help-42

[reef island]

I have a TI-84!

[calm coral]

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[barren nymph]

can someone help me understand how the top one makes the bottom one?

[barren nymph]

I know you have to "expand" n! so its n(n-1)(n-2)! so the (n-2)! cancel out but what about the 2!

[velvet osprey]

it doesn't, the top thing equals n(n-1)/2

need more context!

[barren nymph]

v

i'm following a tutor video

[velvet osprey]

link video and timestamp.

[barren nymph]

its not on youtube

its those paid ones...

that comes with a book

[velvet osprey]

well fuck

[barren nymph]

is this not enough context or

because this is a stand alone

[velvet osprey]

well i can't really see what's being done in the vid

[barren nymph]

oh uh

so they rewrote the expansion to equal 1-3x +4x^2 ....

then they expanded (1+kx)^n to that

and now equating coefficients

this is the other bit and then the tutor just simplifies that expression for binomial into n(n-1)

somehow

[velvet osprey]

ok and what happens right after this?

scroll a few seconds forward

[barren nymph]

ping me when you respond

[velvet osprey]

@barren nymph ah but he multiplied both sides by 2 as well.

[barren nymph]

ah, because 2! is just 2 right?

[velvet osprey]

yes

[barren nymph]

ah I see

just one more quick question about this

I noticed they neglected the first term, why is that?

.close

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[lethal patio]

When i plug the integral into my calculator with the limits i get math error whys that?

And when i plug it into integralcalculator.com it also gives me a different value

[median oyster]

remember to change the bounds of integration if you haven't already

if you're plugging in 0 and 4 into logs, that'll give math errors

[lethal patio]

Wdym

What am i meant to change it to

Im given the bounds no?

[median oyster]

when you do a variable substitution you need to change the bounds to be in terms of the new variable

u is sqrt(x), and the original integral is from x=0 to x=4, so your new bounds should be u=0 to u=2

[lethal patio]

Ah ic

Nah but that still doesn’t change what i get tho

After doing the u sub i get the 1/3 on 5

Ln*

[lethal patio]

But if i try this way its wrong

But y would this not work? What’s wrong with this?

[median oyster]

what's the original function f exactly?

because your working on paper uses 1/(9-x)sqrt(x)

but you've put in 2/(9-x) into the website

[lethal patio]

O

Bruh mb

Plugged it in wrong

Aight ye ur right it works now

Thanks

after i get rid of the sqrt x why can i not then integrate it with ln tho?

[median oyster]

what do you mean by integrating it with ln

[lethal patio]

When i have 2 / 9 -x cant i move 2 outside the integration then do

[median oyster]

because the integral is with respect to u

not x

[lethal patio]

Ok

Get it now

Ty

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[barren nymph]

could someone explain what in the world they are doing ??

[hasty fiber]

for which step?

[barren nymph]

uh sorry, I realised didn't specify, I'm asking for when they rewrite the geometric series and write in that wacky fraction form

also soz for late reply

[hasty fiber]

$\sum_{k=0}^n r^k = \frac{1-r^{n+1}}{1-r}$

[potent lotus]

Steakanator

[hasty fiber]

this doesn't look familiar?

[barren nymph]

thats the equation to find a term in a geometric series...

[hasty fiber]

it's used to find the value of the series as a whole

[barren nymph]

wait no

its used to find the sum

yes yes my mistake

sorry

[hasty fiber]

in your question r = 1+x

[barren nymph]

and 1 is the first term

wait this is the thing were using right?

this is just a general term, not related to anything

but then what is that long line of n+1 c 1 and such

[autumn pollen]

Binomial expansion

[barren nymph]

that long line is only happening because the context is binomial right

if it were anything else it would just stay as (x+1)^(n+1)

[autumn pollen]

Uh I guess

Can you send the rest of the solution

[calm coral]

@barren nymph Has your question been resolved?

[barren nymph]

yes, sorry for late reply

ping me when you reply

[autumn pollen]

@barren nymph is this the end of it

There seems to be more

[barren nymph]

ok hold on

[autumn pollen]

Oh damn

That’s a pretty cool proof

[barren nymph]

Yes

Its very confusing to me a bit 😅

Because the bottom doesnt look like the tip but I assume its om for some reason

And idk how that is the coefficient of x^r

[calm coral]

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[eager acorn]

What should I do next?

[calm coral]

@eager acorn Has your question been resolved?

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@eager acorn Has your question been resolved?

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@eager acorn Has your question been resolved?

[hollow kestrel]

I would rewrite tan^2(u) as sin^2(u) / (1 - sin^2(u)) and then try to make it into a quadratic equation.

(a quadratic equation of sin(u))

[eager acorn]

I guess the question is wrong because when we put π/8 it doesn't give -1

[mighty plank]

yo can u help me from the 2nd last step

[modest pebble]

I tried the same tbh

but the fact is solving for sin(x) is unreal in terms of b^2 -4ac on the quadratic equation

@eager acorn

[meager moat]

did u not understand the condition?

