help-0

[upbeat eagle]

You dont need to know any physics

[hasty creek]

Alright

[upbeat eagle]

U just need look and comapre numbers

anywasy im lost haha

I can help you run this question down to where im at

If you are interested

[hasty creek]

Sure

[versed walrus]

#help-6 message

[upbeat eagle]

Ok so Basically,
The first question was to Prove ε is 1.6V

So we have 22/n = ε /I -r

I turn that into a y=mc + c

This should be very neat?

[hasty creek]

Looks right

[upbeat eagle]

Alright

Now

regarding find the r value

Im a bit confused

Ill sen you a picture one sec

,rotate

[upbeat eagle]

My question can I use method A and B to find r values does that work

And for B

Would it be 1/0.3 or 0.3

And also would you have to similtaneous equation it

@hasty creek

thats where my brain is just like wtf

[hasty creek]

[upbeat eagle]

[hasty creek]

You can just plug in the point (0.9,0)

And solve for r

[upbeat eagle]

Into part A?

[hasty creek]

Sure

[upbeat eagle]

i see

nvm

[hasty creek]

1/I = 0.9, 1/n ~ 0

[upbeat eagle]

yeah

What if you werent given an x intercept

You just plug in any point

right?

[hasty creek]

Then sure you can make two equations

[upbeat eagle]

Oh ok

So that would be part B

Would it be 1/n and 1/I or just n and I

[hasty creek]

So in part B you made y = n and x = I?

[upbeat eagle]

I think so yeah? i guess

Im not sure if it matters

[hasty creek]

It’s better to continue with part A
Less stuff needed to figure out r

[upbeat eagle]

ok but I kinda need to know how B works

just incase

[hasty creek]

🤔

[upbeat eagle]

[upbeat eagle]

Using A r is 16/9

I guess ill just try trial and error?

and ill let you know?

[hasty creek]

[upbeat eagle]

can u double check its 16/9 i dont wanna fk it up

22y = ε x - r

22 (1/0)= 1.6 1/0.9 -r

-( 1.6 x (1/0.9) ) = -r

So r is 16/9

yeah should be right

imma trial and error

[hasty creek]

Err

1/n is 0

And 1/I is 0.9

So you don’t need to do 1/0.9

It should be 0.9*1.6

[upbeat eagle]

errr what

[hasty creek]

1/I is 0.9, doing 1/0.9 will get you the value of I

We are using 1/I

[upbeat eagle]

oh ok

How come in the very first picture i didnt have to convert it?

[upbeat eagle]

when i plugged in x and y values

[hasty creek]

You don’t have to convert it

Keep it as 0.9 rather than 1/0.9

[upbeat eagle]

Which picture r we talking about

Im guessing 2nd with A.

[hasty creek]

Here

[upbeat eagle]

Okok

so 22y = ε x -r

and you r telling me

(0.9,0)

So you put in 1/0.9? as x aka 1/i

thats what i did

[hasty creek]

No

[upbeat eagle]

0 = ε x (1/0.9) - r

[hasty creek]

x is 1/I

Aka 0.9

[upbeat eagle]

oh

OH bc

ok

I understand

[hasty creek]

[upbeat eagle]

so 0 = ε 0.9 - r

[hasty creek]

Yep

[upbeat eagle]

1.6 x 0.9 = 36/25 = r

ok imma do sim eq and see which one it is

[hasty creek]

[upbeat eagle]

i think i alrdy know whcih one

TY !

nah I dont

I threw it in the calc

didnt get any correct answers

Am I doing it wrong lol

0.3 = 5m -r
0.9 = 13.2 - r

can I plug it in into

x + y = 0

-1 + 5 = 0.3
-1 + 13.2 = 0.9

I got the correct y value (aka the gradient matches up)

@hasty creek

Sry last one

Might have to wipe my calculator

[hasty creek]

Actually

Since we know everything we can just plug in any single point lmao

No need for equations

[upbeat eagle]

Oh

[hasty creek]

Let’s say (5, 0.3)
22(0.3) = 1.6(5) - r

,calc 1.6(5) - 22(0.3)

[ocean seal]

Result:

1.4

[hasty creek]

[upbeat eagle]

But that’s different

To what we just got for A

1.44

Probably rounding error

[hasty creek]

Yeah it’s a rounding error

[upbeat eagle]

? But I can’t think of a reason

Ok

🙌

I’ll leave it as that

Well thank you once again

Luv u

[hasty creek]

[upbeat eagle]

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[upbeat eagle]

Im a bit confused on how to finish it

So
When 2 = even/ even

It means that the 2 evens must have a factor of 2 which related to the [2]

But in this case there is no factor therefore it is an irrational number

Is that a correct statement?

