help-17

[graceful scarab]

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[blissful drum]

I have six 3D vectors, and I need to multiply them each by their own scalars, ranging from -1 to 1, in such a way that the result points in the same direction as a 7th vector. At the same time, I must also choose the scalars that maximize the magnitude of this resulting vector.

If someone could just tell me what type of problem this is, I could look up the proper way of solving it.

[lilac pebble]

after multiplying them, are you adding the six vectors?

[blissful drum]

Yes. All together.

There are six different scalars. They all have one.

At least three of the vectors should always point in different directions. But some of the vectors can point in the same direction as eachother.

I can write my current solution. But it has a lot of holes in it, so I would much rather find an official way of doing this problem.

[lilac pebble]

sorry i have to go

[blissful drum]

Oof. Thanks for responding.

[lilac pebble]

interesting problem though

[blissful drum]

I think it can't be too uncommon. Too close to linear algebra.

[vocal sleet]

@blissful drum Has your question been resolved?

[vocal sleet]

@blissful drum Has your question been resolved?

[coral chasm]

As far as I know, this is a constrained optimization type of problem

The constraint is that you need the results points in the same direction as a 7th vector while maximizing the magnitude

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[vast shale]

How do i draw the diagram for this problem? i have a hard time understand bearings related questions

a ship is sailing due north. at a certain point, the bearing of a lighthouse 7.9km away is N38.7°E. later, the captain noticed that the bearing of the lighthouse has become S33°E. how far did the ship travel between the two observations of the lighthouse

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@vast shale Has your question been resolved?

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@vast shale Has your question been resolved?

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[night chasm]

Can anyone please help me solve the determinant

[hollow kite]

just try to get zeroes under a certain column or row

[vast shale]

Do transformations

[night chasm]

I tried converting it into a triangular matrix and got the answer -105

the answer is 0, but I have no clue why

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[night chasm]

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[abstract palm]

how to determine absolute convergence of $\sum_{n=1}^{\infty}\frac{n+2^n}{1+(-3)^n}$?

[twin meteor]

Slowaq

[abstract palm]

I could use limit comparison test with (2/3)^n but i donr kniw how to solve that limit

[spiral turtle]

have you heard about the geometric series?

[abstract palm]

Yes

[spiral turtle]

do you know the formula for the geometric series?

[abstract palm]

Sorry but no

[spiral turtle]

that's ok, let's build up to it

consider a finite sum: 1 + a + a^2 + a^3 + a^4

what happens if I multiply this sum with the value (1 - a)?

[abstract palm]

I’ll get 1-a^4?

[spiral turtle]

1-a^5

[abstract palm]

Ah yes sorry

[spiral turtle]

(1 + a + a^2 + a^3 + a^4)(1 - a) = 1 - a^5

so we have our sum is equal to (1 - a^5)/(1 - a)

[abstract palm]

Yes

[spiral turtle]

obviously this is a pattern that holds for exponents larger and smaller, if we have a sum up to a^n then we have (1 - a^(n+1))/(1 - a)

what happens if n gets very large provided a < 1?

[abstract palm]

Then it goes to 1/(1-a)?

[spiral turtle]

exactly!

so now for your question, we have a = 2/3

[abstract palm]

Why did we omit n in numerator?

[spiral turtle]

well, the n becomes absolutely tiny compared to 2^n eventually, but you do need to consider it, because the limit comparison test requires that you choose a series that is greater than or equal to the original for each term.

[abstract palm]

Yes that’s why I didn’t know how to use limit comparison test

[spiral turtle]

so consider the series sum 2 * (2/3)^n

is this series larger than your at each term?

[abstract palm]

yes because 2^n+2^n>n+2^n for all n ≥0

[spiral turtle]

👍

so do a limit comparison test against 2 times (2/3)^n

[abstract palm]

this is the problem ive encouncered because i dont know how to solve $\lim_{x\to\infty}\frac{(n+2^n)3^n}{|1+(-3)^n|2^{n+1}}$

[twin meteor]

Slowaq

[abstract palm]

,w lim n to inf |(n+2^n)3^n/(1+(-3)^n)2^n|

[twin meteor]

Results provided by WolframAlpha

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Requested by slowaq

[abstract palm]

how should i do it then?

@spiral turtle

[spiral turtle]

you don't need to calculate the limit explicitly to determine absolute convergence

The explicit value of that limit is surely heinous

[abstract palm]

ah so i just need to determine whether its (0,\infty) or infty?

[spiral turtle]

[
\qty|\frac{n + 2^n}{1 + (-3)^n}| < \qty|\frac{n + 2^n}{(-3)^n}| < \qty|\frac{2^n + 2^n}{(-3)^n}| = \qty|2 \frac{2^n}{(-3)^n}| = 2 \frac{2^n}{3^n}
]

well, with absolute values around everything

There.

[abstract palm]

alright alright so it goes to 0?

[spiral turtle]

Well, it's not enough that the value goes to zero, because 1/n goes to zero as well.

[twin meteor]

OmnipotentEntity

[abstract palm]

$\lim_{n\to\infty}\frac{2\frac{2^{n+1}}{3^{n+1}}}{2\frac{2^n}{3^n}}=\frac{2}{3}$

thus it sould converge absolutely?

because this is between 0 and 1

[twin meteor]

Slowaq

[abstract palm]

@spiral turtle

[spiral turtle]

I believe that is sufficient yeah

[vocal sleet]

@abstract palm Has your question been resolved?

