help-26

[pure magnet]

Okay sweet

[ocean pewter]

y is just f(x) for some restriction (i.e. remember how we said this line was to the left of x = -3, that is our restriction

[pure magnet]

Yes

[ocean pewter]

So we can solve for y in the point-slope equation and say x < -3

[pure magnet]

Okay

[ocean pewter]

Which point to you want to plug into the point-slope equation?

[pure magnet]

-6,1

[ocean pewter]

Okay

$y - 1 = -\frac 2 3 (x + 6)$

[thorny flame]

CalculusDude

[pure magnet]

okay

[ocean pewter]

How would you solve for y

[pure magnet]

Distribute

[ocean pewter]

Yup

What would that give you

[pure magnet]

-3/2x-4

-2/3 i mean

[ocean pewter]

So $y - 1 = -\frac 2 3 x - 4$

[thorny flame]

CalculusDude

[ocean pewter]

What's next so solve for y

[pure magnet]

-2/3x-3

[ocean pewter]

The right hand side is $-\frac 2 3 x -4$, what can we do to both sides to isolate y

[thorny flame]

CalculusDude

[pure magnet]

add 4

I think

[ocean pewter]

We can add 1 to both sides (remember, we want a y on the left side, not a y -1)

[pure magnet]

Ohh okay

[ocean pewter]

So our final result for the leftmost line is $y = - \frac 2 3 x - 3$

[thorny flame]

CalculusDude

[ocean pewter]

For x < -3

[pure magnet]

Yes

[ocean pewter]

That's the first part of your answer

We can do the same steps for the rightmost line

First, what value of x does our rightmost line start?

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[heady bolt]

I am struggling on getting a good concept of understanding how to sketch 3D functions. Ex: f(x,y) = x + 2y, z = y^3-1

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[heady bolt]

<@&286206848099549185>

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@heady bolt Has your question been resolved?

[sterile finch]

Best to start with one of the variables being set to zero. This allows you to draw something on the xy-, xz-, or yz-plane.

[heady bolt]

i did that but i only end up getting 2 lines

[sterile finch]

Is your example a constraint problem?

[heady bolt]

it was just asking to sketch the graph of f and f(x,y) = x + 2y

this is what the answer is but im having a hard time conceptualizing a process so i can solve any other ones

[sterile finch]

Shading helps.

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[dry dragon]

Hello I'm stuck on this geometric progression question and would like some pointers

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[drifting swift]

does that mean you figured it out yourself just now

[dry dragon]

yes :)

[drifting swift]

aight

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[sharp meteor]

set An = [0,1/n] show that the intersection of A1,A2,A3,A4...An is just the set contaning 0:
for all x (in (0, 1] here), there exists an n such that x is not in An

[sharp meteor]

guys for this

i was thinking of esp-delta yesterday

I had come to the conclusion that 0 would be in all sets

but was going to prove that no other x would be in the intersection of all sets

ive never encountred eps-delta, this is just from the basis of what i learnt yesterdya

[drifting swift]

you want to prove that for every x > 0 there exists a natural n such that 1/n < x

you need some version of archimedes' principle

[sharp meteor]

im writing it

[drifting swift]

... do not call me "bro" please.

[sharp meteor]

oh sorry

[drifting swift]

edit that out, would you?

[sharp meteor]

mb

so let $x > 0$ what i want to show is that there exists some $n$ such that $x \notin A_n$.

[thorny flame]

Deno

[sharp meteor]

alr the rest idk how to do in latex

so

ik that as n tends to inf, 1/n tends to 0

wait nvm

idt my logic makes sense

yh ill wait til i read on epsdelta

😭

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[strange basin]

is 50N a vertical force?

[finite storm]

according to this representation

no

@strange basin

[strange basin]

according to the image

of the boat

[finite storm]

well

uhh

u kinda need a diagram

describing which line is the y-axis

that way, we can describe the notion of vertical more easily

[strange basin]

but how do i find it from the boat picture

[finite storm]

u have to make ur own axis

[finite storm]

like this

[strange basin]

i know

so can i put either one as x and y axis?

[buoyant forge]

i showed this to my physics friend and yea its vertical force

[strange basin]

okay how did you distinguish that?

[buoyant forge]

.

he didnt say anything after that

he just said "yes"

and left

[strange basin]

wait what did you show him?

[buoyant forge]

This and the 50KiloNewton question

[strange basin]

where did you get the question from?

