help-41

[junior kelp]

Where did the (-2z-4) go?

<@&286206848099549185>

!help

[amber wasp]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

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[exotic olive]

so im doing Part a for this question and this is all i have so far

[exotic olive]

just had a question

will be using the finite geometric series formula here

like this one?

<@&286206848099549185>

[vale moon]

Yeah you have $\sum_{i = 0}^{n} a \cdot r^i = a \frac{1 - r^n}{1-r}$

[grizzled pagoda]

Vaizex

[exotic olive]

okay i just did it does this look good

[vale moon]

Ya

Are you typing this on notepad lol

[amber wasp]

@exotic olive Has your question been resolved?

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[bright hare]

pls help

g(x) = 3 / x - 2

what im doing is

x = 3 / x - 2

then i bring x - 2 to the LFH

but im kind of stuck

[low crypt]

have you tried converting it to quadratic form

ax^2 + bx + c

= 0

[bright hare]

hmm

i c

[prisma ember]

how do you bring x-2 to the left side?

[bright hare]

subject of oformula?

[low crypt]

multiplying both sides by (x-2)

[bright hare]

ill try with quadtric tq

[prisma ember]

i was hoping OP would say that

[low crypt]

oh

well he already said he did

mb

[bright hare]

here

im getting +- x^2 - 2x + 3 = 0

[low crypt]

where did the +- come from

you only have to use that if you do square root btw

[bright hare]

wait nvm

i was gonna square root it

b4 i do quadtric

so thats why

[low crypt]

oh

[bright hare]

when im bring the 3 over

it become negative

right s

x^2 - 2x - 3 = 0

that?

[low crypt]

looks right

[bright hare]

ok just gotta use quadtric formula?

[low crypt]

now you can solve that pretty easily

[low crypt]

try factoring before

[bright hare]

alr just use the trinomials?

[low crypt]

just try factoring the expression x^2 - 2x - 3

[bright hare]

(x-3) (x+1)

that right?

[low crypt]

indeed it is

now you're able to solve the equation

[bright hare]

i see but its saying that

-1 and 3

should be right

where did i do it wrong

[low crypt]

try plug in -1 and 3 into this

you get zero right

[bright hare]

yeah

og bru

im so stupid

i get it

[low crypt]

ur answer was right 👍

[bright hare]

alr thank you uve been a big help

ill close it later

.close

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[bright hare]

aint getting nowhere

im thinking i wanna find x first

like

y+4/7 = x

[low crypt]

have you found the inverse of y = 7x - 4?

[hollow cape]

if i'm thinking about it correctly you don't need to find the inverse function at all

[low crypt]

wait you are

[bright hare]

so what is it

[bright hare]

so how should i do it

[low crypt]

think about the fundamental concept of an inverse function

[bright hare]

if i inverse it its just gonna be well inverse

[low crypt]

what switches?

[bright hare]

y and x

[low crypt]

yes

[bright hare]

so i swithc it first?

oh wait

i think i might ve get t=it

if i switch it an change it to inverse

i might be able to find the answer?

[low crypt]

well there is an easier way

[pseudo tusk]

Flipping x and y gets you an inverse function. So y=7x-4 become x=7y-4 so a function of y would be y=x/7+4/7 or (x+4)7

[bright hare]

i got 10

which is right

[pseudo tusk]

Yup

[low crypt]

yep

[hollow cape]

you didnt have to do all that work tho

[bright hare]

but whats the easier way

[bright hare]

yeah it too kme a couple seconds

but if theres a better way

happyto learn

[hollow cape]

so for a function you know that there's a domain and a codomain right?

[bright hare]

yeah

[hollow cape]

so is h in the domain or the codomain

[low crypt]

if inverse is equal to 2, that means that it is the value where x = 2 for the normal function

(since it is where y = 2 for the inverse)

(also im sorry i interrupted above)

[bright hare]

h is the domain

right

[hollow cape]

you were right the first time

[bright hare]

ho can h be the codomain

then wouldnt that be he output

2 should be the codomain right

[hollow cape]

because g is the inverse function

the inverse function pulls from the codomain and outputs an element in the domain

[bright hare]

so it basiclaly swithces?

[hollow cape]

yep

so if we know that h is in our codomain, where does that put 2?

[bright hare]

domain?

