help-27

[formal quarry]

yes i did that

i solved tghe definite from 0 to 5

[olive snow]

Bounded by the curve means that its either below or above, depending if its below or above the x axis

x axis being y = 0

[olive snow]

So what justifies that we integrate

[formal quarry]

yes so when i did 0 to 5 its this entire region

correct?

[olive snow]

Yes

[formal quarry]

then it says to do the the x-axis? meaning?

[olive snow]

Whats x axis

[formal quarry]

and the line 𝑥=4 meaning this?

[olive snow]

Yes

[formal quarry]

0 1 2 3 4 5

[supple knot]

Can you show the actual question

[olive snow]

More generally

[supple knot]

Is it this

[supple knot]

Amazing lack of parenthesis

[formal quarry]

Then, find the area of the region bounded by the curve, the x-axis, and the line 𝑥=4.

i think its the commas, i think they mean just two methods, the x-axis and the line x = 4.

not that by the curve AND the x-axis AND the line x =4

cuz obvs that bounded by the curve is till the x-axis and the line x = 4 no?

[olive snow]

When you integrate you calculate the area between the curve of a function and the x axis, thats why they talk about x axis

[winter torrent]

no, it's one area. the curves that bound it are: the curve 1/(1-x), the curve y=0, and the curve x=4

[formal quarry]

but they says interval from [0,5]

[a,b]

[olive snow]

No they say to graph it there

Then to calculate smth

[formal quarry]

🤦‍♂️ ohhh right.....

so they want me to find area between 0,4 only?

[olive snow]

Also, it is starting to 0 because it is where the function meets x axis

[formal quarry]

and not like this?

red for find the area of the region bounded by the curve, the x-axis

and green for the area of the region bounded by line 𝑥=4

?

I JUST read it again

i see what you mean

clearly

thanks!

[formal quarry]

SMH 🤦‍♂️ kek

[olive snow]

Both are area of region bounded by x axis and curve, you just stop at different line x = smth

[formal quarry]

yeah understood

thanks! both

[short hare]

you're welcome

[formal quarry]

.close

[devout snow]

Channel closed

Closed by @formal quarry

Use .reopen if this was a mistake.

[formal quarry]

.reopen

[devout snow]

✅ Original question: #help-27 message

[formal quarry]

good?

[light storm]

yes

[formal quarry]

.close

[devout snow]

Channel closed

Closed by @formal quarry

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[cerulean ruin]

\textbf{Lemma 6.3:} \textbf{$\forall$ ordinals $\alpha$, if $b \in \alpha$, $b$ is an ordinal.} \ \
\textit{Proof:} We first check if $b$ is transitive. Choose any $z \in y$ and $y \in b$. We want to show $z \in b$. Since $b \in \alpha$ and $y \in b$, $y \in \alpha$ since $\alpha$ is transitive. Since $y \in \alpha$, and $z \in y$, then $z \in \alpha$, since $\alpha$ is transitive. Thus ${z, y, b} \subseteq \alpha$. Because elements of $\alpha$ are transitive, and we have $z\in y$ and $y \in b$, we get $z \in b$. So $b$ is transitive.
\\
$\in$ is a strict well-order on the elements of $b$. Since $b \in \alpha$, and $\alpha$ is transitive, $b \subseteq a$. Since $\in$ induces a strict well order on the elements of $\alpha$, it clearly induces a strict well order on the elements of $b$. $\blacksquare$

[woven radish]

toast

[cerulean ruin]

hello i have writtent his proof down in my notes

i think i mightve missed some parts of it

specifically the last sentence of the first paragraph

i understand everything up to why can we now assume z in y and y in b => z in b?

oh

hm

?

[tender lodge]

<@&268886789983436800>

[cerulean ruin]

<@&286206848099549185>

[light storm]

what

[cerulean ruin]

.

[slender totem]

beyond my paygrade

[cerulean ruin]

i dont fully understand the portion where its saying because elements of alpha are transitive

[last parrot]

Optional btw

[light storm]

kinda hard lowkey

[cerulean ruin]

I think i get it

So because alpha is well ordered, it must have strict well ordering so we know z, y, b are elements of alpha and we also know z \in y and y \in b Then because elements of alpha are well ordered, z must be in b because strict well-orders are transitive

can someone confirm my understanding ^

[light storm]

yeah that looks correct

honestly props to your for figuring that out

i didnt even have an idea how to do it

[cerulean ruin]

eh its just set theory and following directions

i confused alpha being transitive

and transitivty of well orders

.solved

[devout snow]

Channel closed

Closed by @cerulean ruin

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[versed wyvern]

In this Venn diagram, what does U at the top right mean?

[jade pecan]

the universal set

[versed wyvern]

So what does that mean?

@jade pecan

[jade pecan]

https://byjus.com/maths/universal-set/

[versed wyvern]

.close

[devout snow]

Channel closed

Closed by @versed wyvern

Use .reopen if this was a mistake.

[versed wyvern]

Thanks

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[devout snow]

Please don't occupy multiple help channels.

[crystal dawn]

<@&268886789983436800>

[devout snow]

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.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[safe brook]

does it matter where the limit comes from in these types of question?

[restive river]

what do you mean by where does limit come from

[sturdy fiber]

Yes

It does

[safe brook]

how

[sturdy fiber]

Because it is the primary thing that will decide what sign we get

[safe brook]

like the lim->5+/-

[sturdy fiber]

For eg question 32 of the image

[restive river]

it does

[sturdy fiber]

Since it is 3-, we get a negative sign

Since it is odd power the negative sign stays

Hence the limit approachs $-\infty$

[woven radish]

Itsuki

[safe brook]

so if its even power, and the sign is negative it becomes positive?

[sturdy fiber]

Exactly!

[safe brook]

is there any exception to that?

or is that all

[sturdy fiber]

Nope no exceptions you should worry about for now

[safe brook]

so if its x->0-, per say it becomes positive too right

[sturdy fiber]

0- will be negative

0+ will be positive

[safe brook]

oh

[sturdy fiber]

Just less than zero

For a reference something like -0.00000000...

