Available help channel!
#help-0
lone heartBOT
Available help channel!
digital obsidian
lone heartBOT
digital obsidian
I foolishly tried the ratio test, only to get L = 1
Which I should have seen coming πΏ
Divergence test returns 0 too, obviously
I probably need to do a comparison test
But I cannot tell what I need to compare this with
ornate condor
FOOL
digital obsidian
πΏ Omg
digital obsidian
Youβre breathtaking
digital obsidian
digital obsidian
I shall return at a later date with more foolishness
ornate condor
me 2
digital obsidian
spare comet
I hope this is an appropriate question for this channel. Do any of you have tips on how to study for the upcoming Mathematics Admissions Test for Oxford? For reference of my current skill level, I recently finnished IB with HL math. Perhaps any sort of resources or guides that can get me going? I've looked at the past papers and they seem a bit difficult
lone heartBOT
I hope this is an appropriate question for this channel. Do any of you have tips...
@spare comet Has your question been resolved?
lone heartBOT
@spare comet Has your question been resolved?
lone heartBOT
@spare comet Has your question been resolved?
wispy gale
I hope this is an appropriate question for this channel. Do any of you have tips...
dont go ocford it sucks
cambridge is better
spare comet
in certain aspects maybe so, but for now I do need to figure out how to prepare for this test
chrome plank
π I'm sorry, I can't answer, but it may be better to ask these kind of questions in channels like #serious-discussion or maybe #math-discussion
lone heartBOT
@spare comet Has your question been resolved?
tall topaz
cambridge is better
You do know that the UCAS deadline was like a week ago
ember sky
lone heartBOT
tall topaz
What you do think
ember sky
so its just the numbers inside the matrix that change?
tall topaz
Yes
tall topaz
ember sky
.close
drowsy sedge
Sorry thats a bad screenshot
I just dont know how he got the normal vector n = [2 -1 -1]
aka idk how he went from n1 dot d1 = this to that
<@&286206848099549185>
lone heartBOT
drowsy sedge
nvm
lone heartBOT
Available help channel!
solemn prism
Probability problem:
Inside a π° are 7 π΄ and 5 βͺ.
Balls are extracted randomly without replacement.
What is the probability of the 2nd ball extracted be a π΄?
lone heartBOT
Probability problem:
Inside a π° are 7 π΄ and 5 βͺ.
Balls are extracted randoml...
plain flame
split into 2 distinct possible events
one being that you grab a white ball first and then a red ball
solemn prism
So, there's not a single probability
plain flame
the other being you grab a red ball first and then a red ball again
add those probabilities
solemn prism
There's two different probabilities, is that it?
Ohh, I just add them.
Thanks!
.close
green magnet
$a+b=20$
plain flame
substitute
green magnet
$a^2-b^2$?
ocean sealBOT
DanielCsocsik
green magnet
let me send you
mortal trellis
factor a^2-b^2
green magnet
how i tried to solve it
mortal trellis
difference of squares
green magnet
mortal trellis
its not necessary to calculate what a and b actually are
fringe sleet
easiest way, and the one they might have wanted you to do is to note that $$a^2-b^2=(a+b)(a-b)=(20)(27)=540$$
ocean sealBOT
Duh Hello
mortal trellis
the formula a^2-b^2=(a+b)(a-b) is very important. remember it
green magnet
okay so theres a catch
i know the formula
so
wait guys
these are the asnwers:
$(A) 18 ; (B) 22 ; (C) 24 ; (D) 40 ; (E) 44$
ocean sealBOT
DanielCsocsik
green magnet
the formula a^2-b^2=(a+b)(a-b) is very important. remember it
altought thanks for that
green magnet
easiest way, and the one they might have wanted you to do is to note that $$a^2-...
also thanks for you too
green magnet
yeah that works
also u too
mortal trellis
can you show an image of the whole question?
fringe sleet
i could see myself thinking thats a 7 where the bottom half has been scratched off
green magnet
bro
dont tell me
that is a fucking question mark
$How much is a^2-b^2 if a+b=20 and a-b=2(7?)$
mortal trellis
if a+b=20 and a-b=2 then one of those answers works
green magnet
40?
mortal trellis
yes
green magnet
**DanielCsocsik**
Answer 40?
fringe sleet
need to have the actual math inside the dollar signs and the rest outside it. but yeah you can easily use the technique for the other one here as well
green magnet
need to have the actual math inside the dollar signs and the rest outside it. bu...
okay let me try
How much is $a^2-b^2$ if $a+b=20$ and $a-b=2(7?)$
aye?
