help-33

[bleak ledge]

y+K=x

i.e. positive slope

so yes

[obtuse plume]

Okay great, thanks for the help, I'll try solve the rest!

[bleak ledge]

[obtuse plume]

.close

[marsh citrus]

Channel closed

Closed by @obtuse plume

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[placid prawn]

want help providing intuition for R-modules in general

[placid prawn]

I feel pretty good with ideals, field extensions, polynomial rings, whatever, but modules just don't sit well with me and im wondering if im missing something

[night relic]

for starters, if R is a field, the R-module becomes an R-vector space. so i think of R modules as as a generalization of a vector space, but now your 'scalars' don't necessarily have an inverse, aren't necessarily commutative, don't necessarily have an identity, etc. etc.

[placid prawn]

ye

[whole sleet]

So modules have "vectors" and "scalars". We don't call them that though.

Usually the module itself just kinda refers to the "vectors" and the "scalars" are signified by the R-

One major difference is we lose the concept of basis and dimension. This does make them a lot more difficult to picture. We have some tricks to get some kind of basis back.

[leaden monolith]

<@&268886789983436800>

[whole sleet]

Dang discord just letting the scammers run wild

[placid prawn]

ya i think i get those things but it's still difficult to get past anything more than formalism or symbolic manipulation when working with them

i dont really know how to put the question because the question isn't clear at all to me im just hoping something can be said that would make them seem more natural in a way

[night relic]

are there any examples of modules that don't make sense to you? how is your intuition on module homomorphisms; what do they generalize from vector spaces?

[placid prawn]

I feel pretty good about module homomorphisms. i have no grasp on free modules other than their definition - same as tensor products of modules

other than the clarification of those two things, another more specific question might be what an R-module is to its ring R, in a meaning comparable to what an ideal in R is to its ring R

[marsh citrus]

@placid prawn Has your question been resolved?

[night relic]

i'll admit im not the most versed in module theory, so i don't know much about tensor products of modules. they are a generalization of tensor products of vector spaces, though, so perhaps start there?

free modules are modules with a basis (made of 'vectors' in the module). so what you need is the possibility of a set that spans everything (intuitively to me, the lack of inverses for each element make this hard), and are linearly independent. i think a good non-example helps: Z/nZ as a module over Z is not free, because n * v = 0 in the module, but n is not zero in the ring, so linear independence is moot

as for understanding what R-modules are to R, i like to think of modules as ring actions over the (abelian) group M, so R-modules "extend" R in a sense (of course, I is a 'subset' of R but also an R-module, so 'extending' is probably not the right word). if you are familiar with diffgeo, you can also apparently think of modules as vector bundles with R as the ring of functions, but i dont fully understand that one

[placid prawn]

thank you very much for this answer, i will probably revisit it many times. to be honest, it's been a few months since i last tried to get into modules and only now trying again (with the background idea of a generalized vector space and whatever other experience) do a lot of the things i'm reading in my text seem more natural. especially with the idea of a "basis" for the free modules that you just pointed at. and the "extension" of rings in a comparable sense as vector spaces "extending" their underlying fields

ahh thank you both very much

.close

[marsh citrus]

Channel closed

Closed by @placid prawn

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[tawny geode]

why and when do we do implicit differentiation? for example, normally the derivative of y is 1, however differentiating it implicitly makes it dx/dy

[bitter cave]

the derivative of y wrt what is 1?

also, dx/dy?

[jade sigil]

if y is a function of x then d/dx(y)=dy/dx,
the derivative of y is NOT 1 unless y=x

maybe you are mixing it with d/dy(y)=1, but thats with respect to y, and not x

[vale moss]

It's used if you can't seperate different variables in an equation and one of them is dependent on another. The dx/dy simply means that you differentiated x with respect to y

[tawny geode]

so how would you know what variable to differentiate with respect to?

dy/dx is common but im sure thats not it all the time

[radiant orbit]

The problem will typically specify

[tawny geode]

when doing word problems we did dr/dy, r being any variable we used

[bitter cave]

if it is a rate, then usually it's d(var)/dt, with t being time.

normally the variable to differentiate wrt is indicated by "per {variable}".

[tawny geode]

for example today we were taking up a question

xe^y+ylnx=0

[terse raptor]

Implicit differentiation treats an expression as two variables which change thereby making you consider both variables slope (hence why chain rule kicks in)
however, explicit differentiation takes everything as one variable, which removes that, because dy/dy (the term chain rule introduces) is just 1.

[tawny geode]

and we differentiated implicitly, but im confusing on how we know how to do it

^ to differentiate implicitly, not the math path

part

just having a hard time understanding

[terse raptor]

Alternatively there is a shortcut for implicit differentiation, you get the derivative as
f'(x)= -(dau(x)/dau(y))/(dau(y)/dau(x) where y=f(x)
however, well, the actual method involves you to do the following (sending, one second)

[tawny geode]

so basically we use implicit differentiation when we have two variables?

[terse raptor]

two variables which we think change

[tawny geode]

and which one would we know to put in respect to?

[tawny geode]

hmm ok

[terse raptor]

and in most easy cases we try to convert it all into one variable and differentiate with respect to that one variable

[terse raptor]

for your question i am differentiating with x

it depends, most places usually teach the same algorithm for implicit differentiation

1. Take the function
2. Differentiate with respect to x (with appropriate use of chain and product rules)
3. Group and simplify the derivative

[tawny geode]

so in expressions with x and y, we would always differentiate with respect to x?

[bitter cave]

not necessarily. always look at the question.

[tawny geode]

but then for example, what would we differentiate with respect to in a expression, with lets say a and b

[tawny geode]

alright

[terse raptor]

Sometimes it's easier to diff with y, sometimes with x
it depends on the Q

[bitter cave]

again, everything is context-dependent.

[tawny geode]

could you give an example

not using x and y

[bitter cave]

for instance, if you have distance as a function of time, and you want to know the velocity function, then you diff the distance wrt time.

[terse raptor]

and product rule*

[bitter cave]

eg: x(t) = t^2 + 2t + 3 (distance).
if we want to know the velocity, v(t) = d/dt (x(t)) = 2t + 2.

diffing time wrt distance in my example makes no sense physically. it can be done, but it's not helpful because it doesn't answer the question.

[tawny geode]

so lets say we differentiate the radius with respect to time, that would mean how much the radius is changing when time changes?

[terse raptor]

yes.... of course
dr/dt= (limdeltat tends to 0) deltar/deltat (from the definition of a derivative)

[bitter cave]

correct.

[tawny geode]

so really knowing what variable to put respect to is just context and question based

[bitter cave]

absolutely.