Also let’s say you got

2 = 1even/ 2even
2= (1/2) (even/even)

Would this mean it’s rational

Because these are integer factors

And are a factor of two

Proof is something I tell you

[vapid shuttle]

Suppose sqrt(2) is rational, then sqrt(2)=a/b in reduced form

we showed earlier that a is even and b is even, if this is true

(so you can't write it in reduced form)

contradiction

done

boom

pow

you're confusing yourself

[upbeat eagle]

Oh ok

If you got

This means that it is a rational number

[vapid shuttle]

Why do you keep doing this

[upbeat eagle]

It can produce a rational number

[vapid shuttle]

what are you writing

2=1even / 2even

it doesnt make any sense

What are you trying to say?

[upbeat eagle]

True

It’s more of a question of factors

You need a factor of 2 to be even

So if there is a factor of. 1/2

Is that a factor of 2

[vapid shuttle]

no stop

[upbeat eagle]

Ok

[hot swallow]

uh

[vapid shuttle]

if they're even, they share a factor of 2, THAT IS IT

the contradiction is they share a factor

we assumed they share no factors

[hot swallow]

[vapid shuttle]

if they share a factor of 2

it's over

game over

we win

[upbeat eagle]

[vapid shuttle]

no more need to be thinking about it

we said

[upbeat eagle]

Ok

[vapid shuttle]

sqrt(2)=a/b

and they share no common factors

but then we showed

they share a common factor of 2

so we can be done

that's the contradiction

[upbeat eagle]

Ok ok I gotchyu

For now

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[upbeat eagle]

[vapid shuttle]

https://tenor.com/view/alpha-wolf-sigma-male-gif-26562640

[upbeat eagle]

Everyone says warewolf

But no one asks how wolf

https://tenor.com/view/funny-emo-wolf-werewolf-transform-gif-27196401

[lone heart]

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[silver widget]

I was able to do 3a and 3b

I got stuck on 3c

I started to integrate the integral by parts and did that twice

[safe tartan]

Integration by parts I’m assuming

[silver widget]

However, I got the following value:

$[x^nsin(x)+nx^{n-1}cos(x)-n(n-1)I_{n-2}]^{\pi/2}_0$

[silver widget]

Yep, I did that

[safe tartan]

What was ur u and dv

[silver widget]

u = x^n
dv = cos x

[safe tartan]

Might be x^n-1 xcosx

[silver widget]

When I simplify this further, the last term cancels though

[safe tartan]

Since the previous question does xcosx

[silver widget]

For u and dv?

[ocean seal]

Cayush

[silver widget]

<@&286206848099549185> Please

[civic dragon]

<@&286206848099549185> ASSEMBLE NOW

A FELLOW COMRADE NEEDS US

[ancient vapor]

Which part?

[silver widget]

Part 3c

[ancient vapor]

@civic dragon shut up bruh.

[silver widget]

I was able to simplify it to this

[civic dragon]

We are here to help all our fellow comrades

[silver widget]

However, the I_n-2 term seems to cancel

[ancient vapor]

Well it might form a gp

[silver widget]

In school, the method we learned was direct proof

So, I integrated the integral by parts twice, and substituted the general term

[lone heart]

@silver widget Has your question been resolved?

[ancient vapor]

@silver widget

[lone heart]

@silver widget Has your question been resolved?

[lone heart]

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[grave verge]

My progress:

I am unsure if I did it right (am 60% sure I did smth wrong cuz there cm³ in question but Idk how do I get cm³)

[frigid mirage]

volume is cm^3

notice lbh is (cm) x (cm) x (cm)

and idk why you put weight in cm

[grave verge]

So all I have to do is add cm³ in ans?

[frigid mirage]

no

[grave verge]

Oh shi

[frigid mirage]

the volume should be cm^3

weight should be in grams

actually I think your number is right

just the units

[grave verge]

So in the end I just change it to grams?

[frigid mirage]

,w 105(70)(1.5)8

[ocean seal]

Results provided by WolframAlpha

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Requested by nebula40

[frigid mirage]

yes, and correct volume's units as I mentioned

and change to kg

since the question asks in kg

[grave verge]

Just cm^3 instead of ^2 right

[grave verge]

Oh i didn't notice that ty

Tysm

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[upbeat bone]

hello

[upbeat bone]

9th grade geometry

how to find y, i already know how to get x

[slender gull]

Check out co interior angles.

[upbeat bone]

sorry idk what u mean

[slender gull]

In your notes wherever you're studying parallel lines,

Find the term co interior angles.

In this case, 2x and y are co interior angles.

There's a property for parallel lines that states sum of co interior angles is 180 degrees.

Might wanna check that out.

[lone heart]

@upbeat bone Has your question been resolved?

[lone heart]

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[last aurora]

Hallo this is a q regarding bias of an estimator (in stats)

[last aurora]

This is the question

This is my work

I was wondering if this was right?

