help-17

[livid void]

either but im pretty sure thats the same equation I used, jut converted it to v

[empty delta]

its the total work done in J

[empty delta]

why does this say U_sys

@livid void what formula did you use to calculate the frist question

[livid void]

Oh I forgot a pic for that to make sense 1 sec

[empty delta]

ah
ok so ΔK_sys = w_tot

[livid void]

That was my thought process at the very least.

Yeah, what I was saying. There's nothing about Wtot in my book or notes. I have no clue what that is

[empty delta]

but what formula did you use for the question before this one

[livid void]

This is all my work

Also the way this reads is
W_{tot} = K_sys - uwhat looks like a different form of potential energy (U=1/2 K x^2 or mgy)

Sorry getting ready for school now which is complicating my responses. Forgot I had u_s but when I get a chance I'll plug in what you showed to see the result.

Is there a reason you add the coefficient of static friction to the equation because I haven't been taught this.

[empty delta]

if you rewrite this you get this

now you just need to know the W_tot or in our case ΔK_sys

[livid void]

It's 20N/m

Oh wait sorry no

$frac{1}{2}(0.1)•v^2$

This basically

[empty delta]

i see what you doing and also i dont see what you doing

[livid void]

Kinetic converts to potential

I'm trying to find v

[empty delta]

in your book do you have a formula like this
u_k*m*g*d

[livid void]

Yeah

What I posted

I know it says y but it's the same equation

[empty delta]

ah

[livid void]

I think I'm still misunderstanding but honestly seems like you're doing what I did. I just don't know Wtot or why the coefficient of static is used

Not getting how Wtot= K when K needs velocity.

[empty delta]

so W_tot is the total work done

[livid void]

Or where the -2 either honestly

[empty delta]

-2 is due to rewriting the formula

[livid void]

Both have 1/2 so when bringing the other 1/2 over makes it 1

Yeah, wouldn't it be 1?

[empty delta]

no cause v_2 = 0

right

[livid void]

No

[empty delta]

one whole side become 0

[livid void]

I'm finding v

[empty delta]

you are finding v_1

[livid void]

Which isn't 0

[empty delta]

the glider remains stopped right

[livid void]

For v_2

2nd sentence

Or is that for the spring not the glider.

Also if that's the case wouldn't the answer just be 0?

[empty delta]

that answer for v_1 is correct right

if we ignore the path to it

[livid void]

So I worked the problem wrong, I'll try to figure that out on my own.
Nothing shows me to use the coefficient of K I don't think though.
Also still not sure how the w_tot is working if it requires velocity to find.

I gotta run though if you don't mind me @ you later if I have another question? Honestly just having a route to work off of to help understand is a lot still though so thank you. (Reformatted)

[empty delta]

−ΔU_spring
E _dissipated

do any of those be in your book

[vocal sleet]

@livid void Has your question been resolved?

[livid void]

I thought I posted them somewhere in here but I guess not

[livid void]

Thats all I have on elastic force

Before this is Static and Kinetic force which I get.

I dont think I know what E is

I know U is potential energy

[empty delta]

Hmm

[livid void]

Oh wait

Conservation of Energy?

I just finally found W as well for Work so thats what W_tot is im guessing

[empty delta]

What book do you use for this topic?

[livid void]

Its not technically a book.

[empty delta]

Yes W is work

[livid void]

My teacher condenses the book chapters into a pdf basically

[empty delta]

Ah

[livid void]

One sec I can upload the 2 on this problem

Technically this problem is supposed to be a Lecture 7 problem, but it basically includes all of 8 as well.

Which has been part of the issue. I only really just learned 8 this week. This was due last week 😂

[empty delta]

Aah

[livid void]

I think based on work, the last thing of confusion is the U_k in the problem you posted. Ill grab a screenshot

or sorry u_s, which I dont have

nvm i do have

you use it for distance

Im realizeing it F_s on top

Sorry, I only just got able to look at this again 😅

[empty delta]

No problem

Take your time

[livid void]

So it seems like just work is the issue then. I think if im correct here Im good.

I know its not the variable being looked for, but thats the equation youre using for ⬇️ right.

[twin meteor]

Ousel

[livid void]

(better pic)

@empty delta

[empty delta]

I think my brain is a bit too tired rn

[livid void]

No problem, you've helped me a lot as it is 😅 🙏
I probably actually can figure it out at this point if you wanna stop. I think not remembering/knowing W =work was the main confusion with this.

That's the main reason I come here. I can find the answers usually, but because its newer stuff a lot of the time im not even sure what im looking for. 😅

[empty delta]

For me its also been a long time i think

Mostly self education

[livid void]

im 27 just starting college so I get it on some level lol

[empty delta]

No clue what counts as college

Different school systems :P

[livid void]

Basically it's been 10 years since I've done any school so had to reteach myself a bit 😅

You got me there conceptually though. Which like I said, is the biggest issue usually. So I greatly appreciate it. 🙏
Question was driving me crazy not understanding it. lol

If you can confirm thats it cool, but I definitely think I could handle it now that you showed me work is what I was missing if you wanna move on from it.

[empty delta]

Oh i dont mind. If you get your answer i can check it out

See if its the same

[livid void]

Alright, I cant work on paper atm, but ill let you know when I do😄

[empty delta]

Ew paper 🙃

[livid void]

Lol, I like using latex for notes, but quicker to work on paper.

[empty delta]

I use a program cause im just lazy

[livid void]

which one?

