help-19

[clever fjord]

Ann

[wooden python]

is that what your original problem says?

[clever elm]

Nope it is written in the book just like that

[clever elm]

Yupp

[wooden python]

hmm hold on.

i am ever so slightly suspicious of this. let me actually run it through my calculator to see if it actually matches up.

[mystic saffron]

actually im dumb nvm

Ok with sin11°41'sin18°19' it works

[clever elm]

Tnx

[clever elm]

Its okay people are dummer these days

The very last line

Check that

[mystic saffron]

wait that doesn't even have the minute notation in the 4

[clever elm]

Oh right

Probably a printing mistake

[mystic saffron]

then I guess there's a typo

[clever elm]

Could be 😶

May not be as well idk abt these maths 🥺

They drive me crazyyy

[mystic saffron]

it would be true if the + was replaced with 1'

[clever elm]

Hmmmm.... Ig u have a point

But, it just might not be cuz these writers are weird

They say there is no mistake

[wooden python]

aight so

in the interest of clarity i calculated this and wrote out all intermediate results to as many decimals as my calculator would give me

[clever elm]

I believe it didn't match the given thing

[clever elm]

:O

[wooden python]

and yeah shit doesnt add up

[clever elm]

Wow!!!! Ur handwriting 🙀

Its so nice ^~^

[wooden python]

i wasnt trying to be neat right now but thank you

[clever elm]

👍 you're welcome madame

[mystic saffron]

lol it also looks like the spacing isn't consistent at all

so skibidi

[clever elm]

Thanks for the help ;')

Am grateful

And am super mad about these rumors that there are no mistakes

Screw those typo creeps 🥺 wasted so much time

[wooden python]

yeah that sort of crap is really infuriating

[odd edge]

@clever elm Has your question been resolved?

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[elfin vessel]

help please

[graceful viper]

have you tried any substitutions like e^x + 1 = u so far?

[odd edge]

@elfin vessel Has your question been resolved?

[elfin vessel]

yes i have tired

[molten palm]

And did it work?

$\sqrt{\frac{u-2}{u}}$?

[clever fjord]

jelly v20

[odd edge]

@elfin vessel Has your question been resolved?

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[stoic cloud]

How do I find a formula for $\sum^{\infty}_{k=1}\frac{H_k}{k^n}$?

[clever fjord]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[summer wave]

how did you find these values

[stoic cloud]

I must be honest — wolfram alpha

but they do check out numerically

@rancid moat

plz

help meh

[rough birch]

$\sum_{k=1}^\infty \frac{1}{k^n}\left(\sum_{i=1}^k \frac{1}{i}\right)$

[clever fjord]

snowflake

[stoic cloud]

yes yes!

[rough birch]

(im just tinkering)

$\sum_{k=1}^\infty \sum_{i=1}^k \frac{1}{k^n}\frac{1}{i}$

[stoic cloud]

you can rearange like that?

[rough birch]

maybe?

[stoic cloud]

idk, how would that 𝑘 work outside of the lower limits?

[rough birch]

i always forget the interchange rules

[stoic cloud]

[rough birch]

oh wait yeah that is wrong

[stoic cloud]

isokay ❤️

[clever fjord]

snowflake

[rough birch]

but we could rearrange the summations now and get k on the inside

[stoic cloud]

that’s correct though, Can you merge the fraction into 𝑖/𝑘ⁿ?

[rough birch]

and then evaluate the geo series

[summer wave]

no closed form according to this

https://www.quora.com/How-would-you-evaluate-sum_-n-1-frac-H_n-n-k-where-H_n-is-the-n-text-th-harmonic-number

[rough birch]

or something

oh

yay

[summer wave]

you can always interchange with positive terms btw

[low locust]

https://mathoverflow.net/questions/457508/the-dirichlet-series-of-the-harmonic-numbers

[stoic cloud]

Wait what?

So there’s no formula, but there is closed forms for some 𝑘?

*or 𝑛 in this instance

[rough birch]

$\sum_{i=1}^\infty \sum_{k=i}^\infty \frac{1}{k^n}\frac{1}{i}$

[clever fjord]

snowflake

[low locust]

more or less closed form for integers m>1

[rough birch]

oh that is not geometric what am i doing

[summer wave]

ye

[stoic cloud]

so does a formula exist… or is this a lost cause…

[rough birch]

absolute convergence :D

[low locust]

well the post writes a formula which is about as closed formula-ish as I would expect

I cant imagine that such a sum of zeta values has a nicer closed form

[stoic cloud]

Let me find quickly scroll through MSE and see if I should close this channel or not…

because this was only part of a bigger problem of mine

I was trying to find

[clever fjord]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[summer wave]

what is your definition of H_k/s

[stoic cloud]

Harmonic numbers again

if you extend them with an integral

[low locust]

this really is above the paygrade of a help channel

[stoic cloud]

$H_z=\int_0^1\frac{-1+t^z}{-1+t}dt$

[clever fjord]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[stoic cloud]

forums?

[low locust]

go into an advanced number theory channel

[stoic cloud]

I just don’t want my problem to get shot down…

!close

oop

uh

I forgot

.close?

.close

[odd edge]

Channel closed

Closed by @stoic cloud

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

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[jagged crescent]

guys I messed up both of these apparently.. anyone know where the mistakes happened?

[late dust]

9: 8 became 5 for some reason

10: it looks like x÷2, not x+2

[jagged crescent]

ooppss

thanks for the help

.close

[odd edge]

Channel closed

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[frank tide]

is the vector (0 , 0 , 2) perpendicular on the zx plane?