[terse raptor]

for this just differentiate with respect to x

if you differentiate with respect to y
you'll get dx/dy
flipping it can be a headache

besides in this problem they want f'(x)=dy/dx

[tawny geode]

okok

thank you

[marsh citrus]

@tawny geode Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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 grove]

I did part a

[neat grove]

But i genuinely dont Know how to start b

All ik is that now the integral will be greater

[velvet laurel]

its a similar riemann sum thing

[neat grove]

Wait

I think i gotnit

[velvet laurel]

the k-th interval is still (k-1)/n, k/n and the width is just 1/n but now you evaluate the height at the right* edge

(i presume you used the left edge for part a)

[neat grove]

It would be this right

[velvet laurel]

yup

use sigma notation to sum up the squares and u get a simplified fraction

[terse raptor]

riemann sums and integrals isn't it?

[neat grove]

Does rhe n-1 at the top of the zigma mean anything

[velvet laurel]

now distribute the summation

[neat grove]

Or do i just use these as normal?

[velvet laurel]

?

[neat grove]

Look at my zigma

I put n-1 at the top

Does that change anything

[velvet laurel]

it shouldnt here

[terse raptor]

well instead of n you just substitute n-1

in the sig formulas you mentioned

[neat grove]

Ahhh

[terse raptor]

isn't it?

(Sorry for barging in, but that should finish off ur problem)

[velvet laurel]

yep

[terse raptor]

A-lvls?

These sure look like them

[neat grove]

So much crosses lol

But i got it i think

[terse raptor]

Indeed this is cool

Bravo

now apply the limit and get the lower bound

finish it off

[neat grove]

Yeee

Got it

Thanks lol

[terse raptor]

npnp

[neat grove]

These questions are js hella intimidating bro

But they arent that bad

I always mess em up tho

[terse raptor]

A lvls isnt it?

[neat grove]

Yho

Further math

I get everything but these

Bro the time pressure for a level is horrible

Further is just so stressful w time

[terse raptor]

And it's a descriptive paper

not even MCQ

[neat grove]

Whats that

Oh yeah

Its a 2 hour paper

But everything takes so long

[terse raptor]

Extra marks for good handwriting my guy
crazy shi
I mean y'all have a vast syllabus but easy Qs in the vast syllabus

[neat grove]

😂😂😂

[terse raptor]

Second order LDE in further mechanics for example

[neat grove]

Nothings hard

Besides further mechanics

Bro further mech is fucking horrible

Its whats brings my grade down

[terse raptor]

It's nothing compared to the struggle that is IIT-JEE

[neat grove]

Lol

I hatebit

And itd so boring

[terse raptor]

I have to admit further mech problems are crazy too

definitely above the first level of the JEE

AND you have to write EVERY single step

yeah well good luck

cya

[neat grove]

Yeh bro

My paper wascrazy lol

Cya

.close

[marsh citrus]

Channel closed

Closed by @neat grove

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[quick oyster]

is the answer to this B 142

[quick oyster]

i'm pretty sure the maximum is in an equilateral triangle
so the pairs of triangles can be

30-60-90 triangles (which there are 12 of)
60-60-60 triangles (which there are 5 of)
30-30-120 triangles (which there are twelve of)

so you do 12 choose 2 and 5 choose 2, getting 66 + 66 + 10 = 142.

i'm still trying to figure out how many is in the minimum

k nvm i think it's C

[marsh citrus]

@quick oyster Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[royal hearth]

achaaa

[bitter cave]

hm? why are you replying to a message half a year ago?

and do you have a question for the channel?

[marsh citrus]

@royal hearth Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[marsh citrus]

Please don't occupy multiple help channels.

[cunning fiber]

<@&268886789983436800>

[next ivy]

<@&268886789983436800> and furious I guess

[marsh citrus]

Channel closed

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

[waxen dust]

[next ivy]

no scambot is complete without the Enterprise judgment emote

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[little root]

Hey can anyone help me solve this

[tardy solstice]

domain is your x-values, range is your y-values

so look at the graph and see for which x values is the graph defined, and then do the same for y

[little root]

Ohh

[little root]

Can u pls explain slightly better 8 still don't get it

[tardy solstice]

so your graph starts at (0, 0) right?

[little root]

Right

[tardy solstice]

you know the line doesnt go past that point since it is a dot not an arrow

so that will be your starting point for both your domain and your range, since you won't have any x values less than that nor will you have any y values less than that

does that make sense so far?

[little root]

Kind off

[little root]

My friend asked if I can add you so she can also ask u soemthing if Ur alright with that?

[tardy solstice]

domain means: for which values of x do you have a corresponding y value?

[tardy solstice]

uhh sure

[little root]

I am sorry

[tardy solstice]

no worries you dont have anything to be sorry for

[marsh citrus]

@little root Has your question been resolved?

Channel closed

Closed by @little root

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lean bramble]

how do i solve this question: out of 4 numbers, the average of the first 3 is 16 and that of the last 3 is 15. if the last number is 20, than what is the first number?

[lean bramble]

anyone?

[brave marsh]

Have you tried making the two averages you're given into equations?

[lean bramble]

no

[brave marsh]

Well if we say that the numbers are a,b,c and d, how would you write that the average of the first 3 numbers is 16?

[lean bramble]

so a+b+c=16?

[brave marsh]

The average of a,b and c is a+b+c?

[lean bramble]

no

a+b+c/3?

[brave marsh]

Yes (a+b+c)/3

[lean bramble]

how about 15?

[brave marsh]

Well how do you write the average of the last three numbers?

[lean bramble]

(d+e+f)/3=15

[brave marsh]

The 4 numbers are a,b,c,d

There's no e and f

[lean bramble]

ok

so it will be: b+c+d/3=15?

[brave marsh]

Yes

[lean bramble]

and a+b+c/3=16

[elfin berry]

Azyrashacorki

[lean bramble]

= a+b+c=48 ?

and b+c+d=45?

but shouldnt d be 20?

[brave marsh]

Yes

[lean bramble]

since its the last number

so it will be b+c+20=45

[brave marsh]

45

But yes

[lean bramble]

and then it will be b+c=25?

so 48-25=23?

and a=23?

[brave marsh]

Bingo

[lean bramble]

thank you

have a nice day

.close

[marsh citrus]

Channel closed

Closed by @lean bramble

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[whole grail]

I wanted to ask if someone could help explain this to me. I have an upcoming test on it and have just about everything down apart from arc length and finding values for trig functions. This is pre-calc btw

[vagrant gull]

which specifically are you trying to understand in here?

there are a bunch of examples

[whole grail]

Im trying to understand 2 topics. How to find arc length and how to find values for trig functions. I sent the image in hopes that someone could help explain a problem to me.

