help-0

[warped phoenix]

yeah

this is a really garbage course

i believe you were the one who told me for an earlier question that was also wrong to appeal that the question's answers were all incorrect

if i were to do that that would be a lot of appealing

because to say there are things here being taught incorrectly is an understatement lmfao

the course was recommended to me by my school, i shouldve went with john-hopkins instead 😦

[noble sinew]

Uni course?

[warped phoenix]

its an algebra II course for highschool

im taking it to test out of algebra II so i can go into pre-calc next year

tho idk if i can pass the test to test out of it if a bunch of stuff im being taught is wrong 😅

we'll see

[noble sinew]

Ye well... What you have above is a multionomial model. But I'm curious how your teacher got to that conclusion ever. We can easily see that 80 * 0.223 is not an integer for example so it is impossible for our simulation to be "consistent" if consistent in his mind means exact same probability.

and if he is like oh it just needs to be close to the true probability then there clearly is a difference whether the simulation was for 80 or for 80000 for example (like with the coin thing mentioned above for example)

[glacial hedge]

I have taken certain math courses through CTY and was tryign to take a math course at UW, however they said that the CTY courses weren't "college level" courses and that I couldnt test through the courses.... So i would have to take calculus if I were to take a course at UW. Does anyone know what to do... oviously tkaing calculus, multi, and the following courses would be a huge waste of a year and tons of money. Does anyone have any suggestions... I cannot go to a different college to take courses because UW is the only college without an age requirement (I am going into highschool this year)

[noble sinew]

I mean they even say on there website it doesn’t count as college courses

[solar cradle]

University of Wisconsin or Washington?

[noble sinew]

So not really sure what you expect

[solar cradle]

Many schools do have placements tests that can place you into calc 3 right away. You could also seek instructor consent to take other courses

[glacial hedge]

washington

[solar cradle]

Which course were you considering taking?

[glacial hedge]

they dont have a placement test

I was tryign to take linear analysis

They said I would have to go into calculus 1.....

[solar cradle]

linear analysis or algebra?

or is that the same at UW?

[glacial hedge]

analysis (p.d.e + fourier and stuff)

[solar cradle]

yeah, it's probs pretty unlikely you'd be able to skip into an upper level course like that :/

[glacial hedge]

wdym

[solar cradle]

I was in the same boat, it kinda blows but often taking calc at a good university can be enlightening

[glacial hedge]

but it would be a tremendous waste of time and money?

[solar cradle]

Is there a youth options program in your hs?

[glacial hedge]

nope

[glacial hedge]

wdym by enlightening

[solar cradle]

You could consider reaching out to the prof and ask to audit the class if you just want to learn the material, but if you're looking for credit they'll probably want to vet you to make sure you're able to perform in university level courses

[glacial hedge]

yeah probably want credit unless I want to do this again when i go to college....

[solar cradle]

Depending on how rigorous CTY was, in good math schools the calc sequence is taking pretty seriously and can be a good intro into analysis

That's what i mean by enlightening

Is Calc 1 the only class you have available?

[glacial hedge]

yessir

i cant test out of it

becauser i didnt take the ap

exam

[solar cradle]

After taking calc 1 would other courses open up or would you be stuck in the calc sequence?

What are the prereqs for analysis level courses at UW?

[glacial hedge]

its a pretty low level course... only 200 level

differential and linear algebra are prefequs

I think I would still be stuck... and what sucks even worse is I can only take 1 class per semester because of hs...

[solar cradle]

I think you may just be stuck in the system here, even if you wait until college it's likely you wouldn't be able to test past calc 3 without college credit

[glacial hedge]

:/

[solar cradle]

Have you looked into online courses at other universities?

[glacial hedge]

yes

all of the other universities

dont.. offer courses past calculus

and if i want to take university courses.... all of the other ones have age reqs

[heavy spear]

I need help with this quest8ion

please

aw man i posted here would you mind posting in another section?

otherwise i will its fine

[kindred dock]

I'll post somewhere else

[heavy spear]

its fine ipostred in question 1

[little lotus]

did you do something?

[heavy spear]

no i just need to know how to do iut

<@&286206848099549185> can u help with the above picture

[coral pagoda]

Well, we know the function is continuous everywhere except x=-1.
To make sure the function is continuous at -1, both left and right hand limits need to be the same and the limit is f(-1)

[ocean seal]

dackid (jump king +)

[coral pagoda]

Now, try to determine how to use this knowledge to figure out a solution

[heavy spear]

thx for the life saver

[coral pagoda]

Keep in mind I did not give you an answer, I only gave you a helpful way to think about the problem in order to figure out the answer yourself.

[heavy spear]

ye i always forget the parts i need to solve i know how to

but i forgot the small parts

[coral pagoda]

Sounds like you know where to go from here 🥳

[alpine sable]

Hey everyone. Can anyone help me with this? I dont understand where is underline, where the number 1 is.

[solar cradle]

Are you asking how they go from the second line to the third line?

If so, its just the definition of $Im(z)$ and $Re(z)$. That is, for $a,b \in \mathbb{R}$, then $Im(a + ib) = b$ and $Re(a+ib) = a$.

[ocean seal]

Billy Clintorus

[alpine sable]

Yes!! Omg, i get it now, thx ❤️

[misty thistle]

Fairly easy question Im just kind of stumped.
The start up costs of a farm is $1,840,000. Each harvest costs $560,000 in resources and labour but the produce is sold for $780,000 for $220,000 profit per harvest.

How many harvests will take until they are in the green. (paid for the starting costs and bearing in mind each harvest costs $560,000)

[ionic jewel]

they make $220,000 per harvest, and need to pay off $1,840,000

how many harvests will it take?

maybe that rewording will help?

[misty thistle]

omg it really is that simple

thank you

[red lagoon]

@astral dagger yes its convolution \

[modern wren]

would this be a correct solution?

