help-27

[drifting sierra]

The "plot" of that is just two lines, y=0 and y=1

A plot always has some precision

[sand dove]

computers like desmos can't do that because float type numbers have finite precision, when "x is p/q where q is odd" requires infinite precision

[drifting sierra]

(so no, it's not that it can't be plotted by a computer, it's that the plot itself is not quite well defined)

[rough sparrow]

is x^x defined only for postive integers for convinience?

[drifting sierra]

Note that Desmos can plot n^n for any integer n

[sand dove]

.

[drifting sierra]

Example: https://www.desmos.com/calculator/rasbol96qx

[sand dove]

and that's because desmos works with a different type of data

computers work with integers quite well

[sand dove]

x^x defined for all positive reals

[drifting sierra]

Yeah, you just can't really mix ints and floats (unless you specifically program that, but why bother)

[unborn osprey]

oohh cool

[rough sparrow]

ah yes

reals not just integers

[sand dove]

when you ask to compute f(x) for specific values of x

like x = p/q with q odd

and p negative

desmos responds

but it doesn't plot it

because plotting is done with floats

[rough sparrow]

hmmm

[sand dove]

vs computing f(-1/3), -1/3 is interpreted as a rational number

[rough sparrow]

and then?

[sand dove]

well that's it

[rough sparrow]

i learnt some computer science today yayy

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[spring vessel]

any easy way to solve this?

i tried with that (5(x^2 +4x+ 3) + 5(4x+3))/(x^2+4x+3) but my answer is really different

[pseudo basin]

use ^ for exponents

also 5(x^2 + 4x + 3) + 5(x^2 + 3) ≠ 5x^2 ...

you want to do the polynomial long division first

[spring vessel]

sorry i meant - instead of that +

[spring vessel]

hmm okay

[pseudo basin]

5(x^2 + 4x + 3) - 5(x^2 + 3) still isn't equal to 5x^2

[spring vessel]

omg wait type

typo*

[pseudo basin]

in any case btw, after the long division you'll have a mildly bashy but not terribly hard integral

[spring vessel]

(5(x^2 +4x+ 3) - 5(4x+3))/(x^2+4x+3

[spring vessel]

okay okay

[pseudo basin]

ok

so you have that your fraction equals $5 - \frac{5(4x+3)}{x^2+4x+3}$

[woven radish]

Ann

[pseudo basin]

the 5 is integrable by itself

so you just need to partial-fraction the rest

[spring vessel]

yep

[spring vessel]

i tried but i am getting B as 45/2 and A as -5/2 , after solving with those values i am still not getting the correct answer

or whatever the answer is given at the back of my book

[pseudo basin]

theres like 37,000 different places you could've made an arithmetic fuckup

[spring vessel]

😭

lemme try again wait

[pseudo basin]

which of these goes over which denom btw

[spring vessel]

i am geting (45/2)log (x+3) -(5/2)log(x+1)

[spring vessel]

?

[pseudo basin]

is it A/(x+1) or is it A/(x+3)

[spring vessel]

the first one

[pseudo basin]

uh huh...

well ok, probably easier to differentiate your thing

,w d/dx [45/2 * log(x+3) - 5/2 * log(x+1)]

[woven radish]

Results provided by WolframAlpha

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

Requested by ann_dec

[pseudo basin]

so your antideriv is correct

for 5(4x+3)/(x^2+4x+3)

[spring vessel]

number 16,(answer)

[spring vessel]

yeah

[pseudo basin]

note the final answer will have to be 5 - I where I is the result of F(2)-F(1) with F(x)=

(45/2)log (x+3) -(5/2)log(x+1)

[pseudo basin]

and what's your answer

[spring vessel]

um i didnt get it

[spring vessel]

that one

[spring vessel]

.

[pseudo basin]

wdym "didn't get"...

no i mean like

[spring vessel]

i didnt understand 😭

[pseudo basin]

when you found the definite integral

what did you get

if NOTHING: where did you hit a barrier

[spring vessel]

oh i might be dumb as shi 💀 i forgot its a definate integral

😭 i am sorry

i forgot to do that part

[pseudo basin]

you forgor 💀

[spring vessel]

I GOT THE ANSWER YES

i am sorry 😭

thank you 😭

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[crimson silo]

Can someone help me with part a and b pkease. I have started it but i think its wrong so a bit confused. 🤣

[crimson silo]

X cant =6 and it doesnt move anlong the x axis, only up the Y.

Is Q (6,0)

[hardy trail]

Yep :) Your working out does show it!

[crimson silo]

So how do i do part A?

[hardy trail]

Wellllll x can equal 6, no?

[crimson silo]

For part b yes

But not part a

[hardy trail]

What are the solutions to 2x(x - 6) = 0?

[crimson silo]

2x=0

X=0

And x-6=0
X=6

[hardy trail]

Good. So, what's the x coordinate of R?

[crimson silo]

0

[hardy trail]

Nice. I mean you can also look at the graph and see it's a little obvious:
R lies on the y axis. That means that, you should check x = 0 on both quadratics.

[crimson silo]

Yea but idk how to get the Y axis

[hardy trail]

R lies on the curve y = x^2 - 8x + 12, right?

[crimson silo]

Yea

So do i sub 6 in place of x

And see ehat i get for Y?

[hardy trail]

Hm, why 6?

[crimson silo]

X=6

Oh, nvm

[hardy trail]

Are you sure?