[hollow cape]

exactly

so now think about what that's saying

we have an element in the domain

[bright hare]

ohhh

[hollow cape]

we want to find a corresponding element in the codomain

[bright hare]

u can just solve it

using the formula

[hollow cape]

just plug in 2 to g(x) and you should get the right ansewr

[bright hare]

i see

iget it

but

i still dont understand

how can h be the codomain

its inside gx

[hollow cape]

pay attention. it is inside of g^-1(x), not g(x)

[bright hare]

alr i get it thank you

.close

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[simple drum]

Prove:
Let $a_n$ be a positive sequence, such that $\lim_{x\to\infty} a_n =0$ therefore $\lim_{x\to\infty} 1/a_n =\infty$

[grizzled pagoda]

prograce

[simple drum]

Can I get a hint?
I'm trying to prove by using this: if a sequence is unbounded and montonely increasing then it diverges(?) to infinity

First I tried to prove that it's unbounded using the definition of bounded but I'm stuck

[grand epoch]

bit confused on what the question is, "unbounded and monotonely increasing" seems to be at odds with lim x-> inf a_n = 0

[simple drum]

I have to prove the $1/a_n$ diverges to infinity not $a_n$

[grizzled pagoda]

prograce

[grand epoch]

well you already said 1/a_n -> inf here

[simple drum]

Yes but I have to prove that

[grand epoch]

if you are given lim a_n x->inf = 0, it just follows directly from that

[simple drum]

Yes, intuitively, but this questions asks me to prove that this is correct using theorems and such

[grand epoch]

using this:

you can argue something along the lines of: assume there's a least upper bound N, then come up with a value of n such that a_n > N. that shows there's no least upper bound

n = N + 1 works

or wait

=\

with delta epsilon since lim a_n approaches 0, there must be some P s.t. for every n > P, a_n < 1/N
with that you'd have 1/a_n > N

[simple drum]

Ohhh right

This what I did:
Assume wrongly that $1/a_n$ is bounded from above therefore there exists M such that $|1/a_n| \leqq M
But we know that $\lim_{n\to\infty} a_n=0$ therefore by definition, choose \epsilon = 1/M such that there must be an N such that for every n>N, $|a_n| < \epsilon = 1/N$ therefore $1/a_n > M$
In conlusion 1/a is unbounded from above

[grizzled pagoda]

prograce

This what I did:
Assume wrongly that $1/a_n$ is bounded from above therefore there exists M such that $|1/a_n| \leqq M
But we know that $\lim_{n\to\infty} a_n=0$ therefore by definition, choose \epsilon = 1/M such that there must be an N such that for every n>N, $|a_n| < \epsilon = 1/N$ therefore $1/a_n > M$
In conlusion 1/a is unbounded from above
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.51 But we know that $\lim
                           _{n\to\infty} a_n=0$ therefore by definition, cho...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```

[simple drum]

prograce

This what I did:
Assume wrongly that $1/a_n$ is bounded from above therefore there exists M such that $|1/a_n| \leqq M
But we know that $\lim_{n\to\infty} a_n=0$ therefore by definition, choose \epsilon = 1/M such that there must be an N such that for every n>N, $|a_n| < \epsilon = 1/N$ therefore $1/a_n > M$
In conlusion 1/a is unbounded from above
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.51 But we know that $lim_{n\to\infty} a_n=0$ therefore by definition, cho...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```

[grizzled pagoda]

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

[grand epoch]

yes, exactly, I would just clarify in the 2nd to last sentence: therefore 1/a_n > M ** for n > N**

[simple drum]

Ok

[grand epoch]

but that's it 👍

[simple drum]

Haha now I prove it is increasing

[grand epoch]

that should be easier

[simple drum]

Wait

[simple drum]

Why switch the < sign here wheb you do 1/a_n
Shouldn't it still be 1/a_n<N

Then whay I did is not right

[grand epoch]

because when you take reciprocals of an inequality, if both signs are positive, you flip the sign

thats just algebra

think about it a bit \ come up with some simple examples in your head

2 < 5 => 1/2 > 1/5 etc.

[simple drum]

Ahh yes yes

[grand epoch]

so to prove 2nd part

you know a_{n+1} < a_n

now...just take reciprocals.. : )

[simple drum]

Okay! Will do the same by assuming it is decreasing then reach that it's wrong by doing ^

[grand epoch]

?

$a_{n+1}<a_n$

[simple drum]

Like before, I assumed it's bounded and reached contradiction

[grizzled pagoda]

from math import sqrt

[grand epoch]

this is just a simple inequality, no concepts of boundedness, decreasing etc. is happening here

just take reciprocals of both sides, what do you get

[simple drum]

Yes 1/a_n+1 > 1/a_n

But I have to use theroems lol

[grand epoch]

i mean that inequality holds for all n

so every successive term of your 2nd sequence is larger than the last

[simple drum]

Yws I agree

[grand epoch]

so you've just literally shown the definition of an increasing sequence

that's it

[simple drum]

Okay

Thanks

.close

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[hasty verge]

hi, i am from india, i want to clear ISI exam for doing BSC in it. but i have lot of chapters backlog in maths, should i drop 1 year and then persue for its exam or should i continue my BSC with a normal college and cover my backlog parallely to clear the ISI exam.

[alpine flower]

It would be better if you ask this question in any indian discord server

[hazy roost]

This server is dedicated for math problems

[hasty verge]

i don't where i can find indian server, can you guide me

[split sail]

Quora

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[covert glade]

I'm struggling to start this problem and the next. This is one of the questions I didn't do on my 3rd exam (I'm reviewing for finals).

[covert glade]

I'm not exactly sure what I'm supposed to graph. The integrand? If so, why?

