help-4

[dusky pulsar]

Can I do that?

Whole question ^

I was thinking of finding the relation between distance , and then just using basic 1d

[vale dock]

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[midnight pier]

How do you do a simplex tableau by pivoting?

[vale dock]

@midnight pier Has your question been resolved?

[safe copper]

Google Gemini 2.5 pro answer to get you started

[wraith heart]

!nogpt

[vale dock]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[frank salmon]

Why chatgpt and ai cant solve math

[wraith heart]

#serious-discussion

[frank salmon]

Well well well

[safe copper]

Gemini is always my first ask. It's really smart at math actually.

though it is occasionally wrong

[frank salmon]

Depends on the level

Of analysis

Needed

[wraith heart]

go #serious-discussion

[frank salmon]

[frank salmon]

[wraith heart]

stop spamming OP's channel

[frank salmon]

They re the best

Stickers

Fr

[final adder]

<@&268886789983436800>

oh geez what was that 😭

[frank salmon]

?

Oh that nvm

[vale dock]

@charred sinew Has your question been resolved?

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[ornate sequoia]

how do i get the 2nd value of r

[vale dock]

@ornate sequoia Has your question been resolved?

[distant pulsar]

two points:

1. you are intended to do this problem by hand, not with a calculator
2. your use of the calculator is not correct. r = 21 is not a correct value of r, neither are p = 6, q = 1 valid values of p and q

expand (px + 3)(qx + 4) and compare coefficients to 12x^2 + rx + 12

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[midnight pier]

im back

[slate folio]

ok for this you need a horrible trick

[final adder]

do you know ptolemy's theorem? it makes the question very easy if you do

[slate folio]

no you dont need that

@midnight pier extend AB by 1 unit

[waxen scarab]

ummm
can't we just use pythagorus twice

[midnight pier]

?

[waxen scarab]

I assume that you can use trigonometry, right?

[midnight pier]

no

im sped

[final adder]

ok now im curious lol

[midnight pier]

ye,wat do we get

[slate folio]

fuck that's big

so i extend AB so that BD=1

[waxen scarab]

D is used already by the way : )

[midnight pier]

lol

[slate folio]

me being an idiot lol

[waxen scarab]

do you make that so AC = FC
but how to know that is true

ok I see now

[midnight pier]

ye

[slate folio]

so BE=1

now can you find 2 congruent triangles?

[midnight pier]

uh

CDA and CBE

[slate folio]

why are they congruent

[midnight pier]

SAS

[slate folio]

ok nice

now what angle is ACE

[waxen scarab]

I am curious about how you checked that the angles are equal. It took me some time to realize that

[midnight pier]

ACE?

90

[final adder]

carbonized you are a genius

[midnight pier]

u play obe?

[slate folio]

i am not

[final adder]

yeahh

[slate folio]

top 5% in TSA is nothing impressive

[final adder]

first time someone commented on it and identified it correctly lmaoo

[midnight pier]

clarinet

[final adder]

n o

[midnight pier]

i do

me play clarinet

[midnight pier]

uh top 5% here means u know how to add

[slate folio]

ok let's get back to the problem

[midnight pier]

k

[slate folio]

you've identified ACE = 90

why is that?

[midnight pier]

cuz

dca

and

bce

are same

[slate folio]

and?

[midnight pier]

uh

90-DCA+BCE = 90

[slate folio]

ok nice

you got it

[midnight pier]

idk how to explain rlly

[slate folio]

but you get my idea

[midnight pier]

ye

[slate folio]

now there's one more pair of sides that are equal

[midnight pier]

hmm

[slate folio]

hint:

[midnight pier]

AC BE?

[slate folio]

?? no

look at what side corresponds to AC again

[midnight pier]

CE mb

[slate folio]

now look at triangle ACE

we have CA = CE

ACE = 90

what type of triangle is it

[midnight pier]

iso

45 45

[slate folio]

nice

and what is AE equal to

we got AB = 7 and BE = 1

[midnight pier]

8

[slate folio]

alr so you can get AC now

[midnight pier]

4root(2)

[slate folio]

nice

god this problem is dumb

[midnight pier]

ima take a bath

lol

[slate folio]

idk why they even put it right after an easy and intuitive one

ridiculous

[midnight pier]

ok

.close

[vale dock]

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[slate folio]

if i see this sort of problem i'd def use Ptolemy

[final adder]

yeah

[final adder]

i think i may have started a war in the discussion because of my bio lmao

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[winter wind]

The circumference of each circle is pix^2 + pi4x^2 + pi16x^2

if we call the radius of A to be 'x' then B has a radius of '2x' and C has '4x'

circumfernce is 2pi * radius

[cunning peak]

That's the area, not the circumference

[winter wind]

oh

oops

yeah

thanks

i think i got it from here

.close

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[foggy thistle]

Does anyone know how the calculation works to get a answer? I didn’t pay attention now I’m cooked
(Algebra 2, Logarithim)

[vale dock]

@foggy thistle Has your question been resolved?

[river shale]

Are you referring to the calculation of logarithm?

