help-42

[royal cape]

possible

right

and too choose 5 odd numbers from 9

9 choose 5

[final parrot]

yes

[royal cape]

total amount of ways

5 numebrs from 1-9 and be chosen from 9

and there are 9 times

when they are possible in 3 by 3 grid

[final parrot]

yeah, but how about permutation?

[royal cape]

because the order doesnt matter

for this one

it can be any order of 5 odd

[final parrot]

Are you referring to the final answer?

[royal cape]

yes

[final parrot]

or the ways odds can be arranged

[royal cape]

9 / 9 choose 5

is final i think

ok i just confirmted it

the answer is 1/14

its right

amc 10 2019 question 20

did u make aime?

[final parrot]

nah

[royal cape]

what grade r u

[final parrot]

mb, I'm too rusty at combination lol

Haven't done it in a year+

[royal cape]

lol i js trryna perpare for aime

amc 10

i did pretty good on amc 9

8

last year

[final parrot]

Damn....

[final parrot]

Second of uni lol

Alright, anything else?

Imma help the next one

@blissful field ye, time to claim a channel

[blissful field]

what happened

[final parrot]

He's gone nowhere, but I believe the problem's been resolved at this point

[winter elbow]

.solved

[calm coral]

Channel closed

Closed by @winter elbow

Use .reopen if this was a mistake.

[royal cape]

u play chess wanna play?

[calm coral]

Available help channel!

Send your question here to claim the channel.

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

[remote mural]

hello

[winter elbow]

hi

[rugged pine]

Do you have a question?

[remote mural]

indeed

i just dont understand the second part

dont they technically have the symmetric equation under "Parallel to"

[rugged pine]

They do, but you can add any number to all the equals and get another equation I think I misunderstood helpee’s question

Like if 1=1=1 then 2=2=2

[remote mural]

oh

why would they even do that bruh

[rugged pine]

It gives another point on the line

I think

Tbh too tired to check

I’m going now, hopefully that answered your question! :)

[remote mural]

yes thank you

[rugged pine]

!done

[calm coral]

If you are done with this channel, please mark your problem as solved by typing .close

[remote mural]

wait im not finished

i have another question

ill post

[finite pulsar]

No

[remote mural]

wait how

[finite pulsar]

It says it's "parallel to" that line

[remote mural]

but even when i solve for t i get what they have

[finite pulsar]

Ah well

Okay so

That's not guaranteed

[rugged pine]

In this case the line it is parallel to has the point

[finite pulsar]

Which means it's the same line

[rugged pine]

But in general it is not

[finite pulsar]

You have a line L1 that is parallel to their line L2

And passes through that point

But their line L1 also passes through that point

Which means L1 = L2

But L1 doesn't always equal L2

Just in this weird example

In that case, what BB said about adding stuff to each part will be useful

You need to find an equivalent set of equations to what they've put

[remote mural]

ok im gonna be honest im a little confused

normally id have a direction vector and a point where i can get an arbitrary line from the initial point and scale the direction vector to it to then get an equatioin for the line that passes through that one point given

now here they have an equation already that passes through the point given.. right?? .

[rugged pine]

Yes, I don’t know if they would give that in general though

[remote mural]

okay so in general if they give me another equation, that would mean that i need to extracxt the direction vector from that equation?

right

what they would be giving me at that point is just a seperate symmetrical equation right

that is for a seperate line

right

[finite pulsar]

They would normally give you a line that was a separate parallel line

Rather than a line that was the same as your line

You can get the direction vector from your own line as well

[remote mural]

but i cant cause i only have 1 point

and then im getting an arbitrary line that passes throught that point from that point

right

and that alone isnt enough cause for a line in space we need a point and a parallel vector

do you mean the parallel vector can also be an arbitrary point on the line that passes through the point given?

[finite pulsar]

The parametric equation of a line and the vector equation are trivially interchangeable

Trying writing the vector (x, y, z)

[remote mural]

wdym

[finite pulsar]

Try this

[remote mural]

wdym by writing the vector

i mean you just gave me the coordinates

so thats just that

vector

[finite pulsar]

You have equations for x, y, and z

Write them as a vector

[remote mural]

in this problem?

[finite pulsar]

Yes

[finite pulsar]

Split the t terms off from the constant terms

[remote mural]

like just take it out

[finite pulsar]

I mean split it into 2 vectors

One with the t terms in it, and one with the constant terms

[remote mural]

this is just getting more confusing tbh

[finite pulsar]

Just do it >.<

[remote mural]

idek what it means to split it into 2 vectors

[finite pulsar]

Okay quick example

What is (1, 2, 3) + (4t, 5t, 6t)?

[remote mural]

ohh

like that

[finite pulsar]

Now factor out the t

[finite pulsar]

Does that look like vector equation of a line?

[remote mural]

well to me it looks like a direction vector scaled = a poin parallel to it which a line passes through i guess???

[finite pulsar]

What do you consider to be the vector equation of a line?

Something like:
r = a + t b ?

[remote mural]

yes

[finite pulsar]

Don't we have that?

