help-49

[queen herald]

Yes

[quaint field]

btw how do I check the answer using wolfram

I guess I can try a specific value of the radius

but how do I make it calculate the flux

[queen herald]

There's no command for that (as far as I know?) but you can plug in integrals

[quaint field]

the thing is that I am not 100% confident my integral is right

[queen herald]

Unfortunately I don't know any tools that calculate the flux given the vector field and the contour

[quaint field]

I found this online and they got a completely different answer using green's theorem (I think)
https://math.berkeley.edu/~kwray/teaching/summer_2012/math_53/hw_5_solns.pdf

[queen herald]

Idk why they wrote div(F)=0

That's clearly not the case

Nvm it is

Calculating divergence in head isn't always successful from the first try XD

,w Integrate[(R^2 + R Cos[t])/(1+R^2+2 R Cos[t]), {t,0,2 Pi}]

[grand pond]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by equenos

[queen herald]

Good news is that we get the same answer, actually

[queen herald]

It's not completely different answer, it's the same answer

I checked 😅

[midnight plank]

@quaint field Has your question been resolved?

[quaint field]

oh wow

it's always 2*pi for R>1 and 0 for R<1

how is that even possible lol

[queen herald]

Math

Clearly visible from this integral times R

[quaint field]

so I guess you can just use green's theorem and the problem is 100% easier then

[queen herald]

Yes

[quaint field]

damn

that is one powerful theorem

[queen herald]

Tbf it depends on luck

No one guarantees that div(F)=0

It could be some scary expression which you would have to integrate over the unit disc

[quaint field]

this is how to calculate it, right?

the only issue is at (0,0) the denominator becomes 0

which makes sense because I don't think the divergence would be 0 there

it would be positive since the vector field is radiating outward?

how would I calculate it though

oh, the way they did it was genius

they considered a small circle around the origin, for which the flux is easy to calculate

and then the rest of the region just has div being 0

so it's just becomes the flux of the small circle, which is 2pi

wow

thanks for the assistance btw, @queen herald, I appreciate it

.close

[midnight plank]

Channel closed

Closed by @quaint field

Use .reopen if this was a mistake.

[queen herald]

Correct

[queen herald]

That's a standard technique :)

Gives vibes of complex analysis

[midnight plank]

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.

[deep junco]

How do I rotate a picture here?

[deep junco]

I need to rotate some picture

[hazy parrot]

,rotate

[deep junco]

Turn it to the left side please

Thx!

[hazy parrot]

.close

@deep junco can you do .close ?

[worthy wing]

Why does he has to close?

[latent elk]

what language is that

[hazy parrot]

because he's done

i think

[worthy wing]

He is done turning the image

[hazy parrot]

yeah

[worthy wing]

By the context

So his question is just doing that?

[hazy parrot]

yes

xD

[latent elk]

😭

This is so hilarious

[worthy wing]

@deep junco is that true?

[latent elk]

This is why I pay for my internet

[iron whale]

omg this server is always so judgemental lol

[latent elk]

bedrock or java?

[iron whale]

bedrock

[latent elk]

Can i join

im bored

[iron whale]

I'm making a cake rn

I think I left it logged in

ill be on later once I frost it though

are you good at commands?

[worthy wing]

Don’t talk in this channel

You can go to #discussion

[deep junco]

.closee

.close

[midnight plank]

Channel closed

Closed by @deep junco

Use .reopen if this was a mistake.

[deep junco]

sorry guys

[midnight plank]

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.

[naive aspen]

hello i need help im in factoring cases and doesnt matter what i do the answer never matches with the answer keys so please help

[worthy wing]

You can use the fact that (x-1) is a factor

[naive aspen]

yes i did try that but at the end it doesnt match with the answer key

i asked everyone but all they did was dissapear the -2 for no reason and they got the answer so idk

[worthy wing]

Can u write here the denominator?

I cant read well

[naive aspen]

x4 + x3y - x + y

[worthy wing]

You can’t factor that

[naive aspen]

the numbers are exponents

you can factor it by grouping

[fallow scarab]

x(x^3-1) + y(x^3-1)

[naive aspen]

gcf by grouping

[worthy wing]

Oh it is exponent

I see

[naive aspen]

how do you get x to the power of 3?

wait

what happened to the -2

[fallow scarab]

This only works if you wrote the sign wrong

[fallow scarab]

On the +y term in the denom

[fallow scarab]

This is just the denominator

To save some time take a picture of the original problem

[naive aspen]

i wrote it right

[worthy wing]

Do you have a picture of the original book?

[naive aspen]

yes give me a second

[fallow scarab]

Also show the answer key while you're at it

[naive aspen]

alr

[fallow scarab]

Oh the - is on x^3 y term

[worthy wing]

That makes more sense

[fallow scarab]

This is almost right.

[fallow scarab]

x(x^3-1) - y(x^3-1)

[worthy wing]

Copy the exercise correctly random

And try again

[naive aspen]

what?

BRUH

[worthy wing]

-x^3y

Not +

[naive aspen]

yeah uhhhh

im blind

[worthy wing]

I was upset lol

[fallow scarab]

[worthy wing]

Xd

[naive aspen]

lol

ok

i still need help in the numerator

[worthy wing]

(x-1) is clearly a factor

Do long division

[fallow scarab]

-2 =-1-1

And x^6-1 = (x^3-1)(x^3+1)

[naive aspen]

ok wait

wich factoring case is that?

[worthy wing]

a^2-b^2

[fallow scarab]

Verify my hints. Then figure out your problem with the hints

,calc -1-1

[grand pond]

Result:

-2

[naive aspen]

alr

and then what happens to the x to the power of 3?

