help-0

[lethal canyon]

no

[alpine sable]

Bro

[minor crypt]

so it's actually a game where you do maths?

[lethal canyon]

No

[glacial hedge]

😦 my question got barried

[minor crypt]

what is the game about?

[alpine sable]

Bro

[lethal canyon]

Naruto

[alpine sable]

Bro

[lethal canyon]

What

[alpine sable]

Sup

[lethal canyon]

Yo

[minor crypt]

naruto!???

[minor crypt]

why do you need to solve vector shit on a roblox naruto game?@lethal canyon

[lethal canyon]

For my sharingan

[minor crypt]

?

[lethal canyon]

Like uchiha sharingan

anyways

is the answer no solution or is there one more step?

[minor crypt]

this looks hard

do you study pure maths? @glacial hedge

[lethal canyon]

alr well ima go use brainly

cya

[minor crypt]

no wait

[ionic jewel]

that's calc 3

[minor crypt]

whats the game

[minor crypt]

I'm still in high school

Just give me some basic substitution and partial integration stuff, thanks

[glacial hedge]

@ionic jewel do you know where the *** that stupid pi comes from?

[glacial hedge]

whats partial integration?

[minor crypt]

oh is that not how you call it in english?

[glacial hedge]

you mean multiple integrals?

[lethal canyon]

NEW QUESTION
t = -2/3, s = 5/3, j ≠ 0
Convert to vector form

[glacial hedge]

dude

that doesnt even make snese

neither of them are vectors

[lethal canyon]

is there some other mathematical form for it>?

[glacial hedge]

no

[lethal canyon]

i see

nvm then

NEW QUESTION
t = -2/3, s = 5/3, j ≠ 0
Graph this eqution

[minor crypt]

it's the method where you call one factor u, the other factor dv, then use the formula u×v-intr(v×du)

e.g.
intr(arctan x × dx)=..

say

u=arctan x <=> du=1/1+x²×dx
dv=dx <=> v=x

.. u×v-intr(v×du)
=arctan(x)×x-intr(x×1/(1+x²)×dx

that seems to also be the correct name in english

@glacial hedge

[slender marten]

Did you figure it out?

[glacial hedge]

oh.. you mean that... I thought u were talking about calc 3

[glacial hedge]

yeah forgot a sin(phi) 😤

[slender marten]

Nice. 🙂

[shell heron]

$(-3)^4 = 81, -3^4 = -81?$

[ocean seal]

Elon

[shell heron]

is that correct?

[subtle thicket]

4. An energy company wants to build a natural gas storage reservoir with
   capacity for 75000 liters, with a cylindrical shape with a circular base, with a flat end and the
   another has a parabolic shape with the same base.
   4.1. Assuming that the manufacturing cost (per m2 of metal used) of the end is 2.3 of the
   cylindrical portion, what is the height and dimensions of the base of the reservoir in order to minimize the
   construction cost of it?
   4.2. Assuming the reservoir walls are 19 cm thick, what is the total volume
   of used material?
   someone help me with 4.1 pls

[minor crypt]

I just said I'm still in High School.

[glacial hedge]

u take that in hs?

[minor crypt]

yes

well, I have 2 additional hours of maths a week

so 8 hours total

I also got taught conic sections and homogeneous coordinates, which you dont normally see in hs

[ionic jewel]

yes

[inner token]

If a mass of 300 kg with density 7 kg/m^2 collides perfectly with a mass of 200 kg at 10 kg/m^2, how do you calculate the new density?

[minor crypt]

pretty sure thats physics

[inner token]

no it isn't, i'm dumb and don't know how to do ratios

[minor crypt]

(300+200)/(7+10)
=500/17

is that it?

thats definitely not it

[inner token]

the density isn't evenly weighted like that though

[minor crypt]

let me think this through

(3/5 × 7) + (2/5 × 10)

so 21/5+10/5=31/5

[inner token]

new mass = 300 + 200 = 500 kg
new volume = 300 / 7 + 200 / 10 = 62.86 m²
new density = 500 kg / 62.86 m² = 7.95 kg/m²

[inner token]

got it thanks

[minor crypt]

so it physics

you baited me

[inner token]

well kinda

[minor crypt]

also why do you call it volume, isnt surface the correct term

[inner token]

meant to be m^3 my bad

[minor crypt]

oh

oh that changes a lot actually

[strong furnace]

if it collides perfectly(elastically) why would you have a combined body system?

[inner token]

huh

[strong furnace]

imperfect (inelastic collisions) result in sticking

[minor crypt]

[inner token]

it's for a game i'm making.. when 2 circles collide, they merge into one larger circle

[minor crypt]

cs degree? @inner token

[inner token]

and i'm dumb and cant do math so I was struggling to calculate new density lol

[strong furnace]

this scenario is called inelastic collision but it seems you have figured it out

[inner token]

no, electrical engineering lol. Just making a game for fun

[minor crypt]

now I'm gonna have to look into electrical engineering

it looks fairly similar to computer science

except it is more so focused on the physical part of computers, rather than the software/virtual side of things? @inner token

is that it?

[inner token]

haven't implemented the density stuff yet, but here's what I got for gravity sim

[inner token]

yeah it's more hardware stuff

[minor crypt]

agario

[minor crypt]

sounds hard to me

[subtle thicket]

Prove that $u,v \in \mathbb{C}^1(\mathbb{R}^3 )$,then
$$\nabla(u.v)=(u.\nabla)v+(v+\nabla)u+(u \times rot v ) + (v \times rot u)$$

[ocean seal]

St0ny 420

[subtle thicket]

Can anyone help me with this ?