[crimson silo]

I sub in 0

[hardy trail]

Perfecto.

That's it.

[crimson silo]

Ohh

I was just being stupid and never though of that thanks! 🙂

[hardy trail]

You are good. No problem!

[crimson silo]

Ill fill out the formfor ya too 🙂

[hardy trail]

Thanks :)

Much appreciated!

[crimson silo]

Thanks to you too for the help 🙂

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[woven radish]

Renato

[spring oasis]

. close

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[iron fiber]

I am currently working through a textbook and have the following task

"Show that the equivalence relationships reflexivity, symmetry and transitivity actually are equivalence relationships"

Now I understand the definitions of these three terms as such, what I am struggling with is proving the statement because I do not know how to start. Can someone give me a pointer as to how to frame and think about this problem?

[upper schooner]

(do you happen to have a picture of the question, and what it actually says? I'm not sure whether I'm parsing it correctly - are you being asked to show that some relation is an equivalence relation, and so satisfy those three terms?)

[iron fiber]

It is unfortunately in german. Let me translate it via deepl quickly

[stone stump]

show original

[iron fiber]

ok let me install discord on my phone quickly 😄

Task 3 although I might have realized that I misinterpreted it. The other pages are there for reference

[olive snow]

You want to prove that an equivalence relation has these three propreties verified ?

[stone stump]

"show that the examples of equivalence relations in section 1.2 are indeed equivalence relations"
mentioned examples:
x~y iff x and y live in the same city
x~y iff x and y are represented by the same member of the bundestag
x~y iff x=y
x~y iff x and y are parallel (lines)
x~y iff n | x-y

[iron fiber]

This is probably what I am misunderstanding ... I thought (the question is pretty vague about it) I have to prove the equivalence relationships themselves and was pretty lost so most likely, yes, what you said is correct.

[iron fiber]

Ok then it is much clearer ... I'll go solve the question then. Thanks for the patience and dealing with my lack of interpretation skills haha 😄

I will close this chat then

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[shut crown]

.

can someone please explain to me what a parallel projection is? i understand what a normal projection from say vector v onto z but what is a parallel projection. Yeah it gets right of a component but how is it parallel?

[young spade]

Okay, so

In reality they are basically the same

Normal Projection is used to find the projection of a vector v, to the direction perpendicular to a plane.

Parallel Projection is the projection of a vector v to a direction parallel to another vector
Or onto a plane.

I separeted the two because, if you give it some thought, the first description is quite literally the same process as Normal Projection

The "onto a plane" version is a bit different tho.

I swear there is a prettier formula for it, but you can find it by choosing two coplanar vectors as reference, doing Normal/parallel projection for each and adding both results

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@shut crown Has your question been resolved?

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[atomic idol]

Ok so there’s this thing and I’m supposed to show that the dimension of it is N-1 by utilizing another expression

[atomic idol]

This is the other expression and I was supposed to prove it’s surjective to help with the dimension but I’m not sure how that’s related
I think I have sth showing it’s surjective but it doesn’t seem helpful

The vector w is also complex and not the zero vector

[jaunty mantle]

Think about the properties of tau here

[jaunty mantle]

And what does this mean for S

Surjectivity is nice but surjective isn’t that related to the = 0 part

[atomic idol]

Not sure if I follow

[jaunty mantle]

What’s interesting about a = 0 condition

What else in linear algebra has a = 0 condition?

[atomic idol]

Linear independence?

[jaunty mantle]

True, what else

[atomic idol]

90 degree angle between vectors

[jaunty mantle]

Also now that I think about it you also need the surjectivity later

[jaunty mantle]

We’re in a vector space we have no notion of angles

[atomic idol]

I don’t think I can think of a different thing atm

[jaunty mantle]

Kernel/null space

[atomic idol]

I might not have heard of it before

Nope not a single time

[jaunty mantle]

…

Your course is weird

[atomic idol]

Sorry I have 3 hours of sleep and a professor who demands that I submit homework in a mailbox

[jaunty mantle]

If A is a linear transformation then ker(A) is the subset of the domain of A such that Ax = 0

The kernel of A is everything A sends to 0

The kernel of A is a subspace

You should know these things

This is the basics of linear algebra it’s what everything else is built upon

[atomic idol]

I wish the order in which we learned things made sense

Looks like we’ll both suffer from it

[jaunty mantle]

Well start here

Show that kernel of A is a subspace

The trick I think here is to look at the kernel of tau

Since tau is surjective the image has dim 1

So the kernel must have dim domain - image = N-1

[jaunty mantle]

This uses the fundamental theorem of linear algebra

[atomic idol]

What would that be?

[jaunty mantle]

But S is precisely the kernel of tau

https://mathworld.wolfram.com/FundamentalTheoremofLinearAlgebra.html

You can ignore everything with orthogonality since we have no inner product

[atomic idol]

I should mention that my prof started talking about matrices today

I don’t know anything about those yet

Except for some very basic things I’ve figured out by myself

[atomic idol]

Can you elaborate that part please

[devout snow]

@atomic idol Has your question been resolved?

[jaunty mantle]

The image of a linear transformation is again a subspace

[devout snow]

@atomic idol Has your question been resolved?

