help-0

[lament glen]

think about the condition

[weary wyvern]

No

[lament glen]

no no it's from pi/2 to 2pi

[slender sparrow]

we go the other way around?

ahh i see

so cos is in the 3rd and 4th ?

[lament glen]

sin has to be positive

wait hm

is that given?

[slender sparrow]

yes

[lament glen]

oh it is

yeah sin has to be positive

[slender sparrow]

is that why ?

[alpine sable]

ig its better to use some identities
$tan(\frac{\pi}{2}+x)=-cot(x)$

$sin(\frac{\pi}{2}-x)=cos(x)$

[ocean seal]

∆y/∆x=πy+π^2x

[slender sparrow]

so we are in the 2nd, 3rd and 4th quadrant, but since sin is positive cos is negative

so it's in the 3rd quadrant

[lament glen]

is sin positive there?

[slender sparrow]

i mean second

[lament glen]

yeah

[slender sparrow]

okay thank you

okayy i get it so i was wrong and cos(phi) = -4/5 not 4/5

[lament glen]

#❓how-to-get-help

pick one of these empty channels

[slender sparrow]

.close

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[mild copper]

hi guys, how can I solve this differential equation?

[tacit arch]

what have you tried

[mild copper]

I got these solutions{cos(3x),sen(3x)} from y''+9y=0

using the incomplete DE method

then, I can say the general solution is y = C1.cos(3x)+C2.sen(3x)

now missing the particular solution part

[tacit arch]

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

"guess"

[mild copper]

hmmm

but I have a sum of functions of g(x)

sen(x)-e^(-x)

do I need to solve 2 times the DE?
y''+9y=sen(x)
and
y''+9y=e^(-x)?

and then add up the 2 yp?

[tacit arch]

yea go through solutions in example 10 here
https://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

[mild copper]

yep

ok ty very much

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[reef lantern]

hey guys, can you help me out with this. Is this true?

[last ether]

is c a point or a domain?

[dense sleet]

Does it really matter?

[marsh rapids]

what does your intuition say ?

[last ether]

Not really lol

Just wondering what c is exactly supposed to be

[marsh rapids]

no

[last ether]

I mean

Not really

Doesn't matter though

It'll still be continuous

[marsh rapids]

c is obviously a point because it's one of the 3 most common names for points when talking about continuity, and it definitely isn't a good name for a domain

[marsh rapids]

are you sure about that ?

[last ether]

As far as I'm concerned

Well

I guess if like

Well now that I think about it

Not always

[marsh rapids]

not always

therefore no

[last ether]

I guess if f(x) is like this

And so |f| would fill that hole, per se

[marsh rapids]

that's an example yes

I was thinking of something much more drastic but hey, this works

like $f(x) = (-1)^{1_{\mathbb{Q}}(x)+1}$

which is continuous nowhere but whose absolute value is continuous everywhere

[ocean seal]

themateo713

[last ether]

I mean (-1)^x by itself satisfies

[marsh rapids]

the problem is you have a function whose domain has no interior

so talking about continuity for f(x)=(-1)^x is .... Rather uninteresting

[last ether]

Well no it's not continuous for ... well

Lmao

A lot

[last ether]

This probably is the best example

It's just a line with a hole

[marsh rapids]

your example is almost the simplest yes of course, but not the most interesting/enjoyable

[last ether]

If it works it works

Fine

sgn(x)

[marsh rapids]

that's also quite simple indeeed, though I had in mind f(x) = 1 if x != 0 otherwise -1

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@reef lantern Has your question been resolved?

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[junior talon]

This is from Oscar Levin's open Discrete Mathematics book
The answer for B and e are 6720 and 6660 respectively according to the show answers button

Question is : how do I even begin to get the answers for these? I'm actually totally clueless

[junior talon]

my god something came up

.reopen

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[quiet hull]

8 letters total

8x7x6x5x4

Equal 6720

Calculating possible combinations while removing one from each multiple to account for 1use letters

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[sterile vale]

Could somebody explain me this please?

[sterile vale]

I get the limit on the left but what to do about the cos?

[keen pasture]

cos is in [-1;1] so it doesn't matter regarding the infinity

[sterile vale]

thank you!

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[alpine sable]

HOW?!

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Can someone help me out its pretty simple I know but I'm confused

:\

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[alpine sable]

How..?

[lament glen]

it feels like you cut out way too much from the image

[limpid spade]

^

[lament glen]

what's the context exactly and what are you confused about?

but I feel it's a u = -t sub considering the bounds

not sure why they went with the same variable for the sub though

so I might be wrong

[alpine sable]

1 sec

this is the whole thing

[lament glen]

oh is a a function

[alpine sable]

I'm just a little confused about the 1st part although by graph I can easily see they will both give the same result

[lament glen]

I think it's this

[lament glen]

oh wait you're integrating that

[alpine sable]

this is the question

yes

[lament glen]

oohh

that clears up a lot

yeah it's an even function

since $e^{-2a|t|} = e^{-2a|-t|}$

[ocean seal]

Doggo

[lament glen]

then you can just write it as 2 times 0 to infinity of that function

[alpine sable]

yes but how is this done? :\

Or is it just using the even property of the function

[plain flame]

you mean how to integrate that function?

