help-49

[lavish venture]

ahh

[keen hill]

Ap covers alot of the same content

some things left out

but

[last slate]

Physics ?

No physics in high-school?

[lavish venture]

no there is

[keen hill]

there is physics at mine if you choose to do it

[lavish venture]

yea

it’s optional

[keen hill]

its a chemistry bio sequence or physics

usually

for us anyways

[lavish venture]

my school only offered 2 of the ap courses which basically consisted of regular mechanics

i had to self study for e&m

[last slate]

lol they teach us first semester of physics course at a standarduni in like 11th grade of high-school

[keen hill]

i also took it at college since they skip the calculus

or my school doesnt have calculus phyiscs yet

just algebra based

[last slate]

Wtf

Lmao

[lavish venture]

they only had physics 1?

[keen hill]

its a testing space problem

we have physics 1 and 2

[lavish venture]

ahh

[keen hill]

but there aren't enough rooms to conduct the exams

[last slate]

Physics without calculus

Lol

[lavish venture]

my school had physics 1 and physics c mech

[last slate]

Electrodynamics ?

[lavish venture]

i took physics 2 and physics c e&m independently and just ordered the exam

[lavish venture]

yea i had to self study for that

[keen hill]

the concepts of calculus are referenced, but the ideas aren't explicity covered using differentiation and integration

[lavish venture]

they don’t offer it

[keen hill]

we have ENM but not with calculus!

"E&M"

[lavish venture]

yea physics 2 e&m is a joke

[keen hill]

its dumbed down

as hell

[lavish venture]

lol

e&m requires calc really

[keen hill]

it does

[last slate]

Lmao knowing elementary integrals even I am struggling with e and m as you require alot of vector calculus and ideas like divergence I nit

[keen hill]

the teacher at my school teaches it with calculus to the students who are prepared

[last slate]

I have no idea how you guys had e and m in thay

That

[lavish venture]

yea how are you doing that before integral calculus??

i mean

a lot of it is just symmetry

[keen hill]

physics loves symmetry!

[lavish venture]

so you don’t need to do much integration at all

but

still there are some problems

[last slate]

The physics in jee teaches basic calculus which is enough for physics problem solving in beginning of physics

[keen hill]

yea

[last slate]

Because jee physics is impossible without calculus

[keen hill]

the thing with algebraic physics is it's just all very conceptual and symbolic in nature

[lavish venture]

probably didn’t need the last two words

[full quest]

Have y’all guys challenge csat once

[lavish venture]

wayyy too many words

what’s csat

[keen hill]

is that the korean one

[full quest]

Ye

One of the hardest ones

[keen hill]

have never done it

what does it cover up until?

[lavish venture]

oh isn’t the english part hard?

[full quest]

Math

[lavish venture]

never seen it then

[keen hill]

if it's just calculus and anything before it should be fun

[last slate]

We have pretty good use of calculus in e and m

lol

[keen hill]

looks about right

[lavish venture]

yea this is fun

i thought gauss’ law was cool

[last slate]

Stretches way beyond our math syllabus

[last slate]

No I don't like it

[keen hill]

physics does that in american university too

your physics course almost always outpace your math

[last slate]

Unintuive to me it's only mathematically beautiful to me nothing more

[lavish venture]

yea but with symmetry E is always just constant and gets pulled out of the integral

[last slate]

No

It depends on your choice of gaussian surface

[lavish venture]

well yes

but if you choose it appropriately

[last slate]

Only if dot product is same nature

For all points

[lavish venture]

the problem should work out well

[last slate]

On surface

[last slate]

That's the hard part lol

They give arbitary things

You have to choose some surface then compute the field

Shits wild

[lavish venture]

lol in the ap course we had three scenarios and they were all simple

[last slate]

how is that advanced course if you had simple things

[lavish venture]

🤷🏼‍♂️

don’t let the name fool you

[keen hill]

in reality the courses are meant to expose you to the topics before college level courses

[last slate]

I thought kids who take college courses in us are smart prodigies

[keen hill]

even ap courses

[last slate]

💀

[lavish venture]

probably half of the kids take ap courses

atleast in my area

[keen hill]

AP physics curriculums focus more on conceptual understanding over solving problems

[lavish venture]

but not all of the more "difficult" ones

[keen hill]

and in college it depends on your teacher

[last slate]

But what's conceptual understanding lol

Like

Won't solving problems

Do the same thing

Enhance conceptual understanding

[keen hill]

i mean it would definitely enhance it, but you'll be covering the same things much more in depth in upper division mechanics and e&m with new concepts

[last slate]

As the math used will be elementary and known the only challenge would be to conceptually imagine the physical situation

[keen hill]

well many times you'll be solving problems purely symbolically with no real numbers

[last slate]

I saw a book called Taylor classical mechanics

It was nice

[keen hill]

taylor's is an amazing book

[lavish venture]

this is a sample problem from the exam

[last slate]

Yeah I read some things which I didn't get

[lavish venture]

for e&m

[last slate]

