help-42

[brisk yarrow]

Do you know how to Build a DFA for Numbers that are divisible by 3?

[tender vessel]

yes

[brisk yarrow]

So what i believe you can and Maybe are supposed to do is unite a DFA for the divisibility of 2 and a DFA for 3 and then you should have it

And this should create a NFA

You see what I mean?

[tender vessel]

but wont i create more states by that

for 3 i need 3 states, and for 2 i need 2 states.

[brisk yarrow]

I think you should be able to do it with 4 states

[tender vessel]

i will try it again

[brisk yarrow]

Yes but I think that you can unité a specific state so that you have exactly 4

[tender vessel]

if i need the not 3 not 2 or not both

i will build for each one and then do unite?

like DFA for not divided by 2, DFA for not divided by 3 and then try to unite them

[brisk yarrow]

yeah

[tender vessel]

ok brb

[brisk yarrow]

i think that should make it

[tender vessel]

i am testing it again. might worked

[brisk yarrow]

ok

[tender vessel]

i still got 6 states

[brisk yarrow]

Your doing the product of both DFA right?

[tender vessel]

well this is A or B or AandB

if you ask to do when it is accepted for both DFA then it will be the same but the accpected states wil be [q1p1] [q2p1]

but then its not right

i created A U B

any suggetions guys?

[brisk yarrow]

give me a minute 😭

[tender vessel]

i dont rush you

[brisk yarrow]

but im rushing me haha

[tender vessel]

i was like in case anyone is watching haha

[brisk yarrow]

This should makle it

that's the union of both DFAs

@tender vessel

[calm coral]

@tender vessel Has your question been resolved?

[tender vessel]

but how haha

is my table wrong?

[brisk yarrow]

Usually when you unify two DFA you create a new start and build two epsilon transitions to each DFA and this would be a NFA and then you can see that both DFA have a very similar start. So you erase the epsilon transition and use the same start point for both DFAs

[brisk yarrow]

no but you tried to build a DFA and not a NFA

you did the multiplication of both DFA which is correct but not what you need to do in this case

You should know that each NFA has a DFA but the DFA will probably have more states than the NFA

[tender vessel]

Can you break down the path to build this nfa?

[brisk yarrow]

yes !

[tender vessel]

Like did you use the table

[brisk yarrow]

no

[tender vessel]

Just from the 2 dfa?

[brisk yarrow]

I rarely use them 😅

[tender vessel]

Ok haha

[brisk yarrow]

yeah

let me draw this

[tender vessel]

Ok

You just drew the both dfa but with same starting state?

[brisk yarrow]

So we have those two DFA

[brisk yarrow]

you will get it soon

[tender vessel]

Ok

[tender vessel]

Yes

[brisk yarrow]

now its right

[calm coral]

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[brisk yarrow]

.reopen

do reopen

@tender vessel

[tender vessel]

.reopen

[calm coral]

✅

[brisk yarrow]

We unified both with these epsilon transitions

[tender vessel]

Yeah

[brisk yarrow]

i did write them wrong again 😭

So now they got unified by the epsilon transitions

And if you look closely q5 and s1 are somewhat similar

So i erased the epsilon transitions and got this

[tender vessel]

Well it looks like you took q4 and make him act as q5 and s1

[brisk yarrow]

yeaj

thats what i did

[tender vessel]

Alright

But should have work with table. I did something wrong

But I got it

Thanks man

[brisk yarrow]

there's a bit of trial and error process to in my way to do it 😅 but that's how you can do it usually

[brisk yarrow]

no problem 😄

[tender vessel]

.close

[calm coral]

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[tender vessel]

wait

the number 10010 which is 18 get accepted state

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[tacit brook]

<@&268886789983436800>

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[slim kindle]

What statistical test should I use for the following:
The propability Y that the predictions are correct is the same across the binary group X

P(Y|X1) =µ1
P(Y|X2) =µ2
H0: µ1=µ2

ow my bad

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[wise moss]

hii could someone check if this proof is valid, this subject is really confusing

[wise moss]

visual of the theorem

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[remote mural]

Heyo, me and a friend are trying to solve this, question is "find the inequality", apparently the answer is 4x-2y<-6 but I don't get how it gets there, I've tried solving it using points from the solution (pink is the solution region btw) and from the line itself but to no avail

[zealous lodge]

say gex

[remote mural]

🤨

[inner zealot]

The boundary is linear so make an equation for that line.

[remote mural]

yeah

Y-Y1 = (Y2-Y1/X2-X1)(X-X1)

but the answer comes out to Y=2x+3, which is none of the options

and Y<2x+3 is wrong cuz 3<3 is wrong and 0<-1 is also wrong

I'm using the points (-1.5, 0) and (0,3)

[inner zealot]

Put the equation into standard form.

y = 2x + 3

-2x + y = 3

After that, it's just a matter of finding which solutions are a multiple of the result you found.