[empty delta]

Calcpad

Its just a glorified calculator

I can make variables and put them inside formulas

And it just calculates

And it supports html, svg, css, javascript

So you can basically make your own calculations sheet

[livid void]

Oh, yeah. thats what I use Latex for basically. Just use my graphing calculator for equations.

[empty delta]

Ah. Is latex free?

[livid void]

Its basically a programming language

$X_2 + 5^2 + \frac{1}{2}$

[twin meteor]

Ousel

[livid void]

Thats latex

[empty delta]

Ah

[livid void]

I use it on obsidian, but Overleaf is the simpliest way and online for free.

https://www.overleaf.com/

[empty delta]

But does it actually calculate?

Or just visualise

[livid void]

Visualise. Can make them into pdf's to reference later.

[empty delta]

So you cant say something like this.
a=3
b=6
a*b

If i put that into calcpad it gives the answer

a*b=3*6=18

[livid void]

I think you might, but I only started using it loosely a month ago so I don't know for sure. May look into calcpad more them if it can be formatted well like Latex for reference sheets then assuming Latex actually cant.

Seems like there might be Latex community packages for it.

[empty delta]

This is the output of calcpad

[livid void]

yeah apparently it can.

though sure calcpad is simpler lol

[empty delta]

Ok yea i wont learn that code

Yea calcpad has its own languegr

But its purely textbased

And has interactive possibilities

Like i can type a=?{1}

and in its output i can manually change what a is

So i can do different calculations with a template

And cause it supports svg i can add self make pictures based on the calculations

[livid void]

Ok, I just looked at the calc, looking at the IDE now seems a lot more convenient if thats the case and it supports CSS. Is it a proprietary or open language. Cuz that was the main reason I did latex is its so widespread so seemed like the standard.

[empty delta]

I think it supports css

And say you have additions you want or find a bug you just post it on github

Cause its fully opensource

[livid void]

Yeah JUST found a post saying it's open source. Hm, definitely gonna give it a shot at least then. Seems like a better alternative. Thanks for the recommendation.

[empty delta]

No problem

The more people who use it the better

Then it will become an amazing calculator program

[livid void]

Uses ai im guessing?

[empty delta]

No?

Why would it use ai?

[livid void]

Usually what that means lately, I don't have a issue about it. Just made the assumption. It being open source though didnt consider just more development resources.

[empty delta]

I still dont get how more people using it would count as using ai?

[livid void]

It's not, but if it was ai and more people were using it it would learn more.

That was my thought.

[empty delta]

Oooh

Yea no. Ai is amazing but not to make a program

[livid void]

Like I said, everything uses ai, even for making programs, so thats where my brain went. I have a bad habit of quick assumptions sometimes. 😅

[empty delta]

Ah

No problem

But yea i mean more people using mean more ideas and faster bug reports

[livid void]

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[hoary jacinth]

broken channel?

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[tame pasture]

Can every vector space just be seen as, for a certain set S, the set of all functions mapping elements of S to real numbers?

[vocal sleet]

@tame pasture Has your question been resolved?

[tame pasture]

<@&286206848099549185>

[hybrid flicker]

if you say "all functions" then no. There are always gonna be more functions f:S->R than elements of S

if you're talking about linear functions then it is a more nuanced story

In finite dimension, for an R-vector space S, yes there are as many linear maps from S to R than there are vectors of S

the sets are even isomorphic with this construction:

take a basis of S {e1,...,en}

you can construct unique linear maps $e^_j:S\to \bR$ such that $e^_j(e_i) = 0$ for $i\neq j$ and $e^*_j(e_j) = 1$

[twin meteor]

rafilou is not not born in 2003

[hybrid flicker]

In infinite dimension there are always more linear maps $S:\to \bR$ than elements of $S$

[twin meteor]

rafilou is not not born in 2003

[hybrid flicker]

final layer of complexity: what if you only consider continuous linear maps $S\to \bR$

[twin meteor]

rafilou is not not born in 2003

[hybrid flicker]

in finite dimension it's the same since all linear maps in finite dimension are continuous

in infinite dimension... it depends

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@tame pasture Has your question been resolved?

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[final saffron]

I would like some help with this, can you explain please?

[vocal sleet]

@final saffron Has your question been resolved?

[vast shale]

Our purpose in these kinds of questions is to create a single, variable equation

1. Write the first one in terms of X

2. Substitute X in the second equation with what was found in part (1). You now have a 2 variable equation. Write this equation in terms of y.

3. Substitute y and X in equation 3 with the y and X found in part (1) and (2). For X, replace the y value in the substitution with part (2)

You should now have a single equation ONLY in terms of one variable, that is the variable z(remember a and b are constants here so they don’t matter)

4. Find the value of z, feed it back into equation found in (2) to find y

5. Find the value of y, feed y and z back into equation (1) to find x

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[fast hemlock]

stats question but just asking anyway

[fast hemlock]

does anyone happen to know what the parameter s represents or stands for in this case?

[flat whale]

Show the entire page

[fast hemlock]

sure

In order: page 3, 1, 2

I felt the above 2 provide relevancy

Also I appreciate it

I believe it represents score test

I don't want you to read all of that, if you didn't know from the table it's fine

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[gray herald]

Sl loney exercise 2

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@gray herald Has your question been resolved?

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[untold arrow]

f is diff at x=x0, if f'(x0)>0 , then f(x) is increasing around x0?