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[radiant aspen]

so far ive completed this

[coral dragon]

did you calculate the values of A-B?

i.e.

d_i = A_i - B_i

[radiant aspen]

wym

mb i didnt see this

@coral dragon

this is the data

yo

tales

[coral dragon]

yeah, so did you calculate the values of Sat - Wed?

[radiant aspen]

we use something called stat crunch to make these calculations

but i have no clue what to select

can u help me figure how to do it

[coral dragon]

never seen this in my life ngl

[radiant aspen]

DAMN

[coral dragon]

this yeah

[radiant aspen]

i jksut dont know how to get box plot twin

🥀

[coral dragon]

you were supposed to do a box plot or answer which box plot is the correct one?

[radiant aspen]

idk wihich one

[coral dragon]

uh

I use R/Python code to create statistical plots

mainly R

[radiant aspen]

can u help me do that

yo bro

@coral dragon

how do i find the correct box plot

🥀

[coral dragon]

first calculate Sat - Wed

[radiant aspen]

calculate by

getting the diff?

[coral dragon]

Camera	Sat	Wed	Sat − Wed
2244	2	19	−17
1671	14	8	6
2081	10	3	7
1964	5	8	−3
1743	4	26	−22
1151	1	2	−1
2321	11	4	7
1142	30	8	22
1652	3	11	−8
1514	3	17	−14
2054	3	24	−21
1934	1	9	−8
3082	12	4	8

[radiant aspen]

ok

[coral dragon]

sorry for bad allignment

[radiant aspen]

u good i see it perfectly

[coral dragon]

now you look at biggest/lowest/median values

[radiant aspen]

so biggest is22

lowest is -22

so even?

[coral dragon]

should look something like this

-ish

[radiant aspen]

erm

[coral dragon]

so with the numbers you said

[radiant aspen]

none of them go to 22 and -22

:/

the ones in the left both go to -22

soooo

[coral dragon]

it's kinda like this:

oh wait

I just saw

errm

[radiant aspen]

wait look

past this correct

ok

fixed it to noy be on top

then i

?

golod?

[coral dragon]

wait

why is there a point below -40?

[radiant aspen]

huh

[radiant aspen]

bruhhhh

is my diff not correct

[coral dragon]

hold up, cause now I'm confusing myself lol

[radiant aspen]

ok

🙁

im so cooked

🥀

im studying for my exam tmrw

idk how to even get a box plot

🥀

[coral dragon]

sir

[radiant aspen]

?

[coral dragon]

what program do youuse

[radiant aspen]

stat crunch

[coral dragon]

to generate plots

[radiant aspen]

stat crunch

[coral dragon]

you just need to select the Diff column, not Camera ID, Sat, or Wed

create the “Diff” column

[radiant aspen]

i did select diff column

[coral dragon]

ah ok

[coral dragon]

this matches with D

doesn't it?

[radiant aspen]

oh yea it does

i can see it now

ty

🙂

wait

no

this is bad

[coral dragon]

https://tenor.com/view/punisher-no-no-no-tanklorde-gif-25785566

[radiant aspen]

LOL

wiat no ur right

i almost got it mistakend

i have 2 more pwease help me

ill calculate and just tell me if i got it correct

[coral dragon]

k

gimme the data at least?

[radiant aspen]

e

its fine

why did i getting this?

ok

yo

here is the problem

it will only let me select one tax rate

and i need to do both to get my answers

or

i can just do one at a time

?

1

this what i got

its either b or c?

yo

bro

i think its c

am i correct

ik its c

[coral dragon]

ok lemme see

[radiant aspen]

and i think this is b

[coral dragon]

I got this

[coral dragon]

looks more like a B to me

[radiant aspen]

so im wrong because women is longer

[coral dragon]

but idk

[radiant aspen]

thats where i messed up

[coral dragon]

image kinda bad to read

[coral dragon]

yep

[radiant aspen]

wait

i think its d tho

[coral dragon]

that was my line of thought

[radiant aspen]

wait no

it cant be

so b or c

ima just go with b

but look

look at c

the lines r close

bu b there far

[coral dragon]

pretty sure it's B, cause woman has longer tail + man has outlier

B is the only that matches both

[radiant aspen]

what abt this im done

[coral dragon]

oh lemme se

[radiant aspen]

gemini said it was c 🥀

chat gpt said b 🥀

google said a 🥀

ima just do b fuck it

yo i think im done

i think the other one is correct

[coral dragon]

hold up pls

btw

[radiant aspen]

TAKE YO TIME TWINNN

my bed time is in 13 min tho

[coral dragon]

AI is bad at reading those imgs

[radiant aspen]

its just my sleep time

yea thats true

[radiant aspen]

EHHHHH

WHYS UR SO DIFF

[coral dragon]

doesn't look like a match :despair:

[radiant aspen]

BRO

DO I JUST

THATS IT

be done w it

u think mine correct

or nah

[coral dragon]

yeah

go ahead

[radiant aspen]

okay

[coral dragon]

oh

I got the wrong data lol

[radiant aspen]

i was right buddy

[coral dragon]

ah damn

[radiant aspen]

alr thanks for the help

!done

[devout snow]

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[radiant aspen]

.close

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[full hollow]

!status

[devout snow]

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

[full hollow]

5

where did 90 come from

.close

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[restive river]

i got x = pi/3 or cos(x) = 1/2, can anyone confirm?

