help-39

[worn stone]

i made this

look at this

[woeful shadow]

now we have to write general expression for consecutive odd numbers

useless throw it

[worn stone]

bro what? 😭

[woeful shadow]

define even number

[worn stone]

@maiden zodiac @midnight haven help me im scared

[worn stone]

2

4

6

8

10

like

what

[woeful shadow]

in algebra we define even number as 2x

because all even numbers are multiple of 2

[worn stone]

ok

so even number = 2x

number = x

odd number = 1x ?

[woeful shadow]

consecutive odd numbers mean 1 and 3, 3 and 5

[worn stone]

yes

[woeful shadow]

and we learnt in between 2 odd numbers there is an _____ number

fill in the blanks

[worn stone]

even

[woeful shadow]

good

[midnight haven]

my pleasure

[woeful shadow]

so what can we write 2 consecutive odd numbers as

[worn stone]

help me im scared

[worn stone]

1x, 1x + 2 ?

[woeful shadow]

no

[worn stone]

1x, 1x + 1?

[woeful shadow]

not quite

[midnight haven]

sorry but i am not able to go cross channels and servers so

[woeful shadow]

first write even number 2x

[midnight haven]

i will leave it to the guy with that cartoon icon

idk how to describe

[woeful shadow]

then consecutive odd numbers are 2x+1 and 2x-1

[worn stone]

2x, 2x + 1

so 2 consecutive even integers =
x, x + 1
odd
2x, 2x + 1

?

[worn stone]

okay

[worn stone]

2n - 3 is odd too?

and 2n - 5 ?

[woeful shadow]

yes

even+odd=odd

ok coming back to the question

[worn stone]

man this is so weird

[midnight haven]

yes because no matter what the value is, 2n is even

minus an odd so

[worn stone]

i dont need to do this guys

its nice to learn but i dont need to do this paper

[woeful shadow]

how will you write sum of 2 consecutive odd numbers

[worn stone]

x + x + 1
2x + 1

[woeful shadow]

using this

[worn stone]

uh man

one sec

[midnight haven]

what is wrong with your username

[woeful shadow]

i have kept it like that

[midnight haven]

oh

[worn stone]

man

idk bro

[worn stone]

2x - 1 + 1 = 39?

2x = 39?

[woeful shadow]

it will be(2x+1) +(2x-1)

[worn stone]

like i dont understand bruh

[worn stone]

this is 2x right

[woeful shadow]

4x

[worn stone]

oh right

[woeful shadow]

did you understand why it is 2x-1 + 2x+1

for better understanding

[worn stone]

no i dont understand

[woeful shadow]

2(3)-1=5 and 2(3)+1=7

keep putting values of x

the concept is that between every odd number there is an even number

[worn stone]

x + (x + 1) + (x + 2) = 195  | isolate the x's
x + x + x + 1 + 2 = 195 | there are three of x, so it can be simplified to 3x
3x + 1 + 2 = 195 | add 1 and 2 together
3x + 3 = 195  | subtract 3 from both sides (inverse the sign)
3x = 192  | divide 192 by 3
192 / 3 = 64
x = 64  | this is the smallest of integers
x + 1 = 65 
x + 2 = 66   | this is the biggest of integers
64 + 65 + 66 = 195  | 3 consecutive integers add up to 195, the smallest is 64 (x), and the biggest is 66

[woeful shadow]

(2x)--> even number
(2x-1)-->odd number (because it is number before 2x(which is even))
(2x+1)--->odd number (because it is number after 2x(which is even))

[worn stone]

can you explain why this is useless

[worn stone]

i see

[worn stone]

this is just to calculate any values, even or odd doesnt matter

[woeful shadow]

2x+1+2x-1=48 4x=48 x=12

done

you need 3 steps

[worn stone]

what

[woeful shadow]

the answer is 12

[worn stone]

3 consecutive integers add up to 195

the answer is 64

x = 64

you mean the odd integers for question 7 ?

[woeful shadow]

q7 right?

[worn stone]

12 is not an odd number

man this is so confusing to me bro

the teacher doesnt explain anything

[woeful shadow]

x= 12 so the numbers are 2(12)+1 and 2(12)-1 = 23 and 25

23+25=48

[worn stone]

i see

[woeful shadow]

we can write 2 consecutive odd numbers as 2x+1 and 2x-1
it is given that sum of 2 odd numbers is 48
hence 2x+1 +2x-1=48

[worn stone]

so 2x + 1 and 2x - 1 = 4x = 48 = 12 = x
x = 12

so then why not just 4x from the start

+1 and -1 dont matter if they cancel each other out

[worn stone]

what about 3 consecutive odd integers?

3 odd = 81

how would that work

[woeful shadow]

2x-1 + 2x+1 2x+3

always start from and even number

[worn stone]

2x + 3

2x = 78

[woeful shadow]

6x=78

[worn stone]

oh

right

[woeful shadow]

13 is the answer

x=13 and 14 are the answers

[worn stone]

6x - 1 + 1 + 3

6x + 3 = 81

6x = 78

[woeful shadow]

x=13

[worn stone]

three odd integers

[woeful shadow]

2(13)-1, 2(13)+1, 2(13)+3

[worn stone]

man this is so confusing

[woeful shadow]

x=14 is also an answer

because we could have also written 2x-3 2x+1 2x-1=81

[worn stone]

so then how would i do 4?

