help-13

[cerulean sail]

,w diff arcsin(x)

[wraith dagger]

Results provided by WolframAlpha

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Requested by chartbit#3171

[cerulean sail]

You seem to have done it right but written it wrong here though

Also here the way you've written it (keeping the integral sign after you've integrated, and also forgetting to divide by the power here as well)

Otherwise no real complaints

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

Cries TYSM charbit

🌊🌊🌊🌊

[cedar kiln]

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[knotty panther]

Find the four fourth roots of
− 128 + 128 sqr3 i.
(Give your answer in the form a + bi, where a and b are real numbers. Enter your answers as a comma-separated list.)

[knotty panther]

How would I be able to solve that?

[dire geode]

write it as $re^{i\theta}$ first, then take the fourth root

[wraith dagger]

riemann

[knotty panther]

Ok I understand now thank you

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[rich blaze]

Problem regarding Determinants and its properties

[bright bridge]

[rich blaze]

Det(M) =1 and Det(2M)= 16. What is the dimension of the matrix M?

I'm reading the properties of the determinants, but I dont know how I could figure that out

[karmic cedar]

Uh

Maybe do like det(cIA)

And separate them

And c is a number like 2

[rich blaze]

mmm

I don't get it

isn't 2IM just 2M ?

[karmic cedar]

Yeah but then you can’t find the dimensions

What is the determinant of cI

Det(cI)Det(M)

[rich blaze]

mmm

det(cI ) = c1

right

since det(I) =1

[karmic cedar]

Uh

Ok so I is just a long diagonal of 1s in a matrix right

[rich blaze]

yes

[karmic cedar]

And if you multiply it by c it’s just a long diagonal of c

[rich blaze]

oh, right

[karmic cedar]

The determinate of this long diagonal of c is just the cs multiplied by however many rows and columns

And since c is 2

C has to be multipled by however many rows/columns to equal 16

[karmic cedar]

Yeah

I think that’s how u do it

[rich blaze]

yeah, its right, thank you a lot

[karmic cedar]

Np

[rich blaze]

👍👍👍🥺

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[granite knoll]

you didn't get the right exponents

[granite knoll]

well, for the first term

yes

[rain drift]

Remember this rule: $(a^b)(a^c) = a^{b + c}$ and $(a^b)^c = a^{b \times c}$

[wraith dagger]

MellowDramaLlama

[rain drift]

yep bingo 🙂

[granite knoll]

the second term was fine

[rain drift]

Sorry yes that's correct

nice work 🙂

So this one it's supposed to be $8t^{-\frac{3}{2}}$ rather than $8t^{\frac{3}{2}}$

[wraith dagger]

MellowDramaLlama

[rain drift]

that's probably why the 2nd answer is incorrect

yep np!

[cedar kiln]

@opaque mantle Has your question been resolved?

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[turbid spoke]

how i can solve this

[bold anchor]

Are you able to screenshot the entire thing?

[runic garnet]

Are u asking how they got 1/3 - 1/6?

They plugged in the upper limit into the expression

[bold anchor]

If you pretend that the expression inside the brackets is g(x), then it's g(1/2)-g(0)

[turbid spoke]

If I understand that part, the problem is evaluating it, I don't get 1/6

how i can evaluate this

[bold anchor]

Plug in 1/2 in for x

You can also pretend that the 3/2 on the bottom makes the equation sqrt(2)x^(3/2) * 2/3

Strange syntax they used, but it's not incorrect.

[turbid spoke]

how i can get 1/3

i dont understand

[bold anchor]

It's from the 3 in the denominator.

Have you evaluated (1/2)^(3/2)?

[turbid spoke]

yes

[bold anchor]

What did you get?

[turbid spoke]

4(1/sqrt2)/3

[bold anchor]

So $$\frac{4}{3\sqrt{2}}$$?

[wraith dagger]

MJames31

[turbid spoke]

$$\frac{4(1/sqrt2)/3}$$

[wraith dagger]

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

[bold anchor]

Is that what you got for the entire term, or just the x

[turbid spoke]

only

[bold anchor]

Ignore the sqrt(2) and the 3/2

What is (1/2)^(3/2)?

[turbid spoke]

1/sqrt2

[bold anchor]

That would be (1/2)^(1/2)

[turbid spoke]

?

[bold anchor]

$$(\frac{1}{2})^{\frac{1}{2}}=\frac{1}{\sqrt{2}}$$

[wraith dagger]

MJames31

[bold anchor]

But you want

$$(\frac{1}{2})^{\frac{3}{2}}$$

[wraith dagger]

MJames31

[turbid spoke]

i use radicalization i dont understand

[bold anchor]

The 3/2 power means you need to square root the 2, but also cube it.

[granite knoll]

$x^{3/2} = \sqrt{x^3}$

[wraith dagger]

cwatson

[bold anchor]

Correct.

[bold anchor]

Your work was good up until the last line.

Since 2 times sqrt(2) isn't sqrt(4)

You can't combine them since one is being operated on by the sqrt

[turbid spoke]

is equivalent?

