help-49

[pearl star]

anyway

[grand pond]

Jonath A.K.A Planned Aiphid1621
Compile Error! Click the reaction for more information.
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[pearl star]

<@&268886789983436800>

pls get this guy out

[oak ether]

wat

y

[pearl star]

you know why

[tawny hedge]

@oak ether

[still nacelle]

you should not and is not allowed to use bot to help

[oak ether]

ill delte

[pearl star]

nd ur literally giving the answer away

😭

anyway

no ur supposed ot guide me through it

[oak ether]

oops

[pearl star]

and @still nacelle is already helping me

so pls stop typing here

[still nacelle]

so anyway

yeah you're right with that the determinant of A is det(A) = 3x-6*4

[pearl star]

and we do the same with b right?

or nah

[still nacelle]

yes

[pearl star]

oki

[still nacelle]

but do you know any property for determinant of product and inverse of matrices

[pearl star]

uhh

i think i do yes

[still nacelle]

ok which ones do you know

[pearl star]

u mean like

det(AB)

[still nacelle]

yh

[pearl star]

for the product

oh

yea i think im good with those

i hope so

[still nacelle]

ok can you list it out just to be sure

[pearl star]

list out the things i know?

[still nacelle]

just the ones that you think is enough for this question is okay too

[pearl star]

uhhh

im mostly familiar with product

[still nacelle]

so what is det(AB) in terms of det(A) and det(B)

[pearl star]

just multiplyright 😭

[still nacelle]

yup

det(AB) = det(A)det(B)

[pearl star]

ohh wait so i need to find the det of both then multiply the result by each other

[still nacelle]

what about $det(A^{-1})$ in terms of $det(A)$

[grand pond]

lgkoo

[still nacelle]

yes, except in the question it contains inverse of A, and transpose of B

[pearl star]

oh inverse im not too sure 😢

[still nacelle]

and what about $det(B^t)$ in terms of $det(B)$

[grand pond]

lgkoo

[pearl star]

is that the transpose

[still nacelle]

yes

[pearl star]

yeah im kinda lost sorry 😭

i need to find the inverse right

before the transpose

[still nacelle]

you don't

[still nacelle]

from this we know that det(A^-1) = 1/det(A)

so as long as you know det(A)

[pearl star]

ohh

yes

[still nacelle]

you don't need to find A^-1 and its determinant

[pearl star]

so it would A^-1 = 1/det(3x-24)

[still nacelle]

yup

det(A^-1)

[pearl star]

oh ye

mb

okay

then we find the transpose

[still nacelle]

yes

[pearl star]

which im not too sure of tbh

[pearl star]

oh

[still nacelle]

the determinant of the tranpose of a matrix is the same as the original matrix

[pearl star]

wait so its just det(B)

[still nacelle]

yah

[pearl star]

im stupid

💀 mb

alr

[still nacelle]

nah it's ok, you're still learning

last thing

do you know what's det(kA) in terms of det(A)?

where k is a scalar constant

[pearl star]

uhh

[still nacelle]

(in this case for the question k = 5)

[pearl star]

im not too sure sorry

[still nacelle]

det(kA) = k^n det(A)

where n is the dimension of A

in this case A is 2x2 so n = 2

btw I would suggest you spend time to verify these formulae yourself too

[pearl star]

im tryna process it xD

[still nacelle]

yh that's good

[pearl star]

im kinda confused on how its 2x2

[still nacelle]

the matrix A is a 2 by 2 matrix

so 2x2

as it has two rows and two columns

[pearl star]

OH

THE DIMENSION

i THOUGHT

it was the numbers inside

om

mb i got it now

[still nacelle]

ok, so combining these formula

[pearl star]

so it would be 5^2 det(3x - 24)

for

det(kA)

[still nacelle]

yes

[pearl star]

ohhhh

[still nacelle]

now can you do it for the question?

[pearl star]

OH

so just sub in

since we found the inverse

and transpose

[still nacelle]

yup, so what would you get

[pearl star]

i dont really have a calculator on me rn 😭

[still nacelle]

you don't have a paper to work on?

[pearl star]

i found one its fine

nvm it doesnt work 😭

ill just use a paper

OKAY i think i got it

is it 154/3

nvm

wait

i think i made a mistake

[still nacelle]

for what though, the determinant or x?

[pearl star]

for the det yes

but im not sure

i mightve made a mistake when i was finding x

[still nacelle]

show me your work and we can figure out the mistake together

[midnight plank]

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[daring lark]

why is the unit normal vector N (times dS) equal to that?

[still nacelle]

the oval is the intersection of the cylinder and the plane 2x+2y+z = 3, which means that the oval is on the plane

so it has the same normal to the plane 2x+2y+z=3

[daring lark]

gotcha, thanks!

[still nacelle]

np

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[midnight plank]

Please don't occupy multiple help channels.

[heady flint]

this correct

[surreal moon]

!1c

[midnight plank]

Please stick to your channel.

