help-43

[low pulsar]

do i do 2^-2 or do i do 1/2^2

[hexed hornet]

same thing

[low pulsar]

alright

[hexed hornet]

so we're trying to solve
$-2 = log_c (b)(-1-h))$
$-1 = log_2 b(x-h)$
for $b$

that is the original query, yes?

[low pulsar]

yeah

we got 2 now

[boreal girder]

Mirror

[low pulsar]

b = 0,5/(0 - h)

and b = 0,25/(-1-h)

[hexed hornet]

are we solving for b or h?

[low pulsar]

well that was b

now we need to find h

because we isolated b

[hexed hornet]

i thought we were trying to solve for b

[low pulsar]

well we cant

u cant find b cause as we just tried

it gives these

unless we substitute but substituting 0,5/(0-h) is another monster

so we can find h then b

[hexed hornet]

kk in which case we are now solving $\frac{-1}{2h} = \frac{1}{4(-1-h)}$

[boreal girder]

Mirror

[low pulsar]

we got 2 b's knowing both of them are =

b1 = b2

0,5/(0-h) = 0,25/(-1-h)

[hexed hornet]

great so now we set them equal to each other and solve

[low pulsar]

0,5(-1 -h) = 0,25(0-h)

[hexed hornet]

solving yields $h=-2$

[boreal girder]

Mirror

[low pulsar]

got that too

now we replace h

to find b

0,25 = b

ty @hexed hornet

.close

[compact pewter]

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[sonic wedge]

Is this a infinite sum - i Assume so?

[hexed hornet]

nop

or, rather, it is an infinite sum, but the answer to the question is not infinite

[sonic wedge]

16 + ( 16(0.75)+16(0.75)^2...)
is the the sieries no?

[sonic wedge]

yep alright

Is my Series correct tho?

[hexed hornet]

yes. a better way to say that mathematically is that the ball bounces to a height of 16 + 2$\sum_{1}^{\infty} 16(0.75)^n$

[dusky nymph]

is this taking into account the round trip?

it has to climb up to 75% of 16 meters and then fall the same distance

[sonic wedge]

Ment a 2 infront of the ()

thx

[boreal girder]

Mirror

[hexed hornet]

distance, not height ^^

because now infinite sum woohoo

[sonic wedge]

Is there even a way to use the caculator to caculate the infinite Sigma?

OR you have to use the formula a / 1- r

[hexed hornet]

i would strongly advise you use the formula yeah

[sonic wedge]

Alrigth but i will assume just putting a really large number n the caculator would also work?

[hexed hornet]

it might but it wouldn't be precise

[dusky nymph]

using the formula would probably be faster than trying to get a calculator to compute a sum

[hexed hornet]

make sure you set the formula up right with the a/(1-r)

because it assumes sum from 0 to n and we're summing from 1 to n

[sonic wedge]

Alright but my textbook says if r < 1, Sn = a(1-r^n)/1-r is this true but for finite?

[dusky nymph]

take the limit as n->infinity

the r^n goes away if |r| < 1

[sonic wedge]

Sorry but I still dont understand the actual point for a(1-r^n) / 1- r

[dusky nymph]

wdym by actual point?

that's the formula for $$a \sum_{k=0}^{n-1} r^k$$

[boreal girder]

Bungo

[dusky nymph]

and it's valid for any $r \neq 1$

[boreal girder]

Bungo

[sonic wedge]

When do I use that formila

[dusky nymph]

you use it if you have a finite geometric sum

like this one

[thorny urchin]

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[sonic wedge]

Bots broken

[thorny urchin]

ahk

[sonic wedge]

alright but another question is the Infitiy formula only for GP or Ap? Or is it able to work for both

[dusky nymph]

no we're only talking about geometric series here

[sonic wedge]

Can AP's have an infinite Sum?

[dusky nymph]

nope

well not a convergent sum anyway

a series can't converge unless the terms go to zero, and that doesn't happen in an arithmetic progression unless it's the trivial one 0,0,0,0,...

[sonic wedge]

So if a question gives you a series that is nto a GP and not AP rather a recursive ( i think that what its called) how would you solve that?

[dusky nymph]

depends on the specific series

most don't have closed form formulas for the result

[sonic wedge]

Meaning you need to break it up and make 2 different ones?

[dusky nymph]

no i mean in general, series don't have a formula for the sum at all

do you have an example in mind?

[sonic wedge]

I only have this really simple one
where you just Fidn the difference then you would see the difference is multiple of 3's

7-5 = 2
13 - 7 = 6
31 = 13 = 18
....

[dusky nymph]

try subtracting 4 from every term

[sonic wedge]

Then you just do 5 + Sn = 2 / 1 - 3

[dusky nymph]

i don't understand your formula

obviously the infinite series won't converge, it's asking you to find a formula for the sum of the first n terms

[sonic wedge]

Sorry
5 + (2(3^n-1) / (3-1) ) = 5 + (3^n-1) = 3^n - 4 no?

[dusky nymph]

the formula doesn't work for n = 1, does it?

i found the answer to be $(8n + 3^n - 1)/2$

[boreal girder]

Bungo

[sonic wedge]

How?

[dusky nymph]

hmm wait let me double check that

[dusky nymph]

yea looks right

your answer is the same as mine

[sonic wedge]

That was the solution - i dont actually understand some parts first Why is it 3 ^n-1 and not jst 3^n

[dusky nymph]

well you're summing the first n terms

starting with 0 and ending at n-1

[sonic wedge]

Oh is it because I left out the 5 so i would be double counting another digit in its place if i didnt?