[short terrace]

What does it mean to be perpendicular on the zx plane

[frank tide]

if so why

[frank tide]

is that a question to me or you dont understand the question itself

[short terrace]

That's a question to you lol

I'm asking for the definition

[vernal yacht]

@frank tide is this what you’re asking?

“ Orange perpendicular to purple, yes or no? “

[frank tide]

ah, let me give the original question

[vernal yacht]

Alright 🙂

[frank tide]

"Which of the following vectors is perpendicular on the zx plane?"
1 - vector x
2 - vector y
3- vector z
4- (0 ,0 ,2)

[frank tide]

apparently the answer is vector y and i dont really understand why

original question perhaps

[vernal yacht]

Hmm….do you know the equation that describes the plane xz?

[short terrace]

That is not what (0,0,2) would look like is it

[frank tide]

y=0?

[vernal yacht]

Nah, it was a demonstration. All in all, can you takeover?

[short terrace]

Sure, I just wanted to confirm if I was tripping lol

[vernal yacht]

I shouldn’t hijack your channel 😂

[short terrace]

I don't have a notebook on me unfortunately

No no I disappeared for a while

I'm at a doctor's

Feel free to take over cuz I'll keep disappearing

[vernal yacht]

Absolutely ✅

Can you find me the normal vector of it?

[frank tide]

normal 😭 ?

you mean like- unit vector version of it

[vernal yacht]

Yes, it’s like the vector that is perpendicular to the plane

And its length is 1

[vernal yacht]

yay

[frank tide]

ah yes, just learned the terminology for it

anyways

what do you want the normal vector of

[vernal yacht]

XZ plane

[vernal yacht]

This guy

[frank tide]

(1 , 0 , 0)?

[vernal yacht]

alr, so for every ax + by + cz = 0
The normal vector is <a, b, c>

Keep in mind that <a, b, c> is always the vector that is perpendicular to the plane

[frank tide]

oh you wanted (x , 0 , z)?

[frank tide]

im assuming the <> mean matrices?

im very new to 3d geometry

[vernal yacht]

No, I’m referring it to vector here.

[frank tide]

whats this?

[vernal yacht]

It’s a plane equation!!

[frank tide]

pretty sure i wasn't introduced to that but- ig ax +cz =0 or <a , 0 , c>?

[vernal yacht]

wait fr?

[frank tide]

yeah i wasn't

[frank tide]

started yesterday

[vernal yacht]

Have you been taught how to find a vector that is perpendicular to a plane in a 3D space?

[frank tide]

no, nothing that specific no

i was only taught projection and unit vectors when it came to planes

like how (0 , 0 , 1) is the unit vector for the z axis

[mystic nova]

a vector is perpendicular to a plane if it perpendicular to 2 or more distinct vector parallel to that plane

[frank tide]

yeah i def didnt learn that

[vernal yacht]

Yep, you’ll need this information in the following process

[vernal yacht]

It’s alright, just keep that in mind

[vernal yacht]

Do you need some time to put that in your note?

[frank tide]

what are a , b , and c exactly? like in a vector like (2 , 5 ,11)

[mystic nova]

actually you can look at the corner of your house and imagine that each edge is an axis

[vernal yacht]

They’re variables

[frank tide]

OH

[frank tide]

yes we do that sometimes

[vernal yacht]

For example
For 3x + 7y - 4z = 0, its normal vector is <3, 7, -4>

[frank tide]

oh so thats a plane

and the unit vector thats perpendicular to that plane

is ( a , b , c)

any reason why you type them between < >? is that not a vector

[frank tide]

oooh so this is like a function of x and y in the 2d plane

the "plane equation"

[vernal yacht]

it's easier for me to tell vectors from coordinates 😂

[mystic nova]

vector has a form (x,y,z) respectively to the axis, so for example u(a,b,c) that mean it go along x axis a unit, along y axis b unit and the same for z

[vernal yacht]

be careful, the length of a unit normal vector is 1, while normal vector can be at any length.

[frank tide]

yes!

i understand

everything

proceed please

(super interested tbh)

[vernal yacht]

Right, back to the question

[vernal yacht]

do you know the direction vector of a vector in the direction of x

ik it sounds redundant, but I wanna make sure yk.

[frank tide]

what?

i might know what that is but not seem to recognize it bc of hte language barrier, can you clarify what ur talking about?

[vernal yacht]

the direction vector of the first option

any vector that is parallel to the first option

[vernal yacht]

here

[frank tide]

yeah, any vector with z=0

i... think?

[vernal yacht]

any vector with z = 0 and y = 0

Because the vector is in direction of x

[frank tide]

oh yes i didnt consider the direction while imagining

yes

I already see the pattern

[vernal yacht]

how about the second and the third option?

[vernal yacht]

yay

alr, have you taken the notes?

Let's move on

[frank tide]

ye

a vector that is parallel to for example the z axis has both their y and x = 0

[vernal yacht]

"Which of the following vectors is perpendicular on the zx plane?"
1 - vector x --> (1, 0, 0)
2 - vector y --> (0, 1, 0)
3- vector z --> (0, 0, 1)
4- (0 ,0 ,2) --> (0, 0, 2)

[frank tide]

and what does perpendicular on the zx plane mean again?

[vernal yacht]

As we mentioned previously, the plane equation of xz is y = 0, and its normal vector is (0, 1, 0)

[frank tide]

and the vector that's perpendicular on the zx plane is the same as the normal vector of the y axis

[vernal yacht]

Absolutely

[frank tide]

or... any vector along they axis ig?

does it HAVE to be normal?

is (0,1,0) the only possible vector thats perpendicular on the zx plane

[vernal yacht]

yeah why not?
Normal vector means a vector that is perpendicular

[vernal yacht]

No

[frank tide]

so..?

