun]

If I had a bank called Bank n which gives 1/n the interest but for n times a year as n goes to infinity the number approach’s e but no bank in particular would give e

But because currency rounds to 0.01€ it doesn’t matter

[molten quiver]

so with the power of rounding

they escape

e

was there ever a time

[queen sun]

I suppose if at each step the money gets rounded maybe you could get more than e

[molten quiver]

where they forgot to do that

and people became rich

[queen sun]

Banks don’t offer interest continuously though it’s just an example

[molten quiver]

ohh

okay

[queen sun]

$e=\lim_{n\to\infty}((1+\frac{1}{n})^{n})$

[elfin berry]

BBMaths

[molten quiver]

wait

whats lim

what's n

oh nvm the bank

[queen sun]

Limit

[molten quiver]

is n

by the way

[queen sun]

In our original example bank 2 was actually bank 365

[molten quiver]

who invented the infinity sign

[molten quiver]

Ah

[queen sun]

https://en.m.wikipedia.org/wiki/Infinity_symbol

John Wallis

[molten quiver]

i thought it would be a lot more ancient

oh nvm in math

[queen sun]

The idea is much older

[molten quiver]

it must have pre dated that

[molten quiver]

ye but i meant the symbol itself

like its an Arabic 8

turned upside down

[queen sun]

^

[molten quiver]

that last name scares me

[queen sun]

Why?

[molten quiver]

there was this awful movie

where the main character was named wallice

and i hate it so much

bc it was really sad

[queen sun]

Wallace and gromit?

[molten quiver]

and weirf

[molten quiver]

no

tusk

i didn't even watch it i only watched a

uhh idk what it's called

[queen sun]

Dw it’s fine

[molten quiver]

but i use to watch "what could the main character

do to survive

i think its called hoe to beat or smth

[molten quiver]

basically it was this awful movie about the main character getting kidnapped

and made into a walletuce

walleruce

and then at the end

instead of killing him

or giving him reconstructive surgery

they put him in a zoo

[queen sun]

Weird

[molten quiver]

yeah

[queen sun]

I think we’re done now

!done

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[molten quiver]

byee

ty for the math help

[queen sun]

Make sure to close it

[molten quiver]

.close

[marsh citrus]

Channel closed

Closed by @molten quiver

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.

[delicate light]

Hey

[marsh citrus]

Please don't occupy multiple help channels.

[queen sun]

!da2a

[marsh citrus]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[queen sun]

Don’t start with hey either would’ve been a better thing for me to have said*

[night relic]

hi :) pls close ur other channel first before asking another q

[delicate light]

Ok

Close

[queen sun]

!done

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[delicate light]

.close

[marsh citrus]

Channel closed

Closed by @delicate light

Use .reopen if this was a mistake.

[queen sun]

Would be nice if there was a don’t say hi command

[fervent rampart]

!nohello?

nvm i guess

[outer lodge]

That is an absurd suggestion icl

[fervent rampart]

there is the website i guess https://nohello.net/en/

[marsh citrus]

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.

[dull sable]

I'm not sure how to start this because of the rational numbers condition

[dull sable]

I would've try x_1=a/b and x_2 = c/d

[fervent rampart]

to start out with, do you expect W to be a subspace?

[queen sun]

Maybe do a1/b1 and a2/b2

[dull sable]

well if I remember rational numbers is a subset of real numbers

[indigo nest]

Well what is a vector subspace

[dull sable]

One I've seen so far it has to satisfy three conditions

[indigo nest]

What are the three conditions

[dull sable]

Zero vector has to be in subspace. If two vectors in subspace the addition of two vectors must also be in subspace and multiplying a scalar to a vector in subspace must also be in subspace

[indigo nest]

Good

[fervent rampart]

so do you expect all three to be fulfilled, or if not, which one would you expect not to be fulfilled?

[indigo nest]

Now does the given set satisfy all of them

Oh hi cloud

[dull sable]

By expect do you mean making a guess like not doing anything yet?