[dusky nymph]

i don't know, how did you compute it?

is the purple text screenshot your work or someone else's that you're comparing with?

[solemn matrix]

lemme just derive the formula here

[sonic wedge]

its the solutions

[solemn matrix]

$A = 1 + r + r^2 + r^3 + \dots + r^{n-1}$

$rA = r + r^2 + r^3 + r^4 + \dots + r^n$

$(r-1)A = r^n - 1$

$A = \frac{r^n - 1}{r-1}$

[boreal girder]

1 divided by 0 equals Infinity

[solemn matrix]

detailed explanation why the sum works @sonic wedge

[sonic wedge]

yeah thats the proof? i waas talking about my question

[sonic wedge]

Also what happen to the A

infront ofthe r^n - 1

[solemn matrix]

just wanted to resolve your confusion

[solemn matrix]

subtract $rA$ with $A$

[boreal girder]

1 divided by 0 equals Infinity

[solemn matrix]

the terms at each RHS cancels out

[sonic wedge]

Yep so the other proof is just same thing but you add them / andnot times by r

Confused n this step how did we get from 4 to 4n

[hollow rivet]

there are n terms, so you are adding 4 n times

[sonic wedge]

thx

[hollow rivet]

you are summing from k=0 to k=n-2, so you have n-1 terms here

when they are finding S_n, they are summing from k=1 to k=n, which is n terms

[compact pewter]

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[graceful jay]

How is a/b = (a + kc)/(b + kd) whereas k = 1, -1?

[kind viper]

set k=1 in (a+kc)/(b+kd), what do you get?

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[regal lake]

@kind viper tu parle français?

[regal lake]

comment je fais numéro 6 ici

vraiment difficile

[eternal pulsar]

don't ping helpers specifically unless they asked you to, there's plenty of other french speakers that could help you out here

[hidden root]

Si

[regal lake]

my bad

[thick comet]

Si la tangente est parallèle à L, alors la pente de la tangente doit être la même que la pente de L

Du coup c’est quoi la pente de L?

[regal lake]

aucune idée

pente de L est f’ de C non?

[thick comet]

L c’est une ligne là

[regal lake]

ouais

[thick comet]

x+y-2=0

[kind viper]

!noping

[compact pewter]

Please do not ping individual helpers unprompted.

[eternal pulsar]

i got it covered ann

[kind viper]

ok

[regal lake]

yeah we get it amigo

[thick comet]

Donc avec l’équation de L la pente de la droite ça te dit rien?

Ou taux de variation

[regal lake]

pas vraiment

je comprend que a=1

et b=-2

[thick comet]

En gros si t’écris l’équation de la droite comme y=ax+b, a c’est la pente de b c’est l’ordonnée à l’origine

Du coup là si tu réécris l’équation t’as y = -x+2

[regal lake]

ah ouais

[thick comet]

La pente c’est donc -1, et n’importe quelle droite parallèle à celle-ci aura aussi une pente de -1

[regal lake]

ahh

okkk

[thick comet]

Et justement ta dérivée te donne expressément la pente de la droite tangente à un abscisse donné de la fonction

Du coup tu recherches les abscisses où la dérivée vaut …

[regal lake]

comment

je peu ecrire que pente de L est -1 alors sachant que c est sur L

alors f’(c) est -1?

[thick comet]

Oui. Pourvu que la pente de la tangente à un point est -1, elle sera parallèle à L. Donc ces points sont exactement ceux d’abscisse où la dérivée vaut -1.

[regal lake]

Ok

et comment on obtient y de c

et x

[thick comet]

Trouve x d’abord en résolvant f’(x) = -1

Après pour ces solutions tu peux leur appliquer f pour avoir l’ordonnée correspondant

[compact pewter]

@regal lake Has your question been resolved?

[compact pewter]

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[viscid mortar]

I didn't understand last two

[hushed magnet]

there are a lot less rational numbers than real/complex numbers

[viscid mortar]

Yeah the how did they mention it infinity?@hushed magnet

[hushed magnet]

if you have a finite dim vector space over Q then its still just countable

but R and C are not countable

[kind viper]

what letter is this

it looks like some kind of off-brand japanese hiragana character

[compact pewter]

@viscid mortar Has your question been resolved?

[viscid mortar]

Rational Q

@kind viper

[copper sierra]

using theta for Q is based

[viscid mortar]

Nooo.

It's rational Q

Symbol

[copper sierra]

$\bQ$

[boreal girder]

ロケット・ジャンプ

[copper sierra]

the tail needs to be lower otherwise you get a side profile of a girl from xkcd

[kind viper]

sure doesn't look like such

[viscid mortar]

Fine..

It is Q

Rational

[compact pewter]

@viscid mortar Has your question been resolved?

[compact pewter]

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[boreal girder]

Renato

[kind viper]

which part

[compact pewter]

@strange pendant Has your question been resolved?