[elfin talon]

@modern wren I don’t have the brain power to look at the problem rn, I still have some feedback, the modulus operator is “%” so “1 mod 7” is 1 % 7

Just make sure to add a space between and the other values so it’s not mistakened with a percentage

Although I think the concept is context oriented

[placid zinc]

@slate arrow
First make useful variables. What would the variables be?

[slate arrow]

x

the dad woul;d be 3x

the son would be x

the daughter would be x-3?

[astral dagger]

https://tenor.com/view/michael-scott-wink-yes-आँख-मारना-gif-5795910

[placid zinc]

Yeah very nice! That does work

[slate arrow]

yeah

[placid zinc]

What would their ages be 3 years ago?

[slate arrow]

hmm

oh i didnt see that part lmao

ok so

(3x-3)+(x-3)+(x-6) = 63

[astral dagger]

beautiful

[placid zinc]

And with that, you're basically done. Solve for x

[astral dagger]

or 3x

[slate arrow]

x = 15??

@placid zinc

[slender forge]

Look at what u let x equal

If the son is 15 what would the father be

[slate arrow]

46

45*

oooh

[astral dagger]

well done boy

[slate arrow]

then the daughter would be 12

[placid zinc]

👏

[slate arrow]

no but that doesnt sound right

if its 12 15 and 45

thats 72

not 63

[astral dagger]

well, the sum attends to their ages 3 years ago

[slate arrow]

oh yeah that is right

[slender forge]

U calculated current age correctly u good bro

[slate arrow]

9 years

ok so thats right

x = 15

ayyyy

thanks guys

[slender forge]

Yes and they ask for father

Make sure u put 45

[slate arrow]

father is 45

yep

k thx

[sick phoenix]

can someone explain iv pls

ty

[ocean seal]

SubGui

[idle axle]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[idle axle]

,list

[ocean seal]

My commands!

Use ,ls to obtain a briefer listing, and use ,help <cmd>to view detailed help for a particular command, or ,help to view general help.

If you still have questions, talk to our friendly support team here.

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Page 2/4

[analog gulch]

if I have a tree with 10 layers. each node has 100 children, starting from one top node.

how many will there be in the bottom layer

(I'm to tired to do this right now)

wait

it's 100^10 right?

[sick phoenix]

Anyone?

I don’t get how you find k

[ionic jewel]

first one has 1, second one has 100, third one has 100^2, ..., 10th one has 100^9

[analog gulch]

ah ok thanks

[oak chasm]

You need to figure out where you first get a repeated output. When you get two inputs with the same output, the inverse has one input with two different outputs, which isn't a function.

Does that make sense?

[slate arrow]

How do I write an expression for 6 less than half of x

[vernal flower]

Try to break your problem down. Figure out how to write "half of x", then 6 less than the stuff I indicated in quotes

[slate arrow]

uh

0.5 over x in a fraction???

so 6 - 0.5/x

no

thats not right

[vernal flower]

So let's approach this problem with a simple example

Let's just say that x is $10 in this case

[slate arrow]

how do I write half of x

yeah

[vernal flower]

What is half of x? In this case

[slate arrow]

well 10 / 2

[vernal flower]

Yep, and because of the type of question this is, you can simply substitute 10 for x

[slate arrow]

so x / 2

[vernal flower]

Yep. That's "Half of X"

[slate arrow]

so 6 - x/2

?

[vernal flower]

Let's not try to guess. Try to use things you know to approach things you don't know

Let's use x being 20 now that we're tackling the 2nd part of the question

You know that 20 / 2 is 10

Let's say 20 / 2 is "that", or "y", or whatever you want to call it

[slate arrow]

uh

[vernal flower]

Your question again was "expression for 6 less than half of x"

[slate arrow]

yep

[vernal flower]

So then let's substitute "20 / 2" for "half of x"

[slate arrow]

right

[vernal flower]

So your question for example would be "expression for 6 less than 20 / 2"

What would 6 less than 20 / 2 be?

[slate arrow]

so it would be 4

[vernal flower]

In this case, yep

So then would you get 4 from "6 - 20/2" (your earlier guess)?

[slate arrow]

oh

x/2 - 6 lol

[vernal flower]

Correct. You've learnt to

1. Use a small enough value like 10 or 20 that you can comprehend to wrap your head around a problem
2. Use a small enough problem that you've already solved to solve a bigger one

[slate arrow]

gotcha

thanks!

[vernal flower]

You're very welcome 🙂 Try to use the similar approaches when solving questions in the future. Keep in mind of the techniques you learn because they will be extremely valuable in many aspects of life

Could someone with more teaching experience mention how I could've helped better? I felt like I didn't know how to bridge the gap between the "6 less than 20 / 2" (my own brain has problems wrapping around the question lol) but I felt like my approach was nice, short, and sufficient for what was requested

[tulip sedge]

y=|cosx| is not differentiable at x= (2n+1)pie/2 . can someone explain why is it not differentiable at this point?

this is part of my practice test

[placid zinc]

Note that |x| is not differentiable at x = 0, so you care about when cos(x) = 0

[tulip sedge]

i see 🤔

thank you

[steel palm]

can somone pls check channel 1 once they are done pls

[empty bane]

adakah orang indonesia disini ?

[lapis valley]

hey

need help

so my constraint is 4x+3y = 2

and my equation is x^2+sqrt(3)/8y^2

but when i differentiate i get a different answer to the solution

they used a different method but i should get the same area

,rotate

[lapis valley]

,rotate

[lapis valley]

where did i mess up

sry this stuff is too hectic but i appriciate if anyone can help me

the minimum area should be 0.11, and i got 0.07

[tough hatch]

check the area of the equilateral triangle

@lapis valley

you probably thought of asqrt(3/4) as sqrt(3)/4

[cloud rain]

X x 2 is 2x or x^2?

