help-49

[tiny shale]

Thanks for the help once again

[dreamy lichen]

yeah, then its right

[tiny shale]

You a legend

[dreamy lichen]

np

[tiny shale]

.close

[midnight plank]

Channel closed

Closed by @tiny shale

Use .reopen if this was a mistake.

[dreamy lichen]

oh perhaps one more thing, dont write 0 <= x <= 3. Write either ran(f) = [0, 3] or 0 <= y <= 3

[tiny shale]

Yh true

Or f(x)

[dreamy lichen]

oh and since x > 0, you cant even reach 0

nor can you reach 3

so it should be 0 < y < 3

not <=

[tiny shale]

Yk that was all 2 marks

Crazy shi

Can't i just graphical calculator it

[dreamy lichen]

if you can use that, then it should be possible with it

graph it and eyeball the range from the graph

[tiny shale]

M8 this is cheating no lie

Gonna bring this shi for the final exam

[dreamy lichen]

if its allowed on the exam, then its not cheating

[tiny shale]

Cost 2 bills 💀

[dreamy lichen]

but I'd double check whether graphical calcs are allowed

[tiny shale]

Yh they are

[dreamy lichen]

then you're good

[tiny shale]

.close

[dreamy lichen]

it's closed already, should disappear in few mins

[tiny shale]

Alr, might need your help tmr at sum point till then brother

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[torpid garnet]

¿Que has intentado?

[shell wigeon]

!muéstra

[tidal turret]

y podriamos usar las imagenes para obtener la funcion

tipo,
f(x) = (0,2)
f(y) = (0,-2)
f(z) = (1,2)
f(w) = (1,-2)

is an idea a bit algebraic but

say for example

no I have no idea

I thought I had something but, I dont think it will work

[torpid garnet]

Is I the set of irrational numbers?

[tidal turret]

no

[torpid garnet]

What is I then?

[sullen bolt]

I is an alternate notation for integer

used here instead of Z

[tidal turret]

interval

interval I think

[sullen bolt]

oh

[tidal turret]

well no, I think its the domain

@torpid garnet

well, in this case, the function is a parametrization, where I is an interval of the domain

no?

like r is a parametrisation, where I is the interval the parametrisation is defined in

no?

for example, find r(t) where t in I

at least from what I am interpreting, maybe there is a misunderstanding

[fathom onyx]

"I a subset of R(reals)" typically means "I an interval in the reals"

[tidal turret]

whats with that wires emoji

[west iron]

someone recognized his pfp and reacted with a matching emote

[tidal turret]

I dont have a pfp, so cant relate

[midnight plank]

@tidal turret Has your question been resolved?

[chrome vessel]

translation pls?

[chrome vessel]

a parametrization? this shouldnt be the case. A curve should have measure 0

that is: if the function is continuous, it shouldnt be possible

[tidal turret]

whats with the measure zero topic?

this is not measure theory, terry tao

[chrome vessel]

im just saying that it shouldnt be possible if you mandate r to be a parametrization

[torpid garnet]

It's the border of the rectangle so it is possible

And it is really easy

[chrome vessel]

oh it was unclear in the translation i thought its the whole rect

[shadow schooner]

yeah i would argue the og question itself is a bit unclear

[torpid garnet]

Do you know how to parametrise a segment?

[tidal turret]

NO

[torpid garnet]

The most common way is with a baricentric parametrization

[tidal turret]

can you explain

[torpid garnet]

r(t) : (0,1) → R², t → (1-t)·(x0, y0)+t(x1,y1)

If you see that is a segment that goes from (x0,y0) to (x1,y1)

[tidal turret]

what is a baricentric

[torpid garnet]

A baricentric combinatio of x1, ..., xn is like a1x1+...+anxn with a1+...+an=1

In our case, 1-t+t = 1

[tidal turret]

a linear combination or something

[torpid garnet]

With the propery that the coeficients add up to 1

[tidal turret]

🤔

[torpid garnet]

and the terms are usually points not vectors

[tidal turret]

i dont follow

what should I do now?

why is the question not specific and vague?

I dont think I understand

I dont think I follow

[torpid garnet]

You have to write a fucntion that goes all the way round the rectangle of that vertices

A parametric curve in specific

[tidal turret]

yes

thats exactly what I need to do, precisely

how do I do it?

[torpid garnet]

r(t) : (0,1) → R², t → (1-t)·(x0, y0)+t(x1,y1)

If you see that is a segment that goes from (x0,y0) to (x1,y1)

So in this case you have 4 segments

[tidal turret]

what does this mean in human ?

[torpid garnet]

You can think of a way of adapting and concatenating

[tidal turret]

what?

[tidal turret]

the parametric curve is from I which is a subset of R to R2

[torpid garnet]

r : (0,1) → R², (1-t)·(0,-2)+t·(0,2) =
= (0, -2+2t+2t) = (0, 4t-2)

this is the segment that goes from (0,2) to (0,-2)

[tidal turret]

how does that work?

im not sure i follow the notation

can you elaborate on the simbology

[torpid garnet]

r : (0,1) → R², (1-t)·(0,-2)+t·(0,2) =
= (0, -2+2t+2t) = (0, 4t-2)

this is the segment that goes from (0,2) to (0,-2)

Think of what happens when you substitute t=0, t=½ and t=1

Maybe that helps

[tidal turret]

how do you know the interval of the parametric curve is between 0 and 1

[torpid garnet]

That's standard for standalone segments

[shadow schooner]

maybe think of it like a weighting so if t is 0.25, r(0.25) is 75% (0,-2) and 25% (0,2)

[torpid garnet]

(And more generally for natural parametrizations but that is not a topic you should learn now)

[shadow schooner]

in this context i think you can decide what I is

Categorist made a convenient choice

[torpid garnet]

Yes and he might change it so he get the rectangle more easily in an intelligent way

[tidal turret]

the problem categoric, is that i don't understand the parametric curve you sent, why (0,1) -> R2

[torpid garnet]

Look at this:

r: (1,2) → R², (2-t)(0,-2)+(1-t)(0,2)

that would also work

That is a good hint for you

Look at what happens when t=1, and t=1,5 and t=2

[tidal turret]

(0,-4+2t) + (0,2-2t) = (0,-2)

[tidal turret]

(1,2) segment (0,-2)

[torpid garnet]

What?