[glacial hedge]

Could someone help me do this stupid gosh darn integral... I keep getting -2pi/3

<@&286206848099549185> ?

wtf i got -4pi/3 this time

[minor crypt]

you just pinged like 40ish people

[glass lichen]

yeah.. and?

that's how the helper role works

[minor crypt]

[alpine sable]

use cylindrical coords not cartesian

you should easily get the angle to be 0 to 2pi then just worry about radius and z

it also doesnt complicate the integrand which is z^3 (spherical would be a little tedious so cylindrical is nice [and for cones too])

[glass lichen]

just write the function in terms of n.. and make it an increasing function

f(n)=n

$f(n)=\frac{1}{n!}$

[ocean seal]

Mosh

[glass lichen]

that's what you just described

[steep briar]

wait but ⅓ of ½ of 1 isn't 1/(n!)? Isn't that ⅙ ? ignore me

[alpine sable]

thats decreasing though?

[steep briar]

So it'd be: and ignore this

[alpine sable]

which is 1/n!

[steep briar]

oh

duh yeh

[alpine sable]

if you multiply it out lol

mosh is right for that specific f(n), but i thought eben wanted an increasing one?

ah ok

yeah go with mosh's

[glass lichen]

I was tryping that exact thing out then realized, oh wait

[steep briar]

lol the factorial leads to a wonderful simplification of the amagulus (or whatever it's called)

[plain osprey]

hey i have a question in statistics i really need help with, i think i need to use linear transformation but i dont remember it at all, i have E(x)=200 v(x)=100, E(y)=15, V(y)=10, and the formula is F=5x+y+3

what is the expectancy(E) and variance (V) of F?

and how do i calculate it ofc

[steep briar]

If I'm correct, linear means M(a+b)=M(a)+M(b), so you'd do E(F)=E(5x+y+3) and break it down further.

[plain osprey]

[jagged imp]

https://bookdown.org/kevin_davisross/probsim-book/linear-combinations-of-random-variables.html this gives you the formulas you need.

[steep briar]

oh and M(ca) = cM(a) for some constant c (i.e. E(7z)=7E(z) )

[plain osprey]

im not sure how to apply the formulas correctly since i have X, Y, and the 3 there

also its hard as a non-native english speaker to make sense of all these math terms

if i could see an example of the solution i will understand what u did

[steep briar]

I mean from Wiki this is really all you need to know, just apply both properties (Additivity and "Homogenity"):

[plain osprey]

so E(f) is just E(x)+E(y)+3?

[steep briar]

yee

wait

the constant infront of x

don't forget homogeneity

[plain osprey]

idk what that means haha

im not studying math in english i have gamer english

[steep briar]

from the screenshot I sent: f(αx)=α f(x)

[plain osprey]

yeah so like 5E(x) instead of what i wrote

[steep briar]

ye

[plain osprey]

and the V for the constant 3 would be 0 right?

[steep briar]

dunno about variance but from the name I'd say that'd be intuitive, lemme Google what it is

[plain osprey]

yeah yeah it should be 0

would make no sense to be anything else

[steep briar]

Yep

[plain osprey]

k ty for ur time!

[steep briar]

gl!

[glacial hedge]

I have a rather stupid question, would it be possible to skip undergraduate and apply to a graduate program. And Instead do self study?

[steep briar]

I doubt that, as most graduate programs (I don't know any exceptions so you might say all) require an undergraduate degree.

also applying to a graduate program is more like applying for a research job so just doing self study might not be as beneficial as you may think. NOTE: I am a senior undergrad' so I'm not the most qualified to give advice.

[glacial hedge]

But most of college is spend learning through textbooks? Graduate is where you start research?

[steep briar]

nope

you do research before graduate since that's how you build a resumé to apply

[glacial hedge]

ah, so what if you were to do research too xD with a proffesor just not with a university

[steep briar]

Yeah doing research with a professor is usually the way as an undergrad (and trying to get him to let you do a spinoff project)

Like my university makes it explicit in the requirements to get your PhD

[maiden harbor]

Hey if 7600 people give a test and you get a 82.9 percentile, how many people have scored above or equal to you?

[untold warren]

looking for some help on tackling this problem

part a specifically, says it wants me to use mathematical induction, ive done the basis step but having trouble on the inductive step

[maiden rose]

just look at the n+1-th derivative and write it as (f^(n))' so that you can use the formula of the n-th derivative

[untold warren]

tried something like this

dont know if im allowed to factor in the ^k like that tho

[maiden rose]

I'm not sure what you mean with the notation dx/dy

[untold warren]

dx/dy just means derivative

[maiden rose]

oh you mean you take the derivative of what's in front of it ?

[untold warren]

yeah

[maiden rose]

oh ok

[untold warren]

the k represents how many times im derriving it

but im just not sure if im allowed to do what i did really

[maiden rose]

but then what does it go before the exponential in your second line

[untold warren]

power rule

ehh i guess i cant do that

or maybe I can? lol

[maiden rose]

seems weird to me

Imma write something down so you can understand it better (I hope)

[untold warren]

aight

think i got it

[maiden rose]

what is the 2*d/dx for in the third line

it looks like you just get rid of the derivative

but i feel like you know what to do

I just can't tell if you know how to write it

[untold warren]

d/dx just means derivative, i factored out the 2^k since its a constant

[maiden rose]

yes but it disappeared in the next line

[untold warren]

derivative of 2x = 2

[maiden rose]

I thought the x was for the multiplication, you got it then

[untold warren]

nah x is a var lol

and aight good to know

also 1 other thing if you dont mind

[maiden rose]

Sure

[untold warren]

in part b, whats a horizontal tangent line lol

[glass lichen]

d/dx means differentiate

dy/dx means derivative

[untold warren]

mixed up the terminology

does it just means when f'(x) = 0?

[maiden rose]

yes

[untold warren]

alright, appreciate all the help

[maiden rose]

I'm not used to help in english, the notations are very different from what I'm used to

glad I could still help

[tawny lion]

if you are trying to find the nth derivative

or create a formula for it

[untold warren]

another 1 if you guys dont mind, how would I bring a derivative over to the other side of an eq?

in this case, trying to isolate for y

would I just calculate the integral, then try to do stuff from there?

