help-10

[tall arrow]

(2x)^2 = y^2

2x = y

[silver fox]

Nope

Slight error

[tall arrow]

x^2 + x^2 = y^2

[silver fox]

Yes

But the 2 doesnt get raised

[tall arrow]

2x^2 = y^2
removing the ^2 from both would result in
2x = y?

[silver fox]

No

Sqr(2)x

[tall arrow]

Hypotenuse = sqrt(2) * x
side 1 & side 2 = x

I can make x = sqrt(2) and therefore

Hypotenuse = 2

side 1 & side 2 = sqrt(2)

and that should be enough for me to solve sine (45 degrees)?

[cerulean quiver]

help pelase

which is the answer homework

[tall arrow]

Taken channel, switch to an available one, please.

[thick oracle]

#❓how-to-get-help

[tall arrow]

Anyways, so from @silver fox we know that the adjacent and opposite side in our right triangle in sine (45 degrees) should have the same lenght, and that the hypotenuse is equal to the square root of (2x^2), which simplifies to sqrt(2) * x

am I on the right path here?

[tall arrow]

the reason why the hypotenuse is sqrt(2) * x is because:

sqrt(x^2 + x^2) = hypotenuse
= sqrt(2x^2) = hypotenuse

[thick oracle]

good

now find sin 45

[tall arrow]

with that in mind, it's quite easy to find sin 45

sin = opposite side/hypotenuse

if we consider the adjacent side to be sqrt(2), meaning that opposite side also is sqrt(2)

then the hypotenus is 2

sqrt(2) / 2 = about 0,7071

the rule we made earlier says that hypotenuse is squareroot of 2 multiplied by one of the other sides of the triangle

[warm shale]

The following error occured while calculating:
Error: Undefined symbol sqrt2

[tall arrow]

one moment, i may have accidentally flipped the sides

[warm shale]

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Upgrade to WolframAlpha Pro!

Requested by Master Oogway#0599

[tall arrow]

it's 2 divided by sqrt(2)

[thick oracle]

no its not

[tall arrow]

oh, true

just checked using the calculator, and the answer is infact equal to the calculation we've made

[thick oracle]

👍

[tall arrow]

can this method be used for other angles, though?

sine (22), for example?

[thick oracle]

yes

no

i dont think so

you can try

[tall arrow]

why can't it be applied to sine (x) and not sine (22)?

[thick oracle]

it can be applied to sin 45

not sin x

[tall arrow]

all right, but in case i recieve any other angle, what should I do?

taking sin (22) as an example

[thick oracle]

calculator

[tall arrow]

sure, but here we're told to find exact value for sin (22), meaning that i'll have to get sides of a triangle with 22 as one of its angles

how can i use a normal calculator to solve this, and is there any possible way of finding the sides without the need of any calculators at all, just like how we did find sides of a triangle for sin (45)?

[thick oracle]

yeah

what i said earlier

we cant

i tried

[tall arrow]

all right, i'll rely on you
one last question, I promise

If I have the option to use Geogebra and calculator, how would I be able to find sides of a triangle with 22 degrees in one of its sides?

wouldn't that essentially just be to take an algebra calculator and plug this:

x/y = sin(22)

[thick oracle]

you could use this to get an aproximation

[tall arrow]

i'll try memorizing it

[tall arrow]

but as said, if i had an algebra calculator and plugged x/y = sin(22),

wouldn't i have basically gotten two of the sides, which is more than enough?

[thick oracle]

you wouldnt have gotten 2 sides

it's like saying $\frac{x}{y}=3$

[warm shale]

Master Oogway

[thick oracle]

you cant find x and y

[tall arrow]

x/y = sin(22)

is the same as opposite side / hypotenuse = sin(22)

the calculator would suggest values for x and y, wouldn't it?

[thick oracle]

no

the calculator cant suggest sides

[tall arrow]

I'm aware there are infinite suggestions, but i only need one

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Master Oogway#0599

[tall arrow]

okay, so that wouldn't work

which leads us back to the problem: if know what the value of sin (22) is by using a calculator, is there any way I can find all sides of the triangle?

[thick oracle]

no

[tall arrow]

got it, i'll do research regarding whether this is possible in Geogebra
for now, tons of thanks to you, @thick oracle , and lots of creds to @silver fox

[thick oracle]

np

[tall arrow]

I appreciate your time, both of you

.close

[obtuse pebble]

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[agile island]

I’ve been trying to figure this problem out since last night. I have a general idea that one of the kinematic equations are most likely involved but I keep second guessing and thinking I’m overthinking it anyways. The rest of the questions on the assignment were significantly easier to do but I just don’t know about this one and I kept trying to find it in the textbook or something similar but there’s not really anything very helpful. I just need to know where to start on this and I’m pretty sure I can figure it out from that if push comes to shove

(Ignore my dumb answers it saved, I just put them out of frustration thinking I was overthinking it all again).

