help-26

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@stuck linden Has your question been resolved?

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[hallow sluice]

i dont understand how to build and work through a formula for this

[vernal vale]

yes

it usually involves a chain of substitutions

the important part is that theyre distributed normally with that mean and standard deviation

The easy one starts like

\begin{align*}
E[\overline x}
&= E[ \sum \frac 1 n x_i ] \
&= E[ \frac 1 n \sum x_i ] \
&= \frac 1 n E [ \sum x_i ] \
&= \frac 1 n E[ x_1 + \dots + x_n ]
\end{align*}

maybe one more line would be helpful

@hallow sluice can you think of what to do from here?

[thorny flame]

jan Niku
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[hallow sluice]

yes thank you for the help

[vernal vale]

damn

it wont render the first line

but the sum is just the formula for x bar

[topaz sinew]

@hallow sluice Has your question been resolved?

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[neon iron]

sorry i responding, i was busy with soemthing

as a response to #help-27 message, i say 0

[vital relic]

@drifting swift ^ from crabbo

And no, not 0. Probability 0 guarantees event does not happen.

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

i dont think ti will happen

[wooden matrix]

what work have you done to come to that conclusion?

And work you are willing to actually show us.

[neon iron]

25+4

that is the discriminant

[wooden matrix]

it is not

[neon iron]

what did i mess up

[wooden matrix]

where the fuck did the n go?

[neon iron]

5^2-4(1)(-n)

25+4n

[wooden matrix]

yes.

that is the discriminant

Then what did you do?

[neon iron]

isnt that what i wrote?

[wooden matrix]

...

you're trolling right?

[neon iron]

oh wait, i forgot the n

nvm

[wooden matrix]

.

[neon iron]

its always going to be positive

[alpine mist]

i think it should be 25-4n

[neon iron]

no

[wooden matrix]

oh yeah

[neon iron]

the n was negative

[wooden matrix]

no

[neon iron]

wait

we added it

[wooden matrix]

$x(x+5)=-n\implies x^2+5x+n=0$

[neon iron]

🤦

[thorny flame]

Mosh

[neon iron]

you are right

ok

so now i can find th eanswer

[wooden matrix]

ok.

[neon iron]

4/10

2/5

[wooden matrix]

yes.

[neon iron]

cool

Solve for the rational numbers $x$ and $y$:$$2^{x+y} \cdot 3^{x-y} \cdot 6^{2x+2y}= 72.$$Express your answer as an ordered pair $(x,y)$.

[thorny flame]

crabbo

[neon iron]

how should i get started

[wooden matrix]

attempt it first w/o help.

[neon iron]

i would normally rewrite with same base

but i dont like that 3

[vital relic]

You should notice something about 2, 3, 6, 72

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

2 3 and 6 are factors of 72

what can i do with that tho?

<@&286206848099549185>

[vital relic]

'factor'

That's an interesting word.

[neon iron]

why?

[vital relic]

You should do it.

[neon iron]

ah

but hwo?

how can i use it

pls

[neon iron]

<@&286206848099549185>

[sweet shard]

hint: prime factorization https://www.cuemath.com/numbers/prime-factorization/

and 6 = 2 * 3

[neon iron]

Hmm

Does that simplify things

The annoying thing is

I don’t have paper

[sweet shard]

https://giphy.com/gifs/everyone-brown-shaun-LyJ6KPlrFdKnK

[neon iron]

Where I am at the moment

I’m still confused how to use the factors

[wooden matrix]

Then you shouldn't be attempting math if you don't have something to write on

[sweet shard]

use a napkin?

napkin math is very trendy

[wooden matrix]

However based on what Riemann has said w/ their hint, you should attempt that.

[neon iron]

I don’t know how though

[wooden matrix]

well what is a factor?

and what is a prime factorization?

Read the words, decipher them, do some googling for definitions if needed, then try and link them.

[honest hazel]

reminds me of the time I was I had to go to emergency care cus of a dogbite so I took my geometry book with me to the hospital cus I had an exam the next day

[sweet shard]

"Teacher I don't have my math homework because I was at the ER for a dog bite" sounds like an evolution of the dog ate my homework excuse

not to minimize you being bitten by a dog. that shit is scary

[honest hazel]

shows meat hanging out of leg

gets a notice anyway

[neon iron]

How do I put them together

[wooden matrix]

Could have sworn at one point you said you only wanted hints, and to actually get better at math

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

I think I have it

I think so

[neon iron]

so

$2^{x+y+1} \cdot 3^{3x+y}= 72$
or
$2^{3x+3y} \cdot 3^{x-y+1}= 72$

[thorny flame]

crabbo

[wooden matrix]

there's no or.

nor do I have any idea where an or would have come from

And unfortunately I know if I ask you to post your work it'll be met with hardship and refusal.

[neon iron]

not this time

[wooden matrix]

Then show your work.

[neon iron]

$2^{x+y} \cdot 3^{x-y} \cdot 6^{2x+2y}= 2^{x+y} \cdot 3^{x-y} \cdot 2^1 \cdot 3^{2x+2y}=2^{x+y} \cdot 2^1 \cdot 3^{2x+2y} \cdot 3^{x-y} = 2^{x+y+1} \cdot 3^{2x+x+2y-y}=2^{x+y+1} \cdot 3^{3x+y}$

[thorny flame]

crabbo

[neon iron]

a bit long

[wooden matrix]

I meant take a picture

but 1st equality is already wrong

$6^n=(2\cdot 3)^n$

[thorny flame]

Mosh

[wooden matrix]

not $6^n=2\cdot 3^n$

[thorny flame]

Mosh

[neon iron]

oh

i dont know what to do then

[wooden matrix]

...

