help-0

[red ledge]

I didn't understand ur question

This

What point u mean?

U keep saying facing the point! I don't see any points.

[gentle ingot]

Here

I made the point bigger sorry

[red ledge]

Yeah my bad

Okay

[gentle ingot]

Well if it's facing east, it must turn so that it can face the point

What angle should it turn?

Wait no

That was a bad compass lol

[red ledge]

Movement of the ship is just a straight line so it's like we can't describe a movement and direction at the same time

So I wanted to say go 30 degrees but it doesn't make sense

It must be turn 30 degress

Like go? Go straight? No it doesn't make sense

There's a meaning that we are losing when we say go

We should include the turn and the movment straight both together

In order to satisify the required meaning

But motion or momvent in a straight line

Isn't the same as turning

Therefore, Okay, U know it would be right if he just keeps moving forward and he's making an angle 30

That way he just moved forward, I would say "Keep moving u are making an angle 30"

But move angle 50!

Nah!

That's not right.

[gentle ingot]

?

[red ledge]

We are missing something

That is the rotation

Finally that's the word

[gentle ingot]

Yes the rotation

[red ledge]

Yeah it's the rotation

[gentle ingot]

He must rotate a certain angle

[red ledge]

Then how could u miss the rotation when we are describing both a motion, movement straight movement and at the same time u want to make right or left

Therefore u need to say turn

And at the same time u want to say go forward

So combine that both

To require or make a new word that justify or satisfy the meaning

Or the conceptual or physical

U know?

If we put or draw like rays of the ship movement

Go straight but when it goes to an angle it turns left or right

So I think the word direction is missing a meaning

Direction is just one-dimensional

Right?

[gentle ingot]

So you're saying go forward 2 units. Turn left at a right angle (90°), then move 2 more units

[red ledge]

But when u add a new concept, angle

Then there's a new meaning

[red ledge]

Um

I'm saying we need a new word. Direction isn't the right word

Do u agree?

[gentle ingot]

Sorry I don't understand what you're saying

Argument is that word

[crisp iris]

Sense?

[red ledge]

Do u agree on what I said that the direction is just one dimensional

[gentle ingot]

The math definition of argument means exactly that

[red ledge]

Is direction a quanitiy?

[red ledge]

What do u mean Math definition of argument?

What are u talking about? Is there a field called that?

[gentle ingot]

Direction can be multiple dimensions

[red ledge]

How so?

What is direction?

[gentle ingot]

ar·gu·ment

Mathematics

noun

MATHEMATICS•LOGIC

an independent variable associated with a function and determining the value of the function. For example, in the expression y = F ( x1, x2 ), the arguments of the function F are x 1 and x 2, and the value is y.

For a 2d plane direction is just one dimension

[red ledge]

Is direction just a magnitude or a? Is direction even a quantity?

[red ledge]

Aha? so what about 3d?

[gentle ingot]

In 3d direction is 2d

[red ledge]

Tbh I didn't understand what does that mean but I understand what does argument mean

[gentle ingot]

👍

[red ledge]

Okay wait what are u trying to say bc I lost you

U said direction can be multi dimensiaonal

I wanna know first what is direction

Like is it a physical quantity?

[gentle ingot]

Direction is an angle, or argument

[red ledge]

Direction is an angle?

Wow, Who says that? Who said that?

From where? Like is that the normal definition? Or what?

[gentle ingot]

???

[red ledge]

Like when i imagine direction I just imagine motion in one line straight

It's just a line

It can't break it self or have flexibilty

It's just a line

Right?

[gentle ingot]

Uhm I guess I see your point

[red ledge]

That's direction and what determines it

[red ledge]

Direction! Go left go right

[gentle ingot]

Yes

[red ledge]

Jump on

[gentle ingot]

Left and right can both be directions

[red ledge]

Would be adding a new dimensional

[red ledge]

Okay that's just playing with words

[gentle ingot]

??

[red ledge]

Because it's not about left or right I'm saying

Left and right are respectives..

Like they could be straight as well!

I didn't say left and right

I'm talking about motion

Ofc go left or right is just one dimensional

And direction

Like it doesn't matter where u go

u didn't add a new thing

But an angle

is the new thing, A new flexibility

Like u break the line, U start making an angle

U know what it's like? U know those games that u can only move in one direction

Up or down left or right

But aha

U can't move other than that

That's direction

But in order to add a new motion to like turn ur body

Ah wait!

After u turn ur body and u move

It's still direction one dimensional

But it's about when u rotate ur body

So there's a meaning that being conveyed when rotations happen

That we are missing it or dropping it!

It doesn't make sense!

Do u get me?

I mean we can't combine both direction and angle together?

U can't substitute direction with angle..

I dunno man

Let me see it again

Like I would say move parallel to the angle of 30

Not move at angle 30!

Or go at angle 30!

Lol

Go at angle 30?! that doesn't even make any sense

[wispy solar]

I like your funny words magic man

[red ledge]

An angle isn't a line

[jovial aurora]

You okay?

[red ledge]

These are just my thoughts in my head

[jovial aurora]

checks out

[red ledge]

Okay so what?

What is the conclusion?

What did we agree on? And what did we finally reach to?

@gentle ingot

Man please make me understand.

[gentle ingot]

I still don't really get what you mean

[red ledge]

Hmmm

I'm not convinced that direction is an angle

When u for example, say and find the direction of the object

[icy trail]

just call it an angle then

it dosent matter

whenever you see direction replace it with angle

they're the same

[red ledge]

Wow

Yeah that's direction+angle+ rotaition

Okay we can move on

Mabye we can discuss it later

Okay what's the next problem

Don't tell me orientation is the same as rotation, are they?

