help-38

[sturdy frost]

you would get -6/0 which wouldn’t make sense at all

[cold kindle]

Yeah

[sturdy frost]

and that’s when there’s an asymptote

because there’s no y value when x=3

[cold kindle]

how the hell you even pronounce asymptote out 🗿

[sturdy frost]

ah sim tote

[cold kindle]

sounds like a simp toe

🗿

[sturdy frost]

this would be a hole if values close to 3 don’t go to infinity, but dw about that for now

[cold kindle]

ah okay so if next time in exam they asked me to find horizontal "a simp toe" how I find that

[sturdy frost]

uh

[cold kindle]

is it possible

[sturdy frost]

you need to take limits

[cold kindle]

what is limits

🗿

[sturdy frost]

you won’t be asked for that for now

[cold kindle]

oh okay

so basically all I need to remember when vertical "a simp toe" is asked I need to put denominator as 0 and solve it

right?

[sturdy frost]

yeah basically

[cold kindle]

alright thanks

[sturdy frost]

unless you learned holes

[cold kindle]

ayo

[sturdy frost]

for now that would be fine

[cold kindle]

what you mean by that

"learned holes"

💀

[sturdy frost]

lemme send you example

[cold kindle]

ok

[cold kindle]

🤣 thats a line ain't a hole

[sturdy frost]

it’s in blue text

[cold kindle]

oh nvm

[sturdy frost]

even though denominator is 0 it’s not asymptote there because you can cancel out the (x-1)

so if denominator is cancellable it’s a hole

[cold kindle]

what in the world is this

[sturdy frost]

else it’s an asymptote

[cold kindle]

looks same but complicated

[sturdy frost]

i doubt you need to know that for now but it’s something you need later

[cold kindle]

Calculus?

[sturdy frost]

tbh depends on how your teachers teach

[cold kindle]

I am still taking Algebra 2 in my high school

🗿

[sturdy frost]

holes are in algebra 2 as well but slightly later

[cold kindle]

probably next year I will try calculus if I don't like i might quit math forever

[sturdy frost]

moreso precalculus

[cold kindle]

what there is pre calculus

[sturdy frost]

calculus isn’t the only math

[cold kindle]

😲

[sturdy frost]

preparation for calculus

[cold kindle]

whats beyond calculus?

Zeinfincalclusmaths?

[sturdy frost]

you usually start with one variable calc

then there’s multi variable

and then there’s not a real set thing

[cold kindle]

Would you consider physics or math harder?

[sturdy frost]

but some topics are topics in the advanced math category in this server

[cold kindle]

I mean I know without math there is no physics

[sturdy frost]

physics becomes so much easier with math so i can’t really give you a solid question to that

[cold kindle]

🗿

[sturdy frost]

some physics questions are really bad with just algebra but if you know calculus they can be trivial

[cold kindle]

I learned something new today in my physics class

[cold kindle]

If sun disappears, it will take us 8 mins to realize that sun has disappeared.

[sturdy frost]

you can actually derive that with just d=rt

[cold kindle]

how

[sturdy frost]

t=d/r

[cold kindle]

😲

[sturdy frost]

we know distance to sun and we know how fast light travels

so we just divide them

[cold kindle]

Big brain

but still I can't believe why is like this

[sturdy frost]

that’s why the stars you see in the sky are actually younger

[cold kindle]

yea 😭

they might be destoryed right now

[sturdy frost]

yeah

[cold kindle]

man universe is something that we still don't know

probably a maze

[sturdy frost]

we don’t even know our oceans 💀

[cold kindle]

ong

science is so behind

🗿

[sturdy frost]

fr they gotta step up their game

[cold kindle]

aliens might be comin to us at anytime

who know

🗿

[sturdy frost]

world would end ngl

ours

[cold kindle]

do you really believe there is parallel universe

were people actually exist

[sturdy frost]

tbh i do believe it

[cold kindle]

Me to

imagine myself in parallel universe as a boy 🗿

[sturdy frost]

but if i exist in the other universe

it wouldn’t really affect me

like no matter if my other self is smarter or dumber

i’m still myself

[cold kindle]

if it parallel universe there future will be parallel

They might alright have advance technology 🗿

[cold kindle]

alright I gtg go sleep

see ya

[sturdy frost]

cya

[cold kindle]

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[somber spire]

how do i factor 12x^2 + 11x - 5

[somber spire]

like do i need sum and product?

[worthy eagle]

ye

[somber spire]

11 = _ + _
(-5) = _ × _

i can't think of any numbers

😭

[worthy eagle]

multiple 12 by -5

[somber spire]

OHHH

do u always multiply?

how do u know if it needs to be multiplied

[worthy eagle]

depends on the equation

let me show you a tips before starting factoring

[somber spire]

okk

[worthy eagle]

you only need to check these

[somber spire]

ohh

one question

like is there a specific way to find sum and product?

as i just plug in numbers in my calculator until i find

[worthy eagle]

you just do a times c and add to b

sorry wrong image lmao

[somber spire]

lol

[worthy eagle]

here

so what do think the two numbers are?

