it's time to eat for me XD
#geometry-and-trigonometry
dark sparrow
bon appétit
vestal pine
merci
umbral rivet
Hola~
Es mi chat favorito
I'll google how to say chat in spanish
One sec
Es mi charla favorita *
upper karma
Me gusta pizza ?
dark sparrow
mmmm
umbral rivet
New profile pic :D
dark sparrow
yeah
umbral rivet
:3
dark sparrow
it's a selfie that turned out especially good
umbral rivet
Sure :3
median void
Why are you talking in Geometry anyway?
foggy oxide
lol
finite fossil
completing the square. express in simplest radical form. x^2 -6x +4 =0
anyone wanna lend a hand or brain XD
azure storm
=tex x^2-6x+4=x^2-6x+9-9+4=(x-3)^2-5
charred spearBOT
finite fossil
so (x-3)^2 -5?
azure storm
well yeah
(how i did it :
its gonna be (x+b)^2+c, so i know 2bx=-6x => b=-3, then just make it work)
finite fossil
Alright I got one more for ya. 2x^2 +4x = 12
I would try to learn how to do it myself but i've gotta leave my house in 6 minutes XD
azure storm
not gonna give the answer straight away one more time x)
try to do it and i'll correct
finite fossil
Im not exactly sure where to start. where did you get the +9 -9 from?
dark sparrow
=tex x^2 + bx + (b/2)^2 = (x + b/2)^2
charred spearBOT
dark sparrow
@finite fossil does this make sense to you?
azure storm
its gonna be (x+b)^2+c, so i know 2bx=-6x => b=-3, then just make it work)```
it was just to explain where the 4-9 came from, because i force b=-3, so it leaves a +9@finite fossil does this make sense to you?
finite fossil
I've gotta go for the night. ill be back to figure it out
dark sparrow
...welp ok
foggy oxide
i know this haves a geometric interpretation, but why here if no one showed the geometric one ?
lean girder
=tex x^2-y^2=(x+y)(x-y)
charred spearBOT
charred spearBOT
-0.80115264
lean girder
=calc sin(pi)
charred spearBOT
1.2246468e-16
forest dove
There's bot testing channel, check the side
vale raven
Radians, but use the bo-
forest dove
But this is odd, why not 0?
charred spearBOT
1.2246468e-16
vale raven
They do silly things
It might just be some sort of rounding error, not sure about that one
when sin is implemented it does estimations which are close enough
azure storm
i'd bet on not having all pi decimals, so not exactly sin(pi) but sin(pi-something)
=calc sin(0)
charred spearBOT
0
charred spearBOT
-2.23191218e-10
vale raven
azure storm
=calc sin(10^100*pi)
charred spearBOT
-0.14245226
azure storm
mb
foggy oxide
@vale raven
Kaoffie - Hoje às 07:23
They do silly things
computers don't do silly things
humans do
vale raven
Humans tell computers to do silly things ;o
simple storm
PEBKAC.
Problem exists between keyboard and chair.
there are so many lovely little acronyms for human error 😄
trim belfry
hello, i just have a quick question thing about p-norms, p-norms are defined like this according to this https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm
charred spearBOT
upper karma
yes
trim belfry
i noticed the property that the pth powers and the pth roots cancel out nicely when you nest the expressions for the lengths of lower dimensional vectors into the expressions for the lengths of higher dimensional vectors
charred spearBOT
trim belfry
oh yeah x)
dark sparrow
don't wanna run into troubles with negatives
trim belfry
im wondering if p-norms have any other interesting properties is basically my question
dark sparrow
hmm
they have a limit as p goes to infinity
the chebyshev distance i think it's called
hazy field
isn't it just called the infinity norm?
trim belfry
thats another name for it
dark sparrow
trim belfry
also "maximum norm"
hazy field
=tex ||\vec{v}|| = \max |v_i|
charred spearBOT
upper karma
its usually called the infinity norm afaik
trim belfry
Real infinity_norm_length(Vector<Real> vector)
{
Real maximum_real := 0;
for(Natural i := 1; i <= vector.length(); i := i+1)
maximum_real := max(maximum_real, abs(vector[i]));
return maximum_real;
}
``` 🤔im bad at maths so thats the best way i could express it :P
final prairie
The formatting :(
trim belfry
the formatting?
final prairie
Just person preference :p i like it when the { is on the same line
Space after the word for
{} even n one-liners conditions
Etc lol
final prairie
“Prefer” isn’t enough to tell how much it makes me cringe but nvm hehe
violet nest
who is Masa?
quasi lion
yes
dense crater
Does anyone have a video that takes you through
How to calculate 'X' if you get told CosX = 1/2?