From Taylor like damped oscillations

[last slate]

Not too bad

We have this in high-school

Classes

[keen hill]

yea

for free response anyways

AP c is definitely

tamed

in terms of mathematical complexity

[lavish venture]

the mcq is harder

i took both physics c classes this year

the frqs were so much easier

[keen hill]

yup

[lavish venture]

and much more time friendly

[keen hill]

they don't ask for really precise solutions on frqs all the time

so its nice

[lavish venture]

each mcq was a paragraph long lol

[last slate]

aaa

[keen hill]

its standardized

[lavish venture]

some took up the whole page

[last slate]

you guys be chillin

[keen hill]

for my intro mechanics course

it was

not so nice.

and honestly

I'm not sure I learned more having ugly numbers

because when you have to deal with the number spaghetti it turns into alot more computation and less conception challenge

[lavish venture]

how many courses did you take at a local college?

[keen hill]

I have 40 semester credits

[lavish venture]

jesus

none of those are ap?

[keen hill]

well I have AP credits too

but its for

more trivial courses

none of those are AP though no

[lavish venture]

ok that’s more reasonable

[keen hill]

my aps are humanities

[lavish venture]

oh

nevermind

[last slate]

Jee math is comparatively easier

[keen hill]

I am not sure if that's true

[last slate]

Compared to other subjects

[keen hill]

ohhh

yea

that makes sense

[last slate]

no seriously it's much less complicated like you won't get anything new

Lol

Let me show you ques

[keen hill]

I don't think we are a neccesarily good representation of the US population either

it appears (I think) that both knief and I are from higher socioeconomic areas

[last slate]

You mean you guys are rich and go to better schools

?

[keen hill]

yup

probably not incredibly rich

[last slate]

Here like rich and middle class go to same schools cause the middle class wants their kid to go to a rich so he will be rich lol

[keen hill]

but in the top 25%

or like

40%

[keen hill]

yea same

[last slate]

poor go to poor schools

[keen hill]

that is also pretty much the same here

[lavish venture]

i’m from new york

[keen hill]

I am from socal!

[lavish venture]

yea

makes sense

[keen hill]

these problems seem pretty fun

[last slate]

They are fun

[keen hill]

in reality i don't know how

useful

or like

conceptually reinforcing they are

[last slate]

Not useful lol

[keen hill]

but they are good ways to test your ability to apply them

[last slate]

they're good for concept application and manipulation skills

[lavish venture]

a lot of these don’t seem bad at all

[last slate]

You won't get such things often studying physical phenomenona

[keen hill]

yea

[last slate]

They're not meant to be "useful" is what I mean

[keen hill]

yea of course

well

when I say "useful"

[lavish venture]

this is JEE advanced?

[keen hill]

i don't mean practical in everyday life

I just mean useful in learning the concept

[last slate]

yeah

[keen hill]

are you doing any further math after calc 3?

[lavish venture]

i’m majoring in applied math/stats

[keen hill]

fun!

[lavish venture]

so yes

[keen hill]

will also be a fellow

[lavish venture]

i’m taking calc 3 and linear algebra this summer

[keen hill]

applied math major

applied math/cs

[lavish venture]

lol i was planning on double majoring in cs

i put that down

[keen hill]

I never planned to even be a math major

but my linear algebra professor changed that last semester

[last slate]

No like you could also mean if those kind of problems will ever appear in higher physics or in studying any natural phenomenon and the ans is mostly likely No?

lol

I will be a physics major

[lavish venture]

you want to do research?

[keen hill]

yes I could aslo mean that, but I just meant in the actual homogenization of the concepts

[keen hill]

yes!

for a little bit anyways

oh

you were talking to him

but

i'd assume so yes

too

for him

[lavish venture]

he inspired you?

[keen hill]

he did inspire me

amazing teacher

[last slate]

Nah I wanna teach physics I don't believe in formal research as postdocs

I will research privately maybe lol

[keen hill]

came out of stanford Ph.D program

[lavish venture]

the teacher?

[keen hill]

yes

[lavish venture]

damn

[lavish venture]

why not

[last slate]

Wow you guys have inspiring teachers irl lol I am only inspired by the great American and european minds nothing more

[last slate]

It's a joke lol

[lavish venture]

oh i don’t have any good teachers lol

my teachers are terrible

[last slate]

Literally I believe most of it is time waste

[lavish venture]

they don’t know anything

the college professors are better i’m sure

but high school teachers

yea not it

[last slate]

It's been years of no breakthrough in physics lmao

They discover new particles

[keen hill]

there are breakthroughs every year just less fundamental than they used to be

alot more specific and niche

[last slate]

And shove up 100 papers on them claiming utterly stupid things

[lavish venture]

well there hasn’t been a new quantum mechanics

but

i wouldn’t say nothing

but string theory

can be

[keen hill]

string theory is fake!!!!

