help-49

[mortal mirage]

yea...

hm

are the parts correct??

[blissful trench]

ya

[mortal mirage]

try 35.0

[blissful trench]

also wrong

[mortal mirage]

BRO what

imma find the developer

[blissful trench]

lmfao

[mortal mirage]

im actually so confused

i checked w/ a calculator

[blissful trench]

i will try contacting the teacher who gave me this bc i found 3 like mistakes on her website

[mortal mirage]

OH

wait

ah

[blissful trench]

yes?

[mortal mirage]

that's js the total area of all the triangles

but we wanna find the area of the shape inside

so we gotta subtract the 35 from the area of the rectangle

[blissful trench]

how

[mortal mirage]

which is...

[blissful trench]

subtract 35 from which area?

[mortal mirage]

the area of the rectangle

8x10?

!noans

[midnight plank]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[snow dawn]

Look at the right side of the rectangle, the full dimensions are given

Look at the bottom side of the rectangle, the dimension is given

Apply rectangle area formula

[blissful trench]

hate when ppl just come on my help channel and say the answer

[blissful trench]

35x8?

[mortal mirage]

goes against mathcord rules too

[mortal mirage]

what's the height of the rectangle?

[blissful trench]

10

[mortal mirage]

yes

so the area is..

[snow dawn]

Tada

[blissful trench]

35x10/2?

[mortal mirage]

wh-where is the 35 coming from

[blissful trench]

the stuff we did earlier

[mortal mirage]

ignore that for now

[blissful trench]

do i just need to 10x8/2?

[mortal mirage]

we just need the area of the rectangle rn

no /2

its a rect not a triangle

[blissful trench]

oh ok

that means the area is 80?

[mortal mirage]

and you just subtract the 35 to get...

[blissful trench]

my laptop is lagging so hard lmao

45!!!

[mortal mirage]

yeeee :DDD

[snow dawn]

Wait

Wouldn't the area be only the shaded regions?

[mortal mirage]

what shaded regions

[snow dawn]

The triangles

[blissful trench]

do i still keep this channel open bc i got more questions like this

[mortal mirage]

if you have questions about them, ofc!

[blissful trench]

need to finish this first and then ill come back to u

im sure u wont unless u want to send me a gpt answer

[snow dawn]

What is 5th grader doing on discord?

Should I call the mods?

We'll se about that

[raven zenith]

yeah, I'm very sorry but I feel we have to

<@&268886789983436800>

[snow dawn]

<@&268886789983436800>

[blissful trench]

@mortal mirage here

[raven zenith]

I'm very sorry mrx, but violating the TOS is not acceptable

[blissful trench]

no way kid in discord sounds crazy

i tried doing 4 shapes

i think u also need another rectangle shape?

actually i could do more

right?

[raven zenith]

finding the area of the whole thing?

[blissful trench]

ya

[raven zenith]

you could consider subtracting something rather than adding them all up

[mortal mirage]

it's just a rectangle with a corner cut off, no?

[raven zenith]

i.e. find the area of the big rectangle and then minus the corner

[blissful trench]

o

like this?

[snow dawn]

Something is wrong with the shape

The height of the triangle with sides 2cm and 3cm is 3cm

Adding that up spontaneously with the 3cm remaining width of the rectangle gives us 6cm

Which is clearly greater than 5 cm and is not an expected rectangle

[mortal mirage]

yea, you sure this diagram's accurate?

[blissful trench]

no idea

but its given like this

[snow dawn]

2 parallelograms and a trapezium

[blissful trench]

it wont let me do those except for triangle and a square

[blissful trench]

will that work?

[mortal mirage]

nah this diagram's completely wring

wrong

[blissful trench]

how do u know?

[snow dawn]

.

[blissful trench]

whats spontaneously?

excuse me for bad english btw

[snow dawn]

Naturally*

[blissful trench]

ah

[snow dawn]

I mean, just adding up the height of the triangle and the left width of the rectangle makes it disproportional to the right width of the rectangle which shouldn't be

[fair hornet]

but its the length of the side of the paralellogram

hi im new

I've been watching this

It's the left most parallelogram that gives both sides 3cm

it's not disproportional

[blissful trench]

im not getting anything from u

[fair hornet]

bruh

[blissful trench]

😭

[fair hornet]

alr

[blissful trench]

not u

ill take a break and come back later 🙂

thanks for help @mortal mirage @fathom onyx

.close

[midnight plank]

Channel closed

Closed by @blissful trench

Use .reopen if this was a mistake.

[snow dawn]

The triangle with 3cm height when completed forms a square, not a parellelogram

[fair hornet]

here

the red line is 3cm

[midnight plank]

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[fair hornet]

with that, you can find the area of the parallelogram

[snow dawn]

Oh I see

[mortal mirage]

i think you opened a new help channel

!done

[fair hornet]

so you have 3x2

[midnight plank]

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

[fathom onyx]

wdym you think

[fair hornet]

3x2 is 6

then the next parallelogram

is 3x3

[snow dawn]

3 x 3

[fair hornet]

yep

[blissful trench]

#help-49 message

[fair hornet]

so 9+6 is 15

then the trapezium

uk the formula for it?

[snow dawn]

$$ \text{Area} = \frac{1}{2}(a+b)h $$

[grand pond]

Ultra Necrozas

[fair hornet]

yep

[blissful trench]

let me take a break and ill come back 🙂

[fair hornet]

so you have 5+3

[blissful trench]

close this

[fair hornet]

divided by 2

[fathom onyx]

https://tenor.com/view/will-smith-jada-red-carpet-gif-17859329

[fair hornet]

which is 4

[fathom onyx]

@fair hornet @snow dawn

[fair hornet]

times height which makes 12

ye?