[vale frigate]

it can be differentiable and the derivative can be equal to 0

oh lol

[dull bear]

[brisk moss]

increasing at a point isn’t really a useful thing

to the point where it’s not really a thing

[river kettle]

[untold arrow]

Edited!

Around the point

[dull bear]

[untold arrow]

In the nbhd of the point

[brisk moss]

the neighborhood?

[river kettle]

[brisk moss]

i think if f is continuously differentiable and f’(x_0) > 0 then there is a neighborhood of x_0 where f is increasing

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@untold arrow Has your question been resolved?

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[vast shale]

what does a level curve look like geometrically in relation to a function?

[vast shale]

is it just a horizontal ring around the 3d graph

like the yellow plane is the level curve? or is the projected cross section on the xy plane is the level curve

[rugged hearth]

the level curves are the graph of many planes projected onto a graph

each circle u can imagine as another one of those yellow planes cross sectioning the geometry

[vast shale]

so a level curve is for the entire graph

rather than a level curve being for a constant of k?

[rugged hearth]

yeah the geometric representation of level curves (in 3d) would be adding the function of all the real numbers

[vast shale]

so that would be the level curve for the cone?

[rugged hearth]

yup

[vast shale]

aight ty

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[upper tartan]

this question in my maths textbook feels like it has a mistake in it, i tried to solve it myself and instead got the answer as just 1/2

[upper tartan]

this is the area i got stuck in, because i got the answer for this as √2k² which is just 2k

[woeful igloo]

now you know where you went wrong

[upper tartan]

so cos B would be k/2k, which is 1/2 right

[woeful igloo]

2k and k√2 are different

AB = k√2 is correct

so cos B would be k/(k√2) = 1/√2

[upper tartan]

wait by k√2 do you mean √2k

[woeful igloo]

yeah, but k is not under the square root radical

[upper tartan]

ohhh so it's √2 * k?

[woeful igloo]

√2k is a bit ambiguous notation

[upper tartan]

ohh i see

are you able to explain how √(k² + k²) is done because that's where i got stuck on

[woeful igloo]

k^2 + k^2 = 2*k^2

and then you take the square root

[upper tartan]

√2k²?

[woeful igloo]

$\sqrt{2k^2}$

[twin meteor]

Bacter10Fr4g is not fr0g

[woeful igloo]

That is equal to $\sqrt{2} \cdot \sqrt{k^2} = \sqrt{2} \cdot k$

[twin meteor]

Bacter10Fr4g is not fr0g

[upper tartan]

ohhh okok i think i get it

i didn't know you could split the parts of an equation like that

[woeful igloo]

multiplication can be split

But not addition

thats why you first calculate k^2 + k^2 to get the result in product form

[upper tartan]

so √ab could be split into √a * √b?

[woeful igloo]

yes

Also, its better if you type √ab as √(ab) so its clear to those who read the text

[upper tartan]

ohhhh i see

if you saw √ab² would that technically be read as √a * √b²?

instead of √(ab)²

[woeful igloo]

either that or √a * b²

[upper tartan]

ohh got it

[woeful igloo]

In the textbooks, there is this overline on top of the terms under the square root sign, so its clear what we should take the root of and what not to

[upper tartan]

right so you would only take the square root of 2 here

[woeful igloo]

Here, you can see k is not under that line, so you cannot take the square root of k. Only the root of 2

[upper tartan]

ohhh i see

alr i think i got it now! tysm for helping :D

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[jaunty geyser]

solve system of equation
a^3-6b^2+12b-8=0
b^3-6c^2+12c-8=0
c^3-6a^2+12a-8=0

[bronze osprey]

write a^3 + b^3 + c^3 and a^2 + b^2 + c^2 in terms of symmetric polynomials

[vocal sleet]

@jaunty geyser Has your question been resolved?

[jaunty geyser]

how so?

[bronze osprey]

can you factor a^3 + b^3 + c^3 - 3abc?

it's pretty famous

[jaunty geyser]

(a+b+c)(a^2+b^2+c^2-ab-bc-ca) ig

[bronze osprey]

yeah

[bronze osprey]

actually I just realised

add all of the equations together

[jaunty geyser]

so we got (a-2)^3 + (b-2)^3 + (c-2)^3 = 0

thats where i stuck

[bronze osprey]

yeah

[bronze osprey]

so basically that should imply one of a, b, c = 0

and then WLOG c = 0

a + b = 4

so that (a-2)^3 + (b-2)^3 = 0

[jaunty geyser]

what if none of them equals zero

[bronze osprey]

IDK

this isn't a very good problem I agree

[bronze osprey]

that's impossible by Fermat's Last Theorem actually

[jaunty geyser]

fermat's last theorem works with integer numbers

a, b, c here is real numbers

[bronze osprey]

if we have x^3 + y^3 + z^3 = 0 then x^3 + y^3 = (-z)^3

oh wait right

there must be a ton of solutions then

infinitely many

for any b - 2 and c - 2 there will always be an a - 2

[bronze osprey]

so there has to be some restriction on a, b, c

they surely can't be all real numbers

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[unborn widget]

i need help w this

[unborn widget]

yo u there?

bruh

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[plucky pilot]

pls i need to know thiss

[oak magnet]

You need to evaluate the right expression

?

[plucky pilot]

yas yas

IF x 8/1 = 6

then the equation is eqauls to idk

i really struggle with math and i will give a big exam from math in 4 months...

[oak magnet]

x^1/4 = ?

