help-27

[sand isle]

or the range

Which ones the raneg

and which is the codomain

[pale dove]

no range is [0,36]

[sand isle]

Right

[pure flower]

okay

[sand isle]

whats codomain then

[pure flower]

here i'd like to nitpick

you didn't even write a good relation

[sand isle]

wot

[pure flower]

you don't have proper sets

i dont know what the relation is going to

[pale dove]

codomain is R

[pure flower]

relations are defined in between sets.

[pale dove]

or whatever you set it to be

[pure flower]

you didn't even give us the sets.

[pale dove]

codomain is defined

range would be that part of codomain which is the actual output

[sand isle]

is this not enough

[sand isle]

oh okay

[pale dove]

you define a codomain basically

[pale dove]

meaning if the codomain is R

[sand isle]

so codomain is the real numbrers with x is the element of

[pale dove]

range would 0 to 36

[sand isle]

and the range are the outputs

ohhh

[pale dove]

if codomain is Z

[sand isle]

so range is a subset of codomain

[pale dove]

range would 0 1 4 9 16 25 36

[sand isle]

wait wot

why is it different

[pale dove]

because range would be a part of the codomain only

you take the range out of tue coodomain

[pure flower]

GIVE US THE SETS ON WHICH THE RELATION IS DEFINED

[sand isle]

relax

[pale dove]

yeah, those sets would be the domain and co domain respectively

[pure flower]

@pale dove you're not really helping, it's just confusing them more i think

[pale dove]

if f is mapped from a to b

[sand isle]

wdym give u the sets

[pale dove]

a is the domain

b is the co domain

[pure flower]

relations are mapped from sets to sets

[sand isle]

{ x is an element of R : x^2 <= 36 } is this not enough

[pure flower]

why are you asking about codomains and ranges and such when you dont know how relationships are defined

[sand isle]

whats the problem with it

[pale dove]

its different because i specified the co domain to be integers

[pure flower]

no. that's a set.

sets dont have 'codomains'.

[sand isle]

actually?

wait huh

[pure flower]

yeah newsflash

[sand isle]

wot

these are sets

arent they

[pale dove]

well, their codomains are just the range

[pale dove]

nope, f is a function, A and B are sets

[sand isle]

let me get this straight

[sand isle]

this is a function

f : A -> B

right

A and B are sets?

[pale dove]

yes

[pure flower]

'these' are sets.

[pale dove]

yes

[pure flower]

this is not a set.

[sand isle]

So if I had said like

{ x is an element of R : x^2 <= 36 }

[pale dove]

domain set and codomain set

[sand isle]

isnt it obvious that

x is the A set

[pure flower]

that's a set mate.

[sand isle]

x^2 is the b set

[pure flower]

major fucking no

[sand isle]

because for values of x you're getting an x^2

[pale dove]

but where is the B?

[pure flower]

you just have a set and that too written horribly.

[sand isle]

b's the.. output?

hold on before you two tell me how wrong i am

ill tell u my pov

[pale dove]

output? no, the output is basically the range here, there is no codomain, what you said is just a simple set

[sand isle]

im reading this as, "let there be a number x such that x is an element of real numbers and, x^2 is less than or equal to 36"

[pure flower]

The good set notation is $A={x \mid x \in \mathbb{R}, x^2 \leq 36}$.

[woven radish]

Percy

[sand isle]

OH WAIT

I GOT IT

WAIT

[sand isle]

SO THIS WILL ONLY ASK ME

TO LIKE

TELL ME

WHAT X IS

THATS ONLY 1 SET

OHHHHHHHHH

[pale dove]

yes

[pure flower]

please first learn sets, then relations, then functions

[sand isle]

shiiii

[sand isle]

listen

progressive learning happens

i'm in the midst of learning thi

that's why i come here

[pure flower]

or you could just write weird set notation and pretend it's actually a relation i guess /lh

[sand isle]

to ask questions to understand a concept

[pure flower]

fair

[sand isle]

if i didn't get it

i wouldn't come here

[pure flower]

but yeah now you know to learn set notation though

[sand isle]

yeah

[pure flower]

that's like very important if you're doing set theory

you need to know how to write sets if you're gonna play with em

[pale dove]

easy shit, you can learn it in a an hour or two tbh

[pure flower]

there's really only two things.

one is straight up element listing in braces

you know that

the second is setmaker notation

which might take like 30 minutes with examples

[pale dove]

which you just did

[pure flower]

yeah

[sand isle]

ohh

okay so

back to the original question

if i got a relation

as percy said

one set a is x

one set b is x^2

x^2 can only be less than or equal to 36

[pseudo basin]

[pale dove]

what is this?

