help-33

[lofty gyro]

not bad at all

[wintry gale]

You got this! Just use math

[exotic rampart]

Thank you guys

i rlly appreciate it

<3

ima close this now

.close

[marsh citrus]

Channel closed

Closed by @exotic rampart

Use .reopen if this was a mistake.

[wintry gale]

Forgot to tell them to rate me 5 stars

[marsh citrus]

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[sly bramble]

can anyone help with this?

[sly bramble]

its basically physics, and all i really need help with is the last problem

inclined plains and pullies working together

here is a photo if that is easier

[tough raft]

Where are you getting stuck?

[sly bramble]

its just in finding hte ratio of the incline plane

i understand that its a 2:1 ratio for the pully

[tough raft]

Take components of weight for block a

Write the equation for tension and equate them

[sly bramble]

ok

[tough raft]

Use the information ma=3mb

[sly bramble]

ma(slope)=2(mb)

[tough raft]

Now when you will take components you will get sin theta which is equal to

h/L

[sly bramble]

thats what im confused on

so then is it just 2(mb)/ma?

and then for the other one its just 1.8(mb)/ma?

[tough raft]

This is correct

[sly bramble]

oh, thats lowkey pretty easy

[tough raft]

Sorry mb

[sly bramble]

why?

[tough raft]

I confused a with acceleration

[sly bramble]

so what would be different?

wouldint it still be 1/6?

[tough raft]

Yeaah but i got confused

It would be same

[edgy crescent]

what was ur final answer?

[sly bramble]

1/6 for the first one

and then 5.4

1/5.4

[edgy crescent]

uh thats sin(of the angle)

not the slope or tangent

[sly bramble]

oh,

so it would be sin(1/6) and sin (1/5.4?

[edgy crescent]

yup

do u wnat my working?

[sly bramble]

wdym>

?

[tough raft]

The ratio itself is sin theta

Ig

[edgy crescent]

working do you want?

[tough raft]

So it would just be 1/6

[edgy crescent]

like how to go about the question

[tough raft]

Acc to me

[sly bramble]

ohh, i think i get it

but both of those are viable solutions for it, so i think i get it

basically you just see hte force at which the tension produced by the pully

[sly bramble]

and hten from there you see the ratio between the two forces and calculate the slope needed

thank you so much!

[edgy crescent]

.close?

[tough raft]

Don't provide solutions directly until needed

[edgy crescent]

wasnt the question already sloved ?

[tough raft]

Yup

[sly bramble]

ok, just to recap just to make sure i kinda understand it

you want to basically solve the first force in terms of the other force (which in our case is hte pully system)

then from there, you devide out the weight, so you are just left with a ratio which is the h/l of the inclined plane

and form there you sin(h/l) to get the degree at which the inclined plane is at?

[edgy crescent]

yuep

yeup

[tough raft]

Yup

[tough raft]

Arcsin h/l

[edgy crescent]

and generally the angle as the final answer is better than the ratio so try that

[sly bramble]

whats different between arcsin and sin? im lowkey blanking

[tough raft]

Both are different functions

One is sin another is sin inverse

[sly bramble]

i can look up a video, you both are very busy, so i dont want to take up too much of your time

ohh, sin^-1

[edgy crescent]

yup

[tough raft]

Yup

[sly bramble]

because we are doing it the other way around

i remember that from precalc

[tough raft]

Hm

[sly bramble]

cool, thank you both so much!

ima do a few practice problems rq, and keep the chat open, just in case i need it, but will close it once im done. thanks!

for this, do i just make two mini circles within it, and set them = to eachother

i find the hight by making a mini triangle, and hten i find the length of sign b by doing 100root3?

the incline is sin(60)/100

[edgy crescent]

yup

[edgy crescent]

so the side B is correct

[sly bramble]

and then i set it =, so would it be 100/sin(60)(100)(A(9.8))=(100root3)(100/sin(60))(B(9.8))?

wait, sin(60)/100, not the other way around

oh, wait, im overcomplicating this

[edgy crescent]

hold on

[edgy crescent]

yeah

[sly bramble]

its just the ratio of hight transfer per distance

its just algebra

[edgy crescent]

trigno too

[sly bramble]

so like if i move it 100, then it ends up being (100root3-100)(sin(30))

[edgy crescent]

lets take a basic principle first, movement along the string, aka tension, should be same for both

so if A moves x distance up alomg the incline, B should move x distnace down the incline

[sly bramble]

yea

so lets say it moves 100 up

[edgy crescent]

up the incline right!

not vertiically, else that would complicate things

[sly bramble]

so then the other side length becomes 100root3 - 100

[edgy crescent]

wait which part are we doing

first one or seconf?

[sly bramble]

b right?

[edgy crescent]

second right

yeah

[edgy crescent]

side length?