[vernal yacht]

it can be <0, 2, 0> <0, -1/2, 0> <0, 228492, 0> etc

[frank tide]

yeah so- it doesnt have to be normal

bc ( 0 , 2 ,0) isnt normal no?

yet its perpendicular to zx

[vernal yacht]

Let's clarify the definition.
normal vector: A vector that is perpendicular to the plane.
unit normal vector: A vector that is perpendicular to the plane and its length is 1

I was unclear when I first mentioned it

[frank tide]

ooooooooooh yes yes

[mystic nova]

unit vector is vector with length 1 or what ever the axis unit is

[frank tide]

so an infinite amount of normal vectors and one unit normal vector

wait a minute

nvm

[vernal yacht]

2 actually, it can be in opposite direction

[frank tide]

who has a squareroot of one execpt one

[vernal yacht]

<0 1 0> <0 -1 0> both works

[frank tide]

oh

yes that makes a lot of sense

tysm sky

for your patience and kindness

have an amazing day

[vernal yacht]

Have a good one!!

[frank tide]

.close

[odd edge]

Channel closed

Closed by @frank tide

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[odd edge]

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[elder vault]

I’m deflated

[elder vault]

I’m deflated

I’m deflated

It is so hard

I cannot get through it without any mistake made

I’m so sad

I’m so sad

Traumatized

There’s always something wrong

Help me please

Please

[mystic nova]

I mean to check all of them we have to know mandarin

Or you could provide a translated one

[elder vault]

I had checked it

I missed some numbers

👨🏻‍🦰: it is okay. We all make mistakes

👨🏻‍🦰:move on. Look at the big picture

👨🏻‍🦰:you could do it again a week later, but now you should just move on

I will listen to you

I will move on. Thank you

[odd edge]

@elder vault Has your question been resolved?

[odd edge]

Channel closed

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[odd edge]

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[odd edge]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[vivid wyvern]

What have u tried

[wooden python]

!msgdel

[odd edge]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

[buoyant hollow]

uhh i tried to fine tan theta

[vivid wyvern]

Can u show ur work

[buoyant hollow]

sure

wait

[vivid wyvern]

Also u should open a new channel ,this channel is closed
It will be considered available for help soon

[buoyant hollow]

oh

do i close this first

[vivid wyvern]

Is this 2 or 3

[buoyant hollow]

2

[vivid wyvern]

It's already closed

[buoyant hollow]

wait

it shows occupied to me

[vernal yacht]

The channel will timeout soon

[wooden python]

it's going to implode in like 3 minutes

[buoyant hollow]

oh-

[wooden python]

go claim a new one

[buoyant hollow]

😭 i think i did smth wrong

[vivid wyvern]

No it's okay,js claim a new channel

[buoyant hollow]

i did

[odd edge]

Available help channel!

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[outer cosmos]

i have a question on how plus and minus work in 'u substitution' when intergrating

[obsidian nymph]

anyone could help me

with a problem

[summer wave]

!occupied

[odd edge]

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).

[languid horizon]

You can ask the question and give more context like what is it you dont understand etc..

[outer cosmos]

right

lmao

does that plus and minus js stay there?

also how would i intergrate sin^5(x)

ive tried u subbing but im a little stuck

[vivid wyvern]

Can u show ur work

[vivid wyvern]

Try converting the sin⁴u into cosine

And then u can do a sub for cos

[outer cosmos]

ohh

like sin^2 = 1-cos^2?

[vivid wyvern]

Yes using that

[outer cosmos]

ah ok

i’ll try that

tyyyy🤍🤍

[vivid wyvern]

Np

[odd edge]

@outer cosmos Has your question been resolved?

[odd edge]

Channel closed

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[vestal beacon]

Need help.
This is my 11 years old younger sister's math problem, but we've both forgotten how to solve it.

Calculate B = 2^2 + 2^4 + .... + 2^2024 + 2^2026

I know it's supposed to be some sort of sum, but I don't know how to change it to one.
Thank you if anyone decides to help

[tacit wasp]

That is the sum of a geometric series

[slow whale]

looks like it

[tacit wasp]

So your sister should have been taught the formula for it

[slow whale]

Sn=r(1-r^n)/1-r

[vestal beacon]

She, apparently, forgot (which is why I'm here)

[slow whale]

no sorry im wrong

its not that

[nocturne mica]

think this only applies if |r| < 1

[slow whale]

which it is

in our case

its supposed to be multiplied by a

not r

that was my mistake

[tacit wasp]

$$S_n = a_1 \frac{1 - r^n}{1 - r}$$

[nocturne mica]

are we saying that |r| < 1 here?

because i don't think so...?

[slow whale]

this is the question

[vestal beacon]

What's S, a and r? Sorry I'm really bad at notations (is it what they're called in English?)

[clever fjord]

Alberto Z.

[slow whale]

r is common ratio

S is sum

[tacit wasp]

No no you're right

[serene axle]

|r|<1 is for infinite GP

Only

[tacit wasp]

|r| < 1 is needed if the sum goes on till ∞ values

[slow whale]

nvmd im blind

yeah

you were correct

[tacit wasp]

If she forgot it, isn't she able to find it in the textbook or in the lecture notes?

