help-27

[pastel rose]

If u went from -3 to 3

U would get 0

[kindred mauve]

and how would we know this without being able to draw the graph

[pastel rose]

Try and spot the fact that it’s an odd function and and it’s going from -3 to 3

[kindred mauve]

so

so is it -2 becus theres 2 areas

why not just do it from 3 to -3 and then 0 to 3

like this

[ebon coyote]

So, this is flipped along the y-axis for some reason

[pastel rose]

Oh sorry yes

[ebon coyote]

But essentially, you're not tasked with the integral between -3 to 3

[pastel rose]

It’s should be going up

[ebon coyote]

idk why it's been presented like that

You're tasked with finding the bounded area the function makes in that domain

[ebon coyote]

For starters it's a pretty simple function to graph

Secondly, the right-region will have a negative integral, so we need to negate THIS integral if we wanted the area it makes with the x-axis

[kindred mauve]

ok

[ebon coyote]

yh I'm saying this part isn't well written - this integral is zero lol

[kindred mauve]

equal to 0?

[ebon coyote]

ye

[kindred mauve]

becus its symmetric about the origin

[ebon coyote]

Just to check - do you know what it means to say a function f is an odd/even function?

[kindred mauve]

yh

[ebon coyote]

cool

[kindred mauve]

this function is odd=symmetric

[ebon coyote]

Then the graph is rotationally symmetric here about the origin - so the two areas are equal

But if you were to integrate over the related domains for each, one would be positive and the other would be negative

So if you rawly integrated over the whole [-3,3], they'd cancel

[kindred mauve]

so take the absolute value?

[ebon coyote]

Of the integrand, yes

[ebon coyote]

(in practice, I'd just go straight to the bit after this equals sign btw)

[ebon coyote]

ye

[kindred mauve]

so

becus the graph is symmetric

it would be 2 of these

no

it would be 2 about the origin

[ebon coyote]

If you really wanted, you could even just write this as
$$\int_{-3}^0 x^3 - 9x \dd x - \int_{0}^3 x^3 - 9x \dd x$$

[woven radish]

Waes (Wires)

[kindred mauve]

yeah i think i prefer that way

[ebon coyote]

[It just so happens that since this integrand is an odd function, that this sum is equal to:]

[woven radish]

Waes (Wires)

[kindred mauve]

how does it turn into that

so the graph is symmetric so the interval [-3, 0] is the mirror of [0,3]

[ebon coyote]

The graph is a really useful aid to see this, if graphed properly

[kindred mauve]

yh

so if the function is odd then

[kindred mauve]

this is the case?

.close

[devout snow]

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[devout snow]

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[quartz linden]

Could someone please help me with problem 3?

[devout snow]

@quartz linden Has your question been resolved?

[devout snow]

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[pulsar apex]

Someone pls help me to solve

Find all prime triplets (p ,q ,r)
Such that
pq=r+1 and 2(p²+q²) = r²+1

[devout snow]

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

[grand parcel]

How do I taxes 😭

[devout snow]

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).

[mild comet]

where did you get this problem?

[pulsar apex]

A book

[lunar haven]

You need answer

[pulsar apex]

Ah yes
I am not able to solve this
Pls help

[lunar haven]

You just want answer or explanation with it as well

[jaunty bane]

!nosols, just in case

[devout snow]

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.

[lunar haven]

Cause I have answer just quick thinking

[lunar haven]

alright

[pulsar apex]

Give the soln also
I will understand by myself

[lunar haven]

okay

[pulsar apex]

Also I would like to see handwritten soln

[lunar haven]

You have two triples of numbers:
(p, q, r) = (2, 3, 5)
(q, p, r) = (3, 2, 5)
These two look almost the same except that p and q are swapped.
Why call them symmetric?

[pulsar apex]

Yes p and q are symmetric

[lunar haven]

But why

[pulsar apex]

We can interchange them and the eqn remains same

[lunar haven]

Precisely

[pulsar apex]

How did you solved it
???
So fast

[lunar haven]

Light work

Even a third grade asian kid and do

[pulsar apex]

😂😂😂

Can you send the rigorous proof of it
The soln of it

[pulsar apex]

Zeta function

[lunar haven]

no no no, I just sending you the texting version

Jk

I actually cant

[autumn zodiac]

Send the proving pls

[pulsar apex]

What ???

[lunar haven]

No like literally I genuinelly cant

VEen if i tried

[lunar haven]

idk if its my computer

but I cant send no picture

not even drawn ones

[pulsar apex]

Why 😂😂😂

[lunar haven]

Brother believe me

I dont even know

Ima try fixing

[pulsar apex]

Do you see the plus sign

[lunar haven]

Yes I click that

and then click on the picture I want to click

[pulsar apex]

Did you gave permission

[lunar haven]

but then nothing happens

[pulsar apex]

Oh

[lunar haven]

Yes it worked like weeks ago

Yeah so ima try fixing computer

and if nothing happens screw ti and im buying a new one

[pulsar apex]

Ok just tell what approach should i use

[lunar haven]

Alright

lemme cook

okay im back

Use the method:

1)Substitute r=pq−1 from the first equation into the second.

2)Simplify to a Diophantine equation in p and q.

3)Treat the result as a quadratic in one variable, and check when the discriminant is a perfect square.

4)Test small primes; for larger primes the discriminant fails to be a square, giving no solutions.

