help-23

[stone barn]

Thought I could just leave it as it was

😓

Ty anyways

[fathom jewel]

tbf it's more of a preference

[stone barn]

Yeah

[fathom jewel]

this little nuance doesn't make your solution less correct

[stone barn]

Tbh I’m lazy I couldn’t be bothered

🫠

Guess that’s why I thought it was wrong

Anyways tysm

.close

[safe radish]

Channel closed

Closed by @stone barn

Use .reopen if this was a mistake.

[fathom jewel]

also i forgot this

don't just write integral 1 to 3 solely, just leave it

[safe radish]

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.

[strange cosmos]

Hello

[strange cosmos]

I have a test tomorow in math and i know absolutely nothing

Can i send some pictures on what kind of math it is?

Ignore the written text under. I don’t really know how to translate the text

But the ones at the top should be fine

I know berett anything about this and I really need to pass my test or else I’m really in trouble

[empty gyro]

what do you know about exponents so far?

[strange cosmos]

that if it is for an example 5 elevated to 2 it will be 5 times 5 wich will equal 25

But when its larger questions and with multiple exponents and all that my brain stops

Can you teach me?

[hardy monolith]

youre asking about questions 1-4 right?

[strange cosmos]

Yes

[hardy monolith]

what is your solution for 1.a)?

or are you completely clueless

[strange cosmos]

I just tried to solve and it didnt go that well

I am clueless

[hardy monolith]

!show

[safe radish]

Show your work, and if possible, explain where you are stuck.

[hardy monolith]

can you show what you did?

[strange cosmos]

.

[hardy monolith]

im sorry, i cant read that

[strange cosmos]

so i did 3 elevated to seven times 3 elevated to 5 divided by 3 evelated to 2

[hardy monolith]

can you please redo it or make a better photo

[strange cosmos]

That number 1

Ok

Ignore the written text that was my teacher doing

[hardy monolith]

i dont see answers for question 1

[strange cosmos]

well we dont answer our question in my school. We have a separate notebook for that

[hardy monolith]

can you show where you have written down your answer?

[shell badge]

Is this asking to simplify?

[strange cosmos]

I left that one in school for winter break so i dont have it with me

[hardy monolith]

okay sure

you have a few exponent rules

$a^b\cdot a^c=a^{b+c}$

[flat frigate]

Bonk

[hardy monolith]

$\frac{1}{a^b}=a^{-b}$

[flat frigate]

Bonk

[hardy monolith]

$\left(a^b\right)^c=a^{b\cdot c}$

[shell badge]

a³/a⁵ = a^3-5

[flat frigate]

Bonk

[strange cosmos]

huh?

[hardy monolith]

so, if i give you $3^7\cdot 3^5$ what do we simplify it to?

[flat frigate]

Bonk

[hardy monolith]

and which rule do we use

[strange cosmos]

we simplyfy it to 3 elevated to 12?

[shell badge]

Yesss

[strange cosmos]

yey

[hardy monolith]

indeed

now, what about $\frac{3^{12}}{3^2}$?

[shell badge]

Huh

[flat frigate]

Bonk

[shell badge]

You minus the elevated numbers

[hardy monolith]

to simplify this, we actually need to use 2 rules

[shell badge]

This time

[hardy monolith]

dont spoil the solution please

[strange cosmos]

so it will be 3 evelated to 10

?

[shell badge]

You didn't explain that rule to him

[hardy monolith]

indeed

[strange cosmos]

What run?

[hardy monolith]

@shell badge

so, we have just simplfied 1.a)

$\frac{3^7\cdot 3^5}{3^2}=3^{10}$

[flat frigate]

Bonk

[hardy monolith]

now try doing b on your own

[strange cosmos]

Yes

[shell badge]

That rule would be more like
a⁵/a³ = a elevated to 5 - 3

[hardy monolith]

please, this is not your question, dont try to give the solutions

[shell badge]

That's an example

Dw

[hardy monolith]

for b, try doing it step by step just like we did with a

so, where can we start?

[strange cosmos]

4 evelated to 5 times 4 evelated to 3 divided by 4 evelated to 2 would be 4 evelated to 5?

[hardy monolith]

please dont write like this

[strange cosmos]

Oh

[hardy monolith]

its unreadable

[shell badge]

Wait Berra you can use ^ as elevated

[hardy monolith]

use ^ as exponent and * for multiplication

[strange cosmos]

Ok

so

[hardy monolith]

and just do one step at a time

[upper kettle]

but there is • for multiplication

[hardy monolith]

you dont need to do it all at once

[hardy monolith]

yeah but who tf has that on their keyboard?

[shell badge]

I do

[upper kettle]

i am writing on an iphon

[shell badge]

I am on android

But anyways

• is much simpler

[weary mango]

no there is a power if you're on pc

³⁶⁹½⁴⁴½ⁿ

[shell badge]

Huh

[strange cosmos]

4^5 * 4^3 would be simplyfied to 4^7

[hardy monolith]

guys, please

[hardy monolith]

nope

[strange cosmos]

and 4^7 divided by 4^2 would be 4^5

?

