help-4

[cosmic lichen]

@fickle rose

Can we solve it with mod tho?

[cosmic lichen]

Do u have a take?

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[tiny torrent]

This example lost me after defining the possible isomorphisms, is there a typo when they are explaining a_3?

[tiny torrent]

should it be $3\alpha_1(a + b)$ instead of $3(a+b)$?

[rocky lotus]

Branshi

[tiny torrent]

I wouldn't be suprised, there are so many typos in this book

I wonder if i got a bad edition or something

[ebon glade]

well 3 alpha_1(a+b) wouldnt be wrong I guess

but no

3(a+b) is correct

[tiny torrent]

is that because

[ebon glade]

alpha_3(x)=3x

thats the def

[tiny torrent]

mmm I see

what do you mean by

alpha_3 is well defined

since x mod 10 = y mode 10 implies 3x mod 10 = 3y mode 10

Im not seeing why this part is here

[ebon glade]

generally when you define a function you have to check that the "formula" actually always gives the same result, no matter in which way you write the input

for example, say I define a "function" f on fractions as f(p/q)=p

then this wouldnt be well-defined

cause 1/2=2/4 but f(1/2)=1 and f(2/4)=2

similarly I could define a function f:Z_10 -> Z by f(x) = x

but then this is also not well defined

cause f(1)=1 and f(11)=11 but 1=11 in Z_10

so the question here is, if x=y in Z_10, is then also 3x=3y in Z_10

to which the answer is yes

[tiny torrent]

ok that makes sense thank you

[hazy pivot]

I'd just like to drop in to make this comment slightly more concrete

Whenever you have a function on a domain that is defined using equivalence classes, you want the function to take the entire equivalence class to the same output. ie., you don't want it to depend on which representative you choose

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[modern yoke]

I am trying to find the voltage across each voltmeter in the circuit shown. I have currently come up with the answer 3V in the top and 9V in the bottom,, since as current leaves the 9v battery, it can lose 9v and return with 0v, and as it leaves the 12v battery, it can lose 9v then 3v and return with 0v, however, I am not sure what would happen when current from the 9v battery loses 9v and then goes towards the 12v battery, surely it would then have -3v as it reaches the battery, and this doesn't make sense. Can someone help please

[steady charm]

there's nothing wrong with a negative voltage

[modern yoke]

wouldn't that imply negative energy

or that the charge is moving the wrong way

[steady charm]

negative potential energy is fine

if we define there to be 0J potential energy on the ground, there would be positive potential energy above the ground and negative potential energy in a hole in the ground

[modern yoke]

so would there be some charge/electrons with 9v and some with 12v going aroudn the circuit,

and after going through the resistor, some of them would have 0v and some would have -3?

[steady charm]

we should think of potential as a function of position. every electron in a given position has a potential energy according to the electric potential there

[broken agate]

Yo twin whats sinus bruh😭

[modern yoke]

also if that is the case that voltage can be negative, how do we konw what the voltages are

[steady charm]

we can arbitrarily set one point to be 0V and then calculate the electric potential at every point in the circuit from there

[modern yoke]

I could now set them to be arbitrarily large and it would be fine since it can be negative

[modern yoke]

but how do you decide which position that is

[steady charm]

it doesn't matter really

[modern yoke]

for example here where would you start from

like if you had to approach this problem with no extra info

[steady charm]

because what the voltmeter measures is voltage difference which will be the same no matter what

[modern yoke]

which point would you pic

[steady charm]

so pick somewhere that seems convenient

[modern yoke]

so just to clarify I pick somewhere where the potential difference should be 0?

[steady charm]

i would probably pick the right side just because most voltages would be positive

[steady charm]

where the electric potential itself is 0

[modern yoke]

what does that mean

[steady charm]

we can define the electric potential as the potential difference with an arbitrary reference point, which we decide to have 0V. the electric potential difference between two points is then the difference in electric potential

it's like gravitational potential energy, where we decide on some reference height to have 0J potential energy

[modern yoke]

oh ok

but wouldn't that mean that it can't be zero for all paths

like if i picked the right side before the resistor to be zero

some of the charge would reach it with 0v, but some would reach it with 3v

so how do i pick a reference point which will always have 0

[steady charm]

the voltage of an electron will be the same regardless of the path taken

[modern yoke]

but won't the different batteries provide different electrons with different voltages

[steady charm]

yes but the resistor will make up the difference

that's how you can solve for the voltage across the resistor in the first place

[modern yoke]

so then how can I answer this question, since the voltage would be different depending on which battery the electtrons have come from

[steady charm]

it doesn't

that's what you need to use, the fact that the voltage doesn't depend on path is how you can solve for the voltage at each point

[modern yoke]

so would it be ok for the current to reach the 9v battery with 3v

if they came from the 12v battery originally and didn't go through the second resistor

[steady charm]

can you draw the path you're imagining here?

maybe it would help if we labeled all of the nodes on this circuit

if we set Va = 0V (just as an arbitrary choice), can you figure out what Vb and Vc are?

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[brave urchin]

hi, can someone help me with this integral? i don't see any undefined integral formulas for 1/ctgx or ctg x^-1

[brave urchin]

the first half of it i understand but i dunno what to do about the 1/ctgx

[steady charm]

can you rewrite 1/ctg x into a more familiar form?

[coral ocean]

ctg = cot ?

[brave urchin]

yeah

[brave urchin]

? bring it to -1 power

[steady charm]

like maybe expand it out in terms of its definition with sin and cos

and simplify that

[coral ocean]

$\cot(x) = 1/\tan(x)$

[rocky lotus]

Médicis

[brave urchin]

so it would be cot x^-1 = 1/tan x^-1 ?

[coral ocean]

yes, so tan x

[brave urchin]

=x/tan x?

