help-10

[timid silo]

Ye lmao its a balkan country

[brazen saddle]

When i play geoguessr , Kosovo counts under Bosnia and Herzegovina, or maybe some other country for some reason

They should correct their shit

[timid silo]

I mean…. Kosovo was part of yugoslavia but they went too far putting it on bosnia and Herzegovina 💀💀💀

[obtuse pebble]

@timid silo Has your question been resolved?

Channel closed

Closed by @median jacinth

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.

[timid silo]

I need help studying for finals, especially this one bit

[timid silo]

I have to describe the link between the values n and the rapport of the origin of g / the origin of f

The origin in that case is, I assume the summit

so (5,0) and (5n,0)

n being the amount resulting from the translation

(How many times a line with a value of 5 can fit between the summits)

But I have no idea how to find out the value of n

So the functions are parabolic curves

F(x) = a (x - b)^2

so I assume for function f it would be f(x) = a( x -5)^2 +0

Then idk where to go

<@&286206848099549185>

Oh nvm, i think I got it

But like, I just pulled values out of my ass

[obtuse pebble]

@timid silo Has your question been resolved?

Channel closed

Closed by @plush warren

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[past mantle]

m<j is 120?

how do i find k and i

[thick oracle]

so

u here?

[past mantle]

yeah

[thick oracle]

ok

so

if arc hkj is 128

how big is angle hij?

[past mantle]

232?

[thick oracle]

no

[past mantle]

oh

[thick oracle]

its half of its corresponding arc

right?

[past mantle]

oh

yeah

[thick oracle]

so...

how big

?

[past mantle]

64?

[thick oracle]

yes

BUT

what kind of quadrilateral is ihkj?

[past mantle]

rhombus?

[thick oracle]

no

[past mantle]

a

[thick oracle]

if all the angles are on the circle

it means ihkj is a cy..... quadrilateral

what is it

[past mantle]

im confused sorry

[thick oracle]

cyclic

look at the last sentence

then tell me the answer

[past mantle]

so k is 116?

[thick oracle]

yes

[past mantle]

oh thank you

[thick oracle]

np

[past mantle]

.close

[obtuse pebble]

Channel closed

Closed by @past mantle

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.

[nocturne arch]

To solve this indefinite integral am I forced to replace ln(x) or is there some way to do it using only parts?

[high lily]

let I = your integral
and try 2 iterations of ibp

[obtuse pebble]

@nocturne arch Has your question been resolved?

[nocturne arch]

when I have the 2 iterations

what should I do?

I’ve got them here

But I just keep going in circles

[high lily]

note that your original integral appears again

solve the equation for that integral

[nocturne arch]

Ohhhh that’s right

Thanks

You’re a god

.close

[obtuse pebble]

Channel closed

Closed by @nocturne arch

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[acoustic pawn]

if a matrix A has a right inverse B, does it also, by virtue of it having a right inverse, have a left inverse?

[royal basin]

no

$\bmqty{1&0&0\0&1&0}$ has right inverse $\bmqty{1&0\0&1\0&0}$ but has no left inverse

[warm shale]

Ann

[acoustic pawn]

Hmm okey

what if A is a square matrix

[royal basin]

then yes

[acoustic pawn]

thanks alot!

.close

[obtuse pebble]

Channel closed

Closed by @acoustic pawn

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.

[wintry harness]

Hey um quick very simple question, but how do you find ratio again? XD

[wintry harness]

Q6 ii

I already have the volume numbers btw

[versed cave]

Ratio is another way to say division

So you have to divide the volume of the hemisphere by the volume of the cube

[wintry harness]

and then what

[versed cave]

you found the ratio

[wintry harness]

that’s not what a ratio looks like tho no?

[versed cave]

What do you mean?

[wintry harness]

like ratios usually look like 3:2

or 4:8

[versed cave]

Oh I see what you mean

Like in proportions, right?

[wintry harness]

oh i think i have it now

so when i divide it and then get a fraction

the top would go to the left and bottom to the right

[versed cave]

Yes

$a:b=\frac{a}{b}$

[warm shale]

Nonna

[wintry harness]

ok thanks

.close

[obtuse pebble]

Channel closed

Closed by @wintry harness

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.

[wintry harness]

How do u put that in a calculator

[versed cave]

What calculator do you have?

[wintry harness]

Casio fx-83GT plus

[versed cave]

(By the way try to solve that one intuitively)

[wintry harness]

Why would i do that😭

i jsut need the answer

[versed cave]

You have to think "what's the number that multiplied by itself three times gives 27"?

On your calculator press shift (top left button with yellow text) and then square root

[wintry harness]

ohhh

thank u very much i didn’t see that

[versed cave]

@wintry harness if you don't have more questions remember to .close the channel

[obtuse pebble]

@wintry harness Has your question been resolved?

[nocturne minnow]

Or knowing the fact that $$a^{\frac{m}{n}} = \sqrt[n]{a^m}$$

[warm shale]

dldh06

[nocturne minnow]

You could have typed in 27^(1/3)

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[timid silo]

(this is not a HW) why is the 3x3 determinant / triple scalar product the volume of a parrallelepiped created by the 3 vectors? I know that the cross product gives a perp vector whose magnitude is the area for two vectors, and if you dot that with a third vector it is like taking the component of that cross vector in the direction of the third (multiplied by the thirds magnitude), but it is not something that to me tells me that is parralelipiped volume

[timid silo]

is this something I should try to work out geometrically, or should I use linear algebra, both?

