help-17

[stark meteor]

That’s abt it

Hope it helped!

@slate tinsel

[slate tinsel]

thanks

wait

isnt 5? 1;4?

[stark meteor]

What’s four threes?

[slate tinsel]

??

[stark meteor]

I mean 4x3=?

[slate tinsel]

where did you get that?

[stark meteor]

Just answer it bro

What’s 4x3=?

Nvm..it’s 12

So the initial ratio was 4:12 which is simplified to 1:3

[slate tinsel]

oh okay

[lament tangle]

its 1:4, you need to include the keys

[slate tinsel]

bro came out of nowhere

[lament tangle]

lol

[stark meteor]

Oh dang..it says all of them mb

[vast shale]

So divided?

[viscid thorn]

size is directly proportional to volume

[vast shale]

I still don't get it

[viscid thorn]

which part?

if yk that size is half of the volume of cylinder, req volume = vol of cylinder/2

[vast shale]

V=πr^2h
V = 3.14 × 8^2 × 4/2
V = 3.14 × 64 × 4/2
V = 3.14 × 256/2
V = 804.64/2
V = 402.32 cubic decimeters?

[viscid thorn]

yepp

[vast shale]

AB/2 = 16/2
​= 8units.
OB^2 = OC^2 + BC^2
10^2 = OC^2 + 8^2
100=OC^2 + 64
OC^2 = 100−64
OC^2 = 36
OC = (sqrt)36 = 6units.

no additional information is provided about the positioning of C and D, I assume that CD is another chord in the circle, and if it is parallel and equidistant from AB, then the length of CD would also be 16 units.?

<@&286206848099549185>

[worn stone]

You know DB is 8 and OB is 10 so you can find OD from Pythagoras and OB is is radius of the circle so CD is OB - OD

[vast shale]

Did I do it right?

[worn stone]

OC is not 6

OC = OB

[vast shale]

I don't get it

[proper pelican]

OC and OB both radius here

so they are equal

[vast shale]

100=64+ 64?

[proper pelican]

is it for triangle ODB?

oh, look

[proper pelican]

you need to use OD, but not OC

[vast shale]

Oh

[proper pelican]

if i got your thoughts right

and you was trying to use pythogoras theorem

[proper pelican]

so you have DB and OB, you can find OD and OC - DO will be your answer

[vast shale]

DB AND OB IS 16/2?

[proper pelican]

OB is 10 from the question, AB is 16, and DB 16/2

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[brittle mirage]

How can I solve this question?

[spiral turtle]

This is a separable differential equation.

[brittle mirage]

I did that

However i think i might have done smtg wrong

Could u check for me?

<@&286206848099549185>

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[random basin]

How did sec turn into cos, by reciprocal identity?

Wouldn’t it have just been cosecant?

[full summit]

sec is just 1/cos

[random basin]

Oh wait nvm 🤣

I literally realized it as I was typing it out

I mixed sec with sin

Thx

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[rose fractal]

Hi, where do the values for the two sided significance test come from, the alpha = 10% == 1,64 or alpha = 5% == 1,96 and alpha = 1% == 2,58 ?

[rose fractal]

They just said these are the values by which sigma is multiplied by where do they come from?

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[vocal sleet]

@dull widget Has your question been resolved?

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[vocal sleet]

@somber geyser Has your question been resolved?

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[old spindle]

pretty sure u need to take moments about P for both of the forces

by considering the force perpendicular to P

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[cobalt vigil]

Just wondering why the period is 4pi/5 if the K value is 1/2

wouldn't the period be 4pi or am i wrong

[heavy yoke]

it's 5/2, not 1/2

[cobalt vigil]

thanks

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[halcyon marten]

hey yall,

[halcyon marten]

why did my teacher multiply it by 8!

shouldnt it just be the first part

[wraith python]

I concur.

[halcyon marten]

thats a releif

[wraith python]

Oh no.

[halcyon marten]

NO

NOOOOOOOOOOO

[wraith python]

I just realized. Those 8 picked letters can be in any order.

[halcyon marten]

wdym

[wraith python]

abc
acb
bac
bca
cab
cba

[halcyon marten]

oh

so he did a permuatation

[wraith python]

Yes.

[halcyon marten]

then why did he not times this number by 5!

[wraith python]

The order of the cards in a hand does not change the hand.

[halcyon marten]

Ahhhhh

thankyou very much

[wraith python]

yw

[halcyon marten]

permuatations arent even in my test do i dont have to worry anyway

thanks!

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[brittle jungle]

How do I find part B? The answer is I(x) = 3x^3 + x^2 - 8x + 4 but I don't know how to get there

[brittle jungle]

The hint I was given was to not account for the thickness of the sides

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@brittle jungle Has your question been resolved?

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[manic canyon]

I can’t tell if I’m doing this right??

