help-23

[queen ingot]

It's still there

[fervent hatch]

uh

the enclosed region isnt?

nothings enclosed when you remove a circle

[queen ingot]

I'll make a picture

[fervent hatch]

Okay

[fervent hatch]

Sure okay

[queen ingot]

This is just the area inside the blue circle

[fervent hatch]

I see

Lemme do this in my head rq

Is it uh

Wait hold on

I got pi/4 - 1/4

Don’t think that’s right

[queen ingot]

Doesn't seem right

[fervent hatch]

Uh

$\int_0^{\pi/4}{2sin^2(\theta)}d\theta$

Is this not right?

@queen ingot

1/2 * 2

[queen ingot]

The equation has a factor of 2

[fervent hatch]

Wdym

Oh

Ohh

Okay so

[flat frigate]

Nathan

[fervent hatch]

And then that’s

[queen ingot]

Don't you have to square the 2 too?

[fervent hatch]

I did

Divided by two

[queen ingot]

And times 2 for the reflection?

[fervent hatch]

Ohh

Okay yeah

Uh

So is it pi-1?

[queen ingot]

No

Maybe you were already on the right track before I corrected you

Idk but the answer should be pi/2 - 1 right?

[fervent hatch]

pi/2 -1

Yeah I got that

Had to redo it

Okay I got one more question if you got the time

11

I tried it a couple times and kept doing it wrong let me write out my work

[queen ingot]

this will be another situation where you don't have to subtract

[fervent hatch]

Are you sure?

They subtracted

My book had an example, it was just the outside area instead of the inner

,rotate

[fervent hatch]

@queen ingot

[queen ingot]

yes that changes things

[fervent hatch]

How so

[queen ingot]

see how the ray crosses first the yellow cardiod and then the blue circle?

[fervent hatch]

Yes

[queen ingot]

that's why you need to subtract the blue from the yellow

but if you shade the inside area, the ray just crosses the yellow cardiod

it still crosses the blue circle but not in the area we care about

[fervent hatch]

So what do we do differently now?

Do I need to break it up?

[queen ingot]

yeah

[fervent hatch]

unfortunate

alright give me a second

[queen ingot]

another way to look at it -

see we can calculate the black area without even using the red circle

[fervent hatch]

Okay I got the right answer

[queen ingot]

nice 👍

[fervent hatch]

5pi -8

Thank you 🙏

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[fervent hatch]

Can someone help me with 25

[fervent hatch]

I’m stuck

[safe radish]

@fervent hatch Has your question been resolved?

[stray hinge]

You wrote dr/dtheta wrong in the integral

[fervent hatch]

How so?

[stray hinge]

$\sin^2\theta$

[flat frigate]

Smiley ッ

[chrome bear]

hi any one talks Arabic her?

[versed wave]

!occupied

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

[fervent hatch]

Hmmm

Lemme re do it rq

Now what? @stray hinge

[lean otter]

You got the numerator wrong

[fervent hatch]

How?

Oh

Yeah

One second

Now what

@lean otter

[lean otter]

,w integrate secx tan^2 x

[flat frigate]

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[lean otter]

I can't find any other way

[lean otter]

@fervent hatch

Cos(x) can be written as $2cos^2 \frac{x}{2}-1$

[fervent hatch]

mm

Does that help though

[vagrant ice]

Yes

The integral of secant cubed

Is a very famous integral

[safe radish]

@fervent hatch Has your question been resolved?

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[versed wave]

how can i show that the list is a basis without proving it spans U?

[median vigil]

you would have to know ahead of time that U is 2-dimensional

[versed wave]

which for that..i need to find a basis of U

[desert pasture]

find the general form of a polynomial in P_4, differentiate it twice

[median vigil]

but i'm not convinced that it is actually spanning

[versed wave]

P_4(R) is 5-dimensional

p(6) = 0 makes it four, then every differentiation knocks it down one dimension

so that's 2

[median vigil]

but we aren't requiring p(6) = 0 or p'(6) = 0

[desert pasture]

p(6) doesnt have to be 0

p"(6)=0

like consider (z-6)^3+3

[versed wave]

yeah, but every polynomial in the basis must be third degree or above

[desert pasture]

why

[versed wave]

wait

one sec, this is wrong

my bad. this is actually 4-dimensional

so a basis choice could be z - 6, (z - 6)^2, (z - 6)^3, (z - 6)^4

yeah this is good. thanks

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[nova whale]

How do I find the General solution for this nonhom. equation

[nova whale]

i go on and find r which are the solutions to r^2 + 2r + 1 =0

but I have trouble with getting the yp right and I think it's yp = Ax^2e^-x but i am not really sure

if someone can help me

[violet ocean]

There's a few methods to solve this

[nova whale]

Well the method I know is doing the yp and then getting its derivatives, then finding coefficents and then for the solution its like y = yp + yc

[violet ocean]

That would be a valid method

You would use yp=(Ax+B)e^{-x}

Wait

[nova whale]

But wouldn't this be too close to the homogenous part and result in 0

[violet ocean]

You're right

The homogeneous part is a double root at r=-1, right?

[nova whale]

yes

[empty gyro]

the two most popular methods are guessing, and variation of parameters

both are painful for different reasons

[nova whale]

ikr

[violet ocean]

I think we can just use the next highest power, no?

I'm double checking but if irc we move to use (Ax^2+Bx+C)e^{-x}

[empty gyro]

sometimes it works, sometimes it doesn't.