I sorta just assumed $E[X_1]$ = $E[X_2] = \mu$

[ocean seal]

qwq

[last aurora]

because that seemed like the only possible way to do the question

but i don't get why the statement above is true, since I thought $\mu = E[X_1+X_2]$

[ocean seal]

qwq

[alpine sable]

i mean, no?

the center of the sampling distibution of $\hat X$ is also $\mu$

[alpine sable]

also yeah this is fine

[last aurora]

iiinnteresting

thank you!

I guess ill go read the textbook more

[alpine sable]

no worries haha

[last aurora]

:D

[alpine sable]

The concept of bias is related to sampling distribution of the statistic so maybe its better if u think of it that way btw

[last aurora]

I will note that thank u again :)

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[tight thunder]

guys what is this

[fervent kestrel]

lower case delta

In what context is it being used?

@tight thunder

[tight thunder]

amortization rate of capital in macroecnomics

is it equivavlent to this?

[fervent kestrel]

I'm not familiar with macroeconomics

What are the entire formulas you are looking at

[tight thunder]

hmmmmm

[fervent kestrel]

I think delta is 'depreciation rate of capital'

[fervent kestrel]

Where was this given?

[lone heart]

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[lone heart]

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[lone heart]

@verbal galleon Has your question been resolved?

[verbal galleon]

<@&286206848099549185>

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[verbal galleon]

1

[verbal galleon]

<@&286206848099549185>

[verbal galleon]

<@&286206848099549185>

[verbal galleon]

Tf

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[alpine sable]

!show

[lone heart]

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

[torpid roost]

This is what I did I was kind of just guessing what I had to do

[alpine sable]

,rccw

[torpid roost]

I didnt know how to add them

and subtract

[lone heart]

@torpid roost Has your question been resolved?

[torpid roost]

<@&286206848099549185>

[tardy stag]

you can only really add and subtract them if the stuff under the radical √ is the same

so like 3√x + 4√x = 7√x

but 2√x + 9√y is a dead end, nothing left to do

[torpid roost]

so do i need to make them all the same under the radical

[tardy stag]

yes but conveniently if you reduce it like you're doing that's the most you can do

they'll line up as much as possible

[torpid roost]

so what part of what i did was correct?

[tardy stag]

you reduced the first term correctly

do the same for the other terms

like make a factor tree / look for sets of 4

[torpid roost]

so would the simplified version be xy^2

Are these the correct 3 simplified equations

[torpid roost]

<@&286206848099549185>

@tardy stag

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[alpine sable]

I am having difficulty with units

[alpine sable]

So what are the units of t/6

seconds/watts?

watts = t (seconds) / 6?

[placid zinc]

t/6 is seconds

Note the units do not agree here.

[alpine sable]

so its not dimensionally homogeneous

?

[placid zinc]

ye

[alpine sable]

my brain!!! how?? why??

how is that legally allowed

is it because youre integrating

what does that do to units

[placid zinc]

We haven't even gotten to the integral yet haha

[alpine sable]

i know integration/derivation for things like acceleration

ok bro

youre killing me here

[worn fox]

note that the number 6 has units of s/W

[alpine sable]

yes

so dot_Q_out = t/(6 s/W) ==> t(W)/6(s)

[placid zinc]

True, that's a way to fix it

[alpine sable]

me when "t" is in watts 💀

[worn fox]

t has units s and 6 has units s/W, it cancels out to W

[alpine sable]

well, watts per second, so thats better. (1/6) watts/second

[alpine sable]

wha?? whered they get the seconds in .../12 (s/W) then

at the bottom equation

[worn fox]

because the bottom is 2 * 6 s/W

[alpine sable]

so it doesnt cancel out then?

[worn fox]

i dont know what you mean

[alpine sable]

if youre just left with W then why is the bottom 2*6s/W

[worn fox]

the units of Q are not W

[alpine sable]

where are you left with just W

[worn fox]

the units of Q dot are W

then youre integrating that with respect to time so the units become Ws (or kWhr if you scale)

[alpine sable]

ok so to clarify, Q dot (W) = t(s)/6 right? thats good?

[worn fox]

aslong as you remember that 6 has units s/W

[alpine sable]

so youre telling me that its Qdot(W) = t(s) / 6(s/W)

?

[worn fox]

yes

[alpine sable]

ok so yes it is dimensionally homogeneous technically

because they all cancel out

ok i understand it now, thank you

much appreciated

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[heady robin]

i asked this yesterday

but still didn get en9ough heko

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[tulip oasis]

sry dumb question

but i can just rewrite this right

like put the = alll the way to the right

instead of all the way to the left

cuz i hate it when it looks like this xd

[fallen verge]

yes, but be careful with how you move things around

[tulip oasis]

Ok

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[median cove]

U dont move the equals sign, u just move the values to the left and right of the equals sign

If thats what u r talking abt then yes

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[hollow frost]

stuck on this problem, think i’m in the right track but not sure ?

