help-42

[half trench]

yes

if you have -(-x+y-3z) each of the terms in the brackets gets flipped

so its x-y+3z

[tawdry ruin]

ohhh okok i see

i solved it for 4x + 4z=20

that would be correct right?

[leaden thunder]

Should review
http://www.gimaths.com/Styles/images/Algebra/AlgebraicRules.png

[tawdry ruin]

okayyy ttyy

:)

.close

[calm coral]

Channel closed

Closed by @tawdry ruin

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[empty steeple]

how to read those graphs???

i have an exam in 20 mins

[daring haven]

the solution of two lines on a graph is the point at which those two intersect.

do you know how to plot a linear equation in two variables on a graph?

[empty steeple]

nope

idk the lesson names

[cunning reef]

rearrange the bottom equation to get y = x+1, so one of the lines should look like y = x shifted up by one unit

[chrome reef]

do you know how to read slope form

[cunning reef]

and then do the same for the upper equation to check

[chrome reef]

yeah this

[empty steeple]

is there a quick video? i would greatly appreciated

my exam is in like 10 mins but im gonna be late for it anyways so i will check it otw

[winter elbow]

https://youtu.be/Ft2_QtXAnh8?si=kyyacd4oc1iiTvtx

[winter elbow]

You’re not going to learn it in 10 min

[empty steeple]

i will try

thank you for the video

.close

[calm coral]

Channel closed

Closed by @empty steeple

Use .reopen if this was a mistake.

[brazen elbow]

next time, if possible, please don't put off studying until the last 30min

[empty steeple]

i studying all night didnt even sleep

it's just the test mainly focused on complex numbers and at the end this suddenly came which is odd

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[raven crest]

Benjamin bakes cakes in a triangular pan shaped like a triangle CKS. He cuts along segment AE, which is parallel to CS, dividing segment CK into segments of 2 inches and 5 inches. Then, he cuts along segment AS, creating a total of three cake pieces. If he sells all three pieces at the same price per square inch and prices piece II at $2, how much will he charge for piece III?

[raven crest]

Drawing of the triangle (ignore white box)

please help someone

[small garnet]

what have u tried

[raven crest]

updated image

[raven crest]

i notice that triangle AKE is similar to triangle CKS

ratio of 3.5

[small garnet]

Yes That is

And one more thing

[raven crest]

idk that's all i know

[small garnet]

$\Delta AES \simeq \Delta ACS$

[potent lotus]

Aayush

[small garnet]

Can u find out why or how?

[raven crest]

nah i dont know why

is it because all 3 angles are congruent?

or corresponding i mean

[small garnet]

wait i think i messed up 1 se

Where this question from

[raven crest]

mathcounts school handbook

question #135

[small garnet]

So ake and kcs are similar

Yea so $\frac{Area \Delta KAE}{Area \Delta KCS} = \frac{4}{49}$

[potent lotus]

Aayush

[small garnet]

ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides

ok?

[raven crest]

ok

[small garnet]

so price of I will be 4/49 times total price

[raven crest]

yes

[small garnet]

And triangle KCS and KAS share same Height along AS

[raven crest]

i don't think that's the height

[small garnet]

yea this is tricky

hmmm

I think theres some data missing

[raven crest]

i can send an image of the question if you want

[small garnet]

nup i have it here

[raven crest]

just in case im missing any

[raven crest]

but i don't think i am

oh ok

[small garnet]

So what we have is $\frac{KA}{AC} = \frac{KE}{ES} = \frac{2}{5}
;AE \parallel CS
;\Delta KAE \simeq \Delta KCS$

[raven crest]

how is it 2/5 i thought it's 2/7

[potent lotus]

Aayush

[small garnet]

KA /AC sry

Wait

can we write $7 \big( Area (\Delta KAE) \big) = 2 \big( Area (\Delta KCS) \big)$

[raven crest]

no? KAE has a much smaller area than KCS

[small garnet]

man im hallucinating

[raven crest]

also i have to go to bed sorry

[potent lotus]

Aayush

[raven crest]

feel free to dm me if you have any ideas

[small garnet]

alr

[raven crest]

thanks .close

.close

[calm coral]

Channel closed

Closed by @raven crest

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[old crater]

Q7 .

Let u= inf A , v= inf B and w= inf (A+B)

u≤x for all x ∈A
v≤y for all y∈B
hence
u+v≤x+y for all x and y
u+v is a lower bound of set A+B

Since u is infimum of A
For every ε1 >0 there exists x' ∈ A such that

u≤ x' < u+ε1

Since v is infimum of B
For every ε2>0 there exists y' ∈ B such that

v≤ y' < v+ε2

Adding above two inequalities and
define ε:= ε1+ε2
We have
u + v ≤ x' + y' < v+u + ε

x' ∈A , y' ∈B , so
x' + y' ∈ A+B

Since epsilon was arbitrary. There cannot be a lower bound of A + B greater than u+v .
Hence u+v is the infimum of set A+B .

[rustic osprey]

your proof seems fine, but you could write it a lot more concisely

[potent lotus]

Civil Service Pigeon

[rustic osprey]

(usually, it's more normal to start with saying "let epsilon > 0 be given. choose ...")

[old crater]

The book I m using

They have used these words :
" For ε>0 , there exists x belongs A , such that .....

[rustic osprey]

oh ok (eh it's not that deep so whatevs lol)

[old crater]

Is the idea of proof correct?

[rustic osprey]

your proof seems fine, but you could write it a lot more concisely

[old crater]

Concisely?