[sly bramble]

yea

my thought, is wouldnt the new distance be 100root3-100, so we can then just do sin(100root3-100)/sin(100root3)?

and that is the vertical shift

and then we can devide that by 100 so every unit it moves, it shifts that amount

[edgy crescent]

no no u seem to over complicating it again

[sly bramble]

oh

[edgy crescent]

okay first things first mark all the angles in the incline

[sly bramble]

60 and 30 degrees, along with 100 and 100root3

[edgy crescent]

good

now if the block a moves 100 along the incline, vertically it would move?

[sly bramble]

100 the other direction

ohhhh

wait

i see

one sec

[edgy crescent]

nope

[sly bramble]

let me see

[edgy crescent]

yeah go ahead

[sly bramble]

cos(60)/100?

wait, 100cos(60)

[edgy crescent]

nope you are making a tiny error

draw the mini triangle again seperately

[sly bramble]

cos(60)=x/100

100cos(60)=x

[sly bramble]

ohhh, so sin

i thought we were tyring to find the horizantl shift

[edgy crescent]

nope it asks vertical in the qustuon

[sly bramble]

i see

isnt that just 50?

wait, no

50root3

[edgy crescent]

yup!!

[sly bramble]

so the ratoi is 100:50root3?

[edgy crescent]

no its asking us vertical shift of A and B's ratio

[sly bramble]

ohhh, silly me

so now we do the same thing for the other side, but its 100root3(cos(30))

[edgy crescent]

is that the vertical shift of B or the hypotenuse?

[sly bramble]

i was doing the horizantal again...

but if ichagned it to sin, that would be the virtical of b

[edgy crescent]

yeah so vertical of B should be 100 (sin30) right?

[sly bramble]

100root3(sin30)

but yes

[edgy crescent]

uh no no why the root three

[sly bramble]

qait

ohh

because its the smae length

[edgy crescent]

as i said both the blocks will move the same distance

[sly bramble]

yea, ur right

[edgy crescent]

yeah!!

[sly bramble]

i was thinking the ratio between side lengths

im mixing up the wrong things 🙁

[edgy crescent]

its fine happpens to the best of us

[edgy crescent]

.

[sly bramble]

so, now for the mass of b compared to a, how would we do that

would that just be the slope ratio?

[edgy crescent]

one sec

can you send the Q again i cant find it😭

[sly bramble]

oh, so we can just find b

let me see

isnt it just 1500cos(60)=xcos30?

because the 9.8's cancle out

[edgy crescent]

hm ur messing up your trignometric ratio again

try again

[sly bramble]

im lowkey a little lost

is this where the vectors come in?

[edgy crescent]

okay so gravity's component along the incline acting on the block is sin(theta) not cos(theta)

[edgy crescent]

kind of yeah

[edgy crescent]

memorise this case

[sly bramble]

on, wait, so i just did cos, not sin?

[edgy crescent]

sin(theta) down the incline and cos(theta) is for the normal force acting on the block due to incline

[edgy crescent]

yeah

[sly bramble]

oh, ok, thats another silly mistake by me

that makes sense, but in short you basically need to set each side equal to eachother

figure out the forc as a ratio of the ima/ama multiplied by the weight

and if you have the weights, you can find the ima

[edgy crescent]

yes

[sly bramble]

and sin is gravity force, while cos is for when you are pushing/pulling a force

or how far somthing tavels horizantally on a incline slope

thank you so much for all of your help!

i need to go to bed now unfortunatly because its so late, but you have actually been so helpful! thank you so much!

[edgy crescent]

no problem

gn

[edgy crescent]

cos part is a little off so we will talk about it next time

[edgy tiger]

whats 1x1

[edgy crescent]

sorry this channels occupied

[edgy tiger]

pls

answer this for me 1x1

[edgy crescent]

1?

[edgy tiger]

workin out opls

[edgy crescent]

please ask in some other channel

dont spam here

[edgy tiger]

please your the smartest guy i knwo in this channel

you are a nerd

[edgy crescent]

last warning please use other channel

[edgy tiger]

srry my bad i holy glazd you bye bye bye

[marsh citrus]

@sly bramble Has your question been resolved?

[cunning fiber]

<@&268886789983436800> troll

[cunning fiber]

!done

[marsh citrus]

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

[cunning fiber]

.close

[marsh citrus]

Channel closed

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[marsh citrus]

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[still temple]

i'm trying to calculate this series

[still temple]

i honestly have no idea what to use

[brave marsh]

I know you can do it by considering $f(x) = \sum_{n \ge 0} \frac{(-1)^n x^{3n+1}}{3n+1}$ and trying to find a closed form for $f'(x)$.

[elfin berry]

Azyrashacorki

[still temple]

why would that solve it plus i think that's above the paygrade of this Worksheet

[sinful thistle]

its

really not that difficult

to do what azy said

[still temple]

oki

[tough raft]

Make it in a form of integral

[brave marsh]

In particular, the goal is that you differentiate term by term, compute a closed form for f'(x), deduce a closed form for f(x) by integrating, then compute f(1).

