help-27

[viral lynx]

What about the power of a

[olive snow]

1^a= 1

[dense jay]

1^a is always 1

[viral lynx]

Ah ok

But wait

They didnt even care about me proving this

They only care about the angle

[dense jay]

No its the angle and where it occurs

You proved the where

Now need to prove its a right angle

[viral lynx]

Whats the best way to do that

[olive snow]

Derivatives 👀

[dense jay]

And negative reciprocals

[viral lynx]

Umm

What do I do with the derivatives

[olive snow]

Product of slopes = -1

[dense jay]

sub in 1, then show they satisfy yaku's property

[viral lynx]

Why 1?

[dense jay]

the point is (1,1)

[viral lynx]

Oh

🤦‍♂️

Okok

So I just set them equal, sub in 1, and solve to get -1

[dense jay]

no

[olive snow]

Prove that : f'(1) * g'(1) = -1

[viral lynx]

Ah

But wait sry

The slopes are not just negative, but also 1/x, right?

[olive snow]

The wrong part is "set them equal"

[viral lynx]

Not x but you get what I mean

[olive snow]

Take the derivatives

[dense jay]

negative reciprocals yeah, its equivalent to saying their product is -1

[viral lynx]

Ah ok

[dense jay]

f'(1)=-1/g'(1)

[viral lynx]

I understand now

[viral lynx]

Ahhhhhhhhhhhhhh thats where it comes from

[olive snow]

Yeah you can see it as you want

[viral lynx]

Ok I understand everything now

[olive snow]

Both are the same

[viral lynx]

Thanks guys you explained it really well

❤️

.close

[devout snow]

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[devout snow]

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[tepid geyser]

I was pondering on how to encode any two rational numbers into an irrational number, and I came across this question. I have already proved that any two rational numbers gives a unique encoded irrational number, and that the encoded number will always be irrational, but I do not know how to get the two rational numbers back within a polynomial amount of time.

[tepid geyser]

I had to set up the friend thing, because not every I2 and I1 combo has two rational numbers

[devout snow]

@tepid geyser Has your question been resolved?

[tepid geyser]

nope

I dont think this is possible with standard algebra, and I dont know of any math systems that allow you to work with different classes of numbers like this

because there are 2 unknowns in one equation

but I know its possible because I proved that for any two rational numbers, it gives a completely unique I2

no, not really

[agile wraith]

i beleive it’s impossible, since any nonzero length interval in the real numbers as uncountable irrational numbers, but countable rationals

so you would need arbitrary precision to fully decode

[tepid geyser]

hmm

[agile wraith]

like you must input the irrational number purely based off of decimal expansion i believe

[tepid geyser]

well for the sake of the problem, lets say that is not an issue

your pc can compute things with irrational square roots by defining numbers in terms of them right?

why not do that?

[agile wraith]

hm?

sorry i don’t exactly understand

[tepid geyser]

well a computer cant compute 4sqrt of 2 with 4*1.41..., it has to compute in terms of the square root

oh

so its an impossible question?

[agile wraith]

yup it’s irreversible

[tepid geyser]

is there a proof of that?

[agile wraith]

even if it stores it that way, it’ll be in the form p + q root(2) and it’s trivial to extract from there

[tepid geyser]

oh

[agile wraith]

what exactly are you trying to prove

given an arbitrary irrational?

[tepid geyser]

that the problem is not possible to solve

[agile wraith]

given an arbitrary irrational, your program won’t encode

you need infinite time as well

[tepid geyser]

just choose one, say the square root of 2

[agile wraith]

^

[tepid geyser]

i guess that number is the passcode

without it, it would definitely be impossible

[agile wraith]

ok so hypothetically suppose you were given l2 and l1

[tepid geyser]

yes

[agile wraith]

and your program reads off the first n bits

we can’t determine what r1 and r2 are based solely off of that

[tepid geyser]

just imagine you had infinite bits

just pure mathematics

but you cant get it exactly

[agile wraith]

ok so assuming fast multiplication, addition etc?

[tepid geyser]

yeah

[agile wraith]

are we assuming that there exists a valid r1 and r2

[tepid geyser]

yes because the friend picked r1 and r2 before

and calculated i2 based off of that

[agile wraith]

hmmm

can i see your proof of injectivity?

[tepid geyser]

injectivity?

[agile wraith]

1-1

[tepid geyser]

okay

well you can assume that if you keep r1 or r2 the same, and change the other one by any amount, it will always lead to a different I2 right?

