help-19

[mystic saffron]

Country?

Which one

[balmy dagger]

philippines 😛

[mystic saffron]

I will check your spec ://::/:/ /

[mystic saffron]

No I wont

What your friends doing for this thing.

?

[balmy dagger]

well one thing for sure is they cant help me with this

in my grade lvl precal and calc 1 is taught sooo ig u can imagine the kinda skill lvl i have

we're over polynomials a long time ago

ahauhsuhahahaha i hate my friend for choosing this kind of research topic xDD

the kinda statistical tools our adviser is asking for are stuff like chi square linear regression blabla

but i rlly dk

which kind to use

the stats server aint answering :']

[river pagoda]

linear regression is working here i guess

[balmy dagger]

i thought that toooo i just needed some verification from someone who knows better

my only issue isss

[mystic saffron]

Say you on snow peak
Assume that side of the mountain is flat and ground also a flat, only surface ground is snow let's model the difference of ground level at the bottom across 20 years.

Let's assume that amount of snow growth accordingly to temperature and amount of snow at the top
Let's assume that amount of the snow at the top is constant.

Then simply by measuring rate of change of volume of the snow at the top using camera we can undentify rate of change of snow on the ground

[mystic saffron]

It isn't because we don't know where we are

[balmy dagger]

what if the testing for validity or usefulness of the regression model doesnt have good results

that means i cant rely on it

to form an equation

[mystic saffron]

You mean hypothesis testing?

You need observed value and expected value to aprove or disprove hypothesis

[balmy dagger]

what do you mean by thattt :OO ?

[mystic saffron]

I mean we can't make an equation unless we know any conditions otherwise you can make conditions yourself

[river pagoda]

I'm not deep into that stat but it feels right

[balmy dagger]

ohhh that's true so like for example the equation can only work if the rate of change is constant ryt ?

like disregarding or neglecting other possible factors

[mystic saffron]

No I mean you need to know conditions

Like if you have vulcano explosion obviously rate of change of ground level is different to one at normal whether conditions

[balmy dagger]

ohhhh

[mystic saffron]

Rate of change can be any you want

So we need some context from you

Most of your coursework is not an equation right?

So do you have any idea what will you write?

[balmy dagger]

so like do you think i have to get out of math and look at spatial analysis models?? since it seems more fitting and accurate :3

i just had to make sure if doing stats alone is already enough

if no, i'll go ask the geography people : D

[balmy dagger]

I was assigned the "Statistical Tool" part of the paper

so ahahaudhauha i was rlly

looking for

one to use

[mystic saffron]

What other part of the paper says?

Parts*

You need data for an equation, we don't know what kind of data you have

[balmy dagger]

yerp we dont have data since we're in the methodology chapter :((

we just gotta write

"how" we're gonna

form the equation

shi is tufff

[river pagoda]

can't just first do it with optimal data and get a equation then refine it base on what question want?

or even don't refine it.

[mystic saffron]

That's cool
But we have hypothetical question :

What is the best way to sort out data such that you can form appropriate equation

So I am not sure how accurate they want us to be

[river pagoda]

that's best you gonna get from no data question

[mystic saffron]

You can just say that you will use advanced algorithm which will do everything for you.

So that's clearly impossible question to answer

[mystic saffron]

Yeah

[balmy dagger]

yeahhh no data question is our caseee

[mystic saffron]

If it is not data question than you don't need to prepare for it. Quite obvious

[balmy dagger]

we just had to write an equation where we can plug in 'hypothetical' data

since research and allat

[mystic saffron]

That's wild

https://youtu.be/hGJUFUfu9mA?feature=shared

Here you go

Assume this thing represent what happens on the ground at a distinct point of area A

Just copy this thing

With using t in years

@balmy dagger

[balmy dagger]

ooooo thats so fire

[mystic saffron]

Yeah just use equation he derives

[balmy dagger]

yeahhh seems doable !!

[mystic saffron]

Watch the video and ask me if you don't understand anything. Then we will agree on some simplified version of it. So it will have some context which will be up to teacher to figure out

[balmy dagger]

ooooo i think i can manage : 0

yeahhh this will do i trust it enuff > 3 < yay !!

great help u guyss :3

thanksss (+actually had fun lol i was stressing hours ago abt this)

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[timber socket]

help, just calculate a rectangular`s area acording to the three triangular

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[timber socket]

nope

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[livid perch]

I need help with these questions, because they are sorta different from the first which i solved. just need a little explanation

[open crown]

Cosine Law?

[livid perch]

sine

rule

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[livid perch]

<@&286206848099549185>

<@&286206848099549185>

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[errant ravine]

Hey guys, I'm just wondering if someone would have some work (homework, quizzes or test preps) they did on a STAB22 (Statistics I) class. I'm preparing for it since I'm taking it next semester and I'm not so good with math.

[merry finch]

Not sure what’s in your course and I haven’t watched this playlist before but this guy does pretty good teaching for his calculus playlists https://youtube.com/playlist?list=PL5901C68C96DFCAD1&si=Xx_6SCNGN6hrBlLU

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[odd edge]

@iron tusk Has your question been resolved?

