geometry-and-trigonometry

[steady wyvern]

Hi

$|A^n|=|A|^n$

[somber coyote]

Tioo

[steady wyvern]

What is the proof of this?

[obsidian harness]

det A det B = det AB applied repeatedly

You could let B = A here

[summer hedge]

Anyone know how to solve this pls?

[summer hedge]

Nvm

[copper gate]

so i m in 10th grade and i suck in geometry any tips pls?

[dark sparrow]

step 0 of any geometry problem is to draw a diagram. without a diagram, you will get nowhere.

[sweet spruce]

Ok thanks

[split tide]

analyze the question, draw the diagram, write what is given which will help you lay out whatever you have and help you figure out what method to use for solving the question, and then write what is to be proven. It seems little but really improves how you understand the question.

[tame scarab]

Hi guys
how i find the alpha on the question a) and c)?

[obsidian harness]

set up a linear equation and then use algebra

for part a, the sum of the angles equals 90

solve for x then alpha = x + 40

[topaz shore]

ignore alpha and treat it like a var

[obsidian harness]

for part c, you must have x + y = 2x - y (vertically opposite)

[topaz shore]

its prob just to throw you off

[obsidian harness]

you also must have x + y + 4x - 2y = 180, or 4x - 2y + 2x - y = 180

use either one

[obsidian harness]

no the question is to find alpha

[topaz shore]

yeah

treat alpha as y or any other variable

idk why the person writing the question felt the need to use alpha

[topaz shore]

2x-10 + x + 40 =90

solve for x

then you can get alpha

[obsidian harness]

I answered with trig only for this to happen

they asked before

[dark sparrow]

guh

i mean there is a trig-free solution

i think?

yeah, there is.

[mellow merlin]

Why is the formula of a circle x^2 + y^2 = r^2? ik it has something to do with the pythagoream theorem but when i visualize something like this equation i think of

like i cannot visualize how the pythagorean theorem forms a circle

[dark sparrow]

there's a step between these

do you know how to find the distance between two points on the xy plane?

[mellow merlin]

yes by using pythagorean theorem

[dark sparrow]

right

$x^2 + y^2 = r^2$ says that the distance between the points $(x,y)$ and $(0,0)$ is $r$

[somber coyote]

Ann

[mellow merlin]

why does it go all around tho

[cunning lion]

the circle is the set of all points of a distance r (that distance being the radius) from the center. they can be that far away in any direction

[mellow merlin]

also wdym by between (x,y) and (0,0) i thought x and y is basically 0 until you shift them around like (x + 3)^2 + (y+3)^2

like the center of the circle

[dark sparrow]

no, (x,y) is a point on the curve

all cartesian equations are conditions placed upon an arbitrary point (x,y) on the plane

[mellow merlin]

i think i need a 3blue1brown vid 4 this 😭 🙏

i get the equation but how it works i dont get

[cunning lion]

the equation for a circle centered at the origin is
[ x^2 + y^2 = r^2 ]
where $r$ is the radius.
\begin{itemize}
\item The set of all points $(x,y)$ satisfying this equation is the circle.
\item $\sqrt{x^2 + y^2}$ is the distance from the origin $(0,0)$ to the arbitrary point $(x,y)$ according to the pythagorean theorem.
\item Therefore, the set of points $(x,y)$ satisfying this equation is exactly the points which are a distance $r$ from the origin.
\item if you drew a straight line from the center (origin) to any point on the circle, its length would be the distance between them. this line segment is called a radius of the circle.
\end{itemize}

[somber coyote]

cloud

[cunning lion]

so r is the radius of the circle

[mellow merlin]

hmm maybe its the (x, y) thing thats making me confused on how to visualize it

i get what ur saying on how (x,y) satisfies the equation but should i think of it as a function or something else

[cunning lion]

if you were to pick any point on the circle then its coordinates would satisfy the equation

[mellow merlin]

like -√(x^2 - r^2) = y or something

[cunning lion]

as well, any point which is not on the circle would have its coordinates fail the equation

so the circle is just the set of points whose coordinates make the equation true

[mellow merlin]

im starting to piece things together

but its still kinda hard to like visualize it intuitively

but i get what ur saying 🙏

its just that this is what i see when i try to imagine the equation

[cunning lion]

,tikz
\draw (0,0) nodecirc{} node[above right]{$(0,0)$} -- node[midway, below right]{$r$} (235:2) nodecirc{} node[below left]{$(x,y)$};
\draw[dashed] (O) -- node[midway, above]{$x$} (O -| P) coordinate(X) -- node[midway, left]{$y$} (P);
\draw (O) circle[radius = 2];
\path pic[draw, angle radius = 5]{right angle=P--X--O};

[somber coyote]

cloud

[hazy hare]

Can somebody give me the statements aligned with the reasoning

[mellow merlin]

is this khan academy

[hazy hare]

no

[mellow merlin]

show the statement list

[hazy hare]

ok

[mellow merlin]

r u sure this is the right list i dont see any xyzs on the quadrilateral

[hazy hare]

The xyzs are just variables to fill in the actual variables (BADCE)

[mellow merlin]

im gonna ignore variables 4 now
so you know that BA and CD are equal right
and
AD and BC is the also equal

what triangles can u make with that so AC and BD can bisect each other

[hazy hare]

yes the given information is htat BA and CD are congruent

it already shows AD and BC are congruent

the only triangles i can make so AC and BD bisect is

⃤ BDC and. ⃤ . DBA ?

[mellow merlin]

ok so our apporach is to prove BD bisects CA with triangles
and BDC and DBA cant prove that since itll only include BD

and also what other triangle can we make here

we can also do

do u know where im going with this?

@hazy hare

[hazy hare]

oh my bad

didnt see

[mellow merlin]

wait maybe i approached it wrong

[mellow merlin]

ok scrap this

you were right

[hazy hare]

oh

[mellow merlin]

ok i thought it through

so we want to make 4 congruent trianges

ABC = CDA
and
ABD = BCD

and we know that these triangles r congruent to each other due to SSS, they share a side with each other and they have 2 other corresponding sides

and now we want to prove that BE = ED and CE = AE with these triangles

so the first step would be to make <CEB and <AED congruent since theyre vertical angles

and we know BA is pararell with CD and BC is pararell with AD because their triangles share the same angle so we can use interior angles

so with this we know that they are pararell, and angle CAD and ACB are congruent because of alternate interior angles

and because they share all angles and a side, by AAS congruence they are the same triangles, so therefore BD bisects CA

since theyre the same triangles and corresponding sides share the same length

sorry if my explaination was kinda bad but i hope it gives u some insight

so basically whenever a question asks u to prove BD and AC (or anything like that) bisects inside a parellelogram just create congruent triangles, and try to make BCE and AED (or anything like that) or you could even find CED or BEA congruent

it proves that they bisect each other because well if you have congruent triangles, they have the same side lengths right? so if you have 2 of them then the definition of bisect is divide into 2 equally, and since they have the same side length then it proves that they bisect

@hazy hare

also u should ask in the help channels next time instead of here since its way faster

[visual elk]

Who created maths my head is aching me from just a maths question!

