help-42

[rancid sphinx]

4/log2(6)

now break log2(6)

into

log2(3) + log2(2)

which is 1 +log2(3)

you got log2(3) from the earlier equation

[tiny pike]

Hmm

[tiny pike]

I don't understand this part

[rancid sphinx]

ok.

do you know

loga(b) = 1 / logb(a)

[tiny pike]

Yeah

[rancid sphinx]

so x times loga(b) = x times 1/logb(a)?

[tiny pike]

Yeah

[rancid sphinx]

so 4 times log6(2) = 4 times 1 / log2(6) = 4/log2(6)

[tiny pike]

Ahh

I see it

[rancid sphinx]

$x \log_a(b) = x \cdot \frac{1}{\log_b(a)}$

[potent lotus]

TheAstorPastor

[rancid sphinx]

$4\log_6(2)=4\cdot\frac{1}{\log_2(6)}=\frac{4}{\log_2(6)}$

[potent lotus]

TheAstorPastor

[rancid sphinx]

ok

-# || i use chatgpt to generate latex code 😭 ||

i am bad at latex

🥀

[tiny pike]

I will try to finish it

[rancid sphinx]

yeah sure

[tiny pike]

Thank u a lot btw💞

[rancid sphinx]

welcome

may i know from where this problem is?

[rancid sphinx]

coz i encountered it in the blackbook

[tiny pike]

It's from teacher's course

[rancid sphinx]

ah i see. you might want to check out this

quite great and (some easy) questions

this was question 9

[tiny pike]

Thank uu.
I will try them as well

[rancid sphinx]

mhm

.close

[calm coral]

Channel closed

Closed by @rancid sphinx

Use .reopen if this was a mistake.

[calm coral]

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.

[neat jacinth]

When I calculate y=t-x, can I just remove these parentheses as is or would I have to distribute the negative sign? I tried to figure it out on my own in the 2nd image by using a random example but I feel like I'm not getting anywhere...

[limpid lagoon]

in the first image if you wanted to distribute that out you have to distribute the negative to all terms, if that's what youre asking

[neat jacinth]

Thanks! I wasn't sure

.close

[calm coral]

Channel closed

Closed by @neat jacinth

Use .reopen if this was a mistake.

[neat jacinth]

Wait do I have to distribute them?

[limpid lagoon]

if theres parentheses around it then yes

[neat jacinth]

Thanks, I'm trying to figure out angle x in the image

[limpid lagoon]

.reopen

[calm coral]

✅ Original question: #help-42 message

[limpid lagoon]

lemme just double check rq

quick mistake in your last step, y should equal x-t, not t-x

[neat jacinth]

You're right, tysm!

[limpid lagoon]

if you take the second original equation, y+t=x then it should be x-t

[limpid lagoon]

of course!

[neat jacinth]

Yep

[limpid lagoon]

did you have any other questions?

[neat jacinth]

No, I appreciate it!

[limpid lagoon]

no worries. ill close this channel again then

.close

[calm coral]

Channel closed

Closed by @limpid lagoon

Use .reopen if this was a mistake.

[calm coral]

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.

[rancid cloud]

Is it just me or does this question have a problem? They didn't give an upper bound for X, so the way i interpret it is X \tilde U(a,\infty)

[zealous pier]

$a \leq x, y \leq b$

[rustic osprey]

\leq exists btw

$a \leq x,y \leq b$

[potent lotus]

Civil Service Pigeon

$a \leq x,y \leq b$

Ultimator

[zealous pier]

noice

thanks

[rancid cloud]

Ofc but X doesn't have an upper bound tho lmao

[rustic osprey]

What?

The upper bound is literally b

[zealous pier]

$a \leq x \leq b$

[potent lotus]

Ultimator

[rancid cloud]

is that not for Y?

[rustic osprey]

Comma means it’s for x and y

[zealous pier]

$a \leq y \leq b$

[jovial bridge]

x and y are both bounded by a and b

[potent lotus]

Ultimator

[rustic osprey]

Alright I’m out

[rancid cloud]

Ah

[rustic osprey]

hi

[rancid cloud]

Lmao im rarted sorry

.close

[calm coral]

Channel closed

Closed by @rancid cloud

Use .reopen if this was a mistake.

[calm coral]

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.

[wild prawn]

yo I'm looking for someone who has some free time, knows the AP calc ced, and would like to help with AP calc ab math, I just finished a practice test and would like some review on the wrong questions. I'd really appreciate this, thank you!

[patent tundra]

It is better ask a specific question

[main marlin]

no need for the formalisms! just post a specific question and someone can come along to help you

[wild prawn]

Alright maybe I'll do that, thanks.

[heady quartz]

Can someone help me with this?

[scarlet cargo]

-# please read #rules

[scarlet cargo]

-# this is an occupied channel please just check #❓how-to-get-help so u can open ur own channell!! it will only take a second!!

[calm coral]

@wild prawn Has your question been resolved?

[rain portal]

What have you tried?

[heady quartz]

Like wdym

[rain portal]

What was your working?

[thin hill]

Please do this in dexter's channel not in core's

[wild prawn]

if anyone knows how this works

[heady quartz]

It's done ! But ty

[rain portal]

What?

Ah, I thought this was Dexter's channel.

[wild prawn]

https://cdn.discordapp.com/attachments/833469671557562370/1353518685536653423/uncaption.gif

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[wild prawn]

.reopen

[calm coral]

✅ Original question: #help-42 message

[stray tundra]

why is D circled?

[wild prawn]

wrong answer

or my practice answer

[stray tundra]

yeah, i'm asking why specifically you chose D

[wild prawn]

i tried finding when y = 0

[stray tundra]

okay

[wild prawn]

so finding a vertical line

couldnt find

[stray tundra]

do you have any point where y=0, and have represented?

so you cannot really use y=0 then

[wild prawn]

so just removed all the /y's

eliminated

[stray tundra]

that's not really how it works, you cant just remove things

you have to work with the data you have

[wild prawn]

https://tenor.com/view/m4rkdoll-gif-5238933771739046910

[wild prawn]

aaaaa

well what should i do

[stray tundra]

Let's focus on a much smaller part of the set

now, that's a single data point

roughly, what slope does that circled line have?