[spiral zealot]

yes, you're supposed to graph the integrand

do you know what definite integrals represent

[covert glade]

A definite integral is the area under a graph between the limits of integration.

[spiral zealot]

yes

so graphing the integrand,
you can eval the definite integral by calculating the area

[covert glade]

Yeah, I'm not sure why I overthought that, tbh.

Thanks lol

.close

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[amber wasp]

Please don't occupy multiple help channels.

[slender flame]

help

[lean ermine]

!status

[amber wasp]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@slender flame Has your question been resolved?

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@slender flame Has your question been resolved?

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[echo parrot]

hi guys,

[split sail]

Hi

[echo parrot]

i know that

the limit of that

is 0 right

but

the question says theres an oblique asymptote

how do i

calculate it ?

hello ?

[radiant lynx]

If you plug the f into the limit you get $-x+\frac{ln x}{2x}$

[grizzled pagoda]

LooseEthics

[radiant lynx]

That goes to -infinity

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[amber wasp]

@split sail Has your question been resolved?

[whole lion]

Is that u in ur pfp

[high dawn]

the formula is the right one, but not the execution

[split sail]

Whats the right way I should use?

[high dawn]

,w 640* 0.97^10

[grizzled pagoda]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by clonesolopros

[split sail]

Does that mean its B then?

Ohhhhh

I see where I went wrong

Thanks

.close

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[round dune]

Does anyone know what I did wrong here in the numpy code?

[round dune]

That's the error I get, I'm trying to solve the mass function of a binary star system, to the mass of star 2

[pallid canopy]

sir this is a math server

try #computing-software

or find a python server

[round dune]

Sorry my bad didn't know #computing-software existed here, I mean technically this is apart of my calculus 1 / Practical Physics courses 😅

.end

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[untold tinsel]

can someone help me out on this one?

[amber wasp]

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[glad tiger]

okay wait i accidentally clicked yes

[glad tiger]

one sec ill resend

[shrewd elm]

can try .reopen

[glad tiger]

not sure what to do here

specifically the middle term

wait do I even need to multiply by x/x

wait is this literally just 4

the e^4x term

[swift plover]

Why not use l'Hopital

[glad tiger]

again?

[swift plover]

For the last limit

[glad tiger]

ok

[swift plover]

The denominator would nicely simplify to 1 me thinks

[glad tiger]

on this one?

[swift plover]

Easiest way probably yes

It's in indeterminate form 0/0 so we are allowed to

[glad tiger]

16

[swift plover]

Really

I did it in my head I got 12

Oh nvm

You're right

-1 is indeed a constant haha

[glad tiger]

LOL youre good

wait so im allowed to do lhopital, then trig manipulation, then lhopital again?

[swift plover]

I mean it's all just manipulation

Essentially you're just making it easier for yourself to evaluate

Actually you could just have done l'Hopital repetitively from the start

[glad tiger]

i see

oh i could have?

see im stupid

lmao

[swift plover]

Lol it's okay, maths is best learned the hard way

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@glad tiger Has your question been resolved?

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[nova lion]

Why does the negative sign disappear when the top gets simplified to the bottom? Shouldn't it still be sqrt(30)/-2

[indigo cloud]

suspicious crop

[snow blade]

Is this just me

I can’t see

The pic

[indigo cloud]

did they leave out the minus or did they just move it to the front

[nova lion]

might be my internet sorry and uhm

is this better?

[indigo cloud]

its already plus and minus

flipping that to minus and plus makes no difference

either way you are doing both

[nova lion]

well yeah but it's 1 +- a negative number versus a postive, no?

[indigo cloud]

not like it makes a difference

[nova lion]

wait let me verify but you're prob right

[indigo cloud]

1+-5 is 6 and -4

1+- (-5) is also 6 and -4

[nova lion]

yeah you're right, I feel dumb but thanks 😭

.close

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[hearty sleet]

do you not just sub in x^n / n!

[hearty sleet]

for e^x

[formal harbor]

sure, and then simplify the series

[hearty sleet]

but i somehow ended up at

for sinh

[shadow stump]

yes

[formal harbor]

yeah so you gotta show that that's the same as what they put

[hearty sleet]

am i just shit at algebra

hold on

[shadow stump]

consider what that series looks like for even and odd n respectively

[hearty sleet]

oohhh

even n = 0

right

ahhh icic

thx lol

.close

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[exotic olive]

am i right with B here?

[signal furnace]

,w range of x^2+2x-5+(-2x+4)

[grizzled pagoda]

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Requested by civil_service_pigeon

[exotic olive]

THANK YOUUU

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[exotic olive]

am i right with C here?

[cosmic pilot]

It equals 6/^

[exotic olive]

wait wdym?

[hard monolith]

@exotic olive What have you tried?

[amber wasp]

@exotic olive Has your question been resolved?

[exotic olive]

C and it was the best option

i just wanted to confirm it was correct

<@&286206848099549185>

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[midnight sleet]

When using the 3rd degree taylor polynomial, do I plug in 4.2 or 5.2?