[buoyant forge]

i took a snip and shared it to my friend

[strange basin]

oh ok

so its not horizontal

[buoyant forge]

no

[strange basin]

ok ty

why does my calculation work then

[clear python]

You can align your axis as required

As long as all angles are fine, you'll be fine

[clear python]

Hence this works

[strange basin]

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[sharp meteor]

for this i see that |(a-c) + (c-d) + (d-b)| can be replaced on the LHS

[sharp meteor]

then i can maybe use triagnle ineq?

but im unsure to what I use it to

[finite storm]

triangle inquality works

[sharp meteor]

oh alright

ty

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[sharp meteor]

.reopen

[topaz sinew]

✅ Original question: #help-26 message

[sharp meteor]

but injust realised

i would have like 3 things in there

how do i implement |a-b| <= |a| + |b|

wait lemme think abt this

[worthy storm]

you'll want to use the triangle inequality twice

[opal vault]

maybe can you write a-b in terms of the three terms in the RHS?

[sharp meteor]

ah i see

alright

oh got it

ty guys

was complicating a triv q fr

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[upper raptor]

My teacher wants me to solve this diff eqn but with a real solution but idk how

[upper raptor]

I say idk how bc how do I get rid of the i? In class she did but she never explained why the i disappears and we are just left with sin(wt)

It pmo that she jumps a lot of steps because she assumes we all understand. She is a crappy teacher but nonetheless I'm here to try to understand

I solved the diff eqn by assuming y(t) = exp(kt) where k is some constant. This is the method she taught us

she wants us to have two C constants and no complex term but god knows how. Its easier to assume C1 - C2 = 0 and just have the cosine term. That is the only way possible for the complex term to get removed right?

unless of course C1 - C2 = 0 but then I am left with (C1 + C2)cos(wt)

maybe she made that mistake and made it C1cos(wt) + C2sin(wt) when it was supposed to be both cosines, C1cos(wt) + C2cos(wt)

[mint crescent]

Why not define $C_b$ as $i(C_1-C_2)$ instead of just $C_1-C_2$?

[thorny flame]

Civil Service Pigeon

[mint crescent]

you there?

[upper raptor]

gimme a sec

[upper raptor]

im not sure

she might of did that

[upper raptor]

idk, can you even do that and assume its still a real constant?-

the only way I could see doing that is if the value of (C1-C2) is complex, where multiplying it by i would give a real constant

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[pseudo pond]

can someone explain to me how i would find the bounds of this double integral for 38

[pseudo pond]

cause im a bit lost on what to look for

,w graph x = 2y

[thorny flame]

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[hollow cove]

happy birthday vikky 🥳 🎉

[pseudo pond]

thank you!!

https://tenor.com/view/demon-slayer-kimitsu-no-yaiba-tanjiro-kamado-smile-kind-gif-11822011654669430937

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[pseudo pond]

,w graph y = z

[thorny flame]

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[rare slate]

i dont get what the question asked 😭

[rare slate]

how do i solve the left end point and right endpoint

here is my work

.help

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[rare slate]

@haughty drum 😓

[worthy storm]

what does it want for "left endpoint"? can you show the whole question?

[rare slate]

oh u mean this

[worthy storm]

oh i see, it wants the derivatives at the endpoints

[rare slate]

wait does that mean , f'(4) = 3??

derivate of f(x) is just 3

[worthy storm]

yep it's 3 everywhere

including at both endpoints

[rare slate]

does that mean

[worthy storm]

no, that's the average rate of change of the derivative

the question wants the instantaneous rate of change of the function itself

so that's f'(4) and f'(7)

[rare slate]

oh that would be this

[worthy storm]

yes

[rare slate]

oh i see , thank you for your help

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[fiery scaffold]

how did they get from step 7 to 8?

[fiery scaffold]

im stuck here (im trying to simplify step 7)

[jade thunder]

Is that the full picture?

[fiery scaffold]

no but its correct up to this part

[jade thunder]

Errr

It’s missing the cosine part

And then in step9 it reappeared

[fiery scaffold]

yea that seemed weird

[jade thunder]

Probably just a typo

[fiery scaffold]

but im still confused on what to do

[mint crescent]

$$\int e^{ax} \cos bx \dd{x}=\frac{e^{ax} \sin bx}{a}-\frac{be^{ax} \cos bx}{a^2}-\int \frac{b^2}{a^2} \int e^{ax} \cos bx \dd{x}$$ We want to compute $\int e^{ax} \cos bx \dd{x}$, which we will call $I$. Then,
$$I=\frac{e^{ax} \sin bx}{a}-\frac{be^{ax} \cos bx}{a^2}-\frac{b^2}{a^2} I$$
and now this is a standard algebra exercise.

[thorny flame]

Civil Service Pigeon

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[exotic rampart]

wondering if -123(remainder) impact the question at all?

