help-27

[latent heart]

and 4 we get

4: 1, 2, 4

you following?

[spice island]

yes

[latent heart]

So lets split the term up "greatest common"

For now, lets just identify what's common

List out the common factors

What factors do 6 and 4 share?

[spice island]

1, 2

[latent heart]

Right

Now, what's the "greatest" factor

And by greatest, they mean, largest, biggest

[spice island]

okay so the greatest common factor is the largest number that is a factor by both numbers

[latent heart]

Correct

Let me give you a test

Find the greatest common factor between the numbers 9 and 18

List out the factors first

Identify what's common

Then find the biggest one

[spice island]

9

[latent heart]

Right

https://media.discordapp.net/attachments/903486480075354182/1046057389889175593/image.png?width=1031&height=670

So lets go back to this example

Just to clarify, do you know how to expand this

$3(2x + 9)$

[woven radish]

splooze

[latent heart]

Don't worry about the numbers, it's just made up. Just want to make sure you know how to expand it

[spice island]

I don't know what you mean by expand

[latent heart]

okay

so

do you know what simplified means?

Do you know what the word simple means?

[spice island]

I believe so

[latent heart]

Okay

so lets say we have the expression

[humble chasm]

expand the equation

[latent heart]

he doesn't know what expand means g

[humble chasm]

oh...

[spice island]

I have never heard that

[humble chasm]

what grade are you in

[spice island]

I'm not in school

[latent heart]

bruh

[humble chasm]

?

[spice island]

I graduated

[latent heart]

taking the piss

[humble chasm]

splooze

[latent heart]

is that the monero crypto logo?

[humble chasm]

hes trolling

[spice island]

yeah

[latent heart]

jesus

[spice island]

?

[latent heart]

i remember i mined monero coin a long time ago

[spice island]

yeah same

[humble chasm]

this whole thread could have been ended with a google search

[spice island]

had to switch over to Linux

[humble chasm]

splooze help me on my question instead ;)

[latent heart]

i've literally got my final year exams soon

in 6 days

[spice island]

I have never heard expand before

[latent heart]

and i'm helping someone learn to expand

what the fuck am i doing

[autumn breach]

need solution

[spice island]

could u explain what it means

[autumn breach]

<@&286206848099549185>

[humble chasm]

wtf 💀

bro just sends it in the middle of another persons thread

[latent heart]

@autumn breach read the rules you spaz

#❓how-to-get-help

[spice island]

so how do I expand it then?

@latent heart

[latent heart]

okay

if you have

$6(3x+5)$

[woven radish]

splooze

[latent heart]

expanding it means

$(6 * 3x) + (6 * 5)$

[woven radish]

splooze

[latent heart]

$=18x + 30$

[woven radish]

splooze

[spice island]

okay I have never done that but why not just distribute it

the 6

[gusty merlin]

Wait since ur expanding do u know about BODMAS

[spice island]

order of operations?

[humble chasm]

bodmas??

[gusty merlin]

Yup

It’s the order you solve things in

[spice island]

yeah I think so

[gusty merlin]

B= brackets
O= order (sometimes i for indices)
D= division
M= multiplication
A= Addition
S= subtraction

[spice island]

but isnt multiplication before division?

[gusty merlin]

Hence if your solving 6(3x+5) you will need to get rid of the brackets

[spice island]

or I suppose it doesn't really matter

[gusty merlin]

Pretty sure it’s whatever goes first can be switched around

[spice island]

but you can use the distributive property

[gusty merlin]

Yup, I feel like BODMAS of BIDMAS is easier to remember

Do u know how to get rid of the brackets

[spice island]

I heard something like pemdas before

no

[gusty merlin]

Where I’m from we don’t do that

[spice island]

how can I get rid of the brackeds

[gusty merlin]

How much do u know about this topic

In General

[spice island]

what topic

[gusty merlin]

Just asking so I know what to teach u first before we jump to the problems

[gusty merlin]

This

$6(3x+5)$

[woven radish]

Justt.monty

[spice island]

well I believe I know everything I need to be able to solve my problem I just don't understand the issue

or the rules atleast

[gusty merlin]

Right

So first of all we need to learn how to get rid of the brackets

Can u tell me what we’re solving for?

[spice island]

why

[gusty merlin]

I’ll get to that

I want to see if u understand what we are solving for / solving

[spice island]

okay what do you want me to do

[gusty merlin]

For the moment, I want u to let me know in ur own words what we are finding out about the equation

Can u screenshot the problem?

[spice island]

we are not finding out anything we are supposed to choose a factor of the expression 12x^2 + 8

[gusty merlin]

Oh

Okay we’ll do u know what a factor is

[spice island]

yes

[gusty merlin]

Could u explain it

[latent heart]

norahc

how old are you

[spice island]

19

[latent heart]

what grade did you leave school

[spice island]

anyways it's something that u multiply to get a number

[gusty merlin]

Ss do not judge by age u don’t know what others have been going through

[gusty merlin]

Fab!