[safe brook]

okk, thanks

that's my last question

.close

[devout snow]

Channel closed

Closed by @safe brook

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[drowsy parcel]

please explain this to me

[carmine veldt]

go step by step

can you tell me what you've tried so far?

[twilit comet]

!status

[devout snow]

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

[twilit comet]

!show

[devout snow]

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

@drowsy parcel Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[pine minnow]

okay so I simplified the given term and got (xy)^2, so i want to know whats the thinking process that goes in your mind when you try to find maximum value of (xy)^2 when youre given a restricted domain. I know the answer, but i want to develop my own thinking to it, but im struggling to i would appreciate if you were to guide me to think for it

[lost lance]

Its a well known trick that when x^2+y^2=1, you can substitute x=cos theta, y=sin theta for some theta

so we do just that

and then (x^2y^2=\cos^2\theta\sin^2\theta=(\frac12\sin(2\theta))^2)

[woven radish]

Richard Liu

[lost lance]

and (\sin(2\theta)) is at most 1

[woven radish]

Richard Liu

[lost lance]

so maximum is (1/2)^2=1/4

[restive river]

alternately you can use AM-GM

[lost lance]

yeah but on x^2 and y^2

cuz x and y themselves are not necessarily positive

[restive river]

yh

[pine minnow]

oh yes, one way to solve this is by trigonometry. that clears it up, thanks for the assist

[pine minnow]

i havent studied AM-GM yet actually

will be learning it very soon though

[restive river]

if you are done with the thread and do not have any other query, you can close it by typing .close.
Closing solved threads/help channels helps people know that the query is solved and avoid the need to ask if you still need help

[pine minnow]

oh yea, thanks for the reminder

.close

[devout snow]

Channel closed

Closed by @pine minnow

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[cerulean ruin]

Prove that the collection of all successor ordinals is not a set.

maybe the idea is to create an isomorphism between ordinals and successor ordinals, because we have already proven the fact that all ordinals are not a set, and we can show that theres a 1-1 mapping between oridnals and successor ordinals, then the set of successor ordinals is nto a set?

[cerulean ruin]

I thinkt his idea is right but I'm not sure how to represent it rigorously with the axioms we have discussed in class

Set Existence
Axiom of Extensionality
Pairing Axiom
Separation Scheme
Union Axiom
Axiom of Infinity
Induction Scheme

\textbf{Prove that the collection of all successor ordinals is not a set.}
\\
Assume by way of contradiction that the collection of all successor ordinals is a set, denote this set by $SO$. Observe by a theorem, since $SO$ is a set of ordinals, then $\bigcup SO$ is also a set of ordinals.

[woven radish]

toast

[cerulean ruin]

my next argument was to show that USO = ON

(i.e collection of all ordinals)

😭

[devout snow]

@cerulean ruin Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[devout snow]

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.

[willow helm]

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[pine minnow]

can i get any tips regarding how to approach this problem? im running in a circle tryin to susbtitue value by sum and product, although not getting a clear solution as given in the options. I would apprieciate a small hint on how to proceed with this

[tender kite]

sum of roots, product of roots?

(Hint)

[pine minnow]

running into a circle with that, ending up with the same equation with x = alpha

[tender kite]

Oh you're asking for tips

[tender kite]

Manipulation

[pine minnow]

I would appreciate both tbh

[tender kite]

Did you try to solve it using the quadratic formula?

[pine minnow]

okay so, i basically did x = beta, in the given equation. and subsituted value (in terms of alpha) for beta^2 and left beta as it is, and it gave a much more complicated expression than in the option

[pine minnow]

I did, got the roots but the answer begs in term of alpha does it not?

verifying each option 1 by 1 is unusually tedious and im sure theres a more clever way to solve this

[rain summit]

so viete's identity stated this

$\begin{cases} x_1 + x_2 = \frac{-b}{a} \ x_1x_2 = \frac{c}{a} \end{cases}$

[woven radish]

1 divided by 0 equals Infinity

[pine minnow]

yes

[rain summit]

so if we substitue $x_1 = \alpha$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

then we can solve for $x_2$

[woven radish]

1 divided by 0 equals Infinity

[pine minnow]

i did, but the equation isnt matching with the options. I will redo it rn in case of any errors though

[rain summit]

!show

[devout snow]

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

[rain summit]

show us your work

[pine minnow]

gimme a minute

Using only sum of the roots to get this relation, substituting Beta into the product gives the equation we've started with (4x^2 + 2x - 1)

[rain summit]

okay

so you got $\beta = \frac{-1}{2} - \alpha$?

[woven radish]

1 divided by 0 equals Infinity

[pine minnow]

yes

[rain summit]

substitute into $\alpha\beta = \frac{-1}{4}$

[woven radish]

1 divided by 0 equals Infinity

[restive river]

checking the options one by one is the way here ig unless there's a trick i cant find

[pine minnow]

will only give us the initial equation 4x^2 + 2x - 1 with x = alpha as I have stated before

[tender kite]

Ig there's some manipulation we're not able to find

[restive river]

[rain summit]

i don't think so

[pine minnow]

oof, I guess thats the only way

[rain summit]

just try substituting $\beta = \frac{-1}{2} - \alpha$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

into the product $\alpha\beta$

[pine minnow]

lemme try again, mightve did erorr

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

you'll get a quadratic of $\alpha$ if you did it correctly

[woven radish]

1 divided by 0 equals Infinity

[tender kite]

It's the same quadratic

[pine minnow]

and then what?

[rain summit]

oh wait rlly?

[tender kite]

You just reached the starting point

Again

[rain summit]

well then solve for $x$ directly

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

and then plug and check

[tender kite]

Yeah

[pine minnow]

thats what ive said, like 3 times now

[tender kite]

But that's not fun

[pine minnow]

thats the sad part about this problem

ahem

ig no other way

.close

[devout snow]

Channel closed

Closed by @pine minnow

Use .reopen if this was a mistake.

[tender kite]

I tried completing the square

[pine minnow]

.reopen

[devout snow]

✅ Original question: #help-27 message

[rain summit]

mhm

let's see

[pine minnow]

and?