[dark sparrow]

do you want to complain about it or do you want to solve it?

[steady wyvern]

Excuse me why detA det B=detAB?

[obsidian harness]

https://www.youtube.com/watch?v=Ip3X9LOh2dk

the determinant is the area/(hyper)volume scale factor

https://www.youtube.com/watch?v=Sv7VseMsOQc

[spark heron]

yo does anyone know any good geometry vids to watch on youtube

i try to look but cant find any on the topic i am being tested on tommorrow

[worn scroll]

the goat

[frank rivet]

How to dtetermine the value of a(strech) in the vertex form of parabolas by looking at its graph? Y= a(X-h)^(2)+k

[dark sparrow]

what data do you have access to? another point on the parabola, perhaps?

[frank rivet]

I know, we can use That as refrence, but how do i create a refrence point on the graph which will change reative to a

[dark sparrow]

...

ok, that makes no sense.

!xy

[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.

[frank rivet]

Nvm, let it be

[steady wyvern]

Thanks

[sudden solstice]

Guys I need help pls 🥺

I have a test on this soon and dont understand

[main wyvern]

what don't you understand?

[sudden solstice]

What ever this thing is

[silent plank]

do you know your parallel line theorems?

[sudden solstice]

I think so but like this is a new looking one to me like what is point a looking at?

Like I don’t understand what I do to get the answers

[silent plank]

they're looking for that angle

start with what's given and start doing some angle chasing and see where that leads you

see if you can get any new info from the position of that 62° angle

[sudden solstice]

@silent plank there either gonna be corresponding or alternate exterior right

[silent plank]

you can do many things with that 62°

you can do them all if you want

it won't hurt to get more info, even if some might not be needed

[sudden solstice]

So like vaule of X is 16 cause 80/5 is 16 and cause there vertical there equal

[silent plank]

yes

[sudden solstice]

And value of y is 62 cause it’s alternate exterior

Just don’t know what a is

[silent plank]

y isn't 62

alternate exterior is applicable here,
but that angle at the bottom isn't y

[sudden solstice]

I am confused then

[silent plank]

why do you think just y is 62

tell me which angle the 62° is alternate exterior to

don't overthink

[sudden solstice]

Erm

[silent plank]

it looks like you tried to apply it, you just weren't careful

[sudden solstice]

2y?

[silent plank]

yes

so 2y = 62, not y

[sudden solstice]

Oh

I stupid ☠️

[silent plank]

as for A, don't forget
angle sum on a line / linear pair

[sudden solstice]

What does that mean

[silent plank]

its a common geometric property

one you should know and have encountered before being introduced to parallel lines

how big is that red angle

[sudden solstice]

Linear pair they =180

[silent plank]

the sum will be 180° yes

apply that

[sudden solstice]

180 is the line

A=118

[silent plank]

yes

[sudden solstice]

Ty

[lime girder]

You guys are funny

[dark sparrow]

<@&268886789983436800> potential troll?

[neon prairie]

Please avoid posting huge emojis that take up tons of screen space

For mobile users it makes the channel hard to use.

[hybrid belfry]

If the definition of a straight line segment is the shortest path from a point to another,
then is there any way to rigorously prove that there's no other distinct straight line segment which connect exact those 2 points?

(By the way, i don't care what kind of method or definition you wanna use, as long as it works 😄)

[upper karma]

trigonometry is scary

[upper karma]

are the 2 lines that don't cross each other parallel?

if not i am cooked.

[burnt yoke]

I'm not sure if this is the right place to ask but how do I find out lenght of 2 if 1 is 1425?

[cloud night]

i know i learnt abt this somewhere

but i forgor

a^2+b^2=c^2

ur prolly gonna need that

pythagoreans theorem

[burnt yoke]

well thank u for the answer but I still got no idea how to solve it

[maiden brook]

where does it say they are parallel

[sudden solstice]

Guys can you help me understand this please I am Cooked on this test if I don’t know this

[solid needle]

understand what

[waxen temple]

[ionic depot]

https://youtu.be/slWroky2UYk?feature=shared

[worn scroll]

try working out some angles

[burnt yoke]

and then?

[worn scroll]

a little bit of trig

[wise zodiac]

i’m guessing the assumption is that this is a regular polygon?

if so, you can find the side length from law of cosines with 1

then u can find 2 from the definition of a regular polygon

(it can be inscribed inside a circle)

[bright frost]

assuming line 2 is perpendicular to line 1 (basically its 90 degrees where they intersect)
so join one end of line one to the end of line 2 as ive given here.
in pythagoras theorem
AC^2 + BC^2 = AB^2

dm me if you need more help

[worn scroll]

this is wrong

[worn scroll]

this length is AC - something

pythagoras cannot be used straight away

[bright frost]

you can derive the actual needed equation witht he given info

if BC is 1425

but wait one more important thing you can only use pythagoras is 2 values are given

i guess you cant use it here as only 1425 is given, mb

[bright frost]

but if 2 values are given and you wanna find 2,
then AC^2 = AB^2 - BC^2 (if AB is given)

[mellow merlin]

are angles still inscribed if theyre like this

or this

[sudden solstice]

Can anybody help me understand this?

Idk if I got any of these answers correctly

[dark sparrow]

,rccw

[dark sparrow]

wow that is a LOT of angles they're asking you

An.| Correct?
---+---------
 7 | Yes
 8 | Yes
10 | No
11 | Yes
14 | Yes
15 | Yes
16 | Yes
17 | Yes
18 | Yes
19 | Yes
20 | Yes
21 | Yes
22 | No
24 | No
25 | Yes
29 | Yes
32 | Yes
35 | Yes
36 | Yes
37 | Yes
41 | No
44 | Yes
45 | Yes

@sudden solstice

[icy sigil]

OMG THIS IS BEATIFUL

I wish I had this

[solid needle]

shoutouts and kudos to ann for actually taking the time to list those out

goddamn

[sudden solstice]

What is this?

