help-0

[south sun]

what a roundabout way of saying "they're the same thing"

i rlly hope i don't lose marks for not putting an answer like this in the convoluted form the ms gave it in

[north adder]

you wont

but to make sure ask your teacher!

[south sun]

don't have one sadge

im a private resits student

[north adder]

ask one of your mates then

[south sun]

good call

actually

ill ask my tutor tomorrow

[north adder]

lol yea that works too

[south sun]

with him its hit and miss lol

hes not a teacher

hes an engineer who does maths tutoring

so he cant answer specific questions about mark schemes sometimes or exam content

he can definitely help me understand the work though

anyways back to it

thanks a lot though man

@north adder ❤️

[north adder]

no worries :)

always worth it when they genuinely thank you

[lone heart]

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[small swift]

https://gyazo.com/da13990eba5d424e42115b901cb037d5

[small swift]

Hello for this question

to find the pivots I need RREF form

so I take A and got 2 rows

but I'm a bit confused on the 2nd part

which asks whether the eqn Ax = b has a soln for each b in R^4

how can i approach this?

[lone heart]

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[lone heart]

@small swift Has your question been resolved?

[lone heart]

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[half salmon]

i need prove this identity twice in two diffrent ways

i already proved it once

now i need help to prove in another way

i need someone to hop on vc and help me

so i can show him what i already did

<@&286206848099549185> 'please

[lone heart]

@half salmon Has your question been resolved?

[half salmon]

<@&286206848099549185> someone anyone?

pleaseee anyone

<@&286206848099549185>

i just need to prove this identity

likr 5 minutes

another way than i already did

[half salmon]

<@&286206848099549185>

[sly bolt]

wouldnt it be helpful if you show your first way

[half salmon]

its like 4 pages but i will send

ok this is the first proof

now i need another one

[sly bolt]

honestly just try to use a different identity at the start or start from the other side

[half salmon]

what diffrent identity icant 😭

idk what to use

[sly bolt]

it doesn't actually matter just write cosa / sina squared or something

[half salmon]

ok so i factorised the bottom

what can i do next

@sly bolt

ok i made it easier <@&286206848099549185> what can i do next

[near hollow]

Ur basically there

Your looking to get rid of
$(csc(\theta)-1)$ on the bottom. You also don't want cot on top so it makes sense to convert cot into csc using the Pythagorean identity, then factorise and look for cancellation

And you should get the final result

[ocean seal]

Max..

[half salmon]

how can i convert cot into csc

[half salmon]

this is the pythagorean identity how will i conver cot into csc

@near hollow ?

[proven rune]

divide by sin^2 theta

[near hollow]

Divide both sides by sin^2 and you get one of the other 2 identities

You can do the same for the tan - sec identity by dividing by cos^2

[half salmon]

like this?

[near hollow]

Noooooooo

[near hollow]

Divide this by sin^2

And you form a new identity

[half salmon]

ohhhhh

[near hollow]

Containing cot and csc

[half salmon]

oh okok

so what is the new identity

[half salmon]

ok so on the left side we get this

but what do we get on the right

[near hollow]

Split the fraction

You get 1+cot^2

[half salmon]

?

[near hollow]

Then move the 1 to the other side and get rid of the cot on top

[half salmon]

wait so what is the new identity

its csc^2 = what

[near hollow]

$csc^2\theta=cot^2 \theta +1$

[ocean seal]

Max..

[near hollow]

Then move the 1 to the other side

[half salmon]

how did u get cot^2 +1?

[near hollow]

And you get cot^2 on its own

[near hollow]

It's literally the LHS

[half salmon]

you said divide both sides by sin^2

the left side gives csc^2

how does 1/sin^2 give cot^2 +1

@near hollow

[near hollow]

The right hand side gives csc^2 not the LHS

The LHS gives $sin^2/sin^2 + cos^2/sin^2=1+cot^2$

[ocean seal]

Max..

[half salmon]

OK SO LIKE THIS

@near hollow ok then what do i do

[half salmon]

@near hollow can i do this

<@&286206848099549185> what can i do next

.close

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[proper mica]

So I know what laws to use for all 3 of these, the thing is I know how to solve for certain sides, but not the entire triangle.

[last ether]

Is this a test or quiz

[gray isle]

solving for a while triangle is just doing additional work

[alpine sable]

I have no idea what solving the triangle means

[gray isle]

if youre able to correctly apply to theorems/laws to solve for one side, you can apply it again or other relevant laws to find out everything else about the triangle

solving a triangle just means finding all sides and angles

[alpine sable]

If it means finding all a, b, c, α, β, γ

Ah

Yea, it's just simple process of applying cosine rule sometimes and normally sine rule

Just apply appropriate rules

multiple times until you find all

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[lost coral]

what next?

[tacit arch]

Simplify first

log(ab) = log(a) + log(b)

[lost coral]

but how does that apply to this?

in this case its log(a+b)

its not the same

[tacit arch]

Look earlier

[lost coral]

i see

[tacit arch]

Do you know the derivative of log(7)?

[lost coral]

isnt it natural log?

[tacit arch]

Any base

[lost coral]

log (7)/log(10)?

[tacit arch]

I use log for natural log

[lost coral]

ok

log = log_e

[tacit arch]

Nope

,calc log(7)

[ocean seal]

Result:

1.9459101490553

[tacit arch]

Now do you know the derivative of log(7)?

