help-0

[formal notch]

yes

[warm mortar]

or i can type it out

[formal notch]

send a pic

[warm mortar]

it's sending, my internet is being slow because my laptop is using hotspot

Oh woops I see an issue I made, I did -20 plus 30 not 35

36

[formal notch]

yeah. Just that one addition mistake

otherwise you did it correctly

[warm mortar]

so then its w=4

[formal notch]

yes

[warm mortar]

haha awesome!

my homework said its wrong ;-;

[formal notch]

oh yeah i missed a mistake you made

recheck your distribution of 8

[warm mortar]

oh its -32

[formal notch]

yes

[warm mortar]

so then it is 12 divided by 4 which is 3

w=3

[formal notch]

yes

[warm mortar]

ill do one more just let me go check this car really quick

okay

i did it wrong once because i read my own handwriting wrong -_- but i redid it and i got U=-4

my u and 4 look really similar lmao

[formal notch]

thats right

[warm mortar]

See but then I did this one and I got it wrong but idk what I did wrong

It looks right to me

But the answer can't be a decimal

oh wait, i took the negative 32 and made it posititve for whatever reason

[alpine sable]

Oh, yeah. I realised that as well!

[warm mortar]

just wanna get 2 in a row correct without forgetting something

[alpine sable]

It’s okay, you can do it! What is the equation?

[warm mortar]

this one is 3y+8(y+6)=-18

so i did the distribution which makes it 3y+8y+48=-18

then u add the terms which makes it 11y+48=-18

then you subtract 48 on each side which makes it 11y=-66

then divide 11 by both sides so y=-6?

[formal notch]

yes.

[alpine sable]

Yes!

[warm mortar]

as a 21 year old not knowing this is embarrassing lol, i remember learning about it in like high school but never paid attention

[formal notch]

Dude im on the same boat.

I had to review algebra the summer before starting college.

[alpine sable]

LOL, it’s fine. Just take it step by step, take your time to learn!

[warm mortar]

now its giving me number theory questions

"converting a repeating decimal to a fravtion"?

what does a line above a decimal mean?

[formal notch]

its repeating

[warm mortar]

so its like 0.79999999

[alpine sable]

It repeats without end?

[formal notch]

yes but if the line is over .79 it is .79797979

[warm mortar]

okay, how do you convert that into a fraction if its infinite?

wouldnt that mean the demoninator would be infinite

[formal notch]

hmmm. I'm not exactly sure if this is right but I think you do the following. Given .7 (repeating). x=.7

[warm mortar]

it wants it as a fraction :/

[formal notch]

hm

[warm mortar]

says Multiply both sides of this equation by 10, or 100, or 1000, etc., based on the number of repeating digits

[formal notch]

yes

[warm mortar]

so since its 2 numbers its 100

[formal notch]

so if it it .797979 you multiply by 100

if it is .123123123 you multiply by 1000

and then the 1000 or 100 goes in the denominator

dont forget to simplify

[warm mortar]

then it says it is 100x=79.7979 minus x=0.7979 which makes it 99x = 79.0000...

says the answer would be x= 79/99

so the real question its giving me is 0.2 as a fraction so it would be 0.2 divided by 10

[frosty eagle]

bruh

x= -4

[formal notch]

@alpine sable you can take it from here

[warm mortar]

yes thank you katsu for pointing out my mistake from 10 minutes ago

[formal notch]

lmaoooo

[frosty eagle]

I was eating lol

[formal notch]

@warm mortar i don't remember. I don't want to give you the wrong answer

[frosty eagle]

why u saaits not .777

its not .77*

its -4

[warm mortar]

oh there isnt even a point of doing division for these questions you just remove the decimal, make it a whole number and make the denominator 9, 99 or 999 depending on how big the number is

[frosty eagle]

here one sec

[warm mortar]

so 0.76 would be 79/00

76/99

alright blew through that section, just 56 more sections to go through lmao

[frosty eagle]

wait

no

check ur work

the answer not 0.76

its -4

x=-4

[warm mortar]

bruh

you from the past

[alpine sable]

Wait, what? Where are we on… I thought we were on decimals.

[formal notch]

@frosty eagle if you keep trolling ur gonna get banned

[frosty eagle]

nah not capping

[warm mortar]

i just finished the decimal part, it was only 3 questions because i answered them all correct

[frosty eagle]

2x+4x-8=-32

[warm mortar]

now its consumer mathematics, computing the interest and repayment

[frosty eagle]

6x-8=-32

6x-8+8=-32+8

6x=-24

[formal notch]

@warm mortar I remember is working like this. (Given .76) Therefore, you use 100. 76/100

[frosty eagle]

6x/6=-24/6

which equals -4

bruh

[frosty eagle]

answer

= -4

[warm mortar]

and it depends on how many actual unique numbers are repeating that gives it the demoninator 10,100 or 1000 and so on?

