help-13

[dusk goblet]

just use youtube

you’ll notice that when you set x = 2 however that you have two unknowns still

so just choose another convenient value for x and you’ll solve an easier system of equations

this happens when you have this repeated factor situation

[dreamy void]

what did you do there?

[worldly bolt]

first

i halved the second equation

then i subtracted the first equation from the second equation

[dreamy void]

Why is there still a 4?

[worldly bolt]

ok

there

gimme a sec

yeah

thats the issue

.close

[cedar kiln]

Channel closed

Closed by @worldly bolt

Use .reopen if this was a mistake.

[cedar kiln]

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[pure gale]

i have a question about the concept of second order differtial equation

[pure gale]

for ay''+by'+c=0, there are 3 cases:

1. determinant >0 ,then y=c1e^r1t+c2e^r2t
   2.D=0, then y=c1e^rt+c2te^rt
   3.D<0,y=..........

im confusing about the first case and the second case

in the second case, why y2=c2te^rt but not c2e^rt, there is a multiple of t

[dire geode]

yes D = 0 is a repeated root

[pure gale]

why we cannot say that y=ke^rt, where k=c1+c2

[dire geode]

because there's another solution in D = 0 you'd miss

[pure gale]

just imply the repeated root to case 1

[dire geode]

i don't know what you're saying here

[pure gale]

i don't know why y2=c2te^rt

i couldn't understand why there is a multiple of t

[dire geode]

plug y2 into the differential equation when D = 0

[pure gale]

i've searched that y1 and y2 must be linearly independent but i don't know why y1 and y2 must be like that

i know the solution but i don't know the principle

[iron wren]

is the differential equation with respect to t?

[pure gale]

yes y is a function in terms of t

[iron wren]

kk

[iron wren]

im not too sure of the specific logistics but its supposed to make the equation linearly independent

[pure gale]

but why it must be linearly independent

[iron wren]

like if you just use the same value of r for both parts of the equation there wont be a specific answer

[pure gale]

why a repeated root give out a different y1 and y2

[dire geode]

You can just do this to prove it to yourself

[iron wren]

i dont know how the additional t makes it accurate but it does allow for a single solution

[dire geode]

And try to plug it into the DE when D>0 and see that y2 doesn't satisfy the DE

[iron wren]

the same kind of equation resolution is used in difference equations as well

[pure gale]

i think i have some ideas that y1 and y2 must be linearly independent base on this reply from AI

.close

[cedar kiln]

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[civic coral]

Guys

[nova snow]

hello Tom

[wicked mantle]

Hi hi hi

Mickey Lord !!

[civic coral]

How to calculate this shit

Tip

Tip

[wicked mantle]

可以完整截圖ㄇ

Plz plz plz

[civic coral]

No

Ann

[tropic oxide]

$c_1^4 + c_2^4 + c_3^4 + c_4^4$ ?

[wraith dagger]

Ann

[civic coral]

My lifesaver

Yes

[tropic oxide]

what are these meant to be?

[civic coral]

A single term

Like

They can be written in a different form

And simplify the calculation

[tropic oxide]

who asked you??

[rapid mauve]

wot?

[unreal jacinth]

lol why are you guys asking me this stuff

[honest field]

mf wrote it incorrectly lmaooo

[unreal jacinth]

/j

[unreal jacinth]

casual math error moment

[honest field]

the top and bottom number have to be reversed lol

[tropic oxide]

hold on tho uhh

no but what does this all mean

like right now all i can see is $(c_1)^4 + (c_2)^4 + (c_3)^4 + (c_4)^4$ and i don't know what these $c_i$ are

[wraith dagger]

Ann

[honest field]

They meant 4C1 + 4C2 + 4C3 + 4C4 I think

[civic coral]

This is how Asian people writes combinations

Taiwanese people

[tropic oxide]

$C^n_k = \frac{n!}{(n-k)! k!}$ ?

[wraith dagger]

Ann

[civic coral]

Yes

[tropic oxide]

ok, do you know $\sum_{k=0}^n C^n_k = 2^n$ ?

[wraith dagger]

Ann

[civic coral]

I was looking for it

How should I memorize it, a intuitive association maybe

[honest field]

$C^k_n$ actually, he wrote it incorrectly

[wraith dagger]

36% Carbonized

[tropic oxide]

better off memorizing binomial theorem more generally

i.e. $(x+y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k} y^k$

[wraith dagger]

Ann

[civic coral]

I know this

[tropic oxide]

(replace the notation for combinations with whatever you like best)

ok then you can put x=y=1 and get the earlier thing

[civic coral]

I just cannot recognize that to be 2^n

[civic coral]

Sure

[honest field]

let x=y=1

[civic coral]

I think I should do more practice

Thank you Ann

The certified smart people

Also 36% alcohol

.close

[cedar kiln]

Channel closed

Closed by @civic coral

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[honest field]

36

[hallow pelican]

are you carbonite or crabonite

[honest field]

crab

[wicked mantle]

A family has 4 children.Given that at least one of them is a girl.

Question 1) The possibility that the family has exactly one girl

2)Possibility that the family has at least 3 girls

3. Possibility that the oldest child is a girl.

[tropic oxide]

possibility?