[lost coral]

0

[tacit arch]

Start back after simplifying the log(7x) step

[lost coral]

btw can u use ln

it kinda confuses me

[tacit arch]

Nah

[lost coral]

i dont get it

[lost coral]

what do u mean by this?

what about log(7x)

[tacit arch]

Oh shit I read the whole problem wrong

Start aaaallllll over

[lost coral]

bro

dont troll i swear

[tacit arch]

Write f(x)=7x+5-x^3

Then you have log(f(x))

You can't split log of a sum as a sum of logs

Try it in your calculator

[lost coral]

?

what are u saying

[tacit arch]

Which part

[lost coral]

??

u trying to isolate x?

[tacit arch]

Write this out

It'll help with the derivative

[lost coral]

confusing

[tacit arch]

You're looking for the derivative of log(f(x))

[lost coral]

no

i wanna derive 7x+5-x^3

[tacit arch]

Differentiate* is the verb

[tacit arch]

I'm just calling the stuff inside log a name

[lost coral]

i wanna differentiate this

[tacit arch]

So I don't have to type it out

[lost coral]

nvm

its fine

ill just do it myself

[tacit arch]

g(x) then since you didn't say it was f

.close to free up the channel

[lost coral]

im looking for someone else

cause ur lazy

[tacit arch]

Nah it's useful

You just can't math

[lost coral]

the last thing i want is someone polluting my brain

[lost coral]

okay how is it useful

im trying to differentiate it with this formula

.close

[lone heart]

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[vast bobcat]

Find all primes p such that $$ 5p+2 $$ is a perfect square

[ocean seal]

liviu

[vast bobcat]

so far I've got $$ n^2 - 2 = 5p $$

[ocean seal]

liviu

[dense sleet]

1 * 1 = 1
2*2 = 4
3 * 3 = 9
4 * 4 = 6
5 * 5 = 5
6 *6 = 6
7 * 7 = 9
8 * 8 = 4
9 *9 = 1

Last digits

May be very helpful

[vast bobcat]

pretty sure there's a more systematic way to solve it

[heady void]

yeah

[dense sleet]

Well look at the table your perfect square ends with either 7 or 2

There is no perfect square that gives last number 2 and 7

[vast bobcat]

how would I write this in a proof form

proof by contradiction?

alr thanks

.close

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[visual wadi]

can someone check my work if i did correct

[lone heart]

@visual wadi Has your question been resolved?

[lone heart]

@visual wadi Has your question been resolved?

[lone heart]

@visual wadi Has your question been resolved?

[slender marten]

What work?

[lone heart]

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[raw sigil]

Hello

[raw sigil]

can someone help me with 1st and 3rd option please

[lone heart]

@raw sigil Has your question been resolved?

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@raw sigil Has your question been resolved?

[lone heart]

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[final viper]

when you integrate using substitution , do you consider the variable which you substituted as a constant

[echo socket]

No

[final viper]

like sometimes if i replace say dr with dt , i get some terms of r as well

[echo socket]

Why'd you treat a variable as a constant? Especially in integrating

[final viper]

what to do with that r

[echo socket]

You need to rewrite that r using t

[final viper]

oh

i have a very complex function e^(alpha.x^2) .dx

so cant decide how to replace x completely

🥴

[echo socket]

As I remember you can't integrate that

[tight locust]

you can

[final viper]

alpha is constant btw

[tight locust]

error function

[echo socket]

Without defining any new functions

[final viper]

how

[echo socket]

Yeah that one

[tight locust]

erf

[final viper]

i need to check how to use this erf

btw what are complex numbers doing here smh

actually i have to integrate this

so ilate method

[tight locust]

yeah you don't have to worry about allowing complex values of z

[final viper]

• this erf 🤔

[tight locust]

oh you have a z^2 lmao

[final viper]

xd

[tight locust]

that makes things a lot simpler. why didn't you say so

[final viper]

oh

[tight locust]

just let u = -az^3

[final viper]

i thought its harder

[tight locust]

the u sub gets rid of all the nasty stuff

[final viper]

dayumn

exactly what i needed to know

[tight locust]

because we have that factor everything else cancels nicely

[final viper]

thanks

.close

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[safe island]

can someone explain to me what happened in the 4th line? they're using singular value decomposition here, how did the 2 V and V' come out of the inverse?

[mortal trellis]

we have $(abc)^{-1} = c^{-1} b^{-1} a^{-1}$ which can be checked by multiplying $abc$ with $ c^{-1} b^{-1} a^{-1}$

[ocean seal]

Denascite

[mortal trellis]

and then they use $(V')^{-1}=V$ and $V^{-1}=V'$

[ocean seal]

Denascite

[lone heart]

@safe island Has your question been resolved?

[safe island]

why is this true?

[mortal trellis]

I assume V is orthogonal and V' denotes the transpose?

otherwise it's not true

[lone heart]

@safe island Has your question been resolved?

[lone heart]

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[native venture]

here how come they wrote a + 2c = 0 and b = 2a+b?

if a +2c = 0 then we get 0/0

i did this

to evaluate the left hand one both a and b cannot be equal to zero, then we just get 0/0

hello?

<@&286206848099549185>

[abstract fractal]

For the limit of (a + 2c)/h to exist, a + 2c must be 0. The limit would equal 0

This would make the entire limit b

Then, the left hand and right hand limits must be equal, so b must equal 2a + b

[native venture]

but wont we get 0/0?

[abstract fractal]

Only when h=0, but it won't equal 0. We're only approaching 0

[native venture]

if a + 2c is zero

and h is approaching zero

then how can we compute the limit?