[alpine sable]

No, I was confused on how the limits changed and thought it must be some property to change them that way

I know this is very silly

[lament glen]

if we ignore the fact that it still uses t as the variable, this sub does give you that integral

since as t -> -infty, u -> infty

and t = 0, u = 0

then dt = -du

so you have negative to flip the bounds

and you get that integral, but the variable is u

[alpine sable]

Hmmmmm

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[neat sierra]

What would the identity element be?

[neat sierra]

Since we dont know what G actually is

[alpine sable]

you can give the identity of G a name (a natural choice is 1 or e or 1_G)

[neat sierra]

Ok, so just call it e then

[dry ridge]

Also we know G is a group so we know G has an identity element.

[neat sierra]

But how do we prove the identity in (G', *)?

Take a in G' (or G). Then just stating that ea = a = ae?

Feels kinda weird

[alpine sable]

since there are two different operations here, you should specify which one you are using:
$e\star a=a\cdot e=a$ etc

[ocean seal]

Toby

[alpine sable]

but your idea is right

[neat sierra]

oh I see

thanks

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[edgy flare]

Complex Variables:

[edgy flare]

Attached is the problem and the theorem it is referring to. I’m not sure what I am being asked or were to start.

[verbal juniper]

I do love Euler's identity

[edgy flare]

I would probably love your help then 🙂

[verbal juniper]

I wish I could, but this is beyond my current capabilities at the moment. Sorry!
Just a fan of r*e^(i*theta)

[edgy flare]

<@&286206848099549185>

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@edgy flare Has your question been resolved?

[edgy flare]

<@&286206848099549185>

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@edgy flare Has your question been resolved?

[lone heart]

@edgy flare Has your question been resolved?

[fallen verge]

Hey poisoned! More CV?

[alpine sable]

you'll probably have more luck posting this in #real-complex-analysis

[edgy flare]

@alpine sable I asked about posting a homework question there and someone told me it did not belong there.

[alpine sable]

nah it's fine

people in help channels often come for hs math

if you want help for undergraduate courses you'll likely find it in ''early uni'' or ''advanced''

[edgy flare]

.close

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[wintry vortex]

So im alittle bit confused, i get that it wants to me to get v_x and v_y

So it wants me to do DX/DT

that just comes out to 4d-dt/3d

[alpine sable]

seperate it out find the x component of velocity at the given time similar for the y component

Which is very handy actually it comes out to be

Oh no oops

[wintry vortex]

how do I do that?

I got this

and i know its wrong

but i also dont know how to make it not wrong lol

the examples just kinda snap to a solution, it doesnt show me what they did

[alpine sable]

This is terrible I think you don't know how to differentiate

differentiation of x component of velocity which is 3t would be 3

which is constant similarly you'll get the y component velocity which will be -1

[wintry vortex]

Why is that?

Sorry this is a new concept to me

[alpine sable]

Now take the magnitude and it comes out to be root 10 super apologies I don't know what I did before but

root 10 is correct

[wintry vortex]

So do I not need the whole v_x=dx/dt equation?

[alpine sable]

here

differentiation of ax^n is nax^(n-1)

[alpine sable]

its the same thing

[wintry vortex]

okay so to backtrack, why is X a constant?

[alpine sable]

like ths

this

[wintry vortex]

So I dont set T to 3?

[alpine sable]

which x 3 is the constant you have to differentiate 3t

[alpine sable]

Normally you would after differentiating but as you can see the velocity is not a function of time and hence constant

differentiate it one more time and you will get the acceleration 0

[wintry vortex]

How do I know its not a function of time?

[alpine sable]

because after differentiation You got a constant

re-read this

[alpine sable]

.

Vx comes out to be 3

hence constant

[wintry vortex]

wouldnt it equal 3d?

[alpine sable]

That's not how we do differentiation

[alpine sable]

use this

[wintry vortex]

okay, so how does v_y come out to -1?

along the lines we used last time it should be 4

or -4

[alpine sable]

same way , no

its 4 - t differentiation of a constant is 0 here 4 - t will come out to be -1 which is the coefficient of t and if you apply the formula you'll get it remember you are differentiaing with respect to t so if no t the answer is 0

[wintry vortex]

ok, i think i get it

[alpine sable]

This was the answer to be clear

[wintry vortex]

okay the rest of the formula is alittle easier to understand for me, sqrt v_x^2+v_y^2

[alpine sable]

see this

[alpine sable]

yes

[wintry vortex]

COOL I finally got past the first questions!

TY!

9 more to go by tomorrow and i can have a weekend lmao xD

u rock!

[alpine sable]

Good luck and learn differentiation ,for your own good

[wintry vortex]

Lol im trying, I just got the handle on derivatives last week

[alpine sable]

😄 tc

[wintry vortex]

okay so to see if i understand this, in this case v_x would be 4 and V_y would be -1

[alpine sable]

Yes but you have to find the acceleration for which you have to differentiate one more time

which gives you zero

[wintry vortex]

ok the acceleration part lost me, what do you mean by that?

why would it equal 0 with acceleration?

