help-33

[lyric bay]

I assume

[proper zodiac]

No

[lyric bay]

4

[proper zodiac]

Remember you specifically need it to look like this

[lyric bay]

Ohhhh

[still temple]

split it into lim(x → 0) (sin(4x)/(5x)) / (cos(4x))

[proper zodiac]

Yes but obviously we can't just divide by 4 as that will change the value

[still temple]

yes but we have another cosine

[proper zodiac]

So what do we also need to do

[lyric bay]

$\frac{\frac{\sin\left(4x\right)}{\cos\left(4x\right)}}{x}\cdot\frac{1}{5}=\frac{\frac{2\sin\left(2x\right)\cos\left(2x\right)}{\cos\left(4x\right)}}{x}\cdot\frac{1}{5}=\frac{\frac{4\sin\left(x\right)\cos\left(x\right)\cos\left(2x\right)}{\cos\left(4x\right)}}{x}\cdot\frac{1}{5}$

[elfin berry]

LE SSERAFIM

[lyric bay]

Lost after this

[lyric bay]

Is this right?

[proper zodiac]

You don't need to do all that it's overkill

[still temple]

its overkill

[lyric bay]

Okay

[still temple]

$\frac{\frac{\sin\left(4x\right)}{\cos\left(4x\right)}}{x}\cdot\frac{1}{5}$

[elfin berry]

110101

[still temple]

fix this

this will become

[astral junco]

$\lim_(x->0)(1)/(cos(4x))*(sin(4x))/(5x)

[proper zodiac]

Just go from here

No need to break tan up at all

[still temple]

This should become lim x goes to zero of sin4x/5x which should be 1, frac cos4x

[astral junco]

or this

[lyric bay]

$\frac{\frac{\sin\left(4x\right)}{1}\cdot\frac{4x}{4x}}{\cos\left(4x\right)}\cdot\frac{1}{5x}$

[elfin berry]

LE SSERAFIM

[lyric bay]

Which equals 4/5

I see

[astral junco]

yep

[lyric bay]

Thanks guys

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[marsh citrus]

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[still temple]

Pls help me find acceleration for 8-

[still temple]

8a

.close

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[jagged abyss]

How many binary numbers less than 256 start or end with two 1s

(my answer originaly was infinity because you can write however many 0s you want and then put two 1s at the end)

I think the question is formulated bad or its just me beind stupid rn

[midnight estuary]

That will still be the number 3 or 11 (in binary)

Let's start with counting all the binary numbers less than 256 that start with two 1s

So something like 110101100 will be counted

[jagged abyss]

oh so does binary add upp?

like is 1101010100 = 5

[midnight estuary]

No

[jagged abyss]

hmm

[midnight estuary]

Each place has a place value

Powers of 2

[jagged abyss]

yes

2^8=256

so 8 digits?

[midnight estuary]

Yea so each place except the first two has to be eithed 1 or 0 and there are at max 9 digits

[midnight estuary]

9

[jagged abyss]

why 9?

[midnight estuary]

1 or 0 unit place

[jagged abyss]

okay

oh

[midnight estuary]

hmm so if we fix the first two digits as 1 how many such binary numbers less than 256 there are ?

[jagged abyss]

64?

thanks i found the solution!

.sto

.stop

/stop

hmm

.close

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[radiant stratus]

hello

[radiant stratus]

can u help me prove this trigonometric identity

[summer trench]

tga?

[radiant stratus]

tan

but in my language its country they type tg

[radiant stratus]

so is it true or false

cuz i suck at these 😭

[terse turtle]

yeah use $\sin2\alpha=2\sin\alpha\cos\alpha$ and $\cos2\alpha+1=2\cos^2\alpha$

[elfin berry]

chlamydia

[radiant stratus]

\

can u do this identity as well

tg =tan

[terse turtle]

$\cos^2\alpha+\sin^2\alpha=1=\frac{1+\cos\alpha}{1-\cos\alpha}\tan^2\frac{\alpha}2$

[elfin berry]

chlamydia

[terse turtle]

if you move the cos^2 over

[radiant stratus]

yes?

[marsh citrus]

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[marsh citrus]

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[frozen drum]

Hey

[terse turtle]

[frozen drum]

Can someone help me understand this question

I'll redo my working and send photo

New method I'm trying

Doesn't seem right

I don't understand what it's asking. So 16 + b4 + c = -1. But how do we fit it being a local minimum into all this?

