help-39

[sharp smelt]

Can't use that

[nimble osprey]

why not ?

[sharp smelt]

This is for a proof writing class, so I'll have to prove that first

[nimble osprey]

oh i see

[sharp smelt]

I don't know that there is even something called gcd at this point

I mean I do, but you get what I mean

now to prove $lcm(ka, kb) \leq klcm(a,b)$

[rustic gate]

you're being careless with what you're writing

we already proved that direction

[sharp smelt]

Now to prove $lcm(ka, kb) \geq k lcm(a,b)$

[jolly parrot]

Veni, vidi, perii

[rustic gate]

now it's right

this direction is the harder direction

you'll have to write out some equations possibly

[sharp smelt]

Yeah, sure feels like it

okay, so $\exists lcm(ka) \implies \exists p st p(ka) = lcm(ka,kb)$

we already know that $lcm(ka,kb) > lcm(a,b)$

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

wait

no

let qa = lcm(a,b)

and p(ka) =. lcm(ka, kb)

no

sorry

Can I have another hint

[rustic gate]

since $ka \mid \lcm(ka, kb)$, you can write $\lcm(ka, kb) = kpa$ to find that [ a \mid pa = \f {\lcm(ka, kb)} k ]

[sharp smelt]

I was thinking I could prove lcm(ka,kb) \geq lcm(a,b) first

[sharp smelt]

I don't follow

[rustic gate]

k divides lcm(ka, kb), so lcm(ka, kb)/k is an integer

[rustic gate]

maybe i should just keep it like this

a divides lcm(ka, kb)/k

[pearl pond]

@sharp smelt Has your question been resolved?

[sharp smelt]

I'm so confused

I'll try this again later

sorry

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

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.

[gleaming musk]

context of this conversation was started in another help channel but since it was someone else's channel, i think it is more appropirate to just open a separate one

[gleaming musk]

it is a bit of a vague and general question in regards of substitution and transformations of variables in calc

contexti s highschool scope

an exercise i went through a long time ago was to integrate from 0 to 2pi x dx using u = sinx

if you substituted it directly without checking for ranges, then u yield 0 which is evidently wrong

i can understand geometrically what is happening and then splitting it into separate integrals will work

but my teacher has said subs like this is invalid without checking conditions

so ig my question is kinda what makes a substitution valid? (what conditions)

[rough forge]

,, \int_{-2}^{-1} x : \dd x

[jolly parrot]

bacc

[rough forge]

Imagine I want to substitute

x = e^y

well that would fail

because e^y > 0

and this would be an invalid substitution

you cannot do this transformation

[gleaming musk]

sure, the domains and range doesnt match up

[gleaming musk]

but i dont understand what is inherently wrong in this subtitution

if i disregard the geometry

[rough forge]

,, \int_0^{2\pi} x : \dd x

[jolly parrot]

bacc

[rough forge]

this?

[gleaming musk]

yeah

[rough forge]

So you want to do sin(x) = u

x = arcsin(u)

[gleaming musk]

the problem is with the bounds where u yield 0 to 0

[rough forge]

yea

[gleaming musk]

so what makes this substitution invalid

[rough forge]

because of arcsine

the range of arcsine is between -pi and pi

[gleaming musk]

but thats a different sub then?

letting x = arcsin u
vs
u = sinx

[rough forge]

but with sin(x) = u you are saying essentially x = arcsin(u)

[gleaming musk]

it runs into this problem

if i let u = sinx then shouldnt it be fine

[rough forge]

for this you have to make sure that the bounds are within an interval where sine is bijective

[gleaming musk]

so invertability is also a condition?

[rough forge]

ok now how do rewrite the integrand

[rough forge]

if you wanna express x now in terms of you substitution

this assumes now additionally invertability

else the substitution is kinda useless

[gleaming musk]

oh

that actually clears a few things up

was never taught about conditions for substitutions

[rough forge]

i mean it's kinda natural

[rough forge]

.

,, \int_0^{\frac{\pi}{2}} x : \dd x

[jolly parrot]

bacc

[rough forge]

this should work

let's see

u = sin(x) then du/dx = cos(x) so dx = du/cos(x)

[gleaming musk]

i might be misunderstanding but i've been told before that change of variables in integration doesn't even require monotonicity or invertability before

sry im just still a bit confused

my current textbook print for highschool math does say that invertability is not a condition

[rough forge]

there is a little distinction i believe between substitution by introducing a new variable or substituting a function

yes you are right

we should be mindful about our substitutions

[rough forge]

that's strange

If I recall a few days ago

I had this integral

[ \int_0^1 \frac{1}{\abs{\ln x}^p} : \dd x ]

[jolly parrot]

bacc

[rough forge]

And I substituted ln(x) = t

now the problem is if I differentiate both sides

1/x = dt/dx so dx = x dt

I need to express x also in terms of t

so I have to use the fact that ln(x) is invertible

aka e^t

iit's not necessarily always a condition but sure not negligible

sometimes you just need a transformations that simplifies the integral where you don't require it to be invertible or some

[gleaming musk]

to quote the notes verbatim just so im not accidentally losing any technicality in my wording

"U-substitution or change in variable in the process of integration does not demand the function to be monotone, nor invertable or injective(injectivity is a concept beyond this course)"

[rough forge]

I think it's kinda misleading if you stick by this when you do undergrad math

because high school calculus doesn't do really crazy stuff

[gleaming musk]

mhm ig i will probabyl find out about it when i start math in uni

yeah, my teacher has said the same thing

[rough forge]

like everythings works out and you still have simple functions

[gleaming musk]

since we rarely get questions where this becomes a problem

[rough forge]

i have to be honest

[gleaming musk]

the textbook's explanation for the earlier problem was to define it as a piece wise

[rough forge]

i never really thought about it deeply

[gleaming musk]

so ur integration has to be treated as piece wise

[rough forge]

it just felt naturally right to do

[rough forge]

hmm ok

[rough forge]

you mean 0 to 2pi integral of x?