[bold anchor]

Technically yes, but there's not actually a reason to radicalize this specific equation.

[turbid spoke]

what property is that?

why you move the two to radicalize

[bold anchor]

It's just how exponents work

1/2 is to the 1/2 power, which is the same as square rooting it.

[turbid spoke]

does that always work?

[bold anchor]

Yes, just be careful of syntax.

[turbid spoke]

what syntax

[bold anchor]

How the symbols appear in what order

[turbid spoke]

wdym

[bold anchor]

(3/4)^3 is not the same as 3^3/4

But yes, it's just an extension of the distributive property.

[turbid spoke]

thx for help me

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[fading forum]

hi im a bit confused. can someone guide me? thx

[cedar kiln]

@fading forum Has your question been resolved?

[long swan]

i don't like the way this is written, sort of confusingly worded.

allow me to translate:

Find the plane with the point a and the line l contained within it

let me just give you a high level overview

1. Find the direction vector of the line, let's call this v_1.
2. Find the other direction vector of the plane by choosing a point l_0 on the line. Then your second plane vector is "a-l_0". Call this v_2.
3. Your normal vector to the plane is given by v_1 x v_2.
4. Solve for p by plugging in the point a.

[fading forum]

ahhh

[fading forum]

just curioius, do you think this can be solved any way without the use of cross product?

[long swan]

sure but it's basically doing the same thing.

let A be the matrix [v1, v2] where v1, v2 are column vectors

then just find Nul(A^T)

this gives the orthogonal complement of Span(v1,v2)

[fading forum]

wait whatttttttttttt

i dont think i have learnt these haha

[long swan]

I gave you the lin alg answer and the calc 3 answer

[lunar saddle]

if anyone can help with this please

[long swan]

What more do you want

@lunar saddle #❓how-to-get-help

[fading forum]

yea its fine thanks

.close

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[atomic ember]

I need a little help, I haven't done math in a very very long time.

[atomic ember]

How do I simplify this

[dire geode]

https://www.cuemath.com/foil-formula/

[livid hound]

multiply numerator and denominator by lcd

[atomic ember]

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[plush shore]

can anyone help me figure this out

ive been testing multiple entries and cant ifgure it out

[cedar kiln]

@plush shore Has your question been resolved?

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[flat kayak]

Wondering if anyone can explain what to do in this problme

[flat kayak]

I know you’re supposed to do y=mx+b

But I’m confised

Usually the teacher would have a video that teaches this part. But there isn’t a video

[short blade]

do you know what a piecewise function is

[flat kayak]

Kinda

It’s the one subject I’m kinda struggling on

[short blade]

it just defines what the function is piece by piece, so piece-wise

look at your graph and consider the part where x is greater than or equal to -1

[flat kayak]

Okay I’m looking at it

[short blade]

that should be a function you’re familiar with

[flat kayak]

|x|

?

[short blade]

yes, but shifted around

[flat kayak]

|x|-2

[short blade]

your goal is to find what those transformations are, what the stretch, horizontal and vertical shift are

[short blade]

almost

[flat kayak]

2|x|-1.9

[short blade]

2|x|-2

[flat kayak]

Dang

Okay give me a second

[short blade]

idk why it’s weird like that on the bottom

but anyways, there’s not much more to explain

[flat kayak]

Yeah

[short blade]

you just do the same thing for the left side

find the function

[flat kayak]

Give me a second and I’m gonna try to solve the next one

-(x+2)^2+2

[short blade]

looks right

[flat kayak]

Sweet

You made that seem easier

Can I ask you another question. I think I might have the answers

[short blade]

yes

[flat kayak]

So setting up an equation

Would it be like 6()^x

Well I guess for the first one

6^x-4

[short blade]

(6^x)-4 yes

[flat kayak]

Then the second one would be (6-9)^x

?

[short blade]

no

if we shift to the right by k units we do f(x-k)

[flat kayak]

6(x-9)?

With it being squared by x

[short blade]

raised to the x-9

but yes

[flat kayak]

Wait

6^(x-9)

?

[short blade]

yes

[flat kayak]

Trippy

Then for the last one

-6^x

[short blade]

no

that’s reflection about the x axis

[flat kayak]

-x?

[short blade]

6^(-x) yes

[flat kayak]

Okay

So the outside - is for the reflection of c

X*

And inside is the reflection of y

[short blade]

reflection about the x axis

and reflection about the y axis

[flat kayak]

Gotcha gotcha

[fluid ember]

... hard

[flat kayak]

Dude I be struggling

Thank you

@short blade

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[crimson sedge]

is the e in here the e used in ln(e)

[mighty drift]

What other e could it be ?

e comes up a lot. Get used to that fact

[crimson sedge]

ok

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[tidal wasp]

this is what i have tried

the answer is coming out wrong

nvm i found the mistake

here

lemme try again now 😭

bruh found another mistake 💀

[meager jungle]

tbh

id just use the fact that B is the midpoint of AC

[tidal wasp]

then use the midpoint formula?