[tranquil wasp]

Flipping the inequality can catch you out

[remote mural]

oh my god i just realised that B is just a multiple

thank you

.close

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[livid plume]

I have a question about asymptotes, so the question is (x^3+4x^2-21x)/(x^2+4x-21), which simplifies to x(x+7)(x-3)/(x+7)(x-3). n>d, so there is no horizontal, but there is a slanted asymptote. If we divide n by d we get y=x as the slanted asymptote. Holes at x= 3 and, but the simplified equation is y=x

[livid plume]

How is it possible that the asymptote is the same as the equation? all of the values are the same as the asymptote

[marsh valley]

It is as slanted asypmtote in a way, but in reality your function, whenever it is defined, is just x * 1 * 1

So x=y is a slanted asymptote kind of trivially, just like y = mx would be a slanted asypmtote of y=mx

[livid plume]

so the way I understand it is asymptotes are what the function approaches as it goes to infinity right, but here the asymptote is the same as the function, so it never deviates from that line. How would i even graph this function when the asymptote and function are on top of eachother?

[marsh valley]

Slanted asymptotes are lines your function gets close to (i.e. it grows like a line for large x)

In your case f is a line

So its asymptote is just itself

[livid plume]

okay cool that makes sense, now another question which i have about asymptotes. (x+1)/(x-3)^2 is the function, d>n so horizontal asymptote at 0, and vertical asymptote at x=3 cuz x cant be 3. If i graph this function though, the left part of it starts positive and goes through y=0. I understand that it describes the end behavior, and as x gets closer to -infinity, the y gets closer to 0 again, but is there any way to check for behavior like this beforehand? or just guess and check?

[marsh valley]

Well just from the definition of the function, you should expect that the function is negative whenever x < -1

Since (x-3)^3 >= 0

So it stems from that

[livid plume]

alright yea that makes sense, thanks king

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[hybrid flint]

I need some help on this 💀

[hybrid flint]

for a), to prove bijection, I need to prove it's injective and surjective

It's surjective because f(pi/2) = 1, f(3pi/2) = -1, and f is continuous

for injective, I'm not sure what to do

Injective means that no two inputs have the same output or if f(a) = f(b), then a = b

[serene geode]

the derivative of sin is cos which is negative on (pi/2, 3pi/2) and 0 on endpoints

so sin is strictly decreasing on (pi/2, 3pi/2)

[hybrid flint]

Oh we aren't allowed calc

[serene geode]

bruh

[hybrid flint]

💀

the classes are for comp math

[serene geode]

comp math?

[hybrid flint]

competitve math

[calm coral]

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[hybrid flint]

<@&286206848099549185>

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@hybrid flint Has your question been resolved?

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@hybrid flint Has your question been resolved?

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[unborn stone]

Help

Rn I have |(n+1)(2x-1)| after ratio test and idk what to do now

[drifting seal]

lim n-> inf

[unborn stone]

I got the answer now but doesn’t that become inf times inf

[drifting seal]

how

2x-1 has no n

[unborn stone]

Oh yeah

[drifting seal]

only the n+1 does

[unborn stone]

The IOC is just 1/2?

[drifting seal]

but anyways yea infinity so what’s the radius

[drifting seal]

yea it only converges at its center

[unborn stone]

I don’t need to make it -1/2<x<1/2 right

It’s just 1/2

[drifting seal]

no that would imply the radius was one

it only converges at x = 1/2

[unborn stone]

👍

.close

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[hidden umbra]

I need to do this exercise but i don't know where to continue , it has been 3 hours that i have been working on thid task and I can't find my way out of it

[hidden umbra]

<@&286206848099549185>

[brittle isle]

!15mins

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@hidden umbra Has your question been resolved?

[hidden umbra]

<@&286206848099549185>

[hidden umbra]

Bon

No help then?

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[calm coral]

@dense coral Has your question been resolved?

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[unkempt lagoon]

can anyone check part 2 of this pls (shown below)? thanks

[calm coral]

@unkempt lagoon Has your question been resolved?

[unkempt lagoon]

<@&286206848099549185>

[sweet zodiac]

part 2?

wdym

would you like all the qustions checked?

[unkempt lagoon]

yes pls

[sweet zodiac]

k

ill get back to u in like 5 minutes lol

ok lemme take al ook atthesel ol i was busy

11 is wrong

12 is right

13 is right

gimme a sec igotta finish soenmthing

lol

14 is right

15 is right

so only 11 is wrong

[unkempt lagoon]

hmm what should it be

[unkempt lagoon]

thanks

[calm coral]

@unkempt lagoon Has your question been resolved?

[unkempt lagoon]

is 11 A?

<@&286206848099549185>

[opaque harness]

Yes but do you understand why? What is your understanding of what f’ and f’’?

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[hushed crater]

Why can't we further simplify the answer into x = -6 ± 4√3 by diving the top side by 2?

[shadow tendon]

You can

[drifting seal]

what’s your 2s rank

[shadow tendon]

diamond 1

Hbu?

[drifting seal]

i played for a bit over the summer and was gc1 but i quit way back in 2021

i was gc1 in 1s and 3s and gc2 in 2s

[hushed crater]

What is a 2s...

