help-39

[last moth]

intuitively this makes sense because if you know your signal only contains low frequencies (the most extreme case would be if your signal is constant) then you can space out your samples really far in time and still reconstruct the whole thing

[rose sentinel]

I keep confusing dft and dtft, when we sweep the frequencies in dtft, are we not using Riemann sums rather than integrals for area? Wont this area be off from the actual integral area? And isn’t the effect of this meaning our area isn’t quite reliable for large T

[last moth]

yes our area isn't reliable because of this effect of multiple copies of the frequency spectrum overlapping with each other

[rose sentinel]

And if T is large, our area could represent the area beneath another curve

Or is that just nyquist taking over there

[last moth]

the effect that you're describing where the Riemann sum doesn't approximate the integral well is exactly aliasing from frequencies above the nyquist rate

[rose sentinel]

hmm

I see

[last moth]

I don't know how to intuitively explain why, but that's how it is

[rose sentinel]

so as T goes to 0 we just get back out Fourier transform?

[last moth]

yup

then the width of your frequency range gets infinitely large

so you can resolve higher and higher frequencies

[rose sentinel]

And the aliased copies are so far away they’re irrelevant

[last moth]

yeah

[rose sentinel]

I guess that makes sense

alright that’s all I can think of at the moment thank you for your help!

Much appreciated you beat every YouTube video and website I could find

[last moth]

you're welcome!

[last moth]

I'm guessing this is related to Poisson summation

so look into that if you're curious

[rose sentinel]

Alright I’ll check it out thanks!

im gonna go try and replicate my learning on a whiteboard now, see you later thanks

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[pearl pond]

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[proud kiln]

I have parts A, B, C done, but I do not quite understand part d

[pearl pond]

@proud kiln Has your question been resolved?

[sudden sigil]

A "non-zero quadratic form" refers to a quadratic expression where the coefficient of the squared term (the "a" value) is not zero

So just a quadratic right?

[proud kiln]

I would assume

[sudden sigil]

And google says A "finite dimensional inner product space" is a vector space where every vector can be represented by a finite number of components

[proud kiln]

Well, I decided to turn them into sums

[sudden sigil]

But I don't know how vectors have anything to do with this

[proud kiln]

Do you know how to do all the LaTeX stuff?

[sudden sigil]

Not really

Do it on paint maybe

[proud kiln]

This is pretty bad

And the bottom is where I start

The quadratic form I defined using Sylvester's Law of Inertia

And the norm squared part I worked through on the bottom right, so I am then just stuck with these two sums divided

And I've been thinking

It may have a directional dependence

[sudden sigil]

Bro this is next level I'm sorry

[proud kiln]

Lol you're all good

[sudden sigil]

I thought this was just multivariable limits

[proud kiln]

Ah my course is weird

At my uni they call it Honors Calculus, and it's essentially real analysis, Calculus 3, and Linear Algebra smushed into a year long course

We rarely have nice computational questions like those earlier limit ones lmao

[sudden sigil]

The only thing I know is that if x tends to 0, the square of the modulus will always tend to 0+ due to the nature of the modulus

So it should be infinity unless the top part tends to 0

[proud kiln]

Thats what I was thinking

[sudden sigil]

I will look it up tomorrow

[proud kiln]

I was thinking about maybe something as simple as a unit vector

Taking the form of as Im sure you know, x/|x|

[sudden sigil]

Yes I know that

[proud kiln]

And my thought was that since my lamba terms can be positive, negative, or zero (Sylvester's Law of Inertia), my final answer would depend on how the x term aligns with the eigenvalues

So essentially, I could have tons of different terms

So in general, I think it would not exist

[sudden sigil]

I'm sorry I didn't even know you could do limits with vectors

[proud kiln]

I dont either

[sudden sigil]

I hope someone else helps you

[proud kiln]

Im just guessing at this point lmao

[sudden sigil]

Hahahaha me too

[proud kiln]

Thanks for the thought though!

[sudden sigil]

No problem, good luck!

[proud kiln]

Thanks!

.close

[pearl pond]

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[rose sentinel]

I'm wanting to understand the Z-Transform and its relationship to the DTFT. From my understanding it is a generalized version of the DTFT that is just a lot more useful. It's also like a discrete laplace transform (comes from it being generalized fourier) and I need to learn about it, where it comes from, what it means, and how to use it. Can anyone walk me through it? Thank you so much

[rose sentinel]

@last moth Sorry for bugging you again, if you're available I'd appreciate it if not its fine

[last moth]

Yes a z-transform is a discrete-time Laplace transform.

The Laplace transform differs from a Fourier transform in that it can analyze signals which grow exponentially over time

[rose sentinel]

right

Because of the complex s = alpha +ibeta

[last moth]

Yes

The alpha corresponds to a growth/decay and the beta corresponds to a frequency of oscillation

[rose sentinel]

I get that, where the alpha multiplies everything by an exponential term

right

Yup, I'm familiar with laplace transforms, how does Z do the same thing as S?

[last moth]

You can rewrite z^-n as e^(-(log z) n), maybe that makes it more obvious?

here, n is your time variable

In comparison to the Laplace transform where you have e^(-s t), where t is your time variable

[rose sentinel]

where is log z coming from?

