help-0

[steep pike]

<@&286206848099549185>

[lone heart]

@steep pike Has your question been resolved?

[lone heart]

@steep pike Has your question been resolved?

[lone heart]

@steep pike Has your question been resolved?

[steep pike]

<@&286206848099549185>

.close

[lone heart]

Channel closed

Closed by @steep pike

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.

[simple lion]

Could someone help me with this probability question regarding card draws:

You draw 4 cards, one after another from a 78 card tarot deck. What are the odds of drawing the Emperor card 3 times total? (Odds of drawing the Emperor in a single draw are 1/78)

Here's what I've got:

Number of 4-card hands: (78choose4) = 1426425
Number of 4-card hands with three Emperors: 77*4 = 308
Odds of drawing 4 cards with three Emperors: 308/1426425 = 0.00021592442 =~ 0.0216%

Does this seem correct?

[thorny root]

where did 77 come from

[simple lion]

odds of drawing a card that is not the Emperor

(78-1)

[thorny root]

multiplying that 4 doesn't seem to give you anything of sense

[simple lion]

wait that's a bad explanation

so how would you get the number of 4-card hands that are 3 Emperors and 1 other card

[thorny root]

also how can you draw 3 emporor when you have only 1

[simple lion]

because you draw it and put it back and then re-draw

[thorny root]

I see

well

[simple lion]

there's 77 different ways to have a 4 card hand that's EEEX, and then you have X in all 4 positions, so EEEX, EEXE, EXEE, XEEE; hence 77*4

E = Emperor
X = something else

[thorny root]

oh yeah

[simple lion]

just need someone to verify

[thorny root]

seems good

[lone heart]

@simple lion Has your question been resolved?

Channel closed

Closed by @simple lion

Use .reopen if this was a mistake.

[simple lion]

thanks

[lone heart]

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.

[barren portal]

Can you help me to see that this goes to e^-lambda ?

[echo socket]

Well, it does not

[barren portal]

mbb

[echo socket]

Unless you meant -n in the exponent

[barren portal]

I mean x

cropped the wrong one

[vale wigeon]

if you mean this exactly as stated, then it goes to 1, not e^(-lambda).

[barren portal]

Yes, this going to one makes sense applying the limit properties

as n tends to infy, lambda/n tends to 0

I'm actually looking for ^n

[tacit arch]

Just send the right screenshot then

[echo socket]

Substitute for -n/lambda and recall the limit definition of e

[barren portal]

This was the one I was supposed to send

[alpine sable]

Isn't this how we define e^{-\lambda} ?

[barren portal]

so here x=-lamda ?

[alpine sable]

Yeah

[barren portal]

To be honest, The definition I'm aware is e^x=1+x/1! +x^2/2! + .... +

are they same ?

[alpine sable]

Here, this is an interesting proof @barren portal

[barren portal]

using binomial theorem

i can get there?

[alpine sable]

That's Taylor series

[barren portal]

I haven't studied taylor series yet

A glimpse of it will be helpful

[echo socket]

.

[alpine sable]

Taylor series requires basic of calculus, have u done that ?

[barren portal]

I'm actually about to finish Calculus 3, but the college skipped power series and so

for last semester

[alpine sable]

Ah! Dw, there's an interesting video on Taylor series then, wait lemme pick it up from internet quick

https://youtu.be/3d6DsjIBzJ4
@barren portal

[barren portal]

Sure, I'll watch

probability classes are overwhelmed this.

[alpine sable]

Are u in university or something?

[barren portal]

Yes, 2nd year.

[alpine sable]

Ohh!! That's wonderful ^°^

Good luck

[barren portal]

Yep. Thanks again, Have a great day.

.close

[lone heart]

Channel closed

Closed by @barren portal

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.

[spark prawn]

Can I ask some direction help with 2b ? Trigonometric identities

[last ether]

Try splitting the fraction up

[spark prawn]

And expanding from there or factoring to lead to an identity?

[keen mason]

u wanna expand the left or right side?

[spark prawn]

Right side

[keen mason]

2-2sin^2 = 2cos^2 so thats the denom

(1+cot^2) = csc^2

u can do the rest now?

[lone heart]

@spark prawn Has your question been resolved?

Channel closed

Closed by @spark prawn

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.

[past magnet]

In a graph, is the clique cover number always greater/equal than the max independent set?

[past magnet]

I have tried the following proof:

Given graph G=(V, E)
Let $C_{min}$ be the minimum set that contains the cliques which cover the graph G.
Let $U_{max}$ be a maximum independent set.
Assuming $|U_max| > |C_min|$:
We then have
$\exists v_i, v_j \in U^{max} : v_i, v_j \in C_i, C_i \subseteq C^{min}$
this implies that $v_i$ and $v_j$ are adjacent which then implies $v_i, v_j \notin U^{max}$
which is a contradiction.
Therefore $|U_{max}| \leq |C_{min}|$

this seems plausible but im not sure if i missed something

[ocean seal]

LanPodder

[lone heart]

@past magnet Has your question been resolved?

[past magnet]

<@&286206848099549185>

[lone heart]

@past magnet Has your question been resolved?

[lone heart]

@past magnet Has your question been resolved?

[lone heart]

@past magnet Has your question been resolved?

[alpine sable]

<@&286206848099549185>

Can somebody help me with my culminating tommorw

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[frank merlin]

how did the constant move out of the exponent

[outer lark]

e^c is just a constant

[frank merlin]

thanks

.close

[lone heart]

Channel closed

Closed by @frank merlin

Use .reopen if this was a mistake.

[tacit jacinth]

Hi if anyone can solve this with working steps i will send them 10 bucks on steam, Thank you so much

[lone heart]

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.

[thorny parcel]

.close

[lone heart]

Channel closed

Closed due to the original message being deleted

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.

[surreal lichen]

Find the number of labelled trees on 5 vertices

[surreal lichen]

i found three unlabelled trees

the first one i found was a path graph

so if i want to find the number of labelled path graphs on 5 vertices

is it the same as finding the number of linear arrangements of 5 objects?

[lone heart]

@surreal lichen Has your question been resolved?

[lone heart]

@surreal lichen Has your question been resolved?

[chilly storm]

open a new ticket that's only for you

[lone heart]

@surreal lichen Has your question been resolved?