[hardy monolith]

just bringing it back down

[shell badge]

Yesss

[upper kettle]

wdym no thats correct

nvm its 8 not 7

[strange cosmos]

i didnt take a question from the book

[hardy monolith]

$4^5\cdot 4^3=4^{5+3}=4^8$

[strange cosmos]

i made one up

[flat frigate]

Bonk

[shell badge]

Oh

[weary mango]

xdd

[strange cosmos]

How

[hardy monolith]

but try doing 1.b)

[strange cosmos]

I just putted it in the same format as thwe first question

Ok

[hardy monolith]

$8^5\cdot 8^{-3}$

[flat frigate]

Bonk

[shell badge]

Wait Berra do you know the basics of variable rules?

It should be displayed on the textbook

[strange cosmos]

8^2 ?

[strange cosmos]

Couldnt find it

[hardy monolith]

yes

but are we done?

[strange cosmos]

can it be divided ny 2

by*

[hardy monolith]

we can write 8 as an exponent aswell

which one?

[strange cosmos]

the 8?

[hardy monolith]

yes

[strange cosmos]

so 4^2

[hardy monolith]

not quite

[shell badge]

It should be under Variables

[hardy monolith]

4^2=4*4=16

but youre roughly on the right path

[strange cosmos]

so many steps😢

[hardy monolith]

the thing is, when you get comfortable with it

you can write down the answer immediately

[strange cosmos]

How do you guys and all my friends know math so easily

my friends barely studies and passes

[hardy monolith]

lots and lots of practice

[shell badge]

We started with the basics basics

[strange cosmos]

The problem with me is that i give up fast

[shell badge]

Ok first

[hardy monolith]

you need to find that "aha" moment for yourself

[shell badge]

Let's just try a simple

Equation

[strange cosmos]

true

[shell badge]

2x + 4x = ?

[strange cosmos]

that is 6x right?

[shell badge]

Yes

[hardy monolith]

itll give a really big dopamine rush

[shell badge]

4x/2x= ?

[hardy monolith]

4x/(2x)?

[strange cosmos]

Ive felt that and its lovely. Not to be wierd or anything but when that moment hits you feel like the best

[shell badge]

Same thing

[hardy monolith]

no its not

[strange cosmos]

that would be 2x?

[shell badge]

Right

[hardy monolith]

no.

[shell badge]

Yes

[strange cosmos]

um

[hardy monolith]

$\frac{4x}{2x}=2$

[flat frigate]

Bonk

[shell badge]

No your right

Oh right

Ok now

[hardy monolith]

and btw what you wrote before was $4\frac{x}{2}x=2x^2$

[flat frigate]

Bonk

[shell badge]

Jesus

???

[hardy monolith]

being precise matters

[strange cosmos]

My brain hurts

[hardy monolith]

anyway, were getting sidetracked

[shell badge]

Yea next

[hardy monolith]

i want to introduce an intermezzo

[shell badge]

So you know these simple rules right?

[hardy monolith]

do you know what prime and composite numbers are?

[shell badge]

y × y = ?

[strange cosmos]

Ill never make it to sophomore if i dont pass math uuughhh

[hardy monolith]

youll make it, i believe 🙏

[strange cosmos]

Thaaankk yooou

[hardy monolith]

let me continue

do you know what prime and composite numbers are?

its okay if you say no

[upper kettle]

do you know imaginary numbers?

i am stuck somewhere

[hardy monolith]

those are not related to this

[upper kettle]

yea ik

[strange cosmos]

Nope i dont

[hardy monolith]

if you need help yourself open a channel

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[upper kettle]

i did

[hardy monolith]

then wait for help

[upper kettle]

#help-22

[hardy monolith]

or ping if its been 15 minutes

but dont invade other peoples' channels

[upper kettle]

it has been and i did

[hardy monolith]

then there is nothing more you can do than wait

[upper kettle]

aight

[shell badge]

Listen to music

[hardy monolith]

a prime number, is a number that is only divisible by 1 and itself

[upper kettle]

ill just do the next one

[shell badge]

Okie

[hardy monolith]

a composite number, is a product of prime numbers

for example

5 is prime

[strange cosmos]

Oh is that why 8^1 = 8?

[shell badge]

?

[hardy monolith]

not really

[strange cosmos]

Oh

[hardy monolith]

but youll see where im going at the end

[shell badge]

No we look at the base numbers

[strange cosmos]

Yess

[hardy monolith]

just go along with the intermezzo

[shell badge]

Instead of the elevated numbers

[hardy monolith]

for exmaple, 6 is not prime

its composite

of which two prime numbers is it a composite of?

[shell badge]

A prime number which can't be divided with another besides itself and 1

[strange cosmos]

umm

[shell badge]

Like as in full numbers

[hardy monolith]

so, a*b=6 with a and b whole numbers

then what are a and b

[shell badge]

2 is also a prime number btw

[strange cosmos]

prime?

numbers

[hardy monolith]

what numbers are a and b

such that a*b=6

[strange cosmos]

3 and 5?

[hardy monolith]

where are you getting that from?

[shell badge]

3 x 5 = 6?