[reef bronze]

to prove that it's an equivalence relation, show that it's reflexive, symmetric, and transitive

reflexive: a ~ a
symmetric: a ~ b implies b ~ a
transitive: (a ~ b and b ~ c) implies a ~ c

[strange pendant]

i don't even know how to explain it

for reflexivity

[strange pendant]

a)

[reef bronze]

what you wrote is correct

well, you can just write x = x, no need for x = x iff x = x

[strange pendant]

okay then because of the equality relation is an equivalence relation then the other properties follow

[reef bronze]

yes

[kind viper]

no no no no you dont understand. obviously you need to write a minimum of
⁨```
x = x iff x = x iff x = x iff x = x iff x = x iff x = x

(sarcasm)

i mean it is a general fact that if a relation is defined by x ~ y iff f(x) = f(y) for a function f then ~ is an equivalence relation

here f happens to be the base ten digit sum function

[strange pendant]

how can i justify in short for a)

[kind viper]

a ~ a means ds(a) = ds(a), which is true either obviously or by reflexivity of =

a ~ b means ds(a)=ds(b), which means ds(b)=ds(a) [by symmetry of =], which means b ~ a

[strange pendant]

a R b , b R c => a R c because of transitivity of =

what about b) how many numbers between 1 and 10000 have digits which sum to 2

b) 11000, 10100, 10010, 10001, 01001, 01010, 01100, 00101, 00110, 00011, that's 10

c) 1,2,3,4...,27

@reef bronze

i don't have the answers can someone check my stuff

[reef bronze]

11000 is too big

There's also numbers like 200

[strange pendant]

b) 2000, 00200, 00020, 0002, 01001, 01010, 01100, 00101, 00110, 00011

[reef bronze]

You still have some numbers that are too big

[strange pendant]

no

[reef bronze]

Oh sorry

[strange pendant]

so its 10

correct?

[reef bronze]

Seems right

[strange pendant]

2000, 200, 20, 2, 1001, 1010, 1100, 101, 110, 11

[strange pendant]

what about c)?

[reef bronze]

Yeah 27 seems right

[strange pendant]

wait but it's 27 or 28

@reef bronze

between 1 and 27 there's 27 or 28 numbers?

[reef bronze]

27

[strange pendant]

ok

[reef bronze]

Good thought, though

You wouldn't want to make a fence post error

[strange pendant]

I see, ty for the help.

.solved

[compact pewter]

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[slate bolt]

so thats the answer right

thats what i have, 2 is the det(A)

how did the just delete the second vector

i understand how they got -2

it goes -, -, so its positive and then i take the minus one out

and it goes

-1 * |A|

but why is the second det = 0?

wait

do i just need to calculate it myself?

or is there like a property i can use on it?

[thick comet]

Columns aren't linearly independent

c1 + c2 = c3

[slate bolt]

ohh

so it equals 0

thx man i didnt see it

.close

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[karmic stirrup]

question is asking for the volume of the shape that forms when the highlighted area rotates around the x axis.

what I did; got the equation of the line, being y=3-x, and when y=1 then x = the radius of the cone that will form aka 2. and the height of the cone is just 3-1 = 2.

so the volume should be 1/3 * pi * (2)^2 * 2

[karmic stirrup]

answer choices are

40/3 pi
16/3 pi
10/3 pi
20/3 pi

[karmic stirrup]

and the volume i calculated is 8/3 pi

so, waht went wrong?

wait-

okay the way I imagiend it had it be rotated around y-axis

fml

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[karmic stirrup]

.reopen

[compact pewter]

✅ Original question: #help-43 message

[karmic stirrup]

the radius is still 2 and the height is still 2

so my answer is still teh same

[kind crane]

Maybe show your work

[karmic stirrup]

I thought I did?

[kind crane]

Not all the steps

[karmic stirrup]

give me a bit ig

[karmic stirrup]

riemann can I ask you a question? will the highlighted reigon even rotate into a cone?

[kind crane]

the x axis? no

[karmic stirrup]

ok. so thats where it all went wrong

I guess I do have to integrate this.

[karmic stirrup]

that's what the question is asking for and I assumed that the reigon will rotate into a cone

.close

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[regal laurel]

Can anybody explain this?

[kind crane]

which line exactly

[quiet sentinel]

Its essentially splitting it into circular discs

The radius of any disc is just the current value of the function

So the equation should be that squared times pi

And that needs to be integrated to get the volume of the sphere

[regal laurel]

But why is it 2pi

Instead of pi

[kind crane]

it explains (the integrand is even)

[regal laurel]

.close

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[quartz yoke]

tanx+ cotx=2....bro how do i prove this

[azure vault]

You mean how to solve this?

Try writing the expression on the left under a same denominator

[compact pewter]

@quartz yoke Has your question been resolved?

[quartz yoke]

yes

[quartz yoke]

False

[compact pewter]

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[quartz yoke]

false? bro we have to prove lhs=rhs

[quartz yoke]

tanx+cotx=2 cant be proven

bruh

why

[little isle]

yess

[little isle]

because it is not true for all values of x

instead we might just might have to find the value of x

[quartz yoke]

which would be 45?

[quartz yoke]

but we can still prove it

hasnt the question given you a condition?

no

a proof must be correct for all cases

the question is ass

no?

[little isle]

yes

[little isle]

no

[quartz yoke]

we can turn cotx into 1/tanx and form a quadratic equation

[little isle]

indeed

[little isle]

yes and from that we will get all values of x for which this is true

not prove it

[quartz yoke]

you cant just say that every value of tanx+cotx=2 just because it was correct for x=45

like say for example, x=60

[quartz yoke]

okk i get ...to solve it the way im saying we need the given to be Equal to zero..right.?

no

you have to find x for this

actually same thing

but not making it equal 0 is easier

okk

$\frac{sinx}{cosx} + \frac{cosx}{sinx} = 2$

[boreal girder]

noonebtw

[quartz yoke]

take LCM

$sin^2x+cos^2x = 2cosxsinx$

[boreal girder]

noonebtw

[quartz yoke]

you should be able to find x on your own now

1/cosx sinx =2?

uh huh

so ...

i dont get it

Ok Imma walk you through it

brb amma get a pen and paper

[quartz yoke]

multiply both sides by cosxsinx

2cosxsinx =1

now

$sin2A=2sinAcosA$

considering cosxsinx is not equal to 0

[boreal girder]

noonebtw

[quartz yoke]

so replace 2cosxsinx with sin2x

[quartz yoke]

how

now, what is 1 equals to in terms on sine?

