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[midnight plank]

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[hard burrow]

you have done a calculus course right?

[exotic pendant]

good question

[hard burrow]

.close

[midnight plank]

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[safe onyx]

I have this so far but I'm not sure how to make the x to theta bounds

would it be best to graph it?

https://www.desmos.com/3d/t8mcq9qm3n

ok i got it now

I messed up and didn't put r^2 inside sin

and then it is just pi rad

.close

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[midnight plank]

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[tight citrus]

how is this not A

this is the solution

i don't understand the last sentence of the solution

pls ping

[brave oak]

@tight citrus a length cannot be negative

[tight citrus]

yes

i understood what they did but how can x > 3

which is why is chose A

[brave oak]

because it's not a x>-1/3 AND x<3

if at least one of them is true then it's acceptable

it's x>-1/3 OR x<3

[tight citrus]

wait what

ok i will try plugging x > 3

like 4

doesn't work

12 < 13

[brave oak]

3(4)+1+4+2 > 3*4+1 -> 12+7 >13 -> 19>13

you still have to do side 1 + side 2 > side 1 or 2

[tight citrus]

I think I got the formula confused

This is triangle inequality theorem?

[midnight plank]

@tight citrus Has your question been resolved?

[brave oak]

ye

sorry if I reply late had to do smth

[tight citrus]

Ur good I got it now

Thanks

[brave oak]

nice

[tight citrus]

.close

[midnight plank]

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[midnight plank]

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[boreal parrot]

Verify that |u+v| not uv

[cobalt nest]

show ur work

[boreal parrot]

I did and got v as 2-i

But the verification part isn't coming out

[cobalt nest]

wrong

[boreal parrot]

How

What did u get

[cobalt nest]

what u got is wrong

re do the calculations

[boreal parrot]

Ok

[midnight plank]

@boreal parrot Has your question been resolved?

[midnight plank]

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[languid mica]

hello

[languid mica]

how do we prove this?

do we just take 2 points on C and consider the 2 paths C1 ,C2 that are part of C going from one point to another

and since integral is path independent then they are opposite

[steel crest]

what's the domain and codomain of F

[languid mica]

idk

[steel crest]

are they numbers? pairs of numbers?

triples?

[languid mica]

what

i dont understand what you are asking me

[languid mica]

this is the theorem i have i want to prove it

[steel crest]

what is "F"

[languid mica]

vector field

[blissful pier]

note that if F is path independent then that means there exists an (f) such that (\nabla f=\vec{F})

[grand pond]

PajamaMamaLlama

[languid mica]

why

[blissful pier]

from here apply the fundamental theorem of line integrals and the desired answer pops right out

[languid mica]

are you sure?

that is true if F is conservative

or that nabla f dr is path independent

but path independancy doesnt mean F has a potential function

[languid mica]

unless you are assuming F is continious

[blissful pier]

truthfully I kinda forgot the explanation my multivar calc prof gave us 😅

[languid mica]

so you would be using this theorem

[languid mica]

i just finished proving that theorem yesterday

but for this F must be continious

cause in proof

you split integrals

[blissful pier]

and where does it say F is not here?

[languid mica]

it doesnt need to say its not

but doesnt say it is

so that means the theorem is true for any vector field F

continious or not

so your idea only works for continious what about the rest

my idea was that

if we choose 2 points on the path C

[blissful pier]

I think so... again so long as its conservative

[languid mica]

no

so what id say

[cobalt nest]

a closed path C_0 at point A means that the initial point is the end point

[languid mica]

is we take the path C

[blissful pier]

no need, if F is conservative then the integral only depends on the start and end points of the path

[languid mica]

and we split it in 2 points

[cobalt nest]

parametrize C_0 by y(t) = A for t in [a, b]

[languid mica]

from 1 point to the other lets name it C1

and back C2

means that since its path independent

the integral on C1 is same as on C2

but the direction is opposite

[cobalt nest]

thus integral over C_0 F.dr = integral F(y(t)) y'(t) dt over [a,b]

[languid mica]

so integral on C is integral on C1 and C2

[cobalt nest]

= 0

[languid mica]

and integral on C2 = -integral on C1

since its path independent on opposite direction

so thus its 0

[cobalt nest]

and use the fact that the line integral is independent of the path

[languid mica]

thats what i just said

using defintion

if we use the exact path of C2 but opposite direction

[cobalt nest]

i said parametrize it

[languid mica]

then we have that the integral on C1 = - integral on C2

so the addition is 0

[languid mica]

why would you complicate it even more

[cobalt nest]

no

its 2 lines proof

[languid mica]

what

[cobalt nest]

restructure what i said it will sort itself out

[languid mica]

no point

there is no reason to parametrize it

[cobalt nest]

2 lines though

[languid mica]

what does saying 2 lines mean

[cobalt nest]

short proof

[languid mica]

how bro

why would you parametrize it

[cobalt nest]

as i said

[languid mica]

when you can do 1 line proof

like its just C1 = - C2

so sum is 0

from defition of path independancy

just by picking any 2 points

[cobalt nest]

it takes more than 1 line to formalize what you said

unless u need a sketch of the proof

[languid mica]

one question

when we say integral over C

which direction are we implying

clockwise or counter clockwise

[steel crest]

F doesnt need to be continuous

[languid mica]

i pointed that out

[steel crest]

$F = \nablda \phi$ just needs that $\phi$ is differentiable, not continuously differentiable

oh, sorry, I missed that

[grand pond]

