help-39

[distant pendant]

Right

Ok then thank u soo much for ur help

[pearl pond]

@distant pendant Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[pulsar stump]

can $< \emptyset, 1>$ be an element of the group?

[jolly parrot]

Ayanokoji

[pearl pond]

Please don't occupy multiple help channels.

[pulsar stump]

or set

[last moth]

Please only have one question open at a time

Do you want to close your previous channel, to ask this new question?

[pulsar stump]

I switched questions and this is pretty small (1m or 1 liner)

[hollow cobalt]

Yes, that is an element of R

[pulsar stump]

I mean I can

[pulsar stump]

how's it the condition at the end work then? for any condition I mean

[last moth]

I think the word you're looking for is "relation", not "group"

[pulsar stump]

oh it is, mb

[last moth]

It's vacuously satisfied. It says "check through all the elements of A and make sure they are less than or equal to n"

Since there are no elements of A to check (because A is empty), we are done

[pulsar stump]

great, ty mate I understand now

[last moth]

No problem

[pulsar stump]

.close

[pearl pond]

Channel closed

Closed by @pulsar stump

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.

[pulsar stump]

if I have an odd number n, will n+2 always be odd?

[quiet tendon]

yes

[flint zenith]

yes

[pulsar stump]

great ty guys

[quiet tendon]

the proof for that is really simple too, an odd number is any number of the form 2p + 1 where p is an integer, so let n = 2p + 1, then n+2 = 2p + 1 + 2 = 2(p+1) + 1 = 2q + 1 where q is an integer

therefore n+2 is odd

[midnight haven]

As in trigonometry, if we get an odd nπ/2 and and even nπ/2 how to determine which quadrant to choose?

[pulsar stump]

yeah that's a great proof ty I needed to see this

.close

[pearl pond]

Channel closed

Closed by @pulsar stump

Use .reopen if this was a mistake.

[pearl pond]

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.

[pulsar stump]

can $<\emptyset,\emptyset>$ be an element of R?

[jolly parrot]

Ayanokoji

[tropic saddle]

no

emptyset is not a natural number

[pulsar stump]

thank you

.close

[pearl pond]

Channel closed

Closed by @pulsar stump

Use .reopen if this was a mistake.

[pearl pond]

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.

[brisk marsh]

If the solution of the differential equation $$\frac{dy}{dx} + e^x(x^2 - 2)y = (x^2 - 2x) (x^2 - 2)e^{2x}$$ satisfies $y(0) = 0$, then the value of $y(2)$ is?

[jolly parrot]

♥•♥•♥•♥

[tulip ore]

did you get stuck figuring out $\int e^x(x^2-2)\dd{x}$?

[jolly parrot]

mtt

[brisk marsh]

no

i wrote $x^2 - 2 = x^2 - 2x + 2x - 2$

[tulip ore]

why?

[brisk marsh]

differenciation of $x^2 - 2x = 2x - 2$

[jolly parrot]

♥•♥•♥•♥

[brisk marsh]

then i can use by parts to solve the integral

[tulip ore]

so this edited post still has a typo youre saying?

[brisk marsh]

?

wait lol

[jolly parrot]

♥•♥•♥•♥

[brisk marsh]

that's better :D

[tulip ore]

so what part are you stuck on

[brisk marsh]

i m stuck after tht

when i calculate integration factor and put it in the equation

[tulip ore]

are you stuck at this step

@brisk marsh

[brisk marsh]

yes

[tulip ore]

you see that exponent in e^((x^2 - 2x)e^x)?

it would be nice if that exponent was just u

so let u = (x^2 - 2x) e^x

then from there, figure out how to write the rest of the integral in terms of u and u'

part of it involves splitting e^(2x) into e^x * e^x

[pearl pond]

@brisk marsh Has your question been resolved?

[tulip ore]

@brisk marsh are you still stuck

[brisk marsh]

yeah

[tulip ore]

are you stuck on the integral

[fallen robin]

you only need the integral from 0 to 2, since you know I(0) = 0

[tulip ore]

that doesnt work out when I tried it

the (x^2 - 2x) term on the left prevents any info about y(2) from getting out

@brisk marsh hello?

[pearl pond]

@brisk marsh Has your question been resolved?

[fallen robin]

irrc its supposed to be e^((x^2-2x)e^x)?

[tulip ore]

the integral?

[fallen robin]

the integration factor

$e^{(x^2-2x)e^x}y = I(x)$, not $(x^2-2x)e^xy

[tulip ore]

we already covered the integration factor to get here, what is your point?

[jolly parrot]

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

[tulip ore]

why are you calling that an integration factor?

the integration factor then is $\mu(x)=e^{\int p(x)\dd{x}}=e^{(x^2-2x)e^x}$

[jolly parrot]

mtt

[tulip ore]

thats the convention Ive learned

this was in a previous step

[fallen robin]

yes but here you wrote it as $(x^2-2x)e^x$?

[jolly parrot]

Catted

[tulip ore]

oh tahts a typo, I completely glossed over the missing e^

I really need to take your hints next time

[fallen robin]

i think the guy already got it

[tulip ore]

@brisk marsh did you already figure this out

[brisk marsh]

no i went to watch yt instead of solving it 😭

[tulip ore]

bruh

I pinged you a few times

anyways there was a typo in the image before

this should be the correct version

did you do the u-sub yet?

