help-0

[wanton lily]

i understand

for a more general question

[fallen verge]

oh wait hold on

can you do negative integers?

[wanton lily]

true i think you can

unsure

i dont think so no

[fallen verge]

if so, you have to deal with a few more factors

[wanton lily]

well i recall answering a qeustion like this in class

as in the teacher explained it

i remember only positive integers

[fallen verge]

ah ok

[wanton lily]

ok for a more general qeustion to understand sequences, if i know say a3 is -8 and a14 is 25

what can i do with that

because im looking at the questoins and most of them have something to do with that

knowing 2 of the things then asking for the others

[fallen verge]

ok, so to get from -8 to 25, how much do you need to add

[wanton lily]

33?

[fallen verge]

yes

to get from 3 to 14, how much do you need to add?

[wanton lily]

11

oh its 11 x 3

[fallen verge]

yup

[wanton lily]

what do i do with that information

[fallen verge]

so the common difference is what

[wanton lily]

11?

[fallen verge]

not quite

[wanton lily]

11/3?

[fallen verge]

just 3

[wanton lily]

hmm

ok i understnad but may i know why

[fallen verge]

33/11=3

[wanton lily]

ah ok

so i just divide the amount needed from the aN things

and the results

[fallen verge]

one way to think about it is because its an arithmetic progression, you can think about it like a line on the coordinate plane

[wanton lily]

ohh so like its an equation of a line?

[fallen verge]

a3=-8 can be like (3,-8) and a14=25 is like (14,25)

[wanton lily]

as in if it was an mx + b b would be 3

[fallen verge]

yes

m would be 3

because thats the slope

[wanton lily]

ah ok that mkaes it way more understandable

[fallen verge]

note that only works for arithmetic progressions

[wanton lily]

how about for geometric?

ok wait lets not skip,

[fallen verge]

those are of the form y=a^x

[wanton lily]

il get to geometric after this that would make more sense right

as to not clump up random information

[fallen verge]

sure

[wanton lily]

how would i find the general like

term ?? i guess

[fallen verge]

since we know our line is of the form y=3x+b, we can plug in one of what we know into the equation and solve for b

[wanton lily]

so 9 + what is 8

-1

[fallen verge]

9+what is -8

[wanton lily]

is that how?

ah ok

since y is the result

i get it ok

17?

-17

[fallen verge]

yeah dont forget the sign

[wanton lily]

so basically

i plug in x for y

[fallen verge]

you plug in x and y

[wanton lily]

i see

-8 =3x + b

like thats the equation

[fallen verge]

no

so what did we get for b?

[wanton lily]

-17

[fallen verge]

our line is of the form y=mx+b

we also know m

[wanton lily]

yeah so -8 = 3.3 - 17

that would be the equatoin rihgt?

[fallen verge]

yes, but for any general term, y=3x-17

[wanton lily]

so the common difference

is the slope

[fallen verge]

yes

[wanton lily]

meanwhile the general term is the equation itself

[fallen verge]

yes

[wanton lily]

alright

knowing this

[fallen verge]

an=3n-17

[wanton lily]

how would i go about finding the addition of the first 8 terms

[wanton lily]

hopefully my teacher doesnt care that i do it in a coordinate plane lmao

[fallen verge]

do you know sigma notation

[wanton lily]

i meanyeah?

n = something

[fallen verge]

$\sum_{n=1}^8a_n$

[wanton lily]

and a number at the top of the sigma

[ocean seal]

GarlicBredFries

[wanton lily]

wht do i plug in n as here

[fallen verge]

dont worry about that

yet

[wanton lily]

alright

[fallen verge]

do you remember the general term for an

[wanton lily]

an = 3n - 17

[fallen verge]

ok so we can plug it into our sum

$\sum_{n=1}^8 (3n-17)$

do you know sum properties?

[wanton lily]

not really

[ocean seal]

GarlicBredFries

[fallen verge]

ok so the first thing we can do is sorta "split" the sum

like this

$\sum_{n=1}^8 (3n)-\sum_{n=1}^8(17)$

[ocean seal]

GarlicBredFries

[wanton lily]

but theres no n on the one on the right

[fallen verge]

thats fine

[wanton lily]

so the one on the left is 24 right?

wait

[fallen verge]

not quite

[wanton lily]

doesnt osund rihgt

hmmmmm

the numbner at the top

is the max i can plug in for n right.

?

[fallen verge]

another thing you can do is pull out multiples

$3(\sum{n=1}^8 n)-\sum{n=1}^8(17)$

[ocean seal]

GarlicBredFries

[wanton lily]

uhh

[fallen verge]

gimme a sec lemme fix it

[vague coral]

bad tex

[fallen verge]

$3(\sum_{n=1}^8 n)-\sum_{n=1}^8(17)$

[ocean seal]

GarlicBredFries

[wanton lily]

ah i see

[fallen verge]

you should be familiar with the one on the left

[wanton lily]

so its 1 + 2 + 3 ...

[fallen verge]

up to 8 yes

[wanton lily]

x 3

[fallen verge]

yes

[wanton lily]

what was the fast addition thing again i forogt sorry

[fallen verge]

x(x+1)/2

[wanton lily]

x being the max ?

[fallen verge]

ye

[wanton lily]

72/2

36

so 36 - the one on the right

[fallen verge]

dont forget the 3

[wanton lily]

ah fuck

108

[fallen verge]

on the right, when you sum a number, you just multiply it by the max number

(this is an oversimplification)

in this case 17*8

[wanton lily]

136

108 - 136?