[remote mural]

yeah but

[remote mural]

i just dont understand this

does this example have what you mean?

because there is no direction vector

and you said you can get your direction vector from your line itself

so

since this problem just has the line itself and no direction vector

[finite pulsar]

So we have:
x = 3t + 1, y = -4t -1, z = t + 5

The direction vector of this line is [3, -4, 1]

[remote mural]

it’s just not clicking

all whats in my head rn is that you need a point

and a direction vector

and the direction vector is seperate from the line that passes through the given point

[finite pulsar]

I'm not sure what you mean by that

Okay so there a various ways we can represent a line

We can have symmetric equations, which look like:

$\frac{x - a}{f} = \frac{y - b}{g} = \frac{z - c}{h}$

[potent lotus]

💪 Greenie The Power Queenie 💪

[remote mural]

thats to construct the whole thing

[remote mural]

yeah im saying you get there from having:

A point in space

A direction vector parallel to it

[finite pulsar]

I wouldn't say it's trivial that this is a line, but it is

There are various ways to represent a line

You can start from any of them

And go to any of the others

[remote mural]

besides this you mean?

[finite pulsar]

This is the symmetric equation representation

We also have the vector equation of a line

Which is of the from r = a + t b

a is a point on the line

And b is the direction vector of the line

[remote mural]

im just confused

idk bruh

[finite pulsar]

Which is what you've been talking about

What are you confused about?

[remote mural]

all i know is how to construct the equation for a line in space from having a point in space + a direction vector parallel to it

thats literally ALL i know

like literally

[finite pulsar]

Okay so let me teach you

Ways to define a line:

• 2 points
• vector equation
• parametric equations
• symmetric equations

You should be able to convert between any of these, starting from any other

So let's pick 2 points

I'll say (1, 3, 2) and (5, 11, 4)

Okay

So those are our 2 points

Let's find the vector equation

The vector equation has the form:
r = a + t b

Where r is a variable vector

a is a point on the line

b is the direction vector of the line

And t is a variable parameter

All good so far?

And he's gone

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

mb im back

im reading through it

[remote mural]

uh

well what i learned is the scaling thing

[finite pulsar]

I'm not sure what you've learnt but we can go through stuff now

Does everything I just said make sense?

[remote mural]

idk what a vector equation is and how it works

like i get that i get my line equation in that form, but the general formula i just dont know

[finite pulsar]

So with a normal equation like y = 3x + 5, this provides a connection between a number y and a number x

Happy with that?

[remote mural]

yes

i am

[finite pulsar]

Okay so a vector equation is the same thing

But instead of connecting variables that are numbers, it connects variables that are vectors

[remote mural]

so like its a function?

and the input is what?

[finite pulsar]

I'm not sure I would necessarily approach it that way but you could

Well in this case, the input would be a number t

And the output would be a vector r

So we have a function that takes a number as input and gives a vector as output

I think it's more helpful to think of this as an equation that defines a curve rather than a function though

[remote mural]

i mean you compared it to a xy function

[finite pulsar]

I know

So the equation y = 3x + 5 defines a straight line

[remote mural]

yesyea

yea

it does

[finite pulsar]

Not every equation that defines a curve is a function though

e.g. x^2 + y^2 = 10

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[jovial bridge]

.reopen

[calm coral]

✅

[finite pulsar]

That's an equation that defines a circle

[remote mural]

bro is lurking

[finite pulsar]

But not a function

[remote mural]

yes

i agree

[finite pulsar]

Okay so we have something similar here

Which is r = a + t b

Now we're using vectors

[remote mural]

okay i see now

[finite pulsar]

The curve that defines is also a straight line

[remote mural]

a and b are vectors?

[finite pulsar]

Yes

Constant vectors

[remote mural]

i see

[finite pulsar]

r is a variable vector

a and b are constant vectors

t is a variable number

[remote mural]

yea

[finite pulsar]

So that's the vector equation of a line

We also have a parametric equation of a line

Which looks like:
x = a + bt
y = c + dt
z = e + ft

The way this works is that we put a value of t in

And we get a value of x, y, and z

Which is a point on the line

So we have 3 variable numbers as outputs now

And 1 variable number as input (t)

[remote mural]

yea

[finite pulsar]

(x, y, z) are coordinates of points on the line

[remote mural]

yes

[finite pulsar]

And lastly we have symmetric equations

$\frac{x - a}{f} = \frac{y - b}{g} = \frac{z - c}{h}$

[potent lotus]

💪 Greenie The Power Queenie 💪

[finite pulsar]

Which look like this

It's not immediately obvious that this gives a straight line

But it can be proved that it does

So now we have a triple equation that connects 3 numbers

Like y = ax + b but now it's 3 variables instead of 2

[remote mural]

yes.

[remote mural]

yeah so i get this part, i understand how to get to it through a point and a vector parallel to it though

you know what i mean

like that in itself isnt the issue

[remote mural]

neither is this

its just

how to construct that in the first place

you said you can have a vector from the line itself

and usually im giving a seperate direction vector but parallel

[finite pulsar]

Okay so let's say we have these 2 points

[remote mural]

okay

wait ill post it

look

like this?

