help-39

[quick yacht]

i want it to not do that, because i really like natural deduction

[tulip ore]

bee what definition of definitions does natural deduction have

[quick yacht]

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

particularly the system lk

specifically, i mean, is there a typographical rule which automatically rejects self-reference

because natural deduction operates on suppositions, this just looks really bad for all of nd without any typographical rule

[tulip ore]

looking at that link you sent,

[quick yacht]

thats the form of a judgement

i can replace them arbitrarily

[tulip ore]

they didnt call B "A(n+1)"

[quick yacht]

uhh

[tulip ore]

they didnt call B "An" either

[quick yacht]

what does B "A(n+1)" mean

[quick yacht]

this just means, if i have wffs of a formal language A1, ..., An, B, then it follows A1,...,An |- B is legally syntactic
these are syntactic rules, we want a semantic rule

maybe we want a semantic rule?

even if we couldnt find a typographical rule, thanks bee, this makes me feel a lot better about the reasoning

ill leave this up for a bit in case someone can think of a typographical rule to deal with this type of self-reference

[meager trellis]

just skimming through that page, i don't think any of the systems described have definitions at all

which means there's just no way to form self-reference

[meager trellis]

also, i wouldn't say the thing to look for is to reject self-reference

you just need to not accept self-reference

[quick yacht]

i meant reject it as a supposition

[meager trellis]

as in, if you don't have any axioms you don't have self-reference

so you just need to make sure that each time you add an axiom, that axiom does not add the ability to form self-referential statements

[quick yacht]

X <-> (X -> Y) |- Y

was my issue

this statement holds in lk

[meager trellis]

...yep

that's not a problem? that's just a true inference

[quick yacht]

because it is true in general

[meager trellis]

LK doesn't have a way to use X <-> (X -> Y) |- Y to derive |- Y

so there isn't a problem

[quick yacht]

okay, so there is 100% nothing to be concerned about with this paradox in lk?

[meager trellis]

yep, in LK there isn't a paradox

[quick yacht]

and if i want to assume X = P(X), then i need X -> P(X) to show P(X) -> X, first?

[meager trellis]

...?

uh

are you talking about just logic in general or like, the diagonal lemma

[quick yacht]

that is, what exactly was wrong with saying X := (X -> Y)

[meager trellis]

the problem is that X occurs in X -> Y

[quick yacht]

right

but like X -> X is fine

sorry if im not making much sense, i got a little riled up upon seeing this

[meager trellis]

...?

if you mean X := X -> X, then that's still not a valid definition, because X occurs in X -> X

just the statement X -> X by itself is valid (assuming that X is a statement), and is also true

[quick yacht]

so, we cant just suppose X = P(X), but what if X = P(X) is true, is what im trying to get at

[meager trellis]

yeah that can happen

[quick yacht]

just, i can suppose something and get to X = P(X), and were okay?

[meager trellis]

yep

that's just... how reasoning normally works?

[quick yacht]

right, but i used my standard understand of how reasoning normally worked and ended up showing unicorns exist, i just want to be really precise

i think this covers the issues i had, well see if i find something about this to freak out about again

thanks bee, have a great rest of your day

.close

[pearl pond]

Channel closed

Closed by @quick yacht

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[last pelican]

Hi, to solve the equation sin2x-cos2x = 1, would putting it into harmonic form help?

[pine moat]

what is harmonic form

you probably do need a trig identity

[last pelican]

like Rsin(x-alpha)

[pine moat]

oh interesting

i don't think you need that specific one

there's a different one that lends itself very nicely to this problem

[glacial sequoia]

theres no problem with this btw

it will work well

[last pelican]

oh

I tried using it and go sin(2x-pi/4) = 1/sqrt(2)

[glacial sequoia]

yup

do you know the general solution

[median zealot]

hi

[jolly parrot]

NEON

[last pelican]

normally i just use unit circle to find solutions in interval but i think for this exam i need to know general solutions

are there different ones for sin cos and tan and how would I apply it to this case?

[glacial sequoia]

yeah theyre different for the three

[glacial sequoia]

you keep the term containing the variable on the left

and convert the otherside in terms of sin

for example here

[jolly parrot]

NEON

[glacial sequoia]

now just identify what to put for theta and what to put for phi

$2x - \frac{\pi}4 = n\pi + (-1)^n\frac{\pi}4$

[jolly parrot]

NEON

[glacial sequoia]

now you can do some rearranging and stuff to solve for x

[glacial sequoia]

remember n is an integer

[last pelican]

would there be more than one solution here?

