help-27

[prime narwhal]

I think it's only sin for this

Okay so one of those types of questions is good practice

All of them are similar?

I don't have time so I'm wondering if I should skip those for now

[visual hazel]

yeah

[prime narwhal]

How do I know when this information in this picture applies

Injsut randomly saw this in my notes and didn't know what I needed to know for what type of questions I need to worry about this

[devout snow]

@prime narwhal Has your question been resolved?

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[prime narwhal]

Once you figure out what case you have wtf do you do

How do you find the sides angles etc

I'm sooooo confused

<@&286206848099549185> idk how to find out the two cases when I get two, I assume when it's one I just plug it into the sin law but I need to know if that is correct too

.close

[devout snow]

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[sacred trellis]

how do you factorise this

[exotic viper]

Let f = (x+a), g =(x+b) use these placeholder variables

Easier to see

[sacred trellis]

okay

[exotic viper]

Those who know💀💀💀

[orchid glade]

try to be friendly here

[sacred trellis]

can someone explain to me

i'm so lost

[orchid glade]

did you do the substitution as told above?

[exotic viper]

Yea it should factor nicely

[orchid glade]

or without doing that. you can try looking for any patterns of any formulas you know.

just dont expand that since you clearly dont have the space to do anything

[sacred trellis]

i'm so lost do i take out the common factors first

[orchid glade]

Let f = (x+a), g =(x+b) use these placeholder variables

did you understand this

[exotic viper]

Yea did u do

[orchid glade]

where you see (x+a) put in f and where you see (x+b) put in g

[sacred trellis]

yeah so we haven't learnt that

[exotic viper]

Bruh it’s simple

[sacred trellis]

it's just factorisation i haven't learnt functions

[exotic viper]

It’s just using a variable

There variables

Not functions

[orchid glade]

let's just rename them

[vital dagger]

use any variable like y,z

[orchid glade]

its the same thing; but we're giving a different name

[exotic viper]

I just didn’t want to use x,y ,a,b again to not confuse

[sacred trellis]

oh okay

[exotic viper]

F and g aren’t function they r just variables

[sacred trellis]

okay

.close

[devout snow]

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[exotic viper]

did u get it

[devout snow]

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[inner leaf]

I'm stuck on union part

Like

X+5 can't be 0
X-3 can't be 0
X can't be -5
And x also can't be 3
If so why is it in the union? Also How do I use the minus infinite and infinite sign?

[hazy cradle]

() these brackets mean that they are excluded
[] thse brackets mean that they are included

so the values -inf,-5,3,inf cant be substituted for x

every other number is possible

[inner leaf]

Wait

I understand it now

Thx!

Oh yeah

X can't be inf and - inf

Does it mean that you will not be able to use any negative or positive number at all?

I'm sorry if it's a dumb question

[hazy cradle]

no, putting the value of inf in maths is absurd

like we generally use it see where the function goes if we try to plot it in a graph

[inner leaf]

Oh
I thought infinite things meant like
Every all number

[exotic viper]

no just infinity as a value

[slate ocean]

it's hard to conceptualize how a function acts at infinity so instead we observe a function's behavior as it gets closer and closer to infinity

[inner leaf]

I understand it all fully!

[exotic viper]

called end behavior btw

[inner leaf]

Oh

You guys seem so good at math

Wow

[exotic viper]

those who know 💀 💀 💀

[slate ocean]

If you take 1/infinity, it's kinda hard to imagine (well it's undefined), but if you look at what happens when x in 1/x approaches infinity
1/10 = 0.1
1/10000 = 0.00001
1/1000000... = 0.000...1
You'll notice the function's behavior is to get smaller and smaller

so at 1/infinity it's a bit iffy, but as it gets closer to infinity it approaches 0

hopefully that made sense

[inner leaf]

This make really alot of sense

[valid silo]

(a,b) means anything between all x, such that, a<x<b

-inf < r (for all r in reals)

[slate ocean]

glad to hear it
if you wanna read more about this these are called limits, and they get pretty usefull further on

[inner leaf]

Limit is more than I thought

I will try to learn more on yt

Thanks guys!

Im done with the question

How do I clear this channel?

[hazy cradle]

.close

u gotta type

[inner leaf]

.close

[devout snow]

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[restive river]

3 BEST Rivals Weapons Will Make You UNSTOPPABLE
https://youtube.com/shorts/GUiy-_PsfYI?feature=share

[devout snow]

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[dapper mica]

<@&286206848099549185>

[valid silo]

did you finish the proof for 3?

[dapper mica]

No

It works

I have a grid for 3 which works

[valid silo]

send it?

[dapper mica]

??

[dapper mica]

Yes wait'

[ancient sluice]

Bro

[atomic estuary]

😝😝😝😝😝😝

[ancient sluice]

That was a slang

[atomic estuary]

Yes lol

[dapper mica]

9 6 1
2 5 4
3 1 4

[ancient sluice]

Why would you use that ! No way !

[valid silo]

doesnt work

alo

there are 2 4rs

[dapper mica]

This works

Try it out

Also please mute trustyy

[atomic estuary]

Bro i just used it once and if anyone felt bad then i am sorry i was just doing it for fun

[valid silo]

and also 2 1s

[dapper mica]

Wait

[valid silo]

i did

[dapper mica]

Sorry

Problem solved

.close

[devout snow]

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[strange nimbus]

Yeah, you can only use each number once.

My guess is that there will be two primes in the upper half of the numbers. If so, you can't use both of them in a shared row and then simultaneously in a shared column.

[devout snow]

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[ancient sluice]

Trinomial theorem!