[rare kernel]

ye its correct

u can confirm by urself putting x value in the expression and seeing what it evaluates to

[deep abyss]

Yep

[restive river]

ty frends

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[fervent helm]

I can't see the pattern, can anybody please help

[wild grove]

The bottom looks like n • (4n+3)

[fervent helm]

yea

but what about the numerator

[rain summit]

First term is 2^3 - 1^3

Second term adds in 4^3 - 3^3

Third term = 2nd term + 6^3 - 5^3

[fervent helm]

but there denominators are different right?

[rain summit]

Ye

[fervent helm]

then how?

[rain summit]

So like, each "pair" is just $n^3 - (n-1)^3$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

Try using the difference of cubes identity

[fervent helm]

alright

[rain summit]

So what does a "pair" simplify to

Wait

[rain summit]

Try to simplify each pair

[fervent helm]

my bad

[rain summit]

You should get your first factor as 1

[fervent helm]

i don't get it

[rain summit]

Try factoring this

So you could see what the pattern is clearer

[fervent helm]

alright

$1 \cdot (n^2 + (n-1)^2 + n \cdot (n-1))$

[woven radish]

Prathmesh

[rain summit]

The 1s is self explanatory

[wild grove]

Isn't that (2n)³-(2n-1)³?

[rain summit]

Assuming n is an even number

[fervent helm]

I still don't get it

[wild grove]

Odd work too wdym

[tribal patio]

$\sum_{n=1}^{15} (4n^2 + (2n-1)^2 + 2n \cdot (2n-1))$

[woven radish]

Hunter

[tribal patio]

hmm the first two term would add up so you get sum of square if you know what the formula is

if you expand the last term it would be 4n^2 this's also sum of square

2n is just sum of integers from 1 twice

[fervent helm]

okkkk

got it

so this is for the numerator right?

[glossy dew]

yeah

[fervent helm]

okkkk

[glossy dew]

or you can do
2 x (sum of even cubes from 2 to 2n) - (sum of cubes from 1 to n)

[fervent helm]

got it

[glossy dew]

it all cancels

[fervent helm]

yea got it

can you please tell this one too

[tribal patio]

find a_n close form, then bn-b_{n-1} = a_n = that close form then you could find close form of b_n

It seems like close form of b_n is quadratic sequence

[devout snow]

@fervent helm Has your question been resolved?

[deep abyss]

(2n-1)n²

This might be tje general form @fervent helm

Then u simplify the sigma

And put n=15 at last

[glossy dew]

since sequence for a is 1, 3, 5...
sequence for b would be 1, 1 + 3, 1 + 3 + 5, ...

[devout snow]

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[glossy dew]

which is just n²

[devout snow]

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[devout snow]

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[gleaming gorge]

.close

.close

[pseudo basin]

it's already closed, just leave it

[devout snow]

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[wanton tiger]

is there a way to do this without randomly putting values

[glossy dew]

graph

[wanton tiger]

and i also want to know what f(x) really is because it says min of smth comma smth?

[wanton tiger]

like f of x is min of both of those vlaues ?

[glossy dew]

minimum of the functions at that point

like the smaller of both is the function at that point

[lyric hornet]

if 1/2-3x^2/4 at a particular x-value is smaller, take that value, otherwise take the value of 5x^2/4

[glossy dew]

yeah just draw the graph

[wanton tiger]

oh i see

ohhhh

[lyric hornet]

[\operatorname{min}(a(x),b(x)):=\begin{cases}a(x)&\text{if }a(x)<b(x)\b(x)&\text{if }a(x)>b(x)\\end{cases}]

[woven radish]

ΠαϳαμαΜαμαΛλαμα

[wanton tiger]

so what i do is find x where the function changes to the 2nd definition

[wanton tiger]

yeaaa

i got it]

tysm

.close

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[rain summit]

What if a(x) = b(x)

[devout snow]

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[frozen aurora]

i want to prove that
$$
\int_{x_1=0}^1 \cdots \int_{x_m=x_{m-1}}^m 1 , dx_m \cdots dx_1 = \frac{(m+1)^{m-1}}{m!}
$$

[woven radish]

artemetra

[frozen aurora]

but i don't know how to do this

context: https://math.stackexchange.com/a/5110691/1153468

[frozen aurora]

i tried computing a general
$$
\int_{x_1=0}^1 \cdots \int_{x_m=x_{m-1}}^m f(x_m) , dx_m \cdots dx_1
$$
for any $f$ so that i can substitute $f(x_m)=\int_{x_m}^{m+1} 1 dx_m$ and do induction
but that seems to be harder than the original problem

[woven radish]

artemetra

[frozen aurora]

so i honestly have no idea how to do this

ping on reply

[faint gorge]

can't you use fubini in the inductive step?

[frozen aurora]

how? the bounds depend on the variable w.r.t. which we are integrating?

or am i wrong

my multivar is rusty asf

also $f(x_m)=\int_{x_{m+1}=x_m}^{m+1} 1 dx_{m+1}$

like that

[woven radish]

artemetra

[faint gorge]

oh i see it's not constant

so not a rectangular region

[stone stump]

so if you compute the inner integral then you have int int int ... c-x_i dx dx dx which you can pull apart into int int int c dx dx dx - int int int x_i dx dx dx

where I'm too lazy to type properly

the first one should certainly be doable with induction

and the second also doesnt feel that bad?

[faint gorge]

the goat

[stone stump]

frankly you probably just have to get your hands dirty

[devout snow]

@frozen aurora Has your question been resolved?