In my opinion

I feel like #1 would be easiest

[pulsar apex]

Ok

[lunar haven]

Because that is what the third grade asian kid did to solve the equation in his head

Anyways

If that is all, im glad to help someone out

[pulsar apex]

Thnks

[lunar haven]

I will head to sleeping now, and please if you need help

Let me know

[pulsar apex]

@lunar haven ok

[lunar haven]

Have a good day!

[uncut crow]

how much ai went into this on a scale of 1-10

[mild comet]

Can you please send only one problem at a time

[lunar haven]

bro CHAT GPT IS BLOCKED

Not blcoked

but my computer broken

Barely anything works

[mild comet]

also, it says find all solutions, not just one (2,3,5)

[pulsar apex]

Yes

[devout snow]

@pulsar apex Has your question been resolved?

[devout snow]

@pulsar apex Has your question been resolved?

[devout snow]

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[green vault]

integrate (xdx)/((sqrt(1+x^2+sqrt((1+x^2)^3)))

[lunar harbor]

$\displaystyle \int \frac{x}{\sqrt{1+x^2+\sqrt{\left(1+x^2\right)^3}}} \dd{x}$

[woven radish]

Civil Service Pigeon

[lunar harbor]

(rewritten for readability)

[green vault]

yup

[lunar harbor]

any ideas so far

[green vault]

uh

[flat ibex]

u sub maybe

[green vault]

sub 1+x^2

i did that

[flat ibex]

u = 1 + x^2

yea

what you get

[lunar harbor]

@flat ibex do you want this? If so, I'll let you take it from me since two people helping at the same time is generally bad

[flat ibex]

uh sure

[lunar harbor]

k

[lament kraken]

fyi you forgot the da at the end

[green vault]

🥀

u get the idea

[flat ibex]

rewrite the radicals as exponents

[green vault]

forgot the 1/2

[green vault]

hm

[flat ibex]

bro what

u cant do that

[green vault]

fuck mb

idk what i was thinking

[flat ibex]

lol

first rewrite radicals

should be easier

[green vault]

ookok

(x+x^3/2)^1/2

[flat ibex]

oh wait this does work out mb

u can do u sub from there

u = sqrt a

[green vault]

hm

lemi try

[green vault]

u got me rethinking if i knew math at all 🥀

@flat ibex

[flat ibex]

ya

[green vault]

got it thanks

[flat ibex]

now just sub back

[green vault]

i just didnt spot the root a to sub lol

thank ya

.close

[devout snow]

Channel closed

Closed by @green vault

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[green vault]

.reopen

[devout snow]

✅ Original question: #help-27 message

[green vault]

@flat ibex i have diff qn

integration (sin^8(x)+cos^8(x))/(1-2*sin^2(x)cos^2(x))

[sharp garnet]

!noping

[devout snow]

Please do not ping individual helpers unprompted.

[green vault]

oh my bad

[sharp garnet]

$\int \frac{\sin^8 (x)+\cos^8 (x)}{1-2\sin^2 (x) \cos^2 (x)} dx$

[green vault]

yes

thanks

[woven radish]

Ishmam

[sharp garnet]

the bottom part is equal to $\sin^4 x + \cos^4 x$

[woven radish]

Ishmam

[green vault]

how

thats where im getting confused over and over

other than that i got the question

[shadow bear]

(sin2 x + cos2 x)^2 = 1

[sharp garnet]

you can check for yourself by applying square formulas

[green vault]

uh sin(2x) or sin^2(x)

[sharp garnet]

$a^2+b^2=(a+b)^2-2ab$

[woven radish]

Ishmam

[shadow bear]

squared

[green vault]

complete the square

ohk

got it @sharp garnet mb

silly mistake

thanks

.close

[devout snow]

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[devout snow]

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Remember:
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[pastel rose]

Could I please have help on part b?

[stone stump]

say f=sum a_i x^i and g=sum b_i x^i where g is in I

what can you say about the a_i and b_i?

take h=sum c_i x^i in R arbitrary

can you build h using f and some polynomials from I ?

[pastel rose]

Can we just add f and g?

[pastel rose]

They don’t have a constant so you can factor an x out

Wait so I can have g(x) = g(0) + xh(x)

[vital edge]

What do the units in ℝ[x] look like

[pastel rose]

They’re constant terms

[vital edge]

Good

So if you can produce a constant term in J you are done

(do you understand why)

[pastel rose]

If I can produce a unit then there exists its multiplicative inverse?

So then I just multiply them together to get 1?

[vital edge]

That doesn't exactly help here

[pastel rose]

Oh then I’m not sure

[vital edge]

Ideals aren't closed under multiplicative inverse technically

I mean they are but it's a circular argument

[pastel rose]

Oh yea

[vital edge]

Anyway point is

Oh nvm you said the right argument I just read it wrong

[pastel rose]

Oh what

[vital edge]

You get c in the ideal

c^-1 is in the ring

[pastel rose]

c?

[vital edge]

Then c ⋅ c^-1 = 1 is in the ideal

Let's say c is the produced unit

[pastel rose]

Oh alright

[vital edge]

And once you have 1 you have everything

So our goal here is to produce a unit

[pastel rose]

Yea this is just property of an ideal right?