[slate folio]

think about where 0 should go

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[midnight pier]

I am currently smooth brain, is the matrix
[0 1
1 0]

invertible or no
things in my head:
there is a pivot in every row and column
thus, it is invertible

[midnight pier]

does this logic work or no

[lone furnace]

what is a condition that the matrix is invertible

[next vortex]

[midnight pier]

wait- so while im here, when can I use the diagonal to find the determinant of a matrix

[next vortex]

when a matrix is upper (or lower) triangular, its determinant is the product of the diagonal entries

[midnight pier]

oh,, that matrix is not upper triangular lmao

that's it, thankies

.close

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[midnight pier]

i can help if u want

[sick sequoia]

uhh yeah basically i'm not that familiar with functional equations (like i know the basics of substituting "nice" values and stuff but the f(30)=1 is kinda throwing me off ngl

[sick sequoia]

that would be great thanks

[midnight pier]

you want result or how to do it?

[sick sequoia]

how to do it

[midnight pier]

alr

[sick sequoia]

like im trying to learn as much as i can 🙂

[midnight pier]

Sure okay uhh lemme look at the screen shot

[rigid trench]

!noans

[vale dock]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[rigid trench]

:p

[rigid trench]

is this solved

[sick sequoia]

not yet :p

[rigid trench]

er whats ur progress

[sick sequoia]

so i think the reason im finding it tricky is because

its not like a typical functional equation

like the conditions are kinda weird lmao and so im not really sure how to make progress

[rigid trench]

:p me too

[sick sequoia]

f(30)=1 seems to be the starting point to use the first condition

[rigid trench]

f(7)=1 :p?

f(17)=1? :p

💀 mo tag

:p so f(210)=1 :p

[sick sequoia]

like f(30)=f(30)f(1)=f(15)f(2)=f(10)f(3)=f(6)f(5)=1 implies f(x)=1 for x=1,2,3,5,6,10,15,30

[rigid trench]

uh

oh

[restive aurora]

Yeah that makes sense

[sick sequoia]

and yeah f(stuff ending with 7)=1

[rigid trench]

how to write this

skull

[sick sequoia]

lmao idk bro

but like how do i find all functions

[rigid trench]

f(10k+7)=1 k\inZ+?

[sick sequoia]

yeah pretty much

[rigid trench]

skul skul

[sick sequoia]

this question is cooked lmao

[restive aurora]

So I think you could do something with prime numbers here

[sick sequoia]

mk

[rigid trench]

7 prime 👍

wait

emm

[restive aurora]

Think about how integers are built out of prime numbers

[sick sequoia]

oh so like instead of factoring you kinda build out?

[rigid trench]

let me have a guess

is it f(n)=1 for all n in Z+

just a random guess

[sick sequoia]

so like f(10k+7)f(x)=f(x) kinda thing and if

[sick sequoia]

wait yeah hold on

what if its just that

[rigid trench]

yea

[sick sequoia]

and the rest of the question is proof by contradiction

[scenic peak]

There's a way to do this by looking at last digits of numbers instead.

[sick sequoia]

assume that f(y)=n not equal to 1

[rigid trench]

e

[sick sequoia]

then theres probably some factorisation argument or smth with primes or idk

wait this is helpful

alr i'll see if i can take if from here

[rigid trench]

:p

[sick sequoia]

thanks for the help!!

[rigid trench]

emm

[vale dock]

@sick sequoia Has your question been resolved?

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[vivid sleet]

help

does anyone know how to plot conic sections in desmos😭

[midnight pier]

is this the right channel tho?

[vivid sleet]

wiat what channel is this

[glass kelp]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[glass kelp]

U want checking?

[midnight pier]

Sure

[glass kelp]

Bottom no. 1

And 2

For the table, aren’t there 10 eqs

No 7 seems problematic (table)

[vale dock]

@midnight pier Has your question been resolved?

[midnight pier]

I asked her what it's supposed to say

[midnight pier]

?

[midnight pier]

?

[glass kelp]

Check how u solve the ineuqality

[midnight pier]

Wdym?

Did I swap the signs?

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[midnight pier]

Wha

[midnight pier]

?????

[vale dock]

@midnight pier Has your question been resolved?

[glass kelp]

do u know how to solve

[ x^2 - 6x + 5 > 0]

[rocky lotus]

k

[vale dock]

@midnight pier Has your question been resolved?

[midnight pier]

i JUST USE dESMOS

[glass kelp]

Bruh

Do it the normal way

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[heady egret]

Can someone help me slve this question?

[ivory valley]

What did you try? Can you show your work?

[heady egret]

i dont have my phone w me rn, but i was able to simplify down to integral tan theta

but chatgpt shows the limits changing, which is why im confused

[heady egret]

like after i asked for help

[lyric sundial]

!nogpt

[vale dock]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[lyric sundial]

By the way, why are you confused about change of bounds? Isn't it the standard process when doing substitution?

[heady egret]

yeahh so would it be lower and upper 0 and pi/6 respectively?

[heady egret]

fr though gpt's not that great at math

[lyric sundial]

Yep correct

[vale dock]

@heady egret Has your question been resolved?

[half lake]

Guys is it fine if I ask 10th grade physics?

[tidal swift]

in another channel, please

[half lake]

Okey

[vale dock]

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[half arch]

If x = 1 - √2,find (x - 1/2)³. How do you solve this?

[ebon glade]

just plug in and compute

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[sage kestrel]

is it true or false?

[plush anvil]

What is meant by rational function?