[quartz yoke]

formula

sin 90

exactly, so $sin2A=sin90$

[boreal girder]

noonebtw

[quartz yoke]

therefore, $2A=90$

[boreal girder]

noonebtw

[quartz yoke]

but we don't know the value of A

thus, $A=45^\circ$

[quartz yoke]

A = x

I am just using A because I am used to it

so how can we say 2A=90.

[quartz yoke]

i get it

[quartz yoke]

$A=45^\circ$

[quartz yoke]

I am getting used to it 😅

[quartz yoke]

mhm

no no wait

[boreal girder]

noonebtw

[quartz yoke]

how did we get 1?

oh no i mean

wait😭

what happened to 2sinxcosx

$2sinxcosx=sin2x$

[boreal girder]

noonebtw

[quartz yoke]

bro 😭😭😭😭

what

i dont get it

son

daughter*

have you learned the formula for 2sinAcosB

no?

bro

what is your teacher doing

genuinely

✌️

bro i just got introduced to this chapter man

do you have your book

yes

[quartz yoke]

what is it

find the formula for 2sinAcosB

in your book

expand this yourself

Its a good time to learn

you tell me bro😭

If I told you you'd probably forget it

is it sixcosx=1

no

[quartz yoke]

naah naah tell me

fine

$2sinxcosx=sin(x+x)+sin(x-x)$

[boreal girder]

noonebtw

[quartz yoke]

btw, general formula:

$2sinAcosB = sin(A+B) + sin(A-B)$

[boreal girder]

noonebtw

[quartz yoke]

$2sinxcosx=sin(2x)+sin(0)$

[boreal girder]

noonebtw

[quartz yoke]

therefore, $2sinxcosx=sin(2x)$

[boreal girder]

noonebtw

[quartz yoke]

got it?

nvm .. I'll cry instead

[quartz yoke]

hmm

just know for now that ts = sin2x

no need to cry :)

ok

thnx

mhm

so, $sin2x=1$

[boreal girder]

noonebtw

[quartz yoke]

and whats 1 in terms of sin?

sin 90

good

$sin2x=sin90^\circ$

[boreal girder]

noonebtw

[quartz yoke]

now just imagine that we're cancelling sin from both sides

yeah i got it from here

bruh

[quartz yoke]

we are comparing right?

yeah you can do both

ok

at the end, $2x=90^\circ$

[boreal girder]

noonebtw

[quartz yoke]

and there you go, x!

🙏🏻thnx bro

do remember to remember your formulas

[azure vault]

well, 2x = 90° + k*360°, but that's it

[quartz yoke]

Even I dont know what that is ✌️

I dont think she needs it in her level

[azure vault]

so x = 45° + k*180°, so on [0°,360°) you have two solutions

If the question was to solve for all values of x, it's kinda needed

[quartz yoke]

this works as principal solution

[quartz yoke]

x != 0?

guys..i js realised in the question it was already given tanx+cotx=2 to prove smt else

🫠🫡

cool

[azure vault]

When did I say x = 0

[quartz yoke]

oh wait sorry

[azure vault]

bruhhh

That's why we have !xy

[quartz yoke]

yeah its 270-x and x

CAST type shit

[quartz yoke]

[quartz yoke]

whats the thing asked to prove

lmao

[quartz yoke]

we had to find the value of secx+tanx

[strange ermine]

!original

[compact pewter]

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.

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[thorny urchin]

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Please don't occupy multiple help channels.

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[viscid mortar]

It is saying find the volume generated by these two curves

Around x axis

[blissful tangle]

Firstly you have to eliminate the parameter t from the equations to get the real curve

[viscid mortar]

I see

[blissful tangle]

Have you tried anything further?

[delicate sundial]

hii

can i join?

[viscid mortar]

I need to go out

I'll be in couple of minutes

[blissful tangle]

Now for finding the volume of a curve which is being revolved around the x axis we can integrate πy^2 dx between the limits of intersection of the curve with the x axis

[viscid mortar]

Yes

[compact pewter]

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[viscid mortar]

.close

[compact pewter]

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[pale trout]

why are you supposed equate real and complex derivatives to get riemann cauchy equations? why must real derivative equal complex derivative?

[rotund wave]

let f: U -> C where U is an open subset of C

what do you mean by real derivative

[pale trout]

step 4

ik this is ai lol

[rigid perch]

if a complex limit exists, it must be the same along all possible paths

similar to how in the real case the sided limits must be the same

[pale trout]

i see

thanks for the analogy

[rotund wave]

so you understand the first 3 steps?

ur just equating 2 complex numbers so they must have the same real and imaginary parts

in step 4

[compact pewter]

@pale trout Has your question been resolved?

[pale trout]

yup

[pale trout]

yepp

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[hazy obsidian]

how would i solve this by pure angle chasing and extension of lines?

[hazy obsidian]

i was thinking to drop a height from E to AC but idk

[blissful tangle]

First find angle AED

[hazy obsidian]

i did

[blissful tangle]

Then you can find angle AEC and after that angle ACE

[hazy obsidian]

... i already did..

[hazy obsidian]

^

[blissful tangle]

Oh mb , you have to find x right?

