help-23

[sand minnow]

well, technically eventually you can think of it as a basis vector but thats nothing to think about right now

[fickle trail]

lol

do you think brackets should be mandatory notation for arguments?

[sand minnow]

writing it on its own is just something you would do for defining notation, it isnt uncommon to define notation by writing for example $$\dv{x}\equiv D(\phantom{x})$$

[fickle trail]

i see sinx a lot in math

[flat frigate]

Duh Hello

[sand minnow]

it is not, but you can consider it to be at your current level

[fickle trail]

i wonder if ppl do derivative arguments d/dx without brackets too.. seems risky

rolling the dice

[icy nymph]

are you doing calculus without having done trigonometry?

[fickle trail]

no?

[icy nymph]

oh nvm lol

misread

[fickle trail]

just gave that example: sinx should be written sin(x) as x is the argument of sin

[jade magnet]

ive never put brackets i dont think it matters

just convention

[fickle trail]

for derivatives or for trig functions?

[jade magnet]

for both, sometimes i do sometimes i dont

[fickle trail]

i don't see how writing derivative without brackets could be safe

how do you know when it ends?

if there are other terms after it

[sand minnow]

what if you have $\cos(\omega t+\phi)$

[flat frigate]

Duh Hello

[sand minnow]

would u still omit the parenthesis?

that would be very bad practice

[jade magnet]

no there i would, like i said it depends

[fickle trail]

lol

[jade magnet]

for derivatives

[sand minnow]

same deal goes

$\dv{x}(ax+b)$ vs. $\dv{x}ax+b$

[flat frigate]

Duh Hello

[jade magnet]

well its a linear operator

so i just add it to both

[sand minnow]

consider b to be a function of x

[fickle trail]

oh man, that's playing with fire

what if it was intended to only be d/dx of ax

not b

how would you know?

[jade magnet]

i wouldnt add it to b 💀

[sand minnow]

exactly

but what if you were supposed to?

[fickle trail]

yeah

[sand minnow]

then ud need parenthesis

or brackets

[fickle trail]

I think you should always use brackets for derivatives

[jade magnet]

no i just put it on b aswell

[sand minnow]

what about if you have a disgustingly long equation?

like 10 terms

are you writing that d/dx 10 times instead of just putting 2 brackets?

[fickle trail]

d/dx 10x

[jade magnet]

i might consider it

[fickle trail]

lol

[jade magnet]

i mean it doesnt really matter as long as it is intrepretable

[sand minnow]

yeah, but if you are taking up massive space with unnecessary notation then eventually you wanna start to reconsider the way you are writing things

[jade magnet]

idk is never happened to me really

where i thought i have to, atleast not from what i remember

[sand minnow]

for example in later math you get stuff called tensor notation, so what you could write as this, while it doesnt look pretty im not sure you wanna see what that looks like in normal notation

this is roughly 1/3rd of that when expanded

[sand minnow]

take shortcuts where you can, they will be useful

obviously dont make things confusing by doing that, gotta keep clarity as well

[fickle trail]

Imagine marking this

[jade magnet]

yea i havent stumbled upon tensor notation

[stray socket]

Boreogadus saida, known as the polar cod[1][2][3] or as the Arctic cod,[1][4][5] is a fish of the cod family Gadidae, related to the true cod (genus Gadus). Another fish species for which both the common names Arctic cod and polar cod are used is Arctogadus glacialis.

[sand minnow]

exactly what i was thinking umbra

[stray socket]

Ong

[fickle trail]

Nice to see the Wikipedia references included in the homework

I wonder if there is a website to check if ChatGPT wrote something

probably an issue for homework now, Wikipedia is the least of the teacher's concerns

oh that's good to see

https://openai.com/blog/new-ai-classifier-for-indicating-ai-written-text

by the same makers of ChatGPT

so they would be able to spot it perhaps even with 100% accuracy

.close

[safe radish]

Channel closed

Closed by @fickle trail

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[near oracle]

Hello! I need help with a problem. Let 𝑎∈ℤ. Prove if 3|𝑎2, then 3|𝑎.

[near oracle]

I was thinking on starting this problem using a contradiction, but I'm just a little unsure

[icy lance]

what is a2? is it 2*a?

[near oracle]

a^2

sorry about that

[broken yew]

write out what a|b actually means

there is another way to formulate it that is more helpful

[near oracle]

a|b = b is congruent to 1(mod a)

right?

[broken yew]

dont use = when u dont mean it, just plain words

Not at all, however.

a|b means 'a divides b'

if a divides b, then b is not congruent to 1 mod a

[near oracle]

oh okay

so what is b congruent to then

[broken yew]

well take an example

3 divides 12

12 = ??? mod 3

[near oracle]

4

or 1/4

sorry im confused by the wording

[broken yew]

r u not familiar with modular arithmetic

or have u not learnt it properly yet

[near oracle]

we are just starting to talk about it

its 4 right

[broken yew]

no

[near oracle]

oh so 1/4?

[broken yew]

no....

[near oracle]

?????

oh

is it fr 36

[broken yew]

Maybe dont use it until you learn it properly

[near oracle]

I see now

[broken yew]

its not 36 either

[near oracle]

then what it is

[broken yew]

forget modular arithmetic.