Or
All Xs between two limits
dull egret
i know exactly 12 values of sin and cos and those are the obvious ones
just basing on the circle
more i dont deem neccessary
dense crater
Is there a way to calculate it without a calculator and without memorising?
Struggling a little.
charred spearBOT
dense crater
This is undergraduate maths and that scares me. So I think that it's likely they expected rote memorisation
I guess I'd better learn those same 12 values as you
dull egret
=wolf taylor series for cosx
charred spearBOT
Query made by @dull egret
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=taylor+series+for+cosx
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
dull egret
not much to learn, they repeat around the circle
so really only two to learn
bunch of values on there https://en.wikipedia.org/wiki/Trigonometric_functions#Computation
@dense crater
but ask which you actually need
the one for 1/2 is about the most basic anyways
dense crater
Well it's just an "introductory examination" example from last year for the Maths section of a university course
And it says
"Determine all values of X, so that cosx=1/2
And I remember 5 or so years ago being taught this in school
But for the life of me I couldn't remember how to do it
dull egret
well, cant help you with not forgetting things :P
dense crater
Haha of course.
Which 12 values have you comitted to memory, out of interest?
Just the most predictable ones like cos(x) = 1, 1/2, 1/3, 1/4 etc?
Or?
dull egret
no no no
12 aroud the unit circle
cos(pi/3)=1/2, cos(pi/4)=sqrt(2)/2, cos(pi/6)=sqrt(3)/2
out of which cos(pi/4) is just logical since it s a 45° angle
and by the pythagorean theorem it has ot be sqrt(2)/2 then
cos(pi/6)=sqrt(3)/2 just results directly from cos(pi/3)=1/2
again by the pythagorean theorem and the property that sin(x)=cos(x-pi/2)
dense crater
Thank you very much for this
It is appreciated - I'll try to commit one segment to memory
Or at least, understand one segment, then the rest is easy
Thanks for your help
dull egret
again, i m not in favor of memorization myself so yeah
crude kraken
=tex \tau = 2\pi
charred spearBOT
crude kraken
Worth mentioning for the unit circle that you can express fractions of how much of the circle is taken using tau
dull egret
i dont get the advantage still xD
crude kraken
Easier because you don't gotta remember as much :p
rather than having to know 2pi/3, you can just remember 1/3 and convert to 2pi/3
easier when working with smaller portions too :p
45% of a circle? 45tau/100, 9tau/20, 18pi/20, 9pi/10. Or 45tau/100, 90pi/100, 9pi/10.
dull egret
dont really see the point. i can multiply by two. yes i can. xD
foggy oxide
some things have to be "More difficult"
i think using only pi instead of tau would be better
if someone cant face this kind of difficulty then the teacher (or the student) know there is something wrong that have to be worked
and that's why i think pi works better than tau
dull egret
i just think it s so insignificant that just sticking with what has become the standard is better
upper karma
@dense crater
This is the background to my phone because I use this so much at work
foggy oxide
do you really have to memorize this ?
like
you don't have to memorize all those angles
foggy oxide
well
he don't need more than 30 45 60 and some unit circle knowledge to know all those angles
quasi lion
"This is the background to my phone because I use this so much at work"
" because I use this so much at work"
"I use this "
foggy oxide
he just need 30 45 and 60 so he know all other angles sin cos and tg value
this is useless
quasi lion
How do you know about his job?
foggy oxide
Am i supposed to awnser you ?
quasi lion
No it's rhetor
foggy oxide
Alright
You can show whatever you think
Whatever argument
whatever kind of sarcastic talking
quasi lion
I just say that if he says he uses it for his work, it might not be useless
foggy oxide
this won't change he only needs 30 45 60 and unit circle knowledge to know all those angles sin cos and tg value
quasi lion
At work, you don't want to remember how to switch between angles
foggy oxide
unless he likes to drawn the circle to the scale, it's useless
quasi lion
Just saying that as an engineering student
foggy oxide
This should be something spontaneous
quasi lion
Depends on the field you are working
foggy oxide
If you're going to say about subjective and relative things i could appeal for everything that it depends too
foggy oxide
If you're saying it's not useless, you're right, but it could be simplified
quasi lion
I am saying that in industrial organic chemistry, you don't use trig all day
foggy oxide
¯_(ツ)_/¯
quasi lion
I am just saying that in work, you don't want to remember how to switch between angles in that table and it's more convenient, more HUMAN-shaped and more WORK-efficient to have a table with all angles
foggy oxide
"ALL ANGLES"
foggy oxide
I can not emphasize more than this
quasi lion
It's not because you emphasize that it invalids my point
foggy oxide
Yes it's not a argument
And it's not because you point a fallacy that it invalids the content of the argument, also pointing a fallacy is a fallacy
Whatever, the table he showed does not have "all angles" , i would understand better if it had
foggy oxide
It was a expression
don't take it too literal
WELL, that makes everything even more useless, your argument is contradicted by what u said rn
quasi lion
No it isn't
Just saying, I use the 2pi/3 in geometrical chemistry and I look it on a table. Yes I am too lazy to do the conversion, and that's what human do.