[brisk marsh]

there is only e^2x on the right

so how abt we put it as e^x into e^x

[tulip ore]

I already said that

[brisk marsh]

oh

[tulip ore]

thats correct

[fallen robin]

why not just evaluate the integral from 0 to 2 now

[brisk marsh]

wait lemme catch up

[tulip ore]

they need to take their time

@brisk marsh also are you allowed calculators

[brisk marsh]

dont i need to solve the definite integration first

i mean indefinite

[brisk marsh]

no

[fallen robin]

$e^{(x^2-2x)e^x}y=\int_{0}^{x} (x^2-2x)(x^2-2)e^{2x}e^{(x^2-2x)e^x} ,dx$

[jolly parrot]

Catted

[brisk marsh]

yeah

i got tht part

[tulip ore]

what

[fallen robin]

plug in 2 to get $y(2)=\int_{0}^{2} (x^2-2x)(x^2-2)e^{2x}e^{(x^2-2x)e^x} ,dx$

[jolly parrot]

Catted

[brisk marsh]

wait how did u get the limits

isnt is supposed to be indefinite integration

then i get the value of integration constant by putting y(0) = 0

[fallen robin]

yeah

i forgot that

[tulip ore]

@brisk marsh so did you do the u-sub yet?

[brisk marsh]

no

i hvnt figure out yet wht to sub

[tulip ore]

do you remember what I told you?

about the exponent?

this is your integral

it would be nice if that long exponent in the integral was just a u

so I suggest that you do u = (x^2 - 2x) e^x

@brisk marsh so go u-sub u = (x^2 - 2x) e^x

[brisk marsh]

if i put $ t = (x^2 - 2x)e^x$
then $\frac{dt}{dx} = e^x(x^2 - 2x) + e^x(2x - 2)$

[tulip ore]

keep going

its \frac

[brisk marsh]

oh

[tulip ore]

also you can do \dv{t}{x}

[jolly parrot]

♥•♥•♥•♥

[tulip ore]

to get $\dv{t}{x}$

[jolly parrot]

mtt

[tulip ore]

its shorter to type

[brisk marsh]

cool

[tulip ore]

now simplify dt/dx for me please

[brisk marsh]

$\dv{t}{x} = e^x(x^2 - 2)$

[jolly parrot]

♥•♥•♥•♥

[brisk marsh]

ohhhhh!

I got it

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[brisk marsh]

i fricking got it!

.reopen

[pearl pond]

✅

[brisk marsh]

ayo dont close the channel just like tht

i just got the answer lemme thank all these ppl

THANK YOU SOO MUCH!

[tulip ore]

np

also thank cattedf

[brisk marsh]

it was pretty dumb of me not see tht

yeah thanks to everyone man

[tulip ore]

if you watch youtube then theres a good chance you can forget anything

I can attest to that

[brisk marsh]

lol

i am just not in the mood to do em

so i am half heartedly doin em

maybe i just just commit to watchin yt and do em later

[tulip ore]

or you can commit to finishing this now

so that when you commit to watching yt, you have no time pressure

[brisk marsh]

yeah seems like a reasonable thing to do

.close

[pearl pond]

Channel closed

Closed by @brisk marsh

Use .reopen if this was a mistake.

[pearl pond]

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.

[ivory hornet]

Kacka found a number n that has k divisors (including 1 and n itself). She took all these divisors, sorted them in ascending order, and numbered them as 1 = d1 < d2 < … < dk-1 < dk = n. She found that the following equation holds:

377 * d2 + dk-1 = n

Find n.

[ivory hornet]

I have no idea how can i solve this

[pearl pond]

@ivory hornet Has your question been resolved?

[light helm]

d_2 and d_(k-1) will be factor pairs and multiply to n

[pearl pond]

@ivory hornet Has your question been resolved?

[pearl pond]

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.

[raven spade]

how do i do this question

[raven spade]

lemme share my wirk

[raven spade]

,rotate

[raven spade]

.

[raven spade]

it should be sin^2(2x) in the denominator in the last step mb

but yea

[glacial sequoia]

why did you just split it at the start

surely you know the integrals of csc^2(x) and sec^2(x)

[raven spade]

oh yeahs

forgot about that

but how do i use the integrals of them in the question

∫[(sec^2(x)*cosec^2(x)][3+sin^2(x)] dx

is what im getting

[somber needle]

How r u getting this its not correct

[raven spade]

oh wait

[somber needle]

When u distribute the denominators u should be getting integral of 3cosec^2(x) + 4sec^2(x)

[raven spade]

edited

[raven spade]

wdym distribute the denominators

[somber needle]

I mean like if its written (5+6)/2 u can write 5/2 + 6/2

[raven spade]

right yeahs

[somber needle]

Similarly u do this and cos and sin will cancel out

[raven spade]

uh huh

okay

[raven spade]

yeah so i got 12∫dx/(sin2x)^2 + tan(x)

dunno what to do with that integral though

[pearl pond]

@raven spade Has your question been resolved?

[pearl pond]

@raven spade Has your question been resolved?

[pearl pond]

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.

[lavish flax]

hi! just wondering if anyone could please help me with this question. i've already got 1a, which is 1+5x+10x^2+10x^3+5x^4+x^5

[sly dagger]

right

so ur after 1b?