[kind hawk]

I think 3b1b made a video about that once

[timid silo]

Yeah im actually parsing through his cross product and determinant videos but so far at least I am only finding the what and not the why

whats funny is that when I look up why does triple scalar give volume I get "because it is determinant which is volume" but then when I search why is determinant volume I get "because it is triple scalar which is volume"

[kind hawk]

when I search why is determinant volume I get a math stackexchange post which goes through the math

https://math.stackexchange.com/questions/427528/why-is-the-determinant-the-volume-of-a-parallelepiped-in-any-dimensions

it essentially boils down to reducing it to the "obvious" case and knowing it's true for that

[timid silo]

ahh it looks pretty good, thank you

.close

[obtuse pebble]

Channel closed

Closed by @vernal jay

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.

[timid silo]

I'm looking to seek some help and check if I completed the square correctly to find the vertex

[timid silo]

Here is the photo of my already tried work

[golden oriole]

Didn't you already ask this ?

[timid silo]

I redid it 😆

I think it's right now

[golden oriole]

Yep its correct

[timid silo]

Awesome thank you so much for the help @golden oriole

.close

[obtuse pebble]

Channel closed

Closed by @shrewd token

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.

[pliant wolf]

hey

[pliant wolf]

can someone help me out on this

[harsh remnant]

Which one?

[pliant wolf]

so there is a 1,3,5 rule

for graphin n shit

[harsh remnant]

Arithmetic Sequence?

[restive ridge]

,rccw

[pliant wolf]

yeah so

the form is vertex right?

[restive ridge]

no

[harsh remnant]

It's not?

[restive ridge]

the form of a quadratic function is a parabola

[pliant wolf]

im pretty sure it is bro

[harsh remnant]

I think he was asking if the equation was in vertex form

[pliant wolf]

i just checked it is..

[harsh remnant]

Am I right?

[pliant wolf]

yes u r

[harsh remnant]

It is vertex form

[restive ridge]

oh my bad

[pliant wolf]

how would i start off

[golden oriole]

Hmm
Here we call it completed square form

[harsh remnant]

What's the vertex?

[pliant wolf]

the x intercepts are 2 and 2 right?

[golden oriole]

I don't think so

[harsh remnant]

Hold on

Lemme calculate

[pliant wolf]

but

[golden oriole]

Do you know how to find the domain and the range ?

[pliant wolf]

nvm its not

ik domain is always the same

but idk how to find out range

[golden oriole]

Can you find the vertex ?

[pliant wolf]

i mean lemme try

[harsh remnant]

There are no x-intercepts

[golden oriole]

Ye

[pliant wolf]

how

[golden oriole]

Take the -3 and -2 to the other side
You get a square = negative number

So there are no real roots

[harsh remnant]

It's imaginary

Use the quadratic forumla

[pliant wolf]

wait so what should i start off with

like

[harsh remnant]

Let's start off with the vertex

What is the vertex?

[pliant wolf]

tbh idek

how would i find the vertex

i had to take online classes

[harsh remnant]

What's the vertex form

[pliant wolf]

(h,k)

[harsh remnant]

Yes

[pliant wolf]

for vertex

[harsh remnant]

What's your h

and k

[pliant wolf]

k is the -3

[golden oriole]

a(x-h)² + k

[pliant wolf]

and im not so sure abt the h

[golden oriole]

Yes

[pliant wolf]

how do i found h

[golden oriole]

This is the form you find h from

[pliant wolf]

exactly

how do I find h tho

[golden oriole]

Bro just compare the original equation with this

[pliant wolf]

yeah cool

i did compare it

so now what

?

@harsh remnant

[harsh remnant]

Answer domain and range

[pliant wolf]

domain is

(- infinity, infinity)

idk about the range

[golden oriole]

And what is the h ??

[pliant wolf]

the h is -2

[golden oriole]

No

Its + 2

-h = -2
So h = 2

[harsh remnant]

Why don't you know the range?

You know the vertex

[pliant wolf]

bro idk

[golden oriole]

Ok
Lemme explain

[harsh remnant]

Does a parabola ends both ways?

[pliant wolf]

ik its smth like (- infinity, smth)

[harsh remnant]

A parabola increases or decreases infinitely, right?

[golden oriole]

What exactly is the vertex
A max or a minimum right ?

[harsh remnant]

Yeah

[pliant wolf]

yes ik

[harsh remnant]

The parabola does down

[pliant wolf]

this is a maximum

[harsh remnant]

What was the vertex?

[golden oriole]

-3

The maximum value is -3

[harsh remnant]

Yes

[golden oriole]

So the range is- 3≥y

[pliant wolf]

wait

[harsh remnant]

Do you get it?

[pliant wolf]

so wuts the range

[harsh remnant]

?

[pliant wolf]

wait i dont understand

how the range is not -2

since its -2

[harsh remnant]

What's the vertex, again?

[golden oriole]

First its not - 2 its 2
Second the range is concerned with y coordinate not x

[pliant wolf]

exactly

ik

thats what im saying

[golden oriole]

So you take the value of k 😅

[harsh remnant]

Yes

[pliant wolf]

how is value not -2

since it literally says - 2

[golden oriole]

K is the y cord of vertex

[harsh remnant]

Say the vertex again

[pliant wolf]

ye exactly

[golden oriole]

Can you look at the question again ?

