help-23

[lean otter]

And you'll get the answer.

in option a i am geting ans as -2n , so it will be -inf but its aint a possible ans i think

[lean otter]

I am getting-inf too.

like just taking highest power

then dividing

yea same method

[fast tapir]

(-)infinity

[topaz furnace]

im confused

[rancid lion]

0+ means it goes from some positive value to 0

[edgy breach]

Yeah it has to be -inf, as n increases the n^3 is the only significant part so itll just be infinity

[topaz furnace]

so it is 0-

[floral yew]

just factor out the n with highest power from numerator and denominator simplify and make sure it doesnt end up with an indeterminant form again

[rancid lion]

nope

[fast tapir]

The highest power on n is not same in numanator and dinominator

[rancid lion]

in the denominator you have 2/n + 5/n^2 - 2/n^3 which you know tends to 0

[floral yew]

doesnt matter as long as the result is not an indeterminant form

[topaz furnace]

yea

[rancid lion]

but you can rewrite it as (2n^2 + 5n - 2)/n^3

[topaz furnace]

yess

[rancid lion]

and both numerator and denominator of that are positive as n tends to positive infinity

so it has to be 0+

[fast tapir]

Is the answer 0

[topaz furnace]

ooooo

[rancid lion]

so you have -4/0+

[lean otter]

Yeah.

Which is -inf.

[rancid lion]

please stop talking over the helpeee

you're not helping

[fast tapir]

Yeah I was also telling them the same

[topaz furnace]

that's right

[rancid lion]

alr so imagine if i have -4/x

and x is a positive value

[fast tapir]

Are u high?

[rancid lion]

if x goes closer and close to 0 then -4/x gets more and more negative

@topaz furnace you agree?

[topaz furnace]

yep

[rancid lion]

then we can confidently say that your limit equals to -inf

[fast tapir]

More and more negative simply implies to negetavie infinity

[topaz furnace]

ohhhhhhhhh

[rancid lion]

which also means you dont know how to have a proper convo irl because you keep talking over the helpee

[topaz furnace]

how can i explain it in my homework, i dont think my teacher allows me to write 0+ or something

[normal moss]

Why not?

[dull sequoia]

What have you currently got down for your solution?

[fast tapir]

Silly questions

Huh

[normal moss]

Huh, are you just trolling

[primal bone]

Are you? In any case, you've been told before to stop interrupting the flow of the conversation. Should this persist, I will sick the mods on you on account of trolling.

[topaz furnace]

i dont actually know, my teacher doesnt teach us about 0+ or 0-

[primal bone]

For the lim as n tends to infinity? I think you can get away with then just saying "0"

[lean otter]

Yes.

[topaz furnace]

hmmmk

all of that are helpful to me, appreciate all of you guys

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[hazy sail]

hello, can anybody help me with differential calculus rn?

[near atlas]

!xy

[safe radish]

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.

[hazy sail]

i need help for a quiz not specifically for a problem, it would be about derivatives of transcendental functions then tangent line and normal line to a curve

im having a hard time understanding the whole thing

[ember socket]

for future helpers, might wanna clarify if you meant you need help for the actual quiz, or revising for the quiz

if revising for the quiz, perhaps send some questions over that you're stuck on

but if the actual quiz, probably counts as academic dishonesty

[hazy sail]

oh sorry, the quiz is not given yet it’s done with a proctor so no questions handed yet

[near atlas]

i think for transcendental functions, you might wana look into logarithmic differentiation and stuff

which concept are you struggling with

[hazy sail]

the whole concept of differential calculus🥲 I haven't mastered increment method and differential formulas that may be the reason why i’m not able to get a hold of the lessons we’ve been having

we’re even done with logarithmic differentiation

[near atlas]

then the best you can do is review your notes and redo the example problems again, by yourself. whenever you get stuck, you can come here and resolve your doubts

[vivid flame]

gauyesss i needd heelpp
my exam is tomorrow

[near atlas]

and its better if you get your formulae memorised. although memorization always goes hand in hand with practice. maybe you can memorize them better if you find the logic behind and you can do that by deriving them either by first principles or by the increment method you mentioned

[ember socket]

!occupied

[safe radish]

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).

[hazy sail]

ok ill try

tyy

[safe radish]

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[opaque hamlet]

is there any problem with my solution?

[plucky elk]

did you typo ii)

[opaque hamlet]

dont think so?

[opaque hamlet]

wait nvm i did

(accidently add dx at the end of the first line)

[plucky elk]

x is a constant wrt to u so you just factor the integrand out

int f(x) du = f(x) * int du

[opaque hamlet]

so i can just pull whatever is in the middle out?

[plucky elk]

yes for this reason

[opaque hamlet]

as long as it's not wrt. the d(whatever)

I thinl the prof. has a typo in ii).

Its suppose to be 1+sqrt(u)

[plucky elk]

yea that's reasonable too

[opaque hamlet]

So.. excluding ii). Is there any problem with i). and iii).?

[plucky elk]

no

[opaque hamlet]

alr, thx a lot

appreciate it

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[warped lark]

i am blocked in the last question which is asking to show that 3 is the only solution for the equation in (-1;+ infini)

[warped lark]

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[slate dawn]

When does differential of f(g(x)) = 0 can anyone help

[slate dawn]

I did chain rule for composite function and then null factor law so differential of g(x) = zero once, I just need to find out how many times differential of f(g(x)) is zero

[somber cape]

,rccw

[somber cape]

mm ive never heard the term stationary point before

[slate dawn]

Maybe different terminology that’s when dx/dy = 0

[somber cape]

o ok

[slate dawn]

Ya

[somber cape]

ye I think its 3 also

so you take derivative using the chain rule

[slate dawn]

Ya that’s the answer but I copied that down from when teacher did it idk how to get there lol

[slate dawn]

Ye

[somber cape]

you found that g' = 0 happens once at x = 3 so thats one

[slate dawn]

Ya

[somber cape]

now we want to know when f' = 0

for the other part right

[slate dawn]

Ye the left side

[somber cape]

right

and we see f' has one zero around like 0.9 or something right

[slate dawn]

Yes

[somber cape]

ok but what we are inputting into f' is g(x), we have f'(g(x))

[slate dawn]

Ya

[somber cape]

so we need to find how many y values of g(x) = 0.9

and its a parabola

[slate dawn]

Ohh

So 2

[somber cape]

right

so that gives 2 more

[slate dawn]

And then because there’s the other one from g(x) the total is 3

[somber cape]

ye

[slate dawn]

I seee

Tysm

[somber cape]

np

[slate dawn]

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[hoary seal]

Im not sure if I did the first part of the question correct

the one I circled, please check the answer

[thin bridge]

First part is fine
End value is correct, however you didn't do what the question wanted to get there

[hoary seal]

yeah I had a feeling

how was I meant to do it?