[tribal pumice]

This looks fine to me

[manic canyon]

Ok awesome I’ll submit -77.5 tyyy

[tribal pumice]

Don't forget to round as they asked

[manic canyon]

Oh wait yea It’d be a -77.50 got it

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[sinful pollen]

im on number 18

i got the derivative

$$\frac{d}{dx}[f(x)]=\sqrt{3}cosx-sinx$$

[twin meteor]

Devil Wears Prada

[sinful pollen]

and now i cant find the critical numbers

which is when the derivative is undefined or equals 0

i know its defined everywhere on its domain

but finding when it equals 0 is hard

my teacher said to do it algebraicly

[heavy yoke]

so what do you get if you set that equal to 0?

[sinful pollen]

wdym

like isolating x?

[heavy yoke]

that's what we would like to do, yes

[sinful pollen]

ok give me a second

yeah i cant isolate x

im having trouble

[heavy yoke]

what did you try so far?

[sinful pollen]

i got

$$x=-\frac{\sqrt{3}+2}{csc\cdot sec}$$

but i dont think thats possible

how can trig functions not have x

oh wait

[twin meteor]

Devil Wears Prada

[sinful pollen]

yeah

[heavy yoke]

that does not make sense. csc and sec are functions

what are their inputs?

[sinful pollen]

well i had to isolate x

so i removed them

[heavy yoke]

that does not make sense as a concept. if you had [ x^2 = 3 ] it would be equally nonsense to say [ x = \frac{3}{{}^2} ]

[twin meteor]

cloud

[sinful pollen]

not a good analogy for this

for me

at least]

how do i isolate x

[heavy yoke]

it might look like sin(x) is "sin multiplied by x", but it is not

[sinful pollen]

here

oh

so can i just keep x with them

[heavy yoke]

maybe let's start from the beginning. we have [ \sqrt 3 \cos x - \sin x = 0 ]

[twin meteor]

cloud

[heavy yoke]

what would be a first step for this?

[sinful pollen]

yes

+sinx

[heavy yoke]

ok, so now we have [ \sqrt 3 \cos x = \sin x ]

[twin meteor]

cloud

[sinful pollen]

now how do i isolate x

if its apart of cos

[heavy yoke]

it might be a good idea to divide things so that we have functions of x only on one side

[sinful pollen]

$$\sqrt{3}=\frac{sinx}{secx}$$

[twin meteor]

Devil Wears Prada

[heavy yoke]

not quite

[sinful pollen]

how come

[heavy yoke]

where did sec(x) come from?

[sinful pollen]

dividing is like multiplying by the reciprocal

[heavy yoke]

but you divided by the reciprocal

[sinful pollen]

no

the reciprocal of cos is 1/secx

right

[heavy yoke]

yes no

[sinful pollen]

so why is that wrong

im multiplying by the reciprocal of cos

[heavy yoke]

the reciprocal of cos(x) is sec(x), in other words 1/cos(x) = sec(x)

1/sec(x) = cos(x), that's the reciprocal of the reciprocal, which is the original thing

[sinful pollen]

what

you just said

a = b

but b =/ a

oh i see

ohhh

so sinxsecx

on the right side

now

[heavy yoke]

yes, but it would probably be better to keep it in terms of sin and cos

[sinful pollen]

oh

sinx/cosx

so tanx

$$\sqrt{3}=tanx$$

[twin meteor]

Devil Wears Prada

[sinful pollen]

but its not really isolated still

[heavy yoke]

well once we have an equation in terms of a single trig function we can look at solving it

[sinful pollen]

how

[heavy yoke]

well it happens that $\sqrt{3}$ is a value of $\tan x$ found in most function tables

[twin meteor]

cloud

[sinful pollen]

what

i thought it is sqrt3/2

[heavy yoke]

that is a value which shows up on the function tables of sin and cos

[sinful pollen]

ok got it

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[mortal granite]

how do you solve this

[mortal granite]

the answer is 2/5 but how do you get it

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@mortal granite Has your question been resolved?

[mortal granite]

<@&286206848099549185>

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@mortal granite Has your question been resolved?

[inner osprey]

ABP/PQRS = 1 - PQA/PQRS - PBS/PQRS - ABR/PQRS

[mortal granite]

.close

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[near finch]

Is this correct ?

[tawny nacelle]

yes

,rotate

[tawny nacelle]

looks good to me

[near finch]

Ty!

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[glacial kernel]

what is the working out to transform this first equation into the 2nd more simplified version?

[lone bison]

wait, do we have to convert the 1st equation to the 2nd one?

[gaunt sparrow]

I think it's just a result of $\tan(\frac{\pi}{2} - \theta) = \cot(\theta)$

[twin meteor]

Azyrashacorki

[prisma rain]

$\tan(\theta) = \frac{1}{\tan\left(\frac{\pi}{2} - \theta\right)}$

[twin meteor]

kaue

[glacial kernel]

ah

okay that makes sense

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[heavy wharf]

i thought i was tweaking trying to read that for a sec 😭

[lone bison]

Q19?

first u need to make the intervals continous

uk how to do it?

just simply subtract 0.5 from left interval and add 0.5 to the right interval

in all 4 rows

[upper shell]

(but if you just have to find the mean, theres no need to make class intervals continuous, u straightaway find the class mark and treat it as the value)

[lone bison]

uh... idk i always make the intervals continous because i can't take risk of getting answers wrong

yep!!

now yk what to do

yk right ;-;?

mention not!!

mention not!!

hmm, have u rechecked?