you are smart
so that unfinished fucker was a question mark
mortal trellis
How much is $a^2-b^2$ if $a+b=20$ and $a-b=2(7?)$
ocean sealBOT
Denascite
mortal trellis
dollar signs around each math expression separately
ocean sealBOT
DanielCsocsik
green magnet
yay
fringe sleet
green magnet
i'm grateful for all of you, if not you i would probably think about that 27 for a while
also thanks for telling me to use the formula without calculating
i want to win that competition very much
i go close this chat
goodnight
.close
lone heartBOT
lone heartBOT
Available help channel!
tight locust
let's say we have the 2nd order linear homogenous DE:
lone heartBOT
let's say we have the 2nd order linear homogenous DE:
tight locust
$y'' + by' + cy = 0$
ocean sealBOT
EndTimes
tight locust
and we wish to find the general solution
then let's assume that a solution will be of the form $e^{rx}$
ocean sealBOT
EndTimes
ocean sealBOT
EndTimes
tight locust
so then all we are left to do is solve the characteristic polynomial for the values $r_1$ and $r_2$ that will satisfy
ocean sealBOT
EndTimes
ocean sealBOT
EndTimes
tight locust
but i don't understand how you are supposed to proceed if $r_1 = r_2$
ocean sealBOT
EndTimes
tight locust
what do?
blissful temple
Then the general solution is a linear combination of $e^{rx}$ and $xe^{rx}$
ocean sealBOT
Zanarcane
tight locust
standard case of what
blissful temple
For the case, where $r_1\neq r_2$
ocean sealBOT
Zanarcane
tight locust
yeah didn't i just do that? lol
blissful temple
In general, the solution to a linear ODE system of the form $y'=Ay$ with constant coefficients is given by $y(x)=\exp(A(x-x_0))y_0$, where $\exp$ is the matrix exponential function.
ocean sealBOT
Zanarcane
tight locust
huh
is there a way without busting out all the linear algebra
my prof said something about just taking the partial wrt r
but i don't see how or why that would work
as in
$\frac{\partial}{\partial r} e^{rx} = xe^{rx}$
ocean sealBOT
EndTimes
blissful temple
is there a way without busting out all the linear algebra
Hmm, okay so, if you want the simple explanation, you essentially want another solution to the ODE that is linearly independent of $e^{rx}$. The function $xe^{rx}$ is one of them and lies in the generalized eigenspace corresponding to r.
ocean sealBOT
Zanarcane
lone heartBOT
@tight locust Has your question been resolved?
tight locust
i think i found a simpler way to do it with Heaviside's method
$$ (D-k)^2 y = 0 $$
$$ e^{-kx} (D-k)^2 y = 0$$
$$ e^{-kx} y = \frac{1}{D^2} 0$$
$$ y = \frac{1}{(D-k)^2} e^{kx} \times 0$$
$$y = e^{kx} \frac{1}{D^2} 0$$
$$y = e^{kx} x$$
ocean sealBOT
EndTimes
tight locust
technically we should have: $y = e^{kx}(c_1x+c_2)$, but since those constants are arbitrary they get absorbed
ocean sealBOT
EndTimes
tight locust
wait actually that is the solution
$$y = e^{kx}(c_1x + c_2)$$
$$y = c_1xe^{kx} + c_2e^{kx}$$
ocean sealBOT
EndTimes
tight locust
nice
i'm starting to really like heaviside
treating derivatives as operators makes everything so much simpler
tight locust
Hmm, okay so, if you want the simple explanation, you essentially want another s...
is this valid?
not too sure about if i can use the exponential shift rule there because it's 0
blissful temple
$$ (D-k)^2 y = 0 $$
$$ e^{-kx} (D-k)^2 y = 0$$
$$ e^{-kx} y = \frac{1}{D^2} 0$$
...
I'm not really sure what you're doing here, the explanation I know of involves matrix exponentiation and the Jordan normal form
tight locust
oh, i thought this was common knowledge. i guess some profs don't bother teaching this method then
blissful temple
$$y = e^{kx}(c_1x + c_2)$$
$$y = c_1xe^{kx} + c_2e^{kx}$$
Well, I'm familiar with treating derivatives as operators, but I can't follow how you come to this conclusion.
tight locust
it's the exponential shift rule
blissful temple
The conclusion is correct though, in general, it's $$y(x)=(c_0+c_1 x+c_2\frac{x^2}{2}+...+c_s\frac{x^s}{s!})e^{kx}$$ for an eigenvalue with multiplicity s.
ocean sealBOT
Zanarcane
tight locust
Wow ok that makes a lot of sense
I like how the DE problem essentially just becomes an algebra problem
tight locust
The conclusion is correct though, in general, it's $$y(x)=(c_0+c_1 x+c_2\frac{x^...