[strange cosmos]

I dont knoow

[hardy monolith]

3*5=15 which is not 6

[shell badge]

Ok

[strange cosmos]

Ohhh

[hardy monolith]

theres the aha

[shell badge]

Wait bonk,your going too far ahead

[strange cosmos]

3*3 = 6

[shell badge]

Explain what is a prime number first

[hardy monolith]

i did

[strange cosmos]

so the numbers 3

[hardy monolith]

.

[hardy monolith]

no, 3*3=9

[strange cosmos]

2 for an example?

[shell badge]

2 is also a prime number

[hardy monolith]

2*3=6

[strange cosmos]

oh my days

[hardy monolith]

6 is a composite

[strange cosmos]

im screwed

[hardy monolith]

because multiplying the two prime numbers, 2 and 3, equals 6

[strange cosmos]

Ok

[shell badge]

Is 9 a prime or composite number?

First he needs to identify which is a composite or a prime number

[strange cosmos]

prime?

[hardy monolith]

no

whats your reasoning why its prime

[shell badge]

Nu cuz 9 can be divided by 9 3 and 1

[strange cosmos]

so for an example 12 is a prime?

[shell badge]

Nope

[hardy monolith]

no, 12 is composite

2,3,5,7,11,13,17,etc are prime

[strange cosmos]

i cant think of any numbers that only can be divivded by 1

[shell badge]

And itself

[strange cosmos]

basically numbers you cant cut in half

[shell badge]

So ok let's break it down

[hardy monolith]

not jsut in half

[strange cosmos]

by itself

[hardy monolith]

but also not in thirds, or 5ths, or 7ths, etc

[shell badge]

Break down the highest common factors of 6

[hardy monolith]

you cant cut 9 in half, but you can cut it in 3rds, which means its still not prime

[strange cosmos]

6/2?

so a prime number can only only be divivded by 1?

[hardy monolith]

and itself, yes

[upper kettle]

and by itself

[strange cosmos]

Yes

[upper kettle]

13 can be divided by 1 and 13

[upper kettle]

12 can be divided by 1;2;3;4;6;12

[strange cosmos]

13/13 = 0

[shell badge]

Nah it's 1

[hardy monolith]

=1

[strange cosmos]

composite

[upper kettle]

yeah

[shell badge]

We aren't subtracting

[strange cosmos]

hahah sry

[upper kettle]

self division always equals to 1

[shell badge]

That's different from the exponents

[hardy monolith]

okay, so a bigger example

[shell badge]

27

[hardy monolith]

what are the prime factors of 20

[shell badge]

Bonk... your getting way too ahead

[strange cosmos]

1,2,4,10?

[hardy monolith]

no, i want to go here

[hardy monolith]

not quite

lets go one step at a time

what prime number can divide 20

[strange cosmos]

2

[hardy monolith]

yes

and 20/2=10

so we keep track of the 2

and continue with 10

what prime number can divide 10

[strange cosmos]

2 also

[hardy monolith]

indeed

[shell badge]

And??

[hardy monolith]

and 10/2=5

now, what prime number can divide 5

[shell badge]

Be confident ✨️

[strange cosmos]

non?

[shell badge]

Yrss

[hardy monolith]

it kinda sounds like a trick question, but its not

[strange cosmos]

yep

[hardy monolith]

the prime number 5 can divide 5

and we are left with 1

and nothing else to do

so, taking notes of what we divided by

[strange cosmos]

but 5 was a composite?

[hardy monolith]

5 is prime

[shell badge]

No

[strange cosmos]

Oh

yeah

mixed them

[hardy monolith]

and a prime number is only divisible by 1 and itself

[strange cosmos]

Yess

[hardy monolith]

so, what numbers did we divide by

that we took note of

[strange cosmos]

2 and 5

prime numbers

[shell badge]

Yesss

[hardy monolith]

almost

we counted 2, twice, didnt we?

[strange cosmos]

so 4

[hardy monolith]

nono, keep it as 2*2

we have 2,2 and 5

[strange cosmos]

Ok

[shell badge]

No simplify it further

[hardy monolith]

as our factors

[shell badge]

2²

[hardy monolith]

and remember exponents?

2*2=2^2

[strange cosmos]

yes the ones at the top

[hardy monolith]

so, do you see how $20=2^2\cdot 5$?

[flat frigate]

Bonk

[hardy monolith]

from the steps we followed

[shell badge]

Btw Berra are they still teaching this in school?

The questions you had about simplifying the exponenets

[strange cosmos]

yes i think 2^2 = 4 and 4*5 = 20

?

[shell badge]

The one you struggled with in the beginning

[hardy monolith]

yes, but do you see how we decomposed it?

[strange cosmos]

not quite

[hardy monolith]

we took 20, divided it by 2, got 10, divided that by 2, got 5, divided that by 5, got 1 and we were finished

[strange cosmos]

Yeaahh

[hardy monolith]

this is called prime decomposition

[shell badge]

I'm talking about these questions

[hardy monolith]

we take a number, and write down the prime factors of it

[strange cosmos]

so 30?

the prime number of 30 is

[shell badge]

Wait break it down first

Then identify the prime numbers and if not, simplify that number further

[hardy monolith]

*prime decomposition

[strange cosmos]

oh

[hardy monolith]

if the number is prime, we are immediately done

[strange cosmos]

25?

[shell badge]

Eh?

[strange cosmos]

prime?

