aught just asking, thanks
#help-36
red tree
rugged jay
is this deep enough understanding of division and unit conversion or do I need to go deeper ?
final saddleBOT
is this deep enough understanding of division and unit conversion or do I need t...
rugged jay
zenith shard
hmm
is the speed actually relevant here?
it kinda feels like red herring info
unless theres another q after
anyways
6km/liter
travelling 150km
rugged jay
I tried to solve it using just pure logic and division, I basically pretended like I didnt know what cancelling was or any other rules that I could not explain in words
zenith shard
150/6=25 litres needed
the car already has 20 litres
so you need to find the price of 5 litres
0.60*5=$3.00 of fuel
now, it does say for the entire drive, so if we know 5 litres is a fifth of what’s needed, then $3.00 is a fifth of the price.
$3.00*5=$15.00
soft zealotBOT
WanderingFurr
zenith shard
cheers TeXit
rugged jay
the point is to explicitly avoid multiplication since division (especially with multiple units) is harder to visualize
rugged jay
so the point is to understand division intuitively (basically able to understand perfectly whats happening)
like in this step
[liters-(km)] / [liters-(dollars)] this is basically liters/liters
after my explanation, you can understand intuitively why liters and liters cancel, you dont need to use keep change flip and rely on multiplication to understand it
zenith shard
right
rugged jay
is that a constraint to answering the question or just to avoid confusion?
well its more to expose yourself with using division only
zenith shard
oh i see why i was confused by you’re working. \
you’re saying \ $\frac{6km}{liter}$ = liters_{km} \ $\frac{0.6}{liter}$ = liter_{dollars}
whoops
rugged jay
whoops
ye is there a syntax for that ?
im basically translating both dollars and kilometers to liters
and then doing some work with them, they have a "common language" like that
rugged jay
so you think this is a intuitive enough understanding of division only unit conversion ?
zenith shard
Clear up that you mean 6km/liter = $liters_{km}$ and 0.6 dollars/liter = $liters_{dollars}$ and you’re good
soft zealotBOT
WanderingFurr
rugged jay
Clear up that you mean 6km/liter = $liters_{km}$ and 0.6 dollars/liter = $liters...
nice, are u in uni bdw ? just to make sure that its good even for unit
zenith shard
nice, are u in uni bdw ? just to make sure that its good even for unit
I’m not, to be honest.
rugged jay
well its not like the concept of unit conversion changes there anyways
tnx for the help
zenith shard
Yw!
final saddleBOT
final saddleBOT
Available help channel!
hexed bison
I am having trouble showing uniform convergence for this. I want to bound the f_n by a sequence of supremums of the functions, but I don't know how to show that it goes to 0
final saddleBOT
I am having trouble showing uniform convergence for this. I want to bound the f_...
@hexed bison Has your question been resolved?
final saddleBOT
@hexed bison Has your question been resolved?
granite thorn
Use continuity of S in 1
hexed bison
Use continuity of S in 1
Yeah I know I need to use that but I’m not sure how to relate it to the definition of uniform convergence
Maybe I should use uniform continuity of S(x) on [0,1] since that’s stronger
strange sparrow
You are not given that S is unif continuous though
whole halo
is this what I think it is
strange sparrow
Anyway, do as syssou said, pick some δ so that |f| < ε on (1-δ, 1], then...
|S| not |f| sorry
whole halo
is this your solution
strange sparrow
I think that's their attempt
they showed that fn → 0 but they need help showing the convergence is uniform
strange sparrow
yes just some minor modifications are needed
hexed bison
the first half should already do that if you reword it
really? I don't know how to fix it because my bound is not uniformly convergent
strange sparrow
Anyway, do as syssou said, pick some δ so that |f| < ε on (1-δ, 1], then...
You need to argue separately as in here
hexed bison
You need to argue separately as in here
Ok so once I do that, I think I can get to this, but I want to make sure this isn't bad maths:
Given that $S$ is continuous on $[0,1]$, $\forall \epsilon > 0$, $x, a \in [0,1]$, $\exists \delta > 0$ such that if $|x - a| < \delta$, $|S(x) - S(a)| < \epsilon$. Hence, $\forall x \in [1 - \delta, 1]$, $|S(x)| < \epsilon$.
Then, $\forall n \in \mathbb{N}$, $x \in [1-\delta, 1]$, $|x^nS(x)| < x^n\epsilon \leq \epsilon$
soft zealotBOT
Mr. BananaHead
hexed bison
I guess I need to add that $\delta \leq 1$
soft zealotBOT
Mr. BananaHead
strange sparrow
the wording of your ϵ-δ is a bit strange
you are specifically using the continuity of S at 1 so you should just replace a with 1 from the get go (the way you phrased it makes it seem like S is uniformly continuous, which is not given)
also you want 1-δ < 1, weak inequality is not enough for the next part of the argument
final saddleBOT
@hexed bison Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
calm oxide
hi guys - could i get some help here? i know i need to use cartesian equations of the 3d plane but im a bit unsure how to start
final saddleBOT
hi guys - could i get some help here? i know i need to use cartesian equations o...
calm oxide
cartesian equations should be x, y, z
so i think it would be like 1.5 for z
but how would you establish x and y? or does it not really matter
honest carbon
cartesian equations should be x, y, z
Your drawing, please?
