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@leaden coral Has your question been resolved?

[leaden coral]

<@&286206848099549185>

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@leaden coral Has your question been resolved?

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@leaden coral Has your question been resolved?

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[blissful rapids]

The solutions on the internet use some college level stuff

[blissful rapids]

But I'm in high school

[rigid tree]

First of all, differential equations is not even high school material in the first place

[blissful rapids]

It is in my country

[rigid tree]

You can't expect to find high school level solutions to college level questions that easily 💀

[rigid tree]

It's college level in most countries

What techniques of differential equations have you learnt?

[blissful rapids]

Separable form
Homogeneous form
First order linear differential equations
Bernoulli's equation
Polar form
Exact form

[violet jetty]

looks exact to me

[blissful rapids]

The first term is d(x*e^x)

But xe^xdy

[blissful rapids]

What do I do with that

[pearl current]

nah its not

@blissful rapids try integrating factor

[violet jetty]

not directly but you can use an intergating factor to make it exact

[blissful rapids]

Thats what I saw on the internet

They didn't teach us that

[violet jetty]

It's not a massive conceptual step up from a regular exact ODE, I can't think of any other way to solve it

[blissful rapids]

Ok

Ill learn that

[pearl current]

jee huh

[blissful rapids]

Is this the same integrating factor as e^(integrate P(x) dx)

[blissful rapids]

Yes

[blissful rapids]

In linear differential equations

[plain onyx]

its something like e^(int (N_x - M_y)/M)

maybe google "almost-exact ode"

[pearl current]

similar

[blissful rapids]

Thank you

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[spare beacon]

Halllllloooooooo

[pearl current]

hi

got a doubt?

[spare beacon]

can you german?

[pearl current]

no

send the original question anyw

try translating best you can tho

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[warped topaz]

I just got x = 4 not also x= 0

3 - 6/sqrt(x) = 0

3 = 6/sqrt(x)

3sqrt(x) = 6

[tight pier]

critical points are not just f'(x)=0

[warped topaz]

sqrt(x) = 2

x = 4

[tight pier]

also where f'(x) may be undefined

[warped topaz]

Ahhh

Ok I didnt think of that

Thanks!

❤️

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[ionic yoke]

why's the derivative of ln x is 1/x?

[bleak kestrel]

why not

[north rover]

There's multiple ways to go about this tbf, use the limit definition of derivative though

[lilac dome]

do you know the 1st principle of differentiation?

[proven leaf]

[\frac{d}{dx}[\ln(x)]=\lim_{h\to0}\frac{\ln(x+h)-\ln(x)}{h}]

[ocean seal]

ΠαϳαμαΜαμαΛλαμα

[vale wigeon]

what is your class's definition of ln?

and if it's as exp^-1, what is your class's definition of exp?

[north rover]

(I believe you will have to use the fact that $\lim_{n\to\infty}\qty(1+\frac1n)^n=e$, if I am not mistaken - this might just be for $e^x$ though)

[ocean seal]

;(

[ionic yoke]

ye

[proven leaf]

[\frac{\ln(x+h)-\ln(x)}{h}=\frac{1}{h}\ln\left(\frac{x+h}{x}\right)=\ln\left(\left(\frac{x+h}{x}\right)^{\frac{1}{h}}\right)]

[ocean seal]

ΠαϳαμαΜαμαΛλαμα

[bleak kestrel]

lets say y = ln x

then x = e^y

dx/dy = e^y

dy/dx = 1/e^y

dy/dx = 1/x

[vale wigeon]

this kicks the question down to "why is e^x equal to its own derivative"

[stable relic]

yea that seems circular lol

[vale wigeon]

@ionic yoke please tell us how your class first introduced ln and/or exp to you

[stable relic]

surely log base e?

[bleak kestrel]

then just use the defintion of derivative to find it i guess

[ionic yoke]

we're not obliged to find it i was just curious

[vale wigeon]

well like heres the thing tho.

the answer to "why is ln'(x) = 1/x" is going to depend on how it was introduced to you

cause maybe it was defined as $\ln(x) := \int_1^x \frac{\dd{t}}{t}$. in which case the answer is going to be FTC.

[ocean seal]

Ann

[vale wigeon]

or maybe it was defined as the inverse of $e^x$. in which case the answer is going to be what FishTank said.

[ocean seal]

Ann

[vale wigeon]

or maybe it was defined as ln(x) := d/dt (x^t) at x=0. which then again has to link to e^x. eventually.

[stable relic]

how do u get this from the log base e definition of ln

why are they the same

[north rover]

The whole point is that its defined that way, you don't get it from that if you have a different definition to begin with

Some calculus textbooks do it that way

[ionic yoke]

yeah it's defined as the inverse of e^x

[vale wigeon]

i mean you're gonna need to tell us what e^x is

[north rover]

defining ln and then e^x

[vale wigeon]

ok and e^x is defined as?

[stable relic]

surely we are all working with the same concept if the derivative is 1/x

[ionic yoke]

exponential function?

[vale wigeon]

mmmmmmmmmmmm

that feels circular.

what was e defined as then

[ionic yoke]

euler's constant?

[vale wigeon]

that is a name, not a definition

what is e?

[ionic yoke]

didn't understand

[bleak kestrel]

what is pi?

[ionic yoke]

a constant

[onyx acorn]

what kind of constant? what does it represent?

[ionic yoke]

half a circle in radians?

