help-23

[dense lark]

are we missing something

is it a 'intuitive' question

like a rough logic

[regal igloo]

According to the properties of the determinant for non-square matrices (specifically the Cauchy-Binet Formula), if (A) is an (m \times n) matrix and (B) is an (n \times m) matrix where (m > n):

[proud carbon]

oh i get it

[flat frigate]

Just me

[proud carbon]

@desert pasture calculation is just dirty work

[regal igloo]

Then answer 0

[proud carbon]

rank of a matrix cannot exceed the rank of its factors

[regal igloo]

But i don't know this property

[dense lark]

hmm

[desert pasture]

you're talking about the product?

[dense lark]

search it up?

[regal igloo]

Cab u explain

[proud carbon]

and since rank is less than 4 (AB is a 4x4) its 0

[regal igloo]

What is rank

[proud carbon]

linearly independant rows/columns

like they arent multiples of other rows

or factors

[regal igloo]

How to find it

[proud carbon]

by looking at the matrix

[desert pasture]

I really doubt y'all are expected to know this 😭

like the determinant isn't even defined properly from what I remember

then where is this supposed to pop out of

[proud carbon]

hows my logic

[dense lark]

idk much either tbh, my course was recently rationalised nd i think this was removed

[desert pasture]

I do by the logic of the rank of the product being less than 4, yes

[regal igloo]

I also think so this ncert🗑️

[dense lark]

they rationalised cuz 'Covid19 made kids dumb, nd so much syllabus is difficult for them to learn' 🥀 ✌️

[proud carbon]

calculation is just dirty work

[dense lark]

yea maths is all abt being lazy asf

[proud carbon]

considering its a mains pyq no way you have to calculate that much

[regal igloo]

Can anyone teach how to find rank

[desert pasture]

I know...

[dense lark]

jee rank?

[regal igloo]

U hsve 2min

[regal igloo]

Upcoming

[proud carbon]

thats why

[desert pasture]

that's the best way to do it unless y'all know the defn of a det

[proud carbon]

there had to be some other way

[proud carbon]

man we finished det in like 3 lectures prob

[desert pasture]

because proving it doesn't look very trivial

[proud carbon]

lol

[desert pasture]

maybe it's just the math major in me talking

[proud carbon]

or 2

[desert pasture]

[proud carbon]

yep

from jee perspective its a small and easy chapter

lol

[desert pasture]

okay, but @regal igloo what is intutuvely a det for you

what does it reprsent

at times that can help too

[regal igloo]

What is intutuvely

[desert pasture]

that can help you rationalise a lot of theorems

what physical quantity does it represent

[dense lark]

basically to get a 'feel' tht this will happen

intution

[patent citrus]

hi

[dense lark]

yk 'obvious' things

[dense lark]

arey haze hi

case ho

[patent citrus]

cool whats the question

[dense lark]

determinants

cauchy binet formula lg rha h

[regal igloo]

An collation of number which has no value which can we used to extraxt data like price rank or anything

[patent citrus]

bro what a coincidence ive been helped by all the 3 helpers here

[dense lark]

@patent citrus

[dense lark]

wdym

[regal igloo]

An collation of number which has no value which can we used to extraxt data like price rank or anything

[desert pasture]

It's volume or area

[regal igloo]

Volume my guess

?

[desert pasture]

Depends on if it's a 2 by 2 matrix or a 3 by 3 and so on

[proud carbon]

even i dont know that 🙏

😭😭

[desert pasture]

This would make the theorem Shreya sent more understandable I think

[regal igloo]

2x2 area and 3*3 volume then 4x4 ?

[desert pasture]

Ykw, forget it if I explain this I'll have to explain a lot of linear algebra

[ionic blaze]

is this still the question?

[regal igloo]

What i need to understand to understand that

[regal igloo]

Ye

[proud carbon]

2 simultaneous questions

that 1 and a det 1

[regal igloo]

3

U need to learning whole number

[proud carbon]

which is the 3rd one

[ionic blaze]

you can prove it(not algebraically) by letting c= some real number greater than a and b, and let a=b when both are real numbers and evaluating it then getting contradiction

well that is algebraically now that Im thinking about it

[regal igloo]

I gave 2 differements and 1 algebra

[proud carbon]

oh for the first one yk the method

[desert pasture]

okay imma dip, too many cooks spoil the broth

That and I have an exam in 2 days

[proud carbon]

now only thing left is to solve

[ionic blaze]

cases would be similar for b=c, a=c, and prove it's true for a=b=c? perchance

[desert pasture]

okay, but before I go

[regal igloo]

If u are giving exam next year are u in 12

[desert pasture]

one suggestion for EVERYONE here please

[regal igloo]

I proved it

[proud carbon]

yes

[regal igloo]

I think i will need to grind harder

[desert pasture]

https://youtu.be/Ip3X9LOh2dk?si=OnWkkHzqNtD_pmf0

this is a very important video

it will make the theorms that you can't yet prove very intutive

[regal igloo]

Ok

[proud carbon]

na my maths sucks dw

[desert pasture]

honestly the entire series (the essence of linear algebra by 3b1b) will, but it's not NEEDED as of now

[patent citrus]

it looks like it will make my already cooked determinants even worse

[regal igloo]

If u got this questions easily then u can be in top 50 of allen

[regal igloo]

Ok

[proud carbon]

i mean ive given olympiads

so

[regal igloo]

Is there any properties to solve any matrics easily is diagonal elements are 0 or same

[proud carbon]

i do have little maths experience

[desert pasture]

wdym

[desert pasture]

the diagonal elements are all 0?