[woeful shadow]

think

start from even number 2x

[worn stone]

2x -3 + 2x - 1 + 2x + 1 + 2x + 3

?

[woeful shadow]

yes

[worn stone]

then we solve for x?

[woeful shadow]

yes

[worn stone]

8x

-3 -1 +1 +3

what do we do with this

[woeful shadow]

they will cancel

[worn stone]

oh

i see

[woeful shadow]

+3-3 =0

[worn stone]

yes

8x then

so then

8x = 216?

216 / 8

27

x = 27?

[woeful shadow]

yes

[worn stone]

x = 27 for this

then boom

uh

answer

right?

[woeful shadow]

yes

[worn stone]

thank you

so what about even numbers?

or is my thing okay

[woeful shadow]

you can answer on your own start from even number

even odd even

[worn stone]

so instead of 2x its x

x - 2, x, x + 2

?

or

[woeful shadow]

no

[worn stone]

or is it still 2x - 2 , 2x, 2x + 2

[woeful shadow]

yes

[woeful shadow]

if x is odd number then x+2 is also odd number

[worn stone]

neuron activate

[woeful shadow]

so this cant work

always start with even number

then keep adding and subtracting to reach

[worn stone]

2x = even if x is even

if its odd its odd

epic ty

so

whats the steps for even and odd? so i can write to my friends

[woeful shadow]

no 2x is even for any value of x

[worn stone]

oh

• 1 is the offset

to make it odd

[woeful shadow]

2x+1 always odd

[worn stone]

yes i see

ok ty

[woeful shadow]

2x+999 is odd

[worn stone]

woah lol

[woeful shadow]

2x+999999999999999999999 is odd

[worn stone]

i understand

2x -3 + 2x - 1 + 2x + 1 + 2x + 3

where x = 27

2(27) - 3 + 2(27) - 1 + 2(27) + 1 + 2(27) + 3

51 53 55 57

right?

@woeful shadow

okay so

2x + 2x + 2 + 2x + 4 + 2x + 6

right?

<@&286206848099549185>

gods of mathmatics, save me from failiure 🙏

[maiden zodiac]

sup

[worn stone]

sup

[worn stone]

is this correct

2x + 2x + 2 + 2x + 4 + 2x + 6
8x + 12 = 20
8x = 8
8 / 8 = 1
x = 1

?

idek

[maiden zodiac]

x + x +2 + x + 4 + x + 6 = 20
4x + 12 = 20
4x = 20 - 12
4x = 8
x = 2

[maiden zodiac]

1* aint no even integer 😭

[worn stone]

wat

man idk man

im confused bro

and slow

and dont know this topic

even and odd and this shits annoying

[maiden zodiac]

see, take an integer x such that x is even okay

[worn stone]

2x

[maiden zodiac]

it means you can write x = 2n (the way you are doing it)

[worn stone]

[maiden zodiac]

now, it says 4 consecutive even numbers
so if the first number is x (or 2n)
next even number is x + 2 (or 2n + 2)
then x + 4 (or 2n + 4)
then x + 6 (or 2n + 6)

the ones inside the brackets is how you're doing it

[worn stone]

see bro

he said to forget just x

and do 2x for anything

and then offset by +1 or +2 if its even or odd

[maiden zodiac]

you can either solve for n now, or directly for x (as i did above)
if we solve for n, we do the way you did it and get n = 1, right?
now since x = 2n, we put n = 1 and we get x = 2
which is the least integer

[worn stone]

oh i seee

[maiden zodiac]

is my method hard? he said to use 2x, i prefer using 2n because that seems more comfortable

[worn stone]

id rather solve for x directly

method schmethod

[maiden zodiac]

see? that's how i did it initially

[worn stone]

can you teach me

he is scary

[maiden zodiac]

who is?

[worn stone]

@woeful shadow

this guy

CONSECUTIVE INTEGERS :

this is for calculating them no matter if its even or odd

x + (x + 1) + (x + 2) = 195  | isolate the x's
x + x + x + 1 + 2 = 195 | there are three of x, so it can be simplified to 3x
3x + 1 + 2 = 195 | add 1 and 2 together
3x + 3 = 195  | subtract 3 from both sides (inverse the sign)
3x = 192  | divide 192 by 3
192 / 3 = 64
x = 64  | this is the smallest of integers
x + 1 = 65 
x + 2 = 66   | this is the biggest of integers
64 + 65 + 66 = 195  | 3 consecutive integers add up to 195, the smallest is 64 (x), and the biggest is 66

also he said throw this away

called it useless

[maiden zodiac]

if x is even, no matter what you multiply it with, it will always be even

[worn stone]

\

😔

and she expects us to do this in around 15 minutes

[maiden zodiac]

x + x + 2 + x + 4 + x + 6 = 216
4x + 12 = 216
4x = 216 - 12
4x = 204
x = 51

[maiden zodiac]

it's actually easy

you need to get what the question wants you to do/show

Incase you want any further help, feel free to dm me

gg

[worn stone]

this is for even\

ok good

what about odd

i doi

x + x + 1 + x + 3

etc?

[maiden zodiac]

who said that its only for even
1 + 2 = 3
1 + 4 = 5
1 + 6 = 7
see?