[wild prawn]

ok thats (1, 2) right

a positive slope

[stray tundra]

okay, we know it's positive

now, can you guess roughly the value as well?

[wild prawn]

of the slope?

[stray tundra]

yes

[wild prawn]

45 degrees i guess?

so looks like 1

[stray tundra]

good

now let's go for the one right below it

does it have more or less slope?

[wild prawn]

looks more to me

[stray tundra]

what about the one right above the circled one?

[wild prawn]

looks like the same slope

[stray tundra]

yeah okay that one is not really that clear

what about TWO above?

[wild prawn]

they look less

more horizontal lookin

[stray tundra]

okay, so we can see that the higher we go, the lower the slope, correct?

[wild prawn]

yup

[stray tundra]

okay, we've seen what happens going up

what happens if i move right or left instead?

does it change?

[wild prawn]

no it doesnt

looks the same

[stray tundra]

so if it doesnt change to the left or the right, it doesnt care about x, correct?

[wild prawn]

yeah correct

x = 0

wait

uh

[stray tundra]

okay, with this, so far, can we discard any of the avaliable options?

we currently know that going up in the positive side means less slope, and moving left and right doesnt change

[wild prawn]

we can remove b

I think

wait im kinda tweakin

a horizontal slope means

x = 0 right?

[stray tundra]

no

x=0 means where you are

the slope is dy/dx

[wild prawn]

ah

ok ok yeah

[stray tundra]

so can we actually remove b?

[wild prawn]

we're looking at the slope a nromal thing

i mean

idk tbh

[stray tundra]

i want you to be able to justify it to me

[wild prawn]

slope doesnt change as x changes

only as y

[stray tundra]

it's more important that you understand the reasoning of WHY you answer, than the answer being correct

[wild prawn]

so if x = 0 for example it wouldnt matter for the function

[stray tundra]

so that means that on the right hand side there should be no x

since we've seen that the slope doesnt change depending on x

[wild prawn]

what do you mean on the right hand side?

[stray tundra]

you have four answers, of the form dy/dx=thing

[wild prawn]

yup

[stray tundra]

dy/dx is the left hand side, your slope

thing is the right hand side

[wild prawn]

ah

yes

[stray tundra]

and since you've told me that the left does not change with x, x should not appear on the right

[wild prawn]

so the slope shouldnt have ANYTHING to do with x

[stray tundra]

correct

so B is correctly out so far

can we remove any other answer?

[wild prawn]

so it dy/dx which is the slope cannot equal any x

yes c

[stray tundra]

why?

[wild prawn]

because if x = 0

itll set the slope

to 0

which we cant see on the graph

[stray tundra]

you dont have data on x=0

[wild prawn]

right

[stray tundra]

there's a difference between not having the data and the data being a value

you cant use data that you dont have

[wild prawn]

well uh

any number of x

will make the slope smaller

and we cant see that happening on the graph

[stray tundra]

*on the positive side

[wild prawn]

ah

right yeah

[stray tundra]

on the negative side it would make the slope greater

but that's immaterial here, the point is it would change

[wild prawn]

yup

[stray tundra]

and we've established it doesnt

[wild prawn]

x would affect the slope

we dont want that

[stray tundra]

so now we only have A and D avaliable. Obviously you know D is wrong, so now we're gonna see why

now, we're gonna focus on the positive side only (so y>0)

if you have 5/y, does it get bigger when y is bigger, or smaller when y is bigger?

[wild prawn]

when y is bigger slope gets smaller it seems

[stray tundra]

that's the graph, i'm asking specifically about 5/y

for example, is 5/1 bigger than 5/2?

[wild prawn]

yes

[stray tundra]

so when y is bigger, 5/y gets smaller, right?

[wild prawn]

yup

[stray tundra]

now let's go for the other one

5y

when y is bigger, does 5y get bigger or smaller?

[wild prawn]

why y gets bigger so does the slope

[stray tundra]

so which behavior goes with the graph, the one from 5/y, or the one from 5y?

[wild prawn]

as we go up

the y graph

we can see the slope becoming more horizontal

so we know that y affects the slope negatively

SO A!!

[stray tundra]

there we go

you could use the lower side to confirm as well

[wild prawn]

oh my god

yup negative slope

[stray tundra]

since you're dividing by the negative, so slope goes less slope, but still negative

[wild prawn]

slowly becomes less and less negative

this is amazing

i love you

[stray tundra]

and that's why the reasoning is more important than the yes/no

[wild prawn]

thank you so much, really helped

[stray tundra]

dont forget to close the channel if you're done

[wild prawn]

lf for explanation on this one if anyones available

[stray tundra]

okay i see that you've seen integrals

so, in terms of derivatives and/or integrals, what is the speed, with respect to the position?

[wild prawn]

the absolute value of v(t)

[stray tundra]

okay, my mistake. It is correct that the speed is the absolute value of the velocity. But what is the velocity, with respect to the position?

[wild prawn]

uhhh the derivative

wait gimmie 1 sec

parents

[calm coral]

@wild prawn Has your question been resolved?

[wild prawn]

im back

velocity is the derivative of position

so in order to go backwards

we need to get the integral of velocity at t = 5

v(5) = 2?

[stray tundra]

you dont need it at t=5 only

you have the velocity as a function from 5 to 8

so the variation of poosition would be the integral of the velocity from 5 to 8

[wild prawn]

mhm right

which would be f(8) - f(5)? but idk how that would work

[stray tundra]

start by obtaining the velocity function from 5 to 8

[wild prawn]

i did using the area of triangle formula in the first photo

but I didnt know what to do next

basically the integral is = to -3

[stray tundra]

yes, that is correct

so your variation in position when going from t=5 to t=8 was -3

at t=8, you are at x=10

so if you started at a number, and substracting 3 from said number you get 10, where did you start?