<@&286206848099549185>

[marsh citrus]

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[grave vortex]

what does it mean by behavior

[astral junco]

sup

[astral junco]

its asking you to describe the graph

[grave vortex]

like

as in

[astral junco]

the slope of the graph goes increasing over the value of x

[grave vortex]

yes

[astral junco]

you can prove this by finding the trangential line at x=1 x=2 x=4 etc

[grave vortex]

tangent linr

line

[astral junco]

or use limits, lim h->0 f(x+h)-f(x)/h

[grave vortex]

cant i just di

rise over run

x=2

4/2

=2

or do i have to show the tangent line

[marsh citrus]

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[pulsar saffron]

It is now between 10:00 and 11:00 o'clock, and six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now?

[marsh citrus]

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[spiral quail]

Can someone help me out

[marsh citrus]

@spiral quail Has your question been resolved?

[marsh citrus]

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[elfin niche]

I attempted this problem again but not sure where my mistake is, the answer is supposed to be 225/2

[marsh peak]

I think x is supposed to go from 0 to 5 rather than 0 to 3

And y should go from 0 to 3 instead

[elfin niche]

I got 450/2

[hasty ruin]

you ignored the 15 after factoring out 3/2

[elfin niche]

oh so i factor out the 15 too?

[hasty ruin]

no, you forgot to factor out 3/2 from 15(5)
that term did not have a 3/2 in front as well

[elfin niche]

how would i factor out 3/2 from 15(5)

wait i got it

tysmm!

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[vernal granite]

Hi, I'm learning equipotents sets. I have to proof that ℕ ≈ ℕ - {k}, where k ∈ ℕ
Then I have to find a bijective function f(n) : ℕ ---> ℕ - {k}, so, for example k = 5

1 2 3 4 5 6 7 8 ...
1 2 3 4 6 7 8 9 ...

But, I don't how how to find that function :c how can I have that ease to think for functions that works for what I need?

[stoic saddle]

do you want specifically a formula

bc this table conveys the idea well enough imo

[vernal granite]

what means "imo"?

[twilit grove]

"in my opinion"

[vernal granite]

Ooh I see

[stoic saddle]

like you could say f(n) = n for n ≤ k-1, and n-1 for n ≥ k, or something. but it isnt THAT important to be able to write the formula down

[vernal granite]

Why n <= k-1? Is wrong if I think like n >= k-1?

[marsh citrus]

@vernal granite Has your question been resolved?

[vernal granite]

Ooh I think that I understand this is my function

[marsh citrus]

@vernal granite Has your question been resolved?

[marsh citrus]

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[rustic glade]

May I get info on differentiating this equation and integrating it

[dire spire]

you could pull the -1/2 apart then just ln rule for the x exponent

[cloud iron]

[rustic glade]

Not sure if im familiar with the rule but

Something along those lines?

[dire spire]

thats correct

[rustic glade]

Thank you so what about integrating it?

[dire spire]

separate the constant and then exponential rule for integrals

$a^{x} = \frac{a^{x}}{\ln{a}}$

[elfin berry]

saad

[rustic glade]

Much obliged

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[grizzled orbit]

What do I do with the |20-30| over my expression

[devout mauve]

evaluate it

[grizzled orbit]

I have no idea what that means

[plush willow]

|20-30|=|-10|=10

[grizzled orbit]

OOOH SO ABSOLUTE VALUE

[marsh citrus]

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[grizzled orbit]

Yes

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[north holly]

”Simplify as much as possible”

The values are auto generated

I cant figure it out by myself

And photomath tells me to split 32x into 20x + 12x so that i can factor

But i feel like there is no way in h i will be able to figure that out by myself

Is that really the way to go? Is this problem reasonable? Or is it a very unlucky generated number? Is there a better method? Should i learn how to to like photomath?

[elfin tangle]

photomath is bs

[bright jay]

Normally with big coefficients like that, doing it by hand is not ideal

[north holly]

We wont have calculators on the test

:/

[bright jay]

Your teacher would give more reasonable numbers

[elfin tangle]

are you muslim

[bright jay]

What does that have to do with the question asked?

[north holly]

No? Why lol

[elfin tangle]

wanna go dms

[north holly]

Uh ok

dldh06

What about polynomial division?

Would that be useful?

[bright jay]

If that was on an exam, no

Tests have limited time, if you were to that question by hand, it would take about 5 - 10 minutes depending on how well you can do mental math

[north holly]

Bruh

Im gonna ask my professor tomorrow

Thx for the help!

[bright jay]

Do you know how to factor in general?