[glacial sequoia]

infinitely many

unless youre given a finite interval for x

[last pelican]

$x = \frac{1}{2}n\pi +(-1)^n\frac{\pi}2 + \frac{\pi}{2}

[glacial sequoia]

you can actually make this prettier

actually nvm

[glacial sequoia]

close with $ as well

[last pelican]

cheers

$x = \frac{1}{2}n\pi +(-1)^n\frac{\pi}2 + \frac{\pi}{2}$

[jolly parrot]

Felix

[last pelican]

so like this?

[glacial sequoia]

the last two should be pi/8

[last pelican]

oh yh mybad

[glacial sequoia]

but other than that youre good yeah

[last pelican]

oh cheers

also in the solution its like x = pi/4 + pin and x = pin + pi/2

this is the same right?

[glacial sequoia]

if you mean pi/4 in th second one

then yes

otherwise no

[last pelican]

second one is pi/2

[glacial sequoia]

yeah then theyre different

[last pelican]

oh

[glacial sequoia]

wait are you asking if these two solutions are the same

[glacial sequoia]

or are you comparing it with this

[last pelican]

yh

comparing

thats like the solution they give

[glacial sequoia]

they should say one is for odd integers and one is for even integers

have they?

[last pelican]

not rlly

[glacial sequoia]

well they should

if thats the case then yes

theyre the same

[last pelican]

how would u reach that other conclusion?

[glacial sequoia]

because if n is an odd integer

then (-1)^n is always -1

so it always cancels with the other pi/4

and you're left with n*pi/2

something similar for even

[last pelican]

oh yh

so if its even

(-1)^n is 1

[glacial sequoia]

they would add

yeah

[last pelican]

ah tysm

[pearl pond]

@last pelican Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[midnight haven]

so a set and a number equating is illegal right?

[midnight haven]

The idea when things are represented like that is that these numbers represent the cardinality/size of the set

so the number of elements in A\setminus B is 20-x

[midnight haven]

huh

whaat

[midnight haven]

huh

thing of A being people who are say in the north america

and B as being the set of males

so there are x males in north america

20 -x people in north america who are not male

i just wanna know if equating a set and a number is legal or not

no that's not it

|A| = 20

huuh

[midnight haven]

so i cant do that?

$$ |A \cap B| = x$$

[jolly parrot]

swimmingland

[midnight haven]

no

[midnight haven]

why not

a set represents a collection of items

a number is well a number

doesnt represent a collection of anything

even a singleton set A = {5} is not the same as the number 5

truee

trueee

hope that clarifies the q

how do i do it then

sure

n(A-B) = 20-x

n(A \cap B) = x

so n(A) = 20

similarly n(B) = 8

@midnight haven

and you have n(A \cup B) = 23

right?

n(AuB) is 3

but thats wrong

umm

ikik

no it says n(A U B) = 23

lemme think ig

[midnight haven]

number of elements of A U B

yeah

it says below the diagram

that n(A U B) = 23 right?

yea

ok

so what all do we know

n(A U B) = 23

n(A) = 20

n(B) = 8

nooo

n(A \Cap B ) = x

right?

n(A) = 20 -x

not just 20

no

20 -x

yes

is the number of elements in A that are not in B

but then the number of elements in both A and B is x

so if you sum the two

you get the number of elements in A in total right

[midnight haven]

how

umm that's like what the diagram means

when they write 20-x

in the part that is in A

yea

but see that its not in the common region

it is, x is their common

x is the elements in common

20-x is the elements that are in A

but not common

[midnight haven]

yes

8-x is the elements in B but not common

ok

so 20-x + x = 20 is the number of elements in A

swimmingland

yeah

thid is what they did

yeah they're combining it

i was coming to that

and was first trying to explain it to you

do you want to understand the idea or just get why the answer is as is?

[midnight haven]

oh

why are u saying cup stuff

sorry cup = U (union)

cap = intersection

nevermind

ok

so look n(A U B) = 23

n (A intersect B) = x

so n(A) = 20

[midnight haven]

why 20

20 -x + x is 20 right?

yea

so that's why

n(A) = 20

okay

20-x+x => 20

did it make sense or if there's something specific you're confused about you can maybe say that

yes

and for B

it is

+x+8-x

so its 8

ya

ok

okay

and we know n(A U B) = n(A) + n(B) - n(A intersect B) right?

huh

ok we can do it differently

yes

the number of elements in either A or B, i.e., A U B

are of 3 different types

1. those that are common to A and B = x

2. those that appear in A but not in B = 20-x

3. those that appear in B but not in A = 8-x

and this contains all possibilities

right?

yes

ok

so let's sum up these 3 possibilities

and in total it should sum to 23 yes?

why

A is 20

B is 8

n(A U B) = 23

AUB is the set of elements that appear in either A or B

[midnight haven]

AUB is {20, 8} ?

no

again

AUB is a set

ikk

hut

but

if it was AUB

you cant just make the sizes of the set as the values in the set

i really think you should think of elements in the set as people

20 is not a person

8 is not a person

right?

oh true

So just think of A as Americans

and B as Male

okay?

okay

so there are 20-x Americans who are not Male

x Male Americans

and 8-x non-Americans who are Male

an in total there are only 23 people in the world

ok?