[fathom onyx]

well shiet

[snow dawn]

4 x 3 = 12

[fair hornet]

and add 'em

[snow dawn]

12 + 15 is ?

[fair hornet]

there

alr imma close this

.close

[midnight plank]

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[blissful trench]

back

[fair hornet]

yo

[blissful trench]

this will be just 9x18 right?

that means 81 correct?

[fair hornet]

yep

[blissful pier]

yep but the formula is 9*18/2

[fair hornet]

ye

[fathom onyx]

wuh

[fathom onyx]

no?

[blissful trench]

that worked

thanks

[fair hornet]

formula of rhombus? is it?

or whatever its called

[fathom onyx]

https://tenor.com/view/joe-biden-presidential-debate-huh-confused-gif-9508832355999336631

[blissful pier]

pq/2?

[fathom onyx]

wait those were the whole lengths?

[blissful trench]

this was last question i think

[fathom onyx]

Not up to the centre?

[fair hornet]

Who's good with trig

[blissful trench]

time to do the other ones

.close

[midnight plank]

Channel closed

Closed by @blissful trench

Use .reopen if this was a mistake.

[fathom onyx]

!occupied

[midnight plank]

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

[blissful pier]

oh wait yeah good point

[fair hornet]

could someone pls explain

stupid mathspathway

[fathom onyx]

@fair hornet

ik it's just closed - still, go to a new channel here and open a new request there

[blissful pier]

#❓how-to-get-help

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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• Show your work, and if possible, explain where you are stuck.
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[ivory sigil]

Hello everyone, if anyone can help i'll be forever grateful, for contexte i am currently in last year of psychology masters and need help with some statistics. I tried doing a meta-analysis using 14 different studies. Each study has a pre and post mesure for the treatment group AND the control group. Those studies need to get standartised for me to be able to compare them. So at the moment i am trying to find the effect size of each study (+combined effect size). Therefore I thought i should use hedges-g, and with jamovi (or even jasp... all the software i tried) i cant compare this many measures, which lead me to look for another way. I found this Meta-analysis similar to mine using this formula but the result is ......off :/ am i in the wrong? is there an easier way to find what I'm looking for? how do i compare the studies (with 2 moderators)? If anyone can help, unblock just a bit i would be sooooooooooo grateful. also i will send the screenshots of the formulas and methodology i found (Ayuso-BArtol et al. 2024 and Morris, 2008)
If you need any other info dont hesitate to lmk, THANK YOU

[fair hornet]

yoooo u do psych

[ivory sigil]

yayyyy unfortunately i have to do statistics lol

[fair hornet]

lol

[ivory sigil]

A part of my database if it can help you visualise :))

<@&286206848099549185>

[midnight plank]

@ivory sigil Has your question been resolved?

[midnight plank]

Channel closed

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[ivory sigil]

.reopen

[midnight plank]

✅

@ivory sigil Has your question been resolved?

[ivory sigil]

<@&286206848099549185>

[midnight plank]

@ivory sigil Has your question been resolved?

[midnight plank]

@ivory sigil Has your question been resolved?

[carmine sigil]

@ivory sigil just a heads up, I took the liberty of removing your post from #advanced-stats . It is generally frowned on to advertise help threads elsewhere. And the content of this post is not actually #advanced-stats material. (See the channel description for details of the sort of problems that go in that channel.)

(This is more #probability-statistics material, for the record.)

[ivory sigil]

ok verry sorry

oh thank you for letting me know

[midnight plank]

@ivory sigil Has your question been resolved?

[wind oxide]

well, for starters, do you mind actually writing out exactly what you need?

like

you have a formula and a bunch of values, from what I can understand

[midnight plank]

@ivory sigil Has your question been resolved?

[midnight plank]

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[regal oar]

How to revolve this function on z axis like circular staircase

[eternal pawn]

you need polar coordinates for that

[midnight plank]

@regal oar Has your question been resolved?

[midnight plank]

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[vital quartz]

how the hell is this even solved

[twilit field]

$x^4+\frac{1}{x^4} = \left ( x^2 + \frac{1}{x^2}\right)^2-2$

Can you do something from here

[grand pond]

wai

[twilit field]

Try applying the same idea to simplify x^2+1/x^2

[twilit field]

.

[vital quartz]

idk how

[twilit field]

$\left( x + \frac{1}{x} \right)^2-2$

[grand pond]

wai

[twilit field]

can you see why this is true

[vital quartz]

i cant

[dreamy lichen]

is it really that much easier than direct computation tho

[vital quartz]

?

wdym

[vernal zenith]

not really

[runic hamlet]

well x+1/x simplifies a lot

and from there its trivial

[dreamy lichen]

Yeah, it cancels quite nicely, thats true

[runic hamlet]

so yeah, I would say its easier

[dreamy lichen]

Have you tried expanding it?

[vital quartz]

i dont even know how

my maths teacher didn't teach us shit

[dreamy lichen]

$x^{4}+2+\frac{1}{x^{4}}=(x^{2})^2+2\cdot x^{2}\cdot\frac{1}{x^{2}}+\left(\frac{1}{x^{2}}\right)^{2}$

Do you understand why this is true?