foggy oxide
Of course it doesn't have all angles I meant implicitely all angles of the table
I am just saying that in work, you don't want to remember how to switch between angles in that table and it's more convenient, more HUMAN-shaped and more WORK-efficient to have a table with all angles
Suppose you need a sine
quasi lion
If you don't have the angle you are working with at work, then you just google it and not look at it in your table
foggy oxide
you would have to look into your calc, or do arc sum and difference etc...
That's the point !!!
You don't need the table anymore
quasi lion
Except that you forgot that some angles are work-related
foggy oxide
I didn't got what u mean by that
I think i got it now
nvm
Like, a specific angle for something specific
quasi lion
In some jobs, there are angles that are ALWAYS used.
foggy oxide
i suppose that's what u mean
ok, that's almost what i thought
I don't have job experiencie
quasi lion
Ah
foggy oxide
But ... Well those angles should be spontaneous don't you think ?
quasi lion
No they shouldn't
Spoilers: Most humans don't care about converting
Most humans are lazy
foggy oxide
XD
quasi lion
And lazyness is inherent to humanity
foggy oxide
Yeah, well, i always forget the tg of 30 45 and 60 but that's just mental cancer
sqrt3 1 and sqrt3/3
am i correct ?
quasi lion
Does it matter whatever the result is?
quasi lion
The thing that you forget is that playing with angles and trig is NOT a trivial thing.
foggy oxide
before typing
foggy oxide
But everyone should know that ...
foggy oxide
Everyone that works with trig
i got what u mean
and i understand your point
but some things would be easier ...
quasi lion
Things would be easier if all humans could learn everything perfectly, what's your point?
foggy oxide
when u face something new, you have knowledge to work with it
that's my point
fuck it's 10:41 pm i have to go to school in some hours (i'll sleep b4, actually i have school at 6:00 am)
foggy oxide
do you live in canada xD
quasi lion
I live in France
foggy oxide
thefuck
quasi lion
I work today/tomorrow
quasi lion
Sleeps at 11 pm, bad sleeping 🤔
quasi lion
🤔
foggy oxide
rip
quasi lion
@upper karma How late do you sleep?
foggy oxide
dude
in the vacations
i actually sleep during the day
and keep awake during the night
xD
quasi lion
Spoilers : Most people do that in video games discord
foggy oxide
xDD
foggy oxide
i played the game that u throw balls at people at school and almost fainted (idk how to say this game in english)
quasi lion
Pokémon?
vapid kettle
I've never seen the merits to sleeping late
if your clock doesn't compel you too
seems like a self-made crutch
quasi lion
@vapid kettle It's not a merit, it's a psychological disease
vapid kettle
Hot 😩
wraith fossil
Whats the difference between the resultant and the equilibriant when it comes to vectors?
Trying to solve this problem
topaz valley
the resultant is the sum of all the vectors
the equilibriant is the vector that, when added to the resultant, is zero
so pretty much the equilibrium is -1 * resultant
@TheKingPin#8504
Oh, he's gone.
wraith fossil
@topaz valley still here! just took a lunch break
how did you get -1 as the equilibriant?
when you say its the sum of all vectors do you mean add their magnitude?
which in this case im assuming is in Newtons
topaz valley
Not quite
wraith fossil
then what exactly are you summing?
