help-39

[daring bay]

yes

do i just basically remove the ^2s

[proper nova]

well simplify it first

[daring bay]

1/3 b

[proper nova]

simplify what's in the root first

[proper nova]

oh pretty quick answer i see

that's the answer for the root

b/3

[daring bay]

but what about 4/9

[proper nova]

$\sqrt{\frac{4}{9}b^2 - \frac{3b^2}{9}}$

[jolly parrot]

1 divided by 0 equals Infinity

[proper nova]

to be able to compute this

[daring bay]

but do we have to simplify that in the root

[proper nova]

you should simplify what's in the root first

[daring bay]

cant we do it after

[proper nova]

yea we have to

[daring bay]

oh damn

okay noted

[proper nova]

you can't have $\sqrt{A - B} = \sqrt{A} - \sqrt{B}$

[jolly parrot]

1 divided by 0 equals Infinity

[daring bay]

but 4/9 - 1/3

is 1/9

[proper nova]

it's kinda clear here

[proper nova]

yea

so $\sqrt{\frac{1}{9}b^2}$

[jolly parrot]

1 divided by 0 equals Infinity

[daring bay]

oh

oh ok i get it

so always simplfiy in root first

[proper nova]

yea

it depends tho, but mostly you simplify in the roots first

it makes things nicer to handle like what you had here

you done @daring bay?

anymore questions to ask us?

[daring bay]

like

im still doing

i dont think so no

il open a new channel

.close

[pearl pond]

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[proper nova]

dw

you can continue sending it here

[proper nova]

aight then

[pearl pond]

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[wide pawn]

I need a hint, how do I evaluate the limit of
$\frac{\left(1+x\right)^{\frac{1}{x}}-e}{x}$
as x approaches 0

[jolly parrot]

Aorts

[shadow elm]

take x=1/t to start with

nvm

[wide pawn]

hmmm

[eager jewel]

i remember this question..jee advanced right

[wide pawn]

yep

[eager jewel]

let me try

[autumn fossil]

this is a defn of derivative technically, though im not sure whether it helps

[shadow elm]

oh yes

[wide pawn]

I took the derivative but it's blightful

[autumn fossil]

its the derivative of (1+x)^(1/x) at 0, if you extend it continuously at 0

[shadow elm]

we can solve by definition of derivative

[autumn fossil]

if you're okay with differentiating that thing, then i think its the fastest sol

[wide pawn]

yeah but the derivative is just a worse problem to handle imo

[autumn fossil]

it should be just e^ln(1+x)/x and then chain rule

[wide pawn]

ya, but both the terms have 1/x

and also the (1+x)^1/x doesn't really disappear

[autumn fossil]

hmm, right, we would have to take the lim of derivative and it might not be simpler

[shadow elm]

use logarithmic diff.

[wide pawn]

gang I did just that

[wide pawn]

yep

[shadow elm]

when x approaches 0

[autumn fossil]

are you okay with taylor expanding?

[shadow elm]

write the (1+x)^1/x as e

[wide pawn]

I'm okay but how would we taylor expand (1+x)^1/x

[autumn fossil]

wdym?

[eager jewel]

yeah this is what i did also ^^

[autumn fossil]

its just $\exp\left(\frac{\ln\left(1+x\right)}{x}\right)$

[shadow elm]

after differentiation

[jolly parrot]

MathIsAlwaysRight

[autumn fossil]

oh, i didnt actually fully differentiate it because of my laziness, but then it might actually work

[autumn fossil]

or this + taylor, i tested out this one and it works

[shadow elm]

whats exp

[autumn fossil]

e^sth

[wide pawn]

oh right, I hadn't considered expanding that

[shadow elm]

oj

[wide pawn]

I moved on to differentiating it entirely

[wide pawn]

yess it works

thank you all!!

I will go ahead and close the channel then

.close

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[sinful snow]

How do you find the domain of a function from a graph?

[sinful snow]

For b

Because the last one was just R

[cinder flower]

go along the x axis and ask yourself whether there is a point on the graph associated that with each x value

[nocturne grail]

these are not called functions (b and c) see what layla said.

[sinful snow]

1 or 2?

[cinder flower]

at the point 1 on the x axis, there are two points straight above or below 1

so 1 is in the domain

at the 2 there is also a point on the graph

at 3 there is not

[sinful snow]

So would it be 2 since it's the highest number?

[cinder flower]

well all the real numbers <= 2 are in the relation's domain

the numbers > 2 are not

[sinful snow]

So less than or equal to 2?

I think I understand

[cinder flower]

there is a point on the graph that intersects this vertical line, so 1 is in the domain

so there are no such points when you put the line at 3 instead of 1, so 3 is not in the domain

[sinful snow]

In a the domain was just R, is that when the point isn't at a number on the graph

[cinder flower]

same as what i said before, just with a picture this time

[cinder flower]

it means that at every real number z, there is a point (x,y) on the graph with x = z

[sinful snow]

Ahhhh

So the range for b would also be R

[cinder flower]

yep

[dreamy bobcat]

Do you know hit and try method?

[sinful snow]

I kinda get it now

For c would I do like domain is 3 < x<0

Or something

[cinder flower]

almost

[sinful snow]

Less or equal to

I can't find that sign on my keyboard

[cinder flower]

yes, but also it looks like -4 <= x <= 0

[sinful snow]

Would the range be 4 <= x <= 0

[cinder flower]

almost

you have the signs mixed up

0 <= x <= 4
or
4 >= x >= 0

[sinful snow]

Ohhh whoops

[white veldt]

wsp guys im new to this server

[sinful snow]

Since it dosent say 4 would I be allowed to say 3? Because its really just a guess

[cinder flower]

sometimes you can't be precise but i'd say it should really be 4 here

like it's a circle with radius 2

so the diameter is 4

[sinful snow]

Ahhh okay

Well tysm for helping I understand now

[cinder flower]

yay

[sinful snow]

I'm probably gonna be back in this server about 20 times tonight

[cinder flower]

[sinful snow]

I kinda delayed studying now my test is tomorrow

[cinder flower]

we've all been there

[sinful snow]

Well I'm back

For 13

I looked at the solution and it uses a formula ds/dt

What does d stand for?? I know s and t but how do I type that in

[nocturne grail]

d by itself means "very very small piece of something". dy/dx is the derivative of the function y with respect to x

ds/dt is the derivative of displacement with respect to time.

do you know what that is equivalent to?