[agile wraith]

yes

[tepid geyser]

and you want a proof that there is no way to get 2 different combinations of r1 and r2 that lead to the same I2

i have one

Lemme take a photo of it, its in my notebook

I proved it by assuming the opposite was true, then using algebra to make an inconsistency, such as a rational number equaling an irrational number

i is not sqrt(-1) in this case

[agile wraith]

yup

that works

[tepid geyser]

i and j are just irrational numbers

[tepid geyser]

thanks

say you are trying to guess r1 and r2, you pick an arbitrary r1 that is different than the one your friend encoded, and you find the limit of r2 that gets the answer closer and closer to i2. But at the point where it stops being arbitrarily close to i2, and actually becomes i2, then r2 stops being rational

kind of like how you can get arbitrarily close rational approximations of pi, but at the limit, it stops being rational, and actually becomes pi

that was in response to that

[agile wraith]

ok so wait

[tepid geyser]

?

[agile wraith]

if we are assuming infinite bits

[tepid geyser]

bits

[agile wraith]

yeah lol

what exactly is our input size

usually time complexity is in terms of bits of input

[tepid geyser]

i just mean that we can store the number

and do operations with it

i dont think we should store it in base 10

[agile wraith]

yeah but if you look up algorithms they’ll all be a function of their input size

[tepid geyser]

store it in terms of r1 +r2i2

[agile wraith]

i.e. primality tests are in terms of input digits

[tepid geyser]

that was just an example, and im saying I1 is an arbitrary irrational number, and i have proved that if I1 is irrational, then I2 has to be irrational too

pi doesnt really have anything to do with it

okay, so the computer would store it in terms of r1+r2i2, but it cant just look at the values, it has to perform operations and functions to get the values ont their own

so no need for infinite its

buits

bits

oh god

history repeats itself

[agile wraith]

ok so we have an oracle

[tepid geyser]

oracle?

[agile wraith]

that can preform basic operations

[agile wraith]

sort of a black box that can do whatever you want

[tepid geyser]

so imagine you choose sqrt2 as I1

then you can store the number as r1 + r2sqrt2 , but the 'oracle' cannot look at those values, it needs to use a function (that we dont know yet) to get the values r1 and r2 by themselves

I hope this problem has a really cool solution, or even a solution at all

[agile wraith]

yeah seems interesting

[devout snow]

@tepid geyser Has your question been resolved?

[tepid geyser]

nope

[agile wraith]

ok so far, under the assumption that we are allowed to :

• preform any elementary operation with any arbitrary rational, or i1, it is impossible, since we cannot garuntee that we result with 2 rational numbers

as for any stronger claims im not sure

[tepid geyser]

how do you mean

[agile wraith]

hm?

[tepid geyser]

"since we cannot garuntee that we result with 2 rational numbers"

I2 is not arbitrary

it was precalculated by a friend

[agile wraith]

yes

but

[tepid geyser]

the operations dont have to be elementary, go crazy

[agile wraith]

uhhh

[tepid geyser]

i meant go crazy with the operations

[agile wraith]

technically you can literally just use a function that gives you the answer lol

[tepid geyser]

f(x) = the solution to this problem

[agile wraith]

yeah im not too sure how to approach this tho, im pretty sure its impossible

[agile wraith]

yup

[tepid geyser]

kind of like complex numbers, 'i' = the solution to sqrt -1

[agile wraith]

ok so intuitively

small changes in i2

can result in massive changes in r1, r2

just some food for thought

[tepid geyser]

well, actually any arbitrary irrational for i2 has a 0% chance to result in two rational numbers

[agile wraith]

yup

[tepid geyser]

so you would need to precaclulate it and get a value close to your target

are there any other people that might have better luck with the problem?

[agile wraith]

not sure

[tepid geyser]

alright im going to close this, unless anyone else has something to add?

.close

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[devout snow]

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[frozen stump]

Help with 7a pls

[frozen stump]

Og nvm

.close

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[heavy current]

does my proof have any mistakes?
#1260424130822541403 message

[heavy current]

any suggestions are welcome

hey convergence

[fervent hornet]

honourable asking questions

hello higher

[heavy current]

I wonder how unusual this is

I've been asking well before I got it though

[lost laurel]

Eh, you're the youngest honerable ever so far afaik, bound to happen

[fervent hornet]

very much

[lost laurel]

I mean you're yet to start year 2

[heavy current]

I've gotta be the honourable with the least amount of math knowledge

of course I'm asking for help

[fervent hornet]

[heavy current]

not youngest of all time, but probably at the moment yes

[fervent hornet]

moth was prolly the youngest to get it

[heavy current]

I think so too

[heavy current]

fwiw, I've seen senior mods ask questions in the adv channels

it's just not common to see it in the help channels

[fervent hornet]

yeah thats the uncommon part ,not asking questions

[heavy current]

I see

[lost laurel]

As I've said before you're only in year 2, you better ask as many questions as you can.