[vale wigeon]

ok so e = 6.90420. thats a constant?

[proven leaf]

SA, did you ever see (e:=\lim_{n\to\infty}\left(1+\frac1n\right)^n)?

[ocean seal]

ΠαϳαμαΜαμαΛλαμα

[ionic yoke]

yes

[onyx acorn]

there's a more fundamental definition of pi, but I suppose that's besides the point now

[proven leaf]

that is what Ann was asking for if I'm understanding correctly

[ionic yoke]

Oh you mean what's e equal to

[vale wigeon]

thats a pretty severe logical lapse or misuse of words

but yes sure

e is equal to?

[bleak kestrel]

is it also the ratio of circumference and diameter?

[ionic yoke]

lim x → ∞ (1+1/n)^n

[vale wigeon]

you mean n -> ∞?

[ionic yoke]

yh my bad.

and it's approximately equal to 2.71828

[vale wigeon]

hmm

i think this may be a somewhat arduous journey

but the idea is probably still going to be that e^x is its own derivative and you can calculate ln'(x) from it in this way (with the inverse function rule or otherwise)

[ionic yoke]

Thanks

[ionic yoke]

yes

[proven leaf]

or @ionic yoke if you know that limit, from here let (n:=\frac{x}{h}) then the limit becomes:
[\lim_{n\to\infty}\frac{1}{x}\ln\left(1+\frac{1}{n}\right)^n]

of course now you should recognize the (1+1/n)^n limit

[ocean seal]

ΠαϳαμαΜαμαΛλαμα

[lone heart]

@ionic yoke Has your question been resolved?

[ionic yoke]

and that's lim n→∞ 1/x ln e ?

ln e is 1

[proven leaf]

yep so all that's left over is 1/x

and thus we have (lnx)'=1/x

[lone heart]

@ionic yoke Has your question been resolved?

[lone heart]

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[split seal]

how do i find the angle of the cable?

This one

,rotate

[ionic sable]

subtract 50 from 90 to get one angle, since the cable is perpendicular, another angle is 90

[ionic sable]

use angle sum property to find thr angle

[split seal]

idk what angle sum property is

[ionic sable]

wait mb i misunderstood

[split seal]

oh ok

[ionic sable]

sum of all angles in a triangle is 180 degrees

[split seal]

oh yah. but how would that help with this?

i already got the angle of the bottom triangles. its 50

i just dont know how to get the tension angle

[ionic sable]

can you lable all the vertices, it will help

[ionic sable]

id solve the sum and show the working but im not in the situation to do that

so ill js text it

[split seal]

wait i just reaslied. isnt it just 45 degrees? since its perpendicular

or am i wrong?

[ionic sable]

which angle, it would be 90 if its perpendicular

[split seal]

this one

the cable is perpendicular to the beam

[ionic sable]

u dont know if the line bisects the angle tho

[split seal]

oh ok

so whats the answer?

[ionic sable]

wait

[split seal]

alr

[ionic sable]

lemme do it

[split seal]

k

,rotate

[split seal]

i think i got it

is it 50?

my works super messy sorry

Yo @ionic sable U here?

[ionic sable]

yeah

its 50

[split seal]

Oh ok tysm for the help

I think I know how to get it now

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[ionic sable]

yeye np

i woke up 2 am in the morning to solve this sum 🥀

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[unborn burrow]

Im a bit stuck on the final step of this proof

[unborn burrow]

So

so im positive my proof is right up to this point

let U represent the upper sum and L represent the lower sum

for $\varepsilon > 0$ I have that
[0 \leq U - L + \varepsilon \implies L \leq U + \varepsilon ]

[ocean seal]

Branshi (Hints only plz)

[unborn burrow]

not sure why thats so off centered

but yeah this what I got I just cant figure out how this implies

L <= U

[regal condor]

Let's say it's not

Can you derive a contradiction

[unborn burrow]

ok so say L > U

then L - U > 0

[regal condor]

Yes

[unborn burrow]

and so

[regal condor]

Go on

[unborn burrow]

$L \leq U + \frac{L - U}{2}$ and so $L \leq U/2 + L/2 < L/2 + L/2 = L$

[ocean seal]

Branshi (Hints only plz)

[unborn burrow]

so L < L is the contradiction?

hmm

[regal condor]

Bestie there's a much easier contradiction here

Assume L > U

And we have L ≤ U + ε for any positive ε

[regal condor]

Now using this, do you see a candidate ε

For a contradiction

[regal condor]

I just realized this might come off as condescending. Apologies, that was not my intention

[unborn burrow]

no its ok it wasnt

hmm

let me think about it

oh

ok so

L - U > 0

[regal condor]

It is what you have done, just a bit faster essentially

[unborn burrow]

and L - U <= epsilon

but epsilon > 0

wait

😭

thats not it

[regal condor]

Take an epsilon between 0 and L - U

[unborn burrow]

(L-U)/2

ohh

L - U <= (L-U)/2 is the contradiction?

because L - U is positive

but if we divide by 2 it should be come smaller

[regal condor]

Yeah that works too

[unborn burrow]

what was your contradicition lol

[regal condor]

Wtf my phone autocorrected yeah to ehhh

How often have I been saying ehhh for this to be a thing

[unborn burrow]

lol

[regal condor]

Also intuitively

If L ≤ U + epsilon

Take the limit as epsilon goes to zero

[unborn burrow]

oh does limits preserver inequalities?

like lim L <= lim (U + epsilon)?

