help-10

[obtuse pebble]

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[fathom flicker]

I need help following along with this proof about sequence convergence. $\newline$ If ${x_n}$ is a sequence and it converges to x and to y, then $x=y$. I'll start typing out the proof below

[warm shale]

AustinU

AustinU

AustinU

AustinU

[fathom flicker]

this following step is the step that I am lost at, I don't see where it comes from

[warm shale]

AustinU

[fathom flicker]

Any help understanding where this final equality comes from would be appreciated. Please tag me if you respond.

[sonic anchor]

they added 0

$-x_{M_1+M_2}$ and $x_{M_1+M_2}$

[warm shale]

Køter

[sonic anchor]

and im assuming the the real implication then is that that is < epsilon/2+epsilon/2=epsilon

showing x and y are epsilon close for some m1 and m2

@fathom flicker

[fathom flicker]

ohhhh

because that's 0

gotcha

I was just wondering where those pieces came from lol

yeah, that is what happens next in the proof

triangle inequality

and then we show that |x-y| < epsilon for all positive epsilon

so x=y

Ty Koter!

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[obtuse pebble]

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[tall forge]

Can some one help with question 1

[violet sentinel]

!status

[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[tall forge]

1

[sonic anchor]

find out how big a fraction of the profit comes from the jumping castle

[obtuse pebble]

@tall forge Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[shy agate]

how to prove with part one of FTC

[sage geode]

How to prove what?

[shy agate]

g'(x)

find g'(x) i mean

[sage geode]

Alright, what do you mean by part one of FTC btw?

[shy agate]

part one of fundamental therom of calculus

the easiest one

[sage geode]

According to FTC, y = F(1) - F(1 - 3x) where F'(u) = u^3/(1 + u^2)

So y' = -F'(1 - 3x) * (-3) or simply 3(1 - 3x)^3/(1 + (1 - 3x)^2)

[shy agate]

ok so

basically factoring the negative flip the upper bond and the lower bond of the intergals upside down?

[sage geode]

Yes

[shy agate]

that applies to every intergrals?

[sage geode]

Yes

[shy agate]

thx

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[timid silo]

!status

[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[timid silo]

4

Is the range [0,1)?

[sage geode]

Yeah

[timid silo]

And I can rigorously write that like :
f = {(x, f(x)): x is an element of R}. The range is the set of all the values that f(x) can assume given real x. so, x^2/ (1+x^2) = f(x).
So when x= 0, f(x) = 0.
As x approaches neg infinity, f(x) approaches 1. Similarly when x approaches positive infinity, f(x) approaches 1.
Therefore the range must be [0,1)

I am trying to learn to be more rigorous

Is there something I should change here to do so?

[sage geode]

That is not enough

You just said f(0) = 0 and f(x) -> 1 at infinity

Which does not mean the range is [0, 1)

Instead you just need to prove the inequality 0 <= x^2/(1 + x^2) < 1 for all real x

0 <= x^2/(1 + x^2) is always true because x^2 and 1 + x^2 are both nonnegative numbers

And x^2/(1 + x^2) < 1 is true because x^2 < 1 + x^2

[timid silo]

I understand

But that is a verification that that is the range

How do I frame my answer

[timid silo]

With respect to this

[undone ferry]

I have also been doing this ques since 20 minutes, though it is intuitive that the answer is [0, 1) I am trying to prove this

[timid silo]

i think once we get an intuitive idea, we can just show that its that like Lonely Bean said

[undone ferry]

That doesn't clear concept tbh

I have a solution I am not sure if it works

[timid silo]

Mind sending it in

I was thinking that we could also do this

[undone ferry]

Ya sure 2 mins

[timid silo]

$\frac{x^2}{x^2 + 1} = \frac{(x^2 + 1) - 1}{x^2 + 1} = \frac{x^2+1}{x^2 +1} - \frac{1}{x^2 + 1}$

[warm shale]

Matchstick

[timid silo]

that would be $1 - \frac{1}{x^2 + 1}$

[warm shale]

Matchstick

[undone ferry]

Highly incorrect imo and the range is not even coming correct but i think this is how it would be approached

[timid silo]

but that brings us to the same spot as before, we still have to go the same route

[undone ferry]

sorry i am on PC so can't use camera for photos

[undone ferry]

Here we start with assuming that x^2 is always greater than or equal to zero

I could do it with Sign Scheme method but x^2 will then nvr be -1

bcz root of -1 doesn't exist

[timid silo]

you wrote the incorrect range in the last step

wait

[undone ferry]

I told you range is not even coming correct

[timid silo]

we could let x^2 /(x^2 +1) equal to 0. find x in that case

and then we could use that x^2 > 0

that will do

[undone ferry]

I have an idea

give me a min

[timid silo]

we'll have two cases x^2 = 0 and x^2 > 0

sure

[undone ferry]

Yes

u r right

[timid silo]

bro are you solving ncert?

[undone ferry]

Maybe we could use above x^2+1/x^2 >= 0
and put x belongs to (-infinity, infinity)
Basically to takee very large numbers on both sides and then determine the range

[timid silo]

we could but i was told that wasnt enough

[undone ferry]

I am also in 11th currntly doing this chaptr from Cengage

for JEE

[timid silo]

ahh

[undone ferry]

Why r easiest problems most difficult to prove

[timid silo]

i dont know

[undone ferry]

maybe we can since we have actually proved that range would be greater than orr equal to zero in all cases then we can use values of x to determine range

[timid silo]

but if we use your solution with the two cases it is good as done

[undone ferry]

This would have been very easy if x^2 could be
-1

but that is not possible

Maybe we can put f(x) in a variable

I'll try this approach

[timid silo]

put in what?