[coral ocean]

no

${1\over \cot (x)} = {1\over {1\over \tan(x)}} = \tan(x)}$

[rocky lotus]

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

[brave urchin]

okay i got it, thanks

.close

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[vestal grove]

Discrete maths question

Above is the question and below is the solution

I dont understand what the solution is saying

[keen tundra]

its disproving by giving a coutner example

[vestal grove]

Like why is it a counter example

I thought z = (x+y)/2 was the proof

[keen tundra]

it shows no z can satisfy this

[verbal badger]

37.5 isnt in N

[keen tundra]

because such a z would have to be not an integer

[steady charm]

the exercise is claiming "for any two natural numbers x and y, we can find another natural number z such that x + y = 2z" but for x = 38 amd y = 39, the only real number satisfying that equation is 37.5 which is not natural, so z can't exist

[vestal grove]

Ah true

But I still don't see how we can just disprove with just 1 counter example

[verbal badger]

A proof must hold for any possible x and y

[vestal grove]

Ahh yeye you're right

[steady charm]

the exercise was claiming it's true for all possible x and y, so it would be false if it's false for even one x and y

[verbal badger]

"All cows are brown" is my statement

You can disprove this by showing me a white cow

You don't need to show me multiple white cows

[steady charm]

it's like if i say "it will rain every day next week", if it doesn't rain on Wednesday then i must be incorrect, regardless of whether it rained or not any other day

[vestal grove]

OK I think I get it now 🙂

Thank you, you all explained it really well!

❤️

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[grave night]

Help in evaluating the Efficient Frontier Equation for a portfolio

[coral ocean]

ki are random variable?

[grave night]

i'm not sure

ik that w is the the percentage of the stock in the portfolio tho

and the omega_i is the standard deviation of the stock

<@&286206848099549185>

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[fathom narwhal]

how to solve the koinsberg bridge theory

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@fathom narwhal Has your question been resolved?

[fathom narwhal]

no

[dawn axle]

discrete maths

[fathom narwhal]

?

[dawn axle]

yeah using discrete mathematics

Euler Trails and Circuits

[dawn axle]

There will be a route that crosses every bridge exactly once if and only if the multigraph of the koinsberg bridge has an Euler trail.

[fathom narwhal]

so is it solveable

[dawn axle]

yep

[fathom narwhal]

can u draw me a pic

[dawn axle]

sure

[fathom narwhal]

i have been pondering on this question for 3 years

[dawn axle]

let’s get it down today

[fathom narwhal]

do we have to use fancy math?

[dawn axle]

Nope you just need to know the definition of Euler trail

[fathom narwhal]

ok

[dawn axle]

It’s proved by Euler

[fathom narwhal]

ok

[dawn axle]

Yeah

[fathom narwhal]

i searched it up

[flint phoenix]

,rccw

[dawn axle]

all good?

[fathom narwhal]

but i dont know if it is still solvable or not

[dawn axle]

Wdym?

[fathom narwhal]

you just said if there is an euler trail

[dawn axle]

Then it’s possible

[fathom narwhal]

but is there

[dawn axle]

But there doesn’t exists any Euler trail

[fathom narwhal]

<@&286206848099549185>

[dawn axle]

Thus it’s impossible to across exactly 1 time

[marble arch]

He's already helping you

[dawn axle]

It’s solved by demonstrating the impossibility

[fathom narwhal]

but from point d to point b there is an euler trail

[dawn axle]

It’s not a theory it’s a problem

[dawn axle]

Eulerian trail exists in a connected graph if there are exactly two vertices with an odd degree (number of edges connected to them), or if all vertices have an even degree

There are 5 vertices with odd degrees

Thus it’s not an Euler trail

[fathom narwhal]

cant you chop it up

[dawn axle]

That’s clear enough, @marble arch

Go help him

You got to know the conditions for Euler trail man

[marble arch]

I think you explained it well enough already

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@fathom narwhal Has your question been resolved?

[fathom narwhal]

still dont undersatnd

but whatever.

.close

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[hazy pivot]

!test

[hazy pivot]

Sad

.close

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[pine prairie]

Hi what do you need help with

[hazy pivot]

Life

[hazy pivot]

Living

[river shale]

Hi, welcome to the server

[pine prairie]

Sorry that’s above my pay grade

[river shale]

Enjoy your stay!!

[hazy pivot]

That's unfortunate

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[dusky storm]

hey so I'm really bad with graphs and I just wanted to double check, is this answer correct?

[flint phoenix]

That's not 1

[safe fulcrum]

careful: x = 1 is not the turning point

if you fix x = 1 and replace it with the correct value, you'll get the answer

[fiery tide]

its not 1
its prolly half (by observation)
so like the fn decreases from x belonging to half to infinity

[safe fulcrum]

yeah, x = 1/2 is what I'd also expect

[dusky storm]

oh I see

I didn't enlarge it

[flint phoenix]

Zoom in :))

[dusky storm]

.close

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[fair wing]

can you give brief explanation that why tan5x can be written tan5x = tan(pi/2 - 2x)

[safe fulcrum]

it can't be tan 5x

[river gate]

How am i supposed to go about these type of questions
The example no.27

[fair wing]

!occupied

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[fair wing]

in my textbook to solve the equation tan(5 theta) = cot (2 theta)
it is written that this given equation maybe written as
tan(5 theta ) = tan (pi/2 - 2 theta)

but why

[steady charm]

so that's entirely different, they are saying cot(2 theta) = tan(pi/2 - 2theta)

and this is true because sin(x) = cos(pi/2 - x) and also cos(x) = sin(pi/2 - x)

[fair wing]

since cot2x = tan(pi/2 - 2x) and tan5x = cot2x that is why tan5x = tan(pi/2 - 2x) right?

