help-0

[pseudo ice]

Is that like $\operatorname{Frac}(\bZ[x])$ or?

[ocean seal]

chartbit

[inner path]

no, i'm an highschool student and we can solve that just with bezout theorem and congruence i think

We can resolve maybe $/frac{(n^2 + 1)^{2}}{n^{3}(n^{3}+2n)}$ and if $n^{3}$ and $n^{3}+2n$ are coprimes with $(n^2 + 1)²$ we resolve this

[ocean seal]

phoestaclies

[inner path]

sorry my fraction is not good

[pseudo ice]

backslash for the fractions

\frac{top}{bottom}

[inner path]

We can resolve maybe $\frac{(n^2 + 1)^{2}}{n^{3}(n^{3}+2n)}$ and if $n^{3}$ and $n^{3}+2n$ are coprimes with $(n^2 + 1)²$ we resolve this

[ocean seal]

phoestaclies

[inner path]

ok better

thanks

but don't know how to fix it to

Ok i think i solve this tell me if I'm wrong

[pseudo ice]

You've shown that if you have a common integer factor of both that said factor must be 1, fair enough

Matter of fact I think that's fine for any ideal you choose to quotient out by?

[inner path]

? sorry i don't understand ur question ? my english is not very good, still better than my latex i think

[pseudo ice]

Ignore this bit for now

[pseudo ice]

You're trying to show here that there's no common [positive] integer factor barring 1, right?

[inner path]

yes

[pseudo ice]

Cool, that's fair enough, and clearly they don't have any common polynomial factor, as if $p$ divides $(n^{2} + 1)^{2} = n^{4} + 2n^{2} + 1$ and $n^{6} + 2n^{4}$, then $p$ would divide any combination of both, including, say $n^{2} \cdot (n^{2} + 1)^{2} - (n^{6} + 2n^{4}) = n^{2}$

[inner path]

yes

great !

thanks arthur read

[pseudo ice]

Actually wait error, me no math

[ocean seal]

chartbit

[pseudo ice]

Not quite clearly then

[inner path]

this is true if a equal 1 so it's ok with that

[pseudo ice]

But then I guess you can make an argument along those lines for polynomials anyway tbh

[inner path]

yes I wasn't sure because i feel like i can do that with all polynomials

[pseudo ice]

actually, if $p$ divides $n^2$, then from there you know it divides $n^{4} = n^{2} \cdot n^{2}$ and therefore you do get that $p$ divides 1, right?

[ocean seal]

chartbit

[inner path]

yes

it's what i did before

[pseudo ice]

From it assuming to divide $(n^{2} + 1)^{2}$, just needed to finish off the steps for it

[ocean seal]

chartbit

[inner path]

thanks i will look at it and well writen all of that, (thanks for the latex also)

[pseudo ice]

No worries, have a good one!

[inner path]

.close

[lone heart]

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[fathom girder]

Hello, is this correct?

[fathom girder]

The answer sheet says the answer should be 1/25a⁴-1/49b²c²

I don't know where the a⁴ came from, could be an incorrect answer, though

[hollow sparrow]

seems correct for me

[inner path]

don't know, it's an identity in the form $z²-x² = (z+x)(z-x)$ with $z = 0.2a$ and $x = 1/7bc$ so you're right

[ocean seal]

phoestaclies

[inner path]

the solution are $0.2²a² - 1/7²b²c²$ and it's your result

[ocean seal]

phoestaclies

[fathom girder]

Alright, thanks for confirming it with me

.close

[lone heart]

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[wraith marlin]

how do I solve this?

[tacit arch]

Count the choices for each digit

Or just write them all out

There are only 4! permutations

[lone heart]

@wraith marlin Has your question been resolved?

[lone heart]

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[steady basin]

i have no clue

why

[mortal trellis]

what does skew-symmetric mean

if $A=\begin{pmatrix} a & b \ c & d\end{pmatrix}$, what condition on $a,b,c,d$ does that give

[ocean seal]

Denascite

[steady basin]

if A is a square matrix, then the transpose of A is equal to - A

[steady basin]

wdym?

[pseudo ice]

As in set A to be that matrix [for the 2 by 2 case] and see what happens

[steady basin]

^

[mortal trellis]

yes

so a=-a and d=-d

what does that mean

[steady basin]

acc no

um

[pseudo ice]

acc yes

[steady basin]

well a could anything

[mortal trellis]

that was correct

2a=0

so a= ?

[steady basin]

a is 0

[mortal trellis]

yes

[steady basin]

chartbit

remeber this question earlier

we did?

then could have i just said that ap was 0?

since ap - ap is 0

?

but we did the same thing here no?

[pseudo ice]

You have the statement ap=ap

[steady basin]

ye

here we have a = -a so we did 2a = 0

[pseudo ice]

If you took away ap from both sides, that just becomes 0=0

[steady basin]

ye

surely thats correct since the matrix is 0 in the main diagonal

and 1 in the other

[pseudo ice]

If instead those equations ended up being ap = - ap then you would be fine

[steady basin]

mhm

but here

a doesnt have to be 0 no?

