help-13

[crimson sedge]

pls help

[crimson sedge]

<@&286206848099549185>

.resolve

.close

[cedar kiln]

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[amber mural]

what does the k mean

[deft mirage]

Any arbitrary integer

[amber mural]

how do u find those

[deft mirage]

They are just there for consistency

You arent meant to find them

Its similar to an integration constant

[bright surge]

their point is that, for every integer K, this is true

[amber mural]

how come this 9 just came out of nowhere 😭

[bright surge]

set k = 9

k can be whateer

*whetever

*whatevvr

*whatrev

*whareaer

*whatever

r/ihadastroke

[amber mural]

reddit wholesome big chungus moment

[bright surge]

anyways

[amber mural]

yea but what was the reason why 9 was used?

[bright surge]

@amber mural theta + k*360deg is a coterminal angle for every integer k

[bright surge]

example, i guess? you can replace it with 5 or 6439206 or 3716845947831657483195647831 and it will still work

[cedar kiln]

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[viral basalt]

Someone pls help me how to do this using double integrals

I keep getting answer as 0

<@&286206848099549185>

<@&286206848099549185>

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[jade crystal]

I know that $\int_{-\infty}^{\infty}p(x) = 1$ but idk how to do that integral

[wraith dagger]

nova

[bright surge]

alright

we have $\int_{-\infty}^{\infty} p(x) \dd x = \int_{-r}^{r} p(x) \dd x$

[wraith dagger]

Kanga Gang Advocate Adavocowana

[jade crystal]

oh

[bright surge]

right? @jade crystal? since for |x|>r, p(x)=0

then bring 1/N outside the integral, since it's just a constant

the rest is simple

[jade crystal]

i feel so stupid

thank you

.close

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[sweet wedge]

Match the rational form and expressions with rational exponents

1. 25½
2. 64⅓
3. 81½
4. 27⅓
5. 16¼
6. 8⁰
7. (3x)¾
8. 2⅔
9. 5ab½
10. (125x³)⅓

Column B

A.³/125x³
B.5
C.9
D.²/5ab
E.³/4
F.⁴/27x.³
G.1
H.2
I.3
J.4

[sweet wedge]

help please

[bright surge]

cmon you're shinichi this should be really easy

jk

i don't even understand a eingle expression

send the original question please

this is really hard to read

[sweet wedge]

wait

Match the rational form and expressions with rational exponents on column A to column B

[bright surge]

,rotate

[bright surge]

do you know what $x^{\frac{1}{2}}$ mean?

[wraith dagger]

Kanga Gang Advocate Adavocowana

[bright surge]

@sweet wedge

[sweet wedge]

yeah, maybe

[bright surge]

well

we have $x^ax^b=x^{a+b}$

[wraith dagger]

Kanga Gang Advocate Adavocowana

[bright surge]

therefore, $x^{\frac{1}{2}}x^{\frac{1}{2}} = x^1=x$

[wraith dagger]

Kanga Gang Advocate Adavocowana

[bright surge]

@sweet wedge so what should x^1/2 be?

[sweet wedge]

uhm

[sweet wedge]

wait i ddnt got it

[bright surge]

x^1/2 times itself is x

think of another number that has this property

[sweet wedge]

is this x^1?

sorry im really bad at math

[bright surge]

nope

x^1 times x^1 is x^1+1 = x^2

[bright surge]

choose another username please

[sweet wedge]

okay

[bright surge]

just kidding!

i mean

the other numbers that have this property are $\pm \sqrt{x}$

[wraith dagger]

Kanga Gang Advocate Adavocowana

[bright surge]

since we want f(x)=x^1/2 to be a function, we will only take the positive root (sqrt x).

@sweet wedge

[sweet wedge]

okay

[bright surge]

so $x^{\frac{1}{2}} = \sqrt{x}}$

[wraith dagger]

Kanga Gang Advocate Adavocowana
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[bright surge]

@sweet wedge

[sweet wedge]

okay

[bright surge]

(just a question) what's $x^{\frac{1}{3}}$?

[wraith dagger]

Kanga Gang Advocate Adavocowana

[sweet wedge]

^3 sqrt x^3?

hah idk

[cedar kiln]

@sweet wedge Has your question been resolved?