[frosty eagle]

its not a decimal

The answer is -4

where did u get 76/100

from

[formal notch]

I'm just explaining how I remember it but I'm exactly sure that im doing it right

[alpine sable]

Katsu, we are on another topic…

[frosty eagle]

ohhh

[warm mortar]

katsu, respectfully, we are good here with us 3 🙂

[formal notch]

@frosty eagle we already fixed that

[frosty eagle]

ohhh

[warm mortar]

i appreciate you trying to help

[frosty eagle]

thought u were talking bout that

what topic u on

[warm mortar]

nope lol

[frosty eagle]

?

I'll help

[alpine sable]

Repeating decimals to fractions!

[warm mortar]

right now im on consumer mathematics, computing the interest and repayment of the interest

[frosty eagle]

whats the question?

[formal notch]

@frosty eagle U said you take calc 2?

[frosty eagle]

I'm done that

Don't take it anymorew

anymore*

[formal notch]

and now?

[frosty eagle]

what?

[warm mortar]

sorry back had to search a car

okay yeah consumer math

[formal notch]

@warm mortar u at work or something?

[warm mortar]

yeah

[frosty eagle]

whats the question unnullifier

[formal notch]

you a police?

[warm mortar]

yes

[formal notch]

ah interesting

[frosty eagle]

?

[warm mortar]

yeah im a military police officer, im stationed in south korea rn

[formal notch]

wtf

[frosty eagle]

what

anyways

[formal notch]

thats sounds cool asf

[frosty eagle]

wahts the question @warm mortar

whats*

[frosty eagle]

it isnt

[warm mortar]

the question is

Katsu obtains a loan for home renovations from a bankthat charges simple interest at an annual rate of 7.45% his loan is for 12,700 for 62 days. Assume each day is 1/365 of a year

find the interest that will be owed after 62 days and assuming katsu doesnt make any payments, find the amount owed after 62

[frosty eagle]

lol

[warm mortar]

i have the formula for percentages somewhere in my brain

[formal notch]

I remember using a program on my calculator for this

[warm mortar]

so 7.45% of 12700 is 946.15

cuz 7.45 times 12700 divided by 100 yatta yatta

gimme a sec

and yeah frizzzle were allowed to use a calculator for these questions

but to find the interst that will be owed after 62 days do we divide something by 62 to get the daily amount or?

oh wait

[formal notch]

I have no idea. I used to literally plug in the givens on a program on my ti-84 and it would spit out the answer.

[warm mortar]

the interest owed after 62 days is 946.15

and then if he doesnt pay anything

then he pays the interest adds onto the original loan

nah i got it wrong lmao

no clue

[frosty eagle]

@warm mortar

[warm mortar]

yah i got it

[frosty eagle]

wait

nvm

its not that

I meant

this

12700 + 12700(0.0745) * (62/365)

this is the answer

@warm mortar

by accident

the answer is

12700 + 12700(0.0745) * (62/365)

u got it?

did u get it

?

Unnullifier

u there?

[formal notch]

rip

[lone heart]

@warm mortar Has your question been resolved?

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[faint bone]

Can someone help me with this question

[lone heart]

@faint bone Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[dim sundial]

Uhh can someone help me write smthng digitally like in latez

[dim sundial]

*latex

[remote heron]

huh?

[dim sundial]

Cus i dont know how to write digitally

Like i got this solution on paper but idk how to write it digitally yk

[alpine sable]

#latex-help ok?

[dim sundial]

Oh i didnt know that existed

Mb

[alpine sable]

Can u close this now

[remote heron]

u should know

we have a user here who recently did a talk on latex

for total beginners

[dim sundial]

Ahh I see

Ill look into it after this hell of a week

[remote heron]

https://www.youtube.com/watch?v=CSjVUbVGlA8

if youre interested

has some great resources on it too

[dim sundial]

Alright thanks man

[remote heron]

like detexify ❤️

np

[dim sundial]

.closed

.close

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[alpine sable]

help

[alpine sable]

why am i so shit at maths

[naive valley]

Is that your question? 😆

[raven rover]

#❓how-to-get-help

[tacit arch]

reopen if you have a specific math question. otherwise go to #discussion or #chill

.close

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[oak walrus]

i need help with spss. I just need someone to confirm I'm doing it correctly.

[tacit arch]

[oak walrus]

one moment my stupid computer isn't loading spss

okay it's loading

these are my instructions

I found a website that explains it but it kind of skips the first part, and i had a question about that

https://www.statology.org/z-scores-spss/

how did they get the little ruler on the income, and for my homework question do I have to put the data one at a time or at the same time

<@&286206848099549185>

[lone heart]

@oak walrus Has your question been resolved?

[oak walrus]

damn no one helping me fr 😢

[tacit arch]

Not really a stats server nor a software server

[oak walrus]

isn't stats a math subject tho

tbh idc that much i just want to pass this hw, its 2;30 am im tired af, this stats server i joined isn't answering either

i usually dont ask for help i just try to figure it out on my own but my lessons are empty af and online guides are confusing like the link i sent because theyre missing steps

if you know anyone who knows spss can they message or pm me please

[oak walrus]

.close

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[solemn tinsel]

im doing problem 33 and idk how to go from moivre's theorem to a+bi form

can anyone help me out??