In terms of x^1/8

[plucky pilot]

its

[oak magnet]

Sure

$x^{\frac{1}{4}}$

[twin meteor]

YakuBros

[plucky pilot]

:0 waatt

[oak magnet]

Can you write x^1/4 in terms of x^1/8 ?

[plucky pilot]

uhhh

ii dont know

it goes into root maybe?

or half of 6

[oak magnet]

Hum

[plucky pilot]

answers

[oak magnet]

do you agree that 1/4 = 2*1/8 ?

[plucky pilot]

mmmm

2 * 1/8 equals to 2/8?

yeah yeah

i agreee

[oak magnet]

Fine

[plucky pilot]

1/4 = 2*1/8

[oak magnet]

Put a x^ both sides

[plucky pilot]

x^1/4 = x^2*1/8 ??

[oak magnet]

Yessir

So

[plucky pilot]

hell yeah

[oak magnet]

Now use the fact that $a^{mn} = (a^m)^n$

[twin meteor]

YakuBros

[plucky pilot]

mhm

[oak magnet]

Hint : Let m = 1/8

[plucky pilot]

lemme try solving agian

do i change that to 2/4

[oak magnet]

If you want but what the value of x^1/4 firstly ?

[plucky pilot]

idkk-

i cant solvv

i will just hit randomly

maybe thiss

anyway thanks for help mann, i will skip the question, its not really for me lol

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[dense hatch]

hi

[dense hatch]

i need help with matrix ex

[vocal sleet]

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/

[dense hatch]

m=8

thats the matrixes we need to find first the determinate of A,B and C

[wintry sonnet]

a and b are simple c is also simple but long

do you know how to compute determinants

[dense hatch]

can u help me man i dont understand them i need them done for tommorow

[wintry sonnet]

i mean for determinants there's not much to it all you need to know is the formula and then you can compute them

[dense hatch]

can u send me the formula bro

[wintry sonnet]

theres 2 different ways that are taught in school

you can pick whichever you prefer

[dense hatch]

the next condition of the ex its to find the reverse matrixex of A,B and C

[dense hatch]

im very bad at this wich one do u say to use bro

[wintry sonnet]

its on you to pick they are the same thing, maybe its best to do the one that you were taught in class

[dense hatch]

ok the second one ill try

and any tips of how to find the reverse matrix

[wintry sonnet]

the inverse?

any idea that you remember from class?

[dense hatch]

i was sick and i dont have idea

[wintry sonnet]

do you know what an identity matrix is

[dense hatch]

no

[wintry sonnet]

its a matrix made up of 1's only in the diagonal and the rest is 0's

[dense hatch]

100

110

1110

something like that?

[wintry sonnet]

eeh almost but more like

100

010

001

[dense hatch]

alr

[wintry sonnet]

yeah and what you do is you multiply the matrix by the identity matrix

and that would give you the inverse

BUT

[dense hatch]

can u send me the formula

[wintry sonnet]

there is a condition

[dense hatch]

or something

[wintry sonnet]

if the determinant which you are going to calculate is 0

the matrix cannot have an inverse

[dense hatch]

yes thats the only thing i know

XD

[wintry sonnet]

do you know how to multiply matrices?

[dense hatch]

no idea bro i have to do this ex by tommorow i have to do them right

[wintry sonnet]

well theres also a condition for matrix multiplication do you know of it?

[dense hatch]

no

[wintry sonnet]

ok well a matrix is composed of rows and collums

m x n

m are the rows and n are the collumns

when multiplying matrices

[dense hatch]

ye alr that i have some idea

in my school they use something like this matrix A11(1 row and the 1 of the right its the collums one)

[wintry sonnet]

okay so when you have A(m x n) and B (m x n)

and you want to multiply them

the collumns of A have to be equal to the number of rows of B

[dense hatch]

what??

[wintry sonnet]

this can be seen as A ( 3 x 2)

do you get this?

[dense hatch]

yes the matric its (3 x 2)

[wintry sonnet]

yes okay

so if you want to multiply this 3x2 matrix what condition must the other matrix have in order for the multiplication to occur

[dense hatch]

to be the same type (3 x 2)

[wintry sonnet]

no

[dense hatch]

no idea then broski

[wintry sonnet]

i said it above

you need the number of collums (2) to be equal the number of rows

[dense hatch]

then u say if the mateixes have two collums for etc like matrix (3 x 2) and matrix (2 x 2)

[wintry sonnet]

this is for matrix addition or subtraction

yes that works

[dense hatch]

bro can u solve me the ex if u dont mind i want to see the way u gonna solve it

[wintry sonnet]

sorry i can't

i can guide you through it

i already gave you the formula for the determinant

[dense hatch]

show me the way bro for reverse matrixes

[dense hatch]

appreciate it

[wintry sonnet]

this is the matrix multiplication formula

[wintry sonnet]

well first we need to know if the determinant is = 0 or not

[dense hatch]

bro ill be right back

for now i have to go

if anyone wants to solve the problem ill be thankfull

❤️

[vocal sleet]

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[bitter pilot]

jetzt wirds krass

[tardy peak]

guten abend

wie hat der Lektorat Nullvektor gefunden

er hat direkt Nullvektor definiert

[bitter pilot]

Ja, sieht so aus dass ihr eine neue, eigene Additions- und Multiplikationsvorschrift definiert habt

[tardy peak]

ja aber wie hat er den Nullvektor gefunden.

