help-0

[magic terrace]

5. Now find the derivative of the of the function you simplified

[vale wigeon]

also $C = \frac{10}{r} + 0.14\pi r^2$

[swift shore]

lmao

[magic terrace]

??

[vale wigeon]

$\frac{\pi r}{\pi r^2} = \frac{1}{r}$ not $r$

[ocean seal]

Ann

[vale wigeon]

also wait

,calc 2 * 250 * 0.02

[ocean seal]

Result:

10

[vale wigeon]

yeah, you screwed up the coefficient too. only noticed now.

[ocean seal]

Ann

[magic terrace]

here's what I did

[swift shore]

real 1950s math teacher

[magic terrace]

$C=\pi{r\frac{500}{\pi{r^2}}}(0.02)+2\pi{r^2}(0.07)$

[ocean seal]

Eyesonjune

[vale wigeon]

@swift shore is this meant to be an insult?

[magic terrace]

$C={\frac{500\pi{r}}{\pi{r^2}}}(0.02)+2\pi{r^2}(0.07)$

[swift shore]

no I’m teasing eyesonjune

[magic terrace]

I make that joke because my grandma always used to tell me "math teachers are always picky about hanging decimals" and I have never once had a teacher mark me down for it

And she grew up in the 1950s

[swift shore]

Ah

[vale wigeon]

i personally am picky about more than a handful of notational things.

also were you going to like, live-edit that or what

[ocean seal]

Eyesonjune

[vale wigeon]

ok great

i think you're about to come to the two meaningful screwups i mentioned before

[magic terrace]

$C={\frac{500}{r}}(0.02)+2\pi{r^2}(0.07)$

[ocean seal]

Eyesonjune

[magic terrace]

is that the step I messed up?

[vale wigeon]

no this time you did it correctly

[magic terrace]

0.02*500 = 10

So

$C={\frac{10}{r}}+2\pi{r^2}(0.07)$

[ocean seal]

Eyesonjune

[magic terrace]

I'm not sure what I did here

I think I reversed it and instead of doing 1/rx10, I did 1/10xr

[vale wigeon]

do not use the letter x for multiplication

[magic terrace]

To be fair I have been doing math for the last 9h

I had to because * does italics

discord markup

[vale wigeon]

\* exists

spaces exist

[magic terrace]

and I wasn't about to use backticks retroactively

[vale wigeon]

also maybe you need a break

[magic terrace]

Finals week

I aint got time to slack

[vale wigeon]

9 hours is too long

[magic terrace]

ok now so it's actually

$C=\frac{10}{r}+0.14\pi{r^2}$

I'm desperately trying to avoid quotient rule but I think it is inescapable

in that case I think 10/r makes more sense

[swift shore]

Quotient rule is a rewritten product rule

[magic terrace]

I know

[swift shore]

You have to differentiate this?

[magic terrace]

No

It's = 0 later in the problem

dr/dx or whatever

Actually it would be like d/dr

or something like that

${\frac{-10}{r^2}+0.28\pi{r}}$

I believe that's correct

not 100% sure

[vale wigeon]

grumble grumble hanging decimals...

now this is correct

[ocean seal]

Eyesonjune

[magic terrace]

well now they're out of order

[vale wigeon]

wym out of order

[ocean seal]

Eyesonjune

[vale wigeon]

oh you mean that

[magic terrace]

When I edited them they got out of order

[vale wigeon]

i mean ok yes you got $\dv{C}{r} = -\frac{10}{r^2} + 0.28 \pi r$

[ocean seal]

Ann

[magic terrace]

6. Now set the derivative equal to 0 and solve

[vale wigeon]

now you can (and should) find where this equals 0 --- and while the problem does not say how far you should be rounding, since this is meant to be a real-life (ish) problem i doubt they're looking for the exact value in terms of π

[magic terrace]

hmm

let's see

$0=\frac{-10}{r^2}+0.28\pi{r}$

I don't see anything I can really factor out?

maybe 2?

I don't see how that would help though

[swift shore]

Try clearing the denominator

See what happens

[vale wigeon]

just add 10/r^2 to both sides lmao

[swift shore]

That works too lol

[vale wigeon]

also HANGING DECIMALS!!!

[magic terrace]

R CANNOT GO ON LHS WE ALL KNOW THIS 😭

[magic terrace]

deal with it boomer

[vale wigeon]

what do you mean "r cannot go on LHS"

who told you that and in what context

[swift shore]

What why

[magic terrace]

I'm joking around

[vale wigeon]

curious

how old do you think i am

[swift shore]

Ann the boomer

You should add that to your bio

[magic terrace]

I just always forget that you can place the variable you're trying to solve for on either side

[vale wigeon]

also you missed a pi

who gives a shit what side the variable youre solving for is on lmao

you can switch the two sides of an equation at any point it literally doesnt matter

space after \pi

[ocean seal]

Eyesonjune

[magic terrace]

$\frac{10}{r^2}=0.28\pi{r}$

[ocean seal]

Eyesonjune

[vale wigeon]

great

this equation should now be much easier to solve

[magic terrace]

$10=0.28\pi{r^3}$

[ocean seal]

Eyesonjune

[swift shore]

Yuh

[magic terrace]

$\frac{10}{0.28\pi}=r^3$

[ocean seal]

Eyesonjune

[vale wigeon]

keep going

[magic terrace]

I don't know how to do cube root with latex

[swift shore]

,calc cbrt(10/(0.28*pi))

[ocean seal]

Result:

2.2485231606224

[vale wigeon]

$\sqrt[3]{...}$

[ocean seal]

Ann

[vale wigeon]

this is how you do cube roots

[magic terrace]

$\sqrt[3]{\frac{10}{0.28\pi}}=r$

[ocean seal]

Eyesonjune

[swift shore]

Why is your latex white

[magic terrace]

I am going insane solving this problem and listening to Bonehead's Bank Holiday by Oasis

[magic terrace]

yes I was gonna ask that

but that's racist

[vale wigeon]

config option. ,tex --color white or ,tex --color light

[vale wigeon]

is this statement meant to be serious or joking?