[gleaming musk]

yeah supposedly

it is kinda a bummer that the authors extra notes are super short

they dont really present any working out

or any further writings to what they meant by that

saying that it will be piecewise so the integration has to be treated as such as well

[rough forge]

but then you still have to consider a different substitution for each piece

for example from pi/2 to pi consider u = sin(x-pi/2)

[gleaming musk]

thats essentially what my teacher suggested in his working out

he broke it down into the intervals where it is monotone

[rough forge]

otherwise it doesnt workout

[rough forge]

yea

very ugly thing to do btw

substitutions should be seen as a tool to simplify things

not make matters worse

[gleaming musk]

yeah

probably wont worry baout this for now since it has only cooked me twice out of the thousands of questions in textbooks and exam papers

its quite a niche topic and detail that is rarely examined here so im not rly worried about it

[rough forge]

I honestly think I cannot provide a very good answer to this, was just sharing my experience, but you could ask this in #calculus again

[gleaming musk]

mhm maybe, i asked a similar question a few months ago to my teacher but i think i dont know enough math to really understand it

[rough forge]

everytime i think about things i been doing for years and they work and then suddenly you actually think about them

you realize you dont know actually what you are doing

which kinda sucks now haha

[gleaming musk]

i feel like that in my math exams

i have no idea what is happening sometimes even after getting the right solution

thx for ur time tho

[rough forge]

I mean what I did previously

u = y/x

[gleaming musk]

yeh?

[rough forge]

you were asking me why it's valid

[gleaming musk]

yep

[rough forge]

and what i thought was

why wouldn't it be valid

well i cannot divide by x

if x=0

but that would be naturally the case before the sub

what possibly could make this invalid

why would this then also make sense

y = ln(x)/x

Essentially we are setting a definition

We let that complicated thing be a simple thing

we encode it

let that y/x nuance be u

it's the same thing

and in math if i think about it

we can always introduce a new variable

which is not the same as substituting a function

is there even such thing as explicit and implicit substitution

explicit u = y/x
implicit e.g. sin(u) = y/x

[gleaming musk]

i mean besides naming ig they kinda the same>

[rough forge]

so that would make it by definition valid

if we say u=y/x is the same

but there are of course limitations

u is not really limited

as opposed to e^u

y/x > 0 then

same with sqrt(u)

u=y/x would be for all y and x

except x=0

but that was before the sub anyway the case

y/x yields basically any number

[gleaming musk]

yeah

yields all except for when x= 0 so it makes sense

[rough forge]

so saying that's simply u which is basically linear should not cause any restrictions

[gleaming musk]

that makes a lot more sense

im just trying to fix what my teacher calls "notation abusing" and defintion abusing

[rough forge]

hmm

[gleaming musk]

im a serial offender of this lol

this was actually fairly productive, i think i understood bulk of what makes the subs valid

[rough forge]

i think the high school hint or whatever that was shouldnt be taken at heart

[gleaming musk]

probably

the textbooks aren't really that well written

when it comes to the details

it omits a lot of things tbf

[rough forge]

it was actually a good question you asked

and you deserve better clarity to this

only thing i can transmit is that one should be mindful of their substitutions

[gleaming musk]

hopefully uni math will be more clarifying than highschool

a lot of things i do in my working out is at best 'dodgy' but the teachers says its fine

[rough forge]

also what i wanted to mention previously

y = x would have been also a substitution

but now guess

y may also be other things

may be other solutions too, to this differential equation

so that would be a rather insuffcient substitution

where as with

u = y/x

we still keep y abstract basically

like it still varies

because y is not set

we just encoded that expression

[gleaming musk]

that analogy makes sense as well

[rough forge]

you are making me crazy haha

asking myself, why can we substitute things in the first place

why is that legal

😂

[gleaming musk]

this is going to boil down to counting fingers at some point lol

[rough forge]

exactly

[gleaming musk]

i mostly just stopped questioning after starting this year (final year of highschool)

abusing notation for differentials and probably dodgy algebra that works somehow

[rough forge]

ohh thats what you mean

dy/dx treating as a fraction thing

[gleaming musk]

yeah

[rough forge]

well i wouldnt call that necessarily notation abuse

leibnitz notation to be precise

i think there are also proofs as to why it's possible to treat them as such

[gleaming musk]

my teacher had a really long rant about why abusing it is strictly ok in first derivatives only

it was the whole thing about dy/dx versus (d/dx) y

[rough forge]

yea i never used that with second derivative

but like

[gleaming musk]

treating dy as one object or d/dx as an operator of sort

[rough forge]

that begs the question whats a differntial in the first place

[gleaming musk]

i dont really understand the difference but he did mention about just dy by itself

like dy is just change in y

dy/dx is with respect

with respect or not it is still fine

different notations tho supposedly

[rough forge]

dy/dx change in y with respect to the change in x

[gleaming musk]

tbh the worst offender of this is for complex number questions where i just pretend the complex polynomials can be diff'd as normal

[rough forge]

haha i never really encountered that

at least not yet

[gleaming musk]

anyhow, i need to go back to doing practise papers

thx for ur time tho

it was quite helpful to understand about conditions

your analogy about encoding actually makes it much easier to understand

gonna close this channel since idrh any questions for now

🙏

.close

[pearl pond]

Channel closed

Closed by @gleaming musk

Use .reopen if this was a mistake.