[vagrant gull]

think of it like this: first look at the angle and figure out its reference triangle, then check which quadrant it’s in to get the correct signs, use the point (x, y) where $\cos \theta = x$ and $\sin \theta = y$ to find any trig value (like flipping for csc or using ratios for cot), and for arc length just multiply the radius by the angle in radians using $S = r\theta$ hope this helps

[elfin berry]

# 1 shitmiss hater

[whole grail]

I understood arc length however i still cant really grasp the values of trig functions

[warm pilot]

why do you hate me specifically

[smoky hare]

yeah fr

[whole grail]

Nah its part of a game i play and their really annoying charecter called fred. Srry for any slander towards u

[smoky hare]

nah dude i'm just messing around that's my alt account

[whole grail]

.close

[marsh citrus]

Channel closed

Closed by @whole grail

Use .reopen if this was a mistake.

[vagrant gull]

you just need to find where the angle lands on the circle, take the point, then sin is the y-value and cos is the x-value, and the rest are just simple fractions from those

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[wise oxide]

how u do this

[buoyant jetty]

do you know what image is

[red nimbus]

Try to find another but linear dependent vector of (1,-5)

[wise oxide]

ik how to solve for a basis of one

[wise oxide]

idk how

do i just think of random numbers or is there a way to do it fast

[red nimbus]

You do

Dont overthink it

[subtle dune]

[red nimbus]

What vectors do you get if you consider span(1,-5)

[paper raptor]

not random numbers, do you remember what is means for a vector to be in the span of another?

[wise oxide]

no

[wise oxide]

i dont get it

[red nimbus]

I will let Pajama continue.

[paper raptor]

A vector (\vec{v}\in\mathbb{R}^2) is also in the span of (\begin{bmatrix}1\-5\end{bmatrix}) iff it can be written as (c\cdot\begin{bmatrix}1\-5\end{bmatrix},; c\in\mathbb{R}).

[elfin berry]

ΠαϳαμαΜαμαΛλαμα

[paper raptor]

That is, a linear combination of the basis vectors of your span, in this case we only have one basis vector (so the linear combination is just any real multiple)

[paper raptor]

if you wanna take over you can Adonis, sorry I hijacked ur channel 😭

[wise oxide]

ok so c=1

its 1, -5 still

[paper raptor]

right (1,-5) is in the span of (1,-5) is there another vector?

[wise oxide]

c=2

2,-10

[red nimbus]

You should know that (0,0) is linearly dependent to every vector,,,

[wise oxide]

ngl idk wht that means

[paper raptor]

take c=0

and as above we can take any vector in any dimension vector space

so the zero vector can then be written as a lienar combination of the basis vectors

[wise oxide]

so 0,0 is an answer?

how do i get the 2x2 matrix

[red nimbus]

How do you understand what a basis is,,,

<@&268886789983436800>

[wise oxide]

i dont i just know how to solve for image of one

[paper raptor]

0mod2

[paper raptor]

a key fact from linear algebra is that the image of a matrix is its column space

so for the image of a matrix to be the vectors spanned by (1,-5), we want the column space to be span{(1,-5)}

[wise oxide]

ok so it can be 0,0 and 1,-5 then?

for c=0 and c=1

[paper raptor]

those are perfectly good columns for the matrix yes

In general, for a matrix, the image is the column space. So any matrix with (\text{col}(A)=\text{span}\left{\begin{bmatrix}1\-5\end{bmatrix}\right}) looks precisely like:
[
A=
\begin{bmatrix}
| & | \
c_1\cdot\begin{bmatrix}1\-5\end{bmatrix} & c_2\cdot\begin{bmatrix}1\-5\end{bmatrix}\
| & |
\end{bmatrix}
]

where (c_1,c_2\in\mathbb{R}) are arbitrary scalars.

[elfin berry]

ΠαϳαμαΜαμαΛλαμα

[wise oxide]

so this is the answer?

[paper raptor]

that is a very good example of such a matrix yes

actually I'd just be careful about what I said

if c1=c2=0 then we just get the all-0 matrix

which obviously the column space is trivial instead of span{(1,-5)}

[wise oxide]

wym so i jsut have to make c diff values

[paper raptor]

not necessarily, just that they're not both 0

[delicate prairie]

just specify c1,c2 are not both 0

oop snipe

[wise oxide]

ok so i make one c as 0 and as long as the other c isnt 0 im fine?

[red nimbus]

Why did I not get this-ed

[delicate prairie]

yes that or both nonzero

[paper raptor]

and why that is is because if (c_1=c_2=0) then the matrix becomes:
[A=\begin{bmatrix}0&0\0&0\end{bmatrix}]

[elfin berry]

ΠαϳαμαΜαμαΛλαμα

[paper raptor]

which the column space is (\text{span}\left{\begin{bmatrix}0\0\end{bmatrix}\right}={\vec{0}}) which is just the zero vector

[elfin berry]

ΠαϳαμαΜαμαΛλαμα

[paper raptor]

which is obviously not the span as span{(1,-5)}

[marsh citrus]

@wise oxide Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[final cobalt]

i can't visualize what is question stating on the fig 26-5

specifically confused about distances

can anyone draw the situation for me that question is asking

[main idol]

Did you try physics server

[marsh citrus]

@final cobalt Has your question been resolved?

[delicate prairie]

the question wants u to approximate the E field at very far away points

(the lesson here is that the E field of a dipole decays roughly like 1/z^3 as z gets larger, which is faster than the 1/z^2 decay of a single point charge)

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[gloomy merlin]

Your work? What are you stuck on

[marsh citrus]

@buoyant jetty Has your question been resolved?

[buoyant jetty]

don't know how to begin

[leaden monolith]

What is a C¹ parametrization?

[buoyant jetty]

a c1 parametrization is a parametrization that is continous and his derivative of the parametrization exists and it's continous aswell

first order derivative

@leaden monolith @gloomy merlin

[leaden monolith]

Okay

What’s a circle with radius r centered at (0,0)

[buoyant jetty]

just a circumference where every point is at a distance 1 of the origin

it's a closed curve

[leaden monolith]

Like I don’t know where you’re getting confused

Can’t you show that first parametrisation is C¹

[buoyant jetty]

cos and sin are smooth

[leaden monolith]

So where are you confused

[leaden monolith]

Like how is this a problem

[buoyant jetty]

I'm sorry

how do you prove that this parametrization is of a circle

[leaden monolith]

What is a parametrisation?

[buoyant jetty]

don't know

a way of describing every point of a curve in an interval domain

[leaden monolith]

Okay, so it’s a function from an interval [a, b] to some set of points

The “set of points” part was why I asked what’s a circle with radius r centred at (0,0)

[buoyant jetty]

help

[leaden monolith]

How do you describe this circle as a set of points?

[buoyant jetty]

using a parametrization?

