help-0

[candid thistle]

It's alright, everone starts somewhere

I too

I spent an entire day on one problem and still havne't finsihed :/

Speaking of which i should work on that

[leaden galleon]

Lol

Good luck

I’ll be back next time guys if I end up having questions with math again

[candid thistle]

kk

[leaden galleon]

Cya 🙂

[last narwhal]

how to quickly find numbers that satisfy the equation

[candid thistle]

Set all three of them to be equal

[surreal meadow]

this looks like a 2010 olympiad problem

[wind bane]

like, integer solutions? or just any old numbers

[surreal meadow]

i'm sure there's a solution they provide

[ocean seal]

Eat water it's good

[candid thistle]

If it allows simplest radical form.

It is more likely that they are asking for integer solutions but idk ¯_(ツ)_/¯

[last narwhal]

integer

[wind bane]

would ask in the number theory channel

[quick timber]

help

[alpine sable]

@quick timber please read #❓how-to-get-help , don't multipost. rule 3

[ocean seal]

Eat water it's good

[candid thistle]

Another thing is, you should simplify 66/3.

If <BAQ = <QAC (angle bisector), would r/t = s/u

I see my drawing skills are improving :/

rather, getting worse

[heady tusk]

busy?

you know I could do this but I'm soo tired and this is the last question

so can I please get some help

I really wanna go to sleep

[candid thistle]

I don't speak that language

Factor f(x)?

[heady tusk]

oh ye

mb

you have to find/calculate the numeric values of a and b

[candid thistle]

I got this now, its just r/s = t/u, not r/t = s/u

oh ok

First off

plug in -2 as x

[heady tusk]

and in line 2 it says (x-1) is a factor of f(x)

[candid thistle]

Is that german?

[heady tusk]

ok

1 sec

[heady tusk]

nah but good guess

some things are similar

[candid thistle]

ok lol

its not that hard to understand it after reading it 1-2 times

[heady tusk]

but they already told us what f(-2) would give?

it gives 9

[candid thistle]

yes

[heady tusk]

so why would I plug it in

[ocean seal]

Eat water it's good

[heady tusk]

yes

[candid thistle]

4a - 2b = ?

2a - b = ?

[heady tusk]

uhm

wait

[candid thistle]

Using this find those two btw

[heady tusk]

19

I think

no

28

@candid thistle

[candid thistle]

yea

so 2a - b = 14, that means that a = what in terms of b

[heady tusk]

28?

oh it's 14?

how

oh half

of 28

nvm

[candid thistle]

-19 + 4a - 2b = 9, 4a - 2b = 28, so 2a - b = 14

[heady tusk]

uhm

[candid thistle]

But yeah, using this, what is a equal to in terms of b

[heady tusk]

a=8

b=4

OK wait lemme write down what I got so far

[candid thistle]

thats one possibility but you have to make sure that f(x) has a factor of (x - 1)

also idk if you can guess

[heady tusk]

it says

x-1 is a factor of fx

in the question

[candid thistle]

I was just going to suggest isolating a, then writing f(x) without any a's and only b's

yeah

[heady tusk]

so that's it

[ocean seal]

Eat water it's good

[native temple]

this active?

[candid thistle]

but you cant really guess since a could be 100 and then b = 186

[candid thistle]

I don't think so now.

[native temple]

https://www.amazon.com/Mental-Math-Calculator-Enthusiasts-Interview-ebook/dp/B07S1KLMB8

I have this book….

And it mentions place value

[candid thistle]

as in for example in the number 14, the 1 represents 10 and 4 represents 4?

[heady tusk]

@candid thistle so final answer is a=8 and b=4?

[candid thistle]

not necessarily

because (x - 1) has to be a factor

and a could be anything

for instance plug in a = 100, that would make b = 186

[heady tusk]

but if (x-1) is a factor

[ocean seal]

Eat water it's good

[native temple]

in this section it mentions place value

what is that I forgot

[heady tusk]

wouldn't it be correct in that proportions?

[ocean seal]

Eat water it's good

[native temple]

you said it wasn’t active..

[candid thistle]

how is a = 2b?

[candid thistle]

It wasn't for like a minute, I had assumed they solved it

Sorry :(

[heady tusk]

wdym? b=2a

[candid thistle]

Ahh

how is that?

[heady tusk]

oh wait

[candid thistle]

.

[heady tusk]

should a be a be 4?

[candid thistle]

?

[heady tusk]

but the questions asks for a and b

but it can be more than 1 thing?

[native temple]

@candid thistle No water will slit theough your teeth also you don’t stick your tongue out when eating it’s dangerous and disgusting

[candid thistle]

idk you need to have two values of a and b that satisfy that and when f(x) is factored, (x - 1) should be one of the terms

[candid thistle]

It's a joke :P

[native temple]

sorry for starting small talk in here

[heady tusk]

yes...

[candid thistle]

So you have to find those

[heady tusk]

bruh it feels like I'm so close

but oh so far

lmao

[candid thistle]

Yeah :/ I had that two days ago

[alpine sable]

so

i need some help as im going to the 8th grade in a american school, where i learnt most of my mathematics in a different language.

[heady tusk]

so what do I have to plug In?

[alpine sable]

whats the best video that could probably help me with mathematics 8th grade.

[candid thistle]

not exactly sure

[heady tusk]

busy go to another questions channel

[candid thistle]

Khan Academy is good but yeah the channel is taken

[heady tusk]

oof x_x

[oak chasm]

@alpine sable Sorry, channel is busy. Try Khan Academy. Has video lessons on mathematics classes.