Do you always have a defeatist attitude?

[drifting swift]

person helping you: [corrects your mistake in a way that indicates how to proceed to fix the mistake]
you: i DoNt kNoW wHaT tO dO

one would think that the mistake was pointed out in almost the most direct way possible

[wooden matrix]

Nah, I didn't make it clear enough \s

[neon iron]

i see my mistake

but it doesnt seem to help me

(2*3) is very contained

[wooden matrix]

rewrite your 1st line with the correction.

Then try to apply, correctly, exponent laws.

Look up a list of the laws or refer to your notes if need be.

[neon iron]

ok

$2^{x+y} \cdot 3^{x-y} \cdot (2 \cdot 3)^{2x+2y}=72$

[thorny flame]

crabbo

[drifting swift]

keep going

[wooden matrix]

Now read the other 2 things I said

[neon iron]

this?

[wooden matrix]

...

[wooden matrix]

.

Use context.

Why would I refer to something from 4 hours ago?
You responded to the 1st of 3 things I wrote, then I said read the other 2.

[neon iron]

ok

[drifting swift]

where are you right now

[neon iron]

i got a paper

im trying to find which exponent law would work for this

[drifting swift]

so you still have not moved on from $2^{x+y} \cdot 3^{x-y} \cdot (2 \cdot 3)^{2x+2y}=72$?

[thorny flame]

Ann

[drifting swift]

no answer....

[neon iron]

i cant group anything

[drifting swift]

im going to fucking scream

this is yet ANOTHER instance of me asking a yes/no question and NOT RECEIVING A YES/NO ANSWER

[neon iron]

no

[drifting swift]

okay

so where are you at now?

[neon iron]

i mean, no one will hear you

[neon iron]

tbh, same thing

[drifting swift]

okay

so you're stuck at the same line

[neon iron]

yes

[drifting swift]

you know how in your last attempt you got your equation to look like 2^something * 3^something = 72, yes?

[neon iron]

yes, but it was wrong

[drifting swift]

your exponents were wrong because you fucked up the algebra.

but you were on the right track with expressing the left-hand side as a power of 2 times a power of 3

of course, if you for some reason believe a solution can ONLY ever be 100% right OR 100% wrong with no inbetween, then you might be making it hard for yourself to identify and recover the good parts from a bad solution

[neon iron]

right, and now i dont know how to fix that algebra

[drifting swift]

.

keep this goal in mind

and apply exponent laws, which you should most certainly know by now

[neon iron]

$a^b*a^c=a^{b+c}$ im not sure how to use that one here

[thorny flame]

crabbo

[neon iron]

but it seems like the one i should use

[drifting swift]

there are others

if you're not sure how to use this one, look for other laws that might be more easily applicable

[neon iron]

$(a^m)^n$. that would only give us the same thing

[thorny flame]

crabbo

[drifting swift]

again, you want to have the left-hand side look like a power of 2 times a power of 3

and you currently have a power of (2*3) in your expression

how can you take care of that

ive done everything i could think of to avoid saying it directly and giving you a chance to figure it out

[neon iron]

multiply it out?

[drifting swift]

i don't know what you mean by "multiply it out"

so why don't you do it and show me the result

[neon iron]

its acctually unessacery

wont work

im stumped

[drifting swift]

i think you didn't even try

seeing as how quickly you gave up

gave up on doing something you yourself suggested, i should say

i want to know what you meant by "multiplying it out", because you might have something good in mind or you might not

but now we'll never know because your defeatist attitude got in the way and you made a sitting duck of yourself.

[neon iron]

what have i not tried?

[drifting swift]

i don't know what you mean by "multiply it out"
so why don't you do it and show me the result

to this, you responded by saying it "won't work"

[neon iron]

i cant really say the result

besides saying multiply (2*3) 2x+2y times

[drifting swift]

you had something in mind that you were planning to do. is that the case, yes or no?

[neon iron]

yes

[drifting swift]

so do it

[neon iron]

i cant

[drifting swift]

how can you plan to do something you can't do

[neon iron]

since i dont know what 2x+2y is

[neon iron]

is was false logic

we can forget about it now

im honestly tired

[drifting swift]

if you're tired then why are you doing math?

[neon iron]

i should probably come back to this tommorow

[drifting swift]

are you under a deadline?

[neon iron]

no

[drifting swift]

okay then rest up and come back to this when you're able.

[neon iron]

not a serious one atm

[neon iron]

ok. gn

.close

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[stable tiger]

Can anyone help me with how to go about solving these questions?

[neon iron]

try log base 1/4 of 16

[stable tiger]

Uhm I don’t know what log base is

[wheat laurel]

maybe just guess

it's quite easy

[stable tiger]

Ya that one is but I mean like the steps to solve it

For others like that

[empty sail]

Make both sides into the same base

[stable tiger]

.close

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[broken steeple]

yo could anybody help me rq?