[frozen aurora]

the first one is basically the original one if you take the constnant c out of all the integrals, but the second one is like the original but with x instead of 1, which looks harder...

but I'll give it a try

[frozen aurora]

that's fair :(

[devout snow]

@frozen aurora Has your question been resolved?

[devout snow]

@frozen aurora Has your question been resolved?

[tender kite]

Um hi

Nvm i don't know this

[devout snow]

@frozen aurora Has your question been resolved?

[frozen aurora]

i'll try this later

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[worldly tapir]

How do we turn a sine function into a cos function/ cos function into sin function

[hollow jolt]

you mean put it in that form?

[worldly tapir]

yes switch between forms i can show an example

[hollow jolt]

cos(90-A)=sinA

[worldly tapir]

yea but we do it in radians

[hollow jolt]

then just cos(pi/2-A)=sinA

[worldly tapir]

wait

so then

[worldly tapir]

for this example we dont need to care about the negative sign right

[hollow jolt]

pretty sure it does matter

but pretend 4(x-3pi/4)=A and then swap it

[worldly tapir]

i see, but then for this pretend we only have cos

shouldnt this be 0?

[hollow jolt]

what would be 0?

youre just converting a function right?

[worldly tapir]

it would be pie/2 - pie/2

[hollow jolt]

oh

[worldly tapir]

yes from cos to sine

[hollow jolt]

$2(\theta-\frac{\pi}{4})=A$

[woven radish]

ImOakley

[hollow jolt]

$\frac{\pi}{2}-A=\frac{\pi}{2}-2(\theta-\frac{\pi}{4})$

[woven radish]

ImOakley

[hollow jolt]

$=\frac{\pi}{2}-2\theta+\frac{\pi}{2}$

[woven radish]

ImOakley

[hollow jolt]

$=\pi-2\theta$

[woven radish]

ImOakley

[worldly tapir]

im so confused 😭

[hollow jolt]

this is the bit inside the trig function

[worldly tapir]

wym

[hollow jolt]

you have $y=7\sin{[2(\theta-\frac{\pi}{4})]}-3$

[woven radish]

ImOakley

[hollow jolt]

you need to convert $\sin{[2(\theta-\frac{\pi}{4})]}$ into cosine

[woven radish]

ImOakley

[hollow jolt]

the angle in question is always the entirety of whats inside the sine

so to convert it into cosine you minus the whole thing from pi/2

[devout snow]

@worldly tapir Has your question been resolved?

[devout snow]

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[ashen temple]

I didn't ask 🤣

[ashen temple]

Hell yeah

[jade pecan]

do u have a question

[faint gorge]

a question you didn't ask

[soft umbra]

.solved

[devout snow]

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[soft umbra]

Gotcha

[cold haven]

<@&268886789983436800> check their history.

[winter torrent]

what the heck

[jade pecan]

he didnt ask it seems like

[winter torrent]

find something marginally more productive to do with your time

[cold haven]

...is that for me or for them.

[cold haven]

ohhh my bad.

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[devout snow]

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[jolly notch]

wolframalpha doesn't seem to be accepting delay terms? trying to plot a nyquist

[jolly notch]

works fine without delay

[supple knot]

this is not a wolfram debug server

help channels are for math questions

[jolly notch]

sorry i'll try to find somewhere else

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[spark quarry]

help !

[weak cove]

You just have to keep track of your parenthesis and the order of operations

Do you have a specific example of an operation you want to try

[spark quarry]

this one …. Why isnt it working when i am solving the equation … i manually had to try the options..

[coarse flume]

You divided both sides by 0.05 so it should have become 0.15/0.05=1+B

[weak cove]

put the right hand side of he equation in line 2 inside parenthesis

(0.05+B(0.05)

and then when you divide both sides

you will get something different than what you wrote

[spark quarry]

so even if right side was 0.05 * B(0.05) i should have put it in parenthesis first?

[weak cove]

That is what the right hand side is already

So yes

[coarse flume]

They meant if it was mutiply instead of add

[spark quarry]

yes… will it still become 1*B ?

[coarse flume]

No it would be 0.05*B

[spark quarry]

Thank you very much 🙂

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[faint sage]

I think I might be stupid but how do I justify x^2+x+2 is greater than 0 for all reals
trying to find domain and I know the function x^2+x+2 is greater tha 0 for all reals but not sure mathematically how to come to that conclusion

[fossil locust]

complete the square!

[faint sage]

oh
oh no I completely forgot how to do that
haven't touched complete the square since grade 10 :((((

.close

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[fossil locust]

or you could set d/dx (x^2 + x + 2) = 0

then sub that x-value back in

since it's concave up (*+*x^2) you know that must be the minimum

[fossil locust]

!occupied

[devout snow]

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).

[fringe summit]

Can u explain clearly

[late scaffold]

this channel is in use

[fossil locust]

ask in #help-44｜stanley-🌲-v2-dans

[fringe summit]

Ok

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[earnest rivet]

on the bottom line, i think that if i can show that thing in brackets is equal to 1, then the proof is complete, but im not sure how to show it is equal to 1, as there are so many terms in the bracket, (as its the sum of the recipricol of (k+1) multiplied by any number(x) between 1 and k), or maybe theres a different way to approach this? thanks

[earnest rivet]

oops when n = 3, s_n is also 3

[deep abyss]

I think it would give an exponential series?

