help-23

[cold pilot]

Yess

[lime dust]

Now, you know they are integers

Start by getting the prime factors of 720 and tell me.

[cold pilot]

2
2
2
2
3
3
5

[lime dust]

That means one of the ages of the 3 people has 5 as factor

[cold pilot]

Ok,ok

And the other 2? How can I know?

[lime dust]

You start 1 by 1 testing 1 age

Imagine one age is 30, that would mean the others are 0 and 0, which is impossible because abc would be 0

now 25

then the others would be 2, 3 or 4, 1

[cold pilot]

Ohhh, okok

[lime dust]

and ABC is neither 720

then 20, 15... etc

you will find your solution in the end

[cold pilot]

Tysm

[lime dust]

you are welcome

[cold pilot]

I understand it now

Their age are 5 9 and 16

Tysm

How can I close this?

.Close

.close

[safe radish]

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[cold pilot]

.close

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[restive jacinth]

Need help with understanding this, don't really know where to start

[restive jacinth]

Just need help with a

[mint plume]

cylindrical coords might help.

you know how z is bounded, isolate for r in your condition and see how r is bounded, then try finding the bounds of theta

[restive jacinth]

and then i just integrate D?

Does integrating the density function just give me the volume?

[mint plume]

the density wont be used for this part

do ∫∫∫1dV

express dV in cylindrical coords

express your region bounds in cylindrical coords too

[restive jacinth]

Oh that makes more sense

yea thank you]

[ocean shuttle]

hello i have a test in 2 days i am taking differential equations and linear algebra and have not learned anything my entire duration of taking this class deepseeked all the homework. it is to late to withdraw from the class and i need to speedrun second order linear equations, eigenvalues and eigenvectors matrix exponentials and laplace transformations. i have already reviewed first order differential equations and learned all the mainstream methods to solve them i know this is fucked but plase if any kind soul wants to help me i dont know how to repay you. my dad will kill me if he sees an f in this class

idk where to post this might be the wrong place sry

[restive jacinth]

forgot to close this

but

this isnt the right place i would assume

and if i were to say something (havent taken diff eq and linear algebra) you might be cooked brodigy

might as well withdraw

[ocean shuttle]

i cant

not with a w on my record

i dont have a choice here

i have to try

[restive jacinth]

Then study 24/7

im gonna close this

before trouble

.close

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[restive jacinth]

.reopen

[safe radish]

✅ Original question: #help-23 message

[restive jacinth]

@mint plume hey sorry to ping you, i'd rather just do spherical coordinates and i wanna ask you if this looks right

Because well i tried to rearange this and it just gives me a sphere of inner radius 1 and outer radius 3

[safe radish]

@restive jacinth Has your question been resolved?

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[turbid crag]

um this may be out of the blue but how does adding nodes into smartart shapes in powerpoint shift existing nodes?

[turbid crag]

so for instance

this

turns into this

but this

turns into this

its clear that the added vertex is independent of existing node positions, but it is also evident that existing nodes are somewhat shifted, and i need to know how

(and specifically, if it can help me 5-sect angles)

[Source: Microsoft PowerPoint, I'm using Mac but it shouldn't matter]

[safe radish]

@turbid crag Has your question been resolved?

[turbid crag]

<@&286206848099549185>

[low echo]

Hmmmmmm

[turbid crag]

hmm indeed lol

i believe i should be done here

i say with great joy —

.close

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[turbid crag]

(and you may just see me in a video

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[supple radish]

Hey, i have already solved this problem by just brute forcing out the cases one by one which are not alot

[supple radish]

i was wondering if there is a way to solve this without listing out the cases one by one

and is more efficient hence

[glacial cairn]

What result did you get?

[molten acorn]

Stars and bars

But in the end you'll need to subtract by some cases which have a digit >4

[supple radish]

413

answer

which is correct

[supple radish]

uhh

how exactly do i do that

like do i have to get cases in that too

[glacial cairn]

12 = 1+1+...+1

Mark 6 of the + signs to form 7 groups, which make the 7 digits

That's 11C6

[supple radish]

yeah

[glacial cairn]

Remove 7 cases where there's a digit 6

Remove (7C2)*2 cases where there's a digit 5 (the rest is one 2 and 1s)

[supple radish]

aah

yeah

works better

thanks

better than listing them all down

[molten acorn]

7C6

1 star 6 bars

[supple radish]

yeah i got it

solved it on my own

after hearing u guys

thankss

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[molten acorn]

And mult this by 7

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[rocky pond]

hi can someone please help? Idk what went wrong here with my cofactor 3xpansion <@&286206848099549185>

[cedar widget]

You are multiplying by 3 instead of 3-x

You write Det(A)=3 * |.....
Instead of Det(A)=3-x * |....

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[wary python]

@rocky pond

[rocky pond]

ohhh thanks!

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[strong pike]

Question 10

[strong pike]

This is what I have done.

After removing root I take sin +ve and cos -ve because angle is in 2nd quadrant.

I might be making mistake is assigning +/- sign after removing root because given answer is (d) but I'm getting (a)

[left gyro]

you dont use the rules for sin and cos alone to figure out √((sin x + cos x)^2)

you cant distribute the ^2 and √ like that

remember that √(x^2) = |x|

youre saying |sin a + cos a| = sin a - cos a

an easier way is to consider this as |(sin a + cos a)/(sin a)|

that tells you its |1 + cot a|

then its a lot easier to tell whether this is supposed to be positive or negative

[strong pike]

Ok

[safe radish]

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[barren geode]

Hi, how can this be solved? Im searching the derivative of that function

[noble mango]

Hi! No need for quotient rule: what's the derivative of (x^2 + 2)^3?