[plucky python]

no yeah complex polynomials should just differentiate as normal

[gleaming musk]

@plucky python isnt it purely coincidental that it works just as usual

at least thats what we have been told

i haven't learnt why it works

[plucky python]

ah fair enough

[gleaming musk]

this is a question from a practise paper

[plucky python]

yeah if u haven't learnt it yet then it is a bit of an abuse of notation

[gleaming musk]

part iii A)

my solution was to log it

and diff

[plucky python]

fairs

[gleaming musk]

idek if u can log complex

[rough forge]

LY might give a better answer

to your doubt

[plucky python]

you *can

but in school they won't really care too much about rigour

[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.

[brittle hearth]

Can I get help?

[brittle hearth]

Oh alr

I will send an attachment

The question is

I need to find four numbers so every next number is -4

So its x,x-4,x-8,x-12

And multiplication of first and second number have to be 384 bigger than multiplication of 3rd and 4th

So its

X*(X-4)=[(x-8)*(x-12)]-384

I think that I did everything right but when i checkdd if everything matches it didnt

[lost flax]

288/16 is 18

[brittle hearth]

So im stupid?

And i did it corrctly ?

[finite geode]

um also 0=-16x-288

so 16x=-288

not 16x = 288

[brittle hearth]

But if i multiply both sides by (-1) it doesnt work?

Because i have 0=-16x-288

[finite geode]

well then you get 0 = -1(-16x - 288)
0 = 16x + 288

[brittle hearth]

Yeah

[finite geode]

now subtract both by 16x

[brittle hearth]

Oh

Yeah rookie mistake

[finite geode]

ig yeha

[brittle hearth]

So whats x equal to

It still dont work with 18

[finite geode]

well it seems x = -18

[brittle hearth]

(-18)*(-14)

[finite geode]

um

-18 - 4 = -22

-22 * -18 = 396

the next two numbers are -26 and -30

-26*-30 = 780

780-396 = 384

[brittle hearth]

Wait

So if x is -18

Next is -22

But 1st and 2nd number should be bigger when multiplied

[finite geode]

they are

-18 is bigger than -26

[brittle hearth]

But multiplication should be bigger

[finite geode]

well then

i have no clue 💀

[brittle hearth]

Oh.

[finite geode]

ill try again

[brittle hearth]

I will try to translate the question more accurrately

There are four numbers such that each subsequent one is four less than the previous one. The product of the first and second numbers is 384 greater than the product of the third and fourth numbers. Calculate these numbers and their sum. Write down the appropriate calculations and the answer.

@finite geode

[finite geode]

oh i see

it says 384 greater

now if the product of the first two is greater

that means you should add 384 to the product of the 3rd and 4th

not subtract

subtracting means it is 384 less than

[brittle hearth]

Mb

[finite geode]

so in the beginning add 384 to (x-8)(x-12)

[brittle hearth]

OHHH

Ye

I will try it now alone

[finite geode]

sure

[brittle hearth]

How do i close this ?

This convo so others can ask?

[finite geode]

.close

[brittle hearth]

.close

[pearl pond]

Channel closed

Closed by @brittle hearth

Use .reopen if this was a mistake.

[brittle hearth]

.reopen

[pearl pond]

✅

[brittle hearth]

Need one more thing

To other question

Bottom number is 20 and left is 10

Find BD and DC

I would prefer a hint or maybe some usefuk info rather than an answer

[supple knoll]

BD=10root3
CD=10(root5-root3)

[brittle hearth]

Could you explain it please?

It doesnt have to be long

Because i see you typing a lot haha

[finite geode]

well you know the radius is 20

and what is AB?

[brittle hearth]

Also

20

[finite geode]

oh AB =20?

i thought raidus

nvmnvm

[brittle hearth]

Yeah

So whats next

[finite geode]

well then you can apply pythagroas theorem

for BC

[brittle hearth]

And its root500 right?

[finite geode]

yeah

[brittle hearth]

Im glad because i didnt really learn pythagoras theorem like that lol

[supple knoll]

In the large triangle, let’s denote the sides as follows: side lengths are AB = 10 and AC = 20, with angle B being arcsin(1/2) , which is 30 degree.

To find half of BD, we can use the cosine of angle B:

Half of BD = 10 cos(30)= 10*sqrt(3)/2

Thus, the full length of BD is 10*sqrt(3)

Since triangle ACB is a right triangle, we apply the Pythagorean theorem to find BC:

BC = sqrt(10^2 + 20^2)= 10*sqrt(5)

to find CD:
CD = BC - BD = 10sqrt(5)-10sqrt(3)

[supple knoll]

Just checking my English

[brittle hearth]

;))

Oh so you need to know tryghonometric functions?

I think thats what its called

[supple knoll]

Might have other ways

But I can’t see one yet

[brittle hearth]

Yeah ig, the competition im preparing for doesnt have questions with these from what i know

I can check

[finite geode]

you could also just use properties of similar triangles afaik

[brittle hearth]

How do i do that?