[last moth]

exponent properties

z is the same thing as e^(log z)

[rose sentinel]

ohh

[last moth]

so the z does the same thing as the s in a Laplace transform

you can write z in polar form as r e^(i theta)

then r determines the growth/decay and theta determines the frequency of oscillation

[rose sentinel]

why not just use a complex exponential like we have been before?

[last moth]

it's the same thing

you can write it as a complex exponential if you want

this notation seems cleaner though

[rose sentinel]

so is its derivation similar to how you showed me the DTFT is derived from the CTFT?

[last moth]

either way you can convert between the two notations using an exp/log, so it's good to understand how both work, as both forms come up a lot and are useful in different circumstances (polar vs rectangular form of a complex number)

[last moth]

you pretty much just replace the integral with a sum, yeah

[rose sentinel]

so if I'm following correctly its
$$\int^{\infty}_0{f(t)e^{-(\alpha+i \beta)t}}dt$$

[jolly parrot]

Nathan

[rose sentinel]

as the laplace

[last moth]

yeah

change that to a sum over values of t instead

[\sum_{t=0}^\infty f(t)e^{-(\alpha+i\beta)t}]

[jolly parrot]

synaptERIC_integration

[last moth]

and that's a z-transform

where z = e^(alpha + i beta) = e^alpha e^(i beta)

[rose sentinel]

hmmm

okay

[last moth]

btw, just like how the laplace transform reduces to the fourier transform when Re s = 0, the z-transform reduces to the discrete-time Fourier transform when z is on the unit circle

[rose sentinel]

so they just kind of expanded notation and let z be the complex exponential rather than just letting s be a complex variable in the exponent

[last moth]

yeah

[rose sentinel]

yeah ive seen that, its really neat

Okay so basically

so i just let that whole complex exponential be z and thats it?

or well z^-t

what about it being a polar plane?

why is it different than the s plane?

[last moth]

because of the complex exponential

[rose sentinel]

wait let me guess its because we defined the plane as the entire

yeah

dang

that is not as bad as I thought

[last moth]

you can convert between the rectangular plane vs the polar plane by using exp/log

[rose sentinel]

could you show me an example?

[last moth]

sure

[rose sentinel]

thank you

[last moth]

s = 1 + 2i corresponds to z = e^(1 + 2i) = e * e^(2i)

the further right you go in the s plane, the further outwards you go in the z plane

the further up you go in the s plane, the further counter-clockwise you go in the z plane

[rose sentinel]

right

okay so going to the right aka just sliding along the real axis in the s plane corresponds to a stronger exponential term in the z plane right

stronger real exponential

[last moth]

yes

[rose sentinel]

and that makes it go out why?

[last moth]

further right in s = more magnitude in z

[last moth]

bigger magnitude number

[rose sentinel]

but then you would pass the unit circle if you go to like infinity, yet that is still stable in the s plane no?

[last moth]

what do you mean?

[rose sentinel]

like the right side of the s plane is stable

[last moth]

yes

[rose sentinel]

poles being there are fine

[last moth]

the right side of the s-plane corresponds to outside the unit circle in the z-plane

[rose sentinel]

wait

isnt that unstable

i think i got it backwards

left hand side of s plane is stable

negative exponents

[last moth]

yes

left side of s-plane corresponds to inside the unit circle in the z-plane

[rose sentinel]

okay and so when the real component of s is greater, the magnitude is greater?

[last moth]

yes

[rose sentinel]

and what value is it when its the unit circle?

1?

or 0

wouldnt it have to be zero

[last moth]

yes, Re s = 0

corresponds to |z| = 1

[last moth]

which is why this makes sense

[rose sentinel]

right okay

i see

[last moth]

yeah it's just a different way of looking at things (polar vs rectangular)

but same concepts

[rose sentinel]

so is there any particular reason we decided to define it as the entire complex exponential

cause we didnt do that for dtft

[last moth]

like you mean why we write z^(-n) instead of e^(-sn)?

[rose sentinel]

yea

and just call it DTLT

[last moth]

I don't think these approaches were historically as unified as they are now, the z-transform in particular has many names, such as a "generating function" in combinatorics or a "probability generating function" in probability or a "Laurent series" in complex analysis

it is mathematically convenient to work with sums of this form, due to their resemblance with power series from calculus

[rose sentinel]

mhm okay

[last moth]

as for why the laplace transform uses an exponential

I think it's weird to think about a complex number raised to a fractional power

you start getting into questions of branch cuts and so on

like what is i^(1/2)?

[rose sentinel]

no clue

[last moth]

any square root has two possibilities right

[rose sentinel]

right

[last moth]

with real numbers, we just pick the positive one

with complex numbers.. seems like you have two equally valid options

it's just mathematically more convenient to work with exponentials generally

when dealing with complex numbers and continuous exponents

with the z-transform, the exponent is always an integer because we are working in discrete time, so it's perhaps mathematically more convenient to think of it this way in terms of z^(-n)

[rose sentinel]

i see

[last moth]

there's a straightforward relation between the z-transform and Laplace transform anyways with z = e^(sT) so it's trivial to convert between the polar vs rectangular representations

alright hope this helped

[rose sentinel]

it very very much did thank you

If you have any free time some other time, could you explain to me what it is about poles that gives you the system function, not quite sure what its called, but I saw connections to the characteristic equation in the laplace transform being the coordinates of the poles in the complex plane, I image you have some other stuff to do right now, but maybe some other time?