[worn stone]

what

whatttt

os

[worn stone]

so

my equation was right

and he was just a hater

not really

but

ok i will try your method on this one

[maiden zodiac]

won't work tho, but if you take directly from x + 1, then it will
say x + 1 + x + 3 + x + 5 + x + 7 = 216
4x + 16 = 216
4x = 216 - 16
4x = 200
x = 50
since we assumed x + 1 to be the first number,
hence, x + 1 = 51 (ans)

[maiden zodiac]

sure go for it, but check this msg as well

[worn stone]

x + x + 2 + x + 4 + x + 6 = 216
4x + 12 = 216
4x = 216 - 12
4x = 204
x = 51

---

x + x + 2 + x + 4 = 51
3x + 6 = 51
3x = 45
45 / 3 = 15
x = 15
15 + 15 + 2 + 15 + 4
15, 17, 19

I DID IT

HOLY CRAP

[maiden zodiac]

x + x + 2 + x + 4 = 51
3x + 6 = 51
3x = 51 - 6
3x = 45
x = 15
yes you're right!

[worn stone]

holy moly

neruon

[maiden zodiac]

haha gg

[worn stone]

gg

x + x + 2 + x + 4 + x + 6 = 216
4x + 12 = 216
4x = 216 - 12
4x = 204
x = 51

---

ok so

x + x + 2 + x + 4 + x + 6

4x + 12 = 294

4x = 282

70.5

x = 70.5

[maiden zodiac]

no, you're wrong

[worn stone]

😔

[maiden zodiac]

yk why? because it says sum of 4 consecutive integers

[worn stone]

whatt

[maiden zodiac]

that is, x + x + 1 + x + 2 + x + 3

[worn stone]

oh

[maiden zodiac]

read the question silly

[worn stone]

4 consecutive integers add up to 294

same thing as the sum of 4 consecutive integers is equal to 294

[maiden zodiac]

||4x + 6 = 294
4x = 288
x = 72||
answer, don't look at it yet

[maiden zodiac]

yes

[worn stone]

x + x + 1 + x + 2 + x + 3
4x + 6 = 294
4x = 288
x = 72
72 73 74 75

i didnt look

so then

this is x + x + 1 + x + 2

?

[maiden zodiac]

yes

see, you got it, but make sure you know that you need to find the greatest one this time

[worn stone]

x + x + 1 + x + 2
3x + 3 = 12
3x = 9
x = 3
3 4 5

5

okay so

now what?

[maiden zodiac]

gg

[maiden zodiac]

you already did it
do it with x + x+ 2 ...

[worn stone]

x + x + 2 + x + 4 + x + 6

[maiden zodiac]

[no silly dont let the word "odd" mislead you

[maiden zodiac]

yes exactly

[worn stone]

got it

[maiden zodiac]

bingo

[worn stone]

x + x + 2 + x + 4 + x + 6
4x + 12 = 88
4x = 76
x = 19
19 21 23 25

19

brain activation

ty arpoop

[maiden zodiac]

gg

anytime pal

[worn stone]

so

x + x + 2 + x + 4
3x + 6 = 285

3x = 279

x = 93

93 95 97

i was right

[maiden zodiac]

see? easy right

[worn stone]

yippeeeee

easy yes

[maiden zodiac]

once you get the hang of it, you're unstoppable

[worn stone]

okay so

this

x + x + 2 + x + 4 + x + 6

same thing?

[maiden zodiac]

yes

don't ask, solve

[worn stone]

x + x + 2 + x + 4 + x + 6
4x + 12 = 28
4x = 16
x = 4
4, 6 , 8 , 10

10

[woeful shadow]

we can just ignore the odd and even integers because the questions set up in that way?

[maiden zodiac]

okay so you need to know how you define numbers
if x = 2n, we say this is even
if x = 2n + 1, we say this to be odd
keep this in mind anytime you're stuck

[maiden zodiac]

bingo

[maiden zodiac]

-15, mind the sign

[worn stone]

x + x + 2 + x + 4
3x + 6 = -15
3x = -9

?

6 - 15?

[maiden zodiac]

-15 - 6

[worn stone]

or is it 6 - (-15)

[worn stone]

well

which is it

my way or your way

[maiden zodiac]

my way

[worn stone]

cuz 21 and -21 are different things

ok

got it

so

oh right i see

i remember

[maiden zodiac]

see? easy

[worn stone]

right side go first

yes

x + x + 2 + x + 4
3x + 6 = -15
3x = -21
x = -7
-7 -5 -3

[maiden zodiac]

bingo

[worn stone]

and this is x + x + 1 + x + 2 + x + 3

[maiden zodiac]

yes

[worn stone]

instead of 2 4 6 8

right

[maiden zodiac]

indeed

[worn stone]

ill have to let my friends know

teacher does not teach

tbh

[maiden zodiac]

you only use 2 4 6 8 when its mentioned that they're either odd or even consecutives

[worn stone]

ty

[maiden zodiac]

otherwise, you don't have to use them
go with 1 2 3

[midnight haven]

,w x+x+1+x+2+x+3=10

[worn stone]

wat

[worn stone]

what is he doing

[jolly parrot]

Results provided by WolframAlpha

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

Requested by jl7up

[maiden zodiac]

eh dont mind him

[worn stone]

alr

[midnight haven]

i am using a bot to solve the equation

[maiden zodiac]

he is tryin out stuff

[midnight haven]

but i kept doing mistakes

,calc 1+2+3+4

[jolly parrot]

Result:

10

[worn stone]

x + x + 1 + x + 2 + x + 3
4x + 6 = 10
4x = 4
x = 1

1 2 3 4

??