[glass kelp]

rational function is continuous

[glass kelp]

if P and Q are polynomials, a rational function would be P/Q

[glass kelp]

what do u think

[sage kestrel]

true

[glass kelp]

why true

[sage kestrel]

bcz it is continous

[glass kelp]

right

[sage kestrel]

thanks a lot

.close

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[plush anvil]

Not true like if the denominator has a root it isn’t continuous

[abstract island]

It being continuous is equivalent though, so that’s circular reasoning

[glass kelp]

composition of continuous functions make it continuous tho

[abstract island]

You mean quotient?

[plush anvil]

This isn’t composition and the inverse function is not continuous

[glass kelp]

yes

given that both domains contain x=a

[abstract island]

Yeah, that’s a more insightful answer

I am not saying you are wrong

[plush anvil]

Oh yes I forgot a is in the domain

Mb

[glass kelp]

my wording hasnt always been the best. i understand

[abstract island]

It’s okay

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[turbid wave]

A circular loop of wire with a radius of 0.1m lies on a uniform magnetic field that's perpendicular to the plane of the circular loop. The magnetic field changes uniformly from 0.3T to 1.2T in half a second.
What is the magnitude of the induced emf in the loop?

[turbid wave]

how do i set up an equation for this

[glass kelp]

faraday's law of induction

[ \varepsilon = -\frac{\Delta \phi}{\Delta t}]
Note ${\phi = A \cdot B}$ in this instance

[rocky lotus]

k

[turbid wave]

oh, didn't knew it was just Faraday's, thought it was something else

.close

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[glass kelp]

(for those reading after, no, this is not a dot product. it is the product of the magnetic field strength and the area of the circle)

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[cloud coral]

have you drawn a diagram

[dusky axle]

can't send an image as I'm currently not operating my phone

wait I'll scrap this and solve it later

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[dusky axle]

Let m, n be natural numbers such that m + 3n - 5 = 2LCM(m, n) - 11GCD(m, n). Find the maximum possible value of m + n.

[vale dock]

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[graceful merlin]

not really sure where ive gone wrong here

can someone help

i just used the jacobian to transform the integral

into the form in the image

then i tried integrating it and just ended up with zero

[glass kelp]

hello mr chomper

[graceful merlin]

hey whats up man

lmao i need ur help again

[glass kelp]

jacobian is correct

r dr dtheta dz

x^2 + y^2 <= z^2 => r^2 <= z^2 becomes a cone

are u sure abt the bounds for r?

[graceful merlin]

hmm

lemme think for a sec

is it between -sqrt(x^2+y^2) and + sqrt(x^2+y^2)?

but then again ig thats just -+z

[glass kelp]

think aboout the diagram

[graceful merlin]

ah wait no it is this right?

because its <= z

so its included everywhere within the cone

as a function of (x,y)

[glass kelp]

im not following

[graceful merlin]

r^2 = x^2 + y ^2

[glass kelp]

yup

[graceful merlin]

so r = +-sqrt(x^2 + y^2) ?

oh but z is >= 0

so r is between 0 and sqrt(x^2+y^2) ?

[glass kelp]

r is between 0 and z

[graceful merlin]

oh ig that is fine then as this is just equal to 0 and z ?

i think i was just overcomplicating it

[glass kelp]

[ \int_0^1 \int_0^{2\pi} \int_0^z]

[rocky lotus]

k

[glass kelp]

this yes

[graceful merlin]

yh alr thanks

that makes sense

ill try finish the rest of the integration

also is there any easy way to check answers to these using wolfram alpha or smth

[glass kelp]

dont ur book have an answer key

[graceful merlin]

oh yh acc i can just use that

that would be easier probably...

uhh ok so ive done the integration

but im p sure ive done smth wrong

as im getting 8pi ( ln(1) - ln(0))

in the end

[glass kelp]

should get -5pi/9

[graceful merlin]

thats the correct answer

[glass kelp]

,w int from 0 to 1 int from 0 to 2pi int 0 to z ln(r^2) r dr dtheta dz

[rocky lotus]

Results provided by WolframAlpha

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

Requested by nuclearinteraction

[glass kelp]

wa the goat

[glass kelp]

ln(0)?

[graceful merlin]

yh 😭

[glass kelp]

u did smth wrong defnly

[graceful merlin]

yh ik

idk where ive messed up

lemme send a pic rq

[glass kelp]

okie

[graceful merlin]

ignore the bounds -z and +z in the top line

wait ive just clocked

i mustve messed up the first integration step

bc theres also another ln(0) error before

[glass kelp]

${u := r^2}$?

[rocky lotus]

k

[graceful merlin]

oh yh ima dummy

[glass kelp]

how did u do u:= ln(r^2) sub

[graceful merlin]

so du = 1/r^2 * 2r

= 2/r dr

[glass kelp]

theres no 2/r

[graceful merlin]

oh my gosh

[glass kelp]

in the integrand

[graceful merlin]

im cooked

yh thanks

[glass kelp]

theres only r

[graceful merlin]

yh idk why i did u = ln(r^2) 💀

[glass kelp]

so use this

[graceful merlin]

yh yh

im assuming the rest works out nicely

is there any point in me doing the rest?

[glass kelp]

wdym

[graceful merlin]

like doing the u sub again

and working it out

[glass kelp]

not sure, havent thought abt the rest yet

[graceful merlin]

its just pluggin in bounds right

[glass kelp]

i just wa'ed it

[graceful merlin]

ill do it anyways quickly then

[glass kelp]

plugging in bounds + trivial integration

[glass kelp]

okie

[graceful merlin]

@glass kelp thanks for the help, i should be good now!