I hope basic physics is allowed here. Didn’t see a channel but if it’s not I’ll head out so just let me know 👌

[normal turtle]

you gotta resolve forces in both x and y directions i think

also this is mechanics (best part of maths other than pure)

[agile island]

Can you explain that a little more? I’m not sure I know what you mean

[normal turtle]

so break each force down into its x-direction and y-direction components

or perpendicular and parallel to the way the car is facing

[agile island]

Would the next step be adding them together then? So 448 + 389 for magnitude and 40 degrees for direction??

[normal turtle]

hm not exactly, have you done the resolving bit yet?

cause that involves trig

[agile island]

I don’t think so. I really just don’t know where to start with this one. The other problems were all mainly conversion and basic substitution into kinematic equations,, so I haven’t done anything besides that up to this point

[obtuse pebble]

@agile island Has your question been resolved?

[agile island]

<@&286206848099549185>

[obtuse pebble]

@agile island Has your question been resolved?

Channel closed

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[serene crane]

how do I solve this?, plugging in doesn't seem, to work

I think it uses the indea that lim x-> 0 of (sinx)/x = 1

but Idk how to get that

[lusty cedar]

Try Taylor series

[serene crane]

I don't know that - it is a calc a high school class

(well its BC but reviewing calc A rn)

[warm shale]

R00tKiT

[serene crane]

I thought it converged to 1

??

[lusty cedar]

Yea

Ig

[serene crane]

so I turn denom to ^-1 ?

but dont I want x on the bottom to use that

[lusty cedar]

Just take x common from denominator

[serene crane]

to much ppl talking idk what to do

[lusty cedar]

And then separate limits

[serene crane]

can U write out the seperation of limit

I think I know what u r talking about I just need confirmation

I got it nvm

[lusty cedar]

Ok kay

[serene crane]

factor x, seperate and solve

1 x -1 = -1

thank you guys

[lusty cedar]

No worries

[serene crane]

!close

[lusty cedar]

.close

[obtuse pebble]

Channel closed

Closed by @lusty cedar

Use .reopen if this was a mistake.

[lusty cedar]

This way

[serene crane]

ty

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
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[dry echo]

This is literally basic algebra and I think I'm dumb. I'm supposed to simplify.

[dry echo]

I'm stuck at:

(x^3 - 4x^2 - 4x - 1)^2 + (x^5 + 6x^3 + 9x)

Mainly the squaring of the cubic

[stable rain]

seems a bit annoying to do

[timid silo]

a BiT

[timid silo]

multiply it out and simplify

[dry echo]

uh

[timid silo]

or wait

theres prob a simpler way

u could do x((x-2)^2 - 1/x) and then square ig

idk if thats easier

[dry echo]

I'm slightly confused

i'll give it a go

i'm just confused as to what you meant by multiply out

i forgot wtf to do again when it comes to a polynomial being squared like that

Okay so I did give it ago

but now I'm stuck at

(x-2)^4

oh my god now i realized it

i was never taught

how to multiply it like this

t1 * t1 + t1 * t2 + t1 * t3 ...

.close

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[stable rain]

hi

[stable rain]

is the residue at all zeros of a holomorphic function 0

only poles have non zero residue

yay?

nay?

[royal basin]

a non-pole always has zero residue yes

this includes but is not limited to zeros

[stable rain]

oops meromorphic

holomorphic is 0 residue throughout as it contains no poles

i think~

[royal basin]

yes

well you could consider the function holomorphic in its domain minus the poles

[stable rain]

aite

thankssss ann

.close

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[tall tusk]

can't figure it out

@mint tendon

@wild swallow

[mint tendon]

yo

what's the expression for the area inside an n-gon

[tall tusk]

geez, i think

(n-2)*180

[stable rain]

seems like 0 intuitively idk

isit

[mint tendon]

its got a tan in it

[tall tusk]

wait no

thats angle lol

i don't know the area

[mint tendon]

ok let's derive it

[tall tusk]

okok

[mint tendon]

imagine a polygon

regular one 😂

actually ill just draw it

snow's a tikz master so its a little unfortunate they aren't here atm

[stable rain]

cant we just consider an arc

[tall tusk]

okok

[stable rain]

of 2pi/n radians

[mint tendon]

that would probably be more efficient than computing the direct limit tbh

[stable rain]

and i feel the line thru the 2 ends of the arc approaches the line

but would take some work

mayb~

hf calculating

[tall tusk]

Area = (number of sides × length of one side × apothem)/2?