[tender kite]

(2x+1/2)² = 5/4

[rain summit]

ooh okay

you're just solving for $x$ directly again

[woven radish]

1 divided by 0 equals Infinity

[tender kite]

I was finding a manipulation

[rain summit]

hold up

[pine minnow]

lowkey no other way, it all leads back to it

[rain summit]

lemme try smth rq if it works

[pine minnow]

aight

[tender kite]

I think I got it

[rain summit]

ooh

cook something

[tender kite]

Manipulation

[pine minnow]

enlighten me

[tender kite]

4x²+2x = 1

Divide both sides by x

4x + 2 = 1/x

Now Look at the options

[restive river]

i am looking

[rain summit]

🤯

[tender kite]

Wait😭

[rain summit]

-# prove that x = 0 ain't a root

[rain summit]

tbh substituting's the deal for me

since it's multiple choice

why can't you just find the numbers directly

[pine minnow]

okay- 😭

[rain summit]

it's multiple choice, what's the deal?

[pine minnow]

ofc we have, but if theres a manipulation we can use to get answer more quickly then why shy away from utlising it?

[rain summit]

yea ik

but finding the manipulation takes more time than just solving directly

by the time people are helping, if you did solve the numbers directly then you would've done

[pine minnow]

but also reduces number of errors and expands your thinking capacity when given similar proble

[rain summit]

you allowed to use a calculator?

[pine minnow]

nope

[pine minnow]

except im solving dis at the comfort of my home rn, and if a manipulation exists lemme find it

[tender kite]

Ughhh ultimately you would have to put the value of aplha

But Beta is -1/2 - alpha

[rain summit]

hm

this is multiple choice

[pine minnow]

no other way

[tender kite]

Yk what's the other way

[pine minnow]

staring at the options?

[tender kite]

Equating this with options

[rain summit]

ooh that's genius

[tender kite]

And checking the value of aplha

[rain summit]

a^2 = -1/2 - a

[tender kite]

At least it's faster

[rain summit]

for the sake of simplicity im assuming alpha = a

so a^2 = -1/2 - a

[tender kite]

Nop doesn't fit

[rain summit]

a = -1/2 so definitely not

[tender kite]

Option 2 should fit

[rain summit]

4a^2 - 3a = -1/2 - a

WOLFRAM ALPHA

oh wait no calculator

[tender kite]

It gives one root same

[rain summit]

4a^2 + 3a = -1/2 - a

[pine minnow]

gives a cubic?

[tender kite]

Yeah both roots same

[rain summit]

so probably the

oh wait i forgot

!nosols exists

[devout snow]

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.

[tender kite]

So what, didn't they teach you to divide

[restive river]

bluds lets quit

[rain summit]

also really there's really no way to get a cubic in here

[rain summit]

you quit alone by yourself

[tender kite]

Fastest method we found to solve this problem is using options 💔

[restive river]

https://tenor.com/view/rain-sadness-gif-27348981

[tender kite]

There's no manipulation

Or there is, we're just blind

[rain summit]

the approach might be lying in this spaghetti 🥀

impawssible without solving directly

[tender kite]

Even if you go directly it's kinda hard

I think the trick is to use the options only

[rain summit]

if ts is in SAT

we might be fucked

[pine minnow]

no other way 💔

.close

[devout snow]

Channel closed

Closed by @pine minnow

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[unreal lynx]

can someone give me a hint for part B please

[winter torrent]

what did you get for a?

[unreal lynx]

not possible

I figured for part b of the question I could place this piece so that it is on 3 black tile and the other one on 3 white tiles than that would cancel out

[drifting sierra]

Well, you now think it's possible, right? So try to construct an example

[unreal lynx]

I am. I cannot seem to find a way to get it to work

I made little cutouts and am trying to arrange them

[winter torrent]

hmmmm how would they fit together then?

[unreal lynx]

they dont have to be immediately next to each other

[drifting sierra]

Maybe try starting with this configuration since both Ts cover the same number of black and white tiles

It shouldn't be too difficult

[unreal lynx]

what tool are you using for that?

[drifting sierra]

I just found some random website https://toytheater.com/tetromino/

Found a solution yet?

[unreal lynx]

no

going insane

[drifting sierra]

Try placing the straights and squares first

The Ls and Ss can combine to make a lot of different shapes so they are easiest to place last, filling whatever area is left

[unreal lynx]

I always end up with one piece not fitting

[drifting sierra]

Try with this

[unreal lynx]

ok

are you sure it can be done using each shape twice

[drifting sierra]

I've done it four times now, including once with this

[unreal lynx]

finally got it

that was not fun

just felt like guessing randomly until I got it right

[drifting sierra]

I can't really think of a strategy to give you

Anyway:

[unreal lynx]

thanks

I don't know why I struggle so much with arranging shapes

I say that and then i did this in 30s

anyway, thanks @drifting sierra

.close

[devout snow]

Channel closed

Closed by @unreal lynx

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[devout snow]

Please don't occupy multiple help 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.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[inner marten]

How to do 19a and b

[trail eagle]

Just start from (0,1) and follow flow lines

It's a sketch so not meant to be super precise

[versed juniper]

fr

[trail eagle]

What's already drawn is fairly good I think

[inner marten]

Alr ty

What abt part b?

[trail eagle]

Same process but start from (-3,0)

[inner marten]

How to tell where to draw for the decreasing part

Would it be smth like this

[devout snow]

@inner marten Has your question been resolved?

Channel closed

Closed by @inner marten

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[warm hedge]

Trying to find the value of X, can this be done? If so how can I solve it?

[opaque mortar]

what is x

is it supposed to be the opposite side

as if it were a right triangle

[warm hedge]

Thats what I’m trying to find

[opaque mortar]

like i mean

[warm hedge]

If it helps both lines are 252

[opaque mortar]

like idk what x is pointing to

are we assuming this

yes

right angle on the bottom

yes tangent

[warm hedge]

Wait

[opaque mortar]

ok so x = 252 tan 9

[warm hedge]

So its tan

Thanks guys

Yeah its a right angle

I have the values over the original image if this helps

Yea

I accidentally put 252 on the top one instead of the bottom and forgot to erase

Its still tan tho right?

Thanks guys

.close

[devout snow]

Channel closed

Closed by @warm hedge

Use .reopen if this was a mistake.