[sand isle]

so we just get b = 0,1,4,9,16,25,30

[pure flower]

so neither of these are sets

one is a variable

the other is the same variable but squared

[sand isle]

yes

[pseudo basin]

yeah your notation and phrasing are unfortunately quite far off the mark here so we cannot understand you at all

[sand isle]

let me draw this out

[pale dove]

he basically wants to use setmaker

on R

no on Z

idk lol

[pure flower]

let me stumble his way through what he wants

best case we get it

worst case he learns stuff

[pale dove]

lol, hes constantly dabbling between codomain as R and Z

[sand isle]

this is what i mean

by A being x and B being x^2

[pale dove]

GOSH, this extremely vague

[sand isle]

WHAT

Oh wait

[pure flower]

okay

[pale dove]

what? where is the relation, domain? codomain??

[pure flower]

fair enough i guess

i mean i think the diagram is good enough.

[pale dove]

is that a function?

[sand isle]

yea

f(x) = x^2

A is x

[pale dove]

bro

in a function

that A is not x

[sand isle]

oh

why

[pure flower]

yeah

[pale dove]

A is a set

not a variable

[pure flower]

okay but he got sets though now lmao

[pale dove]

lol

[pure flower]

im wondering if the diagram he drew is accurate to what he means

but at least we know what we're working with now

[sand isle]

okay

uh

[pale dove]

yeah, he still doesnt get what a set is lol

[sand isle]

f(6,-6) = 36

f(5,-5) = 25

[pale dove]

???

bro ???

[sand isle]

f(4,-4) = 16...

[pure flower]

the

what

[pale dove]

mod(xy)??

[sand isle]

huh

OKAY

RESTART

LETS JS RESTART

[pale dove]

okay

okay

[sand isle]

let f(x) = x^2

right

[pale dove]

right

[sand isle]

right right

[pale dove]

mapped from R to R

[sand isle]

sure

[pale dove]

yeah

here A is R

and B is R

[sand isle]

x^2 cant be less than or equal to 36

[pale dove]

this would be a constraint

[sand isle]

yes

[pale dove]

yes go ahead

[sand isle]

so

whats gonna be A and b

[pale dove]

whatever you want it to be gosh

A and B is something you decide

or is generally given in tue question

if not its just considered to be real numbers

[pure flower]

if your function doesnt say anything specific we just assume it's defined on $\mathbb{R} \to \mathbb{R}$

[pale dove]

if A is R

B is R

[sand isle]

so

codomain and range

[woven radish]

Percy

[sand isle]

is js real numbers

[pale dove]

until specified, generally yes

[sand isle]

but what about the constraint

[pale dove]

what about it?

you want a solution set??

[sand isle]

doesn't it say x^2 has to be less than or equal to 36

[pale dove]

yeah, that doesnt affect your codomain or domain

[sand isle]

so what does it affect

[pale dove]

it affects only your range

[sand isle]

got it

so codomain and domain are real

range is affected

[pale dove]

by changing the constraint, yes

[sand isle]

okok

TYY

[pale dove]

youre welcome

[sand isle]

help appreciated

very much

[pale dove]

but go through set theory once

[sand isle]

okok

[pale dove]

youll understand stuff much more clearly

[sand isle]

okkk

tyy

will do

have a gday/gnight

.close

[devout snow]

Channel closed

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[devout snow]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[tall aspen]

small question - does [] and () brackets mean the same in matrices?

[tall aspen]

[1 0 1] = (1 0 1)?

they mean the same

okk thnks

.close

[devout snow]

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[devout snow]

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

[neon dock]

@pure flower bhai notes pade ho ge jee ke?

[neon dock]

@jee-waloon

[thin basin]

bro mujhe bhi bhejna agar mile 😭

[neon dock]

[pure flower]

marks app

[neon dock]

free hai?

[pure flower]

i think so

[neon dock]

ok thnx

[pure flower]

or get revision notes for physics from physics galaxy

[neon dock]

[thin basin]

aap kisi institue mai the kya?

[storm raptor]

allen (fuck allen)

[pure flower]

i was in fiitjee

[storm raptor]

point and laugh

[lost laurel]

Marks was pretty good, yeah

[neon dock]

to bhai fir notes to beje ho ge

[pure flower]

it was good in 10th and never after

but

our maths dude was awesome

[thin basin]

im in allen rn 💀

not rn rn

[lost laurel]

fuck coaching

[thin basin]

but this year

[storm raptor]

my condolences

[neon dock]

bro seriously... is there still any hope now

3 days are left only

i think I should just give up

[pure flower]

drop

[neon dock]

already a dropper

imean in college rn tho

[neon dock]

Im not studying now

im using life hacks

[rocky tapir]

for what bro?

[neon dock]

my exam...