[shadow stump]

you should plug in whatever value of $x$ is appropriate to have [ \sqrt{x-1} = \sqrt{4.2} ]

[grizzled pagoda]

cloud

[midnight sleet]

so 5.2?

[shadow stump]

yes

[midnight sleet]

tyty

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[exotic olive]

am i right with D here?

[exotic olive]

OHH WAIT ITS B

it has to be

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[hollow reef]

Use the formula in this example to determine the sample size, n.

The estimated prevalence is 18%, and the desired confidence level is 94% with a margin of error of 4%. (Round your answer to the nearest integer.)

N =

i got no clue and its due at 12 😭

[compact yarrow]

it tells you what formula to use, and the formula tells you what the variables are

what's giving you issue?

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[clear finch]

pls help I feel like I am banging my head against a wall

[hollow cape]

what have you tried

[clear finch]

i tried finding the equation in terms of x

and then doing 2pi(integral from 10 to 12 (f(x)sqrt(1+f'(x)^2))dx

[cursive spoke]

Integration

[cursive spoke]

Eh around the y means the limits should be x , question wrong?

[hollow cape]

could you put this in mathematical notation? struggling to parce it rn

[fading cradle]

No, he just has to evaluate the x-coordinates

[cursive spoke]

Hm? Can you explain?

[fading cradle]

When y=10, x=8

When y=12, x=64

[cursive spoke]

That's not how it works

[fading cradle]

Is it not

[cursive spoke]

Y = 10 is a line

You can't just put that in the equation and get a x axis line

[fading cradle]

???

[hollow cape]

that's not what's happening...

[fading cradle]

I am a lil rusty on volume integration

Can we wait for a more intelligent being to show up

[cursive spoke]

The limits are given to indicate the lines between which we gonna measure the area

[clear finch]

not volume

[clear finch]

surface area

[fading cradle]

Oh shoot surface area

Mbmb

[clear finch]

np

[fading cradle]

I wasn't paying attention 😭

[hollow cape]

could you write out what you originally said and take a pic or something? or write it in latex? so i can read it better?

[cursive spoke]

? That's what he said tho

[fading cradle]

I am very rusty on SA calculations

[hollow cape]

he was talking about bounds of integration not lines in the coordinate plane

[cursive spoke]

The bounds of integration are lines in geometric visualization

[fading cradle]

He would need ds/dy or ds/dx right

[hollow cape]

but you can change the bounds of integration

to different variables as appropriate

oh wait i see what you're saying

ignore

[cursive spoke]

Probably op made a mistake or there is something we don't know

[cursive spoke]

Yeah but about the y axis

[clear finch]

idk if that works

[cursive spoke]

So the integration should be in terms of x

With limits in terms of x axis lines

[clear finch]

oh

[clear finch]

so When y=10, x=8
when y=12, x=64 like that guy said?

[cursive spoke]

It shouldn't be tbh

I don't think it will be

[cursive spoke]

The question is proper?

[clear finch]

wdym proper?

[cursive spoke]

Like question is correct?

And it got a answer key?

[clear finch]

oh yeah

[clear finch]

isnt that what you mean?

x is actually y in that equation

[cursive spoke]

??

[hollow cape]

tbh i'd just restart the problem i think the fundamentals are wrong

[clear finch]

so, should I get the limits in terms of x or the equation in terms of y first?

or niether

[hollow cape]

i'd look back on your notes. what is the formula for rotating around the y axis?

[clear finch]

for surface area of rotational solid its this

[hollow cape]

correct. so why do you need to solve for x in terms of y?

it tells us we want y in terms of x

[clear finch]

so then we want the limits in terms of x?

[hollow cape]

yes

[clear finch]

Is it like this then?

oh i forgot dx

[craggy sundial]

I think what you did there is the right one

[craggy sundial]

bc here, f(x) is supposed to represent the radius right?

[hollow cape]

we're rotating around the y axis so we need it to be in terms of x

[craggy sundial]

the radius will be x, so we need x=f(y)

[hollow cape]

when rotating around the y axis we need everything in terms of x

[clear finch]

so im on the right track now then

[hollow cape]

looks like you're on the right track just doing it myself to confirm we match 🙂

[craggy sundial]

we want the bottom integral
so ds in in terms of dy there

like here's a visualization

so x=h(y)

[hollow cape]

reading more it looks like we'll need a combination of our methods

we want the first part to be in terms of x but the second part to be in terms of y

[craggy sundial]

see example 2 in that site

[hollow cape]

apparently i'm too tired to do math rn LMFAO

[craggy sundial]

oh wait, so I'm wrong then

[hollow cape]

LMFAO

neitther of us can figure out who's right

[craggy sundial]

wait, lemme read it

[hollow cape]

i think you're right with example 2 solution 2

[craggy sundial]

yea, I think so
but what's solution 1

[clear finch]

so like that?

[craggy sundial]

oh, you can use either one
we're both right

[hollow cape]

we killed it

[craggy sundial]

so either make it in terms of x and the bounds be in x
or make it in terms of y and make the bounds be in y

[clear finch]

so this works?