[grand tangle]

waiting for a helper cuz i'm invested in this one

is this qce specialist

[iron tusk]

figured it out and yes it is qce

[grand tangle]

ah yea I got it

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@lone elbow Has your question been resolved?

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[woeful ravine]

.

[fleet shadow]

I tried this qs through the fourmulas but the answer is wrong and im not getting the right answer, Im basically stuck. HELP NEEDED.

[fleet shadow]

<@&286206848099549185>

[odd edge]

Show your work, and if possible, explain where you are stuck.

[fleet shadow]

4=20+x/2 I added the number of matches all together. It isn't right. I used the median formula but its not correct

Middle point?

Sorry English is not my main language

Yes

I don't think so

No

Uh

No

Yes I guess

5??

3 then?

I don't understand

4 is the median.

Understood

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@mystic saffron Has your question been resolved?

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[mystic saffron]

am i doing it

correct

[nimble blaze]

no doesn't look like it

its also a pain to distinguish your x and u

[mystic saffron]

😅 lmao sorry

from here its du

[nimble blaze]

1 sec

your last line is incorrect

[mystic saffron]

should be (u-1/2)² -1/4

[nimble blaze]

and you shouldn't really be approaching this with completing the square

[mystic saffron]

oh yeh

yeah you can do partial fraction, it's easier

true

[nimble blaze]

you already had the denom in factored form a few lines ago
from there, you'd usually want to do stuff like partial fractions

[charred veldt]

you can change variables

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@mystic saffron Has your question been resolved?

[mystic saffron]

thanks guys

😊

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[thorny junco]

What volume of O2 is required to react with 6.74 g C3H8 at 2230 torr and 125 C? use stoichiometry then ideal gas law C3H8 (g) + 5O2(g) = 3CO2(g) + 4H2O(g)

[glacial inlet]

what

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[primal lagoon]

prolly wrong server

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[thorny junco]

oh shoot mb

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[eager saffron]

any idea how to solve

[frigid canopy]

substitute the values of each of the angles

[frigid canopy]

good

now compute it

[eager saffron]

i came to this conclusion

can anybody verify if i got it right

what did you get

[clever fjord]

faiyrose

[eager saffron]

all i did was multiply the top by two then

alrigh got it now thank you

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[slim raft]

10 question correct answer showing is 2

[slim raft]

Why ? How can it be transitive? If 1,3 belongs to R , 3,2 belongs to R but 1 ,2 doesn't

Anyone pls tell

Chapter relations

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[cloud wedge]

Determine the equation of the ellipse with the x-axis and the y-axis as the axis of symmetry and passing through points P(2, 4) and Q(6, 2)

[frigid canopy]

The equation of such an ellipse is of the form

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

[clever fjord]

ƒ(Why am. I here)=I don't Know

[cloud wedge]

(x²/a²) + (y²/b²) = 1

[frigid canopy]

can you do it from here

[cloud wedge]

yes

No I don't know how to do it

I don't know how to find the values of a and b

[pale stream]

substitute in the values of x and y that youve been given from the two coordinates in the question

then solve the simultaneous equations

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[glossy sleet]

If you’re using t ratio in a hypothesis test

[glossy sleet]

Instead of absolute t value/t value

Does null hypothesis have to be X= 0

Because of that

<@&286206848099549185>

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@glossy sleet Has your question been resolved?

[glossy sleet]

Okay so now i know u can’t use t ratio if null isn’t to do with zero

So how do u use it to calculate the standard error

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[gloomy pecan]

An airplane leaves an aircraft carrier and flies due south at 400 km/hr. The carrier proceeds at a heading of 60◦
west of north at 32 km/hr. If the plane has 5 hours of fuel, what is the maximum distance south the plane can
travel so that the fuel remaining will allow a safe return to the carrier at 400 km/hr?

[gloomy pecan]

So far, I created a Cartesian plane

[zinc glacier]

thats not 60deg west of north

[gloomy pecan]

Oh sorry other side

So 60 degrees

And 30

[zinc glacier]

so then you want to write the sidelengths of the triangles as 32t for the ship side and 400t for the plane side

[gloomy pecan]

Ohh okay

T being time in h

Then use cosine law?

[gloomy pecan]

To find the other side

[gloomy pecan]

Okay cool now Im here

But I can't do 25600t^2cos120

Idk how to do thag

[undone palm]

times by cos120 on the calc and pull out t^2

it should simplify a little bit

[gloomy pecan]

Just do cos 120?

[undone palm]

yeah i havent looked to much into this problem but i couldnt see the fault of doing that

yeah its -0.5

[gloomy pecan]

Okay now i have this

[undone palm]

uhhh was there a value for t?

[gloomy pecan]

Time

[undone palm]

yeahh it disappeared at the bottom of your working

[gloomy pecan]

Kh shoot

But ya it's right on the diagram

416.922t

[undone palm]

yeahhh that seems cool

id check da answers and see if thats cool

[gloomy pecan]

An airplane leaves an aircraft carrier and flies due south at 400 km/hr. The carrier proceeds at a heading of 60◦
west of north at 32 km/hr. If the plane has 5 hours of fuel, what is the maximum distance south the plane can
travel so that the fuel remaining will allow a safe return to the carrier at 400 km/hr?