[heavy current]

I've seen one other person do it in the last month or so

here
#help-14 message

though DM Ashura is an actual teacher 😵‍💫

[fervent hornet]

well this and Zorn asking in help will forever will be remembered in mathcord history

[heavy current]

I am waiting for the day nG asks in one of these

I will straight up resign

[fervent hornet]

who can answer his questions ,maybe delt can understand it ?

[heavy current]

no

[fervent hornet]

not sure if delt can help him tho

[lost laurel]

I'll try to get one of my profs to join mathcord.

[heavy current]

he's told me before that he's had a hard time following nG many times before

[lost laurel]

There are 17 of them , so at least one should be able to do it

[heavy current]

there're a few users I think who can hold a long convo with him though

TTEG comes to mind

[fervent hornet]

who other than CV,sharp and mods?

[heavy current]

probably others like moth too

[heavy current]

not all mods could, for sure

[fervent hornet]

yeah true

[fervent hornet]

TTEG?

[heavy current]

perhaps yamin or potato too?

[heavy current]

topos theory e girl

[lost laurel]

I want to know when I'll be able to answer any other green's question

[fervent hornet]

ah yeah i can see that

[heavy current]

you can for sure

[fervent hornet]

whta abt walter?

[heavy current]

that would probably be another good pick

I don't know how much these users' work overlaps with nG's though

[fervent hornet]

what does nG do ?

idr

[heavy current]

Langlands

[fervent hornet]

[heavy current]

lots of algebraic number theory and arithmetic geometry though

hey evelyn

are you the one I remember?

[fervent hornet]

then not much ig

[heavy current]

bump

I think my proof is sound, but I am not confident

which evelyn is this?

[dense dust]

Hi yes I accidentally typed while clicking btwn channels

[heavy current]

hello!

[dense dust]

Lol

Hello!

[heavy current]

haha, that's okay

would appreciate if you could check my proof though :p

[dense dust]

I'll look

[wicked turtle]

can you explain this part?

why does g(x) have to be in W?

[heavy current]

oh wait

[wicked turtle]

yea g(p) is in W

[heavy current]

I just realized

hmm

[wicked turtle]

but why is g(x)?

[heavy current]

you raise a good point

let me see

right.

this is a problem

[fervent hornet]

hello bungo

[heavy current]

okay hmm

[wicked turtle]

heya convergence!

[wicked turtle]

let me know if you want a hint

[heavy current]

this can't be that hard to fix, right??

[wicked turtle]

possibly not, let me take a look

[heavy current]

I might need a hint...

hold on, cooking...

take 2
#1260424130822541403 message

[wicked turtle]

proof looks good now!

[heavy current]

[heavy current]

how about the counterexample?

[wicked turtle]

i'm not sure i understand the counterexample

first, Y being not hausdorff doesn't automatically mean that every map from X to Y is continuous

Y having the trivial topology does imply that, however

[heavy current]

see what I said

in the channel

I only just realized I made that error, haha

[wicked turtle]

ok

[dense dust]

You would need to show that {0} isn't closed in X, not Y, no?

[wicked turtle]

but the more serious issue...

yes, that ^

[heavy current]

hmm

right, okay.

man, I'm too tired for this

remind me to never do problems at 3am again

[dense dust]

I've figured out a counterexample, if you'd like a hint. It may not be the simplest counter example, though

[heavy current]

I will try to salvage this one first

[wicked turtle]

the good news is that you have a lot of room to play with, since every function is continuous
just think of any two functions from R to R whose set of agreement is not closed in the standard topology on R

[heavy current]

take 3
#1260424130822541403 message

nvm take 3 was a failure

okay, take 4 succeeded

thank you Bungo and evelyn!

.close

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[rose night]

for when u find the critical number, you have to equal the derivative to zero to find the critical Number however, do you find the critical number in the numerator or the denominator?

[rose night]

i know it’s when the derivative is undefined or zero however I get confused as to why some numbers that equal the function to zero before the derivative are not considered as a critical number

[devout snow]

@rose night Has your question been resolved?

[hushed wraith]

a critical point is when the derivative does not exist or is zero...what exactly is ur question?

if f is a function, then a critical point is when f'(x) = 0 or f'(x) DNE. are u asking why x such that f(x) = 0 are not critical points?

[devout snow]

@rose night Has your question been resolved?