[indigo nest]

I'd say let's just start checking

Is zero in the set?

[dull sable]

well if zero counts as rational number then I think so?

[indigo nest]

Good

Now if you add two things in the set are they still in the set

[queen sun]

(0,0)*

[indigo nest]

The zero vector, they got what I meant

But yea should have been more precise

[dull sable]

if you add a rational number and rational number then I would assume you get a rational number so long as denominator isn't zero?

[indigo nest]

Yup

And if the denominator is zero, it isn't rational in the first place

So it satisfies the first two

What about the third

[dull sable]

It makes sense intuitively but not sure how to show it

[indigo nest]

Rationals being closed under addition is a property you should just be able to invoke

Anyway now on to the third one

Does the third property hold

[fervent rampart]

you can justify it to yourself by the fact that you can combine them into a common denominator

[dull sable]

I think it should

[queen sun]

What field are we over

[indigo nest]

Can you spell out the third property for me

[indigo nest]

Subspace of ℝ² so I imagine ℝ

[indigo nest]

^^

[dull sable]

That I need to multiply a scalar and a rational number and get a rational number

[indigo nest]

Yes

And does that work for this

What exactly does a scalar mean here

[dull sable]

it depends what scalar is

[indigo nest]

It's the same as for the ambient field

[queen sun]

The scalar is anything in the field

[queen sun]

^

[indigo nest]

And your ambient field is ℝ², so the scalar is from ℝ

[queen sun]

Doesn’t have to be from R does it technically?

[indigo nest]

So is this true

[queen sun]

But we are saying it is

[dull sable]

well if c =pi or something then you wouldn't get a rational number if you multiply it

[queen sun]

Correct

[indigo nest]

Good

[queen sun]

So is it a vector sub space (after this question)

[indigo nest]

So does it satisfy the third property

[dull sable]

so since it satisfy all three conditions it is a subspace of R^2 I'm assuming

[indigo nest]

I mean yes, the given set is a vector space over ℚ but when taking vector subspace you stick to the same underlying field

[indigo nest]

But you just said it doesn't satisfy the third property

[dull sable]

oh yeah my bad

then no not a subspace

[queen sun]

If the field the vector space is over is the rational numbers, then it is a vector space, as the scalar multiple would be a rational number, so rational times 2 rational numbers giving 2 rational numbers therefore it works

[indigo nest]

Good

When talking about vector subspaces we take them over the same field

[queen sun]

I had that on clipboard for like 3 mins lol

[dull sable]

But how would I show steps can I just say suppose x_1=a/b and x_2=c/d where a,b,c,d are integers. And then do the arithmetic?

[queen sun]

Just give a counter example

[dull sable]

well b and d has to be not zero

[indigo nest]

Just consider a singular counterexample

Consider (1,1) and scalar multiply by π

Gives (π,π) which isn't in the set

Hence done

[queen sun]

You need to show pi is irrational not really but still

Better to use sqrt 2

[indigo nest]

I'm pretty sure you can invoke that lmao

But fair

If a teacher is asking you to prove π is irrational they better give you a long long time

[queen sun]

If you know a fair bit of calculus, Niven’s proof isn’t too hard to follow

[fervent rampart]

you can assume most properties of real numbers in a linear algebra class since it's not really about those

[dull sable]

Well I don't think I have to do that , this is introductory level linear algebra exercise

[indigo nest]

Yeah π is irrational, it's okay

[queen sun]

Breaking News: Scientists discover pi is rational, the last digit of pi is 3, 1 digit in

[dull sable]

But if it isn't a subspace of R^2 what does that look like or mean

[queen sun]

It means it satisfies some properties but not others

[indigo nest]

This is essentially just ℚ² embedded in ℝ²

But in general it means nothing

[fervent rampart]

a subspace of R^2 is either the origin, a line through the origin, or all of R^2. there are plenty of other sets in R^2 (geometric shapes, the quadrants, etc) which aren't subspaces

[indigo nest]

(i didn't wanna tell him that cuz it seems like it's part of the rest of the exercise)

[fervent rampart]

that means that it is not a vector space in its own right using the definitions of addition and scalar multiplication inherited from R^2

[queen sun]

In general R^n is it just like a point line plane or 3D space etc?