If a divides b

then that means ka = b for some integer k

agreed?

that is the usual definition

[near oracle]

yes

I agree

[broken yew]

ok, you should use this

for your question

Write out what it means if 3 divides a^2

and also what you want to show, which is 3 divides a

[near oracle]

3/ a^2

or in b terms, 3/ (b^2/k^2)

but what do we do from here

[broken yew]

thats not wut i wrote

If a divides b then ka = b for some integer k

[near oracle]

oh sorry

okay

[broken yew]

use this directly

[near oracle]

so then 3k = a^2

for some integer k

[broken yew]

ok

and then what do u need to show

[near oracle]

that 3 |a

[broken yew]

which is

[near oracle]

3k = a

[broken yew]

ok, but best to pick another letter

[near oracle]

l

[broken yew]

because its probably not the same k

[near oracle]

not l

how about o

[broken yew]

j

[near oracle]

3o = a

fine

j

3j = a

[broken yew]

3k = a^2 for some k

Need to show
3j = a for some j

Ok, now remember a j k are all integers

[near oracle]

right

could you square the 2nd equation

and set 9j = a^2

[broken yew]

no, nothing like that

[near oracle]

oh alright

[broken yew]

you need to get from the first to the 2nd

not the other way round

[near oracle]

so square root it?

sqrt(3k) = a

?

[broken yew]

So what I would think about is prime factorization

this is number theory so probably not root it

3k = a^2

[near oracle]

divide by a?

[broken yew]

what can u see in terms of prime factorization

[near oracle]

what does prime factorization mean

[broken yew]

mmm

what course is this

[near oracle]

Intro to Math Reasoning

[broken yew]

its strange they havent covered that first

before this

or is this another language

so maybe u dont know the word?

[near oracle]

bro

are u gonna tell me what it is or just continue to insult my intelligence

[broken yew]

like 12 = 2^2 . 3

not an insult to your intelligence at all

im questioning whats been taught on your course

because there are certain things that should be covered before u talk about other things

and its a pain if it hasnt

[near oracle]

gotchu

okay

so

for the question

[broken yew]

this is the prime factorization of 12

2 squared times 3

its splitting it up into a product of primes

[near oracle]

1 * 3

or do you want the variables included as well

[broken yew]

no, i dont mean in terms of variables

so just talking about squares

when u prime factorize squares

each prime factor must have an even power

[near oracle]

oh I see

[broken yew]

u knew this?

[near oracle]

so 2^1 + 1?

no

this is all new to me

[broken yew]

So for example 36

[near oracle]

6^2?

[broken yew]

,,2^2\cdot3^2

[broken yew]

thats the prime fac

[near oracle]

oh I see

so like taking the square root of 8

[broken yew]

each prime has an even power

[near oracle]

making it 2 times square root of 2

in a way

[broken yew]

no, this is number theory

u only talk about integers

no roots no decimals

[near oracle]

ok

well

for 3

wouldnt it just be 3^1

[broken yew]

yes

thats the prime fac of 3

Back to the original question

the point is the left and right are equal

so they must have the same prime factorization

yes?

[near oracle]

because of porime facotization?

oh

okay yeah

I get it

[broken yew]

3k = a^2 for some k

So taking this

and taking what i said about squares

you can deduce something about the prime factorization of k

[near oracle]

k has to have some integer ^2 power?

[broken yew]

Each prime factor in a^2 must have an even power

[broken yew]

no

,,a^2 = p^{2\alpha}q^{2\beta}...

[broken yew]

thats what it looks like

but this is also equal to 3k

[near oracle]

im not gonna hold you bro we have not covered anything even close to this in class lol

[broken yew]

very strange to me

maybe theres an even simpler proof im missing

or they want something simpler

but like i dont see it

Maybe theres some given facts in class u can use

to do this that avoids all of this work

[near oracle]

yeah hold on I'll type something up real quick and run it by you

[broken yew]

But regardless, this all should really have been covered before

[near oracle]

Would this work?

Proof:
Let a=3. We can then say that a^2=9. In this case 3|3, and 3| 9.

[broken yew]

Youve managed to prove the statement for a = 3

but not all the other integer a

[near oracle]

Is there a way to disproof the statement?

[broken yew]

well its true

so no

[near oracle]

right

thats what I thought

[broken yew]

Let 𝑎∈ℤ. Prove if 3|𝑎2, then 3|𝑎.

You start with any integer a

and so u need to prove this works for any a

[broken yew]

back to this, we are almost there

https://media.discordapp.net/attachments/903481106819612714/1081404213415915620/321445119171756033.png

[near oracle]

okay I'll roll with it

what do we do from here

[broken yew]

right so consider what the power of 3 is like

on the right

it must be 3^(2x)

for some integer x

So now what about the power of 3 in the prime factorization of k

[near oracle]

wait what

sorry this is all like foreign language to m e

[broken yew]

mmm

[near oracle]

could we break this proof down into 2 cases

in which one is even

and the other is odd

[broken yew]

What is even and what is odd

[near oracle]

a = 2n

[broken yew]

no, it has nothing to do with a being even or odd

[near oracle]

I see

[broken yew]

do u get whats going on here

ive written 3k as a product of primes

[near oracle]

oh okay

yeah I see now

[broken yew]

a product of primes which all have even power

k itself can also be prime factorised

im saying we are interested only in the power of 3

on both sides of the equation

[near oracle]

3^1

[broken yew]

its 3^1 times k

[near oracle]

right

[broken yew]

So on the right u have 3^2x

on the left u have 3^1 times 3^y

where 3^y is the power of 3 in k

does that make sense?

