help-10

[knotty crow]

pretty easy to solve and it determines the answer

[arctic granite]

but I would have to factorise to find the solutions, wouldn't I ?

[knotty crow]

ah sorry, it says x > 0, mb

[arctic granite]

yeah

[obtuse pebble]

@arctic granite Has your question been resolved?

[brazen viper]

You might be able to make something using Vieta's formula

The sum of the roots is equal to (-a) in this case.

[obtuse pebble]

@arctic granite Has your question been resolved?

[arctic granite]

Actually the solution is very elegant

suprisingly, if you take -x-2 to RHS

and sketch the graphs

[brazen viper]

oh, that is really nice

[arctic granite]

regardless of the 'a', there would be just one positive x-value

[obtuse pebble]

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[spiral yoke]

i need help

plz

i suck at math

[tall tusk]

a more generalized approach is to find the derivative and complete the square to see when the function starts increasing or decreasing

[tall tusk]

this is more or less a coincidence

or u can complete the cube and look for the discriminant

just two thoughts

[obtuse pebble]

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[rare oak]

Im pretty sure this is right, but just wanna double check.

[buoyant musk]

6th grade type sho

shi*\

[rare oak]

well

its

geometry and algebra

but if you can help I would be thankful

Can anyone help?

<@&286206848099549185>

[obtuse pebble]

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[rare oak]

.close

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[silent imp]

https://gyazo.com/f22ee57fe3f875f72a812c469a583854

[silent imp]

how is this wrong!

grrr so angry!

[cold thistle]

Is this in calculus or before calc?

[silent imp]

this is calculus

[silent imp]

why this rong

[cold thistle]

Cool so I assume you've learned about using derivatives to find critical points

[silent imp]

yes yes

is it wrong because its appraoching 0

approaching

[cold thistle]

,w critical points of f(x) = 3/(x-5)

[warm shale]

Results provided by WolframAlpha

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

Requested by lexitorius#4749

[silent imp]

why

[cold thistle]

hmm

Because x=0 is a horizontal asymptote

This function is never equal to zero

[silent imp]

at 5 it does

wait no

it errors at 5

so it cant = 5

[cold thistle]

Let's take the derivative

[silent imp]

ohhhhhhhhh oops wait lemme do that

[silent imp]

ok i got -3/(x-5)^2

[cold thistle]

Good

Now we do run into the same problem here where it never equals zero

[silent imp]

ok we should have a local max yes?

[cold thistle]

Due to its asymptotic behavior I'm not sure

[silent imp]

wait

[cold thistle]

We can however input arbitrary values into the derivative on either side of the discontinuity and see if they're positive or negative

[silent imp]

i got negative for both sides

[cold thistle]

^

[silent imp]

so it never increases

[cold thistle]

That's what you want

Exactly

[silent imp]

oh

i see ty

[obtuse pebble]

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[obtuse pebble]

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[hushed gust]

Hi guys! A bitt stuck on question iii here. Just a bit lost

[hushed gust]

So far I have found the theta for i which is 63.4 degrees using sincostan, and I found the equation for the line which is y = -2x + 240

But I'm just a bit stuck on how my thought process should be for iii. I know I can find the total area of the triangle

The area of the section of the house is 1/2 x 2.4 x 1.2 which is 1.44 meter^2

I'm just kinda lost on how to determine the expression I need to work on

I think I've done something wrong. As the area of the rectangle (trunk) differentiates to -4x which doesn't make sense as I would need to equal the derivative to 0 to find the maximum area

I assumed that the height is 2x and the width of trunk to be x

I tried forming an expression that gives the area of the trunk as a function. I somehow got a negative value for x after differentiating.

[obtuse pebble]

@hushed gust Has your question been resolved?

[obtuse pebble]

@hushed gust Has your question been resolved?

[obtuse pebble]

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[pseudo hatch]

I’m not sure about this is one bc I thought it was d

[obtuse pebble]

@pseudo hatch Has your question been resolved?

[pseudo hatch]

<@&286206848099549185>

[pliant pond]

it is b

its not continuous at 4 bc there is a hole at x = 4

[pseudo hatch]

Ok thanks

.close

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[nocturne karma]

hello I need help

[nocturne karma]

I’m doing partial fraction integrals right now but I have one that’s improper

It’s the integral of x^3-x+3 / x^2 + x - 2

The degree of the numerator is greater than the denominator

[obtuse pebble]

@nocturne karma Has your question been resolved?

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<@&286206848099549185>

.close

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[onyx prairie]

I’m not sure on how to interpret this table and where to start

[onyx prairie]

<@&286206848099549185>

[obtuse pebble]

@onyx prairie Has your question been resolved?

[obtuse pebble]

@onyx prairie Has your question been resolved?

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.close

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[old edge]

I'm trying to understand the limitations I should put on a bipartite graph G such that the complement of G is also bipartite.

[old edge]

I couldn't make of anything since it doesn't seem like the complement of any bipartite graph with more than 2 vertices will be bipartite given that the 3rd vertex will always have to connect to one of the two original vertices

in other words, a triangle can't make a bipartite hence I don't see how it's possible with bipartite graphs w/ more than 2 vertices.