No

[tidal turret]

i dont think i follow the idea

[torpid garnet]

This is a different parametrization for the same segment that which goes from (0,-2) to (0,2)

[torpid garnet]

Have you tried this?

Ok do this

[shadow schooner]

yeah trying points will make it more clear how the function maps points in [1,2] to one of the side of the rectangle

[tidal turret]

ahh the interval is [1,2]

of t

[torpid garnet]

r: (35, 36) → R², t → (35-t)·(0,-2)+(36-t)·(0,2)

Substitute t=35, t=35,5 and t=36. What do you see?

[shadow schooner]

he changed I but the image is the same side of the rectangle

[tidal turret]

t = 35 is (0,2)

[torpid garnet]

So the idea is parametrizing a side on (0,1) the next side on (1,2) the next side on (2,3) and the next side on (3,4) and sum them all on the union (0,4)

[shadow schooner]

I=[1,4] with a function defined by parts

[torpid garnet]

And yes it would be closed intervals. I'm so used to parametrising with open intervals bc of calculus, sorry

[shadow schooner]

now thinking about it would be [0,4] but same idea

[tidal turret]

how did you managed to find a formula based on t for the segment

[torpid garnet]

It's common knowledge, baricentric combinations I learned at uni when I was sophomore

[shadow schooner]

i like the intuition in term of weighting

but i’m not sure you got the idea renato

[torpid garnet]

Yes, it is useful and there are gif on the internet for the triangle case

very visual

[shadow schooner]

image for this sentence

[tidal turret]

yeah im newbie, like I started a week or so, university

[torpid garnet]

No problem

That is too much for second week of uni

[tidal turret]

how does the formula for the segments do that, then we union the segments?

[shadow schooner]

you have to define r(t) in four parts

[tidal turret]

life is tough dude, uni is eating me alive

[tidal turret]

and then what?

wdym in parts?

[shadow schooner]

as far as i am aware, multivarcalculus is usually a very full course, like there is a lot of stuff to cover in short amount of time

uni is like that sometimes unfortunately

mine was like that too, i survived and was rexeposed to the ideas later during undergrad

[torpid garnet]

THIS, @tidal turret

[tidal turret]

r(t) : (0,1) → R², t → (1-t)·(x0, y0)+t(x1,y1)

t = 0

[shadow schooner]

smt like this

[tidal turret]

can you mark the points?

of the rectangle

well, the most important part is how to get to the parametrisation of each segment or sub interval @shadow schooner @torpid garnet

like this (1-t) ...

you guys said baricentric what?

baricentric combinations or something?

[tidal turret]

the interval for t in [0,1) is the segment of (0,-2) to (0,2)

but how do I found a formula for the segments is what I am asking, a parametrisation of the segments or sides of the triangle

@shadow schooner @torpid garnet

I sort of have an idea

[shadow schooner]

https://www.desmos.com/calculator/fj6di7ongl

[tidal turret]

say you have a generic point, (x,y)

(x,y) = (1-t).(0,-2) + t(0,2)

nah, I dont follow dude

[tidal turret]

yes, how to get to find the formula dude

i follow what you guys mean, but I get lost in the baricentric part dudes

[shadow schooner]

do you agree when t=0, r(t) = (0,-2) and when t=1 r(t) = (0,2)?

[tidal turret]

yes

of course

[torpid garnet]

initial point (x0, y0)
final point (x1, y1)
variable t
interval (a,b)
formula
r(t) = (b-t)(x0,y0)+(a-t)(x1,y1)

[tidal turret]

ok, that clarifies a lot

[torpid garnet]

I don't know it by heart I know where it comes from and deduces it anytime I use it. Maybe you don't know, but you will

[tidal turret]

i appreciate the help

but

there is a simpler way I think

just, we have 4 points, we can create 4 lines

let me do a drawing

basically, each of this 4 lines passes through 2 points we will use parametric equation of a line

then, we figure out the intervals for t

but first let me draw and explain

knowing two point a line passes through we can find the line L1

L1 : X = t.((0,2) - (0,-2)) + (0,2)

L1 : X = t.(0,4) + (0,2)

then we write it as a generic point in R2

L1 : (0, 4t + 2)

now we need to find the interval of t such that (0, 4t + 2) passes through (0,2) and (0,-2)

that will be t in [-1. 0]

easy right?

[shadow schooner]

yeah this works also it’s a direction vector + starting point approach

[tidal turret]

you can find similarly the other segments

[tidal turret]

exactly dude

[shadow schooner]

but my guess is yes it will work but it will be clunky to get the precise interval you need

[tidal turret]

?

lets do the other 3 segments

otherwise you are not going to trust

[shadow schooner]

it’s not that i believe this is more efficient for that problem

plug and chug and extra point if you get the intuition

[tidal turret]

it surely is, but my approach uses less machinery, it would depend if you like complexity or simplicity

anyways, I dont want to bore yall, I just wanted to mention other approach

[shadow schooner]

try your thing and see for yourself

[tidal turret]

are you going to watch me or should I close?

we can always go back to categoric solution

[shadow schooner]

i can watch

[tidal turret]

ok

Let A = (0,2), B = (0,-2), C = (1,2) , D = (1,-2) be points in a rectangle!

