help-0

[granite badger]

essentially h(2) - h(0) / 2 - 0

[rocky zealot]

oh

wait

i got it

thxs

[granite badger]

nws

[rocky zealot]

would the answer be -9.8

since 10.4-(30)/2-(0)?

@granite badger

[granite badger]

i don't have my calculator with me but probably yes

[rocky zealot]

ok thxs

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[rocky zealot]

hi can i get someone to review my work before i submit it, math 180 calc

[rocky zealot]

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[craggy token]

Given a triangle ABC where AB =/ AC. The bisector of angle BAC intersects the circumcircle of triangle ABC and line segment BC at D and E respectively. The circumcircle of triangle BDE and circumcircle of triangle CDE respectively intersects line AB and line AC at F and G.
a) Prove that G, E, and F are collinear.
b) If I is the incenter of triangle ABC, M is a point on line segment EB, and N is a point on line segment EG, prove that IM = IN if and only if ME = NE.

[craggy token]

how do i prove part b?

I've proven part a, but I don't know how to proceed with part b

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[placid mason]

.open

.open

please help

[placid mason]

anyone

[round sable]

We would need to see the options in the drop-down menus

Also this looks like a test question, which is not allowed

[placid mason]

its a homework

delta math

@round sable

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[placid mason]

no :C

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[still fjord]

In the quotient rule for derivatives, if g(x) is 5cot(x), does squaring in the denominator it become 25*cot^2(x)?

[kind basalt]

what do the l brackets around the x mean?

[naive valley]

yep

[still fjord]

Did I make a mistake somewhere then?

All of the answer choices I have show the denominator as 5cot^2(x)

[tardy stag]

well there are some common factors you could look for

[still fjord]

Ah

ok i just needed to factor out 5

that makes more sense

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[median oar]

So I’m trying to Fourier transform the pdf of a standard Gaussian right

[median oar]

Now I’m here and I’m stuck

This ibp didn’t work because it looks like their limits don’t converge

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@median oar Has your question been resolved?

[keen plinth]

complex analysis goes brrr

splitting the complex exponential is probably not what you want to do

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[median oar]

;-;

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[alpine sable]

Can someone help me with the octet rule

[alpine sable]

Does this obey the octet rule?

I am confused

What about this one

Not a chemistry server

[tardy stag]

yes to both - electrons in bonds are shared between the atoms

and double count

so the oxygens and chlorines are both satisfied

as for why they double count? pffffft that's like quantum physics or something

[alpine sable]

But I’m confused because doesn’t it have to be 8 to obey octet

[tardy stag]

it is 8

hold on ill mark them

and it's that but horizontally flipped for the right oxygen

[alpine sable]

But the one on the right doesn’t have 8? Is that fine?

OH

okay

[tardy stag]

yeah covalent bonds are weird

[subtle birch]

But you must know that octet rule is NOT always satisfied

It is in most cases but there are cases where it isn't

Take for example the case of NO2

[tardy stag]

(presumably in resonance)

how does that work, just because oxygen is a diva and forces her way into the molecule anyway?

[alpine sable]

For this does it matter whether the top 2 valence electrons are up top, to the left and rights of N or on the bottom?

I mean, logically they should be on the top right?

But I’ve seen images of them on the left and rights of N

[tardy stag]

when you draw lewis diagrams like this it doesn't usually matter where you put them

[alpine sable]

I see

[tardy stag]

on the side looks nicer

probably idk

[alpine sable]

A line is always 2 electrons right?

[tardy stag]

in reality they'll be wherever the bond isn't

[tardy stag]

i'm gonna say yes with the mutual understanding that chemistry is really weird and that's probably not true for some exotic stuff
but yes

[alpine sable]

I’m not liking chemistry

[tardy stag]

i didn't like chemistry until i learned quantum physics

[subtle birch]

Well, we are not yet told the specific reason but as of now we are just said that NO2 by itself is stable

[alpine sable]

And this does follow octet right, because I can count the 6 in the middle and 2 to the left or right depending on which N I’m counting for

[tardy stag]

yep, N_2, O_2, and F_2 all work essentially the same way

[alpine sable]

I see

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

@tardy stag hi r u still there

[tardy stag]

hi yes against my better efforts i'm still awake

[alpine sable]

Is this a sufficient Lewis diagram for MgCl2?

[tardy stag]

those are ionic bonds, right? i don't think you'd usually draw lewis diagrams for those but let me check...

[alpine sable]

Ain’t that covalent?

[tardy stag]

idts because magnesium sheds 2 electrons to get to valence

it doesn't "want" more

[alpine sable]

Well anyways

My question is just this

[tardy stag]

oh usually you'd put a bracket around the element and note its charge

[tardy stag]

that's fine too

[alpine sable]

Is the stuff in the blue necessary?

[tardy stag]

yeah i'd include it

[alpine sable]

Cuz that’s how my tutor writes it but my teacher doesn’t

But is it necessary?

[tardy stag]

everything i'm seeing online includes it

[alpine sable]

If I’m just drawing Lewis diagrams

[tardy stag]

and it makes it clear that it's an ionic bond

rather than just two electrons that are suspiciously close to both Cl and Mg

[alpine sable]

What about for covalent bonds then would that blue stuff be necessary?