I don't know what z refers to in your drawing.
calm oxide
sorry, the drawing im referring to is in the question
honest carbon
The drawing in the question does not establish x y and z
calm oxide
it is a cartesian plane on the 3D plane
sorry i just kind of assumed
not sure how else to start it honestly
honest carbon
Start by redrawing the cube in your 3d plane. My suggestion is that to make things easier, make the chopped corner be at (0,0,0)
final saddleBOT
@calm oxide Has your question been resolved?
boreal hound
hey can i ask physics numerical questions?
final saddleBOT
hey can i ask physics numerical questions?
boreal hound
At what temperature is the root mean square speed of nitrogen molecules equald to the root mean square of the hydrogen molecules at 20 degree celcisu? ( Molecular mass of hydrogen and nitrogen are 2g/mol and 28 g/mol respectively)
tranquil pine
what have you tried so far
tranquil pine
hey can i ask physics numerical questions?
you can ask but they may not get response as math questions do
boreal hound
you can ask but they may not get response as math questions do
ohh cool thanks
eyyy thanks for that
tranquil pine
anyways going back to the question i just solved it
ic
in that case if you dont have any further queries you can close this channel
😄
boreal hound
.close
final saddleBOT
final saddleBOT
Available help channel!
proud igloo
im being very silly but need a nudge.
where x,y are in an ordered field \
If I have $0<x<y$ \
prove $x^2<y^2$ \
I have that by $x>0$ and $y<z$ $xy<xz$ \
$x^2<xy$ and $y^2<xy$ \
final saddleBOT
im being very silly but need a nudge.
where x,y are in an ordered field \\
If I...
proud igloo
but I cant think of any other useful propositions or axioms
soft zealotBOT
Nyxzore
runic needle
how did you get y^2 < xy
proud igloo
by the proposition that if
$x>0$ and $y<z \quad xy<xz$
soft zealotBOT
Nyxzore
runic needle
and what is z here...
strange sparrow
that gives you x² < xy no
runic needle
ok so y^2 < xy is not true
strange sparrow
not y² < xy
runic needle
x^2 < xy, yes
soft zealotBOT
Nyxzore
final saddleBOT
proud igloo
ty lante ❤️
strange sparrow
and mayer-vietoris
runic needle
welcome...
final saddleBOT
Available help channel!
rustic wedge
let $f$ and $g$ be two polynomials of equal degree $n$ with real coefficients. If $f=g$ and $f$ has some fixed value of its discriminant as 'D', then does $g$ also have the same discriminant?
final saddleBOT
let $f$ and $g$ be two polynomials of equal degree $n$ with real coefficients. I...
soft zealotBOT
rak³en
rustic wedge
I am interested particularly in the $n=2$ and $n=3$ case
soft zealotBOT
rak³en
leaden moon
how do you define $f = g$ tho
soft zealotBOT
1 divided by 0 equals Infinity
rustic wedge
oh right should also mention this is a tangent from something called ferrarris method
for solving a quartic
why does this work?
and if it works does this property hold in general?
(y is a numerical constant which is to be solved for to factorise the quartic into two quadratics)
final saddleBOT
@rustic wedge Has your question been resolved?
old quarry
helloo
final saddleBOT
@rustic wedge Has your question been resolved?
rustic wedge
<@&286206848099549185>
weary cosmos
What is the original question
or youre just asking it?
rustic wedge
let $f$ and $g$ be two polynomials of equal degree $n$ with real coefficients. I...
.
pinned it too :\
vital crag
**1 divided by 0 equals Infinity**
Not really enough context to answer your question. You didn't answer this or explain how your question relates to Ferraris method you showed above since the image doesn't contain f nor g
rustic wedge
Not really enough context to answer your question. You didn't answer this or exp...
the ferrari photo is an example i suppose
vital crag
Just guessing without more context that u and y are the variables representing the two polynomials f and g
rustic wedge
Just guessing without more context that u and y are the variables representing t...
uh no, i wrote right after y is a constant we need to figure out
f and g are both variables in u
vital crag
That begs more questions than answers
final saddleBOT
final saddleBOT
Available help channel!
distant turret
hollow
polar spruce
hi what is the question
polar spruce
because it generates atp (energy)
vital crag
Why mitochondria is power house of the cell?
#old-network for biology server
tranquil pine
Why mitochondria is power house of the cell?
to keep your cells alive
keen cradle
Guys can someone help me with this pls
final saddleBOT
Guys can someone help me with this pls
keen cradle
<@&286206848099549185>
leaden moon
!15min
final saddleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
pliant elk
stats is not my thing gng
final saddleBOT
@keen cradle Has your question been resolved?
vital crag
yikes
formal trail
.close on account of op having left
final saddleBOT
vital crag
good riddance
onyx peak
Don't troll in the help channels please, use #chill if you wanna have fun
If you don't have any real question, you can close this using .close
shell condor
If you're stuck in a question or need help with a problem, feel free to ask
Oh god
Okay again, please only ask actual problems you're stuck in, for jest, move to #chill
Now please close the channel unless you have an actual question
onyx peak
<@&268886789983436800>
faint edge
timber plume
final saddleBOT
vital crag
do you know why -1 <= sinx <= 1
timber plume
yes
vital crag
where do you get lost then
timber plume
second line
timber plume
where did he divide by x?
timber plume
I do not see it 😭
timber plume
He divided the whole inequality by x
do u mind explaining me it in vc with a whiteboard if u dont mind? I think i might need visuals
vapid hound
where did he divide by x?
still need help ?