Do u know ur multiplication?

[latent heart]

who says i'm judging

shush

[spice island]

3rd grade in the gymnasium

[latent heart]

this guy's just a troll lmao

he's literally trolling

grade a chimp

🐒

[spice island]

?

[latent heart]

monkey for brains

[gusty merlin]

He literally needs help and I’m bored

Bfr

Just ignore him

[latent heart]

he needs help that can't be attained from a math server

he needs brain surgery

[gusty merlin]

Okay that’s Just out of line rn

[latent heart]

"3rd grade in the gymnasium"

piss taker

[spice island]

I would probably benefit from a whole new brain so a transplant

[spice island]

?

I told you I graduated

but I'm not from the US

[gusty merlin]

Back to this equation

[spice island]

so I didn't learn math in english

[latent heart]

you didn't learn math in english

[spice island]

ok

[latent heart]

.

[spice island]

no

[latent heart]

what country?

[spice island]

so that's why I didn't know what a factor was because I never used that word

Sweden

[gusty merlin]

U defined ‘factor’ as a multiple and it is asking for the greatest common factor, what would that be

[latent heart]

bruh i thought sweden has a good education system

[spice island]

ha

you are wrong about that one

[gusty merlin]

^

[spice island]

but it wasn't the education system at fault here

[latent heart]

other personal issues?

[spice island]

it was me but i'm trying to remedy that

[latent heart]

mmk

[gusty merlin]

Can we solve the equation now

[latent heart]

@gusty merlin i've already explained what a factor is

[spice island]

it feels like you are jumping too many steps

[latent heart]

the fault is that he's not familiar with how to expand

[gusty merlin]

I didn’t ask

[gusty merlin]

Dms then I’ll explain is better

[latent heart]

i don't give a fuck what you asked

i'm pointing out what he already knows so you don't reexplain shit

[gusty merlin]

Check ur dms @spice island

[latent heart]

@gusty merlin teach him how to expand and he'll figure it out

[spice island]

I appreciate all the help I get but what you are saying is something I already am aware of

[latent heart]

^^^^

[latent heart]

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

[spice island]

and you didn't answer me why I needed to expand

[gusty merlin]

Be so fr do u need help or not

[latent heart]

This will provide more help than any of us have to say

[spice island]

I could use the distribute property

[gusty merlin]

Go to dms and I’ll explain why ur expanding my days

[spice island]

ok send me dm then

[gusty merlin]

Because there are interruptions on here

[gusty merlin]

I did

[devout snow]

@spice island Has your question been resolved?

[gusty merlin]

I helped u in dms tho

This guy has to be fr

[spice island]

you offered me help and then gave up on me when I couldn't understand

<@&286206848099549185> could someone help me with this problem please

[devout snow]

@spice island Has your question been resolved?

[devout snow]

@spice island Has your question been resolved?

[devout snow]

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[narrow plank]

what?

[torn valve]

Shouldn't it be 0, roo3a

Or am i trippin

[narrow plank]

I think you're right

Ye

[torn valve]

Where O is the origin

[narrow plank]

It actually looks like there are 2 A points

so to speak

So maybe it's supposed to say (0, ±√(3a)

[torn valve]

Yes exactly but i went to 2-3 sites and it says the same answer here

So ion know

[narrow plank]

This coordinate plane is messed up lol

[torn valve]

Mostly likely

.close

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[restive river]

hi

[stark sinew]

What is the general pattern of the slope in 4? Note it's shallow, then steep, then shallow agaon

so the slope starts small, goes up to a maximum, then goes small again

which one of those histograms does that look like?

[restive river]

i tink it ax^3 or a x^5

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[lavish dew]

can anyone join the mathematics vc?

[lavish dew]

I need help with math

[dark dawn]

https://tenor.com/view/what-the-fuck-wtf-excuse-me-shocked-what-gif-14402529

[lavish dew]

Anyone I really need help

anyone please

please join the math vc cause idk what to do next

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@lavish dew Has your question been resolved?

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@lavish dew Has your question been resolved?

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[muted reef]

how to find what D is?

[muted reef]

i know it's $y=x^2$ and $x=y^2$

[woven radish]

張嘉棋

[muted reef]

but what numbers do I get from that?

[supple knot]

Find the intersection

Graphing the two might help

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[true jasper]

could someone help me with question 7

got stuck

<@&286206848099549185>

[vale dew]

Differentiate the given function y and equate it to 5/4 and then solve for x(which will be your x-coordinate)

Then you can substitute that x value in function and get value of y(which will be your y-coordinate)

[true jasper]

i tried

couldnt work it out

[true jasper]

cant solve for x

[vale dew]

X=3 is a solution

[true jasper]

the last step of ur working

is where im stuck at

what do i do from there

[devout snow]

@true jasper Has your question been resolved?