[dapper mica]

What is that

[dapper mica]

Ive seen binomial

[ancient sluice]

A Google search can surely explain better

[dapper mica]

Okay but then what?

[ancient sluice]

https://www.statisticshowto.com/trinomial-coefficient-theorem-definition/

[ancient sluice]

This is your exact question

[dapper mica]

Understood

[dapper mica]

Whats this

[ancient sluice]

Just a page on trinomial theorem

[dapper mica]

Ok

[uneven talon]

It's the same as the binomial coeff but for three variables

[dapper mica]

Understood

[dapper mica]

Oh

Understood trinomial

Now what

@ancient sluice @uneven talon

[uneven talon]

It all depends on n,a,b,c

[ancient sluice]

Did you open the page I sent ?

[dapper mica]

Yup

[ancient sluice]

K is the n in your question

[dapper mica]

How do i get the a, b and c

Which are for me i,j and k (in my question ofc)

[ancient sluice]

Search general trinomial, it shall give you the formula

[dapper mica]

Okay

[ancient sluice]

https://en.wikipedia.org/wiki/Trinomial_expansion

[dapper mica]

And that is the answer to my ques?

[ancient sluice]

Not exactly but it will take you some thinking

[dapper mica]

Ok, but could yoh helo me through the thinking

[ancient sluice]

But the concept is essential

[dapper mica]

Like I alreadh made a few deductio s

$c_n(0,0,f)=1$

[woven radish]

Abir

[dapper mica]

This is true for all f

Then,

$c_n(f, f, f)=2n$

[woven radish]

Abir

[dapper mica]

@ancient sluice

[ancient sluice]

Wait ! I have some work ! I will be back in sometime !

[dapper mica]

Okay@ancient sluice

[ancient sluice]

Hey hii

So

n!/a!b!c!

Is the coefficient

[uneven talon]

Could we check cases for this

[dapper mica]

I was doin that

[uneven talon]

Since the trinomial expression is permutable for a,b,c

[dapper mica]

Ok, but i am still not able to get it

How do I figure out the a b and c

For binomial, choose any a<n and b would be n-@

[ancient sluice]

a,b,c are the

Powers of

[dapper mica]

Wait

[ancient sluice]

a,b,c

[dapper mica]

Like for then 2nd term

Okay but how do i get em

[ancient sluice]

See (a+b+c)^n will give an expansion where all terms will be homogenous and of degree n

[dapper mica]

Okay and?

[ancient sluice]

So Ka^x×b^y×c^z be any term

Then x+y+z = n

[uneven talon]

Mhm

[ancient sluice]

Where K is the coefficient given by

[dapper mica]

Oh

Now I get it

[ancient sluice]

n!/(x!×y!×z!)

[dapper mica]

So for x^n, a=n, b=0=c

Okay@ancient sluice

Well I expanded the thing

Now what?

How do I know about the parity

[ancient sluice]

To predict if the

Coefficient is even or odd

[dapper mica]

Yea

[ancient sluice]

Depends totally on the values of x,y,z,n

[dapper mica]

Oh

[ancient sluice]

I think we need to break it into further cases

To find some resemblance

[dapper mica]

Ok on it boss

[uneven talon]

I say we look at exponents close to n

Suppose we have a^n as our term

Then of course the coeff is 1

And suppose WLOG since it's all permutable that we have a variable raised to the n-1

Meaning there's some other variable raised to the 1

Then the coeff would be n

If there's only two variables in a term

And the max exponent is n-k

Then its gonna be n-k+1 choose k

And because of that we know that these coefficients are still related to pascals triangle

[dapper mica]

Yes

[uneven talon]

Just as the binomial is

[dapper mica]

I see

Whats WLOG

[uneven talon]

Without loss of generality

[dapper mica]

Oh

[uneven talon]

It's a statement to say that we aren't extrapolating smth

When it may seem like we are

[dapper mica]

I didnt understans rhis part

[dapper mica]

Oh

[dapper mica]

J didnt understans

@uneven talon

[ancient sluice]

I was looking for, if we could establish some sort of relation between x,y,z which tells us about if it's even or odd

[uneven talon]

I think its trying to decide if n-k+1 choose k is even or odd

[dapper mica]

Could we please talk abojt i, j, k

Im getting confused abt x, y, z

[uneven talon]

So how do we know if a pascal number is even or odd

[dapper mica]

Yeah how do we know it

[uneven talon]

Well we know that if i=j=k

Then the coefficient is even

[dapper mica]

Ofc

[dapper mica]

Wait but why

Im kinda noob

@uneven talon

[ancient sluice]

Well we won't be able to say that for n ≠ 3k, so ig we will need cases

[dapper mica]

Ok

But can you show me a case

Forme to figure out to rest

[uneven talon]

Oh truth

[ancient sluice]

For n = 2^k all terms will have even coefficients, except those of a^n,b^n,c^n

[dapper mica]

I dont think a^n, b^n and c^n ever have even coeff

[ancient sluice]

This holds for all k € I

[uneven talon]

Well they do but it's 1

[ancient sluice]

1 is their coefficient

[dapper mica]

Not even

[dapper mica]

How do you know

[ancient sluice]

It happens to be so, because 2^k! always has an extra factor of 2

[dapper mica]

Wait let me ckmprehend

[dapper mica]

But what is the proof of it.

[ancient sluice]

Ig the question needs extensive analysis and isn't that simple, or we're missing something very vital !

[dapper mica]

Its intuitive

[dapper mica]

I think as well

[uneven talon]

Well its

For (2^k)!