[wicked mantle]

@tropic oxide

[wicked mantle]

Yes

[tropic oxide]

are you sure it says that and not probability

[civic coral]

.reopen

[cedar kiln]

✅

[tropic oxide]

and we're also assuming child gender to be 50-50 right

[wicked mantle]

Probability sry

I’m in a hurry rn

[tropic oxide]

bruh

[wicked mantle]

Certainly

[tropic oxide]

ok and OP was calculating the number of possibilities for the children's genders

which he could have done with the sum written

or as 2^4 (all possibilities) minus 1 (the one we can't have, which is all 4 boys)

[worldly edge]

Is this the french defense? Your username? But i think this question can be solved by making the chart of all possible outcomes assuming 50-50 chances of being boys and girls.

[cedar kiln]

@civic coral Has your question been resolved?

[tropic oxide]

!redir

[cedar kiln]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[wicked mantle]

啊哈，你回來的時候再標Ann
@civic coral

她寫了一大串結果你直接把人家晾在這邊==

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[wicked mantle]

.reopen

[cedar kiln]

✅

[wicked mantle]

.close

[cedar kiln]

Channel closed

Closed by @wicked mantle

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• Show your work, and if possible, explain where you are stuck.
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[supple falcon]

,rccw

[supple falcon]

$\alpha = \frac{\pi}{2} - \beta = \beta + \gamma$

[vital lodge]

What?

[tropic nova]

Indeed

[slender ginkgo]

I think its $\gamma$ not $y$..

[wraith dagger]

k

[vital lodge]

And yes it is

[slender ginkgo]

Do u know how tan and cot are cofunctions?

[slender ginkgo]

U should consider this

[vital lodge]

Yeah

[supple falcon]

oh okay

[wraith dagger]

1 divided by 0 equals Infinity

[supple falcon]

consider this

[slender ginkgo]

In conjunction with sum of angle for tan (maybe)

[supple falcon]

basically $\cot{\alpha} = \frac{1}{\tan{\alpha}}$

[wraith dagger]

1 divided by 0 equals Infinity

[vital lodge]

I can see where this is going

But do u know some more faster way of doing it?

I mean this shouldn't be the only way u are telling

There must be better one right?

[supple falcon]

since $\alpha + \beta = \frac{\pi}{2}$

[wraith dagger]

1 divided by 0 equals Infinity

[supple falcon]

then $\tan{\alpha} = \cot{\beta}$

[wraith dagger]

1 divided by 0 equals Infinity

[vital lodge]

I know this one

[supple falcon]

yea

im more used to with degrees

[vital lodge]

Yeah i understand

[vital lodge]

..

[supple falcon]

try to draw a triangle or smth

[vital lodge]

No that doesn't works

Maybe

[supple falcon]

since $\alpha + \beta = \frac{\pi}{2}$

[wraith dagger]

1 divided by 0 equals Infinity

[supple falcon]

then the right triangle should look like this

now since $\beta + \gamma = \alpha$

[wraith dagger]

1 divided by 0 equals Infinity

[supple falcon]

we can split $\alpha$ in the diagram

[wraith dagger]

1 divided by 0 equals Infinity

[vital lodge]

I got the idea

Thanks to u

I can just do something great

[supple falcon]

kind of like this

notice that angle ABD is actually $\gamma$

[wraith dagger]

1 divided by 0 equals Infinity

[supple falcon]

and angle DBC is $\beta$

[wraith dagger]

1 divided by 0 equals Infinity

[vital lodge]

Thank you

[supple falcon]

i think from this diagram

[vital lodge]

Yeah i understand

[supple falcon]

you can visualize what's going on

[vital lodge]

Mhmm

[supple falcon]

np

[vital lodge]

Okay

.close

[cedar kiln]

Channel closed

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[supple falcon]

i didn't even think of this solution lmao

[cedar kiln]

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[lucid zephyr]

I thought Leibniz looks for some L > 0 that is a constant such that |f(b) - f(a)|/|b - a| <= L

[lucid zephyr]

How is this not Leibniz

If we plug in the b and a, respectively, we obtain 1.

[nocturne ravine]

I think the definition of lipschitz is for any a and b in the domain of definition

And when b goes to a your fractions goes to the derivative of f in a

[idle tusk]

lipschitz and leibniz are different surnames xd

[lucid zephyr]

I mispelled it

I meant Lipschitz

[nocturne ravine]

Did you solve your dynamics problem?

[idle tusk]

i did not, but i haven't spent enough time on it yet :)

[lucid zephyr]

Why isn't this Lipschitz

[idle tusk]

plug in u = 0

and consider what happens as x->0

[lucid zephyr]

u?

[idle tusk]

here they use x and u

[lucid zephyr]

Oh, it is usually (point, function of point)

[upper ruin]

Huh? No

[idle tusk]

well you have two points through which you compute a slope

if the slope is bounded then the function is lipschitz

[lucid zephyr]

Wait, hold on

Wait, how does this work

sqrt(1) - sqrt(0)/ (1 - 0)

Absolute value of this whole thing is still 1/ 1 = 1

[idle tusk]

why are you plugging in 1

[lucid zephyr]

What is f(x) = sqrt(x) on?

[idle tusk]

[0,1]

[nocturne ravine]

What do you mean?

[idle tusk]

but that means that all points inside [0,1] need to work

not just endpoints

[lucid zephyr]

Okay, so [a, b] = [0, 1]

Oh

Bruh - why didn't my Professors say that lol

[idle tusk]

otherwise it's a pretty useless definition

[nocturne ravine]

No a and b are any points in [0;1]

[lucid zephyr]

I thought it was plugging the end points in from what he did in class

[idle tusk]

it does say "for all x,u in A" here though

[nocturne ravine]

Yeah that’s not how it works

[lucid zephyr]

So, how does this work then?