(What rule should we use here?)

[barren geode]

Is this?

[noble mango]

Good! So, what's the derivative of 3/5(x^2 + 2)^3?

[barren geode]

Ok ty!

[noble mango]

No problem. By the way, you can clean up the function a little bit :)

(2x + 0) looks a little messy, so might want to move around the terms a bit.

[barren geode]

Should I multiply both terms and develop de power of 2?

[noble mango]

In particular, I would write it as so:
||18x(x^2 + 2)^2/5||

[noble mango]

Oh you don't need to do that, I was just saying some terms are a little useless.

Like for example, 2x + 0 is just 2x

[barren geode]

True, ty!

.close

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[split ether]

What’s your question and status?

[safe radish]

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

[spring wasp]

I’m trying to do part a but It being multiple variable is throwing me off

Because I could do p(a,4)=a and then p(a,5) also = 4 so does that count as a injection still since it’s two different y values

[split ether]

Yes, but can you have (a, 4) and (a, 5) both present in the domain?

The domain of p is the graph of a function f

(a, b) being an element implies b = f(a)

Can you have f(a) = 4 and f(a) = 5 simultaneously?

[spring wasp]

Right that makes sense thank you

For it being surjective though how can I know that all x in X would also be in the graph

[split ether]

For surjectivity, you need to show that for all x in X, there exists y such that p((x, y)) = x and (x, y) is in the graph

The last bit should help you figure out what y is equal to

[spring wasp]

It’s equal to f(x)?

[split ether]

Yup

[spring wasp]

Would this be correct then?

.close

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[graceful wren]

So I'm trying to solve this problem from Gallian. "Let $G$ be a finite group. Show that the number of elements $x$ of $G$ such that $x^3 = e$ is odd. "

[flat frigate]

edg

[graceful wren]

This is my current progress so far, but I don't know if my reasoning for saying so is correct

\begin{proof}
Note that the property of an inverse $x^{-1}$ is $xx^{-1} = x^{-1}x = e$, we could show $x^3 = e$ as follows,
$$x(x^2) = e$$

This implies, that if $x \in G$, it follows that its inverse $x^{-1} = x^2 \in G$. Finally, because this is a group we could say that its identity $e$ is in $G$ as well. Therefore $G$ has an odd number of elements.

\end{proof}

[flat frigate]

edg

[graceful wren]

Would it be possible to say that $x$ and $x^2$ are different elements? (If so) how can I show this more explicitly?

[flat frigate]

edg

[rustic goblet]

you’re unfortunately showing the wrong thing

G doesn’t necessarily have an odd number of elements - finite groups of even order exist, after all

what you’re trying to show is that there are an odd number of elements of G with the property that x^3 = e

the observation that such an element must be the inverse of its square is useful though

some suggestions: if x satisfies x^3 = e, does x^-1? does e satisfy that property?

[graceful wren]

ohh, that means that $x^3 = e$ could imply an even number of elements as well(?)

[flat frigate]

edg

[rustic goblet]

nope

you have a fixed number of elements already, you’re trying to show that there’s an odd number of elements with this special property

[graceful wren]

ohhh i see

[rustic goblet]

my suggestions are here :p

[graceful wren]

can you clarify/expound more on this matter, ifl i dont understand it as much

[rustic goblet]

if x satisfies the property that x^3 = e, does y = x^-1 satisfy y^3 = e? if so, then this means that every element with that property comes in a pair with its inverse, so we know that the number of such elements is even

except it’s not, because e is its own inverse and doesn’t come in a pair, yet still satisfies that property, so the number is actually odd :p

[graceful wren]

ohhh i think im starting to understand it imma js clarify a few things

[safe radish]

@graceful wren Has your question been resolved?

[graceful wren]

suppose that i've shown that $y^3 = e$, where $y = x^{-1}$ then this implies that $x = x^{-1}$ how do i go from here

[flat frigate]

edg

[graceful wren]

wait a minute,, then this also implies that x = e. if so, then this means there only exists one element in group G?

[graceful wren]

.close

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[native flume]

would (b) be impossible if m>n

[quasi bison]

not quite

you can fit n+1 boys and n girls if you have them go like ♂️ ♀️ ♂️ ♀️ ... ♂️ ♀️ ♂️

can't do more boys than that tho

[limpid lodge]

PnC is scary. Hope ur doubt gets resolved fr

[elder moss]

lmao slots look like sluts

[native flume]

whats PnC 😭

[native flume]

😭

[elder moss]

perm and combinations

[native flume]

ohh ok

[limpid lodge]

wait this ones p easy tho

the b part?

[native flume]

?

[native flume]

is b part meant to be p easy as well 😭

[limpid lodge]

idk what ur trynna ask

[native flume]

what did u mean by this

[limpid lodge]

im asking which part is ur doubt

[native flume]

oh yeah part (b)

[limpid lodge]

and what is the doubt.....

[native flume]

gonna have a think

[limpid lodge]

do you the methomethod of gaps?

[native flume]

i dont know the method of gaps

i think im overcomplicating it i was considering considering the total permutations - permutations where there are at least 2 boys adjacenet

[limpid lodge]

well is the ans (n+1) P m × n!