[willow pike]

which eight

oh

not that way

ok wait

lets take a normal example

say we have 7, 8, 9

how would you find the mean

[lone bison]

i think u missed a step

did u calculate the midpoints?

and multiply it with the number of students?

TOT

CMON

[silk osprey]

dawg what are your pronouns

[willow pike]

here were assuming each student to have value as midpoint of the range

[lone bison]

anyways u can redo the question

keep doing

[silk osprey]

🤔

[willow pike]

quesitonable

[lone bison]

and tell if u got correct answer this time

answer is 61.7 indeed

....

[willow pike]

whats the midpoint of 7 and 8

[lone bison]

there will be a different midpoint for each interval

[willow pike]

same way

whats the midpoint of 20.5 and 40.5

yes

[lone bison]

exactly

[willow pike]

youre assuming each student to have the value as that midpoint

so the answer will give you the approximate mean

[lone bison]

then multiply each midpoint with their respective numbe of students

add them up

add up the number of students, which is 50

divide both values

u got ur answer

!!!!

wrong midpoints!!!!!!!

30.5, not 30

same with others

[silk osprey]

bro no one is paying you

people help for free

[lone bison]

it's okay

that's the spirit

nice try diddy

💀 👍

jk jk

[silk osprey]

aint no party like a diddy party

[lone bison]

YES

YES YES

[willow pike]

no

wait

yeah

[lone bison]

YESSSSSSSSSSSSSSSSSSSSSSSS

congrats @stray cave

proud of u idk why

no problem!!

[silk osprey]

wow man very helpful

perfect timing

yo raymond

[lone bison]

[willow pike]

came when we needed the most

🙏

[lone bison]

mention not :D

poor raymond

[silk osprey]

yo raymond

how much money have you made so far

[lone bison]

[silk osprey]

@uncut burrow

[lone bison]

brother ain't leaving him 💀

[silk osprey]

nuh uh

[sharp rain]

Knief hunting today

London style

[lone bison]

make it american🦅

[silk osprey]

https://tenor.com/view/pirate-writing-blackbeard-feather-writing-heresy-gif-4408192544333034740

[sharp rain]

https://tenor.com/view/america-america-flag-sigma-baller-gif-4192599876740220832

[silk osprey]

damn bro

raymond might be ai

[sharp rain]

@stray cave

Just close bruh

[lost yarrow]

.close

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[sharp rain]

Comes in with the save

[silk osprey]

is he banned

uyu

might be

yep

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[valid zenith]

Hi, I have an algebra problem here, How can I demonstrate that [ (1/3)n(n+1)(n+2) + (n+1)(n+2) ] is equal to [ (1/3)(n+1)(n+2)(n+3) ] ?

I'm very bad at these kind of exercises, so I'd like to learn how to solve them.

[maiden iron]

$$\frac{1}{3} n(n+1)(n+2) + (n+1)(n+2)$$

[willow pike]

take (n+1)(n+2) common

[twin meteor]

Herels

[willow pike]

and say what you got

[valid zenith]

sorry, what do you mean?

[lone bison]

he said to take n+1 and n+2 common

[valid zenith]

the common factor?

[lone bison]

yes!!!!!!!!

[valid zenith]

that would be n

i think i can use n to express (n+1)(n+2) in other way

[maiden iron]

not really
just take (n+1)(n+2) as common factor

[valid zenith]

Oh i see

[vocal sleet]

@valid zenith Has your question been resolved?

[valid zenith]

Ok i know i should use the common factor, I just don't know how to use it

[lone bison]

...god

[valid zenith]

heh sorry..

[lone bison]

$$(n+1)(n+2)((1/3*n)+1) $$

[twin meteor]

Baizhi

[lone bison]

@valid zenith

[valid zenith]

Ok i understand better

its like if I see (n+1)(n+2) as just X and (1/3)n as just N, it would be like nx+x, which is equal to x(n+1)

[lone bison]

i didn't get it

[valid zenith]

im seeing (n+1)(n+2) as an X variable

[vocal sleet]

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[tidal magnet]

for the question h(x)=(x^2-9)/(4x^2+2x-15) how do i find the end behavior and how do ik if there is a horizontal asymptote?

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[tidal magnet]

.close

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[digital kayak]

i NEED help desperatly assignment due in 2 hrs

[digital kayak]

please ping me when someone i shere

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[opal raft]

@digital kayak I don't know the solution but I have started thinking about it

[opal raft]

An equivalence class is an element of a quotient set. https://ncatlab.org/nlab/show/equivalence+class

These are from Tom Leinster notes, it is a set theory course going on at the moment at Edinburgh University: https://www.maths.ed.ac.uk/~tl/ast/ast.pdf

These are my twopence for (b)

[vocal sleet]

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[opal raft]

<@&286206848099549185>

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[tardy loom]

can some one help me pls

[vocal sleet]

Please don't occupy multiple help channels.

