Ah this isn't j - 1 sorry
#help-39
compact ridge
This is just j
Cause there are j numbers from 1 to j
In general there are b - a + 1 numbers from a to b
chrome flame
compact ridge
Nah so it's just the sum of i(i + 1)/2
The sum of 1 from 1 to j is j
The sum of j from 1 to i is i(i + 1)/2
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chrome flame
The sum of j from 1 to i is i(i + 1)/2
How?
chrome flame
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narrow bloom
How do I find position of "2"?
upper igloo
draw a line from 0 to 2 and then use trig
unreal blaze
Hello, I am having trouble finding the conjugated form of this can anyone please explain it to me
torpid jungle
Hello, I am having trouble finding the conjugated form of this can anyone please...
whats a conjugated form though
unreal blaze
whats a conjugated form though
Oh I don't know if it's a real term or I just made it up but means that the radical sign is in the numerator and not the denominator
pearl pondBOT
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torpid jungle
So you want to express sec theta in such a way that the numerator is radical?
oh I got you
This is know as rationalisation or rationalising a fraction.
I hope you know that root 3 times root 3 equals to 3
basically whenever we want to remove the radical sign from the denominator the easiest way to do it is to multiply the denominator with another radical sign, which neutralises the previous one
but if we just multiply the radical sign with the denominator the numerator remains unchanged and that would change the entire number
So we multiply the numerator with the same radical sign. Now the number remains the same
Im giving you a small example.
Please understand bro I put a lot of effort into writing all this
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fast shuttle
hey, how can i prove this inequation?
given that x!=0
pearl pondBOT
hey, how can i prove this inequation?
given that x!=0
fast shuttle
using lagrange?
civic saddle
idk what you mean by lagrange but it can be solved using differentiation
since f(x) = 1/(2x) + arctan(x) is an odd function, we only need to observe where x > 0
setting f'(x) = 0 you can figure out when the local minima occurs
(also the question is wrong; the inequality should be reversed)
pearl pondBOT
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narrow iron
can anyone tell em how 2 do this? i kinda get the idea but i dont really understand it lol i have a test in 2 hours
trim coral
hello
trim coral
can anyone tell em how 2 do this? i kinda get the idea but i dont really underst...
hello
narrow iron
i can skip the graph , i need the basic idea lol
trim coral
alright
so the slope
is the gradient
so for every 1 square it goes to the right, it goes 2 squares up
the y intercept is the where the line crosses the y axis
in this case, it is 3
and so the line crosses the y axis at 7=3
the equation for the line would be y=2x+3
is that helpful or do you need something else?
narrow iron
ok !! by any chance can u show ur work ?
trim coral
i didnt do any working out
you can interpret it from what it has given you
have you been taught y=mx+c?
m is the gradient
narrow iron
nope unless u mean y=mx+b
trim coral
c is the intercept
narrow iron
m is the slope
trim coral
guessing you're not from the uk then
narrow iron
lol
trim coral
yeah so
m would be 2
and b would be 3
do you get why they are the answers?
i can explain some more if you need
narrow iron
yup
trim coral
so the y axis is where x=0
and so the y intercept is where the line crosses the y axis
on this graph it would be 0
right?
narrow iron
yes
narrow iron
yes
trim coral
so that sums up the y intercept
and if you want to find the y intercept if you have all the other values
how far have you gotten in this topic?
i dont want to make it more confusing
narrow iron
like we passed it on mar 27 but im a slow learner lol
we start new stuff everyday so
its hard 2 catch up
trim coral
do you know how to substitute into equations, solve equations and rearrange aquations?
trim coral
not quite sure what you been by constants, we probably call it something else
but yeah probably
narrow iron
wait i think i can pull up an example
narrow iron
?
trim coral
trim coral
can you find me the y=mx+b for this graph
trim coral
can you find me the y=mx+b for this graph
?
trim coral
can you find me the y=mx+b for this graph
or not?
trim coral
no
ok
can you find the value of the y intercept
where the line crosses the y axis
narrow iron
the line crosses at 4 ?
trim coral
i think the y = 4 x = 2?
oh right, i see what you did
yeah
so thats where the line crosses the y axis and the x axis
ok perfect
so you understand that part
narrow iron
yep
narrow iron
mhm
narrow iron
like y1 - y2 / x1 - x2?
trim coral
yes!
narrow iron
wouldnt i need 2 other values tho?
trim coral
and -1,1
narrow iron
why would it be -3/-1?
narrow iron
ohh ok
narrow iron
sure
narrow iron
wait mb
trim coral
np π
narrow iron
5 , 11?
trim coral
yep
narrow iron
i didnt see the line lol
trim coral
π
narrow iron
would the slope be -2?
trim coral
so you did the substitution right
narrow iron
would it be 1 / -2?
narrow iron
oh 1
narrow iron
2
trim coral
what would b be?
narrow iron
y=2x + 1
narrow iron
yay
trim coral
are you more confident with this now?
narrow iron
yes i understand it more ^^ can i ask u another question tho?
trim coral
yes
narrow iron
what does this mean ?
narrow iron
sure
also this ^^ pls explain this if u can
ill be back in like 2 mins lol im just transitioning 2 class ^_^
trim coral
ok
trim coral
2 more mins
narrow iron
Sure
trim coral
ok
so
what i can see
is that you plot the line
and then shade in the region which would either be above the line or below the line
sharp tree
π I know I would find u here
narrow iron
and then shade in the region which would either be above the line or below the l...
