help-17

[sly sierra]

it's the law of the unconscious statistician

[rugged orchid]

Or that

[edgy gulch]

was wondering why do you want to open it infinitely, unless you're opening schrodingers box or something

[thin vale]

I just thought that it didnt seem as random if we were throwing out the bad choices

its more like searching

[livid tapir]

,w sum 1 to inf of n^2/2^n

[rugged orchid]

You have also $\mathbb E[g(X)] = \int_\mathbb R g(x)f_X(x),dx$

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by 992qqoloy

frosst

[livid tapir]

Ik we don't need it im just curious

[thin vale]

well I don't understand why this shoud be the definition

why would it not be P(X^2) * value X^2

[urban edge]

remember that you have to be careful when you open a box, the price to no price ratio is not 1:1

[rugged orchid]

That’s true but then you need the pmf of X²

[thin vale]

okay but I know P(X^2)

isn't it 1/2^(n^2)) ?

mixing up my variables

but

[rugged orchid]

I don’t know I haven’t read that far 😭

But I do know you can just let Y = X² then you can do E[X²] = E[Y] = sum P(Y=y)y

[sly sierra]

why would it be times value X^2?

[rugged orchid]

Which would be what you said

[thin vale]

why would it not be? thats my whole doubt

[sly sierra]

expected value of X^2 = mean value of X^2 = sum of nP(X^2 = n)
but P(X^2 = n) is zero unless n is a square

[thin vale]

why weight it with X^2 but not the probability of getting this weight?

[urban edge]

.reopen

[vocal sleet]

✅

[thin vale]

as it should be

[sly sierra]

so let n = m^2

sum of m^2 P(X^2 = m^2)
which is sum of m^2 P(X = m)

[bitter pilot]

YESSSS WHAT INFINITE TIMES

[thin vale]

but why weight the possibility that X=m with m^2 instead of m?

[bitter pilot]

Austin you are cool but I need to sleep

gl

[sly sierra]

because i did the change of variable n = m^2

[thin vale]

⚔️

[sly sierra]

before the change of variable you had the sum of nP(X^2 = n), but that's zero for all non-square n

[thin vale]

I see the issue

E[X^2]
I'm like okay, I want to know what the expected value of the r.v X^2 is so
it can take on 1, 4, 9, 16, ...
1 * P(X^2=1) + 4 * P(X^2=4) + ...
but this is
1 * P(X=1) + 4 * P(X=2) + ...

I seee

thank u dark side gf

[rugged orchid]

@thin vale r u good or u want me to read it

[sly sierra]

yep

[thin vale]

im good

[rugged orchid]

Big

Bingo bongo bungo the incredible doubt clearer

[sly sierra]

tbh, jumping straight to the law of the unconscious statistician makes things easier

[livid tapir]

f_X(x) is like a density function and g(x) is the coordinate, E[g(x)] is like the center of mass

if physics helps

[thin vale]

I understand it now

thanks

.close

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[radiant rock]

How do I find x?

[radiant linden]

can you send a full screenshot

[radiant linden]

with the whole question please

it cuts out at the ends

[radiant rock]

Thanks so much

17c

[radiant linden]

hmm

[novel iris]

Equality

[radiant linden]

im kinda bad at geometry tbh

[urban edge]

how can you write DC in terms of x?

[radiant rock]

20-x

[urban edge]

good

what about AD?

[radiant rock]

64-x^2 then square root

[urban edge]

good

the biker knows what about AD and DC?

[ancient adder]

Ok

I will try

[radiant rock]

Do you draw a line from A to C

[urban edge]

reread the problem statement

[radiant rock]

So from D to B right

That length

[ancient adder]

Well

[radiant linden]

theres another statement in the question

[urban edge]

what does the last sentence say

[radiant linden]

thats the key to solving it

[ancient adder]

Let Hyp = H
Then 20 - x = H (given)

Use pythogoras
H^2 = x^2 + 8^2
Sub and find

Solve quadratic

[radiant rock]

The answer is 8.4km

[ancient adder]

I hate these questions, so calculative

[radiant rock]

I don’t know why tho

[urban edge]

oh my god can we let me finish

[radiant linden]

are there any inequalities you can create

given the 2 lengths

mb not inequalities

but like

2 equations that equal eachother

[radiant rock]

CD = AD

[radiant linden]

yeah

[urban edge]

good

[radiant linden]

and what are the lengths of those

[radiant rock]

20-x

Oh

Right

[ancient adder]

400 + X^2 - 40X = X^2 + 64
Wow
X^2 gets cancelled
400 - 64 = 40X
336/40 = X
X = 8.4

a) AD = 20 - X
b) DC = 20 - X
c) BD = X = 8.4

Bruh pretty easy

Wats the answer

Given?