[vital edge]

Yes

[pastel rose]

c is in the ideal, c^-1 is in the ring

[vital edge]

What does a polynomial not in I look like

[pastel rose]

f(0) !=0

[vital edge]

I mean yea but what does the polynomial itself look like

As a hint, what does a polynomial in I look like

[pastel rose]

Oh u can have a constant, so have it such that it’s of this form

A polynomial in I looks like g(x) = sum a_i x^i

but a polynomial not in I

h(x) = constant + sum b_j x^j

[vital edge]

Ranging over what values of i

[pastel rose]

Yep

[vital edge]

That wasn't a yes no question

[pastel rose]

Oh lol I thought u said ranging over values of x

I mean from 0 to inf?

No

Wait yes

[vital edge]

No

[pastel rose]

No

Greater than 1

Equal to 1asw

[vital edge]

Firstly a polynomial is by definition a finite number of terms

Yeah so i ranges from 0 to some n

Anyway now take some polynomial that isn't in I

[pastel rose]

Wait but if it range from 0 to n then x^0 would give a constant which u can’t have in I?

[vital edge]

Oh shit sorry I meant 1 to n

Lmao

[pastel rose]

Yea alright that makes sense

[vital edge]

^^

It looks like $\sum_{i=0}^n a_i x^i, a_0 \neq 0$

[pastel rose]

Yes

[vital edge]

Now how do we get smth from this that is in I

Actually hold on

[pastel rose]

it will be a_0 plus smth in I

[woven radish]

Xavier 🌺

[pastel rose]

Alright

[vital edge]

Good

So since J is an ideal it is closed under addition and subtraction

[pastel rose]

So that means this is in J?

[vital edge]

We assume that it is in J

Okay let me clear the steps here

1. Assume there is an ideal J that contains I as a proper subset
2. Pick a random element in J that isn't in I (why can we do this?)
3. Produce a unit

[pastel rose]

2. we can do it because I is a proper subset of J

[vital edge]

Yup

[pastel rose]

Alright so when u say produce a unit, that unit in out case is a_0

How does that show that 1 is in J?

[vital edge]

Yes

[vital edge]

Same argument as before

a_0 is in J

a_0 has an inverse in R

[pastel rose]

Oh and since J is an ideal

[vital edge]

Yes

[pastel rose]

a_0 * 1/a_0 =1 which is in J

Ahhhh yes tysm Xavier

.close

[devout snow]

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[devout snow]

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[devout snow]

Channel closed

Channel closed due to the original message being deleted.
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as this action is irreversible, and this channel may abruptly lock.

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[rare wagon]

?open

[rare wagon]

<@&286206848099549185> guys wanna see my today algebra paper?

[true coral]

You did 2 things wrong

well, 3

[rare wagon]

How

[modern wind]

Bro can someone help me with fractions

Its so confusing

[true coral]

first of all, there is no open command, the command opens when you send a message

[rare wagon]

Are you European?

[true coral]

second, you need to send your question, not ask if someone can check it out

[half comet]

your execution date is set for tomorrow

[true coral]

don't "ask to ask"

[modern wind]

Yes

[rare wagon]

How

[half comet]

Send your problem atleast?

[rare wagon]

What country?

[fast estuary]

you just pinged half of this server

[true coral]

third, read the bot message: You may ping the helpers role once after 15 minutes

[modern wind]

France

[true coral]

not immediately at the beginning of the channel to get help

[fast estuary]

@rare wagon what is your problem?

[true coral]

I honestly cannot tell if you're just highly careless or a troll

[fast estuary]

like fr

[rare wagon]

The mcq

[true coral]

like sure these are all mistakes you could make on accident

but 3 at the same time feels intentional

[true coral]

You need to open your own channel, not hop into someone else's

See #❓how-to-get-help

[rare wagon]

.

[modern wind]

K

[rare wagon]

<@&286206848099549185> help me with mcq

[true coral]

bro

you gotta be kidding

[fast estuary]

I swear bro is there any mod

[rare wagon]

No?

[jaunty bane]

I don't think it's a wise idea to rapidfire ping Helpers

[true coral]

<@&268886789983436800> There's a genuine chance the user above is acting in good faith but 4 mistakes in one go is suspicious

[jaunty bane]

also, which one of the four mcqs anyway? and what have you tried? gotta be specific, OP.

[true coral]

^

[true coral]

^

[rare wagon]

Today that is my paper

[true coral]

Not only did you do it once, but you did it again after I told you you shouldn't

[fast estuary]

you need help exactly on what?

[rare wagon]

Tellme the answer

[jaunty bane]

what did I ask and what did you answer?

[jaunty bane]

!noans

[devout snow]

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.

[fast estuary]

..

[fast estuary]

there

see?

[winter torrent]

let's have you take 5-10 minutes to read over the helpful instructions at the beginning of the thread #help-27 message

[rare wagon]

Correct me i f i am wrong
1 ans mode
2 B
3 B
4 B

[jaunty bane]

question 2 is cut off

questions 1 and 4 are guaranteed incorrect

question 3 requires knowledge of the GST rates in your country, which I have no idea.

[devout snow]

@rare wagon Has your question been resolved?

[rare wagon]

No

[fast estuary]

so what is your question?

again

[jaunty bane]

I'm only going to show as much effort as you have, so if you don't even make an effort to reply or show why you've selected certain answers... yeah.

[vital edge]

It looks like these are problems from a textbook. I would suggest reading through the text.

[devout snow]

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[devout snow]

Available help channel!