[surreal lichen]

.close

[lone heart]

Channel closed

Closed by @surreal lichen

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.

[indigo saddle]

Why can there be infinite many solutions to this question? I thought that any homogenous system of linear equations (SLEs) of form Ax=0 will always be consistent

[limpid turret]

Unless A is singular

"singular" is quite the misnomer, as it implies there are many solutions

[indigo saddle]

Sorry, here was the full Question

[indigo saddle]

Sorry, I don't quite get what you mean by "Singular"

[limpid turret]

If the determinant of a matrix is zero, then -by definition- is called singular

[indigo saddle]

Oh okay

[limpid turret]

If a matrix is singular, it can have multiple solutions

[indigo saddle]

Ah, I see

[limpid turret]

Been a while, so I can't remember if "homogenous" means "non-singular"

[indigo saddle]

I think so

because if it's singular, then an inverse of A cannot exist

therefore, there isn't necessarily a unique solution to Ax=b (including Ax=0) (right)?

[limpid turret]

what is an "inconsistent system of equations"?

[indigo saddle]

No solutions

i.e., in ℝ³, you can have 3 parallel planes that don't intersect eachother

[limpid turret]

ah gotcha

Yeah I don't know this one sadly. Guess I gotta review my lin alg.

Give it 5 minutes then ping helpers if no one comes

[indigo saddle]

okay

[pseudo ice]

Consistency is having at least one set of solutions?

Or exactly one set?

[indigo saddle]

at least one

And since we are only dealing with the ℝ³ case, we are dealing with planes

So consistency can only mean "a unique (set) of solultions" or, infinitely many (sets) of solutions

And there can only be 3 types of inconsistencies

[pseudo ice]

Alright fair, so could you elaborate on what's confusing, sorry?

[indigo saddle]

I don't get the written answer explanations that is provided to me

I thought the question is asking in terms of Ax=0, but to me, the answers seem to be answering in terms of Ax=b—as in it is explaining why Ax=b must have an infinite number of solutions

[pseudo ice]

Oh fair no, they're assuming that Ax=b is inconsistent and then from that you can show there would be infinite solutions to the homogenous Ax=0

[indigo saddle]

oh

[pseudo ice]

Do you agree with this statement?

[indigo saddle]

yep

[pseudo ice]

Calm calm, does it all make sense now?

[indigo saddle]

so they're first deducing restrictions on A

and then using the restrictions to find what must then be true on [A|0]

[pseudo ice]

Yeah in particular you know A isn't full rank, else it'd be invertible and you'd have a solution to Ax = b as x = A^{-1}b

[indigo saddle]

yep

[pseudo ice]

Therefore when you REF the matrix A, you'll have somewhere "at the bottom" having a zero row

[indigo saddle]

Then

couldn't you just directly answer by doing:

this is true

Thus for [A|0], we will have at least one row of 0=0 in REF

And since we already know that A0=0 is consistent

i.e. we know a single case

[A|0] must have infinite solutions?

in ℝ³

why then is it necessary to state* these properties of [A|b]?

[pseudo ice]

That's pretty much what I think they're trying to say

[pseudo ice]

This here in particular is saying you can't "fix" one of the coordinates

As in you won't be able to restrict one of them to be a fixed value

[indigo saddle]

But how is that relevant for showing that [A|0] has infinite many solutions

[pseudo ice]

let's say we have like something in $\bR^3$ that turns into $\pmqty{1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 0}$ on REF

[ocean seal]

chartbit

[pseudo ice]

Then that will tell you for the homogenous that x=0 and y=0

so then (x,y,z) = (0, 0, z) = z(0, 0, 1)

[pseudo ice]

That's effectively what the statement is trying to say

Or for $\pmqty{1 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0}$ in REF, we get that $x=0$, and so $(x,y,z)= (0, y, z) = y(0, 1, 0) + z(0, 0, 1)$

[ocean seal]

chartbit

[indigo saddle]

I get it

thanks

I feel like the question

's wording is a bit confusing (to me)

[pseudo ice]

Yea as you have like the hom and nonhom case and they're easy to confuse I guess?

[indigo saddle]

Yeah

[pseudo ice]

Anyways is all of that all good?

[indigo saddle]

Yep

Thanks 🙂

[pseudo ice]

Perfect, have a good one!

[lone heart]

@indigo saddle Has your question been resolved?

Channel closed

Closed by @indigo saddle

Use .reopen if this was a mistake.

[lone heart]

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.

[dawn dust]

how do i find the x intercepts of a vertically transformed equation

and they y for horizontally

[native cloud]

In order to find the x intercepts, you'll need to use the standard equation

[dawn dust]

yea but they will change wont they

[native cloud]

I don't follow

Elucidate please

[dawn dust]

like i found the roots of the original

but they will change once u transform the function

how do i find the new roots

[alpine sable]

find the new function first

[dawn dust]

so -2x+12x-4

oh yea ok that works

that gets me the right roots

wait what if it was a horizontal tranformation

how would i find the new function then

[lone heart]

@dawn dust Has your question been resolved?

[dawn dust]

<@&286206848099549185> ?

[dawn dust]

.close

[lone heart]

Channel closed

Closed by @dawn dust

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.

[long spindle]

can someone help me find (f/g)(x) as well as its domain?

[wraith adder]

is there anything to plug anything in?

[long spindle]

no im just dividing the equations as it is

i got this as the answer and it was wrong

[wraith adder]

hmmm 🤔

[woven plaza]

Just write it with the root

√(49-x²)/(x+4)

Now for the domain the only condition is that x shouldn't be -4 and the whole function needs to be positive inside the root

So that leaves you with 2 cases, either both the denominator and numerator are positive of they're both negative

[long spindle]

oh, i thought radicals weren't allowed in the denominator?

[woven plaza]

Well they didn't ask to simplify the function

[long spindle]

ohh

hmm

ok gotcha

[woven plaza]

,w domain √((49-x²)/(x+4))

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ankit#6969

[woven plaza]

[long spindle]

okok

thank you!

[lone heart]

@long spindle Has your question been resolved?

Channel closed

Closed by @long spindle

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.

[jade dagger]

Can anyone correct these limits for me? I unfortunately don’t have a solution manual. If you can tell me where I went wrong and correct my mistakes, it would help me a lot. Thanks in advance 🙂

[alpine sable]

oh i see now

[alpine sable]

why is $\lim_{x \to 2} x^3 = (1)^3$?