[nova whale]

is that the usual methond

[empty gyro]

It works for degenerate homogenous solutions, but it can fail for particular solutions in specific circumstances

[nova whale]

becuase most of the examples I have are like yp = Ae^x

[empty gyro]

It would be the first thing I try though, with nothing else to go on

[nova whale]

and for this example isn't yp = Ax^2e^-x

[violet ocean]

Yes

[nova whale]

But as I said I am not really sure why

[nova whale]

I will also go on with this example

[violet ocean]

The lower powers would be scooped up in the general constants

[empty gyro]

Yeah I haven't looked deep at the problem yet

[violet ocean]

We have repeated roots at -1

[nova whale]

Do I have to go into the derivative of this

oh god

[violet ocean]

Actually

@empty gyro brings up a good point

We can just use Ax^2 e^{-x}

[nova whale]

but why

[violet ocean]

Since e^-x and xe^-x are part of the general solution, they have general constants C1 and C2

[nova whale]

is it because it normally it would be Axe^-x but that already exists in the nonhom. part

so we just guess x^2 should be in place of x

[violet ocean]

Yes

Exactly

[nova whale]

but why are we making it square

why is that the correct choice

[violet ocean]

We just use the next power

That hasn't been used before

[nova whale]

I understand somewhat

[violet ocean]

It's just a rule of thumb

It works out more times than not

Unless the problem is degenerate but that's unlikely

[nova whale]

on my exams they probably will be simple ones

like the one mentioned in the image

I will write it down to see if it goes well

[safe radish]

@nova whale Has your question been resolved?

[nova whale]

so using Ax^2 e^{-x}

goes to like A = 2x/(2-x)^2

so instead I should go for (Ax^2+Bx+C)e^{-x} right?

[violet ocean]

Can I see the work that gets you that?

A should equal a constant by the end of it

[nova whale]

i write it on textbook rly ugly

but you get that
yp = Ax^2e^{-x}
y'p = 2Axe^{-x} - Ax^2e^{-x}
y''p = -4Axe^{-x} + 2Ae^{-x} + Ax^2e^{-x}

correct me if im wrong

but after you replace in the equation
y'' + 2y' + y = 2xe^{-x}

you get that A is a function of x

[violet ocean]

I think your derivatives are correct

When you plug in yp, you should end up with something like Axe^{-x}=163826xe^{-x}

And then you know A=163826

Obvs A isn't that really but yk what I'm getting at

[nova whale]

let me redo it

[violet ocean]

You should have all your x^2e^{-x} terms cancel

[nova whale]

now I got A = x/(4x+1)

😭

@violet ocean

[violet ocean]

Hi

Sorry

I was working it out on my own

We might have to use the full quadratic

Bc just the x^2 e^{-x} doesn't work like i hoped

[nova whale]

oh thank you

i will try it

[violet ocean]

Some news

The particular solution has x^3 e^{-x} 🙂

I wish i could tell you why right away but I have to think about it

[nova whale]

x^3 ?

oh my god

im cooked for my exams

[violet ocean]

This is just bad for the case of repeated roots with one of the roots being part of the non-homogenous solution

That's at most one question

[nova whale]

theres this other example

y'' +4y = 3cos2x

i think this should be far easier

[violet ocean]

That would probably be find with xcos2x for yp

[violet ocean]

I think this would be easier (at least correct) with the variation of parameters instead

[nova whale]

e^−x[−Ax^2−Bx+(2A−2B+C)]+2e^−x[−Ax^2+(2A−B)x+(B−C)]+e^−x[Ax^2+Bx+C]=2xe^−x.

something like this

[violet ocean]

Yes

But i did it already

I think it fails for the same reason as just x^2 did

That's why x^3 pops up

Bc you would need to do x^3e^{-x}

[lean otter]

hi

[nova whale]

but if you get
e^−x[−2Ax2+(4A−2B)x+(2A−C)] = 2xe^-x

[lean otter]

Im new here

[nova whale]

can you get the coefficients of x^2 and x

hi @lean otter

[lean otter]

hi

[violet ocean]

Assuming your other work was right, yes

You would line up the coefficients like normal

But idk how you would get a cube term like that

Assuming the online solution was correct

,w y''+2y'+y=2xe^(-x)

[nova whale]

No way just got it to be yp = xe^-x

[flat frigate]

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[violet ocean]

I just wolfram'ed the solution

We're missing something if the solution has a cubic

[nova whale]

I don't know why there is a yp = xe^-x

probably did some mistake but all looks legit to me

[violet ocean]

I did the problem with the variation of parameters

And i got the wolfram solution

[nova whale]

so you did it with x^3e^{-x}

or the whole formula for 3rd power

[violet ocean]

I used this

Here y1 and y2 are the homogenous solutions e^-x and xe^-x

[nova whale]

😵‍💫

[violet ocean]

Your class went over variation of parameters right?

[nova whale]

i've got no idea what this formula is honestly

[violet ocean]

Does Wronskian ring a bell?