[twin sapphire]

what do you mean by complement

just to be sure

but if its the graph with edge set E' such that (V,E U E') is a fully connected graph

i think its very hard to have some general result about this

other than, the complement graph can be mmany many things

but not bipartite i think

[obtuse pebble]

@old edge Has your question been resolved?

[old edge]

Yes that's what I meant by complement. This is one answer I've come across, although I'm having a hard time understanding (K2 U K1) paired with P3 and C4 paired 2K2 could be valid parings.

[twin sapphire]

look at the adjacency matrix

i dont even know these notations

but yeah there are a few

that have the property

oh yeah their argument is actually very good

[obtuse pebble]

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[mighty temple]

with

ok

what class

[supple glade]

6th

[mighty temple]

ok

what’s the problems

jus send the problems i can try to help you out

[supple glade]

@mighty temple I'd suggest u stay as far away as possible from this troll

[mighty temple]

just send the problem and i’ll see if it’s a troll

just get the question and put it in the chat

i don’t give a shit where it comes from

ok

just dividing by decimals?

ok

so what i would do is make a box

graph

and something like this is what it should look like

say it’s 7 divided by 19.76

i’ll send a picture

i’m giving an example

that would be for multiplying after to check your work

just set it up now so you don’t have to later

what i would do is divide like you would normally do

except you have to keep your decimal points in place or it won’t work

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[abstract willow]

So basically I'm stuck on getting rid of the square root and the exponent under the square root

[meager yew]

i got x is 23

[abstract willow]

x is going to have 2 different answers

[meager yew]

i dont know about the second one but i hope my first one is correct

i can send work if you wish

[abstract willow]

yes please

[meager yew]

sorry for the poor legibility

here

i hope that is helpful

@abstract willow

[abstract willow]

for some reason its having trouble downloading :/

[meager yew]

oh im sorry

[abstract willow]

nevermind I got it

[meager yew]

i hope its helpful

[abstract willow]

how did you get rid of ^3?

[meager yew]

cube rooted it

[abstract willow]

oh okay thank you

[meager yew]

did it help?

[violet sentinel]

I think you're missing on the RHS. Wouldn't you need to have $64^4$ as well?

[warm shale]

MellowDramaLlama

[meager yew]

oh i think i did something wrong sorry

[violet sentinel]

but the answer is still correct 🙂

[meager yew]

im sorry i dont get what i did wrong

[violet sentinel]

$\sqrt[4]{(4x + 164)^3} + 36 = 100\\$
$\sqrt[4]{(4x + 164)^3} = 64\\$
$(\sqrt[4]{(4x + 164)^3})^4 = 64^4\\$
$(4x + 164)^3 = 64^4\\$
$4x + 164 = (64^4)^{\frac{1}{3}}\\$
$4x + 164 = (64^{\frac{1}{3}})^4\\$
$4x + 164 = 4^4\\$
$4x + 164 = 256\\$
$4x = 92\\$
$x = 23\\$

[warm shale]

MellowDramaLlama

[meager yew]

yes i did that however i got 2^(24/8) = 2^8 = 256

[violet sentinel]

just from the notes I see here

you took one side to the 4th but not the other

that's all I was saying

[meager yew]

ohh okay sorry

😅

[abstract willow]

these are the notes we took in class but im still confused on how to get 2 answers for x

[violet sentinel]

Oh i See. Yeah it's 2 answers if you take an even root

if it's odd it's only 1

[violet sentinel]

so like in this, we take a cube root

which is an odd power

[abstract willow]

ohhh i see thank you

.close

[obtuse pebble]

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[mighty ether]

i'm a bit confused with the vector i've circled in red

[mighty ether]

because Y appears in the place of the x component, i'm not sure what that indicates?

[kind hawk]

well that at the point (3,1) for example you get the vector (2*1, 3)

[mighty ether]

and it looks like that? (black arrow)

[kind hawk]

no

do you know what vector fields are

[mighty ether]

i do but I might have forgotten, i probably need to practice this more. I'm only drawing one point (the one you said before)

[kind hawk]

at the point (3,1) you attach a vector (2,3)

in general at the point (x,y) you attach a vector (2y,x)

[mighty ether]

i thought that was what I did? the initial point of the vector and the final point is what you've said

[kind hawk]

the vector you attached is (-2, 2)

the vector (2,3) goes 2 units to the right and 3 units up

and you need to attach it to (3,1), aka its initial point needs to be (3,1)

https://i.imgur.com/jq5sHlD.png

[mighty ether]

like that?

[kind hawk]

yes

[mighty ether]

and would this be the graph of the vector field overall?

[kind hawk]

no

how does the arrow at (3,1) look even close to what you drew

[mighty ether]

wth i think my lecturer said that this was the graph though?

[kind hawk]

they made a mistake

maybe typo somewhere, no clue

https://i.imgur.com/ujGrvzO.png

[mighty ether]

hmm okay

I'll email them about it

[kind hawk]

https://i.imgur.com/Y6qwY4Q.png

I assume they meant (2y, -x)

[mighty ether]

hmm okay

thanks for your help

[obtuse pebble]

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[obtuse pebble]

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[tepid eagle]

Hi, I have a doubt. I can't remember how to solve this type of easy problem.