[jagged imp]

I'm gonna ignore whatever is going on in the first line.....
so 2 things: you can simplify sqrt(2)^20, and also, you should be able to find a numerical value for cos(5pi) and sin(5pi)

[solemn tinsel]

so i. just find the numerical value and then distribute sqrt(2)^20 correct?

[jagged imp]

yeah

[solemn tinsel]

alright thank u :))

way easier than i thought

.close

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[zenith compass]

I know the radius of the larger circle is a

So do the magnitude of the vector from the centre to the intersection of two circles

The radius of the smaller circle is b

But i dun know how to relate the angle theta

Can anyone plz help me

[lone heart]

@zenith compass Has your question been resolved?

[zenith compass]

<@&286206848099549185>

[zenith compass]

<@&286206848099549185>

can anyone help me

[woven whale]

hold on i'll try

[zenith compass]

Thank you

[hasty elk]

this looks horribly painful

not too difficult if you can power through the calculations, but i don't want to do those calculations

the idea is to figure out first the new centre of the small circle

[zenith compass]

The locus of the small circle centre is just a circular motion

[hasty elk]

then figure out how many revolutions it's gone through, relative to the contact point - this will yield \varphi

[zenith compass]

Umm

[hasty elk]

and then this gets you P

[zenith compass]

The problem is idk how to convert phi to theta

[hasty elk]

the idea is to forget about phi for the moment and focus on theta

travelling by theta means that the small circle has rolled a certain distance on the circumference of the big circle, right?

[zenith compass]

Yes

[hasty elk]

that same distance must be traversed on both circles, meaning that the distance travelled on the circumference of the big circle, equals the distance travelled on the circumference of the small circle

e.g. if the small circle has circumference 1, let's say, and travelling by angle theta means a travel on the circumference of the big circle by distance 1, that means that the small circle completes one full revolution relative to the contact point, i.e. the point P will once again be at the contact point

[woven whale]

this reminds me of that one problem

https://www.youtube.com/watch?v=pOxZX7dQVuk

[hasty elk]

yeah, it's pretty much that problem

[zenith compass]

Oh

[woven whale]

and so i was just wondering if "without slipping" means it would rotate 4 or 5 times

[hasty elk]

so to answer your question on how theta can be related to phi, the answer lies in the distance travelled on the circumference

[zenith compass]

Alright I have some ideas

[hasty elk]

i think that video puts it in a clear diagram way

have fun!

[zenith compass]

Ok

Thank you

I will try

[solemn grove]

5 i think and yeah, i saw the same question ages ago

[hardy moth]

Actually its already given in your picture

[zenith compass]

Wow I don’t even notice that

Thx for noticing

[hardy moth]

(:

[lone heart]

@zenith compass Has your question been resolved?

[little drum]

@zenith compass meow

what's the issue

[zenith compass]

I am stuck on the coordinate

It is easy for the origin to the small circle centre

[zenith compass]

I just dk how to attain point P

[little drum]

._. write P = r(theta')?

and use relative position?

Hint: what is position of P with respect to the center of smaller circle?

[zenith compass]

Am I going wrong?

The r phi is the small circle

[little drum]

._.

[zenith compass]

So in the small circle, r=b

[little drum]

by position

I mean

the x, y coordinates

of P

w.r.t. Center of smaller circle

[zenith compass]

Sth like this?

[little drum]

are you sure about that?

[zenith compass]

Umm is that sth like (rcost,rsint)

Vector equation

[little drum]

well, anyways

[woven whale]

P should be something like ((a+b)cos(theta) + cos(pi - theta - phi), ...)

[little drum]

the idea is to use:

[fallow ibex]

Would it look something like b cos(pi+theta(1+a/b)), b sin (pi+theta(1+a/b))?

Sorry I was just looking at it on my own

[little drum]

$\vec{OP} = \vec{OO'} + \vec{O'P}$

[little drum]

looks better, but can you ascertain what happens when theta > 2πb/a?

because for that value, phi > 2π so you might be

[fallow ibex]

Oof, haven't thought that far yet

I'm just here trying to get the ideas too, the question seemed interesting to me sorry if that's a bother

[little drum]

No no

the questions with circle revolving around circle, parabola on circle, etc. are indeed pretty interesting

parabola on parabola, line on circle, circle on line

circle on ellipse

and they all use relative motion, as a base

[zenith compass]

Similar for o’p?

[little drum]

I don't know your intentions

[turbid sigil]

Keep going

[little drum]

but those coordinates are just

[turbid sigil]

Your thinking is on the right path

[little drum]

wrong if you check their units

[turbid sigil]

I solved this problem earlier and desmos was a big help

[little drum]

a, b are lengths, theta is radian.. cos(length times radian) = cos(length) is just

the only valid arguments for a trig function is degree or radian

[fallow ibex]

Unless you were trying to do (a+b) cos (theta)

¯_(ツ)_/¯

[little drum]

which again gives you r(a+b) cos (theta) = (unit area) times scalar ._.