[buoyant jetty]

don't know

[leaden monolith]

Describe this with set notation

[buoyant jetty]

{x,y in R | x^2 + y^2 =1^2}

@leaden monolith

[leaden monolith]

So you do know

[leaden monolith]

Don’t let your first instinct be to say I don’t know

[buoyant jetty]

help

[buoyant jetty]

.

[leaden monolith]

Well put the words together

[leaden monolith]

This is a parametrisation

[leaden monolith]

This is a circle

Show that what they’ve given you is 1 a parametrisation, 2 it is of the circle, 3 is C¹

[buoyant jetty]

how

[leaden monolith]

How to which step

[buoyant jetty]

1

@leaden monolith

[marsh citrus]

@buoyant jetty Has your question been resolved?

[red nimbus]

Blud

[red nimbus]

Just validate the equation by plugging in x(t) and y(t)

[buoyant jetty]

then what?

I get that r^2(cos^2(2.pi.t) + sin^2(2.pi.t)) = r^2.1 = r^2

[red nimbus]

Simplify it

Also

[red nimbus]

This is for a circle with radius 1 not r

[buoyant jetty]

{x,y in R | x^2 + y^2 =r^2}

[buoyant jetty]

I already did

[red nimbus]

You are trying to simplify x^2+y^2 to r^2

[buoyant jetty]

I did

@red nimbus

what now

[red nimbus]

Whats left

[buoyant jetty]

well

@red nimbus

[red nimbus]

Ok you'd need to also show that parameterization covers actually the whole circle too

Right now you showed that your paramerization is a subset of {(x,y) : x²+y²=r²} to say the least

@buoyant jetty

[buoyant jetty]

how

[red nimbus]

What if t varied from to 0 to 0.5 instead

[buoyant jetty]

what about it

[red nimbus]

Think abou it

What would curve look like

[buoyant jetty]

semi circ

[red nimbus]

Why

[buoyant jetty]

0 to 1 is a circle

0 to 0.5 is upper first half clockwise

[red nimbus]

Ok bruh

[buoyant jetty]

0.5 to 1 is the lower half

[red nimbus]

So you do you realize that it depends on t

If all the angles are covered

Why do you say how then

You just need a small argument if t in [0,1] with 2πt maps to [0,2π]

[buoyant jetty]

one thing is understanding the intuition other thing is proving it

[red nimbus]

You seem to do neither

[buoyant jetty]

can we start from scratch

[digital robin]

starting from scratch would be like

well first its a function

[red nimbus]

You can scratch my back

[buoyant jetty]

I am trying to prove it

[digital robin]

so i think what star is trying to say

is that map t ↦ 2πt sends [0,1] onto [0,2π], and every point of the circle corresponds to some angle in [0,2π]

[red nimbus]

2πt is a linear function bruh

It is monotonous

It is continuous

[digital robin]

same exact argument works for σ₂ with 4πt instead of 2πt — the map t ↦ 4πt sends [0,1] onto [0,4π], which still covers every angle (twice, actually which is the hint for part c)

[buoyant jetty]

wait hold on

[red nimbus]

You can easily show that it's surjective

[buoyant jetty]

how

[digital robin]

You need three things to complete part a, and you've basically already said all of them

1.) It's a function [0,1] → ℝ² which is just trivial

2.) would be proving the image is exactly C

[digital robin]

^

3.) It's C¹

[buoyant jetty]

how

[digital robin]

both components r cos(2πt) and r sin(2πt) are differentiable with derivatives −2πr sin(2πt) and 2πr cos(2πt), which are continuous

[buoyant jetty]

do you prove that

[digital robin]

two directions

Image ⊆ C which you did

and star is saying C ⊆ Image:

so you did for any t, (r cos 2πt)² + (r sin 2πt)² = r²(cos² + sin²) = r²

for star he is saying take any (x,y) with x² + y² = r². Then (x/r, y/r) is on the unit circle, so there exists θ ∈ [0, 2π] with cos θ = x/r, sin θ = y/r. Set t = θ/(2π) ∈ [0,1]. Then σ₁(t) = (x,y)

again, star is trying to say that the map t ↦ 2πt sends [0,1] onto [0,2π], and every point of the circle corresponds to some angle in [0,2π]

[marsh citrus]

@buoyant jetty Has your question been resolved?

[subtle dune]

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[thin coral]

1. I have to draw a pyramid LABCD where LA is perpendicular to the base

I have drawn it as i understand it. Would want to see pointed out if i did that wrong

2. The base is rectangular with side lengts of 5 and 9cm, while LA = 12cm.
   I have to find and calculate the longest side facet. Would need someone to walk me through for help

[serene bramble]

yh you've drawn it wrong, if "LA is perp. to the base"

If ABCD is the base of this pyramid, then L has to be directly above A

[thin coral]

you mean like this or?

[serene bramble]

ye

Also, it would help if (see incoming bot message):

!xy

[marsh citrus]

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.

[thin coral]

have to translate it so hopefully its not innacurate somewhere

[serene bramble]

If the original problem is not in English, then post it anyway
@thin coral

Just in case

[thin coral]

alright

[serene bramble]

But otherwise, yes, it's as I've said

You have a base ABCD, and then the point L lies directly above A

[stable dune]

wasnt thr base a rectangle

[thin coral]

yeah, its an almost-example

to get general idea

[serene bramble]

[yes, but it should be clear that's a different diagram entirely lol]

[the point in question's labelled E]

[stable dune]

yeah im blind mb

[serene bramble]

no worries

[thin coral]

I have constructed it how i understand it, again

would this be accurate

@serene bramble

[serene bramble]

ye

Now it's just a matter of finding the other side lengths

This shouldn't involve anything more than using the Pythagorean theorem

[thin coral]

alr

[marsh citrus]

@thin coral Has your question been resolved?

Channel closed

Closed by @thin coral

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[elfin berry]

Renato

[buoyant jetty]

.close

[marsh citrus]

Channel closed

Closed by @buoyant jetty

Use .reopen if this was a mistake.

[brave marsh]

[delicate prairie]

.reopen

[marsh citrus]

✅ Original question: #help-33 message

[buoyant jetty]

my channel is getting highjacked !!~

[delicate prairie]

@buoyant jetty i suspected that the last time you closed your channel you were evading my suggestion to properly review the material before doing the problem. you doing it again confirms my suspicion. consider this an official warning to not abuse help channels. the next instance of similar behavior will result in a mute

[buoyant jetty]

this might been a misunderstanding. I was closing the channel because this problem is a pain in the ass and I have other exercises from other classes

however you immediately asssumed the worst case possible it seems

[night relic]

that definition is very fundamental to understanding epsilon-N calculus. once you understand that theorem properly, it will lead you to understand other theorems better, in analysis or otherwise. it does take time now, but it's time you are saving in the future, i promise :)

[buoyant jetty]

but there is no delta in the definition

[delicate prairie]

this seems a lousy excuse for closing the channel right after i showed up

[buoyant jetty]

,w lousy

[elfin berry]

Results provided by WolframAlpha

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

Requested by renatoxbz

[delicate prairie]

you can say weak or nonsense

[buoyant jetty]

how is this abusing help channels? I was closing a channel?