[craggy sundial]

for that method, it should just be x outside the root
so x sqrt(1+(f'(x))^2)

[clear finch]

oh

grrrr

[craggy sundial]

what's the integrand that you're working with?

[craggy sundial]

just realized that your dy/dx is also wrong

[clear finch]

oh

well thats probably my problem then

I was wondering why I was so close to the answer

oooooooooooh

[clear finch]

ok thanks so much

[clear finch]

and thank you too!

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[clear finch]

ok, so what did i do wrong here?

[shadow stump]

to be honest it seems like it would be easier to do an integral with respect to x here

[clear finch]

but I thought it had to be with respect to y since it's being rotated around the x-axis

[shadow stump]

you can do it for either

[clear finch]

oh ok ill try that then

[honest dagger]

Basically chain rule

If $y=f(x)$, then $\int g(y)\dd y=\int g(f(x))\frac{\dd y}{\dd x}\dd x$

[grizzled pagoda]

SWR

[honest dagger]

(I hope I did that right)

[clear finch]

oh

ok thanks guys

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[slim briar]

think 4 points on a complex plane a b c d, lines ab and cd are paralel to eachother if they ensure
(a - b)(\bar{c} - \bar{d}) = (\bar{a} - \bar{b})(c - d)
how can we show that

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@slim briar Has your question been resolved?

[slim briar]

<@&286206848099549185>

[formal yacht]

What have you tried so far?

[slim briar]

firstly i can do that for line start from the origin

because i assume that they are all on the same line

but i wonder how is it going if for example ab line passes the x=5

[formal yacht]

One way to go about this is to express these lines using a real parameter, say t in the reals

Are you aware of how to express a line in the complex plane using a parameter?

[slim briar]

not at all i only know the point^s line equation z(alpha_bar)+zbar(alpha)=beta

also my instructer has said that you do not have to use line equation

[formal yacht]

If you’re comfortable with learning how to express a line using a parameter, this result will sort of fall out

I can go through the process of showing u how to express a line using a parameter

If you’ve ever had linear algebra, this is basically just the same idea

[slim briar]

determinant from linear algebra solves this with relation between determinant and area i think

now i am sending my solution

i hope it will have uploaded my connection is so bad

mathematically it is the solution i think but i can not imagine on complex plane

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[split sail]

Can someone tell me how I can write an equation regarding this?

Bc idk how

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@split sail Has your question been resolved?

[tight horizon]

let the number of books read by reece be y and the number of weeks passed by is x

now we know reece has read 3 books already and reads one more every week

so we can write the equation for number of books read as y=3+x

if 1 week has passed then y=3+1=4 books

similarly for nicole the equation is y=1+2x

since she reads 2 books per week

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[minor grove]

How many triplets (x, y, z) (natural numbers) verify the equation:

[minor grove]

It's not like this is hard, but I think it's maybe a combinatorics approach I'm not seeing well

I assume by natural numbers they also mean 0

[cunning birch]

so it includes 0

[minor grove]

Yep

[cunning birch]

have you seen stars and bars?

[minor grove]

Stars and bars...I'm afraid no

All I know is permutations, arrangements and combinations as we call them in romanian

As far as I can see it on google, it kind of makes sense what it is, I also thought of breaking it down to (10, 0, 0), (9, 1, 0)

Wait, so basically a sum of possibilities

[cunning birch]

sum of possibilities is tedious

when you can have an easy formula

ok, suppose x,y,z had to be positive integers

so > 0

[minor grove]

Yes, I just edited it

They are natural

[cunning birch]

natural in the >= 0 sense?

right now I'm supposing > 0 just to show you an example

[minor grove]

Oh, I see

[cunning birch]

so

think of x y z as bags

and you have to fill those bags with 10 undistinguishable elements

[minor grove]

Yes

[cunning birch]

to do that

the 10 undistinguishable elements can be placed from left to right

and we have to place 2 "bars"

to delimit:

on the left of the first bar: the elements that go to x

in between the bars: the elements that go to y

and on the right: those that go to z

[minor grove]

Sure, makes sense

[cunning birch]

so

if we need every bag to have at least 1 element

since the elements look like this:

- - - - - - - - - -

oops

[minor grove]

Yeah, discord is shit at this

[cunning birch]

something like that

[minor grove]

Okay so I have elements

[cunning birch]

yep

[minor grove]

That look like sticks

[cunning birch]

and we have to place 2 bars

to delimit the number of elements x,y and z get

for example we may do

- - - | - - - | - - - -

meaning x has 3 elements, y has 3, z has 4

[minor grove]

Yup

[cunning birch]

but we can't do
| - - - - | - - - - - -

as we need for now every bag to have at least 1 element

[minor grove]

So what is asking me is in how many ways we can place two bars between 10 elements without them on the edge

[cunning birch]

that's kinda it

so if you have 10 elements

how many in betweens are there

[minor grove]

9

[cunning birch]

how many spots can the bars be placed onto

yep

[minor grove]

9*8?