[still temple]

i got the idea thanks i just have a question sorry if i sound dumb we just started series

i got this

[hot rivet]

Prolly smth to do with cube roots of unity

[still temple]

to use the formula of geometric series doesn't the |(-x^3)|< 1 but in this case isn't |-x^3| = 1

because we are taking f(1)

[tough raft]

This is 1/(1+x³)

[still temple]

isn't the condition not satisfied tho ?

[brave marsh]

There's some argument as to why this extends to x=1, but I don't really know how it goes.
I just know you can get the answer by doing that.

[still temple]

hmm i see thanks

the idea does work for sure tho

tysm!

[brave marsh]

Nw!

[still temple]

.close for now

[marsh citrus]

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[marsh citrus]

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[finite forum]

how is U just not sqrt(5^2 + 12^2)

[wintry gale]

why should it be that?

[finite forum]

because tan alpha = 5/12

[wintry gale]

yeah but thats the angle

[wintry gale]

if i say i threw a rock with initial velocity of 5 ms^-1 making tan a = sqroot(3)

you will find that a gives the angle from which the rock was thrown

do you want to know how we find the initial velocity u?

[finite forum]

nah i did it

[wintry gale]

noice

can you give a rating of 5 stars regardless?

[finite forum]

you just say that the vertical component velocity is 5k, and the horizontal is 12k, find k and then do pythag

atleast that worked for me

[finite forum]

wut is this

[wintry gale]

ehh ig?

never tried it that way

the process was to use x = vi cost , and the second equation of motion for y axis

and subsitute in place of t

just throwing this out there

i encourage you try it this way too

[marsh citrus]

@finite forum Has your question been resolved?

[marsh citrus]

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[tired ore]

Is it possible for a continous function R->R to take all real values exactly three times?

[tired ore]

and I managed to show that as x->infty or x->-infty f(x) -> {-infty,infty}

I think it shouldnt be possible

[main idol]

Say what

[tired ore]

$x \to \pm\infty \implies f(x) \to {\pm\infty}$

[elfin berry]

k

[tired ore]

sorry, is this wording clearer? [
\text{Does there exist a continuous function } f: \mathbb{R} \to \mathbb{R} \text{ such that for every } y \in \mathbb{R}, |f^{-1}(y)| = 3?
]

\begin{multline*}
\text{Does there exist a continuous function } f: \mathbb{R} \to \mathbb{R} \
\text{such that for every } y \in \mathbb{R}, |f^{-1}(y)| = 3?
\end{multline*}

[elfin berry]

k

[main idol]

Ah yea okay

Maybe a scaled form of sin(x)

[tired ore]

I SEE THE VISION

crazy function

[main idol]

Like x ^ alpha * sin(x)

[tight furnace]

I think that would hit 0 more than 3 times

[tired ore]

x/5+sinx

is clooose

x/a+sinx

[tight furnace]

how much do you want the function to go up over a period of sin(x)?

oh nvm this is messed up

but yeah I see the vision

[main idol]

,w plot x + sin(x)

[tired ore]

😭

[elfin berry]

Results provided by WolframAlpha

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

Requested by rie.mann

[tired ore]

no idea how to pick that a

[fervent rampart]

we would want to enforce that the first zero after x = 0 is also a turning point, that should be enough to fix a

[tired ore]

yes

okay okay

[tight furnace]

,w plot arcsin(sin(x))+x/3

[elfin berry]

Results provided by WolframAlpha

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

Requested by a_mog

[tight furnace]

here's a funny one

[tired ore]

this odes the trick

how did u come up with it

[tight furnace]

if you want a really fun task try proving that such an a exists for your problem by IVT

for the sine thing

[tight furnace]

I thought we wanted a zigzag function so I tried to think of one

[fervent rampart]

see also https://math.stackexchange.com/questions/2583355/function-taking-on-all-values-thrice

[tight furnace]

Then I remembered composing arc trig functions with trig ones is funny

[fervent rampart]

the first answer does the same strategy and finds a numerical value for a (technically K = 1/a)

[marsh citrus]

@tired ore Has your question been resolved?

[tired ore]

thanks everone

for 2 values the answer is no

.close

[marsh citrus]

Channel closed

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[crystal lintel]

@tired ore

brought to us by the great @fair pond

it also generalizes. replacing 3 with any odd n gives you a function where all preimage sizes are n

[fair pond]

[crystal lintel]

thank you for this beautiful function daddy

[fair pond]

thank you for spreading my holy words layla

[crystal lintel]

this problem came up in helpers and lounge and i provided a proof that it was impossible for even n and pure made this function for odd n

we are such a great team

[fair pond]

[crystal lintel]

[quaint dirge]

<@&268886789983436800> obscene.

