math-help

[timid delta]

Yeah then , log method is better

[night wolf]

right, ty

[timid delta]

Btw y=2.726

[silent snow]

how we calculate

approximately

i mean the log's value

[timid delta]

Uh you mean how do you know log(any number)?

[silent snow]

yeah but like this example

3^y = 20

[timid delta]

oh I just remember basic values , log 2= 0.3010 , log 3= 0.4771 , log 7= 0.845 and for log 20 it's log (2×10)= log 2+ log 10 and log 10 = 1 so log 20= 1.3010

I generally use log ( when it's base 10) , if other base then just use identity and find

And if natural log then lnx= 2.303×logx (base 10)

[silent snow]

i got it

thank you

[timid delta]

Your welcome

[random flame]

Hi can someone help me with part b? Ping if you do, thanks!

[velvet shore]

this one is still relevant

[timid delta]

Uh x= √5 only as X>0

[random flame]

I don’t get the ln 5 + ln x = 3lnx part tho

[timid delta]

ln( pq) = ln p + ln q

[random flame]

Ohh okie thanks

[timid delta]

Np

[random flame]

Umm can someone help with part b? Ping if ya do and Thankiew again! -^-“

[timid delta]

Aah wait

[random flame]

Thanks a lot yo

[ivory heart]

Lol m sorry I don’t

[maiden fog]

Anyone know how to answer this?👉👈

[left knoll]

Can someone explain how to do this 8(5+1)?

Pls

I really dont understand

[modern loom]

8(5+1)
= 8x6
= 48

[left knoll]

Ok nerd

thx

So in math you have priorities when calculating.

1. Anything in brackets
2. Multiplications and division
3. Addition and subtraction

@left knoll Are you Dutch? I could explain it in Dutch as well

Ik maakte maar een grapje

tuurlijk weet ik hoe het werkt

Dijenkletser

Assumptions are dangerous, so I don't assume anything. It might be that you're young and just don't know how to do it yet

[modern loom]

Just making sure... sometimes people don’t actually know how to do it.

[left knoll]

Yeah

yeh

I am so sorry Patatje oorlog

K verveel me gwn

[toxic bobcat]

hello, may i get help

[terse swan]

sure, depends on how hard the question is lol

[toxic bobcat]

pretty easy

you are gonna laugh

[terse swan]

nope

[toxic bobcat]

ill dm it to you

its a pic

of 3 little tasks

[terse swan]

okay sure sure

[waxen forum]

Hey loves lemme know if theres anything yall want help with in math 🙂

[torn torrent]

2. answers is : 41.3°

[terse swan]

can someone help me with question 3 plsss. the answer for this is √3/6

[terse swan]

i don't know how to get there tho

[left knoll]

No one answers your question lol

[terse swan]

it's a tragedy

[waxen forum]

Hold on lemme see

[left knoll]

Wait its blurry

[waxen forum]

oh great job!! 🙂

[timid delta]

Nais

[timid delta]

Use snells law

[waxen forum]

go to #science-help

[terse swan]

thanks man

[timid delta]

And for the first question , c= lambda × frequency

Frequency = c/wavelength

Generally we take c= 3×10⁸ , but you can take its exact value 299792458 m/s

[maiden fog]

Thank youu

[maiden fog]

Thank youu

[vague wave]

So I know how to get to the part when I get 1+ 1/n/3 form but Im not sure how we get the 6 there

[hard jasper]

you understand that?

[steel plover]

2cos^2a - 1 = cos2a

can someone explain how you get that ans please

[timid delta]

cos (2a) = cos²a-sin²a

sin²a= 1-cos²a

cos (2a) = 2cos²a -1

@steel plover

[steel plover]

Thanks!

[timid delta]

Np

[vague wave]

thank you very much! 🙂

[waxen forum]

@timid delta you are OG!!!

on top of all the questions. So goood

[hard jasper]

no problem 🙂

[hard terrace]

could someone see my math guide?

[timid delta]

What is OG? orthogonal?

Am not familiar with abbreviations ;-;

Especially related to memes , I left memes months ago

Aah leave am stupid

[toxic bobcat]

OG is for something old

or old in something idk how to explain

lets say you started playing warzone from day 1

and now after a year or more

i can say for you that YOU are OG

[timid delta]

I Googled it , but it shows original gangster 😂

Ohhhh

[toxic bobcat]

xD

[left knoll]

Hahah

OG means Original Gangster

But it's just used to talk about someone who was there from the start

[timid delta]

Ohhh

That means I have nothing to do lmao

Well am thinking of uninstalling discord now , cuz it's still distraction for me ;-;

But idk

[toxic bobcat]

try turning it off

if it doesnt work, uninstall

xd

[timid delta]

Well at first I was like , atleast I will be connected to studies all the time , now it's like I spend most of the time here ( I don't generally chat much , cuz am not that social) , but now it's like am 90% here ;-; , so I need to reduce that and focus somewhere else

[timid delta]

Uh can you translate

[hard terrace]

Yesss

The quartiles of the data are

Ammm

Quartiles of the following data?

Are respectively

[waxen forum]

Noo thats not what I meant. You are just on it!! Mathematiciian

[left knoll]

@timid delta if you have to write stuff, you can use an app called Cold Turkey Writer

[timid delta]

Aaah I don't understand , well see if you can find someone who knows your native language

[timid delta]

Oh TY :)

[waxen forum]

I wish I could understand the question. Could you translate it?

I don't recommend doing this but I found this online for you

[alpine mulch]

how to find C?

[dry badge]

Because the limit is different from both sides, the limit for c does not exist

[waxen forum]

c?

[alpine mulch]

oh ok thats what i thought, thanks

[dry badge]

no prob

[timid delta]

[timid delta]

Like is it better than notepad?, I generally don't write my thaughts , sometimes I share with classmates , but 99% I just remember them, but yeah I will try to write cuz idk

Or is it for translation?

[left knoll]

It's basically an app that blocks all distractions

[timid delta]

Ohhh

[left knoll]

Ypu can only type, and until you type a certain amou t of words, the only way to escape is turning off the system

[timid delta]

But it will require certain perms , I feel like It will leak personal data or something

[left knoll]

It's just an exe

On windows

Very lightweight

[timid delta]

Oh am on phone ;-;

[left knoll]

Ahhh

Hmmm

Do you have a computer?

