signal flicker Oct 7, 2023, 12:13 PM

#

so its false right?

merry cosmos Oct 7, 2023, 12:13 PM

#

yes

vocal sleetBOT Oct 7, 2023, 12:22 PM

#

@pliant hinge Has your question been resolved?

#

Channel closed

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crimson pumice Oct 7, 2023, 12:29 PM

#

Could someone help to explain the logic of this?

vocal sleetBOT Oct 7, 2023, 12:29 PM

#

crimson pumice Could someone help to explain the logic of this?

crimson pumice Oct 7, 2023, 12:30 PM

#

ok so if you look at question b line 2 to 3, the teacher does it by flipping the dP/dt to get dt/dP, but what is the thought process for doing that?

#

#

this one more close up

#

because I would do it the same as I would do those newton cooling/ heating up questions

#

but I know these popualtion questions you need to flip it at some point because

vocal sleetBOT Oct 7, 2023, 12:47 PM

#

@crimson pumice Has your question been resolved?

crimson pumice Oct 7, 2023, 12:47 PM

#

<@&286206848099549185>

#

aw man 😦

#

anyone?

#

welp

#

.close

vocal sleetBOT Oct 7, 2023, 1:02 PM

#

Channel closed

Closed by @crimson pumice

Use .reopen if this was a mistake.

#

Available help channel!

Send your question here to claim the channel.

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

wraith pelican Oct 7, 2023, 1:38 PM

#

can someone help me solve this like, how should i approch solving this? do i like get A into reduced row echleon form ?

vocal sleetBOT Oct 7, 2023, 1:38 PM

#

wraith pelican can someone help me solve this like, how should i approch solving this? do i lik...

#

@wraith pelican Has your question been resolved?

vocal sleetBOT Oct 7, 2023, 2:23 PM

#

@wraith pelican Has your question been resolved?

vocal sleetBOT Oct 7, 2023, 3:24 PM

#

@wraith pelican Has your question been resolved?

heady ibex Oct 7, 2023, 4:25 PM

#

you just have to apply A to x and equate it to b

#

you then have 3 solutions of which one does not contain an x_i

#

3 equations

#

not solutions

noble lily Oct 7, 2023, 4:27 PM

#

^

#

RREF for this problem is unnecessarily

vocal sleetBOT Oct 7, 2023, 5:29 PM

#

@wraith pelican Has your question been resolved?

#

Channel closed

Closed by @wraith pelican

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Remember:
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

tough kraken Oct 7, 2023, 5:53 PM

#

#

Hello

vocal sleetBOT Oct 7, 2023, 5:53 PM

#

tough kraken

tough kraken Oct 7, 2023, 5:53 PM

#

Can someone help me with this problem

#

I ain't doing so great with fractions

warped gazelle Oct 7, 2023, 5:55 PM

#

ok

#

if you do opposite way, it's way more simple

tough kraken Oct 7, 2023, 5:55 PM

#

opposite way?

warped gazelle Oct 7, 2023, 5:55 PM

#

like you are proving A = B, you could also prove B = A

tough kraken Oct 7, 2023, 5:57 PM

#

Um, a is given to be equal to 3/25 + 3/5*8 + ... + 3/(3n-1)(3n+2)

#

And I have to prove that 3/(3n-1)(3n+2) is equal to something or can be rewrited as smth

#

there is no b

#

also, this is a part of the a, not the whole nr, so, there is no such thing like A = B and opp

#

or, am I wrong?

warped gazelle Oct 7, 2023, 6:01 PM

#

hmm?

tough kraken Oct 7, 2023, 6:01 PM

#

hmm?

split wind Oct 7, 2023, 6:04 PM

#

hmm?

warped gazelle Oct 7, 2023, 6:05 PM

#

ok

#

it's very satisfying sum

tough kraken Oct 7, 2023, 6:05 PM

#

I don't get, am I wrong with smth?

warped gazelle Oct 7, 2023, 6:05 PM

#

for example

#

hmm

#

just 3/(3x-1)(3x+2) = 1/(3x-1) - 1/(3x+2) is calculated

#

and can get something like this: 3/2*5 = 1/2-1/5

tough kraken Oct 7, 2023, 6:07 PM

#

so, what should we do first?

warped gazelle Oct 7, 2023, 6:07 PM

#

we just change everything in the sum like that

#

1/2 - 1/5

#

1/5 - 1/8

#

1/8 - 1/11

#

...

#

1/(3x-1) - 1/(3x+2)

#

then we sum everything

#

1/2 -1/5 +1/5 -1/8 +1/8 -1/11 + ... + 1/(3x-1) - 1/(3x+2)

#

all the middle part is gone

#

1/2 - 1/(3x+2)

tough kraken Oct 7, 2023, 6:09 PM

#

#

so it's smth like that, right?

warped gazelle Oct 7, 2023, 6:09 PM

#

now you know the most satisfying sum in math

tough kraken Oct 7, 2023, 6:09 PM

#

Sorry for my bad writing, it's a pc after all

#

um, what should I do now?

warped gazelle Oct 7, 2023, 6:10 PM

#

it's plus minus same thing

#

results in zero

#

except for

#

very edge parts of the

tough kraken Oct 7, 2023, 6:11 PM

#

um

split wind Oct 7, 2023, 6:11 PM

#

Well, to prove that $\frac3{(3n-1)(3n+2)}=\frac1{3n-1}-\frac1{3n+2}$, you can start from the Right Hand Side first.

twin meteorBOT Oct 7, 2023, 6:11 PM

#

Biscuity

split wind Oct 7, 2023, 6:12 PM

#

first step would be to find the common denominator and expand the fractions

tough kraken Oct 7, 2023, 6:12 PM

#

wait a bit

#

I'm confused at the first part

#

#

how is this 0?

warped gazelle Oct 7, 2023, 6:13 PM

#

ok

#

that's not zero

tough kraken Oct 7, 2023, 6:13 PM

#

warped gazelle results in zero

.

warped gazelle Oct 7, 2023, 6:13 PM

#

oh you confused because of that

#

the MIDDLE PART results in zero

#

for example

#

-1/5+1/5 is 0

#

-1/8 + 1/8 is 0

#

...

#

-1/(3x-1)+1/(3x-1) = 0

#

and the only things left are

#

1/2 and -1/(3x+2)

tough kraken Oct 7, 2023, 6:14 PM

#

#

ooh

#

this and so on

#

got it

split wind Oct 7, 2023, 6:15 PM

#

nice!

tough kraken Oct 7, 2023, 6:15 PM

#

for me, which I ain't dealing so good with this is satisfaying, ain't gonna lie

#

so

#

#

what we doin' from now?

warped gazelle Oct 7, 2023, 6:16 PM

#

hmm

#

is there anything given for that

tough kraken Oct 7, 2023, 6:17 PM

#

a

#

not really

#

Oh

#

Actually yes

#

I have to find a

#

this is the 2nd request

warped gazelle Oct 7, 2023, 6:17 PM

#

then what is n

tough kraken Oct 7, 2023, 6:18 PM

#

the first request of the exercise is this

#

Omg, I don't know how to express myself

warped gazelle Oct 7, 2023, 6:18 PM

#

wait what

#

are you talking about

tough kraken Oct 7, 2023, 6:18 PM

#

#

Problem 3

warped gazelle Oct 7, 2023, 6:19 PM

#

LOL

#

what is the number

tough kraken Oct 7, 2023, 6:19 PM

#

Se considera numarul a means A is given to be equal

warped gazelle Oct 7, 2023, 6:19 PM

#

a = 33/ ?

tough kraken Oct 7, 2023, 6:19 PM

#

at a) we need to prove this equality

#

where n is in N without 0

#

N*

#

b) = to calculate nr a

#

and c) find n which makes part of N* with a=33/70

tough kraken Oct 7, 2023, 6:20 PM

#

warped gazelle a = 33/ ?