LAB = t(A - B) + A = t((0,2) - (0,-2)) + (0,2)

LAC = t(A - C) + C = t((0,2) - (1,2)) + (1,2)

LBD = t(B - D) + B = t((0,-2) - (1,-2)) + (0,-2)

LCD = t(C - D) + C = t((1,2) - (1,-2)) + (1,2)

LAB = t(0,4) + (0,2)

LAC = t(-1,0) + (1,2)

LBD = t(-1, 0) + (0,-2)

LCD = t(0,4) + (1,2)

LAB is (0, 4t + 2) and needs to pass trough A = (0,2) and B = (0,-2)
thus, t = -1 and t = 0, so t in [-1, 0]

LAC is (-t+1, 2) and needs to pass through A = (0,2) and C = (1,2)
thus t = 1 and t = 0, so t in [0,1]

LBD is (-t, -2) and needs to pass through B = (0,-2) and D = (1,-2)
thus t = 0 and t = -1, so t in [-1,0]

LCD is (1,4t + 2), and needs to pass through C = (1,2) and D = (1,-2),
thus t = 0 and t = -1, so t in [-1, 0]

finally we get

,, r(t) = \begin{cases} (0, 4t + 2) \iff t \in \left[-1, 0\right] \ (-t + 1, 2) \iff t \in \left[0, 1\right] \ (-t, -2) \iff t \in \left[-1,0\right] \ (1, 4t + 2) \iff t \in \left[-1, 0\right] \end{cases}

[grand pond]

Renato

[shadow schooner]

this is good apart LAC t=-1 to t=0 (typo?) for parametrizing each line segment individually

[tidal turret]

@shadow schooner

[tidal turret]

?

[tidal turret]

LAC has t = 1 and t = 0 dude

ahh I see what you mean

we are re using the same intervals

like yes

[shadow schooner]

maybe it’s me whose tired on this one

[tidal turret]

nah dude, im also tired asfk

I went for the gym for 2 hours dude

nonstop in the treadmill

[shadow schooner]

but for this exercice this won’t do because it’s not a function same input gets sent to multiple outputs

[tidal turret]

yes

I guess we can re do with better direction vector

and better point that the line passes through

[shadow schooner]

you could try to tweak the starting point but it will get annoying though perhaps you will end up with a formula

tbh idk but seeing those two way to parametrize line is good

[tidal turret]

theoretically speaking if we would have chosen better line equation we couldve gotten a unique interval

is just that I hate this trial and error course

everything is so applied and with applications

maybe im just coping at this point, idk

[shadow schooner]

heads up you will probably do integrals on those kind of line segment later in this course (was covered in mine) and you can do each one with it’s own parametrization

[tidal turret]

king of line segment?

kind*

[shadow schooner]

what i feel they do is they make you play and familiarize yourself at the start with the object you will differentiate and integrate later in the course

so it feels arbitrary right now but it will pay off later type thing

[tidal turret]

maybe, im just been eaten alive by uni

is like first week or so and I am already struggling, tips?

[tidal turret]

Im going to be honest, I feel like I might need to retake this one, ngl

[shadow schooner]

don’t say that already, you didn’t even had your first midterms yet and you seem to grind hard.

[shadow schooner]

that’s one of the thing i disliked math undergrad for. you get blasted this very large amount of information and you get the feeling you can’t appreciate what it all really means

you learn to prioritize things, exercises part of lecture notes, you somehow have to guess what the midterm will look like and study for that based on cue from the teacher

those are like general tips

having people to compare homework or study max 2-3 is insane also if they are good

[tidal turret]

where did this category guy derived the formula

it seemed out of the blue

[tidal turret]

I am so antisocial, unless I meet a nice goth mathgirl I think I will be studying by myself dude, math is lonely

[shadow schooner]

tbh i’m not sure i would call this approach barycentric smt. for me it’s called a convex combination.

https://en.wikipedia.org/wiki/Convex_combination

[shadow schooner]

tbh, there are no better helpers sometimes than the other rats in the gulag with you

but my undergrad was very small

like 15 peoples

[tidal turret]

dude, the day I entered university we were only 4 people counting me in my class, that was starting math this semester

there are a lot from other years, math students, math dept is not small, but in this semester only 4 people were starting math major, for compsi it was like hundreds

[tidal turret]

I just hope I can find a nice girlfriend dude

who is also interested in math

[shadow schooner]

k so it’s different maybe if you struggle to the higher math class late undergrad, what i said about having this kind of math friend will apply more. (call shots for exam, give you deep insight on concept or find the trick in the nasty proof at the end of hw)

[shadow schooner]

i would’nt limit this to a (perhaps nonexistent) math girl. if you spot someone you will seemingly share a lot of hard classes with and they seem pretty good, go get them

[tidal turret]

yeah Im open to it, the day we were welcomed, the other 3 people one was a cute girl, hopefully I can make her my gf dude, she is also studying math, then we can talk about math no problem, about having male friends, well, im not so interested, i can always ask TAs for help so its not a biggie

[shadow schooner]

the 2 other rats i found first semester helped me so much even if they were not there at the end of my undergrad

but tbh this is getting pretty off topic

i need some sleep dude

[tidal turret]

rats = friends

[shadow schooner]

exactly

!rats

[midnight plank]

[tidal turret]

I appreciate the help dude, well its whatever

just hope I can find some gf dude

its funny the rat and the gulag analogy you do jajaj

[lavish venture]

😭

type shit

all of my advanced math courses are just men

[tidal turret]

what would you say its advanced math?

[lavish venture]

go for it

[lavish venture]

i mean like the advanced courses that are intended for advanced/promising undergrads

only ones math majors take

who want to go for a phd

[tidal turret]

damn, seems tough

[lavish venture]

but i’m sure you could find women in stem classes

girls do engineering

cs

💀

wdym?

your school doesn’t let them?

[tidal turret]

i fell in love with her because she is a math major

who tf chooses math?