[mint crescent]

ofc

[exotic rampart]

wait how

[mint crescent]

[https://math.libretexts.org/Workbench/FHSU_College_Algebra/03%3A_Polynomial_Functions/3.05%3A_Dividing_Polynomials]

if you don't have r(x), then you don't have enough to uniquely determine d(x)

[exotic rampart]

the answer didnt include -123

[exotic rampart]

i get that but why didnt the answer not include the remainder?

the answer didnt need remainder

[mint crescent]

actually tbf you don't need the remainder [reinterpret d(x) and q(x) and vice versa]

[exotic rampart]

so for these types of questions we dont need the remainder?

[mint crescent]

aka instead of the quotient being $5x^2-14x+42$ and the divisor being unknown, let the divisor be $5x^2-14x+42$ and the quotient be unknown

[thorny flame]

Civil Service Pigeon

[mint crescent]

and then it's just standard division

but knowing the remainder makes this A LOT easier

since you can say that $$d(x) q(x)=5x^3 +x^2+3+123$$

[thorny flame]

Civil Service Pigeon

[mint crescent]

aka $(5x^2-14x+42)d(x)=5x^3+x^2+126$

[thorny flame]

Civil Service Pigeon

[mint crescent]

you know that d(x) has to be linear

comparing the leading terms gives the coefficient of x is 1

comparing the constant terms gives the constant to be 126/42 = 3

hence x+3

so being given the remainder makes this a 15 second question

[exotic rampart]

im just trying to understand what u saying rn 😭

wait i get this @mint crescent

Thanks bru

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[mint crescent]

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[dense panther]

Hello, how can i know for sure which way it will curve?

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@dense panther Has your question been resolved?

[restive inlet]

if unsure, table if values will help

[dense panther]

Yes thabk you i figured it out in the last min lol

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[exotic rampart]

Why isnt there an x-intercept at -1 ?

[mint crescent]

(x^2-1)=(x-1)(x+1)

Not (x^2+1)=(x-1)(x+1)

[exotic rampart]

Wait im confused

[thin girder]

I mean you can just put x=-1 into the equation and see it doesnt gives out 0

[exotic rampart]

wait

so so im so confused 😭 so whenever its x² + 1 or whatever its like

no xintercepts

[thin girder]

X^2+1
Put x =-1
(-1)^2+1=1+1=2≠0

[thorny basin]

You can try substituting numbers into the coordinate axes to understand.

[exotic rampart]

yes

[exotic rampart]

wait so y = 0?

[thorny basin]

Wait, your image shows only one point where y=0—when x=1, y=0.

[burnt swift]

if there is an x intercept at -1, then it intercepts the x axis at x = -1, any x intercept has y value 0

[exotic rampart]

wait so whenever its x² + something, it always is no x-intercept?

um

[ruby tree]

x^2 is never negative; add something positive and you get something positive, so why would there be an x-intercept?

[exotic rampart]

Ohhh

This is a really good explanation

thank u

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[coral fog]

How can I approach this problem? I already know how to solve for 0^p where p is prime

[drifting swift]

what's your approach for L = {0^p | p prime} and what's the verdict for that language?

[topaz sinew]

@coral fog Has your question been resolved?

[coral fog]

When I solved for 0^p I chose n to be the constant of the pumping lemma. I chose w = 0^n where n is prime, and |w| >= n and w belongs to L. Then I split w = xyz. By the 3 conditions of the pumping lemma, I got w = xy^kz = 0^(n+t(k-1)). Choose k = n+1, after replacing we get n(t+1) is a composite number

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[delicate meadow]

I need help with this math problem, i'm second grade high school

[calm charm]

Hi

[delicate meadow]

hi bro

i cannot solve this question and im using app called photomath but i cant figure it out how he solves this

[calm charm]

Do you now $\sqrt{x}=x^{\frac{1}{2}}$?

[thorny flame]

Richard Mullin

[delicate meadow]

no

[tacit crow]

😭

[calm charm]

rewrite the expression using this thing

[delicate meadow]

half of the root is 1/2

so what about it

[calm charm]

???

[delicate meadow]

wait

im gonna kill mysekf

[calm charm]

⚠️

What

[delicate meadow]

Bro do you want me to write you like from this robot

[calm charm]

???

[delicate meadow]

or?

do you want this math problem to be written like you like this robot or can I use paper and pencil to write you this problems

i dont understand

i will start crying

[calm charm]

Paper

[delicate meadow]

ok wait

i dont know how to do this

[calm charm]

.

[delicate meadow]

wait

[tacit crow]

this is an example but use this

[delicate meadow]

so those are like rules for root?

ok wait

im really bad

[tacit crow]

roots can be written like that

[delicate meadow]

aaaaa

alright

[tacit crow]

now try to simplify

[delicate meadow]

alright

i will try

[tacit crow]

(assuming you know exponents)

[delicate meadow]

would you still be here if i need you?