[trail tendon]

corrections

ig

[mellow merlin]

all those angles 4 what 💔 its just time consuming

[dark sparrow]

a table telling you which ones you got right and wrong

[bleak blade]

NO NO NO

I REMEMBER THIS

no

i remember it being hard

no

i saw some friends doing it

and decided not to do it

[maiden brook]

just use calc

it gets messy but it isn’t that bad

I have seen this question before yeah

[spark plover]

im struggling to remember how identities interact with one another

i understnad now why quoitent identity worked for this

but at the time i could not see it is there like any way for me to be able to recognize these i dentites better?

[silent plank]

-cot(t) wasn't distributed properly
and none of those options seem appropriate for the last part

[spark plover]

thats pearson for you

making things more complicated then it should be

(I really shouldve taken in person classes for this)

[silent plank]

wait, misread the expression

i suppose its technically ok, misread cot for cos
but for the last one, it should be a combination of quotient and double identity

[spark plover]

wdym?

[silent plank]

quotient identity by itself would only lead you to
= -cot(t) + 2sin(t)cos(t)
which isn't quite the final result

[spark plover]

but wait

oh wait nvm

continue

no wait

yeah wait a minute

thats the exact reason why i got confused on why quoitent idenity would work for this

[silent plank]

don't worry about their options
and first focus on what you'd normally do

[spark plover]

i see now

but everytime i try to solve it at the time i cant see the options

i have trouble trying ot piece what the next step should be to get it to the result I want

like just a bit before

[dreamy geode]

I don't get the 5 and I have an answer to 4 but I don't think it's right..

[obsidian harness]

what did you try for 4?

[atomic thicket]

This is pretty obvious

Since angle of depression is 5°

The angle of elevation would be 85°

[atomic thicket]

Is it not?

[silent plank]

no

[atomic thicket]

Why not

[silent plank]

by definition / alternate angles on parallel lines

angles of depression and elevation are congruent

[atomic thicket]

Wdym

[atomic thicket]

Yes

[silent plank]

they'll be the same size

[atomic thicket]

You mean, angle of elevation would be 5°?

[silent plank]

yes

[atomic thicket]

Well

Oh yeah

Sorry dude

Lol

I always mistake angle of depression as the third angle

[dreamy geode]

Tan=26/80
Tan= 0.325
Tan-¹(0.325
=18.00

Or was it

(26)Tan80°
=297.18

I saw these solutions on yt I'm not sure which is true or am I even doing it right

[signal vapor]

Why divide 26 by 80

???

[south garden]

how do i solve this

[obtuse quiver]

Anybody know (b)

I got 22

[obsidian harness]

what did you do to get there?

[ionic cairn]

i forgot how to do these and would like some help if possible

[obsidian harness]

search up similar triangles

by angles in parallel lines, angle QRP = angle STP
angle RQP = angle TSP as well

hence you have angle-angle similarity, between triangles QRP and STP

can you now set up an equation about the side lengths ratios of both triangles?

[dreamy geode]

Idk, what about the other one?

[obsidian harness]

well firstly, you shouldn't be using 85 deg but 5 deg

try drawing the setup out

you should then have the opposite side to the 5 deg angle = 26 m
and the adjacent side to the 5 deg angle you don't know, so we'll call that x

and yes, tan theta = opposite/adjacent is the right trig ratio to use

if you change 80 to 85, one of the methods you wrote is indeed correct

you need to think through this yourself and figure out how to get to the correct answer, not just what the answer is

[dreamy geode]

Oh

It is supposed to be 85 sorry

[dreamy geode]

Yep that's what I need

[obsidian harness]

yep, then continue from here

[ionic cairn]

qs/ps = pr/pt
x/15 = 62,5/25
62,5/25= 2,5
x/15=2.5
x=2.5*15=37,5
this is what i get but x is supposed to be 22,5

[obsidian harness]

you're not being consistent, that's why

[ionic cairn]

eh?

[obsidian harness]

QS and SP correspond to RT and TP

[tiny halo]

sorry to bother but could anyone help to check some of my answers for a trigonometry worksheet (6 questions, the absolute basics)

[obsidian harness]

honestly just go to the help channels

!help

[lime crown]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[obsidian harness]

and you can ask your question directly

[obsidian harness]

if you have QS/PS, then PR/PT is not correct

[ionic cairn]

yeah i noticed what i did wrong

ty

[obsidian harness]

no worries!

[ionic cairn]

have a blessed day mate

[obtuse quiver]

Found the magnitude of oa,ab, and ob and then cosine rule to find aob and then 0.5 x sides c sin (the angle)

but the thing is when there’s |a|=|b|=1 given

Aren’t we supposed to use that only if the vector is in terms of only a and b and not both

That’s just what I wanna understand

[sudden solstice]

Guys I need help my teacher told me to do this and I don’t know how 😭

And I think I got some answers wrong

[solid needle]

did you even see this

[sudden solstice]

Idk what that means

Like that long message he posted

@solid needle

[silent plank]

yes/no answers to which ones are correct

also refer to Ann as she

[sudden solstice]

Wdym by that

[silent plank]

*she posted, not he

[sudden solstice]

Oops

Like how do I find them out is what I am aksibg

Asking*

Not to just give me the answers

And tell which ones are wrong

[silent plank]

your initial request implied you wanted to know which ones you got correct
assuming you used valid methods to obtain those, that cuts the list of stuff you need assistance on

57 is a lot to go through one by one

state specific ones you want to focus on

[south garden]

Deepseek, I gave it the question but I didn't understand the solution

It's C

Here's a better picture

Sorry for the poor quality pictures, my phones front camera is broken

Yes

[honest idol]

This is my type of channel.

[south garden]

So a and b's values ?

I have to hop off rq, you can ping me the explanation if you solve it

[thin hearth]

Apparently they’re teaching us probabilities in geometry now (I’m not sure if they’re supposed to)

I’m not sure how to calculate number four where it says “Tara has 10 pennies, 4 nickels and 6 dimes in her purse. If she were to grab two coins, P(total of at least 15 cents)?”

My teacher told me to make a table to solve it but I really got stumped there

[regal wedge]

here’s my idea. If she every chooses a penny she can’t get to 15, so she has to take a dime and a nickel or 2 dimes. Add up those probabilities and divide by number if possible 2 coin pairs and you got your answer

the table i’m guessing is doing the same thing but drawn out

[dreamy geode]

May somebody help me know how to do the 5th one?
I was confused on how to do the figure and most probably solving it..