[lavish venture]

i thought you said you just met her

[lavish venture]

a wife bro

🙏🏻

[tidal turret]

well, love at first sight

[lavish venture]

🤝🏻

talk to her

[tidal turret]

I cant find her

[lavish venture]

🤔

is she not in your classes?

how do you know she’s a math major

[tidal turret]

the first day of university the profs welcomed every group of people by major

we were four who started math major this semester, one was me

[lavish venture]

oh you’re a math major?

i thought you were cs

[tidal turret]

well, its complicated, I am also doing cs

[lavish venture]

ah

double major

that’s common

[tidal turret]

but only in case I am not able to get a job or something

[lavish venture]

😭

word

is she in any of your classes

[tidal turret]

but basically, our first year courses are so general so, every course has like 300-400 studnets

[lavish venture]

yea my first semester was like that

[tidal turret]

i haven't seen her since day1

will meet her later if she doesnt change her major

[lavish venture]

if you’re on campus enough you’ll see her

[tidal turret]

i am on campus all day, I have class from 9am to 2pm then from 5pm to 10:30pm

everyday

except weekends ofc

[tidal turret]

hopefully dawg

[lavish venture]

maybe she goes to clubs

like math club

not the other kind

[tidal turret]

well its complicated, she was too pretty to be a math major, so I am not having too much high hopes tbh

[lavish venture]

💀

should’ve went up to her on day one

[tidal turret]

need to join those mate, I have been just been stomped by university this first weeks everything is very different from pre university life

[lavish venture]

yea i hear you

you sort of drown in work and forget to do extracurricular stuff

i’m sure youll figure out what works for you

[tidal turret]

thanks dude, appreciate it

[lavish venture]

don’t take too difficult of a first semester

while you’re adjusting

[tidal turret]

wdym? the classes I take?

I cant pick them, like, is a predefined course path

[lavish venture]

oh i see

[tidal turret]

I can only pick classes after I finished all of the prereqs

like in year 5

[lavish venture]

year 5??

[tidal turret]

ye

[lavish venture]

how many years of undergrad are you doing

😭

[tidal turret]

its 1 year of foundations, and 5 years of bachelor, so 6 years

[lavish venture]

oh wow

you don’t even get a masters huh

[tidal turret]

I do

[lavish venture]

oh alright that’s good then

[tidal turret]

well at least we go directly to phd if we finish the licenciatura

university like, prefers to make you a generalist

jack of all trades master of none, so to speak

[lavish venture]

yea that’s strange

at my school we have the ability to choose from day one

[tidal turret]

how is university in where you live?

[lavish venture]

some courses are obviously locked behind prerequisites but it’s not bad at all

and sometimes you can just waive the prerequisites by emailing the professor and demonstrating you’re knowledgeable enough

[tidal turret]

crazy

[lavish venture]

very lenient

[tidal turret]

well I am not even mad brother, I get to study for free, and life is good, uni is filled with cute chicks

maybe its a little bit longer than usual

and like, courses are locked with prerequisites

[lavish venture]

🗣️

[tidal turret]

but you can take, like

some oral exam that skips you an entire course

[lavish venture]

i mean they probably have your interests in mind either way

you could always learn something on your own if it’s that important to you to learn it

[tidal turret]

well there is a lot of optional courses you can take, but thats in the later years

because in the first years is everything foundational

[tidal turret]

you think so?

[lavish venture]

yea the structure they have has probably been tested for years

[tidal turret]

I am liking my Algebra I class dude, but Analysis 1 sucks ass, i dont like it

[lavish venture]

professors usually know what they’re talking about/doing

[lavish venture]

well some parts of math are just a chore

[tidal turret]

they have changed the analysis 1 course to make it less proofy

and more of like, multivariable calc

[lavish venture]

you need to know it to be able to learn more interesting things

[tidal turret]

because every science makor was taking it

[lavish venture]

hmm

[tidal turret]

fair dude

[lavish venture]

they don’t have something separate for math majors?

[tidal turret]

no, math majors need to take analysis 1 to then take analysis 2 to then take advanced calculus and real analysis

and then you can take advanced analysis I guess

[lavish venture]

my favorite

[tidal turret]

its a class that is shared with other majors

that is why every classroom has like 400 students

[lavish venture]

this will probably change in later semesters

the first few courses you take inevitably have people from all over

like my first semester had a course with every kind of engineering student, physics majors, math majors, applied math, economics, chemistry you name it

computer science

everyone

[tidal turret]

engineering 😭

yeah I gotchu

our faculty is like science faculty so I havent seen any engineers from like, pre university classes

but in the other hand, yes, chem majors, physics, cs and data science majors

[tidal turret]

you from america?

[lavish venture]

yea new york

[tidal turret]

i think I kind of prefer the approach america takes, where you can graduate cum laude, like honors, so to speak

and take honor classes and shit

with honor level students

[lavish venture]

yea it’s nice to go at a faster pace and be with like minded students

[tidal turret]

that way, is more liberal, but at the same time you can do what you want

[tidal turret]

the big apple

[lavish venture]

in the advanced classes you can tell all the people are total nerds who love math

do it all day

[tidal turret]

crazy dude, hopefully that shit happens to me, unless I get lost halfway through...

[lavish venture]

nah

study hard and effectively and youll keep up

[tidal turret]

I appreciate it hard brother

[lavish venture]

no worries

[tidal turret]

will close this, I need to wake up tomorrow early asfk because of gymrat schedule, ty for the convo

[lavish venture]

you’re welcome have a nice night

[tidal turret]

.solved

[midnight plank]

Channel closed

Closed by @tidal turret

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[molten bay]

Question number 9

It is saying it is continuous at x=0

[sullen hornet]

One moment, please.

convert cos in terms of sine of the half angle

and then substitute x=0

@molten bay

[molten bay]

Bro they wanted me to find restrictions over alpha?

@sullen hornet

[sullen hornet]

Q's in hindi, not used to that. U typed continuity, so i thought u were asking for that...... but nvm..... sorry again..... my bad.

Alpha is smaller than zero is impossible

for that would give a constant/zero form

that option can be eliminated
now checking the other three.......
=0 is not possible

for that would give 0^0=1

it would break the continuity

so alpha is greater than zero

is your answer

@molten bay

[midnight plank]

@molten bay Has your question been resolved?

Channel closed

Closed by @molten bay

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[urban needle]

Can't catch up with the option C and B and D too

[urban needle]

I'm done with half but it's multiple correct

[sullen hornet]

newton's simplifications?