I have to find if the Domain and the Codomain are limited or unlimited.
I have also to determine the lower and the upper extreme, indicating if they're the maximum and the minimum of the function.

[tepid eagle]

here's the graphic.

I found the Domain and the Codomain yet

Dom: x< -2 V -2 < x < 2

Codom: R

Now I can't remember which is the lower extreme. The upper is 2, but the lower is -∞ ?

[daring rock]

My terminology might be a little different.

Do you mean you're looking for the global maximum and global minimum of the function?

In other words, the greatest output and least output from the function?

[tepid eagle]

yes, I have to find them. Sorry but I have translated badly.

[daring rock]

Wait

The greatest and least x, or the greatest and least y?

[tepid eagle]

x

[daring rock]

Ah okay

[lusty veldt]

x∈(-∞; -2)U(-2; 2)

[daring rock]

I mean, yeah, it looks like there is no lower extreme, and the upper extreme is 2

[tepid eagle]

yes, but the -2 isn't included in the function

[lusty veldt]

it doesn`t matter

and u also can`t say that upper extreme is 2

it also not included

[daring rock]

It really depends the specific definition of 'extreme'. I think it's not really clear.

[tepid eagle]

ah ok, fine. So the greatest output is 2 and the least output doesn't exist in R?
So 2 isn't the maximum of the function, but is the greatest output.

[daring rock]

2 is the upper bound of the input

All of the inputs for which the function is defined are less than 2

[tepid eagle]

yes. I'm italian and we use another lexicon, so I messed up with the terminology.

[lusty veldt]

i`d say that this function has no min and max

[tepid eagle]

yes because 2 isn't included

and there's no lower bound

[daring rock]

Yeah, generally I would say that 2 is a supremum, not a maximum

I just didn't know what is meant by "extreme"

[tepid eagle]

ah ok, in italian we say "massimo", in english is supremum. Ok thanks

[tepid eagle]

is the upper bound

[daring rock]

Supremum means it's greater than everything in the set, but it's not necessarily included in the set

[tepid eagle]

ah ok

perfect

thank u very much

[daring rock]

👍

[obtuse pebble]

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[bold siren]

Hi I would like to know how to do 11a thank you

[plain stag]

Your setup for the 4th week needs a little adjusting

That tells you the amount of the bonus received for that week, but not the total amount accumulated

150 is the sum of the first 4 weeks' rewards

[bold siren]

Am I on the right track?

[plain stag]

You seem to have lost a 1 on the last line

[bold siren]

Oh 😂

[plain stag]

Also, it looks like your use of r has changed

Your initial terms seemed to represent a geometric sequence with ratio (1-r)

Yet your updated work has ratio r

It's not necessarily wrong but be careful

[bold siren]

so I can choose either use ratio or not to use ratio to calculate it right ?

to be consistent in order to get the right answer

[obtuse pebble]

@bold siren Has your question been resolved?

[obtuse pebble]

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[raven carbon]

could anyone give a hand on this? I mean i know how the unit vector is made but adding "t" into there kinda throws me off. Not entirely sure how to calculate the magnitude, and whether I need to calculate the magnitude at all

[knotty crow]

find magnitude of unit vector a (hat) in terms of t and make it equal 1

[obtuse pebble]

@raven carbon Has your question been resolved?

[raven carbon]

man idek what i'm doing somehow i'm getting t = sqrt(1/90)

[knotty crow]

what's your length of a (hat)

(in terms of t)

[raven carbon]

90t^2 ?

i've definitely got it wrong wtf am i even doing

[knotty crow]

should be sqrt( 2t^2 )

[raven carbon]

how'd you get that?

oh shit wait i got it

sorry you've been typing so long lmfao

[warm shale]

Modus

[raven carbon]

yeah

for some reason i decided to take the denominator out and that completely messed it all up

[knotty crow]

now:
$$\sqrt{2t^2}=1$$

[warm shale]

Modus

[raven carbon]

yeah

1/sqrt(2) = sqrt(2)/2

ty for your help man

[knotty crow]

+/-

[raven carbon]

ye

.close

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[rare shore]

how do u know which values are right? help please ;-;

[faint prism]

L: (x-3)(x-2)>=0 . R:(x-1)(x+6)>=0. Make a form to show when each side is negative, positive and equals to zero.

[pure verge]

Yep yep. Find the set of x for which x >=0 for each of these two cases, then take the intersection of these two sets.

I think you have already found out that for x^2 - 5x + 6 >=0, x ∈ (-∞, 2]∪[3, ∞) and for x^2 + 5x - 6, x ∈ (-∞, -6]∪[1, ∞)

[obtuse pebble]

@rare shore Has your question been resolved?

[rare shore]

@pure verge @faint prism well i got these values at the bottom but idk what to do with them

it’s all X >= the value ;-;

i don’t understand sorry 😔

[pure verge]

think about it one more time

[faint prism]

You make a form and use dot-lines for negative, line for positive, and a zero for zeros.