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Remember:
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• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
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[uncut hatch]

help

[fickle magnet]

yes

what happened

?

[uncut hatch]

i need some help on this problem

[fickle magnet]

do you know the formula of surface integeral?

[uncut hatch]

yes do you want me to send a picture of the formula

[fickle magnet]

no just i wnted to ask

did u grt r alpha and r beta

[uncut hatch]

i haven’t done anything for this problem i’m just stuck not knowing what to do

[fickle magnet]

send the picture of formula that u know

[uncut hatch]

it’s the a = double integral one

[fickle magnet]

yes

[fickle magnet]

yes but there is one more form of that formula

[uncut hatch]

there is?

[fickle magnet]

this is for surface

that one is for a para meter surface

lemme pull it up for you

on min

one

[uncut hatch]

ok

[fickle magnet]

it finally becomes in the formula u wrote

top one is the starting point

[uncut hatch]

ok i see

[fickle magnet]

see where r=(x,y,z) is written

we have something like thaat given in wues

ques

[uncut hatch]

ok

so how do i even start this problem?

[fickle magnet]

yeah

so one we find partial diff of the parameter give wrt to eavh variable here alpha and beta

[uncut hatch]

so i partial derive alpha and beta?

[fickle magnet]

with respect to alpha and beta

yea

[uncut hatch]

so if i did that i would get what ? cause am i deriveing it from the r(a,b) = ( a+b) or the top where it says a^2?

[fickle magnet]

pardon?

i didnt quite get u

[uncut hatch]

like where do i start the problem

[fickle magnet]

in your formula there are partial derivatives

[uncut hatch]

the at the D= or the r(a,B) =

[fickle magnet]

oh that D is jut=st specifying the boundary

like u have a parameter it is just telling where to start and stop

we start from r(a,b)

[uncut hatch]

yea and in the problem btw that less than or equal to the one is supposed to be a zero

[fickle magnet]

it cant be

squares are positive always, so if they are less than 0 the alpha=0 and beta=0

[uncut hatch]

idk that just what my professor said

[fickle magnet]

nope i think u heard wrong

did u partially diff the whole thing with alpha and beta?

[fickle magnet]

u wrote less than equal to 0

[uncut hatch]

oh i see now

[fickle magnet]

yea

[uncut hatch]

ok that makes more sense

i did not partially diff the whole thing yet

[fickle magnet]

yea do it and plug it in the formula u wrote

[uncut hatch]

ok

do i have to use the jacobian to derive it

[fickle magnet]

use this one only

i said it first because i use the original one

[uncut hatch]

so it would be 1,1,b and 1,-1,a

[fickle magnet]

oka yeah

mb

[uncut hatch]

so it is right?

[fickle magnet]

yes

now

u do cross product right

?

[uncut hatch]

yes\

[fickle magnet]

yea so do it plaese

then we will find the magnitude

what?

[stable aurora]

sorry

[fickle magnet]

hello, ghost?

[uncut hatch]

yes

im doing the cross product now

[fickle magnet]

okay

[uncut hatch]

(a+B)i + (B-a)j + (-2)k

[fickle magnet]

yes its magnitude is?

[uncut hatch]

root 2(a^2 +B^2 +2)

[fickle magnet]

yes

now they said its a quater disk

did you ever change variables in r cosx AND r sinx?

for polar coordiantes

[uncut hatch]

i have like once its very confusing to do that

[fickle magnet]

a min ill send u a pic

[uncut hatch]

ok

[fickle magnet]

in a cicle we can express any point a r and thetha

[uncut hatch]

yes

so basically i would just change A into r cosx and B into r sinx

[fickle magnet]

yea exactly

[uncut hatch]

is it r cosx or r cos theta

[fickle magnet]

and dA as?

[fickle magnet]

same thing any varible for angle

thake thetha tho

[uncut hatch]

ok

and wdym dA?

[fickle magnet]

what bout this

dA will become?

[uncut hatch]

root 2(r^2 +2)

[fickle magnet]

no

[fickle magnet]

that thing will become that only

[uncut hatch]

idk what dA would become then

[fickle magnet]

i ll send a pic

[uncut hatch]

ok i see now

[fickle magnet]

so final integeral becomes

?

[uncut hatch]

double integral root 2(r^2 +2) r dr d theta

[fickle magnet]

limira of thetha are?

limits of r is?

[uncut hatch]

0 to 1

[fickle magnet]

and thetha limits?

[uncut hatch]

0 to 2 pi

or is it pi/2

[fickle magnet]

pi/2

as it is quarter disk

[uncut hatch]

ok yes

[uncut hatch]

yes

[fickle magnet]

so can you integerate this

?

[uncut hatch]

yes im working on that

[fickle magnet]

no limit of radius is 0 to r

sa now after typo the alpha and beta not bounded

[uncut hatch]

ok so what do now

[fickle magnet]

put r instead of 1

[uncut hatch]

wait so i cant integrate it cause the bound is 0 to r

[fickle magnet]

i mean R

[uncut hatch]

so what do i do now

[fickle magnet]

take R as a constant

[uncut hatch]

ok can you show me what i would do

[uncut hatch]

so i plug in R for r?

[fickle magnet]

yes

[uncut hatch]

so id get get the same thing just with R in it

but with +2

[fickle magnet]

meamns?

