geometry-and-trigonometry

[amber hollow]

fair enough, thank you

[amber hollow]

okay i cant figure this one out pls help

[dark sparrow]

AC = 96m

is the one piece of info not marked on the diagram

[amber hollow]

yeah but idk what to do with it

[dark sparrow]

draw a horizontal line from A to the right until it meets BC

call that meeting point H

you have that ACH and ABH are both right triangles w/ a known acute angle and one of them also has a known side

[amber hollow]

which is the knwon acute angle? 14? how does that belong to one of the right triangles

wait is it 57 for ACH since you just made the triangle smaller but the angle of inclination is the same?

[dark sparrow]

angle CAH is 57° yes

bc AH will be parallel to the ground

[amber hollow]

got it, tysm

[flint ingot]

what does same size independently mean

ive found the angle xby but idk what it wants me to prove

[faint pasture]

just that it is constant

no matter how everything else changes

[flint ingot]

oh ok

[dark sparrow]

Prove that angle XBY has the same size**,** independently of the other angles of the triangle.

they missed a comma that would have clarified things a lot here

[ashen pagoda]

remember kids

a^2 + b^2 = c^2

[flint ingot]

Why is this wrong?

[dark sparrow]

your handwriting is hard to read and your grammar isnt making it any easier.

what do we start with?

[flint ingot]

So I fold point a to point c

Then draw the crease line xy

Then draw cx and ay

[dark sparrow]

ok so you start with a rectangle ABCD and then you draw the line XY which is the perp bisector of AC

[flint ingot]

Then draw vertical lines from point f and e

[dark sparrow]

did i get that right

[flint ingot]

Yes

[dark sparrow]

im unable to follow your angle-chasing at all

[flint ingot]

Then we label the angles

[dark sparrow]

but it's looking like triangles AXY and CXY will be isosceles... with XY as the base

[flint ingot]

Let bcx=a and fcx=b

[flint ingot]

Yes but idk where I went wrong

Why my method doesn’t work

[flint ingot]

Let bcx=a and fcx=b because of alternate angles I can label the rest of the angles

[flint ingot]

Yes

[dark sparrow]

i concede that angles FXC and FCX are labeled correctly. but from where did you get that angles YXF and XYF are what you claim them to be?

[flint ingot]

Fcx is b

So because of alternate angles exy is b

[dark sparrow]

eh?

alternate angles for what two parallel lines cut by what transversal?

[flint ingot]

Oh crap

Ok thanks I get where I went wrong

The diagram I draw made it look like the triangles are similar

[dark sparrow]

it might also help if you organize your reasoning in something better than a wall of text and a giant run-on sentence.

[flint ingot]

How should I organize it

Normally I just write a lot sometimes with a diagram

[dark sparrow]

try individual sentences each on their own line

and showing clearly what follows from what

and get a bigger notebook or smaller handwriting

[flint ingot]

Ok should I draw more diagrams

[flint ingot]

Ok

[deep axle]

I’m having trouble with this especially since I can’t use a calculator on this test.

[blazing veldt]

Just know that sin(30 degrees)=1/2.
You can always rederive it by drawing a 30-60-90 triangle.

[deep axle]

THANKS

[green elm]

how do I dind the period of the graph?

[grave pond]

Visually. How far is there between two points on the graph that are "the same" point but in different repetitions of the repeating shape?

[green elm]

2 1/5?

[grave pond]

Looks closer to 2½ to me.

[green elm]

would that be the period?

[grave pond]

Yes.

[green elm]

or do I put it in the 2pi/k formula?

nvm, thats for k

so my period is equal to pi?

[grave pond]

What? Why?

[green elm]

my teacher usually gives us the period and its usually pi or 2 pi

[grave pond]

x=pi is all the way out here -- there's clearly more than a period between the y-axis and that.

[green elm]

oh

[grave pond]

"Period" means the horizontal distance between corresponding points in neighboring repetitions.

[green elm]

ok, so 2 pi?

[grave pond]

2pi is way wider than your graph even shows.

[green elm]

1/2pi?

[grave pond]

How long is the red line segment in my last image?

[green elm]

5 cubes

[grave pond]

And each grid line is how much, in numbers according to the axis?

[green elm]

1/2pi?

[grave pond]

Aaargh.

There are four grid lines out to the point marked 2.

[green elm]

pi?

[grave pond]

Aaargh.

What. Is. 2. Divided. By. 4?

[green elm]

1/2

[grave pond]

Yes. So each grid line represents 1/2.

And there are five of these in a period.

[green elm]

2 1/2?

[grave pond]

Yes.

[green elm]

ok

thank you

how do I get d?

[grave pond]

What do you mean by d?

[green elm]

thats an example

[little anvil]

ahh i need helelep

[zealous olive]

on #11, #12 or both?

It’s pretty much just use trig functions

for #12 drawing the triangles related to point D may be helpful

[maiden brook]

no

u can’t at this point

by chapter 6 u wouldn’t have done that yet

[little anvil]

11d and 12 for me!

[maiden brook]

mirror the example except use s

do u understand 12a?

[upper karma]

:/

Tetrahedron

Nvm
Solved

[upper karma]

I'm unable to prove it😭

[faint pasture]

well the easy but painful way would be to just apply cos(a+b) = cosa*cosb-sinasinb

[somber coyote]

south

[upper karma]

uhh.. could you please send the whole solution.. like written or typed😅

please

[obsidian harness]

No thanks

[somber coyote]

south

south

[upper karma]

done

[obsidian harness]

oh really? congrats

[upper karma]

I used this

substituted pi/3 value as 60..

and done!

[obsidian harness]

great! it's honestly worth doing it yourself so that you fully understand how it works

[safe plaza]

Why can't I understand euclidean geometry

🙏🤷‍♂️

[faint pasture]

wait till you hear about non euclidean geometry

[dark sparrow]

there could be several different reasons why

[safe plaza]

I DON'T LOVE GEOMETRY

The only obstacle in my life

[faint pasture]

well gotta push through?

life is tough get a helmet

[dark sparrow]

ngl like

did you just want to vent

or did you wanna get help w/ something concrete

[red flax]

Probably just wanted to vent

[dark sparrow]

i would have redirected him to #chill or #discussion in that case.

[spare lagoon]

hey can you give me please some limites whit trigonometry (sin, cos, tan)

[boreal crag]

Hello there I need help

[dark sparrow]

!da2a

[lime crown]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[boreal crag]

ABCD adds to 20m2

I need to find the gray stuff how kuch

Much

[dark sparrow]

#calculus

[faint pasture]

abcd is the area of square right?

