help-13

[edgy heart]

Bro thanks

[scarlet widget]

Yw

[edgy heart]

And if I have another problem like that

[weary vessel]

The table summarizes the signs of both of the factors

And their multiplication

[edgy heart]

Always one answer will be invalid?

[edgy heart]

Ohhh so the other x is the possible answers that won't be

[scarlet widget]

No

[edgy heart]

Right???

[scarlet widget]

Check all the cases

[edgy heart]

That's the case when it collides right?

Or not

[scarlet widget]

I don't understand your question

[edgy heart]

Uhmmm how can I explain it

Well look

[scarlet widget]

Second case is invalid because x has to be less than -1 and greater than 2 at the same time

[edgy heart]

If a have idk let's say

4>x

And

-4<x

in my first answer

But

3>x
And -3<x

In the second

[scarlet widget]

4 > x means x < 4
-4 < x means x > -4
so x is between -4 and 4

[edgy heart]

I can mix the two answers

And logically

I will see that it remains-4<x<4

[scarlet widget]

Yes

x < 4 and x > -4 is possible

[edgy heart]

It doesn't have a hole between 4 and 3?

[scarlet widget]

But x < -1 and x > 2 is not

Wait

[edgy heart]

Or it keeps being an answer

Like idk 3.5

[scarlet widget]

4 > x
-4 < x
3 > x
-3 < x

All the same question?

[edgy heart]

Yeah

[scarlet widget]

x is between -3 and 3

[edgy heart]

That's the only answer?

[scarlet widget]

That's the answer

[edgy heart]

Why not 4

[scarlet widget]

Because x < 3

In one of the inequalities

[edgy heart]

Oh yeah hahaha I understand now

Thanks man

I appreciate it

[scarlet widget]

You are welcome

[edgy heart]

🥹

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

This exercise deals with a self-generating sequence. The sequence, ${\map a n}$, is defined by[
\map a n = n- a(a(n-1)) \textss{for} n \ge 1 \textss{and} \map a 0 = 0
]
I have to prove that $\map a n = \floor{(n+1)\mu}$ where $\ds \mu = \f{-1+\s 5}{2}$

\vs{3 mm}
So far, I have only discovered the fact that $\mu^2 = 1-\mu$ but am unable to proceed. Any hints would be appreciated!

[crimson sedge]

(Asking this again because I couldn't keep up with yesterday's channel)

I'm still stuck and don't see the proper procedure of solving this

[clear berry]

Holy shit, this is one of the questions I've seen today

My only guess is that induction should work

[crimson sedge]

Where? Haha

[crimson sedge]

Someone did suggest me doing it

But, hoooow 😅

You just get like

k+1-a(a(k))

[clear berry]

This would need a pen and paper

Lemme get some

[crimson sedge]

Okay okay no worries

[clear berry]

In the definition of a(n) is it defined as n - a of a(n-1) as in function of function?

[slate lintel]

yes

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[clear berry]

any progress lix

I tried but got stuck in dealing with the floors

[crimson sedge]

really not :(

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

your sequence has a name https://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_G_sequence

reading through oeis, it seems to be related to fibonacci

(which makes sense because of the golden ratio mu)

[crimson sedge]

oh wow thats crazy

[crimson sedge]

also, I agree with this ^ (strong induction probably)

might need to show that a(n) is nondecreasing first tho

[crimson sedge]

still dont see it easily enough

at least with that floor

we want to show $\lfloor (n+1)\mu \rfloor = n- \lfloor (\lfloor n\mu \rfloor +1 )\mu\rfloor$

[wraith dagger]

Toby

[crimson sedge]

uh wait

i thought it was the otheer way around?

huh?

as in show n-a(a(n-1)) = floor((n+1)mu)

yeah

then we can sub in a(n-1) via induction

[crimson sedge]

to get this ^

(provided that a(n) is nondecreasing)

hmm okay

[clear berry]

yeah, I basically got stuck here and called quits

I tried taking [n mu] as k and proceeding but didn't help

[crimson sedge]

if we get rid of all the floors, its true via mu^2=1-mu

but idk if we can retrieve the floor form from that

[clear berry]

yeah but then again there's no property that allows to simplify that

only thing we can do is somehow bring the n out

lemme try again

[keen flax]

can anyone help me solving my equation doubt basics pls

[limpid plume]

Yes why not, just take an unoccupied channel

This one is already occupied

[keen flax]

thank you this one step-step

[limpid plume]

Uhm i meant

Not here

[clear berry]

tune, get your own channel pls

[limpid plume]

.

[keen flax]

like y?did I mean something bad?

[clear berry]

you can find free channels in MATH HELP (AVAILABLE)

[limpid plume]

Nono the thing is there's already someone here who is asking a question

You take an empty room

Like

#help-4

[keen flax]

thank you and sorry

[limpid plume]

It's okay 👍

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

Sorry for the afk guys

[crimson sedge]

How does one

Get rid of floors?

Is there a... Floor inverse 😅

[crimson sedge]

wave wand

idk if its valid to literally ignore all the floors

[crimson sedge]

My math bender!