[broken steeple]

I'm having trouble with this

[empty sail]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/introduction-to-slope

[leaden tusk]

$m=\frac{\text{rise}}{\text{run}}$

[thorny flame]

a disappointing son

[empty sail]

Perfect example video

It shows how to draw it and everything

[broken steeple]

I see

[topaz sinew]

@broken steeple Has your question been resolved?

[topaz sinew]

@broken steeple Has your question been resolved?

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[neon iron]

Hi

[neon iron]

I'm weak in this sort of geometry (although it's technically algebra, maybe?)

I've solved 9a, but have no idea how to start or understand 9b

I understand k is meant to represent the difference in size between the sides of the outer and inner triangles

This was my solution for 9a (what D equals)

I simply don't see the relation yet between k and D, b, c

Just realised, can I just make k the subject of my first answer

Solved my own question

[neon iron]

It was just simply doing this lol

.close

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[merry mason]

What should I do in this question

Have to use purely trigonometric transformations to find limit

L hospital is forbidden

[toxic dust]

Expend it?

[merry mason]

I don't have money

[toxic dust]

Expand

[proven anvil]

he means taylor expansion

[merry mason]

No

[toxic dust]

Nope

[proven anvil]

😰

[merry mason]

This is doable without that

I know because we don't did Taylor in my class

[toxic dust]

I mean only expand the sin(3(….))

[merry mason]

Sin3x= 3sinx - 4sin^3x formula?

Should I expand using that

[toxic dust]

I think there’s another formula for sin3x

[merry mason]

No I only know this one

Can sin3x - 3sinx be simplified?

[thorny flame]