[somber spire]

-4 and 15

thank you for ur helpp

have a good night/day

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[wraith hinge]

Count the number of integers equivalent to b (mod 225) that have
exactly a digits and have no two adjacent digits being equal.

how

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[upbeat pike]

can someone please help me with question 2?

[supple copper]

How can you get from O to P?

[upbeat pike]

de moivres?

[upbeat pike]

P - O?

oh wait

OA + AB

wait no wtf

OA + OB

[supple copper]

Yes

I drew a crappy diagram but you got the idea anyway

[upbeat pike]

what if A and P were switched around?

because I was trying to visualise the combinations in my head

would it still be OA + OB

[supple copper]

Looking at the parallelogram OAPB it’s going to be in that order just flipped or rotated

It doesn’t matter which reflection you have

You know that O is in between A and B

[upbeat pike]

ohh ok

so you just assume that O is between A and B for simplicity

[supple copper]

I assume it because they said OAPB

Not OABP

[upbeat pike]

im blind

thanks for the explanation

I got the answer

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[torpid meteor]

Calculus question - Prove that any open ball in some norm $\lVert \cdot \rVert_\alpha$ contains an open ball in some norm $\lVert \cdot \rVert_\beta$ and contained in an open ball for some norm $\lVert \cdot \rVert_\beta$

[solid kiln]

mtr123

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@torpid meteor Has your question been resolved?

[wise dagger]

very interesting question, what have you tried?

[torpid meteor]

Tried using the equivalence of norms but got stuck in the middle

Like we know there exists a,b such that a|x| <= |x| <= b|x|

Where middle is 1 norm and the rest is the other. I’m not sure what do if a < 1

Same idea as here actually

https://math.stackexchange.com/questions/3152289/equivalent-norms-and-subsets-of-open-balls-proof

[torpid meteor]

@wise dagger Any idea? 🙂

[torpid meteor]

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[spring hull]

Since A and B are bounded intervals, they are either open, semi-open or closed. (Wlog) there exist a₁, a₂, b₁, b₂ ; a₁ ≤ b₁ ≤ a₂ ≤ b₂ s.t. a₂ = sup(A) and a₁ = inf(A) similarly b₂ = sup(B) and b₁ = inf(B), now A∩B is bounded by a₁ and a₂, infact a₁ = inf(A∩B) and sup(A∩B) = a₂ = min{sup(A),sup(B)}.
Is this proof correct?

[subtle lava]

Why did you consider the inf?

[spring hull]

Yeah it was kinda unnecessary, I'll change that bit

Or wait I need inf(B) atleast

[subtle lava]

Can you write it on paper or using latex?

[spring hull]

Alright just a min

Since A and B are bounded intervals, they are either open, semi-open or closed. (Wlog) there exist a$_1$, a$_2$, b$_1$, b$_1$ ; a$_1 \leq$ b$_1 \leq$ a$_2 \leq$ b$_2$ s.t. a$_2$ = sup(A) and a$_1$ = inf(A) similarly b$_2$ = sup(B) and b$_1$ = inf(B), now A$\cap$B is bounded by a$_1$ and a$_2$, infact a$_1$ = inf(A$\cap$B) and sup(A$\cap$B) = a$_2$ = min${$sup(A),sup(B)$}$.

[solid kiln]

Normed

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@spring hull Has your question been resolved?

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@spring hull Has your question been resolved?

[spring hull]

<@&286206848099549185>

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@spring hull Has your question been resolved?

[obsidian hornet]

hey @spring hull I don't know how long you're gonna stay on this channel, but I'll take a look at this question sometime

cause rn Im working on the same topic

either today or tmr

[spring hull]

It will get automatically closed if I miss a single Bot reminder

[obsidian hornet]

aww alright

yea the bot reminders are kinda annoying

Well I already took a picture of the question

so I'll try that one out sometime today or tmr

[spring hull]

hmm you can dm me whenever you want

[obsidian hornet]

wanna take a look at my first section of a proof Im working on?

Been working on it the whole day

doing the second half now

[spring hull]

So yeah when you try this and get a different solution(proof) let me know

[obsidian hornet]

ok

@spring hull any insights?

[spring hull]

Here's what I've done so far
Since A and B are bounded intervals, they are either open, semi-open or closed. (Wlog) there exist a₁, a₂, b₁, b₂ ; a₁ ≤ b₁ ≤ a₂ ≤ b₂ s.t. a₂ = sup(A) and a₁ = inf(A) similarly b₂ = sup(B) and b₁ = inf(B), now A∩B is bounded by a₁ and a₂, infact a₁ = inf(A∩B) and sup(A∩B) = a₂ = min{sup(A),sup(B)}.