[icy trail]

what's the difference between direction and angle?

[red ledge]

@gentle ingot Asher, can we continue? Where were u at?

[red ledge]

Bro angle isn't a direction

[severe beacon]

I need help

[gentle ingot]

Oh Im speaking with friends right now

Sorry I left you

[icy trail]

Collatz conjecture 👀

[severe beacon]

This question…

[gentle ingot]

Lol

[small bear]

Trivial stuff

[severe beacon]

Yea it came in my test yesterday

Soo

[icy trail]

solving it?

[red ledge]

Bro u just interrupted me!

[severe beacon]

Yea

[icy trail]

how many marks was it?

[severe beacon]

10

[red ledge]

Angle isn't direction bro

[gentle ingot]

🐸

[icy trail]

10 marks nice

[red ledge]

U say what is the difference between angle and direction!

[gentle ingot]

If ur joking zaddy I think this belongs in chill

[icy trail]

lmao

[severe beacon]

Lmao maths is sooo hard imma finna take bio

💀

Guys i have a question

Is computer science related to maths

[red ledge]

Math isn't hard bro, Only the reltations that u do it, and mental calculations are hard

[severe beacon]

How much

[icy trail]

computer science is maths

kinda

its discrete maths

[severe beacon]

Oh

[icy trail]

people call it a branch of maths

[red ledge]

Okay pls u interrupted me

And u cut me off

[gentle ingot]

Not to ruin the joke but if you aren't kidding, that's a famously unsolved problem and your teacher could've put it there as a joke. If you knew the answer you could get like 1000000 dollars I believe

[severe beacon]

This shit 😭?

[red ledge]

What makes it complicated is that there are many of them! But each concept is just easy

[icy trail]

i don't think it's a millennium problem? and maybe the question was asking to compute the 12th term for n_0 =5 or something and they just put Collatz in to be cute

[red ledge]

Like a line, U understand or know what is it

The amount of things just overwhelm u

That might mean that the concepts are hard

[gentle ingot]

Oh true

[red ledge]

But that's not why you were astonished or felt hard when u looked at this image

[severe beacon]

Soo is the combo pre med and computer sci good?

[red ledge]

Because u don't even know what are these concepts

U just knew they are hard because of two things

U don't even understand what is this yet you felt it's hard because u know from experience Math is hard and u assumed this must be hard, I'm not saynig they are not hard

Even if they are hard not because u understood they hard, but because they are actually hard.

[severe beacon]

U sound smart

[red ledge]

But just the feeling

[severe beacon]

?

[red ledge]

But I can't solve problems bro, Like literally every time I look at Math problem just my mind goes blank

I don't know what's wrong with me...

Like I'm slower than a turtle when i try to solve it, I think this might help

I dunno like my mind wouldn't connect anything at all when I'm solving

[severe beacon]

💀

[red ledge]

Like it can't connect

But It can like analyze?!

I dunno

I don't really know man it makes me wanna die...

[severe beacon]

I have some friends u can ask them if u need help

[red ledge]

Like I don't know, Many dumb people in my class can solve math

[severe beacon]

What class r u in

[red ledge]

12ht grade!

Is that what u are asking?

Um... Like what topics of Math?

[severe beacon]

Uhm I forgot 💀

[red ledge]

What is that? I dunno

Class name?

What do u mean?

I'm not from US I think...

I don't live in it rn

Give me an example then

I don't know what u are referring to!

I can understand concepts, but it's just a problem of referring.

Ah, I never knew about that, that's why

[gentle ingot]

Math 1 math 2 and so on

[red ledge]

Okay, We just study Math

Yeah lol

[gentle ingot]

Or just 12th grade math

That's valid lol

[red ledge]

We don't have such a thing

But according to ur system

Yeah, Math 1 and Math 2

[red ledge]

Okay, Asher... Are u free?

Like can u explain something to me?

[icy trail]

just ask to the whole channel

they aren't gonna be free 24/7

[marsh shuttle]

DID IT ON MY OWN CANT TAKE IT OFF THIS WRIST NOW IM GWTTING RICH

That’s why everyday we LIT

EVERYDAY WE LIT YEAH CANT TELL ME HIT YEAH

[red ledge]

Okay guys I got it

I guess I don't have the ability to imagine or make sense of numbers in my head

I wouldn't say I "don't" have the ability at all, because it must be there otherwise I wouldn't be understanding anything, but it's very slight, like it's very weak or low.

That's my weakness and my problem! I dunno, does this have to do with how I make sense of abstract things? Should I go to a psychiatric or something or he won't be able to know, I guess this isn't common, so I dunno if therapist or psychiatrics are the right choice!

[vague coral]

tf ?

[red ledge]

And I guess it's also Math anxiety?

[red ledge]

What?

[glass lichen]

"I struggle with complicated stuff, should I see someone" shouldn't be your 1st thought

[red ledge]

Lol, What do u mean?

I didn't say complicated stuff lol!

[glass lichen]

No clue why you're having an existential crisis in a discord server

[red ledge]

And what do u mean by complicated? What does determine a complicated stuff? A hard one?

[glass lichen]

"a complicated stuff"

[red ledge]

That is conceptually hard wise to understand?

Or do u mean bunch of stuff put together that are hard

[glass lichen]

No, there's a distinction b/w computational difficulty and conceptual difficulty.

[red ledge]

Is that ur perception of complicated stuff?

How do u even I have a problem of understanding complicated stuff?

Did u judge that because I have a problem understanding Math?

[glass lichen]

Yeah ending this discussion here.