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[fair wing]

.close

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[fair wing]

to solve sin(9 theta )= sin( theta)
i can write sin (9 theta)= cos(pi/2 - theta) but due to this i am unable to compare angles

[fair wing]

what other way i should do

[jovial edge]

$\sin^9(\theta) = \sin(\theta)$

[rocky lotus]

Alexis_Fx

[jovial edge]

this?

[fair wing]

no

sin (9theta)

[jovial edge]

$\sin(9\theta) = \sin(\theta)$

[rocky lotus]

Alexis_Fx

[fair wing]

yes

[jovial edge]

huh

[fair wing]

.

[jovial edge]

isn't 9\theta=\theta + 2kpi or pi-\theta +2kpi?

Like how we do with sin(a)=sin(b)

[fair wing]

add $

[stark wedge]

2kpi if you are so inclined

not just 2pi

[jovial edge]

oops mb, thanks

[fair wing]

i don't get it

sin(9x) = sinx
sin(x) = cos(pi/2 - x)
sin(9x) = cos(pi/2 - x)

[clever sentinel]

sin A = sin B →

1. A = B ± 2nπ ,or
2. A = π-B ± 2nπ ,or

[fair wing]

yes

[clever sentinel]

did you know that?

[fair wing]

no

[clever sentinel]

I should tell you an easy way to derive relation between A and B if sin A = sin B, cos A = cos B, tan A = tan B

[fair wing]

go ahead

[clever sentinel]

For sin A = sin B

1. Imagine an angle A in 1st quadrant.
2. sin is +ve in 1st quadrant so what is the other quadrant in which sin is +ve? It's 2nd quadrant.
3. In the second quadrant, make angle A from the x-axis(which in this case will be from negative x-axis) and then measure that angle from +ve x axis and you get that that angle is π-A and that's B.
4. Sin of any angle is equal to sin of ±2nπ that angle so our relation is "sinA=sinB" implies either

• A=B → A=B±2nπ
• A=π-B → A=π-B±2nπ

try to draw unit circle and visualise it. It's really simple way

[fair wing]

yes doing

can you tell me a way to write values for angle for different trigonometric equations when required?
because i have to look every single time to unit circle again and again

isn't there a way to do it wihtout looking at it again-n-again

[clever sentinel]

there are different formulas for each and they look ugly, I can write them for you but for real, if you do some practice with this, you can derive them from unit circle in your mind

[fair wing]

i do this but sometimes i get wrong

[clever sentinel]

sinA=sinB → A = nπ + (-1)^n B
cosA=cosB → A = -B + 2nπ or A=B
tanA=tanB → A = B + nπ

[fair wing]

for that question the answer is theta = npi/9 +(-1)^n theta/9

[clever sentinel]

that is what you get from here

[fair wing]

i applied that 1st relation

[clever sentinel]

you need to derive it for sin, cos, tan and I think it's pretty ez once you get it

[clever sentinel]

yes that's correct

[fair wing]

answer in book is npi/4 or (2n+1)pi/10

[clever sentinel]

9x = nπ+(-1)^n x
9x - (-1)^n x = nπ
x (9-(-1)^n) = nπ
x = nπ/(9-(-1)^n)

oh

so it basically broke the solution for even and odd n

[clever sentinel]

this gives a single solution

the book gave 2 solutions

[fair wing]

if i get anyone of from the book then thats also fine

[clever sentinel]

for even n,
x = nπ/(9-1) = nπ/8
for odd n,
x = nπ/(9+1) = nπ/10

notice you can write even n as n=2k and odd as n=2k+1

x = 2kπ/8 = kπ/4
x = (2k+1)π/10

so yes both are correct

[fair wing]

what are you assuming x to be?

[clever sentinel]

again if you did it this way you would have gotten
9x = x±2nπ
8x = ±2nπ
x = ±2nπ/8
x = ±nπ/4
well if you consider n as any integer instead of natural number, you can just write it as
x = nπ/4

or

9x = π-x±2nπ
10x = π±2nπ
x = (1±2n)π/10
again notice if you have n as integer you can write it as
x = (2n+1)π/10

[clever sentinel]

x is theta

[clever sentinel]

you see that (-1)^n formula doesn't give intuition to what angles we are referring to that's why everyone uses this unit circle way. And you are supposed to simplify your answer like this so the reader and you can visualise what angles are being referred

[fair wing]

i agreed this article with reason till point 3. but when i read point 4 i am just agreeing it without understanding reason

reason isn't clear to me for 4th point

[fair wing]

so i can't understand

[clever sentinel]

for 4th, imagine an angle in unit circle, now image that angle + 2π, what do you get? what does adding 2π mean? it means rotating the ray by 360 degrees

and you come back at the initial position

after adding 2π

[fair wing]

yes

same for subtracting?

[clever sentinel]

now what's sin of the that? it's same as sin of theta

you see?

that's why adding or subtracting 2π to the angle doesn't change it's sin, cos, tan

[fair wing]

yes as it comes to initial position on adding 2pi

[clever sentinel]

you can add or subtract 2π any number of times so you write it in general as ±2nπ for n any positive integer but you can write it even better as +2nπ where n is any integer

[fair wing]

😄

[clever sentinel]

try to find relation btw A and B for

1. cos A = cos B
2. tan A = tan B and see if you can do it or not

[fair wing]

interesting property

[clever sentinel]

that's why you must know to visualise unit circle for trigonometry, it's very useful

[fair wing]

btw it is true that if you add or subtract any say (2npi or npi or pi/2) it get's back to its initial position

[clever sentinel]

no

only 2nπ

π means half rotation
pi/4 means one fourth rotation

[fair wing]

why say for any anlge A if i add npi and subtract npi what is the difference

[fair wing]

like this

[fair wing]

are you taking 2npi for sin because x axis has values of 2npi

[clever sentinel]

adding π means rotating the ray 180°

it doesn't come back at same position

[clever sentinel]