[surreal moon]

Do not occupy multiple channels

Stick to one question in one channel

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[mighty vault]

58.03 I guess

12.8 / 4 = 3.2 meters (base side)

Base area = 3.2 * 3.2 = 10.24

V = 1/3 * 10.24 * 17 = 58.026666666... ~ 58.03

[midnight plank]

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[latent hamlet]

Looking for help on where I went wrong for this question

[ivory crescent]

How did you determine your a and b

Also, you did not account for the inner radius in your setup

[midnight plank]

@latent hamlet Has your question been resolved?

[wet pollen]

Did you try drawing a graph?

[latent hamlet]

graph would just be a wider parabola right?

[latent hamlet]

no I don't think I did, I haven't done calc in over a year and have forgotten a bunch of stuff

[wet pollen]

Do you recall the Washer Method?

[latent hamlet]

yea a little, also I'm realizing my a and b should be +/- 1.308 right?

[wet pollen]

No.

The upper boundary is at y = 1.

[latent hamlet]

oh yea yea so it's +/- 1

[wet pollen]

With the Washer Method, you subtract the volume calculated by the inner radius from the volume calculated from the outer radius.

[latent hamlet]

ok yea I'm remembering, so outer radius is π(x^6)^2 right

[wet pollen]

Which is πR^2 - πr^2

Not quite. The radius needs to be calculated from the axis of rotation.

What is that distance?

[latent hamlet]

5?

or 4

ooh hol up

[wet pollen]

What is the distance from the axis of rotation to a point anywhere on the curve y = x^6 on the interval [-1, 1]?

How would you calculate that length?

[latent hamlet]

integral of π(x^6)^2 ?

[wet pollen]

No.

Consider the points at the ends of the orange line segment. Let's say at x = 0 to keep things simple.

[latent hamlet]

yea that's 5

[wet pollen]

What are the coordinates of the endpoints of the orange line segment?

[latent hamlet]

5 and 0

[wet pollen]

The (x,y) coordinates.

[midnight plank]

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[latent hamlet]

.reopen

[midnight plank]

✅

[latent hamlet]

(0,0) and (0,5)

[wet pollen]

And how would you calculate that length?

ahem Distance formula, but you don't worry about the x value because it would zero out.

[latent hamlet]

it's just 5 yea?

[last slate]

its 5 units

[wet pollen]

At that particular point, but that's not what I'm getting at.

How would you calculate that distance using the distance formula?

[latent hamlet]

0-5 = -5 ?

[wet pollen]

Would it make sense to have a negative length?

[latent hamlet]

no

?

[wet pollen]

So what do you think you should do?

[latent hamlet]

5-0=5 ?

[wet pollen]

Yes. ALWAYS subtract the smaller value from the larger value to get a positive radius.

At any point on the curve y = x^6 on the interval [-1,1], the y-value will be less than or equal to y = 5.

[latent hamlet]

Okay, so now what do I do with that

[wet pollen]

Now let's think in more general terms for calculating the length of the radius.

[latent hamlet]

Alright

[wet pollen]

How would you calculate that length?

[latent hamlet]

this is where I'd want to use an integral right?

[wet pollen]

Not yet. I'm teaching you something rather basic right now before we get to the integral.

[latent hamlet]

5-f(x)

[wet pollen]

And what does f(x) equal?

[latent hamlet]

the y value at a given point of x

[wet pollen]

What is the equation given to you by the question?

[latent hamlet]

x^6

[wet pollen]

Yes.

So what is the equation for the Outer Radius?

[latent hamlet]

so 5-x^6

[wet pollen]

Correct.

R(x) = 5 - x^6

[latent hamlet]

and then I'd subtract that from the inner radius

which is little r

[wet pollen]

Now let's find the inner radius using a similar method.

[latent hamlet]

alright bet

[wet pollen]

How would you calculate that radius?

[latent hamlet]

5-1

[wet pollen]

Correct.

So the Inner Radius is equal to 4.

Now you can fill in the integral for the Washer Method.

[wet pollen]

Yes.

And there is a reason why I emphasized using the Distance Formula. There will come a time where you will to need to solve for the rotation about a slanted line. That's long in the future but it will come.

And it's better you understand that you ARE using the Distance formula here.

[latent hamlet]

Yeah I get that

just want to make sure I have this set up right

25x-16x would become 9x

[wet pollen]

You can simplify things by reducing 25 - 16 to 9.

[latent hamlet]

yea yea, thank you so much man

huge help

[latent hamlet]

one last thing if you don't mind, I just want to make sure I plugged in all my numbers right, but I got ~48.056 as a final answer, does that seem right?

[wet pollen]

Spot on.

[latent hamlet]

thank you sooo much for all of this

[wet pollen]

Although it's usually preferable to leave it with pi.

Without reducing to decimal unless asked to do so.

[latent hamlet]

cool beans man, thanks again 🙏

[wet pollen]

So 1392pi/91 would also be acceptable.

yw

[latent hamlet]

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[frozen plume]

Hey! It’s not necessarily a mathematical question but i was just curious to know: so basically im taking linear algebra in my next semester of college and i wanted to know in advance what would generally be the main topics that i could possibly learn during the class. My only guess is that we’ll learn the matrix thing

[sharp coral]

this playlist by 3blue1brown is a good overview of the concepts covered: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

[frozen plume]

Alright thank you so much 😁😁

[sharp coral]

don't worry if you don't understand everything the first time, that's what the class will be for

[frozen plume]

Yeah for sure

Do you think it’s a pretty hard class?