[ocean seal]

♡Lex♡

[jade dagger]

I wonder with e)

[woven plaza]

Pip error no brain found

[echo socket]

The way you did e) is weird

[jade dagger]

How do i approach those? I am confused

[echo socket]

Why'd you plug in x = 1 into x^3 if x -> 2?

[jade dagger]

Ah true, so which x value can I pick? i mean I can’t tell from which graph it’s coming from. Since it’s f(x) I assumed it to be from the first graph

[echo socket]

x = 2

[smoky adder]

this is not the slayest notation

[echo socket]

Yeah that too

[jade dagger]

Ahhh so as x approaches 2 x^3 is 2… right?

[echo socket]

x -> 2
x^3 -> 8

[jade dagger]

How can I correct that?

[jade dagger]

x^3 right?

[smoky adder]

I usually draw an arrow that the denom is zero and then say dne

[jade dagger]

Thank you everyone!

.close

[lone heart]

Channel closed

Closed by @jade dagger

Use .reopen if this was a mistake.

[jade dagger]

.reopen

[lone heart]

✅

[jade dagger]

What about the point on the graph, how will that be defined through notation?

Is it f(2)?

[echo socket]

The red point or the white one?

[jade dagger]

The red

[echo socket]

It's f(2) yeah

Different from the limit

[jade dagger]

Ah okay, now that’s what made me write 1 in the first place, thankyou once again! 🙏

.close

[lone heart]

Channel closed

Closed by @jade dagger

Use .reopen if this was a mistake.

[kindred anchor]

https://tenor.com/view/pepo-the-frog-anime-girl-hammering-sad-pepo-meme-gif-13354961

[lone heart]

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.

[lone coyote]

555% decimal and fraction issue getting right answer

<@&286206848099549185>

[woven plaza]

per "cent" means u just divide it by 100.

so 555/100 would be 5.55

[lone coyote]

what about the fraction?

[woven plaza]

simplify that fraction and you get your final answer for the fraction

[lone coyote]

how?

[woven plaza]

they have 5 as a common factor

so that makes it 111/20

[lone coyote]

111/20 isn't final answer tho right?

[woven plaza]

yea it is

[lone coyote]

What about this?

We didn't get that in class, homework is totally different..

@woven plaza

<@&286206848099549185>

.close

[lone heart]

Channel closed

Closed by @lone coyote

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.

[primal galleon]

How do I find angle v?

[primal galleon]

Could you show me?

[plush lion]

use the pythagoras theorem

[primal galleon]

Yes

[primal galleon]

It’s 3a^2

opp/adj

a/2a = 1/2

tan^-1(1/2)

,w atan(0.5), convert to degrees

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by dgh#0553

[primal galleon]

What’s that?

The answer should be 27

@tulip violet

,calc atan(0.5)

[ocean seal]

Result:

0.46364760900081

[primal galleon]

,calc 0.463647*180

[ocean seal]

Result:

83.45646

[primal galleon]

What’s that?

Cos(adj/hyp)

[plush lion]

,calc 0.46364760900081*180/pi

[ocean seal]

Result:

26.565051177078

[primal galleon]

Okay, why do we divide by pi?

Is it to cancel radians?

[plush lion]

yes that's how you convert radians to degrees

[primal galleon]

Thanks

.close

[lone heart]

Channel closed

Closed by @primal galleon

Use .reopen if this was a mistake.

[lone heart]

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.

[alpine sable]

i have to write and graph a function for this

and im not sure how to

[rocky grove]

Is this a compounding problem?

[alpine sable]

no

[rocky grove]

So it's a simple interest?

[alpine sable]

yeah

[rocky grove]

Okay

Do you remember how does simple interest look like?

[alpine sable]

A = P(1 + rt)

?

[rocky grove]

Yep

What's P and what's r in this case?

[alpine sable]

P = 42, 500

and r = 3%

[rocky grove]

Nice

Now plug in

[alpine sable]

so A = (42, 500)(1 + (3/10)t)

is this what i graph?

,w plot y= (42500)(1 + (3/10)x)

[gray isle]

get rid of the comma

[ocean seal]

Results provided by WolframAlpha

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

Requested by Twerkingbee#7740

[alpine sable]

Nice

huh

nice

thanks 👍

[rocky grove]

[alpine sable]

.close

[lone heart]

Channel closed

Closed by @glacial summit

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.

[tulip hound]

How do I solve this system

Wait I got it I think

x-3 or y-5 should be = 0

so x=3 y=5

[echo socket]

x = 3 or* y = 5

[tulip hound]

so if I take x=3, y=±4

And it woll be (3;-4) (3;4)

[echo socket]

Right

Now consider y = 5

[tulip hound]

x=0

I just remembered I wrote that exact number a long time ago lmao

Ty

.close

[lone heart]

Channel closed

Closed by @tulip hound

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.

[warped topaz]

So I set x(t) to 0 and y(t) to -4, I got +3 and -3 for both x and y. but how do I know if its (-3,3) and (3,-3) or (-3,-3) and (3,3)?

[pseudo ice]

Those are the t values you get right? As in the point in the “track” where you have the same point?

[warped topaz]

yes

I think 🙃

[pseudo ice]

Yep, so you know that t=3 will give you that point, and also t=-3 will give you that point

But you want to find both velocity vectors for that point

Putting in those two t values will get you two different things I think?

[warped topaz]

I got +3 and -3 for x and +3 and -3 for y...

so its 4 values

[pseudo ice]

Those are your t values, remember how there was a question we had and I said that from both you needs to get the same t values?

As in you solved x(t)=0 and y(t)=-4 for the t values

Hold up didn’t we do this question

[warped topaz]

Yes im going over everything again im just stuck on this 1 part

[pseudo ice]

But anyways, these will give you t values, and you want those to be the same, the ones that match for both are the t values you’d accept

So you get t=3 and t=-3

Those are what you’d use, if you get me?

[warped topaz]

ah so theyre not points

ok 1 moment I will try something

Ok I got the answer

thank you so much!!

❤️

.close

[lone heart]

Channel closed

Closed by @warped topaz

Use .reopen if this was a mistake.

[lone heart]

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.