[red ledge]

Well a number just triggers me and it's very hard for me

This part or region of the brain is different

It doesn't have to be I'm dumb because I lack or low at something

I could have symptoms or mental illness or a cause

Doesn't mean I'm dumb or I'm not good at Math

[glass lichen]

Channel's free to use if anyone's wondering

[red ledge]

There might be something that prevents me from... that something u don't have so u understand better than me

[red ledge]

Okay fine. Bye!

[glass lichen]

Yeah I didn't ask for your life story, nor was you starting a soliloquey in a discord help channel necessary

[red ledge]

This isn't a life story, This is just a branch of a branch explaining an argument

Criticized u, what u said as complicated stuff and accusing me of being dumb

[lean reef]

I got 2/3(x+2)^2-5 I feel like it’s wrong

[red ledge]

@glass lichen Move it to another channel.

[glass lichen]

,w calculate (2/3)(6)^2-5

[ocean seal]

Results provided by WolframAlpha

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

Requested by Omegabet_#9771

[glass lichen]

it's right

[lean reef]

Oooo aight

There is no need to simplify or anything else?

[glass lichen]

well you could expand it if you want

but it just says give the equation

[lean reef]

I don’t know what that is?

[glass lichen]

so y=that is sufficient

[lean reef]

Ok thank u

[lean tartan]

to this^

[sick wadi]

ayo how i do dat

[red ledge]

What is this? Are u at high school?

[glass lichen]

looks right too.

[red ledge]

Are u trying to simplify the problem? @lean tartan

[glass lichen]

but just do what I did, plug in the point and check

[lean reef]

Aight thank u

Wait which point?

[glass lichen]

"point on the graph"

just to check if the a value is correct or not, cause everything else should be pretty simple

[lean reef]

Yep

It’s right

[red ledge]

I think that has something to do with "Cos Law"

[glass lichen]

again, plug the values into general vertex form, then solve for k

are you sure that's the expansion?

[lean reef]

Sheesh lmao I tried plugging it in and got 35 this time

I’m lost

[glass lichen]

$-3=-2(-5-k)^2-1$

[ocean seal]

Mosh

[lean reef]

Still lost

Why is the K inside?

[glass lichen]

cause general vertex form is $y=a(x-k)^2+h$

[ocean seal]

Mosh

[lean reef]

Sooo uhh would I distribute the -2?

[glass lichen]

no

you want to isolate for k

[lean reef]

Yeah that’s where I’m lost

Idk how to begin

[glass lichen]

if I asked you to isolate x in $-3=-2x-1$, what would you do?

[ocean seal]

Mosh

[lean reef]

Add 1 to both sides then divide by -2

[glass lichen]

yes, so x=?

[lean reef]

1

[glass lichen]

yep so $1=(-5-k)^2$

[ocean seal]

Mosh

[glass lichen]

then what?

[lean reef]

Don’t know lmao

[glass lichen]

how do you get rid of the squaring?

[lean reef]

U square it on both sides

[glass lichen]

no

[lean reef]

Oh uhh

[glass lichen]

if I square both sides ill have something to the power of 4, not 1

what's the opposite of squaring?

[lean reef]

That’s a good question, umm

Finding the square root?

Idk

[glass lichen]

yes, take square root

[lean reef]

Of what?

[glass lichen]

of both sides....

$\pm 1=-5-k$

[ocean seal]

Mosh

[glass lichen]

though you can just take +1 or -1 since it just asks for a value of k

[lean reef]

Why is it plus or minus?

[glass lichen]

(1)^2=1
(-1)^2=1

so both square to 1

[lean reef]

Oh but how do I find K’s value?

Would I add 5?

[glass lichen]

yes

[lean reef]

So it’s plus or minus 6?

[glass lichen]

no, it'd be 5+-1

so either 6 or 4

[lean reef]

For the value of K?

[glass lichen]

no

for -k

[lean reef]

So in order to find k do I have to square 6 or 4?

[glass lichen]

???

[lean reef]

I’m lost

[glass lichen]

if you have $6=-k$, what do you do to get k?

[ocean seal]

Mosh

[lean reef]

Well since K is negative in order to get it to be positive don’t u multiply by another negative?

[glass lichen]

yes, multiply/divide by -1

so k=-6

(or k=-4 if you chose to use -1 after square rooting)

[sick wadi]

help

[lean reef]

So k is either -4 or -6?

[glass lichen]

yes

[lean reef]

Is there anyway to check which is the correct one?

[glass lichen]

both are correct

[lean reef]

So for the answer choice i could just input them both

[glass lichen]

no

cause it explicitly says a value of k

[lean reef]

Oh use either

[glass lichen]

yeah, use one of them

[lean reef]

Thank u!

[glass lichen]

<@&268886789983436800>

[sick wadi]

golly gee how disrespectful

<@&268886789983436800>

[sly mantle]

b&

[crystal zephyr]

Hey guys

can i help me?

How to find the kernel of matrix

[red ledge]

What happened bro?

[red ledge]

What's going on? What did he do?

[glass lichen]

kernel is defined as the set of vectors which get mapped to 0

$\text{ker}(A)={x|Ax=0}$

[ocean seal]

Mosh

[lean reef]

Is this right lmao

[tiny crown]

I dont see an equation lmao

[lean reef]

Wym

[glass lichen]

well what did eqn did you try to solve?

no

put the information into general vertex form, then isolate for h

[steel scaffold]

how do i draw the polar curves of r=acos^2theta / r=asin^2theta? what rule is there for a squared function?

is it just 2 petals instead of 1 circle if the function is squared

[still vessel]

Can someone help me please it’s my last question I need done and my test is due in 10 mins

[lean reef]

So what would it be then

[glass lichen]

You tell me.