[cunning birch]

not exactly

the bars are undistinguishable too

[minor grove]

Well I thought if I were to overlap bars then y would be 0

[cunning birch]

yes you can't overlap bars

but also

when you do 9 * 8

you're basically saying "9 spots possible for the first bar and 8 spots possible for the second bar"

[minor grove]

Yes, that

[cunning birch]

but the bars are undistinguishable

[minor grove]

Ohhh

[cunning birch]

had I switched the order in which I place the bars

[minor grove]

So it's 298?

[cunning birch]

nothing changes

[minor grove]

2 times 9 times 8

[cunning birch]

2 times?

[minor grove]

Well since the bars are undistinguishable

[cunning birch]

this is computation done when the bars are distinguishable

but the bars are undistinguishable

so when you count 9 * 8

any configuration 'bar 1 bar 2'

is counted twice

because "bar 2 bar 1" is also there

[minor grove]

Yes, that's why I said 2 times

2(9)(8)

[cunning birch]

so when you do 9 * 8, you overcount

[minor grove]

Wait

Ohhhh

Yeah you are right

[cunning birch]

so

what's the correct number of ways

[minor grove]

Alright, I think it's 9*8/2?

[cunning birch]

yes

[minor grove]

Since it'd remove half

[cunning birch]

aka 9C2

[minor grove]

Which is implicitly yea

9C2

That's how to note it online? Always had issues with that

9!/7!2!

Which is 36

Coming back to our problems, now that we know they can overlap and they can be on edges

[cunning birch]

so

there's a way to go around that

but remember

if you have n elements (indistinguishable) to distribute into k bags

and give at least 1 to each back

we have (n-1)C(k-1) possibilities

so now

going back to x+y+z = 10 with x,y,z natural integers

(so >= 0)

what happens when you view this instead as (x+1)+(y+1)+(z+1) = 13?

[minor grove]

Then I can't do the edges nor overlap as previously?

Because now we have a condition of existence

That suggests that x+1 will always be higher than 0

Given that x is a natural number

So, 13C2

?

13*12/2 issss...78

Wait

You literally just told me above

Oh wait no

[cunning birch]

x+1 > 0 yes

[cunning birch]

so yes

[minor grove]

Well, hooray! But that's not one of the answer sets

Closest is 72

[cunning birch]

let's not do 'closest' xd

oh

[minor grove]

Of course 😆

[cunning birch]

didn't apply correctly

?C?

[minor grove]

Ohh, 12?

Because now we'd have 13 elements

From 0 to 12

12C2

12!/2!10!

12*11/2, 66

[cunning birch]

13 elements so 12 in betweens

[minor grove]

Yup

Got 'em now!

[cunning birch]

for future refs

https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

[minor grove]

Thank you! I appreciate the help

Have a great day or night

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[lavish wind]

Hello, comrade, did you have a question today?

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[opal nebula]

We need a solution for at least one number

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[devout ledge]

,, \frac{dy}{dx} = x e^y \ y(0) = 0

[grizzled pagoda]

smeagol

[devout ledge]

How do I solve this?

,, dy \cdot e^{-y} = x dx ?

like that

[night jacinth]

yea sounds good

[grizzled pagoda]

smeagol

[devout ledge]

I don't know what to do from here though

[modern mauve]

Integrate both sides

[devout ledge]

,, \int e^{-y} dy = \int x dx
\ -e^{-y} + C = \frac{x^2}{2} + C
\ y = - \ln( - ( \frac{x^2}{2} + C) )

[grizzled pagoda]

smeagol

[devout ledge]

@modern mauve how's this?

but ln(x) can never = 0 so I am confused

[pallid canopy]

That's where C comes in

[devout ledge]

oh ln(1) = 0

[night jacinth]

& you mean x can never be 0

[devout ledge]

0 = - ln ( - 0 - C)
0 = - ln ( - C)
0 = ln ( - C)
e^0 = - C
- 1 = C

,, y = - \ln ( - (\frac{x^2}{2} -1 ))

[grizzled pagoda]

smeagol

[devout ledge]

Is this good?

.close

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[fading tapir]

I know how to simplifily, I just don't understand what goes where the ... are

It's not a pattern of addition or multiplication, also not squares or cubes

I think the dots mean there is a pattern there

Answer key btw

[blissful swan]

12=2^2*3, 27=3^2*3, 48=4^2*3.... 18=3^2*2, 32=4^2*2 etc

i.e. 12-192 is square roots of [square number]*3, and 18-162 is square roots of [square number]*2

[fading tapir]

Good eye

thank you

[blissful swan]

nw

[fading tapir]

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[languid cradle]

I have a homework question for discrete math and I am unsure if my solution is correct since it did not invoke subsets. Here is the question.