[boreal crag]

Yeah

It's 20m2

[faint pasture]

and is it given that the radius of inner circle equal to thhat of the other four?

[boreal crag]

It's not given anything the question just was ABCD square is 20m2 find the gray stuff how much it is

It's probably the same

Just count it as the same

[dark sparrow]

!status

[lime crown]

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

[faint pasture]

well have you figured out the radius of any circle? ||hint :- sum of two diameters should equal the side length||

[boreal crag]

Now man I don't know nothing

[faint pasture]

well then i would suggest starting with easier problems

[boreal crag]

My professor sent this to me to solve it

That's all he said

[dark sparrow]

you know absolutely nothing?

[boreal crag]

Nope

[dark sparrow]

if you take a square and enlarge its sides 2 times, how many times does its area grow?

[faint pasture]

your proff is just evil

[dark sparrow]

do you know this?

[boreal crag]

Twice

[dark sparrow]

are you sure?

[boreal crag]

It's side

Circle doesn't

Have sides

Os square

Sorry

[dark sparrow]

doubling a circle's radius would not cause its area to grow 2 times either.

[boreal crag]

Oh

Can you help me with that mathh problem pls 🥺

[dark sparrow]

im trying to get an idea of how much you know some basics.

[boreal crag]

I know chemistry that's about it

[dark sparrow]

cause i have an explanation lined up but if you truly know nothing as you say then it will be difficult

[faint pasture]

yea that def not gonna help with maths

[boreal crag]

Just give me the explanation cuz I'm thinking

If it's 20m2

[dark sparrow]

when you double the sides of a square, its area grows by 4 times.

[boreal crag]

It's means it should a circle around 4,5x4,5

[faint pasture]

that problem is not so easy- it would be tough to understand the explanation then there is no point

[dark sparrow]

and the other way, if you take a square with sides equal to half of the original, the area will be reduced to a quarter of what it was.

[boreal crag]

Can you just help me figure out how large is one circle in that box

I'll find the gray part somehow

[dark sparrow]

one moment

oh hold on

[boreal crag]

Thank you you are doing a really good deed

[dark sparrow]

those arcs in the corners

do we know that they are from circles of the same radius as the ones we see in full

cause if we don't then we are in trouble

[boreal crag]

Yes

They are all the same

[dark sparrow]

this grey area can be cut into pieces and rearranged like this

[boreal crag]

Count it thesame

[dark sparrow]

and the same in the other corners

[boreal crag]

Ohhhh

Does that work

[dark sparrow]

it means the grey area is equal to the area of these two squares

which is clearly half of the total

[faint pasture]

damn that was elegant

[boreal crag]

So half of the box

10m2 p

And the other two part I'll give it around 3,5m2

?

Ohhhh I get it

Thank you very much

You those curvers

[dark sparrow]

no

[boreal crag]

In the sides

So it's squares

[dark sparrow]

i erased all the curves with this argument

[boreal crag]

So it's 10m2

[dark sparrow]

yes the grey area is 10 m^2.

exactly half of the big square.

[boreal crag]

Than you very muchhhh

I really appreciate much love

[winter mortar]

Is there any kind of theorem to solve for this? If so, is there any proof and does it apply to any triangles with 2 circles inscribed such as this?

[exotic yarrow]

A good technique when you're working w/ circles and tangents is to draw the segments from the centre to the tangent pts

that basically nukes this

[green elm]

What went wrong?

At the end it’s -2cotA, i wrote ^2 on accident

[exotic yarrow]

With (1), you need to write $\tan^2 A$, not $\tan A^2$

[somber coyote]

Civil Service Pigeon

[exotic yarrow]

However, the bigger issue is with 2

you can't just introduce a division by 1/tan^2 A for no reason

in fact, you were basically done at 1

$-\frac{2}{\tan^2 A}=-2 \cdot \frac{1}{\tan^2 A}=-2 \left(\frac{1}{\tan A} \right)^2=-2 \cot^2 A$

[somber coyote]

Civil Service Pigeon

[exotic yarrow]

I'd think it's fine to jump from the -2/tan^2 A to -2cot^2 A immediately

but I listed out some (excessively granular) detail if you wish to see it

[green elm]

thanks for the help!

[exotic yarrow]

[green elm]

do i do the same for this one?

[exotic yarrow]

wdym by "same"

[green elm]

same process

[exotic yarrow]

as in multiplying by the conjugate?

uh kinda ig

[green elm]

ok, thx

[grave pond]

Most often the LHS will be understood as meaning the arcsine.

[cunning lion]

which is why we have the special notation csc(x) = 1/sin(x) instead

[green elm]

pls help, i have no idea how to do this

prove the trig identity

[echo beacon]

geometry my beloved

i’m hating proofs rn

stupid asf

t table proofs 🤓

[trail tendon]

real

[echo beacon]

i cant fricking memorize the circle geometry laws

[trail tendon]

real

[echo beacon]

like circle chord theorem????

buddy just

😭😭🙏

[trail tendon]

wth even is that 🗿

[echo beacon]

😂

i know the laws

simply can’t memorize the name

😭😭

[trail tendon]

same, sometimes XD

[winter mortar]

Ok bro, I need your help, with a geometry problem

😄

[echo beacon]

sure

[echo beacon]

i’ll try my best

wtf

erm

2am me will try my best

lemme go get paper

[trail tendon]

this is horrible what is this 😭

[winter mortar]

I keep asking chatgpt, but it can't do math 🤷

[echo beacon]

doesn’t look too bad tbh

i just learned a butt ton of circle geo so

[winter mortar]

GL!! 🫵😄

[echo beacon]

maybe it’s a bit hard

[trail tendon]

this is the kind of geometry that i have no idea how to do 💀

[echo beacon]

idk i haven’t tried anything yet

[winter mortar]

I got the answer if that helps? I just want to know HOW to solve it.

[echo beacon]

o

lemme try first

[winter mortar]

Got you.

