And i'll help from there
#help-0
solid fog
ah actually i just got it
topaz tartan
allg
lone heartBOT
solid fog
.reopen
lone heartBOT
✅
solid fog
lone heartBOT
@solid fog Has your question been resolved?
empty stone
what is a null set
lone heartBOT
what is a null set
weary wyvern
Empty set?
vapid shuttle
empty stone
ok
alpine sable
it's the unique set that has no elements. Its size or cardinality is zero
denoted as [
\set{}, \emptyset, \tsx{and a few others}
]
ocean sealBOT
mortal trellis
in what context? in measure theory it also means something else - a set of measure zero
lone heartBOT
@empty stone Has your question been resolved?
echo socket
fast gyro
i know he used newton binomial but i don't know where come from the sign "-"
mortal trellis
1-1/n=(n-1)/n
lone heartBOT
lone heartBOT
Available help channel!
naive linden
How can I calculate 2.5D rotation of a 2D point around a hypothetical Z axis?
I'm trying to rotate a 2D point - for instance X=50, Y=27 - around a pivot point along a hypothetical third Z axis. I'm not entirely sure how I can calculate the end points after rotation. It's important to note that this is all done with 2D, and the 3D rotation is an illusion (this is called 2.5D, for those curious).
For a visual demonstration, see this YouTube video (https://youtu.be/vTTdchYmzJM?si=ac97rY5PVm8FxYSk&t=14) from 0:14-0:23 where it rotates a character in increments of 45 degrees.
Imagine the top of the shoulder for instance, as a 2D XY coordinate and the pivot point being the center of the body. You will notice that the top of the shoulder will rotate around the Z axis (despite being in 2D!). The result of this is a sort of straight line shape as opposed to a circle shape around the pivot point.
mellow grail
**How can I calculate 2.5D rotation of a 2D point around a hypothetical Z axis?*...
Are u rotating a point or a sprite?
naive linden
Are u rotating a point or a sprite?
I'm more or less looking for how to calculate the point. The sprites will all be replaced programmatically, but it's the math that I need help with.
mellow grail
I'm more or less looking for how to calculate the point. The sprites will all be...
Well the video isn't really 2.5D, it's hand drawn sprites
mellow grail
I'm more or less looking for how to calculate the point. The sprites will all be...
Where are u building this?
naive linden
Well the video isn't really 2.5D, it's hand drawn sprites
The environment is 2D and the rotation is 3D, which makes it 2.5D.
naive linden
Where are u building this?
It is for a project I am working on, though I don't think the programmatical details matter too much, do they? I am just looking for help with the math.
naive linden
Well the video isn't really 2.5D, it's hand drawn sprites
The way to visualize it would be like this, where the green squares are being rotated around the theoretical Z axis. (the axis is not there, it is the illusion from moving the points that makes it appear as such).
Whereas for 2D, it would be like this, which is not what I am after:
(pretend that is going around in a circle, like a clock)
mellow grail
The way to visualize it would be like this, where the green squares are being ro...
You could rotate it in 3D and then flatten it and render it on 2D
Like using perspective
naive linden
How do you rotate a 2D point in 3D, then? As in, the math required to calculate the destination.
mellow grail
How do you rotate a 2D point in 3D, then? As in, the math required to calculate ...
Good question
Ray tracing? 
naive linden
Please, no 👀
mellow grail
You can follow sebastian lagues tutorial on youtube if you want to build a basic ray tracer
mellow grail
Please, no 👀
Well that's just crazy
naive linden
You can follow sebastian lagues tutorial on youtube if you want to build a basic...
I'm not sure a ray trace would be appropriate here. I would think of this as more of a trigonometry problem, personally.
mellow grail
I'm not sure a ray trace would be appropriate here. I would think of this as mor...
Well I am not really good at trigonometry 😅
You should do a helpers ping
naive linden
<@&286206848099549185>
lone heartBOT
@naive linden Has your question been resolved?
mellow grail
lone heartBOT
@naive linden Has your question been resolved?
empty stone
f(x)=x-2
vague coral
wide sierra
lone heartBOT
@empty stone Has your question been resolved?
empty stone
ok
welp
b 7g
8y8y
8t h
u9 y
y 9y
y8y y
8t8ug
8g 0g
gu
ougb
u g
worn fox
Wtf are you doing
worn fox
Please don't troll in the help channels
worn fox
Use a calculator
worn fox
Youre on a computer or mobile device, it'll have a calculator
There is even a calculator right here
,calc 1+1
ocean sealBOT
Result:
2
@empty stone Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
twilit inlet
ayy can some1 help me
lone heartBOT
ayy can some1 help me
dull dove
twilit inlet
lone heartBOT
@twilit inlet Has your question been resolved?
alpine sable
4√ 7+4√ 3-4√ 6
4(√ 7+√3-√6)=4*2=8
primal galleon
I'm currently working on a problem involving path counting in the x-y plane, and I could use some guidance on how to approach it. The problem is as follows:
primal galleon
My approach to solving (a) was that we start at the point $(0,3)$ and need to reach the point $(7,2). In each step, we can either move up one unit and to the right one unit (denoted as U), or move up one unit and to the left one unit (denoted as L). To reach our destination, we must take 3 "U" steps and 4 "L" steps. This is because we need to go from a starting y-coordinate of 3 to a final y-coordinate of 2 (a difference of 1), and move 7 units in the x-direction. Now, the question is how many different combinations of 3 "U" steps and 4 "L" steps we can take, where the order of the steps doesn't matter. To count these combinations, we can use combinatorics. One way to do this is by calculating the binomial coefficient "7 choose 3," which is also denoted as "$C(7,3)$." This can be computed as: $C(7,3) = 7! / (3!(7-3)!) = 35$.