[worthy wing]

What do u mean

[naive aspen]

i understand this part but what happens to the x to the power of 3

[fallow scarab]

.

[naive aspen]

ik

[worthy wing]

You have this $x^6+x^3-2$
Which is the same as $x^6-1+x^3-1$

[grand pond]

Samuel

[naive aspen]

hmmm

so the x to the power of 3 -1 is another case then

because i cant divide the exponent by 2

thx

i already know what to do here

[midnight plank]

@naive aspen Has your question been resolved?

Channel closed

Closed by @naive aspen

Use .reopen if this was a mistake.

[midnight plank]

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.

[barren parcel]

how did they get their answer?

[viral dagger]

do you know the geometric progression formula and your supposed to apply it here, or are you supposed to work your way to figuring out the geometric progression formula?

[barren parcel]

i think im supposed to apply the geometric progression formula?

but then wouldnt that be 3(1/10)^n-1?

how do they get from that to 3.1^(1-n)

[midnight plank]

@barren parcel Has your question been resolved?

[robust prism]

i think the answer is wrong? for example to verify, n=1 doesn't even give us 3 with that formula

[barren parcel]

lmao

that checks out

.close

[midnight plank]

Channel closed

Closed by @barren parcel

Use .reopen if this was a mistake.

[midnight plank]

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.

[pastel wyvern]

how to do 13a

ans is (0,2,12)

[west iron]

Do you know how to find the point on the line closest to (8,5,7)?

[pastel wyvern]

i tried finding parametric form of the line

and then dot product with the Q-P

but im not getting a value for the parameter

[pastel wyvern]

hello?

[west iron]

You aren't supposed to know what Q is

So why would you use it

[pastel wyvern]

oh crap i meant dot product with the point closest and p

using those two vectors

[west iron]

So you're taking a point R(t) on the line

[west iron]

You should be taking the dot product of PQ with the direction vector of the line

The direction vector shouldn't depend on lambda

And the dot product of two vectors isn't a vector, it's a scalar

[pastel wyvern]

ohhh crap

so i need to add all the results

bruh i got confused because of cross product

[pastel wyvern]

what is the dir vector of the line

[west iron]

Yeah add the products of corresponding elements

<2, 3, 5>

[pastel wyvern]

why?

[west iron]

from the multiples of lambda in the parametric form

[pastel wyvern]

hmm but why does that become the dir vector of the line? im sorry but idk how it translates

[west iron]

Also works if you take any 2 points on the line and subtract their position vectors

[pastel wyvern]

ok so sub in lambda =1,2

for eg

[west iron]

Yeah

[pastel wyvern]

but why is this the case?

[west iron]

Idk just intuition

Every time you increase lambda by 1 you move (2,3,5) along the line

[pastel wyvern]

oh opk

[pastel wyvern]

alright so my method here would work but it would take longer, i should just let Q be (x,y,z) and do dot product of PQ and the dir vector of the line = 0 to find Q

i think i got it

[west iron]

It wouldn't really work

You need to use the direction vector of the line, not the position vector of a point on it

[pastel wyvern]

Oh yeah, okay

Thanks a lot

[west iron]

Np

[midnight plank]

@pastel wyvern Has your question been resolved?

Channel closed

Closed by @pastel wyvern

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.

[midnight plank]

@leaden matrix Has your question been resolved?

[leaden matrix]

<@&286206848099549185>

[midnight plank]

@leaden matrix Has your question been resolved?

[midnight plank]

@leaden matrix Has your question been resolved?

[midnight plank]

@leaden matrix Has your question been resolved?

[midnight plank]

@leaden matrix Has your question been resolved?

[midnight plank]

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.

[spiral talon]

Hey, there - I have a problem with understanding basic solutions. Given a linear problem in standard-form

$A = \begin{bmatrix}
1 & 3 & 1 & 0 \
-1 & -1 & 0 & 1
\end{bmatrix}
$ and $c = \begin{bmatrix}
12 & 2
\end{bmatrix}^T
$

I have a question, which is asking for the number of max. possible basic solutions to this problem. My intuiton told me, that, since I need an invertable matrix for a basic solution, all possible pairs of the columns of a could lead to a basic solution.
Using the binomial coefficient, I came to 6 basic solutions to this matrix and (n choose m) solutions for a general m times n Matrix.
is this approach correcT?

[grand pond]

Edlingem

[runic hamlet]

in general not every choice of m columns will give an invertible matrix

[spiral talon]

Yes, but if I only got a general matrix without any information, I can't restrict the choices any further, can I?

The question, in this case, asks for what the maximum number of basic solutions is

[midnight plank]

@spiral talon Has your question been resolved?

[midnight plank]

@spiral talon Has your question been resolved?

[midnight plank]

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.

[pallid vortex]

Hi , help me with c pls, combinatorics

[next rover]

c is the opposite of no 1 and no 7

[earnest pike]

numbers containing the no. 1 only = 6C2
numbers containing the no. 7 only = 6C2
numbers containing both 1 and 7 = 5C1

add 6C2+6C2+5C1 to get 35

@pallid vortex

[midnight plank]

@pallid vortex Has your question been resolved?

Channel closed

Closed by @pallid vortex

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.