Yes
trim coral
when it has a line underneath
of th wsymbol
the line on the graph is solid
when there isnt a line underneath the symbol
the line is dotted
right?
narrow iron
Yup
trim coral
what does this mean ?
i mean it seems you understand it from the annotations
satisfying the inequalities
narrow iron
That's not my work
trim coral
oh right
narrow iron
It's the teachers notes
trim coral
you pick a random value either above or below the line
narrow iron
Like not intersecting
trim coral
So like if it's < then the line would be below the middle?
wdym
ok
so to satisfy the inequality
you pick a random coordinate on either side of the line'
and put it into the equation
trim coral
what does this mean ?
y <2x+1
coordinates 5,5
would be
5 < 2(5)+1
5 < 10+1
5 < 11
which is true
satisfying the inequality
right?
narrow iron
Yes
narrow iron
Yes I think I did practice questions with "does it satisfy" stuff
When it's satisfied it's shaded right?
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waxen void
pearl pondBOT
waxen void
could someone help me out with this question
we're studying about gradients and im not sure how to continue this exercise
i got 9-b/-14 = 7-b/-10 so far
and now im stuck
sharp tree
U need to construct the line equation
waxen void
i can solve this easily with numeric solver but im not sure we're allowed to use it in the exam
waxen void
U need to construct the line equation
wdym?
sharp tree
y = ax + b is the general form of a line
waxen void
yeah
sharp tree
Triangle method
waxen void
?
sharp tree
pearl pondBOT
waxen void
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β
west sapphire
do you know what gradient means?
waxen void
not really the definition, no
west sapphire
it's also called the slope
sharp tree
Delta y / delta x
Delta as in difference; as delta y = difference in y; so y1 - y2
The same for x
sharp tree
Delta y / delta x
this = 1
waxen void
like, do i just calculate it as i have done before?
sharp tree
like, do i just calculate it as i have done before?
Not really
pearl pondBOT
sharp tree
Its funny
U know and understand what it is
U just dont know what it called or how it works
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silent bramble
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silent bramble
I donβt get sol 2, not sure why itβs -1<= t <= e^pi
west sapphire
they just want a straight line connecting (0,1) to (0, -e^pi)
check that if r(t) = -tj then when you plug in t=-1 you get the first point and when you plug in t = e^pi you get the second point
personally i would have just used
r(t)= (0,1)(1-t) + (0,-e^pi)t with 0 <= t <= 1
but they're equivalent parameterizations and will give the same answer
pearl pondBOT
@silent bramble Has your question been resolved?
silent bramble
personally i would have just used
r(t)= (0,1)(1-t) + (0,-e^pi)t with 0 <= t <=...
I get (0, 1-t-te^pi)
west sapphire
I get (0, 1-t-te^pi)
yea, with 0 <= 1 <= 1
using that you should get the same answer
silent bramble
sorry how do you get 0<=t<=1
west sapphire
plug in t=0 and t=1
those are the endpoints because i used this convex combination: r(t)= (0,1)(1-t) + (0,-e^pi)t
which is designed to give you the first point when t=0 and the second point when t=1
west sapphire
yea
west sapphire
the example in your book used some other funky parameterization
which also works but it's not the most obvious one
west sapphire
nice
west sapphire
looks good
pearl pondBOT
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forest stone
Trying to get help with these two questions
pearl pondBOT
Trying to get help with these two questions
forest stone
I will pay for someone to tutor me on this
I know that I need to get 4 and -5 to be 0.
and I am not changing R2.
So I need to multiply R1 by I think -.5 and I have no idea what to multiply R3 by.
cyan oracle
I know that I need to get 4 and -5 to be 0.
and I am not changing R2.
So I ne...
im not sure how theyre doing it but when i did simplex youd divide R2 by 2 so that you get 1 in column x2 in R2. That way you can then do R1- 4R2 to get 0 in row 1 and R3 + 5R2 to get 0 in R3. Afaik you dont divide or multiply anything other than the pivot row, only add and subtract
forest stone
im not sure how theyre doing it but when i did simplex youd divide R2 by 2 so th...