But I am not sure if this correct?
As for (b) to (d), I am not really sure how to solve the questions and would like some help.
lone heartBOT
@primal galleon Has your question been resolved?
lone heartBOT
@primal galleon Has your question been resolved?
lone heartBOT
@primal galleon Has your question been resolved?
twin nimbus
@primal galleon your approach to part (a) looks correct to me
For (b) you have 4 Ls total and 3 Us. In order to touch the x axis you have to have either 3Ls before you have 1 U or 4 Ls before you have 2 Us. So for case A we have 1 path down (LLL) then the other 4 can be arranged however (4C1). For case B we have 5C1 paths down (ULLLL, LULLL, and so on) and then all of the Ls are used up, so the second half is locked in place.
Finally, there are two paths that are double counted in this, the ones beginning with LLL in case B. So subtract those two away.
4+5-2 = 7.
From here, (c) and (d) should be manageable for you.
Best of luck and I hope you see this @primal galleon
primal galleon
For (b) you have 4 Ls total and 3 Us. In order to touch the x axis you have to h...
For (b) you have 4 Ls total and 3 Us. In order to touch the x axis you have to have either 3Ls before you have 1 U or 4 Ls before you have 2 Us.
Didn't quite get this part
twin nimbus
So in order to reach the x axis you have to go down a net of three spaces right?
primal galleon
Yes, atleast
twin nimbus
So that means you need LLL or 4Ls and 1U
because you only have 4 Ls to work with
You can't do 5Ls and 2Us
twin nimbus
So you have two parts, the dive down to the x-axis, and then the rest.
primal galleon
LLL + LUUU
and
LLLL+UUU
you mean?
twin nimbus
Well, so you have LLL + other 4 in whatever order
twin nimbus
and (4Ls and a U) + UU
primal galleon
Well, so you have LLL + other 4 in whatever order
so how is that translated into the formula
in my head i'm thinking 7!/4!3!
twin nimbus
It's 4C1, because there are 4 spaces that are free to change, and only one L
primal galleon
Okay can you explain how the numerator and denominator numbers were chosen
twin nimbus
I didn't use numerator and denominator?
twin nimbus
after LLL there are 4 spots left, 1 of them must be an L the other three must be U
primal galleon
after LLL there are 4 spots left, 1 of them must be an L the other three must be...
Okay so the 4 in 4C1 is the " 1 of them must be an L the other three must be U" part, and the 1 is the "after LLL" part?
primal galleon
Well, so you have LLL + other 4 in whatever order
Okay, so if this is 4C1, what's the (4Ls and a U) + UU in that notation?
twin nimbus
5C1 * 2C0
primal galleon
Where 0 in 2C0 comes from?
twin nimbus
There are no choices to make
you must have UU
(there isn't an L to move around within the Us or a U to move around within the Ls)
primal galleon
Okay. T_T
I don't get much smarter from this, but let's say this is the case
How do you then end up with 7Choose1
twin nimbus
If you have one distinct thing that you have to put in one of 7 spaces
fringe sandal
can you help me pls
twin nimbus
can you help me pls
twin nimbus
Then that's 7C0?
7C0 is when you have 0 things that you're trying to put in 7 spots.
primal galleon
7C0 is when you have 0 things that you're trying to put in 7 spots.
Ah I see
How do you determine the "spots" again?
twin nimbus
7C1 is one thing in 7 spots, 7C2 is two things in 7 spots, and so on.
primal galleon
The "things" bit is a bit clearer to me now
twin nimbus
things in this case is either Us or Ls.
I've been using whichever is smaller
but honestly, you can just pick one and it will give you the same result.
The spots is the number of places where you're putting the Us and Ls for this particular situation
So in the case of LLL + (the other 4 in any order)
if we're looking at the second half of this problem
where we're putting 3Us and 1L in 4 spots.
the spots is 4, and the total arrangements is 4C1 or 4C3
these are the same number (4)
primal galleon
I'm lost.
twin nimbus
It would be helpful if you told me where I lost you
primal galleon
I've been using whichever is smaller
but honestly, you can just pick one and it will give you the same result.
the spots is 4, and the total arrangements is 4C1 or 4C3
these are the same number (4)
twin nimbus
sorry
Got called away temporarily
nCk is defined by n!/k!(n-k)!
so if you replace k with (n-k) you get the same value.
nCk = nC(n-k)
4C3 = 4C(4-3)
lone heartBOT
@primal galleon Has your question been resolved?
pale kestrel
nCk is defined by n!/k!(n-k)!