[echo beacon]

what grade is this

i’m only 10th 😭

[trail tendon]

im pretty sure this is high school geometry, but i can't even do it 😂

[echo beacon]

help 🙏🙏

[trail tendon]

this is like the hardest part probably

[winter mortar]

13 to 15 year old math "olympiad" in Sweden

[trail tendon]

thats kind of what i was thinking ngl

[trail tendon]

oh bruh

[echo beacon]

lmfao

[trail tendon]

yeah

[echo beacon]

13 year olds

[trail tendon]

this is one of those harder hard problems

[echo beacon]

😭😭🙏

[winter mortar]

Yess

[trail tendon]

i mean if they know how to do it then thats one thing

if you've never learned it thats another lol

[echo beacon]

i should be able to do it with what i’ve learned

simply can’t because i can’t see it

[trail tendon]

wdym?

[echo beacon]

can’t see solution

[trail tendon]

🗿

[upper karma]

Both the circles are identical

[echo beacon]

when it says “what is the RADIUS” does it mean they have the same radius?

[echo beacon]

UGH

HELPFUL

😭😭🙏

[winter mortar]

yes, they are identical

[echo beacon]

fuck me

[trail tendon]

wait the radius of both circles is identical?

[winter mortar]

yeah

[trail tendon]

bruh

[echo beacon]

gotta read more carefully

[trail tendon]

i guess i thought radius was plural of radius 💀

its like radii tho

or radiuses

not sure

[upper karma]

Radii, radius

I don't which is plural though

[dark sparrow]

one radius, two radii

...because latin

[trail tendon]

and radiuses isn't a thing

[dark sparrow]

radiuses is recognizable as plural but usually avoided in more formal writing

[trail tendon]

Ann do you feel like helping with the problem 😂

[trail tendon]

ah

[dark sparrow]

i have not seen the problem

[trail tendon]

p

[dark sparrow]

weh

[trail tendon]

XD

idk ;-;

[echo beacon]

this is tough

lemme

[trail tendon]

yeh

[upper karma]

Will "tangents from a common point are equal" help in any way ?

[trail tendon]

wdym common point

[upper karma]

From the same point

[trail tendon]

._.

a tangent of a point is equal to the tangent of the point?

[upper karma]

It is marked in here

[echo beacon]

doubt

oh

wait

yeah probably

i thought u meant

nvm

[trail tendon]

i don't get what it means 😭

[echo beacon]

basically a point outside a circle

when u draw a line from the point

that is tangent to the circle

ok it’s easier to explain drawn

[trail tendon]

i know what a tangent is

i don't know what "tangents from a common point are equal" means

like the length of the tangent is equal? the slope?

[halcyon sand]

breh

[trail tendon]

OHH

[echo beacon]

amazing diagram

[halcyon sand]

wut grade level is the problem in

[trail tendon]

you mean tangents that intersect a common point

have equal lengths

[echo beacon]

age 13-15 olympiad

[trail tendon]

ahh

[halcyon sand]

alr

[trail tendon]

yea that is marked in the diagram

it helps

[echo beacon]

y’all

easiest solution

just search up

two circles inscribed in right triangle

easy

hmmmm

i swear i was on to something

😭😭

let’s try now

what the fuck

this is a similar triangles problem

😭😭🙏🙏🙏

i ain’t doing trig at 2:30am

@winter mortar https://www.toppr.com/ask/question/in-the-figure-below-the-triangle-is-a-345-sides-triangle-two-equal-circle-are/

read this

i am too lazy to do this

[upper karma]

Xd

[trail tendon]

so close

only 200 more years and we would have gotten the answer

[upper karma]

Key point

[echo beacon]

^

i swear i could’ve gotten that

but not on a contest where you’re given like 5 minutes 💀💀

[winter mortar]

10 minutes 🤓☝️

[winter mortar]

Thank you!

Also why are they giving trigonometry to 13 yo’s 😭🙏

[lime dune]

this is not trig.

[lime dune]

there is nothing overly unusual about that, i was probably learning trig as early as 12-13 and there are plenty of other students who have done similarly

[winter mortar]

Bro what 😭🙏

[lime dune]

this is just plain ol geometry

a very standard problem type in fact

whenever you see circles in a diagram

your first thought should be "draw in radii in convenient places"

[winter mortar]

I’m going to fail math 🤧

[steady zinc]

Does anyone has any ideas on how to get better at geometry apart from practice espcially the part that requires to draw unimaginable construcions?

[main imp]

you guys know any good books to self study trigonometry?

[maiden brook]

which problem have u seen that requires “unimaginable constructions”

[faint pasture]

Proof of sin(A+B) for one lmao

[trail tendon]

i dont think thats what he was talkin bout

[faint pasture]

Probably not but i was just commenting that shit constructions definitely exist

[trail tendon]

xD

i think he was talking about like drawing lines and stuff on geometric drawings to figure out the problem

[faint pasture]

Yea no i dont have one in mind rn but i have seen enough of those too... like any question from even AMC 10's ending problems require god level constructions

[trail tendon]

if you scroll up a bit theres one X'D

[faint pasture]

Lmaooo exactly my point

[obsidian harness]

I hate how hard the AMC is especially 12

[faint pasture]

Were you talking bout this viper?

[obsidian harness]

For people with no special training in competition maths

like you can do average but certainly you need to be trained to qualify for AIME

[faint pasture]

And then AIME is just pain

And in my country the equivalent stages are even harder

Soo am fucked lmao

[obsidian harness]

India? or no

[faint pasture]

Yea-

[obsidian harness]

ohhhhhhh

[faint pasture]

Lol

Integer type questions are tougher than mcqs

[trail tendon]

yes XD

[faint pasture]

It isnt even that bad acc to aime/amc standards ngl

[trail tendon]

ik 😭

idk how to do geometry like that tho

honestly

[faint pasture]

Yea like sure i can manage enough to get done with it in school

But competition geometry is pain

[trail tendon]

exactly

[obsidian harness]

Ahhhhh that's not bad if you think a bit

I hate how the number of maths enthusiasts in grade school means you need to be insanely good to stick out

[trail tendon]

i thought quite a bit, and its still bad 😂

i didnt read the answer thing but do u know how to do it

[obsidian harness]

Yeah I know how to do the case with only one circle but....

no and I'll try to figure it out if I can

[trail tendon]

alr

[faint pasture]

Ig the same old area trick used for the single circle would work here too?