[crimson sedge]

I'd assume the error would be a bit too large

yeah

floors are really weird to work with

if my working is correct, I've reduced it to $\lfloor -\mu^2n+\mu\rfloor = -\lfloor \lfloor n\mu + 1\rfloor \mu\rfloor$

[wraith dagger]

Toby

[crimson sedge]

so we need to show that there is exactly one integer between the two floored things

[crimson sedge]

[crimson sedge]

$\implies \lfloor -\mu^2n+\mu\rfloor =\lceil-\lfloor n\mu + 1\rfloor \mu\rceil$

[wraith dagger]

Toby

[crimson sedge]

so $-\mu^2n+\mu \leq \lfloor \mu^2n-\mu\rfloor \leq \lfloor n\mu + 1\rfloor \mu$

[wraith dagger]

Toby

[crimson sedge]

i dont follow, how?

pulling the negative sign out flips floor/ceiling

[crimson sedge]

wtf?

i actually

never knew that

HUUUUUUUH

,w -floor(x)==ceil(-x) reals

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Toby#2275

[crimson sedge]

oops signs got f'd up

should mu^2n-mu on left

what is the proof of that

like

just curious

[crimson sedge]

of this?

yes

I think looking at the definition is enough

hmmm?

- changes max to min and swaps inequalities

this is really interesting ty

the more you know with toby

[crimson sedge]

but how do we use this now

somethings not right

desmos giving us wrong things

but we should bound the difference between upper and lower bound to be <1

[crimson sedge]

which gives us "exactly one integer"

and then we would be done I think

but that requires me to be capable of arithmetic, and my brain power is not up for it atm

[crimson sedge]

yeah i am still not up for it with this question LOL

i will message you tomorrow toby about this if possible

after i

try understanding what have u done a bit more

but thanks a lot

.close

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[timber dock]

$\int_{-1}^{0} w^3 \cdot 8^{w^2+1} , dw$

[wraith dagger]

Daniel H.

[timber dock]

I'm trying to solve this, but I can't find a method to use. Any recommendations?

[dire geode]

Use a^b = e^(b log(a))

[inland gust]

Pull out the 8^1 first though

[cosmic steppe]

The 8 is funny

Don't hate it

[surreal cave]

?

[dire geode]

Don't h8 it
FTFY

[dire geode]

Just a silly joke I think

[surreal cave]

smh I haven't unlocked the Dad Joke Detection ability yet

[timber dock]

.close

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[teal echo]

how do i do this

[shadow hedge]

have you come across trig inverses

like sin^-1(x) or arcsin(x)

[teal echo]

yes sin^-1 but not arcsin(x)

i cannot remember

[slate lintel]

those are different names for the same function, it takes a value and gives you back an angle with that sin

[teal echo]

oh then yes i have come across

[slate lintel]

ok, can you use that to find a value of theta that satisfies that equation?

[teal echo]

yes i found the value of theta is that all ?

[slate lintel]

that will give you one answer but there's infinitely many solutions to that equation, and more than one in the range they ask for

[teal echo]

okay i see so how do i calculate the other ones in that range provided

[slate lintel]

here's a picture of what you've got going on, can you tell me another angle that has the same sine?

[teal echo]

im not sure

[inland gust]

Hint there are 3 of them

[teal echo]

i am missing it i am confusing myself i think

[inland gust]

There's one in each quadrant

[slate lintel]

no there isn't, there's just one more angle on there that has the same sin

[inland gust]

Oh oops

I'm working in absolutes 😦

[slate lintel]

sin can be thought of as the height, which is why I've drawn it that way

[inland gust]

I usually construct this view as the triangle and shapes have positive sides :/

[slate lintel]

in this case we're working with \sin\theta = -0.05

[inland gust]

Mm

[teal echo]

sin is negative in quad 3 aswell right is that what you are asking

[inland gust]

I find that locating more roots is significantly easier with the graph

[slate lintel]

true that might be simpler

have you seen the graph of a sine function @teal echo ?

[teal echo]

yes

[slate lintel]

do you see how you can go from one solution to many solutions?

[teal echo]

ohhh i see

[slate lintel]

(i put that 2pi label in the wrong spot; that's 3pi)

[inland gust]

There are actually 4 values 🙃

[slate lintel]

in the range we want (-pi to 4pi) there are 6 i think

[teal echo]

yes 6

[inland gust]

Which is more than 4 🙃

🎉

[teal echo]

okay so how do i calculate those 6 values in that range

and show it

[slate lintel]

do you see how the graph has a lot of symmetries?

[teal echo]

yes

[slate lintel]

can you use that to calculate the remaining 5 values?

or even one more of them?

[teal echo]

yes i am doing it right now

thank you

.close

[cedar kiln]

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[heady spindle]

what can I do to solve this integro-differential equation on wolfram?, I need to check my answer :c

[mighty drift]

If you differentiate it the integral disappears and you get a 3rd order diff eq

[rose swan]

couldn't you differentiate both sides?

[mighty drift]

Then WA can most likely solve it with ease and you can check the answer

Also checking whether the answer is right shouldn't be that hard, should it ?

[rose swan]

looks like you could do method of undetermined coefficients after differentiating

since you'll only have an exponential term on the right hand side

[mighty drift]

It's 6e^t - 4 so it's not just exponential

[heady spindle]

But the exercise is about using convolution

[rose swan]

you're absolutely right on that. misread it

[heady spindle]

but, the integrate is with dx, how can it dissapear differentiate?