[heady tusk]

@oak chasm yooo my man

[candid thistle]

Someone who knows what they are doing :0

[heady tusk]

is there any way that you can help me with this question?

[candid thistle]

I can't help from here as I suck at quadratics

[oak chasm]

@alpine sable https://www.khanacademy.org/math Find your class here.

@heady tusk What's the question?

[candid thistle]

question

[oak chasm]

f(x) = 2x³ + ax² + bx - 3
f(-2) = 9
(x - 1) is a factor

So, if (x - 1) is a factor, then f(1) = 0.

So, use the definition of f(x) to find f(1).

What do you get?

[heady tusk]

the definition of f(x)

uhm

[oak chasm]

Yeah, f(x) = 2x³ + ax² + bx - 3.

[heady tusk]

you get

[oak chasm]

Fill in 1 for x.

[heady tusk]

0

[oak chasm]

No, you don't.

[heady tusk]

cus x-1 is a factor

right?

oops

[oak chasm]

No, use the definition of f(x), not the fact about roots.

You'll see why in a minute.

[heady tusk]

ok

[native temple]

this active?

[heady tusk]

you get

2+a+b-3

[oak chasm]

@native temple Yes.

Good, now simplify.

[heady tusk]

a+b-1

[oak chasm]

f(1) = a + b - 1

f(1) = 0

So, a + b - 1 = 0

Does that make sense?

[heady tusk]

yes

so can I now cculate a and b?

[oak chasm]

Find f(-2) according to the definition of f(x).

Almost.

You need two equations to find two variables.

[heady tusk]

I found this already, can't we use this?

yes cus that's another eqaution

[oak chasm]

OK, good.

[alpine sable]

Is that indices ;w;?

[heady tusk]

OK I'll try now

[oak chasm]

Now you have:
a + b = 1
2a - b = 14

Solve the simultaneous equations.

[heady tusk]

mhm

[oak chasm]

,rccw

[oak chasm]

OK, what's b?

[heady tusk]

uhm

1 second

-4?

[oak chasm]

Right.

[heady tusk]

if you sub it in

[oak chasm]

Now check it with your original equation.

Get f(x) with a and b filled in.

Make sure that f(1) = 0 with that new formula.

Make sure that f(-2) = 9 with that new formula.

[heady tusk]

f(1) works

lemme check the other one

f(-2) also gives 9

or wait

does it

[oak chasm]

Well, do the work on paper.

Let's see.

[heady tusk]

yay it works

the equation is correct

[oak chasm]

OK, so your answer is a = 5, b = -4.

[heady tusk]

tysm again

NOW I CAN SLEEP

[oak chasm]

You're welcome.

Have a good sleep

[heady tusk]

you are amazing

ahhh

bye

[oak chasm]

Bye

[native temple]

This section of this book https://www.amazon.com/Mental-Math-Calculator-Enthusiasts-Interview-ebook/dp/B07S1KLMB8

mentions place value

what is that I forgot

and how does this work

I don’t understand step 1

I would continue

but I forgot what place value is

[oak chasm]

Is this for finding the remainder after division by 11?

[native temple]

okay I guess I can show a few more pages

IDK

tbh

[oak chasm]

OK, so the digit sum method gives you the remainder after division by 9. The digit difference method essentially gives you the remainder after division by 11, though with 10 handled strangely.

You're asking how to do the digit difference method?

[native temple]

Yea

IDK how this works

specifically

Idk what place value is

even odd “place value

[oak chasm]

OK, so you number the places in the number, starting with the place left of the decimal point, like this:

Let's say your number is 1309.567.

1  3  0  9  .  5  6  7
4  3  2  1  .  0 -1 -2

See how the second line starts numbering at 1, then goes to the left 2, 3, 4, 5, 6, 7, 8, 9, 10, etc, until you get to the start of the number?

[native temple]

yes

[oak chasm]

And just like going to the left increases by one each time, going to the right decreases by one each time, which is why we get 0, -1, -2, -3, -4, etc after the decimal point until the last digit of the number.

So, now we add together the digits in the odd numbered places.

1  *3*  0  *9*  .   5  *6*  7
4   3   2   1   .   0  -1  -2

3 + 9 + 6 = 18

See how I added the digits in the odd numbered positions?

[native temple]

oh

[oak chasm]

Then I add the even numbered digits:```
1 3 0 9 . 5 6 7
4 3 2 1 . 0 -1 -2

1 + 0 + 5 + 7 = 13

Then I subtract the even sum from the odd sum:
Odd sum - even sum = 18 - 13 = 5.

Does that make sense?

[buoyant scaffold]

Is this available

Nobody answered me in the question-1 channel

It's been like 25 mins

[native temple]

okay

I see

[oak chasm]

@buoyant scaffold Sorry, you need to keep the question in one channel.

[gaunt magnet]

<@&268886789983436800> i need to change my name

[night geyser]

To?

[gaunt magnet]

i cant change name

[native temple]

so to get digit sum of $ 132197.192$

[night geyser]

Yes, that's intentional

[tall wing]

right this is by design

[buoyant scaffold]

So what should I do even if I pinged the helpers role and nobody showed up?

[gaunt magnet]

can i change

[night geyser]

What do you want it changed to?