[uncut hatch]

idk what the means tbh like does it mean i cant finsih the surface area

[fickle magnet]

it means it gives the equation of surface area of a R radius quater disk

is the exam subjective?

[uncut hatch]

what do you mean by subjective

[fickle magnet]

i maean are all answers numerical

?

or some are in form of equation too?

[uncut hatch]

all are numberical i believe i havent had one not as a number yet

[fickle magnet]

ok first integerate

once we get ourl equation we can think what values can r take and plug in accordingly

[uncut hatch]

ok well check and see if this surface area is right A = pi/6 ( 3 root 6 - 4)

[fickle magnet]

yes

when u took r as 1

R as 1

hlo?

hlo>

ghost

[uncut hatch]

yes

[fickle magnet]

did u get

?

flux is (vector field).(normal)

we have vector field in ques

and u found normal vector, befre magnitude

dot them up

subs r cos thetha and r sin thetha

same limits and integerate

[uncut hatch]

yes

[fickle magnet]

👍

[devout snow]

@uncut hatch Has your question been resolved?

Channel closed

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[brisk finch]

Hey there
How do I interact with these exponents?

[brisk finch]

I know that if they were saying -1, I'd just have to flip the thing upside down

But what about these

[soft umbra]

Do you know what is $2^{-1}$ equivalent to in the first place?

[woven radish]

Entitled Scumbag

[lunar harbor]

hi

[soft umbra]

Hi helpful

Wish I can become one someday 😔

[brisk finch]

1/2?

[soft umbra]

How about $(\frac12)^{-1}$

[woven radish]

Entitled Scumbag

[brisk finch]

1/0,5?

[soft umbra]

Can it be simplified further?

[brisk finch]

1×2?

[soft umbra]

Right

So this is how it works, if the exponent is negative, we swap the denominator and the numerator

So far so good?

[brisk finch]

Yep

[soft umbra]

Here’s an example
$2^{-2} = (\frac12)^2$

[woven radish]

Entitled Scumbag

[brisk finch]

Why does it work this way btw?

[soft umbra]

If I weren’t mistaken, that’s how they are defined

But lemme double check it rq

okay, I’ve found a good way to explain this

Let’s take
$2^4$ as $2\times 2\times 2\times 2$

[woven radish]

Entitled Scumbag

[soft umbra]

Do you agree with this?

[brisk finch]

Yep

Yeah

[soft umbra]

So the exponent mean how many times should we times

When it’s “negative”, that means we have to “take away” instead of adding up

[brisk finch]

So it becomes division?

[soft umbra]

For example
$2^{-4} = 1\div 2\div 2\div 2\div 2$

[woven radish]

Entitled Scumbag

[soft umbra]

Yes

[brisk finch]

Hm

[brisk finch]

Where did that 1 come from?

[soft umbra]

$1\times 2^{-4} = 1\div 2\div 2\div 2\div 2$

[woven radish]

Entitled Scumbag

[soft umbra]

yeah, cuz you need to put something before the division sign

So the 1 cannot be omitted on RHS

[brisk finch]

Why do we change the symbol for 1? 1 isn't a part of 2^-4

Well, we didn't change the sign for the 1

But we changed the action

[brisk finch]

Why not just 2^-4 = 2 : 2 : 2 : 2?

[soft umbra]

Ah I see what you mean

[soft umbra]

By this logic, what would be 2^(-1)

[ocean gale]

Noice evernight pfp

[soft umbra]

Let me clarify it real quick

[brisk finch]

Thanks!
Nice Navia pfp :3

[soft umbra]

For multiplication, there also exists a 1

But got omitted as well

[ocean gale]

Thanky :)))

[soft umbra]

Let’s take
$1\times 2^4$ as $1\times 2\times 2\times 2\times 2$

[brisk finch]

I understand that
Because it wouldn't change anything

[woven radish]

Entitled Scumbag

[brisk finch]

2 = 1 x 2

[soft umbra]

yep

[brisk finch]

-2 = -1 x 2

[jaunty mantle]

Well to be honest, $\left(\frac{1}{3}\right)^{-3}$ kinda doesn’t make sense in this way

[woven radish]

frosst

[jaunty mantle]

Division is a sham and doesn’t really exist

What it’s really saying is $\left(\left(\frac{1}{3}\right)^{-1}\right)^{3}$

[woven radish]

frosst

[jaunty mantle]

First you look at the multiplicative inverse of 1/3, then multiply that with itself 3 times

The multiplicative inverse of 1/3 is the number when you multiply with 1/3, yields 1 (here it will be 3)

So then it becomes 3³ which is 27

[brisk finch]

So

This = 3/1³ = 3³ = 27?

[jaunty mantle]

Sure

Brackets though

(3/1)³

[brisk finch]

Why

[jaunty mantle]

But you can just say the inverse of 1/3 is 3

[jaunty mantle]

Look at what I wrote the ^3 is on the outside of the 2nd bracket

[brisk finch]

So if the brackets weren't there people would be like "oh it's actually 3/1x1x1"?

[jaunty mantle]

Yes

[brisk finch]

Thanks

.close

[devout snow]

Channel closed

Closed by @brisk finch

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

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[hybrid elk]

im lost on what exactly we're doing after we note that H5 and H2 are cyclic

[hybrid elk]

this is in discussion w/ sylow's thm

figured it outtt nevermind!