[glass kelp]

👍

[graceful merlin]

.close

[vale dock]

Channel closed

Closed by @graceful merlin

Use .reopen if this was a mistake.

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[timber echo]

addition is repeated successor functions
multiplication is repeated addition
exponents are repeated multiplication
following this pattern we next get tetration, pentation, sex?tation, and so on
what if anything comes before successor functions in this pattern

[viral idol]

YES

MY TOPIC

finally

😭

PEANO AXIOMS

[stark wedge]

hyperoperations i think is the general name for these

or knuth arrow notation

[viral idol]

oh yea guys

im trying to create my own axioms based off Peano's

i successfully defined addition and subtraction

[west cloud]

#math-discussion

[viral idol]

but not multiplication and division and stuffs

[west cloud]

off topic

[stark wedge]

#math-discussion or open your own channel

[viral idol]

...

[viral idol]

...

[viral idol]

alr now close...

[stark wedge]

don't hog somebody else's channel.

[river shale]

Plz no get too hyped

[stark wedge]

if you keep insisting you might get somebody calling the mods at you

[drifting hornet]

Why should something come before successor?

[dusky axle]

Hey I'm getting the answer as I=-(5pi)/9

[drifting hornet]

all the hyperoperations you mentioned take in 2 inputs, except for successor

i cant even imagine how that would work

[spark vale]

it's called the successor. something has to come before it

[dusky axle]

you mean to say hyperoperations in the negative field

[drifting hornet]

uhh.. in the negative field?

What is that supposed to mean

[dusky axle]

wait I kinda get the pattern, so if we were to extend the hyperoperation hierarchy downward, it would be:
H(-1,a,b) = b --> the identity function - no change basically

[timber echo]

holy crap i left for 15 minutes and ppl are all over this

[dusky axle]

That's the fun part of Maths, a topic can be spoken on and on about and it can never end

[timber echo]

λx.x is my only real hypothesis

although lambda calculus is not necessarily the best thing to communicate with

[dusky axle]

it's like asking if you can finish a game in negative hours and not just 1 or 2

[timber echo]

i dont know what that is but this sounds very lambda

[timber echo]

its fine @viral idol you can blab

[timber echo]

the pattern implies its existence

[viral idol]

it's like an expansion of the peano's axioms

[viral idol]

probably move to #discussion

[drifting hornet]

How can unary operation be repeated anything

[timber echo]

well ish
ish
bSUCC(a) doesnt equal (b)(SUCC(a))
it equals a+b
which is kinda sirta ish how itd go but idkkk

[timber echo]

what

[drifting hornet]

bSUCC(a) doesnt even seem like a well formed expression

at least to me

b and SUCC(a) are both terms

what operation combines those 2 terms

[timber echo]

yea but this is the fabric of math
negative time is abt as validly real as white holes ig idk

[timber echo]

unary?
oh like one input?

[drifting hornet]

yes

[dusky axle]

exactly

[timber echo]

bSUCCa
i just said that
its the successor of succA

[drifting hornet]

SUCC is a unary function?

and in this case it's applied on a

so its essentially b(a+1)

what's meant by that

[timber echo]

whatever
bsucca is binary
succa aint
ANYWAY
thats not the point

[drifting hornet]

i have never seen a notation where bSUCCa is to be interpreted as a + b

[timber echo]

no

[drifting hornet]

oh okay

so you just made SUCC a binary function with a dummy variable b which does nothing

so it's only essentially unary

[timber echo]

its weird
(b)(SUCC(a)) IS NOT bSUCCa
its dumb

[drifting hornet]

so bSUCCa = a + 1?

[timber echo]

no

its a+b

idk ehy its like that

[drifting hornet]

who said its like that?

[timber echo]

but succ(succ(a)) is 2succ(a)

idk why

its just expressed that way

its dumb

[drifting hornet]

who taught you all this stuff?

whats the source

[timber echo]

i dont fucking know

[timber echo]

the internet because math is an autistic obsession of mine

[drifting hornet]

then it seems like you misinterpreted some of the notation (or you read some terrible notation online and you should read better books)

[viral idol]

i knew the peano's axioms because someone posted a video about > 300 page proof of 1+1=2

😭

[timber echo]

imo it should be expressed with a pre-exponent thing
like cubed roots or tetration
so a+b = ^b SUCC(a)
but its not expressed like that sadly

[drifting hornet]

a + b should just be expressed as a + b

i dont see anything wrong with the symbol +

[viral idol]

about my axioms, it didn't go really well

[drifting hornet]

if we want a notation uniting all these so-called "hyperoperations", then we might use $H_n(a, b)$ or sth

[rocky lotus]

MathIsAlwaysRight

[timber echo]

i know lambda calc bc whatever his name is made a video titled what is plus times plus

[timber echo]

o h

[viral idol]

ill say it in #serious-discussion

[timber echo]

im not arguing against +

[viral idol]

lololol

[timber echo]

math discord is for autistic ppl who get frustrated with eachother for asking for help in the area for asking for help

[viral idol]

lol

[timber echo]

none of this bickering has answered my question to sny capacity

idk

[drifting hornet]

Well, i dont get what you're expecting

why should all patterns be extendable in both directions?