topaz valley
hold on, I'm looking for the =tex syntax for vectors
wraith fossil
alright
topaz valley
ok, so given that information, we can make two vectors
=tex \vec{v_1} = 245 \begin{pmatrix}\cos{160}\\sin{160}\end{pmatrix}
charred spearBOT
topaz valley
=tex \vec{v_2} = 138 \begin{pmatrix}\cos{45}\\sin{45}\end{pmatrix}
charred spearBOT
topaz valley
or you can write it like
=tex \vec{v_1} = \begin{pmatrix}245\cos{160}\245\sin{160}\end{pmatrix}
charred spearBOT
topaz valley
then the sum v_1 + v_2 would be
=tex \vec{v_1} + \vec{v_2} = \begin{pmatrix}245\cos{160} + 138\cos{45}\245\sin{160} + 138\sin{45}\end{pmatrix}
charred spearBOT
topaz valley
so that result is the equilibrium
dense crater
@upper karma
"This is the background to my phone because I use this so much at work"
https://cdn.discordapp.com/attachments/326138757474680852/351865759019958272/image.jpg
That is a nice image. I suppose really, all you need to remember is three of them.
topaz valley
Did any of that make sense
topaz valley
Hmm
wraith fossil
I've been trying to brush up on it this past week. I havent seen vectors since precal
topaz valley
i mean, i can try draw a picture
wraith fossil
ok
topaz valley
https://puu.sh/xm9HO/e8f92a9162.jpg so here's the first vector - does that make sense?
decomposing that 245N line into an x,y coordinate, we get this
note that 245*cos(160) is a negative number, because the vector lies on the left of the y axis
wraith fossil
Gimme like 10 to get to my dorm. Im still alive
topaz valley
Lol ok
topaz valley
As a non-American, I'll never understand dorms. Apartments ftw.
wraith fossil
Lol
Im from puerto rico so this is my first semester living in a dorm
Besides the small space its pretty ideal for me
Except for the shitty wifi
I dont understand the second picture
Why do that?
topaz valley
adding vectors is really easy if the vectors point in the same direction
in picture 2, we break down the vector into 2 different vectors x and y
if we can convert vectors into a vector on the x axis and a vector on the y axis, then we can add them up easily
what exactly about the second picture don't you get?
wraith fossil
The x and y are vectors as well?
topaz valley
yeah
wraith fossil
Ok, I get it
topaz valley
does the trig there make sense?
topaz valley
wat no that's just the 245 vector
from the second picture, does this notation make sense now?
=tex \vec{v_1} = \begin{pmatrix}245\cos{160}\245\sin{160}\end{pmatrix}
charred spearBOT
topaz valley
yeah
wraith fossil
Ok, I get it then
topaz valley
=tex \vec{R} = \vec{v_1} + \vec{v_2} = \begin{pmatrix}245\cos{160} + 138\cos{45}\245\sin{160} + 138\sin{45}\end{pmatrix}
charred spearBOT
topaz valley
adding vectors means to add their x and y components together, which makes this your resultant
the equilibriant is just the resultant with a negative tacked on
=tex \vec{E} = -\vec{R}
charred spearBOT
wraith fossil
Wait why the negative?
topaz valley
Because the equilibriant is the vector which, when added to the resultant, is zero
=tex \vec{R} + \vec{E} = 0
charred spearBOT
topaz valley
R being the resultant, E being the equilibriant
quasi lion
One could note is that if such forces exists, there is a high probability that it rotates around its axis.
wraith fossil
So equlibriant is the negative resultant?
topaz valley
yeah
topaz valley
ok
https://puu.sh/xmbOC/1973a47ed7.jpg here is the resultant in blue
the resultant is the result of adding the 138 N vector and the 245 N vector
(ignore the x and y stuff)
https://puu.sh/xmbQR/86d2c12ea8.jpg the equilibriant is in red there
it has exactly the same magnitude as the resultant, but is pointing in the opposite direction
the red and blue vectors cancel each other out exactly, when added together
wraith fossil
The blue is the equilibriant?
wraith fossil
Why is it important to know the equilibriant in general?
topaz valley
the equilibriant is the force that cancels out other forces, which can be useful for things like building bridges
if a strong wind blows on a bridge, it will produce a force in some direction
to keep the bridge attached to the ground, the bridge needs to exert that same force but in the opposite direction, to counteract the wind
if the wind is pulling the bridge along that blue arrow, in that last picture
then the bridge is pulling back, along that red arrow
and if your bridge can't pull back as much as the wind can pull, then you've got an expensive, sometimes fatal problem
wraith fossil
Thats so cool!
topaz valley
yeah!
wraith fossil
Do you think you could help me out with two far more basic vector problems? If its not too late where you're from
topaz valley
heh
quasi lion
how old are you @topaz valley ?
topaz valley
im about to be 20
quasi lion
Rotate pi/4 please
topaz valley
Lol
quasi lion
@topaz valley Then it's normal you don't have any children, no?
topaz valley
Hah yeah I guess
wraith fossil
Eh, in some countries women are suppose to have children in the early 20's or theyre considered a widow
Married*
quasi lion
Like which one?
wraith fossil
Ukraine
topaz valley
Oh, weird. I copy/pasted the image into GIMP. it automatically rotated it
quasi lion
plz roate and resent plz plz plz
topaz valley
ok, so first thing, magnitude is absolute
wraith fossil
I know that, just got frustrated lol
topaz valley
but otherwise, yeah, you got it
quasi lion
Isn't a magnitude defined positive?