I think I see the proof now though thank your for the help, gonna get to the next one

got an analysis test monday

and then an algebra one wednesday 😭

they always line up like this and I ended doing go on analysis but bad on algebra since I couldnt study enough

thanks for the help

.solved

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[fervent sail]

Any good resources to learn formal proofs? ideally digitally bc icbf buying a book. :) thanks in advance

[hushed locust]

https://richardhammack.github.io/BookOfProof/

[fervent sail]

thank you!

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[fading geode]

this is a deferred annuity problem

1. Mr. Lopez wants to sell a piece of farmland. He received an offer: P100,000 down payment now and P80,000 at the end of each year for 6 years, with the first payment starting 3 years from now. If money can earn 6% compounded annually, compute the present value of the offer.

through my solution i used the formula of the present value and multiplied it by (1 + r/n)^-ng to account for the payment gap
where n is the number of times interest is compounded per year, r is the interest rate and g is the gap in years between the first payment
i arrived at a final answer of 430,294.43, but supposedly the real answer is 450,112.09 using the formula (1 + r/n)^-(ng-1), will this formula work for all deferred annuity problems?

[lone heart]

@fading geode Has your question been resolved?

[tiny fable]

can i see your work?

[fading geode]

for present value

for deferral period + down payment

[tiny fable]

you can't directly apply the formula here since the first payment occurs immediately and the rest occur later

so you need to do 100,000 + PV(deferred payments)

@fading geode

oh wait you did that mb

I think your issue is that the formula at the top of the first image assumes the first payment occurs at the end of the first year

so you need to discount it by 2 years instead of 3

[fading geode]

the present value formula or the deferred annuity formula?

[tiny fable]

you just have to be careful with the wording. if the first payment occurs at the end of 3 years, you need to discount your formula 1 year less than that if you use that formula

in general, if the first payment occurs at the end of year n, discount by n-1

(if you use that top formula)

[fading geode]

but in that case if n = 1 and you were to subtract by 1 then youd be multiplying and dividing by 0?

[tiny fable]

I should have said t instead

if it makes it easier, then if the first payment occurs at the end of year t, discount by t-1

so multiply by (1+r/n)^(-n(t-1))

so if t = 1, then you're multiplying by (1+r/n)^(0) = 1 and the formula doesn't change

[fading geode]

hmmm, ok i see isee

its consistent with how the supposedly right answer 450112.09 was reached

thank you for the time and help

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[lethal steeple]

How do i get the right answer for the cosine function of the given graph. i have my work shown but the answer is wrong??

[lethal steeple]

i think the period is 6 pi

because going from the starting value to the max is 3pi

so that again is 6pi

then p=2pi/b

6pi=2pi/b

then 6pi(b)=2pi

then b=1/3

and i’m so lost what i did wrong

is the phase change not +pi/2

for cosine

[lone heart]

@lethal steeple Has your question been resolved?

[opal portal]

you can just use cos x = sin(pi/2 - x)

[lethal steeple]

but i need to see where i went wrong and how to fix it not just a whole different way of doing it

[opal portal]

how did you get +pi/2

normal cosine graph has its peak at x = 0

[lethal steeple]

OHHH

I TRIED USING THE SIN GRAPH FOR MY COS GRAPH

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[odd hound]

i dont understand the mark scheme

[vale wigeon]

it's hard to read the proof from the MS

but the idea is: n is either odd or even.
if it's odd, then ...
if it's even, then ...

[odd hound]

for when n is even, i let n= 2n and subbed it into the equation and then i got 2(2n^2 +1) and for when n is odd, i let n = 2n+1 and got 4n(n+1)+3

[lavish cave]

right, and then you want to show that 2n^2 + 1 is not a multiple of 2

[odd hound]

how would u do that?

[lavish cave]

if 2n^2 + 1 is a multiple of 2, then 2(2n^2 + 1) is a multiple of 4

[lavish cave]

what's the form of any odd number

[odd hound]

n-1

[lavish cave]

uh, no

[odd hound]

im not too sure

[lavish cave]

well, an odd number is always 1 more than some even number, right?

[odd hound]

yes

[lavish cave]

and what's the form of any even number?

[odd hound]

2n? or conversely 1 more than an odd number

[lavish cave]

2n is what we want

so any odd number is 2n + 1

(n must be an integer, importantly)

[odd hound]

yess

[vale wigeon]

not n = 2n

[lavish cave]

otherwise you could have 2 * 1/2 + 1 = 2

[vale wigeon]

n = 2(ANY OTHER LETTER)

[lavish cave]

or 2pi + 1 or some shit

[odd hound]

ohhh right

[lavish cave]

you can also write 2n - 1, that's also correct

even number - 1 = odd number

but for this question, it'd be most helpful to compare 2n^2 + 1 with 2k + 1
(we don't want to use n twice)

[odd hound]

could i also represent it as 2n-1?

[reef wren]

.

[odd hound]

ah i didnt see that thx

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[tired spear]

Hi! I'd like to understand the mathematic rational behind the method used to solve this question:

[sly vale]

Bro what a irony I studied rutherford model today 😅

[tired spear]

I will upload the model answer

[tired spear]

Wow!

