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@cloud kiln Has your question been resolved?

[lone heart]

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[hybrid maple]

is my reasoning for finding f^-1(x) valid

[hybrid maple]

and how do i find g(x)

[lone heart]

@hybrid maple Has your question been resolved?

[cloud kiln]

We have to solve that differential equation, that is the next step, there is nothing else written

[hybrid maple]

ok i showed my work for the inverse nvm but how do i find g(x)

[lone heart]

@hybrid maple Has your question been resolved?

[hybrid maple]

nvm

my question is resolved

[tacit arch]

Do .close

[hybrid maple]

.close

[lone heart]

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[olive sundial]

help

[olive sundial]

how do i find the cis form of 1 + 3i ?

or 1- 3i

[tacit arch]

,tex .demoivre

[ocean seal]

riemann

[tacit arch]

Oh your r isn't 1

[olive sundial]

yep

[tacit arch]

Factor out a real number first then

Use polar form of complex number

[olive sundial]

wouldnt we need to find like arctan(3)

[olive sundial]

like 3? or what

waiiit

i think i factor sqrt(3)

nvm what am i thinking

lol

[tacit arch]

Do this

[olive sundial]

whats polar form?

of complex number

is it the e^pi i

definition or what

[tacit arch]

Should be an r

[olive sundial]

well yeah but i dont know how to isolate for r

[tacit arch]

if z= a+ib, then r = sqrt(a^2 + b^2)

[olive sundial]

waiiit

fuck

[tacit arch]

r is the magnitude of z

[olive sundial]

alr hold up lemme cook

[tacit arch]

You should look for it in your notes or book

[olive sundial]

yeah i knew that just havent touched complex stuff in a long time so the formulas arent coming to mind as easily

wait so i get sqrt(10) times e^i arcsin(3/sqrt(10))

but like how do u get

the rad instead of arcsin stuff

@tacit arch

[tacit arch]

Where did arcsin come from

[olive sundial]

idk i just need the

radian measure

but i dont know

to get it

[tacit arch]

It's your work, you should be able to explain it

[olive sundial]

no i mean like

its a substitute

for

the radian measure

u could just call it sqrt(10) times e^ix in that case and just have x = the radian measure

@tacit arch

?

you there

<@&286206848099549185>

nvm im literally blind

i thought sqrt(3) = 3 kms

.close

[lone heart]

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[alpine sable]

Hello

[alpine sable]

I have been trying this question for like an hour now I just can't set up the first order differential equation

Past that I'd be fine to solve it I understand what I'm aiming for but not how to get there

[elfin fiber]

Relate velocity and distance in a formula

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

how so

[lone heart]

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[muted hornet]

what do you think you should do?

[waxen turtle]

Idk

I don't get the last bullet point

Idk what it means

[muted hornet]

oh okay! what do you think would happen to a boat if you just dropped it into that current?

maybe this will help you conceptualize it

[waxen turtle]

Idk it goes faster

[muted hornet]

yeah. in what direction?

[waxen turtle]

uhhhh

Idk

[muted hornet]

have you learned about vectors at all in your class?

[jade lichen]

Direction and magnitude OH YEAH

[waxen turtle]

yes

[muted hornet]

essentially, the current is moving in some direction, and the current has the property that it pulls the boat with it "perfectly" (as opposed to just flowing under it). you can quantify this direction in various ways, but one good way is by using a vector

[waxen turtle]

Fr

[muted hornet]

if the current was just flowing 12km/hr due east, could you express this as a vector?

[waxen turtle]

uhhh

I guess

idk the argument

Or like

Exact direction

Fr

But I guess east

Fr

[muted hornet]

well, yeah, if its flowing 12km/hr due east, it's definitely flowing east

[waxen turtle]

So true

so like

Now wat

[muted hornet]

i think that the problem is going to be super hard if you're not comfortable expressing velocities as a vector

what do you remember learning about vectors, do you remember any notation or anything

[waxen turtle]

uhh

idk

[muted hornet]

i mean honestly, i think you should learn more about vectors before trying the problem. i can provide some resources, but i'm not going to just unload a bunch of information about vectors.

https://www.khanacademy.org/science/physics/two-dimensional-motion/two-dimensional-projectile-mot/a/what-are-velocity-components
this khan academy article is good, but it does a lot of trig that isn't relevant here

https://www.youtube.com/watch?v=UGTmOCJ0NKI
this youtube video is probably good and applicable to this problem

[waxen turtle]

WHAT

omg I hate physics

anyways

Let's jsut

Liek

Do it

Fr

They call me the vector god

@muted hornet

PLZ

[toxic spruce]

INVERTED

DO YOU KNOW NORTH, EAST, SOUTH, WEST?

