help-4

[mental skiff]

oh sry mb i have been grinding on this since past like 45 mins or so

[stark wedge]

oh yeah ok deg(P) ≤ 2024 is given mb

[mental skiff]

Yes

this means the func

F(n)=P(n)-N!(the summation) also has degree <=2024

at most 2024 roots

could we use this fact?

[stark wedge]

no because F(n) is definitely not a polynomial anymore

[mental skiff]

no like F(n) would have at most 2024 roots right ?

because like as P(n) = n!(the summation) for atmost 2024 numbers

so like diff would be zero for at most 2024 numbers right?

so like we could rewrite F(n) as (n-n1)(n-n2).....(n-n2024 at max

right?

[stark wedge]

you're technically but not morally right

in that alone

and i will repeat

F(n) IS NOT A POLYNOMIAL IN n

[mental skiff]

true

[stark wedge]

no you can't factor it like that

only polynomials can be factored like that

no you can't factor it. no you can't factor it. no you can't factor it.

[mental skiff]

okokokokok

chill ok

so like i discard this fact ok

now we need to analyse from start

P(n) has atmost 2024 roots which are like non negative integers

Lets say even if we write P(n) as P(N)=Q(N)(n-n0)+R

where like n-n0 is a factor

[stark wedge]

what

how do you know the roots of P are nonnegative integers at all

[mental skiff]

Wait so sorry

my bad

i mixed fn and pn

sorry

Ok so

P(n)=n!(the summation) how could we like do something bout this

either we could like focus on simplifying the summation right?

[stark wedge]

dunno

[earnest ingot]

Not sure what you’ve tried yet but you can rewrite the original statement as [ \sum_{k=0}^m \frac{a_{m-k}}{(k+1)!}=\frac1{m!} ] which may be easier to work with

[rocky lotus]

kheer257

[earnest ingot]

Especially since you have a_{n-k} in the second equation

[vale dock]

@mental skiff Has your question been resolved?

[mental skiff]

Right

ok i saw it now thanks

Hello?

[vale dock]

@mental skiff Has your question been resolved?

[mental skiff]

@earnest ingot @stark wedge

So like i did some research and like found that ak is actually B*k/k!

[vale dock]

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[swift barn]

I have a question

[frigid harbor]

yeh

[mystic tartan]

hello

hey mutekius

[frigid harbor]

hellooooooo

[swift barn]

Can anyone solve this

[mystic tartan]

r u interested in fractional calculus

[frigid harbor]

reaplce x with -x ig

[mystic tartan]

do u know the formula for sum and product of roots

[frigid harbor]

i dont remember it properly

[swift barn]

Yeah

[mystic tartan]

yes right

just sub x equal -x

[frigid harbor]

yeh

[mystic tartan]

sum of roots =-q/p

[swift barn]

Yeah

[mystic tartan]

product is equal r/p

[swift barn]

Yeah then

[mystic tartan]

a+b=-q/p then (-a)+(-b)= -(-q/p)

[frigid harbor]

product of roots sign doesnt change

right

[mystic tartan]

-a and -b is new root of new equation

[mystic tartan]

yeah

[frigid harbor]

only sum of roots sign changes

[swift barn]

Yeah how is new quadratic equation formed from these

[frigid harbor]

px^2 -qx +r

sign of sum of roots changes

and sign of product of roots doesnt change

or just replace x with -x

[swift barn]

Yeah I know

[frigid harbor]

if u sub then this comes

[frigid harbor]

this

[frigid harbor]

yes

[mystic tartan]

come to my dm

[swift barn]

Then

What should I do

<@&286206848099549185>

@mystic tartan

@frigid harbor

[mystic tartan]

hi

x^2-(sum)x+product

sum=q/p and product =r/p

sub and get the equation

[swift barn]

Done ✔️

@mystic tartan look now

[mystic tartan]

yeah u did it

[swift barn]

Thanks buddy you helped a lot

[swift barn]

Wanna play chess and chill?

[mystic tartan]

okay

but im not good in chess

[swift barn]

I am 765 only

What's your username on chess.com

[mystic tartan]

i do no

[swift barn]

Let's play from discord

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[ebon blade]

.open

.reopen

[young cosmos]

Isn't this from rd sharma class 10

[young cosmos]

Why are you doing such easy and boring questions

[stark wedge]

this isn't how you open channels btw. you need to send any message in a free channel -- except that starting your message with a period actually suppresses this effect.

now someone else came here so you have to go and open your own by sending your question there directly, no commands

[swift barn]

Yeah it is

[young cosmos]

Hmm

Will i give you an interseting geometry questuon

Question*

[vale dock]

@young cosmos Has your question been resolved?

[toxic ridge]

Because not everybody has the same intelligence? It's his question, let him ask it, no matter how trivial or difficult it may be.