,,\frac{n!}{k!(n-k)!}
ocean sealBOT
lone heartBOT
@primal galleon Has your question been resolved?
alpine sable
@thick basalt
Hehehehehe
Let’s get u to 10K ping 🙂
@thick basalt
I lit have to charge my calculator
alpine sable
What is discussion
mental flame
Srry for the clogging dgh
mental flame
read #❓how-to-get-help , this channel is occupied
your not supposed to go to the exact help channel in the directions, go to one of the available ones listed in the "math help available" section
lone heartBOT
lone heartBOT
Available help channel!
keen egret
Can someone help me figure out 3b (also check 3a maybe afterwards?)
mellow quiver
Can someone help me figure out 3b (also check 3a maybe afterwards?)
it will tend to negative infinity from the left
and positive infinity from the right
keen egret
ok
mellow quiver
limit does not exist
mellow quiver
yes
mellow quiver
there must be a vertical asymptote at x = 1
mellow quiver
is 3a right?
correct
keen egret
ok thx
so how can I show that in my work
like I understand it
but writing it out confuses me tf out
oblique sorrel
What should I do to solve this?
lone heartBOT
What should I do to solve this?
oblique sorrel
Is there like a formula or sum I should use
wary stream
What should I do to solve this?
Are you allowed to be asking for help on a quiz?
oblique sorrel
Are you allowed to be asking for help on a quiz?
Going over our mistakes from the quiz
Like the wrong answers
wary stream
Did you look up midpoint formula?
oblique sorrel
Thanks gang
oblique sorrel
Did you look up midpoint formula?
What i do wrong
wary stream
Because you are given one of the coords and the midpoint
You are looking for the other coord
lone heartBOT
oblique sorrel
Yes
lone heartBOT
Available help channel!
chilly idol
I need to find the inverse of this function
lone heartBOT
I need to find the inverse of this function
chilly idol
I know that you need to switch the y and x variables
and I have gotten to x+4 = 3(2)^y
right now im kind of stuck
ocean sealBOT
hayley!
chilly idol
yes
tardy stag
so what's the next right thing?
chilly idol
using log?
chilly idol
so divide by 3
tardy stag
yeah
tardy stag
$\log_2 \frac{x+4}{3}$ yeah
ocean sealBOT
hayley!
fringe yoke
X
fringe yoke
why is this correct?
I think it could also be (d)
This is a permutation matrix, so its inverse is its transpose, and A*A^T = I, this is true for (d) as well
lone heartBOT
@fringe yoke Has your question been resolved?
lone heartBOT
@fringe yoke Has your question been resolved?
tiny finch
How do I solve this answer ? I plugged the x value in and I’m assuming the answer is undefined but I’m being told otherwise
vale wigeon
and I’m assuming the answer is undefined
why so?
tiny finch
Because -root 2 is not a real number
ocean sealBOT
Ann
fallen verge
however, $\sqrt{-2}$, a totally different number is not a real number
ocean sealBOT
GarlicB
fallen verge
yes
vale wigeon
yes but you do not need a calculator here at all. unless maybe you do not know the first thing about square roots.
tiny finch
How do you do without
vale wigeon
well what's $(-\sqrt{2})^2$?
ocean sealBOT
Ann
vale wigeon
yes but do you know what happens when you square the square root of 2?
vale wigeon
ok, then tell me the definition of sqrt(x).
tiny finch
So like square root of 9 is 3 essentially a number taken to the 2nd power
vale wigeon
bad.
tiny finch
Ow
vale wigeon
this is imprecise and relying on an example again.
sqrt(x) is the positive number whose square equals x.
y = sqrt(x) means y ≥ 0 and y^2 = x.
since sqrt(x) is BY DEFINITION the positive number whose square equals x,
(sqrt(x))^2 equals what?
tiny finch
0
tiny finch
X
ocean sealBOT
Ann
tiny finch
x?
vale wigeon
[LOUDER INCORRECT BUZZER]
pulsar spire
this is getting intense
vale wigeon
square-rooting and then squaring a number brings you back where you started.
do you understand this or not
yes or no
vale wigeon
jeez, finally.
ocean sealBOT
Ann
vale wigeon
(-x) * (-x) = +x^2
tiny finch
I mean
Cuz I took it to the 2nd power so the negative goes away
So 2-2 = 0
Which is the limit
tiny finch
I ain’t plug it in properly
vale wigeon
your limit is not $(-\sqrt{2})^2 - 2$ but $-(-\sqrt{2})^2 - 2$
ocean sealBOT
Ann
vale wigeon
you should go learn and practice square roots though, for real. otherwise you will just suffer endlessly.
vale wigeon
seems so.
hallow mortar
May I ask why angle BAT is 90. Is it because angle BAF is also 90 degrees. Just want to check my methodology
coral flower
May I ask why angle BAT is 90. Is it because angle BAF is also 90 degrees. Just ...