[bitter pilot]

Der Nullvektor soll ja das neutrale Element sein, das heißt x + 0 = x

[twin meteor]

bacc (unhelpful)

[bitter pilot]

Jetzt würdest du die neue Additionsvorschrift anwenden und dann gucken, was a und b sein müssen

[tardy peak]

einen moment

[bitter pilot]

genau

was muss n_2 und n_1 sein

also

[tardy peak]

danke

[bitter pilot]

schönen Abend

[tardy peak]

.solved

[vocal sleet]

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[tardy peak]

.reopen

[vocal sleet]

✅

[bitter pilot]

Was gilt für das inverse Element?

[tardy peak]

was macht klein Lambda hier?

x+(-x) = o

ich habe gerechnet aber es sieht nicht wie es aus.

ich denke, es hat etwas mit Lambda zu tun

[bitter pilot]

So hätte ich es auch

[tardy peak]

aber hier steht anders

[bitter pilot]

Ok entweder sind meine lia kenntnisse komisch

[tardy peak]

es gibt ein lamda

[bitter pilot]

Ok ich verstehe das eine

ist nach Definition

das mit dem Lambda ist mir gerade ein Rätsel

[tardy peak]

aber solange wir die Existenz eines inversen Element gezeigt haben, ist das Problem erledigt?

[bitter pilot]

Sieht so als ob man den Vektor normieren würde um auf (0,1) zu kommen

[twin meteor]

bacc (unhelpful)

[bitter pilot]

Die erste Komponente ist 0 ja, die zweite (x_2)²

[tardy peak]

durfen wir es durch 1/x_2 dividieren, um es schöner zu machen

[bitter pilot]

genau das machen die ja

[tardy peak]

dann es sieht aus, wie hier steht, glaube ich

[bitter pilot]

Aber eig. klappt das mit dem Normieren nicht weil die skalare Multiplikation im Weg steht

[bitter pilot]

das Problem ist dass die zwangläufig die Inverse so definiert haben mit -(x_1, x_2)

Aber so wie du sie definiert hast, geht man diesem Ärgernis besser ausdem Weg

die Inverse ist ja genau das Element, das dafür sorgt, dass das neutrale Element raus kommt

Das muss nicht immer minus dem Element sein

[tardy peak]

ja, aber es ist Lösung des Übungsblatt.

[bitter pilot]

Also ich finde die Lösung merkwürdig

[tardy peak]

ich auch

[bitter pilot]

Weil mit der Inversen kommt man ja nicht zu (0,1) sondern (0,(x_2)²)

es sind zwar grundsätzlich die gleichen Vektoren, nur unterschiedlich skaliert, aber trotzdem

ich würde da die Polizei verständigen

[tardy peak]

danke

[bitter pilot]

right

[bitter pilot]

das problem ist das geht ja nicht haha guck mal wie die die skalare multiplikation definiert haben

das würde nur in die 1. Komponente reingehen, die ja eh 0 ist

das ist so komisch

deine lösung verhindert dieses problem 😄

[tardy peak]

was meinst du?

[tardy peak]

dann ist es falsch?

[twin meteor]

bacc (unhelpful)

[bitter pilot]

checkst du?

[tardy peak]

nein

[bitter pilot]

also ich hab keine Ahnung wie man das rechtfertigt oder schafft,

[tardy peak]

was willst du damit sagen?

[bitter pilot]

lambda kann man reinmultiplizieren und es änder sich nichts

x_2^2 bleibt doch unverändert

[tardy peak]

ach so

jetzt verstehe ich

Die nächste Frage

[bitter pilot]

Sieht sehr komplex aus

Aber eig muss man nur die 3 Axiome nachweisen

Ist der Nullvektor enthalten?
Ist die Addition abgeschlossen?
Ist die skalare Multiplikatoren abgeschlossen?

[tardy peak]

wie

[bitter pilot]

Ok 1. Frage

Wir wissen, alle W_i sind ein Teilraum von V

Ok?

[tardy peak]

ja

alle W_i haben Nullvektor

[bitter pilot]

GENAU

[tardy peak]

was soll ich auf meinem Heft schreiben

[bitter pilot]

Wenn du jetzt den Durchscnitt bildest

dann ist mindestens der Nullvektor enthalten

Das wars

Du benutzt die Tatsache, die gegeben ist, alle W_i sind ein Teilraum

Dann gilt 0 in W_i für alle i

demnach ist mindestens im Durchschnitt, auch der Nullvektor enthalten

[tardy peak]

okay. jetzt wie zeigen wir, dass die Addition abgeschlossen ist

[bitter pilot]

gute Frage

Was wollen wir zeigen?

Wir wollen zeigen

[tardy peak]

ich weiss nicht

[twin meteor]

bacc (unhelpful)

[bitter pilot]

Macht sinn?

[tardy peak]

ja

[bitter pilot]

So

jetzt schreiben wir uns erstmal auf

was gilt für w_1, w_2

Ein Element aus W ist so definiert

Es ist in allen Teilräumen W_i enthalten

[twin meteor]

bacc (unhelpful)

[bitter pilot]

richtig?

[tardy peak]

richtig

[bitter pilot]

Dasselbe für w_2

[twin meteor]

bacc (unhelpful)

bacc (unhelpful)

[bitter pilot]

Das bedeutet

[twin meteor]

bacc (unhelpful)

[bitter pilot]

ok?

[tardy peak]

ok

[bitter pilot]

also macht sinn?

[tardy peak]

ja macht sinn

[bitter pilot]

frage

ist die addition in W_i abegschlossen?