[maiden zodiac]

yess

[worn stone]

epic

im gonna use this as the demonstration instead of what i had on my other one

[maiden zodiac]

i'll take my leave kid, enjoy solving now!

[worn stone]

this is for calculating them no matter if its even or odd

x + x + 1 + x + 2 + x + 3  |  This is the formula
4x + 6 = 10  | Isolate the x's into (amount of x's)x + the amount of offset per every x (1 + 2 + 3) 
4x = 4  | Subtract 10 (right hand side goes first) from 6
x = 1  |  Divide 4 (right hand side) by 4x
1 + 2 + 3 + 4  | Substitute x as 1 in the formula, and you get this

[worn stone]

:(

can you stay

i kinda like you as a teacher bro

[worn stone]

can somebody fact check my work right here

[maiden zodiac]

I wanna play minecraft welp 😢

[worn stone]

lol sorry man

[maiden zodiac]

thanks man i get that a lot

[worn stone]

you can play minecraft but can you help me with one last thing

pls pls pls

[maiden zodiac]

sure tell

[worn stone]

this is for calculating them if the question asks for even or odd integers

x + x + 2 + x + 4 + x + 6 |  This is the formula (4 consecutive integers [x] [x + 2] [x + 4] [x + 6])
4x + 12 = 20  | Isolate the x's into (amount of x's)x + the amount of offset per every x (1 + 2 + 3) 
4x = 8  | Subtract right hand numbers (right hand side goes first) from left hand numbers (4x + a = b) (b - a)
x = 2  |  Divide 4 (right hand side) by 4 (ax = b) (b / a) (x = b / a)
2 + 4 + 6 + 8  | Substitute x in the formula
Done!

sorry i was writing a lot

[maiden zodiac]

yep that pretty much seems correct to me

you got the idea right?

[worn stone]

yes

[maiden zodiac]

another thing to keep in mind, even numbers can be written as 2n and odd ones as 2n + 1
will be helpful in later studies

[worn stone]

yes ty

[maiden zodiac]

gg

[worn stone]

gg

[maiden zodiac]

tc gtg

[midnight haven]

all the best h

remember to close the ticket if you dont have any further enquiries at the moment

[worn stone]

is this good explanation chat

@midnight haven

@maiden zodiac

[worn stone]

sorry for ping again, ik your trying to play minecraft but this is the last question i have

yall have helped me get three 100's, ty guys so much (75's because the teacher is a butt and removes 25% if late but its whatever)

[midnight haven]

wonderful

very

[worn stone]

yaayaayayaya

i shall close this and return to this place if neccessary

also is there a website that shows me the units of everything in alg 1?

so i can get ahead or study what im learning currently

[worn stone]

and preferably every other course like alg 2 and english etc

im gonna rip my skin out

i have to get 100

ive been at this so long bro

and then after this i have to do 140 flash cards

[midnight haven]

all the best

[worn stone]

lets go chat

we got this

1 more 😭

lets goooo

@midnight haven @maiden zodiac

ty guys so much for everything

.close

[pearl pond]

Channel closed

Closed by @worn stone

Use .reopen if this was a mistake.

[midnight haven]

my pleasure

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[worn stone]

how do i do this <@&286206848099549185>

[worn stone]

@midnight haven idk if you are awake but i need help pls

[midnight haven]

its just like 6pm for me ofc i am not asleep bro

[midnight haven]

you do the change of subject

[worn stone]

its 6am for me LOL

[midnight haven]

t = vu
vu = t
u = v/t

[worn stone]

so then

this is

y/x?

[midnight haven]

x = w - y
w - y = x
w = x + y

sorry am a bit busy across channels and servers

what if i leave this channel to jade

[worn stone]

i see

[brave ivy]

Try to keep the operation in mind

[worn stone]

sure

[brave ivy]

Sounds good 🙂

[midnight haven]

ty

[brave ivy]

Np

[worn stone]

what the heck am i supposed to do here 😭

[brave ivy]

How do you initially want to start?

[worn stone]

this is the original problem

[worn stone]

i dont know, you tell me 😭

idk how to do this

[brave ivy]

Fair lol

So you want to solve for x correct?

[worn stone]

yes

wait

this

this is the full thing

yes just moving them

but idk how

[brave ivy]

If we have w=(xu)v do you have an idea of how to just move the v?

[midnight haven]

dont worry, h is a very good one, he has the initiative to try after you teach him one or two questions, not like all others who just ask for answers through their whole assignment

[worn stone]

:D

[brave ivy]

I have no doubt of that, I meant no shade, and am attempting to go slow to help him build an intuition 🙂

[worn stone]

ive been doing math for 6 hours straight

maybe longer

[midnight haven]

bro go get sleep

[worn stone]

but i have gotten 3 assignments done so its worth it

[worn stone]

cant, school in 2 hours

[brave ivy]

Yeah me too man, working on a research project atm lol

[midnight haven]

jesus did you not sleep the whole night

[worn stone]

i slept well, dw

ive been slacking off a lot this week

[midnight haven]

phew much better

[brave ivy]

That’s good

[worn stone]

ok so

in terms of u v and w solving for x

how do

[brave ivy]

Does anything come to mind for this situation?