(It has not been talked about for decades)

[lavish venture]

a bit of a waste of time

[keen hill]

not seriously anyways

[last slate]

They are formalities , people need to publish to get the bread on their table

[keen hill]

there are many formalities

[last flint]

Tru

[keen hill]

but there is also much advancement in the field

[last slate]

I don't believe in quantum physics

[lavish venture]

😳

[keen hill]

quantum physics is definitely real

[lavish venture]

what am i missing

[keen hill]

string theory probably not

[lavish venture]

what do you know that i don’t

[last slate]

How do you anything if it's real when you don't know about it

[lavish venture]

do you mean by observation?

[last slate]

I don't believe in entanglement

[lavish venture]

you don’t think information can travel faster than light

[last slate]

Intuition

[last slate]

Well it literally does

[keen hill]

Trusting human intuition is not great...

[lavish venture]

isn’t that the premise of entanglement

wasn’t there a nobel prize in entanglement like two years ago

[last slate]

idk i will come back to answer that when I have finished studying qm

[keen hill]

in 2022

yes

[last slate]

I am just very unsure of ideas

In qm

They don't make sense to me

[lavish venture]

i thought it was the best theory there was

[last slate]

I believe I need to know alot more

To even start pondering around it

[keen hill]

particles have been observed to behave as if they are "entangled" but I am with him on the fact that ideas that I am not too sure that I believe our current model is the accurate model

[last slate]

I believe I should know lot of math may it be differential equations complex analysis or even real analysis

[keen hill]

real analysis for physics 😳

[lavish venture]

yea i didn’t read that griffiths book i’ve only read an algebra based textbook and watched youtube videos so i can’t say much

[last slate]

Topology differential geometry

[last slate]

YES

they use theorems which have proofs in real analysis

And physicists don't care about proofs mostly

[keen hill]

yes

[last slate]

But I personally do very much

[keen hill]

the fundamental understanding of calculus is nice but it applies less handedly than other math

[last slate]

idk

[keen hill]

of course it wouldn't hurt but its extremely formal for physics

[last slate]

i find it "necessary"

to know it fundamentally

maybe i am brainwashed by my mathematically profound seniors

lol

[keen hill]

math is beautiful

I do plan to take it just because I like math

though saying it's neccesary for physics is pretty farfetched

[last slate]

i think math is necessary

i like it

but yes

like

its not just about liking it for me

[keen hill]

and you will have plenty of math to the point where you will teach yourself real analysis if you ever do need it by the end of your physics major

[last slate]

i dont know what i will do if not study physics or math

[keen hill]

I mean

before real analysis it'll probably do more help to take pdes, complex analysis, numerical analysis, or even algebra

[last slate]

i will do it after i finish differential equations from simmons book but before that i will finish multivariable calc from stewards

and yes complex analysis but its necessary to do before i can do it later aswell

like after real analysis

it won't affect much ive been told

[keen hill]

it shouldn't

[last slate]

okay

i will get started with integration

i have a target to finish it by next month

's end

you both were a great chat , thanks for the information about america

[lavish venture]

mhm

have a nice night

damn it’s 430

💀

[last slate]

its morning for me

lol

[lavish venture]

i guess it’s morning for me too now

[last slate]

i mean afternoon

[lavish venture]

oh

[last slate]

its 2 pm

here

i wake up at 10

lol

am

[lavish venture]

guess i’ll wake up at 2 pm tomorrow

[last slate]

goodluck

.close

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[primal patio]

Can anyone hellpp??

[midnight plank]

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[last slate]

for the rectangular loop why is its differential surface element represented by the phi uni vector?

[midnight plank]

Please don't occupy multiple help channels.

[last slate]

im very confused because this is what it gets represented by

but like, this doesnt make sense? im confused

[hard shard]

i assume its probably the Bflux

[last slate]

yeah but like

how the frick is $\dd \vv s = \vc\varphi h\dd r$

am i going crazy

[hard shard]

that looks like a gamma, but thats beside the point

[last slate]

yeah

[hard shard]

ngl idk what a_0 or a_phi is

i feel like i should

[last slate]

just unit vectors

of the phi component in spherical/cylinderical coordinates

[hard shard]

ah

they are taking vertical slices and finding the flux

[last slate]

im looking around online and this person used the x unit vector instead?

[hard shard]

yeah, flux is perpendicular to the wire plane

[last slate]

fair enough but like

with phi the thing is yk

uh

in all directions

i feel like im definitely missing out on something here

[hard shard]

your a_phi is tuned to be the one perpendicular to the wire plane i think

(btw take everything im saying with a grain of salt, i just finished doing my first emag class)

but yeah i think you pick phi hat to be perpendicular to the wire plane

[last slate]

hmm

why does this make sense actually

[hard shard]

because i said it

[last slate]

love me some physics bullshit that feels inconsistent as fuck as with most things involving this stuff

[hard shard]

correction: you dont pick it, the phi hat is always perpendicular to the wire part (im trying to generalize to more complicated wires and its messing with my head)

[last slate]

im trying to visualise this but like

how?