[gloomy pecan]

The questions asking the maximum distance it can travel

On 5 h of fuel

So do I sub 2.5 as the t

Cuz it can go there and back

[undone palm]

as long as motion is constant

that should be okay

no wait it wouldnt be t=2.5

[gloomy pecan]

Oh why not

[undone palm]

so at t= 0 the distance from carrier and plane is 0

[gloomy pecan]

Ya

[undone palm]

and t increases they would grow further apart

[gloomy pecan]

Ye

[undone palm]

sooooo, when the plane is travelling south it wouldnt head back north to the carrier

it would move NWish

[gloomy pecan]

Ye

[undone palm]

and travel a different distance back

[gloomy pecan]

Correct

[undone palm]

so the distances are different

thus its not half 5 hours

[gloomy pecan]

It's a different ratio

So it's 400/416.922 as the ratio

???

[undone palm]

lemme get a jotter

[gloomy pecan]

Whats a jotter

[undone palm]

a notepad

[gloomy pecan]

Kk thx

[gloomy pecan]

How's it looking

[undone palm]

got an equation for the trianlge found the hypotenouse

just thinking about maxinal travel time now

okaaa

i got it

so 5 hour flight time

so 2000km is the maximal total distance travelled

hypot + disctance travelled south = 2000km

sub in ur numbers

then boom

but the two t s will be different

as it will be time flying south + back to carrier = 5hours

[gloomy pecan]

What number do I sub in for t tho?

[undone palm]

t_1 and t_2

respectively

then u solve with these parameters

and find t_1

[gloomy pecan]

I don't understand

What's t1

[undone palm]

sorry mb on the terminoligy

respectively means in the order i have written things

to time flying south was first

so i called that t_1

[gloomy pecan]

How can I solve t

For t

[gloomy pecan]

How can I solve for t

[undone palm]

i dont have my phone on me i need to go find it

will send in what ive written

will be a wee minute

i used a slightly different method from you

if ur curious of the equations i used feel free to ask what they are @gloomy pecan

[odd edge]

@gloomy pecan Has your question been resolved?

[gloomy pecan]

I have just been informed that the answers 955

Km

[undone palm]

okaa i didnt do working but that method should be solid

[lunar geyser]

Did you get it

[gloomy pecan]

🙏🙏💀💀

Why is bro here

[gloomy pecan]

It's a waterloo math contest problem

Answers r there

.close

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[lunar geyser]

Gang what

Senior question???

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[eternal glade]

Hey guys, i have some sort of strange task to do (i let chat gpt translate, please tell me if something is unclear)

[eternal glade]

Let 𝜑, 𝜓 ∈ End(𝑉) be linear mappings from 𝑉 to 𝑉. Then the following statements hold:
(a) If v ∈ 𝑉 is an eigenvector of 𝜑 ◦ 𝜓 with eigenvalue 𝜆 and 𝜓(v) ≠ 0, then 𝜓(v) is an eigenvector of 𝜓 ◦ 𝜑 with eigenvalue 𝜆.
(b) The endomorphisms 𝜑 ◦ 𝜓 and 𝜓 ◦ 𝜑 have the same eigenvalues.

Arrange the following sentences in the correct order to provide a proof for the above statements, separating them into a proof for part (a) and part (b).

I would think its pretty easy. Imo
7. -> 3. solves a. 5. -> 9. -> 4. -> 6. -> 11. -> 2. -> 1. solves b. but im unsure cause i didnt use 8 or 10. Did i miss something?

[tender bloom]

you did use 8

[eternal glade]

huh?, no haha, im typing 5 but its making an 8 out of it? help haha

5. -> 9.

is my start for b

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@eternal glade Has your question been resolved?

[eternal glade]

<@&286206848099549185>

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@eternal glade Has your question been resolved?

[odd edge]

@eternal glade Has your question been resolved?

[odd edge]

@eternal glade Has your question been resolved?

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@eternal glade Has your question been resolved?

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@eternal glade Has your question been resolved?

[vocal ruin]

@eternal glade ive looked and i think 8 and 10 can be used to justify why lambda is zero or not maybe?

Maybe 5 -> 10 -> 8 -> 9 -> ...

They can also fit after so im not too sure

[eternal glade]

@vocal ruin what exactly do you mean? Because... Well... Imo those dont even say this. Because it only says that lambda = 0 => y(v)=0 and lambda ≠ 0 => y(v)≠0

It doesnt even say that other way around its true as well

In my opinion they dont really fit anywhere in there

[vocal ruin]

Im thinking where to fit them because why would the exercise include them in the first place

[eternal glade]

Yeah, im just lost, im not happy no matter where i put them..

[vocal ruin]

They might fit in the end?

[eternal glade]

After the symmetric one? But which value do they add then?

[vocal ruin]

you're right they bring no value, tbh i don't have a clear answer, i might as well say they have no place, but at the same time i can see some places they could potentially fit in

[eternal glade]

Thanks, it helps that other people struggle too. Im getting the results in a week from now. Ill be pretty mad if i dont get full points. That will be a weird discussion with the corrector

[eternal glade]

@vocal ruin we actually talked about it today in class. The corrector doesnt know why the hell they are in there either lol

[vocal ruin]

wow i thought their intention was to confuse people as like some test but nevermind hahah

that's a relief

[eternal glade]

haha

thank you tho

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[open shore]

Did I mess up or can I turn my solution to the one in blue

[open shore]

F prime =

[odd edge]

@open shore Has your question been resolved?

