help-36

[still drum]

uh

choose small enough epsilon

that it does

well you can choose $\epsilon = \frac{\epsilon_\lambda}{4}$

[soft zealot]

lifelong dumbass

[still drum]

since it was arbitrary

[opaque ember]

that works, so does /3

[still drum]

the result is going to be positive

mmm ok thanks

[opaque ember]

if u use /3 it looks very similar to the proof of fn cont => f cont 😉

[still drum]

oh yea

huh ok

[still drum]

ohh ok

oops

well we got there anyway

[opaque ember]

go ahead with /4 anyway, its not very important

[still drum]

yea

thanks

[opaque ember]

np!

[still drum]

hey do you think this argument works the same way

cause i realise that they're really similar

or if theres anything i could add

[opaque ember]

maybe but im kinda lazy to fully think it out haha

[still drum]

its ok lmao

(man analysis really does fuck you in the head huh)

[opaque ember]

mhm epsilon is pretty hard bc the million quantifiers

[still drum]

uniform convergence is hard because like

you have to worry about two things

instead of just one

[opaque ember]

yep u drown in quantifiers

[still drum]

yea ok

ill close this channel now

thanks so much again

.close

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[opaque ember]

less quantifiers in PDEs, more fun

[final saddle]

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[jagged flare]

i feel wierd on changing a divergent function to a convergent function, then back to a divergent function

how can you do that?

it feels like it defies what i know on functions

[desert mantle]

generating functions dont care about convergence

[final saddle]

@jagged flare Has your question been resolved?

[jagged flare]

eugh thats wierd

alr ty

.solved

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[desert mantle]

are the functions here even divergent

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[bitter zenith]

National geometry olympiad tomorrow, what should i do

[bitter zenith]

send tips plz

[worldly mesa]

Get good sleep

[umbral steppe]

do you have any questions you are stuck with?

[livid solar]

Win

[tired walrus]

sleep.

[bitter zenith]

3.30 hrs and 3 problems

sleep or practice?

[livid solar]

Sleep

[severe canyon]

Sleep, for sure

[bitter zenith]

it's my first time coming so far to national olympiads

kinda shy

[livid solar]

Stress tomorrow

Sleep tonight

[bitter zenith]

what food is recommended

dark chocolate?

[worldly mesa]

Thats good

But not too much

Bring also real food

Sandwitch/hot meal

Maybe a fruit

[bitter zenith]

ah yes

[livid solar]

Dark chocolate is okay if you only eat 1 or 2 squares

[bitter zenith]

what about during the olympiad?

[worldly mesa]

Water

[bitter zenith]

should i start from the easiest?

[worldly mesa]

Start from what you can solve

[bitter zenith]

only 3 problems kinda wild bru

[livid solar]

Eat 2 squares of dark chocolate so you can get the benefits of flavonoids increasing blood flow to the brain without the excess sugar

Solve what you can

[umbral steppe]

don't hesitate to put a question aside for later if you feel stuck doing it.

[bitter zenith]

Wow

[livid solar]

But tbh

That doesnt really matter

If ur that dude ull win regardless so get ur ass in bed and be well rested

[bitter zenith]

hell yeah

thanks for sharing yall

i will cook tonight

[livid solar]

[bitter zenith]

.close

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[ornate tree]

I need a quick confirmation, and I've read the definition of it.
Proposition is like a "claim", and it does not need to be true, is that correct?

[steep hatch]

Propositions can be false yes

[ornate tree]

Alright ty

.close

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[steep hatch]

Proposition: This is sad 😢 is bad at helping
is an example

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[arctic fiber]

What is the sin(x°) when there is rectangle ABCD and length of AB = 2,BC = 8 and CD = 4, and point E is on between point B and C?

[tired walrus]

and where is angle x?

show us a diagram

[tired walrus]

ok so ABCD isn't a rectangle

anyway i think the way to proceed would to be to find some measurements in triangle ADE -- the most straightforward imo is to find all 3 sides and then apply cosine law

[arctic fiber]

I tried flipping the triangle ABE to create a 90° triangle that has angle x°

[final tangle]

how are you flipping exactly?

[arctic fiber]

It creates new 90° triangle I think

Perhaps the 90° triangle formed by the intersection of the extended line of DE and the newly drawn line and points A and E is identical to triangle ABE

√20 / √68 was not an answer

[final saddle]

@arctic fiber Has your question been resolved?

[lime bison]

what is school like in korea?

[final saddle]

@arctic fiber Has your question been resolved?

[pallid birch]

Apply Pythagoras theorem in triangle ABE to get AE,
Apply Pythagoras theorem again in triangle DCE to get DE,
If you draw a perpendicular from point A on side DC(call the intersection F), you'll divide the line DC into 2-2 ratio. Now if you apply Pythagoras theorem in triangle ADF as well, you'll get the third side of triangle AED.

After that use cosine rule to get cos x -> sin x

[arctic fiber]

The heck is cosine rule?

[arctic fiber]

Then cos(x°) is (√32 + √68 - √20) / ( 2 * √32 * √20 )?

[pallid birch]

There is square in the numerator

[arctic fiber]

So the result is sin(x°) = (2 * √32 * √20) /( √((2 * √32 * √20)² - (√32 + √68 - √20)²))

[pallid birch]

Side opposite to the angle you take isn't there in the denominator.

So, cos x would be (68+32-20)/(2 * 8 * root(34))

Then just use the identity of sin & cos to get sin x

[arctic fiber]

I think I solved it

[pallid birch]

Nice 👍

[ripe jewel]

i find the following version easier to remember, btw:

a²+b²=c²-2ab cos(C)

because this reduces to Pythagoras when C=90⁰

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[slow vigil]

I was trying to solve a rational equation by eliminating the LCDs but I came across this problem & I can't figure out what went wrong🫠 I'd appreciate it if someone pointed out what I missed

[random ledge]

.xy

[faint locust]

Why is this a problem?