[native flume]

idk theres no mark scheme / solution fo rthis

[limpid lodge]

oh

[native flume]

howd u get that tho

[limpid lodge]

method of gaps

idk how to explain in text dang

[native flume]

its ok il have a youtube around thanks

[limpid lodge]

IIt is correct i believe tho.

[native flume]

okok ty

[safe radish]

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[north orbit]

i haven't learned this topic yet

how do i find where f(x) is concave

and how do we even determine that

is the range around the first or second turning point?

if i were to guess, it would be the second one

[tiny imp]

You can find the point of inflection using the double derivative of the function.

[empty gyro]

what is the definition of concave?

[limpid lodge]

Double derivative..

[north orbit]

idk mathematically, but from general knowledge i know this

[north orbit]

how does that help me find where f(x) is concave

[empty gyro]

It would help you to know the definition, especially if you are being asked to deal with it in your HW

[plucky elk]

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/05%3A_Curve_Sketching/5.04%3A_Concavity_and_Inflection_Points

[north orbit]

nah this aint my hw

just a random q i found

[north orbit]

okay this helped, understand it now

thanks

.close

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[thin lion]

Is it supposed to say m>=N?

[thin lion]

Also I’m kinda confused on this proof of like using the 1+|x_N|

[plucky elk]

where's your definition of cauchy sequence

[thin lion]

,rotate

[plucky elk]

and convergent sequenc?

[thin lion]

For all eps>0 there exists an N in Naturals such that for all n>=N |xn-x| less than eps

[plucky elk]

yea then n >= N is correct. it's just using this with m fixed

the proof works either way if you fix m or n it doesn't matter

they just picked n probably to fit your definition of convergence sequence

[thin lion]

So it doesn’t matter either way?

[honest perch]

they chose m=N

because obvi N>=N

[thin lion]

Hi

Is this decent

Like I’m trying to understand intuitively

Asw as formally

[fierce nimbus]

unrelated but nice handwriting

[thin lion]

Ty ❤️

But I just wish to be better at math

[noble mango]

Hi! Nice work.

You technically don't need any of that bit below

The fact that |xn| < 1 + |xN| is true for n > N means that the sequence is bounded

Because xN is fixed

Essentially this statement is saying that:
xn < Some fixed number

Which is by definition bounded.

[thin lion]

Yea I mean, the purple is for my own intuition ❤️

[thin lion]

Yep 🙏

Alr tysm

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[real horizon]

This is my understanding of the question. The answer on the answer sheet is -4/7 but

I don’t understand how we’d get tan(POQ)?

[hearty fjord]

is the answer -4/7 or -7/4?

[glacial cairn]

Think of sin(POQ) and cos(POQ)

I mean... I just read what you wrote, you got it right, so what exactly is your question

[real horizon]

The answer is -4/7

Yes but I thought -4/7 would be the answer to QOR

POQ forms an obtuse angle doesn’t it?

How’d you find tan of that

My mind’s legit not working rn

[glacial cairn]

Ah, right

Your A is not -7/sqrt(65)

It's +7/sqrt(65)

It's a distance, it must be positive

And then tan(x) = -tan(pi-x)

[real horizon]

Oh Okok I get it now

Thank you

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[long igloo]

how do i do this

[long igloo]

x= ucos(v) ?

i mean vcos(u)

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[long igloo]

can someone help me with this

.reopen

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✅ Original question: #help-23 message

@long igloo Has your question been resolved?

[austere forge]

have you parametrized the surface?

hint: $0 \leq \theta \leq 2\pi$, $0 \leq \phi \leq \frac{\pi}{2}$

[flat frigate]

c2b7

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[visual bone]

I need a hint to solve the integral of sin(e^(ix))

[visual bone]

Without substitution

[astral glacier]

Why without substitution

[visual bone]

Because that is the task the proffesor assigned

Not sure exactly what she wants

Me to use

[astral glacier]

What course is this

No substitution makes me wonder

Write e^ix as cis(x)

And then angle sum formulae?

And then IBP?

But why would you do that

[visual bone]

This is from complex analysis

[astral glacier]

That was my guess as well

[astral glacier]

Any bounds? Or just indefinite?

[visual bone]

No

I am thinking i might use series for this

[astral glacier]

That was my first thought also but that just looks messy

[visual bone]

Messy is better than no answer

[astral glacier]

Fair enough lol

[visual bone]

And it is correct, so she will have to accept it

[astral glacier]

Yup

[clever gale]

The answer is gonna be in terms of Si

Are you sure it's not definite?

[astral glacier]

Not necessarily

[visual bone]

No it is not in terms of Si

[astral glacier]

It will be a power series

[visual bone]

I am not using substitution

[clever gale]

,w integrate sin(e^(ix))

[flat frigate]

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Requested by lemniscate201

[visual bone]

Roy i know u can read

[astral glacier]

Again, power series

[visual bone]

Maybe if you read the channel dont say wrong stuff

So yes, i just define sin(z) using taylor

The rest is easy

Thx

[astral glacier]

Yeah

[visual bone]

.close

[safe radish]

Channel closed

Closed by @visual bone

Use .reopen if this was a mistake.

[astral glacier]

e^ix is a standard integeal

So it works out

Not as messy as I thought

[visual bone]

Yes

It is normal

.reopen

[safe radish]

✅ Original question: #help-23 message

[visual bone]

Sin(e^(ix)) = z + z^3/3! + z^5/5!