[lean reef]

The other number I’m thinking is 3

That’s it lmao

[glass lichen]

I've given you general vertex form before

[lean reef]

Is 3 right? Lol

I got a decimal this time yeah there is no way that is right

[glass lichen]

you should get 37/5

[lean reef]

How I got 17/9.6

[glass lichen]

yes, cause i know exactly what you did to get there \s

[lean reef]

I used the general vertex form method

And I plugged in the numbers to their respective variables

[red ledge]

Are u at high school, Mosh?

[glass lichen]

ok... what equation did you get?

[alpine sable]

is this differentiable across all real numbers

[lean reef]

17=3/5(-2+2)^2+0

Ah (-2-2)^2

[zealous basalt]

I said the answer to this problem was:

But it says y=8x-6pi-8 is wrong? That makes no sense to me

[buoyant kayak]

what did you get for y'?

[unborn heath]

I cannot figure this out for the life of me

After rationalizing you get (2x^2 + 22) / (x-2) (sqrt(2x^2 + 28) + 6)

But how do you remove the (x-2)?

[zealous basalt]

8 sec^2(x)

[buoyant kayak]

and if you plug in 3pi/4 into that?

[zealous basalt]

yes.

[buoyant kayak]

i mean what do you get

[zealous basalt]

8

[buoyant kayak]

that's not what i got

[zealous basalt]

really?

[buoyant kayak]

what is cos(3pi/4)

[zealous basalt]

about -sqrt(3)/2

[buoyant kayak]

no

that's a reference angle of pi/6

[zealous basalt]

ohhhh

it must be -sqrt(2)/2 then, got them mixed up

[buoyant kayak]

yes

now we know sec(x) = 1/cos(x)

so sec^2(x) is 1/cos^2(x)

and you know cos(x) is -sqrt2/2

so flip the fraction and square it

that's your sec^2(x)

[zealous basalt]

ohhhhhhhhh

ffffffuuuu

my problem

so simple

I put 8/tan^2 (x) in my calculatror, not 8/cos^2 (x) because I was thinking of how the derivative of tan is sec^2

dumb error

thanks for correcting me @buoyant kayak

[buoyant kayak]

👍

[unique peak]

This question doesnt make sense to me

Find the other values for a parabola with the given as focus (5,0) and directrix y = -5

Isnt the focus and directrix supposed to be aligned

[steel scaffold]

how can i find the diameter? 3 chords, ABC=30.1 BAC=43.1 ACB= 106.8

AB not diameter

[light dagger]

sorry cant read

[torn hemlock]

help me with b)

[light dagger]

am absolute trash with languages

[torn hemlock]

a+b+c=3 a,b,c>0

sorry

i'm from Viet nam

[light dagger]

ah nice

[alpine sable]

I need help proving this. Imma put it here and in logic channel just in case

This is where i'm stuck at

Better view

[torn hemlock]

help me :((

[teal pike]

Can someone help me with this question? It is solving for y`

[buoyant kayak]

get everything that has y' in it on one side, then factor out and divide

[teal pike]

I would have to multiply 2 individually with every term right

[buoyant kayak]

when getting rid of the fraction, yes

[lean reef]

May I ask a question here?

[small cypress]

whats the eq

cos when i graph it i get nothing

<@&286206848099549185>

[torpid needle]

what do you think a 7th grader should focus on in math?

[glass lichen]

Algebra

[rancid cave]

Hello, is this already answered?

I just passed by and got curious how to get it 😅

[sturdy glen]

hey yall, was curious as to what to do in set theory when you're subtracting a set from the set of all integers

for example

$\mathbb{Z} - {10x : x \in \mathbb{Z}}$

[ocean seal]

Josephh

[sturdy glen]

thanks !

[tight locust]

so basically the set of all integers that are not divisible by 10?

?

[sturdy glen]

OH im so dumb, so it's just all integers such that it doesn't satisfy {10x : x in Z}?

[tight locust]

yeah

[vernal flicker]

it is 4pi degrees

how could i express that in radians?

[buoyant kayak]

multiply by pi/180

[alpine sable]

could somebody help me with this

[buoyant kayak]

plug in 60

for C

and evaluate

[alpine sable]

so do i multiply the fraction by 60?

[buoyant kayak]

yes

[alpine sable]

okay then

[buoyant kayak]

to do it simply, you could divide 60 by 5 and multiply your result by 9

[alpine sable]

so 12 x 9 + 32?

[buoyant kayak]

yep

[alpine sable]

okay thanks

[buoyant kayak]

👍

[alpine sable]

holy shit its right

thanks fr though

[finite mesa]

How would I solve for the bounds? I’m not sure how to get what x is equal to

[tawny fox]

https://media.discordapp.net/attachments/823200439322935296/893612633901662208/image0.jpg HELP ME TO DO THE LAST PART FOR BOTH OF THESE

thanks

[finite mesa]

Yo I asked first

[pastel forge]

Hey guys I found a bit of a problem in some sources

Who found the method of quadratic formula?

In Wikipedia it is given a long description of names.

But in my school text book it is given Sridharacharya and there is no mentioning of his name in Wikipedia

Which one is correct?

[waxen lichen]

Hi can someone help me with this?

[buoyant kayak]

find common difference then plug into formula

[tiny crown]

u know the formula for arithmetic sequence?

[waxen lichen]

No

[buoyant kayak]

that's something you definitely should know considering you're working on sequences

[tiny crown]

$a_n=a_1+(n-1)d$

[ocean seal]

Ricky

[tiny crown]

plug it in

[waxen lichen]

Oh yeah I know it but I didn’t know it was called that

thanks

[finite mesa]

How do I find the bounds?

Idk how to solve for x in this equation

[buoyant kayak]

could factor

[tepid shale]

Any idea how I could do this

I want the answer and an explanation if possible

[finite mesa]

factor what?