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[hard radish]

For number 6 is there a way to

Quickly do it

Ik to find the lcd first but it's too slow

And I thought maybe there's another method

[tired gate]

The LCD is 20×21×41×53, so you just need to do 4 2 digit multiplications and 3 additions

[hard radish]

? Wdym

<@&286206848099549185>

[vast shale]

hey i have an i dea but how to show it using latex here ?

well anyway my idea is the second half and the last one that will gives you 1/20 x 21 and add the first term with the 3rd one that gives 1/ 21 x 32 then adding the two results gives 52 / 20 x 21 x 32 and i think u can simplify it more

[paper estuary]

japanese?

i cant read japanese

[merry shuttle]

notice 32,53 and 20,41 have the same difference of 21

1/(32*53) + 1/(20*41) multiply and divide by 21, then express 21 as 53-32 and 41-20 as needed to get 1/21 * [(53-32)/(32*53) + (41-20)/(41*20)] seperate the denominator 1/21 * [1/32 - 1/53 + 1/20 - 1/41] if u expand this then 1/(21*53) and 1/(21*41) will cance

[hard radish]

Bro it's chinese 😭😭😭😭

[hard radish]

I'm so confused

[vast shale]

i dunno what u need to get as a result but if u need the sum i think my solutions is easy and quick

there is no need to use the LCD here

[hard radish]

What is it?

[vast shale]

this one

[hard radish]

I don't understand what your saying here ●_●

I'm now more confused then before

[vast shale]

okay i gonna write it in a latex file and send it here (i dont know how to use latex in discord)

[hard radish]

Oh shi your right

[hard radish]

👍👍

[hard radish]

Ty this actually helps so much

I'm gonna still try to find an even faster method (hope fully)

[vast shale]

here it is

[hard radish]

Could I ask how did it become like that I'm super confused on just that part

[vast shale]

ooh okay it is just basic algebra i gonna show u wait a bit

hhh i tried to explain it then ive got lost

:/

[hard radish]

I think I know already

I think

Cus I js now asked chat gpt

And it explain very badly

But I still somehow understood it lol

[vast shale]

is this better

[vast shale]

hhhhh at least u got it

the first "=" it should be "+"

[hard radish]

Yup

Tysm

I hope you have a good day or night cus I need to sleep now it's 1:30 am for me

.close

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[small valve]

Need help with integrating with trig identities and under a root

[small valve]

I am trying to perfect my integration skills but I’m having a bit of trouble with using trig identities

And integrating from under a root

I’ll send the equations I’m currently working on

For the first one, I’m not sure at all. In the second one my instinct is to write the root as a fraction

Like converting the root to 1/2 and adding 1 to make it 3/2 over 3/2. I’m not totally sure what to do with the inside. U substitution I’m not sure if this is an option here.

[odd helm]

no

[vital sable]

My wifi lagged

Sorry

[odd helm]

ok

[vital sable]

I sent that message when the channel was open

[odd helm]

try t²=2sin^2(theta)

no idea how to do the first

[vocal sleet]

@small valve Has your question been resolved?

[small valve]

i wanna know how to solve it tho

[odd helm]

integration by substitution

[small valve]

did you do u substitution?

i'm not sure about that

[odd helm]

yes it's substitution

[small valve]

can you walk through how you solved it

[odd helm]

do the substitution

[cunning saffron]

are you sure you meant for the power to be inside of sin ?

because that sin^3(x) and sin(x^3) is really different, and the later is much more difficult than the first

[small valve]

yes

i'll send the book page for it

wait no

it was sin^3(x)

sorry

[cunning saffron]

yeah, that's what i thought

[small valve]

i am having a bit of trouble integrating trig functions

i can derive them fine but

[cunning saffron]

sin^3(x) is with substitution

[small valve]

i guess the question is how to do trig integration

in general

i'm having a bit of trouble with it

[cunning saffron]

well, there isn't really only one way

for this one, you have to know that sin^2+cos^2=1, and find a good substitution

[small valve]

so the double angle formulas

?

[cunning saffron]

no

[cunning saffron]

just this one

try to expand sin^3 and see if you can find something

[small valve]

i'm not sure how

idk trig makes me a bit anxious

[cunning saffron]

expand sin^3(x) and find a link between what you find and sin^2+cos^2=1

if you're still struggling for this, is you change a bit sin^2+cos^2=1, you can see that
sin^2+cos^2=1 <=> sin^2=1-cos^2

and then you can use u = cos for the substitution

[vocal sleet]

@small valve Has your question been resolved?

[small valve]

So I just break down the trig formulas until it’s easier to integrate with u sub?

[cunning saffron]

yeah

basically

[small valve]

Do you memorize them or

[vocal sleet]

@small valve Has your question been resolved?

[cunning saffron]

yeah

sry for the late reply, wasn't paying attention to this channel

did you managed to get the integral ?

[small valve]

no i still am having trouble

[flat whale]

Read the examples here
https://tutorial.math.lamar.edu/classes/calcii/TrigSubstitutions.aspx

[small valve]

reading them

[nocturne geyser]

!status

[vocal sleet]

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

[vocal sleet]

@small valve Has your question been resolved?

[split cairn]

with which one?

[vocal sleet]

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[eternal glacier]

What do I do here with numerator

[orchid walrus]

$\frac{\sqrt{2x+1}+3}{\sqrt{2x+1}+3}$

[twin meteor]

syecko

[eternal glacier]

Difference of squares is not helping for numerator?

[orchid walrus]

don't be so sure of yourself

[eternal glacier]

I messed it up?

[orchid walrus]

yes

[eternal glacier]

I don’t see how this would help tho

[orchid walrus]

i suggested multiplying your original expression by this

[orchid walrus]

because what you did accomplishes nothing

[eternal glacier]

Oh it’s the conjugate

[orchid walrus]

and it wasn't my suggestion either

[visual marsh]

just use L-Hospital?

[orchid walrus]

$\frac{\sqrt{2x+1} -3}{(x-4)(x+4)} \cdot \frac{\sqrt{2x+1}+3}{\sqrt{2x+1}+3}$

[twin meteor]

syecko

[orchid walrus]

how about no

that's not a good suggestion, this is much simpler

[visual marsh]

ah even yrs is correct

[eternal glacier]

I must have screwed up somewhere

[orchid walrus]

$\frac{\sqrt{2x+1} -3}{(x-4)(x+4)} \cdot \frac{\sqrt{2x+1}+3}{\sqrt{2x+1}+3} = \frac{(2x+1)-9}{(x-4)(x+4)(\sqrt{2x+1}+3)}$

[twin meteor]

syecko

[orchid walrus]

can you finish it from there?