[sharp coral]

it's not super difficult, but it is a bit of a different style from the types of classes you've taken before

[frozen plume]

Ohhh yeah fair enough

alright thank you 😁

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[deep portal]

This is for the master theorem, what is the "2nd term" they're talking about? Not sure what they mean by terms

[deep portal]

Ping me if you reply please, this is for discrete math

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.close

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@last slate Has your question been resolved?

[void copper]

Solved...

Lemme repeat the process clearly

Here

@last slate lemme know of any questions

Did you click at it?@last slate

What did it show?

[void copper]

Exactly here it is... you just click and it will download to you@last slate

[pearl hull]

Is that your pic?

[void copper]

@pearl hull yes it is

@last slate after the v part, we take the v equation and replace the a with a in iii. That gives us the vi down there. And then, you take v and replace it's c with c we made in ii, after which you get vii. From there, you just take the vii and solve it simultaneously with the one from the arrow with terms a and b, and since they have like terms, you get the answers of a and b, and now c becomes easier as you will just take the c we made in ii and replace a and b with values.

Yes@last slate ... so it's well understood now?

We get iv from the second equation in the question. We just make c the subject in that second equation @last slate

We take ii and iv as they have the same terms being a and b on one side, and c on one side. Solving like simultaneous equation while eliminating c now gives us an equation with a and b as the only unknowns which is 1.5a+0.5b=25 which is also same as 3a+b=50

@last slate just to match with the terms there, it's just a zero, so no much significance

Yes, because after that, you just take -25 to the other side and now remove the zero @last slate

Because we just subtracted the two c's on the left hand of both equations so c-c came to 0

Yees @last slate

[void copper]

@last slate from here.... make 1.5a+0.5b=25 and make it to a fraction, and then multiply every term by the lcm which is 2, you get that

Nice @last slate

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[hybrid moss]

can someone tell me what am I doing wrong?

[austere nest]

check if u are using degrees or radians

[hybrid moss]

degrees

pretty sure

[austere nest]

then ill give u a hint

[hybrid moss]

hmm

[austere nest]

think about the question logically

does a negative value for tangent make sense

[hybrid moss]

of course not

that's why I know im doing something wrong

[austere nest]

is your work the 2nd pic?

[hybrid moss]

yep

[austere nest]

well we know tan=sin/cos

sin and cos are both positive in the first quadrant

55 deg is the first quadrant

so by that logic your work is using radians

you might have meant to use degrees but always have to check the calculator settings

[hybrid moss]

ok lemme try desmos calculator

[austere nest]

desmos automatically uses radians unless you specify otherwise

[hybrid moss]

ah yea

[hybrid moss]

I changed it to deg

[austere nest]

this is using radians

sin should be positive with degrees

[austere nest]

yep

[hybrid moss]

aha I see I see

thank you 🙏

[austere nest]

no problem

take care!

[hybrid moss]

I was confused for 10 minutes trying to figure it out

[austere nest]

dw u havent done enough practice if u havent missed a question because of degrees vs radians

everyone has done it

anyone claiming to not hasnt done enough math

[hybrid moss]

real

.close

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[gray gorge]

can anyone answer question 6, thanks

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[last slate]

how can i solve this in a calc?

[midnight plank]

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@last slate Has your question been resolved?

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[terse turtle]

What is your question. Explain me

[last slate]

how can i solve the question by using the calculator? for ti 84

[terse turtle]

Have you tried it in pen and paper

[last slate]

i know how but i’d like to know the calculator method

[last slate]

idk

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[delicate musk]

how can i solve this using pascels triangle

[midnight plank]

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[delicate musk]

<@&286206848099549185>

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[civic moth]

Solve using binomial expansion

[midnight plank]

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[obtuse totem]

the question asks: what is the probability that they need to sample again if 3 of every 5 households in the country have pets?

so what Im thinking, is to use the binomial distribution

where Success= at least 4 households have pets, so the equation I'll use is: 1- h(4;10,0.6) where 4 is the num of successes, and 10 is the sample size, 0.6 is the probability

yea, I think that should be right

more clear when I typed it out, thanks

so bayes theorem would be, prob of F given 0.6 success..

i dont see why you cant just use the formula I typed above?

ok, give me some time to think on it

I think Im getting more confused lmao

I still didnt use bayes..

oh oops btw its b(0;10, 0.6) not h, b for binomial, I dont know why I wrote h

yea I think thats right

[cobalt sigil]

Hey i am really sry

[obtuse totem]

because P(X=1)=b(1,10,0.6) and thats for one pet, we get prob of 1- at most 3 pets, which is prob of atleast 4

[cobalt sigil]

My phone died

[obtuse totem]

oof nw

[cobalt sigil]

Yeah binomial would work for this

P (x<4)

p = 2/5

q=3/5

[obtuse totem]

whats p and whats q?

[cobalt sigil]

p is household doesnt have dogs

n = 10 number of trials

Now you can calc and add for P(x=0,1,2,3)

I am really sorry

[obtuse totem]

like what I did here

nw nw

all good lol

[cobalt sigil]

I was inspecting the question and it just powered off !