[timid delta]

No

[left knoll]

Tablet?

[timid delta]

Well I have a lapi , but I only use it for tests , and nothing else

Tablet one is kinda complicated

[left knoll]

You could use discord only on that, to make sure you don't get distracted

[timid delta]

I have one. But can't do anything xD

[left knoll]

Hahah

So it's a nice paperweight

[timid delta]

Hmmmm, well I will try to only use when I have free time , I can control that , or if I feel that am too distracted , I will just leave server for few months xD ( I just have only one server joined , I left others ages ago)

[left knoll]

Or turn off notifications

[timid delta]

Generally after like using discord , I uninstall it like I just installed it 10mins ago

[left knoll]

If you get value from using Discord, then try to find ways not to get distracted by it

[timid delta]

The prob is I can easily download discord ;-;

[left knoll]

True

It's more about discipline, honestly

[timid delta]

And I don't have any source of entertainment except music , so well when I use phone for like longer period of time w/o discord , I just get bored , so yeah it feels empty kinda , so I download it

[timid delta]

True , I will try to reduce

[left knoll]

So you use it more to get distracted?

[timid delta]

Well you can put it that way , but sometimes i just feel good after solving doubts ,

I like doing questions

But not theory

And nowadays am just reading theories , cuz I feel like I am missing something basic

It might sound stupid ;-;

[left knoll]

Nah

I have that with math

Math is like a knife, you have to keep it sharp

[timid delta]

Yeah , atm I am studying physics and chem more , (organic chem ) and in physics jyst theory before questions , I just get extremely bored , and If I jump directly on questions , it feels like am missing something even if I solve the qyes

Ques*

So am reading theories only

[left knoll]

The thing with math is that you have to apply the theory asap

It's ok to struggle with it

You have to work with it to become proficient

[hardy urchin]

C) 5.5, 10 y 17.5

[left knoll]

But brushing up on the basics is never a bad idea

[trail horizon]

hey guys, do any of you know how to do this?

[timid delta]

Yes , I am trying , 2 days ago I was focused , but I use music to help me focus but I read an article about using earphones too much can damage your ears

[left knoll]

Do you still have this article?

Try to always question articles by looking up their sources

[timid delta]

I Googled it tho

[left knoll]

High volume can definitely damage your ears

[trail horizon]

more than 80 db damages ur ears

[left knoll]

And if they're uncomfortable enough to give you pain, then in the long run you might damage your ears by continuing to wear them

[left knoll]

*70

[trail horizon]

oo

[timid delta]

Yeah that's why I left listening music while studying , if I use em while studying , I go for like 4-5 hrs without stopping ( just cuz I don't realise am listening while studying) without it I just get distracted even with the sound of my fan ;-:

[trail horizon]

you can use a speaker

or just not wear headphones

[left knoll]

They don't have to be loud

[thick steppe]

do you still need help with this?

[left knoll]

Above 70 db can definitely get uncomfortable

[trail horizon]

yes i need help w a lot of question rn lol

[left knoll]

Most phones warn you now when you go above the safe threshold

[thick steppe]

okay so do you know how to write the standard form of the equation or should i walk you through it?

[trail horizon]

no i dont know how

[timid delta]

My phone used to but now It does not

I use bluetooth ones , it only warns if I used wired one

[thick steppe]

okay give me a minute, ill be right with you - kinda in class rn lol, but will try to help you asap

[left knoll]

Then try to stay at 60% and you'll be safe

[trail horizon]

thank youu

[timid delta]

Do you know about differentiation?

I can give you a trick to find the centre of any 2nd degree curve

[timid delta]

Yes ok ty

Is there any setting in phones which show volume percentage?

[trail horizon]

nope but literally any piece of information will be useful at this point

[red glen]

can anybody help?

[pulsar dove]

Can someone help with a Solids of revolution problem?

[timid delta]

Differentiate the curve wrt x and y respectively , you will get two lines , find its intersection , that point will be the centre

[dry badge]

I might be able to. Do you know what method to use?

[pulsar dove]

Yeah. I believe disk method is the correct one for the problem

[pulsar dove]

Is it alright if I PM you the question?

[timid delta]

Do you know about centres (orthocentre , centroid , incentre etc)

[dry badge]

yep

[timid delta]

It's an equilteral triangle

[trail horizon]

what-

[red glen]

I'm learning math in turkish wait i have to search

[timid delta]

Not wet , it's w.r.t

[timid delta]

Ok

[trail horizon]

i am confused

[autumn brook]

What I would do is just draw an imaginary line from the middle to the middle of AC and then just cos

[thick steppe]

okay im currently in the process of solving it give me a couple minutes 🙂

[red glen]

oh thanks i can do with 30-60-90 special triangle... i guess the answer is 12 is it correct?

[trail horizon]

okk

[red glen]

it helped thanks

[autumn brook]

Yupp 6sqrt3/cos 30 = 12

[timid delta]

Aah well I did without any cases considering you only know pythogorus

In short AG = a/√3 ( G is centroid and a is side of equilateral triangle )

And AD = √3 ×(a/2)

[red glen]

wow there is so many way to solve thank you guys. I learned new things

[timid delta]

Did you get it? Well if not maybe once you learn differentiation , it will help alot , if you wanna solve questions in very short time

And w.r.t to x means assuming y is constant and only differentiating terms of x

[left knoll]

Bruh Nuke chill lmao you don't have to help everyone.

Giv3 other people a chance

[timid delta]

Ok yeah

[left knoll]

Hey guys, anybody can help me please... i don't understand why this equality is correct :
2x²+x-1 = 2(x+1)(x-1/2)
apparently we need to use roots : x1 = -1 and x2 = 1/2... but i don't know why

Jk

[timid delta]

Nah , I am just going in 5 min anyways

[timid delta]

Any polynomial = a (x-a1)(x-a2)..... , a1, A2 ... Are the roots of polynomial and a is a constant

[left knoll]

Oh yeahh... so simple 😆 Thank you my friend !

[timid delta]

Yeah np

[near verge]

someone can help in this?