[random ledge]

!xy

[final saddle]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[faint locust]

Also what is that 4b^2 or 2b^2 on the right

You mean multiplying both sides?

[slow vigil]

Because there is a right answer that is 4

[faint locust]

I usually denote that as | *4b^2

[slow vigil]

But I got whatever is on the bottom

[slow vigil]

I multiplied the whole thing by 4b^2 first and then 2b^2

[faint locust]

On the right that should be 4b^3 + 16b^2

After the first multiplication

[faint locust]

Yeah, I usually denote it by | (...), if your class does it like this then it's fine

[slow vigil]

Ohhhh I see

Let me try it out

hol on

[faint locust]

!occupied

[final saddle]

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).

[faint locust]

Post this in e.g. #help-3; after the first message in that channel is from you, you automatically occupied it

[slow vigil]

It worked, thank you very much 🙂

.close

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[final saddle]

@ruby kiln Has your question been resolved?

[ruby kiln]

NOT YET @final saddle

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[craggy plank]

.reopen

[final saddle]

✅

[craggy plank]

Just click on ❌ next time

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@ruby kiln Has your question been resolved?

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[tranquil pine]

yo

[tranquil pine]

when we construct a line equation from 2 vecotrs, our domain on the graph becomes t right?

[plucky rover]

In the sense that you vary t to get all points on the line yes

In some sense, a line is a function in t, where the domain is ℝ and the range is the line

[tranquil pine]

and what makes us able to give it that domain? like as soon as we create the equation we just slam it on its own graph?

[ripe jewel]

same argument that justifies the real numbers being order isomorphic to a straight line in any context

it might be living in a 3d space, but it's still a straight line

[tranquil pine]

can you please elaburate on this a little more

real numbers being order isomorphic to a straight line in any context

[ripe jewel]

have you ever used a number line

or graph paper

im going to assume yes to graph paper

the axes are a representation of (a copy of) the real numbers, associated with an infinite line called the x-axis or y-axis

[tranquil pine]

yes

[tranquil pine]

also can you have 2 inputs on the same graph at the same time?

for example heres the question i was working on

i got up to this point

i had to construct 2 equations for the line

for each line

💀

i just need help finishing this off

thats it

i know i need to figure out if the lines interesect or not

so i equated the pointsa

[tranquil pine]

<@&286206848099549185> how do i solve for this

[willow tiger]

what

which one

[tranquil pine]

i need to solve for if the points equal one anothert

[willow tiger]

a, b or c

[tranquil pine]

heres the original work

[tranquil pine]

a

[willow tiger]

mhm

then you just see if Ax/Bx = Ay/By = Az/Bz

[tranquil pine]

wait i didnt get it

[willow tiger]

sorry

wrote it wrong

[tranquil pine]

its okay

[willow tiger]

so A0 is the starting position, A1 is the finish, the difference is supposed to be A

same with B

[tranquil pine]

are you saying i need to check if the lines are parallel

[willow tiger]

But in this specific case, we dont even need that because Ax is between 2 and 12, Bx is between 1 and -8

which means their x wont intercept

[tranquil pine]

i dont get this

i thought i was supposed to solve for something

like for s and t

[willow tiger]

determine if the 2 paths intersect

they wont because the x ranges dont

[tranquil pine]

yes but how do i do it the algebriac way

[willow tiger]

told you

[tranquil pine]

like by solving the equations

[willow tiger]

the x ranged dont intersect thus there is no way for the paths to intersect

[willow tiger]

idk about that you're overcomplicating

[tranquil pine]

well thats for practice

cause were gonna have questions like that on the test

and they might intersect

[tranquil pine]

can you please explain this

[willow tiger]

whats there to explain

[tranquil pine]

nevermind but how do i do the equation way

[willow tiger]

idk i have never done that

[tranquil pine]

its okay

thanks tho

[final saddle]

@tranquil pine Has your question been resolved?

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[gray yacht]

Hey @tranquil pine

[lethal totem]

?

[bold zenith]

Do you have a question?

[final saddle]

@gray yacht Has your question been resolved?

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[jagged flare]

why is this 1/2? shouldnt it be 1/4?

$\int\frac{1}{u^2+2^2}\dd u=\frac{1}{4}\int\frac{1}{(\frac{u}{2})^2+1}\dd u=\frac{1}{4}\tan^{-1}(\frac{u}{2})$ no?

[soft zealot]

ihave<skissue>

[supple ivy]

consider the constant from the change of variable / reverse chain rule

[vital crag]

are you asking about this step?

[vital crag]

you're forgetting du. do the proper u sub with v = u/2

[random ledge]

wait

on the right side it’s 1/2 not 1/4

$(1/2 \arctan (u/2))’ = 1/2 \times 1/2 \times {1\over (u/2)^2 + 1}$

[soft zealot]

Médicis

[random ledge]

therefore

$\int {du\over ({u\over 2})^2 +1} = 2 \arctan ({u\over 2})$

[soft zealot]

Médicis

[random ledge]

@jagged flare

[jagged flare]

oh yea i see

.solved ty!