[abstract fractal]

We have the limit h->0 0/h

0/h = 0 for all h ≠ 0

That means, for any h really really close to 0, the function 0/h = 0

Remember, the function doesn't need to equal the limit at that point, it just needs to get arbitrarily close. In this case, the function equals the limit everywhere except 0, but sometimes the function never actually reaches the limiting value

[native venture]

got it thankss

.close

[lone heart]

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[rancid trail]

How do I start

[rancid trail]

I tried finding x, y, a and b values and substituting in LHS, but it gave me -1/csc θ - cot θ

[wide raven]

try putting in the parametric form of x and y

[rancid trail]

Para what?

[wide raven]

parametric

[rancid trail]

I don't know it

[wide raven]

x and y are a function of theta

[rancid trail]

Yeah

[wide raven]

it is theta what links the two

for example

equation of a circle x^2+y^2=1

its parametric form is (1 X cos(theta), 1 X sin(theta))

[rancid trail]

I will be honest with you, I don't get it

[wide raven]

okay

[rancid trail]

What is parametric forn in the first place

[wide raven]

say you have a function

okay

[rancid trail]

Okay

[wide raven]

you introduce a third variable and find the function of x and y in terms of the new variable

okay?

you there?

[rancid trail]

I'm here

[wide raven]

yeah so

for example of a circle

do you know what the equation of a circle is like on a graph?

[rancid trail]

Not really

[wide raven]

okay

[rancid trail]

But I guess it is a circle with origin as centre and 1 as radius

[wide raven]

no wait

its fairly ez you'll get it

[rancid trail]

Ok

[wide raven]

so do you know the distance formula

coordinate geometry stuff

[rancid trail]

$$ \sqrt {x^2 + y^2} $$ i think I'm not sure

[ocean seal]

ThickduckPlayz

[wide raven]

umm idts, actually thats only for distance from the origin

[rancid trail]

Oh

Then I don't know

[wide raven]

apply pythagoras

what do you think now?

[rancid trail]

$ \sqrt { (x2 - x1) + (y2 - y1) }$

Umm

Texit

[wide raven]

i get it

a mistake tho

(x2-x1)^2

[rancid trail]

Ahh I'm sorry I forgot it

[wide raven]

no worries

so

say the distance is from origin

put x1=y1=0 in this

[rancid trail]

Ok

[wide raven]

it would be sqrt((x2)^2+(y2)^2)

now say this point lies on a circle

the definition of a circle is that it is a figure or shape whose distance from a point is always the same and the distance is called the radius

so

a circle from the origin with radius 2 would be

[rancid trail]

I have a doubt

[wide raven]

yea

[rancid trail]

Which point

[rancid trail]

This is a function

[wide raven]

no

[rancid trail]

Oh

[wide raven]

x2 and y2 are arbitrary

[rancid trail]

Ok

Then

[wide raven]

you get it right?

[rancid trail]

Kinda

Which point lies in the circle

[wide raven]

those whose distance from the centre is less than the radius

[rancid trail]

Yeah I get it

[wide raven]

yes

[rancid trail]

What does this refer to

The above equation?

[wide raven]

it means the arbitrary point lies on a circle

of radius 2 for example

so

if it is

x2^2+y^2 = 2^2

basic pythagoras

have you followed?

[rancid trail]

Yeah

[wide raven]

okay

so now

we can replace x2 by variable x and y2 by variable y

and it will represent all points

[rancid trail]

Ok

[wide raven]

so

x^2+y^2=4

is the equation

[rancid trail]

Yeah

[wide raven]

so

if we draw a radius at an angle of theta with the x axis

[rancid trail]

Yeah?

[wide raven]

say this

[rancid trail]

Yeah

[wide raven]

what do you think the point it cuts on the circle would be

hint: you have to use sine and cosine in a right angled triangle

what do you think?

[rancid trail]

I have no idea what it will be

[wide raven]

this triangle

[rancid trail]

Idk how to find a point

Oh wait

[wide raven]

i am

[rancid trail]

I think I need to find the base and perpendicular and use the distance formula

What do you think?

[wide raven]

exactly

no wait

why distance formula

we know the radius

[rancid trail]

Lol forgot

[wide raven]

so just use trigonometric ratios

[rancid trail]

So I only need to find the base

And perpendicular

[wide raven]

yep

and they basically are the coordinates of you see closely

should it not be (r cos(theta), r sin(theta))

x=r cos(theta)
y=r sin(theta)

now this is finally called the parametric form

[rancid trail]

Ok wait

I've only taught raw trigonometry

I don't know how to find sides

[wide raven]

dude

what is sine?

[rancid trail]

Perpendicular/hypotenuse

[wide raven]

yes

so if we want perpendicular

[rancid trail]

Oh f

[wide raven]

and we know the angle and the hypo

cant we just

[rancid trail]

P = sin θ x h

[wide raven]

yes

the same way its is that

[wide raven]

and hence this is the parametric form of a circle

[rancid trail]

And similarly cos θ = base / hypotenuse

[wide raven]

yep

so

i did this only because you asked what a parametric form is

[rancid trail]

Yeah

[wide raven]

but we don't actually need the terms here

it's actually my bad that i used it and you got confused

but anyways

now lets get to the problem

[rancid trail]

Okay

[wide raven]

do you want to send what you have done so far?

[rancid trail]

I erased it

[wide raven]

ohh well

anyways

we just put what x and y are

[rancid trail]

Into LHS?