[rose night]

.close

[devout snow]

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[wild imp]

hi

[wild imp]

why are

this term being added in

[stone stump]

thats the lagrange remainder term for the taylor expansion

[wild imp]

what does that mean?

[stone stump]

well when you write $f(x) = \sum_{k=0}^n \frac{f^{(k)}(0)}{k!} x^k$, thats wrong

[woven radish]

Denascite

[stone stump]

its not exactly equal to the first n terms of the series, there is some part missing

[wild imp]

why is it wrong...

this is the formula

a = 0

[stone stump]

well and I only let the sum run until n

not until infinity

[wild imp]

but how would this term make up for all the terms after n to infinity

[stone stump]

well you would have to look into the proof for that

[wild imp]

okay

thanks

.close

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[smoky gyro]

how should i start

[ashen stirrup]

i reckon substitution might help, youre told that the parabola is y = x^2

maybe replacing the x^2 term in the circle equation with y and expanding the brackets can help you

[devout snow]

@smoky gyro Has your question been resolved?

[devout snow]

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[viral lynx]

Sorry about my handwriting 😅

The extra question is the one im on ^^

Only context you need to know from the previous parts of the question is that line l is y = x/2 + 4

And point A (0, 4) is on that line

!status

[devout snow]

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

[viral lynx]

4

So what I did:

I used line l

and subbed in a random number for y (y = 0)

To find the point (-8, 0) on line l

And I used that as my direction vector

So I have the 2 vectors:

(-8, 0)t + (0, 4)

And thats my final answer

Is that correct?

[dense jay]

(0,-8) isnt on the line

also a point on a line isnt a direction vector, it wouldnt work

you would need to either use two points, or just contruct one directly from the gradient/slope you have, 1/2

[viral lynx]

Sorry yes I mixed up x and y

[viral lynx]

How would I do that

[dense jay]

the vector (-8,0) wouldnt be in the same direction as l if you imagine it

[dense jay]

if you had two points on the line, (a,b) (c,d)
then (a-c b-d) would be a valid direction vector

you know the slope is 1/2 though

which means moving across 1 on x is up 1/2 on y

which is the vector...?

[viral lynx]

Ahhh yeye I forgot that step

so the vector (-8, -4) is a valid direction vector?

[dense jay]

it would be, sure

[viral lynx]

Ok awesome

And I write my answer in the form (-8, -4)t + (0, 4) right?

[dense jay]

indeed you do, id probably make the direction vector (2,1) though, just looks nicer on the eyes

just divide by -4

[viral lynx]

Ah I see

Okok I get it now

Thank you!

❤️

.close

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[frosty portal]

hey yall

[frosty portal]

can u help me with this

its a homework problem

pls it would be really helpful

[soft umbra]

!status

[devout snow]

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

[frosty portal]

1

[soft umbra]

Hint.1

[devout snow]

@frosty portal Has your question been resolved?

[mild sorrel]

What is 5cm?

[frozen stump]

thats an S? the left side?

[mild sorrel]

Oh mb

[devout snow]

@frosty portal Has your question been resolved?

[devout snow]

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[regal dust]

help

[regal dust]

sooo i kinda dont get it :)

im kinda slow sorry

ToT

[lavish quarry]

looks like its squared

[regal dust]

but i dont know how to write it in explicit form

[restive river]

1, 4, 9, 16, 25, 37, 52

[regal dust]

i kinda get how i was meant to solve it

[restive river]

growth series of affine coxeter group

[lavish quarry]

maybe an = n^2

[regal dust]

ohh that works

thanks to the both of you T^T

LOVE THE PEOPLE IN DIS COMMUNITY ZXO MUCH <333

.close

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[lavish quarry]

shouldnt it be 36 and 49

[devout snow]

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[modern tide]

help anyone

[modern tide]

in my notes I used trial and error to get to answer letter d

[solid osprey]

you can defidently get d

wait nvm

thats correct

[modern tide]

I might have forgotten how I did it

[solid osprey]

use algebra

[winter patrol]

d isn't correct

[hollow ice]

16 is max possible since square would have the highest area of all rectangle with same perimeter

[modern tide]

really?