[pseudo ice]

That was a specific choice of matrix

[steady basin]

a can be anything

[steady basin]

i see

[pseudo ice]

It does: any real number that's equal to its negative is zero

That's the only number whose negative is the same as itself

[steady basin]

true

true

true

[pseudo ice]

(well, additive inverse strictly speaking, but you know what I mean there)

[molten pivot]

Why does the additive inverse of a number have to be a number? Think about that.

[pseudo ice]

Huh? My comment was a clarification that "negative" wasn't really a good term to use

[ruby current]

as opposed to what?

[steady basin]

could someone mark this for me plz

each step

[ruby current]

seems correct

[pseudo ice]

Yep happy with it

[steady basin]

good progress

[lone heart]

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[craggy depot]

This is the explicit rule

I have an answer but I’m not sure about it

[lone heart]

@craggy depot Has your question been resolved?

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[high ether]

find the nature of the series sum of an

[high ether]

the series in the denominator seem to go to infinity so an ->0

and i think it does so pretty slow so i am guessing it's divergent

[plain flame]

it does it really quickly

[high ether]

as quickly as the series sum of 1

[plain flame]

$\sqrt[k]{k} > 1$

[ocean seal]

Gijs

[high ether]

yeah but very close to 1

[plain flame]

for k > 1 at least

[high ether]

so an is almost like the harmonic series

[plain flame]

$\frac{1}{\sum n} \neq \sum \frac{1}{n}$

[ocean seal]

Gijs

[high ether]

its not sum of n

its sum 1/sum of 1

[plain flame]

thats not the point

[high ether]

cause k^1/k is close to 1

so its 1/n

so harmonic series

anywayyyyy

[plain flame]

a sequence is not a series

[high ether]

to the maths

what do we do

[plain flame]

a_n is a sequence

its not like the harmonic series

[high ether]

whats the solution

[plain flame]

because its not a series in the first place

[high ether]

i mean the series of an ofc

anw, how do i approach this

[plain flame]

$\sqrt[k]{k} \geq 1$

[ocean seal]

Gijs

[high ether]

so?

<@&286206848099549185>

[plain flame]

!15min

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[high ether]

i thought its been 15

[unkempt sundial]

idk if it is correct, but i used the ratio test and reached that it is < 1

ive only recently learned series

[high ether]

how

[plain flame]

this isnt about a series

its about a sequence

[high ether]

no it's the nature of the series an

the seq an goes to 0 it's obvious

[plain flame]

a_n is NOT a series

[unkempt sundial]

they want the nature of $\sum{an}$ no?

[ocean seal]

alihsaas

[high ether]

yes

[plain flame]

where is the series notation\

[high ether]

read my question, the notation was skipped

[unkempt sundial]

watch it all be wrong 🥹

[high ether]

def not a proof

n/n+1 <1

[unkempt sundial]

im gonna join you in waiting for a proof then

[high ether]

yet the harmonic series diverges

[lone heart]

@high ether Has your question been resolved?

[thorn monolith]

i think i found something that can be accepted as a solution

@high ether

and since limit of this is not 0 (its equal to inf), we found a minor series that is divergent thus our series is divergent too

nvm its not the general term

but similiarly if you take limit of this , sum goes to infinty right

and since Sp is greater than inf

then it must be infinity simply

[lone heart]

@high ether Has your question been resolved?

[lone heart]

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[keen socket]

@mellow saffron

[keen socket]

so i have to make a presentation on giralamo cardano for my grade 12 advanced functions class

and i dont understand his mat

can you explain it so that i can make a presenation on it?

<@&286206848099549185>

@lone heart

<@&268886789983436800>

[sly mantle]

pls dont ping mods for math help

[keen socket]

what do i ping for math help

[plain flame]

nobody

you wait

[tacit arch]

Help channels are for math questions, typically homework from textbooks. Make your own presentation.

[keen socket]

so noone would explain his formula?

[plain flame]

maybe they would if you posted it

dont ask for help

ask questions

this server is not a place to match people with personal servants

[keen socket]

can someone explain this

[tacit arch]

That's unreadable

Screenshot the whole page and question

[keen socket]

i didnt ask for anyone to do anyhtinf for me

i just wanted an explanatiob

[gusty gorge]

you want an explanation for how the cubic formula is derived?

Wikipedia has a very good explanation of it

[modern topaz]

riemann blocked me again

[lone heart]

@keen socket Has your question been resolved?

[tacit arch]

What do you want explained

[keen socket]

The whole equation and how I would go about using it to find roots

[gusty gorge]

you don't know how to read the formula?

or you don't know where it comes from

[tacit arch]

It's the same way you use the quadratic formula except with different powers and more terms

Do you understand cubic powers and cubic roots?,

[keen socket]

im in grade 12 so i only know like long division and synthetic to get roots so i dont understand a single thing of this. i only get that the dpressed wuqation is the euqation without the exponent 2

[gusty gorge]

do you know what a cube root is

do you know what a square root is

[tacit arch]

Can you answer our questions

[lone heart]

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[gritty pond]

I got du = dx but I want to include the left x in my du. How can I do that?

[alpine sable]

use x=u-1

then expand

[gusty gorge]

kinda defeats the whole purpose of u substitution

oh wait no it doesn't

im still more of a fan of u = (x+1)^2

[gritty pond]

That is wack

[trim valve]

@gritty pond are you getting it

[gritty pond]

Yeah but that's weird

I never thought of it that way

[trim valve]

Ok

Let U = x + 1

And x = u - 1

Substitute them !