[nova whale]

i think we didn't go over this

the differential equations we went over are with the A,B,C method

coefficients

[violet ocean]

If we were gonna do it with that method

And if the solution had a cubic like this one

We would usually have to use (Ax^3+Bx^2+Cx+D)e^{-x}

But since e^{-x} and xe^{-x} are part of our homogeneous solution, we can just use (Ax^3+Bx^2)e^{-x}

This question is particularly bad in that we didn't know the answer needs a cubic

[violet ocean]

I tried it with this and it worked

[nova whale]

okay

thank you @violet ocean

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[violet ocean]

Np

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[woven stone]

Given that three congruent squares ABEG; GEFH; HFCD are of side a. Prove that angle AFE + angle ACE = 45°

[shadow verge]

Hi

[noble kiln]

Tip draw out the grid

And find equal angles

[shadow verge]

AFE = 90-BAF
ACE = 90- BAC
ACE + ACE = 180 - (BAC+BAF)

BAC and BAF are easily found by trig identities, or you could have used trig from the very beginning

[ebon mesa]

https://www.youtube.com/watch?v=guPXj_Ejya4

easy with trig

fun with geometry

[shadow verge]

A + B = tan^-11/2 + tan^-11/3
= tan^-1(1) = pi/4

[young nexus]

geometric:

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[tame raft]

can anyone reassure me as to why $\mathbb{E} \left[ \prod_{r=1}^{Z_n} Y_{n+1, r} | \mathcal{F}n \right] = \prod{r=1}^{Z_n} \mathbb{E} \left[ Y_{n+1, r} | \mathcal{F}_n \right]$?\

(each of the $Y_{n+1, r}$ are independent from each other and $Z_n$, and $Z_n$ is $\mathcal{F}_n$ measurable)

[flat frigate]

Kaisheng21

[tame raft]

ping me please

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[tame raft]

.close

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[rancid sand]

Seeking help for some resources:
Anyone got '2025 new year' related math question?

[covert yoke]

As in problems that just contain 2025?

We'll 2025 is 45^2 so that's pretty special, it's also the sum of the first 9 cubes (which is related)

But generally, one can simply find an equation that works for a general n, and then substitute in 2025, which is the most common method of generating "problems containing the current year."

[rancid sand]

ye

Ye... probably

But I want some interesting question

more than just substituting numbers into a function or equation

[quick crater]

find $\sqrt{2025\cdot 2026\cdot 2027\cdot 2028+1}$ no calculator

[flat frigate]

skissue.in.a.teacup

[quick crater]

try this

[rancid sand]

oh lol

ah got that

interesting question tho

thx

[quick crater]

actually this is bad

oh

[rancid sand]

it's definitely interesting tho

At least I think

[rancid sand]

Do you got something maybe realated to MI or integration stuff?

[quick crater]

mi?

[rancid sand]

ye?

[quick crater]

whats mi

[rancid sand]

mathematical induction

[quick crater]

for integration no

[rancid sand]

oh

[quick crater]

honestly jyst find any question and change a number to 2025

[rancid sand]

bruh

[quick crater]

ok here

a function $f(x)$ defined on the positive integers such that $f(1)=2025$ and $f(1)+f(2)+\dots+f(n)=n^2f(n)$, find $f(2025)$

[flat frigate]

skissue.in.a.teacup

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[placid wyvern]

I have a question about chi squared distributions, I have just started to learn it but I dont see the significance/intuition behind why we divide by the expected value

[placid wyvern]

I understand the intuition behind why we find the difference in the denominator and why we square it

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@placid wyvern Has your question been resolved?

[placid wyvern]

<@&286206848099549185>

[fathom adder]

<@&268886789983436800>

[glad obsidian]

First one, we square it because we want a positive valor, basically

[placid wyvern]

yes

[glad obsidian]

second, this expression is similar to others in maths, for example, calculate the error

or porcent of error

It's similar, isn't it?

[placid wyvern]

so it shows proportion

to the expected value

since its a ratio

but why is this useful in terms of the probability density function

[glad obsidian]

something likes that, in maths there is mostly the expect valor and the real one

or the real valor and the aproximmate

[glad obsidian]

so yes, that's the answer of your question! or wait, it's a question?

[placid wyvern]

wait but I dont see why this is usefull in making the PDF

[placid wyvern]

did you mean expected value

[placid wyvern]

yeah sorry its a question

[glad obsidian]

yep, sorry English is not my main language

[glad obsidian]

mmmm I understand your point, but let me think how explain you in a easy way

[placid wyvern]

thank you

[glad obsidian]

I learned Statistics for Biotechnology, but i love math, so i'm trying to remember the theory

[placid wyvern]

thats fine im trying to learn it for economics

[glad obsidian]

oh, that's a different way to use it. I learn Statistics for experiments

[placid wyvern]

principle should be the same

[glad obsidian]

chi-square: Compares an observed distribution with an expected one.
Independence analysis: Evaluates whether two categorical variables are independent.
Confidence intervals for variance: In samples from normal distributions, chi-square is used to construct confidence intervals for variance.

[glad obsidian]

yep

well the first sentence could be the answer of your questions?

[placid wyvern]

I mean I understand the purpose behind chisquared, but I dont really see why in the formula what purpose dividing by expected value serves for when we create the PDF function

[glad obsidian]

in other words, you want to understand the concept of chisquared in graphics?

[placid wyvern]

yeah like how it relates to the actuall graph

[glad obsidian]

ahhhh okokok, let me search

mmmm i don't know how to explain you, that formula makes the graphic

[glad obsidian]

or with this, take a look how the graphics depends of the % of error

you can't see directly the difference between the two values because these two values are operated on (subtracted from each other), and as a result, you get a single value, which is the one used for the graph.

Do I make my point?

[placid wyvern]

im really trying to see how we go from the formula

to this graph, and why dividing by E is needed

[glad obsidian]

okeey

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[acoustic goblet]

Is this stable around (0,0)? And how do i prove it?