[pure verge]

just consider x^2 - 5x + 6 first

[rare shore]

oh so it’s greater than zero before 2 and after 3?

[pure verge]

yes

including these two values

[rare shore]

i don’t know what to do with this info tho ;-;

cause there’s a second graph

[pure verge]

well

do you know the domain for the other graph

[rare shore]

oh wait a second

my graphs are like this?

[pure verge]

uh

not these

[rare shore]

did i do the graphs completely wrong

OH

IM AN IDIOT

NEVERMIND

sorry

[pure verge]

i meant the two cases you considered for |5x- 6|

[rare shore]

i know what to do

yeah i was just supposed to do one graph not two of those separately

like draw the graph by getting all the numbers to one side right??

[pure verge]

i...kinda lost you there

[rare shore]

like uh

instead of drawing a graph for x^2 and |5x-6|

i draw a graph for this instead

and the other one

[pure verge]

yes

yes

[rare shore]

yeah sorry i got it thank you!!

[pure verge]

then consider the domain of each graph, then take the intersection of both sets

[rare shore]

got it thanks!

.close

[obtuse pebble]

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[timid silo]

While visiting Newfoundland, Ray notices that that the water level at a town dock
changes during the day as the tides come in and go out. Marking on one of the piles
supporting the dock show a high tide of 3.3 m at 6:30 am., a low tide of 0.7 m at 12:40
p.m., and a high tide again at 6.50 pm.
a) Estimate the period of the fluctuations in the water level at the town dock.
b) Estimate the amplitude of the pattern.
c) Sketch the function.

[timid silo]

Here is my current work

I dont think it is correct

Need some explanation

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[ornate smelt]

Sry

[stable rain]

how do i eval the last 3

...

u alr know to not self insert

i do

[obtuse pebble]

@stable rain Has your question been resolved?

[obtuse pebble]

@stable rain Has your question been resolved?

[stable rain]

nvm

lemme ask smt else

.close

[obtuse pebble]

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[gentle ruin]

Real life examples of Single-dipped preferences, and when to expect bias?

[gentle ruin]

Have no trouble understanding the structure of a single-dipped preference and it's difference to single-peaked preference. However, it becomes a bit shady when I try to apply it in the real world. This is where some assistance would be appreciated

[obtuse pebble]

@gentle ruin Has your question been resolved?

[obtuse pebble]

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[lusty silo]

hy

[lusty silo]

hy

[obtuse pebble]

@lusty silo Has your question been resolved?

[lusty silo]

not here for guestions

[hoary mirage]

Wut?

[rotund rune]

so why did you claim the channel if not for asking 'guestions'

[obtuse pebble]

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[covert orchid]

question d and k

[alpine raven]

,rotate

[alpine raven]

and what is the question ? i dont understand this language

[covert orchid]

i need to find f^-1 (x)

the invertible function

[alpine raven]

ok so what have you tried first ? what do you know about invertible function ?

[covert orchid]

we need do to 3 steps

[alpine raven]

and what are the steps ?

[alpine raven]

well yea if you want
now how do you apply this to your cases ?

[covert orchid]

i dont understand the third step and the outcome

so x = y^2 - 4y + 6

then i need to find y

[alpine raven]

yes

[covert orchid]

so i have -y^2 + 4y = 6 - x

what do i need to do know

[alpine raven]

well, finding y ?

[covert orchid]

i know but how

sqr?

[alpine raven]

there is a lot of algebra method

[alpine raven]

not now

[covert orchid]

then what

[alpine raven]

try to find a way to have only y = something

now i cant say how since I would do your exercises kinda

[covert orchid]

idm

[alpine raven]

but a hint : maybe try factorisation or something else

[covert orchid]

factorisation y?

[alpine raven]

you have y^2 - 4y
you can try to factor this

your goal is to have y only

now this part is tricky

you need to see something

[covert orchid]

well i need a 👓 ig

[alpine raven]

but the goal is to have something like this : (y+a)^2 = ...

with a some constant we dont know yet

use this thing : (a+b)^2 = a^2 + 2ab + b^2

[covert orchid]

what is the outcome

[alpine raven]

did you try ?

[covert orchid]

yeah but i dont understand

im tired asf

[alpine raven]

Dont give up

[covert orchid]

i prob will

gotta go to practice inna bit too

[alpine raven]

To summarize, you have :
y^2 -4y = x-6

and we want to have y alone

but we have two terms with y on the left

so it makes things complicated

[covert orchid]

its -y^2 right or does that dont matyer

not

matter

[alpine raven]