This is just
y = e^(kx) 1/D^s (0)
So e^(kx) times the 's'th antiderivative of 0
blissful temple
Oh okay, I get it, a bit surprised that it yields reasonable results
tight locust
it all makes sense now, thank you
now i just need to refresh myself on why exponential shift rule works and then i will have no holes in my knowledge
lone heartBOT
@tight locust Has your question been resolved?
woven axle
lone heartBOT
woven axle
if dc = db is ad = dc = db?
silent parcel
I think so, the picture makes it confusing though
What do you think the angle at DBC is?
woven axle
i have no info on that
woven axle
abc is 90
woven axle
thats the same question as im asking
rigid smelt
Angle DBC is not half of ABC
silent parcel
how so?
rigid smelt
What you are looking to prove here is actually the triangle ADB and BDC are congruent
silent parcel
thats how I worked out congruence :v
rigid smelt
BD here is the median(but we dont actually know that, we can still prove it) and the median dont bisects the angle
silent parcel
it cuts through the middle because we know angle BDC is 90?
rigid smelt
No
silent parcel
and we know that because DBC is 45?
knotty spire
This is the risk with looking at sketches too much
silent parcel
true
rigid smelt
The median of a right triangle is equal to one half of the hypotenuse
knotty spire
and reading info from that that isn't there and you can't prove
rigid smelt
It doesnt have to bisect the right triangle
knotty spire
Yes, the angle is right. But by no means does it mean BD bisects it
woven axle
its a sketch
the angle isnt necessarily 45 sorry for making it look that way lol
the only thing we know is that angle abc is 90 and bd=dc
silent parcel
I seee
woven axle
im sorry i learn math in another language so i have no idea what the names of things are, but theres a rule that says if ad=dc then ad=dc=bd
silent parcel
sorry, I was working under the assumption DBC was 45 :v
rigid smelt
If AD is a median drawn from B, AD=BD=DC is always true in any right triangle at B. This does not make the emdian bisects ABC
Anyway, the goal is to just prove that triangle ABD and BDC are similar through means of two congruent angles, and then since one of its sides are congruent to each other, they are congruent
Or another thing you can do is to prove that ADB is isosceles through proving that angle BAD is equal to ABD
I would prefer the second one
knotty spire
Well, terminology is important.
rigid smelt
Alright, can you prove that angle CBD + DBA is equal to 90 degrees?
woven axle
Well, terminology is important.
i know these terms just not in english
knotty spire
i know these terms just not in english
So yes, 
Or else you won't understand what's going on.
Or use your favorite online dictionary/translator if need be.
silent parcel
how would you describe congruence?
rigid smelt
Actually nvm on the congruence, I was wrong there
Should just do it through proving that ABD is isosceles at D
You could propabaly do it by drawing the circumcircle around ABC and then prove that the centre is at the midpoint of AC as well
silent parcel
you can prove it is isosceles (a triangle where two sides are the same length) by comparing the angles at DBA and BAD
rigid smelt
But that's not as quick as the isosceles one
rigid smelt
you can prove it is isosceles (a triangle where two sides are the same length) b...
Yeah
woven axle
the original question was (and im trying to translate sorry if its bad) O is a point on the remainder of the right triangle ABC (C = 90) so BO=CO
prove that the point o is the centre of the circle that is surrounding it
im so confused
doesnt BO=CO solve the question because they are both radiuses
rigid smelt
But AO might not be equal to them, you still have to prove that
woven axle
and o is the centre because they are equal
oh i have to prove ao is equal to them okkk
rigid smelt
You can start with proving that angle OBC + OCA is 90 degrees, and then prove that angle OAC is equal to OCA
The rest from there should be fairly obvious
silent parcel
You can start with proving that angle OBC + OCA is 90 degrees, and then prove th...
how do we prove that AB is the diametre though?
like I know that it is intuitively cause ACB is 90, but is there some sort of rigourous proof? Just curious
rigid smelt
Well the question didnt ask for us to prove that it is the diamater, just need to prove that O is the centre. But since O lies on AB and AO=BO, that means AB is the diameter of this circle
silent parcel
that would mean centre of the line though?
rigid smelt
From any midpoint of a line we can create a circle with the diameter being that line
The line AB is straight and we all know that for sure, and since O is it's midpoint, it means there must exists such a circle centered at O such that AB is the diameter, and its radius being AO, or BO
silent parcel
I agree that it is, it just seems the questions bias was to prove that O was the midpoint, not that we were drawing a circle about it
Ignore this part of the convo Erik, i dont want you to get confused on my part - im just trying to understand it myself now :S
rigid smelt
Well that might be the goal of the question, to prove that the midpoint is also the circumcentre
rigid smelt
This part idk, since im not the one making the question
woven axle
idk if that translates good
silent parcel
A right peripheral angle subtends a diameter
yes, thats what I mean
woven axle
oh lmao
rigid smelt
You do not want to use that theorem here, that will make this circular logic (no pun intended)
woven axle
You do not want to use that theorem here, that will make this circular logic (no...