I'm very new to this stuff so yeah this proof is wrong most probably

[obsidian hornet]

no like I mean for my proof😂 I havent looked at yours yet

I will tho sometime today or tmr

[spring hull]

Ohh yours seems like much harder

[obsidian hornet]

yea 🥲

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✅

[spring hull]

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[whole parrot]

Hey guys, I was just trying to work out a way to work out a tournament bracket

I want to have 8 teams with 4 players in each, 32 players altogether

each player will be allocated a game where no player from the same team can be in the same game, and I want to try distribute it as evenly as possible
(note: I want there to be 8 games going at the same time (so groupings of 4)

whats the best way to work this out?

[onyx mist]

What does “no player from the same team can be in the same game” mean, and what are we trying to work out

[whole parrot]

so essentially i’m trying to work out a board game tournament

[opaque lance]

Out of 34 players 8 teams already exist, each with 4 players. And you want these 34 players to players to play 8 games at same time such that team is made of 4? And no player should be from same team previously

[whole parrot]

so i want each of the 8 games to have players from different teams

no i just want 8 total games

[opaque lance]

Each game should have 4 players participating?; You mentioned that in bracket

(so grouping of 4)

[whole parrot]

yeah

but i want it so each game has as diverse of players from teams as possible

so like one team wont have another player in all 4 of the teams’ games

[opaque lance]

I guess there are 2 teams then, one at start and another at game?

since the number of players playing a game is 4

[whole parrot]

oh no

there are 8 teams of 4 players each

32 players altogether

i want them to be distributed amongst 8 different games

so each game will have 4 players each

i want varied players in each game

[opaque lance]

I see

[whole parrot]

so not a case where 4 games have a player from the same 2 different teams

if that makes sense?

[opaque lance]

Yes

So basically you want to change the team such that all players have different new teammates

Both questions will have same answer

but yeah now it makes sense

[whole parrot]

as much as possible

[opaque lance]

I hope our conversation helped that being understood

[onyx mist]

So, if i understand correctly, how many players actually end up playing from the team?

Like in each game

Just one?

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[whole parrot]

well teams are of 4

so 4 of the games will have a player from a team

the other 4 games will be of other teams

so like

1234
1567
1256
1347
8234

where number represents which team it’s from

that’s only 5/8 of the 8 games

but the remaining 3 wouldn’t have team 1 players in it

[frigid lark]

do you want to know how to do it or how many different combinations there are?

bc combinations is easy but if you are asking this for an actual team, you might need to use some sort of calculator to make the teams each time or do it by hand

[whole parrot]

yeah i was hoping someone would be able to help me find a method 😂

or the best approach to it

[frigid lark]

probably the best approach is to just find a generator or you'll just have to do it by hand

bc we can tell you how many different ways there are to do it but to actually figure out the teams is just a hand thing

at least i think so

i enjoy this sort of thing so i can do it for u if u want

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[slate barn]

how should i change LHS to get RHS?

[tepid rock]

$\prod_{i = 1}^n a_i = x$\
$\pl x \cdot x^{\f{1}{n}} \pr ^{\f{1}{n+1}}$

[solid kiln]

! What the hell am I doing here?

[tepid rock]

Is it this?

[slate barn]

well yes

[tepid rock]

Then solve from here.

[slate barn]

$x^1 \cdot x^{\frac{1}{n}} = x^{\frac{n+1}{n}}
\left( x \cdot x^{\frac{1}{n}} \right)^{\frac{1}{n+1}} = x^{\frac{n+1}{n} \cdot \frac{1}{n+1}} = x^{\frac{1}{n}}$

[tepid rock]

Ouch. You copied my text.

[solid kiln]

Slowaq

[slate barn]

alright nvm xd i got it now

thx

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[hybrid kite]

How to start at number 2 of simplify?

[hybrid kite]

I'm really bad at trig identities that's why I don't know where to start 😭

If f(x) = cos (1/2) x, find f(0), f(π/5), f(2x)

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[ionic pendant]

from what i can read it's asking for f(pi/3)

which is a much easier problem

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[hybrid kite]

.reopen

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✅

[hybrid kite]

How 😭

[loud gale]

What how?

Just put x they are standard angles

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[waxen fable]

Are there any conditions that allow me not to check solutions, even after squaring both sides of an equation?

[waxen fable]

For example, if all my numbers are positive

[vague scaffold]

not really sure what oyu mean

[ripe topaz]

can u give an example of an equation ?

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[waxen fable]

For example, 4n+3=sqrt(16m^2+1)

With n and m positive integers

If I am squaring both sides, and if I find solutions, do I need to check those solutions back?