We know that it'll have significantly more factors of 2 than any other factorial less than it

[dapper mica]

Can we do it using pascal's triangle

Like find out which row

And then chdck for coordinates

Whjch are evn and odd

Guys

Can we do like

[ancient sluice]

I think that won't be easy either

It's better to calculate factors of 2, in (i+j+k)!/(i! j! k!)

[uneven talon]

We just gotta see what's greater

There is a formula to see how many factors of a number is in a factorial

[ancient sluice]

Yeah

[dapper mica]

$c_n(i, j, k)= \text{}^nC_i \text{}^{n-i}C_j \text{}^{n-i-j}C_k$

[woven radish]

Abir

[ancient sluice]

Legendres formula

[uneven talon]

Well its explicitly prime

I think

[dapper mica]

@uneven talon @ancient sluice

Can we do thi

[uneven talon]

I think legendres formula might be easier

But we can come back to it if we're wrong

[dapper mica]

Where to get? Googlr

??

[uneven talon]

$\sum_{n=0}^{\infty} \floor{\frac{x}{p^n}}$

[ancient sluice]

I was trying to establish some relation by considering n in different forms

[woven radish]

hiidostuff

[dapper mica]

Whats n and x

[ancient sluice]

But a periodic kind of nature over 2^n says we can't (ig so)

[dapper mica]

Does this work?

[ancient sluice]

I don't think it does

[dapper mica]

How does this woek

Like if x=4, p=2

Im fetting no of primes (2) as 3

Which means I am certainly doing something wrkng

[ancient sluice]

Let me explain

[dapper mica]

Sure

[ancient sluice]

Lets consider n = 100

[dapper mica]

Ok

[ancient sluice]

,calc 10!

[woven radish]

Result:

3.6288e+6

[ancient sluice]

Ok we don't need

We're considering lesser n for simplicity

n = 100

[dapper mica]

Surely

,calc 23!

[woven radish]

Result:

2.5852016738885e+22

[ancient sluice]

so how many factors of 2 in all numbers from 1 to 100

Is our question

First there will be 100/2 = 50

[dapper mica]

Agreed

[ancient sluice]

Next

[dapper mica]

Then there will be 25

[ancient sluice]

All numbers

[dapper mica]

, calc 100/8

[woven radish]

Result:

12.5

[dapper mica]

Then 12

[ancient sluice]

Multiples of 2²

[ancient sluice]

Yeah like this

[dapper mica]

25

[ancient sluice]

Basically this is Legendres formula

[dapper mica]

, calc 100/16

[woven radish]

Result:

6.25

[dapper mica]

And we do this till we vegin to get 0

[ancient sluice]

Yes

[dapper mica]

And then we add them up

[ancient sluice]

So we get

[dapper mica]

Thats the number of that primes we have

Right?

[ancient sluice]

Total factors of 2 in 100!

[ancient sluice]

Yes

[dapper mica]

,calc 100!

[woven radish]

Result:

9.3326215443944e+157

[dapper mica]

Thats too larrge

[ancient sluice]

It's not necessary to calculate

[ancient sluice]

The method works, yk why now !

[uneven talon]

Also fun fact about this

If you find out how many factors of 5 are in a factorial

You get how many zeroes are at the end

[dapper mica]

Yes

[dapper mica]

Oo nice

[ancient sluice]

But

[dapper mica]

Ok does this help mt problem?

[ancient sluice]

This is quite like a computational approach

[dapper mica]

Yeah

[ancient sluice]

I don't see any other easy way, to just look and say if the coefficient is even or odd

[dapper mica]

Agreed

[ancient sluice]

I will try later, if I come up with something, shall share with you

[dapper mica]

Ok

[dapper mica]

In dms?

[ancient sluice]

Or in help channels

[dapper mica]

Ok

[ancient sluice]

Wherever I find you haha

[dapper mica]

Hehehe

@uneven talon

Can u helo till them

[uneven talon]

Sadly not it's super late where I am

Its almost morning and I haven't slept

[dapper mica]

Ok sleep

Bye

Closing this channel

. close

[sharp garnet]

it should be .close

@dapper mica

[dapper mica]

.close

[devout snow]

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[devout snow]

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[slow marsh]

On a German motorway, black cars are four times more common than
cars of other colors. Most black cars are driven by men: 60% of men drive black cars, while 20% of women drive
cars of a different color. We observe the cars on the motorway. State the probabilities in percent, rounded to whole numbers.
What is the probability of observing a man driving a
black car?
What is the probability that the car is not black?
We see a black car. What is the probability of a woman driving it?

1. P(B|M)=P(B∩M)/P(B)
   0,8*0,6/0,8=0,6

2. 1/1-4/5=1/5

3. P(W|B)=P(W∩B)/P(B)
   0,8*0,4/0,8=0,4

Can someone tell me if this is correct?

[fossil locust]

you're not going about this the right way

this table really helps

weird

[slow marsh]

what u mean weird?

[fossil locust]

that gives x = 0 and y = 1

[slow marsh]

.close

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[vapid field]

how do i find the radius or anything here when theres no clear way to find OB. can someone solve this for me.

[undone kelp]

I think you can use the fact that you can write the ratio of the area to the circumference which will be 2pir/pir^2 = 2/r and r should be prime

[ancient sluice]

OC = OA

[last burrow]

It's easy to conclude that OA = AO which implies that the radius of both the circles is the same.

The circle with centre A with drawn to confuse, I guess.

[ancient sluice]

OC= r,
OB = x
x²+6² = r²
r+x = 10

Do you get it now ?

[ancient sluice]

Same, I don't see any use of the new circle !