Actually your gonna have something like this ∫(u-1)(u⁸)dx

[trim valve]

Then try to differentiate u with respect to x and du = dx so that means any where you see dx you put du.
After that you integrate.@gritty pond

[keen socket]

Noq

This is my channels

🥰😃

[trim valve]

But you have to multiply this
(u-1)(u⁸)

you get something like this :
u⁹- u⁸ then integrate .

[lone heart]

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[lone heart]

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[steady basin]

got up to here

and idk wat to do next

[tacit arch]

What does the answer sheet say

[plain flame]

use associativity

also, skew symmetry needs to be applied

which means a matrix B is skew symmetric if B^t = -B

[steady basin]

this was tricky

but i got it

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[sudden hinge]

hi whats troubling you?

[kind nebula]

hi i dont know how to find the volume of the pool

im not very good at maths any help would be good ❤️

[sudden hinge]

the pool will be a cylinder. do you know the formula for the volume of a cylinder?

[kind nebula]

im not sure i do

[sudden hinge]

its the area of the top surface of the cylinder multiplied by its height

[kind nebula]

so how do i find the height

[sudden hinge]

the height is given to you in the problem

[keen mason]

The question

‘90cm deep’

[kind nebula]

oh so the height is 90 cm

[sudden hinge]

right now you also need the area of the circle

[wary stream]

....That is a really shallow pool

[kind nebula]

yeah gotta be a made up scenario

how do i find the area of the pool?

[sudden hinge]

well whats the area of a circle?

[kind nebula]

for that would it be 3.14

[sudden hinge]

yeah or pi to be exact

[kind nebula]

true

so now that i have the height which is 90cm and the area which is 3,14 how do i find the volume of the pool

[keen mason]

Yea I think it’s supposed to be like a jacuzzi

[kind nebula]

V=πr2h=π·12·90≈282.74334??

is the answer for the volume 282.74334???

[keen mason]

What radius did u choose

Root12?

[kind nebula]

2m

is the radius i chose

is that wrong

????????????????

<@&286206848099549185>

2827433.39?

[keen mason]

Ok

If 2m is the radius

The area is pi * r^2

Which is 4pi

And v = pi * r^2 * h

H = 0.9 Meters

So v = pi * 4 *0.9

[kind nebula]

how does that work

11.3097335529??

[keen mason]

Well yea

I don’t have a claim for on me so I can’t verify by 4 * 0.9 = 3.6 so seems right

[kind nebula]

and then how would i figure out how much water i need to fill it

?

i only need to know the form for this tan im finished

[keen mason]

That

Is how much

The volume is how much

Ok well not really

1 m^3 = 1000L

We hAve 11.36 m^3

So times 1000 by 11.36

[kind nebula]

11309.733529 litres of water??

[keen mason]

Yep

[lone heart]

@kind nebula Has your question been resolved?

[lone heart]

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[slow canopy]

Can someone help me understand how the (y-1)(y^2 -1) denominator becomes the one being pointed to

in other words, how does

(y-1)((y^2)-1)

simplify to

(y-1)^2 * (y+1)

[wary stream]

$(y^2-1) = (y - 1)(y+1)$

[ocean seal]

dldh06

[slow canopy]

ohhhhhhh

thank you

.close

[lone heart]

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[noble granite]

<@&286206848099549185>

[alpine sable]

have you tried setting up an equation?

[noble granite]

(3/11)n + 136 = (7/4)(n - (3/11)n - 136)

Not sure if this one is right

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[noble granite]

Oh I'm so sorry

[alpine sable]

equation looks right

are you having trouble solving the equation?

[noble granite]

yes

is the answer 440

440 students?

[alpine sable]

don't think so

[alpine sable]

so try to simplify this equation as much as you can

[noble granite]

i don't really have much knowledge about word problems

this one is hard for me to understand

[alpine sable]

doesn't seem like the problem is you not being able to understand the word problem

bc you were able to accurately write an equation based on the word problem

[noble granite]

(3/11)n + 136 = (7/4)(n - (3/11)n - 136)
(7/4)n - (7/4)(3/11)n - (7/4) * 136 = (3/11)n + 136
(7/4)n - (21/44)n - 102 = (3/11)n + 136
(21/44)n = 238
n = (238 * 44) / 21
n = 440

is this one right?

440 = 440

i don;t really know

[alpine sable]

(7/4) * 136 != 102

[wary stream]

(7/4) * 136
Check that math again

[noble granite]

(7/4)* 136 = 153?

[alpine sable]

uh no

[noble granite]

gosh i'm bad

[alpine sable]

it's alr take it slowly

[noble granite]

why so i still get 440

do*

well i think i could

settle this problem for a bit

how about this one?

my answer is 6.5 hours

[gusty gorge]

he's done 15 km, then at 42 minutes, he's done 5 km, then at 54 minutes he's done 4 km, and at 66 minutes he's done another 3 km and so on

78 minutes another 2

and 90 minutes another 1

so I'd say 90 minutes

6.5 hours seems a little long

[wary stream]

then at 42 minutes, he's done 5 km, then at 64 minutes
You messed up some math here, you added 22 minutes

[gusty gorge]

hmm?

maybe I did

wdym by added 22 minutes?