[north holly]

Yea

But im not that good

I think i know how to factor in general

[bright jay]

What was the method you were taught

[north holly]

But there might be stuff i dont know

Polynomal division

But not for this

I dont think

Just how to do it

Not where to apply it

[bright jay]

Before you learned polynomial division, you learned some factoring method

[north holly]

Yea

[bright jay]

Like for example if you were to factor 2x^2 +9x + 9, how would you do it?

[north holly]

Solve for x using pq

Then have 2 parenthesies

So:

I cant to it in my head

But ill grab a calculator

[bright jay]

If you can't use a calculator on the test, why now?

What is the pq method you are referring to?

[north holly]

To show how i would factor

Top one should be = 0

[bright jay]

That's to find x, I'm asking the process to factor first

[north holly]

Yea

You use that to find the values of x

Where the polynom is = 0

Then you can factor

[bright jay]

And I'm not asking to find x, I'm asking to factor that polynomial

[north holly]

Lets say x=1 and x=2

Then you could rewrite the whole polynomial as: (x-1)(x-2)

(Which is factoring it)

[bright jay]

That's doing unnecessary work, to find the values of x to the make the factors

You can just get the factors

[north holly]

How would you factor it

[north holly]

This

[bright jay]

There are multiple methods, one of the common ones is AC method, where you do A times C, then find the factor pairs that add to B

[north holly]

Looked up a yt video

And that seems to be what photomath did

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[wooden grotto]

Does anyone know how I'd do letter a?

[wooden grotto]

How would I be able to conceptually understand part a?

<@&286206848099549185>

[marsh citrus]

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[daring blade]

Hello. I am composing functions with fractions and I don't know how to algebraically proceed. I understand I have to multiply by the LCD, but I'm just unsure about how to do so for this particular problem.

[daring blade]

Do the denominators cancel out on the top and bottom of the composition?

Here, I made a bit of progress assuming that the denominator of the numerator and denominator was cancelled out

Ended up with x/x-2

And the domain is x ≠ 2 or x≠ -1 from g(x)

So in interval notation that's (-inf, -1) U (-1, 2) U (2, inf)

If the chicken scratch is illegible or you have trouble following the steps I can try to circle things/highlight etc

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[ember loom]

salutations. top reads "determine maximum using zeroes." we have not used any calculus up to this point.

[ember loom]

the factor/interval chart is a tool we have learned in class to determine where the function is positive or negative. these results are consistent with desmos, but the answer of the vertex(s) are large fractions.

[sly zephyr]

is it $y=-x^2+7x+6$ ?

[elfin berry]

deus ex machina

[ember loom]

yes

wait no

x^3

$y=-x^3+7x+6$

[elfin berry]

astronomical

[sly zephyr]

ok

[ember loom]

that's why I went to synthetic division, got the factors

[sly zephyr]

don't you have -2,1 and 3 as roots

oh that's what you did

[ember loom]

yep

(x+2)(x+1)(x-3) are the zeroes

[sly zephyr]

so $y=-x^3+7x+6=-(x+2)(x+1)(x-3)$

[ember loom]

yep

well there's a - in front of the terms

[sly zephyr]

wait

[ember loom]

sorry for my writing lol

[elfin berry]

deus ex machina

[ember loom]

ye

[sly zephyr]

but do you think there's a maximum ?

[ember loom]

and we need to find the maximum from that

well there has to be

a local max, that is

here it is on desmos

[sly zephyr]

ye

[ember loom]

but finding that high point is what we need to achieve

[sly zephyr]

maybe find the derivative ?

[ember loom]

@sly zephyr "we have not used any calc"

this is still advfunctions

trust me if I could and was allowed to I WOULD IN A HEARTBEAT

[sly zephyr]

ok

then i don't see a way

[ember loom]

well f*ck

thank you for trying tho :)

I'll leave the question here for a bit sigh

[ember loom]

.

[marsh citrus]

@ember loom Has your question been resolved?

[ember loom]

.close

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[sudden mauve]

How does line 3 become line 4?

[dim zodiac]

$$8a^3b^{-3}+-24x b^{-4} a^4$$ Would that make it more clear?

[elfin berry]

Good

[sudden mauve]

so its just distributing

[dim zodiac]

I believe so.