[supple knoll]

Actually you don’t

Because ABC and origin,B,half of BD are similar triangle

You only need Pythagorean

[brittle hearth]

So i have root500

Whats next

CB=root500

To be exact

[supple knoll]

CB/AB=origin,B/half of BD,B

[brittle hearth]

Whats origin,B

[supple knoll]

Length of origin to B

[finite geode]

what was cd again?

[brittle hearth]

Thats the question

[finite geode]

no i mean like what did js say it was

[supple knoll]

10(sqrt 5-sqrt3)

[brittle hearth]

I will come back to this convo when i have more time, thanks !!

.close

[pearl pond]

Channel closed

Closed by @brittle hearth

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.

[quasi swallow]

number of 4 digit numbers with 5 and 9 in it

[spiral pivot]

!show

[pearl pond]

Show your work, and if possible, explain where you are stuck.

[quasi swallow]

Its just subaprt of a problem but my brain is not

i thought like maybe first arrange the 2 fixed numbers like 4C2× 2!

And for the remaining 2 spaces there will be 10 possible numbers for each(0-9)

so 10²

[spiral pivot]

Good start

Careful though

You'll double count

(and also not sure if 0000 counts as a 4 digit number)

[quasi swallow]

OH RIGHT

I took none of that into consideration

Dumb me

So i have to substract those cases right

[spiral pivot]

Yes or avoid them entirely and construct those cases separately

[chrome berry]

help please

[spiral pivot]

! occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[quasi swallow]

Okay i first want to deal with the ones which start with 0 at first

Seems easier

So that 10 possibilities for the next 3 numbers

10³ numbers get yeeted?

No wait

sorrt

Only 10 get yeeted

Sorry sorry

[spiral pivot]

Is 0010 a 3 digit number?

[quasi swallow]

no

[spiral pivot]

Ah my bad

Dumb question

Ok we yeet all values from 0000 to 0999

[quasi swallow]

yes but 2 numbers are already 5 and 9

So 10 numbers are yeeted

am i right

[spiral pivot]

So there are two possibilities, either 5 and 9 are in the first digit or no

We yeet 0x59, 0x95, 05x9, 09x5, 059x, 095x. But we need to unyeet a few due to double counting

[quasi swallow]

Oh wait yeah

okay we have 3 spaces aftet fixing 0

and let us first arrange the 2 numbers 5,9 and self arrange them

so 3C2× 2!

and the last space will have 10 possibilities all of which have to be yeeted

So 3C2×2! × 10 rejected?

[spiral pivot]

Yes

[quasi swallow]

60 rejected

[spiral pivot]

Then

We have cases where all 3 digits were either 559 or 599 permuted.

Which we have double counted, so we add them back in

[quasi swallow]

Double counting is allowed tho

Sorry mb for not specidying

repetitions are allowed

[spiral pivot]

As in

You threw out 0x59 and 05x9

You said there are 20 of these

But you counted 0559 twice

So you only threw out 19

[quasi swallow]

OH

damn 😭

This problem didnt look this annoying at first look

Okay i have to add those back in

[acoustic path]

(there exists easy solution)

[quasi swallow]

There does?

can u enlighten me :prayge:

[spiral pivot]

You count the compliment

[acoustic path]

principle of inclusion-exclusion

(number of ways that have a 5 or a 9) - (number of ways that have a 5) - (number of ways that have a 9) + (number of ways that have a 5 and a 9) = 0

[spiral pivot]

Or that!

[quasi swallow]

OHH

Right right

Thats a cool way to do it as well

Thanks a lot both of you i hopefully can do it now

.close

[pearl pond]

Channel closed

Closed by @quasi swallow

Use .reopen if this was a mistake.

[acoustic path]

it takes 2 min max

i.e. (number of ways that have a 5) = (number of ways that have a 9)

so there is very little computation u need to do

[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.

[sonic sigil]

halp

[pseudo oxide]

...?

[plush bramble]

[pseudo oxide]

what is your question

[sonic sigil]

Would f(1) be 1

[pseudo oxide]

no...

[sonic sigil]

ok, then what would it be

[pseudo oxide]

why would it be 1?

[sonic sigil]

let me explain

[pseudo oxide]

okay

[sonic sigil]

wait so

-1

[hot stone]

Piecewise functions say:

When x is taking on these values, the function acts like this

To evaluate a piecewise function the most important thing is to figure out which part of the function you're in

This function has 2 distinct regions

The x =/= 1 region

And

The x = 1 region

If you are evaluating f(1) which of those regions will you use?

[sonic sigil]

the 1st

[pseudo oxide]

that

[hot stone]

So is 1 in the x =/= 1 zone

[sonic sigil]

x =/= 1 region

[pseudo oxide]

isn't much of an explanation

[hot stone]

Or is 1 in the x = 1 zone

[sonic sigil]

yeah but idk why it says its the wrong answer on my part

[hot stone]

Does 1 not equal 1?