[midnight haven]

but it has - x so non americans who arent male too

no

non americans who arent male wouldn't be in either A or B and hence would not be in A U B

so we dont care about those

swimmingland

why did they add them

@midnight haven

swimminglaaaaand

[midnight haven]

because of this

so we added them because we can?

no

because that's what A U B represents

[midnight haven]

why

.close

[pearl pond]

Channel closed

Closed by @trail halo

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[stiff rock]

Whats the first step in evaluating this? I didnt understand the lesson much...

[midnight haven]

you can just substitute x^2 -1 = y

so lim_{y-> 0} sin y /y

and we know that's 1

[stiff rock]

Hmmm wait, why is it possible to subsitute x^2 -1 to y?

[midnight haven]

you can do any substitute you fancy

[stiff rock]

hmmmm ok hold on

[sweet junco]

uhhhh
you know how the limit of sin(x)/x as x approaches 0 is 1*, something similar applies to this scenario

[stiff rock]

is this solution correct?

[midnight haven]

yeah

to be clear

it's lim_{y-> 0} sin y /y

that's missing in your 2nd last step

[stiff rock]

Hmmmm alright...

can you tell me any other ways I can do the same? like turn x^2 - 1 into y?

like does it only work for x^2 - 1? I'm a bit confused how its possible to turn it into y

Yknow what nvm

@midnight haven thanks for the help

.close

[pearl pond]

Channel closed

Closed by @stiff rock

Use .reopen if this was a mistake.

[midnight haven]

sure thing

it doesnt work only for x^2 -1

any transformation via a function is fine

[stiff rock]

alright, thanks

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[visual ravine]

hey guys, Im not sure whether I am missing something obvious here. The task is to determine the max and min fixed point. Now I am quite convinced the set of all even natural numbers has to be a post-fixed point for b) as well resulting in z_max being said set.
Can someone spot if I am missing something or tell me if they'd agree ?

[drowsy harness]

Is that english?

[visual ravine]

you mean whats in the screenshot ?

[drowsy harness]

Yeah.

[visual ravine]

no

[drowsy harness]

Oh ok.

[visual ravine]

its math

badum tzz

.close

[pearl pond]

Channel closed

Closed by @visual ravine

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[upper shoal]

Im stuck here

[upper shoal]

and im trying to turn it into

sryy last channel I made a disaster

[light helm]

show what you've tried

[upper shoal]

Well I did a few steps to get to the first image

[tribal geode]

think of an identity which includes both cos and sin

[upper shoal]

But then I got

sqrt(2) ( cosxcosy + sinxsiny) -1+sqrt(3) sinx
Which is a disaster

[upper shoal]

lemme think

[light helm]

wheres x and y coming from

[upper shoal]

sry x = theta y = Pi/4

looks cleaner

[tribal geode]

now the thing which you've put in a bracket

do you remember it?

is it some identity?

[upper shoal]

yea cos2 (x+y)

/2

[light helm]

where's -1 + sqrt(3)sin(x) coming from

[upper shoal]

+sqrt 3 sin x - 1 sin x

either way its a disaster

[autumn trellis]

Parenthesise it

[light helm]

you're missing ()

also unnecessary to factorise that

[upper shoal]

100%

[light helm]

instead of trying to be fancy with compound angle identites, you could just use the exact values of sin(pi/4) and cos(pi/4) directly

[upper shoal]

oh yeah

I forgot you can do that

man

sorry

im a bit embarrassed

ty

;-;

.close

[pearl pond]

Channel closed

Closed by @upper shoal

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[sharp smelt]

Where do I even start?

[sharp smelt]

I'd probabably want to find a general formula for $n^a$

[jolly parrot]

Why am. I here

[sharp smelt]

's summation

[autumn trellis]

they want you to turn it into an integral

You should know how to write an integral as a limit of a sum for this

[sharp smelt]

hmm, ok

wait, what?

you mean divide by n^a

and multiply by n^b?

[autumn trellis]

$\int_{0}^{1}f(x)dx =\lim_{n \rightarrow \infty} \frac{1}{n} \sum_{k=1}^{n} f\left(\frac{k}{n}\right)$

[jolly parrot]

smidgin

[sharp smelt]

just a minute

hmm, so I get $n^{\alpha - \beta}$ ?

[jolly parrot]

Why am. I here

[autumn trellis]

He just deleted all his messages

[sharp smelt]

hmm

let me see

[autumn trellis]

Have you learnt Riemann sums?