[buoyant kayak]

factor an x-1 out

to (x-1)(2x^2+2x+3)=0

then set both equal to 0 and solve

the quadratic would have a negative discriminant though so you'd have imaginary answers

[finite mesa]

if there are imaginary numbers they wont work for bounds for the integral

if thats the case then i have no idea how im gonna solve this problem

[buoyant kayak]

there is a real answer

with (x-1)=0

i'm just saying the quadratic will have imaginary answers because the discriminant is negative

[finite mesa]

sqrt(4 - (2)(3)(2)) = sqrt(-8)

yeah it will be an imaginary number but for the integral i need a value for both a and b

if i only have +1 = x then how can i solve the integral?

[tame sorrel]

Can someone help with a functions question

[tiny crown]

post ur question in an empty question channel and someone will help

[finite mesa]

<@&286206848099549185>

[tiny crown]

what question

[finite mesa]

ill repost it

trying to find the bounds but idk how to solve for x here

[candid nova]

Is this correct?

[tiny crown]

use the other channels

[candid nova]

i was but no one was responding 😦

[tiny crown]

so based on this, use factoring to find the x

[tiny crown]

did u ping helpers?

[candid nova]

no

[tiny crown]

well ping them there

or wait until I'm done with helping here

[finite mesa]

factoring how though? i was told to factor out a (x-1) but if u do that u will only got 1 real solution for x

[tiny crown]

either way, don't overlap, kinda rude haha

[candid nova]

ok i can wait for you to help him

sorry

[tiny crown]

no worries

[tiny crown]

$2x^3+x-3=0$ is factorable

[ocean seal]

Ricky

[tiny crown]

@finite mesa lmk if you've gotten the factors of this

[finite mesa]

i wouldnt be able to factor this tbh. someone told me to factor out (x-1) like this

Could u tell me what I should be factoring out?

[tiny crown]

From this

$(2x+3)(x-1)=0$

[ocean seal]

Ricky

[tiny crown]

@finite mesa

[tiny crown]

how'd u get to this stage?

[tiny crown]

ignore this, cos it's making yourself confused atm

[finite mesa]

alright urs looks more simple

ill try solving now

[tiny crown]

👍

[chilly veldt]

Can someone help me solve this one

[tiny crown]

what have u written?

$\frac{2x^2+x-6}{2x^2+7x+5}/\frac{x^2-2x-8}{2x^2-3x-20}$

[ocean seal]

Ricky

[tiny crown]

so this is your problem right? @chilly veldt

[candid nova]

are you done helping arf out

[tiny crown]

@candid nova use #help-1, I'll help u out there

[candid nova]

ok thanks

[chilly veldt]

Yeah

[tiny crown]

do u know how to change divide to multiply?

[chilly veldt]

No

[tiny crown]

switching numerator and denominator

[chilly veldt]

I didn't study for two years because covid. I almost forgot math

[tiny crown]

$\frac{2x^2+x-6}{2x^2+7x+5}/\frac{x^2-2x-8}{2x^2-3x-20}$

[ocean seal]

Ricky

[tiny crown]

Back to this

$\frac{2x^2+x-6}{2x^2+7x+5}*\frac{2x^2-3x-20}{x^2-2x-8}$

[ocean seal]

Ricky

[tiny crown]

Switch the numerator and denominator, and you'll get a multiply instead of divide

[chilly veldt]

Ohh

[tiny crown]

Then, left and right numerators can multiply, and so does the denominators

$\frac{(2x^2+x-6)(2x^2-3x-20)}{(2x^2+7x+5)(x^2-2x-8)}$

[ocean seal]

Ricky

[finite mesa]

Can u help me solve this integral for area?

[tiny crown]

@finite mesa #help-4

middle of smth here

[chilly veldt]

I'll try that now

[tiny crown]

👍

[chilly veldt]

Is this the correct answer?

[tiny crown]

denominator should be x+1

[chilly veldt]

Oh I forgot

[lapis valley]

$\sqrt{1+\left(2-\sqrt{3}\right)^{2}}$

[ocean seal]

Nobelaker

[lapis valley]

Can I simplify this any further?

[tiny crown]

Yep

[tame sorrel]

Yeah?

[lapis valley]

$\sqrt{8-4\sqrt{3}}$

[tame sorrel]

Yup

[ocean seal]

Nobelaker

[lapis valley]

How can I simplify any further

[tame sorrel]

Sorry you weren't finished

[lapis valley]

How to express it in $a\sqrt{b-\sqrt{3}}$

[ocean seal]

Nobelaker

[tiny crown]

left and right are multiples of 4

take it out

[lapis valley]

why can i do that

[tiny crown]

because they're multiples of 4

$\sqrt{8-4\sqrt{3}}$

[ocean seal]

Ricky

[tiny crown]

$\sqrt{4(2)-4\sqrt{3}}$

[ocean seal]

Ricky

[lapis valley]

yea

ohh

i see

[candid nova]

hey ricky can u help me at questions 1

[tiny crown]

$\sqrt{4(2-\sqrt{3})}$

[ocean seal]

Ricky

[lapis valley]

ya

[tiny crown]

take out 4 and u have your solution

[lapis valley]

ok

thanks

[tame sorrel]

Can you help me isolate y?

[tiny crown]

np

[tiny crown]

one by one pls, I'm being bombarded

[low topaz]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[tame sorrel]

Is this correct?

[tiny crown]

@tame sorrel what's ur full question?

[tame sorrel]

Inverse f(x) and see if it is a self inverse or no

@Ricky#5461 nvm I solved it

@tiny crown

[tiny crown]

cool

good for u 👍

[stone sail]

hi i need help

[tiny crown]

ask away

[stone sail]

the answer is 35 but I am getting 37

geometry question

[tiny crown]

How'd u get 37?