[undone kelp]

shouldnt it be x^2+6^2=r^2?

[last burrow]

Yeah

[ancient sluice]

Was Just fixing it !

[undone kelp]

hahaha nice

[undone kelp]

this works when the radius is 34/5

[ancient sluice]

Haven't Calculated, Thank you, maybe helpful for the person who asked !

[devout snow]

@vapid field Has your question been resolved?

[vapid field]

after this how would i know the values?

[sharp garnet]

ik this was on bdmo right?

[vapid field]

yep

[ancient sluice]

Have you read through the whole chat?

[vapid field]

yeah

x^2+36=r^2

what would i do to get r

[ancient sluice]

another eqn is there

[vapid field]

area over circum

[ancient sluice]

r + x = 10

[vapid field]

ohh im sorry i get it now

thanks

sorry ion get one thing, the equation is too big to calculate and calculators arent allowed. nd if i just get the radius and do everything what would the point of those whole co-prime a and b integers be

[devout snow]

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[devout snow]

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[last burrow]

Translate

[tropic tinsel]

it says here in dutch p could be anything and will still be bigger than 0

which makes sense

but i added 1 to both sides and then square rooted the whole equation resulting in p + 5 > 1 which then became p > -4 but p is able to be any number not just greater than -4 so i dont know how that makes sense

[dense jay]

that is not how a square root works

sqrt(a+b) is not sqrt(a)+sqrt(b)

[tropic tinsel]

im a beginner chill

[dense jay]

[tropic tinsel]

i dont get it

[dense jay]

$\sqrt{a+b}\ne\sqrt{a}+\sqrt{b}$
$$\sqrt{16}=4=\sqrt{4+12}\ne\sqrt{4}+\sqrt{12}$$

[woven radish]

AℤØ

[tropic tinsel]

wait hol up

imma make an ms paint drawing showing what i did

[dense jay]

i know what you did

it just doesnt work that way

sqrt(2x^2) isnt equal to 2x for example [sqrt(x^2+x^2) isnt sqrt(x^2)+sqrt(x^2)=x+x]

(forgive my lack of absolute values oh merciful gods)

[dense jay]

you cant square root separately either

because that also implies that sqrt(a+b)=sqrt(a)+sqrt(b) which isnt true

[split river]

(P + 5)^2 = p^2 + 10p + 25 not p^2 + 25

You have to factorise

Not square root

[dense jay]

sqrt(ab)=sqrt(a)sqrt(b), which you may have seen, but the property doesnt apply to addition

[tropic tinsel]

you lost me

[dense jay]

you tried to do this

a+b>c
sqrt(a+b)>sqrt(c)
sqrt(a)+sqrt(b)>sqrt(c)

the third line is illegal

cant do that

[tropic tinsel]

why not

[dense jay]

because thats just not how a square root works, in the same sense that (a+b)^2 isnt a^2+b^2

sqrt(3^2+4^2)=sqrt(25)=5

sqrt(3^2)+sqrt(4^2)=3+4=7

5 is not 7

[tropic tinsel]

(a+b)^2 isnt a^2+b^2 explain how it isnt

[dense jay]

(a+b)^2=(a+b)(a+b)=a^2+ab+ba+b^2

=a^2+2ab+b^2

[tropic tinsel]

right

i get that now

but thats not what i did in my eyes

[dense jay]

youre aware that what you do to one side of an equation (or inequality) you must do to the other?

[tropic tinsel]

ye

i square rooted both sides

[dense jay]

yeah so sqrt(p^2+25)>sqrt(1)

but you then separated that root into sqrt(p^2)+sqrt(25), which you cant do

[dense jay]

as i showed you here

[tropic tinsel]

i dont really get why you cant square root seperately but from now on ill just keep that in mind

[dense jay]

you can consider it as being because exponents dont distribute over addition

sqrt(a)=a^(1/2)

sqrt(a+b)=(a+b)^(1/2) which isnt a^1/2+b^1/2=sqrt(a)+sqrt(b)

[tropic tinsel]

i dont get im sorry

[dense jay]

alrighty, so long as you keep this in mind

[tropic tinsel]

i will thx so much

[devout snow]

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[devout snow]

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[crystal fulcrum]

could i get help w a question

[crystal fulcrum]

thats the question

[supple knot]

<@&268886789983436800>

[crystal fulcrum]

nooooo

im sorry

[winter torrent]

.close

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[devout snow]

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[sand quarry]

This is more of a question about definitions. My friend has told me that the "laplace transform" is always defined as the one-sided transform [
X(s) = \int_0^\infty x(t)e^{-st} \dd t
]
but this goes against what I am accustomed with

[woven radish]

Aero

[sand quarry]

What we had learnt, however, is that the two-sided transform is the basis of our consideration. It is true that with the two-sided transform barely any functions converge. However, it gives you the liberty of deciding the region of convergence yourself

[supple knot]

What does two sided transform mean

[sand quarry]

[X(s) = \int_{-\infty}^\infty x(t) e^{-st} \dd t]

[woven radish]

Aero

[supple knot]

And where did this formula come from

[sand quarry]

take for example the two functions [
x(t)= -e^{-at} u(-t), \q y(t) = e^{-at}u(t)
]
Their Laplace transforms are identical. However, to uniquely specify their laplace transforms you need to define their region of convergence of $\Re{s} > -a$ and$\Re{s} < -a$ respectively

[woven radish]

Aero

[sand quarry]

https://en.wikipedia.org/wiki/Two-sided_Laplace_transform

It is the more general Fourier transform

[supple knot]