[earnest rivet]

like e = 1 + 1/1! + 1/2! + ... ?

[deep abyss]

Yeah

[earnest rivet]

so it would end up as k + e?

hmm

[deep abyss]

e-1

I dont think u understand the ques

Reciprocal of product of elements

Not product of reciprocals of elements

[dark talon]

Sorry to intrude but arent these two the same

[deep abyss]

Not really no

[deep abyss]

U find the product first then reciprocate it

Oh wait

I dont understand ur soln dang TT

[dark talon]

[earnest rivet]

the inductive part of the n = 1, n = 2, n = 3 cases?

so like

[deep abyss]

Omg waiti think i misunderstood the ques

Ignore me lol

[earnest rivet]

s_k+1 will contain all of s_k and also contain the sum of recipricols of (k+1), (k+1)(k) and loads of other terms like (k+1)(2), (k+1)(k-5)(4)(1) etc

no its ok my working out sucks

[earnest rivet]

s_k+1 contains s_k and also the sum of all the recipricols or all the possible terms containing a (k+1) 😭 if that makes any sense

[lusty sapphire]

I don't get how you're getting $S_2=2$. Wouldn't it be $\frac11+\frac1{1\times2}$?

[woven radish]

SWR

[earnest rivet]

i think the subsets of (1, 2) are (1), (2), (1,2)

so 1/1 + 1/2 + 1/1x2

[lusty sapphire]

Oh. You are doing every subset

The question is ambiguous because i think it just wants you to do the subsets {1,2,...,n}

[earnest rivet]

whats the difference between subsets and every subset

[lusty sapphire]

My interpretation is that it wants you to do just the sets {1}, {1,2}, {1,2,3} etc

But maybe i am wrong

But it could be the way you are thinking, because you're getting a nice result

[earnest rivet]

i think this works, since every new term involving (k+1) will be the same as the amount in S_k, since its just each term in S_k multiplied by k+1, and then we have the unique 1/(k+1) term

.close

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[torn thicket]

Let $S$ be a nonempty set and let $e \in S$. Define an operation $*$ on $S$ by putting $a * b = e$ for all $a, b \in S$.

(a) Show that $S$ is a semigroup under the operation $*$.

[woven radish]

edg

[torn thicket]

Here's my current progress so far

\begin{proof}
Let us recall that a semigroup is a nonempty set that has associative property. Suppose that there exists another element $c \in S$, we will verify whether $S$ is associative and closed under $*$.
$$(a * b) * c = a * (b * c)$$
Checking the left side, because we know that $a * b = e$,
$$e * c = a * (b * c)$$
\end{proof}

[woven radish]

edg

[torn thicket]

Since we know that a * b = e, how will we know what's e * c or b * c even? This is the part where I'm kinda stuck

[pulsar sand]

You have more than just a * b = e since that is true for all a,b in S

[torn thicket]

the problem doesnt give anything other than that

[toxic grove]

a and b aren't specific elements in S

The question says that for any a and b, a * b = e

i.e. any two elements multiply together to get e

That's what the upside down A means

[torn thicket]

even though it says for all a, b in S? or am i understanding it wrong

[toxic grove]

Yes you're understanding it wrong

Think of it this way

If I want to define a function of the real numbers, I might say that f(x) = 2 * x for all x

x isn't a specific number, it's just a stand in

It's exactly the same here

[torn thicket]

i see

[toxic grove]

a and b don't represent specific elements of S, they're just standins

[toxic grove]

And it's exactly the same for a, b, c here

[torn thicket]

then how should i approach this problem?

am i to say that a * b = e and b * c = e?

since they're just arbitrary

[toxic grove]

That's correct

[torn thicket]

i see

that's interesting hahah, i think i got it

thank you

.close

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[toxic grove]

Oh yeah also another nitpick

[torn thicket]

oh

[toxic grove]

The set does not have the associative property

The operation does

The set is just a set

[torn thicket]

i see, thanks for the clarification

i'll take note of that from now on

[devout snow]

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[junior heron]

for part A, i just have no idea how to parametrize that intersection curve

[junior heron]

i tried plugging in for y in the second equation but got 2 quadratics

[upbeat isle]

you do not need to parametrize the curve of intersection c to evaluate the line integral

[devout snow]

@junior heron Has your question been resolved?

[junior heron]

HUH???

how would you do it

[upbeat isle]

simply because it’s a closed loop

read the question carefully

[junior heron]

so i see on desmos 3d that from the positive y axis its a circle

so that is a closed loop therefore integral is 0 ??

[upbeat isle]

yup

[upbeat isle]

exactly

[junior heron]

if thats true how would i know that without desmos 3d

[upbeat isle]

because in the start it’s already stated

F = delta f

[junior heron]

and how does that tell me its closed

[graceful cosmos]

One curve is a "3d quadratic" and the other is a plane. You might imagine they make some kind of ellipse

[upbeat isle]

oh wait my bad

[upbeat isle]

yes this is the correct response for that question

[grand edge]

It doesn't tell you it's a closed loop, it just tells you it's a conservative vector field

[junior heron]

okay got it thanks

.close

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[karmic sluice]

Hey, I’m stuck and this is starting to feel pretty convoluted, so I’ll try to be clear.

What I have:

A timestamped stochastic time-series (e.g. market prices). It’s noisy but when an event happens the series often shows a reaction (up or down), sometimes strong, sometimes subtle, sometimes nothing, thats what I am investigating.