[mighty plank]

i did not

[mighty plank]

i dont understand anything from the 2nd last step

[meager moat]

we get a new quadratic equation

and as per the conditions given

we want all real values

[mighty plank]

@meager moat

[meager moat]

create a new channel

this is already

in use

[mighty plank]

the thing that i dont understand in this quetions is why did the (m-4)(m-6) =< 0
resulted into 4=< m =< 6

can we talk in dms

[meager moat]

ya

[calm coral]

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[fossil kraken]

hi i need help with naive bayes assignment
Predict using Naive Bayes classifier for the following input attributes. Clearly show your computations and the classifier'sprediction. (i)x1 = 1, x2= 1, x3= 0

[fossil kraken]

is what i did correct or am i missing something ?

this is the full question

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[distant hinge]

How am I getting to the wrong answer here?

I get a = 2 and b = -8 when a is right b is wrong

x = -5/4

10 = a(4(-5/4) + 5) + b(-5/4)
10 = a(-5 + 5) + b(-5/4)
10 = -5/4b

this is what i do to try and get b

[weak rapids]

what a and b dude

[distant hinge]

to get rid of -5/4b would u not multiply 4/5 * 40/4?

partial fractions just

a/3x + b/4x + 5

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.close

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[white pawn]

i have to find the points (if any) at which the graph has a horizontal tangent line, i dont know how to start

[storm stirrup]

set the derivative equal to 0 and solve for x

[white pawn]

thank you

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[glad anvil]

how does one go about doing part c?

see its understandable

but for the injective one i dont get why you equate the x and y

surely calling them x and y implies theyre different

god youre right

screw functions 😢

my brain no understandy the funny symbol

🤓

lol jkjk

ty for the help

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[lone kiln]

where is the additional sin(x) coming from. The final form i have before intergrating is

[lone kiln]

$1-2u^2+u^4$

[potent lotus]

Flamester7 Tv

[calm coral]

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[lone kiln]

<@&286206848099549185>

[hushed tartan]

you forgot the +1 that is in the integral

you need to integrate that too

[lone kiln]

1 becomes x

[hushed tartan]

beaware

you are integrating with u as the variable now

$\int{u^4-2u^2+1}{du}$

[potent lotus]

calculus is fun

[hushed tartan]

after getting the answer in terms of u use u=sinx so that you have it in terms of x

[lone kiln]

OOOOHHH

thank you

[calm coral]

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[paper grail]

Hey, I have a question

[dapper turtle]

!just ask

[paper grail]

My task says to show that these two operations

are well-defined binary operations

but what does that mean?

[dapper turtle]

hmm

well lets see

idk, im not a helper

[dapper turtle]

you can ask a helper

[paper grail]

no hate to you dude

but you came, acted passive aggressive, and left

i am asking helpers

thats why im in the help channel

[fringe reef]

it means that the result of an operation is a unique value i.e. unambiguous

[paper grail]

hmm okay

and do u know what the line above the ordered pairs means?

because if it's important then i'm unsure of the notation

and if not then tysm anyway

[fringe reef]

i think it's the congruence class

[paper grail]

congruence class...?

im not sure if i have learnt that

[fringe reef]

actually nvm

probably not that

[paper grail]

okay i googled it and i know what that means but it is definitely not what the question is sking

asking*

[fringe reef]

yeah i see

seeing the full question might be useful

not sure what either S nor ~ are

[paper grail]

okay

S is just

set of pairs of integers where n >= 1

[fringe reef]

got it, this clears things up

[paper grail]

i'm just a little unsure how to start thinking about this

i've done part i)

showing reflexivity, symmetry + transitivity was very simple

[fringe reef]

honestly

[paper grail]

for ii) though im just

[fringe reef]

i have no clue what the overbar means

[paper grail]

yeugh

ive read thru the lecture notes

and they do not feature

any kind of overbar notation

wait no they do

i missed a page

oh thats so annoying

im sorry for wasting your time lmaoooo

$\overbar{x}$

just means

[potent lotus]

george clooney real account
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[paper grail]

equivalence class of x

overbar x

forgot the latex for it

[fringe reef]

ah lmao

[fringe reef]

$\overline{x}$

[potent lotus]

artemetra

[paper grail]

overline

gotcha

[fringe reef]

i also always write overbar lmao

[paper grail]

ive been trying to write my working on pen+paper and then all my theorems in obsidian using latex

and im still trash at latex

thanks for the help

.close

[calm coral]

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[indigo hinge]

can someone tell me how 2.6672 was obtained?

Because I've plugged in 1 into k and I didnt get that

a better question would be is what did they plug in for k in this example?

[calm coral]

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@indigo hinge Has your question been resolved?

[indigo hinge]

.close

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[indigo hinge]

.

[calm coral]

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[pliant coral]

Well, you need to find the slope first

Do you know how to find the slope?