[tacit crow]

yeah

[delicate meadow]

yes

[delicate meadow]

alr thanks alot bro

[tacit crow]

np

[delicate meadow]

i will send here when i finish

Am I right?

[tacit crow]

,rccw

[tacit crow]

noo look

this whole thing is under this bigger root right

[delicate meadow]

aha

so I dont touch that big root

i do under him

[tacit crow]

so once you write this in the format

theres a multiplication right?

[delicate meadow]

ye

[tacit crow]

so do that multiplication first, then open the squareroot

[delicate meadow]

alr wait

[tacit crow]

you got this

[tacit crow]

solve the inner stuff first, then go for the outer one

[delicate meadow]

,rccw

[delicate meadow]

i got this

[tacit crow]

oh im back

sorry if im late

1s lemme look

[delicate meadow]

np bro

i didnt finish this, this can be more solved

[tacit crow]

wait

[delicate meadow]

i dont know this im getting bad grade again😭

[tacit crow]

tbh bro you're complicating it

[delicate meadow]

i know

[tacit crow]

look

[delicate meadow]

im complicating it my whole life

[tacit crow]

write this in the format i showed youi

then multiply it with x^5 using the exponents

and then once you get a single term in x, write it using the format once again

you got it?

[tacit crow]

nah dw alg

[delicate meadow]

okay let me try it

[tacit crow]

look try something like this

(Sorry for my garbage handwriting, i wrote using my mouse)

[tacit crow]

,rccw

[delicate meadow]

is this good?

[tacit crow]

nope you made a blunder

do the multiplication again

[delicate meadow]

wait let me see this you sent me

[tacit crow]

you are doing it correctly just check this once

[delicate meadow]

I just saw what you wrote to me and I did the same as you

[tacit crow]

yeah you messed up the addition 😭

[delicate meadow]

wait

[tacit crow]

5 + 1/3

this addition

redo it

[delicate meadow]

OMG IM SO STUPID

its 16/3

[tacit crow]

lol

yep

now for the last squareroot

[delicate meadow]

IT WAS THE OLD TRICK

HOW I FORGET IT

sorry bro

[tacit crow]

lol dw it happens

[delicate meadow]

now i look dumber than im really are

sorry

okay

waut

wait

let me write this for you

[tacit crow]

dwdw

you arent dumb

it happens to all of us sometimes

[delicate meadow]

i got the root from x^13

and then i can transform it

and get

this

x^6 root of x

OMG I THINK IM RIGHT

[tacit crow]

show show

lemme verify

[delicate meadow]

wait

just rotate ut

it

[tacit crow]

,rccw

[delicate meadow]

thanks

[delicate meadow]

I knew it

so what i did there cannot be done like that?

[tacit crow]

you cant write like this

[delicate meadow]

so, can I just shorten it like with 3

like 16:3 and 3:3

[tacit crow]

they are completely different values

[delicate meadow]

yeahhh i missed it

i think i need 3 hours for this one math problem and im second grade high school

[tacit crow]

once you get a hold of it, youll solve them real quick dw

[delicate meadow]

bro im alot worried for me and my future for math but i need it alot

[tacit crow]

dw

just practice

[delicate meadow]

can i ask u something

[tacit crow]

use this exponents identity now

[tacit crow]

sure

[delicate meadow]

how old are you

[tacit crow]

16

[delicate meadow]

THE FUCK

im 17 bro

[tacit crow]

dang

[delicate meadow]

can i add u

or you only do on this server

[tacit crow]

but ig not sorry

but i can help you on the server

[tacit crow]

use this to get the answer on one side

[delicate meadow]

alright i dont want anything to harm or else

i just want to do math thats all

[delicate meadow]

i will use servert tgeb

server then

[tacit crow]

im always here

[delicate meadow]

ahahah you are so good

[tacit crow]

np now solve it you're very close

[delicate meadow]

wait

i have it

i will send you solved

idk how are you so good in math

[tacit crow]

the other side is very easy compared to this one

[tacit crow]

im not

[delicate meadow]

bro how are you not im litteraly trash in math you are like professor to me

okay let me do it

wait

[tacit crow]

well we've done all this 2 - 3 yrs ago

thats why

in school

[delicate meadow]

where are you from (if you can tell me)

[tacit crow]

india

[delicate meadow]

BRO YOU ARE WAY AHEAD OF US

IM FROM BOSNIA AND HERZEGOVINA

THE FUCK

SORRY FOR WORDS

[tacit crow]

o

[delicate meadow]

I wrote it again

I think i can solve it now

Do you want me to send you fully solved or?