[harsh remnant]

What was your vertex

[pliant wolf]

bro what

stop

[harsh remnant]

Just answer me

[golden oriole]

Bro thats -h
Not k

[harsh remnant]

Lemme explain a bit

[pliant wolf]

BRO

IM NOT AKSING WUT K IS

[golden oriole]

Write the vertexes coordinates
Then all will be clear

[pliant wolf]

IK K IS -3

WUT IS H

[harsh remnant]

2

[pliant wolf]

how

[harsh remnant]

(x - 2) = 0

[pliant wolf]

explain that

[harsh remnant]

What is x

[pliant wolf]

idk

[harsh remnant]

?????????

This is pre-algebra

[pliant wolf]

wut is x

bro im dumb

help me out

[harsh remnant]

Not until you solve this

[golden oriole]

I was talking about the range
Range means Set of y cords
And that involves the value k
Thats what i was trying to explain
The range

[pliant wolf]

bro wut is x

idk what x is

@harsh remnant how do i find x

[harsh remnant]

I...

x is an unknown variable that needs to be solved

[pliant wolf]

(x - 2) = 0

[golden oriole]

[pliant wolf]

you add 2 to both sides?

[harsh remnant]

YESSS

[pliant wolf]

o

[harsh remnant]

So what is x

[golden oriole]

🥳

[pliant wolf]

x s 2

x is 2

[harsh remnant]

Yes

That x is your h value

That's why your vertex is (2, -3)

[pliant wolf]

alr so here me out

okay

wuts the range then?

[harsh remnant]

Does the graph opens up or down

[pliant wolf]

it opens down

[golden oriole]

So the vertex is ?

[harsh remnant]

Does a parabola stops when going down?

[golden oriole]

A min or a max

[pliant wolf]

ITS A MAX

oops

[harsh remnant]

You gonna answer this or...

[pliant wolf]

no

[harsh remnant]

Yes, right

[golden oriole]

So We know the highest value is -3
And all values below it are part of the range

[harsh remnant]

Then your vertex either represents your graph's highest or lowest point it can go

[pliant wolf]

so its (-infinity, -3]

[harsh remnant]

Yes

Nice

[pliant wolf]

and the axis of symmetry is 2?

x = 2

[golden oriole]

Yes

[pliant wolf]

kk

wut is the max?

[golden oriole]

Also don't write that in coordinate form

[harsh remnant]

Why not?

[golden oriole]

Write it as y ≤ -3

[pliant wolf]

my teacher said write it that way tho

[harsh remnant]

I mean honestly

It depends on the teacher

[pliant wolf]

^

[golden oriole]

The coordinates form means the -infinity is x cord doesn't it ?

[harsh remnant]

No

[golden oriole]

Or is that some notation im not aware of ?

[pliant wolf]

kk so wuts the max

[golden oriole]

What is the max in your range ?

[pliant wolf]

-3?

[golden oriole]

Yes

[pliant wolf]

kk bet

[harsh remnant]

Or just write it like this Range: {y ∈ ℝ | -∞ < y ≤ -3 }

[pliant wolf]

so the max is always the y-value?

[harsh remnant]

Um

Yes, for this function

[pliant wolf]

kk

[golden oriole]

Yes
The y coordinate of the vertex
Its always the max or the min

[harsh remnant]

ONLY for parabolas

Alright, next

End behaviors

[pliant wolf]

how did you know that there were 0

x intercepts

[harsh remnant]

$$\lim _{x\to :-∞}\left(Where:does:y:go:to?\right)$$

[pliant wolf]

?

[warm shale]

AirToastie

[harsh remnant]

Basic factoring...

[pliant wolf]

o so when the parabola goes down, there is always 0 x intercepts?

[pliant wolf]

wym

[golden oriole]

As you said before
It goes towards -infinity

[harsh remnant]

No

[golden oriole]

No

[harsh remnant]

If you graph the parabola

Are there any x values that touch the y = 0 line?

[pliant wolf]

i didnt graph it yet tho

wait help me graph it rq

[harsh remnant]

Is the vertex above the y = 0 line?

[pliant wolf]

no its not

[harsh remnant]

Is the vertex opening up?

Then there should be no x values touching the x-axis

[pliant wolf]

how do you graph it

can you help me

[harsh remnant]

Graphing it is not important

Just sketch

[pliant wolf]

ik but i need to graph it

also

[harsh remnant]

How can you graph it

[harsh remnant]

when you don't know the answers

[pliant wolf]

ok my bad

so

i need the increasing and decreasing

thats left

[harsh remnant]

Is the graph increasing at all?

[pliant wolf]

no

[versed cave]

Do you have to graph that function?

@pliant wolf ?

[pliant wolf]

i figured it out

were good now

ig

[versed cave]

oh ok

The problem was to find a parent function and use transformations

[obtuse pebble]

@pliant wolf Has your question been resolved?

Channel closed

Closed by @pliant wolf

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.

[neon flume]

I'm trying to code a city generator. This is how I calculate the size of the map 40 * ((mapSize) * 1000 / 200) * 5. And if the roadlength is 12 it comes out right. I'd like to be able to change my road length and keep the size the same.

[versed cave]

Is there a reason the size of the map is so specific? Why is mapSize not just the size of the map?

@neon flume

[neon flume]

Because the way my generator sees the number is different than a person would. It's the map size in KM there and then I do all that math to put it in the units my generator uses.