[small yew]

Yes you can…

Just factor out 2x no?

[open shore]

Lh

Oh

Well heres a related questipn

Do these two mean the same thing

[open shore]

.close

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[lost prairie]

Just want to make sure it's right

[odd edge]

Please don't occupy multiple help channels.

[sly juniper]

it doesnt have a y-intercept

[lost prairie]

Alright

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[shell nest]

Can u help me with this

[shell nest]

Can anyone help me with this

[honest turtle]

,rotate

[honest turtle]

Use quadratic formula.

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[cobalt pebble]

HELPP

[cobalt pebble]

48 and 50 please

I’m so confused

[shrewd birch]

What is the step ur stuck at specifically

[cobalt pebble]

all of it

idk where to start

One dice has the prob of 1/6

that’s all I know

[shrewd birch]

Ohk

For 48

When we roll two doce simultaneously there are 36 possible outcomes

[cobalt pebble]

Oh okay

1/6 times 2

1/36

[shrewd birch]

No the probability is not 1/36

[cobalt pebble]

oh

[shrewd birch]

There are 36 total possible cases I mean

[cobalt pebble]

Yes

[shrewd birch]

Se here 1 as a sum of dice is not possible because even if we consider lowest number on both the dice ie 1 the sum is gonna be two so there is no case out of 36 where the sum is one

[cobalt pebble]

oh okay facts

But for 5 we have a lot of them

[shrewd birch]

If we consider 5 , on two dice 5 could appear in the following ways , (1,4) ,(2,3) ,(3,2) , (4,1) only these four cases arise for five

[cobalt pebble]

we have 1 and 4
2 and 3

OH SO

4/36

1/9

IS IT 1:9

[shrewd birch]

Only four cases that tol if we consider both the dice as unique if consider them similai there are only 2 case (1,4) and (2,3)

If we consider both dice similar not unique

So the answer depends weather u consider both as unique or similar

It could be 1/9 or 1/18

[cobalt pebble]

ITS 1/9

JUST CHEKCED

YAAAAA

thanks pcboi

[shrewd birch]

Great so we consider them as unique dice

[cobalt pebble]

yesss

what about 50

can u help me on that

[shrewd birch]

50 could also be solved in. A similar manner by making simple cases

Total outcomes here are gonna be 16

[cobalt pebble]

7/16

are odd

5/16 can be divisible by 3

do i add them

12/16

6/8

3/4

[shrewd birch]

No. U don't listen

[cobalt pebble]

is the answer 3/4

oh

[shrewd birch]

No hold one

[cobalt pebble]

LMFAO

okay..

[shrewd birch]

See here out of 16 cards

1,3,5,7,9,11,13,15 are odd ie 8 cards

3,6,9,12,15 are divisible

We don't add them because

3,9,15 are common number in both

So if we add we count these 3 cards twice

Therefore favourable cases are 12-3 ie 9

[cobalt pebble]

so its 9/16

[shrewd birch]

I believe so

[cobalt pebble]

erm

its 5/8

...

[shrewd birch]

Hmm so it means 10/16 maybe I made a counting error

[cobalt pebble]

im confused

but its oka

can i ask another question

[shrewd birch]

Yes I made a counting error there are 10 cases so it's 5/8 I'm sorry'

[cobalt pebble]

thats okay

u did great

can u help me with 54 - 57..

pls ... exam tmr

might kms

[shrewd birch]

Ok just gimme a sec

I think it's 3/17

In this specific problem we can't pick balls that are red and even numbered

Since all balls from 1-12 are red we skip these possibilities

And 13,14,15,16,17 numbered balls are white

But there exists another constraint

We can't pick even numbered balls

So we also ignor ball no 14,16

There for we only have balls 13,15,17 which are neither red nor even number

So we have 3/17

[cobalt pebble]

for 54

YESSS

IT ISS

so we only take the white balls

pick the odd ones

and bam we have our answer

[shrewd birch]

yes exactly

[cobalt pebble]

okay that easy af

[shrewd birch]

Yes

[cobalt pebble]

55!

9 coins in total

1/9 chance its a nickel - 1/9 chance its a quarter and 1/9 chance its a dime

but the part the fucs me up is the "in that order"

[shrewd birch]

Umm for that question I would use the Ncr formula

[cobalt pebble]

ncr

formula??

ill ask my aMIgo

can we do 56

[shrewd birch]

Lemme se 56

I gotta leave man I'm sorry it's urgent

Sorry I couldnt help u further I hope u figure it out

[odd edge]

@cobalt pebble Has your question been resolved?

[cobalt pebble]

THANKS

ITS OKAY

HOPE UR OKAY

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[full hill]

Can someone explain this? Z is a random variable = X - Y.

[modern sundial]

What do you need explained? Thats just an equation

[full hill]

Is this a definition?