[undone ferry]

Got the answer

let's go

Finally

I'll share it, one second

[timid silo]

alr

[undone ferry]

Basically if you put anything including 1 or above then the solution will be negative but inquality says solution can only be 0 or greater than 0

This one is incomplete actually let me complete it

If you put y < 0 then also the solution will be -ve which goes against >= 0

1 and 0 are the roots of equations y and 1-y

called critical points

and we do not include 1 bcz the 1/0 is undefined

@timid silo Did u understand?

1 hour wasted, phew

i feel worthless

[timid silo]

how did you find the critical points?

[undone ferry]

1-y = 0
Y = 1

y = 0

Critical points r points where these variables will change signs

[timid silo]

ahh

wait leme digest this

[undone ferry]

If you put -60 as y for ex
-60 / (1-(-60) = -60/61 which is ngative and smaller than zero soc an't be the solution

There is a method called Sign scheme or Wavy curve method which is not in NCERT syllabus but is very helpful

where we put signs on the number line

[timid silo]

ahh okay

i think i understand

thank you so much:)

.close

[obtuse pebble]

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[lavish sequoia]

Ok if an airplane covers 7007 miles in 98 upon 35 hours how long did it travel in 1 hour

[lavish sequoia]

ok i simplified it to if a airplane cover 1001 miles in 14 upon 5 hours

[rich plume]

Let the plane cover x distance in one hour

So if in 1 hour it covers x distance, what distance does it cover in 2 hours?

@lavish sequoia

[lavish sequoia]

x times 2

[rich plume]

Yes

Or 2x

So what distance does it cover in 98/35 hours?

[lavish sequoia]

98x?

[rich plume]

No

Notice how many hours

[lavish sequoia]

35x?

[rich plume]

No

Let's see another example

Okay what distance is covered in 0.5 hours

[lavish sequoia]

x upon 2

[rich plume]

Can we write 0.5 as 1/2?

[rich plume]

Yes

[lavish sequoia]

yea

[rich plume]

So in 1/2 hours the distance covered is (1/2)x

[lavish sequoia]

yes

[rich plume]

So can you now answer the distance covered in 98/35 hours?

[lavish sequoia]

im sorry i dont get it 😭

[rich plume]

Okay can you write 98/35 as a decimal?

[lavish sequoia]

2.8 right

[rich plume]

Yes

So the plane covers x distance in 1 hour
2x distance in 2 hours
So what is distance covered in 2.8 hours?

[lavish sequoia]

2.8x?

[rich plume]

Yess

But we are given the plane covers 7007 miles in 2.8 hours

[lavish sequoia]

yes

[rich plume]

So both the quantities 2.8x and 7007 are equal

2.8x=7007

Now you can solve for x

Which is required ans

[lavish sequoia]

oh thank you

[rich plume]

Welcome

[lavish sequoia]

.close

[obtuse pebble]

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[light flume]

I came across an interesting question that asks to express sqrt 2 as an approximation in fraction

[light flume]

or using the words of the question

"Deduce sqrt2 as 1/(2+1/(2+1/2.....)))

i understand that it is irrational so thereby cannot be expressed correctly as a fraction (at least not in a form we can count)

but how would u go about proving this

[rich plume]

Do you have a pic of it?

[light flume]

@rich plume here

scope of my knowledge is yr11 highschool

im not too sure how different australian curriculum is to elsewhere

[rich plume]

The RHS is an infinite repeating series below numerator

[light flume]

yep i recognise that

[rich plume]

Assume this quantity to be x

[light flume]

just before u proceed more into the question

generally when it says deduce, u arent really meant to use the RHS

and supposed to generate it from purely elsewhere

if that makes sense

[runic void]

I see this as recursively replacing \sqrt(2)

Hopefully this will make sense

[night moth]

well you can use the rhs to understand the procedure of getting from the rhs to sqrt(2), and then in the actual answer write the same thing but backwards

[light flume]

ah ok

dang

thats quite neat way

so thereby every irrational number is expressable this way?

[runic void]

isn’t this ramanujan continued fractions?

[night moth]

i suppose that is true only for ones which are not transcendental

[light flume]

right

so all algebraic irrational numbers are expressable in recursive

[night moth]

yep

[light flume]

https://en.wikipedia.org/wiki/Rogers–Ramanujan_continued_fraction#:~:text=The Rogers–Ramanujan continued fraction,of values of its argument.

god dang this cant be it man

im screwed if this shows up intest

T=T

i suppose its still doable without full understanding of the theorem above

thx for the help

.close

[obtuse pebble]

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[edgy needle]

Hi how do i do qb ii

[edgy needle]

ohh wait

[rich plume]

use the exponent rule a^n/a^m=a^(n-m)

[edgy needle]

But before that

Do i add a^5/2 to a^1/2

So its 6/2

OHHHHH

[rich plume]

and a^n*a^m=a^(m+n)

[edgy needle]

CALL ME A GENIUSSSSSS

stop

can u check this question

part b

[rich plume]

all correct

[edgy needle]

ah ok and this one

[rich plume]

correct

[obtuse pebble]

@edgy needle Has your question been resolved?

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[vestal island]

Hey everyone, can someone help me on the topic of multiple regression analysis? I am asked to assess the reliability of my multiple regression model, which I am unsure as to which models/test could best justify this. If someone could help, I could additionally provide the data and context too. Thanks

[obtuse pebble]

@vestal island Has your question been resolved?

[vestal island]

<@&286206848099549185>

[tame narwhal]

how are they defining "reliable"

and yes, some more context and showing the data would be helpful

[vestal island]

this is also what im confused about. I'm guessing it's just whether the regression is valid (not violating any regression assumptions) and is statistically significant, but I'm not entirely sure.

Here is the output of the multiple regression model. Basically we are analysing whether certain variables such as field goal %, 3 point %, free throw %, turnovers, and the introduction of a new ball (dummy variable) impact the scores made by a basketball team in a season.

[tame narwhal]

"statistical significance" should not have anything to do w/ "reliability"

has your textbook and/or teacher defined "reliable" in this context

[vestal island]

no they havent unfortunately

would it be simply whether the model has pitfalls or not?

