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#help-39
upper shoal
Nvm
pearl pondBOT
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olive jasper
does anyone use wxmaxima?
pearl pondBOT
does anyone use wxmaxima?
pearl pondBOT
@olive jasper Has your question been resolved?
olive jasper
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gleaming plank
$$\sum_{r=0}^{n}(-1)^r\times\binom{n}{r}\bigg[\bigg(\frac{1}{2}\bigg)^r+\bigg(\frac{3}{4}\bigg)^r+\bigg(\frac{7}{8}\bigg)^r+.......m \ terms\bigg] = \ ? $$
jolly parrotBOT
Intecules ∮
gleaming plank
!status
pearl pondBOT
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
I know that somehow I have to use the binomial theorem to group them to power of n but I have no idea how
midnight haven
I know that somehow I have to use the binomial theorem to group them to power of...
do you have the formula
i need this shit in pre calc i forgot lol
pseudo oxide
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gleaming plank
do you have the formula
hard crystal
@gleaming plank do you see any pattern in series? ??
gleaming plank
<@1205199381868052561> do you see any pattern in series? ??
the denominator is in gp
gleaming plank
yes
hard crystal
Now try to simplify
gleaming plank
I actually have no idea , do i just multiply by the -1?
hard crystal
What will be the last term can you tell me?
gleaming plank
(m-1/m)^r
oh goddamnit the series starts from r=0
bruh I didnt notice
i thought it was from 1
hard crystal
Np
gleaming plank
yup but that doesnt matter the way I solved it
but i still appreciate the help
.close
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errant shadow
pearl pondBOT
tribal geode
chain rule
errant shadow
how so
jolly parrotBOT
midnight haven
so you can apply the chain rule by substituting u = cos(x)
unborn charm
,, \6{\cos^2}x = \8{\6\cos x}^2
what sort of preamble do you even have to use the commands by using numbers lol
midnight haven
what sort of preamble do you even have to use the commands by using numbers lol
its magic
midnight haven
ok so I get that
can you do it now
errant shadow
not really
midnight haven
ok so like
errant shadow
I don't know this chain rule
midnight haven
remember what the chain rule tells you
errant shadow
not american or british
midnight haven
,, \dv[y]x = \dv[y]u\2\dv[u]x
jolly parrotBOT
midnight haven
for some chosen 'u'
midnight haven
so here. You can pick u = cos(x) for y = cos^2(x)
errant shadow
nah look lemme send a pic
midnight haven
,align
\dv[y]x &= \dv[y]u\2\dv[u]x\[1.5ex]
\9[\big]{\6f{\6gx}}' &= \6{f'}{\6gx}\2\6{g'}x
jolly parrotBOT
midnight haven
those two forms are identical
errant shadow
midnight haven
yeah
errant shadow
like this is the form I know
midnight haven
right you distributed it
errant shadow
I didn't learn that d(x) d thing
midnight haven
do you know the second
errant shadow
I don't think so
midnight haven
do you know the chain rule at all
errant shadow
don't think so
midnight haven
do you know the product rule
errant shadow
yes
errant shadow
can it be done that way?
errant shadow
ok that's what I was doing but I got a different result
midnight haven
alright show what y did
errant shadow
lemme write and I'll send it
midnight haven
oki
midnight haven
ur answer is definitely correct just to be clear
errant shadow
so that's it?
midnight haven
yeah
midnight haven
this could have been a typo unless there is additional context
midnight haven
no worries have a nice one
errant shadow
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jagged burrow
How can i prove a matrix witha column of zeroes cannot have an inverse?
jagged burrow
With regards to the linear combinations of the columns of the matrix
ashen geyser
How can i prove a matrix witha column of zeroes cannot have an inverse?
could you use the condition for a matrix to be invertible
jagged burrow
could you use the condition for a matrix to be invertible
no
potent mist
square matrix, right?
jagged burrow
well ofc
potent mist
I think you might be able to use the condition for a matrix to be invertible
let A be a matrix with a column of zeroes, and let B be the inverse of A such that BA = I...
jagged burrow
well sure
but that ties with uh linear combination of the columns
i just want to know what i'm missing
if A is the matrix with the first column as zero and it has 3 columns
actually let's say the dimension of A and B are 3x3
so I = 3x3 as well
first column of A is a zero column
potent mist
mhm
acoustic path
you could say that the zero vector is linearly dependent with any other vector
jagged burrow
Let A_1, A_2, and A_3 represent the column of the matrices
Similar for B
actually wait i think i know where i'm messing up
jagged burrow
you could say that the zero vector is linearly dependent with any other vector
not discussed in our chapter yet
but yes that's true
acoustic path
weird (actually idk what order i learned this content in)
jagged burrow
lol
jagged burrow
weird (actually idk what order i learned this content in)
i'm near end of chapter 2
3.4 is independence so yeah
acoustic path
oh cool
jagged burrow
but okay i think i got it
i had it the wrong way around
A * B_1 is the first column of the inverse
but that isn't so clear (at least to me)
if you reverse it then B * A_1
this one evidently gives a column of 0s
near pine
pearl pondBOT
near pine
pearl pondBOT
@near pine Has your question been resolved?
jagged burrow
near pine
Wolfram says √2 but idk how
little shoal
You know a choose b means a!/(b!(a-b)!)