[obtuse totem]

thats me and my phone too lol, always low battery

[cobalt sigil]

You have considered having pet as p ?

[cobalt sigil]

?

Then its absolutely correct

[obtuse totem]

so 0.6 is the probability of 3 of every 5 households

[cobalt sigil]

Yeah its correct then

[obtuse totem]

ok

thank you

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[autumn briar]

the question is is there a partial differentiable funktion g: R^2 -> R with the outcome above

[cedar vortex]

yk what's an easy check we can do

[ancient path]

So you are trying find the function?

[autumn briar]

we found a solution where someone took e^x * sin(y) + c
but shouldnt it be
e^x * cos(y) since when you take the derivitive of x you get cos(y)?

[cedar vortex]

we can compare the partials of xy and yx

[ancient path]

Yeah

[cedar vortex]

prob the best way to start off with

[ancient path]

You are right

[cedar vortex]

so let's do xy first

[ancient path]

Becuase you treat the y-part as a constant

[autumn briar]

yes

[ancient path]

and e^x is its derivative

You would be right

[autumn briar]

so you take e^x * cos(y)

[cedar vortex]

no

take the partial derivative respect to y

[ancient path]

hold up

[cedar vortex]

what happens to the negative

[ancient path]

but cosy derivative is -siny

[cedar vortex]

yes

[autumn briar]

ah

[cedar vortex]

the way you show this isn't true

is you take the partials xy and yx

they should equal each other

[ancient path]

Yep

[cedar vortex]

by Clairaut's theorem

[ancient path]

which givves us -e^x * siny + f(x) and e^x * siny + f(y)

[autumn briar]

wait now im confused😅

[cedar vortex]

learn Clairaut's theorem

[ancient path]

i believe there is some khan academy lesson for this

[cedar vortex]

or integrate

ig you can also integrate

[ancient path]

lemme check

it should be like some system of equations

[midnight plank]

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[wooden fossil]

hey everyone

When I saw this lemma I immediately thought of what I wrote down. To my surprise the authors chose to do a "more complicated" proof (imo). Is my version wrong ?

[polar mortar]

your C must be a positive integer, theirs does not

[wooden fossil]

ohh

thats a good point

thank you very much !!

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[plush prism]

heya

[plush prism]

i have to hold a presentation about "Whole Numbers"

it is also requested that we formulate at least 3 quiz questions

[unreal fjord]

ok... whole number

[plush prism]

they should be directed at uni students

(math / education course)

the questions i have right now are:
Which of the following Relations are total Orders on Z? (meaning reflexive, antisymmetrical, transitive and total)
-some options here
Do the whole numbers construct a Field?
-yes / no

but i dont know if these are good questions

i know the subject is weird

the whole course is kinda weird imo

[unreal fjord]

I think it is actually good.

[plush prism]

do you have a third question in mind?

[unreal fjord]

some number theory quiz maybe

[polar mortar]

are there more/less/same amount of whole numbers as rational numbers

or integers

[unreal fjord]

that is a good one.

[plush prism]

yeah that is good

[subtle zinc]

how much time do they have to answer these lol

[dreamy lichen]

and maybe formulate that in terms of cardinality instead, so that it's clear and unambiguous

[plush prism]

yeah true

they have infinite time

[subtle zinc]

"is 0 a whole number"

[plush prism]

they dont have to answer them at all, but i have to create the quiz

[dreamy lichen]

it's for uni students

[subtle zinc]

wait what are whole numbers tho

[plush prism]

-3,-2,-1,0,1,2,3

[unreal fjord]

integer

[subtle zinc]

ohh

[plush prism]

i gotta say tho, the didactics/education courses are all so lame

[unreal fjord]

well, some define that as $\mathbb{Z}$ and some define it as $\mathbb{Z}^{+}$

[plush prism]

the math and physics courses are so much better

[feral sedge]

"whole numbers" usually refers to nonnegative integers

"natural numbers" usually refers to positive integers

[plush prism]

huh

[grand pond]

print("NAME")

print("NAME")

[plush prism]

we call them "Ganze Zahlen" meaning Whole Numbers and for us that means -3,-2,-1,0,1,2,3

[feral sedge]

yeah the definitions are a bit.. ambiguous

[surreal moon]

yeah it is.

at least mention that

[feral sedge]

(though i will admit i've never seen whole numbers include negative integers)

[surreal moon]

"whole numbers sometimes include zero, and sometimes include negative. But they never include fractional or decimal components"

[feral sedge]

cool

[surreal moon]

"mathematicians struggle with naming things"

[plush prism]

in german they are luckily not ambiguous, for us, whole numbers always include the negatives

[dreamy lichen]

wait what

oh nvm

[surreal moon]

For me, a whole number was always a positive integer

0 is "hole" number

[unreal fjord]

even natural number sometimes include 0.

[feral sedge]

yeah

[feral sedge]

lol

[surreal moon]

I include zero

[plush prism]

i like to call them N_0 then

[unreal fjord]

Yeah, but as CS person, we count from 0, not 1.

different field or different people define that differently.