[mighty drift]

Though you can guess that the answer is of the form k e^t + some polynomial of degree at most 4

[mighty drift]

Fundamental theorem of calculus

[rose swan]

FTC baby

[mighty drift]

Never forget

[heady spindle]

yes, but, my function is y'(t) = dy/dt, if I differentiate using dx what happens with that dy/dt, thay is my question

[weary vessel]

Are you asked to solve the differential equation in a normal way

Or using convolution

??

[heady spindle]

Using convolution

[weary vessel]

Then use Laplace transform on both sides

[mighty drift]

If you did things properly you'd quickly realize there is no problem here

[heady spindle]

Yes, I did it, I want to check if what I did is correct

[weary vessel]

Oh, I see, nice!

[mighty drift]

Also maybe change your role to something other than pre-university

[weary vessel]

What did you find?

[heady spindle]

Eeeh, I'm not from USA, so I'm not sure what role I have to choose, I'm from Colombia

[mighty drift]

Most likely undergrad

Basically 18-20 is undergrad

[rose swan]

looks like a problem from an ODE class, which is undergrad

[heady spindle]

y(t) = 3*cosh(t)[cosh(2t)-cosh(t)] + [e^-t(cosh(2t)-cosh(t))][-2t-3]

[mighty drift]

Undergrad -> bachelor's
Graduate -> master's
PhD student / doctorate -> phD

[heady spindle]

[weary vessel]

Oh my god

[mighty drift]

I did not expect that

[rose swan]

either way, i don't think any of us want to grind through this calculation lol

too much trouble to look up laplace transform tables and then apply convolution

makes sense to check it with wolfram alpha

[weary vessel]

Maria, it's false unfortunately

You should not get any cosh

You should get exponentials

[heady spindle]

In the purple underline I need to solve the convolution first and then solve the integral?

[weary vessel]

You do not need any convolution to solve this differential equation

Only Laplace Transform

Find Y(s)

Then its inverse y(t)

[heady spindle]

Why is with exponential? :c the inverse laplace transform of L^-1 (s/s^2 - 1) is not cosh? :c

[heady spindle]

My teacher asked us to solved it using convolution

[weary vessel]

Yeah, but convolution in the time domain

is equivalent to multiplication in the s-domain

in the laplace domain

that's what we are doing here!

if I had a paper and pen next to me, I would solve it for you and show you

[heady spindle]

what is time domain?

[weary vessel]

Okay okay, never mind

Let's just apply the Laplace transform on both sides

y''(t) becomes s².Y(s) - s.y(0) - y'(0)

Right?

[heady spindle]

right

[weary vessel]

Okay

y'(t) becomes s.Y(s) - y(0)

Right?

[weary vessel]

Yes correct, but I do not see any s²-4

s^3 + s² - 4s - 4 gives real roots

-1

2

and -2

(s+1)(s+2)(s-2)

So you will have c1.exp(-t) + c2.exp(2t) + c3.exp(-2t)

I'm talking about homogeneous solution

For the general solution, it's a long tedious process lol

[cedar kiln]

@heady spindle Has your question been resolved?

[heady spindle]

Oooh :0

thank you so much <3

[cedar kiln]

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[finite badger]

hey, trying to find young`s modulus here but i get 200mpa (2/0.01=200) , what am i doing wrong

[finite badger]

.close

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[nocturne field]

Can someone explain part b for me please

If it’s perpendicular go the plane

Would I use the vector product if the 2 direction vectors and find the normal to the plane and make that the direction vector if line l ?

@ me if you know pls

[cedar kiln]

@nocturne field Has your question been resolved?

[cedar kiln]

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[twin flax]

Given f(x) = tan(x) and g(x) = sin(x). What is (f/g)(x). State the domain and range of the combined function

[twin flax]

I see, so then, it can go till 1 / cosx?

[surreal cave]

this can be simplified :))

[violet flume]

let em finish typing haha

theres a real paucity of askers tonite

[twin flax]

And for the Domain, I wrote:

D: { X|X =/ pi/2(n), n e R, x e Z

[surreal cave]

ah I'm sorry I didn't him typing 😂

[surreal cave]

ikr

[twin flax]

What's paucity

😥

[rain drift]

there's not much going on, we're all eager to help lmao

[surreal cave]

scarcity pretty much

[livid hound]

why do you have
x in Z

[twin flax]

So it can go till 1/ cosx then

[twin flax]

U have a point... it would make sense for n, not x

[surreal cave]

usually $n\in\mathbb{Z}$ and $x\in\mathbb{R}$

[wraith dagger]

XxMrFancyu2xX

[twin flax]

Yeah

Btw, when I tried simplifying it again

I got this:

sin^2(x) / cosx

[surreal cave]

just use the fraction properties $\frac{1}{\cos\theta}=\sec\theta$

[wraith dagger]

XxMrFancyu2xX

[twin flax]

Wait whay

tanx/ sinx = sinx/cosx ÷ 1/sinx

Wait...

I think I made a mistake

Yeah it's 1/cosx

[surreal cave]

$\frac{\tan\theta}{\sin\theta}=\frac{\frac{\cancel{\sin\theta}}{\cos\theta}}{\cancel{\sin\theta}}$

[wraith dagger]

XxMrFancyu2xX

[twin flax]

As for the domain, there was sinx and cosx in the process, so would we just look at the simplified answer for the NPV?