[meager jungle]

idk if thats a formula

[tidal wasp]

yeah ig we can do that too

[tidal wasp]

there is one

[meager jungle]

(a+b)/2?

[tidal wasp]

yup

[meager jungle]

pretty much common sense

[tidal wasp]

ig using this also makes sense

[meager jungle]

thats the same thing

[tidal wasp]

yeah i meant using B as a mid point would make sense aswell

fixed my method tho

the answer is correct

these silly little mistakes are someday gunna be the death of me

but thx for the help!

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[hollow trail]

what’s the question here

[safe smelt]

I didn't understand the question either.

[thin galleon]

to show that the function has derivatives of all orders?

[safe smelt]

I guess

[hollow trail]

is this something you were assigned?

[safe smelt]

No, teacher. These are the questions I solved to prepare for my exam.

Teacher, I have thrown the whole problem to you.

[thin galleon]

we are all learning

[sullen saffron]

It's not a question. It's an example by the author to show you something they think will be useful for you to think about.

[thin galleon]

what is the big idea of this?

[crimson sedge]

its been a long time coming

its fearless

BIG REPUTATION

and they said speak now

into folklore

IM TAYLOR

I WAS BORN IN

1989

Evermore..

LOVING HIM WAS RED

NICE NICE

LOVERRR

MIDNIGHTS

ITS BEEN A LONG TIME COMING

[thin galleon]

awesome, it's a poem

[safe smelt]

I don't understand

[thin galleon]

i just meant that i think we are all learners, and there is a lot to understand from this problem

there are different ways to approach it

[safe smelt]

You're right. Can you solve my question?

[thin galleon]

i can try!

i don't understand most of what is written there, where would you use the f(x) function in life?

[hollow trail]

a similar function is actually used to define the gaussian distribution

[cedar kiln]

@safe smelt Has your question been resolved?

[safe smelt]

Please someone help me?

[thin galleon]

is e^(-1/(x^2)) the "Gaussian function" or "bell curve"?

[thin galleon]

@safe smelt what do you want to understand about this problem?

you can also use <@&286206848099549185> to ping helpers

i tried to visualize the f function in Python, is this correct?

[cedar kiln]

@safe smelt Has your question been resolved?

[granite knoll]

it is not the "bell curve". just google the formula

,w plot e^(-1/(x^2))

[wraith dagger]

Results provided by WolframAlpha

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

Requested by cwatson#5438

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[trim shard]

i need help and you people know how to do it

[trim shard]

im more of a english guy, struggle in math can someone please help me thank you

[thin galleon]

read this book, it is awesome https://www.youtube.com/watch?v=Z0k8F9m2pJ8

[odd snow]

do you know the pythagorean theorem

[trim shard]

lxhxw yeah

[trim shard]

thanks but i need help with math

[thin galleon]

that's why i recommend you to read it

[livid hound]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[trim shard]

1

[livid hound]

which question are you on, 3 or 4?

[trim shard]

both

im doing A first

[livid hound]

do you know the pythagorean theorem

[trim shard]

.

[livid hound]

have you tried applying that here

[trim shard]

dwag i look at numbers and its like looking at arabic

just a bunch of scribbles

[livid hound]

doesn't really answer my question

did you make any attempt to find the length of the green line

[trim shard]

no

dawg

you asked what stage im on

i said 1

that = i dont know what to do

[livid hound]

you said you know the theorem

[trim shard]

no shit

[thin galleon]

you can grow the connections in your brain with struggle, effort, making mistakes, and looking at the problem from many perspectives

[livid hound]

knowing that, you should also know that its directly applicable here

[thin galleon]

math can be super fun

[trim shard]

i know the calculations to the theorem

[livid hound]

what's your issue with applying it here

[trim shard]

NOT when to apply it

holy shit

[thin galleon]

and you can learn math too

[livid hound]

state the theorem

if you know it so well

[trim shard]

literally 0 help from a cord server supposed to be providing help, this is why ur not a teacher lmao

[livid hound]

bold assumption

[livid hound]

word of advice: don't antagonise people spending their time helping

[cedar kiln]

@trim shard Has your question been resolved?

[shrewd gust]

thats so nice of you!, a lot of people here are phds in maths, and the probability of your bs being put up with will still be null

[cedar kiln]

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[gilded rain]

2 2 2 2 2=28 have to put an action between each number (not homework or anything) but cant seem to figure it out

[crimson delta]

what actions are you allowed to do

[gilded rain]

like + - / x ^ !

[dusk finch]

parenthesis too?

[gilded rain]

yea

[lyric narwhal]

what about concatenation

it's real easy with concatenation

[gilded rain]

no concatenation

[dusk finch]

I can do it with 4 two's :(

[lyric narwhal]

I can do it with five provided you can use factorials

[dusk finch]

Oh I see

[lyric narwhal]

wait

no

[gilded rain]

?

[lyric narwhal]

it's 4 still

[gilded rain]

yeah

thats why i was stuck

[dusk finch]

oh yh

[tropic oxide]

$(2^{2 \cdot 2} - 2) \cdot 2$?