[fallow ibex]

At this rate I'm just throwing things at random

[little drum]

lmao

I'll just leave it to Trenton to figure. All you gotta do is figure the OO' vectors and O'P vectors correctly

[fallow ibex]

Wait but I didn't quite get this part, why is it r(a+b) not just (a+b) ?

[zenith compass]

Ahhh

[little drum]

For starters, you can at least, with a little more caffeine power, conclude that $$\overrightarrow{OO'} = [(a+b) \cos \theta ]\hat{i} + [(a + b) \sin \theta] \hat{j}$$

[zenith compass]

Am i on the right track?

[turbid sigil]

Yeah

[little drum]

no ._.

only the OO' vector is figured

[zenith compass]

[fallow ibex]

So I'd say phi isn't exactly measuring the angle from the

Right place? Idk how to describe it

[turbid sigil]

First figure out what the center of the little circle is doing, then adjust to point p

[little drum]

of course if you were on the right track and figured O'P, this question wouldn't have been keeping you at bay for this long

anyways, (r cos theta, r sin theta) is the coordinates only when theta is measured from the +x axis or from an axis parallel to +x axis ._.

so,

1. ✅ yeah your expression for OO' vector looks correct now.

and

2. figure how to figure O'P vector

[zenith compass]

How about this?

[little drum]

might as well start guessing the answers now?

can you show me how exactly you arrived at that ?

[zenith compass]

Basically is the alt angle

And phi=a theta/b

[fallow ibex]

Seems like y value should be flipped?

[zenith compass]

You mean the coefficient of the j component?

Oh they are in anti clockwise

[zenith compass]

Umm how about I give a negative sign to the j component of the o’p vector

[zenith compass]

Umm but why? They are rotating in the same direction

[fallow ibex]

Nevermind, both x and y??

Because idk how to explain it in words so Imma just draw like a noob

[fallow ibex]

I was looking at it in this manner

Poorly drawn I know

[zenith compass]

No your drawing is good

I can easily understand

So you mean this?

[fallow ibex]

Probably, yeah

[zenith compass]

Ok

So I get this

And the i,j components are the x,y coordinate respectively

[fallow ibex]

Complicated as hell but it looks okay to me, but then again don't take my words for it cause I was also trying to figure this thing out

Ye

[zenith compass]

Ok

Thank you so much

[woven whale]

i just drew this

[little drum]

That works perfectly

[zenith compass]

Opps

[fallow ibex]

The confirmation we were looking for

[little drum]

not sure why you wanna avoid writing phi during the whole computation thingy when you can just plug in the value for phi in the end while casually using it during the computation for obvious convenience

would be better writing phi during the computation instead of having to keep repeating the a/b theta

[zenith compass]

Sorry my bad

[little drum]

Anyways, this looks right :o you might wanna check up if it works by plugging some obvious values of theta >_<

[zenith compass]

When theta=0, it works

[zenith compass]

Ok so for the part b, just plug in a,b then find the magnitude of the vector?

[zenith compass]

But I cant continue then

The term is too difficult to be integrate

[little drum]

._. why integrate now?

[zenith compass]

I mean part b

The distance travelled

By the point P

[little drum]

for what theta do you think P returns to the original position ._.

Did you solve?

[woven whale]

this don't look so bad

a lot of the sines and cosines combine into 1

and you can compound angle the rest i believe

[zenith compass]

Oh

Perhaps it turns around but go back to the original position after more than one periods

[zenith compass]

So it is equivalent to solving this system of equations

w, 5cosx-cos(5x)=4

[woven whale]

you notice the 5cos(...) - cos(...)

what if the cosines happen to be 1

[zenith compass]

So the general solution is only 2pin? For n belongs to natural numbers including 0

[woven whale]

i think so

i might be wrong though

[zenith compass]

This can prevent the quintic equations indeed

And geometrically it make sense

[woven whale]

i aint gon prove it but take but a glimpse at this wonder

[zenith compass]

As at least theta=2pi so that it is the original position

[zenith compass]

Oh thx

Oh wait a minute

The two equations have different value of theta

[zenith compass]

Geometrically we need to find the intersection point of green, red and blue here

[woven whale]

not where blue intersects red and green is at 0?

[zenith compass]

Simultaneously

[zenith compass]

Oh sorry about that

I forget that green should intersect with y=0

[little drum]

:O

[woven whale]

oh right you could do that

totally4got

[little drum]

so yeah, after theta = 2pi, the point P comes back to its original position

Also, I don't see ANY need of integration here ._.

just be a bit smart about it

[zenith compass]

Oh

[zenith compass]

So at the the distance that P travelled is just the circumstance of the larger circle

[zenith compass]

Yay so I am learning to be smarter

[little drum]

😱

[zenith compass]

Wait did I say sth wrong?

[little drum]

no you were right >_<

[zenith compass]

Yeah

[little drum]

the period of the smaller circle is pi/2 for the bigger circle

so each time P touches the bigger circle, its passed a quadrant of bigger circle >_<

so its basically 4b(2pi) or 1(2pi a)

[zenith compass]

Pi/2 because the ratio of a:b=4:1? Hence 2pi:pi/2?

