help-10

[gilded needle]

so as your screenshot says, w is in f(K) if and only if 1/w is in K; this is because f(z) = 1/z is its own inverse function: f(f(z)) = z. You take the reciprocal of z to get w = 1/z, and you take the reciprocal of w to get 1/w = z

and 1/w is in K if and only if it is a z value that satisfies |z-3| = 1

i.e. 1/w is in K if and only if |1/w - 3| = 1

[timid silo]

hmm

i kinda get it but also dont imma try again later!! thank you!!

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[obtuse pebble]

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[river idol]

Hello

[river idol]

How do I know what a good laptop is 🐣

[cloud berry]

#❓how-to-get-help

[zenith raft]

probably depends what you want it for, but i'm not sure this is the best place for that question haha 🙂

[obtuse pebble]

@river idol Has your question been resolved?

[cloud berry]

which have atleast 100MB RAM , 500MB ROM, screensize atmost 5inch and able to run supermario atmost

[ripe mortar]

A laptop that has at the very least, 4gb ram and an atleast 500gb storage

Thats the

Bare minimum u should have

To run like….

Scratch?

Ms paint?

[cloud berry]

btw i ran unity 3d in a 2gb laptop with 200GB storage also made a game

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[ripe mortar]

Whaa

[obtuse pebble]

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[tardy apex]

Hey guys somone wants to help me with this problem?

[tardy apex]

Quadrilateral ABCD is a rhombus with side length 6 cm and height 4 cm. Point E is
is the centre of side AD, point G is the centre of side BC, point F is the intersection of the lines AG and BE,
point H is the intersection of lines CE and DG.
Determine the area of the quadrilateral EF GH

I ended up with making some 90° triangles and using pythagor but It did not end up well

The intersection of that rhombus is 40cm^2

[river idol]

What’s considered good though?

I have a MacBook but idk what’s good 🥲

[tardy apex]

The answer went negative:D

I Will draw IT for u wait

[river idol]

Are you good at physics?

[tardy apex]

Not at all

U understand?

You need the intersection of red

[river idol]

What about the topic of 95% confidence interval for grouped data and median of grouped data

Wait what are we even doing over here

[tardy apex]

Trying to solve this problem

The geometry one

[obtuse pebble]

@tardy apex Has your question been resolved?

[obtuse pebble]

@tardy apex Has your question been resolved?

[obtuse pebble]

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[nimble harbor]

both my solutioms are extraneous

[robust sleet]

wdym with extraneous

[nimble harbor]

incorrect, i substituted the variable as you can see

its a term my textbook uses

[robust sleet]

did u just do (a-x)²=a²-x²?

[nimble harbor]

which part?

oh wait..

[robust sleet]

sqrt(x+3)=...

[nimble harbor]

actually that's a different of squares i believe

actually you were indeed correct oh the tomfoolery i've endured

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[silver plover]

need some help drawing the tree diagram for this question

started off with this

[obtuse pebble]

@silver plover Has your question been resolved?

[silver plover]

<@&286206848099549185>

[obtuse pebble]

@silver plover Has your question been resolved?

[lost tree]

right

[silver plover]

ive done A and B

stuck on C

[lost tree]

what is C

[lost tree]

1 - P(he doesnt binge today AND doesnt binge tomo) ?

[silver plover]

hmm i did this

but its incorrect

[lost tree]

(B_1 U B_2) U (B_1 n B_2) is the same as B_1 U B_2

[silver plover]

oh yh

[lost tree]

0.36 is the answer then ig

same thing u get with 1 - 0.8*0.8

[hexed stirrup]

hi silversolider

[lost tree]

so B_1 U B_2 and B_1 n B_2 are not mutually exclusive

[lost tree]

hi

[silver plover]

yh cool

[hexed stirrup]

whatsup hru

[silver plover]

so its 0.36

got it right

nice

[lost tree]

lol im good wbt u

[hexed stirrup]

im good too

[silver plover]

@lost tree why is this not valid for part D?

[lost tree]

isnt it B|MES

that D is asking for

[silver plover]

nah its MES given Binge

GIVEN that he binges

[lost tree]

oh

[silver plover]

ur looking at E

i think

[lost tree]

P(MES & B) = P(B | MES) * P(MES)

[silver plover]

bro its Mes given B

not B given mes

[lost tree]

yes

ur numerator

what im saying is

[silver plover]

oh

ok

[lost tree]

P(MES | B) = P(MES & B) / P(B)

= [P(B | MES) * P(MES)] / P(B)

[silver plover]

why cant i just do 0.8 x 0.36 / 0.36?

so answer is 0.8?

[lost tree]

P(B|MES) is not the same as P(B)

B and MES are not independent

[silver plover]

how come?