[lapis valley]

is it wrong?

i wrote it like this sqrt(3)/4

[lapis valley]

yea

i wrote it like sqrt(3)/4

where did i make this mistake

[tough hatch]

work from there

[lapis valley]

ok

thanks

[hollow pelican]

hi is 1a and 1b like this?

[rigid island]

this is a little weird, don’t you usually i for imaginary numbers?

or am is this not it

[hollow pelican]

for engineering is j

i think

[rigid island]

oh hahaha sorry

i’m just a high school student trying to learn

[hollow pelican]

ohh

[rigid island]

but from what ik it looks right all tho 1b it. doesn’t look like it’s (-7,2)

it should be quadrant 2

[hollow pelican]

ohh is it like this?

!rotate

,rotate

[rigid island]

nah um so just think of graphing real numbers

the point (-7,2)

like that

i could be wrong but that’s what it would be

logically

[hollow pelican]

Ohh

ok

i think its correct

thanks

[rigid island]

np

[solar widget]

yo i dont get this

can someone check on it a lil

[alpine sable]

How is this statement correct?

17^2=289

8^2=64

289+64=353

[tough hatch]

no

c=17

[median tendon]

26/4=13/2

[tough hatch]

a=8

b=15

[alpine sable]

I had to calculate the right side

[tough hatch]

c is the length of the hypotenuse

[alpine sable]

the opposite side

I had the adjacent and the hypoteneuse

and I had to get the opposite

so I had a=17 and b=8

That's all I had

[tough hatch]

you are using the theorem incorrectly

you are not listening

[alpine sable]

please enlighten me

[tough hatch]

c is the length of the hypotenuse

what length does the hypotenuse have in your triangle?

hypotenuse is the longest side

[alpine sable]

17

[alpine sable]

I'm aware

[tough hatch]

so why do u insist that a=17 instead

whereas c=17

[alpine sable]

But the hypoteneuse is already given, one second let me send the equation before it got solved

[tough hatch]

and yes, it is correct

[alpine sable]

So I already have the hypoteneuse

I need to calculate the opp

[tough hatch]

so you are finding the length of the shorter side

you need not use angles even, since the triangle is a right triangle

[alpine sable]

yeah

[tough hatch]

a^2+b^2=c^2

c=17

either a or b can be 8

[alpine sable]

yes

[tough hatch]

assume a=8

then what do u get

[solar widget]

ohhhhhh

shit

thanks man

makes sense

[alpine sable]

64+b^2=289

[tough hatch]

yes

so how do u find b?

[alpine sable]

289-64

[tough hatch]

=????

[alpine sable]

then square root

yep, 15

[tough hatch]

🙂

yes

[alpine sable]

Thanks, I never knew c was the hypoteneuse

In a right angle triangle are the angles always 90, 45 45?

all the questions so far have been in this orientation

[sharp barn]

Can we solve this with algebra?

[rigid smelt]

yes

[tough hatch]

no

[tough hatch]

not all right triangles are isosceles (two sides are congruent or two interior angles are congruent)

[alpine sable]

Alright thank you

[sharp barn]

,rotate 90

[sharp barn]

But the negative part i think i did something wrong

[rigid smelt]

you didnt

there are no real solutions for x^2+1=-10

[sharp barn]

But u cant square root negatives right?

cant

[alpine sable]

But then what if I do? Do I have to calculate the ratio here?

[rigid smelt]

ok we should move

this channel is occupied

[sharp barn]

Kk

Where

[tough hatch]

what are you solving for, a and b?

here you use trig ratios

[alpine sable]

I asked in #help-7｜zen1thxyz because I thought this channel was occupied

let's move there

[plucky slate]

hello

if I want to evaluate the formula in normal plot (x, y)

formula of line i use normal formulas

like f(x) = ax + b

when I do such on log scale x I go f(x) = alog(x) + b

and what about when x axis is the square root scale

will it be f(x) = a*square(x)+b?

[tawny totem]

Can someone help me pls

https://math.stackexchange.com/questions/4215600/i-do-you-prove-the-following-formal-adjoint-inner-product-for-this-specific-diff

I stuck on this question

[placid zinc]

Which one is it?

[tawny totem]

@placid zinc 5)

Here is my attempt

https://ibb.co/album/R4NqKx

[placid zinc]

What book btw?

[tawny totem]

Its my professor book,there no answers at the back but here is some context

https://ibb.co/album/BKQyx7

[placid zinc]

Zτ = ∂/∂z + 1/2 τz'
Zτ' = ∂/∂z - 1/2 τz
Using ' for overbars haha

And it looks like (a, b) = ∫ ab dx over the entire domain

[tawny totem]

I know that

how do you solve 5) @placid zinc haha

if you can

[placid zinc]

I'm looking to just simplify the left, and simplify the right. They should come out to the same thing. Does that work?

[tawny totem]

No,i tried :/

[tawny totem]

you need the conjuagte for b for this case

[placid zinc]

Ah I see

[alpine sable]

can someone explain the steps taken to arrive to the answer? thanks!

[surreal meadow]

factor out I(s)

the rest is just moving around terms like usual

[small holly]

how do i do this

[vale wigeon]

make a diagram

it should become clear

[alpine sable]

thanks 🙏

[small holly]

i did

c=sqrt(170^2+320^2-2(70)(320)cos71)
c=342m

but c=310m

[vale wigeon]

70? did you mean 170?

,calc sqrt(170^2 + 320^2 - 2 * 170 * 320 * cos(71*pi/180))

[ocean seal]

Result:

309.6420268553

[small holly]

ohh

[vale wigeon]

also

[small holly]

oops my bad

[vale wigeon]

since you had the calculations

you really really should share them

the way you asked the question it appeared you didn't know how to even start

[small holly]

oh alright ill do that next time

ty

[vale wigeon]

do that all the time for all future problems. share all the progress you have made even if it led you to the wrong answer

[small holly]

alright

[split slate]

How would one do this?