[near oracle]

yeah it does

[broken yew]

,,3^1\times3^y = 3^{2x}

[broken yew]

,,3^{1+y} = 3^{2x}

[broken yew]

ok?

[near oracle]

yeah

[broken yew]

so y+1 = 2x

y = 2x-1

Therefore the power of 3 in k is odd

[near oracle]

🤯

[broken yew]

it could be 1, 3, 5, 7, 9, ...

More importantly this shows knis divisible by 3

[near oracle]

right

so how do I write this in english now lmao

[broken yew]

ngl, idk either

[near oracle]

lmao

[broken yew]

u have to explain these ideas

[near oracle]

right

ill type sometghing up and ill run it by ui

[broken yew]

more important is to understand them first

before attempting to write it

,,3k = a^2

[broken yew]

You had this. k is divisible by 3

[near oracle]

yeah

[broken yew]

so k = 3m

for some m

,,9m = a^2

[broken yew]

NOW you can take square roots

m must be a square

,,3r = a

[broken yew]

and u end up with this which is what you wanted to show

[broken yew]

ngl, I have little idea what they expect from you in the class

So it is hard for me to judge what is or isnt good

In the end, its best to hear the feedback from them directly Id say

[near oracle]

wait wait wait

why do we get r

[broken yew]

It doesnt matter if you score highly or lowly - the feedback given is what matters. I have no clue what they're after.

[near oracle]

why isn't it 3m = a

[broken yew]

,,9m = a^2

[near oracle]

here I can get u something real quick

[broken yew]

square root both sides

[near oracle]

right

+-3m = a

[broken yew]

,,3\sqrt m = a

[broken yew]

no its this

[near oracle]

ohhhhh

I see now

and then the square root of m is r^2

or sorry

m is equal to r^2

[broken yew]

m = r^2

[near oracle]

yeahg

[broken yew]

the reason u can do this is because m is a square

because of the previous way u wrote the product

urgh its hard for me to explain over text

[near oracle]

nah I get it

[broken yew]

https://media.discordapp.net/attachments/903481106819612714/1081404213415915620/321445119171756033.png

[near oracle]

okay

heres an example of feedback

[near oracle]

yo I gotta go get some food rq

is it alright if I brb for like 15 mins?

[broken yew]

i gtg

[near oracle]

oh shit

[broken yew]

maybe someone else can look

[near oracle]

okay

thank you so much though!

I appreciate everything you've done for me!

❤️

[broken yew]

👌 maybe the feedback can give a better proof than the one i outlined

[safe radish]

@near oracle Has your question been resolved?

[near oracle]

.close

[safe radish]

Channel closed

Closed by @near oracle

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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.
• 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.

[safe radish]

Please don't occupy multiple help channels.

[zinc token]

.close

[safe radish]

Channel closed

Closed by @zinc token

Use .reopen if this was a mistake.

[zinc token]

do not open 2 help channels

[lean otter]

ok

mb

[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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• 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.

[thorny thorn]

hello could i please have some help

[safe radish]

Please don't occupy multiple help channels.

[thorny thorn]

okay sorry

[zinc token]

.close

[safe radish]

Channel closed

Closed by @zinc token

Use .reopen if this was a mistake.

[thorny thorn]

.close

[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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[stuck sparrow]

So for this i’m not sure what i’m missing

it’s probably smt very small

F(x) sits description of sinx

so g should be at sinx

arcsinx

integral arcsin^2019x from 0 to 1 but i gs t a huge # that’s probably wrong

[hot thistle]

well

under the assumption that any function satisfying these conditions gives the same integral (which i don't think is the case) can't we just let f(x) = x?

[stuck sparrow]

Wait

that’s true

so integrand is jsut x^2019?

apparently the ans is small between 1-24

[hot thistle]

there's not enough information

[safe radish]

@stuck sparrow Has your question been resolved?

Channel closed

Closed by @stuck sparrow

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[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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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.

[scenic holly]

guys, help

[scenic holly]

sqrt(15^2 - (3sqrt(2))^2)

[quasi bison]

$\sqrt{15^2 - (3\sqrt{2})^2}$

[flat frigate]

Ann

[quasi bison]

is this your problem?

@scenic holly

[scenic holly]

Yeah, sure

[quasi bison]

okay, and what is troubling you?

@scenic holly ?

[scenic holly]

I have a exercise from geometrty

[quasi bison]

please answer the question i ask you.

[scenic holly]

Wait, wait

I have pyramid base is quadrat, pyramid base square = 72cm^2, pyramid apothem = 15cm, find the height of pyramid

If square = 72, the side of the pyramid base = 6sqrt(2)

then we have right triangle, the hypotenuse = 15, and 1 side = 3sqrt(2)

[thin bridge]

okay, and what is troubling you?
by that she's asking you what's preventing you from simplifying what you initially gave us

[scenic holly]

Nothing

I did

[quasi bison]

nothing troubles you?

[scenic holly]

It's sqrt(207), right?

[quasi bison]

if nothing troubles you, then why are you here?

[scenic holly]

Because the answer which I got is wrong

[quasi bison]

then why did you not say so?

also that is something that should trouble you.

[scenic holly]

Okay, it's troubling

[thin bridge]

did you copy down the correct values?
are you looking at the answer key for the correct section?
what's the expected answer?