[sharp smelt]

yeah

[autumn trellis]

Okay, so this is a Riemann sum

[sharp smelt]

yeah, trying to figure out how I'd get it into that form

so I divide the num and denom by n?

[regal flax]

Yes

[autumn trellis]

Yes

[sharp smelt]

hmm, so that would become

$\frac{\left(\int_0^1x^{\alpha}dx\ \right)}{\int_0^1x^{\beta\ }dx}$?

[jolly parrot]

Why am. I here

[autumn trellis]

Yes

[sharp smelt]

hmm, so that's just $\frac{\left(\beta+1\right)}{\alpha+1}$

[jolly parrot]

Why am. I here

[autumn trellis]

Yes

[sharp smelt]

what do I do with the n^(beta-alpha)?

[autumn trellis]

How did you get this then?

[sharp smelt]

oh

just multiplied and divided by n

$n$ as in $n^1$

[jolly parrot]

Why am. I here

[autumn trellis]

Right, but you should know what happened to the n^{beta-alpha} if you managed to get those integrals

[sharp smelt]

hmm, doesn't it flip the sum

when to 1/n^\alpah +2^\alpha/n^\alpha ...+1

and similarly for the denom

[autumn trellis]

Wdym by this?

[sharp smelt]

I have to rewrite $n^{\beta-\alpha}$

[jolly parrot]

Why am. I here

[sharp smelt]

as $\frac{n^{\beta}}{n^{\alpha}}$

[jolly parrot]

Why am. I here

[sharp smelt]

and then divide and apply the rienman sum

[autumn trellis]

Yrs

So f(x)=x^(alpha) in the numerator

And in the denominator f(x)=x^(beta)

[sharp smelt]

yeah, got it, thanks!

I'll close this now

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[wintry pasture]

Im doing differentiability and Im stuck at this question. I basically have no idea where I should start. It would be very helpful if someone just gives me the general direction I should go in to solve the question.

[plush prawn]

L'hopital's ?

[regal herald]

tis possible

[plush prawn]

not sure what you can do after that though

is there no other info?

[wintry pasture]

I have not yet learned it and it has not been in the book the question is from.

[wintry pasture]

nope no hints as well

[vast berry]

what is lt

[plush prawn]

hmm then seems we need to rearrange stuff so we can obtain f'(a) somehow

[wintry pasture]

the photo attached to my question

[vast berry]

what does Lt mean*

[plush prawn]

Limit

[vast berry]

Oh

[wintry pasture]

oh I read that as it

[vast berry]

oh

[wintry pasture]

no the equation is indeed limit Im just justifying why I wrote a reply to it. Just to prevent misunderstandings

[plush prawn]

change limit from x -> a to h -> 0 by using x -> a + h

then evaluate ig. should work out with a bit of manipulation to make f'(a) appear

[wintry pasture]

ah then it becomes kinda like the first principle

[wintry pasture]

Ok I will try

[autumn narwhal]

There should be some trick to rearrange it

No need to substitute h

[plush prawn]

yeah but I don't see it

[autumn narwhal]

Oh this is quite tricky

[plush prawn]

probably L hopital brainrot, my brain cant get past it

[autumn narwhal]

You need to find a term that works nicely with both x^2f(a) and a^2f(x)

Then you can split the limit into 2 limits.

[wintry pasture]

ok

So I've got literally nothing. What other way can I get help for this?

[autumn narwhal]

Try adding and subtracting ||a^2f(a)|| in the numerator

If you wanna try thinking what exactly, go for it

If not, unspoiler

[wintry pasture]

aha ok

[autumn narwhal]

@wintry pasture Did you get it?

[wintry pasture]

so I got till I seperated (x^2 - a^2)f(a)/x-a and (f(a)-f(x))a^2/x-a

[autumn narwhal]

Exactly

That's all you need

[wintry pasture]

and then the first one is just (x+a)f(a)

but what about the second one

[autumn narwhal]

$\lim_{x \to a} \frac{f(x) - f(a)}{x - a}$

[jolly parrot]

RedstonePlayz09

[autumn narwhal]

Do you know what this equals?

[wintry pasture]

no but I think I saw that somewhere

[autumn narwhal]

Try plugging in x = a + h

And changing the limit to be in terms of h

[wintry pasture]

ah thats just first principle then

[autumn narwhal]

Yeah it's f'(a)

Just another way of writing it

Personally I like this way more

[wintry pasture]

and then what about the remaining a^2/x-a

[autumn narwhal]

x - a?