[tardy loom]

PLS HELP ME

WITH SINE COSINE LAW

I NEED QUESTIONS

[fringe quest]

https://dontasktoask.com/

[floral pike]

AHHHHHHHH!!!!

[tardy loom]

bro

[floral pike]

[tardy loom]

I need u to give me some questions for sine and cosine law

bruh

[full summit]

search on google

[tardy loom]

they are too easy

[full summit]

search for hard ones

[tardy loom]

they are easy too

[floral pike]

Because they are easy to use when you know the context

[tardy loom]

there are no hard ones

[tardy loom]

that not the prob

our teacher told us that there will be really hard questions on our test

so I need to practice

[floral pike]

LoC is useful when you know two sides and the included angle, but not the opposite side

[tardy loom]

ty

[floral pike]

LoS is easier than that and is good when you have two pairs of angles and opposite sides where 3 out of 4 are known

.

.

Here it looks like they want you to use area formula

A = (1/2)(base)(height)

Where the height is in terms of sin(theta). It's helpful to flip it over so the 3x is "on the ground" (for me anyway). That way you can draw a height that visually makes more sense

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@tardy loom Has your question been resolved?

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[shut sedge]

hi my first time here I need help with math homework pls, I barely understand the theorems ;-; I need answers but I would reallly appriciate some explanations as to how the answers we're obtained T>T 🙏

[bronze osprey]

for 1, you need the fact that OA = OP

so that means triangle AOP is isosceles and its base angles are..... ?

[shut sedge]

90 degree ?

[bronze osprey]

no, wrong theorem

[shut sedge]

ouh

[bronze osprey]

this theorem doesn't have anything to do with circles

[shut sedge]

they are equal ?

err holdon theres a term for it uhhh wait

[bronze osprey]

yes

[shut sedge]

congruent

yeah congruent

[bronze osprey]

congruent but you don't really need to say that

yeah

actually it's easier to start from angle 4 actually

by definition, angle 4 is 98 degrees

[shut sedge]

ae yeah nevermnd I don't understand the concept can you break it down for me pls 🙏

[vocal sleet]

@shut sedge Has your question been resolved?

[bronze osprey]

go watch a video

https://www.youtube.com/watch?v=nd46bA9DKE0

this is harder than the question you have been given

but it's good to watch

[vocal sleet]

@shut sedge Has your question been resolved?

[shut sedge]

Kk ty ty

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[bronze osprey]

https://www.youtube.com/watch?v=FD9DVFBpCMI

actually go watch this one first

then do your problem

if you have any more circle theorem questions later on, go watch the org chem video

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[devout agate]

A quick question.

Can a 2 dimension vector have a cross product?

Ex: P1 (2,3), P2 (4,6)

[oak magnet]

Yes

2*6 - 3(4)= 0

Thoses are colinear

So 0 isn't a fancy result

[devout agate]

thank you!!

.close

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[hybrid basalt]

is this correct

[mild flower]

,rcw

[mild flower]

sure yeah

idk exactly what they want there

but that seems fine

[hybrid basalt]

thanks

[hybrid basalt]

i have to assign a property to the change to justify steps

its geometric proofs

[mild flower]

yeah that seems like what they want then

[hybrid basalt]

thanks

.close

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[hybrid basalt]

have a good day

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[valid yacht]

what are they looking for in a counterexample?

[brisk moss]

an element m of Z for which there is no n in Z with the property F(n) = m

[low haven]

bad name

[sharp rain]

It's dead

Just like like club penguin 💀

[brisk moss]

fuck you

[valid yacht]

ohhhhhhhhhh

so like an integer where there is no f(n)

so like

1

or 0

[brisk moss]

yea 1 works

[sharp rain]

Yup

[valid yacht]

nice

ty

.close

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[valid yacht]

muah

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[south knot]

Hi

[south knot]

Could you help me out with a question paper

?

[sharp rain]

[south knot]

Here is the question paper with The Fuction

It was in German and i had to translate it.

The translator kept messing with the function so i have it in German too in the second picture

[south knot]

I would be very grateful if anybody could help. I have the test day after tomorrow

This is very similar to a test. Says my professor. But I don't even know how to solve this

[vocal sleet]

@south knot Has your question been resolved?

[south knot]

<@&286206848099549185>

[acoustic vector]

CHARLES LECLERC?!

Anyway..

[south knot]

Yes yes thats me

[acoustic vector]

W, lemme out the same pfp wait

[south knot]

Can you help me? I have to finish this otherwise I won't be allowed to Race in Vegas

[acoustic vector]

This is better

[acoustic vector]

Lemme see

[south knot]

Here's with better quality

[acoustic vector]

I’m too dumb for that..😭😭

Sorry

[south knot]

Damn.