[sly dagger]

.

u first want to find the ratio between each term

[lavish flax]

yes!

[lavish flax]

it's -1 right? but idk how that impacts (1+x)^-1

[sly dagger]

its not necessarily -1

-1 would producee a series of 1-1+1-1+1-1...

[lavish flax]

so -x?

[sly dagger]

yes

knowing that is there some formula u could use?

[lavish flax]

would it be ok if i use the binomial theorem formula? would it still work if the power is negative though?

[sly dagger]

remember that this is a series

[lavish flax]

oh, so would this then be the sum of geometric series? finite

[sly dagger]

<@&268886789983436800>

hmm this finite stuff is throwing me off

hmm is it in reference to this series

[lavish flax]

i'm not actually sure whether to use sum of finite or infinite geometric sequence - i didn't really understand the first line of 1b to be honest, i just took finite from the question.. but technically there should be infinite terms in the power series they've given, right? this is what i'm referencing right now

[sly dagger]

right

that first line also throws me off

i think it should be an infinite series

assuming that its an infinite series, what would be its sum?

[lavish flax]

let me send you a picture of my working out right now

i've proven it's (1+x)^-1 i think, but i'm not sure what it means by state the values of x for which the equality is true. wouldn't it be all real numbers, because x can be anything?

[sly dagger]

not necessarily

note that our ratio, r, must have a magnitute less than 1

since the sum of an infinite series only converges (doesnt go to infinity) if it's ratio has a magnitute of less than 1

[lavish flax]

ohh, i see!! so -1<-x<1? as the ratio is -x

[sly dagger]

correct

[lavish flax]

so it would be like 1>x>-1 if we convert the negative to a positive sign

[sly dagger]

yes

[lavish flax]

ohh i got you thank you so much!! i haven't really looked at 1c so i'll have a look considering the steps for 1b. thank you again :))

[sly dagger]

all good

[lavish flax]

Hi, so sorry to bother you again! I just finished c and d but I’m unsure how to solve for e. There seems like there would be 2 options for either an odd or even power — as in, if the power was odd, the sequence would start with a negative one, whereas it would start with positive 1 if the power was even

[sly dagger]

right

so its good that u noticed it alternates starting positive and negative

do u notice anything about the coefficients of each term?

[lavish flax]

all coefficients seem to be alternating positive and negative? the power of 3 seems like they're triangular numbers and the power of 2 is just consecutive numbers

[sly dagger]

wait

i think u made a slight mistake with the 2nd derivative

ur 3rd sequence should also start with a positive

these are different

[lavish flax]

OH you're so right, i think i copied the wrong sequence, let me fix that real quick

[sly dagger]

yes thats correct, but there is a specific place that they come from

[lavish flax]

pascal's triangle?? could i then use combination to calculate the coefficients?

[sly dagger]

yes

do u see where on pascals triangle that these coefficients are coming from?

[lavish flax]

the diagonals? i am trying to figure out how to represent these using combination

[sly dagger]

yes

it may be easier to work with the diagonals going from top right to bottom left

since the series of 1's are all the first number of each row, and the 1,2,3,4 series are all the 2nd number of each row, and the 1,3,6,10, series are all the 3rd numbers of each row.

[lavish flax]

something like that? i'm unsure if the lower number would be 1, but i'm guessing the top number has to increase by 1 with every variable

[sly dagger]

hmm u have the right concept

but the top number represents the row

and the bottom number represents the position in the row

[midnight haven]

Nice handwriting my guy

[sly dagger]

it may be easier to focus on just the series of 1's then build on from there

[lavish flax]

so 1 would be like the last number in each row, and then the position decreases by 1 with each further term? does this make sense 😭

[sly dagger]

the series of 1's are just the first number of each row, but remember that pascals triangle starts from 0, so they are technically the 0th number of each row, and note that we just have to increase the row number each team so it would be 0C0,0C1,0C2,0C3,etc

[sly dagger]

i think ur getting ur directions mixed up, pascals triangle reads from left to right

[lavish flax]

so 0 is the row number for every term in the sequence? sorry i am a bit confused :((

[sly dagger]

0 is the position in each row

remember that a row goes from left to right

so each row goes like

1

1,1

1,2,1

1,3,3,1

1,4,6,4,1

1,5,10,10,5,1

notice that the 1 is always the first number of each row

but like i said, in pascals triangle we start from 0, so they are the 0th number of each row

[lavish flax]

yes, but 1 is only the first term of the sequence, right? the next term would move to the next row, with the second term and thus the 1st number in a combination representation --

[sly dagger]

lets focus on just (1+x)^-1 for now

each term has a coefficient of 1 correct?

[lavish flax]

yes!

ah so it would be like C (0,0), C (1,0), C(2,0)?

[sly dagger]

correct

now lets take a look at (1+x)^-2, ignoring negatives for the moment, the coffecients are 1,2,3,4,5,6,7,... etc right

[lavish flax]

yes

[sly dagger]

which happen to be the 2nd number of each row?

in pascals triangle

[lavish flax]

oh! yes

so the bottom number would always be 1?

[sly dagger]

correct

like wise for (1+x)^-3 all bottom numbers would be 2

can u notice a correlation between the power and the bottom number?

[lavish flax]

bottom number is 1 less than the power?