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[bleak wraith]

this is the graphh of the present value of some amount of money

[bleak wraith]

when the time tends to infinity

but when i do $PV = lim_{t\to \infty}(\frac{FV}{(1+t)^t})$

[wraith dagger]

Guilhotina

[bleak wraith]

where PV = present value

FV future value

i the interest rate

and t the time

i get 0

not this graph

what i'm doing wrong in the limit ?

i is positive

[elfin hemlock]

What is i?

[bleak wraith]

interest rate

[elfin hemlock]

Why is it not (1+1/t)^t?

That is the formula

[bleak wraith]

because (1 +1/t)^t is when we the interest rate is compound at the mimum time possible

every time

not in years but is continually compounding

wait i stat the formula wrong, it's $\sum_{1}^{t}\frac{FV}{(1+i)^t}$

[wraith dagger]

Guilhotina

[bleak wraith]

and t goes to infinty

but how do I do limits of sums?

[elfin hemlock]

Why wouldn’t present value approach 0? If you had 1 dollar and you let it compound at 5% interest rate for 100 years you would have a lot of money, even more for 1000 years, what about 10000000 years?

And t->inf future value approaches inf

[bleak wraith]

yeoook makes sense

so when i do the limt of a sum of cash flows

the value tends to stabilize because at one point the present value of the cash flow are really smal

[cedar kiln]

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[crimson sedge]

god

[crimson sedge]

how do i do this

Let $f$ be a function such that $f(x+y) = x + f(y)$ for any two real numbers $x$ and $y$. If $f(0) = 2$, then what is

[wraith dagger]

crab

[tight bolt]

what is what

?

[graceful karma]

Simply what is

[tight bolt]

f(k)=k+2

?

[granite harness]

This also gives f(2-2)=-2+f(2), so f(2)=0

I think you can proceed adding zero to find more values of f(y)

Uh no nevermind

So I think it’s something like f(x)=x+2 for x>= c And f(x)=x-2 for x<c, and c is maybe 2?

No that’s not price wise continuous

[crimson sedge]

what should i simplify to?

[crimson sedge]

how did you come up with that?

[granite harness]

If it’s true that f(0)=2, choose y=2, x=-2, then x+y=0

[crimson sedge]

ok

then f(2)=4

[granite harness]

Yes

Ok so maybe my equation is right and it isn’t piecewise continuous

[crimson sedge]

but x and y can be many other things

wait

is the answer 4024

[dense wing]

???

what are you even trying to solve?

You never actually finished your question.. you gave a random functional eqn

[crimson sedge]

wdym?

[dense wing]

I mean... you never finished your question

No fucking clue what you're trying to solve for.

[dense wing]

.

what is..............

[crimson sedge]

oh

Let $f$ be a function such that $f(x+y) = x + f(y)$ for any two real numbers $x$ and $y$. If $f(0) = 2$, then what is $f(2012)?$

[wraith dagger]

crab

[crimson sedge]

f(2012) = f(2012 + 0) = ?

[dense wing]

oh true

[crimson sedge]

so the answer is, 2012?

Nope

but f(y) = y*2

What?

in the example f(0)=2

f(-2+2)=-2+f(2)

f(2)=4

[crimson sedge]

im confused

Ok so f(2) = 4

So what?

[dense wing]

apply the definition of the function to f(2012+0)

[crimson sedge]

It clearly is not the case that f(y) = y*2 in general because f(0) = 2

[crimson sedge]

the answer is 2016

because

f(2012+0) = 2012 + f(0)

and f(0) = 2

[dense wing]

??????

[crimson sedge]

Lol

2014

lol

Yes

[dense wing]

yes, the answer is 2014.

[crimson sedge]

also, why did you split it into 2012+0

and not anything else

i mean, it makes sense

[dense wing]

you dont know anything else a priori

[crimson sedge]

yeah

Because I knew it would be a useful statement somehow

thank you!

[dense wing]

you know what happens to 0 and want to know what happens to 2012

[crimson sedge]

yup

.close

[cedar kiln]

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[crimson sedge]

hey everyone would someone be able to explain exactly what this question is asking for? this is a brand new topic to me and i do not know what i am doing?

[crimson sedge]

i have answer it like this

but again i am really not sure what we are doing or trying to achieve

[obsidian coral]

I believe it wants you to find the zeros of that function

[crimson sedge]

could you expand upon that please?

the zeros of the function?

[obsidian coral]

The roots of the function

X - intercepts?

All mean the same

[crimson sedge]

with the question all i did was change the x-3 to x + 3

and then put that value into the equation then just multiplied them out that then gave me zero?