[stone sail]

ugh can you give solution

[golden nymph]

We don’t give solutions

We give help

[stone sail]

so you help without solving

[golden nymph]

Guess that’s true

[stone sail]

(36)^2 + (1)^2 = 37

[tiny crown]

we're basically not cheatsheets, there's google for that

[stone sail]

sorry (6)^2

[tiny crown]

how did u come to this conclusion?

[stone sail]

google dont have answer i am not here to cheat i have solved but i am confused

[stone sail]

atq the ratio is 2[x+4y root2]
the ratio will be 4(3-2root 2)

[low topaz]

are there more real numbers between 1 and 2 or are there more integers from negative infinity to infinity

[golden nymph]

First one

I guess

[weak talon]

2021 PSLE Math Qn for 12 year olds Singapore

Ping me back when theres a reply, thx

[grizzled timber]

/help

[weak talon]

?

[paper holly]

what is the method for calculating derivative for (a+b)^x?

[supple tundra]

Letting $y = (a+b)^x $ then $\ln(y) = \ln(a+b)^x$

[ocean seal]

azeem321

[paper holly]

oh then i do the ln formula

got it!

thanks!

[elder glacier]

is (A union G^c)^c <=> (A^c intersection G) ?

[torn hemlock]

help meeeee

the problem b) 🙂

[placid zinc]

@elder glacier
Yes

[elder glacier]

how does one factorise/simplify |e^c intersection (A union G^c)^c|

i get up to |(E^c intersection A^c) intersection G|

not sure what to do from here

[placid zinc]

E, A, G all independent? Then there's nothing else you can do

Note that the brackets aren't necessary here.
E^c ∩ A^c ∩ G is correct

[elder glacier]

im given a ven diagram and they want me to evaulate |e^c intersection (A union G^c)^c|

im getting fucked by discrete mathematics lol

[ivory zodiac]

why is it (T cos theta) x 2 = mg

and not

(T sin theta) x 2 = mg

because it's the y component that's keeping it held up

and sin is used to find the y component

i understand to find the angle we can do cos inverse(1.8/3.9)

but once we found that angle should we use (3.9 sin theta) x 2

= mg

[supple tundra]

You have a right angled triangle. If you use $\sin(\theta)$ you will be finding the x component of the force. $\sin (\theta) = \frac{Opp}{Hyp}$. In this case, Opp is the $T_x$ i.e. tension in x direction

[ocean seal]

azeem321

[ivory zodiac]

in right angled triangles sin is used to find x?

[wispy olive]

What is x?

Give more details.

[ivory zodiac]

x as in the graph

x component

[proud estuary]

Can anyone tell me how to work through this problem step by step please, I know the answer but do not understand how they got to it.

[harsh girder]

if |x|=3, then x=3 or -3,

[proud estuary]

Thank you but what I need is for someone to actually write it out to show me or take me through it, step by step. I need to see it visually to get an understanding of how to work through it or else I will not understand,

[fluid knot]

someone help me i hate geometry

[harsh girder]

firstly, you know |3x-4|=8, right?

then you know 3x-4=8 or 3x-4=-8, then you can get the answer

[proud estuary]

How then does the 2 play into the equation?

[harsh girder]

if 2y=16, then y=8

[proud estuary]

This is what I was shown for a step by step, is it correct? if not can you show me how to do the greyed out portion so that I understand it because I have tried all day and still do not understand.

[harsh girder]

it's correct

[proud estuary]

Ok then how do I work out the greyed part? also ty in advance.

[harsh girder]

$$\begin{aligned}
3 x-4 &=8 \
3&x=12\
x&=4
\end{aligned}$$

[ocean seal]

秋水

[proud estuary]

Ok so then how do you work out the part that says x= -4/3

[harsh girder]

Could I know your grade?

[proud estuary]

11th

and I am on an IEP

@harsh girder

[harsh girder]

You should learn how to solve a equation like ax+b=c

[proud estuary]

Ok we have somewhat so what or how do I work it, can you help me or no?

[harsh girder]

$$\begin{aligned}
3 x-4 &=-8 \
3x &=-4\
x &=\frac{-4}{3}
\end{aligned}$$

[ocean seal]

秋水

[harsh girder]

it's the same

[proud estuary]

Thank you but I still do not get it, I give up for now.

[harsh girder]

You should learn from the basics, do you know how to solve 2x+1=8

[elder glacier]

can there be more than one value* for f(x) to make a function considered to be injective?

[lofty juniper]

hi

anyone free?

[elder glacier]

@lofty juniper what do u need

[lofty juniper]

help me with this

[elder glacier]

@lofty juniper im assuming you divide the functions then input 2

i havent learned that yet so do not take my word for it

[devout sigil]

f(2) ÷ g(2)

[brazen parrot]

hey guy s

what is this radically new symbol?

[crimson beacon]

hi, are there any filipinos who can help me explain this? ill send a link of the vid in dms but its in filipino

[silver current]

[alpine sable]

how would i make c the subject?

[sacred sapphire]

divide booth sides by m first of all

then

[alpine sable]

so would that be e over m = c squared

[sacred sapphire]

yes

then take the square root on both sides

then

slap a plus or minus

on the radical

[alpine sable]

oh okay

so wouk

would this be the answer?

[sacred sapphire]

yes

then

put a plus or minus

next to the suare root

[alpine sable]

okay okay

thank you sm

Can someone help me in calculating the length of this thing please?

[wispy olive]

What is wrong here?