[vestal beacon]

My sister still doesn't really understand anything,, I'll try plugging the equation/wherever whatever into the formula to figure it out

[vestal beacon]

Most likely left that at class, I think

[slow whale]

i mean fair enough

we are 15 years old here in my country

and we have just learnt

AP

[vestal beacon]

I'm also 15... whoops.

[slow whale]

oh

[vestal beacon]

(Math was never my strong suit basically)

[slow whale]

well this is a tad bit awkward innit

[slow whale]

same but lets not go offtopic

[vestal beacon]

Indeed.

[languid horizon]

Where are you stuck?

[slow whale]

uhh he just forgot the sum of first n terms for gp , all g now

[languid horizon]

Dont wanna be rude. But you can just google such stuff

[tacit wasp]

a1 is the first term (in your case |2²|) and r is the common ratio (in your case |2²|

n is the number of terms you're summing (which you have to figure out here)

@vestal beacon

[vestal beacon]

What's a?

[nocturne mica]

a represents a term

like a term in your sequence

[vestal beacon]

Ah

[nocturne mica]

the number tells you which term it is

for example, a_3 = third term

[vestal beacon]

Thank you

[nocturne mica]

i guess your first step is to find n

[vestal beacon]

I guess there are... 2026 of them? considering,, it ends at 2^2026

Sorry English isn't my first language

If you all want, I can close this channel (My sister gave up)

She's also saying her teacher gave her a different method asw

[nocturne mica]

not exactly

see that the power goes up by 2 each time, not 1

and also, don't worry about the language! just let us know if you don't get a certain part

[vestal beacon]

Oh so that's what it meant,, the total of numbers inbetween

[nocturne mica]

yep! the total number of numbers in the sequence (or more properly, the total number of terms)

[vestal beacon]

My calculator is... refusing.

[nocturne mica]

what did you type in your calculator?

[vestal beacon]

It's been so long since I last touched something bigger than 2^2 I'm so sorry

[vestal beacon]

I was testing,, I wanted to see if it could handle a massive number

[nocturne mica]

technically speaking, all you need to do is look at the power (the smaller number to the top right)

notice that it starts at 2, and for every subsequent number it increases by 2

and it ends at 2026

[vestal beacon]

Yes,,

[nocturne mica]

so if i ask you how many numbers are in the sequence (2, 4, 6, 8, ... , 2026), what would you tell me?

[vestal beacon]

If nobody minds, I'll close this channel

I think I'm freaking out worse than ever

So sorry everyone

.close

[odd edge]

Channel closed

Closed by @vestal beacon

Use .reopen if this was a mistake.

[nocturne mica]

i apologize if i contributed to it

hope to see you around next time

[vestal beacon]

thank you

[odd edge]

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• Show your work, and if possible, explain where you are stuck.
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[rare crown]

very confused on this

[rare crown]

wha

[short terrace]

!status

[odd edge]

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

[short terrace]

What have you done so far

[rare crown]

i looked at trig identities and im not sure entirely where to modify it to work

cus i know theta is basically x if i can get the right form

i think

[short terrace]

Well what is csc x

[rare crown]

1/sinx

[short terrace]

Good

[rare crown]

which could then be x/cos9x sin4x

[short terrace]

And what is the limit of cos 9x as x goes to 0

[rare crown]

uh

1

oh ok

[short terrace]

Good

Do you see what to do now

[rare crown]

so then x /sin4x

still a little lost, do i just reverse the denom and numerator somehow

[short terrace]

I mean x/sin4x is just 1/(sin4x/x)

Only one more thing you need

[rare crown]

ohhh

1/1?

wait nvm its 4 (1)

ok this makes sense now

thanks

[odd edge]

@rare crown Has your question been resolved?

[odd edge]

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[dense phoenix]

Im doing set theory, its only week two of classes and im stressed the fuck out, havent taken a math class in 5 years pls help

[dense phoenix]

ok so the universal set is A-Z and i just have no clue how to solve this, i dont understand why the fuck the parentheses are here, the comma is the complement but i dont get it

[quasi sparrow]

you can just ask your question here

[dense phoenix]

and heres my other thing, if i get help with these two im sure ill be able to finish the rest of the assignment

[quasi sparrow]

if you're struggling with notation, this is pretty simple https://www.storyofmathematics.com/set-notation/

[fleet tapir]

The parenthesis are there to indicate that you are taking the complement of the entire set A n B. Because A n B' might be interpreted as the intersection of A with the complement of B'

Read the question after the one with parenthesis

[dense phoenix]

BnA'?

[fleet tapir]

That is different from (BnA)'

See the difference that the parenthesis makes?

[fleet tapir]

.

The parenthesis tells you what to do first. The parenthesis around A n B in (A n B)' means you do A n B first, then take the complement

While A n B' means you take B', then intersect with A

I repeat: these two will give you different results

[dense phoenix]

the complement is everything in u that isnt in any sets right

[fleet tapir]

The complement of a set is everything in U that is not in the set

So the complement of B would be all the letters except {r,e,d}

[fleet tapir]

This is not helpful. They don't understand the need for parenthesis which is not covered in this article.

[dense phoenix]

so would B n A' be {f,g,h,i,j,m,n,o,p,q,s,t,u,v,w,z,y,z}?

but b has d and e tho

[fleet tapir]

Yeah

What is A'?

[dense phoenix]

everything not in a

[fleet tapir]

What is B n A' then?

Everything that is in B and not in A

Can you explicitly write the set A' for me?