[sinful snow]

displacement? I have no clue

[nocturne grail]

:((

[sinful snow]

There are no other numbers in the equation or anything

[nocturne grail]

well yes you're supposed to use calculus here.

here's a useful list

d(displacement)/dt = velocity (v)
d(velocity)/dt = acceleration (a)

and you can reverse these operations with antiderivatives.

[nocturne grail]

d(smth)/dt is the derivative of smth with respect to time.

the derivative of displacement with respect to time is velocity. or speed

[nocturne grail]

here, you are given a function of displacement

[dreamy bobcat]

Integration!!

[nocturne grail]

and is directly asking you for speed of the moving thing

now that you know that the derivative of displacement is speed

you can get a function of speed by differentiating the displacement function you're given!

I will explain again perhaps you're back-reading/didnt get something.

we are given a function of displacement,
s= 0.25 e^t

we are asked for velocity. the releationship of velocity and displacement is quite the famous one! velocity is the derivative of displacement.

since we're given a function of displacement, if we find the derivative of it, we can get the function of velocity. which will solve alll of our problems!

displacement ---> velocity ---> acceleration

the arrows represent differentiation/derivative.

[dreamy bobcat]

@sinful snow Is it IGCSE book? Something

[pearl pond]

@sinful snow Has your question been resolved?

[sinful snow]

I'm still so confused

sorry for taking so long I had to grab smth

[nocturne grail]

I'm afraid you're lacking some essentials covered in early calculus and early kinematics.

I'm not sure what I can do about that except i can redirect you to a youtube video,.

[sinful snow]

Yeah we haven't done calculus yet

This formula has never came up before

[nocturne grail]

you cant solve that question without calculus

or I'm really missing something

[sinful snow]

I really hate this book, the examples they give us are simple then the questions have no correlation

[nocturne grail]

@cinder flower can we solve this without calculus (13)

[nocturne grail]

I mean the whole velocity is the derivative of displacement shtick is covered in physics as well.

actually- it shouldnt be covered in math but

oh well- it uses calculus!

[cinder flower]

[sinful snow]

This subject will be the death of me

[cinder flower]

[nocturne grail]

you said your exam is tomorrow?

[sinful snow]

Yea

[nocturne grail]

have you tried studying the material before- solving?

weird question but i wanna make sure

[sinful snow]

I did 😭 😭

I've read through all the examples and notes in the chapter

[dreamy bobcat]

Slayla and carla you know many concepts of maths, you guys are at which year?

[nocturne grail]

well the questionalso expects you to graph

are you familiar with that

like graph of exponentials.

[sinful snow]

Yeah I've done a bunch of graphing

[nocturne grail]

do you know how to differnetiate

take derivatives of stuff

[sinful snow]

I don't

[nocturne grail]

I'm afraid you cant solve that problem then

is there any way you can check your syllabus and see if it has calculus in it

[sinful snow]

So far we've done slgerbra 1,2 and 3

This chapter is functions

Maybe the problem is that we don't go by book chapter, like it's chapter 1, 2,12 then 8

[nocturne grail]

oooooh

well yeah the chapter wont include differentiation. but the question does expect you to know how to differentiate

so ignore it

move on

solve the other ones

and see if you face any problems

[sinful snow]

Okay dokey

I'll do as much as I can before I fall asleep

[nocturne grail]

I cna give you the function of velocity and then you can graph it i guess. thats one part your chapter covers

[nocturne grail]

greatest of luck

[sinful snow]

Thank uuuu

[pearl pond]

@sinful snow Has your question been resolved?

[pearl pond]

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[pearl pond]

@desert silo Has your question been resolved?

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[dark dagger]

Instructions are to rewrite the expression in terms of the first power of the cosine

At first glance I thought this problem requires me to use the Half-Angle Identity

But I don’t think that’s right

[west sapphire]

could use the cos(a)cos(b) formula if you have it

[dark dagger]

Huh

the cos(a)cos(b) + sin(a)sin(b) ?

maybe the power reducing identity could work

although that's basically taken from the cos(a)cos(b) thingy

[dark dagger]

this led me to realize that idk what the half-angle identity exactly is, and when i should use it

😭

[outer canyon]

use the formula for cos(2x)

[sterile python]

If cos(2x) = cos^2(x) - sin^2(x)

then cos^2(x) = cos(2x) + sin^2(x)

you sub pi/2 into x @dark dagger

[outer canyon]

sin²x **

cos(2x) = cos²x - sin²x

[sterile python]

mb haha

[outer canyon]

no worries

also 1 + cos(2x) = 2cos²(x)
so cos²(x/2) = ( 1+cos(x) )/2
ans could be in this form as well

[pearl pond]

@dark dagger Has your question been resolved?

[dark dagger]

Ok I’ll do it that wayyy

Thanks

[dark dagger]

Btw is anyone able to answer this :(

[iron basin]

$\cos(\frac{x}{2}) = \sqrt{\frac{1+\cos(x)}{2}}$

[iron basin]

something similar for sin and tan

[pearl pond]

@dark dagger Has your question been resolved?

