help-0

[alpine sable]

wdym

$x\lor y$

[vale wigeon]

in what context?

[alpine sable]

?

yeah depends on the context

@alpine sable can you show us where you found it

idk in general

just asking what a number and radical attached to each other means

maybe search up logical (inclusive) disjunction

you'll get more info about that

V

whats dat

search it up

x multiplied by the square root of y

[alpine sable]

yeah thats what i meant

Yeah we just use the radical sign (aka radical symbol, root symbol, radix, or surd)

idk if there are any other notations for roots

probably not

One's enough

[vale wigeon]

why is your tex background this eye-searing shade of raspberry

[versed prairie]

I've asked a question

Can smne answer it

..

[alpine sable]

Cause its a custom

[vale wigeon]

my retinae are suffering great pain as we speak

[alpine sable]

% \usepackage{xcolor}

\begingroup \def\begin#1{\endgroup\begin{document}\pagecolor{purple}\color{pink}} % LAST LINE OF YOUR PREAMBLE

[versed prairie]

🥲

[alpine sable]

I don't think its so eye cancer

[lost crane]

https://i.imgur.com/dLBXUYO.png
This is a collection of 50 measurments. Largest is 391, smallest is 221. Range is 170. I want to find the width of the class when I have 5 classes. Obviously its 10 per class but the equation range/#classes = class width gives me 34

Am I using the equation wrong? How can I find the width of classes?

[urban salmon]

What is the smallest number which when divided by 7, 8 and 9 leaves a remainder of 2, 4 and 6 respectively? How do i solve this one

[alpine sable]

@urban salmon 492

[gilded nova]

hello, I'd need some help with this limit

[alpine sable]

Find the LCM OF 7,8 AND 9
LCM(7,8,9) = 504
LCM(2,4,6) = 12
REQUIRED ANSWER = 504–12= 492.

[sturdy bay]

this can only be indeterminate compatible no? (the matrix to the right is just a bunch of independent elements together so u can do many at the same time, for example the independent elements for the first system of equations would be the (0 0) for the second the (1 1 ) and so on

[urban salmon]

but this method is wrong. It only works in a few cases

[sand star]

I am pretty bad at math.

If u have a string lets say: "myString"
and u can place a dot anywhere, but cannot have two dots next to each other, so:
"my.String"
"my.str.ing"

these would be valid but these:

"my..string"
"my..s.ss" would not be.

How would I make a formula to calculate the amount of possibilites

[sturdy bay]

dlscord

bruh

@fading citrus

[kindred lion]

Hes probably hacked

[sturdy bay]

<@&268886789983436800>

ye most likely

[urban salmon]

yes u did

[sturdy bay]

it's in every other channel too

[urban salmon]

its happening to a lot of people

[kindred lion]

Can any moderator just delete all these fake messages in all channels? Cos one might just click the link accidentally

[night geyser]

seems im the only one on rn

bleh

[alpine sable]

please help

[quartz oxide]

Do you know some basic modular arithmetic?

And, how do you express m directly in terms of a and b?

[alpine sable]

i do

[alpine sable]

a and b?

$m = 210^7 + x * 10^6 + 19210^3 + y*10^2 + 20 = 20192020 + 10^6 x + 10^2 y$

[ocean seal]

omeganebula

[alpine sable]

what next?

dividing 20192020 by 41 is sure to be tedious af lol

[radiant jasper]

Elon Sucks

[quartz oxide]

[quartz oxide]

Not sure but there doesn’t seem to be (at the moment) any better way than reducing all the terms mod 41

[earnest panther]

Note that you aren't concerned with the entire result of the division, but only the remainder. Therefore, when you apply mod 41 to the breakdown of the number as Omeganebula did, you can consider only the modulo 41 of each power of 10, and you end up with a sum of numbers made of a digit times a number between 0 and 40, which is much more feasible to deal with.

As an example, suppose you wanted to find out the remainder of 4x86 modulo 41. In this case, the breakdown of the number would be:
4x86 = 4 · 1,000 + x · 100 + 8 · 10 + 6 · 1
when applying modulo 41 on the breakdown of the number, we get:

4 · 1,000 + x · 100 + 8 · 10 + 6 · 1 mod 41 =
((4 · 1,000) mod 41 + (x · 100) mod 41 + (8 · 10) mod 41 + 1 mod 41) mod 41 =
((4 · 1,000 mod 41) mod 41 + (x · 100 mod 41) mod 41 + (8 · 10 mod 41) mod 41 + 1 mod 41) mod 41

and since:
1,000 mod 41 = 16 and 100 mod 41 = 18,
then you get:
(4 · 16 + x · 18 + 8 · 10 + 1) mod 41
or:
(18x + 161) mod 41 = (18x + 38) mod 41
which is more manageable to work with.

[crisp grove]

x-[x] is not surjective

[vestal needle]

Oh sorry for deleting

yh I’m trying to either show that it’s subjective or not surjective

But I’m having trouble finding the range

[steel oyster]

range?

[vestal needle]

For $f(x)=x- \floor{x}$

[ocean seal]

Mani

[steel oyster]

but it just equals the decimals of x?

[vestal needle]

Like I can think about it, it should be from 0 and 1, but can I find it algebraically?

[earnest panther]

I think the best way to show it is to say that for each value between 0 and 1 (not including 1), you can show an example of a number for which the value of f(x) = x - [x] will be that value.
For example, for 0.3, you can pick 2.3 which satisfies f(2.3) = 2.3 - [2.3] = 2.3 - 2 = 0.3.
For any other value, you can explain why the function can't achieve them.
(For example: Why can't a negative value be achieved? Why can't you achieve values equal to or greater than 1?)