[viral patio]

in this particular example, y is what's called a "dummy variable" - that is, if you are able to do the integration* then there wouldn't be any y's in the right hand side

* note, wolframalpha tells me that this integral requires hypergeometric functions, which i know nothing about

[solid sorrel]

How many have no toppings?

Solution to this specific problem:
36 - floor(36/4) - floor(36/5) - floor(36/6) - floor(36/10) + 1 for every shared multiple of 4, 5, 6, 10 in {1, …, 36}

But what is the general solution for every shared multiple of a, b, c, ... in {1,..., N} cupcakes?

[untold warren]

well the q originally said that an answer might not even exist

this is what the original q was

[viral patio]

it's messy to type out, but what you have is basically the process of what you do - you start with N, subtract for every N/a, N/b, N/c, N/d cakes, but you have to be careful with lcm(a,b) cakes and need to make sure you aren't over-subtracting, but then you need to be careful with lcm(a,b,c) cakes and account for that... does that make sense?

[safe kite]

can anyone explain how to do this ^

[viral patio]

so we know that f(x) = 0 precisely when x = r1, r2, r3, right

[safe kite]

yes

[viral patio]

but now we want to know when g(x) = 0
so we can subtitute that and try to solve

[runic citrus]

can u help/

?

[tawny lion]

@runic citrus read the rules

and after that i will help you

[runic citrus]

i hav to say how i tried to do it?

[tawny lion]

no, you need to see #❓how-to-get-help

you don't ping helpers after 5 minutes, read the rules

[runic citrus]

oh so sorr

sorry

[tawny lion]

so, what is the formula for finding the nth term

of an arithmetic sequence

[runic citrus]

a +(n-1)d?

[tawny lion]

you dont even need that

[runic citrus]

oh ok

[tawny lion]

you just need the initial term

what is u1

[runic citrus]

7

[tawny lion]

what is the difference of each consecutive term

[runic citrus]

2

[tawny lion]

so if a = 7

and b = 2

what is your formula

[runic citrus]

a + 2n?

[tawny lion]

you know a

[runic citrus]

7+2n

[tawny lion]

exactly

now b is the exact same concept

you have u1

you need to find d

[runic citrus]

but isnt d 2?

[tawny lion]

d = difference

d = u2 - u1

aka b

[runic citrus]

9-7

b =2

[tawny lion]

we are talking about question b now

[runic citrus]

oh ok

[tawny lion]

you did q a

[runic citrus]

but for a

[tawny lion]

for a it's correct

[runic citrus]

if its 7+2n

if i did it on 2nd term

wouldnt it be 7+2(2)?

[tawny lion]

2(n-1)

my bad

it's 6 am here

[runic citrus]

no problem

wait so 7+2(n-1)?

[tawny lion]

yes

[runic citrus]

ok thnx

[tawny lion]

no prob

[runic citrus]

so for b

[tawny lion]

same concept

[runic citrus]

difference is 9-17

[tawny lion]

u of n = u1 + (n-1)d

you know u1 = 17

you know d = u2 - u1 or d = 9 - 17 = -8

[runic citrus]

yes

so 17-8(n-1)

[tawny lion]

depending on what they define as a, you might need to simplify this

if they mean that a is u1 then keep it as it is

[runic citrus]

yeah they mean a as u1

[tawny lion]

ok then just keep it as such

[runic citrus]

thank you so much for making my brain work!

[tawny lion]

no prob, if you have more questions lmk

[runic citrus]

i do actually

1 second

[tawny lion]

sure

[vast stump]

hi! just wanna ask for help, if u guys are done discussing hehe

[agile prairie]

If they want it in form a+bn wouldn't you have to distribute?

[runic citrus]

could i just ask one mmore?

[runic citrus]

thats what i was confused

[tawny lion]

a is u1

[runic citrus]

is the answer i gave in a+bn form or no?

[tawny lion]

it's quite ambiguous

[runic citrus]

oh ok

[agile prairie]

but then it's in form a+b(n-1) isn't it?

[tawny lion]

i would assume you should distribute but it doesn't say to find an expression for u(n)

[tawny lion]

oh nevermind

[runic citrus]

could i ask for help on this?

[tawny lion]

@runic citrus just include a distributed answer just in case

[runic citrus]

what does that mean?

[tawny lion]

i have to go afk for a minute, 1s

[runic citrus]

sure

[tawny lion]

back, so recall the formula for u(n)

[runic citrus]

sorry which one r we doing

[tawny lion]

the one u sent

what is the difference between every even number?

[runic citrus]

2

[tawny lion]

yeah, so a + (n-1)2

the formula for the sum of an arithmetic sequence is

n/2(2u(1) + (n-1)d)

and we know that n is 160

[runic citrus]

yeah

[tawny lion]

and that d is 2

also that u(1) is 2

[runic citrus]

25760?

right @tawny lion ?

[tawny lion]

no @runic citrus, it's not

how many even numbers are there in 160?

i gave you wrong inputs, forgot to mention some important things

[runic citrus]

oh ok

80 even numbers?

[tawny lion]

yes

[runic citrus]

so n is 80?

[tawny lion]

the formula is n/2(2u(1) + (n-1)d)

yes

[runic citrus]

so i just put 80 instead of 160 in n?

[tawny lion]

40(2(2) + (79)2)

should be 6480 or something

[runic citrus]

6480

[tawny lion]

yeah

[runic citrus]

yeah

[tawny lion]

if you wanna check yourself you can do 2 + 4 + 6 + 8 + 10 ... + 158 + 160 😉

[runic citrus]

its ok

[tawny lion]

just kidding don't do that

[runic citrus]

i trust u

[tawny lion]

it will drive you insane

[runic citrus]

and ill waste 2 hours

yeah

[tawny lion]

yes

is that it

or anything else

[runic citrus]

thats it

[tawny lion]

kk

[runic citrus]

thank you so much

[tawny lion]

npnp

also to shorten that whole process you can always do

n(n+1)

as you know n is 80 @runic citrus

for even numbers

[runic citrus]

ok thanks

[haughty pollen]

hey how can we take the square root of (0.5) in calculator

[jagged imp]

press the square root button then type in 0.5?

then equals?