[sudden mauve]

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[sudden mauve]

What did I do wrong

[twilit grove]

you can't subtract x when the term is $x \dv{y}{x}$

[elfin berry]

cwatson

[sudden mauve]

so i would divide instead

[twilit grove]

yes, once all the other terms are on the other side

[sudden mauve]

makes sense

thank you

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[still temple]

oh god i need help

[still temple]

please someoe uhm

its about circles

and polygons

and its really simple math

i dont want some crazy theories

i have already done that :)

[nova totem]

Post it

[still temple]

thats the thing

theres is no thing to post

its kinda hard to explain

but i have all the knowledge

ik people hate this

but can i go into dms

and explain it

cuz i am a frantic person ill just get banned for spamming if i say it here

and 90% sure ppl wont understand it as well

its much easier in dms cuz i can fastly correct myself

[nova totem]

Then how are we supposed to help

Just say it in here

[still temple]

if you say so

ok basically

[nova totem]

Like what's the goal here though

Before you start

To just make sure you're right on track

Or

[still temple]

the goal is to create the formula for the polygon

thing

[nova totem]

Like the area?

[still temple]

to help me create it

[nova totem]

Of a regular polygon?

[still temple]

not even close

to CREATE the polygon

[nova totem]

Okay

[still temple]

but like that its also

like the output is RAW

itll give you something like

[nova totem]

Wdym raw

[still temple]

0,10 10,10

alot of x's and y's

that youll plug into a grid

is the goal

[nova totem]

Oh

[still temple]

or obviously the computer will plug them

whatever works honestly

[nova totem]

Yeah I see and it's a regular polygon you're tryna construct?

I've made something like that before

[still temple]

basically (i know no shit) but im sort of in the goal of disproving pi and proving that circles are mere high definition polygons

and that also sort of means that circles are squares

but im not here to say my theories i already did that with my friends

im just giving some context

uh basically

i want like

that you can choose how many sides the polygon has

and itll create it

thats as simple as it gets

[nova totem]

Okay so center it at the origin

And then choose the number of sides

[still temple]

i made a formula to create a side of a polygon but its very... conditoinal isnt the word but idk how to get it to be fully interchangeable

[still temple]

basically

[nova totem]

Okay so what you're gonna have to do is set the radius of the polygon to "1"

Just for simplification

[still temple]

radius?

[nova totem]

The center to one of the interior angles

[still temple]

sure yeah

[nova totem]

Do you know vectors?

[still temple]

not really

[nova totem]

Hm

Well you're gonna need to know how to create vectors

[still temple]

i have heard of it multiple times but didnt make the connection to the thing in my brain yet can you refresh me on what it is i probably know it just not the name

[nova totem]

Well assuming it's a regular polygon, then you can splice the polygon into n isosceles triangles where n is the number of sides

Vectors are like direction: they start somewhere and point in a direction

,w define vector math

[elfin berry]

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[still temple]

i have constructed something...

probably not new or anything

but really quite cool

lemme show u

[nova totem]

Utilizing this, you can say that one point will lie on a vector <cos(π/n), sin(π/n)>

Make that a unit bector and place the point on the head

But that's already a unit vector

[still temple]

ok soooo

we have this right

basically

lets draw a point at 0 and call it c

now find the average

not average

center

between a nad b

now find the center of c and d

now connect a e and b

polygon side

or a "curve"

and i presume you can go into much greater detail to create a "true circle" by doing the same for ae and eb

and than just flip them accordingly

and bam

sorry i sort of ignored what u said

let me catch u

up

[nova totem]

Here's what I made

[still temple]

damn witchcraft

im really sorry but what do sin and cos do

aside from fake math

and how the hell is pi involved in this

[nova totem]

Well since I made the radius 1, sine and cosine will tell you the y and x position of the coordinate point

π radians = 180°

[still temple]

ok so π is just 180

[nova totem]

Although I hate to break it to you

If you do this way

And let n be an infinite number of sides

You'll get a circle

[still temple]

thats the point!

[nova totem]

The area of that is still π

[still temple]

no no

[nova totem]

The perimeter of that shape

[still temple]

theres a way to not get pi involved

its just way longer

my problem is that i cant find how to make it into a formula

only describe it in words

[nova totem]

Kinda showed you up here

Just make your program connect the dots

[still temple]

no

thats not what i mean

uh

like

gosh this is hard

like

ok ill explain this

in the most human way possible

and can you try to convert it to math

[nova totem]

Also if I disappear for a bit it's because I'm working out and the gym's busy so I'm texting in between waiting for a machine to be free lol

[still temple]

sure

ok so

a and b

what needs to be done is

draw staright lines between a and b

in a fixed direction (meaning doesnt need to be a variable it doesnt really matter)

lets just say to the left

[nova totem]

So B to A?