Yes pretty straight

.close

[safe radish]

Channel closed

Closed by @visual bone

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[weary latch]

I'm confused on where to place the t in this equation. I know one part is dv, but where do I place the t (or t - 0.25)?

[dreamy urchin]

Is the person who gave it to you schizophrenic?

try differentiation and add 0.25 hours to t.

[gritty atlas]

Dv?

[weary latch]

Wait, is it d/v = t + 0.25?

[gritty atlas]

Yea

Nice

Or

D/v + 0.25 = t

[weary latch]

This was the correct one.

Thank you so much! I forgot about the one formula they teach in science class.

I'll close it.

.close

[safe radish]

Channel closed

Closed by @weary latch

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
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[ruby tulip]

what does that equal sign with the triangle mean?

[median vigil]

the triangle is a Delta to stand for "equal by Definition"

[ruby tulip]

so, is that equivalent to the triple equals "≡" and also ":=" ?

[median vigil]

yes

[ruby tulip]

alrighty then

thank you

.close

[safe radish]

Channel closed

Closed by @ruby tulip

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[noble kiln]

[safe radish]

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[craggy inlet]

hey lmao im in yr 10 and wanted some help

[craggy inlet]

i js joined a random maths server

SOMEONE PLZ HELP I HAVE AN EXAM

[plucky elk]

Just show your entire exam

The whole first page

[craggy inlet]

ion have the exam but like

these r similar questions

plz dont flame me yall ik tis is probs easy af

[plucky elk]

,tex .log rules

[flat frigate]

riemann

[plucky elk]

Have you seen those

[craggy inlet]

yes

wait so'

am i js supposed to find t?

it doesnt specify :(((

[plucky elk]

For the first one yea

[craggy inlet]

ok

lmao ty for ur help i preciate it

[safe radish]

@craggy inlet Has your question been resolved?

[craggy inlet]

NO

[safe radish]

Channel closed

Closed by @craggy inlet

Use .reopen if this was a mistake.

[craggy inlet]

.reopen

[safe radish]

✅ Original question: #help-23 message

[timid trench]

apply the produtct/quotient rules

[austere forge]

@craggy inlet u still need help

[safe radish]

@craggy inlet Has your question been resolved?

[craggy inlet]

if thats ok

[austere forge]

for #1, you first apply the quotient rule right

cause its logx - logy

[craggy inlet]

yes

[austere forge]

then you have log_5(...) = 2

[craggy inlet]

yes

[austere forge]

so what do you do to get rid of log_5

[craggy inlet]

uhhh

gimme a sec

do u involve log 10 into it?

[austere forge]

its log base 5, so you raise each to 5th power

[craggy inlet]

oh shi

[austere forge]

cause $a^{\log_a(x)} = x$

[flat frigate]

c2b7

[craggy inlet]

u raise loga?

log a*

[austere forge]

raise both sides of the equality

[craggy inlet]

okay

wait i think i get it

[austere forge]

$\log_5(\frac{4t+7}{t}) = 2$

$\frac{4t+7}{t} = 5^2$

[flat frigate]

c2b7

[craggy inlet]

yes

[austere forge]

then you just got to solve for t which is easy

[craggy inlet]

and then you cancel dont u?

[austere forge]

wdym

for #1?

[craggy inlet]

like its 4t+7 divided by t

[austere forge]

you multiply both sides by t

[craggy inlet]

so it'll ultimately be 4+7 = 5 squared no?

OHHHH UR SAYIN

[austere forge]

4t + 7 = 25t
-21t = -7
t = 3

[craggy inlet]

BRING THE BOTTOM T NEXT TO THE 5 SQUARED?

ahhh

[austere forge]

yeah

[craggy inlet]

okok ty

thats my bad

[austere forge]

for #2 and #3 you apply product and quotient log rules first as well

[craggy inlet]

ok

do you group them all to one side?

[austere forge]

just combine the logarithms first

[craggy inlet]

oki

holdon im gonna try and send a pic

[austere forge]

remember the log rules

[craggy inlet]

ok i'll try again

[austere forge]

this

log(x) + log(y) = log(xy)
log(x) - log(y) = log(x/y)

[craggy inlet]

2log a (x) = log a (18 multipled by x-4)

Is that bit ok?

[austere forge]

yeah so 18x - 72 right

[craggy inlet]

Because x-4 is its own thing

[austere forge]

yeah 18 * (x-4)

[craggy inlet]

ohh 18 goes into both numbers

ok

Yes

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[craggy inlet]

NO REOPEN

mb

the bot is saying smthb

[safe radish]

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[limpid lodge]

say .reopen

[craggy inlet]

.reopen

[austere forge]

then you use the power rule for 2 log_a(x) right

[limpid lodge]

oh cmon its in my name now

[craggy inlet]

yes

So

log ax = 2loga(18x-72)

??

[craggy inlet]

mb cherry

[austere forge]

no its

$2\log_a(x) = \log_a(18x-72)$

$\log_a(x^2) = \log_a(18x-72)$

[flat frigate]

c2b7

[austere forge]

remeber the power rule

[limpid lodge]

thts ryt now take log base a bboth sides

[craggy inlet]

oh

ok

im sorry im rlly bad 😭

[austere forge]

so once you have log_a(x) = log_a(y), how do you simplify?

[craggy inlet]

Cancel the logs on each side?

[austere forge]

yeah

so you got x^2 = 18x - 72

[limpid lodge]

you cant cancel logs.....