[tame narwhal]

so they say "reliable in terms of predicting the scores made by the team". does that mean they want you to predict total score per game, using the model? is there more to the question?

[tame narwhal]

all models have "pitfalls", technically

[vestal island]

so the overarching question is they gave us a set of data and instructed us to create a multiple regression model with Y variable as scores made by the team, and independent X variables as the ones i mentioned above. Then, they're asking us whether this regression model is reliable in terms of predicting the scores made by the team over an entire season (which is what the data they provided us is)

[vestal island]

so they're not asking us to specifically predict a score (as they provided us this data), but rather assess the "reliability" of the model

[tame narwhal]

so I guess they might be asking about the residuals, perhaps. y - yhat

[vestal island]

yea that was one of my initial thoughts. I was thinking residual analysis, f-test, t-tests, and/or something with r-squared?

here's the residual plot.

[tame narwhal]

those look fine IMO

[vestal island]

yep, i also think that

what do you think about using an f-test?

does that indicate anything about reliability or is that just significance

or arethose two terms interchangable

[tame narwhal]

I don't know what reliable means TBH. it should be defined by the book or teacher

what are TOV and NEWB?

[vestal island]

TOV stands for turnovers, and NEWB is the dummy variable i created which is the introduction of a new ball design. So the dummy variable assigns =1 to games played **before **the new ball, and =0 is games played **after **the new ball.

[tame narwhal]

ok. well anyway, I don't know how to answer it if they don't define "reliable", but given the residuals look reasonable I would say "yes"

you could possibly use the F-test as justification

since the denominator is the mean squared error

which is low relative to the total mean square

[vestal island]

yep, thats what i came to the conclusion of. Residuals look fine and f-stat significance is lower than 0.05, so its "reliable" ig.

But should I worry about the fact that 2 of the variables are statistically insignificant (i.e. p-value > 0.05) and also that multicollinearity exists across these variables?

[tame narwhal]

multicollinearity could be an issue, yes. whether they are stat. significant or not doesn't

[vestal island]

do you mind briefly explaining why stat significance doesn't matter?

[tame narwhal]

because it is usually just an arbitrary cutoff. for an individual predictor, even if p > 0.05 that predictor still might have an important contribution towards predicting your dependent/response variable

[vestal island]

right that makes sense. So it may still have an impact but cannot be distinguished from a statistical standpoint?

[tame narwhal]

I don't know what "distinguished from a statistical standpoint" means

[vestal island]

basically the contribution may not be captured by the p-value completely

[tame narwhal]

all I'm saying is that, while the new ball design might not be "statistically significant" in terms of this model and specific dataset, it might have a real impact on total score

statistical significance and "practical" or "real-life" significance are different things

[vestal island]

yep thats what i was trying to get at, thank you

and just one last qucik question

the y-intercept is 19.881, does this make any sense for this regression model and its practical scenario of a basketball game?

[tame narwhal]

that is the total points scored when all predictors equal 0

so... I'm not sure how that could be possible. because that would mean FG%, 3pt%, and FT% equal 0

and TOV=0, and NEWB=0 (which you said is after the new ball design)

[vestal island]

yea so if we have NEWB=0 when interpreting the intercept, does that mean data before the new ball design is just completely cut off?

[tame narwhal]

cut off?

it just means that, if NEWB 0 is after and NEWB 1 is before, then scores are ~2.7 points higher after new ball design

[vestal island]

yep but in terms of interpreting the intercept, how does that work since we only have NEWB=0?

since we have to set the predictors to 0

[tame narwhal]

it just means it's the value of y (total points) with all predictors equal to 0. it depends on the meaning of the dummy variable, which here is after new ball design was introduced

[vestal island]

so when interpreting the intercept's practical meaning, we're saying that FG%, 3PT%, FT% are all equal to 0. And then the dummy variable in this scenario is set to "new ball design"

[tame narwhal]

it's the same as an intercept of a straight line y = mx + b. it is nothing more than the y-value when x=0

just in the multiple regression case, it's when all predictors/independent variables are 0, including any dummy variables

[vestal island]

yeah i just dont get the dummy variable part. Because when we set that to 0, it's not like we're setting a value to 0. It has a meaning behind it (new ball design introduced) which makes it kind of weird.

[tame narwhal]

it does have meaning. NEWB = 0 is for games after the new ball design was introduced

[vestal island]

yeah that's what i'm saying, but just confused in regards to how that fits in when substituing all predictor values to 0 for interpreting the intercept.

because essentially we get this right;

intercept (19.881) = 0+0+0+(new ball introduced)

[tame narwhal]

yeah. it definitely gets confusing with multiple predictors

[vestal island]

right. So do you think its safe to conclude that the intercept doesnt really make sense from a practical/real-life relevancy viewpoint?

since having a 0 FG, 3PT, FT is really unlikely and unrealistic

[tame narwhal]

yeah, I don't see how that could be the case

what do the data look like?

maybe some of the rows where NEWB=0

[vestal island]

here's a chunk of it when NEWB=0. Sorry i couldnt get the titles in because NEWB=0 is the second half of the data

but yea none of it is really close to 0

[tame narwhal]

oh right. so it's probably an interpolation of the regression line, and would be the value if all the other variables were 0

which won't ever happen in real life

so yeah, I'd say the intercept parameter is not sensible in this model

[vestal island]

yea i think they were hinting at that since they one of the question asks if "the intercept makes any sense given the data you have"

anyways, thanks so much for your help bro. Helped alot, I appreciate it

[obtuse pebble]

@vestal island Has your question been resolved?

[fair notch]

how did they get the f(t + 5) ?

[candid yarrow]

what don’t you understand in #❓how-to-get-help

[obtuse pebble]

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[lean kayak]

question 8 b, i’m completely stuck, have no notes on this and have never done something like this. where do i start?

[candid yarrow]

Do you know how to determine the equation of a line?