I feel like I should know this but idk why I forget over holidays

[dull sable]

So what would this set W look like geometrically

[indigo nest]

It's ℝ^m for m less than n

[indigo nest]

You don't have to answer that for your assignment lol

Read the question properly

[queen sun]

Actually since it’s null you wouldn’t see it

[dull sable]

It says give a geometric description but at same time I'm curious what it would look like

[fervent rampart]

it says if W is a subspace give a geometric description

[indigo nest]

if W is a subspace

[queen sun]

Q^2 contains almost nothing from R^2 (0% of the points) but at the same time you are always infinitely close to any point in Q^2

[dull sable]

This exercise was kind of confusing because it felt like I didn't even use a vector at all

[queen sun]

You used it to show a counter example

[dull sable]

Alright, it makes more sense but I don't think I'd be able to come up with a solution by myself because I didn't know the scalars I'm working with have to be real numbers

[queen sun]

They should say you are working on a real vector space or something, if they don’t it’s probably the implied field

Or whatever is implied in the question

!done?

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[dull sable]

.close

[marsh citrus]

Channel closed

Closed by @dull sable

Use .reopen if this was a mistake.

[fervent rampart]

R^2 is has "standard" operations of addition and scalar multiplication which you should use unless specified otherwise. part of that definition is that the scalars are real numbers

[indigo nest]

To be very fair, ℝ² is technically also a vector space over ℚ

But yeah, what cloud said

[dull sable]

So in linear algebra should I always assume scalars are real numbers

[indigo nest]

No

For a first course maybe

But even then no

[elfin berry]

Xavier 🌺

You assume $\mathbb{F}^n$ is a vector space over $\mathbb{F}$

[dull sable]

can F be any set or has to be something specific

[indigo nest]

A field

[fervent rampart]

F being a field, which is a set like R, or C, or Q which you can add, multiply, subtract and divide the way you expect to

[indigo nest]

Also reopen the channel if you wanna continue the discussion

Or it might randomly disappear

[dull sable]

Last question. It's probably not necessary for this course but should I look into what this field object is just to know

[indigo nest]

Yes

You should know at least the basics of what a field is

[fervent rampart]

for this course you will probably use R as your field 99% of the time and C the other 1% of the time, so it's not necessary to be super familiar with other examples of fields. but it's good to know that you can use other types of scalars and what properties scalars have to fulfill

[queen sun]

There are weird fields like Z_73

[indigo nest]

Z_73 is not a weird field

Try the fields which have a non-prime number of elements

[queen sun]

I suppose

[marsh citrus]

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[hexed silo]

-3x^3 + 17x^2 - 28x + 12

How do I factor this

[quick kindle]

try guessing one of the roots using rational root theorem

then synthetic division leads to a quadratic

[indigo nest]

2 works

By trial and error

[hexed silo]

I used Photomath and it says I can write it as a difference

-3x^3 + 6x^2 + 11x^2 -22x - 6x + 12

And then I can just factor it

But I wanna know why we did that

[runic temple]

because it knows 2 is a factor

based on trial and error

you cannot escape trial and error

[hexed silo]

Bruh

Whole reason I need to do this is cuz I need to find a point of discontinuity in my rational function

Very annoying

[runic temple]

well you can avoid trial and error if you use this

[hexed silo]

Is that rational root theorem?