[wary stream]

42 -> 64

22 minutes

[gusty gorge]

oh whoops

yeah I was wondering why it didn't come out to a nice clock multiple

[noble granite]

so what could be the final answer?

[gusty gorge]

90 minutes

[noble granite]

ohh okay, thank you!!

how about this one

mine's 39/117

[rigid plover]

yeah thats right !

[noble granite]

ohh okay okay thanks!

[rigid plover]

anytime

[noble granite]

sorry if i have many problems

im just making sure my answers are correct

my answer to this is 24 students

[gusty gorge]

seems right

[noble granite]

(41 + 22) - 9 = 54
78 - 54 = 24

right?

[gusty gorge]

yeah that's basically how it's done

[noble granite]

oki oki

how about this one

my answer is 1.5 meters

1.18m + (8*0.04m) = 1.18m + 0.32m = 1.5m

[tall holly]

why did u do 8 * 0.04?if it's 14yrs - 7yrs

[noble granite]

oh my mistake

So is it 1.46m?

[lone heart]

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[quick sinew]

Help

[quick sinew]

Confused

[gusty gorge]

tell your teacher to not write such ambiguous questions

For example

[quick sinew]

Lol

It’s suppose to be grade 12 review for pre calc

Lol

[gusty gorge]

$g(x) = \frac{\sqrt[3]{x}}{2(7+\sqrt[3]{x})}$ and $f(x) = 2x$ work

[ocean seal]

Saccharine

[gusty gorge]

but your teacher will mark it wrong for dumb reasons

[quick sinew]

What?

[wind cloak]

What they're getting at is that the question has multiple solutions

Often laughable

[gusty gorge]

just a poorly worded question

and one I've seen so many times it's annoying at this point

[quick sinew]

Huh

So you guys don’t know?

[wind cloak]

It's not that we don't know

It's just that we don't know what your teacher expects

[quick sinew]

Oh

Lol

What about this one

[pseudo ice]

There's one "obvious" answer to the question that the teacher probably wants, but as per above there are many which are valid too

[gusty gorge]

if you submit what I wrote, the teacher will be like "don't put linear functions"

and then we'll get e^x and log x

[wind cloak]

Most likely $f(x) = \frac{x}{7 + x}$ and $g(x) = \sqrt[3]{x}$

[ocean seal]

NEONPerseus

[median oar]

Lmao this is actually funny

[quick sinew]

Computer science is hard

Just saying

Don’t take it

[median oar]

It depends what kind of environment you’re doing these questions in

If it’s just an exercise with nothing on the line you want to point out it’s ambiguity

[quick sinew]

Alright I’m going to have to buy a tutor

[wind cloak]

No this ain't hard, it's just that the question isn't clear enough

[median oar]

If it’s an exam you want to do the same but also put down the expected answer

You don’t wanna lose marks due to being a smartass

[quick sinew]

Can you help with this?

[median oar]

But you also don’t want to be wrong

[gusty gorge]

actually an even better example of a great function to put in there is g: R -> Rx{0}, g(x) = (x, 0) and then f: Rx{0} -> R: f(x, y) = x

computer science people love those random cartesian products

[wind cloak]

Do you have a basic idea about composition

Of functions

[quick sinew]

Can I get help with this?

[quick sinew]

Yes

[median oar]

What have you tried

[quick sinew]

f(g(x))

=

[wind cloak]

So you just need to find a function such that $2 \times f(x) + 1 = 4x^2 + 4x + 8$ this is something you'd get by intuition tbh

[ocean seal]

NEONPerseus

[gusty gorge]

so actually a neat thing you can do is note that the equality $f \circ g = h$ can be satisfied with something like $f = (h \circ g^{-1})$ and therefore $f \circ g = (h \circ g^{-1}) \circ g = h$

[ocean seal]

Saccharine

[gusty gorge]

which turns it into something more mechanical and boring and time consuming

[quick sinew]

Bro wtf

Y’all are wasting my time

[median oar]

Relax

[quick sinew]

.close

[lone heart]

Channel closed

Closed by @quick sinew

Use .reopen if this was a mistake.

[median oar]

Just start here

[wind cloak]

Damn

[median oar]

What is this equal to

[wind cloak]

Sunk cost

[lone heart]

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[runic forge]

is this correct>

[runic forge]

?

i filled in the y

[gusty gorge]

the y filled in doesn't look right

I guess it's c?

y decreases and then increases

but it increases more

[runic forge]

wait youre saying i did the y wrong?

i basically took the differences and made an equation to find it,
5 - (-2) = y and so on

this is the original problem

[gusty gorge]

the differences are between the y values

not hte y values and the x values

[runic forge]

ohhhhhhhhhh

wait so then is finding the y values not possible?

would the answer be c? the values are increases non linearly as x increases

any help??