[fallen verge]

yes

[wanton lily]

-28

[fallen verge]

should be correct

[wanton lily]

ok lets try to apply that

to this

sending

alright il jsut type it since for some reason discord does not like me sending stuff

[fallen verge]

ok

i have to go soon, so i might leave randomly

[wanton lily]

it is fine

i shall have to ask trig to another

thank you alot for your help

so

[fallen verge]

no problem

[wanton lily]

theres a line of people

in an arithmetic series

the first guy is 7

the last guy is 139

the qeustions asking for the 15th guy

[fallen verge]

how many people are in the line?

[wanton lily]

34

so do i do

[fallen verge]

ok you have to be kind of careful here

[wanton lily]

132/33

?

[fallen verge]

oh good you got it

[wanton lily]

so common difference would be 4

[fallen verge]

is that m or b?

[wanton lily]

so y =4x + b right now

[fallen verge]

yes

[wanton lily]

and lets try

1 , 7

7 = 4.1 + b

b is 3

so an = 3n + 3 right?

i mean

4n + 3

[fallen verge]

yup

[wanton lily]

so it would be 63

the 15th guy

[fallen verge]

exactly

[wanton lily]

alright do you have time for geometric series?

[fallen verge]

maybe one

[wanton lily]

ok then i will ask the last thing of arithmetic instead

fuck

ok lets do fast ineed these two lmao

an = n^2 - n + 5

how many of these lie between

7,17

and the other question is this

arithmetic series

the n n+1 n+2

are the sticks

[fallen verge]

i can get you through the first one

but i might leave

do you know how to get the vertex/turning point of a quadratic function?

[wanton lily]

i just factor it in a form of something(x+-b)^2 + c

right?

[fallen verge]

actually nvm you wont need it

for the first one you basically just need to test values

start from 1 and go up

[wanton lily]

il start from 3 i have a good feeling about it

3 gets me 11

the limit is y 17 right?

like the result a n being 17 is the max i can go to

oh so

i can go until a4 only then

but is 17 included

?

oh noes hes gone..

do not know if im supposed to do this but

<@&286206848099549185>

sorry if it was a ping misuse

[limpid turret]

I don't feel like reading the whole thing

Can you restate what your question is?

[wanton lily]

an = n^2 - n + 5

fuck ok im back

sorry

how many of the temrs of that equatoin

lie between (7,17)

[wanton lily]

this is the question sir / maam

[limpid turret]

sure

hold on

[limpid turret]

Not sure what this means

[wanton lily]

how many results i guess im not sure

like whats the max of n

so that it lies between 7 17

like i could say a1 a2 a3 a4 but then a5 wouldnt be in 7 17

[limpid turret]

Oh you were trying to write this?

[wanton lily]

yes

how do you write that

in text

[limpid turret]

I use Microsoft Word

I don't know LateX

I'm old

I'm lazy

[wanton lily]

can i say like

a down arrow

[limpid turret]

I don't feel like learning new things

Are we given what a_1 is or any of them?

oh derp nvm

I see it now

[wanton lily]

would this be correct

since a_4 would be = 16 - 4 + 5

being 17

would the max be 17 or does it have to be below 17 to be between it

[limpid turret]

good question

What is the original problem?

Pic/Screenshot please

[wanton lily]

how many terms of this series lie between 7,17

[limpid turret]

If you use ( and ), then that normally excludes the endpoints

So it should be values greater than 7 and less than 17

[wanton lily]

OHH i thought

by that it meant

[limpid turret]

[7, 17] should mean greater than or equal to 7 and less than or equal to 17

[wanton lily]

as in a coordinate system

[limpid turret]

yeah I did too

[wanton lily]

would u be able to even solve that?

i mean i guess not since for that equation if you plug 7 in you certainly do not get 17

[limpid turret]

solve what?

[wanton lily]

if it was a coordinate instead of a valuie ting

thing

[limpid turret]

yeah coordinates wouldn't make sense

Kind of a nonsense question if asked that way

[wanton lily]

so tthe only term would be a3?

right

but then what do i do if its like abigger space in between is there a formula for this?

[limpid turret]

ah

graphing would be good

Also solving quadratic is another choice

quadratic with inequalities is kinda tricky, so you just gotta be careful.

[wanton lily]

so 7 < n^2 - n + 5 < 17

2 < n^2 - n <12

uh

what now

[limpid turret]

Nah not quite

Well kinda

You gotta solve both quadratics separately

0<n²-n-2

And n²-n-12<0

[wanton lily]

oh bc of the square?

since it could be negative or positive bc of the thing

[limpid turret]

wym

[wanton lily]

since n^2

n could be negative or positive irght

bc of the

absolute value

[limpid turret]

I guess?

You gotta consider the whole quadratic

Like if you asked me for what n is n²-n+5<10000

[wanton lily]

so 2<n^2 - n and n^2-n<12

[limpid turret]

I would solve for n

Using quadratic formula

[wanton lily]

ah ok

[wanton lily]

what do i do with this

[limpid turret]

solve both quadratics

[wanton lily]

so root 2<n-n

uhh

i might be abit stuck here

[limpid turret]

Do you know how the quadratic equation?

[wanton lily]

do icomplete square?

do you mean the -b +- root b^2 - 4ac / 2a?

so -1 + root 1 - 8 /2

i eman

-1 + root 1 + 8 / 2

so 2 / 2 being 1

cant i just

0 = n^2 - n - n

so n is either 2 or -1

and it cant be -1 since n^2

fuck its 4 11 am

i shall have to sleep

sorry for abrupt ending

but i have to wake up 3 hours alters

good night!!

.close

[lone heart]

Channel closed

Closed by @wanton lily

Use .reopen if this was a mistake.

[lone heart]

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.

[rose rivet]

Does anyone know how this works?