[thin bridge]

By first expressing it as a gp
the hence means they want you to use the summation formula for a gp

[hoary seal]

just as a side note confirmation, gp includes geometric sequence and geometric series, right?

so the question was asking me to derive 11/9 from this part

[thin bridge]

Not quite

That's only the part after the decimal point

To get the final value, add 1 to that

[hoary seal]

wdym?

[thin bridge]

That's for
0.222...
They want **1.**222...

[safe radish]

@hoary seal Has your question been resolved?

[hoary seal]

but we cant get 1.2222... from 0.222...

[thin bridge]

To get the final value, add 1 to that

[hoary seal]

Is this much better?

[thin bridge]

Yes

The last few lines could be structured better

[hoary seal]

how?

[thin bridge]

$\begin{aligned} 1.\dot{2}&= 1 + 0.\dot{2} \
&= 1 + \frac29 \
\therefore 1.\dot{2}&= \frac{11}{9} \end{aligned}$

[flat frigate]

ραμOmeganato5

[hoary seal]

I see

,calc (0.23)/(1-0.1)

[flat frigate]

Result:

0.25555555555556

[hoary seal]

will the 5 be recurring

because theres a 6 at the end

how would u write that as?

[thin bridge]

Use ,w instead of calc

[hoary seal]

,w (0.23)/(1-0.1)

[flat frigate]

Results provided by WolframAlpha

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

Requested by perseverance4

[thin bridge]

The calc rounds values

[hoary seal]

why didnt it round it earlier?

[thin bridge]

Where

[hoary seal]

this over here

thats the same result I got in my calc

[thin bridge]

It did round there

[hoary seal]

0.25556

it coudve did that

or 0.26

[thin bridge]

That would be rounded

[hoary seal]

I see

also how do u subtract reccuring from another recurring

its hard to visualise

ill show you what I mean

first I wrote 23/90-0.02 recurring but changed it back to 0.02

[thin bridge]

Redo the whole question

How did you determine your r value

[hoary seal]

second term divided by first term

third term divided by second term

[thin bridge]

You had your terms listed out
0.23 + 0.0023 +...
How did you get r = 0.1 from that

[hoary seal]

oh

It should have been 0.01

I prob misread it

is the answer from sum to infinty of a GP always give a reccuring decimal?

I never realised that until now

[thin bridge]

um

The repeating component of a number can be expressed as a geometric sum

[hoary seal]

thanks for the help

.close

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[silk cove]

I didn't understand how _ sign mean?

a/b mean?

b divides a?

[lament blaze]

yes, 9/3 = 3

[plucky elk]

,calc 9/3

[flat frigate]

Result:

3

[plucky elk]

Checks out

[silk cove]

For option A

a/b and a/c

a/b=bx and a/c =cx

a/(b+c)

(b+c)X yes it seems correct

a/b =bx and b/c=cx

[silk cove]

How do I check these options?

Should I use random values?

n=1,2,3

[neon vapor]

start there

but be judicious with your numbers

[safe radish]

@silk cove Has your question been resolved?

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[trail mica]

these are just random numbers but does anyone know what this problem is called? i genuinely cant find it but apparently itll be on the exam

[trail mica]

is this like weight networks and algebra or smt

[astral glacier]

...mensuration?

[trail mica]

apperently the total area will be given too

[trail mica]

is that what its called

[astral glacier]

Oh the total area will be given

[trail mica]

yeahh and weretrynna find the a

[astral glacier]

Then it's a mix of algebra and mensuration ig

[trail mica]

ohhh

let me see

idk if it has anything to do with shapes cause this entire term weve only been learning about net works

but maybee

[astral glacier]

What does area even mean in the context of a network

[trail mica]

idrk

[astral glacier]

Actually what even is a network at the pre-uni level

[trail mica]

i couldnt tell you😭 im sorry

i just cant find a question similar to this so now im questioning if it even exists sigh

it should be solvable tho right like smt abt minusing the numbers to the total area and then dividing them all

or something

[open wedge]

heron comes to the rescue

[trail mica]

herons

[open wedge]

this is just 3 triangles

[trail mica]

ohh??

[open wedge]

search up heron's formula

[trail mica]

will that find a

waitt i think thatll work

tysm!!

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[vagrant halo]

Is this double integration right ?

[mossy lotus]

the bounds of theta look a bit off

[vagrant halo]

Ig it should be 0 to COSθ right ?

[mossy lotus]

well yea

[mossy lotus]

not for theta bounds, for the bounds of r you mean right?

[vagrant halo]

Yesss

[mossy lotus]

yea, then thats right

[vagrant halo]

If we take 0 to sin it would be 0 to π/4 right ?

[mossy lotus]

your r = sin theta is the lower curve and cos one is the upper

[mossy lotus]

correct

[vagrant halo]

Thanks bro/sis I have maths exam today

[mossy lotus]

gl

[vagrant halo]

Tyyy

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[trail mica]

does anyone know what this is called

[vagrant ice]

you should ask your teacher after the test for the exact question wording

this is far too vague

[trail mica]

noo this is the exam question based on my friends memory😭

im just wondering if it would be some kind of network algebra thing or smthing else

[vagrant ice]

does your class cover any graph theory?

[trail mica]

graphs i think so

yes

[safe radish]

@trail mica Has your question been resolved?

[kindred dagger]

Are these small a or 9s in your drawing?

[trail mica]

a

[kindred dagger]

Ok, so first you gotta find out what a is.

How would you do that?

[trail mica]

uhh minus all the numbers to the total area?

and then divide it by the amount of lines or smt

[kindred dagger]

Yes, probably the easiest way would be if you summed up all the numbers and a's. So a+5+a+10+a+6+... and then subtracted that number from 320 and - as you said divide by the number of a's. Then you should have the value of a = .... What's next?

[trail mica]

i think thats itt

i just wanted to make sure bc my friend said no one completed that question

so i thought it couldn’t be that easy

[kindred dagger]

Yup - don't forget to still add the 10 to the a for the distance between OP though.