[runic temple]

yeah if thats in the denom, you just gotta bite it

[runic temple]

youve heard of the quadratic formula, this is the cubic formula

[hexed silo]

Oh

I hope I don’t gotta do that

[runic temple]

no its not part of any curriculum

[hexed silo]

Phew

Alright well I appreciate the help

.close

[marsh citrus]

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[marsh citrus]

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[leaden peak]

Not too sure where to start here

I think I need to assign a length somewhere (perhaps a side of the triangle or the radius of the circle)

then find the length of segment ZG

[cunning flint]

Hello guys

I am in high school and I am struggling with math

[leaden peak]

!occupied

[marsh citrus]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[cunning flint]

It’s hard for me to understand it and I try to pay attention but I just feel like my mind is slow

[odd agate]

!occupied, sorry

[marsh citrus]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[odd agate]

please post your question in an available channel like #help-46

[leaden peak]

and then from here determine the n-gon that would fit in the circle with side length ZG

but not really sure where to start

like, what part would be best to assign a length to? and what length (I'm thinking 1)

and why?

[jagged relic]

You don't need any length

Think about the angles from O

[leaden peak]

ohhh true I could just work with angles

ok give me a sec let me try this out

[jagged relic]

(all you really need are the angles AOG, AOZ, AOC, AOF)

[leaden peak]

Well I treid but got a decimal for n

let me explain my work:

first, triangles angles add to 180

so each triangle angle is 60 cuz its equaliteral

thus each arc is 120deg

like arc AB and AC

then do the same with the reg polygon

sides is 5 so (5-2)*180 = total angles

divide that by 5 for 108 each

then double it

arcs there will be 216

so arc GB = 216

then if we go GB - AB = GA, 216-120=96

arc GA=96

arc GC = 120-96 since GA + GC = AC, AC = 120

GC = 24

since Z is midpoint, GZ=24/2 = 12

then solve $\frac{(x-2)*180}{x}=12$

[elfin berry]

UCYT5040

[jagged relic]

Ok hold on

[leaden peak]

this is where i got decimal

[jagged relic]

108 is for the internal angles of the pentagon

[leaden peak]

then the arcs touching that are double that yeah?

216

[jagged relic]

Right ok, but that's not GB

[leaden peak]

oh no

[jagged relic]

G is a vertex of the pentagon, B is a vertex of the triangle

[leaden peak]

yeah i confused those two

let me retry hold on

[jagged relic]

Let me show you something though, you're kind of overthinking it

[leaden peak]

ok, sure

[jagged relic]

If you draw the lines OA, OB, and OC, you divide the circle in three equal parts, right?

[leaden peak]

yes

[jagged relic]

And the entire circle is 360º

So each part is 360º/3 = 120º

You can do the same for any regular polygon

[leaden peak]

then each angle would be 72 (360/5)

[jagged relic]

Yes

[leaden peak]

ohhhhhhhhhh

AOF = 144

AOC = 120

then COF = 144-120=24

[jagged relic]

Yes

[leaden peak]

GOF = 72, sub 24 = GOC = 48

then divide by 2 because midpoint

GOZ = 24

I still get a decimal though?

$\frac{(x-2)\cdot 180}{x}=24$

[elfin berry]

UCYT5040

[leaden peak]

x approx= 2.307692

[jagged relic]

What is that equation supposed to represent?

[leaden peak]

prob better to say x=n

(n-2)*180 is sum of angles for n-gon

then divide by n is the value of each interior angle

[jagged relic]

Yeah ok, but interior angles

24 is the angle from O

[leaden peak]

ohhh true

24 is the wrong angle

wait so how do i do this then?

is it just

360/24?

[jagged relic]

Yes

[leaden peak]

ohh yeah that makes sense

like asking how many can fit within the circle

and its 15, which is correct according to answer key

[jagged relic]

If you really wanted to use interior angles you could check the isosceles triangle OZG

[leaden peak]

it would be 156deg

[jagged relic]

180 = 24 + 2x, so x = 156/2 = 78

Double it to get the interior angle of the polygon

[leaden peak]

well anyways i way overthought this whole thing lol, thank you so much for your help though! makes so much more sense now

.close

[marsh citrus]

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[marsh citrus]

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[ebon lotus]

I’m trying to figure out what it converges to. Do I find 4 terms and find the pattern?