[magic terrace]

What do you think

7. Now plug in the value you found to the original equation you needed to optimize

[vale wigeon]

i don't know, hence why i ask.

[swift shore]

You thought of asking, hence you are racist

Nice try avoiding it though

[vale wigeon]

either you're reading race into the literal color of the background (where there is obviously no race involved) or you're making a shitty joke

either way you're making a dick move

a minor dick move but a dick move nonetheless

[magic terrace]

Someone takes things a little too seriously

[swift shore]

Bruh

It’s whatever

[vale wigeon]

so it was a joke? you could've and should've said it was a joke.

someone doesn't like being direct and transparent. wonder why that is.

[swift shore]

They can’t even keep eye contact

[vale wigeon]

who gives a shit about eye contact

[swift shore]

That was such a brain dead joke lol sorry

Their name is eyesonjune

[vale wigeon]

anyway yeah you found the value of r

[magic terrace]

what are you insinuating here

[vale wigeon]

which i recommend you round to like 2 decimal places

i am not insinuating shit.

you refused to answer directly to my question of whether your statement was serious or joking

when in fact there was an answer you could've given

but you didn't

anyway

you have now found the radius of the can

you have an expression for the height of the can, and for the cost of the can, in terms of the radius.

what remains is simple plug-and-chug.

[magic terrace]

I didn't feel that the unnecessarily critical approach you took to interpreting my joke warranted a serious clarification

[magic terrace]

yes I am aware

[vale wigeon]

if you're asked for clarification you give it.

doesn't matter whether you think it warrants it or not.

[magic terrace]

what do you mean by this?

[vale wigeon]

i mean exactly what i say.

[magic terrace]

so do I

[vale wigeon]

when you're asked to clarify something you said, you clarify it.

[magic terrace]

what do you mean by clarify?

[vale wigeon]

http://wiktionary.org/wiki/clarify

[swift shore]

lmao

[magic terrace]

What do you mean by wiktionary?

ok that's enough

.close

[lone heart]

Channel closed

Closed by @magic terrace

Use .reopen if this was a mistake.

[vale wigeon]

[hidden pier]

boi what

[vale wigeon]

fuck you actually

dunno. OP had some kinda attitude and acted self righteous when called out

[lone heart]

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[alpine sable]

Hello guys, I'd like to solve the following equation for all mu and r, does anyone could help me please ?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[pulsar aspen]

What have you done so far?

[sullen agate]

I just know the basis, if that counts

[pulsar aspen]

Hint:
||W have two basis. Prove it||

[lone heart]

@sullen agate Has your question been resolved?

[lone heart]

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

.reopen

Hellooo

[pulsar aspen]

Repost your question

Also, coincidentially, I played made in abyss song.

[scenic sable]

Hold on the image is loading

How do i solve question 3?

[pulsar aspen]

,rccw

[alpine sable]

Hi, which one is question 3?

[scenic sable]

Oh wait

Question 3 is the one that says the function g is definded as g….

Sry didnt fit the whole screen in the pic

[alpine sable]

alright!

[scenic sable]

Add maths really is hard

[alpine sable]

Alright.

[scenic sable]

If possible can u teach me how to solve the next question too

[alpine sable]

So can you tell me what does "range" mean?

[scenic sable]

From smallest number to the biggest?

[alpine sable]

Um

So range is when you input a domain and you get the output

[scenic sable]

Oh that range

Icic

[alpine sable]

ok ok you do perfecto

so now it gives us the domain restriction

[scenic sable]

Mhm

[alpine sable]

we know that x can only be 0 or MORE

right? it says x >= 0

[scenic sable]

Yeah

So its any number from 0 and above?

[alpine sable]

let's put 0 into $(0)^2 - 5$, what do we get?

[ocean seal]

kav

[alpine sable]

what is $0^2 - 5$ ?

[ocean seal]

kav

[scenic sable]

-5

[alpine sable]

perfect. Now try $(1)^2 - 5$

[ocean seal]

kav

[scenic sable]

-4

[alpine sable]

mhmmm do you know the next one?

[scenic sable]

And if its 2 it would be -1

3 its 4

[alpine sable]

right! so since we know that x is only INCREASING. And when we use 0 (the smallest number), we get -5

and you know, when you put 3 then you get 4. so the number is only getting bigger, we can conclude that -5 will be the smallest number in that range right?

[scenic sable]

Yeahh

In that case, is the range the number where it starts increasing?

[alpine sable]

so the range will be >= -5

Meaning, your range will be all numbers that are above -5 and including -5

[scenic sable]

Oooh

Ah got it

The next question i do not understand the x e ERthing

[alpine sable]

This is how we write it $[-5, \ulti)$

[ocean seal]

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

[alpine sable]

e r thing?

oh question 4?

[scenic sable]

Yeah

Question 4

[alpine sable]

Alright. so the R symbol means "all real numbers"

[scenic sable]

What are real numbers?

[alpine sable]

Good question!