I multiply both sides by -1

so, we want to only have a term with one y on the left

[covert orchid]

yeah

[alpine raven]

since we have a quadratic

I thought about this formula :
a^2 + 2ab + b^2 = (a+b)^2

so we will have something that will look like this : (y+a)^2 = something

with a some constants we still dont know

but the thing is we have y^2 - 4y

the b^2 part of this is missing

so remember this trick : we will add "0" on both sides

in other words :
y^2 -4y + 4-4 = x-6+4-4

why 4 ? because if we look at our quadratic, we have y^2 -2*2
it looks like the start of the formula I just gave : a^2 - 2ab

now I have something I can factorize

y^2 - 4y + 4 = x-6 + 4 = x-2

and y^2 - 4y +4 = (y-2)^2

now i will sqrt both side to get rid of the square

but we will have two solutions

$$y-2 = \sqrt{x-2}$$ and $$y-2 = -\sqrt{x-2}$$

[warm shale]

Ｈｅｒｅｌｓ

[covert orchid]

ig thats a way

[alpine raven]

therefore : $y = f^{-1} (x) = \sqrt{x-2} +2$ because they said $x\geq 2$

[warm shale]

Ｈｅｒｅｌｓ

[covert orchid]

yeah

i hate maths

[alpine raven]

everybody does

but its beautiful, so we kinda like it too

[covert orchid]

no

it makes me tired

[alpine raven]

idk, maybe you want to do something that doesnt evolve maths

but you cant really escape it

[covert orchid]

i can

[alpine raven]

Yea, paying taxes and counting money doesnt involve maths, nice

Anyways

thats the way

[covert orchid]

Dying

But i only hate this theme

[alpine raven]

cool, so do you have any questions ?

I basically did everything at the end

[covert orchid]

nah its good u did more then needed

.close

[obtuse pebble]

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[timid silo]

We have a parabola like this. Why is it (-infinity, 0> in decreasing matter if the infinity is clearly going up?

[timid silo]

In decreasing shouldn't it be (+infinity, 0> as the infinity is going up?

[drifting badger]

When we talk about an interval like (-inf, 0> we are talking about the values in between these numbers on the x-axis. So the "-inf" in this case is to the left on the coordinate-system.

[timid silo]

So its about x not about y

Wow, so simple I'm dissapointed in myself

@drifting badger thank you for bothering about my goofy ass

Appreciate you

.close

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[wanton kraken]

how does it become a*cotg alpha

[silent otter]

does anyone know how to prove stuff like this? Im rly lost

[knotty crow]

tan = 1/cot

[wanton kraken]

oh

ty

.close

[obtuse pebble]

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[obtuse pebble]

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[sullen cradle]

hi i have a question about measures of positions in grouped data, when you do cf do you start from the lowest or just start from the bottom?

[sullen cradle]

just a simple question

<@&286206848099549185>

why does no one want to look at a basic question

https://media.discordapp.net/attachments/432717898843160597/938609313503674438/opa.gif

ima go to sleep

whoever has an answer just dm instead

goodnitf

.close

[obtuse pebble]

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[latent jasper]

Can someone help me with formulas

[latent jasper]

So I am struggling to keep track on combination problem and I need help finding them

I have a formula for different balls in different boxes where boxes can be empty, and for identical balls in different boxes where boxes can be empty and also for if they are not empty. I have a formula for different boxes in identical boxes too. But there are four cases I can't seem to find formula for

They are

Different n balls in different k boxes (no empty box)

Different n balls in identical k boxes (boxes can be empty)

Identical n balls in identical k boxes (No empty boxes)

Identical n balls in identical k boxes (boxes can be empty)

[craggy flame]

Hi, i'm confused. What are you counting? Let's try the first one: You have n different balls and k different boxes, do you need to count what?

[latent jasper]

No I am preparing for an exam

And when I was doing

[tall tusk]

yeh u worded it quite confusingly. The two fundamental principles of counting I think ur getting at are 1)The number of permutations of k types of objects, each type is identical and the ith type has ni
objects, is n!/n1!*n2!....nk! where n = n1 + n2 + ... + nk. and 2)The number of ways to choose r objects from n types of objects (each type of objects is identical and has at least r objects is r + n – 1Cr =(r+n-1 over r)

[latent jasper]

problem solving questions, I kinda felt lost and I kind of need guidance to check if I am doing right and I will definitely need that sort of help on the exam.

[latent jasper]

Lets say I have n different balls that I need to put in k different boxes where no boxes are allowed to empty. Can I then use sterling number like S(n,k)*k!?

[tall tusk]

yes but u have to multiply by k! by the sterling number

its the stirling number of the second kind

[latent jasper]

What about identical n balls in k identical boxes where boxes can be empty?

[craggy flame]

@tall tusk What is this problem counting? Oh, I got it. The "number of ways to partition a set of n elements into k nonempty subsets".

[tall tusk]

yes

[tall tusk]

and the second order sterling number is really just calculating it recursively

[latent jasper]

I already have a formula for that, what I need is the number of ways to partition a set of n identical elements into k subsets where subsets can be empty?

Wait this

the cardinality of the power set right?

No wait it is not because here I said identical elements whilst it is not for the power set

[tall tusk]

(n+k-1) C(k-1)

S(m,n) = S(m – 1,n – 1) + nS(m – 1,n). this is sterling number of the second kind

[latent jasper]

Is it defined recursively?

[tall tusk]

this is

lemme give u an example

[latent jasper]

What about this?