33/70

warped gazelle Oct 7, 2023, 6:20 PM

#

then you did everything except c

#

you just make equation

#

and solve it

tough kraken Oct 7, 2023, 6:21 PM

#

I didn't did a)

warped gazelle Oct 7, 2023, 6:21 PM

#

oh

#

let's take a look at a)

#

1/(3n-1) - 1/(3n+2)

#

is

#

(3n+2)/(3n-1)(3n+2) - (3n-1)/(3n-1)(3n+2) right?

tough kraken Oct 7, 2023, 6:22 PM

#

warped gazelle Oct 7, 2023, 6:22 PM

#

hmm?

tough kraken Oct 7, 2023, 6:22 PM

#

warped gazelle and the only things left are

.

tough kraken Oct 7, 2023, 6:22 PM

#

warped gazelle 1/2 and -1/(3x+2)

.

warped gazelle Oct 7, 2023, 6:22 PM

#

yes

tough kraken Oct 7, 2023, 6:22 PM

#

this is where I've stopped

warped gazelle Oct 7, 2023, 6:23 PM

#

something written you showed to me

#

said

#

if that is equal to 33/70,

#

what is the value of n

tough kraken Oct 7, 2023, 6:23 PM

#

c) - Find N who is part of N* knowing that a = 33/70

warped gazelle Oct 7, 2023, 6:24 PM

#

then, do you need help on calculating that equation?

tough kraken Oct 7, 2023, 6:24 PM

#

um

#

wait

#

warped gazelle Oct 7, 2023, 6:25 PM

#

yes

tough kraken Oct 7, 2023, 6:25 PM

#

i hate this writing

#

um, now,

warped gazelle Oct 7, 2023, 6:26 PM

#

that's my writing 2 years before 💀

tough kraken Oct 7, 2023, 6:26 PM

#

wait

warped gazelle Oct 7, 2023, 6:26 PM

#

let's work out anyway anyway

tough kraken Oct 7, 2023, 6:26 PM

#

um

#

can we do derivate ratios

#

right

#

?

#

I hope this is the thing I'm meaning

warped gazelle Oct 7, 2023, 6:26 PM

#

hmm

#

i didn't study math in english

tough kraken Oct 7, 2023, 6:27 PM

#

#

neither did I

warped gazelle Oct 7, 2023, 6:27 PM

#

unfortunately, that's not possible

#

when you are doing that kind of thing,

#

it should be like this:

#

A/B = C/D

#

so

#

AD = BC

tough kraken Oct 7, 2023, 6:28 PM

#

so

#

then

#

#

let this be the main img

warped gazelle Oct 7, 2023, 6:28 PM

#

ok

tough kraken Oct 7, 2023, 6:28 PM

#

so, what are we doing frm now?

warped gazelle Oct 7, 2023, 6:28 PM

#

we

#

just

#

uh... what's that called....

#

you just do something like this:

#

A+B = C

#

A = C-B

tough kraken Oct 7, 2023, 6:29 PM

#

a and C being which one

#

and B

#

A and B *

warped gazelle Oct 7, 2023, 6:29 PM

#

that's just an example of doing that math thingy

#

in this case,

#

1/2 being A, -1/(3x-2) being -B, 33/70 being C,
A-B = C

A-C = B

tough kraken Oct 7, 2023, 6:30 PM

#

oh

#

the thing is I don't really have any Idea how to calculate

#

1/2-1/(3n-2)

warped gazelle Oct 7, 2023, 6:31 PM

#

so

tough kraken Oct 7, 2023, 6:31 PM

#

oh

warped gazelle Oct 7, 2023, 6:31 PM

#

you do something transposition ( iguess)

tough kraken Oct 7, 2023, 6:31 PM

#

3n is 3 * 33/70

#

right?

warped gazelle Oct 7, 2023, 6:31 PM

#

yes? (sus)

tough kraken Oct 7, 2023, 6:31 PM

#

why sus

#

lol

warped gazelle Oct 7, 2023, 6:32 PM

#

goahead

tough kraken Oct 7, 2023, 6:32 PM

#

a

#

no

warped gazelle Oct 7, 2023, 6:32 PM

#

lol

tough kraken Oct 7, 2023, 6:32 PM

#

I don't htink I'm right

#

think

#

I tought n = 30/70

#

but this is a

warped gazelle Oct 7, 2023, 6:32 PM

#

ok i'll draw the solution on my computer

tough kraken Oct 7, 2023, 6:32 PM

#

we are finding N

#

fuck mslf

warped gazelle Oct 7, 2023, 6:33 PM

#

can you understand this?

tough kraken Oct 7, 2023, 6:34 PM

#

oh

#

Yes

#

I understand what u did

#

I didn't know that was possible

#

Or maybe I did but I couldn't associate

warped gazelle Oct 7, 2023, 6:35 PM

#

well, we usually explain this as weight

#

if we add something on Left Hand, we also add the exact same thing on Right Hand and it's equal

tough kraken Oct 7, 2023, 6:35 PM

#

warped gazelle Oct 7, 2023, 6:35 PM

#

yes good

tough kraken Oct 7, 2023, 6:35 PM

#

still don't know how to calculate

#

um

warped gazelle Oct 7, 2023, 6:36 PM

#

you calculate the number first

tough kraken Oct 7, 2023, 6:36 PM

#

we should amplify first by 45?

warped gazelle Oct 7, 2023, 6:36 PM

#

hmm,

tough kraken Oct 7, 2023, 6:36 PM

#

or it doesn't work like that

#

to have a commo n denominator

warped gazelle Oct 7, 2023, 6:36 PM

#

i think you should calculate the number side; Left Hand Side

#

can you calculate 7/2 - 33/70?

tough kraken Oct 7, 2023, 6:36 PM

#

this is what am I asking you

warped gazelle Oct 7, 2023, 6:36 PM

#

ok

tough kraken Oct 7, 2023, 6:36 PM

#

how to get the same denom

warped gazelle Oct 7, 2023, 6:37 PM

#

7/2 - 33/70 is

#

7x35/2x35 - 33/70

#

did you understand what i did?

tough kraken Oct 7, 2023, 6:38 PM

#

warped gazelle 7/2 - 33/70 is

7/2?

#

isn't it 1/2?

warped gazelle Oct 7, 2023, 6:38 PM

#

no

#

fraction is something like this

tough kraken Oct 7, 2023, 6:38 PM

#

#

oh

warped gazelle Oct 7, 2023, 6:38 PM

#

uh yeah that's true

tough kraken Oct 7, 2023, 6:39 PM

#

I thought u switched 1 by 7 by mistake

warped gazelle Oct 7, 2023, 6:39 PM

#

i think you should have better handwriting 💀

#

well,

#

that doesn't mean that you should get better writing forms

#

you just need to seperate something like 1 and 7

tough kraken Oct 7, 2023, 6:40 PM

#

there is an obv difference from nr to nr in my hwriting

#

just saying

warped gazelle Oct 7, 2023, 6:40 PM

#

e

#

ok

#

1/2 - 33/70

#

anyway

#

(trolll)

tough kraken Oct 7, 2023, 6:40 PM

#

are u balkan? srry to task

warped gazelle Oct 7, 2023, 6:41 PM

#

1/2 is

#

35/70 right?

tough kraken Oct 7, 2023, 6:41 PM

#

a

#

theoretically yes

warped gazelle Oct 7, 2023, 6:41 PM

#

theoretically :skulll

#

ok

#

so

tough kraken Oct 7, 2023, 6:41 PM

#

lmao

warped gazelle Oct 7, 2023, 6:41 PM

#

1/2 - 33/70
= 35/ 70 - 33/70
= 2/70 right?

tough kraken Oct 7, 2023, 6:42 PM

#

yes

#

affirmative

warped gazelle Oct 7, 2023, 6:42 PM

#

so

#

it is 1/35

#

right?

tough kraken Oct 7, 2023, 6:42 PM

#

yes

warped gazelle Oct 7, 2023, 6:42 PM

#

wait i am drawing

tough kraken Oct 7, 2023, 6:43 PM

#

this is satisfaying tho

#

but I don't know how u get this ideas

#

this fast

#

Actually, maybe also is just that I never saw exercises like this

#

maybe If I'd work more on them, I could do them faster

warped gazelle Oct 7, 2023, 6:43 PM

#

lol

tough kraken Oct 7, 2023, 6:44 PM

#

so

warped gazelle Oct 7, 2023, 6:44 PM

#

wait

#

i just noticed that

#

you mistaked something

#

the initial question was 3n+2 but not 3n-2

#

so

tough kraken Oct 7, 2023, 6:45 PM

#

hm?