[upper ruin]

Probably he took that for granted, hopefully it's not the first time you see something similar

[lucid zephyr]

What goes into f(x) and f(u)

[nocturne ravine]

You take any x and u in a he domain

[lucid zephyr]

It is the first time

[upper ruin]

For this theorem

[lucid zephyr]

Abstracting it as a rep?

So, |x - u| just stay that way

[nocturne ravine]

And to show a function is lipschitz, you need to show f(x)-f(u)/x-u is lower than a constant for all x and u

[upper ruin]

But I'm really sure you have already studied/been taught similar theorems dealing with an interval [a, b]
@lucid zephyr

[flint cape]

Suppose f is a function defined on an interval
Draw the graph of this function.
Pick any two points on the graph, draw a line between them, and find its gradient
We say f is a Lipschitz function if this gradient has a maximum (i.e. no matter what points on the graph we took)

[lucid zephyr]

I meant from the definition alone

[lucid zephyr]

Using this.

f(x) = ?, f(u) = ?, x = ?, u = ?

Is it choosing any x, u in the interval? Or is it for all? How is for all representd

[flint cape]

Loosely, we can relate this to a function having a finite maximum derivative (it's not quite this, because our f can be non-differentiable, but it's a good intuition)

[nocturne ravine]

For all

[lucid zephyr]

Cool. How is it represented?

[flint cape]

$\forall$

[wraith dagger]

Waes (Wires)

[lucid zephyr]

Sigh

Nevermind. I am just going to GPT this

[flint cape]

BRUH

[lucid zephyr]

What is a pencil? How is it represented?

Here is an emoji: ✏️

Like - BRUH

Really?

Disingenious

[nocturne ravine]

What do you want to represent even?

[flint cape]

TF sorta explanation did you expect?

[lucid zephyr]

In relation to the problem

Dumbass

[nocturne ravine]

A bit respect would be welcome if you want any help

[flint cape]

When you're the one being taught, you don't reserve the right to call others a dumbass, for one

For two

[nocturne ravine]

I’m not the one who doesn’t understand fkn lipschitz

[lucid zephyr]

Respect this idiot 🖕

Can't understand a basic question

Disingenious prick

[nocturne ravine]

Can’t explain what you want wdym

[crimson delta]

you really have a talent for making people like you

[lucid zephyr]

Bruh. Are you dense?

What is a + b = 2 here?

Oh, a + b is for all here

[nocturne ravine]

Are you able and I formulate anything coherent?

[lucid zephyr]

Okay, but what is a and b here?

DUhhhh

[lucid zephyr]

Are you a bovine idiot?

I think so

[idle tusk]

[lucid zephyr]

Because you can't understand basic questions

What does 2 + 2 mean?

[flint cape]

We say $f:I->\bR$ for an interval $I\subset \bR$ is Lipschitz if
$$\exists L>0 .\forall x, u \in I, \frac{|f(x) - f(u)|}{|x-u|} \leq L$$

[nocturne ravine]

Because you can’t formulate then to be understandable

[lucid zephyr]

Uh.... it means that you are to take for all individual repersentatives and add them

Like - dude is king of speaking indirectly.

A non-answer lol

[lucid zephyr]

You couldn't formulate understanding my questions

[dreamy void]

Not a good way to talk to your interlocutor.

[wraith dagger]

Waes (Wires)

[nocturne ravine]

What kind of three-year-old answer is that

[lucid zephyr]

This is a conversation between A and B, you can C your way out.

[nocturne ravine]

You have your answer

[flint cape]

Call back, nice

[lucid zephyr]

The one you have been giving this whole time? You lack self-reflection

[nocturne ravine]

Damn he be spitting bars like new Kanye

[nocturne ravine]

I’m just trying to help you

[lucid zephyr]

You have your answer

Lol

[flint cape]

@lucid zephyr Regarding this, what question(s) do you have?

[nocturne ravine]

What more do you want then the explicit enunciation of the theorem

[lucid zephyr]

What was my original question

Figure that out

[lucid zephyr]

*than.

[lucid zephyr]

Infer from my previous question what I wanted. Read it slowly.

[flint cape]

Your original question stems from a misunderstanding of the definition of a Lipschitz function

[lucid zephyr]

Follow the conversation till now.

[nocturne ravine]

Dude is correcting me while not understanding simple mathematics

[lucid zephyr]

Okay, and after that, what did I ask once I finally understood we aren't plugging in endpoints.

You are almost there.

[flint cape]

This is already addressed from what I discussed about an informal way to think about this

[lucid zephyr]

Nope. Try again

You will get.

Read it again

[flint cape]

You will get it*.

[lucid zephyr]

Nice.

[nocturne ravine]

Ratio

[lucid zephyr]

Read it again

Do you want a hint?

[nocturne ravine]

Dude your the one asking for help why are you this condescending

[flint cape]

"It" doesn't really work when you've asked multiple questions; let me address them all

[lucid zephyr]

Hmm, I wonder - probably because someone started patronizing and deliberately started being dense and disingenuous.

[flint cape]

This function isn't Lipschitz because by taking a derivative we can show there exists a point where there's no finite L for which the condition can suitably hold

[lucid zephyr]

Here is your hint.

[lucid zephyr]

Wrong again.

You aren't addressing what my concerns were after I found that out.