Where can I do better

[rustic osprey]

"Concisely" means to make it more short/succinct/brief

[rustic osprey]

^ Here's an example of what I mean

[old crater]

Ok I see

[rustic osprey]

[old crater]

The way I define and uses ε is it correct

ε= ε1+ ε2

[rustic osprey]

yeah

[old crater]

Thanks

.close

[calm coral]

Channel closed

Closed by @old crater

Use .reopen if this was a mistake.

[keen flower]

is it?

i feel like it relies on the fact that the function R+ x R+ -> R+ defined by (x, y) -> x+y is onto

[vague trench]

it’s just that you can split a positive number into two positive pieces.

[keen flower]

yeah it can be justified in this case, but for example
" let ε = ε1 + ε2 + 1 " would be wrong, wouldn't it?

[vague trench]

yeah

you always get epsilon > 1

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[arctic igloo]

Hey, can anyone help with this please

[arctic igloo]

I guess it's an easy question, but i just cant seem to be able to solve it

[graceful crest]

de morgan's law ig

[arctic igloo]

Can you please elaborate

[dusky flax]

what about just $P(A\cap B) = P(A)P(B)$ for independent events A, B

[arctic igloo]

Ohh right lemme try that then

[dusky flax]

were you aware of that formula already

[arctic igloo]

No 😅

Can you please tell how to derive it

[graceful crest]

I forget I to type it in Latex lol, here's from Wiki

[arctic igloo]

What does independent event even mean like if they are independent then shouldn't they be disjoint sets

[dusky flax]

something like\
$P(A$ occurs | B occurs$) = P(A)$

[arctic igloo]

So using this im getting A union B=2/3

[graceful crest]

Should be

[arctic igloo]

Can you please type out what you mean 🙏

[arctic igloo]

What to do further then ? Only (AUB), A intersection B are not enough to find them individually

[mortal orbit]

You can also use that not(A) and not(B) are independent too

[graceful crest]

Okay lol yeah it doesn't that helpful, stick to what bluple said

[graceful crest]

You'll still need this

[arctic igloo]

What do independent events mean 😭

[leaden thunder]

https://www.probabilitycourse.com/chapter3/3_1_4_independent_random_var.php

[arctic igloo]

Okayy i got it

Thank you very much everyone

Im getting imaginary answers can someone please tell what i did wrong

Answer key has x=1/2 and y=1/3

Omg im so dumb nvm

.close

[calm coral]

Channel closed

Closed by @arctic igloo

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[drowsy rune]

I did a) correctly, for b) I got 50 (I just threw random things at it till I got 50 which is the correct answer), my method was to finding the tangent line which i did as

y - y1 = m(x-x1) => y - 550 = 50(x-18)
550 is my estimated y coordinate for Q4 and 18 is my estimated x coordinate for Q4,
this equalled to y = 50x - 350
I found the x intercept by putting y = 0. which ended up being 7 and y intercept was then 0.
Point P is at (20,650)
650-0 = 650
20-7 = 13
650/13 = 50

can someone confirm if this correct?

[calm coral]

@drowsy rune Has your question been resolved?

[drowsy rune]

<@&286206848099549185>

[calm coral]

@drowsy rune Has your question been resolved?

[mighty harbor]

Avatar looks good

[drowsy rune]

oh thanks

i will close it now

.close

[calm coral]

Channel closed

Closed by @drowsy rune

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[crisp minnow]

can someone help me make TAC the subject or solve for it

[leaden thunder]

what's tacsin

[vagrant oak]

is tac a variable?

[crisp minnow]

yes

TAC is the vairable

[vagrant oak]

then factor it out

[crisp minnow]

this is what I did

[vagrant oak]

great, now divide both sides by the thing in parenthesis

wait where'd the cos44 go

oh no no

[crisp minnow]

hmmm

[vagrant oak]

you cant just move it over there

if you want, you can multiply both sides by cos44

[crisp minnow]

ooooooh

[vagrant oak]

but you'd have to multiply the left side as well

so that'd give u this

[crisp minnow]

i see

[vagrant oak]

the last step will be this

[crisp minnow]

.close

[calm coral]

Channel closed

Closed by @crisp minnow

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[crisp minnow]

how dowe know that angle is 30 degrees?

[swift laurel]

the horizontal tie is parallel with the horizontal line drawn

[crisp minnow]

oh right

thanks

.close

[calm coral]

Channel closed

Closed by @crisp minnow

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[frosty oak]

For this question how is it x<-48 and x>0

[frosty oak]

like i know u find -48 and 0 but how do u know like which direction is > <

[scenic plaza]

x(x+48)>0 means either both x and x+48 are positive or theyre both negative
For the both are positive case, x>0 and x>-48, the 2 conditions simplify to x>0
For the both negative case, x<0 and x<-48, the 2 conditions simplify to x<-48
Which means x<-48 OR x>0

[frosty oak]

OHHH THIS EXPLANATION IS PERFECT thank u

.close

[calm coral]

Channel closed

Closed by @frosty oak

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[kind plover]

<@&268886789983436800>

[calm coral]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[gray pelican]

last question of today pls we confused

[limpid crescent]

Btw I have the same question, (im F16).

If you help him you help me too

[hollow totem]

ur this?

[graceful dust]

you’re killing me

[hollow totem]

the fighter jets are learning math now its over

[gray pelican]

no they're not, they are seeking help with math

[limpid crescent]

Stoooooooop

[hollow totem]

ok the a:b part should be pretty easy

[graceful dust]

i’m relieved someone normal (you) is helping

[hollow totem]

this is the first time i've been called normal

[gray pelican]

.close

[calm coral]

Channel closed

Closed by @gray pelican

Use .reopen if this was a mistake.