[last moth]

you can ask in #odes-and-pdes I'm sure there are people there that can help you

[rose sentinel]

okay thank you 👍

[last moth]

you're welcome

[rose sentinel]

I really appreciate your help you just helped me skip past like 5 weeks of doom forum scrolling

[last moth]

[rose sentinel]

take care! thanks again

.close

[pearl pond]

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[pearl pond]

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[wraith badger]

I need help with this q 😔

[wraith badger]

oh and if possible, could somebody explain the answer to this question as well?

[iron stream]

Newton's second law ?

[iron stream]

Use the formula, s = ut + 1/2 gt² here u = 0

[rancid depot]

distance traveled when accelerating is proportional to the square of the time

[wraith badger]

If ur referring to C. its not right 🙁

[iron stream]

Rate of change of momentum

F = dp/dt

[vivid flower]

u sure man?

[urban sun]

b

or wait

[vivid flower]

nah its b

[urban sun]

oh

[broken fossil]

The solution set is described by a blood type

[wraith badger]

OHH

[iron stream]

Newton's second law states that

[vivid flower]

im also struggling here with maths

[wraith badger]

is it cuz F=ma=mv/t

[vivid flower]

but im alr alone

[iron stream]

Opened a channel?

[broken fossil]

open another help

[urban sun]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[vivid flower]

yh better

[iron stream]

For easy understanding yes

[wraith badger]

wait but why would it be rate of change in momentum and not just change in momentum

is it becasue of the t

[iron stream]

mv/t

Yes this represents change in momentum w.r.t time

[wraith badger]

okay

but why is C wrong?

oh wait nvm i ujndertsnad

that would be F=a/m

right?

[iron stream]

Yeah

[wraith badger]

yay

[iron stream]

F = ma/m

[wraith badger]

thank you so much for the help

[iron stream]

Wlcm !

[pearl pond]

@wraith badger Has your question been resolved?

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[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[pearl pond]

@stoic imp Has your question been resolved?

[stoic imp]

,w Nullspace[{{-1,1,0,0},{4,0,1,1}}]

[jolly parrot]

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[pearl pond]

@stoic imp Has your question been resolved?

[pearl pond]

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[rancid steppe]

$4x^2 -9-2(2x-3)$ i am stuck on factorizing this

[jolly parrot]

Simon James B

[north talon]

notice that 4x^2 - 9 = (2x-3)(2x+3)

[rancid steppe]

I do not see how we got 2x+3

Yes we have 2x-3 but how did we manipulate the other terms to get 2x+3

[north talon]

difference of squares

[rancid steppe]

I am confusedd

Oh wait

[warm sonnet]

$a^2 - b^2 = (a + b)(a - b)$

[jolly parrot]

asm

[rancid steppe]

Yess i see it now

$(2x-3)(2x+3) -2(2x-3)$

[jolly parrot]

Simon James B

[rancid steppe]

like this?

[warm sonnet]

You can factor out (2x - 3)

$(2x - 3) ((2x + 3) - 2)$

[jolly parrot]

asm

[warm sonnet]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[rancid steppe]

Yess i see it

Now we distribute -2?

[warm sonnet]

Distribute?

What expression are u working with

[rancid steppe]

What is next bec this is is not final answer

[warm sonnet]

Well

[crystal crypt]

wdym?

[warm sonnet]

$(2x - 3)(2x + 3 - 2)$

[jolly parrot]

asm

[warm sonnet]

I suppose

[rancid steppe]

OH

I am stupid

[warm sonnet]

Hold on

[rancid steppe]

Yes i got it

[crystal crypt]

guyz will u help in basics of parabola?

[warm sonnet]

Ok yea it is true

[warm sonnet]

Open a help channel, this is occupied

#❓how-to-get-help

[rancid steppe]

.close

[pearl pond]

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[boreal raptor]

can someone help me solve this integral?
i have a feeling it's a trig sub or something
because of the 1-x^2 at the bottom but idk how to get rid of the -x

don't solve it please
just.. point me in the right direction

[frozen lantern]

it's not

it's just a u sub

no?

[boreal raptor]

u = x+1?

[frozen lantern]

wait no its not nvm

[boreal raptor]

i don't see what the u sub would be

[frozen lantern]

yeah sorry i read the top as 2x+1 :D

[boreal raptor]

i did think about doing u sub and then splitting the x+1 into x + 1/2 + 1/2

but it doesn't work

[frozen lantern]

im thinking about that rn lol

does it not?

[boreal raptor]

u can try but i didn't get anywhere

[frozen lantern]

i feel like it shold

ok lets try

why not

[boreal raptor]

yeah because when u split, u get u's and x's

[frozen lantern]

ok it wont

yeah

[midnight karma]

I think you can use trigonometric substutuion

[boreal raptor]

but how

[frozen lantern]

which

[boreal raptor]

x = sintheta?

doesn't seem to

idk

[frozen lantern]

i dont see it ;-;

[midnight karma]

wait let me try it first

[frozen lantern]

,wolf tan^2 x - sec x

[jolly parrot]

Results provided by WolframAlpha

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Requested by percykel

[midnight karma]

reshape the denominator into vertex form

[boreal raptor]

when i see a 1-x^2 in a square root, i think about trig sub but i don't see how to work it because there's a -x

[boreal raptor]

oh complete the square?