[hollow ice]

so 24 cant be possible so answer is e

[solid osprey]

wait i thought it was the last choice

e is incorrect ye

im fucking tired but i need to study :iirikdf

[modern tide]

I meant e here btw

[solid osprey]

you use algebra

[winter patrol]

e is correct, yeh

[hollow ice]

Also, a cheesy way is if 16 cant be possible, theres no way 24 is possible. So, 24 is the only answer possible [common sense, no math answer ]

[solid osprey]

let x and y be the side lengths
2x+2y=16
xy=24 wont work

[modern tide]

oh

is that all?

yea I got that much better

[hollow ice]

you can convert this into a quadratic equation so that you have: z^2 + (x+y)z + xy = 0
where z is possible sides of rectangle

[solid osprey]

actually 24 works im pretty sure

assuming you let the sides be 4±2isqrt2 :3

[hollow ice]

and when x*y is 24, you cant get real roots to the z, so rectangle cant have non-real roots

so 24 is answer

[modern tide]

uhuhh

but the easier method is

[modern tide]

this?

[hollow ice]

that is a statement, not proof

you need to explain WHY not possible

[modern tide]

I mean but in terms of college exams where its multiple choice

[solid osprey]

can you use amgm here

[modern tide]

and like you only get a minute per question

[hollow ice]

yeah, but if you think you can do it when the numbers are differnt, sure

[solid osprey]

(2x+2y)/2>=sqrt(4xy)
8>=2sqrt(xy)
4>=sqrt(xy)
16>=xy
inequality happens when x=y

mrrow

[modern tide]

fair

[modern tide]

wait so is the solution here not practical

considering the context

[tulip hatch]

My brain would go to derivatives lol

[modern tide]

my brain kinda fried rn

but like at the base of it

its js applying the concept of perimeter and area of a rectangle right?

[cold bone]

?

your problem is still not solved?

[modern tide]

I mean I got it right

but

im kinda fried in figuring out how I got it

and how to solve things like that in a quick way

[cold bone]

that's a strange issue

but anyways

[modern tide]

cus I answered jt abt a wk ago

[lavish quarry]

if you want to prove it u can use am-gm inequality

[cold bone]

Skill Issue's methos is perfect

[cold bone]

fr

[cold bone]

that's literally the most efficient way to get the answer

[lavish quarry]

but since the area is smaller the answer would just be the biggest one

assuming there is 1 answer

[modern tide]

how I did it?

[cold bone]

@modern tide what problem did you find in understanding Skill Issue's AM-GM inequality method?

[modern tide]

what's am -gm

[cold bone]

Arithmetic and Geometric mean

[modern tide]

this one?

[cold bone]

yes

[modern tide]

oh that's the only one I get

all the other's ppl said here I dont

[modern tide]

like this one

[cold bone]

yeah it is the best method here

[modern tide]

I see

and would it be able to be applied to other similar problems?

[cold bone]

yeah ig

depends on the problem

[modern tide]

like that?

[modern tide]

I mean if it was structured like that w other numbers

*different

[cold bone]

what do you mean by different?

[modern tide]

diffirent given I mean

[cold bone]

like different data?

AM-GM inequality is applicable in any problem that revolves around strictly positive numbers

[modern tide]

alright then got it

thanks again!

also why is jt called am - gm

[modern tide]

this

[cold bone]

(a+b)/2 is arithmetic mean of a and b
sqrt(ab) is geometric mean of a and b

Arithmetic mean is greater than or equal to the geometric mean of the same numbers

and they become equal when all the numbers are equal

it's not that useful to remember for now but just for the information

[devout snow]

@modern tide Has your question been resolved?

[devout snow]

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[candid lance]

The top q

[warm breach]

that's pair of straight lines

[candid lance]

Well yeah

[warm breach]

apply the formula

you can also apply this

[devout snow]

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[cosmic junco]

Would P(AnB) be 0 then?

Thats a better photo

since

P(AuB) = P(A) + P(B) which is already 0.55

so

0.55 = P(A) + P(B) - P(AnB)

would leave P(AnB) with zero right??

[topaz axle]

of course

[cosmic junco]

Thank you, I wanted to make sure I wasn't missing anything!

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[restive river]

Why secx cscx can't be 1?

If... then calculate...

[hushed lance]

Where did the + between sec^2 and csc^2 go

i think it should be
sec^2(x)+csc^2(x)-3=-2sec(x)csc(x)

[devout snow]

@restive river Has your question been resolved?

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[restive river]

There is an identity

[restive river]

sec^2(x) + csc^2(x) = sec^2(x)csc^2(x)

You can demostrate it as well

[hushed lance]

Oh i see

[restive river]

Yep

[hushed lance]

ah its because

for sec x csc x to be 1

sin x cos x have to be 1

because sin and cos are always between -1 and 1, the only way you can have sin x cos x=1 is for sin x=1 and cos x=1, or sin x=-1 and cos x=-1 which are both impossible

[restive river]

Ohh you're right, it's impossible
thanks (:

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[silk topaz]

not sure what the first step is

can i set them both equal to 0?

so solutions are

x = -5/3, 3/2

do i plot them on a number line now or what...