[pearl pond]

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[boreal slate]

am i right to say =(2/3)

[honest spear]

ayep

[shell brook]

Did you use the Leibniz integral rule

Yeah you're right

[boreal slate]

thats what i did

[boreal slate]

thx

.close

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[shell brook]

Yeah it's fine

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[scenic crest]

Hello , can someone explain how to solve this by using equation appraoch

[proper nova]

that's just pure grammar 🥀

[scenic crest]

Ig misprinted

[random ermine]

this is correct grammar

[proper nova]

💀

please tell me the plural of person is persons 🥀

but anyways

[scenic crest]

aree who cares

solve na

[proper nova]

i don't really know much

but i think you should consider how many gaps you can make

[scenic crest]

I did

using gap method already

I just wanna know the equation approach

I mean I solved using that

We put 14 gaps

and arrange 10 people in the 15 created gaps

15p10ig

[rare scaffold]

you mean you want a generalization?

[scenic crest]

No.........

wait showing you

[proper nova]

you really want to make an equation out of this?

[scenic crest]

this........

I have no idea what this means

[thorn shale]

oh

[scenic crest]

I didn't get the first inequality x1,x11 greater than equalt to 0

and rest greater than equal to 1

(ignore capitalization , pure accident

[rare scaffold]

are the people independent?

[scenic crest]

well read the question , my guess is as good as urs

tbh I don't know what that means

dependent on whom?

[rare scaffold]

I'm forgetting terminology, I meant distinct

[scenic crest]

yeah ig

[warped violet]

||two persons is actually grammatically correct, but rarely used (usually in legal documents, laws, on signs, etc.)||

[scenic crest]

unless specified otherwise it shud be standard assumption

[scenic crest]

are u fr?

[thorn shale]

x1 is number of empty seats before first person
x2 is number of empty seats between 1st and 2nd
all th eway to x11 being the number of empty seats after last person

because no two people can sit in consecutive seats then there must be at least one empty seat between any two people
so x2 to x10 are 1 or more

x0 or x11 can be 0 because there can be no empty seats before/after the first/last person

[rare scaffold]

there is no standard

[proper nova]

||wait really?||

[scenic crest]

Okay......well you explain the whole solution after this

[scenic crest]

I mean

¯_(ツ)_/¯

Ig people means diff

[rare scaffold]

sometimes the people receiving a donut are distinct but the people who don't are not

[scenic crest]

well now that i have clearly stated there is diff so yea........

[warped violet]

||yes, mostly to emphasize individuals separately rather than as a group of 'people'. But anyway I won't clutter this help channel anymore. Sorry Agape||

[scenic crest]

someone pls explain this

how to proceed after this

[scenic crest]

Omg your grammar

take it else where

[thorn shale]

im assuming its the same method

[scenic crest]

yea yea u r correct

carry on with ur solution

[rare scaffold]

this attitude, man

[thorn shale]

🤷

[rare scaffold]

so demanding

[scenic crest]

Sowwy

I just thought

She thought I was just solve afterward

so I made it clear

well if I send the entire solution would u be able to tell smth

[thorn shale]

probably

[warped violet]

I think the point is you do the work and people guide you when you get stuck and/or explain the reasoning

[thorn shale]

yeah

you subtract 9

had that idea

[scenic crest]

well..... its just that I already tried lol

I don't ask without trying

[thorn shale]

you subtract 1 from x2 to x10 to make them non negative

[scenic crest]

sowwy

I will keep that in mind

[thorn shale]

then do stars & bars

[rare scaffold]

you should define your x_i's

[thorn shale]

this is probably what xi is representing

just a guess

[scenic crest]

Jeez it's not my writing , I am following some unfortunate books

[scenic crest]

I am pretty sure you r right

cuz then the solution makes sense

[rare scaffold]

oh duh the watermarks lol

[scenic crest]

Listen lets not talk abt my pirating habits

too poor man

Anyway ty to all

even to mr grammar who enlightenet me abt two persons lol

.close

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[tired hemlock]

Hello everyone, Am trying to solve a CTF which requires me to prove ( that is not the part of concern) that a point (x,y) exists on a curve and curve has a eqaution of y^2=x^3+ax+b (a and b are given), but the thing is they want me to satisfy few relations y^2=x^3+ax+b mod p1, y^2=x^3+ax+b mod p2....so on where p1,p2... are prime is there a way i can find (x,y) i will use sageMaths to find the solution but like what should be the approch to this?
Thanks 😄

[tired hemlock]

also that (x,y) should be a integer pair

[unborn abyss]

hmm i see an elliptic curve

[tired hemlock]

yea, its based on cryptography

<@&286206848099549185> Anyone?

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[violet terrace]

anyone by any chance knows how to fix this really small tiny iny issue?

[violet terrace]

number aint even that big cmon

[plush bramble]

#computing-software

[violet terrace]

ill try over there ig

!close

.close

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[safe harbor]

I need help with solving for angle of elevation/depression

[safe harbor]

I know it's not a very specific question, I just don't understand how to solve for it in general and none of my resources are helping me

[toxic remnant]

angle of depression is the angle by which your line of sight goes down to look at an object

rest is trigonometry and depends on the structure of the question

[safe harbor]

I get that (mostly) but I can't tell where exactly you'd be "looking down" at something from
Or how to properly do inverse functions

[toxic remnant]

angle of elevation 'from the boat' to the top of the tower

you're standing at the boat and need to look up at the yop of the tower

the angle by which your neck moves up

is the elevation

[pearl pond]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[dense jasper]

(In the future, please make the first message you send the actual question since that's what the bot pins. This saves us the effort of having to change the pin manually.)

[safe harbor]

Ah, I'm sorry
It's my first time asking for help and I wasn't 100% sure how to ask what I needed

.close

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[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

[left vector]

1

[versed mica]

try writing it in exponential form and graphing it

[left vector]

x+5=2^6/2^x ?

but i havent studied graphs of exponential

isnt therre other way?