[alpine sable]

Alrght

[wintry vortex]

sorry 😅 im alittle hopeless with calc, it loses my frequently

[alpine sable]

this is the relation

differentiating position one time will give velocity as velocity is the rate of change of position

differentiating velocity will give acceleration

So differentiating the position two times will Give you the acceleration

A short Video on this topic will help I think

Do watch it

Here r is position , v is velocity, a is acceleration

d/dt just denotes the differentiation with respect to t

[wintry vortex]

is there a video you would suggest?

[alpine sable]

https://youtu.be/pFeuGMMiZWw

Explains with an example

https://youtu.be/4dCrkp8qgLU

explains what is position,velocity,acceleration

[wintry vortex]

so v_x and v_y is showing velocity?

[alpine sable]

yes the x and y components of velocity

respectively

[wintry vortex]

so to get acceleration i take the second derivative

so it would just be x and y equal 0

oh boy that was more complicated in my head

Cool ty! I'm rolling now!

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[wintry vortex]

ugh, I thought i got this one pretty well and somehow the degrees arent right

so i got the magnitude, then i used tantheta=-1/5 to find the degrees like the example says

am i missing something?

[white obsidian]

did you set your calculator to DEG?

[wintry vortex]

yes

I dont need the answer, just confused on why its not right 😦

I was super confident on that answer lol

[white obsidian]

well, if your magnitude is correct, then your angle is correct. could enter -11° or 349° instead 🤷‍♂️

[wintry vortex]

the magnitude is correct, it already told me its right

WHY WAS 349 degrees right?!

[white obsidian]

169+180

tan has a period of 180, not 360

[wintry vortex]

i forgot about that 0_0

ty

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[wintry vortex]

.reopen

[lone heart]

✅

[wintry vortex]

sorry didnt mean to closewhile u were answering 😅

[white obsidian]

np. be careful with the quadrants when using arctan 😉

[wintry vortex]

❤️ TY

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[humble prairie]

Does any1 know this

I've been working on it and I don't know what I would put.

[tacit arch]

Too tiny to read this resolution

[humble prairie]

Let me fix . one sec

[humble prairie]

I need to know what each variable means v

Can anyone help? <@&286206848099549185>

[worn fox]

You are posting more than once problem

[humble prairie]

I deleted

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[humble prairie]

.close

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[proven saddle]

good evening, can you help me with this simplification of radicals

[median oar]

which one?

[median oar]

ok let's start from left to right

do you know about $\sqrt{ab}=\sqrt{a}\sqrt{b}$

[ocean seal]

Frosst

[proven saddle]

a little

[median oar]

what do you mean a little

you either know this or you dont you cant know a rule a little

[proven saddle]

the basics

[median oar]

what do you mean the basics

i asked just 1 rule

[proven saddle]

yes

thanks

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[lethal sinew]

I'm not sure if 14 is correct. I double checked my work but it was wrong
A Quonset Hut's height is its radius.
The volume of a Quonset Hut is the second picture

[tacit arch]

the hut is just a cylinder?

there shouldn't be 1/2.

[lethal sinew]

oh

it was given

[tacit arch]

oh so it's not a cylinder then

then what's your question

[lethal sinew]

half a cylinder

idk how to explain it LOL

[tacit arch]

show your math

[lethal sinew]

i'm not sure how to go about the problem
i plugged in the values but i dont think its how i'm supposed to do the problem bc when i double checked i got 7389 instead of 7540
gimme a sec sorry

[tacit arch]

swap your h and l

[lethal sinew]

lemme try

hmm didn't work
i double checked and got about 253488

[tacit arch]

why would it be larger than 7540

[lethal sinew]

i honestly have no idea 😭

[tacit arch]

use a calculator

[lethal sinew]

i did

[tacit arch]

try it again

[lethal sinew]

this is how I originally did it; not sure how it’s wrong

By swapping the h and l do you mean the values?

nevermind! i got it correct!

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[daring tulip]

The function f has the property that for each positive integer n, the number f(n) is also a positive integer. It is also known that f(n) + f(f(n)) = 2n for each positive integer n.
Find all possible values of f(1000).

Can someone please prove that the only answer is 1000?

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[grizzled vortex]

I did this and got some nonsense... I must be doing something wrong, but I'm not sure where

[vale wigeon]

your 2 looks like a z

also no you didn't get nonsense you got exactly what you were supposed to

the numerator approaches a positive number while the denominator approaches zero

perhaps you could argue the denominator x(sin(x)-sinh(x)) ought to approach zero from below and so the limit is -∞ rather than just nonexistent.

...

,w graph y=sin(x)-sinh(x)

[ocean seal]

Results provided by WolframAlpha

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Requested by Ann#0413

[vale wigeon]

ok yeah

from below

[grizzled vortex]

oh! Then I guess we are supposed to prove by definition that the limit is infinity...

okay thanks I'll do that

.close

[lone heart]

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[grizzled vortex]

.reopen

[lone heart]

✅

[grizzled vortex]

So the right limit and left limit is both minus infiniity, right?