[gusty nexus]

you don't have to "plot" them, I normally prefer getting rid of abs
for example for x's lower than -5/3 the equation will be $-3x-5-2x+3 = 25$

[woven radish]

MetuMortis

[silk topaz]

oh wait cant i do

i know what i can do i think

theres 4 solutions?

[gusty nexus]

I'd write other equations (equations for x's between -5/3 and 3/2 and also for x's bigger than 3/2

I didn't solve it

[silk topaz]

x = 20/3, -10, 14, -11

those are the four solutions no?

[gusty nexus]

put them into the original equation and test them

[silk topaz]

okay well 20/3 doesnt work

nor does -10

nor does 14

nor does -11

what do i do

none of them work

[gusty nexus]

can you try write equations that does not have absolutes

[silk topaz]

so just remove them?

so then

3x + 5 + 2x - 3 = 25

errr

now what do i do

i can find solutions if it was just

|2x - 3| = 25

but an absolute value is being added by another

how is this solved

im still stuck on the first step

im lost

[silk topaz]

?

can you explain what you wrote

i get how x = -5/3, 3/2

but what is y???

[gusty nexus]

y is the result, you will be trying to solve equations for y = 25

[silk topaz]

so can you tell me what im supposed to do?

im still lost

[gusty nexus]

for x values less then -5/3 you will do $y = -5x-2$

[woven radish]

MetuMortis

[silk topaz]

what

[gusty nexus]

for x values between -5/3 and 3/2 you will do $y = -x+8$

[woven radish]

MetuMortis

[silk topaz]

still dont get it

i dont know what ur doing at all

i can solve the equation

|2x +3| = 25

but i cant solve

when its two absolute values being added together

what do i even do because 4 solutions didnt work

theres a step im missing

[gusty nexus]

if x is less then -5/3, $|3x+5| = -3x-5$ isn't it?

[woven radish]

MetuMortis

[silk topaz]

what

im not getting this at all

[gusty nexus]

can you put -10 into |3x+5|, what result do you get

[silk topaz]

25

[gusty nexus]

can you put -10 into -3x -5 what do you get

[silk topaz]

25

[gusty nexus]

yes this is what I'm trying to say

this is how abs works

[silk topaz]

but how does that even sovle the question

i dont know what you jsut did

[gusty nexus]

I doon't think I am able to expalin it, I'd suggest you to tag Helper role (@ Helper)

[silk topaz]

<@&286206848099549185>

okay thanks for your help anyways

[hybrid moth]

wait I swear I've seen this in a roblox game 💀

[silk topaz]

oh fr

regardless someone help me

[quasi mantle]

Lmoooaa

[silk topaz]

oh dam

plz help me tho

<@&286206848099549185>

[hybrid moth]

I got -4/5

[silk topaz]

but explain HOW

[hybrid moth]

ok

so I use the rule of subadditivity

[silk topaz]

and explain

[hybrid moth]

where |x+y|<=|x|+|y|

I'll replace x with m

and y with n

and let 3x+5=n and 2x-3=n

so

the first one

is M

ok so |m+n| <= |m| + |n| = 25

which means that |m+n|<=25

I'll substitute m=3x+5 and n=2x-3 and then simplify inside the absolute value sign to get |5x+2|<=25

then split the absolute value to get 5x+2<=25 AND 5x+2>=-25

I'll simplify both and get rid of the AND to get -27/2<=x<=23/2

wait

no -27/5<=x<=23/5

these are the least and greatest values

and then I add them to get -4/5

[silk topaz]

ohhhh

ok thank you

imma summarize it so i learn it

so

3x + 5 = m

2x - 3 = n

then put them together into one abs

simplify

|5x + 2| = 25

then expand it

|5x + 2| <= 25

[hybrid moth]

less than or equal to

not equal to

[silk topaz]

|5x + 2| >= -25

[hybrid moth]

other way around

and you don't need the absolute value signs anymore

[silk topaz]

5x + 2 <= 25
5x + 2 >= -25

then, solve for x

leaving,

-27/5 <= x <= 23/5

then, find the sum of the highest and lowest values

leaving

-4/5

ok thank you

[hybrid moth]

np

[silk topaz]

.close

[devout snow]