If not that’s totally fine

[worn stone]

no

its my first time doing anything like this

[brave ivy]

Alright

[worn stone]

so i have no clue lol

[brave ivy]

Totally understandable

Well we have 2 main type operations we’ll be dealing with

Multiplication/division
And addition/subtraction

You can view one as the undo button of the other

[worn stone]

w = xu / v?

wait

[brave ivy]

Close, that’s a good start

[worn stone]

x = wu / v

[brave ivy]

Not quite

We start with w=xuv

We want x on its own

[worn stone]

w=xuv
x=wuv
x=w/uv

[brave ivy]

So we will go after one variable at a time

[worn stone]

?

[brave ivy]

Division isn’t the same as multiplication, so those 2 won’t be equivalent

[worn stone]

hm

[brave ivy]

We want to perform an operation on both sides of the equation to make it work

[midnight haven]

division is like $\div$ and multiplication is like $\times$

[worn stone]

oh i see

both sides

[midnight haven]

they are two very different things

[worn stone]

yes

lol

[jolly parrot]

jl7up~

[worn stone]

bot error

[midnight haven]

no its my error

my code error

[worn stone]

your bot error

[midnight haven]

😂

[brave ivy]

So consider

w=xuv
w/v=xuv/v
w/v=xu

where / acts as the division symbol

From here we would want to continue by removing u from the left side to isolate the x

How do you think we would want to do that

[worn stone]

w/vu = xu/u

w/vu = x

?

[brave ivy]

Exactly!!!

[worn stone]

x = w/vu?

[brave ivy]

Yup

[worn stone]

?

[brave ivy]

Yeah!

[midnight haven]

you dont need to put the x = in the box

[brave ivy]

Oh

[midnight haven]

cause its already given

[brave ivy]

Was about to say that lol

[midnight haven]

sorry if my wpm is too quick

[brave ivy]

It’s correct, but just need w/uv

[midnight haven]

my highest peak was 156 💀

[worn stone]

so to clarify,
w = xuv
w/v = xu
w/vu = x
x = w/vu

[worn stone]

mine was 180

200+ if i tried

[midnight haven]

nice

[worn stone]

150 not like locked in

[brave ivy]

Exactly

[worn stone]

on the 30 second tests

[worn stone]

epic

alright so

let me try to cook here

[midnight haven]

physics nuclear energy mentioned in maths assignment
😂

[brave ivy]

Absolutely, give it your best shot

[worn stone]

PV/T = nR
PV/TR = n
n = PV/TR

[midnight haven]

remember to let me try your cooked food later

[worn stone]

?

[midnight haven]

yes

[worn stone]

alr alr

[worn stone]

epic this is so easy

i dont understand why youd need to get these values but

its so easy

[midnight haven]

i feel like changing subjects is easier than solving equations

cause you do a lot less

if you dont need to solve for the number value

[worn stone]

idk what to do here

[midnight haven]

you ignore the negative sign first

but youll need it in the answer

[worn stone]

x = y/z

ok

[midnight haven]

no its negative y over z

not positive y over z

[worn stone]

x = - y/z

[midnight haven]

mhm!

[worn stone]

you said ignore

[midnight haven]

yes i did but still

[worn stone]

ok so then what

[midnight haven]

x = -y / z

xz = -y

-xz = y

y = -xz

[worn stone]

whatt

[midnight haven]

yes

[worn stone]

that is so weird

i understand it

[midnight haven]

i say you ignore the negative sign

[worn stone]

but its still weird

[midnight haven]

because you can just directly add it back at the end of your operations

[worn stone]

how

[worn stone]

yes

[midnight haven]

you do subtraction

b = d + c + a
b - d - a = c
c = b - d - a

[worn stone]

wait

so its literally just inverse operations but like

weirder

?

[midnight haven]

youre lucky enough h
today is probably the last day i will be online cause summer break is ending

[worn stone]

r = p + q

?

[midnight haven]

yea i think you can say so

[midnight haven]

yes

[worn stone]

:(

you are a good teacher

[midnight haven]

my pleasure bud

ykw my dream is to become a teacher when i grow up
so if i were your teacher
😂

[worn stone]

is this good

[worn stone]

epic

[midnight haven]

yes you are right

[worn stone]

become an online tutor tho, classrooms suck bc of bad kids

[midnight haven]

i am very good at maintaining discipline dw

[worn stone]

unless you teach the higher up grades

uh

s = p / 4

?

[midnight haven]

its like when i am in the library and the kids are noisy as shit i just shout at them and they shut up immediately

[worn stone]

lol

[midnight haven]

(i am sort of like a student security guy at the library)

[worn stone]

i see

[midnight haven]

a prefect if you know what that is

[worn stone]

i do not but its oka

[midnight haven]

yes youre right

[worn stone]

dude im on a roll

[midnight haven]

a prefect = a person that maintains discipline of school

[worn stone]

role = over

i have no clue what to do brah

[midnight haven]

this is a bit worse

[worn stone]

LOL i agree

[midnight haven]

for this you need cross multiplication

[worn stone]

whattt

[midnight haven]

q = (-1/p)sr

q/sr = -1/p

qp = -sr

p = -sr/q

[worn stone]

wat da hal man

[midnight haven]

ikr

[worn stone]

lol

nice

same question

[midnight haven]

but different subject

[worn stone]

oh?