[scenic holly]

a^2 = c^2 - b^2; a = sqrt(225 - (3sqrt(2))^2)

sqrt(207)

[thin bridge]

pics of the original problem would help

[scenic holly]

sqrt(207) = 9sqrt(23)

I dont have it )

I have only task condition

[thin bridge]

anyway,

sqrt(207)
can be simplified further

[quasi bison]

this is going to be a long shot, but are you Russian

[scenic holly]

Not Russian

[quasi bison]

and/or do you speak Russian

[scenic holly]

Yeah, I speak

[quasi bison]

давайте тогда продолжим по-русски, если не против

[scenic holly]

А так можно было?

)

[quasi bison]

ну, я русская.

итак, проблема состоит в том, что у вас есть задача, которую вы решили, но ответ не совпал с ответом в задачнике. так ли это?

[scenic holly]

Да

[quasi bison]

скиньте условие и заявленный ответ

[scenic holly]

Периметр основания правильной четырехугольной пирамиды равняется 72, нужно найти высоту пирамиды, если апофема пирамиды равняется 15

[quasi bison]

так

[scenic holly]

Периметр равняется a^2 * 2

[quasi bison]

что такое a?

[scenic holly]

Значит а = 6

[scenic holly]

Сторона основания пирамиды

[quasi bison]

а с чего бы периметр тогда 2a^2, а не 4a?

[scenic holly]

Ой, точно, 4а

тогда а = 18

Имеем прямоугольный треугольник, с нижним катетом 9, гипотенуза 15, sqrt(225 - 81) = sqrt(144) = 12

Стоп

Я понял, в чем ошибка была

[quasi bison]

ну так я вроде бы на нее вам и указала

[scenic holly]

Спасибо большое )

[quasi bison]

пожалуйста

если больше вопросов не осталось, можно закрыть канал командой .close

[scenic holly]

Можете еще с одним помочь?

[quasi bison]

ну давайте

[scenic holly]

Ученик в 1 семетре получил оценки с математики: 8,7,9,8. Какое количество оценок 10 он должен получить, чтобы среднее значение всех оценок было 9.5

Кроме 10 никаких других оценок он не должен получать

[quasi bison]

так

[scenic holly]

Я не понимаю, как составить уравнение

[quasi bison]

чтобы составить уравнение, сформулируйте, что из себя представляет неизвестное

попробуйте сами. если окажетесь неправы, я поправлю

[scenic holly]

Даже не знаю как

[quasi bison]

что в задаче требуется найти?

[scenic holly]

Количество оценок 10

[quasi bison]

именно так. в нашем случае неизвестное -- количество полученных учеником десяток

прекрасно. так давайте назовем это какой-нибудь буквой, например x

вы знаете, как находить среднее набора чисел?

[scenic holly]

Нужно все числа суммировать и разделить на количество чисел

[quasi bison]

да

сможете исполнить?

или мне разобрать с вами по шагам

[scenic holly]

Лучше разобрать

[quasi bison]

хорошо

итак, ученик получил оценки 8, 7, 9 и 8 (всего 4 штуки) и 10-ки в количестве x штук. сколько всего получается оценок?

[scenic holly]

Это получается (8+8+7+9+x) / 4 + x = 9.5

[quasi bison]

во-первых, скобки неправильно стоят

а во-вторых, вы заставили ученика получать не десятки, а единицы

еще вокруг знаменателя скобки не забудьте.

[scenic holly]

А как заставить ученика получать десятки?

[quasi bison]

тьфу, не туда нажала

а чему равна сумма x слагаемых, каждое из которых 10?

все-таки может быть 10x, а не x?

[scenic holly]

10x

[quasi bison]

ага

[scenic holly]

(32 + 10x) / (4 + x) = 9.5

[quasi bison]

то есть уравнение наше все-таки (32+10x)/(4+x) = 9.5

да

решить справитесь?

[scenic holly]

Попытаюсь

Хм, не получается

[quasi bison]

в чем затык?

[scenic holly]

Не понимаю как решить

32 + 10x = 9.5(4+x) -> 32 + 10x = 38 + 9.5x

(1/2) * x = 6

x = 12

[quasi bison]

ну да...

[scenic holly]

Теперь решилось

[quasi bison]

как удивительно

[scenic holly]

Да я опять ошибку допустил

Спасибо большое )

[quasi bison]

пожалуйста

[scenic holly]

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[scenic holly]

.reopen

[safe radish]

✅

[scenic holly]

@quasi bison

Подскажите еще пожалуйста одно: sqrt^3 (128) / sqrt^3 (2)

[quasi bison]

sqrt^3 -- кубический корень?

[scenic holly]

Да, именно

Я хотел поднести оба числа к 3 степени, тем самым убрать корень

И получилось бы 64, но правильный ответ: 4

[quasi bison]

128^(1/3) / 2^(1/3) = (128/2)^(1/3)

[scenic holly]

А почему так нельзя?

[quasi bison]

а вы что, просто возвели в куб и числитель, и знаменатель...?

[scenic holly]

Да

[quasi bison]

ну так вы всю дробь в куб возвели, конечно же

[scenic holly]

А

[scenic holly]

Тогда это действительно правильно, спасибо

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[blazing kindle]

hey guys do u plss give me any resource to learn probability from basics to advance

[safe radish]

@blazing kindle Has your question been resolved?