[rocky tapir]

college?

[neon dock]

32 chapters... studied them 1 yr ago

nah jee

[rocky tapir]

mains?

[neon dock]

yup

[neon dock]

thats last hope

[rocky tapir]

when did you start your preparation?

[neon dock]

I did preperation last yr

then stopped

then continued yesterday

[rocky tapir]

did you need help revising anything?

I am in 9th but am preparing for JEE

tell any chapter

I might know

[neon dock]

bhai so ja school bhi jana ho ga tuje kal

[rocky tapir]

kal sunday hai

bhai tu online hai?

[neon dock]

oh

[rocky tapir]

me koi help kar sakta hu?

[neon dock]

thank you bhai but I dont think there is anything you can do

[rocky tapir]

drop year ya first lik rahe ho?

[neon dock]

drop

ok bhai

gn

take care

see ya

have a nice day

[rocky tapir]

gn

bhai fikar mat kar

clear ho jaye ge

gn

good luck

[neon dock]

.close

[devout snow]

Channel closed

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[devout snow]

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.

[restive river]

Is determining a sequence to be monotonic increasing /decreasing required to find Sup and inferior of the set ?

[restive river]

its not required right ?

[storm raptor]

wdym?

[restive river]

$ Let A={1-\frac{1}{n+1} : n\in N} Find superior and inferior of such set $

[storm raptor]

$A = \left { 1 - \frac 1{n+1} , \vert , n \in \mathbb N \right }$

[restive river]

yeah

yeah

[woven radish]

dyxn

[storm raptor]

you need to find the supremum and infimum of the set

well, do you have any guesses

[restive river]

yeah its pretty easy but my teachers are really picky so I was wandering if its required to find if its monotonic increasing.... One of my mates is bugging me about it , got into a full blown argument , thanks for the help btw

[storm raptor]

there is nothing implicit about determining the monotonicity

but if your teachers are picky, they probably have a set method for you to follow

so check it out with them once

[restive river]

yeah , ok thanks

.close

[devout snow]

Channel closed

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[devout snow]

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.

[visual stone]

!help

[devout snow]

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

[visual stone]

i need help to find function zeros for f(x) = -3(x-4)^2 + 27

i already solved it but im stuck on finding the function zero

[graceful cosmos]

There's only one x, so you can algebraically arrange to get it

[visual stone]

yeah but what about x2

[winter patrol]

wdym you already solved it

what exactly did you solve

[pure flower]

this has equal real roots

[visual stone]

the equation

[visual stone]

wdym

[winter patrol]

wdym solve the equation

[visual stone]

what

[winter patrol]

as that usually means you were able to get the roots

[visual stone]

yeah i did

[winter patrol]

its unlear what you mean if you got the solutions and also saying you didn't find the zeroes

[visual stone]

oh cause

[winter patrol]

if you have the roots you have the zeroes

[visual stone]

ok let me show you

[winter patrol]

they're synonymous here

[visual stone]

f(x) = -3(x-4)^2 + 27

0 = -3(x-4)^2 + 27

-27 = -3(x-4)^2

3/-27 = -3(x-4)^2 / 3

√9 = √(x-4)^2

3 = x-4

im stuck here

[pure flower]

what

thats not the place to be stuck on

[visual stone]

idk man

what do i do next

[pure flower]

transpose the 4-?

[visual stone]

so 3-4?

3-4 = x?

[winter patrol]

also you should have two cases when taking the square roots

[primal elm]

3+4

[visual stone]

oh right

[winter patrol]

$$x - 4 = \pm 3$$

[woven radish]

ℝαμOmeganato5

[visual stone]

so 7 = x?

[primal elm]

Yeah

[winter patrol]

would be one of the solutions, (the +ve case)

[visual stone]

ok wait

i dont get the plus or minus

whats that supposed to mean

[winter patrol]

+3 or -3

[visual stone]

so x1 would be what then

and x2

[winter patrol]

interchangeable
one would be from the result of using +3, the other using -3

[visual stone]

so x1 is 3 and x2 is -3?

[winter patrol]

no

[visual stone]

ahh

[winter patrol]

use +3 in your calculations to get one solution for x
use -3 in your calculations to get the other solution for x

[visual stone]

alright

so i replace the x with 3

and the other calculation

with -3

?

[winter patrol]

no

[primal elm]

No

[winter patrol]

you don't replace the x with 3 or -3

$$x - 4 = \pm 3$$
means \
$x -4 = 3 \ \textbf{OR}\ x-4 = \red{-}3$

[woven radish]

ℝαμOmeganato5

[primal elm]

If x-4=3
Then x=7
Else x-4=-3
Then x=1

[winter patrol]

each of those equations will result in a solution for x

[visual stone]

oh ok so

x1 is 7 and x2 is 1?