Y'all are getting out of topic 😭

But thanks

[drifting seal]

sorry

rocket league

video game

[drifting seal]

also sqrt(6)/2 ≠ sqrt(3)

[hushed crater]

Why not?

Oh okay thanks I get it now

Radicals just simply break the rule

x = -6 ± 4√6 would be correct right?

So 8√6/2 = 4√6

[drifting seal]

yea

[hushed crater]

Okay thanks

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[snow spire]

Can you help understand what is going on here please?

[snow spire]

Is this long division?

This is from Calculus Made Easy - Silvanus P. Thompson https://www.gutenberg.org/files/33283/33283-pdf.pdf, showing how to differentiate quotients

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[polar grail]

how do i evaluate sin(11pi/12) using sin(x+y) identity

[cunning reef]

5/12 + 6/12 = 11/12

[polar grail]

how do i get an exact value for 5pi/12

[cunning reef]

half angle identity

also jtoh mention

[polar grail]

?

[polar grail]

i aint ever seen that in my life

[swift laurel]

alternatively 11/12 = 8/12 + 3/12

[cunning reef]

its derived from sin2x formula if i remember correctly

[cunning reef]

how did i not see that😭

[cunning reef]

if you did want to use this since sin(5pi/12) > 0 use the positive term

[polar grail]

then i reduce that to be sin(2pi/3 + pi/4) ?

so its got the same denominators as the special triangle shit

[swift laurel]

yes

[polar grail]

do i need to find the related angle for 2pi/3 and then just use that

[polar grail]

what jtoh are u talking abt

sounds like sumn i know i js wanna see if its the same

[fleet verge]

3pi/4 + pi/6 @polar grail

[polar grail]

where did u get that

what

[fleet verge]

That is 11pi/12

And is easier

[fluid oxide]

$\cos(2\theta)=1-2\sin^2\theta$, replace $2\theta$ with $A$

[potent lotus]

@fluid oxide

[fleet verge]

This is not A+B

[fluid oxide]

i was telling them where this half angle formula comes from

[fleet verge]

Oh okay

[fleet verge]

But no half angle formula, he wants a+b, so he gotta use this

[fluid oxide]

right

[fleet verge]

@polar grail have u tried this?

[remote mural]

Hii

Uhm I’m a high schooler

So I chose undergrad student

Is that fine?

[fleet verge]

This channel is occupied, not the place to discuss

Go #discussion

[remote mural]

Oh
I’m sorry I didn’t know

[polar grail]

thats 9/12 and 2/12 yea?

[fleet verge]

Yes, but u just do with the original

Sin(3pi/4) and cos(3pi/4) and same for pi/6

[polar grail]

when im finding the exact values do i replace 3pi/4 with its related angle

so pi/4 if im not wrong

[fleet verge]

Good

But for cos is the opposite

Cos(3pi/4) = -cos(pi/4)

[polar grail]

so it should be this once i put it into the formula?

oh

mb

[fleet verge]

Also is pi/6

[polar grail]

right

[polar grail]

if its pi/4 why is cos negative

isnt that in quadrant 1

[fleet verge]

3pi/4 is second quadrant

And how is cos in second quadrant?

[polar grail]

ohh

wait so just to make sure

anytime i have cos i just switch it to negative?

for this question at least

[fleet verge]

No, it depends where it is

But thats other topic

[polar grail]

well for this question the principal angle is in quadrant 2

so anything cos just becomes negative right

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@polar grail Has your question been resolved?

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[orchid ridge]

ik the -< is like 12 to 12.5 range, but why exactly do we write it like this?

[orchid ridge]

if i were to answer a question thats like “What values have a frequency of 5?”, would I write it like 12-<12.5 in my answers?

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[orchid ridge]

<@&286206848099549185>

[unkempt drift]

that's just bad printing

for $12 \le x < 12.5$

[unkempt drift]

do not write this ever

[potent lotus]

southlander!

[orchid ridge]

ic, thx for that. i was so confused when they wrote it weird like that

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[surreal patio]

small physics question , im really bad at this

[surreal patio]

A nonuniform linear charge distribution given by lambda =
bx, where b is a constant, is located along an x axis from x=0 to
x =0.20 m. If b = 20 nC/m2 and V = 0 at infinity, what is the
electric potential at (a) the origin and (b) the point y = 0.15 m
on the y axis?

i dont understand how to do any of it , status : 1

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[hazy wind]

hey guys how can i differentiate this with logarithmic differentation?

.close

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[potent sorrel]

Why?

[gentle imp]

Are you looking for a proof or intuition

A rigorous proof can get rough

Intuition is simple. Just use linear approximation.
f(x0+dx) = f(x0) + dx f'(x0)

[potent sorrel]

Def intuition

Thanks lol

.close

[gentle imp]

XD

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[remote mural]

Goyda

[dire gulch]

what is the qn?

[remote mural]

Goyda?

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

Yes

[calm coral]

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[wintry echo]

How was the formula for $e^z$ thought up?

[potent lotus]

crazytime

[leaden thunder]

https://www.sciencing.com/history-exponents-5134780/

https://www.britannica.com/science/exponential-function

https://www.jstor.org/stable/2974104

[calm coral]

@wintry echo Has your question been resolved?