[chilly cobalt]

Consider parallelogram ABCD, where point E and F are the midpoints of BC, and CD respectively. Let P and Q be the intersection of BD with AE and AF. Show that P and Q split BD into 3 equal parts ( using vectors)

[keen saddle]

Diagram pls

[chilly cobalt]

rn my idea is to let BP : PQ : QD = m:n:p

dont really know what ot do

[mighty viper]

is this also for mental help 🙂

[chilly cobalt]

probably not

[keen saddle]

!occupied

[mighty viper]

(ik it aint)

[midnight plank]

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).

[keen saddle]

Lmao

[chilly cobalt]

and somehow show m=n=p=1 but idk

anyone have ideaass

[keen saddle]

Join AC

Maybe that will help in m=p

[chilly cobalt]

and?

oh

[tepid field]

It will not ig

[keen saddle]

Try letting PE = QF = x

Then use triangle law in ABP, ADQ, ABD

[chilly cobalt]

whats triangle law?

[keen saddle]

https://images.app.goo.gl/GunFQVVoXgE7vrcj6

[chilly cobalt]

oh

oh okay

thanks

.close

[midnight plank]

Channel closed

Closed by @chilly cobalt

Use .reopen if this was a mistake.

[midnight plank]

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.

[prime hornet]

I’m confused by your confusion

[last slate]

😭

[prime hornet]

you only care about finding an N st a_n < e whenever n > N

why do you think your choice of N does not work?

[last slate]

it could be complex

[prime hornet]

wait hold on

okay yeah, it seems like we’re gonna need to break this into two cases, find an N for each one, and then take either the max or the min

note that if eps > 1/3, then a_n < eps always

yeah

it’s the case when eps <= 1/3 that’s hard

[last slate]

thanks

[prime hornet]

sorry, I’m still working the estimate myself

should work

if $\varepsilon < \frac{1}{3}$, then

why

[grand pond]

higher!

[prime hornet]

ahh

the point is that the N works if you write it out

let me try to figure out why my TeX doesn’t work

[last slate]

okk

[prime hornet]

\begin{align*}
n > N \implies \frac{1}{n^2 + 3} & < \frac{1}{N^2 + 3} \ & < \frac{1}{\left(\sqrt{\frac{1}{\varepsilon} - 3} \right)^2 + 3} \ & = \frac{1}{\frac{1}{\varepsilon} - 3 + 3} \ & = \varepsilon
\end{align*}

there we go

I hate everything

[last slate]

hahahah it works but im hoping i dont have to check & show that it does

lol

[prime hornet]

maybe

[grand pond]

higher!

[prime hornet]

finally

but yeah, you can confirm it works like this

[last slate]

thank you

.close

[midnight plank]

Channel closed

Closed by @rare sundial

Use .reopen if this was a mistake.

[prime hornet]

sorry that took me so long haha

[last slate]

npnp f this school and this class

[prime hornet]

have a great day!

[last slate]

u too

[prime hornet]

cat bit is watching, so watch what you say about analysis

[midnight plank]

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.

[livid sonnet]

I need help understanding matrix reflections and how they can be expressed/found through equations. These are examples of the types of questions.

[midnight plank]

Please don't occupy multiple help channels.

[gaunt otter]

stick to one channel

[livid sonnet]

yeah mb

it wasn't registering

[fallow scarab]

.close

[midnight plank]

Channel closed

Closed by @fallow scarab

Use .reopen if this was a mistake.

[livid sonnet]

so i thought it didn't work

[fallow scarab]

.reopen

[midnight plank]

✅

[fallow scarab]

stick to this one stop opening new channels

[livid sonnet]

ok mb

[grand pond]

bacc (unhelpful)

[dawn dagger]

you can rewrite the left side applying matrix multiplication

[grand pond]

bacc (unhelpful)

[dawn dagger]

Now compare

a)

to find a,b,c and d

[livid sonnet]

ok wait

can i write it like this?

[dawn dagger]

a)

are you doing b)?

[livid sonnet]

yes

[dawn dagger]

not quiet

you need to switch some positions

[livid sonnet]

do i just switch the 2 columns?

[dawn dagger]

yes

[livid sonnet]

ok so x coefficients come in first column

[dawn dagger]

yes

[livid sonnet]

and then what do i do

[dawn dagger]

You found the transformation matrix

aren't you done?

[livid sonnet]

ok so i think the question here is incomplete. There's an answer which i need to get to and i need to understand the logic behind it

i have the ansewer scheme

can i share it

[dawn dagger]

yes

[livid sonnet]

so for b that were doing rn

y=4x is the answer that i need to get to

but how do i get there

Im pretty sure it involves something about using tan theta = sin theta/ cos theta but

there's this inequality that i need to consider that goes like: pi<2 theta<3pi/2 or smth

and im not sure how to proceed with all this

and for reflection of matrices the formula is given as:

where a is just theta

.close

[midnight plank]

Channel closed

Closed by @livid sonnet

Use .reopen if this was a mistake.

[midnight plank]

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.

[grizzled elbow]

What does it mean for A and B to be independent given C?

[grizzled elbow]

usually id expect to see this in parentheses but there are none in this case

[merry pewter]

,, P(A\cap B | C) = P(A|C)\cdot P(B|C)

[grand pond]

Bair

[grizzled elbow]

thanks!

.close

[midnight plank]

Channel closed

Closed by @grizzled elbow

Use .reopen if this was a mistake.

[midnight plank]

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.

[limpid slate]

Can someone explain how this works

[limpid slate]

I dont get why its ak

Can someone explain this

Help

.close()

.close

[midnight plank]

Channel closed

Closed by @limpid slate

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.

[limpid slate]

Can someone explain how this is simplfied to
[ 1 ak
0 1]

[fallow scarab]

Use induction

[limpid slate]

Can u explain

[fallow scarab]

Induction?

