help-27

[dark sable]

fun fact, half the people there got less than 1 question correct

out of 30

[sand quarry]

so like

everybody failed?

crazy

[dark sable]

this is like one of 8 questions nobody managed to solve correctly

[sand quarry]

i mean it isn't really difficult but having you do the computations in 90 seconds is rough

[dark sable]

ok what if

Let a and b be positive real numbers, and X, Y be random variables such that Y=aX+b. If E[X]=2ab, E[X^2]=5a^2b^2, Var[X]=6a, Var[Y]=48. Determine E[aY^2-bY+ab]

60 seconds 😭

[sand quarry]

cringe

again not really hard

but its a lot of computations

[dark sable]

I can get the X part but I'm not entirely sure how to transpose it to Y, or rather how is Y doing that

if I'm mkinag any sense

[sand quarry]

like

,, \lm \Var[Y] = \Var[aX+b] = a^2\Var[X]

is that your quesiton

[dark sable]

a bit yes

why is i a^2Var[X]

[sand quarry]

its one of the properties

but you can prove it

[dark sable]

ok so I assume i express Y as a function of X so

[dark sable]

oh man 😔

[sand quarry]

you dont assume

its given to you

[dark sable]

um

is it

[sand quarry]

'and X, Y be random variables such that Y=aX+b'

[dark sable]

E[a^3X^2+2a^2bX+ab^2-abX-b^2+ab^2]=E[a^3X^2+(2a^2b-ab)X+2ab^2-b^2]=

[sand quarry]

that sure is a chungus

[dark sable]

ok in this case, how do I do this

is it 5a^5b^2+2a^3b^2-2a^2b^2+2ab^2-b^2

[sand quarry]

idk what you are doing rn

like

what i'd do is like

1- evaluate Var[X] from Var[X] = E[X^2] - E^2[X} and Var[X] = 6a in terms of a and b
2- Recover a from Var[Y] = Var[aX+b] = a^2Var[X]
3- Recover b from the equation resulting from step 1
4- find E[X], E[Y], and E[Y^2] now that you know a and b
5- use the fact that E[aY^2 - by + ab] = aE[Y^2] - bE[Y] + ab to calculate the lhs

[dark sable]

yk I was trying to figure ouot if 5 was real

kk thanks is this still in the same book

[sand quarry]

yes everythign is there

[dark sable]

6a=5a^2b^2-4a^2b^2 => 6=ab^2
a=2
b=sqrt3
E[X]=4sqrt3, E[Y]=E[aX+b]=aE[X]+b=9sqrt3, E[Y^2]=a^2E[X^2]+2abE[X]+b^2,=240+48+3=291
582-27+2sqrt3=555+2sqrt3

am I right

[sand quarry]

yes

tahts riht

[dark sable]

555+2sqrt 3

crazy

ok what if

Given a random variable X is normally distributed with mean 28 and variance 6, what is E[X^3]-E[X]^3

is this kurtosis

[sand quarry]

i need to go really but you should propbably open up a new help chnanel

[dark sable]

aw

[dark sable]

thanks for all the help

.close

[devout snow]

Channel closed

Closed by @dark sable

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.

[idle citrus]

im kinda confused, is this how u do this?

[dull parrot]

you can't use difference of two squares because they're not the same

so you expand it normally

[idle citrus]

when i do 7y time x does the order of the y and x matter like can it be 7xy

[pure flower]

yes

multiplication is commutative (for real numbers)

[hardy trail]

In other words, no; the order does not matter :)

[idle citrus]

so 4x^2 - 5xy - 21y^2

[pure flower]

me trying to phrase it in the least 'assumes you know what i mean' way possible

[pure flower]

yep

[hardy trail]

Oh that wasn't the issue, you just said "yes" when I think you meant "no" 😭

[idle citrus]

okay ty i wouldve def got that wrong

[pure flower]

oh i thought she said doesnt matter? because she says 'can it be xy', im like yes!

[idle citrus]

i did say can it be 7xy lasy so i assumed yes was for that xD

[pure flower]

but yes order doesnt matter

[idle citrus]

alright tysm!

[pure flower]

and i guess (7x)y = 7(xy) is associativity

so yes multiplication is associative as well (for real numbers)

[idle citrus]

.close

[devout snow]

Channel closed

Closed by @idle citrus

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.

[lament cradle]

How do i do b

[lament cradle]

Vectors gen wanna make me like

💔

[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

[lament cradle]

1

[willow helm]

I assume we begin with a)

[lament cradle]

Ys

That one i got

4b-2a

With the weird lines underneith

[willow helm]

Weird lines underneath?

[lament cradle]

Yk how

U put those dashes

[willow helm]

Oh, above

$\vec{a}$

[lament cradle]

Ya

[lament cradle]

Ya those

[somber trout]

Any genius

[willow helm]

Eh, I don't have reliable internet anymore. Imma let someone else take over instead of you waiting on me every time for 5 minutes. Good luck and sorry!

[verbal wharf]

i can take over if needed

[undone egret]

Not hopping in to help but how are you undergrad & this smart (im just hoppping between help channels to see what people are doing to procrastinate)

MORE MORE JUMP SPOTTED SO PEAK

[verbal wharf]

😟 you flatter me i dont think that im great but i like doing math in my free time

[undone egret]

Are you in hs? I'm in y11 hh I feel so behind

[verbal wharf]

THATS OKAYYY

i finished college here and just looking for a university atm

[lament cradle]

a

i m back

[undone egret]

Ooo gl!! I'm gonna stop clogging up the channel now hhh glglgl

[verbal wharf]

TYYYY AND YOU TOOO

[verbal wharf]

henlo what have you done so far

[lament cradle]

A

[lament cradle]

NOTHING..

