help-43

[kind crane]

don't troll

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[coarse verge]

correct?

[vague sparrow]

We'll see.

[coarse verge]

huh?

[short ferry]

yes

[vague sparrow]

Alright so, we have seen what was shown on the graph.

Can you tell me what function made this graphs?

@coarse verge

[coarse verge]

a quadratic

[vague sparrow]

What type of quadratic function?

[coarse verge]

oh wait no, this isnt a quadratic

i dont think it matters what type of function this is

[vague sparrow]

ok

so

We know that the 2 blue dots shown are the points/domain.

[coarse verge]

yep

so brackets

yea i think im right

[vague sparrow]

Yes.

So it's a polynomial function.

[coarse verge]

quick, right?

[short ferry]

what if it was trig?

You cant know that and it isnt relevant either

[short ferry]

correct

[coarse verge]

ah alr

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[pastel ice]

so basically i know how to do this

the hence part

but im wondering for the top part do i have to just find the derivative of sqrt(x) generally then move onto showing the hence part

or do i just go straight to the hence part and show its not right differentiable at x = 0

i dont have any mark schemes and its worth 4 marks if that helps

[mild sky]

Hence means that you should conclude that from the main result

[pastel ice]

maybe im dumb but idk how id show the hence part after differentiating just generally

unless im confused on how to do the hence part

would i have to do first principles here

[mild sky]

You should see that the limit at x=0 doesn't converge

[azure vault]

I'm gonna criticize the question (not you OP) and say that the limit of f'(x) when x->0 doesn't say anything about right differentiability of f at 0

[pastel ice]

that might be what im saying

if i take the derivative of f(x) i get 1/(2sqrt(x)) which doesnt seem much help for the hence part

since i assumed id have to do first principle differentiation where x = 0

which gives lim h -> 0 of 1/sqrt(h)

then that shows it tends towards infinity unless im doing something wrong

[azure vault]

That's exactly what I would have done

f'(x) when x->0 only relates to if f is C^1 (so it's about the continuity of the derivative)

When what we want is if f'(0) is defined

[pastel ice]

alright thanks for the help guys

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[sacred snow]

Hello

[pastel ice]

hey

[verbal kiln]

You have opened a help channel. Do you have a question?

If not,

[compact pewter]

If you are done with this channel, please mark your problem as solved by typing .close

[sacred snow]

No so piss offf boy

[verbal kiln]

<@&268886789983436800>

[sacred snow]

Cry

About it

[verbal kiln]

ok.

[sacred snow]

What u gonna kick me

[verbal kiln]

just wait till someone shows up so they can get rid of your ass

[sacred snow]

Ha loser

[verbal kiln]

[verbal kiln]

ok.

[sacred snow]

Sure bud

It’s ok to cry

[verbal kiln]

ok.

[verbal kiln]

ok.

[wheat pasture]

Well, that is a good option

[pastel ice]

@verbal kiln how have you put your favourite game on discord

is it a nitro thing?

we have the same favourite game!

[verbal kiln]

yes.

[tranquil prawn]

Jackpot

[pastel ice]

awh boo discord!

[wheat pasture]

Sadly me baby mod so I can't but I can time them out

.close

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[verbal kiln]

i’ll take it!

thank you Chartbit!

this is their bio btw:

I’m quiet, I’m mysterious, I work in the night and sleep in the morning, I watch and observe like shadow

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[young raft]

i am a bit confused with how the dirac delta works in context of ODEs

[young raft]

and laplace transforms

i needed to solve this ODE with laplace transform

and i got this (ugly ass) result with dirac delta

[serene depot]

Is that the dirac delta?

[young raft]

but my question is how do i verify that y(0) = 1 ?

[young raft]

yes

where (n) is the n-th derivative

[kind crane]

do you have a definition of derivatives of the delta function

[young raft]

we haven't covered distributions very formally so not really :(

i just know this as a table laplace transform

[kind crane]

show the table

[young raft]

or like it makes sense when you integrate it

also this is mentioned but i don't think we need it here?..

like it makes sense to include 0-

[young raft]

it's just this is my question

in what way is y(0) = 1

because y(0+) is 64 and y(0) requires evaluation of delta function

idk i hate that they never defined what a distribution even is but make us solve problems involving it

[flat fulcrum]

(\mathcal{L}{y^{\prime }(t)}(s)=sY(s)-y(0^{-})) is the answer

[boreal girder]

Gold_Baconzx

[kind crane]

maybe show your steps how you got here

[young raft]

yeah there might be a problem there, give me a sec

i did verify tho that my inverse laplace transform is correct and matches with WA

but it might be wrong initially

[flat fulcrum]

The initial condition is typically given as (y(0)=1), which is often interpreted as (y(0^{+})=1). The presence of a Dirac delta function at (t=0) can cause a jump discontinuity in the solution, meaning (y(0^{-})) and (y(0^{+})) are not equal. The value of (y(0)) is usually defined by the problem statement, but in the context of the Laplace transform, the initial condition is specified as (y(0^{-})). To verify the initial condition, you would need to evaluate your solution (y(t)) at (t=0) and confirm it matches the required value. The user's statement that (y(0+)=64) is a specific detail from their problem. The verification process would involve checking if the solution (y(t)) satisfies this condition.

[boreal girder]

Gold_Baconzx

[young raft]

is this chatgpt generated?

[flat fulcrum]

i used google lense

[young raft]

"The user's statement" bro 🥀

[flat fulcrum]

what browser u use

[young raft]

firefox, why?