[wild prawn]

so the distance between 5 and 8 is -3 and we know that t = 8 is x = 10, so to get t = 5 we have to remove something from 10 to equal -3 which is 13

idk im tryna visualize it but I cant grasp it tbh

feels weird

[stray tundra]

basically, if i call Z to where i start (t=5), then you have the following:
Z-3=10

which obviously means Z=13

i think you just fucked up where you started and finished, and thats why you got 7 as an answer instead

[wild prawn]

yeah this fucks with my head ngl

anyways thank you

.close

[calm coral]

Channel closed

Closed by @wild prawn

Use .reopen if this was a mistake.

[calm coral]

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.

[primal forge]

How can i book a help??

[primal forge]

Oh i guess i did it.

A merchant sells two kinds of alloy rods: Type A and Type B.
Type A contains copper and zinc in the ratio 3:2.
Type B contains copper and zinc in the ratio 5:3.
The merchant melts some rods of both types together to create a new alloy containing exactly 41 kg of copper and 25 kg of zinc.
However, due to impurities:
10% of the copper from Type A is lost during melting.
20% of the zinc from Type B is lost during melting.
Find the mass (in kg) of Type A and Type B rods originally used.

Question

[scenic plaza]

So does type A not lose any zinc?

[civic dirge]

The tricky part with word questions is always the same:
Define your variables.

It doesn't matter how you define them, but it's important to be precise about it

I think you know you'll need to solve a system here, so you'll need two unknowns. What do you want to use?

[primal forge]

Pair of linear equation in two variable.

[dire violet]

It’s good to meet you. Such a big fan

[civic dirge]

Right. How are we defining these two variables

[primal forge]

yeah yeah , i'm bad at word problems but you can ask me physics , decay , number theory , real analysis btw

[primal forge]

x and y??

[civic dirge]

What is x representing?

[dire violet]

I did all those courses in all throughout HS. lol. I was just talking about your username. Lmao

[primal forge]

mass of type A alloy??

and y = mass of type b aloy??

[civic dirge]

Perfect. That's exactly right

[primal forge]

in kg's*

[civic dirge]

I'll actually use "a" and "b" instead

[primal forge]

I know xd

[primal forge]

np

[civic dirge]

Now let's say we know how much "a" and "b" we're melting. We will get an alloy. Is there anything we want to know about that alloy that can be represented by a single number?

[primal forge]

We know the ratios so we find th compostion of each??

[civic dirge]

You're a little bit ahead of me. Think simpler

We want to know the amount of copper and the amount of zinc in the alloy, at least

[primal forge]

So Type a alloy when calculating gives around

wait lemme calc

[civic dirge]

Can we make an equation that takes a and b, and gives back the amount of copper?

[primal forge]

Oh wait yeah!

as per ration copper =3/5 before loss its 3a/5??

and 10% is loss

so

90/10 * 3a/5

which gives

27a/50??

[civic dirge]

That's the amount of copper you get if you melt "a" kgs of type A! Well done. What about type B?

[primal forge]

I'm calculating :3

5b/8?

[amber bolt]

alloy question

[civic dirge]

Perfect. Now, if you melt both type A and type B, how much copper is in the alloy?

[primal forge]

27a/50 + 5b/8 = 41

[civic dirge]

Exactly. Just their sum

Zinc works in a similar way

[primal forge]

I calculated zinc = 2a/5 + 3/10b =25

[brave grove]

hi

[civic dirge]

I like that you noticed the "= 25" bit. I did forget to mention that's why we're looking for copper and zinc amounts.

It can be handy to look at the numbers you're given and try to find equations that equal them

[primal forge]

https://tenor.com/view/drdonut-floss-lost-free-gif-6891064328548957882

[rain portal]

Is this gif necessary?

[primal forge]

Umm..

maybe yes??

[civic dirge]

We're past the "word problem" bit! Now it's just calculation

[civic dirge]

Of course!

[primal forge]

so i just solve it by elimination method??

or substitution method what do you recommend?

[civic dirge]

Either or! Whatever you like

Do whichever one you feel you need practice with lol

[primal forge]

Just tell the name of the method :3

[civic dirge]

Dang confident. Substitution?

[primal forge]

I've mastered everything.

[primal forge]

AIGHT BET

Just word problems..

b=32.95

a≈37.79

Type A alloy = 37.79 kg(around)
Type B alloy = 32.95 kg(around)

@civic dirge is it correct :3??

¯_(ツ)_/¯

[dire violet]

You knew I did those in hs??? lol

<@&268886789983436800>

[calm coral]

@primal forge Has your question been resolved?

[civic dirge]

,w solve 27/50 x + 5/8 y = 41, 2/5 x + 3/10 y = 25

[potent lotus]

Results provided by WolframAlpha

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

Requested by kaynex

[civic dirge]

,calc 3325/88

[potent lotus]

Result:

37.784090909091

[civic dirge]

,calc 725/22

[potent lotus]

Result:

32.954545454545

[civic dirge]

Yeah that's looking pretty good!

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[slender socket]

what is wrong here? I don't get the right result for the limit but my approximation seem fine and I can't see any mistakes in the rest of the work

[rain portal]

Did you substitute x^2 in?

[eternal shard]

Why o(1)

Multiplying by (1/x⁴) num and denom should give you the correct answer

Also u have x²/2 but wrote x²/4 in the num

[civic dirge]

,w limit x approaches 0 of (1 - cos(x^2))/(xxsin(xx))

[potent lotus]

Results provided by WolframAlpha

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

Requested by kaynex

[slender socket]

I did. I showed sinx^2 and cosx^2

[slender socket]

since o(x^6) = o(1)

[eternal shard]

This doesn't help

[slender socket]

that was it thank you

[civic dirge]

This is exactly it. The mistake starts in the Taylor series of cos(x²)

[slender socket]

Well o(1) = 0 as x goes to 0

so that term disappears

[eternal shard]

Hmm

[civic dirge]

o(x⁴) disappears as x goes to 0.

o(1) does not!