[wintry echo]

@leaden thunder Thank you

[calm coral]

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[main sinew]

|sqrt(x)-2| < Σ ?

[calm coral]

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[main sinew]

.close

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[sweet meadow]

how can I solve this using probability laws such as bayes theorem and LOTP?

[sweet meadow]

2/3 is the answer, but idk how to get it

[strange lichen]

well here's the thing

we can't get anything from that statement

because there's nothing to get

show the rest of the problem lol

[strange lichen]

honestly i'd draw a tree

[graceful dust]

you can just write out permutations of A,B,C where A comes after C

there are only 3

and that’s the space after the condition is met

[sweet meadow]

.close

[calm coral]

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[strange lichen]

i always do bayes with tree ngl, makes it very easy to see

<@&268886789983436800>

@remote mural stop

u are from georgia?

[dreamy lance]

They are spamming here right?

[strange lichen]

they sent a link to their discord

thats why i pinged

it was like some russian discord

[calm coral]

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[manic spear]

I need help

[calm coral]

Please don't occupy multiple help channels.

[willow summit]

with what

@manic spear @manic spear @manic spear @manic spear

[drifting seal]

with what

@manic spear @manic spear

[willow summit]

wake up

[manic spear]

AP calculus

[drifting seal]

!da2a

[calm coral]

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/

[willow summit]

what's the question

please don't die

@manic spear wake up

[drifting seal]

good old lhopital

[willow summit]

yea

[manic spear]

I'm in my secondd year of school and I'm in all honor classes

[drifting seal]

use lhopitals rule

[willow summit]

differentiate both sides

no

[willow summit]

the nominator and the denominator

[manic spear]

Gro

Bro this is hard

[drifting seal]

nah

do you know lhopitals rule

[manic spear]

I'm only in 10th grade yall

[drifting seal]

yo you just keep throwing questions in

answer one at a time

[manic spear]

Lol

So the first on would be B

I feel it's 2 but at the same time im not sure

[drifting seal]

$\lim_{x \to \pi} \frac{-\sin(x) + 2\cos(2x)}{2x} = \frac{1}{\pi}$

[potent lotus]

knief

[drifting seal]

yep so B

if you know then why are you asking?

[manic spear]

But like how did I get be

B

[drifting seal]

here

[manic spear]

I have a lot of qyestions to do on this sheet todays the last day of the tri

[drifting seal]

nice

trimester

haven’t had a trimester since elementary school

[manic spear]

lol, it's end of terms

Now the second one too

[drifting seal]

do you get how i got this

[manic spear]

Not realy

[drifting seal]

it was 0/0 from direct substitution

[manic spear]

Oh

[drifting seal]

whenever you encounter a 0/0 or inf/inf using direct substitution we get the following

[manic spear]

Oh

I now see

[drifting seal]

$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f’(x)}{g’(x)}$

[potent lotus]

knief

[drifting seal]

@manic spear

do you need to do the next one now

[calm coral]

@manic spear Has your question been resolved?

[calm coral]

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[still meadow]

need help! im dying

[leaden thunder]

Use logs

[still meadow]

ik that part but idk how to start off

[leaden thunder]

Do you know how to write 70db and 50db in terms of logs

[still meadow]

no

[leaden thunder]

https://youtu.be/twppI9Eizp8

[still meadow]

gonna start with that, will come back if need more help

thanks

.close

[calm coral]

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[finite oasis]

Does E(XY)= E(X)E(Y) imply that Y and X are independent? I am a bit confused by this

[torn gorge]

no

[finite oasis]

Go on?

[finite oasis]

But intuitively, what is that really saying. How exactly is covariance being 0 and the two variables being independent differ if you could describe it in some analogous fashion

[torn gorge]

I can't answer as I don't have a clear idea either

it seems like independence is a condition on every pair of events... meanwhile covariance being 0 is a single request on the average behaviour

so the latter must be in some sense weaker

[calm coral]

@finite oasis Has your question been resolved?

[ancient thistle]

you can get independence if you require a bit more

Ef(X)g(Y) = Ef(X) Eg(Y) for a large enough class of functions f

[calm coral]

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[lean bay]

I'm stuck on question b

I just don't understand how I'm supposed to solve it

the topic is trig identities

[glacial lily]

What does the right hand side say?

[lean bay]

0.9

[glacial lily]

Oh okay

How do you normally solve these kinds of questions?

[lean bay]

uhhh we use trig identites and replace the cos/sin

/tan

[glacial lily]

I like to solve them by drawing a small unit circle

[lean bay]

ohhh unit circles i find them confusing

[manic sandal]

i tried to use cos angle sum identities, but didn’t really turn into anything useful so uh

[glacial lily]

Okay that's fine we can find another way

[glacial lily]

Maybe we should rewrite it as:
0 < x < 540
cos(x) = 0.9

If you draw the unit circle you can just count how many cycles it takes

Not sure how to find a nice solution otherwise

[manic sandal]

oh inverse trig function why over complicate so much 😔

[lean bay]

i still dont get it......

it keeps giving me the wrong answer

[manic sandal]

what are you getting right now?