[timber echo]

you get a gold sticker

[drifting hornet]

why cant you have a starting point somewhere

https://en.wikipedia.org/wiki/Hyperoperation

[timber echo]

why do negative numbers exist
what number is successor in the pattern?
do we know for sure its 1?

[drifting hornet]

best you can do is check some defns here and try to see what happens when you plug in e.g. n = -1

[timber echo]

...............
does this have an equation for that

[drifting hornet]

1. negative numbers exist because someone found them handy and interesting enough to define them

2. in what pattern?

[drifting hornet]

it has a recursive definition

which includes an equation

[timber echo]

hand through head soyjack

[timber echo]

1. pure mathematics/logic doesnt care what we can percieve, nor what can exist in this universe
2. the pattern of succ + x ^ ^^

[drifting hornet]

if you mean the succ, +, *, ^, tetration, pentation, ... pattern, then the generalization upward is pretty obvious and follows the recursive rule above

[drifting hornet]

notice that $H_n(a, b) = H_{n-1}(a, H_n(a, b-1))$ essentially captures the "repeated operation" part of these hyperoperations

[rocky lotus]

MathIsAlwaysRight

[drifting hornet]

if we plug in n = 0, we get

$H_0(a, b) = H_{-1}(a, H_0(a, b-1))$

[rocky lotus]

MathIsAlwaysRight

[drifting hornet]

applying defn of H0

$b+1 = H_{-1}(a, b)$

[rocky lotus]

MathIsAlwaysRight

[drifting hornet]

or simply $H_{-1} = H_{0}$

[rocky lotus]

MathIsAlwaysRight

[drifting hornet]

not very interesting

[timber echo]

yea i know

[timber echo]

i csnt read that yet

[hot tide]

we have successfully proven that unsucc = succ

[drifting hornet]

lol

[timber echo]

tf this mean

[timber echo]

is
is H0 succ

[drifting hornet]

yes

H0 is succ, H1 is addition, H2 is multiplication...

[spark vale]

every time i hear succ i think of that weird filthy frank video with the alien saying give me the succ

[timber echo]

well i cant check if thats right bc i cant read it yet
but that is a dissapointing answer
also one i dont like

repeated H^-1 cant be itself when its SUCC bc repeated SUCC is +
that
seems to be broken

OR

in the sense of lambda bc we are menipulating and disecring functions....

MAYBE

its the same function
but a different number or order of INPUTS

[timber echo]

i have not seen it
succ is funny and sounds derogatory in my head tho lol

damn you had an acc for 6 years and have no pfp

tf

[spark vale]

sometimes i'm indecisive

[timber echo]

right like
ok
in lambda calc
0 = the false function
which is just
if we put in a, then b, we will get b back
its useless by itself
but 0 becomes a very different thing when we change its application

[hot tide]

the problem is that SUCC is a unitary operation, and unlike addition and higher operations, it doesn't take two numbers as input, where the second one is the number of times to repeat the previous operation

[timber echo]

looks like this lol
⬜⬜⬜
⬛⬛⬛
⬜⬜⬜
⬛⬜

[hot tide]

so if you were to hypothetically define H_{-1}, you would have no way of indicating how many times you can repeat it in the definition of H_0 = SUCC

[timber echo]

yea ik that

[timber echo]

well yea

thats what i didnt get

thats why i asked

its hard to go backwards in the order

[drifting hornet]

There is not much else to get. Now we know that we cant really meaningfully extend it backwards

so we move on

[timber echo]

i think it might be possible to force it to work anyways

[drifting hornet]

and do sth else

[timber echo]

H{-1}

[timber echo]

naw

[hot tide]

another more handwavy reason is that there's quite literally nothing between the number n and the number SUCC(n) when hou work within the naturals

[viral idol]

it's a bit of yippy yappy

[hot tide]

so if you really insist, you should try and look into is not working within just the naturals

[timber echo]

then like how did this happen
did MAR miscalculate this
bc now we have this dilema

[hot tide]

but the successor function isn't particularly special

[viral idol]

#latex-testing has it

[hot tide]

they didn't

[timber echo]

it is to me a little
its dumb and insignificant
but extremely relivant and rarely taught

[hot tide]

sorry i mistyped

[timber echo]

i cannot check thooo

[hot tide]

i meant outside of naturals it isnt special

within the naturals it is special indeed

[timber echo]

wym natruals

[viral idol]

i mean it almost took down discord's limit

[hot tide]

$\bN_0$

[rocky lotus]

artemetra

[hot tide]

non-negative whole numbers

[timber echo]

o h

natural numbers

[viral idol]

in our country

[hot tide]

yea

[viral idol]

$\mathbb N$ are natural numbers from 0 and so on

[hot tide]

don't even start

[rocky lotus]

1 divided by 0 equals Infinity

[hot tide]

man

[viral idol]

$\mathbb N^*$ are natural numbers from 1 and so on

[timber echo]

how does everyone know how to use the bot

[rocky lotus]

1 divided by 0 equals Infinity

[viral idol]

WE USE N*

[hot tide]

practice and that's it, it's not super hard

[viral idol]

oh yea #latex-testing has it

[hot tide]

you find what each character is called and you use it

[timber echo]

weird

[viral idol]

oh you have a github

interesting

[hot tide]

indeed i do

[viral idol]

bro messed with polynomials in one python file 💀

[timber echo]

H{-1} cannot equate to H{0} thats not right that doesnt work

[hot tide]

maybe that's the contradiction you were seeking all along?