[hazy obsidian]

yup

theres probably some line extension going on but idk

[blissful tangle]

I am confused too lol, I will let you know if i get it

[hazy obsidian]

oki :3

[compact pewter]

@hazy obsidian Has your question been resolved?

[blissful tangle]

I had to actually go on stack exchange to find the solution ..The solution is pretty complex and it would be tough to explain here
Here is a video on youtube explaining the solution ..it might help you
https://youtu.be/TXvHHwOCXUs?si=ZiXC__crUvHj0e5I

The first solution is the one without trigonometry

[hazy obsidian]

ohhh yea

the solutions pretty standard, thanks

.close

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[robust flicker]

i have no clue how to solve this

[robust flicker]

how do i find the period of a composite function

the period of sinnx is 2pi/n

the period of tanx/n is npi

[digital crater]

should be n=6

[robust flicker]

yeah

thats the answer

[digital crater]

i think like cos(sin(nx)) is negligible

or just think when the whole thing evaluates to 0

[robust flicker]

wait if i take

cos (2pi/n)

then its period is n

wait nvm

[robust flicker]

i know but i wanna know how to find for composite functions

[normal shuttle]

you know the definition of periodic function right ?

its given fxn is periodic with period 6π
so f (x + 6π) = f(x)

try using this @robust flicker

[robust flicker]

is there a way to work from the inside

[normal shuttle]

i didn't get you

[normal shuttle]

this idea should solve your problem

[robust flicker]

yeah

how did u guess 6pi

[normal shuttle]

bro its given in question that fxn is periodic with period 6π

[robust flicker]

oh ye

mb

ohhh so

if i take

x as something like

i do 0 ?

[normal shuttle]

you find f(x+6π) and equate it to f(x)

[robust flicker]

ohh i got it

n comes out to be 6

[normal shuttle]

to find f(x+6π) put x = x +6π in f(x)

[robust flicker]

tysm

.close

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[severe pelican]

How did it get x=28mod 20

[thick comet]

From 3x' - 20y' = 4 you can mod 20 to get 3x' = 4(mod 20)

[severe pelican]

How ts works

I mean I did get x=28, but that ain't the expression they want

[twilit crane]

they want a linear expression to find all the solutions easily

same way you solve the diophantine earlier

[severe pelican]

Tf is a Diophantine

This?

[twilit crane]

yes

[severe pelican]

Yea but this didn't want anything, just the integers

But now they want an expression which idk whr the mod20 comes from

[twilit crane]

if there is a single solution to a diophantine , then there must be infinite

the solutions of x in
9x = 60y + 12 is your answer

[severe pelican]

Can I assume that whenever I get the value of x, then I just use the modn in formula ax= b(modn) to get x expression ?

[twilit crane]

yeah

[severe pelican]

How u get this

[twilit crane]

but that is solved through a formula

i forgor

[twilit crane]

we know that 12 i remainder after dividing 9x by 60 right

[severe pelican]

Oh nvm jus yea

[twilit crane]

that is definition of mod

[severe pelican]

But the answer is 28mod20 tho, not the converting it into algebraic expression

[twilit crane]

same thing

they js converted the linear expression to mod

by taking mod of the coefficient of the parameter we will use

although doing it by modulo is easier

i forgor how we used to do thay

[severe pelican]

So ur saying 9x =12 mod 60 is equivalent to 9x-12 =60y which also equals to x=28mod20

[twilit crane]

not exactly equal

the solutions of x in the equation

are of the form
x = 28 mod 20

[severe pelican]

Ok so whwt does the mod20 means

[twilit crane]

mod 20 is same as mod 60 but 20

you must be asking how we arrived at mod 20?

[severe pelican]

Yea is it from the first part?

9 60

[twilit crane]

no

[solemn matrix]

god damn it diophantine is a fancy way of saying ts is an equation that wants you to find the integer solutions

🥀

[twilit crane]

the formula that is used to calculate any arbitary solution of a diophantine gives this

[severe pelican]

[twilit crane]

x = x' + (coeff of y)/gcd of coefficients* t

[severe pelican]

Uhm ion think I learn this honestly

t came out from nowhere

[severe pelican]

[twilit crane]

t is the arbitary constant

that gives different values of x

its like a parameter

[severe pelican]

Ohhh

Like vectors

Is it like a point , den when u add lambda, it becomes a line

[twilit crane]

yep

[severe pelican]

So 28 is like the point and mod20 is the lambda so it won't exceed and within that range

[twilit crane]

it does not become a line

it gives out all the points on the line

it is still a point

[severe pelican]

Yeayea

[twilit crane]

but defines the line

[twilit crane]

lambda would be t here

mod is just a shorter way of represeting this

[severe pelican]

Whennit says x=8mod20, it is saying x=8 right which is also the remainder

Correct?

[thick comet]

That's your final expression for the solutions of the equation.
Any x which 8 more than a multiple of 20, i.e . x = 8+20k is a solution.

[severe pelican]

Ayo this is clear now

[thick comet]

The main things to keep in mind are that

• you can divide through your equation by the gcd, so 9x = 12 (mod 60) becomes 3x = 4 (mod 20)
• once you have that you can use the euclidean algorithm to figure out what x value works
• any such value of x you get mod 20 will be a solution

[twilit crane]

where did you learn your number theory from broski @thick comet

[severe pelican]

Oh yea, dumahh teacher tell me to Euclidean algorithm first then extended Euclidean algorithm

[thick comet]

Yeah extended would be more appropriate to get the coefficients back

[thick comet]

I did maths and compsci, so algebra and cryptography

[severe pelican]

Ok gonna practise more

Thanks a lot guys

[thick comet]

It becomes pretty much the same in any similar exercises, so you should get comfortable quickly!