[violet ocean]

By showing x_1'=0 and x_2'=0 at (0,0)

To verify it's a equilibirum point

Then find the Jacobian of the system

And verify the eigenvalues of the Jacobian matrix both have negative real part

[fathom adder]

Bro anticipate the next questions

[violet ocean]

I gave an outline just in case he knows/remembers some of the process. Might jog his memory

[fathom adder]

Honorable process

[safe radish]

@acoustic goblet Has your question been resolved?

[acoustic goblet]

No they dont tho

They both have 0's

[violet ocean]

What did you get for your Jacobian?

[acoustic goblet]

{0,-1}{1,0}

[violet ocean]

Yeah. I got purely imaginary eigenvalues

So we can't say the eq point is stable

[safe radish]

@acoustic goblet Has your question been resolved?

[acoustic goblet]

But it is.

[safe radish]

@acoustic goblet Has your question been resolved?

[queen ingot]

why do you think it's stable?

[safe radish]

@acoustic goblet Has your question been resolved?

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[ocean tapir]

,rccw

[ocean tapir]

Need help w this qu pls

Part b

[safe radish]

@ocean tapir Has your question been resolved?

[lean otter]

for sum of roots taken twice at a time

you can use the property

a^2+b^2+c^2+2(ab+bc+ca) = (a+b+c)^2

just like you used it for part (i)

except a would be ${\alpha}{\beta}$,b would be ${\gamma}{\beta}$ and c as ${\alpha}{\gamma}$

[lean otter]

after substituting and simplifying

see what you get

@ocean tapir

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[nimble lynx]

I am trying to create an isogrid, i know it is made up of equilateral triangles which are strung into a repeated pattern in a 2d space. for reference i have attached a couple photos. however once its 3 dimensional the relationships change across the isogrid. i am trying to make some designs in cad software but i am missing some math education that i would like to learn and fill in. for now ill keep it at that. There is a lot more to this, and i want to use this as a learning experience. I am happy to go study what i need to solve this, i just don't know where to start.

[winter mauve]

hi

[nimble lynx]

Hello!

[frozen shoal]

If I understand correctly, you have a 3D volume and want to create a surface grid of the 3D volume?

[nimble lynx]

yes indeed, but i also want to use this on a flat surface of a 2d object but reprojected with different ratios, photos attached, i had something getting close but it needs to be parametric

i am also missing the rib width and the hole at intersection points

[frozen shoal]

Okay, I don't know if there's an algorithm for exactly what you want, because it seems very niche. But for obtaining a triangulation of the surface of a 3D object, there is an algorithm called "Marching Cubes" and a couple of others you can look up in related literature.

[nimble lynx]

ahh okay, i have heard about ray marching before

we use it at work to offset pixels on a depth map with a search range

someone has figured out some sort of algorithm, check this out

[frozen shoal]

There's an implementation of marching cubes in Scikit which you could try out.
https://scikit-image.org/docs/0.24.x/auto_examples/edges/plot_marching_cubes.html

Oh never mind I think you want something else, because I assume you could get a grid automatically in whatever software you are using if you have the 3D model made in there

[nimble lynx]

yes i need to define some different grids known as isogrids and have those drawn out so i can extrude volumes

[safe radish]

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[nimble lynx]

.reopen

[safe radish]

✅

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[gentle edge]

Is there a better way to solve 32 than multiply by 17 or 19

[covert acorn]

ur doing 32.?

[gentle edge]

Ye

[covert acorn]

hold up ill show u

[gentle edge]

Alr

[gentle edge]

I did this but is there a better way?

[rocky lichen]

Yes

As your can see there is a sort of symmetry in the eqns

[covert acorn]

nvm im dumb

i apologise

[rocky lichen]

Try subtracting and see what happens

[covert acorn]

deeply

[gentle edge]

Lemme see

[gentle edge]

No worry

[gentle edge]

Ah

We get -2x -2y=-2

[gentle edge]

So jus divide by -2

I see thx

[rocky lichen]

Yeah

[gentle edge]

Well ima do more questions

.close

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[gentle edge]

@rocky lichen

In 33 do we have to multiple by 7 or can do something else

[rocky lichen]

Yeah, I don't see an easier way

[gentle edge]

Alr thx

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[sonic dragon]

Help

[sonic dragon]

Here’s an attempt for proving that every real bounded sequence has monotone subsequence

I know it must have many many issues please point them out so I can somehow try to fix

[safe radish]

@sonic dragon Has your question been resolved?

[junior smelt]

I'd say that here that for one, you could have more than one limit point, and it's worth a small justification as to why any bounded sequence has at least one limit point ("it's true by BW")

As for here, I'm not entirely sure what the aim was? It seems that you assumed S1 was infinite, and concluded it was infinite (the very thing you assumed to begin with )

[sonic dragon]

Let s_n < s_n_k<s_n_k_m … if we let a new sequence such that b_n=n, n_k, n_k_m then it follows immediately n<n_k<n_k_m

We have a monotone subsequence s_{b_n}

Because n_k is clearly greater than n etc

[sonic dragon]

since we find a b_n that is infinite and monotone, it shows that every bounded real sequence in this case has monotone subsequence at least s_{b_n} is

Like is it clear that n<n_k for ya?