[sonic sigil]

yeah

[pseudo oxide]

isn't really an explanation
profoundannihilation

[sonic sigil]

thats what im confused on

it all makes sense, the math

[hot stone]

Let's rephrase that question

If i tell you a number does NOT equal something

[sonic sigil]

however it says that 1 is not the answer

I've tried

[hot stone]

Then 1 does NOT equal something that is NOT equal to 1

so if you evaluate f(1)

You can't plug it into the top function

Because that is the function for any number other than 1

Use that function only when x =/= 1

So when x = 1 you can't use it

When x = 1 you switch to the other region

The other region is specifically when x = 1 use that value

[sonic sigil]

ok so it's basically the opposite of what I thought

[hot stone]

I suppose so

[sonic sigil]

so =/= is not equal to

?

[hot stone]

The conditions on the right are telling you which x values correlate with each part of the piecewise

[hot stone]

Yes

Exactly

[sonic sigil]

so how would I list that as an answer

[hot stone]

Ok so again the first question is

Which region are you in

[sonic sigil]

again

[hot stone]

either the

x =/= 1

[sonic sigil]

the the first

[hot stone]

Or the x = 1

[sonic sigil]

we are solving for f(1)

[hot stone]

If x literally is equal to 1 as it is in f(1)

[hot stone]

Then you must be in this region

[sonic sigil]

okk

[hot stone]

Sooo

[sonic sigil]

ye

[hot stone]

What does f do

when x = 1

When you are in the x = 1 zone, what does f act like

[sonic sigil]

u have to plug f(1) into the function

[hot stone]

Yes but the right part

[sonic sigil]

sorry i have a question

[hot stone]

Go ahead

[sonic sigil]

sry nvm I figured

so the answer is -2

[hot stone]

Yesss

[hot stone]

Perfect

[pearl pond]

@sonic sigil Has your question been resolved?

[sonic sigil]

I need more help

would it be (1/3X +4)

[midnight haven]

huh

[pearl pond]

@sonic sigil 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.

[mighty basalt]

Vx = 5 + (0.625(2.15)^2 - 0.625(1.15)^2) = 7.06

That's the next step right?

[oak quiver]

assuming intial position is 0

[mighty basalt]

It's not

[oak quiver]

what is it?

[mighty basalt]

6

[fossil birch]

add 6

[mighty basalt]

I haven't integrated yet

t1 = 1.15 t2= 2.15 x1 = 6

[oak quiver]

i think you forgot a 1/2

alpha * t^2 / 2

[mighty basalt]

For the 0.625 is half of 1.25

[oak quiver]

can you like show step by step calc

instead of directly x

show v too

[mighty basalt]

Not sure what you're asking

[oak quiver]

dv / dt = alpha * t
v = f(t)
dx / dt = f(x)
x = g(t)

[mighty basalt]

That's my paper for the first part

[mighty basalt]

This is V

[oak quiver]

yeah this

[oak quiver]

if t1 and t2 are this

[mighty basalt]

Yes

[oak quiver]

then you havent taken x1 = 6

the limits on x are wrong

should be 6 to x

[mighty basalt]

Yeah, that's just how I wrote it for now

I'm focused on the equation on the right of X atm

[oak quiver]

i think that is correct

no wait

bro 1 suggestion

[mighty basalt]

I know how to better ask I think 1 sec

[oak quiver]

instead of writing t2 write t

now t1 is const

so it will be ax t1^2 * t`

t` = t2 - t1

similarly it should be vi*t`

[mighty basalt]

That's dt at the end

[oak quiver]

one thing

if you have f(x)

and you wanna find f`(x) at x = 5

you find f`(x) then put x = 5

not x =5 in f(x) then find f`(x)

similarly dont put values of t2

let it stay as t

cos it is the only variably

[mighty basalt]

I'm lost, youre focusing on my variable usage, I'm just unsure how to integrate something that's using a previous integration in the initial equation

Because acceleration isn't constant

[oak quiver]

gimme a min

hope you understand this

i didnt put the values of alpha, t1 and x1

[mighty basalt]

I think so but I gotta drive so I'll look at it again in a second

[oak quiver]

drive?

[mighty basalt]

Only thing I can see right away is I do have the a/2

It's 1.25/2 = 0.625

[mighty basalt]

My car

[oak quiver]

im helping a person older than me lol

im 16

ping me if you dont understand my soln

[mighty basalt]

I'm a decade older

[mighty basalt]

Lmao

Just entered college

[oak quiver]

damn

[pearl pond]

@mighty basalt Has your question been resolved?

[mighty basalt]

That's what my teacher did. Basically added the 5 to the initial integration

[mighty basalt]

I was trying to keep it like this which I guess can be done but is more complicated

@oak quiver

[oak quiver]

ohh

is initial v 0?

[mighty basalt]

No

It's 5

[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.

[silent compass]

Guys can i ask

[silent compass]

How can we study a function where we have

A partie entière im not sure what they call it in english

For example we have f(x) = E(x)÷x

we're aiming for to study it for continuation

Floor function

.close

[pearl pond]

Channel closed

Closed by @silent compass

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.

[urban horizon]

Hey, can someone help me with this? I'm trying with the Shell Method, but I'm having a difficult time integrating.

[pearl pond]

Show your work, and if possible, explain where you are stuck.

[urban horizon]

Uh

I got to 2pi int 0->1 [(1-x)(xsqrt(1-x^2))]dx

[pearl pond]

@urban horizon Has your question been resolved?

[urban horizon]

<@&286206848099549185>

please

):

[plush bramble]

what are you having trouble with

[urban horizon]

The integration

Is it integration by parts? or something?

