help-0

[glacial hedge]

I took the laplace transform

getting

$Y(s^2+2s+2) = 1 - e^{-{pi}s}/{s^2+1}

$Y(s^2+2s+2) = 1 - e^{-{\pi}s}/{s^2+1}

$Y(s^2+2s+2) = 1 - e^{-{pi}s}/{s^2+1}$

GRRRRRRRRR

$Y(s^2+2s+2) = 1 - \frac{e^{-{\pi}s}}{{s^2+1}}

$Y(s^2+2s+2) = 1 - e^{-{pi}s}/{s^2+1}$

iOSAdhLKSADJLKKJSAdkfDKJSFj

[chilly zodiac]

can anyone help me with this?

[glacial hedge]

$Y(s^2+2s+2) = 1 - \frac{e^{-{\pi}s}}{{s^2+1}}$

[ocean seal]

Elonmosqito96

[alpine sable]

I'll take a look

Is it diophantine?

[glacial hedge]

ahem

[deft python]

Do you guys know what is the difference of linear and quadratic equation

[glacial hedge]

this is a linear equation...

[chilly zodiac]

yeah just a linear equation system

[glacial hedge]

So just solve it with substitution or some other method of like idk gaussian elim?

[chilly zodiac]

whats the quickest method for solving these kind of exercises in a small amount of time

ive been sitting around solving this for like 20 mins already

[alpine sable]

Ok I do not fully understand how to read the symbol on the left, I understand the definition.

It look like some form of enumeration of sets non fancy M.

[ionic jewel]

guassian elimination

specifically matrix rref-ing

[alpine sable]

cramer's rule.

[deft python]

Wait

[ionic jewel]

that's just gauss elimination but you have to memorize stuff

[alpine sable]

yeah but he said quickest

[ionic jewel]

true you aren't wrong, but it falls apart as soon as it isn't 3 var 3 eqn

you know what fair enough, that's probably the quickest way to do it without a computer, given you have it memorized

[deft python]

What is the meaning of coefficient?

And constant also

[alpine sable]

a constant what is multiply by a variable. Tho I am pretty sure they exist a rigorous definition for it.

[deft python]

Oh

ty

2x^2 - 3x + 6 = 0 please answerrrr

[chilly zodiac]

thanks, ill look into it

[alpine sable]

complete the square, quadratic formula etc.

[ionic jewel]

coefficient is what's multiplied by the variable, a constant is just a value that doesn't/can't change

[glacial hedge]

WHAT AM I doING WronG WITH THIS PROBLEM
I Took the laplace transform
$s^2Y-1 +2sY + 2Y = -\frac{e^{-\pi s}}{s^2+1}$
$Y = \frac{1}{s^2+2s+2} - \frac{e^{-\pi s}}{(s^2+1)(s^2+2s+2)}$

$s^2Y-1 +2sY + 2Y = -\frac{e^{-\pi s}}{s^2+1}$

$Y = \frac{1}{s^2+2s+2} - \frac{e^{-\pi s}}{(s^2+1)(s^2+2s+2)}$

[ocean seal]

Elonmosqito96

[glacial hedge]

And the second term i have no idea how to take the inverse laplace transform of

<@&286206848099549185> ?

[stable merlin]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[stable merlin]

How do I solve this:

1/x + 1/y = 1/4```

<@&286206848099549185>

Sorry if it doesn't make sense I had to translate it

[oak chasm]

@stable merlin Add the fractions on the left.

[stable merlin]

I organized it to come out like 4x + 4y = xy

But dunno how to proceed

A hint says to make an equation about a single variable

[oak chasm]

Well, you have 4(x + y) = xy

[stable merlin]

and then

yeah ive not solved a question like this before

@oak chasm So uh what do I do after?

[vale wigeon]

just out of curiosity

[stable merlin]

yes?

[vale wigeon]

how familiar are you with the concept of completing the square in algebra?

there's a similar but different technique that can be used here

[stable merlin]

yeah no im learning math in a different language

aka korean

middle school

[vale wigeon]

oh god

uh

ok forget about that for now

so you have $xy - 4x - 4y = 0$.

[ocean seal]

Ann

[stable merlin]

yes

[vale wigeon]

now

if you have a particularly keen eye

[stable merlin]

No

[vale wigeon]

you may notice that expanding (x-4)(y-4) will yield something very similar to the left-hand side of that equation

namely, $(x-4)(y-4) = xy - 4x - 4y + 16$

[ocean seal]

Ann

[stable merlin]

im kind of too dumb to do that

ive just learned "the system of equations" as google translate says

the one where question gives you two equations with same variable value

@vale wigeon please help...

[vale wigeon]

...i'm trying to look up the korean name for something

hold on

[stable merlin]

my god this worksheet has so much difficult questions

ill give you a picture

nevermind idk how to take picture on a mac

[vale wigeon]

okay so

are you familiar with the distributive law, or 분배법칙 as it's known in korean?

[stable merlin]

yes

[vale wigeon]

okay great

[vale wigeon]

so you understand how this is true, right?

[stable merlin]

no

[stable merlin]

I understanded to that point

nothing after

[vale wigeon]

...

what happens if you apply the distributive law to (x-4)(y-4)?

[stable merlin]

x-4 X y-4 would be...

darn it

uh

[vale wigeon]

don't use the letter x for multiplication, please.