[true jasper]

@vale dew ??

<@&286206848099549185>

<@&286206848099549185>

[devout snow]

@true jasper Has your question been resolved?

[vale dew]

It’s pretty much substitution of random values
But you can solve it

If you square on both sides and cross multiply, then you finally get a cubic equation in x

x=3 is a solution to this equation

Randomly substituting till it satisfies or you could solve that cubic(which I don’t know how to)

[devout snow]

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[lavish perch]

yo can someone help me out

[hollow pollen]

yeah sure but it'll cost you 1 million dollars 🙂

[lavish perch]

I'll give you 20%

Seems fair to me

[sand dove]

What are you asking for ?

[lavish perch]

^

anyone who helps me out gets 20%

(I deserve all the recognition)

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[random pendant]

First one

[devout snow]

@random pendant Has your question been resolved?

[random pendant]

.close

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[mild basin]

What do these buttons do? And whats the difference between CE and C?

I am impressed with Microsoft's Calculator, there are actually a lot of versions in settings!

One for programming which is nice

[lavish perch]

mc memory clear sets the memory to 0

[mild basin]

But what does that do exactly? Why would I want to do that? And doesn't C do that?

[lavish perch]

m+ takes the number on display and adds memory and puts the result into the memory

[lavish perch]

dude I have no idea

[mild basin]

lol

[lavish perch]

these 2 are all i know

[mild basin]

Oh so it can save values with M?

[lavish perch]

yeah

[mild basin]

Hmmm I will need to play around with that

Could be useful

[pseudo basin]

https://www.google.com/search?q=difference+between+c+and+ce+on+a+calculator

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[stuck birch]

hello can anyone explain this line?

[neon aspen]

This is somewhat vague

[stone stump]

context?

[stuck birch]

cartesian operators to cylindrical operators

[neon aspen]

But assuming f is a function of rho and phi, this is chain rule

[stuck birch]

hmmmm

[neon aspen]

This is kinda abuse of notation but no one really cares. This is really the chain rule applied to a composition of functions and the partial derivatives are wrt the coordinates of each function, which can have arbitrary labels

[stuck birch]

but what is d/dx

there is no f

[stone stump]

it's the operator that you would apply to a function

[stuck birch]

hmmmmmmmm

ok thanks

.close

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[tawdry crystal]

I need help with this question

[dapper gazelle]

So of the 4 do you have any ideas

[tawdry crystal]

no

I don't know how to solve it

[sonic smelt]

If a line is parallel to y = 3 - 2x, it means that it has -2x component too

In this case there's only one option where you can see -2 in front of the x

[tawdry crystal]

wouldnt it be the option that has the ssame slope?

.close

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[misty spruce]

im having a litlte confusion on my calc hw. shouldnt this be f(x) = e^x^3 times x^2 where f(2) = e^2^3 * 2^2 = e^8 * 4 which equals 11923.832? i got it wrong.

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[snow locust]

Please help

I just learned the inverse derivatives and im struggling super hard

[upbeat lagoon]

Do you know the derivative of tan ?

[snow locust]

I think so

arctan(u) is u'/1+u^2

[upbeat lagoon]

And the derivative of sqrt(6x) ?

[snow locust]

1/2(6z)^-1/2 *6

[upbeat lagoon]

by simplifying it can be rewritten 3/sqrt(6z), so your u is sqrt(6z) you just have to apply the derivative of arctan(u)

[snow locust]

kinda confused by what you mean by this

oh

what do i do about that 5?

[upbeat lagoon]

The derivative of ku is ku'

[snow locust]

so just leave the 5 outside?

[upbeat lagoon]

Yes

[snow locust]

and what about the complex fraction

[upbeat lagoon]

You can simplify if you want, but we have our result

[snow locust]

thank you

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[plucky sky]

i don’t know how to make it orthogonal

And I am sure somewhere is wrong

[wild creek]

by the spectral theorem the eigen vectors are orthogonal just normalize them

and then the matrix of basis change will be orthogonal

[devout snow]

@plucky sky Has your question been resolved?

[plucky sky]

Umm

How do I normalise them

Just make them unit vectors?

[wild creek]

yeah

they'll still be eigen vectors

for the right eigenvalues

[plucky sky]

Huh ok thx

I guessed I did missed sth

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[floral niche]

can someone pls help?

[uncut crow]

the first thing i’d try is like completing the square twice

[floral niche]

i tried doing that but it didn't work

[uncut crow]

completed the square for both x and y?