[haughty pollen]

0.25 should come as the ans

[jagged imp]

0.25^2=0.0625

not 0.5

sqrt(0.25)=0.5

but sqrt(0.5) isnt 0.25

[haughty pollen]

in the question it says take the squre root of (0.5)

then he said the ans will be 0.25 if we take the squre root of it

[jagged imp]

the answer was wrong then

i promise you

[haughty pollen]

damn i will check again

[vast stump]

hi! can anyone help me? just need some ideas

[ionic jewel]

kW*h = kWh

read: number of kilowatts times number of hours = number of kilowatt-hours

[alpine sable]

1.5 x 6

@ionic jewel

[ionic jewel]

yes

so how many cents for that many kwh?

[alpine sable]

9$

9 x 23.99?

[ionic jewel]

9 kwh

not dollars

[alpine sable]

Srry

[ionic jewel]

yes

[alpine sable]

9kWh

215.91

[ionic jewel]

ok

[vast stump]

hi i just need some ideas. we were asked to conduct a mini research about the students’ performance on their math test. We need to incorporate our lessons about the quartiles, deciles and percentiles. Do you guys have any thoughts of possible research questions i could do?

[ionic jewel]

someone already answered that didn't they

[alpine sable]

Q15?

Stuffing up with 15

[vast stump]

i'm gathering ideas, so i'm asking other people's thoughts

[stark grail]

May I know how to solve this question The answer is 9/2

[jagged imp]

a lot of unnessecary information there

the important part is that 2/3[h,k] is a unit vector and then recognising that [-k,h] has the same magnitude as [h,k]

and knowing that |3y|=3|y| ig

[fervent grail]

Factorise
(a+b+c)⁵ -a⁵-b⁵-c⁵

Pls help

<@&286206848099549185>

[oak chasm]

@fervent grail Please don't use @Helpers until 15 minutes after you ask your question. See the rules and tips for getting help in #❓how-to-get-help.

[fervent grail]

Okay sorry

Btw pls help

I am in hurry :/

[undone dock]

Just expand (a+b+c)⁵ normally (proabably by using the trinomial expansion formula) and take away the fifth powered terms

oh waif

nvm

i cant read

[fervent grail]

?

I can send u the sol but I am not able to understand it

I am not able to understand it

[fervent grail]

@undone dock

[fallow jasper]

What part are you having an issue with?

[fervent grail]

How a+b = 0 ?

[fallow jasper]

We can express a function by the multiplication of its roots

Roots being the zeros of the function

You can notice that when a=-b the function goes to 0 since it will become c^5-c^5

Therefore (a+b) is infact a root of the function P(a,b,c)

[fervent grail]

Oh yess

[fallow jasper]

And the same applies to (b+c) and (a+c)

[fervent grail]

So we could also take that c+b =0 and a+c = 0

[fervent grail]

Yeah I was asking that only

[fallow jasper]

Exactly

[fervent grail]

But how P1 = m(a²+b²+c²).......

@fallow jasper

[fallow jasper]

Since the main function is degree 5

And we took degree 2 out

[stark grail]

thank you !!

[fervent grail]

But why a²+b²+c² only ?

[fallow jasper]

Hmm

[fervent grail]

?

[fervent grail]

We could take any other poly of degree 3 ; why this only ?

@fallow jasper

[fervent grail]

<@&286206848099549185>

Pls🙏

[fallow jasper]

Alright I'm back sorry for that

[fallow jasper]

Because it's the general form basically

[honest lagoon]

helllo everyone i have a question pls help me out!
can mixed fractions with different numbers and having the same improper fraction be same
i mean equal if ys how

[fervent grail]

?

[fervent grail]

This channel is not free

[honest lagoon]

ok sry

[fallow jasper]

m(x^2+y^2+z^2) is the general form since m is just a constant which we will find later

[fervent grail]

We could have taken x³+y³+z³ also why this only ?

@fallow jasper

[fallow jasper]

Yeah I'm here

[fervent grail]

[fallow jasper]

I'm thinking

[fervent grail]

And this of deg 2 but there was written deg 3

<@&286206848099549185>

Pls help

I am in a great hurry

:/

[sick ledge]

why are people so good at maths

i swear people need 130 iq to understand maths fully

[fervent grail]

<@&286206848099549185>

[versed osprey]

Could someone send their working for this

I keep getting super long decimals

[fervent grail]

Factorise
(a+b+c)⁵ -a⁵-b⁵-c⁵

[sick ledge]

identity:(a^2-b^2)=(a+b)(a-b)

[jagged imp]

oh god tell me you havent been working out what 12.5^2 is

[fervent grail]

Factorise
(a+b+c)⁵ -a⁵-b⁵-c⁵

[jagged imp]

yeah use wandering palace's identity lmao

[fervent grail]

Factorise
(a+b+c)⁵ -a⁵-b⁵-c⁵

[versed osprey]

Nvm thought it said 3 I’m blind

[fervent grail]

Factorise
(a+b+c)⁵ -a⁵-b⁵-c⁵

[jagged imp]

stop pinging random people and spamming

it doesn't make people want to help you more and just annoys the randos your pinging

(they deleted the random pings if any of you that got pinged look at this channel)

[fervent grail]

Am I talking to u ?

[jagged imp]

lol

[sick ledge]

just stop

people are trying to help your question to not be annoying and invasive

you should accept that

anyone who knows the question will come and help you
mass pinging wont help

[mental dune]

how do i go about proving it

[alpine sable]

Like evaluate them?