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[obsidian rivet]

The triangle being stacked on top of a larger segment of a circle instead of a half circle kills me

[plucky rover]

Can you find AB

Like do you know how to

As a hint, read the note

[obsidian rivet]

yes but AB ≠ D or 2r

[plucky rover]

Yeah it isn't

[obsidian rivet]

I really dont know how to find another measurement

if I could, I could probably solbe it

[plucky rover]

Well

Let's start with drawing the image

Also mark the center of the circle and connect it to all the vertices of the triangle

[obsidian rivet]

lets mark the center of the circle as D

[plucky rover]

The convention is O, but do whatever you feel like

[obsidian rivet]

i thought of that I just dont know what to use and how to approach it from there

[plucky rover]

Well send the diagram after doing that

[obsidian rivet]

Forgive me for being bad at kt

at first, I was reminded of a problem where a lying cylinder and figuring out the volume of the water but this one for me really lacks given measurements 😓

[plucky rover]

It's okay

Now we know CA and CB are tangents

What does that mean

[obsidian rivet]

it rests on top of the circle? Is there anything else?

[plucky rover]

It's perpendicular to the radius at that point

[obsidian rivet]

Ohh so since

CA= OA
CB = OB?

[plucky rover]

...no

Perpendicular

So CAO is a right triangle

Same with CBO

[obsidian rivet]

no way really?

[plucky rover]

Do you have any ideas for what to do now

[plucky rover]

Yes that's what tangent means

[sick roost]

any tangent line to a circle is perpendicular to the radius

[plucky rover]

!nosols once again

[final saddle]

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.

[ivory bear]

I got it till here

[plucky rover]

Please let people make observations and solve things themselves

[ivory bear]

Well fine

Whatever you settle on

[plucky rover]

<@&268886789983436800> can one of you delete the solution posted please, thanks

[ivory bear]

I did it myself

Review it

[obsidian rivet]

Pythagorean theorem to find OC

[plucky rover]

Good

Can you do that

[obsidian rivet]

676

So 26

26cm

[plucky rover]

Good

Okay actually, have you done any trigonometry

[obsidian rivet]

actually none lol, they only introduced it to us and started throwing stuff like this

[plucky rover]

Hmm ok so that's off the table

Can you mark the intersection of OC and AB as something

[obsidian rivet]

D

[plucky rover]

Cool

Now we already know DA

We wanna find OD

Oh actually we don't know DA

Have you done congruent triangles

[obsidian rivet]

nope 😓

[plucky rover]

Interesting

How else are we supposed to show DA = DB

Tbf that should be a property you're allowed to use

[obsidian rivet]

We dont know D yet, do we? How do I get it

[plucky rover]

The line joining the point and the center perpendicularly bisects the line connecting the tangent points

[plucky rover]

Well D is the intersection point of OC and AB

[obsidian rivet]

I mean OD

[plucky rover]

And then we use this cuz I'm assuming you're allowed to use it

We don't know OD no

We're trying to find DA and DB here

[plucky rover]

Use this

[obsidian rivet]

i'm sorry what?

[plucky rover]

I gotta leave to grab breakfast, someone else feel free to take over

[obsidian rivet]

Alr thanks!

[pliant shore]

just checking, so you're up to here so far right?

[obsidian rivet]

yes

[pliant shore]

ah, so you actually do need some right-angled trig

you want to find angle POB

[obsidian rivet]

P?

[pliant shore]

I've labelled the top point as P here

oh wait, that's what you've called C

[obsidian rivet]

We havent been taught trigonometry ☹️

[pliant shore]

oh no wonder

[obsidian rivet]

Should I just cry

[pliant shore]

well, you have these similar right triangles

DBO and DCB

ah you still need trig even then

you need to find the area of major circle sector AOB to continue

so that requires finding one of the angles in the diagram

[pliant shore]

maybe

,w arctan(24/10) in degrees

[soft zealot]

Results provided by WolframAlpha

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

Requested by sooouth.

[pliant shore]

alright, if I give you that angle DOB = 67.38 degrees, can you continue?

[ivory bear]

I sent the same pic and Xavier cried over it and made me delete it

What injustice

[pliant shore]

bruh

[plucky rover]

That was before she had solved it

Are you dumb or are you just acting like it

[obsidian rivet]

just r times sin 67.38? Idk im just guessing at this point

[obsidian rivet]

so 10 • sin (67.38°)

[pliant shore]

no, you're not using sin or cos or anything

[pliant shore]

what is angle AOD?
hence, what is major angle AOB (the one more than 180)?

[obsidian rivet]

Major angle?

[tulip coyote]

Can you not antagonise other helpers, and not send full solutions please

[ivory bear]

It doesn't work like that

This server bans/restricts full blown solutions and just impinges on the fact that the person who asked the question learns something rather than just seeing the solution and giving up much further thought on solving it

[obsidian rivet]

Can we go in a different approach and go on from finding OD then finding the chord AB 🥹

[pliant shore]

the issue is, that doesn't let you find the area of the circular sector

[plucky rover]

Yeah we really need the angle here

[plucky rover]

Once again, the reason for nosols is so that people can't just copy shit as homework solutions and not learn anything further

Having access to solutions can be a good thing for specific people sure. But we have no way of knowing that. And guiding people through the solution still leads to the same outcome without the risk of them copying it and moving on.

[ivory bear]

But south also made the same diagram which I had made and sent right? Why not ask him to delete? Why bias?

[plucky rover]

Holy shit

That was after she had already solved for all those values

NOT BEFORE

[pallid birch]

Alright guys, it's a help channel, let's keep it that way.

[ivory bear]

Ok

[plucky rover]

I'm just gonna modping and move on

<@&268886789983436800> hullo second time today

[steep hatch]

If you’d like to complain about server policy you’re invited to do so in meta, otherwise please keep help channels on topic. Arguments with other helpers are best done outside of help channel.

[ivory bear]

Fine @steep hatch

[obsidian rivet]

Is AOD the same angle as DOB then?