[young cosmos]

No not that

I just wanted him to tell to do some interesting sums,though i dont have any problem with his doubt...

Though leave it

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[drowsy lagoon]

Nothing tbh

I dont know where to start

[stark wedge]

well it tells you what it means for two optimization problems to be equivalent

so you need to start with a feasible sol of the 1st problem and cook up a feasible solution of the 2nd problem with the same value of the objective function

[drowsy lagoon]

Hmm okay

Imma try that

[stark wedge]

think about like... how you could turn an ineq constraint into an equality constraint

[drowsy lagoon]

I think I got something

let me write it down rq

is this good for 1 side?

[stark wedge]

ok yeah

[drowsy lagoon]

then I try the otherway around

[stark wedge]

basically the extra variables you add for going from the 1st to the 2nd problem are "slack variables"

[drowsy lagoon]

aaah yes true

[stark wedge]

they quantify how far apart the two sides are in each original ineq constraint

note that your original n variables are kept as is

[drowsy lagoon]

because we picked those as feasible and nothing in the 2nd problem changes them in the constraints?

[stark wedge]

well yeah

[drowsy lagoon]

alright

idk what to do for 2nd problem to the first problem tho

[stark wedge]

not much lol

just drop the slack variables

[drowsy lagoon]

ooooh

ye makes sense tbh

alright thank you :)

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[naive granite]

I have one simple question.
How do I improve problem solving skills?

[neon summit]

by solving problems

[naive granite]

but that's the quantity of problems.

i want to improve quality

[drifting hornet]

You can learn X by doing X in general

[naive granite]

uh, makes sense?

[median sun]

Think about the problem you solved after solving it

[sleek nebula]

Make sure you comprehend the solution fully

Dont't be lazy and skip if you dont really feel like doing

[median sun]

Don’t ever read the solution of a problem before working on it for enough time, otherwise reading it won’t add anything to you

[naive granite]

i mean i can always discipline myself.

[naive granite]

okay. this answer is different. ill try it.

[sleek nebula]

I have that issue as well

[neon summit]

same

[naive granite]

ill close the help then.

.close

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[median sun]

Always think about motivation in solutions, you know “what made us think of trying this?” “what is the motivation behind this step?” “what is a general indication i can look for to understand this type of technique will be useful”. Dont accept solutions like they fell from the sky

[naive granite]

thanks

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[boreal solstice]

Let A and B be events.
Let P be a probability distribution.
Is it always the case that $P(A \to B) = P(B \mid A)$?

[rocky lotus]

! See my about me

[vocal tusk]

what does $A \to B$ mean?

[rocky lotus]

unc

[autumn lantern]

if you mean the implication, then no it isn’t equal

in general

[boreal solstice]

nvm, got it

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[jaunty fox]

Any solution to simplify fractions like this?

[jaunty fox]

Like what should I do when seeing these kinds of problem, etc

I have solved these kinds of problem few months back in highschool but I got washed since graduating and forgot it

Ignore the language ok

Dont forget to ping me thank you

[drowsy lagoon]

1/a + 1/b = ?

[jaunty fox]

What?

[drowsy lagoon]

what is 1/a + 1/b ?

if you try to simplify that

[jaunty fox]

Oh

ab/ab

wait no

a + b / ab

[drowsy lagoon]

alright how did you do that?

[jaunty fox]

I made the denominator the same (idk what do you call it in math)

so

[drowsy lagoon]

perfect

[jaunty fox]

1/a times b/b

like that

Yes

and 1/b times a/a

[drowsy lagoon]

do that in your exercise too :)

[jaunty fox]

Ok hold on

Im stuck @drowsy lagoon

I did what you told me to do and now I have arrived here

[drowsy lagoon]

aaah I just notice

they did some tricky shit

[manic igloo]

(a^3-b^3) = (a-b) * (a^2+ab+b^2)

[jaunty fox]

Yea I literally did some problems with the way you told me to do

But it aint work here

something sus

in this question

[drowsy lagoon]

I didnt see the answer they gave you

but you have to use what IA_MW gave you

[jaunty fox]

Ohhhh my days

Ok let me try once more

Thank you guys

Ok got the results

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[jaunty fox]

Question is this (it tells us to simplify it )

[jaunty fox]

My working is this ( im stuck again)

How do I solve this rightly

[umbral slate]

,, \sqrt{6}=\sqrt{3}\sqrt{2}

[rocky lotus]

ΔCΣ♠

[jaunty fox]

Is this what you are asking me to do

[jaunty fox]

@umbral slate

If yes what is the next step

Hello!