Im so stuck

[dark sable]

I'm gonna be making this intentionally harder since it doesn't make sense
wow whoever made this question hates you, I don't even think a is answerable and expressable as just a and b 🥀, since no angles are given on a technicality(one can assume but do we really want to assume)

[winged hearth]

is this gcse?

[lament cradle]

ya

[verbal wharf]

draw straight line OP and BC, Q would be the intersection

[lament cradle]

Yes i did that

[lament cradle]

BRO IKR

Legit the vectors i did in class is like NOTHING

[lament cradle]

But then now idk what to do

Since like

No value for P

[dark sable]

express OP and BC as a line, Q is the point at which they intersect, find the point at which they intersect
2AP=3PC => AP=3PC/2 => 5PC/2=AC=5AP/3 => PC=2AC/5, AP=3AC/5,
now what we can do is do
with respect to O as the origin,
OP can be expressed as y=tanPOAx I think, then you have BC
similar concept, except it's raised up by a bit, how much?
you can do (y-y1)=m(x-x1) where x1 is the x component of OB and y1 is the y component of OB and m is the slope of BC(or tangent of the angle BC would form against a line parallel to OA, or simply put OBC-(108-BOA)) to which you can then do y= and x= and approximate the values from there(not really approximate)
the issue is expressing it as unit vectors, there is probably a geometry theorem out there that would help you find the sides but here I can only assume from point B to C you have to figure out how much x changes to 2a+b and translate it to the x value you get for CQ

now of course, this is all speculation and you should ask your teacher to specify since it's virtually a "why are we doing this" question

[dark sable]

this is all a bunch of snickerdoodle, though
I'm not sure if you have to do this much, although you probably can

[lament cradle]

Shld i sen the ms

[dark sable]

I mean by the x and y thing is that your units are 2a+b
for a specific x amount you calculate in the question, your hypotenuse is 2a+b or something, if you find the ratio from x:2a+b, then you can apply it to other x vals and y vals to find how to express the vectors as a and b

[dark sable]

what ms

also is there more to the question

[lament cradle]

Mark scheme

[dark sable]

well go send

[lament cradle]

If u wanna deciper this go ahead but i genuinely gave u

Up

[verbal wharf]

do you understand how to find P first?

[lament cradle]

No

Wait

Yes

[dark sable]

idt these are correct answers 🥀

[verbal wharf]

i got the same end answers though 🤔

[dark sable]

why do you randomly have mew and k and the angular torsion symbol

and gamma

[verbal wharf]

you want to come up with equations of OP and BC

that is what they are doing

[dark sable]

it said in terms of a and b, adding another constant or anything like that would ruin the point of expressing it as solely a and b

[verbal wharf]

these arent constants though

[dark sable]

if constants are allowed qa=fb=w(a+b)
where q f and w are constants that allow for the above to be true!!!

[dark sable]

idk I might not understand I'm from another country n I don't see the gamma phi k mew stuffs

they also are constants

[verbal wharf]

they are just a variable being multiplied to (a+b) acting as scalars

[verbal wharf]

thats fair

[dark sable]

which is a constant in the scenario here

it's multiplied by a factor of say k representing CQ or PQ, where since they are collinear with BC and OP respectively, can be expressed as a constant multiplied to the vector quantities of BC and OP respectively plus OB+BC or OP

[dark sable]

it is a findable factor I guess

my wording ain't right prolly

[verbal wharf]

multiplying is okay

adding wouldnt be

[dark sable]

well you ain't finding OQ without breaking the rules of 2d vectors which whatever math this is already has ✌️

you following this OP? the questions don't make sense at least not in conventions I know

[devout snow]

@lament cradle Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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.

[steep agate]

What do the z, x, u, o, and n looking symbols mean? I totally forgot

[shy osprey]

Is this related to statistics?

[steep agate]

yes

[shy osprey]

right x bar is mean

[lethal wraith]

z means z in this case

[shy osprey]

mu is the mean deviation
sigma is variance
n is number of observarioms

i think

[wheat pawn]

z means z
we could never guess that

z is the value after tipification of the variable

[shy osprey]

isnt that phi?

oh well regional differnece ig

[wheat pawn]

no, that's phi(z), which is the value of the normal

[shy osprey]

OH right

-# i hate stats

[wheat pawn]

z is the entry value, phi(z) is the exit value

[shy osprey]

yeah mb

[steep agate]

ok I will see if I get a reasonable answer then I will close

[shy osprey]

Sure

[wheat pawn]

i mean, we already gave you the answer for each of the letters

[steep agate]

yes but the answer for what I needed the letters for

thank you

.close

[devout snow]

Channel closed

Closed by @steep agate

Use .reopen if this was a mistake.

[wheat pawn]

.thats... not what you asked tho?

[steep agate]

I couldve asked for more help

[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.

[cold topaz]

How do i get this?

[supple knot]

you pick convenient values for x in the range and plug them into the function

e.g. x = -5 < -4 and (-5 - 4)(-5 + 4)/(-5 + 2)^2 = some positive number

[rain summit]

Denominator is > 0 so numerator is < 0

And then the rest is sign work

[cold topaz]

x = -3 should be negative

?

-7 . 1 / 1

[supple knot]

yea he makes a good point here. you can do a shortcut and ignore the sign of the denominator because (anything)^2 is always positive unless anything = 0

[supple knot]

yes

[flat ibex]

The work is wrong then right

Should be + - - +?

[rain summit]

Does the latest message counts as !nosols tho

[cold topaz]

ok thanks everyone

.close

[devout snow]

Channel closed

Closed by @cold topaz

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.