[dreamy lichen]

As a set theory uh.. fan? I like to include 0 too

[unreal fjord]

just, make sure it is clear in your presentation

[plush prism]

likes to plot things in matplotlib I'm something of a CS person myself

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[pure gulch]

the question was get the primitive of f(x) = cos(x) - cos(x)/sin^2(x)

[pure gulch]

but why did the cos(x) before the - dissapear

[surreal moon]

,rccw

[surreal moon]

good question. No idea

[pure gulch]

it has nothing to do with it being a constant or smthing right?

bcs I'm still kinda vague on this topic

might also be a book mistake

this is the full answer

oooooooooooooooooooooo

I see it

[subtle zinc]

that's just part of the answer

[pure gulch]

they splitted the thing

right?

[subtle zinc]

right

[pure gulch]

aaaa alr

ty

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[cunning fulcrum]

what should I notice here to prove it?

[midnight plank]

@cunning fulcrum Has your question been resolved?

[cunning fulcrum]

<@&286206848099549185>

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@cunning fulcrum Has your question been resolved?

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@cunning fulcrum Has your question been resolved?

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@cunning fulcrum Has your question been resolved?

[feral sedge]

the relationship between the functions (x^4 + 1)^(1/4) and (x^4 - 1)^(1/4)

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[shut canyon]

is the intersection of two planes, a line, exactly one solution?

or is it a set of solutions, as many as the points in the line?

[midnight plank]

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[last slate]

Do set operations like union and intersection and difference have a priority order? If so what is it

[last slate]

$A \cup B \cap C$

[grand pond]

GinNBread

[last slate]

Which part do I do first

[junior flower]

the first thing you do is scream at the author for writing that

[last slate]

Screaming at myself, done.

I was genuinely curious, is it invalid notation?

[junior flower]

but after that i would interpret it as A cup (B cap C) and then scream at the author some more

[last slate]

Because intersection has higher priority? Is it?

Or do we go left to right

[junior flower]

it’s not really an established thing

just use parentheses

[last slate]

I could use parentheses on first two or last two

[junior flower]

yea

[last slate]

Why would you do it on last two?

[junior flower]

i’m not answering this question lol just use parentheses

i don’t want to say anything that encourages one operation having precedence over the other

[last slate]

You're confident there's no such thing?

[junior flower]

i mean let’s see what’s on google

https://math.stackexchange.com/questions/6505/precedence-of-set-union-intersect-and-difference

[last slate]

I'll stick to parentheses

[junior flower]

[last slate]

Thank you for your time

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[sturdy escarp]

I would be grateful if someone could kindly explain this question

Thank you.

[humble aurora]

is it assumed that you know that lim x->0 sin(x)/x = 1

??

[cunning fulcrum]

You can write is as sin(pi(1-x))/(x-1)*1/(x^2+x+1)

[sturdy escarp]

Yes

[golden cloak]

@sturdy escarp you here?

$\lim_{h->0} \frac{\sin ({\pi\times(1+h)})}{(1+h)^3-1}$

[grand pond]

Monarch of Eternal Night

[golden cloak]

Now numerator is $sin(\pi+\pi.h)=-sin(\pi.h)$

Mb

[grand pond]

Monarch of Eternal Night

[golden cloak]

Then use sin(ax)/ax=1 value as well as binomial theorem in denominator

We can also use a^3-b^3

Or binomial

Both works

That's because to get indeterminate form

Sin(pi.x) when x->0 is 0

But for me they taught the value inside sin should be zero

That's why I took 1+h

Now as h->0, inside also become zero

So now sin (ax)/ax=1

[midnight plank]

@sturdy escarp Has your question been resolved?

[sturdy escarp]

I deeply apologize but pls explain like im 5

🎀

[midnight plank]

@sturdy escarp Has your question been resolved?

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[last slate]

Prove
$A \cap (A \cup B)' = \phi \$
Where A and B are any two sets

[last slate]

I need to prove this using their definitions

[autumn canopy]

What's their definition?

[last slate]

Like starting with x∈

[autumn canopy]

Is there any further information about A' and B'?

[last slate]

What is the term used to call this method, I'm sorry

[autumn canopy]

x \in

[last slate]

No sir

Pardon?

[autumn canopy]

Ah, ' means complement?

[last slate]

What is the correct notation?

[grand pond]

Kepe

[last slate]

I have done some working but I don't know if it's right

[autumn canopy]

Can you show that? We might continue from there then

[last slate]

Ok please wait

I made a mistake in the question sorry

[grand pond]

GinNBread

[junior flower]

i was very confused because i reacted to a message and then couldn't see it but now i realize the message got deleted

[autumn canopy]

Do you know de morgan's laws?

[grand pond]

Kepe

[last slate]

My internet is so slow

My problem is I used the parentheses specifically to reach the answer. My question is how should I appropriately use parentheses

[last slate]

Does that make any sense?

[autumn canopy]

Are you referring to this step?

[last slate]

Yes

[autumn canopy]

The first line is equivalent to [\text{(x in A) and ((x in A') and (x in B'))}] and when having two and's, you can use the associative property: [\text{((x in A) and (x in A')) and (x in B')}]

[grand pond]

Kepe

[autumn canopy]

That's how I would do it

[last slate]

Oh shoot

Associativity

You're right

[autumn canopy]

Thought I think it's not wrong as you did it too?