[regal igloo]

I meant something like this

I atleast know name

[proud carbon]

wait

shit

wrong definition

[desert pasture]

,rotate

[regal igloo]

U just inverse it

[proud carbon]

iont think theres a property but

simplying would be easier

ig

[desert pasture]

what do you wish to do with these matrices

[proud carbon]

if diagonal elements are 0

[regal igloo]

I have seen many matrics in my syllabus so i wish there could be inway to easy solve them

[proud carbon]

then simplify the matrix

with row column operations

[desert pasture]

if the diagonal elemnts are zero I do think it would depen on the values

[regal igloo]

If 0 any nor 0

[desert pasture]

because $\begin{bmatrix}0&1&1\1&0&1\1&1&0\end{bmatrix}$

[flat frigate]

what a wonderful world(wai)

[desert pasture]

well

this is a symmetric matix

so bad example

[proud carbon]

i need to learn latex

damn

[regal igloo]

Use chatgpt to format latex

[regal igloo]

Computer book last chapter latec

[proud carbon]

double work

prompt and copy paste

[desert pasture]

https://youtu.be/Jp0lPj2-DQA?si=T0GWYejkRAFGFtT6

[proud carbon]

o tysm

[flat frigate]

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

[regal igloo]

U know a way?

[flat frigate]

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

[desert pasture]

I need an example..

also stop posting spam

[regal igloo]

Ok

[regal igloo]

\begin{bmatrix}
\textcolor{red}{0} & \textcolor{blue}{a_1} & \textcolor{teal}{a_2} \
\textcolor{orange}{a_3} & \textcolor{red}{0} & \textcolor{violet}{a_4} \
\textcolor{brown}{a_5} & \textcolor{magenta}{a_6} & \textcolor{red}{0}
\end{bmatrix}

[flat frigate]

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

[regal igloo]

This is an e.g

[desert pasture]

no it's not

it's too generalised

[regal igloo]

So we are generalising it

[proud carbon]

if diagonal elements are 0 then why not just open it

[desert pasture]

well, need not be a det

[proud carbon]

those 0s will make your life easier anyways

[regal igloo]

What if x

[proud carbon]

what yall trying to find

[desert pasture]

and I suppose it does have some interesting properties in LA

[regal igloo]

Generalising stuff

[desert pasture]

but idk what property that y'all would care 'bout here would even be worth proving

[proud carbon]

iont think theres any

[regal igloo]

Here we can do something is that it doesn't depend on a5

[desert pasture]

well

these may help?

https://math.stackexchange.com/q/79779/879009

oh well

the sum of the eigenvalues being 0 is somethign useful I guess

[regal igloo]

What is postive definite

[desert pasture]

leave it for now

[regal igloo]

eigenvalues?

[desert pasture]

There are many definitions, it's not worth it rn I feel

[proud carbon]

not needed for jee

icl

[desert pasture]

maybe this

is one accesible to y'all

but I'd use the other defn

but I digress

[regal igloo]

I think i am too dumb

[proud carbon]

i feel you

[desert pasture]

this is uni level LA usually 😭

positive definiteness the way I first learnt it requires something called am inner product space to start

[desert pasture]

though this defn doesm't

just don't worry about it for now

[regal igloo]

Ok

[proud carbon]

btw i gotta go so can i ask a quick q

its a bit off topic

[desert pasture]

in #「the-obsidian-twink-jesus」 ?

ping me there?

[proud carbon]

okay

[desert pasture]

<@&268886789983436800>

[regal igloo]

?ban

This jerks are also in my server

.vlose

.close

[safe radish]

Channel closed

Closed by @regal igloo

Use .reopen if this was a mistake.

[proud carbon]

nvm

its cleared

[safe radish]

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[jade kernel]

the current over here is 920.81 amperes right?

[glossy dock]

yes

100/108.6

(im using kiloohms)

[jade kernel]

but for some reason, I'm getting the same value in micro ampere as well

[glossy dock]

?

$I = \frac{V_{\text{source}}}{R_T} = \frac{100\text{ V}}{108.6\text{ k}\Omega} \approx 0.92081\text{ mA}$

[flat frigate]

thecrumbeler2

[jade kernel]

wait hold on

this solution says otherwise

[glossy dock]

it seems to be a typo

[jade kernel]

so 100/108.6k would be in kilo amperes right?

[glossy dock]

$V_D = \color{red}{V_B} - V_{56\text{k}}$

[flat frigate]

thecrumbeler2

[glossy dock]

^ this is a typo

[jade kernel]

what about this?

[glossy dock]

It should be $V_C$ because you are moving from point $C$ to point $D$. If you use $V_B$, you would have to subtract the voltage drops of both the $10\text{k}$ and $56\text{k}$ resistors

[flat frigate]

thecrumbeler2

[glossy dock]

i wrote mA

[jade kernel]

alright so that means voltage from A to B would be 20.26V right?

[glossy dock]

you are measuring voltage at the points not between

[jade kernel]

oh that means

A is at 100V

B is at 20.26V

[glossy dock]

correct

incorrect

subtract from 100

[jade kernel]

that gives 79.74V

[safe radish]

@jade kernel Has your question been resolved?

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

[errant ravine]

,rcw

[golden nebula]

!status

[safe radish]

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

[median sand]

So you're just gonna drop it here and expect us to do it for you or..?

[safe radish]

@foggy jackal Has your question been resolved?

[foggy jackal]

Noo sorryyy I meant to ask where I went wrong

[foggy jackal]

3

[thin bridge]

can't cancel those s^-2 like that since its part of a difference in the denominator

$$\frac{a\blue{b} + cd}{pq + r\blue{b}} \redneq \frac{a + cd}{pq + r}$$
$$\frac{a\blue{b} }{pq + r\blue{b}} \redneq \frac{a}{pq + r}$$

[flat frigate]

ραμOmeganato5

[foggy jackal]

Ohhh

[thin bridge]

just because a component is present "somewhere" in the numeartor and denom doesn't mean you can just erase it

[foggy jackal]

I understand now

Thanksss

.close

[safe radish]

Channel closed

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• Type the command .close to free the channel when you're done.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[odd solar]

Hi I need some help with finding forces using torques

[odd solar]

Ive done it wrong but im trying to find the force acting on the wheel at Point d and and the wheel at Point c

[open wedge]

,rcw

[safe radish]

@odd solar Has your question been resolved?