@eternal glacier

[eternal glacier]

Could I also solve it this way

[orchid walrus]

why would you do that

[eternal glacier]

Or I need to use denom

[orchid walrus]

2x-8 = 2(x-4)

cancel the x-4

[eternal glacier]

But why do it this way

Seems like more work

[orchid walrus]

and you are missing the sqrt(2x+1)+3 term on the bottom

[orchid walrus]

because it is correct

[vocal sleet]

@eternal glacier Has your question been resolved?

[eternal glacier]

I am shocked with this question

Far too much work involved

Not sure if I did that denominator calculation correctly

[orchid walrus]

this is not correct

[orchid walrus]

look here

[eternal glacier]

Just the denominator?

[orchid walrus]

no

[eternal glacier]

Or all of it

[orchid walrus]

your second line is wrong

i mean ok technically its equivalent but why are you multiplying by that fractional expression again

[eternal glacier]

Oh I put a 9 for some reason

[orchid walrus]

just stop once you get to what is written on the right

then do as i said before

[orchid walrus]

here

[eternal glacier]

Closer

Still not there yet

How do I keep messing this up

[orchid walrus]

your parentheses

[eternal glacier]

Something with the denom is wrong

[orchid walrus]

its (x+4)(sqrt(2x+1)+3)

[eternal glacier]

Oooo

Foil

[orchid walrus]

no just let x = 4 here

[eternal glacier]

Didn’t I already tho?

[orchid walrus]

no

you did (x+4)(sqrt(2x+1)) + 3

$(x+4)(\sqrt{2x+1}+3) \neq (x+4)(\sqrt{2x+1}) + 3$

[twin meteor]

syecko

[eternal glacier]

You mean it should be this?

[orchid walrus]

no it should be that

$\frac{2}{(8)(\sqrt{9}+3)} = \frac{2}{(8)(6)}$

[twin meteor]

syecko

[orchid walrus]

@eternal glacier

do you see your mistake yet

[eternal glacier]

I think so

I added 3 after multiplying

I should have added 3 before multiplying

I'm still getting used to 11" M4 iPad Pro with Apple Pencil Pro, damn thing is more work to use than just typing on MacBook Air

maybe I should get familiar with LaTeX if it saves me a lot of time and frustration

[orchid walrus]

yes

you should

[eternal glacier]

I thought iPad would be superior for math class, but maybe not

[orchid walrus]

there are numerous resources online

[eternal glacier]

I guess drawing diagrams is nice on it

[orchid walrus]

it is for note taking

[eternal glacier]

I'm tempted to return it and just learn LaTeX going forward

[orchid walrus]

that's not a terrible idea

[eternal glacier]

lol

[orchid walrus]

you can type up all of your homework

[eternal glacier]

yeah

[orchid walrus]

and if you self study you can do the same

[eternal glacier]

maybe I should use paper and re-type with LaTeX

[orchid walrus]

yes exactly

[eternal glacier]

damn.. i guess i'm going to the Apple store tomorrow lol

[orchid walrus]

they are overly expensive

[eternal glacier]

ya

[orchid walrus]

did you buy a newer edition as well

[eternal glacier]

ya, i found TouchID on iPad is really horrible, only works half the time

and I wanted to use Pencil Pro, so stuck with newest for that

[orchid walrus]

lol

yea that costs like what 800?

might as well cut your losses

[eternal glacier]

FaceID works great, and ProMotion display is nice too
I may still keep it for the gym, it's good when doing cardio and watching calculus videos

[orchid walrus]

calculus videos on an ipad in the gym

never would have imagined it

[eternal glacier]

not the 13" haha that would be too much

but 11" seems like the sweet spot, and mini is too small for actually writing on

[orchid walrus]

calculus videos were never really my genre of hype music

[eternal glacier]

lol

[orchid walrus]

cardio doesn't require much intensity though so i can see how

[eternal glacier]

ya when i lift i will open up Spotify

sometimes just watch Netflix on treadmill, depends how I'm feeling

i need as much practice as possible with this stuff tho, trying to eliminate distractions

[orchid walrus]

i skip cardio, don't shame me

[orchid walrus]

good idea

[eternal glacier]

how long have you been using LaTeX? worth learning exclusively, or still use pencil for maths?

[orchid walrus]

i have been using it for close to 6 months now i believe

and it is definitely worth learning

[eternal glacier]

maybe i just need to get the Magic Keyboard so i can use LaTeX and the Pencil Pro together

another $300 down the drain for that lol

[orchid walrus]

yes you could always use the ipad as a laptop but if you already have the macair i dont see much of a point

pick one

and get rid of the other

[eternal glacier]

yeah, exactly. i think MBA for non-math classes, and iPad for math class only

[orchid walrus]

i know people who use ipads to serve both functions

[eternal glacier]

I can't use iPad exclusively unfortunately, learning Java and it requires macOS

[orchid walrus]

ahh yea then i don't see much of a point of keeping it

i regret buying mine

[eternal glacier]

or maybe just for the gym and math class, we'll see.. i'll try to give it a go, maybe with keyboard it will be more useful with LaTex and the Pro Pencil

it's so light now, way lighter than MBA

[orchid walrus]

yea i mean i definitely use it over paper

[eternal glacier]

display looks great, 120Hz, Pencil Pro is nice, but locked to iPadOS sigh

if we could run macOS on iPad, that would be ideal
but it will never happen because it would cannibalize laptops

[orchid walrus]

indeed

[eternal glacier]

which size and model do you have?

[orchid walrus]

let me see hold on i forgot

[eternal glacier]

Oh and there is Universal Control, I can use MBA keyboard for iPad, maybe I will just do that

[orchid walrus]

its an 11 inch ipad air

i guess it was the 2024 version?