[floral niche]

yeah

this is what i got

2(x+1/4)^2 = (y+1/3)^2 + 1/72

[uncut crow]

fractions

[floral niche]

haha ikr

it started looking complicated so i just ditched it

[uncut crow]

:c

i was thinking more like multiply by something first to complete the square without having fractions

but i don’t know if that would help anyway

i gtg but i’ll take another look at it later if it doesn’t get resolved

no promises i’ll be any help 😵‍💫

[winter patrol]

something looks off in your equation

you didn't complete the square properly

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[pure bane]

I would like help with graphing quadratic functions pls

[pure bane]

Hello

On the topic in generañ

General

[wooden veldt]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/a/graphing-quadratics-review

[pure bane]

Ty

[devout snow]

@pure bane Has your question been resolved?

[pure bane]

Yes

[devout snow]

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[regal roost]

A toddler has in his hands a playing card with dimensions 8.7 x 5.6 cm. While playing, the child makes a straight fold in the card from the bottom left corner to a point at the top right 1.7 cm below the corner (if you hold the card upright). Calculate the length of the fold. Make the drawing.

[regal roost]

can anyone help me on how too make this drawing?

i just cant get used on too how to do it

Pythagoras

[restive river]

Making the drawing? They probably just want you to draw a square with a line between the corners mentioned in the text

Probably also add the dimensions they write

[devout snow]

@regal roost Has your question been resolved?

[regal roost]

no

idk

their asking an number

[peak parcel]

@regal roost does this image make sense

the red line is how card is folded, from bottom left to top right 1.7 cm below corner. How can u calculate the red lane given that u know other two sides in that right triangle ?

[regal roost]

Omggg

Holy

I was so confused bec there was only a square

But now I get it

So I think

Let me calculate

c^2= a^2+b^2

so

c^2=7^2+5.6^2

c^2= 3185

c= 56.43

is that correct @peak parcel ?

or anyone else

[real grail]

,calcul sqrt(7^2 + 5.6^2)

[woven radish]

Result:

8.964373932406 ul

[real grail]

c = 8.965

[regal roost]

uhhhh

what did i do wrong

[real grail]

c² = 7² + 5.6²
=49 + 31.36
= 80.36
c= sqrt(80.36) = 8.965

[regal roost]

ohh i forget too put the dot

at 5.6

i did 56

thank you!

[real grail]

I 'm not sure it's correct

[regal roost]

wdym/

[real grail]

just a feeling

[regal roost]

i dont understand

oh

its from this

A toddler has in his hands a playing card with dimensions 8.7 x 5.6 cm. While playing, the child makes a straight fold in the card from the bottom left corner to a point at the top right 1.7 cm below the corner (if you hold the card upright). Calculate the length of the fold. Make the drawing.

and this is the answer then

c^2= 7^2 + 5.6^2
=49 + 21.36
= 80.36
c= sqrt(80.36) = 8.965

is that correct ?

i mean with the picture

[peak parcel]

I think it is.

[regal roost]

thank u !

[real grail]

try to do the same thing with a paper

[peak parcel]

I know it makes a weird shape

but they are just asking about the path

yes but it doesn't matter you can still use the length from before you shaped it

[regal roost]

so many of these type of questions, is it that easy too learn fast. like they gave me practice with normal triangles and now i get these full on stories

[real grail]

@peak parcel
the fold is the distance DC , right ?

[regal roost]

would the outcome be different?

i hope ur not asking me i dont know

[peak parcel]

This is how paper looks when u fold it

this blue line is imaginary

but you can still use it to make calculation

bcs it gives u distance

[astral flax]

How do you do Box and Whisker Plots?

[peak parcel]

I added the point M, the fold is MF

[regal roost]

0.o u guys teachers or something or just really good at maths

[real grail]

Ohh right , I thought DC is the fold

[peak parcel]

@regal roost what grade are u ?

take it step by step and it will come naturally

[regal roost]

now i get it yeah

[regal roost]

uhm none

i am in second chance school

for like grownups

theres not rly a grade

[peak parcel]

I see

there's no need to rush, improve step by step. Try a similar problem

[astral flax]

hey

is this channel in use?

[regal roost]

yes

[astral flax]

or is it free now

oh ok

sorry

[regal roost]

okay so i am doing another task rn.. ima try too do it alone but ill show how i do it

To demarcate a football field, Jan steps 20 steps in width and 60 in length. Stijn doesn't trust it completely and asks Jan to go diagonally across the field. Jan has 67 passes. Is their football pitch rectangular? Explain your answer.

yk what i find wierd idk if i do it correct but

it says it is 20 width

and 60 long

and imagine i didnt know it was 20 width

i would do
a^2= c^2-b^2

which is

=67^2-60^2

=889

a^2==889

a=29.816

why is a 29.816 when i calculate it

when it says 20 on the paper

[real grail]

"Stijn doesn't trust it completely"

[regal roost]

?