how exactly
silent parcel
maybe just quote what you said there Erik (that right angle subtends the diametre) and then prove the O is the midpoint of that line is enough to prove that it is the centre
rigid smelt
how exactly
Well in order to use that theorem, you must prove that the hypotenuse of the right triangle is the diameter of the circle, meaning this involves proving that the centre of the circle lies on the hypotenuse. Which is what the question is asking
So if we used that, a person who is reading the proof may ask why is this theorem true
silent parcel
that sounds a bit heavy for the nature of the problem?
rigid smelt
Making a proof is hard, so yes, it is heavy considering the problem might not be very hard
silent parcel
its what I was asking before but probably isnt relevant here xd
rigid smelt
Anyway, proving that the centre is the midpoint of AB is not hard, you just need to prove that AO=BO=CO and that's all. AB being the diameter, (i could say), is pretty trivial to prove, but this is not in the question so you dont need to worry about it
silent parcel
sounds about right
ty for your help @rigid smelt helped me understand my own maths better
good luck Erik!
rigid smelt
Np
woven axle
thanks
i have a test in 4 hours i have no idea how im gonna get any points from the geometry part
rigid smelt
Just remember some useful theorems and try to be creative I guess
cinder depot
Is anyone good at computational complexity? I'm just confused on the notation, what does it mean for a Turing Machine M to accept (x,y) where x,y are just some strings in Sigma* ( so any strings). I'm also curious what the <> notation means. for example langauge A = <M1, M2>. What does this exactly mean? Does A represent the language accepted by M1 and M2?
lone heartBOT
Is anyone good at computational complexity? I'm just confused on the notation, w...
@cinder depot Has your question been resolved?
mossy laurel
Is anyone good at computational complexity? I'm just confused on the notation, w...
It means the automata will always have an action for every letter of (x,y)
Like ot must have a transition from the cell to somewhere else
And it may not be the case
lone heartBOT
@cinder depot Has your question been resolved?
pliant charm
lone heartBOT
pliant charm
I didn't how the equation formed by the roots
lone heartBOT
@pliant charm Has your question been resolved?
alpine sable
is the surface area for this 9450mm^2?
lone heartBOT
is the surface area for this 9450mm^2?
tight locust
this is a square prism?
alpine sable
rectangular
i did the calculating wrong
what i meant to say was
is the surface area 3150 mm^2
alpine sable
4(45*15)+2(15^2)
frozen tree
15 X 15= 225
alpine sable
is that right?
frozen tree
yea thats correct
frozen tree
i thought it was the volume lmao
tight locust
just consider (f-g)(x)
lone heartBOT
@gray creek Has your question been resolved?
ocean sealBOT
dev
odd drift
lone heartBOT
odd drift
Help me find the next three terms
zinc dagger
?
ornate condor
lol
zinc dagger
All of them seem to be geometric sequences
Notice how each term is a certain, constant ratio of the previous
ornate condor
7 isnt
zinc dagger
....
ornate condor
wot
zinc dagger
me is using my thunk to think it over
odd drift
How do i do it
ornate condor
no clue what that means
zinc dagger
i am rethinking how to do 7
rose sigil
how do you know it's not add 2, add 1, add 0, add -1, and so on for the first one?
odd drift
Help pls im stuck on this
rose sigil
or like anything else
zinc dagger
how do you know it's not add 2, add 1, add 0, add -1, and so on for the first on...
usually there are only two types of sequences in math classes: adding by a constant (arithmetic) or multiplying by a constant (geometric)
rose sigil
.-.
long axle
An example like this doesnβt rlly make me think itβs from a math class learning about sequences or series
odd drift
will the answer in #7 be 1/14,1/18,1/22?
oh ok
how about 6? I don't get the pattern
wdym?
sage fractal
or do the opposite and try setting up an equation to figure it out such as 1/4x=3/16
cinder depot
It means the automata will always have an action for every letter of (x,y)
so does that mean it accepts?
if TM A accepts (x,y) that means given input x, and given input y in 2 seperate runs, both will terminate in accepting state riight?
lone heartBOT
@odd drift Has your question been resolved?
odd drift
and for #5 -1/2,-1/4,-1/8?
Will the answer for no. 5 be -1/2,-1/4,-1/8
And for #8 will it be 5/4,5/8,5/16
lone heartBOT
@odd drift Has your question been resolved?
manic coyote
So Iβm not entirely confident if the NM = KM and KL = NL is correct or not
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Hello, I will state my manner in a second.
lone heartBOT
Hello, I will state my manner in a second.
alpine sable
I do have a problem with bionomial coefficients right now. Posting Picture now.
Its german: Calculate n/k for 1 β€ k β€ n β€ 6 and show the x^3 term from (x-1)(3+4x)^6
So far I drew the pascal triangle but that is not really calculating, is it? I really do not know how to approach binomial with a range. If I wanna calculate it I got many many terms, don't I?