[calm coral]

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[severe geode]

Having trouble setting this integral up, kinda got a understanding of what the graph looks like and that its only a portion of the whole given x,y > 0 but cant seem to get the setup

[severe geode]

kinda got a lil mess sketched out

I dont think what I wrote is correct for the bounds

[calm coral]

@severe geode Has your question been resolved?

[severe geode]

<@&286206848099549185>

[solid heron]

?

@severe geode

[severe geode]

wondering about the above, how I can set up the integral for question d

[severe geode]

I see that z is from 2 to 9 but cant quite understand how to get bounds for y and x

[plush sandal]

When discord lags super hard:

[solid heron]

Can you please show an example

@severe geode

By providing more information

It depends

[severe geode]

this was my question

[solid heron]

Oh okay

[severe geode]

my guess or attempt was

these are just the bounds for the integral setup

[still marlin]

Cylindrical coordinates should be easier I think

[severe geode]

I assumed but I have no idea how to do those in 3 planes yet

[still marlin]

ah rip

Have they not taught it in class yet or just don't know yet?

[severe geode]

they went over it breifly havent done many problems with it yet only like 1

[still marlin]

Oh bet time to practice it then

[severe geode]

I suppose

[solid heron]

L (x) = ƒ (a) + ƒ’(a) (x − a)

L(x) = y ^ 2 + 18x - 81

[still marlin]

So first off, $dV$ with cylindrical coordinates is equal to $r dz dr d\theta$

[potent lotus]

992qqoloy

[still marlin]

next, cylindrical coordinates is p much just polar with an added z value

$x^2 + y^2 = r^2$ in particular

[potent lotus]

992qqoloy

[still marlin]

So we have $z = r^2$

[potent lotus]

992qqoloy

[severe geode]

so theta would be 0 to pi/2 in this case since its a quarter circle

[still marlin]

Yeah

and bounds of $r$ given by $z = 2$ to $z = 9$ restraints

[potent lotus]

992qqoloy

[severe geode]

radius from sqrt(2) to 3 and z from 2 to 9? I believe idk I think I may understand how to do this with cylindrical coords now

yeah

^

[still marlin]

yup

[severe geode]

If I run into more problems I will reference the book but htank you

[still marlin]

np

[severe geode]

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[late torrent]

for part b) i got 3.3166666667

but it says its incorrect

cant get c either

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[hollow sphinx]

Tried solving the highlighted above 3 equations simultaneously but I’ve made a mistake somewhere and I can’t seem to find it

[deep pike]

Seems u applied kirchoff voltage law

[hollow sphinx]

Yep, made a mistake when solving the equations simultaneously and I can't seem to find it

Nvm found it finally lol

.close

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[remote mural]

need help with number 16

[remote mural]

helo

[calm coral]

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[remote mural]

@remote mural

[remote mural]

i found it very difficult

with this question

are you at first year uni?

the solution is x=3 and y=2sqrt 5

@remote mural

you need to find x+iy such as x+iy=sqrt(11+12sqrt(5))

this means (x+iy)^2=11+12sqrt(5)

develop (x+iy)^2 and then put imaginary equal imaginary and real number equal real number then solve the system

.close

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[distant musk]

What would the interval [3pi/2 ; 2pi] look like on a trigonometric circle?

[pallid halo]

do you know where 3pi/2 and 2pi are?

[distant musk]

Uh...

I'm just weirded out for 2pi

Does 2 pi mean 0?

[pallid halo]

it refers to the same direction as 0

it means "go all the way around the circle exactly once"

[storm wedge]

4th quadrant

[pallid halo]

and then you end up pointed the same way as when you started

[distant musk]

Ahh I see

[pallid halo]

not helpful

[distant musk]

But do I take the whole thing?

Wait wait

[pallid halo]

[3pi/2, 2pi] is all the points between those angles

[distant musk]

I'll send the exercise I'm trying to figure out XD

[pallid halo]

ok

[distant musk]

Knowing x is part of the interval [3pi/2 ; 2pi] and sin x = -2/5.

Find cos x

[pallid halo]

ok i see

well to work out what part of the circle is [3pi/2, 2pi], i can suggest the following:

[distant musk]

I'm having trouble if I should find cos x and -cos x at the same time ;-;

[pallid halo]

suppose you begin at angle 0 and then you start traveling around the circle counterclockwise (increasing angle)

suppose you have a paintbrush or something

as soon as you reach angle 3pi/2, let your paintbrush touch the circle

then when you reach 2pi, lift the paintbrush

everything you painted is [3pi/2, 2pi]

[distant musk]

Wait so is 2pi 0?

[pallid halo]

yes it refers to the same point

[distant musk]

So is would be like a quarter of the circle right?

[pallid halo]

namely the point x=1, y=0

[distant musk]

Ahhh...