[cinder sundial]

Obviously it’s “the theorem of three perpendicular lines” and im okay with it.
but what had me confused is the teacher says if the angle that were blue circled wasn’t perpendicular, then the other two arrow-pointed angles wouldn’t be perpendicular too.

That sounds like a bullshit to me, just some imagination in mind, you would know it’s not true

Even the blue-circled isn’t perpendicular, the other twos that arrow-pointed would still be perpendicular too

[mortal trellis]

well it depends in what order and how you construct the various points

if the blue angle is not perpendicular, then at least one other thing also has to change. and depending on what you change, you can probably make the other two also not perpendicular

[lone heart]

@cinder sundial Has your question been resolved?

[mortal trellis]

yes that is one possible way to change it

maybe a better wording from your teacher might have been: if the blue angle is not perpendicular, then the other ones don't have to be either

imagine instead moving the black pen towards the camera

[cinder sundial]

What I’m trying to demonstrate from the vid is, even I’d changed the “blue-circled” angle, the other twos (arrow pointed) is still perpendicular

So what the teacher is not true at all

[mortal trellis]

no

maybe the phrasing of your teacher wasn't perfect

but the point is, if blue is not perpendicular, then the red ones aren't necessarily perpendicular either. they can be, but don't have to

so in a general situation you do not know anything about them

[cinder sundial]

u mean a situation like this

[mortal trellis]

that changes one of the red angles, yes

[cinder sundial]

This is the true statement without any flaws, compared to my teacher that didn’t speak his word clearly and make me feel so confused

My problem is solved, Thank you so much

I luv u

.close

[lone heart]

Channel closed

Closed by @cinder sundial

Use .reopen if this was a mistake.

[lone heart]

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.

[alpine sable]

hi hi how do you start getting to learn calulus ?

[pseudo ice]

A question better off in one of the general channels, like #discussion or something tbh

[rocky grove]

True

[alpine sable]

oh sorry idk how this server really works sorryyy

[rocky grove]

But I'd suggest you understand the idea of super zooming into graphs

And the idea of infinity

How to tackle it

[pseudo ice]

Don't worry about it these channels here are for like homework/exercise questions, just so you know

[rocky grove]

And understand the idea of observing behavior of functions

[alpine sable]

hmmm okay thank you!!! :D

[rocky grove]

Also

[alpine sable]

oh thats good to know thank you for telling me ! :D

[woven plaza]

There are some good lecture series on yt

[rocky grove]

To tackle calculus, you need to master Algebra

Because most mistakes that happen in calculus is because of the algebra

[alpine sable]

oh thats fun!! i love algebra ! thank you for telling me that

[alpine sable]

is there?? do you know any good channels are is it easier to search it on yt?

[rocky grove]

More advanced topics will cover slopes of tangent lines, derivatives, max/min, concavity, optimization, area of unfamiliar shapes, anti derivatives, etc...

[woven plaza]

Channel name - Organic chemistry tutor

He's got the BEST pre calc, calc 1 and calc 2 series

[rocky grove]

Also you will tackle series and sequences

[alpine sable]

thank you so much ankit!! :D ill start watching his videos soon thank you!!

[alpine sable]

okay okay!! :D

[woven plaza]

Okok gl

[rocky grove]

You can check out 3 blue 1 brown for more visual intuition into Calculus

[alpine sable]

okayyy thank you Vulcan for all the help!! 😁

[rocky grove]

Happy to help

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[thorny bough]

How does one express a constraint on the signage of a variable with the simplex method ?
like:
x1 >= 0
into the simplex's matrix

[mortal trellis]

well that's assumed for the simplex method

that all the variables are >= 0

if at some point one of the variables is smaller than 0 then you are out of the feasible region

but you can fix that with the dual simplex method

[thorny bough]

it means that there is no solution ?

[mortal trellis]

not necessarily, no

[thorny bough]

I'm new to this stuff, so what I basically did is write down my equations on my problem
Problem: Given a list of crops (with their selling price per unit and required fertilizer per unit) and a list of stored fertilizer, find in what quantity each crop should be grown for the season

x1..x5 the quantity of each type of grain produced
p1..p5 the selling price of each type of grain
f1..f4 the amount of each type of fertilizer available
ax..ex the amount of the x fertilizer the crops needs

Maximize Z = x1*p1 + x2*p2 + x3*p3 + x4*p4 + x5*p5 

Subject to:
a1*x1 + b1*x2 + c1*x3 + d1*x4 + e1*x5 <= f1
a2*x1 + b2*x2 + c2*x3 + d2*x4 + e2*x5 <= f2
a3*x1 + b3*x2 + c3*x3 + d3*x4 + e3*x5 <= f3
a4*x1 + b4*x2 + c4*x3 + d4*x4 + e4*x5 <= f4
---------------------------------------

Objective function:
  x1*-p1 + x2*-p2 + x3*-p3 + x4*-p4 + x5*-p5 + Z = 0

y1...y4 the slack variable (the unused fertilizer)

Subject to constraints:
a1*x1 + b1*x2 + c1*x3 + d1*x4 + e1*x5 + y1 = f1
a2*x1 + b2*x2 + c2*x3 + d2*x4 + e2*x5 + y2 = f2
a3*x1 + b3*x2 + c3*x3 + d3*x4 + e3*x5 + y3 = f3
a4*x1 + b4*x2 + c4*x3 + d4*x4 + e4*x5 + y4 = f4

x1  x2  x3  x4  x5  y1 y2 y3 y4 Z C
a1  b1  c1  d1  e1  1  0  0  0  0 f1
a2  b2  c2  d2  e2  0  1  0  0  0 f2
a3  b3  c3  d3  e3  0  0  1  0  0 f3
a4  b4  c4  d4  e4  0  0  0  1  0 f4
-p1 -p2 -p3 -p4 -p5 0  0  0  0  1 0
--------------------------------


Entering constants:
x1  x2  x3  x4  x5  y1 y2 y3 y4 Z C
1   0   1   0   2   1  0  0  0  0 f1
1   2   0   1   0   0  1  0  0  0 f2
2   1   0   1   0   0  0  1  0  0 f3
0   0   3   1   2   0  0  0  1  0 f4
-p1 -p2 -p3 -p4 -p5 0  0  0  0  1 0

and I get the right answer sometimes

but sometimes I get negative amounts of crops to grow

[mortal trellis]

well you need to add the contraints x_i >= 0

[thorny bough]

do I need to introduce more slack variables then ?