[shell badge]

Nope

[hardy monolith]

if its composite, we decomposite it into its prime factors

can you see why 25 is not prime?

[strange cosmos]

Oh

Ok

[shell badge]

Bonk your just forcing a plant to grow into a tree atp

[strange cosmos]

it cant be divided by 1

[hardy monolith]

not quite, 5*5=25 right?

[strange cosmos]

My brain melts

[shell badge]

He might be fine with these questions but if a more complex question came up, he won't know how to do it

[hardy monolith]

okay okay

lets complete the intermezzo

[shell badge]

💀💀

[hardy monolith]

we discussed prime and composite numbers

a prime number is a number that is only divisible by 1 and itself

a composite number is the product of primes

we can decompose a composite number into its prime factors

[shell badge]

Your going to make his brain go ka-boom

[hardy monolith]

anyway, what i was getting at was

8 is not a prime number

you can turn it into a product of smaller numbers

in particular, 2 * 2 * 2 = 2^3=8

[strange cosmos]

Yes

[hardy monolith]

so in question 1.b)

we arrived at 8^2

now what happens when we turn 8 into 2^3?

[strange cosmos]

Still 8 since 2^3 is the same thing as 2* 2* 2 wich equals 8

[hardy monolith]

yes, but we write 8 as 2^3

[strange cosmos]

What

[strange cosmos]

Yes

[hardy monolith]

because we want it in the smallest base possible

[strange cosmos]

Yes

[hardy monolith]

so $8^2=\left(2^3\right)^2$ right?

[flat frigate]

Bonk

[strange cosmos]

That’s correct

We have ()

Since if we wouldn’t it would be 8^2 but like 64

Right?

[hardy monolith]

yes?

but 64 is kinda worthless for us

we want it in the smallest base possible

[strange cosmos]

Yes

[hardy monolith]

so we want the base to be smaller, and the exponent to be larger

so whats the answer to 1.b)

?

[shell badge]

I'm back

Also ion think the question isn't saying to simplify to the furthest

It's just simplifying the exponents

[strange cosmos]

8^-2?

[upper kettle]

1b is 8^2

[strange cosmos]

Oh

[hardy monolith]

its not

[shell badge]

Yes

It is

The question is asking to simplify the exponents, nothing less, nothing more

[upper kettle]

here

[shell badge]

Yall it's not that complicated

[hardy monolith]

the answer is 2^6, but whatever

[shell badge]

8⁵ × 8^(-3) = 8^(5 + (-3)) = 8²

[upper kettle]

does the book not have answers? ask him

[weary mango]

xDDD

[weary mango]

that is funny

[shell badge]

Fr

[hardy monolith]

if you can just pick whatever base then you can just write 64^1 and call it a day

[weary mango]

when you realize u messed up a school level question but wanna look cool xD

[hardy monolith]

plug everything into the calculator, slap on a ^1 and done

[upper kettle]

i mean its the same thing

[shell badge]

Just too extra

[upper kettle]

does not rl matter

[weary mango]

yes but at first he said no he might've been confused

[upper kettle]

now me, i would write it as lg10^64

[shell badge]

Tf

[upper kettle]

with the zeros

[weary mango]

that is wronge 🙂

[shell badge]

....

[upper kettle]

is the answer not 64

[shell badge]

Ion even know who to defend no more

[weary mango]

that is 100^32

AHAHAHA

[shell badge]

It's log

[upper kettle]

got me

[weary mango]

yes with the log obv

[upper kettle]

lg means log^10

[upper kettle]

under the log

[weary mango]

i was being sarcastic xd

[strange cosmos]

👍🫡

[weary mango]

now i gotta go study my optical courses 😢

[upper kettle]

i have to write 3 more pages

for today

[strange cosmos]

Hard stuff

[upper kettle]

i have written like 17 as of now

[weary mango]

not really but i didn't give much effort to studying this semester

[upper kettle]

14 more tmrw and i will be done

or i will do some more

[strange cosmos]

Oh

[strange cosmos]

💀

[weary mango]

its good to be hard working as someone who was genuinely interested in math even when i was young i studied for the sake of entertainment but keep in mind you can be overwhelmed so try to take it easy a bit and go out from time to time and do something fun

it wont hurt to go out for 1-3 hours

[upper kettle]

i just did 7 all nighters in a row almost

had to write 100 pages

[weary mango]

yes i get u're motivated that is good but

[upper kettle]

almost there

[weary mango]

u have to do something else lil brother

[upper kettle]

yeah i understand that i messed up my sleep schedule

[weary mango]

why u writing this for

[upper kettle]

teacher does not accept normal presents

[weary mango]

what do yo ustudy

[upper kettle]

she said that for a christmas present i could write 100 pages

from like the hardest book

[upper kettle]

that i could write from

[weary mango]

how old are you

[upper kettle]

math

[upper kettle]

almost 18

[upper kettle]

less than 20 days left

[weary mango]

bro she obviously was joking xD

[upper kettle]

15

[upper kettle]

naaah

she is dead serious

[weary mango]

did she ask you only?

[upper kettle]

my math teacher is nuts

[upper kettle]

nope

[weary mango]

everyone in the class?