The map size is converted from kilometers squared to the mapsize my generator would use.

40 * ((mapSize) * 1000 / 200) * 5 this is the conversion where the road length is 12.

[versed cave]

isn't 40 * ((mapSize) * 1000 / 200) * 5
just
1000* mapSize?

[neon flume]

Yeah it seems so

No idea why I did it that way

Oh this is not what I need to change

I just realized

It's actually this transform.GetComponent<CityGenerator>().mapSize = (int)((mapSize) * 1000 / 200) * 5

So it's (mapSize) * 1000 / 200) * 5

Where road length is 12

[versed cave]

What do you mean by road lenght, is it the first or the second?

[neon flume]

Second

[versed cave]

Hmmm ok

how do you actually generate the road?

[neon flume]

I use l-system

I generate the points using L-System. each road has a static length of 10 at that point. But this is in the 2D space. In 3D I take each point and multiply it by 12. And I just realized something.

I have no idea how the 10 relates to the 12.

Well actually it's the same.

So really the length is 10 and then that is multiplied by 12.

I have 2 numbers for the length

Do you think if I change the static length of 10 rather than trying to change the map size it will work?

[obtuse pebble]

@neon flume Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[knotty lodge]

Isn't the direction vector just 2 and -2/3?

the book answer is (3,-1)

[little python]

question asks for vector with integer components though

[knotty lodge]

im not sure what that means

haha

[little python]

if you multiply your answer by -3/2 then you get the same answer as the book

[knotty lodge]

ah

so "integer components"

mean whole number?

[little python]

including negative ones, yes

[knotty lodge]

ahhh

also for this question

(Xo, Yo) would be the run?

[obtuse pebble]

@knotty lodge Has your question been resolved?

Channel closed

Closed by @knotty lodge

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[heavy berry]

Can I get some help with this?

[cedar lichen]

What have you tried?

[heavy berry]

Nothing really, I have no idea what to do

[cedar lichen]

Well, I'm unfamiliar with a table method to find (x + m)(x + n). I assume you are familiar with it? Or at least have done it before?

[heavy berry]

we have never learned this before

[cedar lichen]

I doubt this question is coming out of the blue. Are you at least familiar with FOIL?

[high lily]

have you ever seen a multiplication table before?

[golden oriole]

What does it mean use table ?

[heavy berry]

yeah

[high lily]

something you've probably been introduced to when learning times tables

use a similar structure here

put a multiplication symbol at the top left

x,m for the boxes at the top
x,n for the boxes on the left

do the respective multiplication

and add those 4 results

[heavy berry]

okay thank you

.clsoe

.close

[obtuse pebble]

Channel closed

Closed by @heavy berry

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.

[urban gust]

can someone check this ?

[obtuse pebble]

Please don't occupy multiple help channels.

[plain nacelle]

ok

take my advice with a grain of salt

[urban gust]

jaja okay

[plain nacelle]

but isn't it a maximum or minimum?

[urban gust]

what do you mean by it

[plain nacelle]

instead of and

[high lily]

there are many that are wrong

[urban gust]

really?

[plain nacelle]

also i think there are functions with only one real root, and some that has none

[high lily]

ticked some that you shouldn't have
and didnt tick some you should have

[plain nacelle]

yep

[slim lake]

I recommend reading about the discriminant, it's not a difficult topic but will give you a lot of intuition for this question

[urban gust]

ah okay

ill look into that

[valid crown]

they don't hqve min and max a the same time

also

not all quadratics have 2 solutions

they may have sometimes 1 solution

[urban gust]

thank you for your help

i will see

.close

[obtuse pebble]

Channel closed

Closed by @urban gust

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.

Please don't occupy multiple help channels.

[valid crown]

5cos((pi/270)*(x+75))+3

[cedar lichen]

Don't just give answers

[valid crown]

dunno where you gwt your formula

it's different

that and

why 2×pi would convert to 60?

sine and cosine is just shifted

HOW?

2×pi = 360degree

keyboqrd mulfunction

omega = 2×pi×frequency

omega =2×pi/period

period = (195- (-75))×2

just changed my formula

should be pi/270

pi is angle in radians

degrees are not

pi is just a value of irrational number 3.141592653

so 2×pi = 6.28

[obtuse pebble]

Channel closed

Closed by @hardy swan

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.

[sharp forge]

Very simple question, but I am a somewhat math ignorant person.

Do functions have anything to do with equation systems?

[cedar lichen]

Wdym by equation systems?

[obtuse pebble]

@sharp forge Has your question been resolved?

[sharp forge]

something like this

[cedar lichen]

Well, you can plot both equations. The solution is where they intersect

[sharp forge]

Okay, thank you

[obtuse pebble]

Channel closed

Closed by @sharp forge

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[weary nacelle]

can someone help me with this

[weary nacelle]

it’s so confusing

Length of a rectangle is 2x + 1 and the width is 3x - 2. Find the value of x if the perimeter is 38 inches

i have no clue of what to put

[sharp mesa]

38=4x+2+6x-4

10x=40

x=4

[sharp mesa]

the 2x+1 and 3x-2 are inches right

[tacit vapor]

hey

[obtuse pebble]

@weary nacelle Has your question been resolved?