There's a specific step though where I have a doubt

[sly vale]

Yeah but I don't know this level of maths I read this in chem

Alpha particles are He^+2

[tired spear]

Yeah, so it says

[sly vale]

Which class r u in

[tired spear]

Final year of HS

[sly vale]

Hs?

[tired spear]

highschool

[sly vale]

Oh nice I am in 9th

[tired spear]

Nice

[sly vale]

Yeh

[tired spear]

So basically, I didn't get why we multiply the fraction by 2 instead of squaring it

Should we use the AND operation instead of the OR?

[thorny sable]

i need a buddy to study with is there anyone

pls i really need

[wide cairn]

😭 get your own channel

[thorny sable]

means

i am enw

new

[wide cairn]

i mean i don't think this is the right place to inquire about study buddies

[thorny sable]

ok sorr

y

[wide cairn]

not to mention, you have to first get your own channel like #help-49 if u need help

[ancient sky]

@thorny sable #❓how-to-get-help #help-2 isnt occupied if you wanna take it

[thorny sable]

yes i wanna take it how to do

[tired spear]

So, I got how they approximated the fraction of deflected alpha particles through circular cross section . . . but I don't see how the 2 layers entail OR (*2) instead of AND (squaring)

Or am I missing something there

[thorny sable]

it says seasamak

[tired spear]

Actually, that makes sense . . . I was thinking of it in terms unperturbed alpha particles instead . . .

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[novel tartan]

kielhöfer

[lone heart]

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[remote adder]

A reddit post got 60% upvotes. The shown upvotes are 2. How much down votes did it get?

[remote adder]

I am not a mathematician. I am just interested in knowing

[tulip flame]

how much % do you think were down votes?

[remote adder]

(X+2/2x+2)*100 = 60

Or the opposite

[remote adder]

Is that correct so far?

[tulip flame]

a bit off

[remote adder]

Hmm

[tulip flame]

x is downvotes?

[remote adder]

Yeah

No

Its down votes or the upvotes we don't know

Because there is an unknown number of upvotes that cancelled the down votes for it to be +2

[tulip flame]

so we can consider x to be downvotes total upvotes - x =2

[tulip flame]

so this formula is correct

if x is downvotes

[remote adder]

Correct

[remote adder]

Yeee I am a smartie. I havent opened a math book in 6 years. Kinda miss it

[tulip flame]

lol

[opal jolt]

isnt that formula missing parenthesis?

[tulip flame]

is it?

[remote adder]

Its 16?

Wow that post was really controversial

I was just venting about my medschool being awful

[tired spear]

How'd it be 16?

60% is upvotes which are 2, so then down votes are less than 2, no (40%)?

[opal jolt]

let x be the downvotes
x+2 is the upvotes
2x+2 is the total votes
(x+2)/(2x+2)=0.6

[remote adder]

Thats what I did

[tired spear]

Or do you mean 60 percent less?

[opal jolt]

then you did not do it correctly

[remote adder]

No its not just the 2 upvote. 2 is the only shown upvotes. There are upvotes that cancelled the down votes

[tulip flame]

a bit different, we assume downvotes cancel upvotes

[opal jolt]

x+2=1.2x+1.2
-0.2x=-0.8
x=4 (downvotes)
x+2=6 (upvotes)

[tired spear]

oh

[remote adder]

Right I added instead of subtracting

So its probably 4

Much more comforting

Okay that was fun. Thanks guys

[tulip flame]

!done

[lone heart]

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

[remote adder]

.close

[lone heart]

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[torpid adder]

idk if this type of question is allowed but how do you solve this?

[jagged mantle]

I'll try but don't depend on me solving it

😔 wait

[torpid adder]

sorry if this question is too open-ended!! i am just trying to learn lim for the first time 😭

[jagged mantle]

oh I see

[jagged mantle]

yeh same

hmm

i THINK i solved it

but how do I explain

[tacit arch]

Divide all terms by 5^n

[jagged mantle]

yeah wtv

then try to sipmlify everything

[tacit arch]

Wasn't talking to you

[jagged mantle]

I'm sorry riemann

[vale wigeon]

why would this type of question be disallowed

[torpid adder]

if you can just paste the solution maybe that works too. i am just trying to get a grasp on this

[vale wigeon]

!noans

[lone heart]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[torpid adder]

idk its not a specific question maybe. i am new to this server

[vale wigeon]

it is a specific question

you've got a limit to calculate

so let's see

do you know in general how to calculate limits

[torpid adder]

no

[barren oak]

why is bro always so toxic lol

[vale wigeon]

oh dear

ok right so uh.

[tacit arch]

No one was talking to you either

[tulip flame]

he is the og reimann

[barren oak]

Thats what I mean XD

[vale wigeon]

if i asked you for the value of $$\lim_{n \to \infty} \frac{1}{n}$$ would you be able to tell me what it is?

[jagged mantle]

wait fr?

[ocean seal]

Ann

[torpid adder]

does this mean i should start with something easier than this problem?