[urban needle]

Idk

[sullen hornet]

can you show me some of your work?

so that i may see where you're at

[clever igloo]

a^n - b^n is divisible by a - b

[sullen hornet]

everything here is correct, which is good.

[sullen hornet]

this is also alright..... okay now let me go ahead with the rest

there's a chance only these two options are right, so ill assume the other two are wrong and try to prove them as such. if im wrong, then you know that i am, and u may pick that option too

[urban needle]

A,B and C are right

[sullen hornet]

okay, so let's prove C is correct

i guess D was incorrect and u proved it using the exact same thing u did for A

btw..... did u get B?

[urban needle]

Nope

[urban needle]

No

I hadn't proven D

[sullen hornet]

actually...... there are two ways to do this

i see the JEE advanced label..... so then binet's formula is out of question

and the other is what you're doing

ill send a picture, one moment.

[midnight plank]

@urban needle Has your question been resolved?

[sullen hornet]

wait

catch that~

@urban needle

[urban needle]

Oh great wait

[sullen hornet]

what is it?

tell me

[urban needle]

Oh wait

Now i get it

Thank you very very very much

[sullen hornet]

you're welcome

and thank u!

[urban needle]

.close

[midnight plank]

Channel closed

Closed by @urban needle

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[gusty sky]

Can anyone please help me do this

[gusty sky]

I assumed D, B,A to be going downwards and C to be going upwards

And got A(d) =(A(a) +A(b))/2

And -A(c) =2A(b) +2A(a)

And from the rest of info given in question i got a(c) =-20/3 which corresponds to v=-20m/s at t=3 but in answer key it shows -57m/s

Can anyone please help me understand what I did wrong and how to do this question

Can someone pls help I have to submit my hw by tomr

<@&286206848099549185>

[midnight plank]

@gusty sky Has your question been resolved?

[hard meteor]

Bruh this is mathematics help not physics

[gusty sky]

Okk 🙁

.close

[midnight plank]

Channel closed

Closed by @gusty sky

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[twilit field]

I'm kind of lost

I first thought this is a conditional probabilty probelm

so P(W|A)= P(W \cap A)/P(A)

but that doesn't work

so baye's theorm was my next idea

but for that I need P(A|W)

oh

P(A|W)=0.6

is it not

[modern sapphire]

it is

[twilit field]

$P(W|A) = \frac{ P(A|W) \cdot P(W)}{P(A)}$

[grand pond]

wai

[twilit field]

$P(A) = \frac{0.6 \cdot 0.9}{0.7}$?

[grand pond]

wai

[solar hearth]

how did you get P(W)

[twilit field]

P(W) = P(W|A)+ P(W|A^C)

[solar hearth]

P(W)=P(W|A)P(A) + P(W|A^C)P(A^C)

[twilit field]

oh right

so with that change this would be fine?

[solar hearth]

yea you can solve for P(A)

[twilit field]

Thanks!

.clopse

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[undone vapor]

im not sure how to do this

[grim vector]

whats the definition of odd or even functions ?

[undone vapor]

i dont know

[grim vector]

fine ima write it out

[undone vapor]

i think its talkibg about the degree of the polynomial

[grim vector]

oh well its kinda related to it yeah

[undone vapor]

and the diffrent shapes of graphs can be seen by the degree is it not?

[grim vector]

but what if its not a polynome ?

it can but it has a more general proprety

[undone vapor]

they are polynomials on the title.

"slip 4 polynomial Odd and Even function"

[grim vector]

fine but the degree of the polynomial isn't all

[solar hearth]

not rigorous but whatever
even: f(x)=f(-x)
odd: -f(x) = f(-x)

[undone vapor]

ah yeah

i forgot about that

[cedar mason]

for all x in domain yeah

[undone vapor]

but how do i use that

[clever igloo]

Graphically, an odd function would be symmetric about origin and an even function would be symmetric about y axis, and their domains behave same

[mystic harness]

yep

[undone vapor]

ok

[grim vector]

compute f(-x) and -f(x) and see if there are equal or if f(-x) = f(x)

if there nothing its neither

[clever igloo]

So you just need to check, which one of the graphs

1. are symmetric wrt origin
2. are symmetric wrt y axis
3. none of the above

[undone vapor]

so i just put the same function equal to itself

[mystic harness]

yeah you’re right but be careful this technique only works if the domain is symmetrical to 0

[grim vector]

well ofc, else f(-x) is a no sense and the question wouldn't be one

this admit a coherant domain

[undone vapor]

huh im so confused

what am i suppose to do with that formula

[grim vector]

for each function f, you compute f(-x) and -f(x)

[grim vector]

and see if there is one of the two equality that is true

[undone vapor]

ah ok

thanks i can figure it out now

[grim vector]

if no equality stands, its neither

as a precision, the only function that is even and odd at the same time is the x : x -> 0 function

[undone vapor]

first one is neither

second one is even?

[grim vector]

So far so good

[undone vapor]

and third one i got odd

[grim vector]

yep indeed

[undone vapor]

4th i got nothing

[grim vector]

why so

[bold peak]

Where is the 4th I only see 3 in the pin

[grim vector]

(the graph)

[bold peak]

Oh my bad

[undone vapor]

thanks for the help

.clsoe

.close

[midnight plank]

Channel closed

Closed by @undone vapor

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[twilit field]

I wanted a hint

my first idea was to show that such a group always has an even number of elements

but that seems very hard to prove

Like I get $(n-1)^2 = 1mod(n)$ is probably the desired idea

[grand pond]

wai

[twilit field]

oh that's it, isn't it

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[twin forge]

Can you translate?

[olive matrix]

graph the intersection curve of the following surfaces

[midnight plank]

@tidal turret Has your question been resolved?

[tidal turret]

can I get some help?

[dawn dagger]

I can try to help

[rigid jungle]

hello

[dawn dagger]

hi

[rigid jungle]

i just joined

[dawn dagger]

welcome to mathcord

[grim vector]

#discussion

[dawn dagger]

yeah, this is an occupied channel

[grim vector]

Unless you wanna help renato

[tidal turret]

yes please help me universe

what kind of objects are we dealing with?

i) first is a circle? and then what?

but a circle in r3 is a circular cylinder

[dawn dagger]

a pringle

[tidal turret]

say what?