[slender socket]

how? o(1) represents f(x) s.t. lim x to 0 f(x)/ 1 = 0.

so when goes to 0 f(x) = o(1)

and this f(x) is such a f(x) where f(x)/1 = 0 as x goes to 0

[eternal shard]

Like the second line is 0/0 idk how u evaluate that

[slender socket]

f(x)/1 = f(x) so f(x) = 0 as goes to 0

[slender socket]

we even had an example here

[slender socket]

so what did you do with o(x^2) and o(x^4)

[eternal shard]

f(x)=o(x^6) means f(x)/x^6 -> 0 so in particular we have f(x)/x^6 * x^4 = f(x)/x^2 -> 0

your expression doesnt lead to anything useful in the second last step

[slender socket]

I don't see how this so o(x^2) = 0 as x to 0

because for o(1) I see that o(1) = 0 as x goes to 0

[eternal shard]

here o(1) as mentioned because you are dividing by x, taking an order away, similar how we divide by x⁴ taking away 4 orders

you instead just write o(1) which doesnt make sense here

you are neglecting the other terms

[slender socket]

well if a function vanishes faster than x^2 it will vanishes faster than 1

[eternal shard]

yeah but you are making the expression indeterminate

[slender socket]

how?

[eternal shard]

you lose information

[slender socket]

for o(x^2). we have f(x) = o(x^2) as x to 0 means f(x)/x^2 = 0 as x to 0 . but then o(x^2) = 0 only if we have o(x^2)/x^2 which we don't

[eternal shard]

it's like saying x²/x=o(x)/x oh well o(1) goes also to 0 therefore o(1)/x

but that could then lead to something like sqrt(x)/x which doesnt go to 0 anymore

just because two things go to 0 doesnt mean you can swap them

[slender socket]

I still don't see how o(x^2) goes to 0

and ins't o(x^2) = o(1)

[slender socket]

he has done in this in the book where we have some higher terms and he sets it all equal to o(something of a lower degree)

[slender socket]

ok but that doesn't tell me o(x^2) = 0 as x to 0

[eternal shard]

what

[slender socket]

?

[eternal shard]

0/x²=0?

wdym

[slender socket]

f(x) = o(x^2) means that f(x)/x^2 = 0 when x to 0

so we need f(x)/x^2

[eternal shard]

all o(x²) is a class of functions that behave smaller than x² near 0

[slender socket]

yes

[eternal shard]

goes to 0 not is 0

[slender socket]

I mean the limit of f(x)/x^2

regardless I still don't see how o(x^2) goes to 0 as x goes to 0

[eternal shard]

?

do you know how o is defined

[slender socket]

yes

f(x) = o(g(x)) if f(x)/g(x) goes to 0 as x goes to 0

[eternal shard]

Ok

Let's make it concrete, let's say you'd replace o(x^6) with something specific like x^7 since x^7=o(x^6) then dividing by x^4 yields x^3 which still goes to 0, and for higher terms it's the same

The whole point is that we have an unknown remainder but that we can still deal with, because it has a certain behavior around 0

[slender socket]

ok so your saying o(x^2) can be say x^3 or x^5 etc and all of their limits as x to 0 is 0

[eternal shard]

yes

[slender socket]

is my understanding of o(1) correct?

[eternal shard]

what understandin

[slender socket]

so f(x) = o(1) if lim x to 0 f(x)/1 = 0. so when x to 0 o(1) = f(x). and since f(x)/1 = f(x). then f(x) goes to 0 as x to 0

[eternal shard]

yes

the issue the whole time is how you conclude o(1)

[slender socket]

Ok regarding that the statement o(x^2) = o(1) is true right?

[eternal shard]

limit are basically sensitive to rates, like how fast something approaches something

[slender socket]

any function that vanishes faster than x^2 near 0 will vanish faster than 1 near 0

[eternal shard]

no, f=o(1) doesnt imply f=o(x²), for example: x/1 -> 0 but x/x²=1/x doesnt

o(x²) is a subset of o(1)

[slender socket]

im going to other way f= o(x^2) imply that f= o(1)

[eternal shard]

yes

[slender socket]

ye so that was the sub I was making

[eternal shard]

u cant sub thats my point

you are confusing here something

[slender socket]

so if this is true why can't we use this in the limit?

[eternal shard]

i showed an example

[eternal shard]

this does not mean =

[eternal shard]

example ^

[slender socket]

ok so how can x^2 = o(x^2). as x to 0 the limit is 1

also is c supposed ot be a constant?

and ins't x^2 = o(1)?

[eternal shard]

oh yeah i made a typo

[slender socket]

ok so the example is x^2/x. x^2 = o(1) implies o(1)/x. they both still go to 0 so we still have 0/0. so the sub did not help

I don't see the issue with the sub. This just shows an example where it was not helpful

[eternal shard]

ok i fixed the counter example

so the point is we introduce functions for which the limit doesnt work out necessarily

because you are removing constraints

your substitution doesnt guarantee to hold for the new functions of that class in o(1) you introduce for the limit to work out

[slender socket]

how about here then? I remember when going through this the only way to achieve what he obtained was to set all the higher order terms = o(x^2)

[slender socket]

ok I see. so o(1) has very few constraints and we can introduce many functions that will change the meaning of the limit

[eternal shard]

the thing here is that o(x²) (which lower) is already here, so the o(x⁴) is being absorbed

you are not introducing anything new

[slender socket]

so your saying that if I have o(g(x)) and I have terms of higher degrees I can simply say all those terms = o(g(x)) since I already have o(g(x))

since the problem is meant to be understood with o(g((x))

[eternal shard]

you could technically keep the o(x⁴) but it wouldnt do a thing because o(x²) basically dominates

[slender socket]

no but we also use that to remove terms that are not o

[eternal shard]

for example 1+0.001 approx 1

[eternal shard]

yes

[slender socket]

one more thing how do we know what degree approximation is good enough for the limit

[spare beacon]

You've made this a lot harder for yourself by not using the Calc 1 technique of dividing by the lowest power of the polynomial. Multiplying by 1/x^4 in the numerator and denominator makes the algebra very clear.