謝墨離

$\sin 3x = \4(sin(60-x))(sinx)(sin(60+x))$
```Compilation error:```! Undefined control sequence.
l.55 $\sin 3x = \4
                  (sin(60-x))(sinx)(sin(60+x))$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]```

[toxic dust]

This

[merry mason]

I think this formula only make the work lengthy

But ok

[toxic dust]

I hope it will help

[merry mason]

I hope so

60 is pi/3?

[toxic dust]

And sin(pi-y)=sin y

[toxic dust]

Yea

[merry mason]

Alr

[merry mason]

Right

[toxic dust]

Hey

[merry mason]

Yes

[toxic dust]

I don’t use l hospital rule

But I can prove

[merry mason]

What

[toxic dust]

Sin(x)/x=1 when X is approaching zero

[merry mason]

Using toylar expansion?

[toxic dust]

It’s a bprp video

[toxic dust]

No

[merry mason]

What is bprp

[toxic dust]

Black pen red pen

[merry mason]

Nice

[toxic dust]

Let me find the video

[merry mason]

Ohh

I know that channel

Just calculus and him are one

[toxic dust]

https://youtu.be/mZiPdyHyUvE

I’m going to sleep

[stuck lintel]

0!

cheeky

[toxic dust]

Bye

[merry mason]

Bye

[stuck lintel]

it's a nice geometrical proof by the way

Should make you feel good for a day

[merry mason]

After solving this question I'll watch it

[dawn pelican]

give me kit

😟

[merry mason]

I know that sin(pi-y) is sin y but is sin^3(pi-y) also sin^3 y?

Well it seems my well done answer somehow was wrong.

[abstract wadi]

It is not wrong.

[merry mason]

Answer is -4 but book answer says -1

[abstract wadi]

Maybe you did something else wrong.

[merry mason]

Yeah I'm checking that rn. If I don't find anything wrong, I'll post my work here

[stuck lintel]

I got into the habit of cross-checking with a symbolic calculator, just to make sure the book isn't wrong (possibly).

[merry mason]

Book is rarely wrong though, there was one question for which it was wrong for me

It seems there is nothing wrong

,w limit of (sin3x-3sinx)/(pi-x)^3 as x tends to pi

[thorny flame]

Results provided by WolframAlpha

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

Requested by Ji Ning#8861

[merry mason]

Seems like my answer was correct

.close

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[wary willow]

Is the this a fractal?
Sequence:
0, 2, 0, 5, 3, 8, 2, 11, 6, 14, 0, 17, 9, 20, 5, 23, 12, 26, 3, 29, 15, 32, 8, 35, 18...

Splitting in half gives

0, 0, 3, 2, 6, 0, 17, 9, 20, 5, 23, 12, 26...
2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35

Splitting again gives
3, 6, 9, 12, 15, 18, 21...
0, 2, 0, 5, 3, 8, 2, 11, 6, 14, 0, 17, 9, 20, 5, 23, 12, 26, 3, 29, 15, 32, 8, 35, 18...

[wary willow]

You can then split the final sequence again forever the same way

[topaz sinew]

@wary willow Has your question been resolved?

[wary willow]

eh

I wanna go

.close

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[wintry canyon]

if f is differentiable on the set of real numbers and f(3)=0 and f'(3)=2 what is the value of lim (x -> 3) f(sqrt(x+6))/(x-3)?

[wintry canyon]

3 options were given: a) 0, b) 2, c) 1/3

so i know the limit is actually 1/3 using f(x)=2x-6 since it satisfies all the conditions and calculating the limit then is easy and the result is 1/3

<@&286206848099549185>

[topaz sinew]

@wintry canyon Has your question been resolved?

[wintry canyon]

<@&286206848099549185>

[wintry canyon]

<@&286206848099549185>

[topaz sinew]

@wintry canyon Has your question been resolved?

[vapid lichen]

$\frac{f(\sqrt{x+6})}{x-3}=\frac{f(\sqrt{x+6})-f(\sqrt{3+6})}{x-3}$

[thorny flame]

RokabeJintaro

[vapid lichen]

now recall f is differentiable

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[unborn sundial]

how would you set this up in an equation

[unborn sundial]

Ithink did the sides right amby not 😦

Oh ok tyvm

yes srry

.close

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[unborn sundial]

when is set up equation thing tto get x what am i setting up wrong?

[dim crag]

sin(65°)*28 ist the hight of the touching point, the horizontal distance is cos(65°)*28

[unborn sundial]

Was got that part wrong? Is the set up right

.close

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[grave juniper]

so given to me is a table when x equals a value
x = -2
f(x) = -2
f'(x) = -5
g(x) = 1
g'(x) = 7

[grave juniper]

so i need to find the derivative of the function

$$g(gx))$$

[thorny flame]

heep

[grave juniper]

and so i did chain rule and got

$$g'(g(x)) * g'(x)$$

[thorny flame]

heep

[grave juniper]

now given my table would this be the correct way to enter the values? i know this is basic algenbra but im kinda conufsed

$$g'(1) * g'(7)$$

[thorny flame]

heep

[grave juniper]

so i would get 7 as an answer or would i need to do something with the g'(g(x))

[short mango]

It's 7^2

B/c g'(x) is always = 7, it doesnt even matter what g(x) is

[grave juniper]

see thats what i would think too but my study guide says its -7

[short mango]

Ur teacher made a mistake bc if x=-2 then g'(1) needs to be defined

[grave juniper]

ok wait so the full table also includes
x = 1
f(x) = 1
f'(x) = 3
g(x) = -2
g'(x) = -1

so once i do g'(g(x)) and get g'(1) since x = 1 would i use g'(x) = -1 and then multiply it by 7 to get -7?

[short mango]

Oh

so g(x) = 1 and g'(1) = -1 so you do -1 * g'(-2) = -7

[grave juniper]

alright so if i solve the inside function and it corresponds with another x i would use that tables reference?

[short mango]

Ye

[grave juniper]

word i just tested it out with another problem and it worked

thanks broski

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[pliant lake]

I'm stuck at this point on 22. We have not learned hopitals rule so any other way of getting this answer?

[sweet shard]

,rotate

[honest hazel]

hint: lim x->0 of sinx/x

[pliant lake]

Am I just supposed to do it numerically then?

[honest hazel]

umm

numerically?

[pliant lake]

Like plugging in numbers close to zero from both sides

[honest hazel]

nay nay nay

No such thing is necessary

[pliant lake]

Plugging in 0 would give you div by 0 obv

[honest hazel]

remember arithmetics of limits

and use the hint I gave you

[honest hazel]

you cannot ever plug in your limit subject if your function is not continuous at that point