warped gazelle Oct 7, 2023, 6:45 PM

#

so

tough kraken Oct 7, 2023, 6:45 PM

#

ooh

warped gazelle Oct 7, 2023, 6:45 PM

#

1/35 = 1/3n+2

tough kraken Oct 7, 2023, 6:45 PM

#

warped gazelle Oct 7, 2023, 6:45 PM

#

so we do the ~~holy thingy~~

#

35 = 3n+2

tough kraken Oct 7, 2023, 6:45 PM

#

yea

#

u are right

warped gazelle Oct 7, 2023, 6:45 PM

#

i am sure that you can find integar n

tough kraken Oct 7, 2023, 6:45 PM

#

is the one w +2

warped gazelle Oct 7, 2023, 6:45 PM

#

lul

tough kraken Oct 7, 2023, 6:45 PM

#

so

#

warped gazelle Oct 7, 2023, 6:46 PM

#

simple simple

tough kraken Oct 7, 2023, 6:46 PM

#

so

#

we have n = 11

warped gazelle Oct 7, 2023, 6:46 PM

#

yay

#

finally

tough kraken Oct 7, 2023, 6:46 PM

#

which makes part of N*

warped gazelle Oct 7, 2023, 6:46 PM

#

after 2.539 eternity

tough kraken Oct 7, 2023, 6:46 PM

#

so this is good

#

hehe

#

thank you so much for not feeling to kll yslf after talking w me

warped gazelle Oct 7, 2023, 6:47 PM

#

ok good bye

tough kraken Oct 7, 2023, 6:47 PM

#

lmao

#

have a nice day

#

:))

warped gazelle Oct 7, 2023, 6:47 PM

#

eeeeeeeeeeeeeeeeeeeee

tough kraken Oct 7, 2023, 6:47 PM

#

tysm

#

are u balkan

#

x2

#

x3

#

x4

warped gazelle Oct 7, 2023, 6:47 PM

#

no

#

x2

#

x3

tough kraken Oct 7, 2023, 6:47 PM

#

oh

warped gazelle Oct 7, 2023, 6:47 PM

#

x395302395

tough kraken Oct 7, 2023, 6:47 PM

#

where are u from

warped gazelle Oct 7, 2023, 6:47 PM

#

hehe

#

somewhere east west

tough kraken Oct 7, 2023, 6:48 PM

#

Oooooooh

#

antractica

#

got it

warped gazelle Oct 7, 2023, 6:48 PM

#

(wt0

tough kraken Oct 7, 2023, 6:48 PM

#

antarctica

#

srryh

#

I misspeled cuz I was worried about the cold air from there

warped gazelle Oct 7, 2023, 6:48 PM

#

kills myself for 1 consecutive second by sneezing

tough kraken Oct 7, 2023, 6:49 PM

#

ok bye I love u bye

#

have a nice dayt

warped gazelle Oct 7, 2023, 6:49 PM

#

.close

tough kraken Oct 7, 2023, 6:49 PM

#

nono

#

I am the one who ends it

#

catKing

tough kraken Oct 7, 2023, 6:49 PM

#

warped gazelle .close

.close

vocal sleetBOT Oct 7, 2023, 6:49 PM

#

Channel closed

Closed by @tough kraken

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.

covert ridge Oct 7, 2023, 7:18 PM

#

which one is correct and why?

vocal sleetBOT Oct 7, 2023, 7:18 PM

#

covert ridge which one is correct and why?

paper depot Oct 7, 2023, 7:19 PM

#

can a number be equal to 2 and -1 at the same time?

covert ridge Oct 7, 2023, 7:19 PM

#

No

simple mason Oct 7, 2023, 7:24 PM

#

covert ridge No

Any more questions
If not
Don't forget to close the channel using
.close

covert ridge Oct 7, 2023, 7:26 PM

#

Why is implication true when beginning condition is false?

#

Is it set like that by default?

paper depot Oct 7, 2023, 7:31 PM

#

there are a bunch of different explanations for that concept

#

it's called vacuous truth

#

but basically like

#

imagine that i tell you, "If it rains tomorrow, I'll give you $1000"

#

and imagine that the next day it does not rain, and i don't give you the money.

#

have i broken my promise?

#

@covert ridge

covert ridge Oct 7, 2023, 7:33 PM

#

paper depot have i broken my promise?

No?

paper depot Oct 7, 2023, 7:33 PM

#

exactly.

#

so in that scenario, my promise is kept.

#

i.e. my statement was true.

#

do you agree?

covert ridge Oct 7, 2023, 7:35 PM

#

Yeah.

paper depot Oct 7, 2023, 7:36 PM

#

right

#

in fact, with sunny weather on the following day, i'll have kept my promise no matter what i do.

covert ridge Oct 7, 2023, 7:38 PM

#

so for the second one in that pic it should be true since those are the only roots possible and false for the first one since a number can't have 2 values?

charred forge Oct 7, 2023, 7:39 PM

#

Yes

#

Also Ann that’s a very good example

covert ridge Oct 7, 2023, 7:40 PM

#

What if I do this?

#

What difference does that left head make?

#

can I replace that double sided arrow with the phrase "if and only if?"

vocal sleetBOT Oct 7, 2023, 7:57 PM

#

@covert ridge Has your question been resolved?

vocal sleetBOT Oct 7, 2023, 8:12 PM

#

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.
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jolly mulch Oct 7, 2023, 8:34 PM

#

Its a stupid thing but english is not our first language and it has me stomped that I cant answer my kids homework

vocal sleetBOT Oct 7, 2023, 8:34 PM

#

jolly mulch Its a stupid thing but english is not our first language and it has me stomped t...

sand hedge Oct 7, 2023, 8:35 PM

#

the first part i assume you know means the number is between 56 and 65

jolly mulch Oct 7, 2023, 8:35 PM

#

Yes

#

Is it 64 because it means

#

It needs a 4 at the end?

sand hedge Oct 7, 2023, 8:35 PM

#

yes

jolly mulch Oct 7, 2023, 8:35 PM

#

Because it the ones god damn it

sand hedge Oct 7, 2023, 8:35 PM

#

if you want to explain it to your kid, they were taught about how you can splt numbers into 10's, ones etc

jolly mulch Oct 7, 2023, 8:36 PM

#

I tought it meant it needed 4 one literal 1111

#

I was like wtf

sand hedge Oct 7, 2023, 8:36 PM

#

example:

63 = 6 tens, 3 ones

#

or

#

152 = 1 100's, 5 10's and 2 1's

jolly mulch Oct 7, 2023, 8:36 PM

#

Thanks and sorry for taking from your time

sand hedge Oct 7, 2023, 8:37 PM

#

its better than doing the math im doing rn lol

cyan shadow Oct 7, 2023, 8:37 PM

#

jolly mulch I tought it meant it needed 4 one literal 1111

I am a native speaker and this is how I read it too

#

I only know it means the other way because that way makes no sense

jolly mulch Oct 7, 2023, 8:37 PM

#

Lol its good that I wasn't the only confused then

sand hedge Oct 7, 2023, 8:37 PM

#

this could be good practice for him, its just an image i found on the internet

cyan shadow Oct 7, 2023, 8:38 PM

#

It should say "It has a 4 in the one's place" - that is clear and umambigious

jolly mulch Oct 7, 2023, 8:38 PM

#

But I get it they are learning that and it was obvious that the ones meant like the single number not literal ones

sand hedge Oct 7, 2023, 8:38 PM

#

cyan shadow It should say "It has a 4 in the one's place" - that is clear and umambigious

well they want them to know its multiples of 1's

#

just like you would say 900 has 9 100's

cyan shadow Oct 7, 2023, 8:39 PM

#

yeah thats right, it just doesn't work for 1s

#

once you go to 10 then the meaning switches to the other one

jolly mulch Oct 7, 2023, 8:39 PM

#

sand hedge just like you would say 900 has 9 100's

Yeah thats exactly what this week lessons about I just blanked out

cyan shadow Oct 7, 2023, 8:39 PM

#

but i think the persons question was answered regardless

jolly mulch Oct 7, 2023, 8:39 PM

#

Yes it was answer thank you very much

paper depot Oct 7, 2023, 8:39 PM

#

jolly mulch I tought it meant it needed 4 one literal 1111

i think it isn't your fault btw. in any other context, "has 4 ones" would be understood as "the code contains the symbol 1 four times"

jolly mulch Oct 7, 2023, 8:41 PM

#

Does this closes automatically or do I have to input something?

cyan shadow Oct 7, 2023, 8:41 PM

#

.close

vocal sleetBOT Oct 7, 2023, 8:41 PM

#

Channel closed

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woeful hull Oct 7, 2023, 8:44 PM

#

Getting stuck, not sure how to complete the proof

vocal sleetBOT Oct 7, 2023, 8:44 PM

#

woeful hull Getting stuck, not sure how to complete the proof

woeful hull Oct 7, 2023, 8:45 PM

#

I don't think I am doing this right

#

Wait

#

if I say f^p is int

#

and I write out how exponents work

#

so like d * d *d ... p times

#

then i can factor d

#

so n^p = d * k

#

which proves it

#

but idk if thats write

#

<@&286206848099549185>

amber bridge Oct 7, 2023, 9:08 PM

#

woeful hull but idk if thats write

no, that should be good

woeful hull Oct 7, 2023, 9:08 PM

#

thanks

#

just need to write it out

jovial remnant Oct 7, 2023, 9:15 PM

#

It is just missing more clarification at the end

#

vocal sleetBOT Oct 7, 2023, 9:24 PM

#

@woeful hull Has your question been resolved?

woeful hull Oct 7, 2023, 9:25 PM

#

jovial remnant

so I should write it like that

vocal sleetBOT Oct 7, 2023, 9:55 PM

#

@woeful hull Has your question been resolved?

woeful hull Oct 7, 2023, 10:04 PM

#

.close

vocal sleetBOT Oct 7, 2023, 10:04 PM

#

Channel closed

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astral notch Oct 7, 2023, 10:09 PM

#

Is there a way to somehow represent this as a series of dots in desmos?

vocal sleetBOT Oct 7, 2023, 10:09 PM

#

astral notch Is there a way to somehow represent this as a series of dots in desmos?

astral notch Oct 7, 2023, 10:10 PM

#

Or is desmos only strictly used for functions?