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[silk topaz]

i think the first thing i can do i flip the

1/log_x(3)

to change the base

to

log_3(x)

so now

imma make

log_3(x) = t

so now the equation is

wait hold on'

im gonna do

the denominator on the lhs can be

expanded

to

log_3(x) - log_3(9)

which imma just turn into 2

so lhs is

[harsh trout]

then basically let u=log3(x)

it would become an algebraic equation

then solve for u

substitute to get x

[silk topaz]

(2t) - 4/t - 2

is the lhs

[harsh trout]

and notice x is not 1 and x is bigger than 0

[silk topaz]

wait what

[silk topaz]

i made it equal to t

not u

[scenic surge]

same thing

[harsh trout]

whatever

[silk topaz]

oh nvm

but is this correct for the left hand side

(2t) - 4/t - 2

[scenic surge]

ye

[silk topaz]

ok ok

[scenic surge]

W username btw

[silk topaz]

thank u

[silk topaz]

oh hell naw

[scenic surge]

😭

[silk topaz]

lone aint ever do that

ok anyways

imma simplify rhs

7t - t^2 - 8

is the rhs

[scenic surge]

yuh

[silk topaz]

so now we have

(2t) - 4/t - 2 = 7t - t^2 - 8

[scenic surge]

u can simplify lhs even further

[silk topaz]

imma move everything now

oh how

[scenic surge]

2(t-2)/t-2 and cancel t-2

2 = 7t-t^2-8

[silk topaz]

oh nice

so then,

[harsh trout]

notice when you cancel it out. you should keep in mind t can't be 2

[silk topaz]

-t^2 + 7t - 10 = 0

[silk topaz]

yes thats a hole

on the graph

im gonna use quadratic formuola no

now

[harsh trout]

and it is going to show up in the solutions of that equation. so you have to be careful about that

[silk topaz]

yeah it did

on but now

co so i have 4 solutions but i have to replace t with its variable

[harsh trout]

4 ?

[silk topaz]

oh i mean 2

srry

[harsh trout]

2 ?

[silk topaz]

x = 2, 5

i mean

t = 2, 5

[harsh trout]

yes but t cant be 2

[silk topaz]

so now we replace t

[harsh trout]

so there is only one solution

[silk topaz]

oh yeah

t = 5

time to replace

log_3(x) = 5

so

3^5 = x

x = 243

[harsh trout]

true

[silk topaz]

ok niceee that wasnt too hard

thanks for the help @harsh trout @scenic surge

.close

[harsh trout]

np

[devout snow]

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[wooden meteor]

can someone help me with this question

[wooden meteor]

not even sure how to approach it

ik vietas formula

for sum of solutions

which is -b/a

but im not sure that applies here

maybe im wrong tho

[jaunty mantle]

Well this is a quadratic in x

The sum of solutions is -b/a as you said

So find what b and a are for this quadratic

[wooden meteor]

wud i have 2

multiply

the whole thing out

[jaunty mantle]

Jokes on you

This ain’t a quadratic

Lmao

[wooden meteor]

😭

[jaunty mantle]

Errr

Okay

No problem

They are individually quadratics in x

We can factorise them

Then we can see what every root of this quintic is

Then we can just add them all up

[wooden meteor]

i was thinking about that but 3x+p isnt a quadratic

and it has a constant variable

[jaunty mantle]

It doesn’t matter

(x-a)(x-b)(x-c)(x-d)(x-e) is the general factorised form of any quintic

This quintic has roots a b c d e

[wooden meteor]

OHH

i got it

now

[jaunty mantle]

Every quintic can be written like this (if you allow for complex numbers as well)

Hell yeah

[wooden meteor]

so u wud add the sum of the solutions for the two exists quadratics, then subtract p from them and set them equal to 20/3?

actually wait no

ok wait

wud u do -b/a for 3x+p

[jaunty mantle]

No no no

I’d forget about -b/a

[jaunty mantle]

From here I just go a + b + c + d + e = 20/3

[wooden meteor]

ok yes i get this

and i get

add the solutions from both quadratics

but what am i supposed 2 do

with

3x+p

[jaunty mantle]

Oh actually this is faster

Add p/3

Oh

Add -p/3

[wooden meteor]

genius

ok bet

thank u

[jaunty mantle]

That’s the root for 3x + p

[wooden meteor]

.close

[devout snow]

Channel closed

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[jaunty mantle]

This doesn’t work because a = 0

[wooden meteor]

.open

nvm

wait

nvm

XD

[devout snow]

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[toxic abyss]

quick question how do i figure out what quadrant theta is in?

[toxic abyss]

nvm i’m dumb

oops

[umbral shuttle]

ope

k

[toxic abyss]

it’s 3 right

cause it’s -x -y

[umbral shuttle]

wha

[toxic abyss]

quadrant 3?