And for the x^3 I just lack the foundation to even start I think.
Appreciate anyone, thank you!
lone heartBOT
@alpine sable Has your question been resolved?
charred plover
Calculate $\frac{n}{k}$ for $ 1 \leq k \leq n \leq 6 $ and show the $x^{3}$ term from $(x-1)(3+4x)^{6}$
ocean sealBOT
habukichan
alpine sable
Solved that x^3 on my own actually. Only stuck on actually calculating that (n, k)
charred plover
Solved that x^3 on my own actually. Only stuck on actually calculating that (n, ...
oh its n choose k
alpine sable
charred plover
Calculate $n \choose k$ for $ 1 \leq k \leq n \leq 6 $ and show the $x^{3}$ term from $(x-1)(3+4x)^{6}$
ocean sealBOT
habukichan
charred plover
doesnt look like it has any big problems
alpine sable
Ye I actually do not understand the first thing tho. How do I actually calculate n,k for a range, except drawing triangles
It is a fair bit of n and k's to calculate if I wanna go through the range of 1 to 6 for each n and k
lone heartBOT
@lapis pier Has your question been resolved?
main bolt
Hi! I need help in my homework since I had a busy week. My teacher told us to apply geometric sequence in a real life problem.
main bolt
I need to have my own geometric sequence problem and answer it.
gray isle
does your book have real life examples involving those?
main bolt
Unfortunately no
gray isle
in that case, look up stuff like
compound interest, radioactive decay
main bolt
Hi! I need help in my homework since I had a busy week. My teacher told us to ap...
Okayyyππππ
.close
lone heartBOT
rose sigil
maybe also a probability problem could work
lone heartBOT
Available help channel!
mellow totem
lone heartBOT
mellow totem
on the left is the problem, and on the right is a solution to an extremely similar problem. can I get some help because for some reason I just cant find an answer
craggy token
how can you express 0.25 as a fraction?
mellow totem
1/4
craggy token
and how can you express 1/4 as 2 to the power of something?
mellow totem
see thats where i get lost
craggy token
how can you express 4 as a power of 2
mellow totem
hold on nvm I missed something and now i feel stupid cause i got the answer
craggy token
lmao
strange fractal
how do i do this?
lone heartBOT
how do i do this?
strange fractal
i did this
craggy token
i did this
you can solve the other x-intercept from the 3rd line
strange fractal
im confused
trim wagon
well what u have expanded isnβt quite correct
craggy token
when you have a quicker way
celest hearth
craggy token
well what u have expanded isnβt quite correct
and that as well
trim wagon
craggy token
strange fractal
?
craggy token
then isolate x
strange fractal
so x=6?
craggy token
you have (x-3)^2 = 9
that means x-3 = +- 3
bcs when you apply the square root, youll get |x-3| = 3, which means x-3 = +-3
grave island
ur diagram is wrong
strange fractal
it says the width is 1m shorter than length
grave island
yea
strange fractal
ohhh
strange fractal
im confused again
grave island
"the spa and the pool has a length of 10 m", the width of the pool is -1 of it's length
if u were to say its 9
strange fractal
so is it x-1?
grave island
u would be combining the length of both the spa and the pool
if x is the length of the pool yes
strange fractal
really
grave island
pool + spas length is 10 m
^^^
strange fractal
tbh idk in math i jus tuse waht im given
grave island
ajskfkaflkdsjf
strange fractal
and it works cuz im in 9th
grave island
uh this diagram is correct in the visualisation. the dimensions r wrong igig so try redraw it
strange fractal
okk
strange fractal
uh this diagram is correct in the visualisation. the dimensions r wrong igig so ...
i dont get it
strange fractal
yess
strange fractal
is this righjt
grave island
i mean.
it makes sense
but like
wouldnt u want ur pronumeral to be the thing u want to find out
the length of the spa.
not the lenght of the pool?
strange fractal
not the lenght of the pool?
??
grave island
ye
grave island
so do i make the length of the spa
mhm
grave island
im pretty sure u can put everything in terms of x
correct me if im wrong tho
length of pool is 10-x bc length of spa is x.
therfore width of pool is
10-x-1 which is 9-x
and uh.
yea no idk
im honestly stuck
strange fractal
my teacher always does this to me
the answr is 5.5 so im just gonna back track
.close
lone heartBOT
lone heartBOT
Available help channel!
granite terrace
Can someone help me explain how to factor quadratic equations? I know how to factor but I cant explain it well
grave island
IM HERE DONT WORRY SIR
so
u want to find two numbers that.