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

[languid mica]

so when we say integral over C

which direction are we implying

[cobalt nest]

its path independent

[languid mica]

thats not what im asking

when we have any integral over C

[cobalt nest]

it doesnt matter

[languid mica]

it does

[cobalt nest]

clockwise or not, if its path independent

[languid mica]

bro

going from point A to B

and from B to A

isnt the same

[cobalt nest]

when its path independent

it doesnt matter

[languid mica]

it does

[cobalt nest]

aight

kekw

[languid mica]

if we go from A to B and from B to A

they will be opposite

[blissful pier]

yeah that is one way to do it

then let C=C1+C2

reverse limits

[languid mica]

so ill ask again

[blissful pier]

they cancel

[languid mica]

when we say integral over a curve or path C

which way do we imply that we are integrating over

clockwise or counter clockwise

or how is the way specified

[cobalt nest]

int_a^b f = -int_b^a f

[blissful pier]

counterclockwise

[cobalt nest]

nothing is different generally

[languid mica]

yes they are opposite

so lets say one is 1

other is -1

when i type integral over C

which one do i want

the 1 or the -1

cause 1 isnt equal to -1

[languid mica]

oh ok

but uhm

like if i have a curve thats changing curveture

like can have some like this

[blissful pier]

can you elaborate on what you mean by changing "curvature"?

[languid mica]

do i go from left to right

or the other way around

which way is counter clockwise

[blissful pier]

depends on the parameterization 😅

but that counterclockwise is true for closed curves

[languid mica]

no parametrization

[steel crest]

it's generally a meaningful question for closed loops

[languid mica]

none closed loops i meant

[steel crest]

im saying i dont think the question makes sense

[languid mica]

ok so in the curve above

[languid mica]

ill name this C

if i say integral of F dr over C

which one do i want the one from left to right or right to left

[blissful pier]

for that there is no "correct" way to go like counterclockwise and clockwise

left to right is meaningless here, we simply have a start and end point

[languid mica]

which is the start

and which is the end

is the start on the end

[steel crest]

if i take a road trip from NY to LA, NY is the start and LA is the end. but if i go backwards, LA is the start, NY is the end

[blissful pier]

again... depends on how you parameterize 😅

[steel crest]

there's no canonical orientation

as Pajama is saying

[blissful pier]

this is good example :)

[languid mica]

so here

if i name this C

and i type with this notation

integral over C of F dr

what am i refering to

from A to B or from B to A

[cobalt nest]

as i said just

Assume the line integral is independent of path. Let C be any closed path starting and ending at point A. Consider the constant path C0​ at A, parametrized by γ(t)=A for t∈[a,b].

[steel crest]

it depends on how you parameterize

[languid mica]

without parametrizing it

as it is

[blissful pier]

then we cannot even describe the curve

[languid mica]

what am i saying by writing integral over C of F dr

[cobalt nest]

integral of F . dr over C = integral of F.dr over C0 = integral of F(y(t)) y(t)' dt over [a,b] = 0

[blissful pier]

lest the start and end points

[steel crest]

then the integral is not well-defined

[languid mica]

so how does that make sense

[blissful pier]

.

[languid mica]

you are saying that the result of an integral depends on parametrization?

[languid mica]

so how does it get well defined

or when defining C

we also define the direction

so when saying C

we mean from A to B on that curve

[steel crest]

yes, it has to have a direction as part of it

[languid mica]

ok

yea thats all i understand now

[steel crest]

and the change of variables will preserve the orientaiton becaue you take the absolute value of the jacobian

so in that sense parametrization doesnt matter

but you have to choose a direction

[languid mica]

ok

so when defining a curve C

on an integral

the problem has to also give a direction

[cobalt nest]

no?

[steel crest]

yes. if it's a CLOSED contour, that is, a loop, then by convention the default orientation is counterclockwise

[languid mica]

its not a set direction that we agreed to follow when we use that notation

[steel crest]

so you'll see things like

[languid mica]

ok

[steel crest]

$\int_{\vert z \vert = 1} f(z) , \mathrm dz$

[grand pond]

gfauxpas

[languid mica]

so only there we have default orientation

idk what contour integrals are yet sorry

[steel crest]

and that's a circle and the implied orientation is ccw

[steel crest]

just treat it as a line integral

[languid mica]

i wanna finish my work on integrals over paths

then look at that

i wanna finish first all these theorems so i can better understand how contour works

[steel crest]

$$\int_{\vert z \vert=1} f(z) , \mathrm dz = \int_a^b f(\phi(t))\vert \phi'(t) \vert , \mathrm dt$$

same definition

[languid mica]

yes you type that

but i dont understand anything

[grand pond]

gfauxpas

[languid mica]

so yea

[steel crest]

but thats what you rintegral means in the first plane

what does this mean when you write

[languid mica]

idk what it means |z|=1

[steel crest]

$$\int F \cdot , \mathrm dr$$

?

[grand pond]

gfauxpas

[languid mica]

on the buttom of integral

[cobalt nest]

thats what i've been tryin to tell them

[languid mica]

for open paths it does not have a default orientation

thats what i was asking

[steel crest]

${\mathbf v \in \mathbb R^2 : \Vert \mathbf v\Vert = 1}$

[languid mica]

ok

[steel crest]

i should say in R2

[grand pond]

gfauxpas

[cobalt nest]

dont take open paths

[steel crest]

do you know what shape this is

[languid mica]

🥀

[cobalt nest]

closed path lol

[languid mica]

i told you so many times

bro

forget the problem

[cobalt nest]

i gave u way with closed path

[languid mica]

yes i understand

[cobalt nest]

because the question

[languid mica]

but i moved on from that

[cobalt nest]

asked to prove that

[languid mica]

and i asked for any path

[cobalt nest]

in open path

it isnt true

[languid mica]

i know that

i did the full proof

its over

forget about it

now we are at a completely new chapter

[cobalt nest]

then whats the question?