[pallid halo]

but you wouldn't write [3pi/2, 0]

[distant musk]

Oh-, jeez these mathematicians

[pallid halo]

because intervals like that should have a smaller number first, then a larger number

[distant musk]

Ahhh

Yeah make sense...

[pallid halo]

but yea it means, start at 3pi/2 and then everything is included up to 2pi which is the same as the point called 0

[distant musk]

I see!

Thanks bungo :D

[pallid halo]

so can you describe which part of the circle this is?

[distant musk]

Um the part on the bottom right?

[pallid halo]

yep

aka the 4th quadrant

[distant musk]

Yaaay

[distant musk]

Ahh so that's what he was talking about

[pallid halo]

yea

but it's more helpful to guide you to the answer instead of just telling you

and we're not supposed to just give answers anyway haha

[distant musk]

True true, I definitely liked the paint brush 🖌️:)

[pallid halo]

cool

[distant musk]

Thanks again :)

[pallid halo]

sure, cheers

[distant musk]

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[astral dune]

I have to solve that limit using the definition but I got stuck there

[cunning veldt]

you could also notice that n²+3n+2 = (n+1)(n+2) and 6n+6 = 6(n+1), so you get 6|1/(n+2)| < epsilon
it was easier from there, bc then you have n > 6/epsilon - 2
so you can take N = rounding up of 6/eps - 2

[calm coral]

@astral dune Has your question been resolved?

[astral dune]

Oh that makes a lot more sense

How can I notice easily that n²+3n+2 = (n+1)(n+2) ?

Well, in this case I'll probably just remember it but what if it's (n+3)(n+2), (n-1)(n+2)... ?

[cunning veldt]

the way I think is that, if it didn't simplify nicely, your teacher wouldn't say to find an epsilon proof
and the more obvious case where polynomials simplify nicely is when they share a common factor
6(n+1) has only n+1
and then, n²+3n+2, bc of viete formula, has -3 as the sum of its roots and 2 as their product
so I immediately now that it's (n+1)(n+2) and that the (n+1) will cancel out

and if it wasn't the case, well, it would be a pain

you would still need to do the long division ig, so that you can bound the thing in terms of n

[astral dune]

What's viete formula?

[cunning veldt]

or you use some camel's trick (I think it's called like that in English) where you add and remove the same thing at the same time on the numerator

it's in fact, several formulas, that express some things about roots of a polynomial in terms of the coefficients of the polynomial

if you don't know them you can just factor the way you usually do

[calm coral]

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[astral dune]

Okay thank you so much, I'll look that up

[astral dune]

oh mb

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[icy pumice]

**The displacement from O of a particle moving along a straight line is given by

x=t^2−4t

The distance that the particle has travelled after 4 seconds is ???**

[calm coral]

Please don't occupy multiple help channels.

[icy pumice]

how do i convter the displacement to distance?

[mild jetty]

it is moving along a straight line

which means

[calm coral]

@icy pumice Has your question been resolved?

[river basalt]

you can just sub in t = 4 into the displacement function

[calm coral]

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[icy pumice]

displacement function?

[calm coral]

Please don't occupy multiple help channels.

[icy pumice]

uhhh area under the graph is the distance?

[river basalt]

it's moving on a straight line so the distance is the same as the displacement in this case

i think

[icy pumice]

thanks

wait

is average velocity and acceleration the same?

whats the difference?

oh im guessing

that you find the average of the numbers?

[proud sphinx]

Test

[icy pumice]

huh?

[calm coral]

@icy pumice Has your question been resolved?

[calm coral]

@icy pumice Has your question been resolved?

[calm coral]

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[astral dune]

Which one is correct? Top or bottom? I think it's bottom but I'm not sure

[velvet osprey]

you're right it is the bottom

[astral dune]

Thanks

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[harsh kelp]

im so confused on how to even set this up

[harsh kelp]

Seperation of variables

[stoic oyster]

say S(t) is the amount of substance 1 at time t

S is consumed at a rate (prolly some derivative thing going on here) proportional to S(t)^2, that's what the question says

@harsh kelp

[harsh kelp]

Okay

[stoic oyster]

so we have dS/dt = something involving S(t)^2 pretty much

[harsh kelp]

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[stoic oyster]

got it ? @harsh kelp

[harsh kelp]

yes thanks

[stoic oyster]

aight

[calm coral]

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[orchid abyss]

I need to find the inverse of this function, but after swapping the x to y, i get two y's in seperate functions.. how do i solve for y?

[orchid abyss]

i can do either arccos or arctan to get the y out, but tthen there's 1 y left in either function

and my domain was [0,pi/2]

[potent igloo]

Express tan(y) in terms of cos(y), then solve for cos(y) in your inverse function

[orchid abyss]

is this then the inverse function?

[potent igloo]

no

You must isolate y

Why are you trying to get the inverse function?

[orchid abyss]

i need to calculate this

the derivative of the inverse function evaluated at x = 1

[potent igloo]

You do not need to find the inverse function.