[pure skiff]

Hello so I don't have specific type of question about math, but I got an exam/test coming up tomorrow all about integrals. So can someone teach me all about integrals like ranging from neper's number integration up to X and Y-axis integration

[pure skiff]

I would be appreciate it if someone could give valuable youtube video about integration perhaps

[gloomy aurora]

khan academy

[pure skiff]

Alright

[gloomy aurora]

!done

[devout snow]

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

@pure skiff Has your question been resolved?

[pure skiff]

I guess

[devout snow]

Channel closed

Closed by @pure skiff

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.

[opal olive]

hey

[trail eagle]

What is your question?
Also avoid opening duplicate help channels.

[twilit comet]

do you

have a question?

[trail eagle]

I'll close this one since OP posted their problem in the other channel.

.close

[devout snow]

Channel closed

Closed by @trail eagle

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.

[worthy phoenix]

how to find the equation of circle if I have 3 points that are in the same circle

[trail eagle]

!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.

[winter patrol]

perp bisector theorem twice to get the centre
then distance formula for the radius

[worthy phoenix]

how u calc the perpendicular bisector

<@&286206848099549185>

[crude niche]

!15m

[devout snow]

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.

[crude niche]

do you have the original problem

[worthy phoenix]

I have A= (-2;3) B =(4;5) c =(2;-1) i need to find the circle equation the points are in the cercle

[crude niche]

okay

try and find the midpoint

of every point

[worthy phoenix]

yes

after that?

[crude niche]

then find the slope

of each segment of points

and then find the perpendicular bisector

[worthy phoenix]

yes

[worthy phoenix]

but how u find that

its the perp segment of a segment?

[crude niche]

perpendicular means

create 90 deg

[worthy phoenix]

yes

[crude niche]

basically the slope is opposite

[worthy phoenix]

ahh I see

[crude niche]

eg 3 is slope

so the perp is -1/3

[worthy phoenix]

yes

what should I do after?

[crude niche]

create point slope formula

then you find the center

also i might be so wrong so idk 😭

[lunar harbor]

(In the future, please make the first message you send the actual question since that's what the bot pins. This saves us the effort of having to change the pin manually.)

[worthy phoenix]

found the intersection between the segments

now how do I calc the distance for radius

[tribal leaf]

Hey

So the circle equation is

X^2+y^2+2gx+2fy+c=0

Which is S=0

Now

U substitute the points in the equation

You will be 3 equations and 3 variables

solve them you will get g,f,c values

[worthy phoenix]

whats S?

[tribal leaf]

S is the equation of circle

we denote it that way

[worthy phoenix]

I see

[worthy phoenix]

yes

[tribal leaf]

Do you want me to solve it?

[worthy phoenix]

yes please

if u can

[tribal leaf]

Okay give me few min

[winter patrol]

Distance formula between the intersection point and any of your original 3 points

[worthy phoenix]

ah f yeah

lol

[thick lotus]

if you have found the center you can use the general form :
(x-h)^2 + (y-k)^2 = r^2
sub any one point and you can find radius

[worthy phoenix]

thank you

[worthy phoenix]

I see

ty

[thick lotus]

yh this is distance formula

[winter patrol]

I prefer this method compared to the system of 3 equations above

[worthy phoenix]

can I use this method if I have 2 points and 1 radius

[tribal leaf]

U can also find radius from circle equation

[winter patrol]

As in the length of the radius?

[tribal leaf]

Nah

r = \sqrt{g^2 + f^2 - c}

so the center would be (-g,-f)

[tribal leaf]

It's actually the same method but mine is the expanded version of it

instead of h and k u get f and g

it's only the change in variables rest is same

[winter patrol]

It's pretty different

applying different properties/ideas

[devout snow]

@worthy phoenix Has your question been resolved?

[worthy phoenix]

I see thank you

[devout snow]

@worthy phoenix Has your question been resolved?

[devout snow]

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

[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.

[light plover]

is the 1/4 applied to all of the numbers including both the numerator and denominator? or only the numerator/denominator or there is some sequence

[supple knot]

both numerator and denominator

$\lp\frac ab\rp^x = \frac{a^x}{b^x}$

[woven radish]

pi_day

[light plover]

including the numbers like 162 and 2? also 1/4 being applied through a bracket means that the exponents will be practically divided by 4 right?

[supple knot]

,tex .exp rules

[woven radish]

pi_day

[supple knot]

yes to the numbers by distributivity. yes raising to the 1/4 power is the same as dividing the exponent by 4

[light plover]

thanks

[devout snow]

@light plover Has your question been resolved?

Channel closed

Closed by @light plover

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.

[severe ice]

can someone help me with the bottom 2? the shapes are rhombi

[devout snow]

@severe ice Has your question been resolved?

[winter patrol]

What have you tried?

[severe ice]

.close

[devout snow]

Channel closed

Closed by @severe ice

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.

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.

[cold badger]

can someone help me how to answer this?

[rose granite]

What kind of answer would u need?

One with a solution?

Or just the answer.

[marsh trail]

!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

[rose granite]

@cold badger ?

[small geyser]

!nosols, I don't think we should provide a full solution from the get-go?
(if you were not planning to provide a full solution or just the answer, then please ignore this, and I'm sorry for entering.)

[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.

@cold badger Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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.

[hollow agate]

i honestly have no clue where to start, i don't see a way in that has any meaningful way to break this question.

[hollow agate]

nvm i have a start

.close

[devout snow]

Channel closed

Closed by @hollow agate

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.

[serene forge]

Helloo im kinda struggling here

The farthest i got was 2(√5+√3)

But the answer's not on the options

[serene forge]

No 9

,rotate 180

[serene forge]

<@&286206848099549185>

[zealous ledge]

Is the answer A, perchance?

[serene forge]

Idk, im tryna ask how to do it qwq

[zealous ledge]

Honestly, i think the answer is a
The power of the denominator is greater than that of the numerator

So you end up with something like this (gimme a sec im writing this down)

[serene forge]

Okie

[serene forge]

How'd u get 1/4?