[crystal lintel]

what the blud

[quaint dirge]

you are both blocked. please do not engage with me anymore

revolting

[minor kindle]

hello

idk what to do about this but i guess uhh @crystal lintel @fair pond keep it in dms/private servers please

[marsh citrus]

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[hybrid valley]

Hi i need help

[hybrid valley]

For this, i got 5/7 but its not in the options, what am i doing wrong?

This is how i got 21

NVM

I MISCOUNTED

7×4=28

D

Wait but it has without replacement

Is it combination/permutations?

[quick kindle]

without replacement just means the 2nd time u pick a ball, the total number of balls will be 7 instead of 8

i believe u r already right

with D

[marsh citrus]

@hybrid valley Has your question been resolved?

[hybrid valley]

Oh okk thank you

[marsh citrus]

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[echo basin]

Hey, I have a math competition tomorrow about modelling. I was wondering if anyone was willing to give me some insight since I'm pretty new to this and it's my first time. I have some questions based on past samples and I just wanted to have a discussion about tomorrow's game plan. Specifically, a lot of the questions probably use common data models and I wanted to see if someone with more experience can guide me!

[main idol]

#study-discussion

[marsh citrus]

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[marsh citrus]

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[novel juniper]

Trying to perform a SVD of thid

[novel juniper]

I started with AA^T to fing the singular avlues

I got the singular values to be $1,\sqrt{6}$,0

Then I computed A^TA

[elfin berry]

wai

[novel juniper]

The eigenvalues of A^TA are 1,6

I then found vector in the kernel of A-I and A-6I

(1-2),(2,1)

I should probably show steps

.close

[marsh citrus]

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[marsh citrus]

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[odd agate]

<@&268886789983436800> and here

[marsh citrus]

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[wintry gale]

magnus carlsen?

[marsh citrus]

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[raven bone]

I know this question may be a easy google search, however i dont really understand how AI tries to solve this inequality, I can solve basic inequalities like, 2x + 3 > 11.
I dont even know where to start in this question.

[jagged relic]

You just multiply both sides by x+3, making cases for whether x+3 is positive or negative

[quaint elm]

i think it may be better to simply make cases for when the numerator is positive or negative, and when the denominator is positive or negative

[jagged relic]

Or you can directly check in what intervals x-2 and x+3 are positive/negative

[marsh citrus]

@raven bone Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[bleak pine]

Am I going the right way

[bleak pine]

@me when yall here 🫡

Nvm ima just round it

.close

[marsh citrus]

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[vagrant gull]

channel is already closed, open a new one

[verbal leaf]

oh sorry

[marsh citrus]

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[lofty timber]

was looking at my study guide, dont remember going over this

[still light]

try process of elimination

if x=t^2 when can you say about the sign of x

[lofty timber]

mmmm

positive

so the arrows wouldnt be pointing down

so that leaves top right and bottom left right

[still light]

Well I was referring to the x-component, which yes is positive

x being positive means the graph has to be on the right-side of the y-axis

[lofty timber]

oh

whoops

[lofty timber]

yeye

and the y would also be positive then right?

cus t^3 is positive

[marsh citrus]

@lofty timber Has your question been resolved?

[lofty timber]

https://tenor.com/view/cat-looking-eyes-emoji-let's-take-a-look-gif-16800462008013598153

i need help on this as well

where are my beautiful tutors 😔

[cunning fiber]

you can use the same logic that Ari gave you here to eliminate based on bounding y=1-t^2 for starters

[lofty timber]

ye i got the first question done

second one i need help w the arrows and part b

im assuming on the second one it's the third option where the arrows move towards the negative but idk

and idk how to do part b

[cunning fiber]

Mhm. For positive t, y strictly decreases

you can also do it by seeing that x is a strictly increasing function of t

so the x coordinates must increase

[cunning fiber]

Solve for t in one equation and substitute back into the other

this is just algebra

don't overthink it

[lofty timber]

okok

i got y = 1- (x-2)^2/16

does that make sense u think

[cunning fiber]

you can judge this for yourself using the graph in the first part

[lofty timber]

hmm

oh

i see what you mean

okay yea it makes sense

ty ty

[marsh citrus]

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

[lofty timber]

.close

[marsh citrus]

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[marsh citrus]

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[rose saffron]

why the green side is P(B|A)?

[tawdry rivet]

P(B/A) basically means P(B) given that P(A) happened... so that from this picture im understanding... yellow + green is basically P(A) and the square as a whole is the total probability of every outcome

okay so now... we know A happened definately so we limit our set to just the vertical strip and find p(B) that overlaps with rectangle giving us the green area

and since we got A happened we multiply by by p(A) too ;p

[marsh citrus]

@rose saffron Has your question been resolved?