[obsidian coral]

Did you learn polynomial long division?

[obsidian coral]

Also, you can't just do that

[crimson sedge]

kinda i hate polynomial long division

that stuff made me go mad

[obsidian coral]

That's what you needed to do

[cedar kiln]

@crimson sedge Has your question been resolved?

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[fervent quartz]

Ok, so hear me out it’s a bit embarrassing but can anyone explain to me a/b = c/d
is ad = bc

[kindred sand]

take the reciprocals then cross multiply

[floral thistle]

multiply both sides by bd

[kindred sand]

or that

[fervent quartz]

K

Thx

.close

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[floral thistle]

0 = $4\pi r - \frac{30}{r^2}$

[wraith dagger]

quantum

[halcyon lantern]

hi

[floral thistle]

just multiply both sides by r^2

then add 30 to both sides

[cedar kiln]

@clear grail Has your question been resolved?

[fossil karma]

hello

[cedar kiln]

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[cedar kiln]

@white hornet Has your question been resolved?

[fallen solar]

factorise it as $x^2 (x^3 + a) = 9$ maybe?

[wraith dagger]

Peppermint Demon

[fallen solar]

this implies x^2 and x^3 + a are both factors of 9

and both are integers by the setup of the question

now casework, i guess

[white hornet]

nice

I have another question

so

a+b=5432

lcm(a,b) = 223020

[fallen solar]

lord this is going to be painful

calculators allowed?

[white hornet]

yes

[fallen solar]

great

hmm

a = g * m
b = g * n
where m and n is coprime

so 223020 = ab/g

and g(m+n) = 5432

meaning g | 5432

try using this

[white hornet]

g|5432?

[fallen solar]

g divides 5432

[white hornet]

and also what does g represent

[fallen solar]

gcd of a and b

[white hornet]

okty

wait

what should I do with g/5432

[fallen solar]

it would be better to use g(m+n) = 5432

that's just to say that g is a factor of 5432

[fallen solar]

prime factorise 5432 and see the cases for g and m+n

then use ab/g = 223020

[white hornet]

oh

ab/g?

for example if g is 2

(m+n) is 2716

and then?

[fallen solar]

a = g * m
b = g * n

[white hornet]

then u means

g^2mn？

[fallen solar]

divided by g

[white hornet]

o

so

ab = g^2mn

ab/g

=

gmn

[fallen solar]

and ab/g is the LCM

[white hornet]

how do we know mn

we only know m+n

[fallen solar]

gmn = what?

[white hornet]

ab/g

[fallen solar]

i mean what integer

[white hornet]

223020

[fallen solar]

so gmn = 223020
and g(m+n) = 5432
and m and n are coprime

so what should we try doing now?

[white hornet]

try different g?

and we got m+n and mn

and calculate m and n see if they are comprime?

[fallen solar]

mhm

well its better to choose m and n to be coprime

and then check if they satisfy the conditions

because the other way would be a bit tedious i guess

[white hornet]

so we prime factorization 223020

and try every m and n?

[fallen solar]

yes, and g should be a common divisor of both 223020 and 5432

and m+n should obviously be smaller than 5432

equal also might work

[white hornet]

OK

ty

.close

[cedar kiln]

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[naive spear]

could someone help to work out the moment at b?

[naive spear]

This is what i drew

[cedar kiln]

@naive spear Has your question been resolved?

[naive spear]

<@&286206848099549185>

[cedar kiln]

@naive spear Has your question been resolved?

[cedar kiln]

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[crimson sedge]

I need help with this

I already did this but my teacher kept saying this was wrong so i kept doing it and keep getting the same awser

[cobalt leaf]

@crimson sedge what answers did you come up with?

[crimson sedge]

The first was many the 2 was one the 3 one and the last one no

Can anyone give me the awser for this

@cobalt leaf

<@&286206848099549185>

[void whale]

I disagree with you on the second and 4th one

[snow hull]

Can you take a better picture of the question please?

[crimson sedge]

Yes

[crimson sedge]

There you go

[cobalt leaf]

@crimson sedge solve the equation if you get something like 0=0 then it’s infinite solutions

If you get something like 2 = 75 (obviously not equal) it’s no solutions

[crimson sedge]

I just need the awser cuz we just started learning Abt this

[cobalt leaf]

If I give you the answer you won’t learn

Let me know if you want me to explain further

[crimson sedge]

We just started learning that's the thing

[cobalt leaf]

Okay let me explain

[crimson sedge]

And this counts as 70% as my math grade

[cobalt leaf]

Do you know how to solve equations?