[tardy peak]

ich weiss nicht

[bitter pilot]

Tatsache war

W_i sind Teilräume

was muss dann gelten

abgeschlossen oder nicht?

[tardy peak]

abgeschlossen

[bitter pilot]

auf jeden Fall

[twin meteor]

bacc (unhelpful)

[bitter pilot]

Weil W_i wissen wir ist Teilraum

SO

wenn w_1+w_2 in W_i ist

für alle i

dann sind sie auch im Durchschnitt drinnen, richtig?

[tardy peak]

richtig

[bitter pilot]

Somit

sind sie auch in W

Ist klar?

[tardy peak]

ja klar

[bitter pilot]

https://cdn.discordapp.com/attachments/1080555115066437686/1275095275140026459/1112374071854891058.gif

[tardy peak]

ich versuche 3.

[bitter pilot]

so ähnlich klappts mit der skalaren Multiplikation

[bitter pilot]

vorbildlich von dir

https://tenor.com/view/cat-cuddle-gif-27222129

[tardy peak]

alle w_1 sind in W_i, das bedeutett alpha mal w_1 sind in W_i.

[bitter pilot]

wieso?

[tardy peak]

dann sind sie auch im Durschnitt drinnen

weil alle W_i Teilraum sind.

[bitter pilot]

und die skalare Multiplikation abgeschlossen ist

prima!

[tardy peak]

danke

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[opal scroll]

DE || AC
triangle ABC is Isosceles(?)
There's a more important thing I need to find, but I need to know, does angle C = angle BDE?
like angles between parallel lines?
I'm not sure how to say this in english

[last agate]

did you mean angle BED?

[opal scroll]

uh no

[last agate]

what parallel line thing did you use to surmise angle C = angle BDE

if DE || AC then line segment BC is the transversal

or well AB

[opal scroll]

im not very familiar with these terms, in english

i was suspecting that there was an Alternate angles situation going on

but i wasnt sure that was the case

[last agate]

lines cutting the two parallel lines

[last agate]

no

[opal scroll]

Is it the case that angle C = angle DEB

Corresponding angles?

[last agate]

yes

[opal scroll]

alright i will attempt to finish the entire question now

thank you for your help

.close

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[fair harbor]

Im confused where am i messing up

[fair harbor]

Am i misunderstanding maybe the concentration coming in or?

.close

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[safe sigil]

hello, I need some help with this:

[safe sigil]

Given that AB = 5, AC = 6, AD = 2. DE is parallel to BC, and DF is parallel to AC. Determine the ratio between the area of the quadrant CDEF and triangle ADE

[vocal sleet]

@safe sigil Has your question been resolved?

[jade marsh]

Kinda busy but first thing you can guess is that the triangle AED is the smaller size of ACB bcz of the information u were given that is. So AED= k.ACB=K.FDB
Same thing to the sides so for example AE= k.CA
EC=DF
And CF= ED
These are first infos u can extract from the exercise then u play with them

Also the 3 triangle they re all proportional

Then u can use theorem of thales or whatever u call it so AE/CA=FB/CB=ED/AB etc... There are many ways to solve this

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[vocal frost]

I dont get how to get the inverse function

[vocal frost]

Its task b)

The second pictures are the solutions

[cedar burrow]

Switch x and y, then solve again for y.

[vocal frost]

But how do I get from (x-2)(y-3) to the given solution?

Do I multiply or is there some kind of rule that i can just apply here.

[cedar burrow]

Divide both sides by (x-2), then take the square root on both sides

Then add 3 on both sides

[cedar burrow]

Notice it’s (y-3)^2

[vocal frost]

Ooh got it

Is there a difference between having the root over the whole fraction or only the denominator?

[cedar burrow]

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

[twin meteor]

FirstNameLastName

[cedar burrow]

So yes, there is a difference

But notice that the square root of 1 is just 1

[vocal frost]

But since theres a 1

Yes I just noticed, thank you very much for your help!

[cedar burrow]

Yw

[vocal frost]

I will close it now :)

Wish you a nice evening/morning etc

/close

[cedar burrow]

You too!

.close

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[vocal frost]

.close

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[vocal sleet]

@silver sandal Has your question been resolved?

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@silver sandal Has your question been resolved?

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[cinder dawn]

recurrence relation, i got the u and v values correct but i don't understand how they get the last line

the teacher solution is in black, my attempt was in red

all the things are coorect up to the last line

resolved, thank you

.close

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[thick bear]

Some one pls help me

It's sophomore math

Straight form geometry

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[knotty pelican]

Hey, been stuck on these last two math problems!

[blazing wigeon]

What have you tried/have you graphed them?

[knotty pelican]

I already done the whole process and integered them and found the area hut it keeps saying it’s wrong

😓

[blazing wigeon]

Can you show what integrals you computed

(Your work)

[knotty pelican]

give me 5 mins sorry

[hidden turret]

,tex .int rules

[twin meteor]

Banana Steeler

[knotty pelican]

Hi hi

@blazing wigeon @hidden turret

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[wind jacinth]

My x3 is coming up as 1.02 but the answer sheet says it should be 1.18.

What’s causing that tbh?

I found what’s causing my issue!

The online calculator I was using wasn’t removing the negative sign in my denominator.

.close

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[smoky sage]

got partial point on this what was i missing ? its physics

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[ancient lichen]

Can someone explain why B is false?