[wraith dagger]

Ann

[gilded rain]

ooo

i think thats it

[shrewd gust]

what is concatenation

[gilded rain]

i googled it

[dusk finch]

concat(2,5)=25

[lyric narwhal]

2 || 2 = 22

basically joining digits

[shrewd gust]

oh

[gilded rain]

nah

[shrewd gust]

ty ty

[gilded rain]

thats it

tysm guys

.close

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[gilded rain]

1=3
2=5
3=4
4=4
5=3
6=2
7=3
8=5
9=3
10=?

[gilded rain]

yeah

i got lots of them to answer

[tropic oxide]

is this one of those stupid facebook puzzles

or something similar

[gilded rain]

my friend gave me it

[tropic oxide]

this is going to be a long shot but what's your native language

or your friend's

[gilded rain]

i get 20$ if i find it out

עברית

[tropic oxide]

i think there might be something

[gilded rain]

hebrew

[tropic oxide]

okay in that case

can you write out the names of the numbers 1-10 in hebrew

[gilded rain]

אחד
שתיים
שלוש
ארבע
חמש
שש
שבע
שמונה
תשע
עשר

however

u can pronouns and spell them in various ways

[tropic oxide]

it appears that each number on the right is the length of the hebrew name of the number on the left

[gilded rain]

omfg

ur so right

so 3

good thinking my man

or woman

idfk

ty ❤️

.close

[cedar kiln]

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[tropic oxide]

woman is closer

[gilded rain]

.close

why is it still in occupied

.reopen

[cedar kiln]

✅

[gilded rain]

.close

[cedar kiln]

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[gilded rain]

idfk

[lyric narwhal]

it'll move, dont worry

[cedar kiln]

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[cedar kiln]

Please don't occupy multiple help channels.

[cosmic steppe]

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[cosmic steppe]

You already have one

[narrow merlin]

yea

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[forest portal]

I need to find need to find every point on x-axes

Not every point*

[tropic oxide]

надо указать, какие точки соответствуют значениям выражений слева

[forest portal]

-2a скорее всего это K

[tropic oxide]

другим быть не может, да

[forest portal]

Я просто не понимаю, их нужно по рисунку искать или это формулы какие-то

[tropic oxide]

по рисунку конечно

[forest portal]

Просто -2 * 0.75 = -1.5

[tropic oxide]

из рисунка, например, видно, что a лежит между 0 и 1

и ближе к 1, чем к 0

[forest portal]

|a - 1| = M

[tropic oxide]

значит 1/2 < a < 1

о том, что a=3/4, не известно

[forest portal]

Ну я приблизительно считаю, ведь у нас не так много точек

[forest portal]

В случае если a > 1/2, -2a будет меньше чем -1

[forest portal]

А как найти 3^a ?

[tropic oxide]

не надо его находить

однако можно определить интервал, в котором оно находится

[forest portal]

Как?

[tropic oxide]

1/2 < a < 1 => 3^(1/2) < 3^a < 3^1

то есть 3^a лежит между sqrt(3) и 3

[forest portal]

Я точно не помню, но есть ли такой cheat sheet, где объясняеться какое значение будет в a^x, в случаях если 0 < a < 1 , x > 1 ; a > 1 ; x >1

?

[tropic oxide]

функция f(x) = a^x -- строго возрастающая при a > 1 и строго убывающая при 0<a<1

оттуда следует все необходимое

[forest portal]

То есть 1.4 < 3^a < 3

[tropic oxide]

можно и так сказать, т.к. 1.4 < sqrt(3)

сам sqrt(3) ближе к 1.73, если что

[forest portal]

А как понять, N или P?

[tropic oxide]

N слишком близко к единице, чтобы быть больше sqrt(3)

a и N выглядят примерно равноудаленными от 1

[forest portal]

А, хорошо, тогда только P

Спасибо )

[tropic oxide]

да

[forest portal]

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[forest portal]

(log_2(x))^2 - (a - 1) * log_2(x) - a =0

[forest portal]

Need to find min whole a, when the one of solutions of the equation lies on (30; 100)

[tropic oxide]

#help-18 message

уже было

один в один такая же задача

[forest portal]

Я помню вы мне ее объясняли даже

Но я забыл как решать

[tropic oxide]

ну так диалог наш перечитать же можно

[forest portal]

,rccw

[forest portal]

Я ее почти решил, но у меня не сходиться число

[cedar kiln]

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[tropic oxide]

https://en.wikipedia.org/wiki/Cauchy_condensation_test

this can be useful i think

hmm

can't think of anything else

well ok

maybe integral test?

and then you can accomplish basically the same thing with the integrals by substituting e^x

[cedar kiln]

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[lyric narwhal]

hello, I have this expression

[lyric narwhal]

how do I turn it into an integral?

I'm getting confused on what the bounds of integration should be

or what the integrand should be

<@&286206848099549185>

sorry for the ping before 15m, it's a bit urgent

.close

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[sullen spire]

can i get some help for how to approach this

i think that the function is neither injective or surjective

[cedar kiln]

@sullen spire Has your question been resolved?