[opaque mortar]

wait what

no it's not a right angle

this triangle isnt even possible

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[sinful badge]

Is my math right for this? I still gotta graph

Which I'm probably gonna need help with

[crystal dawn]

,rccw

[crystal dawn]

poor notation. in both questions you seem to write f(x) = transformed function before the g(x) = transformed function final answer.

[sinful badge]

I'm confused

[crystal dawn]

look at your own work, specifically the last two lines of each question

flips x-coordinate, not x-axis

and that would be flipping across the y-axis

that part is correct. what is dubious here is misrepresenting f(x)

[sinful badge]

What should it really be

[crystal dawn]

since |-2x + 3| - 4 is already the transformed function, it can't be f(x) any more

[sinful badge]

I guess that was just me showing my work then changing it to g(x) to box in

[crystal dawn]

if you had put f(**-**x) instead of f(x), I would have accepted it

[crystal dawn]

but then you would be saying that f(x) is now this new function. which isn't the case

[sinful badge]

Hm I don't think I've ever had, wasnt taught to write it that way

I just know the formula mentally

[crystal dawn]

or, you coulf state that g(x) = f(-x), and then write your boxed answer

could*

[sinful badge]

Is the x negative because of it being whatever

I'm not sure what problem so

[crystal dawn]

q6

[sinful badge]

I can't say what it really is

[crystal dawn]

I'm using q6 as an example, but it applies to both questions shown in the image

[sinful badge]

So because its a reflection over the y it's -x

[crystal dawn]

the x is negative because it's the transformation you have made

you are defining a new function, g(x), as the transformed version of f(x)

the transformation is a reflection over the y-axis, which is f(-x)

hence, g(x) := f(-x)

[sinful badge]

I guess I'm confused why the x is negative because I thought you were just referring to like the formula for a reflection

[crystal dawn]

I mean, you went from |2x + 3| - 4 to |**-**2x + 3| - 4. how?

if you can tell me how and why you did this, then there is a high chance you have answered your own question.

[sinful badge]

I made the 2 negative bc that's the rule for a y reflection

[crystal dawn]

what is the rule for a reflection over the y-axis?

[sinful badge]

Uh

I don't have them memorized

But I have a sheet

[crystal dawn]

,rcw

[sinful badge]

Make the x negative

[crystal dawn]

there, see? f(x) becomes f(-x)

[sinful badge]

Yeah I see

Hm I guess I've never done it bc my teacher never has in her examples

[crystal dawn]

g(x) is the transformed version of f(x), and the transformation is f(-x). so g(x) := f(-x)

it's better to write it something like this to illustrate the exact transformations first

then you can do your algebra as necessary

[sinful badge]

In my examples I just go straight to g(x) so

I guess I've never done it bc I didn't know I should

Are my answers okay tho?

[crystal dawn]

6 is fine, haven't seen 7, sec

[sinful badge]

Alright

And I need help with the graphing ig, someone tried but I was confused

I also lost the chat bc I couldn't graph when they were helping

[crystal dawn]

7 is also correct

if you are in doubt about how to graph these, perhaps start with the basic f(x) = |x|

[sinful badge]

Thank you, I think 2 and 4 are too

[crystal dawn]

oh there was a larger image, sorry

the thumbnail showed only q6 and q7

[sinful badge]

No worries I'm sorry

[sinful badge]

So like at (0, 0) right

[crystal dawn]

nt sure what you mean by at (0,0) but perhaps you can graph what you mean?

[sinful badge]

Is this what you mean

[crystal dawn]

yes

you can then transform this graph into what you need in two ways

first, if you are not confident, you can graph the given function, then transform the given function into your answer function. if the graphs of the given and answer functions match the transformation you were asked of (eg. q6 given and answer being mirrored across the y-axis), then you can be sure you are right

if you are confident though, you can graph your answer function directly

[sinful badge]

I also have my graph calc I just don't know what to look at / type on my y's

[crystal dawn]

honestly just use Demos

Desmos*

are you not allowed to use Desmos or Geogebra or anything like that?

[sinful badge]

Would you know what to do on my calc? Bc I use it on my tests

Just my calc

[crystal dawn]

what model do you use? I am only familiar with the Ti-nspire

[sinful badge]

Ti-83 plus

[crystal dawn]

I suppose each y is a function?

if so, type in your original function as y_1 (the given function) and your answer as y_2

[sinful badge]

These two, right?

[crystal dawn]

yes

the same for any other question you wanna check

[sinful badge]

So then what points should I be graphing for what

[crystal dawn]

,rcw

[sinful badge]

So then what points should I be graphing for what

Sorry it was meant to send under that

[crystal dawn]

does your calculator tell you which graph is y_2?

oh it does. then you know you put your answer function as y_2. so graph y_2.

[sinful badge]

Why is -3 two points tho

It's confusing me

[crystal dawn]

look at the graph

[sinful badge]

Yeah, cant use on test tho

[crystal dawn]

it's a V shape

some y-values would be mapped to twice

OP wants familiarity on tests

[sinful badge]

Like me graph these

[crystal dawn]

let's answer her question first

[sinful badge]

What's OP

[crystal dawn]

you

the original poster

[sinful badge]

Ah sorey

Let me graph this

[crystal dawn]

but once you are done you should familiarize yourself with Desmos too

or Geogebra

[sinful badge]

This is what I get from graphing the points

I just graphed what the graph will fit and what it showed me with out scrolling

[crystal dawn]

obviously the graph isn't split though, so you can join the two pieces by extending them

(works because both pieces are straight lines. does not work otherwise!)

[sinful badge]

How do I do that

I'm prob gonna draw it wrong lol

[crystal dawn]

the cheap way is to just extend the two straight lines downwards

the proper way is to find the minimum point of this graph

[sinful badge]

What should I do

[crystal dawn]

I've given you two answers to that question

[sinful badge]

I guess I meant if you were me

[crystal dawn]

if it were me I'd do away with these points and graph the function just using the special points (intercepts and min point). if it were me in exactly this situation, since the points are alrd there, I'd just find the min point. or I'd just extend downwards if I was asked to sketch

the best option for you is to find the min point

[sinful badge]

What is a min point

[crystal dawn]

minimum point

notice that the graph never goes under a particular y-value. that point is the minimum point

[sinful badge]

But if its not going under a particular y value how is there a min point

[crystal dawn]

why would there be no min point if the graph does not go under a specific value (i.e, has a minimum)?

for instance, if I say, the volume of water in a tank will never drop under 10 liters, surely there's a minimum volume of water here?