I don't see why the minimum isn't 7.6-6.1 = +1.5 m ?
topaz valley
i'll draw a thing
quasi lion
@wraith fossil
topaz valley
so consider the first vector fixed
and rotate that 6.1mm vector in your head
think about how the distance between the end of the 6.1mm vector and the origin would change as you rotate it
quasi lion
You forgot to draw the sum of both vector in red saucecode 🤔
topaz valley
lol, I did indeed
quasi lion
In 4. you missed a minus sign in front of 6X^-2 and the 1/X after -3 (since ln(x)' = 1/x)
In 3., that's just summing the vectors, then placing a minus sign, right?
topaz valley
2 b is also wrong -- the resultant goes from the start to the end, not the end to the start
topaz valley
oh, 2 a is wrong too, for the same reason
the resultant vector goes from the origin (in this case, the start line of the race) to the end
in your answer you're pointing from the end to the start
wraith fossil
So just flip the arrow?
quasi lion
Yes
topaz valley
you drew the equilibriants, not the resultants 😛
quasi lion
Do you understand why 1. and 4. are false?
topaz valley
2 would look like https://puu.sh/xmbOC/1973a47ed7.jpg
a line from the origin pointing to the end
quasi lion
Yes
wraith fossil
You can do that?
wraith fossil
Have to arrows join?
quasi lion
Yes
topaz valley
who's Chasles?
quasi lion
Its called theorem of Chasles because he was the first one to popularize it in the francophonia
topaz valley
he also never married, apparently
quasi lion
what's your point?
topaz valley
you're welcome
upper karma
Where is trigonometry needed for conic sections?
upper karma
Purple math says something about needing trig for Bxy
Of the general conic section formula
_the equations for the "slanty" conics get so much more messy that you can't deal with them until after trigonometry. _
Of course. I know trigonometry but not so much conic sections
I also did rotation of axes in Calculus
upper karma
ok I am back
@upper karma
conic sections that are not... neither horizontal nor vertical?
like a parabola which directrix is a diagonal
oh ok
I studied most of them. need to memorize some propierties, as I told you days go
latent turtle
So I'm only in my first year of geometry. And having trouble with the most basic stuff.
kindred sleet
It's okay, we all need help in something.
latent turtle
They want me to do 8 and a few others not on screen
It sucks to not be there the day you go over it
^any help on this would be appreciated
sonic fiber
@latent turtle if the two lines that look like theyre parallel are parallel then you can use supplementary angles and corresponding angles to find the rest
in 8 theres one angle thats 51 degrees, so the angle on the other side of the line should be 180-51, basically
and you proably have the parallel lines properties someplace with you, if youre taking a class on this
just refer back to all of it and apply liberally
sonic fiber
np 😃
latent turtle
Ye we just went over the properties today
umbral rivet
Any more questions, just ask :3
upper karma
@umbral rivet i have a question that i think is very easy
@umbral rivet could you explain absportion law in logic? why does it work
sonic fiber
thanks to you, im gonna start researching boolean algebra lololol
surreal bolt
Hey now ... don't make fun of boolean algebra ...
lilac verge
ye dont make fun of it. lol i dunno what boolean algebra is.
hallow trellis
It is what it sounds like pretty sure
lilac verge
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
so they use that algebra for code i think
sonic fiber
yeah, booleans have feelings too yknow!11!!!!1!
but in all seriousness im curious about what booleans are now.... ive only ever seen them in context of (trying to learn) python/coding in general
analog brook
Its essentially Z/2Z
upper karma
Hello?
dense crater
I've been given a question "What is a weakness of geometric proof of the distributive law?"
dark sparrow
doesn't work well with negatives
dense crater
Oh right
That's a good point
Isn't that true with all geometric proofs though?
Just to check
I mean you can't define something as a "negative distance"
dark sparrow
yeah ig
dense crater
Okay cool, thank you.
I might be asking a lot of questions here because I've just started Uni and our professor has decided to go at the pace of a starving leopard.