[ivory valley]

Was eine Aufgabe

Ich würde zuerst den Nenner ausmultiplizieren, dann rationalisieren, dann mit \sqrt{6}+\sqrt{2} erweitern

[swift barn]

I am very poor in geometry

[ivory valley]

@jaunty fox

[jaunty fox]

warte

[jaunty fox]

ist für ne aufnahmeprüfung

,, \sqrt{6}+\sqrt{2}

,, \sqrt{6}+\sqrt{2}

[rocky lotus]

katan

[jaunty fox]

was meinst du

hab ich versucht wie vorher

das funktioniert nicht

[ivory valley]

Wo bist du

[jaunty fox]

so hier

[jaunty fox]

was??

das ist für ne aufnahmeprüfung

bin kein deutscher

[ivory valley]

,rcw

[jaunty fox]

ok ja also mit rationalisieren meinst du die stpe 2

step 2

die ich gemahct hab

[ivory valley]

Jetzt erweiter mir sqrt(6)+sqrt(2)

[jaunty fox]

ok aber woher bekommst du das

[ivory valley]

Ja du willst das am Ende im Nenner

Wenn du richtig gerechnet hast, sollte dann der Faktor 12 auch sich kürzen

[jaunty fox]

ok warte

[jaunty fox]

ja aber stell dir vor

wenns kein Lösung darin steht

wie kann man das bearbeiten

das wollte ich wissen

[ivory valley]

Ja bro deswegen sage ich ja, was eine Aufgabe

[jaunty fox]

also ich muss das nach und nach bearbeiten

mit komplettem Fortschritt

da steht "Vereinfachen sie so weit wie möglich"

die Lösung ist nur sodass ich überprüfen kann

oder meinst du was anderes

[ivory valley]

Nein

[jaunty fox]

ok so wie kann ich das vereinfachen

[ivory valley]

Ohne die Lösung wüsste ich auch nicht was genau verlangt ist

[jaunty fox]

ok verstehe ich was du meinst jetzt

der wollte nur das wir das kürzen

bis es die Lösung entspricht

aber man kann nicht direkt nach antwort gucken und die nenner davon multiplizieren

aber ist ok weil ich das nicht genau weiß

Can anyone help me

How should I solve this problem

[ivory valley]

???

[jaunty fox]

was

?

I still havent found a way how to

[jaunty fox]

oy was meinst du

meinst du dass diese frage ist echt unklar?

wenns keine Lösung hier gibt

haben wir komunnikation probleme oder was

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[north scarab]

For 1/x, how do we draw the curve

[north scarab]

Like I’m confused why it’s connected

To the parabola

[fierce vector]

you don't know how ot sketch 1/x?

[north scarab]

I do but

[dusky pulsar]

put x= 1 in both

what you get?

[north scarab]

Y should equal to 1 right when x is 1

[radiant garden]

they will be both

[dusky pulsar]

yeah for both the peices

[north scarab]

But y doesn’t look like 1 f

[radiant garden]

connected

[north scarab]

what is y for that point right there?

1?

How is that 1

[dusky pulsar]

you will have to label it , free hand rough diagram can be pretty non scale

[radiant garden]

not drawn to scale

[dusky pulsar]

y = f(x)= x^2
and we are evaluating when x=1
hence
y at 1 or f(1) = 1

same for the other piece

[north scarab]

It doesn’t make sense because on the x axis it’s not the equal length as the y axis

[dusky pulsar]

think about it as zoomed

1 sec

[north scarab]

As both are indicating a unit of 1

[dusky pulsar]

they are yes

but they are not to scale

the diagram is a rough sketch , you will be required to label some points

[radiant garden]

i will let u handle this

[north scarab]

Alr makes sense thank u

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@north scarab Has your question been resolved?

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[latent mortar]

Is that right

I’m not sure if anything else needs to be in parenthesis

[stark wedge]

perimeter is 2a+2b not 2a*2b

[latent mortar]

Oh shit

[stark wedge]

also which letter are you doing rn

[latent mortar]

Uh

[stark wedge]

a), b), c) or d)?

[latent mortar]

A)

I misread the question I think

Ab product is area

And it tells us the area already

So isn’t it just 0.8

[stark wedge]

indeed

[latent mortar]

And for b if we have a+a+b+b = 4.2 isn’t it just half of that?

So 2.q

2.1

Soma means sum btw

[stark wedge]

yes

[latent mortar]

Idk how to do c though

[stark wedge]

you want to find an equation of the 2nd degree for which a and b are roots

[latent mortar]

It’s saying “a and b are roots of which 2nd degree equation

Yep

How do I do that

[stark wedge]

have you done things with such equations before

[latent mortar]

Yes

[stark wedge]

ok

[stark wedge]

can you write this equation in factorized form

[latent mortar]

Uh

Lemme try

Which ewuation

[stark wedge]

an equation which has a and b for roots

leave them as just a and b

and for the unknown use x

[latent mortar]

Like that

[stark wedge]

well that's your first step yes, but it isn't yet the answer

now expand (x-a)(x-b).