[trail mica]

ohh right

thank youu then

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[tough spear]

this is where I got stuck in
I proved the two equations and then I don't know how to move from here
excuse my handwriting 🙂

[junior bobcat]

use vector?

i think

[tough spear]

any other way?
I don't know vectors

[junior bobcat]

ik

here

we have ABC is the isosceles triangle right?

@tough spear

[tough spear]

yes

2 sides are equal

[junior bobcat]

=> ∠ABC = ∠ACB = 80

[tough spear]

yes

[junior bobcat]

=> ∠A = 20

we have ∠ABE = 20; ∠EBC = 60

oke u do it right

now to consider triangle AEC

We have

[tough spear]

AEC is a straight line

[junior bobcat]

wait

oh f

wait me

∠BFE (x) + ∠FEC(y) = 110 | x,y is my called

[tough spear]

what?

[junior bobcat]

we have AEB is isosceles (EAB = EBA = 20)

[tough spear]

I think our naming has a problem

can you tell me which point you name what?

I named points like this

it may be that you named B as E?

then, it would make sense that AEB is isosceles

[junior bobcat]

yes

did u learn about ceva theorem

i think we can only use this to do

@tough spear

[safe radish]

@tough spear Has your question been resolved?

[lone hornet]

You can use law of sines to solve for it

at least in theory...

Actual calculations are nasty

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[jolly sail]

guys I found out that one of the topics I need to learn more is parametrization

[jolly sail]

I absolutely have no idea how they parametrize that

do I parametrize F(x,y)

[safe radish]

@jolly sail Has your question been resolved?

[jolly sail]

<@&286206848099549185>

pls ping methanks

[dim rock]

So we always parametrize the surface/curve we’re interested in integrating over

In this case we have this semicircle which looks a lot like a circle

Do you know how to parametrize a circle, say centered in the origin for simplicity?

[jolly sail]

<cost, sint>

x = rcost

y = rsint

yes I know the basics

[dim rock]

perfect

now two things to determine are i) how can we move our circle to another point which is needed to solve this problem, and ii) how do we add the constraint that its a semicircle

and I guess determining the radius but you can see that it’s 1

[jolly sail]

i) so +1 for the x-component

oh is it x + 1 = cost then?

[dim rock]

exactly!

[jolly sail]

oh........................................................................................................................................................................

ii) so the way t works is it's increasing in an anti-clockwise direction right?

so t = 0 and t = pi

?

oh..................................

[dim rock]

actually need to make one correction

[jolly sail]

BROOOOOOOOOOOOOOOOOOOOOOOOO how is this easier when asking someone

[jolly sail]

yes?

[dim rock]

it should be (x-1)=cos t

for our circle to be centered at x=1, the way we shift it by 1 is to take (x-1)

so x=cost + 1, an easy check is that we know x=0 when t=pi, because that refers to a half cycle right?

[jolly sail]

oh hmm right, this might be counterintuitive for me haha

[dim rock]

Yeahh I get it, for me i like using those concrete examples

like t=pi refers to one full cycle around

but at t=pi we need x to be 0 because that’s where we land

so therefore we need to add 1

[jolly sail]

alr hmmm ok and maybe one more thing that made me confused earlier: Isn't parametrization always start at the origin? This one starts from center of circle, because before asking the question here, I tried finding parametrization t from (0,0) to (2,0)

[dim rock]

they don’t have to

[dim rock]

there probably is a way to find one that starts at the origin but using polar coordinates like we did here is easiest

[jolly sail]

ic

and last thing

is t always increasing in anti-clockwise direction? If so, how does it still apply when the curve C from pic is moving in clockwise direction?

[dim rock]

that depends on how we define things. In most cases we define anti clockwise as the positive orientation

[jolly sail]

what...

I thought its a fixed rule

[dim rock]

right handed systems give anti clockwise as the positive direction

but anyways the important thing is we want to integrate clockwise over c

So our angle starts at pi and ends at 0

[jolly sail]

oh ok got it

[dim rock]

these things can get confusing because there’s many different ways to parametrize

you could use x=1-cost and integrate from 0 to pi and get the same answer as well for example

[jolly sail]

yes but do u know how they got that

oh do they use cos(-t)?

[dim rock]

its kind of like shifting the whole cosine function? we know cos(t+pi)=-cos(t) right? so when we shift cos by pi we move the starting point to t=pi (which corresponds to x=0). in that sense we can integrate from t=0 to t=pi to get the same region

we can see that at t=0 we get x=1-cos(0)=0, t=pi we get x=1-cos(pi)=1-(-1)=2 which is of course what we want

it’s like going backwards? does that make sense lol

[jolly sail]

ohh i see i see, u mean from t = pi to t = 0?

OHH

yea yea I get it

[dim rock]

this time we go from t=0 to t=pi

because cos(t+pi), if we insert 0 we get cos(pi) as our starting point instead

its the same idea but flipping things and going backwards

[jolly sail]

right right

alr thanks bro 👍 see you in the next one haha

.solved

[safe radish]

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[obtuse kettle]

im not sure where i went wrong cuz i got a negative of the answer

[dim rock]

I mean it does say k is just a constant

[obtuse kettle]

can't constants also be negatives tho?

[dim rock]

ohh sorry I misunderstood lol

the actual answer is pi/48?

[obtuse kettle]

yess

[obtuse kettle]

no worries!

[dim rock]

maybe just a slip up somewhere? cant tell since you skipped over some steps

[obtuse kettle]

in the first line, why did u equate arctant to pi/2?

[dim rock]

standard limit

[obtuse kettle]

in general for arctan?

[dim rock]

yeah exactly

it’s like an identity

[obtuse kettle]

ohhh i see

in the last line, where did the 1/2 come from?

[dim rock]

so I replaced the arctan(3/4 t) with pi/2

and I factored out pi and 3/4

[obtuse kettle]

instead of replacing that with pi/2, ik this is a bit lazy but since t tends to infinity, i just assumed it would be 0 in that case so then i just ignored arctan(3/4t) and thats how i got a negative, which now im thinking thats prob where i went wrong by assuming that?

[opaque fern]

yeah well its not being lazy its being wrong

which is why you got that

[dim rock]

yeahh because the limit of arctan as t goes to infinity isnt actually 0!

[obtuse kettle]

ohh

[dim rock]

you can see that clearly from the graph of arctan

it has a horizontal asymptote

[obtuse kettle]

oh so as x becomes bigger, it tends to pi/2

[dim rock]

yup!

[obtuse kettle]

ohhh okok

thanks sm!