[mint tendon]

yep

incircle radius is also the apothem

[tall tusk]

i copied that from the internet

lol

[mint tendon]

💀

[tall tusk]

lemme go to reddit

for a quick proof

[mint tendon]

here it is

@tall tusk come back 😢

[tall tusk]

what about it

[mint tendon]

the side length is 1

since they are all equilateral triangles

[tall tusk]

oh i got how the formula works now

[mint tendon]

oh word

[tall tusk]

1apothemn/2

• in between

those

?

[mint tendon]

what's in between those

[tall tusk]

times

lol, it wasn't typign out

[mint tendon]

apothem * base * number of triangles

[tall tusk]

yes

[mint tendon]

finding apothem is trig

[tall tusk]

a = R \cdot \cos (\frac{\pi}{n})

what's this

formula

[mint tendon]

idk what that is

i'd just use the simple one

[tall tusk]

okok

[tall tusk]

right

[tall tusk]

how did u get that

[mint tendon]

the base of this triangle (aka the side perpendicular to the red)

[tall tusk]

number of sides × length of one side × apothem=cost(pi/n)?

[mint tendon]

is just 1/2

[mint tendon]

thats just the area

[mint tendon]

the base is 1/2, the red line (the height) is the apothem

cot relates the two

[wild swallow]

hey guys

i have a present for y'all

[mint tendon]

🙏

tikz god

[mint tendon]

wtf

[tall tusk]

i forgot trig, fairy, explain to me cotan again😭

[mint tendon]

wait im in awe rn

[mint tendon]

https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/reciprocal-trig-ratios/v/example-the-six-trig-ratios

[tall tusk]

ok give me. 4 min

[wild swallow]

looks kinda bad when its large

[mint tendon]

how does one reach this level of competency jesus

[wild swallow]

that looks nice

[stable rain]

lmao

tex

[tall tusk]

oh so fraction just recipricates

[stable rain]

yall done here?

[mint tendon]

,w lim n to inf of (n * cot(pi/n) / 4 - pi*(1/2 * cot(pi/n))^2)/((1/4 + pi*(1/2 * cot(pi/n))^2) - n * cot(pi/n) / 4)

[tall tusk]

no not even close

[stable rain]

did yall not work with limits

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by S̨̥̫#8871

[mint tendon]

looks sus

whatever

[stable rain]

what why

just show that

[tall tusk]

fairy

sitll dont quite get

this

[mint tendon]

did you watch the video

[tall tusk]

assuming cot is

A over O

agacent over

opposite

yes

[mint tendon]

opposite is 1/2

[stable rain]

nvm

[mint tendon]

its half the side length

nooooo circle

[stable rain]

gambate

jiayou

you can do this

achante

[mint tendon]

https://tenor.com/view/boom-bomb-explosion-iron-man-tony-stark-gif-15429820

[stable rain]

substitution jutsu

[mint tendon]

https://tenor.com/view/kakashi-gif-22059814

[stable rain]

y

[mint tendon]

https://tenor.com/view/pizza-heart-heart-pizza-big-time-rush-gif-7236858

[stable rain]

kinda weird

im out

[mint tendon]

👋

[tall tusk]

BRO What

how

is it

working

fairy

what is

pi/n

from

[mint tendon]

,w pi/n from

[warm shale]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by S̨̥̫#8871

[stable rain]

..

[mint tendon]

he asked me what it was

[tall tusk]

fairy cot(pi/n)

what is that

[mint tendon]

,w cot(pi/n) definition

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by S̨̥̫#8871

[tall tusk]

explain

fairy

fairy

fairy

[stable rain]

@tall tusk have u done limits

[mint tendon]

its literally just adj/opp

[stable rain]

learnt

[mint tendon]

thats just the angle

[tall tusk]

learning rn

[tall tusk]

why is pi

adjagent

adjacent

to whom

[mint tendon]

pi/n is just the angle

[tall tusk]

which angle

[stable rain]

why

[mint tendon]

pi/n is the red theta

[stable rain]

do yall even have

cos

[mint tendon]

idk man

whats the faster way

[stable rain]

so

area of triangle is

[tall tusk]

fairy

why is the length of ajacent

[mint tendon]

listen to the circular man

[tall tusk]

pi

[mint tendon]

it isnt

[stable rain]

r^2 sin (2pi/n)