[ivory bear]

I won't repeat such insistent behavior again

[plucky rover]

That is correct as well

Let's step back a little

What properties of tangents do you know

Maybe you could send images of the parts of your book talking about it

[obsidian rivet]

actually, not that I look at it, there is none 😠 only identities

and formulas

[plucky rover]

Well those could help too

[obsidian rivet]

After finding out the angles, how do I proceed?

[plucky rover]

I gotta run to class now, hopefully someone else helps you out

Sorry, bai

[pliant shore]

from here

[pliant shore]

the major angle is the central angle of the circular sector that is more than 180

so that's still AOB yes

then you can do (sector area) + 2 * (right triangle area) for the total area

search up the formula for the area of a circular sector if you don't know it

[obsidian rivet]

So I do 67.38°/360° x π(10)^2

Or double the angle?

[pliant shore]

doubling the angle gives AOB, but that's not the one more than 180

what do angles around a point sum to?

[obsidian rivet]

360

[pliant shore]

yeah

,calc 360 - 2 * 67.38

[soft zealot]

Result:

225.24

[obsidian rivet]

Ohhh then I use that in the sector formula?

[pliant shore]

yep

feel free to use ,calc to calculate it

[obsidian rivet]

196.559

[pliant shore]

,calc 225.24/360 * pi * (10)^2

[soft zealot]

Result:

196.5589803596

[pliant shore]

yep! and then the 2 triangles

[obsidian rivet]

how? for what? Im sorry im confused

[pliant shore]

.

[obsidian rivet]

ohhh okayokay mb 😓

436.559?

You must be really pissed off based on how bad I am at math 😓

Wait is that it then

@pliant shore sorry for the ping but its done right?

And one last questions, is 67.38° the DOB angle or DBO

[pliant shore]

,calc 196.5589803596 + 240

[soft zealot]

Result:

436.5589803596

[pliant shore]

yep!

[pliant shore]

I'm not angry

[pliant shore]

it's DOB

DBO is 90 - that

anyways well done, sorry there was a lot of drama

[obsidian rivet]

yesyes I got it now, thankyou very muchhh

I will be coming back later with what I think is definitely harder than this one 😓

Thankyou so much

.close

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[stoic totem]

Is it possible to expand this equation into the second equation?
I am not really sure on how to go about this as what i thought of was regular cubic expansion which wouldn't apply for derivatives right?

[umbral hamlet]

usually when we expand powers like this, we’re working with addition and multiplication, and we get nice formulas

part of the assumption of how this works is that addition is commutative and associative, multiplication is commutative and associative, and multiplication distributes over addition (so like a * (b+c) = ab + ac)

If we can replace addition and multiplication with operations that behave in that same way, then we can still obtain the same results

in this case, we replace addition of numbers with addition of operators on functions, and we replace multiplication of numbers with compositions of operators on functions

the operators here are just the derivatives, and we can verify all of those nice addition and multiplication properties still work here

[stoic totem]

(a+b+c)^2 would apply here?

[umbral hamlet]

The big important property we need to verify is distributivity, and the reason why composition distributes over addition here is because the derivative is a linear operator

In case you haven’t seen linear functions before, a linear function f is any function such that

f(ax + by) = af(x) + bf(y)

in other words, f(x + y) = f(x) + f(y), so composition directly distributes over addition

(Here, f is the derivative operator, and x and y are functions)

[umbral hamlet]

because composition and addition of linear functions works like multiplication and addition of numbers, yes we can use that

And this generalizes to any addition and multiplication of numbers

cubic formula works fine etc

[stoic totem]

ah alright

[stoic totem]

tysm man'

i think i got it

but my main query is

d2y/dx2 wouldn't be equal to (dy/dx)^2

that is where my confusion arose

[umbral hamlet]

dy/dx is not an operator, that’s a function

or to be more clear

A function maps some input to some output (like y = x^2)

the derivative operator maps functions to functions (like d/dx (x^2) = 2x )

dy/dx is a function, but it’s not an operator on functions. d/dx is the operator

and (d/dx)^2 is just notation for saying we compose the derivative with itself. In other words, apply it twice to whatever we want to apply it to

[stoic totem]

and operators undergo the same properties as numbers

[umbral hamlet]

not necessarily, we have to verify those properties I mentioned earlier

linear operators behave very similarly to numbers, yes

Specifically when we replace multiplication with composition

linear functions do too

these things are very flexible and can be very abstract

you just have to define your operations conveniently

[stoic totem]

hmm ok

[stoic totem]

Alright ty

[umbral hamlet]

here’s one more example to illustrate the difference between cases a bit better

f(x) = 4x is a linear function from R to R

g(x) = 3x is another linear function from R to R

let h(x) = 2x etc

there’s lots of ways I can combine these functions. I can add them, or I can multiply them, or I can compose them.

If you think about multiplication and addition of generic functions, this behaves like multiplication and addition of numbers

eg f * (g + h) = 4x * (3x + 2x) = 20x^2 = 12x^2 + 8x^2

instead I can think about composition of functions instead of multiplication, and then

f ° (g + h) = 4 (3x + 2x) = 20x
f ° g + f ° h = 4(3x) + 4(2x) = 12x + 8x = 20x

so we can see that composition distributes over addition too

multiplication of functions and composition of functions are clearly not the same thing, but they satisfy very similar properties that we use during expansions, so if we pick one and use that as our interpretation, everything will work out

I could think of d/dx * d/dy as “compute each derivative separately, and then multiply the functions together”

I could also think of
d/dx * d/dy as d/dx ° d/dy, or the composition of the derivatives

there’s lots of ways to interpret this. That latter case is what we actually care about, because we want to compose derivatives together. When I write

(d/dx + d/dy)^2

I don’t want to square functions, I want to apply this sum of derivatives twice. That’s indicating the composition, and we can nicely expand our derivative compositions thanks to linearity

that’s all I have, it’s a little tricky at first but hopefully it’s easier to process the more you see it

[stoic totem]

ye this helped me out

thanks a lot

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[gentle zephyr]

i need help with b, proving that is differentiable in the point 0,0

[fathom meteor]

Translation?