[winter patrol]

yes

[visual stone]

but how do u know that x1 is 7 and not 1

[winter patrol]

doesn't matter

[visual stone]

oh

[winter patrol]

its just a list

[visual stone]

alright thanks guys

🤝

[primal elm]

It has 2 solutions, both are the zeros of the function

[visual stone]

alright so ima try to understand what u and he did

[winter patrol]

the subscript/index just indicates that the value is different

[visual stone]

basically u guys took the parathese of f(x) = -3(x-4)^2 + 27

which is x-4

but how did u get the 3

+- 3

[primal elm]

Square root of a number always has 2 solutions

1 negative and one positive

[visual stone]

its from here

?

[winter patrol]

$\sqrt{k^2} = c \
\gray{|k| = c} \
k = \pm c$

[woven radish]

ℝαμOmeganato5

[visual stone]

this is the 3 u guys took

[winter patrol]

for c>0

[primal elm]

Cuz (-3) x (-3)=9 and (3)x(3)=9

U have to write both, not just the positive one

[visual stone]

ohh

ok thank you guys

[winter patrol]

$(x-4)^2 = \sqrt{9} \
\gray{|x-4| = 3}; \text{this line is usually omitted/skipped}\
x-4 = \pm 3$

[woven radish]

ℝαμOmeganato5

[visual stone]

👍

thanks a lot

how do i close this now

.close

[devout snow]

Channel closed

Closed by @visual stone

Use .reopen if this was a mistake.

[winter patrol]

but in case this leads to any misconceptions, sqrt(9) is just 3,
the +- come from the stuff on the left side

[devout snow]

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.

[visual stone]

!help

[devout snow]

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

[visual stone]

i need help with this

whys my k 27

is it going downwards like this?

[dawn violet]

what

[dawn violet]

i didnt undersatnd your question

what is the question

[visual stone]

my k is 27 so is the lines going downward?

[dawn violet]

what is k here

what is h

[visual stone]

because zero functions are here

[mystic scarab]

!original

[devout snow]

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.

[dawn violet]

what are you trying to find

[visual stone]

-4 , 27

[dawn violet]

bro

!original

[devout snow]

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.

[mystic scarab]

Lol you won't get help if you continue like this

[visual stone]

?

[dawn violet]

!

[visual stone]

its telling me to draw my graph?

[dawn violet]

still not helpful

[mystic scarab]

Do you think we know what exercise you are doing????????

[visual stone]

what more information do u need

[dawn violet]

bro

what even is the question

omg

haha

[visual stone]

theres no question

[mystic scarab]

EVERYTHING

[visual stone]

it says draw the graph

[mystic scarab]

Hence no answer.

[dawn violet]

bro

what do you mean why is k 27

is there a law that says

k is 27

what is the context

[visual stone]

because thats the information i got provided with

[dawn violet]

i give up

[visual stone]

the exercise is telling me k is 27

[tiny panther]

what exercise

[winter patrol]

it says draw the graph
graph of what exactly?
a singular point?
function?

[visual stone]

f(x) = -3(x-4) +27

[mystic scarab]

Maybe tell WHICH graph?

[visual stone]

h is -4

k is 27

[dawn violet]

wow thank you

[mystic scarab]

There we go, finally 🎉

[dawn violet]

lmao

[mystic scarab]

...

[dawn violet]

y=-3(x-4)+27

[visual stone]

i didn't need to type that out

[dawn violet]

totally

[visual stone]

thats the same as saying -4 is h and k is 27

[dawn violet]

we just telepathically know

what the question is

[visual stone]

ok so tell me what have u learned from that

[dawn violet]

yeah no

[visual stone]

theres no question in a equation i fear

[mystic scarab]

YOU DID!

[dawn violet]

its not

[mystic scarab]

I don't think you deserve an answer, then

[visual stone]

notice how u still dont know what to do

[dawn violet]

right

[visual stone]

maybe u just aren't the right guy

[dawn violet]

wow

haha

says the one who gives A POINT

and then

expects us to magically know the equation

[visual stone]

are u the one who told me a minute ago that a equation was a question?

[dawn violet]

what have you tried

[dawn violet]

the question is draw a graph

which you didnt tell us before

now

[visual stone]

yeah i didnt tell u that

[dawn violet]

what have you tried

exactly

so we cant magically konw

if you tell us

[visual stone]

i didnt tell u

[visual stone]

yup didnt tell u

[dawn violet]

soemthing so random as h=something and k=something

that gives us nothing

can you just stop acting like a child

[visual stone]

bro u arent supposed to solve anything

[dawn violet]

and tell me

what you did

[visual stone]

what im asking u requires no maths

its just a question

[dawn violet]

move on to the question fam

[visual stone]

where does it go

down?