[upper kettle]

she has like hundreds of these “presents” collected

[upper kettle]

its a private tutor but yea

[weary mango]

oh i see

[upper kettle]

there are 25~ of us lol

[upper kettle]

at the same time almost

[weary mango]

are you taking bachelor exam or what

[upper kettle]

nationals

i am in the 12th grade

[weary mango]

which country and for what degree

[upper kettle]

i also have daily 4 to 8h math lessons

[upper kettle]

georgia and law

[upper kettle]

minimum 4

[upper kettle]

i can rest for 30m

[weary mango]

does low require this much math work xD

[upper kettle]

lol not at all

everyone goes history

[weary mango]

from private tutoring or school

[upper kettle]

tutor

[strange cosmos]

💀💀

[upper kettle]

she also asks for like minimum 15 pages as homework

[weary mango]

and do yo uget to study for free if u do well

[upper kettle]

nope

[strange cosmos]

I wish I could see studying math as entertainment and any other subject for that matter

[upper kettle]

ohh you mean in uni?

[weary mango]

yes

[upper kettle]

i can get a discount yea

[strange cosmos]

Studying home isn’t fun but listening on the lessons is better

[weary mango]

how old are you and why you can't ?

[upper kettle]

georgia as in the country

not the state

[weary mango]

what percantage u get

[upper kettle]

depends on what ill score

[strange cosmos]

I’m 16, am a freshman and the reason why is that I hate and suck at math even if I don’t want to. There is no problem with any other subjects

[upper kettle]

it can be from 30-100

[weary mango]

i mean foreign countries are so wierd man you need to be very excelent to get to study in a private university xD

[strange cosmos]

My motivation to everything is gone

I mean almost everything

And I’m starting to lose it

[upper kettle]

best law uni in my country is not a private one lol

what did you major in?

[weary mango]

don't worry bro i got 4.5 / 20 when i was your age then proceeded to get full marks straight . you just have to work a little bit and get a good tutor that teaches you how to think . i m studying in one of the best universities in my country and i don't even study that much because its about quality . if you do something while enjoying it it will have much more impact

[weary mango]

computer science

[upper kettle]

i would make a joke about that but nvm

[weary mango]

why xD

[upper kettle]

you helped me quite a lot for that lol

[strange cosmos]

That is true really and yeah my math teacher isn’t the best I’ve had better

[weary mango]

its fine go for it i m down for a laugh

[upper kettle]

there are so many memes about comp sci students not getting a job

[upper kettle]

well mostly cuz they dont choose it things right

[weary mango]

ah i see hahaha . its just memes don't worry there is still a lot of avalaible jobs especially that my university degree is valuable even abroad

[upper kettle]

nice

wya from?

[strange cosmos]

I hope I’ll make it to university

[weary mango]

its fine don't blame the teachers if you can find someone even your brother or something that can help you of how to think rather than give you solutions to your question

[weary mango]

don't worry you will . the most important part is to learn how to think rathar than how to find the solution

[strange cosmos]

Well my family isn’t the nicest to me so wouldn’t me my first solution

[weary mango]

i m studying the whole semester in a week cuz i can understand quickly

[strange cosmos]

Yeah

[weary mango]

i m from tunisia don't think u would know it its in north africa

[weary mango]

where are you from

[strange cosmos]

That’s the thing. People understanding quickly. I would rather have that then any money in the world

[strange cosmos]

Sweden

[weary mango]

don't worry life is fair in the system of education because if yo ureally want to get somewhere you can

all you gotta do is work hard

sometimes your motivation is very down and you don't want to

[weary mango]

but you gotta force it

[strange cosmos]

Yes

[weary mango]

and have your goal in mind

[strange cosmos]

You from Georgia

[upper kettle]

yeah

[weary mango]

yup that is me

[strange cosmos]

How is it there I’ve always wanted to know

[upper kettle]

revolution

[upper kettle]

and good food

lol

[weary mango]

my brother visited georgia last summer actually

[strange cosmos]

What did he think

[upper kettle]

yea not the best time to do that rn

[strange cosmos]

Why

I planned do to

Actually

[upper kettle]

there is a lil revolution going on

[strange cosmos]

Like war or what

[upper kettle]

just dont go to the freedom square if you do

[upper kettle]

ahmmm

gas grenades and water turret thingy

[strange cosmos]

Damn

[upper kettle]

and normal ppl are using fireworks to shoot the police

[weary mango]

i mean he is 6 years older than me so we don't connect that much but he enojyed it and made a lot of friends also the main reason he went with his friend cuz his friend got married there lol

[strange cosmos]

Happens here to

Sweden unfortunately top 3 most criminal countries in Europe

[strange cosmos]

That sound wonderful

[upper kettle]

his georgian friend got married?

[weary mango]

we gotta go sleep both its 1 am for us xD

[strange cosmos]

Hahaha true

[upper kettle]

its 4am for me lol

[strange cosmos]

What did you study for?

[weary mango]

no his friend is marrocan he studied with him abroad near europe he got married to a georgian woman

[strange cosmos]

Go to sleep, you’ve got school?