[modern sundial]

I don't know if I would call it a definition, but you should know that integrating out a variable from a joint distribution gives you the marginal one for the remaining variable

[sleek moth]

it's kinda sus because you essentially have two random variables, X and Z, and therefore you should have a two dimensional integral

or two integrals

keep in mind that spicy notation

my bad I don't actually understand what they're saying

maybe

!xy

[odd edge]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@full hill Has your question been resolved?

[full hill]

yep, its totally this

.close

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[sleek moth]

cool ^^

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[eager crow]

How do I know where I need to find my resultant's angle in questions like these:

[eager crow]

Do I need to find the resultant from it's base where it connects tail to tail to it's first component vector?

[eager crow]

ooop, sorry where would the angle for the displacement of the resultant for my plane be at? would it be from where the angle in between the purple vector and the yellow one?

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[tired ruin]

It is incorrect.

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[tired ruin]

@eager crow it should be this

Use resultant vector formula to calculate it's magnitude

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[tired ruin]

.close

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[eager crow]

Okk thank youuu

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[hazy moss]

Hello, I have a few questions with some linear algebra problems.

for the given question specifically, I'm having trouble figuring out how the kernel is solved, and also whether T(x, y, z) = x(1, 0, 0) + y(1, 1, 1) + z(1, 1, 0) is correct

[torpid owl]

no, the columns of the matrix will be the result of T on the basis vectors

[hazy moss]

im sorry i dont get it 😓

[torpid owl]

the matrix of T will be 3x3

[hazy moss]

okay

[torpid owl]

the first column equals T(1, 0, 0). the second column equals T(0, 1, 0). and the third equals T(0, 0, 1)

you are given T(1, 0, 0). you need to use linearity to find the other two

[hazy moss]

okay that makes sense

would T(0,1,0) be (0,1,1) ?

[torpid owl]

yup

[hazy moss]

okay omg

would T be [(1,0,0),(0,1,1),(0,0,-1)] ?

[torpid owl]

yes, looks right

[hazy moss]

ker(T) should be 0 then, right?

[torpid owl]

the 0 vector, yeah I think so

[hazy moss]

oh right the 0 vector tysm

What does T^3 = T mean?

[torpid owl]

it's asking if the cube of the matrix equals the original matrix

[hazy moss]

OH

should be false then, right? since T is not an identity matrix

[torpid owl]

it happens to be true here

matrix multiplication works differently than scalar multiplication

[tired ruin]

@hazy moss Did you know Pustak literally means Book?

[hazy moss]

im aware haha

[hazy moss]

thats true

[hazy moss]

im unsure about T(0,0,1) the -1 doesnt quite look right

[hazy moss]

should be false, though

[torpid owl]

I think it's right

you can check by multiplying the matrix by the given vector (1, 1, 1). you should get (1, 1, 0)

[hazy moss]

you're right

thank you so much

[hazy moss]

if T is this, would T(x,y,z) be x(1,0,0) + y(0,1,1) + z(0,0,-1) right? just making sure the language is correct.

[torpid owl]

yes

[hazy moss]

perfect

thank you, closing now

.close

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[marble pond]

Already solved for f(x) here

[marble pond]

Does anyone have ideas on what steps are necessary in order to solve for g(x) here

[sweet dagger]

If you intersect the normal line of f(x) with OX, you have a radius of the semicircle. You have to find the point C in OX for which the distance OC is that radius

I would use that idea. But it might be another simpler solution

[odd edge]

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[pale briar]

Is this right

[torpid owl]

I think you need to account for the river's current

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[wanton bison]

I would like to calculate the marginal density or distribution (I don't know what it is called) but I can't figure out how.

My professor defined it as $$f_X(x) = \int_\mathbb{R} f_{(X,Y)}(x,y) \dd{y} \text{ and } f_Y(y) = \int_\mathbb{R} f_{(X,Y)}(x,y) \dd{x}$$

But now all of a sudden they calculated $P(X \leq x)$ and $P(Y \leq y)$ and then differentiated both and I am just lost.

[clever fjord]

𝔸dωn𝓲²s

[wicked kestrel]

what do you mean "all of a sudden"

[wanton bison]

suddenly

They didn't use the definition

Instead they proceeded to calculate P(X <= x) and differentiated it

[wicked kestrel]

how did they calculate it?

[wanton bison]

,,P(X \leq x) = F_X(x) \text{ therefore } \frac{\dd}{\dd x} F_X(x) = f_X(x)

[clever fjord]

𝔸dωn𝓲²s

[wicked kestrel]

i mean in your specific example

also that isn't a calculation

[wanton bison]

I will send

What I did

What they did

Everytime I try to apply what I learnt it fails and when I see what they did it's something new

[wicked kestrel]

they're doing an extra step for whatever reason

they're doing the same integral as you, but then doing an additional integral and then differentiating it

for what reason, I can't tell

[wanton bison]

but then my f_y is wrong

They calculated P(Y <= y) and P(Y > y)

for certain interval

[wicked kestrel]

your f_y is wrong because your bounds are wrong

[wanton bison]

but how

-inf to inf = R

besides -1 and 1

i have íntegrand 0

[wicked kestrel]

the integrand is 0 in certain places within [-1, 1] as well

[wanton bison]

depending on y?