[mortal trellis]

I am assuming you are using a program?

[thorny bough]

because if I understood correctly simplex can only solve equalities

yes I am

[mortal trellis]

that should have a documentation

[thorny bough]

I am making the simplex

the program is mine

[mortal trellis]

the standard form of linear programming is "maximize c^Tx subject to Ax <= b and x>=0"

so I would assume that an implementation of the simplex algorithm would assume that

[thorny bough]

idk I just followed https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/04%3A_Linear_Programming_The_Simplex_Method/4.02%3A_Maximization_By_The_Simplex_Method

how can I express that x_i >= 0 constraint explicitely

[mortal trellis]

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

they are just assumed for the whole algorithm

[thorny bough]

so I shouldn't be ending up with negatives in the C column

and I messed something up

is that right ?

[mortal trellis]

I am not too familiar with this specific notation of setting up the matrix

if you start in the feasible region then you shouldn't leave it

so you made a mistake there if that happens

[thorny bough]

okay thanks for the insight

i'll leave the issue open in case somebody knows more

[lone heart]

@thorny bough Has your question been resolved?

[lone heart]

@thorny bough Has your question been resolved?

[lone heart]

@thorny bough Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[alpine sable]

Find the elements of order $6$ in $\mathbb{R}/\mathbb{Z}$.

[ocean seal]

isomorphism

[alpine sable]

$\mbb{R}/\mbb{Z} = {g + \mbb{Z} : g \in \mbb{R}}$

[ocean seal]

isomorphism

[mortal trellis]

in other words, the real numbers that you have to add 6 times to get an integer

[alpine sable]

yes

1/6 + Z is one such element

[mortal trellis]

yes

[alpine sable]

what else though

[mortal trellis]

lets work in R instead of R/Z

if 6*x is an integer, how can you write x

[alpine sable]

ty

.close

[lone heart]

Channel closed

Closed by @rigid kelp

Use .reopen if this was a mistake.

[mortal trellis]

(dont forget to check that each of them actually has order 6 and not a smaller one)

[lone heart]

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.

[naive leaf]

@remote heron

[naive leaf]

#help-7｜zen1thxyz message

^^ previous convo

[remote heron]

lets pray i did this right because im way too tired to fix it now

right, lemme make a field

[ocean seal]

Awesome_Ruler_007

[naive leaf]

for horizontal one, I solve for $\frac{dv}{dt}=-kv$ as is the norm

[ocean seal]

Awesome_Ruler_007

[remote heron]

oh geez theres directions

i may have stepped in it

okay so you want to start from the differential equation

and get to some equation for s that shows what youre expecting

[naive leaf]

ya, well drag should apply to both direction, but vertically the acceleration due to gravity focks it up

[remote heron]

where you go back to 0 as long as you start positive

[naive leaf]

$$
\text{Horizontal drag:} \frac{dv}{dt} = -kv \implies \frac{dv}{v} = -k\
\implies\int{\frac{dv}{v}} = \int{-k.dt} \implies \boxed{ln(|v|) = -kt+c}\
\text{Using initial conditions,} ;v=u;;t=0;;s_x=0\
\implies \boxed{c=ln(|u|)}\
\text{Thus,}; ln(|v|) - ln(|u|) = -kt \implies ln(|\frac{v}{u}|) = -kt\
\implies \frac{v}{u} = e^{-kt} \implies v = ue^{-kt}
$$
But we need it in terms of $s_x$, so we integrate it again:
$$
\frac{ds}{dt} = v \implies \int ds = \int v.dt \implies s_x = \int ue^{-kt}.dt \implies s_x = u\int e^{-kt}\
\text{Integrating:} \implies s_x=u\frac{e^{-kt}}{-k}+c;\text{, again with the same initial conditions}:s_x=0,:t=0\
\implies 0 = \frac{u}{-e^{-0}k}+c\implies c=\frac{-u}{k}\
\therefore s_x = \frac{-u}{ke^{kt}}+\frac{-u}{k} \implies s_x = \frac{-u}{k}(\frac{1}{e^{kt}}+1)\
\implies \boxed{s_x=|\frac{-u}{k}(1+e^{-kt'})|}
$$

[ocean seal]

Awesome_Ruler_007

[naive leaf]

This is how I solved that differential equation for $s_x$ incase it helps

[remote heron]

ill probably just look at the vertical

im not into physics

but differential equations

[naive leaf]

the second term looks great, its just the first one that's a bit odd

eq. is $\frac{dv}{dt}=-a-kv,:a=g$ for a reminder

[ocean seal]

Awesome_Ruler_007

[naive leaf]

I was given this eq. so it might be wrong

[remote heron]

,w y''=-g-ky

[ocean seal]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[remote heron]

[naive leaf]

damn

[remote heron]

,w y''(t) = -g-k*y(t)

[ocean seal]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[remote heron]

[naive leaf]

,w \frac{dv}{dt}=-9.8-kv

[ocean seal]

Results provided by WolframAlpha

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

Requested by Awesome_Ruler_007#7922

[remote heron]

okay, initial conditions

y(0) = s_0

[naive leaf]

v_0 = u

cuz you've got to throw an object with some velocity to actually make it fly

[remote heron]

$s(t) = A\sin(\sqrt k t) + B \cos(\sqrt k t) - \frac gk$

[ocean seal]

jan Niku

[remote heron]

$s(0) = s_0 = B - \frac gk$

[ocean seal]

jan Niku

[naive leaf]

methinks wolfram alpha is treating g as a variable

[remote heron]

nope

[naive leaf]

which is why your solution looks a bit wonky

[remote heron]

wonky?

[naive leaf]

ya, see this

[remote heron]

they are identical

i think

[naive leaf]

is y'' double derivative?

[remote heron]

yea

[naive leaf]

lets do one order at a time 😅

[remote heron]

its not necessary

[naive leaf]

,w y''(t) = -9.8-k*y(t)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Awesome_Ruler_007#7922

[remote heron]

it leads to a lot of extra constant wrapping

[naive leaf]

fair

[remote heron]

either way the theory for second order linear differential equations is straightforward enough to plonk through it IMHO even if youre clumsy with diff eqs

like me

[naive leaf]

,w y''(t) = -g-k*y(t), y''(0)=0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Awesome_Ruler_007#7922

[remote heron]

okay, solving for constants

[naive leaf]

you can give it init conditions like this right?