[tardy stag]

no, covalent bonds don't involve transfer of electrons in the same way that ionic bonds do

the electrons get thrown away by the magnesium and chlorine picks them up

then they become attracted to each other du eto the charge

[alpine sable]

I see, thank you. You’ve been extremely helpful

[alpine sable]

What did u mean by this

[tardy stag]

that's a 24h clock

[alpine sable]

I see

Well you should try to… go to sleep

[cloud chasm]

i think this form is more standardized

as MgCl2 is ironic bond

[tardy stag]

yeah i've usually seen the brackets

[cloud chasm]

this should be better,as the electrons from Mg is now belong to Cl

[alpine sable]

Thanks guys

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[next cedar]

are my calculations right and its worth playing this case?

[next cedar]

i took each one of the items, multiplied it by the probability for example the first one would be 10* 0.8 and did it witch each item

and if its above the cost of the case means the odds are on my side?

[vale wigeon]

,calc 10 * 0.8 + 275 * 0.05 + 400 * 0.05 + 540 * 0.04 + 600 * 0.03 + 675 * 0.03

[ocean seal]

Result:

101.6

[vale wigeon]

ok yeah

[next cedar]

bro this site gotta be a scam 💀

[vale wigeon]

expected value seems to be +13.6 afaict

[next cedar]

yeah

thanks for the help man

.close

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[obsidian sable]

Hi, im a little confused on how to approach this question on my math hw. For number 2, it says to make a table of values near x = 1 to estimate the instantaneous rate of change of f(x) = -3x^2+12x-5 when x = 1 but im confused on if im supposed to only plug the x value given to me into f(x) or if im supposed to do the (f(b)-f(a)) / b-a thing. I was also wondering if someone would be able to look over my work for the other questions on my assignment to let me know if im approaching this correctly. Thank you so much!

[nimble fern]

for the table you can just plug the x values into f(x) to find f(xl for coorespdoning x values, e.g.
f(0.5) for the first box

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[obsidian sable]

.reopen

[lone heart]

✅

[obsidian sable]

Oh so like this

[nimble fern]

yea, something like that

(I didn't check the numbers of all answers)

[obsidian sable]

ooh ok thank you

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[rapid gate]

why do they choose 1/4 to plot first?

in fact

my general qeustion is

how do i know which values to choose to plot

[gray isle]

considering the definition of log
y = log_2(x) → x = 2^y
you'd get nice integer values for y if x is an integer power of 2

[left wharf]

and you get nice rational values if your input is 2^q for some rational number q

if you were to consider log_2(3) for example then that's not a rational number and doesn't have a terribly nice representation

[rapid gate]

hm?

ok lemem

process

that

[left wharf]

log_2(3) = 1.58496250072115...

and there is no repeating pattern

[rapid gate]

hm?

so take for eg

if i were to plot

log_4 (x)

which values wuld i pick

1/16,1/4, 1.4,16?

[left wharf]

sure, those are pretty nice inputs to the function

[rapid gate]

so basically

wait

[left wharf]

but really, if you wanted to plot log_4(x), what you'd do in practice is use some sort of calculator like Wolfram Alpha

[rapid gate]

,w plot log_{4} (x)

[left wharf]

,w plot the base 4 logarithm

[ocean seal]

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Requested by fwgx

[left wharf]

exactly

[gray isle]

choose things that you can calculate by hand without too much difficulty

[rapid gate]

oOO

cool

is there assymtote

for a function like this?

,w plot base 2 x

[left wharf]

there's a vertical asymptote at zero

[rapid gate]

,w plot log base 2 x

[ocean seal]

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[left wharf]

but there is no horizontal asymptote

the function grows arbitrarily large to the right

[rapid gate]

okay

thanks!

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[timber grove]

graphically represents the following functions on the same Cartesian plane: (N.B makes a signature box for each function).

f1(x) = x-3
f2(x) = 4
f3(x) = 3x

[rapid gate]

?

[timber grove]

I need to know how this would look like

[rapid gate]

dilation factors right

[timber grove]

I don't think it's that, it's more simple

[rapid gate]

??

[timber grove]

it gotta go in this graphic

[rapid gate]

yes

so theres a dilation factors?

that affect thee shape?

[timber grove]

there isn't

[rapid gate]

????????

[ember lichen]

dude will start drawing bunch of straight lines. i did this once in school

[timber grove]

yes that's right

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[rapid gate]

.reopen

[lone heart]

✅

[rapid gate]

Wdym

[native cloud]

?

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[lone heart]

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[median oar]

So I’m looking at exponential order, and my book says that cosh t is not of exponential order.
cosh(x) = (eˣ)/2 - (e^-x)/2
Now clearly the first term is of exponential order, and the 2nd one tends to 0 as x goes to infinity so how come it isn’t exponential order?

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[paper quartz]

Thank yu

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[near apex]

I think it is because it doesn't increase/decrease exponentially.
So, i'm going by the definition of exponential function - A function whose rate of change at any instance is directly proportional to the value of function at that instance, i.e f'(x) = kf(x).
That is not true for cosh(t), as its derivative is sinh(t).