[native temple]

wait until someone else asks a question in that channel

[gaunt magnet]

Change usman 👉 Moshisanidiot

[night geyser]

slightly aggressive

but sure

[gaunt magnet]

ty

[native temple]

so to get digit sum of $$ 132197.192$$

[ocean seal]

Nerdy_Coder

[native temple]

what

uhh

$so to get digit sum of $ 132197.192$

one line

so to get digit sum of $ 132197.192$

so to get digit sum of $ 132197.192 $

there we go?

why isn’t this working!

so to get digit diffrence of $ 132197.192 $

$ 132197.192 $

$$ 132197.192 $$

[ocean seal]

Nerdy_Coder

[native temple]

so to get digit difference of this number

do

$$ 1 + 2 + 9 + 1 + 2$$

[ocean seal]

Nerdy_Coder

[native temple]

which is $$ 15 $$

[ocean seal]

Nerdy_Coder

[native temple]

15 - 3 + 1 + 7 + 9

which is 20

the result is -5

but this can’t be negative os ot’s negative 5 + 11

which is 6 right?

[native temple]

<@&286206848099549185>

[hollow sage]

CAN SOMEONE HELP ME WITH THIS PLEASE

ive been stuck on this for my entire life im now 91 years old and i can't figure it out ]

<@&286206848099549185>

[topaz scaffold]

You know what foil is?

[hollow sage]

no?

[topaz scaffold]

Oh

[hollow sage]

oh like inner and outer

and stuff

[topaz scaffold]

Yea

That's what you would use here

[hollow sage]

oh yea

thanks

[wheat condor]

<@&286206848099549185>

what’s the right answer

[topaz scaffold]

0

For both

Since a tangent line would be flat ther

There*

[brittle wasp]

0 is a straight line :|

Oh wait my bad

Hey can someone help me out with this question pls?

<@&286206848099549185>

[topaz scaffold]

,rotate

[wheat condor]

thank u s much

[topaz scaffold]

The planes seems parallel to each other

So they wouldn't intersect

[brittle wasp]

Thank you ripe@topaz scaffold

[topaz scaffold]

[alpine sable]

hey can someone help me im a little stuck on this problem https://cdn.discordapp.com/attachments/722462948009967677/876974742240915496/Screen_Shot_2021-08-16_at_7.png

[topaz scaffold]

Sum means add

Spam protection lol

[alpine sable]

wait what

[topaz scaffold]

Sum of 1 and 2 means what do you get when you add 1 and 2 together

[alpine sable]

what would i get

[glass lichen]

0

in Z_3 at least

[alpine sable]

okay thank you

wait it says error

[topaz scaffold]

Hopefully he/she didn't actually enter 0

[alpine sable]

are you sure that’s right?

[glass lichen]

yes

[topaz scaffold]

Yes

But

[glass lichen]

Im positive 1+2=0 in Z_3

[topaz scaffold]

1+2=10 in base 3

[alpine sable]

okay i will try that, thank you!

[topaz scaffold]

Are you actually unable to do addition?

[alpine sable]

mf

[wheat condor]

is someone near a pen and apper

paper

[topaz scaffold]

Depends what you define as "near"

I gotta stand up and walk to get the pen so I would say no (?)

[warped phoenix]

is this true?

you can make the exponents of an equation into their own equation

and then solve for x?

instead of doing a log and getting the x out of the exponent area

[topaz scaffold]

Well doing that is basically the same as doing log_2 on both sides

[warped phoenix]

huh

[topaz scaffold]

Kinda like saying 3 * x = 3 * y

So just comparing x and y

[warped phoenix]

so this can only be done if there's an x in both exponents of both sides of the equation?

[topaz scaffold]

x = y

[topaz scaffold]

Doesn't have to be

For example $2^x = 2^2 \implies x = 2$

[ocean seal]

RipeOrange

[warped phoenix]

ah

for the function g(x) = f(1/3x), g(x) would have a horizontal stretch by a factor of 3, and if g(x) = f(3x), g(x) would have a horizontal compression by a factor of 1/3

right?

just to make sure ive got that correct

[topaz scaffold]

Yep

[warped phoenix]

great

ty!!

oooh one more thing

ik something like this depends from person to person

but ive got my alg 2 final tmrw

what do you guys think would be most beneficial for review? taking the khan academy mastery course for alg 2 over and over until i stop getting questions wrong or simply watching a yt vid i found that goes over the entirety of the course of alg 2 (~3 hours)

[topaz scaffold]

I didn't study for mine

Depends how confident you feel about the content ig

If you feel good about it you could probably just review the concepts that you're not as strong in

And I think it's good to review content from the beginning of the year too

Since it's easy to forget them since it's been a while

[wheat condor]

<@&286206848099549185>

[jagged raptor]

if anyone figures this out can you ping me bc im also confused

[alpine sable]

yes please help i have been trying to submit this form for the last 30 minutes

[warped phoenix]

i feel pretty terrible about it

💀

i forgot like...

a lot....

so videos it is then? 😅

[topaz scaffold]

Yea ig

[topaz scaffold]

What's 1+2

[warped phoenix]

,w 1+2

[ocean seal]

Results provided by WolframAlpha

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

Requested by TheMane3#3104

[warped phoenix]

oh wow that actually worked

yay i can use wolfram

[topaz scaffold]

It's 1+1+1

[remote heron]

[loud mountain]

,w 1+1+1

[ocean seal]

Results provided by WolframAlpha

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

Requested by FastSammy2007#6266

[loud mountain]

Lol

[topaz scaffold]

Which is 1*3

[alpine sable]

oh okay how did you get that result though

[loud mountain]

,w 1×3

[ocean seal]

Results provided by WolframAlpha

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

Requested by FastSammy2007#6266

[loud mountain]

Sigh

[warped phoenix]

doesnt this count as trolling???? lmfao

[topaz scaffold]

Well 1+1 is succ(1)

[loud mountain]

No

Please

That's enough

[topaz scaffold]

So 1+1+1 is succ(succ(1))

[loud mountain]

I don't want to lose my helper

[warped phoenix]

LMAO no not you

i meant

[loud mountain]

You can do it

[warped phoenix]

the person asking

[alpine sable]

?

isnt this a math server

[topaz scaffold]

Yep

[warped phoenix]

yeah in which you're asking a blatantly obvious question

[topaz scaffold]

Serious question: Do you know how to do addition?