[versed mica]

you don't know what 2^-x looks like?

[left vector]

it starts from + inf and decreasing?

[versed mica]

yes

if you know what 2^x looks like it's just the same thing but reflected over the y axis

the factor of 2^6 will stretch it of course in our example

[left vector]

ok

but like i need to solve qs withouut graph

[versed mica]

i mean what class is this for

and how do you know you need to do this without a graph

[left vector]

11th

[versed mica]

that's not what i meant but ok

[left vector]

its a qs of 1st ch and we have not been taught to solve qs graphically yet

[left vector]

what u meant

[versed mica]

like the course name

is it just "year 11 maths"

[left vector]

in my coutry there arent diff course

this is js jee math

its diff from most countries

the name of ch is basic maths

[versed mica]

i mean i'd be willing to bet a solution key would graph it

it isn't complicated to do so

just a rough sketch

[left vector]

but the thing is my teacher hasnt taught graphs yet and even if i know the graph how would i see solution on pen paper?

[left vector]

from rough sketch how will i know exact point of intersection

[versed mica]

you don't know how to graph a linear function and a logarithmic function?

or an exponential?

[versed mica]

you don't need to find it

that's the point of graphing

[left vector]

i js kniw rough and only basic

[versed mica]

it only asks how many points of intersection

doesn't ask you where it is

[left vector]

hm yea

2^6-x will start 6 unit left of y axis?

and decrease??

[versed mica]

not sure what you mean by this

[left vector]

nvm wait

[left vector]

is this correct?

[versed mica]

yea looks good

[left vector]

ok thanks 🙂

.solved

[pearl pond]

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[pearl pond]

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[daring bay]

hello whats the derivative of (c-2)/2 x^2

[daring bay]

i had this in an exam and i did something wrong

i really wanna know what i did wrong and it really frustrates me

[silent notch]

do you mean c-2 over 2x^2 or c-2 over 2 times x^2

[daring bay]

no like

[sterile python]

$\frac{x^2(c-2)}{2}$

[daring bay]

as a fraction

no

[sterile python]

This?

[daring bay]

in the bottom

theres a 2

[silent notch]

2x^2?

[daring bay]

and after the fraction theres a x^2

[daring bay]

no just a 2

[silent notch]

$\frac{c-2}{2x^2}$

[jolly parrot]

acacialog123

[silent notch]

oh

[daring bay]

no

[jolly parrot]

Minhh

[silent notch]

so you derive the x^2 first

[sterile python]

This?

[silent notch]

do you know how to do that

[daring bay]

the x ^2 is after the fraction

[daring bay]

yes

i just did the fraction times 2/1

is that correct

[sterile python]

Ts?

[silent notch]

the derivative of x^2 is 2x.

[daring bay]

no

[sterile python]

Then which formula so vague

[silent notch]

so its ((c-2)/2)*2x

[daring bay]

$\frac{c-2}{2}{x^2}$

[jolly parrot]

law

[silent notch]

ok thats clearer

[daring bay]

tbut

there was a bracket

(c-2)

[silent notch]

so whats the derivative of x^2

[daring bay]

2x

so i just multiplied the whole fraction times 2

[silent notch]

ok what do you think would happen next

[sterile python]

So this is literally the same man

[daring bay]

and we have 4/4 then

[silent notch]

the 2 from the den cancels

it leaves you with (c-2)x

which is your derivative

[daring bay]

oh shit

okay

i thought

the 4/4 cancels

and we just have c left

[silent notch]

😭

[daring bay]

but if you have 4/4, isnt that 1?

why does it cancel

[silent notch]

so say you have c/2 times 2x

you get 2cx/2

the 2s cancel

leaves you with x(c)

[daring bay]

oh

if there were no brackets it wouldve made a difference right?

[silent notch]

around c-2?

actually yeah nowhere it will make a difference

[daring bay]

it would? or no

[silent notch]

wouldnt

[daring bay]

but you dont have 2(c-2)

oh

actually yeah

idk

[south ice]

@daring bay

Did you figure it out

[south ice]

Wdym?

[south ice]

@daring bay do you agree with this answer

[silent notch]

?

is it not right

[south ice]

No it is

I’m tryna see if he agrees as in if he knows why that’s correct

[silent notch]

oh

[south ice]

Brackets are inferred in this case

Depending on how you multiply the fraction by x^2

[south ice]

If there weren’t parenthesis here, in this way of writing the problem, it would be a different fraction to begin with

So in that sense it’ll be different

[pearl pond]

@daring bay Has your question been resolved?

[pearl pond]

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[boreal slate]

can anyone help me solve this limt

[boreal slate]

small hint plz

[midnight haven]

lopital

[honest spear]

or we think the french only know how to say baguette and not do maths and we try this without L'Hôpital's

[pastel umbra]

Try and formulate a grammatical sentence and try again

[iron basin]

sabotaged by a comma

[pastel umbra]

But yh, have you tried L'Hôpital yet? @boreal slate

[shadow elm]

L🏥

[honest spear]

"Perhaps we assume the French are better at baking baguettes than solving equations; let's attempt this without using L'Hôpital's Rule." Fit bro's fancy better? English pedants in a maths server 💀

[midnight haven]

bigot

[boreal slate]

@pastel umbra @honest spear

i aint sure lhoptials is the right choice here..

or maybe im doin it wrong

[iron basin]

lhopital always works with enough confidence

[pastel umbra]

Follow-up question - does that limit actually exist?