[vestal needle]

Ahhh ok

That makes sense

Thanks!

[hasty crow]

hi @rustic harness

[rustic harness]

hi

[hasty crow]

how do I solve this

pls help 🙏

[alpine sable]

This is 5/4 correct?

[cyan grail]

i believe so

[stark trail]

Yea I also got 5/4

[orchid python]

can anybody help me?

[alpine sable]

find the animal population in the 4th and 9th year

then find the difference

that'll be the animal population increase in that certain time interval

[orchid python]

yeah I got it

how can I evaluate this

[crisp grove]

white the nominator in terms of A* d/dx(denominator) + B

separate out and u get a familiar form

[jolly stone]

straightforward u substitution

[tall phoenix]

Question Me A Question

[alpine sable]

what's last digit of pi?

[steel oyster]

But it's a transcendental number?

[tall phoenix]

any

[wary stream]

No

[alpine sable]

i was jk

how does these bot works?

[twilit venture]

Can anyone help me with logarithm questions

I am of class 9

[tall phoenix]

uh. uhhhhh don't chuuu Ignor meeeeeeee...

[alpine sable]

just post my g

[alpine sable]

got a q to ask?

[tall phoenix]

yeah

question me any question

[twilit venture]

Can u provide me some proofs of Pythagoras theorm

I want 4 atleast pls

[keen basalt]

Can anyone help me prove this mathematical equation??

[twilit venture]

Hey I know this

Which class r u??

[orchid python]

can you help me?

[keen basalt]

12th grade

[abstract prairie]

why is your book so dirty

il

whats a intergrate

[alpine sable]

integrate?

just means to find the integral of... (verb)

[abstract prairie]

yeah

yeah but whats a integrak

[alpine sable]

in loose words, you can find the antiderivative of an expression, which would be the expression that has been differentiated to get to the original expression

@abstract prairie

[abstract prairie]

yeah

im dutch so idk about that

plus im in like 7th or 8th grade idk how that system works but im just curious i want to learn math further

[alpine sable]

well i'd then recommend to go step by step if you really want to advance in maths on your own.

[abstract prairie]

ah alright

[wary stream]

Integral is a bit advanced for you, at this point in time

[abstract prairie]

where can i do that

[alpine sable]

e.g by following a course or by youtube.

[keen basalt]

Actually the book isn’t dirty, rather it’s ink print which I already found in the book after buying

[abstract prairie]

alright

[wary stream]

Khan Academy has good lessons

[alpine sable]

okay guys this might be the dumbest question ever asked here, but how did we get 16?

second equation

someone please explain

Divide everything by 4

Or factor it out and then divide whatever

4(16-(k-2)(k+4)) < 0
16-(k-2)(k+4) < 0/4

Makes sense?

why do we divide by 4

You dont have to

Just makes stuff simpler to calculate

64 - 4 shall be 60 right?

You can leave it look:
64-4(k^2+2k-8)

But you cant subtract 4 from it

You'd have to multiply each element by -4 in the parenthesis

oh okay wait lemme do it

If you have 6-2×3, you cant say 6-2 is 4 so 4-3 is 1

Yeah go for it

[orchid python]

I don't understand why dx=-du/5

[alpine sable]

du = -5 dx
Divide both sides by -5

[orchid python]

thank you

[alpine sable]

@alpine sable oh i got it

so

64 - 4
-4 gets multiplied by (k-2) and (k + 4)

and 16 * 4 = 64

and 4 divides with 0

right?

[jolly stone]

where are you stuck at?

[alpine sable]

@alpine sable 0 divides with 4

Im not sure where you're at exactly, did you decide to factor out and divide everything by 4 or not

$4×16-4(k^2+2k-8)<0$

[ocean seal]

Em

[alpine sable]

0 divided by 4 is 0

[rustic rock]

ye

rest

$16-(k^2+2k-8)<0$

[ocean seal]

mustapha56

[rustic rock]

then

[alpine sable]

guys

[rustic rock]

$(k^2+2k-8)<-16$

[ocean seal]

mustapha56

[alpine sable]

just reverse the chain rule

[rustic rock]

holly

$k^2+2k<-12$

[ocean seal]

mustapha56

[rustic rock]

then

$\frac{k^2}{2}+k<-6$

[ocean seal]

mustapha56

mustapha56

mustapha56

[deep panther]

https://gyazo.com/cb70e0a19386bc7b44e7bd176b3869a4 does this want me to multiply (n, i) by (1-t)

[rustic rock]

maybe

[orchid python]

what should I do with this question

[stable hound]

I am looking at numerical integration methods and came across weights. However, I am having trouble understanding what they actually are. Any help would be appreciated, thanks.

[astral dagger]

(\underset{t\rightarrow \infty}{\lim}~\int_1^t \dfrac{6,{\rm{d}}x}{\sqrt{x^2+9}})

[ocean seal]

SubGui

[astral dagger]

evaluate the integral and try to see if the limits gives you a number

if it gives you plus/minus infinity, then the integral diverges

or also something that does not exist

[alpine sable]

yes exactly this

thanks @alpine sable

[crisp grove]

bruh

[astral dagger]

[tall phoenix]

Ask Me Any Question I Will Answer.

[alpine sable]

4 + 4 = ?

[tall phoenix]

9

8

[alpine sable]

Oof

You are a semi genius

Pi = 3,14.. ?

[tall phoenix]

hmmm...

[alpine sable]

😂😂

[tall phoenix]

9365

[alpine sable]

pi has over 63.2 trillion digits and it took a supercomputer 108 days to calculate them all

[sudden crater]

Hi, I have a question

This is for context

Why is there an F’’(c)?