BAT is not 90 degrees
BAT = BAF + FAT
if BAF = 90 degrees , there is no possible way BAT can be equal to 90
hallow mortar
if BAF = 90 degrees , there is no possible way BAT can be equal to 90
so the textbook is wrong
?
coral flower
so the textbook is wrong
idk but its common sense
BAF = 90
FAT = 55
BAT = BAF + FAT
= 90 + 55
= 145
dense rampart
Hey there! I don't understand the concept of the dot product in vectors. After some searching I found the layman definition "How much vector a aligns with vector b", but I still can't visualise what i'm doing intuitively.
It would be wonderful if someone could explain the concept to me, please, and thank you in advance!
dense rampart
To elaborate, I kind of get why there's |a|cos(theta), because this allows you to find the 'amount' of a that's in the direction of b, but i don't understand why we multiply by |b| as well -- according to the formula a.b = |a| |b| cos(theta)
mortal trellis
well if we multiply a.b and a.(2b) then the second should be twice as much
also we want it to be symmetric in a and b, i.e. a.b=b.a
lone heartBOT
@dense rampart Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
tiny finch
Find the distance D between each pair of points P and Q:
lone heartBOT
Find the distance D between each pair of points P and Q:
tiny finch
Is this the correct answer?
vague coral
sqrt of a negative number... ?
tiny finch
That would make it a “not real number “ right
vague coral
a distance is always a real number
tiny finch
Ok
vague coral
$D = \sqrt{(x_Q - x_P)² + (y_Q - y_P)²}$
ocean sealBOT
Herels
vague coral
$$D = \sqrt{(9 \times 22 + 4 \times 11)}$$
ocean sealBOT
Herels
vague coral
$$D = \sqrt{11\times 23}$$
ocean sealBOT
Herels
vague coral
$D = \sqrt{253}$
ocean sealBOT
Herels
vague coral
,w \sqrt{253}
ocean sealBOT
tiny finch
I’m trying to plug it in the calculator to see if I get the same thing
On math way it’s comes out as 11 sqrt 2
That’s how I input it
lone heartBOT
@tiny finch Has your question been resolved?
tiny finch
@vague coral
lone heartBOT
@tiny finch Has your question been resolved?
vague coral
That’s how I input it
thats how i did too
alpine sable
i forgot to ask another question :c
lone heartBOT
i forgot to ask another question :c
alpine sable
when an exercise just drops the word continuity, is continuity over R or the domain
for example
f: R --> R
but f = 1/x
nvm i think i got it, just the given assumptions of the book
.close
balmy patrol
can some one explain how to answer this and understand the question.
i know the conditions of totally ordered set, but i am unable to get any answer for this question
alpine sable
well, I think the first one might not be a total order. what happens when you try comparing {7} < {2, 3} and {2, 3} < {7}?
whereas when we take the 4th option, what happens when you try comparing any two elements?
balmy patrol
" {7} < {2, 3} and {2, 3} < {7}" what does comparing these 2 sets mean ?
in 4th option {2,3} < {3} or {3} < {2,3} , what does this imply ?
alpine sable
well, whats your definition of a total order?
balmy patrol
reflexive, antisymmetric, transitive and comparable
alpine sable
mhm, comparable in that for any two elements a, b either a < b or b < a, right?
balmy patrol
yep
alpine sable
but for that first option, it's neither the case that {7} < {2, 3} or {2, 3} < {7} so that doesn't hold
balmy patrol
how can we apply < or > operator to sets ? that is what i did not understand , is it cardinality that we are talking about ? when we use < or > oprator on sets. 7 > 3 makes sense but what does {7} > {3} tell ?
alpine sable
ohh the < symbol I'm using is just a easy way to write the weird sign they use in the image, but on my keyboard
they tell you what their symbol is defined as, it doesn't have to mean "less than or equal to" in the classical sense you know it as
balmy patrol
they tell you what their symbol is defined as, it doesn't have to mean "less tha...
ohh
so in this case are saying < > represent subset or superset ?
alpine sable
their definition of A < B is that A is a subset of B
they haven't defined >
they defined <
balmy patrol
ohh yes
got it thank you, can you hold on i have another doubt
just these 2 also i am having a hard time, i did not understand what does maximal, minimal or covers mean here excatly
alpine sable
I can't answer both but I'll answer the first one rq. if x is maximal that means there's no y that x < y. and the same for minimal, just reversed
balmy patrol
so a set could at most have one maximal or minimal but not more than one. is this right statement?
alpine sable
nah you can have multiple maximal and minimal elements, confusing as that is
have you done hasse diagrams?
they help visualise it
balmy patrol
so the base node in a hasse diagram would be minimal right ?
alpine sable
yeah but you can have multiple
balmy patrol
yeah but you can have multiple
ok lemme try to do it for this and post it here
alpine sable
for example
balmy patrol
for example
thanks that made it clear
wooden epoch
i equated the 2 circle equations and solved for x = 3, but idek what that x =3 means relative to what i had done
wooden epoch
i could've put them in gneral form, but i thought since they equalled the same already, might as well use that.
near apex
What do you mean by "solved for x=3"? Did you substitute x as 3?
near apex
Okay. Well, then you have gotten the x-coordinate of the intersection point/s.
wooden epoch
wait but how?
near apex
All you need to do is just find the y-coordinate.
wooden epoch
to get the x coordinate the intersection wouldn't i have had to equate 2 y=... equations and solved for x?
near apex
wait but how?