[radiant rock]

336=2x^2

[radiant linden]

and then what else can you do to simplify

[urban edge]

!noans

[vocal sleet]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[urban edge]

holy heck

[radiant rock]

8.4^2 isn’t 168 though

What did I do wrong

[radiant linden]

hmm

wait did you root the hypotenuse or no

[urban edge]

how did you get here

[radiant linden]

i might be slow

[radiant rock]

(20-x)^2=64+x^2

[urban edge]

ok

[radiant linden]

retry on the hypotenuse

[urban edge]

how would you expand the (20-x)^2

[radiant linden]

oh wait im dum

mb

[radiant rock]

Oh wait

It isn’t a difference of squares

[radiant linden]

yeah i think you accidentaly pressed - lol

[radiant rock]

Alright

Got it

Thanks so much

[urban edge]

youre welcome

[radiant linden]

im bad at math lmao

well

geometry

[radiant rock]

.close

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[hushed pewter]

!nosols

[vocal sleet]

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[empty plaza]

what does d4 mean

[alpine perch]

4th decile i think

[empty plaza]

ohh alright

do you know how to answer or solve that

im not v good with statistics and percent 😭

[alpine perch]

Do you know how to find median?

[empty plaza]

yes

[alpine perch]

And quartiles?

[empty plaza]

the formula for quartiles is like q1 = (n+1) x 1/4 and so on right

if so then yes

[alpine perch]

Yeah

Then can you guess whar would be the formula for decile

[empty plaza]

same but like 1/10?

or is it wrong

😭

[alpine perch]

Yea

Rightt

[empty plaza]

ok tysmm

[alpine perch]

Also

[empty plaza]

.close

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Channel closed

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[empty plaza]

OH SORRY

.reopen

[vocal sleet]

✅

[alpine perch]

It is asking for D4 so?

[alpine perch]

What would be Q3?

[empty plaza]

3/4

[alpine perch]

Yea

Right

You have got it

May I ask what this book called?

[empty plaza]

oh its not a book

its some link i foudon the internet

[alpine perch]

Yeah practice set

[empty plaza]

yes

wait ill try finfing

[alpine perch]

What is it called

I also need to practice some stat mcqs

[empty plaza]

i can send it to u

the pdf

unanswered

since i cant find the orig

is that ok

[alpine perch]

Sure, if you don't mind

[empty plaza]

dm?

or here

[alpine perch]

Here would be fine

How big is it?

[empty plaza]

2.71 mb

[alpine perch]

Thanks

[empty plaza]

thanks too ^^ !!

[alpine perch]

Now you can close if you want

[empty plaza]

.close

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[restive whale]

hello, i have to do a triple integral in this region x^2+(y-1)^2+z^2<=1, the bounds i set in polar coordinates are
x=rcos(phi)sin(theta)
y=rsin(phi)sin(theta)+1
z=rcos(theta)

jacobian is r^2sintheta

is this correct?

[restive whale]

forget that, so the region is a square right? so in conversion i had theta and phi both run from 0 to 2pi, is this correct?

[boreal remnant]

should be a sphere

[restive whale]

yeah mb

its a full sphere so on conversion the xy plane angle runs from 0 to 2pi, same with the z angle right?

[boreal remnant]

phi goes from 0 to pi

not 2pi

[restive whale]

why is that?

[vocal sleet]

@restive whale Has your question been resolved?

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[cedar canyon]

if im at 100k
and i need 360k
i will exchange 10 stuff for 1500
how many stuffs i need for total 360k?

[cedar canyon]

<@&286206848099549185>

[vocal sleet]

@cedar canyon Has your question been resolved?

[oak magnet]

You need 260k

260000/ 150 = 1733.33

You need 1734 stuff id say, as its better for context

[cedar canyon]

if 100 = 1 stack
so it is 17 stack half?

[oak magnet]

Yes 18 so

[vocal sleet]

@cedar canyon Has your question been resolved?

[vocal sleet]

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[atomic mica]

i’m stuck at f(u)

what i have so far

i just need it to be more clear

[elder scaffold]

ok man, no need to flip us off

[atomic mica]

bruh 😭

[vocal sleet]

@atomic mica Has your question been resolved?

[alpine perch]

Also turn x^2 in terms of u

@atomic mica are you here?

[atomic mica]

yes but i called it quits

imma work on it tmrw

[alpine perch]

Okay

[atomic mica]

can i dm u privately

[alpine perch]

Whay happend with prob befor

[atomic mica]

i ain’t read it properly

[alpine perch]

You should post it here

[atomic mica]

it’s fine i’ll just ask it tmrw

[alpine perch]

As i might not be available

[atomic mica]

yeah lol

okay ty tho

[alpine perch]

Ue

[atomic mica]

.closs

[alpine perch]

Yw

[atomic mica]

.close

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[subtle vine]

I need help to solve these equations

[left portal]

,, \begin{cases} 2(x-1) = 3(y+2) \ 2y + 3 = 2(x-y) \end{cases}

[twin meteor]

938c2cc0dcc05f2b68c4287040cfcf71

[left portal]

well

,, \begin{cases} 2(x-1) = 3(y+2) \ 2y + 3 = 2(x-y) \end{cases} \ \begin{cases} 3y + 6= 2(x-1) \ 2y + 3 = 2(x-y) \end{cases}

[twin meteor]

938c2cc0dcc05f2b68c4287040cfcf71

[subtle vine]

What do i do to find the x and the y

[pallid forge]

isolate the y on one side

2(x-1)=3(y+2)

multiply the 2 through the first parenthese and the 3 through the second

[subtle vine]

Alr

The answer is 2x-2=3y+6

[pallid forge]

you should end up with a y=something for both equations

right

so now isolate the y variable

start by moving the 6 over

[subtle vine]

2x-2-6=3y, is that how i do it?