[astral salmon]

been stuck on this for a while, (diffrential equations btw)

1/2y' +4 =1 where y= 3/4 and x= 1/4

(v Pic for clearer thingy ( its from right to left since its in another language but i removed the thing and replaced it with english in the red marker)

[timid delta]

Is it 1/(2y') or (1/2)y'

[astral salmon]

(1/2)y'

[timid delta]

@astral salmon

[astral salmon]

thank you

[timid delta]

It's 4y

Wait lemme solve again

@astral salmon It's wrong I solved it not taking 4y instead I took 4

[astral salmon]

hm

im confused

i look at an example in the book i got and it shows one way of solving it which i did not understand, then i see my teacher's example which showed something else then i look at yours and its also different

anyways thank you

[timid delta]

Mine is wrong , wait lemme solve for correct question xD

@astral salmon damn , I am getting a function but at the given values it becomes not defined xD

Idk what I did wrong here

@left knoll ty for the advice , I will try to be more productive now

Now gotta go

[left knoll]

@timid delta Good luck! You can do this!!

[trail horizon]

does anyone know thisss

[left knoll]

watch this https://www.youtube.com/watch?v=Rw70zkvqEiE

[trail horizon]

ok ty

[hard terrace]

Thanks, i think that c is the answer

[drowsy rose]

Anyone know how to do part b)?

[wild folio]

integrate both sides wrt "t" from 0 to 10 ?

[summer sierra]

hey, does anyone know how i can study maths independently but also well? cus i'm going to go to a school with only 2h of maths a week and i want more since i want to go to university and i'm pretty sure 2h isn't going to be enough for that?

[vital vessel]

Have u tried khan academy? They have good resources. You can also try finding PDFs of textbooks to practise

[left knoll]

Brilliant has great courses, it's not free though

Kahn is another great one

[summer sierra]

appreciate it you guys

much love

[vital vessel]

Npp!

[summer sierra]

i heard openstax is also a good one, what are your thoughts on that?

[left knoll]

Haven't heard of that one

[vital vessel]

Yea nor have I

[summer sierra]

https://openstax.org/subjects/view-all

[left knoll]

It's open source and peer reviewed, I don't see how it could be bad

Definitely worth a shot!

[vital vessel]

Oh also, there a CEMC courseware that University of Waterloo has (a uni for engineering and their math is rlly good too). They have lessons and practise questions too. U can chevk that out

[fiery widget]

can someone help me with this?

[raven snow]

kinda late to the party but I can also recommend MIT opencourseware. I don't know a lot of courses offered there but this linear algebra course is very good. Heard it mentioned on at least 5 different occasions and it was always positive. Strang is an amazing professor. shouldn't be too hard to understand since it's an introductory class you'd take in your first uni semester (at least the case for me)
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

[summer sierra]

appreciate it man

[left knoll]

Can anyone assist me with Calculus?

[static beacon]

I can try, what's the task?

[vernal meteor]

anyone is familliar with discrete math counting ?

[proven hazel]

yeah i guess

shoot

[vernal meteor]

im struggling with the binomial coefficient, inclusion exclusion and graphing concepts

I have the lecture but still there are sum spots where I dont know

[vernal meteor]

so if there you have some explanation or examples that could help me understand them well it'll help a lot

[proven hazel]

have you tried youtube videos? they can be really helpful

[vernal meteor]

I watched some

I understodd the expanding and pascals triangle for example

but I got stuck in things like this

where the last one is just too annoying

[timid bridge]

Anyone able to help me out?

[raven snow]

if you mean g it helps to replace the binomial coefficients with their definitions n!/(k!*(n-k)!)

[opal bough]

Do you know the answer to the last one?

I came to that m and n can be any positive integers except 1 and 2. But I could be (and probably I am) terribly wrong.

[coral sierra]

Are you trying to show each of them hold true or? What exactly do you need to do for the last part

[alpine mulch]

help how do i do this without graphing

thanks pepe

[opal bough]

Well in the first limit the e^-x goes to zero. And sin(x) for x->infty goes vroom.

[coral sierra]

by looking at it, you ideally want to use the squeeze/sandwich theorem (idk what you call it) since there's a trig function involved

[static beacon]

"b" is easier, it's just an infty 🙂

[alpine mulch]

vroom

wait does sinx even have a limit

[opal bough]

So for a, limit does not exist I think.

[alpine mulch]

idk what ssandwich theorem is

[opal bough]

For this case the e^-x goes very smol, so it is basically sin(x), which repeats into the oblivion and beyond

[opal bough]

Yep.

[coral sierra]

are you trying to prove it or just get a limit?

[static beacon]

Seems legit

[opal bough]

Here is rigorous proof of my statement.

Q.E.D

[reef timber]

Nice proof 😄

[alpine mulch]

oki thank u

just limit

how do u do this algebraically

if possible

the example just shows a graph

wait do u just plug in 0

o wit that doesnt work

[opal bough]

I think it is doable.

[alpine mulch]

cacn i get a hint

[weary arrow]

I think you're supposed to derivative top and bottom of it

It's been a year since I had calculus but there's a theorem that says you can do that iirc and then it is solvable

[opal bough]

L'Hôpital's isn't necessarily needed this case.

[weary arrow]

Hmm yeah it might be possible to just rearrange it so all x are in bottom

[opal bough]

Just try to get rid of the x in the denominator.

[opal bough]

That way everything would blow up to infty.

[weary arrow]

Oh I just saw it goes toward 0 not infinity my b

[ancient agate]

anyone here able to help with statistics (intro)

[opal bough]

This thing can be algebraically simplified to the point, where you can just plug in 0 and get result.

[opal bough]

Try subtracting those two fractions in the numerator and see what happens.

[coral sierra]

You can visualise this as effectively getting the gradient of the function 1/x at x = 3

since it has the same format as differentiation from first principles

you can turn it into a simpler problem of differentiating 1/x and plugging in x = 3

If that didn't make sense, try to compare what your question is with this image,

I think that's the most elegant way to solve it

[weary arrow]

It's also possible to just rearrange it, you will get a constant in the bottom along with x, and therefore you can set x=0 with no problem, it just takes a bit of switching around the fraction to do so

[opal bough]

Dude, legit you can just subtract those two reactions and cancel out x.

And bam

[coral sierra]

u want to subtract 1/3 from 1/(3+x) ? I guess you could do it like that, I just thought that using first principles seemed elegant

[quaint imp]

How is determining the sign of a product the same as determining the sign of a quotient in integers

[left knoll]

if you can translate it to turkish we can get to somewhere

[quaint imp]

kk

[left knoll]

sorry

[quaint imp]

Bir ürünün işaretini tamsayılarda bir bölümün işaretini belirlemekle aynı şey nasıl belirlenir?