Any number is a real number

(well except complex ones, but don't worry about that 🙂)

[scenic sable]

Positive and negative?

[alpine sable]

Yup!

[scenic sable]

Does decimals count?

[alpine sable]

decimals do count yes

[scenic sable]

Ah okok

But since its any number how do we find the smallest one?

[alpine sable]

now that means our "domain" can have any number as it's input right?

[alpine sable]

aha! see now there's isn't a smallest number

[scenic sable]

Yeah

[alpine sable]

you see this is a quadratic

let me show you how it looks like

[scenic sable]

Okayy

[scenic sable]

So its basically a curve in the graph?

[alpine sable]

oh there you go

[alpine sable]

yes, it's a curve. When you see $x^2$, you should think of them as a curve

[ocean seal]

kav

[scenic sable]

Ah i got it now

[alpine sable]

So if we look at it, do you see any values going above 4? no right? well that means our range is 4 and below

you can try to solve it algebraically too.

[scenic sable]

Where does the 4 come from?

[alpine sable]

$4 - x^2$

[ocean seal]

kav

[scenic sable]

Oo

[alpine sable]

yup!

[scenic sable]

Wait hold on ,the equation in the question is the domain isnt it?

[alpine sable]

The thing you need to know is, even if you input a negative number into $x^2$. it will become positive

[ocean seal]

kav

[scenic sable]

Ah

[alpine sable]

? that's the equation, the domain are your inputs. which are your x values

[scenic sable]

Oh ic

[alpine sable]

$(-2)^2 \rightarrow 4 | (2)^2 \rightarrow 4$

[scenic sable]

Since negative multiplied by negative is still positive

Got it

[ocean seal]

kav

[alpine sable]

yup!

[scenic sable]

Okay so whats the next step ?

[alpine sable]

that's it, your range is 4 and below

I'm just explaining the fundamentals haha

[scenic sable]

Yeah

[alpine sable]

Is that all?

[scenic sable]

Yep you may proceed

[alpine sable]

If you're done with your question, you can type ".close". Thank you! @scenic sable

[scenic sable]

Oh wait

Ooooooohhh

Okay thanks

.close

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

@frozen pawn Has your question been resolved?

[frozen pawn]

<@&286206848099549185>

[median oar]

What have you tried

[north adder]

@frozen pawn

[frozen pawn]

Different methods

Cosine rule

Since rule

But it doesn't fit

As there is a value missing

Pythagoras theorem also doesn't fit

[nimble fern]

Which question are we tackling?

If you are talking about Q7a)
You can use cosine formula to find length of BC

Since you have an angle and 2 adjacent sides

[lone heart]

@frozen pawn Has your question been resolved?

[grave mirage]

this question has been solved

on #help-8

same question repeated twice

i solved 7)b)i)

i think t hat's what they needed help with

[lone heart]

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[obtuse fog]

Could someone help me?

[wary stream]

Why does that look test like?

[obtuse fog]

It's a "group exam"

We do it before the real exam in a group

And none of us know how to solve it, really

[wary stream]

Can you not ask your teacher or other groups?

[amber niche]

it's not as hard as it seems

i think what they want to do is
a) get a parametric equation for the line
b) find where the line intersects the plane
c) calculate distance

[obtuse fog]

I did, but couldn't understand what he told us... If we ask him something specific he can't explain it differently

[obtuse fog]

Yeah, that's clear

But how

[amber niche]

i'll try to be more clear

1. basically you have a line that is perpedicular to the plane and that goes through B

[obtuse fog]

You do that with a normal vector, I guess?

[amber niche]

yes

and you make it go through B

so you apply the vector to B

so you get a parametric equation for the line

[obtuse fog]

So you have (x|y|z) = (5|-2|0)+ s(-1|4|1) <- Normal vector

[amber niche]

yes

now you can plug x y and z in the plane's equation to solve for s

[obtuse fog]

and what would these be? 🙂

[amber niche]

x = 5-s
y = -2+4s
z = s

right ?

[obtuse fog]

ah, lol, true

and then you solve for s

[amber niche]

yep

[obtuse fog]

I found that s = 1

[amber niche]

all right now what does that tell you

[obtuse fog]

good question^^

[amber niche]

why did we just calculate s

actually, what does s represent

[obtuse fog]

to find x y and z?

[amber niche]

which ones

[obtuse fog]

how many times you multiply the normal vector with, doesn't it?

[obtuse fog]

these

[amber niche]

yes, but why is s=1

what point does it give you

for s=1, you get a point on the line, but it's more special than just that

because for any s you get a point on the line

what makes s=1 special

[obtuse fog]

(5|-2|0)+(-1|4|1) = (4|2|1) ?

[amber niche]

for s=1, your point is in the plane

it's where the line intersects the plane

[obtuse fog]

okay, that makes sense

so what does that tell me?

[amber niche]

right, so plug 1 in the parametric equation

[obtuse fog]

That's what I did here

[amber niche]

so that's the point right below B

now you just calculate the distance in between them

[obtuse fog]

why is it right below? 😅

[amber niche]

it's easier to see with a drawing

ignore my glorious ms paint skills

all you gotta do is calculate the distance in between B and the new point

[obtuse fog]

oh shit, I think I understand now

Thanks very much

i think the solution is like 4.24?

[obtuse fog]

it isn't that bad xD

[amber niche]

idk

[lone heart]

@obtuse fog Has your question been resolved?