±2nπ is true for any trig function

[fair wing]

for cos A = cosB
it is positive in both 1st and 4th quadrant by convention
A = B +- 2npi

[clever sentinel]

for cos A = cos B

1. A = B or better A = B + 2nπ
2. A = 2π-B or better A=2π-B + 2nπ = 2π(n+1)-B = 2nπ-B

because you measure angles counter clockwise from positive x axis

[fair wing]

for tan A = tan B

1. A = B or A = B +2npi
2. A = B + 2pi or B - 2pi
   A = B +- 2npi

[clever sentinel]

yes that thing was correct that since theta is positive in 4th quadrant that's why we make this diagram and get sin theta = sin 2nπ-theta

[clever sentinel]

no 2nd one is same as 1st

2. should be A = B ± π

[fair wing]

beacause it reamins positive if jumping the angle from 1st to 3rd quad?

and that is difference of pi angle

right?

[clever sentinel]

yes

[fair wing]

there is more question

if sin3x = sin2x

i am writing my steps

[fair wing]

3x = npi +(-1)^n 2x
3x-(-1)^n 2x = npi
x (3-(-1)^n 2) = npi
when n = odd
x(5) = npi
x = npi/5
when = even
x(1) = npi
x = npi

[clever sentinel]

when even looks wrong,
3-(-1)^n 2 = 3-2 = 1

[fair wing]

i am gonna do with inutitive method

[clever sentinel]

now you got
x = nπ/5 (for odd n)
x = nπ (for even n)

But in your answersheet ALWAYS the answer is given assuming n is any integer. So you should write your answers in such a way that you don't need to specify n is even or odd instead just that n is an integer for which for even n write let n=2k since n is even and for odd n, n=2k+1

and get x = (2k+1)π/5 or 2kπ

where k is any integer

you understand this?

[fair wing]

yes

[clever sentinel]

in this method, you don't need to make cases for even, odd n as it's assumed from start that n is any integer so you get ez solution

that's why i prefer that way

[fair wing]

then for this method i will do 3x = 2x +-2npi

x = +- 2npi

x = +- 2kpi
x = +- (2k+1)pi

this is not even rocket science why i am not understanding it

[clever sentinel]

aah you just did that wrong

[fair wing]

sin3x = sin2x
3x = 2x ±2nπ

[clever sentinel]

i said you don't need to make even, odd cases in this method

[clever sentinel]

correct

and the other one?

[fair wing]

wait let me

[fair wing]

x = ±2nπ where n is an integer

[clever sentinel]

you are almost there. Notice that if n is integer that means n itself can be positive or negative so there's no meaning in putting ± in front so you can write x = 2nπ where n is an integer

[fair wing]

x = 2nπ where n is an integer

[clever sentinel]

I know I made that mistake earlier, I should have written it as +2nπ Instead of ±2nπ

good

and the other one?

[fair wing]

x = 4nπ?

[clever sentinel]

show steps

[fair wing]

x = 2nπ + 2nπ

[clever sentinel]

no no no

3x = 2x + 2nπ
3x = π-2x + 2nπ

you get why?

[fair wing]

yes

beacuse 3x and 2x are supplementry angles on unit circle and adding 2npi doen't effect

[clever sentinel]

you need to write like this in exam

sin 3x = sin 2x → 3x=2x+2nπ or 3x=(π-2x)+2nπ for some integer n.
3x=2x+2nπ → x=2nπ
3x=(π-2x)+2nπ → 5x=(2n+1)π → x=(2n+1)π/5

[clever sentinel]

No bruh Not because they are supplementary because sin of theta and sin of π-theta are same because sin is positive in 2nd quadrant and by drawing A angle from positive x axis and A angle from negative x axis in 1st and 2nd quadrant and writing the angle between the ray in 2nd quadrant and positive x axis as B we get A = π-B and adding +2nπ doesn't change angle

Because if you remember it as supplementary angles, you might apply this to cos, tan and mess up. Though not entirely wrong but remembering it from unit circle drawing is better than as supplementary angles so you don't mess up in cos, tan

Is your doubt cleared?

[fair wing]

yes cleared

.close

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[clever sentinel]

close

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[echo oasis]

I need a help with this sequence problem.

a_n + a_{n+1} = 2x3^n, a_1 =1

I need to find the general term...

[shut mirage]

you mean, find an expression for a_n that doesn't involve previous terms?

[reef violet]

What level are you? There are explicit formulas for this stuff

It's pretty similar to a 1rst degree differential equation
Have you learned this method?

[echo oasis]

I have but I don’t know how to solve this one

[bronze moss]

you can try writing out a few terms (don't simplify).
a_2=2x3-1
a_3=2x3^2-a_2=2x3^2-2x3+1

[vale dock]

@echo oasis Has your question been resolved?

[vale dock]

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[crude ermine]

hi

[eternal osprey]

!da2a

[vale dock]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[eternal osprey]

Also, don't greet someone in help channel

[crude ermine]

I need help

with math

[eternal osprey]

Again, just post the problem. Don't do chit-chat

[crude ermine]

okay

[rocky kettle]

xD

[crude ermine]

So I need help with this

[eternal osprey]

!status

[vale dock]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[crude ermine]

1

will u check my answer if I do them?

[eternal osprey]

Yes

[crude ermine]

good

start the lesson pls

[crude ermine]

i have more questions

[eternal osprey]

Note that
$(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a-b$

[crude ermine]

this is part one

[rocky lotus]

Xwtek

[crude ermine]

whats that

can you do one question for me and tell me how you did it

[eternal osprey]

The important property for this problem. I don't know the name, though.