Use the inverse derivative property

Otherwise, this would be your inverse function

[orchid abyss]

oh...

yeah maybe the inverse derivative property is a bit easier

[potent igloo]

It absolutely is

[orchid abyss]

thanks! i have one more question

which is

don't mind the dutch, but i have to prove this inequality by using the mean value theorem. i only got so far

i'm not sure how i'll get any further given that 2/pi is equal to cos(c)

i mean i'll have to talk in terms of sin in the end

[calm coral]

@orchid abyss Has your question been resolved?

[calm coral]

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[honest trellis]

Hi, I need help bc I am not a maths person
context: I am trying to model bacterial growth to make it so that bacteria can grow, reach a plateau and then die bc of nutrient depletion.
I just have 2 components, "sty" which is the bacteria and "nut" which is the nutrients, and I have the following code

reaction_network <- function(t, y, p) {
  dsty <- p[1]*y[1] -p[2]*y[2]*y[1] 
  dnut <- p[2]*y[2]
  list(c(dsty,dnut))
}
y0 <- c(sty = 0.1, nut = 1)
p <- c(1, -0.5)
times <- seq(0, 100, by = 0.1)
out <- ode(y = y0, times = times, func = reaction_network, parms = p)

now, "out" is the output and I can make it so that "nut" decreases, the problem is that it goes to negative numbers and I need it to not go lower than 0... any idea how I can do that?

[honest trellis]

forgot to mention that "y0" is the initial conditions (low bacteria and some nutrients)
and "p" are the parameter of the kinetic constants (how it changes)

[stoic oyster]

nice pseudo you got there ^^

i got 2 questions

1. what's the differential equation that describes your system ? maybe you typo'd idk
2. does nut become hugely negative, or is it very small ?

@honest trellis

[honest trellis]

idk how the system is described as an ODE, I don't even know how to make them (I am just a biologist scared of math)
and nut becomes hugely negative (like 1*10^-200 or something like that)

[stoic oyster]

10^(-200) is ultra small

@honest trellis

like pretty much 0

and 1*10^(-200) is still a positive number

just very very tiny

[thin tendon]

isnt what you need basically a logistic map?

[honest trellis]

this is what I get

[stoic oyster]

ah yeah ok this is problematic

floating point numbers in computers can completely screw up like that sometimes, I'm just throwing explanations around

what does the curve look like for small times ?

[thin tendon]

care to explain your code?

what are those variables?

like t is time i guess but p and y

[honest trellis]

ok so, I am trying to copy this code and logic into bacteria

I tried to do the same but it didn't work apparently

[thin tendon]

so yeah this is the logistic map if you have only one population that starves

we'll do a sequence instead of a function so its easier

unless you want to get fancy

[honest trellis]

ok so it's more a problem with the "formula" (the "dsty =" part)

?

[thin tendon]

its a problem that you are using a predator prey model but with just one population at first

and second, the fact that you are doing that tells me you are lost about the maths you are doing

[honest trellis]

always tbh

ok so I am gonna do more research sinceI am having trouble with basics

[thin tendon]

what is your understanding of differencial equations?

tial*

[honest trellis]

none

[thin tendon]

okay so dont try to do what they are doing

[honest trellis]

my degree just got up to derivatives and integrals

[thin tendon]

are you at ease with coding ?

[honest trellis]

gotcha

yes, I think so

[thin tendon]

okay so you want to code something along those lines

let P_t be the population at time t

$P_t = r P_{t-1} * (1-P_{t-\tau})$ with P inside $[0,1]$ representing the percentage of the max population and $\tau$ representing the time bacteries take to die roughly, r is an adjustable parameter that you can fiddle with

[potent lotus]

Benjamin

[thin tendon]

and you compute for integer values of time t

[honest trellis]

hmmmm I'll try

thanks a lot!

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[main marlin]

can you translate, is that...I'm gonna guess Hungarian?

[final dock]

nope turkish

basically

find cot^2x+cos^2x

[main marlin]

damn wasn't even close

[final dock]

can u solve this?

i was know the methot

but i forgot

[main marlin]

Here's a hint: $\cot\theta=\frac{\cos\theta}{\sin\theta}$

wait

what is this question asking exactly?

like just evaluate cot^2+cos^2?

[potent lotus]

PajamaMamaLlama

[final dock]

yep

just equaliation of cot^2x+cos^2x

equivalent to ^2x+cos^2x*

[main marlin]

$\cot^2\theta+\cos^2\theta=\left(\frac{\cos\theta}{\sin\theta}\right)^2+\cos^2\theta$

[final dock]

oh

there we go

[main marlin]

idk why it's giving me an error

[potent lotus]

PajamaMamaLlama

[main marlin]

oh, is that it?

nice

ok

[final dock]

I think I understand. I need to equalize the denominator.

so the cos need to be positive

because of its between 0 and 90

For this, a unit circle needs to be drawn

.

@main marlin

[calm coral]

@final dock Has your question been resolved?