[quasi plume]

see #books and/or #book-recommendations

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[lean otter]

hi, I was wondering how I can solve this without any differentiation:

[lean otter]

$\lim\limits_{x\rightarrow1}x^{\tfrac{1}{x-1}}$

[flat frigate]

CWolf

[quasi bison]

let f(x) = x^(1/(x-1)), then log(f(x)) = log(x)/(x-1)

[lean otter]

I'm not sure I follow

[quasi bison]

f(x) is what you want to find the limit of

i am suggesting that you find the limit of its logarithm instead

[lean otter]

Oh yeah like that

But doesn't that still go to 0/0?

[pure agate]

Yes, and you apply L'hopital.

[lean otter]

Wish I could, but we can't use any sort of differentiation :/

[pure agate]

Just an arbitrary rule or you haven't learned differentiation yet?

[lean otter]

We haven't learned it yet, so we're also not allowed to use it

Maybe we're supposed to bring it back to a standard form of e if possible

[quasi bison]

not even the definition of the derivative...?

[lean otter]

Nope...

[quasi bison]

[lean otter]

I'll ask our professor what we're supposed to do

Thanks to both of u!

[pure agate]

I'm actually curious about how one would solve this without differentiation. I would assume you have not learned how to use logarithms to simplify problems.

[quasi bison]

you must know either $\lim_{t \to 0} \frac{\log(1+t)}{t} = 1$ or $\lim_{t \to 0} \frac{e^t-1}{t} = 1$

[flat frigate]

Ann

[lean otter]

I'm gonna assume that's what he's looking for

thanks 😄

That makes my original equation e^1

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[lean otter]

Okay I think I get what it is

[lean otter]

I think he wants us to let x = (1+1/y)

which turns the whole thing into

$(1+\dfrac{1}{y})^y$

[flat frigate]

CWolf

[lean otter]

= e

i think

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[desert axle]

I want to be clear on something here.
I have these two matrix:

What kind og matrix are they? B is not a upper triangular matrix and C is not a lower triangular matrix right? But they are instead anti-diagonal, please correct me if Im wrong.

Also, I had to calculate the determinant. And I know when a matrix is either on upper or lower triangular form you can just multiply all diagonal-elements. Does that also work with "all" anti-diagonal matrix.
Because I can calculate the determinant of C by multiplying all diagonal-elements correctly as: det(C) = -3*(23(-1))9 and -3(23(-1))*9 = 162

If I had to calculate the determinant of B, I would not be able to just multiply all diagonal-elements as it gives a result of -22, but I need 22. Which is why Im calculating like this:

[desert axle]

Is there a rule with, if you have an odd number of negative values in the diagonal you need to multiply with -1 also, when multiplying all diagonal-elements?

[safe radish]

@desert axle Has your question been resolved?

[safe radish]

@desert axle Has your question been resolved?

[desert axle]

<@&286206848099549185>

[peak estuary]

you can just imagine it as switching the columns

each time you swap two columns you change the sign of the determinant

in the case of B you have to swap once, 1<->3, so you get a factor of -1

in the case of C you have to swap twice, 1<->5 and 2<->4, so you get a factor of (-1)(-1)=1

[desert axle]

How can you tell which you had to swap?

[peak estuary]

I mean I could have also swapped others

but this seems like a very obvious choice here

[desert axle]

Oh yea sorry, I get it

[peak estuary]

it turns out that you always have to swap either an even or odd amount of times but that's harder to see

[desert axle]

You basically meant this right?

[peak estuary]

what

[desert axle]

Or am I totally wrong

ahah

[peak estuary]

https://i.imgur.com/gG3Hj5U.png

[desert axle]

Ohh

If had to explain the type of these matrix both B and C, would I describe them as anti-diagonal?

[desert axle]

@peak estuary

[peak estuary]

upper left triangular or something. calling something anti-diagonal if it includes values that arent on the antidiagonal is not a good idea

but why are you encountering a lot of matrices like that

are you sure that you cannot simply reorder the columns?

[desert axle]

I can, it's just that I want know what kind of matrices they are - if they had some special name. I'm calculating the determinant, I also have to include text with it - so I was just wondering what I could explain regarding the matrices and with that include some kind of title for the matrix

@peak estuary

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@desert axle Has your question been resolved?

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[cerulean tusk]

Hey, I’m not too sure where I’ve gone wrong on this

[cerulean tusk]

Apparently the answer isn’t correct

[glass carbon]

b = 5/2

right?

[cerulean tusk]

Yes

[glass carbon]

,w int from 1 to 5/2 of 4x^3 - 20x^2 + 29x + 10

[flat frigate]

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[glass carbon]

mhm, maybe post the original problem

[cerulean tusk]

Here

[kind fractal]

,w roots of 4x3-20x2+29x-10

[flat frigate]

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[kind fractal]

The intersections are ok

[kind fractal]

It's asking for the area, so you have to make sure you get positive areas

from 1 to 2, the function is positive

Then from 2 to 2.5 the function is negative

Area must be positive, so you just take the absolute value of that result, and add it to the integral from 1 to 2

[cerulean tusk]

It stays above the x axis between 2 and 2.5 no?

[kind fractal]

No, it says enclosed by the x axis and the function

between x=1 and x=b

[cerulean tusk]

Right ok. But the area between there is positive no? It’s still above the x-axis

[kind fractal]

Check the function

it's -10

[cerulean tusk]

Ok I definitely see that now, that’s fixed all of my problems

Thank you

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[fickle trail]

Not saying it's a good idea to do so, certainly not.. but could you use the quotient rule to solve this?

or it needs to be function divided by function to use quotient rule?