So if you right it in submation notation in that fraction factorial forms and simply
You can probably use ratio test to see it converges
But to sqrt(2) I'm trying to figure out
vague girder
it does converge but i've tried this approach but i personally got stuck
near pine
vague girder
what approaches have u tried?
i tried to see if i can convert it some type of binomial but nah i didn't get anywhere
near pine
Yes i was doin somethin like that
but couldn't simplify any stuff
the solution too dont have much
little shoal
What class is this?
near pine
it just gave a function
vague girder
11 or 12 ig? xD
near pine
12 yee
vague girder
jee if im not wrong lol
little shoal
11 what?
vague girder
12th grade
little shoal
12 what?
vague girder
high school
little shoal
What high school is this?
vague girder
uh uk any identities regarding this?
vague girder
1/sqrt(1-4x) = sigma 2nCn • x^n
like the maclaurin expansion?
near pine
like the maclaurin expansion?
yep it actually gave the same series binomially expanding
ah so they found the function
vague girder
yo i got something
vague girder
uk about the gamma function?
near pine
dang
vague girder
idt they'd ask this in adv tho this far above im guessing
i doubt it xD
vague girder
no they said they probably wont
vague girder
ganma function
well u need it in Wallis' formula so ig
wait im sending my soln but it uses the gamma function
vague girder
i did look some stuff up but yeah
near pine
stuff
vague girder
wallis formula was some integrating rhing right
yeah
vague girder
(-1/2)Cn = (-1/2)!/n!
little shoal
(2n)! / ( 8^n * (n!)^2 )
vague girder
uk what it's a bit complex for me, i'll let someone else answer it
dawn sphinx
I don’t know how to start 1
pearl pondBOT
I don’t know how to start 1
wooden ice
find the derivative on that point
that'll be slope for the tangent equation, which passes through that point
dawn sphinx
find the derivative on that point
So do I just find the deriv of e^e^x then plug in ln(2) for x for m?
wooden ice
yeah
dawn sphinx
Ok I got here but I feel like I’m doing it completely wrong 😭
midnight haven
Ok I got here but I feel like I’m doing it completely wrong 😭
nah u got it right!
midnight haven
So then would this be the answer
yeaaaaa
plush bramble
,w plot y = e^(e^x) and y = 2e^2 * x - 2e^2 * log(2) +e^2 for 0.6 < x < 0.8
jolly parrotBOT
pearl pondBOT
@dawn sphinx Has your question been resolved?
vagrant cape
Why dont they multiply by the primitive of (x+y) at the end?
so in the case of primitivation respective to x.
1/2 x^(2) + y.
so as a whole 1/3(x+y)^(3) * 1/2 x^(2) + y ?
regal herald
im not sure what you mean, but why would you do that?
if i were integrating (x+1)^2 wrtx
i wouldnt get 1/3(x+1)^3 * (1/2x^2+1)
vagrant cape
why dont you have to integrate the inside just like you would with the chain rule?
regal herald
because integration doesnt work like that
you can do a reverse chain rule which is essentially what they do here
integrating (x+a)^n
we divide by (n+1) and increase the power
and we divide by (x+a)'=1
so 1/(n+1) * (x+a)^(n+1)
but theres no chain rule logic directly applying to something of the form f(g(x))
at least not in the same way
pearl pondBOT
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rough abyss
pearl pondBOT
west sapphire
regal herald
west sapphire
should be a -2 down there
rough abyss
Oh
west sapphire
also to be notationally clear you should write "det" instead of just writing matrices
regal herald
or use straight lines rather than brackets
rough abyss
or use straight lines rather than brackets
my bad
rough abyss
seems you kinda drew it but missed it later
i think i corrected it after
regal herald
it made you write this wrong, should be (2-2lambda)
here you also distributed the -1 wrong, if we ignore the previous error
also remember youre trying to keep things as factorised as you can, dont expand stuff if theres no good reason to
rough abyss
it made you write this wrong, should be (2-2lambda)
-2 *-lambda should be 2lambda
rough abyss
here you also distributed the -1 wrong, if we ignore the previous error
yea i think the 2 should be negative
oh wait ur right
regal herald
the determinant of (a,b),(c,d) is ad-bc
youre saying bc is 2 lambda which is fine, but that means you have -2lambda
rough abyss
why
regal herald
because youre trying to factorise it
and youve just expanded it in a way which makes it unclear how to do so
regal herald
by pulling out common factors
rough abyss
wdym
regal herald
rewrite -2+2lambda as a multiple of (1-lambda)
then you can factor out 1-lambda from the whole thing
youll be left with a quadratic which should be quite simple to factorise
jolly parrotBOT
rough abyss
yea thanks , i was confused at the last step before cause i dont how to solve cubic equations
regal herald
just remember not to expand if theres no reason to
always try to see what you can pull out
rough abyss
,w eigenvalues [[1,0,-1],[1,0,0],[-2,2,1]]
how do u know this?