[final dock]

i resolved

[calm coral]

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[icy pecan]

!status]

[calm coral]

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

[torn thicket]

Hello, can someone help me

[icy pecan]

Please send the whole question

[torn thicket]

here you are

[icy pecan]

33?

[torn thicket]

yes

f+g is says

[icy pecan]

x+1

[torn thicket]

How I can solve it

[icy pecan]

with th square root over it

[torn thicket]

both of them or one by one

[icy pecan]

both

[torn thicket]

it will be 25-x^2 and x+a

x+1*

idk the app

which app u are talking about

can you show me on paper is it possible f+g ?

[potent igloo]

no

Replace f with what it is equal to

and same with g

Then you are done

[torn thicket]

(sq root 25-x^2+ sq root x+1)^2

like this ?

[potent igloo]

why are you squaring the whole thing?

[torn thicket]

idk he told me

;/

[potent igloo]

you have no need to square it

[torn thicket]

okay I combine them like f+g

thats all ?

[potent igloo]

yes

that's all

[torn thicket]

it will stay same but I will plug them

sorry f+g

what about times and divide

f*g and f/g

[potent igloo]

same idea, but multiply or divide instead of add

[torn thicket]

so it will nothing change I just multiply divide

yes ?

[potent igloo]

yup

simple as that

[torn thicket]

I confused a little bit `cause I expect that is not easy

[torn thicket]

okay thank you bro

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[torn thicket]

Can u help idk what to do here

I confused

[weary wyvern]

f(g(h(x)))

[calm coral]

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[torn thicket]

in 51?

[torn thicket]

this?

.close

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[lethal radish]

word

[formal canyon]

The answer is m + 14 but I’m not sure how to get that

[remote mural]

4m+ 20-3m-6

[formal canyon]

Why 3m-6?

How*

[remote mural]

u have -3xm -3x2

[remote mural]

U distribute the - also

[formal canyon]

Oh thank you I get it now

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[drifting grove]

I am trying to calculate the odds of getting at least one unique dice when rolling 5 dice. By unique I basically mean a die that is alone in it's set. 

For instance 
[1, 3, 4, 4, 3] has one unique die: 1.
[3, 5, 4, 2, 4] has three unique dices: 3, 5 and 2.

So I am looking for the probability that there exists a unique die in a set of 5, if that makes sense.

My intuition tells me that if we fixate 1 die and 1 number, we can calculate the probability as 

(1/6)*(5/6)^4.

Let's say we fixate "die 1" and a number 5, then could this be called the probability of rolling 5 on "die 1", and anything-but 5 on the remaining 4 dices?

Then in order to account for all the dices and all possible numbers we multiply by 5C1 and 6C1 respectively

(1/6)*(5/6)^4*5C1*6C1 = 2.4112654321

Which obviously isn't correct, but rather the average number of unique dices per 5-throw.

How can I go about solving this correctly?```

[drifting grove]

Also, I know that the answer is very close to 96%, according to my Java simulation which appears to be working correctly.

[amber bolt]

you can notice that there's only 2 ways it doesn't happen: 3+2 or all 5 are the same

,calc ((6)(5)(10) + 6) / 6^5

[potent lotus]

Result:

0.039351851851852

[amber bolt]

i'm curious if there's some cool general way too

[drifting grove]

That is for exactly one unique

correct?

[amber bolt]

no

we exclude no unique, so any amount is fine

it's 4% like you said

[drifting grove]

Oh okay, yeah makes sense

Would it be possible to calculate this with generating functions some how?

[amber bolt]

probably

i've never touched them, but they seem powerful enough

[drifting grove]

Would you mind explaining this? How the exclusion works I mean

I understand that the denominator is the total number of cases

But how did you come up with the numerator?

There are 6 ways to have all 5's, I understood that one

and there are 5*6 ways to pick two numbers for 2+3, but where does the 10 come from

[amber bolt]

then 2+3 you get by choosing a value that appears twice and then a value that appears 3 times, and 5c2 counts the order

i was lazy to write out 5c2 with factorials

[drifting grove]

Ah right

Thank you

[amber bolt]

i think we can calculate it with a table, just like stirling #2, but without creating singles

[drifting grove]

unfamiliar with the concept

[amber bolt]

so 350 is number of ways to assign 7 rolls into 4 nonempty groups
e.g. ABABBCD

[drifting grove]

Like stars and bars sort of?

[amber bolt]

stars and bars would only count the different amounts that would add up to 7

for each shape of 6 rolls we can extend it to 7 by using an existing group
ABABCD → ABABCDA
ABABCD → ABABCDB
ABABCD → ABABCDC
ABABCD → ABABCDD
so we multiply 65 by 4

and also for each shape that has 3 groups we can add D, so we add 90 times 1

the order of letters is not interchangeable, there's no 4!

it just to make thwe numebrs smaller

so i tihnk if do this and just not add 90

[drifting grove]

This is beyond what I can comprehend

But would stirling be covered by an advanced statistics course?

