help-38

[tight prism]

I still don't get the 765 one... since our teacher has not discussed abt the term you were describing..

since it says there how many 3 balls... But my r (selected object) was 7 and my total objects were 7 as well which makes 1

[runic dew]

everything is context dependent. Yes I would say the $765$ is also correct. The key thing is what you want

[solid kiln]

team132

[tight prism]

I'm so confused 🥲🥲

[runic dew]

Do you want combinations or something else?

[tight prism]

Combinations since our teacher said so haha

[runic dew]

then 1

[tight prism]

but that's not in the choices I was given 😭

there was 536.25 I think then there was a 3000+ given... our teacher said we needed to add 7,5, and 3

[runic dew]

I think it would be best if you clarify with your teacher

[tight prism]

you're right but I looked up online, do you think this solution is right?

this was the given

[runic dew]

The question is different now?

[tight prism]

yes but I made it relevant since it's basically the same question with a different given so I can solve the first question in the same way this was solved

[runic dew]

6C3 is the answer they want for the new question

[tight prism]

but was 10 C 3 necessary as well?

then again if I solved them like that the answer would also be 1 lol

wait not 1 nvm

[runic dew]

$(654)/(1098)$

[solid kiln]

team132

[tight prism]

wth now im even mor confused 😭

[runic dew]

Since they want probability of a hypergeometric distribution

[tight prism]

ohh

[runic dew]

My answer above is correct for the probability

The formula I am using is:

num_permutation * probability_of_single_event

The permutation of RRR is just 1

probability of event is fairly easy to calculate

[tight prism]

idk any of those 🥲 but I get ur 7x6x5/3! now

[runic dew]

That was just 7C3

that is what your teacher wants

[tight prism]

Yes but she talked abt adding the 7 red balls, 5 white balls and 3 green balls..

[runic dew]

I prefer the way I think about the content because formula I mention above can be use binomial distribution as well

Anyhow I will leave you to it

[tight prism]

ty ig 🥲

[trim jolt]

@tight prism Has your question been resolved?

Channel closed

Closed by @tight prism

Use .reopen if this was a mistake.

[trim jolt]

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.

[rugged zodiac]

can anyone help on call

[left oriole]

what is your doubt

[rugged zodiac]

i dont know how to do discriminant

[left oriole]

!original

[trim jolt]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[rugged zodiac]

Use the discriminant to determine the number and type of solutions of the following quadratic equation. 64x^2 −64x+16=0

[shrewd vessel]

do you know the formula of discriminant?

[rugged zodiac]

nah

i just started learning them

[shrewd vessel]

for a general quadratic $f(x) = ax^2+bx+c$, its discriminant is $b^2-4ac$

[solid kiln]

lgkoo

[shrewd vessel]

if the discriminant is positve, then two real solutions, negative then two complex solutions, and equal to zero means one repeated soln

[rugged zodiac]

thank you

[shrewd vessel]

you're welcome

[rugged zodiac]

.close

[thorny gazelle]

You have resources?

[trim jolt]

Channel closed

Closed by @rugged zodiac

Use .reopen if this was a mistake.

[rugged zodiac]

what you mean?

[thorny gazelle]

Materials that you learn with, Eg books

[rugged zodiac]

i just go to class

but he did not teach us this yet

and i am trying to do it before he teaches it

[thorny gazelle]

Then you should read it from a book. When you have little understanding. Explanation is easier

[trim jolt]

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.

[rugged zodiac]

Use the square roots property to solve the quadratic equation (w+1/2)^2+4=21 nter exact answers in radical form. If there are multiple answers, list them separated by a comma, e.g.
1,2 . If there is no solution, enter
∅
.

[trim jolt]

@rugged zodiac Has your question been resolved?

[trim jolt]

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[rugged zodiac]

Use the square roots property to solve the quadratic equation (6x-7)^2+4=21 If there are multiple answers, list them separated by a comma, e.g.
1,2. If there is no solution, enter
∅
.

[trim jolt]

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.

[rugged zodiac]

Use the square roots property to solve the quadratic equation (6x-7)^2+4=21 If there are multiple answers, list them separated by a comma, e.g.
1,2. If there is no solution, enter
∅
.

[left oriole]

what is your doubt?

[rugged zodiac]

i got x=7x+sqaure root of 17/6, 7x-sqaure root of 17/6,

nvm

i got it

.close

[trim jolt]

Channel closed

Closed by @rugged zodiac

Use .reopen if this was a mistake.

[trim jolt]

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.

[scenic delta]

Is there a formula for the nth composition of a second degree polynomial?

[trim jolt]

@scenic delta Has your question been resolved?

[unreal elk]

1 den n^2 ye kadar olan sayıların toplamını mı istiyorsun @scenic delta

[trim jolt]

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.

[full moth]

Hey

[full moth]

Somoene can Help me resolve this

I guet the result but I'm not sure about the step

Ty already

[nimble stone]

what step

[trim jolt]

@full moth Has your question been resolved?

[full moth]

When I need to find the constant

I already find the form of the general solution

But im struggling with the constants

[nimble stone]

the two pieces of information on the right are your friends for that part

[full moth]

I know but I don't remember how I have to do it

[nimble stone]

well
x=e^(at)[A+Bt]

x(0)=e^0 [A+0]=0 so A=0

similar idea with the derivative

[trim jolt]

@full moth Has your question been resolved?

Channel closed

Closed by @full moth

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.

[supple copper]

Given : cosα = 24/25, where 3π/2 < α < 2π and sinβ = 4/5 where π/2 < β < π
calculate:
a) sin 2α
b) cos 2α
c) sin(α-β)
d) tg (α-β)

[vapid grove]

double angle identity for first 2

[worthy scroll]

These are going to help you

[supple copper]

.close

[trim jolt]

Channel closed

Closed by @supple copper

Use .reopen if this was a mistake.

[trim jolt]

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.

[solemn sierra]

is (n!) at the power of 2 -------) (n!)(n!) ?

[fallow swift]

I think so

For example

(3!)^2=36

(3!)(3!)=36

[solemn sierra]

okay yes thank you !

[smoky snow]

Just stick to the definition of power of 2, wich is x to the power of 2 equal to xx

[solemn sierra]

!close

[solemn sierra]

thanks!

[smoky snow]

It’s .close

[solemn sierra]

.close

[trim jolt]

Channel closed

Closed by @solemn sierra

Use .reopen if this was a mistake.

[trim jolt]

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.