[maiden brook]

a much easier thing is cos(A-B) from which sin(A+B) follows

[maiden brook]

not so much

imo

[faint pasture]

Uh idk my textbook had the sin(A+B) first and both cosine ones were given as an exercise

[obsidian harness]

spoilers to circle geometry:
||(x + c)/(r + c) = 5/4
x + c = 5/4 * (r + c)
x = 5r/4 + c/4

But also (x + r)/(r + c) = 3/4
x + r = 3/4 * (r + c)
x + r = 3/4 r + 3/4 c
x = -1/4 r + 3/4 c

So 5r/4 + c/4 = -r/4 + 3c/4
6r/4 = 2c/4
And c = 3r
So x = 5r/4 + 3r/4 = 2r

So x^2 + r^2 = (3 - a)^2
(2r)^2 + r^2 = (3 - (5 - 2r - 3r))^2||

[faint pasture]

For non visual thinkers like me it is at least, soo like when i have an idea i have to draw it out cuz i cant just picture an image of it in my brain if this even makes sense to you

[faint pasture]

X is the length of that red thing?

[obsidian harness]

no, I should label x

and there's a sign error but oh well

[maiden brook]

do u have an example of a problem? Just wondering

[faint pasture]

XD i mean its the idea which matters anyways the silly stuff along the way is just boring computations

[faint pasture]

Damn that was cool

[obsidian harness]

I messed up the signs and I'm now getting r = c??? anyways

Basicallly the smaller right triangle to the red side is similar

[faint pasture]

Not really
But just look past rmo papers the geometry problems in there tend to be hellish

[faint pasture]

💀

[obsidian harness]

Oh ok WA tells me ||r = c/3, x = 2c/3||

I swear I know how to do it it's just silly algebra

oh lol I know why

||the quadratic isn't nice but I think the solution is reasonable with the quad formula ||

[obsidian harness]

@winter mortar

hope this helps

Ah wait did I make a wrong assumption

Don't think ||x^2 + r^2 = (3 - a)^2|| is correct sorry but the rest is right

I honestly think the way forward is:
||(3 - a - r)/(4 - c - r) = 3/4 which gives a = 2r and r = 5/7|| but that's super weird

It seems correct but there doesn't seem to be a proof

[worthy acorn]

#8 d, how do you find the second time?

I got 10 just from subbing 17 in

[trail tendon]

what did you get for sin(3t)

like when you solved for sin(3t)

[worthy acorn]

T=10

[trail tendon]

no, like what did you get sin(3t) = ?

wait how did you get 10

oh

this might not be in degrees

[river raptor]

Who can help me with my project?😭 Im badly needed someone help with trinometry cause the deadline is tomorrow

Trigo*

[trail tendon]

ah

sin(theta) = 1/2

do you know the unit circle?

[worthy acorn]

Ooo yea

Forgot about that

[trail tendon]

there are other times when sin(theta) = 1/2

[trail tendon]

also, are you sure they talking about degrees and not radians?

[river raptor]

I need to answer the even no. questions

[worthy acorn]

Its degrees

[trail tendon]

mk

[worthy acorn]

I figured it out, thanks

[trail tendon]

👍

[faint pasture]

Like all of them?

[river raptor]

@faint pasture no

[faint pasture]

Then?

[river raptor]

Just the even numbers such as 2,4,6 and so on

I mean starting from 42

[faint pasture]

No like as in all the even numbered ones?

[river raptor]

Yes 😭

[faint pasture]

No ones gonna help with so many ques at once if am being honest

[river raptor]

I answered 1-40 and my mind is so tired

@faint pasture even one question it will help me alot

[faint pasture]

Idk you can ask the ones you get stuck at, no one is gonna answer them all

[faint pasture]

We arent gonna give out the answer anyways if thats what you want i can help you reach the solution though

[river raptor]

Okay, i wanna know how to solve it

Preparing for my exams

[obsidian harness]

https://www.desmos.com/calculator/zphrvodkfp

[faint pasture]

What are 43 and 44 asking?

[faint pasture]

(Hey what would be a good channel for dknight's problems? I dont wanna ruin geo and trig)

[river raptor]

Can you help me with 46 and 48?

[faint pasture]

Well for 46 you just have to plug in the value

[dark sparrow]

these?

[river raptor]

@dark sparrow yes

[dark sparrow]

ok what's troubling you with 46

[faint pasture]

For 48, i assume you know about (a+b)(a-b) form

[river raptor]

Yeah

[faint pasture]

(Ann i really dont think is the correct channel for his ques)

[faint pasture]

Well yea then expand the brackets and try to make it look similar to that form

[obsidian harness]

idk

isn't this one fine

[faint pasture]

We dont have one for basic complex nums right?

[river raptor]

Yeah thanks, iknow that already but i need to finish other but icant understand some problems

[faint pasture]

I guess even alg will be better how are these related to trig

[dark sparrow]

ok wait hold on

can we perhaps focus on one problem at a time

[faint pasture]

Well just tell which problem you cant understand and we will help with that specific one

[river raptor]

Okay

Btw, i will be back tomorrow i gotta finish different project rn

[dark sparrow]

...

[river raptor]

Thanks

[winter mortar]

Aight, thanks boss.

[obsidian harness]

no worries

[south plume]

Saw a video that involved an equation for sin(5(theta)) which sparked my interest

Is there a general form/equation for Sin(n(theta))? Where n is a constant?

[hoary totem]

https://en.wikipedia.org/wiki/Chebyshev_polynomials

here are examples

and here is how to use them:

you can generate them by writing cos^n(x) as a fourier series using the exponential definition

then solving for cos(nx)

[faint pasture]

Damn there existed smthn like this all along?

But like it all seems random

I dont really see a pattern for generating it

like tan(nx) follows a pretty pattern

[hoary totem]

here is an example with cos^4(x)
cos(x) = (e^(ix) + e^(-ix))/2
so
cos^4(x) = (e^(ix) + e^(-ix))^4/16
= 1/16 (e^(4ix) + 4e^(3ix)e^(-ix) + 6e^(2ix)e^(-2ix) + 4e^(ix)e^(-3ix) + e^(-4ix))
= 1/16 (e^(4ix) + e^(-4ix) + 4e^(2ix) + 4e^(-2ix) + 6)
= 1/8 ((e^(4ix) + e^(-4ix))/2 + (4e^(2ix) + 4e^(-2ix))/2 + 6/2)
= 1/8 (cos(4x) + 4cos(2x) + 3)

now we have cos^4(x) = 1/8 (cos(4x) + 4cos(2x) + 3)
so cos(4x) = 8cos^4(x) - 4cos(2x) - 3

here, we know cos(2x) = 2cos^2(x) - 1 (if we dont, we can simply repeat our steps to find cos(2x))
so we have cos(4x) = 8cos^4(x) - 4(2cos^2(x) - 1) - 3
= 8cos^4(x) - 8cos^2(x) + 1

this is why T_4 (x) = 8x^4 - 8x^2 + 1

[faint pasture]

Sureee the result is interesting and there is a pattern but considering the recursion it can possibly involve for higher values of n, it is just not like doable
Were the polynomials invented this way too like by brute forcing btw if you know?