[amber bolt]

i don't know sorry

[drifting grove]

Well, thank you very much for the help. I'll leave this open for a few more minutes if someone has a general/alternative solution

[amber bolt]

ok it kinda doesn't work

[calm coral]

@drifting grove Has your question been resolved?

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[remote mural]

How to determine the equilibrium P and Q

.close

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[calm coral]

Please don't occupy multiple help channels.

[halcyon ore]

hi

closed other from long tim eago

Wat i do wrong for this plz 😭 the answer is there and my work is here

[calm coral]

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[calm coral]

@halcyon ore Has your question been resolved?

[calm coral]

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[remote mural]

y = -f(1/3x)
how do i find the two points? given 6,5 im confused atm

[remote mural]

i got (18.2,-5) but it's wrong and im not sure what to do or change

[tulip basin]

What two points

[remote mural]

vertex

[remote mural]

this is basically doing transformations

.close

[calm coral]

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[sand dragon]

Hi

[hushed pasture]

Pedestrians approach a crossing from the left and right sides following independent Poisson processes with
average arrival rates of λ_L = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a light
is flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right or
from right to left). Assume that the left and right arrival processes are independent, that the light flashes
every T = 2 minutes, and that crossing takes zero time – it is instantaneous.

What is the probability that in a particular crossing, there are total 10 pedestrian and they are all
crossing from left to right?

wtf

really

just bc u said hi

okay .close

.close

[frank gull]

sorry my dude they beat you here, it's first come first serve

[hushed pasture]

@frank gullin one metric yes and in another no. i asked a question first technically

but it's fine i got another channel

[sand dragon]

How am I supposed to solve this, and what am I doing wrong ?

[kindred estuary]

This is the formula

Don't you need to use the y coord of the focus?

,w plot y =(1/8)(x + 4)^2

[potent lotus]

Results provided by WolframAlpha

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

Requested by captainnova22

[kindred estuary]

Oh wait

[sand dragon]

alr

I just dont get which part of it is wrong ?

<@&286206848099549185>

[kindred estuary]

Isn't p the distance from the directrix to vertex or focus to vertex?

Not from the directrix to focus?

[sand dragon]

Yes

[kindred estuary]

So why is p = 2?

Because the vertex is in the middle of the directrix and focus

[sand dragon]

Is it 1 ?

[kindred estuary]

So if the overall distance between the two is 2, and the vertex is halfway, then p is half that distance

[kindred estuary]

Yeah, I believe so

[sand dragon]

No it is not

Oh maaan 1 last try

[kindred estuary]

Wdym

p is 1

[sand dragon]

Yeah but the final answer is wrong

[kindred estuary]

4 * 1 = 4

So 1/4

[sand dragon]

Oh

[kindred estuary]

I wasn't referring to the k part anymore

[sand dragon]

Right ?

[kindred estuary]

Yes

[sand dragon]

Do I write it with 0 ?

[kindred estuary]

You can but it's not needed

[sand dragon]

Thanks man

.close

[calm coral]

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[polar ether]

The volume V and the surface area S of a sphere of radius r are given by the formulas V= 4/3 πr^3 and S= 4πr^2. Express V as a function of S

[polar ether]

I just dont understand how to get the r^2 to r^3, because theyre very similar equations, but I just don't know where to start

[clear delta]

solve for r

[polar ether]

so would i be solving for r in the surface one? and then just plug in that into the r^3 of the volume one?

.close

[calm coral]

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[next tangle]

I need to find the relative minima for this graph

I believe the relative minima to be (-3, 3) although I am unsure if endpoints are relative minima or if there are any more.

[calm coral]

@next tangle Has your question been resolved?

[next tangle]

<@&286206848099549185>

[next tangle]

<@&286206848099549185>

[calm coral]

@next tangle Has your question been resolved?

[next tangle]

.close

[calm coral]

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[winter jacinth]

can someone tell me what i did/thought wrong in the red squared area? and how to avoid that in the future?

[calm coral]

@winter jacinth Has your question been resolved?

[winter jacinth]

<@&286206848099549185>

[molten crest]

Seems to me like you did nothing wrong

Why do you think you did?

[winter jacinth]

answer i was given was on the right side

left side would be an acceptable answer too?

[molten crest]

They're the same answer

[sweet briar]

both are the same

[molten crest]

multiply by -1/-1 to either to obtain identical solutions

[winter jacinth]

oh and hmmm. if i wrote the answer from the left on a test i should get that right though or is there some formatting convention that i should be aware of that makes the right side answer more correct?

[molten crest]

It would be correct on a test

there is no preferred formatting

in this case

personally I like to have as few negatives signs as possible but that's just for aesthetics

[winter jacinth]

ok tysm

.close

[calm coral]

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[wraith shuttle]

Am I just supposed to differentiate this?