[real grail]

he made a mistake when he was counting steps

[regal roost]

0oh so its not a miscalculation

did i do the drawing good?

and what would be the answer. bec even tho his calculations are wrong whos calculations are wrong

their field will 100 procent stay rectangular

i'd be wierd for them too miss over 40 steps

weird

or over do

[real grail]

I think since 20² + 60² is not equal to 67 ² than it's not a rectangle

[regal roost]

confused

ahhh i understand

but then it would be

7² + 60²?

or

it could be anything

10² + 57²

could i calculate that from what i have of info or not

omgggg i understand

@real grail

they are talking ab the corners???

not the full things

like the angle corner type

it would be wierd for a football field not too have rectangulars tho

could i calculate how big the corner is with that info

how much degrees

[real grail]

if 20² + 60² is not equal to 67² then I will not have a right triangle
and if i don't have a right triangle i can't have a rectangle

[regal roost]

thank u

Dad wants a summerhouse in the back of the garden and digs a rectangular pit of 3.6 m by 4.8 m. To check whether the well has a straight hat, he measures the diagonal. Which is 6 m.

Is the pit rectangular?

ima try one more

then i go

so this

a^2= c^2-b^2

a^2= 6^2-4.8^2

a^2= 12.96

a= √12.96

a= 3.6

b^2=c^2-a^2

[real grail]

true

[regal roost]

b^2= 6^2-3.6^2
b^2=23.04

[real grail]

because:
3.6² + 4.8² = 6²

[regal roost]

do i also have too calculate b^2

or is one enough?

was a^2 enough bec i was ab too do b^2 aswel

just too be sure

[real grail]

you need just to prove that :
c² = a² + b²

[regal roost]

b=4.8

okay

[real grail]

a = 3.6
b= 4.8
c= 6

[woven radish]

The following error occured while calculating:
Error: Undefined function ul

[real grail]

3.6² + 4.8² = 12.96 + 23.04
=36
= 6²

[regal roost]

so ill type in yes the pit is rectangular because 3.6² + 4.8² = 6²

[real grail]

yeah

[regal roost]

okay.. thank you !

[real grail]

welcome mate

[regal roost]

Calculate the length of the third side as c = 12 and b = 9. Write down the steps correctly. Round the result to 2 decimal places.

i think im getting the hang of it

[regal roost]

/close

.close

[devout snow]

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[long kettle]

What's confusing you

A relation R is a set of ordered pairs

xRy is true if (x, y) is in R

If I had the relation {(1, 2), (3, 4)} for example

1R2 and 3R4 are both true

1R3 is false

This notation isn't as foreign as you may think

There's a few relations that use this notation that you are very familiar with

For example, "="

1=1 is a true statement, 1=2 is not

Theres also "<", ">", "≤", and "≥"

A relation is a set of ordered pairs

{5, 7, 9} is not a set of ordered pairs

Yes

Well

Technically (3, 2), (4, 3), and (5, 4) should be in as well

Actually wait there's a few more missing also

Are you sure that's the right answer?

That looks right

[fair flax]

thanks

[devout snow]

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[stark sinew]

What have you tried? It looks like the question is about the values of a and e, what can you tell about them so far?

Note that e is the value when x = 0 i.e. f(0) = e. What is f(0) from this graph?

[devout snow]

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[limpid wasp]

how to solve the system

[devout snow]

@limpid wasp Has your question been resolved?

[devout snow]

@limpid wasp Has your question been resolved?

[limpid wasp]

No

[devout snow]

@limpid wasp Has your question been resolved?

[zenith jacinth]

$\begin{cases} L_2 \frac{d i_2}{dt} = -r i_1 -(r+R_2)i_2 + \epsilon \ L_1 \frac{d i_1}{dt} = -ri_2 -(r+R_1)i_1 + \epsilon \end{cases}$

eh

[woven radish]

Ｈｅｒｅｌｓ

[zenith jacinth]

transform this into a matrix and do some diagonalization I guess

$\begin{pmatrix} \frac{d i_1}{dt} \ \frac{d i_2}{dt} \end{pmatrix} = -\begin{pmatrix} \frac{r+R_1}{L_1}& \frac{r}{L_1} \ \frac{r}{L_2} & \frac{r+R_2}{L_2} \end{pmatrix} \begin{pmatrix} i_1 \ i_2 \end{pmatrix} + \begin{pmatrix} \epsilon \ \epsilon \end{pmatrix}$

oops

forgot i_1 and i_2

[woven radish]

Ｈｅｒｅｌｓ

[zenith jacinth]

$X' = AX + B$

[woven radish]

Ｈｅｒｅｌｓ

[zenith jacinth]

you solve X' = AX first

and then constant variation method for B

@limpid wasp

[devout snow]

@limpid wasp Has your question been resolved?

[zenith jacinth]

you wont come back ? @limpid wasp

[devout snow]

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[limpid wasp]

.reopen

[devout snow]

✅

[limpid wasp]

sorry was busy

[limpid wasp]

i don't understand a word of it

[zenith jacinth]

have you learned about solving differential equation using matrices ?