[crude ermine]

and i will see if I udnerstand

1/root 1 + root 2 x roo1 + root 2/ roo1 + root 2

Thats what the teacher said

I think

idk

@eternal osprey

actually wait

I opened a forum

but it glitched

I will go there

u can close this one

[eternal osprey]

Okay, then.

I close it according to Aden's request, the owner of this help channel,

.close

[vale dock]

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[rocky kettle]

xD

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[north scarab]

what did I do wrong here

[stiff lily]

you didn't evaluate y' at the specified point

[north scarab]

ah got it, ty

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[rose lance]

how to solve this

[flint phoenix]

Re = real part; Im = Imaginary part?

[rose lance]

yep

[lavish aurora]

are you being helped

[carmine swan]

is this how undergrad math looks like ?

[rose lance]

ive done this and im stuck

[rose lance]

wdym

[rose lance]

im in first semester

[carmine swan]

nvm

[lavish aurora]

good that's. a great start

[stark wedge]

one moment...

[carmine swan]

yeah ok

[stark wedge]

$\Im(x+jy) = y$ and not $jy$ btw.

[rocky lotus]

Ann

[lavish aurora]

so let's look at the equation after expanding teverything in complext

ofc we know

[rose lance]

oh

[stark wedge]

also z^2 = a^2 - b^2 + 2abj; z^2 means z * z and not z times its own conj

[lavish aurora]

i see the issue noe thanks ann\

[rose lance]

so its 2a-b?

without the j

[stark wedge]

so you should've had:

a^2 - b^2 + j(2a-b) + 3 = 0

[lavish aurora]

yup

[stark wedge]

and then match real and imag parts separately on this. get two equations in a and b

this is assuming i didnt miss anything else.

[carmine swan]

i wanna ask smtn

[lavish aurora]

yup as ann said

^^^

in the notation you wrote it'll take me a minute to tex the eqn

but you wont need it

[carmine swan]

^

[stark wedge]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[rose lance]

so is it like this?

[lavish aurora]

perfecrto

[carmine swan]

regarding this only

[flint phoenix]

regarding this question?

[carmine swan]

yes

[stark wedge]

ok then ask

[carmine swan]

ive done very few of these

so idk much

but we have to solve it in 2 parts ?

[rose lance]

ok so real part=0 and im part=0

right?

[stark wedge]

.

[carmine swan]

wait no 5

itll take 5 steps ig

involving cross-checking

[stark wedge]

i dont think we should be splitting hairs about the exact number of steps that this takes.

[lavish aurora]

give us the equations after separting the im an re parts

[carmine swan]

yea nvm

[stark wedge]

who cares if it takes 5, 6 or 27.4493 steps.

[carmine swan]

j^2 is -1 right ?

To the OP... there will be 2 solns ?

[lavish aurora]

nope

[carmine swan]

o

[stark wedge]

let OP work thru it and show us what she gets.

[lavish aurora]

they're be conjugate sols

[carmine swan]

yea

conjugate means opp sign right ?

[lavish aurora]

nvrmind

[stark wedge]

conjugate means you flip only the imaginary part

[lavish aurora]

i used conjugate wrongly

[rose lance]

this is my final answer

if i didnt mess up

[lavish aurora]

i have a habit since my alg geometer days

to use the word wrong

[carmine swan]

im getting -1-2j

[carmine swan]

idek half of the words so its fine ig lol

[lavish aurora]

okay so b = 2a

now if you sub that to - b^2 + a^2 +3 =0

you get a eqn ya can solve

you have the perfectly right idea

and you're doing amazing btw

[rose lance]

okay but im wrong cause no way 4^2 - 8^2 + 3=0

lol

[lavish aurora]

imma tex the answer now

because you have it

[rose lance]

ok

im dumb+

wait i correct it

[flint phoenix]

[rose lance]

u think this is sad right

.close

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[rose lance]

thanks :)

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[north scarab]

Im trying to solve for stationary point of

[north scarab]

e^x+1=0

I got e^x=-1

[pine prairie]

does this even have a stationary point

[novel canyon]

can u show the full context

[pine prairie]

think about that

[novel canyon]

well there u go

[pine prairie]

well we certainly did part a right

[stark wedge]

your derivative is correct and your equation is correct

[pine prairie]

what about part b

[stark wedge]

now that you're staring at the equation e^x = -1

tell us: can this ever happen at all and if so for which x

[north scarab]

my prof said e^x does not have a stationary point but I didnt understand why

[pine prairie]

what is a stationary point?

[north scarab]

when the curve isnt increasing or decreasing

[pine prairie]

what does that mean mathematically

[north scarab]

f'(x)=0

the gradient is 0

[pine prairie]

okay

when is the derivative of e^x equal to 0?

-# first question is what is the derivative of e^x

[north scarab]

derivative of e^x is e^x

e^x is basically an exponential

x could be 2,5, 8, etc

e^8 is an exponential

[pine prairie]

okay

now when is e^x = 0

-# if you dont know what to do, draw y = e^x and draw y = 0 and look at where they intersect

[north scarab]

y is an asymptode

y=0

as x aproches - infinity, it approaches 0 but never equal to 0

[stark wedge]

and now you said it

e^x is never equal to 0.

in fact e^x is always positive. its graph is always above the y-axis. (these are two ways of saying the same thing)

capisce?

[pine prairie]

ya unforunately you cant plug -infinity into e^x

the domain of e^x doesn't include -infinity

[gilded stirrup]

Actually e^x=-1 is a condition for being a stationery point. So not even asymptotically

[pine prairie]

and then etc etc look at what ann wrote

[north scarab]

if u put a really small number or a big number, its good enough to be equivalent

[pine prairie]

no its not

if you put in a very negative number

e^very negative number = something bigger than 0

we need it exactly equal to 0 for it to be stationary

[gilded stirrup]

$-\infty$ is not in $\bb{R}$

[pine prairie]

-∞ is not in ℝ

[stark wedge]

is texit down?