[meager portal]

you have 3 y sides and 2 x sides

those are the fences

and the area is x times y

you know $3y + 2x = 1000$

[ocean seal]

TRAMPELTIER

[meager portal]

and you wanna maximize $x \cdot y$

[ocean seal]

TRAMPELTIER

[hollow frost]

yes

im not sure how to though after where I got

[meager portal]

okay

lemme think

we can write x in terms of y (or y in terms of x)

take this $3y + 2x = 1000$ and solve for $x$

[ocean seal]

TRAMPELTIER

[meager portal]

which gives $x = (1000-3y)/2$

[ocean seal]

TRAMPELTIER

[meager portal]

and then, you can in the target function that we want to maximize substitute x by this equation

And then the target function only depends on y

and we can easily maximize it by taking the derivativ, setting to 0 and finding the maximum

questions?

[hollow frost]

so I substitute the x for 1000-3y/2

then derive the new target function and set it equal to zero to find the critical numbers ?

[meager portal]

yes

because you'll see that the target function is a quadratic in y

and it will be a quadratic that grows negatively

so there's a maximum in that quadratic

[hollow frost]

ok thank you

[meager portal]

np

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[tacit barn]

No idea where to start from in this problem ...

Also that, dont know how or if it will help. Very complicated problem for a 12th grade student imo... Help

[lone heart]

@tacit barn Has your question been resolved?

[tacit barn]

<@&286206848099549185> please help me

[wicked sparrow]

sure

is it possible for you to enlarge it?

[tacit barn]

Where do I even start in this?

[tacit barn]

What do you mean

The limit?

[wicked sparrow]

i cant really see the problem well

[tacit barn]

Oh hold on sure

Any idea?

[wicked sparrow]

oooh

thats a pretty hard problem

what grade are you? freshman?

[tacit barn]

im in the last year of high school

This is usually a problem youd encounter on the final exams, and it most likely is one of the final ones if not the final one

Its like the last 6/100 points

In my country the entrance exams to uni have like 4 problems, containing 4-5 sub-questions each of them(each problem is total 25 points) and this is like the D4 or D5

[wicked sparrow]

yeah im doing the problem now

gimme a few miniutes

*minutes

[tacit barn]

Thanks 🙏

[wicked sparrow]

been a while since ive done this

[tacit barn]

Just ping me because I'll close my phone to try it myself

[tacit barn]

Its alr man, most of our professors wouldn't be able to solve this either

[wicked sparrow]

ok

so

when you wrote [a, - inf)

did you mean ( -inf, a]?

@tacit barn

just to make sure

[tacit barn]

Where

[wicked sparrow]

at the top i think?

can you give some context for the problem so i have something to base it off of

[tacit barn]

At the domain and the range of f?

[wicked sparrow]

like a way of thinking

yeah

[tacit barn]

Well we have the function f(x) given to us with a domain of (0,+inf) and a range that ive found by the first derivative which is [1,+inf) (f has a total min value f(1)=1). Then we have the following information about x0 and that f is increasing on the mentioned interval (1,2) and that the tangent line is that of the above form. And it asks us then to prove that the limit above is -infinity

I tried my best translating the problem from greek to english man srry lol

My guess is that we play with the fact that f is increasing in the interval (1,2) not sure tho...

But we both agree the limit is a/0 but what a and what 0

[tacit barn]

Thats the issue

[lone heart]

@tacit barn Has your question been resolved?

[wicked sparrow]

hm

[lone heart]

@tacit barn Has your question been resolved?

[lone heart]

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[dusk umbra]

Are components of an eigenvector orthogonal?

[dusk umbra]

Like for example, if you have an angle and a magnitude for a vector in 3d space

You can write the vectoe components as trig functions

Is this true for eigenvectors too?

[flint pagoda]

For symmetric matrices yes

Eigenvectors for distinct eigenvalues are always ortho

For example, in PCA, we have symmetric matrices for covariance so the representative eigenvectors we get as output are indeed orthogonal

[dusk umbra]

Is this with the caveat that the matrix is symmetric?

[flint pagoda]

Yes

https://m.youtube.com/watch?v=gJhlkEBZsfI

Watch this

[dusk umbra]

ok gimme a min

.close

[lone heart]

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[lone heart]

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[manic ruin]

I could use some help with a statistics problem. I think I understand how to do the rest of this problem, but I straight up do not know how to get part a.

[manic ruin]

I'm trying to wrap my head around part a but I am having difficulty. I know there's 21 possibilities per stop and 4 stops total

I just don't know how to translate that into an actual answer. Unless my base assumption is wrong?

Part b is just 1/N x 1/N where N is the answer from a, right?

like, I feel like I'm almost there on my knowledge but something fundamental is not clicking. Any help is most appreciated.

[balmy grail]

So you’re right there’s 21 possible outcomes [0,20] for the first stop, but then you have to think about what happens on the second stop- if 1 persons gets off at stop 17, only [0,19] people can get off at stop 18

So if you had 1 person on the bus how many possible outcomes are there?

[manic ruin]

8?

I'm confused

or is it 2^4?