[grand pond]

MathIsAlwaysRight

[dreamy lichen]

i just rewrote x^4 as (x^2)^2, 1/x^4 as (1/x^2)^2 and 2 as 2*x^2*1/x^2

[vital quartz]

i understand the first two

but not the last one

[dreamy lichen]

if you mean this, then i can write it like that because x^2 and 1/x^2 cancel

so you are left with 2, which is what we began with

[vital quartz]

makes sense

[dreamy lichen]

After that, it's in the form a^2 + 2ab + b^2

and that equals...?

a^2 + 2ab + b^2 = ?

it's (a + b)^2

(a + b)^2 = a^2 + 2ab + b^2

this is one of the formulas you should definitely remember

[grand pond]

MathIsAlwaysRight

MathIsAlwaysRight

[dreamy lichen]

And $x^{2}+\frac{1}{x^{2}}=\left(x+\frac{1}{x}\right)^{2}-2$ can be proved in exactly the same way, try it

[grand pond]

MathIsAlwaysRight

[exotic berry]

help me find surface area

[zenith snow]

!occupied

[midnight plank]

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

[zenith snow]

Own ur own channel

[exotic berry]

silly

[zenith snow]

Very not silly

[austere blade]

you did this yesterday

and got muted so it's best you create another help channel

[vital quartz]

bruh im so confused

idk even where to start

actually nvm

.close

[midnight plank]

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[graceful ferry]

Help how do i proceed to find the domain?

[graceful ferry]

,rccw

[visual tiger]

Start with the global theta bounds

You've found 0 <= r <= sin(theta)

Which means sin(theta) >= 0

So if the total range is usually [0,2pi]

What are we keeping?

[midnight plank]

@graceful ferry Has your question been resolved?

[graceful ferry]

I thoughr about it i really dont know sorry can you explain how i can know

[midnight plank]

@graceful ferry Has your question been resolved?

[fallow scarab]

Maybe just find the intersection points in terms of Cartesian instead of polar

Plot both x^2+y^2 and 2y

[ivory sigil]

@wind oxide can i dm you? or i can create a new help question

[graceful ferry]

.solved

[midnight plank]

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[midnight plank]

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[rare maple]

If a1 =1 and a_n = a_n-1 + 1/a_n-1 then find the value of floor(a_75)

[wary valve]

3

[rare maple]

?

<@&286206848099549185>

[wary valve]

You're welcome. LMK if you need any more help, I'm free for a while. Love to help kids out :)

[rare maple]

?

The answer is 12

[fallow scarab]

stop trolling

[wary valve]

Of course, I missed a step! I am now getting abt 12.3, although it may be slighly off.

[rare maple]

how do we do it

[wary valve]

Kindly refrain from bothering me. I have work right now.

[fallow scarab]

<@&268886789983436800> troll

[onyx slate]

Knock it off

[midnight plank]

@rare maple Has your question been resolved?

[rare maple]

<@&286206848099549185>

[fallow scarab]

what did you try so far

[rare maple]

i didnt try much

there wasnt any obvious pattern

[woeful turret]

Could u use brackets

[fallow scarab]

you should verify for small $n$, but it looks like $a_n^2$ for large $n$ is approximately $a_{n-1}^2 + 2$. so you can approximate for large n

[grand pond]

riemann

[small jasper]

^ You can show that ||2n-1<a_n^2<2n+ln(n)||

[midnight plank]

@rare maple Has your question been resolved?

[rare maple]

the approximation gives me root 149

[rare maple]

i am not sure how to get this upper bound

[fallow scarab]

,calc floor(sqrt(149))

[grand pond]

Result:

12

[fallow scarab]

looks good

[small jasper]

Square the recursion and then bound by harmonic series

[midnight plank]

@rare maple Has your question been resolved?

[midnight plank]

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[midnight plank]

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[mint ravine]

Can anyone please help me start this question?

[midnight plank]

@mint ravine Has your question been resolved?

[spice geyser]

hey can anyone help me in here?

i got a topology question

[vast cipher]

!occupied

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[midnight plank]

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[void burrow]

!help

[midnight plank]

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

[last slate]

what

[void burrow]

find all integers which are equal to 11 times the sum of their digits

[last slate]

0

is one

u probably know why

it has to be a 3 digit number

Let the number be (100a+10b+c), where (a, (b), (c) are digits.

(a+b+c) sum is

Set up the equation(100a+10b+c=11(a+b+c))

[void burrow]

there are no bounds given in the question and please tell why it has to be 3 digit number

[last slate]

well

its almost impossible for a number *11 to be 4 digit

the sum of digits then has to be more than 90

and 9999 greatest 4 digit number has a sum of 36, not close to 90

got it?

[void burrow]

oh wbt 5 digit numbers

[last slate]

well

it would make it have higer

[last slate]

same thing for 5 digits

[void burrow]

ok

wait

[last slate]

Simplify (100a+10b+c=11a+11b+11c).

i gtta sleep

[last slate]

simplify that

remember a is 1

[midnight plank]

@void burrow Has your question been resolved?

[void burrow]

.close

[midnight plank]

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[midnight plank]

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[chilly cobalt]

Hi! the question asks to consider a rod of plasma of length $l$ and radius $a$ where $l >> a$, having equal positive and negative charges and a current $I$ flowing through it. The force from its own magnetic field makes it so that the radius becomes smaller. Suppose that the rod is in equillibrium of forces, the the pressure $p(r)$ follows the eq $$\dv{p}{r} = -\beta \frac{I^2 r}{a^4}$$, i am to determine the value of $\beta$

[grand pond]

Copter

[chilly cobalt]

is this more suited for the physics server ;-;

[rough birch]

yes...