[compact pewter]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[flat fulcrum]

use chrome since it has google lense and it shows all the work for it

never mind

[young raft]

i sent them above

[kind crane]

where did s^4 in denominator go

[young raft]

fuck my life

thank you

[kind crane]

always send work

[young raft]

jesus christ everything becomes so much simpler

[rigid perch]

i think in general you get weirdness when your numerator has a greater degree than denominator

[young raft]

yeah cuz L^-1[s^n] is delta^(n) (t)

so it makes sense

[young raft]

i'll keep that in mind for the exam

[rigid perch]

so if you get that sort of rational function it's probably a good idea to check whether it's correct (as in this case), because i don't think you should get that when ode solving

[young raft]

thanks you so much guys

.close

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[young raft]

.reopen

[compact pewter]

✅ Original question: #help-43 message

[young raft]

hold up

[young raft]

oo new update

[young raft]

nvm almost made another mistake

i should sleep instead

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[sudden carbon]

can someone explain how to f

idk how to sketch DEs

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[sudden carbon]

<@&286206848099549185>

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[shell cairn]

Am I thinking about this statement correctly

That if a value is in the compact set, then it has a value. However, lets say a value is at infinity and its outsdie of the compact set, then its essentially zero

[frail knoll]

😆

[shell cairn]

Well i could use the extreme value theorm here could I not to prove this?

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[wanton ferry]

is topology induced by metric

[shell cairn]

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[proven wren]

any way to shorten the second expression?

xor might be useful here but i'm not sure how to incorporate it into the proposition

mm that's unfortunate

i heard there's something called iverson brackets, but it's pretty obscure for me

[kind viper]

iverson bracket doesnt rly have anything to do w this

it's basically just a fancier version of an indicator function

in that it turns true and false into the real numbers 1 and 0 resp

[proven wren]

oh alright thanks

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[short lantern]

wait

[proven wren]

yes

.reopen

[compact pewter]

✅ Original question: #help-43 message

[short lantern]

NOT (q XOR q XOR r) AND (p OR q OR r)

that first q should be p

basically this is "Is there an even amount of trues AND is at least one true"

which is logically equivalent to "exactly two of three statements are true"

fungy you still here?

[proven wren]

oh sorry something cropped up

needa take care of it, i'll come back in 10min

[rigid perch]

looking at the karnaugh map (if you're familiar) you have the most efficient map in terms of OR'ing a bunch of ANDterms. if you take the opposite approach (AND'ing a bunch of OR terms together), then you would get 4 terms but on the plus side 3/4 of them would have only 2 propositions each
-# edit: swapped OR's and AND's

[short lantern]

isnt what fungys doing ORing sets of ANDs

[rigid perch]

oh i got it completely backwards

[compact pewter]

@proven wren Has your question been resolved?

[torpid crypt]

So what it is really used for I have seen this first time

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[molten grotto]

f(x)=sinx and g(x)=cosx in R

The multiplication will be Uniform continuous?

[molten grotto]

By lipsctiz i have solved like |f'(x)|<infinity

Which is true

[quaint gulch]

there are several ways to see that yes, like if you calc'ed f' it's kinda obvious that f is 1-lipschitz
you can also notice that sin(x)*cos(x) is sin(2x)/2 because of the sin(2x) identity

[molten grotto]

Which is bounded

[quaint gulch]

so the problem goes back to "is sin uniformly continuous"

and, yes

[molten grotto]

Thanks

Any specific thing related to sin and cos where they are not uniform continuous

[quaint gulch]

you can always make stuff that's not even continuous like sin/cos or whatever

the point is more that if you calc'ed f' you should have looked for 1-lipschitz

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[molten grotto]

Thanks

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[scenic sluice]

I only care about x>L/2 in the question but how would I compute the derivatives including the point x=L/2

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<@&286206848099549185>

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@scenic sluice Has your question been resolved?

[scenic sluice]

.close

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[cunning jetty]

Proof for linear thermal expansion equation (for solids)

[cunning jetty]

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[rugged parrot]

hi, i dont really understand the solution to this problem

[rugged parrot]

I calculated the vector product correctly, but I don't understand the subsequent step where they've set the magnitude equal to 0

[dense dagger]

what must the cross product be for two vectors to be parallel?

[rugged parrot]

OHHH RIGHT

wait a sec

isnt that already being handled by sin(180) though

|v||w|sin(theta)

the sin theta will already make it 0 right

[dense dagger]

Firstly I see no sin in that equation

[rugged parrot]

isnt the equation for the cross product also |v||w|sin(theta)?

[dense dagger]

You're confusing cross product and dot product

[rugged parrot]

Sorry, cross

mistype

OHHH WAIT I GET IT

|vxw| = |v||w|sin(theta)

the RHS will be 0, so I can solve it, cause I already have the LHS

[dense dagger]

dot product, which measures "how parallel" two vectors are uses cosine. cross product, which itself is a vector (not a scalar like the dot product), measures "how perpendicular" two vectors are. because the cross product is a vector & not a scalar, it is not suggested you use the sin definition, since you then need to get the magnitude of it.

yeah, you shouldn't even involve the sin definition to begin with

[rugged parrot]

oh, thats a nice analogy

[dense dagger]

The trick is to set RHS = 0, since cross product = 0 means they have "no perpendicularness", or they're parallel (which is the semantic opposite of perpendicular)

[rugged parrot]

ive been struggling to wrap my head around the dot and cross product, aside from their formulas

[rugged parrot]

that definition isn't used much yea?

ive sorta noticed that most problems ignore it

[dense dagger]

Not really, the cosine definition for dot product is perfectly legit, but the sine definition for cross product is not really useful. you can get the same thing out of doign the "ladder rule" or whatever you call it (thing you did in your photo) without information loss

[rugged parrot]

yea, i was referring to the sin definition for the cross product

[dense dagger]

I would even go as far as to say you should completely forget the sin definition once you're no longer a complete beginner

[rugged parrot]

tbh i find that way kinda irritating, way easier to just diagonlise a matrix

the way the image does it kinda involves memorising the formula which is clanky

[rugged parrot]

the only normally viable usecase would be for finding the angle between 2 vectors right? (assuming that the question doesnt let you solve it using dot product, which is easier)

[dense dagger]

you mean get the determinant of?