[remote heron]

sure but i wouldnt let a bot do it

[naive leaf]

,w y''(t) = -g-k*y(t), y''(0)=0, y'(0)=u

[ocean seal]

Results provided by WolframAlpha

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

Requested by Awesome_Ruler_007#7922

[naive leaf]

lol

[remote heron]

okay we can solve for B

$B = s_0 - \frac gk$

[ocean seal]

jan Niku

[remote heron]

and we let $s'(0) = v_0$

[ocean seal]

jan Niku

[remote heron]

to get A

[dry latch]

Hi guys. Can anyone give me another example for the second question please?

[remote heron]

how to get help

#❓how-to-get-help

[naive leaf]

It fricking works!!

now... just to solve it all with steps

[remote heron]

I get $s(t) = \frac{v_0}{\sqrt k}\sin(\sqrt k t) + \qty( s_0 - \frac gk) \cos ( \sqrt k t) - \frac gk$

[ocean seal]

jan Niku

[dry latch]

I already read the rules and on the picture a person send is post my question on help-0

[remote heron]

no you need to create your own channel

[naive leaf]

go to #help-1

Check the ones with "Math Help (available)"

[remote heron]

yea

any open channel

the numbers change around

[remote heron]

so this is what we want, right?

[naive leaf]

uh

its close ig

[naive leaf]

That's wolframalpha's solution. Now, it if only gave a step-by-step solution in full latex...

[remote heron]

eh i got a small sign error in mine

i cant help you with the actual typing haha

do you understand the steps to solve

[naive leaf]

..maybe?

I guess I don't if I couldn't solve it despite trying multiple times

[dry latch]

So you mean like if any channel has someone’s name on it, then I suppose to pick any channel that doesn’t has a name yet

[naive leaf]

What amazes me is that I took 1'st order solution, solved for constants, but it back into wolfram alpha, and still got it wrong

[remote heron]

oh where the hell is math help open

oh im so tired

yea you got it khai

[naive leaf]

#help-1 is now your channel, since it has your name on it

[remote heron]

i love the pauls notes

have you worked with these before

the process is uhh

intimidating if you havent

[naive leaf]

ODE's? I've just started using them recently

[remote heron]

but its very well documented

[naive leaf]

high schooler

[remote heron]

you have a second order linear differential equation with constant coefficients

theres an inhomogeneity, but its a constant

[naive leaf]

hm? what's an imhogenity

[remote heron]

you may start with a toy equation

like $y''-y=1$

[ocean seal]

jan Niku

[naive leaf]

I think I solved them correctly - since wolfram alpha and I get the correct eqn.

maybe I'm fucking up the constants?

[remote heron]

ah then youre fine

the constants are just some more work

i wouldnt do them with a bot

a bot will guess what you want

start with your general solution

so no solved constants

[naive leaf]

that's the exact initial conditions I use

[remote heron]

say it looks something like

$y(t) = A\sin t + B\sin t + m$ or something

[ocean seal]

jan Niku

[remote heron]

y''0 = 0 😌

[naive leaf]

ya, the constants were solving out much neater

lmao where am I going wrong? I'll prolly post the whole thing here (dw its quite short) and you can take a look ig

[remote heron]

that makes a whole part of your solution fall away

which is nice

no no its easier to start over

[naive leaf]

I meant starting over, by scratch, myself and my solution

[remote heron]

this entire process can be completed on half a sheet of paper if you do it carefully

[naive leaf]

I did it in less, but multiple times cuz things were going to shite

[remote heron]

ye

easier to do it multiple times

[naive leaf]

let's hope for the best ig 🤞

[remote heron]

i will solve it too

idk if you wanna see my solution

or if youre trying to do your own thing

just lmk

[naive leaf]

as long as the solution is simple and doesn't use some otherworldly tricks, I'm more than happy to learn

Just to get on even ground, we're solving for:
$$
\begin{align}
\frac{dv}{dt} = g-kv, v(0)=u, s(0)=0
\end{align}
$$

[ocean seal]

Awesome_Ruler_007
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[remote heron]

s(0) = 0?

i thought your intention was to see this thing fall to 0

this is too many conditions either way

[naive leaf]

ya, $s = \frac{dv}{dt}$. I guess I could write it 2od

[ocean seal]

Awesome_Ruler_007

[remote heron]

isnt s position

[naive leaf]

yep

[remote heron]

but position is the derivative of velocity?

[naive leaf]

wait, what were you solving for?

yes

[remote heron]

are you sure you dont mean $\dv{s}{t} = v$

[ocean seal]

jan Niku

[naive leaf]

that's what I mean

[remote heron]

okay

[naive leaf]

oh, I wrote it wrong above. mb

[remote heron]

youre good

here is what im going to solve

$\dv[2]{y}{t} = g-ky$ with $y(0)=y_0$ and $y'(0) = v_0$

[ocean seal]

jan Niku

$\dv[2]{y}{t} = g-ky$ with $y(0)=y_0$ and $y'(0) = v_0$

[remote heron]

mostley equivalent

[naive leaf]

but

double derivative of velocity is not displacement

[remote heron]

no

but you want to end up with a position equation right

[naive leaf]

ya

[remote heron]

so you should write your de in terms of position

not velocity

[naive leaf]

ya well that was the eq. given to me

[remote heron]

i mean its fine you can change it

theyre the same

$\dv{v}{t} \to \dv[2]{s}{t}$

[ocean seal]

jan Niku

[naive leaf]

that's correct

[remote heron]

right

so make this sub

[naive leaf]

you would, but there isn't any s term in the RHS

[remote heron]

oh

youre right

so we have to write $\dv{s}{t} = v$

[ocean seal]

jan Niku

[naive leaf]

ya, so its an integral of a derivative

[remote heron]

$\dv[2]{y}{t} = -g-k\dv{y}{t}$ with $y(0)=y_0$ and $y'(0) = v_0$

does this seem right

[naive leaf]

looks ugly

[ocean seal]

jan Niku

[remote heron]

nothing to it but to do it

[naive leaf]

y(0)=0 no

[remote heron]

does it?