[chilly cobalt]

apologies😭

ill still leave it here if anyone can answer though

[rough birch]

i wouldn't consider myself to be illeterate in pphysics but i didn't know that plasma generates its own magnetic field

[chilly cobalt]

meh probably a translation error

oh yeah

Plasma is formed when a gas is heated to such a high temperature that electrons are stripped from atoms (ionization occurs), producing positive ions and free electrons. These charged particles can move freely, giving plasma a high electrical conductivity.

When plasma is placed in a magnetic field, it will move under the influence of forces from both the external magnetic field and the field generated by its own motion. In the case where we consider plasma in a cylindrical configuration with an electric current flowing along its length (z-axis), under suitable conditions, the magnetic field will pinch the plasma into a smaller radius. This phenomenon is called the Z-pinch.

the earlier question was to determine the force acted upon a small volume of the rod (subtending an angle delta theta, width delta r and delta l in length)

[grand pond]

Copter

[midnight plank]

@chilly cobalt Has your question been resolved?

[midnight plank]

@chilly cobalt Has your question been resolved?

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[molten bay]

Question number 3

I want to first understand the question properly

What type of elements will appear in HK?

H and K are given non empty subsets of abelian group G

Suppose If I take klien group order 4

[lyric charm]

HK = {xy | x ∈ H, y ∈ K}

[molten bay]

subsets is confusing word for me

xy multiplication?

[lyric charm]

multiplication within the group

[molten bay]

Okay fine

so HK is closed under multiplication

Or let me check first

H={a}

K={b}

HK={ab}

Yes it will be closed

HK will be subgroup of G yes?

[atomic granite]

don't forget to include the identity element in your groups

[lyric charm]

a and b are?

[molten bay]

elements of klien group

[lyric charm]

then none of H, K, HK are closed under multiplication.

[molten bay]

But i am only taking subsets

[molten bay]

Huh how?? They are having elements of G {e,a,b,ab}

[lyric charm]

e does not belong to {a} nor to {b} nor to {ab}

[molten bay]

Yes but we need to check it for HK only

HK is not subgroup because of identity

HK is subgroup so it will have identity and HK so

We must need H and K are having identity

And if H and K have identity then it will automatically become subgroup

So. H and K must be subgroups of G

Am I right ann ma'am

[atomic granite]

your reasoning doesn't justify why a subgroup and a subset with the identity is insufficient

[molten bay]

What??

Subset with identity element is sufficient

[atomic granite]

Could you get outside of closure with a subgroup and a subset?

[molten bay]

No we can't

[atomic granite]

let's say you choose H to be a subgroup and K to be a subset, let e and a be a member of K but a*a not in either K nor H. then HK will have the identity but will not have closure because we can escape by mutliplying the element a contained in HK

[molten bay]

I didn't understand properly what is your subset and subgroup

@atomic granite

K={e,a} and what is H?

[atomic granite]

let us assume that we have G = Z_6 H = {e,5} and the inherented operator and K={e,2}

[molten bay]

Z6 is abelian group and any subgroup of it is abelian

@atomic granite

HK={e,2,5}

[molten bay]

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[tired maple]

the first two are linear

??

[glass chasm]

1

[livid python]

why do you think so ?

[glass chasm]

is not

others area

[tired maple]

^2

[glass chasm]

others are'

[tired maple]

because of the ^2

[livid python]

isn't 9^2 just another number ?

[tired maple]

oh

i read it as 9x^2

sorry

;p

[livid python]

then you found your answer :3

[tired maple]

ty

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[safe notch]

ahmm

[safe notch]

guys

can anyone explain

why there are (N-1) !

permutations

in a circle

circular permutations

[runic hamlet]

you can always rotate the circle so that e.g. the 1 is at the top

and then you are just permutating the rest

[woeful turret]

ABC =BCA=CAB in a circle

[safe notch]

and what abt that 1/2(n-1)!

thing formula

[runic hamlet]

you cant just say a random formula

formula for what

[safe notch]

i mean

[woeful turret]

Do u mean (n-1)!/2?

[safe notch]

its in the topic

so i thought you guys would know it

its

when

clockwise and anticlockwise arrangements

are not distinguishable

[woeful turret]

Yes

Seems like u know it what is the problem

[runic hamlet]

so its the same as the previous situation

just divided by 2

[safe notch]

i didnt get the theory

[runic hamlet]

because 2 different permutations before are now considered the same

[safe notch]

can u elaborate

[woeful turret]

Take a necklace for example

[gleaming spear]

you have to divide by two because you have to account for the fact that all reflections are the same

A B and B A
C C

are the same

[safe notch]

soooo

???

[runic hamlet]

write out all permutations on a circle for n=5

[safe notch]

1,2,3,4,5
2,3,4,5,1
3,4,5,1,2
4,5,1,2,3
5,1,2,3,4

like this

??

[runic hamlet]

well I kinda meant on a paper

and actually on circles

and with the 1 always at the top

[safe notch]

why always one fixed

hm?

[runic hamlet]

well you can also do 3 at the top

[safe notch]

yea i know

[runic hamlet]

then whats the problem

[safe notch]

i didnt get the theory

why is it

[runic hamlet]

I dont want you to write down the same permutation multiple times

and you dont want to do that either

that would be a lot of writing

[safe notch]

huh

[vivid yoke]

you can fix one person and arrange the rest

the rest is n-1

so the permutation is (n-1)!