$123$

[rocky lotus]

Ann

[north scarab]

do u meant above x axis?

[stark wedge]

yes sorry. typo on my part.

[north scarab]

no worries

.close

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[odd gate]

Can the solution to a complex problem be a line like z = x + i (4x-5)/3? (4 + 3i)z + (4 − 3i)z (with a line above it) = 10. This was the original question

[coral urchin]

z(x) = x + i (4x-5)/3
this is a valid complex function

so, if x is unknown, then yes this is reported as a solution

[flint phoenix]

Can the solution to a complex problem be a line like $z = x + \frac{i(4x-5)}{3}?$\
$(4 + 3i)z + (4-3i)\bar z = 10$\
This was the original question

[rocky lotus]

This is sad 😢

[odd gate]

Okay thank you guys 👍🏿

.close

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[stark wedge]

,rccw

[stark wedge]

!status

[vale dock]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[stark wedge]

do you know any trig identities that could help us here

[swift barn]

Identity or value?

[scarlet igloo]

identify

[stark wedge]

identity.

[swift barn]

No no I can't use value

[swift barn]

In my syllabus I only have 3

[hidden terrace]

What is sin(2A)?

[stark wedge]

show these 3

[eternal osprey]

What does 🇹 emoji mean?

[shut mirage]

knight said identify instead of identity

[stark wedge]

knight _f3 misspelled the word

[scarlet igloo]

oops

[eternal osprey]

oh

[swift barn]

Sin²+cos²=1
Sec²-tan²=1
Cosec²-cot²=1

[stark wedge]

that's it?

[hidden terrace]

Those aren't it

[stark wedge]

then you don't have the right tools.

it is unavoidable to work with either the identity for sin(A+B) or for sin(2A).
it is impossible to proceed otherwise.

[hidden terrace]

Unless you derive them yourself

[swift barn]

BTW it is from mcq

I can put the value

[stark wedge]

show the options?

[swift barn]

From all options

[swift barn]

0, 30, 45, 60

Ik the answer is 0

But still I wanna solve it

[stark wedge]

then your only option is to check every single one of these lol

you dont have the tools to solve it properly

(yet)

[swift barn]

That motherfucker textbook is telling me to justify

[stark wedge]

show full photo of page.

[swift barn]

Ok

,rccw

[stark wedge]

where do you see that it says to justify

[hidden terrace]

That's easy then

Just test

[swift barn]

Wait I have to click again

[stark wedge]

(iii) has "justify" nowhere...

btw learn to rotate pictures on your phone before uploading

[hidden terrace]

Justify by testing each value

[stark wedge]

it is infuriatingly vague what the fuck it wants as "justification".

[hidden terrace]

sin(2*0) = 0

[scarlet igloo]

Ais it NCERT?

[hidden terrace]

2sin(0) = 0

0 is a solution

LIke that

[swift barn]

Yeah!

[swift barn]

Yup! I know I already putted it

[hidden terrace]

Test the others and you're done
You've justified them

[swift barn]

Ez

[scarlet igloo]

then you have the identity which was used in it..

[hidden terrace]

Testing case by case is perfectly fine, you don't have to solve it generally

[swift barn]

That's a point

Thanks

[stark wedge]

<@&268886789983436800> eye cue moratorium bypass

[hidden terrace]

What

[fervent dew]

The testbook isn't mf, you are unable to do it

[chrome beacon]

it's.... it's fine

[hidden terrace]

Bruh

[swift barn]

What? Are you complaining?

[idle void]

-# yay hayley is handling stuff for me

[short torrent]

technically I'll delete it since that word isn't allowed on this server but yeah it's fine

[hidden terrace]

Alright just close the channel

It's getting hot in here

[stark wedge]

that's why i pinged, thank you

[hidden terrace]

Why is it not allowed

[swift barn]

Can I ask why it was offensive?

[hidden terrace]

I just read #rules

Apperently you can't discuss intelligence or eugenics under any circumstances

So yeah

[swift barn]

Oh! Jeez she is so strict

.close

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[terse adder]

yooo

[flint phoenix]

yoooo

[flint phoenix]

How can we help you today?

[terse adder]

man im confused with this

holdon

[flint phoenix]

Alright

[terse adder]

answear is log x

but that was 3

is this a typo?

or what

[limber cliff]

Yes

[hazy pivot]

Well the answer is certainly wrong cuz it's in terms of x and not z

[terse adder]

it should be

[fickle rose]

the ans to 1 has many typos yes

[flint phoenix]

quite confusing honestly

[terse adder]

log5 x^2 + y^1/2?

[terse adder]

fr 😭

ive been stuck on this

[fickle rose]

is that log_5(x^2+y^1/2)?

[terse adder]

yes

[fickle rose]

If so, that's wrong, as in general (\log_b(a)+\log_b(c)\neq\log_b(a+c))

[rocky lotus]

PajamaMamaLlama

[terse adder]

is that the correctY?

ohh what the correct ans for 1

[fickle rose]

we cannot give answers, but instead us the log property (\log_b(a)+\log_b(c)=\log_b(ac))

[rocky lotus]

PajamaMamaLlama

[terse adder]

oke thanks

[vale dock]

@terse adder Has your question been resolved?

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[wintry oxide]

Ok so assume O is the center of the circle

[lost oar]

Problem 12 (5 marks). 23 people are selected at random. Find the probability that at least 2 of them
share a birthday (day and month).

[wintry oxide]

OA needs to be orthogonal to the left vertex

[wintry oxide]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[wintry oxide]

Same for OB

[hazy pivot]

Please stick to your own channel

[wintry oxide]

Do you see where this is going ?