[pliant lake]

Honestly never heard that at this point. Either we haven't learned it or it's called something else

[honest hazel]

you haven't learned aobut limit arithmetics?

like

[pliant lake]

Perhaps?

[honest hazel]

Lim a+b = lim a + lim b? etc... ?

or lim a*b = lim a * lim b ?

[pliant lake]

Oh properties of limits

Yeah

[honest hazel]

yea sure potato tomato w.e

[pliant lake]

I know how to split it up

But from there it gets screwy

Bc of sinx/x

Or I'm just Stoopid

[honest hazel]

what about sinx/x... ?

[pliant lake]

How do you solve that? That's really the only part that has me stumped

[honest hazel]

huh ?

were you not taught that limit?

[pliant lake]

If I was it's completely slipped my mind and I just can't find any hint of it in my notes for the past 10 minutes

[honest hazel]

Well.. usually sinx/x as x tends to 0 is one of the elemntary limits that are taught so ill give it to you

Lim sinx/x as x-> 0 is 1.

since.. without that you probably won't be able to solve it..

[pliant lake]

Oh so it's like a trig identity...but limits 🙃

Yep haven't heard it

[honest hazel]

you weren't taught that.. ?

[pliant lake]

But I do appreciate the help

[honest hazel]

so you're expected to solve without it.. ?

[pliant lake]

🤷‍♂️

Maybe he just overlooked something in the lecture

[honest hazel]

@sweet shard would you happen to know anything .. ?

[pliant lake]

@honest hazel is this the one?

So if the angle and denominator match, it equals 1?

[honest hazel]

exactly

if they both approach 0

[pliant lake]

Oh yeah that too

Alright cool

Need to bash that into my head

Thanks a lot

[honest hazel]

you should really watch the proof on that one tho

the geometric one

[pliant lake]

Yeah when I finish this up I'm gonna check it out

[honest hazel]

shows you how beautiful math can be sometimes

[pliant lake]

It really do. Just sucks at the beginning 😂

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[warm sage]

Hey guys I'm trying to show one of the conditions for a converging alternating series test but am having trouble showing this inequality. Can someone give me some pointers?

[topaz sinew]

@warm sage Has your question been resolved?

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@warm sage Has your question been resolved?

[vernal vale]

wow this goes to 0 slowly

@warm sage you still around?

looks like n>=2 is enough

i can type out what i got but i wanna make sure youre still here

😄

[warm sage]

@vernal vale ye

I did graph it and yes it does seem like for n>=2 it is true

[vernal vale]

i mean i just did it backwards

4 <= n(n+1) is true when n>=2

add 8n, 5n^2, and n^3

multiply by sqrt 10

this simplifies to

wait

multiply by 10, then sqrt

this should be fine right? since sqrt is monotonic

then you get

$\sqrt{ 10(n+1)(n+2)^2 } \leq \sqrt{ 10 n(n+3)^2$

[thorny flame]

jan Niku
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vernal vale]

so $(n+2)\sqrt{10(n+1)} \leq \sqrt{10n}(n+2+1)$

[thorny flame]

jan Niku

[vernal vale]

some algebra will turn this into $\frac{a_{n+1}}{a_n} \leq 1$ for $n \geq 2$

[thorny flame]

jan Niku

[vernal vale]

actually, i think you can turn this strict

< 1

since n=2 gives 4 < 6 and n^2+n is increasing

seem reasonable?

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[tired cloud]

What are the steps to evaluate the limit of- lim x->0 from the right (1+sin4x)^cotx? I have been told that the answer is e^4 but i don't know how they come about this answer. Can anyone help me?

[sweet shard]

Write the function as exp(log(...))

[keen osprey]

use logs to move the cot x down and solve using lhopitals

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[neon iron]

hey guys i have angle d, but im unsure how to find angle c

[neon iron]

angle d is 59 degree btw

found from subtracting the 2 angles from 180

how would i find angle c though??

pls help

[restive inlet]

apply parallel line theorems

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[neon iron]

why is the nth triangular number always divisible by n if n is odd?

[acoustic tangle]

Because nth triangular number is n(n + 1)/2 ?

[neon iron]

the upper part is a multiple of n

[wooden matrix]

hence why it's divisible by n

[acoustic tangle]

You can show that the 2 cancels out with n + 1 when n is odd

And the factor of n remains

If n is even, then the triangular number is instead divisible by n/2

[neon iron]

i think i figured it out

[neon iron]

its not always true tho

the second triangular number is 3, which is not divisible by 2

[wooden matrix]

well yeah, but n+1 is even when n is odd clearly

[neon iron]

but if n is odd, it can be written as 2k+1. (2k+1)(2k+2)=4k^2+6k+2

(4k^2+6k+2)/2=2(2k^2+3k+1)/2=2k^2+3k+1

is 2k^2+3k+1 divisible by 2k+1?

[wooden matrix]

yes

[neon iron]

i thought so

[wooden matrix]

n is odd implies n+1 is even, so n(n+1) is divisible by 2 and n.

[neon iron]

How about the +1

Wait

Nvm

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[wanton dune]

hey im trying to solve the quadric form of a 2 variable function, once i do the associated matrix A i can find the determinant, but then it asks me to compute det A1, det A2, and det A3, to assert if A is a postivie semidifinite or indefinite in sign etc, does anyone know what i have to do?

[wanton dune]

3 variable function sorry

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@wanton dune Has your question been resolved?

[wanton dune]

<@&286206848099549185>

should i be more specific?

[sweet shard]

Just take a picture of the original question

[topaz sinew]

@wanton dune Has your question been resolved?

[wanton dune]

the question says

Study the definition of the following quadratic form on $\mathbb{R}^3:q(x,y,z)=x^2+5y^2+z^2-2xy-4yz$

[thorny flame]

James Joyce

[wanton dune]

thats exactl waht is says, ive done the matrix, found the determinant, but i dont know where to go from there

i guess it has something to do with submatrices but idk how to get them\

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[urban wren]

how would i do this question?

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[edgy bane]