vapid hound
ive beeen trying to understand
give me a sec
vapid hound
ive beeen trying to understand
do you know how they went from $-1 \leq \sin x \leq 1$ to $\frac{-1}{x} \leq \frac{\sin x}{x} \leq \frac{1}{x}$ ?
soft zealotBOT
foxxeil
vapid hound
or is that what you are trying to understand
vital crag
because sin(x)/x is in the question
vapid hound
where did they get x from?
we can take it a step back; $2 = 2 \implies \frac{2}{x} = \frac{2}{x}$, as you can divide both sides by x, as x is equal. the same applies to inequalities given that values are real and non-negative.
soft zealotBOT
foxxeil
final saddleBOT
@timber plume Has your question been resolved?
tranquil pine
**foxxeil**
Do you understand this @timber plume
final saddleBOT
final saddleBOT
Available help channel!
hallow gust
I got the right answer but was it correct to do it without any continuity corrections?
final saddleBOT
I got the right answer but was it correct to do it without any continuity correc...
night raft
I got the right answer but was it correct to do it without any continuity correc...
I guess so because some caculators let you caculate the binomial distribution
but this depends on the mark scheme or what your teacher says
final saddleBOT
@hallow gust Has your question been resolved?
hallow gust
but this depends on the mark scheme or what your teacher says
This is the mark scheme
But why tho, why no continuity correction
Is it cuz it’s binomial -> normal -> x bar?
Also (different question) here in part ii why don’t we do poisson -> normal -> x bar?
hallow gust
<@&286206848099549185>
calm ermine
Also (different question) here in part ii why don’t we do poisson -> normal -> x...
Wdym part ii
U got it correct
X bar ≈ N(1.6,1.6/75)
CLT already implies the sample mean and the standardized sample mean is normally distributed so we can go directly from a poisson distribution to a Normal without first approximating the Poisson
Also since lambda=2 is very small appriximating the poisson first using Normal doesn't even make sense its gonna be a garbage approximation
calm ermine
Also (different question) here in part ii why don’t we do poisson -> normal -> x...
u seem to have a small notation error in part i u still used discrete random variable X instead of the discreet random variable T as u defined to be the sum of the poissons
calm ermine
But why tho, why no continuity correction
You dont need to since ur standardizing a Normal ur going from a continuous distribution to another continuous distribution
Via clt x bar follows a continuous distribution
Z also follows a continous distribution
If the og question asked you to find P(X<a) then when u go to X bar using clt ud use continuity correction
final saddleBOT
@hallow gust Has your question been resolved?
tribal nexus
if (f(x+h)-f(x))/h≈f'(x) then
f(x+h)≈f(x)+hf'(x)
is there a way i can get a better estimate of f(x+h) using second derivatives?
final saddleBOT
if (f(x+h)-f(x))/h≈f'(x) then
f(x+h)≈f(x)+hf'(x)
is there a way i can get a bett...
slow coral
if (f(x+h)-f(x))/h≈f'(x) then
f(x+h)≈f(x)+hf'(x)
is there a way i can get a bett...
if you can, please format this in latex next time, this is hard to read
slow coral
if (f(x+h)-f(x))/h≈f'(x) then
f(x+h)≈f(x)+hf'(x)
is there a way i can get a bett...
yes
tribal nexus
how can i do this
trail mango
you may want to google finite difference methods or something
slow coral
i just wrote everything out and you can use a taylor expansion of it
$f(x+h) \approx f(x) + h f'(x) + \frac{h^2}{2} f''(x).$
soft zealotBOT
IdelUser404
final saddleBOT
tribal nexus
you want some motivation on this?
wdym
tender pollen
ok basically
we want the nth derivative to match with our function
that's the motivation
the nth derivative matches with our function
tribal nexus
oh
tender pollen
so for example, our linear approximation
the 0th and 1st derivatives at a match with f
for the quadratic approximation, the 0th, 1st, and 2nd derivatives at a match with f
that's aslo where the n! comes from
soft zealotBOT
nadat12
tender pollen
then $T_1(a)=f(a)$ and $T_1'(a)=f'(a)$
soft zealotBOT
nadat12
trail mango
ts channel will close 🥀
tribal nexus
**nadat12**
ah ok
tender pollen
same with the quadratic approximations
if you do this to infinity, you get the taylor series of f
which matches all of the derivatives of f at a
sometimes, the taylor series even equals f!
tribal nexus
ah i see
tender pollen
(there's a few theorems on how taylor polynomials converge to f)
(taylor polynomials being those "matching" derivative functions)
tribal nexus
thanks
final saddleBOT
Available help channel!
late gazelle
if i take the 4th root of an integer, do I only get the one solution?
sturdy cypress
yes it's also a square root of something
late gazelle
so i get x = +-K^1/4 right
sturdy cypress
sure
proud roost
if i have x^4 = K i get x = K^1/4
multiply that by -1 or -i or i
it would still satsify the given equation
late gazelle
for it being an integer/real number still
proud roost
if i have x^4 = K i get x = K^1/4
if you start the equation from here then you would get 4 solutions
but if the given thing itself is like x= 4th root of K then you would get only 1 solution
i think
late gazelle
yea thats true
okie, ty - was just checking if i had more than just the principle root being a real number still
proud roost
but if the given thing itself is like x= 4th root of K then you would get only 1...
same goes for square root aswell
tahts why sqrtx is always positive
late gazelle
.close
final saddleBOT
final saddleBOT
✅ Original question: #help-36 message
late gazelle
bc i get arctan(3/sqrt3 )
lilac bison
also you can simplify 3/sqrt3 further
proud roost
but its in quadrant 3 so u subtract pi
proud roost
A?