#

Where v is on the y-axis and t is on the x-axis

vocal sleetBOT Oct 7, 2023, 10:25 PM

#

@astral notch Has your question been resolved?

vocal sleetBOT Oct 7, 2023, 10:56 PM

#

@astral notch Has your question been resolved?

vocal sleetBOT Oct 7, 2023, 11:57 PM

#

@astral notch Has your question been resolved?

heady ibex Oct 8, 2023, 1:35 AM

#

desmos can have points

#

and tables

#

afaik

vocal sleetBOT Oct 8, 2023, 2:16 AM

#

@astral notch Has your question been resolved?

astral notch Oct 8, 2023, 2:16 AM

#

heady ibex and tables

That was what I was asking about, but at the same time, I am asking for a way to place them out efficiently.

#

Like, after the expression that I wrote.

#

And it's not like really a function, what I am doing here is kinda different.

#

You can try placing them out yourself after the pattern I wrote here, and you get exhausted pretty early. There has to be a tool for this, why wouldn't there be?

heady ibex Oct 8, 2023, 2:17 AM

#

i cannot really read what you wrote

astral notch Oct 8, 2023, 2:18 AM

#

heady ibex i cannot really read what you wrote

I'll rewrite it, brb

astral notch Oct 8, 2023, 2:20 AM

#

heady ibex i cannot really read what you wrote

heady ibex Oct 8, 2023, 2:20 AM

#

a is just a number?

astral notch Oct 8, 2023, 2:22 AM

#

heady ibex a is just a number?

a, delta t, f
are pre-set numbers.

heady ibex Oct 8, 2023, 2:23 AM

#

you're basically just integrating

#

idk what it's called other than integrating

#

it's numerical integration of differential equations

astral notch Oct 8, 2023, 2:24 AM

#

heady ibex you're basically just integrating

Yeah I got an integrating-ish pattern as I incremented t, but I wasn't really able to turn it into a nice graphical representation. So I am still on square 1, in a way.

heady ibex Oct 8, 2023, 2:25 AM

#

you can do it using python

#

idk if you can do it using desmos

astral notch Oct 8, 2023, 2:25 AM

#

heady ibex you can do it using python

But you usually use libraries with python. Do you have any libraries that are appropriate for this?

astral notch Oct 8, 2023, 2:25 AM

#

heady ibex you're basically just integrating

Can you elaborate on what you mean by this?

heady ibex Oct 8, 2023, 2:26 AM

#

for visualization just use matplotlib

astral notch Oct 8, 2023, 2:26 AM

#

Cause I don't think I can make a nice graph out of this expression like you can with like y = 2^x or something like that

heady ibex Oct 8, 2023, 2:26 AM

#

for the maths just use python maybe use numpy

#

numerical integration

astral notch Oct 8, 2023, 2:26 AM

#

astral notch Cause I don't think I can make a nice graph out of this expression like you can ...

What I am doing here seems a lot more recursive

heady ibex Oct 8, 2023, 2:26 AM

#

is finding the next point using previous points

astral notch Oct 8, 2023, 2:26 AM

#

astral notch What I am doing here seems a lot more recursive

New things appear in the new expression

astral notch Oct 8, 2023, 2:27 AM

#

heady ibex is finding the next point using previous points

Is that it's own field of mathmatics? I would be interested in researching more about it. But I am having a giant break from maths so I have no university teacher or anything like that available so I have to do this on my free-time.

heady ibex Oct 8, 2023, 2:28 AM

#

numerical integration

#

there was a subject in university for using it to solve problems in physics and astronomy in my university

vocal sleetBOT Oct 8, 2023, 4:16 AM

#

Channel closed

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vocal sleetBOT Oct 8, 2023, 4:40 AM

#

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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tardy flint Oct 8, 2023, 5:13 AM

#

vocal sleetBOT Oct 8, 2023, 5:13 AM

#

tardy flint

tardy flint Oct 8, 2023, 5:13 AM

#

where am i going wrong 😭

grizzled halo Oct 8, 2023, 5:14 AM

#

check domain of f as well?

tardy flint Oct 8, 2023, 5:23 AM

#

grizzled halo check domain of f as well?

like by adding another union sign with the domain of the original f function?

vocal sleetBOT Oct 8, 2023, 5:38 AM

#

@tardy flint Has your question been resolved?

#

Channel closed

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vocal sleetBOT Oct 8, 2023, 6:30 AM

#

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idle salmon Oct 8, 2023, 7:20 AM

#

can someone tell me how to prove this question whether it's false/true please? i don't know what kind of formula that i have to use

vocal sleetBOT Oct 8, 2023, 7:20 AM

#

idle salmon can someone tell me how to prove this question whether it's false/true please? i...

pallid zenith Oct 8, 2023, 7:21 AM

#

idle salmon can someone tell me how to prove this question whether it's false/true please? i...

whats the average of the numbers 1 through 7?

idle salmon Oct 8, 2023, 7:22 AM

#

pallid zenith whats the average of the numbers 1 through 7?

4??

pallid zenith Oct 8, 2023, 7:22 AM

#

yes

#

okay, now i select 2 numbers randomly from the numbers 1 through 7

#

will the average of these two numbers always be higher than 4?

idle salmon Oct 8, 2023, 7:23 AM

#

Depends? if i choose 1 &2 it's lower than 4

pallid zenith Oct 8, 2023, 7:24 AM

#

yea

#

and if you choose 6 and 7 then no

#

and if you choose 3 and 5 its exactly 4

idle salmon Oct 8, 2023, 7:24 AM

#

pallid zenith and if you choose 6 and 7 then no

Right

pallid zenith Oct 8, 2023, 7:24 AM

#

so it seems like we could have a case where anything could happen

#

and we cant say for sure

#

you might get unlucky and pick some high numbers or super low ones

#

do you see how this is related to your question?

idle salmon Oct 8, 2023, 7:25 AM

#

pallid zenith do you see how this is related to your question?

yeaa

#

could i answer this question with "false" ?? cause it's not always in a true condition

pallid zenith Oct 8, 2023, 7:27 AM

#

unless im missing the trick yea

idle salmon Oct 8, 2023, 7:28 AM

#

okay got this, thanks!!

vocal sleetBOT Oct 8, 2023, 7:43 AM

#

@idle salmon Has your question been resolved?

vocal sleetBOT Oct 8, 2023, 7:58 AM

#

Channel closed

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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

balmy pulsar Oct 8, 2023, 8:19 AM

#

guys can someone verify if this statement is true or not?

$a^{p-1} \equiv 1 \mod p$ if a and p are coprime

vocal sleetBOT Oct 8, 2023, 8:19 AM

#

balmy pulsar guys can someone verify if this statement is true or not? $a^{p-1} \equiv 1 \mo...

twin meteorBOT Oct 8, 2023, 8:19 AM

#

CrazyCuber217

balmy pulsar Oct 8, 2023, 8:19 AM

#

i know its fermats little theorem but im not sure if it still holds if p isnt necessarily a prime number

#

and the wikipedia page wasn't very clear

proven garden Oct 8, 2023, 8:25 AM

#

if p is not a prime then it becomes Euler's theorem

balmy pulsar Oct 8, 2023, 8:25 AM

#

ohh ty

#

but its still always true right?

proven garden Oct 8, 2023, 8:26 AM

#

if a and n are coprime then $a^{\varphi(n)}\equiv 1 \mod n$

balmy pulsar Oct 8, 2023, 8:26 AM

#

phi?