[cosmic meadow]

Yes

You have to make a restriction before squaring it

If x=1

And you want to square both sides for some reason

You have to specify that x>0 before doing it

Eitherway you are creating a new solution

And if you forgot the original context you might get a false solution

[waxen fable]

so is x=4n+3 in this example?

because if yes, I already know that 4n+3>0

[cosmic meadow]

I gave a different example, your example doesn’t have x

When you square both sides you lose the square root

So you have to put a restriction

Also, your n becomes n^2

And that create two answers

[ripe topaz]

i think in the case of sqrt(A) = B u don't have to check back the solutions when squaring both sides
cause if the expression B is negative then the equation doesn't have any solutions

A and B are expressions of a variable x

[cosmic meadow]

That’s why he has to put a restriction

[waxen fable]

but I already know both sides are positive

so I don't need any restriction

[cosmic meadow]

So when he gets a negative answer he checks the restriction instead of the solution

[waxen fable]

right?

[cosmic meadow]

This is why u use restrictions

[lyric nymph]

you should have a restriction if you have sqrt(x)=x+1 for example then you should have a restriction that x>=-1 bc if a solution is in the interval (-inf,-1) then plugging it will lead to problems

[cosmic meadow]

Exactly

[ripe topaz]

yeah i said that if B is negative then the equation has no solutions in that interval

[waxen fable]

Sorry for the late replies, I am back now

okay so I think my example is a bit different

because this is a diophantine equation

[lyric nymph]

if RHS is not constant then it will not be either positive or negative all the time

[waxen fable]

so my variables on both sides are not tied to each other

so in the case of $4n+3=\sqrt{16m^2+1}$

[solid kiln]

BeeReallyYum

[cosmic meadow]

This one m has two solutions

And n has one solution

[waxen fable]

technically it has more

an infinity of solutions

[cosmic meadow]

I don’t mean infinite solutions

I mean

[waxen fable]

because of pell's equation

[cosmic meadow]

Every two solutions of m you have one for n

[waxen fable]

oh okay

[waxen fable]

but one of the solutions for m will be negative

[cosmic meadow]

Yes

[waxen fable]

and I know that m>0

[cosmic meadow]

No

[waxen fable]

yes I do

m is a positive integer in the problem

[cosmic meadow]

You know that 16m^2 + 1 > 0

Ok

Then that’s a restriction

And now

When I square both sides

I put another restriction

Which is n>0

[waxen fable]

i also know that

from the problem

that's another restriction

[cosmic meadow]

Then u don’t have to check any other solution

That is not n,m positive

[waxen fable]

okay, that was what I tried to mean from the beginning

[cosmic meadow]

That’s why u use restrictions

[waxen fable]

yeah I get it

thank you so much for your help!

[cosmic meadow]

No prob

[waxen fable]

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[deep marsh]

what angle should i be looking for

[fathom bolt]

I'd guess the angle at point C inside the triangle. But not sure about how to interpret "CDH" exactly

Okay I looked it up and typically this means you have to calculate the angle between lines CD and DH

[deep marsh]

i got 29 for it

[fathom bolt]

So, the angle at point D inside the triangle

[deep marsh]

what rules do i use?

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[deep marsh]

<@&286206848099549185>

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[short trellis]

a trapezoids bases are 4 and 12 i got a line that is parallel to the bases and it crosses the touching parts of the diagnals find the lenght of that line

[short trellis]

<@&286206848099549185>

[gusty bone]

any other information given?

[cosmic meadow]

We need the height

[short trellis]

Thats all

How do i find the hight?

[cosmic meadow]

You can’t

[short trellis]

So not enough info?

[cosmic meadow]

No, look at this I image

Just by looking at it u can realize the height can vary

With the same 12 and 4 bases

You just put the top base 4 wherever u want

And the height changes

[short trellis]

I need the line ghag passes thro the diagnals toching spot tho i dont need the hight

[cosmic meadow]

If you don’t have another function as information you can’t find it

[short trellis]

Its parallel to the bases

[cosmic meadow]

I have to go now, show a picture of the original problem and later I’ll check

[short trellis]

.close

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[gaunt temple]

Let A be a non empty subset of R and F be a finite subset of A. Prove that if A doesn't have a maximum also A/F doesn't have a maximum.

[gaunt temple]

By contradiction suppose A/F has a maximum M. Then since A doesn't have a maximum, there must be an element X in A such that X>M

Two cases: if X is in A/F it cannot be true since we supposed M is the maximum of A/F and the maximum is unique

If X is in F....? I'm stuck

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[short trellis]

A right triangles perimeter is 60 the perpendicular to the hypotnus is 12 need to find the sides of the triangle

[slim charm]

Try doing

The hypotenus (The relation)

The summatory of the 3 sides

And the Area formula

[short trellis]

I don’t get it

[short trellis]

Those both are the area right

[slim charm]

Also you have

a.b = 12.c, 'cause d=12

[short trellis]

A*B is 12?

[slim charm]

12 times c

[short trellis]

Why?

[slim charm]

The area formula

[short trellis]

Oh yea

[slim charm]

Here, d equals to 12

[short trellis]

Got that

Yes

[slim charm]

Then you have this

[short trellis]

So i need to solve that system?