[sinful badge]

I just thought then there would be multiple min points

[crystal dawn]

not for an absolute value function. you'll meet minima and maxima in later math

[sinful badge]

Ah okay sorry

So is this acceptable

[crystal dawn]

no, you've drawn both the original and transformed functions here when you are only asked for the transformed version, but the transformed version is correct

but as a guide for yourself, it is fine

[sinful badge]

I was taught to draw both so I did

[crystal dawn]

normally if you're not told to graph both, never graph both. if you have to graph both, clearly indicate the original and transformed functions

[sinful badge]

Maybe not taught but helps me since we do it for like f(x) = |x|

[crystal dawn]

if I was an examiner and I was an asshole I could look at this and ask you, "which is the transformed function?". or worse, I can purposely pick the wrong function as the transformed function and dock you marks

never give a pedantic ass a chance to dock marks

since you already marked the original function as f(x) and the transformed function as g(x), just note the left graph as f(x) and the right one as g(x)

[sinful badge]

Alright

Will you stay for me to graph 8

[crystal dawn]

I think I can

[sinful badge]

Thank you

[crystal dawn]

I just realized we have an unexpected mutual

[sinful badge]

Finished

[sinful badge]

Really? Who

Towa?

[crystal dawn]

mhm

[crystal dawn]

looks ok

[sinful badge]

Yayyy

Okay thank you, I need to try and memorize the formulas, any tips?

[crystal dawn]

what formulas

experiment

[sinful badge]

These

[crystal dawn]

yeah experiment

vary something and observe the new graph

there are only four parameters to remember

af(bx - c) + d

and then from here you can easily divide them into two categories

first, whether the parameter affects the input or the output.

a and d both affect the output of the function (a multiplies the result of f(x), d is added to the result of f(x)), while b and c both affect the input (b is multiplied with x, c added to or subtracted from x)

parameters affecting the output of the function affect its graph vertically (memory tip: output = y, y = vertical), while those affecting the input affect its graph horizontally (input = x, x = horizontal)

second, whether the parameter is a multiplier or an addition

a and b are multipliers, hence they scale the function by some amount. c and d are additions/subtractions, hence they shift the function by some amount

scaling parameters stretch/compress the graph of a function, whereas shifting parameters, well, shift/translate the graph

that's how I see function transformations

[sinful badge]

Ahhh

[crystal dawn]

hope that helps

if you can and want to memorize, you could I suppose, but I am bad at memory and as a teacher I don't encourage rote memorization anyway

[sinful badge]

Well I have a test tmmr and transformations are apart of it so I need to know the formulas to solve

[crystal dawn]

fun fact! memorizing is not the only way to know stuff :D

but that's besides the point Ig

anything else?

[sinful badge]

I don't think so💗

Thank you so so much!

[crystal dawn]

nps

!done if you're done, and see you around!

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[sinful badge]

See you around!!

.close

[devout snow]

Channel closed

Closed by @sinful badge

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 kernel]

I found the formula for power spectral density

[viral kernel]

And It says

$S_x(\nu) = \lim_{N\to\infty} \frac{1}{2N+1} |X(\nu,N)|^2$

[woven radish]

KirbySnack

[viral kernel]

Can someone explain to me what this means?

Also

It says that for periodic sequences

[woven radish]

KirbySnack

[viral kernel]

Can someone explain to me intuitively what the first formula is and how I should interpret it in the periodic one?

<@&286206848099549185>

[jagged harbor]

I can't explain the formula due to not knowing it or any of the context, but what is X(-, -)?

[viral kernel]

Wait

[jagged harbor]

since you're taking a norm/absolute value and squaring, I'm guessing it's like a vector's length?

but then what are its inputs

[viral kernel]

is the Fourier transform of the signal observed only on a finite window of length

[jagged harbor]

is nu the signal and N its length?

[vernal grail]

i think it is

$X(\nu,N) = \sum_{n=-N}^N x(n) e^{-j2\pi \nu n}$

[woven radish]

alee

[viral kernel]

Yes

[jagged harbor]

ahhh, so it's almost like an average

square their sum's absolute value and divide by the number of terms

[vernal grail]

it is the Fourier transform of the finite portion of the signal

[vernal grail]

i mean this

[viral kernel]

@jagged harbor so now can you explain pls

I don't care about the proof

Someone can explain the concept to me in a way that's easy to grasp, even without having to do a lot of calculations or memorize formulas. It should make me think, "Oh, okay, now it makes sense.

[jagged harbor]

I can't, I can only say 2N+1 is the number of terms in this sum and you're dividing by 2N+1 to get some kind of average. I think it's more like variance?

I'm trying to be just wrong enough so someone who knows better corrects it lmao

[vernal grail]

wait

variance measures how much the signal disperses over time around the mean

in this case the power spectral density measures how that power/variance is distributed across frequencies

[viral kernel]

<@&286206848099549185>

[vernal grail]

<@&268886789983436800>

[viral kernel]

<@&268886789983436800>

He removes It !!!

Oh okay

👍

.close

[devout snow]

Channel closed

Closed by @viral kernel

Use .reopen if this was a mistake.

[modest gazelle]

.reopen

[viral kernel]

.reopen

[devout snow]

✅ Original question: #help-27 message

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[devout snow]

Please don't occupy multiple help 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.

[craggy dagger]

i think they got hacked

[arctic field]

not uncommon occurrence

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[noble turtle]

Hello if $A \cap \emptyset$ would the result be

[woven radish]

PainAndLight

[viral kernel]

empty set

[noble turtle]

1. $A \cap \emptyset = \emptyset$ ?

2. $A \cap \emptyset = {\emptyset}$ ?

3. $A \cap \emptyset = \emptyset = {\emptyset}$ ?

[woven radish]

PainAndLight

[noble turtle]

what would it be

it more about notation then what the answer would be

[candid maple]

option 1.

[noble turtle]

but isnt $\emptyset = {\emptyset}$?