[midnight karma]

yes

[stable dune]

$1 - x - x^2 = \frac54 - (x + \frac12)^2$

[jolly parrot]

hiidostuff

[boreal raptor]

but it's -x^2 - x + 1

[stable dune]

And we can go from there

[frozen lantern]

AH

[boreal raptor]

oh rightt

[frozen lantern]

neat

[boreal raptor]

half then square

then divide by 5/4

mm

[stable dune]

Then just factor the 5/4 out

And trig sub the x + 1/2

I think let it equal sin(x)

So we have $\int \frac{x+1}{\sqrt{1-x-x^2}} \dd x = \int \frac{x+1}{\sqrt{\frac54 - (x + \frac12)^2}} , \dd x = \frac{\sqrt{5}}{2} \int \frac{x+1}{\sqrt{1 - \frac45(x + \frac12)^2}} , \dd x$

[boreal raptor]

.close

[pearl pond]

Channel closed

Closed by @boreal raptor

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[boreal raptor]

ty

[stable dune]

Np

[jolly parrot]

hiidostuff

[pearl pond]

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[craggy crypt]

Can someone explain how this works

Why do we set u to that

What happens to 18y^2 -4y +3

Wait I see it

.close

[pearl pond]

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[bright gate]

help a boyo out

[compact ridge]

!status

[pearl pond]

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

[bright gate]

1

[pearl pond]

@bright gate Has your question been resolved?

[bright gate]

pls someone save meh

[leaden marsh]

I think you should try greens theorem for the first one

And the second one is by definition, you can find

[bright gate]

:0

ok

i will tyr

[leaden marsh]

For the third one, you have normal vector as k that means your plane is the XY plane, so you can write dS as dxdy

[leaden marsh]

Got the answer?

[bright gate]

nop

i set up an integral

but i dont think i knowh what to do next

[leaden marsh]

Can you show what you did

[bright gate]

its the closed part thats throwing me

[leaden marsh]

Yeah so apply the greens theorem...

Or if you don't want to do that

Break the path into two different sections

First when it goes from 0,0 to 1,1 on y = x
Then from 1,1 to 0,0 on y = x^4
Find the work done for them individually and then add

You have your F and dr
dr = <dx,dy>
Now if you do F•dr you will get xdx + (x^2 + y)dy
Then for the first path, you have x = y => dx = dy
Now it's easily solvable with x from 0 to 1

Similarily do for the the second path

[bright gate]

would i do the sum of two integrals one with respect to x and one with respect to y/

[leaden marsh]

Ummmm, can you explain....

[bright gate]

;-;

[leaden marsh]

See for the first path
It now becomes

Integration from 0 to 1 of (xdx + (x^2 + x)dx)

And now there shouldn't be any problem in integrating as all terms are in x

[bright gate]

;-;

[leaden marsh]

Yeah you can do this too
But don't forget to rewrite x^2 as y^2 because you're integrating with respect to y in the second integral

[bright gate]

um

i got 10/6 which isnt correct boss

[leaden marsh]

For the first path from 0,0 to 1,1 on y = x

Work = $\int_{0}^{1} xdx + (x^{2} + y)dy =^{x = y, dx = dy} \int_{0}^{1} xdx + (x^{2} + x)dx = \int_{0}^{1} (2x + x^2)dx$

[jolly parrot]

@leaden marsh

[leaden marsh]

For the 'first path' now do similarly for the path from 1,1 to 0,0 on y = x^4

[leaden marsh]

This is for the first path

For the second path from 1,1 to 0,0 on y = $x^4 \$
Work = $\int_{1}^{0}xdx + (x^{2} + y)dy =^{y = x^{4}, dy = 4x^{3}dx} \int_{1}^{0} xdx + (x^2 + x^{4})4x^{3}dx $

Now add both the works
I think you should get -1/3

[jolly parrot]

@leaden marsh

[leaden marsh]

Corrected

Still got a doubt @bright gate ?

[pearl pond]

@bright gate Has your question been resolved?

[pearl pond]

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[stiff mauve]

guys i have a question

[stiff mauve]

7b

this is what the answer says

Is this also correct

[spare lark]

dividing by 2 make it more clearer that you can use a)

but to me its good

[stiff mauve]

alright thanks

i have one more if u dont mind

[spare lark]

sure

[stiff mauve]

on 2c

i dont rly understand why it cannot be determined

[spare lark]

i can't tell

[stiff mauve]

alr thank you for your time

[pearl pond]

@stiff mauve Has your question been resolved?

[pearl pond]

@stiff mauve Has your question been resolved?

[pearl pond]

@stiff mauve Has your question been resolved?

[stiff mauve]

<@&286206848099549185>

[kindred stone]

x fractions

?

[stiff mauve]

.close

[pearl pond]

Channel closed

Closed by @stiff mauve

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[pearl pond]

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[charred dome]

idk how to solve this

[charred dome]

free numbers? but this chapter hasn't covered it yet.. can someone explain plz?

matrix theory. btw.. sry i thought my textbook had it but no they dont in this chapter. idk why they hvae this question in this section.