[stable merlin]

1. Then what should I use?
2. Can't caluclate that.

why did my teacher give this to me

[vale wigeon]

if you want a symbol for multiplication, use *

...this is going to be difficult

as in

[stable merlin]

yes it will and i have swimming in 10 minutes so thats bad

[vale wigeon]

oh no

go do your swimming then

10 minutes won't be enough

[alpine sable]

i can take over ann

[stable merlin]

shoot

[stable merlin]

-4x + xy - 4y + 16

xy - 4x - 4y + 16 = 0

equals 0 right

[vale wigeon]

no

we didn't say (x-4)(y-4) = 0

[stable merlin]

😦

[alpine sable]

xy - 4x - 4y + 16

I got it to that

[vale wigeon]

i was trying to suggest considering the expression (x-4)(y-4) in its own right

the equation we actually have is xy - 4x - 4y = 0

i would then continue by saying to add 16 to both sides,
to get xy - 4x - 4y + 16 = 16,
and so (x-4)(y-4) = 16

[stable merlin]

nvm

this is sad

alright ill do this 5 hours later then cya

[dull wedge]

how do I use the harmonic number formula into the recurrence formula?

[split oriole]

Can you check what T(2) is ?

[dull wedge]

I believe
T(0) = 0
T(1) = 7
T(2) = 17.5

[split oriole]

Juts write it like T(2)= t(0)+t(1)/2=7/2

[dull wedge]

• 7n

[split oriole]

Ohh yes

My bad

[dull wedge]

T(2) = (T(0) + T(1) / 2) + 14

[split oriole]

7/2+14=7+28/2 or 35/2

Next t(3)

We want to see some pattren

[dull wedge]

T(3) = (T(0) + T(1) + T(2) / 3) + 21

[split oriole]

Not 2 it will be 3

In deno

[dull wedge]

oops

yea

T(4) = (T(0) + T(1) + T(2) + T(3) / 4) + 28
for the next...

[split oriole]

This will get complicated

[dull wedge]

I can see that it's the sum of i=0 to n-1 for T(i) but why exactly is that related to the harmonic number thing?

[jolly stone]

Since we have T(n) = something of sum(T(i) from i=0 to n-1), we can find T(n-1) = something of sum(T(i) from i=0 to n-2)
and then we can replace sum(T(i) from i=0 to n-2) into T(n)

probably a very big hint but you can manipulate and make T(n) only depend on T(n-1) + some function

[dull wedge]

Doesn't quite click...

What you described was shown in a very similar example

but uh

[jolly stone]

we have the formula T(n) = 1/n * sum(T(i) i = 0 to n-1) + 7 * n

[dull wedge]

Why it's related to the harmonic number thing I can't understand

[jolly stone]

that term sum(T(i) i = 0 to n-1) = sum(T(i) i = 0 to n-2) + T(n-1)

you will see why you need harmonic number when you derived T(n) = something of T(n-1) + some function

[dull wedge]

tfw it's more or less to what they showed here in the slides

just can't make that link of replacing the recurrence terms with the harmonic thing

seems arbitrary and random

[jolly stone]

is this a different problem?

[dull wedge]

yeah slightly

different constants only

[jolly stone]

yeah what they showed was pretty non-intuitive

[dull wedge]

What's the thinking / reasoning behind swapping the terms with the harmonic thing

or rather redefining them in terms of the harmonic

[jolly stone]

but firstly, we have T(n) = whatever * [T(1) + T(2) + ... + T(n-1)] + whateverver right

[dull wedge]

Yeah that i get

[jolly stone]

and T(n-1) = whatever * [T(1) + T(2) + ... + T(n-2)] + whateverver

[dull wedge]

yeah

makes sense

[jolly stone]

you see the term T(1) + T(2) + ... + T(n-2) right?

[dull wedge]

mhm

[jolly stone]

that term can be replaced as T(n-1) + some stuff

into the original recurrence T(n)

[dull wedge]

Yeah

[jolly stone]

yep

[dull wedge]

That's just like telescoping right

[jolly stone]

kinda yep

just this case you directly substitute the finite sum into some term you know

[dull wedge]

yur

I just can't see how it's equal, the T(0) ... T(n-1) == Harmonic number sum

Am I overlooking something

[jolly stone]

nope T(n) is not H_n

spoiler: T(n) = 14 * n - 7 * H_n

wanna work through on how?

[dull wedge]

what do you mean

[jolly stone]

this is the answer btw, not exactly H_n

or you wanna know why H_n in this recurrence?

[dull wedge]

Yeah I wanna know why

[jolly stone]

have you done T(n) = something T(n-1) + something?

[dull wedge]

I could just brainlessly solve it just like the slides showed me

but I want to understand it

[jolly stone]

so your work is basically the same as the slides?

[dull wedge]

Nah haven't started to work on it

Want to understand why the recursively defined terms

[jolly stone]

you should try that first and you will eureka along the way

[dull wedge]

can be replaced by the summation of i=0 -> n-1 for i^-1

[jolly stone]

i dont quite understand this question

[dull wedge]

so essentailly

you can rewrite that reccurence as this

but I don't understand why you can do that

[jolly stone]

why you can write as summation?

you mean that?

[dull wedge]

yeah

[jolly stone]

well it's a summation from i = 0 to n-1

im not sure what point you're confused

[dull wedge]

oh wait

true

rather

why is it connected to the harmonic number thing

is that just a red herring

[jolly stone]

well a big spoiler but it's from 7*n term

[dull wedge]

i'm working through it now

[jolly stone]

yeah should try that first

[silver current]

help

[shadow mango]

Do you know how to rationalise the denominator?