[still temple]

yeah

but like that

thats the first step

than

define the point

of intersection

lets say like that

so thisi s what we get

than find the center between a and b

like that i guess

than find the center between d and c

like this i suppose

to make this cleaner, c and d are no longer needed

so ill clear them

you are left with something like this

now strech a point betwee a e and b

line*

youll get this

now a formula that could perhpas even

do like

e and b

to create more fractions

e and b

and a and e

and double the fractions

until you have a true curve

with no sin cos pi

an un-infinite curve

[nova totem]

Well yeah that construction involves sine and cosine

That's why it works

I mean you did no sine or cosine

But it works because of sine and cosine

[still temple]

explain

🫵

https://tenor.com/view/side-eye-dog-suspicious-look-suspicious-doubt-dog-doubt-gif-23680990

[nova totem]

How do I this without calculus

[still temple]

huh

sorry i got the brain of a walnut

[nova totem]

You're saying to make more "e"s between A E and B E right

[still temple]

exactly!

but not infinitly just however much u wnat

does that make sense

[nova totem]

I'm just gonna say, to avoid vernacular confusion, that AC = BC and AE = BE

When you made AC, the angle between that and AB is larger than the angle between AE and AB

So the position of e is ultimately dependent by the angle between each constructed segment and AB

Which, if you wanted to find that position, it requires trig

Now bevause I'm on my phone I can't really do vigorous calculations

But you're gonna end up creating some kind of sector

[still temple]

i somehow understood allat

whats a sector tho

[nova totem]

The area between a random ass chord and the intersected part of a circle

That is if you did it an infinite times

If you do it like 500 times, you're gonna have a choppy looking shape

With 2^(500) + 1 sodes

[still temple]

yeah

thats how real life works tho so thats what im tryna do

even if i plug in 90000 intersections

better than infinity

😎

[nova totem]

Wdym better than infinity

[still temple]

well inifnity is not real

even computers dont believe in infinity they do some kind of work around

anyway what ur saying is

this is gonna be very hard

alot long numbers

bla bla bla still not a perfect cirlce

i think

did i read you right

[nova totem]

It'll converge to a circle

Or a part of a circle

Or some curve

[still temple]

yay!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

yeah

for the meanwhile its a curve

than i can write a formula that switches x and y in some ways to like flip it horizantally and vertically and both to create the circle

but u got what im trying to do!

how the hell do i do it 💀

[nova totem]

Probably some recursion formula

But it has to do it 2^(n) times

Which a lot of computers don't like

[still temple]

(n)?

yeah its alright man i know its way way heavier than pi and the workarounds of inifnity

i got a really beefy computer

uhm

would you mind like actually helping me create an actual formula for this in your free time

[nova totem]

Hm

Well I ain't gonna go outta my way to make a whole ass formula but perhaps I can get you started

If AC = BC, then ED is perpendicular to AB

So let's make that easier on ourselves and find the vector AB, and then find the vector perpendicular to that (L)

Place E randomly on L

Make AE and BE

Repeat for AE and BE

[still temple]

wow that actually helps out a ton

those two lines are life savers

[nova totem]

Make sure L passes through the midpoint of AB though, etc

[still temple]

yup

how do u do that

tho

just curious

lets say AB is 10,10

so c (or the midpoint of AB)

is 5,5

?

[nova totem]

AB is a set of two points

You can't say AB is a singular point

[still temple]

thats not what i said

10,10 means x = 10 and y = 10

ph

oh

i got what u mean

yes my mistake

[nova totem]

AB is two points ...

[still temple]

sorry ur right

so ab

is

10,10 10,10

so c is

5,5

SORRY

WRONG AGAIN

LMAO

AB is 0,10 10,0

what will c be

[nova totem]

In that case, (5,5) would work

[still temple]

how do you find that as a calculation

[nova totem]

It's simply just half of Δx and half of Δy

Where Δx and Δy is the difference in x and y between the points

That should work

,w midpoint of (a,b) and (c, d)

[elfin berry]

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[nova totem]

There

[still temple]

tanks!

when im done its gonna be such a massive formula 😭

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

dont you dare close this chat mr @marsh citrus

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

no it hasnt stop asking ong

[still temple]

this is beautiful

its so beautiful

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[still temple]

is csc-1 (-2) equal to sin-1(1/-2) ?

[still temple]

someone in this server told me they are different

[late geode]

who?

[still temple]

so that's the same thing?

[late geode]

,W arccsc(-2) = arcsin(-1/2)

[elfin berry]

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[still temple]

wtf

that exists

well

thankss

.close

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[hexed veldt]

can you please explain how it got to that final answer?