[safe notch]

yea

can u explain why we gotta fix one

[sudden yacht]

Because of rotations

[vivid yoke]

it's quite confusing every times I explain it

[safe notch]

say it regardless ill try

[vivid yoke]

So basically the rotation makes it overcount right? then stop it

[lethal path]

these are just rotations of the same thing

[vivid yoke]

fix one person make it that others can't rotate

[lethal path]

so ABCD, DABC, CDAB, BCDA are all the same

[safe notch]

ok

then

[sudden yacht]

Then you have to divide the n! by n ...

Because you can rotate up to n times and still have the same distribution

Try to think for a while, don't rush. I mean, take your time to see it with small examples (like n=3 and n=4)

[safe notch]

if we consider the arrangement of numbers like this in a circle
this is one arrangement in a circle
but in a line or a row it is n different arrangement
i took numbers upto 5 so 5 different arrangements in a line
fix one number and permute the rest ( arrange the rest)
so we get p number of arrangements in circle total
so total linear arrangement or permutation np=n!
p=n!/n
where p denotes the circular permutation

is this it

[midnight plank]

@safe notch Has your question been resolved?

[midnight plank]

@safe notch Has your question been resolved?

[midnight plank]

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[clever holly]

Hi teachers, why is an empty set an open set according to the definition?

[clever holly]

R is open because (-infinity, infinity) is a open interval, and this implies empty set is closed

Is there any similar way to prove that an empty set is still open?

like, by using intervals

[glacial slate]

it's open directly from the definition: for every x in emptyset, [condition on x]

there are no xs, so the universal quantifier is vacuously satisfied

in more detail, a statement of the form "for all x in X, P(X)" is really hiding an implication: "for all x, x in X -> P(X)", and implications are satisfied when their premise is false

R and the empty set are simultaneously open and closed ("clopen")

[midnight plank]

@clever holly Has your question been resolved?

[clever holly]

so the premise:= \forall x \in X is false, so the statement is correct according to implication

is that correct?

[glacial slate]

the premise is x in X

where X is the empty set, so x can't possibly be a member of it

the quantifier binds least tightly, so:
open(X) = for all x (x in X -> P(X))
= for all x (false -> P(X))
= for all x (true)
= true

[clever holly]

brief and precise

thank you

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[worldly pine]

did i began the solution in the right way?

[keen saddle]

yes it is correct

as you have two variables x and y

you will need two eqns to solve for them

how can you get a second one?

[worldly pine]

no idea

[keen saddle]

can you tell me what x is?

[worldly pine]

one part of 12800

oh

wait

[keen saddle]

the part of x invested under 15%

[worldly pine]

i got the answer

is there any other way to solve this??

ignore the middle one

[keen saddle]

bro i get the first eqn

what did you do after that?

[worldly pine]

second one is wrong..i forgot to cut it

[keen saddle]

ohk

[keen saddle]

yes this feels correct

[worldly pine]

?

[keen saddle]

i dont think so

this should be the fastest and easiest method

[lyric charm]

i think there might be, if you're the kind of person to want to avoid algebra

[keen saddle]

just a tip you should write what x is

because teachers might cut marks for it

speaking from experience

[lyric charm]

imagine you invest the whole sum into the 12% account, how much do you get?

,calc 12800 * 0.12 * 3

[grand pond]

Result:

4608

[lyric charm]

but your actual total interest is 5085

now think what happens if you remove money from the 12% account into the 15% account

you gain an amount equal to 3%*3 = 9% of however much you transferred (or decided to put into the higher interest account to begin with)

,calc 5085-4608

[grand pond]

Result:

477

[lyric charm]

9% of the amount transferred = 9% of the money put into the higher yield account = Rs. 477

,calc 477/0.09

[grand pond]

Result:

5300

[lyric charm]

@keen saddle @worldly pine an alternative solution does exist

[keen saddle]

If you look at his maths

Then you both have done the same thing

[lyric charm]

we have, only he did it algebraically while i spelled my reasoning out in plain English

[keen saddle]

Tomato tomato

[lyric charm]

well there is also the thing where op is slightly scared of decimals and so puts all percentages as fractions with denominator 100

[keen saddle]

I don't think that is true

It's just easier to carry out calc with fractions

[worldly pine]

any idea
how do i know this method i have to use.

i think my question is wrong

.close

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[hoary hamlet]

how do i start to approach this question mathematically?

[lyric charm]

do you mean to say that you have an approach but you do not consider it mathematical enough?

or that you don't have an approach to begin with

[hoary hamlet]

^^

[lyric charm]

ok

consider this: let each ant write a number in the corners of its visible faces -- 0 for a blue face, 1 for a red

zoom out and think what a blue face will look like after this labeling

and what a red face looks like

[zealous schooner]

Is this MAT 2024

[lyric charm]

and think about the total of all written numbers

[hoary hamlet]

yes

[zealous schooner]

Yeah I remember, I gave that paper

[hoary hamlet]

i dont get what you mean, how do you want me to label it

[hoary hamlet]

you.. gave ? the paper?

[zealous schooner]

Yeah

[hoary hamlet]

what do you mean you gave the paper 😭

to who

[zealous schooner]

As in I sat it

[hoary hamlet]

oh okay

did you get an offer

for oxford

[zealous schooner]

Yes

My offer is unconditional, I’m international

[hoary hamlet]

thats crazy

did you manage to get this question

[zealous schooner]

Yeah

Consider that every red face is seen by exactly four ants

So consider the sum of the number of red faces each ant can see

[hoary hamlet]

ohh okay i think i get it

its 4x the number of red faces

but how do we determine which ants see an even amount

of red faces

[zealous schooner]

What if an odd number of ants say yes?