This is what she did to show, but I don't understand how the fuck she's doing this I feel very lost
cyan oracle
i mean shes doing simplex but in a way i wouldnt do it
forest stone
i mean shes doing simplex but in a way i wouldnt do it
So do you think you could help me? Or could we take thisto DMs
Cause I am lost in the sauce
cyan oracle
So do you think you could help me? Or could we take thisto DMs
i probably cant like explain the whole thing since its been a while but ill see if i can find a video with the method i learnt then ill try to answer any question you have
https://www.youtube.com/watch?v=iYAHQINXmuk this video is probably best its a bit long but they just go through many examples
pearl pondBOT
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@forest stone Has your question been resolved?
pearl pondBOT
@forest stone Has your question been resolved?
pearl pondBOT
@forest stone Has your question been resolved?
pearl pondBOT
@forest stone Has your question been resolved?
pearl pondBOT
@forest stone Has your question been resolved?
pearl pondBOT
@forest stone Has your question been resolved?
candid ice
is this programming
marsh vessel
is this programming
it looks like someone needs help with the simplex method, but i have no clue how to help them over messages and its been open for a while now
charred ocean
is this programming
Itβs linear programming, which is a type of optimization, but not computer programming/coding if thatβs what youβre asking
pearl pondBOT
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sleek arch
pearl pondBOT
sleek arch
Pretty simple i know but i forgot how to find midpoint π
hasty osprey
midpoint formula
if the two coordinates are (x1, y1) and (x2, y2)
its pretty much just finding the average between the coordinates
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wind lagoon
pearl pondBOT
wind lagoon
I don't see why we can assume $f$ to have compact support. The DCT states that $$\left|\int f_n \ d\mu -\int f \ d\mu\right|<\epsilon,$$ given certain conditions. Now, convergence in mean means that $$\int |f_n-f| \ d\mu <\epsilon.$$ It looks to me as if the DCT does not imply convergence in mean, or am I mistaken?
jolly parrotBOT
Philip
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brazen crystal
Hey, I need strategies when it comes to solving differential equations, for example this:
y = 2y''
I was not able to solve this, for some reason. I was wondering, how can I solve such equations efficently?
pearl pondBOT
Hey, I need strategies when it comes to solving differential equations, for exam...
@brazen crystal Has your question been resolved?
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@brazen crystal Has your question been resolved?
dusky turret
i don't understand the last part of the momentum flux profile
dusky turret
how did they get it?
pearl pondBOT
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lime chasm
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tulip musk
Do you know what equivalence is ?
pearl pondBOT
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lime chasm
Do you know what equivalence is ?
In this case will it be the dollar value of both set x and set y?
[N] = {N}
[D] = {D,{N,N}}
[Q] = {Q, {N,D,D }}
Is this correct?
tulip musk
Not quite
lime chasm
Not quite
Could you tell me what i'm doing wrong?
[N] = {{N}}
[D] = {{D},{N,N}}
[Q] = {{Q}, {N,D,D }}
is it the curly brackets that i missed?
tulip musk
- ( {N} ): This represents the set containing only a nickel. Its dollar value is 0.05.
- ( {D} ): This represents the set containing only a dime. Its dollar value is 0.10.
- ( {Q} ): This represents the set containing only a quarter. Its dollar value is 0.25.
- ( {N, N} ): This represents the set containing two nickels. Its dollar value is 0.05 + 0.05 = 0.10.
- ( {N, D, D} ): This represents the set containing one nickel and two dimes. Its dollar value is 0.05 + 0.10 + 0.10 = 0.25.
jolly parrotBOT
Gaza
tulip musk
What have you tried?
lime chasm
For 3(a) I came up with
f(x) is defined for all real numbers except x= -3. Excluding x = -3, the function is one-to-one function since for any two different real numbers x1 and x2, f(x1) is not equal to f(x2). This function is not onto because there is no value of x such at f(x) = 0. Therefore this function is also not a invertible function.
(b)
This function is defined for all pairs of integers, so it is one-to-one because for any two different pairs of integers (x1, y1) and (x2, y2), g(x1, y1) β g(x2, y2). However, it is not onto because there are elements in Z^3 that cannot be reached by g(x, y). For example, there is no pair of integers (x, y) such that g(x, y) = (1, 2, 5). Since the function is not onto so, it is not invertible.
(c)
This function is not one-to-one because both the elements 1 and 4 in the domain map to the element 5 in the co-domain.
This function is not onto because the no element in the domain maps to the element 8 in the co-domain.
Since this function is not an onto function, therefore, it is also not invertible
@tulip musk is this okay?
pearl pondBOT
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umbral sierra
Are the observed counts of a chi-squared test poisson distributed or binomial distributed?
umbral sierra
I assumed that they would be binomial distributed because for Chi-Squared tests it is assumed that the count numbers are sampled from a multinomial distribution.