oh

your right

alr one sec

i got this lemme cook chat

[midnight haven]

||PV = nRT
nRT = PV
R = PV/nT||

check later

[worn stone]

R = PV/Tn

[midnight haven]

yes

but do note the n should be small

nice you edited it in time

i gtg now sorry bro

@brave ivy if you are available to continue helping h please

[worn stone]

PV = nRT
PV/T = nR
PV/Tn = R

[brave ivy]

For sure

[midnight haven]

i like how the help between us is like alternate 😂

[worn stone]

so

lol

[brave ivy]

Yeah lol

[worn stone]

b = a + c

sorry lol my hands are weird rn

[brave ivy]

All good lol

But yeah just add a to both sides and you get that 🙂

[worn stone]

idk if this would be b = c + a or b = a + c

we work it right to left to i think a + c

[brave ivy]

Whats the difference between 4+7 and 7+4?

[worn stone]

nothing but idk

some people are weird about having it placed right

[brave ivy]

They’re exactly the same

[worn stone]

yes

so for this one

[brave ivy]

The awkwardness with this one is the negative right? How do you want to approach that?

[worn stone]

t = -srq
t/q = -sr
t/qr = -s
s = -t/qr

like dat

i did this twice, and swapped -s and t the first time

solving for t on accident lol

[brave ivy]

Yup, but we still have that negative we need to deal with

Ah lol

[worn stone]

there

[brave ivy]

Yup!

[worn stone]

idk what to do

wait

cross multiply or something

w = v * u

?

[brave ivy]

Not quite, remember that multiplication and division are inverses, so the best way to start is moving w to the other side

How would you want to only do that

[worn stone]

w = v/u

[brave ivy]

Yup!

[worn stone]

sorry it took so long to respond

[brave ivy]

Do you see why?

All good

[worn stone]

no i dont see why, am just following instructions

[brave ivy]

Fair

[worn stone]

lol

is w = v/u

[brave ivy]

If 2 things are equivalent, when we do the same operation on both sides they should remain exactly the same so it follows like this

u=v/w
u*w=(v/w)*w
uw=v
uw/u=v/u
w=v/u

Yeah you were right, just want to make you sure you get the rational

[worn stone]

brain hurty

[brave ivy]

That’s totally fair

[worn stone]

lol idk

[brave ivy]

We can see that u=v/w means that u should have the same value as v/w right?

[worn stone]

yes

plus and minus??

oh no

[brave ivy]

Then if we multiple or divide 2 things that are the same by the same value they should stay the same

[brave ivy]

Don’t worry you got this!!

[worn stone]

idk if i do mane

v + x - w

u =

thats all i got

its probably wrong too brah

[brave ivy]

Try to take it one step at a time

We know we want the u on its own, so just start by handling the w

How would we handle that?

[worn stone]

x = v + u - w
x - w = v + u
x - w + v = u
?

i do NOT know

[brave ivy]

Hey don’t worry

It’s fine to not know

You are close, but we don’t subtract w from both sides to remove a negative w, we would want to add w to both sides

[worn stone]

o

oh

OH

[brave ivy]

Similarly for adding v 🙂

[worn stone]

x = v + u - w
x + w = v + u
x + w - v = u

u = x + w - v

?

so many letters

😔

[brave ivy]

Yup!!!

Good stuff!

[worn stone]

wait

neruon activation

[brave ivy]

Whats your first thought?

Yeah?

[worn stone]

r/ts = 1/u

wait

😔

idk anymore

lol

r = 1/u ts

r/ts = 1/u

yeah idk

[brave ivy]

That’s true, but when multiplying and we have t in its own it’s best to keep it on the side where it’s multiplying instead of dividing if that makes sense

So focus on moving things from the right side to get things away from t

[worn stone]

r/s = 1/u t

idk where to go next

ru/s = 1 t ?

idk

its becoming daylight

😔

[brave ivy]

Yup! The 1/u is the same as dividing the whole of it by u

So multiplication remains the inverse

[worn stone]

so 1/u = u/u

so ru/s = t

so t = ru/s

[brave ivy]

Not quite

[worn stone]

😔

[brave ivy]

(1/u)ts=ts/u

[worn stone]

ru/s

i swear its ru/s

[brave ivy]

1/u≠u/u

[worn stone]

i got it right

[brave ivy]

Oh this part is legit

[worn stone]

o

[brave ivy]

This part is not

[worn stone]

i see

[brave ivy]

Sorry wasn’t clear

[worn stone]

its alr im done now

i understand fully

ty

@brave ivy

ty for the help

.close

[pearl pond]

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[brave ivy]

No problem man 🙂

Glad you’re getting it

[worn stone]

ty

[pearl pond]

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[dire crater]

This is impossible. The task is to get the area of a perfect hexagon (idk how to translate it, the one where all its lines are the same) where S is in the middle of it and A3 is one of the hexagons dots. How did we get the last line? The sin 60 part is very confusing to me

[compact ridge]

a regular hexagon is just 6 equilateral triangles, no?

then you can do 6 * (1/2 ab sin C), where a = b = distance from S to A3 and C = 60 deg

,w 6 * 1/2 * (1^2 + 0^2 + 4^2) * sin(60 deg)

[jolly parrot]

Results provided by WolframAlpha

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Requested by sooouth.