[gray pelican]

.reopen

[calm coral]

✅ Original question: #help-42 message

[gray pelican]

oops

[graceful dust]

contextually normal

[limpid crescent]

Keep this closed

[hollow totem]

lets set b = 1 for simplicity

can we write each side of this right triangle in terms of c?

[limpid crescent]

I hope so

[gray pelican]

yes

[limpid crescent]

My english is bad I dont understand question

[gray pelican]

they lived in japan until last year

[willow knoll]

.

[limpid crescent]

Greetings

[willow knoll]

Heyyy

[limpid crescent]

Could you please help us

[hollow totem]

ok then use pythagorean theorem to solve for c

[willow knoll]

With what

Yea

[gray pelican]

.close

[calm coral]

Channel closed

Closed by @gray pelican

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[dusk iris]

can someone explain to me what is the cross ratio and help me solve the first question of the exercise pleassseeee

[dusk iris]

high school level

I know it's not past 15min yet but I'm desperate <@&286206848099549185> 💔

[nimble cosmos]

Mdmrmdmmrr

[dusk iris]

le prof il nous met des truc de prépa et il pense que nous allons pouvoir le faire

c un taré

[calm coral]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

@dusk iris Has your question been resolved?

[dusk iris]

no no one is willing to help

[calm coral]

@dusk iris Has your question been resolved?

Channel closed

Closed by @dusk iris

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[elder lance]

is this even possible to solve/

[sacred bear]

4m wire-> 2m 5m pieces

how

[sour saffron]

looks like a badly worded question

[sacred bear]

maybe 2cm 5cm

[sour saffron]

plausible

the rest is just comparing the price per volume of each type of box

[sacred bear]

8 = 222
20 = 225

make cases

[elder lance]

yeah that's what i mean

so guys what's the solution

[sour saffron]

!nosol

oof forgot command

[limber elm]

!nosols

[calm coral]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[sacred bear]

!noans for helpee

[calm coral]

The purpose of this server is to help you learn; please don't ask for direct answers. Ask for guidance, explanations, or feedback instead.

@elder lance Has your question been resolved?

[elder lance]

uh oh

https://tenor.com/view/sad-gif-22469622

[limber elm]

Linear programming I think

So 4m -> 2cm and 5cm ?

[elder lance]

yes

[limber elm]

Hm

Oh hm, that's tough cuz there're 4 variables

[elder lance]

yeah 😭

cant be solved using the normal way

[limber elm]

Basically we want to maximize 3x+5y+6z+9t

[elder lance]

obviously

[limber elm]

Try to find vertex point ig

20*(3x+2y+z)+50*(3t+2z+y) =< 400

[elder lance]

what is the function

[limber elm]

Well 20*(3x+2y+z) is the total length of 2cm wires

Similarly for the other term

[calm coral]

@elder lance Has your question been resolved?

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[plucky fiber]

let tangents at point P(5,5) and Q(-5,10) to a parabola intersect at R, if the focus (S) of the parabola lies at (1,2) then find distance SR

[ivory saddle]

draw it out

[plucky fiber]

i did but im on pc rn so i cant upload a picture

[ivory saddle]

what are u stuck with?

[plucky fiber]

i mean js the process of dealing w these questions

first i thought to check if its a focal chord

and its not

cuz otherwise Q wouldve been

like 1/-5

js dunno how to do it entirely i guess

[odd moon]

find the equation of the parabola

or tangent lines

[ivory saddle]

the tangent lines will help

[plucky fiber]

how do i find it without the directrix?

i dont have the directrix i js have the focus

[odd moon]

you have 3 points which defines a parabola (of the form ax^2 + bx + c)

[ivory saddle]

think about how u can use the 2 points on the parabola and its focus to find the eq of the parabola

[plucky fiber]

would the tangents intersect at the directrix or not?

[ivory saddle]

not

[plucky fiber]

i tried making two equations

[ivory saddle]

<@&268886789983436800>

[ivory saddle]

its indeterminate no?

[plucky fiber]

25a+5b+c=5

25a-5b+c=10

and simultaneously solving it

[ivory saddle]

try, but its not gonna

[plucky fiber]

it doesnt work

they js taught me in the standard forms and stuff

but this different focus stuff

it just doesnt work

nothing works

[ivory saddle]

do this for

me

[plucky fiber]

i can write it like (y-2)^2=4a(x-1)

[ivory saddle]

you have $$y=a(x-h)^2+k$$

can u get what the values of h or k would be

[potent lotus]

Nyxzore

[ivory saddle]

agree that the focus is always at (h,k+p)?

and we are given focus at (1,2)

[plucky fiber]

theres no p

[ivory saddle]

so i know h is 1

[ivory saddle]

yes

[plucky fiber]

yea

[ivory saddle]

but now since we know h we have

$$y=a(x-1)^2+k$$

[potent lotus]

Nyxzore

[ivory saddle]

and u have 2 points

this is a simulatenous u can solve

[plucky fiber]

a=1/4

[magic pelican]

I have a question how do u know if the graph is downward, leftward , rightward or upward??

[plucky fiber]

well the focus is at 1,2 so i naturally assumed its in the first quadrant

[ivory saddle]

I mean u can just solve for the equation as well and that tells

[magic pelican]

yeah right but what's the direcn of graph

[magic pelican]

if it's upward / downward u gotta take 4ay=x^2

[ivory saddle]

just look at a

[magic pelican]

if it's other way around u gotta take y^2

[ivory saddle]

if a<0 its down

if a>0 its up

fr

a=1/4>0 so its up

[plucky fiber]

yes

[magic pelican]

but a>0 doesnt prove it's verticle or horizontal

cant horizontal parabola have a>0??

y^2 = 12x here a>0 is this verticle parabola?