[little drum]

Yep

[zenith compass]

Ok

[little drum]

a theta = b phi

[zenith compass]

Ok

Thanks a lot

Finally solved it

Thank you Ansh for always helping me

[little drum]

here's a better one

a parabola rolling over a parabola

find the locii of the fixed point

mwahahaha

[woven whale]

wait i'm not sure i follow

[zenith compass]

Omg

[woven whale]

isn't it supposed to go like this

[zenith compass]

Is that IMO questions lol
Can’t even imagine

[little drum]

honestly, now that you've shown me that

Yes

[woven whale]

i'm not really sure how to get around integration here

could you enlighten me somehow

[little drum]

can you explain why'd I think the length traversed would be the same :o

[woven whale]

no sorry

i don't see it

[zenith compass]

Umm i forgot but I remember in calculus course there is a formula if u fix a “focus/centre” (i.e. the origin) then u basically do the Riemann sum stuffs

[little drum]

not quite

if I'm following worm right, 2pi(a) actually is the distance covered by the circle as a whole and not the particular point P

since any point P on the circle would be following it's own path during the revolution, when asked about the distance they traversed in their respective paths,

you probably do need to integrate

the arclength formula helps(!?) ig

but thanks to the symmetry, you only need to integrate from theta = 0, to pi/4

[zenith compass]

Suppose that $r=r(\theta)$, for $a\leq\theta\leq b$, defines a curve C.

[ocean seal]

Trenton

[woven whale]

oh no sorry trenton i was referring to uh

[woven whale]

this part

[zenith compass]

Oh

[woven whale]

i get what you mean by the riemann sum though

[zenith compass]

Lol ok

[little drum]

what's the integral setup here tho

integral d(arclength(theta)) from 0 to pi/4?

[zenith compass]

So we take the derivative of the vector $\vec{OP}$

[ocean seal]

Trenton

[zenith compass]

With respect to $\theta$

[ocean seal]

Trenton

[little drum]

tyvm that saved me (@_@;)

[woven whale]

this reminds me of this and i still don't know whether it's gonna rotate around 4 or 5 times dang

[zenith compass]

Lol I also get confused

Intuitively I think it is 4 times

[woven whale]

i like imagine a coin rotating around a point

[zenith compass]

But the video just make me think about 5 times lol

[woven whale]

then it's bound to rotate right

[zenith compass]

Yes

[little drum]

$L = 40$

[sterile idol]

Why a re you supposed to integrate here?

[hardy moth]

Im so glad nobody uses geogebra here

[zenith compass]

No lol we done without it, just kinda playing with integration

[little drum]

._.

[zenith compass]

Ansh is so powerful, simplify such monster in few sec!!!

[little drum]

Answer = 40, not 8pi

😑

[sterile idol]

Can we do something like this?

[zenith compass]

Alright so the game has not end

[little drum]

need to calculate the length of the red curve

we already have the locii for the red curve though

[zenith compass]

By the graph, the flower shaped locus has length longer

[sterile idol]

Oh I see, but I am trying to find out the coordinates of P

[zenith compass]

Than the circle

[little drum]

we already did find the coordinates of P

[little drum]

Yes, so our initial answer was wrong

[sterile idol]

But is what I did wrong?

[little drum]

P doesn't traverse the circumference

[zenith compass]

Opps

[little drum]

but actually, follows its own path

[sterile idol]

What is the equation you get for the flower shaped thing?

[little drum]

$$(x, y) \equiv (5 \cos \theta - \cos (5 \theta), 5\sin \theta - \sin(5\theta))$$

[sterile idol]

5 is a right?

[zenith compass]

Yes

I just put a=4,b=1 into the question

[little drum]

OwO

[hardy moth]

uwu

[woven whale]

this actually looks really neat

could make some desmos art

[zenith compass]

The problem aside, the picture is indeed beautiful

[woven whale]

really cool and well set up

i still don't know whether it would rotate 4 or 5 times though

[little drum]

what though :o

it would rotate 4 times

[woven whale]

the point would go 4 times right

the coin might go 5

[zenith compass]

Wow

[woven whale]

honestly i don't know my brain is out of juice

[little drum]

atheta = b phi so, phi = 2pi => theta = pi/2

so P would go 4 times

[little drum]

wow, da heck is this (@_@;)

Oh btw I can draw a rose petal though UwU

[hardy moth]

nice

[hardy moth]

a=4.1 and b=1

[little drum]

UwU

[sterile idol]

If you know the points how do you plot the graph in desmos?

[little drum]

I used Geogebra lol

Desmos kinda awkward for me :|

[hardy moth]

Grrr

[sterile idol]

Oh

Lol

[hardy moth]

I can give you my desmos link if you want

[little drum]

well, if you can teach me tho-

[sterile idol]

What about this?