[mental dune]

nah i get how it works

just dont know how to "prove it"

[oak chasm]

Evaluating it is a form of proof.

[mental dune]

oh set

too easy

[oak chasm]

Like prove 4 = 2 + 2.

Well, 2 + 2 is 4, so 4 = 4.

[gray isle]

consider the factorial representation
or demonstrate through pascals
or something similar if you don't want to explicitly calculate numerical values

[mental dune]

its a chapter on pascals but i don't think i am meant to show it through pascals yet. but thanks

[surreal delta]

@mental dune that's like a simple formula btw

Want me to show you?

That's the formula of Stifel-Pascal

[misty pebble]

Use first principles to find dy/dx. y=x+3. Anyone able to help?

[gray isle]

where are you stuck?

[fervent grail]

Factorise
(a+b+c)⁵ -a⁵-b⁵-c⁵

[misty pebble]

well i've got f(x+h) = (x+h)+3, and f(x) = x+3. So x+h+3-x-3, then I'm left with h/h?

[gray isle]

h/h = ?

[misty pebble]

And since its h->0 though?

Oh, I'm assuming I evaluate that first, then the limit bit, my mistake

[strong knot]

Derivative 1/c

<@&286206848099549185>

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

Whatchu think your first step would be

@strong knot

[nova dune]

d/dx $x^-1$

[ocean seal]

BelowAveragePlayer02

[nova dune]

Screw LaTeX

[alpine sable]

[nova dune]

d/dx x^-1 makes it easier to differentiate

no, no

like x^(-1)

not 1/x

[alpine sable]

oh

but still he'd have to convert the fraction into a reciprocal

[nova dune]

Yeah, 1/x is weird looking.

[alpine sable]

its what i mean't

when I asked for the first step

[nova dune]

He can just state it's equal to -x^-2

oh

[strong knot]

How?

[alpine sable]

Write the fraction in terms of exponents

[strong knot]

Can u do step to step please

[alpine sable]

All you have to do is apply an exponent rule

then the power rule

ok still want me to show it to you

or

[nova dune]

Pretty sure he does

[alpine sable]

All you have to do is apply an exponent rule
then the power rule
this still insufficient for you

[alpine sable]

your amazing Latex skill is off the chart please print it out 🙏🏾

[strong knot]

Yes

[nova dune]

lmfao, I have never learnt LaTeX

[alpine sable]

yeah it was sarcasm (joking, please don't hate me)

[nova dune]

$x^{-2}$

[ocean seal]

BelowAveragePlayer02

[nova dune]

LET'S GO

@strong knot

d/dx $x^{-1}$

[alpine sable]

lol

\dv

[ocean seal]

BelowAveragePlayer02

[alpine sable]

$\dv{abc}{def}$

[ocean seal]

Πολλά άτομα είναι

[nova dune]

$\dv{c^{-1}}{c}}$

[strong knot]

I just want to know Derivative 1/c

[ocean seal]

BelowAveragePlayer02
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[nova dune]

apply the power rule $-1*c^{-1-1}$

[ocean seal]

BelowAveragePlayer02

[strong knot]

{-1-1}?

[nova dune]

-2

-1-1 = -2

[strong knot]

That's Derivative?

[nova dune]

ye

wat

the derivative is -1/c^2

[alpine sable]

$$\dv c\qty[\dfrac1c]$$
Firstly you'd convert the fraction into an exponent knowing that $\dfrac{1}{a^b}=a^{-b}$. $\therefore$ you will have $\dv c\qty[c^{-1}]$. Converting the fraction into an exponent makes differentiating much easier and clear. After doing this you would apply the power rule for derivatives that being $\dv x\qty[x^a]=ax^{a-1}$. So you will have $-1\cdot c^{-1-1}\implies -\dfrac{1}{c^2}$.

[nova dune]

not -2

[strong knot]

Okay

😂

Thx

[ocean seal]

Πολλά άτομα είναι

[nova dune]

@alpine sable Have u ever used the quotient rule of derivatives?

[alpine sable]

Yup

[nova dune]

I have only used it 3 times in my life

[alpine sable]

Was in english doing them

I was like fuck english time for quotient rule

that was like a year ago

[nova dune]

I usually change my equation to use product rule

[alpine sable]

any number theory lover?

[nova dune]

Whats number theory

[alpine sable]

#elementary-number-theory , #advanced-number-theory

[alpine sable]

just a branch of pure mathematics

[nova dune]

ill probably do it next sem

[alpine sable]

devoted primarily to the study of the integers and integer-valued functions.

[nova dune]

oh like series and sequences?

yeah i have done that

[alpine sable]

Something like this

Analytic Number Theory

[nova dune]

uhh wtf

that looks hard

[alpine sable]

whatchu doin now in math

in your uni

[nova dune]

I did Advanced Calc and Algeb (Calc and Alg III) and Differential equations this sem

I will do Computational Mafs and Fundamental Concepts of Mathematics next sem

Fundamentals of mathematics important to many branches of the subject and its applications. Topics include equivalence relations, elementary number theory, counting techniques, elementary probability, geometry, symmetry and metric spaces. This is an essential course for all students advancing beyond Stage II in pure mathematics, and highly suitable for other students in the mathematical sciences.

oh, look, some number theory

nice

[spiral estuary]

which order DE?

[nova dune]

? infinite order

[spiral estuary]

lol okay there's first order and higher order that we have in syllabus

[nova dune]

like $y^{n}+y^{n-1}+.....+y^{'} + y = f(t)$

[nova dune]

ya thats what we did

[ocean seal]

BelowAveragePlayer02

[spiral estuary]

hmmmmmmm

[nova dune]

we mostly focused on first order ODEs tho (and systems of ode)

[alpine sable]

I do have the same query your status states

[spiral estuary]

yea take a look at my questions lmao

idk about systems...