[left knoll]

ı cant stop laughin at this translation sorry you need another one ı would love to help you

[quaint imp]

its google translate

Bir ürünün işaretini tam sayılarda bir bölümün işaretini belirlemekle aynı şey nasıl belirlenir?

better?

[left knoll]

well turkısh is complicated a littel bit for it

[minor sluice]

Quality

[quaint imp]

yes

can u answer plz?

y turkish ur speaking english rn tho

How is determining the sign of a product the same as determining the sign of a quotient in integers

[minor sluice]

Cross multiply lmao

[left knoll]

oww its like this ıf you are dividing -/- its+ and if it is -/+ its - is that it

[left knoll]

I got -1/3

[nocturne prism]

Soz for bad hand writing lol

[left knoll]

sorry, typo, -1/9

just like the answer of @nocturne prism

[nocturne prism]

true dat

[left knoll]

it is a derivative problem f equals 1/(3+x) find F'(0)

[coral sierra]

f equals 1/x find f'(3) is easier to differentiate

but they are equivalent

[left knoll]

+1

[alpine mulch]

Sorry wut did you do here

@nocturne prism

[quaint imp]

r u guys solving my problem?

[nocturne prism]

Gimme a min I'll write it in detail for you

[quaint imp]

k

[nocturne prism]

What is your question dude :))

[alpine mulch]

Ohhh ok got it

Tysm

[nocturne prism]

yw

[left knoll]

@alpine mulch

thats one another way to put it

[summer sierra]

where'd that come from

the minus

and why'd it become -2

damn am i retarded or what

[supple island]

f=x^a, f'=ax^(a-1)

so if a=-1

f=x^(-1), f'=(-1)x^(-1-1)=-x^(-2)

if you're still not conviced do the limit of the difference quotient

[shadow mural]

guys ive been slacking off algebra 1 for a really long time and never took it serious do u guys have any youtube courses or something that does everything?

[supple island]

didn't your professor suggest a book?

books are generally better than youtube courses

also, what are the subjects of the course? it may vary, depending on where you are

[full surge]

Look up Professor Leonards youtube channel

he has everything you need for learning math from prealgebra to calculus 3

Literally the best math teacher ive ever had.

that i've never had*

[tropic topaz]

the rule is f'(x)= nx ^(n-1) right? so after applying the rule, the value raised to -(3+x) would be (-1-1) which equals to -2

[left knoll]

Exactly👌

[left knoll]

you need to be consistent about it if you have collage enterance exam nearbyi dont want to discourge you but i dont think you can do anything about it now but I belive you can get to the level you can full your tests in 1.5 year if you study continously
those guys at the top will stop rising at some point its the time for you to catch and annhilate them I belive you can learn it from beggining if you study hard after all its just highschool math

[lusty tundra]

hey guys, any idea on how to change the normal distribution to the exponential distribution in this question. This is a probability course.

[west plinth]

hi

im having my first math test in a long time, soon

please let me know what good studying techniques are

btw the test is on statistics and data (z scores, frequency, standard deviation etc)

please PING or dm if you have any advice, thanks

[static beacon]

Why do you need normal dist here? It's just about MLE question, you need to multiply probs, and so on

[left knoll]

find derivative of ax+b/x^(1/2) by from 1st principle method

[lusty tundra]

so do i jus take log in for the function?

[lusty tundra]

am i right

[static beacon]

You have 5 observations (light bulbs lifetimes), you need first to construct the likelihood function (just multiply f(x), substituting values, so your L(\lambda) = f(2) * f(3) * ... * f(4)), and only then, yeah, you can take log (log(L(x)) = log(f(2)) + ... + log(f(4))). Then you need to find max in respect to lambda, and that's all

[lusty tundra]

cause my friend gave me the solution and i do not understand it. how did the f(x) turn into lambda to the power of n

[static beacon]

Your friend's solution is right and I just wrote it 🙂
lambda to the power of n appears when you construct Likelihood function

[lusty tundra]

ok thanks. everythings clear! thank you very much

:)

[static beacon]

np

[left knoll]

Someone get me out of this pain😭

[twin bolt]

Does anyone know the solution to this?

[high tusk]

i mean sin function ranges from -1 to 1, so 1 being maximum should be the solution

[drowsy rose]

Anyone know how to solve first order differential equations?

having trouble getting a solution for this one

dx/dt= (x(400-x))/400

when t=0, x=100

[timid delta]

Ok

[drowsy rose]

the question is find x when t=10

[mossy crane]

1?

[timid delta]

I will try solving after lunch@drowsy rose ( going to eat rn)

[drowsy rose]

thanks! no rush, really appreciate it i've been stuck on it for a while...

[timid delta]

@drowsy rose do you have the answer?

My answer is kinda complicated ( exponential terms are there)

[drowsy rose]

I got 400e^10/3+e^10

[timid delta]

Yes

[drowsy rose]

awesome

the question was asking for a number of fish

so i think its 399 right?

[drowsy rose]

Thanks guys!

[supple island]

Didn't properly check so i could be wrong, sorry

[timid delta]

You r right

[supple island]

oh nice

[ornate copper]

guys i dont get the area of the shaded region...

[timid delta]

Yes it would be something like that cuz rounding off I am getting 400 , it will be around 399.9

[ornate copper]

i think im hella off

wait is it " pie/2 - 1"

[supple island]

Are you doing what option D says?

[ornate copper]

yes

its pie/2 - 1 ?

[timid delta]

Yep

I am getting that too

[ornate copper]

hue thx

tyty

[supple island]

Yep

[radiant tree]

can someone help me

?

Yeah I'm here

I kinda getting the hang of it

wait lemme try solving it

i think i got it

lemme put it in

wait

[timid delta]

Parabola is a second degree curve ,I think you misunderstood the question , pls re read ty

Am getting (y-2)²= 28(x-5) , idk it's correct or not , I just did mental calc , someone pls verify

[supple island]

the equation of a parabola is y=ax^2+bx+c and the coordinates of the focus are F=(-b/2a , ( 1-b^2+4ac)/4a )

@radiant tree

this should help

[timid delta]

That is focus or vertex?