[silver current]

yes

[shadow mango]

cool so let's start off by rationalising the first term

or have you made any progress with this problem so far?

[mossy agate]

i think it should be root(46)

not the value of s

but instead of root(47)

[silver current]

Thats confusing yes

[shadow mango]

hmmm valid
I'm assuming it's a typo

[silver current]

im trying

[shadow mango]

When you rationalise $\frac{1}{\sqrt{1}+\sqrt{4}}$ what do you get?

[ocean seal]

Mochi

[mossy agate]

rationalise each term and add

all except for first and last should get cancelled

[silver current]

root(1) - root(4)/ -3

[shadow mango]

yup that's right

[mossy agate]

now do this for every term

[shadow mango]

If you rationalise the other terms you'll notice that they all end with a common denominator of -3

[silver current]

got it

Thanks

[dull wedge]

I've arrived at T(n) = 7 * H_n

[ebon finch]

As $x\to 0, \sin\left(x\right)\to x \ $ and as $x\to\infty, \frac{1}{x}\to 0$.
$\ \therefore$ as $x\to\infty, \sin\frac{1}{x}\to\frac{1}{x}$.
$\ \implies\lim_{x\to\infty}\left(x\sin\left(\frac{1}{x}\right)\right)=1 \ $
Is this a correct proof (like the $\sin\left(x\right)\to x$ part)?

[ocean seal]

VardhanR

[jolly stone]

does it make sense with T(2)?

nope so something went wrong

[dull wedge]

Wait how wouldn't it make sense with T(2)

[silver current]

my answer's 2

[jolly stone]

your T(2) was 17.5 right? but 7 * H_2 = 10.5

[dull wedge]

o

[shadow mango]

that's right

[silver current]

thanks for the help

[empty portal]

I hate math

Im really bad there

Math sucks

Who agree?

[alpine sable]

so
shifting equations
the constant is just shifting the y value
but to shift the x value you replace x with x- something. can someone explain why

why, not how

[dull wedge]

I'm getting very close, Got T(n) 14 * n but can't work out the other side of the equation... something * H_n

Can't spot the pattern haha

[jolly stone]

if you need help detecting bug you can show me your current work

[dull wedge]

mostly the last couple of lines

and the numerator of those fractions

[jolly stone]

yep the last three lines are

but yeah you got T(n) = T(n-1) + 7*(2n-1)/n

simplify and you get 7*(2n-1)/n = 14 - 7/n

that should be easier to deal with

[dull wedge]

true

[jolly stone]

this should be straightforward:
T(n) = T(n-1) + 14 - 7/n
T(n-1) = T(n-2) + 14 - 7/(n-1)
T(n-2) = T(n-3) + 14 - 7/(n-2)
...
T(1) = T(0) + 14 - 7/1

[dull wedge]

hmm I'm stil getting like

T(n) = 14(n - 1...2...3) - 1/ harmonic

[jolly stone]

hmm how?

[bleak meadow]

Hey is this channel occupied?

[dull wedge]

oh wait

I can do one more simplification first

xD

[jolly stone]

that thing 7(2n-1)/n is not a harmonic term

[fair socket]

very easy question that i am lazy to do right now, i have 6 years so how much will have to study to complete 40 hours of study in 6 years?

[jolly stone]

so yeah you definitely need to simplify

[bleak meadow]

Was looking at a year 9 test

This is one of the questions

However

I’m a bit confused on 21 c/d

Anyone mind helping

[fair socket]

guys please help me i am too tired

[bleak meadow]

It says if x=8 and the output =70 find y

[dull wedge]

Ah, I got it thanks. I see how using the harmonic thing allows you to subtract terms to get that (n-1) thing but I still don't quite see how you're meant to know to put the harmonic thing into the recurrence in the first place

[stable merlin]

Like how

[jolly stone]

[stable merlin]

What's the question

[fair socket]

please help me my mind is draining

[bleak meadow]

This is the formula to work out the question however the question is if x=8 and the output = 70, find Y

[stable merlin]

Make an equation I guesS?

[bleak meadow]

Such as?

[stable merlin]

are you looking at the top one

or the bottom one

[bleak meadow]

Top one

[stable merlin]

or nevermind

[bleak meadow]

That’s the formula

[stable merlin]

ok

$3x * 2y + 3y - 4x$

[ocean seal]

garodueng

[stable merlin]

@bleak meadow

[bleak meadow]

uh

huh

[stable merlin]

@bleak meadow Also you can't solve an algebra without the right side

or whatever you call the thing

[bleak meadow]

My first guess was to work backwards

Start with the output which is 70

[stable merlin]

What's the full equation lol

oh I see

[bleak meadow]

The answer is 2 but I don’t know how to get 2

[stable merlin]

alright

you don't know how to solve an equation?

algebra*

$3x * 2y + 3y - 4x = 70$

[ocean seal]

garodueng

[stable merlin]

right?

[bleak meadow]

i do

[stable merlin]

Basically, put 8 in the x position

and solve it

[bleak meadow]

Wha-

[stable merlin]

So it would be

[ocean seal]

garodueng

[stable merlin]

Which comes out to be:

[bleak meadow]

uh

[pearl fern]

what's the question?

can u tag it

[ocean seal]

garodueng

[stable merlin]

and its easy now

[bleak meadow]

@pearl fern

[bleak meadow]

I’m still confused

[stable merlin]

x is a variable, it can be changed

put 8 inside the x

[bleak meadow]

8x

[stable merlin]

no

x = 8

[pearl fern]

put x = 8 bro

[stable merlin]

my brain

wants to teach you

but im too dumb to teach

[bleak meadow]

im dumber

[stable merlin]

x = 8 right? put 8 instead of x

[bleak meadow]

8 = 8

??