Because n is natural number

Like n_{any natural number n} > n

[junior smelt]

Alright happier

[junior smelt]

(greater than or equal to )

[sonic dragon]

Yes

[sonic dragon]

This is a stronger theorem compared to BWT but I am not sure if I have done it correctly in term of proving it

Actually it’s not the strongest yet

You can even prove that every real sequence has monotone subsequence

But I haven’t figured how I can do it yet

And bcs again I’m not studying mathematics as a math major so it’s so hard 😭

[junior smelt]

I think I see what you're trying to get at here, at the very least

[junior smelt]

(if you can figure out the one we're doing now, then it's not too difficult to extend to all real sequences: if it's bounded, you're done, if it isn't bounded, then...)

[junior smelt]

As for here, are you like trying to cook up a subsequence? That you take one term, and choose the next one from the set S1 such that it's closer to s than the first one is?

[sonic dragon]

Because the union of S_1 s_2 and s_3 is complete natural number

So it’s either one of the cases

Which is the center of my argument in this proof

[junior smelt]

That at least one of them is infinite?

[sonic dragon]

yes

Like one must be infinite

[junior smelt]

That is fair, though of course it's worth making clear why (at least) one of them being infinite means you can get a monotone subsequence, which is what I was asking

[sonic dragon]

Yes, it’s kinda a scratch work bcs I feel like I spent way too much on this one

But still I kinda wonder how I can extend it to the entire real line

[junior smelt]

Awww, that one you'll get it almost instantly (with a few questions )

But for the bounded one here, at least personally, the way I'd think about it is that at least one of the S1, S2 or S3 is infinite (given a limit point you chose)

-wait, do you count constant sequences as monotone? (i.e. do you count "non-strictly" increasing/decreasing sequences as monotone?)

[sonic dragon]

Since yes

[junior smelt]

Cool then, in that case, if S3 is infinite, you're done

Otherwise one of S1 or S2 (or both) are infinite, then if it were S1, similar to what you were doing, choose some n1 and then pick n2 from S1 such that s_{n2} is closer to s than s_{n1} was, and keep going, which you should be able to do, but-

-if you weren't, then do similar with S2, keep choosing terms such that you get closer to s, if you aren't able to do that with both S1 and S2, then s can't be a limit point of the sequence, which is a contradiction

[sonic dragon]

of course bcs constant sequence is monotone

So it’s quite counterintuitive for many I think

[junior smelt]

(note that S1 being infinite does not immediately mean you could "keep going", those infinite terms could be related to another limit point instead, for example)

[sonic dragon]

Oh that’s a good idea for infinite case though

[sonic dragon]

Like showing one of them is infinite should be sufficient I think

Like if s_n is not bounded

In either of the 3 cases

Shouldn’t they still be monotone?

like I can even omit s as a limit point

Which isn’t needed

Since these are all 3 cases of all possible case scenarios

[sonic dragon]

Like if I omit the part of s being limit point and let it be arbitrary and let it unbounded then they all should be monotone

But still for the bounded case I must assume limit point to craft argument

Since they are oscillating

[junior smelt]

You don't need to consider (finite) limit points for the unbounded case, at the very least

You don't really need the sets S1, S2, S3 either

[sonic dragon]

But this is the only proof I came up with cuz I’m dumb 😭

[junior smelt]

You aren't

Anyways, thinking about an unbounded sequence, that's basically like saying you can find terms that get as large (in absolute value) as you want, right?

[sonic dragon]

Yes like I must find a subsequence that’s monotone

Like b_n=n, n_k, n_k_m,…,

[junior smelt]

Yep, do you at least agree that if you have an unbounded sequence, you can either make it get "large positive", or "large negative" (or both)?

[sonic dragon]

Yes

I agree

[junior smelt]

Well, then if you had it getting "large positive", do you think you can then make a monotone sequence?
(the idea is basically very similar for "large negative")

[sonic dragon]

Yes I actually got it now

To be honest I actually think even if my proof is right it’s too complicated

Like the case bounded actually somehow does it

I saw a rare proof for BWT online and I knew there’s a stronger version of BWT

So I used that method

Which kinda work out since I found the cases but… there should be easier method

[junior smelt]

Awwwww well as they say, the most important part is that it works, once it does then you can consider refining it to be smoother

[sonic dragon]

Thanks so much though I have been on this one for almost 24 hours, since I was so stubborn to look up for help and kinda ruined my new year

I think I will sleep for now 😭😭😭

Thanks so much

Like I am still too scared that I will fail the RA course next year in the spring in 2026

I feel like always my preparation isn’t enough like even my friend somehow said it’s enough you should just rest and that study doesn’t matter 😭

[junior smelt]

Awww, it can be like that for maths for sure, that it feels like you still haven't done enough no matter how much you've done I'm sure that you'll end up fine though, you've done quite a lot as it is, and at least in my experience, things don't go as terribly as I'd have thought for the most part

Hope you get a good well deserved rest (and sorry that this problem ruined your start to the new year )

[sonic dragon]

Thanks it’s fine I am a workaholic so

Have a sweet dream too please 🥰🥰

[junior smelt]

Awwww thank you catch ya later

[safe radish]

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[storm dew]

how to solve this

!status

[safe radish]

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

[storm dew]

2

i can get the area of the quadrant

and of the square

but the intersecting area

[storm dew]

1764 cm^2

[storm dew]

1386 cm^2

[rotund robin]

To solve the question, try draw the whole circles.
After that, you can find the area of intersection of these two. (main part, tell me if you're stuck).
Now, you shall solve for the intersecting area that is asked in the question.