[wide raven]

a^2/a^2 sin^2(theta)

yep into lhs

[rancid trail]

Yeah

[wide raven]

do it

[rancid trail]

And the same with y?

[wide raven]

yes

and really with practice you can do this one in your head as well

[wide raven]

1/sin(theta) cosec

cancel out a and b

[rancid trail]

Ok

[wide raven]

did you?

[rancid trail]

Thank you

[wide raven]

voila

[rancid trail]

I'm such a narrow minded piece of crap

I'm sorry

It was a simple question

[wide raven]

no worries bro we're good

[rancid trail]

Thank you

.close

[lone heart]

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[woven hamlet]

Can someone explain how these inequalities are converted into a equality contraints?

[woven hamlet]

Like if I have x1+x2>0 I can just say x1+x2=0 and how can I even determine such slackvariable to make it be x1+x2+y=0?

It could had make sense if i had two constraints x1+x2=> 0 and x1+x2<=0 then it can be converted into an equality constraint simply saying x1+x2=0.

I hope someone can give an example.

[lone heart]

@woven hamlet Has your question been resolved?

[shell widget]

@woven hamlet You have x1+x2 > 0. Obviously we would need to subtract something positive from x1+x2 in order to get 0. Hence x1 + x2 - y = 0, where y > 0

[woven hamlet]

But y is arbitary how do we know what y is?

[shell widget]

y will actually be equal to x1 + x2

in order to get 0

[woven hamlet]

or is y evaluted after x1 and x2 is known so to make it zero

x1+x1-(x1+x2)=0 I dont know if this is a bad example but does this constraint not always turn true?

[shell widget]

If I recall correctly, I don't think what y is matters

[lone heart]

@woven hamlet Has your question been resolved?

[woven hamlet]

.close

[lone heart]

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[wise canyon]

Can anybody pls solve that?

[high rapids]

do you know discrimant?

[oblique spire]

if the graph never touches x axis

the discrimant is always neg

for those ms

so u can rewrite what values of m satisfy the equation

$6^2-4m^2<0$

[wise canyon]

so I need to solve it by discriminant?

[ocean seal]

idk7

[oblique spire]

ya

u will require discriminant

[wise canyon]

okay, i'll try to do that

thanks

.close

[lone heart]

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[spare plaza]

2 nd one

[high rapids]

what have you tried?

[lone heart]

@spare plaza Has your question been resolved?

[spare plaza]

Nothing yet idk how ti Start this

<@&286206848099549185>

[alpine sable]

had you tried it @spare plaza

[spare plaza]

No

[alpine sable]

okey...

well you can make it to the form
sqrt(a^2 +x^2) or sqrt(a^2-x^2)

[spare plaza]

Can u give me a solution pls

[alpine sable]

sure..

[woven wraith]

Factor out e^x out of sqrt

Then substitute $e^x=t$

You will get $e^xdx=dt$

[ocean seal]

GG・Goof

[spare plaza]

Can u give a solution pls

[woven wraith]

Uhh

Do till this then you will get a hint for next

[nocturne dove]

It's a little more complex than that I guess

[woven wraith]

Wait

[nocturne dove]

Not the complete solution, but you can do it from here.

Integral sec³udu =I, the 2√a is not included

[woven wraith]

Got it

Giving solution

[spare plaza]

Ok lemee try

[woven wraith]

Uhh

[alpine sable]

why don't you use e^x as A for a while and then make it similar to the formula

$ sqrt(X^2 + A^2)

[nocturne dove]

Where do you think the formula of √(x²+a²) comes from xD

Indian student vibes coming from you

[alpine sable]

what??

[nocturne dove]

Yea mugging up the formulae been there done that

[alpine sable]

look at this then

[nocturne dove]

Yea how you think this formula came into existence?

It's not obvious is it?

[alpine sable]

isn't it making things simple

[woven wraith]

ig you can substitute $a=e^xtan^2(\theta)$

[ocean seal]

GG・Goof

[nocturne dove]

Dude u remember a formula. You take cannot take it as a fact that everyone knows it

[alpine sable]

i know how to derive that formula very well..i am just saying when we have formula why don't use it

[nocturne dove]

I'm pretty sure the asker doesn't know this formula

[woven wraith]

It might work :?

[alpine sable]

so now you will teach the asker how to derive the formula..or make things simple for them

[nocturne dove]

I'll show them where the formula comes from

I bet that's what your teacher did when he first taught u indefinite integration right?

[alpine sable]

it dosen't matters...

[nocturne dove]

Or he just wrote this formula down and told you to remember it.

[nocturne dove]

XD understanding is more important than mugging up formulas in mathematics.

What grade u in?

[spare plaza]

.close

[lone heart]

Channel closed

Closed by @spare plaza

Use .reopen if this was a mistake.

[alpine sable]

what the heack...how do you know i am only mugging things..when someone had asked some thing we should make things easy for them..not complicated

[lone heart]

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[tender basin]

can somebody help me figure out how to get the answer on number 3? i've already got the answers for everything else except that one

[tender basin]

how do you get the possible means

i think it means the sample means, but all of the possible means as an answer isn't an option in the google form, so i'm thinking that's not the exact answer

<@&286206848099549185>

[lone heart]

@tender basin Has your question been resolved?

[tender basin]

.close

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[sick python]

If i have a line can i find out if its convex or concave and increaseing or decresing just from having a points?

[supple tundra]

eh?

[sick python]

...?