[hard shard]

i forget how direction pops out of a dot product integral

[last slate]

the phi unit vector changes direction at every point in space

[hard shard]

lets think about that later

[last slate]

so how can it be simultaneously changing direction everywhere and still be always perpendicular

[hard shard]

ill sleep on it

speaking of, im going to bed, hope i helped

[last slate]

lmao aight no worries

sleep well

still pretty confused though if anyone wants to chime in

[hard shard]

about what

[last slate]

this

[hard shard]

wait isnt flux B.dA

integral of

ointegral of*

area vector is normal to the surface

idk, good night

[midnight plank]

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[zealous schooner]

how many times will you guys post the same thing

lmaooo

I think all of you should create a group chat and discuss your paper over there, insteda of creating 6 different channels asking for just the answers of the same test...

[midnight plank]

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[zealous schooner]

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[drowsy nova]

I thought the answer was C as the dimension of the subspace is 6 (i think) and 6 =! 2 so its not isomorphic. Whys is c correct

(the real answer is e)

[midnight plank]

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[tribal temple]

Well, considering you can e.g. write 4 + sqrt{2} as a rational linear combination of 2 - sqrt{2} and 2 + sqrt{2}...

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[tidal basalt]

not sure if this is correct so far, but can anyone give me a hint on how to find the coordinates of D? thanks

[tidal basalt]

if the ab = dc thing is wrong pls lmk

[primal granite]

idk

[tidal basalt]

thanks

[primal granite]

миллионы умрут сука

[tidal basalt]

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[undone mulch]

1²+(1²+3²)+(1²+3²+5²)+.......sum of n terms of the series. help please

[undone mulch]

umm

hello?

@here

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[misty marlin]

Hello again . Sigh...this is not correct right? The question is: If 10 people do a job by working 5 days for 6 hours, how many hours a day should 15 people work to finish the job in 4 days?
Key: 5hours

[midnight plank]

@misty marlin Has your question been resolved?

[misty marlin]

<@&286206848099549185>

[heavy monolith]

Use Unitary Method

[misty marlin]

Please remind me

[heavy monolith]

Sure

Take 10 on one side

Then take 5 days 6 Hours on other & convert days into hours

5*24

[misty marlin]

I think that is not right tho

[heavy monolith]

Wait let me try

[misty marlin]

Because they work 5 days 6 hours not 24 hours

[heavy monolith]

But can't 5 Days be converted into Hours?

[misty marlin]

Why would you

It's not like they work 24/5

Non stop

[heavy monolith]

Then is it given how many hours do they work?

[misty marlin]

Yes. It's 6 hours

A day

[heavy monolith]

Okay

Should have told earlier

Anyways

Let me try

[misty marlin]

Alright

[tiny drum]

it is stated in the problem

[heavy monolith]

I just read it

Still, Thanks

Got it @misty marlin

[misty marlin]

What metod did you used

[heavy monolith]

10 Days times 5 Days times 6 Hours Daily = 300 Man Hours

[misty marlin]

Okay

And then what

[heavy monolith]

Now, we need to find out how many hours a day 15 people should work to finish the job in 4 days:15 people * 4 days * x hours/day = 300 work hoursSolving for x:60x = 300x = 5 hours/daySo, 15 people should work 5 hours a day to finish the job in 4 days. Therefore, the correct key should be 5 hours.

[misty marlin]

Ooo okay

Thank you

[heavy monolith]

&

[misty marlin]

?

[heavy monolith]

@misty marlin in which grade are you?

[misty marlin]

Uh...12

Idk actually

[heavy monolith]

So you're in High School?

& are you an American Citizen?

[misty marlin]

Yes

No

[heavy monolith]

Which country?

[misty marlin]

Does it matter?

[heavy monolith]

It does

[misty marlin]

Why?

[heavy monolith]

Just tell me I am really curious

[misty marlin]

No

[heavy monolith]

Fine

[misty marlin]

That's not why this server exists

[heavy monolith]

In my country

[misty marlin]

but anyway thank you

[heavy monolith]

This is 4th grade Math

[misty marlin]

Ig

Great 4u

[heavy monolith]

Anyways

Glad you got the answer

[misty marlin]

.close

[midnight plank]

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[tiny drum]

don't harass people for personal info

[heavy monolith]

Wasn't harassing

Just asking the name of her county

[midnight plank]

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[last slate]

A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2 m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2 m3 /min. Find the rate at which the water level is rising when there is 8π m3 of water.

[last slate]

is this asking for rate of the volume (because of the unit?) or do i solve for dh/dt

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@last slate Has your question been resolved?

[tribal temple]

They're asking for dh/dt when V = 8pi (where h is the water height, V is the volume of water etc etc)

[midnight plank]

@last slate Has your question been resolved?

[last slate]

okay, I think I am getting thrown off by the cubic metres but that helps

i ended up getting 0.07m as an answer and idk if it’s correct

but i did work for dh/dt

[midnight plank]

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[fresh ice]

hi! My question is a little tricky, i want to re-learn maths from the beginning and i dont know how and where should i start from, Can anyone give me a guide or something? I appreciate it! thx!