Yea this is different from Laplace transform

"ordinary" Laplace transform
https://en.m.wikipedia.org/wiki/Laplace_transform

[sand quarry]

Pretty odd to be honest

my signals and systems class takes the former as the "ordinary" transform

It seems more insightful once you realise how many variations of the same laplace transform you could have depending on your chosen ROC? For example this attached image implies 4 signals can uniquely define the laplace transform

It just seems super odd why 0 to infinity is "forced upon you" with the ordinary laplace transform instead of having you choose the suitable ROC yourself

[supple knot]

Use whatever definition your class uses. If you're in a math class, you're learn a different definition

[devout snow]

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[copper hamlet]

hey i need help. im supposed to make a small presentation on main axis transformation in the 2nd dimension and my teacher gave me a specific example on which i should explain it but i dont understand his notes and all the youtube videos are using terms i never heard

[copper hamlet]

I understand these two

But the second half of the second sheet and this one are unclear

[tame palm]

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

I'm not sure exactly what you are looking for.

[copper hamlet]

thank you hope this helps because i am german and the german videos are much weirder

.close

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[flat surge]

I got this wrong because I missed the absolute value sign. But now i'm confused how to do this, all I know is the answer is 2 but how?

I did the mean value theorom f(b)-f(a)/b-a which got me -1 but this was before I realized there was an absolute sign

[misty crest]

were you given a graph

[flat surge]

nop

[misty crest]

so they want you to graph this yourself?

also f(1)-f(0)/1-0 = 9-8 = 1

ok you realized that

[slender mirage]

Technically you could graph it

Graph y = (x² - 4)(x² + 2) = x⁴ - 2x² - 8 and flip the curve that goes below y = 0

Moreover this is an even function, so you only need to plot for x > 0 and mirror it on x = 0

[flat surge]

is there a non graphing way cuz my teacher wants us to do it with no graphing

[slender mirage]

,w graph y = x^4 - 2x^2 - 8

[woven radish]

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[slender mirage]

Hmm, non graphically

[flat surge]

no basically what I did before I saw the absolute value sign was this

f(1)-f(0)/1-0 = (-9)-(-8) = -1

Now I double check if -1 falls in interval [0,1] by doing f'(x) = -1

The answer was 0.2 which was why i chose 1 solution --> coordinate (0.2, -1)

idk if that's right, but that was before I realized there was an absolute value sign

[misty crest]

i mean you could of course take the derivative lol

[flat surge]

could you elaborate please

is this before or after using the mean value theorem equation

[misty crest]

what

using mean?

ok

[flat surge]

lol mb

[misty crest]

well i mean you can solve f’ = 1

[flat surge]

how do i find the derivative of absolute again?

for that equation at least

[misty crest]

but again it says to use the graph so you could graph this by hand

[misty crest]

$|x| = \sqrt{x^2}$

[woven radish]

knief

[misty crest]

differentiate the right

$\frac{x}{|x|}$

[woven radish]

knief

[misty crest]

but you have a product

[slender mirage]

,w 4x^3 - 4x + 1 = 0

[woven radish]

Results provided by WolframAlpha

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[slender mirage]

Two solutions in [0,1]

[misty crest]

yea you could do that actually

don’t even need ||

[slender mirage]

Yeah, correcting your solution after plugging f'(c) = 1 would give you 2 solutions

You're not so off

[misty crest]

but finding the zeros is rough

[slender mirage]

No need to find zeroes

Can judge from nature of curve

[flat surge]

ok wait so the steps are
find derivative of the absolute value equation. Make that equal to 1. and then what? There's no need to use the MVT equation?

[slender mirage]

Yes

[flat surge]

where did f'(c) = 1 come from

[slender mirage]

Equating f'(c) = 1 is the MVT

where 1 = (f(1) - f(0))/(1-0)

[slender mirage]

Wait, why you acting so lost? You just need to redo it by rectifying [f(1) - f(0)]/[1-0] = 1 and checking f'(c) = 1 for some c in [0, 1]

[flat surge]

Lost cuz I need help finding the derivative of I(x^2-4)(x^2+2)I

and then I can do the MVT equation right?

wait

waitt let me backread rq

[slender mirage]

No

Since you're using the derivative in [0, 1] where the absolute value will open with a negative sign

[flat surge]

I originally wrote [f(1) - f(0)]/[1-0] = -1

u guys wrote [f(1) - f(0)]/[1-0] = 1 because u took the absolute value of -1 right?

[slender mirage]

Yes. Because f(x) = |x⁴ - 2x² - 8|

[flat surge]

ohh bruh

lmao

ok got it now

tysm guys appreciate it 😭

[trim berry]

Do .close

[devout snow]

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[devout snow]

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[unkempt sandal]

i dont really gert how to start this quesrtion

[slender mirage]

You can start by plotting f(x) roughly

[unkempt sandal]

alright

i got sometring like this

if i remember how to graph a piecewise lol

[slender mirage]

Yep. So now calculating integrals is pretty sweet

g(-8) is the area under curve from -4 to -8 going backwards, so it's -(0) = 0
g(-3) is area under y = 2 between -4 to -3 so a rectangle, that is 2 x 1
g(0) is area under y = 2 b/w -4 to -1 minus area over y = -3 b/w -1 to 0

[slender mirage]

Like that

[devout snow]

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[granite anvil]

confused on how to do this

i did 7C1x7C3x7C2x7C1

but the answer is 420

is it supposed to be

7C1 x 6C3 x 3C3 x 1C1

No thats getting me 140

[alpine python]

3C2 rather than 3C3?