​ N
W E
​ S

[waxen turtle]

Fr

[toxic spruce]

fr fr

so do this for me

get a paper

[waxen turtle]

NOO

[toxic spruce]

and draw this situation

FR

[waxen turtle]

idk wth the last bullet point means

how is a single current going two distinct directions with completely diff velocities

[toxic spruce]

it's okay. One step at a time

remember our compass

so we are going 12km/h ---> that way and 7km ^ that way

so the result of the motion might look like / that

fr

fr

[waxen turtle]

so like

wat should I do

[toxic spruce]

draw a picture fr

with arrows

like that

[waxen turtle]

is the last bullet point like

One vector

Is it giving me x and y

To find magnitude

Idk

[toxic spruce]

it's enough to determine a vector

u gotta draw the picture

fr

[muted hornet]

i don't think this will help

the numbers in the last bullet point specify the components of the vector, so how much the boat is moving in the x-direction and how much it's moving in the y-direction

[toxic spruce]

teased them with the picture of the situation

and then deleted it

[muted hornet]

this helps draw the picture

[toxic spruce]

it's gonna help

it's gotta help

who even cares about vectors

i'm sure inverted knows how to add perpendicular velocities

the answer is triangles, triangles, triangles!

[waxen turtle]

Omg so it's one vector right

Ez

now wat

[toxic spruce]

wait! you have several vectors lying around

you have to draw the picture

[waxen turtle]

WHY

[toxic spruce]

SO YOU KNOW WHAT'S GOING ON

FR

[waxen turtle]

NOOO

[toxic spruce]

DO YOU KNOW WHAT'S GOING ON

[waxen turtle]

SORT OF

[toxic spruce]

SO YOU SORT OF DON'T

BECAUSE YOU HAVEN'T DRAWN THE PICTURE

FR

[waxen turtle]

NO

Never

[toxic spruce]

If anything, the one thing you should take from this is to draw pictures for these questions!

you gonn' learn

^
|
|
|----->

like that

[waxen turtle]

Nah

wat should I do

should I find the magnitude

[toxic spruce]

of what

this situation is lousy with vectors

magnitude of what

you should draw a pic to sort out all of the info

[waxen turtle]

the last

bullet point

[toxic spruce]

yes, there is a last bullet point

[waxen turtle]

yes

that

[toxic spruce]

fr

[waxen turtle]

the magnitude

of that vector

[toxic spruce]

sure what's the magnitude of the vector

given in the last bullet point

[waxen turtle]

√193

I think

[toxic spruce]

alright. now what

[waxen turtle]

idk

[toxic spruce]

right

because that's irrelevant

you need to draw a picture

fr

[waxen turtle]

no

[toxic spruce]

okay. Suppose you are an treadmill going 10km/h south and you're running 11km/h north

how fast are you going

[waxen turtle]

Idek wat that msans

[toxic spruce]

okay

what about

[waxen turtle]

how u run faster than the treadmill

and in a diff direction

[toxic spruce]

well if you were running in the same direction as the treadmill, you'd be going really fast

[waxen turtle]

Fr

[toxic spruce]

fr

have you ever been at an airport and gone on one of those treadmill things that let you get across the airport really quickly

or like an escalator

[waxen turtle]

Yes

[toxic spruce]

like you feel really fast when you go in the same direction a the escalator

or if you want to go up the down escalator, you have to go really fast

[waxen turtle]

Fr

[toxic spruce]

fr fr

so you have to go faster than the escalator is going down

otherwise you're just going to go down too

so like what do you think happens when you are going up a down escalator and the escalator is going -10m/s and you're going 10m/s

[waxen turtle]

idk no progress

[toxic spruce]

yeah, you will be going -10 + 10 m/s

0m/s

fr

[waxen turtle]

can I achieve infinite velocity

[toxic spruce]

uhh if you had infinitely man escalators, no

some weird speed of light stuff happens

it's stupid

it'd be cool if we could achieve infinite velocity

alright, so what happens if sally is on a boat going 35km/h north that's beeing pulled forward by the current another 7km/h north

how fast is the boat going

[waxen turtle]

faster

[toxic spruce]

yes!

faster north!

what's its speed northwards?

[waxen turtle]

idk 42

[toxic spruce]

FR

so the boat is going 42km/h northwards

[waxen turtle]

Fr

[toxic spruce]

now sally is going 5km/h westward and boat is being pulled 12km/h eastward by the current

so if i'm on the shore looking at sally, what direction and what speed does it look like sally is travelling horizontally

​ N
W E
​ S

REMEMBER THE CARDINAL DIRECTIONS

never eat sour weiners

[waxen turtle]

sus

[toxic spruce]

fr

[waxen turtle]

idk 7 east

😭

[toxic spruce]

yeah i'm gonna be like "SALLY, YOU'RE TRAVELLING 7KM/H EAST" when i see her go past

because that's my relationship with sally

so it looks like she's going 7km/h east and 42km/h north

what is her speed

[waxen turtle]

idk

[toxic spruce]

you gotta draw the picture!!!

[waxen turtle]

37 north💀

Idk

northeast

😭

[toxic spruce]

look at that beautiful picture

how do "add" those

[waxen turtle]

√1813

[toxic spruce]

yes

[waxen turtle]

42.6

[toxic spruce]

probably something like that

[waxen turtle]

now wat

[toxic spruce]

what do you think

what do we have right now

[waxen turtle]

idk

her speed

[toxic spruce]

yes

[waxen turtle]

Is that the answer

[toxic spruce]

what does the question want

[waxen turtle]

her absolute speed

[toxic spruce]

so that doesn't really mean anything

but I assume they mean from someone observing on teh ground

like if we were on the land looking at her go, how fast would we see her going?

and that's what we found

[waxen turtle]

.

so

now what

[toxic spruce]

do you want to like hangout or something

[waxen turtle]

.