[austere pendant]

Suppose n > 1 is an integer such that 4((n − 1)! + 1) ≡ 0 (mod n). Prove that n = 4 or n is prime.

[austere pendant]

I found out that my first step is wrong lmao. What did I do wrong?

$$ 4((n-1)!+1) \equiv 0 (mod n) $$

[solid kiln]

thiccyoshi4568

[austere pendant]

$$ \frac {4(n!)}{4n} + 4 = nk $$

[solid kiln]

thiccyoshi4568

[austere pendant]

$$ (n-1)! = \frac {n!}{n} $$

[solid kiln]

thiccyoshi4568

[zinc dove]

You shouldn’t put 4 in the denominator

[austere pendant]

Oh haha I'm a dumbass

Thanks

.close

[trim jolt]

Channel closed

Closed by @austere pendant

Use .reopen if this was a mistake.

[austere pendant]

.close

???

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[deft oyster]

where a and b are just trivial integers to represent p for the purposes of another question

[ionic pendant]

in spherical coordinates $\odif V = \rho^2 \sin \phi \odif{\rho,\phi,\theta}$

[solid kiln]

pnoןɔ

[deft oyster]

tysm

[trim jolt]

@deft oyster Has your question been resolved?

[deft oyster]

the same thing for sin there now that i mentioned it

shouldnt it be sin phi?

why are they both in theta

[deft oyster]

as per this definition of dV even, it should be sin tau, not sin theta as given here

[ionic pendant]

seems to be a mistake, they write it as sin φ in the next line

[deft oyster]

you are absolutely right and i just clocked that myself, the rest is Fubini theorem

thank you so much for your helkp

.close

[trim jolt]

Channel closed

Closed by @deft oyster

Use .reopen if this was a mistake.

[trim jolt]

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.

[terse cipher]

Can i work on this with someone

[wraith hinge]

Do you know the probability that an ace is drawn out of the 52 cards?

[trim jolt]

@terse cipher Has your question been resolved?

[somber onyx]

Calculate probability for when you draw Ace then a 'ten' value,
calculate probability for drawing a 'ten' value then an Ace
then combine the probabilities

[trim jolt]

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.

[frigid lark]

help

I tried taking moments but i kind of forgot how to

can someone walk me through it?

[trim jolt]

@frigid lark Has your question been resolved?

[frigid lark]

<@&286206848099549185>

I have to go to class in a minute so I won't be able to respond to follow up questions for a bit but I still need help on this question

[frigid lark]

<@&286206848099549185>

[trim jolt]

@frigid lark Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[trim jolt]

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.

[nimble wind]

Super confused on where to start on this

[nimble wind]

should i be splitting the intergral into 2?

[cunning timber]

yeah

essentially your integrand changes based on the bounds

[nimble wind]

okay and then like one is for up to pi/2

and the other is for pi/2 to pi

and i add the answers together

[cunning timber]

yeah

so for 0 to pi/2 integral you integrate sinx

then for pi/2 to pi you integrate cosx

[nimble wind]

idek why i asked that all i needed to do was stare hard enough lol

[nimble wind]

ohh okay and id do like anti derivative

make it nice and easy

Thanks Jaxx!

[cunning timber]

👍

[nimble wind]

.close

[trim jolt]

Channel closed

Closed by @nimble wind

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.

[shrewd otter]

I'm on this problem, now I get to P = e^(Gt)

which gives me P = e^(-λt λt λt -λt)

Then I use Maclaurin series, but it's hard to that for matrix

some notes.. take it but don't understand

<@&286206848099549185>

[trim jolt]

@shrewd otter Has your question been resolved?

[trim jolt]

@shrewd otter Has your question been resolved?

[trim jolt]

@shrewd otter Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[trim jolt]

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.

[wraith hinge]

Hello

[wraith hinge]

I just have a quick question,

If the x needs to be five units bigger to compensate from being subtracted by 5, would that not make it the same as the first function f(x)=1.2^x

[wraith hinge]

It’d be the same shape, but shifted right 5 units

Since x = 5 is the new x = 0 and blah blah blah so forth

[wraith hinge]

So, does the -5 have no effect on anything?

It does have an effect

It shifts the graph 5 units

Then, what is the x there for?

In 1.2^x, when x = 1, y = 1.2

In 1.2^(x-5), when x = 6, y = 1.2

It reaches the same values, just 5 units later than the original

[wraith hinge]

Okay, this makes a lot of sense now

behaviour and asymptotes remain the same.

👍

[trim jolt]

@wraith hinge Has your question been resolved?

Channel closed

Closed by @elder gorge

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.

[wraith hinge]

...

[wraith hinge]

i need help with surface areas

[orchid wagon]

do you know the formula for surface area of a cylinder

[wraith hinge]

yes SA = 2nr2+ 2nrh

[orchid wagon]

um

i get what you mean

but please write pi as pi, not n

and the r in the first term is squared

[wraith hinge]

oh sorry

[orchid wagon]

so the surface area is

$2\pi r^2+2\pi rh$

[solid kiln]

فطر

[orchid wagon]

so what are you waiting for? just apply the formula

[wraith hinge]

okay give me a minute

SA= 2 πr(14)²+ 2π(14)(6)

SA= 392π+168π

SA=560π

now i multiply 560x3.14 right?

@orchid wagon

[orchid wagon]

remind me what r is in the formula

[wraith hinge]

radius

[orchid wagon]

and do you think 14 is the radius?

[wraith hinge]

no

[orchid wagon]

so...?

[wraith hinge]

6

its 6

[orchid wagon]

what

no lol

[wraith hinge]

the radius is 6

[orchid wagon]

6 is the height

[wraith hinge]

huh

[orchid wagon]

can you tell me what the radius is

like, its definition

[wraith hinge]

A line that runs directly from the middle to the edge of a circle or sphere.

cylinder*

[orchid wagon]

<@&268886789983436800> um sus link

[orchid wagon]

but anyway

this checks out

and what about the diameter?

[trim jolt]

@wraith hinge Has your question been resolved?

[trim jolt]

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.

[latent axle]

Why isn’t the 1/2 distributed to the C in step 3?