[alpine sable]

Seems right

[sacred sapphire]

nothings wrong

[quartz oxide]

Nothing wrong

[sacred sapphire]

but if your trying to isolate for x

[quartz oxide]

But there’s still x on the right side lol

[sacred sapphire]

thats not how u do it

cuz you have to complete the square

[wispy olive]

Then why do not we use this instead of the Quadratic Formula?

Let me try substituting with values.

[alpine sable]

Where would you get x from?

[sacred sapphire]

because x isnt alone on one side

[wispy olive]

It is.

Oh wait.

I am dumb.

[alpine sable]

Lel

[quartz oxide]

Lol

[sacred sapphire]

lmao

[wispy olive]

xD.

[alpine sable]

That's how we realise :)

[wispy olive]

Anyone has any website or anything to show how we get from ax + bx + c = 0 to the quadratic formula?

[quartz oxide]

Khan academy might be a good idea

[wispy olive]

I have basics.

[quartz oxide]

Another way is to replace x with t-(b/2a) for an easy proof: the result should be a quadratic in t with no degree 1 term

[sacred sapphire]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/v/proof-of-quadratic-formula

[alpine sable]

https://youtu.be/mDmRYfma9C0

[glass lichen]

complete the square then isolate

[quartz oxide]

Or, make it x(x+b/a) = -c/a
Then apply difference of squares identity to the left side

[wispy olive]

Ohhh.

So that is how you get that thing.

Thanks guys.

[glass lichen]

yeah, standard proof shown is comp the square

[wispy olive]

I will do more exploring of Quadratics after doing my Biology school project.

I will ask here lol.

[alpine sable]

hello

i need help

in math

ratios of decimals

can anyone explain me

pls help me 😦

😦 😦 😦 😦

[wispy olive]

Send.

[alpine sable]

what

i already sad\

[glass lichen]

send your question??

[alpine sable]

said

up

ratios of decmails

decmials

[glass lichen]

Do you have a question yes or no?

[alpine sable]

yes

how to do ratios of decmials?

grade 6

[gritty pine]

https://cdn.discordapp.com/attachments/844681108473118750/893779313353195540/688032319235293196.png

can someone tell me if this is correct? i have to check if the line that passes throught the point (-7, 2) is perpendicular or parallel with the given equation 3x-14y=4

[alpine sable]

There can be a lot of lines passing through just one point I think

Is that all the information given?

[lethal lichen]

Can someone help me state the range?

[gritty pine]

yes

[gritty pine]

in another topic it asks if it is perpendicular

i found the equations i guess

y = 3/14x - 4/14
and y = -14/3x-92/3

[alpine sable]

That's a different question than you asked

[gritty pine]

yeah sorry i noticed it now

i wrote it in #prealg-and-algebra

[alpine sable]

You can just calculate m of the given line

[gritty pine]

but it was still used

[alpine sable]

And then y=mx+c

[gritty pine]

didn't i?

[alpine sable]

And calculate c by substituting thr given point

[gritty pine]

can u make an example?

also did i check if the line is perpendicular correctly?

[alpine sable]

Yes they are perpendicular

M1m2=-1

Is the rule

[gritty pine]

oh nice, atleast that

i have 1 month and half of experience in math lol

[alpine sable]

Does someone know what does this weird function mean?

[supple tundra]

Let $k = x^2+4x+11$. This implies that $x^2+4x+11-k=0$. Calculating discriminant $4k-28$. You should know that the discriminant determines whether your quadratic will have real roots or not. The discriminant for this is $4k-28$ this tells us that $k \geq 7$ otherwise the discriminant would be $<0$ and hence no solutions. So $f(x)\geq7$

[ocean seal]

azeem321

[lethal lichen]

i dont completely understand how you go from $x^2+4x+11-k=0$ >> $4k-28$

[ocean seal]

NiLo

[supple tundra]

Do you know how to find discriminant of quadratic?

[lethal lichen]

can you explain that step please

yeah

using $b^2 - 4ac$

[ocean seal]

NiLo

[supple tundra]

Right, so $4^2-4(11-k)$. b = 4. c = (11-k) a = 1

[ocean seal]

azeem321

[lethal lichen]

ok, so for question b, the range would be f(x) <= 7 ?

[lethal lichen]

ok this makes sense

[supple tundra]

You can think of it like this, the question wants us to find out the values of $k$ for which the graph $y = k$ intersects with $x^2+4x+11$. Therefore if we equate them, we find that they intersect when $x^2+4x+11 = k$. But notice, this is a quadratic equation and we can use our techniques that we learned for dealing with quadratics. We know we can find the discriminant of a quadratic and it tells us the number of solutions for when the quadratic will intersect the line y = 0

[lethal lichen]

why is k negative in this: $x^2+4x+11-k=0$

[ocean seal]

NiLo

[lethal lichen]

will k always be negative when using this method to find the range?

[ocean seal]

azeem321

[lethal lichen]

ok i understand now that $x^2 + 4x + 11 = k$

[ocean seal]

NiLo

[supple tundra]

You could also think of $4k-28$ as a discriminant function. It tells you the discriminant for different values of $k$. So when $k = 10$ discriminant is $12$. and so the function must be greater than or equal to 10. But when $k=-10$, we have the discriminant $=-68$. So the negative discriminant, no real solutions. So function cannot have any solutions when k = -10

[lethal lichen]

ok i understand

but for the purpose of question b, would the range be: $x>-7$

[ocean seal]

NiLo

azeem321

[orchid python]

Find the point on the line y = 10x + 9 that is closest to the origin.

how can I solve it?