[latent mortar]

Ok

I used completing the square

Is that right

Wait but now i can substitute cause i know what a+b and a*b is

I think I got it

But isn’t that just for a?

Oh nvm there’s b in there too

I just wrote it as a different way

.clsoe

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[slim coral]

hello I am trying to prove this statement is true using the mean-value theorem. I thought I had to find c for both functions; sqrt(x) and 1/2(x-1) but that doesn't seem to be working. I would like some guidance please.

[ivory valley]

By the looks of it 1+(x-1)/2 appears to be a tangent line of sqrt(x)

Since they meet at x = 1 you may consider the intervals [0,1] and [1,oo)

[vale dock]

@slim coral Has your question been resolved?

[slim coral]

ok, do i split into cases?

[ivory valley]

I would say so, also react to the bot message!

[noble anvil]

React ❌ or your channel will auto-close

[ivory valley]

or rather ❌

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[ivory valley]

ok lol

[noble anvil]

Oops.

[noble anvil]

O yeah lmfao

[ivory valley]

I thought OP needed help still

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[latent mortar]

27 a)

It says to use the other page example to help but it doesn’t help much

Idk what to do tbh

[noble anvil]

I cant read

What does it say

[latent mortar]

Lemme tryna,set

Tenalstw

Translate

Based on the example of the plot from the previous page, think and answer.
If we wanted a plot of land with an area of 624 m², what would its dimensions be?

Do you want the other page top

Too*

Can’t it have multiple dimensions

Like many numbers multiplied together gets 624

[velvet lake]

Well, you're given that the perimeter of the plot must be 100m, since half the perimeter is 50m

[latent mortar]

What

[velvet lake]

so you know that the sides are (x), and (50-x)

[latent mortar]

??

The question doesn’t say that

[noble anvil]

Do we have to maximise perimeter or something?

While keeping the area 624

[velvet lake]

the question does say that pretty clearly

[latent mortar]

Oh we’re supposed to use the other page to help us

[noble anvil]

That's not the question

[velvet lake]

The question says "using the example of previous page". That's on the example of the previous page. So it's part of the question

[latent mortar]

That page is the explanation of the conecept

[latent mortar]

That does make sense

Lemme try that then brb

Uh something went wrong I think

Oh

I put 625

It’s 624

😭

I think it worked

Lord Felix big brain

Would’ve been stuck there for a while if it wasn’t for him telling me it was using the other page too

What is the maximum possible area that can be used in the calculation of the dimensions? Why? In that case, what would be the dimensions of the plot?

Idk how to do this one though

If I were to try

I’d say 25x25

Why?

Cause they’re the biggest numbers possible together

The dimensions of the plot would be 625 right

Idk if that’s what the question wants

<@&286206848099549185>

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[pseudo python]

how do i solve this ? i asked someone and they explained a method with product notation but i havent learn that yet so how do we do this

[spark sluice]

cot 5 * cot 85 = 1, cot 10 * cot 80 = 1 and so on

pair up terms like this

they will all become 1 except the middle term which is cot 45 = 1

[pseudo python]

how are they all 1 if u dont mind me asking

is there any cot(90-x) identity

[spark sluice]

because cot (90° - x) = tan(x)

and cot x * tan x = 1

[pseudo python]

wait isnt tan x = 1/cot x

[spark sluice]

it is

i dont see the problem here

cot (90° - x) = cos(90° - x)/sin(90° - x) = sin x / cos x = tan x

[pseudo python]

ok i got the rest but what does this mean

[spark sluice]

what did you simplify the product to finally

[pseudo python]

didnt u say itll all become 1

[spark sluice]

...i said all the pairs will become 1

but one term will be left unpaired

because there are an odd number of terms in the product here

[pseudo python]

so do i have to write all the terms out and do it ?? bc thats alot

[drowsy kraken]

you can convert half of the terms into tan

[spark sluice]

no

[drowsy kraken]

by using

cot x = tan (90-x)

[spark sluice]

hello, are you reading the help channel? that is exactly what we are doing

[pseudo python]

so how am i supposed to know which pair is left if i dont write them all individually and see if they multiply to produce 1

[spark sluice]

there are 17 terms, the first and last pair up, the second and second last pair up and so on

[pseudo python]

theres 17 terms right

yeah

[drowsy kraken]

umm?