[lone heart]

@median oar Has your question been resolved?

[alpine sable]

A student of mass 50kg walks up a slope inclined at 30° horizontal.find the work done by the student if he walks 25m along the incline

Can anyone answer this

[near apex]

This channel is occupied. Please open another help channel. Refer #❓how-to-get-help

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[undone ledge]

i dont know how to aproach this

[mortal trellis]

how do you decide if there is a min or max at a certain point

[undone ledge]

first check with second derivative test , if fails first derivative

[mortal trellis]

then compute the second derivative

[undone ledge]

right donw now?

getting something like 2(x-a) g'(x)+g(x) +g'(x).2(x-a)+(x-a)^2 . g''(x)

[mortal trellis]

and what do you have to check now?

what is the second derivative test?

[undone ledge]

puting the critical points of the first derivative, in the second derivative

and if its > 0 then minima , if smaller then maxima

im not able to get how will i find thoese critical points

[mortal trellis]

well the question is about the point x=a

oh I just noticed they don't say that explicitly

but well its clearly the interesting point here

why else should g(a) matter

[undone ledge]

o yeah

that makes sence

so like f double differentiation a = g(x)

wait no -

f(a) = 0

na idk-

[mortal trellis]

what is f''(a) ?

plug a into the expression from above

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[undone ledge]

i think i got g(x)

[lone heart]

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[undone ledge]

.reopen

[lone heart]

✅

[undone ledge]

oops sorry

[tacit arch]

show your calculation

[undone ledge]

when i double differentiated i got this

then i substituted x = a

and got g(x)

i dont have a phone atm to share a pic sorry

[maiden glen]

I think you may be missing a factor of 2 from the g(x)

but I don't think that will really affect the question much either

rest of that looks good

[undone ledge]

oh? ic

how will i proceed to get an answer tho

[maiden glen]

plug in x=a into f'(x)

and show that you get zero

[undone ledge]

oh cool 1 sec

yeah deff a zero

[maiden glen]

then, we also have f''(a) = 2g(a) as you've said

and if g(a)>0, then f''(a)>0 and if g(a)<0, then f''(a)<0

so second derivative test applies

[undone ledge]

oh yeah 2g(a) missed the bracket

ahhhh

damn

i was overthinking

so A and D?

[maiden glen]

yes

[undone ledge]

cool ty!!

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[alpine sable]

Can someone please show me how you would evaluate this?

[undone ledge]

is that 1 + 9 sin^2 3x

[alpine sable]

,rotate

[alpine sable]

Yes

No

[alpine sable]

Have you learnt about Elliptic integrals yet?

First week in Calc II

As far as i know you need to know how what they are to solve this

[tacit arch]

looks like you wrote down the problem wrong or made a mistake earlier

[alpine sable]

My hw software said that it’s written out correct, I just don’t know how to evaluate. I’ll go watch some videos on elliptic integrals I guess

[tacit arch]

screenshot what you mean by "hw software..."

[alpine sable]

It should be easy to solve

[tacit arch]

,w int 0 to pi/2 of sqrt(1+ 9sin^2(3x))

[ocean seal]

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[tacit arch]

here's a good start
https://mathworld.wolfram.com/CompleteEllipticIntegraloftheSecondKind.html

[alpine sable]

Thank you

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[cosmic hull]

Sorry, this was a glitch

Due to internet connection

[lone heart]

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[alpine sable]

how does one even begin to prove this?

[alpine sable]

isn't this just riemann sum, but now n could equal to 1 and you don't have to make any sums at all

do I just show that this is true by giving an example?

Does the exercise want me to write a proof?

I heard some people talk about how proves are really hard

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[proven leaf]

Does anyone know a constant familiar to this? I cant help but I feel like I've seen it before: −1.15710298351...

[naive sorrel]

is it terminating after that

[proven leaf]

no it's non-terminating, the program just didn't compute any decimal palces after the 1 😅

sorry abt that, I added the ellipses now

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@proven leaf Has your question been resolved?

[proven leaf]

so it begins...

[naive sorrel]

no exist!!

http://wayback.cecm.sfu.ca/projects/ISC/ISCmain.html

[proven leaf]

I see also thank you for website mein freund

I check on WolframAlpha, they also appears to have nothing

[naive sorrel]

[proven leaf]

I might have been thinking of Euler-Mascheroni

[proven leaf]

well thank you again!

.close

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[opal ruin]

in part C, why isn't is (6 choose 4)(6 choose 3)

[remote heron]

theres only 10 total questions

oh wait

[opal ruin]

my logic is that he chooses 4 from the first 6, and then he gets to choose 3 more, which 2 of those three more can either be from the first 6, or the remaining 4

[remote heron]

is this the entire answer?