Non-permissible value

[surreal cave]

because both sin and cosine are in denominators

check when both cosine =0 and sine =0

[twin flax]

That's never

They can't be 0 at the same time

Cosx is 0 at pi/2

[surreal cave]

yes but when either of them are 0

[twin flax]

Sinx is 0 at pi

I see
So if we add by pi/2 each time for the npv, we would be getting them

So then the domain is

D: {X in R| x =/ (pi/2)n, n in Z}?

[surreal cave]

yep! :))

[twin flax]

As for the range

[surreal cave]

from this maybe consider using interval notation rather then set builder

you may find it easier 😅

[twin flax]

Is it this:

Y: { y | y =/ 0, y in R}

[surreal cave]

y=1/2 is not in range

[twin flax]

Now I'm confused

[surreal cave]

just start with the range of secant 😅

what is the range of secant?

[twin flax]

To the real numbers

[surreal cave]

nope, there is not $\theta$ such $\sec\theta=0$

[wraith dagger]

XxMrFancyu2xX

[surreal cave]

so 0 is not in the range

[twin flax]

Ohh

True

[surreal cave]

remember $\sec\theta=\frac{1}{\cos\theta}$ is $\cos$ has it's maximums at 1

[wraith dagger]

XxMrFancyu2xX

[surreal cave]

and can never get larger

what happens to the denominator and hence the fraction?

[twin flax]

It's undefined at pi/2

[surreal cave]

alright back up a little, cosine goes from [-1,1] right?

[twin flax]

Yes

[surreal cave]

so the denominator goes from [-1,1] then of secant, yes?

[cedar kiln]

@twin flax Has your question been resolved?

[cedar kiln]

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[timber dock]

$\int_{3}^{7} u(2u-5) , du$

[wraith dagger]

Daniel H.

[timber dock]

I have to solve using Riemann sums.

I already rewrite it as:

$\int_{3}^{7} 2u^2-5u , du$

[wraith dagger]

Daniel H.

[weary vessel]

Did they specify to you how many sub-intervals?

To divide the interval [3,7] into sub-intervals

[timber dock]

No, I usually have to create the limit to the infinite.

But I can't get the answer to be 382/3

[agile kettle]

What step us causing you trouble?

Is*

[timber dock]

Idk, but when I evaluate the limit it tends to the infinite and not to the right answer.

Maybe I was wrong somewhere, but I don't know where

[weary vessel]

Show us!

[timber dock]

Here

[weary vessel]

The line f(ui)

The formula is: (a+b)² = a² + b² + 2ab

You missed the +2ab part!

[timber dock]

Awww 🫠 thankss!

[weary vessel]

Also, right after that, you have -15 - 20i/n

You distribute the minus sign on both!

Not only the first

[timber dock]

Right

Thanks a lot!

[weary vessel]

other than that, your work is awesome

try again with those slight changes

and check

[timber dock]

Thank u! I will.

.close

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[crimson sedge]

How do I find the star height of [
(((((\vb 0^)\vb 1)^\vb0)^)\vb 1)^
]

[muted bear]

Whats star height

[crimson sedge]

hmmm i get [
\max(\max(h(((\vb 0^),\vb 1)^), \map h{\vb 0}) + 1, 0) +1
]
but how the hell do you progress from that:

[muted bear]

Wtf

[crimson sedge]

lemme give the definition one sec

[umbral hull]

I am curious in this star operation too

[sacred grail]

[slate lintel]

it's a recursive definition right? start with the innermost things and work your way out

ie h(0) = 0 because 0 is an alphabet symbol

[crimson sedge]

@muted bear

[sacred grail]

that took you a while

[umbral hull]

Oh is this language math?

[crimson sedge]

yes

[crimson sedge]

yeah it just gets too messy idk

lemme try again

[sacred grail]

apply the last step recursively

[slate lintel]

you shouldn't have any max in there at all

[sacred grail]

there's basically nothing for you to do apart from the last thing

[muted bear]

O.O ...oh

[crimson sedge]

oh what so i have to try and eliminate the max's right?

okay hmm

[sacred grail]

evaluate as you go

outside in or inside out doesn't matter

[slate lintel]

no you shouldn't have any max in the first place, that should never show up

[tropic oxide]

h(0) = 0, yes?

er

i mean ok intuitively i think the answer should be 4 but im not gonna be able to justify that formally without any work

[sacred grail]

4 seems right

[umbral hull]

I need to read up on this math

[crimson sedge]

how are you meant to evaulate it otherwise? like wouldn't you need to use this?

[sacred grail]

yeah you will

[slate lintel]

no, why would you need to use that?

[crimson sedge]

those are two...very different answers 😅

[sacred grail]

you will need it to split the expression

[slate lintel]

you don't have any concatenation or unioning in that regular expression

[sacred grail]

(0*)1 is (0*) followed by 1

[slate lintel]

oh i didn't even see that

yes you will need that sorryyyyyy

[crimson sedge]

oml i was worried that i just bullshitted everything i did 😭

okay

[sacred grail]

h(0) = h(1) = 0

use this wisely

[crimson sedge]

yes uh

sir

[slate lintel]

max(x, 0) = x is also useful here

[umbral hull]

Forgive me if I'm wrong as I just learned this off a wikipedia page 5 seconds ago and what you're saying here but is h(0*)=1 then?