It doesn't remain

[wintry pasture]

oh yea mb

[autumn narwhal]

$\lim_{x \to a} \frac{x^2 - a^2}{x - a} f(a) - \lim_{x \to a} \frac{f(x) - f(a)}{x - a}a^2$

[jolly parrot]

RedstonePlayz09

[autumn narwhal]

This is what you have now

[wintry pasture]

And then thats as far as we can simplify right. Cause we dont know f(x)

so In total I have (2a)(f(a)) - f'(a)a^2

[autumn narwhal]

Yeah

That's it

[wintry pasture]

and if thats it. Thank you very very much. This really helped. I was stuck on this for so long

[autumn narwhal]

2af(a) - a^2f'(a)

np

It is tricky, I can see why you were stuck

[wintry pasture]

Thanks again. but I will close now

[autumn narwhal]

Also

[wintry pasture]

yeah_

?

[autumn narwhal]

Like the reason I saw this is because this is similar to the proof of the derivative of a product

Derivative of f(x)g(x)

[wintry pasture]

oh I just know the rule but I havent seen the proof

very interesting

[autumn narwhal]

Anyways np

gl

[wintry pasture]

thanks bye

.close

[pearl pond]

Channel closed

Closed by @wintry pasture

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[lucid frost]

why do we not change the bounds here?
this? ⤵️

[lucid frost]

I mean we did u-sub for integration

should the bound not be u=5-2 = 3

[turbid moss]

what u-sub

[lucid frost]

u = x-2

du = dx

2sqrtu

[turbid moss]

they didnt use that in their version tho

[lucid frost]

they didn't?

[regal herald]

can you see a change of variable?

[lucid frost]

how did it go from dx/sqrt(x-2) to 2sqrt(x-2)

[turbid moss]

you couldve used a u-sub in your calculation but they didnt need it here so no bounds changed

[lucid frost]

yeah when it is 2sqrt(u) it has changed its variable

[regal herald]

(there is no 2sqrt(u))

[lucid frost]

how did they integrate it then

[regal herald]

it was always in terms of x

[regal herald]

its quite a standard integral, just a reversal of differentiating (x+a)^n

most can do it just by looking at it

[turbid moss]

they couldve used u sub but skipped it bc its not the main focus of the problem

[lucid frost]

so if i had done it my way with u-sub i would have to change the bounds right

and that would be right as well

[turbid moss]

yeah should be

[lucid frost]

could you link me a youtube video explaining this

i never thought i could do it without u -sub

[regal herald]

its just an experience thing

theres no issue using a u sub

but they just havent done that here, the limits didnt change because the variable was never changed from x

[lucid frost]

oki 👍

ty

.close

[pearl pond]

Channel closed

Closed by @lucid frost

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[frank bison]

I'm not sure what to do next-

[dusty light]

hmm

Here u go

[frank bison]

soo the sinx from 1/sinx can make 4sinx into 4sin²x?

[dusty light]

I multiply the whole equation by sinx

[frank bison]

ohh icic

[dusty light]

Yup

[frank bison]

thankss

[dusty light]

U should be able to solve the rest

Np

[frank bison]

yep

.close

[pearl pond]

Channel closed

Closed by @frank bison

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[lyric glen]

how to solve

[eternal tulip]

do you know how to find the volume of a regular cylinder?

[lyric glen]

it says half tho not regular

[eternal tulip]

yes

we can just divide it by 2

[lyric glen]

pi x r^2 x h

[eternal tulip]

mhm

so what would the volume be if it were a regular cylinder

[lyric glen]

621.72

wait no

this is with

divide

by

2

[eternal tulip]

,calc pi * (36) * 11/2

yes

[jolly parrot]

Result:

622.03534541078

[lyric glen]

so this is ans

[eternal tulip]

yep :)

[lyric glen]

i want to check ym ans

can u just tell me

if

im]

correct

or

wrong

[eternal tulip]

sure!

[lyric glen]

i got 1354.4

this is the total

surface area

is it correct

..

[eternal tulip]

no

[lyric glen]

what did u get

[eternal tulip]

wait

yes its correct

i misread

[lyric glen]

oh ok thanks

[eternal tulip]

idk how much it wants you to round

[lyric glen]

no need roujnd

[eternal tulip]

I got something along the lines of 1354.35131368 ish

approximately 1354.4

[lyric glen]

1354.4 in^3

in^3 is correct right

[eternal tulip]

in^2

we're calculating surface area

[lyric glen]

oh

oh alr thanks for helping me

[eternal tulip]

np

[lyric glen]

.close

[pearl pond]

Channel closed

Closed by @lyric glen

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[vapid sail]

I’m not sure how to do 32

I’m thinking ratio test

But some of the terms

I can’t cancel out

[plush bramble]

should be alternating series test

[vapid sail]

Oh

Ok

.close

[pearl pond]

Channel closed

Closed by @vapid sail

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[viscid mural]

This is probability and stats the standard normal distribution

I have the answer of .8726 but how would I know which z score do I subtract from

I have z score 0.9977 and 0.1251 and I subtract both of them

The answer would be the same but would it be negative or no

Nvm I got it

.close

[pearl pond]

Channel closed

Closed by @viscid mural

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[rain flame]

Helllo

[rain flame]

So I solved this problem my own way

Instead of a 4 that’s a 25 I noticed after I took the pic

So pretend that is rigut lol

I found the d= 4 and a1 is 9.