regal herald
wdym
rough abyss
is that the eigenvector values?
rough abyss
ohhh
pearl pondBOT
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hollow scroll
could someone help me with this
pearl pondBOT
could someone help me with this
indigo pewter
9 or 12?
hollow scroll
12
indigo pewter
are we simplifying?
indigo pewter
first factor both the quadratics in the denominators
hollow scroll
could u show/explain
edgy wren
what two number added together will give us -2 and when we multiply them we get -8 ?
hollow scroll
-8 -4
edgy wren
yep
hollow scroll
so wat would i do next?
edgy wren
same denomenator (can't spell it right )
hollow scroll
im lost
edgy wren
on what specifically ?
hollow scroll
same denomenator (can't spell it right )
this
i think
i dont know what to do next
we got -4 2 and -8 -4 but idk wat to do next
edgy wren
you got the common factor ?
hollow scroll
no
edgy wren
i want to ask you a simple question first
hollow scroll
ight
edgy wren
what is the least common multiple
between 3 and 4
hollow scroll
12
edgy wren
ok then LCM of
x and x+1
hollow scroll
x^2+1?
edgy wren
its ok to write as x(x+1)
and its x^2+x
ok now i'll ask two more then we get back to our original question
LCM of (x-4) and (x-4)
hollow scroll
x^2+16
edgy wren
check again
hollow scroll
x^2-8x+16
edgy wren
that right but isnt the LCM of 2 same expressions just the same expression
hollow scroll
idk
hollow scroll
k
edgy wren
same implies even when we have a lot of expressions
we write the recurring ones as one expression
so then back to our question
the LCM of (x+2)(x-4) and (x-8)(x-4)
you dont need to expand the expressions
hollow scroll
so would the left or the right would be (x+2)(x-4)
edgy wren
so would the left or the right would be (x+2)(x-4)
missing one expression
hollow scroll
wat would that be?
edgy wren
x-8
hollow scroll
im so confuse
edgy wren
from what point
hollow scroll
why is there 3 expressions?
edgy wren
the lcm of (x+2)(x-4) and (x-4)(x-8)
hollow scroll
and what would i do with the 3 expressions
edgy wren
and what would i do with the 3 expressions
to get the common denominator
hollow scroll
how?
edgy wren
ill send a pic
hollow scroll
k
edgy wren
Here
edgy wren
yep
hollow scroll
and left by 1/ no mutiplying?
edgy wren
and left by 1/ no mutiplying?
also yes
edgy wren
yep
hollow scroll
so wat would i do next
edgy wren
multiply the left expression by x+2
hollow scroll
ight appreciate everything
pearl pondBOT
@hollow scroll Has your question been resolved?
potent monolith
Hi, can I get a little help with the 3rd one
pearl pondBOT
Hi, can I get a little help with the 3rd one
worldly glacier
Hi, can I get a little help with the 3rd one
If X+Y converges and X converges, consider subtraction
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cedar dove
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ashen geyser
I divide both sides by loga and got p=19
why
ashen geyser
uneven smelt
I think they literally cancelled away the 5 log a. that's how you get 19
ashen geyser
like it has to be of the form log base a (b)
cedar dove
I just divide both sides by log base a
ashen geyser
you cant do that
uneven smelt
yes. it doesn't have a value.
ashen geyser
its not multiplication
ashen geyser
yes
cedar dove
log a (p(1/16)) = 0
cedar dove
16
ashen geyser
yes because?
cedar dove
so I multiply both sides by 16
ashen geyser
once you remove the log
cedar dove
and to remove the log i
cedar dove
p/16 = 1
ashen geyser
yes
cedar dove
oh ok ty
cedar dove
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dawn drum
How to solve?
pearl pondBOT
How to solve?
dawn drum
Im just very very lost
<@&286206848099549185>
i might have pinged a bit too early
but it was urgent
regal herald
why so urgent
acoustic path
How to solve?