[slate lintel]

that's correct

[umbral hull]

Ok then I understand all this now neat! Have no idea what it's used for tho xD

[crimson sedge]

oh okay i think i got it all down to max's

[slate lintel]

formal languages, pattern matching, linguistic pedantry

[umbral hull]

I think AMS had an article on this this month, or featured book I've been meaning to look into it

[crimson sedge]

i have [
\max(\max(\max(1, 0)+1,0)+1,0)+1
]

[crimson sedge]

unless i somehow fricked up my algebra somewhere

this like

[slate lintel]

looks right to me, now time to pretend to be a computer and evaluate it

[sacred grail]

use this wisely

[crimson sedge]

becomes [
\max(\max(2,0)+1,0)+1\
\max(3,0)+1
]

[crimson sedge]

sooooooooooo

3+1

=4

[umbral hull]

Based off this wouldn't the first inner term be the max(h(0*),h(1))=max(1,0)?

[crimson sedge]

dw about it u will never use this probably

im just obsessed with discrete shit

[umbral hull]

Ahh yeah you have that just erased the h

[crimson sedge]

i did it in-and-out basically

though i dont think it matters

anyways tysm @slate lintel and sir snow sir

[umbral hull]

Hmm wait

[sacred grail]

[umbral hull]

Logically

We have four *'s and everything is 0 otherwise

Hence you coulda looked at this and said 4 from the getgo

Since everything else involved is a normal letter

[sacred grail]

specifically four nested *s

[umbral hull]

Yeah

At each step you're deciding between the star of the previous thing or something with value 0

[crimson sedge]

wait guys

follow up question

wait uhh

maybe i should reopen so people dont get lost

.close

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[minor bear]

hello

[minor bear]

i dont understand this

can someone explain please

[hasty aurora]

What exactly do you not understand?

[minor bear]

the theorem

why is that the answer?

[hasty aurora]

I see

Okay so the thing is first of all we need to understand what we're working with here

Or rather how this is constructed

First there are 4 points M,N,P,Q

[minor bear]

yep

[hasty aurora]

which are connected so that MP is orthogonal to NQ, orthogonal meaning the angle between the lines is 90°

[minor bear]

oh right

i dont know what orthogonal means but i searcehd it up

we didn't take it

i'm year 10/grade 9

[hasty aurora]

Ok do you want me to give you some more examples on that?

[minor bear]

sure

man geometry is so hard and i have finals tomorrow god damnit

[hasty aurora]

you can do it

[minor bear]

brio

if you help me get through this geometry

i will pay you 200$

not even messing around

[hasty aurora]

even if you would i wont take it

[minor bear]

we'll see lol

anyways

so back to the example

i just dont undersatnd like

the reasons of why

like why is AD parallel to BC

[hasty aurora]

First of all this is orthogonal

[minor bear]

aha

okay

so that means

[hasty aurora]

this too

[minor bear]

QN is orthogonal of uh

MP

[hasty aurora]

this is not

[minor bear]

this is not what

an orthogonal?

[hasty aurora]

orthogonal

[minor bear]

oh

so it has to

cut the line

DC has to cut line AB?

for it to be orthogonal?

[hasty aurora]

nut directly cut it

*not

the lines must have a common point

[minor bear]

which would be the 90 degrees

right

right

it doesnt matter

so

i apply this theory

to find the answer?

[hasty aurora]

not really

[minor bear]

so what's this used for then

[hasty aurora]

Or wait

Yeah you will use that fact

[minor bear]

oh ok

so how will i use it

what's the statement and reason

[hasty aurora]

So the thing is in this case that you can just look at it and know whats going on. this might not be true for all cases however

Anywys

Lets talk about AD being parallel to BC because here our orthogonality will become important

[minor bear]

yeha

[hasty aurora]

As MP and QN are orthogonal, the triangle enclosed by M, N and the intersect between MP and QN, lets call it X, is the same triangle as the triangle betwenn M, Q and X

[minor bear]

yeah

[hasty aurora]

This is what I mean with X

[minor bear]

right

[hasty aurora]

Same goes for the Triangle NPX and PQX

Meaning that the midpoints A and D as well as B and C must be equal

[minor bear]

ohhhhhhhhhhhhhhhhh

im so stupid bro

[hasty aurora]

So AD = BC

[minor bear]

i get it now

tysm

ill use this theorem

and ill apply it to anything i dont understannd

[hasty aurora]

because the object is orthogonal AD and BC must be parallel to one another

[minor bear]

yeah

[hasty aurora]

Because if they weren't MP and NQ wouldn't be orthogonal

[minor bear]

mhm

alr

thanks cyrol

[hasty aurora]

and as for the rectangle yeah well thats obvious isnt it

np

[minor bear]

ye

ok

how do i close this lol

[hasty aurora]

.close

just write that and itll be closed

[minor bear]

alr

.close

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[merry heath]

hi so I would like to check if I've done this question correctly

[merry heath]

I'll send my solution after I'm done doing it brb

[tropic oxide]

ok, waiting

[crimson sedge]

you could've opened your channel when you finished your solution

[merry heath]

yeah mb

will do next time

can you guys spot the mistake

[tropic oxide]

bruh the decimals

,calc 64 * (1 - (-1/2)^8)/(1 + 1/2)

[wraith dagger]

Result:

42.5

[tropic oxide]

did you maybe mean to ask "can you guys spot the mistake, if any?"