[toxic spruce]

!

[waxen turtle]

so like

did we get the answer

[toxic spruce]

yes

[waxen turtle]

I don't think we did it right

but ok

OMG

It's right

Hurray

[waxen turtle]

wat is ur fav food

[toxic spruce]

poutine. what about yours?

[waxen turtle]

Idk wat that is

I liek orange chciken

Do u think I got it right

[toxic spruce]

yes

[waxen turtle]

hurray

[waxen turtle]

wat is difference between an array and a matrix

[toxic spruce]

what's an array

[waxen turtle]

Umm

Idk

It's like a grid I think with things in it idk

[topaz nacelle]

a matrix is a two dimensional array

[waxen turtle]

wat does that mean

[waxen turtle]

Plz help

[toxic spruce]

can you break it down so you can add the horizontal components

[waxen turtle]

I got 6.4

idk wat ur drawing are

[toxic spruce]

i drew two perpendicular directions

[waxen turtle]

am I correct

[toxic spruce]

and the force of 3.5 N

,w 3.5 sin(10) + 6

[ocean seal]

Results provided by WolframAlpha

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

Requested by asmallgirl

[waxen turtle]

wat

[toxic spruce]

look at my drawing!

[waxen turtle]

uhh I just liek copied watever this was

law of cosines

The example problem

Fr

[toxic spruce]

fr that works

but i don't like it

i want you to understand decomposing forces into their components

[waxen turtle]

WE GOT DIFF ANDWERS

[toxic spruce]

i only just started

i got the x-component

[waxen turtle]

oh

Law of cosines seems easier anyway fr

[toxic spruce]

,w sqrt((3.5cos(10 degrees))^2 + (3.5sin(10 degrees) + 6)^2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by asmallgirl

[toxic spruce]

that would be my answer

[waxen turtle]

rip I got it wrong

I put 80 instead of 100

u r correct

.close

[lone heart]

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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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[swift raptor]

Got this question as a part of my IB packet on geometry and trig. I got up to this point and couldn't figure out where to go for a while, so I looked at the answer key and somehow I'm even more confused

[swift raptor]

How did they plug it in this way to the quadratic formula?

[tacit arch]

,tex .quadratic formula

[ocean seal]

riemann

[tacit arch]

c is x, a is 1, b is -a

[swift raptor]

But then how does (a^2 - b^2) plug in as ac in 4ac?

[tacit arch]

What

Where exactly are you lost

[swift raptor]

Third step in the answer key

What i mean is, if your definitions of the inputs are correct, then how are they plugging in (a^2-b^2) for 4ac?

[tidal lichen]

cuz c is the "constant terms" which is basically the parts of the quadratic without c

[swift raptor]

By the way, that's meant to be a -b^2 on line three. I miswrote that.

[tidal lichen]

so a = 1 and c = a^2-b^2

[swift raptor]

Got it. I never realized the constants in the quadratic formula worked that way

Thank you so much.

By the way, do you think there's anything in the question that would've made you think to plug it into the quadratic formula to begin with? What would be your thought process going into this type of question?

Asking so I can understand better how to identify the steps I need to take for a problem in the future.

[tardy stag]

i guess just seeing that it's a quadratic in the variable you care about

it's tricky because you have to use the letters a, b, and c for two different things at the same time

but that's a thing you'll have to do in math a lot

actually, seeing the form of the solution would have given me a little hint since it has the form of (thing) ± √(other thing)

[swift raptor]

Fair enough. Thanks

[lone heart]

@swift raptor Has your question been resolved?

[lone heart]

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[trail summit]

I need help with this physics question

[trail summit]

A box sits on a ramp. The ramp exerts a force of 15N on the box. If the coefficients of friction are 0.2 and 0.3, what is the friction force?

i dont know how to solve this question at all

[lone heart]

@trail summit Has your question been resolved?

[trail summit]

<@&286206848099549185>

[haughty sun]

!status

[lone heart]

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

[trail summit]

1

[haughty sun]

first step is to draw the diagrams

[trail summit]

ok

Is this good

[haughty sun]

!original pls

[lone heart]

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

[haughty sun]

i don't know what you mean by the force applied to the box from the ramp

like in which direction

[trail summit]

A box sits on a ramp. The ramp exerts a force of 15N on the box. If the coefficients of friction are 0.2 and 0.3, what is the friction force?

this is all i have

[haughty sun]

then we have to assume that the 15N is the reaction force

the reaction force is perpendicular from the ramp at point of contact

it's in reaction from the force of gravity*masse of the box

[haughty sun]

perfect

[trail summit]

Nice

[haughty sun]

now what's the angle of the ramp?

[trail summit]

I don’t know

What does the coefficient of friction mean exactly?

[trail summit]

What’s that

I never did that in my class

[haughty sun]

F frott means force of friction, $\mu_c$ means coefficient of friction dynamic (cinetique), and $\mu_s$ means coefficient of friction static.