[astral bay]

well, starting with a i guess

what's the definition of an injective function?

[sullen spire]

f(x) = f(y), x = y

[cedar kiln]

@sullen spire Has your question been resolved?

[astral bay]

...maybe be more specific than that

i don't even know what that means

what are x and y? what's ","?

[cedar kiln]

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[dusk finch]

would be good to see the sequence defined in previous question...

[astral bay]

yeah what's the sequence

[green niche]

oh sorryyyy

[cedar kiln]

@green niche Has your question been resolved?

[green niche]

<@&286206848099549185>

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@green niche Has your question been resolved?

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[dull pewter]

How do I find integer values of x and y that solve this equation

[dull oxide]

Find integers for y that make the right side an integer

Look for a pattern

[dull pewter]

I mean yeah but how

I can just do it with a calculator but how am I gonna form my answer on an exam for example

[frail thistle]

how do you make the right side an integer value

[dull pewter]

Well he just means plugging in integer values of y that gives an integer value of x

[frail thistle]

ok lemme simplify this

for y/3 what values of y would give you an integer

[dull pewter]

Yep

[frail thistle]

?

[dull pewter]

but in this case you have (2+5y)/3

[frail thistle]

yeah but

[frail thistle]

answer this first

[dull pewter]

Ok

Well

I guess it has to be equal to or bigger than 3

[frail thistle]

more specific

y should be a multiple of 3 right

so 3, 6, 9, ...

now what does that say about the 2 + 5y in your problem?

[dull pewter]

My internet just went off

[frail thistle]

damn

[dull pewter]

Ok so

[dull pewter]

Yeah true

I guess 2+5y has to equal a multiple of 3?

[frail thistle]

correct

[dull pewter]

But that could also take some time to find

If you don't get lucky

[frail thistle]

not necessarily

if you start plugging in values

2, 7, 12, 17, 22, 27, 32, 37, 42

do you notice a pattern

which numbers are multiples of 3 here?

y=2, y=5, y=8, etc...
so y=2 + 3k, where k can be any integer

[dull pewter]

Wait

Lemme understand this

Ok so

Then what

[frail thistle]

well

[dull pewter]

Wait is that the y from the equation or just the multiples of 3

[frail thistle]

wdym

that's the y from the equation

2 + 5y

[dull pewter]

Wait this is revolutionary

[frail thistle]

lol

if you plug 2 + 3k in for y in the original equation

[dull pewter]

I dont understand this part

[frail thistle]

you get an equation for the values of x too

[frail thistle]

okay so

[dull pewter]

How you do that

[frail thistle]

if you start plugging in values

for y = 2, it outputs a multiple of 3

for y = 5, it outputs a multiple of 3

and for y = 8, it outputs a multiple of 3

it's pretty easy to see that this pattern will continue, right

for y = 11, y = 14,

[dull pewter]

Yeah

[frail thistle]

etc

so

you notice there's a common difference of 3 between each value of y

[dull pewter]

Yes

[frail thistle]

and the first value is 2

so you can say y = 2 + 3k

if k = 0

y = 2

if k = 1

y = 5

if k = 2

y = 8

for all integer values of k

itll spit out a valid value of y

[dull pewter]

How do you know the first value

[frail thistle]

well

we started from plugging in y = 2

y = 0*

and y = 2 was the first value where we got a multiple of 3

so i'm just using that as the first value

[dull pewter]

OOoh I see

Ok so to recap

You just need the first value that gives you a multiple of 3 or whatever number you have

[frail thistle]

yes

[dull pewter]

then you can just extract the formula thing

[frail thistle]

you should look for a pattern first

like y = 2 y = 5 y = 8

its pretty obvious you're adding 3 to each

[dull pewter]

Yeah ofc

[frail thistle]

and then you can extract a formula for y

in terms of k where k is any integer

[dull pewter]

Ok so question

[frail thistle]

mhm

[dull pewter]

Does the pattern have to be equal to the number we have like in this case we have multiples of 3 and the pattern is 3

[frail thistle]

hmm

[dull pewter]

Youcef88

heard he's a great mathematician

[frail thistle]

im not sure if that pattern persists but

just plug in values of y and you'll find the pattern regardless

[dull pewter]

Yeah it doesn't matter

So is there always gonna be a pattern

[frail thistle]

in these types of questions theres usually some kind of pattern you can find

[dull pewter]

Or can the pattern for example be *3 instead of +3

[frail thistle]

wdym?

hm

for like

y = 1 y = 3 y= 9 y = 27?