[balmy grail]

They have to get off eventually, so if we count the number of exits per stop you’ll see 4 possible outcomes: last stop: 0001, third: 0010, second: 0100, first:1000

So what happens if there’s a second person?

[manic ruin]

I have no idea. Does it double?

or square?

[balmy grail]

Try and reason your way through it, what choices can each person make?

They only get off once

[manic ruin]

off or not off at every stop

[balmy grail]

Or off at which stop?

[manic ruin]

so each individual person has 4 possibilities?

[balmy grail]

Yes

[manic ruin]

so it's 4^n where n is the total number of people?

[balmy grail]

Stops^number of people yes

So for 20?

[manic ruin]

Okay, that makes sense. I had it backwards on my paper. I was doing 20^4 and the answer felt wrong

4^20 = 1.1E12

[balmy grail]

In that case 1 person would have 1 possible outcome 1^4
11 billion looks about right though

[manic ruin]

Okay, cool. What about part b?

Is it 1/N x 1/N where N is 4^20?

Or do I have to figure out the total number of possibilities per individual stop?

So if no one gets off at stop 17, that's 1 out of the 21 total possibilities there

And if it happens again that is another 1/21 chance for the next stop?

so is it 1/21 x 1/21 or is it the first thing I said?

Oh, wait, maybe I'm misunderstanding the question. It's asking for the number of possibilities in the event that no one leaves in the first 2 stops, not the chances of it occuring.

[balmy grail]

Right, also I don’t think it’s either of those options

[manic ruin]

yeah, it isn't. Would it just be what we already did but for only 2 stops instead of 4?

[balmy grail]

That looks good to me

[manic ruin]

And then for c, if half the passangers leave in the first 2 stops, then all we have left are 10 passengers and 2 stops, so 2^10 possible outcomes?

[balmy grail]

That I’m not so sure about

[manic ruin]

oh, hm...then I'm not sure what it would be.

[balmy grail]

Is it exactly half or at least half?

[manic ruin]

exactly half

"the event that half of the passengers leave by stop 18"

Would it be double my original answer? Cuz either "half" could be in either place?

So 2^10 x 2 = 2048?

hello?

[balmy grail]

I’m not sure, I’m getting 48/128 for the case of n=4

[manic ruin]

wait, what?

for the probability of occurrence?

or for the total number of possibilities?

[balmy grail]

96 / 4^4 = 96/256

[manic ruin]

I have no idea what I am looking at...

I'm confused as to how the total number of possibilities could be less than 1

the questions is asking me to count how many different possibilities exist if half the people on the bus get off in the first 2 stops

So wouldn't that just be the number of ways exactly 10 people can get off in the first 2 stops + the total number of ways the other 10 could get off in the last 2 stops?

[lone heart]

@manic ruin Has your question been resolved?

[balmy grail]

96 of the 256 possibilities have exactly 2/4 riders getting off on stop 1 or 2

You have to imagine the fourth column because it wouldn’t fit

[manic ruin]

I thought there were 20 riders?

How did we get to 4?

or does it not matter as long as the ratio is 1/2?

[balmy grail]

Because I was using 2 as a simple case but then I was worried about that being too small / similar to other things

[manic ruin]

okay, so how do I apply that to my answer?

Do I multiply the total number of possibilities obtained in part a by 96/256?

[balmy grail]

No

[manic ruin]

I am very lost

[balmy grail]

On the case of n=2, 8 have exactly 1 person getting off at stop 17 or 18, which looks like 1/2 of the cases, but let’s check another case, eg n=4 for exactly 2 people getting off at stop 17 or 18, which when we go out and count them there are 96/256 = 3/8 ≠ 1/2. So we know this is more complicated than it looks

[manic ruin]

okay, so then how do I figure it out for 20 people where 10 get off at stops 17 and 18 without counting as that seems difficult?

without counting by hand that is. I must be missing a formula somewhere along this process

Is the total number of possibilities 20 C 10 x (something)?

cuz the first 2 stops eat 10 of the people but it doesn't matter which 10 so it's just a nCr thing?

is it just 20 C 10 x 2?

idk, I think I'm not understanding something more fundamental here maybe. I think I'm just gonna talk to my professor about it tomorrow during her office hours.

[balmy grail]

Yeah it looks like the pmf = 0.5 for the sum of 20 uniform variables from 1:4 but I don’t have a simple solution

[manic ruin]

okay, well I still appreciate all the help you gave me. Thank you. I have some other questions for my professor anyway so I think it'll work out with me going to her office hours tomorrow morning.

.close

[lone heart]

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[lean river]

help

[keen pasture]

#❓how-to-get-help

[gray isle]

if you need help with a math question,
ask asap.
(before people lose interest and start skipping this channel when browsing)

[lone heart]

@lean river Has your question been resolved?