[lavish venture]

what have you learned so far

[fresh ice]

i learned a lot of things in math but i did it just for the time, so the only things that i always remember are just addition, subtraction, multiplication and division

i'll probably get used to more of the topics because i may remember some of them, but i want to go step to step from the very beginning

[lavish venture]

so you don’t know any algebra

[fresh ice]

yep :(

[lavish venture]

maybe go to khan academy

they have everything from the very beginning

to early uni level math

[fresh ice]

they have it in order?

[lavish venture]

yup

[fresh ice]

like a path

[lavish venture]

by grade level

[fresh ice]

OH

that's seems to be the thing that i was searching for

thank you knief!

[lavish venture]

you’re welcome

[fresh ice]

how do i put the channel available again?

[lavish venture]

i’ll close it but in the future do what i write

.close

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[craggy ice]

hi

[craggy ice]

ignore the spanish text

shouldnt theta go from pi/4 to0?

topic: triple integral spherical coordinates

[sharp coral]

the y-axis is theta = pi/2

[craggy ice]

so thats wrong?

[sharp coral]

theta = 0 is always the positive x-axis

[craggy ice]

oh so like this?>

[sharp coral]

yes

[craggy ice]

ok bro ily

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[last slate]

When you convert a trig function into phasor form, is the frequency information lost?

[last slate]

I.e., [
A\6\cos{\omega t + \varphi} = A e^{j\varphi}
]

[last slate]

is omega just not recoverable after doing this?

[surreal moon]

This is not quite correct

[last slate]

how so

[surreal moon]

It needs to be $Ae^{j(\omega t+\varphi)}$

[grand pond]

SWR

[last slate]

i dont think so?

unless im misunderstanding something of course

oh wait

this makes sense

[hard shard]

that table does not make sense

oh nvm

[last slate]

so that gets effectively ignorred in phasor domain?

heh

[surreal moon]

Oh yeah. So it does.

The $e^{j\omega t}$ is just discarded. It's up to you to remember to reinsert it when going back to time domain.

[grand pond]

SWR

[last slate]

i see

makes much more sense

[hard shard]

it looks like the information is the domain

[last slate]

wait so how does this work

im new to this stuff so like

[surreal moon]

sometimes the phasor included the time component, sometimes it does not, at least from what I'm reading

[last slate]

ahhh

u mean that

[hard shard]

idk, i read the paragrapg and thats how i read it

brb

[last slate]

btw just a curious question but what is this like

triangle notation they are using for the phi

what does it actually mean

,,<steinmetz>
z = 1.19 \phase{-78.2039\degrees}

[last slate]

i guess this is jsut phasor notation

ok thanks yall

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[inland patio]

In probability, when we want to obtain the marginal distribution of the joint distribution, there is this identity (in the discrete case) $$\left{X=x\right}=\bigcup _y\left{X=x{,}Y=y\right}.$$Suppose the union consists only of two sets, with points $y_1$ and $y_2$. Then, if we write ${X=x}$ as statement $p$ and ${Y=y_1}$ as $q$, we can write the RHS of the above equation as $$(p\land q)\lor (p\land \neg q),$$and this is equivalent with $p$, so it proves the set identity. How does one extend this to more points than two?

[grand pond]

Philip

[runic hamlet]

show double inclusion

[inland patio]

ok, I guess a key assumption then is that $X,Y$ must have the same domain then (they are part of the same random vector), since if $\omega\in{X=x}$, then $X(\omega)=x$ holds, and likewise $Y(\omega)=y$ for some $y$ in the range of $Y$, so $\omega\in {X=x,Y=y}$ and thus it is in the union. Conversely, let $\omega\in\bigcup_y {X=x,Y=y}$, which means it is in some ${X=x,Y=y}$. How do we know from this that $\omega$ is in ${X=x}$?

[grand pond]

Philip

[runic hamlet]

well X(omega)=x

[inland patio]

ok, I think I see {X=x} is a subset of {X=x,Y=y}, is that right?

[runic hamlet]

other way around

[inland patio]

ah yeah, ok, thanks 🙂

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[grand pond]

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

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[last slate]

bruh,

😭

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[inland patio]

Let $(X,Y,Z)$ be a point chosen uniformly within the three-dimensional unit sphere. Determine the marginal distributions of $(X,Y)$ and $X$. \

I'm tempted to consider the joint density $f_{XYZ}(x,y,z)=\frac1{4\pi}$ when $x^2+y^2+z^2=1$ (as the surface area of the sphere is $4\pi$), however, this function will integrate to $0$ over the unit sphere. So this can't be the joint density. I'm a bit lost on how else I should proceed with the problem. Any ideas are appreciated.

[grand pond]

Philip

[rare pine]

how did you do the integral?

[inland patio]

well, for lebesgue integrals we have $$\int_{A}d\mu=\mu(A).$$Let $A$ be the sphere, then it has 3-dimensional Lebesgue measure $0$, or?

[grand pond]

Philip

[midnight plank]

@inland patio Has your question been resolved?