[odd solar]

<@&286206848099549185>

[novel stag]

do you mind posting the problem?

[odd solar]

yeah ofc

[ionic blaze]

is C the center of mass/point of rotation

and is this a rigid body

ok I'm gonna go read that

[odd solar]

im at vi

[ionic blaze]

-# as it turns out I forgot I hate physics

[odd solar]

same ahaha

[ionic blaze]

-# 10 damn subparts I ain't doin all at bro

[odd solar]

yeah i just need help with vi haha

just givimg context to the question

[prisma elk]

so did you take the sum of torque about point D

[odd solar]

nooo

[prisma elk]

so I think you have to assume the system is in static equilibrium

[ionic blaze]

I assume from the previous part but it seems like a weirdly placed question... although I'm probably just tsupid

[prisma elk]

um

[ionic blaze]

-# I'm not the brightest with torque

[prisma elk]

prob, cant tell tbh. My book just gives straight 1 paragraph of text.

for some questions

[prisma elk]

meh, same here tbh

[novel stag]

did you get v) right?

[odd solar]

sorry im confused, should i assume its static or not? i thought it seems like it would be tipping

[odd solar]

i hope so ahah

[novel stag]

what did you try for vi)?

[odd solar]

i got that there is 500n pushing on the trailer from the rail

[ionic blaze]

from the prev question it's prolly tipping just slightly

[odd solar]

i used point c as the pivot and calculated the torques

[novel stag]

,rccw

[odd solar]

would that mean there is no force on point d?

[prisma elk]

um: Assume the ramp and trailer are stationary throughout and do not move relative to each other is this not?

[odd solar]

ohhh right i forgot it said that

ah but the next questions r about it tipping

[prisma elk]

N_d < 0, it tipps

I think

[odd solar]

yeah that seems right

im just confused how to find Nd and Nc witout knowing if its static

[novel stag]

if you found the trailer to be tipping clockwise, what would $N_D$ be?

[flat frigate]

caspar

[odd solar]

would it be 0?

[novel stag]

yup!

could you share your calculations for the force on point B?

[odd solar]

yup gimme a sec

[novel stag]

,rccw

[novel stag]

do you know that your solution is wrong?

[odd solar]

ah what

nooo

damn

how wrong

[novel stag]

no im asking, calculations seem right to me but you mentioned you did the task wrong

for vi)

[odd solar]

oh oh

[odd solar]

this is my solution i think is wrong for vi

[novel stag]

why do you think its wrong?

[odd solar]

idk

i was just guessing lol

guessing how to solve it i mean

i dont know if negitive t means its rotating lol

[novel stag]

it seems like you put the torque from the left side of C as positive right? Then if you end up with negative total torque your trailer would be rotating in the opposite direction, clockwise

[odd solar]

yeah is that right? omg did i guess the correct thing ahah

[novel stag]

pretty impressive if this was just guesswork, you seem to have the general idea of the calculation steps down

[odd solar]

i kinda know the basics but im not too sure what im doing lol

[novel stag]

i think it would help if you structure your calculation steps and try to get an understanding of why you are doing them, helps in the long run and makes it easier to do more complicated calculations

and reduces guessing methods and hoping its right

[odd solar]

i will def work on it haha rn im trying to get this done before its due in an hour and a bit lmao

[novel stag]

well good luck!

[odd solar]

Thank you!!

[dense lark]

has ur question been resolved?

[safe radish]

@odd solar Has your question been resolved?

Channel closed

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[safe radish]

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

[dense lark]

Is there a better solution to this?

[dense lark]

cuz I did it thru venn diagrams

i did prove it

but i think i need to do a 'mathematical proof' i dunno

[median sand]

Well let start with for any arbitrary x in U.

Do you know what U is?

Venn is a straightforward one though, but want to know how it actually work then you use formal proof.

[dense lark]

yea cuz i rlly cant say '' Here's a venn diagram, its so obvious''

[dense lark]

union

[median sand]

Eh... No.

[dense lark]

I mean depends

[median sand]

U is the universal set.

[dense lark]

yea

[dense lark]

I thought tht U symbol used here

anyways yea ik all the sets basic stuff

les get on the solution

[median sand]

Then the first step you need to say is: Suppose we pick an arbitrary $x \in \mathbb{U}$.

[flat frigate]

Mercury (ヤフォダ)

[dense lark]

jst spam me w the solution

fas fas

[median sand]

We want to show that $(A \cap B) \cup (A-B)=A$.

[flat frigate]

Mercury (ヤフォダ)

[dense lark]

if ion get anything ill stop u

[median sand]

What?

[dense lark]

.

[median sand]

You know what, just do it by yourself then.

[dense lark]

...

hmmmmmmmm

i wonder how i can contact the mods

[median sand]

Since you think you can have the solutions, then you better think it by yourself.

Feel free to ping mods.

[dense lark]

ah alr

<@&268886789983436800>

aye sup

[median sand]

Helpee want me to "chop chop" and handle him the solutions.

[junior smelt]

Why the pingeth

[median sand]

Threatening me to give him solutions.

By pinging mods.

[dense lark]

scuse me what

[polar lynx]

The purpose of these channels is not to give you solutions

[median sand]

Read above please

[dense lark]

hey yea so acc to this insult rule i lowk think she violated one

[median sand]

I didn't do anything, lol.