Look at the hint

[flint cape]

This is wrong, again, because of the definition - Lipschitz requires you to find L sufficient for ANY two points in the interval the function acts on

[lucid zephyr]

Lol. You can't read

[lucid zephyr]

.

[nocturne ravine]

The derivative is going to infinity when approaching zero si taking a=0 and b going to a f(a)-f(b)/a-b is going to infinity which means you can’t find any L bigger than f(a) - f(b) /a-b for all a and b

[lucid zephyr]

How many times do I have to say "look at the hint".

[flint cape]

Aid, you lack basic comprehension skills; these need more addressing than your university mathematics.

[lucid zephyr]

Dude - look in the mirror. This is more reflective of your illiteracy skills than mine. Stop deflecting.

You can't even answer my basic point of contention.

[nocturne ravine]

What don’t you understand in that

[lucid zephyr]

Because you don't understand how to look at the hint that I specifically directed you over 5 times loool

[flint cape]

I've addressed any and all questions thus far from when I first started talking here; if you're still adamant in your unaddressed questions being unaddressed, the fact is you haven't even asked them, let alone succeeded in making clear where your confusion lies.

[nocturne ravine]

If you came to insult people then just go somewhere else what is your problem dude

[lucid zephyr]

Why should I address a strawman?

[lucid zephyr]

Did you know I addressed your concerns about dragons being real? I've addressed any and all questions thus far from when I first started talking here; if you're still adamant in your unaddressed questions being unaddressed, the fact is you haven't even asked them, let alone succeeded in making clear where your confusion lies.

[flint cape]

Oh hey, yes I did know, because it's vacuously true that you did address these, BECAUSE I DIDN'T ASK ABOUT DRAGONS.

[lucid zephyr]

This is another hint where it is practically the answer.

[nocturne ravine]

f(x) having x? Really?

[flint cape]

How is that a "hint", per se?

[lucid zephyr]

Oh hey, yes I did know, because it's vacuously true that you did address these, BECAUSE I DIDN'T ASK ABOUT THE LIPSCHITZ THEOREM!

[flint cape]

If you have a point "x", and a function "f", then you have "f(x)"

[lucid zephyr]

Come on. You can do it!!!

[flint cape]

That is literally the definition of what functions do

[lucid zephyr]

You are almost there you illiterate and benighted idiot!

[nocturne ravine]

ITS THE DEFINITION OF LIPSCHITZ WHICH YOU HAVE BEEN ASKING FIR YOU MORON

[lucid zephyr]

What is point x!!!!

[dreamy void]

<@&268886789983436800>

[lucid zephyr]

Come on. ALmost there 👏

[nocturne ravine]

Thx

[limber marsh]

wtf

lol

[flint cape]

Any point on the interval that the function f acts on

[nocturne ravine]

Dude just went completely crazy out of nowhere

[nocturne ravine]

I think he’s gone

[slate lintel]

@lucid zephyr There is no need to talk to people like that, especially when misunderstandings come from you not expressing your desires in any sort of understandable way. You've had issues with helpers before and they don't seem to have improved. I don't know what the core problem is, but it seems like you aren't willing to carefully read what texts say, or pay attention when being taught in class. You need to work on all of those things, and fast.

[cedar kiln]

@lucid zephyr Has your question been resolved?

[pastel vault]

.close

[cedar kiln]

Channel closed

Closed by @pastel vault

Use .reopen if this was a mistake.

[cedar kiln]

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

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

[true wasp]

Hi i need help ASAP w my hw😭😭

[void sand]

hi! just post your problem!

[silk gust]

hii could you post your specific question?

[true wasp]

HELLO SORRY TO BOTHER YOU BUT UHM ITS CURRENTLY 11:30PM HERE IM ABT TO SLEEP AND I JS REMEMBERED I HAVE A HOMWWORK

i lowk forgot what to do here

[open grove]

Try to get rid of the denaminator

Wait, which equation are you solving

[true wasp]

sorry guys i ws too busy w other subs, havent had enough sleep and i ended up sleeping in math

[true wasp]

Both

[silk gust]

lets start with 1 then

[true wasp]

OK

[silk gust]

how would you clear denominators?

[true wasp]

HEH IDK

Tbh the teacher havent teached that yet, so he made it our homework so we can study it and present it to the board tmrw

[silk gust]

ok, have you heard of lcd before? (least common denominator)

[true wasp]

yes

[silk gust]

mk, do you know how to find it in this case?

[true wasp]

I think so?, btw do u know what to do there?

[silk gust]

can you find it?

[true wasp]

6?

[silk gust]

hmm, your answer should contain x

[true wasp]

6x

[silk gust]

not quite, could you tell me where you got that from?

[true wasp]

3x and 2..

[silk gust]

ah, well those are the numerators. you want to multiply the denominators together to get a common denominator

[true wasp]

Oh

x² ?

what..

[silk gust]

so close!

how would you expand (x-1)(x+1)?

[true wasp]

like standard form?

[silk gust]

mhm!

[true wasp]

x² + 2x

?

;;

[silk gust]

hmm

lets take this step by step

[true wasp]

OK

[silk gust]

(x+1)(x-1) = x(x-1) + 1(x-1)

ok?

[true wasp]

Oh yes that

Yea..

how did u get that

[silk gust]

you just expand the first parentheses

similar to how 2(x+1) = 2x+2*1

[true wasp]

what grade and quarter is that lesson in

i somehow cannot remember it😭

we just finished factoring quadratics

[silk gust]

ok, so if i gave you $x^2+3x+2$, would you be able to factor it?