[nova dune]

systems are easy

[spiral estuary]

never heard about it too

[nova dune]

$dx/dt = ay + bx$
$dy/dt = cy+dx$

[spiral estuary]

ohhhhh yeaaaaaaaaaa i secretly searched on google but couldn't find it XD and memory too weak so i need to be reminded every other day

[ocean seal]

BelowAveragePlayer02

[spiral estuary]

hmmm

[alpine sable]

lol he can't latex

scrub

$\dv{x}{t}=ay+bx,\dv{y}{t}=cy+dx$

[nova dune]

lmao

[spiral estuary]

yesss

[nova dune]

latex is for nerds

[oak chasm]

Seems like there should be a comma.

[nova dune]

watch this

$\dv{x}{t}=ay+bx, \dv{y}{t}=cy+dx$

[ocean seal]

BelowAveragePlayer02

Πολλά άτομα είναι

[nova dune]

where did the comma go

wtf

[alpine sable]

lol your comma didn't render

https://media.discordapp.net/attachments/738548949488762954/818299625182199878/image0.gif

[spiral estuary]

[nova dune]

Screw LaTeX

y'all are nerds

[spiral estuary]

[alpine sable]

https://tenor.com/view/marvel-gif-21698421

[fervent grail]

Factorise
(a+b+c)⁵ -a⁵-b⁵-c⁵

[alpine sable]

I'm asked to evaluate this limit using Taylor expansion. We usually have functions like cos(x) to replace with it's series expansion and then simplify. Can anyone explain how I'm able to use Taylor expansion here?

$$\lim_{x \to \infty} (\frac{2x+1}{2x-1})^{2x}$$

[ocean seal]

Mouhib

[nova dune]

You want Maclaurin expansion right?

[alpine sable]

Oh yes

[nova dune]

ok gimme a min

is the answer e^2?

[alpine sable]

I don't have the answer

But wait, I can verify it

[nova dune]

this is what wolfram alpha spits out

[alpine sable]

Yes it is

[nova dune]

T(x) = f(0) + f'(0) (x)

1+f'(0)

[alpine sable]

I didn't think for a second to do the expansion myself...

Now I get it. I just got used to find a function like cos(x) in a limit, replace it with it's usual expansion and then simplify

[nova dune]

ya

[alpine sable]

Thank you for your help.

[nova dune]

np

[prime mist]

Hello I have an integral question, how did the $$k\left[\frac{x^3}{3}\right]_{-2}^0: become k(0 - ( - 8/3)) $$?

[ocean seal]

foreverbeginner

[prime mist]

how so?

[gray isle]

oh edited

evaluate bounds

$=k\br{ \frac{0^3}{3} - \frac{(-2)^3}{3}}$

[ocean seal]

ℝamonov

[prime mist]

ohhh i see

i thought I missing something

thanks for clearing up

[karmic pine]

what is k times 2.6 recurring?

i'm not sure

[hexed solar]

Hello

I have problem in finding mean of a question

Can Anyone help?

The mean of three numbers x, y and z is 6 and the mean of 5 numbers is x,y,z and a is 8. Find the mean of a and b

[oak chasm]

@hexed solar Please don't post to more than one channel. See the rules and tips for getting help in #❓how-to-get-help.

[gray isle]

@karmic pine$\frac{8k}{3} = \frac{8k}{3}$

[ocean seal]

ℝamonov

[ivory otter]

Hey, so i have a question about solving triangles

so i got this question

so my thought process is

if i can find out the length of BE, i will get the length of the half circle above BC

So i did

[alpine sable]

So the minor segment and the rectangle make the panel?

[ivory otter]

wdym?

[alpine sable]

my wifi is so ass

[ivory otter]

lol

[ivory otter]

idk, thats what i uynderstood tho

so look what i basically did was

i got theta angle to be 56.3

and ofcourse the triangle to the left is a right angle which means its 90

[alpine sable]

right

[ivory otter]

then i got B angle of that right angle

which was 33.7

90-33.7 to get the remaining of B

i have no problem getting the angles of the rectangle

but im confused on how to calculate the are (assuming we include the segment)

i got the hypotenus of the triangle to the left to be 1.58

so i know the radius of the segment is 1.58 cm

because it says that the length of BE is the lenght of the radius

[alpine sable]

how'd you get 1.58

i get an irrational number

[ivory otter]

lemme see

[alpine sable]

oh wait

nvm

I typed in the wrong values

[ivory otter]

ahh ok

[alpine sable]

hit an extra number accidentally

[ivory otter]

so you are getting similar numbers like me?

so we can assume they are correct?

or i can assume

[alpine sable]

nope

Wait

ugh

[ocean seal]

Πολλά άτομα είναι

[ivory otter]

lemme see how i got 1.58

i just used pythogoras

1.5^2 + 1^2 = 2.5

sqrt(2.5)

[alpine sable]

uh

[vale wigeon]

1.5^2 + 1^2 is not 2.5

[alpine sable]

wot

yeah not 2.5

[ivory otter]

omg

3.25

shit

[alpine sable]

yup

now root that

[ivory otter]

so i guess sqrt(3.25)

ye

[alpine sable]

which gives you this

[ivory otter]

which is 1.8 ye

right

but anyways, how can i calculate the segment tho

getting the rectangle is no problem

the segment is the problem

we know now the radius of the segment is 1.8

[alpine sable]

how do you get the radius of a segment? We have the radius of a circle, but BC is the segment, we have a sector EBC

we can find the area of that

[ivory otter]

im not sure ik what segment means

i thouight they meant the half circle

[alpine sable]

half a circle is a semicircle

[ivory otter]

what is a segment

?

[alpine sable]

A segment is a region bounded by a chord of a circle and the intercepted arc of the circle

[ivory otter]

ahaa

[ivory otter]

i see, but do we have a segment or a half circle?

[alpine sable]

we have a sector

I mean we can find the area of the segment

if you want

but we'll find the area of a sector since we got less steps to do

[ivory otter]

doesnt the question want us to do that?

ahh ok

so what should our first step be in your opinion?

do we first calculate the area of that rectangle?