"can you spot the mistake" implies you know for certain there is at least one mistake

[merry heath]

so are there any mistakes

[tropic oxide]

there don't seem to be, except for the awful decimals

why not write (-1/2)^8 as 1/256..?

[merry heath]

I mean yeah I agree it could be simplified but the way *

I did it is not wrong right?

I kept the decimals to minimise the room for mistakes because I got a differenct answer the first time I did it

[tropic oxide]

i think decimals will NOT minimize room for mistakes

[merry heath]

is it because there is a chance I will write the decimals wrong?

or something else

also, separate question, which one is correct

.close

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[crimson sedge]

Question related to Stats

Is this how coefficient of determination (R^2) is calculated?

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

I guess I’ll just close it

.close

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[sleek saddle]

can someone help me understand where the 1/T normalising factor goes when taking the limit of the fourier series to turn into a fourier transform
there exists a derivation from fourier series to transform but what they do in it is derive the inverse fourier transform and they take the fourier transform as the definition
i cant find anyone showing the fourier transform as a direct consequence of extending the periodicity to infinity and the "disappearance" of the normalising 1/T factor

[cedar kiln]

@sleek saddle Has your question been resolved?

[sleek saddle]

<@&286206848099549185>

[cedar kiln]

@sleek saddle Has your question been resolved?

[dire geode]

Can you write out exactly what math you're implying

[sleek saddle]

the fourier transform

[dire geode]

Yes you mentioned that

I'm asking for exact formulas

there exists a derivation from fourier series to transform

Show this resource you're talking about

[sleek saddle]

this i will show

ok so this is the question

[sleek saddle]

https://math.stackexchange.com/questions/45883/fourier-transform-from-limit-of-fourier-series

[sleek saddle]

https://en.wikipedia.org/wiki/Fourier_transform#Fourier_transform_as_the_Fourier_series_of_an_aperiodic_function

[cedar kiln]

@sleek saddle Has your question been resolved?

[sleek saddle]

<@&286206848099549185>

[dire geode]

https://math.stackexchange.com/questions/1335309/dirac-delta-function-inverse-fourier-transform

You need a little distribution theory to prove it rigorously, but that's essentially the idea

[sleek saddle]

okay ill see more into it

.close

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[sleek saddle]

thanks for the help

[cedar kiln]

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[red pumice]

suppose you are using the finite difference method to solve a PDE

[red pumice]

and you are able to write it as a system of linear ODEs

like this

with your original PDE being

with the w vector being (del p)/ (del t) values

how do i find the values of (del p)/ (del t)

this might be a stupid question

but how do i find the value of $\frac{\partial p}{\partial t}$ for lets say p = 2 and t = 2

[wraith dagger]

heavy

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[red pumice]

.close

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[zinc stag]

How do I do these problems?

[crimson sedge]

recall that complex roots of real polynomials come in conjugate pairs

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

^ Consider reviewing the fundamental theorem of algebra to get a better, general idea too

[zinc stag]

tysm

.close

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[halcyon spire]

@fierce hound

[halcyon spire]

Can u help me with my desmos art assignment

This is what i got rn

[zinc mural]

Ah you’ve made progress. Good job man

Probably shouldn’t ping specific people unless you know the are fine with it tho

[halcyon spire]

this guy told me to ask the verus dude he said he knows all about this

[zinc mural]

Fair enough

What the problem

[halcyon spire]

I found out that i have to put the details of the tiger too

So like the skin lines and colours

[zinc mural]

Get the general outline of it done first

For the stripes maybe you can get away with a single line cause you can change the thickness to make it bigger

[halcyon spire]

Alright

Do u know what i got to change in the second equation to get the second ear

I feel like i can finish the whole left side but idk about the right side

Cause i can’t rotate it

[zinc mural]

You can try and use the same equation

But change to domain more left

So you get the left curve more

Also make the curve thinner

You could the the right ear with a quadratic facing down (negative) like an upside down u

Then join it with just the right side of a quadratic facing up

[cedar kiln]

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[viral fox]

Hello math flows, got a question about number theory, here is the question

[viral fox]

The solution by textbook is a burtforce mode, checking all values of set S to tell if result is an even or odd

I'm wonder if there is better solution for that? here is my attempt, but I'm stuck at last part

I think my solution is not completed, any suggestion how may I come up with a conclusion to include those 3, and 4 values?! sorry I'm not smart

[crimson sedge]

(6 calculations is small enough for brutforce to be a good solution)

[crimson sedge]

one of n or n+1 must be divisible by 4

(follows from coprimality)

[viral fox]

Yes I was thinking of that, so can I say

[crimson sedge]

I dont like your notation

I think $8\mid n^2(n+1)^2 \implies 4\mid n \text{ or } 4\mid (n+1)$ is more clear

[wraith dagger]

Toby

[viral fox]

Oh, sorry may I should have used ∨(OR) instead edit: ∨.

[crimson sedge]

yeah, be explicit that its 'or' and not 'and'

[viral fox]

Awesome, yes, and one last question, about 4|n, and 4|(n+1) parts, proofing is required?