[languid cradle]

<@&286206848099549185>

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[noble burrow]

can someone walk me through the steps and explain how we integrated this

[pallid canopy]

Which line did you get lost first

[noble burrow]

line 2 after the arrow

[pallid canopy]

They did chain rule or substitution

u = 3-x for the first one and u=1-x for the second integral

[noble burrow]

sorry i dont understand

oh

so theyre using u substitution for both terms

[pallid canopy]

Yea forgot to say they split the integral of a sum as a sum of two integrals

But you figured it out

[noble burrow]

thanks

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[cedar eagle]

what does it mean graphically to take the integral of a linear function. what physical systems does it describe?

[pallid canopy]

Area of a triangle

[cedar eagle]

why do i get a y-value of 8 on the parabola and a y value of 4 on the linear function

what does it mean?

like how can i apply this in real life

[little widget]

where is that from

[cedar eagle]

wdym

[little widget]

the blue graph is the area of the green line?

[little widget]

the area of the triangle is 8

[cedar eagle]

oh

what can i describe physically with this example

?

[leaden sonnet]

you estimated the area under the curve from 0 to 4

[amber wasp]

@cedar eagle Has your question been resolved?

[cedar eagle]

i know, but physically could you say that my acceleration went up from 0 to 8 in the span of 4 seconds.

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@cedar eagle Has your question been resolved?

[amber wasp]

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[dark portal]

🤨

[long vessel]

what r u having a problem with?
how far r u in the question

[dark portal]

I’ve been stuck on this for like 10 minutes

Idk where to start tbh

[long vessel]

okay

do you know the equation for the slope of a line?

[dark portal]

Not really

[long vessel]

okay

the slope is how fast the line is going up or down

[snow blade]

Hey huzz

[long vessel]

hello?

[dark portal]

Ok

[long vessel]

uh

a small number

like 0.2

means that it's increasing very slowly

[dark portal]

Okay

[long vessel]

whereas a big number like 3 means it's increacing very fast

[dark portal]

Ohh okay thank you

[snow blade]

Pick those two points and use the formula
(Y2 - y1)/(x2-x1)

[long vessel]

this number measures how much the y changes for each x change

a slope of 3 means that for every 1 unit you move in the positive x direction (right)

you move 3 units in the positive y direction (up)

[dark portal]

Okay thank you so much!!

[long vessel]

have you got it from there?

[dark portal]

I think so

[long vessel]

also for "downhill" slopes it's negative

so if you move to the right and end up doing down the slope is negative

[dark portal]

Alright thanks

[long vessel]

you can probrably see how ooferms formula matches it lol

gl!

[dark portal]

Thanks!

.close

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[unreal escarp]

Hello

[unreal escarp]

I'm trying to solve this system using the normal equation:

Using A^T * Ax = A^T * b

and then trying to find the error vector

I've found this vector for the x_hat:

but it seems to be giving me the wrong error vector

and I'm not sure why my solution doesn't work

I plugged in A and b into the normal equation, and got this

which I believe is correct

[unreal escarp]

and this is the x_hat I got, which seems to be giving me an incorrect error vector, and I'm not sure why

[celest cove]

if its solving Ax=b then im relatively sure theres no solution

it would demand x=-1
then -2+2y=8 so y=5
and also -1-y=3 so y=-4

As for the method youre using im not too familar

[shadow stump]

what do you get as your error vector and how do you know it's incorrect?

[unreal escarp]

i might have just figured out

my x_hat is wrong i think

the error vector is [6 2 -1]
and the one i got was crazy, like 44/9, -7/9, and -29/9

wow, im sorry guys

complete typo on my part lol

i was solving b = [5 13] instead of [15 13]

now im getting the correct x_hat of [1 2]

appreciate the help nonetheless

.close

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[modern torrent]

What is the adjoint of a matrix? Concretely and abstractly.

[pallid canopy]

https://mathworld.wolfram.com/Adjoint.html

Can also be https://en.m.wikipedia.org/wiki/Adjugate_matrix

Gotta infer from context of usage

[amber wasp]

@modern torrent Has your question been resolved?

[modern torrent]

Proposition: Let $R_0 = {\alpha \in R: \alpha$ is integral over $S}$.
Then $R_0$ is a subring of $R$, i.e. closed under addition and multiplication.

[grizzled pagoda]

utop!a

[modern torrent]

I guess, why specifically choose adjoint? I'm curious it if has any abstract properties similar to properties of diagonalization.

[pallid canopy]

Depends on what's being proved

[pallid canopy]

Looks like it's this one

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[modern torrent]

okay, thanks

was just wondering particulary if there was anything special intuitively about the adjoint.

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[dusky sigil]

I feel like I still don't have a grasp on change of basis. I kind of know the basics and what they represent from the 3b1b video. I could do change of basis problems that just involve tuples of numbers but I'm stuck on this question.

Consider the following equation 2x^2-2xy+5y^2=1 where the (x y) coordinates of vectors are relative to basis e1, e2.

consider another basis:
e'1 = (1/3)e1 - (1/3)e2
e'2 = (2/3)e1 + (1/3)e2

Write the equation relative to e'1, e'2.

I've basically just written the matrix

( 1/3 2/3 )
( -1/3 1/3)

but thats it

[dusky sigil]

<@&286206848099549185>

.