.close

[safe radish]

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[normal moss]

[opaque fern]

ok nvm

[rigid blaze]

[ember socket]

uh?

[opaque fern]

was testing something

[ember socket]

ah

[safe radish]

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[lyric marten]

$\sum_{n = 1}^{\infty}\left(\frac{(a-3)^{2n}}{4^n \cdot (n + \sqrt{n})}\right)$

[flat frigate]

squared_apple

squared_apple

[lyric marten]

Using the Ratio test, I have gotten to here.

I just stupidly don't know how to check for when a = 1 or a = 5 (same thing here)

[charred summit]

Substitute in the original series and check for convergence again. (but don't use ratio test again)

[lyric marten]

Ah right I see

By the way, is everything up to this part correct?

[charred summit]

The ratio test looks correct

So yeah probably

[lyric marten]

okay thank you very much 😄

!solved

Right

.solved

[charred summit]

It's .solved i think

[safe radish]

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[safe radish]

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[exotic charm]

im confused for the 2nd part

[safe radish]

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

@exotic charm Has your question been resolved?

[fickle yoke]

what make u confused brotha

yk what dense and closed mean?

[safe radish]

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[exotic charm]

everything

[exotic charm]

idk where to start 😭

[plucky elk]

What second part exactly

Closed nor dense?

[fickle yoke]

ye he asking for that

[plucky elk]

Wasn't asking you

[fickle yoke]

bro he answers late just wanted to tell u

dont be toxic

[plucky elk]

Blocked

[exotic charm]

not closed

but in reality

idk how to do subspace now

i thought it was as simple as cts functions on a compact set are bounded

but then i realised compact support isnt the same (i think)

[plucky elk]

Do the first part and show it here

[exotic charm]

acc i got it now

it's cz i didnt rly understand what support acc was

now i get it, it's just the space s.t. for all points outside the support f = 0

[safe radish]

@exotic charm Has your question been resolved?

[safe radish]

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[lean otter]

Calculating two weapon damages to decide which one is better at what point

Target info:

Health aka HP: 20
Info: one damage removes 1 hp

Armor points: 20
Armor toughness: 8
Info: armor reduces the damage you take, here are the formulas on how to calculate it https://minecraft.wiki/w/Armor#Damage_formulas
There is also a 64% damage reduction coming from the armors enchantment called protection, this is applied after the armor's damage reduction. more info: https://minecraft.wiki/w/Protection

Weapon info:

We have 2 weapons, both are a weapon called the mace, which increases your damage based on how many blocks you're falling:
A successful smash attack causes a mace to deal 4HP extra damage for each of the first 3 blocks fallen, 2HP extra damage for each of the next 5 blocks fallen, and 1HP extra damage for each block fallen after that.
More info: https://minecraft.wiki/w/Mace
The difference between these 2 is that they contain 2 different enchantments

The 1st mace has the enchantment Density 5, which does the following:
Density increases smash attack damage by 0.5HP per block fallen per level of enchantment.
More info: https://minecraft.wiki/w/Density

The 2nd mace has the enchantment Breach 4, which does the following:
Breach reduces the effectiveness of the target's armor points and armor toughness by 15% per level. Specifically, Breach deals damage as though the enemy's damage reduction from armor was 15 percentage points lower per level. For example, if the enemy's armor reduces damage by 50%, and they are hit with a mace with Breach I, their armor reduces the damage by 50% - 15% = 35%. However, this reduces the effectiveness of only the armor itself, which does not include damage reduction from enchantments such as Protection.
This is the formula used to calculate the damage for the breach enchantment:
damage taken=weapon damage×(1−max⁡(0%,armor effectiveness−level×15%))
More info: https://minecraft.wiki/w/Breach

[lean otter]

I can easily calculate the damage for tthe density enchantment myself, the part im struggling with is the breach enchantment because the armor point formulas are a bit too complicated for me
I am really bad at math, i have tried using LLM to solve this but they all failed, i need a bit of help to solve this

My goal:

My goal is to find the point where the density mace becomes superior to the breach mace in terms of damage and the block fallen, for your information: breach deals more damage at less blocks fallen and density at more blocks fallen, and i want to find the exact point where this change happens

[north raven]

Do you know the armour of the target?

[lean otter]

Yes i provided the exact information under target info section

[north raven]

ah mb

[lean otter]

Those are values for full netherite armour

[north raven]

I'm looking into it rn, there's quite a lot to read

[lean otter]

Okay thank you, i provided all the necessarty information, the rest, aka wiki links are fyi
Please ignore the weapon base damage which is 6 and critial hits (which multiplies damage by 1.5), only provided on the wiki page, not on my explanation

[trail field]

just make up a function in desmos and see where they intersect

if they even do

make a formula for the damage, with y being ur damage and x ur blocks fallen

the rest would just be constants

[north raven]

i'm sure he or she understands that

[trail field]

then whats the goal of this post lmao

thought he didnt know how to find where 1 is better than the other

[lean otter]

Hey, im ground 0 in math, i only know basic stuff like - + x / and %, i dont know any more
Thats why i came here to get help

[trail field]

so he did infact not know it

okay ill give u a hand

lemme make 2 functions quickly for u

[lean otter]

thanks a lot
if you had any questions about what my goal is and how any of the elements i explained function, i would be glad to answer them

[trail field]

nah i know minecraft, i get what ur trynna find out lmao

[lean otter]

alright great

Please ping me on response

<@&286206848099549185>

Imo to make this simpler lets just help me make a formula for breach damage that takes the following arguments:
Blocks fallen
Armor points
Armor toughness
breach level

And outputs the damage

[north raven]

that's literally what we're doing

for a standard unenchanted mace, the weapon damage (excluding base damage of 6) can be represented the piecewise function
$$m(x)=\begin{cases}4x&0<x\leq3\6+2x&3<x\leq8\14+x&8<x\end{cases}$$
and similarly for a density V mace, the weapon damage (excluding base damage of 6) is
$$d(x) = \begin{cases}4x+2.5x&0<x\leq3\6+2x+2.5x&3<x\leq8\14+x+2.5x&8<x\end{cases}$$

where $x$ is the height of the blocks fallen.

Note that when $x < 1.5$, smash attack doesn't occur but we can just ignore that.