[merry depot]

binomial theorem

[strange meadow]

what the heck is r tho?

[merry depot]

it's just written out explicitly instead of using choose notation.

[merry depot]

arbitrary term

[strange meadow]

what?

[rose rivet]

how did it come about

[strange meadow]

theres no r in (1+x)^n

[merry depot]

that's what the r'th term will look like, whatever r is

r runs from 0 to n

[rose rivet]

im still unsure about how it links in with pascals triangle

how does it actually work

[strange meadow]

what?

[rose rivet]

it cant just be a coincidence

[strange meadow]

do you know what you're talking about?

how can there be an "rth" term

im very confused

[pliant cedar]

theyre asking how the numbers in pascals triangle are also obtained by nCr

ig

[strange meadow]

oh wait i get it

@merry depot sorry

i get it

im dumb as shit

shouldn't be helping people

[merry depot]

it's two different ways of working it out
(1+x)(1+x)(1+x), how do you get a term with x^2? You look at each term (1+x) in the product and choose two of them to have an x, and the last one must be a 1.
So you get 3 choose 2 ways to get x^2

[pliant cedar]

u r literally a helper lol 😁

[strange meadow]

im dumb as hell tho

[merry depot]

for pascal's you are adding up down paths. The number in each spot is the number of paths to get to that spot.
so each value represents the number of paths you can choose to get there

[rose rivet]

im still unsure

i dont get any of it, do you think you could think of an analogy to break it down?

is there a reason why nCr and pascals triangle are linked

i dont think im smart enough to get it

[tacit arch]

https://youtu.be/s19dWIHficY

[rose rivet]

thanks

[merry depot]

thanks, i was looking for something that could explain it waaaaay better than I could

[tacit arch]

Resources don't have to explain better than you always, they can just provide a starting point and you can fill in gaps

[rose rivet]

did nCr come first, or did pascals triangle come first

[pliant cedar]

i dont think this video answers the question

i believe the question is why you are able to obtain a term somewhere in pascals triangle using nCr

"why"

[rose rivet]

yeah

[strange meadow]

i think this is the way to go

[tacit arch]

Just Google your math history questions

[rose rivet]

please may someone explain what this person meant from 4:10 to 4:30. I understood the first part at 3:45
https://youtu.be/WeSwIp-_ozY
Thanks

[tacit arch]

nCr = nC(n-r) part?

With n as 5 and r as 2

[rose rivet]

yes

the number of ways of choosing two objects out of a selection of five is the same as the number of ways of choosing three out of a selection of five

i understood it when he showed it in the formula, but i can't picture it

5!/3!2! = 5!/2!3!

[naive valley]

intuitively, suppose you have five items and you want to choose two of them to put into a bucket. There are (5 choose 2) ways to choose the two that go into the bucket. But choosing which two go into the bucket is the same as choosing which three do not go in the bucket

so (5 choose 2) = (5 choose 3)

[rose rivet]

ah

beautiful explanation

.close

[lone heart]

Channel closed

Closed by @rose rivet

Use .reopen if this was a mistake.

[lone heart]

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.

[lone heart]

@silver robin Has your question been resolved?

[hollow shale]

Might need translating.

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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.

[grand lagoon]

If the x^2 and y^2 term coefficient of equation of circle is 2 , do I divide the whole equation by 2 to help find the coords of centre ?

[rose sigil]

you don't have to but you could if you want to make it look more familiar ig?

[lone heart]

@grand lagoon Has your question been resolved?

[hollow shale]

If you want a more explicit form for the coordinates, then sure

But as Layla says, it isn't necessary

[rose sigil]

any circle $(x-a)^2 + (y-b)^2 = r^2$ has centre $(a,b)$ and any circle that looks like $p(x-a)^2 + p(y-b)^2 = r^2$ has the more familiar form after division by $p$

[ocean seal]

💜𝓁𝒶𝓎𝓁𝒶💜

[rose sigil]

then you can see the centre (also lol didn't realize i was subconsciously using that spelling after seeing it in the original post) will still be (a,b)

[lone heart]

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.

[tribal oxide]

Im confused, i never really learnt formulas for this topic

Wouldnt statement 2 have been c(mn,m)m!?

As in what s2 is referring to

Or maybe not

If i consider that distributions have in the ratio r:r:r:r.. m times

Not that

This should be the N if N represented total number of ways of equal distribution of (mn) distinct objects among n person

[rose sigil]

is r there n/m?

[tribal oxide]

r is the ratio in the which the distributions happened

Oh wait r should just be

Yesss

[tribal oxide]

Just realized this

💀

[rose sigil]

lol

i was just thinking about it and had the same thing as you but with n/m instead of r so that's what i figured haha

[tribal oxide]

Ok time to replace r with n/m and see what it comes out as

Hm just noticed something

Tried to do this question on a smaller scale and realized

[tribal oxide]

This should evaluate to (mn)!/(m/n)!(m/n)!(m/n)!...m times

[rose sigil]

the meaning of that expression is very unclear to me

[tribal oxide]

No wait not mn

M!

N!*

[tribal oxide]

Wait

I meant this

The example i thought about was 9 pencils distributed to 3 girls equally

Let me try 12 pencils 4 girls just to be safe

Does seem to match

[rose sigil]

i'll also try one numerical example and see if it agrees with the problem

[tribal oxide]

i cant write (m/n)! As m!/n! Can i?💀

[rose sigil]

no haha

try 10 and 2 or something

[tribal oxide]

Hm then this form doesnt seem equivalent to the one in statement one

Which must mean statement 2 is wrong

[tribal oxide]

YEP S1 DOESNT WORK

As in doesnt work for whats asked for in s2

[rose sigil]

how do you know?