I guess i can't race now in Las Vegas

Anyways thanks

[acoustic vector]

Sad

[south knot]

<@&286206848099549185> cmon be Useful for once atleast

[vocal sleet]

@south knot Has your question been resolved?

[vocal sleet]

@south knot Has your question been resolved?

[dusky mural]

Bis wann ist das, ich kann tatsächlich morgen helfen falls es morgen nicht abgegeben werden muss 👍

[south knot]

Bro ich schreibe übermorgen

Also habe noch morgen eigentlich, aber ich will ja meine Antworte vergleichen und sehen ob es richtig ist oder nicht.

Dann halt verbessern wo ich Fehler gemacht habe.

Danke dir

[vocal sleet]

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[crisp schooner]

How is angle D = 120 degrees? The explanation makes it seem obvious but I can't figure out how they got it immediately.

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@crisp schooner Has your question been resolved?

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@crisp schooner Has your question been resolved?

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[crisp schooner]

.close

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[meager basin]

can someone pls help me with this

[meager basin]

i keep getting random ass numbers

please my friend is struggling too

we need help

[spiral turtle]

!show

[vocal sleet]

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

[dark kiln]

x - (3/4)y+(2/4)z = 4
so x = 4+ (3/4)y-(2/4)z
then (32 + 6y - 4z) - 6y + 5z = 37
32 + z = 37
z = 5

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[open igloo]

@naive ingot

[open igloo]

here

definite

[naive ingot]

yo

[naive ingot]

send

[open igloo]

hold

letme translate

[naive ingot]

where are you from

[open igloo]

México

[naive ingot]

Nice

makes the question 30 × harder XD

[open igloo]

the text say: Find the area of the graph bounded region of the given functions

[open igloo]

fr

i just need help to know how to solve one of it

[naive ingot]

I don't think I took that yet

[open igloo]

like what are the limits and the integral

[naive ingot]

like as a definition?

[open igloo]

i think the same for me 😭😭

but anyways i have it like homework

[open igloo]

yeah

[naive ingot]

Well for a function to be differentiable the limit from the left gotta equal the limit from the right

and integrals are known as anti-derivatives

which is literally the opposite of differentiation

so if $\frac{d}{dx}(3x-1) = 3$

[twin meteor]

Daddy| |matr!x

[naive ingot]

integral is the opposite of it

which is $3x + C$

[twin meteor]

Daddy| |matr!x

[naive ingot]

c is the arbitrary constant

in this case

$C=-1$

[twin meteor]

Daddy| |matr!x

[open igloo]

yeah

i understand that

[open igloo]

the problem its where are the integral here

[spiral turtle]

To get the function to integrate along with the bounds, you subtract the two functions (top one first), And the bounds are the points of intersection

This works because if you imagine the area as sliced into vertical strips, we can move them around up and down without changing their area, so if we line them all up on the x-axis then we have an easy to integrate area. And this is equivalent to subtracting the bottom function from the top

@open igloo ^

[open igloo]

hold on

i'm processing

i think

i get it

nah

i get how to get the bounds

like the intersection

but i don't understand the last part

[spiral turtle]

That's fine, it's a little bit difficult to visualize

Let's call the top function f(x) and the bottom g(x)

[open igloo]

"the equivalent to substracting the bottom function..."

[spiral turtle]

Now here's a question. Does the area change if a choose a value C to add to both?

In other words, instead of the area between f(x) and g(x), I'm considering the area between (f(x) + C) and (g(x) + C)

[open igloo]

i think it doesnt

[spiral turtle]

Indeed it doesn't

Next step, what if I only apply the value partway?

In other words,

Let's say the two intersections are -2 and 2. Does the area change if I consider the area from 0 to 2 to be between (f(x) + C) and (g(x) + C) but from -2 to 0 it's just between f(x) and g(x)?

Is that the same as the area between f(x) and g(x) from -2 to 2?

[open igloo]

yup

[spiral turtle]

Ok cool, what if I have an arbitrary function h(x)?

Is the area between (f(x) + h(x)) and (g(x) + h(x)) the same as between f(x) and g(x)?

[open igloo]

yup

[spiral turtle]

Ok now consider the case when h(x) = -g(x)

Do you see what is going on here?

[open igloo]

i think

[spiral turtle]

So in the case where h(x) = -g(x) what is your top function?

And more importantly, what is your bottom function?

[open igloo]

f(x) + h(x)

[spiral turtle]

Which is f(x) - g(x) after we use the identity.

[open igloo]

g(x) + h(x)

[open igloo]

yup

[open igloo]

and this g(x) - g(x)

[spiral turtle]

Which is?

[open igloo]

0

and g(x)=0

right?

😭

[spiral turtle]

Yes!

Well g(x) isn't 0

But g(x) - g(x) is

So now your top function is (f(x) - g(x)) and your bottom function is 0.

But 0 is just the x axis

[open igloo]

yeaah my fault

[spiral turtle]

So now you're trying to find the area between a function and the x-axis

But this is just the integral!