[lethal lichen]

How would I do this? @supple tundra

[flat vale]

Use distance formula

and find the min

root(x^2-y^2)

gotta sleep but should be enough of a info to get you going

[flat vale]

just let f(x) = y and swap x and y

[supple tundra]

If I gave you this $x = \ln(y)$, could you find y as a function of x? i.e. $y = ...$

[ocean seal]

azeem321

[lethal lichen]

no i couldnt

would $f^-1 x = 1/x$

[devout sigil]

did u learn the rules of logarithm

[lethal lichen]

yeah but i cant remember the rule for the inverse of a logarithm

[devout sigil]

because it should be obvious that y=e^x

[lethal lichen]

i know that $ln(x) = log_e(x)$

[ocean seal]

NiLo

[spring condor]

Hey y’all how do I answer these

[elder glacier]

@spring condor times the length and the width together and you get area in terms of x

@spring condor for the third one do long divison

[spring condor]

how

[supple tundra]

The inverse is defined as the function which maps you back to the input of the original function. So $f(x) = e^x, f(0) = e^0 = 1$. Now if we want to find a function which maps us back to 0 i.e. $g(1) = 0$. If two functions have that property for their entire domains, then they are said to be inverses of each other

[ocean seal]

azeem321

[elder glacier]

@spring condor or you can factor your area

to get into 2 factors

[red ledge]

Guys I have a question about vector and forces?

Can someone help me?

[elder glacier]

one being ur given length and the other one being width

[red ledge]

Should I post the question?

[spring condor]

sure

[spring condor]

How do I do that too

[elder glacier]

do you know how to factor equations?

[spring condor]

Yea

I think

[lethal lichen]

If $f(x) = ln(x)$ then what is
$f^-1(x)$

[ocean seal]

NiLo

[lethal lichen]

Is it = to $e^x$

[ocean seal]

NiLo

[supple tundra]

If two functions satisfy $f(g(x)) = x$ then they are inverses of one another

[ocean seal]

azeem321

[supple tundra]

don't we all

[lethal lichen]

how to state the domain of $e^x$

[ocean seal]

NiLo

[lethal lichen]

@supple tundra

[supple tundra]

Do you know what the graph of e^x looks like

[unkempt umbra]

how is the set different from this one?

[orchid python]

please help me with question

[unkempt umbra]

oh so i get it, U means union of intervals for all possible n
whereas ∩ means intersection of intervals for all possible n, which is actually the smallest possible interval

right?

[orchid python]

can anybody help?????

[glass lichen]

You haven't posted what you've tried to do...

[sacred sapphire]

pretty much

[sacred sapphire]

what have you tried

how long have you worked on the problem?

i have the solution

desmos verified

use implicit differentiation

instead of isolating

otherwise its a mess

[orchid python]

yeah I calculated dy/dx = -x/4y

but I don't know what to do next

[glass lichen]

Find the slope at the point

[sacred sapphire]

by inputting the values

[glass lichen]

No shit

But yeah... it's just any other "find the tangent" problem

You also should not be struggling with this given you're in calc 2

[orchid python]

wdym

[glass lichen]

You don't know what inputting values means...?

[sacred sapphire]

dy/dx = -x/4y, now for the point given where x = 2 and y = -sqrt(3), you just plug those values in

as x and y

to find dy/dx

which represents the slope of the tangent at the given point

[orchid python]

so it will be -2/-4sqrt(3)??

[alpine sable]

any math tutors can help me? Can pay money I have a test tomorrow I really need help please dm me if you can. :)

[slender root]

Hi

[sacred sapphire]

yeah which simplifies to (1/2*sqrt(3))

now thats ur slope

[orchid python]

now I have to plug in into a formular?

[sacred sapphire]

so for any linear function in order to find its equation all you need is a point and slope. You have your point (2, -sqrt3) and the slope 1/(2 sqrt 3) the rest should be fairly straightforeward

does that make sense?

[orchid python]

do I have to use this formular: $f\left(a\right)+f'\left(a\right)\left(x-a\right)$

[ocean seal]

Nam V. Do

[sacred sapphire]

pretty much

[orchid python]

what is f'(a)?

[sacred sapphire]

is the slope

which we already calculated

at the point a = 2, and f(a) = -sqrt3

[orchid python]

what is f(a)?

ok

so a will be 2?

oh yeah'

ok

[sinful relic]

$\frac{a^2}{a}=0 \ 1 = 0$

[ocean seal]

Sachi

[sinful relic]

Is this a rule

Can someone tell me how taking the square root of both sides to get rid of ^2 works

[orchid python]

how can I solve it

[woeful pulsar]

calculus?

please don't just give answers directly

[pearl sun]

ok

[woeful pulsar]

engage the person who asked the question

[unkempt umbra]

is Z or Q a neghborhood of -1?
i think Z is not because it only includes integers and we can't really have an open ball of 1/2 radius, for example
but i don't know about Q

[oak chasm]

@unkempt umbra What's the definition of neighborhood?

[orchid kayak]

is this chat being used?

[oak chasm]

Yes.

[unkempt umbra]

well this is how i understand it
we have a set A = (a, b)
we set a point p
and if there exists an open ball of radius r > 0 such that B(p, r) is included in a A
then A is a neighbourhood of p

[alpine sable]

hi

36 as a percentage of 8 mins

[oak chasm]

@alpine sable Sorry, this channel is busy.

[alpine sable]

help

k

[oak chasm]

@unkempt umbra What is the definition of ball?

[unkempt umbra]

it's the set of all points with a distance < or equal than r from p

the metric space is not defined in the exercise so that was my main concern

i guess it is R

and then Q would not be a neighbourhood

but it is not mentioned

[wispy olive]

For general use, how to derive the quadratic formula -
https://www.chilimath.com/lessons/intermediate-algebra/derive-quadratic-formula/.