trick to problem like this is reflect one of the path endpoints points across the "river"
this preserves distance while making it a lot easier to calculate the minimum needed
dawn drum
so basically ur saying teh fastest way would be from (2,10) to (10,-5)?
dawn drum
i kinda get that but i still feel as if there would be shorter ways to reach
acoustic path
to travel between two points what is shortest path
dawn drum
to travel between two points what is shortest path
line
dawn drum
ok
acoustic path
u can think of it as, for instance, label the point the rider touches the river as point O or smth
dawn drum
So the shortest distance between the point (3,5) and (9,6) if you had to ross line y =2 would be sqrt61
acoustic path
u can think of it as, for instance, label the point the rider touches the river ...
and label the 2 endpoints as A and B
the rider must go from point A to point O, then from point O to point B
dawn drum
and label the 2 endpoints as A and B
ok
dawn drum
the rider must go from point A to point O, then from point O to point B
ye i understand now ty
i do math olympiads and i was struggling on such an easy problem😭
acoustic path
So the shortest distance between the point (3,5) and (9,6) if you had to ross li...
i don't think this is right
bcz height is 7 not 5
dawn drum
i don't think this is right
sqrt85?
acoustic path
ye
acoustic path
welcome 🎉
dawn drum
how do i close this help thing
acoustic path
u tytpe .close
dawn drum
.close
main terrace
how do I even do this question
pearl pondBOT
how do I even do this question
main terrace
well I do understand these 2:
because of the drawing but without the drawing I don't know how to do it
pearl pondBOT
@main terrace Has your question been resolved?
inner peak
does antone know how to solve this please!!
pearl pondBOT
does antone know how to solve this please!!
unique ibex
does antone know how to solve this please!!
Do you know how to do implicit differentiation?
pearl pondBOT
@inner peak Has your question been resolved?
smoky saffron
Do i find the time at 10 hours in the derivate or normal equation? Im confused on why
ashen geyser
theyre asking for rate of growth at t=10
so you have to sub t=10 in the rate expression, that is the derivative
ashen geyser
here you have population as a function of time
so dP/dt
is rate of change of population with respect to time
so thats why the derivative is the rate
ashen geyser
so if anything says rate i immediately think of derivative
somewhat, yes?
ashen geyser
np
smoky saffron
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pearl pondBOT
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drowsy leaf
How is this wrong
pearl pondBOT
How is this wrong
drowsy leaf
severe adder
you might wanna put in the entire question
pearl pondBOT
@drowsy leaf Has your question been resolved?
daring wedge
if AB = 20, find A + B . A nd B are natural nos
pearl pondBOT
if AB = 20, find A + B . A nd B are natural nos
wooden ice
if AB = 20, find A + B . A nd B are natural nos
there are multiple answers for that
20 can be made by 3 pairs of natural numbers, 2x10, 4x5 and 20x1
so a+b can be either 12, 9 or 21
daring wedge
so tese are da only 3solutions?
wooden ice
so tese are da only 3solutions?
yeah
daring wedge
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woeful raven
why is this vector A - B? I dont get it
worldly glacier
why is this vector A - B? I dont get it<:sadcat:547124024585486359>
well what do you know about vector addition
graphically
cursive wraith
I mean look at what B+C is
woeful raven
well what do you know about vector addition
is b+c =a
woeful raven
what if im looking at it as c=a+b
woeful raven
how do you look at the graph and tell which adds to get certain letter
sorry i dont get physics
worldly glacier
how do you look at the graph and tell which adds to get certain letter
it's a method called tip to tail
woeful raven
ohh, how do you use this on word problems?
worldly glacier
ohh, how do you use this on word problems?
uh it's more of a graphical method
pearl pondBOT
@woeful raven Has your question been resolved?
pearl pondBOT
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midnight haven
i got a ti84 calculator question about binomialcdf
pearl pondBOT
i got a ti84 calculator question about binomialcdf
midnight haven
I type in binomcdf(7,.403,3) in the calculator, but the answer is not what I expect
what am I doing wrong?
is this the wrong function for this problem?
<@&286206848099549185>
I have a test I have to do later today, want to be prepared. anyone?
i got it, its fewer than, so i need to insert a 2 instead of 3 for the third arg. thats confusing
.solved
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vivid pilot
im not sure where to start with this
pearl pondBOT
im not sure where to start with this
keen rain
im not sure where to start with this
assume you were to know the 'radius' of the heptagon, can you determine AB?
likewise, can you determine AC & AD as well?
vivid pilot
assume you were to know the 'radius' of the heptagon, can you determine AB?
im honestly not sure
trig?
keen rain
ys, let's say radius=1, and the center is M
then you know MA = 1
MB=1
the angle between MA and MB is 2π/7
and you seek AB
:)
are the steps unclear?
vivid pilot
and you seek AB
in terms of the sidelengths?