But I found an answer online that seems to suggest that they are poisson distributed?
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weary dragon
Can someone help me with this
pearl pondBOT
Can someone help me with this
weary dragon
tall flint
You're integrating with respect to y but your integrand is in terms of x
weary dragon
i'm pretty sure this is wrong
tall flint
That's an issue
weary dragon
so do i j replace x with y
weary dragon
yea
tall flint
Which is equivalent to x = ...?
weary dragon
sqrt of y
tall flint
Better
weary dragon
so would it be the integral from 0 to 4 of sqrt y?
tall flint
It would
weary dragon
i got 16/3 and it was wrong
tall flint
Can you show me the full problem?
tall flint
That would've been nice to know beforehand
You're not just finding an area, you're revolving that around the axis
weary dragon
would it be like 2pi integral of 0 to 4 of sqrt y?
tall flint
How have you been taught to solve these solids of revolution questions?
tall flint
You sure about that?
weary dragon
Not really, we started this topic yesterday
tall flint
You should probably go confirm this formula
weary dragon
on what?
pearl pondBOT
@weary dragon Has your question been resolved?
torn mountain
@weary dragon check this out https://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx
you will find that the formula you're wanting to use is the integral of pi*r^2
empty sigil
its like a bunch of little circles when rotated around an axis
weary dragon
you will find that the formula you're wanting to use is the integral of pi*r^2
can u help me finish the problem
pearl pondBOT
can u help me finish the problem
torn mountain
yeah one second ill give it a shot
weary dragon
yeah one second ill give it a shot
any luck?
torn mountain
i believe this should be correct
symbolab wasnt loading for checking purposes
if you cant read/dont understand anything please ask
weary dragon
okay let me take a look
i see, so it's basically the same conept but you just have to use the formula
would it be the same concept for this one?
torn mountain
yes essentially the way to tell if you are integrating with respect to x or y is what the thickness of the disc you are using is
weary dragon
so in this case would it still be y
torn mountain
so for these ones where its rotated around the y-axis (or more broadly x=a where a is a number) you would be integrating with respect to y
and the opposite for rotations around the x-axis
torn mountain
so in this case would it still be y
yes correct
and then your integration bounds are also with respect to the same variable that you are integrating with respect to
weary dragon
so it would be y=x^2/3 or would u have to get it in terms of x
torn mountain
you would have to get it in terms of x so your radius only consists of y's
weary dragon
i'm kind of lost for this one ngl
torn mountain
do you remember what the method was for getting y=x^2 in terms of x
weary dragon
u just isolate x, no?
torn mountain
yes by square rooting both sides, what that did for us was multiply the exponent by 1/2 which was the inverse of what was happening to the x
so in order to get y=x^(2/3) in terms of x we want to multiply each exponent by 3/2
weary dragon
okay i see
torn mountain
i hope that makes sense
weary dragon
ya i got it
torn mountain
awesome!
weary dragon
I'm guessing there is more we have to do before we set up the integration, right?
actually wait
the graph goes from 0 to 1
torn mountain
as long as you have your radius in terms of what you are integrating to you're good to go
weary dragon
so i think we can j set it up
torn mountain
correct :)
weary dragon
Hows this
torn mountain
on first look i think thats correct
weary dragon
what about on second look?
torn mountain
second look its still checking out
weary dragon
yup its right, tysm!
torn mountain
awesome!
weary dragon
u actually explained it quite well with the example
torn mountain
thank you :)
i just had my final exam for this class a couple weeks ago so im glad i still remember how to do some stuff
weary dragon
oh really? what math class
torn mountain
calc 2
torn mountain
I have to either take intermediate calc for comp sci or calc 4 and im thinking i might go the calc 4 route and also take calc 3 as an elective so i can say i completed them all lol
and then also matrix algebra
torn mountain
yes i am
weary dragon
i'm computer engineering lol
torn mountain
i enjoyed calc a lot more than i enjoyed discrete math so i might go down that route a little bit
weary dragon
i enjoyed calc a lot more than i enjoyed discrete math so i might go down that r...
ye i took discrete math
torn mountain
thats sick where at if you dont mind? feel free to dm me for privacy
weary dragon
.close
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high geyser
How do i do this?
pearl pondBOT
How do i do this?
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frank hound
give us your norm
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potent wasp
Hi I need help where I'm stuck halfway and don't know what to do
potent wasp
the above diagram shows a pyramid container with square base of area 36cm^2 and height of 4cm. water is poured into the container such that the height of the water level is h cm and the square area of the water is 4p^2cm^2f
show that the volume of the sapce that is not filled with water vcm^3 is given by v=3/4(64-h^3)
sorry if it's a bit confusing, it is translated from another language
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potent wasp
<@&286206848099549185>
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dense cedar
x=2^1/3 -2^-1/3 , then 2x^3 + 6x = ?
pearl pondBOT
x=2^1/3 -2^-1/3 , then 2x^3 + 6x = ?