[warped phoenix]

thus trolling

[alpine sable]

@jagged raptor

i think they helped but they didnt ping you

so there you go

[topaz scaffold]

Is it possible to be able to use Discord without knowing addition?

[warped phoenix]

hmmmmmmmmmmmmmmmmm

yes?

[topaz scaffold]

Hmmmm

[warped phoenix]

you dont need to know addition to make an email and register to the site ig

[topaz scaffold]

Seems plausible yeah

[alpine sable]

if it's so "blatantly obvious" then why did you need to ask a bot to do it lol

[jagged raptor]

okay thanks

[warped phoenix]

because i didnt know wolfram worked for me lol

so i tested it out

[topaz scaffold]

It works for everyone

[alpine sable]

yeah no problem

[warped phoenix]

yeah i had no clue lmfao

[topaz scaffold]

I mean why not?

[alpine sable]

true, true

[topaz scaffold]

Fancy technology

[warped phoenix]

i wonder

if you know your life's career

[alpine sable]

oh wait this makes sense
if i use the formula δ(ψ) = ωψ + π, ω, π ∈ R

[warped phoenix]

why get taught things you dont need for that career

[topaz scaffold]

Oh thank goodness

[warped phoenix]

im pretty sure i dont need AP Calc BC for orthopedics......................................

[topaz scaffold]

Is that like a bone doctor?

[warped phoenix]

yeah

[topaz scaffold]

Ah

[warped phoenix]

idk man im with elon on this one

his school teaches you specifically towards your interests

[topaz scaffold]

Is calc required at your school?

[alpine sable]

yeah after applying tai's method this problem is super trivial, thanks for the help

[topaz scaffold]

What's his point?

[topaz scaffold]

Np

[warped phoenix]

no but colleges apparently expect you to have it done by senior year on your hs transcript so im forcing myself to do it 😦

good colleges*

lol

[topaz scaffold]

Ah

I'm stuck in AB Calc because of Covid

[warped phoenix]

calc sounds fun

[jagged raptor]

you can combine that with kai's method too using χ−γ = ((γ−η)/(ξ−ζ))(ψ−ξ)

[warped phoenix]

not really

but yk

sounds terrible tbh

but yeah

LOL

[topaz scaffold]

And my consoler won't let me skip it

Oof spelling

[alpine sable]

holy shit thats revolutionary

[topaz scaffold]

Calc was pretty fun for me

[jagged raptor]

thanks you too

[warped phoenix]

man if i could take all science classes that didnt require math i would 😦

no chem, no physics

just bio ❤️ ❤️ ❤️

[topaz scaffold]

Doesn't bio use math later on?

[warped phoenix]

hope not

[topaz scaffold]

I'm not sure but I think I've heard something about it

Ripppp

"We have developed a set of application examples for Calculus, which are more biology oriented. These include: growth/decay problems in any organism population, gene regulation and dynamical changes in biological events such as monitoring the change of patients' temperature along with the medications."

[astral dagger]

population growth = differential equations = perfection

[topaz scaffold]

Cool

[warped phoenix]

😦

me no likey math

me hatey math

very much

[topaz scaffold]

Me likey math tho

🥲

[warped phoenix]

like..i have no problem with complex rhetorical analysis of english literature or describing how in the period 1450-1750 certain states in Asia and Africa adopted policies to limit European power and influence

but when it comes to "what is 1 + 1?"

[abstract portal]

lol

[warped phoenix]

i hate it

[quick spoke]

heyaa, a friend sent me this question with solutions and I’m trying to do it myself but I’m a little stuck

[placid zinc]

Just looking for the area?

[quick spoke]

oh no just in general like how can I find the coordinates of D?

or how did they find the rule of AD

[placid zinc]

What's the line that connects B and C?

[quick spoke]

shouldn’t it have the same gradient as A and D but with a higher y intercept?

[placid zinc]

Yes

[quick spoke]

but how do I continue from there?

I don’t know the coordinates of B or D and I’m clueless as to finding it 😅

[placid zinc]

Or, sorry, you already have the equation AD. Okay, what's the intersection of AD and CD

[quick spoke]

wouldnt you do simultaneous equations

but the equation for AD is kinda

not known

[hushed blade]

ad is just -0.5x

oh it says that

[quick spoke]

I know, the answers are there

I just want to figure it out how they got that :)

[hushed blade]

its perpendicular so the gradieent is the negative reciprocal

[quick spoke]

so the reciprocal of the gradient of y=2x-6 is 1/2

and then negative

so -0.5

ohhhggg

[hushed blade]

yup

[quick spoke]

tysm it’s clear now

:D

[manic glade]

why is it {i} and not just i?