[finite pulsar]

Let's not worry about that rn

[remote mural]

alright

[finite pulsar]

Do you know what the parts of the vector equation of a line mean?

[remote mural]

not really

[finite pulsar]

Okay so we have r

r is a vector that points from the origin to any point on the line

Remember r is like our output variable, like y

a is a fixed vector, which points from the origin to a single point on the line

b is also a fixed vector, and points along the line

Because b points in the direction of the line, it's called the direction vector of the line

Like this

Now what the equation is saying is as follows

It's saying that we can get to any point on the line (r) by going to a single point on the line (a) and then moving in the direction of the line (b) by some amount (λ)

Does that make sense?

[remote mural]

uh

[remote mural]

i thought you said r is a vector

[finite pulsar]

It is

r is a variable vector that points from the origin to any point on the line

r is this

[remote mural]

im just confused on how they appear like this

man

look this is how i understood it all along

thats all what my brian can understand]

[finite pulsar]

Okay so imagine we have a specific point on our line

[remote mural]

okay

[finite pulsar]

The vector a points at it

Okay?

[remote mural]

okay

okay

[finite pulsar]

The vector b points along the line

Is that okay?

[remote mural]

uh

how does it do that

[finite pulsar]

So the line goes off in a particular direction, right?

[remote mural]

what causes them to point in that poarticular way

is what i dont get

how

[remote mural]

yes

[finite pulsar]

So we choose a vector that points in that direction

[finite pulsar]

Each possible line goes off in a particular direction. And each possible line has a corresponding direction vector

[remote mural]

...

what properties of a make it point on any point of the line

@finite pulsar what are the components of a

[finite pulsar]

So for a, we just need any point on the line

Any point on the line will do

a is our starting point

We need to start on the line

But any place is fine

[remote mural]

ohh

okay i see how a works now

okay

yeah i mean any point on the line does serve as terminal values for a vector a from the origin

right

[finite pulsar]

Okay

And then b points along the line

Which allows us to move along the line

Here's another way of thinking about this

Imagine we don't have a line yet

[remote mural]

at which point exactly

tho

[remote mural]

ok

[finite pulsar]

We just have an empty cartesian space

We're now going to start adding some points to our space

And we're going to do so by specifying vectors that take us to those points

So we start off by adding a single point A

A is pointed to by the vector a

And we're going to the collection of all our points r

So r is our collection of points

[remote mural]

okay

a is our first point from the origin

[finite pulsar]

Each point will have a vector that points to it, and those will be each value of r

So now we've added a single point A

[finite pulsar]

Which is pointed to by the vector a

Okay now we're going to stay at A

[finite pulsar]

And we're going to move in the direction of another vector b

[remote mural]

so we are modifying A's components? or?

[finite pulsar]

No a is still the same

We're adding a new point now

[remote mural]

okay

[finite pulsar]

And let's say we move 1 unit in the direction of b

And add a new point there

[remote mural]

wait im still at a

how do i create the b vector

[finite pulsar]

Just pick any vector you like

And move from A along that vector 1 unit

[remote mural]

i dont understand the "moving from a" part

i see vectors as starting from the origin

[finite pulsar]

They can start from anywhere

[remote mural]

do you mean its initial points would be a's terminal points?

[finite pulsar]

You can pick up a vector and move it wherever you like

A vector is just a quantity with a magnitude and direction

Which you can think of as an arrow if you like

[remote mural]

yes

[finite pulsar]

You can pick up the arrow and move it anywhere you want to

It doesn't have to start from the origin

[remote mural]

true but graphically b's initial points would be a's terminal points right

[finite pulsar]

There is a particular class of vectors call position vectors, which do start from the origin

[remote mural]

for this case

[finite pulsar]

So position vectors start from the origin

But other vectors can start from anywhere

[remote mural]

i see

[finite pulsar]

And you can move them to anywhere

[remote mural]

?

[finite pulsar]

r is a position vector btw

[finite pulsar]

So b is a vector (which we can place anywhere), but we're going to place it at A

[remote mural]

so this means its initial points are a's terminal points

mechanically

right

[finite pulsar]

I'm not sure exactly what you mean by that but I think so yes

The end point of a is where we're going to put the start point of b

[remote mural]

like moving the vector on the graph keeps the same components but they are expressed in terms of the units they lie on

right?

[finite pulsar]

The vector won't change at all if you move it

[remote mural]

yes

[finite pulsar]

You have to keep the direction it points in the same

[remote mural]

but its component's representation will

[finite pulsar]

And the length the same

[remote mural]

not the actual value

[finite pulsar]

No

The components won't change either

[3, 4, 5] will be [3, 4, 5] wherever you put it

[remote mural]

well yeah

[finite pulsar]

Actually nvm

At this point, we now have 2 points, right?