[granite anvil]

oh

wait

ya

yep got it

thanks

.close

[devout snow]

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[granite anvil]

.reopen

[devout snow]

✅

[granite anvil]

also confused on this

i am acc not sure where to beginw ith this since its not immediately obvious how the 10 paintings can be split

like he could do 3 3 4

but

also

8

1

1

the number of paintings each child gets

[alpine python]

i think you don't need to use a binomial coefficient for this

[granite anvil]

idk what that is yet lol

[alpine python]

the nCr thing

[granite anvil]

oh

how do i do it i am still confused

i thought of it now as, arrange numbers from 1-9 in pairs of 3 such that their sum = 10

with the exception of the case where he gives all 10 to one heir

wait

this is like the same thing as the number of possible nucleotide base combinations 💀

its just 3^10

[alpine python]

ye

[granite anvil]

ok ok thanks

.close

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[devout snow]

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[slim tree]

guys ik im doing something wrong

[ocean viper]

What are you trying to do?

[slim tree]

find the value of theta

[ocean viper]

Solve for theta?

[slim tree]

yes!

[autumn fjord]

why do you suspect that you're doing something wrong?

[slim tree]

because im not getting the right answer!

[ocean viper]

Looks right to me

[autumn fjord]

is your calculator set to the right mode

[slim tree]

oh lemme check

[supple knot]

,rotate

[autumn fjord]

you're getting something less than 3 i bet

[slim tree]

yea

[autumn fjord]

yeah

[ocean viper]

Switch to degrees then

[autumn fjord]

your calculator should be set to degrees :P

[slim tree]

this is the answer btw

[ocean viper]

Ur in radians mode

[slim tree]

ok!

im still getting 3.36 ;-;

ik the gdc is in degrees

im typing (sin^-1)(8.5/145)

i converted to cm to mm

so thats how i got 145!

[bleak lake]

1cm = 10mm

[slim tree]

omg.

[autumn fjord]

oh wait, why is one in cm lol

[slim tree]

i read that as 14.5

ok wait lemme try again

[autumn fjord]

the answer given depends on them having the same units

[slim tree]

idk!

[ocean viper]

Why are they in different lengths

That’s trippy

[bleak lake]

Because math textbooks like adding extra unnecessary steps

[slim tree]

OK WAIT IT WAS JUST THAT

THANK YOU SO MUCH!

[slim tree]

bro fr 😔

guys i sat here for 15 minutes like a fool

[ocean viper]

Uhhh does 36 degrees look right?

Actually it does nvm

[slim tree]

i think it looks ok, is it not-?

oh ok!

[bleak lake]

You can never get a problem right if you don't have the right problem 🤔

[slim tree]

thank you!!

https://tenor.com/view/catthankyou-cat-gif-24824893

[iron kindle]

would be strange for the sidelength to be smaller than the base wouldnt it

[slim tree]

yea

.close

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[solar goblet]

why is 0 a member of L(V, W), while I is a member of L(V)?

[olive snow]

[solar goblet]

ah wait i'm dumb

.close

[devout snow]

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[olive snow]

[devout snow]

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[karmic creek]

I checked the answer key but it says something different from my answer. I think theirs a problem with my setup for this question?

I used 20 = 2y + x and A = xy for my two equations

The answer key says: 250/3 ft x 125 ft

i don't get it, i need some help -_-

[graceful stone]

Note that the fencing is $20/ft

So if the amount of fencing you get is x+2y, its price will be 20(x+2y) and you need make sure that quantity is at most 5000

[karmic creek]

ah

let me try that

im a bit stuck. Should I change my 20 = 2y+x equation to instead F = 20(x+2y) ?

F for fencing

I need to go, thank you for trying to help me!

.close

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[graceful stone]

Since you share one of the fences you should 20(x+1.5y)=max cost

[devout snow]

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[fiery dove]

how do you put y= x^2 + 2x into simpler terms to graph?
it’s been so long since i’ve been given a question in standard form

[fossil locust]

try completing the square

so y = (x + 1)^2 - 1

[fiery dove]

how do you complete the square again

[fossil locust]

ah, so you need to divide the middle term by 2, and then square it

so (2/2)^2 = 1

[fiery dove]

ohhhhhhhh

[fossil locust]

what happens now is we add and subtract that number

(x^2 + 2x + 1) - 1

[fiery dove]

it’s coming back to me sort of

[fossil locust]

and yeah

[fiery dove]

awesome thank you so much!!

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[jovial geyser]

Need help

[muted mural]

Need help with what?

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[muted mural]

The more you say, the easier it is too help you

[wheat bough]

First, plot out each of the four missing points

Recall that each line on the number line represents an additional 1/4

Is this 4th grade math?

[jovial geyser]

There are many missing length for which there is no x on top

[wheat bough]

yeah there are 4

[jovial geyser]

Why question says only 4 lengths

[wheat bough]

it explicitly says on the paper

wdym

[wheat bough]

don't overthink it like that

just follow what it says on the paper

[jovial geyser]

I understand but how will u put x for the given length

[wheat bough]

the missing length without the x just means that there are no recorded lengths for those distances

[wheat bough]

Do you know how to plot numbers on a number line?

[jovial geyser]

Yes I do

[wheat bough]

Okay, first plot 2 3/4 on the number line

lemme write that a little better

$2 \frac{3}{4}$

[woven radish]

RamenNoodleMan21

[wheat bough]

plot that on the number line

[jovial geyser]

For this how many x I put on top

[wheat bough]

just 1

there is only 1 recorded distance for it

sorry I don't have any more time in my hands to help you anymore

try using the helpers command so other people can help you

good luck!