[zealous pike]

Can't one of the sides be given by solving for:

4x + 2y = 400
xy = 400?

it is giving me an imperfect square which is making me think that it is a wrong approach

[south garden]

Yeah

[normal sierra]

nah it seems correct

[sudden solstice]

Help me understand this

[dark sparrow]

,rccw

[dark sparrow]

@sudden solstice have you made any changes on this since i wrote down that table detailing what you got right and wrong?

[zealous pike]

So it will indeed give square root of 147200

[sudden solstice]

I only need someone to tell me how to do it not what I get right and wrong

[dark sparrow]

apply various properties of angles formed by intersecting lines, or by angles formed when two parallel lines are intersected by a third.

[sudden solstice]

I still don’t understand

[zealous pike]

I'd try finding the right angles first

That question can be solved through the notions of property of angles alone

[vocal charm]

Do you still need help?

[pale girder]

This looks fun

[sand marlin]

have yall ever tried heroin

its fun

[gentle haven]

Like the area of a triangle formula?

Pretty cool but really impractical for what I used it for

But it works

[trail tendon]

that one triangle drug addict guy?

[gentle haven]

For what I used it for

It was not very good

But yeah it can help in other cases

I don't remember exactly but I remember it involved trig and could be solved a lot quicker with b*h/2

Ohh ok

[somber coyote]

Vanellope von Schmugz

[upper karma]

I need help rearranging sectors

[south garden]

I haven't gotten the opportunity but I doubt they'll test us on something like that today

[topaz shore]

polynomal 🏁

how about

chat gpt solves it for us 😏

geometry did not teach me that 🙏🙏

seems like just simplifying it

foil 🗿

[topaz shore]

ok
foil the left expression to
2(cos yx)

make sure to use inspection method on ur exam if theres any systems 👍🏻

[somber coyote]

Vanellope von Schmugz

[topaz shore]

ok then

foil left to

erm

😭

dawg

honors algebra 2 w/ trig

is my level

THAT

is not

i know what all the funny little triangle side formulas are

no idea what doa is

ok now i know

mensa brain has absorbed it

im evolving

[rapid rampart]

Just came back after missing a whole chapter used ai ngl.. I need to know not sure on any of these

[rapid rampart]

Alright I ended up redoing some of my answers

[rapid rampart]

I think I’m goood now

[signal vapor]

How do we prove the identity cos(x+y) = cosxcoy-sinxsiny without the unit circle?

[dark sparrow]

there is a way to do it using nothing but right triangles actually, one moment

@signal vapor

[sudden solstice]

Yes @vocal charm

[sudden solstice]

Yes cause I doing know how to do anything on this page ☠️ and I think I got some wrong 😑

[radiant anchor]

so like the given radius is 4cm and the central angle is 45 degress what is the area of the sector

i was wondering if my answer is correct 0.62cm squared

cuz the formula given to me by my teacher was the area of the sector - area of the triangle

[silent plank]

did you mean you wanted area of the segment?

[meager glacier]

I might be trash, but trig proofs have been kicking my ass lmao

[meager glacier]

I think I got them, one i didnt even know how to approach because i wasnt taught the difference of cubes formula

im a lil nervous on skipping precalc so im investing hours into trig

[somber coyote]

Vanellope von Schmugz

[meager glacier]

i do have a bit of a question on an identity
SinXCosY
And
CosXSinY
Are two different identities which seems weird to me because you can move around multiplication due to the commutative property of multiplication

product to sum ID

[south garden]

yeah ?

oh yeah I wrote my trig test today

[meager glacier]

I guess its just a context thing

[south garden]

I don't wanna 😫 . I wrote my last math test for the term today

and I'm writing physics tomorrow so I gotta lock in for that

yeah

It was a pretty easy test

[somber coyote]

Vanellope von Schmugz

[meager glacier]

so glad i dont have to memorize all these, im close to laminating my unit circle sheet with all my IDs written on them

[somber coyote]

Vanellope von Schmugz

[meager glacier]

I was so relieved to find out most engineering courses allow you to have formula sheets

yeah i need to look up what the functions mean physically, im visual learner so SEEING cosine (as being just a plotted value of your x coordinate) on the unit circle was super helpful
Wonder if i can do the same with the identities

[signal vapor]

Thanks

[remote wyvern]

hello guys is some of you all had problems with math and how you solves them? cause I don't know why but don't matter how hard I try I'm still not good(especially with geometry...)

[livid plaza]

start with simple questions. Solve a lot of them. Slowly move on to harder ones. This will make it easier to solve tough problems. Never start with hard questions. You'll feel like quitting if you do so. Hope this helps :)

[civic pond]

dawg i suck at matrix 😿

just watched like 2 videos i dont get it much

[livid plaza]

did you try to solve some questions?

[civic pond]

im so slow at it tho

i did

[livid plaza]

well, atleast you can do it

[civic pond]

the formula is confusing

its so weird

[livid plaza]

PrACtIce mAkeS A mAn PerFEcT

I don't know about matrix

I just started 10th so..

[civic pond]

i dont need this in life ugh

same im in year 10 as well

i gotta give igcse tests in april im gonna die

[livid plaza]

I mean 10th class

in school

[civic pond]

me too dawggg

[signal vapor]

What is that

[livid plaza]

matrix in 10th? That's weird

[civic pond]

yehh its different education systems ig

[civic pond]

UK school test but for international schools

its so hard omg

[signal vapor]

Oh

Best of luck

[civic pond]

thank uuu 💙

[livid plaza]

When I search matrix in google, I get the movie lol

[remote wyvern]

alright, I'll try

[civic pond]

search matrix math lol

[signal vapor]

There are no formulas in that

Determinants ??

[livid plaza]

ik

[civic pond]

there was

like for adding them

u gotta criss cross it

[signal vapor]

Oh

[civic pond]

so weird

[signal vapor]

I remember watching a 3blue1brown video

It is really good

[civic pond]

ohhh this channel is nice

ill def watch some vids later

[livid plaza]

I wanna learn too

pls share the channel

[civic pond]

https://www.youtube.com/@3blue1brown

[livid plaza]

oh ok

[livid plaza]

didn't see this message

[livid plaza]

yeah this guy's good

[sudden solstice]

Explain this to me pls

[sudden solstice]

Please explain how I get the answers and not just tell me which ones I got wrong

[hollow lichen]

Uhhhh

[dusty loom]

Wut du hell

[livid plaza]

Is this a joke or is this actually serious 💀 ?

[neat wigeon]

it's not that hard

just a lot

[neat wigeon]

u really just need to know correspondencing angles, vertical angles, that a straight line has 180°, triangles add up to 180°, opposite angles of a parallelogram are congruent, and more

[chilly glacier]

you just have to use the properties such as that of corresponding angles, alternate angles, complementary angles n all

[trail tendon]

if 16 is 45, what does that tell you about 31?