[eternal glacier]

i started with that one but TouchID is what just didn't work for me

[orchid walrus]

really?

[eternal glacier]

95% of the time it requires passcode

ya

[orchid walrus]

haven't had a problem once

[eternal glacier]

hmmm, maybe mine was just faulty
but now that I have 120Hz it is kinda nice, feels smoother when writing

unlocking is no problem, it sees me before I even try to use it

[lilac pebble]

IMO latex isn't a great choice for note-taking

[eternal glacier]

ah OK

lol

[orchid walrus]

take notes by hand first

[eternal glacier]

on the iPad 😄

[lilac pebble]

latex is for making stuff look pretty

[orchid walrus]

yes

[eternal glacier]

https://www.youtube.com/watch?v=gITRodzr704
iPad with practice too

[lilac pebble]

if you want your notes to look pretty you could use latex, but the downside is you probably won't be able to take notes as fast

[eternal glacier]

I am using white ink on black, like this video, and I like it a lot better

the text is easier to read at small size

[orchid walrus]

i think it is a good idea to copy handwritten notes into latex

[eternal glacier]

i may do that from iPad (GoodNotes) to MBA (LaTeX) if I have the time

[orchid walrus]

if you have the time

[eternal glacier]

on the treadmill

https://tenor.com/view/ellen-treadmill-desk-exercise-working-gif-3527839

[lilac pebble]

oh it's from the ellen show
she talked about "the hawaii chair" and it was just hilarious

[eternal glacier]

https://tenor.com/view/wearing-fedora-hat-gina-rodriguez-carmen-sandiego-outfit-covering-face-gif-2666498570089878549

tyvm @orchid walrus

[lilac pebble]

there's a mistake in the distribution but it didn't affect the answer

you have 12 twice instead of 3x

(actually you don't need to distribute anyway, you can already substitute at that stage)

[vocal sleet]

@eternal glacier Has your question been resolved?

[vocal sleet]

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[vocal sleet]

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[magic crater]

what do i do here? help please

[merry shuttle]

f(x) = x^(67-f(x))

plug in n for x and find n

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[minor gorge]

Hello. I am trying to understand the proof of the rule of differetiating composition of two functions

[minor gorge]

There is the following equality and for the love of god I cannot wrap my head around how this is derived.

Can someone try to explain it to me

There are some obvious things to do: you can take the f+alfa part of the outer sum and bring it in

then you could swich the order of the sums

but I do not know further

[surreal basin]

try reasoning through this completely separate algebra, where all variables involved are natural, to see if it's any easier[\begin{array}{rl}
=&\sum_{i=1}^3(x_i+a_i)\left(\sum_{j=1}^2(y_{ij}+b_{ij})t_j\right)
\=&\sum_{j=1}^2\left(\sum_{i=1}^3x_iy_{ij}\right)t_j
\&+\sum_{j=1}^2\left(\sum_{i=1}^3((x_i+a_i)b_{ij}+a_iy_{ij})\right)t_j
\end{array}]

[minor gorge]

ok, thanks, I'm gonna try

in the top line there is b_{ig}

[twin meteor]

mtt

[surreal basin]

big mistake on my part

[minor gorge]

np

i got it!

its true

big thank you!

[surreal basin]

np

[minor gorge]

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[magic crater]

how would i do this without a calculator, and what are the procedures

[bronze osprey]

so you get 2024! / 594!

or 595 * 596 * ... * 2024, using the definition of nPr they gave you

now you want to count how many multiples of 11 there are

these multiples may not only have 11^1, but also 11^2 and 11^3

,calc 11^3

[twin meteor]

Result:

1331

[bronze osprey]

so there are no numbers which are a multiple of 11^4 in here, that's too big

[bronze osprey]

if you know anything about Pascal's triangle this should be quite natural

worst case you multiply 121 * 11 by hand

[bronze osprey]

have you heard of the problem about finding the number of trailing zeroes at the end of 100!

it's the same strategy

[magic crater]

how can i apply pascals triangle into this?

[magic crater]

ill look into it

[bronze osprey]

you don't apply Pascal's triangle except for calculating 11^3

what is useful is the alternating divisibility test for 11

5 - 9 + 4 = 0, so 594 is a multiple of 11
similarly 2024 is also a multiple of 11

so then you need to calculate 594/11 and 2024/11, more specifically, (2024 - 594)/11

to find how many multiples of 11 there are

[hard atlas]

(and dont make an off-by-one error)

[bronze osprey]

very true, luckily we leave out the 594 endpoint and include the 2024 endpoint

but yes if you want to find the number of multiples of 5 in 5, 10, 15

the answer is not 15/5 - 5/5 = 2

this will be very useful for finding the number of multiples of 11^2

the off-by-one concept

[visual marsh]

what are you guys getting x as?

[bronze osprey]

313?

[visual marsh]

i got 143

[vast shale]

ya 143

[visual marsh]

ig u are overcomplicating stuff

[bronze osprey]

,calc (2024 - 594)/11

[twin meteor]

Result:

130

[bronze osprey]

ah not 300 but 130

yes I get 130 + 13 = 143

[visual marsh]

https://www.youtube.com/shorts/jIa_TjxNdVM
just use the concept shown in this vid

[vast shale]

finding x was easy but how do we find k now?

[visual marsh]

we only need x

[vast shale]

oh right

[vocal sleet]

@magic crater Has your question been resolved?

[magic crater]

okay so we will count how many multiples of 11 there are in both 2024 and 594, for 2024 is 11^3, 11^2 and 11^1 and for 594 its 11^2, 11^1

[magic crater]

so why exactly do we do this?, we are finding the multiple (k) of 11^1 i believe but we already found 11^3 and 11^2

[vast shale]

Watch this video, you simply need to calculate the highest power of 11 in 2024! and then in 594! and then simply subtract them

[magic crater]

okay thanks i will see

[bronze osprey]

yes, we are finding how many times 11^1 appears

you still need to do 11^2 for yourself using the same method

11^3 = 1331 so there is exactly one copy

[magic crater]

multiple 11 appears 3 times in 2024 i thought?