[viral idol]

i thought that's the best suitable channel that no one's messing around

[hot tide]

bro's actually stalking

but yeah that code is old as hell

[timber echo]

if H{-1} = repeated H{0}
and repeated H0 is H1, so on and so forth, addition equals multiplication
which is wrong

[viral idol]

uhm move to dm

[hot tide]

iirc it has a bug in long division lol

[hot tide]

sure

[hot tide]

so maybe the assumption that H_-1 exists is false?

[viral idol]

lol

[timber echo]

well maybe
but again
i dont know how to do this shit

which is why im here

what the hell is # latex testing

[hot tide]

well i am confirming that the idea of H_-1 isn't very well defined

at least with the way H_n is defined

[timber echo]

i need to make a labda calc block for tetration
maybe thatl be the project for the next few days

[timber echo]

and i believe you

[viral idol]

i made the peano axioms simulator in golang

[timber echo]

i just dont know what conclusion to come to yet

[viral idol]

oh it's slow as hell

[hot tide]

I'm sure there's some alternative system where it makes sense

but definitely not like the usual succ + * ^

[hot tide]

i am by no means an expert in that tho

[timber echo]

im half thinking of this in lambda
and idk if you know what that is actually
but i think itd make a ton of sense for it to work and also not work/exist in lambda

[timber echo]

yea

[hot tide]

i know what lambda calculus is

[timber echo]

can you do lambda calc

[hot tide]

a little bit

[timber echo]

can you read/decipher/convert john tromp diagrams

[timber echo]

this is λx.x in the john tromp crap

which is [false,0]

except as ive found (unless im doing it wrong) the 0 doesnt work completely as 0

[timber echo]

im wrong

no

[hot tide]

that no

[timber echo]

its λx.λy.y

[timber echo]

i said it wrong

[timber echo]

o h

im sorry

[hot tide]

don't apologise lol

[timber echo]

its really weird shit
and raw logic is helpful here and almost needed to do this

although i do find it weird

[timber echo]

this uh

ok

in order of how complicated the functions are (ammount of details most to least)
it goes like
addition, successor, multiplication, exponent
im rather certain

tetrations GOTTA be smaller than + and biggerr than ^ tho

im tired as crap tho
so ill likely figure that out tomorrow or at least try

i know a little abt how it should be structured

[vale dock]

@timber echo Has your question been resolved?

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[plucky grotto]

I need help with d). Feel free to speak out if I made a mistake on a previous question too but rn I’m struggling with d)

[glass kelp]

g is the derivative of f

[plucky grotto]

yes

[glass kelp]

so f''(x) is g'(x)

[plucky grotto]

In my head i was thinking that it would be when the graph of g crosses the x axis, however im not sure when exactly that would be

[glass kelp]

how do we find point of inflection

[plucky grotto]

when the slope changing from increases to decreasing so in this case when g crosses the x axis?

or vise versa

[glass kelp]

cool

so from the graph

[plucky grotto]

g stays at y=0 from -1<x<0, how would i go about that

[glass kelp]

does it change from increasing to decreasing or vice versa?

[plucky grotto]

it would be decreasing to increasing

[glass kelp]

at any particular point on the interval

not taking the whole interval as a point

[plucky grotto]

so when it wants to know the x-coord of the point of inflection, its any point on that interval -1<x<0?

[glass kelp]

if i pick the point x = -0.5

is there a change in f'(x)?

[plucky grotto]

no

[glass kelp]

so is any point in this interval a point of inflection

[plucky grotto]

no..

because theres no changing from pos ->neg/neg->pos

[glass kelp]

so from the graph wheres the point of inflection

[plucky grotto]

There would be none then

theres no exact point that marks the change in pos/neg

[glass kelp]

hmm. that seems really weird..

lemme refresh my brain rq

we are looking at f''

which is g' not g

@plucky grotto

fucking hell, im high

[plucky grotto]

wait

so would it just be when g changes from increasing->decreasing or dec->inc

that just clicked

[glass kelp]

yes

theres only one point here

[plucky grotto]

x=4

what about x=1

it stops increasing there

[glass kelp]

went from 2 to 0

[glass kelp]

but never went decreasing

[plucky grotto]

yeah i suppose, not until x=3 but im assuming it must go directly to decreasing after x>1

[glass kelp]

what

oh ye

for it to be point of inflection, yes

[plucky grotto]

alright

makes sense to me

[glass kelp]

i did some searching

its the uhh

ap calc ab 2018 frq #3

u can go check that out in case i am blurry

and my answers wrong

[plucky grotto]

sounds good, i appreciate it

.close

[vale dock]

Channel closed

Closed by @plucky grotto

Use .reopen if this was a mistake.

[vale dock]

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[next vortex]

if E is a vector bundle of rank k over a fixed space M, must every vector bundle over M be of rank k?

[next vortex]

my assumption is no, but I'm really not sure

okay, it's indeed no

we can take the Whitney sum of E with itself

.close

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

13th one

[glass kelp]

u sub first?

${u := \frac{1}{x} \implies \dd u = -\frac{1}{x^2} \dd x}$

@timber swan

[rocky lotus]

k

[noble anvil]

[glass kelp]

then u do conjugate and stuff

[timber swan]

[glass kelp]

?