You are the one who is threatening and insulting me.

[junior smelt]

And what was the insult then?

[polar lynx]

This reads like a threat to me

[median sand]

OP was the one who says: "Give me sols quick, else I stop you".

Then: "Or I call mods".

[polar lynx]

This reads like you trying to find reasons for us to punish the other user in this case

[dense lark]

I said ' i wonder ' 😭 cuz i cant see any help desk

[dense lark]

hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

[polar lynx]

Gotcha. Well now you know.

[dense lark]

https://tenor.com/view/yuji-itadori-yuji-jujutsu-kaisen-thinking-yuji-thinking-gif-8634259671603096188

[polar lynx]

It is best to move on from this issue.

[dense lark]

+1

[median sand]

Now OP either let me explain the question, or you can work by yourself.

[polar lynx]

The help channels are not for giving you solutions to problems. They are for helping people learn math. Just doing math problems for you is counterproductive to that goal.

[median sand]

But anyways, I don't feel like helping this guy anymore, good luck on finding other people to help.

[dense lark]

yea i agree

[dense lark]

aye same

finally we agree on smthin

[median sand]

What do we agree here, exactly?

You were the one with disrepectful behavior.

I think the mods are treating you lightly.

[junior smelt]

I also want to make clear that all the helpers here are volunteering their free time, and do not get paid to help. If someone does choose to help you, you really should treat them with respect (and not say things like this to them).
Mercury was nothing but respectful to you in her interaction with you.

[polar lynx]

Move on

[dense lark]

Alr so yea

See

I jst said you can spam me with the soltions

If i get a doubt ill stop you

Not big of a deal

[junior smelt]

We literally just told you that we do not give solutions here, no? If you want solutions, you're better off trying to get them elsewhere.

[dense lark]

I made it easier for you to jst go on typing and not stop for me to understand after every step you typed

[dense lark]

Alr dude "help"

[polar lynx]

What you are suggesting is not a useful method of help

[dense lark]

Where was the disrespect again?

[polar lynx]

Move on

Neither of you benefit from bickering about this

[dense lark]

Ik, but ion think they're gonna let me

Gosh

Lets end this

[polar lynx]

You framing it like this is just going to piss them off and prolong this. The solution as of now is for me to force you to move on.

[junior smelt]

At the very least, the role of the moderators is not for answering questions (and see the point I made previously)

Anyways-

.close

[safe radish]

Channel closed

Closed by @junior smelt

Use .reopen if this was a mistake.

[median sand]

https://tenor.com/view/chomp-bite-arm-gif-7083692912057941766

Cat bit.

[safe radish]

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

[north fulcrum]

did i make some mistake, why does doing dydx or dxdy give different results?

[north fulcrum]

t<0 and Z = X - Y

[safe radish]

@north fulcrum Has your question been resolved?

[fathom jewel]

I think your bounds for the left are not correct

,w plot x-y<-1 and x>0 and y>0

[flat frigate]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 4nzon

[fathom jewel]

y starts here from 1 not 0, or generally y starts at t

so y=t to y=oo

[safe radish]

@north fulcrum Has your question been resolved?

Channel closed

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[safe radish]

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[hard kettle]

<@&286206848099549185>

[manic patrol]

!15m please.

[safe radish]

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

[errant ravine]

!15m

[safe radish]

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

[hard kettle]

hello guys

oh okay

i thought we tag

is this occupied

[manic patrol]

now it is, by you.

[visual linden]

it's fine, please remember this for later though

[hard kettle]

okay sorry again

you guys know polyminals right

the long division one

[still stone]

could just show the problem, that will be more helpful

[hard kettle]

no I wanted to ask something about it

cause I might have a problem

I was absent when the teacher explain it further

can u guys like teach me

like the full long division theorem thing

I know how to do long division tho

I just don't know how we do it further

I was told it had surds and discriminant

so can I have help on those

nvm just close it I'll figure it out myself

.close

[safe radish]

Channel closed

Closed by @hard kettle

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[dense lark]

hi

[dense lark]

oh

[hard kettle]

.reopen

[safe radish]

✅ Original question: #help-23 message

[hard kettle]

holdup

buddha

come back

[upbeat swan]

https://tenor.com/view/buddha-gif-23893013

[stoic torrent]

-# LMFAO i was abt to send this😭😭

[hard kettle]

HELP ME

[dapper shell]

can anyone can explain me set bulider form😭 🙏

[hard kettle]

can y'all teach me long division polyminal full

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hard kettle]

bruh

[dapper shell]

what bro?

[stoic torrent]

see a yt vid?

[honest perch]

i suggest just doing examples

[dapper shell]

canya teach me set builder from

[stoic torrent]

ask in another channel

[hard kettle]

hey bro do u think I can learn calculus in under a month

[stoic torrent]

Thsi one is occupied

[stoic torrent]

no

[dapper shell]

like what

[stoic torrent]

#help-44｜stanley-🌲-v2-dans

[honest perch]

no, open a new channel

[hard kettle]

.close

[safe radish]

Channel closed

Closed by @hard kettle

Use .reopen if this was a mistake.

[honest perch]

yes

[dapper shell]

how?

[honest perch]

💀

[stoic torrent]

just ask your qsn there

[honest perch]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[dapper shell]

where?

[stoic torrent]

thats how you open a new channel

[stoic torrent]

.

Just ask your question in that channel

[rugged cave]

<@&268886789983436800>

[stoic dune]

<@&268886789983436800>

[lilac crane]

dont ping it

[stoic torrent]

<@&268886789983436800>

[rugged cave]

oops

[stoic dune]

Dang

[lilac crane]

you bastafrds

OPKO

[stoic torrent]

oops

[stoic dune]

Fast

[safe radish]

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[buoyant shadow]

more derators please

[whole hill]

<@&268886789983436800>

[safe radish]

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[cyan trout]

hi guys i had AI generate me some practice problems but I don't want it to grade them so i was hoping someone here might help me check if everything is correct

[cyan trout]

here are my answers

i know the noai thingy but i didn't know where else to get practice problems exactly like these

[exotic bolt]

Lowkey u got too much work

For each problem

Like for one

[cyan trout]

really?