[ivory saddle]

a horizontal quadractic is technically not a function

so its not described by the same formula

[magic pelican]

it's a fucntion just defines in terms of x

[ivory saddle]

no

a function is mapping of x to y. One x cant map to multiple y

[magic pelican]

ik but when take output at x then we look at graph sideways

[ivory saddle]

when its side ways you have +-sqrt graphs

and you can just look at that coefficient

[magic pelican]

plus man how can u assume it has to be fucn

[ivory saddle]

?

[plucky fiber]

uhh i have a midterm tmrw

[magic pelican]

like u are saying the graph has to be a function

[plucky fiber]

how is it not a function mate 😭

help pls i dont wanna fail ts i been stuck on my problem sheet since early afternoon please

[ivory saddle]

no it doesn't have to i'm just saying its not describe by the same formula

[magic pelican]

okay lets just do question

[ivory saddle]

if a>0 its open to the right if a<0 its open to the left

[magic pelican]

if answer comes then ok ig

[magic pelican]

yeah

[ivory saddle]

work out the equation of the 2 tangents

[plucky fiber]

is it ok if its in terms of t?

[ivory saddle]

?

i mean sure

[plucky fiber]

common parameter?

[ivory saddle]

oh nop

you are introducing a new variable called t

[plucky fiber]

:(

[ivory saddle]

u can just solve the equations in terms of x

[plucky fiber]

yea

alright

[plucky fiber]

oh theyre coming a bit weird

[ivory saddle]

now it should be obvious how to work out distance

[ivory saddle]

?

do u need help finding them?

do u have the first derivitive?

$f'(x)=\frac{x-1}{2}$

[potent lotus]

Nyxzore

[plucky fiber]

well i computed one of them as x+2=0 and the other one is x-1=0

idk if thats right

[ivory saddle]

no

[plucky fiber]

oh wait

[ivory saddle]

so the first derivitive gives us the gradient to the slope at a point x

[plucky fiber]

i know

wait wait

5x+y+10=0
5x-y-5=0

[ivory saddle]

no

[plucky fiber]

ok

[ivory saddle]

yes?

[plucky fiber]

ok

[ivory saddle]

know how i got 2 and -3?

[plucky fiber]

nope

[ivory saddle]

the equation of the tangent it y=f'(x)x+b

[plucky fiber]

oh you used the gradient

[ivory saddle]

yeah

and $f'(x)=\frac{x-1}{2}$

[potent lotus]

Nyxzore

[ivory saddle]

so $f'(5) and f'(-5)$

[potent lotus]

Nyxzore

[plucky fiber]

yeah

[ivory saddle]

good good

so the equation for your tangents are?

[plucky fiber]

y=2x-5 and y=-3x-5

[ivory saddle]

very good

now it should be obvs

[plucky fiber]

now if i solve them simultaneusly i can get the point

[ivory saddle]

yes and then you can

...

[plucky fiber]

and then just use the distanace formula

[ivory saddle]

well equating them

[ivory saddle]

yes!

vv nice

[plucky fiber]

i got one more

[ivory saddle]

i gtg ...

but theres other helpers

just open a new channel

and close this one

!done

[calm coral]

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

[plucky fiber]

okay thankyou so much

.close

[calm coral]

Channel closed

Closed by @plucky fiber

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[plush kindle]

At which points it will be comtinuous

So my work x=1/x

And two points x=+-1

But my doubt is how can we say it is continuous because part second is irrational?

How can we put that rationals into it

[robust sedge]

what do you mean part second is irrational?

[remote wigeon]

that "$x\in \mathbb{R}\setminus\mathbb{Q}$" means x is irrational, i guess

[potent lotus]

bsharp

[steep zinc]

yep

i usually write that as $x \in \mathbb I$

[potent lotus]

1 divided by 0 equals Infinity

[remote wigeon]

hm, never seen mathbb{I} for irrationals

[steep zinc]

my country does that

[remote wigeon]

sick!

not doing any working but google seems to agree with OP

[steep zinc]

my best assumption is that $x \in \mathbb R \setminus \mathbb Q$ is my best guess that it will be continuous

[potent lotus]

1 divided by 0 equals Infinity

[robust sedge]

Well not really

[robust sedge]

You have the right idea

[plush kindle]

Indian?

My country uses both ways

[steep zinc]

no

[plush kindle]

Okay so tell me how can we put rationals

[robust sedge]

You can prove a slight generalisation without much extra effort. Write ℝ = U ∪ V, where U and V are dense, disjoint sets. Let f and g be R -> R continuous functions. Define h = f on U and g on V. Then the points of continuity of h are precisely the points where f and g agree.

[robust sedge]

this is just a restatement of your correct idea that the points of continuity are where x and 1/x agree

[remote wigeon]

piecewise coincides at x = \pm 1, so it should be continuous at those points

[plush kindle]

But how can we put rationals into a function which takes only irrational numbers?

[remote wigeon]

?

[robust sedge]

what do you mean only takes irrational numbers?

[remote wigeon]

f(x) accepts reals, it looks like

[sonic rose]

Youre assuming that 1/x is only-rationals?

[plush kindle]

Yes

[sonic rose]

Not the case

[plush kindle]

noo

[robust sedge]

blud doesn't think 1/π is real

[plush kindle]

Only irrationals

R/Q mean?

Irrationals

Am I right?

[sonic rose]

The section at the right is basically the domain of each.