[stable merlin]

mhm

[bleak meadow]

Uh

[stable merlin]

x is equal to 8

[bleak meadow]

Yeah

[stable merlin]

so you can put 8

inside where x is

[bleak meadow]

ah I see

[stable merlin]

3x -> 3 * 8

or 3(8)

[bleak meadow]

24

[stable merlin]

yep

[bleak meadow]

ah

[stable merlin]

'Zat good enough explanation?

[bleak meadow]

Yeah

So how do I go about it from there

[stable merlin]

or are you hungry for more

[bleak meadow]

Yes

[stable merlin]

ok so you ar

so change every x inside the equation

multiply the coefficient with the value

aka

if 3x

and x = 8

[bleak meadow]

Right

[stable merlin]

3 * 8

[stable merlin]

make that for every x

[stable merlin]

try to make it like this

and i have to do my algebreic homework now

[bleak meadow]

8(3) * y(2)

[stable merlin]

just ping me when you need me

[stable merlin]

yes, but not with the y

[bleak meadow]

oh k

why

[stable merlin]

but it is same

[bleak meadow]

I don’t know what the variable is

[stable merlin]

so it doesnt matter

variable is x and y

[bleak meadow]

The

Number

What’s the mathematical term

For the number

Before a variable

[stable merlin]

coefficient is 3, 2, 3, and 4.

[bleak meadow]

ah

Thanks

[stable merlin]

constant is 70

[bleak meadow]

kk

[stable merlin]

woo im ready for middle school math

in united states

if i ever go there

[bleak meadow]

How old are you

💀

[stable merlin]

oh im 13

im in the 6th grade

[bleak meadow]

Nice

[stable merlin]

learning 8th grade math

[bleak meadow]

Nice

[stable merlin]

which is driving me crazy now

aw shit 30 minutes of work gone

[hollow swift]

Wow

I'm also 13

[stable merlin]

nice

tbh the most helpful thing in math

is learning how to code

basically teaches you stuff you'll learn later

but more fun

[bleak meadow]

3(8) * 2(y) + 3(y) - 4(x) = 70

[stable merlin]

now im back to my equation: how the frik do I solve 1/x + 1/y = 1/4

I came to 4(x + y)= xy

nothing further

[bleak meadow]

Are you trying to find x

or y

[stable merlin]

im trying to find both

as a set

[bleak meadow]

Ah

[hollow swift]

You can't solve that with one of it

[stable merlin]

you can

[hollow swift]

It's have infinity value

[stable merlin]

it actually doesn't when there is a requirement

it has to be an integer

[bleak meadow]

@stable merlin I got this

[stable merlin]

for my question

[hollow swift]

Oh

[stable merlin]

= 70

[bleak meadow]

3(8) * 2(y) + 3(y) - 4(x) = 70

[stable merlin]

change the x with 8

and then rest is just like solving algebra with one variable

MATH SUCKS

aafaaasfadfads

my brain

my time

my hand

[bleak meadow]

3(8) * 2(y) + 3(y) - 4(8) = 70

[stable merlin]

= 70

24 * 2y + 3y - 32 = 70, move the constants to the right, then calculate

make sure you multiply 24 with 2y

and add minus signs

[bleak meadow]

Why to the right

[stable merlin]

to organize it

[idle rune]

how am i supposed to right 1° inside the rays

[bleak meadow]

How do I do that though

[stable merlin]

24 * 2y + 3y = 70 -(-32)

48y + 3y = 70 + 32

51y = 102

y = 2

done

[bleak meadow]

.

Why did it become 70 - (-32)

[hollow swift]

You have infinity solutions

[idle rune]

can someone answer?

[hollow swift]

1 degree?

[stable merlin]

sorry, 2 requirements.

[idle rune]

yeah

[hollow swift]

It’s very small

[idle rune]

yeah

[stable merlin]

• must be natural number
• you have to count them

[idle rune]

how to right 1° inside its ray

[stable merlin]

use a compass lol

[idle rune]

?

[bleak meadow]

@stable merlin

[hollow swift]

But it’s very small

[stable merlin]

we moved the constant to the right

[bleak meadow]

Yeah

Meaning it’s -32

[stable merlin]

BUT

you change the sign

[idle rune]

then where to right 1° @hollow swift

[bleak meadow]

Why is it 70-(-32)

[bleak meadow]

Yeah

Where’s the 70- from

[stable merlin]

its

[hollow swift]

Write it somewhere

[bleak meadow]

It should just be -22

32

[stable merlin]

70 -(-32) = 70 + 32

[idle rune]

oh

outside the ray?

[bleak meadow]

Yeah

A minus and a minus make a plus

[stable merlin]

yes

[bleak meadow]

but I still don’t get why

It’s 70-

Where do you get that from

[stable merlin]

ITS

[bleak meadow]

YES I KNOW

[stable merlin]

70 -(-32)

not 70-

[bleak meadow]

-1(-32)

[stable merlin]

yes

that works too

[bleak meadow]

WHY IS IT - OUTSIDE THE. RACKET THOUGH

[cloud olive]

Hi

[stable merlin]

BECAUSE

yes

[bleak meadow]

It’s just like that?