[chilly glacier]

16, 31, 35, 20 all are 45°

37 n 34 too

[trail tendon]

you're just giving the answers away 😔

[chilly glacier]

16, 31, 35, 20 are corresponding angles so they are equal

[chilly glacier]

37 is vertically opposite to 35 and 34 to 31, so they're also equal

bruh u need to learn these angles and properties

[vocal charm]

No need to be rude

[chilly glacier]

uhm... sorry... I didn't mean to..🙂

[vocal charm]

Like it’s quite apparent

[chilly glacier]

sorry dude...

[scarlet osprey]

Wait

Is this the wrong channel to send doubts?

I deleted it, I just read the rules my bad
I got confused by 'occupied'

[trail tendon]

this channel is fine, only help channels can be occupied not these

afaik

[scarlet osprey]

Oh I see

[idle goblet]

i have this demonstration
I have an isosceles triangle ∆ABC
CH is the height relative to AB
I have to trace the projection of H to AC and the projection of H to CB

the projection to AC is P
to CB its Q
if i project Q into AB (Q') and P into AB (P')
by construction it means that P'H = Q'H right?

[idle goblet]

oh
im the worst in class and the BEST one in class told me that im wrong

fucker

[vague token]

Did you learn what you were wrong about?

If yes, that's it

[idle goblet]

ah

what did i get wrong

[idle goblet]

yes but i aint the sharpest in maths
i always had a few problems with it

noo i got ghost pinged

😭

[bleak blade]

yeah because its symmetric

ofc theyre equal

idk what the so called best one in class is saying

[idle goblet]

my dude said 'how do u prove that' like twice
then said 'believe what u wanna believe'

bro..

[plain marten]

anyone knows how to do this?
its about the area of an arch with given angle and radius

[wet pond]

Anybody doing silly triangles

[fast junco]

Guys,can we use the menelaus theorem for any case(provided we choose the components correctly)?

[idle goblet]

its symmetry,
theres nothing to believe

H is the median of AB , and is also a point of the height, CH,
since the rectangle is ∆ABC isosceles (given by the book) projecting H into the two long sides, AC and BC, (thus forming a 90° angle) will have the same length for both (since H is median of AB)
and if i project the two projections on the base (AB) where H is located in, (lets call them P and Q) we get P' and Q' that by symmetry are equidistant from H, thus making them congruent

its not to prove

its by construction

if you want to school me on this

tell me at least why im wrong

oh wait

youre acting like

AAAA

sorry its not even 7 am im not thinking

sorryyy

im just going off what i wrote yesterday

lol

happens often to me too

[vague token]

You need a formula to solve it

As seems you understand Spanish, I give you a web in Spanish: https://www.areasyvolumenes.net/area-de-un-sector-circular/

[livid plaza]

translate.

[tough reef]

I don't know spanish but from the words here and there, it feels like they gave the radius and angle of each sector and asked the areas

[vague token]

It's about having to calculate the area of a circular sector having Radius and Angle

[visual elk]

Bruh how we supposed to understand when its Spanish explain pls.

[dark sparrow]

i would imagine that these:

R = 2
tan(EF) = 4/3
FB * BC = 3 sqrt(2)
calcule ("calculate") BG
are self explanatory

[obsidian harness]

it's Portuguese and you can use Google Translate on the image

I don't actually know Portuguese but I can figure it out from my knowledge of Spanish

"no gráfico a seguir" = "on the | graphic | to | follow" ~ on the following diagram
"se" means if and "e" means and

also Portuguese does have "diagrama" if that helps in any way

||sine rule on the triangle formed by AE and AFB gives BF = 4/sqrt(5)||
||so I can now find AF and BC of course, what's next?||

||AG/BG = BG/BC so I know if we find AG we're good||

there's just so many damn computations

[obsidian harness]

sure

I feel I'm going about this the wrong way due to it being inefficient

angle EOF is (EAF)/2 then there's a formula for sin(arctan(x)/2)

cause I have all this technology I just used WA or equivalent, but by hand it's sin^2 x = (1 - cos 2x) / 2 and now sub x = u/2 and square root both sides

so sin u = sqrt((1 - cos(u) / 2) = sqrt((1 - 3/5) / 2)

yeah I mean I knew the solution had to be a lot more elegant

ah wait that's a brilliant observation

so you can let opp = sqrt(5), hyp = 5, and hence adj = sqrt(20) = 2 sqrt(5)
so tan theta is indeed 1/2

I did not notice that yeah

yeah I figured out that the line was collinear but I didn't know how to use it

[upper karma]

Does anyone have spare exercises relating to this lesson? This topic in our school usually entails finding the measures of the sides and angles. I have exams tomorrow and I would appreciate some exercise resources. Thank you!

[obsidian harness]

there are formulas for $A \circ B$ and $B \circ A$ where $A$ = regular trig functions and $B$ = inverse trig functions

[somber coyote]

south

[plush surge]

someone gave me this in a work as a challange. I have no clue how to calculate the side X. Basically, the length of the square is 100 meters and the width is 50 meters, the surface of the curved section down is 2500m↑2 and the length of the leg of the right triangle is 25 meters and I need to calculate the hypotenuse X. Annoying is the curve, there is no informations to the curve

please help someone

This is the original paper

[lapis moon]

@tulip bone continued from your question: #help-3 message
my desmos graph shows that this step is wrong
https://www.desmos.com/geometry/ejctcuojx6

This type of questions is textbook exercise on the Co-side Theorem (共邊定理, a.k.a. Dovetail Theorem (燕尾定理))
https://baike.baidu.com/item/燕尾定理/10828082

[merry vessel]

hey does anyone know if it's possible to solve this, btw diagram isnt drawn to scale

[cunning lion]

what are you trying to solve for?

[covert ermine]

Can someone tutor me?

[brave dirge]

Everytime I ask ChatGPT to calculate cos(2x), it never can on the first try, lol. Anyone else notice that?

[trail tendon]

wdym by "calculate cos(2x)"?

[brave dirge]

For example, if I ask it to calculate cos(2x) given that tan(x) = -20/21, it hasn't been able to for like 5 different times I've asked it, lol

[lime dune]

well that should be a strong sign to

not use GPT?