[plush kindle]

??

[robust sedge]

Have you seen a piecewise function definition before?

[plush kindle]

Yes of course

Many times

but my doubt is related to their domain

I meant i found two points

X=1 and -1

[robust sedge]

Sure

[plush kindle]

But these are rationals

[robust sedge]

and?

[plush kindle]

And how can I put into other piecewise?

[remote wigeon]

Q is contained in R, where's the question?

[robust sedge]

what do you mean "put into other piecewise"

[plush kindle]

x takes rationals

1/x takes only irrationals

[remote wigeon]

f(x) takes reals. if x happens to be a rational as well, then f(x) returns x, otherwise 1/x

simple

[plush kindle]

I'm sorry my doubt is not clear

[robust sedge]

I don't know why you need to "put it into" anything

So your guess is that f is continous at 1 and -1 right? Why not start working to prove that

[plush kindle]

Yeah sure sure

How we will check it?

by putting in both function?

It will be same for both function

I meant the graph it crosses

[robust sedge]

wait

Are you in a real analysis class or a calculus class

[plush kindle]

No one class

[remote wigeon]

cool, formalize this idea

[robust sedge]

What do you mean

[plush kindle]

My doubt is....did they form the question correctly?

[robust sedge]

Sure they did

[remote wigeon]

so are you self-studying?

[robust sedge]

Are you doing proof-based maths?

[plush kindle]

Yes@remote wigeon

[plush kindle]

On my own yes after my graduation

[robust sedge]

Like does proving that f is continuous entail epsilon-delta style arguments?

I know you're self studying but what kind of level are you studying at?

[plush kindle]

I am just thinking my own

[robust sedge]

That's not the question

[lusty jungle]

You must be studying something surrounding this or some particular textbook???

[plush kindle]

I am graduated poorly and studying all stuffs on my own

[robust sedge]

Do you know what epsilon delta means?

[plush kindle]

Yes. It is definition

Used in limit and continuity

But i didn't understand it properly

[remote wigeon]

(revise it?)

[plush kindle]

|fx-l|<epsipon

[plush kindle]

I am not understanding

Revise is other thing na

[robust sedge]

OK so you want to prove that f is continuous at 1, can you expand out the epsilon-delta definition to see what this means?

[plush kindle]

So we can put rational numbers into 1/x?

[robust sedge]

What?

[plush kindle]

Or we have to assume surrounding values?

Could you gues please show me how can I prove?

By epsilon delta

[robust sedge]

Write down the ε-δ definition for what it means for f to be continuous at 1

Just copy it

[calm coral]

@plush kindle Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[valid vigil]

what's the most important part of the proof of lim x-> 0 (sin x / x) = 1?

[valid vigil]

and so is the proof of lim x->0(1-cos(x)/x) = 1

[leaden thunder]

all steps are important

[valid vigil]

wdym

the squeeze theorem is applied only after sector classification

[leaden thunder]

there is no most important

[valid vigil]

so what is there?

[leaden thunder]

all steps are important

unless you have a faulty proof

books don't usually have faulty proofs

[valid vigil]

can you please explain to me

how is the proof is constructed?

[leaden thunder]

too vague without the actual proof. show the one you learned

and "is constructed" is probably still too vague

[valid vigil]

Can you explain why does -x ≤ x sin(x) ≤ x imply that -|x|≤x sin(x) ≤ |x| when x ≥0?

[teal drift]

Are you sure you were given this? Because if x ≥ 0, there's no need of the absolute value

Not that it's wrong, but it's somehow weird

[leaden thunder]

you need to do this

[valid vigil]

So it's then become:
$\displaystyle -\frac {1} {|x|} \leq \frac {sin(x)} {x} \leq \frac {1} {|x|}$

[potent lotus]

macwindow

[valid vigil]

this

[leaden thunder]

that image shows almost nothing you've typed so far

[teal drift]

Where's the absolute value? 🤔

[valid vigil]

it's using the sector of the circle

it's what it becomes to from the sector

[calm coral]

@valid vigil Has your question been resolved?

[pulsar wing]

well you can see it as: (sin(X)-sin(0))/(x-0) which is cos(x) when x→0 so it's 1

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[vagrant oak]

<@&268886789983436800>

[calm coral]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[vagrant oak]

that was literally gone in a blink

i looked away for just a millisecond wth

[dull wagon]

Was already here before you pinged.

[vagrant oak]

oh, makes sense

[sacred bear]

gaate keeping

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[restive perch]

ive done (i) but I am not sure how to do (ii) I can show how i did the first part

[restive perch]

i showed (i) by assuming the expression is some value L > 0, then L - epsilon < n a_n ≤ L (by the definition of lim inf, and then choosing epsilon = L/2 makes the sum of the sequence a_n diverge, which is untrue hence L = 0

[vagrant oak]

consider some very sparse subsequence of the harmonic sequence (and set the other terms to 0)

the idea is that if we take any (strictly positive) sequence whose partial sums converge, by moving the terms far to the right and adding 0's to the gaps, it'll still converge to the same number, but we can make na_n as large as we wish

[restive perch]

we can make it as large as possible because we are shifting those a_ns to the right, right?

so the product takes a larger value since larger n

[vagrant oak]

exactly

[restive perch]

hmm

[vagrant oak]

by shifting it far to the right enough, you can increase n as much as u want and so make na_n as big as u want

try doing that e.g. with 1/2^n, whose sum clearly converges

[restive perch]

so something like 1/2^{n-1} if n ≥ 2 and 0 if n =1

[vagrant oak]

this would have na_n = n/2^(n-1)

which tends to 0

you gotta make gaps

1/2, 0, 0, ..., 0, 1/4, 0, 0, ..., 0, 1/8, 0, ....