<@&286206848099549185>

[gritty talon]

السلام عليكم @runic forge

[runic forge]

و عليكم السلام ورحمة الله وبركاته

[gritty talon]

تريد أن نكمل بالانجليزي أم بالعربية؟ 😁

[runic forge]

englishh

[gritty talon]

OK then

So let us assume first that this function is linear

As far as I understand (because I didn't study maths in English) the first difference is basically taking f(6)-f(5) for example

[runic forge]

mhm

[gritty talon]

So for a linear function, even an affine function for the matter, the first difference between x1 and x0 will always be a*(x1-x0), where a is the slope

That's because f(x) =ax for all x in IR

[sage quail]

Never seen such type of question before

[gritty talon]

In this case, all the xs are consecutive integers, that means that the 1st diff should be equal to the slope, which is a constant, but as you can see, the slope is changing

[sage quail]

Yea

[gritty talon]

That means that we should rule out the possibility of a linear function

[sage quail]

Yupp

[gritty talon]

Now for the second part, is it decreasing or increasing?

[runic forge]

it seems to be increasing?

[gritty talon]

Yup, can you provide an explanation as to how you figured it out?

[sage quail]

It given f(5)-f(6)=-2 right?

[gritty talon]

It should be f(6)-f(5)

[sage quail]

Alright, thx!

[runic forge]

im not exactly sure how i found out, more of a guess

[gritty talon]

Well, it starts with: f(6)-f(5)= - 2

That means that f(6) is smaller than f(5) by 2

[runic forge]

yes

[gritty talon]

Then f(7)-f(6)=0

That means they are equal

[sage quail]

I conclude f(8)>f(5)>f(6)=f(7)

[gritty talon]

Then f(8)-f(7)=4 that means f(8) is bigger

Yeah, if we exclude f(5), we can see that it is increasing

[sage quail]

f(5) is making problem but

[gritty talon]

Perhaps it is considered as an "initial condition"

[sage quail]

Therefore it's not increasing...

[gritty talon]

Yeah but I guess he has to pick one of the choice there

[runic forge]

wait what

[gritty talon]

@runic forge do you have to pick exactly one answer?

[runic forge]

this is only grade 9 math why is it so confusing??

yes only 1

i mean, it asks for one of the statements that best describes the relationship

[gritty talon]

Wow... Do 9th graders even study functions?

[runic forge]

idk, self taught myself the basics

i doubt others know

[gritty talon]

Cool

Well, you gotta start with plots

Plot a lot of functions

And get a feeling / intuition for their behavior

[runic forge]

oh

whatt

that much??

[gritty talon]

I mean if yiu went the self teaching route

Because in class that would be done for you

[runic forge]

i just went on khan academy and finished the first courses on functions

[gritty talon]

You start out with linear functions and plot it

[runic forge]

yes

thats how i started out

[gritty talon]

Then you go to parabolas

[runic forge]

yes that too

[gritty talon]

Then learn about limits and derivatives

Then start plotting whatever function you want basically

[runic forge]

didnt learn those yet

[gritty talon]

Yeah those are a little advanced

[runic forge]

so for this, can we conclude the answer is c?

[gritty talon]

But they basically are the core of math

Yes

[runic forge]

yea thats what i went with

[gritty talon]

OK then

[runic forge]

man i really need to review slopes

could u help with another question?

[gritty talon]

Yeah, and plots

Sure go ahead

[runic forge]

im asked to plot this equation, and so far i found 3 possible coordinates, are they correct?

[gritty talon]

Yup

You jusy pick an easy x and replace in your equation

[runic forge]

alright

how would i plot this? not enough space on the graph

[gritty talon]

Add me if you want

Well you're forced to pick the bad xs here hhh

[runic forge]

oh

[gritty talon]

Pick fractions

Like 1/3 and - 1/3

[runic forge]

would these be correct

[gritty talon]

Or negative numbera work better

Yeah good job

[runic forge]

alright

[gritty talon]

BTW

All you need is 2 points

[runic forge]

btw if you dont mind me asking, could i ask some further questions in dms? im a little curious on a few things

yes 2 points to create a segment, and you can extend it further

[gritty talon]

Yeah of course, do add me then

May I close this channel?

[runic forge]

yes

.close

[lone heart]

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[tacit arch]

Pain

,w int cot^5(2x)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by riemann#2529

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[tacit arch]

It isn't fun
https://youtu.be/V9NVISCMQGQ

Integrate by parts twice to reduce 6 to 4 to 2

And maybe once more to 0

[tacit arch]

Would be easier if you did u=2x first

[tall holly]

I think u only do that once

so u get (csc^2-1)(cot^4

so csc^2cot^4 - cot^4

then for the left u do u = cot

and u have to repeat for the right

*cot^2?

[lone heart]

@thorn jungle Has your question been resolved?

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[plain heart]

A factory produces electrical components, one after another. The time in hours to make one electrical component is Exp(6).
What is expected time that the first electrical component will be ready?

[plain heart]

The answer I'm getting seems wrong. I get 1/6

[wanton pebble]

what is exp6

e⁶?

[plain heart]

Exponential distribution

[lone heart]

@plain heart Has your question been resolved?

[plain heart]

<@&286206848099549185>

.close

[lone heart]

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[dire gale]

how do I find limits for these kind of question without a calculator

Is there a trick that I could use?

[balmy elbow]

For these, you should just know that the limit of ln(0) is negative infinity.

[balmy elbow]

Should also mention that ln(1) is 0.

[dire gale]

Thank you

.close

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[fathom sluice]

Checking notes, I'm not sure where x^2 + 8x -209 came from, can someone please explain and whether I'm correct?