[alpine sable]

As far as i'm concerned this is the panel

[ivory otter]

without the sector

[alpine sable]

well we could approach this many ways

we could find the area of the sector

then find the area of 1 of the right angled triangles

then double that

Cause triangle ABE is congruent to EDC

or we could find the area of the rectangle

then the area of the segment

[ivory otter]

ye didnt think of that

but wouldnt finding the area of the rectangle be easier

since we know the length

of each side

[alpine sable]

i mean thats up to you

on how you'd approach the problem

ok so if you wanna find the area of the rectangle then segment so be it

find the area of the rectangle

then we can continue off by finding the area of the segment

[ivory otter]

ok

but how do we get the segment

area of the rectangle is 1.5 cm^2

oh wait

its

[karmic pine]

how have they done that?

[ivory otter]

3 cm^2

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

Is used

[ivory otter]

is that the area of a segment?

[alpine sable]

Yeah

[ivory otter]

aha

[alpine sable]

or you could find the area of the sector, and area of the triangle then subtract

[ivory otter]

i like the formula u gave

ill go with that one

[alpine sable]

alr

[ivory otter]

wait

whats sin going to be in this case

[ocean seal]

Πολλά άτομα είναι

[minor crypt]

can you also not see it as just a part of the full circle

so you're gonna try to find alfa, you know that the angle of the complete circle is 360°

so you divide 360/alfa to find how much of the are of the circle you actually need

[alpine sable]

Central angle

[minor crypt]

1. use tangent to find theta
2. use theta (2theta+alfa=180°) to find alfa
3. divide alfa by 360°
4. calculate the area of the entire circle (using pi×r²)
5. multiply this with ur answer in 3.

[alpine sable]

whats alfa

alpha?

or something else

[ocean seal]

Πολλά άτομα είναι

[minor crypt]

ye mb

[ocean seal]

Πολλά άτομα είναι

[alpine sable]

test

fucking

[ocean seal]

Πολλά άτομα είναι

[ivory otter]

https://www.mathsisfun.com/geometry/circle-sector-segment.html

is was following this formula here

area of a segment

i keep getting soem weird numbers

like 0.4

i first got the arc length by doing

$67.4 \cdot \frac{\pi}{180} \cdot 1.8$

the dots are multiplication btw

so

then i did

[glass lichen]

\pi

[ocean seal]

MEOWBRO 父

[ivory otter]

nice

then i calculated

the area of that segment

by doing

$( \frac{67.4 \cdot \pi}{360} - \frac{\sin 67.4}{2}) \cdot 1.8^2$

[minor crypt]

you're overcomplicating this

[ocean seal]

MEOWBRO 父

[ivory otter]

but this should still give me the answer no?

[minor crypt]

assuming that formula is correct, yes

but there's no reason to use such a complicated formula

[minor crypt]

when you can just calculate the area of the circle and divide it by the ratio of 360°/alpha

formulas are great when the exercise is too abstract to visualize, but for an exercise like this one you don't really need any formulas

so unless your teacher asked you to use this formula specifically, just use 'logic' to solve it

[ivory otter]

i see what you mean

ye this formula was probably not the idea

[minor crypt]

I don't like formulas because it makese feel like I don't know what I'm doing. I don't know where the formula came from, so I'm just filling in some random stuff until I find the answer.

It's mich better to understand the problem and find a way to solve it yourself, that's what maths is about (imo)

[alpine sable]

can't disagree

[raven lodge]

Hi i need some help with logarithmic function and graph. which i have a hard time understand it >~<

I have the answers to it but I dont know how they get the answers >~<

This the 1st question.
why lg(k+18) isn't lg(18k)?
and why the 1 become lg 10?

[oak chasm]

@raven lodge Let's say k is 100.

[raven lodge]

then it would be 1+lg 100 = lg(100+18)

[oak chasm]

Never mind.

Let's see.

[raven lodge]

i super lost in log >~<

[oak chasm]

@raven lodge What's the base of lg?

[raven lodge]

my default is 10 right?

*by

[oak chasm]

Yes, in this problem, it's 10.

So, what's lg(10)?

[raven lodge]

to make it base 10

for the 1

[oak chasm]

Sorry?

[raven lodge]

but i thought is like algebra.
1+lgk=lg(k+18)
lgk- lg18k=1

when do log everything must change to log?

[oak chasm]

Yes, but you asked why 1 became lg(10), right?

[raven lodge]

yeah

[oak chasm]

So, what does lg(10) evaluate to?

[raven lodge]

because i did in a algebra way @.@

[raven lodge]

lg(10) = 1

[oak chasm]

Right, that's why 1 became lg(10), because they're equal. You can replace something with what it's equal to.

[raven lodge]

so when doing log
everything must be in log and same base before solving it?

[oak chasm]

It depends on the problem.

For this problem, that way helps.

[raven lodge]

0.0

ooo
i think i only face this kind of problem >~<

[pine lake]

Nah log needs alot of practise

[raven lodge]

o.o

gg

fail in log

[pine lake]

Im also struggling a lil bit in log

[raven lodge]

~<

my classmate from the other class says is easy

i only had one day of learning it >~<

[oak chasm]

Oh, that's probably why you're having trouble with it.

[raven lodge]

yeah

do you have any questions related to log?

which uses this

since my exam on 30 june T^T

[oak chasm]

@raven lodge If you want more than a day of instruction, there's this: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs.

[raven lodge]

thank you ❤️

[oak chasm]

No problem.

[pine lake]

U can search for it in online or watch organic chemistry tutor

He has practice questions at the end of the vid

[raven lodge]

i still got like graph questions

[raven lodge]

thank you ^^

how do i do parallel questions >~<

[oak chasm]

@raven lodge Parallel means same slope, different line.

Or same gradient if you use that term.