[languid mica]

i was asking when we say integral over any path C

[cobalt nest]

u should open new channel tbh if u got new question ig, but nvm

[languid mica]

of F dr

do we have a default orientation

[cobalt nest]

depends on param

[languid mica]

or that needs to be defined with C

it doesnt

an integral cant depend on parametrization

parametrization is something we use to get an equal integral to the first and calculate it easier

if i use 2 different parametrizations that get 2 different results yet being equal to the first integral i have a contradiction

what it depends on is direction

but my question was if there is a default one when using that notation

and the other guy already answered there isnt it needs to be defined

@steel crest

so

we use z

as an imaginary number?

or vector

meaning this is all on 1 plane right? 2D so its a circle

with radius 1

.close

[midnight plank]

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[midnight plank]

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[rancid vigil]

im playing a game that you can either win lose or draw , played it 5 times ,
what are the chances of me winning 3 times
its equiprobable

[rancid vigil]

should i use newton binomial ?

[viral dagger]

are the chances of winning, losing, and drawing equal?

[rancid vigil]

yep

[lyric charm]

do you want EXACTLY 3 wins or AT LEAST 3 wins

[rancid vigil]

that what i meant by equiprobable but ig its french lol

[rancid vigil]

exactly

[viral dagger]

oh i read that diffrently

[lyric charm]

so during each game you have 1/3 probability of winning, 1/3 of losing and 1/3 of draw

yes?

[rancid vigil]

yep

[lyric charm]

ok then your number of wins follows a Bin(5, 1/3) distribution

[rancid vigil]

so yeah its gonna be solved with the binomial

[rancid vigil]

can we approach the formula with logic ?

like i just use it , but dont understand it

[runic hamlet]

well it doesnt come out of thin air

[lyric charm]

wdym "approach with logic"

do you want the binomial pmf explained logically or...?

[rancid vigil]

yep

like why we multiply all the stuff to get the exact probablity

or you know what ,thx

ig i need to go

.close

[midnight plank]

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[midnight plank]

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[urban needle]

hi

[blissful pier]

hello

[urban needle]

hi

my question as follows

2015/2 + 2016/4 + 2018/8 + 2022/10 + upto infinite
all terms in Box, greatest integer function

each term in gretest integer f^n

my my

[lyric charm]

do you have a picture

[urban needle]

again sorry im from laptop
i know series is pretty awkward

[urban needle]

all terms are in greatest integer function like in [.] such brackets

[lyric charm]

ok but are we supposed to just magically guess the pattern

[rare maple]

How did it go from 8 to 10

[lyric charm]

i don't see it at all

[urban needle]

thats also a mystery
its a module so it can also be like error in question

[lyric charm]

a module?

[rare maple]

Is this the exact question

[lyric charm]

can you maybe take a screenshot of the question

[urban needle]

believe me

[lyric charm]

if you're on laptop it should be doable

[rare maple]

I assume he is talking about a physical module

[urban needle]

its module a thin book from school

[rare maple]

If i had to guess it should have been 16 instead of 10

[lyric charm]

are you able to skip this question at all

or do you risk your teacher being mad at you

[urban needle]

obviously he will solve our doubts tomorrow

also [log 1]+[log 2]+[log3] + ............+ [log 66]
log's base is e

[.] represents greatest integer f^n

[pine wave]

$\sum_{n=1}^{66}\lfloor\log_e(n)\rfloor$?

[grand pond]

Element118

[pine wave]

do you have the powers of e

actually it's not too hard to calculate the powers of e using power series for e^x

[urban needle]

yes

[urban needle]

no

[urban needle]

ik the series of value of e^x

[pine wave]

use it to estimate the powers of e

then you can use it to calculate the terms of this summation

[urban needle]

how

[pine wave]

$e^3=\sum_{n=0}^\infty\frac{3^n}{n!}$
take enough terms until you are sure it converges

[grand pond]

Element118

[urban needle]

sry i truly cant get that

how shall i implement em

[pine wave]

just add until you see the new terms shrink really quickly

[urban needle]

i apologize
can u pls show me how
may be idk the things u r telling me

[brittle valley]

loge instead of ln

[urban needle]

they all r same

[urban needle]

what do u mean exactly

[brittle valley]

yh ik its js nicer to write ln

[urban needle]

i just wrote whats was in question

btw can u help me solve it

[brittle valley]

let me see

[rare maple]

They are telling you to find the powers of e so that you can use them to approximate the logs

[urban needle]

oh

ty

[urban needle]

naah man how is it possible it runs till infinite

.close

[midnight plank]

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[rare maple]

The powers reduce quickly we need an approximate one

[urban needle]

.reopen

[midnight plank]

✅

[urban needle]

but how

its like

[rare maple]

We find only till like he first 3 or 4

[urban needle]

how mane e's value to find

[rare maple]

After which the powers reduce quickly

[urban needle]

e=2.7

e2=7.29

e3=19.683

e4=53.1441

e5=enough

now just tell me to use such in that question which i already knew

will answer be 136

[urban needle]

by counting the terms etc

.close

[midnight plank]

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[midnight plank]

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[molten bay]

(2,0)(0,1)(4,5)(0,C)

If four points are concylic then what will be value of C?

[molten bay]

I can do it by distance formula but I need something time saving method

[lyric charm]

you can find the eqs of the perpendicular bisectors of two segments joining known points

then intersect those

and that you can do w/o distance formula but rather with some slope/intercept/whatever magic

[midnight plank]

@molten bay Has your question been resolved?