[dull pewter]

Yeah

[frail thistle]

off the top of my head i cant think of a case where that would be true, but if you did come across this case you could use that pattern yeah

[dull pewter]

Bro you're like a saver

cuz

To get that formula I had to do so much shit

And now I can just get it quick

[frail thistle]

lol

[dull pewter]

Thx

[frail thistle]

np

[dull pewter]

Youcef88 writing an essay

[frail thistle]

writing his phd dissertation on math in this channel

[lethal coral]

Hhhhhh, Just a hobby and curiosity

[dull pewter]

Naaah man it took you 8 years to write that

[frail thistle]

bro types at 1 wpm

[lethal coral]

Hhhh, my english

For X=5k+4

[dull pewter]

Nah its good man

[dull pewter]

Yeah its easy to get the x value

anyways imma close this

@frail thistle gonna need you

.close

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[kindred hornet]

@radiant topaz if i multiply n-4 by 2 i get (n-4, -3)

[kindred hornet]

which doesnt really make sense

link to the original problem: #help-22 message

[cedar kiln]

@kindred hornet Has your question been resolved?

[astral bay]

how did you get -3?

you have 2n+5 and n-4

n-4 multiplied by 2 is 2n-8

what operation is there on 2n+5 and 2n-8 that gets you -3

[cedar kiln]

@kindred hornet Has your question been resolved?

[kindred hornet]

oh yeah it should be 13

[radiant topaz]

Now there

[kindred hornet]

cool

so the numbers need a gcd of 13 ig

hm not sure how im gonna find these numbers

[cedar kiln]

@kindred hornet Has your question been resolved?

[cedar kiln]

@kindred hornet Has your question been resolved?

[cedar kiln]

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[crimson sedge]

Please explain me everything after b2 - 4ac = labda2

[radiant topaz]

What is even - odd and odd - odd?

[crimson sedge]

Even - odd is odd and odd - odd is even

??

[cedar kiln]

@crimson sedge Has your question been resolved?

[thin galleon]

did you try proving it? what is lambda?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[still oracle]

is every point inside the circle a midpoint of some chord of that circle?

[still oracle]

i believe this is true

since infinite chords

but i need confirmation

[mighty drift]

Yes

Just take the perpendicular to the radius

[crimson sedge]

yes but im not sure about the points on the circle

[still oracle]

typo that was

[mighty drift]

The chord has 0 length

[still oracle]

ah

[crimson sedge]

yeah but like it doesnt feel satisfying

[still oracle]

perpendicular from centre bisects the chord

[mighty drift]

Feel free to exclude it

[still oracle]

that was very obvious nvm

got it

thanks

.close

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[steep umbra]

I need help finding total number of transitive relations from N to N having n elements

[steep umbra]

Here's what I have done till now but I dont know if it is 100% correct

The order of the images is reversed :/

Here i have found non transitive ones then I'll subtract them from the total number of relations

[cedar kiln]

@steep umbra Has your question been resolved?

[steep umbra]

<@&286206848099549185>

[grizzled hawk]

Yes?

[steep umbra]

.

[steep umbra]

.

I want someone to see if my workings are okay

[grizzled hawk]

It is ok but a bit messy.

No offence.

[steep umbra]

i mean is everything mathematically correct?

[grizzled hawk]

I think so.

[steep umbra]

thenks then

.close

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[smoky stump]

Could someone please explain why is it that the line L is not parallel?

and does not intersect?

[cedar kiln]

@smoky stump Has your question been resolved?

[smoky stump]

<@&286206848099549185>

[vague rapids]

Bing Chliing

[cedar kiln]

@smoky stump Has your question been resolved?

[cedar kiln]

@smoky stump Has your question been resolved?

[cedar kiln]

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[bright flame]

I am just genuinely very confused

[bright flame]

Why is the first picture wrong? Or is it not?

I mean the answer is different but I used a correct method right?

also this is it, I forgot the - at some point but still

[cedar kiln]

@bright flame Has your question been resolved?

[lethal bison]

it's the same

they only differ by a constant which makes them both valid antiderivative

as cos^2(x)+sin^2(x)=1

@bright flame

[bright flame]

How do you get that information out of this?

[lethal bison]

you can try plotting the graph

blue is sin^2(x) red is -cos^2(x)

[bright flame]

is it like cos^2(x)=1-sin^2(x) but because of the Constant you have anyway the 1 doesn't matter so cos^2=-sin^2?

[lethal bison]

-cos^2(x)*

[bright flame]

I edited my message, it works like that?

[bright flame]

they look the same but they're off by 1 tho?

[lethal bison]

in this scenario yes because your looking to find the area under the curve

the area stays the same

but I mean

try to take the derivative of -cos^2(x)/2 and sin^2(x)/2

and you'll see they both give same answer

[bright flame]

ah yea I guess you're right on that one

Thanks mate!

.close

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[pearl crest]

How do they get this?

[granite eagle]

1/3 = 3*1/9

also root(ab) = root(a)*root(b)

[pearl crest]

Oh sii i get it now

They made it 1/9 so you can remove the root

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[modest wind]

Help

[granite eagle]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@modest wind Has your question been resolved?

[cedar kiln]

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[summer agate]

.reopen

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[oak pecan]

My working out

Can someone double check thank you much appreciated

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[oak pecan]

4

<@&286206848099549185>

[cedar kiln]

@oak pecan Has your question been resolved?