[opal ruin]

yup

[remote heron]

well like

it seems reasonable they would do maybe uhh

6C4 * 4C3 + 6C5 * 4C2 + 6C6 * 4C1

but if thats all they wrote

then yea it seems wrong to me

[opal ruin]

oh wait

lol yea they eventually write that my bad

I thought u meant for that first part

of the entire sum

I don't get why it's 6C4*4C3 though

[remote heron]

theyre just doing cases

at least 4

[opal ruin]

ohhh I see

yea that makes sense

[remote heron]

so they can choose 4

or 5

or 6

and thats exhaustive

[opal ruin]

yea that's right

that makes alot of sense

thank you

[remote heron]

[opal ruin]

.close

[lone heart]

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[hot bluff]

highlighted part

[hot bluff]

if i understand right, isn't Span{u,v} the set of all linear combinations in R^2?

Since it's not asking for the Span{u, v}, then can I assume that there are vectors which aren't a linear combination of u and v, since Span{u, v} is the subset of R^2 that contains all linear combinations of u and v?

[remote heron]

yea i think you could visually reason this

[hot bluff]

right, but what I'm getting at, is that basically a Span of 2 vectors in R^2 is simply a "rearrangement" of the coordinates in terms of the 2 vectors, right?

[remote heron]

not necessarily

[hot bluff]

so would a 2 vector span in R^2 also contain ALL spans in R^2?

[remote heron]

what if the vectors are 0 and <1,0>

or <1,0> and <2,0>

[hot bluff]

hm

[remote heron]

or 0 and 0

[hot bluff]

would a span of {(0,0), (0,0)} even be a span?

well wait

[remote heron]

sure

[hot bluff]

isnt the zero vector present in all spans of a space

[remote heron]

i believe so, yea

[hot bluff]

so a span of 0 seems kind of redundant

[remote heron]

well its degenerate

im just making a point lol

you cant just pick any two vectors and say the will span the entire plane

[hot bluff]

1,0 vector and 0,1 vector is basically a cartesian coordinate system isnt it

[remote heron]

you could pick 0 and 0 which is extraordinarily degenerate

[remote heron]

i guess yea

[hot bluff]

but as soon as we get vectors of two non zero values, i.e. (x, y) then we get a new coordinate system from a span

so knowing all this, can ANY vector in R^2 be described with a linear combination of two other vectors?

i feel like the answer is yes, since there are infinitely many combinations aren't there?

[remote heron]

youd have to put conditions on the two vectors

[remote heron]

i mean what about <1,0> and <2,0>

theres infinitely many linear combinations of these

describe <0,1> using one

[hot bluff]

well, 2,0 is within the span of 1,0

[remote heron]

right

[hot bluff]

in that case the span is a line within the plane of R^2 right?

[remote heron]

it is, yea

[hot bluff]

the x axis pretty much

[remote heron]

so you need to put a condition on the two vectors

youve found one way to say it

the second vector cant be in the span of the first

this seems sufficient for what you want to do: describe any other vector in R^2 using some 2 vectors youve chosen

[hot bluff]

as long as u and v are different nonzero vectors, they would contain all vectors within R^2?

[remote heron]

no

[remote heron]

go back here

[remote heron]

what about this

[remote heron]

i just stole your idea from here

[hot bluff]

hm

but given something like Span{ (nonzero, nonzero), (nonzero, nonzero) } that still would not contain all vectors of R^2?

[remote heron]

it might or might not

you need to put an additional constraint on the relationship between the two vectors

its not enough that youve chosen 2 of them

[hot bluff]

how is that possible when infinite combinations of scalars can be used?

how can there be "holes" in the coordinate plane created from a 2d span (all nonzero values)? isn't it just a transformation of the cartesian plane?

[remote heron]

i feel like were kind of going in circles

[hot bluff]

let me reword it another way

[remote heron]

it is a transformation of the plane

the problem is if you choose 2 vectors that are in each others span right

then you squish the plane down to a line

[hot bluff]

right

i understand that entirely

[remote heron]

its not sufficient to just require that none of the coordinates be 0

or that you pick 3 or 5 or however many

[hot bluff]

oh i see

[remote heron]

you need to also require something about the relationship between the vectors in your set

[hot bluff]

would a restriction then be that the two spans cannot be parallel?

[remote heron]

well theyll go through 0 right

[hot bluff]

right, all spans contain 0

[remote heron]

so if theyre parralel, theyre equal

parallel

[hot bluff]

so barring parallel vectors, would a 2d span then contain all other vectors within R^2?

[remote heron]

yea i think id really desire a better definition of parallel here

but i believe youre getting at the meat of it

[hot bluff]

hm parallel in terms of vectors im not sure.

[remote heron]

youre in linear algebra?

[hot bluff]

i guess that would mean

they would be scalar factors of each other?

yes this is intro to linear algebra this is the first week lol

[remote heron]

if youre in LA i wouldnt worry too much about it, this is kind of a central concept of the entire course

[hot bluff]

so two vectors must scalar factors of eachother to be parallel?

[remote heron]

one way to say parallel might be like

if you can find a couple nonzero constants, say a and b

such that a of the first vector, and b of the second, gets you back to 0

like you can walk some distance along the first vectors span, then back along the second vectors span, and get back where you started

if this were true, then theyd be parallel

with this formulation you can eventually link this problem into invertible matrix theorem

[hot bluff]

hmmm, so a - b and b - a would both be 0 in this case?

errrr

[remote heron]

which if youre in a normal LA course will be like the majority of the course is IMT and its consequences

[remote heron]

think like

u=<1,0> and v=<0,1>

now write au + bv = <0,0>

and a and b cant be 0

[hot bluff]

that can't be consistent is it?