[lean otter]

yea i know i already have a claculator for enchanted and density

[lean otter]

As i mentioned here, my problem is the breach mace

yes we also do ignore the x < 1.5

[north raven]

i know, having it as a function makes it easier to plot

[lean otter]

yes

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[north raven]

The damage taken by the player with the density V mace accounting for armour is:
$$\mathrm{dmg}\text{density V}(x) = d(x)\times0.36\left(1-\min(80,\max\left(0.8\times20,4\times20-\frac{16\times d(x)}{8+8}\right)\right)$$
which simplifies down to
$$\mathrm{dmg}\text{density V}(x)=d(x)\times0.36\left(1-\min(80,\max(16, 80-d(x))\right)$$
lemme know if you want me to explain that

The damage taken by the player with the breach IV mace is given by
$$\mathrm{dmg}_\text{breach IV}(x)=m(x)\times0.36\left(1-\max\left(0,\min(80,\max(16, 80-m(x))) - 0.6\right)\right)$$

[lean otter]

reading

so those are the two complete formulas for density and breach with armour? thats all?

[north raven]

wait

hmm i think i might've calculated something wrong

[lean otter]

yea that didnt make sense for a bit

[north raven]

The damage taken by the player with the density V mace accounting for armour is:
$$\mathrm{dmg}\text{density V}(x) = d(x)\times0.36\left(1-\frac{\min(80,\max\left(0.8\times20,4\times20-\frac{16\times d(x)}{8+8}\right)}{100}\right)$$
which simplifies down to
$$\mathrm{dmg}\text{density V}(x)=d(x)\times0.36\left(1-0.01\min(80,\max(16, 80-d(x))\right)$$
lemme know if you want me to explain that

The damage taken by the player with the breach IV mace is given by
$$\mathrm{dmg}_\text{breach IV}(x)=m(x)\times0.36\left(1-0.01\max\left(0,\min(80,\max(16, 80-m(x))) - 0.6\right)\right)$$

should be corrected

[lean otter]

oh thank you so much

if possible, i would like a small explanation of where some numbers come from

[north raven]

0.36 comes from the armour protection-- 100% - 64% = 36% = 0.36 so 0.36 of the damage is actually taken

the rest just come from plugging in numbers into the formulae

[lean otter]

durability?

[north raven]

not durability

protection i mean

whoops

[lean otter]

oh yea i get it

what about 16

[north raven]

that's 0.8 * 20

[lean otter]

How much can i rely on LLMs explaining functions

[north raven]

not much

[lean otter]

what im asking is do they flop too much or they can explain decently?

okay

let me play with the function a bit and if i had any questions i will ask, are you okay with pings?

[north raven]

sure

[lean otter]

x is the number of blocks fallen? if so why do i get 1.08 when i feed the function the number 10? i should get 55

sorry its my first time using math functions
i understand how it works for the most part, i just dont know what d is for and where some numbers come from

[north raven]

which function are you feeding it into?

[lean otter]

density

[lean otter]

this density one

[north raven]

it takes into account armour

[lean otter]

yea but

Density V mace: A critical hit after falling 10 blocks.

[north raven]

You're looking for the d(x) function i defined earlier

[lean otter]

this is for doing 20 or more damage with a density 5 mace on prot4 netherite armour

[north raven]

here

also you said not to take into account base damage and crits so i didnt include that

[lean otter]

yes i know, the image i sent is no armour

but still

[lean otter]

i know,

crit is 1.5 multiplier

1.08 and 55 are so different

even if we count armour

and crit

look at the prot4 netherite, even if we add the crit which is 1.5 multiplier, we still dotn get close to 2 dmg

Do you understand the point im trying to make?

[north raven]

at x = 10, dmg_{density V}(10) is about 17.5 hp

maybe you typed something in wrong

[lean otter]

How can i do it right? is there a calculator i can use?

[north raven]

https://desmos.com/graphing

[lean otter]

idk how any of this works
i tried to figure it out on my own but failed
what do i need to do?

[north raven]

do you know how to define piecewise functions in desmos?

[lean otter]

i dont

f(x) = d(x) * 0.36 * (1 - min(80, max(0.8 * 20, 4 * 20 - (16 * d(x)) / (8 + 8))) / 100)

this is what i entered, i got it by LLM

[north raven]

!nogpt

[safe radish]

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).

[north raven]

do you know what piecewise functions are?

[lean otter]

#help-23 message

However, im a programmer and i understand most of these stuff

i just dont understand the math specific ones

[north raven]

okay that's amazing

piecewise functions are basically sort of like if-else statements

[lean otter]

oh yea

i think i get it now

a little bit, i may be wrong

[north raven]

in this case,
$$d(x) = \begin{cases}4x+2.5x&0<x\leq3\6+2x+2.5x&3<x\leq8\14+x+2.5x&8<x\end{cases}$$
is the same as
$$d(x) = \begin{cases}4x+2.5x&\text{if }0<x\leq3\6+2x+2.5x&\text{if }3<x\leq8\14+x+2.5x&\text{if }8<x\end{cases}$$

[lean otter]

i get it

[north raven]

you can type them out in desmos like d(x) = {condition 1: return value 1, condition 2: return value 2, etc}

[lean otter]

kinda like json

[lean otter]

i am having a lot of problems using and understand math functions
i think i need to ask for assistance its been an hour or two that i have been trying to figure this out on my own with tutorials but i failed

[north raven]

What level of math do you know? In terms of grades

"Basic math" could mean anything

[lean otter]

I did not go to school

[lean otter]

this is what i know

[lean otter]

i understand stuff like this because of my programming, but i cant understand any further

[north raven]

What programming language do you know? I might be able to give an analogy in that language

[lean otter]

lets go with python so it will be easier to explain, i know some more like golang and java but explanation will be easier in py

at the end i want to turn the functions into code so it will be easier that way, what language do you know?

[north raven]

This is essentially equivalent to

def d(x):
  if 0 < x and x <= 3:
    return 4 * x + 2.5 * x
  elif 3 < x and x <= 8:
    return 6 + 2 * x + 2.5 * x
  elif 8 < x:
    return 14 + x + 2.5 * x
  else: 
    return None # function is not defined for any other case

[lean otter]

oh my god

this is so my easier

thank you so much

thank you, we shoulve done this earlier lol

[north raven]

plotting this out on a graphing calculator gives you the return value of d(x) for each x-value on the number line

you will notice that the graph doesn't extend into the negatives, because the function isn't defined for such

[lean otter]

yea i get it

[lean otter]

I'd much rather stay on this side, this seems to be more understandable for me, when i read these i understand the math too

[lean otter]

I would like to lift the weight as much as i can off your shoulders, youve helped alot
Thats why i tried to figure most of it out on my own but that didnt seem to solve anything, is there any chance that i can get a translation of these main functions to code too?