hello I want to go sleep

[edgy bane]

Radiocarbon Dating

$y(t)=y_0e^{-kt}$

[thorny flame]

cakeee

[edgy bane]

How to calculate t if i know
y_0=18%=0.18
k=0.00012097

and half-life of carbon-14 is about 5730 years

[outer gyro]

is it not just ln(y(t)/y0) = -kt

[novel token]

indeed

[edgy bane]

I have to calculate time

[edgy bane]

Can you explain little

I have to calculate how old the bone is

[novel token]

ok so what does y(t) represent here

[edgy bane]

y(t) equation

[novel token]

ok sure but what i meant is when you plug in t into the y function does it give you the half life back or full life

can you show me the fll problem?

[edgy bane]

This is all I got.

[edgy bane]

i dont get it

[novel token]

alright so basically your formula for radiocarbon dating says:

y(t) is the half life after some time t

no

y0 is the half life at t =0

[edgy bane]

lol i dont know what to do

[outer gyro]

its been a while since i did physics but y0 is not 0.18

y0 is the initial mass surely

y(t) is the mass at time t

or rather the proportion of the mass

[crude patio]

yea. y(t) at the current time is now y(t)=0.18y_0

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@edgy bane Has your question been resolved?

[crude patio]

you have found k using the half-life already right? now solve for t using y(t)=0.18y_0

[edgy bane]

0.18y_0=y_0e^-0.00012097t
t=-(ln(9/50)/0.00012097)=14175 years

that y_0 confused me somehow

but thanks

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[signal bough]

To graph I just simply graph 2x+1 and x but remove part to satisfy the condition, right?

[signal bough]

(for 2x+1 the left side of the plot will be erased since it's only looking for values < 1)

[marsh mortar]

To graph

You first look at the section of the function where x<1

and sketch 2x+1 for that part

and for x>=1

you just sketch x

At x =1

You need to include an open circle at F(1) = 2(1)+1

and closed circle at F(1) = (1)

[signal bough]

For x >= 1 why is it only at x=1?

[marsh mortar]

What do u mean

[signal bough]

"you just sketch x
At x =1"

[marsh mortar]

The way you read this is the following

$F(x) = 2x+1$ when $x<1$

and

[thorny flame]

azeem321

[marsh mortar]

$F(x) = x$ when $x\geq 1$

[thorny flame]

azeem321

[signal bough]

correct

[marsh mortar]

Because the function 2x+1 is not defiend at x=1

only x is defined at x=1

[signal bough]

is this correct?

[marsh mortar]

The point where you've included the open circle

looks like

(0,1)

[signal bough]

oops

[marsh mortar]

The circle should be (1,0)

[signal bough]

yea

[marsh mortar]

also dont forget the other function

and 2x+1 only holds for x<1

when x>=1

you need to start drawing the graph of f(x) = x

[signal bough]

I'm more confused than I was before 😂

[marsh mortar]

hmm

what confuses u

[signal bough]

your explaining lol

[marsh mortar]

Ok. You know that a normal function $f(x) = 2x-3$ for example is defined for all x values

right

[thorny flame]

azeem321

[signal bough]

yes

[marsh mortar]

The image above is called a piecewise function

[signal bough]

2x+1 is the same except for values less than 1

correct

[marsh mortar]

It's called piecewise because different functions exist for different intervals of x

In the 2x-3 example, only the one function existed

[signal bough]

yes

[marsh mortar]

Can you sketch the graph of $2x+1$ but only for values of $x<1$

[thorny flame]

azeem321

[signal bough]

sure sec

[marsh mortar]

good

Now sketch the graph of $x$ for $x\geq 1$ on the same graph as above

[thorny flame]

azeem321

[signal bough]

I think I was confusing myself xD

because now it makes sense lol

[marsh mortar]

Is that a horizontal line

or is it just a low slope

[signal bough]

low slope

my bad xD

[marsh mortar]

ok good

[signal bough]

yea the other has a slope of 2

so I just made it look lower

[marsh mortar]

Yup you seem to have got it

any other questions about it?

[signal bough]

nah I got it thanks 😄

appreciate the help

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[marsh mortar]

cool

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[craggy tendon]

can somebody help break this solution down for me?

[flat zodiac]

Well without even knowing n, what is the median of the set that was given?

In terms of n

[craggy tendon]

idk

i suck at sets

[flat zodiac]

What does median mean

How does one find the median

[craggy tendon]

the middle value

[flat zodiac]

Ok so what's the middle value of the set they provde?

In terms of n

[craggy tendon]

OH

i see now

thanks

[flat zodiac]

Yep no problem

[craggy tendon]

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[hearty wraith]

kjnjkn]

[hearty wraith]

.close

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[hearty wraith]

u = cis (-pi/6)

[hearty wraith]

find the smallest positive interger, n, such that u^n=1

would it be 12k = n

or n = 6k

[mortal thunder]

$u=e^{-i\frac{\pi}{6}}$

[thorny flame]

Ansh

[mortal thunder]

hmm

[hearty wraith]

so i did cos(pi n/6) = 1

so pi n /6 = 2pi k

so n = 12k

[mortal thunder]

right

[hearty wraith]

but also '

[mortal thunder]

so, what's the problem?

[hearty wraith]

if sin ( -pi n/6) = 0

would this be valid to

?

cause 1 + 0i

[mortal thunder]

Yes but

For example: $\sin 0 = 0$ and $\cos 0 = 1$ works here

[thorny flame]

Ansh

[mortal thunder]

however, $\sin \pi = 0$ and $\cos \pi = -1$ won't work

[thorny flame]

Ansh

[hearty wraith]

oh

[mortal thunder]

n(pi) is a solution to sin x = 0, correct

but it need not necessarily be a solution to cos x = 1

👀

[hearty wraith]

ohh oooofo

[mortal thunder]

that's why you need the cosine argument to determine your "n"

[hearty wraith]

oh

so wait

so sin(-pi/6n) = 0, when n = 12k

?

[mortal thunder]

plug it in and check for yourself +_+

Don't you get, sin(-2kpi)?

[hearty wraith]

-sin(2pi k )

[mortal thunder]

yeah

[hearty wraith]

ye

[mortal thunder]

and that's zero

[hearty wraith]

burh im high

yes

fk

okk thabksnsknknss

sksk

thank you @mortal thunder

[mortal thunder]

[hearty wraith]

.close

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[vernal vale]