[little drum]

wdym what about that (@_@;)

[sterile idol]

That is desmos I believe

[little drum]

oh worm prolly made that on desmos yes

[sterile idol]

How did worm plot it on desmos

[hardy moth]

It is desmos

[woven whale]

oh uh

[little drum]

teach me 💀

[sterile idol]

Me too

[little drum]

show me your command list

show me what sorcery you typed in there

[woven whale]

you can do (cost, sint) for a circle with r=1 and center (0,0)

just use t for the parameter

[hardy moth]

I‘ll just send a link

I think its intuitive from just looking at it

[sterile idol]

What about the flower

[sterile idol]

Oh

[hardy moth]

https://www.desmos.com/calculator/blemambore

[sterile idol]

Oh I see

[little drum]

noooo

make it moving

make it move

[sterile idol]

Yay

[hardy moth]

Press the start button thingy for phi

[sterile idol]

I think you have to add this

[hardy moth]

And maybe a different a because its a bit messy

[little drum]

(@_@;)

[hardy moth]

https://www.desmos.com/calculator/urcp9vwqkp

[little drum]

UwU

[hardy moth]

Ok now its better

[little drum]

@zenith compass

Check this out

https://www.desmos.com/calculator/6tfrwjvsa9

[zenith compass]

A bit cant follow

[little drum]

click on the play button on 'phi'

that's the locii of point P

[hardy moth]

Wait

[woven whale]

try setting a < 0 lol

[hardy moth]

Making the upper bound of t just phi makes it way better

[little drum]

da heck

[hardy moth]

Lol

[little drum]

https://www.desmos.com/calculator/ffliapted5

The UwU Circle thingy upgraded

Let's gooooooooooooooooooo

[hardy moth]

Are fractals possible to render in geogebra?

[little drum]

many thanka Verus

[hardy moth]

Because in desmos they are

Thats why i believe in desmos supremacy

[hardy moth]

[little drum]

obviously desmos superior but Geogebra for Geometry stuff

good tools accordingly so

[woven whale]

geogebra is good when you have to construct points

[little drum]

[zenith compass]

Thank you Verus

[hardy moth]

np (:

[little drum]

https://www.desmos.com/calculator/ffliapted5

check this out Trentonnnnnnnnnn

[zenith compass]

Also thank you Ansh

[little drum]

nuuuuuuu

check that outtttttt

[zenith compass]

It’s so satisfying

[little drum]

[zenith compass]

Checked. That’s genius

[little drum]

show you what satisfying is XD

[hardy moth]

I have a suprise for you

[zenith compass]

Among us😅😅😅

[little drum]

showmieeeeeeeee

[hardy moth]

Go in desmos and type „betchacant“ in a line

[woven whale]

oh no

[hardy moth]

Oh yes

[woven whale]

waiit is this an easter egg

[hardy moth]

Yes

There are multiple

[zenith compass]

Lol

[little drum]

doesn't workkkkkkk

aaaaaaaa

[zenith compass]

But the graph is kinda SUS

[little drum]

in what line??

[hardy moth]

Doesnt matter

[little drum]

[hardy moth]

Without „

[little drum]

challenge accepted let's goooooooo

[alpine sable]

Holy moly beautiful!

[hardy moth]

The easter eggs are really nice in desmos

[alpine sable]

Wait UwU circle th

Pog graphs

But what is the question

[zenith compass]

Lol

Enjoy!

[little drum]

oh wait

Did you get how to do the integral

that was where you were stuck the last time I believe 🤔

[zenith compass]

When a math help channel turns into an art basel lol

[little drum]

Lmao

[zenith compass]

I get it lol, just use the Riemann sum will do

[little drum]

Okie

showmieee when you're done UwU

[zenith compass]

Ok!

[zenith compass]

@little drum QED!!!

[little drum]

perfect

[zenith compass]

Thank you so much guys

[little drum]

gg

[zenith compass]

The artworks are really fantastic

[sterile idol]

I just came from eating dinner and you're done

Great timing

[zenith compass]

Yay

[sterile idol]

Could someone explain why you integrated?

I thought integration being finding the area under a curve

[zenith compass]

Wait

[sterile idol]

Oh did you find an equation for the points and then integrated to find the length?

[woven whale]

integration is just the sum of infinitely many little things

[sterile idol]

So what are those little things here?

So if I understand correctly, integration is just summation but not discrete?

[vital crown]

Somewhat not really, but the Riemann-sum integration is more than enough for what you need right now

[sterile idol]

What is Riemann-sum integration?

[zenith compass]

Hope this prove is legal

[sterile idol]

Is it the name of the integration we do usually?

[vital crown]

In here, the idea of summing small things

[woven whale]

you could say that

[zenith compass]

Lol this help room is bustling with noise and excitement today

So many people

[woven whale]

yeah it was fun

[zenith compass]

The artworks are just elegant

They motivate me a lot

Once you get better at math, you can draw better pictures XD

[woven whale]

take a look at this picture i found online

please don't report me to the copyright guys

[sterile idol]

This was a nice problem

But I couldn't solve it

[woven whale]

it's tricky in more than one way

[sterile idol]

hopefully one day I'll be able to solve it

[woven whale]

you'll definitely be able to

[sterile idol]

thank you

[zenith compass]

What is that?