3. The width of a rectangular vegetable garden is 4 feet less than its length. After a 3-foot cement border is placed around the garden, the area of garden and border is 221 square feet. Find the original dimensions of the vegetable garden.

[lone heart]

@fathom sluice Has your question been resolved?

[lone heart]

@fathom sluice Has your question been resolved?

[gray isle]

its the result of setting up the equation representing

After a 3-foot cement border is placed around the garden, the area of garden and border is 221 square feet

@fathom sluice

[fathom sluice]

OH sorry,

It took so long i solved it myself,

i forgot to close the channel sorry

.close

[lone heart]

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[lone heart]

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[lofty citrus]

how do I find another point on a line equation if I have the line equation and a point on the line?

[echo socket]

Could you show how the exercise is stated if that question is coming from one?

[lone heart]

@lofty citrus Has your question been resolved?

[lone heart]

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[high ether]

A is an orthogonal matrix, can someone explain why this goes to 0

[high ether]

why the rhs goes to 0

they explained below that its because the euclidean norm of any orthogonal matrix is sqrt(n)

but it doesnt really clear up things for me

here's the question for the french readers(tho it doesnt really matter)

and the answr

[marsh rapids]

Passe à la norme puis applique l'inégalité triangulaire. Ça revient à sqrt(p) / p -> 0

[high ether]

norm of the rhs?

[marsh rapids]

Yes

Oh nvm I overlooked the power

[high ether]

and the minus sign makes it bigger than sqrt(p) not less

[marsh rapids]

On est un groupe donc A^p+1 est dans On(R) donc sa norme est encore sqrt (n)

[high ether]

oui je voiss ca

[high ether]

mais l ineg triang ne marche pas..

[marsh rapids]

Si

Maintenant en norme c'est 1/(p+1) * (un truc inférieur à ||I|| + sqrt(n)) <= cst / p+1 -> 0

[high ether]

alors j utilise le fait que |a-b| =< |a|+|b|

[marsh rapids]

Yes

[high ether]

okayy

merciii

et on utilise le fait que 1 n est pas vp pour que I-A soit inversible ouii

?

[marsh rapids]

Sinon tu diagonalise A et tu a une entrée ou tu somme que des 1. Ça va pas tendre vers 0 en moyenne

[high ether]

ah oui

okay

mercii

.close

[lone heart]

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[high ether]

.reopen

[lone heart]

✅

[high ether]

wait

l autre choix pour les vp est seulement -1 oui?

dans R

[marsh rapids]

J'ai pas encore revu On donc si tu le dis

[high ether]

D'accord

[marsh rapids]

Car c'est U inter R ?

[high ether]

U?

[marsh rapids]

|z| = 1

[high ether]

Ah oui je crois c'est ca

ca conserve la norme alors necessairement les vp sont les racines de l unite

[marsh rapids]

À ce moment 1 est la seule valeur propre pour laquelle il n'y a pas de compensation dans la moyenne de Cesaro

[high ether]

oui

mercii de nouveauu

.close

[lone heart]

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[high ether]

if the only proper values for a symmetry s are 1 and -1 how come | s(x)|=|x| only for orthogonal symmetries

[marsh rapids]

Probably a drawing like that if you don't force the direction to be orthogonal to the symmetry space

[high ether]

i dont see what the drawing is representing

also can you show me a non orthogonal projection

[marsh rapids]

It is non-orthogonal

[high ether]

and a matrix associated to one

[high ether]

it's a nonorthogonal symmetry?

[marsh rapids]

Because otherwise I can draw a right-angle at the intersection of s's line and xx'

[high ether]

and for non orthogonal projections?

can you show me one first cause i am having trouble drawing it

also a matrix representing one that is non orthogonal would be also super cool

[marsh rapids]

If it's not orthogonal, you can have a symmetry in a direction that brings x closer or farther away from 0

[high ether]

i m failing to see this geometrically

or mathematically

[marsh rapids]

Well...

An orthogonal projection maintains distance. Because visually you stay on the same circle

[lone heart]

@high ether Has your question been resolved?

[high ether]

can you draw a non orthogonal one

just a vector, and a non orthogona projection

[marsh rapids]

It's the first thing I did

[high ether]

those are just 2 lines

explain what you mean

where's the projection

and where's the vector

write something other than literally 2 lines so i can understand

[marsh rapids]

s symmetry perpendicular to F and parralel to G

F is the vertical, somewhat left-leaning line

G is the line xx'

x' being the symmetric of x by s

[high ether]

okay i got symmetry. I am saying a projection

p^2=p

[marsh rapids]

Oh

Lmao

I overlooked that twice, sorry

[high ether]

its fine😆

[marsh rapids]

Simply stop on the line instead of going through

[high ether]

okay, thank you very muchhhhhhh

.close

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[final minnow]

Can anybody help me with this eigenvector answer?

[pliant oak]

Eigenvector v is satisfying identity：
Av=λv (λ is the eigenvalue of the matrix A)

[final minnow]

So i just find the eigenvector , but i'm not sure

[pliant oak]

What you wrote is not the identity...