[tall tusk]

so it's not the angle of theta

[stable rain]

then the area of the circular bit is pi r^2/n

[tall tusk]

bro he doesn't speak enlighs😭

use latex

circle

[stable rain]

just show the diff of these -> 0 as

[mint tendon]

oh man

[stable rain]

im bad at latex but i can try

[mint tendon]

$\begin{tikzpicture}[scale=5]
\path [name path=inner] (0, 0) -- ({360/(212)} : 1);
\path [name path=ngon] (0 : 1) foreach \t in {1, ..., 11} { -- (\t360/12 : 1) } -- cycle;
\draw [color=green, name intersections={of=inner and ngon, by=X}] let \p1 = (X) in (0, 0) circle [radius={veclen(\x1, \y1)}];
\draw [color=purple] (0, 0) circle [radius=1];
\draw [color=blue] (0 : 1) foreach \t in {1, ..., 11} { -- (\t*360/12 : 1) } -- cycle;
\end{tikzpicture}$

[tall tusk]

$\begin{tikzpicture}[scale=5]
\path [name path=inner] (0, 0) -- ({360/(212)} : 1);
\path [name path=ngon] (0 : 1) foreach \t in {1, ..., 11} { -- (\t360/12 : 1) } -- cycle;
\draw [color=g, name intersections={of=inner and ngon, by=X}] let \p1 = (X) in (0, 0) circle [radius={veclen(\x1, \y1)}];
\draw [color=p] (0, 0) circle [radius=1];
\draw [color=b] (0 : 1) foreach \t in {1, ..., 11} { -- (\t*360/12 : 1) } -- cycle;
\end{tikzpicture}$

what

[warm shale]

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

[tall tusk]

why is it not working

OHH

[warm shale]

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

[tall tusk]

WOW

[mint tendon]

lol

stealing snow's code has never been more fun

[tall tusk]

ok fairy, go back to question

how

how

how

[mint tendon]

ok

idk where circle went but idk that method so i

[stable rain]

yea can u latex what i said

[mint tendon]

oh

[stable rain]

anw

as n->inf it shld get to 0

[stable rain]

lmao exactly what i said but in an image

nice

[mint tendon]

he's a visual learner i suppose

[stable rain]

bru no

i just realised

this is a

[tall tusk]

bro what

wtf

[mint tendon]

idk whats happening

[stable rain]

weird method lol

[tall tusk]

fairy

[stable rain]

we gotta use ratio

[tall tusk]

how do do

the questio

[mint tendon]

is this function meromorphic

circle

[tall tusk]

@wild swallow help me out

[stable rain]

what thats

[tall tusk]

fairy is useless

[stable rain]

random

[mint tendon]

bro

[tall tusk]

[wild swallow]

is there no better way to do this

than to just brute force the limit

[tall tusk]

snow think of it

[mint tendon]

😂

[stable rain]

but yes this is true but no not what to show

i think i said it wrong

D:

[mint tendon]

ok chris

CHRIS

listen close

[tall tusk]

okok

[mint tendon]

SO

[stable rain]

i was saying the difference in areas

anw

[mint tendon]

let's look at a hexagon

[stable rain]

i guess we shld take diff and *n

show its 0

[tall tusk]

ok

[stable rain]

u prob get a 0/0 n l hopital it

[wild swallow]

yuck

thats such a bad blue

[mint tendon]

agreed

cyan is the way

[tall tusk]

what is alpha, idk

[mint tendon]

wtf

[stable rain]

..

[tall tusk]

360/6

lol

[mint tendon]

yeah that's it

[mint tendon]

idk how you got rid of the brace argument

[tall tusk]

OH

lol

[tall tusk]

im so dumb

[mint tendon]

wait wtf

WTF

[tall tusk]

pi/n

is just the

alpha

[stable rain]

..

[tall tusk]

u were confusing me

with trig

[wild swallow]

fairy's mind is being blown rn

over a completely different thing

[mint tendon]

i didnt know that was a thing 🤣

[mint tendon]

bro you need trig

to get the apothem

[tall tusk]

ok the cot of the angle

is the apothem

[stable rain]

trig is to get triangle area

[mint tendon]

😵‍💫

[stable rain]

pi is to get my area

[tall tusk]

is it

is it what

[mint tendon]

circle is trolling

[tall tusk]

broo, im the only one confused, just explain to me

[mint tendon]

ok you got what alpha is

now we can move on

[tall tusk]

okok

[mint tendon]

do u have saturday school or something

[stable rain]

with an arbitrary r, a circle has radius pi r^2

[tall tusk]

no, thats why im on apex

[mint tendon]