[stable merlin]

hold on

look at this

[bleak meadow]

kk

[stable merlin]

lets say there is an equation called x + 10 = 20

[bleak meadow]

Yes

[stable merlin]

in order to move it

you have to do this

x = 20 - 10

right?

[bleak meadow]

Yes

[stable merlin]

it's a rule that you put brackets around negative numbers

well

its not a real rule

just a conventional one

just to get it organized

[bleak meadow]

x = 20 -(-10)

[stable merlin]

no

because 10 isn't -10

[bleak meadow]

but

you switched it to the other side though

so shouldn’t it be -10

[hollow swift]

@stable merlin

[stable merlin]

YES

[stable merlin]

thank you sir

[bleak meadow]

kk

[stable merlin]

i dont know how to

do that

[hollow swift]

🐧

[stable merlin]

though

ok ima cool my brain down

with a daily dose of roblox

[turbid harbor]

does that mean this channel is free? 😄

if so: im just practicing some integration by integrating factor, and im not really entirely sure what is happening in the circled area, but for context I should also add that I don't really know (dont think i've been taught, or if i did it was super briefly) what the meaning of d(x^-2y)/dx is, of course it's something to do with differential but i just dunnoooo what it means, or how the lecturer jumped from the first line in the circle to the second :))

[dull oak]

how do i do b and c

[turbid harbor]

do sketches of the triangles you should be able to figure out the height based on the angles and distances^

and dont forget the 200m between the two people, with one being directllly south (so making a right angle with the other person)

[stoic hamlet]

what does this symbol mean

[turbid harbor]

sum of

[stoic hamlet]

i dont get it

[turbid harbor]

sum of 2^1 + 2^2 + 2^3 + ... + 2^10

i THINK

[stoic hamlet]

so thats equivalent to

2^11

[turbid harbor]

unsure maybe

dont think so tho

[stoic hamlet]

yes it is

[turbid harbor]

welll sheeeyip

[turbid harbor]

HALP XD

<@&286206848099549185> can someone spoon feed me

OMG its because its the product rule, right? i think it just clicked 😂

still not entirely sure what this means other than maybe differential of mu.y?

ok yeh it definitely does, ok i think im sorted xd

[thin kayak]

can someone help w this?

[lyric ocean]

i need help

[red phoenix]

a?

[lyric ocean]

yea

[red phoenix]

well is a Real ^2 a Real? And is it always 1-many

[hollow swift]

I think 1) answer is 5

[red phoenix]

You know what the range is? It's the set where the function outputs to

[hollow swift]

I think it's 0 to infinity

[lyric ocean]

im not really sure

i have little understanding about domain

and range

i just got this homework

[hollow swift]

Range is the output of the function

So the question is to find possible answer of x^2

[lyric ocean]

i dont get it man

[hollow swift]

So you have to know where do x^2 can be

x^2 is always positive

[kindred herald]

It is (2^11 )- 2. Just see this as appending ten ones to the left of 0 in binary.

2^11 would be a 1 with 11 zeroes to its left.

[lyric ocean]

can ya solve itforme

[hollow swift]

Answer is [0,infinity)

[lyric ocean]

Thanks

[hollow swift]

Because x^2 can't be negative

[lyric ocean]

thats the range

?

[hollow swift]

Yes

[lyric ocean]

this is the second part from the samee question

[hollow swift]

fog and gof right?

[lyric ocean]

whats that

[red phoenix]

f o g and g o f is just a notation thing

meaning f(g(x)) or g(f(x))

assuming they are functions of x

[lyric ocean]

Oh

ive heard of that

but no clue about that

[lyric ocean]

can you help me get the awnser xD

[red phoenix]

so what it is, using f and g defined in the above picture?

[lyric ocean]

yeah

[red phoenix]

f(x) = x^2, g(x) = sqrt(4x-3)

so what is fg(x), well that is f(g(x)), which is f(sqrt(4x-3))

so whats a f(sqrt(4x-3))?

[lyric ocean]

fg?

how about gf

[red phoenix]

same process

[red phoenix]

substitute that sqrt(4x-3) into f

[sly nebula]

7x+3y = 10, 3x - 4y = 7
Do this math with the method of substitution?

I tried many times but cant plz helpp!!!

[vague coral]

write x in terms of y first

with the first equation

and sub the expression of x in the second equation

you'll be able to solve for y

[sly nebula]

I did but when goes to solve x it doesnt match

I said to my friends

[vague coral]

how ?

[sly nebula]

They also said

Cant

U try

Then comment

[vague coral]

3x - 4y = 7 --> 3x = 7 - 4y --> x = 1/3 (7-4y)

then 7(1/3 (7-4y)) + 3y = 10

and I solve for y

after this, when I find the value of y, I plug this value in the expression of x

there is no problem

[sly nebula]

Maybe i did mistake I wil dm u aftwr doing the math again k?

[vague coral]

k

[sly nebula]

U r description😑

[vague coral]

what

[sly nebula]

@vague coral

Why cant dm

@vague coral

Help me

😗

[vague coral]

oh I disable DM xd

cuz there is a lot of scam in discord these days

[sly nebula]

Oh

I cant post here my handwriting is...

[river radish]

this is a very simple question, how do i calculate the absolute error from this table?

i need the error from x

the anwser is apparently anywhere from 0.5 to 0.05cm

[finite scroll]

is anyone using this?

if not

need some help with this

[oak chasm]

@finite scroll Which parts?

[finite scroll]

from b onwards

i get a but i don't understand the rest

these are the answers

so im thinking that 3 red dics selected would be (6/10)(5/10)(4/10)

but that gives me 120/1000 = 3/25 which isn't right

[oak chasm]

OK, your numerators are right.