[visual marsh]

or u can just see this

[bronze osprey]

no, 11^3 * 2 > 2024 already

[mental egret]

2024!/594! -> [2024/11] + [2024/121] + [2024/1331] - [594/11] - [594/121]

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[magic crater]

.reopen

[vocal sleet]

✅

[magic crater]

i suppose shes working with 2 and 5 cause they are the only prime factors of 100

why did she use the minimum number (24) instead of 97

[visual marsh]

because for getting a 0 u need a 2 and a 5

so whichever is minimum, there will be that many number of zeroes

[magic crater]

why is that the case

[visual marsh]

factorials are being used here

so 100! = 1.2.3.4.5.....99.100

so 2 and 5 are not the only prime factors

for getting a trailing 0, we need it to be a multiple of 10

and for getting something ending with 0, we need minimum 2x5, which is basically multiplying by 10

do u understand what im saying

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[magic crater]

okay, in that case why didnt they just find the multipple of five

[magic crater]

what was the point in finding multiple of 2

they chose 5 anyways at the end

[visual marsh]

to check the power of 2

incase if it comes less than 5

then we take the power of 2

[magic crater]

why we always gotta pick the lesser number

[visual marsh]

bro

[magic crater]

my bad man im dumb ash

[visual marsh]

think on it a litlle bit

u got it?

[magic crater]

thinking

[visual marsh]

suppose 5 has more powers

and 2 has less powers

or lets assume 5 has 6 powers, ie $5^6$

[twin meteor]

ЯεтιяεĐ

[visual marsh]

and 2 has 4 powers, ie $2^4$

[twin meteor]

ЯεтιяεĐ

[magic crater]

yes

[visual marsh]

now to make a ten u take 1 power from 2 and 5 each

[magic crater]

yep

so we can take max four

[visual marsh]

now how many 10s can u make

yes

[magic crater]

wow

[visual marsh]

cuz the other 5^2 which is left, wont have any 2 with it to become 10

understood?

[magic crater]

yessir

tysm

[vocal sleet]

@magic crater Has your question been resolved?

[magic crater]

okay, sorry, another question
why exactly are we finding the power of 11 in 594 and later subtracting it from 2024?
is it because 594! dividing 2024! makes the factorials start from 595*596 and so on?

[visual marsh]

no

we find power of 11 in 2024!

then we find power of 11 in 594!

[magic crater]

yea

[visual marsh]

so we get k* 11^something/ 11^ something

like basically we dont care abt anything other than 11

[magic crater]

what

oh i sort of get it i think

so 2024!/594! is equivalent to 11^x/11^y * k

[visual marsh]

yes

[magic crater]

oh i get it

[visual marsh]

so power of 11 = x-y

[magic crater]

what exactly is k

is it an integer

or is it the other prime factors that make up 2024!

[visual marsh]

k is the other term which doesnt contain any power of 11

we basically extracted all 11, so whatever we were left with is k

[magic crater]

yeah so from
10! = 2^a 3^a 5^a ...
if we extracted 2^a we'd be left with 3^a 5^a nd so on?

[visual marsh]

yes

just that its a,b,c,d and soo on

[magic crater]

yeah my bad

so 3^a 5^b etc those are what make up k in this scenario

[visual marsh]

did u understand how to get power of anything from any factorial?

[visual marsh]

yes

[magic crater]

yeah you do
[n/p] + [n/p^1] and so on untill p^x is greater than n itself

[visual marsh]

yes

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[dense blaze]

Hello! I have a math test tomorrow and I do not understand how to solve these questions. For this exercise, we have to go on demos, note down the data, and make a quadratic regression. I understand how to find the max point, but I do not understand the other questions or how to solve them. I am mainly struggling on questions d and e.

[atomic jasper]

i think in d) theyre asking to find the intersection between your curve and y=2000

and e) isnt rly a mathematics question

[dense blaze]

why 2000?

[atomic jasper]

thats 2 billion in sales

[dense blaze]

ohhhh

[dense blaze]

ahhh okay!!

thank u smm

.close

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[candid socket]

Hello I was trying to solve this linear Diophantine equation, but I only got a subset of the solutions according to wolfram. Why?

[half imp]

Why do you think there are more solutions

[candid socket]

I put it into wolfram.

[half imp]

Oh

you didn't look at the negative factors

[candid socket]

Ahh negatives

[half imp]

-2 * -4 is also 8

[candid socket]

Yeah I just realized

[mental egret]

!original

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[candid socket]

Lmao thanks

.solved

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[half imp]

np

[mental egret]

Oo

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[cinder valve]

Guys, which site or software do you use to "translate" expressions to LaTeX?

[jagged cargo]

chatgpt

[ebon lotus]

yo

[cinder valve]

Or you simply learned how to write this

[cinder valve]

Oh

[ebon lotus]

i need help with my math test

[cinder valve]

Thanks

[jagged cargo]

!occupied

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

[ebon lotus]

can someone help me with my math test,

[jagged cargo]

<@&268886789983436800>

[jagged cargo]

kinda, yeah

[ebon lotus]

jk

[cinder valve]

.close

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[jagged cargo]

this can help you https://detexify.kirelabs.org/classify.html

[ebon lotus]

?

[atomic jasper]

#rules

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[velvet cove]

yo how do i do this

[vocal sleet]

@velvet cove Has your question been resolved?

[oak magnet]

do what ?