[last slate]

Yes

Thank you

[autumn canopy]

Might wait for what @junior flower has to say (if she is still here?)

[last slate]

Hey

[radiant tiger]

i think u pinged the wrong layla

[autumn canopy]

oh, sry

[last slate]

I have another question

[radiant tiger]

no problem 😭

[last slate]

I think that this one is wrong

x not in (A and B)

That part

Right?

[grand pond]

Kepe

[last slate]

x not in (A and B)
x in (A and B)'
x in A' or B'

[autumn canopy]

You can also write it like they did it

[last slate]

Did I do something wrong?

Because it covers the universal set in Venn diagram 😭

[autumn canopy]

It's correct. But it doesn't cover the universal set

The middle will still be missing

You can try drawing it

It will look like this

Now if you read this again,

you also have the requirement "x in A u B"

So the entire area around the two circles falls away

[last slate]

What does \ mean

[autumn canopy]

"without"

[last slate]

oh -

[autumn canopy]

Yes

[autumn canopy]

So yeah, you did everything correctly but went wrong in saying

Because it covers the universal set in Venn diagram

[last slate]

So the definition given in text is wrong

[autumn canopy]

No it's correct too

[last slate]

It's says x not in A and B

[autumn canopy]

Ah, that part. Yeah, it should say {x in A u B | x not in A n B}

You want to represent the shaded part of Figure 1.11

[last slate]

Yes

[autumn canopy]

Like this, everything around the shaded part is included too (except A n B)

[last slate]

I just wanted to find a simple way to represent it, sorry

Thank you for your time

.close

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[autumn canopy]

Btw, it's generally a bad idea to define a set using {x | ...} without specifying what x is in. Look up Russel's paradox (or Barber's paradox).

You only do that in non-rigorous settings where the reader is assumed to know what x is in

[last slate]

Hey

Is there a good resource to learn sets

My guide is not cutting it

I have been most things outside and from this server. God bless you all

[autumn canopy]

https://www.khanacademy.org/math/ncert-class-11/xea4762213f311c5e:sets

He does have some stuff on it, it seems

Other than that, just Google I guess

[last slate]

Oh boy

It's time to grind khan academy again

[autumn canopy]

#proofs-and-logic message

[autumn canopy]

Though not sure if he has much on proofs

[last slate]

I'll still spend some time on it the unit tests help

[autumn canopy]

Depending on your class the proof exercises are also really important

[autumn canopy]

So yeah, just google "set proofs" and I'm sure you'll find something

[last slate]

I've been struggling with proofs

[midnight plank]

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[quiet spire]

Hello! I'm trying to study some statistics in my free time and I have a question about multinational coefficients. My book explains binomial coefficients (regular combinations) as an attempt to perform an experiment $k$ without replacement, and I get that analogy; however, when it comes to a multinomial coefficient, I struggle to use the same analogy, as for some reason with multinomial coefficient, unlike with the binomial, we start to account for the items that are left out (unchosen), and I cannot understand why, since the derivation of the multinomial coefficient from the binomial coefficient (which I have attached) seems to omit the unchosen items.

[grand pond]

RIGIK93

[runic hamlet]

from those which are left out at first you want to choose in the next go

[midnight plank]

@quiet spire Has your question been resolved?

[quiet spire]

? I'm sorry, but I don't fully understand

I understand that part, however, what I do not understand is why we are choosing from those unchosen too (conceptually)

In a regular binomial coefficient, it is (n-1)(n-2)(n-3)/3!, so we don't really care about the "unchosen" items; however, with the multinomial coefficient it does not seem to be the case

So this is why I'd like to find an appealing analogy

[runic hamlet]

that formula is the same as n!/(3!(n-3)!)

so the unchosen items also "appear" in the formula

[runic hamlet]

well ok not the same cause your formula is wrong, but this would be the correct one

intuitively, not choosing items is the same as saying: I pick those elements as those I dont want to choose. so you "chose" them as your unchosen items

that sounds weird but hopefully makes sense after reading it a couple of times

[quiet spire]

Yeah, sorry the corrected formula would be:

$$
n(n-1)(n-2)/3!
$$

[grand pond]

RIGIK93

[quiet spire]

How I view this is:
We have n choices when we are picking the first object, then n-1 for the second, then n-3 for the third, and we also divide by the number of possible arrangements. I don't understand where in this reasoning unaccounted items are included.

[runic hamlet]

lets say we have 10 objects. and we want to pick 3 of them

then we could say, ok 10 for the first, 9 for the second, ..

like you said

or we could say, I instead pick 7 objects and afterwards choose the leftover 3 items as the actual 3 items I wanted to choose

which would be n(n-1)(n-2)...(n-6)/7!

[runic hamlet]

to get from this formula to the one I wrote, multiply by (n-3)! on top and bottom

$\frac{n(n-1)(n-2)}{3!}\cdot\frac{(n-3)!}{(n-3)!} = \frac{n(n-1)(n-2)(n-3)!}{3!(n-3)!} = \frac{n!}{3!(n-3)!}$

[grand pond]

Denascite

[midnight plank]

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[bright grail]

guys am i allowed to ask z-transform question here yes or no?