[lyric charm]

what do you mean label

[hoary hamlet]

you say write in the corner the number of its visible faces, 0 for blue 1 for red

[lyric charm]

no

[hoary hamlet]

uh

[lyric charm]

i mean that each ant writes 3 numbers

on each corner of a red face that it sees, the ant writes a 1

on each corner of a blue face it sees, the ant writes a 0

i am suggesting that you imagine the faces as physical, writable surfaces

[hoary hamlet]

okay im following

[lyric charm]

what will end up written on a red face when you zoom out?

[hoary hamlet]

then an odd number of ants see even number of red faces

[hoary hamlet]

1111

[lyric charm]

right

and on a blue face?

[hoary hamlet]

0000

[lyric charm]

right

so the total of everything the ants write will be 4 times the number of red faces

[zealous schooner]

This is basically the same as what I said

[hoary hamlet]

yeah i get it

[lyric charm]

now the ants who say they see an even number of red faces see either 0 or 2

[hoary hamlet]

okay yeah

[lyric charm]

while the ones who say no would see either 1 or 3

think about the yes-ants' total and the no-ants' total

[zealous schooner]

So can the sum be even?

The sum has to be a multiple of 4 but that’s no bueno if an odd number of ants say no

[midnight plank]

@hoary hamlet Has your question been resolved?

[hoary hamlet]

is there an obvious reason why this cannot be true bc just for example 20 is a multiple of 4

and also divisible by 5

i kinda get what youre saying but like just as an example

[hoary hamlet]

i understand the question but how would you determine the amount of ants that say yes or no in this case given that yes ants see 0 or 2, and no ants see 1 or 3

[zealous schooner]

Why does this matter?

If an odd number of ants say no, then the sum of the number of red faces the ants see must be odd

To find out the parity of a sum of integers, you only need to know the parity of the number of odd numbers

Because adding an even number doesn’t change the parity

[hoary hamlet]

whats parity?

[zealous schooner]

Odd or even basically

[hoary hamlet]

oh wait

i think im onto smth

bc if an odd number of ants see an odd number of red faces

its odd * odd which is odd

is that the logic here

[zealous schooner]

Yes

you also have to add the contribution of thr ants who see even number of red faces

[hoary hamlet]

but that doesnt change the parity

?

[zealous schooner]

But it goes back to the fact that adding an even number doesn’t change the parity

Exactly

[hoary hamlet]

YES

im so smart

fr

okay wait lemme see

so the question asks why an even number of ants see an even number of red faces

we eliminated an odd number of ants seeing odd number of red faces

what about the other 2 cases? even number of ants seeing odd number of red faces

or odd number of ants seeing even number of red faces

[zealous schooner]

Remember that there’s a total of 8 ants

[hoary hamlet]

ohhhhhhhh

so the number of ants must be even

[hoary hamlet]

wait ive been thinking about this for like a long time

idk if this is the correct way of thinking

but if theres 8 ants, and each can see 3 sides

then the total amount of sides that can be seen is 24

so then you go from there?? or no

[midnight plank]

@hoary hamlet Has your question been resolved?

[delicate helm]

Part 1 hint:
||For the first argument you can just consider inductive base to be there are no red faces, and inductive step to be flipping color of a face (given an arbitrary starting coloring).||
Another part 1 hint:
||Then consider the 4 ants at the corner and they were saying either:

1. 4 no-s, 0 yes
2. 3 no, 1 yes
3. 2 no, 2 yes
4. 1 no, 3 yes
5. 0 no, 4 yes
   Show that none break parity||

And clearly you can get where you want using inductive step now

Actually idk if that's too much of a hint, so i spoilered it just in case

Part 2 hint:
||Construct an example, duh||

Actually if you want to properly formalise p1 ||you should say you are only allowed to go blue -> red, that way you get to order them simply by the number of red faces||

[midnight plank]

@hoary hamlet Has your question been resolved?

[midnight plank]

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[clever holly]

Hi teachers, in class, our professor proved that:

[clever holly]

how can i prove, if a set open and closed is, then the set should be one of them

[visual tiger]

a subset of R you mean?

[clever holly]

yes

sry for my ignorance

[visual tiger]

the general gist is that, supposing the open and closed set is not empty, we have to prove it's R

so take A a non-empty open and closed subset of R

and let's go prove every real number is in it

so take a an element of A

and x an element of R that isn't a

we'll treat the case a < x first

what happens if you consider the set $T = {b\in A,, b \leq x}$?

[grand pond]

Raphaelisius Maximus MMIII

[visual tiger]

tell me all you can about the set T

[clever holly]

well, i don't understand why we're introducing a new set T 😭

[visual tiger]

it'll be relevant soon

[clever holly]

then x is the sup(T)?

[visual tiger]

well x is an upper bound of T

but we have no idea if x is the supremum

(that's what we're going to prove though)

first of all, why does T have a supremum

what do we need for existence of sup(T)

[clever holly]

wait a sec Master Raphaelisius Maximus MMIII, i need to figure out first: we are dealing the set A right now, ain't it?

