yeah it's my code
#help-0
vocal hawk
vocal hawk
are you rotating 90 degrees each time?
cinder tundra
Yes but it’s double direction
One o clock other anti o’clock
It’s the only way u get this sequence
vocal hawk
that's what I meant by impossible
is that you can't have the same center for all 4 rotations
cinder tundra
If you go the same rotation 90 degrees no
If u do double rotation yes
If you rotate more than 90 degrees yes
So there are two possibilities
1->2 image = 90 degree 2->3 =270 degree
Or
90 degree one direction then 90 degree inverse direction
ember isle
I'm having issues with solving this differential equation:
\begin{align}
\frac{dv}{dt} = \frac{1}{245}(49^2 - v^2)
\end{align}
ocean sealBOT
Trouser Zipper
ember isle
i get to:
\begin{align*}
\frac{1}{49^2-v^2} \frac{dv}{dt} = \frac{1}{245}
\end{align*}
ocean sealBOT
Trouser Zipper
ember isle
After that I try integrating both sides with respect to t
and I do a substitution on the left with v = 49sinx, so that v^2 = 49^2 sin^2x
that way, I end up with \begin{align*}
\frac{1}{49^2} \int \frac{1}{1-\sin^2{x}}dx = \frac{1}{49^2}\int \frac{1}{\cos^2{x}}dx = \frac{1}{49^2}\tan{x}
\end{align*}
ocean sealBOT
Trouser Zipper
golden canyon
ember isle
ah, that's huge, thanks
o that might be helpful
ty, but i am going to try to work it out with what you both have given me for now
yeah i uh went back and changed my thing so that i use x = v/49
so right now my work looks like [ \frac{1}{49^2} \frac{1}{1-(\frac{v}{49})^2} \frac{dv}{dt}]
ocean sealBOT
Trouser Zipper
ember isle
there is what you sent earlier
which would be the same as if i had never done what i did...
ah i had to search it up
derivative of inverse tanh^-1x... i'm sad that i had to search it up but i don't think i ever would have gotten it otherwise
anyway big thank you for the help
.close
lean plover
lone heartBOT
lean plover
i know how to do this question
but i have no idea what its actually doing
so what i did was
r = parmetric equation of c2 = (x, -x^2 + 4)
then i substitute that into vector field F
and then i do dr/dx dx = (dr/dx) dx
dr/dx is derivative of r with respect to x
i sub it in
F(r(x,y)) dot product (dr/dx) dx = that formula
boom there u go
but i dont understand whats going on
im substituting the equation of a line, into a fector field, then taking the integral of that line on the vector field?
so what exactly is the value im calculating working out?
is it summing up each of the individual points of the vector field on that line?
mellow knoll
you're summing up each individual vector field point, dotted with your tangent vector
eg if the vector field was a force
this would give you the work done to move from point A to B
lone heartBOT
@lean plover Has your question been resolved?
deep harbor
what did he do wrong since he only got one answer when he should get two
deep harbor
-3
0
i didnt do it
but its the task
that asks us to show what he did wrong
0
How do i know that it should be 0
using the abc- formula?
How did you find that x=-3 and x=1 cuz idk if i did it correctly
yes the abc thingy
quadratic formula
ax^2+bx+c=0
I dont understand why
worn fox
when you divide by x+3 you are implicitly saying that x is not equal to -3, otherwise you would be dividing by 0 and thats not allowed
so you are missing out on the possibility that x=-3
deep harbor
when you divide by x+3 you are implicitly saying that x is not equal to -3, othe...
what value is given to it
worn fox
given to what?
x is still unknown at the point you divide by x+3
but you have missed out on the possibility that x=-3
deep harbor
but you have missed out on the possibility that x=-3
since it becomes 0?
i dont get this part quite
worn fox
so you would need to check whether x=-3 is as solution, as it could be a solution in addition to the ones you get going forward
deep harbor
so you would need to check whether x=-3 is as solution, as it could be a solutio...
i know that the answers is 1 and -3 by using the quadratic formula
worn fox
Fredrick arrived at x=1 by assuming that x is not -3, as thats what allowed him to divide by x+3
he still needs to check whether x=-3 is a solution
deep harbor
so he needs to do the quadratic formula first to check what the different answers are?
worn fox
no, he needs to check any options that he assumed x cannot be when he does division
in this case -3
deep harbor
so he needs to check every single number till he finds out?
i dont understnad
understand*
worn fox
you only check the options that you had to exclude in order to do the division
he excluded x=-3 so that he could divide by x+3
he needs to check x=-3
exotic canopy
what did he do wrong since he only got one answer when he should get two
at the second step, we are dividing by $x+3$, implicitly assuming $x+3\neq 0 \implies x\neq -3$, because otherwise it will be division by zero. however, $x=-3$ is a valid answer, because you have $(x+3)$ on both sides which could be both 0, effectively making 0=0 which is true.
ocean sealBOT
artemetra
exotic canopy
so every time you divide by something like that, you need to also check if you didn't get rid of a root
worn fox
if in a different question you were to at some point divide by say x-5, then you would need to check whether x=5 is a solution
in this case he divided by x+3, so needs to check if x=-3 is a solution. it happens to also be a solution in this case, sometimes it might not be, but you still need to check
still ibex
Hi, I was trying this question and decided to approach it using a coordinate system and calculating the distances, then proceeded to calculate the left hand side and right hand side separately and seeing if they were equal, but they weren't. I retried it a few times and I can't find any errors, so why won't it work? Have I accidentally made an assumption or something?
woeful lake
still ibex
LHS ends up being 4px and RHS ends up being 2 similar but messy roots subtracted from each other (the inside of the roots only differs by a minus, but there's not relaly a way to combine them)
lone heartBOT
@still ibex Has your question been resolved?
lone heartBOT
@still ibex Has your question been resolved?
still ibex
Hi, I was trying this question and decided to approach it using a coordinate sys...