[north raven]

do you know what min and max are?

[lean otter]

yes

min(30. 80) outputs 30

[north raven]

i dont see why you aren't able to translate the rest into code with that

[lean otter]

let me tell you what i dont understand

as far as i understood, dmgdensity is the func name, x is the arg, but what is that v floating there?
ik its the density enchantment level but is it a argument, is it part of the name, what is it?

[north raven]

it's just part of the name

like

def dmg_density_V(x):
  ...

mathematicians do that sometimes

[lean otter]

oh yea it was confusing
all 3 words had different sizes and places

[north raven]

You can think about $\mathrm{dmg}\text{density V}(x)$ as the damage function for density V and $\mathrm{dmg}\text{breach IV}(x)$ as the damage function for breach IV

[lean otter]

yea im trying to turn them into code

[lean otter]

is ther supposed to be a minus or something after d(x) * 0.36? seems like something between d(x) * 0.36 and the opening bracket next to it is missing

[lean otter]

a = d(x) x 0.36
b = 1 - 0.01
c = min(80, max(16, 80 - d(x))

I dont understand how to combine these
this is the simplified density one

[north raven]

oh yeah there looks like a missing bracket

[lean otter]

0.01 and min are connected
idk how that part works its like 0.01min()

[north raven]

d(x) * 0.36 * (1 - 0.01 * min(80, max(16, 80 - d(x)) ) )

[north raven]

it just means 0.01 times min(...)

Like how e.g. 5d(x) is the same as 5 * d(x)

[lean otter]

yea but there one no * in 2 places, is that intentional and how math works?

[north raven]

?

[lean otter]

nvm

[lean otter]

m(x) * 0.36 * (1 - 0.01 * max(0, min(80, max(16, 80 - m(x))) - 0.6 ))
is this correct for the breach one?

[north raven]

looks like it is

[lean otter]

intresting

lets do a final clean up and get this over with 😄

for a standard unenchanted mace, the weapon damage (excluding base damage of 6) can be represented the piecewise function
$$m(x)=\begin{cases}4x&0<x\leq3\6+2x&3<x\leq8\14+x&8<x\end{cases}$$
and similarly for a density V mace, the weapon damage (excluding base damage of 6) is
$$d(x) = \begin{cases}4x+2.5x&0<x\leq3\6+2x+2.5x&3<x\leq8\14+x+2.5x&8<x\end{cases}$$

where $x$ is the height of the blocks fallen.

Note that when $x < 1.5$, smash attack doesn't occur but we can just ignore that.

[flat frigate]

i.8.i
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[lean otter]

def d(x):
  if 0 < x and x <= 3:
    return 4 * x + 2.5 * x
  elif 3 < x and x <= 8:
    return 6 + 2 * x + 2.5 * x
  elif 8 < x:
    return 14 + x + 2.5 * x
  else: 
    return None # function is not defined for any other case

def m(x):
  if 0 < x and x <= 3:
    return 4 * x
  elif 3 < x and x <= 8:
    return 6 + 2 * x
  elif 8 < x:
    return 14 + x
  else:
    return None

def dmg_density_v(x):
  return d(x) * 0.36 * (1 - 0.01 * min(80, max(16, 80 - d(x)))

def dmg_breach_iv(x):
  return m(x) * 0.36 * (1 - 0.01 * max(0, min(80, max(16, 80 - m(x))) - 0.6))

this should be it, but one thing, i need a bit of an explanation of what each number is so i can attach them each to a variable

i only know what 0.36 is, which is the remaining of our 64% for the protection enchantment

@north raven sorry for ping, if you dont like ping tell me

[north raven]

yeah this looks right

[lean otter]

i need to assingn names to each variable

[north raven]

honestly i have no idea where each constant comes from i just plugged in numbers from the wiki you linked earlier

[lean otter]

so you use their formulas

[north raven]

yes

and did a little bit of simplification

[lean otter]

let me check and ill let you know if i need help

i am just realising if i locked in i couldve made the same formulas you made for me in the same time you did it for me but in code

lmao

[north raven]

well

[lean otter]

im trying to figure out what d and m funcs are

[north raven]

it's good being able to know how to translate between math and programming sometimes

[lean otter]

so basically

d is for calculating falling damage + density, but not taking armor into account

then dmgdensityv comes in and takes armor into account

am i correct?

[north raven]

d(x) is the weapon damage for density V (which has a 2.5 bonus damage per block)
m(x) is the ordinary weapon damage (unenchanted)

[north raven]

yes

[lean otter]

yes, i learnt how to do math now lol

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

nah bru hang on im codin

What do you call like the 0.36 in our formula?
its the oposite of 64%, what is it called? like the opposite, i want to name the variable

[north raven]

hmm

i guess you can call armour_protection_factor

[lean otter]

ik but

i dont get why its like in reverse

like the other half of 64%

its 0.36

Fuck. i just had to scroll 1 cm down to see this exists

and not have to spend 4 hours or more making the formula

atleast i learnt math

[north raven]

let $x$ be the damage amount. Protection will reduce the damage by 64%. This is the same as $x \times (1 - 64%) = 0.36x$

[north raven]

hopefully that explains why you multiply by 1 - 64%

[lean otter]

This formula

better image

i dont understand this

and this part

what is that weird line

@north raven

[north raven]

that is division

$\frac ab = a\div b$

[lean otter]

armor points / 5

[lean otter]

(4x weapon_damage) / (min(toughness, 20) / 8)

did i understand correctly?

[north raven]

that's a plus symbol on the denominator, not a division symbol

[lean otter]

apart from that, did i understand correctly?

thank you

[north raven]

yeah pretty much

that 'x' symbol is multiplication

just to be clear

not a variable named x

[lean otter]

yes i understand

thanks

[lean otter]

numbers like 1 and 0 and 20, 25, 4 are static in the formula? anything that dosent have a name is static and will never change or be dynamic right?