[rose saffron]

i dont understand

the height is 1

[tawdry rivet]

the area of the whole square is say 1 (entire sample space) yellow+ green + blue + grey = 1 alright?

and the strip on left.. basically green+ yellow represent P(A)

[tawdry rivet]

yes

[tawdry rivet]

now lets just focus on the event A parts

green part is basically the portion of A

where B happens

and the yellow where B doesnt happen

so

[rose saffron]

i mean this height

[tawdry rivet]

P(A and B)/P(A) = green / green+yellow

so ...

P(A and B) / P(A) = P(B/A)

[tawdry rivet]

ahem

[tawdry rivet]

ahem

[rose saffron]

how can i find the height of the green?

[tawdry rivet]

the height of green is basically P(A and B) right...

[rose saffron]

but the area is P(A and B)

of the green

[tawdry rivet]

yea my bad area

not height

[rose saffron]

yes

[tawdry rivet]

whyd u even need the height ;-;

this picture based explaination is

area based

anyway

ull prolly do bayes theorom and total probability using the picture based explanination too i suppose

[rose saffron]

But why is height an area? We have defined probability as area.

@tawdry rivet

[tawdry rivet]

what r we even bout ;-;

u were the one who brought up height ;-;

i was workin with areas ;-;

[rose saffron]

okokokok

so P(B|A) is an area?

@tawdry rivet

[tawdry rivet]

its a fraction of areas

specifically P(A and B) and P(A) ;-;

basically probability = area
and conditional probabilties = fraction of areas

from this picture explaination of urs

[rose saffron]

@tawdry rivet i dont understand

[marsh citrus]

@rose saffron Has your question been resolved?

[marsh citrus]

@rose saffron Has your question been resolved?

[rose saffron]

.close

[marsh citrus]

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[gaunt lynx]

hello can someone help with the -)

[gaunt lynx]

a)

im confused about what to multiply the matrix with

there is no vector given

[copper raven]

the text in the beginning describes what vector you should use

[gaunt lynx]

the 180?

but

i dont understand

is it x y or z

how do i know

[plain vault]

"in the area W"

[gaunt lynx]

oh my god

[copper raven]

and area W corresponds to the first row/col of the matrix

[gaunt lynx]

oh my god ty

illl keep this channel open as i go bcs im definetly gonna have more questions

[copper raven]

sure

[gaunt lynx]

btw can i just do m^2 * v0

or do i gotta get v1 first

[copper raven]

you can

[marsh citrus]

@gaunt lynx Has your question been resolved?

[marsh citrus]

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[elfin badger]

not sure where -1/1 came from

wwould it be this?

[brave marsh]

Yes that's why

If you think of it as reversing the chain rule, you need a -1 there to "cancel" the -1 that will pop out when you differentiate ln|9-y|

[marsh citrus]

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[spare shoal]

hello can someone please help me graph these following characteristics!! 😭

[spare shoal]

thats the exact question idk

[wintry gale]

I think we have to draw the graph of f(x) from these 4 limits

[spare shoal]

I THINK SIO TOOO

i dont know where to start

yes

no

😭

oh

AYY

yes

OMG..

OK IMA DRAW IT RN

????

DNE

WAHT DOES THAT MEAN

ohhhh okay

[queen spade]

im a part of the same question and idk what to do next

???

the other problems

idk what to do for this one

[marsh citrus]

@spare shoal Has your question been resolved?

[valid gull]

I think he was asking what you have tried so far to solve this one

[queen spade]

well i havent done anything on that one bc idk what do

so nothing

[marsh citrus]

@spare shoal Has your question been resolved?

[wary kite]

@spare shoal what is your question

[spare shoal]

like how do i graph an infinity for c. and d.????

[wary kite]

well for the first case it would be a horizontal asymptote

do you know what that is

[spare shoal]

yes

[wary kite]

ok so do you have any idea how you might draw one

is the only requirement that it satisfies c?

oh i see it has to be all of them?

[spare shoal]

yah

[wary kite]

ok can i see your graph so far

[spare shoal]

um like a line

[wary kite]

maybe it's best if you show your idea by drawing it out

[spare shoal]

okay hold on

[spare shoal]

ts is wat we got rn

[wary kite]

hmm so where is the rest of the graph for your lim x -> 5 DNE bit

looks like you haven't decided how to draw it yet?

[spare shoal]

yes

we have no idea

[wary kite]

ok i see

you can pretty much do anything to connect to those two open circles you drew from either side

just make sure it doesn't get in the way of parts c and d

but let's focus on part c first

i mentioned that it should be a horizontal asymptote for part c

do you know the equation of the asymptote for part c?

[spare shoal]

y=2??

[wary kite]

yep

nice

[spare shoal]

OMGGG

[wary kite]

ok so now just draw any curve that asymptotically approaches y = 2 and connects to that lower open circle on the right side

[spare shoal]

???

[wary kite]

hmm no it has to on the right and extending off to infinity on the x axis

let me give an example of what i mean

[spare shoal]

okay thank you

[wary kite]

,w plot -e^(-x) + 2

[elfin berry]

Results provided by WolframAlpha

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

Requested by kniefy

[wary kite]

ignore the left part to the left of the y axis

do you see how it just extends all the way to the right and approaches y = 2

maybe on desmos it would be clearer

[spare shoal]

???