[ocean seal]

nico

[haughty sun]

oh and N is force of reaction

coefficient don't have units

[trail summit]

So how do u solve for it

[haughty sun]

$\mu_s$ is usualy biggerthan $\mu_c$

[ocean seal]

nico

[trail summit]

What would that mean

multiply

[haughty sun]

if the Ffrott is bigger than the force that would make the box move than use $F_{frott}=\mu_s*N_{reaction}$

[ocean seal]

nico

[haughty sun]

if there is movement than $F_{frott}=\mu_c*N_{reaction}$

[ocean seal]

nico

[trail summit]

so this problem is an exception?

or we do this with all the problems

[haughty sun]

i think since the box "sits" than there is no movement

[trail summit]

ok

[haughty sun]

wait i made a mistake

[trail summit]

4.5

oh

[haughty sun]

if there is no movement than $F_{frott} \le \mu_s*N_{reaction}$

[ocean seal]

nico

[trail summit]

and in our case there is no movment

[haughty sun]

yes

[trail summit]

what if there was

also is it 4.5 and 3

[haughty sun]

4.5N in static and 3N in dynamic yes

in static Ffrott $\le 4.5$ not necessairly equal

[ocean seal]

nico

[haughty sun]

don't forget to specify if it's in static or dynamic

[trail summit]

So are you sure I will have to do that

Cuz I do have a quiz coming up soon

Ok so I guess since I do

[haughty sun]

don't forget

[trail summit]

Can you tell me in simple terms how I can decide which is static and dynamic

[trail summit]

Sorry I don’t really understand this. My bad I really need to get a good grade on this quiz or ima fail the mp

That’s why I have so many questions

I’m new to physics

[haughty sun]

force that you push on the box < or = force of friction (mass * gravity) * coefficient static on the ground than static

that's if it's not on a ramp

if it's on a ramp you need to make a diagrame and with a little (moderate/big for you) trigonometrics calculate the force of reaction

[haughty sun]

that means that the symbole on the left should be $F_{friction.statc}\le 4.5$ rather than $F_{friction.static}=4.5 $

[ocean seal]

nico

[trail summit]

and f friction dynamic = 3

[haughty sun]

indeed

[trail summit]

alr

thanks

[haughty sun]

but don't forget your units at the end in (Newton)

[trail summit]

so 4.5N

[haughty sun]

yes

[trail summit]

alr fixed it thanks

wait

could Uk also mean dynamic

because in my class we don't use Uc

@haughty sun

[haughty sun]

still here

[trail summit]

alr my bad

[haughty sun]

by U you mean $\mu$ right?

[ocean seal]

nico

[trail summit]

yes

[haughty sun]

then makes sense that we probably don't use the same symboles since we're probably not in the same country

[trail summit]

im in the US

[haughty sun]

what symbole do you usualy use ? from canada btw

[trail summit]

cool

we use

Uk

and Us

whats that symbol called btw

[haughty sun]

yeah they mean the same thing

k for kinetic and s for static

[trail summit]

alr good

so

Uk = dynamic? and Us = static?

[haughty sun]

Uk = coefficient of friction in dynamic and Us = coefficient of friction in static, yes they don't have any units btw

[trail summit]

what you mean by they dont have any units

like N

[haughty sun]

yes

Ffrott is in Newton, Nreation is also in Newton, and Us or Uk don't have any

[trail summit]

what do you mean can u give me an example

so its Ffriction dynamic = 3N

[haughty sun]

yes

[trail summit]

alr ima send my work

see if its correct

[pliant cedar]

hello

so

so u know that 15 is the normal force

do u know the component along the plane? due to the weight

[haughty sun]

it's all correct

[trail summit]

Nice

[trail summit]

No I don’t think I need that

[haughty sun]

it's not the question, there's no need for that

[pliant cedar]

well it can be necessary right

coz if the force of tendency is less than us*normal force

then friction = force of tendency

[haughty sun]

what exactly do you mean by force of tendency

[pliant cedar]

the force which is trying to get the box to move

the component of the weight force along the plane is trying to move the box

[haughty sun]

oh so the force Nreaction

[pliant cedar]

Nreaction is the force exerted by the plane on the box right?

[haughty sun]

yeah

[pliant cedar]

thats not what i am calling the force of tendency

[haughty sun]

https://amesweb.info/Physics/Inclined-Plane-Calculator.aspx

there's no force of tendency there what your source?

[pliant cedar]

mgsinalpha

mgcosalpha = Nreaction

which is why the box doesnt move into the plane

but coz of mgsinalpha

the box is trying to go down the plane

the maximum achievable static friction is Nreaction * Us

[pliant cedar]

if this is bigger than mgsinalpha, a friction force equal to mgsinalpha would act on the box and keep it in place, without making it go down the plane

if not

the box will start to move down the plane

and a constant friction force of Uk*Nreaction will keep acting against the direction of motion

[pliant cedar]

while it is still moving. so the net force in the direction of motion would be mgsinalpha - Uk*Nreaction

thats what happens right?

[teal comet]

To solve this problem, we must know the quality of the box and its motion state

Then you can use Newton's laws

[haughty sun]

since the box "sits" then we should use the static domain rather than the dynamic right?