[weary nacelle]

wait

[weary nacelle]

yes

[weary nacelle]

wait that’s just the length

they width has to be included i think

the

if it’s 4 then 4*4 is 16+1= 17x2 is 34

for length

width is 3*4 is 12-2 is 10 so that’s 20

20+34 is 54

It’s supposed to be 38

@sharp mesa

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[weary nacelle]

.reopen

[obtuse pebble]

✅

[timid silo]

@weary nacelle

x = 4

It's perimeter, we'll take both sides which are "2x + 1" and "3x - 2"

Now let's render it out.
$2(2x + 1) + 2(3x-2) = 38 \rightarrow (4x + 2) + (6x - 4) = 38 \rightarrow 4x + 6x = 40$

[warm shale]

kav

[timid silo]

You get the idea? now we add 4x + 6x = 40, we get 10x = 40 and it's simple, divide 10 and boom. 4

[reef knot]

@weary nacelle
Permter = 2(l+b)
2(2x+1 + 3x-2)
2(5x-1)
10x-2 = 38
10x = 40
X = 4

[timid silo]

^

[obtuse pebble]

@weary nacelle Has your question been resolved?

[weary nacelle]

h ty

oh

wait

i got 1 last one

[timid silo]

Wussup

[timid silo]

cute pfp btw, I like it 🙂

[weary nacelle]

What’s this

[timid silo]

ah

[weary nacelle]

Length is +5 more than width and perimeter is 9x more than the width

[timid silo]

so this should be set algebraically

[weary nacelle]

oh

[timid silo]

Hm. so since we know the length is 5 units more than the width

that would be x + 5 and x right?

[weary nacelle]

yes

[timid silo]

uh huh and the permiter is 9 times of width, so that's 9(x + 5)

[weary nacelle]

Yes

[timid silo]

$x + (x+5) = 9(x) \rightarrow 2x + 5 = 9x \rightarrow -7x = -5 \rightarrow x = 5/7 $

[digital moat]

Shouldn't it be 9x cause it's 9 times the width

[timid silo]

yeah

I messed up so I'm fixing it

[digital moat]

So 4x+10=9x

[timid silo]

it should be better now (originally I thought it was 9x the length

[digital moat]

5x=10

[timid silo]

wait.

it's perem

nevermind, take over @digital moat I fked up

[weary nacelle]

Ok

[digital moat]

X=2

Length

=2+5=7

[weary nacelle]

Ty

So the answe is 2

right

[digital moat]

Yeh

[weary nacelle]

ok ty

.close

[obtuse pebble]

Channel closed

Closed by @weary nacelle

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.

[urban kiln]

but the real formula which is derived algebraically by flipping the same series and adding it gives a (2a)
then where am i going wrong?

kindly ping me while replying

[hearty terrace]

@urban kiln the outcome you want is $\frac{(a_1+a_1(n-1)d)\cdot n}{2}$?

[warm shale]

🙛𝕍ѳrtєx🙙

[urban kiln]

yess

but m getting a single a instead of 2a

then is my geometrical analogy wrong?

[hearty terrace]

@\

@urban kiln analogy seems a bit off

if you just do a_2 the area is supposed to be 4*2/2=4 but the sum of 2 and 4 is 6

[urban kiln]

hmmm i see

then how else can u geometrically derive the sum of n terms

[hearty terrace]

smth like this possibly

https://www.maa.org/press/periodicals/convergence/geometrical-representation-of-arithmetic-series-terminology-and-trapezia

this article has an answer if you wanna see it but you might also wanna leave it as an exercise

[urban kiln]

hmm i see

[hearty terrace]

actually

your diagram just cuts out a small triangle out of each of those rectangles which may be where the a_1 is lost

@urban kiln

[urban kiln]

m still wondering if i cud rearrange it into a triangle

[hearty terrace]

i cant see any immediately but it's also 1:00 am lol

dm me if you find anything!

[urban kiln]

sure!

can i add u as a friend?

cuz u dont seem to be accepting req's frm well not friends

[obtuse pebble]

@urban kiln Has your question been resolved?

Channel closed

Closed by @urban kiln

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[kind hawk]

you would maybe call it a degenerate rectangle

[knotty fjord]

there are 2 lengths of 0 so wouldn't that just be one line

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[mighty ether]

can someone explain what is going on in the red part?

[mighty ether]

ill send my solution through

[sick pelican]

*-1 on both sides

[summer spire]

and adding 2 after this

[sick pelican]

basically making y as the subject

yes yes

[mighty ether]

but i get this??

[summer spire]

you didnt apply log rules properly

[mighty ether]

which log rule did i mess up

[summer spire]

run me through how you got from your first line to second line

[mighty ether]

i raised e to both sides

[mighty ether]

e^ln(2-y) = e^ln(sinx)

[timid silo]

normal stuff

$-ln(2-y)=ln(sin(x))+C$

Raising both sides to e

$\frac{1}{2-y}=e^{ln(sin(x)) + C}=Ce^{ln(sin(x))}=Csin(x)$

taking reciprocal of both sides

$2-y=\frac{1}{Csin(x)}=\frac{1}{C}*\frac{1}{sin(x)}=\frac{C}{sin(x)}$

[warm shale]

0/0=:Hmmcat:

[timid silo]

@mighty ether

[summer spire]

okay i think the answer is wrong

[timid silo]

[summer spire]

your method should be correct cheese

[summer spire]

@timid silo can you check this

[timid silo]

the thing is

the C chesse is using

is not the same C

in the answer

[summer spire]

no but the sign is totally different

[mighty ether]

yeah that part i can kind of reason in my head why the c is wrong

beacuse its just a constant so

[timid silo]

it can be simplfied

[mighty ether]

the c can be left there

the sign is what is messing with me

[summer spire]

oh

OH

bruh.