[pallid forge]

so far so good

the 2 and 6 can combine

and then you need to deal with the 3

[subtle vine]

That makes 2x-8=3y

[pallid forge]

yep!

now what

the 3 is multiplying the y, so how do you undo that

[subtle vine]

Y ÷ 3?

[pallid forge]

yes, but make sure to divide the other side by 3 as well

what exactly is the question?

[subtle vine]

Im solving (1)

[pallid forge]

lol

no i know

what does it say

[subtle vine]

2(x-1)=3(y+2)
2y+3=2(x-y)

Im solving 2 equations

[pallid forge]

ill translate it myself then

what language is this

[subtle vine]

Indonesia

[pallid forge]

oh it just says "solve"

ok

alright so the first first equation, what did you get?

after dividing both sides by 3?

[subtle vine]

Wait lemme calcculate

[pallid forge]

fractions will probably work best

[pallid forge]

please dont solve the equation for them

[subtle vine]

2/3(x/3-1/3)=1(y/3+2/3)

[pallid forge]

uh'

[pallid forge]

from here

[subtle vine]

I dont learn fraction yet

[pallid forge]

divide both sides from 3

what

okay

decimal is fine

[subtle vine]

If i remember correcty, 1/10 = 0,1

[pallid forge]

divide both sides by 3

[left portal]

it might be better to solve the system of equations by elimination of 2x, no?

[pallid forge]

1/10 is a fraction btw

[subtle vine]

So pecahan is fraction

Alr

2x/3-8/3=3y/3

[pallid forge]

right

[subtle vine]

Now, what do i do about it

[pallid forge]

well you have 2x/3-8/3=y

now i would start the second equation

[subtle vine]

Alr

[pallid forge]

and isolate y again

[subtle vine]

Wait a min lemme capculate it

2y+3=2(x-y)

So since theres 2 y's, waht do i do

[pallid forge]

well what did we start with last time

you will combine the y's eventually

but we need to get rid of those parentheses first

[subtle vine]

So, 2y+3=2x-2y

Now, do i move the y?if yes, what y?

[pallid forge]

it doesnt matter which y

[subtle vine]

Alr

3=2x-4y

[pallid forge]

great

now you need to isolate the y on one side

[subtle vine]

Dont tell me we have to divide both sides with 4

[pallid forge]

not yet, but yes

need to move the 2x over

[subtle vine]

Alr

[pallid forge]

and you'll be dividing by -4 on both sides once youve moved the 2x

[subtle vine]

-2x+3=-4y

[pallid forge]

yes perfect

[subtle vine]

2x/4-3/4=y

[pallid forge]

yep!

[subtle vine]

Does it have to do something with 2x/3-8/3=3y/3

[pallid forge]

well 3y/3 is just y

but yea

you are given two equations and are asked to solve

[subtle vine]

2x/3-8/3=y
2x/4-3/4=y

[pallid forge]

if you were to plot these equations, they are two straight lines on a graph

[subtle vine]

Just saving it

[pallid forge]

yea np

[subtle vine]

Do i need to subtract both equation?

[pallid forge]

now set them equal to each other

[subtle vine]

8x/12-32/12=4y
6x/12-9/12=3y

Is that how i do it?

[pallid forge]

no

since y=2x/3-8/3 and y=2x/4-3/4, then 2x/4-3/4=2x/3-8/3

[subtle vine]

Alr

2x/4-3/4=2x/3-8/3

What do i do with it?

[pallid forge]

solve for x

i hope you're comfortable with pecahan

[subtle vine]

2x/4 -2x/3 = 8x/12 - 6x/12 = 2x / 12, or x/6

Am i right?

[pallid forge]

no

WAIT

sorry

for one side of the equation yes

what does x/6=?

[subtle vine]

x/6 = x÷6, or do i need to turn it into decimal

[pallid forge]

no there should be another side to your equation

[subtle vine]

Oh wait

Yea

[pallid forge]

i see what you did, you did it correctly, but you forgot about your other numbers

[subtle vine]

-3/4+8/3

[pallid forge]

8/3-3/4

yeayea

that's what x/6 is equal to

[subtle vine]

-9/12 + 32/12 = 23/12

x/6 = 23/12

[pallid forge]

close

32-9

wait

a;sdlfkj

sorry yes

that is correct

sorry my brain is shutting down

[subtle vine]

do i need to turn the x/6 to 2x/12?