@craggy dagger
Is there anything wrong with my setup?
Unless like did i label the square wrong
lone heartBOT
@still ibex Has your question been resolved?
nimble fern
Hi, I was trying this question and decided to approach it using a coordinate sys...
asssumptions are fine, just that you have messed up a bit on the distance formula
still ibex
How exactly?
nimble fern
e.g.
you've assumed A to be (-x,x)
then |PA| should be √((-x-p)²+(x-q)²) which is √((x+p)²+(x-q)²)
Side note: Since your setup is really nice, you should make it even more decent by setting up A,B,C,D in Q1,Q2,Q3,Q4 respectively to make it easier to calculate next time 😛
still ibex
I thought it would work like this?
Oh wait
is it because
q is gonna be a negative number
so it ends up being x minus something
I calculated all of the distances using a similar logic
nimble fern
so it ends up being x minus something
you can say that, but that's what you do after the setup and calculations
also, P is a point on arc CD
so p might be negative too
still ibex
true
see i'm bad at learning formulae so i kinda wanted to do it by intuition instead of using the distance formula
and i figured if i treat them all as positive quantities, it'd work out
nimble fern
you can first setup correctly, then start to use the fact that (p,q) is on arc CD and it's properties to prove
e.g.
if you really want q to be positive, and conside p in the positive side, you can split cases
like
Case 1: for p>0
Case 2! for p<0
Case 3: for p=0
and you can also set P as (p,-q) for q>0
but that's another story
😆
still ibex
that makes sense
but i don't entirely understand why my method didn't work
like if we just assume that p>0
that case
and q is just a distance
then is my way of calculating AP right?
then i calculated the other ones in the same way
but didn't get the two sides to be equal after i evaluated them
nimble fern
but i don't entirely understand why my method didn't work
e.g. if q is just a distance and p>0, then P will actually be (p,-q) and -q=-√(2x²-p²), which come back to q√(2x²-p²), which is still good up till now
but then since (p,-q) is on CD, you might have to use some fact that p<x and q>x
which might mess up the calculations somewhere
still ibex
oh yeah that's true
that probably is it yeah
it's hard to use an inequality in solving an equality tho
i can't imagine how that could be done
nimble fern
can you show the rest of your work so that i can check?
still ibex
it's like 2 pages of messy scribbles all over the place lol
but i did it twice and got the same answers each time
so i think all the algebra was right
but as you said, it doesn't take into account the fact that P can only be on CD, so i don't think my method would work anyway
nimble fern
it's like 2 pages of messy scribbles all over the place lol
you can try and show it if you want 😛 I don't mind reading
nimble fern
lets see
still ibex
They were the exact workings I had (the guy beside me kept doodling on the page, sorry about that)
nimble fern
reading
still ibex
i tried it like a normal geometry problem too, but didn't have any luck, which is when i swapped to trying to coordinate system
Perhaps if the point P was written as (x + p, x + q) instead?
Which then gives the restriction that P is on the arc CD?
Given that p is an integer and q is a natural number
I feel like that could actually work
I don’t see any problems with it
I’ll give it a go tomorrow hopefully if I have the time
But it’s almost midnight here now lol
nimble fern
finished reading
a few things:
- you can keep the q as q all untill you've done simplifying, but in this case, it won't be much easier😆
- this is a very decent of work, and please don't feel bad posting, it's definitely not "messy scribble"
and Finally
2x²±2p√(2x²-p²)
= (2x²-p²)±2p√(2x²-p²)+p²
= ( √(2x²-p²) ± p )²
and you're done
nimble fern
2x²±2p√(2x²-p²)
= (2x²-p²)±2p√(2x²-p²)+p²
= ( √(2x²-p²) ± p )²
this is the final step for proving, hope that helps!
still ibex
Wait so this method will work?
nimble fern
right now, i think P is in CD is a constraint helps you to make it easier to solve using geometry only, the fun fact is that it's useful for all points on the circle
still ibex
2x²±2p√(2x²-p²)
= (2x²-p²)±2p√(2x²-p²)+p²
= ( √(2x²-p²) ± p )²
I was acrually thinking to myself “the only way this could work out is if I could somehow complete the square”
But I couldn’t see how
And thought it was more likely that my workings had an error
But then I did something
nimble fern
And thought it was more likely that my workings had an error
your working is decently fine
still ibex
But then I did something
Actually wait nvm lol
Is it formal enough to just say 4px = (that mess) and simplify?
Or do you need to evaluate each side separately
I think you have to do the latter
nimble fern
Or do you need to evaluate each side separately
?
still ibex
But idk if I’d ever spot completing the square like that lol
nimble fern
But idk if I’d ever spot completing the square like that lol
you will, there are a lot of times
still ibex
So would we have to get an equation that says RHS = 4px
nimble fern
you will, there are a lot of times
that you'll encounter something like that
still ibex
Or can we just take 4px = (the other stuff) and square both sides etc. and show that they’re the same?
nimble fern
So would we have to get an equation that says RHS = 4px
ah i see, you don't need to do both sides in this case
nimble fern
Is it formal enough to just say 4px = (that mess) and simplify?
you just need one way
e.g.
|PB|•|PD|-|PA|•|PC|
= that mess
= something
= another something
= ...