[lone heart]

@trail summit Has your question been resolved?

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[cerulean junco]

Can't understand what it is trying to do with that (1+Δ)(-²) .

[lone heart]

@cerulean junco Has your question been resolved?

[cerulean junco]

<@&286206848099549185>

explain please <@&286206848099549185>

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@cerulean junco Has your question been resolved?

[teal comet]

(1 + difference) * u(3) = u(4) according to this operation can be deduced u(2)

It's just a calculation that is defined

[cerulean junco]

I am talking about that (1+Δ)^(-2) -----(i)

how did they get that (1-2Δ+3Δ²) from (i) ?

I wan to know the skipped steps and logic behind that calculation .

[teal comet]

matrix

[cerulean junco]

???

[teal comet]

wait

[teal comet]

u(x) is optional

u（x)=(03,9)He identified the entire system，This is valid and you can calculate it

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[teal comet]

You're a bit abstract

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@teal comet Has your question been resolved?

[teal comet]

Guess

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[past violet]

hi, ive got this relation right here and the excercise says prove itf its equivalent or an order relation

[past violet]

problem is, this isnt even reflexive

at least according to what i did

[mortal trellis]

and thats a problem why?

[violet orchid]

it is symmetric, yet not reflexive
therefore it is neither an order relation nor an equivalent relation

[mortal trellis]

not all orders need to be reflexive

[past violet]

idk in my lecture slides

orders are partial orders+totality

and a partial order needs to be reflexive

[mortal trellis]

do you have strict orders?

[violet orchid]

it doesn't fit "<" or "<="

[mortal trellis]

for example < is a strict order

and its not reflexive

[past violet]

no not really

we only defined partial and linear(full) orders

[mortal trellis]

(well ok it isnt one of those either. but just wanted to point out that not being reflexive is in general not enough)

[past violet]

this is an old exam, maybe they also defined strict orders in the past and this question was about that

[mortal trellis]

!original

[lone heart]

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

[past violet]

well its in german

and all i did was translate

[mortal trellis]

well prüfen translates to check, not prove

[past violet]

does it

damn

[mortal trellis]

check whether ...

[violet orchid]

anyways it isn't transitive at all

[mortal trellis]

and you did check

and saw that it is neither

so all good

[past violet]

thought it had to be one of them

german isnt first language lol

anyway thanks

.close

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[livid jewel]

I've a question about physiscs. About the difference between couple en moment

[livid jewel]

when you have a couple the net moment would be 0, but there is still rotation? how could this bne

be

[lethal belfry]

net force, the force moment would still be non-zero , unless I'm missing something

i.e the torque

[real parrot]

couple might not be colinear

[livid jewel]

it's just when you have to calculate equilibrium for the moments a couple will give you equilibrium, but this will always provide rotation?

[real parrot]

no?

the couple might be colinear

[livid jewel]

you have a force F , distance H from a rotation point. Now you have another force -F also distance H from rotation point

this will lead to a couple

but the sum of moments will be 0

[real parrot]

but a couple can even be non colinear

[livid jewel]

yes ok

but in this example

it is?

[real parrot]

no rotation will be here

[livid jewel]

how???

[real parrot]

sum of moments is zero

so no rotation

[livid jewel]

take a pen, apply one force +h from point O and the same negative force -h from point O

it will rotate

[real parrot]

this is a couple

[real parrot]

wait

oh

I thought you meant the same point

[livid jewel]

no +h and -h

my bad

[lone heart]

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[bold token]

I was trying to find the radius of the circle, however im stuck to the step where im trying to find the lines in which it passes the center. Im guessing I equate both the x and x1 to get the center of the circle, is it the right direction?

[lone heart]

@bold token Has your question been resolved?

[bold token]

I tried doing this, but I think theres something fundamentally wrong. Can someone help?

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@bold token Has your question been resolved?

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[unkempt vector]

hey can someone help me with #5 on this

i started with partial fraction decomposition then idk what to do after

[slender ridge]

write 1 = (n+2)-(n+1)

then split

[unkempt vector]

why would it be - though

[buoyant saddle]

just 1/(n+2)! starting at n=1

[unkempt vector]

so bc it's minus it'll keep cancelling out right

i got 1/2 - 1/n+2

and because n approaches infinity i got 1/2

my answer matches with the book of the book so i think its right ty guys

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[alpine sable]

Let G = (V,E) be a simple, connected, planar, 4-regular graph.

 In planar embedding, G divides the Euclidean plane exclusively into squares (with 4 corners) and triangles (with 3 corners) (including the surrounding area).  The number of squares is exactly 18.

 Using the Euleric Polyhedron Formula, determine the number of triangles
.```


F - |E| + |V| = 2
S is the amount of squares (18)
T is the amount of triangles.