[dawn wraith]

Use the law of cosines bud

[split slate]

Gonna quickly google that

[dawn wraith]

Law of cosines*, sorry.

[small holly]

i cant do a), i did

cosC=(9.5^2+8^2-15^2)/2(9.5)(8)
cosC=0.4654...
   C=cos^-1(0.4654...)
   (I made a triangle BCD, D is left horizontal of C to the B line and named the bottom right angle theta)
   theta=117.74000/2
   theta=58.87 degrees
   ∴ bearing from B to C = 148.87 degrees

but the answer is 145.9 degrees

[vale wigeon]

is CD meant to be perpendicular to AB?

[small holly]

no

[surreal meadow]

@small holly what is the bearing from B to A?

[small holly]

180

[surreal meadow]

good

and can you somehow find angle ABC?

because if you can, you should be able to construct an equation for the bearing from B to C with that information

[small holly]

yeah i can

ill try do that and see if i do it right

yay i got it correct

ty

[surreal meadow]

👍🏻

[tawny totem]

Advanced Textbooks in Mathematics
The Wigner Transform
https://doi.org/10.1142/q0089 | May 2017
Pages: 252
By (author): Maurice de Gosson (University of Vienna, Austria)

Anyone has this book

Can someone DM me pls

Lib gen doesnt have it

[alpine sable]

I need some help with part c of this question

[split slate]

Sorry if it seems dumb, but I still haven't been able to do this...

Even after trying the law of Cosines

[surreal meadow]

can you show your work?

[split slate]

In ∆ABC, a = 10, b = 11, c = 13. Find the 3 missing angles (2 d.p).

Here's what I tried to do:

[alpine sable]

Me ?

[surreal meadow]

no, @split slate

[alpine sable]

Ok

[split slate]

$13^2 = 10^2 + 11^2 - (2\times10\times11) \times cos(x)$

[ocean seal]

HappyAlt

[surreal meadow]

\cos{x}, for future refrence

but yes

did you do anything else?

[surreal meadow]

oh sorry

[split slate]

That's all I've tried so far

[surreal meadow]

that image is wrong

[split slate]

And if I put it in my calculator

Am I doing this wrong?

[surreal meadow]

this: $13^2 = 10^2 + 11^2 - (2\times10\times11) \times cos(x)$

[split slate]

Like...

[ocean seal]

maximo

[surreal meadow]

implies that x is opposite of the side length 13

[split slate]

mhmm

But it's the opposite of 11

I see that now

[fading shadow]

Need help with q15

This is my progress for (a) so far

[alpine sable]

yo

can someone please help me!

Online learning kinda sucks!

Well not kinda, it sucks

[indigo jetty]

Working is fine, so just simplify that expression you have to get it in the form that the question asks for

[fading shadow]

@indigo jetty stuck

[indigo jetty]

open up the brackets

then simplify

[split slate]

Thanks bud! I got the answers I was looking for and I (kind of) understand it now! I can ask my teacher tomorrow for anything I am unsure about.

[surreal meadow]

awesome 🙂

[fading shadow]

Aight thks

15b still having problems tho

[indigo jetty]

for 15b u have two choices: calculus, or completing the square

[fading shadow]

Worksheet is on related rate of change so I gotta do by calculus

[indigo jetty]

then go forit

[indigo jetty]

yup, then express x in terms of k

[split slate]

Sorry

[indigo jetty]

then sub that value of x back into the expression for A

[split slate]

Didn't realize channel was occupied

[fading shadow]

I got A in terms of K now

[indigo jetty]

that would be the answer

[fading shadow]

For part c I got dA/dt = dA/dx ×dx/dt

[indigo jetty]

ok

so your task is to find dx/dt

You know dA/dt, which is given in the question

so now you have to figure out the value of dA/dx

[fading shadow]

If my answer for k is 1 doesn't that mean dA/dx = 0

[indigo jetty]

you are not supposed to solve for k

so basically find the value of dA/dx at x = 1/2

that 1/(2k) only applies to the previous part, where dA/dx is a minimum, but we are not told that dA/dx is a minimum for this part

[fading shadow]

They want the answer in K right

[indigo jetty]

yes

[fading shadow]

I missed out the 2pi

[indigo jetty]

yup correct

well done

[fading shadow]

Thks a lot of the help 👍

[indigo jetty]

👍

[split slate]

This is the diagram I drew for it:

[tough hatch]

dont post your question on top of someone else's recently posted one

[surreal meadow]

looks good

[split slate]

And so are the sides?

So... would I do: tan(9°15') = 112/x

?

[surreal meadow]

that works

[split slate]

Oh well

Why does this make a difference though?

One is negative, the other is positive

[surreal meadow]

radians vs degrees

[split slate]

Ahhh

Ok

That makes a lot more sense now...

Thanks!

[surreal meadow]

np

[tough hatch]

nope, the triangle should be flipped vertically.

[split slate]

Sorry to cause trouble here, but could you please do a rough sketch of what you mean?

Like MS Paint if you're on windows or screen sketch, anything (including paper)

[split slate]

Now that I think about it...

That would've made it a bit easier to understand

Thanks for the illustration and your time!

[surreal meadow]

it says angle of depression though, no?

[split slate]

True

But what they just did is kinda the same thing

Angle of elevation would be different to the 9°15'

It's still in the corner that's going down, so in my opinion, still valid

But, you probably know more, so I won't argue too much

[tough hatch]

hmm, i doubt they would be the same answers

[surreal meadow]

they are not

take this

theta ($\theta$) does not equal 9 15'

[ocean seal]

maximo

[tough hatch]

nvm, my diagram is also wrong

[surreal meadow]

unless 9 15' is = 45 degrees, but i don't think it is

[tough hatch]

editing.

[split slate]

9°15' = 9.25°

Also, another question has risen

I figured out a to be 176.4m

But now, would b just be 176.4 - 24?