[snow dawn]

!done

[midnight plank]

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

[tawdry laurel]

what was this for

[molten bay]

I didn't understand ann comment

[lyric charm]

do you know what perpendicular bisector means

[midnight plank]

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[molten bay]

.reopen

[midnight plank]

✅

[molten bay]

Yes a line which divide equal and 90 degree

[lyric charm]

ok so just for convenience let's give your points names:
i'll call (2,0) as P; (0,1) as Q; (4,5) as R; (0,C) as S

find the equations of the perpendicular bisectors of any two of PQ, QR, PR.

intersect them.

that'll be the center of the circle.

[merry agate]

Given that it asks for only 1 value of C I'd guess that C is the y coordinate of the center of the circle

Normally for a given circle, a line at a given x or y coordinate would intersect at 2 places. Since the question only asks for 1 value of C I'd guess that the x/y value given is tangent to the circle

[lyric charm]

that's an unjustified guess

hm i am getting something ugly here

[midnight plank]

@molten bay Has your question been resolved?

[molten bay]

I am not understanding reasoning behind perpendicular bisector

Can anyone make it easy by graph?

[midnight plank]

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[lyric charm]

.reopen

[midnight plank]

✅

[lyric charm]

1. perp bisector of PQ consists of all points which are at the same distance from P as from Q
2. since your 4 points are concyclic then the center of their circle must be at the same distance from all four points.
3. you can claim point 2 even if you do not know where the center is yet
4. the center must in particular be at the same distance from P as from Q, and at the same distance from Q as from R

[molten bay]

But what is credibility of perpendicular bisector will pass through center?

[lethal path]

proof is by SAS congruence

[lyric charm]

"perp bisector will pass thru center" == "center will lie on perp bisector"

[molten bay]

I am asking why?

[lyric charm]

call the center O

[molten bay]

Ohh thanks

[lyric charm]

then OP = OQ, agree?

[molten bay]

Yes

[lyric charm]

... wrong reply?

[molten bay]

Agree

[lyric charm]

anyway.
perp bisector of PQ consists of all pts at same distance from P and from Q

OP = OQ says O is at same distance from P as from Q

therefore O lies on perp bisector of PQ

[molten bay]

Ohh now i got it

Thanks Ann

Gukesh is winning that's enough for magnus

The crown wall is moving from bottom

[lyric charm]

#chess-go-shogi but also <@&268886789983436800> this looks kinda scammy

[warm hazel]

We don’t allow advertising of personal services on this discord and you should not be interrupting a help channel.

[solid iris]

take a day off too

[molten bay]

Off from which jobM

[exotic pendant]

i wanted free chess classes for a cheap cheap price of 5 USD D:

[lethal path]

GothamChess is free

like there's so much free chess stuff honestly

[exotic pendant]

-# see the joke is i said free and then proceeded to say a price

[molten bay]

What if we ban you for fun?@exotic pendant

[exotic pendant]

https://cdn.discordapp.com/emojis/1241929902199017535

[midnight plank]

@molten bay Has your question been resolved?

[midnight plank]

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[rapid imp]

I need someone I can DM anytime to ask stuff about trigonometry and exponential equations, logarithms and probably quadratic equations and system of equations for 1 or 2 weeks pls I have 3 exams in that span

[livid python]

you could just come here again and again and ask it's ok

[rapid imp]

Ok

.close

[midnight plank]

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[rapid imp]

.reopen

[midnight plank]

✅

[rapid imp]

Can someone help me relearn trigonometry I have exercises like calculate value of Cos(120) + tag(-330) / sec(1125) + csc135 also have exercises like prove the trigonometric identities and stuff like that I need to relearn everything for an exam and then I'll have two other exams of other topics the same week 😭

Man I also struggle when I have to like cancel out stuff I don't know what can cancel out with what

[fallen sparrow]

Do you know in which quadrants sin cos and tan positive/negative?

[rapid imp]

Yeah

[fallen sparrow]

Then its just simple reduction of the angles like 1125

Tan(-330) is just -tan(330)

330 degrees is in 4th quadrant

So tan must be negative there

Tan(330) = tan(360-30) = tan(-30) = -tan(30)

[rapid imp]

Man sorry I have lots of questions I don't want to bother anyone do u know like a youtube video or something where I can learn everything in 1 or 2 days

[fallen sparrow]

Like what portion

Trigonometry is a vast chapter

Theres sections of it

[rapid imp]

Like what

[fallen sparrow]

Uh

[rapid imp]

I don't know where to begin

[fallen sparrow]

Trigonometric identities
Trigonometric equations
Periodicity and stuff

[rapid imp]

Sorry

Yea identities

[fallen sparrow]

What grade are you

[rapid imp]

I'm not in USA it's different here wait let me check

[fallen sparrow]

Me neither

[rapid imp]

I think it would be 10th grade

Yea

[fallen sparrow]

https://youtube.com/playlist?list=PLj7p5OoL6vGwh4_Y8yP64vIRIMn68XXXl&feature=shared

This is bprp

Pretty good for beginners

Scroll down you'll find identities

He's also discussed the question you were asking earlier

[rapid imp]

Thanks also If I don't know what I'm getting in the exam what specific things do I have to learn?

Because I spent a week learning those formulas like sin^2= cos^2-1 just to fail the exam anyway

[ebon mica]

knowing pretty much every trig identity usually comes in handy

[rapid imp]

So other than the exercises themselves in the youtube channel what do I really need to understand?