[remote heron]

theres no way to do it right

you cant walk up, then walk right, and end up back where you started

now try u=<1,0> and v=<2,0>

au+bv=<0,0>

[hot bluff]

that can def work

u-(1/2)v, etc.

[remote heron]

so yea youll spend a lot of time on this

i think you have the right idea

youll spend weeks drilling this concept from different angles so

[hot bluff]

now back to this

its no

[remote heron]

why not?

[hot bluff]

... okay, since u and v are not parallel, they DO contain all vectors of R^2?

[median oar]

They don’t contain but they do span

[hot bluff]

tbh im not sure if its referring to the vectors in the picture or every possible vector in R^2

[remote heron]

the latter

[remote heron]

hi frosst

[hot bluff]

geometrically speaking, the span of this u,v would be a plane covering the cartesian plane, right?

my original thinking was the span of u,v covers the coordinate plane, so it should contain all 2d vectors

[remote heron]

yea

i mean idk i like this wording

[median oar]

Hi jan

[remote heron]

but maybe its silly to talk about wording

[median oar]

It covers ℝ² yeah

[remote heron]

i dont like covering i mean it gives some kind of idea that span({u,v}) is different than R^2

but good enough

[median oar]

Well I mean

You can think of it as span({u,v}) is a subspace of ℝ²

But it’s the entire space

[remote heron]

ah yea

[hot bluff]

besides the obvious case of the span being a line, is there 2 vector spans in R^2 that won't cover the entire space?

[median oar]

“Covers” is not a very linear algebra way to say things

[remote heron]

yes

well

[hot bluff]

lol, "fills?"

[median oar]

And when you’re in linear algebra you want to use linear algebra terminology

[remote heron]

okay {0,0} isnt a set of 2 vectors

to be clear

but if you chose 0 and 0

itd be degenerate

[hot bluff]

we haven't covered degenerate

[remote heron]

im so excited for you

[median oar]

A line is a less degenerate case than a plane

[remote heron]

i wish i could go back and take LA for the first time

[median oar]

It’s so cool isn’t it

[hot bluff]

it is pretty interesting. i like how it can connect so many different fields and branches of math

[remote heron]

span({0,0}) doesnt make sense but thatd be like

thatd be even worse than a line

[hot bluff]

"worse?"

[median oar]

I mean it is

[remote heron]

i dont think you accepted span({0}) as legitimate lol

[hot bluff]

0 is a vector

[median oar]

They just aren’t distinct or unique

[remote heron]

but elements in a set have to be distinct

[median oar]

Ah

That’s a good point

[remote heron]

like even lower dimension than a line

[median oar]

He did say span

[hot bluff]

so when a vector is degenerate, does that mean it contains less dimension than the space in occupies?

[remote heron]

dont worry about degenerate right now

[median oar]

besides the obvious case of the span being a line, is there 2 vector spans in R^2 that won't cover the entire space?

[remote heron]

i shouldnt have used it

[hot bluff]

like a line in R^2 or a plane in R^3?

[remote heron]

no

[median oar]

A vector must have equal dimension to the space it lives in

Or it doesn’t live in the space

[remote heron]

i get what youre askin

[median oar]

The span of a set of vectors however is different

[remote heron]

the span is either a point, or a line, or a plane

[hot bluff]

can a span be a cube?

[remote heron]

sure

[median oar]

Not if your vectors are in ℝ²

[remote heron]

ah yea

but i mean

theres no reason your vectors cant be 3d or 4d or infinite d

[median oar]

But if your vectors are in 3 or more dimensions

Then yes you could span a “cube”

[hot bluff]

would R^4 be used for something like 3 dimensions + time?

[median oar]

Not necessarily

There’s really no difference between ℝ² and ℝ¹⁰

[remote heron]

i think just wading further into the course will answer a lot of the immediate questions youre having

[hot bluff]

i agree. mainly i wanted to be sure my understanding wasn't too far off.

[remote heron]

LA has a good progression to it most of the time

[median oar]

Pretty much all the math is the exact same regardless of how many dimensions you got

(Finite)

[remote heron]

no I think you're doing great 😄

[median oar]

Some wack shit happens with non-finite dimensional vector spaces

[hot bluff]

does calculus ever get involved in LA?

[median oar]

Absolutely

[remote heron]

[median oar]

You bet your ass everything is connected to LA

[hot bluff]

[remote heron]

LA is foundational

[median oar]

Otherwise you wouldn’t be studying LA

[remote heron]

dynamic systems my beloved

[median oar]

Everyone studies LA because LA is used everywhere

[remote heron]

actually thats where i was taking degenerate from

theres interesting bifurcations where linearizations of nonlinear systems are degenerate

[median oar]

Those are certainly words

[hot bluff]

are linearizations approximations like tangents in calc?

[remote heron]

yes of course

kinda

youll see a lot of LA flavored calculus in differential equations

if you take it

which you should

[median oar]

I think the first LA you see in calculus is probably partial derivatives?