[lone heart]

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[lone heart]

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[gloomy stream]

can someone help me with any of the 2

[keen bear]

,rotate

[keen bear]

see if you can start by simplifying the arguments of the trig functions

[gloomy stream]

i can't

the basic steps are

1: convert it to arctan()
2: manipulate it and split into arctan(x) - arctan(y)
3: put r= 1, 2, 3.. till n. all terms except 2 will be cancelled
4: put lim n→∞

i need help with step 2

the formula is:
arctan(x) - arctan(y) = arctan((x - y) / (1 + xy))

[keen bear]

well, this gives you a system of equations: x-y=6^r, xy+1=2^(2r+1)+3^(2r+1)

solve for x and y

it's nasty and rude, but you can do it

[rugged sun]

For the first series, I started with cosec^2(x)=cot^2(x)+1

You can rearrange to x=arccosec(sqrt(cot^2(x)+1))

[gloomy stream]

hmm I'll try

[rugged sun]

Let y=cot^2(x)+1 and substitute

So arccot(sqrt(y-1))=arccosec(sqrt(y))

Putting this into the series gives

The same argument but with -1

Expanding (r^2+1)(r^2+2r+2)-1 and refactoring

[gloomy stream]

yeah i got that

now arccot(x) = arctan(1/x) i guess?

[rugged sun]

Gives (x^2+x+1)^2

[gloomy stream]

ohhh

[rugged sun]

The you have a simpler series as the sqaure cancells with the root

[gloomy stream]

that's clean now

[rugged sun]

Thats all I have rn

Hope that was useful

Sum arccot(r^2+r+1)

Is the series currently

[gloomy stream]

can you tell how you factored that?

[rugged sun]

Expanding (r^2+1)(r^2+2r+2)-1

Then put into wolframalpha

Gives (r^2+r+1)^2

I was hoping it would do that tbh

[gloomy stream]

r⁴+2r³+2r²+2r

[rugged sun]

+1 on the end

[gloomy stream]

no?

[rugged sun]

The coeficients from r^4 to r^0 go 1,2,3,2,1

[gloomy stream]

1 and -1 cancel tho

[rugged sun]

It's 2-1 you might want to check again

[gloomy stream]

ohh right

[rugged sun]

I need to do something rn, will be back later

Sorry

[gloomy stream]

alr thanks

nope idk how to factor this

[lone heart]

@gloomy stream Has your question been resolved?

[rugged sun]

Hi again

I will show in more detail

We want to show that
(r^2+1)(r^2+2r+2) - 1

= (r^2+r+1)^2

Expanding the first function

(r^2+1)(r^2+2r+2) - 1 = r^4+2r^3+2r^2+r^2+2r+2-1

Or

r^4+2r^3+3r^2+2r+1

[gloomy stream]

alright

[rugged sun]

Now we need to factor this

Honestly, I am not sure of an easy way to get to the factored form. I kind of hoped it could be factored and put it into wolframalpha

We can check that expanding (r^2+r+1)^2 gives the same result

In any case, (r^2+r+1)^2 is the factored form

I guess you could assume that it was to be of the form (r^2+ar+b)^2 with a view to cancelling the square root, but this is quite a big leap of faith

The series simplifies to

[gloomy stream]

that's not the point lol

[rugged sun]

,,\sum_{r=1}^{\infty} \acot(r^2+r+1)

[ocean seal]

Social Capital Gainer

[gloomy stream]

the result would be same but expanding it but i need to know how to factor it

I'm supposed to do this question in less than 90 seconds 🥲

[rugged sun]

Really, what is this question from?

[gloomy stream]

it's really easy from here

[gloomy stream]

I'm not sure, my teacher gave it to us. it is for JEE mains or advanced

[rugged sun]

Hmm, not something I've heard of

[gloomy stream]

should I open another thread about how to factor it, and close this one?

[rugged sun]

No it's fine, we can get this

[gloomy stream]

you haven't? that's strange, because it's one of the hardest exams

[gloomy stream]

alrighty

[rugged sun]

I haven't heard of it in my country

[gloomy stream]

yeah JEE mains is conducted by the Indian government, and advanced by IIT
they're entrance exams for engeneering colleges

[rugged sun]

Yeah

I looked it up now, I'm interested bc these questions look really good

Anyway

For factoring the quartic

The pattern I can see is this

If we write it in a specific way, promped kind of by the fact that the coefficients go 1,2,3,2,1, it is like the repeated terms have been stacked

[gloomy stream]

yeah

we need to split them in a way

x³ can be written as x².x

[rugged sun]

,,\begin{align}r^4&+r^3&+r^2&&\ &+r^3&+r^2&+r&\
&&+r^2&+r&+1\end{align}

[ocean seal]

Social Capital Gainer

[rugged sun]

Ignore the big gaps

[gloomy stream]

(A + B)² = ((x²)² + B² +2.x².x)
A = x²

but well now I know what it factors to so I'll think to form that

now B² = 3x²+2x+1

no waitwr

wrong

[gloomy stream]

this image is not loading for some reason

[rugged sun]

Oh

I'll repost

,,\begin{tabular}{ccccc}r^4&+r^3&+r^2&&\ &+r^3&+r^2&+r&\
&&+r^2&+r&+1\end{tabular}

[ocean seal]

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

[rugged sun]

Is that ok?

So we factorise r^2 from the top row, r from the second and nothing from the third

[gloomy stream]

yeah

wow that looks beautiful

[rugged sun]

Thanks :)

[gloomy stream]

alright

[rugged sun]

You said that the question is easy from there, what do you do next as I haven't looked to much into it yet?