[iron basin]

should be ln x + 1 within the brackets

[boreal slate]

perhaps not

[pastel umbra]

Check the left and right side of those limits

[honest spear]

your numerator should be $\ln(x)+1$

[jolly parrot]

Nyxzore

[honest spear]

not -

[boreal slate]

youre right

[boreal slate]

lmao so i still get 0/0

[honest spear]

do it 1 more time

famous last words

[boreal slate]

i get -2

thx

.close

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[ashen slate]

Helloo what's this formula for? I heard it has something to do with the ratio but i forgot 😅

[sweet schooner]

It’s just a sequence

If that’s an inequality, then it’s a family of sequences with that as the lower bound

Nothing special really if I’m not mistaken

[midnight haven]

looks like general term of sequence

an hp with alternating plus minus terms

[pearl pond]

@ashen slate Has your question been resolved?

[ashen slate]

Ouh, would u mind telling/showing me an example of a question that requires us to use that formula?

[pearl pond]

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[blissful brook]

not sure how to do this

[full wadi]

Have you drawn out the diagram and all the relevent forces, including friction?

[blissful brook]

yeah

lemme redraw it on paint

cus i have it on apper

paper

not sure what to do now

[full wadi]

As you need the ladder to be stationary, consider the moments about the point where it contacts the ground, to find X

Are you working on that?

[blissful brook]

yeah so

M(about A):

a * wcos(th) = 2aX * cos(th)

[full wadi]

You balance the vertical forces, so R = W, then use the moment to calculate X from W, then balance horizontal forces using X = mu R

[blissful brook]

so i will get something in terms of R = mu R?

[full wadi]

Something in terms of f(W) = mu R

Then the mass will apparently cancel, I haven't done these in a while

How's it going?

[full wadi]

Yes you'll get k*R = mu R, then equate them to get the equation it wants

[pearl pond]

@blissful brook Has your question been resolved?

[pearl pond]

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[shell brook]

show your work

[toxic remnant]

after squaring

[slender stream]

try x^2 - y^2 = xy^2 - yx^2 and factoring (its a small trick that will let you get the desired derrivative)

[toxic remnant]

its factorisable

x≠y so ignore the x-y factor

[shadow elm]

,rcw

,rcw

[shadow elm]

what did i do wrong

oh

right

[slender stream]

you did (x-y)/(y-x)=1 when it should be -1

[shadow elm]

the -ve ofc

[slender stream]

yep

[shadow elm]

thanks

.close

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[grizzled matrix]

how would these 2 graphs look like if i would graphical intergrade them?

[autumn fossil]

what exactly do you mean?

Like interpolate between them?

[grizzled matrix]

ugh i mean these are f(x) right now and i want to draw F(x)

idk the english words for it

[main oriole]

integrate?

[autumn fossil]

oh

[grizzled matrix]

could be yea

[full wadi]

Not this?

[grizzled matrix]

absolutely

[full wadi]

You want us to teach you how to integrate or how to draw the integral numerically?

[grizzled matrix]

how to draw the integral of these graphs

does that makes sense?

[full wadi]

I don't have much experience drawing integrals numerically

[grizzled matrix]

aight nw

[full wadi]

You could use the graphs to determine the equation, integrate that, then plot it

[grizzled matrix]

how could i determine the equation of this graph?

[full wadi]

It is quadratic

So using some points you can find the equation

[midnight haven]

Graphically integrate is a new term

[grizzled matrix]

with the roots as example?

[midnight haven]

Left looks like cubic integrating it will give graph of a quartic with 3 turning points

[grizzled matrix]

prolly yea but i think i give up on that one, it will most likely not get asked in examen

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[green aurora]

What do those red vertical axes mean?

And why are they in that position?

[hollow magnet]

sigma is the standard deviation

the red vertical axes show $\mu-\sigma$ and $\mu+\sigma$

[jolly parrot]

gribble19

[green aurora]

What does it measure?

That is, what do those numbers we just found measure?

[rough stream]

The standard deviation is a measure of "spreadness". A large standard deviation means you are likely to sample far away from the mean

[green aurora]

You are likely to sample?

@rough stream

What It means

[rough stream]

Like, in this case, if you rolled a die.

I think, judging by that bottom axis, this is based on dice rolls

Large standard deviation: You will probably not roll close to the mean. The data is very spread out.

Small SD: You will probably roll close to the mean. The data is very concentrated.

[green aurora]

That is, you are saying if the mean is 0 and σ is small, I often draw numbers like 0.5,0.2,0.1 if the mean is 0 and σ is large, you often draw numbers like 3,2.5,4

[hollow magnet]

this might help illustrate

[rough stream]

Yeah pretty well said

SD and variance measure the same thing, if you know variance

[green aurora]

many values are often close by, but it is not guaranteed and it is not a “always valid” rule?

[rough stream]

SD has the same units as the data though, so it's used in more calculations

[green aurora]

I ready this

[green aurora]

.

[rough stream]

What is not guarenteed?

[green aurora]

it is not always true that the values often come out in that range

[rough stream]

No not guaranteed. SD just controls how probable it is

[hollow magnet]

if you roll a die, there is a 68,27% chance the result is between the red lines

so it is not guaranteed it will be in there

but lets say we have two different sets of values

A:
1: 10
2: 10
3: 10
4: 10
5: 10

B:
1: 1
2: 4
3: 40
4: 4
5: 1

both A and B have the same Mean, but they have a different Standard Deviation

when you roll a die in A, the chance of getting a result far away from the mean (so 1 or 5) is much bigger than in B

[green aurora]

Why 68,27%

[hollow magnet]

actually i have to note, this is only the case if the distribution is a normal distribution

so it wouldn't apply in the example you showed

[green aurora]

@rough stream @hollow magnet So small σ → more concentrated values ​​near μ, large σ → more dispersed values ​​μ. But then what is
μ±σ (the arrows in my image)?

would these be the two intervals where the values fall?