[prime bramble]

do you know how matrix multiplication is defined?

[charred dome]

yea but im not doing matrix multiplication

this is elementary operattions to solve

sry this is a bad picture

[charred dome]

here this is the question i need to solve

idk how to make latex for that

for the matrix

i was in another help but i closed it bc i thouhg it was gona be in my textbooksection but its not

they told me to use free variables

[spare lark]

Yes

[charred dome]

how do i do that then

plz jiust help me solve it so i can apply it to the next question

[spare lark]

So

[charred dome]

do i just make x3 = 1?

[spare lark]

No

x3 will be a free variable and you express x1 and x2 in terms of x3

[charred dome]

how so..

i tried reducing the matrix they said not to

[spare lark]

No need

[charred dome]

like i divided 1/2 R1

ok

ya

[spare lark]

Just send x3 to the other side

For both

[charred dome]

what doe tha t mean

so 2x1 + 2x2 = 7 - 9x3?

[spare lark]

Yes

[charred dome]

and x2 = -2 -5x3?

[spare lark]

Indeed

[charred dome]

ok but how do u solve for x3 then

[spare lark]

You don't

[charred dome]

the b ook has an answer tho

lol

it says the solution is

(5, 3, -1)

[spare lark]

Can you show it ?

[toxic fractal]

the whole thing

!original

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[charred dome]

that is it

it doesn't show how to solve

[spare lark]

This is just one solution among infinity solution

[charred dome]

this is all they give you

[toxic fractal]

that should have instructions

[charred dome]

pretty crazy

[toxic fractal]

like "solve this" or "do this"

[charred dome]

should i just skip it

like idk wut to do

[spare lark]

Why ?

[charred dome]

and the next one is basically the same as this

well how did they get that as answer

[spare lark]

You have it

[charred dome]

but how do you get (5, 3, -1)

[spare lark]

Its not correct

[charred dome]

uh

it's in the answer key tho

[spare lark]

There are infinite answers

[charred dome]

so how do i produce one

and why are there infinite answers

we learned abt infinite answers in this section actually

[spare lark]

Take x3 = 2 and replace here

What x2 value ?

[spare lark]

And after replace value of x2 and x3 in this to get x1 value

[charred dome]

well , since x2 = -2 -5x3

[spare lark]

And you have the triple

[charred dome]

there is no value though

[spare lark]

I said take x3 = 2

[charred dome]

oh

so you can choose any value then?

[spare lark]

Or x3 = 1

[charred dome]

they chose -1

[spare lark]

Thats why its infinite

[charred dome]

ok that's weird they didn't cover it in this section

[spare lark]

Thats why its stupid to write it as unique answer

[charred dome]

lol

what can i write as evidence it is infinite

[spare lark]

that you let x3 in R

[charred dome]

can i not solve it as a system of eq.?

[spare lark]

And express x1 and x2

In terms of x3

Its enough

[charred dome]

it's weird bc

like it's aasking me to verify the values i got..

in q. 17

whatever

.close

[pearl pond]

Channel closed

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[pastel haven]

write 512 as a power of two different bases each base less than 512: so i got an answer but it seems too simple. I got 2^9 and 4^4.5

[plush bramble]

,calc 2^9

[jolly parrot]

Result:

512

[plush bramble]

,calc 4^4.5

[jolly parrot]

Result:

512

[warm current]

4.5

[pastel haven]

is there anything else to it

[warm current]

$e^{\ln 512}$

[jolly parrot]

SWR

[warm current]

nope

[pastel haven]

alr thanks, it seemed too simple for 4 marks so... thanks anyways

.close

[pearl pond]

Channel closed

Closed by @pastel haven

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[pearl pond]

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[pastel haven]

-49 = p^2
so I took the square root of this and I'm wondering whether to put the +- sign or just put 7. I have had a similar conversation before and moral of the story a square root symbol calls for the positive value. but this is a negative value so im confused

[wet osprey]

There’s 2 solutions to this equation

[pastel haven]

yeah, so do I put the +- sign?

[wet osprey]

p = 7i and -7i both solve the equation

[pastel haven]

but then again the square root symbol

[wet osprey]

The point of the +- sign is to say there are multiple solutions

[wet osprey]

And to contract this statement so it’s quicker to write

[spare lark]

Sqrt symbol over a negative number ?

[pastel haven]

uhh im not sure

[wet osprey]

$\pm\sqrt{-49}$

[jolly parrot]

frosst

[wet osprey]

What

[pastel haven]

im so confused

[spare lark]

To me the problem is using the sqrt symbol

[pastel haven]

and keeping the 49?

[wet osprey]

@warm current what’s wrong

[pastel haven]

or should i go ± 7

[glossy trellis]

4b

[warm current]

I just liked that you omitted i

[spare lark]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[glossy trellis]

sorry

[pastel haven]

it ok

[wet osprey]

Oh I was trying to show that you can have the +- outside a square root

Without evaluating the square root first

[pastel haven]

[wet osprey]

Is your question -49 = p² or is it 49 = p²

[pastel haven]

-49 = p^2

how do you write the exponent in discord

[wet osprey]

And what is the instruction

[spare lark]

²³⁴

[wet osprey]

I have a special keyboard on my phone that lets me do it

[pastel haven]

solve the variable in each of the following (there were other questions hence the word following)

[wet osprey]

Well then do you understand that there are 2 solutions?