[gloomy stream]

shall i tell that first?

we had arccot(r²+ r +1)
arccot(x) = arctan(1/x)

= arctan(1/(1 + r(r+1)))
= arctan(((r+1) - r) / (1 + r(r+1)))
= arctan(r+1) - arctan(r)

doing r=1 + r=2 + r=3 + ... + r=n
let arctan(x) = f(x)
f(1+1)-f(1) + f(2+1)-f(1+1) + f(3+1)-f(2+1) + ... + f(n+1)-f(n)

= f(n+1) - f(1)
now n tends to infinity:
f(∞) - f(1)
= pi/2 - pi/4
= pi/4

i just need help with the factoring

[rugged sun]

Aaah, do you mean the factoring we were talking about above?

[gloomy stream]

yeah

[rugged sun]

So does this image make sense, as in why I split the terms in that way?

[gloomy stream]

yeah sure does

[rugged sun]

Ok, so we factorise r^2 from the top row, r from the second row and nothing from the third, then we get (r^2+r+1) three times

[gloomy stream]

what how

we get r(r+1)

[rugged sun]

So it looks like this

[gloomy stream]

oh you mean 1 from the third?

[rugged sun]

Yes

[gloomy stream]

how do we get that 3 times

[rugged sun]

,,r^2(r^2+r+1)+r(r^2+r+1)+1(r^2+r+1)

[ocean seal]

Social Capital Gainer

[rugged sun]

Factorise all three instances of (r^2+r+1)

[gloomy stream]

oh let me see

alright cool

that was.. fairly simple

[rugged sun]

Yeah, but it took some inspiration that I wouldn't have got by myself. Seeing the result helps a lot hehe. That was a very cool question

[gloomy stream]

ikr

it used so much concepts to get it

thanks a lot man

[rugged sun]

Yea, no problem at all, good luck with your entrance exam too

[gloomy stream]

maybe you can look into the second one as well--

[gloomy stream]

yeah thanks

[rugged sun]

Oke, I'll look into that, but this channel might close, can I dm you?

[gloomy stream]

sure you can, but i had to go to sleep now

I'll close this channel

[rugged sun]

Ok, no problem, good night for now

[gloomy stream]

byee

.close

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[rapid nova]

Where on $E = (0, 1)$ is $F(\alpha)$ continuous?
[ F(\alpha) = \int_0^1 \frac{\sin(\frac{\alpha}{x})}{x^\alpha} \dd{x} ]

[ocean seal]

rept1d

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@rapid nova Has your question been resolved?

[rapid nova]

<@&286206848099549185>

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@rapid nova Has your question been resolved?

[rapid nova]

:(

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[cedar field]

Can you help me with this?

[cedar field]

My working so far is that from the left it is 5 and from the right it is -5

[karmic rapids]

undefined

[karmic rapids]

yea exactly

[cedar field]

why

[karmic rapids]

if it's different from the left side than the right side then there exists no "neutral" limit

[cedar field]

but how could the limits be the same?

[karmic rapids]

if it's a continuous function

or at least continuous around that point

[cedar field]

is it always undefined if one limit is under the other?

[karmic rapids]

yes you could say it like that

but a limit from the left/right side still exists nonetheless

[cedar field]

wdym?

[karmic rapids]

$$\lim_{x \to 0} h(x) = \text{undefined}$$
$$\lim_{x \to 0^-} h(x) = 5$$
$$\lim_{x \to 0^+} h(x) = -5$$

[ocean seal]

illuminator3

[cedar field]

oh

[cedar field]

this is an example of the only way you could get a equal function right? And are there any other ways?

[karmic rapids]

don't get what you're trying to say

[cedar field]

equal limits sorry.

[karmic rapids]

f(x) = x

that's an example where the limit for any value is equal from both sides

and the neutral limit is well-defined

[cedar field]

is the one that i said an example?

[karmic rapids]

no

that has a gap between two values lol

well

depends on where you want to get the limit

[cedar field]

in the middle of them?

@karmic rapids

[karmic rapids]

b-but that doesn't even exist

like even the values around it

$\pm 1$

[ocean seal]

illuminator3

[karmic rapids]

don't exist

[cedar field]

oh

[cedar field]

finally can you explain what this looks like?

(show me)

[karmic rapids]

,wolf plot x

[ocean seal]

Results provided by WolframAlpha

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

Requested by illuminator3#0001

[cedar field]

thanks

.close

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[native cloud]

Do you know that sin(2x) = 2cos(x)sin(x)?

[tacit arch]

Yes it is

I don't recommend skipping precalculus if your plan is to take more science classes

[native cloud]

2cos(x)sin(x)/sin(x)

tada

Woah you're in college?

Dang

How's college

Oooo

You must have a great milieu

You are too 🙂

Anyways, did it help?

[lone heart]

@glass bay Has your question been resolved?

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[surreal lichen]

what is the difference between ¬∀x∀y(x<y ∨ y<x) and ¬((∀x∀y(x<y ∨ y<x))

[surreal lichen]

in the first scenario is the negation not distributed?

[lone heart]

@surreal lichen Has your question been resolved?

[remote heron]

have you tried making a truth table

just a thought

[surreal lichen]

yeah i thought of making one

[remote heron]

alternatively you can distribute that negation right

you dont need to just be able to see if its the same or not

you can confirm it through experimentation

[surreal lichen]

ahh i see i see

[remote heron]

i say this since idk either

it doesnt look the same

[surreal lichen]

bc i'm just curious abt the negation if it gets distributed or not

[remote heron]

but idk

yea

its very odd to write $\neg \forall$ there right

[ocean seal]

jan Niku, Researcher in LinAlg

[remote heron]

lets think

so

$\neg \forall x \forall y: p(x,y) \lor q(x,y)$

[ocean seal]

jan Niku, Researcher in LinAlg

[remote heron]

this would be the same as uhh

$\exists x \forall y : \neg(p \lor q)$ i think?