[cedar mason]

hyperboloid

well

hyperbolic parabloid actually

[dawn dagger]

i was unsure how to call it

but it comes from a quadratic form

[cedar mason]

but we dont have that here

[tidal turret]

in spanish this quadric surface is called silla de montar

[cedar mason]

we do indeed just have a cylinder

with a circular trace

[dawn dagger]

silla de monster

[tidal turret]

a saddle

[dawn dagger]

yea

[cedar mason]

yeah hyperbolic paraboloid

like

[dawn dagger]

if you put a circle on it you get a pringle

[cedar mason]

,w plot z=x^2/4+y^2/9

[grand pond]

Results provided by WolframAlpha

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

Requested by percykel

[cedar mason]

welp

oh thats eliptic lol

[dawn dagger]

i am so smart ong

[tidal turret]

guys no wolfram dude

[cedar mason]

,wolf plot x^2/4-y^2/9

[tidal turret]

guys, no wolfram allowed

[grand pond]

Results provided by WolframAlpha

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

Requested by percykel

[cedar mason]

there you go, pringle

[tidal turret]

guys no wolfram

[dawn dagger]

z=xy you can figure some traces for y=x, z=0, z=1

[tidal turret]

then what?

[dawn dagger]

it's just to get an idea of how to draw it

z=xy

[sudden yacht]

So it means you already know the shapes

[dawn dagger]

do you have to draw it in 3d or 2d

[tidal turret]

well, I know the one of the circle

[tidal turret]

it doesnt specify

im asumming r3

[dawn dagger]

the easiest is to just draw the circle and then draw the contour lines

we are mathematicians, not artists (although i would actually say a mathematician is an artist in another sense )

[robust isle]

or just work in cylindrical coordinates, no need to know what z=xy looks like in full

[tidal turret]

lol

[robust isle]

x=2cos(theta), y=2sin(theta), then find the correct z for each theta using z=xy

[dawn dagger]

i wanted a challenge

[robust isle]

ok mate

[tidal turret]

no but I think the exercise wanted us to use traces and level curves

[dawn dagger]

then 2d is fine

[tidal turret]

annyways, what traces should I try for z = xy

z=xy you can figure some traces for y=x, z=0, z=1

then we get z = x^2, z = 0, xy = 1

how will the graph of xy = 1 look like?

in the xy plane?

[sudden yacht]

Haven't you been taught it in precalculus?

[tidal turret]

oh, you mean y = 1/x

isnt this an homographic function?

like we have some horizontal asymptotes at x -> 0

[dawn dagger]

3d is hard ngl

i think 2d suffices for your purposes

[midnight plank]

@tidal turret Has your question been resolved?

[tidal turret]

so its not a pringle?

this is what my classmate sent me for this

[dawn dagger]

it would be if it was x^2+y^2 =< 4 but we have equality, so it's the boundary

[tidal turret]

the circle in r3 is a circular cylinder because z is free btw!

[dawn dagger]

yea

[tidal turret]

wait, this are the traces of z = xy

[dawn dagger]

some

[tidal turret]

umm I see

[dawn dagger]

i wanted to show how it would kinda-ish look like

[tidal turret]

how did you graphed the z = xy surface out of the y = x and y = 1/x traces

[tidal turret]

what would be the intersection then?

[dawn dagger]

I didn't quite draw the actual surface but traces of them

[tidal turret]

what about the intersection between the circular cylinder and the z = xy?

more less what will that be?

roughly speaking ?

[tidal turret]

is tricky drawing this just out of the traces themselves, like pulling out the graph of the quadric surfaces in r3 without looking at desmos or ggb

[tidal turret]

I see red and blue are traces of z = xy when z = 0 and when z = 1

[dawn dagger]

the boundary curve of a pringle

If you moved the line x or mathematically, you have x-c

the parabola traces go down

[tidal turret]

wait a second dude, how did you found a trace y = x when z = xy, did you set z = 0 or z = 1 or what?

because I am not finding it, if you do z = 0 then y = -x

also you are drawing the trace y = x at a height z = 0 so I thought thats what you mean but then y = -x

[dawn dagger]

In the plane y=x you get z=x²

if we move that plane back or forward the parabola moves diagonally and descends as well

For y=x-1 (in that plane) we get z=x(x-1), it intersects with y=x-1 at points (1,0) and (0,-1)

[tidal turret]

wdym boundary?

[dawn dagger]

this is how you could do it in 2D you would have to denote the z levels

[tidal turret]

also, nice drawing, is just that,the green should be living inside the plane y = x

[dawn dagger]

the red curve is called boundary

[tidal turret]

though I guess, is hard to draw by hand such that it looks like a pringle

[dawn dagger]

because we have x^2+y^2 = 4 not x^2+y^2 =< 4

[tidal turret]

i would say, only thing I dont understand is the arbitrary decisionship of using the y = x trace

[dawn dagger]

adding more traces makes it better visually too

but hard to draw

[tidal turret]

quite literally a saddle

but since its not a surface we cannot say its a pringle

its just the intersection between the surfaces

[dawn dagger]

yes

[tidal turret]

I appreciate it

[dawn dagger]

that is called boundary

[midnight plank]

@tidal turret Has your question been resolved?

[tidal turret]

.close

[midnight plank]

Channel closed

Closed by @tidal turret

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[exotic ridge]

#help-22 message

I'd like to continue with this problem I had yesterday night

[midnight plank]

@exotic ridge Has your question been resolved?

[midnight plank]

@exotic ridge Has your question been resolved?

[exotic ridge]

.close

[midnight plank]

Channel closed

Closed by @exotic ridge

Use .reopen if this was a mistake.