[crimson sedge]

Not really since I was out of school for a while since I got sick due to covid

[snow hull]

Ah yeah

[crimson sedge]

So like I really need the awser for this one cuz I was sick so my grade it pretty bad

[cobalt leaf]

@crimson sedge This should help https://youtu.be/v5c-YkZtlZw

[snow hull]

The first one is a linear equation,did you solve it?

[crimson sedge]

I guess since I don't know algebra

My buddy said the first was inf

[crimson sedge]

Can I get the awser for the 4

[cobalt leaf]

@crimson sedge Have a look at the video I sent you and then after solving check if it meets with what is mentioned in this message

[crimson sedge]

Kk

[crimson sedge]

Wait I can't see a vid am at school and am texting while doing this test

So I can't hear anything

[cobalt leaf]

#❓how-to-get-help #rules

Can’t help with tests sorry. Well hey try your best in this test and if you can’t manage to get it right comeback and have a look at the material suggested above and you can be prepared for the next test

[crimson sedge]

Kk

[snow hull]

It has one solution

1

[crimson sedge]

Already submitted ty tho

[cedar kiln]

@crimson sedge Has your question been resolved?

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[echo briar]

how can I multiply X by something every certain amount of units using a piecewise function?

[echo briar]

e.g. multiply X by 1.02 every 3 units

[floral thistle]

heaviside step function possibly

[graceful karma]

On average or all at once

[floral thistle]

https://tutorial.math.lamar.edu/Classes/DE/StepFunctions.aspx

only look at the top of this page

[graceful karma]

That might be a bit on the heaviside

[floral thistle]

everything else is laplace transform stuff which you don’t want lol

asks a simple question, gets an answer about odes

[graceful karma]

Who even needs laplace transforms though just use pure brainpower

Tbh

[floral thistle]

why use derivatives just guess the slope

[graceful karma]

Use a ruler

[floral thistle]

you would definitely need to use a summation to get what you want though

and this would really only work for consistent steps in that case

unless you want it over an interval, in that case whatever works

i feel like i over complicated this question

[echo briar]

I take it there’s no easy way to do this -_-

[graceful karma]

Depends

[floral thistle]

not that i can think of

[graceful karma]

Wait and to be sure you want like steps

Not on average

Cause on average would be easy peasy

If that works for your application

[echo briar]

I don’t know what the difference is so I’ll go with the on average option

Both would probably work

[graceful karma]

Like a straight line vs a staircase

A ramp vs a staircase ig

Well not a straight line

An exponential line

[echo briar]

on average. I feel that a staircase leaves out info, I was expecting to get a line that wasn’t truly exponential (no straight lines) but was instead exponential made up of straight lines… if that makes sense

[graceful karma]

Like a bunch of sticks end to end in the rough shape of an exponential function?

[echo briar]

exactly

[graceful karma]

Hmm

What application is this for?

You could make nodes of a pure exponential function

And just interpolate between

If for programming

[echo briar]

not for programming, this is just a question that has been bugging me for months

for fun.

[graceful karma]

Hmm

Would you mind a pure exponential

[echo briar]

not at all

[graceful karma]

Lemme think about this rq

Ok so uhh

$y=h^{\frac{x}{w}}$

[wraith dagger]

PapaBread

[graceful karma]

Is the general form

Where w is the width it goes before multiplying by h

You could also add on an extra variable multiplying the whole thing by the starting value

So like if you had a function of like radiation

It starts at 5000 units of radiation and decays by one half every 7 days

$R(t)=5000 \cdot 0.5^{\frac{t}{7}}$

[wraith dagger]

PapaBread

[graceful karma]

,w plot r(x)=5000 * 0.5^(x/7)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[echo briar]

This will do, thanks.

.close

[cedar kiln]

Channel closed

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[graceful karma]

Np

[cedar kiln]

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[pure quartz]

God damn my geometry is far back

[pure quartz]

If I got 2 points and the radius for a circle

Then I should be able to figure out the center, right?

Technically I should be able to get 2 centers

If I think about it, the opposite one

[void whale]

Yeah

It's the intersections of :

• The circle of center one point and radius r
• The line perpendicular to the segment that goes through its middle

[cedar kiln]

@pure quartz Has your question been resolved?

[pure quartz]

Thanks, gimme a sec to look into that

[cedar kiln]

@pure quartz Has your question been resolved?