[tardy solstice]

(highly recommend you don't get into an argument with a mod because they are probably right and that's their job)

[delicate prairie]

apart from my suspicion of you avoiding my suggestion to review material, you opened a channel without posting any of your own work then closed it the instant a helper appeared

[buoyant jetty]

fair enough I can take the blame for that, I forgot to include my previous work

thats a bad habit of mines

[delicate prairie]

the last time you posted the same problem you had no work at all. you didnt understand the definition of limit and we spent an hour reviewing it

[buoyant jetty]

its the first exercise on sequences for this homework problems

and the professor like: quickly glanced it today in class, but didnt explained fully. The examples from the book are helpful but are also a pain to decrypt

anyways, I get your point. Though I still believe my excuse is valid enough aswell as your suspicion, I will try to be more careful before misusing the help channels

[delicate prairie]

i suspect you havent fully understood the examples in the book. i suggest going over all of them with classmates or helpers who can clearly explain the material. that way you can formulate at least one correct concrete idea for solving a problem before asking us for help

[buoyant jetty]

I asked for a classmate of mines to share me how she did it, but she is way too handwavy with proofs and I dont trust her work, I prefer to go at my own pace

[delicate prairie]

and from now on i would like you to post at least one concrete idea for solving a problem every time you open a channel

[buoyant jetty]

but yeah I will definitely re read that chapter of the book, maybe ask prof next week about what I dont understand

[buoyant jetty]

but status 1: IDK how to begin, is not possible?

[delicate prairie]

based on your history of interactions with helpers its clear that you very often underprepare the material related to your problems

for example today you showed that you fundamentally misunderstand the definition of limit along with the textbook’s examples. that means you are far from capable of solving the problem you just posted

[buoyant jetty]

well, this problem is certainly hard for my level, but I still gotta do it because is part of my weekly homework

I am dedicating a lot of time to this class yet, I feel like I am progressing really slow compared to my other classes

[delicate prairie]

i strongly suggest that from now on you seek help on reviewing material as many times as you can BEFORE doing a problem

ideally ask the professor first. emails, office hours, right after lectures etc… any form of contact

then ask helpers here for help reviewing material

for example what you shouldve done was recognize your lack of understanding of the epsilon definition and examples, then ask the professor to help you understand those, then ask helpers here for the same… repeat this cycle as many times as you can BEFORE doing the above problem

this is a study habit that you have not developed during your several years on this server. it has cost many helpers’ time and much of your own time, but it is still possible to put every ounce of your effort into turning around this situation

[marsh citrus]

@buoyant jetty Has your question been resolved?

[delicate prairie]

you do not learn by spamming problems here and expecting us to help you solve them from scratch… you learn by checking your understanding of the material RIGHT AFTER lecture ends so that you are as ready for assignments as you can possibly be

[buoyant jetty]

to be Frank today we had the first class and i am so behind in catching up with everything

maybe i should check on my understanding more often, but is tough work

i am taking like 4 classes simultaneously i might be going to explode sometime soon

doing this for all my classes is tough

i just need a study buddy from my class but since i am antisocial is tough

sorry for being a horrible helpee

though all this 2 years i have requested a lot of help from you guys but as homework gets tougher i might have went more stressed with my courses, i used to have fun with the problems but is hard when they bomb you with gazillion exercises weekly

[delicate prairie]

during ur 2 years here, u and the helpers spent LOTS of time on problems in linear algebra, logic, modular arithmetic, etc. but real analysis will be ur hardest class ever. epsilon is famous for being EXTREMELY hard for new students to fully learn. u will spend INFINITELY more time learning it than other topics. thats why its so important for u to develop the study habit that i mentioned above RIGHT NOW

[buoyant jetty]

i shee

quick question what is the difference between limit definition of convergence of a sequence and the popular epsilon delta definition?

[delicate prairie]

epsilon n0 is for sequence. epsilon delta is for function on interval

[buoyant jetty]

say for example, I am trying to prove that 1/(2n+1) -> 0

n >= n0 => 2n >= 2n0 => 2n + 1 >= 2n0 + 1 => 1/(2n + 1) <= 1/(2n0 + 1)

|1/(2n+1) - 0| = 1/(2n+1) <= 1/(2n0 + 1) < ?

Now what I would like is that 1/(2n0 + 1) < e

however it is getting tough, I used Arquimedes propety that forall x in R there exists some n in N such that n > x

[buoyant jetty]

.

[delicate prairie]

1/(2n0+1) < 1/(2n0)

now easy choice of n0 is clear

[buoyant jetty]

this is for time saving? I can always just clear n0 in this 1/(2n0 + 1) < e

[delicate prairie]

yes. but in epsilon delta its strictly necessary to guarantee positive delta

this is common trick in epsilon proof. smaller bottom = bigger fraction

[buoyant jetty]

however we dont deal with deltas in the sequence convergence proofs right? or wdym exactly

[buoyant jetty]

why

[delicate prairie]

smaller bottom = bigger fraction

[buoyant jetty]

suppose 1/(2n0) < e
then
1/(2e) < n0

basically, by Arquimedes property I get that forall x in R there exists some n in N such that x < n

so by Arquimedes, forall 1/(2e) there exists some n0 in N such that n0 > 1/(2e)

then we go back again and from there deduce that

[delicate prairie]

its nonsense to say "forall 1/(2e)"

we say "for all e>0 there exists n0 in N such that n0 > 1/(2e)"

[buoyant jetty]

this ^

yep and from there we do algebra and get that 1/(2n0) < e

we basically proved it!

[delicate prairie]

archimedes property is the right idea but we need good math grammar too

yep we're done

[buoyant jetty]

I think I am getting the gist of it, is just the tip of the iceberg

🤯

[delicate prairie]

its good progress, keep up the review

[buoyant jetty]

thanks, I got help from a classmate

he already passed this class

what he told me about Arquimedes property blew my mind

I was like, so its like that, huh?

crazy

[buoyant jetty]

I appreciate the help as always roketto, we will see how this class goes for me because I find it extra hard for my level

this is supposed to be "advanced calculus workshop" then if you pass this you get to take "advanced calculus" or whatever it is

my upperclassmen are telling me this class is tough, they suffered through it but at the end you come out stronger than b4

[delicate prairie]

getting help from ppl who did well in the class is one of the best things u can do. if u can find ppl to help u review lecture material as often as possible that will be key to success

[buoyant jetty]

I appreciate the help dude, even the tips I really cant thank u enough

math is really cool huh

but at the same time is a pain jaja

[marsh citrus]

@buoyant jetty Has your question been resolved?