[wraith dagger]

Frances

[true wasp]

yes

( x + 2 ) ( x + 1 )

do i have to complete it

[silk gust]

good! now can you go backwards? (i.e. if i gave you the (x+2)(x+1) would you be able to write it in standard form?)

[true wasp]

x² + 3x + 2 = 0

[silk gust]

ok, now can you do the same to (x-1)(x+1)?

[true wasp]

x² + x + 1?

...

am i hopeless

[silk gust]

hmm, can you walk me through your process?

[true wasp]

cuz like

[silk gust]

NO

[silk gust]

dont say that about yourself

[true wasp]

its negative and positive, so if u add that its 0

so it shouldnt be x...

x² + 1?

[silk gust]

you got the x^2, now you have a -x and a x added together, what happens

[silk gust]

closer!

whats -1 * 1?

[true wasp]

negative

oh yea

i always forget those

[silk gust]

so the expanded form would be...

[true wasp]

of x² - 1?

[silk gust]

yea, it would be x^2-1

you saw nothing

[true wasp]

def

i would understand if its enclosed w parentheses

like (x - 1)² stuffs

[silk gust]

reposting so i dont have to scroll up

[true wasp]

BUT IDK HOW X² - 1 WORK

[silk gust]

alr, so pretty much youre going to multiply (x+1)(x-1) on both sides

[true wasp]

oh

[silk gust]

mhm

[meager dock]

x^2-1=0

what value would be x?

[true wasp]

what

[meager dock]

wait no

nono

[true wasp]

oh

[silk gust]

alr so the left side doesnt really need the expanding we did earlier

[true wasp]

my brain is shutting down its 12am

[true wasp]

oke

[silk gust]

so can you tell me what each fraction becomes?

[meager dock]

me i would just multiply everything by 3x+1 to get rid of the denominator

[silk gust]

we're working on the first question ^^ :)

[meager dock]

oh

[true wasp]

😁

[silk gust]

ill write it for you like this: $\frac{3x(x-1)(x+1)}{x+1}+\frac{2(x+1)(x-1)}{x-1}$

[wraith dagger]

Frances

[true wasp]

why did it suddenly teleported there

help im so dumb

[meager dock]

two things cancel out here

what are they?

from the numerator and denominator

[true wasp]

Its

numbers

[silk gust]

@true wasp ^^

[true wasp]

okey

[meager dock]

take $\frac{3x(x-1)(x+1)}{x+1}$

[wraith dagger]

Tan

[meager dock]

what do you see here

which is the same

[true wasp]

its like

[meager dock]

in the numerator and denominator

what is same?

like ditto

[true wasp]

X + 1

[meager dock]

correct

so they cancel out

[true wasp]

it lowkey looks like the quadratic formula something something

[true wasp]

Yes

[silk gust]

leaving you with...?

[meager dock]

so now we're left with?

[true wasp]

3x(x - 1)

[meager dock]

yes!

now apply this same logic to the other one

[true wasp]

now i multiply?

oh

2(x+1)

[meager dock]

$\frac{2(x+1)(x-1)}{x-1}$

[wraith dagger]

Tan

[meager dock]

good

now what do we have?

[true wasp]

now i multiply?

[meager dock]

we have

[true wasp]

3(x-1) + 2(x-1)

[meager dock]

you're forgetting something

the + sign

[true wasp]

wait

[meager dock]

@silk gust help

[true wasp]

3(x-1) + 2(x-1) = 4

[meager dock]

yes

[silk gust]

ack sorry i dipped for a second

[true wasp]

what next

[meager dock]

what does this tell u abt x

[silk gust]

waitt youre forgetting something on the rhs

[true wasp]

can i pin this

nvm cant

[true wasp]

rhs what

[meager dock]

your question is already pinned by the bot

[true wasp]

Oh

[silk gust]

right hand side, you forgot to multiply by (x+1)(x-1)

[meager dock]

nvm the bot pinned this

cuz it thought thats ur question

[true wasp]

wut

[true wasp]

Oh ..

[silk gust]

when you have this, the lhs got multiplied by the lcd but the rhs did not

it should be 4(x+1)(x-1)

[true wasp]

What happened to the 3

😓😓

[meager dock]

the 3 is still there

he is talking abt rhs

[true wasp]

idk im not from the us we dont use those terms 🥹

[meager dock]

3(x-1)+2(x-1)=4(x+1)(x-1)

[true wasp]

Oh

So that

[meager dock]

lhs= left hand side of the equation

[true wasp]

OK what next

[meager dock]

rhs=right hand side of the equation

[true wasp]

im gon be honest.. idk where my left and right is

[meager dock]

3(x-1)(+2(x+1) is ur left hand side here

[true wasp]

okey

4 is right

[meager dock]

cuz its the left side of ur equation

[true wasp]

Okok

btw

[meager dock]

2+3=5

what would be the rhs here?

@true wasp

[true wasp]

5

[meager dock]

yes

thats how it works

[true wasp]

what r we supposed to do in that equation? Is it like get the standard form and solve?

[meager dock]

@silk gust

$3(x-1)+2(x-1)=4(x+1)(x-1)$

[wraith dagger]

Tan

[true wasp]

yes

what next

are we getting its standard form

[silk gust]

ok now expand all parentheses

yes

[meager dock]

expand

[true wasp]

ok wait i br

how do u expand x - 1

[silk gust]

well you distribute the constant in front into the parentheses

[true wasp]

oh that

multiply

yes

3x - 3 + 2x - 2 ?..