[hoary totem]

well cos^n(x) follows a pattern
its 1/2^(n-1) (cos(nx) + pascals triangle...../2)

[faint pasture]

And cos(2^n(x)) is still easy to calculate cuz cos(2x) =2cos²(x) -1

Shit like cos(17x) yea thatd be a mess

[faint pasture]

Dayum that sounds fun
Whats the patterns name so i can look it up?

[hoary totem]

hell if i know ¯_(ツ)_/¯

[faint pasture]

XD

[hoary totem]

but u can easily derive it using this method

[faint pasture]

Hmm true!

To think of it
There cant really exist such a polynomial pattern for sin right? Since sin(nx) is usually so intertwined with cosines

[hoary totem]

cos^1(x) = 1/1 (cos(x))
cos^2(x) = 1/2 (cos(2x) + 1)
cos^3(x) = 1/4 (cos(3x) + 3cos(x))
cos^4(x) = 1/8 (cos(4x) + 4cos(2x) + 3)
cos^5(x) = 1/16 (cos(5x) + 5cos(3x) + 10cos(x))
cos^6(x) = 1/32 (cos(6x) + 6cos(4x) + 15cos(2x) + 10)
cos^7(x) = 1/64 (cos(7x) + 7cos(5x) + 21cos(3x) + 35cos(x))

it all comes from pascal's triangle

[hoary totem]

sine is just shifted cosine

so i dont see why not

[faint pasture]

I mean sure you could just replace the x in cosine's pattern with pi/2 - x but thats kind of cheating

Oh wait

You couldnt

Nvm

(You kinda could but after it is all reduced to cos^n(x) form)

But that's kinda far xD

[hoary totem]

sin^2(x) = cos^2(x - pi/2) = 1/2 (cos(2(x - pi/2) + 1) = 1/2 (cos(2x - pi) + 1) = 1/2 (-cos(2x) + 1)

there u go

[faint pasture]

Um could you explain how? It doesnt look like anything like pascals triangle to me after the 3rd row

[hoary totem]

sin^3(x) = 1/4 (cos(3(x - pi/2)) + 3cos(x - pi/2))
= 1/4 (cos(3x - 3pi/2) + 3sin(x))
= 1/4 (-sin(3x) + 3sin(x))

u can just shift them and simplify

[faint pasture]

Damn that's cool

[hoary totem]

if odd power: take 5 as an example
2^(5 - 1) = 16
1/16 in front
row 5 in pascal's triangle is 1 5 10, these are the coefficients, reduce frequency by 2 each time
cos(5x) + 5cos(3x) + 10cos(x)

[faint pasture]

Ohhh iseee that makes sense

[hoary totem]

if even power: take 6 as an example
2^(6 - 1) = 32
1/32 in font
row 6 in pascal's triangle is 1 6 15 20, these are the coefficients, reduce frequency by 2 each time, except the last one gets halved
cos(6x) + 6cos(4x) + 15cos(2x) + 10

[faint pasture]

That was fricking cooool

You never fail to amaze me

[hoary totem]

sine series comes out to be:
sin^1(x) = 1/1 (sin(x))
sin^2(x) = 1/2 (-cos(2x) + 1)
sin^3(x) = 1/4 (-sin(3x) + sin(x))
sin^4(x) = 1/8 (cos(4x) - 4cos(2x) + 3)
sin^5(x) = 1/16 (sin(5x) - 5sin(3x) + 10sin(x))
sin^6(x) = 1/32 (-cos(6x) + 6cos(4x) - 15cos(2x) + 10)
sin^7(x) = 1/64 (-sin(7x) + 7sin(5x) - 21sin(3x) + 35sin(x))

odd powers only have sine

even powers only have cosine

and then when frequency mod 4 is 2 or 3 u flip the sign

[faint pasture]

And the fact that cos(2nx) can be written entirely in the form of sine is a cherry on top of the cake

[hoary totem]

lol

i just like trig a bit

[faint pasture]

XD can say the same now but i usually do an extremely different kind of trig

So yea

[hoary totem]

like what?

[faint pasture]

The textbook kind

[hoary totem]

im sure u could find this in a textbook somewhere

[faint pasture]

Shit like cosec 10 + cosec 50 -cosec 70

(In degrees)

[hoary totem]

idk how to do that

lol

calculator to the rescue

[faint pasture]

XD well its mostly just formula based

[hoary totem]

are there angle addition formulae for cosecant?

[faint pasture]

Convert it to sine first!

[hoary totem]

1/sin(10) + 1/sin(50) - 1/sin(70)

those chebyshev polynomials could come in handy

lol

u could express this all in terms of sin(10)

[faint pasture]

Hmm yea take lcm
You get sin10sin50 +...
And then since 2sina*sinb = cos(a-b)-cos(a+b)
Just do this a few times and yea

[hoary totem]

i see..

[faint pasture]

Lmaooo
The algebra would be just hell then tho lmao

[hoary totem]

this is about all the trig i know

[faint pasture]

I mean these results are derived from the formulas you know too

[hoary totem]

yeah i can see

[faint pasture]

These are just commonly used so i kinda remember them now

XD

Damn look what i found in my textbook lmao

[hoary totem]

lmao

[faint pasture]

The official solution derived the polynomial from the basic too(they used trig identities tho since well n is small here instead of the complex num definitions) 💀

[hoary totem]

i see

[hoary totem]

my textbook

is...

confusing me

im wondering if this is even necessary

[faint pasture]

Yea no i definitely dont know enough non euclidean geometry to even realise what half this ends up doing

[hoary totem]

i really just dont wanna have to figure out how 17.30 is derived

cuz the textbook states it without any derivation

oh wait 13.12

[faint pasture]

It is the authors way of flipping you off

I would guess

[hoary totem]

oh thank god theres derivation

[faint pasture]

💀

How th did you remember the exact definition where the derivation you wanted lied

[hoary totem]

well it says "by equation 13.12"

so i checked chapter 13

[faint pasture]