A sequential list of events (ordered list). There are 5 possible event types (call them 1..5). I know the sequence and the type at each position, but no timestamps — just the order (e.g. 3 → 2 → 3 → 4 → 1 → ...).

I expect each event (usually) causes a reaction in the time-series.

Goal:

Align each event in the ordered list to the most likely reaction in the time-series and learn how each event type (1..5) typically affects the series (direction, magnitude).

Why this is hard:

The timeseries is stochastic many spontaneous moves that are not caused by events.

Reactions vary by event type and magnitude.

Events only come with order, not time.

Lag is unknown and non-stationary. Between each event.

Any help will be appreciated

[supple knot]

yea there's not enough information to help you unless you give more information to "reaction in the time-series." that's uninformative to the problem

[devout snow]

@karmic sluice Has your question been resolved?

[devout snow]

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[bold vale]

i found EX1 and EX2 using conditional expectation and im recognizing a pattern but im struggling to find a closed form for the pattern

[winter torrent]

what pattern are you seeing?

it might help to compute EX3

[bold vale]

i did

its

so x1 is 1 + 2/9, x2 is 1 + 4/9 + 4/27

x3 is 1 + 3(2/9) + 3(4/27) + 8/81

[winter torrent]

hmm

so 1 -> 1 + 2/9

[bold vale]

its def some sort of geometric series but im struggling to find a closed form

[winter torrent]

yea

i'm not sure where x2 came from

i think i get it as 1 + 4/9 + 4/81

[bold vale]

For X_2?

[winter torrent]

ya

[bold vale]

hm

my exact thing is $9*\frac{1}{9} + 2*\frac{2}{9} + \frac{14}{39}$

[woven radish]

uni

[winter torrent]

ya where did that 3 in the denominator come from

[bold vale]

if you lose twice in a row you have 1/3 dollars

oh wai

ur right

[winter torrent]

you'd have 1/9

[bold vale]

cuz 1/3 is from 1 loss

thank u

[winter torrent]

so you mentioned geometric series

[bold vale]

r is 2/some faactor of 3

[winter torrent]

why do you think that?

[bold vale]

it seems like ur multiplying by 1/3 each time

[winter torrent]

on some level sure

ex0 = 1 right

like you start with $1

[bold vale]

yes

[winter torrent]

and ex1 = 1 + 2/9?

[bold vale]

yes

[winter torrent]

and ex2 = 1 + 4/9 + 4/81

[bold vale]

yup

[winter torrent]

do you see a pattern there?

[bold vale]

kind of

1 + (2/3)^2 + 2^2/3^4

[winter torrent]

hmm that is true

could also be 1 + 2 * 2/9 + 2^2/9^2

[bold vale]

so r = 2/9

[winter torrent]

try computing ex3

[bold vale]

yeah i need 2 redo that

cuz i did it wrong

[winter torrent]

yawp

[bold vale]

1 + 2/3 + 4/9 + 8/9^3

[winter torrent]

instead of 27^2 let's say 9^3

one thing that's interesting about this problem is that it's kinda symmetric

it doesn't really matter what you start with, right? like it's all the same

if you started with $100

then your ev after 1 round would be 100 (1 + 2/9)

[bold vale]

okay

hmm

[winter torrent]

so what if you started with 1 + 2/9?

[bold vale]

ur ev would be (1 + 2/9)^2?

[winter torrent]

yawp

[bold vale]

So is EX2 just EX1 as if you started with (1+2/9)

Ohhhhhhhhh

Thank you

do u have any tips for recognizing patterns like this cuz i feel like this is the part i sometimes struggle w

[winter torrent]

hmm

sometimes it's just experience but in this case there's something called linearity of expectations

i didn't recognise it immediately

[bold vale]

wait how does linearity of expectation apply

[devout snow]

@bold vale Has your question been resolved?

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[devout snow]

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[restive river]

im stuck pls helppp
i got a+b+c = 64a-14 but idk what to do from here

[restive river]

only thing i know about a is that it should be positive

[solemn cloak]

@restive river

You there?

[restive river]

ya

[solemn cloak]

What is a vertex?

[restive river]

9, -14

[solemn cloak]

I'm not asking for the coordinates

I'm asking what is a vertex

[restive river]

like its min/max

here its min

btw i found a+b+c by doing vertex form eq = given eq

[solemn cloak]

There's a much more straightforward way to do it here

[restive river]

oooh

howww

[solemn cloak]

What are the properties of a turning point?

[restive river]

yo are we doing like calc or sm

[solemn cloak]

Yeah

[scarlet fern]

Nvm

[restive river]

like when dy/dx = 0?

[solemn cloak]

Yes

[scarlet fern]

It’s either a or b

Since the vertex is at 9 14

A must be negative

So

[restive river]

bruh its D

[solemn cloak]

😂

[scarlet fern]

Bruh

9 -14

Then it’s so ob D

Using the same reasoning

A must be positive

64a-14 and a is positive

Only possible answer is D

[restive river]

can you explain this

[solemn cloak]

Wait you didn't learn calc?