[pastel haven]

7 and -7 right?

[wet osprey]

Where’s the i

7 and -7 are both 49 when squared

We want -49 when squared

[pastel haven]

what i

[wet osprey]

Imaginary number

[pastel haven]

uhh i dont understand what that means

[wet osprey]

Look at -49 = p²

How can something squared be negative

[pastel haven]

yeah i understand that now

cuz two negatives make a positive ovb

[wet osprey]

If you have not learned about imaginary numbers then there would be no solutions

[pastel haven]

is there a way you could give a small description for my curiosity

[wet osprey]

It is exactly what we want from this i

It has the property that when you square it it’s negative

i² = -1

From this you can do a lot of crazy stuff

So if we allow this use of i, then (7i)² = 7² * i² = 49 * -1 = -49

[pastel haven]

oh i see

so you can set anything to i

[wet osprey]

No

[wet osprey]

i is defined by this

[pastel haven]

or is i^2 always -1

[wet osprey]

Always

[warm current]

If $n=0$, then $n^2=0$, if $n>0$, then $n^2=n\times n>0$. If $n<0$, then $n^2=n\times n=(-|n|)\times(-|n|)=|n|\times|n|>0$.\
\
In any case, $n^2\ge 0$. So, the square of no number can be negative. We therefore define some "imaginary number" whose square would be negative. That is, we define the value $i$ such that $i^2=-1$

[jolly parrot]

SWR

[pastel haven]

i see, so just i is imaginary

[wet osprey]

It’s called the imaginary unit

[pastel haven]

wow thats so cool

[wet osprey]

Cos it’s like the number 1

1 is 1 lot of “real” numbers and i is 1 lot of “imaginary” numbers

2i is 2 lots of imaginary numbers

Or 2 lots of the imaginary unit

As in 2 * i

[pastel haven]

we have not learned about this

idk what to do

[wet osprey]

Then i suppose there are no solutions

[pastel haven]

do you want me to give u the full question

[warm current]

!xy

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[wet osprey]

It’s not solvable then

[pastel haven]

ok

Its e)

,rotate

[warm current]

!show

[pearl pond]

Show your work, and if possible, explain where you are stuck.

[pastel haven]

ok

Ignore the last step

bruh i hope I didnt mess up otherwise this would be for nothing

[warm current]

here

[pastel haven]

omg

wait

wut

[warm current]

add 52 to both sides of -3=p²-52

[pastel haven]

thats insane 😭

how did I mess that up

mb guys, atleast I learned about i. it always confused me. thanks

.close

[pearl pond]

Channel closed

Closed by @pastel haven

Use .reopen if this was a mistake.

[warm current]

yup. Always fun to learn stuff

maybe one day you will learn why $i^i=e^{-\pi/2}$

[jolly parrot]

SWR

[pastel haven]

bruh thats too much

[pearl pond]

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[small cape]

I no want to write it twice

Anyone help?

[open rivet]

!status

[pearl pond]

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

[small cape]

If you read what I wrote, you would know my status

😭

1

I don’t know where to begin

[open rivet]

Do you know what an arithmetic sequence is?

[small cape]

Yes

I wouldn’t be doing this if I didn’t

Tbh

[open rivet]

,w arithmetic sequence

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by .bonk__

[open rivet]

So something like, 5,6,7,8, would be an arithmetic sequence

[willow chasm]

you know what r is

[small cape]

🤨

[open rivet]

And so would be 9,5,1,-3,-7

[small cape]

Yes

I said I knew

[small cape]

Right here

[willow chasm]

you also know what a_21 is

[small cape]

What is the _

[willow chasm]

subscript

[versed mica]

key word "didn’t"

[willow chasm]

like ^ but for below

[open rivet]

Oh, mb

[small cape]

Never really had to use it. What is it for?

[willow chasm]

its hard to format math in plain text

[versed mica]

subscript, he already told you

[willow chasm]

so people use ^ for exponents and such and _ for subscripts

[versed mica]

$a_{21}$

[jolly parrot]

knief

[small cape]

That’s what it is named. I don’t know what function it serves.

[willow chasm]

sorry

[urban galleon]

That's what @jolly parrot is for :)

[versed mica]

to denote which term in the sequence it is

[small cape]

Oh

OH

yeah

I know that

I just do t_n

Term and subscript is the term number

[willow chasm]

that makes sense

regional language difference probably

[small cape]

Yeah

[willow chasm]

im guessing you know the arithmetic sequence formula

[small cape]

Yeah

And geometric and both series

[willow chasm]

$a_n=a_1+k(n-1)$

[jolly parrot]

CrEpasPmkinPie

[willow chasm]

have you seen the general formula for it?

[small cape]

Yeah

[willow chasm]

$a_n=a_k+d(n-k)$

[jolly parrot]

CrEpasPmkinPie

[small cape]

T_n = t_n-1, n>- 2, t_1

Or somethig Ng similar

Or that’s something else

[small cape]

Seen this

Yes

General term

Or whatever

[small cape]

That’s recursive

My bad

[willow chasm]

so you know a_1 = g_1

and r=2

[small cape]

What is g

?