[sly dagger]

correct

[lavish flax]

like this?

[sly dagger]

yeah that looks fine i think

[lavish flax]

then the generalized eq would be like this? (on top)

[sly dagger]

yes

[lavish flax]

ohh okay thank you so much for the help!! i'll have another look at this to consolidate my understanding 💙

[sly dagger]

aight all good

gl

[lavish flax]

thank you :)

.close

[sly dagger]

dont sweat

it

[pearl pond]

@lavish flax Has your question been resolved?

[pearl pond]

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.

[unborn cosmos]

How do you use stoke's theorem on a cylinder-like surface?

[unborn cosmos]

for e.g., this question:

the answer is apparently -16π

[spiral pivot]

@unborn cosmos Stoke's theorem can only be applied on surfaces with no holes in them. In order to get the area of the surface with a hole you can apply Stoke's theorem twice and subtract.

Imagine a fully connected surface, bounded only by C2, then consider just the hole bounded by C1. If we find the integral of C2 to be I and C1 to be J, wouldn't it stand to reason that the integral of the surface with the hole in it is I - J?

[pearl pond]

@unborn cosmos Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[unborn cosmos]

.reopen

[pearl pond]

✅

[unborn cosmos]

where is the "hole" coming from>

[spiral pivot]

@unborn cosmos the surface has a hole through it, topologically

[unborn cosmos]

yeah that's what i thought

hmmm

[unborn cosmos]

why I-J?

gahh

i'm getting confused with the orientations

and which one is negative

[spiral pivot]

Clockwise is negative

[unborn cosmos]

anwyays

so the basic idea behind this is that

topologically, this is equivalent to consider a disc with a hole in it

outer boundary = C2

inner boundary = C1

[spiral pivot]

Yup

[unborn cosmos]

for the line integral or the surface integrael?

oh wait

[spiral pivot]

The line integral, right hand rule to the normal vector of the surface

[unborn cosmos]

and so for the "hole", I just pretend that it wasn't a hole

[spiral pivot]

Yup

[unborn cosmos]

and compute the line integral on that

[spiral pivot]

Exactly

[unborn cosmos]

but it's actually a hole

so I minnus it away

[spiral pivot]

Exactly

[unborn cosmos]

THANKS!

[pearl pond]

@unborn cosmos Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[mint tiger]

I need help

[quiet sentinel]

what do you need help with here??

[mint tiger]

Dis

[boreal patio]

ok so r=13 , A=pirr

so you'll have 169 * pi

calculate it

[mint tiger]

I'll try

[boreal patio]

530.929

and it needs to be in 1 decimal place

so the answer would be 530.9

[mint tiger]

Thx

[boreal patio]

np

[mint tiger]

Wait

What if its 21

[mint tiger]

Instead of 13 it's 21

Cuz I'm on the 2nd question now

[boreal patio]

ok so put 21 instead of 13

21 * 21 * pi

[mint tiger]

Which is?

[boreal patio]

use calculator if you're stuck on simple questions

[mint tiger]

But idk how to put equations

[boreal patio]

21 * 21 * pi = 441 * pi = 1385.44236

[mint tiger]

O_o

[boreal patio]

but be careful what the question wants

[mint tiger]

My mind is mush now

[mint tiger]

Is that the answer?

[boreal patio]

no

the question might ask for 1.d.p

maybe 2.d.p

[mint tiger]

It's 1dp

[boreal patio]

ok so you tell me what should it do

[mint tiger]

Umm

Idk

Would it be 1385.5

[boreal patio]

exactly

and continue the other questions like this

[mint tiger]

It says its wrony

[boreal patio]

I don't see clearly

[mint tiger]

The radius of the circle below is 21mm

[boreal patio]

😄

you should've told me that before

[mint tiger]

Calculate the area of the circle

[mint tiger]

What?

[boreal patio]

that it's 21mm not cm

[mint tiger]

What's the dif?

[boreal patio]

you have to convert the units

[mint tiger]

O

[boreal patio]

21mm is 2.1cm

so Area=pirr

so 2.1 * 2.1 * pi = 13.8544236

in 1d.p = 13.8

[mint tiger]

It's wrong ot says now

Is it cuz it wants he answer in mm2

[boreal patio]

I gave you the answer in cm

[mint tiger]

Want ste answer in mm2

[boreal patio]

that's the answer in mm

[mint tiger]

K

Wait

I'm confused asf

[boreal patio]

?

[mint tiger]

That's clearer

[boreal patio]

yeah I think that would be the answer

[mint tiger]

It's wrong it says

[boreal patio]

I don't know why let's ask others

<@&286206848099549185>

[boreal patio]

hmmm

[mint tiger]

?

[boreal patio]

let me think

[mint tiger]

Ok

[boreal patio]

.4

[mint tiger]

Huh?

[boreal patio]

1385.4

[mint tiger]

Yess

[boreal patio]

you round it wrong

[mint tiger]

Mb

[boreal patio]

when you round something be careful

[boreal patio]

same work

7.3 * 7.3 * pi

in 1.d.p

if the 2nd.d.p = 5 or more , you add 1 to the first d.p

[mint tiger]

What's the answer cuz I don't understand *

[boreal patio]

the radius is 7.3

the area of the circle is pi * r^2

right ?