[cedar kiln]

@pure quartz Has your question been resolved?

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[cedar kiln]

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[tame turret]

how can i prove that f(x)=(x-1)/x is injective? im having trouble showing how i can prove it

[sonic sapphire]

Assume f(a) = f(b) and show that a=b

[stray stag]

if f(a) = 0 and f(b)=0 then a=b

[dense wing]

that's not injectivity

[stray stag]

is there any values?

[dense wing]

nope

[stray stag]

aw man

[dense wing]

just f(a)=f(b) implies a=b

[sonic sapphire]

Or the contrapositive of

[cedar kiln]

@tame turret Has your question been resolved?

Channel closed

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[crimson sedge]

how do u use FTC 1 on non constant value?

we have 2 variables

3t and t^2

[floral thistle]

$\int_{t^2}^{3t} = \int_{a}^{3t}+\int_{t^2}^{a} = \int_{a}^{3t}-\int_{a}^{t^2}$

[wraith dagger]

quantum

[floral thistle]

@crimson sedge

[crimson sedge]

oh

i didn't know you could do that

thanks quantum

How do u find what a is?

[floral thistle]

it’s any number

this is just an integral rule

[crimson sedge]

?

but how would I go about solving the one above?

It's not graded btw

we already finished the graded quiz portion

[floral thistle]

you need to use the chain rule

[crimson sedge]

nope i don't follow

[floral thistle]

let’s focus on $\int^{3t}_{a} f(x) \dd{x}$ for now

[wraith dagger]

quantum

[floral thistle]

with f(x) being the integrand i don’t feel like writing out

[crimson sedge]

hmm yeah

[floral thistle]

so we would sub in u = 3t

[crimson sedge]

tbh im tired too

[floral thistle]

$u = 3t$, $y = \int^{u}_{a} f(x) \dd{x}$

[wraith dagger]

quantum

[floral thistle]

now just the normal chain rule

$\dv{y}{t} = \dv{y}{u}\dv{u}{t}$, of course

[wraith dagger]

quantum

[floral thistle]

@crimson sedge are you still confused?

[crimson sedge]

no ill get some shuteye and look over this tomorrow

[floral thistle]

ok, close the channel then

[snow hull]

.close

[cedar kiln]

Channel closed

Closed by @snow hull

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[pliant orbit]

https://i.imgur.com/JXG80Al.png

[pliant orbit]

What is extrema + how does one know what the leading coefficient sign is?

[dense wing]

extrema = turning points

leading coefficient dictates direction.

[pliant orbit]

What does turning points mean?

[dense wing]

points.... where you turn.

[pliant orbit]

Ok.. so vertex

[dense wing]

yes.

the vertex is a turning point

[pliant orbit]

Ok, thanks

.close

[cedar kiln]

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Channel closed

Closed due to the original message being deleted

[pliant orbit]

.close

[cedar kiln]

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[bright surge]

do you have a question?

[wise storm]

which question

[bright surge]

aight

7x-3=4x+3

move all the x's to either LHS and RHS

you're done

[wise storm]

they gave you an example:
7x-3=4x+3
subtract 3 on both sides
7x-9=4x
subtract 7x
-9=-3x
divide -3
-9/-3 = 3
x=3

[crimson sedge]

c) -4m + 2 = 6m + 12

2-12 = 6m +4m

-10 = 10m

-10/10 = 10m/10

-1 = m

m = -1

That's what the question said if you're talking about question 1c

I just rewrote the question

[glad kestrel]

have you tried writing down the question

and trying it yourself

let's see your work then

you just subtract 2 from both sides

what

it's not a matter of "where"

?

subtract 2 from both sides? you're just taking each side individually and subtracting 2

what do you mean with what

??

i don't know what that means

you're subtracting 2

from both sides

the left side and the right side

you subtract 2 from both expressions

what?

where did you get -4 from

take both sides of the expression

subtract 2 from both sides

there's a -4m but not a -4

yeah you're solving for m

why are you taking the coefficient and subtracting 2

you're taking the coefficient and subtracting 2 from it

that does nothing

$-4m+2 \textcolor{red}{ -2}=6m+12 \textcolor{red}{ -2}$

[wraith dagger]

a disappointing son

[glad kestrel]

you're just subtracting

2

from

both

sides

try it first

huh

same route we went with the last one

that's ambiguous

what is -2+3

what

huh??

what

you gotta go back

https://www.youtube.com/watch?v=TMubSggUOVE

i just asked you what -2+3 was and you said 3r

if you lack a basic understanding of math, i'm not here to teach you everything

if you'd like to teach yourself on your own time, by all means, go ahead

[cedar kiln]

@zinc adder Has your question been resolved?