[pallid forge]

no

x is being divided by 6

how do you undo that

[subtle vine]

X × 6

As for 3 is multiplying y

[pallid forge]

exactly

[subtle vine]

Y÷3

[pallid forge]

yep yep

and do it to both sides

[subtle vine]

multiply it by 6?

[pallid forge]

both sides yes

x/6=32/12

[subtle vine]

x=46

[pallid forge]

multipying by 6 would just leave you with 6x/6 or x

no

32/12*6

or

[subtle vine]

hol up

[pallid forge]

$\frac{23}{12}\cdot\frac{6}{1}$

[subtle vine]

32 × 6 = 192

[pallid forge]

hmmmm

[twin meteor]

Wumbo

[pallid forge]

shoulda been 23 right?

[pallid forge]

from here

[subtle vine]

Then, 23×6

[pallid forge]

i copied it down wrong. my b

yea

then divide by 12

[subtle vine]

138?

[pallid forge]

yea

[subtle vine]

Lemme do what i call in my language porogapit

12×1 = 12

138
12

18

Some problom here, 18 cant be divided by 12

[pallid forge]

the answer is not a whole number

[subtle vine]

Oh

[pallid forge]

it's a fraction

[subtle vine]

11,5

[pallid forge]

yes

alternatively you couldve done the calculation with the fractions

23/2=11.5

so x=11.5 yes?

[subtle vine]

So, x=23/2?

[pallid forge]

yes

[subtle vine]

Alr, now we found the x, we need to find the y

[pallid forge]

correct

all you need to do is plug that value of x back into either one of those first two equations

[subtle vine]

It can be any of hose 2 equations?

[pallid forge]

and solve for y

it can yes

what you're actually finding is the intersection point of two straight lines

[subtle vine]

2x/3-8/3=y
2x/4-3/4=y

[pallid forge]

sure you can use one of those

or you can use the very very first ones

[pallid forge]

.

[subtle vine]

Iemme use 2(x-1)=3(y+2)

Since x = 23/2

2(23/2-1)=3(y+2)

1 = 2/2 right

[pallid forge]

yes

[subtle vine]

So, 23/2 -2/2 =21/2

21/2 ×2 = 21

21=3y+6

-3ý=6-21

-3y=-15

Y=5

[pallid forge]

perfect

[subtle vine]

So,

X=23/2
Y = 5

[pallid forge]

well done!

[subtle vine]

Alr thanks

[pallid forge]

no problem!

[subtle vine]

Wait whats the command again

.close

[vocal sleet]

Channel closed

Closed by @subtle vine

Use .reopen if this was a mistake.

[pallid forge]

for what?

(:

wp

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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[boreal remnant]

John has 4 apples in one hand and -1 apples in the other. Now suppose he puts the 4 apples through a square rooting machine and the -1 apple through a squaring machine. How many apples does he have now?

[bold hound]

!status

[vocal sleet]

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

[bold hound]

@boreal remnant

[boreal remnant]

.close

[vocal sleet]

Channel closed

Closed by @boreal remnant

Use .reopen if this was a mistake.

[tawny hollow]

@boreal remnant is such a troll lmao

[bold hound]

wdym?

i mean, the task makes no sense, but still

i say we would have 0 apples, but 3 apples^2

[tawny hollow]

i think theyre trying to spread wildberger propaganda through this idk, have seen them claim real numbers are not real etc

[bold hound]

lol

what is wildberger?

[left portal]

channel is already closed

[tawny hollow]

a mathmetican who well has a certain grudge against analysis for example, but for really odd reasons

a google search would be better tbh

[bold hound]

ah now i find him, google only showed my a german manager lol

[tawny hollow]

ah lmao

[elder scaffold]

well this depends, when it says 'now' are we implying that this is after they have ran through the machine, for all i know they could still be in the machine being processed

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[silent vigil]

hey chat, i am once again stuck in a basic trigonometry question

[silent vigil]

the question wanted me to find all the sides

no idea how to start this, so any help would be appreciated ^_^

AB=x
BC=8
angle ABC=60

[outer warren]

what's the exact wording of the question
are you omitting anything

[tawny hollow]

yeah bcuz atm it seems theres not enough information?

[silent vigil]

? :D

thats everything tho?

[outer warren]

are you sure?

please triple check

that what you've sent here matches exactly whats been given to you

[left portal]

!original

[vocal sleet]

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

[outer warren]

or if possible, send a pic of the original

[gray willow]

then write it is impossible to calculate

if x is variable

[silent vigil]

its in another language so i cant really post it here, ill just skip this question

[gray willow]

x is variable?