[silk gust]

yep, thats the left side!

[true wasp]

OK

[meager dock]

combine like terms

what is 3x+2x

what is -3+(-2)

[true wasp]

5x²

[meager dock]

what the

no

ur adding them

not multiplying

[silk gust]

left side shouldnt have x^2 terms

[meager dock]

is 3+2=6?

x+x=2x

not x^2

x*x=x^2

[true wasp]

but 3x + 2x is not 5x²?

[meager dock]

@true wasp

[true wasp]

Kh

oh

[meager dock]

it isnt

[true wasp]

So no ²

[meager dock]

yes

[true wasp]

Ok

[meager dock]

whats 3 chocolates + 2chocolates

is it 5 chocolates

[true wasp]

5 chocolates

[meager dock]

or 5 chocolates^2

[meager dock]

same logic with variables

[true wasp]

Oh..

so uhm

5x

[meager dock]

yes

[true wasp]

And positive 6?

[meager dock]

👍

no

no

[true wasp]

WAHT

[meager dock]

whats -3-2

[true wasp]

but it has ()

is it not multiply

[meager dock]

show it

[silk gust]

theres no () anymore once youve expanded it

[meager dock]

isnt it 3x-2+2x-3

[true wasp]

But he said😭😭

[silk gust]

constants are the other way around but yh

[meager dock]

theres is a + sign ahead of it

plus + minus =???

minus

so its

-3-2

=-5

[true wasp]

what ws the +) for

()

[meager dock]

if it was like -3(-2), then it would be 6

but its

-3***+***(-2)

[true wasp]

OK im gon do questions later

so 5x and -5

[meager dock]

never mind

just do

-3-2

[silk gust]

yes, thats correct

[true wasp]

oke

[silk gust]

replied to wrong message oops

now for the right side

as we said previously, (x+1)(x-1)=x^2-1, right?

[true wasp]

Yes

4(x² - 1)

[silk gust]

so what do you get if you multiply that thing by 4?

and expand it?

[true wasp]

4x² - 1?

,,,,,,

[silk gust]

distribute the 4 to both terms :)

[true wasp]

4x² - 4

[silk gust]

yep

[true wasp]

Oke

WAIT

I try

[silk gust]

so now youre solving the quadratic 5x-5=4x^2-4

[true wasp]

-4x² + 5x - 1 = 0?

..

[silk gust]

yes!

[true wasp]

WOAH

I GOT IT

[silk gust]

although normally we like a positive x^2 term

just easier calculations

[true wasp]

oh

but how will it turn positive

[meager dock]

no its fine

you did good

[true wasp]

OK

Waht we do nkw

do we solve the quadratic

[silk gust]

since you learned factoring, go ahead and factor it :)

[true wasp]

Ok

[meager dock]

instead of 5x-5-4x² -4=0,
you do 0=4x²-4-5x+5

you shifted 4x² -4 to the left hand side

[true wasp]

Yes

[meager dock]

but you can also shift 5x-5 to the right hand side

[true wasp]

so to the right?

but will both uhm have the same outcome

[meager dock]

and the coefficient of x² will be positive

[meager dock]

try it

[true wasp]

Oh😭

i dont rhink i have time since its 12:30am and im gon start prepping for school at 4am

i barely have time for sleep

🥹

[meager dock]

okay sorry

[true wasp]

noo sorry im taking way too long

😭😭

[meager dock]

no its ifne

i struggled way more than you

use .close to close this channel

so other people can occupy it

[true wasp]

ok

me not done yet

[true wasp]

so i just factor it and im done?

How would u factor it..

[silk gust]

but if you get a solution that is 1 or -1, reject it

so denoms dont become 0

[silk gust]

hmm

[silk gust]

trial and error ig

[true wasp]

oh no

;;;

[silk gust]

like just try factors of 4 (leading coeff) and 1 (constant)

[true wasp]

OK ill work on it

Thankyu(ill js copy from my cm’s) BUT I ACTUALLY learned how to standard form it tyy

.close

[cedar kiln]

Channel closed

Closed by @true wasp

Use .reopen if this was a mistake.

[true wasp]

.reopen

[cedar kiln]

✅

[true wasp]

hi

so um

[true wasp]

Where did the x from the 3 go

[silk gust]

which 3

[true wasp]

Cuz like it ws supposed to be 3x ( x - 1 ) ( x + 1 )

right?..

[silk gust]

uhm

which side?

[true wasp]

This

U cancel x + 1 right but where did the x from the 3 go

[silk gust]

oh uh

crap

uhh

uhhh

geez

[true wasp]

oh

wat

sorry my brain is not functioning anymore

maybe ill just fail math

ok that was not a good joke

[silk gust]

u want me to explain the process (but with the correct problem ofc) or figure it out yourself?

[true wasp]

math is my first sub

Idk if i can do it within 4hours with no sleep

sorry

ill just pray that i dont get picked

[meager dock]

bro

SLEEP

🙏

[true wasp]

ill get humiliated in math if i do😭😭😭

[silk gust]

we dont want you to die <3

[true wasp]

I can sleep during lunch time

its 45minutes

ok nvm i have research to cram

[meager dock]

you've been doing this for 1 hour

[true wasp]

bruh

[true wasp]

what ..