[sly mantle]

the notation is for preimages of subsets of the codomain

[manic glade]

i guess the notation only works for sets?

beat me to it

is "uphold" or "fulfilled" used when you want to say something [] a definition/requirement?

for example in this

is there some other term?

[sly mantle]

satisfy

[manic glade]

👍

[misty holly]

what does this mean for rational numbers? b≠0

𝑎 ≠ 0 for reciprocals

[misty holly]

b≠0 = b cannot be equal to 0
is that the right meaning/definition for it?

can anyone confirm this pls?

[wary stream]

If a rational number is $$\frac{a}{b}$$ then the denominator can't be 0, hence $$b \neq 0$$ because you can't divide by 0

[ocean seal]

dldh06

[gaunt magnet]

[misty holly]

oh okay, thanks for confirming!:)

[wary stream]

Same logic with $$a \neq 0$$ for reciprocals because it'll be $$\frac{b}{a}$$

[ocean seal]

dldh06

[misty holly]

you know what? my module is irritating me, it keeps putting in things without even saying what it means

[alpine sable]

is the projection of v onto u equal to the projection of u onto v?

[stark trail]

U meant vectors?

[stark trail]

If you’re talking about vectors, so the answer is no

[hearty aurora]

No they are different, if you are expecting a vector after your “projection.” They point in different directions unless u and v point in the same direction, in which case they would only be the same if they had the same magnitude

[manic glade]

if i have sets A_i which are sets of functions

and i want to say there are functions which belong to more than one of these sets

what is the phrasing

different A's? different A_i's?

belong to? are in?

[stone pond]

I'd write something like 'f belongs to several of the A_i'

[manic glade]

isnt it super weird to say several A_i's tho?

A_i kind of implies its a specific A which is indexed by some i

[warped phoenix]

is this channel free

[manic glade]

ish, i wouldnt mind more input on the phrasing but its not being actively discussed atm so ask away

[sly mantle]

@warped phoenix occupied

[warped phoenix]

the other person said i could ask

[sly mantle]

the discussion isn't completely closed so it's best to treat the channel as occupied

[warped phoenix]

oh ok

[sly mantle]

it's a common lazy way to say f belongs to many sets in the family {A_i}

[manic glade]

i dont quite know what family is yet besides context based intuition

but what if i is only 1 to 4 and a function can be only in up to two A's

[sly mantle]

@wicked gazelle occupied

[wicked gazelle]

Qn. 1.(iii)

[manic glade]

this is what i am trying to rephrase

[wicked gazelle]

Alright np

[sly mantle]

family is a common name for a collection of sets

[manic glade]

belong to the family {A_i}?

still leaves the second sentence there

i need the emphasize the two

[sly mantle]

ok if that's all you want to reword, then

[manic glade]

just dont know if i can refer to it as A_i or A is better

[sly mantle]

there exist distinct indices i,j where f is in A_i and f is in A_j

[jovial forum]

Does what I've done here make sense? Trying to solve for y

[sly mantle]

@jovial forum occupied

[manic glade]

hm

would i need to define and explain j or would it be self explanatory as is

also as a general phrasing thing, should i just always avoid saying different A_i's?

[sly mantle]

the sets are implicitly defined over an index set. i,j are elements of that index set

[manic glade]

sounds good

[queen nova]

I can't tell what the coeffcient of c is

I think I'm just stupid

<@&286206848099549185>

[sly mantle]

@queen nova pls wait 15min before pinging helpers

[queen nova]

Oh sorry

[willow wadi]

ty for unmuting me

so kind

of u

sir

[clear vessel]

How do I solve |x-2| = |x+2| algebraically?

[novel crag]

Make cases for x>_2 , x<2 respectively

[clear vessel]

wdym

[novel crag]

Coz that’s modulus function

[clear vessel]

I know how to solve it graphically but for algebraically im confused

[novel crag]

for x>_2 , x-2=x+2 , and for the other case , 2-x=x+2

[clear vessel]

wdym haha

[novel crag]

|x-a| , means it will open either x-a or a-x , that’s the property of modulus function

[clear vessel]

oh

[novel crag]

If x>_a , then x-a , or else a-x

Refer to the definition of modulus functions again

[clear vessel]

How do I write 02≤x≤12 in the form |x-a|≤b

I've forgotten lol

[novel crag]

Wait a sec

[gray isle]

wdym by 02

[hearty aurora]

find the midpoint of 2 and 12 first and then half of the distance between the endpoints should also be useful

[clear vessel]

yeah I just figured

after that

I just subtract right to find the difference

[wheat condor]

<@&286206848099549185>

[clear vessel]

so for this |x+5|≤7

[hearty aurora]

hm no

[novel crag]

That means -5<_x+5<_5

I mean 7

[clear vessel]

x-5*

[novel crag]

x+5€[-7,7]

[hearty aurora]

wait 7 is the midpoint though...

so it should be

[clear vessel]

|x-5|≤7

[hearty aurora]

|x - 7| < 5

[clear vessel]

I think should be other way rnd -7+5 = -2

oh wait I sent wrong questio

-2≤x≤12 in the form |x-a|≤b

[hearty aurora]

gotcha in that case, then i think youre correct

[clear vessel]

thanks for the help

[hearty aurora]

no worries 🙂

[warped phoenix]

so

the vertex of a quadratic in vertex form

is just (h, k)

[ocean seal]

TheMane3

[warped phoenix]

be (-2, 3)?