[supple tundra]

,w what is convex function

[ocean seal]

Results provided by WolframAlpha

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Requested by azeem321#9772

[alpine sable]

...Can you make a diagram of what you mean? This is probably a lot more confusing than it sounds

When you say "line", do you mean "curve"? And "a points" isn't very English, although I can understand the struggle if English is not your native language

[sick python]

concave or convex @alpine sable @ocean seal

[alpine sable]

Ah, I see

[sick python]

🙂

I was eating fish with my hands btw.

[alpine sable]

So, what do you mean by "having a points"?

[alpine sable]

That's not relevant, but kinda funny

[sick python]

A line is made of points.

But I have a numpy serries of values for the y and Im using the index for the x values.

[alpine sable]

Oh, so you need this for a program... That's interesting, most people need help for school

[alpine sable]

So, basically, you have a bunch of x-y pairs and you need to use them to figure out whether or not the curve is concave or convex?

[sick python]

https://tenor.com/view/yeah-excellent-extra-hello-hello-u-gif-21823546

yes!

[sick python]

https://paste.pythondiscord.com/ecoleluhac

[alpine sable]

Are we assuming that the curve is always either strictly increasing/decreasing?

Ah... I see, could you perhaps give us a visualization of your data?

[alpine sable]

Oh wow, can that even be called concave or convex? It looks like it's neither

Unless you have a different definition in mind

[sick python]

This is clearly convex increasing!

Im asking what is the best option to get that category?

[alpine sable]

The general trend is, but it is going up and down a lot

[sick python]

I remember in math class using a point but using a line whats the usual option.

People use the first and second deriviative or something.

[stone glen]

How can a line be convex or concave?

[alpine sable]

What if the trend looked like this? Would this be considered concave or convex?

[alpine sable]

They meant a curve

[stone glen]

Oh

[sick python]

lines can be cuved.

[stone glen]

Again what is convex and concave in a curve either?

[alpine sable]

This

[stone glen]

Am i underqualified for this?

[alpine sable]

Probably not, it's just a bit confusing

[alpine sable]

Again, would this be considered concave or convex?

[sick python]

im not sure tbh it looks intentionally dificult

[tacit arch]

This channel's occupied. Read #❓how-to-get-help

[stone glen]

I think from that logic , it's concave in a certain range , and it's convex in a certain range

[alpine sable]

Oh oh didn’t realise

Yea sorry

[sick python]

https://tenor.com/view/dj-khaled-you-smart-smart-gif-4495825

im looking for a basic tool in math to do it im sure there is

i dont think a cuve can be perfectly both

/ine

line*

[alpine sable]

Oh, sorry, I am just asking them so that we can agree on the definitions, the question wasn't meant for me

[stone glen]

Bish send me a request cuz i can't send u

I cant type

[tacit arch]

Nah I don't dm

[stone glen]

Wow

[sick python]

thanks for fogging up the post where im actually trying to ge actual work done

[stone glen]

Oh yeah sorry m8

[sick python]

should of know someone with the handle 'sexy man' was trouble

GET OUT OF HERE

[alpine sable]

Okay, chill 👁️👁️

Anyways, if we're not sure what convex/concave means, how could we put it into code?

[sick python]

mathematically how does one categorically say a line/curve is concave or convex?

increasing or decreasing

[stone glen]

if a curve is convex , then it's derivative is an increasing function in that region where it's convex. And vice versa for concave

[alpine sable]

Depends on your needs, to be honest

[sick python]

can the region be the entire line?

/curve

[alpine sable]

Yes, in theory

[stone glen]

It could be

[sick python]

i think thats only for a point

[alpine sable]

What do you need this for, by the way?

[stone glen]

Derivative being a function doesn't go for a point

[sick python]

dy=np.diff(y,1)
dx=np.diff(x,1)
yfirst=dy/dx
#And the corresponding values of x are :

xfirst=0.5*(x[:-1]+x[1:])
#For the second order, do the same process again :

dyfirst=np.diff(yfirst,1)
dxfirst=np.diff(xfirst,1)
ysecond=dyfirst/dxfirst

xsecond=0.5*(xfirst[:-1]+xfirst[1:])

[stone glen]

It goes for a function , as in a curve

[sick python]

if i have the points not th equation how can i? I got this code from a post online idk if you all know python

https://stackoverflow.com/questions/40226357/second-derivative-in-python-scipy-numpy-pandas

[alpine sable]

@sick python It's important you tell us what you need to know this for, otherwise there's some edge cases that we can't really figure out

Such as this

[sick python]

can you define the edge cases?

i dont have a definition for anything so i cant give you the answer

[stone glen]

He doesn't even have a function, he just has a set of points, and he wants to figure out which is concave and which is convex. Right?@sick python

[sick python]

but like anything there would be caviats etc

[sick python]

Can you convert points to a function?

[stone glen]

Depends, not always

[alpine sable]

An "edge case" is just a case where the general rules don't apply. In my screenshot, for example, the rules for determining whether or not something is concave/convex don't work

It's not really a Math thing

[sick python]

yes but in your example we dont have the typical yardstick or standard so lets first try to figure out that then get to the edge cases

[tacit arch]

You can try fitting polynomials or logarithms to your points first

Then once you have a function, then you can talk about concave/convex

[sick python]

sounds rational

[alpine sable]

Well, then you could check if the middle point is below the line between the first point and the last point. Also, can your points be decreasing?

[sick python]

that sounds super basic sorry

something 15 year old use in algebra class

:/

[alpine sable]

What's wrong with it being basic?

Is it too innacurate for your needs?