Handshaking Lemma:
sum of all degrees = 2|E|
4 regular so 4|V| = 2|E|
|E| = 2|V|


Formulas I made up:
• 4S + 3T = the sum of all degrees = 2|E| = 4|V|
Solve by |V|:
S + ¾T = |V|
• S + T = F

now put them in the euler:
F - |E| + |V| = 2
(S+T) - 2|V| + |V| = 2
(S+T) - |V| = 2
(S+T) - (S+¾T) = 2
¼T = 2
T=8
Whats my error? Why does it stay the same regardless of S?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[strong leaf]

I don`t understand your question, T is 8 i do see a issue with the step where you substitute the expressions for |V| and simplify, but even when i did it i got T=8

ping me if you reply

[alpine sable]

@strong leaf but S simplifies out of the equation, logically I am pretty sure not every 4-regular graph has exactly 8 triangles

I assumed I made a mistake in the calculations somewhere

Can you elaborate on the issue in the step where I substitute for |V|?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

@strong leaf ?

[lone heart]

@alpine sable Has your question been resolved?

[strong leaf]

Sorry

[strong leaf]

It seems there's a consistent error in the formulation. The correct substitution should lead to an equation where both (S) and (T) contribute. Please double-check the substitution, and if needed, we can work through it step by step.

@alpine sable

[alpine sable]

It seems that way, I guess the 3T + 4S = 2E part is wrong? I have no idea why though

I guess a triangle and a square can share an edge? so the formula would need to be <= and not =

@strong leaf any hint?

[strong leaf]

Certainly! To better capture the relationship between the number of triangles ((T)) and squares ((S)) in a 4-regular planar graph, considering shared edges, you could use the following inequality:[ 3T + 4S \leq 2|E| + 2C ]

[strong leaf]

Ah, you've identified a crucial insight. In a planar graph where squares and triangles coexist, an edge can indeed be shared by both a square and a triangle. This implies that the sum of degrees formula (3T + 4S = 2|E|) might need to account for the fact that some edges are counted in both triangles and squares.

[alpine sable]

I feel bad asking this but are you pasting my messages into chatgpt or do you just text like Ai

[strong leaf]

🤣 Using text from text books

[alpine sable]

haha

[strong leaf]

Sorry

Lazy

[alpine sable]

guess I'll think over it a bit then lol

[strong leaf]

Here, (C) represents the count of shared edges between squares and triangles. This ensures that each shared edge is counted only once in the sum of degrees.With this adjustment, the inequality reflects the sum of degrees being less than or equal to twice the number of edges plus twice the count of shared edges.

Try this, i am not home so i can't do it my self

Dont use chatgpt, i know from experience that MF get shit wrong and when you correct it it acts like a child, oh yes like don't text books are better

[alpine sable]

yeah chatgpt isnt really good with more advanced math

i just know its style from programming-related stuff

I'll try, thx

[strong leaf]

Your problem is called a Euleric Polyhedron Formula you am google it

[strong leaf]

Dont even code using it 🤣 i trid making a CI/CD pipeline, it make me make a docker hub account( note, i didnt need it), ill try your problem

[carmine reef]

Bro gonna deny using gpt then paste a gpt generated paragraph and say "try this"

💀

[strong leaf]

I'm lazy wtf you expect

Now help green overlord 🤣

[carmine reef]

<@&268886789983436800>

[strong leaf]

https://tenor.com/view/bruh424019499-gif-25675566

[tardy stag]

yeah that kind of attitude isn't goign to fly here

[strong leaf]

I wont even

[tardy stag]

we also have a policy against posting gpt answers, and especially without disclosing it

[strong leaf]

Bye

[carmine reef]

Bye

[lone heart]

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[vapid steppe]

ik that II is correct and III is incorrect so it must be B but hdyk I is incorrect

[tacit arch]

Find a counterexample

[unkempt mica]

a constant function obviously verifies $h(x)=h(2-x)$

[ocean seal]

LF

[vapid steppe]

oh ye

h=-3

[unkempt mica]

sure

any h < 0 would work

[vapid steppe]

ty

.close

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[grizzled wigeon]

Hi, I was wondering, for the Gram Schmidt process, when we change the matrix V into an orthonormal matrix E, the basis vectors of E are not necessarily i hat and j hat… but they’re just all unit vectors right?

[grizzled wigeon]

And are perpendicular to each other*

[unkempt mica]

exactly

[grizzled wigeon]

oh that clears up thanks!

.close

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[grizzled wigeon]

.reopen

[lone heart]

✅

[grizzled wigeon]

wait nvm 💀

.close

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[faint monolith]

Alina writes the numbers $1, 2, \dots , 9$ on separate cards, one number per card. She wishes to divide the cards into $3$ groups of $3$ cards so that the sum of the numbers in each group will be the same. In how many ways can this be done?

[ocean seal]

sxer

[faint monolith]

I have no idea

[unkempt mica]

what would that common sum be?

[faint monolith]

idk

[unkempt mica]

what is the sum of all the cards?

[faint monolith]

45

[unkempt mica]

yes

there are three groups

so each group must have a sum of 15

[faint monolith]

yes

[unkempt mica]

can you think of one way to do that?

when you do find one, is there any other way to do it?

[lone heart]

@faint monolith Has your question been resolved?

[faint monolith]

9+4+2

[faint monolith]

cant think of any other

tha dont use the same numbers

[lone heart]

@faint monolith Has your question been resolved?