[silent vigil]

yes

[outer warren]

was an image provided to you

what was the original language

[gray willow]

i think i got what it meant

[gray willow]

you can calculate other side in terms of x

so i think that's what question want you to do

[silent vigil]

[outer warren]

the best you can do is express AC in terms of x

[gray willow]

cos(60) = (8^2+x^2-AC^2)/16x

[tawny hollow]

Oh, yeah thought x was to be found

[silent vigil]

huh, i see

[gray willow]

you can get AC

[tawny hollow]

Better to say what theorem youre using than to just give the answer

[silent vigil]

aight, thanks ^_^

[outer warren]

(also starting with a suboptimal form of said formula/rule)

[gray willow]

i think it is basic equation, not the answer, you simply it yourself

[outer warren]

not the issue being addressed

[tawny hollow]

yeah that too lol

[silent vigil]

ok everyone thank you for your time

.solved

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[tawny hollow]

i hope you learned anything?!

lmao

[silent vigil]

i learned that i dont like this question! ^_^

[outer warren]

the relevant formula here in case you didn't already know is
cosine rule
aka law of cosines

[silent vigil]

yeah, thats the topic im supposed be learning

its okayish for me but when variables come in im just lost

hopefully ill get it til tomorrow ^_^

[elder scaffold]

bruh the new champ aint even out yet

[silent vigil]

[elder scaffold]

yasuo>>>

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[molten remnant]

pls help me out in this

[sudden compass]

use a new chanel

[sudden compass]

.

[sudden compass]

good question tho

[sudden compass]

@molten remnant read

[molten remnant]

yes

[sudden compass]

go use a new help channel

this one will get removed in a few minutes

[molten remnant]

ok

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[hard wren]

all atomic propositions are compound propositions. this is wrong, am i right?

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@hard wren Has your question been resolved?

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@hard wren Has your question been resolved?

[warm path]

yes. compound proposition is more of the combinations of the atomic propositions

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@hard wren Has your question been resolved?

[hard wren]

I know compound proposition is combination of 2 or more atomic proposition but atomic propositions are unbreakable so how can they be considered compound
Sorry I don't get your reasoning

[warm path]

I am saying yes to your "this is wrong"

[hard wren]

Ooh

My bad then sorry

[hard wren]

Btw can I say all compound propositions are atomic propositions?
No right?

[warm path]

Atomic is irreducible but compound is still reducible, no?

[hard wren]

Yes compound is reducible

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[deep bough]

Wanted to know if my proof is correct

[vocal sleet]

@deep bough Has your question been resolved?

[deep bough]

<@&286206848099549185>

[ancient adder]

Not this again

[odd helm]

my first comment would be to justify the use of a change of eps

so mention eps>0 anyway

[azure kraken]

If you managed to right this , then I don't think you'd need correction

It looks just right

[odd helm]

just write*

[deep bough]

I’m asking in case I made some type of error in an implication somewhere in my proof

[odd helm]

no errors in logic

looks fine

(i am assuming that says lim sup for lim with upper bar)

[deep bough]

Epsilon is defined to be 1/k where k is positive so I kinda just assumed I would be fine without writing eps greater than 0

Yeah that means lim sup

[odd helm]

yeah you're fine then

[deep bough]

Alright thank you

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[stuck moss]

question is prove that (1) and (2) are equivalent

for 1 implies 2, I was a able to prove the left hand part of the inequality, but dont know how to show the right hand part

[vocal sleet]

@stuck moss Has your question been resolved?

[pallid zenith]

@stuck moss my guess is that

its possible to immediately get $\frac{f\qty(x_1 + t(x_2-x_1) ) -f(x_1) }{ t } < f(x_2) - f(x_1)$

[twin meteor]

jan Niku

[pallid zenith]

which suggests a substitution

but hmm id have to track it out its not really jumping out at me how it sorts out

obviously at some point you need to scale that interval

so you could maybe even do that immediately

[stuck moss]

yea I did that already

[stuck moss]

But it would only give the left hand inequality

I don’t know what to do for the right hand

[pallid zenith]

sorry ill have to mess with this a bit

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[stuck moss]

.reopen

[vocal sleet]

✅

@stuck moss Has your question been resolved?

[stuck moss]

i swear this question is impossible to do

[hybrid flicker]

x is between x1 and x2 strictly

so x = x1 + t(x2-x1)

for some t

[stuck moss]

yea that would only prove the left hand inequality

we need also to show

[hybrid flicker]

you can exchange them as well

so x = x2 + t' (x1-x2)

have you applied it to that?

[stuck moss]

wdym

[hybrid flicker]

like

you used 1) writing x = x1 + t(x2-x1)

to justify f(x) < ...

and get the first inequality

but what if you wrote x = x2 + t' (x1-x2) instead

and applied 1) writing x like this

[stuck moss]

what I did was let t = (x-x1)/(x2-x1)

[hybrid flicker]

sure and you got " x = x1 + t(x2-x1)"

what I'm telling you

is to let t' = 1 - t

and see where it gets you

[stuck moss]

ok ill try, ty

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[foggy pier]

It has been a while since I have graphed piecewise functions and I can not remember how. I tried looking it up and doing some practice problems but still can not figure it out.