Oh nvm i didnt read that
Isee isee

Imagine if the author just forgot to write 13.12 thingy

[hoary totem]

but tbh i dont think this is necessary

all i need to know is this

[faint pasture]

Aha

[hoary totem]

this looks like this which is just spherical law of cosines

[faint pasture]

Just barely but okay yea

[hoary totem]

this is all

very overcomplicated

i dont see why spherical law of cosines doesnt work

¯_(ツ)_/¯

[faint pasture]

Probably cuz author just wanted to show off their skillz lmao 💀

[hoary totem]

no its probably because its useful to format it this way

[faint pasture]

Maybe i guess yea there is a chance it is used again in further chapters

[hoary totem]

or its just useful

[faint pasture]

XD true

[steel anvil]

I haven’t seen this formula in months and I thought I finally escaped geometry

[hoary totem]

lol
ur fault for looking in this channel

[faint pasture]

Bro wtf is up with my textbook, it had a que which was relatively easy i got x =8
Though what it asked me was 3x³ + 2x² + x +1
And im not allowed to use a calculator for this either 😭

[dark sparrow]

what is causing you such confusion

3 * 512 + 2 * 64 + 8 + 1 is not that bad to calculate, is it

[hoary totem]

its pretty bad

[dark sparrow]

it is a four digit addition

since when did those become impossible to do by hand

!xy @faint pasture

[lime crown]

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.

[faint pasture]

But why th make me do that? There is no point in that, is there?

[dark sparrow]

idk it just doesnt register as particularly hard arithmetic

[maiden brook]

u can still do the problem in less than a minute

[faint pasture]

Well i solved the problem? It was just a rant on how some authors are just cruel

[dark sparrow]

just show the original problem

again this is nowhere near cruelty imo

[faint pasture]

And i have to do the entire problem in like 2 mins, including this shit

[maiden brook]

wdym u have to do it in two minutes

[dark sparrow]

show the problem

[dark sparrow]

,rccw

[faint pasture]

Dont get me wrong finding k is relatovely easy

But dont shit in the end is pain

[dark sparrow]

and this is free response?

[faint pasture]

Yep

[dark sparrow]

mm

ok so it's annoying fluff then

[faint pasture]

Not cruelty maybe but just wasting the time of the students, definitely

[faint pasture]

Exactly my point!

And i saw another one just like this where i mean it was sorta simpler cuz coefficients were set for it to be not just pain, but the ans was like 17xx

[summer oak]

DID ANYONE TAKE THE GEOMETRY EOC

[steel anvil]

In florida? Years ago

[summer oak]

oh god its u

[steel anvil]

U forgot the comma

[summer oak]

doesnt matter its discord

[steel anvil]

And the exclamation point

[summer oak]

🤓

[steel anvil]

What do u want RIZZLER

[summer oak]

oookay

i just want to know what was on it

[steel anvil]

Formula sheet gives you everything you need most of the time
Very little SAS, SSS, ASA, AAS congruency questions / generally 2 max if there is
Know difference between area / lateral area
Remember chords

Incredibly easy exam

Getting a 3 is easy as well. You barely need anything to pass

You’re talking abt FL right?

[summer oak]

yes

how do u remember if its so long ago

[steel anvil]

I tutor kids bro

[zealous olive]

damn brother you 2800 bullet?

[steel anvil]

Used to be on lichess

But lichess banned for having a lot of accounts

[obsidian harness]

Wow

[obsidian harness]

this triangle is symmetrical about the y-axis

So the y-coordinate is the same ofc

What do you think happens to the x-coordinate?

[broken crescent]

from the y axis to T or U its the same distance

[obsidian harness]

exactly

And the distance from T to the y-axis is f

[stuck sleet]

What does it mean by ***characterization ***in this context I read in a book by Moise (Geometry Metric Edition, page 501):

Theorem 6-2
"The perpendicular bisector of a segment, in a plane, is set of all points of the plane that are equidistant from the end points of the segment."

In this theorem the book said::
"Briefly, we say that the points of the perpendicular bisector L are characterized by the condition PA = PB........................................ Characterization appear not only in theorems but also in definitions........................... For example, the sphere with center P and radius r is, by definition, the set of all points Q such that PQ = r. Thus we say that the sphere is characterized by the condition."

[obsidian harness]

they are defined by the condition

characterise means that something has some defining property

So all of the points on the perpendicular bisector L (and no other points) have PA = PB

All of the points on the sphere and no other points have radius r

the theorem/definition split just means whether that something is actually the definition, or rather it's another thing that isn't the definition but is always true for these points

[stuck sleet]

Thank you.

Is point of concurrency and point of intersection are just the same?

[dark sparrow]

probably

where did you see "concurrency" tho

[steady orchid]

How do I do this?

[dark sparrow]

can you say what the dimensions (i.e. width, length and height) of the box will be?

all in terms of x, obviously.

[stuck sleet]

Geometry by Moise and Downs Metric Edition page 507 Chapter 15.3: Concurrence Theorems

[dark sparrow]

i wanted a screenshot of the relevant page

[stuck sleet]

wait I'll take a picture

[lime dune]

“concurrency” is usually used in the context of three or more lines

although as stated there it is trivial for two nonparallel lines to be concurrent

[stuck sleet]

Triangles have too many centers though....

[lime dune]

tell that to people grinding olympiad geometry 😭

[dark sparrow]

i mean

doesnt this page tell you what concurrency means

like right at the top lmao

[stuck sleet]

no, also the word characterization is not defined.

but I understand it now

thanks!

[dark sparrow]

literally right here

Definition
Two or more lines are concurrent if there is a single point which lies on all of them. The common point is called the point of concurrency.

[faint pasture]

Tbf those doing olympiad geometry dont mind that cuz they usually have a deep rooted interest

[lime dune]

“characterized” i take to mean “uniquely determined by” here

[stuck sleet]

yeah but its like intersection

[lime dune]

for two lines/curves, yes

[dark sparrow]

two or more lines

also the word "concurrent" is literally mentioned

i dont understand what you are objecting to

[lime dune]

reading is hard™️

[stuck sleet]

I'm not objecting and I'm not mad, maybe I'm just sleepy at that time

[dark sparrow]

...what time is it where you are

[stuck sleet]

2:00 P.M. just have eaten lunch

[serene hedge]

how much longer will you be banned from help channels for?

[dark sparrow]

don't reply-ping me with a question that has absolutely nothing to do with the message being replied to.

also this is not #「helpers-lounge」, why are you asking me out in the fucking open?