[cunning basin]

$x^{-\frac{3}{2}}=\frac{1}{x^{\frac{3}{2}}}=\frac{1}{x^1x^{\frac{1}{2}}}=\frac{1}{x\sqrt{x}}$

[hexed veldt]

?

[elfin berry]

WhereWolf(ping if needed)

[hexed veldt]

TYSM

.close

[marsh citrus]

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[rich herald]

how do i solve this inequation

[marsh citrus]

@rich herald Has your question been resolved?

[rich herald]

.close

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[wanton cloud]

what are the number of trees that has {1,2,3,...,2n} as vertices and the leaves of the tree are only {1,2,..n} ?
isn't the answer just n^(2n-2) according to Cayley's formula because there is a bijection between words and trees of n different vertices and we want to use only half of these vertices.

[wanton cloud]

never mind we have to use inclusion and exclusion principle its still not hard

.close

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[crude jackal]

well i have taken the derivative of f(x) and idk what to do from there, i see that (1,0) and (2,0) are roots so (a+b) and (2a+b) are roots of f(ax+b) but not sure what to do

[marsh citrus]

@crude jackal Has your question been resolved?

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<@&286206848099549185>

[marsh citrus]

@crude jackal Has your question been resolved?

[rapid escarp]

maybe just put the ax+b in to the function first

[crude jackal]

yep did that

i have the derivative f’(ax+b)

but not sure where to go from here

[marsh citrus]

@crude jackal Has your question been resolved?

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[wet laurel]

Where's my chain rule mistake? I thought that the derivative of f(g(h(x))) would be f'(g(h(x)))•g'(h(x))•h'(x)

[still temple]

Why'd you even take the derivative of the inside? The derivative and the integral cancel each other out

If f(x)=int{g(x)dx} then f'(x)=g(x), not g'(x)

[marsh citrus]

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[humble pivot]

i think you can do the forward direction directly and save yourself a lot of typing

but, since you've already typed this... one thing i notice is that you say x is arbitrarily chosen, then you consider a specific case (x \in A \B), then you say x was arbitrarily chosen at the end. that's not really what's happening --- once you assume x \in A \ B, then x isn't an arbitrary element of A u B

you have basically the right idea, though. it could just be worded better

[frank crypt]

how would you do it directly

[humble pivot]

i can walk you through it. suppose that A u B = A n B. how do you show A = B?

[frank crypt]

you'd have to show that A is a subset of B and B is a subset of A

[humble pivot]

pog. so lets start with the first inclusion

so, you have some x \in A. then what

[frank crypt]

if x is in a then x is also in a union b

[humble pivot]

pog. then what do you know about A u B? (if you got it at some point you can tell me and i'll stop the walkthrough)

[frank crypt]

that x has to be in A or x has to be in B

?

[humble pivot]

well, you're assuming something specific about A u B, at the start of the proof

[twilit grove]

hint: use your assumption

[frank crypt]

idk im confused lol

[humble pivot]

here, i started with "suppose ..."

and then said something about A u B

this tells you some further information about A u B that you can use

i'm gonna go now. but i think the fun way to write this direction is ||A ⊆ A u B ⊆ A n B ⊆ B ⊆ A u B ⊆ A n B ⊆ A. so A = B||

[marsh citrus]

@frank crypt Has your question been resolved?

[frank crypt]

is this the right idea

[marsh citrus]

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[mint sonnet]

correct?

[mental panther]

no

check your n=2 case for example

[mint sonnet]

its 10?

[mental panther]

yes

[mint sonnet]

how tho?

[mint sonnet]

so p(1)=5?

[mental panther]

p(1)=6

[mint sonnet]

so for the second hexagon, how is it not 6 again?

[mental panther]

because by placing the two tables next to each other, people can't sit where they meet

[mental panther]

as shown in this diagram

[mint sonnet]

ohhh

[mint sonnet]

and so a recursive equation is

P(1)=6
n≥2
P(n)=P(n-1)+4

[mental panther]

exactly!

[mint sonnet]

and nth term?

[mental panther]

since you add 4 each time

we get 6 + 4(n-1)

[mint sonnet]

i got this

P(n)=4*P(n-1)+6
n≥1

[mental panther]

i think you mean P(n) = 4*(n-1) + 6

[mint sonnet]

ohh ok

but im kinda confused is this correct?

[mental panther]

seems like it

[mint sonnet]

so hexagon 1 sits 6 people, correct?

[mental panther]

mmhm

[mint sonnet]

like this?

[mental panther]

the answer is correct

[mint sonnet]

so hexagon 3 has 15 people?