[dire crater]

but I dont get how this works, why can we put (ab sin C) instead of ||axb||/2 to calculate one of the triangles?

[compact ridge]

oh I can show you

[dire crater]

ok I understand now but damn idk how I would even remember this :/

thank you 🙂

[compact ridge]

practice I guess

no worries

[dire crater]

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[neat harbor]

what is l‘hospitals rule for solving limits? Ive seen the term a few times, and the research i’ve done just leads to a lot of different formal definitions I dont understand

[gleaming moss]

When you try to evaluate a limit and find it gives an indeterminate form, you can apply l’hopital. Just get it into a fraction and differentiation the numerator and denom separately

[neat harbor]

and then just try again

[gleaming moss]

Try to evaluate the result, if you get indeterminate form again then apply l’hopitals again yes

Or you might find some other way to continue algebraically

[neat harbor]

ok thanks

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[oak patrol]

Solve in whole numbers: a^2 + b^2 + c^2 + d^2 = 2abcd

[sly dagger]

aint this just AM-GM?

doesnt this hold when a=b=c=d tbh idk

[autumn fossil]

not homogenous, not AM-GM

[sly dagger]

oh wait im blind

[next dove]

what type of question is it supposed to be?
like is it all about hit-n-trial thing or some legit method?

[pearl pond]

@oak patrol Has your question been resolved?

[sly plover]

Why not im curious

By AM-GM we can get the answer as √2 for each one

[next dove]

how exactly did you got sqrt2

?

[sly plover]

AM-GM ;-;

[next dove]

I mean explain about it

[sly plover]

All terms will be equal

[next dove]

wait that's a weird line

[next dove]

why?

[sly plover]

So you get 4a^2 = 2a^4

[sly plover]

Cuz the arithmetic mean is equal to the geometric mean

[next dove]

why will it even be equal?

[sly plover]

Cuz of the question 😭

[next dove]

bruh, check your calculations again

[sly plover]

Alr wait

[sly plover]

They are correct ig

√2 also satisfies the equation ;-;

[next dove]

I mean it works but it is not a valid answer

[sly plover]

How ;-;

[next dove]

whole numbers*

[sly plover]

Ohhhh

Mb then 😭

[next dove]

and also you're somehow making a mistake in the inequality too

[sly plover]

I'm pretty sure that it is correct

[next dove]

can you share your work?

[sly plover]

Alright

[next dove]

okay the mistake is clear

it is supposed to be 4th root

[oak patrol]

Find all possible combinations (a,b,c,d)

[next dove]

and how are you even dividing geometric mean thing by 4?

[oak patrol]

Sqrt 4th degree

Lol what’s not am gm

[sly plover]

My bad my brain isn't working 😭

[sly plover]

I'm just dumb nvm

[oak patrol]

I think only solution (0,0,0,0)

[next dove]

but how can we prove if there are any more than that or not

[oak patrol]

No 4*4 = 2^5?

[next dove]

okay I'm dumb sorry

[oak patrol]

The only solution using 0 is (0,0,0,0) otherwise on the right 0, and on the left is greater than zero, then we will continue with a,b,c,d≠ 0. I Tried To Write Viet's Theorem And Got That If There Is A Suitable Four, We Can Build Them Endlessly

<@&286206848099549185>

[oak patrol]

.

[pearl pond]

@oak patrol Has your question been resolved?

[spiral pivot]

Hint: Consider a, b, c, and d mod 4.

Click to reveal, try to follow along and guess the steps before seeing what I did.

||If x is even then x^2 mod 4 = 0, if x is odd then x^2 mod 4 = 1.||

||I will leave it to you to check that the only way this formula could possibly hold is if (a, b, c, d) are all even, but it's straightforward to calculate.||

||Assume for the sake of contradiction that there is a solution in the positive integers (a, b, c, d)||

||We have a = 2m, b = 2n, c = 2o, d = 2p and||

||4(m^2 + n^2 + o^2 + p^2) = 32mnop||
||m^2 + n^2 + o^2 + p^2 = 8mnop||

||We have by a similar argument to the first that m, n, o, and p must also be all even or all odd.||

||Iterate this process until we get m, n, o, p all odd (n.b. we use the assumption of positive integer solutions here, as if (a, b, c, d) = (0, 0, 0, 0) this iteration does not terminate) notice that the factor of 4 on the right hand side increases with the number of iterations, let there be k iterations.||

||Let m_k = 2w+1, n_k = 2x + 1, o_k = 2y + 1, and p_k = 2z + 1||

||From our formula of m,n,o,p and substituting in the above values and simplifying we get:||

||w(w+1) + x(x+1) + y(y+1) + z(z+1) + 1 = 2^(2k - 1) (2w+1)(2x+1)(2y+1)(2z+1)||

||Notice that the left hand side is odd, as it is the sum of 4 even numbers and 1. However the right side is even, because it has a factor of 2^(2k-1)||

||This is a contradiction. Thus our original assumption is false. There are no positive solutions (a, b, c, d).||

@oak patrol ^

I do not know if this is how you are intended to solve this problem. But it seems overly complicated. There might be a more simple solution.

Interesting problem, thanks for the diversion.