[restive river]

i learned ts

[scarlet fern]

Derivatives on this function is dumb

We already know the vertex

[restive river]

i did calc bc last year

[scarlet fern]

Derivatives can be used to find the vertex

Thats all

[restive river]

yo but 64a - 14 how does that gives D

like i know that a > 0

im so dumb

lol

[scarlet fern]

Since a is positive 64a is positive

[restive river]

ya

[solemn cloak]

Nah we can manipulate it to help find the coefficients

[scarlet fern]

There is no way a,b,c are possible\

Thats it

[scarlet fern]

How?

[restive river]

?

[solemn cloak]

How is a positive guys?

[restive river]

k=-14

that means a > 0

[scarlet fern]

The parabol intersects the x axis 2 times

[restive river]

cuz U shape

min is -14

[scarlet fern]

And vertex is at 9 -14 meaning a must be positive

[solemn cloak]

Ok

[scarlet fern]

Elaborate on this

[solemn cloak]

Ok

What happens if you diff the function?

[scarlet fern]

We find the slope?

I’m not sure how you would calculate it

[solemn cloak]

We already have the slope

[scarlet fern]

The coefficients

[restive river]

wait i get why its D

i got it

thanks yall

[scarlet fern]

Did you understand my explanation

[restive river]

yaya

.close

[devout snow]

Channel closed

Closed by @craggy summit

Use .reopen if this was a mistake.

[scarlet fern]

It’s derivative is 2ax+b

How would you calculate the coefficients

@solemn cloak

[solemn cloak]

There's a turning point at (9,-14)

[scarlet fern]

18a+b = 0 then

[solemn cloak]

Gradient at that point is 0

[scarlet fern]

Now what

[solemn cloak]

Sub in (9,-14) to the original equation

[scarlet fern]

81a+9b+c = -14

You need another eq

There are many equations that satisfy these parameters

[restive river]

yo why are we using calc for ts 😭

[scarlet fern]

Our question was to find the possible answer

[scarlet fern]

Idk that what I am trying to find out

[restive river]

ts like using a bazooka to kill a roach

🥀

[scarlet fern]

Calc ain’t all that

[solemn cloak]

Vertex is -b/2a

[scarlet fern]

Dude

Thats literally what I wrote

18a = -b

[restive river]

what math are yall in

[scarlet fern]

12th grade

[restive river]

i did calc bc last year

[scarlet fern]

You?

[restive river]

now im doing mvc

[scarlet fern]

Are you taking the sat

[restive river]

ya

[scarlet fern]

This looks like sat problem

December sat?

[restive river]

i did allat just to redo algebra

[restive river]

ya

[scarlet fern]

I see what grade are you in?

[restive river]

11th

[scarlet fern]

Are you aiming for 1500+

[restive river]

uh im aiming for 1550+ but its my first time so smth like 1500

[solemn cloak]

Oh wait my bad guys I didn't read the question properly

Yeah you convert it to vertex form, expand and compare coefficients

[scarlet fern]

I got 1530

[solemn cloak]

Then find the discriminant which must be positive due to 2 real roots

[scarlet fern]

Sat is not easy

The English especially

[restive river]

ayyyy

im bouta bomb rw

[scarlet fern]

800 on math is ez

[restive river]

i need like 750+

[scarlet fern]

But 700+ on rw is hard

[restive river]

im mocking 730-750 rn

[devout snow]

Available help channel!

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[lost heart]

I would like help understanding how, in audio engineering, sine sweeps recorded in a space are smushed into a single point in time to create an impulse response, to then use in convolution reverbs.

I understand that the sine sweep will go from 20Hz up to 20kHz over the span of let's say 6 seconds.

Then this is "deconvolved" into a single point somehow, containing all the frequencies in one moment, but minus the sine itself. Apparently this uses some kind of inverted sine sweep, but I'm not understanding any of this part.

How does this work? What is this inverted sine that it's being "deconvolved" with? I saw some mentions of the fast fourier transform. How is that involved?

An example shown in this video at 5:10 to 5:30
https://youtu.be/BLKWy-U6iQY?si=XEroyKvGb0sbgfDY

I'm just trying to understand audio software a little better at the lower level, and the math behind it.

Thank you!

[devout snow]

@lost heart Has your question been resolved?

[devout snow]

@lost heart Has your question been resolved?

[lost heart]

I might log off and check this tomorrow morning.

[devout snow]

@lost heart Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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• Show your work, and if possible, explain where you are stuck.
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[restive river]

How can I solve these kinds of problems correctly and quickly? I try using formulas, but I still dont really understand them

[restive river]

welp

[rain summit]

wait

[rain summit]

use this root property:

$\sqrt[n]{\frac{A}{B}} = \frac{\sqrt[n]{A}}{\sqrt[n]{B}}$

[calm blade]

1/n

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

this one

[rain summit]

@restive river

[lyric hornet]

Roots obey the same properties as exponents. Notably because they can be represented as exponents: (\sqrt[a]{b}=b^{\frac1a})

[woven radish]

ΠαϳαμαΜαμαΛλαμα

[devout snow]

@restive river Has your question been resolved?

[restive river]

Yes ik

[rain summit]

have you done any question now?

[restive river]

Tomorrow I have a test on nth roots. Are there any important formulas or key points I should know?

[rain summit]

this one is the key to roots

if you can remember exponents properties then you can remember roots properties

[restive river]

Wow alr

[devout snow]

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[fierce ruin]

am i doing this right?

idk about the graphing ngl

[frigid shale]

I got a video that is suitable for that hold on

hope it helps

[late scaffold]

looks about right