[rugged parrot]

yup

i keep on muddling up terms in my head

[dense dagger]

Yeah I guess... I really doubt you'll ever get asked to find the angle between two vectors and not be allowed to use a dot product though. The dot product is a really important tool that actually defines the angle between two vectors (which you'll learn more generally as an "inner product" if you take another linalg course after this), so being asked to find the angle between two vectors without the dot product would be like asking for you to multiply two numbers without using the multiplication operator. Prof might do something wonky though so who knows.

[rugged parrot]

haha nothing like thats gonna happen here, this is a high school math class

I'll be fine then. we've mostly used the cross product to find stuff like shortest distance between 2 vectors and such

[compact pewter]

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[onyx pulsar]

does part b look right

[onyx pulsar]

i don’t have ms

,w rotate

Ok

,rotate

[cinder wing]

i am really confuse i just dont see ever like math in this groups are you a secondary school student , if yes i can if no i cant

[onyx pulsar]

I don’t think it comes up often

I don’t have the ms but

it says use answer from part a

would i not use

1-4theta-8theta^2

[elfin finch]

Welp i dont see anything wrong

[onyx pulsar]

Im in year13 so idk

oki thanks

gauth maths says to plug in 0.14

that’s why im confused

[elfin finch]

Oh wait

OH

Ye my bad thats wrong

[onyx pulsar]

lol

where do u get 0.14 from

i can’t see that

[elfin finch]

You would put theta as 0.07

Idk why it say 0.14 tho

[onyx pulsar]

OHH wait

i think

2theta =0.14

[elfin finch]

Sure but why put in 2 theta

[onyx pulsar]

isn’t tan2theta there

idk

[elfin finch]

Yeah but you just plug theta into the equation you proved in a

[onyx pulsar]

fuckass teacher hasn’t uploaded ms

[cinder wing]

whats mean that circle symbol

[onyx pulsar]

theta?

[cinder wing]

yes

[elfin finch]

Just a symbol thats a placeholder for an angle
Kinda like x or y

[cinder wing]

you want the question a or b answer

[onyx pulsar]

b

[cinder wing]

just replaced theta with 0.07 and you have solved the a question < and fill the second equation with the previous A B C which you have calculated

i am sorry my english is a little bit bad do you understand it or i need to write it on a paper ?

[elfin finch]

Nah nah thats good

[onyx pulsar]

.close

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[kind hollow]

Hello. Is there a proof as to why induction works? If so, what kind of proof is it? Please don't include the proof itself in your answer as i dont feel that my brain is active enough currently to handle it. I just wanna know if its provable without circular reasoning or similar problems

[vivid breach]

I have a dumb intuitive way if you want to hear it

[kind hollow]

sure

[vivid breach]

if you start at 1

and you want to go to 5

you repeat the argument 4 times

each time it goes to 2, then 3, then 4, then finally to 5

[mild sky]

sure there is a proof

But I think you need to go back to foundations

[vivid breach]

repeating the same operator over and over again has some importance to it

[native shard]

yea it follows from the well ordering principle

[kind hollow]

I think this is pretty much how i think of it too. It makes a lot of sense. But because we always prove everything in maths i was searching if there was a way to justify the sufficiency of assuming n is true and blah blah leading us to the conclusion

anyways, I'll look up info regarding it. i just wanted to know if it exists

[native shard]

i think it can be confusing for many people who first learn induction to understand why we "assume P(n) is true for some n"

like you think how is that justified?

[kind hollow]

ye thats my problem with it

[native shard]

the whole point of the implication is that the statement is true for the successor whenever its true for an integer and if we show its true for some base integer (usually 1) then it being true for 1 implies its true for 2 which implies its true for 3...

[kind hollow]

ohhh I remember this successor predecessor stuff

[native shard]

if a domino falls then the one after it falls, the first domino fell, therefore all of them in front of the first one fell

[kind hollow]

yeah thats how i think abt it, just way informal-like

[cosmic crypt]

In any cases, I think it's better to fully understand the technique first before being interested by the proof

[mild sky]

yeah induction is basically: You want to prove P(n) for all natural n.
Assume by contradiction there is a counterexample,
take the minimal counterexample,
that counterexample satisfies P(n) because of the induction step and the base case

[kind hollow]

I've learned the basics, i like to think. Is there more to learn about it before proceeding to the proofs?

[native shard]

when we assume its true for some n try not to think of it like we are finding some far out integer for which the statement holds like its just a placeholder to be able to extend the idea of the next domino falling to all integers

[native shard]

🤔

what

oh

you mean in the proof

using well ordering

considering the set of integers for which P(n) is false

👍

[short ferry]

now prove well ordering principle

[kind hollow]

yeah ive been acclimitizing to this idea since i got in uni cuz we use arbitrary values a lot

[carmine garden]

fun fact Induction is equivalent to well ordering

[short ferry]

and usually, induction is proven first

[carmine garden]

so really depends on what you wanna take as your axiom

[kind hollow]

so it is circular reasoning?