[cyan coyote]

Bruh you straight up dumb

[stone hearth]

Don't be mean

[cyan coyote]

This dude said -2+3 = 3r

[stone hearth]

can you post the original question

its too far up

You should start by making the equation simple

since the variable y is on both sides

you should make it so it is on only one

to simplify it further

what can you add on both sides to make it so that the variable is only on one side?

You can do that, but it's best to make it so that the variable is one side first

add 2y on both sides

do it on paper and send what you get after adding 2y on both sides

exactly

no, add 2y on both sides of the equation 😓

lemme show you

$$ 5 - y = 3 - 2y $$
Add 2y on both sides
$$ 5 - y + 2y = 3 - 2y + 2y \
5 + y = 3$$

stop

focus

$$ 5 - y = 3 - 2y $$
Add 2y on both sides
$$ 5 - y + 2y = 3 - 2y + 2y$$

$$5 + y = 3$$

[wraith dagger]

Daw

[stone hearth]

do you understand

look at the what I did

do you understand what I did

I added it already

Just look at what I did

I added 2y to both sides of the equation

to simplify it

because -2y was on one side of the equation

and adding 2y makes the -2y disappear

hence simplifying it

and now you're left with 5 + y = 3

how would you make the 5 on the left disappear

yes

it's best to write it as another equation

underneath it

wait

,rotate

[stone hearth]

write it like this

you're supposed to add the variable terms now

what do you get when you add -y and 2y

look at the left side of the equation

what do you get

No

5 - y + 2y

no

you have to simplify it

not solve it

you can add variable terms to each other

you have 2 y's

and you take one away

how many y's do you have left

yes

1y is just y

so LHS becomes 5 + y

understood?

LHS = left side of the equation

and now look at the right side

the right side is

3 - 2y + 2y

what do you get when you simplify it

no

you can only add and subtract variable terms to each other

so you cannot do anything with the 3 for now

and you have 2 y's

but you have to take 2 y's away

how many y's do you have left

yes

so 3 - 2y + 2y = 3

because you don't have any y's left, you just have the 3 left

you just write it down

after solving the two sides

let me show you

,rotate

[stone hearth]

do you understand how we got here

We got it after adding 2y on both sides

5 - y + 2y = 5 + y

okay so now

we need to make it so

there's only y on the left side

but there's 5 also 😮

what will we subtract from 5 + y to make the 5 disappear

no

5

5-5=0

so there's only y left

[broken canopy]

i have a question about logic. i think it has priority over this guy struggles with 2nd grade equations 💀

[stone hearth]

now subtract 5 from both sides

[stone hearth]

use an open channel

from this equaltion

what did you get

yes

5 + y - 5 = 3 - 5

y = -2

that's the correct answer

this is how you're supposed to do every other question too

so read my messages again

[broken canopy]

tbh i can solve this equation without even thinking lmao

that was not meant to offend u ☠️

11th

[stone hearth]

please start another channel for the question you need help with @broken canopy

[broken canopy]

no its ok im gonna wait for u to finish this trivial equation

[stone hearth]

brackets is nothing but multiplication, in that case you will just divide both sides of the equation @zinc adder

[stone hearth]

I think we're done 🙂

[stone hearth]

#❓how-to-get-help

[broken canopy]

how can i prove this

[stone hearth]

use an open channel

🤦‍♂️

[broken canopy]

u said you guys are done

[stone hearth]

but the channel is not closed

[broken canopy]

then close it

if youre done

💀 uh

[stone hearth]

even if the channel is closed, there's a window where it can be reopened before it's open

[broken canopy]

what? yall are done. stop messin around and close it ugh- ☠️

how does that add information

💀 💀

i want this one 💀

[stone hearth]

#❓how-to-get-help

[broken canopy]

im 16 duh 💀

[broken canopy]

ill wait for you to close this channel ☠️

lol wdym hard? they are so simple dude uh how the hell-

weird 💀

[celest seal]

.close

[cedar kiln]

Channel closed

Closed by @celest seal

Use .reopen if this was a mistake.