[mint tiger]

Idk

[boreal patio]

If you feel tired or something go rest or sleep maybe

[mint tiger]

Nah I need to do this first

It's due tmr

My hw

[boreal patio]

ok so you need to focus

I can give you the answers

but you need to understand the questions

[mint tiger]

Yes plz

[mint tiger]

Ok

[boreal patio]

very simple question

Area of circle = ?

[mint tiger]

7.3

[boreal patio]

😦

that's the radius

[mint tiger]

Shit

Maybe 14.6?

[boreal patio]

The area of the circle = Radius squared times pi

= r * r * pi

if r = 7.3

[mint tiger]

I still don't understand

[boreal patio]

what's the area ?

[mint tiger]

Prob 7.3cm

[boreal patio]

7.3 is the radius

we need the area

[mint tiger]

Ugghhhhh I need a shower still I get dis shi

[boreal patio]

to find the area we have to know what is the law of the area of the circle

[mint tiger]

Welp idk

[boreal patio]

I will go now , try to focus more and you'll get everything

[mint tiger]

Can u get another helper?

[boreal patio]

<@&286206848099549185>

[mint tiger]

?

<@&286206848099549185>

[steel mural]

So, what is the question?

[balmy oracle]

?

[mint tiger]

I got 30mins

Plz I need dis

It's due tmr(homework)

[steel mural]

Don't you know how to calculate the circle area?

[mint tiger]

No

I'm stupid

[steel mural]

You don't know the formula, or don't understand the formula?

[mint tiger]

Both

Can u give me the straight answers?

[steel mural]

The area of the circle is
πr^2

You used that before

Sec

[mint tiger]

?

[mint tiger]

Plz

[steel mural]

I have to calculate this?

[steel mural]

.

[mint tiger]

Well idk how

Plz if u can

[steel mural]

Just use the formula

πr^2

[mint tiger]

What's the ^

[steel mural]

Squared

r×r

r•r

[mint tiger]

Not working

[steel mural]

Why?

[mint tiger]

Idk

[steel mural]

Where is the problem

?

Answer is not correct?

[mint tiger]

I'm doing what ur saying

[steel mural]

So

[mint tiger]

Pi×7.3²

And I did Pi7.3²

[steel mural]

And

Your answer is not correct?

[mint tiger]

Ye

Should I just skip this

[steel mural]

Write me this number

[mint tiger]

?

Wym

[steel mural]

You got

[mint tiger]

It says syntax error on my calculatr

[steel mural]

Why?

[mint tiger]

Idk

[steel mural]

π~3.1415926535

So

[mint tiger]

Should I skip this part

[steel mural]

I don't know, can you use another calculator?

[mint tiger]

Nope this my only one

[steel mural]

Phone?

[mint tiger]

Idk how to use phone calc

[steel mural]

Ok....

[mint tiger]

Ima skip this

[steel mural]

167.41547250980

That's the answer I got, but you must know how to use phone calculator

[mint tiger]

That's right

[mint tiger]

That's hw answer

[steel mural]

Sorry, for my bad english

[mint tiger]

Tysm

It's nw

How do I play it if it's 16.9

[steel mural]

Translate please

[steel mural]

This one

I don't understand

[mint tiger]

Thank you so much^

[steel mural]

Ok

[mint tiger]

Tysm means Thank You So Much

[steel mural]

Thanks

[steel mural]

This?

nw

[mint tiger]

What's this

[mint tiger]

Nw means No Worry

[steel mural]

So, you should use the same formula

πr^2

π multiplies by 16.9 and multiplies by 16.9 again

[pearl pond]

@mint tiger Has your question been resolved?

[steel mural]

So do you have more questions?

If you need, you can write to me later

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[kindred flame]

I’m not sure if I solved this right… or the right way to solve this. Can anyone help?

[sterile turtle]

when you do f(x+h), replace the x with x+h

you just did f(x) +h

[kindred flame]

Are you saying to do

(5 / x+h) ?

or what do u mean by that @sterile turtle

[light helm]

5/ (x+h)
with the whole x+h in the denominator

[sterile turtle]

lmao fair the brackets are off but we get what they mean

[kindred flame]

LMAO im actually so bad at functions

[light helm]

without them its exactly the same as what they did

[kindred flame]

its so confusing

ok one sec

lemme rewritre and sec anoter pic

[light helm]

and that misinterpretation is what lead to the error

[sterile turtle]

tru

[dapper kraken]

$\frac{5}{x+h}$ btw

[jolly parrot]

Skill_Issue

[kindred flame]

ok i rewrote it at the bottom

now is the next step to find the LCD of all the values in the numerator?

[sterile turtle]

remove the h

[light helm]

still incorrect

[kindred flame]

really?

[sterile turtle]

yea :(

[kindred flame]

if its

f(x+h)

and f(x) = 5/x

wouldnt i just plug in 5/x where the X is?

why would i remove the h

[sterile turtle]

plug in x+h where the x is

[light helm]

you remove the extra +h you have

[kindred flame]

OHHH

ok

i see.

so itd be

(5/x + h) - (5/x)

/ h

[sterile turtle]

the brackets are off still :(

try write it out of paper

[kindred flame]

isnt it what i wrote above without the h in the denominator?

[sterile turtle]

uhhh

lets break this down

[kindred flame]

yes please 😭

[sterile turtle]

youre subbing in x+h where the x is right?