[short ferry]

induction is very closely tied to the definition of natural numbers

[short ferry]

how can you prove something about natural numbers if you dont know anything about them in prior?

[native shard]

no

[short ferry]

You either gotta give a precise enough definition of naturals, or accept some axioms about them

[native shard]

the well ordering principle is just like the most basic assumption you have about the naturals

[kind hollow]

fair enough

[native shard]

if you don't take anything as an axiom then there is no math to do, some things have to be assumed without proof

[carmine garden]

You can either take well ordering to be your axiom or strong induction or weak induction

[kind hollow]

oh I see. yeah havent read abt it yet

[native shard]

the point though is that whether you assume induction or well ordering you can prove the other from that assumption

[kind hollow]

okay that sounds good enough for me

[native shard]

that is the sense in which they are equivalent, the truth of one implies the truth of the other

[carmine garden]

*each other

[kind hollow]

I think they mean, taking one as an axiom, we imply the other

and reverse

[native shard]

yea

[carmine garden]

yes

[native shard]

mhm

saying each other reads to me as p -> q and p -> p

p -> p doesn't need mention

[kind hollow]

now youre frying me man

[native shard]

induction implies well ordering
well ordering implies induction

is that i was trying to say

[kind hollow]

yes i can live with that

thanks for the help everyone

.solved

[compact pewter]

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[kind viper]

law of total probability

uhhh let me look up the name again

yeah that one

[cosmic crypt]

It has multiple names

Because it's true?

[kind viper]

!redir

[compact pewter]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[cosmic crypt]

[infinity]

[strange ermine]

Have you looked at your notes if you have it?

Well, do it then 😅

Are you doing the exercises without knowing the theory?

[kind viper]

sure is

you can't roll a 1 and a 2 at once on the same roll of a die

congratulations point missed successfully

idk if this was sophistry or a legit counterargument.

Y=1 and Y=2 are always mutually exclusive no matter what kind of RV Y is

but yes that is the idea

tf you been doing in your prob course lol

[strange ermine]

@copper loom

Check at least if you have some similar concept/theorem given to you

[strange ermine]

I don't believe your teacher gave you this assignment without explaining anything about how to solve it or giving you the math instruments

Sorry, I was referring to your question which is a theorem

My bad

[kind viper]

chapter 1, like, all of it?

no you're way overthinking it

and trying to say things that sound like they make sense but actually don't

ok. look.

lets forget about any random variables for a moment.

imagine youve got a bag full of counters, each of which is painted say one of three colors (red, green, blue) and has a number written on it.

im gonna leave it deliberately unspecified what type of counter appears how many times in the bag

the probability of drawing a counter labelled 5 may be viewed as:

P(any 5) = P(red 5) + P(green 5) + P(blue 5)

"formulaism"

how does it define a random variable

ok good

X=x as an event is short for {ω ∈ Ω : X(ω) = x}

i.e. when we speak of the event X=x we mean the set of precisely all those outcomes on which the random variable X returns the value x

same story with events like X>x or X<x or X ≥ x or X ≤ x...

proof of what

the event {X=x} is the disjoint union of the events {X=x, Y=y} where y ranges over all possible values of Y

[compact pewter]

@copper loom Has your question been resolved?

[mild sky]

looks fine

consider using $\bigcup$ and $\bigcap$

[boreal girder]

ExpertEsquieESQUIE

[compact pewter]

@copper loom Has your question been resolved?

[mild sky]

big version

instead of writing a big union

sigma notation for union/intersection

[compact pewter]

@copper loom Has your question been resolved?

[copper sierra]

instead of saying define $B$ as the union of $B_n$’s u can say define $B=\bigcup_nB_n$

[boreal girder]

ロケット・ジャンプ

[compact pewter]

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[astral aurora]

I dont get why the common monomial factor is 3 instead of 6?

when ur getting the cube of binomial

cuz isnt it 3x^2y + 3xy^2

[kind crane]

what is it here

[native shard]

yea 6 seems right to me

🤔

[astral aurora]

but… idk…

this is a solution manual

wait ill show u what i got, i used a diff method but i got a diff answer

[native shard]

solutions manuals can be wrong

[astral aurora]

i paid for big bucks for this for my competition 😞

That would suck if it is wrong

[native shard]

💀

[kind crane]

demand refund.

[astral aurora]

excuse the bad handwriting

[native shard]

https://tenor.com/view/yaburnt-joker-burn-burnward-calltheburnunit-gif-5274995

[astral aurora]

its 4 am and my competition is at 9

[astral aurora]

is it wrong?

bro but hes an olympiad trainer

[native shard]

no seems fine to me

[native shard]

he’s not a robot

[astral aurora]

So -301 is the answer?

[native shard]

i mean compare with this, if you instead had the factor be 6 youd add an additional 21 to the right

and get -301

so it checks out

[native shard]

👍🏻

go to sleep

[astral aurora]

bro i need a refund

[native shard]

word

[astral aurora]

how is discord more helpful

[native shard]

just put your money in the blender next time

[kind crane]

knief is taking donations

[native shard]

🤣🤣

[astral aurora]

omg

its knief not knife

[native shard]

yea

[astral aurora]

i just realized

i havent had sleep

[native shard]

get to that

[kind crane]

knief also hands out life advice in addition to math help. Donate extra to him

[astral aurora]

Im halfway done

5 sets

[native shard]

are you watching old zoom recordings

[astral aurora]

i feel like hamilton

[astral aurora]

yes….