[dawn violet]

y=-3(x-4)+27

[visual stone]

because function zeros aren't above

[dawn violet]

for that

you have something called slope

and this is a linear equation

y=mx+c

are you familiar

[dawn violet]

whats a function zero

[winter patrol]

the direction of the parabola depends on the blue sign
$$y=\blue{-}3(x-4)^2+27$$

[visual stone]

let me show u

[woven radish]

ℝαμOmeganato5

[dawn violet]

he didnt mention square

[visual stone]

the purple lines

are my function zeros

and the slope has to go through them

so its going down?

[dawn violet]

you mean the intercepts?

[winter patrol]

also your h here will be 4, not -4

[visual stone]

why 4

[visual stone]

uhh

most likely

sounds like it

[winter patrol]

compare x-h to x-4

[dawn violet]

its not a parabola

y=-3(x-4)+27

thats the equation

[winter patrol]

clear typo

[dawn violet]

its a linear equation

[winter patrol]

seems like its a continuation from the previous question

[visual stone]

it is

the other time we found the intercepts now im tryna draw the graph

so its 4 and -27?

[winter patrol]

no

compare +k to +27

k is still 27, there wasn't an issue with your k value

there is however an issue of your plane not being big enough to be able to show it

zoom out if you can and plot your points
(4,27)
(1,0)
(7,0)
and you should have a clearer idea of what to do after

[dawn violet]

@visual stone you can get an idea of where the concave side will be looking at the sign

and which term is squared

y2=4x, rightward, y2=-4x, leftward,
x2=4y, upward, x2=-4y, downward

and then the rest is the matter

of plotting

[dawn violet]

as he said

[visual stone]

im back

[winter patrol]

seems like its a continuation from the previous question
don't know if it was a miscommunication or something but,
but newcomers don't bother looking above the "channel available indicator"
so are unlikely to know this was related to your previous question
in future if people question insufficient info and/or ask for more clarity, always repost the full question

[visual stone]

lemme read

[visual stone]

no its because

its a graph i took online

so the numbers are random

dont worry about the numbers

[visual stone]

so h is -4 and k is 27

?

[winter patrol]

no

[visual stone]

why is h 4

[winter patrol]

compare x-h to x-4

[visual stone]

what is x then

[winter patrol]

x is x

[visual stone]

but we dont know the value of x

are u saying x is 8

[winter patrol]

no

x is x

[visual stone]

ok lets say it was (x+4)^2

then h is 4 or -4

[winter patrol]

compare (x-h) to what you have in that component
compare
x - h to x+4

or what do you get when you solve
x -h = x+ 4

$$y = \red{a}(x-\blue{h})^2 \violet{+ k}$$
$$y = \red{-3}(x-\blue{4})^2 \violet{+ 27}$$

[woven radish]

ℝαμOmeganato5

[visual stone]

so even if its -4 or 4 in the paranthese

when u solve it

its 4?

[winter patrol]

wdym even if its -4 or 4 in the parentheses

[visual stone]

cause look

it says -4 but ur saying 4

im having trouble understanding how is it 4

[winter patrol]

solve
x-h = x-4

[visual stone]

4 = x

[winter patrol]

no

how are you getting that

[visual stone]

wdym solve x-h = x -4

that whole thing

?

[winter patrol]

yes

[visual stone]

x and h included?

[winter patrol]

simplify / solve / eliminate unnecesary components

give the simplified equation

and if only one variable remains, isolate that variable

[visual stone]

ok ill try

[winter patrol]

and that equation will tell you its value

[dawn violet]

you can compare

from the image itself

[winter patrol]

or compare and the value of h is trivial
especially with my colour coding

[visual stone]

i dont think ive physically learned

how to solve x-h = x - 4

or like

stuff like that

[winter patrol]

same operations to both sides

[mystic scarab]

There's nothing hard, just compare colours... It's a very basic logic task

[winter patrol]

you've demonstrated earlier you've been able to manipulate equations

do NOT overthink this

i've seen what you're capable of
you should have ZERO issue with this

[visual stone]

im getting x + 4 = h + x

[winter patrol]

how did that happen

how did x-h turn into h+x

[visual stone]

mb

x + 4

[visual stone]

flipped it to the other side

[winter patrol]

ok, that edited equation is still valid

[visual stone]

so its good?

[winter patrol]

can be simplified further

do something about those x

[visual stone]

4 = h?