[stuck sleet]

Chill dude

[dark sparrow]

do not call me "dude".

[serene hedge]

oh no

[dark sparrow]

please edit that word out of your message @stuck sleet

[stuck sleet]

ok what should I call you bro?

[lime dune]

💀

[serene hedge]

chill

don’t be antagonistic

[lime dune]

not that either

[dark sparrow]

<@&268886789983436800> transphobia

"bro" is LITERALLY the worst alternative to "dude" you could have possibly picked if you tried

[stuck sleet]

woah

[obtuse field]

Okay please just don't call her masculine-sounding words

[stuck sleet]

I just call anyone on internet "bro" or "dude"

Ok I call you ma'am

[dark sparrow]

well, some people don't like that.

[obtuse field]

I get that you call anyone that, but different people see those words as meaning different things, so it's best just to be respectful of whatever they want to be called

[dark sparrow]

i would prefer being just called by my name over "ma'am"

[lime dune]

the pronoun roles here exist for a reason

[stuck sleet]

Ok thank you ann

[lime dune]

please respect that

[stuck sleet]

I do not really want to offend someone.

Sorry

[dark sparrow]

you had the sense not to double down on it all, so you're fine.

[stuck sleet]

Ok thanks for the help though

[steady orchid]

what does that mean, exactly?

[dark sparrow]

it means that your expressions for the length, width and height should all contain the letter x.

as opposed to being just numbers.

[steady orchid]

oh alright, just literally have x. appreciate that

[dark sparrow]

well again

i... asked you a question

are you able to answer?

[steady orchid]

sorry, didnt see. I suppose length would be like 10x, width would probably be 7x and height 1x (all in cm obviously).
Sorry for not answering earlier, its a bit late

[dark sparrow]

this is all wrong.

well, no. the height is x.

how did you get 10x for the length?

[steady orchid]

well I assumed that those boxes take off 1cm from both sides, as a guess. Also I did not know that the height is x, but I do appreciate it. I assumed it while taking away the boxes. with the boxes the length is 12x, width-9x.
I am not sure or I wouldnt be asking

[dark sparrow]

no

the length pre-folding is 12, not 12x.

and the width is 9, not 9x.

and no, you don't know that x = 1cm.

[steady orchid]

oh alright

how do you figure that out then?

Is there a formula for that?

[dark sparrow]

the 0th step is to tone down the whats-the-formula-ism.

then the 1st step is to understand that the rectangle's width of 12 cm is shortened by x cm on both ends, so it becomes 12 - x - x, or 12 - 2x.

[steady orchid]

Okay

[dark sparrow]

do you understand this

[steady orchid]

yes, I do

[dark sparrow]

like, what you told me earlier was full of unjustified assumptions instead of just reading and understanding exactly what the diagram says

[steady orchid]

See I don't know what to do here, thats why I did assume and said it

I wouldn't be previously asking if I didn't understand lol

@dark sparrowHow would I use desmos to estamate estimate the value of x here, though?

[dark sparrow]

your box has the following dimensions:

• width: 12 - 2x
• length: 9 - 2x
• height: x
  what is its volume?

(don't overthink it)

[steady orchid]

(12−2x)(9−2x)x

I mean it would be this, this is as simple as it goes really

[dark sparrow]

yes exactly.

[steady orchid]

oh alright

[dark sparrow]

now you have a function of x that you can plot in desmos.

some people live in timezones other than yours, stampcake.

[steady orchid]

what?

[dark sparrow]

it is 10:54 where i am, for example.

[steady orchid]

also yeah, its 12 pm* for me

I mean i didn't sleep all night but regardless

[dark sparrow]

people do not usually go to sleep at eleven in the morning, stampcake.

[steady orchid]

school is more important

[dark sparrow]

also like

!redir

[lime crown]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[steady orchid]

good for you bud, whats your problem?

like good for you man, but i dont get your issue here

[dark sparrow]

anyway, go to desmos and input the following on one line:

f(x) = x(12-2x)(9-2x) {0 ≤ x ≤ 4.5}

the {0 ≤ x ≤ 4.5} will make it only show you the part of the function between those values of x, since we only care about those values (do you understand why?)

[steady orchid]

I am not particularly sure, no, I am exhausted so my brain in't calculating but I assume its because it should be in between 0 and 4.5?

if I was asking at a more sensible time, i probably would have a better understanding but understand I have been up all day yesterday and all morning up to 12pm, so I am exhausted due to schoolwork so I do apologize.

[dark sparrow]

x ≥ 0 because x is a length and cannot be negative
and x ≤ 4.5 because 9-2x is also a length and also cannot be negative (9 - 2x ≥ 0 solves to x ≤ 4.5)

do you understand now?

[steady orchid]

I do, yes

[dark sparrow]

why are you doing math while exhausted

are you on a due-yesterday deadline or sth

[steady orchid]

yup, I was busy writing a 12 page no double spaced essay all week so I wasn't able to do any of my schoolwork yesterday

*not yesterday but on friday

[steady orchid]

I put this function in and it was 1.7, that should be right, correct?

[dark sparrow]

you shouldn't overuse the word it

[steady orchid]

i suppose

[dark sparrow]

but yes, the value of x which maximizes the volume is about 1.7

[steady orchid]

alright, thanks

[dark sparrow]

... yeah they ask for nearest-tenth rounding

1.7 is correct

[steady orchid]

Okay, thanks a bunch, you're a life saver :)

Good night, thank you :)

[river raptor]

Is this correct?

[dark sparrow]

is this just polar->cartesian conversion that you're doing? @river raptor

if it is, then your answers are correct, but with two things worth pointing out:

1. you should put a stroke through the middle of your 7's so that they do not look like 1's.
2. for #6, you could have just avoided all the computation and said that r=0 already means your point is the origin, regardless of what theta is.

[faint pasture]

not that relevant to his problem but i have had my physics proff ask me the direction of a null vector, soo theta might matter

[dark sparrow]

in what context

[faint pasture]

he was basically saying that when we just wanna point out the direction just we could add a null vector pointing in that direction, i dont really remember the exact specifics of that problem though

[weary palm]

@brazen mountain

Post here

[faint pasture]

well just repeatedlly apply radius = diameter/2 for the white one

[river raptor]

Thanks

[golden trout]

quick question, when working in space, is there a more efficient way to obtain a point and a vector from a line given as a two-plane intersection rather than solving the indeterminate system?

[grave pond]

How are the planes given?