lilac bison
complex roots always come in pairs
late gazelle
then do i do polynomial long div?
late gazelle
complex roots always come in pairs
conjugate pair right?
late gazelle
id only need to do long div if it wanted the other root
old quarry
id only need to do long div if it wanted the other root
not really..just sub in the values n see if it satisfies
lilac bison
well just from knowing this you can immediately find the answer but yeah what the other peple are saying
late gazelle
oh it does want the other root
so, polynomial long div or whats the thingy called where you check like 0, 1, 2, -1, -2
old quarry
trial and error
proud roost
so, polynomial long div or whats the thingy called where you check like 0, 1, 2,...
brev
late gazelle
where did the x come from?
proud roost
-3-i
-3+i
and lets say x are roots
.
late gazelle
yea i realised that it was a degree 3, then deg 2, then deg 1 and 0... bc i thought the rhs had stuff we needed to use
i got cisx/sinxcosx
oh wait nvm
it should be cis(-x)/sinxcosx
hmmm, a = 2i is not one of the answers
do I not just subst. Z = -2+i and simplify then solve for a? by setting the resulting thingy to 0
proud roost
yea i think thats the only way
late gazelle
what am i doing wrong 😭 i get 2+9i + a(-2+i) = 0
is a not equal to 2i?
oh wait nvm
oh thats funny
i wrote my 9 too much like a 4 and it became a 4 on my final step
proud roost
lol
late gazelle
-1 +4i is 100% more reasonable loll
a question that looks like this should be illegal
is the fastest way to find the modulus just by expanding everything and then simplifying or is there a trick to make it faster?
proud roost
do you know modulo properties
if there are multiple products in a given expression and if your asked to find the modulo of the expression then you can just find each terms modulo individually and multiply them
it works no matter how many there are
late gazelle
i got something like mod(a/b) = mod(a)/mob(b) where mod(b) = mod(b1) * mod(b2) * mod(b3)
proud roost
modulus of cis of anything is 1, modulus of i is 1 aswell i think you can figure out the rest
proud roost
i got something like mod(a/b) = mod(a)/mob(b) where mod(b) = mod(b1) * mod(b2) *...
yep
late gazelle
modulus of cis of anything is 1, modulus of i is 1 aswell i think you can figure...
is that actually true?
mod (cis(a)) = 1
late gazelle
thats if its {cis(a)}^2 tho
late gazelle
cos^2a+sin^2a is 1 so ye
where does cos^2 + sin^2 come from?
i dont see how we get that
proud roost
cisa = cosa+isina right
late gazelle
yes
proud roost
take mod now
late gazelle
ohhhhhhhhh
late gazelle
that makes more sense now
proud roost
this makes alot sense because for me i was taught as e^ix=cosx+isinx which maps out a unit circle
late gazelle
i havent learnt that but ive seen countless videos about that expression
oh yea, bc for any x its always 1
late gazelle
bc if x = pi, we get the vector at -1 on the unit circle so e^ipi = -1 so e^ipi + 1 = 0
proud roost
its very easy to derive tho because
e^x has the expansion 1+x+x^2/2!+x^3/3!... infinity now if you keep x=itheta and if we serperate the real and imaginary parts in the taylor expansion we get costheta expansion in real part and sintheta expansion in imaginary part
late gazelle
yea the taylor series of e^x evaluated at itheta
sooo, im getting 3/4 but its obv not the correct answer
late gazelle
hmmm, a = 2i is not one of the answers
this is just the same thing as this one right
proud roost
almost
late gazelle
lemme try it rq
oh wait
how do we do that, bc its got an x in there and we also need to know what a is
should we get something like:
$(x-3+i)^2 + a(x-3+i) + 10 = 0$
soft zealotBOT
KB
soft zealotBOT
KB
late gazelle
i dont understand sorry
late gazelle
x^2=ax+10 = (x-3+i)(smth)
i dont recall seeing something like this (ever)
proud roost
this is just the same thing as this one right
they said x-3+i is a factor of x^2+ax+10
do you know what factor means/
late gazelle
i should >.<
proud roost
is 3 a factor of 9
late gazelle
yes
proud roost
why
late gazelle
bc 3*something = 9 alt. 9/3 = something which is a constant integer?
proud roost
is x+1 a factor of x^2+2x+1
late gazelle
yea
proud roost
why
late gazelle
bc (x+1)*something = x^2 + 2x + 1
proud roost
what is that something
late gazelle
so we divide x^2 + ax + 1 by x-3+i and get an expression which should find a?
proud roost
bro do you understand the point that x^2+ax+10 = (x-3+i)(smth) ?
late gazelle
ye
proud roost
so if we set x^2+ax+10 to 0 then 3-i would be a root
but if x^2+ax+10 has all real co-effs then the roots are conjugates meaning
the other root is??
late gazelle
x-3-i
late gazelle
hmm, this sum of roots sure does come up a lot...
oh so a = 6
tysm for the help! i'll be fine with the rest
.close
final saddleBOT
final saddleBOT
Available help channel!
radiant oxide
The school asked company C to consider the issues and submit a proposal for the construction. Company C decides that they will charge $45 per metre for computing cable if it is laid in trenches which they dig, rather than using the covered walkways. The trenches would use the shortest possible distance between buildings and all buildings would be connected via trenches so they would be connected in the computer network. Draw up company Cs proposal, including a network diagram of the trenches that would need to be dug, and a costing. Justify your answer by calculations and network theory.
final saddleBOT
The school asked company C to consider the issues and submit a proposal for the ...
radiant oxide
I dont understand what its asking me to do
I have spent like 7h trying to figure things out and i dont get it
I understand its asking for a minimum spanning tree but what trips me is that i cant use the black lines
Ive tried to use an existing MST consisting of the 'walkways' (blacj lines) and tried to make my own lines to make it smaller in distance but it didnt seem right
I then tried to do the whole thing and highlight MST path but somehow got a longer length
i've also asked like 5 of my friends and they keep doing a MST with the black lines - not what the question is asking
timber leaf
The school asked company C to consider the issues and submit a proposal for the ...