[winter patrol]

yes

[visual stone]

ohhhhhh

oh my god ur a life savior for that

[winter patrol]

stop overthinking

[visual stone]

ok so everytime i wanan find h i gotta do x -h = x (number)

[dawn violet]

@visual stone

you dont need to do that much

[visual stone]

yeah

[dawn violet]

you can just compare equations

[dawn violet]

like look

[visual stone]

how do i compare it

[dawn violet]

you know the equations are same

[winter patrol]

red = red
blue = blue ; the thing being subtracted from x
purple = purple

[dawn violet]

yeah

[visual stone]

colors

but what do i do

[dawn violet]

you just equate

a=-3

h=4

k=27

thats all you needed to do

[visual stone]

but how did u get 4

[dawn violet]

till now

[visual stone]

ik its 4 but

how did u get 4

just by looking

[winter patrol]

blue = blue ; the thing being subtracted from x

[visual stone]

at it

[dawn violet]

i know that both the equations are same

both represent the same kind of parabolas

so you can just equate like that

[winter patrol]

in that vertex form,
h represents the value being subtracted from x in the ()
what is the value being subtracted from x in (x - 4)
that value is easily identifiable as 4

[visual stone]

so 4-4

[winter patrol]

no

[dawn violet]

no no no

[visual stone]

oh

wait

ok nvm scrap that

[winter patrol]

you're overthinking again

[dawn violet]

let me give you an example

y=mx+c

y=2x+5

find m and c

how will you do that

[visual stone]

m is 2 and c is 5

[dawn violet]

eah

we're doing the same thing here

[visual stone]

oh wait

u guys mean

[dawn violet]

yeahhhh

EUREKA

[visual stone]

the minus has nothing to do with the h

[dawn violet]

YES

YSE YES

[visual stone]

ohhh

[dawn violet]

we're just comparing the equations

to find waht is what

[visual stone]

ty dude

[dawn violet]

waht you just did is called comparing

and also

to plot it

i mentioned the concave side part above

that helps to know

and to find the intercepts

you can subtitute x =0, find y and y=0 find x

[visual stone]

i already found them dw

[dawn violet]

and pot

[visual stone]

it was 7 and 1

[dawn violet]

plot*

yeah

in this case

[visual stone]

-7 and 1

i mena

[dawn violet]

parabola is facing downward

becaues

x2=-4y form

[winter patrol]

it was 7 and 1, you had it right the first time

[visual stone]

oh nvm

alr thank u guys

[winter patrol]

really, stop overthinking this

[visual stone]

its hard ngl especially cause im taking the highest level of math for my grade

[dawn violet]

its all in your head

because i felt the same

but once you get a hang of it

everyhting becomes clear and easy

[visual stone]

ill remember this from u

ty goat

[winter patrol]

focus on applying basic properties
combine and apply more complex only as required

[dawn violet]

and also next time

if you're asking for help

give context

[visual stone]

yeah my bad

[dawn violet]

and dont just you know

[visual stone]

alr 👌

[dawn violet]

act like they dont know stuff

cuz we had no idea

[visual stone]

yh sorry 😭

[dawn violet]

you were referring to a parabola

or what the question even was or what you even wanted to do

[visual stone]

alr bro

thanks 🔥

.close

[devout snow]

Channel closed

Closed by @visual stone

Use .reopen if this was a mistake.

[devout snow]

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Send your question here to claim the channel.

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• Show your work, and if possible, explain where you are stuck.
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[marsh bloom]

Can anyone give me a thorough explanation on how to solve these questions using 10th Grade Math? We’re just learning about exponents and radicals. I’m completely lost.

[hushed sparrow]

underroot of x means x^1/2

wait ill solve

[marsh bloom]

alr

[rotund umbra]

,rotate

[rotund umbra]

1/5

but yes, nicely done

[hushed sparrow]

yeah change it to 1/5

[marsh bloom]

ohhh this makes much more sense!

so a square root is basically just ^1/2?

[rotund umbra]

exactly

[marsh bloom]

oh i see

[hushed sparrow]

yes

[marsh bloom]

wait can you help me on one more question?

[hushed sparrow]

sure

[marsh bloom]

d)

[iron kindle]

!nosols

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[marsh bloom]

i did the work but my answer was different

[rotund umbra]

$$x^2 = 5 \implies x = \sqrt{5}$$
But also
$$x^2 = 5 \implies (x^2)^{\frac{1}{2}} = 5^{\frac{1}{2}} \implies x = 5^{\frac{1}{2}}$$

[hushed sparrow]

sry my bad

[woven radish]

Shuba

[hushed sparrow]

what did u do after the first step?

[severe bolt]

I think u forgot one negative solution

[marsh bloom]

i used exponent laws to subtract same bases when dividing

[hushed sparrow]

hes doing basic exponents, i dont think he needs to worry about that just yet

you messed up the exponent of 4

the subtraction

you did 4^(2-3)

but u had to do 4^(-2-3)

[marsh bloom]

ohhh i see it now

let me try again

so the answer would be x^2/1048576 ?