[eternal shard]

Yeah that was mentioned

[spare beacon]

I would have hoped the problem should have been obvious by instead making a bad choice and dividing by a larger power than x^4 so that you have terms like 1/x^n in addition to the higher order terms

[eternal shard]

I would say until you can factor out the leading term, which here would be x⁴ around 0, because it grows the slowest to 0

[slender socket]

thanks. .solved

[calm coral]

@slender socket Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[azure elbow]

Help me find where did I go wrong?

[rustic osprey]

the normal vector is not generally the normalised position vector

this holds for a circle sure

but it doesn't hold for all ellipses

also this is wrong

$\frac{1}{\sqrt{1+15\cos^2 t}}$ is not a constant with respect to $t$

[potent lotus]

Civil Service Pigeon

[rustic osprey]

so computing $\dv{\mathbf{T}}{t}$ would require an annoying quotient rule

[potent lotus]

Civil Service Pigeon

[rustic osprey]

I stopped reading at this point

[azure elbow]

Ahh dang I might be cooked

Thanks

[rustic osprey]

[azure elbow]

Ok got the answer thanks

.close

[calm coral]

Channel closed

Closed by @azure elbow

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.

[rustic osprey]

[rustic osprey]

.close

[calm coral]

Channel closed

Closed by @rustic osprey

Use .reopen if this was a mistake.

[calm coral]

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.

[hybrid lagoon]

any tips on how to start

[mortal walrus]

Apply the rules of logarithms: \\
$\log (x^n) = nlog(x)$ \\
$\log (ab) = \log a + \log b$ \\
$\log (a/b) = \log a - \log b$

[potent lotus]

Sarin

[mortal walrus]

You'll also need this one: $\log_a b = \frac{1}{\log_b a}$

[potent lotus]

Sarin

[mortal walrus]

Use the first one to get rid of the fourth roots, then the next two to get rid of the products ab, and the fractions a/b and b/a

[calm coral]

@hybrid lagoon Has your question been resolved?

[hybrid lagoon]

no mr. bot

im tyring

[mortal walrus]

Click on the x

[hybrid lagoon]

tysm sarin

[mortal walrus]

No problem

[rancid sphinx]

you should convert 4th root into powers

[rancid sphinx]

then apply prop 1 of this

then take the common out

then try to group the terms in sqrt in the form of (a+b)^2

[hybrid lagoon]

what r ur views on Nietzsche's will to power?

[hybrid lagoon]

ok

[amber wedge]

bro nietzsche talk about all that stuff but he himself is a weak and pathetic man

he basically a really bad larper

i mean if ur gonna larp at least larp till the end

right

[sleek vessel]

One is compelled to say that this is perhaps not a fitting conversation for a help channel in this server

[rancid sphinx]

!redir

[calm coral]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[calm coral]

@hybrid lagoon Has your question been resolved?

[calm coral]

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.

[icy seal]

im confused on asymptotes

[icy seal]

like how to get em

[amber wedge]

well

for vertical ones

just look where the function isnt defined

in other words where the denominator is 0

cuz u cant divide by 0

[icy seal]

how do i get it from f(x)= 2 +1/x+1

[amber wedge]

.

[icy seal]

the steps in general

[amber wedge]

this

[icy seal]

yea im failing

can u explain it all ;-;

[amber wedge]

so you have

2 + 1/x+1

can the denominator of the fraction be 0?

[icy seal]

ummm

yea

[amber wedge]

so you can have

1/0

[icy seal]

and now what

[amber wedge]

whats 1/0

[icy seal]

0

[amber wedge]

[icy seal]

undifined??

[amber wedge]

yeah

this is why i said

the function will have vertical asymptoites

at the points for which it is not defined

[icy seal]

mmmmm

ye im fried

test tday

in an hour

[amber wedge]

yeah probably

ur cooked

[icy seal]

THERES MORE

i got the top, i just forget the min max n range

😭

[misty lily]

it's questions?

[icy seal]

yea

test in an hour

im cooked

im writing stuff on my hand😭

[amber wedge]

who knows bro maybe they can help

[amber wedge]

lmao

[misty lily]

not geg

i quadriliterallly dud things like this

[amber wedge]

what anime character is that

[misty lily]

*did

[amber wedge]

tears

[icy seal]

.

[misty lily]

from elfen lied

[amber wedge]

hm ok i will look into it

[misty lily]

manga pls

anime is shit

[misty lily]

do you have more if test in an hour?

[icy seal]

theres a lot more

[amber wedge]

i dont really like manga

[misty lily]

jesus bless you

what year @icy seal?

[icy seal]

gr9 at the moment

[misty lily]

cool

[icy seal]

30 more mins 😭

ggs

.close

[calm coral]

Channel closed

Closed by @icy seal

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.

[limpid lagoon]

<@&268886789983436800>

quality on these pics seem to be higher, theyre evolving

[calm coral]

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.
• 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.

[calm coral]

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.
• 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.

[azure elbow]

I don’t quite understand how the answer sheet got 8pi instead of 5pi

[leaden thunder]

Show the answer sheet

[azure elbow]

It just has the answer

For b specifically it’s circ1=0 flux1=8pi circ2=8pi flux2=0

[leaden thunder]

How did you get your integrand in the "circulation =..." step

You left out some work

[calm coral]

@azure elbow Has your question been resolved?