#

where'd that come from?

proven garden Oct 8, 2023, 8:27 AM

#

it's euler's toitient function

balmy pulsar Oct 8, 2023, 8:27 AM

#

wouldn't it just be n-1 in the exponent?

balmy pulsar Oct 8, 2023, 8:27 AM

#

proven garden it's euler's toitient function

oh what's that?

twin meteorBOT Oct 8, 2023, 8:27 AM

#

WhereWolf(ping if needed)

proven garden Oct 8, 2023, 8:27 AM

#

phi(n) is the number of natural number coprime to n that is smaller then n

balmy pulsar Oct 8, 2023, 8:28 AM

#

T-T

proven garden Oct 8, 2023, 8:28 AM

#

The Euler's formula is a generalization to Fermat's little theorem

balmy pulsar Oct 8, 2023, 8:28 AM

#

okok

#

i didn't rly understand the phi thing, but as long as a and p are coprime, the theorem holds right?

#

even if p isnt prime

#

for a^(p-1) only

proven garden Oct 8, 2023, 8:29 AM

#

if p is a prime then a^(p-1) is congruent to 1

balmy pulsar Oct 8, 2023, 8:29 AM

#

yep

proven garden Oct 8, 2023, 8:29 AM

#

if p is not a prime then no

balmy pulsar Oct 8, 2023, 8:29 AM

#

if a and p are coprime?

proven garden Oct 8, 2023, 8:29 AM

#

then you can only say that a^phi(b) is congruent to 1

balmy pulsar Oct 8, 2023, 8:29 AM

#

then?

#

u sure? sorry for doubting but google's giving varied results and i wanted to clarify

#

WhatsApp_Image_2023-10-08_at_13.58.51_db86ff8c.jpg

proven garden Oct 8, 2023, 8:32 AM

#

I think they assumed p is prime

balmy pulsar Oct 8, 2023, 8:32 AM

#

ohh ok makes sense

#

tysm!

#

.close

vocal sleetBOT Oct 8, 2023, 8:32 AM

#

Channel closed

Closed by @balmy pulsar

Use .reopen if this was a mistake.

proven garden Oct 8, 2023, 8:32 AM

#

no problem

vocal sleetBOT Oct 8, 2023, 8:33 AM

#

Available help channel!

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• Be polite and have a nice day!

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balmy pulsar Oct 8, 2023, 9:00 AM

#

random question

vocal sleetBOT Oct 8, 2023, 9:00 AM

#

balmy pulsar random question

balmy pulsar Oct 8, 2023, 9:00 AM

#

related to previous question

#

fermats little theorem is only applicable if a is not a multiple of p, and p is prime

#

but what if a and p are merely coprime?

#

i randomly tried a few examples where p isn't prime but a and p are coprime and all of them still were congruent to 1 mod p

#

is this just a coincedence? if this new conjencture is false, could someone give an example where it's not true?

proven garden Oct 8, 2023, 9:03 AM

#

what examples have you tried?

balmy pulsar Oct 8, 2023, 9:05 AM

#

a = 13, p = 6
a = 13, p = 4
a = 2, p = 9

#

oh nvm i found one

#

a = 7, p = 9

#

tysm

#

.close

vocal sleetBOT Oct 8, 2023, 9:05 AM

#

Channel closed

Closed by @balmy pulsar

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noble lynx Oct 8, 2023, 9:14 AM

#

vocal sleetBOT Oct 8, 2023, 9:14 AM

#

noble lynx

warped gazelle Oct 8, 2023, 9:15 AM

#

hmm

#

did you learn sum

#

formulas

noble lynx Oct 8, 2023, 9:15 AM

#

yaya

warped gazelle Oct 8, 2023, 9:15 AM

#

ok

#

r(r+1) = r^2 + r

#

you can just split them

noble lynx Oct 8, 2023, 9:15 AM

#

i lied what is that

#

IM SORRY

warped gazelle Oct 8, 2023, 9:16 AM

#

so

noble lynx Oct 8, 2023, 9:16 AM

#

what is r^2 + r

warped gazelle Oct 8, 2023, 9:16 AM

#

hmm

#

$r(r+1) = r^2 + r$

twin meteorBOT Oct 8, 2023, 9:16 AM

#

A_Note

noble lynx Oct 8, 2023, 9:16 AM

#

yes makes sense

warped gazelle Oct 8, 2023, 9:16 AM

#

then

#

you use formulas

#

of

#

r^2

#

and r

noble lynx Oct 8, 2023, 9:17 AM

#

wait why

#

did you convert it

warped gazelle Oct 8, 2023, 9:17 AM

#

hmm?

#

let's suppose

#

there's sum called a

#

and another

#

called b

noble lynx Oct 8, 2023, 9:18 AM

#

just write sigmaew

warped gazelle Oct 8, 2023, 9:18 AM

#

ok

#

just doing a+b

#

like

#

sigma k=1 (r^2 + r) = sigma k=1 r^2 + sigma k=1 r

noble lynx Oct 8, 2023, 9:19 AM

#

ya

warped gazelle Oct 8, 2023, 9:19 AM

#

makes sense?

noble lynx Oct 8, 2023, 9:19 AM

#

yes

warped gazelle Oct 8, 2023, 9:19 AM

#

so

noble lynx Oct 8, 2023, 9:19 AM

#

got it

#

understand

warped gazelle Oct 8, 2023, 9:19 AM

#

sigma k=1 r^2 = n(n+1)(2n+1) / 6 did you learn that?

noble lynx Oct 8, 2023, 9:20 AM

#

what

#

okay wait i've learnt everything

#

but i dont understand

#

what method of proving i need to use

#

pmi?

warped gazelle Oct 8, 2023, 9:20 AM

#

you use something.. called..

noble lynx Oct 8, 2023, 9:20 AM

#

contradiction?

warped gazelle Oct 8, 2023, 9:20 AM

#

no

noble lynx Oct 8, 2023, 9:20 AM

#

what

warped gazelle Oct 8, 2023, 9:20 AM

#

you dont use contradiction when getting the exact value

noble lynx Oct 8, 2023, 9:21 AM

#

inductionnn?

warped gazelle Oct 8, 2023, 9:21 AM

#

k

#

you just some everything of these:

#

suppose you are working out

#

sigma k=1 n (k^2)

#

so

#

$2^2 - 1^2$

twin meteorBOT Oct 8, 2023, 9:22 AM

#

A_Note

noble lynx Oct 8, 2023, 9:22 AM

#

THIS'LL TAKE SO LONGGUHUHUHUH

warped gazelle Oct 8, 2023, 9:22 AM

#

$3^2 - 2^2$

twin meteorBOT Oct 8, 2023, 9:22 AM

#

A_Note

noble lynx Oct 8, 2023, 9:22 AM

#

CAN YOU DO IT FOR ME

#

🙏

#

i'll understand from working

#

promisuh

warped gazelle Oct 8, 2023, 9:22 AM

#

uh

#

i think i'll just write down in my note and show you

#

lol

noble lynx Oct 8, 2023, 9:23 AM

#

yes ty

#

solve please

#

i have sm work and its all due tom i'm legit crying

#

not really

warped gazelle Oct 8, 2023, 9:23 AM

#

wait it might take minutes

#

do some other things

noble lynx Oct 8, 2023, 9:23 AM

#

yesuh ty

warped gazelle Oct 8, 2023, 9:28 AM

#

ok i'm transporting the image through the device. would take 2 more minute

#

#

i dont know

#

lol

#

#

#

#

IF you dont understand sigma k=1 n (k) =n(n+1)/2,

#

1,2,...,n the average is (n+1)/2 and the amount is n

noble lynx Oct 8, 2023, 9:32 AM

#

i

#

i think im gonna cry

warped gazelle Oct 8, 2023, 9:32 AM

#

uh

noble lynx Oct 8, 2023, 9:32 AM

#

THANK YOU

#

but i think im gonna go take a nap

warped gazelle Oct 8, 2023, 9:32 AM

#

lol

noble lynx Oct 8, 2023, 9:32 AM

#

i'll go through it later yty

warped gazelle Oct 8, 2023, 9:35 AM

#

i think the last part is a little dark for you

vocal sleetBOT Oct 8, 2023, 9:47 AM

#

@noble lynx Has your question been resolved?

vocal sleetBOT Oct 8, 2023, 10:02 AM

#

Channel closed

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vast shale Oct 8, 2023, 10:05 AM

#

vocal sleetBOT Oct 8, 2023, 10:05 AM

#

vast shale

autumn quartz Oct 8, 2023, 10:05 AM

#

Hi

#

oh come on

vast shale Oct 8, 2023, 10:05 AM

#

Lol sorry

vocal sleetBOT Oct 8, 2023, 10:20 AM

#

@vast shale Has your question been resolved?

coarse gust Oct 8, 2023, 10:29 AM

#

So both of the triangles are similar

#

Small triangle with have hypotenuse 5

#

Then what will be the length of n with similar triangles?