[lost tree]

whether he binges or not depends on whether he wtches MES or not

like

[silver plover]

oh i see

[lost tree]

rather, how likely he is to binge depends on whether he watches MES or not

[silver plover]

ye i see

[silver plover]

this is wrong i think

btw

shouldnt it be P(Mes given B) x P(B)

acc nah

ur right

nvr mind

[lost tree]

it can also be P(B given MES) * P(MES)

[silver plover]

u can do both ways

ye sry mb pal

[lost tree]

yes

[silver plover]

the part i highlighted is that just 0.4?

otherwise not reall sure

[lost tree]

u want P[ (B_1 U B_2) | MES ]

its a union

[silver plover]

ye sry

mb

anyway

[lost tree]

anyway

[silver plover]

how would u find that

[silver plover]

lmao same time

[silver plover]

so how do u find this

[lost tree]

wait im tihnking

[silver plover]

okok

[lost tree]

😦 im not quite sure

[silver plover]

yh this is pretty tough icl

[lost tree]

dont u think a tree diagram like this

will be helpful

0.8*P(B|MES) + 0.2*P(B|TA) = 0.2

[silver plover]

r u sayin the answer is 0.2?

for D?

[lost tree]

no

[silver plover]

oh u said prob of binging

ok ok

yh it is 0.2

but idk how we'd use it for part D

[lost tree]

okay u shud probably get somebody elses help lol

[silver plover]

ok

thx for ur help anyway

<@&286206848099549185>

@royal basin sry to ping u Ann, youve helped me on a few stats questions before so was wondering i u could help me with this

its pretty difficult

[royal basin]

gonna need to be filled in on all context

[silver plover]

just to recoup its part D i need help on and ive done this so far

[silver plover]

^

[royal basin]

eugh

[silver plover]

that says 0.36 btw

[royal basin]

okay sorry i dont feel like doing this rn

[silver plover]

ah ok dw

[obtuse pebble]

@silver plover Has your question been resolved?

[obtuse pebble]

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[winged glen]

https://i.gyazo.com/a72c8aaf5f8b310594f90108f6fe1ca1.png

[winged glen]

Can anyone help me solve this, I don't understand how to solve it with nx^n-1

[brave bluff]

What have you done so far?

[winged glen]

I did it with my mates, but I can't really figure out, I thought we would have to solve for continuity

with Limes

I don't get it

[brave bluff]

pdfs do not have to be continous

What is the definition of a pdf you were given? The solution you gave seems essentially correct

[winged glen]

I know pdf as 'Portable Document Format'

No idea why they write pdf

[brave bluff]

lol

in this case a pdf is a "probability distribution function"

[winged glen]

oh

[tardy epoch]

https://en.m.wikipedia.org/wiki/Probability_density_function

Density

[brave bluff]

in other words, a pdf is a function that gives the probability a random variable takes a value within a certain range

i.e if X is the the height of a person, and f(x) is the pdf, then the integral of f(x) between 180 and 181 is the probability a person will have a height between 180 cm and 181 cm

[winged glen]

Ah I seee

[brave bluff]

that's just an informal definition

if you have notes with a proper definition, you just need to make sure the function you were given satisfies all properties that pdfs must satisify

[winged glen]

So we have to use integral to get all of the possible outcomes

[brave bluff]

one of these is that overall they must integrate to 1

[winged glen]

What I don't understand is, aren't each one of them supposed to be 1 to be continously connected ?

0, x > 1

doesnt that equal to 0, since x is not defined ?

[brave bluff]

I don't think pdf's need to be continuous necessarily. Is there not a definition from your course/notes that you can use?

[winged glen]

Hmm okey, I was not talking about the pdf, I meant the first and last one

why are they defined as 0 ?

[brave bluff]

well if they weren't 0 then the pdf wouldn't integrate to 1 (and probabilities need to add/integrate to 1)

it would probably have been better if they only defined the function from 0 to 1 in the first place

but this just means the probability of the random variable being greater than 1 (or less than 0) is 0

[winged glen]

Hmm I see, okey thank you!

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[earnest tulip]

Is this working correct for finding the equation of the normal at point (2, -2)

The first bit I'm just proving that (2, -2) lies on the curve

[obtuse pebble]

@earnest tulip Has your question been resolved?

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[graceful quail]

I would really appreciate help with this question: If I have a deck of 100 total cards and 31 of the cards In the deck are the same , how many different/ unique combinations of 7 card hands are possible?

[obtuse pebble]

@graceful quail Has your question been resolved?

[upbeat gazelle]

You must disjoint the cases :

1. you have cards that are the same. In that case how many?
   2)you don't have cards that are the same

[obtuse pebble]

@graceful quail Has your question been resolved?

[graceful quail]

31 cards are the same
Is disjointing them a mathematical procedure?

[upbeat gazelle]

You just say that 100 cards = different cards + similar cards

If you want to do thing thoroughly you would have to build bijections

[obtuse pebble]

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[thorn elbow]

can anyone help me graph this question because im having trouble imagining this scenario

[teal turret]

What do u have so far

@thorn elbow

Draw some vectors

[thorn elbow]

I can send an image of what i have so far, its just different interpretations of what i think the question is trying to convey, im just confused as to which one is correct

[teal turret]

Sure if u could send that, we can go from there

[teal turret]

Ok hmm

Alright, first draw a vector that’s heading northeast

Then draw another vector, not connected to the first one, that’s heading from the southeast

[teal turret]

Perfect

Now, split the vectors up into their horizontal and vertical components

After u do that, calculate the magnitudes of each of the individual components

@thorn elbow

[thorn elbow]

kk give me a few mins ty

[thorn elbow]

ok so for the N45E triangle i had 600km/h as the resultant, and the horizontal component and vertical component both being 424.26km/h.

and,

for the S30E I got 75 for the horizontal comp and 129.90km/h for the vertical comp

so what do i do now

[teal turret]

Now, for the horizontal components, treat the component that goes ‘right’ as positive and the one that goes ‘left’ as negative

Find the sum of the horizontal components applying that^

Then for the vertical components, do the same thing instead ‘up’ as positive and ‘down’ as negative. In this case, both vectors are heading up, so just add the 2 vertical components

What did u get @thorn elbow ?