Didn’t they already choose to make it a maclaurin series

And so shouldn’t it be F’’(0)

[remote drift]

How can i see the source code of app

[alpine sable]

second derivative = unknown number c

[wary stream]

This is a math server. Ask in some programming server or Google that question. But honestly, most apps, the company that produced it, won't have the code online

[remote drift]

Thnx for info

[jolly stone]

you mean like android app? havent tried this but there might be a way to decompile apk file

i have no idea about ios app

oh it's iap file but no idea

[remote drift]

Tell me

[jolly stone]

which os you're talking about?

[remote drift]

What is it

[jolly stone]

ios or android

[remote drift]

Android

[jolly stone]

and mostly you wont get the full source code from decompiled version anyway

first you need apk of that app

[remote drift]

Oh

[remote drift]

Ok thn

[jolly stone]

as a package file, not just app

[remote drift]

Hmm

[jolly stone]

https://www.youtube.com/watch?v=VLsJETb3m4M

[remote drift]

Okk

Thnxx

[jolly stone]

can i ask what specific app you want the source code?

[remote drift]

Any app

[jolly stone]

no need to specify if you dont want to

[remote drift]

I am learning

How they work

About backend

[jolly stone]

oh you want the backend code? it mostly wont be in the source code

at most you will see what api routes the app sends the request, then receives response

especially the logic layer will definitely need to be on server side

[remote drift]

Oh

It is

It means source code and backend cide is different

[jolly stone]

if you really want to learn backend, you can learn how to do backend directly with web dev

yep

[remote drift]

Ok

Can u tell me how backend code is different from source code

[jolly stone]

"source code" is basically just a code, but if you want the code from the apk file, you will get the frontend code

frontend aka the thing you see up front (buttons, recyclerviews, navigationbar, etc)

for example, if i have an app with button that adds 2 numbers together, you will find the source code of that button that takes arguments, sends to server, waits for response, and displays the result

the backend code in the server side will handle that requests by performing actual logic, and sends result back to client side (your app)

[remote drift]

Backendcode keeps in server?

[jolly stone]

yep

[remote drift]

Ok

[wary stream]

This has gone way to much towards CS related then math

[remote drift]

I am still noov lol

[wary stream]

Just dm each other

Or go to #chill

[jolly stone]

i would suggest asking different channel actually, yeah was about to say that

sorry about that

[wary stream]

Or something

[remote drift]

Ok bro see you

[jolly stone]

if you want to continue, dont dm me, just #chill channel will do

[remote drift]

i am confused so i will ask later

Lol

[jolly stone]

any more info?

that doesnt look like the solution is unique

you can move point B around as you want as long as AB is still 12, the length CB always changes

so yeah if no info is given then there are infinitely many answers

[grizzled path]

you can

[jolly stone]

trace circle center at A, radius 12

that's all the location B can be

yep

now B is fixed at that point only, so yep there is 1 single answer

you know law of cosine?

notice that angle ACD = angle CAB

[alpine sable]

i dont know i quite get this

how can the bounds of a set A not be included in set A?

[crisp grove]

@alpine sable ex (0,1)

sup is 1 but 1 is not an element of (0,1)

[alpine sable]

oh because its an open interval right

[crisp grove]

hmm

[alpine sable]

wait what was the name of that

uh i think i got it now

TY👍

[crisp grove]

👍

[alpine sable]

When the question isn't hard but its just long

I made a mistake

ffs

[alpine sable]

Lmao i thought that was the solution for the triangle above

forgot to multiply the sinx by 1/4

either way someone asked before u

😭😭😭😭

above is similar triangles

[wary stream]

So? Someone asked a question before you, respect the rules of the server

[alpine sable]

dude I literally just said their question was similar triangles

[astral dagger]

remember polynomial remainder theorem

[alpine sable]

why are u getting so pressed im respecting the rules smh

[wary stream]

I'm not getting pressed, seems like you're getting upset because no one is helping you at the moment

[alpine sable]

I'm really not, i said their question was similar triangles and I'm willing to help them

however they haven't replied

[dense kite]

i got the answer already

[tough ice]

Can someone please explain the working highlighted here, how did he go from 1-x>0 to 1+x>=0?

[jolly stone]

divide into 2 cases: if the denominator 1-x > 0, then the numerator 1+x also >= 0

another case is 1-x < 0 then 1+x <= 0

[tough ice]

Ahh I see thank you

[jolly stone]

[alpine sable]

does anyone know why it is solved like this? I didn't understand it ;;

[small bear]

is there a specific part that is bothering you, or all of them?

[alpine sable]

I get b i), I kinda understand a) I think it refers to the units it moves to? but I have no idea about b ii) :(

[rustic rock]

k \in

[small bear]

b) ii) is all about the period of the function. As you know the period here can be easily calculated since we are given a maxima and a minima. The distance between the maxima and minima is 16-4=12, and the period will be 2*12=24

makes sense?

since the period can also be calculated as P=2 pi / |q| and we know what P (the period) is, we can find q easily

[alpine sable]

OHHHHHHHHHH

I'M so silly HAHAHAHAH

thank you so much!!!! everything makes sense nonw

[small bear]

No worries, I'd just comment on b) part 1 as well since there is an easier arguement

I mean the arguement in the picture is brilliant, however an easier method would be the following

since we know the maximum occurs at x=4 and is 18, the value of the functions p*cos(smth) + 10 will equal 18 only when p=8

the reason why is because the maximum value of cosine is 1, and we need to have 10+p*1 = 18

[alpine sable]

oh that makes so much sense too, thank you! I just used the formula and didn't know why it was like that at all, but it is so clear now :)

[green thicket]

what's the best way to study for a math quiz i have on monday

i barely understand the content

[alpine sable]

then see some online vids on it

then do the questions that you have on it

do enough qns for you to get a good amount of practise

[wary stream]

It doesn't disappear, it got factored

Like $$(x^2 + x) = x(x + 1)$$

[ocean seal]

dldh06

[wary stream]

I factored the GCF

Pulling out that GCF, and then divided by that GCF

In your problem the GCF was (x - 1)

[rustic rock]

yes

[wary stream]

Do you understand my example?