[lime gorge]

idk much else, but u should probably define what you mean by 'salty springs': do u want the entire circular zone of salty or just one specific building

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[frail violet]

Guys just point out what i am doing wrong to solve Ax = b
i made an augmented matrix [A|b] and applied gaussian elimination to turn it into reduced row echelon form which turned out to be the left side now i saw the right linear combination (the particular solution) which is (5,3,0,-1,0) transpose but when i multiply the original matrix why doesnt it turn into b MANNNNNNNNNNNNNNNNNNNNNN LIENAR ALGEBRA AAAAAAAAAAAAAAAAAAAAAAAAAAAA

[daring needle]

I think you row reduced wrong

[atomic jasper]

,w {{1,-1,0,0,1,3},{1,1,0,-3,0,6},{2,-1,0,1,-1,5},{-1,2,0,-2,-1,-1}} row reduce

[twin meteor]

Results provided by WolframAlpha

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

Requested by .bonk__

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[frail violet]

.close

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[strong wharf]

can someone help me out with this

[brazen crest]

Do you know how to use the substitution method?

[strong wharf]

i think i do? i learnt it recently and i'm not getting anywhere near the final answer when i try it

[brazen crest]

Can you try finding what's dx after substitution?

[strong wharf]

is it 2 du x^1/2 ?

[brazen crest]

Yes

[strong wharf]

okay so then

i take x/u and divide that by 2x^1/2

yes?

[brazen crest]

I don't quiet understand what you mean

[brazen crest]

Let's think about what we are left with after this

[strong wharf]

okay

[brazen crest]

Have you found it?

[strong wharf]

one second

sorry mum was calling

got till here

[brazen crest]

So we still have x left but we can find x in terms of u by manipulating u = 1 + √x

[strong wharf]

hm

[brazen crest]

Also you should also change the bounds because you've substituted

[strong wharf]

okay yeah

how do i write x^3/2 in terms of u?

[brazen crest]

In u = 1 + √x -1 on both sides

And then square it for both sides

You'll find x

[strong wharf]

alright i'll try it

aye i've gotta go for dinner

i got the general idea so thanks for the help

.close

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[austere lantern]

Where does the minus come from?

[austere lantern]

i get +1/2 and not -1/2

[lilac pebble]

the sqrt will be positive and the 1/(x-1) will be negative

so it will have to be negative

maybe you changed the sign accidentally when you were manipulating the expression

[austere lantern]

i don't get it.
If i simplify the function, for any x the result is 1/2

[visual marsh]

when u sqrt the numerator u get 1-x

not x-1

[lilac pebble]

maybe there is a mistake in your work

[dull bear]

(Note that sqrt{y^2} is |y|, so depends on the sign of y)

[austere lantern]

the function is: $\sqrt{(x-1)^2/4(x-1)^2}$

[dull bear]

\sqrt btw

[lilac pebble]

you brought x-1 into the sqrt

[twin meteor]

Quantum

[austere lantern]

And?

Oh

fk it

[lilac pebble]

that will be equivalent to $\frac{1}{\lvert x-1 \rvert}\sqrt{\frac{x^2-2x+1}{4}}$

[austere lantern]

i get it

[twin meteor]

Axe

[austere lantern]

So, only cause i know what sign the x will assume, i can remove the module?

So, if i simplify the sqrt i get |x-1|/4(x-1)

[lilac pebble]

i see

[austere lantern]

but since i know x -> negative number, i remove the module and adding a - beyond?

[lilac pebble]

yes

exactly

[austere lantern]

Damn

[visual marsh]

why not go the other way around? instead of compliacting stuff?

[austere lantern]

i have some skill issue with basic theorems

[austere lantern]

?

[visual marsh]

like convert the sqrt part into normal

instead of putting x-1 inside the sqrt

[austere lantern]

Yeah, that's what i've said

[austere lantern]

.

.clsoe

.close

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[novel hearth]

This Question Is About Double U Substitution,
As you can see the question is written on the top, first u sub is easy, then comes the 2nd one, here you can find “problem” there’s one and two, if you substitute the 2nd u as e^-u or -u you get different final results as shown by the arrows, now my question is, which one is correct and why

[novel hearth]

Btw w is just u2 but I wrote it w cos it’s easier

[flat whale]

when you substitute w = e^(-u), you need to replace du in terms of w and dw. did you do that?

when w = -u, dw = -du is simple

[novel hearth]

Yes

Will they both give the same answer ?

If yes then it should be a problem from me, if no then there’s something I don’t know

Here’s a clearer pic

…

[flat whale]

i don't see where you replaced du with dw in the w = e^(-u) substitution

shouldn't skip steps. that's how you make mistakes

[novel hearth]

Hmmmm

One second

Here look

My brain hurts why does that happen

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@novel hearth Has your question been resolved?

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@novel hearth Has your question been resolved?

[flat whale]

this does not equal to the starting integral

$u = -\log(w) \Ra du = -\frac{dw}{w}$

[twin meteor]

riemann

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[vast shale]

Factoring problem. I’m kinda new to factoring and saw the man in the YouTube video did -10 and -3.
I tried it before him and did -15 and 2. I was struggling. Does it still work?

I couldn’t figure it out

[twin horizon]

-15*2 gives -30 so it doesn't work.

[vast shale]

Ohh shii. You’re right

Thanks

.close

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[hollow sparrow]

Hey!
could anyone help me out figuring a certain relation between the exponential distribution and a poisson process ?

[hollow sparrow]

.close

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[mental egret]

No, the class size is not 20 ._.

[rough surge]

it is

how?

it is...

[mental egret]

Hmm, can you explain how?

Because from what I see, 619 - 600 = 19

[rough surge]

lets say we have 5-15

5,6,7,8,9,10,11,12,13,14,15

eleven numbers, not 10

15-5=10

[stone gazelle]

What is the question?

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[rare swift]

What are the closest integer coordinates to x and y

[quiet echo]

,rcw

[quiet echo]

question?

[rare swift]

What are the closest integer coordinates to x and y where x and y are given and here a b c d are integers

Well it's a part of the que I'm solving

Someone help

[brittle wasp]

Those are some confusing fraction lines

Also, this looks like an xy issue

!xy

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[rare swift]

?