[exotic bolt]

Just graph a little cord system if u want to show work

And put an x on the angle

[cyan trout]

oh, that's all i need to do?

could u give me an example if you wouldn't mind?

[exotic bolt]

Like first one 2pi/3

[cyan trout]

mhm

[exotic bolt]

I marked it

You know it’s quad 2

[cyan trout]

yep

so, im supposed to answer the questions in 1. a bit shorter?

[exotic bolt]

I mean in an actual exam I would

No reason to waste time on the easier ones

[cyan trout]

i understand

makes sense, thanks
ill try do them shorter next time

are there any mistakes btw?

[exotic bolt]

Nah they all fine

[cyan trout]

okayy thank you!!

can i close?

[jolly sail]

if ur finished u can close

[cyan trout]

alright, thank you guys

.close

[safe radish]

Channel closed

Closed by @cyan trout

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[slow marlin]

I first started by calculating the midline which is 2, the amplitude is 2, the maximum value of 2. I calculated the period of 2pi/2pi

[brave wolf]

the issue is that its shifted a bit

2sin(x)+2 looks like this

[slow marlin]

Oh I see

[brave wolf]

notice that at 0, it's in the middle of the wave

[slow marlin]

So there is a horizontal compression?

[brave wolf]

you might have to use cos here, or add some phase shift

[brave wolf]

no, not really, thats handled by period

[slow marlin]

Oh I see, what type of shift is it then if you don't mind me asking

[brave wolf]

phase shift

[slow marlin]

Ohhh I see

So it is quite literally shifting the entire graph

[brave wolf]

yeah, its a horizontal shift

are you familiar with that? The equation can look e.g. like y = sin(x + pi/2)

[slow marlin]

That makes sense

[brave wolf]

alternatively, you could use cos to model it

[slow marlin]

I am not familiar

[brave wolf]

and can you use cos (cosine instead of sine)?

[slow marlin]

i have not gotten to that section yet, I have worked mainly on sine functions in this chapter

[brave wolf]

i see, yeah, then we will just shift the sine function

[slow marlin]

although I do know that they can have identical graphs with different equations

[brave wolf]

yet another pic

[brave wolf]

Given how the 2sin(x) + 2 function looks like, what shift would you need to apply?

By how much do you need to shift it left / right?

[slow marlin]

I see, that makes more sense

Let me try to think about this one moment

[brave wolf]

-# you probably mean trigonometric functions btw, not hyperbolic

[errant ravine]

-# oh i thought this was true for both hyperpolic and sin function.. sorry

[slow marlin]

would it be left?

[brave wolf]

it can actually be both, it just depends on how much

[slow marlin]

oh okay, this is a new concept for me

would it be shifted by 1pi?

[brave wolf]

hmm not really

just added some points for reference

[slow marlin]

I think I need to be more familiar with the unit circle to understand this more

[brave wolf]

if you look at this, we need a U bump to be at 0

[brave wolf]

where is the U-bump in here? (there are many a lot of them, so just pick one. Ideally one close to 0)

[slow marlin]

is it between -pi and pi?

[brave wolf]

yeah, but where specifically is the minimum

like the vertex of the U bump

[brave wolf]

oh actually no, not quite what i meant

[slow marlin]

right before -2?

[brave wolf]

yeah, perfect

thats what i meant

can you express it using pi?

[slow marlin]

ohh i see, I apologize if I am veing frustrating

[brave wolf]

no need to apologize

[slow marlin]

tbh I dont know where to begin when expressing this with pi

[brave wolf]

well, you know the period is 2pi

[slow marlin]

yep

[brave wolf]

and sine goes like this:
goes up - max - goes down - min -
goes up - max - goes down - min -
...

[brave wolf]

at 0, it goes up. Then at 1/4 of the period, it achieves maximum. Then at 2/4, it goes down and at 3/4 it achieves minimum. Then at 4/4 it goes up again...

and it repeats like this

so this minimum in particular is achieved at -1/4 th of the period

[slow marlin]

Ah so this is represented on the unit circle?

[errant ravine]

-# math if i may add a bit onto this

[errant ravine]

yes!

https://tenor.com/view/matematica-gif-7322246

[slow marlin]

Wow!! so cool thanks

[errant ravine]

-# sorry for interupting continue

[slow marlin]

i love this visualization

[brave wolf]

there is also the one drawing the waves

https://tenor.com/view/sinusoide-gif-26675443

[slow marlin]

I need a protractor and a compass

Ok I love this

Absolutely amazing visual

[brave wolf]

i dont think you should rely too much on the unit circle, this is more about knowing how to work with graphs. You only really need to know how the basic sine wave looks like (which, if you want, can be deduced from the unit circle)

[errant ravine]

-# THIS IS SO GOOD i am stealing thiss!!

[slow marlin]

I can now visualize the 1/4, 2/4, 3/4 and 4/4 of the circle on each part of the sine function

[brave wolf]

yeah, thats great

[slow marlin]

so going back to the original equation, to express the minimum using pi, it would be 3/4?

I know that is not quite right since I don't have the pi in there

[brave wolf]

it's 3/4 of the period

or alternatively -1/4 of the period (the nice thing is that it doesn't matter! because of the periodicity)

and the period is... ?

(btw visualizing it oon the unit circle would look like this, sin is the y-coordinate and its minimum is here, at -1/4 or alternatively 3/4)

[slow marlin]

that makes a lot of sense

[brave wolf]

great, can you now find 3/4 of the period as a number?