Ugh.
vale raven
Well
vale raven
It's likely that the pace of your professor is normal and the teachers you've had before your professor all teach like turtles
upper karma
Usually first years of uni you do in one month the same amount you did over a semester or a year of content in highschool
dense crater
Quite true Kaoffie
And SEV
Just feels at the moment like I have so little time
So much to cover and so little of my own time to go over it
dense crater
Looking forward to the weekend just to have a solid block of time to study solidly
upper karma
My first year after highschool first semester half the class wasnt writing fast enough to follow the teacher, they had to copy after class on other peoples notes to have a full course
dense crater
Didn't it feel overwhelming for you?
upper karma
not for me but for some it did
foggy oxide
i thought about a cool problem
Let ABCD be a retangular trapezoid with perpendicular diagonals AC, BD, where AB = k CD= j , and both AB and CD are bases, let P be the point of the intersection that is created if u extend the both non parallels sides of the trapezoid, what is the volume of the solid created by the rotation of ABCD and CDP around AC and CP respectivly
unique tapir
hi im trying to teach my self trig and how to use it because i like math class but im in the class with the kids who dont know any thing and i was wondering if anyoen could link me to some good vids i already cinda know the basics like sin cos and law of sins and cos could anyone link me some vids going more in deph please
analog brook
Sheep draw a picture
Draw two triangles, one corresponding to the triangle traced out by the ladder and the wall before the ladder is pulled, and the other corresponding to after the ladder is pulled
Note that the hypotenuses of both of these triangles are the same due to the fact that the ladder doesnt change length
rugged moat
I am able to draw the diagram but I am not bale to prove that
@AlexsandrRodriquez#5387
analog brook
Let the length of the horizontal in the first triangle be x and the length of the vertical be y
rugged moat
analog brook
The lengths of the second triangle are x+a and y-b
rugged moat
Here AC=ED
analog brook
Let the hypotenuse of both triangles be h
What is cos(A)
?
In terms of the lengths
rugged moat
@analog brook
analog brook
the definition of cos(a) is adjacent/hypotenuse
Whats the adjacent side to a?
Whats the hypotenuse of the ffirst triangle
rugged moat
X/h
rugged moat
X+a/h
analog brook
Whats cos (A)-cos (B)?
rugged moat
-a/h
analog brook
Can you see how to do the rest?
rugged moat
Actually the problem is our teacher says that we cannot directly pit values in what we have to prove, if we do that the solution is wrong and we:get a 0
We have to modify the equations to get to the prove
And that is hard as there are many ways through which you can arrive to the prove
analog brook
What do you mean?
Obviously checking one case isnt a proof, but it still might help get the ideas into your head
analog brook
Is the issue that you have to write the proof out?
analog brook
Thays what I was helping you do right?
*thats
Have you done a proofs class before this?
rugged moat
Apparently I was absent
analog brook
Ridiculous
They cant be having you doing trigonometric proofs without having learnt how to lay out a proof clearly
rugged moat
I know how to do proofs other than in trignometry
analog brook
Do you have issues with trig?
rugged moat
Nope, but I need practice as I make a lot of mistakes
rugged moat
I can do proves like these
But the question above asks us to modify the trignometric ratios by substitution and stuff to get to the desired equation
analog brook
Thats really vague
rugged moat
A better example
My teacher says you cannot put values into the prove to prove that it is right as you are basically assuming that the prove is right
analog brook
Thats complete bullshit
You arent assuming the proof is right
All youre assumin is that the ratio is invariant
Which might be easier to prove
rugged moat
:/
Anyway, can you help me in modifying the ratios to get the prove?
@analog brook
analog brook
I dont know what you mean by modifying the ratios
The propf we were leading up to would have been correct
Restricting which proof methods you can use is silly
It restricts creativity
rugged moat
For example we have Sina=b+h/x and cosa=y/x-->x=ycosA
Replacing x in sinA
We get Sina=b+h/ycosA
@analog brook
analog brook
Idk man, maybe someone else can help
latent turtle
So, this question has me stumped.