[surreal meadow]

that is the same diagram

[tough hatch]

same diagram but correctly labeled angle of depression

[split slate]

Not according to the answers however:

[surreal meadow]

how is this incorrectly labeled?

[tough hatch]

i did not say yours was incorrectly labeled

[surreal meadow]

this is his

[digital raft]

hey , anyone familiar with python ?

[surreal meadow]

ayman, read #❓how-to-get-help, also, not the server

[tawny totem]

anyone,pls need some help

[surreal meadow]

@tawny totem #❓how-to-get-help

[digital raft]

@surreal meadow already read them i just want to know if its possible to help with python on here

as its maths related

[surreal meadow]

you clearly didn't

[tough hatch]

dont ask to ask

[surreal meadow]

this channel is in use

[tough hatch]

lol

[surreal meadow]

don't ask to ask

[digital raft]

okay

[surreal meadow]

go reread them and ask again 🙂

[surreal meadow]

it seems like it

[surreal meadow]

its close enough to where it might be a rounding error/typo

[split slate]

Ah okay

I just didn't think it could a typo

But yeah

Thanks!

[tough hatch]

yeah, they are a bit off

[small holly]

i need to find the area of this. I did

A=1/2x5x6xsin65 (half of the shape's area)
A= 13.59461681m^2

then i got the angle of the 65 degree's opposite corner:

cos0=(4^2+2.5^2-13.59461681^2)/2(4)(2.5)
cos0=0.9899542372
   0=cos^-1(0.9899542372)
   0=8.128180311 degrees

after that i got the second half of the shape:
1/2x4x2.5xsin8.128180311

[sacred marlin]

@lofty stump

[arctic laurel]

Hey so guys, we got a small project to work on for school, i understand help with projects and such may not be allowed, but i need help in understand what the fk a question is asking of us to do not really needing help with calculations.

I need help with the bridge design 2, part of the project, i don't understand if for the right side it will also decrease by 55% of the previous and if shortest one is to be atleast 1 m long aswell, or are they leaving it up to us to decide what we want to do with it.

[tough hatch]

your lighting is cool lmao

[arctic laurel]

❤️ purple light

[unborn dome]

can someone help me out on this?

[dull oak]

Someone help pls

[dull oak]

since i will sleep now and wake up, this message is likely to be lost

please dm me any help if u are going to do so thank you!

[tepid jungle]

what does the d on top of the = sign mean?

[subtle mantle]

it probably means equal to by definition

[alpine sable]

its 1/cos im dumb nm

[alpine sable]

bye bitches

[covert berry]

Wow, everyone posts in one channel.

[fossil shoal]

Hi, I'm trying to understand a solution to a fluiddynamics problem. We basically have polar coordinates $(r,\theta)$ whereas we have rotational symmetry i.e. basically $\frac{\partial}{\partial \theta}=0$. We want to find some velocity $\vec{u}=(u_r(r), u_\theta(r))$.

The solution at one point does
[
0 = \frac{\partial}{\partial r} \bigg(\frac{1}{r} \frac{\partial }{\partial r}(r u_\theta) \bigg) \quad \Rightarrow \quad u_\theta = \frac{1}{2} C_1 r + \frac{C_2}{r} \tag{1} ]

I'm trying to see how I'd get to that systematically without "starring at it and just guessing it".

My approach is: $\frac{1}{r} \frac{\partial }{\partial r}(r u_\theta) = C$ whereas $C$ is some constant. We get

[
u_\theta + r\frac{\partial}{\partial r} u_\theta = rC \tag{2}
]

that's an inhomogeneous Euler-Differential equation right? So my approach would be to first solve the homogeneous case and the the particular case and then "add them up" but that seems way too involved for this lecture (they basically don't expect people to solve anything beyond sep. of variables).

So my very simple question is: Is there some easier simpler way to solve it, like some trick I don't see right now? Thanks 🙂

[ocean seal]

balance

[wispy olive]

What does [] mean in Geometry?
Does it mean perimeter or area?

Like for example here.

What do these mean.

Anyone?

[oak chasm]

@wispy olive It's area: https://artofproblemsolving.com/wiki/index.php/Area#Notation.

[wispy olive]

Okay.

Thanks!

[oak chasm]

No problem.

[solid fox]

what are the odds of getting tails on any of 10 coins

[fast patio]

its 1 - the chance of getting all of the 10 coins heads

i thing its called complementary odd or something?

you either get at least one tails or no tail at all

so:
P(at least one tail)+P(no tail at all)=1
P(at least one tail)=1-P(no tail at all)

[proper quail]

a^x=b^y to a=b^(y/x)

how does that work

im trying to understand a proof

wait i can use latex

How do you get from
$a^x=b^y$
to
$a=b^{y/x}$

[ocean seal]

Epicmania

[fast patio]

i dont think you do...

im trying to think a situation where this is false

[proper quail]

its in a proof in an aops textbook

so im just trying to understand it

[fast patio]

maybe you should use log?

[minor heath]

$(a^x)^{\frac{1}{x}}=(b^y)^{\frac{1}{x}}$

[proper quail]

its proving a log property

[ocean seal]

G3oG0dly

[minor heath]

can you continue from there

[proper quail]

yeah

i get it

thanks

you multiply both exponenets by 1/x and get $a=b^{y/x}$

[ocean seal]

Epicmania

[manic glade]

this is correct right?

[minor heath]

raise*

then multiply using law of exponents

[tough hatch]

yes

[wind zinc]

Hello

[candid dagger]

Two equations have at least one solution in common. How can I translate that information into math stuff?

My english is pretty bad lol

The equations contain a parameter , so I tried to make the solutions equal, but i dont know how to deal with the roots

I realized I could make delta=0 and get one of the answers, but I dont know how to get the second one

[cinder sonnet]

i see this one not on use so imma proceed
this is conjugate question, rationalize it

I just learnt this today but still bad at it. Im stuck on after i multiply the numerator [ 1-√2 ] * [ 1-√2] (result of denominator conjugation [1+√2] )which will get
1 -√2 - √2 + 2 and i have no clue on how to solve -√2-√2

sorry for the inconvenience and i appreciate your help.
i have whole week so deadline is not a problem and maybe i could learn myself by that time. but your help might fast forward it.