[zealous ledge]

Wdym?

Its always been there

Not that it affects the answer

[serene forge]

Oh

So i just ignore that 1/4

?

[zealous ledge]

You dont ignore it

But this limit, according to me, evaluates to zero

[solemn gorge]

hey freinds needed help for explaination

[serene forge]

What does the chinese 8 stand for?

[verbal wharf]

!occupied

[devout snow]

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).

[serene forge]

Uh, do u use it all the time qwq?

[zealous ledge]

Use what?

[serene forge]

1/4

[zealous ledge]

Brother

[solemn gorge]

what ?

[zealous ledge]

Re read the question

[serene forge]

Or whenever there's a number at the bottom

Like something something but it's root
Denominator is 8x
you write 1/8?

[serene forge]

Ok

[zealous ledge]

Ah thats what you meant

I mean you dont have to, i did it for clarity

[serene forge]

Oh okk thanks

[solemn gorge]

that's lambda

[zealous ledge]

I thought you meant whered i get the 4 from 😭

[serene forge]

Its ok 😂

[solemn gorge]

why did you ask that?

[serene forge]

My teacher never taught us that

He just taught us

Use the x with the highest exponent

Like

In the question its x³

So 3x³/x³ -> 3
5-> 5/x³ ->5/0-> 0

And so on

Is it correct tho?

[zealous ledge]

Whats the answer?

[solemn gorge]

6

[serene forge]

Ghis is the notes qwq

[solemn gorge]

maybe

[zealous ledge]

The logic behind this is basically that finite/infinute tends to 0

[serene forge]

Oh ok thankss

[serene forge]

-# ignore

Why'd it become 4²?

[solemn gorge]

me?

[zealous ledge]

So if the denominator has more power, all the finite terms get divided by infinity and so its zero

[serene forge]

Nono I'm just doing that to easily check it again

[serene forge]

Ah i see thank you

[zealous ledge]

Im gonna have to ask you to circle it

[zealous ledge]

Thats an x 😭 🛐

I dont even blame you, its my handwriting

But yeah thats an x

[zealous ledge]

Checks out

Whats your answer?

[serene forge]

Ouh

Okie thanks holdon

[serene forge]

So one of the 4x becomes just 4? Why?

[zealous ledge]

Lemme write that step by step

[serene forge]

Why does 1 of the 4 has x and the other doesn't?

[zealous ledge]

Theyre both x's

Youre getting firsthand experience on why my classmates prefer not to take notes from me

[serene forge]

Wait so there are no 4? It moves to 1/4?

[zealous ledge]

I honestly dont know what you mean by that

[serene forge]

They're not 4 but x right?

Just realized i say wait alot

[zealous ledge]

I circled all the 4s for you

Anyways, i should go get lunch

[last parrot]

number 4 slowly transforms into 3 or 5

[serene forge]

Why is it 5/x meanwhile the ine next to it is 4/x²?

Why does only one of each get x²?

[serene forge]

Ok enjoyy

[serene forge]

Uh, can u give me an example qwq?

[last parrot]

i was being sarcastic with the handwriting

[serene forge]

Oh

[thick lotus]

do you need help

[devout snow]

@serene forge Has your question been resolved?

[zealous ledge]

x/x² = 1/x

[serene forge]

Ohhh okok thank youu

[zealous ledge]

Amything else?

[serene forge]

Uhm

I'll try to proses that ine rq

[serene forge]

I'm struggling w no 10 though 💀

I got 0 but the answer's not in the options

[zealous ledge]

10 shouldnt be zero imo, lemme try it

[zealous ledge]

My answer is 2

Are you familiar with the concept of binomial approximation?

[zealous ledge]

Also your answer isnt zero, your answer is undefined

[serene forge]

No

[serene forge]

Oh

[zealous ledge]

BRO

You evaluated it for limit x tends to 0

[zealous ledge]

Are you aware of the binomial theorem?

[serene forge]

Kinda

I forgot how to do it lowkey

[zealous ledge]

I think you need to revise your concepts first 💀

[serene forge]

Ye 😭

[zealous ledge]

Do you remember the expansion for (1+x)ⁿ

I could walk you through it, but if you dont, id honestly recommend you to review your notes first

[serene forge]

I'll review 💀👍🏻

Thank you :'

[devout snow]

@serene forge Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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.

[summer harbor]

hello again

[summer harbor]

is the potential graph correct? im unsure about a decreasing function yet concave up

[tribal leaf]

draw on a graph paper

[summer harbor]

i dont have 😭

i dont have a graphing notebook either

[tribal leaf]

there's one website

[summer harbor]

LOL

[tribal leaf]

To plot graphs*

ill send it (if I get it)

[summer harbor]

but is the graph correct based on the

table?

[tribal leaf]

It's worng

[summer harbor]

i see.. which ones in the table did i get it wrong?

[tribal leaf]

I plotted the graph

[summer harbor]

damn

[tribal leaf]

$1. At x = 0: wrong nature of point

Given: f'(0) = 0, f''(0) = 0
So, (0,0) is a stationary point of inflection

Error: Graph shows a slanted straight crossing
Correction: Curve must have a horizontal tangent (flat touch) at (0,0)

2. Concavity change not clearly shown at x = -1 and x = 1

Given: inflection points at (-1,1) and (1,-1)
Error: Curve looks almost straight → no visible change in bending

Correction:
At x = -1: concave down → concave up
At x = 1: concave up → concave down
→ Show clear change in curvature

3. Segment near origin drawn almost linear

From table, curvature keeps changing
Error: Middle portion looks like a straight line

Correction: Curve must be smoothly curved throughout, not linear$

[woven radish]

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

[tribal leaf]

These are the mistakes

[summer harbor]

thanks

[tribal leaf]

I might have gotten wrong, like double derivative, in the graph*, just change those ig,

[devout snow]

@summer harbor Has your question been resolved?