[wicked kestrel]

why were your bounds for computing f_x not just -1 to 1 as well?

[wanton bison]

because i thought in terms of y

and y is between x-1 and x+1

that was the logic

[wicked kestrel]

now you have to flip it around

x is bound between two line segments as well

[wanton bison]

yea I thought x = -1 and x = 1

so I have to do x <= y+1 and y-1 <= x

?

I just dont understand the logic

and what's happening

it's seems so arbitrary i am losing my mind

[wicked kestrel]

it's the same deal as with the first bounds, f_XY is not 1/4 for every single x value within [-1, 1]

the relevant bounds are either (x between the line segments) and -2<y<2, or (y between the line segments) and -1<x<1

the two are equivalent

[wanton bison]

I don't know what I did in the first integral it was luck that I got that right

gambling

but it seems to not work always hence it's not correct my thinking

I realized that for some reason

[wanton bison]

looking at this when I say -1 to 1 for x and define y -2 to 2 that would be a rectangle

but else how can I avoid that

it seems to me that i maybe i need make the region in terms of x now

instead of y

so from y-1 to y+1

[wicked kestrel]

well the bounds were setup so that you could just copy them over

but for the second one you just have to convert them to the equivalent form in the other direction

[wanton bison]

So I need to consider this?

basically 90 counter clockwise rotation and then mirroring the region

and then I get two integrals

[wicked kestrel]

that looks about right

[wanton bison]

ok it's funny I in terms of x i only need one itnegral but in term of y in need to split it

and i forgot the reason

why wouldnt it work in one integral

[wicked kestrel]

because your bounds change

on the left, the lower bound is always -1, whereas on the right it becomes a new line

[wanton bison]

what would y+1 to y-1 do

oh

[wanton bison]

where as here -1 to 1 it's like continuous

[wanton bison]

here it cuts off

[wicked kestrel]

If the original region were like this then it would be 1 integral

(but then the other way would be 2 integrals)

[odd edge]

@wanton bison Has your question been resolved?

[iron bear]

sus af notation

[wanton bison]

What exactly

[iron bear]

integration variable x

[wanton bison]

That P(X <= x) = integral?

[wanton bison]

That we integrate from -1 to x?

[hushed gate]

The notation are fine

[iron bear]

the integration variable should not be x

x is already taken by the number used in P(X <= x)

[hushed gate]

Nop my bad it sus

[iron bear]

they integrate over x for both integrals

but it is unclear which x is which

[wanton bison]

But it's dydx or do you mean the bounds I am lost

How should have been the integral instead

[odd edge]

@wanton bison Has your question been resolved?

[odd edge]

@wanton bison Has your question been resolved?

[iron bear]

,, P(X \le x) = \int_{-1}^x \int_{t - 1}^{t + 1} \f1y \dd y \dd t

[odd edge]

@wanton bison Has your question been resolved?

[odd edge]

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[vital palm]

Hey can someone help give me instructions to form a graph on excel. I know this is probably a dumb question but I’m really having troubles 💀. It’s for chemistry.

[vital palm]

So to the left is my table right, then the pic on the right is the temperature of the water and the rate of reaction in order from lowest to highest right. But that graph looks stupid 💀

[steel dragon]

As long as the data you collected was reasonable, the graph should be fine, nothing much you can do about that

[vital palm]

Okay, thanks

.close

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[eternal herald]

Hello! I kinda need help on question d

[eternal herald]

i used guess and check for c

but obv that wont work for d

so im trying to find a way to do this systematically, but im stuck

I would really appreciate some help. Thanks!

[odd edge]

@eternal herald Has your question been resolved?

[eternal herald]

help- 😭

[eternal herald]

bruh

ive been stuck for such a long time im taking a break

[eternal herald]

<@&286206848099549185>

Is there a way i can do this systematically, as i need to complete q. D as well?

pls ping me if someone has an idea, i gtg

[cinder elk]

I mean have you tried using the same setup that is given for c, for d? @eternal herald

[eternal herald]

no, since i used guess and check for c

[cinder elk]

like the A/B < 7/B < A/7?

[eternal herald]

yes

i ended up getting (6,10) (6,9) and (5,10)

[cinder elk]

for?

[cinder elk]

oh, for c

I'm looking more at d

[eternal herald]

yea, i need help with that

[cinder elk]

I mean, you know that it is ?/? < ?/? < 1/?, and I can guarantee you that 2024 is the denominator on the smaller two fractions ?/2024 < ?/2024 < 1/?, and the other one would go over the 1 as it makes it the smallest so, 1/2024 < ?/2024 < 1/?

2024 would be the denominator as it is the largest number possible and would make the smallest possible number if it is in the denominator

similar with 1, it is the smallest number possible that would make the smallest number possible if it is in the numerator

So now it is just what number would fit that is 1. larger in the form ?/2024 than 1/2024 and 2. smaller in the form ?/2024 than 1/?

@eternal herald

You also can tell it won't be 1/1 as it has to be less than 1, so follow the rule of proper fraction

[eternal herald]

im comprehending...

[cinder elk]

Do you want a second or a hint?