We have A and 1 other point, which we got by adding b to a

[remote mural]

this is what i mean

[remote mural]

yse

yes]\

[finite pulsar]

a = [a1, a2, a3]

b = [b1, b2, b3]

[remote mural]

actually wth is this

[finite pulsar]

If we move b around, the components of b won't change

It doesn't matter where we put it

[remote mural]

if you wanna move it to the origin though

youre gonna have to do terminal - intial

thats what i meant

[finite pulsar]

It'll still be [b1, b2, b3] whether it's at the origin or anywhere else

The vector from the origin to the point A is a

The vector from the origin to the point B is a + b

Now we have 2 points, A and B

Is that okay?

[remote mural]

yes

[finite pulsar]

Now let's add another point C

Which is a + 1/2 b

Happy?

[remote mural]

yes

[finite pulsar]

Now let's add another point D

Which is a + 3/4 b

[remote mural]

yea

[finite pulsar]

All good?

[remote mural]

i guess

[finite pulsar]

What's wrong?

[remote mural]

its just how the vectors are positioned

[finite pulsar]

You can put a vector anywhere. It doesn't have to start at the origin

I'm putting them so they start at A

Okay so if you look, we've basically been adding points of the form a + t b, right?

With t = 0, t = 1, t = 1/2, t = 3/4

[remote mural]

yes

[finite pulsar]

Now imagine we do this for all real values of t

[remote mural]

yeah

[finite pulsar]

We get a line like this

[remote mural]

i still cant get over the positioning

i get that vectors are the same everywhere

[finite pulsar]

What's wrong with the positioning?

[remote mural]

but the component expressions are gonna be different though

[finite pulsar]

They aren't

You're confusing the coordinates of the end point with the components of the vector

Let's say we have vector [3, 4, 5]

If we put it at the origin, it will take us to the point (3, 4, 5)

If we put it at (1, 7, 9), it will take us to the point (4, 11, 14)

But wherever we put it, it will have the components [3, 4, 5]

[remote mural]

yeah youre right, but like

ill show you what im struggling with

@finite pulsar see how they are the same whether at the origin or anywhere else

so how do i know that its pointing from the blue vector

and not from the middle

shoot i changed its directions

[finite pulsar]

You changed it completely

[finite pulsar]

Okay so u = [0, 2]

Well if it equals [0, 2] it would point directly upwards by 2 units

[remote mural]

right

i was out of my damn mind

@finite pulsar so what i understand now is because the vector is the same everywhere in space, its behaviour will produce a line nonetheless

[finite pulsar]

If u = [0, 2], then it means u is an arrow that points directly upwards and has a length of 2

[remote mural]

like

[finite pulsar]

Wait a second

So we have a position vector r

[remote mural]

yes

[finite pulsar]

Now r is a position vector, which means it starts at the origin and takes us the a point in space which has the same coordinates as the components of the vector

r is a variable, and is going to contain all of our points (each point has its own value of t)

Okay

So if we say r = a

That means we have a single point, which is pointed to by a when a is placed at the origin

Okay?

[remote mural]

thats gonna give 1 point

yes

[finite pulsar]

If r = a + b, we have a different point, which we can get to by starting at the origin, going along a, and then going along b

That's point B in our earlier diagram

[finite pulsar]

This

[remote mural]

wait r is a + b?

[finite pulsar]

r is a variable

So it can have different values at different times

Like if we have y = 3x

y has a different value for each value of x

Right?

[remote mural]

right

[finite pulsar]

So r has different values for different values of t, in this case

If t = 0, we have r = a

If t = 1, we have r = a + b

If t = 1/2, we have r = a + 1/2 b

[remote mural]

whats the purpose of r

[finite pulsar]

r is like y

r is our output

Except that y is a number output

r is a vector output

So it's like y = 4 + 3t

[remote mural]

the scaling of b i get it

but

not the rest of the whole shape

so like when i wanna construct the points how do i do it

like how do i do the vectors

[finite pulsar]

Wait a second

[remote mural]

yea

[finite pulsar]

We'll do an example in a minute

Actually we can do it now I guess

[remote mural]

yes please

can we do it with this

[finite pulsar]

I'd prefer if you understood vector equations first before we do that

If you understand what you're doing, that example will be trivial

[remote mural]

i dont wanna sound presistant but, im not getting it 😂

llmaooo

[finite pulsar]

I feel like you're kinda resisting too

You keep trying to go back to the same thing from before

[remote mural]

its cause when i learn something new and it makes sense im afraid itll go away

[finite pulsar]

Does it make sense?

Okay let's do a quick example

You're familiar with cartesian equations of straight lines, right?

[remote mural]

ok

ye..

yea

[finite pulsar]

Like y = mx + c

Let's say we have the line y = 3x + 5

What's the gradient of that line?

[remote mural]

(delta)y/(delta)x

[finite pulsar]

You should just be able to tell me

No?

[remote mural]

💀

[finite pulsar]

It's 3

[remote mural]

why is it 3

[finite pulsar]

Because y changes by 3 units if x changes by 1 unit

You haven't covered y = mx + c before?