[slim charm]

Work with the first one equation

Then, is just replace

[short trellis]

So a system

[slim charm]

Yep

[slim charm]

Upps, I forgot to "c" on the third equation

[short trellis]

I don’t think thats solvable

[slim charm]

You need to do something to the first equation

You have a + b isolate

Then looks at the other ones below

[short trellis]

(60-c)^2 equals c^2?

[slim charm]

Nope?

The would be c^2 + 60^2 - 120c

[short trellis]

Then what

?

[slim charm]

Bruh

[short trellis]

Ok

So? How would the system i can solve go

The correcg final system

[slim charm]

Wut

Doing that you will find C

[short trellis]

From this?

[slim charm]

Yep

[short trellis]

I need to solve only that?

[slim charm]

What do you mean with "Only that"?

You'll find C doing It

[short trellis]

Dowing what

[slim charm]

xd

[short trellis]

Thag cant find c

[slim charm]

Have you at least tried?

[short trellis]

Yes

Yoh will not get cs value from that

[short trellis]

Idk what you’re even telling me

[slim charm]

Replace

[short trellis]

Replace whatttt?

[slim charm]

The values of ii and iii

[short trellis]

Did you try doing it

[slim charm]

Yes?

I wouldn't be typing if not

[short trellis]

Did you get the answer?

[slim charm]

Do you need the answer or what?

[short trellis]

The sides

No

I need to solve it and get the answer

Im just trying to make sure your answer is correct

[slim charm]

What are you answers?

[short trellis]

The coorect answers?

[slim charm]

If you are trying to make sure my answers are correct, you must already have you own answers, right?

[short trellis]

Yes but i need to do it not just the answers

[slim charm]

Alright, tell me your answers

[short trellis]

15. 20. 25

Are the correcg answers

[slim charm]

You did It, right?

[short trellis]

No I checked in the book

Did you get those numbers

After solving?

[slim charm]

Yes

[short trellis]

Ok now pls help me to solve it

So what do i do

[slim charm]

I was helping solving It 😅

[short trellis]

Yea ik im sorry

Ok so where where we

[slim charm]

That's what I was doing

[short trellis]

Ok i get how tou found c

What about a and b

[slim charm]

Now, replace a with 35 - b

You'll get a cuadritic equation

[short trellis]

Ok

[slim charm]

After solving It, you'll find b, thefore, a

[short trellis]

How do we find c again can you explain it real quick from the start

[slim charm]

First, I relate them with the area formula

Second, I took the fact: a + b + c = 60

Finally, I do the Pythagoras' formula

I'mm move onto Discord servers, so tag/ping me when you reply

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[polar trail]

i need help with part b

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[polar trail]

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@polar trail Has your question been resolved?

[blissful helm]

@polar trail could you give me the formulas you have been using in school

[polar trail]

F=ma
fk = Uk*Fn

[blissful helm]

So basically if i rembember right

the force that the heavier jeep exerted on the lighter one is elephants force combined with the force of the jeep

if u did the acceleration on both jeeps u should easily get the force of the heavier one using F=m*a

Im not completely sure tho

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[polar trail]

okay ty

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[high plank]

When taking moments how do u know where to start

[high plank]

for example

1a where do i take the moment of

cause when doing diffrent questions i always start at diffent points

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[wraith hinge]

how can i find the following 8 sequences series of following z transform?

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[zinc ginkgo]

Your equation is confusing

Is f(x) the constant or is the derivative a constant

Yes the derivative of a constant is zero

Yes

You can check yourself using the limit definition of derivative

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[versed obsidian]

|(x^2-8x)/x-4|<0.1
I've gotten this far and even then I'm not sure if this is right...

Figured it out! delta= 0.1

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[surreal eagle]

shouldnt the answer be 0?

[surreal eagle]

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[slate star]

I'm working on some Calculus I homework with trig limits and I just figure out how to evalualte this limit

[slate star]

I know I need 7h to just be h so that the limit will equal 1. I just can't figure it out and my notes aren't that great

[bright quarry]

well

the 7 on the bottom

can be rewritten as

(1/7)(sin(h)/h)

then you can use limit laws

to be specific

the limit of a product is equal to the product of the limits

[slate star]

So basically, when I rewrite it'll look like

1.    sin(h).      
__. * ______        
7       h.   

wait I think I got
I'm literally dumb
1/7 * 1

is 1/7

bro

I'm gonna close it now and if I ned to open it for another problem I'll do that

.close

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[slate star]

.reopen

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✅

[slate star]

I'm reopening it because I have another issue

[grizzled vine]

Whats the issue

[silk dawn]

just use the tex bot

[slate star]

The second problem, Am I on the right track with it? Also it may not be clear but the denominator is a t

[slate star]

what's the tex biot

[grizzled vine]

Can I have context

[slate star]

bot*

[grizzled vine]

What is the original problem

[slate star]

I gave you it

under the line

[grizzled vine]

Ok

Sure

Lemme grab a paper

Wait

@slate star isn’t cos^2(x) = 1 - sin^2(x)?