[tribal oxide]

I took mn=9

n=3

9 distinct pencils being distributed to 3 girls

Answer should be 9!/(3!)^3

But the formula in s1 gives 9!/(3!)^4

So s1 represents something else and s2 is false

[rose sigil]

yep looks like that does it for showing 2 is false

[tribal oxide]

I think i understand thanks

.close

[lone heart]

Channel closed

Closed by @tribal oxide

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.

[hazy totem]

How do you solve this?

[wanton pebble]

what is this

what does y' mean

[wary stream]

Pretty sure you're convert to degree, minute, second

[gray isle]

in this context,
minutes

[wanton pebble]

okiee

so like 60x+y=63?

[hazy totem]

That's exactly why I'm confused

Oh and btw

This is a trigonometry 1 question

[ornate condor]

bru wot

[hazy totem]

Me rn

Lemme send some other questions that have these symbols and I have no idea what they're referring to

Maybe it helps

[wanton pebble]

these are degree and minutes

[gray isle]

Pretty sure you're convert to degree, minute, second
in this context,
minutes

[vale wigeon]

@hazy totem do you know how degrees, minutes and seconds work?

[wanton pebble]

yp they are angle

[hazy totem]

Angles, alr

[hazy totem]

Then how do we solve this?

[vale wigeon]

do you know how degrees, minutes and seconds work?

[hazy totem]

Separately, yes. Together, no

[wanton pebble]

can you solve questions about time

[gray isle]

wdym by

together, no

[wanton pebble]

like what is 5:29 +6:54

something like that

[vale wigeon]

degrees, minutes and seconds of arc have the exact same relationship among themselves as hours, minutes and seconds of time
1 degree equals 60 arc-minutes and 1 arc-minute equals 60 arc-seconds

[hazy totem]

Idk
(I'm trying to prepare for an exam, and I have a book of its tests (that I'm solving) but idk exactly what subjects they're covering. And I sometimes need to learn new things)

[hazy totem]

Aha

[wanton pebble]

like how many minutes are in 5 hour 25 minutes

[hazy totem]

No I didn't know this

Wait minutes

Yes I do lol

[hazy totem]

So 1 degree is like 1 arc-hour?

[wanton pebble]

same it is like how many minutes are in x degree y minutes

[hazy totem]

So in 63 minutes we have 1 degree and 3 minutes

Alr thanks

This is weird though, what's the usage of this?

[wanton pebble]

what is usage of all of this?

idk

[vale wigeon]

if you wish to put it that way, yes.

[vale wigeon]

define "this"?

[wanton pebble]

this whole maths

[vale wigeon]

two of these problems are "add/subtract these angles given in d-m-s" and the other is "convert this angle in arc-seconds to d-m-s"

also you measure angles this way in navigation usually

latitutde and longitude

[hazy totem]

Oh I see

Alr made sense

Thanks

.close

[lone heart]

Channel closed

Closed by @hazy totem

Use .reopen if this was a mistake.

[lone heart]

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.

[alpine sable]

How to calculate relation matrix of R.R

[lone heart]

@alpine sable Has your question been resolved?

[mighty zinc]

By definition

Find all $(x,y) : x,y \in A$ so that $k(x + y) = 24$ for some $k \in \mathbb{N}$

[ocean seal]

fifty_two

[mighty zinc]

To create the relation matrix for the relation $R = {(x,y) \mid x+y \text{ is a divisor of } 24}$ on the set $A$, we need to determine which pairs of elements in $A$ satisfy the condition for the relation. The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, so we can form the following pairs:

[ocean seal]

fifty_two

[mighty zinc]

$(1,23)$
$(2,22)$
$(3,21)$
$(4,20)$
$(5,19)$
$(6,18)$
$(7,17)$
$(8,16)$
$(9,15)$
$(10,14)$
$(11,13)$

[ocean seal]

fifty_two

[mighty zinc]

and $(12,12)$

[ocean seal]

fifty_two

[mighty zinc]

We then represent these pairs in a relation matrix by setting the entry in row $x$ and column $y$ to 1 if $(x,y)$ is in the relation, and 0 otherwise. The resulting matrix would be:

$$
\begin{bmatrix}
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0
\end{bmatrix}
$$

[ocean seal]

fifty_two

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

[mighty zinc]

this is broken

[ocean seal]