[summer harbor]

i see

i cant draw ts 😭

[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.

[viral kernel]

$|z|=|a+ib|\leq|a|+|ib|\leq|a|+|i|\cdot|b|\leq|a|+1\cdot|b|\leq|a|+|b|\to|z|\leq|a|+|b|$

[woven radish]

Mr. Penguin

[viral kernel]

is it correct?

[trail eagle]

Yes

[viral kernel]

👍

thanks

.close

[devout snow]

Channel closed

Closed by @viral kernel

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.

[frozen solar]

question 7

[frozen solar]

max value is obvious

it would come at x=6

[hidden torrent]

diffrentiate

and equate to 0

[frozen solar]

any other method?

haven't don't differentiation yet

done*

[hidden torrent]

hmm u know to plot graphs ?

[frozen solar]

not really

[hearty yoke]

if you havent done differentiation try substitution x+2.5 = t

the function will look easier to understand

[hidden torrent]

maybe i think

[frozen solar]

yep it looks easier

but what do we get from it?

do i hv to open brackets in the end?

[hearty yoke]

fuck around and find out

[hidden torrent]

we can pair up x+1 and x+4 & x+2 and x+3
then t = x^2 + 5x + 5

[frozen solar]

🥀

[hidden torrent]

lol

[frozen solar]

I've heard shi like that

but not in maths

[hearty yoke]

you wont build intuition if you just ask for everything, try different things you'll get what works

[frozen solar]

in the end just opening up brackets

but with bik brain

[frozen solar]

true

but I was hoping to not have to open the brackets

i alr know the way to open these brackets

take pair with constant sum same

well if that's all that's coming in you all's mind then ig I'll jus make quadratics

kk min value iz 4

at x=-5

thanks and adios

[hidden torrent]

well

1+2+3+4/4 =2.5

and minima is at x=2.5

[frozen solar]

eh

[hidden torrent]

a coincidence

i think not

[frozen solar]

oh it's at t=5

not x=5

for x you get q quadratic which I don't need to solve

[frozen solar]

last step checked the "D"

.close

[devout snow]

Channel closed

Closed by @frozen solar

Use .reopen if this was a mistake.

[frozen solar]

<@&268886789983436800>

[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.

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.

[candid mica]

In our book we have the numerator of the correlation coefficient simplified as on the attached picture. How do we get to the last part where only xi*yi is inside the sum

[lunar harbor]

So
$$\sum (-x_i \bar{y}-y_i \bar{x}+\bar{x} \bar{y})=-\bar{y} \sum x_i-\bar{x} \sum y_i+n \bar{x} \bar{y}$$

[woven radish]

Civil Service Pigeon

[faint gorge]

typo?

[lunar harbor]

$$=-\bar{y} n \bar{x}-\bar{x} n \bar{y}+n \bar{x} \bar{y}$$

[woven radish]

Civil Service Pigeon

[lunar harbor]

$$=-n \bar{x} \bar{y}$$

[woven radish]

Civil Service Pigeon

[lunar harbor]

$$=-\sum \bar{x} \bar{y}$$

[woven radish]

Civil Service Pigeon

[lunar harbor]

@candid mica

[candid mica]

how did we get here ? did u remove a message ?

[lunar harbor]

sums are linear

\begin{align*}
\sum (-x_i \bar{y}-y_i \bar{x}+\bar{x} \bar{y}) &= \sum (-x_i \bar{y})+\sum (-y_i \bar{x})+\sum \bar{x} \bar{y} \
&= -\bar{x} \sum y_i-\bar{y} \sum x_i+\bar{x} \bar{y} \sum 1 \
&= -\bar{y} \sum x_i-\bar{x} \sum y_i+n \bar{x} \bar{y}
\end{align*}

[woven radish]

Civil Service Pigeon

[lunar harbor]

Hello?

[candid mica]

ye gimme a sec, im checking on paper

[candid mica]

what am i missing

thats not correct is it?

o wait im stupid

[lunar harbor]

yeah $\sum x_i=\boxed{n}\bar{x}$(don't forget the factor of $n$)

[woven radish]

Civil Service Pigeon

[candid mica]

ye forgot that one, but is that really the same result as they give in the book? shouldnt the product of the two means be inside the sum aswell? in the book it is outside (because no parenthesis)

[lunar harbor]

ye forgot that one, but is that really the same result as they give in the book?
Yes, see what I said [above](#help-27 message).
shouldnt the product of the two means be inside the sum aswell? in the book it is outside (because no parenthesis)
Observe what I did [here](#help-27 message) (same as the attached image) and/or the last line of [this](#help-27 message).

If you're asking something else, you need to clarify because I don't follow then.

[candid mica]

oh i see where the problem was, i forgot to multiply the leftover sums by 1/n, now it makes sense

[candid mica]

thx a lot

!close

[lunar harbor]

[devout snow]

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

[candid mica]

.close

[devout snow]

Channel closed

Closed by @candid mica

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.

[raven swift]

Help? is Y also 1?

[supple knot]

Y is not 1

1 is the horizontal line right above the point A

[raven swift]

Is AC 1 or just AB?

[supple knot]

AB is 1 yes. AC is the vertical length from the x axis to point A on the circle

[raven swift]

Is BC .375?

If i dont know the angles, how do i even work this out

[supple knot]

you eyeball it and guestimate

[raven swift]

How tho

Would B be false?