[lean bay]

guahtmath told me the answers were x = 30, 90 and 150. but it didnt tell me how to get there

[glacial lily]

It only gives 1 solution though

[lean bay]

i have a test on trig identites tomorrow

and i dont wanna be stuck on the same type of question

[manic sandal]

that’s not right

[lean bay]

is it not..

oh

[manic sandal]

cos(90) = 0

not .9

[lean bay]

cos3x = 0.9

[glacial lily]

Maybe it's 0 * 9

[lean bay]

i needa get x on its own

[glacial lily]

No, no

[lean bay]

nahh we dont use that in the wjec exam board

[lean bay]

oh?

[manic sandal]

where x = 30

[lean bay]

wh#

[manic sandal]

i checked these

and none work out to .9

[lean bay]

really?

[manic sandal]

yes

those all will line up other values on the unit circle and none are .9

[lean bay]

oh

[zinc plover]

it's just 1/3x arccos(0.9)

[lean bay]

whats arccos

[manic sandal]

inverse cosine

[zinc plover]

cosine inverse

[lean bay]

OH

[manic sandal]

i wasn’t sure if ur allowed to use it tho

[lean bay]

i am dw

[zinc plover]

that is one of the solutions

[manic sandal]

alright

[lean bay]

wait so

how would it look

[manic sandal]

others are + 2kpi/3 where k is an integer

[zinc plover]

theres 2 more which is 2pi/3 - 1/3arccos(0.9) and 2pi/3 + 1/3arccos(0.9)

ye

[lean bay]

guys im in year 12 pls...

[zinc plover]

hold old is year 12

how

[lean bay]

16

[glacial lily]

I was 12th grade like 4 months ago

[zinc plover]

yeah you should be able to do this

[lean bay]

I know yall it just a little confusing

[zinc plover]

do you even know inverse trig

without it you can't solve these

so learn that first

[glacial lily]

They thought us to do this in 12th grade

[lean bay]

unit circle

[glacial lily]

Drawing a snail and counting the cosine's positive parts which are first and fourth quadrant

[lean bay]

YES I K WHAT IT IS

[glacial lily]

And every dot that is in a line has 360 degree difference if you want to find their values

[lean bay]

did you guys get 8.61 or 72.54 as an answer

[zinc plover]

i literally gave you the answer above

[lean bay]

where

[glacial lily]

^

[lean bay]

yeah i dont understand tho..

[zinc plover]

yeah that implies you dont know inv trig

[lean bay]

WHERE DID THE PI COME FROM

inv trig is like cos^-1 right

sin^-1

[manic sandal]

yea

[zinc plover]

do you even know what principle domain is

[lean bay]

nope

[zinc plover]

yeah so LEARN INV TRIG first

[lean bay]

im from the uk maybe we have a different curriculum

I KNOW HO WOT USE INV TRIG

[zinc plover]

you clearly dont

[lean bay]

i just dont undertstand the way u wrote it

and how pi randomly appeared

[manic sandal]

trig functions are periodic

[lean bay]

periodic...

[manic sandal]

repeats over and over again.

[lean bay]

oh

[manic sandal]

up and down and up and down

[lean bay]

ohhh yeah

[manic sandal]

the period of cosine is 2pi

[lean bay]

it is? we havent learnt that yet

[manic sandal]

uhhh

[zinc plover]

you dont know that and you claim to know inv trig

😭

[lean bay]

inv trig sin^-1

i know that part

[zinc plover]

wow!!1

omg you know inv trig

👏

[lean bay]

uhm

[glacial lily]

Not nice

[lean bay]

i just need help with this question😢

[manic sandal]

$cos(3x) = .9 \ 3x = arccos(.9) \ x = \frac{arccos(.9)}{3}$

[lean bay]

DOLLAR SYMBOL???

HELLO??

[manic sandal]

it’s a latex bot

idk why it isn’t working tho

[glacial lily]

I think you should first study the sine and cosine functions' properties

[manic sandal]

bot is being dumb 😐

[lean bay]

our curriculums might jsut be different

[glacial lily]

Do not put spaces around $

That tells the bot to not send the result image

[lean bay]

OH I UNDERSTAND

[potent lotus]

Climb

[lean bay]

cos^-1(0.9) / 3

[manic sandal]

yes

[lean bay]

8.61

[manic sandal]

okay good

[lean bay]

I GOT THAT

when i first did it

[manic sandal]

but there are other solutions

[lean bay]

but i thought i was wrong

[glacial lily]

Now that I think of it

They thought us the period of the functions in the form: Csin(Bx), Ccos(Bx), Ctan(Bx)

2pi/B, 2pi/B, pi/B respectively

[manic sandal]

taught but yea same here

[glacial lily]

You should know this to solve it

[lean bay]

h..............😨 ...

[lean bay]

they havent taught us that yet

IM IN YEAR 12??

[manic sandal]

,w cos(3x) = .9

[potent lotus]

Results provided by WolframAlpha

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

Requested by climb.