[spark sluice]

all the pairs become = 1

[drowsy kraken]

you don't have to write its an mcq just show the working by using the dots

show the conversion of last 2-3 terms

[spark sluice]

if i have an odd number of things and i start making pairs one thing will be left unpaired

[drowsy kraken]

and explain how tanx cotx is 1

hence all pairs are 1

hence the answer is 1

[pseudo python]

yeah but im kinda confused how did u guys know all the terms are 2 pairs of cotx . tanx and thus the full ans is 1

[spark sluice]

there are 17 terms

5,10,15,20,...,85

[drowsy kraken]

oh yea

[karmic yacht]

1 term is unpaired

[drowsy kraken]

so 85 = 5 x 17 hence 17 terms

[drowsy kraken]

mid term is 17+1/2

9th term is left

[karmic yacht]

so 9 * 5 = 45

[drowsy kraken]

which is cot 45deg

and cot45 is 1

since all the terms are 1

hence ans is 1

[pseudo python]

ahh okay i got it now

[drowsy kraken]

total terms are 17 hence you can make 8 pairs while one term is left

[pseudo python]

can u tell me again whats the way to find the middle term in an odd list

[drowsy kraken]

all the 8 pairs are 1

so only unpaired is left

now the unpaiored is ofc the mid term

formula for mid term is (n+1)/2

out n is 17

hence mid term is (17+1)/2

[pseudo python]

okay got it thanks : -)!

[drowsy kraken]

18/2

9th term

[pseudo python]

thank you so much

.close

[drowsy kraken]

no prob

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[neat sigil]

a, k, v is known

a > 0
0 < k < 1  
v > 0

f(x) = a*k*(1-k^x)/(1-k)
y(x) = f2(x)*f(x)
0 <= f2(x) <= 1

Need to find a function f2(x) such that the function y(x) is linear until y(x) reaches the v.

need y(x) to reach v as quickly as possible.

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[neat sigil]

<@&286206848099549185>

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[neat sigil]

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[neat sigil]

a, k, v is known
y(x)=a*k*(1-k^x)/(1-k)

F(x, f) = int 0 -> x_0 f(x)y(x)dx
у(x_0) = y(x_0)f(x_0) = v
y(0) = 0

Need to minimize the functional F.

[autumn lantern]

what did u try

[neat sigil]

express x_0 from a, k, v:

x_0 = log(1-v(1-k)/(a*k))/log(k)

This is generally above my level of knowledge in mathematics. I know that it can be solved using the Euler-Lagrange equation, but I don't understand how yet.

[wraith heart]

then learn euler lagrange

[neat sigil]

Where can I find good material for studying (and with translation into Russian)? From what I managed to find, nothing became clear.

[wraith heart]

no idea i don't speak russian

[neat sigil]

<@&286206848099549185>

[neat sigil]

I also found a function f that makes f(x)y(x) linear. But I don't know if it minimizes the functional F or not.

f(x) = v/x_0 * x/y(x)

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[vocal valve]

How can I even start solving that?

[vocal valve]

Obviously, you need simplify it. 324=18², but it doesn't seem to help much

[vocal valve]

Ohh

That's really helpful, thx

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[gleaming kindle]

what part do u need help on?

[buoyant jasper]

Finding (f*G)’(x) well proving it

This is how much I have so far

Anybody know what my next step should be

I know that f(x0)G(x0) is constant so it disappears

[tender sphinx]

is it saying prove chain rule?

[buoyant jasper]

No prove part ii

Part ii on this page

[tender sphinx]

ohhh

[buoyant jasper]

Am i on right track

Anyone know?

Help

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[quasi zinc]

Hey, can someone help me with this problem regarding generating functions? I'm not quite sure, if my approach here is correct.
The last image is a drawing for the last line involving all the combinations for building blocks -- I think, this is easier to read 😄

[quasi zinc]

If this approach was correct, I just need to do a bit of partial fractions and series expansion - but I would want to check if my approach is correct first 😅

[median sun]

Okay lets say you used the shape 3

How will you fill the hole at the top

[quasi zinc]

With shape 2

[median sun]

Yes

So you cant use shape 3 without shape 2

Can you use shape 2 without shape 3?

[quasi zinc]

Yes, just stack two of them

Like in my drawing

[median sun]

Oh yeah in your last drawing you listed all 4 ways to fill

Way 1 is 2x1 way 2 is 2x2 way 3 is 2x3 way 4 is 2x4

So it is like
Option 1) go 1 step up
Option 2) go 2 step up
Option 3) go 3 step up
Option 4) go 3 step up
How many ways are there to climb a ladder with n steps?

Try to answer this for n=1 n=2 excetra and see if you can notice any pattern

[quasi zinc]

sounds like catalan numbers

i'll try

But so I dont need to use the generating function here?

[median sun]

Oh wait idk how to solve with generating functions so you can ignore me

The image you posted talks about them too

[median sun]

But your last drawing here lists all 4 options to fill so you’re correct I can say

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[modern wren]

hi guys simple question whats the diffenrece between sin P and sin Q

[timber swan]

Isn’t it obi?