[jovial geyser]

Why one x

[devout snow]

@jovial geyser Has your question been resolved?

[jovial geyser]

Not yet

[misty crest]

stay here

what part are you stuck on

[devout snow]

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[devout snow]

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[hoary moon]

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

[hoary moon]

Is there any way to simplify the Area function?

I got inspired by @oak stump's work on analytical disk motion blur, but here’s the deal: I’m integrating u(x, y, t) / (b - a) from t = a to t = b. My approach involves turning the inequality condition in u into equality, solving for t, and getting two sets of solutions: A(x, y) + B(x, y, k) and -A(x, y) + B(x, y, k) (the first is larger)

Then, I compute n1 as the smallest k where the larger solution is > a, and n2 as the largest k where the smaller solution is < b. After that, I sum the areas for all intervals in between, excluding n1 and n2, and add the partial areas at n1 and n2. Finally, I divide everything by (b - a) and simplify

It works beautifully, but the function is way too long. Is there a way to make it more elegant?

[devout snow]

@hoary moon Has your question been resolved?

[devout snow]

@hoary moon Has your question been resolved?

[oak stump]

@devout snow shut up knitter

[devout snow]

@hoary moon Has your question been resolved?

[hoary moon]

<@&286206848099549185> I’m desperate. Heartbroken. Shattered into pieces, like glass dropped from the highest tower. Why? Because the world has conspired against me. Because fate, with all its cruel twists, decided to remind me how fragile I truly am. I sit here, staring at the remnants of what could have been—a dream undone, a hope crushed, a vision blurred. Why? Oh, why? My soul aches for an answer, but all I hear is silence.

[glossy sun]

Call 911

[gusty merlin]

Real

[glossy sun]

Talk to a trusted adult

[gusty merlin]

Post that on wattpad

[austere oriole]

Babe you need a snickers

[dusky coral]

You need to accept your fate

[formal delta]

I agree

[plucky bloom]

pray to God

He will answer you

[hoary moon]

Uhm… back to topic

Can you guys… please answer my question for me? Pretty please 🥺

[hoary moon]

<@&286206848099549185>? Anyone?

[iron kindle]

!15m

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[hoary moon]

Huh? I sent my question 2 hours ago, and no one’s answered? What do you mean, not 15 minutes? 😭

[iron kindle]

ping once

[hoary moon]

ohhhhh

[iron kindle]

but yeah at this point might aswell make a new channel lol

or close and reopen it

or reword it so that people are inclined to help you

[hoary moon]

.close

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[magic briar]

@iron kindle

[devout snow]

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[compact hawk]

Can someone help me here with 17,18 and 19

I mean 17,18 and 20*

[merry patio]

Let's do 17!

First of all do you know when a quadratic has real roots?

[slender mirage]

,rotate

[compact hawk]

Uhhh ●_● wdym? Do you mean like how to find the roots

[merry patio]

Yes how would you normally find the solutions to that equation

[compact hawk]

For me just quadratic formula If it's ax² + bx + c and if it's ax³ + bx² + cx + d I just do fraction of d/a

[merry patio]

Yes let's take the quadratic formula

It is asking us about the real solutions

that means whatever is inside that root must be positive

b^2 - 4ac must be positive or 0

[compact hawk]

Ok 👍 so how do we do this one since normally it's easy to find but I got confused when it said 4<a

[merry patio]

lets plug in what we know!

121 - 12ac > 0 or = 0

We want to know the maximum value for c!

[compact hawk]

Uhhh so c is around 10?

[merry patio]

not quite

because a > 4

[compact hawk]

Oh

[merry patio]

i mean the answer would technically be any negative huge number

im assuming it wants it positive

[compact hawk]

Oh wait c is 2 then

[merry patio]

and im assuming a is also an integer

[merry patio]

yes

[compact hawk]

Ohh tysm

[merry patio]

question was worded weird but im assuming this is what it's asking

[compact hawk]

Yea they always do that to confuse people

[merry patio]

since a > 4 and since im assuming a is a whole number, the smallest value of a to make c the biggest would be 5

[merry patio]

nah its just worded poorly

[compact hawk]

No like literally the whole point of this paper is to confuse people

They purposely make it worded poorly

And add symbols people probably never saw before

So more people fail

[merry patio]

its not confusing its just a bad question that doesnt rly mean anything

i could have said -1000000

[violet flower]

is the answer of 18 36

[merry patio]

oh its saying the maximum ig

so negative doesnt count

[compact hawk]

:v it says maximum value

[merry patio]

am stoopid

alright lets do 18 now!

[compact hawk]

How did you find the anwser to it?

[merry patio]

first of all what is a sector?

[compact hawk]

👍

[violet flower]

ok so first draw a sector

[merry patio]

and how do you find its perimeter

[compact hawk]

Uh ●_● 🥲

[compact hawk]

Okay done 👍

[merry patio]

great!

[compact hawk]

I had to check Google for this ●_●

[violet flower]

now write the radius as 4..

[merry patio]

oh all good!

[violet flower]

as given

[merry patio]

ill leave it to Pacifix!

[violet flower]

thankss

[compact hawk]

K done

[violet flower]

so noww

given the perimeter.. we can find ? right

[compact hawk]

Oh uh

[violet flower]

perimeter is just length of boundary

[merry patio]

note the perimeter sector is made out of radius + radius + the arc in between!