[timber swan]

What will this sub do

[glass kelp]

reduce to the thing to radical only

will become

[ \int \sqrt{\frac{1-u}{1+u} } \dd u ]

[rocky lotus]

k

[glass kelp]

where u can conjugate with 1-u

and get into arcsin form

[timber swan]

Linear by root

Quad

Ahh

So trivial

My bad

@glass kelp thanks

[glass kelp]

[timber swan]

.close

[vale dock]

Channel closed

Closed by @timber swan

Use .reopen if this was a mistake.

[timber swan]

Folded under exam pressure

[vale dock]

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Remember:
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[modest anvil]

hey guys..m new here

[glass kelp]

Hi

Welcome

#discussion for discussion
#math-discussion for math discussion

If u wanna ask, a problem feel free to drop it here

https://tenor.com/view/cat-gif-12450451651611168773

[stark wedge]

@modest anvil do you have a question to ask right now? if not, then you should type .close here. @glass kelp outlined channel usage above

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@modest anvil Has your question been resolved?

[vale dock]

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[somber sequoia]

@obsidian ginkgo Have you drawn the FBDs?

[craggy mist]

Typical jee studs

[stark wedge]

do you have progress so far? y/n

[obsidian ginkgo]

yes but cant solve pls provide me the solution there is no solution for this question

[vale dock]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[obsidian ginkgo]

so help me

[somber sequoia]

well can you show me the FBDs

[obsidian ginkgo]

yes let me send

[hoary panther]

4.0 m/s²

[obsidian ginkgo]

ans is 5.0 m/s square

[stark wedge]

!nosols also don't blurt out answers anyway

[vale dock]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[somber sequoia]

,rotate

[somber sequoia]

you're not confident on the direction of friction?

[obsidian ginkgo]

yes kinda

also tension is quite confusing

[somber sequoia]

yeah your tension arrows are incorrect

you've flipped them

[obsidian ginkgo]

in both the fbd

[somber sequoia]

Yeah

Remember the tension is pulling on the block

It's not pushing on it

[obsidian ginkgo]

also in the question cofficient of friction is given so there should be two f max right

and my friction direction right

[somber sequoia]

Yeah just assume that for simplicity

You also don't need to worry about the direction of friction

Since when you solve the equations the sign will tell you

[obsidian ginkgo]

i got two equations 12 +t = 6a and second 89 -2t =2a

my ans is coming 8.07

[somber sequoia]

$$F - (2T + f_1) = m_1a$$
$$f_2 - T = m_2a$$

[rocky lotus]

maison

[somber sequoia]

like this?

the signs of f_1 and f_2 may be flipped doesn't matter

[obsidian ginkgo]

yes just in eq two its + T

[somber sequoia]

okay that should be fine then

maybe you made a mistake in your calculations

[obsidian ginkgo]

nup

[somber sequoia]

Okay let's do it then

[obsidian ginkgo]

ok

ans is 5

[somber sequoia]

$$93 - (2T + 0.2 \cdot 2 \cdot 10) = 2a$$
$$0.2 \cdot 6 \cdot 10 - T = 6a$$

[rocky lotus]

maison

[somber sequoia]

did I get any of the values wrong

Ohhh wait

I made a mistake

The acceleration won't be the same because of the pulley

It will be 1/2

[obsidian ginkgo]

why

[somber sequoia]

Do you know the pulley equations

[ a_p = \frac{a_1 + a_2}{2} ]

[rocky lotus]

maison

[somber sequoia]

it was something like this, I don't remember

It's been a while

[obsidian ginkgo]

nup i dont know this

our eq s are same but only in second eq its +T

WHAT SHOULD I DO

[somber sequoia]

there should be something like this in that module

[obsidian ginkgo]

NUP JUST QUESTIONS

HELPPPPPPPPPPPPPPPPPPPP

[somber sequoia]

[vale dock]

@obsidian ginkgo Has your question been resolved?

[vale dock]

Channel closed

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Send your question here to claim the channel.

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

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

[obsidian ginkgo]

nup

[hot tide]

ask it again

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[limber sparrow]

Hi, I need help with 51 b. I dont know how to include the transformation on the x axis in the new equation

[limber sparrow]

I know how to include the translation of y-axis which is just adding how many it went up by from f(x) i just dont knwo how to do the horizontal translations

[midnight pier]

for every x in f(x) put x-a
-> f(x-a) = (x-a)^3 - 3(x-a)²

it shifts a to the right

[limber sparrow]

ok thank you!

.close

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[tidal moat]

Could I be walked through this problem?

[scenic peak]

The sqrt(36-36sin^2) one?

[tidal moat]

Well that where I ended up from the very top integral using trig sub.

[scenic peak]

One might start by factoring out the 36

[tidal moat]

It has now been factored out. Look like Pythagorean Identity = cos^2x.

[scenic peak]

Indeed

[scenic peak]

So once we use this, we get...?

Seems we've dropped the square root somewhere

[tidal moat]

woops

[scenic peak]

Right

Now is there an obvious simplification here?

[tidal moat]

Well Cos over Sin is Cot, but the square root...maybe not the right track

[scenic peak]

You're on the right track

How might we easily simplify the square root

[tidal moat]

Turn into exponent then distribute across the two terms?

[scenic peak]

...I guess?

You're looking at the expression $\sqrt{6^2(\cos \theta)^2}$

[rocky lotus]

Buzzing Hornet

[tidal moat]

oh

[scenic peak]

So, simplifying this gets us?