[naive leaf]

if y is displacement

[remote heron]

i thought you wanted to see this thing fall

[naive leaf]

ya, but it hasn't moved in t=0

[remote heron]

oh displacement from starting

[naive leaf]

ya, its a projectile going up in an arc - not falling down

[remote heron]

well then shooting off to infinity is what you want, isnt it?

going up in an arc

okay

[naive leaf]

so here's the tricky bit: its $a=-g-kv$ when the object goes UP, $a=g-kv$ I guess when it goes down

[ocean seal]

Awesome_Ruler_007

[naive leaf]

but we won't worry about that for now

[naive leaf]

the solution should be looking like this - object moving in arcs

,w \frac{d^2y}{dt^2} = -g-k\frac{dy}{dt}, y(0)=0, \frac{dy}{dt}(0) = u

[ocean seal]

Results provided by WolframAlpha

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

Requested by Awesome_Ruler_007#7922

[naive leaf]

,w y''(t) = -g-k*y'(t), y''(0)=0, y'(0)=u

[ocean seal]

Results provided by WolframAlpha

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

Requested by Awesome_Ruler_007#7922

[naive leaf]

[remote heron]

hmm?

some kinda stupid sign error or something

k is positive right?

i get a reasonable solution with negative initial velocity

which dont make sense

but it is what it is

[lone heart]

@naive leaf Has your question been resolved?

[naive leaf]

but that wouldn't be correct

[remote heron]

[naive leaf]

I guess I'll just stick with what I have (this project's due tmrw)

many thanks for the help though

[remote heron]

,w y''+ky'=-g, y(0)=0, y'(0)=m

[ocean seal]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[remote heron]

[naive leaf]

I tried it here

[remote heron]

i should just use matlab but it takes so long to boot

[naive leaf]

nah, leave it. don't destroy your sanity over this :berk:

[remote heron]

berk?

you mean bearlain

[naive leaf]

matlab is a hell that I wouldn't wish anyone

[remote heron]

ah it suits me

lemme give it a go

[naive leaf]

lmao its an emoji. nvm

[remote heron]

it will just take maybe 2-3 hours to boot up

and remember how to do it

[naive leaf]

haha. well, if you can solve it then sure - but it isn't mission critical

[remote heron]

 
(g + k*v0)/k^2 - (g*t)/k - (exp(-k*t)*(g + k*v0))/k^2```

$y(t) = \frac{g+kv_0}{k^2} - \frac{gt}{k} - \qty( \frac{g+kv_0}{k^2} )e^{-kt}$

[ocean seal]

jan Niku

[remote heron]

ye 😌 small sign error

so solve your homogeneous portion

[ocean seal]

jan Niku

jan Niku

jan Niku

jan Niku

jan Niku

[remote heron]

so $y(t) = A+Be^{-kt}-\frac{g}{k}t$\

this is where i need to check for sign error

[ocean seal]

jan Niku

[remote heron]

@naive leaf hows that first part

getting to the general solution

[naive leaf]

honestly, I have no idea

[remote heron]

you are intended to solve this right

[naive leaf]

Not really - You can use an online calculator (this is for a modelling project) but I'd wanna learn how to solve them myself

[remote heron]

okay

theres a lot of theory that does the heavy lifting in these

have you taken a course in diff eq? or just seen them

its not completely un-straightforward but also day before a project IDK

you need to know i guess just

particular and homogenous solutions

principle of superposition

and the weirdness of

i mean unfortunately you also have independence of solutions here too lol

so its a lot to learn the day before

[naive leaf]

well, I guess that's a bit above the standard High school stuff

I do wanna learn this stuff though. any resource you recommend??

[remote heron]

you can use an online solver

or say you used matlab

[remote heron]

say you used matlab to get to here

then solve your initial conditions by hand

thats some work on its own

[remote heron]

IMHO you really need a course, or at least to heavily follow a syllabus

its a very large topic and a motivated teacher is really helpful

[naive leaf]

hm. I don't think my uni would cover this

self-study and all

[remote heron]

any self-respecting uni will have a course on diff eq

[naive leaf]

I don't think its a module

[remote heron]

well you can self study too

its just not ideal but

you can ask in #book-recommendations

im sure theyll give you some impossible book

theres quite a few just straight up free books, too

id lean into whatever youre most comfortable with and find a resource with a guided like

list of topics

as in like, if you like physics, find one that uses a lot of physics and applications

i like coding, so theres quite a few books that take a more numerical approach

or if you are just into raw math

etc

[naive leaf]

here it is: https://rentry.co/foa5s

[naive leaf]

no, I like deep learning mostly. So yea, math in general

[remote heron]

if you want to site something

% it was created in collaboration between YOU and N. Michaels

% declare variables symbolically
% g - gravitational constant
% k - drag coefficient
% v0 - initial velocity
syms g k v0
% declare symbolic solution and differential
syms y(t)
Dy = diff(y);

% specify initial conditions
cond1 = y(0) == 0; 
cond2 = Dy(0) == v0; 

% specify differential equation
ode = diff(y,t,2) == -g-k*diff(y,t,1);

% solve
s(t) = simplify( dsolve(ode,[cond1 cond2]) );```

 
s(t) =
 
(g + k*v0)/k^2 - (g*t)/k - (exp(-k*t)*(g + k*v0))/k^2```

this is basically an online solver

IMHO

if youd rather solve the constants yourself

remove the initial conditions, and replace the last line
s(t) = dsolve(ode)

 
C1 + C2*exp(-k*t) - (g*t)/k```

https://www.desmos.com/calculator/bhkdjqju6g

[naive leaf]

which site is this?

[remote heron]

sorry, not site

cite

this is matlab code

i wrote a script that solves either the general or entire thing

you can cite it as an online solver or give the code, if you want

[naive leaf]

impressive, seems like matlab isn't so bad

[remote heron]

its nice

[naive leaf]

nah, I think I'll pass on that. I don't think adding this level of complexity is a good idea the day before

[remote heron]

well

either way

you have the full solution

[naive leaf]

but nice to know I can solve ODEs

[remote heron]

if you dont have to solve it yourself

[naive leaf]

yep. do want to learn it at some point

[remote heron]

id honestly just pause on the like

learning to do it yourself

[naive leaf]

technically, we're taught fundamentals of ODE's at school

[remote heron]

sure

how about superposition

[naive leaf]

(in Applied Maths for which the project is)

the quantum one? 😆

[remote heron]

no i mean

well thats the usual process of solving these kind of equations

you find two solutions

[naive leaf]

nah, I get what you mean - like solutions imposed on to other?