[azure elbow]

As shown above ds = |v|dt and T=v/|v| so circulation = integral of F dot product v dt

Which equals to sin^2t + 4 cos^2t

Sorry for the late reply I was commuting

[calm coral]

@azure elbow Has your question been resolved?

[leaden thunder]

This is wrong but because you've left your steps I can't find where your error is

[azure elbow]

Oh I’m dumb thanks

.close

[calm coral]

Channel closed

Closed by @azure elbow

Use .reopen if this was a mistake.

[azure elbow]

Basically I took x=-sint and y=cost thanks for having patience I was thinking for over an hour

[calm coral]

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.

[frosty hollow]

Is for the pressure a is Pa=(62.4)(6)?

Then for pressure is Pb=(62.4)(8)

Is my understanding correct?

[wind gate]

Where did 62.4 come

[frosty hollow]

For the density of a water

Water having 1 sp.gr

Then need to make it lb/ft³

[wind gate]

Are Pa and Pb the pressures on A and B?

You have to give more information

[frosty hollow]

Yess yess

[frosty hollow]

This is the whole given

[wind gate]

We use the metric system. Can you explain sp.gr

[frosty hollow]

Specific gravity

[wind gate]

Ok

Water has 1 gm/cm^3 in metric by the way so it will be 2200/(33)^3 in lb/ft^3

You got that as 62.4 I guess

It needs a calculator. Its nowhere near 62.4

I know specific gravity

Did you check your calculations? @frosty hollow

[frosty hollow]

Ohhh

Wait, im just basing it from the lesson of our teacher

[calm coral]

@frosty hollow Has your question been resolved?

[calm coral]

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.

[glacial garden]

Calculate the center and radius of the circle x^2 − 8x + y^2 + 14y + 1 = 0.

How do I factor this?

[valid stratus]

you dont have to factor it

[dull wagon]

you want to complete the square, not factor

[calm coral]

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).

[valid stratus]

theres several help channels free

@glacial garden keep that in mind btw

its useful

sometimes saves time of factoring

[dull wagon]

radius not quite right

[valid stratus]

it is

[dull wagon]

root needs to extend over the c

[valid stratus]

oh

shit

yea true

mb

[dull wagon]

also shouldn't blindly apply formulae

[valid stratus]

i derived it

by completing the square

[dull wagon]

but op shouldn't apply it without doing that themselves

[valid stratus]

you mean like help OP derive it?

[dull wagon]

yes

[valid stratus]

oh

ok

mb

[valid stratus]

well would you like to take over?

[dull wagon]

depends if op is still here

[valid stratus]

tht thing imo can be remembered as a result

cuz of how useful it is in certain cases

[glacial garden]

I need to put it in canonical form

[valid stratus]

x^2 − 8x + y^2 + 14y + 1 = 0.

ight

[glacial garden]

How to factor the x’s?

[valid stratus]

you can write x and y terms individually and complete squares on both of them

[glacial garden]

I’m gonna do it

x^2 - 8x

[valid stratus]

like you can write -8x as -(2)(4)x right

[glacial garden]

Isn’t it -4?

[valid stratus]

yeah

now since you have that

[glacial garden]

,w (x-4)^2

[valid stratus]

make it into an algebraic identity by adding the 3rd term to both sides

[potent lotus]

Results provided by WolframAlpha

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

Requested by addisontarna

[valid stratus]

??

[glacial garden]

Bruh it’s x^2 - 8x + 16

[valid stratus]

yea make this

add 16 to both sides

[glacial garden]

I don’t have 16

[valid stratus]

and do the same for y

[valid stratus]

^^

[glacial garden]

What should i do with this 1?

[valid stratus]

well

add 15 then

you can either add 16 rn and then subtract 1 from the number you will add to complete the square for y

[glacial garden]

How should I write it? Cause he’s gonna grade

It

[valid stratus]

both ways work

[glacial garden]

What should I begin with to do it professionally?

[glacial garden]

Ok but I need to show calculations

Mathematical

[valid stratus]

just subtract by 1

on both sides

[glacial garden]

Not just writing stuff and answers

Ok

[valid stratus]

and add the whole squares on both sides

[glacial garden]

So should I write (x-4)^2 + 16 + y^2 + 14y + 1 = 0 next?

[valid stratus]

no

here you added 32 to 1 side

so thats incorrect

[glacial garden]

Where’s 32?

[valid stratus]

should be (x-4)^2 -16 + y^2 + 14y + 1 = 0

[valid stratus]

because if you add 16, you need to subtract it too right?

you added another 16, which made it incorrect

we're basically completing this identity

twice

[glacial garden]

Bruh there’s +

And 4^2 is b^2

[valid stratus]

yes

[glacial garden]

That rule tells us that 16 should be positive

[valid stratus]

so since you wrote this term

it already told that you added 16

and then you wrote it that way

[glacial garden]

So it should be 16 instead of 0 then?

[valid stratus]

yess

because you want to add to both sides to equalize the equation

not only 1 side

left side is what was to be done and right side is what you did

see the difference?

[glacial garden]

But if I’m gonna do -16 then the answer is gonna change to =-16 if the OG was 0

@valid stratus

[valid stratus]

how will it be equal to -16

you are supposed to add 16 to both the sides

[valid stratus]

the initial statement you wrote is wrong, so -16 will only make it worse

the +16 on LHS shouldnt be there unless you add +32 on the RHS

thats the only way you can equalize the equation

@glacial garden you understanding what i mean?

if i have 2 = 2, i cant say 2 + 16 + 16 = 2, but i can say 2 + 16 = 2 + 16

[calm coral]

@glacial garden Has your question been resolved?

[valid stratus]

man what part didnt u understand exactly

@glacial garden start from the very start

so you dont get confused

[limpid lagoon]

<@&268886789983436800>

[valid stratus]

i dint mess up right?

[limpid lagoon]

@glacial garden don't press ❌ without saying anything when a helper is trying to respond to you.