And then you can see if i missed it

[tacit crow]

looks good

go on

[delicate meadow]

alr

wait

bro listen

i can put here on 16/3 rule n root of a= m*n root of a^m

idk how

[tacit crow]

alright

let me show you an example

[delicate meadow]

alr

[tacit crow]

where do you think this comes from

[delicate meadow]

i litteralz know a rule but i dont knoiw how to do it

aha

oh sorry

[tacit crow]

can i write it like this

[delicate meadow]

it came from x 3/2

[delicate meadow]

this one is =x 3/2

[delicate meadow]

no

i think no

[tacit crow]

why not

i can write this

then why not that

[delicate meadow]

i think because the 3 in front of an root is dividing this number so that one cannot be square of x

oh

[delicate meadow]

this one can be

because every number has its own potency right?

[tacit crow]

alr look

so this is correct

and then i used the same exponents identity here

[delicate meadow]

so this one is right?

[tacit crow]

to get this furthur on

[tacit crow]

yep

[delicate meadow]

AAAA

alr

so

[tacit crow]

so similarly

do the one in the q

[delicate meadow]

what it has to do with rule n root of a= m*n root of a^m

[tacit crow]

its the same thing i showed 😭

[delicate meadow]

aaaa

i have to focus

wait

[tacit crow]

gl cmon

you can do this

[delicate meadow]

alr i got this

im doing it and i will send you finished

wait

[tacit crow]

aight

[fallow heart]

,rccw

[delicate meadow]

then i partially root

and i get this one

[tacit crow]

whats this

[delicate meadow]

;rccw

,rccw

[delicate meadow]

which one

[tacit crow]

no no no

you messed up something

[delicate meadow]

let me check

[tacit crow]

why did you square it

[fallow heart]

It's correct, at least by eyeballing it

[tacit crow]

??

no itsn ot

[delicate meadow]

where did i square it

[fallow heart]

Wait, which is the original question?

[delicate meadow]

I have a root from an expression that is already squared

[tacit crow]

wym

[fallow heart]

,w simplify x^(8/3) / x^(3/8)

[thorny flame]

Results provided by WolframAlpha

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

Requested by zuanon.alberto

[delicate meadow]

because 16/3 multiplied with 2

[tacit crow]

i have 2 questions

1. why is it squared
2. where did the 4th root come from

[tacit crow]

where?

[fallow heart]

Yeah, you did it correctly 👍

[tacit crow]

?

[fallow heart]

(even though quite messy, honestly speaking)

[fallow heart]

#help-26 message

[tacit crow]

yea then im tweaking probs

[delicate meadow]

I have a rule which is a on m multiplied is eqaul to a on m*n and here i have (x on 16/3) on square

[tacit crow]

can you like explain this part then

[delicate meadow]

(x316​)2

(x316​)2=x332​

[delicate meadow]

fucc it doesnt use my formulas

[fallow heart]

That had to be made aside, not as part of the equality chain

[delicate meadow]

I have an x which is on square

so there i can get 4 in front

[fallow heart]

That's one of the messy (and wrong) things I was referring to

[delicate meadow]

4 on root of an 16/3

[tacit crow]

nope i still think he has 100% blundered

[delicate meadow]

what the hell this word does

[fallow heart]

Only that blue marked thing, the rest is completely fine (even though really badly written, not the handwriting but for the notation)

[delicate meadow]

It is squared because the expression
𝑥 16/3 ​ was raised to the power of 2, so

(x on 16/3) ^2 is aqual to x on 32/3

[tacit crow]

how did it go from squareroot to 4th root

ive never heard of such identity

[delicate meadow]

Im writting it baddly

[tacit crow]

this is the original q

[delicate meadow]

sorry about that guys

[heavy timber]

(genuine question)
how did this

turn into this

[delicate meadow]

yes

[tacit crow]

exactly my point

[tacit crow]

thats not how it works

[fallow heart]

He has used this identity @tacit crow

[tacit crow]

nope

he blundered

[fallow heart]

Yes, it is...

[tacit crow]

bro

its not like that

this is the identity

[fallow heart]

Yeah and that's what he has solved as well

[tacit crow]

and this is how its used

[delicate meadow]

The fourth root appeared because the square root of the square root gives the fourth root

[fallow heart]

This is not the only existing identity!

[tacit crow]

.

yea bro then you go on w this

im out

peace

[fallow heart]

Yeah but I don't understand your point at all

[tacit crow]

squareroot cant be changed into 4th root

thats completely incorrect

[delicate meadow]

how

[tacit crow]

theres no such identity to change like that either

[delicate meadow]

look

root of and root of a

is 4 root of a

[fallow heart]

@tacit crow

[delicate meadow]

i will write it for z

u

[tacit crow]

yea then thats correct

i havent learned that probs

[delicate meadow]

i just used the rule here in my math problem

then i had the square

which have me 4

i think im getting better

[tacit crow]

idk such identtity

[fallow heart]

$$\sqrt[n]{a^k} = \sqrt[n{\color{red}{m}}]{a^{{\color{red}{m}}k}}$$

[thorny flame]

Alberto Z.