[ocean seal]

SubGui

[astral dagger]

I meant 6/-1, there's a typo

[candid dagger]

Wow good tex skills

[astral dagger]

still improving, but thanks

[cinder sonnet]

Thanks a lot, i'll learn from this

[astral dagger]

also, you could have proceed by multiplying each fraction by the denominator conjugate

as you have learned

but I still prefer to do like I did

[cinder sonnet]

alright i'll find my preference, thanks

[candid dagger]

Has anyone got time for this? Or the information I give in that message and in the ones below is too little

[feral crypt]

If you make the two equations equal to each other and then solve for x

[cinder sonnet]

sorry i did not realize it was a question, pardon the intrusion man

[candid dagger]

Like that I would find x=a+... , why would I need that?

[feral crypt]

Can you show the problem?

[candid dagger]

Yeah it's not in english, I'll try my best to translate it

[feral crypt]

But do you have the equations?

[candid dagger]

"For which values of "a" do the two equations x²+ax+2=0 and x²-x-2a=0 have at least one common solution?"

[feral crypt]

Ok let me try

[candid dagger]

Thanks

[misty mortar]

Is there an error to this problem?

[feral crypt]

Ok I got it

I think that’s right

[candid dagger]

That's one of the solutions

Pretty interesting how you got it

[feral crypt]

Hope that’s helps 😄

[candid dagger]

Oh I think I got it

You divided by (a+1), implying that a must not be -1

[feral crypt]

Actually a can be -1

[candid dagger]

And -1 is actually the other solution

Hmmm

Enlighten me

[feral crypt]

Just by plugging -1 into the equations we will see that they are equal

[candid dagger]

Yeah, to show that tho? I did it by calculating the 4 solutions of the two equations separately, then assuming delta=0 and solving

Does it make sense?

And delta>0 is the case you showed

Via the system

[feral crypt]

I see

Well this is how I would’ve gotten to -1

[candid dagger]

Yea makes absolute sense

[feral crypt]

How were you able to calculate 4 solutions for the equation?

[candid dagger]

I think I used the wrong word

[feral crypt]

Did you just plug into the quadratic formula?

[candid dagger]

Yrp

Yep

I had got -1 as my first result but I didnt know what to do next

So thanks a lot

[feral crypt]

Well the question is just asking for 1 solution no? So I guess you had it 🙂

[candid dagger]

I would have got half a point I guess lol, its asking "which values"

[feral crypt]

Ahh I see. Well glad I could help 😁

[candid dagger]

Thanks and bye

I have another completely unrelated question.
i⁴=1
Take the fourth root of both sides
i=1

I dont know pretty much anything about how imaginary and complex numbers work, but what's wrong here?

Or maybe I dont know how roots work lol

[feral crypt]

So i is equivalent to sqrt(-1)

If I put the sqrt(-1) to the power 4 than it simplifies to 1

[candid dagger]

Yea but then right here I get i=1

And it is wrong

Why

[feral crypt]

Well I always equals sqrt(-1)

[glass lichen]

you're solving $z^4-1=0$ with a root already plugged in

[ocean seal]

Mosh

[glass lichen]

$z=\pm 1, \pm i$ are all the solutions to that

[ocean seal]

Mosh

[candid dagger]

Oh my bad I'm treating i as a normal variable

I think that's the mistake

[glass lichen]

yes

[candid dagger]

Ye thanks guys

[glass lichen]

$z^4-1=0 \ (z^2-1)(z^2+1)=0 \ (z-1)(z+1)(z-i)(z+i)=0$

[ocean seal]

Mosh

[random pelican]

quick question, what is (2a+3b)² expanded? is it (2a+3b) or (2a-3b)? and with (2a-3b)²?

[alpine sable]

$4a^2+6ab+6ab+9b^2$

[ocean seal]

Lambdalo

[alpine sable]

for (2a+3b)²

[random pelican]

oh, okok, ty
but when i want to use the foil method, to expand it do i invert the signs of the 2nd parentheses?

[alpine sable]

foil?

first outside inside last?

[random pelican]

to use the foil method you need to expand it like:
(a+b)²
(a+b)(a+b)
what sign is the wrong here?

what should be minus

[alpine sable]

nothing

[random pelican]

oh, okok

ty

[alpine sable]

(a+b)² = a²+ab+ab+b²

[random pelican]

okok, ty

like this right?

[alpine sable]

for mutliplication (-n) times (-n)= n but negative times negative = positive you can't use that principle for n*n=-n

$(-n) x (-n)=n,n x n ≠ -n $

$(-n) x (-n)=n,n x n ≠ -n $

alright it doesn't want to compile

[alpine sable]

yes that is correct

[random pelican]

okok, ty

[alpine sable]

no problem

[willow wadi]

hi guys

[alpine sable]

you might want to go to https://discord.gg/physics

[willow wadi]

oh its calculus and vectors not physics

[alpine sable]

oh then my bad nevermind

[halcyon geode]

where are you stuck?

[willow wadi]

i try solving it and

(4√3 I + 29j)

this what i got

[halcyon geode]

sounds about right

[willow wadi]

thanks

Hey 1 more ques

i need help with this

[feral crypt]

Calculate vertical and horizontal forces then use pythag

[livid knot]

can someone help me with calculus (limits and continuity)

[willow wadi]

#❓how-to-get-help

[willow wadi]

Ok

[feral crypt]

This room is busy rn

[livid knot]

Ok

[willow wadi]

do u get 206.2

[feral crypt]

I'm checking now

Sorry I’m a little slow lol

[alpine sable]

do u need answers or like.. proper solved solutions ?