[restive perch]

I can do 0 for odd n and 1/2^{n/2} for even n

[vagrant oak]

that'd be a slight improvement, but still by not so much

[restive perch]

why is that

[vagrant oak]

n/2^{n/2}

[vagrant oak]

this would be your na_n at even n

still tends to 0

you need to make these gaps increasingly bigger

[vagrant oak]

you know what, let's say you want na_n to be always 1 at the non-gap terms

try writing out the first few terms of the sequence

figure out exactly how big gaps you need to make na_n = 1 at the non-0 terms

I'll start:
0, 1/2,
Here the n=2th term is 1/2, so n a_n = 2 * 1/2 = 1

continue, add enough 0's and then 1/4

at whatever index n you place 1/4, you will want n a_n = n * 1/4 = 1

[restive perch]

n = 2^k makes sense where k is the index

[vagrant oak]

perfect

this makes sure that every non-zero terms (i.e. the terms at powers of 2) have na_n = 1

and therefore the limsup na_n is gonna be 1 as well

[vagrant oak]

na_n = 2^k * 1/2^k = 1

[restive perch]

I mean can't I just say a_n = 0 forall n but n = n_0 where a_n is 1/n_0 ?

would this not work also

[vagrant oak]

nope

recall the defn of limsup

limsup isnt just the "max" or "sup" of your sequence

roughly speaking, limsup is whatever the sup tends to as you cut smaller and smaller tails of the sequence

[restive perch]

$\lim_{k \to \infty} sup(a_n : n \geq k)$

ouch

[vagrant oak]

\geq instead of <= maybe

[restive perch]

ah yeah

something like this

[vagrant oak]

idk why the infk is there

[vagrant oak]

it should look more like this

what does inf_k even mean

[restive perch]

ah mb

[vagrant oak]

maybe u were trying to write this

[potent lotus]

ginny

[restive perch]

yes

but more importantly

since k is to approach infinity

of coure the sup x_n is 1

after k ≥ n_0

hence 1

[vagrant oak]

in your sequence?

[vagrant oak]

in this one?

[restive perch]

n x_n

is 1

mb

sup of this

[vagrant oak]

say a_n = 0 forall n but n = n_0 where a_n is 1/n_0 ?
not in this sequence. If we consider e.g. k = n_0 + 1, a_n will be 0 for all n > k, so na_n will also be 0

in fact, if you consider any k > n_0, na_n will be always be 0 for n >= k

and so the sup cant tend to 1

the sup mightve been 1 at k <= n_0, but after it its just gonna be 0

so it will tend to 0

[restive perch]

makes sense

[vagrant oak]

i think the wikipedia pic illuminates it quite well

your graph would look like long sequence of 0's, then a single 1 at n_0 and then another long sequence of 0's

so the red line would be 1 until n_0 and then drop suddenly to 0

[restive perch]

ah makes sense, this is why limsup is (loosely speaking) inf of sup (for n ≥ k), so always ≤ global supremum and so on

[vagrant oak]

yep

the sups of n >= k form a decreasing (or rather non-increasing) sequence, so their limit is gonna be the same as their infimum

[restive perch]

yes, I read that

it makes more sense now

so what we want is that no matter the choice of k, our supremum should not tend to 0

[vagrant oak]

yes

[restive perch]

which works for the construction you gave

and could be done for any sequence really

i mean converging and all that ofc

[vagrant oak]

yep, you can always choose gaps which are big enough

except when it's a 0 sequence or sth like that

it must be converging, but not literally eventually-0 sequence

converging, but not way too quickly

[restive perch]

wdym

like where we explicitly define it is 0 after a given n etc

[vagrant oak]

if we had 1,2,3,5,0,0,0,0,0,0,0,0,0,0,0,... then the gap trick wouldnt work anymore

[restive perch]

yes ofc

[vagrant oak]

but the sum of this sequence still converges to 11

[restive perch]

we just saw why

[vagrant oak]

mhm

[restive perch]

damn

I could have seen this exact solution on an LLM and still not have understood it like this lol

thanks!

[vagrant oak]

np

[restive perch]

.close

[calm coral]

Channel closed

Closed by @restive perch

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[foggy elbow]

anyone know where I would start with this question?

[mellow crater]

Ugh, control systems, I have unpleasant memories of it

So, firstly you have to write down the input-output relationship

In the domain of time

How can you describe u(t)? Generally you just have to write the equation for this summation node

[calm coral]

@foggy elbow Has your question been resolved?

[foggy elbow]

how would you do that i practically forgot this topic😭

[mellow crater]

Just follow each path, remember that u(t) = y''(t), e.g. for the top path we'd obtain:
-a1 * y'(t)

[foggy elbow]

so theres 3 paths
integral of -a1y(t)
integeral(integral(y(t))
-a2y''(t)
is that correct?

[mellow crater]

Integrators cancel subsequent derivatives, here you won't have integrals, only derivatives of the output signal

For the summation node you have:
u(t) = y''(t) = x(t) - a1 * y'(t) - a2 * y(t)

If you take y''(t) as input and integrate it you get y'(t) etc.

[calm coral]

@foggy elbow Has your question been resolved?

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[trail wagon]

hello! can someone please help me understand how my answer is wrong?

[rustic osprey]

$\frac{1}{2\sqrt x}=\frac{1}{2}x^{-1/2} \neq 2x^{-1/2}$

[potent lotus]

Civil Service Pigeon

[trail wagon]

ohoh i see

thank you!!