[thorn elbow]

so the horizontal components added are 424.26km/h and the verticals added are 554.16km/h

[thorn elbow]

¨¨

[teal turret]

How did u do the horizontal part

Did u treat to the left as negative and to the right as positive

[thorn elbow]

so 424.26 is positive as its going right and -75 is negative because its going left

yea

and yea for the verticals theyre both going up so i just added them

[teal turret]

Correct

[teal turret]

What’d u get after adding these

[teal turret]

Cuz then 424.26 can’t be it here

[thorn elbow]

oh my bad i meant 349.26

[teal turret]

Ah

Ok np

Now there are ur components of the new resultant vector

Calculate the new magnitude of the resultant vector

[thorn elbow]

so just pythagoream i got 655.04, which im guessing will be my ground velocity right

[teal turret]

Ye

Now u need direction

Draw a triangle that has the direction of the components and the resultant vector

So since both our horizontal and vertical components are positive, draw the horizontal component to the right, and vertical component up

Then draw the resultant vector

Then use arctan to compute the angle

[thorn elbow]

the direction is 57 degrees anticlockwise to the horizontal axis right

[teal turret]

From the notation in ur problem, we’d say: N32.221 ° E

But yes 57.779 degrees north of due east

Hopefully u can visualize how the wind vector essentially pushed the tip of our plane direction vector into that direction^

[obtuse pebble]

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[thorn elbow]

tysm

.close

[obtuse pebble]

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[tardy epoch]

<@&268886789983436800>

Spammer

[amber spear]

nice video

https://www.youtube.com/watch?v=-K-mWQ7oBS8&ab_channel=ロズ

10 views

日本語はわかりませんが、あなたのIPアドレスは知っています

[tawny fog]

uvuvwevwevwe onyetenyevwe ugwemuhwem osas

[obtuse pebble]

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[dusk trout]

Hey guys, I have a question.

[tardy epoch]

[dusk trout]

Gimme 2 mins

[royal basin]

@dusk trout next time, your opening message should contain your question

[dusk trout]

Yes ma'am, I'll keep that in mind and not repeat my mistake.

[royal basin]

okay

1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

what stage are you on?

[dusk trout]

1

[royal basin]

you have here an equation with some fractions in it

therefore you might want to multiply both sides by something

a well-chosen something will make it so that all these denominators cancel away and you are left with something hopefully more manageable

do you understand this idea?

[dusk trout]

Yes

I'll try solving the equation and let you know?

[royal basin]

okay, sure.

[dusk trout]

Gimme like 5 mins.

[royal basin]

when you ping me, show all your work

preferably as a picture

[dusk trout]

Sure

I'm not sure if my answer's right.

@royal basin, help me.

[royal basin]

why does this need to be an assumption?

anyway ok let's just check

,w 5/(2-x) + (x-5)/(x+2) + (3x+8)/(x^2 - 4) = 0

[warm shale]

Results provided by WolframAlpha

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

Requested by Ann#0413

[royal basin]

your answer is correct @dusk trout

[dusk trout]

Thanks a lot @royal basin

[obtuse pebble]

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[mystic forum]

Can someone please explain to me what my teacher did here? He is saying that you could get the result by doing the product of the two functions (when x=2), but how did he get both 1/32 and 7/8?

[mystic forum]

(he obviously used Taylor's series)

[lunar tide]

I don't understand mathematics in Spanish

[mystic forum]

It's italian :[

[lunar tide]

he multiplied the two things in the series

[lunar tide]

I'm so sorry

You're right

It's Italian

[mystic forum]

He got the taylor's series of the two functions and multiplied the two together

[lunar tide]

you look at the coefficients and multiply them

yea that's correct

that's how you do it

[mystic forum]

but how did he get 1/32 from cos((x-2)/x^2)

[lunar tide]

that's the taylor series expansion for that expression centered at 2

[mystic forum]

Never heard it before

so he substituted x with 2 and did the whole series? correct?

[lunar tide]

no he did the taylor series of that function

and then put in two

if you put in two, you just get a value

[mystic forum]

Also, from what you said, we would need to multiply the two coefficient together, so for example we would have -1/32*1 (because they have in common (x-2)^2)

so how did he get 7/8?

[lunar tide]

I'm not sure because I didn't solve it myself but it's just combining coefficients

for example

x^3 can be derived by multiplying x and x^2 or 1/x and x^4

similarly, when you multiply two taylor series, you can get the same term in different ways

[mystic forum]

oooh okay i understand now, thank you

.close

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[lunar tide]

np

[lunar tide]

.close

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[hexed stirrup]

hello i need help

[hexed stirrup]

with algebriac expressions

[tacit shadow]

yes

ill try

[hexed stirrup]

hi hi

hru

[tacit shadow]

im fine

whats ur question

[hexed stirrup]

sorry i have posted wrong topc

topic

its linear equations with 2 variables

[tacit shadow]

yes

question?