[delicate prairie]

yep its a big pain if u dont have ppl to help u review

btw i have a process for epsilon proofs. maybe it will help u

keep in mind i use N instead of n0

[buoyant jetty]

ok

[delicate prairie]

,tex \epsilonN

[elfin berry]

ロケット・ジャンプ

[buoyant jetty]

it doesnt seem thaat hard

but is about practice, innit?

[buoyant jetty]

math really is cool huh

[buoyant jetty]

i mean as long as you know arquimedean property everything is possible

[delicate prairie]

the sequences can get MUCH more complicated than what u saw

[buoyant jetty]

[delicate prairie]

but this scratchwork process will still apply

[buoyant jetty]

i think, i did a bunch of progress today

however, i still need to do more progress

math is tough work but very rewarding

[buoyant jetty]

we will see, I think I kind of understand the gist of it, innit?

[delicate prairie]

yes but the world of limits is large. besides more complicated sequences there are also limit properties, sequence properties, series, series properties etc

[buoyant jetty]

🤯

[delicate prairie]

in calc class u accepted the rules of limits, sequences, series, derivatives, integrals etc without proof. but in real analysis u prove ALL of em

and epsilon is the key

[buoyant jetty]

fair enough, shit will get tough

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[delicate prairie]

VERY tough but doable as long as u have mentors to help u review everything

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[marsh citrus]

Please don't occupy multiple help channels.

Channel closed

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[worldly vale]

Pls anyone solve this SASMO 2024 P14

[faint creek]

!status

[marsh citrus]

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

[jade sigil]

try to minimise the sum of the hidden sides

[marsh citrus]

@worldly vale Has your question been resolved?

[worldly vale]

can you pls explain

[worldly vale]

1

[worldly vale]

hmm, thanks sir

!ban

<@&268886789983436800>

[cobalt sedge]

<@&268886789983436800>

[wary zenith]

Ban these kids br

Thank you.

[jade sigil]

<@&268886789983436800>

[worldly vale]

Pls anyone solve this

and explain

<@&286206848099549185>

[faint creek]

What have you tried

[gloomy merlin]

Any thoughts?

We don't solve things for you

[sharp plank]

what do you think of how to solve it?

its the idea that makes the outcome

[worldly vale]

5 by 5 by 5 cube

[faint creek]

Yup, it's 5 by 5 by 5

[bitter cave]

try drawing an image of the cube.

[faint creek]

And which of the smaller cubes have been painted red and yellow?

[worldly vale]

the top , front and right faced cubes are red

[gloomy merlin]

Hint 1: ||Notice that every red face is opposite to a yellow face. If this is the csse, how can a cube be both yellow and red?||

[jade sigil]

<@&268886789983436800>

[marsh citrus]

@worldly vale Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[tawny knot]

Wait nvm I see my mistakes

.close

[marsh citrus]

Channel closed

Closed by @tawny knot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[rose saffron]

when do the two functions take on the same value in the circumference?

try writing the cosine in another way

[reef fable]

,rccw

[tawny knot]

Wdym

[rose saffron]

try to reduce it to 2 equal functions (like only cosine), so that you compare the arguments

[rose saffron]

why 40+360k?

[tawny knot]

Showing it repeats after every 360

Till infinity

Unless im wrong?

Is it 120?

[rose saffron]

in reality

its all the solution

not only the periodicity

[tawny knot]

😮

[rose saffron]

i mean in the second

how you obtained this?

[solid brook]

because sin(x) = sin(180 - x)

[tawny knot]

Ye

[solid brook]

equating the arguments gives 40,
sin(x) = sin(360 + x) gives 40 + 360k,
and sin(x) = sin(180 - x) gives 160 + 360k, which should be all the solutions

[tawny knot]

Is it not k.120?

[rose saffron]

x-30=90-2x+360k

[tawny knot]

Huh

[rose saffron]

https://www.quora.com/How-do-I-solve-cos2x-sin-x-30

you can take a look here

[tawny knot]

Its confusing 😕

[rose saffron]

also

x-30=180-(90-2x)+360k

[tawny knot]

.close

[marsh citrus]

Channel closed

Closed by @tawny knot

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[sinful pier]

Right so I know both ends are going to positive infinity

But I’m not sure how to like….write it

[normal moss]

Do you know limits?

[sinful pier]

Possibly- you’d have to give me more of a definition

[minor kindle]

$\lim_{x\to+\infty}f(x)=+\infty$

$\lim_{x\to-\infty}f(x) = +\infty$

is how id write it

[elfin berry]

rays

[normal moss]

If you haven't seen limits at all you shouldn't worry about them yet.

[sinful pier]

Right I don’t think….limits is smth we’ve done

[normal moss]

"As x tends to infinity, then f(x) tends to infinity" would be one way to say part of it.

For ex

[sinful pier]

This is precalc if that gives you any idea if we should have or should not have

But I missed the instructions on this assignment

[normal moss]

Yeah limits are thing u will see in calc the

[minor kindle]

ah then i would just say this:
"f approaches +infinity as x approaches +infinity. f approaches +infinity as x approaches -infinity."

[sinful pier]

Is there a not so wordy way to write it

[minor kindle]

well this is the best you can do "informally"

note that i wrote two statements: one for the limiting behavior to the left and one for the right (which is which?)

[sinful pier]

I vaguely remember doing smth similar to it in….algebra- but I don’t remember exactly

[normal moss]

The idea is just to describe what f does as x heads off arbitrarily far in the positive or negative direction.

Yeah often in algebra you talk about end behavior of things like polynomials or rational functions.

[sinful pier]

So if I wrote like…. F(x) -> inf, x -> [answer]?

[minor kindle]

what is "answer"

[sinful pier]

Do you think that would work?

[minor kindle]

f(x) -> infty should be the answer

[sinful pier]

Idk yet I left the room to use the bathroom

It’s a stand in

[minor kindle]

with "end behavior" you want to consider what happens as x -> + infty and x -> -infty

and your answer will be the behavior of f under these conditions

[sinful pier]

And do I write it the same way for y or is f(x) y in this scenario and I can just write one thing

[minor kindle]

yeah youd write the same thing for y replacing f(x)

[sinful pier]

So f(x) for x and just x and y for y?

Does “f(x) -> inf, x -> inf and f(x) -> -inf, x -> inf” seem correct?