[small cape]

Yes

[willow chasm]

geometric series

[small cape]

Assuming g is constant siff

Oh

A is arithmetic

G is for geometric

[willow chasm]

yes

[small cape]

?

Yes

[willow chasm]

some people i know use a_n for both but i think that's weird

so you know a_1 = g_1

find the formula for a_1

[willow chasm]

like this

[small cape]

Okay

[willow chasm]

keep in mind you also know a_21 = 72

[small cape]

Let me see

I got it

[willow chasm]

show me

[small cape]

Alright

Thanks

[willow chasm]

oh you solved it?

[small cape]

I’m working on it

One sec

@willow chasm

[willow chasm]

thats not the method I thought you would use so im going to do it out myself to see if the answers match

[small cape]

Okay, sure!

It’s the one that made sense to me

Let me know when you do yours

[willow chasm]

I ended up actually using that same method 😅 but I somehow got a different answer

,rccw

[willow chasm]

let me find where we went different

[small cape]

Oh, lol

had to be positive yeah

It's laright

As long as I understand it

it should bees fines

[willow chasm]

do it from there to see if you get a different answer

[pearl pond]

@small cape Has your question been resolved?

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[pearl pond]

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[mellow idol]

hi!

i need to solve this:

prove that, if (x,y) are integers, and (x^2+y^2+1)/xy is also an integer, (x^2+y^2+1)/xy =3

[mellow idol]

here i proved that the thingy can't be lesser than 3 we get xy<1

which is not possible

if its greater we get 4xy<4xy

also not possible

is that enough to prove it?

[gleaming moss]

Why is xy < 1 not possible

[mellow idol]

writing down

wait mb

n<3 i made a mistake but what abiut the 2nd one

[hot canyon]

!show

[pearl pond]

Show your work, and if possible, explain where you are stuck.

[mellow idol]

i just said i made a mistake w that case

[mellow idol]

i think we'll get the same inequality in both cases

wait nvm found another solution, thanks!

.close

[pearl pond]

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[pearl pond]

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[radiant whale]

how does one do this integral

[drowsy adder]

what are you struggling with exactly

the exponential or the polynomial

[radiant whale]

polynomial

The book said this is an expansion-type problem

Idk if that’s messing me up

[drowsy adder]

expand the whole square

[radiant whale]

is that it

[drowsy adder]

yes

[radiant whale]

am I overcomplicating this that hard

[drowsy adder]

since after that you will just have powers of x you will have to deal with

i thought youre tripping over the 2^x

lol

[radiant whale]

does this seem correct..

so far anyway

wait

5x/x^2

is

5/x

right

[drowsy adder]

you tell me

[radiant whale]

okay yes

im telling u that

is this a W final answer

.close

[pearl pond]

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[pearl pond]

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[silent bramble]

again i’m getting a diff value..

am i trippin

im pretty sure mine is right??

[plush bramble]

,w 55C10

,w (55 choose 10) / (65 choose 10)

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[silent bramble]

ok

thanks

.close

[pearl pond]

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[tribal shale]

can someone explain me how does it works?

[bitter herald]

If you don't like the geometric approach, using Euler's formula is also a neat, algebraic alternative

[tribal shale]

what does Cos(b · Cos(a -Sin(b · Sin(a

[brave sluice]

?

[tribal shale]

oh got it

.close

[pearl pond]

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[pearl pond]

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[split badger]

hello

[split badger]

im having trouble setting up double integrals

so far i know that the points of intersections are (0,0) and (2,4)

and i can choose either the x values to represent a bound or the y value

if i choose x=0 and x=2 for one integral

then the bounds for my second integral would be y=x^2 and y=2x

the video im watching tells me that i need to choose the lower curve as my lower bound and the upper curve for the upper bound

how do i choose the upper and lower bound

[unborn abyss]

figure out which one is bigger on your interval

if you get it wrong it'll just be negative

[split badger]

im a little confused by these terms

like bigger or lower

[unborn abyss]

well, which one is larger at x=3? x² or 2x?

[split badger]

x^2 is larger

[unborn abyss]

ok so that's your upper bound

[halcyon venture]

lmao

[split badger]

do you mean at x=1? inbetween the interval

[halcyon venture]

I thought it was my channel

[split badger]

oh LOL hi hi

[split badger]

x=3 is not between the area of the curve

when i choose x=1 then 2x would be the upper bound

help

x^2 is my lower bound right?

elp

[pearl pond]

@split badger Has your question been resolved?

[unborn abyss]

oh. yeah, whoops

I misread it

again, if you get it wrong you'll get a negative number

so it's pretty easy to identify

[split badger]

why are you reacting to the bot my question wasnt answered...

does it always have to be the lower bound? im confused on how that works

and when if i chose the y variables instead, like (0,4) would i then choose x^2 to be the upper bound instead?

[pearl pond]

@split badger Has your question been resolved?

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[fossil badge]

I have about 40 numbers, lowest = 600 and highest 890. I need to do a table with a range of 20 between

[fossil badge]

So i got i need to do 14,5 rows

I'm gonna do 15 rows

how do i know from which number do i start?