Mr. Gamer

$$
\begin{bmatrix}
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \
\end{bmatrix}
$$
```Compilation error:```! Extra alignment tab has been changed to \cr.
<recently read> \endtemplate 
                             
l.59 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 &
                                             0 & 0 \
You have given more \span or & marks than there were
in the preamble to the \halign or \valign now in progress.
So I'll assume that you meant to type \cr instead.```

[lone heart]

@alpine sable Has your question been resolved?

Channel closed

Closed by @languid radish

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.

[molten pivot]

Similar

Triangle

Parallel lines

Transversal

Corresponding angles

If you know what all those words mean then this should not be an issue for you

[hazy totem]

I understood how to solve the question

And get the right answer

[wanton pebble]

so what u want

[hazy totem]

But this is not the way you help others. It feels more like humiliating them

.close

[lone heart]

Channel closed

Closed by @hazy totem

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.

[shut pelican]

what's happening in the third step? to my knowledge, the intersection is the common solution in both sets which is x > -2 or (-2, inf), but im not sure what it means in the third step

[molten pivot]

That was not meant to humiliate, but to guide and encourage

The deal is that math is really about language, the words that you know

If you don't know what the words mean then you can't do the math

[shut pelican]

can you help me 😄

[wanton pebble]

can you send full question

or do you want to find intersection of x>-6 and x>-2

[shut pelican]

i'm just not sure how they get x < -3 or x >= 1

[wanton pebble]

send question

[shut pelican]

i feel like (-2, +inf) is a satisfying answer

[wanton pebble]

yeah

[lone heart]

@shut pelican Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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.

[alpine sable]

in maths if you get the same answer does that always mean you did the steps correctly

[alpine sable]

i like the first method and the second one is out of my head

[silver dock]

lim x -> -∞ of x² × -1 = -∞ or +∞

[rose sigil]

hard to tell what's happening in the second one haha

[hard patio]

Why are you equating -b = -7

[hard patio]

#❓how-to-get-help

[alpine sable]

i have done this before in some questions

[alpine sable]

this one

[hard patio]

No you are finding b, by equating -b=-7

That would imply b=7

You can’t just put equal to sign

Anywhere you like

[alpine sable]

oh

[hard patio]

and

b=16

Cause there’s an equal to sign there

[alpine sable]

so what i did in first one is incorrect

[vale wigeon]

may i suggest for the future that you should write b and 6 in a way that makes them not likely to get confused for each other?

[alpine sable]

its not b and six

its actually this expression: - 7 - b = - 16

[vale wigeon]

your original equation is supposed to read -7 - b = -16, no?

that's an equation, not an expression.

and my point still stands:

the way you write the characters "lowercase letter b" and "digit six" makes it easy to confuse one for the other

criticizing only your handwriting here, not the content

[alpine sable]

i wrote it in a different way so that was showing as if it was 6

[rocky grove]

Can you differentiate between the 6 and the b?

[alpine sable]

six is entirely different and b is different too

[rocky grove]

What do you notice about the b that makes it different from the 6?

[alpine sable]

its shape

[hard patio]

Oooh Can I say? Can I say???

[rocky grove]

Sure lol but I want Ameena to notice it

2 things in the b that make it different from 6

And both lie in the stem

[rocky grove]

[alpine sable]

i was looking at this circle thing like in b you write whereas in six you turn it here isn’t any much of a difference

[rocky grove]

Alright

[alpine sable]

this exactly

[rocky grove]

Notice that there is a notch near the circle part in b

Notch that continues the stem down

Small but very distinct

[hard patio]

Write a cursive ‘b’ or some other variable

[alpine sable]

i think i didnt understand this

[rocky grove]

Or a β

[rocky grove]

Which part?

[alpine sable]

this one

[alpine sable]

oh i get it you said about a point i think what you mean by the word ‘notch’

[rocky grove]

The stem goes down a bit after hitting the circle

Also

[pliant cedar]

lol

[pliant cedar]

how it started

[pliant cedar]

how its going

[rocky grove]

When you write a b, you write it as if you are writing h but you curve it

[rocky grove]

We're trying to give advice only lol

[hard patio]

(At this point, we’re pretty much trolling)

No offence

[rocky grove]

Nah I'm genuinely trying to help

[pliant cedar]

lol i know

[rocky grove]

I don't like trolling

[pliant cedar]

its just that we are at an entirely different place right now lol

[rocky grove]

Well if there was a rude person asking for help in a math question, I'd point out the attitude first and try to help with that first.

Then we tackle the math problem

Anyways lol

@alpine sable

[hard patio]

Where’s Ameena?

[rocky grove]

Ameena left damn

[hard patio]

If we still on the same page after the attitude correction

[rocky grove]

Yep exactly

Well looks like Ameena left

[pliant cedar]

😦

[rose sigil]

aww omg this is the first handwriting help session i’ve witnessed in this server, so cute 😭

[hard patio]

I need plenty of those

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

the internet of mine went into some serious trouble so now it got connected, anyhow - thank you so very much to everyone who actually took their time answering the questions of mine, thank you @rocky grove.

[lone heart]

Channel closed

Closed by @deft eagle

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.

[lethal berry]

I just want for rectangular and cylindrical

[pliant cedar]

,rotate

[rocky grove]

Transcript: Set up triple integrals for the volume of the sphere $x^2 + y^2 + z^2 = 4$ in (I) Spherical, (II) Cylindrical, and (III) Rectangular coordinates and evaluate any one of them.

[ocean seal]

VulcanOne

[rocky grove]

Spherical coordinates should be simple I think

$r$ = radius of the sphere \
$\theta$ = angle of rotation in the horizontal plane \
$\varphi$ = angle of the slope from the vertical