Hmm, even though you can find a direction vector as a cross product of the normal vectors for the planes, you'd still need to solve the system of equations to find a point on the line -- and if you've gone that far, just basing the entire answer on that solution is probably the least work in general.

[golden trout]

well, yeah, but i didn't realise i could've used the cross vector, I think it might help me, cause there are also exercises in which i don't need the point and just a vector

so it might end up being faster and more efficient

thanks

[grave pond]

Actually, if you start by finding the direction vector, you can decide that you want either x=0 or y=0 or z=0 for the fixed point, and once you know the direction vector you can choose a coordinate that you know is not constant along the entire line.
Then, setting the chosen coordinate to 0, you only have a 2×2 system left to solve.

[golden trout]

omg, that's actually really good

it'd save me a lot of time solving the system and messing it on the gauss method

[summer oak]

okay okay so whats mostly on the eoc

[upper karma]

Given area of a triangle is 5.If two of thr coordinates of the triangle are (2,1) and (3,-2) and the third point is (x,x+3) . Find the value of x

[dark sparrow]

!status

[lime crown]

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

[upper karma]

2

Sorry for the delay

Is this formula right ?

[dark sparrow]

what are all of these letters

[upper karma]

Oops

Coordinated

Coordinates

(xi,yi)

[dark sparrow]

(x_i, y_i) for i = 1, 2, 3?

[upper karma]

Aye

[dark sparrow]

i cant tell for sure whether this formula is correct but i think it is overcomplicated

[upper karma]

Except for finding the perpendicular distance and base length , any method is fine

[dark sparrow]

why that exception

[upper karma]

Lazy

Hehe

[dark sparrow]

i was actually going to suggest exactly that

[upper karma]

Jk

It's takes time

[dark sparrow]

anything here will take time

[upper karma]

Let me try that method

[dark sparrow]

intuition tells me there's gonna be two possible values of x btw

[upper karma]

Is there a modulus in the perpendicular distance between a point and a line ?

[dark sparrow]

yes

[upper karma]

Okay

[dark sparrow]

bc the formula is supposed to return a distance

and those things tend to be ≥0, or at least were since this morning

[upper karma]

Got it

Is there any other method for finding the area using coordinates ?

[dark sparrow]

can probably do some determinant-flavored bullshit if you really want to.

[upper karma]

Wrong formula

I kept on using it in the exam

[west radish]

1 by 2 determinant and putting the coordinates accordingly with 1 1 1

[upper karma]

Simple question but just couldn't solve it

[upper karma]

?

[west radish]

I thinked i bugged the conversation

[upper karma]

???

[west radish]

U can use the determinant formula andgaussion elimination further and find the area

[upper karma]

Is this the determinant formula ?

[west radish]

On the right theres another coloumn

Of 1

Depending upon how many coordinates

Number of ones

Are placed

And 1by 2 is being multiplied by

Dtermniant

[upper karma]

Okay,thank you

Thank you Ann

[dry star]

What major topics should I study for my geometry eoc tomorrow?

[grave pond]

The ones taught in your course.

You know better than we what those were.

[clear owl]

How can I determine the length with these two cases? I know one, but I’m confused on finding the other

The black pen is what I wrote down trying to figure this out

[clear owl]

Well thanks for the help, even if the problem has to deal with sine law rather than cosine law

[hoary totem]

wait

i misdrew my diagram

😭

[clear owl]

Yup, my mistake, should’ve clarified that this was a sine law problem 🗿I am so sorry rn

[hoary totem]

no i just misread the problem

this problem is impossible

there are two possible triangles with the info given

A could be either at the green place or the red place

[vital cypress]

can we do case 1, and then case 2

sorry to interrupt

[hoary totem]

we could

[vital cypress]

case 1 would be angle C = 38 degrees, case 2 would be angle C = 180 - 38 = 142 degrees

Yeah

[hoary totem]

ok ik u said law of sines but just for a quick check
in this case the law of cosines gives us
9^2 + b^2 - 2 * 9 * b * cos(38) = 6.8^2

this quadratic has 2 positive real solutions

giving us two possible values for b

corresponding to the green and red triangles

[hoary totem]

what?

angle C stays the same for both triangles

[vital cypress]

oh yes

what was I thinking

hold on

[hoary totem]

with law of sines:

we have
sin(A)/9 = sin(38)/6.8

so sin(A) = 9 * sin(38) / 6.8

which has 2 solutions

giving two values for b, corresponding to the green and red triangles

[stray willow]

hola

alguien habla español?

[bleak harness]

si

[upper karma]

hi there, i just started learning inverse trigonometry, and i find myself struggling to get comfortable with it. can anyone recommend me some videos that i can watch to strengthen it? also what are some things i should be careful about while learning inverse trig?

[trail tendon]

be careful about the domain restriction

theres prob some organic chemistry tutor video on it

or khan academy

[upper karma]

there are

okay thank you so much

[faint pasture]

And the range too

[west radish]

Hey guys can i get help in permutaion

Permutation*

?

[dark sparrow]

!da2a but probably #precalculus or #discrete-math is better for that.

[lime crown]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[west radish]

Kk

What about probability

A theif is about to rob a locker containing 3 rings with 6 digits on each ring probability of him being unsuccessful

Is?

[dark sparrow]

i mean #probability-statistics is very obviously named, but whatever

[dark sparrow]

this is a little unclear in how it is stated

are you translating? or is it written like that in English?

[west radish]

Lemme send u the orginal pic of question

[dark sparrow]

as you should always do

without exception

[dark sparrow]

,rccw

[dark sparrow]

"mashed with 6 different digits" sure is an interesting way for them to put it

[west radish]

Yupp

[dark sparrow]

but ok we have a combination lock whose code is 3 digits long and each one has 6 possibilities

[west radish]

Yeah

18 sample space

Ithink

[dark sparrow]

are you sure?

[west radish]

Nope

The answer is written on the back

Want me to tell

[dark sparrow]

imagine the lock instead has 2 rings of 10 digits, how many combinations would be possible then? 20?

[west radish]

Yes the sample space would be 20 digits ithink

[dark sparrow]

incorrect

a code on this type of lock is a 2-digit number. you select a digit on the first dial and a digit on the second.

10*10 = 100

not 10+10.

[west radish]

Ok ok

Now the question

[dark sparrow]

well there's three dials of 6 digits each

how many possible codes are there

not 18

[west radish]

6 to the power 3 😂