Tan cant be greater than 1 right since only AB is 1

[thick lotus]

tan = opp/adjacent = AC/BC ,tan can be greater than 1

[raven swift]

Ah yes, im wrong

[supple knot]

this is one form of geustimating

keep going assuming that's true

[raven swift]

How about C

Sin of B would be

So if BC is .375

AC would be .927

Sin = opp/hyp

So is D false?

C is true

[thick lotus]

yes

[raven swift]

Thanks

Wait D seems true

No

Sorry

[tribal leaf]

D is false

[devout snow]

@raven swift 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.

[pale gull]

How can I slove the piecewise function

[trail eagle]

!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.

[pale gull]

Actually there is no original problem but I dont speak English enough to understand the YouTube so asked here in chating

There should be a problem?

[lunar harbor]

piecewise function

[devout snow]

@pale gull Has your question been resolved?

Channel closed

Closed by @pale gull

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.

[stark spruce]

what is my constraint function here?

[versed juniper]

draw a diagram

[stark spruce]

i did

i only have the volume function rn, which is the objective im p sure

V(x) = (16-2x)(7-2x)x

i guess the constraint can be represented as an inequality, but we haven't been taught how to solve inequalities yet

is there any other form that it can take?

[junior flax]

what is x in this scenario?

[devout snow]

@stark spruce Has your question been resolved?

[stark spruce]

the length of one of the squares cut out the corner?

[devout snow]

@stark spruce Has your question been resolved?

[devout snow]

@stark spruce Has your question been resolved?

[devout snow]

@stark spruce Has your question been resolved?

[rich sluice]

umm what is the constraint on x as mentioned in the question

[steady night]

well yeah that's it

[devout snow]

@stark spruce Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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.

[patent jay]

if the dot product is commutative, how come $\vec{\nabla} \cdot \vec{F} \neq \vec{F} \cdot \vec{\nabla}$? I understand nabla isn't exactly a vector, and is just an operator, but if we treat it as a vector in operations, why is this the case?

[woven radish]

prfn

[pure flower]

the latter is just notation iirc

nabla really isnt a vector

it's just convenient enough to think of as a vector

[sand dove]

As you write, the dot product is commutative between vectors of scalars because multiplication between scalars is commutative. Nabla is a differential vector, and if you have $f$ a function, then $\partial_x f$ and $f\partial_x$ aren't the same object

[woven radish]

Rafilouyear2026

[pure flower]

the latter is the directional derivative iirc

[patent jay]

yeah it is

[patent jay]

this makes sense

L notation though

[pure flower]

yeah i found it weird too but its convenient

[sand dove]

I do use it a lot though, because it's good enough and convenient

[pure flower]

there's a thread of me not getting this in hlounge for like 1 hour straight lol

until i realised its just notation

[patent jay]

also

in hs I would have just manipulated one side to get to the other

but genuinely i dont even know how to work to that

is it fine for me to get them both to a point where they equal each other?

[pure flower]

sure

[pure flower]

yeah this was the thing i was tripping up on too lol

[patent jay]

stewart right

[pure flower]

there's a thing written for it in griffiths

and i just didnt get it

[patent jay]

ah ic

whatever

[pure flower]

well i was doing physics not calculus

so i was happy enough to just leave it at 'ok notation'

[patent jay]

uni forces us to take calc III in second sem of uni

got my exam in like a week

[patent jay]

i mean this is fine, but 6 weeks for the whole of calc III is a cram fest

thanks guys though

.solved

[devout snow]

Channel closed

Closed by @patent jay

Use .reopen if this was a mistake.

[smoky gyro]

u australian or what

[patent jay]

europe

[smoky gyro]

oh ok

[patent jay]

i mean its also one thing if its like a math course but im an engineering student who has to do 5 other courses at the same time </3

[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.

[robust bobcat]

So I don't see how c can be any constant. Shouldn't it be f'(1). Also can someone explain why b≠1

[devout snow]

@robust bobcat Has your question been resolved?

[robust bobcat]

<@&286206848099549185>

[quaint creek]

ok so i didnt really understand your doubt but, the reason why b is not equal to 1 is becouse log (1) with any base gives us 0

which in this f(x) since its log(x)/log(b) b should not be equal to 1 since it makes the function tend to infinity

and hence we remove 1 from b's domain

and also b > 0

[devout snow]

@robust bobcat Has your question been resolved?

[robust bobcat]

Ok thank you

.close

[devout snow]

Channel closed

Closed by @robust bobcat

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.

[inner zenith]

help

[modern blade]

Follow PEMDAS

1. Parentheses
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction

[inner zenith]

and what now

9?

[faint gorge]

you also start from the left, usually

[verbal wharf]

[inner zenith]

oh

[verbal wharf]

what if its in arabic

[faint gorge]

what if the expression is intentionally ambiguous

[verbal wharf]

flip a coin

[modern blade]

what if today is April 1?

[hearty yoke]

What if math?

[glass canopy]

What math

[hearty yoke]

Math math

[glass canopy]

what what

[hearty yoke]

Math what

[glass canopy]

if

[hearty yoke]

What

[glass canopy]

hat

[inner zenith]

at

[hearty yoke]

t

[hearty yoke]

https://tenor.com/view/abell46s-reface-john-cena-gif-18864860

[glass canopy]

|| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| ||

[gleaming topaz]

this ones too hard idk if I can help

[hearty yoke]

7

[inner zenith]

right? idk my calculator was giving me some wrong answer

[glass canopy]

the answer is some number, one can assume that much

[inner zenith]

how

[hearty yoke]

Black magic

[glass canopy]

6/2(1+2) = 6/6/7 = 7

[verbal wharf]

67

[summer summit]

67

[gleaming topaz]

67

[glass canopy]

67

[inner zenith]

67

[hearty yoke]

67

[summer summit]

jesus this generation is so cooked

[glass canopy]

can't even do a simple abuse of notation problem??? smh

[verbal wharf]