You know what the period is, so now you can actually find the number (it'll include pi)

[slow marlin]

hmmm is it 3pi/2?

[brave wolf]

that's exactly it

okay so now we know by how much we need to shift it

we need to get that 3pi/2 bump to 0

so we need to shift it by 3pi/2 to the left

does that make sense?

[slow marlin]

YES

I am on track now, even though these concepts may not be completely solidified yet, I can at least understand that the lowest point is 3pi/2 and I know that the lowest point got shifted to 0 on the graph

[brave wolf]

great, so now to actually perform the shift, we use this

sin(x+c) shifts it to left by c

[slow marlin]

Yes, I remember this from the sine function

[brave wolf]

so if we wanna shift it to the left by 3pi/2, what will our c be?

[slow marlin]

would it be 3pi/2 (sorry if this sounds stupid)

[brave wolf]

correct

so what would the equation look like?

[slow marlin]

Ah yes, let me try

f(x) = 2sin(x + 3pi/2) + 2

[brave wolf]

that is correct :)

[slow marlin]

YES

thank you so much you are the best

[brave wolf]

np

btw you can try plotting the equations on desmos to check your work

[slow marlin]

yes I did!

[brave wolf]

good, if you dont have other questions, you can close this with .close

[slow marlin]

.close

[safe radish]

Channel closed

Closed by @slow marlin

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[safe radish]

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[rare flume]

ineed help understanding how to determine angles like 7pi/4 and 7pi/3 etc on an unit circle

[golden nebula]

Write it as an expression like $a * pi+b * pi/c$

[flat frigate]

-TimeLord-

[golden nebula]

Then you can use a to figure out the quadrant and b/c is just the fraction which you can turn into the angle

Make sure b<c

[rare flume]

ooghh okay thanks

[golden nebula]

!done

[safe radish]

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

[golden nebula]

This isn't the best way, but it's a start. Over time you may be able to do it much quicker without any calculations

[rare flume]

i hope so😭

.close

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[hot stone]

How do I do problems like 11-29?

[wind cypress]

do you know some basic limit laws?

[hot stone]

Uhh likee ? 😭

[dim wraith]

there is qr

maybe scan🖨️

[wind cypress]

well some basic properties are that limits respect addition

so taking the limit of f(x)+g(x) as x goes to infinity is the same as taking it separately for each function

[hot stone]

I don’t have the textbook with me rn
Not sure if I can get to the link using a photo but I’ll try?

[dim wraith]

first is like 0 + 3

[outer pollen]

-# I would probably first ask OP what she's actually struggling with.

[dim wraith]

second is -7

[outer pollen]

are you just spewing out answers?

[dim wraith]

like lim(1/x) is 0

[hot stone]

I don’t remember if I learned this, but i think this makes sensee

[hot stone]

This part makes sense

[dim wraith]

so you understand my answers 100%

or you still don't fully understand why so?

[outer pollen]

!nosols, by the way, as a gentle reminder, whether the OP understands you or not.

[safe radish]

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.

[dim wraith]

if op fully understand my answers - it's crime, if they are not please let them say

because it's important to understand if they 100% understand why so

[wind cypress]

another hint for a few of the problems, when computing the limit $\lim\limits_{x\rightarrow \infty}\frac{p(x)}{q(x)}$, where $p(x), q(x)$ are polynomials of degree $n$, there are some easy hints:

[outer pollen]

I have no problems with letting them say their misunderstandings, but nosols is about not providing solutions directly whether they understood it or not.

[dim wraith]

oh 😳

[flat frigate]

TestTickler

[wind cypress]

• if the degree of p(x) > degree of q(x), then the limit goes to infinity
• if the degree of p(x) < degree of q(x), then the limit goes to 0
• if the degree of p(x) = degree of q(x), then the limit is the ratio of the leading coefficients, which is just the number attached to the highest degree term

these ones are crucial to know

[dim wraith]

explain why limit is ratio?

we devide each numerator and denominator by highest order x^n

so kinda get other terms vanish lim(1/x)

only coefficients remain

[wind cypress]

yeah, essentially the highest degree term in the polynomial affects the value of the graph as we go to infinity, so we mainly focus on that

[dim wraith]

-# my t9 is braindead sorry

for example

,tex $\frac{1+2x+3x^2}{4+5x+6x^2}$

[flat frigate]

feel_in_tears

[dim wraith]

,tex we can $\
\frac{1/x^2+2/x+3}{4/x^2+5/x+6}\
$
right?

[flat frigate]

feel_in_tears

[hot stone]

I don’t understand why we must do that

[dim wraith]

which part you exactly don't understand?

[outer pollen]

-# I'll be on standby if OP needs another point of view.

[dim wraith]

,tex like you don't understand why do this multiplication $\
\cdot \frac{x^2}{x^2}\
$?

[flat frigate]

feel_in_tears

[hot stone]

Why do we divide by highest degree variable

Oh

Wut 😭😭😭

[dim wraith]

we devide/multiplcate by x²/x²

do you understand we can do that without spoil the equal sign

[hot stone]

Yes

[dim wraith]

,tex now look at this, for example $\lim_{x\rightarrow\infty}(1/x^2)=0$

[flat frigate]

feel_in_tears

[hot stone]

So this would be 3/6?

1/2

[dim wraith]

yeah

[hot stone]

Hmmm okok

Why is it hard to evaluate the limit without changing it by dividing/multiply by highest degree variable

[outer pollen]

you'll get inf/inf.

[dim wraith]

inf/inf is kinda banned

[hot stone]

Ohh ok

[outer pollen]

-# (more precisely, inf/inf is an indeterminate form, so you will need extra work to find the true limit if it exists.)