It's probably trig sub

But i don't know how to get to it

[plush bramble]

,w int (1-x) * x * sqrt(1-x^2)

[jolly parrot]

Results provided by WolframAlpha

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

Requested by rie.mann

[plush bramble]

yea looks like parts a couple times

[urban horizon]

what about the arcsin?

[plush bramble]

do the parts and it'll come out

[urban horizon]

ugh

why is this problem in the trig sub hmwk if it's just int by parts

[plush bramble]

the arcsin will come after a trig sub

[urban horizon]

oh

how fun

alrighty then

thanks

.close

[pearl pond]

Channel closed

Closed by @urban horizon

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.

[wispy talon]

I was able to answer the first question

[neon blaze]

Had you used chatgpt

[wispy talon]

I used it to translate from french to english

[wispy talon]

the exercise

Whereas the second I was able to find the answer

[neon blaze]

Okay as try that to see if can help yourself out as some of my problems show that

[wispy talon]

but I just don't know how formulate my answer

[wispy talon]

Sorry i didn't understand

[neon blaze]

Meant like try to use chatgpt to help answere the question as I used it to help give me some answers for my probelsm

[wispy talon]

Well it's not dependable

the way it formulates it's answer, even the logic behind can be sometimes flawed

[neon blaze]

Makes sense for that then

[wispy talon]

.close

[pearl pond]

Channel closed

Closed by @wispy talon

Use .reopen if this was a mistake.

[wispy talon]

.reopen

[pearl pond]

✅

[wispy talon]

my instructors have very high demands and standards regarding the formulation of the answer and the logic behind it

<@&286206848099549185>

[tired violet]

Never ever ever recommend gpt for math questions you are seriously going to lead people astray with that

If you can’t help don’t reply

[neon blaze]

I been using it to help myself out and had math people overlook it

[tired violet]

So what? If you need to ask math people to look it over then you can’t trust it first off, and second off I’ve seen countless examples where Gpt makes up some serious bs that sounds correct to someone who is ill experienced

Trust me gpt is not your friend for math problems

[limber ravine]

You first need to check if it's reflexive, i.e. does it hold that (x, y)R(x, y)?

[tired violet]

He already proved the equivalence relation part

Just needs to find the classes

[limber ravine]

Oh, lol, sorry.

[wispy talon]

yes it is

np

[limber ravine]

I read it as unable. My bad.

Have you found the equivalence class [(0, 0)]?

[limber ravine]

Okay, Jesus, you did. I should learn to read.

[wispy talon]

it's null right?

[tired violet]

No

It’s the singleton {(0,0)}

[wispy talon]

oww so it can be itself?

[limber ravine]

The element x is always an element of the equivalence class [x].

[wispy talon]

Oww okay

thanks for the information

[tired violet]

Think about it like this if you plug in (0,0) to x^2+y^2 what value do you get?

0 right

[wispy talon]

yeah

[tired violet]

And since they’re both positive then you can only have 0 if both x and y are 0

So there’s only pair that can be in equivalence class

I think a. Similar line of reasoning works for the others

For example if you have (1,1) then the value of that in the function is 2

What other pairs allow you to reach 2

[wispy talon]

i got (2^0.5 , 0), (0 , 2^0.5)

[tired violet]

There’s more than that

[wispy talon]

we got also (1 , 1)

[tired violet]

You could also have -1,1

I think the best way to think is geometrically

What shape does that function represent

On a graph

[limber ravine]

Hint: you need to use setbuilder-notation or a geometric argument to describe it.

[wispy talon]

Owww yes thats true

[tired violet]

You can recognize it?

[wispy talon]

sorry No idea

[tired violet]

A circle

Recall equation for circle is x^2 + y^2 = r^2

[wispy talon]

yes

[tired violet]

So essentially the equivalence class of 1,1 is a circle with radius 2

Does that make sense to you why?

[wispy talon]

yes

[tired violet]

Great!

[wispy talon]

thanks man

i'm so impressed by you

[tired violet]

Do you think you could use a similar reasoning for (1,2)

[wispy talon]

so it has a radius of 3 right?

[limber ravine]

Remember that the elements of the equivalence class [(1, 1)] are all the elements (x, y) that satiesfies (1, 1)R(x, y) - this is the definitions of an equivalence class. And since you know that (1, 1)R(x, y) iff 2 = 1² + 1² = x² + y², you need to find all (x, y) that satisfies x² + y² = 2.

[tired violet]

Sorry earlier I said radius of 2 I shoulda said root 2

[wispy talon]

np

[tired violet]

Mikkel gave you a really good argument that you should be able to provide to your prof

[wispy talon]

So i guess i need to think like this

[tired violet]

Yeah exactly

[wispy talon]

Thank you so much for your help

[tired violet]

The intuition is geometric the proof is algebraic

As is usual in mathematics

[wispy talon]

I hope one day i can attain your level

for real it's so amazing

[tired violet]

Hehe well assuming you’re in first year then I have a head start on you

Don’t fret, you’ll get there

[wispy talon]

I hope so

[limber ravine]

For a rigorous approach, yes. But a geometric thought process is okie dokie when it comes to intuition.

[wispy talon]

Thank you man

.close

[pearl pond]

Channel closed

Closed by @wispy talon

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.

[elder knoll]

can someone help

[elder knoll]

so essentially i've been wondering why the statement that "if a function is differentiable at point a, then its derivative function must be continuous at point a" is not true

[tired violet]

The most common counter example is the function f(x) = |x|

It does have a derivative which is the sgn function or f(x) = x/|x|

This function is discontinuous at 0

Since it is undefined there

[limber ravine]

That function is not differentiable on all of ℝ.