[craggy inlet]

because they are common no?

[austere forge]

yes you can, if they are the same base

[craggy inlet]

and then transfer to one side and use the null factor law

[limpid lodge]

"cancel" might not be thhe ryt word tho

[craggy inlet]

Idk how else to say it 😭

mb

[austere forge]

idk what null factor law is but yeah you just solve for x

[limpid lodge]

thts just comparison, you comoare the bases and conclude that the expressionexpressions must be equal

but yeah

[craggy inlet]

Its like u transfer all the numbers to one side, and the other side is left with 0. then u factor it to get the answer

Im pretty sure u get 2 answers

[limpid lodge]

yep

[austere forge]

you put -72 instead of +72 but yeah

[limpid lodge]

but make sure to double check the ans

[austere forge]

and you got x=2 instead of x=12

[craggy inlet]

huh is it not -?

oh shi

[austere forge]

the factoring is correct, i think you just wrote it wrong by mistake

[craggy inlet]

ohh wait

Sorry ur right

i see what ur talking about

i'll try do the last equation and show u

i think i did smthn wrong

[austere forge]

yeah you canceled out y wrong

[craggy inlet]

was i not supposed to cancel y?

[austere forge]

so you got

$\frac{y^2}{5y-24} = 4$

[flat frigate]

c2b7

[austere forge]

that is correct

[craggy inlet]

yes

[austere forge]

you cant cancel out y there

[craggy inlet]

Oh what

Why?

[austere forge]

because -24 does not have y in it

[craggy inlet]

Ohhh

so u can only cancel when all numbers have a y?

[austere forge]

yeah, you cancel when everything is in common

so you bring the 5y - 24 over and multiply to the right hand side

$y^2 = 4(5y-24)$

[flat frigate]

c2b7

[craggy inlet]

so even if 5y-24 was in the numerator, u still cant cancel?

[craggy inlet]

oh

Okay

[limpid lodge]

omg idk whwhy it bothers me sm when u cancel logs. Just write on comparison😭

[craggy inlet]

Wym comparison?

thats what my teacher does lolol

[limpid lodge]

ur teacher cancels logs?

[craggy inlet]

She crosses it out like that

To make it visually easier

[austere forge]

its fine

[astral glacier]

What's the problem with cancelling logs

[craggy inlet]

LMAOO

[limpid lodge]

you could've cancelled it like 5-24/y

my teacher would kill me if i cancel logs

[craggy inlet]

im confused

[limpid lodge]

its not in product

[craggy inlet]

yea it isnt

[astral glacier]

And why is that a problem

[austere forge]

the logarithm is injective, so it is mathematically fine to cancel them like that

[astral glacier]

It's an injective function

[astral glacier]

Sounds like your teacher needs to be taught what logarithm is

[craggy inlet]

LMAOAO

[limpid lodge]

I hv no idea bro my teacher just scolds me when i do

[craggy inlet]

Im crine bro

[astral glacier]

think of it not as cancelling, but exponentiating both sides

a^log_a(b) = b

[craggy inlet]

@austere forge so i shld probably remember not to cancel unless all numbers in thr fraction have a y

[austere forge]

yeah, plus its easier to just multiply by the denominator

[craggy inlet]

yes

Okok

[limpid lodge]

im an awful teacher dang

[craggy inlet]

LMAO ITS OK U HELPED CHERRY

Literally thank u guys sm i know im pretty slow

[austere forge]

also make sure to memorize the log rules

log(x) + log(y) = log(xy)
log(x) - log(y) = log(x/y)
c * log(x) = log(x^c)

[craggy inlet]

I owe u my could

[astral glacier]

You learnt smth

[astral glacier]

On that note

[craggy inlet]

Yes will do

[astral glacier]

,tex .log rules

[flat frigate]

Xavier 🌺

[austere forge]

why didnt that work when i did it

[craggy inlet]

Question

For base change

[astral glacier]

You gotta initialise it

[limpid lodge]

ik its just 2 3 steps skipped

[craggy inlet]

Cannu explain base change

[astral glacier]

Well the end result is the same

[austere forge]

no, thats like saying

2x = 2y
x=y

is "skipping steps"

[astral glacier]

Also cherry, if you wanna avoid claiming a channel, start your message with a dot (.)

Since I noticed you claimed this channel on accident

[limpid lodge]

yepp its the cut the line lmao tht bothers

[craggy inlet]

LMAO TJE CUT LINE

OOPS

[limpid lodge]

i didn't realized the bot already made it available mb

[astral glacier]

No worries no worries

[limpid lodge]

UUhh what

[austere forge]

f(x) = f(y) implies x = y for any injective function f. all logarithm functions are injective

it is fine to "cancel" f in this sense

[limpid lodge]

i think im distractdistracting attention frm light srysry

[craggy inlet]

Guys sry to cut u off can someone explain the base change rule plz 😭

[craggy inlet]

NO ITS OK

I fw the discussion

[limpid lodge]

technically it isnt exactly cancellcancelling tho you arent dividing both sides by log or wtv

but wtv lol not tht imp

[astral glacier]

Division is the inverse function of multiplication

[austere forge]

@craggy inlet you use the rule when you have two different bases and need to convert from one to the other

[astral glacier]

Exponentiation is the inverse function of logarithm

It's the same idea

Cancellation is the general idea

[austere forge]

yeah, multiplication is not special

[craggy inlet]

Isnt that when log10 comes into play?