[delicate meadow]

i will send you full picture

im just making it messy here

[fallow heart]

It's just an application of the invariantive property of fractions

[delicate meadow]

rotate it

[tacit crow]

even if the identity is correct he has made blunders in calculations i think

,rccw

[delicate meadow]

se here

i writted rule here

left

[tacit crow]

is this final ans or its in a ratio

[delicate meadow]

in my exercise book yes

[fallow heart]

This is completely acceptable

[delicate meadow]

i can ask my professor to send you completed math problem

i was

doing this math problem

since 3 hours

[tacit crow]

nah dw

im tweaking

then

[delicate meadow]

no bro

relaxed

[heavy timber]

does the question force you to write the answer out in this clean form?

[tacit crow]

no clue

[heavy timber]

or can you simplify it

[delicate meadow]

so guys

A LOT THANK TO YOU ESPECIALLY @tacit crow

[tacit crow]

nope

nvm

the ans is correct

im tweaking

[tacit crow]

nah bro i messed up hard

[delicate meadow]

nah

bro

i have alot bad grades

but

i just writted

[heavy timber]

my previous question was directed at you actually, do you have to write the answer out exactly like that?

[delicate meadow]

yes

[heavy timber]

Because you can do this in around 4-5 equal signs- nvm

ok that makes it a lot harder

[delicate meadow]

it makes

i just

wasted like

[heavy timber]

good job on solving it!

[tacit crow]

tbh i messed up cuz i had no idea such identity exists 😭

[delicate meadow]

8 pages of my book

[tacit crow]

never learned

lol

[delicate meadow]

bro

[heavy timber]

wasted? learning math is about the struggle you know

[delicate meadow]

i just writted this rules u send me on another paper

they helped me alot

[delicate meadow]

i mean

[heavy timber]

its about the quality and efficiency not the time/amount of paper taken

[delicate meadow]

I could have used less notebooks

[heavy timber]

you did great eitherway.

you learned new things

[delicate meadow]

yeah bro i know but it makes me so much frustrating not knowing or not able to do math

im doing this with my bro @tacit crow since 3 hours

1 math problem lol

[heavy timber]

you're doing it pretty well! just keep practising.

[delicate meadow]

listen

i have exam in 2 days

[tacit crow]

you did it pretty well

dw

[heavy timber]

i mean- it is very complicated to get into that specific form

[delicate meadow]

to be honest

[heavy timber]

like i would take hours to put it like that too.

[delicate meadow]

I don't practice math as much as I should

thats why im bad

sometimes i calculate 6*4 on fingers

can you image

[heavy timber]

nah, use your calculator

[delicate meadow]

imagine*

[delicate meadow]

im trying not to use it

[heavy timber]

last time i didnt use my calculator I evalauted 2-4 as 6

[delicate meadow]

YEAH AS 6

[tacit crow]

i think you should remember the tables

[delicate meadow]

you are 100% right

you can blame me guys and i know that

[heavy timber]

I'm a few months away from collage and i only know the 2x and 3x tables.

actually idk half of the 3x

[delicate meadow]

i want to complete my college so baddly

im now second grade high school

[heavy timber]

you're in collage?

[delicate meadow]

no

[heavy timber]

oh

[delicate meadow]

I really like and I know alot about computers but math wasnt my subject

[tacit crow]

so do i say im in college or high school

im 16

high school probs

[heavy timber]

no... algebric manipulation in "advanced" math doesnt require the tables. just calculators

[delicate meadow]

here in bosnia college starts when you finish 4 years of high scchool

school

im now second grade i have 2 more years for college

[heavy timber]

good luck.

[delicate meadow]

thank you guys so much

[heavy timber]

I literally did nothing. I had no idea the sqrt(sqrt(x)) identity existed

but ig so,

ok if you're done

type .close

[delicate meadow]

alright

just one more message

thank you guys alot again, especially my brother @tacit crow

i love you guys

❤️

[tacit crow]

nah i messed up 😭

• you solved it

soo

yea

[delicate meadow]

No bro

[tacit crow]

gl on your exam btw

[delicate meadow]

you litteraly

helped me solve like

60% of problem

thanks

im closing it

goodbye thank you so much so much!

[tacit crow]

aight

[delicate meadow]

.close

[topaz sinew]

Channel closed

Closed by @delicate meadow

Use .reopen if this was a mistake.

[tacit crow]

gl on your exam

[delicate meadow]

thanks

[topaz sinew]

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[marsh rapids]

I need help with this... How can I prove that f(x) = 3x/2

[topaz sinew]

@marsh rapids Has your question been resolved?