[cedar kiln]

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[summer kayak]

Compute $∫_{γ} −y^3 dx + x^3 dy$, where γ is the positively oriented edge of the unit circle.

[wraith dagger]

afeAlway

afeAlway

[summer kayak]

So I used Greens and got $\int\int_{D} 3r^2\cos^2(\theta) + 3r^2\sin^2(\theta) dr d\theta = \int_0^{2\pi} d\theta\int_0^1 3r^2 dr = 2\pi$. But the correct answer is $\frac{3\pi}2$

[wraith dagger]

afeAlway

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@summer kayak Has your question been resolved?

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[summer kayak]

Calculate the curve integral $∫_{γ} y dx + x dy$ if γ is the positively oriented edge to the region given by the inequalities x2 ≤ y ≤ x

[wraith dagger]

afeAlway

[summer kayak]

This is what I did using Green's Theorem: $∫{γ} (y, x) (dx, dy) = ∫∫{D} 1-1 dx dy= ∫∫_{D} 0=0$

[wraith dagger]

afeAlway

[summer kayak]

Is this right? You can't integrate 0 with respect to anything so do I say the answer is zero or there is no answer?

[astral bay]

you can't integrate 0
why not?

there's definitely an antiderivative of 0

i don't actually know what a curve integral is but i would think that the integral of 0 is just 0

[summer kayak]

But in this case 0 * dxdy= 0. Which variable do I integrate it with respect to?

[sullen saffron]

You're integrating the function f(x, y) = 0 over the region D.

$\iint_{D} 0 \dd{S} = 0$.

[wraith dagger]

stabulo

[summer kayak]

wdym?

I mean like how does that help me?

in this case

[sullen saffron]

You can write the double integral as the iterated integral

$\int_{0}^{1} \dd{x} \int_{x^2}^{x} 0\dd{y} = 0.$

[wraith dagger]

stabulo

[sullen saffron]

You just destroy the dy and dx part of the integrated integral which does not make any sense to do so.

You effectively just did this:

$\int_{0}{1} \int_{x^2}^{x} 0$

[wraith dagger]

stabulo

[sullen saffron]

This doesn't have meaning unless you understand this to be the above iterated integral and say its obvious it means that as it's the only way to get a numerical output.

[summer kayak]

so are you saying that $∫∫{D} 0 = \int_0^1 dx \int{x^2}^{x} 0 dy = \int_0^1 ( \int_{x^2}^{x} \dd{y})\dd{x} = \int_0^1 [y]_{x^2}{x} dx = \int_0^1 x-x^2 dx = [\frac{x^2}2-\frac{x^3}3] = \frac16$

[wraith dagger]

afeAlway

[sullen saffron]

No.

$\iint_{D} 0 \dd{S} = \int_{0}^{1} \dd{x} \int_{x^2}^{x} 0\dd{y} = \int_{0}^{1}\left[ 0\right]{x^2}^{x} \dd{x} = \int{0}^{1} 0 \dd{x} = \left[ 0 \right]_{0}^{1} = 0$.

[wraith dagger]

stabulo

[summer kayak]

but first of all how is the integral of 0 with respect to y 0? Any why did you do $\int_{D} 0 \dd{S} = \int_{0}^{1} \dd{x} \int_{x^2}^{x} 0\dd{y}$ and not $\int_{D} 0 \dd{S} = \int_{0}^{1} 0 \dd{x} \int_{x^2}^{x} \dd{y}$

[sullen saffron]

This is my code so you don't have to correct it each time
\iint_{D} 0 \dd{S} = \int_{0}^{1} \dd{x} \int_{x^2}^{x} 0\dd{y} = \int_{0}^{1}\left[ 0\right]_{x^2}^{x} \dd{x} = \int_{0}^{1} 0 \dd{x} = \left[ 0 \right]_{0}^{1} = 0

Oh they disappeared anyway.

[summer kayak]

lol why do I get error when I copy & paste your code?

[sullen saffron]

Discord uses _ to make things italic and stuff like that.

[wraith dagger]

afeAlway

[summer kayak]

Okay finally got it correct. So why?

[sullen saffron]

It can be shown the double integral can be calculated as a iterated integral if the region is appropriate, R_x means it can be described by the inequalities a <= x <= b, φ <= y <= ψ.

A double integral is not a iterated integral but it can sometimes be evaluated using one.

[summer kayak]

aha ok but why did you say the integral of 0 is [0]^x_x^2?

[sullen saffron]

The integral of 0 with respect to y is 0.

[summer kayak]

isn't the integral of 0 a constant

[sullen saffron]

We have bounds so it's not necessary to include the constant of integration. You of course can but they will cancel.

[summer kayak]

oh yeah

[sullen saffron]

$[c]_{x^2}^{x} = c - c = 0.

[summer kayak]

True

Yeah thank you so much. I got it now!!