[limpid wasp]

nope

[zenith jacinth]

well sadge

[fallen quiver]

Add k times second eqn to first eqn
And equate the ratio of coeff of di1/dt and di2/dt to ratio of coeff of i1 and i2.
That will give you k and will help you solve the eqn.

[limpid wasp]

ok thanks

no sure i understand it

what after getting k

its a lengthy value tho for k

[devout snow]

@limpid wasp Has your question been resolved?

[devout snow]

@limpid wasp Has your question been resolved?

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[tranquil basin]

Good evening,
How to prove that two simultaneously diagonalizable endormorphisms commute

[celest verge]

pako was my nickname one time

[gloomy mica]

1 over 4 plus 2 over 3 is 11 over 12 right?

[celest verge]

ok bye

[tranquil basin]

^^

[gloomy mica]

1 oover for pluss 2 over 3

=11over12

[tranquil basin]

@gloomy mica what are you doing ?

[gloomy mica]

?

[tranquil basin]

pls, just get out if you just spam my channel

[gloomy mica]

i'm not spamming

[rotund heron]

#❓how-to-get-help

[tranquil basin]

then, i will repost : How to prove that two simultaneously diagonalizable endormorphisms commute

only on the direct way

[arctic field]

show that diagonal endomorphisms commute?

[tranquil basin]

yes

[tranquil basin]

simultaneously diagonalizable

this means that there exists a basis of E which diagonalizes them simultaneously

[arctic field]

no i'm saying you should show that diagonal endomorphisms commute

[tranquil basin]

well

this is the problem

[tranquil basin]

i don't know how to begin

I was thinking about eigenvalues ​​and characteristic polynomials but it doesn't work

and i don't how to use the argument of the same basis

[arctic field]

they're simultaneously diagonalisable so you only need to worry about when they're diagonalised

[tranquil basin]

i don't understand

why ?

[tranquil basin]

yes

and AB = PDEP^-1

BA = PEDP^-1

[arctic field]

so you just need D and E to commute

they're diagonal

[tranquil basin]

(sry don't speak fluently english, a bit hard to understand)

[arctic field]

prove they commute

[tranquil basin]

okkk

[tranquil basin]

well, only use AB = PDEP^-1 is not enough

[arctic field]

?

[tranquil basin]

i can't proove that D and E commute with only this

wait

well, i don't know where you would like to know with this

i want something at the end ED = DE right ?

[arctic field]

yes

they're diagonal

very specific form

use the fact that they're diagonal to show they commute

[tranquil basin]

yes, ED = DE = diag(diei)

with D = diag(d_i)

and E = diag(e_i)

[arctic field]

yeah that looks about right

[tranquil basin]

well, i have another question^^

Justify the existence of a complex upper triangular matrix T and an invertible matrix P such that A = PTP^-1

is it a easy question like before ?

i spent 1 hour on it

[devout snow]

@tranquil basin Has your question been resolved?

[tranquil basin]

well, the problem, this proove is only for matrix and not endomorphism

so didn't work^^

[neon aspen]

JCF

[tranquil basin]

JCF ?

what this mean ?

[neon aspen]

Jordan canonical form

[tranquil basin]

weil

i can’t use that

didn’t saw this theorem

[devout snow]

@tranquil basin Has your question been resolved?

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[devout snow]

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[loud ingot]

Im using this but getting the incorrect answer

The answer is: [3 -4 -1]', but i'm getting [1.5 -4.5 3]'

[wooden veldt]

Your calculations seem correct

v_1 and v_2 do not form an orthogonal basis

So you can't directly apply the theorem

[loud ingot]

If i can't use that theorem is it even possible to answer this

[wooden veldt]

Yeah make the basis orthogonal

[loud ingot]

something like this?

[wooden veldt]

No you'd need to do gram schmidt

[devout snow]

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[wooden veldt]

Composition

[polar bolt]

f o g(x) means f(g(x))

[devout snow]

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[loud ingot]

Still struggling with this... gram schmidt is giving me some weird numbers and i ended up not getting the right answer... it seems weird having to do 4 pages of work for this question so i feel as though i am definitely doing something wrong

should i be using least squares solution?

do i treat A as [v1 v2]

[torn vessel]

That’s certainly one way to do it, yes

[devout snow]

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[raven herald]

Need help with understanding fourier transform f(t)

[raven herald]

With finding this fourier transform shown above ,I'm super confused as to how to apply it to the one below, as the one below the format we've always done so I'm super confused as to which numbers start off where

[supple knot]

have you tried plugging in f(t) into the definition of fourier transform

[raven herald]

With trying too apply the f(t) into the definition I'm struggling to understand the meaning of which numbers of the question go where into the definition

[supple knot]

plug f(t) into here

[raven herald]

I think I'm confusing something I'm asking how is it I find what ft is out of this

What are these numbers relations to f(t) to which I then use on the F(w)

[supple knot]

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

[raven herald]

Thank you I'll watch it now

With the understanding of evaluating the functions now, may I ask what is the 1/4 and 0 meanings within the function?

does it just mean if f(t)<=3, it's = 1/4 and t>3 = 0?