[limpid slate]

How you get the answer

[fallow scarab]

Try using induction

https://brilliant.org/wiki/induction/

[limpid slate]

Btw ive started matrices

[fallow scarab]

Yes this is a 2x2 matrix multiplied by itself k times

[limpid slate]

Are you talking about proof by industry or something else

*induction

[fallow scarab]

This is what I'm talking about

[limpid slate]

So do i test k for positive integer values

…

[midnight plank]

@limpid slate Has your question been resolved?

[fallow scarab]

you can try that first yea. but to actually prove the statement you should do the induction

[midnight plank]

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.

[past wraith]

This is the exercise

This is the explanation

And I get all thr steps until the fourth step. Idrk what their doing

How did they get to this equation they are solving?

[midnight plank]

@past wraith Has your question been resolved?

[midnight plank]

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.

[icy spoke]

ik what parameter form is, but how would you turn equations for a plane into parameter form

[icy spoke]

like which is the origin and which is the direction

[wise belfry]

find the relationship, plug in, and solve for the parameter form

youll know the direction from the coefficients

[icy spoke]

ok ik the direction is <1,1,1>

[icy spoke]

and maybe im stupid but is x and z just 0?

[icy spoke]

its not correct here

[wise belfry]

your direction vector might not be correct and you have a syntax issue

[icy spoke]

why is the direction/normal vector not right?

is it not just the coefficients of xyz \

[midnight plank]

@icy spoke Has your question been resolved?

[midnight plank]

@icy spoke Has your question been resolved?

[reef nacelle]

The direction vector is <1,0,-1>

Also Syntax error, you can write

<t, 7, -t> instead as the vector function

[icy spoke]

Why is that the direction vector

I don't get how you got it

[midnight plank]

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.

[fathom marsh]

I need help with a question

[fathom marsh]

How do I sketch this equation f(x)=-0.5(x+3)(x)(x-4)

[midnight plank]

@fathom marsh Has your question been resolved?

[fathom marsh]

No

[midnight plank]

Channel closed

Closed by @fathom marsh

Use .reopen if this was a mistake.

[fathom marsh]

.reopen

[midnight plank]

✅

@fathom marsh Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

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.

[orchid dust]

Can anyone figure out what's going on here? Why is average force force of gravity = ma?

[last slate]

!original

[midnight plank]

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.

[orchid dust]

(This isn't mine, I was absent the day the class did it so I'm asking a friend what he did but he claims he doesn't know what he did even though he literally wrote this all out???)

From what I'm understanding he's done mg=Fg, then ma=F and those combined are the average force? Is that like a thing??

Isn't that just all the forces acting while jumping? Would that not be like net force instead of average force?

[midnight plank]

@orchid dust Has your question been resolved?

[midnight plank]

@orchid dust Has your question been resolved?

[orchid dust]

I give up I'm just gonna copy whatever he did. The teacher didn't mark it wrong on his so maybe he was onto something

.close

[midnight plank]

Channel closed

Closed by @orchid dust

Use .reopen if this was a mistake.

[manic bison]

I don't think you have learned about impulses , which is another force which acts while jumping

But yes , gravitational is kind of the only force here

[midnight plank]

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 root]

im a bit lost on how to set up the integration to find the volume rotated on y axis

[thin slate]

So you have to find the volume of that area from 0 to e underneath both lines

when its spun around the y-axis

[drifting root]

yea

im testing uh

the integ of x from 0 th e then minus the chunk rn

[thin slate]

this area

me personally I would calculate

*volume

and subtract the triangle bit (which is a cone)

this volume is a cylinder + the curve of 1/x from 1 to e revolved around y-axis

[drifting root]

how would i calc that

i trief thinking that way but couldnt set an eq for it

[thin slate]

can you imagine this?

[thin slate]

what's the formula for the volume of revolution around the x-axis?

also instead of a cylinder

and subtracting the volume of the cone

you can consider the interval from 0 to 1 the volume of revolution of f (x) = x around the y-axis

[drifting root]

what way is there to set up an eq for this using y values

the part thats throwing me off is the xy=1

[thin slate]

xy = 1

y = 1/x

[drifting root]

like

an integral eq

[drifting root]

the 1 to e doesnt make sense to me

how can i make an eq with it

if i make an eq, its easy for rotate on x

[thin slate]

what's the formula for the volume of revolution around the y-axis?

[drifting root]

how to do for rotate ony

[thin slate]

for some function f(y)?

[thin slate]

use that formula

and set the bounds accordingly

[drifting root]

why tho?

im rotating on y axis

[thin slate]

oh my bad

read again

[drifting root]

ik formula for volume

how can i set up my integral tho

i cant find a nice way to cut the shape so i can calculate

[thin slate]

]

find the volume of the black shape + red cone - red cone

the volume of the shape is equal to the red area from -1 to -1/e revolved around the "new x-axis"

• a cylinder whose height and radius are known

[midnight plank]

@drifting root Has your question been resolved?

[drifting root]

This was the perspective i needed

Thank you

.close

[midnight plank]

Channel closed

Closed by @drifting root

Use .reopen if this was a mistake.

[midnight plank]

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.

[twilit field]

I'm trying to prove every real number , lies between two consecutive integers

[twilit field]

So essentially, let $a \in \Z; x \in \R$. so $a \leq x < a+1$

[grand pond]

Mr bean is not $\R \setminus \Q$

[civic scroll]

You could use the well ordering of N

[twilit field]

That would work for positive reals

[civic scroll]

If x is negative, you can consider -x

[twilit field]

mhm

I was actually thinking of using the completness axiom

[tribal temple]

(how are you trying to prove it? What's available to you - e.g. the whole "[least] upper bound" thing?)