Oh nvm

[gentle zephyr]

.close

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[native crescent]

What is 2. 8
_. - _
9 7

[final saddle]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[native crescent]

Like photo?

[craggy plank]

Yes

[native crescent]

Its bad photo

[native crescent]

Why is it not working

Its a iraqi

[dawn plover]

which part dont you get?

currently

[native crescent]

This

On the photo

At first a was checking

Now the photo

[dawn plover]

ok so you have to solve the brackets first you know how?

the -6/5 + 21/10

[native crescent]

Nah

[dawn plover]

ok

so you write 2 and 1/10 into improper fraction which is 2 times 10 + 1

[native crescent]

I think we have to remove the 2 on the left of the 1/10

I think u mean 1×2+10

Ye?

[dawn plover]

no

[native crescent]

Then how

[dawn plover]

you miltiply the 2 by bottom and add the top

imagine the 2 as full fraction meaning 10/10 and now multiply it by 2 giving it 20/20

[native crescent]

In iraq the teacher say to remove the 2 we have to do the up × 2 then the number we got plus the down number

Btw i dont understand u

Im not that good at english

[dawn plover]

ok no

just do 2 times bottom + top not the other way

[native crescent]

U speak arabic?

[dawn plover]

no..

[native crescent]

Ok

Bye

And sry

I wasted ur time

[craggy plank]

.solved

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[civic sundial]

A

[civic sundial]

xy + 7z

[ornate tree]

yes, what's the entire question?

[radiant walrus]

lol

[unreal anvil]

Hello there @civic sundial do you have a math question/exercise that you would like to get help with?

[craggy plank]

.solved

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[civic sundial]

.reopen

[final saddle]

✅

[civic sundial]

Sorry my net is slow

[ornate tree]

Brother, we need the question

[valid carbon]

https://tenor.com/view/trickywi-tricky-vtuber-xiboo-ghost-gif-557455749108232190

[civic sundial]

Wait a sec I am getting question pic

[lucid nymph]

are you deliberately getting us to not see the problem

[ornate tree]

Nice ragebait

[steep hatch]

Either send an unobscured picture or stop hogging the help channel

[valid carbon]

hi raphael

[scarlet sequoia]

watch the question just be "if xy+7z = 9 then what is xy+7z + 1/6 * 1?"

[valid carbon]

seems believable

[plucky rover]

I'm just gonna close this I think

.close troll

[final saddle]

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[valid carbon]

eh

[plucky rover]

It's not like any progress was made or lost in the process

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[soft heart]

help me please

[runic tulip]

15 rs/kg in the big 25 🥀

What have you tried?

[soft heart]

no idea what to do

the page where i tried is messy

[valid carbon]

how many rasgullas even is a fucking kg of them

,w density of rasgulla

[soft zealot]

Results provided by WolframAlpha

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

Requested by percykel

[valid carbon]

okay

i see

thanks

[runic tulip]

Lmao

Try to find the cost price first

[valid carbon]

god today is mixed fractions haunting me day

[soft heart]

2/3

[valid carbon]

also isnt that like a crazy profit

achhe din apparently math books mein aaein hain

[runic tulip]

2/3 rs?

[valid carbon]

anywa

question

[soft heart]

fraction form of percentage

[valid carbon]

hi ann

[runic tulip]

Tell me in ra

Rs

[tired walrus]

cost prices of flour and sugar are 7x and 3x rupees per kg respectively

[gray yacht]

Converting this to fraction is easy

[tired walrus]

in addition to this, the fact you're making 66⅔% profit (a.k.a. profit equal to 2/3 of CP) means SP = 5/3 * CP

[valid carbon]

https://tenor.com/view/sherlock-sherlock-holmes-benedict-cumberbatch-yes-thank-you-gif-15426484

we know

[tired walrus]

work out:

• for 1 kg of rasgullah, how much of each ingredient you need
• how much that'll cost you, in terms of x
• an equation which says 5/3 of that total cost equals the sale price (per kg)

[valid carbon]

its just a joke about how a helpee earlier insisted on using mixed fractions and it threw me off majorly

[tired walrus]

in this order

let's see if i get drowned out again

i hope not

[soft heart]

https://tenor.com/view/struggle-fml-the-struggle-is-real-gif-12981234

[tired walrus]

ok so it is. can you name which of my 3 steps you're stuck with

[soft heart]

i am selling a kg rasgullah at 15 rs per kg..and getting a profit of 2/3..
so CP = 3, Profit = 2, and SP = 5

?

with x

14 /kg is the answer

[tired walrus]

!nosols

[final saddle]

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.

[tired walrus]

1. you have it rather deeply backwards
2. you did not follow my instructions

[soft heart]

i did

[tired walrus]

for 1 kg of rasgullah, how much of each ingredient you need
i see this nowhere in what you've written

or maybe you decided to do your own thing or something and then you also dont think to tell me that

[soft heart]

is this right

my internet!!

is this correct

[tired walrus]

,rccw

[soft heart]

idk

[tired walrus]

can you tell the meaning of this 35:9 ratio which you got?

if you can then maybe it's a step in the right direction! but if you cannot then it is not.

i might need to disappear now.

[runic tulip]

im back

do you still need help?

[soft heart]

I am coming back to this..after 15m..(dinner time)

[tranquil scarab]

Sugar price = 7x = 7 × 2 = ₹14 per kg

[tired walrus]

!nogpt

[final saddle]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[tired walrus]

actually <@&268886789983436800> GPT answer

[steep hatch]

Left the server?