[upper kettle]

nah

[strange cosmos]

How old are you

[upper kettle]

15 days away from 18

[weary mango]

u realize that its proven by doctors that your lifespan decreases when you don't sleep during the time and you lose focus

[strange cosmos]

Nice

[upper kettle]

yes

[weary mango]

what do you mean

[upper kettle]

i do sleep 7h

[upper kettle]

comp sci

[strange cosmos]

Like what are you planing to work with in the future?

[weary mango]

its not about how much u sleep its about when

[upper kettle]

that too

[strange cosmos]

Valid

[upper kettle]

but oh well

[weary mango]

computer science what i do this year will dectate what i'll study exactly

[upper kettle]

i dont even go to school anymore

[strange cosmos]

That’s interesting

[upper kettle]

almost

[strange cosmos]

Dream

[weary mango]

why

[upper kettle]

i just go to my tutor instead

[weary mango]

he has private tutoring so u shouldn't do what he is doing

[upper kettle]

school is 100 times ezer than what i am doing

[strange cosmos]

What you do

[upper kettle]

private tutors

[strange cosmos]

Oh

[shell badge]

Yt videos

[weary mango]

if u want close this chat and send dms this is not the place to talk about that

[strange cosmos]

Interesting ö

[strange cosmos]

Sure

[shell badge]

.close to close this channel

[safe radish]

@strange cosmos Has your question been resolved?

[safe radish]

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[somber cape]

What do they mean by only listing the colors of successive balls

[somber cape]

so like if we have 5 balls

red blue blue red blue

only blue blue

will be listed?

[covert yoke]

I think it's saying that it will list RBBRB

Not R1 B1 B2 R2 B3
Or equivalently R2 B3 B1 R1 B2

[somber cape]

ohh

I see

yeah that makes sense

[safe radish]

@somber cape Has your question been resolved?

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[dry tusk]

On an ellipse EE with foci FF and F′F′, and center OO, let DD be a point on the ellipse. Prove that the following lines are concurrent: the tangent tt at DD to EE, the perpendicular from FF to tt, and the line through OO parallel to DF′DF′. Once you find the three equations and write them in matrix form, why must the determinant then be zero?

[safe radish]

@dry tusk Has your question been resolved?

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[spiral crescent]

i dont understand the rewriting part

also the last step, how does the 2nd argument of the gcd become just a2?

[peak estuary]

are you sure its not just cut off?

otherwise its a typo

[spiral crescent]

so the last step, the second argument of gcd is a2-a1 only?

[hardy monolith]

yeah i think it should be gcd(a3-a2,a2-a1) for the cut off one

[peak estuary]

its still a2-a1, yes

[spiral crescent]

max refers to the max number among given n numbers btw

okayyy i get it i think

yep

.close

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[analog urchin]

Could some one give me a starting point for this integral?

[hardy monolith]

,rotate

[analog urchin]

that x on the top is bothering me

[final loom]

Start with the most obvious substitution

[analog urchin]

yeah, u = arcsinx

[final loom]

nd the integral becomes?

[analog urchin]

e^u*x du

right?

[final loom]

e^u (sin u) du

[analog urchin]

oh right right

thats some progress

[final loom]

That's end of question ✓

integrate e^u sin u, substitute back x, you done

[analog urchin]

thanks for the idea!

<3

.close

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[lean otter]

Part a

[hardy monolith]

!status

[safe radish]

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

[lean otter]

Probability of x = 3 is 1/38

You go on from there

？

?

<@&286206848099549185>

[hardy monolith]

!status

[safe radish]

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

[bronze gust]

@lean otter can you also express the probability of x=3 in terms of n?

[lean otter]

Yes thank you for sending the same message twice

[hardy monolith]

and thank you for not answering twice

[lean otter]

@hardy monolith okay!

I already told you what I got

Clearly I can't continue from there..

all question？

all need answer？

[bronze gust]

Native language Chinese?

[lean otter]

It's not his question btw..

[bronze gust]

Oh

It's yours?

[lean otter]

yes

Indeed

[bronze gust]

Mb cuh

Alright so

Can you express the probability of x=3 in terms of n?

[lean otter]

I just have a question by x = 1 for example do they mean 1 green marble chosen from the n marbles

[bronze gust]

Yeps

[lean otter]

Ah so (7/n)(6/n-1)(5/n-2) = 1/38 and just solve right

[bronze gust]

Yea

[lean otter]

I just wasn't sure what x meant here

Alr ty

[bronze gust]

Exactly

Np

[lean otter]

.close

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[untold eagle]

calculate the vertical, horizontal and oblique asymptote at +infinity

[untold eagle]

I dont know how to continue pls help

[hardy monolith]

what is the question?

[untold eagle]

calculate the vertical, horizontal and oblique asymptote at +infinity

<@&286206848099549185>

If i found that the asymptote is vertical should i check if it is also horizontal or oblique?

.close

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[warm finch]

Let $A$ be a Noetherian ring, $a_1, ..., a_d$ be a regular sequence. Then, every minimal prime over $a_1, ..., a_d$ has height $d$.

How do I prove this? Krull's height theorem gives height $\leq d$, but how to prove height $\geq d$?

[flat frigate]

DavidL1450

[warm finch]

assume ring is commutative

[peak estuary]

you will have more luck in the advanced channels

[safe radish]

@warm finch Has your question been resolved?