[rough stream]

The arrows are just μ±σ

A place where a lot of values happen to be

I think they just want to give you a picture to see what μ and σ can look like

@green aurora

[pearl pond]

@green aurora Has your question been resolved?

[pearl pond]

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[odd sparrow]

idk if i am being slow but how would i do this i just have no idea where to start

[steel flume]

$$\prod_{k=1}^{n-1} \frac{k+1}{k}$$

[jolly parrot]

akeanti💕

[steel flume]

it simplifies

'produit telescopique'

$$\left(\frac{2}{1}\right) \times \left(\frac{3}{2}\right) \times \left(\frac{4}{3}\right) \times \dots \times \left(\frac{n-1}{n-2}\right) \times \left(\frac{n}{n-1}\right)$$

[jolly parrot]

akeanti💕

[odd sparrow]

ooooo i get it i think

thank you very much @steel flume

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[south ice]

Hello I need help with something

[south ice]

I’m trying to visualize the geometry of these unit vectors and how the come about

In terms of the definition of a derivative

[full wadi]

Each one?

[south ice]

Tbh that would be great

[full wadi]

For the tangent, you can picture it similarly to how to the derivative of an equation is the tangent of the graph

So the tangent is the direction (although not directional) of travel

[south ice]

Question tho, why would the vector not be measured from the origin and be tangent to the graph?

[full wadi]

If you did define it that way would it would give the same tangents

As it doesn't measure the position of the vector but its change

[south ice]

So you’re saying the position wouldn’t matter and that’s why

[full wadi]

Picture the discrete delta y delta x method of approximating a tangent on a graph

so you're moving a small amount along the graph using that to approximate the slope

it is the same for the vector definition, where you start and make a small movement using the equation for r, then measure the direction

so the derivative gives that exact value

[south ice]

What about the unit normal

Why is it perpendicular to the unit tangent

[full wadi]

the normal is defined as being perpendicular to the tangent

[south ice]

Yes but why

[full wadi]

because that is what a normal vector is

that is just an equation for finding the normal

[south ice]

How do you know that using the derivative definition

Because it’s defined as the unit tangent vector’s derivative normalized

T’(t)/|T’(t)|

You’re deriving T’(t)

[full wadi]

Yes

[south ice]

So like

[full wadi]

I'm trying to think of an intuitive way

[south ice]

The derivative of the graph of the unit tangent vectors for all t???

[full wadi]

The normal is again the direction of change of the tangent. Suppose at some point the tangent is pointing at (0,1) and then shortly after pointing at (0.01, 0.99)

I'm trying to explain it without drawing it

Visually you would intuit that the shape has to have 'bent' in the direction of the normal and so the change of the tangent can measure the normal

[pearl pond]

@south ice Has your question been resolved?

[south ice]

Look

Is it the same logic for why the unit tangent vector is normal to the position vector at some point t

[full wadi]

It is if you're considering circular motion

[pearl pond]

@south ice Has your question been resolved?

[south ice]

Is the unit tangent vector not always normal to the position vector at time t?

[full wadi]

No, only in circular motion

*perpendicular

[south ice]

I see. One thing tho. Can you think of the unit normal vector, as the full definition of the derivative (limit of the difference quotient as h approaches 0) for some point t on the derivative function ?

[full wadi]

I don't know what you mean by that

[south ice]

Then that vector you get you just divide by its magnitude

[midnight haven]

Hello ppl

What u need help with I can help a lil

[full wadi]

The normal from the derivative gives the direction, then you normalise it to length 1 using the division

[midnight haven]

What r u guys talking abt I can help a lil

[south ice]

Trying to understand the unit normal vectors intuitively

[midnight haven]

Ohhh

Lemme check my book to see any thing equivalent to that

[full wadi]

You can check pinned messages to see the topic of discussion

[midnight haven]

My mom just told me to tell u this bc she's a teacher

So

[south ice]

Okay

[midnight haven]

Unit normal vector or dt is always a orthogonal curve and also unit tangent vector T is contained in the vector substance defind by the two units...... Idk if she's correct well she should bc she's a teacher

If u don't understand I'll tell her

[full wadi]

I think you misheard her because vector substance doesn't mean anything

[midnight haven]

Probably

[south ice]

What I was asking tho is how to think of all this in terms of derivatives, like when we define the unit normal vector to be: N(t) = T’(t)/|T’(t)|

How should we imagine the derivative of T(t) on the graph? And why does that give us a vector that’s directly perpendicular to it when divided by its magnitude ?

[full wadi]

Think about it instead as the second derivative of the position vector

[midnight haven]

Can u guys text out the pinned comment

Am confused now

[south ice]

Just ask her this please

If you can

[south ice]

Hmm alright?

[full wadi]

Given the calculation above the normal is pointing toward the 'interior' of the curve at that point, and so describes the behaviour of the curve in the same way the second derivative of an equation describes the behaviour of the slope, in that it curves up or down

[full wadi]

You don't have to help in this channel 🙂

[south ice]

Idk

I mean

I’m trying to think of how you’re supposed to graph the derivative functions

Then from there

How the derivative behaves

Like the vector at that point

[midnight haven]

I got smth

Jsn

[south ice]

Okay

[full wadi]

If you're trying it out on a circle at the origin then the tangent derivative is another circle at the origin that starts 90 degrees from the original

And the unit normal the unit circle starting another 90 degrees from the tangent circle's start

[midnight haven]

Right she told me smth

[foggy meteor]

Can I have this channel?

[south ice]

Lemme ask you this, what’s the point of the unit normal vector ? To show how a particle is turning correct ? So why is the derivative of the unit tangent vector / by its magnitude give you that information????

[foggy meteor]

Ong

[full wadi]

The unit normal is very important, you can look at lots of computer science examples to see why

[south ice]

And then why is that turning defined by a vector perpendicular to the tangent vector ?