[wary kite]

better but like start the curve at the bottom open circle and make sure it's beneath that dotted line you drew and draw an arrow at the end once you get past x = 7

i'm mentioning the open circle because i want it to also satisfy the earlier parts

[queen spade]

????

[spare shoal]

are we eating or nah

[edgy crescent]

Ye looks fine

[wary kite]

🤔

[queen spade]

ummm

idk guys

i guessed

[edgy crescent]

but remeber to break the line in middle

[queen spade]

wait what

[wary kite]

you didn't start it at the open circle

you started it at the origin

at the bottom open circle you drew

that's where you start drawing

[spare shoal]

???

[edgy crescent]

Doesnt matter does it?

[wary kite]

no

[wary kite]

brother

no of course it's not necessary but it's convenient

now leave

i don't need your help dawg

[queen spade]

IM DEAD

[spare shoal]

WE JUST WANNA PASS THIS

OMG

[queen spade]

pls sm1 help

anyone

[wary kite]

no you started it at the origin again

[queen spade]

bru

[wary kite]

pick up your pen at the bottom open circle you drew

[wary kite]

then continue like you did

at x = 5

[queen spade]

OK ILL DO IT RN

[wary kite]

🤔

[queen spade]

IDK ANYMORE

[wary kite]

a few things

that is the top open circle

also

you drew to the left

draw it asymptotically approaching y = 2 from below

start at the bottom one

and draw to the right

[spare shoal]

OKAY

[queen spade]

???

[wary kite]

thank the lord

nicely done

[spare shoal]

AYYYY

[queen spade]

HELPPPP

[wary kite]

😭

[queen spade]

ok so next?

[wary kite]

part d

so we need lim x -> - 1 f = -inf

this time we have a vertical asymptote

can you tell me the equation of the vertical asymptote

[queen spade]

x=-1????

[wary kite]

nice

ok so an example would be something like

,w plot -1/(x + 1)^2

[elfin berry]

Results provided by WolframAlpha

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

Requested by kniefy

[wary kite]

ok of course it cuts it off a bit

but i think you get the point

[queen spade]

lololll

i thimk idk

[wary kite]

from both sides of x = -1 it goes down to -inf

[queen spade]

yess

[wary kite]

mhm

so draw something like that

[queen spade]

BRO

IDK

[spare shoal]

😭

[wary kite]

and then make sure on the right side of x = -1 your curve connects back to the top open circle you drew here

[wary kite]

you can do this

graph -1/(x + 1)^2 on desmos if you need to

to get a better picture

[queen spade]

UHHH OKKOK

[spare shoal]

where does it start??

x=-1??

[wary kite]

yea just draw it like the function i gave you

[queen spade]

huh

[wary kite]

but once you get to the other part of the graph at x = 5 make sure what you just drew connects to the top open circle

[spare shoal]

huh

[wary kite]

😭

[queen spade]

bro

i hate calc

what is thsi

[spare shoal]

why did we take rhis

[wary kite]

i'm not sure wym

look at x = -1

[spare shoal]

IM NOT SURE WHAT YOU MEAN

[wary kite]

that's where your asymptote is

[queen spade]

im not sure what any of this measn tbj

[wary kite]

you're just copying what you see in the function i gave you

a rough sketch

[spare shoal]

OK SHE NOT THAT

GOT

SHES GUNNA DO IT RN

[wary kite]

let me see

[queen spade]

BRO

IMA TRY

THIS ABT TO BE BAD

BRO UGH

[wary kite]

you'll get there eventually

[queen spade]

ya eventually

[spare shoal]

do you think we are gunna pass this class

[wary kite]

for sure

[queen spade]

be honest

[spare shoal]

wow thanks

[wary kite]

are y'all in uni

[queen spade]

wow so inspirational

no

[wary kite]

🤔

[spare shoal]

dual enrollemtn

[wary kite]

oh but it just started recently for spring semester

[spare shoal]

recently as in like 2 months ago??

[wary kite]

more like a month ago

but sure

[queen spade]

PLS BE NICE

I TRIED

[wary kite]

yes the left side looks great

[queen spade]

BROOOOOOo

[spare shoal]

AYYYYY

[queen spade]

omg

thanks

POMG

[wary kite]

put an arrow at the left end of it

[queen spade]

okok

bro i feel so like academic

[spare shoal]

https://tenor.com/view/glasses-academic-cat-i-see-smart-gif-21289556

[wary kite]

ok now for the right side do the same thing basically but as you go right from x = -1, draw the curve so that it connects to the top open circle at x = 5

[wary kite]

studious

[queen spade]

literallyyyy

[queen spade]

wait what

oh

[wary kite]

read what i said a few times if necessary

[queen spade]