[eternal herald]

hold up

probably a hint

would vcing be a better option? im quite slow at this type of stuff...

[cinder elk]

at some point, some "random" number in there, ?/2024 will equal 1/?. So at what point will ?/2024 = 1/? (x/2024 = 1/x)

[eternal herald]

i cant even think abt the first sentence u said kind of

😭

why would 2024 be the smallest?

and in the question what does it mean by "one other pair"

[cinder elk]

2024 can't be in the numerator since it is the largest possible number. if it is in the numerator it would always make an improper fraction

so it would have to be in the denominator and since it is in the denominator it makes the fraction incredibly small

[eternal herald]

mhm

ok

[cinder elk]

1/2024 is incredibly small

[eternal herald]

yes

[cinder elk]

in fact it is the smallest possible number you can get from those pairs and set ups

[eternal herald]

yes i understand

[cinder elk]

Do you think you got it from here?

[eternal herald]

what do you mean by this?

and btw for the quesion what does it mean by the "unknown number"

what number

[cinder elk]

x/2024 isn't going to remain smaller than 1/x at all points, at some number it is going to be larger like 2/2024 is smaller than 1/2 but 2023/2024 is bigger than 1/2023. and at some point x/2024 has to equal 1/x

[cinder elk]

Solve for that number and it will tell you all of the numbers that fit x/2024 < 1/x

[eternal herald]

oh

and youre helping find the number?

[cinder elk]

yes, I think? I don't really know what you mean by that

[eternal herald]

hm

[cinder elk]

do you know algebra?

[eternal herald]

yes

[cinder elk]

so how would you solve this ^

[eternal herald]

im stuck on this

[cinder elk]

wdym?

I put random cause it is a seemingly random number but it is a finite (almost, it technically is a ongoing decimal) number

I guess "At some point, some number x will make x/2024 equal 1/x"

would be a better statement

[eternal herald]

ooh

ok

yes

so i find x?

[cinder elk]

yes

[eternal herald]

i cross multiply, x^2 = 2024*1
x=sqrt2024
appox 44.96

[cinder elk]

I would use the rounded down whole number as rounding up make x/2024 > 1/x

[eternal herald]

hm?

[cinder elk]

would number larger than apporx 44.96 make x/2024 larger than or smaller than 1/x?

you know 44.96/2024 = 1/44.96

[eternal herald]

larger?

[cinder elk]

yes, so would 45/2024 be > or < 1/45?

[eternal herald]

45/2024 > 1/45

right....

[cinder elk]

yes, what about 44 = x?

[eternal herald]

<

[cinder elk]

Yes

and what about any number between 2024 and 45?

[cinder elk]

*2023, not 2024. can't use 2024

[eternal herald]

wym any number netween 2023 and 45

between*

[cinder elk]

will any number between 45 and 2023 make x/2024 > or < 1/x?

[eternal herald]

right

[cinder elk]

yep

[eternal herald]

because its bigger than 44

[cinder elk]

Yes

[eternal herald]

oo ok

[cinder elk]

so what about any number between 44 and 2?

[eternal herald]

< because its smaller than 44

[cinder elk]

how many whole numbers are there between 44 and 2 (counting 44 and 2 as well)?

[eternal herald]

43

...

or is it +1

[cinder elk]

44 would be 44-1

44 through 1

[eternal herald]

mb

so the answer is 43?

[cinder elk]

Yep

2 through 44

[eternal herald]

okk

[cinder elk]

Visualization

(this does include 1/1 as it will also do improper fractions)

[eternal herald]

stay here for like 10 more minutes i might have some quesitons

[cinder elk]

You can ping me again

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[slim skiff]

Hello,
I don't fully understand how to get at the end from $\frac{1}{|x|}rf''(r)+2f'(r)$ to $\frac{1}{|x|} cos''(|x|-ct)$.

If you insert $|x|$ for $r$, you get $\frac{1}{|x|}\cdot\left(|x| f''(|x|)+2f'(|x|)\right)$. I kinda understand how $\frac{1}{|x|}\cdot \left(|x| f''(|x|)\right)=\frac{1}{|x|} cos''(|x|-ct)$, but what happens with $2f'(|x|)$?

Thanks

[clever fjord]

Sheymes

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[mystic saffron]

Is it dot product?

Isn't it

[slim skiff]

.close

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[umbral gale]

Is this a valid way to calculate the volume of a rectangular based pyramid? The formula begins by estimating the volume using an endless number of thin slices with decreasing bases as we move up along the height of the pyramid

h - pyramid's height
L - the length of the base
l - the width of the base

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@umbral gale Has your question been resolved?

[mystic saffron]

Probably correct since you get correct answer.

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[raw moat]

Can someone help me with this question please? (Analysis)

[fresh ruin]

lower sum is, between every number in P, the smallest value of x^3 times difference between the two numbers in P, added all up

and if you look at the graph of x^3, it just keeps increasing because it's / shaped, so the smallest value of x^3 is going to be x^3 at the left values of P you have

[raw moat]

so the smallest value of x^3 would be -1 right?

[fresh ruin]

it changes for the rectangles -2 to 0, 0 to 1, and 1 to 2

[raw moat]

so which do i choose?