[past river]

Because 1/2 times a constant is another constant

[lapis ivy]

this might be crazy but (1/2)*C = C

[latent axle]

I think you might be right

[supple copper]

You can think of them as different C’s

[past river]

1/2 = 1 confirmed

[latent axle]

But shouldn’t they attract specify c/2

At least

[lapis ivy]

[supple copper]

Yes and then they let D = c/2

Then they rename D to C

[latent axle]

Where’s that

[supple copper]

It’s a bit bad notation but it’s commonly done

[supple copper]

Hidden in the background

[lapis ivy]

naw cuz in really complex integrals that C is gonna be messed with a lot

[past river]

You can say $C_1 * \frac{1}{2} = C_2$ and then say C_2 = C. It‘s just another constant

[solid kiln]

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

[supple copper]

“c/2 is another constant” is saying let d = c/2 then d is a constant then let’s call it c instead

[lapis ivy]

slappin a C at the end of an indefinite integral is usually good

[latent axle]

Yeah I see but I feel like it’s being manipulated so it should at least be put down

[past river]

Eh, not everyone explicits everything in their work

Especially when it‘s a common thing

[latent axle]

Alr well I get it thanks

[supple copper]

It should, but it is acknowledged to be what we mean

And it isn’t a main idea of indefinite integration

So we don’t put much weight on writing that explicitly

[latent axle]

Alr

[trim jolt]

@latent axle Has your question been resolved?

[trim jolt]

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.

[glad yacht]

if x is an eigen value of a real skew symmetric matrix then prove that |1-x|/|1+x| = 1

[onyx wedge]

If u add the 2 by 1 and multiply the 6 divide the 8 you will get the answer

[glad yacht]

it can be proven that for a matrix A, A and A^T has the same eigen values. if x is an eigen value of A, x is also an eigen value of A^T. again as x is an eigen value of A, -x is an eigen value of -A and also A^T = -A, so actually -x is also an eigen value of A^T. idk if i am dum but can we say x = -x in that case? or x = 0 actually

[glad yacht]

bro what

<@&268886789983436800>

[trim jolt]

@glad yacht Has your question been resolved?

Channel closed

Closed by @glad yacht

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.

[craggy ocean]

how can i do this?

i really need help

[vagrant marsh]

direct sub

oh nvm

[craggy ocean]

what?

can you help me?

[main sigil]

hmm

[main sigil]

can you use lhopital?

[craggy ocean]

nop

[main sigil]

aw :/

[craggy ocean]

i only can use transformations

[main sigil]

alright, lemme check then

[craggy ocean]

ok

i wait

[grave pagoda]

will x + pi/4 = t work?

[craggy ocean]

i do this

[vagrant marsh]

thinking about it

[craggy ocean]

but i stuck after it

[main sigil]

it can be theoretically simplified to this limit $\frac{\cos\left(9x\right)+\sin\left(9x\right)}{\sin\left(4x\right)}$ times some constants

[solid kiln]

MethIsAlwaysRight

[craggy ocean]

how?

can you a the resolution, in a notepad?

[main sigil]

rewriting tan(4x) as sin(4x) / cos(4x)

then just putting the cos(4x) in the front of everything

[craggy ocean]

ok

[main sigil]

and it's just -1

so you can treat it like a constant

and also take 3 from the too

top

$\frac{3+3\cos\left(9x\right)+3\sin\left(x\right)-3}{\tan\left(4x\right)}=\frac{3\cos\left(9x\right)+3\sin\left(x\right)}{\frac{\sin\left(4x\right)}{\cos\left(4x\right)}}=3\cos\left(4x\right)\frac{\cos\left(9x\right)+\sin\left(9x\right)}{\sin\left(4x\right)}=-3\frac{\cos\left(9x\right)+\sin\left(9x\right)}{\sin\left(4x\right)}$

[solid kiln]

MethIsAlwaysRight

[main sigil]

it uses the limit of product is product of limits rule

[vagrant marsh]

what if you try multiplying by (cos(9x)-sin(9x))/(cos(9x)-sin(9x))

[main sigil]

Would it simplify it?

[vagrant marsh]

idk

[grave pagoda]

the tan(4x) at the bottom is still there

or sin(4x)

[main sigil]

thats the problem

It's 4x

if it was 9x it would be solved by now

and no lhop for me

i suppose not even taylor expansion can be used

[craggy ocean]

and after this?

[main sigil]

not sure yet

[craggy ocean]

substituion the variable?

[main sigil]

might be worth a try

$\frac{\cos\left(9\left(t-\frac{\pi}{4}\right)\right)+\sin\left(9\left(t-\frac{\pi}{4}\right)\right)}{\sin\left(4\left(t-\frac{\pi}{4}\right)\right)}=\frac{\cos\left(9t-\frac{9\pi}{4}\right)+\sin\left(9t-\frac{9\pi}{4}\right)}{\sin\left(4t-\pi\right)}$

[solid kiln]

MethIsAlwaysRight

[main sigil]

limit as t -> 0

[craggy ocean]

right

[main sigil]

it can be simplified a lot ig

or at least a bit

[grave pagoda]

aight done ig

[craggy ocean]

how

[main sigil]

$\frac{\sin\left(9x\right)}{\sin\left(4x\right)}$

[solid kiln]

MethIsAlwaysRight

[main sigil]

i simplified it to this

as x approaches 0

[grave pagoda]

uh

[main sigil]

but since im idiot i still cant solve that

[grave pagoda]

mine is different

[main sigil]

mine is multiplied by few constants

its not exactly like this

[grave pagoda]

taking a shit ton of time to type

f

[main sigil]

\f?

ohh

frac

\frac

is it like that?

[grave pagoda]

where's the missing }

[main sigil]

im just typing it in desmos

its faster

its in latex so you can copy paste it

[solid kiln]

Dyssrupt

[grave pagoda]

ok done

[main sigil]

similar to my approach ig

[grave pagoda]

now multiply and divide by that numerator

[main sigil]

wait

ye ic

[grave pagoda]

and apply cos double angle

[solid kiln]

Dyssrupt

[grave pagoda]

now standard limits

t tends to 0

[round mango]

cos9x+sin9x=√2 cos((pi/4)-9x),
Then we put x+pi/4=t, giving us,
√2cos(5pi/2-9t) or just √2 sin (9t)

[round mango]

And in the denominator we just have sin(-4t)

And another -1 due to the cos π

[main sigil]

mine was similar

$\frac{3+3\cos\left(9x\right)+3\sin\left(x\right)-3}{\tan\left(4x\right)}=3\cos\left(4x\right)\frac{\cos\left(9x\right)+\sin\left(9x\right)}{\sin\left(4x\right)}=-3\frac{\sqrt{2}\cos\left(9x-\frac{\pi}{4}\right)}{\sin\left(4x\right)}=-3\frac{\sqrt{2}\cos\left(9t-\frac{10\pi}{4}\right)}{\sin\left(4t-\pi\right)}=3\sqrt{2}\frac{\sin\left(9t\right)}{\sin\left(4t\right)}$

[solid kiln]

MethIsAlwaysRight

[main sigil]

t = x + pi/4

[craggy ocean]

the answer is right

what apened here?