[ebon mica]

every big one

[fallen sparrow]

They are very short videos i don't think you'll have a problem visiting all of them

[ebon mica]

like double/half angle, pythagorean, etc

and educate yourself well on the unit circle

[fallen sparrow]

Also a lot of the videos are connected so you can actually prove some of them on your own after learning a bit

[rapid imp]

Man Ik but I had this exercise where I had to prove some identities or something and even knowing them all I got stuck and ended up doing nothing

[fallen sparrow]

That way you won't have to worry about not remembering stuff when you can just prove them logically

[ebon mica]

those can be tricky sometimes

but all you really need are the main identities

and then there are some tricks to approaching them

like always work on the more complicated looking side, try to condense whichever side of the equation you're working on, etc

[fallen sparrow]

Also one more thing and do not take this offensively but, crying about not being able to do anything is not going to solve anything

[rapid imp]

How long do u think it would take me to learn because I'm really rushed I have trigonometry exam for monday and then some logarithm crap for thursday and some other crap for friday

[fallen sparrow]

I suggest you start now

[ebon mica]

but if you look at some practice problem workthroughs you'll get the hang of it

[rapid imp]

I try turning every tan into sen/cos but then it makes the exercise bigger and it overwhelms me

[fallen sparrow]

That really depends on your abilities and willpower

But I'd say about a day or 2 to brush up

[rapid imp]

Then everytime I watch a yt video there's suddenly a new rule I didn't know about oh suddenly I can change this and put it up in the fraction or something

[ebon mica]

well I guess you'll have to practice dealing with those too

one helpful tip would be to convert whatever you have into whatever terms you are trying to get

[fallen sparrow]

No new rules
Just one expression converted into another

[rapid imp]

like that dumb (a^2 + b^2) (a^2 - b^2) or something like how do I even know when to use that

[ebon mica]

for example if you have cosines on the left and secants on the right and you're working with the LHS, write the cosines down as 1/sec

[fallen sparrow]

That's not trig thats just algebra

[rapid imp]

No I swear I saw a youtube teacher do it

Thanks

.close

[midnight plank]

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[rapid imp]

.reopen

[midnight plank]

✅

[rapid imp]

Can someone give me something for logarithms as well some tutorial

I don't know how my teacher expects me to learn all of this in 1 week

[ebon mica]

https://www.youtube.com/playlist?list=PLSwBOUuVxVwDMGbPge9IMccKfvFdPVhKS

the organic chem tutor is good

[rapid imp]

And the exponential functions

[ebon mica]

he should have good resources for exponents too

and trig

just look him up on youtube and you'll find his videos

[hardy mason]

Yeah he got me through my algebra class last year.

[rapid imp]

Thanks

.close

[midnight plank]

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[desert siren]

@rapid imp Welcome to the server!

[rapid imp]

Thanks

[midnight plank]

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[tidal turret]

how would you show this two things are equal to each other? two sided subseteq inclusions like they both need to be subsets of each other, but how?

[surreal moon]

A truth table or Venn diagram could help

[tidal turret]

to gain intuition?

.close

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[silk bison]

why in transfer function when we take the z transform is input over output?

[silk bison]

is that contradictory?

[languid mica]

Can you show the full problem

[silk bison]

there u go

[languid mica]

so you are just trying to solve this?

[silk bison]

yes

[languid mica]

i didnt realise its laplace transformation sorry

i havent taken that yet but i can show you how to solve the differential equation if you want?

[silk bison]

no need bro i just want to know why it happen

thank you

[silk bison]

<@&286206848099549185>

[languid mica]

ok

[dawn spire]

hi

i need help

[fresh sparrow]

see #❓how-to-get-help

[fallow scarab]

What formula are you referring to that contradicts H = Y/X

[dawn spire]

can someone help me

[silk bison]

the output is at the denominator!

[dawn spire]

why yall ignoring me

[fallow scarab]

Show the formula you think is right

[dawn spire]

i nned help

[fresh sparrow]

go to #help-22

[silk bison]

it says output over input , and when we apply the z transofmr it becomes input/denomiantor

[fallow scarab]

You're still not showing anything

https://en.m.wikipedia.org/wiki/Transfer_function
Something like this

Or notes from a book

[silk bison]

see brother

[fallow scarab]

Where does it say (s+3) is the output

[silk bison]

y'+3y=2x

[fallow scarab]

I didn't see where that implies output = s+3

[silk bison]

it has the y

the coefficient 3

[silk bison]

huh?

[midnight plank]

@silk bison Has your question been resolved?

[silk bison]

<@&286206848099549185>

[fallow scarab]

y is the output, not whatever you're saying

Y / X is the transfer function

[silk bison]

but its on denominator

the y(s(

[fallow scarab]

You're confused. s+3 is not the output

[silk bison]

but it says y(t-3(

explain me then please whats the output

[fallow scarab]

y is the output

Y/X is the transfer function

[silk bison]

and x(t) is the input so at this differential equation

dy/dt + y(t-3) = x(t) = >
the x(t( is the input which at the transformation it becomes =>

Y(s) -(s-3) =x(s)
=> Y(S) =x(s) /(s-3)

[silk bison]

huh?

[fallow scarab]

Your parentheses are problematic

[silk bison]

fixed that.

[fallow scarab]

This isn't Y alone. That's Y in terms of X

[fallow scarab]

Also this is different from the problem in the screenshot

[silk bison]

cant comprehend it

could you elaborate further please?

[fallow scarab]

You should read this

[silk bison]

i have done

[midnight plank]

@silk bison Has your question been resolved?

[midnight plank]

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[midnight plank]

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

[lyric charm]

rightmost part is cropped off

[molten bay]

Nope

It is just incorrect*

[lyric charm]

so we need to find the incorrect statement from these 4

[molten bay]

Yes ma'am

I only feel like AB correct

[lyric charm]

what about C

[molten bay]

Not getting it means

Ohh wait

B and D is suspicious

Could you explain it?