Is that a statistic problem

[woven whale]

no i was just trying to explain the riemann sum

i totally forgot about this

imagine if you will that the gap between each x_i goes to zero

this is the idea of a riemann sum

[zenith compass]

Oh yes

[woven whale]

you approximate the area under a curve with rectangles and take the limit of the dx := delta x -> 0

that's basically how it works

you'll learn more in mathematical analysis if you pursue math in college

[zenith compass]

Yes can! Once you understand calculus and vectors, you can even do it in n-dimensional space

[zenith compass]

Are you European or from USA?

[little drum]

what is the curve for the normal distribution :o

[zenith compass]

My college study Riemann in year 1

[little drum]

e^ something

[woven whale]

e^-x^2

scaled by a 1/sqrt2pi or something

[zenith compass]

1/sqrt(2pi)

Yay

[woven whale]

nah im from hong kong

[sterile idol]

oh my god

[little drum]

,w plot y = e^{-x^2}

[woven whale]

1am right now so i'm about to head to sleep

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Ansh#3502

[sterile idol]

https://www.youtube.com/watch?v=pOxZX7dQVuk this explained it

[zenith compass]

Omg I am also from Hong Kong

Lol

[woven whale]

yoo i linked this like 7 hours ago

heyo

don't give me your address please

[zenith compass]

Lol

Lol I wont find u neither nor u

[woven whale]

alright that's cool

i'm heading to sleep so yeah seeya

[zenith compass]

Yay

Hong Kong time 1:19 now

[sterile idol]

Oh sorry

[zenith compass]

It’s time to sleep for us

[woven whale]

yeah

good night

close the thread

[zenith compass]

Goodnight

[sterile idol]

Oh lol

[zenith compass]

U mean this room?

[woven whale]

no it's totally ok i was just surprised how good this video is

yeah whtever you call it

been going on since like 3

[zenith compass]

Lol yes

I keep this room cuz you guys showing artworks lol

Actually problem solved

XD

Goodnight

[woven whale]

do the .close thing

[zenith compass]

.close

[lone heart]

Channel closed

Closed by @zenith compass

Use .reopen if this was a mistake.

[woven whale]

the end of a chapter in life

good seeing you bud

[zenith compass]

Me too

[lone heart]

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[flat gust]

Can someone explain why it’s B and not others

[lone heart]

@flat gust Has your question been resolved?

[lone heart]

Channel closed

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[knotty spire]

congratulations

you opened a channel

https://tenor.com/view/next-bored-move-on-on-to-another-one-boring-gif-10228847

#❓how-to-get-help

Then post the work

So

What is your problem

And I sincerely hope this isn't a computerized test

what is the base of a triangle?

[lone heart]

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[alpine sable]

https://i.imgur.com/hH8TDqf.png

[alpine sable]

I got no idea how to do it

tip says to change base a to base e

[knotty spire]

we have a function f(x)

What are we supposed to do with it

[alpine sable]

derivative

https://i.imgur.com/NDdFk5v.png

gotta take derivatives from each

but dont know how to do (d)

[knotty spire]

Well then, have you tried this?

[alpine sable]

idk how to change to base e

[knotty spire]

$a^x = e^{\ln{a^x}} = e^{x\ln a}$

[ocean seal]

Remavas

[alpine sable]

damn

XD

[placid zinc]

In general, the derivative of a^x is ln(a)a^x

[alpine sable]

hm actually

[placid zinc]

Can use that algebra above to get that too

[alpine sable]

wouldnt a * a^ax be a^a * a^x

nvm

[placid zinc]

You mean "the derivative of"

[alpine sable]

yes

[knotty spire]

well first off, you should make your life simpler

[knotty spire]

$(cf(x))' = cf'(x)$

[ocean seal]

Remavas

[alpine sable]

okay I dont have enough knowledge rn for this stuff I think

[knotty spire]

I think you do

You just don't know it yet

[alpine sable]

bruh I got dyslexia + I usually do math in wrong order and mess up rip

• ADD

XD

[knotty spire]

So we have $f'(x) = \left( a \cdot a^{ax} \right)'$

[alpine sable]

well dont know what those brackets are and why it became a derivative

[ocean seal]

Remavas

[knotty spire]

I like brackets

Changed it to parentheses so it's easier

[alpine sable]

ah got you

[knotty spire]

we are calculating the derivative of f(x) right

[alpine sable]

yes

[knotty spire]

So we need to differentiate the whole thing

[knotty spire]

now here, we can make our lives simpler

[knotty spire]

Looking at this rule

What do you think we can do?

[alpine sable]

emm

[knotty spire]

the a * in the beginning is quite annoying

Maybe we ought to somehow get rid of it inside the derivative

[alpine sable]

a(a^ax) ?

[knotty spire]

$f'(x) = a\left(a^{ax} \right)'$

[ocean seal]

Remavas

[knotty spire]

Yes, we can pull constants out

[alpine sable]

huh

[knotty spire]

Now we only have to differentiate a^{ax}

[alpine sable]

idk how the (...)´ works

[knotty spire]

' marks differentiation, and the parentheses show what we are differentiating

[alpine sable]

havent done it before but lets go on so

a^ax = 'ax*a^(ax-1) ?