[fiery plover]

dont ask to ask

[bright grail]

i dont wnat to get banned

[fiery plover]

worst that can happen is someone not available who knows how to answer

[bright grail]

if it's nota llowed

[obtuse basin]

You will not get banned by asking to ask

[subtle zinc]

why would you get banned for that lol

[prime rapids]

!da2a

[midnight plank]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[golden cloak]

@bright grail just post the question

[bright grail]

what would the process look like if i inverse transform this

this is my question pls dont ban me if not allowed

[golden cloak]

Relax

Nothing of the sort

[midnight plank]

@bright grail Has your question been resolved?

[obtuse basin]

What exactly do you mean by transforming?

[untold gale]

I do it via table…

There is a definition but it’s a yucky surface integral idk your purpose for this if it’s just to learn the math you can do it by definition if it’s for signal processing … just use a table bro

[golden cloak]

@bright grail

[bright grail]

i am bro

but i need to ask something

when you do partial fractions

are you expressing the denominators with complex roots as 2 binomials multiplied or only 1 quadratic

that's where im stuck right now

solving for the coefficients

or you use cover up method?

[untold gale]

Well honestly the goal is to get into a form that matches the table… you can split up partial fractions into fractions of any residues that are multiplicative elements of the the polynomial in the denominator… I’d suggest going down to binomials if convenient as there are pretty convient rules in that table for them

If you need a review of partial fractions (as in you don’t remember how to do it … it’s probably quickest to watch a video example)

[bright grail]

i know how to do it

but not using cover up method

for z transforms i noticed almost all the time people use cover up method

why is that so?

[untold gale]

Use whatever method you want man … dont worry about what other people do so much if it works it works

If you can get a right answer you can. Get a right answer

https://math.mit.edu/~jorloff/suppnotes/suppnotes03/h.pdf

This is the method they use it’s quick so I get the utility

[bright grail]

yeah that

ok man i will use that starting now

thanks

i am used to just making a system of equations and get all the coefficients

[bright grail]

can i ask what u are searching to get acces to this

what keywords

[untold gale]

Idk I probably searched “Heaviside cover up method for partial fraction decomposition “ or something like that

Knowing the full name of the method and what it’s used for is generally enough for a good google search

[midnight plank]

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[midnight plank]

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[last slate]

Why and how can we do this?
Because we are changing the elements so the matrix won't remain the same only right so how determinant would be same?

[subtle blaze]

it's one of the properties of determinants

when you add rows together the determinant doesn't change

[last slate]

But here we didn't add rows no?

[subtle blaze]

we added row 2 and row 3 to row 1

[last slate]

We added elements of same row you mean?

Here we SUBTRACTED the same column elements
Still the determinant won't change?
@subtle blaze

[tiny drum]

correct

[last slate]

Can I multiply 2 columns tho?

[tiny drum]

they are doing row operations. but no, you cannot

[last slate]

Oh damn, thanks man
Btw is there any proof available that if I add or subtract 2 columns in a matrix
Determinant don't change

Because it's hard for me to digest something as it is unless proof isn't given

I am not asking to prove this
Just asking, is there any proof available
If yes, then I'll try myself for fun

[tiny drum]

I'm sure there are proofs of that, yes

[last slate]

Thankx 🥳🥳🥳🥳🥳🥳🥳

[last slate]

Gracias

[tiny drum]

yw

[last slate]

@tiny drum last help

Can u share a site or pdf or can u name anything where I can get ALL properties of matrices and determinants?

[tiny drum]

sorry, no. try asking in #linear-algebra

[last slate]

Real, thanks man!

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[marble plinth]

The , means?

[sharp coral]

a comma is used to separate every 3 digits before a decimal point

[marble plinth]

And is called?

[sharp coral]

it doesn't have as much of a common name (unlike the decimal point it doesn't change the meaning of a number), although it acts as a "thousands separator"

some styles prefer to use spaces rather than commas or just leave it out entirely

[marble plinth]

k.

[midnight plank]

@marble plinth Has your question been resolved?

[bitter tide]

whats not answered?

[midnight plank]

@marble plinth Has your question been resolved?

[midnight plank]

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[twilit flint]

help

[twilit flint]

i conceptually dont understand how to do it

[tribal temple]

"it" referring to? everything, or a particular part?

[twilit flint]

like i know suvat

and that

but when you use s = vt -0.5at^2

my brain dies on choosing acceleration

bc in one part the acceleration is g and the other is -g

in question 1 part a

[tribal temple]

Cool cool

[twilit flint]

my exam is this month and i do fm im prolly cooked

[tribal temple]

You could, e.g. find the "additional" height the ball rises to before it starts to drop again, then use this to find the velocity on hitting the ground, for example

[tribal temple]

Awwww, did you have the maths one today?

[twilit flint]

nah im year 12 right

icl im confident on everything bar these little aspects of suvat

pure carries me

[tribal temple]

Oh

[twilit flint]

i see that makes sense

but im wondering right

the mark scheme did it in one equation

[twilit flint]

this

[tribal temple]

How did they do it?