.close

[calm coral]

Channel closed

Closed by @trail wagon

Use .reopen if this was a mistake.

[rustic osprey]

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[unique tundra]

does this only go if f''(x)... then f(x) and f'(x) or can it go the other way too

[unique tundra]

like if f'(x) has rel extrema

can i say it has inflection

[primal smelt]

great question

Try to think of counterexamples, why this might not be the case. The true answer is a bit more abstract.

[unique tundra]

i mean i think u know that f(x) has inflection if f'(x) has rel extrema

then i dont think lknowing weather f'(x) is increasing or decreasing will tell you f(x) concavity

but im not sure, the last exam i had the idea of this totaly stumped me

[primal smelt]

there are a lot of things missing in the if then statements for my taste sorry :(

for all x,

defined on R or on an interval

bounded or not

so the answer is kinda, it depends

[unique tundra]

hmm

[unique tundra]

would what i said here accurate?

[primal smelt]

so if f'(x) has a local extrema

then f(x) has an inflection point

makes sense logically

[mortal orbit]

take F(x) = x^4 if x > 0, F(x) = 0 else
F'(0) = 0 is a relative minimum (even absolute)
and yet 0 is not an inflexion point of F

[primal smelt]

Yeah this for example ^

we can just define a function such that the statement does not hold

it needs more restriction

for the opposite to be true

[unique tundra]

oh that makes sense

[calm coral]

@unique tundra Has your question been resolved?

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[frosty oak]

Can someone explain why they did h=8

[royal raft]

he did 10-2 to get 8

f(10)-f(2)/8

[frosty oak]

I get that but how do they know to sub in that for h

[royal raft]

so we have f(x + h) - f(x) / h right

for the formula

[frosty oak]

oh this was the original function

[frosty oak]

yea

[inner zealot]

The original interval was 2 <= x <= 2 + h

They substituted in 2 <= x <= 10

Inferring that 2+h = 10

[frosty oak]

Ohhhh

one more question

for this

how is it 0?

Couldnt it only be 0 if X = 9?

[inner zealot]

How is what zero?

[frosty oak]

h

[inner zealot]

Do you understand the difference between a secant line and a tangent line?

[frosty oak]

yes

[inner zealot]

And what is that difference?

[frosty oak]

we find an instant for tangent and we find an average for secant between intervals?

[inner zealot]

A secant is a line that intersects a curve at two points. A tangent line touches a curve at a single point.

The gotcha with a tangent line is that we usually need two points to determine the equation of a line.

Because a tangent line only touches a curve at a single point, we need a method to determine a value for that "other point".

This is where the limit steps in. You have two points, (2, f(2)) and (2+h,f(2+h)).

If you decrease h such that is it near 0, you find those two points near x=2.

Which gives you the slope that you need to find the equation for the tangent line at x=2.

And because the difference, h, is so small it is effectively one point.

[calm coral]

@frosty oak Has your question been resolved?

Channel closed

Closed by @frosty oak

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[median cloak]

I saw this on the internet

[median cloak]

Why it works

[graceful dust]

what is it?

[median cloak]

I suppose it is a tangent line and a circle.

[remote wigeon]

alternate segment theorem

[calm coral]

@median cloak Has your question been resolved?

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[daring heart]

I have this question here

[graceful dust]

[daring heart]

Where S is the sought-after sum

Does this look correct

[graceful dust]

not quite

[drifting seal]

should be below 1000

[daring heart]

dammit

[graceful dust]

no knief

it asks for the sum

[drifting seal]

no

he did 200

as the upper bound for the 5s

[jolly pilot]

5x from 1 to 199 not 200

[daring heart]

ah below 1000

[drifting seal]

im saying you're only including multiples that are below 1000

[daring heart]

Not less than or equal to

[graceful dust]

oh

i see what you meant now

[daring heart]

So it's not $\floor{\frac{1000}{n}}$ it's $\ceil{\frac{1000}{n}} - 1$

Dammit I forgot the fraction

[potent lotus]

Coolempire93

[daring heart]

Okay let me alter

[graceful dust]

yea

[graceful dust]

yep

cue project euler correct screen

[daring heart]

Idk how to actually submit

[graceful dust]

there is an answer box right below the question

[daring heart]

Where

[graceful dust]

oh

you need to make an account

[daring heart]

I'll make sure to do that

[graceful dust]

wow i did this problem 6 years ago

[daring heart]

Speaking of floor and ceiling

Another question

If I have $n \cdot \floor{\frac{1000}{n}}$

[potent lotus]

Coolempire93

[daring heart]

Oh I can use the inequality definition to deal with this I suppose

Like a

\begin{align*}
& \frac{1000}{n} - 1 &< \floor{\frac{1000}{n}} &\leq \frac{1000}{n} \
& 1000 - n &< n \cdot \floor{\frac{1000}{n}} &\leq 1000
\end{align*}

Good enough

[potent lotus]

Coolempire93

[daring heart]

Okay I'd better go to bed

.close

[calm coral]

Channel closed

Closed by @daring heart

Use .reopen if this was a mistake.

[graceful dust]

[sacred bear]

Good night

[sacred bear]

You sleep as well

[graceful dust]

no

i don't take orders from you scoob

[sacred bear]

Ok

But you should sleep

[graceful dust]

no

[sacred bear]

,w plot n*floor[1000/n]

[potent lotus]

Results provided by WolframAlpha

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

Requested by scoob09979

[sacred bear]

Hm..

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[umbral nimbus]

Let $S_n$ act on $\mathbb{Q}(x_1, ..., x_n)$ by permuting the (transcendental) variables. Is the fixed field equal to the field generated by the elementary symmetric polynomials?