(which you have not specified)

[sick python]

i can see now why you are so fixed on your edge* concpet

lol

[sick python]

tell us more!

i how can you convert points to an equation!?

[sick python]

you use python?

[alpine sable]

You want us to help you figure out whether or not a curve is concave or convex without defining concave or convex or giving us any more information...

[stone glen]

U can approximate it by using different functions and applying graphical transformation and what not. But i need to looks at ur points and then we may talk about how to do that

[sick python]

https://paste.pythondiscord.com/ecoleluhac

[tacit arch]

https://en.m.wikipedia.org/wiki/Runge–Kutta_methods

That's a popular one. Of course whether or not it works for you depends on your data

[sick python]

You have any other ideas you are thinking if? Ill look for this in python btw.

[alpine sable]

i need to looks at ur points and then we may talk about how to do that

Of course whether or not it works for you depends on your data

Those are both versions of "We need more info". Seriously, what kind of data are you actually working with? And what are you gonna do knowing that the trend is concave/convex? The last question is to know how we should define concave/convex

I'm clearly not the only one who needs more information here

[sick python]

i can share with you another example and give you more points but youll have to plot them!

[alpine sable]

Sure. Give me a couple more, please

[sick python]

[0.00047463 0.00047463 0.00087793 0.00087793 0.00150821 0.00150821
0.00213118 0.00213118 0.00239674 0.00239674 0.00261027 0.00318741
0.00318741 0.00319582 0.00333306 0.00371975 0.00374742 0.00374742
0.00408505 0.00408505 0.00443729 0.00452068 0.00452068 0.00475548
0.00484594 0.00484594 0.00505191 0.00505191 0.0052329 0.0052886
0.0052886 0.00532525 0.00551006 0.00551006 0.00569897 0.00574929
0.00599291 0.00599291 0.00617421 0.00617421 0.00678657 0.00678657
0.00703946 0.00705741 0.00722215 0.00722215 0.00736094 0.00736094
0.00746109 0.00746109 0.0074931 0.0074931 0.00760732 0.00792821
0.00829208 0.00829208 0.00835589 0.008433 0.008433 0.00861644
0.00861644 0.00873116 0.00890034 0.00902182 0.00902182 0.00927195
0.009429 0.009449 0.00965975 0.00983825 0.00983825 0.01050859
0.01050859 0.01071541 0.01071541 0.01098189 0.01098189 0.01111307
0.01153451 0.01156762 0.01209603 0.01264033 0.01268287 0.01292867
0.01366593 0.01366593 0.01371995 0.01397526 0.015054 0.015054
0.01538239 0.01538239 0.01545759 0.01545814 0.01545814 0.01552308
0.01557143 0.01557143 0.01629146 0.01629146 0.0164267 0.0164267
0.02022059 0.02023321 0.02023321 0.02109235 0.02129123 0.02182878
0.02182878 0.02450314 0.02450314 0.0281505 0.0281505 0.02825794
0.02825794 0.02908498 0.03088286 0.03574755 0.0370494 0.04209969
0.04209969 0.04414231 0.04687367 0.05148901 0.05148901 0.05686447
0.05686447 0.05853808 0.06005517 0.06181409 0.0688954 0.07178449
0.07306158 0.07698107 0.10353118 0.10479846 0.10607547 0.12230598]

[sick python]

https://paste.pythondiscord.com/inacuwuweq

[alpine sable]

Ah fudge I'm trying to code and Windows is lagging
Imma just switch to Linux once I get the opportunity

[sick python]

ok im here

what are you trying to do plot the values?

[alpine sable]

Yes, using matplotlib

But Windows decided to do stuff in the background for some reason

[sick python]

You are using windows 11?

[alpine sable]

No, Windows 10

[sick python]

ok that still terrible but its not as bad!

[alpine sable]

Once 2025 comes around and they stop updating Windows 10, I'll just hop over to Linux

I'd even use MacOS if I had to

[sick python]

windows has gone to the dogs 100% stupid garbage OS its so slow now windows 11 clearly they are whrehousing user data and doing 'updates' to disguse

[alpine sable]

Good enough... Is this what the data is supposed to look like for the second one?

I guess not. This is what it's giving me for the first one

I suck at programming

[sick python]

:/ idk

i didnt plot them

[alpine sable]

With the power of ugly code, I fixed it

Ah, the last one looks convex, but only if you ignore that tail at the beginning

Day 2 of not having any idea how to define "convex"/"concave" in this scenario

[sick python]

what did you do?

[alpine sable]

Turns out not only was I plotting strings, but some of them were empty strings

[sick python]

lol!!!!!!!!!!!!!!!!!!!!!!!

https://tenor.com/view/bitch-you-scared-me-maurice-sistas-you-frightened-me-i-got-scared-gif-21920021

[alpine sable]

So many exclamation points... Back to business, where are you getting this data from?

[sick python]

https://tenor.com/view/no-nope-gif-18629308

its a decomposition

im trying to use a method called dbscan

but i want to find the elbow!

https://pypi.org/project/kneed/

automatically! so i have to pass 2 parameters through the funciton

you get me? @alpine sable

[alpine sable]

Oh, then that's trivial!

There's 2 things you need to know:

• Is the end point above or below the starting point?
• Is the knee above or below their average?

If you though checking whether or not the midpoint was above or below the average was too simple, this one should be 5x more reliable (and cool)

[sick python]

what?? why do you sound releaved?

[alpine sable]

...It's a genuinely reliable solution?