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[quiet smelt]

Im learning asymptotes now but unsure how to read the graphs fully

[quiet smelt]

like I know the first 2 have x=-2

and the 3rd one have x=2

but I am unsure how to decide y

[hardy monolith]

wdym first two?

[quiet smelt]

the first two asymtotes the left ones

[hardy monolith]

there is only one asymptote

x=-2 is just one

there are 3 asymptotes in total

in the graph

[quiet smelt]

is the the answer sheet

Im assuming the right one goes to 2? no?

anyhow what I need help is how to read 0.5x from the graph

[valid scroll]

is this correct for metric regularization

[safe radish]

@quiet smelt Has your question been resolved?

[hardy monolith]

!occupied

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[safe radish]

@quiet smelt Has your question been resolved?

[safe radish]

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[gleaming grotto]

Hi all. Can you help me figure it out?
I need to find such a , h , k
for the function f(y)=a(x-h)^3 + k
that if y = 0 then x = 0 and if y = 1 then x = 1

[fathom adder]

f(y) ? Not f(x) ?

[gleaming grotto]

I'm sorry. The example looks like this y =a(x-h)^3+k

[icy lance]

what seems like a natural move?

[gleaming grotto]

Sorry, I didn't understand what you mean

[icy lance]

what do you think you should do

[gleaming grotto]

Well, I substituted numbers for x and y and equalized

[icy lance]

what did that look like

[red delta]

@gleaming grotto

[gleaming grotto]

Yes

[red delta]

This

[red delta]

What did it look like after you did this?

[gleaming grotto]

Is this the right thing to do?

Having solved the system, it turned out that h = -1 and h = 2/3

[red delta]

ah³=k right
And a(1-h)³ = 1-k
But k=ah³
Well you can find a and k and plug in the values of x to check if you're correct

[gleaming grotto]

yes, I did that and it turned out that for h=-1 a = -9/8 k = 9/8

oh man I was stupid

I put the numbers in wrong

[red delta]

Try again

I feel there's more details on this question.

[safe radish]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[red delta]

@gleaming grotto

[gleaming grotto]

Yes

what did you want?

[red delta]

Send the original question

@gleaming grotto

[gleaming grotto]

Find a, h, k, in the function y=a(x-h)^3 that for x = 0 y = 0 and for x =1 y = 1

[red delta]

Please show the original problem, exactly as it was stated to you, with the entire original context.
A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[gleaming grotto]

OK

[red delta]

A PICTURE OF IT

[red delta]

Are you sure this is an actual question and the original question?

[gleaming grotto]

Yes

I just need to find points so that the graph looks something like the picture

if this is possible of course

if not, tell me what function should I use so that the graph looks something like the one in the picture?

I figured out how to solve everything

I went a little overboard with the drawing

[red delta]

,w plot y= ⅐(x+1)³ - ⅐

[gleaming grotto]

in terms of?

what does w mean

Okay thanks

Best wishes

.close

[safe radish]

Channel closed

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[red delta]

It's just a command

[gleaming grotto]

yes I understand

how to close the chat

[red delta]

It has been closed

[gleaming grotto]

oh yeah

Bye

[red delta]

I feel there's at least 2 answers to this

Or even several which is why I asked if this is the original question.

Or an actual question

[gleaming grotto]

well, I found that a = 1 h = 0 k = 0
and it turned out that f(x) = x^3

and thanks for the help

[red delta]

Try h=1 and solve

[gleaming grotto]

OK

what about a and k?

they are known or as

[red delta]

try k=1, h=1
And a = 1

[gleaming grotto]

well that's cool

so it’s true that there’s more than one there

Thank you

[red delta]

Where did you get this question from?

[safe radish]

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[gleaming grotto]

I just wanted to do procedural generation and thought about it

[gleaming grotto]

.close

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[inner spear]

how do you get y=x^2 + 2x into graphing form? i think i completed the square but i am missing something

i got to y= (x^2 + 2x + 1) -1 cuz u have to put it outside as well right? or am i missing something

[brave wolf]

That's correct

[severe pond]

that’s fine but now you can express that as something else

the x^2 + 2x + 1 bit

[inner spear]

oh

oh

oh

oh my god

[slim vault]

or you can just take x common , get the 2 zeroes and plot the quadratic..

[severe pond]

vertex form is most useful

[inner spear]

i forgot to factor it 😭😭

no wonder i was so stuck

[shadow verge]

Have you learnt about parabolas ?

[inner spear]

i have i just haven’t had to convert from standard form in a looooong time and i totally forgot lol

[shadow verge]

Ok

y+1 = x²+2x+1
or, y+1 = (x+1)²
So, vertex at (-1,-1)

And it is towards the positive y axis

And at x = 0 ,y = 0

[inner spear]

yes

[slim vault]

how did u added -1 to lhs and +1 to rhs?