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finite geode
x=2^1/3 -2^-1/3 , then 2x^3 + 6x = ?
$x = 2^{\frac{1}{3}} - 2^{\frac{-1}{3}}$
jolly parrotBOT
math X meth β
finite geode
This is correct?
finite geode
x=2^1/3 -2^-1/3 , then 2x^3 + 6x = ?
Multiply it out, its not too hard
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buoyant shore
Pure resonance occurs in underdamped system? true or false
pearl pondBOT
Pure resonance occurs in underdamped system? true or false
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cerulean flower
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cerulean flower
im supposed to do this on the CAS, i have everything define as f(x) and f'(x)
but not sure what point to start with this
this was the example given, they start with 4 here but not sure what to start with on the other qs
woeful stump
if you have a CAS it's just a matter of plugging in the formula
which is $x_{2}=x_{1}-\frac{f\left(x_{1}\right)}{f'\left(x_{1}\right)}$
jolly parrotBOT
b
trim willow
but not sure what point to start with this
It wont matter
magic hearth
calculus II) if we have a scalar field (function with many independent variables) which is defined in E , given that E β R^3 , is it possible that E = R^2 ? (ping me)
pearl pondBOT
calculus II) if we have a scalar field (function with many independent variables...
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oblique river
onyx moat
An aeroplane is flying horizontally, directly towards the city of Melbourne at an altitude of 400
metres. At a given time the pilot views the city lights of Melbourne at an angle of depression of 1.5Β°. Two minutes later the angle of depression of the city lights is 5Β°. Find the speed of the aeroplane in km/h, correct to one decimal place.
onyx moat
plz help
woeful stump
have you set up drawings?
onyx moat
not rlly idk how to draw a diagram for this
woeful stump
first one:
- right triangle
- angle with 1.5 degrees
- 400 tall
second one: - right triangle
- angle with 5 degrees
- 400 tall
onyx moat
would i use sin to calculate them?
woeful stump
your drawing looks something like this right
onyx moat
yes
woeful stump
ok so what side do you have and what do you want
onyx moat
you have the opposite and ur tryna find the hypotenuse?
woeful stump
uhh in this case you'd want the adjacent side
onyx moat
you youd use tan?
onyx moat
what would i do after i get bothe the values
woeful stump
$\sin(\frac{opp}{hyp}) = angle$
jolly parrotBOT
b
jolly parrotBOT
b
woeful stump
yeah you're looking for opposite
onyx moat
you do total distance/time right?
onyx moat
.close
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midnight haven
pearl pondBOT
midnight haven
as per the marking scheme given for this question, x isnβt 180 - (77+50), but is actually 27 (77-50)
why is that?
angles around a line would add up to 180 right?
27 + 50 + 77 = 154
light helm
you've miscalculated <CBE, that isn't 77
midnight haven
you're confusing this with corresponding angles
oh
light helm
these are cointeriorangles
regardless getting that angle wasn't needed
they applied alternate interior angles directly
midnight haven
50 was not known
only numbers provided was 65 and 38
itβs a whatβs it called triangle so itβs same angle for two sides so 65 65 = 130
light helm
50 can be determined from angle sum of a triangle and that triangle being isosceles
midnight haven
50
pale timber
BED and CBE is same because itβs parallel
midnight haven
BED and CBE is same because itβs parallel
oh
light helm
after getting the 50Β°, apply alternate interior
midnight haven
after getting the 50Β°, apply alternate interior
whatβs that one
Iβm not good with names
light helm
Z shape
light helm
vague wording
just look at whatever the pic tells you when you look up alternate interior angles
pale timber
Yes
midnight haven
now that makes sense
pale timber
And 180-153
pearl pondBOT
pale timber
Bye
pearl pondBOT
Available help channel!
steady walrus
what is the diffrence between Original number - new number = difference
( Difference / original number ) * 100 = Percentage decrease (%) and just taking the new number/original number
sleek perch
So you are saying that if $O = 4$, $N = 1$, hence $D = 3$. And $D/O = 3/4 \cdot 100 = 75$ is equal to $N/O = 1/4$?
steady walrus
So you are saying that if $O = 4$, $N = 1$, hence $D = 3$. And $D/O = 3/4 \cdot ...
whatπ
sleek perch
O = Original number
N = New number
D = Difference
jolly parrotBOT
NotRealJohnny
steady walrus
So you are saying that if $O = 4$, $N = 1$, hence $D = 3$. And $D/O = 3/4 \cdot ...
wait let me think
steady walrus
wait i can give task example
sleek perch
That will be better.
steady walrus
Find the percentage.