add up to -24
and multiply to 4 * 27
granite terrace
so 6 and 18
grave island
u mean
grave island
so 6 and 18
-6 and - 18
granite terrace
ye ye
grave island
also that is not quite right
so
nvm me dumb
ok so
we have
now
$$(4x^2-6x)(-18x+27)=0$$
granite terrace
Ye
ocean sealBOT
Mothy
grave island
factorise it like this
factorise first bracket and then second bracket
and tell me wha tyou get
granite terrace
so (2x - 3) (-2x + 3)
lone heartBOT
@granite terrace Has your question been resolved?
gray isle
very bad notation
missing + sign between those ()+()
$$(4x^2-6x)+(-18x+27)=0$$
are you able to factorise the $4x^2-6x$
ocean sealBOT
βamonov
alpine sable
hello can someone help for my home work please
lone heartBOT
hello can someone help for my home work please
alpine sable
question 11
velvet cliff
these 2 angles are the same
then you can make 1 equation in terms of x using the sum of angles in triangle
astral knoll
how can i factor 3x^5+x^4-9x^3-9x^2-2x=0?
lone heartBOT
how can i factor 3x^5+x^4-9x^3-9x^2-2x=0?
velvet cliff
how can i factor 3x^5+x^4-9x^3-9x^2-2x=0?
well you can take out an x
mortal trellis
rational root theorem
gray isle
first thing to look for is whether all terms have a common factor
astral knoll
well you can take out an x
ok then?
velvet cliff
well that's complicated
gray isle
and then
rational root theorem
astral knoll
well that's complicated
yes
velvet cliff
just use this
astral knoll
ok i will see
velvet cliff
velvet cliff
it's better to just use numerical methods to find roots
slow sleet
I want to rotate a 3d cube with matrices. Now the rotating of the cube itself doesnβt seem too hard and I understand how that works. But then you have the cube in a 3D matrix. But how do I get it displayed on your 2D screen? Like I need to turn x y z into x y. Ive heard something about projection matrixes but they just look really complicated and seem to be diff for every scenario.
alpine sable
the easiest thing you could do is the project to the x-y plane, ie just drop the z coordinate from the x,y,z coords
slow sleet
but if the cube is rotated that would become 2 rectangles?
alpine sable
it depends which way you rotate it
slow sleet
i gues rotating it on the z axis would still work if you got a right on view but rotating on the x or y axis wouldnt?
slow sleet
just a cube you can freely rotate
alpine sable
any other projection matrix is equivalent to rotating first, then the x-y projection. so its sufficient to use the x-y projection
slow sleet
any other projection matrix is equivalent to rotating first, then the x-y projec...
i get the rotating first part
but the x y projection wouldnt work with perspective
atleast idk how it would work
its kinda hard to imagine in you rhead
alpine sable
by perspective, do you want shading?
slow sleet
nah
alpine sable
then why doesnt it work?
slow sleet
but something like this would work?
alpine sable
choosing a projection is arbitrary, so why not make it easy on yourself
alpine sable
but something like this would work?
yes, you just need to rotate it to that position first, then apply the projection
slow sleet
and the projecction is?
alpine sable
drop the z coord
slow sleet
just only writing x and y
alpine sable
yes
slow sleet
ill try
clear trench
lone heartBOT
clear trench
Hey, I am quite new to probability and because of a language barrier I dont really know how to treat these coherent packages, can someone help me?
The question is: How many different combinations are possible.
plain flame
In how many ways can you take 2 different items from 10 different items
blazing granite
1200kg car moving at 100 kph (27.7 m/sΒ²) suddenly stops upon hitting a post. How much work is done ln it by the post to make it come on a stop?
help.. this has math so technically its math π¦
plain flame
plain flame
exactly
clear trench
45
plain flame
which can also be written as 10 choose 2
clear trench
so the final answer for the question would be.. 1/45 x 1/6 x 1/5 x 1/4?
plain flame
and now the same idea for picking 3 distinct items out of 6 distinct items
plain flame
so the final answer for the question would be.. 1/45 x 1/6 x 1/5 x 1/4?
well multiplied by 3!
plain flame
is the answer 10!/8! x 2!?
like you did here
plain flame
yes
clear trench
Alright, thanks a lot Gijs!
plain flame
np
thin venture
can this $ x(x^3-1) =0 $ contain complex numbers?
lone heartBOT
can this $ x(x^3-1) =0 $ contain complex numbers?
thin venture
$x(x^3-1) =0$
ocean sealBOT
γMariusγ
swift terrace
yes
sand sky
ayo sulfuric= SO3
lone heartBOT
ayo sulfuric= SO3
golden canyon
sand sky
::C
oh sorry
can u sovle this
i think it is not dark enough to see
if u can pls help me
lone heartBOT
@sand sky Has your question been resolved?