[supple knot]

no

|t| <= 3 means -3 < t < 3

[raven herald]

sorry for my ignorance on this but it also was never explained to me by my prof, what is the meaning of |t| as opposed to t

[supple knot]

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/cc-6th-absolute-value/v/absolute-value-of-integers

[raven herald]

Got it, thank you very much

So then for example in this question shown

[supple knot]

you don't need to keep sending the screenshot of the same thing

[raven herald]

Sorry it's just so I don't get myself mixed up

Is there a video or explanation of what is the meaning behind the 1/4

[supple knot]

it's a number

,calc 1/4

[woven radish]

Result:

0.25

[raven herald]

Ok I think I actually get most of it now

For the expressions here prior I was given the range -1<=t<=1 so prior I'd have -1 on bottom then 1 on top

Since the questions now it's just an absolute t is it just a 3 on top, or does it include a 3 on top -3 on bottom

It'd be a 3 on top then -3 on bottom right?

Then I go about rest of formula all as normal

[supple knot]

yes

[raven herald]

Thank you so much for both being helpful and patient with me

.close

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[pine nimbus]

I have to find the gradient of this product, where x and b bar is both vectors and A is a matrix

should i treat A as a vector?

[devout snow]

@pine nimbus Has your question been resolved?

[pine nimbus]

I have treated the matrix as a vector

<@&286206848099549185>

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@pine nimbus Has your question been resolved?

[devout snow]

@pine nimbus Has your question been resolved?

[devout snow]

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[cunning roost]

what do the symbols mean and whats the difference between them ?

[tall knoll]

They're just different greek letters

Treat them like any other variable

[cunning roost]

oh okay

what is supposed to be in the variable

degrees or something ?

[tall knoll]

Usually it's in radians

[cunning roost]

oh

[tall knoll]

It doesn't matter as long as it's consistent

[cunning roost]

okay ty

.close

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[restive river]

Do we have any alternative to gaussian elimination? to to the computation faster? e.g. a fancy method.

[prime egret]

We have wolframalpha as an alternative

[restive river]

How it is doing gaussian elimination?

I mean an alternative algorithm

[devout snow]

@restive river Has your question been resolved?

[stone stump]

well we have eg QR or cholesky factorization

and in practice (i.e. for huge and often sparce matrices) we often just approximate a solution well enough with iterative solvers of which there are a lot

jacobi, gauss-seidel, cg, gmres and stuff

[restive river]

But QR is more costly also cholesky is not general as GE

[stone stump]

aren't QR and LU both 2/3n^3 ?

fair point about cholesky. but I mean if you know about them then you presumably had a class about stuff like this, no?

[restive river]

QR has some extera cost 2/3n^3 + n^2. Yes I had. GE is a sequential process. So for today parallel computer it means waste of resources..

[stone stump]

who cares about n^2 terms

[restive river]

reducing 1 cycle is 1 cycle.

[stone stump]

yes but no

if you have to do 1 million cycles you don't care about doing 1 more

[restive river]

yes but no. If I am repeating it many times so 1*x is something.

[stone stump]

well the point is you are not doing it that many times. n^2 is nothing compared to n^3 for big n

not that I've ever seen anyone use non-iterative solvers for big systems

[restive river]

Thanks. Which size is big? I am asking becasue I am not sure about real application.

[stone stump]

for stuff like PDEs you easily run into matrices with millions of entries

or well, most of them are 0

[restive river]

30Kx30K is large?

[stone stump]

I mean I don't know about industry but I doubt it. 30kx30k is something my shitty pc could handle

[restive river]

Actualy my PC no. It requare >10GB memory.

In which area do we have dense matrix?

[stone stump]

not sure

haven't seen any

[restive river]

OMG, so why we have LU?

[stone stump]

well probably better for midsized problems

or if you for example have to calculate lots of solutions with different RHS

only need to compute the same LU once

[restive river]

Correct.

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[cyan mulch]

the product of uncommon real roots of two polynomials p(x)=x^4+2x^3-8x^2-6x+15 and q(x)=x^3+4x^2-x-10 is

[woven radish]

FearleSS

FearleSS

[cyan mulch]

<@&286206848099549185>

<@&286206848099549185>

help me please

i dont know how to start

[rotund heron]

Look at q(x). Use factor theorem to see if something works.

(Something does work)

[cyan mulch]

u mean i try putting in some numbers

[rotund heron]

Yes

Got it?