[vale wigeon]

yes

[grizzled vortex]

thanks

.close

[lone heart]

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[oak fiber]

help

[tacit arch]

What math help do you need

[vale wigeon]

something something snell's law?

🐌 📜

[oak fiber]

this

[vale wigeon]

pointing back at the problem isn't going to help us help you at all

are we to understand you have no idea how to even begin this problem?

[tacit arch]

There's no math yet. Set up your physics equations

[oak fiber]

ok

.close

[lone heart]

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[obsidian kayak]

can i just post it here?

[river fossil]

yeah

[alpine sable]

Mhm

[obsidian kayak]

alright so

[river fossil]

what have you tried

[obsidian kayak]

i guess what i was thinking of doing now is

in the example

first example

[alpine sable]

Let's take your example

Yeah

[obsidian kayak]

i set S ={1,2,3}

so now i just have to set epsilon as = 4

right

[alpine sable]

Yes

[river fossil]

umm no

[clever folio]

Any epsilon

[river fossil]

you can NOT set e

[clever folio]

I can pick epsilon = 0.5 and your set won't work.

[river fossil]

as a fixed constant

because

you need it to work for ANY epsilon

[obsidian kayak]

fuck

i thought so

god damn it

[river fossil]

so for example, it doesn't work for e = 0.5

[obsidian kayak]

right

[alpine sable]

If your set S is {1,2,3}, then max(S) = 3
So set epsilon ≥ 3 (epsilon can be anything ≥ 3), and this is your example. S is also a subset of R+

[river fossil]

what you want is a subset such that if i pick any epsilon > 0, there exists an element in that subset that is smaller than that epsilon

[alpine sable]

[obsidian kayak]

right that's what confuses me

because epsilon can be .0000009

so i was thinking the empty set

as one example

[clever folio]

There's a pretty cheeky choice of S listed in the problem..

[obsidian kayak]

but then the empty set has no elemtns

so there would be no s

[river fossil]

well, there's no element in the empty set that is smaller than e =1

[clever folio]

You can also consider infinite sets in general.

[river fossil]

so you might try an infinite subset!

you can think about why no finite subset satisfy this condition later

[obsidian kayak]

ohhhh

[clever folio]

You can also try and construct a set that works from a finite set that doesn't.

[obsidian kayak]

so can i since all integers are part of all real numbers

can i just take the set of all postive integers

[clever folio]

No

I can pick e=0.5 again

[river fossil]

no positive integer is smaller than e = 0.5

[obsidian kayak]

fucking a

[river fossil]

lol

[obsidian kayak]

so e can just be any real number huh

[river fossil]

yes, bigger than 0

[obsidian kayak]

is 0 part of the empty set?

[river fossil]

here's a hint, do you know about sequences?

[river fossil]

it

s not

[obsidian kayak]

mhmm vaguely

[clever folio]

Try this use S={1}, I pick e=0.5, so you say "Damn! I'll pick instead S'={0,0.5}" then I pick e=0.25 and you do what?

[river fossil]

ooh, try doot's idea

[clever folio]

Is there a pattern here?

Try and follow this pattern..

[obsidian kayak]

mhmm okay but just one thing

S has to be all positive real numbers right

so it can't include 0

[alpine sable]

Yeah

[river fossil]

yes

[clever folio]

Well not all positive reals

Just a subset

[obsidian kayak]

right

[alpine sable]

But S' cannot contain 0

[clever folio]

Oh shit oops

Typo mb lol

[alpine sable]

Lol

[obsidian kayak]

so if you pick .25 i pick .25 then you pick .009 and i pick .009

and we gon forever and ever

[clever folio]

S'={1,0.5} is what I meant.

[alpine sable]

[obsidian kayak]

[alpine sable]

I'm thinking S is then R+ itself

That could work ig

[clever folio]

Yeah but 0.09 is ugly what if I pick something easier like e=1/8 instead lol?

Then 1/16

Then 1/32 and so on.

[clever folio]

This was the cheeky answer I mentioned lmao

[obsidian kayak]

ahhh

but wait

[clever folio]

But does fear see why?

[alpine sable]

Oh

[obsidian kayak]

i need three examples

that satisfies one

[river fossil]

try to construct more following doot's example

[obsidian kayak]

bet

[alpine sable]

xD

[river fossil]

so doot did
{1/1, 1/2, 1/4, 1/8, ...}

[obsidian kayak]

huh

i thought he did

0

so it can be less than 1

[alpine sable]

0 < 1/n ≤ 1 for any positive Integer n

[obsidian kayak]

right

[clever folio]

Positive integer n

[alpine sable]

Yes

Interger

[obsidian kayak]

okay i just put all real numbers for my first example

time to use the old noggin

[alpine sable]

Fear just focus one more time on doot's pattern

[clever folio]

All reals won't work

[alpine sable]

How so

[obsidian kayak]

wtf

[clever folio]

It has to do with props the q says S must satisfy.