Why that -

[slate star]

oh yeah

I was just using the pythagorena identity sin^2(theta) + cos^2(theta) = 1

[grizzled vine]

Ok. What problems are you having with the limit

[grizzled vine]

Btw it is not required to solve the limit

It is much easier

[slate star]

Basically I can't figure out how to get it to the point where it'll look like this formula : (1- cos(theta) ) / theta = 0

[grizzled vine]

Is the result 1/2

[slate star]

no

[grizzled vine]

Wait lemme check if i wrote the limit correctly

Its sus

I’d factor (sorry im not english native so my terminology sucks) the cos2t

[slate star]

Oh alright yeah that makes sense

I should've tried that lol

[grizzled vine]

So you get cos2t(1-cos2t)/t and you can use the notable limit 1-cosf(x)/fx^2 which approaches 1/2

Just do some algebra stuff

Ping me if its necessary

[slate star]

after factoring I get (1 - cos(2t) / t. And I don't really know how to explain it but it'll look like a similar problem I solved in my notes and I think I would've come up with 0.

[grizzled vine]

So

What is your f(x)

[slate star]

0 right?

[grizzled vine]

No

It is cos2t

In this case, cosf(x) so your fx is just 2x

I will write for you a note ok? Wait

[slate star]

Ok

[grizzled vine]

f(x) can be anything fr

So, you have 2t as your fx

But in the denominator, what do you have?

[slate star]

Oh I see

In the denomiator it is t and I was trying to get t to match the top which was 2t

[grizzled vine]

Just multiply both numerator and denominator

By 2

[slate star]

hold on I think you're on to something (perfect timing since interstellar is literally playing in my ears)

woah

[slate star]

that's cool trick

[grizzled vine]

Eheh

See?

[slate star]

Thanks for your help

[grizzled vine]

No problem! Anytime

[slate star]

.close

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[remote bloom]

i need help for this i have been stuck in this question for a while now

[earnest breach]

I don't think I'm following how to round using these definitions

Yeah can someone help analyze def 1.13 and 1.14 with me? I don't think I'm following why tests look different for x

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[dusk dew]

claim

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[dusk dew]

<@&286206848099549185>

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[olive horizon]

what do elements of P_2 look like?

[lean depot]

Since any element in $P_{2}$ looks like $p(x) = ax^{2}+bx+c$, and we know $T(p(x)) = (p(0),p(0))$, what can we conclude about what $p(x)$ looks like? Remember that the null space will be the collection of all $p(x)$ that gets mapped to the zero vector in $R^{2}$.

[solid kiln]

twitch.tv/pencenter

[dusk dew]

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[dusk dew]

claim

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[crude ether]

Can someone explain why the sector of the area is multipled by 1/4

[zinc ginkgo]

That comes from the angle in radians

[crude ether]

Isn't it pi/4 tho?

[zinc ginkgo]

Yes

pi/4 = pi * 1/4

[crude ether]

So same thing?

[zinc ginkgo]

What two things are you saying are the same

[crude ether]

Pi/4 and 1/4

Or nah

[zinc ginkgo]

No

pi is a number

pi /4 is pi divided by 4

[crude ether]

Hm

Ohhhh

@zinc ginkgo is it because the pis cancel out during cross multiplying

[zinc ginkgo]

I don't see any cross multiplying

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[exotic gorge]

See they have given the length of arc

The formula for finding arc is
Central Angle/360 * 2Πr

After substituting i am getting radius as 7.7Cm

the area i am getting as 103.17Cm^2

@crude ether

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[lean depot]

So the 1/4 is finding the area of a sector that is 90 degrees, and the extra 1/2 basically halves this area so we get an area for 45 degrees. Basically, 45 is 1/8 of 360, so we need to multiply by 1/8 eventually

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[hollow bloom]

pls help

[sly pewter]

make some equations

[dry holly]

use systems of equations

[hollow bloom]

how

[slender shard]

The sum of each row, column, and diagonal are the same. That means you can pick any row, column, or diagonal and set them equal to each other.
eg.
Column 1
v + 18 + 25
Row 3
25 + z + 21

v + 18 + 25 = 25 + z + 21

[hollow bloom]

ohh

ok

thanks

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[mild stirrup]

im confused how to solve these types of problems

[mild stirrup]

im not sure where to start

[solid kiln]

help a sad kid | desi

[mild stirrup]

im confused

how do i use that for this

[solid kiln]

help a sad kid | desi

[mild stirrup]

ohh

so is it just x(x+2)=15?

srry i think my brain is sleepy 🥲

but i get now

ty

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[real gale]

Let v be a family of linearly independent vectors in a vector space V.
How do I prove that v* in V* exists?