[ocean seal]

VulcanOne

Something went wrong!

An unexpected error occurred while processing your command!
The error has been reported and should be fixed soon.
If the error persists, please contact our friendly support team at our support guild!

Exception

AttributeError: 'NoneType' object has no attribute 'remove_reaction'

[rocky grove]

[lone heart]

@lethal berry Has your question been resolved?

[rocky grove]

For cylindrical you apply rcosθ = x and rsinθ = y and z = z

For the equation $x^2 + y^2 + z^2 = 4$

[ocean seal]

VulcanOne

[rocky grove]

And write z's bounds as a function of r and theta

[lethal berry]

Will z's lower limit be 0?

[rocky grove]

Nope

Try rewriting the equation in terms of r, θ, and z

[lethal berry]

So - root ( 4- r^2 )?

[lethal berry]

What will be r's limits?

Theta will be 0 to 2pi , i think

[rocky grove]

plus minus

[rocky grove]

Yep

[rocky grove]

r should vary from 0 to sqrt(4)

[lethal berry]

Thnx alot

[lone heart]

@lethal berry Has your question been resolved?

[lethal berry]

.close

[lone heart]

Channel closed

Closed by @lethal 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.

[deft owl]

Heya, couple of questions:
Is this a finite region? Do I assume a new restriction on x, [0,2], to make the region finite?
Is this double integral possible (without calculator)?
Thanks!

[lone heart]

@deft owl Has your question been resolved?

[lone heart]

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.

[swift lichen]

Can anyone help me with this?

[swift lichen]

Sorry wrong one

Here

[wild trail]

where?

[swift lichen]

Damn the loading is long

Should I reset it?

Wait a min

Here finally

[wild trail]

,rotate

[wild trail]

Is this constrained with respect to the above statement that x + y = 1?

[swift lichen]

Yea

[wild trail]

Then, just put the value of either x or y in the equation you want to minimise

say, y = 1 - x

[swift lichen]

Well that could work

Lemme try

Ok I’m at this part and I have no idea where to continue

[wild trail]

How did you get square in the second fraction

[swift lichen]

Ohhhh

Damn

Sorry

Ok I’m good now

How can I leave the room once I finish?

[limpid spade]

.close

[wild trail]

.close

[lone heart]

Channel closed

Closed by @wild trail

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.

[olive canyon]

what esoteric magic is this?

[olive canyon]

if i had to guess it's the double angle formule bing used twice but i can't manually get to it :p

[solemn juniper]

Start by combining everything (sans C) into one fraction and see if an obvious double angle opportunity jumps out

[limpid spade]

Steak is french confirmed

[solemn juniper]

Je parle un peu français

(Canadian moment)

[limpid spade]

Oui,moi ussi baguette

[solemn juniper]

Hon hon etc

[olive canyon]

pls put a trigger warning before usiong french

thank you

[lone heart]

@olive canyon Has your question been resolved?

Channel closed

Closed by @olive canyon

Use .reopen if this was a mistake.

[lone heart]

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.

[steady basin]

hello

[steady basin]

right at the top is the taylor series expansion

my question is, if we had made x - theta = pi/3 and made theta = pi/180, why do we get differing answers for the approximation?

[waxen osprey]

we want x-theta to be small

[alpine sable]

pi/3+pi/180 is much further away from pi/180 than it is pi/3

[waxen osprey]

or else you cant ignore all the terms

[steady basin]

ok thanks

also

[steady basin]

WE R TOP OF THE LEAGUE SAY WE R TOP OF THE LEAGUE

[waxen osprey]

come on ggggg

been a painful couple of years until now

[steady basin]

.close

[lone heart]

Channel closed

Closed by @steady basin

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.

[lavish monolith]

According to a dietary study, high sodium intake may be related to ulcers, stomach cancer, and
migraine headaches. The human requirement for salt
is only 220 milligrams per day, which is surpassed in
most single servings of ready-to-eat cereals. If a random sample of 20 similar servings of a certain cereal
has a mean sodium content of 244 milligrams and a
standard deviation of 24.5 milligrams, does this suggest at the 0.05 level of significance that the average
sodium content for a single serving of such cereal is
greater than 220 milligrams? Assume the distribution
of sodium contents to be normal.

[lavish monolith]

why did we use t distribution not normal one

it says standard deviation not sample standard deviation

shouldn't we use z table not the t-table ?

[swift halo]

To determine whether the average sodium content for a single serving of the cereal is significantly greater than 220 milligrams at the 0.05 level of significance, we can use a one-sample t-test.

In this case, the null hypothesis is that the average sodium content is equal to 220 milligrams, and the alternative hypothesis is that the average sodium content is greater than 220 milligrams. The test statistic is:

$$t = \frac{\overline{x} - \mu_0}{s / \sqrt{n}}$$

where $\overline{x}$ is the sample mean (244 milligrams), $\mu_0$ is the hypothesized mean (220 milligrams), $s$ is the sample standard deviation (24.5 milligrams), and $n$ is the sample size (20).

Plugging these values into the formula, we get:

$$t = \frac{244 - 220}{24.5 / \sqrt{20}} = 2.44$$

To determine the p-value for this test statistic, we can use a t-table or a computer program to find the probability of observing a value at least as extreme as the test statistic under the assumption that the null hypothesis is true.

At the 0.05 level of significance, the critical value for a one-tailed t-test with 19 degrees of freedom is 1.725. Since the test statistic (2.44) is greater than the critical value, we can reject the null hypothesis and conclude that the average sodium content for a single serving of the cereal is significantly greater than 220 milligrams at the 0.05 level of significance.

I hope this helps! Let me know if you have any more questions.

[ocean seal]

ArBo

[lavish monolith]

my question why did we use t-test not z-test

[worn fox]

yeah they blindly threw your question at an ai bot

[swift halo]

We use a t-test in this case because the population standard deviation is unknown. A t-test is a statistical test that is used to compare the mean of a sample to a hypothesized mean when the standard deviation of the population is unknown and the sample size is small (typically less than 30).