S=6/(2*3)=1
S=6/2*3=9
S=S
1=9
0=8
0=1
0=7
S=7```

[glass canopy]

https://tenor.com/view/coffee-marshmallow-gif-13281603

[summer summit]

colon at the beginning suggests this may be a ratio. x : 7

[glass canopy]

place a \ before any * or the like if you want to cancel markdown^^

[verbal wharf]

didnt know that

tyty

[glass canopy]

np:)

April fools!!!!!! haha tricked you

[verbal wharf]

:(

[glass canopy]

*or did i?*

[verbal wharf]

mods reading this channel:

[gleaming topaz]

is this game good? I wanted to play it for a while now

[verbal wharf]

Yes

[glass canopy]

Nes

[inner zenith]

yes

[summer summit]

yes (i have no clue what this game is)

[glass canopy]

here is my dog i love him very much

[gleaming topaz]

its "No I'm not a Femboy"

[inner zenith]

ask him

what the answer is

[glass canopy]

he said woof

[summer summit]

$wo^2f$

[woven radish]

Krish

[summer summit]

gotta simplify

[glass canopy]

ah of course

[inner zenith]

what a cutie

whats his name

[glass canopy]

Rutherford

[verbal wharf]

Hi Rutherford

<@&268886789983436800>

[glass canopy]

<@&268886789983436800>

[verbal wharf]

the icon is sakurako oomuro from yuruyuri btw

[inner zenith]

dont invite them there

shhh

[glass canopy]

he says hi

[inner zenith]

he looks very fluffy and huggable

[glass canopy]

He's not as fluffy as he used to be

[inner zenith]

why

he had a haircut?

[glass canopy]

Yeah :(

He's very huggable though

literally never even growled at a person

[verbal wharf]

ill be the first

[glass canopy]

Oh I'm sure not 😊

[inner zenith]

damn its only hair no dog

he mor estylish now tho

[inner zenith]

he almost got it!

[glass canopy]

he's gotten so good at catching

like... he's caught those cubes from a room away

[inner zenith]

woah thats crazy

[jaunty mantle]

So this is a help channel not for discussing random stuff

[inner zenith]

i am getting help

[jaunty mantle]

There’s #chill if you want to yap

[inner zenith]

we still dont know what the answer is

[glass canopy]

the dog was helping

[inner zenith]

yes

[summer summit]

in all seriousness, might wanna close this channel now

[inner zenith]

sure thing

bye Rutherford was nice meeting you

.close

[devout snow]

Channel closed

Closed by @inner zenith

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 crow]

I’m having difficulty determining dv/dt when there are two unknowns dr/dt

And dv/dt

How do I relate this back to the water’s change in volume with respect to time, based on the given information?

[woven vale]

<@&268886789983436800>

[graceful cosmos]

You do have dr/dt! It can be related to dh/dt.

[unreal crow]

Is this to do with triangles?

[graceful cosmos]

That's actually a great strategy. Similar triangles can get it

[unreal crow]

Ok, uhh lemme try and look back at lecture notes

This is what I kinda looked over, and then I plug back into the volume possibly of the cone

Am I on the right track or did I make any mistakes?

[muted sapphire]

dh/dt is given in the context

which is 0.05

[unreal crow]

Yes

The work on the left is the problem and this is what I ended up with

[muted sapphire]

I agree

[unreal crow]

Thank you

[muted sapphire]

np

[unreal crow]

Was there another way to solve it without using similar triangle ratios?

I’m curious, cuz I wasn’t like told about that

With the given information

[muted sapphire]

yeah

you can write everything in terms of h\

and solve it

[unreal crow]

If so, is there a video/guide to that?

Just h?

[muted sapphire]

you can google it, just keep in mind that r scale proportionally with h

[unreal crow]

Got it

[muted sapphire]

and substitute back, the ratio is basically the same, geometric facts

[unreal crow]

Ah. Alright

[devout snow]

@unreal crow Has your question been resolved?

Channel closed

Closed by @unreal crow

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.

[small geyser]

<@&268886789983436800> discussion of banned topic as per #changelog + using images to evade possible filters.

[delicate dust]

take a day to read #changelog. also, dont post nonsense in help 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.

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.

[dapper fable]

Determine the smallest $n$ such that for all subsets $S$ of ${1,2,...,30}$ where $|S| =n$, there is atleast two elements of $S$ that are coprime

[woven radish]

Copter

[dapper fable]

the original question was n = 16, but that was pretty trivial so i was curious to what the lower bound could be

[worthy raft]

Well for {1,2,...,30} it can't be 15 or lower, because for those numbers there will be a set of only even numbers

[dapper fable]

oh right

then its 16

[worthy raft]

Do you know it's 16? I only know that it's more than 15 right now

[dapper fable]

yes

split {1,2,..,30} into {n,n+1} by pigeonhole they must contain atleast one of {i,i+1}

what if S were subsets of {1,2,...,m} tho what would that look like

same thing?

[tribal patio]

probably

You might have to do a bit more on the case where m is odd I think

[dapper fable]

floor(m/2) + 1 or something

[vital edge]

Yeah that should be it

[dapper fable]

so the answer is floor(m/2) +1 for all m

thats cool

.close

[devout snow]

Channel closed

Closed by @dapper fable

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.