native nebula
help
native nebula
harsh girder
the slope of the line is $\frac{-2-(-1)}{4-3}=-1$
ocean sealBOT
η§ζ°΄
harsh girder
$\tan(135 ^ \circ)=-1$
ocean sealBOT
η§ζ°΄
native nebula
the slope of the line is $\frac{-2-(-1)}{4-3}=-1$
tan 315Β° is also -1
harsh girder
Usually we choose angles within 0 to 180 degrees
native nebula
Usually we choose angles within 0 to 180 degrees
why so?
harsh girder
More convenient, otherwise there will be a lot of results
dense oasis
lone heartBOT
dense oasis
CAN someone explain this?
vale wigeon
reindexing
dense oasis
Yeah but how
vale wigeon
in $\sum_{k=1}^n (k-1)^2$ take $k' := k-1$ and reindex your sum in terms of $k'$ to get $\sum_{k'=0}^{n-1} (k')^2$
ocean sealBOT
Ann
vale wigeon
since k goes from 1 to n, k' will go from 1-1 to n-1
look up index shifting in summations
tall topaz
Open your own channel 
keen linden
Open your own channel <:sad_think:899608203736780821>
sorry im still new hereπ«
tall topaz
Dw read #βhow-to-get-help
keen linden
Dw read <#488120190538743810>
alright
lone heartBOT
@dense oasis Has your question been resolved?
thin venture
can somebody explain to me why the domain of definition is E
lone heartBOT
lone heartBOT
Available help channel!
late jay
Hey Hello. I was working on a problem that I need to solve and I've been working on it for a while and I got stuck. In the attached image I have copied the statement and the values that I have found in English so that it can be understood.
Please if someone could tell me which way to go to develop it.
lone heartBOT
Hey Hello. I was working on a problem that I need to solve and I've been working...
@late jay Has your question been resolved?
light spoke
Hello can anyone tell me how this formula is derived
Especially the second part, that is The present value of infinite stream of returns of investments made from retained earnings
lone heartBOT
@late jay Has your question been resolved?
lone heartBOT
@late jay Has your question been resolved?
late jay
Anyoneeeeee
late jay
Bro, what happens is that when determining the equation of the sum of all the interior angles of the triangles, it gives me 180 = 180
and you can't move on
happens with the 3 smaller triangles
vague mirage
Yeah in every that I am doing 180 is getting cancelled and I can't find the value of x
Ok wait
BECD is a Quadrilateral
And its sum is 360
πΉπΉπΉπΉ
late jay
The same thing happens to me, I have tried to set up a 2x2 system of equations but even so I only have two equations that are actually the same
late jay
BECD is a Quadrilateral
I have not thought of it as a quadrilateral, let me see
vague mirage
But I need Angle c π₯²π₯²π₯²
vague mirage
Yeah that's the issue
late jay
I found all three angles of the quadrilateral now that you mention it
late jay
hm?
late jay
60 or 60-2x
60 - 2x
vague mirage
But in the question it's 60
late jay
Bro, in the sentence where it says AC = BC = AD, I wrote it wrong when translating it into English, it is actually AE = BC = AD
vague mirage
Oh ok
late jay
I made a mistake when translating it into English and I forgot to put the -2x xd
vague mirage
Wait then if AE=BE angle ABE = BAE iscloses β property
πΉ
60-2x=120-x
Oh it's bc isss
Shit
late jay
i found this
late jay
Wait then if AE=BE angle ABE = BAE iscloses β property
AE = BC
vague mirage
i found this
How?
Oh yeah
Got it
Great
Good
Very good
Appreciate it
You are genius
late jay
How?
when you said about the quadrilateral I found the EBDC, so 120 - x + x = 120 and that angle is supplementary to the 60Β°
late jay
You are genius
thanks, still I can't use it because I don't know what else to do, I need to find the ADC angle, the one at the tip
late jay
They tell us that there are some sides equal to others, there must be some relationship between them to establish some property between the missing angles, but I don't know what that relationship is.
late jay
How did you get that that exterior angle is (180 - 2x)?
vague mirage
Forget it
late jay
ok
vague mirage
It is 2:20 am in my country I am ded that's why I can't focus
late jay
It is 2:20 am in my country I am ded that's why I can't focus
Ok bro, don't worry, if you have time and you can think of something you can write me to dm.
vague mirage
Yeah
late jay
Go to sleep
late jay
ok bro, thanks
vague mirage
π«π«π« don't mention it
urban tulip
I will do this
I need help on a problem do i post it here ?
vague mirage
I need help on a problem do i post it here ?
I am not a staff of this server I am just a 9th grader so maybe you should post it in any help channel
late jay
I need help on a problem do i post it here ?
Post it in the help channel number 0
vague mirage
Is there any way to proof AB=BD or BE||DC so I can take the help of mid point theorem
vague mirage
Yeah
This is really hard
Really hard
We could only take out one angle
Till now
weak coyote
Bro, in the sentence where it says AC = BC = AD, I wrote it wrong when translati...
then rewrite the problem
and post the correct version
delete the old one
if the problem is not even stated correctly, it does not give confidence for people trying to help you
late jay
if the problem is not even stated correctly, it does not give confidence for peo...