[fleet tapir]

@dense phoenix

[dense phoenix]

{D,E,F,G,H,I,J,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}

[fleet tapir]

And B is {R, E, D}

So B n A' is the intersection of B and A'

[dense phoenix]

oH so i myself just intersect them

so it would be that list plus r e d

[quasi sparrow]

no single article is going to explain every single thing

feel free to add to the article instead of complaining

[fleet tapir]

That's not how intersection works

[fleet tapir]

I just added it- an explanation

[fleet tapir]

You may want to read riemanns article or just this:
The intersection of two sets are the common elements among them

[dense phoenix]

my brain just isnt built for this

[fleet tapir]

What's common among {R,E,D} and {D,E,F,G,H,I,J,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}

[dense phoenix]

r e d

[fleet tapir]

Yeah

So what's B n A'

[dense phoenix]

what i dont understand is why is e and d still in it

i just dont understand

bc thats not in set a

[fleet tapir]

Yeah

[dense phoenix]

and neither is r

i just

ughfsd

[fleet tapir]

So they're in A'

Then you are looking at what's common in between A' and B

You are doing B n A'

Not B n A

B n A' is what is common in between B and A'

A' is stuff that's not in A

So B n A' is stuff that's common in between B and (stuff that's not in A)

[dense phoenix]

im so lost man

i think im just gonna fail this class fuck it

.close

[fleet tapir]

Being frustrated will not help. If you think my explanation is not helpful you can read the articles or wait for someone else

[odd edge]

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[fleet tapir]

Neither will this help

[odd edge]

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[frozen musk]

idk how to sketch vectors please help

like where did theta spawn from

it says heading due east why is theta not just automatically 0

[quasi falcon]

Do you know how to do basic vector operations?

Sum mostly

[frozen musk]

yeah but drawing for some reason I can't do

[quasi falcon]

Well, in the most basic sense, vectors are essentially arrows pointing to some place with a certain direction

you have two ways to express that fact:

1. You find the X,Y coordinates the end of the vector points to.
2. You find how long the vector is, and in what angle is pointing to. Which is usually known as 2d polar coordinates R,θ

Youll 99% of the times be using the first one

[frozen musk]

okay, so how would I go about this problem?

[quasi falcon]

The boat is being moved by two "forces" right?

1. Its own motor
2. The current

[frozen musk]

yeah

[quasi falcon]

Sadly, when doing this sort of problems, you are usually given the second form of the two vectors

R,θ,
R = the force/speed, θ = the angle in which that is applied

[frozen musk]

okay

uh

[quasi falcon]

There is a way to convert it to x,y anyways
for a pair R,θ, the "equivalent" X,Y pair is
X = R (cos θ)
Y = R (sin θ)

[frozen musk]

okay yeah that I remember

but I'm still confused on the drawing

how do I know I needa use the 45 degrees

[quasi falcon]

The drawing is poorly done anyways btw

like, the math is good, but the drawing is completely skewed

[frozen musk]

bruhhh

[quasi falcon]

For drawing vectors, you just chain them together

Specifically, the end of the previous must be the start of the current

Which you can prob see is not done in the drawing

The blue vector should be below the "east" line

[frozen musk]

bruhhh

yeah that's kinda wild

[quasi falcon]

something like this

[frozen musk]

ahhh I see

[quasi falcon]

Well, thats basically how to graphically sum vectors

the end of the blue point connected to the (0,0) is the new vector

[frozen musk]

yeah that makes more sense

[frozen musk]

yeah

eventually the book computes theta to be ~9 degrees

so ig the red is not directly on the east line

[quasi falcon]

If you give me a sec ill fact check that

[frozen musk]

okay bet

[quasi falcon]

about ~13 deg, they got lost with the drawing

[frozen musk]

9 and 13 is a pretty significant difference no?

[quasi falcon]

maybe i got the problem wrong and is not just summing speeds, but i think the text could be wrong

[quasi falcon]

Yeah, i tried doing doing as they did and i get 9.03 deg, the "correct" way (the one i stated) leads to 13

[frozen musk]

hmm interesting

can you share your work for this question?

[quasi falcon]

oh, my bad

its not absolute speed

Its relative to the water itself,

then its ok, since, if the water is moving past us, we are moving past it from that perspective, you use the opposite vector

[frozen musk]

I see

yeah I think I'm just gonna spam some problems and look at other books

it really doesn't seem like a difficult concept

I'm just selling the bag

[quasi falcon]

The vector sum should look like this if we stick to how vectors are added geometrically, but the result will be the same

The problem is kinda strange by asking relative to the water, but it makes sense ig.

[frozen musk]

okay cool, noted

[quasi falcon]

yeah, the ~9 deg is correct then, mb, thought it was relative to the shore

[frozen musk]

okay cool perfect

yeah I understand it a bit better now I'll just keep practicing

tysm for the help

.close

[odd edge]

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[robust olive]

how can u prove cos(2x) = 2cos^2(x) - 1 without using pythagoream identity?

[languid horizon]

So without $\sin^2 x + \cos^2 x = 1$?

[clever fjord]

casework

[robust olive]

yea

[languid horizon]

Idk why would you wanna do that

Like surely whatever you use will just be equivalent to that identity

I mean here is 1 take ig

You can take the derivative of $\cos^2 x $

That is -sin(2x)

Now integrate that. That is cos(2x)/2 + C

And fix up the constant to its 1/2

[odd edge]

@robust olive Has your question been resolved?

[odd edge]

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[winter mesa]

Hello

[winter mesa]

I need some assistance, with the point slope equation

This so far is the problem. And what I’ve done on it

[mystic saffron]

that handwriting tho lol

[winter mesa]

Sorry my hands keep shaking I feel really uncomfortable right now but Still trying to push thru my work

[mystic saffron]

ok lets see, first step is good 4x+7y =9 you do y from here
y= (-4/7) x + (9/7)
the slope : -4/7

[winter mesa]

Wait so I got it wrong?