[crimson sedge]

you could add some explanation

it follows directly from coprimality

you should have some sort of theorem/definition to help you

[viral fox]

Thank you so much sir for your great help, explanation, and your time. Math bless us all

.close

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[rich flint]

Hi, I need some help with this please. I'm trying to solve it with Divergence theorem but I cant find my variable change

[silent bobcat]

I only see the definition of a function from R^3 to R^3, with the definition by cartesian equation of a certain plane S

There is nothing to be solved here

[rich flint]

?

I have to use divergence to solve find the flow from F to the outside

maybe i'm translating something wrong

It's in spanish, so I tried translating it with google

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[slender dock]

the given function f(x)=2x²+3x For what values ​​of the variable x we ​​have: f'(x) = f(x)

[slender dock]

so do i derivate it first?

.close

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[crimson sedge]

so basicly i dont know what the tensor product is

[crimson sedge]

i know that u can reconstruct the tensor from its components and the basis like so

okay so my question is, how would u reconstruct the tensor from its components and the basis using the tensor product

or if that question makes any sense

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[icy anchor]

Hi

[icy anchor]

Can I get some help

Basic maths

Coffee is put in at a ratio of 1 to 5

[barren harness]

like a put option?

[icy anchor]

How much grams of coffee for a 250ml cup of coffee

Yes

Like Would it be 50grams

[barren harness]

yes

[icy anchor]

Or 41.7g

?

[barren harness]

why 41.7

[icy anchor]

Like 1+5 = 6

250÷6

[barren harness]

thats wrong

[icy anchor]

41.7

[barren harness]

dont think like that at all

its 50

set up a proportion

[icy anchor]

Ok

Or does this depend on how the question is read

?

/close

.close

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[marsh pond]

what formula should I use to solve this?

[crystal raptor]

remind yourself what the cross product can tell you geometrically

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[upbeat elbow]

.Ask

.open

[cyan vortex]

.Ask

[quasi jungle]

.close

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[quasi jungle]

.close

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[upbeat comet]

Can anyone make any sense of part b? I just cannot understand what they have done...

[upbeat comet]

This is what I did for qa

[cedar kiln]

@upbeat comet Has your question been resolved?

[upbeat comet]

<@&286206848099549185>

[cedar kiln]

@upbeat comet Has your question been resolved?

[cedar kiln]

@upbeat comet Has your question been resolved?

[ember mesa]

seems right?

what's wrong

@upbeat comet

[upbeat comet]

Im saying i dont get question b

and thats the working for a

[ember mesa]

just take the limit from the left and right side of 0

and compare the two, their will be a 'hole' and you can say that the partial derivative of dg/dx and dg/dy doesn't exist at that point

[upbeat comet]

I don't understand why they are introducing h & k in the third line of their answer for b

[cedar kiln]

@upbeat comet Has your question been resolved?

[cedar kiln]

@upbeat comet Has your question been resolved?

[turbid lynx]

The same as you introduce h for the limit approach in 1 dimensional differentiation

This time you dont approach in 1d but in 2d

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[old monolith]

Hey math friends

[old monolith]

I need some help interpreting this question

Would it be fair to assume that the function I'm being asked to use is sqrt(x + y)?

[rose swan]

yep

[old monolith]

And I'm using the linear approximation formula...

Awesome. Alright, let me try this

.close

[cedar kiln]

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[scarlet ginkgo]

Why does $Σn - 2^i$ equal to $Σn - Σ2^i$?

[wraith dagger]

Willow

[tropic oxide]

this notation feels imprecise

[scarlet ginkgo]

https://youtu.be/alJswNJ4P3U?t=1764

I'm confused on the step here

[tropic oxide]

do you mean

$$\sum_{i=1}^n (n - 2^i) \overset?= \sum_{i=1}^n n - \sum_{i=1}^n 2^i$$ maybe?

[wraith dagger]

Ann (glomed)

[tropic oxide]

let me watch the video

[scarlet ginkgo]

you can just watch the portion I linked, I think

[tropic oxide]

right ok

[scarlet ginkgo]

you probably understand the rest already

[tropic oxide]

this is a more general thing

$\sum_{i=m}^n (a_i + b_i) = \sum_{i=m}^n a_i + \sum_{i=m}^n b_i$

[wraith dagger]

Ann (glomed)

[tropic oxide]

a 'small' example of this would be:

(a_1 + b_1) + (a_2 + b_2) + (a_3 + b_3) = (a_1 + a_2 + a_3) + (b_1 + b_2 + b_3)

[scarlet ginkgo]

It's actually this: $Σ(n - 2^i)$

[wraith dagger]

Willow

[scarlet ginkgo]

?

[tropic oxide]

...yes? like you are still dealing with a single summation being split into two, the guy was just a tiny bit sloppy notation-wise in not putting parentheses around the summand

[scarlet ginkgo]

ah, ok

not having the parens confused me

sorry about that

.close

[cedar kiln]

Channel closed

Closed by @scarlet ginkgo

Use .reopen if this was a mistake.

[scarlet ginkgo]

and thank you

[cedar kiln]

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[harsh plaza]

how do i find the domain for this algebraically?

[cunning loom]

What is the domain of the logarithm function

[harsh plaza]

it's asking you to find the natural domain

[cunning loom]

Can't say I've ever heard of that do you have a definition

Otherwise I can only assume its the domain? Perhaps the domain restricted to $\mathbb{N}$?