[modern wren]

yea it was

[heady pawn]

sin P = p/r and sin Q = q/r

[modern wren]

this is a topic i havent done in like months

thank u doe

I watched chem tutor but the problems were diff

[heady pawn]

yeah not sure if thats right

[spark sluice]

remove the sine on both rhs

[heady pawn]

never known this notation

[modern wren]

wait so sin P is p/r

[heady pawn]

yeah thanks

[modern wren]

lowkey my answer to sin P was q/r

💔💔💔

[heady pawn]

in my country we have like soscastoa

[modern wren]

yeah its soh cah toa

[heady pawn]

which means sin = over / hypothenouse

yea

[modern wren]

yup same thing

[heady pawn]

just remember that

[modern wren]

OHH wait so whats the diff between

q/r and p/r

[heady pawn]

well

the thing left has a reversed p

which is q

🔥

[modern wren]

is it q/r when theres no labels

on the outside

[heady pawn]

what

[modern wren]

the PQR

[heady pawn]

it's sin of point P

right

so soh

[modern wren]

yes

[heady pawn]

sin = over / hypotheneuse

the overside of the point P is p and the hypotheneuse is r

[modern wren]

wait isnt opposite the opposite of hypot

or is it supposed to be the opposit of P

[heady pawn]

I think opposit of P?

now im questioning myself

[modern wren]

rahhh im making this sound complicated

my bad

is there anyone else here who can prolly help

[heady pawn]

it's from the point

[modern wren]

so P

if its sin P its p/r

[heady pawn]

yea

because p is on the other side of point big P

and the hypotheneuse is r

[modern wren]

wait wtf then whats tan P

if im right sin P is p/r

cos is q/r

whats tan

[heady pawn]

tan is toa

[modern wren]

OHH my bad

[heady pawn]

so tan of p is over and adjacent

[modern wren]

i accidentally did toh

[heady pawn]

and over is p and adjacent is q

so it's tan P = p/q

[modern wren]

got it

but then when its

sin Q

[heady pawn]

sin soh

[modern wren]

q/r

?

[heady pawn]

so sin Q = over / hypotheneuse

[modern wren]

yes

[heady pawn]

over of Q is q and r is hypothensue

so it's q / r

nice

[modern wren]

OHH alr bet i get it now

thank u gang

[heady pawn]

nice gng

gl twin

[modern wren]

my quiz is like either tom or tues

thanks

.close

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[frozen shuttle]

I know this is a physics question but i think only the mathematics part is left someone pls help

[timber swan]

Yes

U take the velocity component

Along the diagonal

Divide it by distance

[frozen shuttle]

I think i did that but in a different way

I took the relative of A w.r.t B and divided it by total distance

@timber swan please help me understand what i did wrong

[timber swan]

Ye I’m trying

[frozen shuttle]

Okk ty

[timber swan]

I don’t think this is correct

Cause the particles won’t travel a distance

a

Rather they will travel the distance along corner to centre

[frozen shuttle]

Why it's relative motion to collide particle A will travel a distance "a" if b is put to rest

[timber swan]

Oh yea

I missed that

I got it

Rel velo is

V*=V+vcos2pi/n

[frozen shuttle]

How though ??

Relative velocity would be smaller than original velocity wouldn't it ?

[timber swan]

Particle b will have a velo towards b always

Let’s say

I’ll draw it out

And explain

[frozen shuttle]

Okk

[timber swan]

@frozen shuttle

[frozen shuttle]

So basically we have took projection of a along b right ?

[timber swan]

Yes

[frozen shuttle]

Ohh I see thank you for your help

[timber swan]

Np

Physics is not really my strong suit

It’s been a whole 6 months since I have done

all this

I’m dealing with electro dynamics now

[frozen shuttle]

Damnn

So your in college now ?

[timber swan]

Mhm

[frozen shuttle]

Damn

[frozen shuttle]

Tbh I like electrical engineering way more than cs

[timber swan]

[frozen shuttle]

Cs is just too boring and electrical is just too interesting 🙂

[timber swan]

Physics in uni is 🥴

[frozen shuttle]

Damn well im very far before from uni now so not my worry 🙃

[timber swan]

2 more years?

[frozen shuttle]

Ya

[timber swan]

2027

[frozen shuttle]

Damn 2027 jee 😭

[timber swan]

Good luck

Ts is easy

(Jk)

[frozen shuttle]

Ty

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[royal narwhal]

I'm trying to calculate the oblique asymptote for an rational function, but I'm stuck on my euclidean division:

[royal narwhal]

anyone able to help and write this for me, so I can use it as an example and learn that way?

[glass kelp]

its like normal division

so what multiplies x^2 - 1 that best fits x^3 + 4x - 5

@royal narwhal

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@royal narwhal Has your question been resolved?

[royal narwhal]

Wait

Im still a bit confused

[glass kelp]

so..

[royal narwhal]

Wait, I get it now

so

It would just be x

and than a bit of rest right?