= 4px
= |PA|²-|PB|²
still ibex
e.g.
|PB|•|PD|-|PA|•|PC|
= that mess
= something
= another something
= ...
= 4px...
Rigjt okay
nimble fern
|PB|•|PD|-|PA|•|PC|
= that mess
= something
= another something
= ...
= 4px
= |PA|²-|PB|²
still ibex
2x²±2p√(2x²-p²)
= (2x²-p²)±2p√(2x²-p²)+p²
= ( √(2x²-p²) ± p )²
AHHH YES ITS SO SATISFYING
nimble fern
2x²±2p√(2x²-p²)
= (2x²-p²)±2p√(2x²-p²)+p²
= ( √(2x²-p²) ± p )²
hint for your further studies:
you can try to split the non-squareroot term into the 2 piece of the sqrt term ÷ 2 to see if it works
still ibex
A problem that I first attempted 4 months ago, finally found the answer 😄
nimble fern
A problem that I first attempted 4 months ago, finally found the answer 😄
congratulations!
now sleep 😛
good night!
still ibex
hint for your further studies:
you can try to split the non-squareroot term into...
I don’t exactly get what you mean by this 🗿
nimble fern
e.g.
√(3+2√2)
still ibex
And do what with that?
nimble fern
it's more like completing square XD
nimble fern
Cheers!
still ibex
And for being both really patient and encouraging
I really appreciate it!!
Enjoy the rest of your day :D
nimble fern
Enjoy the rest of your day :D
you too!
still ibex
.close
misty dome
lone heartBOT
tardy stag
yeah that's correct but two stylistic points
- you should get out of the habit of using x for multiplication, especially if you're using x as a variable in the same expression
- i'd probably write that as $3e^{2x} + 2e^{-x} + 1$; just looks cleaner to me. but what you have is equivalent so nbd
ocean sealBOT
hayley
lone heartBOT
@misty dome Has your question been resolved?
misty dome
2) i'd probably write that as $3e^{2x} + 2e^{-x} + 1$; just looks cleaner to me....
Aight then
Thank you
deep harbor
Can someone help me do c
lone heartBOT
Can someone help me do c
balmy grail
Can someone help me do c
Can you translate it to English?
deep harbor
what does it mean create a program?
program in spyder
full nimbus
this is a math server but if you want you can keep waiting and someone might help you but its not likely
deep harbor
this is a math server but if you want you can keep waiting and someone might hel...
I think its still math
but inside a coding program
simple program
spyder
balmy grail
You could frame this question in a more mathematical way
How do you find balls(n)
Sum(2*(k-1)+1) for positive integer k?
And if you want to be comp sci about it you could draw the ball diagram to the terminal, then count the output too
lone heartBOT
Available help channel!
rustic holly
lone heartBOT
lone heartBOT
@rustic holly Has your question been resolved?
tacit arch
i need help
!show
lone heartBOT
i need help
Show your work, and if possible, explain where you are stuck.
lone heartBOT
@rustic holly Has your question been resolved?
cinder sundial
Yee
I got a feeling for the right side
Let’s convert them into cos and sin
Of course
Of course my gentleman
I want to get it out of the denominator
So
Let multiply the top and bottom by cos
nimble fern
hmmm this feels weird
,w (sinA-cosA+1)/(sinA+cosA-1) = 1/(secA-tanA)
i just check Wolframalpha
I don't think it is true for all theta
proven leaf
I don't think it is true for all theta
on Desmos they have the same graph
austere snow
Just multiply both numerator and denominator with sinA + cos A +1 . You'll get it.
random wraith
Sohcahtoa baby
nimble fern
on Desmos they have the same graph
my bad
congratulations
sorry can't help much
i think that's the "usual way"
and i bet there isn't for this Q
just do ,w at the front
but don't do it everywhere in the server
you can try in #bots
you can try in #latex-testing
quote your stuff with $$
lone heartBOT
lone heartBOT
Available help channel!
molten anchor
AP question no clue how to do this one been trying for a while
nimble fern
AP question no clue how to do this one been trying for a while
did you try to name all the unknows for the two AP's ?
molten anchor
did you try to name all the unknows for the two AP's ?
yes
nimble fern
oh.
molten anchor
AP question no clue how to do this one been trying for a while
I don't even get how you can find the common difference from what's given
nimble fern
$$S_1=\frac{n}2(2a_1+(n-1)d_2)$$
$$S_2=\frac{n}2(2a_2+(n-1)d_2)$$
ocean sealBOT
Biscuity
nimble fern
$$S_2-S_1=\frac{n}2\left((2a_2+(n-1)d_2)-(2a_1+(n-1)d_1)\right)$$
molten anchor
oh ok hold on I think I get it from here
ocean sealBOT
Biscuity
nimble fern
sorry, typo
lone heartBOT
lone heartBOT
Available help channel!
stark hollow
how do i determine whether the orthocenter is inside, outside, or on the triangle using coordinates of the vertex and the orthocenter
hidden fable
so a triangle can be defined on the cartesian plane as the solution of a system of inequalities
we can set up those inequalities and plug in the values for the orthocenter, and if it follows all 3, it must be inside the triangle
that's an idea
stark hollow
we can set up those inequalities and plug in the values for the orthocenter, and...