#

@vast shale

coarse gust Oct 8, 2023, 10:33 AM

#

coarse gust So both of the triangles are similar

As equiangular

vocal sleetBOT Oct 8, 2023, 10:35 AM

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ebon idol Oct 8, 2023, 11:10 AM

#

In the figure, ABCD is a square and △EDC is an equilateral triangle. Prove that
(i) AE=BE
(ii) ∠DAE=15

vocal sleetBOT Oct 8, 2023, 11:10 AM

#

ebon idol In the figure, ABCD is a square and △EDC is an equilateral triangle. Prove that ...

ebon idol Oct 8, 2023, 11:12 AM

#

#

help

#

pls help

#

or i cry

warped gazelle Oct 8, 2023, 11:25 AM

#

lol

#

△ADE≡△BCE for the first

1, ∠ADE = ∠BCE = 150°
2, AD = BC
3, DE = CE

#

△ADE is isosceles triangle so ∠ADE = 90° + 60° = 150°
∠DAE = (180°-150°)/2 = 15° is for the second

ebon idol Oct 8, 2023, 11:32 AM

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how is ade isosceles trianogle

#

tell fast

warped gazelle Oct 8, 2023, 11:45 AM

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because

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AD = DE

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because

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AD = DC and DC = DE

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sorry but i was eating 🍞

ebon idol Oct 8, 2023, 11:47 AM

#

warped gazelle AD = DC and DC = DE

why an i stupid

vocal sleetBOT Oct 8, 2023, 12:02 PM

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winter bison Oct 8, 2023, 12:18 PM

#

Hello! I need help with this exercise:


- There are an infinite number of numbers that belong to the interval```
From my point of view, this statement is true. I think it is true because between the value -2 and -3 for example, there can be -2.5, -2.005, -2.99......

I know that maybe this statement refers to intervals that have the infinity symbol [-∞, +∞], but I'm stuck because maybe the statement can be true in this case.

Thanks!

vocal sleetBOT Oct 8, 2023, 12:18 PM

#

winter bison Hello! I need help with this exercise: ```(2) Given the interval [-4, -2], mark...

fleet ember Oct 8, 2023, 12:27 PM

#

it's true

vocal sleetBOT Oct 8, 2023, 12:33 PM

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winter bison Oct 8, 2023, 12:54 PM

#

thanks! @fleet ember

vocal sleetBOT Oct 8, 2023, 12:54 PM

#

winter bison thanks! <@249632691564183553>

winter bison Oct 8, 2023, 12:55 PM

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.close

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thick wolf Oct 8, 2023, 1:08 PM

#

vocal sleetBOT Oct 8, 2023, 1:08 PM

#

thick wolf

thick wolf Oct 8, 2023, 1:08 PM

#

#

Is this correct?

#

Oh

#

First term is 22

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1150

mint crypt Oct 8, 2023, 1:15 PM

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Yes, 1150 is correct

thick wolf Oct 8, 2023, 1:21 PM

#

Part b

#

#

First 10 rows at 20 dollars each

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*40 dollars

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Got it

#

.close

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warm swift Oct 8, 2023, 1:44 PM

#

Hey, I'm doing this exercise for Fourier analysis. So far I'm a bit stuck on the hint. Where can I apply this?
(\bf{Exercise:}) Let (f_k : [-\pi, \pi] \to \mathbb{C}) be a sequence of continuously differentiable functions, and let (f'_k \to g) uniformly as (k \to \infty). Suppose (a \in [-\pi, \pi]), (c \in \mathbb{C}), and (f_k(a) \to c) as (k \to \infty). Then, (f_k) converges uniformly to a function (f : [-\pi, \pi] \to \mathbb{C}) with (f' = g).

vocal sleetBOT Oct 8, 2023, 1:44 PM

#

warm swift Hey, I'm doing this exercise for Fourier analysis. So far I'm a bit stuck on the...

warm swift Oct 8, 2023, 1:44 PM

#

So please give me some pointers to get started :)

twin meteorBOT Oct 8, 2023, 1:46 PM

#

Vepnar

warm swift Oct 8, 2023, 1:47 PM

#

The hint is to use the fundamental theorem of calculus

#

<@&286206848099549185>

vocal sleetBOT Oct 8, 2023, 2:17 PM

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@warm swift Has your question been resolved?

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proven garden Oct 8, 2023, 2:35 PM

#

Let ≤ be the relation defined on the set A={1, 4, 13, 17, 221, 52} by the rule: x≤y iffx|y.

vocal sleetBOT Oct 8, 2023, 2:35 PM

#

proven garden Let ≤ be the relation defined on the set A={1, 4, 13, 17, 221, 52} by the rule: ...

proven garden Oct 8, 2023, 2:36 PM

#

Guys how is this antisymmetric?

vocal sleetBOT Oct 8, 2023, 2:51 PM

#

@proven garden Has your question been resolved?

heady ibex Oct 8, 2023, 2:57 PM

#

if x <= y

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then x | y

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but if x != y

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then y !| x

#

so y !<= x

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$\begin{rcases} x \leq y \Rightarrow & x | y \ & x \neq y \end{rcases} \Rightarrow y \nmid x \Rightarrow y \nleq x$

twin meteorBOT Oct 8, 2023, 3:09 PM

#

Katharine

heady ibex Oct 8, 2023, 3:09 PM

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@proven garden I hope that helps

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I hope it's clear too

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cuz idk if it is

proven garden Oct 8, 2023, 3:10 PM

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proven garden Let ≤ be the relation defined on the set A={1, 4, 13, 17, 221, 52} by the rule: ...

Thanks but I don’t really get it, I mean obviously here there are antisymmetric pairs cuz every number divides itself, however there are also pairs like 17|221

#

So I am not sure if I can claim this is antisymmetric

heady ibex Oct 8, 2023, 3:11 PM

#

what's the problem with 17|221

proven garden Oct 8, 2023, 3:13 PM

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17/=221

heady ibex Oct 8, 2023, 3:14 PM

#

i'm not sure i understand what you're saying

proven garden Oct 8, 2023, 3:17 PM

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The relation R is antisymmetric, specifically for all a and b in A if R(x, y) and R(y, x), then x = y

heady ibex Oct 8, 2023, 3:18 PM

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Exactly

#

Your relation is defined as

#

If xRy then x is a divisor of y

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Yes?

proven garden Oct 8, 2023, 3:43 PM

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yes

heady ibex Oct 8, 2023, 3:54 PM

#

if x | y then y = nx

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in order for y | x, x = my

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y = nm y

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so n = 1 and m = 1

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as both need to be natural numbers

#

meaning only when x = y can x | y and y | x both be true

#

and so the same applies for the relation you have

#

unless your relation has some other properties

vocal sleetBOT Oct 8, 2023, 4:13 PM

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nova delta Oct 8, 2023, 4:29 PM

#

hi

vocal sleetBOT Oct 8, 2023, 4:29 PM

#

nova delta hi

nova delta Oct 8, 2023, 4:30 PM

#

im having trouble with induction. let me just grab the photo

#

#

its mainly the k-3

#

#

I get this^ but how do i express the formula of C(k+1)

stable sigil Oct 8, 2023, 4:33 PM

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its written above?

#

3Ck

nova delta Oct 8, 2023, 4:42 PM

#

where did you get that answer? i only have one shot at this since webassign allows 5 tries and i used up 4/5 of them lol

#

at first i thought it was 3c+1

vocal sleetBOT Oct 8, 2023, 5:00 PM

#

@nova delta Has your question been resolved?

nova delta Oct 8, 2023, 5:02 PM

#

<@&286206848099549185>

vocal sleetBOT Oct 8, 2023, 5:32 PM

#

@nova delta Has your question been resolved?

gleaming hare Oct 8, 2023, 6:11 PM

#

r_n+s_0=124 ig

vocal sleetBOT Oct 8, 2023, 6:37 PM

#

@nova delta Has your question been resolved?

vocal sleetBOT Oct 8, 2023, 8:38 PM

#

@nova delta Has your question been resolved?