[hollow cobalt]

so like this?

[wintry oxide]

Yeah give the edges names to make it easy

[hollow cobalt]

the sides of the triangle?

[wintry oxide]

Here I named it for you

[hollow cobalt]

ah ok ok thank you

so what do I do next?

[wintry oxide]

I’m thinking of an easy way

Think with me

[hollow cobalt]

hmmm

is it ok to assume that the chord bisects the 90 deg tangent angle equally?

wait

this is an isoceles trapezoid so angle D and C are equal right? @wintry oxide

[wintry oxide]

Yes

Omg I didn’t see the 5 inch height

[hollow cobalt]

does that change anything from here?

[wintry oxide]

Hmmm

[hollow cobalt]

(im not very familiar with all geometric theorems soo) ToT

[wintry oxide]

I’ll keep thinking about it. I’m sure there’s a way I just don’t want to brute force it. Let’s keep this open for a while ok ?

[hollow cobalt]

alright alright

ill try to think

@wintry oxide I think my professor messed up

i found the exact same problem online, but it has 1 more thing given

yeah ill just clarify this to my prof 😭

[wintry oxide]

Hmm ok ok

[hollow cobalt]

alright thenks for helping me anyways

.close

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[uncut sorrel]

Hello,

[uncut sorrel]

I would like help

[river sapphire]

!da2a

[vale dock]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[unborn sable]

ask away

[vale dock]

@uncut sorrel Has your question been resolved?

[fallow tiger]

💀

[vale dock]

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[exotic token]

Hiiii

[exotic token]

anyone knows something about LightGCN ?

My goal is to build a recomendation system using LightGCN

but my question is how the model "learns"

i think i know how to make the predictions, i am currently working with 2 layers

But from my understanding hi^(0) , which is a vector of the user/book i, in the layer 0 should be the feature vector

my english is not that great so i hope you can understand me

[cinder creek]

You feed data?

[exotic token]

and from then the model is completly deterministic

[cinder creek]

If it's deterministic, then you do have labels. Use them with datas.

[rocky kettle]

is this an ai model or what

[exotic token]

I dont really know, this is my first project working with ML ( Graph neural networks in this case )

[rocky kettle]

if it is i suggest you go to computer science server

[exotic token]

What do you mean by "feed data"

i see! I will try there also

[cinder creek]

Are you familiar with ML knowledge, or did you just dive into Pytorch?

[exotic token]

not much i would say

from ML i only know basic things

like Logistic Regresssion , One vs Rest ( i am having a course on that ( i am on the beginning ) )

SVM

also i learned in other courses LDA, linear regression etc

[cinder creek]

You know the part where models are trained using data, right?

[exotic token]

but this is one course in which i have to make a research in this case it is this topic GNN aplied to system of recomendation

[exotic token]

Loss function ?

[cinder creek]

No. How models are trained is that they are fed data.

You need data to train model.

That's how they learn.

[exotic token]

Ahhh ok yes! i see yes! But when i give the model the data the process is completly deterministic, shouldnt be a part where my model updates coeficients ( like logreg for example ) and tris to minimize some function ?

[cinder creek]

Are you familiar with the pipeline?

[exotic token]

i dont really know how to explain it sorry

Not really

[cinder creek]

Then you should probably take a step back and grasp the basic first. A model learns by data and the pipeline are probably the things you're introduced at the beginning.

[exotic token]

Ok i will search thank you!

have a nice day!!!

[cinder creek]

So do you.

[vale dock]

@exotic token Has your question been resolved?

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[gilded summit]

For this proof is there anything wrong with just saying through additive and scalar multiplicative closure?

[merry crystal]

u will indeed use closure but do u understand what u r being asked here?

this is precisely the equivalence of span defined through linear combinations and span defined through the intersection of all subspaces of V that contain the subset

u would wanna use a double inclusion to show that intersection of all subspaces containing the subset of V = all linear combinations of that subset

[gilded summit]

@merry crystal why is it not seficient to show something like this:

Through scaler multiplicative closure, each $\lambda _jv_j$ is in each subspace containing $v_j$. With additive closure, the sum of all such $\lambda _jv_j$ must also be in each subspace containing $v_i,...,v_n$. thus, this must be in the intersection as scaler multiplicative and additive closure says the linear combination of $v_i,...,v_n$ is in every subspace containing $v_i,...,v_n$.

[rocky lotus]

BOSS

[gritty sinew]

that's just half of the story if anything

ok you've shown the set of all lin combos is inside the intersection

that doesn't show equality

@gilded summit

[gilded summit]

wdym

we just have to show the linear combinations are in every vector containing v_1,...,v_n right

[gritty sinew]

as dj said

you need the inclusion the other way also

intersection is inside the set of all lin combos

that's the other half

[gilded summit]

Im lost, why is that needed?

[gritty sinew]

cause the question asks you to show set/vector space equality

the "is" in the question specifies equality

[gilded summit]

oh

[gritty sinew]

show that [some set] is [another set]

[gilded summit]

yeah i get what you mean

its not asking if its in the interection its saying it is the intersection

[gritty sinew]

yea

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[nimble python]

I need help we just started learning force and motion so I need to know everything to solve this problem

[ashen prawn]

watch this:https://www.youtube.com/watch?v=6dG5ScVtllQ or this:https://www.youtube.com/watch?v=_DD3zh0_L0M or both

or wait indefinetly for someone to come

[nimble python]

okay ill be watching

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@nimble python Has your question been resolved?