[twilit flint]

ill show you

lie they chose g

and my brain dies there

right because they set downwards as positive

bc overall displacement is postiive according to them

so we know that

meaning they saying acc

wait

acceleration is always down

wtf

then how come im using negative g before when it goes up and its right

[tribal temple]

Hmm, those arrows what on earth-

[twilit flint]

bro how has mechanics got me high

[tribal temple]

Nah, mechanics is generally pain tbh, unless you get someone who's really good at teaching it

[twilit flint]

because my initial instict is in the first section

[twilit flint]

got you bro

[twilit flint]

first instict* is because the ball is rising

it goes against g

so is decelerating

so in that part g is negative

then after reaching its maxmima

accelerates with g

so its now postive

[tribal temple]

also seems like they're choosing a = -g here, or expecting you to use that(?)

[twilit flint]

yeah aswell

[tribal temple]

Which makes sense, as you're shot up, gravity is acting downwards throughout

[twilit flint]

mabye because they took gravity downwards as negative

yeah like displacement

mabye im overthinking it

[tribal temple]

Actually wait no they didn't

[twilit flint]

they did tho

-0.5at

became positive

no negative time

hopefully

[tribal temple]

Yeaaaa I really don't know about these

[twilit flint]

ah i see

dont worry you helped

thanks really anyway man

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[short cove]

can someone help me please

[short cove]

I am very confused

i figred out the first part but not the other

[midnight plank]

@short cove Has your question been resolved?

[short cove]

please help me

[midnight plank]

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[midnight plank]

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[obtuse wing]

I have to use partial fractions to evaluate this fraction. When we divide the nominator by the denominator we get f(x) = (2x^3 - 4x^2 -x - 3)/x^2 -2x -3 = 2x(x^2-2x-3) + 5x - 3.

[obtuse wing]

My question is why do we rewrite is as 2x + (5x-3)/x^2-2x-3

And not 2x(x^2-2x-3) + 5x - 3

[tribal temple]

This is what the numerator is equal to, so when you replace and split up, it…

[tribal temple]

…turns the fraction into this expression

[obtuse wing]

You mean we get 2x(x^2-2x-3) + 5x - 3 from dividing the numerator by the denominator, and we can divide this expression by x^2 - 2x - 3 to get the fraction?

.close

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[rapid cairn]

i need help in this problem

[midnight plank]

@rapid cairn Has your question been resolved?

[rapid cairn]

<@&286206848099549185>

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[livid crystal]

Hey guys
I get the stuff in green but then the red stuff happens and idk what it means 😭

[livid crystal]

Like if I was given a problem like that I wouldn’t be able to do the red stuff ykwim

So can someone explain what it is

[torn compass]

Tbh it should specify that B is mid point

[livid crystal]

Oh ok

[torn compass]

Basically, B is mid point and distance of AB = BC
AC = AB + BC
= 2(AB)

[livid crystal]

Okay

Got it

I see now

[livid crystal]

Can I say AC = 2(BC) instead of AB

Does it matter?

[zinc spear]

Ofcourse

[midnight plank]

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[abstract cairn]

Hey how do I prove that this thing is a trapezoid (using vectors)

[abstract cairn]

I drew a really vague sketch and also proved that diagonals are perpendicular

Then I also tried doing something something equals 180° but it didn't turn out right

[wary epoch]

In LaTeX, please?

[abstract cairn]

What?

[abstract cairn]

Don't mind the language only the coordinates are important

[last slate]

There will be only 3 vectors

[wary epoch]

Wait, why did you prove that the diagonals are perpendicular?

[abstract cairn]

huh

[last slate]

Like every other vector formed by lines will be collinear to these three

[abstract cairn]

there was another question asking me to do that lol

[last slate]

Phh sorry

I read the question wrong

[abstract cairn]

wait wdym three 😭 its a trapezoid isnt there supposed to be 4

oh

[last slate]

Ohh sorry mb lol

I read it as parallopiped

Sorry

[abstract cairn]

ohhh

okok

i searched up that a pair of adjacent angles must be equal to 180 degrees and that would make it a trapezoid

[last slate]

2 vectors collinear and one side perpendicular to both of them

[abstract cairn]

but when i tried doing it that way it didnt rlly end up being 180

[abstract cairn]

why perpendicular?

[last slate]

Not perpendicular sorry lol

[abstract cairn]

huh im confused 😭

[last slate]

Damn sorry i read it as right trapezoid

Only two sides need to be parallel any two and other two should not be parallel

[abstract cairn]

hah i think its time to rest 😭

[abstract cairn]

would this prove?

cuz like what if its another shape

or is only trapezoid like that

[last slate]

Trapezoid is defined like that

It has two parallel sides and two non parallel sides

[abstract cairn]

how do i prove that they're parallel

[last slate]

Ya i only slept 4 hrs in 2days 😢

[last slate]

Wait

U need to

Find vectors of side

[abstract cairn]

ah what

[last slate]

Subtract v1 with v4

And v2 worh v3

See v1-v4 and v3-v2 are scalar multiple of each other

Did u get it ??

[abstract cairn]

wait

what did you do with them

howd they turn into that

shouldnt it be 2i+4j?

whys it 10

[last slate]

I subtracted v1 with v4

And v2 with v3

[abstract cairn]

oh wait