[foggy meteor]

Faxx🔥🔥🔥

[south ice]

Lol

[midnight haven]

Take some point P1=(S1) on a curve C. Let T1 be the unit tangent at this point. Now move a tiny distance along the curve to get to the point P2=c (s2) and let T2 be the unit tangent at this point now draw the vector V=T2-T1 if P1 and P2 are very close together T1 and T2 will be almost equal and V will be roughly perpendicular to both of them because the triangle with sides T1 and T2 will be almost isosceles and very skinny.......... She wrote this btw

[merry carbon]

Seems like you're being deliberately annoying, you can have some time to think about not intruding in other channels

[midnight haven]

[midnight haven]

I was gonna say that but I was writing smth down

Gng why am I even writing this down

Lol

War beast do u understand

Or just send a pic of the hw

So I can understand better

Or just show my mother

[midnight haven]

This will be much better ngl

[south ice]

Why do we consider the unit tangent vectors and not just the vectors themselves without normalizing them?

[south ice]

There isn’t any because my questions are conceptual

[midnight haven]

Lemme ask her

[south ice]

Alright thanks

[full wadi]

We normalise the vectors to simplify the mathematics

As all normalised vectors have length one

If the normal hadn't been normalised then the 3rd equation (binormal) wouldnt be correct and we would have to scale it down

[south ice]

Wait let’s get to binomial after the unit and normal

So wait

Normal tangent vector: tells us how a particle’s direction changes

Unit normal vector: tells us how a particle is turning

Correct

[full wadi]

The binormal

[south ice]

@full wadi

Okay so

Alright so when we talk about the unit tangent vector

We are considering the velocity of the position function

Then we normalize that velocity vector

@full wadi right

unit tangent vector = unit velocity vector

If I’m not wrong

[full wadi]

I have never personally used the binormal for anything

unit just means normalised to length one

[midnight haven]

In Riemnannian geometry for example one defines the unit normal of a local parametrization (under the right circumstances) as
N:=∂1X×∂2X|∂1X×∂2X|
As the name says, it is a unit vector. I mean, one advantage of normalizing basis vectors is that we can easily calculate the coefficients in the linear combinations, but I think there are more. Sorry it took long she's a slow typer

[full wadi]

Tell her she can do LaTeX on here!

[south ice]

No worries at all tell her I appreciate her replies

[midnight haven]

Ok

She said np

She asked if u need more help

She is not busy

[south ice]

@full wadi Okay, so do we care about speed here then? When talking about where a particle is heading ?

Because velocity = speed + direction

Are we only utilizing the direction part ?

[full wadi]

The tangent is the velocity yes

[midnight haven]

Yea

[full wadi]

Atleast the direction of the velocity

I can't remember if that equation gives the correct magnitude

[midnight haven]

[midnight haven]

For what? I can ask my mother

[full wadi]

Is the length of the tangent vector the speed?

[midnight haven]

Lemme ask

[south ice]

Of the velocity vector yes

Good question btw

I don’t think it’s the full speed

I think it would be a constant speed of 1

[south ice]

Wait the tangent vector on it down without normalizing it?

Yes it’s the speed

Magnitude of velocity = speed

Speed is a scalar

[full wadi]

Yes but I can't remember if that equation gives the tangent vector of the same length as the velocity vector

[lavish bay]

is the tangent velocity

[midnight haven]

The tangential velocity is usually the length of the tangent vector

Why do I feel so smart

[south ice]

Lol

[south ice]

.

[south ice]

@midnight haven do you think you can ask her this

[midnight haven]

Will ask

[south ice]

Starting from here

[midnight haven]

Choose one paragraph

[south ice]

Wait lemme ask it here again for better understanding

[midnight haven]

Yes pls

[south ice]

Unit tangent vector: tells us how a particle moves as far as it’s direction
(How its direction is changing)

Unit tangent vectors come from velocity/ magnitude of that velocity

But what we also know about velocity is that it’s a speed + magnitude (speed going a certain direction)

Do we care about this information when considering how a particle changes direction ? Do we utilize this information about what a velocity is in relation to how a particle changes directions? Since that’s our main goal

[midnight haven]

Alr lemme ask

[south ice]

Thanks a lot

[midnight haven]

We care about the velocity to find the direction but we intentionally strip away the speed

[south ice]

Ohhh

That’s why we take its magnitude?

[midnight haven]

Yes basically

Replied - mom

Am I the only person here gng

https://tenor.com/view/brain-hurts-gif-12096381820083648834

[south ice]

Your mom is awesome

Wait I got another question

[midnight haven]

Oki

[south ice]

If that’s fine with her

[midnight haven]

She said yes

[south ice]

Alright so when it comes to the unit normal vector: this tells us how a particle is turning

Now what does turn here mean?

And when it comes to that turning , why do we obtain that turning information through taking the derivative of the unit tangent vector and dividing it by its magnitude ?

[midnight haven]

I'mma ask

In the world of calculus, "turning" has a very specific geometric meaning. It isn’t about how fast you are spinning your wheels; it’s about how much the direction of your travel is deviating from a straight line...... ( basically means it doesn't means that it not abt how fast u go if uk then uk)

She said basically

[full wadi]

the dividing by the magnitude isn't relevent to the turning information.

[midnight haven]

Am just explaining for fun ngl

[full wadi]

it describes turning in the same way the second derivative describes turning of a function

[south ice]

When we talk about a particle deviating from a straight line what’s that supposed to mean on a space curve (I’m using the definition of what turning means that was provided)

[full wadi]

If the particle continued on a straight line without turning then it would have constant tangent vector (direction)

[midnight haven]

On a space curve, a straight line is the path the particle would take if it stopped turning and just kept its current heading forever. This is the tangent line.