[lean kayak]

what do you mean by that? i might have not sure

[candid yarrow]

Do you know how to find the equation of a line?

[lean kayak]

y=mx + c

??

[candid yarrow]

This is the equation of any line, and now you need to find m and c for these specific lines

[lean kayak]

right, but what i’m confused is that in 8 b the line is under 6

so it’s (0,-5)and what?

what would be the x

[candid yarrow]

this is the y intercept

Next you need to find the slope, m

[lean kayak]

using rise over run?

[solid oxide]

Or you can use a few points and solve equations

[lean kayak]

how would i do that? not sure what u mean

[solid oxide]

As in you already have (0,-5)
y= mx+c
-5=0x+c
c=-5

[lean kayak]

m would be -1/2?

[solid oxide]

Where did u get that

[candid yarrow]

as a sanity check, if the graph is going up, your slope should be positive

[lean kayak]

right right my ba

[solid oxide]

So just use a different point for example (4,-3) to find m

-3= 4m-5

[candid yarrow]

reverse for negative slope: graph goes down

[lean kayak]

rise over run
rise of slope = 3
run = 6
3/6 = 1/2

so answer should be y= 1/2 x -5?

[lean kayak]

not sure what this is i’m super confused now😭

[solid oxide]

Thats just another (x,y)

[lean kayak]

oh yeh yeh

[solid oxide]

But yeah you get the same result anyway

Im just lazy

[lean kayak]

so answer is y=1/2x -5

i think i got it

[solid oxide]

Yep

[lean kayak]

okay thanksss

.close

[solid oxide]

Np

its .close

[lean kayak]

.close

[obtuse pebble]

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[late flare]

for the derivative of sin(x+y)

[obtuse pebble]

Please don't occupy multiple help channels.

[late flare]

can I do derivative of sinx+siny

so cosx + cosy'

[high lily]

no

[late flare]

why

[high lily]

first step is already wrong

[late flare]

distributive property

[paper anvil]

What’s your issue ?

[high lily]

sin isn't a magic value being multiplied tio (x+y)

[late flare]

this

[paper anvil]

Tell fast

[paper anvil]

Cos x + 1

[high lily]

sine is a funnction

[paper anvil]

Done

[late flare]

so how do i find the derivative

[high lily]

distributive property doesn't apply

chain rule would be the most efficient

[paper anvil]

Do you know differentiation to begin with

[late flare]

also the derivative of 2y

[paper anvil]

2

[late flare]

people say 2 dy/dx

[paper anvil]

Stop letting us complete your homework

[late flare]

is it 2 y'?

[paper anvil]

Do you know what you’re doing

?

[late flare]

i dont want you to complete my homework

i want to understand

[late flare]

no

[paper anvil]

You got photomath?

Download it

It’ll tell you everything

Don’t have to ask here

[late flare]

i still dont know how to find derivative of sin(x+y0

[paper anvil]

Use chatgpt then

[late flare]

is it capable of solving everything?

[paper anvil]

Sin derivative is cos btw

[late flare]

chatgpt is the shittet

thing to use use

in math

[paper anvil]

Yes just ask it to explain in simple terms

Don’t have to ask here

[high lily]

<@&268886789983436800> slaysec being very intrusive, past logs/messages aren't desirable either

[paper anvil]

??

I’m helping the guy out

[teal turret]

by recommending chatgpt

Yea Aight

[paper anvil]

Chatgpt literally helped me in my math understanding for a whole sem

[high lily]

are you familiar with chain rule?

[paper anvil]

I didn’t have to ask people compared to before it came around

[late flare]

yes i am

f'(gx) multiply gx'

[paper anvil]

Yes correct

[late flare]

the x + y is the gx

[high lily]

(f(g(x))' = f'(g(x)) * g'(x)
can you apply that here

[late flare]

what is the derivative of y?

y' or 1

[paper anvil]

1

[late flare]

why

[high lily]

no

[late flare]

that what confuses me

[paper anvil]

Any variable derivative is 1

[high lily]

ignore them

[paper anvil]

?

[high lily]

they're feeding you all the wrong info

[paper anvil]

You’ve studied derivation ?

[late flare]

oh so its y'?

[paper anvil]

And differentiation ?

[high lily]

yes y' is literally the derivative of y

(wrt to your variable)

[paper anvil]

If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x"

[late flare]

so it should be cos(x+y) multiply 1+y'

[paper anvil]

Yes

[high lily]

cos(x+y) * (1+y')

[late flare]

i got it , thanks @high lily and @paper anvil

[plucky swan]

stop encouraging people to use photomath or chatgpt for the things they ask here slaysec

[paper anvil]

No worries

Happy to help

[paper anvil]

I learnt math that way and it’s good to encourage platform than discouraging others users

[trim portal]

This is what happens when you use chatgpt. This is the precisely the kind of missinfo it would give you

[paper anvil]

It helped me why couldn’t it help him

[paper anvil]

I meant differentiation not derivative

[candid yarrow]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[trim portal]

when you differentiate y wrt x, you get dy/dx, not 1.

[paper anvil]

Ok sorry my bad won’t provide answers anymore

[plucky swan]

Said platforms will not do anyone good who is actually trying to learn things. Especially chatgpt even gets maths wrong a lot. Do not tell people to use it

[paper anvil]

But I learnt differentiation and integration that way no one taught me

I could understand faster than watching YouTube tutorials

[plucky swan]

This is not a discussion about it's usage, we don't want this here on this server and i'm enforcing it the next time i see it

[paper anvil]

Ok fine sorry

[candid yarrow]

what are you going to do about this?

[paper anvil]

Photomath is still good though I did learn a lot from this

It gives detailed steps and explanations for each step

Chatgpt might be flawed like huh said though so my bad

[obtuse pebble]

@late flare Has your question been resolved?