[hexed stirrup]

no no

i need

explaination

[tacit shadow]

explanation

i reccommened u watch yt vids

explaining them would be too long

personally im not a good teacher

[hexed stirrup]

ok

thnx

what is the basic way to solve a equation with 2 variables?

[robust sleet]

just watch youtube vids

[hexed stirrup]

why i joined this server

?

[robust sleet]

https://www.youtube.com/watch?v=oKqtgz2eo-Y if u meant system of equations

[hexed stirrup]

🙁

[hidden fossil]

it's easier to learn through videos cause you can see the illustrations laid out and if you have any doubts after watching the video, you can ask

[hexed stirrup]

i like teaching of you guys here there are world-class teachers

okay if you dont want to explain

leamme know if you have any solutions in a few minutes sir\mam

[hidden fossil]

bruh, it's not about us not wanting to explain, you should be able to learn using multiple sources

sometimes you might come across a question that no one the answer to and you might be forced to watch a video instead

[robust sleet]

Solutions to what?

[hexed stirrup]

okay

[hexed stirrup]

nvm sir\mam

.close

[obtuse pebble]

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[hexed stirrup]

.reopen

[obtuse pebble]

✅

[hexed stirrup]

.close

[obtuse pebble]

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[hexed stirrup]

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@hexed stirrup Has your question been resolved?

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[rotund canyon]

can someone explain when i would use ≡ instead of =

[fickle turret]

In modular arithmetik

You write like 12 ≡ 2 Mod 5 instead of 12 = 2 Mod 5

[rotund canyon]

ok

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[normal forum]

can someone please explain me how to solve this

[ruby path]

Take the LCM and combine the two on the right

And equate the coefficients

[normal forum]

i did

[timid silo]

uh what did you get?

[normal forum]

is the leading coefficient 0 then

13

[normal forum]

13

[ruby path]

Yes the leading coefficient is 0

Which is a + b

[timid silo]

uh how did you get that answer?

[normal forum]

16x-3=(a+b)x^2+cx+a

is this correct?

[timid silo]

yep

[normal forum]

0+16-3

?

[timid silo]

but the question isn't asking what the coefficients of all the terms added are

it's asking for a+b+c

you already know the value of (a+b) right

as you said, leading coefficient is 0, and leading coefficient is (a+b)x^2

[normal forum]

ohhhhh

thank youu xdd

[warm canopy]

the idea here is most likely to plot both functions

[wind furnace]

@normal forum It has 2. 1/2 and 1/4

[normal forum]

4x-3=logx/log2

[ruby path]

Yup looks like it

[normal forum]

i dont get it

[warm canopy]

the fact that question is asking you to just state how many solutions there are, not what those solutions actually are, suggests you dont need to actually find them

[normal forum]

ohhh

[wind furnace]

@normal forum What exactly you don't get?

[normal forum]

its okay

now i get it xdd

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[lime moon]

Im trying to do this question

[lime moon]

I've gotten to the point where i have

to this point

with this

now im not sure what to use as my integrating factor

I divide both sides by 5

So do i use e^yhat/5 as the integrating factor ?

<@&286206848099549185>

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[fluid snow]

$(x^x)' = x^xln(x) + x^x$

$(x^{\frac{1}{x}})' = f'(g(x)) \cdot g'(x)$ where $f(x) = x^x$ and $g(x) = \frac{1}{x}$.

$(x^{\frac{1}{x}})' = (\frac{1}{x}^{\frac{1}{x}}ln(\frac{1}{x}) + \frac{1}{x}^{\frac{1}{x}}) \cdot -\frac{1}{x^2}$.

[fluid snow]

But

,w derivative x^(1/x)

[lost tree]

$f(g(x))=f\left(\frac{1}{x}\right)=\left(\frac{1}{x}\right)^\frac{1}{x}\ne x^\frac{1}{x}$

[warm shale]

SilverSoldier

[fluid snow]

Yeah

[lost tree]

oh wait

i think i misunderstood what u wrote

[fluid snow]

WolframAlpha seems to say something else though

[lost tree]

but f'[g(x)] * g'(x) is the derivative of f(g(x))

[fluid snow]

yes

[lost tree]

not the derivative of x^1/x

[fluid snow]

f(g(x)) is x^(1/x)

where f is x^x and g is 1/x

[lost tree]

this is f(g(x))

[fluid snow]

oh

thank you!

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[tawny tree]

How do I proceed?

[tawny tree]

a,b,c>0

[spiral knot]

you want to show that :
a^3 +b^3 + c^3 > a + b+ c when a,b,c >0 ?

[tawny tree]

yes given the above

[obtuse pebble]

@tawny tree Has your question been resolved?

[tardy epoch]

Looks like AM-GM inequality

[obtuse pebble]

@tawny tree Has your question been resolved?

[tawny tree]

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[rugged pelican]

Exercice a8, show the monotony of that series

[tardy epoch]

,rotate

[tardy epoch]

Show your work so far

[rugged pelican]

sure

I've solved point a) and then from that I tried to show that I_{n} < I_{n-1}

yet after all the transformations I only arrived at e/(n+2) < I_{n}

and I don't know how to prove that

Here

<@&286206848099549185>

[somber gate]

Ai demonstrat că (I_n) este un șir descrescător?