78kr is ? of 325 kr. here im supposed to use methode 2
sleek perch
π€¨
steady walrus
Oda is considering buying a pair of mountain trousers for NOK 899. In another shop, she finds the same trousers for NOK 699.
How many percent cheaper are the trousers in the other store?
here im supposed to use 1
but i dont understand why
bc
sleek perch
π€
sleek perch
That was your answer?
steady walrus
no
i used methode 2 on both bc
i thought it was the same
so i tok 699/899 and got 0,7775
steady walrus
for context what grade are you in
uh that depends on the country does it not
sleek perch
I do not think grade matters.
(899-699)/899 = 0.22, my instincts say this is the answer. But I cannot explain it.
woeful stump
kinda but i remember learning percentages and stuff before formal algebra
steady walrus
but if you take 77,775+22,25 u get 100 ish so there has to be a connection between the methods
woeful stump
you get exactly 100
steady walrus
(899-699)/899 = 0.22, my instincts say this is the answer. But I cannot explain ...
yes thats the answer
woeful stump
you get exactly 100
see if you can find out whyπ
steady walrus
oh i think i get it now
first method gives the decrease percentage while second method gives the percentage
steady walrus
huh
oh
since i got 77,775 i could just take that and minus 100 to get the decrase %
.close
pearl pondBOT
pearl pondBOT
Available help channel!
sand robin
How to solve this?
pearl pondBOT
How to solve this?
sand robin
Well I know how I just donβt know how to get rid of absolute value when integrating 1/(xlnx)
steep saddle
what is z(x)
sterile tusk
this is a first order linear differential equation
we would use an integration factor
sand robin
yes i know
sterile tusk
so what are you confused about?
sand robin
that
sterile tusk
how they integrated it?
sand robin
,w integrate 1/(xlnx)
jolly parrotBOT
sterile tusk
and itβs raised to the e
sand robin
where is the absolute value
hm could you elaborate
what is mok function
ugh never heard of it sorry
hm
wraith hare
I'm doing a maths degree and I have never heard of a "Mokudu" function, so idk what's your point, and not really helpful
sand robin
sterile tusk
fr
wraith hare
even after I googled this "Mokudu" function nothing came up
fathom saffron
real
sand robin
xd
sterile tusk
probably different language or something
wraith hare
probably different language or something
that would be my guess
fathom saffron
nor do i find this conducive helping, even if this were true
sand robin
wraith hare
if you insist
sand robin
either way why does wolfram omit absolute value here?
without mokudu function explanation
xdd what happened to him?
pls help
<@&286206848099549185>
sand robin
<@461113398915104769> hey hi
hi
sand robin
i need help solving differential equation
sand robin
i dont understand why absolute value is ommited here
when integral of 1/(xlnx) is ln|lnx|
waxen condor
ok i got you
Now when you are integrating , its thr question right ?
But to what extent is your calculation correct ?
ln 0 or ln - ve is not defined
So ypu mention the modulus function
sand robin
Now when you are integrating , its thr question right ?
yes i guess so
sand robin
ln 0 or ln - ve is not defined
yes but i can have x from interval (0,1) and then lnx will be negative
and then i can not have ln(lnx)
waxen condor
Thats another case we re not concerned of it
sand robin
yes
sand robin
ah so we get two cases ln(lnx) and ln(-lnx)
but the second one does not exist so we omit it?
waxen condor
No we need to apply modulus two times
sand robin
hm could you shownme how
waxen condor
Just use the symbols again
waxen condor
hm could you shownme how
What ?
sand robin
No we need to apply modulus two times
how to do this
waxen condor
sand robin
ah yes from some other part of the same problem i know that x must be greater then 0 so i dont have to worry about that second absolute value
waxen condor
Okk
sand robin
ah so we get two cases ln(lnx) and ln(-lnx)
then isnt it just this?
waxen condor
see
Integration csn continue up to infinite times
Isnt it ?
So each time we integrate we must make sure the function is defined for all x
sand robin
hm yes
pearl pondBOT
@sand robin Has your question been resolved?
woeful fern
hi
woeful fern
looking back at my teacher's notes. whats the difference between each side
woeful fern
thats it?
woeful fern
ok just wanted to make sure. thanks
waxen condor
π
woeful fern
.close
pearl pondBOT
pearl pondBOT
Available help channel!
midnight haven
if f(2x+3)+f(2x+7)=2, period of f(x) is?
pearl pondBOT
if f(2x+3)+f(2x+7)=2, period of f(x) is?
waxen condor
Hiii
midnight haven
but f(2x+3)=f(2x+11) so if the period of 2x is 8 shouldn't that mean f(x) has period 16?
hollow cobalt
i got f(2x+3)=f(2(x+4)+3)
How did you get that though?