[open igloo]

yuup

[open igloo]

and the space between top and bottom its another function right?

the curve

[spiral turtle]

I don't follow the question

The curve is f(x) - g(x)

[open igloo]

it wasnt the top?

[spiral turtle]

Isn't the curve in question the top function shifted down by the bottom?

Or are you talking about something else?

[open igloo]

like the red line

[spiral turtle]

The red line is f(x) - g(x)

[open igloo]

and what is the top limit

like the green line

YOOOO

i got it

[open igloo]

in the first case

f(x)= x

and

g(x) = -2x

[spiral turtle]

https://www.desmos.com/calculator/muzfwu6oro

[open igloo]

they are two curves

[open igloo]

yoo

now i understand

the two was 2 functions

2 curves

not the two limits

[open igloo]

of one function

😭😭

[spiral turtle]

https://www.desmos.com/calculator/eqhww2dq9x

Slightly better version

[open igloo]

thhhx

so the thing

[spiral turtle]

You're very welcome

[open igloo]

it's calculate the área where are green and red as the same rime

[spiral turtle]

The area of the green and red are the same

[open igloo]

i mean that area

the orange one

[spiral turtle]

Oh no sorry

[open igloo]

now i remember i saw it on class

!!

but it was a lot 😭

but i got the thing

calculate the area between 2 curves

[open igloo]

its the topic

[spiral turtle]

https://www.desmos.com/calculator/ambacowdwj

The area between the curves is in red

We want the red area

The green is the area we get when we just let the area drop to the ground.

[open igloo]

what do u mean with

curve drop to the ground

[spiral turtle]

Ok one more plot, one second

[open igloo]

okey

meanwhile

[open igloo]

back yo this case y=x is f(x)=x and y=-2x is g(x)= -2x

right?

[spiral turtle]

https://www.desmos.com/calculator/fnvvjoszif

Press play on t

[open igloo]

ohhh

right

like green area is the red are but displaced to y=0

thats how i Will get

[spiral turtle]

Exactly

[open igloo]

haha

[open igloo]

@spiral turtle

[spiral turtle]

For that problem, there is only one intersection between those two points. So which one on top depends on the x values being examined.

If you're looking at 0 to 3 then f(x) = x and g(x) = -2x as you supposed.

[open igloo]

this one intersection right

[spiral turtle]

Yes and you also have x=3

So I suppose they want the triangle.

[open igloo]

https://www.desmos.com/calculator/sxuuarxhp0

[spiral turtle]

Yup

[open igloo]

but

how i calculate it

integral of g(x) with limits 3,0

[spiral turtle]

$\int_0^3 f(x) - g(x) , \dd{x}$

[open igloo]

• integral of f(x) with limits 3,0

[twin meteor]

OmnipotentEntity

[open igloo]

oh

how

do u say

?

[spiral turtle]

"minus"?

[open igloo]

okey

i don't know that

haha

[open igloo]

so this all? right

[spiral turtle]

Yup

That's all

Just replace f and g and you're good to go for this problem

[open igloo]

okay, just wait a second letme se another case

now

on this case

https://www.desmos.com/calculator/ij6e0gss8i

what are the limits

cause we dont get x=
and the intersection inst on 0

@spiral turtle

[spiral turtle]

The intersection is where 2(1-x^2) = x^2 - 1

[open igloo]

yooo

[open igloo]

https://www.desmos.com/calculator/dzhctmztt3

like that

[spiral turtle]

https://www.desmos.com/calculator/iskifvzklk

Yeah, you can find it using a graph, but you should be familiar with simply solving the equation

[open igloo]

thxxx

[spiral turtle]

2(1-x^2) = x^2 - 1
2-2x^2 = x^2 - 1
3 = 3x^2
x^2 = 1
x = ±1

(as you found)

[open igloo]

x=+1 the right limit

(top)

and x=-1 bottom

right?

$\int_{-1}^1 f(x) - g(x) , \dd{x}$

[spiral turtle]

x = -1 is the left vertical black line on your graph

Good effort, you need to surround the -1 in {}s

[twin meteor]

JJUASSI

[open igloo]

yeah

one of the limits

[spiral turtle]

✅

[open igloo]

for the areas

this*

its only replace f(x) and g(x)

right?

and calculate the limits

[spiral turtle]

The integral, yes

[open igloo]

@spiral turtle

[open igloo]

with the graph how much it is

the area

can u see it please

[spiral turtle]

"you can find it using a graph"

I was referring to the intersection points.

[open igloo]

oh

YOOOO

i do it

!!

its 4u² btw

hahaha

thank You so much @spiral turtle

i rlly love u

at the end it was more easy than i thought

😭😭

@spiral turtle thxxxxx

u make me happy

prob i come back in a few hours

hahaha

i got a Lot more integrals

.close

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[vast shale]

(Water clock) A water tank is obtained by rotating the curve y = kx^4, k>0 about the y-axis.
Water drips through a small hole according to Torricelli's law. dV/dt = -m√y
Show that the water level decreases at a constant rate.