Dacă da, împreună cu hipoteza că $I_n\ge 0$ (este ușor de verificat) vei ajunge la concluzia că $\lim I_n = L$. Deci, din a), ai egalitatea
$I_n/n+I_{n-1}=e/n$, pentru orice $n=1,2,...$. Când $n\to\infty$ vei avea că $L=0$.

[warm shale]

RaD0N

[obtuse pebble]

@rugged pelican Has your question been resolved?

[unreal musk]

Would also be enough to show that I_n is bounded too, if there's a way to do so...

[somber gate]

I_n is obviously bounded below, since the integrated function is nonnegative.

[unreal musk]

True, though seems like OP is trying to show I_n forms a decreasing sequence, but is struggling to get that it is. At which point they can follow your steps (That said my brain can't seem to figure out how to show it's either bounded above or decreasing atm! )

[somber gate]

induction in n might help

it's the most obvious response, I guess

If not, try the bazuka: DOMINATED CONVERGENCE

[obtuse pebble]

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[topaz violet]

conversion help in trigonomotry

[topaz violet]

40 degree sin

15m hyp

looking for opposite

so bassically

sin (40) = h/15

somehow the answer is 9.6 meters?

basically the question is how high on the pool (opp) should the guide wire be attached

[rigid lintel]

,calc sin(40)*15

[warm shale]

Result:

11.17669740719

[topaz violet]

if the angle of the ground is 40 and the wire is 15 metres

yea wtf

see they say its 9.6

[rigid lintel]

hmmm

[topaz violet]

but they didnt do any conversions

[rigid lintel]

could you draw it

[topaz violet]

hmmm

how on here

ok ill retype the whole question

[rigid lintel]

windows shift s to screenshot

[topaz violet]

determine the height to attach a guide wire to a pole if the wire is 15 meters long and runs at an angle of 40 degrees from the ground

so again

sin (40) = 15/h

so it should just be
15* sin (40) right?

[rigid lintel]

yes youre right

i think theyre mistaken

[topaz violet]

yea thats basically it

i get the same answer as you

but their answer is 9.6

are they somehow converting 11.17 to 9.6?

[rigid lintel]

well actually this is the wrong way around, its h/15

but you wrote it right before

[topaz violet]

ok

so to move 15 away from h you have to multiply it to sin 40 though right

[warm shale]

Result:

20.131170398802

[topaz violet]

aw snap see. even further

[rigid lintel]

exactly

[topaz violet]

https://www.youtube.com/watch?time_continue=351&v=ovDM5WcBtQw&feature=emb_title

if youre really curious

its super short

idk how theyre getting 9.6

i appreciate you taking the time. its hiccups like this that cause so much headache

[rigid lintel]

its just a miscalculation i guess

,calc 15*0.754

[warm shale]

Result:

11.31

[rigid lintel]

or wait

they have it in radians

,calc 15*sin(2/9 * pi)

[topaz violet]

oh fantastic, they never taught me that part

[warm shale]

Result:

9.6418141452981

[topaz violet]

love that

so how do they expect me to know that,

[rigid lintel]

welp

[topaz violet]

ill lookup what radians are

[rigid lintel]

yep

[tardy epoch]

,calc 15 sin(40 deg)

[warm shale]

Result:

9.6418141452981

[topaz violet]

wooah what

what in the heck just happened, how was i typing it wrong

[tardy epoch]

Radians vs degrees is a common issue

[topaz violet]

ohh i was missing the degree term?

okok ill lookup and compare. thank you both

does anyone ever expect you to manually calculate it?

[tardy epoch]

Depends on the angles and teacher

Just study whatever your teacher gives you

[topaz violet]

roger, thanks again

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[topaz spruce]

Hey! Why is this true?

[topaz spruce]

Ignore the second dxe mistake, should be dye

Is this the multivariable chain rule?

[rigid lintel]

thats kind of weird notation

[topaz spruce]

Yeah exactly

Got it from some sort-off guide

[rigid lintel]

but yeah that looks about right

[topaz spruce]

So, is it the multivariable chain rule ?

[rigid lintel]

yeah looks like it

but i would a different source because that looks overcomplicated

[topaz spruce]

Yeah they eventually boil it down to the jacobian multiplied by a vector of changes in angles

$d\vec{x} = J \cdot d\vec{q}$

[warm shale]

sentinel

[topaz spruce]

Something like that

[rigid lintel]

my calc 2 is kind of rusty i will not lie

[topaz spruce]

Other question, would it be fine to use the transpose of the jacobian matrix as an inverse in all the cases?

Inverting the matrix is quite costly

[rigid lintel]

i dont think that works

[topaz spruce]

Because I read $J^{T} \approx J^{-1}$

[warm shale]

sentinel

[rigid lintel]

oh it do?

well then

[topaz spruce]

Not sure, seen people do it

[rigid lintel]

i guess you can

[topaz spruce]

I don't get why it works

[rigid lintel]

if the jacobian is an orthogonal matrix it works

but

[robust sleet]

isnt that only applicable when its an orthonormal basis or something like that

[rigid lintel]

i dont know if it is

[topaz spruce]

Yeah right

[rigid lintel]

weird that they wrote $\approx$ as well

[warm shale]

Gijs

[rigid lintel]

because $J^T = J^{-1}$ if it is orthogonal

[warm shale]

Gijs

[topaz spruce]

Yeah right, hmm ...