[supple island]

focus

[timid delta]

Uhhh

[supple island]

oh need vertex too

[radiant tree]

I already solved it

but thanks

[supple island]

okay no probs

delta/4a is the y axis of the vertex

[timid delta]

So yeah the point ( -b/2a, -D/4a ) is the vertex right?

[supple island]

(1-delta)/4a is the y axis of the focus

[supple island]

yep

[worn mist]

There is a new rule (rule number 5), please read it before using the help channels! #welcome-verification

[supple island]

seems a fair rule

[molten star]

Yooo i had a silly doubt , in probability I seem to get confused with the question..can anyone help me on how to approach a question ( probability) ?

[steel plover]

can someone explain why we divide the numerator and denominator by cos(ϕ)cos(θ) in the third step?

[nocturne prism]

to make it simpler so that the tan of (x+y) it's trig identity must include the tan of both angles you know

[steel plover]

what does cos(ϕ)cos(θ) cancel out?

[nocturne prism]

gimme amin im writing it

[steel plover]

yeah thank you!

[nocturne prism]

Tell me if it's not clear

[steel plover]

no I got it, thanks again

[left knoll]

does somebody know to solve this?

[nocturne prism]

yw 🙏

[left knoll]

i have a big test tomorrow

[supple island]

holy cow that seems annoying

have you done polynome divisions?

[left knoll]

no

im 15

this s for facultative mathematics

[supple island]

what's the other part of the equation?

[left knoll]

nothing

thats all

[supple island]

it's no 0?

[left knoll]

nope

[supple island]

so what's the question?

[left knoll]

calculate

[supple island]

ok from what i'm getting you just have to try simplify everything

[left knoll]

yes

[weary arrow]

I can give it a go, I think you're supposed to just rearrange it lots until you get a simple answer

[supple island]

for example 9-x^2=(3+x)(3-x)

[left knoll]

yes i agree

[supple island]

try to do the best you can, if you get stuck, post a pic of what you've done so far

[left knoll]

ok ty

[nocturne prism]

This is it with common factors and stuff out so give it a try from here

[left knoll]

ok thanks a lot

[nocturne prism]

wlc

[supple island]

the x+3+3 is kinda decieving, you can't do much with it

[nocturne prism]

it can be 1+ 3/x+3

but yep maybe it doesnt help i just couldnt get the idea of it so i did that maybe his problem was taking out common factors or reforming it xD

[opal bough]

I tried to simplify this, it isn´t that nice, so I probly made a mistake. I can send it here if anyone wants to compare.

[opal bough]

Yep. Same result.

[nocturne prism]

That's probably true yep

[wanton shadow]

Determine the solutions x and y of the following equation system

i tried to put the question in english does anyone know how to solve this if been struggling on this.

[supple island]

ok so, this is a very simple system, are you familiar with the basic concepts on how to solve equation systens?

like can you solve the system
a+b=3
a-b=1

without guessing the numbers

[sharp ferry]

x.y=14
4xy=56> eq 1
x+y=-9
x²+y²+2xy=81 eq 2
eq2-eq1
x²+y²-2xy=81-56
(x-y)²=25
x-y=5, x-y=-5
x+y=-9
2x=-4 or 2y=-4
x=-2 or y=-2
y=-7 or x=-7

[supple island]

let them reason, if you just give them the solution they probably won't learn how to do it next time

[sharp ferry]

Ohhh ohh yeaa sorry my badd

[lethal slate]

Thats a very good solution but i think you can just say y=x/14 and put it in the x+y=-9

[sharp ferry]

y=14/x but I got your point ye

[lethal slate]

Sorry

[wanton shadow]

kinda but if you can explain it agaib mabey i will understand more i struggle whit my new math teacher

[supple island]

https://www.youtube.com/watch?v=oKqtgz2eo-Y

it's difficult to explain it by message

[wanton shadow]

oh oke thank you very much

[quaint imp]

How is determining the sign of a product the same as determining the sign of a quotient in integers

[timid delta]

🙌

[potent moth]

Can anyone please help me in this problem:
Find the relationship between a and b so that the function f defined by
f(x) = ax + 1 , if x less than and equal to 3
f(x) = bx = 3 , if x greater than 3
is continuous at x = 3

[waxen forum]

Sure one sec

[potent moth]

Thanks😌

[waxen forum]

Wait this is bx+3

[potent moth]

ya

sorry for mistake😐

[waxen forum]

No worries

[lethal slate]

Is it a-b=2/3

[timid delta]

[potent moth]

please explain bro @lethal slate

[waxen forum]

I got a=b+2/3

[lethal slate]

Yep

[timid delta]

Yeah that is same

[lethal slate]

I will try but my english is very bad

[timid delta]

Do you know about continuity ? Iike when we call a function to be continuous at x=a?

[waxen forum]

Oh okay lots of steps

[potent moth]

no problem bro just please explain me beacause I know what the answer is but I can't able to solve it in a proper manner

which is required

[lethal slate]

If it is continuous at 3 it means if you get closer to 3 in the left and right it will give you the same result

[potent moth]

Ya, I exactly have done the same but I want to explain this question in a proper manner because its important, isn't it?

[lethal slate]

Yes but i dont have enough english to explain this sorry :(

[potent moth]

o

ok no problem

Thanks for help

[waxen forum]

Hold on I’ll write it out for you

[lethal slate]

Your welcome

[potent moth]

ya please

[glacial robin]

how to solve it

?

[supple island]

translate please @glacial robin

[potent moth]

@waxen forum are you there?

[glacial robin]

L - Circle x = 2cos(t), y = 2sin(t), with positive bypass direction

[potent moth]

ya I know continuity very well but I need process of this question

[timid delta]

Ok wait

Lemme send

[supple island]

what's the question?

[timid delta]

@potent moth

[glacial robin]

mb just solve it

I dont know

[potent moth]

O thank you

[timid delta]

Yw

[supple island]

sorry pal, i don't even know what i have to solve

[solid anvil]

which grade question is this

[timid delta]

12th basic

[potent moth]

Yes

[timid delta]

Or you can do in 11th if you know limits

[potent moth]

its basics of calculus

[solid anvil]

your indian right

[potent moth]

Ya

[solid anvil]

in asian countries we are taught this at young ages

[timid delta]

Ohhh

India is in Asia too

[solid anvil]

our theory is good but practicals not that good

[supple island]

[supple island]

that's... strange, is it because you learn things by heart rather than actually understanding them?