Find shortest route is the main point
rare island
But idk what to draw and where
the black lines refer to the paths you can't use?
rare island
its math right
radiant oxide
idk why its asking me to be an architect and build own trenches
timber leaf
Lowkey vague
rare island
have you been taught prim's algorithm?
radiant oxide
Yes
rare island
ok that might be a good starting point then
radiant oxide
I used kruskals for question 2 which was find MST using black lines
rare island
i see
radiant oxide
But this is asking for same thing without black lines and i feel like i dont evne know where t start and where to draw what
rare island
from what im seeing literally all the edges are blacked out
maybe its asking for the shortest hamiltonian path
trenches can be your edges
radiant oxide
I feel like i should be using my mst using black lines as a 'guide' but at the same time idek what the question is asking
rare island
but yea this is uneccessarily vague
radiant oxide
i asked like 4 different ai's and it all gave me diffenrent answers
radiant oxide
but yea this is uneccessarily vague
So the question is like unclear
rare island
yea very
do you have office hours with your professor?
maybe ask for help on this one cause i dont understand exactly what the question wants us to do
radiant oxide
Um yea but its like due tmr so i cant rlly ask anyone
rare island
ok firstly, what's the scale of this graph you've given us
radiant oxide
ok firstly, what's the scale of this graph you've given us
1 cm is 2000 cm
rare island
yes yes but you realise how the scale of the image is different across different screens?
rare island
that would help you with the calculations once you have the shortest path
rare island
The school asked company C to consider the issues and submit a proposal for the ...
ok so first things first, let's assume those buildings are the nodes and we need to build a network that visits every node with the shortest possible path
radiant oxide
MST and network diagram
radiant oxide
they have high schoolers doing this stuff
making me feel like im working towards a phd
That migjt be clearer
rare island
so your job essentially is to make a path that visits every node. the distance between each node is what we'd call the cost(this refers to your building cost)
radiant oxide
yes
rare island
your job is to minimise said building cost
the hard part is finding an optimal path that visits every node
radiant oxide
yes
rare island
could you tell me what path you made here
radiant oxide
could you tell me what path you made here
minimum spanning tree
rare island
yes could you tell me the exact path you followed
because to me it looks like you made a cycle in there which violates the conditions of a tree
and does the path even need to be a tree?
a tree is not neccessarily the most optimal path here
radiant oxide
Wait what cycle
rare island
to me it looks like EJPCB forms a cycle
which violates the criteria of a tree
a tree cannot have any cycles in it
which is why i ask for clarification on what the red path exactly is
tribal stratus
bad questrion
rare island
like tell me what the path is
rare island
bad questrion
i think its a good question but its poorly phrased
this is the defintion of a real life application
radiant oxide
MST and network diagram
Wait does this one also have cycle
rare island
MST and network diagram
the first image does not
that first image is a satisfactory spanning tree
radiant oxide
Uhhh ok cus my friend drew this one
😭
I thought it was the same
so I sent it
Ok so i drew the paper one, a minimum spanning tree
That fllws the walkways
radiant oxide
yes
rare island
MST and network diagram
over here
now just bring out the calcultor
and multiply the total length
and add up the costs
radiant oxide
It was like378m and $13230
rare island
sounds about right?
radiant oxide
yea
rare island
well then we're done
rare island
wtf is q3
radiant oxide
q4 says dont use the walkways u have to create ur own vertices
rare island
wdym create ur own vertices?
that would mean creating my own buildings/halls
you mean your own edges right?
rare island
alright
so the game is to figure out the cheapest route
with no restrictions on what our path will be
radiant oxide
and the edges u create are suppose to be smaller in length than 378m at the end
yes
rare island
unless you've been taught some algorithm for the shortest possible path
ok first things try just making small improvements on the existing path
radiant oxide
unless you've been taught some algorithm for the shortest possible path
umm there is an algorithm but i havent learnt it and i dont thinkwe will cs we moved nto a diff topics
isnt it like
dijkstra
idk
radiant oxide
ok first things try just making small improvements on the existing path
ok so if i look at my mst and for eg i see A-B is a slanted walkway measuring 12m but would be smaller in length i would draw a perfect horizontal line which is 10mto represent a 'trench' thats it?
and ishld i js repeat the process for each edge in my mst
rare island
yes, try any possible optimisation
radiant oxide
but if for eg the legnth between A-B is like 10m and cant get any smaller i leave it as it is
rare island
ye
you can either use your own hands to find a shortest path, or use an algorithm from the internet to give you the shortest path using a recursive algorithm
if you do end up using an LLM, tell it to create an algorithm that accepts an adjacency matrix for the graph along with a corresponding graph of the cost of every possible edge and then finds the shortest path possible using recursion
final saddleBOT
rare island
you're welcome
final saddleBOT
Available help channel!