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[candid thorn]

HEY! Can i get some help?

[grizzled vine]

"Ask your math question in a clear, concise manner"

[candid thorn]

Whats 699 divided by 7?

[left oriole]

we are not your calculator

do you have an actual question?

[grizzled vine]

lmaoo

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[slate barn]

how come these two are equal?

[proper kernel]

are those variables real or complex

[slate barn]

real

[proper kernel]

B - g(x) = -(g(x) - B)

[slate barn]

alright

but is |a/b| = |a|/|b| ?

[proper kernel]

can you come up with an example where thats wrong?

all || does is make a number positive

ignore b = 0

assume b ≠ 0

[slate barn]

hm i dont think so because |-a/-b|=|a|/|b|, |a/b|=|a|/|b|, |-a/b|=|a|/|b|, |a/-b|=|a|/|b|

[proper kernel]

yea

|| forces a number to be positive

so either way you get the result of dividing a and b but made positive

[slate barn]

so this holds always?

[proper kernel]

yes if b ≠ 0

it also holds for complex numbers for similar reasons

[slate barn]

alright

[proper kernel]

same with |a||b| = |ab|

also holds for complex numbers as well

[slate barn]

yes i see

alright thx for help

[proper kernel]

np

[slate barn]

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[real gale]

Maybe u calculate the variance of the residuals and then compare?

nvm

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[fading pebble]

I don't understand this question

I understand that multiplying it all and simplifying leaves me with a quadratic form for q1, q2, q3

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[gaunt wave]

Did the moderators get pinged in that? <@&268886789983436800> sorry for the double ping if so...

No, sorry. You shouldn't advertise servers in other servers

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[fair bison]

(thanks)

[fair bison]

.close

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[lost ledge]

Help

[lost ledge]

I am dying and I have no idea what to do. There's too many ys and xs

[nova spire]

have you tried implicit differentiation?

[lost ledge]

I sort of did but I'm not really sure how to

[nova spire]

like d/dx both sides

[lost ledge]

I have 1 - d/dx(xylnxy)

now

[nova spire]

yes

now you have to d/dx the thing

rules of differentiation

[lost ledge]

how tho?

[nova spire]

composition rule, product rule, etc...

for example, d/dx(g o f(x)) = dg/dx(f(x)) * df/dx(x)

and product rule :

d/dx(f*g)(x) = g(x)df/dx(x) + f(x)dg/dx(x)

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[mental lodge]

I have some doubt with the $U(0, \theta) , g(\theta) = \theta$

so how we found the unbiased estimators were using the indicator random variable, for example the second sub question can be solved by saying that the event $X_1 = 1, X_2 = 1$ , then the expected value of the indicator variable will be $p^2$

[solid kiln]

13wrc

[mental lodge]

I do not understand how it can be approached in a similar way

[solid kiln]

13wrc

[mental lodge]

<@&286206848099549185>

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[sturdy portal]

e^{40}-e^{13} how to simplify this?

[sturdy portal]

it is not e^27 is it?

[ornate swan]

2^4-2^2=16-4

See what I mean?

[sturdy portal]

yeah but e is not an easy number to work with

i can't just do the process you did

[ornate swan]

The only way I think you can simplify this is using natural logs,

[sturdy portal]

go ahead please

[ornate swan]

X^b = e^blnx

A quick way to simplify any shit

[sturdy portal]

is it not 40ln(e)-13ln(e)?

[ornate swan]

So you take the natural log of both sides?

[sturdy portal]

yeah bc what you did gives the same result

[ornate swan]

ok

[ornate swan]

This looks much nicer

[sturdy portal]

so what would the next step be how do i simplify that

i was gonna say 27lne but that be dumb

[ornate swan]

Well it shouldn’t be such a small number right?

[sturdy portal]

yuh

[ornate swan]

Shit I have to go

I’m very sorry

Sorry

Sorry

[sturdy portal]

nah u good

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[cobalt cape]

I don’t understand this one. So what do I suppose to do with a? In the function fx? I’m integrating in terms of a small change in x. So what do I suppose to do with the random a in there lol.

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[nova spire]

What is the average value of f on [0,a]?

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[cobalt cape]

Yes

[valid mesa]

Help

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[kindred pier]

!occupied

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[cobalt cape]

.reopen

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[cobalt cape]

I reallly need help with this question

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[neon sierra]

Alright so

[neon sierra]

How can I calculate this limit:

,rotate

[neon sierra]

Sorry for the awful quality lol

,rotate

[tiny valve]

This limit is the definition of e

[neon sierra]

Uhmm

Lets say I dont know that, how could I evaluate it?

Like how do you even differentiate a function like that

To use lhopital’s

[haughty oasis]

rewrite f(x) as e^ln(f(x))

[tiny valve]

What's your definition of e^x then

Let's work with your definition

[neon sierra]

We havent even seen one, just plugged in sone formulas

Or maybe saw it in highschool, but dont remember

[tiny valve]

This is the definition of e

So now you know

[neon sierra]

Ig yeah lol

[haughty oasis]

is that a 1 or 2 in the exponent?