[timid delta]

Hmmm, idk about any other country , I never researched about education system of other countries

[supple island]

because if theory is good practice is good too

[solid anvil]

no i mean related to programming

[supple island]

you can have good practice without theory cuz its jjust applying a pattern/formula

[supple island]

oh

[potent moth]

OMG what are you guys doing?

stop it

[timid delta]

@supple island you know electrostatics?

[supple island]

yah, i'm 3rd year in physics

[timid delta]

Can you spot any mistake?

I got Q= 0 , and it doesn't make any sense

[potent moth]

I am the junior in between you guys

[supple island]

can you provide the text of the problem?

[timid delta]

Well question is to find capacitance between plates 1 and 3 ( numbered from left to right)

It is connected to cell of emf V

[potent moth]

Thank you so much

[sharp stump]

i convert you image to jpg

discord dont support .heic

[potent moth]

@waxen forum Thank for doing a lot for me☺️

[supple island]

kinda rusty on electrostatics, ngl, it may take some time

[waxen forum]

I tried to break it down

[timid delta]

Np , although I asked from my classmates , they are not responding , take your time

[supple island]

ok so, Q, q and a are the charges on the respective surfaces of the cells?

cuz i'm not getting if these cells are plates or circuits or whatever

[timid delta]

Q is the charge I gave to the positive plate ( connected to postive electrode of cell) , q and q' are the charges at surfaces of each side of conducting plates (unknow charge , to be calculated in terms of Q)

The big rectangular polygons are conducting plates

And a normal cell notation

d= separation between each plate

A= surface area of each plate

e0 = permittivity of space

[supple island]

So if i've understood correctly your drawing, if you were to draw the circuit, It would look something like this?

[timid delta]

Yep

I can do this with this method but I was trying with charge distribution method

Btw thanks For your time 😄

[supple island]

Ok but with this configuration the charge on the left of the first plate and the right of the third should be the same

The same goes for second and the forth

[supple island]

Np

Also i guess that if you use kirchoff, the difference of voltage should be Q2d/eA

For the capacitor

[supple island]

Also i think that this charge should be 0 because that capacitor is attached to a circuit without anything else, and if se use kirchoff for a charge that's not 0 we have some Q'2d/eA=0

Which doesn't seem right

[surreal basin]

Hell0 everyone kinda new here

[supple island]

@timid delta try with this, i don't know if i helped because idk if i completely understood the problem, gtg back to my own studying

[fading copper]

Hey GuНЫ

Hey guys*

[vague wave]

Could anyone check if this is okay?

[fading copper]

I've some problems with this one
60 * (-9)^2 + 10 * (-9)^2 + 45
How do I take the total multiplier out of the bracket in this case?

[timid delta]

Yeah Good luck , ty for your time

[icy spindle]

45 = (-9)*(-5)

[near furnace]

i need help with

can anyone help

[surreal basin]

Here, factor the left hand side , so its should be (2cosx-3)(3cosx-2)=0. then find the roots of each term separately

[icy spindle]

Let u = cos(x) , then 6u^2-13u+6=0, then solve for u using the quadratic formula, then you get two values for u = cos(x)

Thus, x = arccos(3/2) and x = arccos(2/3)

[icy spindle]

First, sin(pi/4 + x) - sin(pi/4 - x) = sin(pi/4)cos(x) + sin(x)cos(pi/4) - ( sin(pi/4)cos(x) - sin(x)cos(pi/4) ) = 2sin(x)cos(pi/4). Then, you know that sin(pi/4 + x) - sin(pi/4 - x) = sqrt(2)/2; thus, 2sin(x)cos(pi/4) = sqrt(2)/2. Solve for x and you should get x= pi/6. 🙂

[near furnace]

would this be positive 3/2

and positive 2/3

[icy spindle]

Actually yes, I made a mistake

[sly shadow]

hi

can someone help me with complex numbers

[icy spindle]

I can try!

[sly shadow]

question 1 : Function : C--> C given by f(u) = (4+3i)u+(4-3i)u^-1
explain geometrically or otherwise why f(u) ir real whenever |u|=1

@icy spindle

[icy spindle]

Are you in a complex analysis course?

[sly shadow]

intro calculus and alebgra course

algebra*

[icy spindle]

Ah ok, I'm thinking about the question 1 min

[sly shadow]

ok thanks!

[icy spindle]

Ah ok, so...
F(u) = (4+3i)u + (4-3i)u^-1 can be expanded into => 4u +3ui + 4u^-1 - 3iu^-1 = 4(u+u^-1) + 3(u-u^1) , If |u| = 1, then (u-u^-1) = 0.

[frozen karma]

I cant get this

[icy spindle]

Hence, since the imaginary part is 0, the number will have the form f(u) = a + 0i for |u|=1.

[sly shadow]

ohhhh damn

it was that easy?!

[icy spindle]

Pretty cool huh?

[sly shadow]

yeah pretty cool!

[frozen karma]

Impressive

Im poopoo at geometry

[icy spindle]

Not sure what a labeled net is, but do you know how to find the surface area of a 3d shape?

[sly shadow]

the second part of the question is evaluate |(4-3i)+u|^2-f(u) for any u with modulus 1

[frozen karma]

uhm jeez am i this dumb?

@icy spindle not really no

[icy spindle]

Give me a second while I try to answer scratchsniff question real quick

[frozen karma]

@icy spindle okay appreciate it

[icy spindle]

You just need to expand everything, then group them up depending on whether they are real or not. Note that |x|^2 = x^2.

[icy spindle]

Well, to find the surface area, you can imagine it like this. Suppose you had an orange, and you wanna peel it. Assume you peeled it perfectly, i.e. in one big piece. Let's say the size of the peel is x cm^2. That is essentially what the surface area is.

[sly shadow]

so |(4-3i)+u|^2 will just be (4-2i)^2+u^2?

[icy spindle]

No, it will be (4-3i)^2+2(4-3i)u+u^2

[frozen karma]

Ohhhhhh, i see thats it??

[icy spindle]

Yes, so surface area in 3D is pretty much area in 2D.

[frozen karma]

Okay thanks bossman

[icy spindle]

No problem 🙂

[frozen karma]

[sly shadow]

" Note that |x|^2 = x^2" where does this apply?