[twilit field]

I mean now that I have proven it , yeah

and that $\Z$ doesn't have a lower bound in $\R$ , along with the completness axiom

[grand pond]

Mr bean is not $\R \setminus \Q$

[civic scroll]

You mean applying it to Z \cap (-infinity, x], right?

That would also work

[twilit field]

Not exactly

I was thinking of first considering $A =(- \infty,x) , B=(x ,\infty)$

[grand pond]

Mr bean is not $\R \setminus \Q$

[twilit field]

Then firstly by the completness axiom , such an x exists

And I then find $\Z \cap (A \cup B)= \Z$

[civic scroll]

But you already know that x exists, right?

[twilit field]

Oh right

[grand pond]

Mr bean is not $\R \setminus \Q$

[twilit field]

now let's consider two arbitrary integers a and b, a \neq b b>a

[civic scroll]

It is not always Z

There is the case x \in Z

[twilit field]

I think I'll first deal with the case wherein $x \notin \Z$

[grand pond]

Mr bean is not $\R \setminus \Q$

[civic scroll]

The other case is trivial anyways

[twilit field]

yeah

what am I doing

sorry

wait, by the ordering of the real numbers , and the fact that the integers aren't bounded from below, I can say there exists an integer $s$, such that $a<x$

[grand pond]

Mr bean is not $\R \setminus \Q$

[twilit field]

After showing that $\Z$ isn't bounded from above, we can show that $\exists b$ st $a<x<b$

[grand pond]

Mr bean is not $\R \setminus \Q$

[twilit field]

So firstly this shows that every real lies between two integers

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

Now we know that $b>a$. We also know that $\frac{b+1}{b} \geq 1$ so $a<x< b+1$

[grand pond]

Mr bean is not $\R \setminus \Q$

[twilit field]

nvm

Again, we know $a<x<b$ ; $b>a$

[grand pond]

Mr bean is not $\R \setminus \Q$

[twilit field]

OOh

shit

[twilit field]

. close

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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 root]

so im finding the volume of the shaded area rotated around the y axis

[drifting root]

im pre sure this gives the right answer

but my poor integ skills prevent me from reaching it

oh wait a sec

i see my problem

fixed it

.close

[midnight plank]

Channel closed

Closed by @drifting root

Use .reopen if this was a mistake.

[midnight plank]

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 root]

hi how do i do this?

[drifting root]

ik $f’(x) = 1 + ln(x)$

[grand pond]

Sho

[drifting root]

but idk what to do after

[sinful trout]

therefore what do you think the integral of ln x is?

note that x' = 1

and -x' = -1

[drifting root]

sorry im not familiar with the x’ terminology

[sinful trout]

that just means the derivative of x

[drifting root]

ah

[sinful trout]

same as you used here; except x is a function equal to x

[drifting root]

gimme a sec

it makes sense to me if i do this

but cause its a definite integral

idk how to deal with f(x)

[last slate]

F(x) = int(ln(x)) + int(1)

[drifting root]

this is just me isolating the int(lnx)

[novel lion]

where are the limits

[last slate]

Bro gonna get + c1 & c2 no?

Why u isolating ln(x) doh

[drifting root]

this is what made sense to me for indefinite but idk how to deal with this as definite

hence why i left out the limits

[last slate]

Just + c1 +c2

[novel lion]

$\int_{1}^{e} ln(x)dx = [f(x)]{1}^{e} - \int{1}^{e} 1dx$

[grand pond]

Astar777

[drifting root]

oh

actual?

[last slate]

Why did u input these limits

[drifting root]

i just sub in the limits to f(x)?

[novel lion]

because the question asked to find integral of lnx from 1 to e...

[last slate]

I see

This is ez if i can remember ibp

[novel lion]

thats how integral works, no?

[last slate]

😂

[novel lion]

$\int_{0}^{1} 1dx = [x]_{0}^{1}$

[grand pond]

Astar777

[novel lion]

same thing here

[last slate]

Yurp

[drifting root]

oh

ic

thanks for the help

.close

[midnight plank]

Channel closed

Closed by @drifting root

Use .reopen if this was a mistake.

[midnight plank]

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.

[cinder path]

need help

[cinder path]

what's the conic, the focal point and the summit

[midnight plank]

@cinder path Has your question been resolved?

[midnight plank]

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.

[gusty falcon]

Hi, what is the minimum number of elements in a List such that range and interquartile range will be distinct?

[gusty falcon]

4?

Consider [1,2,3] then the IQR is 3-1 = range = 2

[steep hinge]

mmm

[gusty falcon]

hi

[midnight plank]

@gusty falcon Has your question been resolved?

Channel closed

Closed by @gusty falcon

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.

[dry ore]

kinda need help i dont rlly understand his last step ik the derivitive of sec^2 is tan but how the did the intergral and du just dissapear?

[shrewd tundra]

cuase he didn the integral

so derivative of tan x = sec ^2 x

integral is the opposite

of differentiation

so hes going back from

sec^2 x and asking, what function if differentiated gives this

this is nkown as the primitive function

[dry ore]

hmm im not sure i understand not sure if my way of thinking if right since the derivative of tan x =sec^2 x that means the integral of sec^2 x is tan x but bow does the du just dissapear?