[tall tusk]

it's just a formula

for the question ur asked

[latent jasper]

But how do you use it?

[tall tusk]

u asked u questions. lemme explain the first

so what's S(3,1)

[latent jasper]

1

[tall tusk]

yes and S(3,2) is is 3

if we have S(3,1) and S(3,2)

we can recursively define S(4,2)

by the formula I gave you: S(4,2) = S(3,1) + 2 * S(3,2) = 1 + 2 * 3 = 7.

[tall tusk]

u just plug the number in???

lets say there are 4 boxes and 2 balls

[latent jasper]

but that formula is for different n balls in identical k boxes?

[tall tusk]

(2+4-1) C(4-1)

[tall tusk]

n identical balls in k boxes such that there may be any number of balls in each box

and can be empty box

and the recursive one is putting n objects in k boxes with no empty sets

[latent jasper]

are the boxes distinct or identical

or does it work for both?

[tall tusk]

wait

i think it's just k^n

since empty sets are allowed

so if u have n objects divindg into k subsets

empty sets allowed

the total ways would just be n^k

[latent jasper]

I think that is for when the balls are different because in this case

we think all the balls are the same so 3 balls in box 1 and 3 balls in box is the same combination

[tall tusk]

yeh it is for different

for same, the ways will be less

idk a formula for it

@viral blade

maybe he can help

[viral blade]

wat

identical balls in distinct boxes?

[tall tusk]

Yes

[viral blade]

stars and bars method

https://brilliant.org/wiki/integer-equations-star-and-bars/

[tall tusk]

Bruh I’m dumb

[viral blade]

lol

this is a pretty hard one to just figure out

if you don't already know it

you end up getting like (n+k-1) choose n

for n balls and k boxes

[tall tusk]

I knew it just didn’t realize it’s the same thing

[viral blade]

n^k is for distinguishable balls and distinguishable boxes

if both are indistinguishable you get https://en.wikipedia.org/wiki/Partition_function_(number_theory)

tl;dr it's very hard

i can't remember if there's a good way to do it when only boxes are distinguishable

[latent jasper]

under which title can i find it

[latent jasper]

There is one i found that is recursive but it apparently only works for non empty boxes

[viral blade]

for non-empty boxes you could try to calculate the distinguishable boxes case first

then divide by k!

since every arrangement where all boxes are non-empty for indistinguishable boxes there'll be k! ways to assign labels to the boxes

also if only 1 box is empty it's still ok

[obtuse pebble]

@latent jasper Has your question been resolved?

[obtuse pebble]

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[cedar lichen]

What have you tried

[cedar lichen]

#❓how-to-get-help

If you increase by 20 dB, the sound is 10x as loud

The rock concert is more than 20 dB louder than normal conversation, so how could it be less than 10x?

[tired summit]

Classic set theory question

[cedar lichen]

Normal conversation is 60 dB

80 dB is 20 more than 60

So 80 dB is 10x as loud as 60 dB

What if you go another 20 dB?

[tired summit]

Can be done easily considering the venn diagram

[cedar lichen]

This isn't their channel

Who said we were decreasing?

[tired summit]

Sorry I'm new to the server

[warm bough]

captain

can you call me for 1 sec pls

[cedar lichen]

Get your own channel

60 dB

Go up 20

Now youre at 80 dB

[vagrant mantle]

Real the how to get help section

[cedar lichen]

Go up another 20

What do you get?

I just want you to add 20 to 80

That's all

Yes

100 dB is 20 dB more than 80 dB

So 100 dB is 10x louder than 80 dB

And 80 dB is 10x louder than 60 dB

So how much louder is 100 dB than 60 dB?

I mean like how 80 dB is 10x louder than 60 dB

I'm looking for "100 dB is (something)x louder than 60 dB"

No

We know 80 dB is 10x louder than 60 dB

And 100 dB is 10x louder than 80 dB

No

No

100 dB is 10x louder than 80 dB

80 dB is 10x louder than 60 dB

If Jim was 10x faster than John, and John was 10x faster than Jake, how much faster is Jim than Jake?

No

Let's say Jake could go 1 m/s

If John is 10x faster, how fast could he go?

Yes

But how fast in m/s

Yeah

So how fast does he go in m/s

I gotta go, I'll be back in like 10 min

I'm back

If John runs at 10 m/s, and Jim is 10x faster, how fast does Jim run?

So if Jake runs at 1 m/s, how much faster is Jim?

I'm looking for (something)x faster

Jim runs at 100 m/s and Jake runs at 1 m/s, so how much faster is Jim

Yep

In short, if A is 10x B, and B is 10x C, then A is 100x C

So if 100 dB is 10x louder than 80 dB, and 80 dB is 10x louder than 60 dB, how much louder is 100 dB than 60 dB?

100 dB is 1000 times louder than 60 dB?

No

Decibels aren't linear so that doesn't work

Remember, if A is 10x B and B is 10x C, then A is 100x C

So if 100 dB is 10x louder than 80 dB, and 80 dB is 10x louder than 60 dB, how much louder is 100 dB than 60 dB?