so for example if the triangle has the vertices (-2, 1) (2, 1) (0, 4)
the inequalities we can set are like
-2 <= x <= 2
0 <= y <= 1
but then don't those theoretical inequalities form a rectangle
hidden fable
so for example if the triangle has the vertices (-2, 1) (2, 1) (0, 4)
the inequa...
we can use x and y in the same inequality, too
for example if we wanted to express the triangle with vertices (0,0), (1,0), (0,1), we have this:
x >= 0
y >= 0
x + y <= 1
we just have to find the equations for the lines connecting each of the points and turn those into inequalities
stark hollow
OHHHH
hidden fable
based on the location of the third point
stark hollow
that makes sense
okay i think i get it now
but how do i decide what to convert into inequalities
hidden fable
so for example if the triangle has the vertices (-2, 1) (2, 1) (0, 4)
the inequa...
let's do this case as an example
i think you'll understand the ide after that
the easiest line to solve is the one between (-2,1) and (2,1)
it's just y=1
stark hollow
mhm
hidden fable
since the third point is above this line, then all points in the triangle must follow y >= 1
then we do the next line
stark hollow
do i need to use the slope intercept form of the side as an inequality
hidden fable
you can use the slope intercept form yeah
hidden fable
almost
hidden fable
yeah
stark hollow
okay
hidden fable
and the final one is pretty much the same
hidden fable
np!
stark hollow
.close
alpine sable
lone heartBOT
alpine sable
How do i find impulse and momentum on the middle one
brittle ember
Did you figure out momentum for 2nd and 3rd situation?
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
alpine sable
Did you figure out momentum for 2nd and 3rd situation?
yes
lone heartBOT
Available help channel!
alpine sable
Hi
lone heartBOT
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
ok
alpine sable
sxt
alpine sable
oop
alpine sable
yes
exotic canopy
where s is distance and t is time?
alpine sable
wdym?
exotic canopy
what is s in your formula?
(asking cuz different schools might use different notation)
alpine sable
speed
alpine sable
ok
exotic canopy
this is equivalent of saying that Ethan travelled one part of those 203 and Noah travelled the other
alpine sable
Ok
exotic canopy
so we get $v\cdot t + (v-64)\cdot t=203$
ocean sealBOT
artemetra
alpine sable
okie ty
split mantle
**artemetra**
You sure? Using your method, v would be 104 km/h, $v \cdot1.4$ would be 145.6km, and $65km/h \cdot 1.4h$ would be 94km, they don't add up to 203km.
ocean sealBOT
Good
exotic canopy
,w v*1.4 + (v-64)*1.4 = 203
ocean sealBOT
exotic canopy
,w (104.5)*1.4 + (104.5-64)*1.4
ocean sealBOT
exotic canopy
You sure? Using your method, v would be 104 km/h, $v \cdot1.4$ would be 145.6km,...
you did something wrong
split mantle
Exactly, v would be 104.5. And vt+vt= 203 wouldn't work.
exotic canopy
Exactly, v would be 104.5. And vt+vt= 203 wouldn't work.
?
it's not supposed to be vt+vt
it's supposed to be vt+(v-64)t
are you confusing it with $v_1 t + v_2 t$?
split mantle
Supposing Ethan and Noah goes in the left and right direction. The distance Ethan travelled is $65km/h \cdot 1.4 h=91$, and Noak $v \cdot 1.4h$. Their sum distance would be 91 + 1.4v = 203.
exotic canopy
Supposing Ethan and Noah goes in the left and right direction. The distance Etha...
ethan doesn't have 65 km/h as his speed
the only thing we know is that his speed is 65 km/h SLOWER THAN Noah's speed
split mantle
Ops, my bad. I misread that.
exotic canopy
it's okay lol
alpine sable
yall so smart lol
exotic canopy
i dont get it
you don't get how to solve it or what i wrote?
alpine sable
i got it now
exotic canopy
awesome
split mantle
you don't get how to solve it or what i wrote?
You wrote 64 instead of 65.
lone heartBOT
@alpine sable Has your question been resolved?
ocean sealBOT
flint furnace
What are the difference between local maximum and absolute maximum?
mortal trellis
a local maximum is bigger than all nearby points
an absolute maximum is bigger than all other points
an absolute maximum is also a local max, but not vice versa
flint furnace
an absolute maximum is also a local max, but not vice versa
so basically, local max is the highest y in the interval and absolute max is the highest y in the whole function?
so the absolute max can be a local max but not other way around?
mortal trellis
close but not quite. you maybe mean the correct thing
the whole function could still be defined on an interval
so you need to be precise with your language
flint furnace
the whole function could still be defined on an interval
let's say it's a continuous function?