[tulip flame]

his ghost

[vale wigeon]

@barren oak @jagged mantle if yall aint gonna talk about the question at hand then please move to #discussion

and @tulip flame too

[tulip flame]

my bad

[torpid adder]

no i don't really know how to solve that

[vale wigeon]

ok so you just have zero experience with limits.

yeah you should definitely drop to something similar.

review your notes from class on the concept of a limit.

https://www.youtube.com/watch?v=YNstP0ESndU

perhaps also give this a watch

simply put, youve got a lot of ground to cover

[torpid adder]

i don't really have any prior experience to refer to so literally anything is a step in the right direction

[vale wigeon]

...do you at least know algebra

like are you comfortable manipulating algebraic expressions and perhaps also solving equations

that sorta thing

[torpid adder]

i will say yes

i think i am ok with that

[vale wigeon]

yeah ok

so uhh yeah watch ochem tutor, do limit stuff (should be in calculus or maybe precalc) on khanacademy, review your class notes

i will say prioritize class notes

[torpid adder]

i am not taking this class yet, its for 2nd semester

i just want to get ready so i cracked open the book and 1 of the first problems is this

[vale wigeon]

one of the first ones?

[torpid adder]

yes

[vale wigeon]

huh.

got a pdf of the book by any chance?

[torpid adder]

its for analysis 1 and everyone says its extremely challenging and most ppl fail it it seems.

i dont, its from my uni library

ok i will just brush up on basic limits then. that'll do it for this question. thanks

[torpid adder]

that is ominous lol

may i also ask, the video you linked it shows he is doing limits with x➡2 or some other number, but in the one I pasted it shows x➡♾ like infinity. do i need to know how to do it with normal numbers before i move onto infinity?

@vale wigeon

[vale wigeon]

mmm

im gonna say the methods for these are like... somewhat different but not drastically so.

so i don't think these are like, dependent on each other in either direction

[torpid adder]

even this example is like that

could you also perhaps link a video that is relevant to the infinity part? i could also find it too, just wondering

[vale wigeon]

look it up on khanacademy i think it has "limits at infinity"

[torpid adder]

okay great

.close

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[molten pivot]

Loge

[lone heart]

@shy ore Has your question been resolved?

[lone heart]

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[undone whale]

not sure wether my answer is right or not

[lime spear]

???

[undone whale]

im also not very good at system of differential equations , so im walk my thought proccess thru , stop me anytime im wrong or off

[undone whale]

i think the ans is C

[lime spear]

i not speak english bro

[undone whale]

to start, we look at the eigen value , raise it to e^

e^3t e^2i

multiplied by the eigen vector

[lime spear]

ok

[undone whale]

use euler formula to to expand the e^2i to cost2t + isin2t

now ,

its just algebraic manipulation, sperate out the stuff with i , and no i ( real and imaginary )

il send a pic of my work

the only thing that matches is C

but gpt and google ai say D

[undone whale]

sorry thats unrelated

[undone whale]

was part of diff problem

[lime spear]

OK

<je reflechi un peu

[undone whale]

?

[hushed locust]

@lime spear this channel is for helping a kar with his problem. if you want to get help with that problem, please open your own channel (see #❓how-to-get-help for details)

[undone whale]

no sorry, i think i confused them cuz , my scartch work had that written down , i think they were confused abt why thats written down

[undone whale]

here that was a excess, scartch written down

[undone whale]

if anyoen can help verify the solution , id be grateful

[lime spear]

ok

[north rover]

i agree

Ah damnit, my wifi

There we are

[undone whale]

yayyy finally an answer

C , ur sure of it right

im not tripping hopefully

[north rover]

Yes, iv doesn’t make sense

[undone whale]

chat gpt regressing my knowledge

and gaslighting me

[north rover]

Haha

I wouldn’t recommend using gpt

[undone whale]

yea , i just use if for verification on practice , which i dont have answers to

[north rover]

I gotta do smth rq but I can explain my thought process to help you understand

[north rover]

you can always come here :)

[undone whale]

sure, does my work seem right tho?

[undone whale]

thanks lol

[undone whale]

its rough

i just learned this yesterday , and tried hand waving this a lil, but seperating the real and imaginary parts

right

[north rover]

Ye

Like for example, you could have a root of the characteristic equation be like 1+2i

All that means is that we consider e^((1+2i)t)

Which would inherently be e^t(cos(2t)+isin(2t))

But for real components we simply delete the i portion

[undone whale]

yes that euler expansion

[undone whale]

wait what

[north rover]

And it magically becomes a solution to the DE

yes lmao, its quite silly

[undone whale]

yea how come they just combine i into c

[north rover]

Because they can haha

At the end of the day i is a constant as well

[undone whale]

yea, thats why i like using the elemination method , for system de

it makes sense, and theres nothing wierd, just straigh integrating , and 2nd order de

[undone whale]

i see

ok thanks

if i want to ask another question

can i just ask it here

[north rover]

uhh sure, I just gotta pin it

[undone whale]

related

ok

now i think this is matrix exponential or something

thing is, im not very good at it, and only learned how to pattern recognize it

like in this case

i can tell itl be D , but no idea how that te^t term appear in the bottom left

all i just learned from recognizing the pattern was that, calcluate eigen values, and e^ eigenvalue t across the diagnal

[north rover]

(I actually do not know what a fundamental matrix is, sorry! :( )

[undone whale]

and anything else thats on the bottom left or top right, just multiply t to e^eigen value t

sht, matrix exponentional

[north rover]

Meaning what

[undone whale]

no idea tbh

[undone whale]

its ok , lol thank you sm for ur help

[steel geyser]

I think you can use $\begin{pmatrix}1 & 0 \ 1 & 1\end{pmatrix} = I + \begin{pmatrix}0 & 0 \ 1 & 0\end{pmatrix}$

[ocean seal]

flynger

[steel geyser]

Since $N=\begin{pmatrix}0 & 0 \ 1 & 0\end{pmatrix}$ gives $N^2=\begin{pmatrix}0 & 0 \ 0 & 0\end{pmatrix}$

[undone whale]

i see?