[shrewd tundra]

yes its right

the du dissaperas cause he did the integral

like he actually integrates it

think of like activating a machine and getting the outpute

before he was tinkerring settings inthe machine (subbing stuff in the integral) then he pessed the button and got the result (tan u) and doesnt care about the machine anymore

[dry ore]

ohh so if i think it as lets tan intergral of sec^2 x dx then it wld just be tan x but what if i had smth like intgeral of sec^2 x du then can du just dissapear or?

[shrewd tundra]

no the du dissapeared

cause he integraetd it

how do i explain this

like he did the integration

like actually did it

he got the answer

[worn blade]

if you integrate integral(xdx) it's just x^2 /2 not that and dx

[midnight plank]

@dry ore Has your question been resolved?

[dry ore]

ohhh ok tks!

[midnight plank]

Channel closed

Closed by @dry ore

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.

[last slate]

am i doing something wrong?

[upper void]

,rotate

[upper void]

yes this is correct so far i believe

are you stuck on what to do next?

[last slate]

yes

[upper void]

i would do a substution and replace x with u^2

and also make it so the y is on its own

[last slate]

whats that

[upper void]

so let x equal some number u^2

[last slate]

ohhh

[upper void]

then replace all the x's in your equation with u^2

[last slate]

like this?

[upper void]

,rotate

[upper void]

almost but it wouldnt be -10u^2

[last slate]

what is it]

[upper void]

if we had root(x)

and we replace that with u^2

it becomes root(u^2)

[last slate]

so 10 root (u^2)

[upper void]

what is root(u^2)

[last slate]

x

root x

[upper void]

yeah but in terms of u

[last slate]

that would be u

[upper void]

yes

so we would have -10u

[last slate]

yeah

[upper void]

so all together we have u^2 - 10u + 25 +20root(2) = y

does that remind you of anything

[last slate]

quadratic formula

[upper void]

yes

so we can use quadratic formula to solve for u

[last slate]

okay

wait so is c 25 plus 20 root 2

[upper void]

yes

[last slate]

it says maths error

[wintry shoal]

What did you put in?

[upper void]

yeah sorry i just realised my method wouldnt work

[wintry shoal]

Why wouldn’t that work?

[upper void]

but im not sure how you would solve this as we just have an equation of a line so i dont know how were meant to get to positive interger values for x and y

[upper void]

it would be imaginary roots

i was trying to solve for when y=0 but thats not what we want

it feels like were missing some information for this to be solved

but i might just not know how to do it tnh

tbh*

[last slate]

-(-10)-root (-10^2)-4(1)(25+20root2) / 2(1)

[wintry shoal]

Wait

[last slate]

r u gcse

[upper void]

ive done up to alevel

[last slate]

damn

[wintry shoal]

No this should be u^2-10sqrt(u)+25+20sqrt(2)

[upper void]

how

[last slate]

itwont be quadratic formula ahlie

[wintry shoal]

(5-sqrt(x))^2
5•5=25
5•-sqrt(x)=-5sqrt(x)
5•-sqrt(x)=-5sqrt(x)
sqrt(x)^2=x
25-5sqrt(x)-5sqrt(x)+x

=25-10sqrt(x)+x

[upper void]

yeah

[wintry shoal]

Oh I didn’t realize you replaced x for u^2

I thought you did x for u

My bad then

[last slate]

that says maths error tho

[upper void]

yeah its not the way you would solve this i dont think

ok i got the answer but im not to sure on the method

i dont know how valid a method this would be so you might want to check with your teacher but ill explain anyway

[last slate]

okay

[upper void]

so we know we want two interger/whole number so we need to cancel out the 20root(2) on the right hand side

so we need the value of (5-root(x))^2 to end up with 20root(2) as well leading them to both cancel out

so that means after expanding when we get -10root(x) we need this to equal -20root(2)

so root(x) must equal 2root(2)

see if you can solve it from there

[wintry shoal]

Wouldn’t we need -10sqrt(x)+25=-20sqrt(2)?

[upper void]

no cause the 25 is a whole number and were only concered with the square roots

the 25 will just help give us the value of y at the end

[wintry shoal]

Hm

[last slate]

25 + x = y

[upper void]

did you get a value of x though?

by solving root(x) = 2root(2)

[last slate]

25 + (2root20)^2 = y?

[wintry shoal]

Nope

[last slate]

if root x is 2 root 2

then x is (2 root 2)^2

am i wrong

[wintry shoal]

That’s what the sqare root of x is

[last slate]

yes

[upper void]

yes that is right

[wintry shoal]

Oh wait yeah you’re right

Sorry, misread what you said

[upper void]

oh i think you just made a typo when you wrote this

[last slate]

y is 33

[upper void]

yes

[last slate]

oh yh lol

[upper void]

so the two values are 8 and 33

[last slate]

okay

ty guys

.close

[midnight plank]

Channel closed

Closed by @shadow copper

Use .reopen if this was a mistake.

[midnight plank]

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.

[last slate]

I'm just going to claim this and I'll write down the questions since it's long

[last slate]

1. 33^2x - 3^2x times 3^-1 = 18
2. 3^x+2 + 3^x = 1-/81
3. (2^x2/2^5x) = 1/16
4. 4^2x - 20.4^x + 64 = 0
5. 0.001^x = (1/10)^x-3
6. (2/5)^x-2 = (5/2)^3x+2

I don't understand how to answer these questions

[keen sphinx]

is the first one 18 or 81?

[last slate]

18

[keen sphinx]

ok so its 33^2x-3^2x x 3^-1 =18

[keen sphinx]

have u done practice questions?