[ocean seal]

jan Niku, Researcher in LinAlg

[remote heron]

did you see this in a problem somewhere?L

it seems like just poor writing to me

[surreal lichen]

yeah it was a reddit post

someone one was asking a question

yeah prolly poor writing tho

thank you

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[fallow charm]

Is it just me or is the question too vague?

[drifting hull]

Do you know something more, like what does n(...) mean and what does E (or whatever the last letter is) usually stand for in this course?

[fallow charm]

N referring to the number of elements within a set & xi being the universal set?

But that simply “what can you say about this” sounds like it isn’t asking for something specific

Unless there’s something I’m missing

[drifting hull]

My idea (which isn't stated in the question) would be that Xi is a set of natural numbers from 1 to some unknown number k. And using $n(A \cap B \cap C)=1$ one could say something about k. But of course, this is only my guess and i agree that the question is kind of vague

[ocean seal]

Alexander42

[fallow charm]

I see

Makes sense

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[cinder crescent]

Hello, How do i solve this please

[wary stream]

Use $$(n - 2) \cdot 180$$ to determine the sum of interior angles of a shape, where n = number of sides

[ocean seal]

dldh06

[wary stream]

Then you can use that to find the missing angle

[cinder crescent]

so (4 - 2) * 180?

[wary stream]

Yes

And that's the sum of interior angles of that shape

[cinder crescent]

ok i gotchu thanks

I appreciate you man ive really lost all my knowledge of middle school math

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[alpine sable]

Q. If three chairs are occupied what is the expected time until it changes

I have made the transition matrix and have also found the stationary distribution

On Google it says
U_jj= 1/pi_j

Where u_jj us the expected recurrence time
I got pi_3 as 4/65
So should the expected time until it changes be 65/4? Can anyone please confirm?

[tacit arch]

You need to give more information about the distribution of change of chairs

[alpine sable]

I was given the rate diagram which is as follows

0 to 1: 1
1 to 2: 1
2 to 3: 1
3 to 4: 1

4 to 3 is 4
3 to 2 is 3
2 to 1 is 2
1 to 0 is 1

[tacit arch]

And what is pi_3 and how did you get it?

[alpine sable]

Exponential distribution

I formed transition matrix using the generator matrix I formed

Used piP=p

To find Stationary distribution and value of pi_3

Pi_3 is Stationary distribution of the 3rd chair

Like after doing pi (transition matrix)=pi
I got pi_3 as 4/65

[tacit arch]

What does 0 to 1 mean here

[alpine sable]

A roadside Dhaba has 4 chairs. Customers come according to a Poisson process with a rate of 1 customer per 10 minute and take anempty chair and eats, occupying the chair with an exponential distribution with mean of 10 minutes. If all chairs are filled, the customer just leaves. The rate diagram isshown in figure 2 below where each state is the number of occupied chairs.

[alpine sable]

Number of chair occupied

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[alpine sable]

<@&286206848099549185>

[alpine sable]

Question

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[pure jacinth]

Silly question here

How come the first integral gets the correct answer, but the second integral doesn't?

Do I always have to factor out constants for this?

[amber niche]

10(y-y^3) = 10y-10y^3

[pure jacinth]

I am sad to admit I didn't realize there was a second 10 by the y^3 twice in a row...

Thanks for letting me realize the folly of my foolish ways

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[pure jacinth]

actually follow up question

.reopemn

.reopen

[lone heart]

✅

[pure jacinth]

nevermind I am still stupid

.close

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[shell urchin]

I was wondering if I got these correct or need to change?

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@shell urchin Has your question been resolved?

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@shell urchin Has your question been resolved?

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@shell urchin Has your question been resolved?

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@shell urchin Has your question been resolved?

[hoary haven]

<@&286206848099549185> ^

actually why don't I just try helping

A - Yes

B - Yes

don't know how to the the rest of it...

uhh

sry

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[silent zephyr]

Hello, hope y'all are doing well! Would anyone be able to explain the steps in this a bit, a bit confused heh. Mostly confused how they got r=11

[normal ingot]

Do you know the definition of circumference?

[lone heart]

@silent zephyr Has your question been resolved?

[silent zephyr]

Yes

[normal ingot]

can you write the circumference in terms of the radius (i.e. r)?

[silent zephyr]

No

[normal ingot]

have you seen the formula circumference = 2 * pi * radius ?

[silent zephyr]

yes sir

i tried doing that

but i get

one second

108.565648412

[normal ingot]

how did you get that?

[silent zephyr]

22pi/2pi

[normal ingot]

yes, that should give you 11

[silent zephyr]

hmm

[normal ingot]

unless you typed 22 * pi / 2 * pi into the calculator

brackets are important

that is not the same as (22 * pi)/(2 * pi)

[silent zephyr]

ohhhhhhhhhhhhhhhhh

i got it now

thank u man

@normal ingot

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[half smelt]

Factored my triniomial. Now what?

[median oar]

what did you do from question to your paper

can you write it out in more simple steps

[half smelt]

Yeah I’ll show you

[median oar]

write the question then do each step one at a time

[half smelt]

Alright

Writing rn

[median oar]

👍

[half smelt]

The first thing I did was factor this trinomial.