.close

[devout snow]

Channel closed

Closed by @hybrid elk

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[devout snow]

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 heath]

hi i need help finding the derivative

[empty heath]

im aware that i take the 6 and move it up front causing there to be 6 times 5 sin^5 (4x)

and then i take the derivative of sin (4x) which is cos (4x) times 4

and i then have

30 cos^5(4x)

oops

forgot to multiply by 4

so 120 cos^5 (4x)

im not sure what i did wrong

[rain summit]

chain rule

if $h(x) = f(g(x))$ then $h'(x) = f'(g(x)) \cdot g(x)$

[woven radish]

1 divided by 0 equals Infinity

[empty heath]

where am i applying that

though

[rain summit]

so for $\sin{4x}$ first

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

then $5\sin^6(4x)$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

chain rule on this first

[rain summit]

then on this

hope that helps

[empty heath]

yes

ty

[rain summit]

glad i can help you

especially when im self-learning derivatives

[empty heath]

one thing

i just dont get

imma send my work

rq

hold on

[steel sage]

f=g•h•k, k(x)=4x, g(x)=5x, h is of the form p^n, use induction to find (p^n)’

((p^n(x))’=p’(p^(n-1)(x))(p^(n-1)(x)’, so you see it will be a factorial ish product in the end)

[empty heath]

mb im fresh off bio

going back and doing these for the finals is frying me

idk how i forgot this stuff

thank you guys tho

🙏

[rain summit]

np

!done

[devout snow]

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

[empty heath]

.close

[devout snow]

Channel closed

Closed by @empty heath

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Remember:
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• 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.

[neat spruce]

asking for help again for these questions since i forgot about my last ticket 😭

[neat spruce]

i don't really know where to start

[devout snow]

@neat spruce Has your question been resolved?

[neat spruce]

<@&286206848099549185>

[uneven coral]

which one is it?

[uneven coral]

okay what have you tried in 15. ?

[neat spruce]

my math teacher said to find corresponding height and base for each triangle

[uneven coral]

Alright, so what all sides have you found?

[neat spruce]

i can't find any ough

[uneven coral]

okay so we know AC and CF to start with, what should AF be?

[subtle thorn]

Basically, first of all you have to write in sequence, the corners, which correspond. Like in 16th, in triangle ABE and triangle FAC , A=A, E=F, B=C... Therefore, triangle(AEB) ~ triangle(AFC) .. Once you get to this, you can safely write, AE/AF = AC/AB.. Or any possible combination accordingly .. Hope it helps

[neat spruce]

hmmm i see

[uneven coral]

TBH a combination of yours and mine method would be the fastest

okay first find AF

[neat spruce]

ok hold onnn

[subtle thorn]

Instead of wondering what to find, just start finding anything you can

especially in geometry

[neat spruce]

i got af = 4.47214 cm?

[uneven coral]

sqrt(20), yes

okay, now prove similarity between triangle(AEB) and triangle(AFC) like mate here said

[neat spruce]

similarity?

[uneven coral]

wait do you know about similarity and congruency yet?

[neat spruce]

i don't think so

[uneven coral]

ahhhhh

[subtle thorn]

wait, how old are you

[neat spruce]

i acc think i learned it b4 but forgot the terms

im in 9th grade but haven't started math yet since my school has a semester system

this is extracurricular stuff

oof

[uneven coral]

So can you use it here, we can't use it if you've never studied it before

[subtle thorn]

I didn't know this, sorry for the friend request I sent you

[neat spruce]

OH i just looked it up and i remember it now

[neat spruce]

oh no worries lol

similarity is same shape diff size

[uneven coral]

Are you sure, we can use another method if you're not supposed to use similarity, it'd be a bit longer

[neat spruce]

no its ok 👍

[uneven coral]

Alright then

so now prove similarity between triangle(AEB) and triangle(AFC)

[neat spruce]

lemme do that rq

[uneven coral]

sure (Hint:VOA and right)

[neat spruce]

wait nvm im rusty 😭

[uneven coral]

Alright, so do I help you here with it or the other method?

[neat spruce]

with the similarity method please

[uneven coral]

sure

Okay so one method we use for similarity is the AAA method (or simply AA method)

where we prove that the angles are equal

when we've proved that 2 angles are equal, we can say that the triangles are similar

So tell me, which angles in these two triangles are equal?

[neat spruce]

the right angles?

they're congruent

[uneven coral]

I mean not congruent

they're equal

[neat spruce]

is there like,, a difference between congruent and equal?

[uneven coral]

so that's one pair, with our reasoning being that they are both right angles

[subtle thorn]

its all about congruent and similar

[uneven coral]

congruent might refer to something else

[subtle thorn]

yes

[uneven coral]

No they're asking about the right angles being equal or congruent

there ig equal would be more appropriate

[subtle thorn]

Ohh okay

yes

I thought its about triangles being equal, nevermind

[neat spruce]

ahh ok

so we have afc = aeb

[uneven coral]

yes, write (right angles) next to it

now are you aware of Vertically Opposite Angles?

[neat spruce]

ya, these

[uneven coral]

yes

[neat spruce]

so do i have to prove those as equal as well?

[subtle thorn]

No you can simply write a=b {vertically opposite angles}

[uneven coral]

I mean you just have to identify angles that are like this and write "Vertically Opposite Angles" in brackets next to it

[neat spruce]

ahhh uhuh

ok

ok so we have the vertically opposite angles and the right angles?