[lyric charm]

explain what exactly

[molten bay]

How can I discrad C and D?

[lyric charm]

i didn't say anything about discarding

also i did not understand your message of

Not getting it means
feels like you swallowed like 50% of the words or punctuation there

[midnight plank]

@molten bay Has your question been resolved?

[molten bay]

I am not getting what it means

.close

[midnight plank]

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[midnight plank]

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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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[pliant wharf]

my answer is 30

but there isnot a option

[verbal pumice]

Is the 50 degrees meant to be the minor arc PQ? Or is it something else?

[pliant wharf]

APQ angle is 60 degree ig

[lyric charm]

blurry unreadable picture

[verbal pumice]

Well then 30 does seem right

60 + x = 90

[pliant wharf]

sorry i dont own the paper

[verbal pumice]

is the circled answer 60 degrees lmao

[pliant wharf]

for some reason chat gpt insists on 60

[pliant wharf]

no option

[verbal pumice]

That would require AB || OQ so yeah that's not right

[verbal pumice]

¯_(ツ)_/¯

[pliant wharf]

thanks

.close

[midnight plank]

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[midnight plank]

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[hushed mauve]

i'm trying to gear up for university math (i'm nowhere near uni yet, but i'm studying in advance)
this is a problem i have with the concept of improper integrals

according to my understanding, improper integrals have one or both bounds at infinity (+/-). as i understand it, this then requires determining whether the limit of the integral exists at those bounds.
if the limit exists, the improper integral resolves to that limit (or at least for that bound).
what if the limit does not exist?

[hushed mauve]

limit of the integral at infinity (+/-)*

[dawn dagger]

then it diverges

for example 1/x over [0,1] diverges because ln|x| goes to -inf

[hushed mauve]

how would we describe such an integral if one comes up?

should we just say that the integral has no fixed value because the limit at infinity does not exist?

[dawn dagger]

We just say it's divergent

because geometrically the area is not finite

[hushed mauve]

i see.
another related concept i have problems understanding (or rather require confirmation about) is multiple integrals (if i'm allowed to continue asking in here).

[dawn dagger]

Also for improper integrals it can also be normal number where the integrand goes to infinity like 1/x at x = 0

[dawn dagger]

Ofc you are

[hushed mauve]

regarding multiple integration, are we supposed to do them from inside to outside? i don't fancy the idea of chunking multiple integrals in one go

[dawn dagger]

You mean like double integrals?

[hushed mauve]

double, triple, etc.

[dawn dagger]

Yes, you work your way from inner to outer

sometimes in double integrals, you can even write them as a product under certain conditions (Fubini's theorem)

but that's too much overload haha

[hushed mauve]

if that's the case, i suppose any variable that isn't part of the current integral (as in, the current integral is not being done with respect to those variables) are treated as constants for that integral?

[dawn dagger]

Yes

[hushed mauve]

i see, that simplifies the scary bits a lot hahah

for the longest time i have been unduly scared of multiple integration and seeing two or more integral signs is a nightmare

[dawn dagger]

The process of integrating is really no different from the one dimensional case, the scary part is more finding the bounds, when giving a region imo

[hushed mauve]

but onto my last question for now:
what are partial derivatives? i know they are marked with a kind of reverse cursive d sign (not sure what the actual name is, sorry), but what should we do with them?

[dawn dagger]

You basically differentiate wrt one variable and treat the rest constant

that's also why we use partial sign

[hushed mauve]

in that case, what's the difference between normal differentiation and partial differentiation?

i know normal differentiation is where you express a function completely in one variable and differentiate wrt that variable

[prime hornet]

you cannot take the “normal” derivative of a multivariable function

[hushed mauve]

and that things can get complicated when two or more codependent (?) variables are in the function statement

[prime hornet]

the partial derivatives tell you the rate of change of a multivariable function in the directions of each component

for example, the partial derivative of f(x, y) with respect to y tells you the rate of change of f in the y direction

there’s no meaning to the ordinary derivative for functions of multiple variables, only partial derivatives

[hushed mauve]

if i were to visualize such a function, i'm guessing i would require a 3D space

[prime hornet]

yes, if it’s a function of two variables

[flat veldt]

Sometimes

[hushed mauve]

so in such a space, does a partial derivative form a plane or a line?

assuming a two-variable function

[prime hornet]

oh, I was just about to post the same image

[hushed mauve]

because to my understanding, the derivative of a univariate function is its rate of change, usually represented by a tangent line

oh i see that image now

[flat veldt]

What textbook is this?

[prime hornet]

it’s the rate of change in each direction

[dawn dagger]

Say you hold y constant so like f(x,b) then the partial derivative of f(x,b) forms lines into the direction of x, so yes, and combing both partial derivatives would give you a plane

You can imagine the lines as vectors spanning the tangent plane at a point (x0,y0,z0)

[hushed mauve]

i was about to ask if vectors are related

but i dropped the idea because i don't see a specific direction

since derivatives are meant to be rates of changes, wouldn't they produce scalars?

or is it because of the presence of the other variable(s) in there that turns partial derivatives into vectors pointing in the direction of the other variable(s)?

[flat veldt]

I think one of the last chapters of calculus deals with vectors

[hushed mauve]

i understand, but i'm actually jumping beyond my grade here hahah

[dawn dagger]

There exist directional derivatives, indeed and they are very important actually

[hushed mauve]

i'm not even supposed to be touching calculus at school yet, but i do not wish to suffer when i eventually do, so i'm studying ahead of time

[dawn dagger]

In one dimensional case it's straightfoward

[hushed mauve]

and these are a type of partial derivative, i presume?