i need some help on 2 😅

I'm curious how I know the original variance here? I'm kind of confused about how it changes with the sampling

i know its not just lambda from the original variance

unless it is

in which case i need help figuring out exactly which function is happening here

[topaz sinew]

@vernal vale Has your question been resolved?

[vernal vale]

<@&286206848099549185> any advice

[sweet shard]

isn't there an R discord server

[vernal vale]

i mean

its not really an R question

i think its just stats

I'm just including the instructions so its clear

I guess i just need to ask like

the instructions say this process:

1. Take a hundred million iid poisson samples

2. split them into a million rows of a hundred each

3. Take the mean of each row (a million means)

4. Take the mean of the means

5. Take the variance of the million means

I'm just trying to figure out variance at the moment

its just what im calculating is off from what the program is giving me by a factor of a million

\begin{align*}
V(\bar E)
&= V( \frac{ E_1 + \dots + E_{mil} }{ 1,000,000 } \
&= V( \frac{E_1}{mil} + \dots + \frac{E_{mil}}{mil}) \
&= \frac{1}{mil^2} ( V(E_1) + \dots + V(E_{mil}))
\end{align*}

[thorny flame]

jan Niku

[vernal vale]

heres my thought to begin with

then since each E_i should be a mean of a hundred, you get another 1/100^2 factor out front

and theres a million of the E_i, each evaluation to 100 lambda...

[sweet shard]

Oh you mean b)?

[vernal vale]

yea

[sweet shard]

Have you tried CLT?

[vernal vale]

Well i know it involves clt

like the asymptotic thing uhh

$\sqrt n ( \bar x - \mu ) \longrightarrow N(0, \sigma ^2)$

[thorny flame]

jan Niku

[vernal vale]

then if you have $g$ some function of $\bar x$

[thorny flame]

jan Niku

[vernal vale]

you get to the asymptotic business

but im having trouble finding g

can xbar here be a mean of means?

why thonk

[sweet shard]

Trying to remember if mean of means is the mean of the total

[vernal vale]

i was thinking

it shouldnt matter right

but it will impact the variance obviously

like you can take the mean however you want, and youll get to the same answer i think?

but the variance is going to change depending on how you box out your samples

idk can you confirm that my calculation of what variance should be is correct?

R is reporting that the variance of the million means is lambda/100

I'm calculating it should be lambda/(100 * 1,000,000)

[vernal vale]

<@&286206848099549185>

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@vernal vale Has your question been resolved?

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@vernal vale Has your question been resolved?

[topaz sinew]

@vernal vale Has your question been resolved?

[vernal vale]

maybe i can explain more and it will help?

[vernal vale]

heres what im attempting to explain

> y = rpois(50000000,1)
> xmat = matrix(data=x, nrow = 500000, ncol = 200)
> ymat = matrix(data=y, nrow = 500000, ncol = 100)
> estx = apply(xmat,1,mean)
> esty = apply(ymat,1,mean)
> var(estx)
[1] 0.004999411
> var(esty)
[1] 0.01003218```

but then compare to

> estx2 = apply(xmat2,1,mean)
> var(estx2)
[1] 0.01000021```

i anticipate that variance will change based on the number of columns

why is it only a function of the number of columns

and how do you find this numerically

please don't be scared away from helping because its code, i dont need any help with the code, its just a poisson sample

[sweet shard]

Maybe phrase your question in terms of random variables and ask in #probability-statistics

[vernal vale]

okay

[waxen flame]

mean of each row has variance lambda/100, mean of the means has variance lambda/100 million, since mean of the means is actually just the mean of all of the samples

not sure if your R code works the way you think it does

[vernal vale]

wait, how do you mean?

doesnt work the way i think it does

it says like

i mean idk im assuming how it works

but it doesnt make sense because like

are you saying that the variance if i take 100 million samples should be lambda over 100 mil?

since its not

it obviously changes depending on how i size the matrix

[waxen flame]

why would it change depending on how you size the matrix?

if you split the 100 million into groups of 100 and then take the average of the group averages, you're just taking the average of all 100 million

[vernal vale]

sure but the variance should change right

[waxen flame]

why would it change?

you're computing the exact same thing

[vernal vale]

i mean if you lumped them all into one mean it'd have no variance right

[waxen flame]

no? it would

[vernal vale]

oh

well

[waxen flame]

Say $X_1, X_2, ..., X_{1000}$ are iid random variables

[thorny flame]

Saccharine

[vernal vale]

sorry im very tired because ive been working on this a long time

sure

[waxen flame]

the sample mean is given by $\hat \mu = \frac{\sum X_i}{1000}$

[thorny flame]

Saccharine

[waxen flame]

it definitely has a variance

[vernal vale]

but then each of them hide a factor of 100mil/nrows

[waxen flame]

not sure what you mean

[vernal vale]

the way i was figuring, one factor gets squared, and one doesnt

like its mean of means

variance of mean of means

[waxen flame]

okay but the mean of means is just the mean

Let's say Var(X_i) = 1 in the example I gave

then Var(mu hat) = 1/1000

but let's say you split the Xs into blocks of 10 and compute mu_1, ..., mu_100

[vernal vale]

you pick up a different number of lambdas

[waxen flame]

no you won't

$\mu_j = \frac{\sum\limits_{i=10j - 9}^{10j + 1} X_i}{10}$

fuck

[vernal vale]

wild

i can try to type out what i have

it might take me a sec

[thorny flame]

Saccharine

[vernal vale]

idk if youre interested in seeing it

[waxen flame]

basically split it in blocks of 10

$\text{Var}(\mu_j) = \frac{\text{Var}(X_1)}{10}$

[thorny flame]

Saccharine

[vernal vale]

wait what is this sum 👀

[waxen flame]

basically sum X1 to X10 for the first mean

X11 to X20 for the second

and so on

[vernal vale]

ah, okay

so this is

[waxen flame]

so you split the 1000 Xs into 100 blocks of 10

[vernal vale]

1000 total samples?