@main sigil

[main sigil]

it's some kind of identity

cos(x) + sin(x) = sqrt2*cos(x-pi/4)

[round mango]

cos x+ sinx= sin(pi/2-x)+ sinx
And then apply sinC+sinD

To arrive here

Quite useful to remember this as an identity

[main sigil]

agreed

i use this a lot

[trim jolt]

@craggy ocean Has your question been resolved?

Channel closed

Closed by @craggy ocean

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.

[formal blaze]

how to solve for x? i moved 4^2x to the other side. i forgot how to do this with exponent rules, do i cross out the 4s?

[dusty gate]

a^m / a^n = a^(m-n)

so itll be 1/16 = 4^(6x + 18 - 2x)

[formal blaze]

oh ok, thanks sm!

[wraith hinge]

And to follow up on inf1425's message you can just take the base 4 logarithm on each side.
log_4(1/16) should just be (-2)

[formal blaze]

oh ok, and how can u tell log_4(1/16) = -2 just by looking at it?

[dusty gate]

4^2 is 16

so 4^-2 will be 1/16

[wraith hinge]

4^-1 = 1 / 4
4^-2 = 1 / 4^2
4^-2 = 1 / 16

[formal blaze]

makes sense. thanks u guys this was really helpful

[wraith hinge]

You can also solve it without logarithms if you want by rewriting 1/16 as 4^-2

then the bases would cancel out and you're left with (-2) = 4x + 18

[formal blaze]

oh ok thanks!

.close

[trim jolt]

Channel closed

Closed by @formal blaze

Use .reopen if this was a mistake.

[trim jolt]

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.

[earnest breach]

I'm not sure I understand this table

So for the first two columns, are they N/A because there's no p coordinate?

[cunning timber]

No

The first box of the left column is asking what is the x component of something in polar coordinates if I understand the table correctly

Below that is the y component in polar form

[trim jolt]

@earnest breach Has your question been resolved?

[earnest breach]

I don't think I understand still.

The x coordinate would just be p

[trim jolt]

@earnest breach Has your question been resolved?

[earnest breach]

.close

[trim jolt]

Channel closed

Closed by @earnest breach

Use .reopen if this was a mistake.

[trim jolt]

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.

[fringe marsh]

for 9.4

[fringe marsh]

I understand how to do it by induction, but i think my reasoning is off

based on the definition of N, you can repeatedly map it to another vertex

by mapping it to the vertex of it / 2 (which depends on if its even or odd)

and you can technically do this repeatedly

minus like 1/2 since its not in the domain

is there a flaw in my understanding

[trim jolt]

@fringe marsh Has your question been resolved?

[stoic iron]

you might have better luck in #discrete-math

grab the undergrad role in id:customize

[trim jolt]

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.

[long basalt]

what does the =sign with a slash threw it mean and what is the first step in solving this?

[fluid cosmos]

It means that x is not 0

It's very important because you can't divide by 0

[long basalt]

oh

[fluid cosmos]

I would say there are 2 steps

1 step consider x<0

[long basalt]

im lisining

[fluid cosmos]

2 step consider x>0

[long basalt]

?

so do i plug 0 in for x?

[fluid cosmos]

Nvm

It's easier

[fluid cosmos]

No

You cannot plug 0 in

X isn't 0

[long basalt]

oh right

[fluid cosmos]

a≠b means that a 100% isn't b

[long basalt]

okay so 0 is not a choice right?

[fluid cosmos]

Yes

Just give me a minute

[long basalt]

k

[fluid cosmos]

The answer is A

[long basalt]

thank you but what did you do to get that?

[fluid cosmos]

1st step

[long basalt]

oh now i understand

[fluid cosmos]

Then you can just divide 3x2+2x by x because if x is negative it will not affect the result the same if x was positive

[long basalt]

oh now this all makes sense

and you got -4(3x by spliting the 12 in two parts right?

.close

[trim jolt]

Channel closed

Closed by @long basalt

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.

[true bridge]

Does this look correct?

[true bridge]

for b) why do we need to condition on $\mathcal{F}_S$ isn't it as straightforward as the solution I have posted?

[solid kiln]

Master Wanky

[trim jolt]

@true bridge Has your question been resolved?

[true bridge]

<@&286206848099549185> anybody whos strong at probability can verify?

[upbeat violet]

I am having bad flashbacks

Looks good to me

[true bridge]

Ok not sure why hte hint says to use Strong Markov Property in order to deduce something about $E[B_T - B_S | \mathcal{F}_S]$

[solid kiln]

Master Wanky

[true bridge]

oh

is it because you cant say $B_S$ and $B_T- B_S$ are independent if htey are stopping times...

[solid kiln]

Master Wanky

[trim jolt]

@true bridge Has your question been resolved?

[trim jolt]

@true bridge Has your question been resolved?

[trim jolt]

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.

[pure drum]

,rotate

[pure drum]

how do I do this 😭?

[split chasm]

do you know any theorems related to angles being subtended at the circumference by the diamter

[pure drum]

I dont think so

[split chasm]

what circle theorems do you know

or are you looking at a reference list

[pure drum]

might be a bit small but i know those

[split chasm]

ok, the first and second one would be applicable

[pure drum]

Ok. So where would I plug the numbers in?

[split chasm]

apply angle on a line in combination with that

[pure drum]

sorry for the late response. What is that?

[split chasm]

do you know the angle on a straight line

basic geometric property

[pure drum]

180?

[split chasm]

yes

[pure drum]

so what would I do with that?

[split chasm]

apply property one

[pure drum]

wait so would I do 6x=180?

[split chasm]

no

[pure drum]

oh

wait would I do 6x+180=360?

[split chasm]

no

you're not applying what i'm saying

[pure drum]

I dont really understand what your saying. Im sorry.

[split chasm]

do you know the angle on a straight line
180?
apply that in combination with the first property in your list and show your diagram

[pure drum]

by the first property do you mean the center one?

[split chasm]

yes

[pure drum]

where would I apply it though

sorry that im not getting it

[split chasm]

180° will be your central angle

[pure drum]

wait so will x be 180?