That’s where I messed up I think

Yeah

[median oar]

ok first off

how did that 2nd line come to be

[half smelt]

Yup. I see now what I did

Idk what I was thinking

I’m gonna try again real quick

[median oar]

i also dont believe that is called a trinomial

[half smelt]

It is. It’s three different terms. Tri=3. Correct me if I’m wrong

[median oar]

that's just a 2nd degree univariate polynomial or a quadratic

anyway it's not that important

actually maybe it is, though i've basically never heard it be called a trinomial

[median oar]

there u go

[half smelt]

Yes! Thank you Frost!

[median oar]

also

first line is wrong

there should be a plus sign between the brackets

[half smelt]

Ahh okay gotchya

[median oar]

so should the 2nd line actually

[half smelt]

Cancel the x+4’s

Is that right?

[median oar]

and then

with the 6x^2 and 20x

[half smelt]

Okay

Is that right? 3x and 10?

[median oar]

yeah

expand that and u get your answer

[median oar]

yes

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[trim oracle]

Does the bit circled in red look correct?

[willow canopy]

yes but it's easily verifiable for you, no?

4(x-3) + 5(x-3) = 4x - 12 + 5x + 15 = 9x + 3

[trim oracle]

Oh ye thx

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[winter oyster]

could someone explain me how the freak those are eigenvectors?

when lambda = 2 the matrix is going to result {{0, 0}, {0, 0}} i.e. there are infinite solutions?

infinite eigenvectors associated to lambda = 2, even tho that's always the case?

no idea tbh

there are always infinite eigenvectors associated to one eigen value but

i don't see the reduced form of the eigenvector here, like it doesn't make any sense to do lambda(0, 0) cuz i won't get any vector nevertheless

but there it says there are two eigenvectors <0,1> and <1, 0>

[vale wigeon]

well your matrix is literally 2I

so every vector in R^2 is an eigenvector for it

but generally we work not with an eigenspace itself but with a basis for it

[winter oyster]

so

All the vectors of the plane are eigenvectors of eigenvalue 2?

cuz according to what i'm seeing here in wa

Only (0,1) and (1,0) are eigenvectors of eigenvalue 2.

when trying to diagonalize the matrix with lambda = 2 i get {{0, 0}, {0, 0}} . {{x}, {y}} = {{0}, {0}}

which i don't know how to interpret it

[lone heart]

@winter oyster Has your question been resolved?

[winter oyster]

<@&286206848099549185>

[vale wigeon]

cuz according to what i'm seeing here in wa
Only (0,1) and (1,0) are eigenvectors of eigenvalue 2.

no, that is not what WA is claiming

S doesn't consist of ALL eigenvectors, only a basis for each eigenspace.

[unkempt pagoda]

Hi

[vale wigeon]

@unkempt pagoda this channel is occupied. if you have a question of your own then please take a channel in the Math help (AVAILABLE) category. also read #❓how-to-get-help

[unkempt pagoda]

Thanks @vale wigeon

[shell urchin]

…

[winter oyster]

i see

nevertheless i'm not able to solve for those vectors by hand i don't know what am i doing wrong

for those 'basis for each eigenspace' sorry

if they asked to draw the eigenvectors associated to a matrix

i should answer this one right?

the 'basis for each eigenspace' in this case is B = {alpha_1, alpha_2} with alpha_1 being < -4,1> and alpha_2 = <5, 2>

[vale wigeon]

what do you mean?

am i understanding correctly that you think there is some process you could follow that would give you specifically the basis {(0,1), (1,0)} and not any other basis for this matrix in particular?

[winter oyster]

yes

[vale wigeon]

well you're wrong because there is no such process

the eigenspace for the eigenvalue λ=2 for your matrix is all of R^2

any basis of R^2 can serve as a basis for the 2-eigenspace of A

no basis is inherently worse or better than any other in this respect

[winter oyster]

and how did you know that?

[vale wigeon]

A - 2I = 0 and ker(0) = R^2

[winter oyster]

better yet, why did WA took those vectors as basis of this matrix

[vale wigeon]

the zero matrix, by definition, sends EVERYTHING to zero. so what could its kernel possibly be if not EVERYTHING?

i don't know. WA chooses them in some way, whichever is most convenient for its algorithm to calculate.

i don't think it's worth dwelling on why it chose this and not that.

i feel you're really overthinking this stuff right now.

[winter oyster]

alr

thanks for your time, appreciate it

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[dim vine]

How do u do this?

[dim vine]

Apparently answer is 60

So cos it's 2 tailed, I guess you're finding at what values the rejecting region is below 0.025

[lone heart]

@dim vine Has your question been resolved?

[lone heart]

@dim vine Has your question been resolved?

[dim vine]

<@&286206848099549185>

[willow canopy]

well

you're assuming the distribution of sample proportion of panthers to be mean = 0.06 and variance = 0.06*(1-0.06)/n

(this comes from the binomial distribution if you do some work on it)

then you approximate it with a normal distribution

[dim vine]

hm ok

Let me think about it a bit

[willow canopy]

there's also just straight up a formula for it

but you can get to that formula by thinking about it the way I mentioned above

[dim vine]

Do u mean like np= mean and npq = variance

[willow canopy]

that's if you let your random variable be the number of panthers out of the n-tries you do

let's call that X

what this is giving you is sample proportion

which is X/n

that's why the mean = p and variance = pq/n

[dim vine]

Gotta think abuot this one

[willow canopy]

if you just want the formula, let me know

but I think it's a cool process that you can reach by applying a normal approximation