[wary stream]

.

Here

[glass lichen]

So you don't 100% understand factoring...

Yeah... so it isnt 100%

This is just factoring

[green thicket]

okay

thanks

[glass lichen]

You have ab-cb^2, clearly you can factor b out

Yes...

No

Where are you getting x?

Yes....

That's (x-1)(x-1)

Not x(x-1)^2

You factored it out.....

(x-1)(stuff)

It's just factoring

I have no clue what you just wrote, cause it's wrong

[desert moon]

-3(x-1)^2
-3*(x-1) * (x-1)
((-3x) - (-31)) * (x-1)
(-3x +1) * (x-1)

[glass lichen]

-3x-3

Don't cross-post

[alpine sable]

ok

[desert moon]

(x-1)^2 = (x-1) * (x-1)

[glass lichen]

They said they understand it...

[woven echo]

if it helps imagine the (x-1) is temporarily another variable

[desert moon]

a theorem for power series
one series may be substituted in another provided that the values of the substituted series are in the interval of convergence of the other seris
how is this substitution done?

[wintry wolf]

Hi guys whats (2x-3)²

Please

I keep finding 4x² + 12x + 9 but google says its 4x² - 12x + 9

[alpine sable]

its 4x² - 12x + 9

[wintry wolf]

How

[alpine sable]

if it were (2x+3)² then it would be 4x² + 12x + 9

but since there is a minus there, it's 4x² - 12x + 9

[wintry wolf]

But the 2 minuses cancel each other so its a plus

[alpine sable]

(2x-3)(2x-3) = 2x times 2x + (2x times -3) + (2x times -3) + (-3 times -3)

Does the null hypothesis assume two values are the same and only differing due to random error?

the minuses cancel each other out only in the last term

[wintry wolf]

I did it with (a-b)² = a² + 2ab + b² ill try with your method and see if it works

[alpine sable]

(a-b)² = a² + 2ab + b²
this formula is actually wrong

[wintry wolf]

Why

I mean -

[alpine sable]

it should be (a-b)² = a² - 2ab + b²

[wintry wolf]

I missclicked yea

[alpine sable]

the formula gives (2x-3)² = 4x² - 12x + 9

[wintry wolf]

In that formula b ls 3 or -3

[alpine sable]

b is 3

[wintry wolf]

Oh ok my mistake comes from that

[placid zinc]

Don't use a formula, use FOIL

[alpine sable]

yeah, np

[wintry wolf]

Thanks for helping

[placid zinc]

If you're just learning how to expand squared binomials

[wintry wolf]

What is foil

[alpine sable]

foil

[wintry wolf]

I have to use those formulas cuz of my teacher lol

[somber token]

hello guys

[wintry wolf]

Hi

[alpine sable]

wdym by FOIL

[somber token]

I am new in this forum

[alpine sable]

what's that an acronym of, is that something you learn in American schools?

[placid zinc]

Agreed, it may not be taught the same everywhere

Just a way to remember how to distribute something like the above

[placid zinc]

Wtf #help-0 has been empty for 20mins

[crisp grove]

wait let me bring my microscope

still can't read

[alpine sable]

can someone check

[crisp grove]

take the time to be t

[woven echo]

that sounds deep

take the time to be t

take some time to urself to become t

[crisp grove]

u need another variable to represent time

bcz in the mean time, the child will get carried by the stream while the boat approaches

i feel sleepy

<@&286206848099549185>

[restive glacier]

A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.75km/h. The child is 0.530km from shore and 0.775 km upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of 18.8km/h relative to the water, what heading relative to the shore should the captain take? 3.44*10^1 deg
What angle does the boat velocity make with shore?

[restive glacier]

<@&286206848099549185> Is this diagram correct for what angle does the boat velocity make with shore?

I dont know if i am reading the question wrong or if the diagram is incorrect, but I keep getting the wrong answer

[ancient saddle]

Hello, are you finding the angle in this instant? By doing that, you are considering that the child stays still in that position

Remember the child has a horizontal speed due to the river's drag

[restive glacier]

@ancient saddle oh but how would i show that on the diagram\

[north adder]

i dont think your diagram is incorrect

just, why cosine law?

wait have you done calc

[restive glacier]

yes

is there another method?

@ancient saddlei will draw the velocity triangle one sec

[fleet axle]

This is just a stats question im interested in if I have a list of numbers with mean 5 and i add 2 more numbers with a value of 10 how does that affect the variance?

[restive glacier]

channel is in use

[ancient saddle]

Oh I see now, Pandya's diagram is correct

I didn't notice the velocity of the boat was relative to the river

[restive glacier]

I still keep getting the incorrect answer

[ancient saddle]

Then this is ok, the angle must be the arc tangent of 0.53/0.775

,calc atan(0.53/0.775)*180/pi

[ocean seal]

Result:

34.367091016121

[restive glacier]

@ancient saddle I got that question. I need help with What angle does the boat velocity make with shore?

[ancient saddle]

oh, so there we use the actual velocity of the boat, not the relative one

so we have a vertical component of 18.8*sin(34.367) km/h

and a horizontal component of 18.8*cos(34.367) + 2.75 km/h

,calc atan(18.8*sin(34.367 *pi/180) / (18.8 *cos(34.367 *pi/180)+2.75))*180/pi

[ocean seal]

Result:

30.153283971869

[alpine sable]

Hi

I have one question

A relation

$f: \mathcal{M}{mxn}(\mathbb{R})\to\mathcal{M}{mxn}(\mathbb{R})$

Can be considered a function?