HELP

[spare shoal]

😭

wait

[queen spade]

she got that

she gonna do it rn

[wary kite]

great

[queen spade]

do u think we will get an a on the test

[wary kite]

without a doubt

[queen spade]

mhmmmm

[wary kite]

watch sal khan

[queen spade]

OMG I LOVE HIM

HES SO PRO

[wary kite]

fr

[spare shoal]

UM

[queen spade]

OH PERIOD

U GOT THAt

[wary kite]

so that's the bottom open circle

😭

[spare shoal]

BRO

[queen spade]

bye

[spare shoal]

OK HOD ON

[wary kite]

connect it to the one above it

and you're good

oh wait

also

you drew your vertical asymptote a bit off

[queen spade]

like instead of the bottom circle its the top??

[wary kite]

you drew it at x = 0

make sure it starts near x = -1

the dotted line

[queen spade]

what

[wary kite]

see here you drew the red bit to the right of x = 0

[wary kite]

yes

perfect

[spare shoal]

wow

[wary kite]

great

[spare shoal]

OMG

[wary kite]

congratulations

you're done

[queen spade]

OMG

[spare shoal]

OGM

[wary kite]

just part e now

[queen spade]

PERIOD

[spare shoal]

QAHAR

oh

[queen spade]

U ATE

[spare shoal]

i forgot about e

[queen spade]

bye

[wary kite]

i think they mean the behavior of f at x = -1

it's not so bad

you can do this

are there any words above the screenshot you gave btw

like do they say anything about f

or does it just say complete the following parts

[queen spade]

thats all

[spare shoal]

YA

[wary kite]

ok

any ideas for part e

[queen spade]

no

[wary kite]

what can we say about f(-1)

anything?

[spare shoal]

um thats the vertial aytmpoteoe thing

sorry for spelling

[wary kite]

nono that would be the limit thing that they said don't worry about

i mean

f(-1)

did they say anything about the value of the function at x = -1

[spare shoal]

no

[wary kite]

exactly

so that's your answer

[spare shoal]

is it dne

[wary kite]

well not necessarily

it might not be defined there

you could also define it there

it's just that the conditions they gave you didn't specify anything about f(-1)

[queen spade]

so just say that????

[wary kite]

yes

[spare shoal]

no

?

just no

?

[queen spade]

bro im actually done with math

[edgy crescent]

hold on

[queen spade]

UGH

[wary kite]

say no, nothing more can be said of the behavior/value of f at x = -1

[edgy crescent]

you can very much say that lim x-->-1 (fx) dne

[wary kite]

are you sure about that sir

[edgy crescent]

yes

[wary kite]

waffling

[spare shoal]

erm

[wary kite]

😭

[queen spade]

HELP

[wary kite]

brother don't type if you don't know what you're talking about

[spare shoal]

can we flip a coin or

its been like 3 hours

[edgy crescent]

its tending to infinity i think so we can say that limit doesnt exist at -1

[queen spade]

thats what ims aying

[wary kite]

they literally said the limit is defined

😭

[queen spade]

IM DEAD

[edgy crescent]

okay then go ahead sorry to interuppt you

[wary kite]

BROTHER IT SAYS LIM X -> -1 F(X) = -inf

😭

[queen spade]

oh my

[edgy crescent]

-inf is not a defined limit

[spare shoal]

oh my

[wary kite]

fym not defined

[wary kite]

they don't use this convention

[queen spade]

im cruing

[spare shoal]

shitting

[wary kite]

stop trying to salvage this

[queen spade]

bro lets js agree pls

im tryna gts

[spare shoal]

THIS IS 80% OF MY GRADE

[wary kite]

this is your answer

[queen spade]

im abt to start tweakinggggggg

ok thanks king

[wary kite]

at best you can say it's not continuous

🤷‍♂️

if you wanted to say something

maybe put that

nothing can be said of the value of f(-1) but f is not continuous at x = -1

[spare shoal]

wow

#kingshit

[queen spade]

so academic

[spare shoal]

thank you

[queen spade]

deadss

[wary kite]

you're welcome

[queen spade]

thank u

[marsh citrus]

@spare shoal Has your question been resolved?

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[uneven prawn]

Pls can someone tell me why they wont add up to 1?

[wild socket]

What do you think it would mean if the probabilities added up to 1?

[runic temple]

did they cover all cases?

[uneven prawn]

Idk i dont even understand all this task really

[wild socket]

alright. do you understand what it means in "the real world" if something has a 0.4 probability?

[uneven prawn]

Im not sure

[wild socket]

If something has a 0.4 probability, that means it has 40% chance of it happening

[uneven prawn]

Oh yea

[wild socket]

similarly, if something has a 0.3 probability, that means it has 30% chance of it happening

[uneven prawn]

Ye

Okay that i know

[wild socket]

So what about a probability of 1

what would that mean?