Wat I mean the whole function is referring to a continuous function
mortal trellis
this doesnt really have anything to do with continuity or not
so, the function is defined on some domain
which might mean an interval or all real numbers
a local max is the biggest point on a smaller subinterval
the absolute max is the biggest point on the whole domain
flint furnace
this doesnt really have anything to do with continuity or not
I thought it does cuz let'say there's a hole where the y value could be inf
mortal trellis
well then the function wouldnt be defined there and has no local or abs max there
which isnt an issue
flint furnace
the absolute max is the biggest point on the whole domain
so absolute max could also happen in an interval where it indicates the highest points of all the x which are one of the critical points?
flint furnace
which isnt an issue
ohh I see I see
mortal trellis
the absolute max is just the biggest of all the local maximums
flint furnace
I thought the local max is indicating the highest point in the interval?
flint furnace
yeah that's why it is in a certain interval? Did I get the idea wrong?
mortal trellis
if you imagine the function as some kind of landscape. then the hills are the local maximums. and the biggest hill is the absolute max
flint furnace
it reminds me of noise map and I think I kinda get it
so whenever there's like a curve up or curve down in the graph
it's indicating a local max there
am I correct?
mortal trellis
not technically because it could be something like an upside down V which has no "curve"
but in practice its good enough to think like that
flint furnace
not technically because it could be something like an upside down V which has no...
so it's a point where it turns from increasing to decreasing?
or other way around
jovial flax
Where do I go wrong 🫠
lone heartBOT
Where do I go wrong 🫠
tardy stag
ok clearly if it started at 50 and it's filling up then it won't be 25 at the end
how did you get C = 50?
also pay attention to hours vs minutes
jovial flax
- Is there some gap in my understanding
lone heartBOT
12. Is there some gap in my understanding
tacit arch
12. Is there some gap in my understanding
Why is C=0
You probably have to assume V(0)=0
jovial flax
I just assumed c was zero since I didn’t know the initial volume
tacit arch
I just assumed c was zero since I didn’t know the initial volume
Yea the problem is underspecified
lost flax
hi, i think this is the answer but could someone give me a second opinion, thank you!
alpine sable
hi, i think this is the answer but could someone give me a second opinion, thank...
whats wrong with D
lost flax
since the number under the square must be 0 it cant be 0 or a nonzero value
unless im misunderstanding the question
lone heartBOT
@lost flax Has your question been resolved?
lost flax
<@&286206848099549185> pls! ty
stoic terrace
tiny bay
when i want to inverse a function f(x)
i have the function
((y^2)-1)/5
do i just switch the y value for x?
tiny bay
ionic oak
More or less
Switch the x and y, then solve for y
Or in your case, first solve for x, then switch the x and y
tiny bay
does this work for every inverse or just mine
wintry coyote
It works for every function (whose inverse exists)
cinder tundra
Does each input of one corresponds exactly with each output of the other?
ionic oak
If I understand you correctly: You ask if f(x) = y always implies that x = f inverse (y) ?
ionic oak
Actually, this is false. Let f(x) = x^2. Then f(-3) = 9, but f inverse (9) = 3.
cinder tundra
Ok that’s because sqrt(x) and x^2 are not inverse functions
cinder tundra
Sqrt(x) only gives and accept positive values
lone heartBOT
@tiny bay Has your question been resolved?
tiny bay
how do you know if a funchions inverse exists?
cinder tundra
Checking if it’s bijective
ionic oak
In other words: Checking that no two x values give the same y value
In other words: Horizontal line test
cinder tundra
The inverse function of( f(x) = \sqrt{x} ) is ( f^{-1}(x) = x^2 ) with the restriction ( x \geq 0 ).
ocean sealBOT
Samuel
junior panther
Evaluate
solemn juniper
You do not
junior panther
You do not
solemn juniper
You're conditioning on them failing the exam, not getting less than 6 hours sleep (as the exam result is what's known)
junior panther
You're conditioning on them failing the exam, not getting less than 6 hours slee...
10/120?
10/18
solemn juniper
Pick one
junior panther
10/120??
solemn juniper
That's the probability that they failed and got less than 6 hours sleep
solemn juniper
P(failed | less than 6) = 10/120?
This is not true
P(failed AND less than 6) = 10/120
Not the same thing
solemn juniper
$\cap$
junior panther
For it
ocean sealBOT
Steakanator
junior panther
Anything else need to be added?
solemn juniper
What do you mean added?
junior panther
I mean that’s it?
solemn juniper
What's "that"?
solemn juniper
Well the question asks for P(failed | less than 6), which you haven't yet found
junior panther
Well the question asks for P(failed | less than 6), which you haven't yet found
What that
solemn juniper
Well how is P(A|B) defined?
junior panther
Well how is P(A|B) defined?
AB
solemn juniper
What?
junior panther
Idk
solemn juniper
How have you historically been taught to compute conditional probabilities?
junior panther
How have you historically been taught to compute conditional probabilities?
No I think
solemn juniper
The question started with "how," it's not a yes or no question
junior panther
How have you historically been taught to compute conditional probabilities?
Idk
solemn juniper
Well then you have something you need to go back and review
If you can't differentiate between P(failed AND less than 6) and P(failed | less than 6) then you need to revise a little
solemn juniper
That's also something for you to review
junior panther
We just started that recently
tardy stag
then you should have notes you can review
junior panther
.close
lime hemlock
Hi, how do I solve these? Just give me an idea, and I'll do the rest
Show that the following sequences are convergent and determine their sums
lime hemlock
Show the divergence of series (using the condition of divergence of series):
Using the comparison criterion, examine the divergence of the series
Using the d'Alenbert criterion, examine the convergence of the series
Using the Cauchy criterion, examine the convergence of the series
Using the Cauchy criterion of compaction, examine the divergence of the series
<@&286206848099549185>
lone heartBOT
@lime hemlock Has your question been resolved?
undone ledge
Hi, how do I solve these? Just give me an idea, and I'll do the rest
Show that ...
for the first one you can think of spliting it into terms like vn , v(n-1) such that vn - v(n-1) would be some constant times the Tn
i think you can use the same for the second one
you can use the same method in 4th too i think
(ping when here)
undone ledge
yeah
undone ledge
Tn -> nth term of the series
lime hemlock
we're doin this, right?
lime hemlock
undone ledge
yeah so here for a
Tn---> 1/(2n-1) (2n+1)
lime hemlock
okay
undone ledge
can you split it into two terms
lime hemlock
yes, 1/(2n-1) * 1/(2n+1)
lime hemlock
can you split it into two terms
?
lime hemlock
idk
could you pls solve the 1st one on paper
and then explain your reasoning
i think it'd work better
lone heartBOT
@lime hemlock Has your question been resolved?
sage hound
open
sage hound
hello, i need some one to explain radicals and their rules
sleek girder
clarification question: are you talking about this?