[uneven coral]

Yes

which angles are vertically opposite?

[neat spruce]

ÂEB and ÂFC?

[uneven coral]

No, those were right angles

[subtle thorn]

He/she has actually put a cap

on A

[uneven coral]

which two angles in those two triangles look like this

[subtle thorn]

indicating angle A

[uneven coral]

I see, okay then

So we have two angles that are equal, hence the two triangles are similar

[neat spruce]

yay

[uneven coral]

now which two pairs of sides do we use for this?

[summer ridge]

The left side and the right side

[uneven coral]

Sorry but the question was meant for op

[summer ridge]

What does op mean

[subtle thorn]

Redditor?

[uneven coral]

the person who asked the question basically

[summer ridge]

Oop sorry

[neat spruce]

me

[uneven coral]

Nope, just acquired it from here

[subtle thorn]

oh alryt

[summer ridge]

Ok can somebody teach me how fractions work

[uneven coral]

you can open a new channel for that

[subtle thorn]

that's not how you ask, go to an available channel

[uneven coral]

Dude

[summer ridge]

Who do u think u are

[neat spruce]

means original poster i think, anyways is it sides eb and fc?

[summer ridge]

I’m not tryna make enemies

U sassy ass guy

I’m jk

I luv u

[uneven coral]

Whatever it is, kindly do not fill someone else's help channel with slop

[neat spruce]

son 😭😭 ur like supposed to ask ur question in like https://discord.com/channels/268882317391429632/359052604149465088 ig

its free atm

[summer ridge]

Shut up

[uneven coral]

okay then

Anyways he's gone, let's continue

[summer ridge]

I’m not

U doctor stranger

[uneven coral]

<@&268886789983436800> disrupting someone else's help channel with bs

[winter torrent]

busy but I muted for a while

[uneven coral]

Alright thanks mate

okay, let's continue

which two pairs of sides do we use here?

[neat spruce]

uhhhhh eb and fc?

[uneven coral]

Not like that

okay see

if any two triangles ABC ~ DEF, then AB/DE = BC/EF

so ratios of any two corresponding pair of sides are equal

[neat spruce]

yup

[uneven coral]

Okay, so which two pairs do we use (Hint : try to use the ones that includes the side we're trying to find and the sides we already know)

[neat spruce]

uhhh eb ab and ac cf?

ough im stumped

[uneven coral]

Okay I'll help you with this one

so AEB ~ AFC

we use EB/FC = AB/AF

EB we're trying to find

it's corresponding side in AFC (whose value we know)

and AB and AF because they're corresponding sides and we already know their value

now just put in the value of FC, AB and AF here, and you would have EB

If this confuses you then we can do it with another method too

[neat spruce]

is eb 14.47cm?

WAIT

8.47cm?

[uneven coral]

I got 3.6 sqrt(5)

let me put it on a calculator

8.05 cm

[neat spruce]

damn where'd i get the extra .42 from 😭😭

[uneven coral]

okay it's 36/4.47214 yes?

[neat spruce]

yea

[uneven coral]

Nope, even still I'm getting the same result

8.0498, which I rounded to 8.05

[neat spruce]

oof so where did i go wrong

[jaunty bane]

when a discrepency occurs, it's best to show your working to see how you got here

[uneven coral]

did you calculate it by hand or did you use a calculator?

[neat spruce]

i like added 9 cm with 4.47

then subtracted 6 from that

uh

[uneven coral]

what

why

you have ratios, so you multiply or divide, specially when you know the values, why would you add or subtract

okay let's do it step by step

we had

$\frac{EB}{FC}$ = $\frac{AB}{AF}$

[woven radish]

doctorstrangejr

[uneven coral]

we know that, $FC$ = 4,
$AB$ = 9,
$AF$ = sqrt(20) or 4.47214

[woven radish]

doctorstrangejr

[neat spruce]

hmm uh huh

[uneven coral]

okay, now we put in the values

[jaunty bane]

(quick hint: if you wanna quickly stick newlines in latex, stick two backslashes \\ at the end of a line, in case that was what you needed
sorry to interrupt for this and sorry if that was not what you intended)

[uneven coral]

$\frac{EB}{4}$ = $\frac{9}{4.47124}$

[woven radish]

doctorstrangejr

[neat spruce]

OH

[uneven coral]

No no you're fine, thank you, I tried to do that but I gave up after seeing that it got the idea across

[jaunty bane]

ah okok

[uneven coral]

now we send 4 to the other side

EB = $\frac{9*4}{4.47124}$

[woven radish]

doctorstrangejr

[neat spruce]

wait hold on short afk be back in 15 ish minutes!

[uneven coral]

Sure

[neat spruce]

my mom's calling me upstairs

[uneven coral]

yeah no problem, take your time

ping me when you're back (incase I don't respond you can wait for someone else)

[jaunty bane]

which question is this? I'll stand by if necessary

[uneven coral]

15th one, we're yet to do 14

[jaunty bane]

sure thing. how did you establish similarity there, if I may ask?

just wanna make sure I'm not drunk in case I step in

[uneven coral]

between AEB and AFC, angle A through VOA and angle E&F through right angles

[jaunty bane]

ah gotcha

[neat spruce]

ok back!

more like 30 minutes 😭

@uneven coral

[jaunty bane]

welcome back

[soft umbra]

$\frac{\overline{EB}}{4}$ = $\frac{9}{4.47124}$

[woven radish]

Juggernaut

[soft umbra]

For reference

[uneven coral]

Alright thanks mate

[uneven coral]

you still here?