[manic sandal]

wolfram being extra but

[lean bay]

woa

[glacial lily]

Perhaps you weren't listening to the class, I don't see any other way of solving this

[lean bay]

i was DEFINITELY listening dw they for sure havent taught us the 2 pi thing yet

[manic sandal]

okay then ur fine i would talk to your teacher

[lean bay]

alra

[glacial lily]

,w cos(3x)=0.9 where 0 < x < 540deg

[lean bay]

hope i dont fail tomorrow😇

[potent lotus]

Results provided by WolframAlpha

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

Requested by oguzhanumutlu

[lean bay]

ohhh yeah

[manic sandal]

0 to 180

[glacial lily]

Was it 540

[manic sandal]

nah

[lean bay]

180

0 - 180

[glacial lily]

Oh I was like why are there so many solutions

cos(3x)=0.9 where 0 < x < 180deg

,w cos(3x)=0.9 where 0 < x < 180deg

[potent lotus]

Results provided by WolframAlpha

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

Requested by oguzhanumutlu

[manic sandal]

3 solutions

[lean bay]

thank you guys IM NOT FAILING WOOHOO

[manic sandal]

alrighty

[glacial lily]

Wait was this your exam

[lean bay]

my test is tomorrow

[glacial lily]

Oh okay good luck

[lean bay]

thank you😓

[manic sandal]

no thanksgiving break

rip

[lean bay]

wtf is thanksgiving

thats not a thing in the uk.......

[manic sandal]

holiday in america right now

[lean bay]

lucky..

i wanna be on holiday'

[alpine solar]

i'm celebrating thanksgiving w my family rn lmao

[manic sandal]

se

same

lions winning

[lean bay]

LUCKY...........................

thanks yall tho forthe help

how do i close this

.close

[calm coral]

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[calm coral]

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[sturdy edge]

Hello

[sturdy edge]

I used this method for variation of parameters

But this question made me kinda confused

[sturdy edge]

Does that method works for it too or just for 2nd derivative ? And is it really good to use such a method ? cuz I think with higher order DEs it will take alot of time to find the determinant of W

[calm coral]

@sturdy edge Has your question been resolved?

[calm coral]

@sturdy edge Has your question been resolved?

[sturdy edge]

Hi

[sturdy edge]

I use this rule for finding 2nd order y_p part for variation of parameters

Can we expand this rule to apply to any higher order DEs?

Chatgpt gave me this but I wanna make sure it is mathematically applicable for any problem

<@&286206848099549185>

Sorry for pinging

[calm coral]

@sturdy edge Has your question been resolved?

[calm coral]

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[primal flume]

I need to find the module of z which is a complex number and the arg (z) using trigonometry (basically i need to simplify the expression and write z in the trigonometric form). I've tried a lot of ways but without success

[calm coral]

@primal flume Has your question been resolved?

[gray smelt]

Simplify inside before applying power

multiplying and dividing by denominator's conjugate

once simplified find arg(z) and also trig form,

[primal flume]

I tried that but seems to go nowhere, maybe i made a mistake

Just to be sure i should have
(1+i)(1+√3-(√3-1)i) Divided by (1+√3)^2+(√3-1)^2. Right?

[gray smelt]

yes

[primal flume]

Yeah so clearly i made a mistake, now i ve gotten to the correct answer.

Thanks

[gray smelt]

np

[primal flume]

.close

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[trim elm]

I have constructed the figure, my question is
in the first subpart, it says measure the angle
How can I measure it without Protractor?

[dusky flax]

straight edge (scale/ruler) and compass

[trim elm]

is it possible to measure the angle with them?

[dusky flax]

hold on

[trim elm]

ok

[dusky flax]

did you learn how to construct angles like 90 degrees?

[trim elm]

yea

[dusky flax]

so first you need to construct 90 degrees

and then bisect it

[trim elm]

yeah I have drawn the figure

now it says to measure the angle

[dusky flax]

where?

[trim elm]

which idk how to measure without protractor

[trim elm]

lemme show wait

@dusky flax

[dusky flax]

but they didnt ask to measure anything

only to construct

[trim elm]

no no in the subpart (i), they told to measure

BCD

[dusky flax]

they asked to construct without protractor

but you can measure with protractor

[trim elm]

Oh I see

Got it thanks for the help and sorry I didn't understand the question properly

.close

[calm coral]

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[sullen skiff]

Where did this - 8y come from?

[gray smelt]

(a-b)^2 = a^2 + b^2 - 2ab

[sullen skiff]

Huh

[gray smelt]

?

[sullen skiff]

Oh lmao

I forgot that one

[errant grove]

bros are cooking

[sullen skiff]

Thanks

[calm coral]

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

[sullen skiff]

.close

[calm coral]

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[hybrid solar]

Let A toss a coin 10 times and B tosses a coin 9 times....Find the number of different ways they can toss the coins if number of heads obtained by A is greater than number of heads obtained by B.

[oak elm]

Let's simplify the problem... How many combinations would there be if 10 head were flipped by A?

You repeat the same process for decreasing number of heads spun by A

[calm coral]

@hybrid solar Has your question been resolved?