[ocean seal]

xd nope

[restive glacier]

@ancient saddle so it would be 30 degrees

[ancient saddle]

30.15 approximately

did you understand the vertical component?

[restive glacier]

I did

@ancient saddle thanks

[slim fog]

$\cross$

[ocean seal]

Welldunn Biff

[slim fog]

Do you mean $f: \mathcal{M}{m\cross n}(\mathbb{R})\to\mathcal{M}{m\cross n}(\mathbb{R})$?

[ocean seal]

Welldunn Biff

[restive glacier]

why

[slim fog]

why what?

[alpine sable]

Yes

I know that $f: \mathbb{R}^2\to\mathbb{R}$ is a function

[ocean seal]

xd nope

[alpine sable]

I think this type of relation isn't a function

[slim fog]

What’s M(R)?

[alpine sable]

The set of matrices with real coefficients

[sick scaffold]

would i distribute the negative or expand the (1+sqrtx) first?

[jade birch]

You'd expant the (1+sqrt(x))^2 first

[sick scaffold]

mind explaining why?

[jade birch]

It's the order of operations

Powers before multiplication

[sick scaffold]

i forgot a lot -_-

well thanks for the help

[jade birch]

np

[restive glacier]

It is opposing flow, so it should be -2.75km/h right?

[ancient saddle]

oh you are right, I didn't notice the boat was going upstream

[glass lichen]

dont crosspost

[restive glacier]

Thank you @ancient saddle it’s correct

[sick scaffold]

kinda confused on where to start on this one

[prisma dove]

I hope they are asking for distinct functions with this property

Because if so, it would be trivial

You could take f : R -> R to be T and f,g to be both the identity on R

If we want distinct functions tho

We can take $h(x) = \sqrt{x}$, $g(x) = \sqrt{1+x}$ and $f(x) = \dfrac{1}{x}$

[ocean seal]

MisterSystem

[sick scaffold]

they are asking me what f(x) g(x) and h(x) are

i think

[prisma dove]

No

Because they are not unique

Except if you like

Make some constraints

[sick scaffold]

um

[prisma dove]

Anwyays

[sick scaffold]

how did you get this?

[prisma dove]

Try to check this works

[prisma dove]

I just went for the most straightforward non trivial answer

So

Think about this

If you went to calculate T(x) at a certain value

What order of operations would you do?

Well

[sick scaffold]

i'm sort of lost here

[prisma dove]

First you would have to take the square root of x right?

[sick scaffold]

yea?

[prisma dove]

Then you would take sqrt(1+sqrt(x))

[sick scaffold]

so the first function is based on the OOO

[prisma dove]

Yeah, sort of

I am just trying to give you some intuition

On why I chose those functions

Because like

$f \circ g$ means that "you first do g and then f"

[ocean seal]

MisterSystem

[prisma dove]

So if you think about the order of operations

[sick scaffold]

so g(x) would be sqrt 1+x?

[prisma dove]

You have an order of "you first do this operation and then that one"

[prisma dove]

Yeah

Then you would take the inverse of the whole thing

And f(x)=1/x

[sick scaffold]

why is g(x) just sqrt 1+x and not sqrt of 1 + sqrt of x like in the original equation

[prisma dove]

Let's do this slowly

We want $(g \circ h )(x) = g(h(x)) = g(\sqrt{x}) = \sqrt{1+\sqrt{x}}$

[ocean seal]

MisterSystem

[sick scaffold]

so is g(x) sqrt 1 + sqrt x or just sqrt 1 + x?

[prisma dove]

What would happen if $g(x) = \sqrt{1+\sqrt{x}}$ ?

[echo geode]

🤯

[prisma dove]

Sqrt(1+x)

[echo geode]

_9€%$/8^"

wuttt

[ocean seal]

MisterSystem

[echo geode]

impossible

[prisma dove]

Try to calculate the composite g \circ h

[sick scaffold]

would you have a 4 root?

[echo geode]

im 13 and this is impossible

[prisma dove]

Yeah

But we want a square root

@echo geode Please, this channel is occupied

You are being unfortunate

[sick scaffold]

so you would end up plugging sqrt x for x in the final equation?

[echo geode]

wUt

[sick scaffold]

i think i see it

[prisma dove]

Yeah

Then

$(f \circ g \circ h)(x) = f\left(\sqrt{1+\sqrt{x}} \right) = \dfrac{1}{\sqrt{1+\sqrt{x}}} = T(x)$

[ocean seal]

MisterSystem

[sick scaffold]

would that be f(g(h(x))?

[prisma dove]

Yeah

Just different notation

[gray apex]

Hey

[sick scaffold]

so f(x) is 1/x

[gray apex]

is khan academy a good place for self-learning some math such as calc 2 and mult variable calc?

or are there better resources

[sick scaffold]

its definitely not bad but idk if there are better ones

[gray apex]

Does it cover all i need to know ?

or is it missing things ?

[sick scaffold]

i dont really know, sorry

[prisma dove]

There are Paul Lecture Notes too

But Khan Academy is definitely a good place to learn this kind of math

[gray apex]

How long do you think one can learn calc 2 selfstudying ?

like how long it would t ake

[prisma dove]

Maybe 2 months

You could take less time tho

[gray apex]

ok because im reviewing calc 1 rn

since i forgot a lot

then its calc 2

[stiff echo]

Ok so for 1b I made a table and got its instantaneous velocity

But I don't know if that's what the question asks

[twilit ocean]

how many times is there 100 in 92

wait no

how many times is there 230 in 250

[quiet basin]

hi

[twilit ocean]

wait no

[quiet basin]

pls help

[tidal sail]

did I do all these right, answers are circled

[quiet basin]

wats the formula to find the answer

[glass lichen]

<@&268886789983436800> exam.