(why does that look like a weak CAPTCHA)
sage hound
yes 2^2 is 4 because 2 x 2 is four
sleek girder
that's great
give me more examples
sage hound
that's great
give me more examples
2^3 is 8
sleek girder
alrighty
radicals answer the question of "?^3 is 8. what is ?".
is that enough for a start?
sleek girder
from there, a lot of rules will follow
sage hound
im currently learning on how to simplify radicals
sleek girder
good luck
for the moment, tell me what you're struggling with in particular
sage hound
good luck
for the moment, tell me what you're struggling with in particular
sorry for responding late
so uhhhhh
like the rules of radicals and how to simplify them
sleek girder
well, give me a few example problems
then we can do it better
sleek girder
that, you need rule 4
so, it's "?^3 = 2; ?^2 ="
a nice thing to notice is that you can square the ? and the 2, to make "(?^2)^3 = 2^2"
as for why a^b = c then (a^d)^b = c^d, I'll just use a concrete example
2^3 = 2 * 2 * 2 = 8
(2__^4__)^3 = (2 * 2 * 2 * 2)^3 = (2 * 2 * 2 * 2) * (2 * 2 * 2 * 2) * (2 * 2 * 2 * 2) = 4096 = 8__^4__ = (2 * 2 * 2)^4
so the base and the result can both be exponentiated :)
sage hound
ok thanks
sleek girder
:)
merry glade
Hello, I've this problem that I can't solve and I don't know where to start
formal oracle
Hello. Maybe not the math question but how can i get this graph data points into excel easiest way?
I know i can make x, y tab and manually enter but thats a lot of work
sleek girder
Hello. Maybe not the math question but how can i get this graph data points into...
!occupied
lone heartBOT
Hello. Maybe not the math question but how can i get this graph data points into...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
sleek girder
(it was close, but still, you will have to ask in a different channel)
rough jungle
guys whatzup!
lone heartBOT
guys whatzup!
rough jungle
└─$ python main.py 3
100
010
001
100
001
010
010
100
001
001
010
100
4 3.552436828613281e-05
matrix size: 3
vale wigeon
what is this
rough jungle
this is a symmetric matrix
I need an algorithm, preferably using permutaitions or recursive functions, that can detect how many symmetric matrices are possible in a determined matrix size
the matrices should be symmetric to the main diameter
and there can only be 1 checked cell (with the 1 mark), on each row
rough jungle
what is this
can you solve it?
this is another output
└─$ python main.py 2
10
01
01
10
2 3.719329833984375e-05
matrix size: 2
I already know how to calculate it,
but the time complexity of my solution is too high
can't get past 12
I want to reach at least 30
vale wigeon
sorry i don't understand the problem in the slightest
do you have the problem in writing
rough jungle
wait a minute
The problem is asking for a recursive solution to find the number of symmetric matrices of size n×n filled with zeros and ones, such that each row contains exactly one element with the value of 1, and the matrix is symmetric with respect to its main diagonal.
for exmaple
10
10
this matrix is not symmetric
10
01
but this one
01
10
and this one is
rough jungle
sorry i don't understand the problem in the slightest
here is some other examples
10000
01000
00100
00010
00001
10000
01000
00100
00001
00010
10000
01000
00010
00100
00001
10000
01000
00001
00010
00100
the problem asks for the total number of possible symmetric matrices, given a matrix size
for example if the matrix size is 5,
there can be 26 possible symmetric matrices in it.
out of 5^5 which is 3125
and for 2 it is 2. out of 2^2 which is 4
@vale wigeon here is explained it
I think this is the hardest problem I've encountered in my life lol
vale wigeon
The problem is asking for a recursive solution to find the number of symmetric m...
ok this statement is clearer
can you show your code
rough jungle
sure
rough jungle
can you show your code
@vale wigeon did you read it?
do you think its possible to make it as fast as they want?
lone heartBOT
@rough jungle Has your question been resolved?
vale wigeon
<@183668144404037632> did you read it?
do you think its possible to make it as ...
sorry, i only got out of class just now
do you want to only COUNT them or are you also required to display each one?
rough jungle
don't be,
will you be able to guide me through this?
vale wigeon
i would like a straight answer to this
rough jungle
do you want to only COUNT them or are you also required to display each one?
yes,
only count them
vale wigeon
??
ok only count
then all of that code you wrote goes out the window
iterating over what seems like all (or a huge subset of) zero-one matrices is not the way to go at all
rough jungle
then all of that code you wrote goes out the window
great so you know a solution
vale wigeon
anyway, im gonna have to present it to you in a decidedly not programmer-like fashion.
vale wigeon
what is a "permutation math formula" specifically?
regardless, here is what i am thinking of...