[obtuse pebble]

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[bright cosmos]

Good evening/ day

My probability theory/ statistics is a bit rusty. I was hoping someone could help me with the following problem, where I need to decide on a sampling method to minimize the overlap between sets.

I am a teaching assistant who needs to feed 600 student submissions to a specialized plagiarism-detection software. Unfortunately, the plagiarism detection software only allows me to process 100 submissions per day. The plagiarism detection software has no memory of the previous submissions and therefore only considers comparisons between each the 100 submissions in a given batch. Therefore, I need to decide on a sampling strategy to minimize the likelihood of the plagiarism software not detecting plagiarism between two submissions. My idea was to use systematic sampling whereby I divide all submissions into k groups. Due to time constraints, I cannot create k sets, for a enormous k-value. Assuming the plagiarism detection software always detects plagiarism cases (since I will manually investigate all flagged cases to prevent false positives), is there a way I can minimize the likelihood of the plagiarism software not detecting plagiarism between student submissions?

My initial methodology was to divide the 600 submissions into k sets of 100 submissions each, such that each set is chosen to minimize overlap between all other sets. When a pair of submissions are flagged, they are removed from the original set and added to a flagged set. The flagged set will then later be used to check against all other submissions. This method assumes already-flagged cases will be more-likely to match with non-flagged cases.

Any suggestions?

Thanks!
Killa

[bright cosmos]

PS. The plagiarism software works by comparing submissions and producing a similarity score (expressed as a percentage) between each two pairs of submissions. If the similarity score is above a certain threshold, it is flagged for further investigation.

[next reef]

I think you should ask this in #math-pedagogy

[kind hawk]

100 per day is a harsh restriction.

how likely is it that more than 2-3 people copy from each other

if you flagged some of them you probably already caught all the ones that did it

per group

[timid silo]

(the simplest solution is to ask your department to cough up money and get proper plagiarism software)

[kind hawk]

i mean even to check each assigment once this already takes a week

[obtuse pebble]

@bright cosmos Has your question been resolved?

[bright cosmos]

Will do. Thanks

[bright cosmos]

Only had three such cases last time.

[kind hawk]

how did you do it last time

[bright cosmos]

We do have access to other plagiarism detection software, like Turnitin, but it does not work well with code. The software associated with my question highly specialized, free, and produced best-in-class scores when compared to other plagiarism detection softwares. They don't even have a paid version, which is weird.

[bright cosmos]

The method I described above and lots of manual checking. This time around, we are much more time constrained, unfortunately.

[kind hawk]

how big are these assigments?

I dont even wanna know how often software flags code for plagiarism because two people use the same algorithm with the same obvious variable names

[tame narwhal]

"best-in-class scores" I'm sure that's the company's marketing speak 😑

[bright cosmos]

The file size varies from 2000 lines of code to 10000.
This software is quite accurate. We use base-code to exclude commonly used code from the comparisons.

[kind hawk]

is there a size restriction for the software?

[bright cosmos]

The best-in-class-score was determined by an independent party published in a respectable journal. Also, the software is free, so they don't market it at all.

[bright cosmos]

Nope, but combining submissions would not work according to the original paper they published

Well, I'm sure there's a theoretical limit. But the software is executed on Stanford's servers.

[kind hawk]

when you say "does not work well with code", what exactly does that mean. could you maybe use it to "preflag" stuff and then use the other one for a second opinion?

[bright cosmos]

Yes. That is what we are doing.

The other plagiarism detection leads to numerous false negatives/ false positives. We cannot solely rely on that -- too inaccurate.

[kind hawk]

(good that you mentioned that in your post btw)

[timid silo]

reading around, it is possible to get a paid local version of moss if you email the author. this probably wont be useful for you this time, but might be worth getting for the future

[bright cosmos]

Oh nice! Thanks for letting me know. I'll definitely pass it on to the department head.

Ok, thanks everyone. I'll do some reading.

.close

[obtuse pebble]

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[latent fjord]

show your work

[obtuse pebble]

@late herald Has your question been resolved?

[obtuse pebble]

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[idle current]

I was working on a question on a quiz about cylinders (can of food in the context of the question) there was 4 questions and one of the questions got me very confused. The question is "A can of beans has a Surface Area of x square inches. The can of beams also has a volume of x cubic inches, what is the value of x?" I have 0 clue of what to do and I didn't even try, after the quiz, I asked my classmates about the questions and they all responded with all different answers and saying that question was stupid. Any help?

[knotty gulch]

so

what are the formulae for both quantities

[idle current]

For SA and volume?

for SA it was 6pir^2

and volume was 2pir^3

[knotty gulch]

are you sure

[idle current]

yeah

the other question has nothing to do with the question i need help

[knotty gulch]

i need more context

is there any more

[idle current]

Thats the issue, thats literally what they provided

no

oh right

cylinder

it is a cylinder

[knotty gulch]

yes

[knotty gulch]

.

[idle current]

well

they provided with 6pi

thats what was given in the formula sheet

[knotty gulch]

6pi for what

[idle current]

SA

it was written as "SA: 6pir^2" and "Volume: 2pir^3"

as the formula

[knotty gulch]

well the surface area of a cylinder is 2 pi r² + 2pi r h

[idle current]

yeah i looked it up after

but thats not what the quiz provided as a formula

[knotty gulch]

ok

[idle current]

thats literally the only context i can provide

[knotty gulch]

i’m not sure how i can help you then sorry

[idle current]

okay

.close

[obtuse pebble]

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[steady patrol]

hello

[steady patrol]

Sorry i didn't send the question here

if your free i'd like to hop on a call and for u to explain please

im desperate

[obtuse pebble]

@steady patrol Has your question been resolved?

[obtuse pebble]

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[vale pilot]

When a question asks for an angle in degrees "below the horizontal" does that essentially just mean I take away the negative?

[vale pilot]

I got to an answer in the 4th quadrant, -50.9061384 degrees

Would they want the answer just 50.9061384 degrees?