[prime hornet]

the partial derivatives only point in the direction of their variable

[hushed mauve]

i see. so if i have f(x, y), and i take the partial derivative wrt x, i get a "vector" that points in the direction of x?

sorry if i'm not using some terms correctly, i'm very new to partial derivatives as a whole

[dawn dagger]

Not quiet

The partial derivative of a scalar function, is a scalar function again

[prime hornet]

formally you get the slope of the tangent line in the x direction at each point

the slope is a scalar

[dawn dagger]

I just used "vectors" to explain how a tangent plane is formed

[hushed mauve]

hm i might need an example to understand. can we try using the formula of a circle as a two-variable function and take the partial derivative of that function wrt x?
eg: x^2 + y^2 = 1

(if this makes sense)

[dawn dagger]

That would not be so intuitive I think because you would implicitly differentiate

You can take f(x,y) = x^2 + y^2

[prime hornet]

mhm

[hushed mauve]

ah alright

so going by your example, the partial derivative wrt x would be 2x?

[dawn dagger]

x^2 + y^2 = 1 would be a level curve

[hushed mauve]

or 2x + y^2?

oh i just realize that by "keeping other variables constant" it actually means to treat the other variables as actually constants and not just let them sit there as they are
so i believe it's 2x

[dawn dagger]

yes

[hushed mauve]

and the partial derivative wrt y would be 2y

so this means that the rate of change of f(x,y) = x^2 + y^2 in the x-direction is 2x, and in the y-direction, 2y
is this right?

[prime hornet]

(fwiw, I do want to mention there is a perspective of treating the partial derivatives operators on the graph of a function as vectors that span the tangent plane at each point, but I don’t believe this perspective is super helpful for you at this stage )

[dawn dagger]

Yes

[hushed mauve]

i will keep this in mind when i get to that stage, thank you! i don't mind learning all of this ahead of time as long as i have scaffolding hahah

[hushed mauve]

i see. i get it now. thank you so much!

[dawn dagger]

You can imagine it like locally if you had f(x) = x^2 + c you get 2x and f(y) = y^2 + c you get 2y

[hushed mauve]

yeah that makes complete sense now

[prime hornet]

so at a fixed point (x_0, y_0), the slope of the tangent line in the x direction is 2x_0, and the slope of the tangent line in the y direction is 2y_0

[dawn dagger]

If you treat y as a constant, you basically get this projection which is a parabola again

[hushed mauve]

i think i will need to play around in geogebra a little bit more

[dawn dagger]

actually meant this haha

[hushed mauve]

makes sense, since the whole function turns into ax^2 + c

[dawn dagger]

Yea something like that

It's constant in one direction, as you see

[hushed mauve]

hm i now get the numerical concept of partial derivatives

but i'll still need to play around with graphing tools to get a geometrical feel for what they actually are

thank you for the help though!

i think that will be it for the time being

[dawn dagger]

You can watch this
https://www.youtube.com/watch?v=GkB4vW16QHI
and also learn about the gradient too

[hushed mauve]

saved, thank you!

alright i think i'll free this channel for others

.close

[midnight plank]

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[tight citrus]

pls ping

i got x^y = 2
and y = (1+x)^y

i don't think that's neccesary tho

like there is a faster way right

[lusty python]

set ${1 + x}^{{1 + x}^{{1 + x}^{...}}}$ as $t$

[tight citrus]

i set that as y

[grand pond]

1 divided by 0 equals Infinity

[tight citrus]

^

[lusty python]

or you can set that as $y$

[grand pond]

1 divided by 0 equals Infinity

[tight citrus]

yes

[lusty python]

so you got $(1 + x)^y = y$?

[grand pond]

1 divided by 0 equals Infinity

[tight citrus]

right here

yes

[lusty python]

oh okay

so $x^{{(1 + x)}^y} = 2$

[grand pond]

1 divided by 0 equals Infinity

[tight citrus]

yeah

yo

are you there

[lusty python]

im here

[tight citrus]

can u guide me

[lusty python]

im thinking

[lusty python]

from that try $1 + x = \sqrt[y]{y}$

[grand pond]

1 divided by 0 equals Infinity

[lusty python]

and $1 = \sqrt[y]{y} - x$

[grand pond]

1 divided by 0 equals Infinity

[tight citrus]

ok then

[lusty python]

so $2 = 2\sqrt[y]{y} - 2x = x^{(1 + x)^y}$

[grand pond]

1 divided by 0 equals Infinity

[lusty python]

nah nah nah

oh it's multiple choice?

[tight citrus]

yeah

[lusty python]

sub each number

[tight citrus]

but im tryna solve it algebraic

[dreamy lichen]

how about not introducing any new var

[floral star]

its jst $x^{1+2} = 2$ right?

[grand pond]

Sypse

[lusty python]

wdym 1 + 2?

[tight citrus]

that's the solution

[dreamy lichen]

exactly ^

[floral star]

x^1+y, y is 2?