[kindred flame]

correct

[sterile turtle]

lets say the x+h is 5

then itd be 5/5

[kindred flame]

wait

wait

actually

[sterile turtle]

just an example

[kindred flame]

i thought we were subbing in

5/x where x is

[sterile turtle]

?

[kindred flame]

oh ok

f(x) = x/5

so wherever i see x in the function

i put x/5

[sterile turtle]

f(x)=5/x?

[kindred flame]

yes

[sterile turtle]

or we just doing an example

ok

heres the thing

i think you might have the f(x) mixed up

[sterile turtle]

whatever the f(x here) is, we sub into the x of the equation

[kindred flame]

is it possible to get into a call with u and explain with voice by chance

if not thats ok just thought id ask

[sterile turtle]

nah sprry

[kindred flame]

ok

np

ok that makes sense

in the f(2)

u replaced x with 2

so u put 2 wherever x is

[sterile turtle]

yep

yep exactly

then if you have f(x) = 5/x

and were trying to do f(x+h)

wed sub the x+h into where the x is

can you try write that

[kindred flame]

i thought that if f(x) = 5/x and we are trying to solve f(x+h)

we'd just put 5/x where the X is

so f(5/x + h)

thats wrong?

[light helm]

is wrong

[sterile turtle]

yea thats wrong

[kindred flame]

i see..

ok

[light helm]

you put x+h where x was

[sterile turtle]

its the same thing as this

just instead of f(2), its f(x+h)

[kindred flame]

ok yes give me that exampole

with a whole number

may be easier

[sterile turtle]

ok

uh

[kindred flame]

pretend f(x) = 2

instead of x/5

[light helm]

to get f("whatever that is")
replace all x initially present with "whatever that is"

[sterile turtle]

there needs to be an x in the equation

[light helm]

there doesn't

[sterile turtle]

so ill give you f(x)= x^2

[kindred flame]

ok

[sterile turtle]

if you want to find f(x+h), what would you do

[kindred flame]

f(x) = x^2 / f(x+h)

so like i did before, if i didnt know better. id do

f(x^2 + h)

but ik thats wrong

so what do i do instead?

[sterile turtle]

yep

so the x is being squared

then we want to replace the x with whatever is inside the f()

we see that its f(x+h) so w replace the x with (x+h)

[kindred flame]

so would it be (x+h)^2

[sterile turtle]

yep

exactly

[kindred flame]

how do you know which function to sub into which

cause apparently theres 2

f(x) = x^2

and f(x + h)

how do know which goes into which

[sterile turtle]

thats the main function

[sterile turtle]

this is a translation of the main function

so we will sub it into the the f(x)

[kindred flame]

so the translation always goes back into the main function?

[sterile turtle]

uhhh

its more like

finding a point

on the function

nah thats wrong

cant explain it clearly lmao

[kindred flame]

its ok

lets just use this case

f(x) = x/5 is the main function

[sterile turtle]

yep

[kindred flame]

the f(x+h) - f(x) / h

is the translation?

[sterile turtle]

this is a formula

not a translation

[kindred flame]

ah

so am i supposed to take parts of the formula and put it into the function?

[sterile turtle]

dont think about what i said about rtanslaion

thats wrong

[sterile turtle]

the formula is made up of parts

there are parts f(x+h) and f(x)

so we need to find both these parts and subtract

[kindred flame]

okay

i see

i just always thought you put the function into the formula..

main function

ok so in this case

I do

[kindred flame]

lemme send a pic

[sterile turtle]

like this

[kindred flame]

i see

ok

so the new equation is

(5/x+h) - (5/x) / h

is that correct?

[sterile turtle]

the brackets on the whole numerator right?

wait

[kindred flame]

i can send a pic

[sterile turtle]

yea

thatd help

[sterile turtle]

yep exactly

[kindred flame]

ah.. ok

ok

would the next step be

multiplying the numerators

by each other

so (5/x+h) * x

(5/x) * (x+h)

so they have a common denominator?

[sterile turtle]

remember when writing these you need to put brackets around the whole denominator

so 5/(x+h)

[kindred flame]

ok

gotcha

[sterile turtle]

but yea

its just algebra from there

[kindred flame]

would the denominator on the 5/x

be in parantheesis

so 5/ (x+h)

5 / (x)

?

[sterile turtle]

the x is stand alone

so you know its just x on the denominator

[kindred flame]

oh alr

so now multiply

so i get the same denominator

in the numerator right

[sterile turtle]

yep

you wanna try it and if you have any problems just send your working out

[kindred flame]

yep will do itll be quick

[sterile turtle]

i can look over it to see if theres anything wrong

[kindred flame]

Does this look right so far @sterile turtle

[sterile turtle]

mmmm

5(x+h) doesnt equal 5x +h

[kindred flame]

ahh

5x + 5h

[sterile turtle]

yep

[kindred flame]

ok

so in the end

id get

(5h/x^2+hx) <--numerator

/ h

is that correct?

its the same as the last part of my work above but 5h instead of h

[sterile turtle]

lmao even inside the numerator 5h/(x^2+hx) but yep youre on the right track

[kindred flame]

ah ok

and then i used the formula thing

(a/b) / c

=

a / (bc)

so heres my new answer

[sterile turtle]

you added not times

[kindred flame]

ah ur right

ok

[sterile turtle]

dont open the brackets btw

[kindred flame]

so just do

5h <--- numerator

(x^2+hx) (h) <--- denominator

is that right?