[rigid smelt]

because the vertex form of a quadratic equation is said to be y = a(x**-** h) + k

if you plugged in h=2, it would have been x-2 and not x+2

[warped phoenix]

ohhhh

the x-h is a part of the vertex form so the negative doesnt apply to the x itself for the vertex

if that makes any sense

lmfao

[novel crag]

What?

[rigid smelt]

it doesnt make sense but as long as you get it then

🤷‍♂️

[warped phoenix]

ok so

(x-h)

wait

nvm

i get it lol

[clear vessel]

How do I solve |x-3| < |x+3|

[rigid smelt]

try to "remove" the absolute value appropriately

[gray isle]

consider the 3 cases

[clear vessel]

do I just 3-x < x+3

[rigid smelt]

no, do what ramonov suggested

[clear vessel]

how

[rigid smelt]

|x-3| and |x+3| has x=-3 and x=3 as their breaking points accordingly

consider what happens when x<-3

-3<x<3

and x>3

[clear vessel]

still confused haha

[rigid smelt]

for example when x<-3, |x-3|=-(x-3) and |x+3|=-(x+3)

this is how you are supposed to remove the absolute value sign

[willow wadi]

@ionic jewel

[alpine sable]

hi everyone i just joined the server cause i just got into collage

[willow wadi]

@ionic jewel

[ionic jewel]

dont ping me

[astral dagger]

congratulations

[rigid smelt]

the channel is currently occupied so try not to interrupt the conversation, and please dont try to ping random users

[ionic jewel]

oh nvm

[rigid smelt]

unless you are friends or closely related

[ionic jewel]

nice image

i appreciate it

can go with

okay im done spamming this chat but thanks

[wheat condor]

yo

[willow wadi]

[neat haven]

How do I factor this?

https://cdn.discordapp.com/attachments/872292083342393345/877030163693580358/fac.PNG

[wind bane]

can u factor 2y^2 + 3y - 2?

[alpine sable]

<@&286206848099549185>

[neat haven]

Yeah

Its the e to the xth which is messing me up

[wind bane]

then ur done

[neat haven]

Do I just treat it as a whole?

[compact hornet]

let $y=e^x$

[wind bane]

let y = e^x

[ocean seal]

juliandroske

[wind bane]

yea

[wind bane]

is there any reason u pinged helpers?

[candid thistle]

They probably wanted to annoy them or smth

[alpine sable]

@wind bane yes

@candid thistle no mate i need help lol

[candid thistle]

Ahh okay

#❓how-to-get-help

[alpine sable]

i just joined so idk who to ask where to ask

[wheat condor]

any1 know this ?

[wind bane]

what have u tired so far?

[warped phoenix]

hey all

im trying to factor $6x^2 + x -15$

[ocean seal]

TheMane3

[warped phoenix]

using the slide and divide method

can anyone help me understand why im not getting a reasonable answer?

i multiply -15 with 6

to get $x^2 + x -90$

[ocean seal]

TheMane3

[thorn kindle]

Thats not how factoring works lmao

[warped phoenix]

do you know what the slide and divide method is

[thorn kindle]

Find factors of ac that add to equal b

[warped phoenix]

i tried replicating this

with $6x^2 + x -15$

[ocean seal]

TheMane3

[warped phoenix]

and im curious as to why it wont work

[wheat condor]

ay @compact hornet mad appreciate it g tjanks alot

can u clairify that some things said the i cant read it

[thorn kindle]

Ok so the problem is you need factors of -90 that add to equal 1

So -9 and 10

(x-9)(x+10)

[warped phoenix]

right

[warped phoenix]

but trying to divide both -9 and 10 by 6 gives you a decimal, so according to the rules you have to drag it to the x, so (6x - 9)(6x + 10)

and for obvious reasons

thats wrong

but i was told this method should be fine for all factoring

but apparently not, so i want to know under what condition can i not use this method

is it when the middle x has a coefficient of 1?

[thorn kindle]

9/6 = 3/2
10/6 = 5/3

Then you will get (2x-9)(3x+10)

Which should work

[warped phoenix]

omg

ughhhhhhhhhhhhhhhhhh im so fucking dumb

[thorn kindle]

,w expand (2x-9)(3x+10)

[ocean seal]

Results provided by WolframAlpha

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

Requested by AMD#4434

[warped phoenix]

yeah idk why i kept dragging the a term to the x's instead of the number you're dividing by

lmao even though it says right there what to do

🤦‍♂️

[thorn kindle]

No that doesnt work either

[warped phoenix]

oh wait

yeah

ur right

hmmm

welp

then it goes back to "under what condition can I not use this method"

[ocean seal]

TheMane3

[warped phoenix]

anyone else know?

[thorn kindle]

Ok let me show you how this method actually works

I read up on it its actually pretty nifty

Ok let us start with the polynomial

$6x^2 + x - 15$

[ocean seal]

AMD

[thorn kindle]

Now let us multiply through by the leading coefficient

$6(6x^2 + x -15) = 36x^2 + 6x - 90$

[ocean seal]

AMD

[wheat condor]

anyone here know calc

?