[dim vine]

Nah cos I sort of see what ur saying. I know with sampling with variance you SD as sqrt(variance/n) but I thought variance was approximately npq so it would just end up equalling pq

Suppose I wouldn't mind to formula tho :1

That would be nice

I meant pq in that bit i just wrote sry

[willow canopy]

n >= (k/<something is here shit i forgot>) ^2 sqrt(pq/n)

uhh give me a sec

ah

that something is the margin of error

[dim vine]

I got 0.06n = X+0.877 now But am just taking X as 1 for minimum value

[willow canopy]

but uh idk what margin of error you would use for this question

[dim vine]

Sorry I am getting lost in the sauce

[willow canopy]

alright so

when you wanna show that the population is 6% or not

what margin error would be appropriate

(i'm asking because idk myself)

I could also be misunderstanding this problem as well and just making a mess of things

[dim vine]

Sorry is margin of error standard deviation

[willow canopy]

like

let's say the true proportion is 6%

then maybe your experiment comes up with 5% or 7%

those answers would have a margin error of 1%

[dim vine]

Oh right like when it has those error bars on a graph. So would it just be proportional to the standard deviation

[willow canopy]

nah the marign of error here doesn't involve the sd

[dim vine]

I suppose the margin of error would be 0.005% so u have it between 0.055 and 0.065?

Oh ok

[willow canopy]

at least with how I know it

[willow canopy]

that would be a marign error of 0.005

not 0.005%

[dim vine]

Oh mb.. Used 2 different systems

[willow canopy]

but yea uh

from how I know of it, the minimum sample size needed to determine if it's 6% or not with 95% confidence definitely depends on how tolerant you are about the proportion as well

if you know how tolerant you wanna be

the formula is

[dim vine]

.. tbh, I think this question might be a bit out of my depth since there's just so much new stuff flooding in. This formula is my last hope for understanding lmao

[willow canopy]

$n \ge (\frac{1.96}{\epsilon})^2 \sqrt{p(1-p)}$

[dim vine]

Is 1.96 just a constant there?

[willow canopy]

yea that's the constant you'd use for 95% confidence

or evidence at the 5% level

[dim vine]

And what does epsilon represent?

[willow canopy]

epsilon is the margin of error

n is the sample size

wait

oops there hsoudl not be a /n there

[ocean seal]

Azzurala

[willow canopy]

fixed lmao

[dim vine]

Ah ok

So for it to be valid, it has to be greater than whatever value pops out fo the formula

Hmm... I have to say the fact that I've never seen margin of error in a q before is hindering me

[willow canopy]

nah it could be that there's another formula for it

or maybe I'm just out of my depths and missunderstanidng the question

I'll let another person with a clearer head answer definitively instead

you should repost your question here

[dim vine]

Thanks a lot for your time. That question is a bit hellish

[willow canopy]

gl mate

[dim vine]

Thanks, have a gud day

.close

[lone heart]

Channel closed

Closed by @dim vine

Use .reopen if this was a mistake.

[dim vine]

.reopen

Whoops

[willow canopy]

oh also, maybe you should contact your professor/teacher about this as well @dim vine

[lone heart]

✅

[dim vine]

Yeah that might be a shout

[willow canopy]

if you find the solution for it can you msg me? I'm quite curious

[dim vine]

Yeah sure. I'll message my teacher now although he's not exactly known for replying fast

And I probably won't get it until Monday if he does

[lean plover]

good luck on tuesday oatlord

[dim vine]

Thank ya. I'll need it

[lone heart]

@dim vine Has your question been resolved?

[lone heart]

Channel closed

Closed by @dim vine

Use .reopen if this was a mistake.

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[dusky blaze]

<@&286206848099549185>

[dusky blaze]

a=17
d=11

i tried using

Sn=n/2(2a+(n-1)d)

but got nowhere

[balmy warren]

$100000 > \frac{n}{2}(2a + (n-1)d)$

wait hang on

[dusky blaze]

$S_N < \frac{n}{2}(34 + (n-1)11)$

[ocean seal]

riad

[dusky blaze]

for the frist part

ok

[ocean seal]

IntelligentCake

[balmy warren]

$100000 < \frac{n+1}{2}(2a + (n+1-1)d)$

[ocean seal]

IntelligentCake

[dusky blaze]

yup

[balmy warren]

are you given a and d?

[dusky blaze]

yeah

first term is 17

and commond diffrence is 11

[balmy warren]

so for the first equation you get

[dusky blaze]

u get this right

[balmy warren]

yes

then do same for second inequality

[dusky blaze]

and the other

$100000 > \frac{n}{2}(2a + (n)11)$

[ocean seal]

riad

[balmy warren]

sub in a too but

[dusky blaze]

oh yeahhh mb

[balmy warren]

also inequality should be other way round for second one

as it is 100000 < Sn+1

[dusky blaze]

$100000 > \frac{n}{2}(34 + (n)11)$

[ocean seal]

riad

[dusky blaze]

i see

so <

[balmy warren]

yes

but this still isn't quite correct

[dusky blaze]

ohh that makes sense

[balmy warren]

as it is Sn+1

[dusky blaze]

oh

[balmy warren]

so it should be (n+1)/2 outside the bracket

[dusky blaze]

oh yeahhh

and the other

$100000 < \frac{n+1}{2}(34 + 11n)$

this?

shit

a 34

i copy and pste my writing 😭

[balmy warren]

this is for Sn+1

[dusky blaze]

but the a aprt is 34

[balmy warren]

yes

[dusky blaze]

yes