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sudden pike Oct 8, 2023, 8:55 PM

#

hi

vocal sleetBOT Oct 8, 2023, 8:55 PM

#

sudden pike hi

ornate ember Oct 8, 2023, 8:56 PM

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hi, did you have a question?

sudden pike Oct 8, 2023, 8:56 PM

#

#

#

.rotate

#

anyways i have no clue how to get x

ornate ember Oct 8, 2023, 8:57 PM

#

,rccw

twin meteorBOT Oct 8, 2023, 8:57 PM

#

cold breach Oct 8, 2023, 8:57 PM

#

um

#

that is 4 squared

#

not 6

sudden pike Oct 8, 2023, 8:57 PM

#

cold breach not 6

where do you see a 6

cold breach Oct 8, 2023, 8:57 PM

#

sudden pike

this

sudden pike Oct 8, 2023, 8:58 PM

#

4^2 = 16

cold breach Oct 8, 2023, 8:58 PM

#

yeah but, you are supposed to square 6, not 4

sudden pike Oct 8, 2023, 8:58 PM

#

what 6

#

there is o 6 in the image

sudden pike Oct 8, 2023, 8:58 PM

#

sudden pike

this is the problem

#

OH

#

FUCK

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i put 4

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instead of 6

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im a dumbass

cold breach Oct 8, 2023, 8:59 PM

#

yeah

sudden pike Oct 8, 2023, 8:59 PM

#

thanks for helping me realize

cold breach Oct 8, 2023, 8:59 PM

#

lol

sudden pike Oct 8, 2023, 8:59 PM

#

.close

vocal sleetBOT Oct 8, 2023, 8:59 PM

#

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fiery wasp Oct 8, 2023, 9:20 PM

#

this author uses nonstandard terminology: he calls a "tower" a chain of sumodules of the form {0} \subset M_0 \subset \dotsb \subset M_n = M and he calls the "height of the jordan-holder tower" the length of the composition series (which he calls a jordan-holder tower). so M being an R-module of finite height means that there exists a (finite) composition series

i can do this problem easily just by using the fact that h(im f) + h(ker f) = h(M), where h(M) is the height of an R-module M and f : M --> N is an R-morphism. i don't need to do what the hint says at all. what is he trying to get me to see with this hint?

vocal sleetBOT Oct 8, 2023, 9:20 PM

#

fiery wasp this author uses nonstandard terminology: he calls a "tower" a chain of sumodule...

fiery wasp Oct 8, 2023, 9:20 PM

#

maybe this is better in the algebra channel. i didn't think of that

vocal sleetBOT Oct 8, 2023, 9:36 PM

#

@fiery wasp Has your question been resolved?

vocal sleetBOT Oct 8, 2023, 10:06 PM

#

@fiery wasp Has your question been resolved?

vocal sleetBOT Oct 8, 2023, 11:07 PM

#

@fiery wasp Has your question been resolved?

vocal sleetBOT Oct 9, 2023, 1:09 AM

#

@fiery wasp Has your question been resolved?

valid void Oct 9, 2023, 5:16 AM

#

fiery wasp this author uses nonstandard terminology: he calls a "tower" a chain of sumodule...

The hint just want you to see that these chains stabilize, but what you did works yes

vocal sleetBOT Oct 9, 2023, 6:36 AM

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@fiery wasp Has your question been resolved?

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tribal holly Oct 9, 2023, 10:51 AM

#

yo

vocal sleetBOT Oct 9, 2023, 10:51 AM

#

tribal holly yo

tribal holly Oct 9, 2023, 10:51 AM

#

boys

#

fact or cap

#

strong grove Oct 9, 2023, 10:51 AM

#

,rccw

twin meteorBOT Oct 9, 2023, 10:51 AM

#

tribal holly Oct 9, 2023, 10:52 AM

#

strong grove ,rccw

wow cool command

hard atlas Oct 9, 2023, 10:52 AM

#

well ^ is never written out on paper

tribal holly Oct 9, 2023, 10:52 AM

#

ik but i did because

#

i put the numbers next to

strong grove Oct 9, 2023, 10:52 AM

#

seems ok, u can simply the power tho

tribal holly Oct 9, 2023, 10:52 AM

#

too*

viral copper Oct 9, 2023, 10:53 AM

#

hard atlas well ^ is never written out on paper

gonna have to tell that to gen alpha

tribal holly Oct 9, 2023, 10:53 AM

#

i can simplify more?

hard atlas Oct 9, 2023, 10:53 AM

#

simplify 4/12

tribal holly Oct 9, 2023, 10:55 AM

#

by divde by 4

#

1/3

#

?

strong grove Oct 9, 2023, 10:56 AM

#

yeah

tribal holly Oct 9, 2023, 10:56 AM

#

#

,rccw

twin meteorBOT Oct 9, 2023, 10:56 AM

#

tribal holly Oct 9, 2023, 10:56 AM

#

is this fact or cap?

strong grove Oct 9, 2023, 10:56 AM

#

seems good , u can simplify 2/4 further also

tribal holly Oct 9, 2023, 10:57 AM

#

but im confused

#

look

#

--?

strong grove Oct 9, 2023, 10:57 AM

#

same base multiplying , powers add

proven garden Oct 9, 2023, 10:57 AM

#

why --

#

when multiplying you add

tribal holly Oct 9, 2023, 10:58 AM

#

oh

real pagoda Oct 9, 2023, 10:58 AM

#

isnt it +-

tribal holly Oct 9, 2023, 10:58 AM

#

its not minus

#

because

#

the exponent tihngs

#

isnt in fraction

#

mb

tribal holly Oct 9, 2023, 10:58 AM

#

real pagoda isnt it +-

ye

tribal holly Oct 9, 2023, 10:59 AM

#

strong grove same base multiplying , powers add

wdymn same base mulyplying?

strong grove Oct 9, 2023, 10:59 AM

#

x^2 . x^3 = x^(2+3)

tribal holly Oct 9, 2023, 11:00 AM

#

oh ye

strong grove Oct 9, 2023, 11:00 AM

#

same base (x)

tribal holly Oct 9, 2023, 11:00 AM

#

when multiply same base and you have powers

#

you can just add

#

ok

#

ty boys

#

.close

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#

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odd scaffold Oct 9, 2023, 11:09 AM

#

vocal sleetBOT Oct 9, 2023, 11:09 AM

#

odd scaffold

odd scaffold Oct 9, 2023, 11:09 AM

#

How do part ii I don’t know where to start

#

,rotate

twin meteorBOT Oct 9, 2023, 11:09 AM

#

proven garden Oct 9, 2023, 11:11 AM

#

notice that a^2+b^2 can be factored into (a+bi)(a-bi)

odd scaffold Oct 9, 2023, 11:12 AM

#

Ya

#

Now what?

calm lantern Oct 9, 2023, 11:19 AM

#

odd scaffold Now what?

Another solution involves noticing that |wz| = |w| |z| = 1
In other words, (-33/65)^2 + (56/65)^2 = 1

#

And from this equality, you can deduce 65^2 = ......

odd scaffold Oct 9, 2023, 11:20 AM

#

Lemme try that

#

Okay

#

I got $33^2 + 56^2 =65^2$

twin meteorBOT Oct 9, 2023, 11:24 AM

#

Sukiie

odd scaffold Oct 9, 2023, 11:24 AM

#

But how would I proceed finding the other solution?

calm lantern Oct 9, 2023, 11:27 AM

#

Well that's a good question 😂

#

Are parts (a) and (b) related?

odd scaffold Oct 9, 2023, 11:27 AM

#

Yea

calm lantern Oct 9, 2023, 11:27 AM

#

How did you do?

odd scaffold Oct 9, 2023, 11:35 AM

#

Actually nvm

#

Idk how to get the other one

#

<@&286206848099549185>

winter canyon Oct 9, 2023, 11:41 AM

#

quiz pls

odd scaffold Oct 9, 2023, 11:41 AM

#

Huh

winter canyon Oct 9, 2023, 11:41 AM

#

mention it

odd scaffold Oct 9, 2023, 11:42 AM

#

It’s just tutoring homework from a company called Dr du

winter canyon Oct 9, 2023, 11:43 AM

#

twin meteor

is this the quiz?

odd scaffold Oct 9, 2023, 11:43 AM

#

No

#

Just hw

winter canyon Oct 9, 2023, 11:43 AM

#

thn

#

bruh

odd scaffold Oct 9, 2023, 11:46 AM

#

.close

vocal sleetBOT Oct 9, 2023, 11:46 AM

#

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tropic anchor Oct 9, 2023, 11:57 AM

#

no.1 I'm stuck halfway

vocal sleetBOT Oct 9, 2023, 11:57 AM

#

tropic anchor no.1 I'm stuck halfway

tropic anchor Oct 9, 2023, 11:58 AM

#

#

<@&286206848099549185>

#

<@&286206848099549185>

vocal sleetBOT Oct 9, 2023, 12:24 PM

#

@tropic anchor Has your question been resolved?