😂

[tall tusk]

and listening to u

[mint tendon]

YO

get tf off apex

[tall tusk]

bro ive played 30 min

[mint tendon]

focus

focus

focus

[tall tusk]

the entire day

okokok

[mint tendon]

i will not help

[tall tusk]

im focusing

[mint tendon]

GET OFF

APEX

idc if ur in ranked

[tall tusk]

jeez, im in a game tho

[mint tendon]

THROW

abandon

[tall tusk]

okok

okokokok

[mint tendon]

circle's a godtier troll

[tall tusk]

what relation

[mint tendon]

what is theta in terms of alpha

[stable rain]

while area of polygon is $nr^2\sin(2pi/n)$

[tall tusk]

wouldn't tangent alpha be

A

[mint tendon]

bro trig only works for right angled triangles

[tall tusk]

given opposite of alpha is just 1

[stable rain]

so we want to show

[tall tusk]

oops

right

[stable rain]

the area of circle-polygon=0 (educated guess)

equivalently

[mint tendon]

what is going on bruh

[tall tusk]

fairy

just continue

explaining their relationship

circle is just a pathetic person

[mint tendon]

LOL

让我儿子冷静下来

[tall tusk]

are u chinese fairy

[mint tendon]

idk am i

i love jiaozi

ok anyway

[tall tusk]

ok continue explaining

[wild swallow]

LOL

[tall tusk]

u ghosted all my DM

[mint tendon]

this entire channel is a shitshow

[tall tusk]

fuck snow

[mint tendon]

what is going on

[stable rain]

$lim{n \to \inf} \pi r^2 nr^2\sin(2pi/n)$

[tall tusk]

why is it

[tall tusk]

dividing by 2

[mint tendon]

bro NO

LOL

[stable rain]

oh nos

[mint tendon]

i cant stop laughing

WHAT IS HAPPENING

[stable rain]

latex time

[wild swallow]

circle you absolute clown

[stable rain]

hey

[mint tendon]

this is too much

im wheezing

[tall tusk]

snow is the real clown

[stable rain]

chill there

[mint tendon]

LOL

[stable rain]

u are melting rn

[mint tendon]

我要死了

[stable rain]

no

[wild swallow]

circle can you even read that

[stable rain]

jokes of suicide

yes i can

[mint tendon]

ok sorry

[stable rain]

im a true blue

japanese

[mint tendon]

bruh wtf

[tall tusk]

fuck u

[stable rain]

call me

[mint tendon]

BRUH

[mint tendon]

yo i think you got blocked

[tall tusk]

why is it dividng

by 2

[mint tendon]

cuz the triangle is isosceles

dropping an altitude cuts the base in two

[wild swallow]

its symmetrical

[tall tusk]

a is the length of the line right?

[mint tendon]

aka isosceles

[tall tusk]

shush

[mint tendon]

LOL

[wild swallow]

LOL

[mint tendon]

no way

circle's still typing

[tall tusk]

fairy, clarify what even is a

again

[mint tendon]

https://tenor.com/view/laughing-crying-emoji-laugh-cry-emoji-cry-laugh-emoji-gif-19935705

[mint tendon]

scroll up

[stable rain]

\begin{align}
lim{n \to \inf} \pi r^2 nr^2\sin(2pi/n)
{align}\end

[mint tendon]

like a million miles

USED BEGIN

HAHAHAHA

[tall tusk]

just type it

whats a

[stable rain]

D:

how

[tall tusk]

what am i playing rn

guys

[mint tendon]

尊重

[tall tusk]

https://tenor.com/view/not-my-business-cool-sunglasses-deal-withit-makise-gif-11974944

anyway

[mint tendon]

true

[tall tusk]

whats a

fairy

[mint tendon]

a is alpha

[tall tusk]

LOG

[mint tendon]

fairyexp

[tall tusk]

wtf??

alpha=alpha/

[mint tendon]

😭

[tall tusk]

2

?

[mint tendon]

no

theta = alpha/2

[tall tusk]

no

[mint tendon]

you asked what alpha was

[tall tusk]

alpha

is the

[mint tendon]

alpha is alpha

[tall tusk]

angle

right

[mint tendon]

alpha is 2pi/n

[tall tusk]

Oh

ok

[mint tendon]

what does that make theta

[tall tusk]

half of the

right

right

snow is right

[mint tendon]

god bless snow

[tall tusk]

shut up snow

[stable rain]

just

[mint tendon]

CIRCLE

[stable rain]

use r^2 sin

[mint tendon]

HAHAHAHA

[tall tusk]

fairy what then

[stable rain]

why are u like this

[mint tendon]

area

nice one

nooooo

[stable rain]

..