[ebon lotus]

also i js realized i did r wrong

https://tenor.com/view/angai313-spongebob-sad-spongebob-crying-gif-21679826

[fervent rampart]

what do the numerator and denominator approach individually?

[ebon lotus]

a real number (i forgot) over infinity

[fervent rampart]

do you know the general rule for limits in the form (some number)/infinity?

[ebon lotus]

0? i think

i forgot that too

😭

[stoic saddle]

you forgor 💀

[steep whale]

[fervent rampart]

well we can consider what happens when you divide a normal number by a really huge number

[stoic saddle]

anyway $\lim_{x \to \infty} \arctan(x) = \frac\pi2$

[fervent rampart]

,calc 45/99999999999

[elfin berry]

Result:

4.500000000045e-10

Ann

[ebon lotus]

https://tenor.com/view/angai313-spongebob-sad-spongebob-crying-gif-21679826

OHHHHH

UR RIGHT

the larger the denominator over a smaller numerator, the closer u get to 0

so it converges to 0

[steep whale]

for questions like these, try subsituting n for infinity as that's what the limit is approaching

[steep whale]

yaya

[ebon lotus]

ty i understand it now

.close

[marsh citrus]

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[weary dirge]

!status

[marsh citrus]

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

[weary dirge]

1

not sure how to begin

[noble geyser]

lemme try

ok i got it

@weary dirge

[weary dirge]

yeah

[noble geyser]

so

you can see that these 5 numbers, there is always one thats divisible by 5

and the only prime number that is divisible by 5 is 5

so one of the numbers must be 5

[weary dirge]

how

[noble geyser]

which step how

[weary dirge]

there is always one that's divisgble by 5

[noble geyser]

ok look at it

if a is lets say 5k+1 where k is an integer

[weary dirge]

yeah

[noble geyser]

then a + 24 is 5k + 25

which is divisible by 5

[weary dirge]

yea

does that work for 7k+1

[noble geyser]

no

because theres 5 numbers

[weary dirge]

yeah

so it won't work for 7

[weary dirge]

but 7 also works

wait nvm

so only 5 works?

[noble geyser]

and all of them divided by 5 gives a different remainder thats why one must be divisible by 5

[noble geyser]

yes

[weary dirge]

but why does nothing else work

[noble geyser]

i just told you

there has to be a number that is divisible by 5

[weary dirge]

ye

[noble geyser]

and only 5 is divisible by 5 and prime

[weary dirge]

oh ok

thanks

[noble geyser]

np

[weary dirge]

is there a notation for prime numbers

[noble geyser]

oof

i think its small p normally

[weary dirge]

kk

so like

[noble geyser]

yea there is none but usually we use p

[weary dirge]

k thanks

.close

[marsh citrus]

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[iron ocean]

@helper

[iron ocean]

help I don’t get this

it’s for our project

[turbid mica]

which part

[iron ocean]

the whole thing

so that I can start it

[queen sun]

Do you know what the words in bold mean? (For step 1)

[marsh citrus]

@iron ocean Has your question been resolved?

[marsh citrus]

Channel closed

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[marsh citrus]

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[verbal iron]

hello

[marsh citrus]

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

[verbal iron]

7

[indigo nest]

Interesting

What have you done so far

[elfin stone]

hmm

[verbal iron]

i tried

but i coudnt reach to smth by which i could get answer

[weak surge]

Show your work

[verbal iron]

hmmm

it is very bad

[indigo nest]

It's okay

[elfin stone]

it's alright

[verbal iron]

i did by co-linear base sharing same vertex

[weak surge]

What did you get

[verbal iron]

nothjing

[weak surge]

Do you know how to transform ratios of areas to ratios of side lengths?

[indigo nest]

That doesn't work unless the triangles are similar no?

[verbal iron]

simialrty right ?