[orchid fog]

Yooo

[marsh rapids]

hey

[ruby tree]

You can't since that is not true

!original

[topaz sinew]

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

[topaz sinew]

@marsh rapids Has your question been resolved?

[marsh rapids]

Nvm i figured it out lmao

[topaz sinew]

Channel closed

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Remember:
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[topaz sinew]

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.

[rugged saffron]

.close

[somber oasis]

What

[acoustic pecan]

dont mind it

[topaz sinew]

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Send your question here to claim the channel.

Remember:
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[brittle lark]

So I'm confsued for 4

How are inequalities supposed to be gotten

[acoustic pecan]

think about what sign each factor must have

[brittle lark]

Well x = -2, 1/3, -1

But

The issue is that

How is the inequality supposed to be written

and also

We know it's -x^3

[rancid jasper]

1/3?

[brittle lark]

Meaning that it goes from Q2-Q4

Oh damn

Yes

1/3

ait no

x=3

[rancid jasper]

mb what question u on specifically

[brittle lark]

no x = 1/3

[brittle lark]

4a

[rancid jasper]

wait i thought this quesiton said solve using integrals and i got scared

[brittle lark]

😭

Idek what those are

So thank God it didn't

[rancid jasper]

u can try drawing this out did u try that?

like graphing it

[brittle lark]

The issue isn't drawing out, rather how to state inequalities

Lemme draw it out though just to show my understandingh

[rancid jasper]

like how to state the intervals using inequalities?

[brittle lark]

Yes

[rancid jasper]

oh ok. u know how to state it out without inequalities and just parenthesis right?

[brittle lark]

I mean ik that

above zero: -2 < x < -1, x > 3

That's all ik

or

(-2, -1)

Like as an example

[rancid jasper]

ye that's right

let me try translating it maybe it will help

[brittle lark]

Like why or though

Why are there these certain formatting stuff

I don't get it

[rancid jasper]

u don't get it on the line?

here brother

state me all the questions u got in ur mind

i'll try to answer them

[brittle lark]

Nah like

Why is it or and also

Let me draw it on the line

[rancid jasper]

oooh or and and?

[brittle lark]

Cause I"m afraid I don't understadn it as well bro

[brittle lark]

Yessir

Like why does it say or x > 3

In the answer

Isn't it both?

It has to be both bro

it has to be "and" no? Not "or"

[rancid jasper]

yeah or includes both

[brittle lark]

Oh

Okay and then

Can you give me a sec

To draw a number line for it

[rancid jasper]

think about it like this

[brittle lark]

Just to see if I get it?

[rancid jasper]

a single number x cannot satisfy both the intervals you just gave me

so it can be in -2 < x < -1 OR x > 3 to satisfy being less than 0

so i guess or is more like at least one of these is true

whereas and is they must happen at the same time

does that even make sense?

lmk if u want me to rephrase it

[brittle lark]

Thank you

Sorry french 😭

So I guess

the way it works is that

It cannot be both x > 3 or -2 <x < -1

So thus it's or

[rancid jasper]

wait are u including infinity with that closed dot? (btw that's + infinity right?)

[brittle lark]

Yes

Sorry my handwriting isn't very good

[rancid jasper]

you can't inculde infinity tho

[brittle lark]

Oh why

It goes on for infinitiy

theoretically speaking

[rancid jasper]

infinity is not a real number so u can't include it

[brittle lark]

So until where does the number line have to be

Or do I just draw an arrow

Ohhh wait

So I just draw an arrow instead?

On the inifinity symbol?

[rancid jasper]

ye i don't see why not

maybe don't write infinity just draw the arrow instead

[brittle lark]

Thank you bro

For your help

Appreciate it

.close

[topaz sinew]

Channel closed

Closed by @brittle lark

Use .reopen if this was a mistake.

[topaz sinew]

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[stiff knoll]

Based on this question (#help-31 message) I tried creating some set $\mathbb{R}^{-1}$. I defined it as such:

$\mathbb{R}^{-1} = {x | \forall y \in \mathbb{R}^*, x\times y = 1_{\mathbb{R}} }$.

I managed to prove by contradiction that the distributivity law didn't apply for $\mathbb{R}^{-1}$, but what about commutativity and associativity ?

[thorny flame]

Médicis

[stiff knoll]

@grand solar @prisma cairn @rancid jasper

[prisma cairn]

...

oh

sorry im busy

[stiff knoll]

it's fine

[grand solar]

im a beginner so I wont be of much help 😭

[pseudo sonnet]

commutativity of which operation?

I'm assuming usual addition?

[spice seal]

huh why should it hold for all y?

[pseudo sonnet]

the problem I feel is that x + y needn't even live in R^-1

[pseudo sonnet]

and this too

[spice seal]

u wont have any element in ur set

[pseudo sonnet]

idk what * is defined as though

I know what commutativity means

but yes, your set is empty, isn't it?