[violet flower]

tru

[compact hawk]

👍 so uh the arc is 18

[violet flower]

dope

now do u know the formula of length of arc

[compact hawk]

Uh is it (18+4+4)/2 for s

Then square root of s(s-a)(s-b)(s-c)

[violet flower]

huh :v

[compact hawk]

= area

[compact hawk]

🥲

[violet flower]

thats herons formula for area of triangle

this is a circle

[compact hawk]

🥲 idk then

[merry patio]

we want to find the angle of the sector in order to find the area

[violet flower]

we can derive it if you want

[compact hawk]

18 degree then?

[merry patio]

draw the whole circle!

first

[compact hawk]

Uhhh 👍

[merry patio]

sorry stealing it from here

[compact hawk]

Done

[merry patio]

alright

there is a very cool proportion

(2pi r)/(360) = (arc)/(angle)

[violet flower]

do u follow this unitary method

[violet flower]

oh yeah it fine

[merry patio]

we have the radius and the arc

and we would like to find the angle

[compact hawk]

Nope I have no idea what that even is 😭

[violet flower]

oh lol

[compact hawk]

So the area is 8pi over 360?

Oh wait pi over 45

[merry patio]

basically if you know that a whole circumference is 360 degrees, the proportion will be the same with arclength and the angle that forms

to find the area of the sector we can use proportions still!

you know that in 360 degrees the area is just a whole circe

so in a specific angle the area will be something else with still the same proportions!

[compact hawk]

Uh 🥲 I kidda have no idea what your saying

[merry patio]

(pi r^2)/360 = (area of sector)/(angle)

[violet flower]

[merry patio]

lemme draw it

[compact hawk]

Ty

[compact hawk]

I'm grade 7 🥲 I know I'm kidda dumb

[violet flower]

its like 5 toffee for 10 children so 1 toffee for 2 children

[violet flower]

oh its alr lol

[merry patio]

ugly citcle

[merry patio]

the area of the red thing / 360 degrees

is the same as

the area of the yellow thing / the yellow angle

cool proportion!

so if you know the angle

you can find the area of the yellow thing

problem is we dont have the angle

[compact hawk]

Ye how do we find it

[merry patio]

and this is where we can also use the other proportion for circumference and arc length

we know that

the length of the red thing / 360 degrees

is the same as

the length of the yellow ARC ONLY thing / yellow angle

[violet flower]

just plug the theta / 360 value from arc length formula into the area formula 🙂

[merry patio]

i like explaining it with proportions easier to visualize

[merry patio]

ratio is always the sameb

[compact hawk]

So the length of the circle divided by 360 is the same as the sector divided by its angle?

[merry patio]

only the lenght of the arc

yes

not including the radius that makes up the sector

[merry patio]

drew it lower to not overlap red and yellow but theyre on top of each other

[violet flower]

do u know about unitary method like.. if we have 10 chocolates for 5 children how much each child get if distributed equally

chocolate is length here and children is theta (angle)

[compact hawk]

Length = 18 so using the atc length formula it's 18 = theta

18 = 4 theta

So theta is 4.5 radians

[merry patio]

idk where that came from tbh

[compact hawk]

Same

[merry patio]

2pi r is 8pi

8pi/360 = 18/x

[compact hawk]

Cus pacifix said something about arc length formula

[merry patio]

x is the angle

[compact hawk]

So I went online to check rq

[merry patio]

and then you can use that angle to find the area

pi r^2 is 16pi

16pi/360 = A/x

we can find A from here!

[violet flower]

hii

[merry patio]

bro gonna get jumpscared by integrals

[compact hawk]

So uhh it's 2 pi over 45?

🥲

[merry patio]

A is x * 16pi/360

x is also 18 * 360/8pi

so A = (18 * 16pi * 360) / (8pi * 360)

[merry patio]

cancelling everything

we get that the area of the sector is uhhhh 36 yea

[compact hawk]

Uh 36 pi?

[violet flower]

[merry patio]

no pi

[compact hawk]

Oh wait pi got canceled

[violet flower]

36 units

[compact hawk]

Oh so 36

[merry patio]

think thats correct right

[compact hawk]

●_● that took quite a long time

[violet flower]

how do they give that question to u without teaching you the formulas?

[merry patio]

did you understand the process i did though?

[compact hawk]

Yes (maybe)

[compact hawk]

Uhh the thing is I'm grade 7

We learn this at grade 10 and above

I'm entering a competiton across Asia

So like yea ●_● basically im learning something 3 - 5 years ahead

Cus there's grade 10 - 12 questions here

[merry patio]

proportion

Area of circle in 360 degrees
Area of circle/360

same ratio as
Area of sector/angle of the sector

same thing with circumference and arc length

[compact hawk]

I just went to memorize the method pacifix was talking about eariler ●_●

Cus eariler I couldn't understand it

[merry patio]

not a fan of memorizing tbh

[compact hawk]

Then after u explain it became easier to understand

So I was able to understand the method and memorize it

[merry patio]

if you understand the thought process behind you dont even need to memorize it as long as you remember the formula for circumference and area of a circle

[compact hawk]

Same but oh well

[compact hawk]

I memorize it just in case

[merry patio]

sure!

[compact hawk]

Cus if in the competiton I forget it then I just wasted 100+ hours

Cus for the competition you have to get 100% or you fail

[violet flower]

💀

u should get to know the theory first

[merry patio]

damn

oh yeah i was using degrees but if you used radians the formula is a little different but still the same

[compact hawk]

Uhhh that's what im doing rn ●_● I spent like 80% of the time understanding everything

Even tho I alr memorize the formulas I js took the time to understand everything

[merry patio]

because 360 = 2pi and stuff might simplify

[compact hawk]

So I can use it in the future not js now

[violet flower]

good luck for exams

[merry patio]

gl!