jagged flare
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jagged flare
ok... wtf? why do i only get the solution the second i post them
smj
ok actually, what did we define n as at the start?
is it just some product p^a(p) for some a(p)
then d(n)=2^k iff a(p)=2^(b(p))-1 and the sum of b(p)=k?
honestly im having a hard time grasping the solution as its really abstract for me
raven marsh
nice problem
oh
go on aops
i remember there being better sols
mont is being fancy
jagged flare
mm sure
jagged flare
forums right
jagged flare
i had apmo today
wtf??
is apmo invitational like imo
ik its prestigious and the questions are hard
desert mantle
ok actually, what did we define n as at the start?
its just the prime factorization of n
alpha(p) is just whatever the exponent of p turns out to be
you should know the formula for the number of divisors given the prime factorization
jagged flare
mm ok yeah
desert mantle
so the first few sentences really just write themselves
jagged flare
then why is n the product of subset T of S, where S is primes in the form of p^(2^i), when the above statement implies n is the product of primes in the form p^(2^i-1), or is that just a mistake?
raven marsh
is apmo invitational like imo
yes
raven marsh
forums right
mhm
jagged flare
are you eligible for imo yet
raven marsh
theres people much much better than me
desert mantle
then why is n the product of subset T of S, where S is primes in the form of p^(...
lets say alpha(5)=7. then n has as factors 5^7 = 5^(1+2+4)=5^1 *5^2*5^4
raven marsh
also advice is dont try to comprehend those sigmas and products all at once
the author is just cooking with complicated notation
see if you can break it doen
desert mantle
into S we are putting the numbers 5^1, 5^2, 5^4, 5^8, 5^16, ...
so T would include 5^1, 5^2, 5^4 here
jagged flare
ohh wait ok i see
raven marsh
sigma
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whole jungle
help, this problem makes me think if i should pursue engineering
final saddleBOT
help, this problem makes me think if i should pursue engineering
soft zealotBOT
low snow
help, this problem makes me think if i should pursue engineering
2cotx/sinx will become 2 cotx cosecx
And
3 sin^2x / sinx will become 3 sinx
Rest is simple integration
whole jungle
can't find cot x in here, im basing on what my teacher taught us, so uhm google says that the integration of cot x have natural logarithm but we haven't gotten there...
low snow
Uh it's cotx/sinx which is equal to cotx*cscx
whole jungle
ohh
low snow
can't find cot x in here, im basing on what my teacher taught us, so uhm google ...
Yes derivation log|sinx| is cotx
final saddleBOT
low snow
No problem
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north spear
hi i need help with this math problem
final saddleBOT
hi i need help with this math problem
north spear
here is the translate on it in english
i know every step how to solve this type of question but i struggle to understand when reflection in the line x_2=-2x_1
what this mean and how i need to think about this step
anyone who know how to think on this step?
i asked gemini and he told me just to have 1= x_1 and x_2= -2
so it will be v= [ 1 -2]
is it just this simple?
night raft
i asked gemini and he told me just to have 1= x_1 and x_2= -2
Shouldn't use Ai btw 
north spear
Shouldn't use Ai btw <:catglasses:1037770587235434567>
yea ik bro but nobody is answering xD
i need to learn how to think about this part just
i know the rest of the question how to solve it
night raft
so it will be v= [ 1 -2]
yeah you can think of the line of reflection as a vector along the line
north spear
yeah you can think of the line of reflection as a vector along the line
okay if its in R3 tho how would it apply it there then?
versed crater
In R³ I recommend using projections to help you think about this
north spear
In R³ I recommend using projections to help you think about this
like this question?
where the reflexion is on the x_3-axis?
what i understand on this is that x1 and x2 changes but nothing happens to x3
versed crater
Yeah so imagine this
If you want to know how the map transforms vectors you want to see what it does to basis vectors
So pic a basis vector red one and look at its projection onto the line of reflection
north spear
If you want to know how the map transforms vectors you want to see what it does ...
yea i know this exist but i dont understand it when i am drawing it but its possible to solve this type of question without drawing it right?
versed crater
Now if you add twice the difference to red you get the reflected vector
versed crater
yea i know this exist but i dont understand it when i am drawing it but its poss...
No the idea in 3D should be the same
north spear
No the idea in 3D should be the same
so i need to understand the drawing part for the exam?
versed crater
No I said imagine this
north spear
uhhh okay i see
versed crater
You can see it in 2D but surely you can try to formulate it for higher dimensions
north spear
You can see it in 2D but surely you can try to formulate it for higher dimension...
but in general which rule should i remember the diffrent between a R2 and R3 when it comes to reflection?
versed crater
What do you mean which rule
north spear
in R3 its always that i need to this [ 1 0 0 ,0 1 0, 0 0 1]
on the type of questions but for R2 its always just [1 0] (example)
versed crater
Why is it only [1 0]
north spear
And in R2 it just like reflection on x1 to -x2
north spear
Why is it only [1 0]
it was just example could be [1 -2]
versed crater
What do these brackets even mean
north spear
but on R3 it just a reflection just on 1 x-axes
versed crater
In this picture you need to do the (0, 1) vertical basis vector as well
north spear
what i mean is in R3 we always think about the general rule of [ 1 0 0 ,0 1 0, 0 0 1] and thats what u change based on the information on the question right? it cannot be like R2 where reflection on x_1 to -2x_2 for example
north spear
In this picture you need to do the (0, 1) vertical basis vector as well
do u understand what i mean lol?