[ornate tree]

What's the current process?

[runic tulip]

op is having dinner

then he will have dessert (rasgullas)

[soft heart]

ok..now..let me see this again

is this the order of the solution

@tired walrus is this correct?

[soft heart]

1. I need 7a : 3a of sugar and flour resp. to make 1 kg of rasgulla

[soft heart]

2. 9x

[tired walrus]

7:3 is the ratio of COST PRICES. not masses.

mass ratio is 5:3.

im afraid all of this is just full of mis-steps and i will just need to tell you how to do it right

mass ratio of flour and sugar is 5:3

[glad seal]

you lined up your ratios wrong

in the question, they purposely altered the order in the other sentence

[tired walrus]

therefore for 1 kg of rasgullah you need 5/8 kg of flour and 3/8 kg of sugar.

[tired walrus]

honestly i dont think even lining up ratios is a good approach, but i think i'll soon give up on trying to preach that because subjectively my success rate with it is low

[glad seal]

mm i see. it's just that in the end, when you multiply the 7x and 3x, you might mix up the sugar and flour 🙂

[tired walrus]

thank you for pointing out the reversal anyway

cause i was about to get bamboozled by it

[glad seal]

haha

[tired walrus]

the CP ratio of flour to sugar is 3 : 7 therefore sugar costs Rs. 3x per kg and flour costs Rs. 7x per kg.

therefore total cost price for 1kg of rasgullah is 3x * 5/8 + 7x * 3/8.

rupees.

[soft heart]

oh..

[tired walrus]

i feel as if i should not continue the solution so much that i just do the entire question for you.

but the next step will be to use the info about profit % and sale price

[soft heart]

I will try

[final saddle]

@soft heart Has your question been resolved?

[final saddle]

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[chilly carbon]

I am wondering why the thing I wrote is true, you can find the full theorem in 2.1.5

[chilly carbon]

If something is not clear I can translate

[final saddle]

@chilly carbon Has your question been resolved?

[chilly carbon]

.close

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[ivory island]

Best way to integrate this?

[gleaming anchor]

first thing that comes to mind is simplification via roots of unity

[ivory island]

no idea what that is

[severe canyon]

A simple u-substitution

[gleaming anchor]

actually nvm, i doubt that would work

[ivory island]

what do I make u

[severe canyon]

Think a bit

[ivory island]

thinking

[severe canyon]

Don't let yourself be spoon-fed 😉

[ivory island]

its either x-1 or just x right?

[worthy wren]

u ideally wanna cancel out something when doing a u-sub

also u-subbing x would just give u the same integral in terms of u

[ivory island]

omg yo

im an idiot

its x^7

yeah?

[worthy wren]

might as well put x^7 - 1, no?

[ivory island]

u right

[worthy wren]

since when u differentiate, u'll end up with the same derivative

[ivory island]

then its ln u

[late laurel]

wait would you even need to u sub

[worthy wren]

yups

[late laurel]

bcs its in the form of x^n/(x^(n+1) +c)

i would think you can directly integrate it without any substitutions

[delicate sorrel]

X = cos (x) and use linerisation

[worthy wren]

how would u direct integrate this?

[late laurel]

the numerator is a scalar multiple of the derivative of the denominator so its derivative would be a ln function + C

[worthy wren]

yes that is what a u-substitution does

[ivory island]

.solved

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[tranquil pine]

hello

[tranquil pine]

im doing quadric equations and surfaces and stuff

im just trying to understand the graphing more

so if i had an equation for a cylinder x^2 + y^2 = a^2

to me this looks 2D

but then its also graphes in 3D

bruh

[candid hull]

<@&268886789983436800>

[atomic moon]

<@&268886789983436800>

[solemn rune]

Oh so u want to understand how the graph of x²+y²=a² extends in 3d?

[formal trail]

if you have an equation not involving z, then it will just be the same 2D equation solutions copied for every value of z

if you go on desmos 3D and enter that equation, then click the "extend to 3D" button, it has a nice little animation of this

[final saddle]

@tranquil pine Has your question been resolved?

[tranquil pine]

yes

i dont see how thats possible

[tranquil pine]

i just dont understand how thats possible when the book says the standard equation of a cylinder is x^2 + y^2 = a^2

thats just a circle to me

[formal trail]

since z is not mentioned, for the purposes of 3D all values of z are solutions

[tranquil pine]

but z isnt even there

[solemn rune]

How does the graph of x=1 look like?

[tranquil pine]

so how does it extend

[tranquil pine]

a striaght line

in x

[formal trail]

yeah but y isn't mentioned is it?

[tranquil pine]

yes

[solemn rune]

A straight line parallel to y axis. Yea.

[tranquil pine]

wait what does that mean

[formal trail]

so we figure out from context that our "base space" for y = 1 is in 2D with (x,y)

if it was in 3D with (x,y,z), it would still be a straight line but we would graph it in a 3D space

so what the graph looks like depends on the context of what coordinates we're assumed to be using

[proven panther]

are we being serious

[tranquil pine]

i dont think i understand tbh

can we go over the x = 1 analogy

that is similar

[desert mantle]

in the context of being 2d, x^2+y^2=a^2 is a circle. i nthe context of being 3d, its a cylinder

[tranquil pine]

but how

even in 3D 2D exists

i can graph 2D in 3D

[desert mantle]

for every possible value of z its a circle

so lots of circles stacked on top of each other

aka a cylinder

one circle for every possible "height" z

[tranquil pine]

how does it go up and down though

[formal trail]

in a 1D context, x = 1 is just a point (on the number line). it's only a line in 2D and 3D and so on

[formal trail]

since y isn't mentioned, we just "copy" that point for every value of y, since every value of y is automatically a solution

[tranquil pine]

but y will just become 0

[solemn rune]

Y is not 0

[tranquil pine]

y*0?