[shadow verge]

This is all the info you will need to plot a rough graph, and can be told from the eqn of parabola

[shadow verge]

Ah sorry

at y = 0 , find the values of x then

[inner spear]

i started with y=x^2 + 2x
then you have to “complete the square”
so you take the x term (2x)
divide the coefficient (2) in half
so you get 1, and then you square that
so 1^2 =1
then you add one to the equation on the end and bracket the whole thing, then you put one on the outside too but the opposite sign so y = (x^2 + 2x + 1) -1
then you factor the brackets to get y=(x+1)^2 - 1

sorry that’s a bit long and a lot to take in if you don’t know parabolas yet

but that’s how i was taught basically

it just took a bit for it all to come back

[slim vault]

yeah i get it

it was just a mistype from his side

[inner spear]

ohhh

okay

.close

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[lean otter]

do i just type in my problem here or what

[flint fiber]

Yes

[lean otter]

I've had a math teacher try to explain to me for 10 minutes how 3^3 3^3 3^3 =9n

n=2

what math video do i need to learn to understand this, because no matter how much the math teacher explains i dont understand these made up rules that are coming out of nowhere and just is so

[plucky elk]

Which rule are you having trouble with

,calc 3^3

[flat frigate]

Result:

27

[plucky elk]

3^3 = 3 * 3 * 3 = 9 * 3 = 27

[lean otter]

that is 3x3^3
which is 3^1x3^3

I don't understand this however, so is there a video to learn more?

[slim plinth]

Do you have a photo or something, it’s really unclear or is it just me

[plucky elk]

https://youtu.be/kITJ6qH7jS0?si=V93TFb9B8B-he7TI

[lean otter]

Do i just close this now or what?

[slim plinth]

If you’re done with your question

[lean otter]

.close.

close

/close

[plucky elk]

.close

[safe radish]

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[coral dagger]

Am I correct? Cuz da negative sin is tripping me out

[icy lance]

2[1/2 cos(x) - sqrt(3)/2 sin(x)]
sin(A)=1/2
cos(A)=sqrt(3)/2

2sin(x-A) 2sin(A-x)

[smoky nacelle]

just rearrange to cosx - sqrt30 sin x.

[coral dagger]

Yeah this is what I did no? I just converted to degrees

[coral dagger]

Wym?

[icy lance]

not really, for some reason you have everything inside a sin, and A wouldnt be 60

[coral dagger]

Oh

I must actually replace the whole sin?

Oh you're right you're right

I got confused

[coral dagger]

Why did you subtract here?

[icy lance]

i didnt

i just changed the order

-a+b=b-a

[coral dagger]

I see

[icy lance]

since i want the form sinAcosB-sinBcosA=sin(A-B)

[coral dagger]

Yeah true

[icy lance]

might actually be 2sin(A-x) then

or -2sin(x-A)

[coral dagger]

So right here the A we want is the angle which would be 60 or pi/3 yeah?

[icy lance]

A isnt 60

[coral dagger]

What it is it then? How do we get that?

[icy lance]

by setting it up like this

its equal to 2sin(A-x)

we know sin(A)=1/2
cos(A)=sqrt(3)/2

[coral dagger]

We solve for A?

So do an inverse trig function?

[icy lance]

yeah

[coral dagger]

Ahh

I see

Thank you

.solved

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[neat salmon]

Discrete Math / System of Congruences

I'm trying to solve:

x ≅ 2 mod 7
2x ≅ 3 mod 9
4x ≅ 5 mod 11

calculating the inverses etc i get:

x ≅ 2 mod 7
x ≅ 6 mod 9
x ≅ 4 mod 11

the general solution i got is x = 114 + 231n

but chatgpt says its 114 + 693n

what's the right answer here?

[neat salmon]

wait i saw my mistake lool

.close

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[lean otter]

In the graph shown, triangles PSB and CHB are congruent. If HC=8, find the largest integer value of AS.

[lean otter]

I am comparing it with the triangle that is formed above

it has to be less than 8 - m

if m = 1

5 - 4 - 3

maybe

so m = 3

then x = 4

could x be equal to 4??

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[cunning epoch]

how do i solve for x whne the exponent is a fraction

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Please don't occupy multiple help channels.

[plucky elk]

i closed your other channel.

!xy

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[cunning epoch]

is this one still available?

[plucky elk]

yes keep this one

[cunning epoch]

]

how do i solve for x when the exponent is a fraction?

[hardy monolith]

try squaring both side

[plucky elk]

maybe divide by 3 first

[desert juniper]

okay, no

[fresh wasp]

Ok so your exponent is 1/2, what do you multiply it by to make it 1?

[fresh wasp]

Yes great first step

[cunning epoch]

well 1 half could be 0.5 so multiply by 2?

[fresh wasp]

Yesss

Ok so put everything to the 2nd

What do you get?

[desert juniper]

no

you're multiplying by 2 on the right, but squaring on the left

that's not the same operation

[fresh wasp]

Ok so exponents to eachother multiply, when you do (x^1/2)^2 within the exponent you will get x^1 and on the other side 4 is also known as 4^1 it’s just not written down you’re doing 4^1x2 but you should write it as 4^2

You’re squaring everything

[fresh wasp]

Yessss

Good job

[cunning epoch]

my answer sheet says i should get positive 2 🤔

[fresh wasp]

Huh

[desert juniper]

hm?

[desert juniper]

okay, you copied it wrong

[cunning epoch]

2b.)

[fresh wasp]

Yea

[cunning epoch]

pfft lol mb

[fresh wasp]

3x^2 =/ 3x^1/2