[unkempt mica]

think of them in a 3x3 grid

[unkempt mica]

it would work, but you need three groups

[faint monolith]

oh yeah

i got another one

9,4,2

8,6,1

7,5,3

theres only two right

because the second number after 9 cannot be bigger than 5 or smaller than 4

@unkempt mica

[unkempt mica]

you got it

[unkempt mica]

well put

you might want to justify why that is

but you got the idea

[faint monolith]

ok thanks

.close

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[west girder]

Deal with each digit in binary separately

Well First deal with all of the 6 digit binary numbers

And then you can do some casework on the 7 digit numbers since they have to be less than 100

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[cinder sundial]

What the teacher did from 1 to 2

[unreal meteor]

2log2 cancels out

fact of life

3log3 also cancels out etc

[cinder sundial]

do you mean 2 log2 = 1

2 multiplied by log2 = 1

[harsh lintel]

no, 2^log_2(x)

[cinder sundial]

is it what you mean

[harsh lintel]

not times

[cinder sundial]

$2^log_(2)$

[harsh lintel]

2^log_2(x) = x because exponentiation and logarithms are inverses

[ocean seal]

Please Correct My Grammar

[cinder sundial]

and that equals to 1

[harsh lintel]

not 1, x

[atomic stirrup]

it equals whats inside the parentheesis

[harsh lintel]

kinda like this... exponentiation and logs are inverse, so it's whatever in the parenthesis

[noble ruin]

awwwww

[cinder sundial]

shit

[cinder sundial]

I see now

[atomic stirrup]

that works out, also nice handwriting

[cinder sundial]

So what the teacher did on both side during "1"

[atomic stirrup]

they set both expressions as an exponent of 2

so how from 1. to 2. 3/2 turns to 2^(3/2)

log2(x) turns into 2^(log2(3))

but 2^(log2(3)) is equal to 3

sorry, got 3 and x mixed up

i hope that makes sense

[cinder sundial]

it does makes sense

and it is such a clever manipulation

I think the question is solved

thank you so much!

[atomic stirrup]

np

[cinder sundial]

.close

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[cinder sundial]

.reopen

[lone heart]

✅

[cinder sundial]

you are still typing, so i reopend it

[atomic stirrup]

oh lol

[cinder sundial]

is there anything you would like to supplement on this quesitons

[atomic stirrup]

i just wanted to add that just like how addition and subtration are opposites

exponents and logs are opposites as well

[cinder sundial]

does addition and subtraction have a inverse relationship

[atomic stirrup]

yes

[cinder sundial]

I see

[atomic stirrup]

same with multiplication and division

starting from 1, say you multiply by 5, you can go back to 1 by dividing by 5
1 * 5 = 5
5 / 5 = 1

[cinder sundial]

I see

but they have a more strict meaning in geometry i suppose?

[atomic stirrup]

wdym?

[cinder sundial]

like two inverse functions are symmetric in terms of x=y

[cinder sundial]

If my memory serves me right, thats the geometric definition of inverse functions

[cinder sundial]

So when you said that addition and subtration are inverses

emm

[atomic stirrup]

do you want me to explain?

[cinder sundial]

yes, im not sure if there are functions that can be used to represent addition and subtration

So i can put them on the plane to see if they match the circumstance(definition) of inverse functions

[harsh lintel]

that's true

actually I'll let @atomic stirrup do it lol

[atomic stirrup]

thx lol

[atomic stirrup]

i think it works

you have a line like y = 3x +1

no wait

(x -1)/3 = y would be the inverse

[cinder sundial]

yes

[cinder sundial]

rather than just -y=-3x-1

[atomic stirrup]

ig you have to be wary of pemdas and of course laws of multiplication

[atomic stirrup]

yes, inverse means(at least in simple algebra) changing the spots of x and y then solving for y

[cinder sundial]

yes exactly

[atomic stirrup]

not just putting y to a negative

[cinder sundial]

does it means addition and substraction are not inverse

[atomic stirrup]

they are

see how in the inverse we are subtrating 1 instead of adding

[cinder sundial]

for y = 3x +1 and -y=-3x-1 do not fit the definition of inverse functions

[atomic stirrup]

they do not

[cinder sundial]

it is quite arbitrary, but I think we can say that addition and subtraction are not inverse functions by that

or there's something wrong in my way of thinking

if we define y to be addition then -y would be the subtraction.

[atomic stirrup]

you're confusing inverse functions(symmetry along y=x) with inverse operations(+/-, mult/division)

[atomic stirrup]

subtration is adding negative numbers

[atomic stirrup]

but through inverse operations you can get inverse functions

[cinder sundial]

I suppose the "inverse operations" is you swapping the position of x and y in a function

emm

[atomic stirrup]

no, inverse functions are defined by swicthing the x and y

[cinder sundial]

ohh

Then I think i have a quite abstract and self-made defination for inverse opetations

[atomic stirrup]

it happens lol

[cinder sundial]

lets define operation A as a step forward, then if operation B is a step backward, then A and B are inverse operation

[cinder sundial]

but i disagree with with that tho

[atomic stirrup]

i meant that in isolating variables after switching the x and y, but yes standalone my statement was wrong

[cinder sundial]

yes

then integral is the inverse operation of differential

Now i have the knowledge of what a inverse operation means

I will close the channel now

[atomic stirrup]

thank you for your patience

[cinder sundial]

no, I appreciate your explanation of these terms

.close

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[cinder sundial]

im glad to learn them

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[amber violet]

I am stuck with part b. How do i start it? Thank you.