[limpid lagoon]

no no not at all, some scammer posted something here. it got deleted by a mod now

[valid stratus]

ah

okay

[glacial garden]

I’ll answer

[sudden parrot]

@valid stratus ill take over if its alright

[valid stratus]

um sure

[sudden parrot]

ight

[sudden parrot]

@glacial garden

[sudden parrot]

how long do i wait man

[rain portal]

You jumped in and asked how long to wait?

[sudden parrot]

?

ill take this 1

i can explain well from the scratch

if the OP responds

[rain portal]

No one is going to steal the channel from you, relax.

[sudden parrot]

that isnt my concern lol

they reacted with a cross but didnt say why

thats what i wanted to know

[calm coral]

@glacial garden Has your question been resolved?

[rain portal]

@glacial garden Why do you not reply?

[sudden parrot]

thats what i meant man

how can you help when you dont even know the doubt

[rain portal]

One more time then modping.

[sudden parrot]

but they react with

[sudden parrot]

ight

[limpid lagoon]

?

[limpid lagoon]

if you want help please respond to the helpers, or close the channel and come back when you have time to actually learn

[rigid pilot]

Ain't this shit been going on for the past 3 or so days

[sudden parrot]

look at the chat above

prev helper explained in such detail

man is just not explaining whats the doubt

lmao

im genuinely feeling like this is a troll

[rigid pilot]

Son 😭

[limpid lagoon]

technically this is a new channel, which is completely okay, but seems like they are never responding.

but you are right in that this is not the first time it's happened with OP

[glacial garden]

There are like 10 other channels

[sudden parrot]

then please close the channel

if your doubts are cleared

100% troll

[balmy bane]

<@&268886789983436800> Some assistance? OP has consistently marked the bot with an ❌ yet refused to explain when prompted either why their issue isn't resolved or why they're unavailable...

[valid stratus]

i tried to explain in as much detail as i can

alas

[dreamy lance]

You should explain what you're stuck on so people can actually help you.

Otherwise you are wasting channels and other people's time.

[sudden parrot]

they prob wont reply to you aswell

[valid stratus]

lets give the op some time i guess

[sudden parrot]

ight man if you say so

[dreamy lance]

If they don't I can just smute em and let them explain in @raven nest

[sudden parrot]

can modmail be used for a suggestion/idea

cuz i had 1

[dreamy lance]

Yeah you can send suggestions to that inbox.

[sudden parrot]

ight

[dreamy lance]

Hmm this is at least the 2nd time this has happened with this user actually. I'll just smute and close the channel now.

.close

[calm coral]

Channel closed

Closed by @dreamy lance

Use .reopen if this was a mistake.

[calm coral]

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.

[cunning reef]

is this right?

[finite oasis]

Seems perfect

[cunning reef]

it wouldnt work for infinite collections of sets because the minimum might not exist?

i think

[finite oasis]

Youd be considering the infimum in that case

For infinite sets the infimum can be exactly zero so yeah

[cunning reef]

oki!

.close

[calm coral]

Channel closed

Closed by @cunning reef

Use .reopen if this was a mistake.

[tight nest]

intersect_n=1^\infty (-1/n, 1 +1/n) = [0, 1]

[rugged eagle]

-# ps you have very pretty handwriting i love it

[calm coral]

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.

[frail light]

can anyone help me with statistics derivation

[umbral gorge]

please post the question

[frail light]

i want to understand first part first

[umbral gorge]

,rccw

[dire violet]

You're a wizard harry

[frail light]

need to learn spells

[dire violet]

So, is Mr. Harry Potter learning stats?

[frail light]

@umbral gorge u there?

[dire violet]

They're in another help channel atm

[calm coral]

@frail light Has your question been resolved?

[calm coral]

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.

[fair cargo]

Hi

I dont know how to start this exercise

<@&286206848099549185>

[calm coral]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[calm coral]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[shrewd magnet]

Hi

[fair cargo]

hi

[oak nymph]

Only use the ping ONCE per 15 minutes please. 😃

[shrewd magnet]

Have you thought about reductio ad absurdum

[fair cargo]

?

I dont understand

[shrewd magnet]

Reductio ad absurdum dude

The most trivial proof method

[fair cargo]

Never heard of that name tho

[oak nymph]

Basically

[shrewd magnet]

Well are you a real mathematician?

[oak nymph]

You have to hit the equation with a counter reductio

[fair cargo]

wtv are u talking about

[shrewd magnet]

Don’t waste my time please

[fair cargo]

I get maths in dutch

its just this course that is in english

holy

no need to be rude like that

[rain portal]

If you are wasting time then do not need to stay here.

[fair cargo]

can we take away their role

[shrewd magnet]

I go to Harvard lol

[fair cargo]

cuz theyre not cool

[shrewd magnet]

I know what i’m doing

[fair cargo]

tuff

https://tenor.com/view/ishowspeed-speed-random-kid-random-kid-gif-10698606526004440975

[rain portal]

What do you think you would solve?

[ivory saddle]

XE

[oak nymph]

Please stop threatening people, they were simply trying to help, not to mention that they go to a better school than you, so stay respectful, thank, you, Ma'am! 🙂

[shrewd magnet]

He should use reductio ad absurdum, lol.

Obviously only Ivy league students would know of this proof method anyway.

[rain portal]

I am truly respectful, do not teach me what to do.

[shrewd magnet]

Drop that ego lol

What college do u go to

[oak nymph]

This is elementary level stuff anyways, I wouldn't call myself a mathematician if I have never even heard of reductio ad absurdum.

[shrewd magnet]

Exactly lol

[rain portal]

!redir by the way.

[calm coral]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[fair cargo]

i get maths in another language

[shrewd magnet]

Even a toddler on the streets could tell you how to do reductio ad absurdum

[fair cargo]

like bro

[oak nymph]

Well, okay. They go to a better school than you, so they probably know more about this topic than you do, exit this channel and let the professionals handle it, thank you.