[limpid lodge]

makes sense

[austere forge]

yeah, if you're converting from base 10 to smth else

[limpid lodge]

dont tell me my schls teaching wrong TT

[astral glacier]

Bestie you're gonna find out how much "wrong" maths is taught in school

[craggy inlet]

Because on my calc only log10 actually solves, so we're taught to automatically resort to log10 as a base change

[limpid lodge]

depends on the ques but generally thts convenient i believe

[craggy inlet]

so in my case on the right side of the equation, the base wld be 10?

[limpid lodge]

ouch

[craggy inlet]

Okok

[austere forge]

log_b(x) = log10(x) / log10(b)

[craggy inlet]

that seems correct right?

regarding my case

OKOK

shi bro yall deserve my soul cause no one helped me before

[astral glacier]

Also I love how chaotic this channel was 5 mins back

[craggy inlet]

🥹🥹

[craggy inlet]

LMAO YEA

[astral glacier]

I give you full permission to tag me in the future

[austere forge]

or tag <@&286206848099549185>

[craggy inlet]

aw ty xavier i appreciate it

[craggy inlet]

WHAT THE

[austere forge]

@ "Helpers"

[astral glacier]

That's the helpers role? There's a 15 min timer on that

[craggy inlet]

Ohj

[austere forge]

without quotes

[astral glacier]

!15m

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[astral glacier]

You can tag me directly I don't mind

[ornate wyvern]

?

[craggy inlet]

Is helpers like the ppl in this channel

[austere forge]

wait did that ping 💀

[craggy inlet]

idrc how discord works lol

[astral glacier]

It's a self role people can choose

[craggy inlet]

Ohh

[astral glacier]

But yea, feel free to tag me directly in the future

[ornate wyvern]

continue guys im busy in a test

[craggy inlet]

is the setup tuff family

[craggy inlet]

yo what 😭

[elder moss]

Ji

[craggy inlet]

Good luck gang

Na guys but tysm again i rlly appreciate ot

it

especially you @austere forge

Thank u sm dawg u helped me alot

[austere forge]

np

[astral glacier]

Can I close this channel then?

I'm guessing yes

.close

[craggy inlet]

I think?

[safe radish]

Channel closed

Closed by @astral glacier

Use .reopen if this was a mistake.

[astral glacier]

Feel free to claim another in the future

Also react to the bot. Saying no doesn't achieve anything

[safe radish]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[silk cove]

How can I start the problem?

[quasi bison]

what does morera's thm say

[quasi bison]

so you need uhh. i guess you need the integral of that crap over a circle around the origin to be 0

i guess maybe try writing down the laurent series of this function centered at 0

[silk cove]

I see

That looks better idea

[quasi bison]

you want the z^-1 term to be 0 in that

[safe radish]

@silk cove Has your question been resolved?

[safe radish]

@silk cove Has your question been resolved?

Channel closed

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

[hybrid citrus]

Help

[safe radish]

Please don't occupy multiple help channels.

[quasi bison]

duplicate channel #help-21｜아리스킨충1

[safe radish]

Channel closed

Closed by @quasi bison

Use .reopen if this was a mistake.

[quasi bison]

.close

[safe radish]

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Send your question here to claim the channel.

Remember:
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[solar oar]

My teacher was teaching P&C seating question and I asked him, “What if two people can sit on one chair?”
He acted like I broke math, so I went home and made a full general formula out of spite.
I defined s = number of students, c = number of chairs, p = number of pairs, treated pairs and singles as groups, and counted how many ways the groups can be formed and then seated.
Now I’m trying to extend the same idea to capacity 3, where I’ll have singles, pairs, and triples, and have to count groupings using p = number of pairs and q = number of triples.

[charred jetty]

So c chairs and s students.

And you want to put s students in c chairs/

Just that?

No restrictions?

Or do you want to restrain it down to triplets—maximum?

[safe radish]

@solar oar Has your question been resolved?

[solar oar]

no restriction i want total combinations that can be formed

when 3 students can sit in one chair

[solar oar]

this one is the total combination that can be formed when 2 students can sit in one chair

including all 3 cases lets take 4 students 4 chair

the combinations can be
1+1+1+1
2+1+1
2+2 these 3 cases can be formed

each of them comtaining the groups

now i want 3 in one chair so combinations will be
1+1+1+1
3+1
but the chairs can hold 2 people too soo all the above cases should aslo be added

excluding 1+1+1+1 bcs that will come 2 times then

[safe radish]

@solar oar Has your question been resolved?

[calm ferry]

saving this thing to look at it later

[solar oar]

ok

[grim plover]

can each chair hold three students?

or only some chairs can hold three/two students?

assuming the first case, first thing you need to know is in how many ways can u divide/group the students

[safe radish]

@solar oar Has your question been resolved?

[grim plover]

@solar oar

[mystic leaf]

!done

[safe radish]

If you are done with this channel, please mark your problem as solved by typing .close

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

[radiant rover]

c++ doubt (competitive prog)

Problem: https://codeforces.com/problemset/problem/1903/A

My solution:

#include <iostream>

using namespace std;

int main(){

int test;
cin>>test;
while(test>0){

int len,sub,i,repeat{0};

cin>>len>>sub;


int arr[len];

for(i=0;i<len;i++){

    cin>>arr[i];

}




for(i=0;i<len-1;i++){

    if(arr[i]==arr[i+1]){
        repeat++;
    }

}

if(repeat==len-1){

    cout<<"YES\n";
}


else if(sub>=2){

    cout<<"YES\n";

}

else{

    cout<<"NO\n";
}




test--;


}





return 0;







}

i have attached the image regarding exactly where it fails.