How would I find that in an actual format

If that makes sense ?

Like mathematically, not just guessing and being right

[regal herald]

well

do you know the general form of the nth term of an arithmetic sequence

[rain flame]

Wat do you mean?

[regal herald]

theres a formula for it, like $A_n=...$

[jolly parrot]

AℤØ

[rain flame]

The recursive formula or the explicit?

[regal herald]

explicit ig

[rain flame]

Yeah I think so

[regal herald]

what would it be

btw you got the wrong answer

or am i high edit: I was

actually one moment

youre fine, i cant divide properly apparently

[rain flame]

Rigut..

Lmao

So if I don’t have a1 OR d I can’t just solve for one or the other you know what I mean? Like I can’t get a1 alone cuz the d is also there so how would I do that

[regal herald]

this

whats the general form of the nth term

[rain flame]

an= 9 + (n-1)(4)

[pearl pond]

@rain flame Has your question been resolved?

[regal herald]

well yeah

but pretend you dont know a1 or d

its just an=a1+(n-1)d

you have two terms, so you have two equations to solve for two variables

seems reasonable, no?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[pearl pond]

@rich plinth Has your question been resolved?

[pearl pond]

@rich plinth Has your question been resolved?

[acoustic path]

it helps to reframe the question

[pearl pond]

@rich plinth Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[pearl pond]

Please don't occupy multiple help channels.

[hexed canyon]

.close

[pearl pond]

Channel closed

Closed by @hexed canyon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[visual canyon]

what is common factor and why does it happen?

[near echo]

they divided by -1

to make the coefficient of x^2 positive

this

turned into

[pearl pond]

@visual canyon Has your question been resolved?

Channel closed

Closed by @visual canyon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[digital smelt]

i understand converting polar to cartesian coordinates but i dont know why they added pi onto the pi/3, can anyone explain please?

[unborn abyss]

it's because the radius was converted from negative to positive

[digital smelt]

ohh

ok

so in all instances where you want the radius to be positive, you add pi to the other term?

[unborn abyss]

if you face northeast and walk 4 steps backwards, it's just like you were facing southwest and walked 4 steps forward

[digital smelt]

alright

.close

[pearl pond]

Channel closed

Closed by @digital smelt

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[silent bramble]

I dont get the solutions..

actually, the solutions make sense..

but

for 11, its linearly dependent because sin^2x and cos^2x make up to be 1

but I can set x=pi/2 for question10, and sinx +cosx =1...

im getting confused

because linearly dependent means you can make one of the vectors in the set from linear combinations of others in the set

[near echo]

what about 10 confuses you

[worldly glacier]

Hey Aff

How are you doing

[silent bramble]

im doing ok

[near echo]

the equation of dependence looks for coefficients a,b,c, such that
a * 1 + b * cos(x) + c * sin(x) = 0, for all x

the "for all x" is important

[worldly glacier]

Can you first write out a relation for these functions

[silent bramble]

well, I can still probably find other x that works for 10, I just change the coefficients?

[near echo]

the problem is not finding x

it is finding a, b, and c
that work for all x

so a,b, and c are fixed

and the left hand side has to be 0 always

the strategy here

is to assume a,b,c satisfy
a + b*cos(x) + c*sin(x) = 0

for all x

then plug in x = 0, and x = pi

[silent bramble]

ok

[near echo]

you'll see that a + b = 0, and a - b = 0, so a = b = 0

then you have c*sin(x) = 0, for all x, so what must c be?

[silent bramble]

so 0

[near echo]

yes

so since a,b,c have to be 0

[silent bramble]

ok

so I was sort of trying to do the same here

for this one

I set x=1 and 1/2

but in the solutions, they 'seperated' ln

I got a=-bln(2) and a= -cln(1/4)

[near echo]

you can note that
ln(2x) = ln(2) + ln(x)

and ln(x^2) = 2ln(x)

[silent bramble]

i see, because I thought then yoou could just say b=c=0

but it doesnt have to be the case

thank you!

@near echo and @worldly glacier

[worldly glacier]

Ofc lmk if you need anything

[pearl pond]

@silent bramble Has your question been resolved?