Actually let's take it back..

I think I can see these rules

all kind of come from the Product Rule

One Rule to Rule Them All

[obtuse jackal]

Fun fact about differentiation rules: it's never wrong to apply them

[fickle trail]

x/7 could be written as (7^-1)x

[obtuse jackal]

More like 1/(7/x))

[snow robin]

you could use any of the rules if you can turn it into that form

[obtuse jackal]

That's what I meant

[obtuse jackal]

This is then subject to the chain rule and the quotient rule for instance

[fickle trail]

wait, it's not ((7^-1)x)/1 ?

[obtuse jackal]

Also

[fickle trail]

I'm bringing 7 from the denominator up to the numerator

not talking about d/dx here, just how to rewrite this

or 1/7x^-1

[fickle trail]

but i don't see how it could be this?

[plucky elk]

Dividing by a fraction is multiplying by the reciprocal

[fickle trail]

x/1 * 1/7 ?

I will write this out, may be easier for me to see..

[obtuse plover]

$\frac{1}{\frac {7}{x}} = \frac 11 \cdot \frac {x}{7}$

[flat frigate]

Stephen

[plucky elk]

Always a good idea with fractions

[fickle trail]

Interesting...

I need to work on that last one more

but it's true

it's like pulling a 1/1 out of any expression (can always be done)

[dull sequoia]

If you take your fraction

And take it to the -1 power twice

You flip the numerator and denominator

Then put it 1 over

[fickle trail]

interesting...
I think it's the third example is the hardest one to interpret, but maybe because I'm just not used to it

obv x/7 is gonna be the easiest form

anybody find 1/(7/x) really easy to see what it means? or takes a minute

[obtuse jackal]

It's often overlooked in 7th grade yes

[dull sequoia]

I try to keep my fractions only 2 high

[obtuse jackal]

But after middle school ? Cmon

[dull sequoia]

Any more gets confusing

[misty coral]

if you apply numbers to it , it becomes quite intuitive

1 / (1/2) for example

[dull sequoia]

I think this is fair

[plucky elk]

,calc 1/(1/2)

[flat frigate]

Result:

2

[plucky elk]

[misty coral]

[dull sequoia]

Stacking fractions on fractions makes it a bit hard to see things

[plucky elk]

this is good advice for you avid

[obtuse jackal]

For everyone

[dull sequoia]

Sometimes it’s not possible but I will try my best always

[fickle trail]

well, if I treat division like multiplication (reciprocal of the second term) it makes total sense

[obtuse jackal]

But we were talking about uselessly complicating an expression

[fickle trail]

but I think an extra step is happening here, which is why it can throw ppl off a bit

[dull sequoia]

(a/b)/c is the one I’d struggle the most with

[fickle trail]

yes, true

[dull sequoia]

I always put that as (a/b) * (1/c)

[misty coral]

(a/b)/(c/1) = (a/b) * (1/c) = (a/bc)

[fickle trail]

we all learn at a different pace. no need to feel bad when comparing to others

[obtuse jackal]

Math is THE subject where you can't afford to not know the stuff you've seen before

[plucky elk]

avid had bad teachers

we're the undoers of those bad teachers

[obtuse jackal]

Bad teachers or not. Can't afford

[dull sequoia]

To be really really proficient at arithmetic and manipulating fractions, indicies and forms of expression can get you a very long way in math

[misty coral]

tbf it can somtimes be hard to undo a terrible foundation

[dull sequoia]

Especially all throughout high school

[obtuse jackal]

Yes. That's why a lot of people are bad at math. I didn't say it's easy to fix. Only that it's necessary to keep studying math

[fickle trail]

it's interesting how Symbolab processes this

1/b/c = 1/1 * c/b

[sand minnow]

i you write fractions like this $$\f{a/b}{c}$$then its fine to have fractions within fractions, but $$\f{\f{a}{b}}{c}$$is horrible

[flat frigate]

Duh Hello

[dull sequoia]

I do that too

[dull sequoia]

a/(b/c) = (a/1) * (c/b)

[fickle trail]

but if I saw it like this, I don't think I would know.. is fraction in numerator or denominator?

[obtuse jackal]

That's when big fraction lines come into play

[dull sequoia]

Extremely cringe and definitely make the main divider bigger

[fickle trail]

it will change the answer right?

[obtuse jackal]

Clearly 1/ by the size of the lines

[fickle trail]

oh ya it's like 2 pixels bigger, i didn't see that at first

[dull sequoia]

Or

Use brackets

!!

[obtuse jackal]

Never done that

[dull sequoia]

Brackets are really helpful, use them

[dull sequoia]

Wdym @obtuse jackal

[fickle trail]

@sand minnow yeah this is better practice to avoid skyscraper fractions

[obtuse jackal]

I just use longer fraction lines

[dull sequoia]

On text id use brackets unless it’s getting complicated

Then latex is my friend

[obtuse jackal]

$\frac{\frac{a}{b}}{c}$

[fickle trail]

brackets are a requirement for latex

[flat frigate]

mateo713

[obtuse jackal]

Latex does it just like me

[dull sequoia]

I dislike using / for divide outside of 1 line text math

[sand minnow]

on latex its generally fine

but writing by hand its really hard to tell

[dull sequoia]

Latex formats it okay

[fickle trail]

can you format like this with latex?