thin sigil
What exactly is f refering to?
midnight haven
How did you get that though?
f(2x+3)+f(2x+7)=2
put x=x+4
f(2x+7)+f(2x+11)=2
Then subtracted both
hollow cobalt
Subtracted what?
midnight haven
both the equations
hollow cobalt
You need to subtract something from both sides of the equation
midnight haven
You need to subtract *something* from both sides of the equation
f(2x+3)+f(2x+7)=2
f(2x+7)+f(2x+11)=2
f(2x+3)+f(2x+7)=f(2x+7)+f(2x+11)
Then subtracted f(2x+7) from both
waxen condor
f(2x+3)+f(2x+7)=2
put x=x+4
f(2x+7)+f(2x+11)=2
Then subtracted both
X = x+2
Made mistake here
hollow cobalt
I see
hollow cobalt
Should be 8 yeah
waxen condor
Yeah same
hollow cobalt
Replacing x with x+2 in f(2x+3) + f(2x+7) = 2 yields f(2x+7) + f(2x+11) = 2
midnight haven
Yup
midnight haven
Should be 8 yeah
The period of f(x)?
hollow cobalt
Hmm, not necessarily actually
hollow cobalt
The period needs to be the smallest positive number satisfying f(x + p) = f(x) for all x, finding out solution doesn't really confirm it's the period
waxen condor
oh sry
hollow cobalt
f(x) = f(x+4)
f(2x+3) = f(2x+11) => f(x) = f(x+8)
midnight haven
f(x) = f(x+4)
Yeah I got that.. but if f(2x) has period 8 then shouldn't f(x) have period twice as much as that?
midnight haven
f(2x+3) = f(2x+11) => f(x) = f(x+8)
Can we just put 2x=x?
Wouldn't that change the period
waxen condor
yeahh
hollow cobalt
Wouldn't that change the period
No
You are not finding the period of f(2x)
But of f(x)
Again, the period p should satisfy f(x + p) = f(x) for all x
If x is arbitrary, so is 2x+3 (and vice versa)
midnight haven
ohh got it
waxen condor
So period will always be 8
midnight haven
alright one last question
if f is a function satisfying f(x)+f(x+2)=f(x+4)+f(x+6)
waxen condor
Yes
midnight haven
then would the period be 2?
Because when I solve it I get f(x)=f(x+8)
I'm not sure if that is the fundamental period
hollow cobalt
Right, that is the issue I pointed out
midnight haven
hmm π
waxen condor
Because when I solve it I get f(x)=f(x+8)
What steps you did
hollow cobalt
Hmm, is the question asking for a period or the fundamental period?
midnight haven
What steps you did
f(x)+f(x+2)=f(x+4)+f(x+6) - (i)
x=x-2
f(x-2)+f(x)=f(x+2)+f(x+4) - (ii)
Then added (ii) and (i)
f(x)=f(x+8)
midnight haven
Hmm, is the question asking for a period or the fundamental period?
It's an MCQ question. Just says period but the options are 6, 8, 2 and 12
waxen condor
No
waxen condor
so I got f(x-2)=f(x+6)
and then put x=x+2
You dont get it
midnight haven
Alright wait
waxen condor
Okk
midnight haven
It's f(x)+f(x+4)=f(x+2)+f(x+6)
Then when I put x=x-2 I get
f(x-2)+f(x+2)=f(x)+f(x+4)
And then when I add both I get f(x-2)=f(x+6)
I think I wrote the wrong question earlier π€¦ββοΈ my bad folks
midnight haven
Alright thank you
waxen condor
anytime
midnight haven
π
shadow monolith
How does this probabilistic reasoning work? How do we fill in the gaps?
From: the assumption there are more things that could exist than tings that actually exist.
To: saying x exists has a lower prior than saying x doesn't exist.
My solution is:
The outcomes are equally probable. So,
p(x exists) = # of existing stuff / # of possibly existing stuff
p(!(x exists)) = # of not existing stuff / # of possibly existing stuff
# of existing stuff < # of not existing stuff
So: p(x exists) < p(!(x exists))
If that's correct, what I'm trying to figure out is: Why isn't the equation the following instead?
p(x exists) = # of existing stuff / # of possible stuff
Is there a special reason why the bottom equation doesn't work?
thin sigil
Idk if I get this correctly, but technically the set of things that exist is a subset of the things that could exist at all times because logic
All things that exist can exist because they already exist, if they didn't they couldn't
Like, assume thing x that exists can't exist, look at it, it exists, contradiction, hence it can exist
Now what the probability of things existing is or isn't is really up to the assumptions you're willing to make
thin sigil
Well the things that exist are a subset of the things that could exist, so the question boils down to what are the odds of that subset being bigger or smaller in terms of the parent set, which in itself is a philosophical question that requires assumptions to work from
Do you assume the universe to have infinite possiblities of things that can exist with a finite space? Then most things that can exist probably don't, but why would you make that assumption in the first place?
shadow monolith
Sure. You might dispute the underlying assumption. My question isn't about that. I'm just asking about how A follows from B.