[heavy yoke]

we should start by verifying whether it's a subspace of P3 at all

[ancient lichen]

wait nevermind can u explain a diff question acutally

i just got that one

here's how far I got:

T(t^2-1) = -3t

T(t) = t^2 - 2t - 1

T(1) = t^2 - t + 1

then im done for

[heavy yoke]

so we need to then express those outputs relative to the given basis

[ancient lichen]

yea so I got

[0 -1 1 ;
-3 -2 -1 ;
0 1. 1]

which isnt even an option

answer is D btw

[heavy yoke]

so let's verify each of those:

1. is -3t = 0(t^2 - 1) - 3(t) + 0(1)?

2. is t^2-2t+1 = -1(t^2-1) -2(t) + 1(1)?

[ancient lichen]

oh wait is that how you're supposed to think about it in this scenario

ohhh

wait ok

i was too used to doing it with {1, t, t^2}

didnt knwo its different with this

lemme do that method and see what i get

okay i got the answer

tysm i had no clue thats how you actually find the columns for matrix

that actualyl makes intuitive sense now

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[knotty pelican]

Please help if you can (:

[knotty pelican]

🙏🏻

Plsss

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[knotty pelican]

<@&286206848099549185>

[knotty pelican]

.close

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[inner ferry]

can anyone help me

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[inner ferry]

<@&286206848099549185>

[raven helm]

Hello!

[inner ferry]

hi can u help me

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[dusky saffron]

.

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@inner ferry Has your question been resolved?

[inner ferry]

I need with drawing plan, side and front elevation

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[inner ferry]

<@&286206848099549185>

[inner ferry]

bruh

[inner ferry]

ok basically i just need help with these i hv no idea how to draw plan, side and front elevation of these. Please help me if you could

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[lilac pulsar]

answer is 120 how do i solve?

[minor finch]

I assume it refer to the angle going outside?

like going down

there is a property where if you have an angle going from the corner of the circle to an arc then its measure is half that of the angle of the arc

so the angle in red is inscribed in the circle and subintends(idk if thats the right word) the 15º arc, so it measures 15º/2

same thing for the other side

that lets you find the angles alpha and beta because the sum of the internal angles of the triangle is 180º

and then if you consider OABC that's a quadrilateral so its internal angles must sum 360º(you can see that because its really two triangles glued together), which you can use to find A^BC

I am very dumb you could just consider the triangle formed by the corner angles and B lmao

that's much more straight forward

(105 / 2) + (15 / 2) + ABC = 180, 60 + ABC = 180, ABC = 120

I got overfixated on the mouse pointer-like quadrilateral

[vocal sleet]

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[limpid plover]

If we have a 3D object in terms of x,y, and z, and we project this 3D object onto a cardinal 2D plane xz, what is the 3x3 transformation matrix T?

[flat whale]

xz plane has all 0 for all its y values

[limpid plover]

so its
[1,0,0]
[0,0,0]
[0,0,1]
?

[flat whale]

that's one way to project vectors onto the xz plane yes

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@limpid plover Has your question been resolved?

[limpid plover]

dubs

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[limpid plover]

.reopen

[vocal sleet]

✅

[limpid plover]

if I want to perform first transformation B and then transformation A onto vector v, would the complete transformation matrix be AB or BA?

I thought it was AB

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[viscid ore]

Hey guys, quick question here:

Let a, b, c be positive real numbers such that abc = 1. Show that if
a + b + c > 1/a + 1/b +1/c,
then exactly one of the three numbers is greater than 1.

If anyone can give me a good hint as to how to solve the problem, that would be appreciated!
Ive already worked on it and there seems to be 4 cases for how many numbers are above one (all 3, 2, 1, or none) and i have disproved the all 3 and none cases
Thank you!

[viscid ore]

<@&286206848099549185>

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[inner patrol]

!15min

[vocal sleet]

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.

[viscid ore]

2

Let a, b, c be positive real numbers such that abc = 1. Show that if
a + b + c > 1/a + 1/b +1/c,
then exactly one of the three numbers is greater than 1.

[quaint comet]

easy

[viscid ore]

ok.

?

could u please provide a solution?

[lilac pulsar]

i fell asleep ty

also u have really nice handwriting

[viscid ore]

?

[lilac pulsar]

nice circle and triangle

[viscid ore]

he closed that discussion Rip

what

<@&286206848099549185>

its been much more than 15 minutes

[fervent sphinx]

i think this is a substitution problem

like if abc=1

a=1/bc

b=1/ac

c=1/ab

[viscid ore]

ok

[fervent sphinx]

and substitute and try something

[viscid ore]

hmmm i went with casework

[fervent sphinx]

idk the actual answer it just looks like a problem that substitution would do

[fervent sphinx]

it's a variable you can't casework it

[viscid ore]

Ive already worked on it and there seems to be 4 cases for how many numbers are above one (all 3, 2, 1, or none) and i have disproved the all 3 and none cases

btw its not a problem witha solution

its a proof

[fervent sphinx]

nice

[fervent sphinx]

sorry i meant proof

[viscid ore]

ok

i mean its obvious, if all 3 numbers are above or below one, the abc=1 isnt satisfied

[fervent sphinx]

yeah ik

[viscid ore]

ok

helpppppp

[dark rune]

actually can you just do counterexample

trying to prove this hurts my brain

[viscid ore]

ok

so sry

lemme send a pic of what i have so far

[dark rune]

holy crap counterexample is so much easier

[viscid ore]

oh ok

[dark rune]

i spent like 30 min trying to direct prove omfg

[viscid ore]

rip

[dark rune]

well you can for the 2 numbers > 1 case

not sure how to approach the 1 number > 1 case

[viscid ore]

yeah

here ya go

everything i have so far is quite obvious...