rough jungle
in my 11th grade in math class there were problems like:
how many 6 letter words can be made using "abcd" that start with "b" and end with "c", and etc
the solution of them was using permutations
vale wigeon
ok but i don't know what you mean when you say the phrase "permutation math formula".
and you are kinda throwing me off with that alone.
rough jungle
give me your solution ignore that lol
vale wigeon
regardless...
let f(n) be the count of symmetric 0-1 matrices of size n. then the following are true:
f(1) = 1, f(2) = 2
and for n >= 3, we have the following recurrence relation:
f(n) = f(n-1) + (n-1)*f(n-2)
and here is how i derived that recurrence
rough jungle
also in each row there can be only 1 one
the rest are 0
rough jungle
regardless...
let f(n) be the count of symmetric 0-1 matrices of size n. then t...
so if i convert this to code it's done?
vale wigeon
sure, but are you interested in hearing how i got this?
rough jungle
yeah. i didn't write that but i did account for it. sorry
don't be!
you are a life saver thank you!
you don't know how hung up on this i am
rough jungle
sure, but are you interested in hearing how i got this?
yes
vale wigeon
right
rough jungle
but i think i know,
because you are smart
vale wigeon
so every one of your matrices has either a 1 or a 0 in its top left corner
if the top left corner is 1, then the rest of the first row and first column are full of zeros, and the rest is a matrix of the same type (0-1, symmetric, single 1 per row/col) but of order n-1
if the top left corner is a 0, then there is a 1 in exactly one of the n-1 spots remaining in the first row, and a 1 in the corresponding spot in the first column. strike out that row and the first row, and that col and the first col, and what you will be left with will be a symmetric 0-1 permutation matrix of order n-2.
i am on the go rn so can't draw it. otherwise i would.
rough jungle
what if in the first row, the third column is 1.
in this case the first column of the third row has to be 1.
vale wigeon
... yeah? that's part of my second case.
vale wigeon
and a 1 in the corresponding spot in the first column
i am aware that a 1 off the diagonal forces a 1 at its reflection
by symmetry
rough jungle
regardless...
let f(n) be the count of symmetric 0-1 matrices of size n. then t...
I don't understand your formula at all
what are the inputs of the function
can you simplify it a bit, or give me a small code
vale wigeon
what are the inputs of the function
there is only one input: n, the size of the matrices to be counted.
rough jungle
there is only one input: n, the size of the matrices to be counted.
def f(n):
if n == 1:
return
if n == 2:
return
f(n-1) + (n-1)*f(n-2)
am i doing it a bit right?
vale wigeon
anyway here is a naïve implementation that will run slow but adheres closely to the formula:
def matrix_count(n):
if n <= 0:
# throw some error or NaN or whatever
# ig also handle non integer input somehow
sys.segfault()
elif n == 1:
return 1
elif n == 2:
return 2
else:
return f(n-1) + (n-1)*f(n-2)
oh my god
Ann
you are a genius
thank you so much
it worked!
omg it calculated 30
vale wigeon
i hope you don't take the segfault thing seriously, but you're welcome.
rough jungle
i hope you don't take the segfault thing seriously, but you're welcome.
close
.end
.close
polar prism
$Let \ ( f ) and ( g ) be monotonically increasing functions. It always holds that \g(n) = \Omega(f(n)) ) or ( f(n) = \Omega(g(n)) ).$
how can i prove or disaprove this pls
mortal trellis
try some examples first. see if it is true for those
if yes, try to understand why its true for those
if not, then you found a counterexample already
vale wigeon
\f isn't a command btw
polar prism
wtf haha
ocean sealBOT
Moaen Ism🐝
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vale wigeon
Let $f$ and $g$ be monotonically increasing functions. It always holds that $f(n)=\Omega(g(n))$ or $g(n)=\Omega(f(n))$.
Ann
vale wigeon
should we also assume f(n), g(n) > 0?
vale wigeon
so as not to get any silly edge case bullshit with negatives...
polar prism
so its disprove i guess
vale wigeon
not given i mean
is this in the context of like algorithm complexity
vale wigeon
sounds like a yes to me
if so then you can probably assume the functions are positive
cause the ones you care about are like, time or space complexity for algos. and those are positive
polar prism
got any idea on 2 functions for example?
it dosnt really matter if its time or space its just a math question
even if its algo course
where i study algo course is 95% math
if not 99%
vale wigeon
i mean ok like
alright
i have an idea but it might be a little too spoilery
bc i know of a pretty elegant way to characterize big Omega and other asymptotic notations
on the condition that neither function takes on the value zero too often.
polar prism
I can draw a graph of 2 functions which show that its not correct
but i dont know how to define the 2 functions
vale wigeon
can you show me the graph you have in mind
polar prism
sure sec
vale wigeon
maybe i can come up with something fitting
polar prism
Here
got my idea? x.d
wait haha actually
I can just do sin and cos? lol
@vale wigeon
polar prism
ye something like this
but wait its more easy just o pick sin and cos? no?
to*
oh wait
no
lol
vale wigeon
and the points where g(n) goes down to zero, does have a vertical tangent there?
fickle heath
Big Omega doesn't just mean "one function is above the other"
polar prism
i can draw another 2 graphs
fickle heath
You are trying to find a counterexample, which is fine, but I'm pretty sure the statement is true
fickle heath
Get to the definition of Big Omega
vale wigeon
polar prism
Hahaha
fickle heath
Big Omega doesn't just mean "one function is above the other"
.