Plugging in m1 and m2

Im left with

F = G * 36/r^2

[winged verge]

I think you should just take the derivative

yeah just plug in the two masses and then take dF/dr

[still marlin]

yeh u should try takin the derivative

Could just do implicit differentiation

Tho

[calm coral]

@wraith shuttle Has your question been resolved?

[wraith shuttle]

I see, thank you both then

I appreciate it

[calm coral]

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[rustic blaze]

pleaze help

[rustic blaze]

and show work

<@&286206848099549185>

[hollow mural]

take common denominator

[hollow mural]

that’s your job 👀

[rustic blaze]

since youre going to tell me stuff i slready did

ill show you my work

and you tell me the error

[velvet osprey]

!15m

[calm coral]

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

[velvet osprey]

that's how things are supposed to be done here anyway lol

[rustic blaze]

pleade

@velvet osprey

pleaze

what did i do wrong

[hollow mural]

thats not common denominator

you multiplied by

[rustic blaze]

what is

[hollow mural]

(x+2)(x+8)(x+1)

just multiplying it changes the equation

so what u have is not equivelant to what they have

[rustic blaze]

so

whqt the cd

whats

im so confused

[hollow mural]

for common denominator youre just multiplying by 1, cuz anything multiplied by 1 is the same. you need to rewrite 1 so that when multiplied it gives the same thing

[rustic blaze]

whats the common denominator

if its not ehat i had

what

what is it

please tell

[ripe escarp]

ok

so

multiple the denominators

by each other

[hollow mural]

a/b + c/d for example
simplest way to get cd is the multiple of denominatiors, which is bd.
for b to become bd, you need to multiply by d. for d to become bd, you need to multiply by b.
so you multiply a/b by d/d, and c/d by b/b. then both fractions have the denominator bd. if its difficult to factor out you can also multiply both denominators by bd/bd (the multiple of the denominators)

[velvet osprey]

,rcw

[velvet osprey]

(reposting so i could rotate it)

[rustic blaze]

please man

whats the common denominator

please tell me

please just tell me

[hollow mural]

this isnt chegg

[velvet osprey]

try to calm down first

and exercise some patience

[dark plover]

how do we ask for help-?

[hollow mural]

the point is to help you figure out how to do these on your own

[dark plover]

sorry for the bother

[velvet osprey]

!help

[calm coral]

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

[velvet osprey]

take your own channel

[dark plover]

ohh tyy

[rustic blaze]

its midnight i want to sleep but im bot sleeping until i figure this out

not

i had work until 9 and ive been doing math since i vot hone

home

[hollow mural]

@rustic blaze

simplest cd us the product of denominators

then multiply by cd/cd (cd = comon denominator)

[rustic blaze]

you want me to myltiply all three denominatore

[hollow mural]

only 2

you’re trying to prove LHS = RHS

consider LHS on its own and manipulate it to equal RHS

[rustic blaze]

ok ill do it

[rustic blaze]

does it matter which two i multiple

multiply

come back

@hollow mural

ok

[hollow mural]

you’re only considering one side of the eq at a time

either consider left and make it equal to right, or the opposite

in this case, since the right is a single fraction, it’s easier to consider the left

so consider the left side alone

and simplify it into a single fraction by taking cd

[rustic blaze]

is the cd 2(x+8)(x+1)

[hollow mural]

yes

[rustic blaze]

?

why

forget why

now how to i get rid of the deniminatore

[hollow mural]

^

[hollow mural]

? you don’t. you take common denominator and then simplify into a single fraction

youre trying to prove the right side, which has a denomiator

[rustic blaze]

what would the 5/x+2 turn into

[hollow mural]

5/2x+2

?

multiply by cd in the top and bottom

[rustic blaze]

?

[hollow mural]

is that y?

[rustic blaze]

the one below y

ignore 13

[hollow mural]

if you just multiply by 2(x+8)(x+1), the function changes. you can only multiply by 1. so multiply by 2(x+8)(x+1)/2(x+8)(x+1)

basically multiply top and bottom by cd

otherwise the function changes

[rustic blaze]

can you pls solve it on paper

ive done every other problem

[hollow mural]

i dont have paper

[rustic blaze]

but this one

im so lost

[hollow mural]

this is correct. multiply the top and bottom of each fraction by this

[rustic blaze]

2(x+8)(x+1)/1

yes

[hollow mural]

thsts just mutiplying the top

and changes the expression

you can only multiply by 1

[hollow mural]

^

multiply the top AND bottom

by the same thing

thsts the same as multiplying by 1, so you doing change the expression

otherwise what you do is wrong

[rustic blaze]

but

[rustic blaze]

whyve the other problems been rivht

whats different about this one thwt makes me have to multiple both

[hollow mural]

show the other problems and your work

[hollow mural]

this goes for any problem

[rustic blaze]

ignore everything about 13

[hollow mural]

wait its not a proof 🤦‍♂️

i men still no problem