[north raven]

pretty much

note that i didn't use that form of the formula just now though, i used the simplified form they gave if you scroll up a little on the wiki

[lean otter]

damage_taken = weapon_damage * (1 - (max(0, (min(20, max(armor_points / 5, armor_points - (4 * weapon_damage) / (min(toughness, 20) + 8)))) / 25) - breach_level * 0.15)))

did i do it? 🥲

[north raven]

yeah bro im not interpreting that for you

my brain stack is limited to 3 brackets at once

[lean otter]

i got tangled in the brackets too

but it seems to be correct now

time to translate this last one i guess

damage_taken = damage * (1 - (min(20, max(armor_points / 5, armor_points - ((4 * damage) / (min(toughness, 20) + 8))))) / 25)

[north raven]

looks about right

imma go eat my breakfast now

if you have doubts, just google it

[lean otter]

ok bon apetite

a = min(20, max(armor_points / 5, armor_points - ((4 * damage) / min(toughness, 20) + 8))) / 25

density = damage * (1 - a)
breach = damage * (1 - (max(0, a - breach_level * 0.15)))

my brain is not braining anymore

but i think thats correct, just gotta code it tommorow after i wake up

thank you so much @north raven for helping, really appreciate it

!close

.close

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[jolly sail]

From this picture, I do not understand the "set G(x,y,z) to be identically equal to 1"

[jolly sail]

I have been staring at this page for long now, pls help

[quasi bison]

<@&268886789983436800> troll

[open wedge]

!noans

[safe radish]

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.

[sinful tangle]

Who?

[quasi bison]

youve been doing surface integrals right

[jolly sail]

yes im currently studying this topic

[exotic anvil]

@sinful tangle don't troll in help channels. We keep logs of deleted messages.

[quasi bison]

yeah so to get just the area of a surface you simply integrate the constant function 1 over it

same as for a triple integral you'd integrate 1 to get the volume, or for a singlevar integral you could integrate 1 over a segment and get back its length

[jolly sail]

yes but I do not get how does moving the variable to the other side make G(x,y,z) to be 1

[quasi bison]

it doesnt

we are not moving anything anywhere

all we are saying is, the area of a surface $S$ is $\iint_S 1 \dd{S}$. that's it!

[flat frigate]

Ann

[jolly sail]

so the equation z = sqrt(10-x^2) is not the consequence of making G(x,y,z) to be 1?

from the statement in pic

[quasi bison]

it is in fact not the consequence of that at all

[jolly sail]

WHATTTTTTTTTTTT

then hold on

pls hold

look at number 4), why is it not set to 1 then

why they plugging G(x,y, f3(x,y)) into G(x,y,z) = xyz?

why not make G(x,y,z) = 1 in the first place

[quasi bison]

because it says to integrate G(x,y,z) = xyz

not to find the area of any surface!

it says explicitly what to integrate!

[jolly sail]

fahhh ur right

ahhhhhhh

but these things are actually just stepping stones for my real problem

this question asks me to integrate right

not to find surface area

yes or no @quasi bison I will figure this out again alone after ur confirmation

[quasi bison]

yes, it asks you to integrate and it tells you what function to integrate

[jolly sail]

tysm 👍

.solved

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

need help on part b please

[lean otter]

accidentally cropped it out but its the second question

pretty axiomatic

but anyway

[hidden parcel]

what is the probability that alex is on team a

or b

[lean otter]

idk tbh bro

[hidden parcel]

if there are 10 kids

and 5 are put on each team

whats the probability that any kid is placed on team a?

[lean otter]

50%?

Idek

[hidden parcel]

yeah

[lean otter]

1/2

[hidden parcel]

b/c there are 5 kids each with an equally likely chance of being on team a (or b.)

[lean otter]

but i dont get how to calulate that via counting techniques

[hidden parcel]

Pnaive(a) is # favorable outcomes for a / length of sample space

[hidden parcel]

what is the length of our sample space

[lean otter]

10!/(5! · 5!)

[hidden parcel]

no?

you overcounted

[lean otter]

the thing is are we supposed to distribute the kids into each five group at once or what

[hidden parcel]

once you pick for team a you dont need to count for team b

[lean otter]

i dont get it

how is the counting process here

@hidden parcel

[hidden parcel]

your sample space is gonna be the number of possible outcomes for team a

because you dont need to count for team b once you've chosen for team a

[lean otter]

Why

i dont get it

[hidden parcel]

because once you've chosen team a team b is predetermined

if you have 20 people and someone tells you to split them into groups of 10

after you choose the first 10 you dont need to count for the 2nd 10

does that make a little sense

[lean otter]

But im putting them into two groups

[hidden parcel]

yes but because order doesnt matter

once youve picked the first group the 2nd group is already predetermined

[quasi bison]

once you decided who gets to be team red, everybody else is auto assigned to team blue

[lean otter]

But its still 2 groups though

[quasi bison]

so what.

[hidden parcel]

yeah but in terms of the length of your sample space

you dont need to account for the 2nd group

[lean otter]

But thats if we were looking at one group at a time or something

but I thought they wanted for the 3 groups

i mean 2

[hidden parcel]

it doesnt matter

[lean otter]

i think im not understanding their question in the first place, can you please explain it to me

maybe I’ll understand it

[hidden parcel]

You have 10 kids who want to play 5v5 soccer, so you split them into 2 groups where each grouping is equally likely

i dont know if that really helps lol

[lean otter]

okay i see so the sample space is all possible outcomes of the splitting

but like what counting technique do i need here

like i would say premutation of the 10 kids into a group of 5 · 2

[hidden parcel]

How many ways can you pick 5 from a group of 10

[lean otter]

but order doesnt matter so / 2!

so (P(10,2)/2!)*2

but that’s wrong pretty sure

yo

[hidden parcel]

P(10, 2)?

[lean otter]

i mean 5

mb

[hidden parcel]

why is that wrong

[lean otter]

(P(10,5)/5!)*2

[hidden parcel]

huh

[hidden parcel]

this is what you had before

which was wrong

[lean otter]

But why

[hidden parcel]

you're picking 5 from 10, why are you dividing by 5! again?

[lean otter]

to map to a single set of each duplicated one

[hidden parcel]

nCk already accounts for overcounting by k!

[lean otter]

Because permutation assumes order matters so

[hidden parcel]

does order matter?

[queen ingot]

which part of the question are you working on?

[lean otter]

yeah but i derived the combination

[lean otter]

no?

[hidden parcel]

right

[hidden parcel]

wait why not just use nCk

[lean otter]

because i hate that goofy notation

am i right though

[hidden parcel]

just use the combination formula

lol

[lean otter]

then * 2?

[hidden parcel]

u dont need to account for group b

[lean otter]

but then that way you account for the outcomes of splitting them into 1 group

i dont understand

[hidden parcel]

you're overcounting

If i give you 10 cards and i tell you to choose 5

I dont need to worry about how the other 5 were chosen

thats determined when u picked the 5 i told you to pick

[queen ingot]

you're doing part A right?