[midnight plank]

@inland patio Has your question been resolved?

[midnight plank]

@inland patio Has your question been resolved?

[inland patio]

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[finite jolt]

I'm in calc 3 and we are going over surface integrals. One of the ways we do surface integrals is using the gradient for an implicit function, but I'm not sure how to know which is the independent variable?

[finite jolt]

$\frac{|\grad{g|}}{|g_z|}$

[grand pond]

tric

[finite jolt]

this thingy as the $d\sigma$ in the surface integral

[grand pond]

tric

[finite jolt]

but sometimes you use gz, sometimes gy, sometimes gx? idk whadda do lol

[sharp coral]

you generally integrate over a region of the surface projected onto one of the 3 unit planes (the xy plane in the image)

note that $g_z = \nabla g \cdot \hat k$, we are taking the dot product with the normal vector of the unit plane we are integrating over

[grand pond]

cloud

[sharp coral]

so for example the xy plane has normal vector k, the yz plane has i, and the xz plane has j

which plane we choose is influenced by the shape: since we are taking its "shadow" on a unit plane, we can't have it "overshadow" itself

[finite jolt]

We set it up by doing a parametrization and taking cross products—is gz the dot product of the gradient and normal vector because k = <0, 0, 1>?

[sharp coral]

yes

[finite jolt]

Integrate the function $f(x, y, z) = z$ over the cylinder $y^2+z^2=4$ for $z\ge 0$ and $1\leq x \leq 4$

[grand pond]

tric

[finite jolt]

for this, the shadow would be the yz plane right?

But when you take the gradient of the function for the cylinder, the x component of the gradient is 0

So in class, we just used z, but how can you use z if the shadow of the cylinder is in the yz plane?

The TA said either x or z would work but not y, and I was confused why

[sharp coral]

the surface should lie above the plane it's being projected onto, and not cross it, and the surface crosses the xz plane (whose normal is j)

[finite jolt]

doesn't it cross all the planes?

[sharp coral]

not with the restrictions in place

[finite jolt]

Then wouldn't x not work either bc it crosses the zy plane as well?

[sharp coral]

we only care about the surface with the restrictions z ≥ 0 and 1 ≤ x ≤ 4, and with those restrictions it doesn't cross the other unit planes

[finite jolt]

hmm okay i'll see if i can apply this to the homework

thank you!

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[last slate]

Anyway to go about this guys ?

How do I evaluate the last integral expression

[marsh galleon]

What's the original question?

[last slate]

I miswrote that phi as theta in numerator

Can you tell me

How do we integrate this

Rather than the original que

I wanna do it my way

[marsh galleon]

I'm asking because I see a strange substitution in line 1

What's the original question?

[last slate]

Yeah that's what i am trying

A strange substitution

Sqrt(tantheta)

Is original question

[marsh galleon]

How did you get from the integral of sqrt(tan(theta)) to the first expression on your page?

[last slate]

write tantheta in complex polar form

Divide numerator inside sqrt by e^itheta

Then put e^-2itheta = cosphi

So you can then write the whole term inside the sqrt as tan(phi/2)

And as a result of substitution we get a tan(phi) outside aswell

@marsh galleon

[marsh galleon]

This isn't clear to me

[last slate]

Tantheta = (e^itheta - e^-itheta)/(e^itheta + e^-itheta)(i)

<@&286206848099549185>

[marsh galleon]

What's this exp(-2i theta) = cos(phi) stuff?

You've literally just written random scribbles and are leaving everyone else to figure it out...

What is phi? Where did it come from?

[last slate]

It's some arbitrary variable I've chose to substitute

[marsh galleon]

You're more likely to receive good assistance if you write out your attempt properly

[last slate]

don't help if you don't get it someone else will

I sent what I wrote

That's how i write

Not my problem if you don't get it

also why do you even need the previous stuff i asked how to integrate the last expression lol

[wary trail]

• Asking a question:
• Write out the original question
• Write out your attempt
• State what you need help on

And make it legible or noone will want to help you.

[last slate]

Is the integral at the last not clear enough?

[wary trail]

absolutely not.

[last slate]

What's not clear

[wary trail]

What is what

[last slate]

Wait I'll write it on a paper

[wary trail]

now: do this, all in separate parts so it is clear what is going on. We aren't psychic, we can't mindread.

I just need you to label what you have and what you want

[last slate]

I wrote the simplified version of what i want

[wary trail]

this is the question?

[last slate]

yes

[wary trail]

great

[last slate]

for me

[wary trail]

now show me your attempt

[last slate]

Tried creating a perfect square in the denominator

[wary trail]

and then what specifically you are wanting

[last slate]

Didn't seem to work

[wary trail]

preferably a picture, you say that but you'd be surprised by the number of times algebraic errors were made that wasn't spotted because they didn't show their working.