[severe pelican]

I'm doing SE and ts so annoyimg

.close

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[twilit crane]

what are p adic numbers essentially about , how to get an intuitive idea of them

[kind crane]

https://en.wikipedia.org/wiki/P-adic_number

[twilit crane]

i cant quite understand written material very well

do they have a video on this

[long vigil]

someone does have a video actually

maybe it was veritasium

[patent yoke]

The short handwavy explanation is that they are decimal expansions that goes infinitely to the left instead of the right

[twilit crane]

yes there was one

isnt that infinity

nvm ill maybe try and read the article

thanks

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[gritty zephyr]

Hello

[forest token]

hello

[gritty zephyr]

Need help with this topic particularly finding the goodness fit and x2 test for independence and dependence

[rotund sphinx]

(In the future, please make the first message you send the actual question since that's what the bot pins. This saves us the effort of having to change the pin manually.)

[gritty zephyr]

sorry

[gritty zephyr]

pls do not recommend me any YouTube videos… I have checked em out and I still don’t understand

would be best if someone here took me step by step with this

thank you

[compact pewter]

@gritty zephyr Has your question been resolved?

[gritty zephyr]

<@&286206848099549185>

[compact pewter]

@gritty zephyr Has your question been resolved?

[compact pewter]

@gritty zephyr Has your question been resolved?

[compact pewter]

@gritty zephyr Has your question been resolved?

[versed chasm]

I probably won't answer, because I'm busy, but what questions do you need specific help with

(for the next helper)

[gritty zephyr]

everything

Ive sent there

I need help with basically almost everything

[gritty zephyr]

next helper has to be ready to sit and go through question by question

[last pasture]

Then you might become 45 when you get a reply

If you have one question, it's more likely for people to respond since everyone's busy.

[gritty zephyr]

More like 100

miss when people would sit you through and help you out

13k helpers and not a single soul can help me through this

[last pasture]

I could if I were free

Try pinging helpers

Nvm you did already

[gritty zephyr]

I did

[gritty zephyr]

Yes

[compact pewter]

@gritty zephyr Has your question been resolved?

[sharp trench]

Do you understand the formula for calculating Chi squared?

@gritty zephyr

Calculate the expected frequency for each variable

And apply the formula

Then use a chi squared table

[split ember]

Do you know how to construct the Expected Frequency Table?

[compact pewter]

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[upbeat pond]

Where’d I go wrong?

[thick comet]

Any context?

[upbeat pond]

Just a system of equations

Practicing

[boreal girder]

Elliot Pixel

[upbeat pond]

Damn 😂

wait

I asked chatgpt and I think the problem was that I wrote this:
$o^2p^2=15x^{-2i-2j-1}$
$o^3p=-\frac{15}{4}x^{4-3i-j}$
$o^4=x^{10-4i}$
Eq 2 yields $p=-\frac{15}{4}o^{-3}x^{4-3i-j}$
Eq 3 yields $o=\pm(x^{10-4i})^{\frac{1}{4}}$
$o=\pm x^{\frac{5}{2}-i}$
$p=-\frac{15}{4}(\pm x^{\frac{5}{2}-i})^{-3} \cdot x^{4-3i-j}$
4p=\pm \frac{15}{4}x^{-\frac{7}{2}-j}$

[boreal girder]

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

[upbeat pond]

I can't do latex

$o^2 p^2 = 15 x^{-2i - 2j - 1}$ \
$o^3 p = -\frac{15}{4} x^{4 - 3i - j}$ \
$o^4 = x^{10 - 4i}$ \
\text{Eq 2 yields } p = -\frac{15}{4} , \bigl(o^{-3} , x^{4 - 3i - j}\bigr)$ \
\text{Eq 3 yields } o = \pm (x^{10 - 4i})^{\frac{1}{4}}$ \
$o = \pm x^{\frac{5}{2} - i}$ \
$p = -\frac{15}{4} (\pm x^{\frac{5}{2} - i})^{-3} \cdot x^{4 - 3i - j}$ \
$p = \pm \frac{15}{4} x^{-\frac{7}{2} - j}$

[dense mason]

<@&268886789983436800> nsfw

[upbeat pond]

So apparently I think the last one is supposed to be
$p = \mp \frac{15}{4} x^{-\frac{7}{2} - j}$

[boreal girder]

Elliot Pixel

[upbeat pond]

So yeah I think I got it

[boreal girder]

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

[upbeat pond]

Hate latex

Anyway I think I figured it out

.close

[compact pewter]

Channel closed

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[thick comet]

You're squaring both of them, so if anything the the sign you get for p doesn't matter

[upbeat pond]

.reopen

[compact pewter]

✅ Original question: #help-43 message

[upbeat pond]

It's $^{-3}$

[boreal girder]

Elliot Pixel

[thick comet]

I mean that after in the end when you check equation 2, it shouldn't matter whether you chose plus or minus, so that's not where it went wrong

[upbeat pond]

Oh right

Yeah so idk where I went wrong then

[thick comet]

Since o has no coefficients, all the coefficient comes from p, which has coefficient -15/4.
But that squared is 225/16 != 15.

[upbeat pond]

Yeah I wrote 225/16

[thick comet]

Yeah and that's correct

My point is that the first equation can't be satisfied

So if you're looking for functions o(x) and p(x), there aren't any.