[twilit ocean]

That looks like homework

Idiot

[meager lark]

Sorry fam, exam

[glass lichen]

it clearly says exam.

[twilit ocean]

Its a file

[meager lark]

Looks at the top left

[twilit ocean]

It also says 2011

[tall wing]

lets not insult each otler

[slender marten]

A nice 2011 exam. 🧐

[glass lichen]

oh shit

[twilit ocean]

Fr

[quiet basin]

this isnt a exam

[glass lichen]

yeah my bad lol

[tall wing]

👍

[meager lark]

u

[tidal sail]

It's probably an old exam that the teacher used for homework

[meager lark]

Prob

[quiet basin]

i need help pls

[twilit ocean]

Wow you guys have no brain

[glass lichen]

no need for ad hominum.

mistakes happen, dont be a dick

[meager lark]

Thx

[quiet basin]

can someone pls help

[meager lark]

So, on the first one, you multiply both denominators and upper number then simplify

Like

2/4•4•8=8/32

Then

Ops

[quiet basin]

kk

[random eagle]

@quiet basin are you trolling lol

[quiet basin]

no why

[meager lark]

8/32=1/4

Get it

?

[random eagle]

what grade yu in

[quiet basin]

ye

7

[meager lark]

oh k

Np

[quiet basin]

can u help with one more pls

The red, green, and black lollies in a packet
are in the ratio of 2:3:5
How many green lollies and black lollies are
there, if there are 10 red lollies?
A. 6 green lollies and 15 black lollies
B. 15 green lollies and 25 black lollies
C. 25 green lollies and 15 black lollies
D. 20 green lollies and 25 black lollies

[random eagle]

b

idk tho im in the dumb classes so

[quiet basin]

nah ur proably rlly smart

[coral moss]

anyone here good with statistics? i've put my question in #help-8 but i havent got a response after 45 minutes

[quiet basin]

@rich kraken srry for ping could u maybe help me

please

[wary stream]

Stop begging for help and don't ping people

[quiet basin]

k

[rich kraken]

What’s the question?

[rich kraken]

Okay so if you have a 2:3:5 ratio that means for every 2 red lollies you have 3 green lollies and 5 black lollies.

[quiet basin]

o kk

[rich kraken]

Wait what question are you asking?

[quiet basin]

this one

[wary stream]

There's 4 questions on there

Which one?

[alpine sable]

and the file is called exam

[glass lichen]

(it's from 2011)

[alpine sable]

time traveller

[quiet basin]

2011

[glass lichen]

I made the mistake already

[rich kraken]

Uhhh if this is an exam then I prob shouldn’t help sry

[quiet basin]

the circle question

[alpine sable]

renamed file to not seem sus

[quiet basin]

its not

[wary stream]

It's from 2011

Pay attention

[alpine sable]

do you know formula for area of circle

[quiet basin]

A = \pi r^2

[alpine sable]

excellent

since you have half a circle, you halve that area

how much is r for your circle?

[quiet basin]

14

[alpine sable]

diameter is 14

[wary stream]

Do you know what r means?

[alpine sable]

what is radius?

@quiet basin

[quiet basin]

idk

[alpine sable]

radius is half of the diameter

[quiet basin]

7

[alpine sable]

plug into formula to find area. divide by two to find half area

for half circle

[quiet basin]

kkk

thanks!

[alpine sable]

youre welcome

whatd you get?

[quiet basin]

3

.

5

[alpine sable]

?

final answer

[alpine sable]

@quiet basin

[quiet basin]

ye

[wary stream]

What did you get as a final answer?

[alpine sable]

,rotate

[alpine sable]

Would be nice thanks :))

[wary stream]

Just plug in the numbers

[alpine sable]

sub in x, see if you get y as solution

[alpine sable]

how do i plug in the numbers

[alpine sable]

wdym

how much is x

[wary stream]

You have coordinates

(x, y)

[alpine sable]

for question a

um im not sure i know that

y = gradient - y intercept?

you are given a formula:
y = 7x + 2
and coordinates:
(1, 9)

coordinates are written in the form (x, y). how much is x?

1?

oh bruh

so just plug them in

yep

y = 7(1) + 2

good

like that?

ahhahahahaha

thanks man

swelcome

I got stuck on this 😭

when you multiply 4 by -3n

you should get a -

Alright is this right? If so what do I do from here

[coral moss]

move the "n"s to one side of the equation

[alpine sable]

move the terms with the variables to one side of the equation and numbers to the other

Would this be right?

the sign should have changed when you moved the -14n

for example:
2x -1 = x - 3
I would need to subtract x from both sides:
2x - 1 - x = x - 3 - x
on the right, x-x is 0 so we get:
2x - 1 - x = 3

if you look at step 1 and step 3, the x moved to the other side and changed signs

the intermediate step is usually skipped

Is this graph correct?

when x is 2 y is 0

oh yeah thats what i meant

so does the bottom function line connect with (2,0)?

yeah, and as it approaches 0 it goes to plus inf

statement 4

[autumn rivet]

How do I solve this limit? i get stuck at the second step

[alpine sable]

@alpine sable so this is good?

better

@autumn rivet why not just evaluate the limit at 4?