[last slate]

maybe a good manipulation or substitution for this

[wary trail]

they were asking something about exponentials before which is why i asked this

[last slate]

no the exponentials are all before this

that has nothing to do with this

i am asking you how to integrate this

they were curious about how i got here but ia m not

so i dont care

you may tell me how do i proceed from here

and thats the only thing i asked in the first place

they got onto me for something i didn't even ask

[wary trail]

who are you...?

[last slate]

i person asking for help in something "particular"

[last slate]

oh

nvm

yeah

sorry

help

that was other acc

[wary trail]

that was you

cool

[last slate]

right

[wary trail]

let me write it out

[last slate]

Okay thanks

[last slate]

if we add and substract 1 in numerator we get cos2x -1/1-(tanx)^2

so it can simplify to solving for integral 1/1-(tanx)^2 now

but i am not sure how

[wary trail]

okay

just done it and can confirm u=tan(x) works as a substitution

[last slate]

lemme try

thanks

it works

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[last nebula]

Can someone double check this?

especially the second one

not rlly sure if I did it right

[midnight plank]

@last nebula Has your question been resolved?

[last nebula]

<@&286206848099549185>

[steady trail]

Hi

What is the problem ?

Do you have to find that all y's are the same?

[cold wind]

shouldn't circle be 31 in 1st

[steady trail]

If so, do the calculations and see if they are the same

[last nebula]

no it’s like factoring

like idk how to explain

[last nebula]

why? 36+5 is 41

[steady trail]

The last of the b seems wrong

Even the penultimate one

For the rest the others in b are correct

then the last one of the a is wrong

because it comes out -5

Not +5

[last nebula]

how does it come out as -5

[last nebula]

how do i fix it?

[steady trail]

Can you add some symbols?

[last nebula]

wdym?

[steady trail]

for example in the last of the b, subtract other additional symbols in addition to the star

[last nebula]

yea

does symbols mean numbers?

i don’t rlly get what u mean by symbols

[steady trail]

for example at the last of b Subtract the star 2 times and once the circle

So

$4(x+3)^2-24-24-3=4x^2+24x-15$

[grand pond]

BobTheBuilder

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[midnight plank]

@rare wharf Has your question been resolved?

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[steep mirage]

did i do this correctly?

[tiny drum]

no, you have to divide everything by -5

[steep mirage]

-4/5x+4=y?

[tiny drum]

(-4/5)x + 4 = y, yes

[steep mirage]

i don't need to rewrite it with y first riht?

right*

[tiny drum]

rewrite what with y first?

[still nacelle]

as in y = (-4/5)x + 4?

where y is on the left hand side?

[steep mirage]

yes

is it fine to leave it or do i need to put it as that

[still nacelle]

it should be fine

[tiny drum]

it's the same thing, just convention

[steep mirage]

for this one slope would be 1/5 right>

[tiny drum]

yeah

[midnight plank]

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[steep mirage]

.close

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[open sedge]

I don't understand how they found the answers

[open sedge]

thx!

could you help me with another problem?

also do u have tricks for these types of problems cuz idk when to use permutation or combination

[small jasper]

Just send it

[small jasper]

Idk it just kinda made sense tbh ._.

[open sedge]

for this idk how to approach it 😭

[small jasper]

Let’s start with part (a)

Let’s say we have n distinct objects

How many ways are there to arrange them in a row?

[open sedge]

8!?

n!

[small jasper]

yup

[small jasper]

So yeah that’s part (a)

For part (b), the couples have to sit together

[open sedge]

ok nice

[small jasper]

So we’re going to want to rethink what we’re ordering

What are we ordering in this case?

[open sedge]

uh the couples?

would it be 4! * 2!?

[small jasper]

How did you get that?

[open sedge]

because theres 4! ways to arrange the couples

and * 2 if the man or woman switches

[small jasper]

Close but no cigar here

Note you need to do it for each couple

[open sedge]

wdym? :/

would it be 4! 2^4?

ok ty how about c)?

[small jasper]

Hint: consider how to order the men and then how you can place them in the line

[open sedge]

would it be 4! to order the men and then 4! to arrange the women?

it doesnt make sense in my head tho idk what im saying

[small jasper]

Yeah, if you consider the men and women individually, then there’s 4! ways to order both

Now you need to figure out how many ways there are to put the men amongst the women

[open sedge]

idk how to figure that part out :/

why cant it just be 4! * 4!?

[small jasper]

Hint: Think of all the men as a single thing

[open sedge]

5?

so 4! * 4! * 5?

@small jasper how do you do them so easily?

like do u draw the situation or do u just know

or do you have a trick to know? 😭

also up till now are they all permutations and no combinations yet?

[small jasper]

Idk this is just expected knowledge for me

If you can’t do this in < 30 sec then you’re dead

[open sedge]

wtf

😭

[civic bough]

There is a secret trick

[open sedge]

what is it pls

[civic bough]

Keep doing lots of questions and understand how to do them

[open sedge]

.

[civic bough]

[open sedge]

can you help with e)?

[civic bough]

Mr pigeon

[small jasper]

oh just

Alternate the strings of men and women

Basically what you did in (c) but easier

[open sedge]

would it be 4! * 4! * 2?