I really need to go to bed x.x

[remote mural]

i didnt learn algebra in school lol

it is what it is though

i actually started with pre calc

most things i did so far didnt require me to scrutinize the line equation

until now

so

[remote mural]

no worries

i appreciate your help

[finite pulsar]

It's kinda important to have the pre-requisites in place

[remote mural]

youre right

thanks for the help though i see what i can do to figure this out

[finite pulsar]

Have a look at y = mx + c stuff

[remote mural]

i gotchu

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

okay i think i figured it out

from this we can see that tv = P - P_0

<@&286206848099549185> right?

i just dont get why we need to represent the points by vectors when we just have points

right?

whjy

im tempted to open another help channel

.close

[calm coral]

Channel closed

Closed by @mortal shadow

Use .reopen if this was a mistake.

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.

[graceful stirrup]

Can anyone help me understand what do i do here

[graceful stirrup]

Pls @ me

[void umbra]

!status

[calm coral]

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

[void umbra]

@graceful stirrup

[graceful stirrup]

1

I don't understand so I can't start it

[void umbra]

The question asks you to find the corresponding y values for the x values given on the table

Plus x and y intercepts

And use these points to plot a graph

To fill in the table, sub x with the number given

To obtain the y value for the given x

[graceful stirrup]

So the x and y values are different from the x and y intercept?

[void umbra]

Yes

the x intercept are the points on the graph where y=0 but we can do that part later

[graceful stirrup]

So for the x -4 to get the y below it i should subtitute x=-4?

[void umbra]

Yes

[graceful stirrup]

How should i get the y values then?

[void umbra]

As you said

Sub x=-4 into the equation

Then just use calculator or mental math

[graceful stirrup]

Wait lemme try it first

I got -36

That will be my y value below -4 then right

[void umbra]

Yes

Then you can do this for the rest of the x values to fill up the table

Tell me when you're done

[graceful stirrup]

How do i then get the x and y intercept do i need to solve the table first?

[void umbra]

No the table is the easier part

So we just do that first

[graceful stirrup]

Okay wait for me

I got (-4,-36)(-1,12)(3,-36)(6,54)

[void umbra]

Correct

Now we can try y intercept

y intercept is the point of the graph where the function intercepts the y axis

[graceful stirrup]

Yes

[void umbra]

Any ideas on how you could get it

[graceful stirrup]

Uhh

I graph it

[void umbra]

No

Sub x=0

[graceful stirrup]

For the polynomial function?

[void umbra]

Yes

[graceful stirrup]

Uh alright wait

[void umbra]

This is because the y axis is at x=0 on the graph

[graceful stirrup]

I got 0

[void umbra]

Correct

[graceful stirrup]

Y intercept is 0 okay

[void umbra]

Yes

Then finally x intercept

[graceful stirrup]

Yes

[void umbra]

x intercepts are points where the graph intersects the x axis

So when x(x+3)(x-5)=0

[void umbra]

Can you solve this equation?

[graceful stirrup]

Hmmm wait

Am i supposed to find the roots?

[void umbra]

Yes x intercepts is another name for roots

[graceful stirrup]

Can't i just transpouse it?

Since the x from start has nothing its x=0 the x+3 can be x=-3 and the x-5 can be x=5

[void umbra]

Yes that's the answer

x=0 or x=-3 or x=5

[graceful stirrup]

Yes

So that's my x intercept?

[void umbra]

Yea

Then you can draw those points on some graph paper

[graceful stirrup]

Oh alright

[void umbra]

And attempt to connect them

[graceful stirrup]

Wait lemme

[void umbra]

What class is this btw

[graceful stirrup]

I guess polynomial or some type

[void umbra]

Ok yea then you're done I guess

Just draw the graph

[graceful stirrup]

Alright thanks bro

.close

[calm coral]

Channel closed

Closed by @graceful stirrup

Use .reopen if this was a mistake.

[calm coral]

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.

[upper iron]

I currently have a piecewise defined function, from this I need to find the coordinates of 4 dots in total
A, B, C, D.
Image 1 is the original photo
image 2 is a graph
image 3 is what I put into a math program to better understand what I am looking at (maple)
Could I get some aid in how I figure out these points of B and C?

[upper iron]

I'm still mind boggled by looking at this because I barely understand what and where I should go

graphed in the same program btw

I just need to figure out where B and C are, as well as understanding what to do next time

aha hold on

Yeah no I figured it out

Vores x altså til højre er
0 start
1 midt
8/3 midt
3 slut
Vi regner venstre side altså y
0+3 = 3
1.21+0.8 =2
68/3 - 12 = 4
6*3-12 = 6
A = (0, 3)
B = (1, 2)
C = (8/3, 4)
D = (3, 6)

different language but its whatever

.close

[calm coral]

Channel closed

Closed by @upper iron

Use .reopen if this was a mistake.

[calm coral]

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.

[void umbra]

Sir this is not google sir

You can find the intro interactive R course to the right of the intro interactive Q course

[pale blade]

freecodecamp.org usually has good coding courses

[balmy bane]

http://giybf.com/ is a good site too

[final parrot]

Bruh, just google it

[calm coral]

@old plover Has your question been resolved?

Channel closed

Closed by @old plover

Use .reopen if this was a mistake.

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.

[chrome locust]

Can sm1 help do u need to divide 3/3?

[mossy raptor]

We have to find x ryt?