[umbral shuttle]

uh

yes

and 1

actually

[toxic abyss]

okie ty

[umbral shuttle]

wait

[toxic abyss]

o

(i thibk just 3??)

might be lying

[umbral shuttle]

I think it's quadrant 1 cause of the range of tangent

tangent inverse*

I might be wrong

[toxic abyss]

idek

the answer key only has one

as in

[hollow ice]

Yep, you are right max

[toxic abyss]

ok thank you bacter

[umbral shuttle]

woops

mb

[toxic abyss]

no worries lol

[umbral shuttle]

I really need to refresh my precalc

[hollow ice]

the direction vector goes into 3rd Q coz signs of coeff

[toxic abyss]

ooooo

thank you guys for help!

.close

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[restive river]

What’s the best advice you have for becoming a good mathematician?

[boreal helm]

Be lazy

[cold bone]

bro's literally asking most Overpowered questions today

[restive river]

wa da fuq

[boreal helm]

Instead of your hands moving fast

Your brain should move fast

That's why I said be lazy

[restive river]

so basically be efficient 💀

[boreal helm]

2nd advice know what you are studying

Some people just study

[restive river]

true

[boreal helm]

They don't actually know all about and around what are they studying

3rd chill and keep preparing

4th be simple

Maths is not a subject it's art

One shall not complicate himself by his words

[restive river]

bro do you do mathsmatics and philosophy?

💀

[restive river]

ur words is inspiring me rn

[boreal helm]

The most important thing

[deep vortex]

the four principles of mathematical success huh

[boreal helm]

Ponder

About things

But upto a limit such that they don't waste or eat your time

[restive river]

fr

all i do is pondering about women

i need to change fr

[boreal helm]

💀

[rancid cave]

💀

[boreal helm]

Actually

Imma not lie

In this small world

Neither maths nor woman could take u anywhere

The thing which can take u is

money

[restive river]

🔥

FR

[rancid cave]

What about Pilots

[boreal helm]

Na bruh i depress myself

[rancid cave]

They can take you almost anywhere

[restive river]

.....

[boreal helm]

Bro they earn money too

[rancid cave]

As long as there's an airport

[boreal helm]

And that too a hefty amount

Fr

[restive river]

dude r u a uni student?

u sound like very old philosopher

[boreal helm]

Fr

[restive river]

who realised that money is the way

[boreal helm]

Seen too much

[restive river]

fr

[boreal helm]

Money gives u everything

[restive river]

FR

[boreal helm]

But everything eats money

[restive river]

lol

[boreal helm]

U urself think

U are using your selfphone

It's self phone ofc

You are using internet

U pay data bills

[restive river]

[rancid cave]

[boreal helm]

Nothing is free everything has a cost

💀

[restive river]

💀

fr

[rancid cave]

You even pay for funeral

[restive river]

you even pay for marriage

[boreal helm]

You pay your whole life for funeral ⚱️

[restive river]

bro u can't actually live without spending money in each day

😭

[rancid cave]

You forgot about monks

[boreal helm]

They be good

[restive river]

BRO they can't live wiithout food

[boreal helm]

They focus

[restive river]

food = money

[boreal helm]

And strengthen their aura

[rancid cave]

Nahh

[deep vortex]

What did this help channel turn into lmao

Anyways, you don't need that much money imo

[boreal helm]

A 3am session

[rancid cave]

Think about those who live in mountains

[boreal helm]

Fr 💀

[rancid cave]

And eat fruits and stuff to survive

And meditate all day

[boreal helm]

See

They have given up this worldy life

[rancid cave]

They don't pay shit

[deep vortex]

Just be able to rent a flat or something and still have some left over

[boreal helm]

U cant

[rancid cave]

They don't do taxes

[boreal helm]

I am not taking bout monks of sants

[restive river]

bro ngl people tells me that i should do what im passionate about

[boreal helm]

I am talking bout us

[restive river]

im passionate about making moeny

[boreal helm]

A general person

[rancid cave]

That's wild

I just wanna be happy

[boreal helm]

Let me tell u the logic

[restive river]

MAKING MONEY = HAPPINESS

[boreal helm]

Money gives financial freedom

[restive river]

yh

[boreal helm]

That freedom gives happiness

[restive river]

ffr

[boreal helm]

Like imagine having millions of bills in the accounts

[cold bone]

bro wants that Crypto advertisement in the chat

[boreal helm]

Just enjoy

[rancid cave]

This looks like one of those Andrew tate podcasts 💀

[boreal helm]

Do whatever u want

[restive river]

💀