[native shard]

been there

[astral aurora]

i paid for 5 sessions

20 bucks

For wrong solutions

[native shard]

oh no wonder

😭

[astral aurora]

Wait im finding the other one

I think they used the same thing there

ok nvm i give up

[compact pewter]

@astral aurora Has your question been resolved?

[real hull]

https://tds.azuroaffiliates.org/132/5?l=4

[compact pewter]

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[terse linden]

I have problem with learning math

[verbal kiln]

What’s troubling you?

[terse linden]

When i study
And I gain information that I am surprised that I will lose it after a week a month…

[verbal kiln]

Well are you cramming or studying naturally?

You should be able to retain knowledge a lot longer than a week, so are you sure you’re studying healthily?

[terse linden]

Tbh cramming

[verbal kiln]

That’s your answer. You should want to study, and want to get good scores, assuming you’re doing tests or something.

[terse linden]

Idc about tests

[fickle hornet]

it's probably because you are learning something you dont understand enough to keep it in a long time

[terse linden]

Im just loving math

But forgetting information is something that confuses me

[verbal kiln]

Could also be this.

[fickle hornet]

and its ok because thats how the education system works

[terse linden]

It makes me feel like what I'm doing is useless

[verbal kiln]

You shouldn’t cram. You should be “in the zone”. You should learn because you want to learn.

[terse linden]

Wdym?

[fickle hornet]

learning methode to resolve something or find something when you dont understand the concept behind, it could be hard to remember this

i mean

[terse linden]

I really take to understand one theorem or definition at least 1 hour

[fickle hornet]

in geometry, you learn a lot of methode to find a lot of things

but there's no explication behind 99% this methodes

and you just apply

and you forget

because you forget why you are doing this

[terse linden]

Mean i need to apply my informations?

[fickle hornet]

it depends of how you work

i mean

i was as same of you

when i began to do real maths

but when i try to find relations behind methodes

it is very simple to me

because i link things

between them

hhhh english

did you understand ?

[terse linden]

But i do what you said

I really study mathematics with high accuracy.

I don't miss a part unless I understand it

But I'll find out later that I forgot 40% of what i study

It makes me doubt that I am sick with alzheimer or something like that

[fickle hornet]

you forgot or you dont remember ?

[terse linden]

Isnt the same?

[fickle hornet]

mmh

not exactly

[terse linden]

Wait

I think i understand what you mean

Like when we see a question

[fickle hornet]

exactly

[terse linden]

But

When i try to remeber without question

Make no sense

Try to remember without goal

[fickle hornet]

ye

ofc

u cant be that accurate

without working actively

its ok if you cant remember a demo in your head

unless you can write it with a pen and a paper

[terse linden]

Who’s that

[fickle hornet]

an app

for studies

yep it could be helpful

but it requiered a bit of time and rigourous

[terse linden]

Maybe

[fickle hornet]

yep i agree

[terse linden]

Then i conclude from that discussion
That to test myself if i still remember math informations i need to apply

[fickle hornet]

yep

you cant do everything in your head

take a pen

a paper

and an excercise

[terse linden]

Yea

Thanks for help

[fickle hornet]

https://tenor.com/view/american-psycho-patrick-bateman-talking-gif-25364693

[fickle hornet]

np dude

its ok to question yourself

i wont say that

but if you want mate

[compact pewter]

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[vocal idol]

@rotund sphinx

[vocal idol]

can u help me w a couiple more plz

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@vocal idol Has your question been resolved?

[compact pewter]

Please do not ping individual helpers unprompted.

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[compact pewter]

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[calm light]

Hiii, can I have some helps

[calm light]

My thought is to find area where a point in that area has the distance from P to AB less than distance from P to 2 other sides

But I'm not sure how I can find that

[open plaza]

you can draw an angle bisector like this

if P lies on the angle bisector then PE = PG

[wanton ferry]

first consider when abp has a greater area than acp. then consider the same with abp and bcp.

[calm light]

what is that for

[open plaza]

if P lies in this red area below the bisector then PG > PE

[calm light]

btw I found a solution, I'm a bit curious about your method

[wanton ferry]

and take the the intersection

[calm light]

yes

what about PF

[open plaza]

do the same with PG vs PF

[calm light]

oh

So we're also finding the intern of all cases?

[open plaza]

you mean intersection?

[calm light]

oh yeah that's what I meant mb

[open plaza]

yeah exactly

[calm light]

okay I see,that's also a nice way

[open plaza]

yeah you get that P has to lie in this area

[calm light]

Mine doesn't deal with intersection

[calm light]

yes I also got that

Thanks

.close

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[steady hill]

67

[chilly basalt]

.solved

[compact pewter]

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[compact pewter]

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[icy nymph]

how do u find the Sn of
1 + 2 + 4 + 7 + 11 + 16 + ...

[icy nymph]

note that common difference increases by 1 every time

[grizzled geyser]

First you find the difference of the differences.

And then there is a formula for the "stacked" arithmetical progression.