[ocean seal]

flynger

[undone whale]

ok

[steel geyser]

$e^{At}=e^{(I+N)t}=e^t e^{Nt}$ and apply taylor series

[ocean seal]

flynger

[undone whale]

(I+N ) + (I+N ) ^2/2 + (I+N ) ^3 / 6 +(I+N ) ^4 /24

[steel geyser]

Since we can factor out the $e^t$ beforehand what is $e^{Nt}$

[ocean seal]

flynger

[undone whale]

(N ) + (N ) ^2 /2 + (N ) ^3 / 6 +(N ) ^4 /24

[steel geyser]

$N^2=0$ implies

[ocean seal]

flynger

[undone whale]

OH shi i see

so anything past N^2 is useless

[steel geyser]

yes so $e^{Nt}=I+Nt$

[undone whale]

N^3, N^4 etc

wait

one sec

lemme process this

[ocean seal]

flynger

[undone whale]

Nt?

howd we get that

I + Nt

[steel geyser]

The taylor series of $e^{Nt}=I+Nt+\frac{1}{2}N^2t^2+...$

[undone whale]

e^Nt = N right?

oh yes

yes for abt the t term

[ocean seal]

flynger

[undone whale]

ohhh

ohhh wait

yea no i get it

[steel geyser]

yea

[undone whale]

then u go back to I +NT

and thats how the t term is there

is this the procedure for every type of matrice

[steel geyser]

Not really

This only worked because it was so simple

[undone whale]

oh

so

for uhm a diff eqs class

would they do anything harder than this?

[steel geyser]

That i do not know... I never took diff eq past introductory

[undone whale]

is this introdcutory diff eqs?

im not in the class

so its kinda hard to gauage

[steel geyser]

This isnt the typical introductory diff eq

at least from what i know since it has some linear algebra

So probably not

[undone whale]

ok ok thanks

.close

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[prisma swift]

So I know how to find angle I, by considering the full triangle. The blue angles would both be supplementary and be 90 degrees, how do I find red angle?

[prisma swift]

Could someone tag me when they answer

I’m thinking it has to do with corresponding angles and stuff like that, but no clue

[fair anchor]

for angle HEG, the triangles HEG and ABI are similar so use inverse trigonometric functions (5, 12, 13 triangle)
and angle FEG is just 90° - HEG

[prisma swift]

Someone else said that since they are the same shape, the angle I and angle GEH

[fair anchor]

yeah its the same triangle just mirrored

[prisma swift]

So it’ll be same angle correct

[fair anchor]

yeah
sin^-1(5/13)

[prisma swift]

Alright one more question

Angle F, it would be corresponding angle with angle I correct. So it’ll be same angle

[fair anchor]

yep

[prisma swift]

Got it, thank you

Oh one more

I will also need to find angle D

If I draw an x axis across

Same as I did with the black mark

[fair anchor]

it would be the same again

[prisma swift]

Same as angle I?

[fair anchor]

yeah because you have 2 parallel lines with a singe line intersecting them
opposite angles are the same

AI || DI_2 lets say
and BI is intersecting both

[prisma swift]

I seee

So if I create the same idea with point B

It’ll be same as angle I?

[fair anchor]

yea

[prisma swift]

Got it thank you

.close

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[clever raptor]

HELP I HAVE 11 MINS TO TURN THIS ASSIGNMENT

[clever raptor]

IS IT CORRECT

ESPECIALLY b) IM DONE WRITING THE GRAPH

[tight pier]

you gave urself 11 min

[clever raptor]

IS IT WHAT BE MEANS BY

“Let GeoGebra draw the function for you. Then draw the function on the paper in a grid and label the function values ​​clearly on the diagram.”

@wraith ferry Can you check?

[tight pier]

,rccw

[clever raptor]

AM I DONE?

I WROTE THE DIAGRAM AND LABELS OUT

[limpid fiber]

whats the question lol

[clever raptor]

HERE

…

[limpid fiber]

oh its just the graph?

[clever raptor]

Let GeoGebra draw the function for you. Then draw the function on the paper in a grid and label the function values ​​clearly on the diagram.

IS IT WHAT THEY MEAN?

[limpid fiber]

yh looks good to me

[clever raptor]

omg really

OMGGG

[limpid fiber]

yeah!

[lime spear]

wooo

[clever raptor]

YAASSSS I TURNED IT IN

ON TIME

[limpid fiber]

nice work!

are you done with this channel, or do you have another question?

[clever raptor]

No thanks so much

[limpid fiber]

alright, then you can type .close to close this

[clever raptor]

.close

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[spring cedar]

101010101
101010101

• 111001011
  111111111

[spring cedar]

i need help with addition of binary numbers to explain

[steel geyser]

are those two 18 digit binary numbers?

[spring cedar]

i dont know broo thats what my teacher wants me to solve i know how to do with 2 rows but not with 4 i dont know how its done

[steel geyser]

send a pic to confirm notation but you can just treat it like two rows if you want

carry the 1 over from the bottom row to the end of the top

[steel geyser]

Oh maybe its adding 4 numbers?

or is it 2

[mighty matrix]

pretty sure it looks like 4 numbers...