I'll round ofc I just copied and pasted it fromt he calculator

[atomic hornet]

yep!

below the horizontal means how far you rotate clockwise from the horizontal (initial line)

[obtuse pebble]

@vale pilot Has your question been resolved?

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[golden current]

hi everyone! 🫶

[golden current]

so on khan academy, i had questions in solid geometry to find the cross section of a solid perpendicular/parallel/diagonal to the base

im pretty good with knowing what the cross sectional shape will be parallel to the base

and perpendicular

but for diagonal, im not so good

like i just dont like visualising every time

it gets too confusing

and i cant really do it

is there a way i can know what the cross sectional shape of a solid will be diagonal to the base?

like proving it

not by memorisation

so that anytime i get a new solid, i can find the cross sectional shape

[fathom flicker]

if you had the shape, you could cut it yourself

[golden current]

yes

[west sierra]

Is it important to visualize, you can draw as well..(although I'm not knowing the topic you asked)

[timid silo]

So your solution is to bake a cake?

[fathom flicker]

which solids specifically do you have issue with?

[fathom flicker]

this is always a handy solution

[golden current]

like triangular prisms

[fathom flicker]

Could you send an example question maybe?

[golden current]

i literally cannot visualise lol

okay, brb!

[fathom flicker]

https://youtu.be/GFYVnu70PfI

this lady doesn't provide much value because she is bad at cutting through foam somehow, but hopefully the idea isn't lost on you

https://youtu.be/DkvdMkR8V8g?t=111

this one might be better

[obtuse pebble]

@golden current Has your question been resolved?

[obtuse pebble]

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[quasi harness]

state the amplitude, period, phase shift and vertical displacement for the trig function with equation y= -sin(20 + Pi/3)-2 . Use this information to graph. Please show a graph for at least -2π ≤ θ ≤ 2π.
Choose appropriately sized scales.
I need help with this

[whole dock]

Period is $\frac{2\pi}{B}$

[warm shale]

ColdTee

[whole dock]

$Asin(Bx - h) + t$ is the general form, A is the amplitude, h is horizontal shift, t is vertical shift.

[warm shale]

ColdTee

[quasi harness]

yes

is the amplitude 1

@whole dock

[whole dock]

Yeah

[quasi harness]

vertical displacement 2 units downward.

whats the phase shift?

[whole dock]

Is that just 20

Inside the sine

[quasi harness]

what would it look like

-20?

@whole dock are you still there

[whole dock]

Should be 20x

[quasi harness]

20x?

[whole dock]

Yeah

[quasi harness]

I got -20 - π/3 units to the left.

[whole dock]

-2 becomes your middle line and the graph is between -2 + 1 and -2 - 1

[quasi harness]

can you show me how that would look like

[obtuse pebble]

@quasi harness Has your question been resolved?

[obtuse pebble]

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[timid silo]

Need help proving this

[timid silo]

one way to do this is to show that every vector in S is in U, then show that U is a subspace, then show dimensions match

I didn't write it but I already know U is a subspace. Also, every vector in S is in U tells me that U contains span(s), no? I need to prove the opposite

show that U and span S have the same dimension

Also, every vector in S is in U tells me that U contains span(s),
yes you are correct

but it seems to me that it is easier to show that U = span(S)

[timid silo]

The end goal is really showing that, but I already prove that U contains span(S) and I wanted to show that span(S) contains U

[timid silo]

.

once you do that, you get equality straight away

[timid silo]

You can derive that from a therom or something?

yes, its a very standard result

if a subspace has full dimension, then its everything

I see, thanks I will look it up

.close

[obtuse pebble]

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[keen sonnet]

can i get some help just explaining this i haven't been paying attention in class and i just need to know how to solve tis

[obtuse pebble]

@keen sonnet Has your question been resolved?

[keen sonnet]

nope it hasnt

[obtuse pebble]

@keen sonnet Has your question been resolved?

[craggy raptor]

Since BC is a tangent, angle PCB has to be 90 degrees

and it should be straightforward to go from there

however ask me if you can't proceed

[obtuse pebble]

@keen sonnet Has your question been resolved?

[obtuse pebble]

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[buoyant ether]

cant you just calculate the integral from here?

why does it split in partial fractal

can i not just say: 4/x²-4x+3 = 4*ln|x²-4x+3|

and 2x-1 = x²-x

x²-x + 4*ln|x²-4x+3|

[empty hull]

you cant

think of if you differentiated ln(x^2-4x+3)

since there is the chain rule it would be (2x-4)/(x^2-4x+3)

[buoyant ether]

ooooooooooooo

let me proces 3 seconds more

so i have to split into partial fractals

am i correct if i said: When there is a kwadratic function under the line (idk what is called for fractal) your answer never would be a ln||?

no ok its ok i understand

thank you

.close

[obtuse pebble]

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[buoyant ether]

Hello

[buoyant ether]

when can i know if there is a rest?

A/B =========>>>>>>> Q + R/B

rest is R

this Bx + C should only be added when you know there is a rest

but how do i know there will be a rest?

[fathom flicker]

what do you mean by "a rest" ??

the
"Bx+C"
Term comes from when there is a irreducible quadratic factor

[buoyant ether]

when you devide with euclidian, but cant animore

yes irreducible that is what i mean with rest

in belgium we call it rest, now i know irreducible quadratic factor

so how do i know there will be an irreducible quadratic factor

[fathom flicker]

look at your question

you see x^2+4x+5

can you reduce it?

if not, it is irreducible

x^2+4x+5 doesn't factor into linear factors

so it is irreducible

[buoyant ether]

OOOOOOOOOOOO

a quadratic cant be reduced?

[fathom flicker]

quadratics can be reduced

but some can't

for example

[buoyant ether]

like here for example there is no irreducible

[fathom flicker]

x^2+4x+4

can be reduced to

(x+2)(x+2)

but x^2+4x+5

can't be factored into two linear factors

[buoyant ether]

ah yes

how do you call the number under the line of fractal?