[hushed sparrow]

u can also think of the power as this

[rotund umbra]

no. sqaure roots have two solutions, so not missed there. raising to fractional powers have multiple solutions (fundamental theorem of algebra), so again not missed there.

[marsh bloom]

alr

thx sm for ur help

i didn’t know square roots were like ^1/2 and stuff

[sand dove]

the square root function has a single output

[hushed sparrow]

no

[sand dove]

square root of a positive number is THE positive root of that number

[marsh bloom]

that’s what it said on the back of the textbook for me

[hushed sparrow]

oh wait nvm yes

i forgot the ^2 at the end

[marsh bloom]

oh alr

[hushed sparrow]

no

[rotund umbra]

we only use the principal solution by convention. so yes, the function does because otherwise it's not a function. but roots aren't functions

[marsh bloom]

im kinda new to the server do i close it

so others can use it

[hushed sparrow]

.close

i think

[sand dove]

sqrt(a) with a > 0 is by definition the principal root

[marsh bloom]

.close

[devout snow]

Channel closed

Closed by @marsh bloom

Use .reopen if this was a mistake.

[rotund umbra]

squrt(a) isn't defined for a<0 on the real domain

[sand dove]

yes

so?

[hushed sparrow]

yes but sqrt(a) = ± sqrt(a)

[sand dove]

we're not dealing with square roots of negative numbers last I checked

[rotund umbra]

f(x) := y : y^2 = x is the principal root of x. the root notation isn't a funciton.

[sand dove]

you literally wrote something = ± itself

[hushed sparrow]

simply put,

sqrt(4) = +2
and
sqrt(4) = -2

[sand dove]

it is? $\sqrt \cdot :\bR_+\to \bR_+$

[woven radish]

rafilou is not not born in 2003

[sand dove]

sqrt(x) is THE principal square root

[rotund umbra]

is it? $\sqrt[n] \cdot : \bR_+ \to (\bR_+)^n$

[woven radish]

Shuba

[hushed sparrow]

ok but then underroot() is not sqrt()

[sand dove]

wrong codomain?

$\underroot x$

[woven radish]

rafilou is not not born in 2003
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sand dove]

what is "underroot"

[hushed sparrow]

mate wtv idk semantics and names of stuff, i just know how to do maths

[sand dove]

if you don't know semantics then don't argue with them xdd

[rotund umbra]

why not have the square-root notation be a functor to vector spaces?

[hushed sparrow]

who is arguing lul

[rotund umbra]

if you really want it to be a function

[hushed sparrow]

i was helping the kid who had the doubt

[rotund umbra]

I think we've strayed from the original question quite a bit XD

[sand dove]

in any case this is wrong as written here if a is positive

sqrt(4) = 2, -sqrt(4) = -2

You can always give another name or notation to what you were trying to argue

[hushed sparrow]

ok who cares tho, his question does not even require the negative root

leave it, go study, gl

[sand dove]

well as soon as was said "square roots have two solutions"

I'm rectifying false information that was given to the helpee

once that is corrected, my job is done

[devout snow]

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• Show your work, and if possible, explain where you are stuck.
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[half current]

Can someone tell me if I'm on the right track?

[pseudo basin]

your value for cos(alpha) is wrong

(5/13)^2 = 25/13^2 not 13/13^2 as you did

[half current]

Oh

Yeah seems I have made a mistake in writing it

I wasn't careful here

Other than that..I did it correct which I'm proud of thank you for noticing my mistake

Oop I didn't erase one bit but that's okay

Okay closing now

.close

[devout snow]

Channel closed

Closed by @half current

Use .reopen if this was a mistake.

[devout snow]

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

[visual stone]

!help

[devout snow]

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

[visual stone]

how can i put f(x) = 2(x-4)(x+2) in general form

[steady veldt]

wdym general form ?

[visual stone]

f(x) = ax^2 + bx + c

[steady veldt]

you can just developp it

[midnight echo]

multiply it out

[visual stone]

so (x-4)(x+2)

?

[steady veldt]

first do x*(x+2) and add -4 * (x+2)

[visual stone]

what?

[steady veldt]

uh im explaining the steps

you don't understand it ?

[visual stone]

where did u get a 3rd x from and where did u get another 2 from

[smoky nimbus]

Do you know FOIL?

[visual stone]

are u talking about what i was previously sayingso (x-4)(x+2)

[smoky nimbus]

Yeah so you can apply FOIL

[visual stone]

ok i did

[smoky nimbus]

What did you get?