[chrome locust]

dude whay

[velvet osprey]

what's the question

[chrome locust]

Do u divide the 3/3

or nah

[sharp narwhal]

yes

[mossy raptor]

Just divide it

[chrome locust]

oml thank u so much

[mossy raptor]

It's too easy

[velvet osprey]

if you really want to divide 3 by 3 for no reason then nobody can stop you

[chrome locust]

my nerd said no

I had issues

[velvet osprey]

but you haven't made clear what you're asked to do!

[mossy raptor]

Listen do the algebraic division

[velvet osprey]

all we can see is two polynomials

no written instructions given

[mossy jetty]

what is the goal of this question?

[velvet osprey]

this btw is never appropriate to say

[mossy raptor]

I think it's factorisation or something for values of alpha beta and gamma

[mossy raptor]

Ahh ok

[velvet osprey]

don't invent things. let OP speak.

[mossy jetty]

I don't think we should assume what OP was asked to do.

[velvet osprey]

it is OP's responsibility to tell us the question in full

[mossy raptor]

Bruh it is literally cubic polynomial

[mossy jetty]

lest he actually have a different question, and we just tossed him down the wrong rabbit hole.

[velvet osprey]

ok and? so what.

[mossy raptor]

Ok let him yell

[sharp narwhal]

what do u think is the answer to op's question?

[velvet osprey]

@chrome locust still here?

[chrome locust]

Yes

Wait am solving it

[untold flint]

!original please, if you still need help.

[calm coral]

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.

[chrome locust]

Is the answer this

[velvet osprey]

show us the original question please

[mossy raptor]

I haven't solved it yet but I think we have to divide the expression 3x +3 to 12x³+6x²-18x-9 and after that put in lemma u will end up factorisation and frm there get the value of alpha beta and gamma

[chrome locust]

I did

[velvet osprey]

bc again we don't have any idea what to do

[mossy jetty]

there's no question statement here.

this is just two polynomials.

[chrome locust]

Um final answer

[velvet osprey]

stop posting the same uninformative image for the 6th time in a row

[chrome locust]

Synthethic

[mossy jetty]

so you're asked to do synthetic division?

[velvet osprey]

were there WORDS anywhere??

[chrome locust]

Wair mv

[sharp narwhal]

oh yeah. i worked it out and i think gamma = 69

[mossy raptor]

Bro just tell if u want the values of X or wt

[chrome locust]

(3x÷3)÷ the upper part

[mossy raptor]

That wasn't funny 😑

[chrome locust]

Using synthethic

[sharp narwhal]

wasn't trying to be funny

[mossy raptor]

Then ur prolly wrng

[chrome locust]

Pls solve it

[mossy jetty]

I assume you meant the upper part divided by the lower part, because the lower part divided by the upper part makes no sense.

[sharp narwhal]

show ur steps

[chrome locust]

Ok

[sharp narwhal]

nah i worked it out

[mossy raptor]

By getting gama 69 it is wrng

[chrome locust]

Wait ill get on a paper to clear it out

[mossy raptor]

That's wt i said

[upper sparrow]

Could we focus on OP for now please

[sharp narwhal]

what do u think is gamma

[mossy jetty]

I'm not responding to you.

[mossy raptor]

Zero of the poly

[mossy raptor]

Okay

[mossy raptor]

Ahhhh u rick rolled me

[sharp narwhal]

what number

[sharp narwhal]

???

[mossy raptor]

I didn't solved it yet but ik how to do it

[mossy raptor]

Sorry sir I indulged in a Convo With u

[chrome locust]

Brub wair

I sent

[mossy jetty]

,rccw

[chrome locust]

Am i correct?

[mossy raptor]

Wait I ll solve it by my own

[upper sparrow]

Btw you might want it the other way around, (12x^3 + ... )/ (3x + 3)

[molten crest]

If you're not helping OP with the problem they have, please leave this channel

[sharp narwhal]

what the heck is going on here

[molten crest]

@mossy raptor @whoeverelse

[mossy raptor]

Wy people r so sensible here I just told him the way to proceed the question wy yall mad

[chrome locust]

btonplsss answer

[dull wagon]

not quite

[chrome locust]

Can yall help fr

[molten crest]

The fact that I cannot find the last message you even sent to OP or what your original engagement is in this channel is evidence enough that you're not being particularly helpful right now.

Any off topic posting in this channel after this message gets muted

[dull wagon]

note that using -1,
the synthetic division gives you the quotient and remainder when dividing by (x+1), not 3x+3

[mossy raptor]

Really it's me who told him the Geniune way first how to proceed the question here wtever leave it i m solving it rn

[chrome locust]

Wats the final anderr

[velvet osprey]

people are indeed sensible here as a rule. did you mean sensitive?