[storm dew]

it would be half for a whole circle

i think

so then it would be 2 quadrants - half quadrant

but that isn't correct

[rotund robin]

Like this

Hint: Triangle EAB is equilateral.

So angle EAB = 60 deg

[storm dew]

ohhh

but the arcs

ill have to search the formula

segment*

it's theta/360*area

[rotund robin]

yeah

[storm dew]

and for equilateral it's

[rotund robin]

root(3)/4 * a^2

[storm dew]

ye

[rotund robin]

So, are you able to do it now?

[storm dew]

so first equilateral triangle area

1.7/4 * 1764

749.7

then the segments

[rotund robin]

so now you can get the area of the figure EAFB

[storm dew]

wait this is of sector

[rotund robin]

yeah

[storm dew]

so i subtract the triangle's area

that is

[rotund robin]

yeah

now you get the segment's area

[storm dew]

749.7 - (1/6*1386)

that's 231

so 749.7-231

518.7

[rotund robin]

wait

[storm dew]

wait no

i messed up

theta/360 of area - triangle area

[rotund robin]

yeah

[storm dew]

60/360 is 1/6

where am i messing upppp

[rotund robin]

well

the area of the sector = 1/6 (22/7) * 42^2

[storm dew]

wait sht

i was using quadrant area

not circle

so 5544

divided by 6

that is

924

924-749.7

174.3

we double that cos two same segments

348.6+749.7

that is

uhh

1098.3

subtract this from the quadrants

[rotund robin]

Now just subtract this from the quadrant's area and double it
yeah

[weary igloo]

Can anyone help me at help 14 if ur done

[storm dew]

almost

[weary igloo]

K ty

[rotund robin]

!noadvertising

[safe radish]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[storm dew]

gimme a min

575.4

well ty

[rotund robin]

np

[storm dew]

help appreciated

.close

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[storm dew]

!status

[safe radish]

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

[storm dew]

1

[snow robin]

The sides of the innermost square are all the hypothenus (long side) of special triangles

does that help?

[versed wave]

there's a pretty nice observation you can make here

[storm dew]

nvm i can just work my way up

[versed wave]

if you shift the side of the innermost square leftwards so that it aligns with the penultimate square, you'll see it's half of the penultimate square side

[storm dew]

and then calculate the diagonal

[versed wave]

likewise, if you shift the side of the penultimate square so that it aligns with the outermost square's diagonal, it's half of the diagonal

thus you can conclude the side of the innermost square must be 1/4 of the outermost square's diagonal

[storm dew]

but that would be 4/root 2

[versed wave]

simplify it, what do you get?

[storm dew]

42 root 2

[versed wave]

wrong

wrong

[storm dew]

2 root 2*

[versed wave]

correct

[storm dew]

this keyboard ahh

[storm dew]

ye if u rationalize it

[versed wave]

and you are done

[storm dew]

ty

very much appreciated help thanks

.close

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[vital sedge]

can anyone help me with getting the coverage/topics specifically on Quarter 3 | Quarter 4 math || second semester basically
also from the philippines specifically, just saying because i dont know if its different for other countries

[versed wave]

the help channels are for asking a specific question, not for reviewing a whole topic

[vital sedge]

i was asking for just the topic names titles... i was told it was okay to ask for them but i guess it wasnt this channel, my bad

[versed wave]

ah, i misunderstood. i'm not sure if that is allowed, but i feel like you won't get an answer here for something THAT specific

why don't you try asking your peers?

[vital sedge]

dont have anyone close enough

ill try searching for it ig

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[deep depot]

What does this actually signify

[deep depot]

What "does the square of the unit vector from the origin" signify

Does the formula for complex slopes have any derivation

Like C=-a/conjugate(a)

Does this have any derivation? Or it is there by defination

Definition*

[safe radish]

@deep depot Has your question been resolved?

[deep depot]

<@&286206848099549185>

[plucky elk]

Definition

[deep depot]

What is the square of unit vector

What does it have to do with coordinates

Okay like the unit vector I get it , it gives the direction but what does the square of unit vector do ?

[safe radish]

@deep depot Has your question been resolved?

[safe radish]

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[tame zephyr]

I dont understand this standard deviation calculation

[tame zephyr]

hey @junior smelt !!

[hardy monolith]

!original

[safe radish]

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

[junior smelt]

Hiii happy new year as well

[tame zephyr]

happy new years!

heres question

[junior smelt]

What's the x you're dealing with?

[tame zephyr]

so little x is nw/2000

I did my calculation of stadard deviance based on this formula

[junior smelt]

cool cool, and which bit is confusing?

[tame zephyr]

im not sure why my answer is not matching?

they got 999.635 and mine is 1413.955235

[junior smelt]

Hmmm, also how comes you have that sqrt{38} inside the outside square root?

[tame zephyr]

OMG

mybad

wait

i got it

yesyes

😭 i deferred my stats exam to jan, ive actually been dragging out this course for so long

nothing can be worse than stats man

literally, ive done ra, calc, lin alg, discrete math, odes nothing beats this

i actually rlly like odes

its very systematic

[junior smelt]

Awwwww I don't blame you one bit

[severe pond]

odes has a ridiculous amount of algebra

longest algebra problems ever

hot take but stats is better

[tame zephyr]

yes but its very organized, its just a bunch of conditions, if this equation is in this form, then you do this...

at the end the whole course is just a tree of conditions you have to memorize

[severe pond]

nah it’s just hell

usually if the algebra takes that long you’re probably doing something wrong but for odes it was the realization of how much algebra you’d have to do for the problem knowing it was the correct way to do it

felt like a good amount of it was memorization too

[tame zephyr]

exactly😂 like i said, you literally just gotta remember all the conditions and you're good to go

no need to do the prac problems or anything as long as you know the methods

maybe i just like memorizing more?