[visual tiger]

we picked a subset A of R

[visual tiger]

has these properties

and we're trying to prove it's R

[visual tiger]

because remember we're trying to prove emptyset and R are the only open and closed subsets of R

so if a set that's open and closed is not empty

it should be R

[clever holly]

i've understood the last two sentences

we are assuming the set a is not empty

[visual tiger]

set A

[clever holly]

set A

[visual tiger]

and is like this

so we pick some random element a in A

and now we want to prove A = R

so... trying to prove A contains every real number x

[clever holly]

uh-huh

[visual tiger]

so pick x at random

let's show it's in A

we're gonna do first case scenario: x > a

and then we'll deal with x < a

is that alright so far?

[clever holly]

yes

[visual tiger]

ok

[visual tiger]

in this first case

we know there are elements of A below x

[clever holly]

mm-hmm

[visual tiger]

because a is one of them

[clever holly]

yes

[visual tiger]

so an idea would be to look at every element of A below x

and maybe find out stuff about the supremum of that set

Let's say we manage to prove x = sup(T)

what could we do with this info?

[clever holly]

x <= sup(T) and x>=sup(T)?

[visual tiger]

uhhh

I think you're mixing up "how do we prove x = sup(T)"

with "what do we do KNOWING that x = sup(T)"

If I'm wrong please tell me

[visual tiger]

I want to focus on this

how could knowing that x = sup(T)

[visual tiger]

help us with showing what we want

meaning x is in A

here's a hint: we can rewrite T as $T = A \cap (-\infty,x]$

[grand pond]

Raphaelisius Maximus MMIII

[visual tiger]

what kind of set is T?

[clever holly]

open

we had an assumption: x < a

[visual tiger]

no... not quite

[visual tiger]

a < x actually

that's what we started with

[harsh storm]

what is ♾️ +♾️

[visual tiger]

A is both open and closed, I'll give you that

[visual tiger]

!occupied

[midnight plank]

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

[visual tiger]

but (-infinity,x]

[visual tiger]

is that open, is that closed?

[clever holly]

in my script, it's not open nor closed

[visual tiger]

(a,b] or [a,b) when a and b are both real numbers is neither open nor closed

but when one of the bounds is infinite...

[clever holly]

what will it be 🥹

[visual tiger]

(-infinity,x] is closed

you should check your notes again in case you missed it

[clever holly]

i did miss this point...

[fathom onyx]

look for the definition of "closed"

[clever holly]

closed means not open

[visual tiger]

no

[fathom onyx]

Not with sets

[visual tiger]

you clearly said there are sets that are neither closed nor open

[fathom onyx]

And yes, I realise it's a shitty definition

[visual tiger]

look again for the correct definition

[clever holly]

weird

complement is open

[fathom onyx]

yee

[visual tiger]

yes

so complement of (-infinity,x]

what is it

[clever holly]

(x, +infinity)

[visual tiger]

you might notice it's an open interval itself right

so it's open

ok

[visual tiger]

so this is closed

because complement of open set

[clever holly]

yes

[visual tiger]

so

A intersected with closed set

what does that give us for sure

[clever holly]

wait, i should remember this

[visual tiger]

A is open and closed

pick the property that applies the most here

[clever holly]

it's that closed? because a<x

[visual tiger]

?

T is closed

but I don't know what you mean by

it's that closed?

[clever holly]

i have no idea what am i doing right now 😭

[visual tiger]

(-infinity,x] is closed

A is closed (among other things)

so yes

closed intersected with closed

gives us closed

T is closed

so... do you see how it's going to be used?

[clever holly]

not really

[visual tiger]

right now we're supposing that we managed to prove x = sup(T)

[clever holly]

😟

[visual tiger]

if x = sup(T)

and T is closed...

[clever holly]

so x = max(T)

[visual tiger]

yes

so x is in T

so x is in A

and we win

because that's what we wanted to prove

I can do a recap if you want to

of what we said so far

[clever holly]

yes

[visual tiger]

We want to show emptyset and R are the only open and closed subsets of R.
So naturally, if we take an open and closed subset of R that isn't empty, then it should be R.
That's exactly what we're gonna prove now:

take A a non-empty open and closed subset of R
and let's go prove every real number is in it
give yourself a in A
and let's first show every real number x > a is in A.
let T = ...
T is closed

....
[Work in progress here]
....

we proved x = sup(T)
but T is closed, so x is in T
so x is in A.
Now similar proof for when x < a...

does that make sense?

[clever holly]

i maybe understand the idea already

[clever holly]

if we take an open and closed subset of R that isn't empty, then it should be R.

this one is delightful

so we continued to consider the x > a and x < a

[midnight plank]

@clever holly Has your question been resolved?

[clever holly]

wait an hour

[midnight plank]

@clever holly Has your question been resolved?

[proper bloom]

Wut u studying @clever holly

[clever holly]

We want to show emptyset and R are the only open and closed subsets of R.
So naturally, if we take an open and closed subset of R that isn't empty, then it should be R.
That's exactly what we're gonna prove now:

take A a non-empty open and closed subset of R
and let's go prove every real number is in it
give yourself a in A
and let's first show every real number x > a is in A.
let T = { t | t \in A, t \leq x }
T is closed, because (x, +infinity) is open.

try to prove x = sup(T)
...

we proved x = sup(T)
but T is closed, so x is in T
so every x is in A, therefore, no elements greater than A: (a, +infinity)

Now similar proof for when x < a to have conclusion that: (-infinity, a)

x becomes to the supremum of T, and T is a closed, so T contains x

for every x, they're in A, therefore, there is no x > A

analog. x < A

then A = R

.close

[midnight plank]

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[midnight plank]

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[viral dagger]

ok maybe dumb but how do you write/prove the fact that if n is an odd number and there are n seats in a round table, if you choose atleast (n+1)/2 then there will be two chosen that are adjacent to eachother

[viral dagger]

it seems so obvious yet im kinda baffled by how you would prove it? can i just write it as is without proof

[peak herald]

start with an even number of seats, choose every other one.

now take one (unchosen) away

[viral dagger]

ok fair, thank you!