[hot canyon]

Canonically, we start in an ascending order: 600-620, 620-640, so on and so forth

[fossil badge]

Someone said that ur allowed to go above and below the minmumim and maximum number

[fossil badge]

incorrect!

ur supposed to do 600-619

[hot canyon]

Yes you may go above or below the max. or min of your data, but the idea is counterproductive as it effects how you deal with the data.
After you're done organising the data in a continuous distribution table, you'll be interested in class marks and herein, the addition of extras would err your boundary class marks

[hot canyon]

Exactly, as stated above, a class size of 20 is not feasible. Instead you might want to use a class size that divides (max - min) = Range of data

As it's 290 here, a class size of 10 or 29 would be ideal

So 600-610, or 600-629 is nice

[fossil badge]

20 is MANDATORY

In the equation

[hot canyon]

Can you post the question you're dealing with?

!original

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[hot canyon]

The addition of context would enable us to better help you

[hot canyon]

,rotateccw

[hot canyon]

Alr. You're required to go:
600-620
621-640
641-660
.
.
.
860-880
880-900

As the class size is given and FIXED, you are not allowed to go 600-619 ^^"

[fossil badge]

600-620 is 21 numbers btw

600 counts as a number

[pearl pond]

@fossil badge Has your question been resolved?

[fossil badge]

.close

[pearl pond]

Channel closed

Closed by @fossil badge

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[wet swallow]

What

[regal herald]

hm

[open rivet]

!da2a

[pearl pond]

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/

[regal herald]

are you asking to help cheat on a test?

[wet swallow]

[plush bramble]

take a picture of the whole thing

[regal herald]

show us

[open rivet]

just take a pic of the whole page

[regal herald]

[wet swallow]

Is this a past paper or a test you are doing rn

I'm pinging mods

[regal herald]

lmao

[versed mica]

brother is this a banned from math discord speedrun

[regal herald]

how do you have that?

[hot canyon]

Not likely, he's already at least 10mins in

[versed mica]

yea he could do better than that

we got you bro trust🤝🏻

[wet swallow]

I can't wait

[regal herald]

think thats enough lol

<@&268886789983436800>

[versed mica]

now we need to help bro

[wet swallow]

@versed mica (sarcasm)

[versed mica]

yep

[wet swallow]

🫠

Why skull

[versed mica]

because

it was funny

let’s help him!

yea bro for sure

[wet swallow]

Yes

[versed mica]

the mods are coming to help rn

[plush bramble]

go study then

[wet swallow]

Should he dm mod mail for more help

[plush bramble]

come back when you have a concrete math problem

[versed mica]

yea sounds like a good idea

[plush bramble]

also nobody knows what time zone you're in

lots of time to study

easy peasy just read book

[regal herald]

light work

[plush bramble]

do home wook

[warm current]

(you might be missing the part where OP is asking us to do his test. I don't think he'll be coming back...)

[plush bramble]

my best rhyme ever

[wet swallow]

~~DM mod mail if you need help with the questions ~~

[versed mica]

he’s gone

[opal lantern]

.close

[wet swallow]

Modded

[pearl pond]

Channel closed

Closed by @opal lantern

Use .reopen if this was a mistake.

[opal lantern]

yall dont need to come in and joke around

just ping mods and let us handle it

you make it messier by shitposting for 40 messages

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
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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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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pastel raven]

how can i prove it rigorously?

[pastel raven]

what should i use

it's pretty obvious intuitively, that to turn a face down card to face up, you need a face up card to the left to be turned down

[shadow stag]

probably you need to find a monovariant

[pastel raven]

hmm

[brave sluice]

mathologer has a video on a similar problem

https://www.youtube.com/watch?v=04x4ZdLpN-0

[cobalt hinge]

potd

[pastel raven]

yup

[pastel raven]

okay, it works, thx!

.close

[pearl pond]

Channel closed

Closed by @pastel raven

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rain river]

If f(x + 1) = 2x² + 4x - 1, then f(x) is...

[cobalt hinge]

subsitute

[rain river]

What??

[cobalt hinge]

what value of x would make x+1=u

i.e. solve the equation for x

[rain river]

the value of x will be u - 1 then right

this is hard

I cant

[cobalt hinge]

yes

[rain river]

I don't understand the concept behind this type of problem...

[cobalt hinge]

its just subsitution

[rain river]

Let x + 1 = u, then to find x, wich is u - 1.

And then I substitute x = u - 1 into the f(x).
f(u-1) = 2(u-1)² + 4(u -1) - 1

Substitute x-1 in x of the function 2x² + 4x - 1

Im confused

[cobalt hinge]

yes

[rain river]

Can you give me some visualization?

[cobalt hinge]

k

[rain river]

What is the name of this topic?

[gleaming musk]

Translations?

idk if theres a strict name for the topic

[cobalt hinge]

just translations

or

uhhhhhhhhh

(idk)

[rain river]

Nvm I've found it, transforming function

Thanks anyway

[cobalt hinge]

k

[rain river]

.close

[pearl pond]

Channel closed

Closed by @rain river

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[shell tapir]

for which interval is the second derivative of f(x) = 2x^3 - x^2 + 5x negative ? if possible shown without a graph

[cobalt hinge]

take..the derivative twice

dont know what else to say

literally just solve f''<0

[shell tapir]

12x-2 < 0

so x < 2/12

[cobalt hinge]

2/12=1/6 but yes

thats good

[shell tapir]

ok thank you ver much 🙂