[fathom flicker]

the denominator?

[buoyant ether]

thx

so the denominator should be a line

if its not

then there is a irreducible factor

[fathom flicker]

In your denominator, you want to reduce it to as many linear factors as possible

linear factors contain a "x", not any x^2 or higher terms

[buoyant ether]

i will remember this , but i cant imagine why

[fathom flicker]

if there are terms containing x^2 or higher degree polynomials that cannot be reduced, then these are irreducible

[fathom flicker]

linear = line

if you have x^2, or x^3 ....

it isn't a line

any "x" is

5x, 10x, 1/2x

still lines

[buoyant ether]

aaaaaaaaaaaaaaaaaaaaa ok ok ok ok ok ok ok respect man

thx

[fathom flicker]

no problem

[buoyant ether]

.close

[obtuse pebble]

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[bold siren]

how I would like to ask how 0.0228 come from

I did a) and calculate the calue of the test statistic is z=-2

and I checked the z score table is 0.4207

[tardy epoch]

two tailed z table probably

or just double/halve your test statistic

[bold siren]

it is a two tailed one

but having and doubling doesnt help to get the culmlative one

i tried both -1 N -4

[tardy epoch]

just look at a z table

[tardy epoch]

-2 = -2.00

https://www.z-table.com/

[bold siren]

OH NO

i mislook the -.2 and -2

smh

thankss

.close

[obtuse pebble]

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[ionic summit]

This is a practice problem =3

Not sure how to do this one. The current understanding I have is that if two lines are parallel then the cross product is zero.

[ionic summit]

I was also thinking that maybe if the plane contained the line it would be parallel but thats not true either

this makes no sense

what the heck

i guess im thinking of this wrong

im thinking that the line has to be parallel to the plane such that like the edges of the plane (that i guess does not exist) are parallel to the line

[balmy mortar]

you can only take cross products of vectors

[ionic summit]

ye

[balmy mortar]

yes, if 2 vectors are parallel their cross product = 0 vector

[ionic summit]

the only way i suppose it cant be parallel if its pointing in like another direction like if the plane was on the x-y plane and the line was x-z or something

[buoyant zealot]

of course this makes sense.
this is the same idea of if 2 lines perpendicular the a line perpendicular to one is parallel to the other

[balmy mortar]

you're checking for parallel planes. 2 planes are parallel iff the normal vectors to the planes are parallel

[ionic summit]

im sorry i dont understand what u mean

[ionic summit]

i thought it was a line and a plane

[balmy mortar]

Oh I misread.

[ionic summit]

well

yeah i think i was just mis intepreiting

like if the plane contains the line

then its parallel

[balmy mortar]

In which case, you can check if the vector in the direction of the line is perpendicular to the normal vector of the plane

[balmy mortar]

yes

I mean well

The plane doesnt have to contain the line

[ionic summit]

i guess above or below it

[balmy mortar]

if the line doesn't intersect the plane anywhere, they are parallel

[ionic summit]

aswell

idk i had the misconception

for some reason i thought like the line had to be parallel to the edges of the plane

but that makes no sense cus it goes off forever

but y'know when like u are taught

what a plane is and its a fat square on the chalkboard

[buoyant zealot]

if red and blue vectors are ortho then the line and plane are parallel

red is director vec of line
blue is normal vec of plane

[ionic summit]

ye

it makes sense now

okay

next step

(I hope i get to draw the cat)

do they intersect

perhaps

lemme think what to do

uhh hmm

i guess to set the direction vector equal to the plane

and see if there is a solution

[buoyant zealot]

if you want a hint say

[ionic summit]

i understand that :3

im trying to figure out if they intersect

well how to figure out if they do

supposedly

i just plug in the parametric equations into x,y,z into the plane

and solve for t

would my method also work

[buoyant zealot]

yess that is the questions intended solution

if they do intersect all

[buoyant zealot]

try it out and see if you get a parameter

[ionic summit]

would my method of

setting the vector equation to the plane equal to eachother still work?

wait

like

hold on im not thinking

[buoyant zealot]

never heard that before xd

[ionic summit]

i understand now!!

thank you!!

[buoyant zealot]

glad i could direct you to understanding

[ionic summit]

🙂

.close

[obtuse pebble]

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[steady owl]

hey guys, i need help solving the following integral:

[balmy mortar]

partial fraction decomp?

[obtuse pebble]

@steady owl Has your question been resolved?

[obtuse pebble]

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[opaque galleon]

sinx = cos2x
how to solve this algebraically because I ain't allowed to say "oh that's pi/6"

[opaque galleon]

wow

RGB

[warm canopy]

you've got yourself a quadratic in sin(x) now

[opaque galleon]

.close

[obtuse pebble]

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[warm canopy]

okay?

[opaque galleon]

.reopen

yes

[obtuse pebble]

✅

[opaque galleon]

( 1 + sqrt(2) sin x) ( 1 - sqrt(2) sinx)

[opaque galleon]

okay?

[desert sinew]

Think about it, from this you can get

$$\sin x = \cos 2x$$
$$\sin x = 1 - 2\sin^2x$$

[warm shale]

jimmy1234

[desert sinew]

Then how will you go about solving that? 🙂

[opaque galleon]

all good now

i can do it now guys dw

.close

[obtuse pebble]

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[warm canopy]

"thanks for trying to help!"

[obtuse pebble]

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[timid silo]

why is lambda = 1/5?

[warm canopy]

because the mean of an exponential distribution is 1/lambda

[timid silo]

so its because when you find lambda it should be on a per/rate basis?

also how do I do 2.3?

[desert sinew]

Thats just how exponential distribution behaves.

Quick ref in case you don’t have this in your notes or textbook: https://en.m.wikipedia.org/wiki/Exponential_distribution

[timid silo]

how do I do 2.3

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

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[timid silo]

I believe those are the answers

To get other answers you would just add or subtract $$2n \pi$$ to them. but that's outside the range of the question right?