[severe pond]

probably and torturing yourself with tedious work

would’ve been better if it was less computation

but i guess that’s just because it was a first course in DEs

[tame zephyr]

i also rlly like integrating and differentiating. I also did really good in multi var calc, and i did better in real analysis than linear algebra😭 or complex variables

real is calc based

stats is not fun🥲

[safe radish]

@tame zephyr Has your question been resolved?

[tame zephyr]

not sure how this is

this is what I got

@junior smelt

[junior smelt]

Not super sure for these ones sorrryyyy

[tame zephyr]

ok! nw

also

the expected value doesnt match

[junior smelt]

Think that might be an error on their part

[safe radish]

@tame zephyr Has your question been resolved?

[safe radish]

@tame zephyr Has your question been resolved?

[tame zephyr]

also i dont think the mean and var are right..

<@&286206848099549185>

i have 49.48 and 188.0896

[warm lodge]

did the calculations and agree with these 2 numbers

[tame zephyr]

perfect, thank you!

@warm lodge not sure how they got this value

[plucky elk]

That's just the alpha value for 95th percentile you have to memorize

[tame zephyr]

shouldnt it be mean+2SD?

[plucky elk]

You're thinking of middle 95%

95th percentile is something else

P(mean - 2 SD < X < mean + 2 SD) = 0.95

[tame zephyr]

yes I was referring to this

oh but we want X <= to

oh yes, so we gotta use z-table

@plucky elk right?

[plucky elk]

That works too yes

[tame zephyr]

wait whats the way you were thinking of?

[plucky elk]

This

[tame zephyr]

what i dont get it

you'd still have to use z-table to find z-score

[plucky elk]

If that's all you know then do it that way

[tame zephyr]

ok

there is no next slide in the slide deck

but you need the pdf to find a) right?

oh no you dont

damn the log-normal distrib really 'distorts' the data

like if you showed this to someone they would think the actual distrib is normal too

[safe radish]

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[tame zephyr]

thank you to all who helped

[safe radish]

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[lean otter]

I can’t get it

I know the answer but I don’t understand it

[neat patrol]

lets say 2/a = c

then we can say that lydias height is c*francine's height

c of x -> c*x

then we replace the c back in as 2/a

[lean otter]

What does “a” represent

[lean otter]

Ohh shit I get it now

[lean otter]

Thanks for your help

.closepl

.close

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[soft lava]

I’m really confused on this. I did not get this answer I got it from a video. I’m confused how we got to this ANWSER.

Number five

[plucky elk]

,rotate

[soft lava]

I really don’t understand this unit at all

And I’m worried I’m going to fall more behind

[plucky elk]

If the price of a stock is $100, what's the price after 1 year?

[soft lava]

I mean it would increase by 80 percent which is this equation 100•(.8)^1 or would the growth factor be 1.8?

[plucky elk]

Can you just answer this

[soft lava]

Isn’t that the answer??

it would either be 80 or 10800

Wait

I forgot a zero

180

[plucky elk]

8% = 0.08

[soft lava]

Oh

Woudk the equation be 100•(.08)^1

Wait

Then the stalk woudk be 8

I’m so confused

Why do it decreasing now

Do I need to add a one?

[plucky elk]

Do you learn anything at all like
A = P(1+r)^t
P = principal, r = rate, t = time

[soft lava]

Umm

Maybe with different words

We are using words like incial amount , growth factor, rate of change, time

So the main equation for this unit it incial amount • (growth factor) ^ time

We haven’t gotton to that fully yet

Part of it

[severe pond]

what because there’s an n?

[plucky elk]

I missed the n

[soft lava]

Wait I’ll draw it out one sec

[plucky elk]

n=1 in my question

[severe pond]

don’t need it here

yep

[soft lava]

This is a fake equation I made up the numbers just to show what I’m thinking

[severe pond]

you realize that multiplying by a number less than one would result in a smaller number right

[soft lava]

If it was decreasing that would be correct right? So if we are increasing it would be 1.6?

[severe pond]

0.6 is not decreasing by 60%

[soft lava]

Is it decreasing by 40%

[soft lava]

So how would you write increasing by 8 percent? I know increasing by 80perbent would be 1.8

[plucky elk]

The answer is $108

[soft lava]

What would be the growth factor?

[plucky elk]

Do you see why 108 is an 8% increase of 100

[plucky elk]

The one in #5

[soft lava]

Yea I just don’t know how to put it into a equation

[plucky elk]

108 = 100+8

[plucky elk]

Then use this

[soft lava]

So then how did we get the increase after 10 years?