im not sure how to end up with the given equation
keen rain
But it's clear why MA=1 MB=1 and the angle is 2π/7 right
@vivid pilot
we can't progress if you answer every 5 minutes 🐣
vivid pilot
But it's clear why MA=1 MB=1 and the angle is 2π/7 right
sorry. why is the radius 1?
oh we are
assuming
yeah i understand that
keen rain
yea :D
k if you draw it out then we now have a triangle with two equal sides
The triangle MAB
MA=1 MB=1 angle(MA,MB)=2π/7
with these values you can determine AB.
or shall I draw it out
vivid pilot
Do we then use cosine law?
keen rain
yes, but preferably sine
which directly yields the answer
do you have AB = 0.8678 (rounded) in that case?
which, if the radius Rwere arbitrary would be AB = 2 * sin(pi/7) * R
then for AC:
AC = 2 * sin(pi*2/7) * R
likewise for AD:
AD = 2 * sin(pi*3/7) * R
keen rain
are the above steps clear so far?
keen rain
and then we plug these in?
ys
vivid pilot
are the above steps clear so far?
im confused about the 2pi*2/7 angle
and how you got the values of AB, AD, and AC
keen rain
k, for AB first, the angle between MA and MB is 2pi * 1/7 right?
keen rain
which means if we look at half the angle
vivid pilot
or 2pi/7
keen rain
we have pi/7
vivid pilot
oh yeah
keen rain
and there is a right triangle
vivid pilot
yeah
keen rain
so we can get AB/2 = cos(pi/7) * 1
or generalised AB/2 = cos(pi/7) * R
multiply by 2:
AB = 2 * cos(pi/7) * R
the same applies when trying to calculate AC and AD
for AC we have an angle of 2pi * 2/7 (because we take two of the seven sides into account)
each of these two angles are 1/7 of 2pi
vivid pilot
ohh
keen rain
which means the angle from MA to MC is 2pi * 2/7
vivid pilot
but we dont have a right triangle
keen rain
exactly, however:
now we have :)
we regard the line connecting A to C
which is AC
and again split the angle
to get two right-angled triangles
vivid pilot
we can multiply both sides by 2R
keen rain
is this true?
ah nvm you meant how to continue from there
vivid pilot
yeah
keen rain
are you familiar with the trig identity for addition with sine?
sin(A+B) = sin(A)*cos(B) + sin(B)*cos(A)
vivid pilot
oh
vivid pilot
`sin(A+B) = sin(A)*cos(B) + sin(B)*cos(A)`
where would i use that though?
pearl pondBOT
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quiet valve
i want to get the best input that will give most output,
pearl pondBOT
i want to get the best input that will give most output,
quiet valve
im working on program that have a function that i can pass input and will give me output, now i think about ratio like i pass small input and store the output then pass big input and store output and check the ratio
what u think guys
quiet valve
i want to get the best input that will give most output,
the input ouput function work like this image, at some point input to output ratio will start falling
keen rain
the input ouput function work like this image, at some point input to output rat...
if it's strictly increasing and then decreasing after the turning point, you can always eliminate sections where the maximum can't be
quiet valve
there is no data know for any point, but at some point it will start fail thats the only known thing
keen rain
there is no data know for any point, but at some point it will start fail thats ...
sure, your algorithm can repeatedly reduce the relevant area
such that you get increasing precision of the maximum value with each iteration
quiet valve
speed is critical, what i think of is test with diff inputs and see what output comes and by two points i could get the ratio ?
i dont want to iterate until last value is bigger than current value
keen rain
Let f be the function.
Let [a,b] the interval of possible inputs for f.
interval = (a,b)
n = ... # iteration count
for _ in range(n):
a,b = interval
test_position1 = a + (b-a)/3
test_position2 = a + 2*(b-a)/3
test_value1 = f(test_position1)
test_value2 = f(test_position2)
interval = (a, test_position2) if test_value1 >= test_value2 else (test_position1, b)
trinary splitting allows you to reduce the interval of possible values by a third each iteration
so for instance if your range of inputs is [0,1] at first, it has length 1
after the first iteration it'll only be 1 * 2/3
after the second iteration 1 * (2/3)²
then 1 * (2/3)³
etc
which yields precision incredibly quickly
@quiet valve shall I visualize how the algorithm works or is it clear?
quiet valve
yes, pls
keen rain
so let's say we currently are during any iteration and have the interval [A,B]
meaning we know that the maximum is between A and B.
now we'll split that interval into 3 and determine the two intersection points:
each subinterval is 1/3 of the size of [A,B]
so x1 = A + (B-A)/3
and x2 = A + 2*(B-A)/3
so far clear right
quiet valve
yes yes
keen rain
now we'll evaluate the function at x1 and x2
giving us v1 and v2
now we'll check which of v1 and v2 is bigger
in the case of the image you can see that v1 is larger than v2
that means that we know that the maximum CANT be between x2 and B.
that's the crucial part
quiet valve
and keep doing that until hit most point
keen rain
yea so in this case our new Interval would be [A,x2]
if instead v2 were larger than v1
then the new interval would be [x1,B]
repeat until desired precision is acquired.
quiet valve
can u show python example or pseudo code
keen rain
as above: ```py
Let f be the function.