[celest seal]

pls use another channel though

bot doesnt work well if you try and post soon after a channel is closed

just pick an available channel

[cedar kiln]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
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[tiny cave]

floor(x/1999)=floor(x/2000), solve for x. Thanks!

how should I write the answer?

i just know that it shouldn't be a multiple of 1999

[cedar kiln]

Channel closed

Closed due to the original message being deleted

[stone hearth]

type .reopen @tiny cave

[tiny cave]

.reopen

tq

[glad kestrel]

doesn’t work if you delete your message

just gotta get another channel or wait for this one to expire

[tiny cave]

oh dear

.close

[broken canopy]

lmao thats some karma 💀

[tiny cave]

excuse me?

[broken canopy]

wrong convo ☠️

[cedar kiln]

Available help channel!

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Remember:
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[modest wing]

help

[cedar kiln]

@modest wing Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[modest wing]

.reopen

[cedar kiln]

✅

[modest wing]

<@&286206848099549185>

[cedar kiln]

@modest wing Has your question been resolved?

[modest wing]

bruh is everyone sleeping?

ig ill wait

[fallen solar]

Hint: If both roots are integers, determinant is a perfect square

*discriminant

[modest wing]

i did it

already

[fallen solar]

👍

[modest wing]

p+q is perfect square
pq is divisble by 2

and p^2q^2 > 4p + 4q

now what

@fallen solar

[fallen solar]

p+q is perfect square? how?

$p^2 q^2 - 4(p+q) = k^2$ for some $k \in \mathbb{Z}$

[wraith dagger]

Peppermint Demon

[modest wing]

yea

[fallen solar]

$(pq-k)(pq+k)=4(p+q)$

[wraith dagger]

Peppermint Demon

[fallen solar]

pq and k have to be of the same parity

[modest wing]

ok

so here is the explanation

of why p+q is also perfect square

D> 0 right?

[fallen solar]

yes

D = 0 is also possible

both integer roots

[modest wing]

yea

so 2

[fallen solar]

they dont have to be distinct

[modest wing]

true

ok p+q is not

perfect

[fallen solar]

how about take D>0 and D=0 cases separately

D=0 case should be pretty easy ig

[modest wing]

ok

[fallen solar]

lol

(pq)^2 = 4(p+q)

[modest wing]

lol

[modest wing]

yes

[fallen solar]

hmm now what

xd

[modest wing]

lmao ikr

[fallen solar]

lets see hmm

[modest wing]

what if

we use

arithmetic mean

and geometric mean

relation

[fallen solar]

hmmm

yeah maybe

but

[modest wing]

AM> GM

[fallen solar]

that only works for positive integers

[modest wing]

and

p and q is positive integers

lol

it said

[fallen solar]

true

sorry

[modest wing]

lol

[fallen solar]

continue

[modest wing]

p+q/2 > sqrt(pq)

[fallen solar]

mhm

p+q >= 2 sqrt(pq)

[modest wing]

yes

[fallen solar]

(pq)^2/4 >= 2 sqrt(pq)

(pq)^2 >= 8 sqrt(pq)

[modest wing]

both base is same

lol

[fallen solar]

pq^(3/2) >= 8

[modest wing]

yes sir

wait but

[fallen solar]

pq >= 8^(2/3)

[modest wing]

NVM

[fallen solar]

pq >= 4

[modest wing]

ok this is good

[fallen solar]

now what

[modest wing]

we got that

and

pq is divisble by 4

nvm nvm

pq was divisble by 2

[fallen solar]

yep

let p = 2k

?

[modest wing]

yes

kq >= 2

[fallen solar]

4(kq)^2 = 4(2k+q)

(kq)^2 = 2k+q

nicee

wait

[modest wing]

wait how did u

[fallen solar]

frick typos

[modest wing]

it was >= lol bcoz yea

we taking D>= 0

[fallen solar]

ah

then replace = with >=

[modest wing]

ye

and now what

WAIT

nvm

[fallen solar]

that is a good question

[modest wing]

yea

my friedn gave it

friend

[fallen solar]

how about

[modest wing]

wait wasnt pq>= 4

[fallen solar]

$(x-r_1)(x-r_2) = x^2 -pq x + p+q$

[wraith dagger]

Peppermint Demon

[modest wing]

what is thats just the answer

[fallen solar]

is it?