[tight citrus]

literaly just

[dreamy lichen]

the red thing equals 2

[lusty python]

oh yeah

DUDE WE'VE BEEN CALCULATE IT WRONGLY 💀

[floral star]

[tight citrus]

brooooo lmao

[lusty python]

we thought it's like

[tight citrus]

this makes perfect sense thank you bro

[lusty python]

$x^{(1 + x)^(1 + x)}$ and so on

[grand pond]

1 divided by 0 equals Infinity

[tight citrus]

just like i have bad vision

it's hard to see things like this

[floral star]

well u did had x^{1+y} so 🤷‍♂️

[tight citrus]

do you think i could've solved it from there

thye algebra there is wierd

[tight citrus]

sry if it sounded rude

[floral star]

its quite a standard problem so yea after seeing it once its quite simple

[tight citrus]

can you help me with the algebra from there

more practice

i got (x-1)^(1/(x-1)) - x = 1

then its kinda hard

no real solutions???

but thats the algebraic aproach

so ig the way is to see the red thing

have a nice saturday everyone

.close

[midnight plank]

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[lusty python]

!nogpt

[midnight plank]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[midnight plank]

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[hybrid crow]

I know some things

The list doesn't span Pm because 1 is not included within its span

The list is length m+1, as is the length of the shortest spanning list

And all linearly independent lists here must be shorter than m+2

But yeah not sure how to prove

I have some intuition behind it though

For example suppose m = 4

Then we have 5 polynomials with roots at z=2

Clearly, we can't include the constant 0

So what this means is that there must be two (or more) polynomials

Of the same degree

And I think this is behind the linear dependence

I even have an example of desmos if thats helpful

Matter of fact i might have a good start

Basically write out every polynomial as

(x-2)(something)

And show that when u subtract two of same degree

U get a lower degree that is a scalar multiple

Of the other lower degree

[glass notch]

Do not ping mods for no reason and do not delete mod pings.

[hybrid crow]

Thats probably not clear tbh

[hybrid crow]

I didn't?

[frail carbon]

was unware of the latter sorry

[slender walrus]

i dealt with it, but don't delete pings

[frail carbon]

unsure what you mean by the last this (and the previous two lines)

[frail carbon]

but this is definitely on the right track

[hybrid crow]

Okay

Imagine u have

(X-2)(x-3)

And (x-2)(x+5

And (x-2)

When u subtract the first two

U get

(X-2)(8)

Which is a linear combination of (x-2)

Okay i found an interesting way

1, z,...,z^m spans Pm and it has length m+1

Assume p0,p1,...,pm is linearly independent.

Then 1 is not in span(p0,...,pm) so (p0,...,pm,1) is linearly independent with length m+2(a contradiction)

So our original assumption is wrong and the list is linearly dependent

I believe it's correct

[midnight plank]

@hybrid crow Has your question been resolved?

[midnight plank]

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[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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

[slate oriole]

If 4x<12 and -4x<A, and if solution set of this inequalities is 1 element, what is A?

[silent zodiac]

-4x>12

But less than A

Should be obvious

[placid spoke]

are there equal to signs anywhere there? otherwise i'm pretty sure that's not possible

[woeful turret]

-4x>-12

[woeful turret]

yeah thats what i was thinking.u get a set as a soln

not 1 element

[runic hamlet]

!original

[midnight plank]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@slate oriole Has your question been resolved?

[slate oriole]

this is the whole question.

[runic hamlet]

well as written its not solvable

[slate oriole]

interesting then question should be incorrect or I did some typo and didn't realise

[runic hamlet]

reasons why I asked for an image

[slate oriole]

Original one is in turkish

[tired osprey]

no problem

[runic hamlet]

If the original problem is not in English, then post it anyway! The additional context might still be helpful.

[slate oriole]

Then I guess I translated wrong or something my bad let me check again

[chilly cobalt]

is x an integer

[slate oriole]

it's a natural number

mb I didn't see extra info

[chilly cobalt]

knew it

A probably has to be an integer as well? from first look

[slate oriole]

so we have -A/4 < x < 3

right?

so x can be either 2 or 1 I guess

[tired osprey]

could you just show the original problem?

[slate oriole]

how will you understand it

do you speak turkish

[tired osprey]

translate?

or just from the context

mathematical notation is pretty universal

[slate oriole]

there is no mathematical notation, it's mostly verbal

[chilly cobalt]

gpt translation is a thing, and its also to prevent you from misreading the text

[slate oriole]

Is it still unsolvable?

These are the all infos I think

[chilly cobalt]

yeah cause theres technically infinitely many values of A if it isnt an integer

[slate oriole]

if it's still unsolvable let me check

actually there are options, is it possible that it asks for possible A?

[runic hamlet]

there are options?

so much wasted time...

[slate oriole]

Yes, it was asking for me to find which option would work

-4 -8 1 4

[runic hamlet]

we have been asking you for 20 minutes to post the entire original problem

[slate oriole]

it would take more than 20 minutes that's why I didnt send you

[midnight plank]

Channel closed

Closed due to timeout

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[slate oriole]

okay it's -4 got it myself

.close

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[woeful turret]

i need to tell no. of points this is not differentiable

and those brackets surrounding the 4x^2-8x+5 is greatest integer function

our domain is (1/4, 1/2)

[lyric charm]

find all pts in (1/4, 1/2) at which 4x^2-8x+5 is an integer

[woeful turret]

so i put these end points and i found 3 and 2 respectively

yeah

[lyric charm]

where is the vertex of y=4x^2-8x+5? is its x-coordinate contained in the interval (1/4, 1/2)?

[woeful turret]

(1,1)

no its x coord is not contained

[lyric charm]

you forgor the brackets

ok

so you found that the values of the quadratic at the endpts of your interval are 3 and 2

and it's monotone on the interval

therefore?

[woeful turret]

these are the only vales the function gives in that interval?

so its non differentiable at only these 2 pts?

[lyric charm]

the domain does not even include those two points

so they do not count

[woeful turret]

huh

oh ok

[lyric charm]

lemme guess, answering 0 to the original q is illegal?

[woeful turret]

not illegal but its wrong

[lyric charm]

can you ss the full question just in case

[woeful turret]

yh

[lyric charm]

...