What does the denominator count?

@finite scroll

[finite scroll]

ohh

i see

i was keeping them 10

when it should have been 9 and then 8

thanks

[oak chasm]

You're welcome.

[finite scroll]

are you in uni?

[oak chasm]

No, I'm out of school.

[sly nebula]

Anyone

Here

To

Hlp

[finite scroll]

surely let me try

im not that qualified but im free

[finite scroll]

what was the question

[ivory otter]

Correct?

[oak chasm]

@ivory otter Nope. What's the probability of the first item they buy being defective?

[ivory otter]

0.2

so 0.2+0.2?

[oak chasm]

Nope.

Better to keep as fractions, so 2/10 = 1/5.

Let's do a case analysis right quick.

If the first is defective, at least one is defective.

If the first is fine but the second is defective, at least one is defective.

F = fine, D = defective

DF
DD
FD
FF

Those are the cases we have to cover.

If the first is defective, that's 2/10.

Now, how many items are remaining after the first?

[ivory otter]

8

[oak chasm]

Nope.

[ivory otter]

9

[oak chasm]

Right.

So, if the first is defective, how many defective ones are remaining after the first?

[ivory otter]

1

[oak chasm]

OK, so DD is 2/10 · 1/9

[ivory otter]

ye

[oak chasm]

Let's do DF.

How many items are remaining after the first is defective?

[steady arch]

i’m a junior in high school doing independent and dependent ik the equations i jus don’t know if they’re are independent or dependent can anyone help?

[oak chasm]

@steady arch Sorry, channel is busy.

[steady sequoia]

I need help on how to solve a union of set thingy on a venm diagram-

[oak chasm]

@steady sequoia Sorry, channel is busy.

[steady sequoia]

Ok

[ivory otter]

9

[steady arch]

so do i go to another one or jus get no help

[ivory otter]

another one

[oak chasm]

How many are left fine if the first is defective?

[steady arch]

ok thanks

[ivory otter]

8

the rest is fine

[oak chasm]

OK, so DF is 2/10 · 8/9

Now we do FD.

[ivory otter]

ok

[oak chasm]

How many are fine at the start?

[ivory otter]

0

[oak chasm]

No.

[ivory otter]

sorry

not 0 wow im stupid, its 8

[oak chasm]

How many are defective after the first fine is removed?

[ivory otter]

the defective has to be 0 no?

they are taken

[oak chasm]

Sorry?

How are they taken?

[ivory otter]

there are no defective anymore?

[oak chasm]

Sorry?

How are you getting that?

[ivory otter]

from DD and FD?

[oak chasm]

Yes, those are different timelines.

[ivory otter]

but why are they decreasing then

[oak chasm]

Decreasing what?

[ivory otter]

9 to 8

etc

[oak chasm]

We've never decreased from 9 to 8 on anything.

[ivory otter]

hmm

[oak chasm]

Let's start over.

What' are the possibilities for the first two choices if F = fine and D = defective?

[ivory otter]

DF ?

[oak chasm]

OK, what else?

[ivory otter]

i meant are we talking about DF first?

what first 2 choices?

[oak chasm]

No.

We're starting over.

Like completely over.

[ivory otter]

yes

[oak chasm]

What are the possibilities for the first two items if F = fine and D = defective?

[ivory otter]

ok i really dont understand the question :d

man idk why my brain is shut down

its tilting lol

[oak chasm]

Do you want to come back later?

Rest could help.

[ivory otter]

ok ill just walk around for few min drink water and stuff

can i ping u?

[oak chasm]

Sure.

[ivory otter]

thank you

[oak chasm]

No problem.

[rocky spindle]

hey i have a quick question

can x be negative?

like the whole sum

inside

negative

[small bear]

The sum inside mustn't be negative

meaning x+1>= 0

This is of course if we are talking in the set of real numbers

[oak chasm]

Yeah, and you can solve that inequality for x.

[rocky spindle]

so it automatically defines X domaine?

[oak chasm]

If that's the whole function, yes.

The part under the square root can't be negative, right?

So, x + 1 ≥ 0.

That makes it not negative.

Then solve for x.

That'll tell you what x can be.

Which is your domain.

[stable orbit]

k

[rocky spindle]

im using it on derivation expression

not function

[oak chasm]

OK, what are you differentiating?

[rocky spindle]

this is the expression

[oak chasm]

OK, why do you need the domain?

[rocky spindle]

so i should just ignore?

im supposed to find the function variations

using derivate is the way i think

heres the function

[rocky spindle]

i need to know the signs of this expression , that's why im asking about the domain

[oak chasm]

OK, so get the intervals where the top is positive and negative and zero.

Get the intervals where the bottom is positive and negative and zero.

Combine them.

[rocky spindle]

but can sqrt root be negative?

[oak chasm]

Sure, if you're fine with imaginary numbers.

[rocky spindle]

no im working on R only

[oak chasm]

OK, then no.

4x + 4 < 0
4x < -4
x < -1

4x + 4 = 0
4x = -4
x = -1

4x + 4 > 0
4x > -4
x > -1

3 - x < 0
3 < x
x > 3

3 - x = 0
3 = x
x = 3

3 - x > 0
3 > x
x < 3

So those are the intervals.

Now we combine them.

x < -1 has the top negative and the bottom positive, so the whole thing is negative.

x = -1 has the top zero and the bottom positive, so the whole thing is zero.