When, you equated, equation gave you coordinates of point of intersection as at intersection points only, the equality will hold.
wooden epoch
oh right because the whole equation is equal to the other
at that point
having 0 =... is the same basically as have y =...
in the sense that if you equate them it means the same thing
if you equate two 0 =... equations or 2 y= .... equations
near apex
If you need abstraction, then assume that (x1, y1) is a point of intersection of two circles. Now, since this point lies on both circle, we substitute into both equations and you'll get zero.
Since both equations are zero at intersection points, you can equate equations of circles to get intersection points.
wooden epoch
right if you sub in the values when you equate them 0=0
what would it mean if i subbed them in and instead of having 0 = 0 i had 5 = 5 or whatever
would that change anything?
or same meaning?
near apex
I mean... that is still the same thing.
Just subtract 5 from both sides.
Anyway, you are not supposed to put values and equate.
That'll give you nothing.
You equate them and try to find out the points for which the inequality will hold.
Basically,
$$x_{1}^{2} + y_{1}^{2} - 2x_{1} - 2y_{1} -2 = 0$$
$$x_{1}^{2} + y_{1}^{2} - 8x_{1} - 2y_{1} +16 = 0$$
Now, since LHS of both equations are equal to zero, then the LHS's can be equated with one another.
So, we get -
$$x_{1}^{2} + y_{1}^{2} - 2x_{1} - 2y_{1} -2 = x_{1}^{2} + y_{1}^{2} - 8x_{1} - 2y_{1} +16$$
ocean sealBOT
Enemagneto
near apex
This gives you x1 = 3
Since (x1, y1) was intersection point, you have gotten the abscissa of intersection points.
wooden epoch
what made sense about have 2 y = equations and solving for intersections, was that when i was equating them i was doing it because at the intersention the y values are going to be equal
so idk this doesn't make sense as much that did.
near apex
What do you mean by " 2 y = equations" ?
wooden epoch
intersection betwen y = ax^2 +bx +c and a line. y = mx + c
if i was to find the intersection between those, in my head it would logical to equate them, because at the intersection y values are the same. but i'm not seeing the same logic here because i just = 0 at the end of each equation which in my head doesn't mean anything
sorry if i'm not making sense
should i not try to relate those two concepts because they are different?
near apex
Well, you are making sense. However, that analogy is easier to work with in case of functions.
Here also, it can be made to work but issue is that here it's not possible to isolate y.
If you could write each circle equation in form of y = (sth) and y=(sthg), then you could have equated those y's essentially like you did in your example.
wooden epoch
yeah that would make the equations look really ugly
near apex
You can think of it like this.
Let's say $z = x^2 + y^2 -2x -2y -2$, and $z = x^2 + y^2 -8x -2y + 16$.
Now, you can equate z's.
But remember that z is zero here.
Does this help?
ocean sealBOT
Enemagneto
wooden epoch
by saying both equations are = 0, i am saying that the functions are equal at what point?
near apex
Although, to be honest, i think that this might be more confusing than helpful. First explanation that i gave you is more apt.
near apex
by saying both equations are = 0, i am saying that the functions are equal at wh...
Firstly, they aren't functions.
near apex
That's the issue. There's not a single y for a single x value.
wooden epoch
yeah
alright thank you for your help, i keep thinking about what you have explained, but it may take a while for it too click for me
*i'll
.close
alpine sable
Anyone know the solution to this problem?
lone heartBOT
Anyone know the solution to this problem?
alpine sable
vale wigeon
what's troubling you with it
alpine sable
what's troubling you with it
i dont get what its asking you
vale wigeon
which part(s)?
alpine sable
all the parts i guess
These type of questions will be in a exam i have tomorrow and i have absolutely no clue about how to do them
vale wigeon
oliver has three machines that convert blocks into other blocks
the problem describes how each of these machines work, and it also tells you that all machines' transformations are reversible.
do you understand that part of the statement?
alpine sable
yes
vale wigeon
ok
so then
a) Show how Oliver can convert 1 red brick into 3 red bricks [using his machines].
which part of this instruction is unclear to you?
alpine sable
> **a**) Show how Oliver can convert 1 red brick into 3 red bricks [using his ma...
i kind of get it now
so Oliver can manipulate his machine to produce more blocks
vale wigeon
he doesn't manipulate his machines
the machines are already there
he uses them
by putting bricks in and getting bricks out
alpine sable
so he can do something liek this = Input A Output 2B?
vale wigeon
no, you are overthinking this.
alpine sable
so he puts bricks in and he gets more bricks of different colours
vale wigeon
yes
alpine sable
and different colours can get different blocks
and he can get more blocks by using this method
OH
i seeeee
twin nimbus
Oh, interesting string automata question. Interesting as rearranging the string into any permutation is allowed at any step.
alpine sable
Oh, interesting string automata question. Interesting as rearranging the string ...