[mint tendon]

use trig

[tall tusk]

how

[mint tendon]

find steins gate

its all up to you now

[tall tusk]

geez how to ues trig

[stable rain]

oh no

my

chuuni tendancies

[mint tendon]

NOOOO

SNOW IS A TROLL

THEY FLIPPED ITTTT

LOL

[stable rain]

my left eye is acting out again

[mint tendon]

how do you consistently find the most funny things to say circle

[stable rain]

i am just

[wild swallow]

what is this chuuni

[stable rain]

all rounded

[mint tendon]

can confirm

[tall tusk]

stop barking

jesus

[mint tendon]

wtf

[stable rain]

..

[tall tusk]

https://tenor.com/view/anime-kurisu-makise-headache-thinking-gif-12655079

[stable rain]

bit wild

[mint tendon]

i dont think your problem will ever be solved chris

i cant stop laughing

[tall tusk]

fairy can we pl

do the question

first

[stable rain]

ye

[mint tendon]

ok do this

listen closely chris

this is the key

[tall tusk]

ok you get the alpha

[stable rain]

chris needs it for the exam

[tall tusk]

now what

[mint tendon]

oh my

[stable rain]

omg u r finding the exact length?

just leave it as r

[mint tendon]

r^2 sin whatever

✅

[stable rain]

when finding limit its a constant that cancels anw

well doesnt cancel but lim goes to 0

[tall tusk]

i think snow is a tsundere, he loves me but has high ego

so he

[mint tendon]

LOL

[tall tusk]

still helps me

[mint tendon]

HAHAHAHAH

[tall tusk]

haha

[wild swallow]

y'all are struggling too much here

[mint tendon]

its completely voluntary

[tall tusk]

lol hes still ignoring, tsundere level infinity that is monotonically increasing

🥰

[mint tendon]

but how can infinity be monotonically increasing

[tall tusk]

wait i got it

why it's

cot alpha*1/2

what now

after apothem

[mint tendon]

multiply

[tall tusk]

like would''t the entire area be

apothem/2 * n

[mint tendon]

snow leaves a residue at every pole

never walk with snow

[tall tusk]

fairy

what do i

do

then

[mint tendon]

ok wait

🤔

u got the apothem

now multiply by the base

which you did

then multiply by number of triangles

which si n

good job!!

[tall tusk]

ok

what then

1/4 cot(alpha)*n????

[mint tendon]

yes good thats the area of the n gon

now find the area of the incircle

the radius of the incircle is the apothem

[tall tusk]

u sure about that?

[mint tendon]

why wouldnt i be

[tall tusk]

wouldn't it be 1 miniminiminimini less than the apothem

given it's inside

[mint tendon]

,w miniminiminimini

[warm shale]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[mint tendon]

wtf

[tall tusk]

ok fine

it is

the same

what then

so

[mint tendon]

it shouldnt be the same

in circle area < n gon area

[tall tusk]

it shouldnt>?

ok

[mint tendon]

ur tryna find this limit

[tall tusk]

so basically

pi r squared

r is the

apothem

[mint tendon]

yes

[tall tusk]

OH

i got what u mean

[mint tendon]

why didnt i add \inf as a shortcut

[mint tendon]

tsk tsk

[tall tusk]

im writing n->w

[mint tendon]

k

[tall tusk]

but whatever

[tall tusk]

that seems annoying

to plug in numbers

mind fairy u help me

[mint tendon]

idk how else to do it

ur the one with the reading steiner

not me

[tall tusk]

nah just thata i cant use latex

🥺

[mint tendon]

that's disturbing

[tall tusk]

simplify fairy

[mint tendon]

,w simplify fairy

[warm shale]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by S̨̥̫#8871

[tall tusk]

to practice

latex

efficiency

[mint tendon]

hmmmmm

[warm shale]

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

[mint tendon]

💀

[tall tusk]

what even is the radius

of the outer cifrcle

anyway

[mint tendon]

thats the hypotenuse

[tall tusk]

wtf

is that

[mint tendon]

hypotenuse of this

u dont know what a hypotenuse is?!

[tall tusk]

fairy

the radius of the outer circle is apothem??

right

the inner circle is less

than apothem

radius

[mint tendon]

yeah

right

[tall tusk]

ok

so whats

the inner circle

radisu

[mint tendon]

idk maybe you could use complex numbers to make things nicer

roots of unity

whatever

[mint tendon]

apothem

circumcircle radius is hypotenuse

[tall tusk]

incomcircle radius=apothem

circumscirle radius=hypotenuese?