[autumn rivet]

it will be indeterminate form 0/0

[alpine sable]

lhospital

should be -4 - x?

in the denominator

[quiet basin]

can u solve this
1, 4, 9, 16, R, 36, 49 …
wats r in the pattern

[alpine sable]

i can

[quiet basin]

rlly

[alpine sable]

yeah

[quiet basin]

wat is it

i been trying for like 20min

[alpine sable]

what's 1^2?

[quiet basin]

?

[alpine sable]

$1^2$

[ocean seal]

Em

[quiet basin]

ye

thats 2

[alpine sable]

1 times 1 is not 2

[quiet basin]

o

o

o

1x1=1

[alpine sable]

@autumn rivet do you see the mistake in the denominator

@quiet basin what's $2^2$

[ocean seal]

Em

[quiet basin]

4

[alpine sable]

keep going

[quiet basin]

8

[alpine sable]

no, i meant 3^2 now

[quiet basin]

o

6

[alpine sable]

3^2 is 3 times 3

[quiet basin]

9

[alpine sable]

1, 4, 9

[quiet basin]

o

wow

thx

o

sooo

25

yea

i think 25

thx

no im on to my finally quetion

*finl

*final

umm

idk

wat

[autumn rivet]

not really

[alpine sable]

$(\sqrt{29-x}-5)(\sqrt{29-x}+5)$

[ocean seal]

Em

[alpine sable]

MB im deaf

do lhospital

why

[autumn rivet]

we haven't started derivatives yet

[alpine sable]

our curriculum was different

dont be, i can use lhospital. he cant

☢️

[tawny lion]

0?

Also I had a question:

The base case, inductive hypothesis are fine but I don't know how to proceed with the inductive step

[alpine sable]

@autumn rivet have you tried rationalizing the other one

top part

[glass lichen]

Use the hint, then apply the strong hypothesis

[alpine sable]

multiply top and bottom by sqrt(20-x)+4

sorry mosh

[tawny lion]

I already tried and I got nowhere

sorry

[glass lichen]

$a^{n+1}-1=(a+1)(a^n-1)-a(a^{n-1}-1) \ = (a+1)(a-1)(a^{n-1}+a^{n-2}+...+a+1)-a(a-1)(a^{n-2}+...+a+1)$

[ocean seal]

Mosh

[glass lichen]

then it's just (painful) algebra

[tawny lion]

hmm

[glass lichen]

$(a-1)[(a+1)(a^{n-1}+...+a+1)-a(a^{n-2}+...+a+1)]$

[ocean seal]

Mosh

[tawny lion]

I'm not sure how you got that part

[glass lichen]

1st equality was hint, 2nd was strong hypothesis

Like I said

[tawny lion]

strong hypothesis?

[glass lichen]

yes, it says use 2nd principle

which is strong induction

[tawny lion]

is there any method to do it without that seeing as my teacher hasnt covered it

but still assigned that

[glass lichen]

no clue

However I doubt they never covered it.. it usually comes a bit after 1st learning induction

[tawny lion]

it's just to see our knowledge prior to taking the course so idk

anw i'll watch some videos, thank you

[alpine sable]

@autumn rivet got it?

[glass lichen]

<@&268886789983436800>

[slender marten]

:/

Hopefully they don't forget to remove messages or that will be a lot of manual deleting.

[dreamy cedar]

Banned

[errant tangle]

what does "in ratio of 6" mean?

[slender marten]

Maybe means a multiple of 6.

[errant tangle]

i mean tried it but it doesn't work

[alpine sable]

Let's say this got me a defined answer, like 2, but the limit as x approaches -1 from the left wasn't the same, or maybe it's even undefined.

Would that nullify this existing, or would -1 from the right still exist?

[proud kestrel]

How many ways can I divide a group of 12 people into 4 teams of 3?

[fair mesa]

Multiply of all NC3 for each team, 12C3 * 9C3... etc, then divide by the number of team combinations possible to discount the order

[proud kestrel]

Yeah ok nice I got that one down then 🙂

Thanks

What about: There's 10 toppings for pizza, including banana and tuna. How many different pizzas can you make if you don't combine tuna and banana?

[woven echo]

i do not like this question

oh ok don't combine banana and tuna

[fair mesa]

no limits on how many toppings you can put on one pizza?

[proud kestrel]

Well I assume max 10

Or I mean 8

Since you can't combine tuna and banana

[woven echo]

or would that be 9

[fair mesa]

9

[proud kestrel]

Yeah 😄

[woven echo]

haha

[proud kestrel]

My bad

Noticed it as soon as I hit Enter

[fair mesa]

All combinations - combinations with both tuna and banana

for the latter you it depends on how many toppings was on one pizza

[proud kestrel]

All I know the answer is 186

But this question is also written in garbage grammar (cant show question since native language)

No wait I honestly believes this question asks

There's 10 different ingredients, he must choose 4, but not banana and tuna together

[untold tapir]

what about pineapple

[proud kestrel]

He's not fking crazy

😄

[untold tapir]

pineapple on pizza is nice lol

[proud kestrel]

Yeah it's decent actually :)

I don't think I ever had a bad pizza tbh

[untold tapir]

nice

[alpine sable]

hello

I need help finding the range and domain of a composite function

but it's incredibly complex

Would it be ok if I could dm someone?

I've done most of the calculations, just wanted to check where i went wrong is all

[restive tendon]

how would i find whether or not the function is continuous over this interval?

algebraically

[lapis valley]

How to export a csv file to gnuplot?

[proud estuary]

Can anyone help me on how to work through this problem? A gallon (gal) of paint will cover 350 ft2. How much paint is required to paint the walls and ceiling of a room 15 ft 15 ft by 8 ft, given that the room has three windows 2 ft by 3 ft and and two doors 3 ft by 6.5 ft?