[upbeat pond]

I'm not sure what you're trying to say sorry

[thick comet]

I'm just not sure exactly what you're solving for

[upbeat pond]

I'm solving for o, p, i and j

not x

[thick comet]

That's just a very weird problem

In any case

My point above is that o is pure x.
The only coefficients out the front of o^2 p ^2 are from powers of p.

[upbeat pond]

Yeah ik I'm just playing around to get intuitive

[thick comet]

If those are equations you came up with I'm afraid you're losing your time with this. I guess the algebraic practice is good

You have 3 equations in 5 unknowns

[upbeat pond]

4 unknowns but yeah

So I'm guessing it's not possible then?

[thick comet]

I mean even if you fix x you'd still be solving in terms of it so you'd get an answer in terms of x and some other variable

And as you can see from your last line they're not compatible equations

[upbeat pond]

I think my last line might've been wrong

[thick comet]

It's not.
As I said the only way coefficients pop out the front of o^2 p^2 is for (-15/4)^2 to be the same as 15, and it's not

[upbeat pond]

Could you elaborate on "coefficients popping out"?

[thick comet]

If you take powers of o

You'll never get coefficients in front of it

Since its coefficient is 1

[upbeat pond]

Right

[thick comet]

So if o^2 p^2 has a coefficient (i.e. 15), it has to have come from coefficients of p

[upbeat pond]

And there's no constants

[thick comet]

But p has coefficient +-15/4, so p^2 can't possible have coefficent 15

[upbeat pond]

Right

Let me show you the actual problem

This came from

Honestly I figured it out atp

Thanks for your help

.close

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[thick comet]

That's why I asked for context.

[compact pewter]

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[gritty zephyr]

No I don’t know

[gritty zephyr]

sorry but my question was not answered and this channel closed for no reason

[split ember]

It closes on inactivity

could you post the question again

[gritty zephyr]

Need help with this topic particularly finding the goodness fit and x2 test for independence and dependence

[gritty zephyr]

Can you pin this ?

bot pinned something else

[split ember]

The first message is what is pinned

Do you know what a Hypothesis is?

[gritty zephyr]

yes, I do also know about null hypothesis and h1

[split ember]

so to construct the EFT you need to figure out what your particular null hypothesis is

and then assume your testing data would fit the same distribution as the other data

[gritty zephyr]

Okay.. so how do I particularly do that

[split ember]

For the first question on your second picture

you suppose that the individual data have the same distribution as the sum data

So in particular the ratios stay the same across men as they are across females

[compact pewter]

@gritty zephyr Has your question been resolved?

[gritty zephyr]

Could you please do it so I can see, like work some question out step by step and send here..

im currently heading to school and do not have time to work them out

[split ember]

Consider the first box, it has value $\frac{46}{80} * 44 = 25.3$

[boreal girder]

WeAreIngram

[split ember]

So the proportion (46/80) is applied to the row's population (44)

continue that across the table

then for the chi squared tests you simply use your created values (expected) with the given (observed) and perform the necessary calculations

[compact pewter]

@gritty zephyr Has your question been resolved?

[gritty zephyr]

ahhhh

[compact pewter]

@gritty zephyr Has your question been resolved?

[compact pewter]

@gritty zephyr Has your question been resolved?

[compact pewter]

@gritty zephyr Has your question been resolved?

[gritty zephyr]

.close

[compact pewter]

Channel closed

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[crude orbit]

.start

.close

[gritty zephyr]

it is closed

[compact pewter]

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[small remnant]

is this here true ?

V is the set of all recurrent sequences of order 2

[small remnant]

a and b are parameters

[small remnant]

i dont know but i am just afraid this point here makes me a problem
i showed that if r exists as a double root then it must sutisfy the two equations in terms of a and b

a=2r
b=-r^2

then i used this to show that the sequence satisfies the reccurence relation

so is it true?

what

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[past trellis]

I am getting a local maxima at f(3,6) = 369

how to identify if it is also absolute maxima?

ban ban ban ban

[fresh tapir]

https://tenor.com/view/execute-the-commands-gif-4793667087061102870

[kind crane]

!show

[compact pewter]

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

[kind crane]

Second derivative test

[past trellis]

that hessian matrix thing?

doesnt it only tell abt local extrema

[kind crane]

Yea find local extrema first

[past trellis]

well there is only one critical point

that is (3,6,369)

[kind crane]

.

[past trellis]

js trust me 😭

i dont hv camera on me rn

also i made no mistake im confident

its not like that riemann sum problem you helped me doing a few months ago

[kind crane]

¯_(ツ)_/¯

[drifting flax]

of course riemann helped you with the riemann sum problem

[winged lion]

Notice it's a quadratic form, maybe you can make some argument about how the function should behave

https://en.wikipedia.org/wiki/Concave_function#Functions_of_n_variables

the 4th should help here

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[spice spoke]

Can I please get some help with this question?

[spice spoke]

This is my work so far, I don't know if this helps me. I don't know how to solve for x or d here or what to do.

Maybe I'm just overthinking it and I'm supposed to solve for d through inspection?

[winged lion]

You could plug in x=-3 and solve for d

[azure vault]

if x = -3 is an extraneous solution to your new equation

[azure vault]

then

[spice spoke]

Oh thank you. I misunderstood what the question was

[spice spoke]

Thanks

Can I plug -3 here for all x?

Or do I have to do that before squaring?