On the other hand, a z-test is a statistical test that is used to compare the mean of a sample to a hypothesized mean when the standard deviation of the population is known and the sample size is large (typically 30 or more).

In this case, since the population standard deviation is unknown and the sample size is less than 30, we use a t-test to compare the mean of the sample (244 milligrams) to the hypothesized mean (220 milligrams).

[lavish monolith]

i'm not trying to be rude but chatgpt is so bad when it comes to math.

but i appreciate it

[swift halo]

Really? Im just testing it seems really good

[lavish monolith]

no it's sucks believe me

.close

[lone heart]

Channel closed

Closed by @lavish monolith

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.

[alpine sable]

wha?

[alpine sable]

how did he change it

[vale wigeon]

factor out 3x

[alpine sable]

OH

LMAO

Fair enough thank you so much

.close

[lone heart]

Channel closed

Closed by @still mulch

Use .reopen if this was a mistake.

[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

I'm not fully sure how he was able to say that 3x is 0

is it because its technically x-0 so its 0??

I get the x-2 but not the 3x

[outer lark]

0/3 = 0

[alpine sable]

but why did he devide 0 by 3??

[outer lark]

so you can isolate the x

3x = 0 -> (3x)/3 = 0/3

x=0/3

[alpine sable]

Oh wow I see I see

Thank you clarkie

.close

[lone heart]

Channel closed

Closed by @still mulch

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.

[remote kelp]

Hello

[remote kelp]

In math can an equation Form second degree have real solutions and yet cannot be solved in factoring?

and i said hello first because if i don't somebody will take the chat 🦆

[gray isle]

depends if you're using conventional factoring methods

[remote kelp]

And what is non conventional way? (i probably know it, just my first language isn't English so i don't know the terms)

[wary stream]

I mean technically x^2 - 12x + 6 has real solutions but can't be factored so the only method would be graphing or quad formula

[gray isle]

*can't be factored over the reals/rationals

for basic factorisation you'd only be considering nice values

[remote kelp]

oh 🦆 so if the Discriminant is positive that doesn't necessarily mean i can factor it so i would have to use the quadratic formula

[gray isle]

if the discriminant is a perfect square, there'd be a nice factorisation

[remote kelp]

oh that's such awesome note, i don't know why they didn't mention in it in the textbook

https://cdn.discordapp.com/emojis/844594907033501756.png?quality=lossless&size=56

[gray isle]

i mean if you already started work with the discriminant, you might as well use the whole formula

[remote kelp]

but you mentioned having another ways to factories? What are those methods?

[gray isle]

for

x^2 - 12x + 6
you could start with completing the square
=(x - 6)^2 - 30
and factor that as a difference of two squares
= (x-6 + sqrt(30))(x-6 - sqrt(30))
(which technically counts as factorising, and you can get the solutions from that)

[remote kelp]

Sometimes i can do it in my head so it would save some time

like if a Was 1

or if b isn't that large (i mean I already have memorized up to 15²)

from day to day in school experience i never actually tried to memorize it

OK so is this always true?

i mean i guess it's, it does make sense cuz if a is perfect square the square root will cancel

[remote kelp]

Didn't see your message, and Yup i already knew Completing the square and I'm actually using it sometimes (the question demands me to solve it like this)

so my question is there's a situation where i can't solve it with completing the square (if i have to) yet the Discriminant > 0

[gray isle]

no

[remote kelp]

thanks human!

.close

[lone heart]

Channel closed

Closed by @remote kelp

Use .reopen if this was a mistake.

[lone heart]

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.

[alpine sable]

How do I solve

2y-5(y-2)=-8```
I get different results every time and the answer should be ``p=26``

[vague mirage]

How did you solve
$2y-5(y-2)=-8$

[ocean seal]

Arnab Pal

[vague mirage]

Show me your process

@alpine sable

[alpine sable]

@vague mirage here

[vague mirage]

I know what you did wrong

It is +10 not -10

$2y-5y+10=-8$

[ocean seal]

Arnab Pal

[vague mirage]

Not -10

[alpine sable]

How?

[vague mirage]

Observe

[alpine sable]

Ah

I see

[vague mirage]

You have to multiply each thing by -5

[alpine sable]

Yeah i see

[vague mirage]

What's -5 times -2

Yupp

[alpine sable]

10 of course

Thank you

.close

[lone heart]

Channel closed

Closed by @steady crystal

Use .reopen if this was a mistake.

[vague mirage]

Welcome

[lone heart]

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.

[open marten]

limit (x+1)-((x+1) ln (x+1)) Derivability at -1?

[lone heart]

Please don't occupy multiple help channels.

[open marten]

yea pls

ok I just hope you understood my question

[worn fox]

<@&268886789983436800>

[devout summit]

<@&268886789983436800>

[tall wing]

banned

[open marten]

????

[tall wing]

they posted a very gory video

[open marten]

who ?

[worn fox]

the person who was pretending they were going to help you

[open marten]

lol

Anyway, can you help me ?

[worn fox]

what exactly is your question

[open marten]

limit (x+1)-((x+1) ln (x+1)) Derivability at -1?

Something we call derivability

[worn fox]

you're gonna need to be more specific

or send a picture

[open marten]

limit of (f(h-1)-f(-1))/h

f(-1)=0

[worn fox]

f(x) = ln(1+x)

?

[worn fox]

oh

gross

[open marten]

hahaha

[worn fox]

you want to find the derivative (from the right) of that function at x=-1

[worn fox]

so plug into here to start

[open marten]

ok

I try and found it

+inf but i think it wrong

[open marten]

yea

[worn fox]

looking at the graph that should be correct yeah

[worn fox]

yeah the slope is getting steeper and steeper the closer you get to -1

[open marten]

that mean, it accept derivation or not at x = -1?

[worn fox]

what are you asking?

[open marten]

it accept a tangent at -1 or not?

[worn fox]

no it is not differentiable at -1

y=-1 is a tangent to the graph at x=-1 but its not unique

[open marten]

oh ok

[open marten]

ok so for this one
is there asymptotic straight y=0 or not?

[worn fox]

not sure what you mean