Let [a,b] the interval of possible inputs for f.
interval = (a,b)
n = ... # iteration count
for _ in range(n):
a,b = interval
test_position1 = a + (b-a)/3
test_position2 = a + 2*(b-a)/3
test_value1 = f(test_position1)
test_value2 = f(test_position2)
interval = (a, test_position2) if test_value1 >= test_value2 else (test_position1, b)
print(f((a+b)/2)) # outpout
thanks, now what if f is a external API, that need to be called form network, for my case that take time and speed are critical, is there any other way to make calls for f function low ?
keen rain
hm I'd say it's already fairly optimized
the only thing we could change is to eliminate the second function call by getting a bit less efficient
by reusing the evaluated values at x1 & x2
however then the reduction factor is probably closer to 1/4 rather than 1/3
quiet valve
py example pls
jolly parrotBOT
Result:
910.23922662684
,calc -1000/log(1/4)
jolly parrotBOT
Result:
721.34752044448
there another way to get some data, there a multicall thing for that API so i can make one network call, with multi input and will give me the outputs for every input so now we have some data, that could help ?
keen rain
there another way to get some data, there a multicall thing for that API so i ca...
so it's cheaper to just call with multiple inputs?
quiet valve
mostly yes, because the speed fall comes from Network not from the code
keen rain
hm do you happen to know the delay times for calculations and a call?
if so then we could specifically optimize
eg if the call costs a lot and a calculation almost nothing
then we could just call the API with ~1000 inputs
and thereby eliminate 99.8% of the interval each iteration
quiet valve
for my tests 100 input are fair delay
keen rain
dym 100 inputs takes a lot longer than 1 input?
quiet valve
nope 100 input are far network latancy, 1000 will take longer (more latancy)
keen rain
can you test the delays
call the API with 1 input and then with 1000 inputs
and test the delays
quiet valve
give me min
keen rain
k
quiet valve
input: 100
duration: 428ms
-------
input: 1000
duration: 3063ms
could you also lastly test input:1 and input:10000?
then we have enough information
keen rain
ok so now we know that the base delay is about 100ms
and that going from 1000 inputs to 10000 is irrelevant (although actually faster)
so we can do something between 1000 and 10k inputs per call
which gives us an elimination factor of 99.8% or 99.98% of the interval per call.
quiet valve
nice!!
keen rain
do you need any specific precision for the output?
because in theory we could also do like 1 million inputs
which would be faster than 100 times 10k inputs
keen rain
both inputs and outputs?
quiet valve
yes both are integers
keen rain
actually wait I realized it can be solved much quicker since the function is linear ._.
keen rain
its very linear
= linear or approximately linear
keen rain
quiet valve
pub fn find_optimal_input(&self, max_count_in: u64, step_size: usize) -> (U256, U256) {
let input_token: &CryptoToken = self.get_input_token();
let input_token_unit: U256 = input_token.input_token_unit();
let mut optimized_in: U256 = U256::zero();
let mut profit: i128 = 0;
for amount_in in (0..max_count_in).step_by(step_size) {
let amount_in: U256 = U256::from(amount_in) * input_token_unit;
let Some(amount_out) = self.get_amount_out_v2(amount_in) else {
continue;
};
let amount_out_i128: i128 = amount_out.as_u128() as i128;
let amount_in_i128: i128 = amount_in.as_u128() as i128;
let this_profit: i128 = amount_out_i128 - amount_in_i128;
if this_profit >= profit {
optimized_in = amount_in;
profit = this_profit;
} else {
break;
}
}
(optimized_in, U256::from(profit))
}
its rust lang
the input will just fall
keen rain
ok but it isn't strictly linear?
quiet valve
so like in this iterate are input incresing, next iterate it less than the last one
keen rain
because if it's linear then we can solve it in under a second to the exact value
quiet valve
mostly first triangle
keen rain
mostly or exactly :D
quiet valve
lol xD
keen rain
if it's exact then:
f(1) - f(0) = f(2) - f(1) = f(3) - f(2) = ...
the difference would be constant up to the maximum
is it some form of task where you're given that the function is linear?
or do you have an API whose function's properties you don't actually know
keen rain
ok so you only know it's rising and then falling.