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@dusky sigil Has your question been resolved?

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@dusky sigil Has your question been resolved?

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[rancid parrot]

Could someone please explain to me why x_1 = 3/4?

[full elk]

The first row tells you that $x_1 - \frac{3}{4} x_2 =0$, so you get $x_1 = \frac{3}{4}x_2$.

[grizzled pagoda]

Azyrashacorki

[amber wasp]

@rancid parrot Has your question been resolved?

[rancid parrot]

Why do it like that?

I don’t understand still

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[exotic olive]

am i right with D here?

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[humble topaz]

how do I simplify this:
(n/3) * ((n-1)/3) * ((n-2)/3)

[amber wasp]

Please don't occupy multiple help channels.

[leaden sonnet]

multiply n x n-2 x n-2

and 3^3 (denominator)

[humble topaz]

Oh I asked wrong, sorry of cause you would say that.

I mean if

n is 3 for example

[leaden sonnet]

huh

[humble topaz]

can I write 3! / 3²?

[leaden sonnet]

um no

3! is 3 factorial which is 1 x 2 x 3

is that what youre asking?

oh youre saying if it continues

so like ............... *(n-x)/3

then yes and it would be 3^x

[humble topaz]

Ah I see my error

Thanks

[leaden sonnet]

youre welcome 🙂

[humble topaz]

I am trying to simplify this:

1 / (0.5 * (3/3)) +
1 / (0.5 * (2/3)) +
1 / (0.5 * (1/3))

Instead of writing every time the next part like here.

E.g. if there are three parts I need to write three lines:
One with 3/3, one with 2/3 and one with 1/3

[leaden sonnet]

i dont understand where youre getting your numbers from

are you talking about writing a summation?

ok so like i described before you are right about the numerator being a factorial

but the denominator isnt

@quick ridge you done hating me now lmao

[humble topaz]

Hating? 😅

[vague thorn]

[leaden sonnet]

he was shitting on my methods before

[quick ridge]

!noping

[amber wasp]

Please do not ping individual helpers unprompted.

[leaden sonnet]

lmao

[humble topaz]

xd

What is going on between you two?

[vague thorn]

@amber wasp help me!!!!

[leaden sonnet]

nothing just jokes 🙂

[humble topaz]

haha

[leaden sonnet]

huh

[trim crypt]

You got your answer?

[leaden sonnet]

so back to your math

[leaden sonnet]

noooo

[humble topaz]

No, I am thinking

[leaden sonnet]

you want a summation right?

[trim crypt]

https://tenor.com/view/hmm-dr-iggy-frome-new-amsterdam-thinking-wondering-gif-14163078457894789635

[leaden sonnet]

shhh its a library!

[vague thorn]

https://images-ext-1.discordapp.net/external/j3bH5O1yOXs5CAwR-npF-JkV7inr-K5nuNukdkKqVag/https/cdn.weeb.sh/images/BJvTXR1Tb.gif

[scarlet trail]

n starts at 1 and ends at 3?

[leaden sonnet]

no they just didnt put the infinite form at the end

[trim crypt]

Seems like we truly have limited numbers of help askers

[leaden sonnet]

fr

[scarlet trail]

p sure its just 6/k

[leaden sonnet]

just happy i got here before diamond 😉

[trim crypt]

And we too many helpers

[scarlet trail]

from n=1 to whatever it goes to

[leaden sonnet]

no

[scarlet trail]

assuming this is what u wanted in summation

[leaden sonnet]

its a factorial of n

[scarlet trail]

wheres the factorial

[leaden sonnet]

that was an example

[leaden sonnet]

omg

[scarlet trail]

they literally said they are trying to simplify that

[leaden sonnet]

just because im female diamond doesnt mean idk math

[scarlet trail]

are you sure its an example

[vague thorn]

💀

[scarlet trail]

I personaly love woman but your not doing them justice rn

[trim crypt]

💀💀💀

Oh

It’s a show

But my phone gonna die

[vague thorn]

I'm guessing the original question is $\prod_{i=0}^{n-1}\frac{n-i}{3}$

[grizzled pagoda]

@vague thorn

[leaden sonnet]

you would have said the same earlier, but yk there is a reason youre here and not with someone else

[trim crypt]

I’ll come back 💀

[quick ridge]

*you’re

[trim crypt]

Knief whose side are you on

[vague thorn]

wat are we doing 💀

[trim crypt]

Bet on someone

[leaden sonnet]

wasting time...

[quick ridge]

neither

[vague thorn]

cute

[scarlet trail]

if what he said he wants simplified, is what he wants simplified, i am correct

[trim crypt]

My money on the guy getting his answer

[leaden sonnet]

he said to simplify

[leaden sonnet]

...

[trim crypt]

Is this english

[vague thorn]

no catalan

[leaden sonnet]

and the infinite form is n-x/3

or (a) whatever you want to call it

[leaden sonnet]

i hope you are simplified, and i see you learned how to type in sentences thank you ❤️