Well, me being a huge idiot

If a matrix is orthogonal, will it always stay, even when tweaking parameters?

[dark stirrup]

Jacobians are not always orthogonal

[topaz spruce]

Crap

Time for some super expensive gaussian elimination

If that was the thing

I think it was that, but then with an identity matrix appended to it

Nevermind, thanks for helping

[rigid lintel]

oh haha

well good luck

[topaz spruce]

Thans

Need to make a computer do this thousands of times a second

[dark stirrup]

what are you trying to do

[topaz spruce]

On the short term, tracing a 3D curve with a given velocity, translating the coordinates to changes in parameters of a robotic leg

[dark stirrup]

thousands of a times per second is a pretty simple task so shouldn't be too bad

[topaz spruce]

Yeah the thing is, it's not a normal computer

[dark stirrup]

Ah pretty non-trivial. Good luck to ya. I think inverse kinematics is what this is? But I could be way off.

[topaz spruce]

It will be an ARM system, that doesn't support SIMD or anything like that

With a primary system clock of around 216Mhz

[topaz spruce]

Yes inverse kinematics

[dark stirrup]

I had someone else here a few weeks ago with an inverse kinematics robot leg problem. But their task was far more trivial when explained

[topaz spruce]

Yeah right

Well I need to do something else too

I need to create a model that also involves the handling of changes in orientation / positioning of the origin

[obtuse pebble]

@topaz spruce Has your question been resolved?

[obtuse pebble]

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[stark falcon]

im stuck on this

[fickle turret]

What have you tried?

[stark falcon]

ive factored it

sin^2 x(-2+sin^2 (x))

i just dont reall understand how to factor it

[fickle turret]

Use the 2nd binomial formula

[stark falcon]

uhhh

ive never done that

is it factored wrong?

oh ok

[unreal musk]

(if you're trying to factor the whole thing)

Maybe it might help to substitute u=sin^2(x) into the original to see if that helps you?

[stark falcon]

would i factor out the -2 only

[fickle turret]

No

[stark falcon]

oh

[fickle turret]

Can you try what chartbit suggested?

[stark falcon]

yes i did

i just dont see what other way to factor it

[unreal musk]

What do you get?

[stark falcon]

it wont make sense but

u x (-2 + u x)

[unreal musk]

is that x at the end a multiplication or the variable x?

[stark falcon]

variable

[unreal musk]

Shouldn't have any x in what you get

[stark falcon]

so

[unreal musk]

Try to substitute it in straight in without factoring it first

Hint sin^4(x) = (sin^2(x))^2

[stark falcon]

im still confused

[tranquil sonnet]

$(\sin^2(x) - 1)^2 = (-\cos^2(x))^2 = \boxed{\cos^4(x)}$

[warm shale]

kappa

[stark falcon]

how did you get the first part?

[unreal musk]

Alright, for what we have, it's $1 - 2 (\sin^2(x)) + (\sin^2(x))^2$, do you agree?

[warm shale]

chartbit

[stark falcon]

why the 1?

[tranquil sonnet]

$u^2 - 2u + 1 = (u - 1)^2$, where $u = \sin^2(x)$.

[warm shale]

kappa

[stark falcon]

theres no 1 in the original problem

sorry im a bit slow :((

[unreal musk]

There isn't? @stark falcon

[stark falcon]

no

[tranquil sonnet]

uh what

[stark falcon]

its just the -2

[tranquil sonnet]

there is a 1

[stark falcon]

how?

OH

[unreal musk]

Look at my picture

[tranquil sonnet]

Look at this @stark falcon

[stark falcon]

I DIDNT EVEN SEE THE 1

OOPS

SORRY

[unreal musk]

Hahah it happens, don't worry! But does it all make more sense now?

[stark falcon]

sort offf

did we get the -cos^2 bc sin^2x - 1 is equal to that?

the identity?

how did we get (sin^2x-1)

[unreal musk]

You agree we start off with this, right?

[stark falcon]

yes but how did we get it in that form

[unreal musk]

It's basically rewriting the powers slightly, to make life easier

[stark falcon]

but wasn't the 1 positive

and whered the 2 go?

[unreal musk]

In my statement I quoted here, 1 is still positive and the 2 is still there

But are you familiar with factoring quadratics at least?

[stark falcon]

why the -1 though

yes

a little shaky on it

[unreal musk]

So could you factor $u^2 - 2u + 1$ for me? (Note that's the same as $1 - 2u + u^2$)

[warm shale]

chartbit

[stark falcon]

uhhhh

im a little confused :((

[unreal musk]

Alright, another question, which might help: can you expand and simplify $(u - 1)^2$ for me?

[warm shale]

chartbit

[stark falcon]

its another way of saying (u-1)(u-1) right?

2u+u^2-1

[unreal musk]

Now, notice that's the same as what I asked you here, right?

Now, if I ask you to factorise $u^2 - 2u + 1$, can you do it for me?

[warm shale]

chartbit

[unreal musk]

Actually pause ⏸️

[stark falcon]

oops

[unreal musk]

Almost, but not quite

[unreal musk]

Try expanding it again please?