tidal trail Oct 9, 2023, 12:35 PM

#

tropic anchor <@&286206848099549185>

Nvr ping like that.
They will help out when they're free

#

Why did you equate your 2 unknowns? (idk y but ended up same as my working so meh)
Ur doing pretty well up till now

Now after ur last line, compare "a" and "b" respectively (compare the coefficient, make sure the signs match)

vocal sleetBOT Oct 9, 2023, 12:39 PM

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knotty kestrel Oct 9, 2023, 1:42 PM

#

vocal sleetBOT Oct 9, 2023, 1:42 PM

#

knotty kestrel

knotty kestrel Oct 9, 2023, 1:42 PM

#

lemme just work thru it first

#

so its 2(cos(2x-1)) * -sin(2x-1) * 2

#

2 times 2 = 4 times -1 [from the -sin] = -4

#

where does the cos go

#

it disappears

livid tapir Oct 9, 2023, 1:46 PM

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Sin(2theta) = 2sin(theta)cos(theta)

knotty kestrel Oct 9, 2023, 1:46 PM

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oh right

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ok thx

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.close

vocal sleetBOT Oct 9, 2023, 1:47 PM

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Channel closed

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hollow thorn Oct 9, 2023, 2:01 PM

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vocal sleetBOT Oct 9, 2023, 2:01 PM

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hollow thorn

hollow thorn Oct 9, 2023, 2:02 PM

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Can somebody teach me part (a)

paper depot Oct 9, 2023, 2:04 PM

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!status

vocal sleetBOT Oct 9, 2023, 2:04 PM

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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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

hollow thorn Oct 9, 2023, 2:05 PM

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rn_image_picker_lib_temp_0a0fa4e4-8b28-4077-888d-0cfe28e80754.jpg

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I have no idea how to get 15.86 % as well

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Since I probably know that the probability is 0.1586

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Oh I knew it 0.5793 - 0.4207

vocal sleetBOT Oct 9, 2023, 2:21 PM

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@hollow thorn Has your question been resolved?

hoary arch Oct 9, 2023, 2:34 PM

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hollow thorn Can somebody teach me part (a)

ALRIGHT, SO THE VARIABLE HERE IS "TIME TAKEN TO COMPLETE RACE" AND WE'LL LABEL THE VARIABLE X

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THEY SAY X IS NORMALLY DISTRIBUTED. THIS MEANS X CAN BE DESCRIBED USING 2 VARIABLES: MEAN, μ = 15 & STANDARD DEVIATION, σ = 5

vocal sleetBOT Oct 9, 2023, 2:36 PM

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vocal sleetBOT Oct 9, 2023, 2:53 PM

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hoary arch Oct 9, 2023, 2:54 PM

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vocal sleetBOT Oct 9, 2023, 2:54 PM

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hoary arch

hoary arch Oct 9, 2023, 2:56 PM

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hoary arch THEY SAY X IS NORMALLY DISTRIBUTED. THIS MEANS X CAN BE DESCRIBED USING 2 VARI...

MATHEMATICIANS HAVE MADE A TABLE OF PROBABILITIES FOR A NORMAL DISTRIBUTION OF MEAN, μ = 0 & STD.DEVIATION, σ = 1, THIS IS THE Z-TABLE

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~~
IN ORDER TO USE THAT Z-TABLE FOR OUR X-VARIABLE WE NEED TO "STANDARDIZE" IT.
TO STANDARDIZE X INTO Z WE USE:

Z = X - μ / σ

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FOR YOUR QUESTION, WE NEED TO FIND 2 PROBABILITIES:

P(X < 16) STUDENT GETTING AT LEAST 1 STAR
P(X < 14) STUDENT GETTING 2 STARS

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TURNING THAT INTO Z:

|| P( X - μ / σ < (16-15)/5 ) , P( Z < 0.2 )||
|| P( X - μ / σ < (14-15)/5 ) , P( Z <-0.2 )||

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FROM THERE READ OFF THE Z-TABLE , I ASSUME YOU KNOW HOW TO

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AND THE QUESTION IS ASKING FOR STUDENTS WHO ONLY GOT 1 STAR , SO ITD BE THOSE WHO GOT AT LEAST 1 STAR - THOSE WHO GOT 2 STARS

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@hollow thorn

small valley Oct 9, 2023, 3:07 PM

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y'+2/x+2 y= 3

vocal sleetBOT Oct 9, 2023, 3:14 PM

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@hoary arch Has your question been resolved?

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vocal sleetBOT Oct 9, 2023, 4:09 PM

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mellow rampart Oct 9, 2023, 4:34 PM

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Prove that if the limit of a sequence exists, then it is unique

vocal sleetBOT Oct 9, 2023, 4:34 PM

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mellow rampart Prove that if the limit of a sequence exists, then it is unique

mellow rampart Oct 9, 2023, 4:34 PM

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Attempt:

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Suppose $(x_n) \to a$ and $(x_n) \to b$. Then for all $\epsilon > 0$, there is $N \in \mathbb{N}$ such that for all $n \ge N$, $|x_n - a| < \epsilon$. Similarly, for all $\epsilon > 0$, there is $N \in \mathbb{N}$ such that for all $n \ge N$, $|x_n - b| < \epsilon$.

twin meteorBOT Oct 9, 2023, 4:36 PM

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KN

mellow rampart Oct 9, 2023, 4:36 PM

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How can I go about showing some contradiction?

paper depot Oct 9, 2023, 4:37 PM

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assume a ≠ b for the sake of contradiction

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wlog let a < b, or something

mellow rampart Oct 9, 2023, 4:40 PM

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If $a < b$, then the $N_a$ such that for all $n \ge N_a$, the sequence should be trapped between $a \pm \epsilon_a$

twin meteorBOT Oct 9, 2023, 4:40 PM

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KN

mellow rampart Oct 9, 2023, 4:43 PM

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hm I think I have something else

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.close

vocal sleetBOT Oct 9, 2023, 4:48 PM

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mighty dust Oct 9, 2023, 4:54 PM

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what exactly is a derivative and how do I get it

vocal sleetBOT Oct 9, 2023, 4:54 PM

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mighty dust what exactly is a derivative and how do I get it

mighty dust Oct 9, 2023, 4:56 PM

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I know these equations
$$ lim_{x\to x_0} \frac{f(x)-f(x_0)}{x-x_0} $$
$$ lim_{h\to 0} \frac{f(x+h)-f(x)}{h} $$

twin meteorBOT Oct 9, 2023, 4:56 PM

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N1x1T4

mighty dust Oct 9, 2023, 4:56 PM

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But what do they even mean?

pale perch Oct 9, 2023, 4:57 PM

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theyre basically the formula m=(y2-y1)/(x2-x1)

mighty dust Oct 9, 2023, 4:57 PM

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you mean the slope?

pale perch Oct 9, 2023, 4:58 PM

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but as h->0 or x->x_0 youll get the exact derivative of the point (basically) of x

pale perch Oct 9, 2023, 4:58 PM

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mighty dust you mean the slope?

yeah

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the derivative of a function gives you the slope of whatever point

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the slope of the tangent to that point to be specific

mighty dust Oct 9, 2023, 4:59 PM

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But what is a slope

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I know it can be seen

pale perch Oct 9, 2023, 4:59 PM

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rate of change of y with respect to x

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dy/dx means a small change in y over a small change in x, ie the slope (when i say small i mean infinitesimal)

mighty dust Oct 9, 2023, 5:00 PM

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so the derivative is the slope of a specific value in the function

pale perch Oct 9, 2023, 5:01 PM

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if you drew a tangent line to any point of a function, the derivative gives you the slope of the tangent of said point

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which is the same as the slope of the function at that point

mighty dust Oct 9, 2023, 5:03 PM

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but why would I want to know the slope of a function at a certain point (except for when it's zero i.e. the peak or bottom of the function)

pale perch Oct 9, 2023, 5:04 PM

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https://en.wikipedia.org/wiki/Differential_calculus#Applications_of_derivatives

Differential calculus

In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve.The primary objects of study in differential calculus are the derivative of a function, related notions ...

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you basically cant do advanced physics without using derivatives, they come up everywhere

mighty dust Oct 9, 2023, 5:06 PM

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Well I know that It is used when calculating acceleration. But so basically it's application is mostly in physics?

pale perch Oct 9, 2023, 5:07 PM

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its extremely used in applied maths and physics etc, basically any stem field will have you using derivatives in some way

mighty dust Oct 9, 2023, 5:08 PM

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ok, ok

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well thank you

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.close

vocal sleetBOT Oct 9, 2023, 5:08 PM

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Channel closed

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wait what

are you talking about