[plucky elk]

You should try to understand 108 fully before moving on

[soft lava]

I mean I got more class tommrow so we are going to move on from this 😭😭😭

[plucky elk]

¯_(ツ)_/¯

[severe pond]

who is we

[soft lava]

My class

[plucky elk]

I don't have class

[soft lava]

😭

I just don’t understand how we get the factor after a certain amount of years

Because I also had it for this equation

Which I did not understand

[plucky elk]

108 = 100(1 + 0.08)

[severe pond]

understand how to get it after one year first

[plucky elk]

Follows from this

[severe pond]

,rotate

[plucky elk]

Guess she's moved on then

[severe pond]

lol

[soft lava]

This is the same homework 😭😭😭

Like this is all from one class

[severe pond]

how do you expect to understand how to do this if you can’t do the simpler problems

[soft lava]

Idk

I think I underaged it better then I did

Like I underaged how to writ ehr equation

[severe pond]

underaged

[soft lava]

I just don’t understand how to know the factor and it’s increased

Like for the one I just sent why are we doing 1.1

[severe pond]

10%

which is 0.1

1+0.1

[soft lava]

Ohhhhhh

Since we are increasing we add one

Then what’s with the fraction

[severe pond]

since we’re doing months we consider it as a fraction of a year

one month is 1/12 of a year

[soft lava]

Ohhh

So the irs months over years

[severe pond]

also did you use chatgpt or some shit?

[soft lava]

Wait

[severe pond]

the irs

[soft lava]

No?

[severe pond]

then how do you not know what you’re writing

[soft lava]

So it’s base amount of time over time your determining

[soft lava]

Our teacher posts links to YouTube videos but the lady is bad at describing

She kinda just writes it down and doesn’t teach

[severe pond]

NA education

🤝🏻

[soft lava]

I was also maybe playing the sims while doing the homeowrk

I was also wicked dizzy during class today so I doubt fid not learn as well as I could

[severe pond]

i forgot high school goes back this early

tough

[soft lava]

It’s horrible

Idk why we are going for a two day week

[vagrant ice]

nah my HS would definitely start on the Monday

so not all high schools

[severe pond]

mine was always january 2nd so long as it wasn’t a weekend of course

[vagrant ice]

sadge

wait which country are you from again

[severe pond]

america

[vagrant ice]

ah interesting

I bet it depends on state

[severe pond]

probably

[vagrant ice]

like Texas and the south start summer early

like it's not uncommon for June to be already summer

and northeast starts summer late from what I can remember

[severe pond]

yea some states further west have a long winter break and also end in like early/mid may

[vagrant ice]

oh lmao early May that's insane

[severe pond]

yep

[vagrant ice]

and goes back late

[severe pond]

yea usually right after AP exams i think

[vagrant ice]

ah yeah for seniors of course it's earlier

[severe pond]

which is first/second week of may

[vagrant ice]

IB exams worldwide finish around mid May

so there's some similarities

[severe pond]

yep the month after AP exams in high schools in the northeast consisted of doing absolutely nothing

waste of a month

[vagrant ice]

no way

you still had school after AP exams??

oh right, not everyone does APs

that's good then, spend some time planning a getaway and figuring out what to do with your life

while you're not totally on your own yet

post exam slump is real

[severe pond]

yep

i mean there were state exams i guess for earlier years

and yea not everyone was taking APs

[vagrant ice]

yeah we had public exams also, and some of those public exams could last until late June

which is why we only started summer at that time

like July 1 is a holiday so we had to start by then at the latest

[severe pond]

still a waste of time though, i showed up once maybe twice last year after exams

[vagrant ice]

lmao what's the attendance requirement at your HS

[severe pond]

i mean if im being real i was absent for about 45% of the school year and received like 4 letters saying theyd do something but they were automated i think

its only an issue if youre failing

[vagrant ice]

ah that makes sense

at mine we had 80% attendance but like not many people would get down that low

like it was never really mentioned anyways

[severe pond]

i had over a 100 in every class besides english so i just didnt care

[safe radish]

@soft lava Has your question been resolved?

[safe radish]

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[static yacht]

Hi.
Been stuck for embarrassingly long.
How does the formula (11) turn into the graph on Figure 1? I have not been able to replicate this graph using the function in either Geogebra or Python (Matplotlib).

Edit: Elaboration: I get like an s-graph, but it diverges after the first two extremas, it doesnt bounce in the band like figure 1 shows it to do.

[static yacht]

One of many failed attempts. Also, the article states A must be negative to achieve the graph, however it seems to work against me. Im quite lost.

[olive heron]

It did work while a was negative

[static yacht]

Still diverges after the two extremas. In Figure 1, the striped line projects the function to stay within the band

[safe radish]

@static yacht Has your question been resolved?

[safe radish]

@static yacht Has your question been resolved?

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[sand tree]

On a),
OP = 2OA - OB

why was it OB instead of 2OB?

[safe radish]

@sand tree Has your question been resolved?

[sand tree]

<@&286206848099549185>

[final loom]

$a = 2\hat{i} + 2\hat{j}$ and $b = 2\hat{i} - \hat{j}$ so, to get $OP = 2\hat{i} + 5\hat{j}$ you can solve sletv ha + kb = OP to get h = 2, k = 1

[flat frigate]

Arya

[sand tree]

like this?

[final loom]

Yes

[somber knot]

k is -1!

[sand tree]

thanks!

.close

[safe radish]

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[sand tree]

.reopen

[safe radish]

✅

[sand tree]

@final loom so only the lines in between (OA) can be extended and the sides (OP and OB) remains unchanged?

does it apply to all vectors?

[final loom]

No.

This might help better your understanding - https://youtu.be/kYB8IZa5AuE?si=_xbFc5zZHGxqtcba

[safe radish]

@sand tree Has your question been resolved?

[safe radish]

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[safe radish]

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[chrome cedar]

Does anyone have a free pdf of vectors from basics to complete advanced?

[devout scroll]

how basic? search "linear algebra textbook"

[safe radish]

@chrome cedar Has your question been resolved?