[woven radish]

PainAndLight

[candid maple]

no.

[dull parrot]

They're different

[noble turtle]

i remember talking about that...

[dull parrot]

The other one contains the empty set as an element

It's kinda confusing at first

[candid maple]

an empty set is, well, empty.
the one on the right is the set containing \emptyset, so that set has 1 element.

more specifically, the set on the left here has cardinality or order 0, while the one on the right has cardinality or order 1.

[noble turtle]

but isnt it stated that every set contains atleast the emptyset?

[candid maple]

the empty set is a subset of every set, not an element.

[noble turtle]

whats the difference between subset and beign element of (have been asking this for the last days, but didnt try to find an answer yet)

[fluid stag]

a subset of a set is a set containing the elements of another set. an element of a set is a member of that set.

[dull parrot]

I got confused and was wondering what a beign element was

[fluid stag]

I'm fluent in typos 😅

[noble turtle]

so one looks like a member the other one is the member

[candid maple]

er.... what exactly do you mean here?

[noble turtle]

forgot that? idk

[dull parrot]

Suppose you have set A as ${1,2,3}$ and set B as ${1,2}$, we would say B is a subset of A

[woven radish]

MxRgD

[noble turtle]

yes

[candid maple]

building off MxR's example, 1, 2, 3 are elements of A (with 1, 2 also being elements of B).

[rotund umbra]

$\emptyset$ and ${\emptyset}$ are not the same.
$\emptyset$ is the set containing nothing.
${\emptyset}$ is the set containing the emptyset.

[woven radish]

Pfhrohug

[noble turtle]

maybe im thinking simple rn but wouldnt that mean $\subseteq = \in$ in this case

[candid maple]

no.

[woven radish]

PainAndLight

[dull parrot]

They are different

[candid maple]

still no.

[noble turtle]

ok this is really weird to grasp

[candid maple]

subset-superset relationships are relationships between sets.
elementship is a relationship between a value and a set.

[noble turtle]

but ill accept it

[rotund umbra]

No. $A \subseteq B$ means $\forall; a \in A.; a \in B$.

[woven radish]

Pfhrohug

[noble turtle]

ok ive seen this one before

thank you

[rotund umbra]

For example ${1,2,3,4,5} \subseteq \mathbb{Z}$. And $2 \in \mathbb{Z}$.

[woven radish]

Pfhrohug

[noble turtle]

ok ok

this looks now different

so $\emptyset$ is a symbol for a set

[woven radish]

PainAndLight

[candid maple]

a special set, namely ${ }$.

[dull parrot]

that contains no elements

[rotund umbra]

\emptyset is the symbol for "the set containing nothing".
it is not the symbol for "nothing".

[woven radish]

trilunar arithmetic (Columbina)

[noble turtle]

like A can be a symbol for a set

[candid maple]

and I suppose some syllabi really do use {} as an alternative to \emptyset.

[dull parrot]

it can be any arbitary letter you want to reperesent a set

[noble turtle]

and $A = {\emptyset}$ would be the set a containing no Elements? or an set containing the emptyset

[dull parrot]

there's special ones like the set of natural numbers which is denoted as $\mathbb{N}$

[woven radish]

PainAndLight

MxRgD

[candid maple]

a set containing the empty set.

A itself would therefore have one element - the empty set.

[rotund umbra]

$A = {\emptyset}$ is the set containing $\emptyset$.
REMEMBER $\emptyset$ IS SOMETHING

[candid maple]

so A is not empty.

[woven radish]

Pfhrohug

[rotund umbra]

It's not empty!

[candid maple]

since two Helpfuls are here, I'll step back. good luck OP!

[noble turtle]

So I would have a basket with no elements, and $\emptyset$ is not even having the basket

[woven radish]

PainAndLight

[rotund umbra]

$\emptyset$ is a set.
$\emptyset$ is empty.
${}$ is a set.
${}$ is empty.
${\emptyset}$ is a non-empty set containing exactly $\emptyset$.

[woven radish]

Pfhrohug

[rain summit]

ya

as one helpful mentioned, the empty set is a BASKET with nothing in it

it is still something

[rotund umbra]

No. ${}$ is the basket. ${A}$ is a basket containing A. ${\emptyset}$ is a basket containing an empty basket

[woven radish]

Pfhrohug

[rain summit]

$\emptyset$ is the empty basket

[woven radish]

1 divided by 0 equals Infinity

[noble turtle]

so ${\emptyset} = 0$ since we also have 0 to say I dont have anything on my bank account and saying $\emptyset$ is like saying i dont even have a bank account

[rain summit]

it's just a basket that has nothing in it

that latex issue

[noble turtle]

bruh

[dull parrot]

no but you can say the cardinality of the empty set is 0

[rain summit]

\emtpyset

🥀

[woven radish]

PainAndLight

[rain summit]

a set can't be equal to 0

a set is never equal to a number

[noble turtle]

oh

[rain summit]

good image illustration

[noble turtle]

wtf

xD

[candid maple]

alternatively, {\emptyset}.

[rotund umbra]

{} is an empty basket.
{A} is a basket containing A.
{{}} is a basket containing an empty basket.

[rain summit]

https://www.youtube.com/shorts/SUqVxZA_EgA

i recommend watching this

to get a grasp of what's going on

[rotund umbra]

$\emptyset$ is not "nothing". It's an empty set.

[woven radish]

Pfhrohug

[rotund umbra]

<- this is nothing

" " <- this is an empty quote

[rain summit]

[devout snow]

@noble turtle Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[cerulean ruin]

Can someone review my proof?