[sick python]

we still dont have a valid method of gtting if the curve is convex or concave

[alpine sable]

Oh, shoot... My bad, I though it didn't require you to know in advance whether or not the function was concave or convex :/

Well, at least now I know what you need it for

[sick python]

_>

[sick python]

so you see what you wanted to see

tell me what about the ideas you had

[sick python]

i posted more data

[alpine sable]

Honestly, the last example makes it all the more difficult. It looks concave and convex at the same time, and both answers from kneed are reasonable

I guess... Maybe one way would be to check the double derivatives at the points you get for concave and convex and take the bigger one

Kind of an ugly solution, but it sounds like it works

[sick python]

Dude Im asking you what will we use to check the curve to say if its concave or convex?

without looking at it with out human eyyes

[alpine sable]

That's what I answered. Let me explain it more clearly

Suppose you use kneed to check the elbow, assuming first that it is concave, then assuming that it is convex. One of these answers will be useless. To figure out which, check the double derivatives at both elbows, and keep the higher one

[sick python]

dude im passing concave or convex before i run kneed

[alpine sable]

I know, what I'm saying basically is that you can run kneed on both assumptions and check which answer is closer to reality

It's kind of a sucky solution, I admit

At this point, you should probably ping helpers

I'm trying to figure something out, but very slowly

[sick python]

<@&286206848099549185>

[sick python]

Thats not my intention.

[alpine sable]

It can tell you whether or not a curve is concave or convex, though. But scratch that, I think that matching it to a polynomial idea could actually work better

So, turns out kneed has an option to "interpolate" by matching the curve to a polynomial, which is a numpy thing

Then you just need to check whether or not the leading coefficient is positive or negative

Oh well... I'm not too sure about this either

[sick python]

If you are tired or giving up jus say that. Its fine.

[alpine sable]

Yeah, I'll just leave you alone until I find a solution that actually works

[sick python]

The interp_method still didnt negate them asking or requireing curve and interp_method

[alpine sable]

@tacit arch Do you think using the sign of a leading term in a polynomial is a good way to determine concaveness/convexness?

To be more precise, the method I'm using approximates the data using an nth degree polynomial and then checks if the leading term is positive or negative

Actually, I guess you also need to know whether or not the data is increasing or decreasing, but that's trivial

[lone heart]

@sick python Has your question been resolved?

[alpine sable]

@sick python I take it back, the polynomial method works well. Could I have some more data to try it on?

[lone heart]

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[zenith sparrow]

How would i go about integrating this?

[dawn birch]

u = sin(t)

so what do you get for du? @zenith sparrow

[zenith sparrow]

i tried doing it by parts

but im not sure how to integrate sin^t

oops

sin^2 (t)

[dawn birch]

what im asking is not by parts

if u = sin(t) then what is du

[zenith sparrow]

cost x dt

[dawn birch]

cos(t) dt correct

so if you replace sin(t) with u and the cos(t) dt with du

what do you get

[zenith sparrow]

u^2 x cost x dt

[dawn birch]

replace cos(t) dt with du

what does that then give

oh also there’s a times 2 factor but we can just factor that out of the integral

[zenith sparrow]

u^2 du so (2u^3)/3 is integral and then replace with u = sint

[dawn birch]

2/3 u^3 + C

and now yes you replace u back with sin(t)

[zenith sparrow]

i see, is this the only possible method to integrate this?

[dawn birch]

you can make other u-substitutions

like u = sin^2(t) gives du = 2 sin(t) cos(t) dt

[zenith sparrow]

so only by substitution. thank you

i wonder why it doesnt work for parts

[dawn birch]

oh oops i accidentally multiplied *2 again here

fixed

[zenith sparrow]

oo yes thats what i got and was confused for a sec haa

thank you a lot

i'll use substitution from now

[dawn birch]

yes integration by parts is generally used for 2 unrelated factors

like x e^x

[zenith sparrow]

i was confused since my teacher integrated it with no working in between

[dawn birch]

since sin and cos are both trig you can (in many cases) use u-sub

[zenith sparrow]

x^2 * e^x + e^x ?

[dawn birch]

don’t use x as a variable and a times symbol in the same expression lol

[zenith sparrow]

o true

[dawn birch]

but yes (x^2 + 1) e^x would be integration by parts

[zenith sparrow]

mhm thats the method i got taught for these things

my teacher solved it in a line hah

super genius! or something

[dawn birch]

lol

[lone heart]

@zenith sparrow Has your question been resolved?

Channel closed

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[night pumice]

pls help 😭😭

[abstract fractal]

Rewrite the root as a power

[chrome plank]

$\sqrt[q]{x^{p}} = x^{\frac{p}{q}}$

[ocean seal]

Nonna

[night pumice]

is the answer c

[supple fiber]

yes

[night pumice]

yassssssss

I’m officially smart now

[supple fiber]

u are

[abstract fractal]

It's better to give a little room for discovery over giving the answers

[chrome plank]

I'm sorry

[high rapids]

@night pumice please change your profile

[night pumice]

why ):

[high rapids]

Your dog nose ugly

[night pumice]

So mean

it’s cute doggo

[high rapids]

Jk

But it's not cute

[night pumice]

why not

it’s a cute roblox doggo

[high rapids]

Cringe

Fuck Roblox

[night pumice]

it’s my doge

jk

[high rapids]

I'll eat it

[night pumice]

:0

[high rapids]

What is a dalmatian

[night pumice]

WHAT

oh yes it’s a type of dog

[high rapids]

Ok

[night pumice]

tall buff dog

with black and white spots

[high rapids]

Wow

[night pumice]

jkjkjk

[high rapids]

Ok

My gf is also asian btw

[north adder]

.close

[lone heart]

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[lone heart]

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[tough fulcrum]

Could somebody show me how to do 96 so I can do the rest of the problems like it

[north adder]

pythag, double identity

[tough fulcrum]

could you explain it step by step for me?