[modest wing]

idk the answer

he also doesnt

only know the question

[fallen solar]

that isn't the answer

number of ordered pairs

[modest wing]

yea

so it is finite

finite number of ordered pairsd

[fallen solar]

mhm

[fallen solar]

how about this

r_1 + r_2 = pq

r_1 r_2 = p+q

which is a bit weird

[modest wing]

ok and

[fallen solar]

hmm wait lemme try to solve it

[modest wing]

oki

what we get quadratic equation

[fallen solar]

ok i have an idea

how about we prove that

[modest wing]

ok

[fallen solar]

after some point

(pq)^2 > 4(p+q)

which means

(pq)^2 - 4(p+q) < 0

which is not possible

[modest wing]

uhhh

[fallen solar]

then we will have only a few cases to check

wait fuck

im stupid

[modest wing]

it should pq^2 -4(p+q) >0

yea

xd

[fallen solar]

NEVERMIND

[modest wing]

lol

we just need one relation that shows the ordered pairs are finite

litterally cant find this question on internet either

so its not from a book

rather a question made by a profesor or smth

[fallen solar]

p = 2, q = 2

[modest wing]

yup it works

[fallen solar]

x^2 - 4x + 4

hmm

ok so i think i got somewhere

[fallen solar]

from here

wait nevermind fuck

aaaaaaaaaaaaaaaaa this is painful

wait no

hmm

[modest wing]

am back

[modest wing]

true

[fallen solar]

ok look at my method @modest wing
(kq)^2 = 2k+q
q = k(kq^2 - 2)
k | RHS -> k | LHS -> k | q
q = km
km = k(k^3 m^2 - 2)
m = k^3 m^2 - 2
2 = m(k^3 m - 1)

now we can check the factors of 2

[modest wing]

i amma just post this again bcoz yes

[modest wing]

looking

[fallen solar]

(keep in mind that is only for the case D = 0 LMAO)

[modest wing]

lmao

now there is another variable m

xd

[modest wing]

fun fact

we already got pq is a factor of 2 and u took p = 2k

[fallen solar]

ok but if we find m and k then we can find everything else

[fallen solar]

no that dont matter

i am saying like

[modest wing]

if we would have found p and q question would have been done but ok

[fallen solar]

m = 2
k^3 m - 1 = 1

[fallen solar]

im trying man im trying

[modest wing]

same

what if

we look in arithmetic mean and geometric mean once more

WAIT

WAIT

WAIT

p^2q^2 >= 4p+4q

p+q/2 = A (arithmetic mean)
sqrt(pq) = G

so G^4 >= 8A

and we also knowA>G

[fallen solar]

mhm

[modest wing]

A^4 > G^4

[fallen solar]

=

ok smart

[modest wing]

A^4 >= 8A

well yes

A^3 >=8

YOOOO

A = 2

YOI

[fallen solar]

or A = 3

or A = 4

[modest wing]

i mean A>=2

[fallen solar]

ye

[modest wing]

ok perfeect

p+q >= 4

waIT

i remmber

a formula

when A and G are arithmetic and geotric means of a and b then
a, b = A+- sqrt(A^2-G^2)

$a, b = A+- sqrt(A^2-G^2)$

[wraith dagger]

S.Bolt

[fallen solar]

hmmm

[modest wing]

ok cool

[tropic oxide]

$A \pm \sqrt{A^2 - G^2}$

[modest wing]

we got A

[wraith dagger]

Kanga Gang Annihilator Ann

[tropic oxide]

here, to make your latex not suck

[fallen solar]

thanks Ann

[modest wing]

lol

[modest wing]

here is the question btw

HEY

G IS ALSO GREATER THAN EQUAL TO 2

[fallen solar]

...yes?

[modest wing]

sopossiblesolutions are

A+- sqrt(A^2 - G^2)

where A>=2 and G>=2

and A>G

[fallen solar]

those are infinite solutions

hmmm

[modest wing]

true

[fallen solar]

i wonder if it actually has infinite solutions

[modest wing]

same

what if it does have

the thing is i dont know the solution

[fallen solar]

it would require a much more rigorous proof

[modest wing]

i mean answer

[modest wing]

yea

wait

i got a idea

[modest wing]

we use this

try to find a solution where the other one bcomes negative

itwill never be negative

like bruh

[fallen solar]

ok i give up

ping me if someone solves it

[fallen solar]

<@&286206848099549185>

[modest wing]

wait

@fallen solar

bro

we fforgot

the main probelm

the quadratic equation that we got

@fallen solar my friend said the answer was 2

reeee

[fallen solar]

its from the fucking RUSMO