[fair cargo]

isnt this server here to help people

no matter their level

[shrewd magnet]

Yes but you’re wasting my time

[fair cargo]

you are not obligated to talk to me

[shrewd magnet]

If you don’t know reductio ad absurdum why are you pinging me

Lol

[rain portal]

Okay? Better school indicate better education? Sounds sacarstically credible enough.

[oak nymph]

Dude lol. I learned about reductio ad absurdum before I learned addition.

[shrewd magnet]

If you want help you should be prepared to learn

[fair cargo]

BECAUSE I GET MATHS IN ANOTHER LANGUAGE

[shrewd magnet]

Better school MEANS better education, lol.

[shrewd magnet]

Ok?

Then learn english math

I learned math in chinese, lol.

[sweet spoke]

Can we not argue please or else ive to ping nods

[fair cargo]

so I probably have another name for it

[shrewd magnet]

She’s being mean to me

[oak nymph]

You're speaking english perfectly fine and math is a universal language. Please do not waste me and @shrewd magnet time with these petty excuses.

[sweet spoke]

Doesnt mean we can argue

[visual bear]

reductio ad absurdum: negate that something that is true/false (like lie), then keep making conclusions based on that until you find a contradiction

[rain portal]

I feel so sorry for you. Well then, let these guys take over, I will not fight over these individuals.

[fair cargo]

<@&268886789983436800> can you mute the rude people, they are not here to help out, but just being rude to me

[ivory saddle]

^

[shrewd magnet]

Thank you

@fair cargo I shall take you on as my discipline

I see potential

[fair cargo]

Im not talking to u anymore

im blocking u

[shrewd magnet]

Maybe you can go to an elite institution one day, like me. Lol

Ok, your loss. Lol

[oak nymph]

There's no need to be rude they were simply trying to help.

Anyways, what do you need help with?

[fair cargo]

they were the ones being rude

nothing

gfys

[hard lagoon]

Guys stop fighting pls

[fair cargo]

.close

[calm coral]

Channel closed

Closed by @fair cargo

Use .reopen if this was a mistake.

[potent smelt]

Hi

[visual bear]

Reductio ad absurdum: negate that something that is true/false (like lie), then keep making conclusions based on that until you find a contradiction

[oak nymph]

So why did you make a math help ticket if you don't need help

[potent smelt]

One moment

I'm reading up.

[sweet spoke]

Anyways i would recommend you go to the advanced mathematics section, you might find an answer there

[fair cargo]

I did need help

[potent smelt]

There's a lot of yap and not a lot of details about what's wrong.

[fair cargo]

but ur not helping me

i'll just ask claude lol

[visual bear]

@arachi

[potent smelt]

!nogpt

[calm coral]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[hard lagoon]

The one with heart emoji name keeps saying they are good and say OP wasting their time

[sweet spoke]

I would not recommend that

[hard lagoon]

This guy here @shrewd magnet

[visual bear]

@fair cargo Reductio ad absurdum: negate that something that is true/false (like lie), then keep making conclusions based on that until you find a contradiction

[fair cargo]

I understand

I know what that means

[balmy bane]

...So then what was the language issue about?

[visual bear]

Try that, Im willing to help within my range

[potent smelt]

@fair cargo for your question, I was under the impression that this was the definition of a group generated by a set?

[visual bear]

lets focus more on helping than arguin

[fair cargo]

They're giving me a hard time because I don't know the name of that evidentiary technique

[fair cargo]

yes

[potent smelt]

How do you prove a definition exactly?

[oak nymph]

sorry if anybody came off as being rude, nobody meant any harm.

[fair cargo]

sure bro

[hard lagoon]

-# Reopen the channel btw

[fair cargo]

idk man I just want to know how to do it so I can move on

[limpid lagoon]

(this channel is closed not sure if you wanted to reopen it)

[potent smelt]

Ok, so I've timed out the two users who were harassing you

.reopen

[sweet spoke]

Anyways if you wanted to continue please do .reopen as this channel might close

[calm coral]

✅ Original question: #help-42 message

[fair cargo]

I have a lot to do

[potent smelt]

I reopened just in case it was about to be locked

[fair cargo]

okay

[potent smelt]

If you don't want to use it, feel free to close it again. Also check with #groups-rings-fields

[fair cargo]

Can someone just tell me how to do it, not the solution

[sweet spoke]

They can help you in there

[fair cargo]

I have to study a lot more of this course today and I wanna move on

[potent smelt]

Anyway, it might be useful to determine if your book uses a different definition for a group representation.

[balmy bane]

I mean the iss-

That

[fair cargo]

https://github.com/vendramin/group

[balmy bane]

Since this feels like a definition, that doesn't sound like something to "prove" per se

[fair cargo]

heres the repository

[balmy bane]

Meaning that we need to know what definition is already provided for <X>

[cunning veldt]

I think <X> is defined as the subgroup spanned by X

[balmy bane]

I mean, we need to know what definition this course is operating under

[cunning veldt]

Yeah I think it's this

[fair cargo]

Let $G$ be a group and $X$ a non-empty subset of $G$.The \textbf{subgroup generated} by $X$ is the smallest subgroup of $G$ that contains $X$, that is $$\langle X\rangle = \bigcap{S:S\leq G,X\subseteq S}.$$

[potent lotus]

arachi

[tight nest]

whats the question? OwO

[old isle]

okay so proving that <X> is equal to the set in the exercise amounts to showing that this intersection of sets is equal to that exercise set

the overall structure of the proof is showing the equality of two sets
you do this using a double inclusion argument i.e. to show that A = B, you show that A is a subset of B and B is a subset of A

let x be an element of \cap { S : S <= G, X <= S }, then ....

[potent smelt]

Here is how I would approach this problem.

Call the group G and let H be the subgroup of G generated by X. Call the group generated by the expression within the question K. Clearly H ≤ K (why?)

Can you prove also that K ≤ H?

[old isle]

and then vice versa