[ABC] = (AB)^2 and all that

[indigo nest]

We should first work on showing similarity

[verbal iron]

but there will be no similiarity\

[weak surge]

Not only that

Area of BEF to area of BFC is EF/FC

[indigo nest]

Ah right

[weak surge]

Can you work this out?

@verbal iron

[verbal iron]

ill try

[weak surge]

Good

[verbal iron]

nah i didnt get it

[weak surge]

The height is common

Since EFC collinear

[verbal iron]

height will not be common

[weak surge]

Why?

[verbal iron]

they both hv same side

BC

[weak surge]

I will draw for you.

Can you see that the area of ADB to the area of BDC is AB/BC?

[verbal iron]

oh

i understood now

EF/FC = 4/5

DF/FB = 2/5

[astral hornet]

í finaly uderstand

under

[weak surge]

Good

[weak surge]

Correct

Now can you do?

Connect AF

[verbal iron]

AE/EB = [AEF]/[FEB]

[weak surge]

Yes

[verbal iron]

[AEF] = P
[AFD] = Q

can i cosider this

[weak surge]

Wait we have the same server tag

[weak surge]

Yes we just need P+Q

[verbal iron]

yeah

AE/EB = P/8
AD/DC = Q/4

hello ?

@weak surge sorry to tag

[weak surge]

Yes?

[verbal iron]

is it correct

[weak surge]

You know FEB area already

[verbal iron]

yeah

[weak surge]

Yes

[verbal iron]

what should i do further

[weak surge]

Plug the values in

[verbal iron]

i m not getting it

[weak surge]

Can you find [AEF]?

[verbal iron]

nah

@weak surge

hello

[weak surge]

I am thinking

Ah this will be a bit uglier

[verbal iron]

its ok

i will try to understand

[weak surge]

EF/FC is [AEF]/[AFC] which is P/(Q+4)

And you know what EF/FC is already

Now do the same for the other side and you have 2 equations

[verbal iron]

ohk

i will do

the second equation i got is
[AFD]/[AFB] = Q/P+8

[weak surge]

Goood

[weak surge]

You know the ratios already

[verbal iron]

yeah

[weak surge]

Can you solve?

[verbal iron]

now

i got ratios of P and Q

P/Q = 9/7

[weak surge]

Mhm

[verbal iron]

bro

is this correct

[marble gazelle]

man you didnt respond to my ping earlier this day?

i still couldnt comprehend why you said that

[verbal iron]

earlier work

@weak surge

@weak surge

just ping me if someone comes

[weak surge]

Apologies i kinda have to go

[verbal iron]

is it correct

[marsh citrus]

@verbal iron Has your question been resolved?

[verbal iron]

<@&286206848099549185>

@weak surge hlo

[verbal iron]

@weak surge

@indigo nest

@elfin stone

<@&286206848099549185>

[marble gazelle]

!noping

[marsh citrus]

Please do not ping individual helpers unprompted.

[calm harbor]

Bro, don’t harass my alt

[marsh citrus]

@verbal iron Has your question been resolved?

[slim trail]

Hi

I got question

Can you check my answer to see if right or wrong

[queen sun]

!occupied

[marsh citrus]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

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[tall pond]

i dont understand the question

what is considered the "outer surface"

as in the base

or what

because if its just anything on the surface

the shortest distance would technically be 0

but that doesnt make sense

oh wait it says from p

mb

.solved

[marsh citrus]

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[finite forum]

1/4 * arctan(3/4) is not 0.94...

[harsh scroll]

,w (1/4)*arctan(3/4)

[elfin berry]

Results provided by WolframAlpha

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

Requested by yobi_fx.

[finite forum]

x = multiple solutions

i just dont know why they chose x = 0.9463

[amber birch]

cause of the domain restriction

$\frac{\pi}{4} \le x < \frac{\pi}{2}$

[elfin berry]

south

[finite forum]

there is still more than 1 answer in this domain

[amber birch]

no there isn't

https://www.desmos.com/calculator/iq9ybnyhaq

really what they should have done is tan(4x) = 3/4

then the principal solution, x = 1/4 arctan(3/4), doesn't fall in domain

so the next solution is x = 1/4 arctan(3/4) + pi/4

[finite forum]

.close

[marsh citrus]

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[shell tulip]

Comment on peut determiner le determinant d'une matrice de taille n?