[sullen saffron]

This is what a double integral is and it's clear that f(ξ_k, η_k) ≡ 0 for all (ξ_k, η_k) so it follows the double integral is zero if you know what the other things in the definition mean. I just don't want to be sending walls of text. 🙂

[summer kayak]

wait btw again just to double check, when it comes to iterative integral. The reason we integrated with respect to y first is because we have numbers as bounds for x right?

[sullen saffron]

Well a analogous version exists for regions R_y in hypothesis of Theorem 2 above.

This is what is meant when people say change the order of integration.

Appropriate regions such as the one we have can either be R_x or R_y, i.e., a <= x <= b, a <= x <= b, φ(x) <= y <= ψ (y), or c <= y <= d, a <= x <= b, φ(y) <= x <= ψ (x).

I arbitrarily chosen the order I did but I would have been justified to choose the other version.

[cedar kiln]

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[ember rover]

How find the equations

[brisk dagger]

can you do the linear parts?

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[ember rover]

what you mean

[brisk dagger]

three parts of the piecewise function are linear

[ember rover]

how do i find what the equations are

[brisk dagger]

on which intervals is the functon linear?

[ember rover]

every

[brisk dagger]

no, we have an exponential piece on [0,2]

[ember rover]

the first and third

[brisk dagger]

you see it's curved instead of a straight line

that's a start

okay so the first part

the blue line

what's the slope of this line?

[ember rover]

how do i find it if it only hit one point

[brisk dagger]

it's 4/3

and the y intercept is 1

[ember rover]

i dont see it in anypoints

[brisk dagger]

f(x)=4/3x+1 when x=(-infinity,0)

[ember rover]

ok

[brisk dagger]

f(x)=3^x when x=(0,2)

[ember rover]

what

[brisk dagger]

f(x)=-x+11 when x = (2,infinity)

and i can't tell what's going on

is there a piece of the function on the x axis?

[ember rover]

what you mean

how did you get the slope in the first function

[brisk dagger]

the function looks like it's goig through the points (0,1) and (-3,-3)

[cedar kiln]

@ember rover Has your question been resolved?

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[open vine]

Where did i go wrong here

[cerulean sail]

Is it wrong?

[cedar kiln]

@open vine Has your question been resolved?

[open vine]

Well the answer for question f says this

[cerulean sail]

Think it might be mistyped

,w diff e^(u^(1/2)) ln(u^(1/2)) wrt u

[wraith dagger]

Results provided by WolframAlpha

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

Requested by chartbit#3171

[cerulean sail]

This here is equivalent to yours, when you factor out another $u^{-\frac{1}{2}}$ and bear in mind the power rule for logs $\ln(u^{1/2}) = \frac{1}{2}\ln(u)$

[wraith dagger]

@cerulean sail

[cerulean sail]

Then common denominator everything

[cerulean sail]

Suspect that it's supposed to be $\frac{1}{2} e^{\sqrt{u}} \pqty{\frac{1}{2\sqrt{u}}\ln(u) + \frac{1}{u} }$ or equivalent I think?

[wraith dagger]

@cerulean sail

[cedar kiln]

@open vine Has your question been resolved?

[open vine]

thanks!

[cedar kiln]

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[light pine]

im buggin rn big time

[light pine]

why is this not allowed?

my mind has gone blank

[cerulean sail]

Need to be multiplied together to do that

[cosmic steppe]

Because ln(e^x + e^x) is not 2x

[light pine]

Ofc

And

[light pine]

Thought so

Sorry for the dumb question, bit fried rn

Thanks

[crimson sedge]

Dw, no dumb questions

[safe laurel]

k?

[light pine]

.close

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[drowsy mango]

i need help ong

[drowsy mango]

this is the question

[cerulean sail]

Separate variables

[drowsy mango]

how exactly?

[cerulean sail]

You have a differential equation of the form $\dv{y}{x} = f(x) g(y)$, so you can convert that to $\frac{1}{g(y)} \dv{y}{x} = f(x)$

[wraith dagger]

@cerulean sail

[cerulean sail]

Both sides should be "easy" to integrate (in theory anyway!) with the left hand side, bearing in mind the chain rule...

[drowsy mango]

so i put the y´s onto the left and keep x on the right

then integrate?

ok i will try

can i leave the chat open if i have another question regarding the same question?

[cerulean sail]

Yea sure thing!

If you need help feel free to ping me too

[drowsy mango]

i seperated both x and y

[cerulean sail]

,rccw

[drowsy mango]

but im not sure what approach to use for this integration

maybe by parts? idk

[cerulean sail]

By parts is a good idea yea

[drowsy mango]

but then what would be the differentiate for 1/sin2(x...

[cerulean sail]

$v'$ is what you wrote, $\frac{1}{\sin^{2}(x + \frac{\pi}{6})}$, just need to realise what that's the differential of(!)

[wraith dagger]

@cerulean sail

[drowsy mango]

yep thats what im not sure of

[cerulean sail]

do you have a list of common differentials anywhere?

[drowsy mango]

i mean we are given a equation booklet i can check there

[cerulean sail]

Otherwise, if not, then bear in mind what 1 is in terms of trig functions

[cerulean sail]

Might be an easier idea to!