versed crater
I do not know of this general rule you speak about
north spear
of [ 1 0 0 ,0 1 0, 0 0 1]
idk what its called in english
but its a rule
right @night raft ?
night raft
I don't get what you mean either 
night raft
are you talking about the identity matrix?
north spear
yes
in this type of question i get for example in R3 they ask me just do a reflection of the identity matrix
north spear
like this question?
like i showed in the picture
where here i need just swap x2 and x1 and let x3 be
north spear
are you talking about the identity matrix?
so i am on the right step now xD?
or i am just a delulu
versed crater
It’s like you didn’t even read what I wrote
north spear
It’s like you didn’t even read what I wrote
i did bro but i dont understand the drawing cause i never done it
i never draw in linear algebra...
versed crater
Surely you have learned about projection one vector onto another vector
north spear
Surely you have learned about projection one vector onto another vector
yea i have but i havent paid attention to it ngl
versed crater
Then go revise it
versed crater
Then all you become is a very bad computer
north spear
Then all you become is a very bad computer
yea true but its a rexam i have only 2 days before the exam so i just need to understand how to do it
.close
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robust hollow
A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m2?
final saddleBOT
A flooring tile has the shape of a parallelogram whose base is 24 cm and the cor...
robust hollow
someone help?
final saddleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
manic leaf
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
what have u gotten so far
robust hollow
1080m^2
robust hollow
by dividing it?
manic leaf
yes but can you divide it directly?
manic leaf
looks right
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dense coral
just seeking a clarification: should the argument of either f_j or g_j be x instead of y?
final saddleBOT
just seeking a clarification: should the argument of either f_j or g_j be x inst...
dense coral
surely, right? otherwise the statement seems false? 
vital crag
yea you should assume f_j(x)
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fast ocean
hey, i am solving for question c
final saddleBOT
hey, i am solving for question c
fast ocean
and when i solved it
i think the answer from the teacher is incorrect
This is the teacher answer
and this is my answer
so which one is correct ?
drowsy epoch
,w 3x^2-6x<0
soft zealotBOT
drowsy epoch
and this is my answer
endpoints dont really change anything
that's why you can include them
fast ocean
so both are correct ?
drowsy epoch
i'd say yes, since it doesn't make a difference for strictly monotonous functions
i would ask your prof tho seems like a matter of preference
dire narwhal
How would I even approach a question like this:
Given some random draw of five distinct numbers (repeats allowed) from {1,2,...,20}, what is the chance that a true arithmetic equation can be formed using ALL of the five numbers, the operations +,-,*,/,^,! and parentheses?
details:
- Five numbers are drawn (for instance, we might get
(1,1,5,8,20) - Their order is irrelevant
- If a number is drawn n times, it must be used exactly n times.
- We must form a true arithmetic expression, eg.
20+5+17=(4!)+18
Follow-up question: Given that the numbers are each drawn uniformly, what is the expected value of one side of such an expression?
My only insight thus far is that we only need to consider partitions of (1,4) or (2,3) numbers on each side of the equals sign, respectively. An equation with 0 numbers on one side is not an equation at all and (3,2) or (4,1) are equivalent because equality is a symmetric relation.
final saddleBOT
How would I even approach a question like this:
Given some random draw of five ...
dire narwhal
You may use only the 5 numbers (once each), the operators +,-,*,/,^,! and parentheses.
so no arbitrary functions are allowed. In that case it'd trivially always be possible and the expected value would be... whatever you want it to be
pliant elk
if we are only using + -
modular arithmetic can help us deduce cases where it is not possible
- and / make it a lil tougher
and ^ , ! makes it hell
in anycase
we would have to find cases where it is not possible
final saddleBOT
@dire narwhal Has your question been resolved?
dire narwhal
I mean intuitively it seems likely that 16,17,18,19,20 would be a counter-example? But how would I prove or disprove that, let alone find some sort of general rule to apply?
desert mantle
are you doing this just for fun?
I dont see any reason to believe that there should be any nice way to solve this
the four fours puzzle shows that shit can get crazy
dire narwhal
But it also shows that some combinations are unsolvable using only the operations allowed in this
final saddleBOT
@dire narwhal Has your question been resolved?
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Available help channel!
heavy grove
The Dirichlet Problem for a Rectangle:
hey I’m stuck on equation 4, I don’t get where sinh is coming from, but I kinda get where sin is coming from. From my understanding case 1 is the only of the 3 cases to meet the BC because we can let c1 be 0 without u being zero always. Then it’s
$$c_2sin(bx)\left(d_1e^{by}+d_2e^{-by}\right)$$
Which I can see why we’d be tending towards cosh, but I feel like they have some bias for choosing sinh beyond it looking nice matching sin(bx). I get I can just let d2 be negative and then boom I have a sinh but I just don’t get why we’re doing that. I feel like what follows 4 is more of a justification for why it works rather than why it is what works as opposed to alternatives
final saddleBOT
The Dirichlet Problem for a Rectangle:
hey I’m stuck on equation 4, I don’t get...
soft zealotBOT
Nathan
final saddleBOT
@heavy grove Has your question been resolved?
candid hull
The Dirichlet Problem for a Rectangle:
hey I’m stuck on equation 4, I don’t get...