[rare swift]

Here x and y are coordinates of 3rd vertex

In terms of coordinates of other 2 vertices which are a,b and c,d

I can't seem to find the closest integer coordinates

<@&286206848099549185>

[brittle wasp]

Are you doing the first part of the second part?

[rare swift]

Second

x and y came irrational so 1st part is done

[brittle wasp]

Pick easier first two points, like a,0 and -a,0

Then look at the the point and see what happens

[rare swift]

Hmm

Nice I think I'm done

Thanks

.close

[vocal sleet]

Channel closed

Closed by @rare swift

Use .reopen if this was a mistake.

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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• Be polite and have a nice day!

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[wild meteor]

Example 4: Two stations A and B are tracking a boat. The two stations are 4500 m apart on the N-S line. Station A sees a direction of S * 40 deg * W while B observes a heading of S * 60 deg * W If station A is north of station B, how far is the boat from station B?

[wild meteor]

Did I did draw this correctly

I'm not entirely sure

[vocal sleet]

@wild meteor Has your question been resolved?

[wild meteor]

This is someone else's work, Ik mine is wrong now but

I don't understand how one of the West angles goes down so we actually need to find the other one

<@&286206848099549185>

[ripe estuary]

Well it looks like they give you the degrees and direction, what do you mean by "one of the west angles goes down"?

[flint storm]

The angles are relative to the station. For example, for station A, since it's SW 40°, it's just like facing west when standing on station A, and then facing south, so the angle goes below station A.
Similarly, when you are at station B, and the boat is SW 60°, you look west, and then turn South, making the 60° angle below Station B.

[wild meteor]

Okay thanks

.close

[vocal sleet]

Channel closed

Closed by @wild meteor

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[glossy hatch]

Hi. is anybody here? I’m going to start getting the question ready now

[lunar pecan]

😭 Just ask your question.

[glossy hatch]

They aren’t good at explaining this. This is for Calculus “Determining Differentiability Graphically”

Sorry took a bit long because mobile otherwise i would’ve had this instantly

[lunar pecan]

Just ping the helpers if nobody responds in 15 mins from now.

[glossy hatch]

These examples are also are explained in a way where Im not able to understand them very well

[glossy hatch]

💯 Will do if that ever happens. Thank you!

[wraith python]

Have you learned about limits?

[glossy hatch]

Yes

[wraith python]

And have you learned about the Limit Definition of Continuity and the Limit Definition of Differentiability?

And that's a no. 🙂

[glossy hatch]

I don’t see anythin with a similar title so nope

[wraith python]

One moment, let me write something up real quick.

[glossy hatch]

💯

[wraith python]

Tell me if you understand what these mean.

If you don't understand, that's fine. I will explain.

[glossy hatch]

First 3 are familiar

[wraith python]

Do you understand what it means though?

[glossy hatch]

Yeah those

I have seen the f’ from looking ahead into the lessons but I haven’t gotten into those yet.

[wraith python]

So the second set of three are essentially the same as the first except it is applied to the derivative of a function f(x).

Ok, so you have not learned about the Limit Definition of a Derivative then?

[glossy hatch]

Not yet

[wraith python]

Hmm, it's interesting that a question about differentiability would be asked without teaching derivatives. 🤪

[glossy hatch]

The chapter i’m in is about Derivatives but i’m on the first ones currently

This is the first lesson to it

[lunar pecan]

I have a question.

[wraith python]

?

[lunar pecan]

Is discontinuity and differentiability the same thing?

[wraith python]

No, discontinuity is a property in which there is a "break" in a line.

[lunar pecan]

Okay!

[wraith python]

So visually, a point is differentiable if the slope at a point and at some infinitesimally nearby point on both sides are "equal".

For this equation, there are several points at which the slope of the curve would not be equal as you move from x to x + 0.00...001.

[wraith python]

You still with me?

[glossy hatch]

Still here just reading along the course section again as well

[wraith python]

So at x = 0, on the left side, the slope will be some positive value. It's actual value doesn't matter here. On the right side of x = 0, the slope will be some negative value.

Because the slopes would not be equal at x = 0, it would not be differentiable.

[lunar pecan]

So if the slope of left hand and right hand limit is equal then it’s differentiable?

[glossy hatch]

Understood.

[wraith python]

The value of f(c) must also equal L.

[lunar pecan]

Okay so the slope of function value must also be equal?

[wraith python]

Here I have a piece-wise function f(x) with its derivative in orange.

The orange line has a break which means f'(x) is discontinuous.

That means it is not differentiable at x = 0.

[wraith python]

This pretty applies to any line in which there is a corner or a cusp.

If any point is discontinuous, then it is also non-differentiable at that point.

[viscid thicket]

Unrelated question say f(x) is differentiable at x=0, does f'(x) have to be continuous or is that not necessary?

[lunar pecan]

So the difference between continuity and differentiability is that in continuity the left hand side limit = right hand side limit= functional value and with differentiability the slopes of the 3 things must of equal or did I misunderstand?

[wraith python]

If f(x) is differentiable at x = 0, then continuity is implied.

[viscid thicket]

Yes for f(x), but is it continous for f'(x) at x=0 (the derivative)?

[viscid thicket]

Since this example shows if f'(x) is not continous then f(x) is not differentiable

[wraith python]

If x = 0 is differentiable then continuity is implied, it's a requirement in fact.

Sorry, responded to the wrong person.

[lunar pecan]

I got that part.
But I asked for the difference😭

[glossy hatch]

Can you show an example of them being differentiable too?

[wraith python]

Continuity and differentiability have the same requirements to be true, but they are property of a function and the functions derivative, respectively.

[wraith python]

One moment, let me think of an equation.

[lunar pecan]

Okay, maybe I don’t understand because idk derivates?

[wraith python]

Yeah, it's weird that differentiability would be brought before learning about derivatives.

It's literally the cart coming before the horse.