[mint tendon]

ye

[tall tusk]

how the incircumcircle radius should be less than it

a tiny bit right?

[mint tendon]

it is

[tall tusk]

at each like angle of the n-gon, there is a little space between the circle and n-gon

so that makes the radius not the same of the apothem??

[mint tendon]

incircle radius is apothem

circumcircle radius is hypotenuse

[tall tusk]

how is this statement true

[mint tendon]

look again

[tall tusk]

draw it

out

[mint tendon]

ok

$\begin{tikzpicture}[scale=5]
\path [name path=inner] (0, 0) -- ({360/(212)} : 1);
\path [name path=ngon] (0 : 1) foreach \t in {1, ..., 11} { -- (\t360/12 : 1) } -- cycle;
\draw [color=g, name intersections={of=inner and ngon, by=X}] let \p1 = (X) in (0, 0) circle [radius={veclen(\x1, \y1)}];
\draw [color=p] (0, 0) circle [radius=1];
\draw [color=b] (0 : 1) foreach \t in {1, ..., 11} { -- (\t*360/12 : 1) } -- cycle;
\end{tikzpicture}$

[warm shale]

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

[tall tusk]

yay that's

circumscircle??

[mint tendon]

oh my

[tall tusk]

am i

[mint tendon]

ur right

[tall tusk]

understanding

terms wrong

@wild swallow , MUA

[stable rain]

still here wow

[tall tusk]

just secretly kissed you

[tall tusk]

oh wow

[mint tendon]

incircle touches midpoints of the sides

[tall tusk]

ohhhh

ok

okok

that's clever

[mint tendon]

lol

[tall tusk]

my mind was dead

but for the outercircle

[stable rain]

$\lim_{n \to \inf} \pi r^2 nr^2\sin(2pi/n)$

[mint tendon]

yesssss

we got the gang back

[stable rain]

how do i align

[mint tendon]

underscore

[mint tendon]

LOL

HAHAHAH

[wild swallow]

wow

[mint tendon]

that looks so stupid

[mint tendon]

woah

[tall tusk]

guys i got it

[stable rain]

$\lim_{n \to \inf} \pi r^2/n - r^2\sin(2pi/n)$

[stable rain]

ok so thats what we wanna show is =0

[tall tusk]

is this correct

[mint tendon]

yep evaluate that guy

[stable rain]

if we show that we essentially show that we get 1

[tall tusk]

ok evaluate

how tf do u evaluate

[stable rain]

@tall tusk do u know how to evaluate limits

[tall tusk]

kind of

[mint tendon]

use epsilon delta defintiion

be very rigorous

[tall tusk]

what

[mint tendon]

,w epsilon delta

[stable rain]

u being weird here

[warm shale]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[tall tusk]

maybe not really

[mint tendon]

bruh

,w epsilon-delta definition

[tall tusk]

fiary

[warm shale]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[tall tusk]

go from where i ended

[acoustic notch]

you can simply take an equivalent of sin(2pi/n) at infinity

[tall tusk]

how to

[mint tendon]

im sick of seeing sin everywhere

[tall tusk]

fairy

[mint tendon]

cleanse thy sin

[tall tusk]

how to go from

where i ended

my pic

[mint tendon]

wrestle it into 0/0

then l'hopital

tho that looks painful af

[tall tusk]

bro, plz write out the steps

🥺

[mint tendon]

that's disturbing

[acoustic notch]

sin(2pi/n) is equivalent to 2pi/n when goes to infinity

it simplify nicely with your expression

[mint tendon]

listen to the corbak man

[tall tusk]

god

i gotta go play golf

😭

@mint tendon , ill see u

[tall tusk]

i dont even have sin

in my thing tho??

ive csc

[stable rain]

$\lim_{n \to \inf} \pi r^2/n - r^2\sin(2pi/n)
\\= r^2\lim_{n \to \inf} \pi /n - 1\sin(2pi/n) $ as r is independent of n
$\\= r^2(\lim_{n \to \inf} \pi /n -\lim_{n \to \inf} - 1\sin(2pi/n)) $

LES GO LATEX

wait

it

didnt even render

OMG NU

yea

sad

[acoustic notch]

what is csc ? Show me your problem

[stable rain]

prob cosec lol

[tall tusk]

it's ok corbak, i gotta go play golf

.close

[obtuse pebble]

Channel closed

Closed by @tall tusk

Use .reopen if this was a mistake.