[formal trail]

why should y be 0? y could be anything unless we specifically restrict it

[tranquil pine]

thats just 0

[formal trail]

anything * 0 = 0 innit

[tranquil pine]

yeah but it simplifies to 0

its literally not there

[solemn rune]

When u plot the graph of x=1 in 2D , it contains points like (1,2) (1,3) (1,-2)

y is not 0

[formal trail]

y * 0 = 0 has the solution set y = all real numbers

[solemn rune]

if x = 1 and y= 0, the graph would just be a point (1,0) not a line

[formal trail]

bc all real numbers multiplied by 0 are 0

[tranquil pine]

okay so wheres the y in x=1

is it added is it subtracted?

[formal trail]

it is only there from the context that we are working in 2D

it's not actually in the equation itself

[tranquil pine]

now that i think of it i dont even understand why x = 1 is a line

[formal trail]

when graphing equations, you need to know the context in which you're doing it. this context is usually implied/not stated explocitly

[tranquil pine]

and not a point

[formal trail]

if you plug (x,y) = (1,4203) to the equation x = 1 you get true, don't you?

the graph of x = 1 in the xy-plane is by definition the set of all points such that plugging in (x,y) to the equation returns true

[tranquil pine]

where is y going though

theres no y

[solemn rune]

x= 1, this equation just says x is 1, and ntg else.
It says ntg abt y.
There's is no constraint on y coordinates.
Just x has to be 1.

y is just chilling, it can be anything since x=1 says ntg abt y.

So the graph of x= 1 would contain points like (1,0), (1,1) (1,2) (1,2.3) etc

[tranquil pine]

but wheres the y 💀

[solemn rune]

Dude there is no y.

[tranquil pine]

so then

how is it graphed

[solemn rune]

i think i confused u sry :c

y can be ANYTHING

y can be 1, 2 ,3 , pi , e anything

because x=1 doesn't tell us what y is

[formal trail]

if there is no y in the equation then it just isn't used when plugging in

it doesn't prevent you from plugging in (x,y)

[tranquil pine]

it’s ok

[tranquil pine]

yeah but when you say y can be anything

youre inplying there a y to even be able to be something

[formal trail]

why can't y be something?

[tranquil pine]

but there isnt a y so how can nothing be something

[tranquil pine]

.

[solemn rune]

Lol that's smart but when we plot the graph of x= 1 , we plot the points that satisfies this equation

Does x= 1 and y= 2 satisfy it?

[formal trail]

y exists in the first place because of the outside context (not in the equation itself!) that we are working in 2D with (x,y)

[desert mantle]

if I write it as x+0y=1, are you now happy that "there is y in the equation" ?

[tranquil pine]

isnt the graph tied with the equation

[formal trail]

graph = equation + context

[tranquil pine]

okay so equation is there

and no y in equation

[tranquil pine]

yeah 😂

I thought thats what it was initially

but theyre saying no

[solemn rune]

Well 0*y = 0 right

[tranquil pine]

right

[solemn rune]

that's why theres no y, but u can leave it as 0*y cuz u like it that way

that's fine

[tranquil pine]

Okay

got it

[solemn rune]

u got it?

[tranquil pine]

so if i solve for y

wait

so

[solemn rune]

ye

[tranquil pine]

the equation then becomes what

x + y0 = 1?

[solemn rune]

yea

[tranquil pine]

so x = 1 - y0

[solemn rune]

umh ya

[tranquil pine]

and then -y0 = x + 1

divide both sides by 0

[solemn rune]

No

[tranquil pine]

boom

🤣🤣🤣

im jk lmao

[solemn rune]

dude stop u r hurting maths

[tranquil pine]

bro what is this

[solemn rune]

maths is crying

[tranquil pine]

how am i even able to divide by 0 here

[solemn rune]

you cannot

wdym

[tranquil pine]

im doing simple algebra

[solemn rune]

that's apparently not simple algebra

[tranquil pine]

and the equation should hold true

[solemn rune]

not if u divide by 0

Lol

[formal trail]

you can solve for x but you can't solve for y here

[tranquil pine]

so how can i graph y

if i cant solve for it

💀

[solemn rune]

when i say to u to bring me a red apple. And u bring me a red apple and a potato, would that be fine to me?

[tranquil pine]

no because you want an apple?

well it depends

if you dont like potatoes you’re gonna complain

but i get what youre saying though no you’ll be fine lol

[solemn rune]

😭 lemme give u diff example brother

[tranquil pine]

😂

okay

[solemn rune]

Suppose you go for a job interview

[tranquil pine]

ok

[solemn rune]

And they want u to atleast know java language

And u know java and python both

is there any problem?

[tranquil pine]

no

[solemn rune]

similarly

when i say x=1

i just want x to be 1

I dont give a damn abt y and z

idc what they become

until and unless x is 1 x=1 equation is happy

[tranquil pine]

oh wait so

for every domain in y

its just x = 1

[solemn rune]

yea

that's why the graph is a line and not a point

Can u think of how would x=1 would look in 3d?

[tranquil pine]

well for all z and y

itll be 1

the output

for x

[solemn rune]

yea x would be 1

And what abt y and z

they can be anything right?

now think of the graph of x= 1 (which looks like a straight line in 2d)

[tranquil pine]

yes

[tranquil pine]

yea

[solemn rune]

how would it look in 3d

x=1

Sry i need to go now byee

[tranquil pine]

like a rectangle

[tranquil pine]

its okay thank you tho

[final saddle]

@tranquil pine Has your question been resolved?