[hushed pewter]

Graph y=6x+1 but only for x<-1

[outer robin]

You follow the function in the range thats given, so for all values less than negative 1 (to the left of negative one) you would graph it as 6x + 11 until that point

Open/closed circle is also important if you don't remember that I can help as well

[foggy pier]

I do not remember that either

It's been a while for most of my algebra topics so I may be unfimilar with some of the basics. I'm just trying to regain some of my previous skills due to upcoming classes.

[outer robin]

Alright well lets start with 6x + 11 do you know how to graph that confidently up until x = -1

[foggy pier]

Yes

What I understand is the 6x+11 part and all that and I believe its saying I need to do something for every x value less than -1 but im not sure if thats correct or how to procede from there

<@&286206848099549185>

[rare hatch]

Correct. You are supposed to graph it for all values less than (to the left of) x=-1

And as the other definition for all values greater than (to the right of) x=2

In between those two, it's not defined, so you don't draw anything

[foggy pier]

so for 6x+11 i how would I graph that

[rare hatch]

As y=6x+11

[foggy pier]

like I know what the question says and how to read it but I do not understand how to put it on paper

oh okay

yeah I see now

thanks

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[edgy gulch]

Is there any intuition behind this skyscraper of a formula

[rugged orchid]

I’m pretty sure there is, but I can’t quite recall atm

[edgy gulch]

tried searching for something online and found a formula to approximate degrees of freedom that is way above my pay grade

[rugged orchid]

i think the main idea is that you want to standardize the 2 samples, which gets you to the bottom of this

then now you want to compare 2 T(n-1) distributed numbers

but it's T(n_1 - 1) and T_(n_2 - 1)

[edgy gulch]

T is the t-distribution?

[rugged orchid]

yeah

then if you look at how the t-distribution arises

it happens when you divide a standard normal by a chi-squared/it's degree of freedoms

and you need the standard normal and chi-squared to be independent

it turns out using the unbiased estimate for the sample variance is indepdent to the sample mean

so you standardize the sample mean (now it's Z(0, 1))

but when you expand it on the bottom from the standardisation you get a chi^2 distribution

that gives you the t-statistic and you look at the ugly ass denominator for what the df of this statistic is

[edgy gulch]

sorry im kinda a dumbass, what does this mean really

[edgy gulch]

and how would you go about standardizing the sample mean

[warm path]

I think you also need the Welch–Satterthwaite equation that approximates the degree of freedom of chi-squared.

[edgy gulch]

oh yeah thats the complex formula that i found

[rugged orchid]

um

[rugged orchid]

this guy is not exact i dont think

because we're just estimating the population parameters

but the distribution of the things is still good

[warm path]

So, suppose you have $X_1,\dots, X_n \overset{\mathrm{iid}}{\sim} \mathcal{N}(\mu,\sigma^2)$ then $\frac{1}{n}\sum_{i=1}^{n} X_i \sim \mathcal{N}\left(\mu, \frac{\sigma^2}{n}\right)$

[twin meteor]

nobody

[warm path]

Since the sample mean is normally distributed, Let$\bar{X} = \frac{1}{n} \sum_{i=1}^n X_i$, then $\bar{X} - \mu \sim \mathcal{N}\left(0,\frac{\sigma^2}{n}\right)$

[twin meteor]

nobody

[edgy gulch]

and thats standardized?

[warm path]

well, you need to divide that by variance

I meant, SD

Because $Var(aX) =a^2 Var(X)$

[twin meteor]

nobody

[warm path]

We want variance to be 1, so we divide it by $\sqrt{\frac{\sigma^2}{n}}$

[twin meteor]

nobody

[edgy gulch]

oh so basically its that z formula from normal distributions

[warm path]

yes

that what they meant by standardizing

https://www.itl.nist.gov/div898/handbook/prc/section3/prc31.htm here is one of the derivation of similar pool variance

[rugged orchid]

hmm

i've gotten up to here

but you can't just compare these z's since they aren't the same degrees

[warm path]

you can't really do analytical work to get there because that is approximated

[rugged orchid]

oh right

[rugged orchid]

im pretty sure there's a way to get to this in a very sensible manner

i just cant remember off the top of my head atm

[warm path]

I remember there is one if you do it in high dimensional

like there is a nice property of chi-squared and Wishart you can use to get there

but also don't have that on top of my head

anyways, just in general. People in statistics use Welch–Satterthwaite equation to estimate the degree of freedom (as that can approximate the degree of freedom of the chi-squared)

Problem with the two-sample t-test is that the it is not exactly chi-squared but can be approximate using chi-squared

[rugged orchid]

im gonna try find my notes on this

[edgy gulch]

sorry had to help my dad with some stuff

damn statistics kinda complicated huh

[warm path]

first answer here can give you the rough idea on how they approximate that chi-squared distribution https://math.stackexchange.com/questions/1746329/proof-and-precise-formulation-of-welch-satterthwaite-equation

[rugged orchid]

ah yeah im getting there

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@edgy gulch Has your question been resolved?