[meager dock]

yeah..

just sleep

[true wasp]

oh

[true wasp]

Dudee but what abt my homework

😭😭😭

[silk gust]

please sleep 🙏

[true wasp]

what will i answer tommorow

🥹

[meager dock]

humiliation is only when you choose to suffer

[silk gust]

i have to go as well so uh

[true wasp]

BUT HEAR ME OUT,

[silk gust]

meow you should really sleep

[meager dock]

you dont have to be humiliated for not being able to solve questions after getting 4 hours of sleep

[fading charm]

you might answer with a gravestone if youre deprived of sleep like that

[true wasp]

real

my teacher does not care tho

he will prolly say

"guys math is so ez blabla"

WHAT SHOULD I DO

im legit gon cry

i cant w the pressure

[meager dock]

is this the last question you have?

[true wasp]

i have 2 more

[meager dock]

or do u have more hw

[true wasp]

Total of 3 questions

[fading charm]

just this once is fine

[meager dock]

either sleep or pull an all nighter

[fading charm]

you gotta just remember next time to do the homework before the deadline hits you like a metal club

[meager dock]

math is about understanding logic

once u get the logic

its easy

when you dont

its impossible to solve

[true wasp]

Oh btw uhm, the hw he gave he did not teach it, he said "study this equation you must solve it in the board you cant say no"

[silk gust]

but then again the chances of anyone thinking logically at 1 am is pretty low

[meager dock]

just be clear with the concept

and you can solve it

[true wasp]

YES THATS IT cuz yesterday i did not sleep too because i had so much to do

i had research, projects, and asynchronous

[silk gust]

i uh

i dont think you should be not sleeping for 3 days in a row

[true wasp]

the other day too

[silk gust]

...

[true wasp]

i was cramming our ppt

[silk gust]

omg

[true wasp]

and had to study my explanations and stuff

[silk gust]

please go to sleep

pretty please

[true wasp]

no hw=no sleep

[fading charm]

theres this saying

[true wasp]

Ok i wont bother u guys ill js watch a tut and hopefully i understand it

[fading charm]

that forgiveness is easier than permission

[silk gust]

good luck soldier

(and please try to get at least 1 hr of sleep)

[true wasp]

ok guys goodmornight

[fading charm]

good luck and try and get some sleep

[true wasp]

how is that connected to math

i swear u never had like a strict strict teacher before who would humiliate their students

Infront of the board

[fading charm]

im asian

[true wasp]

😭

i js wish i can vanish

I hope im alive 3years from now

ok bye guys

how do i close

[fading charm]

i know what it is like to study 3 months in a row with less than 4h of sleep per day

[silk gust]

type .close

[silk gust]

good luck!

[true wasp]

.xlose

[silk gust]

have a good night

[true wasp]

.xlose

[fading charm]

that was close

[true wasp]

.

[silk gust]

almost there

[true wasp]

.close

[cedar kiln]

Channel closed

Closed by @true wasp

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

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

[karmic helm]

can someone help me with this

[karmic helm]

i put log x+1 with base 3 as t

i am getting t= -2 and t= 1/2

can someone solve now and tell me what the answer is coming

[wicked mantle]

Sure, but one of them is apparently invalid

[karmic helm]

why

[wicked mantle]

oh wait, nvm

mb

[karmic helm]

so what will be the answers

[edgy spire]

One of them will be invalid as log base and input cannot be negative

[karmic helm]

why base isnt coming negative if u put x = -8/9

[wicked mantle]

no, it's about t

t = $log_3 (x+1)$

[wraith dagger]

e4 e5 Qh5 Nc6 Bc4 Nf6 Qxf7#

[karmic helm]

also when i put log 3 with base x+1 as t i am getting different answer

[wicked mantle]

I'm not really in a good condition to do math rn, I'll dip out.

[edgy spire]

Oh i see, I thought it was just x + 1

[karmic helm]

ok np

[karmic helm]

can u help

[edgy spire]

To get the answers, raise both sides of this equation to power 3 and sub in the values of t you got

[karmic helm]

but t is log 3 with base x+1 so how can i raise it like that i put t = log 3 with base x+1 so i get quadratic and get roots then put value of t to get x

[edgy spire]

oh you did it that way

[karmic helm]

yea

[edgy spire]

Um in that case you will have to raise it to the power (x+1).

[karmic helm]

.

[edgy spire]

I think you should have instead put t as log of x+1 with base 3

That will be much better to work with

[karmic helm]

oh yes sry mb yes i put that as t

so i am getting -8/9 and root3-1

but when i am putting log 3 with base x+1 i am getting diff answer

like then i am getting a 8

[edgy spire]

Why do you want to do that?

[karmic helm]

what

[edgy spire]

You said you got roots as -8/9 and root 3 - 1

Aren't those the answer?

[karmic helm]

the answer does have root 3 -1

but not -8/9

this is what it looks like

[edgy spire]

Hmm, I think you messed up with one of the roots.
If t = 2, you get the answer 8

So you put the wrong sign

[karmic helm]

hm

[edgy spire]

!show

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[karmic helm]

2tsquare +3t -2

what will be its roots?

oh yes wait i think i did mess up one sign

[edgy spire]

You can factor it as (t -2)(2t+1)

So the roots are 2 and -1/2

So, in fact, you got the wrong sign for both of them

[karmic helm]

yea

[edgy spire]

Wait

No

[karmic helm]

?