Are you talking about this question?
twin nimbus
Yes
alpine sable
i have absolutely no bloody clue of how to solve it
actually
i know some parts its saying
twin nimbus
My suggestion is just to start playing with the rules, and a single red brick
alpine sable
yes im tying to do that
i have to sit a 4hour exam on this stuff tomorrow and im prob gonna fail bc i barely know anything about these topics 
twin nimbus
So from a single red brick you only have one possible move
twin nimbus
My bad, I have no idea why I wrote two
vale wigeon
you have two possible moves: convert one brick into two bricks of the other two colors, or convert two different-colored bricks into one brick of the third.
alpine sable
Right now im stuck between solving this question or going to sleep
alpine sable
its 10pm for me right now
twin nimbus
My bad, I have no idea why I wrote two
Halting. I was counting halting.
alpine sable
This problem is patient, it will wait for you
its supossed to be a year seven AIMO question
Anyone have some advice for long four hour maths olmpiad tests?
worn fox
#competition-math will probably have advice for you
lone heartBOT
@alpine sable Has your question been resolved?
forest cobalt
💀
forest cobalt
Why are YOU here? 😂
true merlin
Sorrii LOLOLOL
I am confused about ur pfp then I realized it was a dog
its weirf
Weird
tardy tapir
close your previous channel!
true merlin
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left olive
I'm not sure if I'm missing something here, I'm supposed to say which of these statements is false ? it could be that I don't know what the {} mean and maybe that's the problem but those weren't shown in the video at all
vale wigeon
do you know what a set is
left olive
I've never seen this before and its in the "review" so I'm a little bit thrown off 😭
vale wigeon
weh
left olive
yes ?
vale wigeon
ok so then like
the easiest but sometimes cumbersome way of describing a set is just by listing everything that is in it
so for example {1} is a set whose only element is the number 1
{4, 20, 69} is a set of three elements: 4, 20 and 69
etc.
vale wigeon
yes
left olive
ok then -3 to 5 intersection with natural numbers does include all those right ?
but I can't find the problem with any of the others either
vale wigeon
yes
left olive
okayy
that makes sense
perhaps I should wear my glasses while i do math 😭
thanks for the clarification
.close
surreal trail
I need help with my objective function. It needs to consider the entire distance traveled, even if the variable multiplied with the distance, is >0 but <1
lone heartBOT
I need help with my objective function. It needs to consider the entire distance...
@surreal trail Has your question been resolved?
forest cobalt
Can you elaborate?
surreal trail
Hi. I have a mathematical model which considers a distance to a pallet place, as well as how many pallets are allocated to that place, out of a certain demand. If there are allocated any percentage, the entire distance to that palletplace needs to be considered, and not only, for instance, 0.4 of it (if that's what's allocated).
My current obj. function is this then (which of course won't work as model.x.value = 0,4 and then...
model.obj = pyomo.Objective(
expr=sum(model.distance_matrix[j][l] * model.x[i, j, l]
for i in model.retailers for j in model.loading_ports for l in model.palletspaces))
then I tried with adding a variable which rounds up model.x if > 0,01 but its a mess and doesn't feel like the right approach
I'm using python and pyomo
forest cobalt
I have no idea what I'm looking at lmao
surreal trail
XD
do u know if someone in here might know python
I can also write it lioke this if its easier?
with x being
surreal trail
<@&286206848099549185>
lone heartBOT
@surreal trail Has your question been resolved?
lone heartBOT
@surreal trail Has your question been resolved?
tacit arch
I can also write it lioke this if its easier?
What do you mean "consider"
tacit arch
I can also write it lioke this if its easier?
What do you want with this min?
tacit arch
with x being
pyomo isn't exactly popular. Try #old-network for CS server where to look for programming questions
shrewd fox
would love help explaining this to me
i know i have to multiply but im not sure what it means by formula a^2+b^2=c^2 correct?
austere sluice
i know i have to multiply but im not sure what it means by formula a^2+b^2=c^2 c...
what are u finding here?
shrewd fox
what do you mean
shrewd fox
i think it wants me to multiply i believe
i can post an example that i dont really understand
austere sluice
u have to find the height?
shrewd fox
shrewd fox
u have to find the height?
im trying to solve for the height
austere sluice
yeh
shrewd fox
austere sluice
yeh
austere sluice
;-;
wild umbra
asking you find CA
austere sluice
oops sorry ig
austere sluice
where did i go wrong?