[neon sierra]

2

[austere cedar]

Ah. When it's 1, then that's the definition of e

But when we change it to 2, the limit is now e²

[haughty oasis]

you can do it with L'Hopital though

[neon sierra]

But how would you differentiate it? We learned briefly about logarithmic differentiation the other day, but not sure im getting anywhere rn

[haughty oasis]

how do you start with logarithmic differentiation?

[tiny valve]

You need to know how to differentiate e^x

[haughty oasis]

do you usually write y = lim ... and then ln(y) = lim ...?

[haughty oasis]

don't think so

[tiny valve]

What is ln x?

If we don't know how to define e^x

[neon sierra]

Ig thats how I start

,rotate

[neon sierra]

If that makes any sense

[haughty oasis]

did you change 2/x to x/2

[neon sierra]

uhh no

Was I supposed to

[haughty oasis]

no, and you did

[neon sierra]

Oh

Shit mb one sec

Lol sorry

[haughty oasis]

we're just supposing that we don't know the limit

I can "define" it using power series or whatnot

[neon sierra]

I dont feel like im getting any closer no?

,rotate

[haughty oasis]

remember that you are not asked to find the derivative, but the limit

[neon sierra]

Yeah, but differentiate the function before no?

Oh damn lets see

[haughty oasis]

where we passed the ln inside the limit because ln is continuous

and the RHS you can evaluate using L'Hopital

[solid kiln]

Tushar

[neon sierra]

Why do we need to differentiate the limit here? I only ever differentiated the function when using L’hopital’s

Kinda confusing me a bit

[haughty oasis]

there is no differentiation happening anywhere

[neon sierra]

Huh

[haughty oasis]

I just took the natural log of both sides

you only differentiate in L'Hopital

[neon sierra]

Oh yea im tripping hard

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[neon sierra]

I guess im making some sense of that, but now when differentiating, how will the form change if the denominator is x? When doing the quotient rule, itll just end up growing exponentially, no? Like x^2, x^4, etc, so itll always divide by 0?

[haughty oasis]

quotient rule?

[neon sierra]

Is that what its called kn english

Just assumed lol

[haughty oasis]

L'Hopital's rule involves differentiating the numerator and denominator separately

[neon sierra]

OH FUCK

[haughty oasis]

no need for quotient rule

[neon sierra]

Yeahhhhhh

I dont even know what to say lmao

[haughty oasis]

this is your one job right now

[neon sierra]

Yeah i got it lol

Well if i miss that idk what ill do

But that doesnt get me e^2 at all tho

[haughty oasis]

what does it get you

[neon sierra]

2

[haughty oasis]

ln(y) = 2 indeed

[neon sierra]

Oh

[haughty oasis]

but you want y

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[neon sierra]

.reopen

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✅

[neon sierra]

I think I’ll give up for tonight, my brains dead, ill just check with my teacher next class

[haughty oasis]

you are already there lol

[neon sierra]

I mean i know but like

Im barely understanding where im coming from

[haughty oasis]

if ln(y) = 2, take e^ of both sides

[neon sierra]

Well, wouldnt have guessed it cause of how little work we did with logs

[haughty oasis]

you just get y = e^2

[neon sierra]

Think i should revise logs lol

Yeah

Anyways, thanks a lot bro

Appreciate the help

[haughty oasis]

happy to help

[neon sierra]

,close

.close

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[swift drum]

how am i supposed to graph this

[unique minnow]

Use the definition of |x|

As in |x| = x if x >= 0, |x| = -x if x<0

[swift drum]

could u show me a example i dont really know what u mean

[unique minnow]

Right

This is just how we define the absolute value

|5| = 5 since 5 >= 0

|-20| = -(-20) = 20 since 20 < 0

So here, you want to split it into two pieces : try to see what the equation of the function looks like for x >= 0

And then do the same when x < 0

[swift drum]

i know what IxI looks like but

idk how to scale the 3/4 bc its asking me to pick a point on the graph

[unique minnow]

|x| is just two line segments.

This will be the case too.

Let's do the x >= 0 case together.

If x >= 0, then x is positive, so |x| = x right?

But then that means that when $x \geq 0$, we have $f(x) = \frac{3}{4}x$

[solid kiln]

Azyrashacorki

[unique minnow]

Is that something you can draw?

[swift drum]

yes

its like /

crossing theorgin

[unique minnow]

Yes. A line of slope 3/4 going through the origin.

Now if x<0, we have |x| = -x (since x is negative).

Then what is f(x) for x<0?

[swift drum]

omg im so confused im sorry]

[unique minnow]

It's ok!

Right. From the first bit we did, we know f(x) looks like a line of slope 3/4 going through the origin for x >= 0.