I can't tell if im smoking or not

oops

Consider the 'induced structure' $(Y, \epsilon)$, i.e., for all $a, b \in Y$
\begin{center}
$(Y,\epsilon) \models a = b$ if and only if $a =b$ \
$(Y, \epsilon) \models a \in b$ if and only if $a \in b$.
\end{center}
\\
\subsection{Problem 5:} \textbf{Suppose $X$ is a transitive set and let $(X, \epsilon)$ be the structure induced by $\epsilon$ (see HW #3).
In the verifications of a), b), clearly indicate where the transitivity of $X$ is used.}
\\
\textbf{a) Prove that for all $a, b \in X$, $(X, \epsilon) \models b = \bigcup a$ if and only if $b = \bigcup a$}
\\
An equivalent statement would be $(\forall c \in X)( c \in \bigcup a \iff c \in b) \iff \forall c( c \in \bigcup a \iff c \in b)$
\\
$(\implies)$ Assume that $(\forall c \in X)(c \in \bigcup a \iff c \in b)$ $()$. We want to prove $\forall c(c \in \bigcup a \iff c \in b)$. We know that $c \in b$ and $b \in X$. Then by transitivity of $X$, $c \in X$. Then by $()$, $c \in \bigcup a$. Conversely, we know $c \in \bigcup a$. This means there exists some $x \in X$ such that $x \in a$ and $c \in x$. But because $X$ is transitive, $c \in a$. We also know that $a \in X$, so $c \in X$ by transitivity of $X$ again. Then by $()$, $c \in b$.
\\
$(\impliedby)$ Assume $\forall c (c \in \bigcup a \iff c\in b)$. Take any $c \in X$. Then $c \in \bigcup a \iff c \in b$ by $()$ is trivially true. $\blacksquare$

[devout snow]

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.

[cerulean ruin]

bruh ok

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[sour furnace]

Consider the 'induced structure' $(Y, \epsilon)$, i.e., for all $a, b \in Y$
\begin{center}
$(Y,\epsilon) \models a = b$ if and only if $a =b$
$(Y, \epsilon) \models a \in b$ if and only if $a \in b$.
\end{center}
\
\subsection{Problem 5:} \textbf{Suppose $X$ is a transitive set and let $(X, \epsilon)$ be the structure induced by $\epsilon$ (see HW #3).
In the verifications of a), b), clearly indicate where the transitivity of $X$ is used.}
\
\textbf{a) Prove that for all $a, b \in X$, $(X, \epsilon) \models b = \bigcup a$ if and only if $b = \bigcup a$}
\
An equivalent statement would be $(\forall c \in X)( c \in \bigcup a \iff c \in b) \iff \forall c( c \in \bigcup a \iff c \in b)$
\
$(\implies)$ Assume that $(\forall c \in X)(c \in \bigcup a \iff c \in b)$ $()$. We want to prove $\forall c(c \in \bigcup a \iff c \in b)$. We know that $c \in b$ and $b \in X$. Then by transitivity of $X$, $c \in X$. Then by $()$, $c \in \bigcup a$. Conversely, we know $c \in \bigcup a$. This means there exists some $x \in X$ such that $x \in a$ and $c \in x$. But because $X$ is transitive, $c \in a$. We also know that $a \in X$, so $c \in X$ by transitivity of $X$ again. Then by $()$, $c \in b$.
\
$(\impliedby)$ Assume $\forall c (c \in \bigcup a \iff c\in b)$. Take any $c \in X$. Then $c \in \bigcup a \iff c \in b$ by $()$ is trivially true. $\blacksquare$

[woven radish]

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

[vital edge]

Would be helpful to send a picture of the original problem, cuz I'm slightly confused by what's going on

Wait this is the same problem as #help-44｜stanley-🌲-v2-dans

Why are you reposting it here

<@&268886789983436800> you guys should probably take a look at this

[arctic field]

what the blud

[split stream]

huh

[green crypt]

Huh who pinged

[split stream]

sup dude, welcome to mathcord,

can you confirm you're not a bot in some way?

[green crypt]

can you say ooga booga?

[worn moat]

In the meantime I am going to close this thread since it doesn't seem to have been started in good faith, and the OP is gone anyway.

.clos

🗿

.close

[devout snow]

Channel closed

Closed by @worn moat

Use .reopen if this was a mistake.

[green crypt]

i wanted them to say ooga booga

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[mystic scarab]

How difficult (from 1 to 5) would you rate this question? Just for curiosity

[mystic scarab]

And can you confirm the solutions are $z = x \pm i e^x$, with $x \in \mathbb{R}$?

[woven radish]

Alberto Z.

[green crypt]

whaaaaaat

hmm 5

[arctic field]

what is a 1 and what is a 5 though

[craggy dagger]

1: needlessly tedious

difficulty wise it's easy with no difficult insights required, just standard manipulations

[glossy dew]

looks like a problem brushing on every concept

[runic prawn]

replace exp(i pi/2) with i

[glossy dew]

although easy

[runic prawn]

z - bar(z) = 2*Im(z)

[glossy dew]

rate it

[runic prawn]

and the rhs is a real number?

[craggy dagger]

I'm getting y^2=e^(2x) for z=x+iy, so looks about right

[runic prawn]

mb

forgot to square lhs

[devout snow]

@mystic scarab Has your question been resolved?

[mystic scarab]

Lol true, 1: easy, 5:difficult

[arctic field]

that's not what i meant

what do you consider difficult

for the average highschooler, this might be the hardest question they've ever seen

but for others, this might be a completely trivial question

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[mystic scarab]

.close

[devout snow]

Channel closed

Closed by @mystic scarab

Use .reopen if this was a mistake.

[mystic scarab]

,That was exactly my intention, the big number such as 2023 was to "scary" and force the student to think deeply

[mystic scarab]

I invented that exercise for a student doing the first year of uni

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[neon wagon]

how do i derive this function?

[neon wagon]

im confused with the bracket

[rain summit]

?

!xy

[devout snow]

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.

[versed juniper]

with respect to x?

you treat everything else as a constant

[neon wagon]

so

do i multiply the bracket with -2 and x

or

[versed juniper]

2(b - 1) is effectively a constant

[neon wagon]

is it not -2 * (b-1) * x?

[versed juniper]

yes but you're differentiating with respect to x right?

so -2(b-1) is a constant

[neon wagon]

yes i guess

b is just a number

basically

is that what u mean

[versed juniper]

yes

[neon wagon]

yes so

wait do i just multiply with the number before the bracket and the one after the bracket

generally

[versed juniper]

what

you dont need to distribute

[neon wagon]

like -2 timest he bracket and x times the bracket

[versed juniper]

the order doesnt matter it's commutative

[neon wagon]

yes but

yea

ok ty

[neon wagon]

also i ended up with x^2 - b/2 + 1/2 = 0

is this correct

[versed juniper]

heavens no

wait did you divide everything by 4

[neon wagon]

yes

[versed juniper]

you shouldn't have an x^2

[neon wagon]

oh

my god

yo

im fried

why is this happening i dont undesrtand

[versed juniper]

4x - 2b + 2 + 2b = 4x + 2

[neon wagon]

i keep getitng mistakes like these even in the exam

[versed juniper]

thats what i got...