[vocal raft]

cx²+bx+a
cx²>0, a is fixed term
all depends on bx
max will be when bx is max → at 10b when b>0, and at -10b when b<0

[exotic ridge]

i gave up and looked at the mark scheme

ill be quite honest i dont really understand it myself

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[hybrid crow]

I need help proving forwards implication

and unfortunately there's no specification that V is finite dimensional so I cannot just specify some basis of V

Anyways

Suppose null S = null T, then dim null S = dim null T so dim range S = dim range T

That's about all I have rn

Maybe we could specify bases of both ranges of S and T

[midnight plank]

@hybrid crow Has your question been resolved?

[spiral rock]

maybe something with the first isomorphism theorem

since $W \cong V/ \ker(S) = V/ \ker(T) \cong W$

[grand pond]

ExpertSqueeSQUEE

[hybrid crow]

That wasnt yet introduced

[spiral rock]

yeah I guessed so

it doesn't even work what I said xD

[eternal pawn]

try to define E in terms of the image of a basis

[hybrid crow]

Yeah i thought about that

[eternal pawn]

did it work?

[hybrid crow]

Not for me

[spiral rock]

Take a basis of ImS and a basis of ImT

you want to map one basis to the other

[midnight plank]

@hybrid crow Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[rich yew]

Let me just clean up that notation rq…

[grand pond]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[cedar mason]

much better

uh !no sols

[midnight plank]

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.

[rich yew]

oops sorry

[midnight plank]

@upper lily Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[gusty sky]

hey can someone please help with this illustration

[gusty sky]

how does the equation at the last step become 0

sorry, if this is too basic but i just started binomial theoram chapter

[twilit jetty]

the identity used is nC0 + nC1 + ... + nCn = 2^n for all n

a way to justify this is "number of ways to gather anything from a group" is 2^n and also would be nC0, nC1, nC2, ..., nCn depending on how many things you gathered

[gusty sky]

but arent the odd terms in negative?

[twilit jetty]

oh they are, I dont know how I didnt see that

[steel crest]

you can also do binomial theorem on (1+1)^n

[twilit jetty]

then do binomial theorem on (1 - 1)^n or something idk

[gusty sky]

wait so then this terms becomes 2^(n-1) -2^(n-1) which then cancels out right ?

[twilit jetty]

few things up with that,

first, if we were using +s instead of -s, itd be 2 * 2^(n - 1) - 2^n instead

[twilit jetty]

second, I mentioned the wrong identity here

thats nC0 + nC1 + nC2 + ... + nCn which is all +s

nC0 - nC1 + nC2 - ... with alternating signs is a different identity

conveniently nC0 - nC1 + nC2 - ... = 0 regardless of n

you can prove this by using binomial theorem on 0 = (1 + -1)^n

[gusty sky]

okk then here odd terms become -ve and even terms become positive and that is =0

[twilit jetty]

yea, regardless of n

for example 4C0 - 4C1 + 4C2 - 4C3 + 4C4 = 0

since 0 = (1 + -1)^4 =(use binomial theorem)= 4C0 - 4C1 + 4C2 - 4C3 + 4C4

[gusty sky]

okk i got it thank you very much for your help

[twilit jetty]

np

[gusty sky]

.close

[midnight plank]

Channel closed

Closed by @gusty sky

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[steel cedar]

No.3
I don't understand why showing h = af + bg has the period of p necessarily leads to "all functions of period p form a vector space"

[steel cedar]

I thought that all functions of the period p form a vector space if every function of period p can be written as linear combination of f and g?

[runic hamlet]

a (nonempty) set is a vector space if any linear combination of elements in that set is again in the set

so if f and g are in that set, then af+bg needs to be again in that set

as it is a linear combination of some elements in the set

what you are thinking of is that f,g are a basis/generating set of that vector space. thats a different condition (and not true here)

[steel cedar]

So what I thought can be phrased as "functions of periodic p is a vector space" which is different from the book which says "functions of period p form a vector space"?

[runic hamlet]

the set of functions with period p is/forms a vector space

usually "set of" is omitted

but doesnt change much

[steel cedar]

Ahh i see it now

But we can't find a basis for functions of period p?

[runic hamlet]

maybe we can but I doubt it

it definitely wouldnt be easy

[steel cedar]

Yeah i guess it's pointless like saying to find a basis for any possible functions f(x)

Anyway this is pretty much solved

.solved

[midnight plank]

Channel closed

Closed by @steel cedar

Use .reopen if this was a mistake.

[steel cedar]

Oh and ty

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[gusty sky]

hey, I don't get what they have done in this solution can someone please help

[lyric charm]

$\binom{n}{k}$ is the coefficient of $x^k$ in $(1+x)^n$, agree?

[grand pond]

Ann

[gusty sky]

can you please write in the C_k expression

im unaware with the above one

[lyric charm]

fine

[gusty sky]

okk nvm $\binom{n}{k}$ is the same as C_k right ?

[grand pond]

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

[lyric charm]

$\binom{n}{k} = {}^nC_k$

[grand pond]

Ann

[lyric charm]

it is still n choose k but way less cringe

[gusty sky]

dw write in whatever way ur comfortable with i just had no clue about this notation until now

[lyric charm]

anyway then they viewed (1+x)^(2n) as [(1+x)^2]^n

[gusty sky]

how did they transend from the 1st to the 2nd step ?

[gusty sky]

ohh and then we just get a series by doing this in every term

thank you very much i got it

[midnight plank]

@gusty sky Has your question been resolved?

Channel closed

Closed by @gusty sky

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[hollow canyon]

hi

[next mulch]

hi

[livid python]

hi

[hollow canyon]

can someone tell me why my steps r wrong

the other one is from the textbook answer sheet

the point r collinear

collineeer

however u spell it

[next mulch]

The -r^2 + 6r + 5

it should be -r^2 +6r -5

oh wait

nvm

you forgot the integer rules

[hollow canyon]

nuhh i mean likeee

[next mulch]

i know

[hollow canyon]

ahhhh ok this is the answer i wanted lol

[next mulch]

r=1 or -5

[hollow canyon]

interger rule

[next mulch]

but it should be 1 and 5

[hollow canyon]

whatstht

[next mulch]

so

1/2(-r^2+6r-5) = 0

and

t should be

-1/2(r^2-6r+5) = 0

[hollow canyon]

huh

[next mulch]

then r = 1,5

[hollow canyon]

WHATS HAPPENING

hold on im kinda dummm

[next mulch]

.

so

yoo have ti

multiple the equation by -1

and remember

a.a = -a.-a

[hollow canyon]

which part issit

[midnight plank]

@hollow canyon Has your question been resolved?