[cedar heron]

if you were to subtract the increase in the common difference you can say it’s an arithmetic progression, so you could subtract 1+2+3….+n

[icy nymph]

is it possible to use only AP and GP formulas to solve this

[cedar heron]

which is just n(n+1)/2

[haughty trout]

The second differences are constant
So it’s a quadratic sequence
Let a_n = an^2 + bn + c
We know a1 = a+b+c=1
a2 = 4a + 2b + c= 2
a3 = 9a + 3b + c = 4
Subtract the first from the second
second from the third
Subtract those
Then:
3(1/2) + b = 1 => 3/2 + b = 1 => b = -1/2
Now plug into a + b + c = 1
So the nth term is
a_n = (1/2n)^2 - (1/2)n + 1
Or a_n = (n^2-n+2)/2

[calm light]

||the sum is 1/6n(n^2+5) I think , you could try induction proof for this||

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[dim plinth]

i need help with geometry. we have to make a pyramid, know information is K coordinates are (50,40,40), diagonal AC (horizontal) is 60 mm at 45 degree angle, diagonal DB (frontal) is 60 mm at 30 degree angle. height of the pyramid KV is 65mm. i have to construct the pyramid, ive done the both bases in frontal and horizontal projection but i dont know where to draw KV and how long to draw it because it not the real length

[inland nacelle]

!occupied

[compact pewter]

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).

[inland nacelle]

this channel is being used by someone else. Claim another

[elfin finch]

#❓how-to-get-help

[inland nacelle]

mb didnt understand. Follow #❓how-to-get-help

[compact pewter]

@dim plinth Has your question been resolved?

[dim plinth]

still need help

<@&286206848099549185>

[gaunt lynx]

You there?

[dim plinth]

yess

still struggling

[gaunt lynx]

Wait

Im trying to figure out myself first🤣

[dim plinth]

🥲 all good

[gaunt lynx]

Can we make some assumptions?

[dim plinth]

i think im gettin somewhere lemme show u

[gaunt lynx]

I think assuming that the base is at the horizontal plane and AC is 45 degree on horizontal plane

[dim plinth]

could this be a way to find the real lenght of KV?

[gaunt lynx]

K is the topmost point of the pyramid

[dim plinth]

yeah

[dim plinth]

its the diagonal inetesection

[gaunt lynx]

Yeah

The KV i think is creating the problem

Projections of KV, im thinking of that

[dim plinth]

yeahh its very confusing

[gaunt lynx]

Chill, lets try to figure it out

I think we gotta create an auxiliary view

[dim plinth]

can u check this tho, becuase technically im getting the real lenght using this method or i might just be schizo who knows

[gaunt lynx]

It looks correct but my gut says you’re missing something

[dim plinth]

probably yeah 😔

[gaunt lynx]

I just woke up so my system is not fully working

[dim plinth]

its okayy, ill just keep working on it and if something is not gonna add up ill find the mistake that way

.close

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[gaunt lynx]

Wait i got it

[dim plinth]

yeahh tell me

[gaunt lynx]

A and D at the front left and right corners

60 mm length

B at the back right corner and C at back left

45 and 30 degree

[dim plinth]

so should i draw the whole thing again that way?

[gaunt lynx]

Yeah, K is the apex

And exactly below that is V if you see from top view

I hope you get what i mean

[dim plinth]

yeahh i think i got it, ill try

thanks

[gaunt lynx]

Lmk when you’re done

It’ll be good if you send your work

[dim plinth]

okayy hopefully wont forget to, ill take a break for now tho

[gaunt lynx]

Yeah no worries, have a nice day mate

[dim plinth]

ty so much

[gaunt lynx]

I’ll close the ticket for now

.close

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[echo nymph]

Hey

[echo nymph]

I need help to understand probability

[viscid shard]

any questions you particularly need help with?

[echo nymph]

B i and ii

[viscid shard]

right

what's wrong with (b)(i)?

[echo nymph]

I dont know how i did it

I used chat gpt

But I didn’t get the point

[viscid shard]

well... I don't recommend using ChatGPT without understanding the material in the first place, but at least you've come to ask about it, so props to you

anyway

die A is labelled 1, 2, 2, 2, 3, 6
and die B is labelled 2, 2, 3, 4, 4, 4

[echo nymph]

Yep

[viscid shard]

you want a total of exactly 6 from both dice

let's get the low-hanging fruit out of the way first

which two numbers on die A make it impossible to get a total of exactly 6?

[echo nymph]

1 2 2 3 6
2 3 3 4 4

[viscid shard]

on die A, my friend.

and there should only be two impossible numbers

[echo nymph]

I can’t understand

What i have to tell?

[viscid shard]

what are the numbers on die A?

[echo nymph]

1 2 2 2 3 6

[viscid shard]

cool

[echo nymph]

Wrong?

[viscid shard]

no, cool as in yeah, correct

now, for each number on die A, can you tell me what number the other die must show for the two dice to get a total of exactly 6?

for example, 1 + ? = 6

do this for each of the numbers on die A.

[echo nymph]

2

3

Only idk i am right or not

[viscid shard]

neither of those get you 6 when added to 1, though

ok let's make it simple then

[echo nymph]

Means no one

[viscid shard]

1 + ? = 6

[echo nymph]

Ready

5

[viscid shard]

replace the ? with a number

good

2 + ? = 6

[echo nymph]

4

[viscid shard]

3 + ? = 6

[echo nymph]

3

[viscid shard]

and 6 + ? = 6

[echo nymph]

0

[viscid shard]

good

now, 1 needs a 5 to get 6

is there a 5 on die B?

[echo nymph]

Nah

[viscid shard]

that means we cannot roll a 1 on die A, otherwise we will never get a 6

likewise, is there a 0 on die B?