[split chasm]

no

forget about x

for now

first mark the 180˜ on the line around the centre
then apply that centre property as shown

[pure drum]

ok

so the sector on the outside is 180 degrees then right?

[split chasm]

try drawing it and show me

[pure drum]

,rotate

[split chasm]

numbers aren't in ideal locations

[pure drum]

should the 180 in the middle be in the inside?

[pure drum]

the image is loading lol. hold on my wifi sucks

ok

[pure drum]

ohh ok I see

so after that then what?

[split chasm]

the second property in your list

[pure drum]

wait so I would divide it by 2?

sorry if im still not understanding it or getting it wrong 😭

[split chasm]

depends on what else you're doing

write full equations

[pure drum]

it just wants me to find x

how do I find it though

[split chasm]

apply property two and set up an equation

as menntioned

[pure drum]

wait so just 360=6x?

[split chasm]

no

[pure drum]

I dont understand how to use that property to make an equation

[split chasm]

what's your arc measure here

what's the expression of the angle here

plug those in

[pure drum]

oh wait so 90=6x?

[split chasm]

yes

[pure drum]

ohhh ok

so the answer would be 15?

[split chasm]

yes

[pure drum]

ok. Thank you for the help :)

[split chasm]

combining those, this is a special case of the inscribed angle theorem
angle at the circumference subtended by the diameter is 90°
which also goes by thales' circle theorem

[pure drum]

Ok. Thank you for all the help! have a good rest of your day or night :)

.close

[trim jolt]

Channel closed

Closed by @pure drum

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.

[strong horizon]

Could someone help me with this problem?

[jade berry]

Lagrange's Theorem does the trick.

[strong horizon]

This is what I have thusfar, what are your thoughts? "For any group of order 25, any nonidentity element must have an order that divides 25, thus the order of any nonidentity element must be 5, as it cannot be 1 (the order of the identity) or 25 (which would imply the group is cyclic)..."

[jade berry]

good

[trim jolt]

@strong horizon Has your question been resolved?

[whole coral]

I would reword that slightly, as the group G being cyclic is fine and one of the possibilities stated

[strong horizon]

Thank you! Can I share with you my solution for this problem as well?

[strong horizon]

Could I ask for your advice on problem 1 as well?

[whole coral]

Sure do you have any ideas for it so far?

[strong horizon]

I have this thusfar:

[whole coral]

I think I'm happy with that so far, looks good to me

[trim jolt]

@strong horizon Has your question been resolved?

[trim jolt]

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.

[trim jolt]

@copper acorn Has your question been resolved?

[hard juniper]

@copper acorn Here is an attempt to explain. The notation $A=(a_{ij})$ is used to describe A by its entries where $a_{ij}$ is the entry at row i, column j. This is just to emphasize the entries of A.

The other part is describing sub-matrices consisting of some subset of the rows and columns of A. Your professor defines $I$ to be the set of rows in the submatrix and $J$ to to be the set of columns. That is $A_{IJ}$ is a matrix with the rows in the set $I$ and columns in the set $J$. The, determinant is just the determinant of this matrix.

Here is an example. Let
$A = \begin{pmatrix}
1 & 2 & 3\
4 & 5 & 6\
7 & 8 & 9
\end{pmatrix} $
Then, if we set $I = {1, 2}$ and $J = {2,3}$ (assuming we index rows and columns from 1) then this gives the submatrix:
$A_{IJ} = \begin{pmatrix}
2 & 3\
5 & 6\
\end{pmatrix} $

[solid kiln]

Owen

[copper acorn]

Alright, I had that feeling but whenever we wrote $A = a_{ij}$ it gave me the feeling that $a_{ij} \in F^{nxn}$ rather than $\in F$

[solid kiln]

Bean Man

[copper acorn]

alright thank you, I was having a very hard time with understanding that

.close

[trim jolt]

Channel closed

Closed by @copper acorn

Use .reopen if this was a mistake.

[trim jolt]

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.

[short trellis]

Two trains left the two cities to meet each other the distance between the citys one goes in 3 hours second one 4 hours. What part of the entire road is left 1 hour after exiting? the road between the trains

[autumn trout]

Total distance - (distance covered by train 1 + distance covered by train 2)

[trim jolt]

@short trellis Has your question been resolved?

[trim jolt]

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.

[lapis blade]

can someone help me prove a sequence that diverges to infinity or negative infity cannot converge for my analysis class

[subtle lava]

Sure

Post it

[wraith hinge]

If you write the definition of convergence and divergence, you'll see by the later that there is M > 0 such that forall x, M < |f(x) - f(a)|. Hence if you take ε < M, you cannot satisfy the definition of convergence

[lapis blade]

ok

is there a general definition of convergence and divergence

that i could look up online

@wraith hinge

[marble wharf]

I mean just google it?

it pops up pretty much immediately

[wraith hinge]

Yeah, have you learned about the ε-δ definition in class?

[trim jolt]

@lapis blade Has your question been resolved?

[trim jolt]

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.

[lapis blade]

@human sorry can you post the definition of convergence that you used here so I can take a look at both

[lapis blade]

@wraith hinge also maybe I will need to look it up and see

I am not super good with these kind of names because I am new to analysis

Assume that the sequence converges to a finite limit L. Then, by the definition of convergence, for any ε > 0, there exists an N such that for all n > N, |a_n - L| < ε. However, since the sequence diverges to infinity or negative infinity, it will eventually exceed any bound, contradicting the assumption of convergence. Therefore, the initial assumption is false, and the sequence cannot converge.

is this a good enough proof?

[knotty locust]

No

you basically just said

"assume the series converges.... but it diverges so this is a contradiction"

[wraith hinge]

That's actually not direct since convergence is not defined as being the negation of divergence to ±infinity (which is not always true btw)

[wraith hinge]

Yes that's exactly it !

[knotty locust]

What are you talking about?

[past comet]

What?

[knotty locust]

That's not a proof at all

[past comet]

^

[knotty locust]

@supple copper

[wraith hinge]

How so?

[knotty locust]

That isn't a proof it proved nothing

[supple copper]

Show that 1/2 is an integer

Suppose it wasn’t an integer, well it’s an integer so that can’t be right

[knotty locust]

Proof: assume that it is an integer, but 1/2 is a fraction which is not an integer, so a contradiction.