[north adder]

okay so you have sin^2 theta + cos^2 theta = 1
16/25 + cos^2 theta = 1
cos theta = 9/25
then use double angle cos
to find cos(theta/2)

and use that for sin(theta/2) in the double sin angle identity

[tough fulcrum]

oh also why did you change -4/5 to 16/25?

it's supposed to be negative btw

[north adder]

because sin theta = -4/5

sin^2 theta = 16/25

?

[tough fulcrum]

oh right thanks

[north adder]

do you understand the rest of the steps

[tough fulcrum]

I'm trying to understand them rn give me a min

how does using the double angle identity for cos help to find cos (theta/2)?

because you could say cos(2theta)=9/25- sin^2theta but I don't see how that helps

[north adder]

let u = theta/2

does it make sense now?

[tough fulcrum]

not really no

[north adder]

ok.... so in the case of trying to find cos theta/2

cos theta = 2 cos^2 theta/2 - 1 right

3/5 + 1 = 2cos^2 theta/2

4/5 = cos^2 theta/2

makes sense now?

2/sqrt(5) = cos theta/2

I really wanted to avoid spoonfeeding you

[tough fulcrum]

I'm trying to understand it rn

[wary stream]

Is this $$\frac{3}{5} + 1 = \frac{2 \cos^2(\theta)}{2}$$
Or $$\frac{3}{5} + 1 = 2 \cos^2(\frac{\theta}{2})$$

[ocean seal]

dldh06

[north adder]

latter

was too lazy to put proper brackets

[wary stream]

Well, as you can tell, lazy made it much more difficult to read

[north adder]

nah, i clearly specified what I meant previously, so there should be no miscommunication.

[tough fulcrum]

alright I got it thanks

idk why I had such a hard time with that but I'll try some of the other problems now

.close

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[north adder]

no worries, keep it up it will pay off :)

[tough fulcrum]

I've got my final on thursday and I"m currently studying fo rit

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[north scaffold]

how to solve this partial equation

when i put v=-1

still b vanishes

[nocturne dove]

B vanishes and gives u a value of A

After finding A put v=0 and find B

[north scaffold]

can i do that

[nocturne dove]

Why not

[north scaffold]

a = 2 and v = 0 to find b

[nocturne dove]

Well v=anything to find B if you know A

[north scaffold]

i thought it is against the rule

thank u

[nocturne dove]

Nah idts

[nocturne dove]

Yw

[north scaffold]

.close

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[visual stag]

what this mean

ignore the r

[alpine sable]

N is natural numbers

[nocturne dove]

n belongs to the set of natural numberz

[alpine sable]

1, 2, 3, 4...

etc

[visual stag]

can it be negative

[alpine sable]

no

its natural

[visual stag]

oh right ok thanks

[nocturne dove]

Not zero

[alpine sable]

yea not 0

my bad

[visual stag]

.close

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[north adder]

:D

[nocturne dove]

Arctan a - arctan b formula

[north adder]

doubel angle?

[nocturne dove]

Nah

tan-1(a) - tan-1(b)

[north adder]

nvm

im balding

[nocturne dove]

ab<1

Well read the ncert it's given in there

[north adder]

yea i see

thank u

i have another question tho

[nocturne dove]

Yw

Yep

[north adder]

why are the domain restrictions like this

[nocturne dove]

An inverse of a function is defined only in a domain where the original function is bijective

So sin is not bijective for all x

But in -1, 1 it is

So arcsinx is defined for x belonging to -1 to 1

[north adder]

right, but wouldnt that imply that its 2x/(1+x^2)

not for x

[nocturne dove]

Yes depends on the argument

-1≤2x/1+x²≤1

Solve for x now it's a simple inequality problem

[north adder]

alright give me some time

[nocturne dove]

Sure

[north adder]

0<=(x+1)^2<=2(x^2 +1)
discrediting the lhs since its true for all real numbers
(x+1)^2 <= 2(x^2 +1)
0 <= (x-1)^2?

which is still true for all real numbers

or am i balding

[nocturne dove]

Okay

So

This is the double angle formula I suppose, but what's your question lol

x can be all real because of arctanx being R in (-π/2 to π/2)

[north adder]

i understand how the domain restriction works for the normal arcsin graph, however shouldnt it change when its not just x but rather 2x/(1+x^2)? sorry im talking about the first eq with sin for clarifcation

[north adder]

this makes sense

[nocturne dove]

Well 2x/(1+x²) is always bounded between -1 and 1

Same case for 1-x²/(1+x²)

[north adder]

right but thats not bounding x between those numbers

no?

[nocturne dove]

it's the double angle formula for 2arctanx

And the x you have here

[north adder]

no ok uhm I understand the derivation

[nocturne dove]

Yea I understand your question

[north adder]

the thing is I understand why and how the domain is

[nocturne dove]

But when it's converted to that form

x is already all R

From the arctan equation

[north adder]

uhm

[nocturne dove]

2x/(1+x²) always lies between -1 to 1

For all x

So there's no need

[north adder]

mhm

[nocturne dove]

To bound this x

[north adder]

i see

so techinically the statement is incorrect?