[open sedge]

:/

[small jasper]

[small jasper]

Yeah

[open sedge]

so the reasoning would be theres 4! ways to order both men and women and we multiply by two cuz it can either be a man or a woman that starts first?

[open sedge]

is this university math 😭

[small jasper]

high school

[open sedge]

cuz im gonna take stats again in uni and i dont wanna do this

WHAT

aint nobody in highschool doing that?? 😭

[small jasper]

that’s the easy stuff

But on a more srs note

Combi is weird

[small jasper]

Ik this is cliche

But it’s especially true for combi

[open sedge]

wait what i just did is combi?

[small jasper]

You need to acclimate yourself with the common setups

Because what happens is when you do harder combi

You’re often looking back on those common setups

And seeing how you can relate things to those

Sometimes you even reframe the question in terms of those common setups

Also there’s this things called “combinatorial arguments”

Which is using combinatorics to show something is true

More specifically, creating a situation that you can use combinatorics on to show something is true

The classic example is showing that $$\sum^{n}_{k=0} \binom{n}{k}=2^n$$

[grand pond]

Civil Service Pigeon

[small jasper]

Ok maybe not the classic example but it’s pretty famous and standard

[small jasper]

Yeah

[open sedge]

i wouldnt be able to do that

[small jasper]

You’re counting the numbers of ways to arrange people

[open sedge]

isnt combinations like

5C4

liek the C

but the problems didnt need the C

[small jasper]

The combinations formula is used in combinatorics

But combinatorics as a whole is counting the number of ways to do stuff

You don’t necessarily need the combinations formula

[open sedge]

oh ok

thx for the help

[small jasper]

In fact, in the trivial cases, when you can technically use it, you don’t rlly need it

[open sedge]

are u a math major

[small jasper]

Eh idk

[open sedge]

ur in highschool???

[small jasper]

Pure math -> not a lot of money

Being a teacher is meh

And I tried research

Don’t rlly like it

So I’ll prob do data science/comp sci

Smthn like that

Maybe throw some AI in there

I def need to get better at coding tho

[open sedge]

wait what are u doing rn?

[small jasper]

But yeah

[open sedge]

WTF

im in college rn 😭

are u in the US educational system

[small jasper]

Yeah

Hence why I said being a teacher is meh

It’s all going 📉

Both student quality and admin support

[open sedge]

and theyre teaching you these advanced stuff in AP stats

[small jasper]

I don’t do AP stats ._.

Also this is the very basics

[open sedge]

then how did u learn all these stuff

[small jasper]

Tbf I do go to a specialised hs tho so

We’re all tryhards

[open sedge]

oh ok

[small jasper]

Comp(etition) math

Picked it up my first year of hs with no experience and just kinda

Stayed with it

Got some more influence on the scene as the years passed

And now here I am

[open sedge]

have u done calculus?

[small jasper]

Won’t disclose what I do since that can dox me but let your imagination wonder ig

[small jasper]

Yeah

I actually took the bc test today lol

Pretty easy, there were a few questions I appreciated seeing

But most of it was the same bland flavor as always

[open sedge]

ok yall way too smart

c'est assez

anyways ty for the help

.close

[midnight plank]

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✅

[open sedge]

.close

[midnight plank]

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[midnight plank]

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[fast gust]

**is this attachted image correct judging by the following probability problem? **A letter is chosen from the word LEVEL without replacement and then a second letter is chosen from the same word.

[midnight plank]

@fast gust Has your question been resolved?

[low escarp]

Looks right to me

[fast gust]

thanks!!

[midnight plank]

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[velvet wraith]

Yo

Got answer key for this one too or what

Yea that's correct as I see it

Oh damn

Yep

Okay so we are given r = (1,4) and + s(0,2) now for this we need to eliminate s which is the parameter

Our equation is a 2 dimensional space line where r is a position vector in our line (remember that 1,4 are only specific points in our line) and our (0,2) is the direction our vector takes in the line

Ur getting it so far?

Okay so how do u think the cartesian form of the line can be expressed as?

We'll use good ol' y = mx + c

Now next step would be finding our slope but since our vector is (0,2) and x is 0 and y is 2 which means that our line is vertical and parallel to the y-axis

so yes with what I told u above m (slope) is undefined

Okay since we know that our line is parallel to the y-axis what would that mean for x in (1,4)?

Yep but to give more clearance since our line is parallel to y

That means our x is constant

Now to find the constant we used (1,4) because it's the coords that passes through our line

Which is why x = 1 (constant)

So in summary, the Cartesian form of the line is x = 1

Yep! When the slope is undefined, it typically means the line is vertical, in this case, the line is parallel to the y-axis, so the only thing that changes as you move along the line is the y-coordinate, not the x-coordinate, so the x-value remains constant, which in this case is x = 1 as it passes through the point (1,4)

Yep that's basically it

12th Grade

No lol

Yea I just converted it we don't use grades in my country

The year I'm in is equivalent to 12th grade apparently