[pseudo ice]

First off, is this supposed to be $\lambda I - A$? If so sign error I think (doesn't affect the characteristic polynomial tho as it's lower triangular)

[ocean seal]

chartbit

[pseudo ice]

Then from here, we want what $\pmqty{v_{1} \ v_{2}}$ is, and this gives you a relation between $v_{1}$ and $v_{2}$ (when you correct it anyway)

[ocean seal]

chartbit

[lone heart]

Please read #❓how-to-get-help

Please read #❓how-to-get-help

[pseudo ice]

Read it and take a new channel, not this one

It's occupied

And please remove your posts, thank you

nobody's going to help you if you stay in someone else's channel

[pseudo ice]

Anyways, back to the point, this will give you a general form of the eigenvector from the relations on $v_{1}$ and $v_{2}$ so pick a non-zero eigenvector at random

[ocean seal]

chartbit

[final minnow]

Hmm i think my answer is correct in this part

[pseudo ice]

The (2,1) entry should be -2 though shouldn't it?

Same with the one for the eigenvalue 3 and the characteristic matrix?

[ivory mica]

P=bxr

Yeah

[final minnow]

So 3-1?

[ivory mica]

So p is missing you use P=BxR wait lemme solve

[pseudo ice]

Both of you get out of this channel, there's #help-16

[pseudo ice]

See here

[final minnow]

Ummm why is it also matter?

Ohhh okay

[pseudo ice]

Because if that's $\lambda I - A$, if you don't fix it, your eigenvectors will end up different

[ocean seal]

chartbit

[ivory mica]

@steep stump wait

[pseudo ice]

The eigenvalues are the same tho (from before, lower triangular) so you just need to change the sign there

[final minnow]

Okayyy , then how about lambda = 3?

[ivory mica]

16.666667%

[pseudo ice]

Just change the signs like this

And you should be all good

[ivory mica]

@steep stump theres an .006 extra

[pseudo ice]

Swear down if both of you don't get out of here

[ivory mica]

@steep stump 16.666667% extra .006 on 9th

So? Got the answer?

[pseudo ice]

<@&268886789983436800> please

Thank you 💜

[pseudo ice]

Oh yeah also you should check as that should give you $v_1 = 0$ and $-2v_1=0$ I think?

[ocean seal]

chartbit

[final minnow]

Like this??

[pseudo ice]

For the eigenvalue 3

[final minnow]

Is it true about my matrix in eigenvalue = 3?

[pseudo ice]

Oh you changed it to $A - \lambda I$ instead, fair enough

[ocean seal]

chartbit

[pseudo ice]

Yep that's all fine

[final minnow]

Okay , then what the next step?

To find eigenvector

Lambda = 3

I still don't have any idea :v

[pseudo ice]

That there should tell you, if you do the matrix multiplication right, that $-v_1 = 0$ and $2v_1 = 0$

[ocean seal]

chartbit

[pseudo ice]

So effectively you'll have something like $\pmqty{0 \ v_2}$ and pick $v_2$ to be nonzero

[ocean seal]

chartbit

[final minnow]

Why it should be non zero?

But
2v1 = 0
Is that should means 2 * ... = 0
... is 0?

[pseudo ice]

By definition eigenvectors are non-zero vectors

[final minnow]

So (0,0)?

[pseudo ice]

Property of real numbers

[final minnow]

Or v1 = 0?

How about v2?

V2 dont have any value? What should i do?

[pseudo ice]

Choose it to be any value you like, except zero

[final minnow]

Maybe 1 ?

Hmmm how it can be 1?

Can't i pick a number except number 1?

[pseudo ice]

You can pick any number, except zero, any would do

[pseudo ice]

1 is perfectly fine to choose

[final minnow]

Ohh, so if v2 or v1 that don't have a value we should pick number 1 ?

[pseudo ice]

You can, but you can pick anything else you want to (except zero)

[final minnow]

Okay thank you :))

.close

[lone heart]

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[karmic dawn]

For question 2 im unsure what they want

[karmic dawn]

velocity?

[outer lark]

that would be the diffusivity

I would suspect its more about whats actually spreading

[marsh rapids]

Temperature ?

[outer lark]

ie your farts or o2 etc

molecule size is a good bet

[karmic dawn]

why is the question so vague

[marsh rapids]

Since it's the average speed of the particles

[karmic dawn]

like surely it could be a ton of things

[outer lark]

depends how simple you want your system

[karmic dawn]

yea I dont think they want us to consider temperature or anything

[outer lark]

how so

[karmic dawn]

its not said anywhere

and the system in question 1 is simple

[marsh rapids]

Question 2 is about physics culture/intuition

[karmic dawn]

i guess temperature then

just feels kinda goofy

the question

[lone heart]

@karmic dawn Has your question been resolved?

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[rigid plover]

Can someone help me with the 12th q

[rigid plover]

<@&286206848099549185>

[deep moon]

Oh

Just go berserk

[deep moon]

Use tan=sin/cos

And sec= 1/cos

[rigid plover]

alright doing that

[alpine sable]

That would get us stuck in a similar situation

[rigid plover]

okay now I think we place the identity in place of 1 in numerator ??

1+tan^2 = sec^2 is that right

[alpine sable]

But there is no power here

[rigid plover]

Can we right sec^2 - tan^2 in place of 1

[alpine sable]

Yep

Where did you reach?

[lone heart]

@rigid plover Has your question been resolved?

[rigid plover]

I solved it thank u !!!