[dense echo]

basically just draw the free body diagrams for each of the objects, the only important thing to solve this is realizing that tension is the same for both objects

calculating x and y components of the net forces of each object + using F =ma solves rest of it

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[hazy pivot]

Well what does Newton's law of cooling tell you

[flat locust]

rate of loss of heat is directly proportional to temperature difference bw surrounding and body

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[timid hamlet]

i need help with this question

[hazy pivot]

We don't know the radius of the circle huh

Have you done trigonometry

[timid hamlet]

i have

[hazy pivot]

Nice

Join OA and OC

And tell me what happens

[timid hamlet]

wdym

ohhh

[queen rover]

construct the radii

[timid hamlet]

you have like a diamond shape or like two triangles

[hazy pivot]

Good

Now what's the property of tangents

[timid hamlet]

the radius is perpendicular to it

[hazy pivot]

Good

So you have two right triangles

[timid hamlet]

yeah

height of 7.7

[queen rover]

youll need to know value of tan 27 for this

[hazy pivot]

Well it asks for the value up to decimal places

So I'm guessing calculators are allowed

[timid hamlet]

can i assume that its 27 27?

[hazy pivot]

Cuz if not I don't think there is a way to solve this

[hazy pivot]

The angles are 27 each yes

[queen rover]

oh

angles

hsit

[timid hamlet]

how would you know that

[hazy pivot]

It's a property of the line joining the center to the point the tangents are drawn from

But also you can prove it using congruent triangles

[queen rover]

^

[hazy pivot]

Anyway are you allowed to use calculators

[timid hamlet]

yeah probably

[hazy pivot]

In that case yeah find the sides of your right triangle

You know one of them is 17

And the angle is 27

[timid hamlet]

i did tan 27 x 17 i got 8.7

but i thought the height was 7.7

oh shi nvm

no way i did that forget that😭

[hazy pivot]

Good that's the radius

[timid hamlet]

wait how

[hazy pivot]

Look at your triangle

And recall the definition of tan

[timid hamlet]

o/a

but are you sure the angle is 27 because when i did inverse sin(7.7/17) i got 26.93

and not 27

[queen rover]

did you take the exact value of tan 27 to get the answer

[timid hamlet]

yeah i used my calculator

[queen rover]

used this?

the entire

?

[queen rover]

here you can round it off

because the more decimal places you take the closer you get

[timid hamlet]

alright so can you help me get p please im stuck icl

[queen rover]

what step you on

like what all youve obtained

[timid hamlet]

i got the height of the triangle is 7.7

could i use cosine rule 1 to get the radius

[queen rover]

ok hold on

you have the value of OA?

[timid hamlet]

nope

[hazy pivot]

...yes you got that from the tan formula

[queen rover]

tan 27 is OA/AB

[hazy pivot]

This is OA

Actually I got class, gonna leave this to you euh

[timid hamlet]

yo hold up i just realized

i understand now

[queen rover]

use distance formula to find OA

[queen rover]

alright

[queen rover]

^

center of the circle is the origin O

its coordinates are (0,0)

so equate the value of OA you got with the distance formula

to find p

[queen rover]

coooll

[timid hamlet]

yo thank you

[queen rover]

got it?

[timid hamlet]

yeah

[queen rover]

kind of bad calculations tho

you will need a calculator

or log table if yk what that is

[timid hamlet]

bro idk why i didnt realize it was a right angle triangle from the perpendicular lines

i thought i was working with a non right angle triangle😭

[queen rover]

lol

[timid hamlet]

and then i realize when you were talking about it

[queen rover]

radius is perpendicular to a tangent

[timid hamlet]

yeah i knew that idk why when i drew my triangles i never put the right angle

[queen rover]

so what ans did you get?

[timid hamlet]

sorry for wasting your time😭

[timid hamlet]

4

[queen rover]

nah np lol

[queen rover]

you rounded it off?

[timid hamlet]

it was 3.96 it asked to one dp

[queen rover]

yea just write 3.9 then

if rounding is allowed then sure

[timid hamlet]

you gotta round up tho

[queen rover]

yea then 4.0

works

[timid hamlet]

yeah

alright thank you

[queen rover]

np

[timid hamlet]

imma close it now?

.close

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[haughty copper]

Hey got this proportionality question

Really really stuck on it

[stark wedge]

whoever wrote this doesn't know about \propto

[glass kelp]

${\alpha, \propto}$

[rocky lotus]

k

[stark wedge]

also apparently c vs. C??

[haughty copper]

yeah i know i was so confused

[stark wedge]

no idea if those are meant as the same or different...

[haughty copper]

same

[stark wedge]

try rewriting the prop between B and C tho

C is propto some power of B. which one?

[haughty copper]

i dont understand how i connect these two

[lyric sundial]

Use the definition of proportionality

And the fact that $\frac{1}{X} = X^{-1}$

[rocky lotus]

Alberto Z.

[vale dock]

@haughty copper Has your question been resolved?

[bold dock]

,tex You have $C = \alpha_1 B^{1/3}$ and $A = \alpha_2 C^{-1/2}$ for constants $\alpha_1$, $\alpha_2$ so what is the obvious thing to do

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[supple terrace]

Hello , I am currently taking Logic in college and we are dealing with syntactic and semantic consequences and so on which includes inferences rules , i want to understand whether those inference rules can be proven from a set of axioms (for example hilbert style axioms) + a single inference rule (for example modus ponens) or they are given by definition to just work in a logical proof system ? in case they all can be proven to hold true (which is something i didn't manage to do) please refer to any resource that deals with such topic , thank you

[worn sparrow]

rules of inference and axioms are pretty much the same

the only real difference is that axioms don't work on antecedents

but that's just a function of how you choose to write them, for example

you can write

a, b |- a and b

or you can write

|- a=>(b=>(a and b))

it doesnt really matter that much

let me look up if these terms mean something specific in model theory so I can make sure im giving you a correct answer, one moment

okay so

here's what I found

[worn sparrow]

rules of inference are defined as true, not proven true