-1 < x < 3 has the top positive and the bottom positive, so the whole thing is positive.

x = 3 has the top positive and the bottom zero, so the whole thing is undefined.

[rocky spindle]

this i guess?

[oak chasm]

x > 3 has the top positive and the bottom negative, so the whole thing is negative.

So, nonnegative is fine.

So, which intervals were zero or positive?

x = -1 or -1 < x < 3

-1 ≤ x < 3

Does that make sense?

[rocky spindle]

yes

[oak chasm]

So get the regions for the signs on top. Get the regions for the signs on bottom. Combine them.

[rocky spindle]

so if the -1 is included , wouldn't the bottom equal 0?

[oak chasm]

What's the expression for the bottom?

[rocky spindle]

3-x

[oak chasm]

When is that zero?

[rocky spindle]

but on the derivation its sqrtroot (x +1)

[rocky spindle]

3

[oak chasm]

That's not the derivative of sqrt((4x + 4)/(3 - x)).

[rocky spindle]

https://tenor.com/view/breaking-bad-walter-white-gif-20348263

so the expression was wrong this whole time

let me redo

[dense snow]

is this channel free right now?

[rocky spindle]

yes

[dense snow]

ok

Can anyone do this? I only need to find CF

[warped phoenix]

how am i supposed to know if this is a vertical or horizontal stretch if there are no parenthesis?

am i simply to assume that it's vertical if there are no parenthesis?

[oak chasm]

@warped phoenix Factor out the x coefficient from the whole expression.

Oh, they're doing it as a stretch followed by a translation.

So, the stretch is 3 times the magnitude.

Then it moves it up 2.

f(x) = x
Stretch it 3 times as large:
f(x) = 3x
Move it up 2:
f(x) = 3x + 2

Assuming f(x) = x is the parent function.

[desert moon]

is open?

to confirm: Y = Y1 - Y2?

Y1 - Y2 in the theorem is equal to the Y that is the general solution?

uwu

[upbeat helm]

hi

[desert moon]

hi

[upbeat helm]

How do I know if two angles in a circle are subtended by the same arc?

[oak chasm]

Well, when will the arc lengths be the same?

[upbeat helm]

So this question

i know f must be 40

cause of the circle theorem stuff

[split oriole]

Half of 80

[upbeat helm]

but how are they subtended by the same arc?

[oak chasm]

OK, they're subtended by the same arc, not angle.

[upbeat helm]

typo

[oak chasm]

The lines of the angle hit the endpoints of the arc.

That's why each angle is subtended by the arc.

See how the lines of the left angle hit the endpoints of the arc?

The left angle is subtended by the arc.

See how the lines of the right angle hit the endpoints of the arc?

The right angle is subtended by the arc.

So, both angles are subtended by the arc.

[upbeat helm]

oh ok

so the one in the center

is times 2 the on that is on the circumfrence

[ivory otter]

@oak chasm Hi, can we continue?

[oak chasm]

Let's continue in #help-9.

[ivory otter]

ok

[main slate]

Hi, I haven’t understand a correction. If you can help me :)
Here they are talking about disjoint cycle but I don’t understand how they are finding (321) and why (321) is equal to (132)

(My first question is : i don’t understand why ((1)(23))(123)=(321)

[oak chasm]

OK, (321) means you convert 3 to 2, 2 to 1, and 1 to 3, right?

(132) means you convert 1 to 3, 3 to 2, and 2 to 1, right?

So, the same conversions are made, so the cycles are the same.

@main slate

(1) doesn't change anything. (23) converts 2 to 3 and 3 to 2. (123) converts 1 to 2, 2 to 3, and 3 to 1.

So, (1)(23)(123) first does nothing, then converts 2 to 3 and 3 to 2, then converts 1 to 2, 2 to 3, and 3 to 1.

So, we do this.

We start with each value.

Start with 1.

(1) does nothing to it. It's 1.

(23) does nothing to it. It's 1.

(123) changes it to 2. It's 2.

Start with 2.
(1) does nothing to it. It's 2.
(23) changes it to 3. It's 3.
(123) changes it to 1. It's 1.

Start with 3.
(1) does nothing to it. It's 3.
(23) changes it to 2. It's 2.
(123) changes it to 3. It's 3.

[main slate]

Aw yes, that s smart 😅

[main slate]

I m not sure to understand, I thought we needed to start from the right then go to the left…

Because with what u wrote the result is (12)(3), no ?

[oak chasm]

The standard is left to right.

,w (1)(2 3)(1 2 3) as permutations

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

We can do right to left if you wish.

1 goes to 2, which goes to 3, which goes to 3.
2 goes to 3, which goes to 2, which goes to 2.
3 goes to 1, which goes to 1, which goes to 1.

[main slate]

Yes but the final result is (12)(3) and we should find (321)…

[oak chasm]

(1 3)

[main slate]

Or (13)(2)

[oak chasm]

So, left to right, it's (1 2). Right to left, it's (1 3).

[main slate]

Yes

[oak chasm]

Neither is (3 2 1).

[main slate]

So there is a mistake in the correction ?

[oak chasm]

Yes, I think so.

[main slate]

Ok

[oak chasm]

After they got (3 2 1), that is equal to (1 3 2).

Because it converts the same way.

You can rotate a cycle.

(3 2 1) rotate one to the right (1 3 2) rotate one to the right (2 1 3) rotate one to the right (3 2 1).

It will remain the same cycle when you rotate it.