[tacit arch]

Answer was given in #discussion

[obsidian kayak]

https://tenor.com/view/epic-meme-kermit-suicide-gif-20626092

[clever folio]

All reals is real close ur just mixing up the q

For ex -1 can't be in S according to the q.

[river fossil]

that's one example that we've also given

[alpine sable]

Yeah all positive real numbers will work

[alpine sable]

partial answer only, it was mostly to make sure you understood how what you were saying was wrong

Can I give one more example

[tacit arch]

I already said it like two times

[tacit arch]

Are you just here to gloat?

[obsidian kayak]

[obsidian kayak]

but R+ works right

all positive real numbers

[clever folio]

Yeh

You see why?

[obsidian kayak]

okay just making that clear

yeah because S can be a subset of R+

and all positive real numbers is a subset of itself

[river fossil]

nice

[obsidian kayak]

[clever folio]

Yeah, and if I pick epsilon>0 by density you can pick some real t between my epsilon and 0 too ofc.

Or just midpoints or whatever

There's multiple ways to pick t lol.

[obsidian kayak]

cool

i'll take a crack at the other 2 examples

following the pattern

[river fossil]

the key here is to have a subset that can contain arbitrarily small elements

[tacit arch]

There was nothing special about the right endpoint here

[obsidian kayak]

for the other example i pick, epsilon can still be any positive real number right? AKA .00009

[clever folio]

Yeah

[obsidian kayak]

okay so what about

the set of all irrational numbers

[alpine sable]

Fear what do you think about doot's example on S = {1/1, 1/2, 1/3,...}

[river fossil]

woah

good job

[clever folio]

Yeah that would work

[alpine sable]

Nice

[obsidian kayak]

[river fossil]

can you reason a little why that would work?

[clever folio]

But there are simpler ones feeds is trying to lead you to.

[obsidian kayak]

well

i was thinking about it before

but

i thought about

R+

and all irrationals

but when you said R+ worked

it made me think maybe irratoinals work

since we don't really know the smallest irrational

[clever folio]

Mmm so there's a property I mentioned earlier about R^+ that the irrationals have too.

[obsidian kayak]

right

b/a

[clever folio]

But try feeds's example it's good lol.

[obsidian kayak]

mhmmm i know this pattern

[obsidian kayak]

lemme see

[alpine sable]

What can you observe here

[obsidian kayak]

it's getting infinitely smaller

[alpine sable]

Hence you can take any epsilon, where there will always exist some element s ≤ epsilon

[clever folio]

Can you write it out as a sequence and take the limit?

[obsidian kayak]

ohhh shittt

mind blown

[alpine sable]

Fear do this

[clever folio]

U might see it better if u do

[obsidian kayak]

for the irrationals?

[clever folio]

Because really we're just doing that.

[clever folio]

No no for the other examples

We're just tossing sequences at you basically.

[obsidian kayak]

right

[obsidian kayak]

okay i see now

i was confused at first

i thought u meant small elemtns as in

a small number of elements

i see it's now the value of the elements themselves

to be small

[alpine sable]

You just like need at least one element in S, where if I say any epsilon, your set will always have some s where s≤€

[obsidian kayak]

right

and since the example 1/1, 1/2, 1/3 will get infinitely smaller

it will work

[alpine sable]

Yes

[obsidian kayak]

essentially i guess i'm a person that has to KNOW the values

so when it comes to stuff like this

where we don't know the smallest number

i suck at it

[alpine sable]

You'll get used to it gradually

[tacit arch]

Now you can give 1000 examples instead of 3

[obsidian kayak]

hehe

easy boys

[alpine sable]

[obsidian kayak]

alright then i'm gonna make the set of all irratoinals as my second one

and for the third i'll go with the 1/1,1/2

[tacit arch]

The bottleneck is your wrist endurance

[obsidian kayak]

is there a name for this sequence?

or can i jsut write it as {1/1,1/2....}

[tacit arch]

Harmonic

[clever folio]

So like here's one way to do what riemann said take arbitrary elements out if this to produce a new different example set.

[alpine sable]

S = {1/n : n is a positive integer}

[obsidian kayak]

beautiful

see fuck

[clever folio]

Here's another way. I divided 1 by 2 repeatedly here.

[obsidian kayak]

my brain can't work like that yet

so simple

[clever folio]

So pick a different integer larger than 2 instead.

[tacit arch]

Find the 3 answers that take the minimum amount of writing

[obsidian kayak]

right i should've thought of that

since it's greater than 0

any infinite fraction sequence

will satisfy it

[clever folio]

In this prob you really just want inf sequences that have all pos terms and converge to zero

[tacit arch]

The one in #discussion was $(0, \infty)$

[ocean seal]

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

[clever folio]

For ex 1/n! works too

[alpine sable]

R+
(R+)\{1}
(R+)\{2}

[obsidian kayak]

we didn't cover any infinite sequences yet so i was confused

but good to know

i'm getting a head start on this hw

[obsidian kayak]

is this actually legit?