[wraith dagger]

KB0

[harsh plaza]

question 22.2

[dawn junco]

or maybe the biggest possible domain

[harsh plaza]

i think it's just asking what x values could this function accept

[dawn junco]

sounds more like it

[cunning loom]

Right, so what is the domain of log?

[harsh plaza]

the thing inside the log is greater than 0

wait let me show u my working

[cunning loom]

Sure

[cunning loom]

It's definitely not always >0 else you broke cubics

[cunning loom]

Okay so you seem to be almost there

[harsh plaza]

oh but isn't a log graph assumed to have a positive base?

[cunning loom]

We just need to put your statements together

[harsh plaza]

that's what the function looks like

[cunning loom]

The base of the log won't matter

[harsh plaza]

yeah like idk what to do with those inequalities

[cunning loom]

So we know that if x<-4, then the first bracket is 0, right?

Sorry

[harsh plaza]

like for log_3(x) = y, x>0 because 3^y = x and 3 to the power of anything has to be positive, right?
what do u mean?

[cunning loom]

Less than 0

[harsh plaza]

yeah

[cunning loom]

Then what, necessarily, happens to the bracket with the degree 2 term?

Looking at the x bounds you have

I mean the bracket (x^2 -9), if that was unclear

[harsh plaza]

oh so $$x>-4$$ AND $$x^2-9>0$$?

[wraith dagger]

choufleur ❦

[cunning loom]

Well, ultimately, the thing on the inside (the factorised cubic) is always going to be defined right? It's domain is all of R you agree?

[harsh plaza]

yeah

[cunning loom]

So the only way we can make this function not be defined, I.e. not have domain which is all of R, is due to the 'log' part

Because log is only defined for positive inputs

So the question is asking when the whole inside is positive

Which you can deduce from the inequalities you have

For example, if x<-4 as before, then it's definitely also <-3, so x^2-9 >0, but x+4<0, so the inside is negative... uh oh!

And from your plot you can see, the function is not defined after -4 and has an asymptote at -4

[harsh plaza]

wait i'm still confused on this step

so x^2-9 >0
how did you conclude this

[cunning loom]

Well, we've picked x to be something less than -4, say, -5 (for example)

But now we've picked x

This is a function of one variablr

We can't have 'another' x

And you deduced yourself that x^2-9 >0 when x<-3

In particular this would be true for this chosen x=-5

[harsh plaza]

oh ok yep

[cunning loom]

Maybe it's good for you to try to either convince me or yourself of why the function isn't defined between -3 and 3?

[harsh plaza]

wait if i originally said that x+4>0 then how does it change to being less than 0??

[cunning loom]

You haven't permanently fixed x, you've said that in order to look at where the sign changes for the function on the inside

The fundamental observation is that if (x+4)(x^2-9)<0, then the function is not defined

[harsh plaza]

i think it's because
if -3<x<3 then x^2-9 will be negative

and then x+4 would have to be positive because x<-4

so in the log function, there's pos x neg = neg which doesn't work

[cunning loom]

Is x<-4?

I think you may have written that the wrong way round!

[harsh plaza]

given -3<x<3, x>-4 oops

okok i get why there's a gap there

[cunning loom]

Yeah, your justification is correct

[harsh plaza]

but i don't know how to get the asymptote at x=-4, and why it doesn't have a graph from x<-4

i think i'm kinda stuck on what i do with all the inequalities once i get them? like how do i know which bits don't work

[cunning loom]

It really is a casewise thing, you have three inequalities right? I would always start by checking the weakest bound, which in this case is x<-4

Then move in

[harsh plaza]

so would i basically have to check these parts (non-purple)

like treat the values that i get as "reference points" and check in the intervals to see if it works?

@cunning loom

[cunning loom]

Yes that is absolutely what to do, you find some 'reference points' dictated by the particular functions in the question, and check around them to figure out whether functions are defined there

[harsh plaza]

ohhhhhhhh ok thank you so much 🙇‍♀️ ✨ KB0

[cunning loom]

No worries! Feel free to come back if you have more questions.

[cedar kiln]

@harsh plaza Has your question been resolved?

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[cedar kiln]

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[limber stone]

why is the inequality answee

[surreal cave]

first off consider how the region is being bounded by the x-axis and the parabola

[limber stone]

$ −2≤x≤2 and 0≤y≤4−x^2 $

ffs

[surreal cave]

this gives the y inequalities

[limber stone]

but u know what i mean

my answer would be to solve the inercepts

and thats my inequality region

but thats incorrect in the answer

$−2≤x≤2 and 0≤y≤4−x^2$

[wraith dagger]

wizrdhndrxx

[limber stone]

this is the answer

but my answer did not have 4-x^2

it was simply 4

[agile kettle]

your bounds are giving you a different region

think about it, you are refering to anything betwen 0 and 4 in the y-axis

but the area shadowed is more specific than that

[limber stone]

so why can i do -2<x<2?

[agile kettle]

because you take x from -2 to 2, and for those given x you evaluate the function and get the area betwen the function and 0 (the x-axis)

[limber stone]

okay thank you

.close

[cedar kiln]

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[surreal plume]

I’m confused on how you do the notations. How do you do the set notation, interval notation and inequality notation? And what does IR mean?

[crystal raptor]

,rccw

[buoyant latch]

Set notation looks like this {}

Interval notation looks like this (a,b]

Inequality notation looks like this 3<x<=80