[tardy carbon]

mainly confused on part a

[frozen aurora]

write out the lhs

[restive river]

the index is in the function argument

[tardy carbon]

you wpuld get an alternating parttern

[frozen aurora]

you'll notice a pattern

[frozen aurora]

yes

[tardy carbon]

so when r is od its negative

then when even its positive

[frozen aurora]

yes

which is what the RHS is talking about

[tardy carbon]

im just not sure how u would explain it in the question

[frozen aurora]

if r is an integer then 2r is even and 2r-1 is odd

[frozen aurora]

$$
\begin{aligned}
\sum_{r=1}^{2n} &= -f(1) + f(2) - f(3) + f(4) - \cdots - f(2n-1) + f(2n) \
&= (f(2) - f(1)) + (f(4) - f(3)) + \cdots + (f(2n) - f(2n-1) \
&= \sum_{r=1}^{n} (f(2r)-f(2r-1))
\end{aligned}
$$

[woven radish]

artemetra

[frozen aurora]

this is sufficient

[tardy carbon]

so would this be fine?

lmk if u canrt read anything

i just didnt add it up to n.

[frozen aurora]

huh interesting! yes that also works

you might need to elaborate on the bounds tho

[frozen aurora]

you should

because the first sum is until 2n while the second one is until n

[tardy carbon]

sorry i dont understand

[frozen aurora]

you write f(2) + f(4) + ....

that makes it look like an infinite sum

[tardy carbon]

ph i see

[frozen aurora]

write down the last terms using n

[tardy carbon]

so i should go on until 2n

[frozen aurora]

like here

[tardy carbon]

yeah got it 😉

Thanks!

.close

[devout snow]

Channel closed

Closed by @tardy carbon

Use .reopen if this was a mistake.

[frozen aurora]

ofc

[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.

[keen estuary]

I would like to resolve this
f(x) = \frac{x^3 - 3x + 1}{x^2 - 1}

[lean crater]

perform a polynomial long division first

[last parrot]

$f(x) = \frac{x^3 - 3x + 1}{x^2 - 1}$

[woven radish]

Minλ

[upper schooner]

(worth asking, what do you mean by "resolve"?)

[devout snow]

@keen estuary Has your question been resolved?

[keen estuary]

find the limit of f(x)

[gusty sparrow]

x tending to?

[upper schooner]

(also react to the bot with ❌ please, so you don't lose the channel)

[keen estuary]

.close

[devout snow]

Channel closed

Closed by @keen estuary

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.

[velvet rain]

in v=E/(B*sintheta) shouldnt the value of theta which minimizes v be -dx? this will make the denominator a very tiny negative value (based on magnitude) which after division gives a negative value with a large magnitude which is a very small number.

[trail eagle]

!xy In particular, is there a specified domain for theta or other restrictions?

[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.

[velvet rain]

no

wait mb

its based on the lorentz force formula when force = 0 and so that we get E = -(v X B) and then by using a X b = absintheta and rearrangement we get the above result

there isnt a domain restriction for theta at least its not explicitly mentioned

[velvet rain]

my textbook says that theta should be 90 degrees

[trail eagle]

The angle you put into a cross product is usually an angle in [0, 180], so your v should only be defined for like theta in (0, 180).

[winter torrent]

negative value with a large magnitude

what exactly are you trying to minimise here? v makes me think it's a vector (velocity?) which doesn't really have a "negative value". Are you trying to minimise the magnitude of v?

[trail eagle]

At least for magnitudes, which I assume is what we're considering

[velvet rain]

velocity vector

[winter torrent]

right, okay. so we're trying to minimise the magnitude of the velocity vector, right?

[velvet rain]

hmm makes sense cross product represents the area of a parallelogram and area cant be negative

[velvet rain]

oh wait yea thats the magnitude formula

sorry mb

[winter torrent]

yes, and magnitude cannot be negative

[velvet rain]

.close

[devout snow]

Channel closed

Closed by @velvet rain

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.

[sturdy yew]

if B^2 + B is similar to B, and B is an nXn matrix, then what are thr permissible values of n?

[frozen aurora]

wdym by similar

is it $B^2 + B = \lambda B$ for some $\lambda$?

[graceful cosmos]

Means there's some invertible P such that:
P'(B^2 + B)P = B

Where I'm using ' for "inverse"

[frozen aurora]

ohh right i forgot about that one

[graceful cosmos]

Obv we can distribute but I'm not sure what to do after that

[stone stump]

eigenvalues but op doesnt know those

[devout snow]

@sturdy yew Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[sturdy yew]

.reopen

[devout snow]

✅ Original question: #help-27 message

[sturdy yew]

i know eigenvalues

[stone stump]

i dont know much abt them tbh

probably not enough if you said that

[lusty sapphire]

<@&268886789983436800>

[karmic flicker]

[lusty sapphire]

If B is a zero matrix, is this not always true for any n?

[devout snow]

@sturdy yew Has your question been resolved?

[spiral moss]

i think it has to be a zero matrix

you might want to check my notes tho

this is assuming rankB=n

[stone stump]

which your conclusion is immediately contradicting

[lusty sapphire]

$C^{-1}BCB^{-1}\ne I$ in general

[woven radish]

SWR

[spiral moss]

oh yeah mb

[lusty sapphire]

@sturdy yew you still with us?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[sturdy yew]

.reopen

[devout snow]

✅ Original question: #help-27 message

[sturdy yew]

yes yes

mb

so

the sets {v_i^2 + v_i} = {v_j}

from the arguement that the eigenvalues of similar matrices are equal

what do i do from here

v_i represents an eigenvalue of the matrices

<@&286206848099549185>

[gritty terrace]

swr mentioned that B = 0 always works

[sturdy yew]

shit mb B has to be real and invertible

so B = 0 is rules out

[gritty terrace]

ah, i see

so B is real, invertible, and similar to B^2 + B

[sturdy yew]

yes

[lusty sapphire]

My gut tells me n needs to be even, but I have no proof

[sturdy yew]

why does ur gut say so

[lusty sapphire]

1. because n=1 doesn't work
2. even square matrices kind of give you a way to fake imaginary numbers, but this is all instinct

[sturdy yew]

i wish i had ur instincts