[tired violet]

Ahh yeah you’re right I think I got the implication backwards

Womp
Womp to me I guess haha

[acoustic path]

https://en.wikipedia.org/wiki/Smoothness#Example:_Differentiable_But_Not_Continuously_Differentiable_(not_C1)

[pearl pond]

@elder knoll Has your question been resolved?

[elder knoll]

so why is it that we consider the function as not continuous simply because it continuously oscillates as it approaches 0? (note: i understand that you would not be able to find the limit as it approaches 0)

oh wait is it because we cant find the derivative at that point because we cant use

since the limit doesn't exist?

<@&286206848099549185>

[elder knoll]

anyways also i think you missed a point in my question

if a function is differentiable at point a, then its derivative function must be continuous at point a

the wikipedia page says a function that is differentiable doesnt have to be continuously differentiable. but the if its differentiable at a point, wouldnt the derivative function have to be continuous at that point specifically, not the entire derivative funciton?

[elder knoll]

he's incorrect btw, an abs. val function is differentiable everywhere but at that vertex point

[pearl pond]

@elder knoll 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.

[rare edge]

And for the second formula is it

CaCO_3

[plush bramble]

sir this is a math server

#old-network for chem server

[plucky python]

yeah

[plush bramble]

https://discord.gg/eexdsFw

[versed mica]

he’s already in it

he just doesn’t ask there

[rare edge]

Are the other ones correct

[plucky python]

yeah

[rare edge]

And the last one

I think that’s Lithium Acetate

How would that formula be written tho

[plush bramble]

i see. he just has LY on demand

[plucky python]

what does it say?

[rare edge]

Ok I’m in

[rare edge]

The name?

For the last one

I think

[plucky python]

as in u've covered what it says at the end

[rare edge]

But idk how to find the formula

[plush bramble]

take your conversation there, thanks

[rare edge]

Yea

[rare edge]

Stop being subjectist

[plush bramble]

@plucky python join too so jj can get help from you

[rare edge]

Ignore Rine

[versed mica]

💀

[rare edge]

He’s mad I’m smarter

[versed mica]

something like that

[plush bramble]

<@&268886789983436800> my feelings are so hurt

[rare edge]

Stop attacking me

I feel targeted

[plucky python]

i mean, you did post a chemistry question to the maths discord server

[rare edge]

Don’t take his side

[plucky python]

expect to get memed

[rare edge]

He’s not letting you hit

@lilac jackal ban them

[lilac jackal]

@rare edge please go to the chem server

[rare edge]

Hypothetically what if I don’t

[plucky python]

anyway if it says C2H3O2- underneath that, then yeah ur correct for both

[rare edge]

That’s the formula for Lithium Acetate?

[lilac jackal]

i will mute you and close the channel. thats no hypothetical

[rare edge]

Ngl ur badass

Can I get mod

[lilac jackal]

.close

[pearl pond]

Channel closed

Closed by @lilac jackal

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.

[lethal vigil]

How would I begin solving this?

[midnight haven]

1. define the curve of intersection
2. line integral

[lethal vigil]

how would I define the curve?

[midnight haven]

hmm

parameterization?

[lethal vigil]

Would that equation be the equation of the purple area?

[midnight haven]

it should be a line, no?

"curve of intersection"

[lethal vigil]

But if a cylinder is intersected by a plane, wouldn't we have a slice of the cylinder?

[midnight haven]

we would have a curve along the surface of the intersected plane and cylinder

[lethal vigil]

so would it just be the purple curve I drew without the shaded part?

[midnight haven]

yeah

[lethal vigil]

ah I see

and then we would find its equation like you mentioned earlier

[midnight haven]

Define $x$ as $t$ so, $y = \frac{t^2}{2}$

[jolly parrot]

icannotdoanymorecauchy

[midnight haven]

yes

[lethal vigil]

so z = (t^3)/3?

[midnight haven]

$z = \frac{xy}{3} = \frac{t(t^2)}{2 \cdot 3} = \frac{t^3}{6}$

[jolly parrot]

icannotdoanymorecauchy

[lethal vigil]

do we now say S(t) = (t^3)/6

and then solve for t in order to reparameterize?

[midnight haven]

The curve is there $<t, \frac{t^2}{2}, \frac{t^3}{6}>$, no?

[jolly parrot]

icannotdoanymorecauchy

[lethal vigil]

yup

[midnight haven]

did u take line integral?

[lethal vigil]

would we integrate from 0 to 6?

I'm doing that

Did I mes up somewhere or is the magnitude actually this nasty?

[midnight haven]

,w integral from 0 to 6 of \sqrt{1+(2x) + x^2/2} dx

[jolly parrot]

Results provided by WolframAlpha

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

Requested by icannotdoanymorecauchy

[lethal vigil]

Can you specify where I went wrong here

[midnight haven]

its the length of the curve

not the magnitude from the origin to the point

[lethal vigil]

you didn't reparametarize right?

[midnight haven]

this is a result of parameterization?

[lethal vigil]

so this is r(t) and not r(S)?

[midnight haven]

yes?