@wild umbra ?
shrewd fox
oops sorry ig
its okay! lol you did better than me LOL
wild umbra
you didnt do anything wrong
austere sluice
exactly
wild umbra
the ques was asking for the area
wild umbra
not the length of CA
shrewd fox
austere sluice
hes like we find cz
shrewd fox
2pie times r
shrewd fox
raduis correct?
austere sluice
yeh
shrewd fox
in that problem would 7 be my radius
austere sluice
44?
austere sluice
in that problem would 7 be my radius
yeh
shrewd fox
im not sure how to solve this problem
austere sluice
this is how u solve it
its 2*22
as 7 and 7 gets cancelled
@shrewd fox
its 44 cm
shrewd fox
it was 14 cm
shrewd fox
14 pie cm
austere sluice
i mean yeh
shrewd fox
austere sluice
that works too
cause 14*22/7
i just cancelled out 7 and 14 that leaves 2
so 2*22 is 44
austere sluice
bruh yeh u gotta type it that way cause its mentioned type an exact ans in terms of pie
surreal trail
what happened with my help chat lol
austere sluice
u didnt ask me that ;-;
shrewd fox
sorry
shrewd fox
no you
austere sluice
what happened with my help chat lol
lol
surreal trail
What do you mean "consider"
It needs to use the entire distance from j to l and not a fraction of it, if only a fraction of jl was delivered
tacit arch
What do you mean "use"
surreal trail
I mean sum
It needs to sum the entire distance and not distance*0,4 for instance
so the distance from one port to the pallet place may be 100 cm. And then I may allocate 40 out of the 100 pallets demanded, to that palletplace. Then xijl = 0,4.
And so the distance becomes 100*0,4 = 40 but I want it to become 100 because no matter the allocation to the pallet space, the distance is the same
I tried adding a variable which assumes the value 1 if xijl > 0 but that just messed up things
Do u want to see my entire model?
tacit arch
probably not
you just need to translate what you're trying to say into a constratint
then use convex optimization techniques
surreal trail
I think I realize the problem..
lone heartBOT
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.
surreal trail
model.allocate_all_demand = pyomo.Constraint(expr=sum(model.ad[l] for l in model.palletspaces) == sum(model.demand[i] for i in model.retailers))
I thought I had added a constraint for the model, forcing the allocated pallets on palletspaces to be equal to the demand required for retailers but apparently not
crazy how u can overlook such an obvious mistake and use 4 hours
still seems to be some problem with my workaround though
thanks for the help though! 🙂
austere sluice
As a helper, please do not give out answers that could be copied as a homework s...
yesh
lone heartBOT
@surreal trail Has your question been resolved?
shrewd acorn
hi i need help with math can i send it here?
lone heartBOT
hi i need help with math can i send it here?
Please read #❓how-to-get-help
glossy gazelle
How do u do this
brisk urchin
i need help with this linear algebra problem
lone heartBOT
i need help with this linear algebra problem
brisk urchin
what i've done so far is plug the given ordered pairs to give me a system of equations
and then converted that system into an augmented matrix
i'm confused as to how this system could be consistent if all numbers to the right of the bar are zeros
and as to whether or not i actually set it up correctly to begin with
<@&286206848099549185>
nvm got it
.close
azure glen
Any algebric system A*x=b is compatible if b is a column of zeros
foggy stirrup
my textbooks arent in english so but if compatible means at least 1 solution then that is correct
azure glen
compatible or consistent
lone heartBOT
@azure glen Has your question been resolved?
broken fossil
Hello
last ether
Post it.
broken fossil
What do you mean
Oh wait my question
Yeah sor at
Sorry
Lmy question is what does dialatiing mean and factor of 1/2 and using the rule
lone heartBOT
@broken fossil Has your question been resolved?
echo shuttle
Thanks
smoky lark
lone heartBOT
@echo shuttle Has your question been resolved?
lone heartBOT
@echo shuttle Has your question been resolved?
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lone heartBOT
echo shuttle
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lone heartBOT
✅
lone heartBOT
@echo shuttle Has your question been resolved?
balmy stag
lone heartBOT
ocean sealBOT
balmy stag
are you sure the polynomial is correct
yes
im looking for the roots and not the graph
rational roots perhaps
balmy stag
so is it like gonna be some sort of imaginary number?
or theres just really no answer to it
frigid mirage
look at the solutions wolfram is giving
you have 2 real and 2 complex solutions
note that the real solutions are NOT rational
somber peak
lone heartBOT
somber peak
Am I lost cuz there is no f(t) or g(t)
atomic harbor
x and t are just dummy variables you can have any symbol to represent the variables
somber peak
x and t are just dummy variables you can have any symbol to represent the variab...
ahhh so why is 5e^x* x^3 wrong
atomic harbor
f(t) means the variable is represented by the symbol t
so f(t) = 5e^t
Similarly g(t) = t^3
lone heartBOT
lone heartBOT
✅
somber peak
.close
jaunty herald
i’ve got a mathematics exam tmrw and i’m really struggling with 2 things. Related differentiation and Perms and Combs. Any tips and tricks for them? Year 11 math btw
jaunty herald
<@&286206848099549185>
lone heartBOT
@jaunty herald Has your question been resolved?
lone heartBOT
@jaunty herald Has your question been resolved?
dull dove
i’ve got a mathematics exam tmrw and i’m really struggling with 2 things. Relate...