O did you leave @sterile turtle

[sterile turtle]

sorry

yea

thats right

ams if you see

You have 5h/(h(x^2+xh))

so why not cross out the h

[kindred flame]

Do I distribute the h?

OHHH

I can remove 1 from the top

So 4h / (x^2 + xh)

Right

[sterile turtle]

mmmmmm

not quite

thats minus

were doing divide

eg.
3a/a = 3, not 2a

[kindred flame]

Oh

What?

O_o

Oh

[sterile turtle]

?

[kindred flame]

If it was h^5

Then it would be h^4 after

[sterile turtle]

yea

[kindred flame]

If it was h in the denominator

But 5h = 5 x h

Ohhhh

Okay

[sterile turtle]

ye

are you doing an intro to calculus?

[kindred flame]

So 5 / (x^2 + xh)

[sterile turtle]

👍

[kindred flame]

I took pre calculus 7 years ago

In high school

And then

I didn’t take much math since

[sterile turtle]

ahhhh

[kindred flame]

Now I’m taking precalclus again

To prepare for college

[sterile turtle]

fair enough lmaoooo

[kindred flame]

But I’m rusty on everything

😭

[sterile turtle]

nah good on you mate

[kindred flame]

And would that be the final answer since we can’t simplify anymore

[sterile turtle]

yep

[kindred flame]

Thank you sir ❤️

[sterile turtle]

npnp

[kindred flame]

Wait lemme put it in answer

To test if it works

Need to load up my pc one sec

It says that it was wrong @sterile turtle

[sterile turtle]

uhh

try not factorise the denominator

AH

WAIT

WE FORGOT

THE NEGATIVE

[sterile turtle]

LMAOOOO 5x-(5x+5h)

=-5h

whoops

[kindred flame]

I’m so depressed

This always happens cause I miss the small details

[sterile turtle]

lmao dw

ur just rusty

youll get back there

[kindred flame]

So it’s just -5 in the numerator right? And same denominator

[sterile turtle]

aight im not gonna be able to help anymore so gl

[sterile turtle]

yep

[kindred flame]

Ok thank you

I APPRECIATE IT

[pearl pond]

@kindred flame Has your question been resolved?

[pearl pond]

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.

[solid pier]

do you want to know how to find such a factorization

or do you just wanna know why they're equal?

[tranquil badger]

MATERIALS:

1 This is a relational quadratic function) that, when graphed, can show input vs output growth.

2 As with all functions, I'd imagine you could just plug in a value and check the result.' Why is it they'd want to factor the answer if they logically should be able to just plug in a few values to find what the operations would come out to?```

CORE CONCEPTS (that I''m aware of):

relational graphing x,y difference

factorization: breaking numbers down into parts that multiply to make a whole

algebraic factoring: reforming problems into quantities or a n y form that, so long as it multiplies to get the whole, is correct.

algebraic operations: attempts to narrow down an answer via various methods, typically involving inverting or manipulating the problem in some way.```

indevelopment

[solid pier]

sorry what is your question exactly, are you asking why we care about factoring?

[tranquil badger]

my understanding: Functions are given input and produce output. Why would we need to factor to find what input would create zeroes when we could just input values to figure that out?```

[solid pier]

i mean good luck finding 5/2 and -1/3 without factoring (or some other technique using the polynomial itself)

you won't find it by guessing and checking, unless you're using the rational root theorem (which I'm 90% sure you don't know)

[tranquil badger]

FAULT: Did not use if & if not operator reasoning to check for usage.

UNDERSTANDING: You are saying that they simply use it because they can't any other way? It is more complex than it appears?```

[tranquil badger]

Q: You mean fractions or whole numbers of the form 5 and 2?```

[solid pier]

i mean that the solutions to these quadratic equations won't be integers in general

it just makes you less likely to find it, unless you pick an enumeration of the rationals and then start checking, which is EXTREMELY inefficient

also, what is FAULT? is that for you or for me?

[tranquil badger]

me

[solid pier]

got it

[tranquil badger]

Meta Calculations

[solid pier]

but yes, it is more complex than it appears, and you have to learn how to factor becuase it's an easy-to-understand version of the "real" technique for finding zeroes of polynomials (without relying on the quadratic formula)

which generalizes to higher-degree polynomials

and is computationally more efficient

[tranquil badger]

Q: How is it that factoring the polynomial ends up producing the roots? 

simplified: How does breaking a problem into smaller pieces and finding the values you could break it into that would negate all values generate the zeroes for X?```

[solid pier]

no need to ask the simplified question, the original is coherent (unless the simplified version is again for you)

[tranquil badger]

It mostly is, as I was attempting to word it in such a way that the answer would be more attainable. It may also make my thought process more visible.