They want me to find the value of X
Not really sure what it could be
upper karma
wait
thorn talon
Wasn't that it?
thorn talon
They're vertically opposite aren't they?
latent turtle
I understand that
upper karma
pretty sure
latent turtle
Nope. All of this is new to me. First year of geometry lol
upper karma
did you take algebra 1
peak sigil
umbral rivet
Ooh
I know how to do that problem :3
Yee, so
Like they said, just set those two equations equal to each other
10x + 10 = 8x + 30
And now you need to simplify this
You can subtract the 8x on the right side and add it to the left side
So you get 18x + 10 = 30
This works because you're not changing to amount of "x" in the problem
You're simply moving it from one side to the other side
You can now do the same thing with the 10 and the 30
Subtract 10 from the left side so that 18x is isolated from everything else
I feel like I made a mistake explaining this
x_x
vapid kettle
10x + 10 - 8x ?
umbral rivet
Agh
Ignore that entire paragraph I typed up there
Let me try it again >.<
10x + 10 = 8x + 30
Subtracted 8x from both sides
2x + 10 = 30
Subtract 10 from both sides
2x = 20
Divide both sides by two
x = 10
Boom
azure storm
last step : verify
umbral rivet
I like, completely forgot how to do that for a second
Ooh hes
Checking your work
If x = 10, then the equation 100 + 10 = 80 + 30 must be equal to each other
And they are
110 = 110
:)
Also
If we relate our final answer back to this picture, we can conclude that both of these angles shown are 110 degrees
unique tapir
hi im trying to teach my self trig and how to use it because i like math class but im in the class with the kids who dont know any thing and i was wondering if anyoen could link me to some good vids i already cinda know the basics like sin cos and law of sins and cos could anyone link me some vids going more in deph please
vast fern
So uh
I've been doing rational functions
How do I determine the transformation of a function of the numerator has x in it
All the previous examples have just been a whole number as the denominator
None of the examples have had something like 3x in the numerator
dark sparrow
...what's tripping you up?
vale raven
I'm assuming there's some sort of grid or box that contains three labeled points X, Y and R
upper karma
@pale crow
pale crow
No there isnt @vale raven
dark sparrow
so what's tripping you up?
can you draw two points and label them X and Y, and then trace a line through them?
@pale crow
dark sparrow
do you know when two rays are called opposite?
pale crow
No
dark sparrow
two rays are called opposite when they lie on either the same line or a pair of parallel lines, and don't point in the same direction
dark sparrow
if you just draw a line and mark a point on it, that gives you a pair of opposite rays
upper karma
Charlie plans to build a square pyramid like figure using unit cubes. The top level will have one cube. Given any level, the vertices of the largest bottom square coincide with the centers of the top face of the four corner cubes. When Charlie finishes gluing together all the unit cubes of the first eight levels, what is the total surface area of all the faces of the resulting solid?
I need help :/
upper karma
yeah
dark sparrow
if you look at it from above, you see an 8 by 8 square, and since all faces are either vertical or horizontal that just gives you 64 units of area
if you look at it from any side, you see 1 face from the top layer, 2 from the second, 3 from the third, etc up to 8
so that gets you 36 units of area
or well, 4 times that
since your pyramid is four-sided
dark sparrow
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
dark sparrow
yeah, and then there's the bottom surface
which is another 64 units of area
== 64 * 2 + 36 * 4
charred spearBOT
272
dark sparrow
that's the total
upper karma
let k be a finite field let's say F_p for some p, look at k[x] as a ringed space in the canonical way, describe the topology, and find the residue fields. How many points have a a given residue field ?
umbral rivet
Uh wat
The triangle with circles one
It doesn't give any information
Just a shape
umbral rivet
;3;
foggy oxide
but as a hint, i'll ask you something
umbral rivet
👀
foggy oxide
umbral rivet
Ohhh
dull egret
nah would ve been to easy
foggy oxide
jewe
umbral rivet
THERES A FORMULA
foggy oxide
don't tell them
umbral rivet
:T
dull egret
did i guess correctly? oops
dull egret
didnt know that was featured
hazy field
@foggy oxide stop.
foggy oxide
Sorry, i tagged wrongly
hazy field
not what I meant
foggy oxide
stop with what ?
dull egret
so what now?
umbral rivet
👀
hazy field
you're being unnecessarily rude and I really don't appreciate calling people retards
dull egret
oh, yeah no idc
hazy field
I do
umbral rivet
foggy oxide
I think i have the "freedom" to call him retard as a joke
umbral rivet
It's not your server fam
foggy oxide
since he is the one that is supposed to give me the "freedom"
dull egret
i m not gonna complain
hazy field
@foggy oxide I don't want you to do it, so stop
foggy oxide
but well, sorry ...
hazy field
cool, thanks
foggy oxide
Jewe u guessed correctly 😭
foggy oxide
yeahh
dull egret
intuition ftw. just that i have no idea how to prove it lol
foggy oxide
i have
but i solved it by intuition too
i tried to prove after answering LOL
let me send one more
dull egret
the one thing i dont get why it is the case although all the circles could be turned outside fo the triangle right?