[calm coral]

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[minor seal]

im hopeless at math help me pls

[pseudo wedge]

!status

[calm coral]

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

[pastel sapphire]

help pls?

answer is 70

[oak elm]

You just find the area under the lines and subtract the area above the line, ie between the x-axis

We can clearly see that (0-3)t=(3-6)t

Therefore we just cancel out 0-6, the area we must find is 6≥t≥10

You can seperate the area between 3 rectangles and 1 square

Then just calculate for each individual area of the shapes

[calm coral]

@minor seal Has your question been resolved?

[calm coral]

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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.

[hollow geode]

find $sin \alpha \pm \beta$ and $cos \alpha \pm \beta$ if sina 8/17, cosB = 4/5
0 < a < 90; 0 < B < 90

[potent lotus]

asm

[hollow geode]

my bad I wrote it wrong

$sina(\alpha \pm \beta)$ and $cos(\alpha \pm \beta)$

[potent lotus]

asm

[remote mural]

If sin(a) = 8/17, then sin^2 (a) = 64/289
1 - sin^2 (a) = 1 - 64/289 = 225/289
cos^2 (a) = 225/289
cos(a) = 15/17 (can't be negative).

[hollow geode]

oh I see

then you can just apply the formula right

[remote mural]

Yup.

[hollow geode]

for sin a + b

yea alright

thank you 👍

.close

[calm coral]

Channel closed

Closed by @hollow geode

Use .reopen if this was a mistake.

[remote mural]

Ni problem

[pastel sapphire]

pls any1?

[wooden tinsel]

Won't it be 0?

[pastel sapphire]

the answer is -9

value of m

[wooden tinsel]

As after that area is negative

[pastel sapphire]

ye

[calm coral]

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.

[wintry echo]

$$
I = \int_{0}^{\infty} \frac{e^{-x^2} \cdot \sin(x) \cdot \cos(x) \cdot \ln(x) \cdot \sqrt{x}}{x^2 + 1} , dx
$$

[potent lotus]

Scruffy

[wintry echo]

How to solve this ?

[wet urchin]

yea ngl that looks like something

i would avoid doing

what have u tried

[wintry echo]

I don't know where to start

[wet urchin]

i would bring x^2 + 1 to the top

[atomic quarry]

You dont solve integral

[wet urchin]

to avoid quotient rule

[atomic quarry]

You evaluate integral

[wet urchin]

thats just

not what that symbol means

|

[wintry echo]

$$
I = \int_{0}^{\infty} {e^{-x^2} \cdot \sin(x) \cdot \cos(x) \cdot \ln(x) \cdot \sqrt{x}x^2+1}, dx
$$

[wet urchin]

means evaluate

[potent lotus]

Scruffy

[wintry echo]

Then

[wet urchin]

hm

[atomic quarry]

He wrote solve

[wet urchin]

yes

solve the integrakl

lol

[atomic quarry]

Its wrong verb

[wet urchin]

it really isnt

but this is just semantics

[wintry echo]

So the exercise can't be done?

[wet urchin]

def

no it can

[wintry echo]

Because it says calculate

Nice

[atomic quarry]

It can be evaluated

[wintry echo]

In fact it seemed impossible

[wet urchin]

give me a min

[atomic quarry]

Lemme see

[slender gate]

You moved it up wrong

[wet urchin]

im gonnna put it through a integral solver to help u

[atomic quarry]

I dont like this method

[wintry echo]

Why

[slender gate]

Nah there’s fs a trick to this

[wet urchin]

im not gonna give him the solution

just give him hints

[wintry echo]

But the integral seems oscillating to me

[slender gate]

It prob diverges or smth ☠️

[wintry echo]

If I put +∞ I have everything that varies

[atomic quarry]

Lemme see

[wet urchin]

😭

5 hours of alegbra

for it to diverge

also

[atomic quarry]

Prob Just use wolfram

[wet urchin]

this is not solvable

[atomic quarry]

[wet urchin]

on a pretty advanced

math tool

so

[atomic quarry]

Really?

[wintry echo]

He said it can be done

I trust him

[wet urchin]

it might not

be able

to get done

i mean

[atomic quarry]

Who

[wintry echo]

You

[atomic quarry]

I didnt

[wet urchin]

are there any like calc wizards in this server

who like really hard problems

thats ur best bet

[wintry echo]

.

[wet urchin]

yea i was lokey just being optimisitic

[pastel light]

Where is this question from?

[atomic quarry]

Whats this , Just use wolfram

[wintry echo]

Why can't it be solved?

[wet urchin]

idk how to use it

u do it

[atomic quarry]

...

i Guess so

[wintry echo]

Maybe I can see on chatgpt

[atomic quarry]

No

[marble pendant]

!nogpt

[calm coral]

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).

[pastel light]

chatgpt is probably more clueless than you are

[pastel light]

.

[atomic quarry]

Are you a bot or something?