[zenith snow]

Modulus over an algebraic expression refers to the positive value of the whole expression, not its individual terms

[hollow canyon]

ahhh

[zenith snow]

For example |x²-2x+1|=x²-2x+1
Not x²+2x+1

[hollow canyon]

wait how do i say this

ok lets take |-x²-2x+1|

[dusty arrow]

show wat you did , and why you did , we can show where you went wrong

[hollow canyon]

does is equals to x²-2x+1

[zenith snow]

Nope

[dusty arrow]

no it equals to
|x^2+2x-1|

[hollow canyon]

uhuhhh

ohhhh

sooo

ok idk how to say it

but basically positive turns negative and negative turns positive?

if its an expression

[zenith snow]

See |x²-2x+1| means that the whole expression needs to be positive, not each terms(as in x²,2x,1)
The whole expression (-x²-2x+1) could be written as -(x²+2x-1)
But putting a modulus over it,gives u the positive value the negattive sign gets removed, so u get x²+2x-1

[hollow canyon]

ahh ok i think i got it alreasdy

thank u victim

.closed

.clsoes

urgrhgrwiph

[zenith snow]

Type .close

[hollow canyon]

.clsoe

.close

[midnight plank]

Channel closed

Closed by @hollow canyon

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[tardy bloom]

I thought the points were -1/2, -2, -1
But it became differentiable at -2. Why?

[shell wigeon]

Factor that quadratic

[clever igloo]

|| X = -2 is an even times repeating root.|| do what @shell wigeon told you to do so, it helps

[tardy bloom]

(x+2)(x-1)

[shell wigeon]

Right, and at -2, what is x-1?

[tardy bloom]

-3?

[shell wigeon]

So |x^2+x-2| becomes...?

[tardy bloom]

0

[shell wigeon]

Ok fair... not what I meant

[tardy bloom]

Non differentiable

[shell wigeon]

Which term is a problem at -2

[tardy bloom]

?

[shell wigeon]

Of f(x), which term becomes a problem for differentiability at x=-2?

[tardy bloom]

|x+2| and |(x-1)(x+2)|

[shell wigeon]

Ok but it's not just |x+2|, it's -3|x+2|

And |(x-1)(x+2)| = |(x-1)| |(x+2)|, right?

[tardy bloom]

Yeah

[shell wigeon]

And at -2, |x-1| = ?

[tardy bloom]

3

[shell wigeon]

Do you see where this is going?

[tardy bloom]

The terms will cancel out?

[shell wigeon]

Exactly

Perhaps a better way to view it is to factorize the terms

(|x-1| - 3) |x+2|

Around -2, you can get rid of the abs:
(-x+1 - 3) |x+2|

[tardy bloom]

So the other terms becomes 0 and makes it differentiable??

[shell wigeon]

Well, the true justification is to take the limit of the derivative on both sides

[tardy bloom]

Thanks

[shell wigeon]

Or you can see that -(x+2)|x+2| is a quadratic on either side of -2

It's a quadratic going up on the left, and the same quadratic going down on the right, but at -2 it's derivative is 0, just like the derivative of x^2 at 0 is 0

(all this is intuition, the justification needs a bit more rigor, but I'm sure you can do that)

[tardy bloom]

Yeah

Thanks again

[midnight plank]

@tardy bloom Has your question been resolved?

Channel closed

Closed by @tardy bloom

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[blazing geyser]

someone help me with this please

[lyric charm]

a or b?

[blazing geyser]

both lowkey

[lyric charm]

ok

[blazing geyser]

can we start at a

[lyric charm]

yes we should do that

can you draw me a circle with a square inscribed into it

[blazing geyser]

im on laptop so i cant send photos

[lyric charm]

...

i mean i would need to see pictures of your work anyway so... this is gonna make things difficult unfortunately

[hushed mauve]

try using paint

[blazing geyser]

whats paint

[errant cliff]

i’m also stuck here

would it be um.. 1 divided by 4

[hushed mauve]

are you a windows user

if you are, i'm referring to MS Paint

[blazing geyser]

im a mac

[errant cliff]

hmmm

is it really not 1 divided by 4 omg

[lyric charm]

no, the square's side is not 1/4.

[zenith snow]

Do u know the formula of finding diagonals

[lyric charm]

1 meter is the diameter of the circular base; it appears as the diagonal of the square.

[errant cliff]

i don’t think so no

[zenith snow]

Or u could use pythagoras to find ot if u dont know that is

[errant cliff]

ohh

[lyric charm]

does either of y'all know such a thing as the pythagorean theorem

[blazing geyser]

yes

[errant cliff]

i’ve heard of it yeah

is that c= a^2 + b^2

[lyric charm]

you stated it wrong just now

c**^2** = a^2 + b^2

[errant cliff]

ohh yeah

[blazing geyser]

but u can also do the square root instead of c^2

[lyric charm]

you can write it as c = sqrt(a^2 + b^2)

[blazing geyser]

ye

a

[lyric charm]

in any case, y'all should know the ratio of a square's diagonal and side length

this ratio is sqrt(2).

[blazing geyser]

ohh

yea

right

[errant cliff]

what

OH

soo..

how do we use pythagoras theron for this

[errant cliff]

OK

[blazing geyser]

ok so um

[errant cliff]

soo

[blazing geyser]

how do we use pythag on that

[lyric charm]

write it out first

your two legs are both equal to x

[errant cliff]

okayy

[lyric charm]

your hypotenuse is equal to 1