vale wigeon
how do these continue tho
polar prism
how do these continue tho
I think in the end one function will win
ye true
one function will always be on the upside of the another one
vale wigeon
you have not specified them in full so it's impossible to evaluate this as a counterexample or not
polar prism
you have not specified them in full so it's impossible to evaluate this as a cou...
right
well here is the definition of big omega:
$we say that (T(n) = \Omega(f(n))) if there are positive constants (c) and (n_0) such that (T(n) \geq c \cdot f(n)) for all (n \geq n_0), $
ocean sealBOT
Moaen Ism🐝
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
polar prism
should i to assume negatively that its not true?
vale wigeon
i don't know to be honest
i can't tell intuitively if we should be going for proof or disproof
fickle heath
The fact that both functions must be monotonically increasing makes it tricky
polar prism
Im trying to prove assuming negatively that its not true
im trying to say that there is no c > 0 and n0 in N
fickle heath
That's not how negation works, you need to keep the n0 part
polar prism
I think im stuck x.d
wait can i assume that if g(n) is not big omega of f(n) and then i prove that f(n) is big omega of g(n) ?
fickle heath
Yes that's what the statement means
polar prism
same thing if f(n) is not big omega of g(n) and then prove that g(n) is big omega of f(n)
fickle heath
That's exactly the same thing, you just changed the names of your functions
polar prism
dont tell the answer pls lemme try
sec
ye ye
if I say that g(n) is not big omega of f(n) then i can say that there is no c (constant) > 0 g(n) >= c*f(n)
@fickle heath
fickle heath
Yes for all n > n0
polar prism
so if i also calc g(n+1)
then i substract
i got that its wrong lol
sec lemme screenshot
@fickle heath
<@&286206848099549185>
lone heartBOT
@polar prism Has your question been resolved?
polar prism
can I divide the problem to 2 cases?:
case1 when f(n) > g(n) and then I can pick c = 1 and say that g(n) is big omega of f(n) @fickle heath
or 3 cases even
case 2 when g(n) > f(n) and then if we pick c = 1 and say that f(n) is big omega of g(n)
case 3: g(n) = f(n) then we can say that the function is big omega of itself
@vale wigeon
and since f(n) and g(n) are monotonoically increasing then for every n0 > n f(n0) >= f(n)
so its true to every n >= n0
.close
dim vine
lone heartBOT
dim vine
Is that valid at all? Right now I'm trying to practice this notation as much as I can because my brain goes to mush as soon as I see it
The answer is 0 but that's not a typical amount of working for a 5 mark question so I worry I've fluffed it a little
yeah for sure
appreciate it
jade lance
can some one help me in comma calculation
dim vine
.close
unborn lark
lone heartBOT
echo socket
!status
lone heartBOT
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
1
unborn lark
no....
quasi willow
have you tried looking it up or looking in your book or do you just not understand it?
unborn lark
we have a wiki on it and i cant seem to grasp it
quasi willow
The antiderivative of that function, is the function which when you differentiate you get your original function.
and you want it to be general, so we attatch the +c.
does that help?
unborn lark
it does ill try that
why would u need to dm? seems sus
mah boi sent the answer i wanted to solve it but welp
.close
pine ether
help 21
vale wigeon
!noadvert
lone heartBOT
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
dim vine
!noadvert
Hey Ann, can you explain why this is wrong? It feels as though it should not be 5 marks worth of working but I am at the correct answer
vale wigeon
Hey Ann, can you explain why this is wrong? It feels as though it should not be ...
you're gonna need to open your own channel for this.
also don't ping me or other individual helpers.
dim vine
also don't ping me or other individual helpers.
My bad. Will do thanks
pine ether
nd help in this ex
let q1 be in N-{0;1} show that : 1/-2<q1/q2 - 1/q2<1/2
?
<@&286206848099549185>
lone heartBOT
@pine ether Has your question been resolved?
tawny radish
dicrete math
lone heartBOT
dicrete math
buoyant dirge
It represents the composition of functions.
echo socket
I think r and s are relations rather than necessarily functions
Pretty weird to name relations with lowercase letters though
Anyway, given relations $R \subseteq A \times B$ and $S \subseteq B \times C$, the relation $S \circ R \subseteq A \times C$ is defined by $(a, c) \in S \circ R$ for some $a \in A$ and $c \in C$ iff there exists $b \in B$ such that $(a, b) \in R$ and $(b, c) \in S$
ocean sealBOT
A Lonely Bean
lone heartBOT
@tawny radish Has your question been resolved?
lone heartBOT
tawny radish
.reopen
lone heartBOT
✅
tawny radish
Pretty weird to name relations with lowercase letters though
well I am learning relations so I dont think they are functions
.close
late maple
How do I do 3?
lone heartBOT
How do I do 3?
vale wigeon
<@&268886789983436800> we got a troll here
lone heartBOT
real gazelle
.close
lone heartBOT
Available help channel!
fallow wadi
Given the set ( A = {2, 3, 6} ), define a relation on ( A \times A ) such that ( aRb ) if and only if when ( 3 ) divides ( b ), then ( a = b ).
ocean sealBOT
Fate
fallow wadi
2 is in relation with 3 right
Cuz implication is false only if A is correct and B is not
But 3 isnt relation with 2, cuz thats the only thing where implication gets false
Can anyone check?
alpine sable
what is aRb
lone heartBOT
@fallow wadi Has your question been resolved?
lone heartBOT
@fallow wadi Has your question been resolved?