[wintry echo]

Okay

[marble pendant]

im not lmao

[wet urchin]

i dont think this integral has a expressible solution in elementary functions

[atomic quarry]

You literally spawned like this

[wet urchin]

at the very least

[marble pendant]

somehow i opened the chat as soon as he said gpt

[wintry echo]

I took this exercise from chatgpt

[wet urchin]

u

[atomic quarry]

[pastel light]

Well there you go

[wet urchin]

gpt gave him a unsolvable integral

thats funny afg

[atomic quarry]

[marble pendant]

bro there are many books you can refer

[wintry echo]

I wanted to raise the difficulty a little

[marble pendant]

if you wanna learn integration

instead of gpt

[pastel light]

or just google

[wintry echo]

Wait I'll go and see

[wet urchin]

u can simplify sin(x)cos(x) to 1/2 sin(2x)

if ur serious about trying to solve this

[wintry echo]

It doesn't solve it gg

What am I doing

[pastel light]

futile effort imo, just forget about the question and get problems from better sources

[atomic quarry]

Tell him to give you the wolfram code

[wet urchin]

yea your right

[atomic quarry]

@wintry echo

[ebon pagoda]

yeah it does look like some slop it would say when asked "give me a very hard integral to solve"

ofc it has no way to actually gauge the difficulty and whether it's solvable, in a closed form expression

[wintry echo]

Wolfram solved it

integrate e^(-x^2) * sin(x) * cos(x) * log(x) * sqrt(x) / (x^2 + 1) from 0 to infinity

[atomic quarry]

,w integrate e^(-x^2) * sin(x) * cos(x) * log(x) * sqrt(x) / (x^2 + 1) from 0 to infinity

[potent lotus]

Results provided by WolframAlpha

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

Requested by jandro0103

[wet urchin]

its ln

x

not log

[ebon pagoda]

numerical integration exists

[remote mural]

Interestingly Desmos gave the same float here, but I am not sure if it has a "nice" representation.

[ebon pagoda]

it's what WA defaults to when it can't figure out a closed form expression

[marble pendant]

doesnt matter that much

[wet urchin]

i guess

[atomic quarry]

Wolfram doesnt use ln

[wintry echo]

So are there any integrals that cannot be solved manually?

[wet urchin]

i see

[marble pendant]

ofc

[wet urchin]

many

[wintry echo]

$$
\int_{0}^{1} x^2 e^x , dx
$$

[potent lotus]

Scruffy

[wintry echo]

This one is done in parts right?

[atomic quarry]

Thats Easy

[wintry echo]

I lowered the difficulty

[ebon pagoda]

yes, for instance sin(x)/x has no antiderivative in terms of elementary functions, there's a way to precisely say this: https://en.wikipedia.org/wiki/Nonelementary_integral

[atomic quarry]

Can you do this ?

[ebon pagoda]

yes.

[atomic quarry]

Do you know how to use IBP?

[wintry echo]

Mmm yes

[atomic quarry]

You can also use DI method there Is a shortcut

Derive x^2 until you get to 0

[wintry echo]

$e^x*x^3/3-\int e^x x^3/3$

[potent lotus]

Scruffy

[wintry echo]

Looks easy

There is integration by parts and this is it

This was easy

[remote mural]

I think you went the wrong direction. Try making u = x^2 and dv = e^x

[wintry echo]

but I'm done

I applied the formula correctly

[remote mural]

But now you have to integrate e^x * x^3 which is even more time consuming

[wintry echo]

Why?

[leaden thunder]

Try to integrate it and see

[calm coral]

@wintry echo Has your question been resolved?

[wintry echo]

see what?

Why didn't I finish?

[leaden thunder]

Wut

[calm coral]

@wintry echo Has your question been resolved?

[wintry echo]

?

why

I just don't understand why I haven't finished

<@&286206848099549185>

Georg Friedrich Bernhard Riemann help me pls

[atomic quarry]

Bro Is cooked

[wintry echo]

What

Is this the whole solution?

[heady rapids]

Yep.

[atomic quarry]

<@&268886789983436800> ai user

[ebon pagoda]

!nogpt

[calm coral]

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).

[wintry echo]

Thank you

What

Where did it end up

@heady rapids

[ebon pagoda]

I deleted it, for one we don't encourage people to post whole solutions since it may incentivize cheating (not saying this is the case here)

[wintry echo]

How to know 100% who used chatgpt

[ebon pagoda]

it's easy to recognize LLM output

from the mannerisms in writing and because often users copy-paste the entire thing which leads to math being all funky

[atomic quarry]

Why did he have to insert random [ , ]?

[ebon pagoda]

and looking like multiple lines where one line suffices

[wintry echo]

Maybe he used chatgpt to write better

[ebon pagoda]

I'm not sure if discussing this is productive -- either way feel free to use GPT yourself to see what it has to say about your problem

[ebon pagoda]

our only issue here is with users using AI tools to "help" people here, often by lazily handing out solutions that might even be inaccurate or wrong

[wintry echo]

Right

Can a human help me pls

<@&286206848099549185>

[leaden thunder]

#help-42 message

#help-42 message

[wintry echo]

I mean why I haven't finished ?

Isn't it enough that I use this?

@leaden thunder