[oak patrol]

It's probably easier to say this: according to mod 4 we get that a,b,c,d are all even (if 0 are even, then the left part is divided by 4, and the right part is maximum by two (except in the case of zeros) if 2 is also a slight contradiction, then repeating this, we see that they are infinitely divisible by 2

[spiral pivot]

Well, yes, that sums up the argument, but you have to show that if you reach the all odd case it results in a contradiction

Because it's "fine" mod 4 to get all odd after the first iteration

[oak patrol]

Thanks!

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[tawny pewter]

how owuld i do this

[whole moat]

you know that sin(x) is negative right

and that cot(x) is positive

so that means that cos(x) has to be negative as well

using the unit circle it has to be in the third quadrant because that's the only location cos and sin are both negative

then label the values of your triangle and use Pythagoras to find the hypotenuse and thus cos(x)

[tawny pewter]

why does cosine have to be negative

[whole moat]

cot(x) is cos(x) / sin(x)

the negatives need to cancel out if cot(x) is positive

[tawny pewter]

do u know what this type of problem is called

[whole moat]

no idea but its a precalc problem I think

a unit circle problem?

[tawny pewter]

it is

[pearl pond]

@tawny pewter Has your question been resolved?

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[robust cedar]

hey i have this problem where im trying to find the dot product between vector u and w. i tried to solve it using u = (0,7,0) and w=(7,7,0) and got 49 but that was wrong. how do i solve this?

[robust cedar]

oh i just noticed the direction of the vectors i wonder if that changes my answer

yep, -49 is the answer

-close

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[robust cedar]

the equation to use here would be work = the dot product of F vector and displacement vector right? displacement would just be (35,0,0) but im struggling to find the F vector. its 9N but how do i work out the x/y that combines to that

[plush bramble]

have you taken trig?

[robust cedar]

its been a few years

the physics questions are just messing with me bc i havnt taken physics

idk if i could take force as a distance and say since that side is 9N the bottom side should be 7.8 and right side should be 4.5

[plush bramble]

,calc 9 * cos(30 deg)

[jolly parrot]

Result:

7.7942286340599

[robust cedar]

got it 🙂 i wish my professor would use more common units so it didnt confuse me so much 😭

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[silver sequoia]

Help, im not used to roots

Give me hints..

Please

[west haven]

derivate of g(f(x)) is g'(f(x))f'(x)

[silver sequoia]

Im not in there yet

Its trigonometry solutions

[compact veldt]

Product rule

[cloud zephyr]

this time it's really about conjugate...

[silver sequoia]

Oh my

[merry carbon]

(in general, problems with roots involve e.g. multiplying and dividing by the conjugate to get something "easier" to work with)

[west haven]

its in numerator

no need here

[merry carbon]

Well, here, it does make the problem easier to do (with a bit of work, there's cancellation that happens)

[silver sequoia]

This?

[merry carbon]

Yep (but you have 2sin(x) rather than the (x - 10) in the denominator, and some would help)

[silver sequoia]

Oh right

😭

[merry carbon]

You end up with
[
\frac{ (1 - \sin(3x)) - (1 - \sin(3x)) }{2\sin(x) (\sqrt{1 + \sin(3x)} + \sqrt{1 - \sin(3x)} ) }
]

[jolly parrot]

@merry carbon

[silver sequoia]

Right

[merry carbon]

With the , can you simplify that numerator, maybe?

[silver sequoia]

Ohh

[merry carbon]

Did you really use loptial

[west haven]

yea why?

[sinful nebula]

for some schools you shouldn't use l'hospital

till you reach that topic

[silver sequoia]

Hmm what do i do next? Should i get the 3 out from the numerator so i can cancel 2sinx?

[merry carbon]

How do you mean "get the 3 out of the numerator"? There's an idea there, you may be on to something, if you rewrite sin(3x)...

[silver sequoia]

Hmm

[silver sequoia]

Like that?

[merry carbon]

Not like that

[silver sequoia]

Ohh dang

[silver sequoia]

How?

[merry carbon]

sin(3x) is not 3sin(x), but there is an identity for sin(3x)...

[silver sequoia]

3sinx-4sin^3x ?

[merry carbon]

Yep that's it

[silver sequoia]

Ohh

[merry carbon]

Now that should make life a bit nicer

[sinful nebula]

bro

just use standard limit

[silver sequoia]

Oh

[sinful nebula]

you know limit x tends to zero sin(nx)/nx = 1

[silver sequoia]

Yeah

[silver sequoia]

What do i do with the root tho

[sinful nebula]

put x = 0

[silver sequoia]

Oh right

[sinful nebula]

wait

[silver sequoia]

So its 3/2?

[sinful nebula]

no wait

[silver sequoia]

Oh..?

[sinful nebula]

answer is correct but you will LOSE marks

your step is nor correct

[sinful nebula]

I will start from here

if you put sin(3x) formula you will get the same answer

[silver sequoia]

Ohh

[sinful nebula]

but its unwanted calculation

instead

2sin(3x) can be written as 6*sin(3x)/3x

divide by x in both numerator and denominator

I will show you in whiteboard

[silver sequoia]

Oh okay

[silver sequoia]

Where?

[sinful nebula]

rewrite in that form

the trick is to manipulate so that you can use standard limits

[merry carbon]

(you don't need to do that with the square roots, just split that and work it out as "product of limits")

[sinful nebula]

yeah you can do that too

[silver sequoia]

Oh hm

[silver sequoia]

How?

[sinful nebula]

took 1/2 outside of limit

[silver sequoia]

Ohh