[restive tendon]

omfg bruh

nobody responding to my fucking question ;/

im going to fail

[placid zinc]

Not too sure how your class expects you to do this.

[restive tendon]

do what

[placid zinc]

It is continuous, but nothing in the algebra reveals that

[restive tendon]

so i should

graph?

i would just do that but i want to learn the concept

i didnt know if i had to do extra work or smoething

[placid zinc]

Well, graphing wouldn't be allowed

[restive tendon]

eek

so then how do i do this

[placid zinc]

Unless "algebraically" isn't important

A graph would work

But that's not an algebraic proof

[restive tendon]

bro 💀

[restive tendon]

should i be doing an algebraic proof?

it didnt specify what method i should be doing

just asked me if it is or isnt

guessing i might be able to use a graph

[placid zinc]

Okay well, it is, lol

[restive tendon]

.?

[placid zinc]

x is continuous, and ³√x is continuous

[woven echo]

lol man the algebraically part confused me too

[restive tendon]

well you dont have to do it that way

here

[woven echo]

i was thinking it is continuous but no idea what to do to show it

[restive tendon]

thats all it says bruh

[placid zinc]

It's odd, as continuity is a very "non-algebraic" property haha

[woven echo]

yea lol

[restive tendon]

i guess my quesiton is

what process would i use to come to the answer

[placid zinc]

You'll memorize what functions are continuous. Remember, that just means "graph is connected everywhere"

[woven echo]

figure out the domain for the function

and then if the interval falls within it

[restive tendon]

mhm

[placid zinc]

x is continuous, and so is ³√x, so their sum is as well

[restive tendon]

yeyeye

so its

continuous then

right

whats the process in which i would solve this?

just want to know so i can complete the problems + gain knowledge

ping me when u have an answer if someone responds, thank you very much

[clear vessel]

if 3^(x+1) . 2^(x-2) = 21, show 6^x = 28

can someone help me? I am so confused

[restive tendon]

what is that period

multiplication/

?

[jagged imp]

To be continuous, the left and right limits at every point must be equal and must equal the value of the function. The only place where you really need to question whether that would be true for this function is at x=1

so, you can find what the value of the function is there, and find the left limit in terms of k

and set them equal to each other

[restive tendon]

wait so like

x+3 = kx

and then put in 1

1 + 3 = k(1)

4 = k

?

[main zephyr]

what is the formula for calculating the percentage value of a number? like 20% of 100 is 20

[jagged imp]

pretty much

[woven echo]

ye

[restive tendon]

oh ight cool

thanks you

[jagged imp]

20%=0.2

20% of 100 is 0.2*100

[main zephyr]

so whats the formula? percentage / 10 ?

[woven echo]

/ 100

[main zephyr]

oh

[jagged imp]

x% of y is x/100*y

[main zephyr]

oo aight thanks

[restive tendon]

how would i find

a value of k

[pliant lava]

X% of Y = Y * X/100

[restive tendon]

in this piecewise function

[jagged imp]

if you're given the same thing that the function must be continuous, then exactly the same way

[restive tendon]

ok so we plug in pi

k * sin pi = pi + 4

k * 0 = pi + 4

0 does not equal

pi + 4

therefore i am confused

[jagged imp]

Oh uh show the full question? That function cant be continuous at pi whatever value of k you choose lol

[restive tendon]

?

[jagged imp]

uh so yeah there might be an error there? It can't be continuous on [0,5] since the limit as x approaches pi never exists

[restive tendon]

lemme graph it and see whats up

not graphing it

ill cross it off nd move on

[fast wraith]

So I need to simplify ((4/x+h)-(4/x))/h to -4/x(x+h) so I can use lim x-> 0

[jagged imp]

as h approaches 0 you mean? I'm assuming you're calculating a derivative

[fast wraith]

yeah my b

[jagged imp]

Ok, so in general when you dont know what to do with fractions, you probably want to get a common denominator

thats your first step

see what you can do there

[fast wraith]

yeah to 4/x(x+h) right?

[jagged imp]

numerator should be -4h/(x(x+h)) if you've done it right

[fast wraith]

that'll also get rid of the all over h right?

if it's 4h

[jagged imp]

sorry -4h i meant, and yes that h will cancel with the h in the denominator

[fast wraith]

wait

so getting the common denominator gets it to ((4x/x(x+h)-4(x+h)/x(x+h))/h?

[jagged imp]

yes.

[fast wraith]

okay and what am I supposed to do with that?

[jagged imp]

now since you have a common denominator, you can combine the fractions on the top and write

$\frac{\frac{4x-4(x+h)}{x(x+h)}}{h}$

[ocean seal]

Sneaky

[jagged imp]

then expand the -4(x+h) on the top and work from there

[fast wraith]

ok ty

[proud estuary]

Can anyone help me on how to work this problem? A land surveyor measures the distance across the center of a circular pond to be 318.31 ft. Find half the distance around the pond.

no

is this what you asked about? C = π* D = π D

if so no i do not recognize it

yes and I do not understand it

[ocean seal]

marc

[proud estuary]

318.31

distance

D?

not sure

1000?

so half would be 500?

[lapis valley]

can someone explain this?

[slender marten]

2/sqrt(2) = sqrt(2)sqrt(2)/sqrt(2) = sqrt(2).

[lapis valley]

oh yea

thanks a lot

got it

[vestal hawk]

hey guys how to find general solution of this equation : 2dy/dt + 3y =7
so i got ln|-7+3y| = -t/2 + c so far idk what to do next

[slender marten]

What method did you use? I assume you approached it as a separable differential equation?

[vestal hawk]

yup

answer is 7/3 +Ae^-3t/2 but im getting Ae^-t/2 / 3 + 7/3