[alpine sable]

Ye

[tacit arch]

Yes lol

[obsidian kayak]

smh

idk why i think the answer is harder than it is

i just got raped in linear algebra and diff eqs

[river fossil]

it's alright, our sequence approach is more enlightening

[slender gull]

There could be more than one answers.

[obsidian kayak]

yea you guys helped a lot

[slender gull]

So you can go for the harder or easier one.

[obsidian kayak]

thanks for real

[slender gull]

It's upto you lol.

[river fossil]

no problem

[alpine sable]

[river fossil]

[tacit arch]

$(0,1), (0,2), {x \in\R^+ \ | \ x\notin \Q}$

[ocean seal]

riemann

[obsidian kayak]

one more thing

for the {1}

[alpine sable]

Yes

[obsidian kayak]

does that mean it's just 1

wouldn't that make it equal to R+

[alpine sable]

It means you excluded {1} from R+

[obsidian kayak]

interesting

never seen that before

[alpine sable]

Like say in a Set S you have {1,2,3}
Then S\{1} is {2,3}

[obsidian kayak]

ohhhh

ohh wait

we did learn that

[alpine sable]

Exclusion

[obsidian kayak]

right

damn thanks boys

[alpine sable]

You can also write S - {1}, another notation

Welcome

[obsidian kayak]

appreciate it for real

i'll be back haha

[alpine sable]

xd

[obsidian kayak]

[lone heart]

@obsidian kayak Has your question been resolved?

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[opaque inlet]

How do I do question 5?

[vale wigeon]

write out all possible outcomes and the resulting totals in a table

[opaque inlet]

I didn’t know how to write it in table form, so I used tree diagrams

[vale wigeon]

ok sure you can do a tree diagram if you want

you're rolling two dice, and you ignore the second dice unless the first rolled 1 or 2

[opaque inlet]

Yes

[vale wigeon]

\begin{tabular}{c|cccccc}
&1&2&3&4&5&6\
\hline
1&2&3&4&5&6&7\
2&3&4&5&6&7&8\
3&3&3&3&3&3&3\
4&4&4&4&4&4&4\
5&5&5&5&5&5&5\
6&6&6&6&6&6&6
\end{tabular}

[ocean seal]

Ann

[opaque inlet]

Yes

[vale wigeon]

do you understand how i constructed this table?

[opaque inlet]

So 11/36

Yea

[vale wigeon]

11?

[opaque inlet]

We did something similar to this

[vale wigeon]

i count 13

13/36

[opaque inlet]

How’d u get 13

[vale wigeon]

wait, hold on. we were both wrong.

it's 19.

3 in the first row + 4 in the second + 6 in the fifth + 6 in the sixth

[opaque inlet]

Oh yea

Ok I understand

How do I do question 1

[vale wigeon]

how many ways are there to seat 5 people at a round table?

[opaque inlet]

24 ways

[vale wigeon]

and in how many of these ways are the people seated in order of age (cw or ccw)?

[opaque inlet]

That’s the part where I don’t know how to calculate it

[vale wigeon]

sounds like you're overthinking it

bc there's only two such arrangements

youngest to oldest cw and youngest to oldest ccw

that's it

[opaque inlet]

Oh

So 24 * 2?

48

[vale wigeon]

what is that number meant to be?

[opaque inlet]

How many ways 5 people can be seated around a round table, considering both clockwise and anticlockwise.

[vale wigeon]

then this not only makes no sense but also is not what the problem asks for.

[opaque inlet]

Yea Ur right it makes no sense

[opaque inlet]

What does ccw mean

[vale wigeon]

counterclockwise.

[lone heart]

@opaque inlet Has your question been resolved?

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[tribal oxide]

im getting the correct answer through lcm removal technique, but im not getting the correct answer through period reduction

[lone heart]

@tribal oxide Has your question been resolved?

[lone heart]

@tribal oxide Has your question been resolved?

[lone heart]

@tribal oxide Has your question been resolved?

[alpine sable]

I can't help you

Neither seems to anyone else

Rip

Sorry

[lone heart]

@tribal oxide Has your question been resolved?

[tribal oxide]

its alright i can wait

[arctic sail]

Hello, I'm not really comfortable in period reduction at all so I'm sorry if my help is futile.
However, it seems that if you make a linearization of the cos^4 term, the expression of f(x) is easier

Maybe that doing a period reduction is easier with this ? I hope it is x)

[tribal oxide]

what is linearization of cos^4

but what ur doing here in the end is, what in my class the teacher calls it "avoiding lcm technique", manipulating f(x), so the fundamental period can be easily found, as taking lcm is where the problems between period and fundamental period comes

[tribal oxide]

which i have also done in this, maybe not with the linearization of cos^4 term, but in a different way

as idk what linearization means

[arctic sail]

English is not my native language so I'm sorry if the explanation is messy. The thing is you express a cos^4 term with a sum of cos^1 terms and a constant.
It's the same process that gives the formula cos^2(x) = (1/2)(1+cos(2x)).