[chrome lichen]

understand the method of solving

[mossy raptor]

Jss leave it

[dull wagon]

thus what that synthetic division is actually saying is
$$\frac{12x^3+6x^2-18x-9}{x+1} = 12x^2-6x-12 + \frac{3}{x+1}$$
to get $\frac{12x^3+6x^2-18x-9}{3x+3}$, divide both sides of that equation by 3

[chrome locust]

AM CORRECT

Finally

[potent lotus]

ραμOmeganato5

[chrome locust]

yall kept ignoring my question

[dull wagon]

a lot of time was wasted since you didn't post a clear question

[chrome locust]

I did bruh

idk what r u on abt

[dull wagon]

and i don't know if there was a formatting isssue and the horizontal fraction line wasn't shown

[chrome locust]

oh ue

Mb

[dull wagon]

which is why peopel kept repeatedly asking

[chrome locust]

bruv

sory

[dull wagon]

but anyway, read what i wrote

[chrome locust]

Wth

[dull wagon]

that generated the image below, read that

and the message above

note that using -1,
the synthetic division gives you the quotient and remainder when dividing by (x+1), not 3x+3

[chrome locust]

ok

I got the correct answer anyway

[dull wagon]

did you make adjustments to what you sent earlier?

[chrome locust]

No but I follow what my teacher does

[dull wagon]

the image you sent, is wrong

[chrome locust]

then what

im confused brah

[dull wagon]

did you read what i wrote up?

[chrome locust]

where dagw

the kmage?

[dull wagon]

yes

[chrome locust]

Bro wdym divide by both sides

I did it like this

I did whay my teacher does

[dull wagon]

yeh and i'm saying the conclusion you're reaching is wrong

[chrome locust]

Ok

It's still correct right

[dull wagon]

no

the final answer is not correct

i'm not going to say that again

[chrome locust]

how tf

[dull wagon]

your synthethic division is correct though
it just doens't give you what you want directly

again posting this again

note that using -1,
the synthetic division gives you the quotient and remainder when dividing by (x+1), not 3x+3

if you were asked to divide by x+1, instead of 3x+3,
this is the result you'll get
$$\frac{12x^3+6x^2-18x-9}{x+1} = 12x^2-6x-12 + \frac{3}{x+1}$$

[potent lotus]

ραμOmeganato5

[dull wagon]

now to get what they actually asked
divide both sides by 3, or multiply both sides by 1/3
so that you actually get division by 3x+3 on the left side, (instead of x+1)

[untold birch]

hello

[dull wagon]

e.g.
2p = 4
dividing both sides by 2:
2p/2 = 4/2
p = 2

[untold birch]

can you help with my homework

[dull wagon]

!occupied

[calm coral]

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).

[jovial bridge]

!occupied, sorry! please use a channel like #help-33

[calm coral]

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).

[untold birch]

i need factors of 25&55

hard one

[dull wagon]

please claim your own channel

[jovial bridge]

hi, but this channel is in use atm

please use an available channell, like #help-33!

i've pinged you there

[chrome locust]

Teacher said it's correct

[dull wagon]

well the teacher is wrong

[chrome locust]

.

[dull wagon]

,w expand (3x+3)*(12x^2-6x-12 + 3/(3x+3))

[chrome locust]

WYF

I meant synthethic bro

It's not like that

Facotr

mv

Mv

[dull wagon]

i said the synthetic itself was fine

what you're doing after that is not

[chrome locust]

??

Dude im going insane

[dull wagon]

again posting this again
note that using -1,
the synthetic division gives you the quotient and remainder when dividing by (x+1), not 3x+3

[chrome locust]

Synthethic divis0n

[dull wagon]

i'm aware

[chrome locust]

brub why did u usebthe hard method

[dull wagon]

wdym

[chrome locust]

It's so different from whay I learned

[dull wagon]

which method

[chrome locust]

nvm

[dull wagon]

i didn't really give an alternate method

i'm just saying what the division actually says

[chrome locust]

im going insane

[dull wagon]

and what you should actually do
to get the correct answer

but it feels like you're not really reading what i'm saying

[chrome locust]

it's so different from wat I leanted

[dull wagon]

whats so different

[chrome locust]

Show me the pic

This is whay I LEARNED

[dull wagon]

well its wrong, or you're conflating stuff

the division is fine.
thus what that synthetic division is actually saying is
$$\frac{12x^3+6x^2-18x-9}{x+1} = 12x^2-6x-12 + \frac{3}{x+1}$$

[potent lotus]

ραμOmeganato5

[chrome locust]

Dude

[dull wagon]

read those numbers carefully

[chrome locust]

It literally the picturenisntjere

[dull wagon]

its different

[chrome locust]

yes

I followed this from JG too

[dull wagon]

you can't just change those two x+1 to 3x+3
and call it a day

that's not mathematically valid

[chrome locust]

idk what ur on abr

[dull wagon]

do you at least agree with the above image?

[chrome locust]

Yss

Yes

[dull wagon]

ok good

[chrome locust]

It's the same answer I got

[dull wagon]

no it snot

It is not

[chrome locust]

...