[supple copper]

Hence it’s an integer

[wraith hinge]

That's exactly the proof I sketched earlier

[supple copper]

That’s your argument

[knotty locust]

Okay well it's wrong then

[past comet]

Its not a proof at all

[supple copper]

Assume that the sequence converges to a finite limit L. Then, by the definition of convergence, for any ε > 0, there exists an N such that for all n > N, |a_n - L| < ε. However, since the sequence diverges to infinity or negative infinity, it will eventually exceed any bound, contradicting the assumption of convergence. Therefore, the initial assumption is false, and the sequence cannot converge.

This part

You claimed without proof

And used it in your proof

[knotty locust]

Also, this isn't even "your" proof

[supple copper]

So you just claimed the statement to be true without proof

[knotty locust]

that was what mark wrote

[wraith hinge]

Which statement?

[knotty locust]

the one in bold?

[supple copper]

I’ve bolded it

[wraith hinge]

That's the definition of divergence to ±infinity

[past comet]

That part is fine? You need to show it can’t both be a convergent and a divergent one

[supple copper]

That’s true

But you don’t know that it’s divergent

[wraith hinge]

It's an hypothesis

[supple copper]

Well you can’t claim a proof on a hypothesis

[past comet]

What? That part is fine.

[knotty locust]

what's the hypothesis, assume a sequence is divergent and prove that it isn't convergent?

even if so, you did not prove that

[past comet]

The problem is he just says well divergent so can’t be convergent contradiction

[wraith hinge]

What we want to show is:
Convergence => not divergence to ±infty

[past comet]

Not that you use your assumption that it is divergent

[wraith hinge]

We are showing this by the absurd

Whats wrong then?

We assume that it's both convergent and divergent and grt a contradiction

[past comet]

This is the proof just with added filler words that do nothing

Nothing was shown

[wraith hinge]

How is this not valid? He used the two hypothesis and found a contradiction. It's pretty straightforward to me

[past comet]

No contradiction was found. He just wrote it. Show it formally

[wraith hinge]

That's a simple extra step I wrote for him earlier

[lapis blade]

ok hold up does this still ahve the same issue if i do this

Choose ε = 1. Since (a_n) diverges to infinity, there exists an M such that a_M > L + 1. But this contradicts the assumption that for all n > N, |a_n - L| < 1. Therefore, the sequence (a_n) cannot converge if it diverges to infinity.

[past comet]

Okay? Like it is not at all a proof

[lapis blade]

I am still not proving anything

I was supposed to add this before sorry

Now, assume by contradiction that the sequence (a_n) converges to a finite limit L. By the definition of convergence, for any ε > 0, there exists an N such that for all n > N, |a_n - L| < ε.

[wraith hinge]

Mathematics always has a level of informality. What actually matters is that we know how to fill in the details

[past comet]

Yes now its better

[wraith hinge]

I really don't get why people got upset for your proof. It trully was pristine, albeit not totally formal, but again no one can be totally formal, unless you wanna get involve in some serious set theory, which is ok to me

[wraith hinge]

That's how implication works

[past comet]

Lmao it really wasn't.

[lapis blade]

yeah i am super new to proofs so I am really just trying to figure things out slowly

I have no idea whats good or not

[wraith hinge]

Whatever

[knotty locust]

The proof was very bad

But no one was upset about the proof being bad

Actually no one is upset at all

We were just pointing out that you were calling his proof correct when it was very lacking

[supple copper]

@lapis blade im sorry i really really needed to go to the toilet and didn't scroll up to see context because you didn't reply to anything i just read it out of context

[wraith hinge]

It's all about how strict you want to be

You could have asked many more details, like the space where the sequence takes its values, whether it is well ordered, and so on

[knotty locust]

I mean if it can be that lax then why even call it a proof. You’re basically just saying well yeah if it converges then it can’t diverge really large, which is like heuristically correct but in no means a proof of anything

[wraith hinge]

I'll have to disagree in regard of the fact that his argument combined to my sketch is sufficient enough of a proof in my book

[supple copper]

@lapis blade just a comment on how you go about proofs like this, a sequence that diverges to infinity or negative infity cannot converge the keywords you want to look at is diverges to ±inf and converge

from here to look back to your notes on what these words mean, then construct the proof from those definitions

you consider what it means for a sequence to diverge, then what it means for a sequence to not converge, these will be 2 separate statements

[past comet]

The point of intro to real analysis is pretty much just learning to write proper proofs.

[supple copper]

then what you want to do is construct arguments to go from the first statement, and chain implication signs until you reach the 2nd statement

[wraith hinge]

I understand where this is coming from, but really there will always be lacking details in a proof at this point if you ask me

And I am definitely not against going full on technical details on set theory and predicate logic, but mathematics is also about drawing the line

[lean prawn]

It's crucial that the M that you find is greater than N, that's what yields the contradiction. But of course that's not an issue since if M is smaller than N, then you can just bump M up to N, i.e. choose M' = N, and that will suffice, since diverging to infinity does not guarantee just one M for which a_M > L + 1, but rather every M' >= M will have a_M' > L + 1

[trim jolt]

@lapis blade Has your question been resolved?

[lapis blade]

ok

[wraith hinge]

I feel like a synthesis of all this discussion would be valuable, so here is a proof that I hope will satisfy everyone:

Let (a_n) be a sequence of real numbers that converges to some real number L. Suppose also that it diverges to ± infinity (WLOG to +infty). This means by definition that for any real number M, there is a rank N s.t. M < a_n forall n > N.
Since the sequence also convergences, we have that forall ε > 0 there is a rank N' s.t. forall n > N', |a_n - L| < ε, i.e. -ε < a_n - L < ε, in particular a_n < ε - L

If you take M > ε-L, you have M < a_n < M

[lean prawn]

As for the meta discussion, I think saying "the proof needs more detail/rigor in my opinion" is completely fair but saying "that's not a proof at all" is pretty discouraging in my opinion since you can certainly be on the right track, have the right picture in your head, even if your formal proof is missing a few steps. I don't see a reason to get hostile, there is no objectively right answer to what suffices as a good enough proof and I think there's plenty good reason to be encouraging by saying something like "I like your proof, but I would justify this and that in more detail"

[wraith hinge]

For every n > max{N, N'}

[lapis blade]

@lean prawn could you write this M=N out fully so I could see it by chance

M'=N srryy

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lean prawn]

.reopen

[trim jolt]

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.

[lapis blade]

like just the rephrasing of my statement

[lapis blade]

.reopen

[trim jolt]

@lapis blade Has your question been resolved?