[hot stone]

Im a lil slow so im gonna ask again to be sure I understand
How does multiplying the original by x^2/x^2 get us to this 😅😅

[outer pollen]

-# sorry to interrupt, but perhaps thinking of this as a mult by x^2 on top and bottom is not the best idea.

[hot stone]

Would it be multiplying 1/x^2 in top and bottom

[dim wraith]

yeah i think so, maybe there other, better pov

[outer pollen]

better still, dividing both top and bottom by the highest degree.

the idea is that you want terms to approach 0 so that you can stop considering them, instead of inf where it gives you 10 years of headache.

[dim wraith]

like first notice highest degree of what is • in •→inf

[outer pollen]

-# I'll use a picture if needed, but otherwise I'll step back for now.

[hot stone]

Sorry i don’t understand the notation you’re using 😭😭😭

[dim wraith]

my gboard doesn't support earthling notation

[hot stone]

This might the the moment it’s needed that u step in 😔

[outer pollen]

please give me a moment to draw my idea.

[dim wraith]

-# maybe it's because it's Google Japan April's fool version of it like from temu

[outer pollen]

so we have this fraction, as an example.

now, a naive substitution of this will lead to inf/inf, as we've found out earlier.

[hot stone]

Yes

[outer pollen]

but let's look at the form we obtained by dividing by the highest degree.

this is going to take me a moment, sorry.

on cancellation of common factors, this turns into:

now let's look at our situation.
earlier, when we direct-subbed inf, we got (inf + inf + c) / (inf + inf + f).
but now we're getting (a + 0 + 0) / (d + 0 + 0).

and this happens because now all of the x terms are in the denominators of each term in the fraction, so they all approach 0 instead of inf.

so all you are doing is that you want each term to be divided by x instead of being multiplied by x.

[cloud notch]

Ok

?

?

?

[hot stone]

So for the example problem uhhh

[dim wraith]

there also notation like ↓0

not just 0

[hot stone]

Yeah 1/2 for the example

[outer pollen]

correct.

this is applicable any time you have two polynomials being divided (or in other words, a rational function).

[dim wraith]

am i right about this?

[outer pollen]

also, you may be wondering if we can actually do that, given we don't know the value of x.

[dim wraith]

we can't write 0 under lim sign

there are properties of limits

[outer pollen]

well, if that is your worry, you can rest assured it's legal - since x tends to infinity, we are definitely not dividing by 0 here.

[dim wraith]

i mean we can't directly write 0

[hot stone]

That makes sense

[dim wraith]

or inf

[dim wraith]

like we can't really write 0s here

[outer pollen]

and that concludes the explanation of how to deal with limits of most rational functions.

[hot stone]

Awesomeeee

Tysm 🙏🙏

[outer pollen]

(I say most - I'm very sure there's some weird edge case that I would not have seen, so just in case I missed any.)

but it should suffice for most of the problems in your text, if not all. happy solving!

[hot stone]

Okk

Oh wait

How will I know if something end up being undefined

[outer pollen]

division by 0.

[hot stone]

Ah

[outer pollen]

or if you mean the indeterminate forms...

[hot stone]

Yes that

[outer pollen]

there are 7 indeterminate forms.

[hot stone]

💀

[outer pollen]

these are all of them.

a bit of a note regarding 1^inf, however.

1^inf can be determinate or indeterminate, depending on the context.

[dim wraith]

you not always have easy way to reach even them btw

[outer pollen]

if the base is a constant 1, then 1^inf is determinate and equals 1.
if the base is a value that approaches 1 as the exponent grows to inf, then 1^inf is indeterminate.

all of the other forms are simply indeterminate, no ifs, no buts.

[hot stone]

😭😭 okkk

[dim wraith]

and also you can hop from one to other sometimes

[hot stone]

Tysm for all the help

[outer pollen]

alright, I'll step back now, as I think I've interrupted too much. I'll be on standby if you have further questions.

[hot stone]

.close

[safe radish]

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[fallen matrix]

1a and 1b are for context

My problem is the x coefficient where my answer is 65 not 104

[nimble wyvern]

one sec

[fallen matrix]

I think ive just realised what I’ve done wrong in writing my problem on here

For some reason I took (alpha)beta + Beta(gamma) as the same thing and wrote down ((alpha)beta)2

Silly me

[nimble wyvern]

oh yeah youre right

i verified all the calculations just now, after that correction you should be getting 13x13x8/26=52

[fallen matrix]

It’s 5am and I can’t sleep but I fixed it thank you

[nimble wyvern]

!done

[safe radish]

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

[fallen matrix]

.close

[safe radish]

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[shell oxide]

anyone know how to use this?

[median sand]

Use what?

[brave wolf]

if you mean the help channels, you can just ask your question right now

[normal moss]

Everything is written out nicely here

Just gotta read a little

[safe radish]

@shell oxide Has your question been resolved?

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[shell oxide]

The bot thinga ma jing

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[ionic blaze]

ok so now this is a culmination of weierstrauss, again, I got stuck at like ln|(c-a)z^2+2bz+a+c)|+integral (2b/(a-c))/((c-a)z^2+2bz+a+c)) dz

[ionic blaze]

how do I integrate (2b/(a-c))/((c-a)z^2+2bz+a+c)) dz

basically

wait

oh no

sigh

4b^2-4(a+c)(c-a)=4b^2+4(a^2-c^2)>0
I did get that c^2-a^2>b^2 so -b^2<a^2-c^2 so

ok wait

c^2-a^2>b^2

c^2-a^2-b^2>0
-c^2-

so it's less than 0 thus imaginary which would mean arctan-able I imagine

so oh dear god

can someone correct the math of my logic

[ionic blaze]

since we were given the c>a things

[safe radish]

@ionic blaze Has your question been resolved?