[timid delta]

For real numbers

[icy spindle]

Take any integer a from the real numbers. Then, (a)^2 = (-a)^2. This is also why we say sqrt(x) = plus/minus (integer)

For example, sqrt(9) = +- 3

[timid delta]

Noooooo

Sqrt9 = 3

[icy spindle]

(-3)(-3) = 9

[bronze edge]

no, (-3)² = 9

[timid delta]

sqrt x²= |x|

[bronze edge]

and 3² = 9

therefore, Sqrt9 = +/- 3

[timid delta]

sqrt 9 = |3|or |-3| = 3

[icy spindle]

'For example, sqrt(9) = +- 3' by this i meant +/-

lol

[bronze edge]

Just "1" fits here...

[timid delta]

?

[icy spindle]

I think we are all arguing the same point lol

[bronze edge]

because you are saying sqrt x² = |x|
therefore x = |x|
Actually any real number sorry

[bronze edge]

yeah lol

any positive number

R+

Any positive real number

because modules don't take negative numbers

[timid delta]

? I don't understand what are you trying to say?

[bronze edge]

Let's say x = -2

therefore, -2 = |-2|

-2 = 2

[timid delta]

Nope

[icy spindle]

My point is |x|^2 = x^2 for any x in R

[timid delta]

Yes

[bronze edge]

This yes

[icy spindle]

because (-3)^2 = 3^2 = 9

[timid delta]

√9 = +3 not -3

[bronze edge]

But he said sqrt x² = |x|

that's why

then x = |x|

[timid delta]

yes sqrt of x² = |x|

Nooooo

[icy spindle]

'sqrt x² = |x|' this only works for x in R+

[bronze edge]

yes!

[timid delta]

Ehhhh wait lemme Google

And share link

Am lazy af to explain ,and if am wrong I will learn something new

[icy spindle]

Because if |x| can only take positive values, x can, however, have negative values

[bronze edge]

the sqrt of a square number is itself

Basicaly i think

[icy spindle]

sqrt((-3)^2) =/= 3

[bronze edge]

for R+

sorry

[timid delta]

https://en.m.wikipedia.org/wiki/Square_root

[bronze edge]

oh no wait i'm saying bs sorry

[timid delta]

We use √ as postive root

and I can prove by complex ✓x² = |x|

[icy spindle]

sqrt((-3)^2) =/= 3 this example contradicts what you are saying

[bronze edge]

Wait me or Nuke?

[icy spindle]

Nuke

[bronze edge]

oh ok

[timid delta]

Uh read wiki

[icy spindle]

oh lol

wait

I thought you were saying something different

that is indeed right, but thats the same as saying |x| = |x|

[bronze edge]

therefore, only R+

right?

[timid delta]

Yes |x|= |x|

[icy spindle]

Even though it isn't entirely correct, since sqrt((-3)^2) = +/- 3

[bronze edge]

R -> R+

[sly shadow]

what does R+ mean

[icy spindle]

Yeah it's a map from R -> R+

[icy spindle]

positive real numbers

[bronze edge]

Positive real numbers

[mossy crane]

we use conventional rules to avoid blunders in calculations

[sly shadow]

so R is just a real number right

[bronze edge]

But (-3)² = 9

[icy spindle]

sqrt(9) = +/- 3

so -3 is a totally acceptable solution

[bronze edge]

Any real number to be exact

[timid delta]

We only take positive root , -3 will be = -√9

[icy spindle]

Thats wrong, why would you only take positive root?

[ancient epoch]

no its not

[bronze edge]

That's wrong

[icy spindle]

In the quadratic formula they also use +/- for example

[supple island]

if i say x^2=9 than x=+/- 3, if i do sqrt(9) the only correct answer is +3

[timid delta]

Yes

[mossy crane]

yea because algebraically mod x can rep plus and minus x

[timid delta]

This is true

[bronze edge]

X can be any Real Value but Y just R+

[bronze edge]

R -> R+
-3 is valid for X

[icy spindle]

Its inherently wrong since square root is the inverse operation of "squared"

[bronze edge]

but not for Y

[mossy crane]

yep this sums it up

[supple island]

it doesn't work like that

we only accept positive solutions to square root functions

[sly shadow]

sqrt(9) = abs(+/-3)

[supple island]

and that's it

[bronze edge]

Ok so the thing we are trying to solve is

sqrt(x²) = |x|

Right?

[ancient epoch]

yes

[mossy crane]

sqrt(x²) = |x|

this is the algebraic form of it and this makes complete sense, to make a consistent definition we only take R+

[icy spindle]

R -> R+ defined by sqrt(x^2) |-> |x| , it is more correct to write only the positive root, but it is algebraically a correct midification

[bronze edge]

It's R -> R+

everything squared is positive

then the module accepts only R+

So Y is R+

[mossy crane]

sqrt(x) is a function and it can't assume multiple values, but they way it;s defined fits the definition of a relation and not a function thats why we set a conventional rule to restrict it to positve values to use it as a function

[bronze edge]

Ooh I get it, alright

[timid delta]

Yes

[bronze edge]

yeah yeah

now i get it

We cant define it R -> R+ because it's not a function

I just forgot about that 🤦‍♀️

[timid delta]

It is a function

[bronze edge]

wait no I'm confused

[timid delta]

y=√x is a function

[mossy crane]

only when its defined

[icy spindle]

|-3|=3

[timid delta]

Yeah only when it is defined

[bronze edge]

no it's R -> R+ no?

[mossy crane]

all the conics can also behave like functions if you restrict it to certain values tha makes it pass the vertical line test

[bronze edge]

like it can be any X value but not every Y value because modules

[mossy crane]

yep

just use layman terms lol its more confusing

[bronze edge]

So x can be -3 like we are saying no?

[mossy crane]

yes

[safe ruin]

what are we talking about here?

[mossy crane]

y cant be -3

[icy spindle]

Saying sqrt(9) = +/- 3 is correct

[mossy crane]

yea

we do use it

[supple island]

no

[bronze edge]

sqrt(x²) = |x|

[timid delta]

No

[mossy crane]

hol up

[timid delta]

Sqrt (9)=3

[bronze edge]

nuke

[mossy crane]

if you are doing calc use only positive no.