[dull sequoia]

Yes

[dull sequoia]

That’s in latex

Wdym

[fickle trail]

i mean, lol

how did you format like this, @sand minnow ?

[dull sequoia]

Use /

[fickle trail]

oh

[dull sequoia]

@fickle trail look at this message

You can see out people formatted things

[fickle trail]

oh ya

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[safe radish]

Please don't occupy multiple help channels.

[thorny dock]

How do you even start with this question?

Thoughts: By Lagrange's theorem, 18 | G and 24 | G => lcm(18,24) | G

so 72 | G?

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@thorny dock Has your question been resolved?

[zinc token]

yes

but now thats not the order of H cap K

H cap K is a subgroup of H and of K

@thorny dock

so this should tell you all you need

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[misty bay]

Suppose ammunition costs approximately $0.30 a round (the exact cost is not so relevant, but I hope it motivates this question). Suppose I model the trajectory of a bullet after it is fired from a firearm as v'(t) = -g*e_2 - f(v), where e_1 is the basis vector pointing forward, and e_2 is the basis vector pointing upward, and f(v) is some function to be estimated. Note that f(v) = kv is typically used at lowish speeds and f(v) = kv^2 gives drag at higher speeds. It's anticipated that f(v) will be somewhat continuous. We don't have any fancy technology, except a protractor / angle measurement device and a GPS unit. Perhaps in the future, we'll acquire some sort of accurate timing system if we need it, but basically this means that we can only measure two things:

1. the angle that the bullet is shot at
2. the starting and ending positions of the bullet, but only to a reasonable accuracy (let's say we're only about accurate to 5 cm).

We, however, are allowed to fire perhaps 500 rounds out of the firearm at varying angles, keeping in mind that the firearm also has some intrinsic inaccuracy.

Are these measurement devices enough to estimate:

1. the muzzle speed of the bullet
2. a curve for f(v)?

My gut says no, but I don't have much more than that. What's a good way to estimate/interpolate f(v) without expending too much ammunition? Something like fitting a spline through whatever points we get?

[misty bay]

(this is like part 4 of a really long discussion with country hillbilly friends of mine who own firearms)

[safe radish]

@misty bay Has your question been resolved?

[spiral bane]

Muzzle speed you only need one shot

That’s just projectile motion

[misty bay]

given that you basically only know the distance it travels before falling down to the ground

[spiral bane]

Why do you want to estimate drag

[misty bay]

how would you distinguish from the scenario where there's high drag and a high muzzle speed or low drag and a lower muzzle speed?

[spiral bane]

You know the angle too

You’d have to ignore drag to keep it simple

[misty bay]

clearly I can't do that

[spiral bane]

You can maybe integrate f(v) though

Since you can use the drag equation

[misty bay]

what would integrating f(v) give

[spiral bane]

Impulse

Have you taken physics before

[misty bay]

how would it give impulse

[spiral bane]

Oh sorry I thought f was a force

[misty bay]

it's proportional to force, yeah

[spiral bane]

I think you can do something with it

Find either the change in velocity or the acceleration from drag

Find the surface area of bullet, air density, etc

[misty bay]

what would that tell me?

[spiral bane]

The drag equation

[misty bay]

that would only allow me to possibly extrapolate f(v) to other bullets

[spiral bane]

Based on v

[misty bay]

and I probably will do something like that, but for now, I'm concerned with only one bullet

[spiral bane]

Yeah

[misty bay]

or rather I have 1000 bullets that are identical

[spiral bane]

We’re only talking about one bullwt

[misty bay]

so what would the surface area tell me

nothing

[spiral bane]

You need it for the drag equation

You can find k basically

[misty bay]

what are you talking about

[spiral bane]

f(v) = kv

[misty bay]

this issue here is that the drag coefficient is not a constant coefficient when it comes to bullets

this is why you cannot say that f(v) = kv or f(v) = kv^2

[spiral bane]

How come

[misty bay]

because it just isn't

[spiral bane]

So then f(v) is like parametric?

[misty bay]

in particular, there's a marked difference in drag when the bullet goes from the supersonic to subsonic

f(v) is probably some weird-looking curve

[spiral bane]

You know a lot more than I thought

Probably ask this in a physics server then

[misty bay]

this is a math problem

[spiral bane]

Sounds like physics to me

[misty bay]

the stuff about drag is just for context

but ultimately this is just a differential equation with some undetermined stuff, and you're given points of a very specific form

[spiral bane]

Can you abstract your question then to a purely mathematical question

[misty bay]

I literally did

you were the one who wanted to say that f(v) = kv, and I told you why that doesn't work

[spiral bane]

I thought you were going to use different ones at difffernet launch speeds

Not midway through

[misty bay]

I have identical rounds, and I cannot feasibly control the launch speeds, and measuring them directly is actually pretty painful to do, so I'd prefer not to

[spiral bane]

yeah I get that now

This is definitely something physicists could also do so I don’t think it would hurt to ask there as well

[misty bay]

this is not about physics anymore

well yeah because physicists know stuff about DEs

[spiral bane]

physics is mostly math

Plus they have experience with your context

That’s all I’ll say

[safe radish]

@misty bay Has your question been resolved?

[safe radish]

@misty bay Has your question been resolved?