[lean otter]

both a and b i guess

[queen ingot]

isn't this correct?

[hidden parcel]

Oh wait

[lean otter]

but thats just one group tho

im so confused bro i don’t understand why im overcounting

[hidden parcel]

that is right

My bad

[lean otter]

its okay but even i forgot why i stopped there 💀

[hidden parcel]

😭

[lean otter]

broooooo

[hidden parcel]

ok so now

have u learned LOTP

[somber cape]

im with you im terrible with counting problems

the sample space is 10!?

[lean otter]

Counting is so freakin complicated

[somber cape]

fr, I can do everything in my probability class but combinatorics

[lean otter]

whats that

[hidden parcel]

law of total probability

[lean otter]

nope

[hidden parcel]

it might help here but its not the counting approach

[somber cape]

I think part a is 10! right?

[lean otter]

well the sample space is all the possible outcomes from an experiment

[somber cape]

maybe not though 😭

right

[hidden parcel]

unfort not

[lean otter]

so that would be

[somber cape]

we have two teams

10 kids

oh

10! * 2?

[hidden parcel]

ill write it in eqn form then explain it

[lean otter]

all the possible combinations of thr arrangements of the kids in the 2 groups

[hidden parcel]

no..

10! is overcounting, once you've picked the first team you dont need to worry about the 2nd team

[lean otter]

so im thinking the first arrangement + another remaining one = sample space

[hidden parcel]

also order of kids doenst matter

[somber cape]

I was doing it with order

[hidden parcel]

you were right with 10!/(5!*5!)

[somber cape]

hmm why doesnt order of kids not matter?

are we not treating each kid indivisually?

[astral glacier]

Me and you being in a team is the same as you and me being in a team

[hidden parcel]

LOTP: $P(A) = \Sigma P(B_i)P(A|B_i)$

[lean otter]

not even 10! Because you’re arranging in a group of 5. Also * 2 would make it 4 groups of 5 I think which is off

[somber cape]

oo I see

[hidden parcel]

if you have an event a which can be broken up into subevents you can use hte law of total probability to find the total p

[lean otter]

you mean this thing

[hidden parcel]

So in this case, our event a is that jose is on the same team as alex

[hidden parcel]

no

my dumbass wrote the equation wrong

[flat frigate]

uni

[lean otter]

because theyre just in the team, there’s no special property about them being in that team except be there

[somber cape]

so were looking at a ordered pairs of sets ({},{}) as our sample space?

[queen ingot]

ye i believe so

[lean otter]

Thats the thing idek

[somber cape]

ok I see

[lean otter]

how am I supposed to arrange them

[queen ingot]

are you asking about part A or part B?

[lean otter]

both at this point

[queen ingot]

sorry i was just away from the conversation for a minute

[lean otter]

its okay

[queen ingot]

i'm pretty sure you got A right, 10! / 5! 5!

[lean otter]

but why did i not multiply by 2

like why is that rigjt

imagine forgetting your own work

[fickle yoke]

what's the problem?

[queen ingot]

choose 5 players to be on the first team

you have now chosen the teams

10 Choose 5

[lean otter]

But bro its like the sample space = { (5 kids ) , ( 5 kids) }

right

[somber cape]

its ({5 kids}, {5 kids}) are the elements

[hidden parcel]

once you've chosen the first set the 2nd set is created automatically

Idk if analogies help

[lean otter]

@hidden parcel is this right

[hidden parcel]

But lets say i were to ask you to split up your favorite artists songs into two categories

[hidden parcel]

yeah

[hidden parcel]

Once you've picked your favorite 3, the other set is already created

[somber cape]

mmmm

now im confused 😭

[lean otter]

the sample space is supposed to be a set of sequences not a sequence of sets

[fickle yoke]

this?

[lean otter]

Yes

[fickle yoke]

which part confuses u

[queen ingot]

shouldn't we finish part A before moving on to part B?

[lean otter]

okay so see why I multiplied by two

[hidden parcel]

yes but you dont need to

[lean otter]

but im only creating one sequence

what about the second one

[hidden parcel]

its created once youve created the first one

[lean otter]

Wait

[queen ingot]

sets, you mean

rather than sequences

[fickle yoke]

u fix one person in one group then we place jose in the group of his friend

[queen ingot]

well you can count sequences and then divide by the ways to order a sequences

[hidden parcel]

Can we do one question at a time pls

[lean otter]

wait this is confusing so i kinda get what youre saying but for each random combination in sequence 1 there exists another 1 in sequence 2, like I get what order is in the first sequence works for the second but theres still 2 copies of all that

[somber cape]

yeah the sample space elements are ({}, {})

[fickle yoke]

arent we talking about sec question?

[lean otter]

1

[hidden parcel]

no

[queen ingot]

part A

[fickle yoke]

size of sample space?

[queen ingot]

yeah

[fickle yoke]

u choose 5 of 10 people to go to team A then the rest will be chosen themselves to go to the other team

easy

[lean otter]

no its {(),()}

Set ⇒ { some elements }

Sequence ⇒ ( some elements )

Sample space ⇒ a set of all possible outcomes ∴ { elements of all possible outcomes }

The outcomes are represented via sequences () , ∴ sample space = { (), () }

[lean otter]

Yes

[somber cape]

oh sorry I see where your confused with my notation

im saying

[lean otter]

I don’t get the choosing themselves thing

[fickle yoke]

@lean otter

[somber cape]

the sample space elements are of the form ({}, {})

so we have { ({},{}), ... } as the sample space

[hidden parcel]

im tryna think of an example that makes sense

Wait this might help

[fickle yoke]

look if u choose 5 person C(10,5) the rest will be assigned to the group B

[hidden parcel]

Imagine someone gives you a list of 100 songs, and they ask you to make a playlist with some of those songs

[lean otter]

ohh but why are you adding a set notation inside the ()

[lean otter]

okay

[queen ingot]

because the teams are sets

the teams are unordered

[fickle yoke]

so the whole answer is u just need to choose 5 ppl for the group A

[hidden parcel]

You pick 15 songs for the playlists, now you have the space [{playlist}, {not playlist}]

Once you've picked the songs for the playlist, you dont need to pick the songs for {not playlist} do you?

[queen ingot]

too many cooks, i'm out

[lean otter]

yea true,

[lean otter]

no

[hidden parcel]

Its the same thing

[fickle yoke]

bro what u talking about

[lean otter]

but if were talking about making 2 playlists that’s a different story