[minor kindle]

no you got it backwards

f(x) -> inf, x -> -inf

[marsh citrus]

@sinful pier Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[latent flicker]

6. Suppose that Smartphone A has 256 MB RAM and 32 GB ROM, and the resolution of its camera is 8 MP; Smart- phone B has 288 MB RAM and 64 GB ROM, and the resolution of its camera is 4 MP; and Smartphone C has 128 MB RAM and 32 GB ROM, and the resolution of its camera is 5 MP. Determine the truth value of each of these propositions.
   a) SmartphoneBhasthemostRAMofthesethreesmart- phones.
   b) Smartphone C has more ROM or a higher resolution camera than Smartphone B.
   c) Smartphone B has more RAM, more ROM, and a higher resolution camera than Smartphone A.
   d) IfSmartphoneBhasmoreRAMandmoreROMthan Smartphone C, then it also has a higher resolution camera.
   e) Smartphone A has more RAM than Smartphone B if and only if Smartphone B has more RAM than Smart- phone A.

[latent flicker]

Discrete maths question, I want to understand how to translate from logic to english better

[rose saffron]

do you have example?

@latent flicker

still help?

[marsh citrus]

@latent flicker Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[scarlet sluice]

Can someone help me understand this problem please? Let’s say the first day arrangement is A, second day is B, knights 1 and 2 switch seats to reach arrangement C, then knights 3 and 4 switch seats to reach arrangement D. On the third day, let’s say the arrangement is called E, now, if two knights switch seats to reach arrangement C, is the seating over? Also, can knight 2 switch seats with 3 after switching seats with knight 1 on the same day given that knights 2 and 3 weren’t sitting next to each other on the same day

[burnt abyss]

Also, can knight 2 switch seats with 3 after switching seats with knight 1 on the same day given that knights 2 and 3 weren’t sitting next to each other on the same day

yes

all that matters is whether 2 and 3 were neighbours on the first day

and if they are neighbours today

On the third day, let’s say the arrangement is called E, now, if two knights switch seats to reach arrangement C, is the seating over?

yes

[scarlet sluice]

Hmm

So let’s say F is the arrangement after 2 switches with 3 on the second day, on the third day, if we reach C or F again, the meeting would be over right?

[burnt abyss]

the day you reach an arrangement that happened before the meeting ends

its unclear to me though if a knight can switch seats multiple times per day

i guess they can

right

[burnt abyss]

so yes

[marsh citrus]

@scarlet sluice Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[covert scarab]

$a,b,c\in\Z$, then (\gcd(a,b)=1) \land (\gcd(a,c)=1) \implies \gcd(a,bc)=1?$

[covert scarab]

no idea where to start

[red nimbus]

tf

[elfin berry]

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

[red nimbus]

Have you heard of Bezout

[carmine sedge]

(i think it's the Z that's the compiling error)

[scarlet ingot]

(\mathbb{Z} gives the integers btw, same with N and R and stuff)

[covert scarab]

[covert scarab]

$1=am+bn$
$1=ap+cq$

[elfin berry]

Nyxzore

[covert scarab]

xa+y(bc)=1

[red nimbus]

yeah

[covert scarab]

2 = am+bn+ap+cq\

$1 = \frac{1}{2}(am+bn+ap+cq)$

[elfin berry]

Nyxzore

[covert scarab]

1/2(am+bn+ap+cq)=xa+y(bc)

1/2a(m+p)+1/2(bn+cq)=xa+y(bc)

1=(am+bn)(aq+cq)

$1=(a^2mq+amcq+bnaq+bncq)=xa+y(bc)$

[red nimbus]

this form

[elfin berry]

Nyxzore

[covert scarab]

$1=aX+(bc)Y=xa+y(bc)$

[elfin berry]

Nyxzore

[red nimbus]

\prpl[a \cdot \underbrace{(amq+mcq+bnq)}{\in\Z}+;bc\cdot \underbrace{(cq)}{\in\Z}=1]

[covert scarab]

#Q.E.D

.close

[marsh citrus]

Channel closed

Closed by @covert scarab

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[knotty trellis]

Can I get a hint?

[knotty trellis]

It would be trivial if I had continuity everywhere

oh wait can i just limit the delta on x and thus make x close to x0

[cunning fiber]

For every $\varepsilon>0$, there is a $\delta>0$ such that having $|x-x_0|<\delta$ and $|y-y_0|<\delta$ implies
$$f(x_0,y_0)-\varepsilon<f(x,y)<f(x_0,y_0)+\varepsilon.$$
What happens if you fix $x$?

[elfin berry]

Civil Service Pigeon

[cunning fiber]

oh

welp

https://giphy.com/gifs/viralhog-viral-hog-pigeon-catches-the-sydney-train-kS1rILGKhd0JGsKuNZ

[red nimbus]

lol

[knotty trellis]

nvm i still dont get it

[knotty trellis]

I probably cant assume that the limits exist, right?

they wouldnt even necessarily exist if it was lim instead of limsup, right?

[knotty trellis]

I honestly dont know what happens when i fix x

except for having fixed x

oh i think i get what you mean

ill fix x within delta of x0

[knotty trellis]

then i take limsup y of that inequality ig

oh yeah i can do that since it holds whenever |y-y0| < delta, so for sufficiently small neighborhoods the inequality is gonna hold

then i have f(x0, y0) - eps <= limsup f(x,y) <= f(x0, y0) + eps

and now i can just take the x limit

[knotty trellis]

that inequality holds in sufficiently small neighborhoods, so that should be okay

and then i take lim of epsilon -> 0

and im done

[knotty trellis]

Thanks

you're a very smart pigeon

.close

[marsh citrus]

Channel closed

Closed by @knotty trellis

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[autumn seal]

Hey guys, I am a Cambridge International A level (CIE) student, giving maths P3 and M1 this may/june. Does anyone have any tips? Particularly for M1 as I do not have physics. Any notes, channels or resources would be greatly appreciated 😄

[prime ivy]

this channel is for homework help but ight

[tardy solstice]

i would ask in #study-discussion , this is more for asking help for a specific math problem that you have.

or #math-discussion

[autumn seal]

Oh alright, thx

[autumn seal]

Says I don't have access to this

[tardy solstice]

oh oops no worries, go over to study discussion then

you can close this channel by typing .close

[autumn seal]

Alright

.close

[marsh citrus]

Channel closed

Closed by @autumn seal

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[ripe shuttle]

how would u proceed using complex numbers?

[ripe shuttle]

i broke em down in telescopic, not understanding what to do next

[marsh citrus]

@ripe shuttle Has your question been resolved?

[cunning fiber]

,w power series arctanh x

[elfin berry]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[cunning fiber]

I'm assuming you meant partial fractions when you mentioned telescoping

since otherwise you'd be done

[ripe shuttle]

yes

[marsh citrus]

@ripe shuttle Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[rapid bone]

How many values of Y are possible? what does (o) mean here?