[lone heart]

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[full apex]

hey

https://prnt.sc/aba2ve

[full apex]

i need help factorising this

someone please help

[ebon sparrow]

you can factor by grouping

[full apex]

i tried

[ebon sparrow]

!show

[lone heart]

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

[full apex]

but i keep getting the wrong answer

one sec

this is the answer

what i did was

i grouped it

and i used binomial products to seperate -3xy^3 - 9y^4

[ebon sparrow]

I know what's the answer is like but I asked you to show your work

[full apex]

im doing that just give me time

actually ill show you my written working out instead of retyping it all

alr dnoe

done*

cant factorise further 😭

[tardy stag]

in this line, replace $(2x^2-3y^2)$ with $\rsq$ and try to factor it again

[ocean seal]

hayley!

[full apex]

replace it what? sorry

its a red box

[tardy stag]

you seem to be struggling with factoring it out

[full apex]

indeed

[tardy stag]

if you replace it with something abstract like a colored box (or another variable i guess) it can make it easier to see what you need to do

[full apex]

hm

lemme try

oh should i expand?

yoo

@tardy stag

[tardy stag]

why would you expand when you just factored

[full apex]

idk 😭

[tardy stag]

$(2x^2-3y^2)\blue{u} - xy\blue{u}$

[ocean seal]

hayley!

[jovial wind]

💀

that do be crazy

[full apex]

hush

lemme think

[jovial wind]

i need help

😭

[full apex]

no

uuuuh

i still dont get it

@tardy stag

[jovial wind]

@tardy stag where did u pull u-xyu from ???

[tardy stag]

basically

[full apex]

jump

[tardy stag]

you're getting really confused with the subexpressions

[full apex]

yeah

[tardy stag]

you're trying to factor out (2x^2 + 3y^2) right

[full apex]

2am moment

[full apex]

yes

[tardy stag]

so i replaced that with u

so that you can easily see what you need to do

[jovial wind]

💀

[full apex]

ill turn ur head into a skull irl stfu

[full apex]

what do I Need to Do

[jovial wind]

😭

she replaced that w u

hell nah

this aint math

[tardy stag]

factor out u

[jovial wind]

where does u come in when the question is this

[full apex]

oh shit

[full apex]

im so dumb

[jovial wind]

there is no U

[full apex]

no there is no YOU!!!!

gtfo here

[jovial wind]

hush random

this is my helpine now

[full apex]

i did this

@tardy stag

[tardy stag]

that with parentheses around the (2x^2 + 3y^2) is correct

[full apex]

act like a normal human being for once

[tardy stag]

replace the d back

[full apex]

yeah

so substitute

[full apex]

alr

lemme try solving it

jump

[unkempt sundial]

This channel is wild

[full apex]

ong

oh you want that?

😼

no

kys

[summer dirge]

easy now

[full apex]

ong

ing

[summer dirge]

no need to insult others or give them death threats

[full apex]

true its just the 2am math getting to me

[lone heart]

@full apex Has your question been resolved?

[viral acorn]

do u need help with this?

everything

sorry go on

so like

what exactly is the question

ong bro

wait

[unkempt sundial]

This is like the first ever successful channel hijacking

fr

[viral acorn]

all ive got

are you okat

ok bet

certainly

im going to kill you

that is ok

some people find it hot

[north perch]

u are definitely not ok if u want to kill someone

[viral acorn]

my bad brither

all is said in a not meant fully manner

boobs yea

[unkempt sundial]

[viral acorn]

ive heard of that show

[lone heart]

Channel closed

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[north perch]

not watched that shit

i am busy gambling in gacha games

[unkempt sundial]

Im a e-kitten

[lone heart]

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[twin compass]

Could somebody help me with this please?

[split spire]

try expanding

[twin compass]

The equation?

[split spire]

yes

[twin compass]

From here I don't know what to do

[split spire]

use sin(a+b) and cos(a+b) formula

[twin compass]

Oh, you are rigth

Thank you

[lone heart]

@twin compass Has your question been resolved?

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[scarlet drum]

Let △ABC, M ∈ (AB),
AM/AB = 2/7
Knowing that MN ∥ BC, NP ∥ AB, P Q ∥ AC, QR ∥ BC,
RS ∥ AB, N, R ∈ (AC), P, S ∈ (BC), Q ∈ (AB).
a) Calculate AN/NC, CP/PB, BQ/AQ.
b) Show that AM = BQ.
c) Show that SM ∥ AC

[swift grail]

Seems like a fun problem. What did you try / got already?

[lone heart]

@scarlet drum Has your question been resolved?

[scarlet drum]

Thales' theorem and simillarity fundamental theorem

I get stuck a lot

[swift grail]

Did you get AN/NC?

[scarlet drum]

No.

[swift grail]

AB/AM = AC/AN

You can get AN/NC from here

[scarlet drum]

Is it 7/2

[swift grail]

Not really

You should write AC as AN + NC

From there you get
AB/AM = 1 + NC/AN

7/2 - 1 = NC/AN

[scarlet drum]

Right.