[wanton sun]

A list of 9 real numbers consists of 1, 2.2, 3.2, 5.2, 6.2, and 7, as well as x, y, and z with The range of the list is 7, and the mean and the median are both positive integers. ordered triples (x, y, z) are possible?

[vocal sleet]

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

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[vocal sleet]

@vast shale Has your question been resolved?

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[torn oracle]

do both of these rules only apply for X and Y being independent?

[torn oracle]

or does rule 1 apply for all cases

[opal raft]

I would like to know this as well.

[haughty shuttle]

The first doesn't require any sort of assertions of independance @torn oracle @opal raft :)

[torn oracle]

thanks !

.close

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[opal raft]

Thank you @haughty shuttle

[hybrid flicker]

in general Var(aX+bY) = a^2 Var(X) + b^2 Var(Y) + 2abCov(X,Y)

the first formula as already stated is already generally true

[torn oracle]

so in the case where X and Y are indept 2abCov(X,Y) = 0 hence making the formula provided by the textbook true when X, Y indept?

[desert hornet]

.reopen

[vocal sleet]

✅

[hybrid flicker]

X and Y independent => Cov(X,Y) = 0

(converse can be false)

[desert hornet]

could you provide a proof of this?

[hybrid flicker]

I'll do it for Var(X+Y) then, I'll leave proof for aX+bY since it's just about linearity of expectation

[desert hornet]

sure

[torn oracle]

just checking, does this reopen your question or my question?

[hybrid flicker]

Var(X+Y) = E((X+Y)^2) - (E(X+Y))^2
Var(X+Y) = E(X^2) + 2E(XY) + E(Y^2) - (E(X)^2 + 2E(X)E(Y) + E(Y)^2)

we'll close afterwards don't worry

[desert hornet]

it's your channel, I just reopened it because otherwise the channel would time out

[desert hornet]

ah okay, I see it now

that's pretty neat

[hybrid flicker]

Var(X+Y) = E(X^2) - E(X)^2 + E(Y^2) - E(Y)^2 + 2(E(XY) - E(X)E(Y))

[desert hornet]

coincidentally I very recently learned what covarience is from my mom

although I didn't get a very good understanding of it I guess

[hybrid flicker]

would you believe it if covariance and variance acted a lot like scalar product and norm?

(notably cauchy-schwarz inequality)

[desert hornet]

woah what

[desert hornet]

hmmm

|Cov(x,y)| <= sqrt(Var(x)Var(y))

is this what you mean?

[hybrid flicker]

yep

[desert hornet]

I didn't quite understand what this means though

[hybrid flicker]

If you only allow X,Y to be centered

then Cov and Variance are respectively the inner product and norm for the "L^2" variables

(meaning of finite variance)

[desert hornet]

ohhh okay

so covarience is analogous to a dot product?

[hybrid flicker]

in many ways yes

[desert hornet]

that makes sense actually yeah

Cov(X,X)=Var(X)

[hybrid flicker]

you just need to consider centered variables for the analogy to be complete

[desert hornet]

what do you mean by a centered variable?

[hybrid flicker]

E(X) = 0

otherwise Var(X) = 0 -> (X = 0 almost everywhere) is not true

[desert hornet]

oh okay

so we can just replace X with X - E(X)

to center it?

[hybrid flicker]

yeah

just note that random variables don't all have finite expectation and variance

[desert hornet]

what's the use of this notion of covarience and varience being the inner product and norm?

are there other results like CS inequality which can apply?

[desert hornet]

yep

[hybrid flicker]

There are more applications with gaussian random vectors

Not going into too much detail about what it is yet

but when you consider normal distribution vectors

then independence is the same as Cov(X,Y) = 0

[desert hornet]

that makes sense

[hybrid flicker]

so delves into orthogonality, orthogonal projection and all

[desert hornet]

hmm

sounds a bit too high level for me

thanks for explaining though!

[hybrid flicker]

alright let's close then

.close

[vocal sleet]

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[elfin pendant]

Hey guys. Does anybody have an idea on how to do this?

[vocal sleet]

@elfin pendant Has your question been resolved?

[heavy wharf]

use stokes theorem

[vocal sleet]

@elfin pendant Has your question been resolved?

[elfin pendant]

But why is dF = {0} (boundary)

[heavy wharf]

Because F, being a bounded level set of a smooth function with a non-vanishing gradient, is a closed, compact surface in R³. Closed surfaces have no boundary (∂F = ∅)

[elfin pendant]

Wait

Closed surfaces have a boundary

Or am i wrong?

[elfin pendant]

Why is that?

[heavy wharf]

A closed surface has no boundary. The term "closed" in this context means the surface is a complete, self-contained entity without any edges or breaks. Think of a sphere or a torus: they are closed surfaces. A disk, on the other hand, is not a closed surface because it has a circular boundary.