Yes

100 dB is 100x louder than 60 dB

Yes

No

Decibels aren't linear

Let's go another 20 dB

120 dB is 10x louder than 100 dB

And 100 dB is 100x louder than 60 dB

So how much louder is 120 dB than 60 dB?

What's the answer in terms of "120 dB is (something)x louder than 60 dB"

Yes

That's your final answer

[obtuse pebble]

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[noble berry]

idk how to go about it

a chart??

[untold flax]

no, represent their ages algebraically

for example J for jerones age, K for keenan's age and L for Leitha's age

[noble berry]

so how do i go about the quetion?

a system with like, k=18-j, k=21-l?

[untold flax]

so we have 3 equations

J + K = 18

J + L = 19

K + L = 21

[noble berry]

yeah

[untold flax]

so if we have 2 equations with 2 unknowns we can solve it easily

we need to make sure K is one of the unknowns

if we get J in terms of L using the 2nd formula

we'd get J = 19 - L

so then (19-L) + K = 18
and K + L = 21

do you know how to go from here?

[noble berry]

do i solve same as how i solve other systems?

[untold flax]

yeah

nothing special about this oen

[noble berry]

alr, i think i can do that

k=10?

[untold flax]

yes

[noble berry]

nice, ty

[untold flax]

no

problem

:)

[noble berry]

.closese

.cloese

.close

[obtuse pebble]

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[timid silo]

how do you get from this top equation to the bottom

and also why is the -1 grouped with the x?

[knotty crow]

arg of z in the form z = x + yi is given by tan(y/x)

[knotty crow]

because it's Re(z) (real part)

[timid silo]

okay thank you

.close

[obtuse pebble]

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[hazy grove]

I wonder whether it is possible to define a graphical model that would find optimal parameters of y=ax+b+eps with an estimation of paramaters a, b, eps, their mu and sigma. The input is set of (mu_n, sigma_n) normal distributions. Normally when we have just set of x_n points it is relatively easy to estimate a, b, eps with bayesian network and for example NUTS solver. Can we however estimate those parameters when x_i isn't determined exactly but is somewhere in a normal distribution (mu_i, sigma_i)? I don't want to do monte carlo with selection of x_n from (mu_n, sigma_n). Can I construct a more general graphical network to solve this task?

[obtuse pebble]

@hazy grove Has your question been resolved?

[hazy grove]

hm

[obtuse pebble]

@hazy grove Has your question been resolved?

[hazy grove]

maybe solved by https://stats.stackexchange.com/a/418373?

[obtuse pebble]

@hazy grove Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Please help me to understand the difference between t and tau here?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

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[obtuse pebble]

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[golden sierra]

i tried inputting f(16) to f(2x+1) but i didnt get anything

or should i enter 16 into x

where the first function is

[daring rock]

What do you mean you didn't get anything?

[golden sierra]

i put it in and then said 2x+1=16

and then 2x=15 which is just 7.5

but i assumed thats not what its asking

[daring rock]

Sounds good to me

Well, that's not the answer to the question but it is the correct first step

Now you know in order for 2x + 1 = 16, x must be equal to 7.5

How does that help you find f(16) ?

[golden sierra]

u have to use 4x^2+4x and 7.5 is x?

[daring rock]

Right

Because if you take

Take $f(2x+1) = 4x^2 + 4x$, and substitute x=7.5, you get
$f(16) = 4(7.5)^2 + 4(7.5)$

[warm shale]

tatpoj

[golden sierra]

i just got 90.25

wait i did it wrong

255*

[daring rock]

👍

[golden sierra]

Thxsm for ur help

❤️

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[obtuse pebble]

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[dense pewter]

the sum of two integers is 10, and the sum of their squares is a minimum. Find the integer
all I really have is x+y = 10 and that x^2 + y^2 = a minimum but I'm stuck trying to figure out how to go on from here

[drifting wraith]

use one variable

[reef garnet]

you mean something like y=10-x?

[drifting wraith]

sure

then it's a parabola

[obtuse pebble]

@dense pewter Has your question been resolved?

[dense pewter]

but like what are the exact like steps to to find those integers?

[obtuse pebble]

@dense pewter Has your question been resolved?

[paper merlin]

Hey

So can i post a doubt here?

New to the server guide me lol

[obtuse pebble]

@dense pewter Has your question been resolved?

[obtuse pebble]

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[haughty drift]

Can someone help me with the 9?

I dont understand what I should do in this because I can only do it when I know the ratio

[teal turret]

does denominations mean bills

10 and 20 rupees bills?

[hollow willow]

Start with 10a + 20b = 800

[teal turret]

dont give answers

ye thats better

[obtuse pebble]

@haughty drift Has your question been resolved?

[obtuse pebble]

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[wet magnet]

how do i do this

[obtuse pebble]

@wet magnet Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[astral garnet]

this a really simple problem\

but I don't know how to do it

what would you do

with teh 2theta

right now I'm at cos2theta = 1/2

[supple glade]

Cos 60 degree is 1/2 so 2 theta = 60 theta = 30

[astral garnet]

is that the only answer

cause cosxx of 300 degrees

is also 1/2

[supple glade]

Yeah u can have multiple answers cuz it's a periodic function.. what's the issue?