[mighty ether]

i know the c should be at the top

[summer spire]

it doenst matter doesi t

[timid silo]

$2-\frac{1}{c sin(x)}=2-\frac{1}{c}*\frac{1}{sin(x)}=2-\frac{C}{sin(x)}$

[warm shale]

0/0=:Hmmcat:

[summer spire]

C could be the negative inverse of c so its fine

but just to be sure cheese's answer is also correct right?

just different ways of representing it

[timid silo]

$2-\frac{C}{sin(x)}=2+\frac{-C}{sin(x)}=2+\frac{C}{sin(x)}$

[warm shale]

0/0=:Hmmcat:

[summer spire]

yup

great

[timid silo]

so they are the same the same thing

it's just that cheese has a different C

which should be simplfied I suppose

[mighty ether]

okay so basically i have the same answer, theirs is just simplified?

[timid silo]

ye

[mighty ether]

okay sweet, thank you !

[timid silo]

$2-\frac{1}{c sin(x)}=2-\frac{1}{c}*\frac{1}{sin(x)}=2-\frac{C}{sin(x)}=2-\frac{C}{sin(x)}=2+\frac{-C}{sin(x)}=2+\frac{C}{sin(x)}$

[warm shale]

0/0=:Hmmcat:

[timid silo]

this is all

[mighty ether]

thanks a lot !

.close

[obtuse pebble]

Channel closed

Closed by @mighty ether

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.

[polar vapor]

How do you turn a complex number into a quadratic, is it x^2-(sum)+product? I think it is, just want to be sure

[warm canopy]

yes, these are vieta's formulas for roots of a quadratic

you mean -(sum)x

[polar vapor]

Yeah, -(sum)x, oops, but yeah, so it is right? I didn't know the proper name of the formula tbh

[warm canopy]

yes its correct, good to know the name to look up stuff about it

[polar vapor]

Yeah, you're right there, thanks, for the help!

.close

[obtuse pebble]

Channel closed

Closed by @polar vapor

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.

[low halo]

(a + b + c)^10 , all i need to know is how many a, b, c combined are in this is equation

[timid silo]

can u explain a bit more clearly?

like

[low halo]

i need to find number of additions in the developed form of expression

[timid silo]

how many a^n*b^k pairs are there where n is not 0 neither k

?

[timid silo]

then use the binomial theorom?

[low halo]

i think n can be zero

[timid silo]

oh mb

there are three 3 terms

[low halo]

i know i can get there this way but i think its very long and tidius, so was just wandering if there is other idea how to get there

[timid silo]

(a+b+c)^10=((a+b)+c)^10=11 terms, with 10 terms of (a+b) that can be expanded

this is using binomial theorom

or pascals triangel

all u need to do now is figure out the number of terms in a and b after each of them are expanded

[low halo]

and then expand a + b

[timid silo]

which can also be done using binomial theorom ig

[low halo]

ok yea yea i get it, thank you for help

.close

[obtuse pebble]

Channel closed

Closed by @low halo

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.

[uneven scaffold]

what is the answer for this

[rancid dust]

i cant tell you the answer directly

are these + or - signs

[uneven scaffold]

like the test is over and i tried some ways but i just marked one cuz i dint have time

[glossy basalt]

Is it $p_{n+2}=α^{n+1}-β^{n+1}$?

[warm shale]

OldBiscuit

[grizzled shore]

Yes

That’s what it says

[glossy basalt]

Then @uneven scaffold , you can make use of the fact 4α²-7α+9=0 (also for beta) to solve it

[uneven scaffold]

yes

[glossy basalt]

Hint2:||4α²+9=7α, (also for beta)||

[uneven scaffold]

ok gonna try solving again thanks

.close

[obtuse pebble]

Channel closed

Closed by @uneven scaffold

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.

[thick wharf]

@random pecan

[thick wharf]

why is this wrong

:\

[random pecan]

bro im grade 7

[restive ridge]

lmao

[grizzled shore]

What is a polynomial @thick wharf

[thick wharf]

a polynomial is a multi term expression?

[grizzled shore]

Not quite

[thick wharf]

or just

any expression

[grizzled shore]

Is 2ˣ a polynomial?

[random pecan]

in wich grade am i going to get this?

[grizzled shore]

Go back to your channel don’t get distracted

[thick wharf]

no right?

[random pecan]

cuz it looks hell

[thick wharf]

this is 6th grade

[grizzled shore]

Is 1/x a polynomial

[random pecan]

sorry

[thick wharf]

no

oh

its not a polynomial

bruh

[grizzled shore]

Is sinx a polynomial

[thick wharf]

no

[fierce lagoon]

Isn't this debatable

Whether or not sin(x) is

[grizzled shore]

No

It is not a polynomial

[fierce lagoon]

Idk I though it was due to the Taylor expansion of it

[thick wharf]

-c/5 isn't then

so its not a polynomial

thanks man

[grizzled shore]

Taylor expansion is an approximation

[fierce lagoon]

That's true yeah

[thick wharf]

I like your taylor pfp too

[grizzled shore]

Me too but that part is only part of an expression

[fierce lagoon]

It is if c is a variable

It just has a coefficient of -1/5

[thick wharf]

wait then I'm still confused

thats what I thought

[grizzled shore]

Is $-\frac{1}{5}c$ a polynomial

[thick wharf]

okay

[warm shale]

Frosst

[thick wharf]

then -c/5 + 9c^3+d^4+c^2d^3 is a 4th degree trinomial right?