So AN/NC is 2/5

CB/CP=CN/AN

Which is 5/2

Too

Right @swift grail

[swift grail]

Yes

[scarlet drum]

Alright, what about BQ/AQ

[swift grail]

You will get that once you get BP/PC as its equal

And BP/PC = AN/NC by similarity

[scarlet drum]

BP/PQ is also 5/2

So BQ/AQ is 5/2 too

[swift grail]

2/5

[scarlet drum]

Yeah, sorry

What about point b?

@swift grail

[swift grail]

I dont quite get it as AM is not BQ

Did you maybe mean AM/MB = 2/7

That would make way more sense

[scarlet drum]

No... AM/AB

[lone heart]

@scarlet drum Has your question been resolved?

[scarlet drum]

<@&286206848099549185>

[scarlet drum]

What about point c?

We have to prove that BMS is simmilar to BAC

[lone heart]

@scarlet drum Has your question been resolved?

[lone heart]

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[hot bison]

does anyone know what this symbol means in calculus?

[hot bison]

the loopdy loop thing

its not a limit

and its in the limit section

.close

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[alpine sable]

Hey, to prove that $\sqrt{2}$ is irrational, I need to proof by contradiction

[ocean seal]

∞

[alpine sable]

Setting sqrt(2) as p/q, etc.

Does this same proof apply to all irrational numbers?

For instance, sqrt(6), sqrt(15)...

[ivory pivot]

yes

[woven harbor]

it should

[alpine sable]

I tried with sqrt(2) and sqrt(5), seems to work

Why does the proof work though?

[ivory pivot]

in fact you can prove that $\sqrt n$ is rattional $\iff$ n is a perfect square

[ocean seal]

everg

[alpine sable]

Is there a way I can explain?

[ivory pivot]

because you are basically using the principal prime property "p divides ab then p divides .."

[alpine sable]

The problem I'm trying to solve is:

Can you modify the proof that you used to show that √2 is irrational to show that √5 is irrational? What about √6? √15? √16? If you can do so, please explain how and why; if not, please explain why you are unable to do so

[ivory pivot]

sqrt 16=4

[alpine sable]

Is there a way I can put things simply? I'm not well versed in proofs, this is legit my first discrete math problem

I'm just trying to understand how the proof can possibly be generalized to all irrationnal numbers

[limpid turret]

Yes and no. For all "rootable" numbers, the proof is the same. But some irrational numbers are hard to prove irrational, are have so far not been proven. But they do all so far seem to have the same idea of "assume rational and find a contradiction"

[alpine sable]

I get it

[alpine sable]

How would you answer this part of the question then? "If you can do so, please explain how and why"

[limpid turret]

Do you understand how the sqrt(2) irrationality proof works? If so, replace 2 with 5 and see if you get the same outcome? Why would you not get the same outcome for 16? What changes?

[alpine sable]

The question specifies that what it's asking is whether the proof to show that sqrt(2) is irrationnal works for other "rootable" numbers (/can be generalized)

[alpine sable]

I can maybe argument this way

No step in the proof that sqrt(n) is irrationnal is changed for all integers n

Nothing in the proof changes aside from the integer in the square root, same steps, same reasoning applies

[ivory pivot]

pretty sure that it is needed to use the fact that n is a prime number ..

[alpine sable]

And for perfect squares like 16 (let's call them z), we don't reach a contradiction, but are rather able to prove the fact that sqrt(z) is indeed rational

[alpine sable]

Would the explanation above be fine to state this condition?

The question that comes after is this one, so I guess it's a generalization that's expected after all

Formulate a conjecture of the following form: “Let N be a positive integer. Then √N is irrational if and only if N is... [Complete the conjecture].”

Describe how you came up with your conjecture. Did your work on the previous questions contribute to your formulation of it? What other approaches did you take? Please describe. Then try to prove your conjecture.

[ivory pivot]

you just don t reach a contradiction, but you can t even do all steps of the proof without n's primality

[ivory pivot]

.

[alpine sable]

I'll try to figure this out by myself

And I'll come back later

[ivory pivot]

👍

[alpine sable]

Do you mind if I ping you if I encounter issues?

[ivory pivot]

sorry but here it s pretty late ...1 a m

[alpine sable]

All good, no worries

Thank you!

[ivory pivot]

but i think a lot of helpers can help you with that problem

[alpine sable]

Got you

Thank you

.close

[lone heart]

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[kind pelican]

Can someone explain how?

[kind pelican]

The second line I mean

[main ruin]

it's the equivalent of expanding out (x-3)(x-3)(x-3) so you can do the first two, like a (x-3)^2, then multiply that by the last one if you'd like

I say if you'd like since there are other ways to distribute as well, but that may be the easiest way to see it

[kind pelican]

I get that (I also solved it irl and keep getting that answer)

[river badger]

so what is the problem?