[astral garnet]

I was just confused what the 2theta

was supposed to mean

what if the problem was like this]

I simplified it down

to

[supple glade]

when is cos theta 1/root 2?

[astral garnet]

|cos 1/2 theta| = rad2 / 2

[supple glade]

Just look for values of theta which give 1/root 2 or -1/root 2

[astral garnet]

what happened to the

1/2

infront of the theta

[astral garnet]

anyway for the posititive 1/root 2 i got 45 and 315

[supple glade]

And look for -ve 1/root 2 and all of those are ur answes

[astral garnet]

i got

135 and 225

so my answers are 45,315,135, and 225

how would you solve this

without a calculatort

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[astral crescent]

i need help on my home work

[robust crow]

Are you old enough to use discord ?? No offense

[astral crescent]

yes

[unique spear]

this is like

a kindergarten’s homework

[nova bane]

This is calculus level stuff

no 4d calculus

on a stick

[royal basin]

@astral crescent how old are you?

[astral crescent]

13

[unique spear]

oh yeah this is so hard bro

it’s calculus max level shit

[royal basin]

can we please not joke about the difficulty level of this worksheet

[robust crow]

Bear the age limit is 13 for a reason

There can be some bad stuff sometimes

Just ask your teacher

[royal basin]

anyway this seems to be about place value and translating numbers between english and numerals

[robust crow]

But while your here

Let’s just solve the question

For reference

[unique spear]

3 tens is 30
3 tenths is 0.03 right

[nova bane]

isnt 3 tenths 0.3?

since oneths dont exist

[robust crow]

3 tenths is 0.3

[unique spear]

oh yeah

yeah that makes sense

[robust crow]

Bear it would be a bit tedious to write out all the answers

Just use this to solve the questions

So for example

If it asks you to find the place value of some digit

so for example let’s use

5.0379

It asks you to find the value of 3

The first digit is Obed

Ones

The second one after the dots is tenths

Third one is hundredths

Fourth one is thousands

And etc

[royal basin]

and you should not do that anyway

[robust crow]

Why

[royal basin]

we don't give answers here

that goes both ways

[robust crow]

I get he’s undersheriff, but just give the man the answer

[royal basin]

you should not ask for answers

[robust crow]

underage*

[royal basin]

and you should not give answers

[robust crow]

I thought that was the point of these channels

To help people

[royal basin]

no, it is not

well

it is to help people

but it is not to just give answers

there is a difference between those

[robust crow]

I didn’t give him the answers

Just the way to find the answer

[nova bane]

its like giving a man a fish

sure he can eat for one day

but how about tomorrow

[robust crow]

Yes but if you teach you the man how to fish

Which is what I did

[royal basin]

it would be tedious to write out all the answers

thats what set me off

[robust crow]

Mb

I won’t give the answers next time

Just the way to find the answers

[astral crescent]

yall cant help i just put radum asurs

[nova bane]

you did?

[timid silo]

are you here to get answers to your homework, or to ask for help to learn how to do it on your own?

[obtuse pebble]

@astral crescent Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[novel knoll]

Put them on common denominator

[wild chasm]

how 😭

[novel knoll]

For 1st one you have 7 and 8 in denom

[wild chasm]

yes

[novel knoll]

So multiply 4/7 by 8 in num and denom

And 5/8 by 7 in num and denom

[wild chasm]

omg

yes

got it

ty ;-;

.close

[obtuse pebble]

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[obtuse pebble]

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[fleet gorge]

A coin is tossed then a Dice is rolled, then another coin is tossed and another dice is rolled. One possible outcome is H,5,T,1
In how many of the sequences do the 2 dice show the same number ?

[fleet gorge]

Could you pleasse help me

[royal basin]

have you made any progress thus far?

[fleet gorge]

i made a progress of knowwing there are 144 diffrent prmutations

[royal basin]

and how did you calculate that?

||2 * 6 * 2 * 6||, no doubt.

[fleet gorge]

yep

[royal basin]

well, a similar principle can be used to count the sequences where the dice values match

it's just that now for the second dice roll you have no choice

[fleet gorge]

so 6 2 1 *2?

6x2x1x2

?

[royal basin]

6 * 2 * 2, yes

[fleet gorge]

OMGGG ANN THABKS now i can do the rest, HEHEHEHEHEH QUANDALE DINGLE OUT

https://tenor.com/view/quandale-dingle-quandale-dingle-bignleton-gif-25683238

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[obtuse pebble]

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[mystic fiber]

Hi so i have this markov chain and want to calculate the steady state by hand

What should be my next step. I have a general idea but im not sure if it is correct

[royal basin]

you want to do this by HAND?

eugh.

so it's got 31 states, huh.

can you present it as a weighted directed graph maybe

perhaps that way it will be easier to see what is going on

[mystic fiber]

unfortunately i need to show algebraically

ive calculated through excel

[royal basin]

you are forced to solve a system of 31 equations in 31 variables algebraically?

what kind of maniac is your teacher