[heavy wharf]

In our problem, the level set F is a closed surface because it is a smooth connected surface without self-intersections, ensuring that it has no boundary.

[vocal sleet]

@elfin pendant Has your question been resolved?

[vocal sleet]

@elfin pendant Has your question been resolved?

[vocal sleet]

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[cobalt valve]

@gaunt fable

[cobalt valve]

ill make one now

x^2 +x -6 = 0

solve for x

@gaunt fable 💀

ive made this question for u, dont pull out now💀

[queen root]

is this some sort of challenge

[sharp rain]

X= -3,2

[sharp rain]

Idk honestly

The challenge is to see who passed elementary school ig💀

[queen root]

literally

[sharp rain]

"Don't pull out now"

Lmao

That's kids is how one sentence from your mother led to your birth.....💀

[vocal sleet]

@cobalt valve Has your question been resolved?

[cobalt valve]

nah this guy told me he was struggling with factorising

so i made him a question, told him id tag him in it

he claimed he "didnt have a foundation" so i wanted to see what was cutting

[sharp rain]

Still, phrasing it as "Don't pull out now"

Like come on

[cobalt valve]

😂

[vocal sleet]

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[queen root]

crazy a non helper helps a helper

[vocal sleet]

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[signal pendant]

im not able to figure out why the "note" is given. i suppose any "deviation" from this function should give us our required points, so i tried considering the difference $f(x)-\frac{1}{2}(x^2+x^3)$ and applying taylors theorem to it, but didnt get anywhere

[twin meteor]

quicdoom

[signal pendant]

let $g (x) = f(x) - \frac{1}{2}(x^2+x^3)$ applying taylors theorem upto the second derivative on points 0,1 and 0,-1, i get that there exist $c\in (0,1),d\in(-1,0)$ such that $g(1) = 0 = g(0) + g'(0) + g''(c)/2! = 0 + 0 + (f''(c) - 2 - 6c)/2! \implies f''(c) = 2+6c$ and likewise $f''(d) = 2+6d$ but i dont see where this goes, applying the mvt doesnt seem helpful

[twin meteor]

quicdoom

[signal pendant]

nevermind, i get a point whose 3rd derivative becomes 6/2=3

.close

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[leaden saddle]

I am struggling to wrap my head around the concept of bijective functions in the case of infinite sets. Obviously they would need the same cardinality for there to be a bijective function, but what does that even mean in the case of infinite sets?

[signal pendant]

we say that two infinite sets have the same cardinality if they have a bijective function between them. the point is to "generalise/extend" the concep of cardinality of finite sets to infinite sets because like you pointed out in the infinite case that doesnt make sense, but a bijection between infinite sets makes sense

[vast shale]

cant u just take f(x) = 4/3 *x ?

idk

from A to B

like, f is bijective form A to B

[signal pendant]

!nosols

[vocal sleet]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[leaden saddle]

I understand that makes more sense. How can I be sure the function I provide covers the whole co-domain?

[vast shale]

no but idk if we talk about the same topic

[signal pendant]

well what does it mean for the function to cover the whole co-domain? every value "c" in the codomain is achieved by providing some value "x" as "input". so take whatever function "f" you want to check, and see if there is some "input" x such that f(x) = c for every c in the co-domain

[potent beacon]

U can use continuity

Or just see that f(x)=y

Has a solution for all y

[signal pendant]

this whole thing translates to what notaportal guy just said. that is, f(x) = c has a solution in the domain for every c in the codomain

[leaden saddle]

okay

thanks

.close

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[vocal sleet]

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[torn spoke]

Is there a way to find the maximum of 3 numbers using their arithmetical average instead of nesting max functions?

[spiral turtle]

If you allow abs, then you can construct a function for max that involves averages, and doesn't involve directly using max.

max(a, b) = avg(a, b) + abs(avg(a, -b))

[peak matrix]

and for 3 numbers,
max(a, b, c) = max(max(a, b), c)

[spiral turtle]

You can then use the linearity of expectation to simplify

[vocal sleet]

@torn spoke Has your question been resolved?

[torn spoke]

I know that you can do it this way, but what I wonder is whether there is a method which doesn't involve this nesting of the max function and which uses the arithmetical average of all 3 numbers. Just like said in the initial message

[vocal sleet]

@torn spoke Has your question been resolved?

[potent beacon]

And what would you like to do with that average?

If its of all 3 it doesnt distinguish between them

[torn spoke]

Honestly no idea. I tried to come up with an idea but it with futile. Web search and AI didn't help either. I thought people here might have an idea

I saw that average is used in the max function for 2 numbers so I thought there might be a similar solution for the max function for 3 numbers

[vocal sleet]

@torn spoke Has your question been resolved?

[vocal sleet]

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[simple maple]

wait nvm lol

It's just phrased like aids

[vocal sleet]

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[dull geode]

hello can someone give me a hint on how to do this

[low haven]

linearization

L(x) = f'(a)(x-a) + f(a)

[sonic escarp]

yup that's the formula of a general tangent line which you can use