[mystic saffron]

i can't understand most of your handwriting to know

lol

[winter mesa]

Bruh I put 9 instead of 7

how can I get rhe slp[e from the problems?

The slope

[mystic saffron]

it's from 4x+7y=9 you do y from here: 7y=-4x+9

y= -4/7 x + 9/7

you can see here m = -4/7

[winter mesa]

So just the x and y ??

[mystic saffron]

yeah it's the slope

so parallel line through 4 and -2:

y -(-2) = -(4/7) *(x-4)

[winter mesa]

Thank u

[winter mesa]

This is the next part right?

[mystic saffron]

yes

you need to do it for (4, -2)

there is next part after that for perpendicular line through (4, -2)

it's reverse/negative reciprocal of -4/7

that's 7/4

se we're here now:
y -(-2) = -(4/7) *(x-4) for parallel line

[winter mesa]

Yes

[mystic saffron]

so now y+2 = (-4/7)x + (16/7)

i hope my brackets are clear

[winter mesa]

I’m on this step rn

It’s stuff after that confuses me

[mystic saffron]

ok so we do y from here:
y = -(4/7)x + (16/7) -2 just shift the 2

[winter mesa]

Subtract 2?

[mystic saffron]

y+2 you need to put it on the right side

[winter mesa]

From both side?

[mystic saffron]

the 2

to get y

[mystic saffron]

yes now you need to get y

so +2 goes right and becomes -2

[winter mesa]

So subtract 2 from both side?

To make it disappear from left

[mystic saffron]

no

[winter mesa]

And add 2 to the right ?

[mystic saffron]

y = -(4/7)x + (16/7) -2

here

[winter mesa]

Ahh

I see

[mystic saffron]

then you * the 2 with 7/7 so it becomes 14/7

basically same

you're multiplying it with 1 but that one becomes 7/7

and the whole becomes 14/7 which is 2

so that you can do 16/7 - 14/7

[winter mesa]

I don’t have a 14/7

[mystic saffron]

and that's 2/7

you have it

it's the 2

[winter mesa]

Ah I get it yeah

So I simplify with 2?

[mystic saffron]

so parallel line: y= -4/7 x + 2/7

that's that

are you confused about some part of this?

[winter mesa]

Yes

[mystic saffron]

ok which part?

[winter mesa]

I’m at the 14/7 part

Do I divide it by 2?

[mystic saffron]

that's the 2

no

y = -(4/7)x + (16/7) -2

see the -2 here?

[winter mesa]

Yea

[mystic saffron]

it's same as -14/7

we make it -14/7 to do 16/7 - 14/7

get it?

[winter mesa]

Im just not good at this types of things

[mystic saffron]

14/7 is practically 2 mate
so we have 16/7 and a 2
we need to make that 2 -> x/7 so that we can calculate those numbers
so we do 2*(7/7) (7/7 is practically 1)

2*7/7 = 14/7

14/7 = 2

so you don't change anything of value

just the equation

if you divide this 14/7 you get 2 so think of it as 2 transforms into 14/7

because of the 16/7

[winter mesa]

Yeah

I get how to get the 2/7 u simplify

To get the 14/7 out of 16/7 tho I don’t

[mystic saffron]

2/7 is because 16/7-14/7

16-14 = 2

2/7

[winter mesa]

Now how do u do perpendicular lines?

[mystic saffron]

so final for parallel is y=-4/7x + 2/7

is everything clear or?

[winter mesa]

I guess but on the exam I’ll forget

That’s just how it is

[mystic saffron]

it's really simple mate so i'll go through it again ok?

[winter mesa]

Nah I’m fine I’mtired of math

[mystic saffron]

first you find slope:
4x+7y=9
you do y from here, transfer 4x on the other side:
7y=-4x+9 (when you transfer it becomes - if it was +)

so from here you find y, transfer 7 on the other side:
y=-4/7x +9/7

if 7 was * on the one side it becomes /7 on the other

and the slope is -4/7

so we have (4 , -2) as point
y-(-2) = -4/7(x-4)

in other words y-(second number) = -4/7(x-firstnumber)

[winter mesa]

It’s alright I don’t want any,ore help I’ll just accept it

[mystic saffron]

-*- = + so
y+2 = -(4/7)x+16/7 -> 16/7 is because -4/7(x-4) -> we multiply -4/7 with x and with 4

transfering the 2 on the other side:
y=-4/7x + 16/7 - 2

we multiply the 2 with 7/7 because of 16/7:
y=-4/7x + 16/7 - 14/7

y=-4/7 + 2/7

that's for parallel

perpendicular you need perpendicular slope
so you do negative reciprocal of the slope:
-4/7 -> 7/4

and do the equation:
y-(-2) = 7/4(x-4)

y+2 = 7/4x - 28/4

[winter mesa]

Ohh that’s what I messed up

[mystic saffron]

y = 7/4x - 7 - 2

y = 7/4x -9

that's for perpendicular

that's that

[odd edge]

@winter mesa Has your question been resolved?