[edgy spire]

I think I factored wrong

[karmic helm]

lmfao what is happening

[edgy spire]

It should be (t+2)(2t-1)

So nvm

You did get the correct roots

[karmic helm]

ok wait the equation will be 3+2/t=2t

so that will become 2tsquare -3t -2

can u factor that

[edgy spire]

Yeah

[karmic helm]

so we would get roots -1/2 and 2

[edgy spire]

And if you sub that in, you get the correct answers

[karmic helm]

yes

dayum i messed up so hard

[edgy spire]

Notice how one mistake messed up the entire solution

[karmic helm]

yea fr

thnx man

u helped me sometime ago too appreciate it

[edgy spire]

Np

!done

[cedar kiln]

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

[karmic helm]

.close

[cedar kiln]

Channel closed

Closed by @karmic helm

Use .reopen if this was a mistake.

[cedar kiln]

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

[hallow valley]

So I understand how to find all 6 ratios for the inverse functions in the parentheses, but I don't know how it helps solve the problem. Obviously I can leave it in terms of asin and acos but I don't think that's a complete solution.

[stoic ferry]

You can find it by changing cos-1 into sin-1 and tan-1 to sin-1

[slender ginkgo]

Sum of angle

[dusty wren]

Bruh

Please don't repeatedly close and claim a new channel with the exact same question.
This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you.
Please be patient, even if your channel has not received much attention.

You've done this twice already

What about the previous explanations confused you

We've literally given you like three different methods

[stoic ferry]

Pythagoras theorem

[slender ginkgo]

??

[stoic ferry]

a^2+b^2=c^2

[hallow valley]

so you're saying I still end up with inverse function, there's no way to get a "numerical" angle?

[stoic ferry]

It’s not angle it’s ratio

Inverse are ratios

I think your theory part is weak

[hallow valley]

Probably :/

[stoic ferry]

Sin(sin-1(x))is

X

[hallow valley]

x

of course

[slender ginkgo]

…

[hallow valley]

No confusion about that

[stoic ferry]

That’s formula can be applied

[slender ginkgo]

Sum of angle..

[royal finch]

You need to study something like this: https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/06%3A_Periodic_Functions/6.03%3A_Inverse_Trigonometric_Functions

You've already been told what to do not just geometrically but also have been given explicit formulas you can just plug in by multiple people multiple times at this point.

[stoic ferry]

Cos-1 in terms of sin-1 will be 5/4

[stoic ferry]

No bro there is range in inverse functions

[dusty wren]

we're taking principals here

[slender ginkgo]

Up to u m8

[stoic ferry]

Just try reading it you will get some clarification

[hallow valley]

Sorry if I'm being extra thick, I will go through the text

[slender ginkgo]

Js saying but
$\arcsin(\sin(x) - \sin(y)) \neq x - y$

[wraith dagger]

k

[hallow valley]

.close

[cedar kiln]

Channel closed

Closed by @hallow valley

Use .reopen if this was a mistake.

[slender ginkgo]

Wonderful

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[untold sluice]

I think I get the general idea with this problem is to ibp from negative infty to positive infty but i keep going in circles - I have to use the statement in order to prove it if that makes sense

[subtle harbor]

what step are you specifically confused on in the IBP?

!showwork

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[subtle harbor]

note that the dirac delta is 0 at anywhere but 0, not approaches, is 0.

[untold sluice]

integrating i get $x \delta (x) - \int_{-\infty}^{\infty} \delta(x) dx$

[wraith dagger]

doublevcodes

[subtle harbor]

yes

[untold sluice]

so the first part becomes 0

[subtle harbor]

yes

[untold sluice]

im unsure how the second part gets me to - delta(x)

[subtle harbor]

you're integrating the other side as well

[untold sluice]

oh i get you

[subtle harbor]

to preserve equality

[untold sluice]

so there's not really anything else to do

thats it

[subtle harbor]

yeh :)

[untold sluice]

ahh okay it just didnt feel like i was done

thanks for your help

[subtle harbor]

you can show both sides are equal to -1 via properties of dirac delta but that's pretty much it

[untold sluice]

.close

[cedar kiln]

Channel closed

Closed by @untold sluice

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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.

[cedar kiln]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[cedar kiln]

Available help channel!

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• 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.

[azure shadow]

i have an idea on this, just wanna confirm if my answer is correct

[opaque harbor]

can't confirm the final number but the working out seems correct

[azure shadow]

oh, thank you

thats all i needed

.close

[cedar kiln]

Channel closed

Closed by @azure shadow

Use .reopen if this was a mistake.

[cedar kiln]

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.

[true wasp]

hi my hw is due in an hour can someone directly give me the answers and solution🥹 I WILL LEARN IT I SWEAR

[silk gust]

hi again!

[true wasp]

FRANCES

HI

IM AT SCHOOL RN

[silk gust]

hiiii

[true wasp]

HI

😭😭😭

even my cm r not done yet

[silk gust]

hmm, i dont know if im allowed to give you the solution directly (per mathcord rules) but i can guide you as fast as i can :)

okok

[true wasp]

OK

can u do it within 6minutes?.. class starting soon i cant use my phone

[silk gust]

gotchu

[true wasp]

OK

[silk gust]

for the first one

[true wasp]

yes

[silk gust]

left side simplifies to 3x(x-1)+2(x+1) after clearing denoms

which becomes 3x^2 -x+2

[true wasp]

............. Based from what i learned uhm earlier

[silk gust]

yea u add them up

[true wasp]

ye