[visual stone]

it gives me f(x) = 2(x^2 - 2x - 8)

after simplifying

[smoky nimbus]

Now distribute the 2

That's on the outside

[visual stone]

f(x) = 2x^2 -4x - 16

[smoky nimbus]

That's it

[visual stone]

thank you

[steady veldt]

what is foil ?

[visual stone]

.close

[devout snow]

Channel closed

Closed by @visual stone

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[devout snow]

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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>.
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[alpine mist]

How do I proceed with this? (I have to write in rectangular form)

[somber heron]

use euler's form

[woven radish]

jesko

jesko

[alpine mist]

is there any way to use demoivre’s theorem since im not suppose to use any other method than that

[somber heron]

yes, the above problem will be best to solve with demoiver's theorm

[somber heron]

now raise both sides to the power of 5

and lastly don't forget to multiply 3^5

[misty crest]

bro did you use \dfrac?

[somber heron]

yeah

kinda look wonky

[woven radish]

jesko

[misty crest]

yea

like that just looks goofy

[misty crest]

much better

[somber heron]

agreed

$e^{i \sfrac{\pi}{3}}$

[woven radish]

jesko
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[somber heron]

no sfrac?

[misty crest]

idk what that is

[alpine mist]

what do you mean both sides? like the (3/2 + 3/2 sqr 3i)^5?

[misty crest]

what’s sfrac

[alpine mist]

wait am I even doing this correctly? cuz u did say raise 3 to power of 5 😭 like am I suppose to raise 3^5 before
(3/2 + 3/2 sqr 3i)^5

[upper schooner]

(if you want it you probs can get it included in your TeXit preamble)

[misty crest]

$e^{i\tfrac{\pi}{3}}, \quad e^{i\frac{\pi}{3}}, \quad e^{i \dfrac{\pi}{3}}$

[woven radish]

jesko

knief

[misty crest]

never heard of sfrac those are the only three i’m aware of

[somber heron]

sfrac is like 3/2 in line

[misty crest]

what package?

[woven radish]

jesko

[somber heron]

i'll have to check but probably amsmath

[acoustic leaf]

xfrac

[somber heron]

oh yeh

[woven radish]

jesko

jesko

jesko

jesko

[somber heron]

i think you can proceed further yourself now

[alpine mist]

so I just have to multiply that by 3^5 and solve for cos(5pi/3) and cos(5pi/3) and then distribute everything?

[somber heron]

yeah

[alpine mist]

is this correct

[somber heron]

it is

[alpine mist]

alright tyy

.close

[devout snow]

Channel closed

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[devout snow]

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• Show your work, and if possible, explain where you are stuck.
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[supple light]

Did everything outside of a b to get 21

Then added everything outside a nd b plus the intersect to get 31

Then tried everything but the intersect still wrong

[rustic jetty]

what region of the graph is $A^C \cap B^C$

[woven radish]

Dork9399

[supple light]

I assumed everything outside of those two circles at first but that was wrong

[somber heron]

is it (universal set) - (A union B)

[rustic jetty]

specifically what do you mean by "outside of those two circles"

[somber heron]

14+5?

[supple light]

• 5

That was my first try

Said incorrect

[somber heron]

is it wrong?

oh

[rustic jetty]

is it not just 14?

[supple light]

It could be I don’t know I tried 3 times and got locked out and it was one of those that doesn’t tell you after just wanted an explanation

[somber heron]

there is a small 5 ouside C

[rustic jetty]

oh oop

[rustic jetty]

wait its not 19?

[somber heron]

it should be but it's not

[supple light]

Hold up

[somber heron]

i can't see anything wrong with this

[supple light]

lol cause i definitely put 21 it probably was 19 and im just silly

[somber heron]

bruh

[supple light]

I’m old !

[somber heron]

it's okay (jk)

[supple light]

Thank you for your the insight lol

[devout snow]

@supple light Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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[supple light]

can someone explain what the first part of this question is asking

[strong plume]

correct me if im wrong but i swear the basic angle/reference angle should be 0 not pi

[devout snow]

@supple light Has your question been resolved?

[somber heron]

what's the lower limit?

@strong plume

[strong plume]

0

[somber heron]

should be

[strong plume]

so whatchu reckon

[somber heron]

that the given answer is wrong and you're right

[strong plume]

aight thx

[supple light]

<@&286206848099549185>

[wise scarab]

well, you're not showing us the dropdown

but if I had to guess

I'd say it's asking you to describe the shape of the distribution (||binomial probably, since it'd the sum of iid rv||) and the range of values it could have

[supple light]

i can show it

[wise scarab]

||which is integers between (inclusive) 0 to 32||

[supple light]

actually nvm that one expired

but the drop down had a bunch if letters X ,N, P