[odd edge]

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[nocturne scaffold]

not sure whats wrong

[nocturne scaffold]

the heck

i put in 2n-1

(still wrong btw)

[wooden python]

what the fuck do they want fr

[nocturne scaffold]

what im saying

[wooden python]

do they somehow want "odd number" to refer only to positive odd numbers implicitly

[nocturne scaffold]

guys it looks like i just left it blank i swear i had 2n-1 in before

[nocturne scaffold]

errr

[wooden python]

but like 2n-1 would be correct

except they reject it

what the hell

[nocturne scaffold]

yeah exactly

im not too sure whats goin on

[wooden python]

is this the entire question or part of a bigger one

[nocturne scaffold]

its part of a bigger one

lemme send the wehole thing

whole

[wooden python]

yeah let's take a look at the whole thing

[nocturne scaffold]

dunno why the other parts would matter as much tho

[wooden python]

oh so

critical info actually!!!

you're encoding the sequence 9, 11, 13, 15, ...

[wooden python]

2n+k should give 9 at n=1, that's how you get your k

[nocturne scaffold]

ohhh

okok

.close

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[proper maple]

@silk fox

[proper maple]

Hi - sorry about that

It does add up to 6

I also don't know how to prove it

I know chatgpt is discouraged but I use it for these cases

[silk fox]

damn

[proper maple]

yeah

its pretty uh

ugly

but i guess it works

[serene torrent]

So may I ask what's your question here?

[proper maple]

well

i've decided to skip it

we were trying to solve the series n^2/2^n

[serene torrent]

Other then like this?

[silk fox]

well i got to $\sum_{n=1}^{\infty}\frac{n^2}{2^n} = 2 + 2\sum_{n=1}^{\infty}\frac{n}{2^n}$

[clever fjord]

creeperdoesredstone

[serene torrent]

I am also getting somewhere like that.

Using n = n+1

[warped glacier]

If you write the sum of n/2^n in a triangular array

You get 1 + 1/2 + 1/4 + ... for each geometric sun

*sum

[odd edge]

@proper maple Has your question been resolved?

[serene torrent]

You sure it is 2+?

Maybe I am also doing something wrong.

Oh wait right it is +2

Here is a whole solution.

[proper maple]

jesus

okay yeah that works

thanks

[serene torrent]

Do you even know what did I do?

[proper maple]

no not previously of course i'm looking at it trying to understand but i get the gist of it

you "pushed back" the series

then expanded

split the sums

[serene torrent]

Yes but also realize that we used the fact that the sum is 0 at n=0. Otherwise you also need to add it.

[proper maple]

ah i see

yeah

[serene torrent]

I mean subtract.

I would suggest you to try it on other examples as well to see the details or do this without looking.

[proper maple]

thank you.

i'll save this for future reference when these situations come up again

thanks!

.close

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[proper maple]

@serene torrent

i've just realized something

i'm so stupid

the exercise asks whether the series converges or not

nothing about finding its sum

🤦‍♂️

regardless this proves really useful as i'm sure i will need it in the future

it's good to know

[serene torrent]

It is only useful if the series converges tho.

[proper maple]

true

[serene torrent]

I am a bit rusty with my series convergence tests but a ratio test should solve this.

[proper maple]

yeah no it's relatively easy

ratio should solve

also no need to prove an >= 0

well i mean

i do need to prove that still

to be rigorous

but you get me

see this is what confuses me

how do i say n^2 >= 0 for example

can i say oh well its a natural number starting in 1 which then only grows

and on top of that its squared

of course all that in math lingo

[serene torrent]

Foe reals n^2 is positive.

[proper maple]

that's just

an implicitly true statement?

like of course it is

[serene torrent]

I would say abs(...) = ... maybe.

[proper maple]

im not debating that

same for 2^n

like i know for a fraction if both terms are always positive then the fraction is always positive

same for if they're both always negative

[serene torrent]

I am not good with proofs so someone else can help you better. Sorry.

[proper maple]

no worries

its all good

[odd edge]

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[frank tide]

in this triangle (ABC) of lengths sqrt(2) , sqrt(2) , sqrt(6), theta=?

ik you can get (180 - theta) by one of the trig identities that includes cosine(180-theta) but! when i first attempted to solve this question, I didnt use trig and I used anotehr approach and i got a terrible answer, i just wanna know what i did wrong.

area of ABC = 1/2 x length x length x sine of whats between them. lets call whats between them here "180-theta" or just "theta" considering that e sin(180-theta)=sin(theta)

OK- so 1/2 * sqrt(2) * sqrt(2) * sin(theta) = area.

so sin(theta)= area.

theres a formula relating the lengths of a triangle to its area (its called her##ne formula? idk his name sounds weird in arabic)

anyways... area of this whole triangle is sqrt(3)/2

sin(theta)=sqrt(3)/2

theta = 60

[frank tide]

Wrong. why?

forgot to attach the triangle

[near socket]

car

[frank tide]

ignore the guy on the left

[near socket]

can i buy you

i want a car

[frank tide]

https://tenor.com/view/black-girl-stan-twitter-red-meme-memes-gif-23478789

[vernal yacht]

Don’t…leave him alone

[narrow crypt]

,calc sin(2pi/3)

[clever fjord]

Result:

0.86602540378444

[narrow crypt]

,calc sin(pi/3)

[clever fjord]

Result:

0.86602540378444

[narrow crypt]

,calc sqrt(3)/2

[clever fjord]

Result:

0.86602540378444

[frank tide]

aha?