[main slate]

Yes I understand this part now

I ve looked again at the correction and yes there is a mistake

Because at the end they wrote smth which is different from what they found

Thanks a lot @oak chasm 👍

[oak chasm]

It looks like both left to right and right to left are used by different people.

You're welcome.

@main slate Ahh, I figured it out.

They're doing the individual cycles backwards, too.

(1)(2 3)(1 2 3)

We go left to right, but at each cycle, we go backwards.

[main slate]

Ah ok

[oak chasm]

So, 1 converts to 1, which converts to 1, which converts to 3.

No, even that doesn't work.

Never mind.

I don't know what they did.

[main slate]

ah ok ^^"

[oak chasm]

2 or 3 will always be unchanged, no matter what orders you go in.

(1) does nothing, so we have (2 3)(1 2 3).

Let's say the individual cycles go in standard order.

Left to right, we have 3 going to 2 and 2 going to 3, so 3 is unchanged.

Right to left, we have 2 going to 3 and 3 going to 2, so 2 is unchanged.

Let's say individual cycles go in reverse order.

Left to right, we have 2 going to 3 and 3 going to 2, so 2 is unchanged.

Right to left, we have 3 going to 2 and 2 going to 3, so 3 is unchanged.

So, any way you look at it, it's (1 2) or (1 3).

[main slate]

Ok

It s what I should have, the goal of the exercise is to find the matrix multiplication of S3

[umbral kindle]

Is x²= 0 a quadratic func, but if x=0 isnt it will not be a quadratic?

[oak chasm]

It's a quadratic equation.

f(x) = x² is a quadratic function.

A quadratic is based on all values of x, not just one.

[umbral kindle]

Oic

Thanks

[oak chasm]

No problem.

[stable orbit]

Can someone teach me how to do q21

[umbral kindle]

My f(x) will get a minimum value , so if -f(x) ,will I turn to maximum value?

[ionic jewel]

yea

[alpine sable]

Convert the whole equation into cosA and sinA then square it u will get quadratic equation in terms of cosA then find out cosA then find SinA using fundamental identity .

ok

I need some help

@alpine sable

[analog locust]

guys

[alpine sable]

you can help?

[analog locust]

why is the slope is equal to sqrt(x^2 + y^2)?

why is it not the sum of x + y?

hypotenuse* not slope sorry

[alpine sable]

Coz of Pythagoras theorem

[grave saddle]

Quick question. How useful is implicit differentation?

It seems kinda niche now that im learning about it

could I skip it without fearing any bumps in the future

[alpine sable]

Used in economics says google

[grave saddle]

Hm

[ionic jewel]

don't bother skipping it

[turbid harbor]

important

in engineering too

[ionic jewel]

it's super low effort compared to other stuff you do and it comes in handy sometimes

[turbid harbor]

its a building block rly

[alpine sable]

Used everywhere

Skip nothing

If you skip it, it will be on the test

[grave saddle]

Alright good clarification

and lol

[ionic jewel]

it's basically glorified chain rule

[alpine sable]

Golden rule

[grave saddle]

yeah thats why i felt like sorta skipping it

but alright. i wont. thanks

[ionic jewel]

nah just pick it up

another tool in the box

[alpine sable]

Happy to help

[grave saddle]

true:D

[flat halo]

What's going on here with the small x's and y's?

What kind of calculation is that?

[topaz scaffold]

It means either the x or y component

[flat halo]

What's that?

[glass lichen]

Are you doing stuff w/ vectors?

[flat halo]

Yes, I'm trying to learn vectors.

[glass lichen]

yeah, so the components of the vectors...

$A=[A_x,A_y]$

[ocean seal]

Mosh

[topaz scaffold]

A and B are 2 dimensional vectors

So they can be described with a x value and a y value

[flat halo]

Ok, so it's like the math way of doing that. I'm not super familiar with the math notations. I'm more familiar with how they are represented in programming languages.

[glass lichen]

this is more the comp-sci concept of vectors

[flat halo]

Really? Well, I've never seen it written like that before 🤔

[glass lichen]

Well.. how have you seen vectors written?

if not the standard array

[flat halo]

For example: Vec2(2,3)

[glass lichen]

yeah, that's the same

that has x component 2 and y component 3

[flat halo]

Yes, that's right.

This formula is about getting the dot product.

[glass lichen]

yes

[flat halo]

Another example was:

[glass lichen]

yes

[flat halo]

Which I don't understand at all.

[glass lichen]

that's the geometric definition

[flat halo]

With angles?

[glass lichen]

yes..

the angle b/w the 2 vectors

[flat halo]

I think I'll stick with the other one. It seemed easier to understand.

[topaz scaffold]

You'll want to know both

[flat halo]

They have different type of use?

[topaz scaffold]

Sometimes it comes in handy

[flat halo]

All right. Thank you for the tip.

Dot product seems rather complex. So I think I'll have to do a lot more reading before I have this figured out.

[glass lichen]

I mean.. wait til cross product

[flat halo]

I haven't heard of that.

[topaz scaffold]

Welp learn dot product first

[glass lichen]

[flat halo]

And of course there are pre-made method so I can do something like:

float d = b.Dot(a)

But I would much rather understand what is actually going on there.

Then I can use the methods with confidence that I know what it actually does 🙂

Thank you everyone. I think I can take it from here.

[topaz scaffold]

You need to get the normal force big enough so that the friction force can balance out the gravitational force

$F_f = \mu \cdot F_N$

[ocean seal]

RipeOrange

[topaz scaffold]

And you need $F_f = F_g = m \cdot g$