then the initial code is the best approach we can hope for likely
quiet valve
the pool desined to be something like that, the more u spend USDC, the more ETH will get high in price and u will get lower rate of USDC -> ETH ratio
so optimal amount is the best USDC u input to get most ouput of ETH
keen rain
,calc log(0.002)/log(2/3)
jolly parrotBOT
Result:
15.327109470451
,calc 15.3271 * 150 - 3063
jolly parrotBOT
Result:
-763.935
k yeah 1000 inputs will be the way to go
so our initial code
only needs to be modified
to split [A,B] into ~1000 intervals instead of 3
AND the inputs need to be turned into integers.
import numpy as np
interval = (a,b)
n = ... # iteration count
for _ in range(n):
a,b = interval
subintervals = np.linspace(a, b, 1000, dtype=np.uint8)
test_positions = f_multicall(subintervals[1:-1])
max_index = test_positions.index(max(test_positions)) + 1
interval = (subintervals[max_index-1], subintervals[max_index+1])
@quiet valve
steps are: take interval [A,B]
split the interval into 1000 intervals with np.linspace (and convert to int using dtype)
get all function values via your call for the inputs subintervals[1:-1]
then determine the maximum index for the inputs
and that index-1 to that index+1 is the new interval
quiet valve
time to write some Rust code xD
keen rain
if your inputs range from 0 to 1 million for example
then this algorithm will find the exact maximum after two iterations.
quiet valve
then this algorithm will find the exact maximum after two iterations.
that HUUUUGE
keen rain
or in other words, if your inputs range from 0 to about 1000^N, it'll need N iterations
quiet valve
O(N)
keen rain
depends on how we define the problem
if the problem would say "given an input range from 0 to N"
then our runtime is O(log1000(N))
= O(log(N))
quiet valve
mostly from 0 -> 50K at very rare case
keen rain
wdym
quiet valve
the pool desined to be something like that, the more u spend USDC, the more ETH ...
^^
keen rain
such a relation doesn't need to be linear yeah
if you have no additional information
then the curve could look very complex
quiet valve
no additional info
will test the code and see what i can get,
i really appreciate your help ❤️
keen rain
kk np
after the loop finished btw you'll have an interval like for instance [701, 701] or [701, 702]
if the interval bounds are the same then you know the max is at x=701
but if the interval bounds aren't the same
then you can do one last API call that tests all of the remaining values
in this case 701 and 702
and takes the maximum from those.
quiet valve
sorry my baby wakeup
got it
time to write some code
what interval = (a,b) are ?
the init values?
a = 0
b = 50_000
?
@keen rain
keen rain
what `interval = (a,b)` are ?
yes
once it runs I'd also experiment with n = 3 and interval splittings of 100 instead of 1000
just to see which is faster
quiet valve
will do, but that will take some times, as the service around that function are not ready yet
but will keep u in touch
keen rain
was a neat question, didn't think I'd solve CS instead of maths problems here but happens :D
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quiet valve
.reopen
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quiet valve
was a neat question, didn't think I'd solve CS instead of maths problems here bu...
u handled it so its good experiance xDD
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warm canopy
Im conducting an analysis on this graph . the relationship should be displacement is proportional to v^2 - so velocity is proportional to the square root of displacement. How would I describe this relationship iwith regards to velocity without saying square root?
pearl pondBOT
Im conducting an analysis on this graph . the relationship should be displacemen...
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rose sentinel
Is normality when n>=30 or just n>30
pearl pondBOT
Is normality when n>=30 or just n>30
rose sentinel
If I have a sample size of 30 on the dot can I consider it normal
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.close
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warped flicker
hey, i have a problem with my trigonometry task, i have totally no idea what to do with the circles when there are no specified lengths of the sides of the triangle (the task is translated from polish so idk if its described correctly)
The measure of the angle between the arms of an isosceles triangle with an area of the root of three is equal to 120 degrees. Calculate the area of the circle inscribed and described in this triangle.
warped flicker
im stuck,,,.
pearl pondBOT
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warped flicker
<@&286206848099549185> 🌭🌭
dim ridge
Sorry, my bad, didn't notice the area is given as well ... First, try to find the side lengths. One way to do this, is drop the median from the center angle, you would get two 30-60-90 triangles. Using basic trig for those triangles, you can find out all the lengths of the triangle
warped flicker
.reopen
pearl pondBOT
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warped flicker
Sorry, my bad, didn't notice the area is given as well ... First, try to find th...
so i got lenghts of the 'a' sides
dim ridge
If you've got, you can use sine law to get the 'b' length as well, which I see in your working
dim ridge
The faster method is basically, the 30-60-90 triangle, no?