[tidal moat]

Integral 6 CotxCosx dx

[scenic peak]

Right

But looking at this as cot is actually not quite as nice

Do you notice anything if you write it in terms of sin and cos instead

[tidal moat]

well if we go back a step, then I suppose we could multiply the two Cos terms together, then use the pythagorean identity.

[scenic peak]

Right, do you see why that's going to be nicer?

[tidal moat]

Well, It would allow cancelation.

[scenic peak]

Exactly

So after our cancelling, what do we have?

[tidal moat]

integral 6 - 6sinx dx

[scenic peak]

Hmm

You've dropped an /sin somewhere

Mind showing me the calculations?

[tidal moat]

yee one moment

Well there's actually not much to show, I thought the 36/6 = 6. And Sin^2 x / Sin X would reduce to Just Sin X.

[scenic peak]

As the saying goes, algebra is the hardest part of calc

[tidal moat]

yeahhh

I figured

Many of my mistake have been algebra.

[scenic peak]

Though uh I have no idea why those are 36s instead of 6s

[scenic peak]

We were good up here

[tidal terrace]

the more you look at it the more you find lol

[scenic peak]

So as you've observed this is $\int \frac{6(1-\sin^2(x))}{\sin(x)}dx$

[rocky lotus]

Buzzing Hornet

[scenic peak]

Now we can pull the 6 out of the integral to disregard it for now

[tidal moat]

Is 6cos x time 6 cos x not 36 cos^2 x?

[scenic peak]

No

Well, it is

But where is that second 6 coming from?

[scenic peak]

This expression is correct

[scenic peak]

And it expands to this

[scenic peak]

Which you've (sort of?) observed

Oh ok sorry I see

I thought we had cancelled those 6s

Ok I will point out that everything is simpler if we realize that 6/6=1 and that we can pull the remaining 6 out of the integral

Which gets us $6\int \frac{\cos^2 \theta}{\sin \theta}d\theta$

[rocky lotus]

Buzzing Hornet

[scenic peak]

(You should make sure you follow that)

@tidal moat Still here?

[tidal moat]

yah

[scenic peak]

Ok so do you get how we got here

[tidal moat]

yes

Pythagorean ID

[scenic peak]

Right

[tidal moat]

then cancel a sin x?

[scenic peak]

So then the expression inside the integral is $\frac{1-\sin ^2\theta}{\sin\theta}$

[rocky lotus]

Buzzing Hornet

[scenic peak]

Now, remember that $\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$

[rocky lotus]

Buzzing Hornet

[scenic peak]

So how do we simplify?

[tidal moat]

Well, 1/sinx is Csc. And Sin^2 x / Sin x = Sin x.

[scenic peak]

Right

So what's our full integral looks like now?

[tidal moat]

6 integral Csc x - Sin x dx

[scenic peak]

Right

Now how can we do that integral?

[tidal moat]

Well for Csc x I'm not sure.

[scenic peak]

Hmm I was thinking you'd have this off of the top of your head

I can walk you through that if you'd like

But are you sure this isn't in your book already?

[tidal moat]

I'm learning all of this litterally just last week. From dereivatives.

[tidal moat]

I would like that.

[scenic peak]

Alright so I'm not really sure how to socratic method this one since it's not an easy trick to see

So I'll outline some steps and have you fill in the details

[tidal moat]

yee

[scenic peak]

We start with $\int \csc xdx$

[rocky lotus]

Buzzing Hornet

[scenic peak]

The key insight is that we can multiply by 1 to get $\int \csc x \left(\frac{\csc x-\cot x}{\csc x-\cot x}\right)dx$

[rocky lotus]

Buzzing Hornet

[scenic peak]

Now, what happens when we simpify?

(We just want to multiply everything out)

[tidal moat]

well it would distribute in then reduce to Csc x - Csc x / 1 - 1?

I'm not very goood at algebra.

Def gotta work on that.

[scenic peak]

Uhh ok so we have an expression which looks like $a\left(\frac{b+c}{d+e}\right)$

[rocky lotus]

Buzzing Hornet

[scenic peak]

When we multiply this out using the distributive rule, what do we get?

[tidal moat]

Well the top would be ab + ac

[scenic peak]

Right

And the bottom?

[tidal moat]

d + e

[scenic peak]

Right

[tidal moat]

you would be multiplying by 1 because a / 1.

[scenic peak]

So going back to this, what happens when we multiply this out?

[tidal moat]

Well, Csc^2 x - Cot x Csc x / Csc x - Cot X

[scenic peak]

Right

[tidal moat]

But the terms on the bottom make me want to reduce.

[scenic peak]

Mm you'll want to resist that instinct

Do you have a guess at what integral technique we might apply here

[tidal moat]

Pythagorean I guess

[scenic peak]

Well this is difficult so it's fine that you don't see it

We're going to use u sub

Specifically, we'll use $u= \csc x -\cot x$

[rocky lotus]

Buzzing Hornet

[scenic peak]

Do you think that you can work out the rest of the u sub?

[tidal moat]

I think so

[scenic peak]

Perfectly done

[scenic peak]

So now, how do we finish up?

Though I guess we should be using theta instead of x

[scenic peak]

You're so close

Do you see the algebra error in your last step

[tidal moat]

I didn't distribute properly.

[scenic peak]

Mhm