!nogpt

[lime crown]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[brave dirge]

I use that and Deepseek to check my work sometime, haha

[lime dune]

don’t

they legitimately have no idea what they’re doing

[brave dirge]

Deepseek doesn't have the same issue, I thought it was interesting, lol

[brave dirge]

Not beyond a certain depth, but I'm fairly certain both of them can calculate a double angle 💀

[lime dune]

you just said gpt couldn’t do it consistently

if that isn’t a red flag idk what is

[brave dirge]

For cos(2x), specifically

The others were fine

[lime dune]

and let me ask you

is that a sign of a well designed calculator/assistant?

of course not

[brave dirge]

It depends on ratio between valid/invalid responses

[lime dune]

it cannot actually do math, all it’s doing is pattern recognition “hmm what word should go next?”

[lime dune]

if properly used wolfram will always be 100% accurate

[brave dirge]

What are we to make of AI providing the same answers a textbook would then?

[lime dune]

why have so many grade school students so blindly embraced gpt usage 😭

[brave dirge]

Assuming the textbook is correct, then the AI would be as well

I'm not arguing that it is reliable at any depth or complexity, but for fairly standard Trig exercises (like calculating double angles), AI seems proficient

[lime dune]

why is your first instinct to use a “tool” as unreliable at gpt

[brave dirge]

Thats probably the equivalent of asking it to calculate the integral of 1/x^2 from 2 to 5, lol. I'm willing to bet it will return the correct value

[lime dune]

is it really too much effort to just look up the double angle formula and then plug it into wolfram or smth

[brave dirge]

Thats the thing, I'm arguing against the notion that it is unreliable across all depth

[brave dirge]

Never said that 💀

[maiden brook]

most textbook problems arent meant to be hard

like it has potentially the right approach for this but messes up badly

[fervent pine]

how can i prep for honors geometry next year

[upper karma]

how old ru guys

[trail tendon]

6300

[primal flare]

omg pls help 💔

[upper karma]

can someone explain to me how hyperbolas work

I don't get how to find the constant and the x,y values

[inland tangle]

do you know what $FC$ here equal to?

[somber coyote]

C

[primal flare]

no 💔

i swear thats all i need 🥀

[inland tangle]

you know AF = radius F circle and BC = radius C circle right?

[primal flare]

yeah????

OMG

ITS 7+17

OMG

YOU SAVED MY LIFE

THANK YOU SO MUCH

[solid needle]

why dont you just use wolframalpha, seriously

if you're going to check your work, use something that we know is reliable

even if chatgpt is reliable at certain depths (which im still not convinced it is), at what point does it start to become unreliable?

why not just use something that is reliable

"hey im gonna use this tool that has a 2% chance of cutting my finger instead of this tool that has a 0% chance"

why

this generation smh

[brave dirge]

Lmaoo, I actually never used it!

I've mostly just taught myself Math all this time actually and none of my classmates ever recommended it to me before

But I just checked it out and I love what I'm seeing, definitely going to being using this while doing math from now on

[solid needle]

are you referring to wolframalpha

because if so, good

[brave dirge]

Yeah!

Its reallyyyy good

[solid needle]

ive been using this thing since i was in high school

its insane that this thing exists and students are still using chatgpt

like actually mad

[brave dirge]

I know!

I feel the same after seeing it 💀

[solid needle]

good, tell your friends

[brave dirge]

Sadly, I don't have any math friends, lmao

No one in my life would gaf 😂

Its a lonely road

[solid needle]

or just mention it when it comes up

whenever its relevant

[brave dirge]

How reliable do you consider ChatGPT or Deepseek to be in explaining math concepts?

[sinful shoal]

yo guys can someone tell what square root of squareof ....-1 is?

[trail tendon]

i

[dark sparrow]

can you write that properly?

when you say ``square root of square of $-1$'', do you mean $\sqrt{(-1)^2}$? bc this is $\sqrt{1}$, or just $1$.

[somber coyote]

Ann

[trail tendon]

didn't read that properly

[dense pilot]

Hi, this is all correct right?

Was a bit confused about the placement of the square

[obsidian harness]

Yep all cor

*correct

[livid plaza]

yup

[obsidian harness]

you just would write $\sin 3^2 = \sin 9$ btw

[somber coyote]

south

[high vault]

what's the best way of expressing angles? radians or degrees?

also how on earth do i memorize the unit circle

[dark sparrow]

depends on context but probably radians are better

[dark sparrow]

definitely don't memorize the entire thing

[silent plank]

depends on what you're doing/whom you're communicating with

memorise the first quadrant, you can get the rest through reflections

[dark sparrow]

silly mnemonic for the first quadrant

[obsidian harness]

funky ass hand

[dark sparrow]

funky how

it's literally mine

[obsidian harness]

oh.

[obsidian harness]

you just have small hands

I had a friend with tiny hands like yours

[silent plank]

Diagram not drawn to scale

[dark sparrow]

where are you getting that i have small hands

[obsidian harness]

the watch? idk

[dark sparrow]

there's no scale reference in the pic is there

[obsidian harness]

the proportion just doesn't look right on your hand idk

[dark sparrow]

ok we are off to #「helpers-lounge」

[crystal oar]

guys can someone teach me circular measure, im about to have a mental breakdown

[dark sparrow]

1. what do you mean by "circular measure"?
2. are you able to calm yourself down enough to not be on the brink of mental breakdown?

[clear sedge]

guys, who can help with stereometry?

[left plover]

Is khan academy trigonometry good if you forgot everything

[worn scroll]

for sin and cos just remember it is always sqrt 1 2 or 3 divided by 2

then just imagining unit circle cos is the x length and it is longer with smaller angles

[obsidian harness]

yep

also org chem tutor has better videos than Khan

[obsidian harness]

hard to measure objectively, sure

but omg Sal Khan talks at a snail's pace

if I watch org chem tutor I know I'll see 2 fleshed out examples or more in 10 minutes and I'll actually be learning new stuff each minute

like 2x speed is not a permanent solution for a bad video

same I can't judge

I was really turned away due to a few bad impressions

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-2/v/trapezoidal-approximation-of-area-under-curve

fuck this is really shit compared to org chem tutor

I'm not saying he's the best, but like there's so much better out there

they're still using 10 year old videos? after so much funding??

omg

that's goated

yeah mmm at what point is that just tutoring then hmm

like connecting different topics with each other is really nice tho

and making corollaries as you said

damn, send me a link to the site

wow

do you think that Spanish speakers would want to use it

if it's really that good

just turn on auto-generated subs to understand the videos

so much maths online

oh yeah science but you don't need to do experiments to know stuff, haha

nah thanks for the offer

but Aus is a lovely enough country for me

[half zenith]

anyone can help with the answer (want to check against someone else's)