[narrow crypt]

,calc sqrt(2)*sin(pi/2 - 2pi/6) * sqrt(6)*1/2

[clever fjord]

Result:

0.86602540378444

[frank tide]

am i supposed to be catching something

[narrow crypt]

,calc sqrt(2)*sin(pi/2 - pi/6) * sqrt(6)*1/2

[clever fjord]

Result:

1.5

[narrow crypt]

Yes

[frank tide]

care to elaborate further? i dont quite understnad

[narrow crypt]

Is 60 degree the only valid input of sin whose output is sqrt(3)/2

[frank tide]

no

180-

OH

.

oooh 😭

ok so

after confirming that 60 iswrong

i shouldve checked for the other equivalent angle

ok- failed at 6th grade math

nice

ok ty

.close

[odd edge]

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[severe pine]

The heat of combustion of ethane gas is 373 kcal per mole. Assuming that 60% of the heat is useful, how many litres of ethane measured at S.T.P. must be burnt to convert 50 kg of water at 10°C to steam at 100°C ? One mole of a gas occupies 22.4 litre at S.T.P.

[odd edge]

Please don't occupy multiple help channels.

[potent nexus]

What’s the density of ethane

It should be using q=mcdeltaT

[calm hedge]

Q1​=mcΔT=(5.0×104)(1)(90)=4.5×106 cal=4500 kcal

[potent nexus]

what’s going on there

[severe pine]

not given

[potent nexus]

Yeah you don’t need

[calm hedge]

Q2​=mL=(5.0×104)(540)=2.7×107 cal=27000 kcal

[potent nexus]

Just find moles

And then litres

[calm hedge]

therefor total = Q1​+Q2​=4500+27000=31500 kcal

and then find n ( moles )

[potent nexus]

Wait does this require latent heat asw

[silk fox]

yes

since water gets converted to steam

[potent nexus]

I’m asking on the basis of the question

[severe pine]

is this for water

[calm hedge]

to raise temp

and to vaporise

after finding moles use find volume v= moles * 22.4

[severe pine]

540 from where

[calm hedge]

yes man its for water

[severe pine]

no im asking how did you get 540

[calm hedge]

That 540 cal/g is the latent heat of vaporization of water at 100 °C (at 1 atm)

[severe pine]

oh

[calm hedge]

now bye bro i am playing Lord of the fallen

[severe pine]

after i find total heat

i have to find 60% of it right

[silk fox]

divide by 60%
since 60% of the heat from ethane combustion is useful

[severe pine]

ohhh

i thought 60% of heat from water was useful

thanks

.close

[odd edge]

Channel closed

Closed by @severe pine

Use .reopen if this was a mistake.

[odd edge]

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[wide pollen]

hey, i need to prove that q has a global min and its <0

so ive shown that it has a global min

but <0 is harder

[wooden python]

$q(0) = -2$

[clever fjord]

Ann

[wide pollen]

ik

[wooden python]

whatever the global min is, it cannot be greater than q(0).

[wide pollen]

but how to prove thats the global min

[potent nexus]

Bruv

[wooden python]

you don't prove that the global min is achieved at 0

it could be achieved at x=0.42069666867530911111131415 instead

[potent nexus]

You agree that the minimum is less than or equal to -2 right

Cuz it’s minimum

[wooden python]

but whatever your global minimum is, it cannot be greater than any value of q at any particular point.

[wide pollen]

agreed to this

[wide pollen]

and this

[potent nexus]

Then qed

[wide pollen]

but a,b,c are just parameters and we dont know if its <0 or >0

[wide pollen]

oh i get u now

thx

q(0) lowest

as the def of a global min

.close

[odd edge]

Channel closed

Closed by @wide pollen

Use .reopen if this was a mistake.

[wooden python]

no

we dont know that min q = q(0).

[wide pollen]

.reopen

[odd edge]

✅

[wide pollen]

right im sry what im sayin is that if s is the min then q(s)<=q(0)

[wooden python]

we know that min q ≤ q(0), yes.

[wide pollen]

thx !

.close

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Channel closed

Closed by @wide pollen

Use .reopen if this was a mistake.

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[shrewd trellis]

My answer is in the red circle

[shrewd trellis]

!status

[odd edge]

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

[wooden python]

show original problem too

[wooden python]

it seems that the 96 in this snippet is also sus -- shouldn't it be 96t instead?

this part is correct btw. you applied the product rule correctly. but you fumbled the algebruh that follows it.

[shrewd trellis]

oh damn bruh let me redo it rq

[wooden python]

dont be quick about it

[shrewd trellis]

carefully I mean

[wooden python]

yeah be extremely careful

brain surgeon level careful

[shrewd trellis]

I was careful

this is still wrong

[wooden python]

time to go papers please on your thing to sniff out even the slightest error

so this expansion is legit

but then your like-term collection got fumbled

in particular the t^3 terms

-64 - 3 - 1 - 64 = -128 - 4 = -132 and not the claimed -120

and then also

[shrewd trellis]

got it

thanks needa work on my fumbles

.close

[odd edge]

Channel closed

Closed by @shrewd trellis

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
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[wooden python]

hmmm hold on. there's some big question marks in there.

• is X withdrawing the whole lot at the end of '10, or only part of it? (or even, when is he withdrawing?)
• does X also have to pay 30% tax on whatever he withdraws? or, maybe more sensibly, on just his interest?
• is this interest simple or compound? (i'm guessing compound, but explicit confirmation would be nice)

do you by any chance have the original problem exactly as written

cause i really really think there's some weaselry here

like

X and Y are both withdrawing at the end of '10 right

it's not explicit in here

so wait. X pays tax on the principal as well? is that what you're saying?

the second that X's €8440 lands in his deposit account, X knows he's already on the hook for 30% of that to the tax man even before he gains any interest?

that sounds monumentally stupid.

so 30% tax applies only to the interest.

[dense topaz]

yes

[wooden python]

and we want the net payout (post-tax) to be the same.

[dense topaz]

yes