[elfin stone]

hi, English?

How can we determine the determinant of a matrix of size n?

[queen sun]

I think that is it

[elfin stone]

can you pin it?

[shell tulip]

How can we determine the determinant of an n × n matrix?

[shell tulip]

yeah

[pliant willow]

ez merguez

ya une formule

attend deux secondes

anon

je suis autiste

je connais que pour taille 2

déso boss

[shell tulip]

...

tkttt c est pg

[pliant willow]

sah demande à chat gpt

[shell tulip]

j ai demandé et j ai pas tout compris justement

[pliant willow]

ptet youtube alors

[shell tulip]

moe encore pire

[marsh citrus]

@shell tulip Has your question been resolved?

[shell tulip]

.close

[marsh citrus]

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[outer granite]

are my teacher's units incorrect? from my understanding, you can't add m/s to m. what i feel it should be is v(t) = 2.00 (m/s) + 3.00 * t (m/s^2 * s) - 1.00 * t^2 (m/s^3 * s^2). am i stupid?

[jagged relic]

The unit of t is s

[outer granite]

yes but did my teacher make a typo

to be able to add velocities together they have to be the same unit

[jagged relic]

Oh, right, should probably be /s² in the second term and /s³ in the third

[queen sun]

The units are not that important really

[jagged relic]

Or something like that, I don't know the context

[outer granite]

true, really just a typo. would be still cool to get it pointed out tho

but thank you guys for answering !!

[queen sun]

!done?

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[outer granite]

.close

[marsh citrus]

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• 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.

[wintry aspen]

!status

[marsh citrus]

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

[calm harbor]

No bro

[queen sun]

!noans

[marsh citrus]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[stoic saddle]

extremely loud incorrect buzzer 😭

[wintry aspen]

show said calcs

[queen sun]

!show

[marsh citrus]

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

[civic echo]

46.2%​=1.55%=0.0155. 834,000​=4,250€. 34,000×0.0155=527€. 4,250+527=4,777€. 34,000−4,250=29,750€. 29,750×0.0155=460.13€

29,750 not correct

[queen sun]

Do you have a photo

[civic echo]

no

[marsh citrus]

@civic echo Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

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.

[vague jay]

If there exists an injective linear map T from V to W, and W is finite-dimensional, does V have to be finite-dimensional?

[queen sun]

I’d also like to know the answer to this

Feels like there might be a trick for V infinite dimensional

[vague jay]

lol

Review this while your at it

specifically the second part starting with "Conversely, suppose..."

[marsh citrus]

@vague jay Has your question been resolved?

[restive sun]

T(V) is a subspace of W, so T(V) is finite-dimensional, and T is an isomorphism from V to T(V), so V is finite-dimensional

[queen sun]

Conversely suppose should be on a new paragraph imo

[night relic]

there is also an isomorphism from the preimage of W to W, by injectivity. say there were n basis vectors spanning the preimage and V was infinite-dimensional. then an infinite number of (basis) vectors would not map to W, which means T isn't a linear transformation on V

[queen sun]

I’m assuming you didn’t make it but it’s easier to follow if converse is not on the end of the first direction so that’s a tip when you’re writing proofs

[vague jay]

sure but why wouldn't axler just specifcy this in the exercise definition

[vague jay]

Thank you, I'm not good at formatting and learned latex recently

/help

bro how do I close this channel

[pallid dome]

!done

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[vague jay]

oh dot

.close

[marsh citrus]

Channel closed

Closed by @vague jay

Use .reopen if this was a mistake.

[marsh citrus]

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.

[lyric kelp]

is there a way to completely remove the negation signs from this?