[uneven prawn]

Its 100%

[wild socket]

yes exactly

In this exercise we have a bag with 3 black balls and 2 red balls and they are looking to describe after how many draws they pick the first red ball

If W = 1 that means the first ball is a red ball

if W=2 that means the second ball picked is the first red ball

etc.

[uneven prawn]

The fourth ball is guaranted red?

[wild socket]

i think you're getting close

[uneven prawn]

Why is the probability for the 2nd ball is red smaller than first one?

[wild socket]

So the probabilities shown in the table are for W=1, W=2, W=3

[uneven prawn]

Wouldnt it be 50%

[runic temple]

you also have to account for the fact you dont get a red ball first

[wild socket]

If the first ball was a black ball, then there is 2 red 2 black left so it would be 50%

[runic temple]

if you get a red ball first, you dont need a second pull

[wild socket]

but, there is only a 60% chance to get a black ball the first time

so it's 60% * 50% because in the other 40% we already found a red ball, so the second ball isn't the "first" red ball

although for this exercise, you don't need to know where the probabilities in the table come from

[uneven prawn]

Okay

[wild socket]

If we add up the numbers in the table, we get the probability that we either draw our first red ball on the first try, second try or third try

does that make sense?

[uneven prawn]

Ye

[wild socket]

now we know that if those numbers added up to 1, then that would mean this

Looking at the experiment, why would this not be the case?

[uneven prawn]

Uh, because after drawing 3 times there is an 100% chance of getting red, because there are no more black balls?

[wild socket]

hmm

we are not looking for the chances after x times

basically what the W shows is

imagine i had a bag with 3 black balls and 2 red balls

and I was asking you to keep picking from the bag until you pulled out a red one

what are the options on how many pulls this would take you? (remember that once you pick out a ball, you don't put it back in, so it stays out for the rest of that attempt)

[uneven prawn]

At the fourth try

[wild socket]

yes, so it could be on the first, second, third, or fourth try, right?

[uneven prawn]

Xe

Ye

[wild socket]

so we know that there is at least some % chance for all these options, even if we don't know the exact amount

[uneven prawn]

Ye

[wild socket]

which of these options are all covered in the table with W's?

[uneven prawn]

1,2 and 3?

[wild socket]

yes!

I think it's important to remember that when you add probabilities, you get the result of what happens if one or the other option is true

[wild socket]

So if we add the probabilities of the first, second and third try being the result here, we get the chance that one of those is the right answer

now if they all added to 1, that means the chance of 1,2,3 combined is 100%

like you said before

[uneven prawn]

Oh i know get it i thi n

That would mean that u get the red ball in the first 3 draws guaranted, which would makrd no sense

[wild socket]

yes exactly!

[uneven prawn]

Its an 90% in the first 3 tries

Wow

[wild socket]

well done

[uneven prawn]

Thanks

W

.close

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[uneven prawn]

What id the derivate?

[uneven prawn]

Is*

[devout mauve]

it helps to write it as 2 x^(-1)

[uneven prawn]

If it would be 4x?

[devout mauve]

no. what was your thinking behind that?

[kind tendon]

$2 * x^{-1}$

[elfin berry]

Daniel Hurbet Marvin IV

[kind tendon]

diff that

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[gaunt lynx]

hello, can unstable processes also be cyclic?

[gaunt lynx]

in matrices

like for example when a * b * c is less than 1 or greater than 1

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[gaunt lynx]

is there a way to find out the fixvektor of a matrix without doing a linear equation system?

[copper raven]

well there's numerical methods, but good luck using them with pen and paper

otherwise not really

[gaunt lynx]

hmm

not even with a calculator?

oh yeah

okay i get it

btw whats the difference between a markov chain and a normal matrix thing

[devout mauve]

the context

a markov chain uses a matrix as part of it

but thats not what a markov chain is

[gaunt lynx]

hmm yeah

its basically

like its independant of the previous stater ight

[devout mauve]

basically, yes

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[gaunt lynx]

yo here for the b) im supposed to find the fixvector but what did i do wrong cuz i dont think x y or z should be negative

[quaint elm]

well... it's easy to check your work right

just see if M * v = v

[gaunt lynx]

wdym?

the vector (180,0,0)?

[quaint elm]

you;re trying to find x,y,z to make this equation true right?

[gaunt lynx]

yes

[quaint elm]

so once you find them it's very easy to check

[gaunt lynx]

oh

yes ok ill check

[gaunt lynx]

no its wrong

wtf did i do wrong

[quaint elm]

dunno, its hard for me to trace your work but go back through and find the error(s)

[gaunt lynx]

okay

[quaint elm]

right away this doesn't make sense to me, shoudlnt this be = z?

[gaunt lynx]

my teacher wrote it like that

this is another example

he does it like this

[quaint elm]

ummm yes that comes from multiplying the matrix times the vector

[gaunt lynx]

but see

he did = 0 too