[solid pier]

but we factor a polynomial so that we can use a particular fact about real numbers, namely that if ab = 0, then either a = 0 or b = 0, and also a fact about polynomials, namely that linear maps have exactly one value of x such that f(x) = 0, and if you take a product of nonzero numbers, the whole result is also nonzero

so if i have like, x^2 - 1, then it's a quadratic, and these facts don't say anything about quadratics, but if i factor this polynomial into (x + 1) (x - 1) , then i can use the fact that f(x) is 0 if and only if x is either 1 or -1 by the two facts above

this is why we try to factor stuff first, because it's clear now that f(x) and the factored version have the same outputs, but the factored form makes it REALLY CLEAR where the roots are, and that the solutions to the factors can be the ONLY roots

this is if you can factor the polynomial in the first place. But we would like to check for it whenever we can because this theory is very nice

polynomials have such a rich theory just becuase we really like computationally efficient methods for computing their properties (and also because geometrically they're very interesting, but if you're looking for immediate applications in areas of math that are understandable or practical in science, then i think that being computationally efficient as an algorithm is a great place to start)

btw

[tranquil badger]

map generation (games)?

[solid pier]

perhaps yes, maybe not for this algorithm specifically, but there is a nice theory of approximation that might be applicable in map generation

I don't know much about game creation

or the cutting-edge when it comes to that

[tranquil badger]

Ok, it's just that someone was using it for that interestingly.

Thank you! I believe I need to deeply think about this for a while.

Gl!

Meta-Flow

[solid pier]

have fun exploring

[tranquil badger]

.close

[pearl pond]

Channel closed

Closed by @tranquil badger

Use .reopen if this was a mistake.

[pearl pond]

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.

[vast berry]

how do i turn left to right?

[vast berry]

theyre equivalent but idk how to turn it

[sly dagger]

start by using double angle on sin

[vast berry]

sin ( 2theta/2)?

[sly dagger]

yes

[pearl pond]

@vast berry Has your question been resolved?

[pearl pond]

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.

[sharp smelt]

here am I allowed to use the polar form of a complex number $(re^{ix})$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[summer gorge]

I don't think so

[sharp smelt]

ok

thanks

[summer gorge]

You gotta first define it

[solid pier]

why would or wouldn’t you, it just depends on if you’ve covered it

[sharp smelt]

This is the first chapter of LADR

[summer gorge]

For that you have to use these

[solid pier]

oh then you can’t

[sharp smelt]

ok

thanks

[summer gorge]

Use the normal definition

[solid pier]

i’m assuming that you can’t because axler is terrible and probably didn’t define polar form

god i hate axler

[summer gorge]

And prove that they are equivalent

[west sapphire]

if you want to do it the based way, identify a complex number a+ib with the 2x2 matrix [a -b; b a]

then it comes from associativity of matrix multiplication

[summer gorge]

Lol that's based

[sharp smelt]

thanks

[solid pier]

there’s a nice spot the mistake question related to this

this is from a friend who came up with this a few years ago: Everyone knows we can prove matrix multiplication is associative by considering matrix multiplication as a function: let f(x)=Ax, g(x)=Bx, h(x)=Cx, then (AB)C represents (f o g) o h which is f o (g o h) which represents A(BC), so (AB)C = A(BC). We specialize to the case of 1D matrices, plug x=1 into both sides, let the matrices be over octonions, and voila, octonions are associative! Where's the mistake?

[sharp smelt]

what are octonions ?

I should probably skip this until I finish LA, sorry

[solid pier]

you could, in theory, do this question right after learning about how matrix multiplication is in 1-1 correspondence with linear maps

but whatever

[sharp smelt]

👍

[solid pier]

it’s just a funny aside

[sharp smelt]

sorry

wait, so some books define $e^{ix}$?

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[summer gorge]

Like the derivation?

[sharp smelt]

I mean while defining complex numbers

[summer gorge]

If so yes

[sharp smelt]

because this is rather painful without euler's form

[west sapphire]

offhand i'm guessing it's because validity of matrix multiplication as the way to calculate compositions depends on the fact that you're in a vector space over a field, or at least a module over a commutative ring?

[solid pier]

yes thats the key, but you don’t need the ring to be commutative, just associative (for matrix mult to be composition)

[sharp smelt]

can I close this now?

I think I'm done

[solid pier]

yes, and good job

[summer gorge]

Yes

[west sapphire]

ah nice

[sharp smelt]

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

Use .reopen if this was a mistake.

[midnight haven]

help

[summer gorge]

!status

[pearl pond]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[west sapphire]

this channel's gonna go away, you need to open your own

!help

[pearl pond]

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

[midnight haven]

i get no answer

[summer gorge]

Oh yeah

[pearl pond]

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.

[agile ridge]

Let $A$ and $B$ be $n \times n$ matrices. AB=BA. Given that $\xi_1, \cdots, \xi_{r_1}$ and $\eta_1, \cdots, \eta_{r_2}$ are the fundamental solutions of the systems $Ax = 0$ and $Bx = 0$, respectively, and for the $n \times n$ matrices $C$ and $D$, it holds that $r(CA + DB) = n$.
How can I prove that $\xi_1, \cdots, \xi_{r_1}, \eta_1, \cdots, \eta_{r_2}$ is a fundamental solution set of the system $ABx = 0$ ?

[jolly parrot]

nino

[pearl pond]

@agile ridge Has your question been resolved?

[agile ridge]

Can i ping <@&286206848099549185>

[cursive wraith]

I saw that you edited, n-rank is very different from 'n x n matrices'

[agile ridge]

Translation error, sry

[cursive wraith]

ok