[peak herald]

👍

its basically just pigeonhole principle

the most you can choose w/ no adjacent for even n is half. if you remove any from there you necessarily put two chosen chairs together

[viral dagger]

yeah thats what i was expecting but i wasnt sure on how to pull it off

.solved thank you again

[midnight plank]

Channel closed

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Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[last slate]

guys is there a formula for-
summation of k.k!, r tending frm 1, extending till n?

[feral sedge]

sure, there is a very simple way to express this

assuming you mean "k tending..." not r

[twilit jetty]

:)

[feral sedge]

you can prove it, or guess it by trying n = 1, 2, 3. it will not take you long

[twilit jetty]

if not, you can at least combine the k and k! together to make the sum slightly easier to read

[last slate]

yeah

[last slate]

there's another method to it frm wht ive heard

it's called the Vn method

u js write k as k + 1 - 1

and apparantly stuff cancels ou

out

but i don't know how to apply it

[verbal pumice]

Have you tried doing it

[last slate]

i have not

😅

[verbal pumice]

Give it a go then

[last slate]

OHHHH

WAI

WOW

I GOT IT

THX

.close

[midnight plank]

Channel closed

Closed by @thick trail

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[digital ore]

What did I do wrong

[digital ore]

The answer is 64/3 somehow

I integrated and then used the roots formula

[vivid yoke]

Must the wrong somewhere in the last two line

[astral canyon]

Without even looking at the math, is it possible you forgot to make this region + ve?

[digital ore]

It’s not tho right

[lyric charm]

op subtracted the cubic from the linear

[digital ore]

I interpreted from -2 to 2

Integrated

[lyric charm]

idt the red thing is any issue

[astral canyon]

Oh yeah your right

[digital ore]

Hey it’s u again I’m having trouble with that thing again

[astral canyon]

It’s 2am I’m being a dolt

[vivid yoke]

Could you write down how you get to the second last line to the last line

this part

[digital ore]

I used like

The formula

[digital ore]

Ann can u send it

[lyric charm]

yeah how did this happen though

[digital ore]

Idk how to do it

[lyric charm]

i dont get wtf you did

[digital ore]

Like the code

ANN REMEMBER

U TOLD ME A COUPLE OF DAYS AGO

[lyric charm]

oh jeez.

did you try to use the formula for integrating (x-a)(x-b) from a to b.

$\int_a^b (x-a)(x-b) \dd{x} = -\frac16 (a-b)^3$

[grand pond]

Ann

[lyric charm]

did you try to do this

[digital ore]

This

[digital ore]

Yes

[lyric charm]

!nogpt

[midnight plank]

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).

[lyric charm]

your function isnt even a quadratic, so the formula is inapplicable!

[digital ore]

Oh shit

[lyric charm]

please do not call me "bro".

[digital ore]

ur right

[last slate]

what is gradient of a curve at a point

[digital ore]

sorry

Wait I get it now

It’s not quadratic

[lyric charm]

are you asking your own thing or trying to help too

[digital ore]

thank you everyone

.close

[midnight plank]

Channel closed

Closed by @digital ore

Use .reopen if this was a mistake.

[last slate]

my own thing

[lyric charm]

@digital ore instead of trying to recall any of 10 bajillion formulas you should just do the integration as normal tbh

[lyric charm]

claim your own channel then

[digital ore]

yeah I thought so and I might do that from now on

it’s probably better

[last slate]

money?

[twilit jetty]

lol what

[lyric charm]

no, no money

see #❓how-to-get-help for instructions

[digital ore]

.close

[midnight plank]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[gaunt nimbus]

i would set the vertex of the parabola at (0,0)

so would get ${2 = a\left(\frac{3}{4} \right)^2 }$

[grand pond]

k

[fiery onyx]

But then I have to introduce a rectangle to my equations to find areas and I don't want to overcomplicate it 😓

[gaunt nimbus]

why rectangle?

[fiery onyx]

if Im finding area using integrals you get area under the graph

[gaunt nimbus]

mhm

so using ur method

[gaunt nimbus]

what did u determine the eq for the parabola to be

[fiery onyx]

y=32/9x^2-2

[fiery onyx]

Oh I did my graph wrong

[gaunt nimbus]

...

[fiery onyx]

nvm no i didnt

i just looks funny

the line y=k is a halfway point not the x axis

Like this

[gaunt nimbus]

i think the water level is parralel to the x-axis so we should be integrating wrt y not x??

[fiery onyx]

my course doesnt teach that

we're meant to do another method

[midnight plank]

@fiery onyx Has your question been resolved?

[fiery onyx]

.close

[midnight plank]

Channel closed

Closed by @fiery onyx

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[last slate]

I've got log(x) = +-2 , log(y) = +-1, log(z) = +-7
How do I reason further?

I am particularly having trouble with checking and verifying what set of values I would get?

[last slate]

How do I know for one that this set, -2, +1, +7 doesnt form the eventual solution set?