[mental panther]

no 14

[mint sonnet]

how

[mint sonnet]

wait so how do u know how many people sit on hexagon 1?

.close

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[steady current]

Not sure how to find the radius of convergence and sum when |x| < R

[steady current]

this is what i have so far

[marsh citrus]

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@steady current Has your question been resolved?

[marsh citrus]

@steady current Has your question been resolved?

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[elfin berry]

Madashi

[willow oxide]

Well for one if you fill in the values with placeholder numbers it might make things easier

a/c is greater than or equal to b/d

Meaning that a+b/c+d does not change the values of either of them

Pretty sure theres a property for this but i cant recall off the top of my head

But my point is

For instance, plug in a=4, b=6, c=1, and d=2

4+6=10

1+2=3

3 1/3

in this scenario 4/1 is 4

6/2 is 2

3 1/3 is in between both

Are you getting where im going

Proving it with variables can be summarized by saying “since the variable of a over c is always greater than b over d, we can assume that the fraction of a over c is always going to be greater than the fraction of b over d, and adding the proper values to the variables in this scenario will not impact them when removing the center”

Thats goofy so if you dont understand my summary just ignore it

No problemo

[marsh citrus]

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[meager grotto]

I need to find the roots

[marsh citrus]

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[meager grotto]

<@&286206848099549185>

Please help

Ignore the photo

2x²-56x+512

I know it leads to 16 and 16

Idk how though

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[elfin berry]

Madashi

[marsh citrus]

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[muted narwhal]

is what I did here the same as what the answers wrote?

[muted narwhal]

wait nvm

.close

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[muted narwhal]

can someone explain to me the logic behin 26C)?

[muted narwhal]

because when I look at that question, isn't that the probabillity of A happening given B has happened?

but why is it just 1/8 divided by (1/8 +3/8)??

[unreal oyster]

it is, they are just applying the formula

[muted narwhal]

what

shouldn't the formula be P(A)P(B)/P(B)?

why is it reversed?

[unreal oyster]

$$P(A/B)=\frac{P(AB)}{P(B)}$$

[elfin berry]

Luna

[muted narwhal]

ah

uh shouldn't be 1/16 on the top then?

[unreal oyster]

So, in our case, we got
$$P(X<-2 / X \le -2)=\frac{P(X<-2 , intersection , X \le -2)}{P(X \le -2)}$$

[elfin berry]

Luna

[unreal oyster]

Nooo D:

Tell me, what is the intersection of the two intervals

X< -2

With X <= -2

it is X< -2

Right?

[muted narwhal]

the intersection of two intervals if found by P(A)P(B) right?

[unreal oyster]

it's not P(A)P(B)

it is P(AB)

P(A x B)

P(A and B)

P(A intersection B)

All these

[muted narwhal]

intersection is the n looking symbol right?

[unreal oyster]

yes, the upside down U

$$P(X<-2 / X \le -2)=\frac{P(X<-2 , intersection , X \le -2)}{P(X \le -2)}$$

[elfin berry]

Luna

[muted narwhal]

hmmm

[unreal oyster]

So, you tell me, what is the intersection

[muted narwhal]

my formula sheet shows me that the intersection is multiplication of P(A) and P(B)

[unreal oyster]

Not always

[muted narwhal]

i'm taking this one

[unreal oyster]

yeah, it's not always true!

[muted narwhal]

wwaat

[unreal oyster]

it's true if events A and B are independent

[muted narwhal]

dangg

[unreal oyster]

only

[muted narwhal]

I see

so since these are related, the intersection is just P(x<-2)

[unreal oyster]

did you also ask yourself, if P(AB) was always equal to P(A).P(B)

Then why didn't we just simplify the P(B)

And get P(A/B)=P(A)

it's P(AB)/P(B) for a reason

[muted narwhal]

no....

[unreal oyster]

😋

cuz not always P(A).P(B)

if you understood what i meant well

[muted narwhal]

I see

[unreal oyster]

yes

Which is basically P(X=-4)

[muted narwhal]

ahhh

[unreal oyster]

There's only X=-4 which is < -2

And for the denominator, P(X <= -2)

P(X=-2)+P(X=-4)

Cuz -2 and -4 are <= -2

[muted narwhal]

I get it now

dang

[unreal oyster]

Awesome!

[muted narwhal]

thanks for the help

[unreal oyster]

One thing

I said that P(AB)=P(A).P(B) only when A and B are independent, right?

[muted narwhal]

yea

[unreal oyster]

Let's try something

Suppose A and B ARE independent

compute P(A/B)

What do you find!?