[stiff knoll]

because $\mathbb{R}^{-1}$ is the inverse of the entire set $\mathbb{R}$

[thorny flame]

Médicis

[spice seal]

can u give me an example for the existence of such an x

[pseudo sonnet]

there are no real numbers that are an additive inverse to every real number though

you can't find a single element of the set

[stiff knoll]

there wouldn't exist one in |R no

[pseudo sonnet]

if your elements aren't real numbers, then what are they?

[stiff knoll]

sorry then, I had multiplication in mind

[stiff knoll]

you could name them anti-numbers ?

[pseudo sonnet]

how is multiplication defined for these numbers?

[stiff knoll]

idk

[pseudo sonnet]

[stiff knoll]

I supposed they worked like between real numbers, but distributivity doesn't hold so...

[pseudo sonnet]

then how are we going to determine if multiplication is commutative if we don't know how it's defined?

[pseudo sonnet]

mhm

[stiff knoll]

i don't even know how addition would work

how am I supposed to know it 😭

[pseudo sonnet]

usually the onus is on the author to define their set and operations

[stiff knoll]

you mean the ring operations?

what is onus

[spice seal]

responsibility

[stiff knoll]

oh thanks

[topaz sinew]

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[smoky pivot]

Hi is there someone here who is decent at college algebra?

[acoustic pecan]

a couple at least

[grand fulcrum]

Like topology and real analysis?

[smoky pivot]

Ahh still at the starting point

Im currently dealing with functions

[ruby wedge]

whats the question?

[smoky pivot]

I have a test tomorrow but I was sick most this week

I guess how do I graph this correctly?

[acoustic pecan]

whats your understanding of what |f(x)| means

[smoky pivot]

The absolute value

[acoustic pecan]

which does what

[smoky pivot]

Which eh- shows the real value of a number and never can make something negative as a result?...

[ruby wedge]

|f(x)| means that the output of the function will always be positive therefore the only viable options are where the y values are positive, which do you think is best?

[ruby wedge]

technically it is the distance of that number from 0 on the number line

[smoky pivot]

So perhaps... D is the correct answer?...

[acoustic pecan]

D has negative values

and its translated right

[smoky pivot]

Ah-

So then A?

[acoustic pecan]

if x>=0 then |x|=x if x<0 |x|=-x

[smoky pivot]

I hope I'm not overthinking this

[acoustic pecan]

nope, thats moved up

[acoustic pecan]

a little

[ruby wedge]

it has to be a function that preserves the position of the function but forces the output to be positive

[acoustic pecan]

wherever f is negative
it will have been 'reflected' in the x axis essentially

[ruby wedge]

since it is moved it is not the same function

[smoky pivot]

Its not a reflection so it cant be B

Oh-

[ruby wedge]

you see how the minimum of the original function is -2

for |f(x)| it would be 2

what option shows that?

[smoky pivot]

So it would be C?

[ruby wedge]

yes

[smoky pivot]

Ah.

Its jarring to see the function bend like that though

[ruby wedge]

yeah lol

[acoustic pecan]

makes derivatives quite unhappy

[ruby wedge]

indeed

integrating can become a pain sometimes too

[smoky pivot]

I haven't touched math in 4 years I genuinely wonder if I am cut out for going for a biology degree

[ruby wedge]

your good man, just keep practicing

[smoky pivot]

Thanks am I allowed to ask multiple questions? Or is it preferably one simple question?

[ruby wedge]

go ahead

[smoky pivot]

If I cant see the phyical numbefs how do I find the domain of this?

[acoustic pecan]

what do you think it is

just looking at it

[ruby wedge]

first what type of function is it?

[smoky pivot]

I want to say... maybe (-&,&)?

[acoustic pecan]

whats &?

[ruby wedge]

i think it is infinity

[smoky pivot]

Pretend those are infinity signs

[acoustic pecan]

in that case, si

[smoky pivot]

Ah

[acoustic pecan]

those arrows on the line means it just goes on, so theres no bounds on the input
and theres no undefined points on the visible region, so its just R

[smoky pivot]

Oh wait-

Nevermind this is wrong

[ruby wedge]

that's why i asked what function it was so that you could try and base a answer off of that because usually cubic function dont have undefined points

[smoky pivot]

Its a cubic function

But then I suppose it turns into a square function

[ruby wedge]

yes

why do you think that is

[smoky pivot]

Because the absolute value?

[ruby wedge]

correct

it forces outputs to be positive flipping the negative side of the original

[smoky pivot]

Maybe I should go with all real numbers- the points are there to throw me off

[ruby wedge]

yes

[smoky pivot]

Uh... well give me a minute my keyboard is not working for the second time today