[lethal vigil]

I was taught to reparametize like this

to first let z = S(t), then solve for t and then instead of having r(t), I change the input variable to S

[midnight haven]

i see

once u reparameterize it

u still have to take the line integral

[lethal vigil]

this is what I got

I don't know how to further simplify the magnitude

[midnight haven]

$\int_{t_0}^{t} \sqrt{\frac{dx}{dt}^2 + \frac{dy}{dt}^2 + \frac{dz}{dt}^2} dt$

try this

[jolly parrot]

icannotdoanymorecauchy

[midnight haven]

try checking this out

https://youtu.be/GbYKsP87cr8?si=D2F1G04YMJAA4vSn

the first one is very similar to ours

[lethal vigil]

this guy didn't reparameterize

I don't think we need to reparameterize either

[lethal vigil]

Is this your final answer?

The book says the answer is 42

[midnight haven]

hmm

interesting

,w integrate from 0 to 6 \sqrt{1 + x^2 + (x^2/2)^2 }dx

[jolly parrot]

Results provided by WolframAlpha

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

Requested by icannotdoanymorecauchy

[midnight haven]

@lethal vigil

i differentiate wrong dawg

[lethal vigil]

ah that's where we went wrong

xd

[lethal vigil]

np np

it happens

thanks for your help though!

.close

[pearl pond]

Channel closed

Closed by @lethal vigil

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.

[coral nova]

can someone help me find the surface area of this shape

[pure rapids]

s.a. is all the sides added up

so the two rectangles and the two circle segments

[coral nova]

but thats not a circle segment because it the 20 cm is not the diameter,

i dont know how to find the diameter of rhe semicircle

[pure rapids]

hmm did you learn sine rule

[coral nova]

ye

[pure rapids]

okay so the blob thing is a isoceles triangle and a semicircle attached right

[coral nova]

ye

[pure rapids]

then sine rule

let the diameter of the semicircle = d

d/sin 40 = 20 / sin ((180-40)/2)

if you have calculator its not hard to solve for d

[coral nova]

ohhhhh

thx

wait

but the diameter is not 20?

20 is the hypotenuse of the isselese triange

[pure rapids]

yes

connect the diameter

we have the triangle that we're gonna use sine rule on

[coral nova]

oh

👍

[pure rapids]

have fun

[coral nova]

thx

wait

i dont think that works

shouldn't it be : sin(40/2)= d/2/20= sin(20)=d/40

wait no

i dont think that works either

[pearl pond]

@coral nova Has your question been resolved?

[coral nova]

.close

[pearl pond]

Channel closed

Closed by @coral nova

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.

[neon rover]

prove using mathematical induction: 4^3 + 8^3 + 12^3 +... + (4n)^3 = 16n^2 (n+1)^2

[acoustic path]

any progress so far?

[neon rover]

i am stuck after i do the substitution for k+1
16k^2 (k+1) + (4k+4)^3 =16(k+1)^2 (k+2)^2

[brittle tinsel]

from this equation, all you need to do is add (4k+4)^3 to both sides

then show that the RHS simplifies to 16(k+2)^2(k+3)^2

[neon rover]

is this correct?

[brittle tinsel]

yeah, just show the RHS simplifies to what I typed and you're done

[neon rover]

this method always works? because if i can always just substitute the left side in and add a term i dont see how this proves anything

and why should i be simplifying it to that, because that isnt what the left side is equal to

i figured it out, but i would still like to know why your way works.

[brittle tinsel]

it does for sums. for a sum, you know P(k) is true, i.e.

$\sum_{i=1}^k a_i = b(k)$

to prove P(k+1) is true, you need to show that

$\sum_{i=1}^{k+1} a_i = b(k+1)$

but the LHS is just

$(\sum_{i=1}^k a_i) + a_{k+1}$

replace that sum with your assumption, and show that this above expression is equal to b(k+1), and you're done

[jolly parrot]

doaby

[brittle tinsel]

if you wanna be general about it, hopefully that helps

[neon rover]

okay thank you for the help!

.close

[pearl pond]

Channel closed

Closed by @neon rover

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.

[noble wren]

does anyone know how to know if a piecewise has removable or jump discontinuity. (I think those r the only two types)?????

[noble wren]

like for this for example, no idea

and for removable

im pretty sure infinites can't come from piecewises

[plush bramble]

That's not correct, but not relevant to your problem

[noble wren]

wdym

so there are infinites?

[plush bramble]

In other piecewise functions yes

[noble wren]

bruhhh

[noble wren]

then how do ik if something is infinite, jump, or removable?

in piecewise functions

[plush bramble]

One sided limits at each piece they intersect

[noble wren]

idk what that means (one-sided limits)

[noble wren]

for my problem could you also explain?

[plush bramble]

https://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx

[pearl pond]

@noble wren Has your question been resolved?

Channel closed

Closed by @noble wren

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.

[buoyant garnet]

One message removed from a suspended account.

[buoyant garnet]

One message removed from a suspended account.

[heady finch]

(1-1+h)/((1+h)/h)

use your KCF

[buoyant garnet]

One message removed from a suspended account.

[heady finch]

keep change flip

for fraction division

sorry

[buoyant garnet]

One message removed from a suspended account.

[heady finch]

have you done fractional division

I assume so?

[buoyant garnet]

One message removed from a suspended account.

[heady finch]

you're missing the fraction in the first denominator

[buoyant garnet]

One message removed from a suspended account.

[heady finch]

well you should just use fraction division

flip to multiplication

also cancel out the 1-1 in the numerator

(h*h)/(1+h)

[buoyant garnet]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[cosmic charm]

well you have a fraction in the numerator