[remote heron]

and then add them together

[naive leaf]

right

[remote heron]

so yea you may be able to solve this its just a pain in the butt

focus on the project

im gonna go back to reading

feel free to dm if you run into something

my last day off before semester so im gonna drink tea and doze off

[naive leaf]

sorry for the whole thing. and thanks for the offer! I've sent you a FR

[remote heron]

youre good gl

[naive leaf]

👍 technically, I didn't need to do diff eq. (all my classmates chickened out) but I've learnt a lot about ODEs by solving the same one in 50 different ways

[remote heron]

well the theory builds up nicely

all the way up to solving systems of linear diff eq's

you can get into nonlinear diff eq's and dynamics/control/stability analysis

which is where the real fun is

or pain if you dont like analysis

[naive leaf]

and pain, where I'll die solving anything

I've heard horror stories for solving PDEs

[remote heron]

you dont generally solve them

nonlinear diff eq's dont generally have solutions

you analyze them as objects in their own right

[remote heron]

you heard from losers

PDEs are fantastic

[naive leaf]

I've never done any analysis - looks like I'll have to find out

[remote heron]

if you ever get a chance to take a PDE course even if it adds some time you should jump on it

its a beautiful course and has the potential to change the way you see the world

[naive leaf]

tbf, I'm quite conflicted between taking an undergrad in math vs. Data science. I know I wanna research in Deep learning later on

[remote heron]

IMO do math

its more work and you have to put in the work to specialize yourself

[naive leaf]

says everyone. I don't know how much I'll like it

[remote heron]

but you will learn what you need to know to do anything

[remote heron]

its a short period of your life

if youre willing to put in the work to specialize yourself it will pay off

[naive leaf]

I find math beautiful, but that sort of elegance isn't really present in uni

[remote heron]

but its more work than a normal degree

[naive leaf]

hm.

I mean, CS fundamentals would definitely help for research

[remote heron]

you will probably gain mostly the same abstract skills

like problem solving time management etc

if you do math your specific skills like the things you pick up from classes will generalize better

but youll probably see mostly the same topics, too

like core of datasci is all stats right

so not much of an option there

[naive leaf]

yea, but that stats isn't really that deep

[remote heron]

dont u kid urself

[naive leaf]

atleast what's employed in DL. In practice, simpler stuff works - occam's razor

[remote heron]

in fact you could just major in stats

nahhh

[naive leaf]

that's an idea

[remote heron]

majoring in stats or applied math is a move for sure

[naive leaf]

mathematical sciences?

[remote heron]

yea although idk who would call it that

applied statistics is a super marketable degree

challenging though

it is very data science-y though

if thats what youre into

you may look at #discussion or

dont take my word for it theres a lot of ppl in secondary here

[naive leaf]

I'm just into deep learning

[remote heron]

but if you are into machine learning and data science an applied statistics degree will satisfy you for sure

[naive leaf]

ya. but I wonder if a CS+data science degree is better

[remote heron]

up to you

reach out to more ppl

i can say

dont mull it too much

its a short period of your life

and your degree doesnt define your job etc

it is fun aesthetically but you will ultimately get to define what u get out of school ya know

anyways

[naive leaf]

ya, but a good course can surely accelerate my undergrad research and get better schools for masters

[lone heart]

@naive leaf Has your question been resolved?

Channel closed

Closed by @naive leaf

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.

[vast arrow]

I am stuck here, I have solved it 2x and got 2 different answers and now I am confused

[alpine sable]

Can you show your work?

[vast arrow]

My answers were the following:

y= 3/x+5/8

and

y= -45x-225

yes

one second

its hard to read because I did it on a little note pad but should be good enough

if not let me know

[alpine sable]

they're both wrong

[vast arrow]

ok

Im not sure what to do now because the -x/3 is throwing me off

[alpine sable]

mmh I don't understand exactly what you did

You should first find m

[wicked warren]

@junior blade can I get fucked up at your wedding

[vast arrow]

that is the issue I am having

finding M

[alpine sable]

When two lines are perpendicular, $m_1=-\frac{1}{m_2}$

[ocean seal]

HPH_Bulko

[molten pivot]

m = (y-b)/x

[vast arrow]

and m 1 in this case is -x/3 correct?

[alpine sable]

the x is not included, it's just -1/3

[vast arrow]

oh okay

So we would just take the reciprocal of that right?

[alpine sable]

the reciprocal and then the opposite

see there's a minus sign

[vast arrow]

so it would just be 3

[alpine sable]

yes

[vast arrow]

which means the second lines M is = 3

[alpine sable]

Now you know m and the point through which it passes, so do you know the formula for this?

[vast arrow]

hmmm

would it just be y=mx + b

where we subsitute

to find b

[alpine sable]

no

[alpine sable]

You actually wrote that formula at the top here

[vast arrow]

oh the y - y1

[alpine sable]

yes $y-y_P=m(x-x_P)$

or with a 1, it's the same

[ocean seal]

HPH_Bulko

[alpine sable]

(P as in Point)

[vast arrow]

so we would have $y-1=3(x-8)$

[ocean seal]

Synx

[vast arrow]

substituting them in

[alpine sable]

yes

[vast arrow]

and then we just solve for y

which would give us our equation

right

which would be y = 3x-23?

im guessing that is the answer

[alpine sable]

nvm

it's right

[vast arrow]

phew

had me lost again lmao

thank you very much for your help

.close

[lone heart]

Channel closed

Closed by @vast arrow

Use .reopen if this was a mistake.

[vast arrow]

.reopen

[lone heart]

✅

[vast arrow]

hey @alpine sable would you be free really quick to double check over another problem

[nocturne cypress]

i can help if u dont mind

[vast arrow]

all good I just wanted to double check my answer

[nocturne cypress]

mhmm go on

[vast arrow]

wrong one

I think

nvbm

it was that

the way I got it

ill put here one sec

I used this

A = L * W

392 = 2 w * w

196= w^2

W= 14

[nocturne cypress]

yaa seems correct

yup correct