[lone heart]

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Closed by @rigid plover

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[craggy gorge]

There are 3 high quality parts, 7 normal and 2 defective. Three are chosen at random
What are the chances of picking one defective part?

[craggy gorge]

Why is all of this so hard for me? Like I literally spent like 4 hours on two questions

[low quartz]

try case making

if you stuck in probability questions

it helped me alot

i was also low in this type of question

total parts =12

case:1 )3 high quality

case:2)1 high quality + 1 normal + 1 defetcive

case:3)2high quality + 1 normal +0 defective

[tribal oxide]

Asking for picking exactly one defective part?

[low quartz]

yes bruhh

[craggy gorge]

Yes

[tribal oxide]

What do you think the denominator is

[low quartz]

case:4) 3 normal

case:5)2 normal + 1 defective

[tribal oxide]

@craggy gorge

[craggy gorge]

How is that related?

[craggy gorge]

Wouldn't there be like a bunch of those?

[tribal oxide]

Well like i study probability in a very surface level manner, but you would agree the denominator is the number of ways to pick 3 objs out of the 12 given right?

[craggy gorge]

And...

[low quartz]

no

[tribal oxide]

So what do you agree the denominator is c(12,3)?

[low quartz]

i think its better to create cases

because it will solve the problem logically

or you can go with @tribal oxide bros method

[craggy gorge]

I don't get where it's going so far

[low quartz]

what is the answer i need to match

my answer

[tribal oxide]

What did u get

[craggy gorge]

9/22 should be the answer

[low quartz]

1/6

[tribal oxide]

Yep thats what i got

[low quartz]

ithink some cases

i left

[tribal oxide]

Are you familiar with nCr notation

[low quartz]

to see

[tribal oxide]

And what it represents

[craggy gorge]

Kinda

[tribal oxide]

so in probability in a way you could say identical objects are also considered distinct because we're counting frequency

The denominator is usually the action performed in the question and the numberator is the favourable outcome

The action performed here is choosing 3 random parts from 12 parts

Which if you relate it to ncr is c(12,3)

[craggy gorge]

Ok, now I'm thinking that I messed up the formula

[tribal oxide]

Formula for what

[craggy gorge]

With the nCr stuff

[tribal oxide]

You can google the formula

What did u think was the answer?

[craggy gorge]

I didn't get a right one. I got like 5 different wrong ones

[tribal oxide]

But now do you agree the denominator is c(12,3)?

Im asking so we can move to the numerator 💀

[craggy gorge]

Think so

[tribal oxide]

Ok now the numerator is the favourable outcome

You have 2 defective parts

You need to pick exactly one

So c(2,1)

But if you remember ur original action is pick 3 parts

But uve only picked one till now

Now the other two parts cant be defective

Cuz the question says only 1 defective

[craggy gorge]

Yeah

[tribal oxide]

So with the 3 high quality and 7 normal you have 10 parts and so you do a c(10,2)

,w (c(2,1)c(10,2))/c(12,3)

[ocean seal]

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Requested by idontsleepanymore#8460

[tribal oxide]

Do you get it?

[craggy gorge]

No

[tribal oxide]

Which part did i lose you

[craggy gorge]

Putting everything together

[tribal oxide]

What

[craggy gorge]

This part

[tribal oxide]

You get the denominator right?

[craggy gorge]

Yes

[tribal oxide]

In the numerator you want the favourable outcome, u have 2 defective and 10 non defective

And when you pick 3 only one can be defective

So c(2,1) picks one def out of 2 def

c(10,2) picks 2 non def from 10 non def

Ensuring you pick 3 and ur selection always has only 1 def

[craggy gorge]

Ok

Now I think I got it

And if a second part needs to pick at least one high quality part?

[tribal oxide]

What is the exact question for the second part

[craggy gorge]

Everything is the same, but at least one of the three parts needs to be high quality

I think that the C(12,3) still works here

[tribal oxide]

You mean they also still want you to pick exactly one defective as well?

[tribal oxide]

For denominator yes

[craggy gorge]

Nop

[tribal oxide]

So find probability at least one part high quality?

[craggy gorge]

Yeah

[tribal oxide]

Theres two ways

I can think of

One would be p(at least one part high quality)=1- p(no part high quality)

Which is a pretty gamer move instead of method 2 which would be to consider cases

Do you want to use method 1

[craggy gorge]

Yeah

[tribal oxide]

So whats p(no part high quality)?

[craggy gorge]

12,9 ?

[tribal oxide]

What

Lets start with the denominator

What is the denominator

[craggy gorge]

3

[tribal oxide]

How

Its still c(12,3)

[craggy gorge]

Yeah...

[tribal oxide]

The question is still randomly picking 3 parts right?

[craggy gorge]

Yeah

[tribal oxide]

Okay and whats the numerator

[craggy gorge]

No idea then

[tribal oxide]

U have 3 high quality and 9 non high quality

And ur trying to pick 3 such that none are high quality

What would you do

[craggy gorge]

Pick from the 9?

[tribal oxide]

Write in c

[craggy gorge]

C9,2?

[tribal oxide]

Why do you think its c(9,2)?

Youre supposed to pick 3

You are familiar with nCr combinatorial meaning right?

[craggy gorge]

I'm supposed to be