[steel geyser]

Just do addition like normal then, but your carry can be 1 or 2 (10 in binary)

[mighty matrix]

or im pretty sure you can add two of them and then add the other two and add the results

[steel geyser]

yes

that works too

[spring cedar]

is it option 2?

[steel geyser]

you have mistakes in your second sum

1 + 1 + 1 gives you 11, you don't leave a 0 there

[spring cedar]

this is 100% right

[steel geyser]

looks right

[spring cedar]

finally

thanks broo ❤️

.close

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[woeful pulsar]

ah idempotents

Maybe do something like consider image and kernel

maybe rank

[woeful pulsar]

Well you can consider the dimension of the image and kernel (secretly, these are your eigenspaces)

Once your rank and nullity are 1, your goal is to choose the basis

That's why you need to carefully choose your basis here

Consider what happens to a vector in the image/kernel

more specifically?

You have to use the fact S^2=S

if v is in the image of S, how do you find S(v)

and if u is in the kernel of S, what is S(u)?

[woeful pulsar]

remember that v is in the image of S

this is also very conceptual - recall what the kernel means

[lone heart]

@wooden crane Has your question been resolved?

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[spare thistle]

Where did I go wrong

[lavish cave]

that's not how you take the dot product

[spare thistle]

How do I do it?

[lavish cave]

you need to multiply the coefficients of the is together

then the coefficients of the js

then the coefficients of the ks

[spare thistle]

Ohh

[lavish cave]

then add all the numbers up

[spare thistle]

I’ll try that

Do I have to do 90 minus 75.47

I used the normals

Do I

Pls someone lmk

I don’t right? Since I used normals of both vectors

@lavish cave

[lavish cave]

you don't! that's exactly why

[spare thistle]

Ok thanks, might reopen when I’m stuck again

[lavish cave]

if a vector on the plane has some angle u (to the horizontal), then its normal vector has angle u + 90

similarly for v and v + 90

so what you're doing by finding the angle between the normals is (u + 90) - (v + 90)

but that's just u - v !!

[lavish cave]

one more hint

if the angle that you get is obtuse, just do 180 - angle to make it acute

[spare thistle]

Uh is u = x and v = y

[lavish cave]

what are x and y?

[spare thistle]

The coordinate

[lavish cave]

no

[spare thistle]

Ill look into it when i get home

Ty for helping me

.close

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[lavish cave]

when you get home

no worries!

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[digital yoke]

how to do

i got

[digital yoke]

siny=sinx

and siny=-sinx

dont now what to do

[pallid scarab]

This one is wrong

[pallid scarab]

But anyway, we can just focus on this part of the graph

how do you solve sin(a) = sin(b)?

When do two angles have the same sin?

[digital yoke]

how come

[lavish cave]

well, you should get $\sin y-\sin x=\left(\sin y-\sin x\right)\left(\sin y+\sin x\right)$

[ocean seal]

south

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@digital yoke Has your question been resolved?

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[steel heron]

how do u solve this

[steel heron]

i get as far as a u substitution making 1/sqrt(1-u^4)

[signal jackal]

$$\int\frac{1}{\sqrt{x - x^3}}\mathrm{d}x = \int\frac{2}{\sqrt{1- u^4}}\mathrm{d}u = \int\frac{1 + u^2 + 1 - u^2}{\sqrt{1-u^4}}\mathrm{d}u$$
$$= \int\sqrt{\frac{1+u^2}{1-u^2}} + \sqrt{\frac{1-u^2}{1+u^2}}\mathrm{d}u$$

[ocean seal]

Herzog

[signal jackal]

do you see what substitution to make now

[gaunt atlas]

Better to use trig substitution

[signal jackal]

well this suggests trig substitution

but that was a question for the person who asked, not you

[gaunt atlas]

Can do that right away

[signal jackal]

ofcourse you can.

[steel heron]

u^2= cos2t

?

[lone heart]

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[full pine]

when n tends to infinity

[full pine]

am i correct?

[ivory igloo]

how did you go from the third expression to the fourth one

[full pine]

one second let me add that extra step so its cleaner in the photo

[full pine]

here

[tulip flame]

Its correct

[full pine]

alright

thanks

[ivory igloo]

notice the last step carefully

[full pine]

hm?

sum k=1 until n of 1/k! when n tends to infinity is e

[ivory igloo]

well yes but notice how many 'e's you will get

[full pine]

4

oh wait 5

im stupid

thanks

[ivory igloo]

and um

im not sure if factorials like (n-3)! are very valid to use in your summation

although youre safe here

because the values below k = 1 somehow evaluate to zero when you split the terms at each step

just saying though

[full pine]

oh

alright thanks

ill make sure to double check if i can do it next time

not sure if i shud leave this open since im gonna open another one in about 10 mins

asking for help in another problem

[ivory igloo]

like are you expecting to be needing help sooner or later

[full pine]

yup since this is olympic level of exercises

and im kind of just learning

[tulip flame]

If its related keep open

[full pine]

here idk what to do
same thing limit of this when n tends to infinity

[ivory igloo]

when you have two adjacent reciprocals subtrated in a summation

its best to write out the first few terms

oh wait

oh no

[full pine]

it was already written out i just contracted it and did some wanky stuff to hopefully solve but no luck

[ivory igloo]

its some series

i forgot which one

ah yes

[full pine]

oh wait you are saying x[n+1]/x[n]

[ivory igloo]

ln(1+x)

[full pine]

now im confused what

[ivory igloo]

you know how e^x expands?