I feel like what follows 4 is more of a justification for why it works rather than why it is what works as opposed to alternatives
it's not like they give any justification for why 4 is true, they're just stating the result
they did the work, they're just not showing it to you
so it's a good opportunity for you to check they didn't fuck up somewhere by doing the work yourself
final saddleBOT
candid hull
.reopen
final saddleBOT
✅ Original question: #help-36 message
candid hull
From my understanding case 1 is the only of the 3 cases to meet the BC because we can let c1 be 0 without u being zero always.
like ok you might be able to intuit that c1 has to be 0 by eyeballing it
why can b be only n*pi/L though ? at some point you gotta struggle with the BCs
heavy grove
Is it cause it makes it always 0 at the endpoints of the side?
And I think I derived it properly, I’ll show a photo in a sec, but I just spammed BCs until I solved for d2 in terms of d1 and was able to factor and manipulate some stuff to get me that sinh
candid hull
yeah indeed
candid hull
aight
final saddleBOT
@heavy grove Has your question been resolved?
chilly rover
Can someone explain me 13 and 14, I dont understand them
final saddleBOT
Can someone explain me 13 and 14, I dont understand them
chilly rover
I am confused at the plotting part
dapper hull
Can someone explain me 13 and 14, I dont understand them
What part of them do not understand?
dapper hull
i mess that up so much
They putting dashes to indicate the coordinates you are traversing
dapper hull
i mess that up so much
It’s not that best
But small indicators like this help a lot
chilly rover
This is so weird
dapper hull
This is so weird
I get you, it’s weird.
But these two vectors are parallel and got the same length so yeah they work
chilly rover
lemme draw mine and show u
final saddleBOT
@chilly rover Has your question been resolved?
vague bear
How would we go about checking if two graphs are isomorphic
final saddleBOT
How would we go about checking if two graphs are isomorphic
rocky tusk
by finding the isomorphism
if it exists
if not just see if it violates some of the necessary conditions for
the graphs being isomorphic
vague bear
Yeah I mean
How would we go about finding the isomorphism function
Or it's lack thereog
Thereof
rocky tusk
so you’re mapping corresponding vertices in the graph
it would help if you checked the degrees and found where the edges were in each
vague bear
Uhh
vague bear
I wanna build towards that but rn I just want an intuitive way I can check two graphs isomorphic or not myself
short talon
there are some crazy state of the art algorithms, but there isn't anything significantly better than just brute force checking each possible mapping
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hollow gust
What is calculus (for simple explaining) lesson 1
final saddleBOT
What is calculus (for simple explaining) lesson 1
hollow gust
Link pls for calculus
final saddleBOT
drowsy epoch
Link pls for calculus
You may check out the pins in #calculus
hollow gust
.close
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Available help channel!
tender heart
I need help with b), I need to prove whether the function is even or odd, idk if what i did was great
final saddleBOT
I need help with b), I need to prove whether the function is even or odd, idk if...
drowsy epoch
,rccw
soft zealotBOT
drowsy epoch
Why did +1 become -1
tender heart
Oh wait im stupid
I accidentally did smth similar to multiplying the function with -1, oopsies
tender heart
So sin -x is equal to -sin x and then it becomes sin x with factorising the -
Right?
drowsy epoch
sin(-x)=-sin(x) because sine is odd
tender heart
Indeed
drowsy epoch
so then we would have $-\sin(x)(1+2\cos(x))+1=-(\sin(x)(1+2\cos(x))-1)$
soft zealotBOT
tender heart
And cos -x id cos x because cosine is even?
drowsy epoch
yes
drowsy epoch
As a clue: I tried to pull out - to see if we can conclude f(-x)=-f(x) for example, but that doesn't seem to be the case
tender heart
Indeed
drowsy epoch
So it seems to be neither even nor odd
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inland flame
Hi does anyone know why the answer is a?
I guessed a & my tutor said correct & im too scared to ask him why because he sounded mad already 💀
final saddleBOT
Hi does anyone know why the answer is a?
I guessed a & my tutor said correct & i...
inland flame
It just looks like it makes sense
inland flame
Hi does anyone know why the answer is a?
I guessed a & my tutor said correct & i...
For no 9
inland kettle
for inverse functions, just swap around x and y
for example, if my inverse function is y = sin(x^2) the inverse function will satisfy x = sin(y^2)
what equation would the inverse function satisfy here?
inland flame
what equation would the inverse function satisfy here?
?
inland kettle
!nosols
final saddleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
inland kettle
oh my god
inland kettle
As a helper, please do not give out answers that could be copied as a homework s...
@proud roost
inland kettle
thank you
inland flame
i have no idea what you did there
I swapped around the x & y 😅
Idk if i did it right tho
inland kettle
not
quite
i meant for your question
unfortunately, i have to go eat dinner
so i won't be able to help
apologies for the abrupt departure
but i'm pretty sure someone else will stop by
inland flame
Oh okie enjoy your dinner!
inland flame
i meant for your question
Oh ok
proud roost
Idk if i did it right tho
there is another method
take f inverse on both sides
you would x=f inverse of (x^3+3)
but u need to find f inverse of x
so say x^3+3= alpha and solve for x and replace it on lhs
try doing it
proud roost
so say x^3+3= alpha and solve for x and replace it on lhs
we do this to single out the term inside f inverse
inland flame
What's lhs?
proud roost
left hand side
inland flame
Like this? Im sorry idk what you're talking about 😭
pliant elk
!status
final saddleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