[hidden marsh]

can any tell me what eccentric means

[solid needle]

there is a technical definition for the eccentricity of a conic section

but we are going to skip that for now

but basically it is a value that describes the shape of the conic section

for circles its 0

ellipses are between 0 and 1, where the more flat it is, the closer to 1 it is

if your eccentricity is 1 or higher, you'll get other shapes like hyperbolas or parabolas

for ellipses in particular, the eccentricity is e=c/a

c is distance from focus to center, a is semimajor axis

this definition can extend much further to generalize to all conics but you can go look that up if you want

[sharp viper]

I'm starting to learn about optics, and I saw Newton's equation for a curved mirror f^2 = x_o x_i where x denotes the horizontal distance to the focus. I recognize that for a point on the principal axis, this means its image is the circular inverse of itself with respect to the circle with diameter spanning from the center of curvature to the mirror vertex.
Is there a simple geometric proof for this fact?
Is there a similar geometric relation for points not on the principal axis (maybe for simplicity, we consider the paraxial approximation)?

I found this post related
https://physics.stackexchange.com/questions/552648/circular-inversion-and-spherical-mirrors

[woeful shell]

circle

[upper karma]

Who can help me

[open flame]

send the question I might be able to

Though I wasn't great at geometry

[latent gull]

@upper karma What you need help with?

[upper karma]

its a lot of questions

I cant find an AI to help me with it

Is this correct

[latent gull]

give me a sec... let me look into it

[open flame]

oh it's just that

no it's wrong

[upper karma]

Damn

[open flame]

hypotenuse is in front of the 90 degree angle

imagine a line going forward from the 90 degree square mark

it's the diaganol line

[latent gull]

LN NM = leg

[open flame]

yeah

[latent gull]

LM = Hypot

[open flame]

no LN is the altitude

not a leg

[open flame]

the mean is just taking the average

it would be D

[frosty lintel]

geometric mean is different

nah

geometric mean is not average

[open flame]

oh it wouldn't?

[frosty lintel]

thats arithmetic mean

its stupid

geometric mean is like

u add rhe numbers up

and take the root

like

ok if u have

3 4 and 5

u go

cube root of 3+4+5

not add im dumb

multiply

cube root of 345

[open flame]

oh it's root n of all the number mulitplied together

[frosty lintel]

if u have 3 4 5 and 6

u go fourth root of 345*6

[frosty lintel]

yeah

[open flame]

is there latexer here

[upper karma]

this was right the first time

[open flame]

,,\sqrt[n]{a * b * c... etc}

[frosty lintel]

it made the 4 italicized instead of multiplying thats dumb

[upper karma]

and it wasn’t D 💔

[somber coyote]

rey

[open flame]

that's the best way I can explain it

your problem would be

,,\sqrt[2]{2 * 8}

[somber coyote]

rey

[open flame]

do you get it?

[rapid valley]

Is that not a?

Geometric mean is a triangle that has an altitude if I remember correctly

[polar solstice]

What’s the answer to this?

[wet pond]

!noans

[lime crown]

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

[wet pond]

it’s asking you how you’d manipulate triangle U so that it was a perfect overlay of triangle V

given the options you should be able to determine the answer

[pliant monolith]

How do i solve this?

[bleak blade]

Take ln

[pliant monolith]

what after that?

I tried it but had to use L'Hospital too many times

[bleak blade]

Hmm

[pliant monolith]

is there any other easy way to do it?

[bleak blade]

I dont thunk so

Also wrong channel

#calculus

[pliant monolith]

ah sorry

[somber coyote]

Vanellope von Schmugz

[rapid valley]

A translation then a rotation

[neat kelp]

How to solve this?

https://youtube.com/shorts/0n2cpp5K1ms?feature=share

[obsidian harness]

turns out this diagram has this fact

[spark plover]

im lowkey struggling cause I forgot something

im in the middle of doing trig equations and i forgot how to turn

,,\2sqrt{3}/2

ill figure it out at some point

this

into these

i forgot how to convert from secant to something that would be in sin,cos, or tan

to get my radians

[dark sparrow]

sec(t) = 1/cos(t)

[spark plover]

yeah but i think the way i was doing it was wrong

since i switched the numerator and denominator around

[dark sparrow]

show your work

[dark sparrow]

2 sqrt(3) * 2 sqrt(3) isn't 4

and also you went about this rationalization in a way that i can only describe as laborious

[spark plover]

thats a one

mb

[dark sparrow]

2 sqrt(3) * 2 sqrt(3) isn't 1 either

[spark plover]

i figured

i just didnt know what to do

[dark sparrow]

you overthought it and forgot how arithmetic with radicals works

[spark plover]

yeah ive been going at it all day

i think my brain is done for today

[spark plover]

well i dont really have a teacher tbh

i have the material from pearson and have been using that

and sometimes i do that

[dark sparrow]

that's your mistake

you are tired

[spark plover]

yeah i see it now

loooorrrrrdddddddddd

1

its supposed to be 1

[spark plover]

yeah but can you explain to me a less labrorous way to go about it?

i see too many issues now

my brain is catching up to why this screwed me up

[spark plover]

thank you so much

i think what messed me up was the 2*sqrt(3) being together

and then like you said i began overthiking

im gonna go to sleep now and make sure i dont do that again 😭

[sharp viper]

Beyond this you can construct vectors (1,2) and (3,1), the cosine of the angle gives 1/sqrt(2) hence 45 degrees

Alternatively tangent difference identity works with m1 = 2, m2 = 1/3

[obsidian harness]

yeah a synthetic way is probably very inventive

[obsidian harness]

next step: ||use similar triangles to conclude that ABC is 4 times larger than AFE and hence AC:AB = 2:1 ||
||but CD:DB = 2:1 also, so AD is an angle bisector and the result follows||

[obsidian harness]

,w sqrt((2 - 1.2)^2 + (2 - 0.4)^2)

[somber coyote]

Results provided by WolframAlpha

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

Requested by sooouth.

[obsidian harness]

your coordinates of E are wrong: they should be (1.2, 0.4)

I think you know the idea but that minor error changes everything

[obsidian harness]

yes y = x/3 after all

oh I see I didn't know you took the origin to not be at the bottom left

that makes sense, I just assumed haha

IDK anymore

[obsidian harness]

Oh right yes it is 45 degrees

Don't know how you got there but yep

[outer reef]

<@&268886789983436800>

[spark yacht]

I want to prove that angle D = 90-1/2A

lines bisect angle a b and c

nvm im done

[granite marsh]

aah

i just saw the question

any other question?

anyone

[spark yacht]

@granite marsh

this one is easy

[granite marsh]

it will use pythagoras theorem

butw what's AO2?