[last slate]

WAIT IM SO SORRY

[keen sphinx]

whats wrong

[last slate]

1. 3^2x - 3^2x times 3^-1 = 18
2. 3^x+2 + 3^x = 10/81
3. (2^x2/2^5x) = 1/16
4. 4^2x - 20.4^x + 64 = 0
5. 0.001^x = (1/10)^x-3
6. (2/5)^x-2 = (5/2)^3x+2

[keen sphinx]

that makes it easier

ok so lets start with the first one

[last slate]

These are practice questions. I know the answer Idk how to solve them

[keen sphinx]

you're familiar with the laws of indices correct?

[last slate]

kinda yes

[keen sphinx]

that alr

so when I say a^-1

what do i mean

if i expand the indices what will it look like

[last slate]

okay idk

I only know laws of exponent

[keen sphinx]

heres an idea

[keen sphinx]

same thing

[last slate]

Welp this is going to be a challenge

We weren't taught about laws of indices

[keen sphinx]

laws of indices and laws of exponents are the same thing buddy

[keen saddle]

$3^{2x} - 3^{2x} /mul 3^-1 = 18$

[keen sphinx]

dont stress on it

[grand pond]

Wumpus Man

[gaunt otter]

use a latex code generator if not familiar with texit

[keen sphinx]

you weren't taught them?

wait then why r they giving you that exercise

[keen saddle]

$(3^{2x} - 3^{2x} )\times 3^{-1} = 18$

is this your eq?

this seems wrong

[last slate]

I mean I know the laws of exponent I just- don't like getting confused...

[keen sphinx]

oh ok

[grand pond]

Wumpus Man

[keen sphinx]

so to put it simply

$3^{-1} = 1/3$

lol i tried

anyways

it's just 1/3

[keen saddle]

put a dollar in the end and it will work

[keen sphinx]

huh yea that doesn't look right

[grand pond]

mompwomp

[last slate]

Negative Exponent law but used backwards.

[keen sphinx]

yea

so that means you have

$(3^{2x}-3^{2x})/3=18$

[last slate]

Okay

[grand pond]

mompwomp

[keen sphinx]

cross multiply

$(3^{2x}-3^{2x})=18\times 3$

[grand pond]

mompwomp

[keen sphinx]

$(3^{2x}-3^{2x})=54$

[grand pond]

mompwomp

[keen saddle]

bro LHS in zero

RHS is non zero

the ques is wrong

[keen sphinx]

yea

ik

i realised that

[grand pond]

faiyrose

[last slate]

yes

[keen sphinx]

yea

[last slate]

im so sleepy I can't concentrate properly

[keen sphinx]

no

[keen sphinx]

.

these are the questions

[last slate]

KINDLY STOP ANSWERING THE QUESTIONS THAT ARE GIVEN TO ME??

[keen sphinx]

sorry

[last slate]

but my quiz is tomorrow

[last slate]

@prime hornet Help me out again. the same problem as last time

wait my head hurts..

nvm

.close

[midnight plank]

Channel closed

Closed by @jaunty lotus

Use .reopen if this was a mistake.

[prime hornet]

yeah... you might want to go to bed haha

I'm not able to help you rn cause I have class

[midnight plank]

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.

[fair kayak]

guys, some modulus functions like |2x-5| > |3-x| can be solved by just squaring both sides right, but i remember there are some modulus functions that can't be squared. what is it and why?

[dawn dagger]

any examples?

since modulos is always non-negative, squaring should be fine

at least in the realm of real numbers

[fair kayak]

i can't find any examples right niw

what if one side has modulus and the other side don't

like |2x-1| = 3

i can't square it right?

[dawn dagger]

that works as well since 3 is positive

[fair kayak]

oohhh

how about |x-4| = 2x+1

[dawn dagger]

if you have a negative side then it's critical

[dawn dagger]

yes

then it is

[fair kayak]

i can't square it?

bcs x is unknown and it can be both positive or negative?

OHH i seee

okayyy thank you so much bacc and alberto

.close

[midnight plank]

Channel closed

Closed by @fair kayak

Use .reopen if this was a mistake.

[dawn dagger]

You would basically introduce a new additional solution, since you squared both sides, but that solution wouldn't hold for the equation prior to squaring

You can test it and see for yourself

[lethal path]

just saying, if you solve for when both sides are equal

then use a sign diagram

you can't go wrong

[midnight plank]

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.

[dim dagger]

What’s the difference between constant function, where different x values give one y and y^2 = x not being a function because one y can’t be determined by two x values? It’s kind of stupid question xd

[fallow scarab]

yes they're different. try plotting it to see

,w plot y=5

[grand pond]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[fallow scarab]

,w plot y^2 = 5

[grand pond]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[dim dagger]

But why isn’t y^2 = x a function

Its so Basic I cant wrap my head around it somehow

Like I get it but don’t

[heavy wagon]

,w plot y^2 = x

[grand pond]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by tomb5530

[dim dagger]

It fails the vertical line test right

[heavy wagon]

correct

A function is specfically defined as one-to-one

[dim dagger]

How could This create a graph

How Can √1 be y = 1 and -1 at the same time

Sorry for Basic questions

[heavy wagon]

From what I see here, they have plotted the graphical solution to y^2 = 5

[heavy wagon]

When you take the square root (as an expression) you take strictly the positive solution (known as the principal root) if you have some equation you wish to solve (e.g. x^2 = 1) then you can have that x = 1, -1

[dim dagger]

Thanks for answering I think I finally get it

[midnight plank]

@dim dagger Has your question been resolved?

[midnight plank]

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.