[ionic blaze]

alr I'm just gonnna

.close

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[worldly flower]

can aynone help

[crude bear]

spherical coordinates

better cylindrical

call r = sqrt(x^2 + z^2)

[worldly flower]

so it just become r

[crude bear]

Yeah

And leave y

[worldly flower]

ok

im gonna solve it now thanks

[shell spade]

Help now please

[errant ravine]

!occupied

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[shell spade]

Well fuck you

[errant ravine]

there are many open channels if u open ur own channel so poeple can help!

[safe radish]

@worldly flower Has your question been resolved?

[median sand]

That's not a nice way to speak to others.

[shell spade]

My apologies

[median sand]

No problem.

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[still frigate]

Hi guys, I’m in Calc one and my teacher is making me do this integral. I tried a lot of ways but it doesn’t seem to get me to the final answer. If anyone could help me that would be amazing

[tardy mango]

Note that the denominator can be written as
$$1+(\sin x-2 \cos x)^2$$
and also
$$6-(2 \sin x+\cos x)^2$$
this motivates the substitutions $u=\sin x-2 \cos x$ and $v=2 \sin x+\cos x$.

[flat frigate]

Civil Service Pigeon

[shell forge]

I feel like you can divide both up and down by cos^2 x

[tardy mango]

Further hint:||try to express the numerator as a linear combination of these two||

[shell forge]

ok it is another way

[tardy mango]

If you're trying to do the trick where you substitute for $\tan x$ since there's a factor of $\sec^2 x$ in the numerator, that doesn't entirely pan out because
$$\frac{\sin x+\cos x}{\cos^2 x}=\tan x \sec x+\sec x,$$
which doesn't easily lend itself to that.

[flat frigate]

Civil Service Pigeon

[shell forge]

$sec^2 x = 1+ tan^2 x$

[flat frigate]

夜靈

[shell forge]

then it is enough for us to let u = tan x

[tardy mango]

eh ....

try doing it yourself

you'll see what I mean

the surviving sec x messes things up

[shell forge]

ok

[safe radish]

@still frigate Has your question been resolved?

[shell forge]

@tardy mango I hope I didn't mistake on algebra, but yes it will anyway downgraded to simple integral

[median sand]

Are you OP, or?

[shell forge]

no

[median sand]

Why are you the one doing the work?

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[atomic basin]

help number 7 c

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[warm warren]

What have you tried?

[grave cargo]

cant find x

it 3^x = (root 5) - one / 2

anyone...

[zealous tundra]

log

[grave cargo]

yes im getting it

[zealous tundra]

both sides

[grave cargo]

but cant find x

[grave cargo]

...

[zealous tundra]

x will be log root 5 - 7/2

[grave cargo]

okk

tysm

.close

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[upper forge]

how do i quickly figure out if $\frac{100}{365}$

[flat frigate]

TheAstorPastor

[upper forge]

larger

or $\frac{3}{8}$

[flat frigate]

TheAstorPastor

[cunning pasture]

Cross multiply.

[plush spruce]

You can separate this fraction into smaller factors

[upper forge]

"quickly"

like 10-20 seconds

not more than that

[cunning pasture]

Or you can see that 100/365 < 1/3 < 3/8, so 100/365 < 3/8

[plush spruce]

I mean, for this particular case you can see that 100/365 is 1/3.65

As Meolve says, the quicker is cross multiplying

[upper forge]

hmm. yeah 100/300 = 1/3 . 100/365 < 100/300 or 1/3 ,and 3/8 i can covert to decimals quickly .37 which is larger than 0.33

i think that's good enough

.solved

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[cunning pasture]

3/8 = 3/(9 - 1) > 3/9 = 1/3

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[copper shadow]

how can you stop overleaf from cutting text?

[shut gust]

Hwo to do it mean instead of multiple we can cel 5 but how

if not smae numbers then what

<@&286206848099549185>

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[shut gust]

sry

[tardy mango]

Try wrapping it.

[copper shadow]

will look into this rn. Thank you

.close

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[copper shadow]

.reopen

[safe radish]

✅ Original question: #help-23 message

[copper shadow]

so I am already using aligned and I have a fraction so we can't have that line by line

[plucky elk]

#latex-help

[copper shadow]

could I also get some help with the limit? It is not clear to me how I can factor out x^3 on the top

[zinc hornet]

The way you are writing it out is such a nightmare. You should expand each piece one at a time.

Expand Sin(x) to O(x^5) or more if you aren't confident that is enough. Write down e^xlna and expand that separately, then plug in Sin(x) etc. It's just a lot of busy work to get it down to a polynomial with an x^3 and some higher order terms

Moreover, just set ln(a) = c or something. Its a constant and you are trying to write a fraction so long that you overflow your hbox

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[fringe drift]

can someone help me with ii

[jade birch]

Find AB and CD vectors

[fringe drift]

how do i figure out if they intersect

[jade birch]

Find the equation of both lines

then solve the system made of both equations

and see if there exists a solution or not

.c lose ?

[fringe drift]

let me try

[dim wraith]

extra minus ruining everything again

-# z=4 @fringe drift

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[chilly condor]

I need some help with factoring polynomials. for some reason, I cannot understand it despite being in tutoring for the past year

[thin narwhal]

do you have any specific problem you'd like to work on ?

[dim wraith]

what are your questions exactly?

[safe radish]

@chilly condor Has your question been resolved?

[chilly condor]

Give me one min

sorry

4x^2 (x^2-100x^2)

[thin bridge]

press ❌ if you don't want the channel to close on you

$4x^2(x^2 -100x^2)$

[flat frigate]

ραμOmeganato5

[chilly condor]

yes

[thin bridge]

Is that the Original question you were given?

[chilly condor]

Wait i typed it wrong