[neon wagon]

wait

now i got x - 1/2b + 1/2 = 0

so x = 1/2b-1/2

right?

[versed juniper]

,w differentiate w.r.t. x 2x^2 - 2(b - 1)x + 2b

[neon wagon]

so yeah

[versed juniper]

man

im goin on website

ok i c i c

[neon wagon]

okay so x = 1/2b-1/2 but

[versed juniper]

actually i dont

[neon wagon]

so

[versed juniper]

arent you supposed to put it into vertex form

[neon wagon]

i dont have to do that right

or do i actually have to

[versed juniper]

well isnt it easier if you do

[neon wagon]

ive never learned it

[versed juniper]

idk how the derivative finds the vertex

[neon wagon]

the vertex is just the extreme points

[versed juniper]

ur right maybe im the fried one

[neon wagon]

so

[versed juniper]

solve what you get for 0 to find extrema

then plug back into original equation for an inequality in b

[neon wagon]

i got x = 1/2b-1/2 but

ye

dont i need a case

2 cases

or

[versed juniper]

what

set equal to 0

[neon wagon]

yo wtf

i plugged it into rb(x)

[devout snow]

@neon wagon Has your question been resolved?

Channel closed

Closed by @neon wagon

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[upbeat marsh]

the red are my notes while the black is from the question itself. I solved this problem before but now i cant even remember what i did to get the answer.

[devout snow]

@upbeat marsh Has your question been resolved?

[devout snow]

@upbeat marsh Has your question been resolved?

[jagged ledge]

@upbeat marsh what can you say about two radii, ehat do they form

in a circle

[devout snow]

@upbeat marsh Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[sharp fiber]

$\prod_{i=1}^n i = n!$

[woven radish]

rafael bombelli

[sharp fiber]

$\prod_{i=inf}^n i = n!$

[woven radish]

rafael bombelli

[trail eagle]

Hi is there anything you need help with?

[uncut crow]

what is is this expression

[faint zinc]

You can use #latex-testing to test these expressions

.close

[devout snow]

Channel closed

Closed by @faint zinc

Use .reopen if this was a mistake.

[faint zinc]

Factorial for n ≥ 1

[uncut crow]

i meant this one

[drifting sierra]

Clearly n=f=1 or n=f=-1, but since (-1)! is undefined, n=f=i=1

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[iron glade]

Hi

[iron glade]

explain how I would do this

cmon spit it out

[winter patrol]

depends what you're being asked to do with this

[iron glade]

I mean

it told me to “solve.”

[winter patrol]

then you walk away

[vital edge]

Solve what

[iron glade]

How to do it thooo

[vital edge]

!original please

[devout snow]

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.

[vital edge]

"solve" doesn't mean anything in this context

You're given a function

[winter patrol]

because someone seems to want you to solve a million dollar problem

[iron glade]

IK

[vital edge]

It just exists

[vital edge]

I just noticed it's collatz oof

[iron glade]

idk where to begain

[vital edge]

Nowhere

You walk away

[iron glade]

doddy blud

[vital edge]

Ideally hit the person who gave you the problem in the face

[winter patrol]

without more info, someone is trying to get you to solve collatz conjecture,
In which case you should throw the problem in their face and walk away

[vital edge]

Since a mod is already here

[vital edge]

@winter patrol does this count as automod bypassing

[winter patrol]

yes it does.

.close

[devout snow]

Channel closed

Closed by @winter patrol

Use .reopen if this was a mistake.

[winter patrol]

Don't make those comments or troll

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[jagged barn]

Hey y'all! I have been tasked to examine the relations of the mean value theorem for integrals and differentials - I do not have a teacher for this and have some struggle with the lack of structure and clarity for my assignment so bear with me please - and I have gotten to a point where I would love to give a mathematical definition / proof for why a function would need to be continuous and differential within and around the intervel respectively for the MVT to apply. It is immediately obvious with a visual, but I lack the mathematical language / skill to describe this off the cuff and I have a hard time finding any sources on it directly, making it a hassle atm!
Picture for reference, how do I explain this with math rather than "look at it" (maybe it would become easier with a different discontinuous function?)

[supple knot]

Try to come up with an intermediate value or mean value for the Signum function on [-2, 1]

[jagged barn]

"riemann is typing" is so funny to me in context. Hi! I do not know what a Signum function means, I study in danish, I could look it up real quick?

I will move on with this and consider it closed for now, it seems there are sources related exactly to my question available when searching related to this - thank you so much!

.close

[devout snow]

Channel closed

Closed by @jagged barn

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[analog yacht]

i need help

[analog yacht]

!help

[devout snow]

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

[analog yacht]

can someone solve it with desmos?

[topaz beacon]

why desmos

[analog yacht]

cuz im shit at math

[wicked turtle]

solve it with your brain

[analog yacht]

how

please help with desmos

[wicked turtle]

what does the quadratic formula tell you?

[analog yacht]

at least one sol

and find ac

[topaz beacon]

thats what the problem tells you

[wicked turtle]

no, that's what the problem statement tells you

[analog yacht]

greatest value of ac

[topaz beacon]

do you know the quadratic formula

[analog yacht]

ax^2+bx+c

[topaz beacon]

thats a quadratic polynomial

[analog yacht]

yh

[topaz beacon]

what is the quadratic formula

[analog yacht]

x=-b-√b^2-4ac/2a

[wicked turtle]

use some brackets

[analog yacht]

do ts have tricks?

[wicked turtle]

or screenshot if necessary

[analog yacht]

ik this

[analog yacht]

.

[wicked turtle]

so what has to be true in order to have real solutions?

[analog yacht]

b=0

atleast one

[wicked turtle]

no

[analog yacht]

can u solve and send me photo

[wicked turtle]

no