I should have said that Instead of this

[south ice]

Ohhh so basically we can say that the turning is the path that “curves”the particle along the curve

Right

[midnight haven]

https://tenor.com/view/cansado-boa-noite-gif-10363364936698022286

[full wadi]

You can imagine that the normal vector is applying a force

[midnight haven]

Yes

Am sure @full wadi is stressed lol

[full wadi]

https://giphy.com/gifs/baby-sleepy-face-first-xT8qBvH1pAhtfSx52U

[south ice]

Okay, now why does T’(t)/|T’(t)| give us that information about turning?

[midnight haven]

https://tenor.com/view/jonah-hill-wtf-i-guess-bro-man-i-guess-smh-gif-4106492938199795190

[full wadi]

As T is the first derivative, that equation means the normal is the second derivative

the devision is just making the length one to make future maths more convenient

[midnight haven]

To understand why \frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)|} captures the "turning" information, we have to look at what the derivative of a direction ACTUALLY REPRESENT SSSSSSSSSSSSSSSSSSSSSSSSASSSSSSSSSS

https://tenor.com/view/cat-annoyed-stare-side-eye-gif-16732086699915766519

[south ice]

I’m gonna put this in latex

I think it is but you missed the $$

$$To understand why \frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)|} captures the "turning" information, we have to look at what the derivative of a direction$$

[jolly parrot]

warbeast002

[full wadi]

$\frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)|$

[south ice]

Oops

[midnight haven]

bro

[full wadi]

$ \frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)| $

what is breaking

[south ice]

To understand why $$\frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)|}$$ captures the "turning" information, we have to look at what the derivative of a direction

[jolly parrot]

warbeast002

[full wadi]

the classic missing bracket

what a fool i am

[midnight haven]

Lol

[south ice]

I don’t think I understand this properly

[midnight haven]

Sighhh lemme ask her to explain a more simple way

SIGHHH

[full wadi]

Consider the standard derivatives, position derives to velocity and then to accelleration

Im sure you can intuit why accelleration would be a 'turning' value

[midnight haven]

She said and I quote think of it as a car steering wheel

[south ice]

Okay

[full wadi]

https://giphy.com/gifs/space-alien-spaceship-r88w2d7tHqazFwNEGN

Space ship steering wheel

[midnight haven]

Lol

[south ice]

We wanna take the derivative of velocity is that what she means ?

I mean that’s the thing I don’t understand why the derivative of velocity gives us insight on Turning

[midnight haven]

NOOOO

[full wadi]

the derivative of velocity is accelleration

[midnight haven]

No

https://tenor.com/view/cat-no-nonono-noooo-cat-no-gif-13597132752790194338

[south ice]

Wait no no

Derivative of the unit tangent vector

Divided by its magnitude

Which is the formula for the unit normal vector

[full wadi]

Where are you getting unit tangent vector

[midnight haven]

Yes

[south ice]

Formula

[full wadi]

Its not a unit vector though

[south ice]

But why does that give us information on turning to begin with

[south ice]

It is

[full wadi]

The tangent wont have length one

[south ice]

T(t) is a unit tangent vector no?

[full wadi]

A 'unit' vector is one with length one

[south ice]

Yes

T(t) = r’(t) / |r’(t)|

[full wadi]

Which the tangent vector doesnt (probably)

[midnight haven]

Bro idek anymore bro it was me giving all the ans from the begging my mom left since last week

[full wadi]

that isn't what the equation shows

[south ice]

Bro WHAT

[south ice]

Wait actually ?

[midnight haven]

Yes

Am tired

[south ice]

That’s actually crazy

Man

[midnight haven]

They call me 𝕡𝕣𝕖𝕞𝕚𝕦𝕞 for a reason

[south ice]

Is your mom also not a teacher

[midnight haven]

No it was just me using my brain cells

[south ice]

I figured

Alright then do you know why

[midnight haven]

AY WHAT U MEAN

[south ice]

Who else was gonna answer if it was you other than you

[midnight haven]

Idk

Anyway the only reason am helping is bc am bored

[full wadi]

https://giphy.com/gifs/the-brain-ararestuserx-noob-FVPcaOuMZo3aKkhnj4

[south ice]

💀

[south ice]

Thanks

[midnight haven]

Bruh

[south ice]

Why do we use that formula

[midnight haven]

No

Np

What formula

For what exactly

[south ice]

The one for unit normal vector

[midnight haven]

Ok lemme look in mi books

[full wadi]

Why not ask ur mum 🤔

[midnight haven]

Cant u not read

Well I can still ask bc she may not be a teacher but she is very good in maths

But for the rest of the question s I was answering for myself

[full wadi]

Idk man ur mum seemed to be giving pretty good answers 👍

[midnight haven]

That was me.....

Cant u not read

I figured

Anyway

[south ice]

He’s trolling

[midnight haven]

Who

[full wadi]

https://giphy.com/gifs/STRAPPEDUS-druski-druski2funny-meme-n4FCJYLldGPC95d4ku

Not me

[midnight haven]

\mathbf{N}(t) = \frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)|}= the formula for de unit nrml vector or V

[full wadi]

$ \mathbf{N}(t) = \frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)|} $ = the formula for de unit nrml vector or V

[midnight haven]

Bro

[full wadi]

oma god the bot hates me

[midnight haven]

Lol

[full wadi]

$$\mathbf{N}(t) = \frac{\mathbf{T}'(t)}{|\mathbf{T}'(t)|}$$ = the formula for de unit nrml vector or V

[jolly parrot]

WeAreIngram

[midnight haven]

Bro what is happening

[full wadi]

https://giphy.com/gifs/cameo-halloween-ghost-ghostbusters-Hs4pCdfhNk28UEOIvk

[midnight haven]

Who bro

Not me

[full wadi]

Me

[midnight haven]

U bearly explained anything

GNG