[eternal bolt]

signs mixed up a bit

[south trout]

Yeah, i missed that too and reacted wrongly to it.

[stark falcon]

2u-u^2+1?

[eternal bolt]

not quite

[stark falcon]

ahhh

[eternal bolt]

(u-1)(u-1) = u(u-1) - 1(u-1) using distribution

see if that helps

[south trout]

Uhh, shouldnt second one also have an u before ()?

[eternal bolt]

no

[stark falcon]

2u-u^2+1

[eternal bolt]

if it helps ill put a 1

[south trout]

Okay, ig am geting something wrong then

[stark falcon]

whattttt

[eternal bolt]

how abt this

using

(a+b)^2 = a^2 + 2ab+b^2

[unreal musk]

You got that last time

[eternal bolt]

can you substitute?

[eternal bolt]

try substituting u for a and -1 for b

[stark falcon]

u^2-2u+1?

YAY

i saw what i was doing wrong

when i was multiplying the U's i should have squared them

silly me

sorrrry

[eternal bolt]

yup

nice job

[stark falcon]

thank you 🥲

[south trout]

All right in the end, all that matters.

[eternal bolt]

now go the other direction

[unreal musk]

Hey, when I was trying out a problem of my own earlier on, I kept making silly mistakes, until I paused and took things slowly. Don't worry about it, happens to many of us

[eternal bolt]

if you can distribute, try factoring

[stark falcon]

thank you guys

[eternal bolt]

nice job

[stark falcon]

so for the original problem

the (sin^2x-1)^2

did we get that by squaring the 2

and subtracting the 1?

[unreal musk]

Basically, for that, try as per the previous suggestion that @eternal bolt said before

[unreal musk]

Here, but with e.g. $a = \sin^{2}(x), b = -1$

[warm shale]

chartbit

[neon eagle]

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

[warm shale]

ed

[stark falcon]

im still a bit confused

[unreal musk]

Or set $u = \sin^{2}(x)$ as per before

[warm shale]

chartbit

[stark falcon]

what happened to the 2?

[unreal musk]

It gets "absorbed" into the brackets

[stark falcon]

so it goes away?

[unreal musk]

Remember, when you expand $(u - 1)^2$, you get $u^2 - 2u + 1$

[warm shale]

chartbit

[stark falcon]

OH

[unreal musk]

So that means when you factor $u^2 - 2u + 1$, it becomes $(u-1)^2$

[warm shale]

chartbit

[stark falcon]

okok i think i get it

so once we square it we get back to

1-2 sin^2x + sin^4x

[neon eagle]

yes you're getting it

👍

[stark falcon]

okok

[nocturne minnow]

Might be easier to demonstrate that $u^2 - 2u +1 = (u-1)(u-1) = (u-1)^2$

[warm shale]

dldh06

[stark falcon]

yes yes

omg i finally got it

thank you guys so much

[unreal musk]

Yea, we did it that way earlier

[stark falcon]

literally the best

[unreal musk]

Awww, thank you does it all make sense now?

[stark falcon]

yes i really appreciate your help a lotttttt

i get it now 🙂

[neon eagle]

didn't do anything but great job

[stark falcon]

thank youuuu

[unreal musk]

Perfect anything else you'd like to go through?

[stark falcon]

yes

sorry trig is not my favorite

how would i go abt simplifying this

(3 cot y+1) (cot y-2)

[nocturne minnow]

Technically it has nothing to do with trig, it's just factoring but it has trig functions involved

[warm shale]

ed

[stark falcon]

yes

[neon eagle]

what is the expansion

[stark falcon]

ac+ad+bc+bd

[neon eagle]

Ok

[warm shale]

ed

[stark falcon]

ohhh wait

i get it

its pretty easy

uhhhh

ac-ad+bc-bd?

the subtracting ones get to me

its correct?

[neon eagle]

good job

its correct

[stark falcon]

yayayayay

[south trout]

Ones wheres the -one are with -

[warm shale]

ed

[stark falcon]

3 cot^2 y - 5coty -2

[neon eagle]

great job!

[stark falcon]

YAYYYY

getting it slowly but surely

[neon eagle]

epic

[stark falcon]

those were my two questions for now 🥲

i may have a couple later but for now, im good

[eternal bolt]

nice job!

[stark falcon]

thank you again so much you guys

yall were a very big help couldn't have figured it out without you 🥲

[neon eagle]

its alright we're glad to h elp

😄

[south trout]

Can i ask something

[stark falcon]

yes?

[south trout]

What are the cot tan and sin, am not familiar with those.

[neon eagle]

they are trigonomtric functions

[stark falcon]

trig stuff

[south trout]

Okay, but how to use them

For what purpose

[stark falcon]

finding certain measures for example

or the distance of them

[unreal musk]

Can be used for modelling, or like Fourier Transforms etc

Mind you, I'm poor at explaining the "why" of things, better at the "how"

[south trout]

Example?

[south trout]

Cus this sounds like alien thing for me

[neon eagle]

maybe lets start with right angled triangles

[south trout]

90°?

One angle

[neon eagle]

ok so imagine a right angled triangle

[robust sleet]

You can approximate functions globally with sum of trigonometric functions like sin or cosinus.