[cyan mulch]

no

nothing

i tried numbers from -5 to 5

in first one

-2 is satisfying second eqn

hmm

so next two roots will be -1+-root6

so if they have common

so first equation should have both of these

so it forms quadratic after division

thanks i got it @rotund heron

[rotund heron]

Was what I said helpful?

I thought it was a bit vague

[cyan mulch]

i thought it was useless to try numbeers out

you pointed that out

thanks man

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[high chasm]

ε − N

[high chasm]

could i have some help on how u do this plz

[long kettle]

What have you tried

[high chasm]

i understand that when u sub infinity into the thing u get infinity / infinity - 7.5

which is essentially infinity / infinity

which is 1

but i dont get how u do it with e - N

[long kettle]

No, it's indeterminate

But you can show its 1 with other methods

[long kettle]

Do you know what ε N is

[high chasm]

epsilon and is N natural number?

if thats wrong im unsure

[long kettle]

It's an ε-N proof

[high chasm]

ye

[long kettle]

It's the definition of an infinite limit

Tell me, what does that definition say

[high chasm]

when functions increase or decrease without bound near certain values

[long kettle]

What is the ε-N definition of an infinite limit, exactly

[devout snow]

@high chasm Has your question been resolved?

[long kettle]

Are you going to answer my question

[high chasm]

Sry I ended up Acc trying to do it

Idk if this is correct

[long kettle]

You say N > (7.5 + ε7.5)/ε, and that n ≥ N. How does that imply n < (7.5 + ε7.5)/ε? It would be greater than, not less than

Must be a typo

Looks right despite that, but I might be missing something

[high chasm]

is this better?

[long kettle]

Yes

[high chasm]

for part a would the limit just be 2

[long kettle]

Yes

[high chasm]

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[stiff ferry]

I'm looking for the equation of the line

(0,3); slope = -2

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[stiff ferry]

<@&286206848099549185>

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[solemn hound]

How would I convert XY=16 to polar form

[muted reef]

well polar form is of the form $x=rcos(\theta)$ and $y=rsin(\theta)$

[woven radish]

張嘉棋

[solemn hound]

So would it be

[muted reef]

its $r^2$ yh

[woven radish]

張嘉棋

[solemn hound]

Where did the h come from

[final drift]

yeah you can simplify this tho

[muted reef]

oh it's just me saying yh

like yeah

lmao

[final drift]

its r^2cos(theta)sin(theta) right

can you simplify cos(theta)sin(theta)

[muted reef]

YUP

[solemn hound]

So like this

[final drift]

um you can simplify it more

remember what sin(2theta) is?

[solemn hound]

2sin(theta)cos(theta)

[final drift]

yeah

so sin(2theta)/2=sin(theta)cos(theta) right?

[solemn hound]

I suppose

[final drift]

so we now have r^2*sin(2theta)/2=16

so then you would have that sin(2theta)=32/r^2

this form is slightly more simplified

[solemn hound]

So would the answer just be

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[midnight bear]

Is anyone familiar with finitely intersecting closed curves?

[supple knot]

[midnight bear]

hi riemann! I know i was asking about this yesterday, but I am still not sure about patterns in fi-closed curves

we're given parametric curves of the form x(t)=sin(pt)+cos(qt) and y(t)=sin(rt)+cos(st) and asked to make generalizations about how certain values of p,q,r, and s result in a fi-closed curve, or symmetry about the x or y axis or the origin

I've tested abunch of different values of p,q,r and s but i cant seem to see any patterns emerging for some reason

[supple knot]

what is a fi-closed curve

[midnight bear]

its a parametric curve that traverses it's path only once, and has a countable number of intersections with itself. It also has to start and terminate at the same point. If it traverses it's path more than once, it intersects an infinite amount of times so it is not finitely intersecting

this is one, where (p,q,r,s)=(1,3,1,1)

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[queen comet]

can anyone help me pls

[restive river]

Do you know the rule of three?

[queen comet]

no

what is rule of 3?

[queen comet]

yes i know this

[queen comet]

what does it have to do with this tho

[restive river]

I mean, can't you just solve $\frac{300}{5}=\frac{2}{x}$ and get $x$?

[woven radish]

3317

[queen comet]

x = 25

[restive river]

,w solve for x (300/5)=(2/x)

[woven radish]

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[restive river]

Nah.

[queen comet]

oh

x is 1 by 30?

,w solve for x (300/5)=(x/2)

[woven radish]

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[queen comet]

x = 120

,w solve for x (300/5)=(1800/y)

[woven radish]

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[queen comet]

hmm

,w solve for x (300/5)=(1800/x)

[woven radish]

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[queen comet]

,w solve for x (5)=(x/12)

[woven radish]

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[queen comet]

,w solve for x (180/4)=(x/3)

[woven radish]

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[restive river]

You can just go to https://www.wolframalpha.com/, you know?

[queen comet]

hmm ok

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