You know the length of the side opposite to the 90 angle, you can find out all sides this way?
warped flicker
yeah
@dim ridge okay, what should i do to find the areas of an inscribed circle and a described circle
dim ridge
The inscribed circle is called an incircle
google it up, find it's radius, you have everything now to compute it
sick saffron
Hi guys, I am trying to solve the integral and I get sligtly different answer than it should be. My teacher takes 1 + 2e^x as u and I take just 2e^x as u and I suppose I am doing everything right and get another answer. Could someone explain what's wrong there? Thank you!
vague girder
um u can't split the denominator like that
wild fable
Hi guys, I am trying to solve the integral and I get sligtly different answer th...
also why not take 1 + 2e^x as u.
vague girder
1/(1+u) isn't 1/1 + 1/u
sick saffron
um u can't split the denominator like that
ohh im dam dam
wild fable
you overcomplicate things by not letting the denominator be u
sick saffron
also why not take 1 + 2e^x as u.
I was just trying to solve it by myself and got interested why I get different answers
then I checked
vague girder
i mean this method will work too but u can't split the denominator like that lol
sick saffron
yeah now I see
wild fable
yeah im not saying it wouldnt work but its just more annoying
vague girder
u can integrate f(1+x) just like f(x) but yeah
pearl pondBOT
wild fable
if you wanted to do a different way
$\int_{ }^{ }\frac{e^{x}}{1+2e^{x}}dx=\int_{ }^{ }\frac{u}{1+2u}\cdot\frac{du}{u}=\int_{ }^{ }\frac{u}{u+2u^{2}}du$
jolly parrotBOT
water beam
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Available help channel!
regal sequoia
can somebody help me solve this? "Determine the 2 × 2 matrix A that has the eigenvectors v1 = (3, 1) to the eigenvalue λ1 = −5 and v2 = (5,2) to the eigenvalue λ2 = 7. Then verify that the matrix A also satisfies its own characteristic equation A^2 − 2A − 35I = (A + 5I)(A − 7I) = 02×2. (Masterclass: Coincidence? If not, why?)"
regal sequoia
am i right in thinking i can put up an equation A(3, 1) = -5 (3, 1) and then (a b , c d) (3, 1) = -5 (3, 1) and then (3a+b, 3c+d) = (-15, -5) to get the equation 3a+b = -15 and 3c+d = -5?
pearl pondBOT
@regal sequoia Has your question been resolved?
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prime bramble
am i right in thinking i can put up an equation A(3, 1) = -5 (3, 1) and then (a ...
yes
that works
regal sequoia
okay so i get four equations 3a + b= -15, 3c + d = -5, 5a + b = 35, 5c + d = 14
then i solve them and get a=-5, b=-4, c=-1, d=-2 and a = 7, b=35, c=3, d=-1
and then do i just choose one of them and try the condition i am given to see if it is correct?
prime bramble
choose one of what
regal sequoia
either the first a,b,c and d or the second one and put it in to (a b, c d)
for example (-5 -4, -1 -2) and check the condition
regal sequoia
becuse we have 3a + b = -15 and 3c + d = -5 for the first one and 5a + b = 35 and 5c + d = 14 so i solve both of them and get two of each
prime bramble
uhh
you have 4 equations, 4 unknowns..
how are you getting two values?
can you show your work?
prime bramble
what happened between the system
3a + b = -15
3c+d = -5
and the answers
a = -5, b = -4, c = -1, d = -2?
how did you come to that conclusion?
regal sequoia
I solved out b from the first equation and put that back in to the second equation
But maybe I did it wrong
prime bramble
I solved out b from the first equation and put that back in to the second equati...
b isnt in the second equation!
regal sequoia
Oh sorry
prime bramble
neither a nor b are in the 2nd equation, and neither c nor d are in the 1st equation
you need to solve the system of 4 equations
not just 2
well, actually
you only need to solve the system of 2 equations containing a and b to get their values
and likewise for c and d
hoary meadow
do i really have to sketch all 12 cases
pearl pondBOT
do i really have to sketch all 12 cases
hoary meadow
surely im missing something here there's no way the qu is asking me to sketch 12 graphs 😭
(12 graphs because 3 cases for the determinant and then choosing whether A or B is positive or negative for each one)
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restive bluff
pearl pondBOT
restive bluff
I need some help with this
trig subs are really not making a lot of sense for me
I will show what I tried but it's not much
I'm stuck here
what do you guys do when you can't solve a problem?
I have spent the past 5 hours trying to solve three problems I don't know how to do and I can't figure out how to approach solving problems I don't get differently
ok I fugred this one out in particular
finally
2 more to go
.close
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cedar scarab
Is anybody able to help with these? I just need some type of direction.
pearl pondBOT
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cedar scarab
Did I do this right?
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wind meadow
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swift olive
can someone dumb this down for me