[bronze edge]

you are thinking wrong

[icy spindle]

Then explain to me how magically (-3)(-3) is 9?

[mossy crane]

if you are doing co-ordinate geometry

you use +-

[supple island]

think it this way if x^2=9, then x=+/- sqrt(9)

this is how it works

[bronze edge]

Sqrt [(-3)²]=|x|

[mossy crane]

goddamit the math is not wrong the context is

[safe ruin]

when minus signs multiply with each other, it gives a positive integer :O

[bronze edge]

|-3|*

[supple island]

this is what we use and accept, check wikipedia or whatever

[bronze edge]

(-3)² = 9
therefore sqrt(9)

no?

[supple island]

no

[timid delta]

I never said (-3)² is not equal to 9

[timid delta]

?

√(-3)² = |-3| = 3

[bronze edge]

I'm just trying to prove that R -> R+ :' )

[supple island]

if x^2=9 then x=+/- sqrt(9) so =+/- 3

[bronze edge]

YES

[mossy crane]

dont

whats the question

[mossy crane]

you are proving f:R->-R which is correct becuase you are defining a function

[supple island]

hence this, sqrt(9) can't be a negative number

[mossy crane]

if you are defining a relation

it can take + and minus values both

[bronze edge]

YES! But y can

[mossy crane]

the context is what matters

[bronze edge]

sry

x

not y

[timid delta]

Idk what is happening here anymore

[bronze edge]

neither do I

xd

[mossy crane]

dude

you dont need complex numbers for this

[timid delta]

When this concludes , I will read conclusion , till then cya

[bronze edge]

Lol

[mossy crane]

lets say you are defining a circle

you would need 2 values of y for the same value of x

so you will have to say sqrt(9)=+-3

[icy spindle]

It’s more like +/-3 = +/- sqrt(9)

So sqrt(9) = 3 and -sqrt(9) = -3

[timid delta]

Yes

[bronze edge]

Dude, for real, you guys know square functions?

[timid delta]

Eh idk , if I know it or not

[icy spindle]

Functions and equations are different

[timid delta]

Yes

[icy spindle]

An equation must pass the vertical line test in order to be a function

[timid delta]

Function are only defined at specific values , equation holds true for every value

[mossy crane]

relation holds true for every value

[bronze edge]

Anyhow the concept of the square function aplies here, i just want nuke to understand that sqrt(9) = +/-3

[supple island]

the opposite?

[timid delta]

Ohhhh

[icy spindle]

The function x=sqrt(y) has no negative answers, but the equation x=sqrt(y) does

[timid delta]

Identity*

[mossy crane]

YES YES YES YES

goddamit at least someone understood that

[timid delta]

Use relation instead of equation ;-:

[supple island]

oh ok

[bronze edge]

what is literally what i'm saying until now?????????

[icy spindle]

Both points are correct btw

[bronze edge]

R -> R+ (?)

[timid delta]

Function can be only defined for the values in domain ;-; not other values , that's what I was trying to say

[bronze edge]

The awnsers are only positive

[mossy crane]

.

[sly shadow]

guys i need homework help

[deep kernel]

it's R+ -> R+

[bronze edge]

Why R+?

[deep kernel]

sqrt is not defined on R-

[bronze edge]

if the x is squared

every value squared is a positive value

[icy spindle]

It’s R->R+

[timid delta]

Yes √-1 is not defined

[deep kernel]

oh nvm i miss understood

[mossy crane]

no you didnt

[bronze edge]

No worries

[mossy crane]

what function are we defining lol

[supple island]

ask and ignore these guys

[timid delta]

But function we are talking about is √x²

[bronze edge]

sqrt(x²) = |x|

[mossy crane]

ya conclude this i guess

[icy spindle]

Ask @sly shadow

[bronze edge]

Ok conclude this, go ahead scratch

[mossy crane]

people studying precalc will crack their brains if they read this

[supple island]

things heating up in the sqrt fandom

[bronze edge]

LOL

[timid delta]

[bronze edge]

[icy spindle]

[sly shadow]

okay the question is
1.) f(x) = 1 , find f'(1).
2.) Is f'(x) differentiable at x=1 ? if so give reasons for ur answer.

[left knoll]

x^(2/n) is awlays in mod, where n is any integer

[bronze edge]

Please we just finished that lol

[mossy crane]

i will nopt discuss this

[deep kernel]

d(1)/dx = 0

[sly shadow]

f'(x) isnt continuous so im assuming its not differntable?

because differentiation implies continuity and vice versa?

[mossy crane]

no f(X) is constant so its continuous everywhere

the derivative will be 0

[supple island]

ok so first of all, do you know what differentiabilty is and how to calculate a derivative?

[sly shadow]

yes

[mossy crane]

which in the neighberhood of point 1 is the same

[supple island]

ok so what's the geometric meaning of the derivative?

[sly shadow]

the tangent

[mossy crane]

continious everywhere no sharp corners

[timid delta]

Slope of tangent

[mossy crane]

hence differentiable

[supple island]

hm, kinda, the slope is more accurate

[sly shadow]

hmm true

[supple island]

so if a function always stays the same

what's its slope?

[sly shadow]

the slope is the derivative of the function

[supple island]

yeah, but how ripid is a function that is flat?

[sly shadow]

0

[supple island]

correct

[mossy crane]

what is ripid

[sly shadow]

was thinkign the same thing lol ^

[supple island]

how fast does the function goes up or down

basically

[icy spindle]

If f is constant then the preimage of any set is either empty or the whole of X, so it is continuous.

[mossy crane]

were you taught continuity before methods of derivating

[sly shadow]

yes

[mossy crane]

yep

just use the graph bro

[sly shadow]

yep i got it

i got another question

how would i go about solving this?

[supple island]

i hate beau, can't help them

lol

/s

[timid delta]

Beau?

[supple island]

yeh the text is "help Beau find a value"

[mossy crane]

how the hell did you go from continuity to a differential eqn real smooth

[timid delta]

I don't understand abbreviations ;-; , pls use fullform

[sly shadow]

u talking to me lol

[mossy crane]

ya

i just started calc

[sly shadow]

idk man my course is poorly designed

[icy spindle]

I’m doing multi variable calculus at university atm lol

[deep kernel]

hmm maybe start with solving the cubic

[mossy crane]

guys

i just remembered that question