[lapis blade]

are you still here @lean prawn if not its ok I might sleep soon

[lean prawn]

Feel free to go to sleep this is taking me a little longer than I was expecting

but it's a good exercise for me as well

[lapis blade]

ok yeah I will probably be up for like another 15 minutes because I am solving another proof so feel free to ping me or dm me if you figure it out

if not its ok

[lean prawn]

I can DM you the proof if I figure it out :p

[lapis blade]

ok ty

ill add you so it doesnt go to my message requests

[lean prawn]

We want to show that convergence => does not diverge to infinity (the minus infinity proof is similar)

We will show this by contrapositive, by showing that

diverges to infinity => does not converge

Since (a_n) diverges to infinity, we have that for any value K that we'd like to reach, we have an M such that n >= M implies a_n >= K

We will use this M for a special K to show that the sequence does not converge.

If the sequence were to converge, then there would be some L (that the sequence converges to) such that we would have some N such that n >= N implies |a_n - L| < 1 (this is with epsilon=1)

How do we find a contradiction?

Well, let's first try to understand our objective. We would like to have |a_n - L| >= 1 for sufficiently large n, since that would yield a contradiction.

By plotting L on the real number line (remember, it can be negative as well), we clearly see that if a_n >= L + 2 then that should work since you start two units to the right of L and keep going to the right. Let's try to show formally that it actually works.

So, by our assumption, for K = L + 2, there exists some M_big such that n >= M_big implies a_n >= L + 2.

Geometrically it is quite clear that
|a_n - L| >= 1 <=> a_n >= L + 1 OR a_n <= L - 1

Algebraically, the => direction is quite clear. The <= direction is what we need, though.

If a_n - L >= 1, then in particular it is positive, and thus we're clear. If a_n - L <= -1, then in particular it is negative, and thus we're clear.

Okay, good.

Since n >= M_big implies a_n >= L + 2 which is the same as a_n - L >= 2 we certainly satisfy the first inequality.

This means that we also satisfy |a_n - L| >= 1

...

Therefore, for n >= M_big, we have |a_n - L| >= 1, which is a contradiction IF n >= N

Well let's see.

If M_big >= N, then n >= N, and thus we find a contradiction.

If M_big < N, then we can choose M_bigger = N. Note that M_bigger > M_big, and therefore for n >= M_bigger, we can derive exactly the same results as for n >= M_big. Then, at the end, we find a contradiction if the index is greater than or equal to N. But it will be greater than or equal to N because M_bigger = N. Therefore, even in this case, we can derive a contradiction

I suppose I get a little handwavy near the end but I hope it clarifies the idea

[lapis blade]

ok ok

I will sc this and look at it in the morning

tysm

[lean prawn]

no problem

hmm I think I overcomplicated that actually

because obviously if you just choose a large enough index, one larger than N and M_big, then obviously you reach a contradiction, and obviously you can do that

but yeah I need a break tbh so I'll just leave it here

[trim jolt]

@lapis blade Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lone mauve]

are both of these vectors considered points?

(1,0,0) and (0,-1,1)

Wait nvm, these two vectors make the basis set
I was trying to find a point from this simple example

Would RREF not be used to find a point?

[trim jolt]

@lone mauve Has your question been resolved?

[trim jolt]

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.

[wraith hinge]

A particle moves along the curve x^2/9 + y^2/4 = 1, with constant speed v. Express its velocity vectorially as a function of (x,y).

[wraith hinge]

Ik what the answer is

But question is
Here what is x?

Is it a function of t?

So can anyone frame question exactly similar to this
But but but
Kindly also provide the function of time for position in x and y axis so that i can but up and better understand it

[brazen forge]

as in the question, its the function of (x,y)

[white kestrel]

Can someone help me with https://discord.com/channels/268882317391429632/1230167216872489090

PLEEAse

[brazen forge]

its two variable function

[brazen forge]

!occupied

[trim jolt]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[wraith hinge]

Ofc but position of x and y would be also independently be function of time no?

[brazen forge]

the hell going on here

<@&268886789983436800>

[tacit bough]

wdym by that

[brazen forge]

someone just started spamming here

[trim jolt]

@wraith hinge Has your question been resolved?

[wraith hinge]

<@&286206848099549185>

[trim jolt]

@wraith hinge Has your question been resolved?

[stone kiln]

Try differentiate both side of equation with respect t

[wraith hinge]

That's what I said
I know the answer
But what x and y mean
Are they also individually functions of time for displacement is x and y axis?

[stone kiln]

Sorry

Given time what is x and y coordinate

You are right x and y are function

[stone kiln]

What you dont understand?

[wraith hinge]

Hard for me to explain
Just that

Can u frame a simple problem like this one
Just that provide the functions for time too

So that i can put the values and understand

[stone kiln]

Like circle sint cost ?

@wraith hinge

It is good for you?

[wraith hinge]

Try if it's like t^2 2t something simple
Because I have quite new to high school calculas

[stone kiln]

Parabola (t,t^2) ?

[wraith hinge]

Works

[stone kiln]

But it is not very interesting because you can express y by x

[wraith hinge]

I don't even what interesting I just want to clear my concepts
That's why I asked

[stone kiln]

Okay

What you want to clear?

[wraith hinge]

@stone kiln this answer is quite complicated
Very much actually
So if I had functions for x and y w.r.t to time
So I could cross check

I don't mean cross check
But yeah.. I. Wanna see how it works

[stone kiln]

You diff both parts and get relationship v_x and v_y

And you have another relation that it has constant v speed then v_x^2 +v_y^2=v^2

And just solve

[cyan oxide]

this part is not correct

however the rest of the soul is correct

[cyan oxide]

well, a short explanation: he diff the equation then got a relation between Vx and Vy

then he used the fact that Vx and Vy is the x and y components of the velocity vector itself

so Vx^2 + Vy^2 = V^2

using this he got Vx in terms of x and y, the same with Vy

[trim jolt]

@wraith hinge Has your question been resolved?

[wraith hinge]

Why?

[wraith hinge]

Thanks a lot man!

[wraith hinge]

Oooo
Got it!

[cyan oxide]

he wrote some symbols wrong, like dz/dt = Vx

but eventually he fixed it and got the right answer

[wraith hinge]

Real
Can u form a question like this
Because the velocity that came at last I wanna crosscheck it
So it would be great if similar question was there with function of time for x and y co-ordinates there

[cyan oxide]

u can simply say that if u have y = f(x)
then say x= t
and y =f(t)

[cyan oxide]

and what do u mean by question?

like u arent sure about the answer?