[thorn kindle]

Then let us rewrite the expression

[jaunty crane]

please help me on 3 questions

[warped phoenix]

why do we multiply it through everything?

isnt it just the 6 times the -15

or were the instructions wrong

[thorn kindle]

$(6x)^2 + (6x) - 90$

[ocean seal]

AMD

[thorn kindle]

Now let $p = 6x$

[ocean seal]

AMD

[thorn kindle]

so now we have $p^2 + p - 90$

[ocean seal]

AMD

[thorn kindle]

We factor and get $(p-9)(p+10)$

[ocean seal]

AMD

[thorn kindle]

then we substitute back in for p = 6x

$(6x-9)(6x+10)$

[ocean seal]

AMD

[thorn kindle]

but now we have to divide by the leading coefficient again because we multiplied through by the leading coefficient

so it is really

$\frac{1}{6}(6x-9)(6x+10)$

[ocean seal]

AMD

[thorn kindle]

,w expand 1/6(6x-9)(6x+10)

[ocean seal]

Results provided by WolframAlpha

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

Requested by AMD#4434

[thorn kindle]

@warped phoenix

understood?

[warped phoenix]

so have i been doing it wrong?

[jaunty crane]

help pls

[warped phoenix]

channel in use

delete ur msgs and post in a free channel

[thorn kindle]

this process gives you the correct roots. but in order to get the original polynomial back you must divide by the leading coefficient again

so in this case you have to multiply by 6, then divide by 6

[warped phoenix]

so what should i change in the instructions given to me

divide by 6 a second time?

and at the beginning should i multiply the whole polynomial by the "a"?

[thorn kindle]

you start with $ax^2 + bx + c$ $\newline$
then you multiply through by a:$\newline$ $a^2x^2 + abx + ac = (ax)^2 + b(ax) + ac$$\newline$
then you introduce a variable $p = ax$, and substitute: $p^2 + bp + ac$$\newline$
then you factor normally and get the following expression in terms of p: $(p-r)(p-s)$$\newline$
and then you substitute back in for $p=ax$, which gives you: $(ax-r)(ax-s)$$\newline$
but this is the polynomial that has been multiplied through by p. in order to get the original polynomial you need to undo the multiplication by dividing, yielding: $\frac{1}{a}(ax-r)(ax-s)$

[ocean seal]

AMD

[thorn kindle]

it still gives you the correct roots though even if you don't divide. it's just that the polynomial will not be the same

in our example we arrived at: $\frac{1}{6}(6x-9)(6x+10)$

[ocean seal]

AMD

[warped phoenix]

so what you've just written out here is basically the fixed version of what i sent you

that should work for all factoring right?

[thorn kindle]

yes

[warped phoenix]

oh ok

awesome

also yeah i read through it a couple times

but

[thorn kindle]

do you understand why it works? it's actually really cool

[warped phoenix]

it seems that the final answer ends with 1/a(ax-r)(ax-s) every time

is that allowed as like an answer

just having the 1/a out there

if im factoring

[thorn kindle]

that's what i was about to tell you.

[warped phoenix]

ah

[thorn kindle]

if you really want it without the leading coefficient in front you do this:

1/a(ax-r)(ax-s) = (x-r/a)(ax-s) = (ax-r)(x-s/a)

it will not always be an integer though. what you were given assumes that either r or s is divisible by a. which is not always the case

[thorn kindle]

this is actually a really cool method though, thanks for sharing

$\frac{1}{a}(ax-r)(ax-s) = (x-\frac{r}{a})(ax-s) = (ax-r)(x-\frac{s}{a})$

[ocean seal]

AMD

[warped phoenix]

ohhh

so either the r/a or s/a works

and like you said r or s has to be divisible by a

[warped phoenix]

np ❤️

[thorn kindle]

yeah otherwise this method doesn't work as described. r/a or s/a will not always be an integer

[warped phoenix]

ohhhh ok so that's the condition then

awesome

ty!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

so if thats the case btw

i should just stick with the ac method?

or some other way of factoring

[thorn kindle]

your choice really. i was personally taught another way

[warped phoenix]

oh ok

[thorn kindle]

which imo i prefer. but i see the logic behind this one

[warped phoenix]

dang it i was hoping this method would work for everything because i despise all other forms of factoring but not in this life it seems 😠 😭

[thorn kindle]

it does work

as i described it to you

[warped phoenix]

but you said only if r or s is divisible by a

[thorn kindle]

no it still works for all quadratics.

[warped phoenix]

ohhhhhhhhhhhh

YAYY

[thorn kindle]

it's just that you will have rational numbers inside the parantheses instead of just integers

if you want i can show you the method i learned. it's actually a lot easier

[warped phoenix]

easier than this?????

than yeah absolutely

[thorn kindle]

alright

let's use the same quadratic

$6x^2 + x - 15$

right?

[warped phoenix]

sure

[thorn kindle]

or wait no

[ocean seal]

AMD

[thorn kindle]

this is it?

[warped phoenix]

yep

[thorn kindle]

alright. now find the product ac

[warped phoenix]

a*c = -90

[thorn kindle]

alright. now find two factors of ac that add to equal b

[alpine sable]

hey guys

oh wait u guys in the middle of a conversation sry for interupting

[warped phoenix]

10 and -9

[thorn kindle]

now watch.

[warped phoenix]

[jaunty crane]

ok

[thorn kindle]

made a typo gimme a sec

$6x^2 + x - 15 = 6x^2 + 10x - 9x - 15 = 2x(3x+5) - 3(3x+5) = (2x-3)(3x+5)$

[ocean seal]

AMD

[jaunty crane]

ok

[thorn kindle]

basically you factor by grouping. and it always works regardless of how you split the linear term

@warped phoenix

[warped phoenix]

ohhhhhhhhhhh

i see

i think ive seen this before yeah

so you just need to find a*c, the factors of ac that add up to the middle term, and then replace the middle term with + ax + cx, put it into 2 groups, factor out if factorable (actually nvm it has to be factorable for this to work which im assuming it would be factorable every time) and then put the repeating part into its own group and then what was factored out into its own group

is that right? the process i wrote out @thorn kindle

[thorn kindle]

yeah pretty much i think you get the idea

[warped phoenix]

oh ok

wow this is quicker

ty!!!!!!