UR ONTO NOTHING BRO

[dull wagon]

lets take this one step at a time

[dull wagon]

instead of assuming that i have nfi what i'm talking about

[chrome locust]

COMPARE THIS TO THE PICTURE ABOBW

WHATS THE DIFFERENCS

NONE

[dull wagon]

there are difference

[chrome locust]

WHERE

[dull wagon]

the pic i have,
has division by x+1

not 3x+3

[chrome locust]

when did I give x+1

[dull wagon]

that's effectively what you're doing when using -1 in your synthetic division

[chrome locust]

yes because I divide 3/3

= 1

But i chnahe it

TO -1

[dull wagon]

you can't just change those two x+1 to 3x+3
and call it a day
that's not mathematically valid

ok, so what's actually happening is:
$$\frac{12x^3+6x^2-18x-9}{3x+3} = \blue{\frac{12x^3+6x^2-18x-9}{x+1}} \cdot \frac 13$$

[potent lotus]

ραμOmeganato5

[dull wagon]

and your synthetic division is saying that blue part is this
$$\frac{12x^3+6x^2-18x-9}{x+1} = 12x^2-6x-12 + \frac{3}{x+1}$$

[potent lotus]

ραμOmeganato5

[dull wagon]

so your actual result would be
$$\br{12x^2-6x-12 + \frac{3}{x+1}} \cdot \frac 13$$

[potent lotus]

ραμOmeganato5

[chrome locust]

ur def onto nothing

[dull wagon]

whatever that simplies to

[chrome locust]

DUDE ITS LITERAY RIGHT THERE

[dull wagon]

what?

[dull wagon]

and if it wasn't already clear
$$\br{12x^2-6x-12 + \frac{3}{x+1}} \cdot \frac 13$$
is NOT
$$\br{12x^2-6x-12 + \frac{3}{3x+3}}$$

[potent lotus]

ραμOmeganato5

[chrome locust]

ITS LITERALLY THE SAME THING

[dull wagon]

it not

distributive property

the 1/3 multiplies to ALL terms

not just what happens to be closest to it or whatever you feel like

[chrome locust]

oml bro

[dull wagon]

a(b+c) = ab + ac
not ab + c

[chrome locust]

I give up

I didnt even ask that

[dull wagon]

you seem to have a mindset that you're right no matter what i say

its a cruicial property that applies directly here

[chrome locust]

ur using advanced English id even know

[dull wagon]

and you're saying stuff is the same, where there a slight difference, so stuff is in fact not the same

[chrome locust]

ur basically onto nothing

is u graduates

Graiyed

Graduated

[dull wagon]

yes

[chrome locust]

Wayncountry

[chrome lichen]

yo whats the ques

[dull wagon]

if you are going to insist that you're right no matter what i say
i'm not going to bother anymore

i've already outlined all the relevant details above

listen to be or ignore me, i don't really care anymore

[chrome locust]

bruh ur basically useless

[chrome lichen]

bro

tell me

[chrome locust]

ok

Is this the same final answer?

Wrong image

[chrome lichen]

lemme solve the question

[dull wagon]

going to let that slide this time, but don't insult anyone else in this server in the future.

[chrome lichen]

yh fr be respectful

[chrome locust]

I did bro but bro is literally onto nothing

synthethic

[void umbra]

Sir bro is literally helping you out of pocket sir

[chrome locust]

I asked for help and he showed something I never learned

[void umbra]

What even was the question anyway

@chrome locust

[chrome locust]

Ques and answer

Here

[void umbra]

Uh did you copy this from somewhere

[chrome locust]

No

I answered it by myself

[chrome lichen]

is the ans correct?

[chrome locust]

Im pretty sure

[void umbra]

So you just uh want this checked?

[chrome locust]

yesss

That's all I asked

Not hard right?

Js yes or no

[void umbra]

You're trying to do synthetic division right

[chrome locust]

yes

[void umbra]

So firstly the question itself is wrong

[chrome locust]

how tf

[chrome lichen]

yh your ans is wrong

[void umbra]

You've taken (3x+3)/yadayada

Where yadada is a higher degree than 3x+3

[chrome locust]

wait no need to divide?

no need to divide 3/3

?

[void umbra]

So in that case you can't even do synthetic division

[chrome locust]

I js did what my teacher does

[void umbra]

Sir sometimes

You can see your teacher do one thing

But you can do another

Is very normal

[chrome locust]

it's correct bruh

Teacher said it correcf

[void umbra]

If we all were able to copy our teacher exactly

Ok then if so why you ask here

[chrome locust]

bruv

[void umbra]

Did your teacher look at your answer

[chrome locust]

umm

[void umbra]

And tell you it's correct

[chrome locust]

Uhhh

[void umbra]

Or are you saying you did what your teacher did

So that's why it's correct

[chrome locust]

Yes

[void umbra]

Sir

Come on man

[chrome locust]

I followed my teacher steps

[void umbra]

If a kid says 1+1=3

And you tell him it's wrong

But he says he followed the teachers steps

[chrome locust]

im sorry im going insane

[void umbra]

Is he then correct

Maybe he just misinterpreted the teachers steps yah

Alright

Don't think so highly of yourself can

We are not perfect

I can make this mistake

You can make this mistake

We can all make this mistake yah

[chrome locust]

if a person is black is he black? No he's white

[short salmon]

babapro, I think you're just not internalizing the idea that it's not generally true that (a+b)c=a+bc