[edgy gulch]

oh well guess you cant understand everything in a first year statistics course

thanks guys

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[lavish river]

is there a way to uniquely define each knot up to ambient isotopy, assign each knot to something such that any two knots assigned to the same thing are the same knot up to isotopy

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[wicked nacelle]

guys help me ah

[urban edge]

do a change of variables to polar

[left sparrow]

Yeah I'm also seeing a radius

[wicked nacelle]

alr do that tho but idk if it correct or no(so bad at complex thing) $\int_{0}^{2\pi} \int_{0}^{1} \frac{r}{(r^2 + 1)^3} , dr , d\theta$

[urban edge]

looks right

[twin meteor]

Kol

[urban edge]

do you know how to solve the inner integral?

[wicked nacelle]

yes

substitue the u =r^2 + 1?

[urban edge]

yup

[wicked nacelle]

ok thanks then i have no problem

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[tawny nacelle]

does this proof work?

[tawny nacelle]

the problem statement is at the top of the first screenshot

[thin vale]

you made a typo in the inverse and said its from X->Z instead of Z->X

Maybe include more details about why the composition of inverses is fine. Otherwise it looks good

now do homotopic

@tawny nacelle

[tawny nacelle]

ah, did I?

shoot, I did

[tawny nacelle]

which details are you talking about?

which section needs more?

[thin vale]

why is psi compose phi inverse well defined

[tawny nacelle]

hm

because psi and phi are bijective, so their composition is too

[thin vale]

it might not be necessary to include but its just because all the domains and ranges line up

[tawny nacelle]

right?

[thin vale]

well if psi:X->Y and phi:Z->W bijective it doesnt mean u can compose them if W!=X

thats all I mean

[tawny nacelle]

right, but the codomain of phi is the domain of psi

[thin vale]

exactly

[tawny nacelle]

so it's fine

I see

[thin vale]

im saying maybe just say that

[tawny nacelle]

alright

can do

[tawny nacelle]

maybe later on...

when I get to alg top properly

[thin vale]

the proofs like the same

haha

[tawny nacelle]

[thin vale]

🔠

[tawny nacelle]

@thin vale is this okay?

[thin vale]

looks good to me although i dont really know if thats the proper usage of "well defined", its just what I called it

[tawny nacelle]

whatever close enough

🔡

thank you!

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[slim oracle]

The point P has position vector (1, 5, 6). show that the perpendicular distance from P to the line AB is equal to root3.

[slim oracle]

and previously i solved AB position vector is (1, -2, -3)

all i wanna know is the answer let’s PQ be (3, -5, -5) + landa(1, -2, -3)

why is PQ that

they let Q be the point on AB that makes the perpendicular line PQ btw

[vocal sleet]

@slim oracle Has your question been resolved?

[slim oracle]

help pls

[knotty lynx]

What's the vector equation for AB

[vocal sleet]

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[bleak sapphire]

I'm trying to use Mayer-Vietoris to compute cohomology of S^n (n > 1) using induction (so H^q(S^(n-1)) = R for q = 0, n, otherwise = 0). But I'm getting the dimension of H^0(S^n) = 0?

[bleak sapphire]

The long exact sequence starts $0 \rightarrow H^0(S^n) \xrightarrow{i} H^0(U) \oplus H^0(V) \xrightarrow{\delta} H^0(U \cap V)$

[twin meteor]

Wheeler

[bleak sapphire]

U, V are hemispheres diffeomorphic to R^n, and UnV deformation retracts to R^(n-1). Then using Poincare lemma, H^0(V) + H^0(U) is just R^2 and H^0(UnV) = R by induction hypothesis

However it seems the dimension of im(delta) is 1, and by exactness the

Oh nvm.

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[spiral mist]

I gotta integrate this

[oak magnet]

Integration by parts would work

Let u = ln(t+1) and v'= 1/(t+1)

Put the 80 infront of the integral by linear propriety

[spiral mist]

,w integrate (80ln(t+1))/(t+1)

[twin meteor]

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[spiral mist]

i could js substitute ln(t+1) = u

that would give me the same ans as wolfram

[oak magnet]

As you want mate

[oak magnet]

It will

[spiral mist]

i will also try this usin integration by parts

lets see

,w integrate tanx

[twin meteor]

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[spiral mist]

,w derivative of lnx

[twin meteor]

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[spiral mist]

@oak magnet it worked haha

thanks

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[spiral mist]

,w integrate (tanx)^4

[twin meteor]

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Requested by ilovecocomelon_

[spiral mist]

How to integrate this?

Tanx to the power four

[oak magnet]

Integration by parts

Or no

Wait

Tan^4 = tan^2 * tan^2

Tan^2 = sec^2 -1

So tan^4 = tan^2(sec^2 -1)

Tan^2 * sec^2 - tan^2

Let u = tan(x)

du = sec^2 x dx

So its 1/3(tan^3(x)) - tanx + x +c

[oak magnet]

So ye no need ibp for this one

[vocal sleet]

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[vast shale]

the question how can the circle showsn in the figure help us to locate pi on a number line

is that like

C = 2pi*r

as radius is 1 then

C = 2pi

so if we got the circuomference by rotating the circle on the number line

then divide it by 2

we get the pi

is thats the solution?