[potent lotus]

bvghfgjfg

[calm coral]

@umbral nimbus Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[plush kindle]

5th question

[plush kindle]

Which test should I use?

.close

[calm coral]

Channel closed

Closed by @plush kindle

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[wheat wyvern]

I'm stuck finding the force of tension

[fading stirrup]

what's the question

[wheat wyvern]

I need to find the magnitude of the electric field

[fading stirrup]

ok so the downward force is your weight (mg)

[wheat wyvern]

My current goal is finding the force on the charge

[fading stirrup]

and your upward force is Tcos(theta) where theta = 17.4 degrees

equating them you get T = mg/(cos 17.4)

and you can ignore electric field here as it exerts no vertical force

[wheat wyvern]

yeah it's only horizontal

[fading stirrup]

yep

so you can find tension that way

[wheat wyvern]

Thank you

I don't need to worry about length at all right?

Thanks I got it

.close

[calm coral]

Channel closed

Closed by @wheat wyvern

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[restive perch]

idk how to begin

[toxic stump]

what kind of groups do you want to be looking at for this?

[calm coral]

@restive perch Has your question been resolved?

[restive perch]

H must not be normal, G should not be abelian etc

[toxic stump]

coolio

before we delve into an example, do yk WHY H must be infinite?

[restive perch]

i think so

because of H were to be finite

gHg^{-1} has to be H as it is a one one map

conjugation basically is a one one map

anf that being a subset of H ensures it has to be H

which is a contradiction

[toxic stump]

okay cool

now that we've got that squared away, what kind of G do you want to try out?

or at least, what kind of infinite nonabelian are you comfy with working with?

[restive perch]

no preference so far, since this is my first course in this, I guess I could do GL_n(F)

[toxic stump]

okay sounds good, so lets take gl_n(f)

do you have access to any kinds of special subgroups within GL_n(F)?

[restive perch]

special how?

[toxic stump]

like has your course ever defined any notable subgroups

sorry maybe not special per se, but common subgroups

[restive perch]

determinant 1

SL_n(F) was it?

[toxic stump]

oh okay cool

unfortunately, that one wont work since SL_n(F) is normal in GL_n(F)

[restive perch]

yes exactly

[toxic stump]

do you know upper triangular matrices?

[restive perch]

yes I do

[toxic stump]

why dont you try playing around with those

specifically, consider the subgroup H of upper triangular matrices with 1's on the diagonal, and any element of F in the top right

\[
\begin{bmatrix}
  1 & f \\
  0 & 1
\end{bmatrix}
\]

[potent lotus]

blanketism

[toxic stump]

so elements of this form

[restive perch]

sure

[restive perch]

isn't this also normal

since the det here is also infact 1

[toxic stump]

no, subgroups of normal subgroups need not be normal

you can have that occur if subgroups are characteristic, but otherwise, no not necessarily

[restive perch]

makes sense

so just so we are on the same page out original group is still GL_n

and H the subgroup is upper triangular matrices of this form

[toxic stump]

yes

[restive perch]

and now we show that this is the sort of example we are looking for

so just find a g \in G

[toxic stump]

yep

ill give you a hint, it looks a lot like the form i gave you

not the same, but it looks a lot like it in its "simplicity" i guess

[restive perch]

no I don't have trouble finding g

[toxic stump]

oh gotcha

[restive perch]

although

I must ask

[toxic stump]

yea

[restive perch]

how was I supposed to think of smth like upper triangular matrices for example

like

see

if you tell me this is an example

I can see yeah it is.

but to come up with one of my own

[toxic stump]

gotcha, so the way i see it (which is helped by the fact that ik this is an example), is that i understand that the question is looking for an injective but not surjective map

now a first thought might be okay, why not try scaling maps? those usually prove to be injective all the time, i.e., if phi(x) = mx for some m in Z, then it can be injective

so clearly they'll map via conjugation

the reason we chose matrices is because theyre nonabelian, and im assuming you've worked with them enough to know that they can naturally scale things so long as theyre diagonal matrices

does that help?

[restive perch]

how does a scaling map prevent surjectivity?

I agree it will be injective, but why not also surjective?

[toxic stump]

we choose a group where closure by division is not always guaranteed

aka inverses

but even then, this might not be a guarantee

which is why its just up to you to make attempts and try things out

[restive perch]

damn that is some hard to think of sequence of ideas

but I understand what you said

this was helpful

thank you

.close

[calm coral]

Channel closed

Closed by @restive perch

Use .reopen if this was a mistake.

[toxic stump]

np

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[small agate]

How do i find the reactions at point A and C

[rustic osprey]

discord.gg/physics

wrong server

[small agate]

oh

thx

[calm coral]

@small agate Has your question been resolved?

Channel closed

Closed by @small agate

Use .reopen if this was a mistake.

[calm coral]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[obsidian void]

how are you supposed to get pi/4 in degrees

im confused

[coral aurora]

mb

[still haven]

pi =180 deg and 2pi =360

[obsidian void]

alg

[still haven]

I think u can solve from there

[obsidian void]

ya right ok

brain fart

so 45 degrees

sin of 45

[still haven]

Yes

[obsidian void]

was entering in the answer

thank you

.close

[calm coral]

Channel closed

Closed by @obsidian void

Use .reopen if this was a mistake.

[obsidian void]

.reopen

[calm coral]

✅ Original question: #help-42 message

[obsidian void]

so for the conversions

how can i divide it cleanly into pi

my brain moves slower when looking at pi in an equation