[grizzled shore]

No no

I’m getting there

[thick wharf]

okay

sorry

[grizzled shore]

Can you tell me what makes a polynomial

Because if u can’t then you can’t possibly know if something is a polynomial and why

I asked you a bunch of different expressions, and they all weren’t, so what gives?

[thick wharf]

sure so isn't a polynomial just an expression of that contains terms?

variables and coefficients added or subtracted from eachother?

[grizzled shore]

Ok

Is x² + y² = 1 a polynomial

[thick wharf]

no because it's not an expression?

[grizzled shore]

That’s the equation of the unit circle if you didn’t know

[thick wharf]

I did

but yeah

[grizzled shore]

Ok can you give me an example of a polynomial?

[thick wharf]

4x^3 + 4x^2 + 4x + 4

[grizzled shore]

So what’s the different between that and x² + y²

[thick wharf]

x^2 + y^2 itself is a polynomial but when it is set equal to something it becomes an equation no?

[grizzled shore]

No you’re thinking about expression

x² + y² is not a polynomial

[thick wharf]

wait why not?

[grizzled shore]

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

This is still a polynomial

So it being equal to something doesn’t make it not a polynomial

[steep harness]

the equation for a circle is a polynomial in two variables. it is not a functional polynomial

[thick wharf]

ohh

okay

sorry about that

[grizzled shore]

I mean it’s not within the scope of this discussion

[steep harness]

doesn't make it a non-polynomial

[grizzled shore]

Some technicalities have to be omitted or we’ll be here forever

[steep harness]

omission is not the same as false statements

[timid silo]

@steep harness It's a binomial no?

[thick wharf]

isn't every binomial a polynomial?

[timid silo]

well even monomials count

[steep harness]

yes. It is not expressible as a functional polynomial though, meaning it can't be expressed as a single variable polynomial

[timid silo]

3 is technically a monomial 😄

[timid silo]

yup! just wanted to confirm, I was confused for a bit

[steep harness]

every binomial is a polynomial, yes

[steep harness]

the technicality being omitted here would change the answer

[grizzled shore]

Yea actually you’re right upon further consideration

Thanks for chiming in 👍

I was hasty and didn’t read the question fully

[steep harness]

apologies for being blunt. oversimplification of definitions is a pet peeve of mine. I trust you got it from here

[grizzled shore]

No no it’s all good

Ok disregard the circle one, what else differs

Actually upon reading the question that’s not even the problem

The problem is just knowing what the degree of said expression means

[thick wharf]

I think the problem is with the terms right? I wasn't sure if when you have multiple exponents within a term you add the exponents to get the degree or something

[steep harness]

y= sqrt(1-x^2) is not a polynomial

[grizzled shore]

And that’s just kinda something you just have to know and remember, you just add the indices

[thick wharf]

would the degree be 7 then?

[steep harness]

this is exactly correct

[thick wharf]

oh perfect

thank you so much guys

[grizzled shore]

Yeah sorry about my confusion there

[thick wharf]

.close

[obtuse pebble]

Channel closed

Closed by @thick wharf

Use .reopen if this was a mistake.

[steep harness]

definition: a polynomial is an expression that can be expressed using only multiplication, addition, subtraction, division, and positive integer powers

[thick wharf]

perfect

thank you

[obtuse pebble]

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.

[glossy ibex]

is there any easy method to compute the volume of a prism like shape but the other face is a bit slanted?

[glossy ibex]

is there a name for this shape?

[steep harness]

are you imagining something like a cube with the top face tilted?

[glossy ibex]

yeah

and you know the area of the base

does it help if the base is convex?

[steep harness]

well, we can break it into a few parts and think of it a couple ways. Either we can shave off the tilted bit to make a prism again, then add the bit we shaved off, or we can cut into a taller prism and take away pieces until we're left with the shape

[glossy ibex]

the shaved off part is what im interested in

[steep harness]

what level of math have you taken?

[glossy ibex]

i know calculus, some linear algebra

[steep harness]

are you familiar with multivariable calculus?

[glossy ibex]

somewhat

i know it can be phrased as an integration

i want to avoid considering an integral for each case, i want to know if theres a general method for this shape

[steep harness]

the problem here is that we don't have restrictions on what direction the face is tilted

is it tilted on an axis parallel to two of the edges?

[glossy ibex]

no, theres no restriction

[steep harness]

it also doesn't help that the wedge we have on top can be any base

[glossy ibex]

damn

[steep harness]

I'm thinking that with some kind of symmetry, we could use the average of the highest and lowest points, kind of like a trapezium extended into 3d, but I don't know for sure

nope, nvm

doesn't work with triangular prisms, therefore it has counterexamples

yeah, I'd probably just define it as the double integral of the plane

[glossy ibex]

would it be true that if i found the volume of different slants, i could use it to calculate every variation by linearly combining them?

same shape with a slant in the x direction, then in the y direction. to get a slant diagonally for example youd add those volumes together

i mean the height

As a function of x,y

[steep harness]

not necessarily, because in a diagonal case, the tilt in the x direction doesn't add up to as much volume as if the tilt was orthogonal to x