[neat spruce]

yea, sorry for the wait!!

[uneven coral]

no problem

[uneven coral]

you got it until here?

[sturdy fiber]

If math branches were chess pieces, what would each branch be?(considering multiple knights, horses, etc)

[jaunty bane]

!occupied, also this kind of questions would be best in #discussion or #chill.

[devout snow]

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).

[sturdy fiber]

oh sorry i didnt realise

omg

[jaunty bane]

nw

[sturdy fiber]

no wonder no one was talking

[devout snow]

@neat spruce Has your question been resolved?

[uneven coral]

Well, I have to go out in 48 minutes, in case op isn't here by then, if they return later then someone else can help them

[jaunty bane]

I'm still here on standby and waiting for OP to resurface

[soft umbra]

They’re not likely going to come back

just say adieu and call it a day

[jaunty bane]

there they are

[neat spruce]

i have to go to bed, so sorry guys

[soft umbra]

Good night

[neat spruce]

thank u very much for ur help tho very appreciated!

[jaunty bane]

see you around next time!

[soft umbra]

.solved

[devout snow]

Channel closed

Closed by @soft umbra

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Remember:
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• 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.

[uneven coral]

.whoops looks like I missed out

[devout snow]

Channel closed

Channel closed due to the original message being deleted.
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as this action is irreversible, and this channel may abruptly lock.

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[smoky gyro]

Hello

[smoky gyro]

A dice is rolled one time. What is the probability of rolling a 2 or a 6?

[dry oxide]

what have you tried so far

[errant harbor]

Is it weighted?

[vagrant skiff]

[smoky gyro]

Yes the Dice weighs 0.25g

[vagrant skiff]

[smoky gyro]

why are you sullying me

[smoky gyro]

its 1/6

[vagrant skiff]

.close

[smoky gyro]

i got 1/6

[errant harbor]

Water beam wth

[smoky gyro]

you dont have helpful

[errant harbor]

[smoky gyro]

you cant close it pure

[errant harbor]

Ur an undergraduate

[dry oxide]

blud thinks blud has helpful

[vagrant skiff]

[sand quarry]

Don't troll in the help channels, please!

[errant harbor]

Just close this

[sand quarry]

.close

[devout snow]

Channel closed

Closed by @sand quarry

Use .reopen if this was a mistake.

[smoky gyro]

P(a or b)

[mystic scarab]

That would mean that it's the same probability of having only a 2. That's quite weird, right?

[dry oxide]

it might be a genuine question though

[smoky gyro]

yes because probability is from 0 to 1

[sand quarry]

Yeah just dont read obsidian

[mystic scarab]

Exactly, this is the formula needed

[errant harbor]

Water beam is an undergraduate dude

[mystic scarab]

Mmh so? I don't get your statement

[smoky gyro]

P(a or b) = P(a)P(b)?

[faint gorge]

add

[dry oxide]

he sucks in probability though

[sand quarry]

Blud is trolling you. Dont bother

[mystic scarab]

Nope

[smoky gyro]

P(a) + P(b)

[errant harbor]

He's trolling

[smoky gyro]

Stop

1/6 + 1/6

[dry oxide]

maybe we should mod ping then

[mystic scarab]

I don't think so at all, he always behaves correctly

[smoky gyro]

so its 2/6

= 1/3

[sand quarry]

As if you wont get screwed over by it too yajat

[smoky gyro]

Thank you alberto

my doubt is cleared

[devout snow]

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[zinc mirage]

is f(x) is continuous in all real numbers?
"ve" means "and"

[polar chasm]

(x^2 - m^2) / (x + m) can be simplified for x =/= -m

[zinc mirage]

since we gotta find out if the f(x) is continous or not, we just gotta give the value m to the x and since the m is element of all real numbers, shouldn't we can just assume its continous

[polar chasm]

What?

no

how does m being a real number imply that its automatically continuous?

[zinc mirage]

i see

[zinc mirage]

no like i was trying to say
if the x is equal to m or -m, the function will be having a value at every number that we provide

its been a really long time i study lim

im trying to re-learn it

in the book, it says

"Since its like that, the f(x) function is is continous"

[polar chasm]

huh

it should be to -m

and to m

the lim should be to both

is there somethign else

or is it the whole solution

can u send the book's full sol

[zinc mirage]

Genuienly its the whole solution 😭

let me show

[polar chasm]

and the full question?

does it really ask exactly this "is f(x) is continuous in all real numbers?"

[zinc mirage]

It asks "Is f function continous in the x=m? absolutely"

third one

question asks "Which are ABSOLUTELY CORRECT"

[polar chasm]

Okay, so it asks only for continuity at m. Not at all real numbers

[zinc mirage]

yeah

[polar chasm]

so the criterion for continuity at some point m is that:

1. the limit x->m f(x) exists
2. the limit equals f(m)

so you need to find the limit x->m f(x)

what's the limit?

[zinc mirage]

it asks is the f function is contunious in the m
f(m) is equal to the 0 so thats fine
i gotta find out the limit from left and right

to find out if its continous

my friend says "you can't make it continous at the values that is at right and left of -m"

[polar chasm]

he is right

if he means "you can't make it continuous at -m"