[remote heron]

if you can

[hot bluff]

just when i think im getting deep into math i realize im in a puddle not even up to my ankles

[remote heron]

LA is pretty deep tbh

maybe dense is a better word

i wouldnt minimize it for sure

[median oar]

I’ve been looking at LA for the past 6 months and I haven’t even touched Complex vector spaces at all

Still got some ways to go before complex stuff

[hot bluff]

complex spaces are where fractals live right?

[median oar]

Wel I wouldn’t know

I haven’t done them yet

[hot bluff]

thanks for the explanations guys. you've gotten me excited for the rest of this course.

🫡

.close

[lone heart]

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[hot bluff]

back again. why is this not a linear combination? free var?

[hot bluff]

answer

finding a linear combination should mean solving the augmented matrix, in this case it has many solutions. shouldn't that prove that a linear combination exists?

or is it a wording thing because it said linear combination and not combinations

but at least one must exist

[tawny condor]

Yeah, b is a linear combination of those vectors.

[hot bluff]

book wrong then?

[tawny condor]

Take for example, 2a_1 + 3a_2

I guess, unless I'm dumb

[hot bluff]

no i think we are right

book probably has a mistake, ill message prof

thanks

.close

[lone heart]

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[tawny condor]

np lol

[lone heart]

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[lusty thunder]

hi again:)

[lusty thunder]

Get several complex roots for the 7 polynomium. Write the polynomium fully factorised and give the algebraeic multiplicity of the roots

This relates to this equation somehow:

Since I already know a z0 i dont know if i should repeat this equation above over and over or what ?

<@&286206848099549185>

[maiden abyss]

Hello

[lusty thunder]

factor out z^3

moment

and then use the ladder

@alpine sable

Not sure where to go from here

😛

i use the ladder to go from z^3-z^2+z-1 to z^2+1

The answers can also be complex

i, -i, etc

@maiden abyss could you maybe also take a look just in case? 🙂

hmm alright

Not sure if I should ping helpers again ? @alpine sable

<@&286206848099549185>

we're stuck x)

[junior citrus]

so do you remember

the formula for (a+b)^3

[lusty thunder]

no, we've never learned this

sadly

[junior citrus]

wait nah that wouldn't apply here

you'd do factorization by parts

(z^3-z^2+z-1), what can you factor out of the first 2 terms

@lusty thunder

[lusty thunder]

you can write it as:
(z^3-z^2+z-1)(z^3-0)(z-1)

And then you can use the ladder method on the first one, which ends up as z^2+1

hmm

[junior citrus]

just look at the first term for the time being

what can you factor out of the first 2 terms within that nomial

so what can you factor out of z^3 - z^2

[lusty thunder]

z

[junior citrus]

it is

[junior citrus]

okay, so you're left with z(z^2-z), can you factor anything else out?

[lusty thunder]

ehh wait

(z^3-z^2+z-1)

you cant factor out z because of -1

[junior citrus]

i said to ignore those

for the tim being

[lusty thunder]

oh okay

[junior citrus]

just factor z^3-z^2

[lusty thunder]

z

and from z(z^2-z)

[junior citrus]

^^

[lusty thunder]

you can say

[junior citrus]

what else can you factor out

[lusty thunder]

z^2(z-1)

[junior citrus]

yep

so now the equation is [z^2(z-1) + z-1] right?

how about i rewrite it

to look a bit more like this

[z^2(z-1) + 1(z-1)]

again

as i have stated 3 times

i am ignoring the rest of the equation for the time being

to simplify things

[lusty thunder]

right

[junior citrus]

so

[lusty thunder]

Yeah

[junior citrus]

so what would be the factorized form of this equation?

[lusty thunder]

[z^2(z-1)+z-1]

uhh

[junior citrus]

Treat (z-1) as a single variable, like x or something

[lusty thunder]

z^2(z-1)+1(z-1). like this?

okay

z^2(z-1)+x

z^2 * 3x

nvm

z^2 2x

oh

[junior citrus]

(frac{1}{2}

what was the command

for latex

ohh okay

$2

$2$

[ocean seal]

PyroShock

[lusty thunder]

so we have now (z^2+1)*(z-1)

[junior citrus]

$[z^2(z-1) + 1(z-1)] = ? Assume x = z-1, therefore (z^2*x + x)$

[ocean seal]

PyroShock

[lusty thunder]

(z^2+1)*(z-1)(z^3-0)(z-1)

#❓how-to-get-help

yeah

its for the purpose of knowing a root

[junior citrus]

correct

now you can simplify the whole thing to z^3(z^2+1)(z-1)^2

[lusty thunder]

right

<@&268886789983436800>

[junior citrus]

thats crazy

[lusty thunder]

where to proceed from here?

I need to write in in a factorised way so I can find the roots

[lone heart]

@lusty thunder Has your question been resolved?

[lusty thunder]

Gonna ping <@&286206848099549185>

😛

[tacit arch]

Do you know complex numbers

z^2+1 can be factorized

[lone heart]

@lusty thunder Has your question been resolved?