[kind pelican]

That this is the “right” answer and it doesn’t make sense to me

[kind pelican]

This make sense

[river badger]

what doesn't make sense?

[kind pelican]

The second line in this image

[river badger]

subtract 8 from both sides?

[kind pelican]

No the second line

[main ruin]

oh yeah that's interesting, it should distribute out to -9x^2

[kind pelican]

I thought I was going crazy fr

☠️

[main ruin]

wondering if it could be a mistake?

bc now I think I'm crazy

[kind pelican]

Maybe, I’m looking at a website with answers for my homework assignment (not cheating, just checking my answers, again, not cheating 😭😭)

[swift grail]

Probably is a mistake

[river badger]

x^3 - 9x^2 + 27x -18

[swift grail]

Any why would you expand it and not factor it?

[river badger]

is what I got

[swift grail]

You litteraly have cubic on LHS and cubic on RHS

[kind pelican]

Same

[kind pelican]

Yea but the teacher said “do it this way 🤓☝️”

[main ruin]

tell the teacher they're wrong and get extra credit points my friend

[swift grail]

You goona use the cubic formula?

[alpine sable]

Hey, just joined

[kind pelican]

I meannnnnn

[kind pelican]

Nah, I could but imma just do it this way

To get full credit

[swift grail]

And what happens once you expand it?

[kind pelican]

I lowkey don’t know how to do cubic formula anyway, but I know 2^3 is 8 so 🤷‍♂️

[kind pelican]

If this is what you mean by expanding it, then this is what i get

[kind pelican]

So it would he x - 3 = 2

If I’m not mistaken

[swift grail]

No i mean what do you get when you write it like
[x^3 - 9x^2 + 27x - 35 = 0]

[kind pelican]

And you add 3 to the other side so X = 5

[ocean seal]

casework

[swift grail]

How will you solve that

[kind pelican]

Oh we’re tryna find the possible rational solutions

So imma just use synthetic division

With guessing and checking

[woven harbor]

yeah

since it's a difference of cubes

there should be one factor for sure

and you can use quadratic formula after you divide

[swift grail]

Or you can expand it then factor it again then solve it

Theoretically you should get full credit

[kind pelican]

Yup, did this

[kind pelican]

That’s a certified W

[lone heart]

@kind pelican Has your question been resolved?

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[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[quartz rapids]

Does the fact that 49 is the square of 7 help you to seeing where to go with this?

[signal swift]

yeah so its 7^x-5=7^2

right

[quartz rapids]

7^(2x) on the right but yeah

So what can we do on both sides to bring those exponents down?

[signal swift]

x-5=2x

[quartz rapids]

Yeah exactly

So whats x

[signal swift]

-5

thanks

[quartz rapids]

Nw

[signal swift]

.close

[lone heart]

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[lone heart]

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[storm cove]

I need help

[storm cove]

Geometry

.close

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[tired bone]

need help trying to set equal to 0?

idk how to make common denominator?

or however to find when it equalszero..

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@tired bone Has your question been resolved?

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@tired bone Has your question been resolved?

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[high wolf]

Could I go over this problem with someone?

[high wolf]

or at least my solution to it

[alpine sable]

go ahead yes

[high wolf]

This is what I've got so far:

[alpine sable]

why did you make it k+1 for your inductive step

you are simply assuming that [
P(k): ; 1^2+\dots + k^2 = \f{k(k+1)(2k+1)}6
]
holds

[alpine sable]

you want to prove that the implication $\m Pk \Implies \m P{k+1}$ is legit

[high wolf]

we made the assumption that the formula is true for some positive integer k, shouldn't we then the formula must also be true for k+1?

[alpine sable]

we want to show that if our assumption holds, then the next step is possible

induction is akin to dominos in the sense that, if you can make sure that the first domino is falling down (basis case) and also can prove that the first domino can make the second domino fall (P(k) -> P(k+1)) then you can assure yourself all the dominos would fall eventually as well

induction is NOT simply just substituting in k+1 into your proposition P(k) if that's what you mean. You are not using your inductive hypothesis

[high wolf]

This is my full work.

[alpine sable]

ok yes that is correct now

[high wolf]

Thanks!

[mystic swallow]

@high wolf if done do .close

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[austere warren]

im confused as to why the shell method doesn't work here

ignore the respect to y integral

i also tried it as just a solid of revolution but doesn't work either

[tardy stag]

something fundamentally changes at y=0

needs to be two separate integrals

this is also true at x=2 if youre going that way

[austere warren]

im still confused

isnt the formula (integral symbol) 2pi(x)(f(x))dx

and in my case, i sbtract the outer integral from the inner integral

the outer integral being y=9x-19

[lone heart]

@austere warren Has your question been resolved?

[tardy stag]

yeah but "the inner function" doesn't always exist

at the base

like the base of the cup

since the parabola only goes so low

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[snow cobalt]

ok

is it an exam?

then?

then why do you have 7 minutes for revising-