Here I just did it with a higher power. You can obtain these expressions using this formula:

[tribal oxide]

but in class, we were taught a different technique where say P is the period of of a function, like say f(x)= sinx + cosx, then the individual periods are 2pi, 2pi, we take lcm (2pi,2pi), which is 2pi, and then we divide this P by every prime number and check if any of those work as the period, and if something matches, then that becomes the new P and we divide it by every prime number and so on, its usually only helpful if theres options in the questions, or if the conditions in question, which make elimination easy,

[tribal oxide]

is i = sq root of -1?

ive never seen this formula before💀

[arctic sail]

I see, I'm sorry that I can't help you more, I just saw that the expression could be simplified and I thought it could maybe help...

[arctic sail]

Yes it is, there are actually two formulas, called Euler's formulas that are deduced by the relation e^ix = cos(x)+isin(x)

[tribal oxide]

basically i want to prove f(x+ 2(pi)^3)= f(x)

[tribal oxide]

it does help, your technique gives the correct ans

[tribal oxide]

I tried to find out cos^4(x)

Im getting this

Now i have to replace x?💀, Or maybe this can be simplified further

[arctic sail]

That's it, and then you need to make another use of the formula to get this result:

It's really useful because you can get formulas like that for any cos^n with n a positive integer

[tribal oxide]

i understsnd your process now

[tribal oxide]

but can you help with this

while using the original form of f(x)

[arctic sail]

Yes I get it now, it's easy with the expression I got, I'm searching for the original form of f(x)

[arctic sail]

Alright, so first thing: I see that you tried to break fractions within the cos^4 the cos terms into sums of 3 other terms. Because you want to prove f(x+2(pi)^3) = f(x), I would advice you to break the fractions like that:

Here I wrote it for the cos^4 term, you'd need to do the same thing with the other cos term

And then, using angle addition formulas, I think that you'll be able to find back f(x)

[tribal oxide]

i just noticed

once we broke away the pi/2 term

we cant join it back anymore?💀

because the lcm of 4(pi)^2 and 2 doesnt exist...?

but then again i am assuming that

2pi^2 is irrational

but im not very sure abt that claim

[arctic sail]

You can multiply numerator and denominator by 2(pi)^2 and join it back can't you ?

[tribal oxide]

right.., im probably thinking too much

basing things of a childhood concept, so im not very sure

ill look into it, once i finish my current workload, thanks for your help tho

.close

[lone heart]

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[arctic sail]

Np, don't hesitate to reopen if you need more help

[lone heart]

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[alpine sable]

This is the graph of c part .I don't know how this was done

It is a unit impulse signal btw i.e δ[n] = 1 for n = 0 and 0 for every other n

[tacit arch]

Do you know how to find n such that n-4k=0?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[gaunt eagle]

Can anyone see what I'm doing wrong here?

[languid bolt]

,rotate

[viral cairn]

Hard for me to read but trig sub if thats what your doing your good

[lone heart]

@gaunt eagle Has your question been resolved?

[tacit arch]

,w integral (x+1)/sqrt(1-x^2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

Your integral of 1/(1-u)^(1/2) should just be solved with power rule

[gaunt eagle]

but you could technically also use a trig integral to solve it, right?

by using u^1/2

[tacit arch]

No

[gaunt eagle]

why not?

[tacit arch]

Differentiate it and find out

[gaunt eagle]

I think I got it

its because the derivative of sqrt(u) isnt 1

in arcsin(sqrt(u)/1

[lone heart]

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[cyan mountain]

What did I do wrong?

[gray isle]

you randomly used the point(3,2) for some strange reason

[cyan mountain]

Oh my gosh

I was looking another example 😹

No wonder

Ty

.close

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[thick lynx]

Factor $-a^2b^2 + 2ab^3 - b^4 + a^2c^2 - 2abc^2 + b^2c^2$

[ocean seal]

Kepe

Kepe

[thick lynx]

But I don't really see what I can do after that
Hints only please.

[mortal trellis]

write it like $(-a^2b^2 + 2ab^3 - b^4) + (a^2c^2 - 2abc^2 + b^2c^2)$. can you factor something out of the first and second term to get something nice for each one?

[ocean seal]

Denascite

[lone heart]

@thick lynx Has your question been resolved?

[thick lynx]

Hmm

[thick lynx]

b^2 for the first one, c^2 for the second one

But it still wont be very nice?

[mortal trellis]

and then what are you left with?

maybe factor out -b^2 out of the first one

[thick lynx]

$$-b^2 * (a^2 - 2ab + b^2) + c^2 * (a^2 - 2ab + b^2)$$

[ocean seal]

Kepe

[mortal trellis]

those terms should scream "I am nice" into your face

[thick lynx]

oh

$$-b^2 * (a - b)^2 + c^2 * (a - b)^2$$

[ocean seal]

Kepe

[mortal trellis]

also they are the same which is extra nice

[thick lynx]

so it's
$$(a - b)^2 * (c^2 - b^2)$$

[ocean seal]

Kepe

[mortal trellis]

yup

[thick lynx]

thx!