[lusty thunder]

Yes

I solved it now 😄

[lone heart]

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[lusty thunder]

Thanks for all the help guys

.close

[lone heart]

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[winter wing]

Weird question

[winter wing]

I have $$ -(x + h)^2$$

[ocean seal]

geoxcaliber

[winter wing]

When u foil out does it look like

$$-(x+h)(x+h) $$

How do u place the minus lol

Do u put another set of parenthesis

[ocean seal]

geoxcaliber

[winter wing]

Whats the logic

[somber eagle]

you can put it in either set of parenthesis

[tardy stag]

it's all getting multiplied right so it doesn't matter but yeah you can write it like $-((x+h)(x-h))$ if you want

[ocean seal]

hayley!

[somber eagle]

did you mean to write x+h?

[tardy stag]

oh yes

[smoky lark]

hi

how do u reflect images without squared paper

[somber eagle]

!help

[lone heart]

Please read #❓how-to-get-help

[smoky lark]

y use this discord if theres google

?

[somber eagle]

google can make things confusing i suppose

plus it can be easier to understand if you are able to ask questions and get quick answers

[lone heart]

@winter wing Has your question been resolved?

[smoky lark]

ccan u help me

[gray isle]

read #❓how-to-get-help, claim your own dedicated channel and someone may come along.

[smoky lark]

bro it wont work

[gray isle]

what won't work

[lone heart]

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[smoky lark]

bro

.repon

.reopen

how to create one

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[real ice]

can somebody give me an equation on the pythageorean theorem?

[smoky lark]

hi

[tacit arch]

,w pythagorean Theorem

[ocean seal]

Results provided by WolframAlpha

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Requested by rie.mann

[lone heart]

@real ice Has your question been resolved?

[long axle]

,w spherical Pythagorean theorem

[ocean seal]

Wolfram Alpha doesn't understand your query!
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Requested by northsteve

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[alpine sable]

Can I get help with these problems please

[alpine sable]

20-24 I’m unsure how to solve it

Help would be appreciated thank u

[outer kite]

do you know what it means by rate of change is positive and decreasing

@alpine sable

[alpine sable]

Yes

[outer kite]

if the rate of change is decreasing

that means the second derivative is negative

it tells us the concavity of the function

rate of change is decreasing = concave down

rate of change is increasing = concave up

[alpine sable]

Is it looking for points like -1,1

Since that’s where it increases

[outer kite]

no its asking for x values

x value intervals where the rate of change is decreasing

just sketch the first and second derivative graph

[alpine sable]

Ah

So like -1

And 1 and 4

[outer kite]

hold on lemme uh

do some antidiff

nvm I can't be bothered bye

I'm not working out what the function is

but uh

20 isn't -1 to 4

because from 1 to 4 while it's concave down the rate of change is also negative

[alpine sable]

Ah

[outer kite]

so yeah try gain

[alpine sable]

So just to be sure this guy is wrong correct? @outer kite

[outer kite]

they're correct

[alpine sable]

What

[outer kite]

but you probably shouldn't have just asked for the answer like that

[alpine sable]

I didn’t

I said help and he gave me that

Most helpful helper ever

[outer kite]

q20 is basically
find the values for x where:
d/dx > 0
d2/dx2 < 0

[alpine sable]

The voices

.close

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[vapid steppe]

is integral of e^-x^2 / x^2 possible

[soft finch]

is it e^(-x^2) or (e^-x)^2

[vapid steppe]

former

[soft finch]

k

i'll try

[tepid drum]

@vapid steppe

[vapid steppe]

ye

[tepid drum]

This integral can't be written in terms of elementary functions

[vapid steppe]

is e^(x^2) / x^2 possible?

[tepid drum]

Do you $\frac{e^{x²}}{x²}$

[ocean seal]

calculus is fun

[vapid steppe]

yes

[tepid drum]

The integral that can't be written in terms of elemtary functions is $\int{e^{-x²}}dx$

[ocean seal]

calculus is fun

[tepid drum]

Lemme see

[soft finch]

i dont think so

maybe im just not well versed enough in integration but i dont think so

[vapid steppe]

ok ty

.close

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[soft finch]

np

[lone heart]

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[grizzled ermine]

can someone explain how these work?

[red ocean]

Probably 1 = X + Y + Z

X = Vanilla
Y = Chocolate

1 = 0.45 + 0.35 + Z
1 - 0.80 = Z
Z = 0.20

Also

1 = Milkshake + Cone + Cup
1 = 0.2 + 0.4 + 0.4
1 = 1 ✓

The values of Milkshake, Cone, and Cup is not (Main Branch) divided by 3

[lone heart]

@grizzled ermine Has your question been resolved?

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[balmy geyser]

hi

[balmy geyser]

idk how this is wrong

when i put in the calculations i get -9.20050

but its telling me that it is -9.20049

i checked my answers on my calculator and mathway and they both say -9.20050

[tardy stag]

computers are actually kinda bad at decimals like that

,calc (-4.9(4.0001)^2 + 30(4.0001) - (-4.9(4)^2 + 30(4))) / 0.0001

[ocean seal]

Result:

-9.2004900001541

[tardy stag]

,w (-4.9(4 + 1/10000)^2 + 30(4 + 1/10000) - (-4.9(4)^2 + 30(4))) * 10000

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by kitten.in.a.teacup

[tardy stag]

rounding issue, check your inputs

[native cloud]

Don't round in calculator

Just use "ans"

[lone heart]

@balmy geyser Has your question been resolved?