What a nice guy. 
late jay
Here is it
thanks bro, i was afk
late jay
I think that is the exterior angle
vague mirage
I think that is the exterior angle
So Angle BDC +60 = 180 which is not possible
Wew
late jay
So Angle BDC +60 = 180 which is not possible
but BDC + 60 can't give 180, we don't know the measure of either of the other two angles.
vague mirage
Yeah
late jay
but how can we use the exterior angle?
vague mirage
<@&286206848099549185> Please help us please save us find the value of x
Maybe there's no way @late jay
late jay
Maybe there's no way <@686551838480400386>
maybe
late jay
maybe it has to do with AE = BC = AD
vague mirage
Yeah
late jay
yes
weak coyote
there is a way
weak coyote
pls wait
vague mirage
Still the same π₯²π₯²π₯²π₯² who made this maths
late jay
Still the same π₯²π₯²π₯²π₯² who made this maths
My teacher takes it out of a book. It's a university course I'm going to. they're supposed to be easy
late jay
Bro you are going to be the next Einstein
haha, thanks. but If I am going to be the next Einstein, I must study much more and improve the level I am at now.
vague mirage
Yeah you will do it
late jay
thank you
weak coyote
I'm betting the answer is 90 degree
let me prove it
before I do
is this required homework or something the teacher uses to find gifted students?
vague mirage
I don't know but I am curious to know the answer
weak coyote
because if it's the latter case, I would want you to be honest to your teacher that you asked for help
weak coyote
just experience. I did geometry for olympiads
vague mirage
Which property did you used can you tell me?
weak coyote
try to construct it and spot the relations between things
is what geometry boils down to
weak coyote
let me prove it first
weak coyote
obviously
vague mirage
Oh I haven't read that chapter ππ₯²
ebon trench
Do u have da solution to that problem
Its 3:30 am here and my mind is stuck on this question π₯Ί
late jay
sorry i just got back
ebon trench
@vague mirage he slept due to frustration
late jay
Its 3:30 am here and my mind is stuck on this question π₯Ί
I can imagine it bro, I've been stuck all day thinking, it has me unfocused in my other jobs.
ebon trench
Cant even sleep cuz of this 
late jay
before I do
is this required homework or something the teacher uses to find gif...
it is a compulsory task, we gain nothing by doing it
late jay
Cant even sleep cuz of this <:blobcry:971797574916907028>
@weak coyote Bro, How did you do it?
weak coyote
ebon trench
Watttt is disss
ebon trench
Cant understand anything πΏ
weak coyote
it should be 90
late jay
it should be 90
but what did you use to get it?
weak coyote
you can think about it while I write
ebon trench
I have a 9th grade olympiad on 22 nov, and i am very weak ππΏ
late jay
you can think about it while I write
ok bro
late jay
I have a 9th grade olympiad on 22 nov, and i am very weak ππΏ
I have 16
ebon trench
16?
late jay
yea
ebon trench
Like 16th nov?
late jay
what
ebon trench
Nvm
late jay
i dont understand
ebon trench
Nevermind
thorn fjord
help
(10x^3) * (8y^-2)
x=6. y=4
weak coyote
@late jay
I thought the answer was supposed to be nice so I said 90
but it turns out the solution is approximately 92.12 degree
x=10 degree
to solve that x is 10 you use the fact that sin(60-2x)/sin(2x)=sin(120-x)/sin(3x) , which is from BC/AB=AE/AB
once you have x, you can explicitly construct and determine the length of everything (by WLOG setting AE=1)
late jay
Voy a verlo
weak coyote
it's funny that they set up x to be nice but the final answer isn't nice. meh.
for the final step, to calculate the angle y, I know I used the sine formula (which gives 2 solution) but it's better to use the cosine formula instead (which gives 1 solution)
I will leave you to think about what I did.
thorn fjord
whats that app or software
weak coyote
geogebra, onenote and wolfram alpha
thorn fjord
thanks
lone heartBOT
Available help channel!
distant nymph
y=(2x-8)^2/3
lone heartBOT
y=(2x-8)^2/3
distant nymph
How I change that to square root?
vague spindle
change what to quare root?
distant nymph
y=(2x-8)^2/3 <β this
vale wigeon
wdym by "change to square root"
heady pollen
the power
lapis ingot
$$y=(2x-8)^{\frac{2}{3}}$$
vale wigeon
show the original problem statement in its entirety
ocean sealBOT
Asagao ζι‘
heady pollen
lapis ingot
and the numerator as the power
alpine sable
x^p/q = qth root of x^p
distant nymph
For example, y=(5x+25)^1/3