Just practice questions
Over and over
Switch up the values
Try harder ones
lone heartBOT
@jaunty herald Has your question been resolved?
static birch
Hello,
I need help with proving tge quadratic formula
lone heartBOT
Hello,
I need help with proving tge quadratic formula
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
minor needle
https://en.wikipedia.org/wiki/Quadratic_formula - many proofs here
static birch
2
coral flower
well he sent many proofs to the quadratic formula
but if still dont understand , send the picture of ur working and someone might see ur mistake and correct it
static birch
https://en.wikipedia.org/wiki/Quadratic_formula - many proofs here
I mean i got all of the steps right but i dont get this part
Why we multiplied it by half
Im watching this
coral flower
I mean i got all of the steps right but i dont get this part
we are trying to make a square using the formula
a^2 + b^2 + 2ab = (a+b)^2
but u cant add random numbers to the mix
static birch
Its
ax²+bx+c=0
coral flower
so u need to have ur value b with a 2 in denominator so in the step
"2ab" ur denominator 2 cancels with it and the equation remains the same
coral flower
Its
ax²+bx+c=0
yes then u divide a to all
static birch
yes then u divide a to all
Yes so it becomes
X²+b/a x = -c/a
coral flower
yes
now u have to make a "perfect square"
aka complete the (a+b)^2 formula
u are missing the entire "b" term , so u add it
static birch
aka complete the (a+b)^2 formula
Ooh
I see now
coral flower
as the "2ab" term has x , b cant be x , so the other term (b/a) becomes term "b"
and u need to have 2 in denominator
so u get "b/2a"
coral flower
and u need to have 2 in denominator
unable to express why 2 is needed but ill try my best
coral flower
Yes so it becomes
X²+b/a x = -c/a
right here u have a^2 term and 2ab term
what u are missing is the b^2 term
and ur goal is to complete the (a+b)^2 formula
static birch
and ur goal is to complete the (a+b)^2 formula
Yes i get it now
But can you explain more how to get it cuz i feel a little bit lost?
static birch
Ok
Which is preferred as a
coral flower
Ok
Which is preferred as a
"a" as in the square formula , (a+b)^2
static birch
so that means that
b/a is the b term
I dont get how is b/a is b
coral flower
b/a is the "b" term in the square formula
static birch
Ohh yes
coral flower
ok when a term is in the square formula , ill encase it in "" these
static birch
So
X² is A
B/a X is B
And we have to get 2ab?
coral flower
A is x
B is b/a
2AB is (b/a)x
static birch
Oh ok
coral flower
This 2AB came from the quadratic quation
coral flower
A is x
B is b/a
2AB is (b/a)x
But see here 2AB is equal to AB which is impossible
coral flower
The x in b/a x is for a
And the b/a from the b/a x is for b?
Yes
coral flower
But see here 2AB is equal to AB which is impossible
So to counter this we divide 2AB by 2 so it becomes AB (1/2 b/a)
static birch
Ok i its clearer now and how we gor the ² on it
And ww divided it by 2
Because its 2b?
We*
1m lemme just write it
coral flower
2AB = b/a x
2B(x) = b/a x
2B = b/a
B = b/a (1/2)
static birch
So like this?
coral flower
2AB = b/a x
2B(x) = b/a x
2B = b/a
B = b/a (1/2)
This is a simpler way
Sorry if i complicated stuffs trying to understand that to you
static birch
I get it now
Thank you so much you've explained it to me
coral flower
Np
lone heartBOT
coral flower
Yeah
lone heartBOT
Available help channel!
void walrus
This was an assignment which was discussed before however I haven't any memory of what the answer shared with us was, the question is
Give an example of a sequence having two subsequences converge to the same limit l, but the sequence may not be convergent.
void walrus
.close
delicate knot
How many different passwords of length from 6 to 14 characters can be composed without restrictions (repetitions are therefore allowed) from the symbols A, G H, 4, and 5?
lilac thicket
no guarantee its correct but I think I got this
so
first of all I'd say the only relevant info we need to draw from having A,G,H,4,5 is that we have 5 distinct characters
which one they are isnt relevant
now lets consider a simpler example
how many possibilities would you have if lets say you wanted to construct a 3 letter password with 5 reusable characters ?
delicate knot
I'm not sure but i have an idea in my head how it would work
basically if we have 5 reusable characters eg 1,2,3,4,5.
It would be 1,1,1 then 1,1,2 then 1,1,3 etc?
Something like that?
lilac thicket
well ok you could bruteforce it
but what would you say how many possibilities are there
for a 3 letter password with 5 characters
how many possibilities do you have to pick the first character ?
delicate knot
5
delicate knot
5 again
lilac thicket
right making it 5*5 = 25 already
and then for each of those 25 you have 5 again for the third right ?
making it 3^5
delicate knot
Don't you mean 5^3
lilac thicket
ok now you have 6 to 14 characters password
delicate knot
the most amount would be 5^14 ?
lilac thicket
but 5^14 would only consider 14 character long passwords
lilac thicket
I'd say its the sum over all those
delicate knot
You are a GENIUS
lilac thicket
but again no guarantee , I might have missed something
lilac thicket
alright nice
delicate knot
What would the sum be ?
5^6 + 5^7 + 5^8 + 5^9 + 5^10 + 5^11 + 5^12 + 5^13 + 5^14 ?
Is there a command here i can use ?
frigid mirage
,w 5^6 + 5^7 + 5^8 + 5^9 + 5^10 + 5^11 + 5^12 + 5^13 + 5^14
ocean sealBOT
frigid mirage
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