.close

[lone heart]

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[hollow fossil]

pls help

[slender gull]

L'hopital's rule.

Just use that.

[north adder]

@hollow fossil

[lone heart]

@hollow fossil Has your question been resolved?

[hollow fossil]

i dare you to try it. its insanely complex

[slender gull]

Definitely is, but still doable.

Just with the rule you can compute the limit.

Now you have to brute force it, that is a different story.

I didn't look into other ways.

But just with the rule I did get th answer and then left.

So yeah unless this is preparation for some exam which requires you to solve this in very less time use the rule.

Or if you simply want something else, people will of course help you.

[rotund plank]

I have absolutely no idea how you’d go about this without l’hôp

Do you have any kind of indications from a teacher or something?

If not I’d just hold my breath and use l’hôp

[fallen verge]

Lhop is le hope here i think

[carmine shuttle]

@hollow fossil I have done it for you. You only need to apply L'Hospital Rule 2 times.

(but before posting my answer, please submit your answer here first)

[hollow fossil]

i got it guys

[hollow fossil]

here it is :)

[carmine shuttle]

great!

[hollow fossil]

nice :)

woah which app do you use to get it like that?

in a digital form

[carmine shuttle]

Microsoft word

[hollow fossil]

ahh

[carmine shuttle]

"Alt" + "=" for equation func.

You can also use LaTeX for mathematical notation, but I usually use MS word to sketch my work since it is faster for me to write something.

[hollow fossil]

i see. its been so long since ive used word haha

anyways thanks for the help guys :)

[carmine shuttle]

My pleasure!

[hollow fossil]

ill sleep its late night for me. thanks again and bye :)

.close

[lone heart]

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[lone heart]

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[tepid drum]

Hi

[tepid drum]

What's the meaning of the notation x belongs <3;6>

Does this mean that both 3 and 6 are have opened boundaries

[worn fox]

Send context

[tepid drum]

So both 3 and 6 are excluded from the interval ?

https://media.discordapp.net/attachments/990290695359188993/990322872163643464/935748580768092210.png

Does this mean that 3 and 6 are excluded from the interval in which x lies in

[worn fox]

Where is this from? Doesn't look like standard notation

[karmic rapids]

I'd read it as $x \in ]3, 6[$

[ocean seal]

illuminator3

[tepid drum]

Idk someone sent me this exercise and needs help but it's the first time i see this notation

[tepid drum]

I read it like that

I'll read it this way

Not [3;6]

Thank you so much for your info

[karmic rapids]

it looks like "x is smaller than 3 or bigger than 6"

[dense sleet]

Nah i learned similar notation

Its just closed interval

[slender gull]

No it's open interval

] is used for (

In some places.

]3,6[ means (3,6)

Or so I've been told.

[vale wigeon]

the french use outward-pointing square brackets for open intervals yes

[dense sleet]

<> is closed interval at leasz in notation i was taught

[vale wigeon]

this notation varies by region

[slender gull]

It does. And yes I was talking about French notation.

[tepid drum]

So is <> closed or opened

[tepid drum]

Yea ik this

[tepid drum]

I am just talking abt this bc the one who asked the question had the interval in this form so I want to know what to answer him

[vale wigeon]

best see your textbook about that

[dense sleet]

Id say closed

[tepid drum]

Which textbook

It's not my question

Someone sent me a pic of the question

[dense sleet]

Same country?

[tepid drum]

No

I knew him today in this server

[dense sleet]

What country is he from?

[vale wigeon]

oh so it's actually a game of broken telephone...

[tepid drum]

Idk in fact

I Didn't ask him

[vale wigeon]

i've seen angle-brackets used as closed, and also used as open, and also used as intentionally ambiguous

so we really cannot tell

this is NOT a math issue

this is a language issue

[tepid drum]

XDDD

[vale wigeon]

now

is there an actual math question at hand here

or just this

[tepid drum]

No it's just the inequality I sent

It's easy but I wanted to know the notation just

I want to be sire of something small here

[high rapids]

I thought language of math was universal

[vale wigeon]

notation varies by region.

[dense sleet]

Some countries dont even use base 10 numbers

[high rapids]

Fr?

[dense sleet]

Idk if they learn base 10 in school or do math in other bases

[tepid drum]

XDDD

anyways tysm for ur answers

I gtg now cya do I close before I go

[high rapids]

Preferably yes

[tepid drum]

Ok

.close

[lone heart]

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[sullen dock]

stuck in c

[lone heart]

@sullen dock Has your question been resolved?

[alpine sable]

You can calculate the lowest possible value of LHS to be 4 using parts a) and b)

[sullen dock]

a guy just gave me the method in a WhatsApp group well ty anyways

!close

.close

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[hot bison]

is the answer to this x^2 + 16x + 64

[hot bison]

or x^2 + 64

[coarse hemlock]

yes

[hot bison]

thankyou

.close

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[coarse hemlock]

@hot bison i meant the first 1

[hot bison]

ok

[coarse hemlock]

x^2+16x+64

[hot bison]

ok