[wintry eagle]

I need help with convergence of fourier series. The situation I am in is that I have an assignment. And my teacher keeps failing me on it, due to him not recoginizing my argument or the theorom I'm using apparently doesn't exist in our course literature

[wintry eagle]

Since he doesn't consider that showing that the function f, satisfies the dirichlet conditions to be valid argument, to why the function converges to all values of f where it is continous

[fallow scarab]

you want us to change your teacher's mind?

[wintry eagle]

No, I want help with a theorom I found in my book

and see how I can apply it to my function

since for me it currently isn't making sense

[fallow scarab]

show the theorem then

[wintry eagle]

It's in Swedish, but I'll try to translate it

The theorom says: Assume that f is C^2 and T-periodic. Then the fourier series converges uniformally towards all f(t)

C^m means that the function f and all of its derivatives up to order m exist and are continuous.

This is my function

And my issue is that it's a piece wise function, which is not continous

and if I take the derivative, I'll have a f that is not continous

I don't really know if I can maybe work with anything here? Maybe prove that it's contious piecewise, and then explore the points of discontinuity with the left and right-hand limit at that point over 2

[fallow scarab]

yea the last idea about piecewise is right

[wintry eagle]

Okay so show that this theorom is true for each piece of the function

Now what conclusions can I draw using the method of left and right hand limit over 2?

at these points?

[midnight plank]

@wintry eagle Has your question been resolved?

[wintry eagle]

<@&286206848099549185>

[winged meadow]

<@&286206848099549185>

[fallow scarab]

!occupied

[midnight plank]

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).

[midnight plank]

@wintry eagle Has your question been resolved?

[fallow scarab]

what are you stuck on? did you find the values?

[wintry eagle]

No, my question is what conclusion I can draw by doing that?

[fallow scarab]

what conclusion are you asked to draw

[wintry eagle]

I need to show that the fourier series converges to the function

taking the first derivative, I'll have 4 points which are discontinous, on my function f

[wintry eagle]

This theorom says that the function f has to be continous and the derivative has to exist

Can I do something with the theorom? show that it is continous piece wise? but then what?

[fallow scarab]

show the original question

[wintry eagle]

Here it is

[fallow scarab]

what about this?

[wintry eagle]

You want the fourier series as well?

[fallow scarab]

you should provid all information you know that i don't

that's relevant to your questions and original problem

[wintry eagle]

I mean, I don't really know what is relevant to my question since I am lost

But sure

That's f(t) and that's the fourier series

I don't think we need the fourier series for my question

[fallow scarab]

yea so you need to do it for the entire domain, including points of discontinuity

just looks like t=0 unless there's more in swedish you're not translating

[wintry eagle]

Point t=0 is discontinous yes

that's the only point in the function

[fallow scarab]

so plug t=0 into the series

[wintry eagle]

which is discontinous

[fallow scarab]

and verify it equals your result here

[wintry eagle]

how come?

[wintry eagle]

Yes? I need to show that it converges for all values, my question is how verifying it at t=0 will do that

sure, we need to explore the point of discontinuity, but what about everywhere else where f is continous?

[midnight plank]

@wintry eagle Has your question been resolved?

[midnight plank]

@wintry eagle Has your question been resolved?

[wintry eagle]

<@&286206848099549185>

[midnight plank]

@wintry eagle Has your question been resolved?

[midnight plank]

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.

[viral dagger]

find all positive integers triples (a,b,c) such that abc=2^4×5^2

[viral dagger]

idk why but im blanking on this

.close gtg whoops

[midnight plank]

Channel closed

Closed by @viral dagger

Use .reopen if this was a mistake.

[viral dagger]

wtf why is the next question an imo 2023 one 😭

[midnight plank]

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.

[viral dagger]

find the smallest n such that
$\tau(n^2)=3\tau(n)$

[grand pond]

Skill_Issue

[viral dagger]

so like if tau(n)=(a1+1)(a2+1)....(ak+1) then tau(n^2)=(2a1+1)(2a2+1)...(2ak+1)

thats where im stuck

tau(n) is ammount of factors of n btw

not sure if thats stsndard or not

[midnight plank]

@viral dagger Has your question been resolved?

[runic hamlet]

given that you want to find the smallest solution, it would be a good idea to limit the amount of prime factors to a small number and then see what you can do with that

[astral bough]

Brute-forced a solution, it's 144. Not sure how to properly get to it tho.

I'd wager a guess that tau is a function of the powers of the prime breakdown. All numbers with this ratio up to 1000 have 15 divisors and factor as x^2*y^4.

[runic hamlet]

the a_i are those powers

[astral bough]

Checked up to 100k, something like 40 numbers satisfy this, all with 15 divisors.

So the problem is showing that only one multiset of numbers, namely $S = {2, 4}$ satisfies $\prod_{i}^{a_i \in S}{\frac{2a_i + 1}{a_i + 1}} = 3$

[grand pond]

LooseEthics

[runic hamlet]

no no

the problem only asks for the smallest solution

that is way easier than all solutions

if k=1 then you can quickly check that there is no solution

[astral bough]

If you don't care about how you arrive at the solution, then that's 144.

[runic hamlet]

if k=2 then you quickly find (4,2) as a solution which leads to 144

if k>=4, then your number is at least 2*3*5*7=210, which is too big

so then you only have to think about k=3

[astral bough]

What about (3, 3)?

Nevermind, the smallest there is 216

[runic hamlet]

anyway, @viral dagger isn't here anymore anyway

[viral dagger]

fuck sorry forgot i made this

[viral dagger]

ohhh

ty