.close

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[royal narwhal]

Sorry @glass kelp , I didn't mean to waste your time

[glass kelp]

thats fine. no time wasted

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[latent mortar]

Question 45 D

How do I factor this

[pure mirage]

Write it as 3x^2 - 6x - x + 2

Do you know the method I used?

[latent mortar]

Uh

[proven wasp]

ab = 6
a + b = -7

[latent mortar]

I know this one

[pure mirage]

It's basically the same

[latent mortar]

Ab isnt 6 though

Oh it is

But

A+b is 3+2

[proven wasp]

How?

All of my statements are correct.

[latent mortar]

A and b should be the same numbers

How is a a number in one of them

A=3
B=-7
C=2

Right

Hello

[cloud turret]

i couldn't understand what said but i beleive it's something like : (3x-1)(x-2)

[latent mortar]

Ye

How’d u get to that

[latent mortar]

Oh wait

Why did u do that though

[cloud turret]

I put it like that (x +)(__x+____)
then try to figure it out

[pure mirage]

One sec, let me link you to an article about this

[latent mortar]

😭

I’m in grade 9

Is there an easier way to explain this

The step by step

[pure mirage]

https://www.mathsisfun.com/algebra/factoring-quadratics.html

Scroll down to 'A Method for simple cases'

[latent mortar]

Wow that’s good

I don’t get how he factored them though

[pure mirage]

Which?

The first example is 2x^2 + 7x + 3

We need two numbers a, b so that a + b = 7 and ab = 2 * 3 = 6

[latent mortar]

I get that

I don’t get the factor

[pure mirage]

From 2x^2 + 6x, you can for example factor out x, right?

That gives you x(2x + 6)

But you can also factor out 2

[pure mirage]

The x + 3 is just there from the previous step

you factor the first two terms and leave the last two as they are

[cloud turret]

he just put the () on it nothing changes

[latent mortar]

Oh

[radiant garden]

the tutorial didnt include the x + 3 on the other pic

[latent mortar]

U just forget about the last 2

[pure mirage]

yeah, at first

[latent mortar]

Why’d he say “the last 2 terms didn’t actual change in this case?

[pure mirage]

Forget about that sentence, this entire website isn't really mathematically rigorous, just tries to explain things in simple terms

They are trying to say to ignore the last 2

[latent mortar]

Ok lol

[pure mirage]

Now try to apply this method to your problem: 3x^2 - 7x + 2

First write out what you need

[latent mortar]

A*b=6

[pure mirage]

yes

And

[latent mortar]

A*b=-7

You know why

[latent mortar]

I a,ways did this method with the first number being 1

So I never took the term with x^2 in consideration

My tscher said u couldn’t do this method when the x^2 term wasn’t 1

[pure mirage]

Yeah, that's wrong, you can

[latent mortar]

Dang

Ok well

A+b=7

[pure mirage]

-7

[latent mortar]

That means -1*-6=6

-1+-6=-7

[radiant garden]

what grade are you?

[pure mirage]

yes

[latent mortar]

9

[radiant garden]

i have a feeling we are close in age

[pure mirage]

So now re-write 3x^2 - 7x + 2

[radiant garden]

i see

[latent mortar]

3x^2-1x-6x+2

[pure mirage]

yes

[latent mortar]

So the terms u found go in the middle

In between term A and C in the quadratic formula

[latent mortar]

Wbu

[radiant garden]

im in 10th grade

[latent mortar]

Now I need to

[pure mirage]

Factor the first part

[latent mortar]

Yeah

How do I know up to where I factor

[pure mirage]

Factor as much as possible

[latent mortar]

Ok

[pure mirage]

In this case, that's only x

[latent mortar]

Always?

Up to as much as possible

[pure mirage]

Always factor as much as possible, yes

[latent mortar]

Ok

In this case it’s 1x right

[pure mirage]

Yes, though you usually don't write 1x but just x

[latent mortar]

Right

[pure mirage]

3x^2 - x - 6x + 2 = x(3x - 1) - 6x + 2

Now also factor the last part

[latent mortar]

X(3x-1-6)+2

Is that right

[pure mirage]

It's right but it's not what we want to do, we want to look at the first 2 terms and the last 2 terms separately

[latent mortar]

U said as much as possible

Ok

[pure mirage]

So look at -6x + 2 now separately

Can you factor that as much as possible too

[latent mortar]

So i leave the last 2 terms out

Always?

[pure mirage]

yes

[latent mortar]

Ok

2(-3x+1)

[pure mirage]

Yes

[radiant garden]

uh

[pure mirage]

Maybe even pull out a - so that it matches something in the first part

[latent mortar]

?