[echo nymph]

Alr

[echo nymph]

No

[viscid shard]

so for the same reason, we also cannot roll a 6 on die A

so these two numbers are the impossible numbers for die A that I asked for earlier

[echo nymph]

Yeah okkk

[viscid shard]

so if they come up, there is no chance of getting a 6

[echo nymph]

it means No chance

[viscid shard]

now, 2 needs a 4 to get 6

[echo nymph]

Yea

[viscid shard]

how many 2s are there on die A?

[echo nymph]

3

[viscid shard]

good, so the probability of rolling a 2 on die A is...?

[echo nymph]

3/6

[viscid shard]

good! now, to get a 6 total, we also need die B to show a 4.
how many 4s are there on die B?

[echo nymph]

3/6

3 fours in dice b

[viscid shard]

so, to get a 6, one option is to roll a 2 on die A (3/6 chance) AND a 4 on die B (also 3/6 chance)

what is the overall probability of this happening?

[echo nymph]

3/6 x 3/6

[viscid shard]

that gives us?

[echo nymph]

9/36

[viscid shard]

good! keep that in mind for later

[echo nymph]

Alr

[viscid shard]

now, the other way to get a 6 total is to get both dice to show 3

[echo nymph]

Yeah

[viscid shard]

what's the probability that die A shows a 3?

[echo nymph]

1/6 x 2/6

[viscid shard]

(do the same for die B, separately)

oh ok sure

and the overall probability of this case is?

[echo nymph]

2/12

1/6

[viscid shard]

eh?

1/6 x 2/6 = 2/12?

[echo nymph]

2/36

1/18

[viscid shard]

ok don't simplify yet

keep 2/36

[echo nymph]

Ok

[viscid shard]

now, either 2 and 4 OR 3 and 3 will get us 6, so the total probability of getting a 6 total is?

[echo nymph]

9/36 x 2/36

🥹

[viscid shard]

unfortunately, you only multiply when there's an AND

[echo nymph]

Oh we need to add

[viscid shard]

but for OR conditions, you add

yes

[echo nymph]

Am i right?

But we use or as add in compiter science

11/36

This is my answer

[viscid shard]

well if you want to get into the technical details, OR itself is not adding in terms of bitwise operations

and that would be correct

and that's how you get to the answer of 11/36

[echo nymph]

Wowww amazing

Uhh can u plz also guide how to get ii answer?

[viscid shard]

so the answer of (i) gives us 11/36

[echo nymph]

Yes

[viscid shard]

now, that means that 11 cases out of 36 possible cases end up with a total of 6

now, we are given the total of 6

[echo nymph]

Yeah

[viscid shard]

this means we no longer need to care about any case that isn't 6 total

[echo nymph]

Ok

[viscid shard]

this shrinks the numbebr of cases we need to consider from 36 to 11

now, what was the probability of getting 3 and 3 that you calculated earlier?

[echo nymph]

9/36?

[viscid shard]

sure that's 3 and 3? or was that 2 and 4?

[echo nymph]

1/6 x 2/6

?

[viscid shard]

so the probability is...?

[echo nymph]

2/36

1/18

Wrong?😑

[viscid shard]

chill.

just because I stop replying for like one minute doesn't mean I'm gone lmao

patience, my friend

ok so yeah, that's the correct answer

now, 2 cases out of 36 sees the two dice show 3 each

[echo nymph]

Tomoroow is my paper that’s why i am worried

[viscid shard]

one minute won't be too bad, I hope?

anyway

[echo nymph]

And my teacher is even not attending my call noe replying to my texts

[viscid shard]

but that original comparison we made was 11 cases out of 36 showing a total of 6

[echo nymph]

I know other topics like functions graphs etc

[echo nymph]

Hm

[viscid shard]

so, are you gonna interrupt me or shall we continue?

[echo nymph]

Sorry

Srry

[viscid shard]

anyway

so if we knew that 11 cases out of 36 has the dice totalling 6, of which 2 of them have the dice showing 3 and 3, can you now tell me the probability of the dice showing 3 and 3 if we knew the total is 6? (which is what the question is asking)

[echo nymph]

1/6

[viscid shard]

your answer should have a denominator of 11

(since that is the number of cases in consideration here)

[echo nymph]

Can’t understand

[viscid shard]

do you get this part?

[echo nymph]

Uhhh

Maybe no

[viscid shard]

then do you know what we did in (b)(i)?

[echo nymph]

Yes yes

We took the numbers that we making 6 by addition

[viscid shard]

use the context and answer of (b)(i) on this message

(which, for reminder, is 11/36)

[echo nymph]

Can u plz summarise it in easy wording

Like the one u did before

Its only 2 mark question

[viscid shard]

the idea is that there's an 11/36 chance of getting a 6 total

[echo nymph]

Okk

[viscid shard]

in other words, 11 of 36 possible cases have a 6 total

[echo nymph]

Alr

[viscid shard]

now, (ii) tells us that we know the total is 6

so we don't care about any case that is not 6 total

[echo nymph]

1 minus 11/36
Chance of not getting 6

Okk

[viscid shard]

well yes, but we don't care about those cases and thus there's no need to calculate that

[viscid shard]

so since we only care about total 6, from here, we know there are 11 interesting cases

[echo nymph]

How did 11 come?

[viscid shard]

^

[echo nymph]

Oh 11/36

Ok ok

[viscid shard]

so any probability we do is /11, not /36, because we are only interested in those 11 cases

[echo nymph]

Okkk

Okk

[viscid shard]

good

[echo nymph]

Taking 11 as a total probability means total

[viscid shard]

now, tell me the two probabilities of getting a 2 and 4 / 3 and 3 case from part (i).

[echo nymph]

Like our answer will come as numinator and denominator will be 11

[viscid shard]

right idea.