[thorn kindle]

😎

[mystic hemlock]

Hello I am new here

who is owner of this server

[alpine sable]

damn @thorn kindle u are very smart and helpful !

[warped phoenix]

hey guys

does anyone know how i could turn a number into a simplified radical using my ti84?

[candid thistle]

wont it just be basic normally?

[warped phoenix]

well like 6.923i = sqrt(-48)

[tight locust]

you can't do it on a ti84. it's not designed that way

unless you have a special app

[candid thistle]

oh stuff like that nvm

[warped phoenix]

oh 😦

where could i find such an app 😈

[tight locust]

look for CAS calculators. (computer algebra system). these work in the same way wolfram alpha does where they are able to manipulate math symbolically instead of just using floating point numbers

[mystic hemlock]

derivative of log(sin(cos x))

[alpine sable]

sus

[tight locust]

you can just google "(your model of calculator) simplifying radicals app"

something like that

is it the ce?

[warped phoenix]

it is yeah "Ti-84 Plus Ce"

[warped phoenix]

what

so yeah i want something to where if i wrote in "sqrt(-48), instead of giving me "6.928i" it gave me "4i*sqrt(3)"

[quaint edge]

Hi, I was just wondering in Gauss' elimination method in linear algebra, how can we do stuff like do (1-2)row1 + row2 and still have row1 be completely unchanged?

[hollow sage]

https://media.discordapp.net/attachments/831394897692459018/877054193003810856/image0.jpg?width=503&height=671

. rotate

wat

.rotate

[wheat condor]

<@&286206848099549185>

[vale wigeon]

it's ,rotate with a comma fyi

,rotate

[trail mantle]

How do u reduce an ODE to an ODE with constant coefficients?

[shell iron]

any clue what this table is?

<@&286206848099549185>

[alpine sable]

What’s the surface area formula for a triangular prism?

[wind bane]

do you want to derive the formula or do you just want to know it? because you can always just google that

[gray isle]

apply the definition of surface area

[manic glade]

why is k=n-1?

[vale wigeon]

nobody is claiming that

here the identity $\binom{m}{r} = \binom{m}{m-r}$ is used

[ocean seal]

Ann

[manic glade]

and why is that true

[tight locust]

symmetry

[vale wigeon]

what's your definition of the binomial coefficient?

is it the factorial formula or is the combinatorial one

[manic glade]

whats that

[vale wigeon]

this thing were talking about

$\binom{n}{k}$

[ocean seal]

Ann

[tight locust]

look at pascal's triangle

[vale wigeon]

are you defining it as $\frac{n!}{k!(n-k)!}$ or are you defining it as the number of subsets of $1:n$ of size $k$

[ocean seal]

Ann

[manic glade]

this?

[vale wigeon]

okay so youre defining it through factorials

great

$\binom{n}{n-k} = \frac{n!}{(n-k)!(n - (n-k))!} = \frac{n!}{(n-k)! k!} = \binom{n}{k}$

[ocean seal]

Ann

[manic glade]

neato

thanks

wait actually, how do you solve that

[willow wadi]

hi

[vale wigeon]

solve what

[willow wadi]

#latex-help

#latex-help

#latex-help

now

emergency

[manic glade]

oh nvm lel

[willow wadi]

lock down

[manic glade]

just sleep deprived

[willow wadi]

?av

[wide raven]

Why are matrices multiplied the way they are?

I've heard they are used somehow in vectors

I need some elaboration

[wind bane]

matrix multiplication is defined in exactly the right way to correspond to the composition of linear maps

[tough hatch]

https://www.youtube.com/watch?v=XkY2DOUCWMU

[gritty cave]

how do i solve this

[gray isle]

apply factor theorem

[gritty cave]

@gray isle is it 7?

[gray isle]

yes

[wide raven]

thank you

[wide raven]

thanks man, will surely see it

[rancid nexus]

@alpine sable ?

[alpine sable]

Because the third loop is not inside the second loop their times arent multiplied, they are added

tô hảd

too hard

So indeed the time complexity is n^2

Actually not even, it is at most n^2

Looks like it’s actually min(A.length,B.length)

@rancid nexus

Although this is quite a weird algorithm

yes

[slow haven]

can I post a question here?

[rancid nexus]

@slow haven yes i am done

[slow haven]

thanks

got this sent to me

dont know where to start

[jovial forum]

Starting with dP/dt = 0.0005P(2000-P), find P(t)

how do I do this?

[stark trail]

Multiply dt for both sides

then integrate both sides

[jovial forum]

So I wind up with P = Pt-0.0005P^2*t

or P(t) = Pt-0.0005P^2*t I guess?

Do I need to do anything else?

anyone?

[icy gyro]

this is correct @jovial forum

[jovial forum]

Thanks

[icy gyro]

just

the t is not a part of the power

[jovial forum]

oh yeah

ty

[icy gyro]

np!

[jovial forum]

So there should actually be a constant there. So P(t) = Pt-0.0005P^2*t + c, if P(0) = 100 then c = 100 right?

[icy gyro]

yep

[jovial forum]

So let's say I wanted to find when P=500, do I just sub 500 in for each P, then solve for t?

[icy gyro]

yess