[lunar pecan]

No, I have only learned about limit and continuity.

[wraith python]

This would be an example where you have a piece-wise function(blue) that is continuous at x = 0 and also differentiable at x = 0.

The slope at x = 0 is "equal" as you take the limit as x -> 0 on either side of the line.

This satisfies the continuity requirement.

There is no break or corner at x = 0 so visually you can say that it is differentiable at x = 0.

Once you learn about derivatives, you can look at the orange line and apply the same limit rule to see that

Visually though, if you see an open circle (break) or a corner or cusp, then it will not be differentiable at that pont.

On this line, there is a cusp at x=0 and x=6, so it is not differentiable at those two points.

There is also a break at x=1, x=3, and x=5; so it is not differentable at those points either because it is not continuous at those points.

[glossy hatch]

Back, going to read up now.

[vocal sleet]

@glossy hatch Has your question been resolved?

Channel closed

Closed by @glossy hatch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[dim sinew]

I keep going wrong somewhere and I don't know how. I also don't really know how to do the sum of cubes when something is the power of 6. The goal is to get it in factored form

[swift bane]

a is equal to 6x^2

[dim sinew]

Could you explain

[swift bane]

the exponents get multiplied

(x^2)^3

So the problem you have is

what power do you take 6x to

ni order to get 216x^6

you have to refer to these properties

[dim sinew]

3

[swift bane]

a = 6x^2
a^3 = 216x^6

[dim sinew]

Hold on im just trying to process it

[dim sinew]

so does that mean the power of 6 is being devided by the root power of 3 since we need to find just a

or is that not the case

[swift bane]

What do you mean by divided

[dim sinew]

6/3

[swift bane]

It's just that

[dim sinew]

for the power of 6x^2

[swift bane]

the exponents are being multiplied

We need to find what a is in order to plug it into the formula

We found that a = 6x^2

If you cube both sides, you get 216x^6

[dim sinew]

so (6x^2)^3 = 216x^6

[swift bane]

Yeah

[dim sinew]

So I just should remember that when I'm using the 6th power and factoring, a should have x squared?

[swift bane]

Can you write a example down

I don't understand what you're asking

We have that a^3 = 216x^6 right

[dim sinew]

yeah and we need to find the cube root

[swift bane]

From that we know that a = 6x^2

[dim sinew]

yes and the ^2 is because I need to multiple the exponents to get a power of 6

[swift bane]

Sure

now we just plug it in the formula

[dim sinew]

Okay let me try that real quick

[dim sinew]

so how would I plug in 6x^2 into the (a^2) part of the formula

[swift bane]

You just

[dim sinew]

what woudld that euqla

[swift bane]

(6x^2)^2

$a = 6x^2$

[twin meteor]

asm

[swift bane]

what would $a^2$ be equal to

[twin meteor]

asm

[dim sinew]

36x^3

[swift bane]

$a = 6x^2 ====> a^2 = (6x^2)^2$

[twin meteor]

asm

[swift bane]

The exponents get multiplied

2^2

[dim sinew]

6x^4

[swift bane]

Yea but u gotta square 6 too

[dim sinew]

right i see that

[swift bane]

6 and x are seperate things

u can view it as that

[dim sinew]

okay

36x^4

[swift bane]

Sure

u just plug it in

Also, why did you make it equal to 0

[dim sinew]

i got it mixed it up the difference

[swift bane]

They're just asking for a factored form so

[dim sinew]

or something

ive watched so many videos man i had no idea this was called the sum of cubes or whatever until 15 minutes ago 😭

[swift bane]

Yea there's also (a + b)^3

Don't get it messed up, it's a whole different formula

[dim sinew]

jeez super similar

[swift bane]

I would say memorize this when your exams are getting closer

Not sure if they would include it

I would memorize it for entrance exams tho

[dim sinew]

luckily they give us the formulas for tests

[swift bane]

Oh

[dim sinew]

until the next year I believe

[swift bane]

that formula is pretty rare

[dim sinew]

interesting

[swift bane]

I never saw it show up in my problems

100% it'll be in entrance exams

[dim sinew]

noted

I'm going to attempt another one, just because last time I said I understood, as soon as I closed it I was stuck.

so im gonna leave it open for like 2-3 min

Alright now I'm supposed to cube root 48

[swift bane]

I suppose you just simplify it

[dim sinew]

just in case you'd like to see:

oh this is difference

[swift bane]

yea

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

[twin meteor]

asm

[dim sinew]

how would I find a for this one?

[swift bane]

All you can do is just simplify

48 is not a cube so

a = 2 cbrt(6) x^2

[dim sinew]

cbrt 6?

[swift bane]

Yea u gotta simplify it

You can make a tree or whatever they call it

Like 48 = 24 * 2

etc

keep on going down til you can get a cube out

[dim sinew]

okay

[swift bane]

48 = 6 * 2 * 2 * 2

Notice how 2's repeat three times

u can take it out

[dim sinew]

oh

6(2^3)

?

[swift bane]

Yeah

[dim sinew]

I'm not really sure where i'm going with this

im gonna pull up this video real quick itll only take a minute

it didn't help he used x^6 without a constant

[swift bane]

What video is it?

[dim sinew]

https://www.youtube.com/watch?v=ADj8sGSjewg

it says perfect cubes

so thats why it didnt work

i think

[swift bane]

Ok wait

We can divide this by 3

3(16x^6 - 25)

[dim sinew]

oh

[swift bane]

yeah

kind of hard to spot

[dim sinew]

yea

[dim sinew]

apparently it cant be simplified more

[swift bane]

I think we can

Yeah we can

[dim sinew]

how so

[swift bane]

Well

In that case

a = 4x^2 right

i meant ^3

a^2 = 16x^6

[dim sinew]

wait

im lost

[swift bane]

Then u can just plug in

Are u familiar with

The difference of squares

$a^2 - b^2$

[twin meteor]

asm

[dim sinew]

yea