[balmy geyser]

I never round tho

its so weird

i re did an extra question and got it fine

idk

[lone heart]

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[warm patio]

can someone explain how they got this arg(z) plz?

[warm patio]

<@&286206848099549185>

[tacit arch]

It's just arctan of the imaginary part over the real part

[warm patio]

yeah but wouldnt that be pi/6 not -5pi/6

unless i cant do exact values to save my life

[warm patio]

.

[tacit arch]

No

What quadrant is z in

And what quadrant is the angle pi/6

[warm patio]

its 3rd quad>

'?

[tacit arch]

For z yes

[warm patio]

wouldnt that mean the theta is pi plus pi/6

[tacit arch]

Yes I was wrong here. I missed the +pi you brought up

7pi/6 and -5pi/6 are the same angle

[warm patio]

oh bruh

classic from me

thanks man

.close

[lone heart]

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[thick mesa]

use substitution method

[prime solstice]

Thats where I'm stuck
I dunno what to substitute

[thick mesa]

try u = x^2 + 5x + 4

[prime solstice]

Hmm so...
(2x+5)dx = du or dx = du/2x+5
I'm stuck again :/

[serene junco]

you sure? the 2x+5 is in the denominator

[prime solstice]

This complicates it further :/

[thick mesa]

yea, becomes 1/u√u du

[limpid spade]

Does it?

[prime solstice]

Umm no?

[serene junco]

i'm not sure, i don't see that route

It's tempting and it's what I tried first but I didn't get very far

[prime solstice]

Would've been very easy if 2x+5 was in the numerator

[serene junco]

yeah that's why my brain went there first lol

fairly sure it's meant to be a trig sub

[prime solstice]

Probably, the answer is in inverse trig function

If that helps :/

[serene junco]

I haven't finished yet but I'm pretty sure you want to complete the square in the sqrt and then perform a trig sub

[prime solstice]

Alright lemme know when you're done

[serene junco]

yeah a trig sub should definitely work out

@prime solstice

are you comfortable with trig sub / completing the square?

[prime solstice]

Yep

[serene junco]

Do you see where you would maybe want to apply it in this integral?

[prime solstice]

Under the sqrt term?

[serene junco]

yeah

in my opinion, a quadratic under a square root, expecially in the denominator, is a sign to try trig sub

[prime solstice]

I still don't know what to substitute x with

Which trig function?

[serene junco]

well did you complete the square?

[prime solstice]

Ahm hold on

[prime solstice]

(x+5/2)^2 - 9/4

[serene junco]

Yeah

so that's equivalent to the expression under the sqrt

Does that help you identify a trig sub to make?

[prime solstice]

Umm no

Im really weak with this part

[serene junco]

ok no worries

are you comfortable with pythag identities

sin^2 + cos^2 = 1 etc

[prime solstice]

Yes

[serene junco]

So you can rearrange that to 1 - sin^2 = cos^2

also tan^2 + 1 = sec^2

and consequently sec^2 - 1 = tan^2

those are the three forms of the identity that are useful for trig sub

[prime solstice]

Yes im aware of it

[serene junco]

so if you have something that looks like constant - x^2, you probably want to substitute sin somehow

etc

you have (x + 5/2)^2 - 9/4

[serene junco]

see how that matches this form?

sorry, I had a - instead of a +, fixed now

[prime solstice]

I still dont get it

[serene junco]

sec^2 - 1
(x+5/2)^2 - 9/4
variable^2 - constant

[prime solstice]

Ohh

Alright i see it now

[serene junco]

so you want to substitute x+5/2 = (some kind of sec function)

but you want the coefficient to be 9/4 after it gets squared

so we do
x + 5/2 = (3/2) sec(theta)

If you're not sure where the 3/2 came from, try the substituion and I think you'll see

[prime solstice]

Ye i get it

Now what

Hmm also 2x+5 becomes 3sec theta

[serene junco]

right lol

awfully convenient isn't it

[prime solstice]

Ye

So now 9/4 out of the root becomes 3/2

And we have tan^2 theta under the root

Which is tan theta

What about the dx though?

[serene junco]

x + 5/2 = 3/2 sec(theta)

differentiate both sides

dx = ?

[prime solstice]

Ahh yes

NICE

So i got theta/3 + c

[prime solstice]

And theta = arcsec 2x+5/3

And its the answer

[serene junco]

🎉

[prime solstice]

THANKS A LOT

[serene junco]

no problem 👍 good work

[prime solstice]

Alright thanks again, I'll close this

.close

[lone heart]

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[lime sluice]

If (4,1) is an eigen vector then (-4,-1) also eigen vector?

[vale wigeon]

sure is

even with the same eigenvalue

[lime sluice]

Because variable k can be either positive negative but not 0

[vapid shuttle]

no

[vale wigeon]

what is k

[lime sluice]

Multiple of vector

[vapid shuttle]

because eigen vectors come from the nullspace of A-lamdba I

any eigen vector is in this nullspace