[latent mortar]

What

[pure mirage]

-2(3x - 1)

[radiant garden]

it would be better to leave the negative in the number outside

[pure mirage]

I can say that aswell

[radiant garden]

yes

[latent mortar]

Ok

[pure mirage]

So you got x(3x - 1) -2(3x - 1)

[radiant garden]

though you're not wrong

[pure mirage]

Now look at the entire thing and factor

[latent mortar]

Uh

[pure mirage]

There is a common factor in both parts

[latent mortar]

So Rn it’s x(3x-1)-2(3x-1)

Right

[pure mirage]

Yes

[latent mortar]

Ok so it’s 3x-1

[pure mirage]

That's the common factor, yes

[latent mortar]

How do u factor smth in the factor

[pure mirage]

You want to write (3x - 1) * (something)

Do you know the distributive property?

[latent mortar]

Yeah

[pure mirage]

Use that

[latent mortar]

Isn’t it just 3x-1(1)

Idk what u want me to factor rn

[radiant garden]

x and -2 multiply to the same thing right

[pure mirage]

We have $x(3x - 1) - 2(3x - 1)$ right now. The common factor is $3x - 1$, so you can write this as [(3x - 1)\Big(x - 2\Big)]

[rocky lotus]

Kepe

[latent mortar]

Yeah

[radiant garden]

x(3x - 1) -2(3x - 1)

[radiant garden]

yea

this guy wrote it down for you

[latent mortar]

Ohhh

Ok

[tranquil zephyr]

if ur confused, after writing (3x-1) just put the remaining stuff in another bracket and multiply, that's your other factor in extremely simple terms

[latent mortar]

Wait isn’t that also the answer

[pure mirage]

We are done after this

[radiant garden]

👏

[latent mortar]

Ok imma try to do the other ones on my own

[pure mirage]

With some practice, it becomes trivial. For example, for h) it's just $a + b = -6$ and $ab = 9$, so $a = -3$ and $b = -3$, giving us [3x^2 -6x + 3 = 3x^2 - 3x - 3x + 3 = 3x(x - 1) - (x - 1) = (x-1)(3x - 1)]

[rocky lotus]

Kepe

[latent mortar]

For e)

[radiant garden]

remember to practice these basics

you'll need them up until uni

[latent mortar]

Ab=12

A+b=8

[pure mirage]

Yes

[latent mortar]

I don’t remember how to divide the middle part now

[pure mirage]

You need to find possible a, b

[latent mortar]

Oh

6 and 2

[pure mirage]

yes

[latent mortar]

Ok lemme write it down

I’ll send pic

Uh

I got this rn

[pure mirage]

That's what you divide the middle part into. 4x^2 + 8x + 3 = 4x^2 + 6x + 2x + 3

[latent mortar]

But the 2 outer terms aren’t the same as the once’s inside

[pure mirage]

Yes, but you forgot a + after the bracket

[latent mortar]

Wait I messed up

[pure mirage]

Also the x after 3 shouldn't be there

[latent mortar]

Yeah

[tranquil zephyr]

can i know what type of sum he's solving?

[latent mortar]

Uh

[radiant garden]

it is basic factoring

[latent mortar]

Idk how to answer that

I feel Like a lab rat and y’all are giving me stuff to test me and I’m being observed

[tranquil zephyr]

ic

[latent mortar]

https://tenor.com/view/tv3-no-pot-ser-tv3-baste-no-pot-ser-jordi-baste-gif-16947004

[radiant garden]

no no do your own thing

[latent mortar]

I’m joking lol but it’s what i think it would feel like

[radiant garden]

this is very intriguing

[tranquil zephyr]

i would love to be a lab rat so consider yourself lucky

[radiant garden]

i was once like you

[latent mortar]

They die most of the time

[pure mirage]

I'll head out now, the procedure is always the same; after this factor out (2x + 3) and you are done

[latent mortar]

What’d I do wrong

Ohhh

[radiant garden]

there is an invisible 1 outside the 2nd 2x+3

[latent mortar]

Right

Ok f)

This time I think I’ll get it 0 error

[radiant garden]

goodluck

[latent mortar]

👍

[radiant garden]

once you get your answwer, remember to verify it by multiplying your factored expressions and seeing if it matches the original expression

[latent mortar]

Yeah ik that part

[radiant garden]

i will head out now 🫡

[latent mortar]

Cya man tysm

[radiant garden]

goodluck, practice these alot

and you will be ahead of everyone else

[latent mortar]

Wait

1 last thing

@radiant garden

[radiant garden]

yes?

[latent mortar]

How do i find a number that Ab=-30

A+b=13

10 and 3 but

It’s negative

Ohhh

15 and 2

15*-2=-30

[radiant garden]

yea

[tranquil zephyr]

does he know how to form the quadratic?

[latent mortar]

15-2=13

[radiant garden]

wait. im thinking how to put it into words

[latent mortar]

I know how to factor

[tranquil zephyr]

i meant forming the equation from your data

[latent mortar]

I just didn’t know how to do it when a≠1

[latent mortar]

Uh

I think so