[waxen flame]

yeah

[vernal vale]

okay

but square works out nicely

[waxen flame]

don't see how that makes any difference

would you rather it be 50 and 20?

[vernal vale]

lemme try to send what i have

just so i can point to it

if youre amenable

[waxen flame]

okay

[vernal vale]

fug its a pdf

one sec

okay this might be super wrong and i fudged some of the indexing you got right

oh

am i missing a factor on the first line

lemme see what happens

it makes the result $\lambda \cdot \frac{n}{m^3}$? for an mxn matrix

[thorny flame]

jan Niku

[vernal vale]

this seems way worse

[vernal vale]

can we go back to what you were saying in the example

i dont think my work is going to lead anywhere

sorry about that

one chance and i blew it

[waxen flame]

as I've already said

it doesn't depend on the size

okay, you have Var(mu_j) = 1/20, since you'd rather have it 20 and 50

and then the Var(mu), where mu is the average of all of the mu_j, is Var(mu_j)/50

and that is 1/1000

same difference

and it would be much better if you used a quick lemma: the variance of the average of n iid random variables X_1, ..., X_n is simply Var(X_1)/n. You can prove this pretty easily

[vernal vale]

damn

youre right

i just fixed my work

well

wait different n's

ill have try that proof

I'm getting that for a mxn matrix the variance should be lambda/n

which corresponds to what im seeing in R

@waxen flame i cant tell if this is what youre saying too

i think youre saying the code cant tell that its taking the variance of sample means

it just sees that there are n many rv's

another typo

should be lambda/mn

youre right and im dumb

but have answer now

i think happy

[waxen flame]

good

[vernal vale]

so uhh

i mean how does that explain how high the variance is

in R i mean

[topaz sinew]

@vernal vale Has your question been resolved?

[onyx spade]

Your variance that you get is just one realisation of the variance distribution

I'm not sure which variance you are referring to now

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[queen cipher]

been stuck on proving $4xyzw \leq x^4+y^4+z^4$ for 2 weeks now

[thorny flame]

alshfik

[queen cipher]

i cant do any other problems at this point because when i try i always come up with some new thing to try with the inequality

please free me

[keen osprey]

Is that inequality even true

Let w x y z all be 1
4xyzw = 4
x^4 + y^4 + z^4 = 3

Did u miss out a w^4 or something

[queen cipher]

oh yea

$4xyzw \leq x^4+y^4+z^4+w^4$

[thorny flame]

alshfik

[topaz sinew]

@queen cipher Has your question been resolved?

[topaz sinew]

@queen cipher Has your question been resolved?

[tardy jay]

this looks like am gm inequality question

[queen cipher]

yes

how do i prove it

[tardy jay]

just apply the theorem, you know that $\frac{x^4 + y^4 + z^4 + w^4}{4} \geq \sqrt[4]{x^4 + y^4 + z^4 + w^4}$

[thorny flame]

zLmk

[queen cipher]

no i dont

i only know $2ab \leq a^2+b^2$

[thorny flame]

alshfik

[queen cipher]

.close

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[serene hound]

A and B are Real Number,is IV True?

[honest hazel]

yes

[serene hound]

Oh Thanks

.close

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[sage kernel]

My friends and I have decided to pool our money into a joint fund in order to buy hardware for crypto mining, and sharing the generated profit has now become a bit of a problem, and I wanted to develop a sharing mechanism such that it is "fair" in some mathematical sense.

I modeled the profit generated as

[sage kernel]

where t is time, I is money invested and r is the rate of mining (coins/hour) and is represented by

where p_r is the price of the rig and p_g is the price of one graphics card

these equations model the fact that no money is generated until p_r is paid, and afterwards money is generated proportionate to the number of graphics cards bought (assuming fixed rate of mining for each graphics card)

now, the first way of sharing profit fairly i thought of is proportional sharing, where if someone has contributed I to the joint fund and everyone else has contributed U, they should get I/(U+I) times the generated profit

so their profit becomes

how can i determine if this method of sharing is fair

i've look into fair division problems from game theory a bit, but i'm not sure how to apply any of it to this problem

[topaz sinew]

@sage kernel Has your question been resolved?

[sage kernel]

<@&286206848099549185>

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@sage kernel Has your question been resolved?

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@sage kernel Has your question been resolved?

[topaz sinew]

@sage kernel Has your question been resolved?

[sage kernel]

.close

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[neon iron]

Can someone please help me

[empty sail]

Use a calculator

[neon iron]

canyou show me

the steps to put

on the calculato

[empty sail]

Do you know how to solve for theta?

[topaz sinew]

@neon iron Has your question been resolved?

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[balmy zephyr]

I have a question

[balmy zephyr]

So, if we have a double integral

and the bounds on both integrals are from -infintiy to infinity

How would we evaluate that in general

So for example, if we have the double integral from -inf to inf (on both bounds) and two functions fg how would we start?

[wooden matrix]

same way you evaluate a single integral over the entire R line

[balmy zephyr]

So would we just apply that method first to the inner integral, and then to the outer integral?

[wooden matrix]

yep

double integrals are just 2 iterated integrals

[balmy zephyr]

thank you!

.close

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[wooden matrix]

alternatively you can switch to polar and get $\int_0^\infty\int_0^{2\pi}f(r,\theta)r\dd{\theta}\dd{r}$

[thorny flame]

Mosh

[balmy zephyr]

I see got it

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[toxic marsh]

not sure where I went wrong

[neon iron]

Just set y equal to the output and solve for x in terms of y

It’s honestly a bit hard to understand what you were doing