[wraith hinge]

I am
But I want to check it
To see how it goes

The correctly understand the relationship between all

[cyan oxide]

maybe some sort of visualisation for this system

we can set, x = 3cos(t) and y = 2sin(t)

[trim jolt]

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.

[lone mauve]

do all of these mean the same thing?

[knotty locust]

The last one is incorrect

v*u is a scalar

and so is ||u||

but the projection should be a vector

[wraith arch]

the third one rather gives the magnitude of the projection, not the projection vector

[trim jolt]

@lone mauve Has your question been resolved?

[knotty locust]

Yes, you left off the magnitude bars

[lone mauve]

would this formula be considered the same as the first two?

[knotty locust]

No

It’s the magnitude of the first two

Do you see the bars around proj in that?

| proj | instead of just proj

[lone mauve]

ya

[knotty locust]

The projection is a vector but that formula gives the magnitude of the vector

[lone mauve]

so it's the same as this

[knotty locust]

That’s an example of taking the magnitude of a specific vector yes

[lone mauve]

why do we need this formula

if this will solve it

[lone mauve]

does absolute value really matter?
if the answer is 3 or -3 isn't it kinda the same thing?

distance cannot be negative, so 3 is the difference either way

for example:

I wonder if prof would be forgiving with marks if D was this

[stoic iron]

yes most people would mark you down for putting -3 because like you say a distance cannot be negative

[lone mauve]

OK

tyvm

.close

[trim jolt]

Channel closed

Closed by @lone mauve

Use .reopen if this was a mistake.

[trim jolt]

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.

[frail yarrow]

More of a general question, so I was sent this photo, could someone either tell me what noise type is and how it affects the degrees of freedom? Either that or point me to a resource.

[frail yarrow]

Actually, if you could also point me to where this formula for chi squared comes from, that would also be appreciated

[trim jolt]

@frail yarrow Has your question been resolved?

[frail yarrow]

<@&286206848099549185>
I'd ask for more context, but the person who sent me this is in a time zone where they should really be sleeping.
Can someone at least point me towards a resource for the formula used?

[frail yarrow]

Someone at least tell me if I'm unlikely to get an answer?

[trim jolt]

@frail yarrow Has your question been resolved?

[trim jolt]

@frail yarrow Has your question been resolved?

[frail yarrow]

<@&286206848099549185>

[frail yarrow]

Eh whatever

.close

[trim jolt]

Channel closed

Closed by @frail yarrow

Use .reopen if this was a mistake.

[trim jolt]

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.

[zinc raft]

Is y^-3 = 1/3y ?

[acoustic sphinx]

no

[zinc raft]

Ok

Actually

Can you help me with the whole question

[acoustic sphinx]

y^-3 = 1/y^3

what is the whole question

[zinc raft]

Ohhhh ok

So far I’m just factoring it out

[orchid wagon]

law of indices

[zinc raft]

Don’t know

[acoustic sphinx]

a^-1 = 1/a

ok

thats the main rule there

[zinc raft]

Oh ok

[acoustic sphinx]

for that question

[acoustic sphinx]

what have you got so far

[orchid wagon]

wtf

[zinc raft]

That’s how they taught us

[acoustic sphinx]

it works but it's no tthe best way

[zinc raft]

Oh ok what should I do instead?

[acoustic sphinx]

you can leave it how it is as 4x^5y^2 * (2x)/y^3

[delicate pagoda]

4x^5y^2*2xy^(-3)
=8x^6y^(-1)

so 8x^6 over y

[acoustic sphinx]

8x^6/y

yeah thats it

[trim jolt]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[zinc raft]

:( idk what to do

[onyx forge]

damn

pretty easy

ngl

[solid kiln]

faiyrose

[delicate pagoda]

it's literally just calculation of the answer!?

[onyx forge]

do you know how

you add or subtract

powers

[orchid wagon]

my man, easy for you doesnt mean easy for others

[onyx forge]

basically exponent rules?

[orchid wagon]

!nosols

[trim jolt]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[onyx forge]

last time i checked an infant can do addition

[delicate pagoda]

x^a+x^b =x^(a+b)

[acoustic sphinx]

@zinc raft

[delicate pagoda]

which works for negative a or b, too

[zinc raft]

How would I combine y^2 and y^-3

[orchid wagon]

,tex .freshman

[onyx forge]

how do you think?

[orchid wagon]

somewhat similar but its the same

thats not how exponent work

[acoustic sphinx]

@zinc raft do you know the index laws

[zinc raft]

No sorry

[onyx forge]

so many people here

[onyx forge]

Then why are u even asking

[acoustic sphinx]

all good look at these

[onyx forge]

how to solve

an exponential question

[zinc raft]

Ok ok I see

[onyx forge]

when you don't know its rules

😭

[acoustic sphinx]

those are the main rules that you'll use

[zinc raft]

So I kind of combine like terms?

[delicate pagoda]

$y^2\cdot y^{-3} = y^{2-3}=y^{-1}=\frac{1}{y}$

[solid kiln]

Bob Goldham

[acoustic sphinx]

when there's multiplication you add the powers if the base is the same

[onyx forge]

ur giving out

the answer-

that's what shes supposed to do herself

😭

[delicate pagoda]

no I'm explaining a general rule of algebra

[orchid wagon]

you help op do the work, you do not do the work.

[onyx forge]

then use

a different example

[delicate pagoda]

$\forall x,y,z \in \mathbb{R} $

better?

[onyx forge]

oh lord its so cold

[zinc raft]

Ok

[onyx forge]

close it too

if u dont need help

[zinc raft]

.close

[trim jolt]

Channel closed

Closed by @zinc raft

Use .reopen if this was a mistake.

[trim jolt]

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.

[drifting rose]

coudl someone help explai the logic of this step

[drifting rose]

so we want that left equation to look like the one in blue, so we add 2 onto the bottom, but we need to equate another fraction so it not like we added it out of nowhere

why is it 2x^2/x^2?

[worldly wing]

It could be anything

It just needs to be equivalent to 2

[drifting rose]

oh

so whats another example off it?

wait

if it need to be equivalent to 2, can't it just be 2?

[onyx forge]

omg

my teacher taught me that

this is nostalgic

[onyx forge]

you're basically making the number (2x^2) in the numerator and the denominator same

[onyx forge]

oh

hold on

ill give u

[drifting rose]

its more confusion that they added the 2 to the already x^2, why would you want to balance it out with an 2*x^2/x^2?

[onyx forge]

hollon

Im tryna find my own docu

😭

odd

cant find it