[safe radish]

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[covert merlin]

idk why but when i complete the square, and even try the quadratic formula, i get 0.835 as my positive answer, but its not right and idk what im missing, can someone pls help? ty

[arctic condor]

What formula are you using?

@covert merlin

!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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[arctic condor]

This seems correct, what did you do next?

[covert merlin]

i did this but i dont think its rihgt

[arctic condor]

It isn't

What is the standard form? Can you recollect it?

[covert merlin]

like this?

[arctic condor]

This is the formula but what needs to be the original equation to apply this formula?

[covert merlin]

ax^2 + bx + c

[arctic condor]

Forgot the equals to zero

Anyway, now tell me what is a, b and c in your original equation?

[covert merlin]

oh mb

[covert merlin]

a = pi
b = 5pi
c = -20

oh

OH

wwait imma do it agaiin

and see

[arctic condor]

👍

[covert merlin]

wait so

i think i did smth wrong again

i definitely did something wrong

wait im like

BIG dum

omg

[covert merlin]

tytyty

.close

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[arctic condor]

No problem

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[halcyon plover]

Can someone check if this is correct?

[safe radish]

@halcyon plover Has your question been resolved?

[halcyon plover]

<@&286206848099549185>

<@&286206848099549185>

[halcyon plover]

<@&286206848099549185>

[halcyon plover]

<@&286206848099549185>

[twin ravine]

Very Sorry

[halcyon plover]

<@&286206848099549185>

[hasty wagon]

hello there, do you still need help with your question ?

[halcyon plover]

Yes

Could u check if its. Right

[hasty wagon]

let's do it one by one

for the first one

what do you need to enter?

[halcyon plover]

( a,b)(e,f)
(c,d)

[hasty wagon]

it says to perform matrix product

does it mean that you'll have to multiply the two matrixes for you to answer the question?

[halcyon plover]

No

[hasty wagon]

oh ... then i don't really understand what it is asking

[halcyon plover]

I think we just have to setup

[hasty wagon]

i see

then i think your answer is correct

next question

[halcyon plover]

Yep

[hasty wagon]

do you have any workings to show so that we can check it?

[halcyon plover]

I did it on a calc

Should I write it out

[hasty wagon]

nah

maybe ill use excel to check

it'll take a while

[halcyon plover]

Alr

[hasty wagon]

correct

both questions done and correct!

Great job! @halcyon plover

[halcyon plover]

Ty

Are you good

With linear alg?

Or nah

[hasty wagon]

so so

if you have other questions, you can post it in a new help channel

[halcyon plover]

Alr

[hasty wagon]

that'll give you better chance having ppl to answer.

[halcyon plover]

It usually takes long to answer my questions lol

But thx appreciate it

.close

[safe radish]

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[safe radish]

@keen peak Has your question been resolved?

[safe radish]

@keen peak Has your question been resolved?

[keen peak]

<@&286206848099549185>

[safe radish]

@keen peak Has your question been resolved?

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[safe radish]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[stoic tree]

What's the probability of winning 1st, 2nd or 3rd place in a contest with 10 players by random chance (all players having the same chances of winning)?

[compact ferry]

3/10

[potent bay]

i think he meant separately, like 1/10 1/10 1/10

[stoic tree]

yea

i saw

of desired outcomes / # of possible outcomes but im confused

is it

1/4 (given you could not win either of the three)

[potent bay]

no, this is the sol

[stoic tree]

then in percentage it would it be 30% chance of winning and 70% chance of losing, correct?

[potent bay]

if winning means standing on the podium somewhere, then yes

so we have 3 winners in your case

[stoic tree]

dawg im dumb 💀 i originally thought of 30% but was unsure

thank youu

.close

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[frail elm]

Hi guys i’m stuck here, i need to find BS, AB is parallel to DE, i found that i could use pythogras to find BC, which could help me find CE cuz DEC and ABC are like the same thing, and then i can find DE with pythagoras, but after that i’m stuck

[safe radish]

@frail elm Has your question been resolved?

[frail elm]

<@&286206848099549185> :(

[young nexus]

you can caluclate DE. can you?
you can calculate DB, can you?

[frail elm]

Oh wait i can do DB

And via that use a table to cLculate ds, right?

[young nexus]

DS:SB = DE:AB

[frail elm]

wait one second please, i’m going to try

I come out on BS ≈ 9

I took another way than what the answerbook said, but i still got it right, thanks

.close

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[keen mural]

How could I prove this identity in the least amount of steps?

[keen mural]

(Only using trig.)

I just keep trying to solve it and it expands to ridiculous lengths without ever finding a solution

wait

I think I got it, actually

the identity of tan(a-b) is (tan(a)-tan(b))/(1+tan(a).tan(b))

the formula on the left is that but with a+b instead of a

so I write it as tan(a+b-b)=tan(a)

it was so easy

[obtuse plover]

Good work

(Assuming ur right)

[keen mural]

I keep struggling with trig identities, though

Sometimes I get really stuck

[obtuse plover]

It’s okay, everyone gets really stuck sometimes

Keep working on them

[keen mural]

.close

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[safe radish]

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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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.

[halcyon plover]

How would I start off this problem

[hot thistle]

do you know what being a member of that vector space entails?

[halcyon plover]

Could u explain

Wdym by that

[hot thistle]

do you know what "(x,y,z) is a member of V" means?

[halcyon plover]

U have to reduce row right

Its 3 elements in a set