[open wedge]

Use ```cpp and ``` please

You need to format your code so we can see it 🙏

[radiant rover]

😭

no idea how to do it
ill try tho

yes

check now

[open wedge]

```cpp
// your code goes here
```

[open wedge]

What's up with the span of newlines im seeing 💀💀💀

[radiant rover]

😂 its just idk why sorry about that

for me its easy to understand

mb

[limpid lodge]

Wow

[dense tinsel]

You assume that any array can be sorted if k >= 2, which is not always true

[radiant rover]

i am pretty sure if k>=2, it can be a bubble sort type of thing. so it WILL sort the array

[dense tinsel]

k = 1 you can’t reverse anything, so only already sorted arrays YES.

k >= 2 you can always swap adjacent elements (like bubble sort), so any array can be sorted YES.

no need to check middle positions

[radiant rover]

wait..... what if k =1

i did not mention anything

hmm

[dense tinsel]

k = 1 you can’t change anything, so only arrays that are already sorted YES, otherwise NO.
k ≥ 2 you can sort any array using swaps of adjacent elements (like bubble sort) YES.

[radiant rover]

i got it

ty

.close

[safe radish]

Channel closed

Closed by @radiant rover

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
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• 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.

[proven shadow]

Hey I need help with a efficient method to find the hcf and lcf of numbers, can use anything that is time efficient

[open wedge]

Use a calculator

[proven shadow]

No like is there a mental solution?

That will speed things up

[open wedge]

Make a b into prime integers

Which should not take too long

[proven shadow]

Kk

[open wedge]

And apply the definition

[quasi bison]

how efficient do you NEED to be

[proven shadow]

Pretty efficient

[quasi bison]

are you participating in an olympiad where the questions are nothing but hcf and lcm

[proven shadow]

No I’m just curious

But it’ll come on my test

…

[quasi bison]

you can prime factorize each number and then take the minimum of each prime's exponent for hcf, or maximum for lcm

[open wedge]

import math

# self-explanatory

Super efficient

[proven shadow]

Ty ann

[open wedge]

< 1s

[ember socket]

had you not said exam and mental math, I would have thought the urgency in which you want some methods meant that you were trying leetcode problems

[proven shadow]

Lol

.close

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[latent mountain]

My method: We know that tangent to a parabola is ** y = mx + (a/m)**

Equation of tangent to circle is** y = mx± r * sqrt(1+m^2)**

on comparision:** (1/m) = 3*sqrt(1+m^2)** [ since a = 1 and radius = 3]

on solving im not getting an answer which matches the options

[proven shadow]

Math.

[latent mountain]

?

[proven shadow]

Idk what I’m saying gng idk wtf this even is

[worn pollen]

LMAO I MADE THE SAME MISTAKE ONCE

You have to compare with ratios

And not exactly the coefficients

a1/a2 = b1/B2 = C1/c2 = K(constant)

And then solve

[latent mountain]

Uhh

Why tho

the equation of the tangent will remain same

[worn pollen]

Okay so

[worn pollen]

The constant changes

The y intercept

[latent mountain]

how?

Its the common tangent

[worn pollen]

Y = mx + c

The "c"

[latent mountain]

So it shouldnt change

[worn pollen]

Is y intercept

It could have many values

[latent mountain]

okay\

so in this problem

even if you compare coefficients your getting the same thing

[worn pollen]

See

I'll give you an example

[latent mountain]

K = 1

[latent mountain]

k

[worn pollen]

See

Are these the same equation ?

?

[latent mountain]

yes

[worn pollen]

Yes

Here the k is 1/2

[worn pollen]

Yes****

They are exactly the same equation

But see

The coefficients are different

[latent mountain]

yes

[worn pollen]

So you just did 1=2

[latent mountain]

2nd one is 1st multiplied by 2

[worn pollen]

Do you get it?

[latent mountain]

Hmm yess

[worn pollen]

You'll get 2 linear equations after comparing, then solve them

[latent mountain]

So in my problem you get:

m/m = 1/1 = (1/m) /3*sqrt(1+m^2)

[worn pollen]

Opps

Yep

Solve for m

[latent mountain]

Which is yeilding the same result

[worn pollen]

Wait

[worn pollen]

Why did you do this

It's a shifted circle

[latent mountain]

um

[worn pollen]

This formula was only applicable if the circle had centred at origin

[latent mountain]

oh shit

your right

[worn pollen]

I mean you just have to modify the equation a bit

[latent mountain]

How do you generalize it for any circle?

[worn pollen]

(3,0) is the centre

[latent mountain]

yes

[worn pollen]

So y = m(x-3)±√(1+m²)

[worn pollen]

There's a thing

[latent mountain]

?

[worn pollen]

It's a whole new concept

Forget about that now

[latent mountain]

what is it?

I might be familiar with it

[worn pollen]

xx1 + yy1 -3(x + x1) =0

Direct equation of tangent

[latent mountain]

ah

[worn pollen]

T=0

[latent mountain]

Ik this

T=0

[worn pollen]

Iykyk

Yeah

But we don't know what's x1 and y1

[latent mountain]

But i want it in slope form

[worn pollen]

So we use that

[worn pollen]

Just shift the x coordinate then

Like I did here

[latent mountain]

Ohh i got it

[worn pollen]

By 3 units

[latent mountain]

wait lemme see if i get m

yup got it

Learnt a new thing too

Ty man

.close

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[north sundial]

Alguien en español?