[muted narwhal]

A/B?

the probably of a given probably of b or like division

[unreal oyster]

given

[muted narwhal]

kk

[unreal oyster]

Suppose A and B are independent, i.e: P(AB)=P(A).P(B)

[muted narwhal]

P(A)P(B)/P(B)

[unreal oyster]

Yep, then it becomes?

[muted narwhal]

P(A)?

[unreal oyster]

yesss

So, when A and B are independent, P(A|B)=P(A)

Read it

[muted narwhal]

ohh I see

[unreal oyster]

Probability of A given B is Probability of A

Makes more sense now?

[muted narwhal]

yes

[unreal oyster]

A is independent of B

[muted narwhal]

so when they're related just take the intersection

[unreal oyster]

given B has happened, or has not

always = P(A)

That's the meaning

[muted narwhal]

but since they're independent they don't affect one another

ahhh I get it

[unreal oyster]

Yesss

[muted narwhal]

Thanks so much for the help

[unreal oyster]

we say dependent generally

[unreal oyster]

You are welcome!

[muted narwhal]

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[marsh citrus]

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[late wraith]

i just thought of this in the shower

[late wraith]

are all regular numbers (5, 258, 19257) 1 dimensional?

[late wraith]

and follow up question, by this reasoning would be volume of a tesseract be a^4?

[marsh citrus]

@late wraith Has your question been resolved?

[terse turtle]

volume of a tesseract - Google Search

(yes)

[late wraith]

so i am a genius

got it

.close

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[rich lily]

is it?

[late wraith]

seems so

[devout mauve]

in which sense do you mean 1 dimensional

in terms of linear algebra, the real numbers form a 1 dimensional vector space. but that probably doesnt mean anything to you

following your image, what about square numbers

[trim quest]

You can say that the reals are 1-dimensional in the sense that a line is 1-dimensional, and a real number can completely describes a position on a line

in the same way that it requires two real numbers to completely describe a position on a 2-dimensional plane

[late wraith]

i have no clue, im high asf rn

[wet holly]

hi high af I'm dad

[marsh citrus]

@rich lily Has your question been resolved?

[marsh citrus]

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[hexed veldt]

please help with how to reach that answer

[late geode]

what's your issue with the multiplication?

[hexed veldt]

oops nvm i realised what i did wrong

ty anyways

.close

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[marsh citrus]

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[cinder whale]

how do I solve this? Binary in computer science

[molten compass]

do you know how to represent repeating decimal expansions like 0.999... as rational numbers?

i.e. as fractions

buddy you there?

@cinder whale

[marsh citrus]

@cinder whale Has your question been resolved?

[marsh citrus]

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[sullen ice]

if we have a<b<c

can a = c ?

[sullen ice]

is it by definition no?

[hard gull]

nop

[tacit fjord]

can you define x = y

in terms of inequalities

[sullen ice]

wdym

[tacit fjord]

well not define tbh

but like

[feral forge]

if a < c then a cannot be c

[tacit fjord]

x = y if and only if x ≤ y and y ≤ x

[sullen ice]

$a\le b \le c$ would work tho

[late geode]

\le or \leq

[feral forge]

\leq

[elfin berry]

Joshii

[tacit fjord]

so you want to know if
a ≤ c and c ≤ a
is possible when a < b < c

[sullen ice]

yes

[tacit fjord]

Now, a < b < c implies a < c.

And so you need a < c and c ≤ a to be simultaneously true

by trichotomy of the real numbers, no.

im assuming real numbers here

===
tbh a bunch of stuff I wrote was unnecessary

a < c
a = c

By trichotomy of the real numbers, these can never simultaneously occur

Exactly one of
x < y
x = y
x > y
are true for any pair of real numbers

[marsh citrus]

@sullen ice Has your question been resolved?

[sullen ice]

tysm

i kind of knew but i just wanted to make sure lol

it also helped me figure out what was wrong with my friend's solution to the problem

talking it out ^

[marsh citrus]

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[sullen cypress]

Super confused on how to go about part b. I recognize the total mechanical energy here is 18.7, but I’m not sure how to get an accurate answer based on this graph.

Or if there is some equation that I’m not recalling to solve for this.

[marsh citrus]

@sullen cypress Has your question been resolved?

[marsh citrus]

@sullen cypress Has your question been resolved?

[marsh citrus]

@sullen cypress Has your question been resolved?

[opal stump]

https://discord.com/channels/268882317391429632/1159940087237333012

[marsh citrus]

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