[static quarry]

what do the bars mean

repeating digits?

[rapid bone]

Yes..

[static quarry]

what is the context? what tools do you have available to work with?

[rapid bone]

a pen and paper with a tiny brain

should I expand it like...x00+y0+x?

(xyx-x)/990+ (zyx-z)/990=164/99

[main idol]

Should write xyx as 100x + 10y + x

[rapid bone]

oh nice....

let me proceed
((100x+10y+x-x)/990)+((100z+10y+x-z)/990)=164/99

(101x+99z+20y)990=164/99

[cobalt sedge]

you forgot an x from the 0.zyxyxy in your sum

and I suggest you clear the denominators by cross multiplying too

as next step ofc

[rapid bone]

i guess they cancels out no?

(101x+99z+20y)=1640

[cobalt sedge]

+x-x from first part cancels out, but there is a +x that still remains in the next term from the 0.zyxyxyx

[rapid bone]

ahha thanbks

[rapid bone]

how do I solve it?

[cobalt sedge]

recall that you took x,y,z as individual digits thus 0 <= x,y,z < 10 and not as any random number

so you dont have to exactly solve it, just look digit by digit

[rapid bone]

x should be 9

[cobalt sedge]

compare each digit of 1640 wrt the left hand side and what parts of the sum contribute to the individual digits

not really. try to work thru like I said, and youd see for yourself

[marsh citrus]

@rapid bone Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[rapid bone]

I tried to solve it but could'nt get answer in Integer form

[cobalt sedge]

take a look at the last digit, 0. Can you tell me which of x,y,z contribute to making the last digit of the sum as 0?

[rapid bone]

z and y

[cobalt sedge]

your equation was
(101x+99z+20y)=1640

[rapid bone]

yes

[cobalt sedge]

so you sure y and z contribute to the units place?

[rapid bone]

20y into 2

[rapid bone]

not really

[cobalt sedge]

20y means y shifts to tens place

[rapid bone]

10 multiple is absent

[cobalt sedge]

we are only considering the units place right now

[rapid bone]

no one is contributing

[cobalt sedge]

not really

[rapid bone]

101x?

[cobalt sedge]

you have 101*x which means there is a contribution of 1x in there

[rapid bone]

because it will be 100x+x

[cobalt sedge]

indeed

[rapid bone]

so x would be 0

[cobalt sedge]

similarly, theres 99z which is 100z - z

[rapid bone]

x-z=0

x and z would be same

[cobalt sedge]

yep

now its time to turn back to the original statement

[rapid bone]

200x+20y=1640

[cobalt sedge]

now that we established z and x are same digits, its simplifies this a lot

[cobalt sedge]

yea, this works too

you can directly find x and y now

[rapid bone]

x would be 8

y would be 2

[cobalt sedge]

indeed

[rapid bone]

is there any other possible values?

[cobalt sedge]

did you find any step which may have led to a second set of solutions?

[rapid bone]

i did not find any

[cobalt sedge]

so this makes it the only solution

[rapid bone]

hmm true

thanks a lot

.close

[marsh citrus]

Channel closed

Closed by @rapid bone

Use .reopen if this was a mistake.

[cobalt sedge]

np

[rapid bone]

i am new over discord and mathematics server

so it is amazing

lovely

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[fierce smelt]

guys if x+1/x = 4 then what is x^3+1/x^3

[fierce smelt]

ik that we have to use (a+b)^2 formula but i dont know how to get x^3+1/x^3

[devout mauve]

well probably (a+b)^3

[safe seal]

$a^{3}+b^{3} = (a+b)(a^{2}-ab+b^{2})$

[elfin berry]

lils ཐི༏ཋྀ

[safe seal]

did you learn that yet

[fierce smelt]

i remember that my sir used (a+b)^2 formula to solve this question but i cant remember it now

[devout mauve]

(a+b)^3=(a+b)(a+b)^2

[fierce smelt]

wait ill send a screen shot of that question

the 5th question

and 7th

anyone can help?

plz guys tmrw is my unit test

im having a problem with these type of questions

[devout mauve]

use the formula for (a+b)^3

either you know it or you can find it using (a+b)^3=(a+b)(a+b)^2

[fierce smelt]

ill try

wait a sec

18

i solved it so it came 18

[devout mauve]

no

[fierce smelt]

.close

[marsh citrus]

Channel closed

Closed by @fierce smelt

Use .reopen if this was a mistake.

[stable dune]

🥀

[red nimbus]

It's a paradox, right? Because he didn't figure the correct answer, but his doubt was resolve, right?

[stable dune]

the answer was right 🥀 for 5th

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[mighty venture]

$3+1

[mighty venture]

Bro

That was without

[fair stump]

<@&268886789983436800> trolling

[upbeat topaz]

can you not

[glass silo]

[upbeat topaz]

these channels are not for low quality trolling

.close

[marsh citrus]

Channel closed

Closed by @upbeat topaz

Use .reopen if this was a mistake.

[red nimbus]

high quality

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[blissful moat]

Among the whispers and light this channel's been seized for the night

[prime ivy]

what is thine question

[main idol]

See

[red nimbus]

It high quality

[crystal lintel]

we can afford to read one line of creative prose before the question gets posted

[blissful moat]

A circle passes through points (0, 0), (0, -16) and touches the parabola y ^ 2 = 8x If radius of the circle is r then what is the value of r^2/5

[brave marsh]

ghost always has a fun hook

[main idol]

Impossible to distinguish prose from troll

[harsh scroll]

What have you tried

Blurple has asked this problem b4 I think

[blissful moat]

ugly

algebra

[harsh scroll]

#help-28 message

Exact problem

3 months ago

[last crest]

yeah i would like do x^2+y^2+2gx+2fy=0 (c must be 0 if goes thru origin), then sub (0,-16) to solve for f, then use the condition of tangency...

[blissful moat]

ty i will look at it

[last crest]

sub in y for x with the tangency thing then solve the cubic and calc the r^2... ||ik how i would do it but i dont rlly wanna cus its a lot of work-||

[marsh citrus]

@blissful moat Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[blissful moat]

Yes you dont want to ts is a cubic

[blissful moat]

Fuck

This is a lot manipulation

Is there a way

<@&286206848099549185>

[late geode]

what's the origina question

[hollow snow]

.

[blissful moat]

Yes

Nvm i sleep

Good night

.close

[marsh citrus]

Channel closed

Closed by @blissful moat

Use .reopen if this was a mistake.

[hollow snow]

gn

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[keen girder]

hello

[keen girder]

i don't know how to start with this problem

[red nimbus]

I would substitute 1+x² and then try ibp

[keen girder]

okey one moment then

say whaat

how to progress

[red nimbus]

Hmm okay