[full pine]

not really-

i barrelly know math fyi i just have a lot of logic which is why im trying to do good in this year's olympics

[tulip flame]

Olympics?

[full pine]

yes in romania we have olympics curently on the county stage

[tulip flame]

Oh

[ivory igloo]

olympiads?

[full pine]

yup

didn't know that was a word in english

[tulip flame]

Mammamia

[ivory igloo]

ok so theres no set syllabus

[tulip flame]

What grade you in?

[full pine]

11 hence why limits and stuff

[ivory igloo]

ok so

you need to know some important series

for summations

you'll catch on after a few examples

they look a bit scary

but you can focus on the denominators for now

[full pine]

ill save these real quick

[ivory igloo]

because we'd mostly substitute x = 1 into all of these and the numerators would become 1

[full pine]

yeah but the limit here tends to infinity

not towards 1

[tulip flame]

Hmm.. you will be introduced to series

[full pine]

im a bit confused as i never heard or seen these kinds of series

[tulip flame]

Ig they fall under maclurian series

[full pine]

anyway so how do these help in my problem?

[tulip flame]

Look at ln series

Put x = 1

[full pine]

ohh

wow

so it would be ln(2)?

or would it be infinity since n tends to infinity and so ln(n+1)=n

im confused if i replace x wiht one on both sides or only on right side

alright thanks

ill try and do the rest tomorrow so yeah thanks

.close

[lone heart]

Channel closed

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[green lintel]

hello does anyone know any good websites for practicing maths problem solving ability idealy year 12 - 13 knowledge

[tulip flame]

Search it or ask in discussions

[green lintel]

alright

cheers

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[leaden valley]

anyone can help me with this, im really struggling

[leaden valley]

i drew the image at the bottom to show how i understand, it might be wrong but im pretty sure im right

[cursive kayak]

hi everyone

[leaden valley]

wrong channel i think you want to message in here #discussion 😭

[lone heart]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[crystal leaf]

@leaden valley okay so

[cursive kayak]

can you answer me whats the difference between classic math and not claasic math !!

[crystal leaf]

@leaden valley u there?

[leaden valley]

ye

[leaden valley]

wrong chanel twin😭

[leaden valley]

mhm?

[crystal leaf]

P should be

P = 3s + 2h + s = 4s + 2h

[leaden valley]

can you explain a bit further?

[tulip flame]

Why?

[leaden valley]

thats what im wondering

[tulip flame]

Looks right

[leaden valley]

ye so now how do i find the optimal proportion of x and y in relation to P

its a derivative but idk how to do it tbh

[tulip flame]

Hmm.. you know derivatives?

[leaden valley]

i should, but not really thats why im asking for help here,

[tulip flame]

Derivatives are simple

Are you introduced to them?

[leaden valley]

assuming i dont really know them, can you help me find the answer? or point me in the direction of how to find the answer

[tulip flame]

What would be area of square?

[tulip flame]

What grade you in btw

[leaden valley]

square x^2 and the rectangle is 2x*y

[leaden valley]

idk what it is in other places, this is my first class with derivative

[tulip flame]

Ik the differentiating method

Maybe someone else would solve without differentiation

[leaden valley]

the class is name differential math so i think thats the way to solve it

would the answer be x=p/10 and y =p/5?

[tulip flame]

Yes

Comes to that

[leaden valley]

ok i just wanted outside verification of my math to be sure thx

[tulip flame]

Np

[lone heart]

@leaden valley Has your question been resolved?

[crystal leaf]

.close

@leaden valley close the channel mate

[lone heart]

Channel closed

Closed by @leaden valley

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[pine cave]

can someone help me

[pine cave]

i need help with this equaltion

can someone help me???

<@&286206848099549185>

[flint zealot]

Hey

[pine cave]

can you help me solve that?

i also need help with another equation?

[vale wigeon]

1. do you know how to multiply fractions
2. do you know how to work with exponents / indices

[pine cave]

yeah i do

[vale wigeon]

yes to both?

[pine cave]

no

only 1.

[vale wigeon]

ok

do you know exponent laws / index laws

[pine cave]

kinda..

[vale wigeon]

such as $a^{m+n} = a^m \times a^n$

[ocean seal]

Ann

[pine cave]

YES I DO!

[vale wigeon]

ok good

[pine cave]

i know

[flint zealot]

(8p³q² ÷ 2p²q) * (3pq ÷ 4q²)

Multiply numerator with numerator and denominator with denominator

24p⁴q³ ÷ 8p²q³

24÷8 is 3, p⁴÷p² is p^(4-2) so p² and q³÷q³ is 1 since they're the same so its:

3p²

[vale wigeon]

!nosols

[lone heart]

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.

[vale wigeon]

help ≠ doing everything for OP, jsyk.

[flint zealot]

Alright

So

You multiply them

[pine cave]

i also got 3 x p square ? is that right?

[flint zealot]

number by number

the variables

[pine cave]

i got 3 x p2

[flint zealot]

when you multiply y

you add their powers

and when you divide

you minus their powers

[pine cave]

okay

[vale wigeon]

3p^2

use ^ to write exponents on discord

and DONT write multiplication as x

[pine cave]

i dont have that in my keyboard

[flint zealot]

like a⁴ x a³ would be a^(4-3) so a¹