[final saddle]

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[final saddle]

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[tranquil pine]

hi

[tranquil pine]

can someone please explain this to me

[versed crater]

What don’t you understand

[tranquil pine]

the z = z_0 thing

and how the equation changed

[versed crater]

You’re gonna have to be a bit more specific

[tranquil pine]

the trace of the surface

and then the circle equation

[versed crater]

I can’t read your mind

Can you point to which part of the picture you are lost on

[tranquil pine]

i dont get how they came up with that the trace of the surface is z = z_0

and idk what z= z_0 is

and idk what happened where they plugged into the circle equation

[odd seal]

can you imagine this surface of revolution as a stack of rings?

each of the ring has a different radius, and all those rings are stacked along the z axis

[versed crater]

z=z₀ represents a horizontal plane slice

Like the level sets to the surface

[tranquil pine]

yes and those stack of rings are called traces right

[odd seal]

idk, I never heard of the traces thing. But thats not very important here tbh

lets say its called traces ok?

so each of these traces correspond to a specific z coordinate

and are all circles of different radii

so the radius r of such a trace is entirely dependent on the z coordinate

you might as well write the radius as a function of this z coordinate, r(z)

[tranquil pine]

yeah

i see

but then

[odd seal]

so you obviously know the equation of a circle very well, its x^2 + y^2 = r^2 when the center is located at x=0 and y=0

[tranquil pine]

how do you come up with all those radii

[tranquil pine]

yes

[odd seal]

from the given generating curve

r(z) is something you would need to know to get such a surface of revolution

just like you know what is x, y and z axis, you would also know the r(z) function that tells you the radius at each location

[versed crater]

This is the r(z) you need to be given

When you spin that line around the z axis you create a surface of revolution

The surface area of this surface is the goal of these problems

[versed crater]

The point is if we know this then we can find the surface area when you spin the curve

[tranquil pine]

i see

like integration?

btw whats a cross section

[odd seal]

what you called a trace is cross section

[final saddle]

@tranquil pine Has your question been resolved?

[versed crater]

No

Well

Normally cross section refers to the cross section of a 3d object (which would be a plane)

But I guess the cross section of a surface would be curves, which are level sets

[odd seal]

the surface of revolution forms a boundary of 3d solid

[versed crater]

Well you need to integrate this r(z) later to get the surface area so it’s not like integration it is integration

[versed crater]

Yes but then the cross section will include the interior not just the boundary, but here the boundary is the trace

[odd seal]

everything in the plane of cuting is just the trace in this case, so the trace would be the cross section here

[odd seal]

its a surface here, not a solid so the cross section has only the curve

[tranquil pine]

so the circles stacked up?

[odd seal]

no

just a single circle

that would be the cross section

[tranquil pine]

yeah i meant each one

btw

@odd seal is the equation of the circle here with the radius function plugged in what forms those cross sections or traces? the circles?

for all values of z

i think the screen shot just answered my question

but also

why do they have z_0

and not just z

cause its supposed to be for all values of z right

[odd seal]

they are looking at some specific z coordinate with value z_0

[tranquil pine]

i see, btw do we always use the circle equation for this

[odd seal]

its revolution of the curve

so thats always gonna be a circle

[final saddle]

@tranquil pine Has your question been resolved?

[final saddle]

Channel closed

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[mortal shoal]

Hi

[mortal shoal]

can anyone help me?

[craggy plank]

yes, post

[mortal shoal]

Ok 1 esc

well i know i can use a graph to complete this quesiton , but i want to know how to read the graphs without using calculator, better for my undersatnding like how can they tell what function complies with whatever graph its so confusing

[still wyvern]

well here u can use limits

[mortal shoal]

I dont understand that sry

[tranquil pine]

They probably never took calculus.

[mortal shoal]

Ya sry this is pre calc

[still wyvern]

for eg
for the graph of C(x)
we know as x tends to infinity graph y tneds to 0
we have 2 graphs fulfilling this
and as x tends to 0 the value of y will be -2
and that is only the case with graph (c)
hence the graph of C(x) is option c

[mortal shoal]

sry 😭 i dont take caculus ever

[still wyvern]

no no limits ain that complicated like how should i put it

[tranquil pine]

For example, we know B works because the graph is undefined at -1.

Do you see how it blows up on both sides?

That's called an asymptote.

[still wyvern]

well in that case u'll need to find values at particular valies of x and then try to like plot the graph a bit uk

[mortal shoal]

Yes

[mortal shoal]

Sry i don understand much 😭

[tranquil pine]

The others work similarly.

C works the same way. It's undefined at 1.

So it blows up at 1.

[mortal shoal]

AHHHH

it doesnt touch one

+1

on the right graph

[tranquil pine]

For A and D, it's basically the graph of 2/x but they just moved it up or down.

[mortal shoal]

also i have a quesiton , so the 2/x is a horizontal stretch of 1/2?

[tranquil pine]

I think it's better to say a vertical stretch of 2.

[mortal shoal]

yeah i can see

it makes sense now

[mortal shoal]

Same my teacher said that

OK i understand now

[tranquil pine]

Good good.

[mortal shoal]

thanks alot ❤️ 😃

[tranquil pine]

No problem!

[mortal shoal]

are. u a teacher?

[tranquil pine]

Yup.

[mortal shoal]

So sick

can i ask where?

high school.?

[tranquil pine]

High school yeah.

[mortal shoal]

Wow

im from canada

and u?

[tranquil pine]

Same.

[mortal shoal]

Wow

im from alberta

[tranquil pine]

Same lol.

[mortal shoal]

Whaat

calgary

[tranquil pine]

30-1?

[mortal shoal]

Yes