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@amber violet Has your question been resolved?

[tacit arch]

You just integrate

Like I said last time, you just do it by cases like the hint says

do one case first

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[real panther]

Q138?

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@real panther Has your question been resolved?

[alpine sable]

bhai

directrix me image lele

focus ki

aur vertex ki

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[bold token]

I was trying to find the radius of the circle, however im stuck to the step where im trying to find the lines in which it passes the center.

[bold token]

Then I tried doing this but got a wrong answer, Am I missing some rule? please someone help

Is it safe to assume that the center of the circle is at the half angle of the three angles and the sides opposed to the half-angle are also halved?

[lone heart]

@bold token Has your question been resolved?

[bold token]

<@&286206848099549185>

[stark path]

I usually use r = (area of triangle) / s (Half the perimeter of triangle) to solve for the radius of the circle inscrbied

[stark path]

The center of the inscribed circle indicates the intersection point of three lines which bisects each 3 angle

[lone heart]

@bold token Has your question been resolved?

[bold token]

Ooo I didnt know this, thanks

[bold token]

Yeah thats what i was thinking aswell, but my formula says no

[lone heart]

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[weak plinth]

Suppose you are planning to attend a party on New Year's and you got a new trim, $t$, the day before. Does the following proposition hold?
$$
\exists M \in [0, 1).\ \textrm{clappedness}(t) > M \implies \textrm{you dodge the party}
$$

(With $\textrm{clappedness}: {\textrm{trims}} \rightarrow [0, 1]$ having the obvious mapping)

[ocean seal]

gkn1

[alpine sable]

what

[tall topaz]

gkn what

is this related to chris

[alpine sable]

is this guy an mg dude

[tall topaz]

nah

but

oh well

[lone heart]

@weak plinth Has your question been resolved?

[rose sigil]

tf

jesse what the fuck are you talking about

[tall topaz]

no idea what the obvious mapping is

[rose sigil]

plus t doesn't seem to be defined...

how are we supposed to evaluate clappedness(t) even if we knew the mapping

[tall topaz]

[tall topaz]

check gkn1's message history

[rose sigil]

william

[tall topaz]

People in chris's circle

[lone heart]

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[shut saddle]

Am I right? Cuz I'm losing my braincells rn

[echo socket]

Are you sure about
[ (y - 3)^2 = y^2 - 6x + 9? ]

[ocean seal]

A Lonely Bean

[shut saddle]

idk

I guess I'm wrong

[echo socket]

Yeah cuz where does the x come from

[shut saddle]

wait

that's y

[echo socket]

Well you wrote x there

[shut saddle]

💀

but my solution is still correct right assuming you ignore the x

Just pretend x isn't there and it's y

[echo socket]

Once you replace -6x with -6y everywhere, yeah

[shut saddle]

It's still correct right

[echo socket]

Actually wait

[shut saddle]

Oh no

I hate algebra

[echo socket]

You forgot to subtract 32 from the right hand side

[shut saddle]

Wait what

= 9?

wtf

😭

[echo socket]

Second line in the right column; You subtracted 16 from the left hand side twice, but not from the right hand side

[shut saddle]

so it's supposed to be x²+y²-8x-6x-7=-7

[echo socket]

Anyway, you could just cancel the 9's and get $x^2 + y^2 - 8x - 6y + 16 = 0$

[ocean seal]

A Lonely Bean

[echo socket]

No, you subtracted 16 from the right hand side now

You should subtract 32

Whatever you subtract from the left hand side, should be subtracted from the right hand side

[shut saddle]

you mean 3²?

Okay so x²-8x+16-16+y²-6x+9-16=9-16

Right

[echo socket]

No, again

You are subtracting 16 twice on the left

But only once on the right

[shut saddle]

Oh okay so I don't subtract here

💀

[echo socket]

You don't even need to subtract that much

Just subtract 9's from both sides

[shut saddle]

do I have to subtract 16 with 9s too?

no need right

[echo socket]

No need

[shut saddle]

so it goes like this then x²+y²+16x-6x=0

[echo socket]

1. You mean -8x?
2. Where does -6y go?

[shut saddle]

So this is pretty much it?

This is the standard form?

if I try to solve this I get (x-4)²+(y-3)²=3²?

Jesus I wrote 6y as 6x again

[echo socket]

That's pretty much it, yeah
[ x^2 + y^2 -8x - 6y + 16 = 0 ]

[ocean seal]

A Lonely Bean

[lone heart]

@shut saddle Has your question been resolved?

[lone heart]

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[lone heart]

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[cosmic acorn]

hi

[cloud nacelle]

can you re write

like

[cosmic acorn]

what?

[cloud nacelle]

why power 4

[cosmic acorn]

its readable

bcs if you derv v, it will be ()^4 : v'. But the other fraction do not have ^4 to get the same denominator

the left fraction does not have ^4