foggy oxide
i didn't get what u mean i think
try this one, it does have a very clever solution :
dull egret
rotate the circle around its corresponding vertex of the triangle until it isnt on the triangle anymore
foggy oxide
yes, well, that's why he gave a pic i think
🤔
wait, that's very confusing, you're right
🤔
dull egret
well, a hexagon always has an inner angle of 720 degrees. so each angle is 120 degrees
(too lazy to work with radians)
foggy oxide
you don't need to use radians
dull egret
we can now get the width via the fact that sin(30) is 1/2
so for the first segment at the bottom it is 2 units
then you just have the line
which is another 18
and do the same trick for 7 to get another 3.5
foggy oxide
Wait, wait i kinda lost myself in your thoughts
dull egret
so the thing is 23.5 wide
now get the hight
same trick again
cos(30)=sqrt(3)/2
so 2sqrt(30) for that height
same for 15
that is 19sqrt(3)/2 then
height of the segment of 7 therefore is 7sqrt(3)/2
so a total of 6sqrt(3) for the bottom of the ?
foggy oxide
i have no idea what you're doing 😂 but i hope you get the correct answer
dull egret
now for the height it s just the 23.5-10-15/2
which is 6
then pythagoras
sqrt(6^2+6^23)=sqrt(46^2)=12
that is the quesion mark
foggy oxide
omg 😂
dull egret
correct?
dull egret
i have weird ways of doing things, but they work 😛
dull egret
nope. no geometrical arguments for me
dull egret
i always do things this way xD
dull egret
let me think
foggy oxide
don't do the calculations
just tell me the way you thought about the sol
that's the fun part, isn't it ?
dull egret
well also 12
foggy oxide
¯_(ツ)_/¯
dull egret
cause it scales with the square
dull egret
ok then let me see
dull egret
i m noone for geometry. i m anchored in algebra and arithmetic. let me try think of a different method
foggy oxide
Alright, but i suggest you to use triangle sim
dull egret
the triangle with area three must have side lengths which are sqrt(3) times longer than those of the one with area one.
the one with two sqrt(2) times longer
foggy oxide
am i the only one who did the inverse, starting with the triangle with area 3 as reference ?
upper karma
@umbral rivet F_p is F subscript p indeed
foggy oxide
where is @umbral rivet btw ?
dull egret
so we have a total of 1+sqrt(2)+sqrt(3) for the sides of the large one
charred spearBOT
dull egret
lazy
charred spearBOT
Query made by @dull egret
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=(1%2Bsqrt(2)%2Bsqrt(3))^2
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
foggy oxide
😂 wtf, too much info hahaha
dull egret
is it around 17.19
dull egret
again, rooted in algebra and arithmetic
yeah, a bit harder
i always try and go for some strategical way of solving things
dull egret
hahaha
foggy oxide
"only"
dull egret
you think makes me confident
foggy oxide
:D:D:D:D
dull egret
btw, what was the geometrical one for this one?
dull egret
i see
foggy oxide
their area ratio is related as the square of their sides ratio
dull egret
yeah
foggy oxide
that's how i did
foggy oxide
(sqrt1/3*a + sqrt2/3*a + a ) (sqrt 1/3 * h + sqrt2/3*h + h) * 1/2 = A
that's what i ended up with
dull egret
uhmmm
foggy oxide
(i save my solutions, so i don't forget what i thought)
dull egret
i say my solution was neater
foggy oxide
well 😂
one minute
let me find the "more geometric" one
Oh
did i send you
the incircle one ?
this one is cool too
but, it's easier
foggy oxide
i'm facing difficulty in finding the problem i told u ...
dull egret
ok this makes it really tempting to go for geometry
dull egret
ok, whatever, let me try that then, what would ve been the solution to the other?
foggy oxide
This one, my solution was very geometric
dude, my solution was retarded trust me ...
i did like this
by triangle sim xy = 64, x+y = 20 and x>y
=> x = 16 , y= 4
then
i used the formula for the incircle in rectangle triangle
2r = a + b - c (c is the hypotenuse)
this was very retarded
i felt very embarrassed when i saw the clever sol
dull egret
dont even know that formula :P
dull egret
i guess
foggy oxide
but i remember a guy, showed one deduction more algebraic
in the comment section
you will like it i think
dull egret
meh, as much as i like algebra, it is mostly just cause elaborate geometry is beyond me.
xD
foggy oxide
Alright buddy