are you asking if y=0 is an asymptote?

[open marten]

this one

[open marten]

yea but for this new one

[worn fox]

that is not a graph of this function

oh ok

well recall what it means for a line to be an asymptote

[open marten]

sorry it is x=0

[open marten]

i think limit of function = inf

where x->number

[worn fox]

for a vertical asymptote, vaguely yes

could be plus or minus inf on either side

[open marten]

I calculated on both sides and got +inf and -inf

so x=0 vertical asymptote ?

[worn fox]

well you calculated it wrong, look at the graph

[open marten]

i calculate it with the f((x)-1)

[open marten]

this

[worn fox]

which has this graph

and the limit as x goes to 0 is clearly not inf or -inf

[worn fox]

You should know yourself, just by looking at the blue graph, that the limit as x tends to 0 is not infinity or -infinity

[open marten]

it 0

[worn fox]

it is 0

[open marten]

so there is no vertical asymptote x=0 ?

[worn fox]

you tell me

[open marten]

i think there is no but the same time h(x) 'the blue one' = 0 is undifined

[worn fox]

all you need to know is the definition of vertical asymptote

[open marten]

I will look for him now

[lone heart]

@open marten Has your question been resolved?

[lone heart]

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.

[steady basin]

why is my radius of convergence wrong?

[pseudo ice]

What'd you do here? What happened to the n at the top? (I do see you cancelled out the 3's)

[steady basin]

silly me

we gotta use l hopitals rule here

isnt it?

[pseudo ice]

Remember, you can, but you don't need to

[steady basin]

since its infinity over infinity

[pseudo ice]

Change it to
$$
\frac{n}{n + 1} = \frac{\cancel{n}}{\cancel{n}}\frac{1}{1 + 1/n}
$$

[steady basin]

true

but if i use l hopital rule

[ocean seal]

chartbit

[steady basin]

1/1

bosh

[pseudo ice]

Yep, that works too, whichever gets you to the answer(!)

I'm just old school and prefer the algebra of limits method tbh 😂

[steady basin]

so to find the interval of convergence

i understand itll be 0,1

but how do i know whether to use square or circle brackets?

[pseudo ice]

Ah, that is a very good question there!

Initially, you know that it'll converge at least on (0,1), however the ratio tests don't tell you anything about the endpoints 0 and 1

You would have to test those endpoints 0 and 1 separately to find out whether they'd be included or not

Which from a quick look and doing no work whatsoever, I'm guessing they're not (at 0 you get (-1)^n 3n, and at 1 you get 3n, and neither of those converge to zero)

So here, assuming I've done no boo boos, it would be exactly (0,1) as your convergence interval, and the endpoints aren't included!

(There's me going off on a long answer to a simple question but hope that made some kind of sense!)

[steady basin]

so ive got this

just still confused on how we check it converges?

and to what value r we checking it converges to and why?

[steady basin]

haha

[pseudo ice]

It doesn't converge, because the sequences $(-1)^{n} 3n$ and $3n$ do not converge to zero

[ocean seal]

chartbit

[pseudo ice]

If a series converges, then the sequence it's made up of must converge to zero

(but not necessarily vice versa)

So if the sequence doesn't converge to zero, you know the sum cannot converge

You're familiar with that right?

[steady basin]

so is convergent when n approaches infinity, it approaches 0?

[pseudo ice]

Basically let me state it a bit more carefully: if the series $\sum_{n=n_{0}}^{\infty} a_n$ converges, then the sequence $a_{n} \to 0$ as $n\to\infty$

[ocean seal]

chartbit

[steady basin]

is it always 0?>

when we tlak about converging

for any sequence?

ight

and is diverging when the sequence approaches infinity?

[pseudo ice]

Yes - a way to see it is via partial sums and taking limits in that

[pseudo ice]

If the sequence does not converge to zero, then the sum doesn't converge at all

[steady basin]

so is it divergent then?

[pseudo ice]

It can converge to any other number, diverge to infinity or -infinity

Or just be generally divergent, if it's not got zero as a limit, that series will not converge

[pseudo ice]

Yep, those series are divergent!

[steady basin]

so what would be the definition of divergent

as n tends to infinity, sequence tends to infinity?

[pseudo ice]

The definition of the series $\sum_{k = k_{0}}^{\infty} a_k$ converging is that the sequence made up of partial sums $s_{n} = \sum_{k=k_{0}}^{n} a_k$ converges

And the series diverges if s_n diverges

[ocean seal]

chartbit

[steady basin]

is this for all sequences or just this sequence only?

[pseudo ice]

Well, that's a fact that holds in general, but in this case we just happen to meet it

For other general power series, it might be that we converge at the endpoints

But if you're given a general question and you test the endpoints, and notice that you're summing a sequence that doesn't converge to zero, you already know that the series diverges there

(sorry I'm being long, but I'm being very careful with my words so that I don't become misleading!)

[steady basin]

nah np

this makes sense now

thx alot

[pseudo ice]

No problem hopefully that helped, and didn't get you considering life

[steady basin]

for this limit do u reckon repeated versions of l hopitals rule would be faster than expanding the brackets out and splitting the fraction?

[pseudo ice]

For me, I'd just do $\frac{n^{3}}{(n+1)^{3}} = \left( \frac{n}{n+1} \right)^{3}$ then algebra of limits impo

[ocean seal]

chartbit

[pseudo ice]

Inside the brackets do this

No need to binomially expand or anything

[steady basin]

wait so what do i do from this

[pseudo ice]

Change that to $\left( \frac{1}{1 + 1/n} \right)^{3}$ as per my previous "up there" quote

[ocean seal]

chartbit

[pseudo ice]

Obviously $x \mapsto x^{3}$ is continuous therefore you can just take the limit of the inside cubed

[ocean seal]

chartbit

[pseudo ice]

So get $1^3 = 1$

[ocean seal]

chartbit

[steady basin]

yep kl

cheers

[pseudo ice]

No probs

[steady basin]

.close

[lone heart]

Channel closed

Closed by @steady basin

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.

[azure leaf]

This problem originated from openstax calculus 3 section 2.1. I have attempted the problem and when I compare my answer to the book, it was wrong. Could you please help me find where I messed up?