[hard atlas]

or you just rotate it halfway around

[vast shale]

🧠

lol

yeah

true

thank you

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[velvet zephyr]

or take 0.5 as the radius.

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[lethal warren]

any idea how is this solved? (im asking for a friend so i don't know the specifics)

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[lethal warren]

<@&286206848099549185>

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[steel forge]

is this correct

[oak magnet]

it is correct yes

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[vast shale]

!status

[vocal sleet]

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

[vast shale]

my solution:

5c^(2/5) - 11c^(1/5) + 2 = 0
u = c^(1/5)
(5u^2)^1/5 - (11u)^(1/5) + 2 = 0
5u^2 - 11u + 2 = 0
5u^2 - 1u - 10u + 2 = 0
u(5u-1)-2(5u-1)
(u-2)(5u-1) = 0
u - 2 = 0 or 5u - 1 = 0
u = 2 or 5u = 1
u^(1/5) = 2 or u^(1/5) = 1/5
u^(1/5)^5 = (2)^5 or u^(1/5)^5 = (1/5)^5
u = 32 or u = 1/3125

eliminate the extraneous solution

u = 32

<@&286206848099549185>

am i right or wrong?

[rich anchor]

Yes!

[vast shale]

hmm?

[rich anchor]

That is completely correct

Oh

[vast shale]

i forgot to replace some variables

[rich anchor]

You asked for wrong or right lol

[rich anchor]

I don’t see anything wrong here

umm

your last step is little weird

you have written

u^1/5 = 2

In fact

You substituted u=c^1/5

[vast shale]

yes

[rich anchor]

so you replace u with c^1/5 and then solve for c

you get c^1/5 = 2

how would you get rid of 1/5?

@vast shale

[vast shale]

I've mentioned it in my solution?

u = 2

c^(1/5) = 2

c^(1/5)^5 = (2)^5

which eliminates the 5 and

c = (2)^5

c = 32

[rich anchor]

Ok nice job

[vast shale]

actually both are a solution..

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[waxen shell]

how do i know when to use integration by parts vs. u sub? Practicing for a test but then i encountered this: integral (10/(xln(x)))dx

[hard atlas]

you dont always know before what will work

with some experience you can often have a feeling for which is more likely to work

but sometimes you just have to try a few things

generally speaking of course, ibp is for products and u-sub is when you have a composition of stuff

[waxen shell]

i see

ty :D

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[fading perch]

i drew possible counter example but idk if i am right or the "right answer" is right

[drifting scroll]

the correct answer is False

[fading perch]

How do you determine that Sand is a subset of Tiger

A is a subset of B
Some element of A (and B) is NOT an element of C
Some element of C is not an element of B

All cats are felines
Some cats are not diabetic
Therefore, some diabetics are not felines (True or False)

[vocal sleet]

@fading perch Has your question been resolved?

[dark kiln]

i assume you can't determine it either way

it means false in that sense, not that all sand is tiger

[fading perch]

makes sense ty

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[red ravine]

This is the question I’m working on

This is my workings so far

the answers are correct but

how can i have tangent line y = 12x -16

and then lower down it has 12h+8

arent they supposed to be the same

because the approximation is the tangent line

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[red ravine]

Proof of tangent

.close

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[sinful swan]

hii

[sinful swan]

can i get some input as to whether my proof is correct?

(for the converse I already have a solid answer, it's the forward statement I had some trouble with)

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[vast shale]

how do you solve this

[vast shale]

i tried sin

but it doesn't even give an answer

[whole oasis]

show your work if possible

[vast shale]

i got 17sin(beta)=8

[whole oasis]

sin(beta)?

[vast shale]

yeah basically sin(A)

i just named it beta

[whole oasis]

ah, ok I thought you misread it and did sin(B)

[vast shale]

oh no lmao

[whole oasis]

sin(A) = 8/17

that's right

[vast shale]

but its asking for an exact answer

[whole oasis]

now it's enough to do arcsin(8/17) in your calc

[vast shale]

whats arcsin

[whole oasis]

sin^-1

[vast shale]

oh

why would u do that tho

[whole oasis]

make sure you're in the degree mod and not radians

[vast shale]

to cancel out sin(a)

so its left with a=sin^-1(8/17)?

[whole oasis]

yes, if you aren't familiar with it, you can also read the answer from an appropiate table of trig values

[whole oasis]

yes

[vast shale]

question though

why wouldn't u divide by sin

or is that not possible haha

[whole oasis]

it's not possible, because sin is a function, sin(A) doesn't mean sin * A

[vast shale]

im pretty new to this mb i just know how to find the "equation" not use a calculator