[livid knot]

@alpine sable i just need help understanding the 3rd question

[alpine sable]

okaY

[glass lichen]

$\lim_{x\to 0}\frac{3^{\sin(x)}-3^{\sin(0)}}{x-0}$

[ocean seal]

Mosh

[feral crypt]

Yes I got 206

[livid knot]

woah whats that

[glass lichen]

rewriting the 3rd limit

[livid knot]

okay thanks

[willow wadi]

and if u round it u get 206.2

ty

[livid knot]

@glass lichen would you use the L'Hopitals rule for this quesiton 3?

[glass lichen]

no

[livid knot]

oh I used L Hop for question 2

[glass lichen]

Ok well you can, but you dont have to L'H either 2 or 3

[livid knot]

can you tell me how to solve it without using L'H

[glass lichen]

solve 2 or 3?

[livid knot]

just 2 for now and then ill attempt 3

[glass lichen]

Ok $\lim_{x\to 0}\frac{\sin(x^2)}{x}=\lim_{x\to 0}\frac{\sin(x^2)-\sin(0^2)}{x-0} \ =\dv{x}\sin(x^2)|{x=0} \ =[2x\cos(x^2)]{x=0} \ =2(0)\cos(0)=0$

[feral crypt]

Yes np 😉

[livid knot]

so that would be the final answer?

[glass lichen]

no clearly not

[livid knot]

would it still be sin(x^2)

just making sure i got it right using L'H

[ionic jewel]

this is lhopital with extra steps

[ocean seal]

Mosh

[glass lichen]

it technically isnt, it's recognizing a derivative

[gaunt magnet]

https://tenor.com/view/cat-leaving-leave-oops-bye-gif-17519616

karen alert

[ionic jewel]

fair enough, different method but they both end with taking the derivative of sin(x^2)

[glass lichen]

then yes, in that regard

[gaunt magnet]

can i get this chanel

channel

[glass lichen]

No

[gaunt magnet]

😋

[glass lichen]

it's in use

[gaunt magnet]

by who

[glass lichen]

unless Yang is done w/ it

there's also 9 other channels

[gaunt magnet]

10

[glass lichen]

10 total, 9 other

[livid knot]

so how is question 3 different from 2

[glass lichen]

you can do 3 with the same process I demonstrated, recognizing the limit as a derivative

[livid knot]

its the same concept right?

[glass lichen]

yes

[livid knot]

okay thanks

[gaunt magnet]

ok

hi

Resolve a force of 200N in the direction S 22 degree E into its regular componets

[unkempt prism]

Hi

[tranquil parcel]

Hi

[gaunt magnet]

<@&286206848099549185>

[strange oasis]

@gaunt magnet Use sin and cos

[gaunt magnet]

i got

[strange oasis]

what did you get?

[gaunt magnet]

y componet should be -200sin22 and the x is 200cos22

[strange oasis]

Is the angle 22 degrees east of south or 22 south of east?

double check that

[gaunt magnet]

south of east

[strange oasis]

then you're right

[gaunt magnet]

#❓how-to-get-help

[gaunt magnet]

so y componet should be -200sin22 and the x is 200cos22

[normal idol]

Oh, sorry 😅

[strange oasis]

@gaunt magnet yes

[willow wadi]

Hey

guys

so

question

i got

[glass lichen]

which one?

[willow wadi]

a)1/3v
b)2/3v + u
c)2/3v - u
d)(1/6)v+u
e) v/2-u
f)-u

[glass lichen]

yes.

[willow wadi]

so that right?

[glass lichen]

Given I said yes...

[willow wadi]

check how to get help

[willow wadi]

ok ty

[gaunt magnet]

next time say its correct

better then yes

[glass lichen]

didnt ask the peanut gallery

[ebon quail]

wdym

[gaunt magnet]

lol

[willow wadi]

channel is in use

[glass lichen]

Not sure why you also feel the need to constantly harass me whenever you get the chance

[gaunt magnet]

its the opposite u harassed me for asking if my answers were right

[willow wadi]

still using this

use another channel

[livid knot]

alright

[willow wadi]

A mass of 60kg is suspended from the ceiling by ropes.The angles between the ceiling and the ropes are 31 degree and 59 degree.Determine the tensions in the ropes include a diagram.

The acceleration due to gravity is 9.8m/s^2
Include a diagram

[wary stream]

Did you draw and FBD yet?

[willow wadi]

no not sure how to do this question

[wary stream]

First draw an FBD

[heavy spear]

i think you are going to use a calculator for this one since you are prob going have to do sin , cos , tna

tan

so ye 🙂

my input i dont know anything else though

[wary stream]

Yes, that's the diagram you're going to but not the FBD to use

[wary stream]

Now make a FBD then equilibrium equations, sum of forces in the x and y direction

[random pelican]

quick question, what is 2 * x^2

[wary stream]

Exactly that

[random pelican]

ok, ty

[willow wadi]

so now
m= 0.60kg

what do i do now

[wary stream]

That m is wrong

[willow wadi]

what should i do

[wary stream]

Use the proper m

Then equilibrium equations

[willow wadi]

how shall i start

[wary stream]

Do you know what an equilibrium equation is?

[wary stream]

Not chemistry, physics equilibrium

[willow wadi]

then im not sure

[wary stream]

Sum of forces

In the x and y direction

[willow wadi]

ok

ill try

[light quartz]

logx+logx is 2logx right

right?

and how is derivative of 1/x -1/x^2

[glass lichen]

those are 2 seperate questions

[slender forge]

Yes

[light quartz]

yeah

[slender forge]

1/x= x^(-1)

Use power rule

[minor dagger]

can someone show me what c/cos(45) looks like on the unit circle

[craggy steeple]

https://gyazo.com/ae980c0cc9b7b0703edeef8d069b435e

#11 pls help

[placid zinc]

cos(45) is the length of the base of this triangle

[craggy steeple]

can you help me with #11 too?