[knotty spire]

ah, the power rule

Not a bad choice

but

$(x^a)' = ax^{a-1}$

[ocean seal]

Remavas

[knotty spire]

Notice how the variable is the base

and the exponent is a constant

in the power rule

So we can't use it here

[alpine sable]

oh

right cuz Im looking for derivative of x

true

hmm

well

a^ax = a^ax ln a

I guess?

[knotty spire]

The rule is $(a^x)' = a^x \ln a$

[ocean seal]

Remavas

[alpine sable]

cant (a*x) be used as x?

man online courses are so ass, gotta pass this to get into university and I dont have any lessons

only some online book and assignments every 2 weeks to give

and I havent done math for 2 years cuz I did finals in my 1st grade and got A

and didnt have to do math anymore lmao

[knotty spire]

No worries

[alpine sable]

and now I cant even remember correct order when there is a lot of powers, roots and stuff

[knotty spire]

No, because we have to use the chain rule or something else.

There are two options I can see

One involves the chain rule, the other doesn't.

Which one do you want 😄

[alpine sable]

emmm

havent worked with chain rule before

[knotty spire]

Alrighty, algebra it is

Can you tell me what $a^{bc}$ equals to

[ocean seal]

Remavas

[alpine sable]

(a^b)^c ?

[knotty spire]

Exactly

So now

$f'(x) = a\left(a^{ax} \right)' = a\left((a^a)^x \right)'$

[ocean seal]

Remavas

[alpine sable]

yeah

[knotty spire]

Now, can we use the exponent rule for differentiation?

is the base a constant, and is x the exponent

[alpine sable]

oh

yeah

(a^a)^x = (a^a)^x ln (a^a) ?

[knotty spire]

$a\ln{a^a}(a^a)^x$

[ocean seal]

Remavas

[knotty spire]

yup, times the a from outside the differential we had

[alpine sable]

https://i.imgur.com/886S657.png

a((a^a)^x) = a * (a^a)^x ln (a^a) ?

[knotty spire]

yes

now, do you know what $\ln{a^b}$ equals to

[ocean seal]

Remavas

[alpine sable]

em

[knotty spire]

It's a pretty useful property of logarithms

[alpine sable]

oh its ln

em

idk actually

xD

didnt work with ln only log's

[knotty spire]

it's the same property

$\ln = \log_e$

[ocean seal]

Remavas

[alpine sable]

oh

right

so

b * ln a ?

[knotty spire]

yes

$a\ln{a^a}(a^a)^x$ so in this expression

[ocean seal]

Remavas

[knotty spire]

try simplifying it on your own

[alpine sable]

a^a ln a^1+ax? XD

[knotty spire]

do it step-by-step

[knotty spire]

^ using this property in the beginning

and going from there

[alpine sable]

a*a ln a(a^a)^x

or wait

is everything in ln ?

[knotty spire]

$a\ln(a^a)(a^a)^x$

[ocean seal]

Remavas

[alpine sable]

a ln a^2a+x ?

a*(2a+x) ln a

[knotty spire]

close

Let me do one step

$a\cdot a \cdot a^{ax}\ln(a)$

[ocean seal]

Remavas

[alpine sable]

huh

[knotty spire]

ln(a^a) gives you aln(a)

[knotty spire]

and from here you should be able to get the simplified answer

[alpine sable]

ln(a)a^ax+2

thanks man

you are legend

gonna go through it 10 times

and try to understand haha

[knotty spire]

Differentiation is fairly simple once you become accustomed to the needed manipulations

[alpine sable]

do you know how to train the order of stuff

I sometimes like

do stuff in wrong order idk

[knotty spire]

What do you mean by that?

[alpine sable]

well I cant give you example rn but

idk might be dyslexia or something

cuz I usually think one thing do the other

I guess I just gotta train more

[knotty spire]

Yeah, just differentiate as much as possible

Same with integration once you get there

although integration is much more difficult

And be sure to compare your answers to https://www.derivative-calculator.net/

They also have a nice step-by-step

[alpine sable]

oh thanks

[knotty spire]

They for example used the chain rule

for our problem

Many ways lead to Rome as they say

[lone heart]

@alpine sable Has your question been resolved?

Channel closed

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[lone heart]

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[alpine sable]

I believe I need to use the ratio test? but im not sure how to solve the exact sum of the series.

[sterile ravine]

multiply by -2 in the numerator and denumerator

[alpine sable]

(-2)^n-1 (-2) / 6^n (-2)?

[sterile ravine]

yes

so it will be (-2/6)^n*(-1/2)

[alpine sable]

what do i do next?

[alpine sable]

Do i plug in a number?

[sterile ravine]

and you will the first formula

[alpine sable]

Is my n term infinity?

[alpine sable]

.

[sterile ravine]

Yes

[alpine sable]

then the answer is just infinity over 8/6

How do I find the sum from this?

[sterile ravine]

sorry for the handwriting and the image quality

[alpine sable]

Got it. Thank you

[sterile ravine]

you're welcome

[alpine sable]

.close

[lone heart]

Channel closed

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[thin stag]

can i please have a hint on how to show this integral exists or doesn't exist?