[stable rain]

they went a weird way

lmao golf

hf

[tall tusk]

thx CIRCLE

ur face is a circle

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[serene furnace]

$\sqrt[2]{ \frac{a^2 \cdot \sqrt{a}}{a^\frac{7}{2}}} = a \cdot (\frac{a^\frac{1}{2}}{a^\frac{7}{2}})^\frac{1}{2} = \frac{a \cdot a^\frac{1}{4}}{a^\frac{7}{4}} = \frac{a^\frac{5}{4}}{a^\frac{7}{4}} = a^{-\frac{1}{2}}$

[warm shale]

Raid

[serene furnace]

Hey is this correct?

[tall tusk]

def correct raid

[serene furnace]

oh yea

[tall tusk]

🥰

[serene furnace]

❤️

The fact is

[tall tusk]

u should pin fairy

or snow

to confirm

[serene furnace]

oh ok chris ❤️

[tall tusk]

but i gtg to play golf

yes gl gl

[serene furnace]

gl 🙂

[tall tusk]

ill pin them for u

[serene furnace]

❤️

[tall tusk]

@mint tendon

@wild swallow

[serene furnace]

sorry guys xd

[obtuse pebble]

@serene furnace Has your question been resolved?

[obtuse pebble]

@serene furnace Has your question been resolved?

[serene furnace]

Is this correct?

[serene furnace]

<@&286206848099549185> sorry guys xd

[serene furnace]

Is this also the best way to solve it? I've solved it in 3 different ways, what, in your opinion, is the best solution? That you would do

[severe dune]

Yes

It's correc5

[serene furnace]

ty ❤️

Is this the best solution? Is this the one that you'd go?

[severe dune]

What do u mean

As in explaining why jts that

[serene furnace]

There are different solutions. I could use all radicals for example and only at the end use rational exponents

I mean not different solutions

[severe dune]

I'd do everything inside the square root first not removing anything just to avoid silly errors

[serene furnace]

Different methods

Oh got it

Maybe I would also

ty Omar ❤️

.close

[obtuse pebble]

Channel closed

Closed by @serene furnace

Use .reopen if this was a mistake.

[severe dune]

Nw

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[true oyster]

$g\left(x\right)=\left|\frac{x+4}{x^2-4}\right|$

[warm shale]

m4x70

[true oyster]

use the continuity of abstract values and determine intervals when continues

[obtuse pebble]

@true oyster Has your question been resolved?

[obtuse pebble]

@true oyster Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fierce lagoon]

What is R10 and R4

[celest mantle]

sorry what

im on 1

[fierce lagoon]

Yeah he says "Matthew guys a laptop for R10 500"

What is R10

[celest mantle]

like money

10 500 of a currency

[fierce lagoon]

Oh I see

That's just a shit way of writing it

[celest mantle]

oh why

i think the % is 15.23809524 rounded of being 15.23? or would it round of to 15.24?

[fierce lagoon]

$\text{Percent Change} = \frac{x_n-x_0}{x_0}$

Frick

[warm shale]

Umbraleviathan

[celest mantle]

btw im not too advanced in math btw

[fierce lagoon]

They're just variables

[celest mantle]

but i think its 10 500 - 8900 over 10500 x 100?

and thats the %?

so like 1600 over or divided by 10500 x 100?

[fierce lagoon]

Yeah

15.2%

Well

Read the question

[celest mantle]

oh ye sorry

[fierce lagoon]

"Round to one decimal place"

[celest mantle]

but then i dont get the questions

[fierce lagoon]

The second is saying to express the selling price as a percentage of the buy price

And then the third is saying "what's the actual monetary loss"

[celest mantle]

lost me again, im very tired

[fierce lagoon]

8900 is what percentage of 10500

[celest mantle]

ohh

[fierce lagoon]

Tbh if you're tired, go to sleep, pick it up tomorrow

I really don't wanna run in circles

[celest mantle]

ye ik its 3 am but im out most the day tmrw and got a test on monday

[fierce lagoon]

Don't stress yourself out

Unless you have school tomorrow for whatever reason

I fucking hate the wifi here

[celest mantle]

forgotten how to do this

its like something over or x by a 100

oh wait

[fierce lagoon]

$\frac{a}{A} \cdot 100%$

[warm shale]

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

[celest mantle]

is it 84.76

or rounded of 84.8

[fierce lagoon]

Yes

[celest mantle]

ok and number 3

[fierce lagoon]

Express the loss as a percentage of the final price

So

The answer is a percentage of the final price

So

What's your final price

[celest mantle]

8900?

[fierce lagoon]

Yeah

And then how much money did Matthew lose

[celest mantle]

1600

[fierce lagoon]

So 1600 is what percent of 8900

[celest mantle]

ohh now i get the question