!helpers

[vocal sleet]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[viscid ore]

<@&286206848099549185>

<@&286206848099549185> Please help me out i am so stuck and this is due very soon

<@&286206848099549185>

its been an hour!!!

[vocal sleet]

@viscid ore Has your question been resolved?

[viscid ore]

no

it hasnt 😭

[vocal sleet]

@viscid ore Has your question been resolved?

[viscid ore]

no

<@&286206848099549185>

[viscid ore]

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[bleak quarry]

stuck in no.9 and unsure if 10 is correct

[jagged cargo]

do you know what $\frac{\dd^2y}{\dd x^2}$ means?

[bleak quarry]

yes

[jagged cargo]

well...?

what is it...?

[bleak quarry]

at last i get $4e^{2x} \sin 3x = 0$

[jagged cargo]

use \sin

put 2x in {}

[twin meteor]

Mirdas

[bleak quarry]

yea so i got this as last line in no9

[jagged cargo]

show your work?

[bleak quarry]

oh both sides don't have to be zero?

[jagged cargo]

no it should be 0

show your work

[bleak quarry]

alr 1 sec

sry for bad handwriting

[jagged cargo]

,rccw

[jagged cargo]

this part is wrong

check your work

[bleak quarry]

ty for help, silly mistakes as always

[jagged cargo]

what about 10?

what did you get

[bleak quarry]

i did it before and the ans was probably wrong so im going to redo it rn

[jagged cargo]

you have two ways to do 10, the smart way or the dumb way

im guessing you did the dumb way

which is just taking the derivative of the fraction without a second thought

[bleak quarry]

guessing the smart way is quotient rule + chain rule?

[jagged cargo]

no, the smart way is to reduce the fraction before differentiating

if you want a hint, ||take 2x out as factor on the numerator||

[bleak quarry]

you can do that to numbers with powers?

[jagged cargo]

why not?

[bleak quarry]

oh nvm im dumb

omg

it was this easy

tyvm

.close

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[leaden scroll]

how do i approach this problem he graph of the first derivative f ' of a function f is shown. (Assume the function is defined only for
0 ≤ x ≤ 9.)

(a) On what interval(s) is f increasing? (Enter your answer using interval notation.)
b) at what value(s) of x does f have a local max and local min (comma-separated list)
c) on what interval(s) is f concave up and concave down
d) what are the x-coordinate(s) of the inflection point of (enter you answers as a comma-separated list)
Image

[torn oracle]

What have you done so far?

[cedar bone]

A function is definitionally increasing on an interval if its derivative is nonnegative there.

[leaden scroll]

honestly nothing 😭 the photo threw me off

im kinda confused on what to do cuz theres no like equation

[torn oracle]

That's fair

Remember when the derivative is positive that gives the gradient or rate of change of the function

A derivative equal to 0 indicates a stationary point which implies local max, min or stat point of inflection

[leaden scroll]

so would i be inceasimg at 1,3,7,9

[vocal sleet]

@leaden scroll Has your question been resolved?

[tame wadi]

a) f is increasing when f' is positive. Find the intervals where f' is positive.

[silk rampart]

Find the intervals

[leaden scroll]

is f positive at 2?

[tame wadi]

You're finding points
Instead focus on the area where it is positive.

[leaden scroll]

its positive on infinity?

[tame wadi]

f' is positive in [2,4], isn't it?

And also on [6, inf]

[leaden scroll]

how did we get the x value

[tame wadi]

You don't have to get x value for answering a) rather you need intervals

[leaden scroll]

isnt an interval x,y

[tame wadi]

Okay let me ask you something.

For which values of x, f' is positive?

[leaden scroll]

all positive numbers ?

[tame wadi]

You should look at the graph and tell me when it's above x axis, that's when it's positive

[leaden scroll]

3,7,8,9

[tame wadi]

It starts from 2 and goes upto 4 right?

[leaden scroll]

ohhh

yes

[tame wadi]

So the first interval is [2,4]

[leaden scroll]

yes

[tame wadi]

See if you can find second interval

6,7,8,9,...right?

[leaden scroll]

yes

[tame wadi]

It's above the x axis for every x> 6

[leaden scroll]

would the third interval be [9, infinity]

[tame wadi]

If you combine [6,9] union [9,inf)...what will be the final interval?

[leaden scroll]

inf to infinity?

[tame wadi]

What?
No.
It'll be [6, inf)

[leaden scroll]

ohhh

[tame wadi]

So you got the answer for a) right?

[leaden scroll]

i think so

[2,4], [6, inf]

would the local max be inf too

[tame wadi]

The point when f'(x) changes it's direction from positive to negetive, we get local maxima at that point.

Can you find points when f' changes it's direction from + to -

[leaden scroll]

3 and 7 ?

[tame wadi]

What about local minima?

[leaden scroll]

5, 8

1,5,8

it concaves up at 2, 6, 8 right?

[tame wadi]

Concave up when f' slope is positive.
Concave down when f' slope is negative

Look closely slope is upwards from 1 to 3

So first interval when the slope is upwards is [1,3]

[leaden scroll]

1,2,5,6,8

[1,2] [5.6] [6,8]

[tame wadi]

Why should it be [1,2]?

[leaden scroll]

cuz it goes up

[1,3]