[fresh ruin]

for the first one -2 to 0, the lowest is at -2 to (-2)^3

for x^3 it's always the left value and you plug it into x^3

looks like this

[raw moat]

ahh i see

so in the case, the lower sum would be 8?

[fresh ruin]

(-2)^3=-8 for the first rectangle yea

[raw moat]

and thats the left value?

oh right -8

[fresh ruin]

yea the left side is always lower for x^3

[raw moat]

i see

[raw moat]

gotcha, thank you for this

.close

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[languid cairn]

can anyone help me with like the steps of solving this, i missed a week of school and have a math quiz tomorrow and i don’t even know what slant height is 😭

[steel dragon]

Slant height is h

[languid cairn]

is it different from actual height?

[steel dragon]

Yeah the height H is different from the slant height h, as you can see in the diagram

[languid cairn]

yes

so do i have to use pythagorean theory to solve?

or something like that

[steel dragon]

Which part?

[languid cairn]

the volume

[somber jackal]

yeah

[steel dragon]

Do you know the formula for volume of a square pyramid?

[languid cairn]

1/3BxH

[steel dragon]

Yeah, you have everything you need so just use the diagram to help

To find H though, youll need to create another triangle and use Pythagoras yeah

[languid cairn]

wdym create another triangle

[steel dragon]

So look at the pyramid

You can see how H and h are two sides of a triangle with base 0.5a

[languid cairn]

0.5?

i got the base area to be 36

oops

[steel dragon]

Thats right

[steel dragon]

Im saying 0.5a is the base of the new triangle, not the pyramid

[languid cairn]

ohhh

ok

[steel dragon]

So draw another triangle with height H, hypotenuse h, and base leg 0.5a

[languid cairn]

alright

is it gonna be a^2 = (0.5)^2 + b^2

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[fair bridge]

hi

[fair bridge]

got a questino

no

.closed

closed!

[mystic saffron]

/report @fair bridge

/report @fair bridge took multiple channels

[fair bridge]

i have not .

you did

you took mine thus I have gone to another channel

[azure turtle]

Anyway don't fight

[fair bridge]

could you help me ?

@azure turtle

[azure turtle]

Sure

The question

[fair bridge]

not sure what would be the equation

[azure turtle]

Seems like sin function

So canu understand how it's sin function?

[fair bridge]

yup

it starts from midline

i guess

am I wrong?

so there is no phase shift

?

[azure turtle]

Yes

So

It's A sin(Bx+c)

[fair bridge]

so would iit be correct: 5 sinx

?

midline is zero so that would not matter

[azure turtle]

How is it 5sin x

The maximum value of A sin() is A

And here it's 4

[fair bridge]

oh it would be 4 sin x

[azure turtle]

And

[azure turtle]

The B here

You have to find it

[fair bridge]

oh. just a second

4?

is b 4

i think it is

[azure turtle]

Put pi/8 in the equation to find out B

Yes

It's 4

As for C it's 0 since nophase change

[fair bridge]

yup

just give me a second

if i got it right

ok?

i will tell you the answer

[azure turtle]

Sure

[fair bridge]

4sin(4(x)

i am kinda confused what d would be ?\

[azure turtle]

That's crct

[fair bridge]

is d the midline or c?

?

[azure turtle]

What's midline?

[fair bridge]

equation of ais

axis

[azure turtle]

Oh

Isn't it x-axis?

I'm not familiar with this concept

[fair bridge]

ok. never mind.

so this would be the correct answer just to make sure

right?

4sin(4(x)\

[azure turtle]

Yes

[azure turtle]

That's correct

[fair bridge]

It told me its wrong

Not sure why though

[azure turtle]

Wait rly?

[fair bridge]

Yup

[azure turtle]

But seems like crct tho

[fair bridge]

Could be that i put extra brackets

Its definitely cuz i put alot of extra brackets

So i will write it like this now

Thanks anyways

@azure turtle could you help me with an assignment as well?

[azure turtle]

Which one?

@fair bridge

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@covert adder Has your question been resolved?

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[mystic silo]

im learning laplace transforms and kinda stuck on some unit step/dirac step function stuff - in one problem i got to this step:

Y(s) = (e^(-2πs)+1)/(s^2+1)
y = L^-1[Y(s)] = (U(t-2π)+1) sin(t)```
this is correct i think, so all good - but then in the next problem i got to a similar point
```[original problem: y''+2y' = δ(t-1)]
Y(s) = (e^(-s)+1)/(s^2+2s)
pfd: L^-1[1/(2s) - 1/(2(s+2)] = 1/2 - 1/2e^(-2t)
y = L^-1[Y(s)] = (1/2 - 1/2e^(-2t))(1+U(t-1))```
however this isnt correct apparently, the correct answer is `1/2 - 1/2e^(-2t) + (1/2 - 1/2e^(-2(t-1)))U(t-1)`. im not really sure, why is it needed to substitute t-1 into the inverse laplace in the second case but not in the first?

[mystic silo]

or is my work for the second case just wrong?

maybe the substituion only applies to the frequency shift e^(alpha*t)?

[odd edge]

@mystic silo Has your question been resolved?