To: saying x exists has a lower prior than saying x doesn't exist.```The assumption isn't that there are more things that could exist, it's that MOST things that could exist don't, re read the tweet
So the most makes the odds in the favor of things that don't
shadow monolith
So the most makes the odds in the favor of things that don't
I'm just trying to figure out how that follows
The formal derivation
thin sigil
Because MOST in the english langauge means vast majority
So if you assume the vast majority of things that could exist don't, then you're making an assumption that stacks the favor in terms of things not existing
It's the assumption itself that makes it that way
shadow monolith
So if you assume the vast majority of things that could exist don't, then you're making an assumption that stacks the favor in terms of things not existing
I'm asking you about the formal details of how this follows.
No worries if you're not aware of the specifics.
thin sigil
Formally the assumption says : p(x exists) << p(!(x exists)), that's the assumption
Or rather
x exists << # x that doesn't
formatting, bah
, # x exists << # x that doesn't exist
From there
, # x exists / # x total << # x that doesn't exist / # x total
and then p(x exists) << p(!(x exists))
shadow monolith
I see. Yeah that makes sense. So how are we deciding # x total? Is it just the total possibly existing xs, or is the total possibly existing xs, and including the total possible not existing xs?
thin sigil
It's the total number of things that could exist, regardless of whether they do or not
shadow monolith
Why is the set the total number of things that could exist, and not the total number of thing sthat could exist, and could not exist?
thin sigil
Think about it this way, let's say the things that exist are blue balls, the things that don't are red ball, you have a pool of 100 balls and you declare there are way more red than blue balls, are the odds of you pulling out a red ball higher or lower than those of pulling out a blue ball?
Think about it in terms of balls, it will become clear, balls never fail me
Balls are what can be, red one aren't, blue are, but they both can
shadow monolith
I understand your example because 100 balls is the total sample space.
thin sigil
Yes, now just assume the sample size is unknown, but you have the assumption still
shadow monolith
You have the assumption still?
thin sigil
Yes, the assumption must be made for it to make sense
If you don't make the assumption you have nothing to work from
shadow monolith
Which assumption?
thin sigil
Of course, the sollution is only valid within the space of that asumption
that most things that can exist don't
shadow monolith
Oh yeah. I agree. I think we're talking past each other.
I understand that much. I'm asking specifically about the denominator here:
p(x exists) = # x exists / # total possibly existing xs
Why is it this equality, rather than the following inequality?
p(x exists) = # x exists / # total possibly existing xs AND # total possibly not existing xs
Is there a reason why the 2nd equality doesn't hold?
In other words, why set the denominator in one way rather than the other?
thin sigil
Well we have to make another assumption that all things are equally likely to exist
shadow monolith
That's fine.
pearl pondBOT
@shadow monolith Has your question been resolved?
pearl pondBOT
@shadow monolith Has your question been resolved?
shadow monolith
<@&286206848099549185>
shadow monolith
hola
waxen condor
habibi where is the Question
shadow monolith
pinned
shadow monolith
Here too #help-39 message
I'm asking about why this is the correct way to set the denominator in this equation:
p(x exists) = # x exists / # total possibly existing xs
There are different ways to set the denominator, like this:
p(x exists) = # x exists / # total possibly existing xs AND # total possibly not existing xs
So why is this way improper?
(Assuming equally likely outcomes.)
pearl pondBOT
@shadow monolith Has your question been resolved?
void sandal
@shadow monolith I may be misunderstanding the notation slightly but:
is this what your asking?
shadow monolith
is this what your asking?
Yes! That's a much clearer way to ask it.
void sandal
?
Ah, but I suppose that doesn't truly answer your question (I've just read it again)
shadow monolith
Yeah that looks makes sense to me. Are you saying that both equalities can't be true? I think that's correct. I'm asking like why is the denominator choosen like that rather than the other one. Like I think there should be some reason having to do with the sample space, or something. But I'm not sure
void sandal
Well the top one I believe to be true as the P(z) = number of z/sum of things in sample space
shadow monolith
Right.
So is P(x exists) = # of existing xs / # of total possibly existing xs an instance of P(z) = number of z/sum of things in sample space?
void sandal
hmmm. Does P(x exists) mean the probability that x is in your taken sample of things out of a larger set? Or the probability that x is in your set?
shadow monolith
I was just thinking about it as, for any x, the probability that x exists. Not sure what you're getting at?
So it'd be the probability that an x in my set exists?
void sandal
So it'd be the probability that an x in my set exists?
That makes sense. I can understand this