Channel closed

Closed by @silent bramble

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[tawdry wolf]

i have to find area enclosed by y = [2 sinx]

why is my answer different when i use integration vs doing by graph?

oh wait nvm i understand why

my bad, i confused Greatest integer function and mod function

.close

[pearl pond]

Channel closed

Closed by @tawdry wolf

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[median shadow]

Im supposed to find the slope of the tangent line of this function without using chain rule or difference quotient. I need urgent help

[near echo]

urgent

[signal atlas]

sqrtx is same as x^(1/2)

[pseudo oxide]

slope of the tangent line is the derivative of the derivative

do you mean that, or just derivative?

[near echo]

[pseudo oxide]

e.g. the tangent line to x^3 is 3x^2.

the slope of 3x^2 (the tangent to 3x^2, i'm assuming) is 6x

[near echo]

no

[median shadow]

i dont even know

[pseudo oxide]

yes

[median shadow]

i just know i have to find the derivative

[near echo]

3x^2 is not a tangent line

[pseudo oxide]

first derivative or second derivative

[median shadow]

the one where theres no x term

[pseudo oxide]

well not strictly speaking but a general version of a tangent line for x^3

[near echo]

a tangent line takes the form T_a(x) = f(a) + f'(a)(x-a)

[median shadow]

the answer for the derivative is apparently 9

[near echo]

the slope of which is f'(a), not f''(a)

[median shadow]

at first i tried to differentiate it inside the square root with the product rule

and it didnt work. i got 27

[pseudo oxide]

that... won't work

[median shadow]

i dont know what to do

[pseudo oxide]

$\sqrt{3x^3} = \sqrt 3 \cdot x^{1.5}$

[signal atlas]

Just use this and its power rule from there

After applying some algebra of course

[median shadow]

i tried that

and still failed it

[jolly parrot]

ren

[median shadow]

1/2(9x^2) ^(-1/2) is what i got

[median shadow]

and differentiate these separately?

3/2(x)^1/2

[pseudo oxide]

wait hang on @median shadow you said the answer was 9?

[median shadow]

yeah

[pseudo oxide]

tangent line at 3, 9 for sqrt (3x^3), correct?

[median shadow]

yeah

[pseudo oxide]

check again

can't possibly be the answer

[median shadow]

idk, thats what the answer key said

[near echo]

can you share the answer key

[median shadow]

the m term is 9

[near echo]

that is not a slope

[median shadow]

it asked for the equation but

[pseudo oxide]

agreed

[median shadow]

i only wanted the slope

so i can plug that into y =mx+b myself

[pseudo oxide]

what...?

[near echo]

notice the y has a coefficient which is not 1

example:
2y = 2x
what is the slope?

[median shadow]

ok basically i want the m value from the differentiation. then i plug it into y = mx+b to find the eq of the tangent line

[near echo]

hint: not 2

[pseudo oxide]

i've never seen this; my school didn't do this lmao

[median shadow]

2

lol wait

mb

[near echo]

did you miss my hint

[median shadow]

its 1

[near echo]

ok

do you see why the slope for your original question is not 9

[median shadow]

oh wait

OHH WAIT

I FORGOT ABOUT THAT

[pseudo oxide]

lol

this what i was saying

[median shadow]

i kept getting 4.5 but i was wondeirng

[pseudo oxide]

that's correct

if you diff sqrt 3 * x^1.5, you get 1.5x^0.5 * sqrt 3

when you plug in x = 3, you get 1.5 * (sqrt 3)^2 = 4.5

[median shadow]

wait a minute

[median shadow]

this

i ended up getting 1.5(x)^-1/2

[pseudo oxide]

no

[median shadow]

which ends up being 1.5/sqrt(x)

[pseudo oxide]

1.5 - 1 = 0.5

not -0.5

[median shadow]

i did a^1-n instead of a^n-1

so i guess thats why

anyway

now i got 1.5(x)^0.5

(4.5)^0.5

which is the wrong answer

[pseudo oxide]

no

you forgot the sqrt 3

;-;

1.5x^0.5 times sqrt 3

[median shadow]

i thought i was supposed to differentiate the sqroot 3

anywya i got 4.5 now...

To close off, I have a few questions @pseudo oxide

[pseudo oxide]

...

[median shadow]

Why did we not differentiate the sqroot 3?

thats about it

actually, dont worry about it

thanks for the help

[pseudo oxide]

np

wait no

WRONG PING

[tall ruin]

💀

[median shadow]

its a ghost ping now

[pseudo oxide]

mb mb

[tall ruin]

naww

[pseudo oxide]

sorry

[tall ruin]

im right here

np XD

[median shadow]

lol

i need some rest. its 1am

gn

[pseudo oxide]

@median shadow

because (c* f(x))' = c * f'(x)

gn

[median shadow]

nice

.close

[pearl pond]

Channel closed

Closed by @median shadow

Use .reopen if this was a mistake.