[north sundial]

Para que alguien en ayude con las funciones de rango y dominio

I need someone to help with the range and domain functions.

[safe radish]

@north sundial Has your question been resolved?

[elder moss]

What help you need

[north sundial]

A brief explanation of domain and range functions for an exam

Something like that

[elder moss]

Domain means the set values you can put in a function

eg ln(x) the set of values of x that are accepted is domain of ln(x)

here x belongs to positive values

Range is the set which contains all possible output values of a function

eg y = f(x) all possible values of y is the range

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@north sundial Has your question been resolved?

[north sundial]

Gracias aunque entendí muy poco

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[somber cape]

I dont see why taking mod p preserves the factors

hmm if I have c = ab in Z

then does c = ab in Zn or Zp

let me see if I can show that

if that is the case then I can see why it would be preserved I believe

oh wait

[snow ice]

what do you mean but preserving factors?

[somber cape]

yeah it is equal

😭

[snow ice]

happens to the best of us

[somber cape]

I dont know why I thought they wouldnt be lol

thanks

.solved

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[fading mural]

.you can ask here @wary dagger

[wary dagger]

can someone help me with translations ?

[wary dagger]

exercise 1

ABCO, CDEO, EFGO and GHAO are squares. 1. what is the image of triangle ABC under the reflection across the line (AE)?………………………………………

2. what is the image of triangle ABC under the reflection with center O?………………………………

3. what is the image of triangle ABC under the translation that sends B to O? …………………………

No justification is required.

exercise 2 : construct the image of the figure with respect to line (d1) then with respect to line (d2)

3 : same thing but with point o1 , then with poijt o2

exercise 4 : construct the image of the figure by the translation that sends F to Pconstruct the image of the figure by the translation that sends K to M

im failing my classes and this is due tomorrow , none of my classmates are willing to help

the teacher cant explain stuff well so im really struggling

[fading mural]

What have you tried for ex1

[wary dagger]

umm

hold on

i literally dont know what im doing

[fading mural]

if no one helps in around 15m you are allowed to ping helpers

[wary dagger]

ill do that

thank u!

[fading mural]

Okay, so what's the reflection of point B and C w respect to AE

[wary dagger]

umm HG?

[fading mural]

Yeahh

And A lie on AE so its reflection is itself

[wary dagger]

Ohhh

LOL i didnt figure that out

oh so its this? AHG?

[fading mural]

Yeah

[wary dagger]

ohhhh

[fading mural]

Iirc

[wary dagger]

is this the reflection of the triangle ABC under the reflection of center O or am i wrong 😭

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@wary dagger Has your question been resolved?

[safe radish]

@wary dagger Has your question been resolved?

[nimble wyvern]

Reflection of ∆ABC will be ∆GEF

[nimble wyvern]

Reflection with respect to Origin O*

[wary dagger]

THANK U!!

i have the last three exercises then im done , but for that im gonna ask for my classmates paper so i can copy off of it

[nimble wyvern]

Good luck!

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[jaunty mural]

pessoal para vocês o que seria a definição de uma reta na matematica?

[open wedge]

English pls

[jaunty mural]

So, what would be the definition of a straight line in mathematics for you?

[golden cloak]

Hello everyone, I'm sorry to bother you but I need help. For some reason I fell in love with mathematics and I would like to actually understand it and know how to solve big problems. I'm 19 years old and I started to study software engineering and that's where I really need, in addition to what I want, mathematics. Most people, websites and etc. say practice practice and practice. But I don't know where to find literature and I consider mathematics like a pyramid and I think that it is necessary to go gradually, but also leave room for adaptation and returning to the old one and connecting the concepts. So I would like to hear your advice on how you started and how you managed if it is not a problem for you. Also tag me so that I can see it instantly.Thank you

[plucky elk]

try #math-discussion

[jaunty mural]

For you, what would be the definition of a straight line in mathematics?

[plucky elk]

https://en.wikipedia.org/wiki/Line_(geometry)

[jaunty mural]

This definition seems strange to me.

[safe radish]

@jaunty mural Has your question been resolved?

[primal bone]

Well, I don't know what to tell you then, O @jaunty mural - but that is the mathematical definition of a straight line

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[primal onyx]

I dont quite have an idea how to do the last one

My guess rn is 0,025*0,03

[split kayak]

its basically P(A|B)

Theres a known formula for it, or you can think about it from sample-space set

[primal onyx]

Like a tree diagram?

[primal onyx]

or what do you mean exactly

[split kayak]

yeah, i believe you can use them to solve for this, but it isnt really needed.

[split kayak]

Im surprised you have gotten this question without knowing what P(A|B) is

Well, to clarify what it is

P(A|B) reads as:
P() "the probability of"
A "Event A happening"
|B "Knowing Event B happened"

Basically sets off a condition

[primal onyx]

Okey

[split kayak]

I wont bore you with the details in set-theory

But this venn diagram here represents the whole "Sample Space", aka, the collection of all possible outcomes

Where we define events A and B as two "parts" of the whole sample space.

For a really foolish interpretation of it, its basically a board, into which you can randomly throw darts

|B is basically telling you that the dart landed in B

We still dont know precisely where, but we are in B

So we get a "sub-diagram"

[primal onyx]

Okey yeah