[raven lodge]

the only thing i have is this >~<

[oak chasm]

Right, see how they have the same slope on the parallel section?

Or same gradient.

[alpine sable]

gotta ask how are you doing common logs and natural logs at the same time as you're learning about parallel lines and perpendicular lines

[pine lake]

Maybe diff chap?

[raven lodge]

yup

@.@

[pine lake]

Hope this will help

[oak chasm]

Are you taking a final exam for the year or something?

[raven lodge]

since i do the quest together i ask question in one go >~<

[oak chasm]

I mean in several days?

[raven lodge]

mid year ...

[oak chasm]

Oh, OK.

[raven lodge]

T^T my first exam

been long since i study math

[pine lake]

Gl!

[raven lodge]

thank you ^^ now im more clear about it

[pine lake]

Np

Can someone help me with this

Ik the formula

[oak chasm]

What's an arithmetic progression mean?

[raven lodge]

i learn this

[proud burrow]

You know general formula for arithmetic series

[raven lodge]

wait i see my note

[pine lake]

A sequence

[oak chasm]

Well, yes, it's a sequence.

[pine lake]

Yes a + (n-1)d

[oak chasm]

Right.

[pine lake]

And ik for sum too

[oak chasm]

What is it for the sum?

[pine lake]

There is 3

[proud burrow]

Then it's given 2nd term is 1/2 put it in formula you will get a equation

And sum is given then you will get other equation solve both the equation you will get value of a and d

[pine lake]

Ok

Im doing it

[raven lodge]

ooooo @.@ thanks ^^ that why they only give that >~<

[oak chasm]

No problem.

[pine lake]

Correct?

[proud burrow]

Yes

[pine lake]

Thanks! @proud burrow @oak chasm

[silk terrace]

n is odd

[noble sinew]

show it is in D_{ST} - so show it is 2pi periodic, piecewiese-differentiabel and normalized in discontinuity-points

[silk terrace]

We have shown that

but is that enough?

[silk terrace]

So it is piecewise C^1 and normalized at discontinuity points. thus pointwise

[noble sinew]

Yes your book should mention a theorem about that

[silk terrace]

It is really not well written regarding this part unfortunately :/

For uniform converges we just consider the complex mod right?

[noble sinew]

If f is in C_{ST}^1 and also continious it is uniform convergent

[silk terrace]

hmmm I guess it can not be then

[raven lodge]

is this question like this?

[vale wigeon]

with all due respect

what the actual fuck happened in your work?

[raven lodge]

idk@.@

i cancel those that becomes 0

[vale wigeon]

your idea of 'cancellation' seems to be carelessly crossing out similar-looking things with a minus sign somewhere between them

how exactly did $\log_{10}(x) + \log_{10}(y)$ become 0?

[ocean seal]

Ann

[silk terrace]

it is piecewise c^1 right but not continious

[raven lodge]

Then is it like this? the question is asking to find log(x)
log10(x) +log10(y)+2log10(x)-4log10(x)+4log10(y)
log10(x) +2log10(x)-4log10(x)=-log10(y)-4log10(y)

[vale wigeon]

wait, can you post the full question?

exactly as it is stated

you've made me doubt that you copied it accurately.

[raven lodge]

this the question

[vale wigeon]

is that the entire question?

no instructions posted for it?

[raven lodge]

yeah

[feral raven]

There is no question here

[vale wigeon]

just this expression?

NOTHING else?

[gray isle]

what's

the question is asking to find log(x)
about?
that doesn't make sense in this context

[vale wigeon]

nothing that says "simplify"? where did you get "find log(x)" from if there truly were no instructions?

[noble sinew]

Yes it isn’t continious and hence can’t be uniform convergent

[vale wigeon]

were you given a piece of paper that bears just this expression and nothing else?

i.e. completely blank except for that?

[azure thunder]

wat is a trapeziod

[celest zinc]

log(x) + log(y) = log(xy)

[frigid lagoon]

Can anyone help me

[raven lodge]

so does it makes logx and logy =0?

[raven lodge]

since i got this question just now

[sterile widget]

I am very new to this stuff

Photo from Arkaan

Need help in this I am rlly new to this stuff

[celest zinc]

\begin{align*}
\log(x) + \log(y) + \Big( \log(x) \Big)^2 - 8 \log(xy) &= 0
\
\log(x) + \log(y) + \Big( \log(x) \Big)^2 - 8 \Big( \log(x) + \log(y) \Big) &= 0
\
\Big( \log(x) \Big)^2 - 7 \Big( \log(x) + \log(y) \Big) &= 0
\
\Big( \log(x) \Big)^2 - 7 \log(x) -7\log(y) &= 0
\end{align*}
it's a quadratic in $\log(x)$

[ocean seal]

Fede Bosio

[raven lodge]

but the answer the question paper says is 8

[noble sinew]

There is an infinite amount of solutions

[gray isle]

is that how the question is given exactly as stated?

no adjustments/omissions etc?

[raven lodge]

is in other language

there is like 4 different options A-8 B-4 D-1 C-zero

[gray isle]

oh geez.

[jaunty plover]

I can try to explain it

[gray isle]

you copied the question incorrectly

[raven lodge]

ahhh i helping somone

[jaunty plover]

I guess but I'm not knowing what's the equation

[gray isle]

you mistook a multiplication symbol for a plus sign

$\log(x)\red{\times}\log(y) + (\log(x))^2 - 8\log(xy) = 0$

[ocean seal]

ℝamonov

[raven lodge]

but im lost @.@

like still lost on how to do this @.@

[gray isle]

consider factorisation by grouping

$\underbrace{\log(x)\red{\times}\log(y) + (\log(x))^2}_{\text{factorise this first}} - 8\log(xy) = 0$

[ocean seal]

ℝamonov

[fickle pier]

ok so this might seem a little weird but, how do i multiply two numbers without using multiplication but just addition?

[vale wigeon]

are they both integers