[flat inlet]

safer to do it in original eqn

[spice spoke]

[flat inlet]

also you don't need to square

[winged lion]

The thing is, for x=-3 to be extraneous, you want also d+2x<0, so to cause a contradiction. Hence, after squaring both sides you should solve for d, I was a bit vague

[spice spoke]

10 because LHS=4 and RHS=16?

[winged lion]

But that wouldn't be extraneous, would it?

[spice spoke]

What is d+2x?

[winged lion]

Your right side

[spice spoke]

Ah

[winged lion]

They want you to find such d, for which x=-3 would work on your squared equation, but not on the original

[spice spoke]

sqrt(3x+25)-2x?

I don't understand

sorry

[winged lion]

When you square both sides of this, you assume d+2x >= 0

[spice spoke]

Otherwise there'd be a contradiction?

like 5=4?

[winged lion]

But if d+2x < 0 you can't do that, else you derive false solutions, or here extraneous solutions possibly

[spice spoke]

How do I figure out what value of d satisfies this contradiction?

[spice spoke]

Does the transitive property of equality fail here because of squaring?

[winged lion]

You would square both sides and keep in mind that you want d+2x < 0

[winged lion]

yes

[flat inlet]

misinterpreted what it means for x to be extraneous I apologize

[spice spoke]

all good

[spice spoke]

Like this?

[spice spoke]

Oh I see, tysm!

[winged lion]

Yes!

[spice spoke]

Can I plug -3 here?

[winged lion]

yes and you should

[spice spoke]

I think I did something wrong

[winged lion]

There is a mistake

The right sides becomes -9+25=16, so you end up with 20 on the left

[spice spoke]

Oh I thought 9x4 was 45 i'm sorry

[spice spoke]

Thanks!

[winged lion]

Then you should get nice solutions, and one that you already know

[spice spoke]

I did it!!!

Tysm

[winged lion]

Yes

Now the important question you should ask is, which causes x=-3 to be extraneous, so you need to pick the one, that causes a contradiction

Which means right side must become negative, since square roots yield non-negative results

So the answer is then d=2 indeed

[spice spoke]

The answer must be 2, because inputting it into the original equation makes LHS=4 and RHS=-4 so 4=-4 which is a contradiction!

Thanks everyone

.close

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[manic geode]

Hey guys how would I get started in deriving the formula for the corrective tilt angle to level out a turret to the horizon (or any other angle really) if the entire platform is not on level ground?

[spark wigeon]

what does it mean?

[manic geode]

@spark wigeon

The error between the tilt of the turret and the horizon changes as the turret sweeps through its local azimuth angle

azimuth here referring to the vertical Z axis' axis of rotation, left to right, right to left, etc

[timber cipher]

90 - the ground angle, probably

Depends on where exactly you're taking your angle from. Try it and see if that gives you what you want

[manic geode]

1 sec

[timber cipher]

Wait I assumed you wanted tilt angle as a function of ground angle, but now I am re-reading and am less sure

Why might there be error values?

[manic geode]

$E_{c}(\alpha)$, alpha being the azimuth, is what im after

[manic geode]

$when E_{c}(\alpha) = 90 - \beta (the angle of the base relative to the ground)$

[boreal girder]

Koja Mori

Koja Mori

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[daring axle]

kinda a dumb question but does necessity imply possibility in modal logic?

[daring axle]

like uh consider the statement "you are looking at a screen"

is "it is a possibility that you are looking at a screen" a true/false statement

Axiom T tells you that if P is necessary then P is possible

but grice's maxim probably would say that this is false

which model is the more conventional one..?

[snow finch]

why would grice's maxim (which one?) say that's false

[strong folio]

I suppose you mean the maxim of quantity. but I would highly caution mixing a pragmatic concept (a Gricean maxim) with a logical one (modal logic).

[daring axle]

maxim of quantity

if you know smth is 100% a fact then saying it is a possibility kinda goes against 1), no?

[snow finch]

um yeah exactly, since it's implied

"i went to the store.... and i might have gone to the store" sounds like i'm being tricky or trying to communicate some hidden information

like i imagine saying it with a

[daring axle]

😭 lol

but hmm okay so 1) takes precedence over athelic logic (axiom T) in a "day-to-day" regular context, right?

[snow finch]

wdym

these support each other

the fact that i didn't mention it means it must have been implied

[daring axle]

i mean in formal logic doesn't the necessity of P also say that P is possible

[snow finch]

sure

[daring axle]

so this is a true statement

but in the linguistic context

[snow finch]

yeah it's just to say

[daring axle]

aka the maxim one we would say it's a false statement or the conclusion doesn't really from the premise

so now i'm curious which one is the more conventional one to fall back on

[snow finch]

no we wouldn't

what?

we would just not mention it out loud

because why tf would i tell you something i already know you kno

[daring axle]

wait you're right 😭

[strong folio]

Gricean reasoning would tell you that the "possible" statement would be misleading, but I don't think it would be outright false.

[daring axle]

okay in hindsight idk why my teacher said it was a false statement

it agrees philosophically/linguistically and mathematically

wait is there any modal framework where "necessity implies possibility" is actually false?

[daring axle]

yeah i think it'd still be true

i was thinkinga bout smth else oops

[strong folio]

I believe system K (Kripke) does not include axiom T by default.

[daring axle]

yeah okay fair

i'm guesisng it doesn't involve both axiom T and axiom D

just looked it up

okay hmm i think i can live with smth like this

thank you both!

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[cerulean sinew]

Guys quick question

[cerulean sinew]

If you have an integral in the form

1/ √(1+x^2)

Can you use u sub

If so how

[forest token]

Yes why not

Probs x=tan theta