[pseudo oxide]

@median shadow (c is a constant, by the way)

[median shadow]

ohk cool. i'll make a note of that

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[vivid lark]

I need help with c

[vivid lark]

I know I need to calculate the complete area, but I don't know how to start

[stoic path]

,rccw

[pearl pond]

@vivid lark Has your question been resolved?

[pearl pond]

@vivid lark Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vivid lark]

I need help with c, can someone help me?

[vivid lark]

Idk how to start

[bold steppe]

you can start by plugging the given values in first

[vivid lark]

I have:
b3 = 27,7m
gamma = 57,2°
alpha = 90°
Also i calculated beta = 32,8°

Now I don't know how to calculate the area A

<@&286206848099549185>

I need this till 1 pm

I thought I could solve it using the law of sines, but it gives the wrong result

[pearl pond]

@vivid lark Has your question been resolved?

[pearl pond]

@vivid lark Has your question been resolved?

Channel closed

Closed by @vivid lark

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[blissful orbit]

at a party, each guest shook hands with every other guest exactly once. how many guests were there if there were a total of 300 handshakes

Is my solution correct?

[waxen talon]

What is the other solution you got

[blissful orbit]

-24

[waxen talon]

Seems correct

[blissful orbit]

I simply crossed out because it is invalid

[waxen talon]

Wait

[blissful orbit]

And I tried inputting 25 into the combination formula as n and got 600

300*

[waxen talon]

,w 25 choose 2

[jolly parrot]

Results provided by WolframAlpha

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

Requested by coldtee

[waxen talon]

Yeah

Seems correct

[blissful orbit]

woah

is that how you input the combination formula in Wolfram alpha?

[waxen talon]

I guess

,w \binom{25}{2}

[jolly parrot]

Results provided by WolframAlpha

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

Requested by coldtee

[waxen talon]

Works too

,w 25C2

[jolly parrot]

Results provided by WolframAlpha

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

Requested by coldtee

[pearl pond]

@blissful orbit Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[paper flume]

are you allowed to do an interchanging row manipulation as circled?

[paper flume]

i have look it up

and i cannot find an answer

[pearl pond]

@paper flume Has your question been resolved?

[paper flume]

<@&286206848099549185>

oh well

.close

[pearl pond]

Channel closed

Closed by @paper flume

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[vagrant raven]

i need help with this graphing equation for Alg 2

[vagrant raven]

<@&286206848099549185>

[lilac quartz]

actually there is cool down before you can ping helpers

[vagrant raven]

oh

[lilac quartz]

What have your tried?

[vagrant raven]

i only tried domain

i don’t know how to do the rest

[lilac quartz]

Set of all reals?

[vagrant raven]

all real numbers?

[lilac quartz]

Yes

[vagrant raven]

yes that’s what i put

[lilac quartz]

So for range, it’s the set of all possible outputs from the function

what do you think it should be ?

hint: look at the y axis and see if you are getting them as input of some number in x axis

[vagrant raven]

-1.4, 5.7?

[lilac quartz]

what’s smallest output you can expect from the function?

[vagrant raven]

(0,0)?

or (0.7,-.8)?

[lilac quartz]

y value is number

not a coordinate

can you get -10 as an output in from your function?

like is there ‘a’ such that f(a)=-10?. Look at the graph

notice, you cannot get a output smaller than -5.7

do you see that?

[vagrant raven]

yes

you mean the lowest minimum?

[lilac quartz]

yes, the global minimum of function

you cannot get y values below that

now what about the upper bound?

[vagrant raven]

what’s a upper bound? sorry some of these terms i’ve never heard of before

[lilac quartz]

do you get every real number greater than -5.7 as an output?

like can you expect y= 1000000?

[vagrant raven]

no

[lilac quartz]

why?

the graph actually goes above though it’s not depicted what matters is f(x)=2x^4+2x^3-4x^2.

[vagrant raven]

oh

i thought it wouldn’t because of the minimums

especially the lowest one

[lilac quartz]

essentially your range is ${y \in \mathbb{R}: y\geq -5.7}$

[jolly parrot]

.doc

[lilac quartz]

you can verify you will get every element above global minimum as your output thus they belong to range set

[vagrant raven]

how would you know for graph if every real number is greater or less than a output though?

[lilac quartz]

here, your outputs cannot be lesser than -5.7 right?

notice, i’m taking about the outputs, the values you get when you plug x

[vagrant raven]

so as long as it’s not bigger or smaller then the y coordinate, it determines if it’s greater or less than?

[pearl pond]

@vagrant raven Has your question been resolved?

[pearl pond]

@vagrant raven Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.