[glossy ibex]

but its reasonable

i think you mean the +C

[steep harness]

we're right up at the edge of my math knowledge here, I'm thinking in terms of geometry rather than numerically

[glossy ibex]

let me rephrase

the function for the height at each (x,y) point of the shape combined with another variation will yield every possible gradient, and every variation of the shape can be expressed as a linear combination of the 2 functions (plus or minus a constant)

im quite certain this is true, and volume should add too like finding the area between 2 graphs

[steep harness]

the problem here is that the gradients here are described within f(x,y), and I'm not sure you can pull that gradient out of the function easily, since it's defined across two variables

[glossy ibex]

we know the gradient is constant based on the top of the shape

Its flat

[steep harness]

in the planar case, f(x,y)=ax+by, right? but a and b are independant, and can't be factored out to get some gradient g to get gf(x,y)

[glossy ibex]

thats the planar case, tho im still not getting what u mean

adding 2 planes would yield a plane

can we not find the slope of that?

[steep harness]

so you're saying we're making some arbitrary function g(x,y) to get f(x,y)+g(x,y)? both being planar

[glossy ibex]

yes something like h(x,y) = f(x,y) + g(x,y) should imply volume(h) = volume(f) + volume(g) + C

[steep harness]

and why are we separating this out? is it so we can set f(x,y)=K where K is some arbitrary constant, so we're only interested in the wedge on top?

[glossy ibex]

the wedge at the top yes

thats the only tricky part

[steep harness]

just set f(x,y) to 0 to get a pure wedge

[glossy ibex]

yeah

well

[steep harness]

which would still be the double integral of the curve across the base, we've just made it easier to find the bounds

[glossy ibex]

the point was to express the volume of an arbitrary wedge as a combination of 2 known cases

[steep harness]

given that it's a planar wedge, we could just be judicious in how we set our coordinate system, such that the gradient of the wedge always aligns with the basis

[glossy ibex]

Yes

[steep harness]

that way we only have to focus on cases of f(x,c)

where c is some height shift

so now it's a double integral over the base of a monovariable function

which makes it easier

[glossy ibex]

IDK man it doesnt sound like i need to integrate at all now

the case i was dealing with was a square

[steep harness]

with a square you have symmetries that can make it work as the average height times base

I was thinking to generalize

[glossy ibex]

if i compute the volume of it slanted in x, then slanted in y, i can express the volume of every slant as a linear combination

im kind of shocked that this will work so im looking for verification of this idea now

oh wait

am i shocked?

maybe this doesnt even solve my problem

i think it solves what i originally asked

but now i want to ask what if the shape is cut again by a plane through the slanted part

[obtuse pebble]

@glossy ibex Has your question been resolved?

Channel closed

Closed by @glossy ibex

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.

[dusk turret]

Integers 1-64 are placed in a 8X8 chessboard. How many ways are there to place them such that all numbers in the 1st row and column are in AP?

[dusk turret]

The annoying thing is that the numbers can't repeat.

[drifting wraith]

that sounds straightforward

[dusk turret]

Can you give a hint?

Rather than a solution?

[drifting wraith]

must be misunderstanding

[dusk turret]

My thought was that suppose 1 is in the top-left corner.

We have to enumerate all the possible valid combinations of a and b such that (1+a, 1+2a.... 1+7a) and (1+b, 1+2b... 1+7b) have no elements in common.

[drifting wraith]

oh, so like you want two progressions that have exactly one repeat

that's what it means

[dusk turret]

Also, 1+7a and 1+7b <=64.

[drifting wraith]

i thought it's just these 15 numbers can be shuffled to make 1 progression

yeah yours makes sense

essentially you want A and B that have a large lcm, then they won't intersect too early

it doesn't need to be 1, well maybe it does just not immediately obvious

why can't they start with 2

could be 12 or 27

it's harder

so are you sure it's your interpretation that's intended?

[dusk turret]

I'm fairly sure. I think I have an idea about how to go about it.

We want {a, 2a,.... 7a} and {b, 2b, ... 7b}, where a and b are distinct integers from the set {1, 2, ...9}. (For the case of the top-left number being 1)

[dusk turret]

This doesn't work, incidentally. You've used 37 twice.

And here's the rub.

[drifting wraith]

oh thanks

[dusk turret]

There are actually a very, very limited set of possibilities.

[drifting wraith]

right

1, 8

not much more, maybe a couple

[dusk turret]

I need a rule to enumerate these.

[royal basin]

the common diffs of either sequence may well be negative

[dusk turret]

That's not allowed; we have to use integers from 1 to 64 only.

OH

Yes, I hadn't considered that!!

[royal basin]

who said we needed to have the number 1 in the corner tho

[dusk turret]

Right, right. I follow.

I was trying to see if having 1 allowed for a general rule for solving.

I'm definitely stuck, then.

Got any clue?

[drifting wraith]

nope

[dusk turret]

It gets worse.

You can have the row increasing and the column decreasing.

Question from hell!!

[drifting wraith]

yes, you have both increasing, both decreasing and going different directions

ok, so the case with both increasing

1,8; 1,9 are possible

what else?

[dusk turret]

9, anything is possible—except 3 and 6.

[drifting wraith]

tru

[dusk turret]

But 9 itself is only possible if 1 is in the top corner.

[drifting wraith]

tru

3,8 is fine?

[dusk turret]

In general, if the two numbers are coprime, we want the smaller to....