[final hornet]

yea i think thered be 2 solutions within the range

[warm shale]

Brandon H

[final hornet]

oh

can i see your work

[zenith raft]

idt those are right

also i think there should be 4 solutions

what’s 0.71 from?

[final hornet]

probs 0.91?

[zenith raft]

what did you get out of the quadratic formula idea?

like… what did that lead to

why are you giving decimal approximations?

[timid silo]

they're probably using a calculator

[final hornet]

i got (6±√12)/12

[zenith raft]

same thing?

[final hornet]

think so

yes sorry

[zenith raft]

it’s ok 🙂

so you want x’s such that sin(x) = (3+sqrt(3))/6

so taking arcsin gives you one

can you see how to decribe the others if you look at the graph of sin?

what’s reference angle?

ok sure

[zenith raft]

so one of the solutions is arcsin((3+sqrt(3))/6), and that plus multiples of 2pi

but that’s only “half” of them and it’s missing the one that’s approximately 2.234

which is one that you want

following?

ok so let’s let arcsin((3+sqrt(3))/6) = t so i don’t have to write that again

can you see the one you’re looking for is pi/2 (that’s where the peak between them is) plus the distance between t and pi/2?

yea i guess you could go through the same thing on the unit circle

i can’t really draw anything rn

but umm

if you take a point on the circle

and then ask which angles take you there

one of them will be arcsin of the y value of the point or something

but just call that angle theta

the other one will be -theta + pi

you’ll probably need to draw it to see

[obtuse pebble]

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[pure walrus]

I’m looking for metrics that could be potentially useful for quantifying and comparing graphs. I don’t know a lot about graph theory but the problem I am working on can be translated into a comparison of simple graphs that can be either connected or disconnected, where the number of nodes is always the same. One metric that is somewhat relevant is the total number of edges.

[obtuse pebble]

@pure walrus Has your question been resolved?

[timid silo]

graphs as in graphs of functions

or graphs as in trees

[obtuse pebble]

@pure walrus Has your question been resolved?

[obtuse pebble]

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[fathom flicker]

Hi, I am working on proving the statement in white. My idea is to do something along the lines of the blue sketch

my problem is, other than sketching that, I'm not sure what to do. Is that even the right idea? I might be overcomplicating this tbh

[royal basin]

is this your handwriting

[fathom flicker]

yeah I can type if you want

sorry

[royal basin]

no thats not the issue

the issue is that you arent writing \in properly

[fathom flicker]

yeah I don't know that one

[royal basin]

it's supposed to be a flattened C with a tongue, not an epsilon

[fathom flicker]

$\notin$

[warm shale]

AustinU

[fathom flicker]

like this?

[royal basin]

that's $\notin$, not $\in$

[warm shale]

Ann

[royal basin]

i'm talking about ∈

[fathom flicker]

oh

[ruby path]

omg blackboard

Respect

[fathom flicker]

my epsilon and in are bad

I am just bad at writing them differently

sorry Ann

There is no epsilons in the sketch so far though I'll tell you that

[royal basin]

anyway your idea is meh

[fathom flicker]

fair

Do you have any suggestions on either improving my idea, working forward from it, or perhaps a different idea?

[royal basin]

do you know how to show the existence of a rational between two real numbers

[fathom flicker]

yes

[royal basin]

do you also know how to show the existence of an irrational between two rationals

[fathom flicker]

No, I don't think I do

[royal basin]

try doing that then

then you will be able to reason as follows:
LEMMA 1. between every two reals there exists a rational
LEMMA 2. between every two rationals there exists an irrational
THEOREM. let x, y ∈ R s.t. x < y, then there exists an irrational between x and y
PROOF: by lemma 1 there exists a rational q s.t. x<q<y and again by lemma 1 there exists a rational r s.t. q<r<y, then by lemma 2 there exists an irrational i between q and r...

[fathom flicker]

Yes okay nice. I was definitely overcomplicating it

trying to work supremums into everything

I need to prove the existence of an irrational between two rationals then

I will work on that

ty Ann

[muted holly]

does it require the chain rule

[obtuse pebble]

@fathom flicker Has your question been resolved?

[fathom flicker]

Okay, I think I have figured it out

If I have proven density once before, is it something I should be able to reprove at whim?

I don't think that I could do it without looking at notes

but, since I have proven it before I used that proof to finish this one

.close

[obtuse pebble]

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[fathom flicker]

I am having trouble considering what this function is doing. To me it looks like it is making every x into f(x)=0.222222.....

but I must be seeing it wrong

[zenith raft]

isn’t f just taking the “locations” where the digit is 2?

the j’s such that d_{-j} is 2

[fathom flicker]

and doing what with them?

keeping them?

[kind hawk]

puts them in a set

a subset of N

aka an element of p(N)

[zenith raft]

send x to a set containing all the “locations”

[royal basin]

f is a set-valued function

[fathom flicker]

so for like x=0.1212, f(x) takes the 2 and 2 and places them in sets? So f(x)={2} and {2} ?

[kind hawk]

f(x)={2,4}

(not that this x is in E cause after that it continues as x=0.121200000..)

[royal basin]

0.1212 isn't in E

[fathom flicker]

0.1212000000...

[royal basin]

0.1212111111... is in E and f(0.121211111...) = {2,4}

[fathom flicker]

oh right

and

okay

I understand now

Thank you everyone

Okay so I am now trying to prove injectivity for that function

Does the following sound good?

so, f(x1) = {a,b, ....... n}

f(x2) = {c,d, .......m}

if f(x1)=f(x2) then f(x1) is a subset of f(x2) and vice versa

[royal basin]

notation is already meh

[fathom flicker]

why?

I did mean to put an m for the last element of f(x2)

[royal basin]

{a, b, ...... n} at best is a set of cardinality 14