[echo nymph]

2 in both dices?

[viscid shard]

no, 2 in both dice will give us total 4, which is not what we want

we found out earlier that to get total 6 with these two dice, we want die A to show 2 and die B to show 4, or both dice show 3

[echo nymph]

We want total of 3?

[viscid shard]

no. where did you get that from?

[echo nymph]

Question

[viscid shard]

question said total 6

[echo nymph]

Both numbers are three

Have a total of 6

[viscid shard]

yes, and we are getting there

[viscid shard]

so what are the probabilities of these two cases separately?

[echo nymph]

3/6 x 3/6

1/6 x 2/6

11/36

?

[viscid shard]

put this into /36

[echo nymph]

I can’t understand i think i will not understand this

[viscid shard]

and this too

[viscid shard]

this is not necessary

[echo nymph]

Ewwwwwww

Unable to do what u are asking 😭

[viscid shard]

just multiply these two numbers

[echo nymph]

9/36

[viscid shard]

I don't think what I asked is particularly hard or anything 😅

[viscid shard]

there we go. what about that other one?

[viscid shard]

this one

[echo nymph]

Ik but idk math will make me mad

[echo nymph]

2/36

[viscid shard]

then you need to learn to chill a bit perhaps

[viscid shard]

cool. now remember that these 2 cases were the (3 and 3) case

[echo nymph]

Ok teacher

[viscid shard]

so, 2 cases show 3 and 3 out of the 11 cases that make 6 total

so the probability of 3 and 3 given total 6 is...?

[viscid shard]

you can get the answer from this message

[echo nymph]

What are u asking😭

Can u plz ask this in simple english

[viscid shard]

I'm asking what question (ii) is asking

question (ii) basically tells you that you know the dice total is 6 already

[echo nymph]

Yes

[viscid shard]

so now that you know the two dice add to 6, what is the chance of the (3 and 3) case happening (and not the (2 and 4) case)?

[echo nymph]

1/6 x 2/6?

[viscid shard]

well, on the right track, except now you only have 11 cases to think about

[echo nymph]

3 3 in both dices?

[viscid shard]

2 in the numerator is correct

[echo nymph]

Oh okkkieeee

[viscid shard]

yes, as the question wants

[echo nymph]

2/11 x 1/11

[viscid shard]

that 1/11 was not necessary

2/11 is the correct answer

[echo nymph]

Both numbers are 3

[viscid shard]

mhm

[echo nymph]

Dice a has 1 three while dice b have 2 three

[viscid shard]

that's already accounted for in 2/36

we already know that based on die A having one 3 and die B having two 3s will give us 2 cases out of 36 to get 3 and 3

but now we only care about a small part of those 36 cases

[echo nymph]

Okkk

[viscid shard]

that is, we only care about total 6

that's why the denominator becomes smaller, because we have less cases to think about

2/11 is correct

[echo nymph]

2nd dice 3+3=6

2/11 answer?

[viscid shard]

yes

[echo nymph]

Is this correct?

[echo nymph]

Thank you so much dear teacher for helping me

[compact pewter]

@echo nymph Has your question been resolved?

[compact pewter]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[compact pewter]

Available help channel!

Send your question here to claim the channel.

Remember:
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[heady spruce]

idk where to start lol

[open plaza]

in a triangle, the bigger the angle, the longer the opposing side

for example here, angle A > B so BC > AC

another factor you have to consider is the length of each side > 0

[heady spruce]

ye

so 3x-3 < x+4

[open plaza]

oh you also have the triangle inequality as well

[heady spruce]

ye

[heady spruce]

so i got it?

(3.5, infinity)

wait

<@&286206848099549185> help

[slate wyvern]

Do you know the sine rule?

[clear marsh]

i think it's x + 7 > x+ 4 > 3x-3

[heady spruce]

*3x-3

yea

[heady spruce]

no

[clear marsh]

ok

[slate wyvern]

Okay, it's basically a way of motivating the "bigger the side, the bigger the angle"

[heady spruce]

ye but we need to find X

[heady spruce]

oh yea

x + 7 > x+ 4 > 3x-3 so we need to solve that

[slate wyvern]

It says that a/sin A = b/sin B = c/sin C where A is the angle at A, and a is the side opposite A and so on.

[heady spruce]

so its (-inf, 7/2)

right?

[clear marsh]

yeah i think so

[heady spruce]

it says its wrng

hmm

[clear marsh]

yeah im not sure tbh, ive never done a problem like this

[heady spruce]

ye

[slate wyvern]

um... 3x - 3 < x + 4 ⇒ 2x < 7 ⇒ x < 7/2. but you also need all the side lengths to be positive: 3x - 3 > 0 ⇒ x > 1

[heady spruce]

wait the sides cant be less than 1

oh ye

[slate wyvern]

And the sides to satisfy a + b > c for any triple of side lengths a,b,c

[heady spruce]

(1, 7/2)

so its that

wait

[slate wyvern]

The triangle inequality thing gives 3 extra inequalities:
2x + 11 > 3x - 3
4x + 1 > x + 7
4x + 4 > x + 4

[heady spruce]

oh

[heady spruce]

wait so now what

its 3x btw

wait nvm

[heady spruce]

(2,3.5)

The altitudes in an acute triangle have lengths $2,$ $3,$ and $h.$ Find all possible values of $h^2.$

[boreal girder]

✪~nano-rōnin~✪

[heady spruce]

i have this now

<@&286206848099549185>

im stuck

i got it nvm

<@&286206848099549185>