[south trout]

Omg am overwhelmed

[neon eagle]

just listen to me im saying the simpler stuff

[south trout]

Yes yes

[robust sleet]

Take for example the boxcar function.
Your task is to approximate it! Gl 😍

[neon eagle]

ok so in a right angled triangle you have two non right angles lets call them angle A and angle B

[south trout]

Whats right triangle

[neon eagle]

right angled triangle sorry

[south trout]

And whats that

[neon eagle]

a triangle with one right angle

[south trout]

90° one angle?

[robust sleet]

Yes

[south trout]

Okay

Got that thing.

[neon eagle]

yes

lets start with sin

[warm shale]

ed

[neon eagle]

so you put in one of the angles that isn't the 90 degree angle into this function and then it outputs the ratio between the opposite side and the hyp

[south trout]

Um, oke

[neon eagle]

probably better to google it to be honest

[south trout]

No no

[nocturne minnow]

And you should have probably opened your own channel, because now you cluttered the OP's channel

[south trout]

Whats op?

[robust sleet]

Occupied Person

[nocturne minnow]

Original poster

[south trout]

Sorry

[neon eagle]

just open a new one

[nocturne minnow]

And use Google

[obtuse pebble]

@stark falcon Has your question been resolved?

[obtuse pebble]

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[carmine fjord]

Hi, im doing compound/composite functions right now but I've been struggling to recreate this line

[carmine fjord]

I've tried everything with sinx and cosx but i still don't know

[obtuse pebble]

@carmine fjord Has your question been resolved?

[tardy epoch]

,w plot e^(-(x-pi/2)^2) + e^(- (x-2pi)^2) + .5

[warm shale]

Results provided by WolframAlpha

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

Requested by riemann#2529

[carmine fjord]

does that work?

[tardy epoch]

Define 'work'

[carmine fjord]

sorry should this fit the line?

because it doesnt look like the max fits

[tardy epoch]

You can scale and shift the second exponential term so it matches your min and max

[tardy epoch]

Then take the template I gave and tweak it

[obtuse pebble]

@carmine fjord Has your question been resolved?

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[obtuse pebble]

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[mystic forum]

Could someone please show me how we go from this

[mystic forum]

To this?

[trail musk]

More context

[mystic forum]

This is the whole problem

I dont have anything else

[sage geode]

Perhaps e^(2/k) - 1 - 2/k and 2/k^2 are asymptotic? Wait let me check

Yep, they are

[mystic forum]

So it's some sort of rule?

Because i get that the denominator is equal to 1/2*(e^7k)

but how i don't understand the reasoning behind the numerator

[sage geode]

Yeah you can replace those since they're asymptotic at infinity

But only when k -> infinity

[mystic forum]

I see, thank you

[trail musk]

Ok

[final thunder]

Series expansion for e^2/k

[trail musk]

Why would you not post the whole thing in the first place haha

This changes everything

[mystic forum]

I'll do that next time then

Ty all

/close

.close

[obtuse pebble]

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[trail musk]

👍

[obtuse pebble]

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[honest vine]

3x * x = 96 first number is 3 times as large as the second number. what are the two numbers

[sage geode]

And it's given that their product is 96?

[honest vine]

yes

[sage geode]

And what are you having trouble with?

[honest vine]

finding the numbers

[tawny fog]

Your question is
$3x×x=96$

[warm shale]

Arnab Pal

[tardy epoch]

Good bot

[tawny fog]

Or you made this equation by that question?

[honest vine]

i made the equation

[tawny fog]

Oh then bro you should do something like that

Leta assume the other number is y

3x=y

Ok

Now solve it

[tawny fog]

Solve this equation for x

[tawny fog]

Then solve this for the other number

[honest vine]

ty

.close

[obtuse pebble]

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[tawny fog]

Welcome

[obtuse pebble]

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[woeful kite]

Im trying to find functions that will be derived from a dataset.
I posted the question on Mathematics StackOverflow.
https://math.stackexchange.com/questions/4606688/find-formula-from-known-input-values-a-and-b-to-get-known-result-c

But basically I have known Input A and Input B, with known Output C.
I think I need an "algorithm" of sorts or even AI software, for larger and more complex datasets. For simple ones like in the question it can be done by ahnd ofcourse by looking at correlations.

But I have a lot of different datasets (hundreds) so I really need an algorithm I think?

[woeful kite]

<@&286206848099549185> greetings from capital city
bang bang bangladesh

[fallow smelt]

@ everyone, there is anybody to teach calculus.

[tawny fog]

Bruh 🙂

[tawny fog]

I'm here

[fallow smelt]

So accept my friend request

[tawny fog]

Ok

[woeful kite]

Wauw, symbolic regression looks very promising.

Is there any online service that can do this, or will I have to writemy own program?

I suppose, linear regression could solve the example dataset aswell, I will have to search online if there is any service like that..

[obtuse pebble]

@woeful kite Has your question been resolved?

[woeful kite]

I resolved my question thanks to help from @timid silo .
Using this website: https://www.statskingdom.com/410multi_linear_regression.html
I was able to have the dataset correctly solve to the equation in the attached image.

.close

[obtuse pebble]

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[obtuse pebble]

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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.

[hexed stirrup]

hi

[hexed stirrup]

here helpers didnt help me out

i tried out myself

[robust sleet]

good job heres your medal