[spark yacht]

can I get detailed soln

with diagram btw 😏

[granite marsh]

I just want to ask that AO2 is included in the equation ar not

[granite marsh]

working on it

[obsidian harness]

not included

[spark yacht]

not included

I mean why would it be

[granite marsh]

done

just doing it in systematic way

[spark yacht]

send pls

[granite marsh]

yes

the photo with diagram is 1st page

@spark yacht ☝️

[spark yacht]

yes

[granite marsh]

is it clear enough?

?

should I explain anythying ? @spark yacht

??????

[spark yacht]

yes from the start pls

[granite marsh]

We just used pythagoras theorem

in triangle AOM and BOM to get AM^2 = BM^2

then we again used Phythagoras theorem in triangle AON to get AN^2

then I found a relation between AM and AN with the information given:- AB=2AC

then equated equation 1 and 3

and got the answer

simple

[spark yacht]

hm nice

[sudden solstice]

I am cooked guys I got a 40 on my test in geometry

[granite marsh]

out of?

[spark yacht]

I suck at geometry so its okay

[sudden solstice]

40%

[granite marsh]

oh

[sudden solstice]

We doing this thing hold on let me find picture of it

[spark yacht]

out of 100

[sudden solstice]

I got this wrong and ik I did lol cause when I put it into ai now it says this is answer

I am cooked

[granite marsh]

Are TS and VW parallel?

[spark yacht]

it was easy how did u mess up

[sudden solstice]

.

[obsidian harness]

yeah I assume those are the parallel arrows

[granite marsh]

If yes then AAS is correct

[obsidian harness]

I mean

easy for you lol

easy for us but not htem

[sudden solstice]

Yea

[spark yacht]

yea

but good luck for next test

i want a 100 from u

[sudden solstice]

I was using 1% of my brain

[spark yacht]

how do I improve my observation

in circles

I can grasp whats going on in other shapes like triangles and quadrilaterals

[sudden solstice]

Yea my brother is in the same class as me and he told me when he got a 57% “I am gonna run up the hallways naked” and in front of our teacher

[granite marsh]

Just apply all theorems that can be used in the question or check which theorem can be used in the question, rest is practice

[sudden solstice]

Ayo

[spark yacht]

I thought angle ade is equal to abe which is true

[sudden solstice]

Oh

[spark yacht]

But I ignored it idk why

can someone drop some algebra on algebra

[little oriole]

1. Understand the Basics Thoroughly
   Before you can observe patterns, ensure you have a solid grasp of foundational math concepts. The better you understand the core principles, the more easily you'll spot important details or trends in problems.
2. Look for Patterns
   Geometric Shapes: In geometry, observe how different shapes relate to each other, how angles change, or how symmetry plays a role.
   Algebra: In algebra, notice how certain variables behave. Look for patterns in equations or factorization.
   Functions: Observe how a function behaves, especially when graphed. Does it have symmetry? Are there any periodic patterns?
3. Work with Visuals
   Draw Diagrams: Especially in geometry or calculus, sketching out problems can help you see things more clearly. Visualizing math can help in spotting key relationships between elements.
   Graphs: Plotting equations and looking at them visually often reveals trends, slopes, or asymptotes that might be hard to spot algebraically.
4. Practice Mental Math
   Training your brain to quickly recognize patterns in numbers or equations helps improve your ability to spot errors, shortcuts, or important relationships when solving problems.
5. Examine Problems from Multiple Angles
   Break it down: In word problems or equations, try different methods to approach them. Sometimes a geometric approach works better than an algebraic one, or vice versa.
   Try Simplifying: Simplify complex expressions or equations and see if any patterns emerge. For example, factoring quadratics or simplifying radicals might give you new insights.

[spark yacht]

yeah I didnt see the arc

[little oriole]

6. Study Solutions Carefully
   When solving problems, take time to understand the steps involved. If you made a mistake, try to figure out where your observation went wrong.
   Review examples and try to reverse-engineer the solution. This will help you notice strategies or techniques that can be applied to similar problems.
7. Look for Symmetry or Invariance
   In mathematics, many problems have symmetrical or invariant properties. Whether it’s symmetry in algebraic expressions, geometric shapes, or number patterns, recognizing these can help simplify your work.
8. Play with Problem Variations
   Try solving slightly altered versions of the same problem. For example, change the numbers in an equation or modify the geometry of a shape. This will train you to observe how small changes affect outcomes.
9. Use Problem-Solving Strategies
   Apply various problem-solving strategies such as working backward, making substitutions, or breaking problems into smaller parts to notice how the structure of a problem evolves.
10. Practice Regularly
    Like any skill, mathematical observation improves with practice. Consistent exposure to different types of problems helps sharpen your observational and problem-solving skills.

[spark yacht]

chat gpt ahh answer

[granite marsh]

Wdym

[little oriole]

blud i typed it for ya

[spark yacht]

yea thanks tho

[little oriole]

i dont have nitro so had to copy half way

lawl

chat gpt tf evn is that tbh ?

[spark yacht]

some cool

like fe

[spark yacht]

!chatgpt

!nogpt

[lime crown]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[spark yacht]

what was it

[little oriole]

what is it....lawl ?

[spark yacht]

If they said

other lines were altitudes

I couldve bashed orthic triangle

[sudden solstice]

I study with it I don’t use it as answer cause my teacher is smart ☠️

[spark yacht]

I struggle with geometry

[spark yacht]

what

[spark yacht]

yeah i got it dw

[sudden solstice]

Fr

[sudden solstice]

Alr

[spark yacht]

😂

[sudden solstice]

.

[spark yacht]

how old are u bud

[granite marsh]

.

[sudden solstice]

Erm

.

[spark yacht]

bro

u finna get banned

[granite marsh]

should we report?

[sudden solstice]

On god

[spark yacht]

<@&268886789983436800>

this is for your own safety bro

[sudden solstice]

lol

[spark yacht]

minimum age for discord is 13

[granite marsh]

bro discord has age restriction

[little oriole]

lawl

[granite marsh]

come when u r 13

[little oriole]

dude just gave up

[spark yacht]

lol

u got any

fe

[granite marsh]

?

[little oriole]

fe ?

[spark yacht]

oh he was in grade 6th

how would he have fe

functional equations

[granite marsh]

what is ur grade?

12th?

[spark yacht]

9th

[little oriole]

dayum bro...............creating ur own short terms

[granite marsh]

gud