[placid zinc]

Do you know what the first term is?

[craggy steeple]

uhh

yes

isnt it 38?

wait no

its 28

the first term is 28

[placid zinc]

Right! Then the second term:

[craggy steeple]

oh yeah i knwo that part

but i need help with the explicit

formula part

[placid zinc]

28 + 10(n - 1)

[placid zinc]

Memorize this haha

[craggy steeple]

uhh

[placid zinc]

Or, at least understand why it works by plugging in a few points

[craggy steeple]

so did u get that by

doing

a1 + d(n-1)

is that how u got

it

also, i dont think thats explicit

[craggy steeple]

so can u put the problem into that

[placid zinc]

So I just have a lot of experience with this, and can sus out the form haha. You will be able to too

[craggy steeple]

like plug it in

so i can see

the reference

[placid zinc]

That is explicit

[craggy steeple]

28_10(n-1)

[wary stream]

All you do is plug in a1 and d into the formula

[craggy steeple]

ok

so a1 is

28

and so it would be

28+10(n-1)?

[wary stream]

Yes

[craggy steeple]

ok

thank you!

[willow wadi]

Hi

this question i did it

but

A mass of 60kg is suspended from the ceiling by ropes.The angles between the ceiling and the ropes are 31 degree and 59 degree.Determine the tensions in the ropes include a diagram.

The acceleration due to gravity is 9.8m/s^2
Include a diagram

i made a diagram

then

so i got

T_1 cos31+ t_2 cos59=0

Pls someone tell me if i made any mistakes

[hidden seal]

It looks good friend

Use the second equation to get a nice expression for T_1 in terms of T_2 and plug that in the first equation

[willow wadi]

T_1 cos31+ t_2 cos59=0
this?

[hidden seal]

Yes. This equation tells you that T1 is exactly $\frac{\cos(59)}{\cos(31)}\cdot T_2$

[ocean seal]

navessss

[gaunt magnet]

,w cos(59)/cos(31)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Usman#0988

[willow wadi]

and then?

[jolly lark]

What percentage is 2,800 out of 10,300? *

[willow wadi]

go to another channel in use

[willow wadi]

<@&286206848099549185>

[hidden seal]

Since you have T1 in terms of T2, you can plug in whatever expression you got for T1 into the first equation

Then you solve for T2

Then you plug in the value you got for T2 into the expression you got for T1 and that should be it friend

[willow wadi]

i got T1 = 645.1
T2 = 1073.6

[hidden seal]

Plug both values into your original equations, and the equalities should hold if you did it right

[willow wadi]

how sorry if im being dumb

[hidden seal]

its ight I've been in your place many many times before believe me lmao

[hidden seal]

the equations here

Plug in the values you got in those, and you should get something like 0=0

that's how you check these things

[willow wadi]

so T_1 cos31+ t_2 cos59=645.1
T_1 cos31+ t_2 cos59=1073.6

[hidden seal]

No, no

So,

When you see an expression of form x=k, you're stating that x and k are the exact same object. When you know, for example, that x=123, you can use the symbols "x" and "123" interchangeably. They are two different names for the same thing.

So $T_1\cdot\cos(31) = 645.1\cdot \cos(31)$

[willow wadi]

ohh

[ocean seal]

navessss

[willow wadi]

,w T_1\cdot\cos(31) = 645.1\cdot \cos(31)

[ocean seal]

Results provided by WolframAlpha

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

Requested by yungdagger#3426

[static glen]

Hey

Im rlly confused on this

So what i think its that its between the height

or yearly income

im not sure tho

[sleek elbow]

I would tend to say yearly income

cause I feel like height is less spread out

[static glen]

hm

well

[sleek elbow]

not sure tho cause I didnt do that in school yet

[undone pond]

what is the result of 5 - 4 x 12

[sleek elbow]

do you know about order of operations?

if not this should help

[undone pond]

ok ty

[noble sinew]

its height

[static glen]

Are you sure?

[noble sinew]

yes

[sleek elbow]

how so? im curious

[static glen]

Same

[noble sinew]

height is a common example of something being normal distributed

[sleek elbow]

and income isnt?

[noble sinew]

no?

[sleek elbow]

okay

[glass lichen]

Height has a clear mean value based on demographic and history of the people

[static glen]

oh yeah

because some people have a much larger income then others?

while someone being much taller than an average is rare?

[static glen]

^?

that about right?

[glass lichen]

yes, extreme heights are rare genetic mutations

[static glen]

ok tysm

[sleek elbow]

stretches far to the lower incomes, interesting

[cinder lily]

what country is that?

[sleek elbow]

its the different regions colored in, dunno which ones were which tho as I already closed it

[cinder lily]

oh ok

[willow wadi]

hello

this ques

having alot of troubles

😭

this question is pain pls help

[glass lichen]

can you write OB in 2 different ways?

[gaunt magnet]

forget about 2 ways ask him to do it in 4 ways

[willow wadi]

mark a point centrosymmetric to O relative to B
we can call it O'
then O'A||OC and AC|O'C
AOCO' is a parallelogram
then express OO' in terms of OA and OC and find OB knowing that the diagonals of a parallelogram intersect in the middle
hang on you will need a better argument to prove the parallelogram
prove that triangles OBC and ABO' are congruent, and prove ABO and BCO' are congruent (both pairs side-angle-side)
then |AO|=|CO'| and |OC|=|AO'| (segment lengths, not vectors)
AOCO' is a parallelogram

[glass lichen]

I mean yeah, make a geometric argument, however you can do it in like, 2/3 lines of quick algebra

[willow wadi]

in the question we just need to prove allgebrically how to do it right, we didnt need to like solve anything right

[glass lichen]

yeah, prove algebraically

[willow wadi]

so what i said is correct?

[glass lichen]

you took a geometric approach

not an algebraic one

[willow wadi]

Ohh

[glass lichen]

refer back to this.