That if 1 minute costs you 10 dollars, 5 minutes costs you 50
#help-36
pliant shore
robust fulcrum
b dollars -> a minutes
1 dollar -> a/b minutes
glass ember
so its C times the cost per minute?
pliant shore
Yes
robust fulcrum
c dollar -> ca/b minutes
robust fulcrum
so its C times the cost per minute?
yes
glass ember
would the cost per minute be B/A?
robust fulcrum
thats called unitary method
pliant shore
would the cost per minute be B/A?
No
robust fulcrum
would the cost per minute be B/A?
no
pliant shore
If you check the units it has units dollars per minute
glass ember
why not A/B tho
pliant shore
Misread as a/b sorry
pliant shore
would the cost per minute be B/A?
You wrote B/A here
robust fulcrum
check the units
pliant shore
Wait the cost per minute yeah
Sorry we're tired
glass ember
but lets say the cost for 5 minutes is 10 dollars
for 1 minute it would be 2 dollars
pliant shore
Yeah exactly yep
glass ember
i did B/A
robust fulcrum
or 2 dollars for 1 minutes
pliant shore
So that is B/A yes
robust fulcrum
1 dollar for 1/2 minutes
glass ember
ohhh
there is a difference between 1 dollar per 0.5 min and 1 minute for 2 dollars
like
robust fulcrum
let me send you by doing it in paper
glass ember
okay
pliant shore
there is a difference between 1 dollar per 0.5 min and 1 minute for 2 dollars
Well yeah, 1 dollar per 0.5 min and 0.5 min per 1 dollar
The units are different
Depends if you're trying to find the number of dollars or minutes
glass ember
Well yeah, 1 dollar per 0.5 min and 0.5 min per 1 dollar
yes i am asked tho how many minutes you can buy in C dollars.
pliant shore
Yep so you would use the second one
robust fulcrum
@glass ember
robust fulcrum
np
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crude tendon
Calculus: need help with if sum of a series converges or not
the series is: sinx + sin^3(x) + sin^5(x) + ... where x tends to pi/2.
I am getting two different results by 2 different methods:
method 1:
since in this case my common factor is less than 1, I can use the infinite GP sum formula which gives me the result positive infinity.
method 2:
if first, I take the series to be till n terms and use GP sum formula, it gives me 0/0 form. Applying L-hospital to it gives me the sum to be:
n*((sin(x))^(2n-2))
where x tends to pi/2 and n tends to infinity
this gives the sum to be 0 as anything less than 1 to the power 0 tends to be 0.
yelp
final saddleBOT
Calculus: need help with if sum of a series converges or not
the series is: sinx...
@crude tendon Has your question been resolved?
tranquil pine
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gloomy thistle
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prime mortar
Isn't that Like f(-x) odd function reflection along the origin ?
I don't know transformations tbh
final saddleBOT
@gloomy thistle Has your question been resolved?
lunar skiff
if u have a point (x, y)
what will it transfer unto if u rotate ut 180 around origin
crimson sparrow
Let ABCDE be a convex pentagon with side lengths a, b, c, d, and
e respectively on the sides AB, BC, CD, DE, and EA. Suppose it is an inscribed pentagon, meaning there exists an inscribed circle, denoted by k, which is a circle inside the pentagon and touches all of its sides. Let P, Q, R, S, and T be the points of tangency on the respective sides.
Express the lengths of tangent segments drawn from the vertices of the pentagon to circle k in terms of the side lengths.
final saddleBOT
Let ABCDE be a convex pentagon with side lengths a, b, c, d, and
e respectively...
@crimson sparrow Has your question been resolved?
wintry talon
Draw the shape and set one of the tangent distances to x
Then, you progress around the shape. Knowing the power of a point theorem, two tangents draw to a circle from the same point have the same length. Therefore, you can simply solve around the shape
We get that $e-d+c-b+a-x=x$. You can solve this for x and find the rest.
soft zealotBOT
AkishBrabus
wintry talon
@crimson sparrow
crimson sparrow
Thank you very much, I had a hunch yesterday to maybe try it like this, but got distracted.
.close
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jaunty adder
help
nova iron
log_2 (x) and 2^x are inverse functions
if you can draw one then you can reflect that over y = x and get the other one
nova iron
so the first y point for y=2x is 0.25?
what's 2^(-2)?
to fill this
oh i didn't see what you meant
nova iron
so the first y point for y=2x is 0.25?
yes first y point for 2^x not 2x
final saddleBOT
@jaunty adder Has your question been resolved?
jaunty adder
yes first y point for 2^x not 2x
Oh okay got it
final saddleBOT
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dire gale
What is the easiest way to solve squares by hand? I’m struggling with squares and square roots and I want to be able to do it by hand for my Math 8 SOL (pre-algebra).
final saddleBOT
What is the easiest way to solve squares by hand? I’m struggling with squares an...
tranquil pine
What is the easiest way to solve squares by hand? I’m struggling with squares an...
there's a trick for finding squares
dire gale
like finding 17^2?
Yeah things like that
tranquil pine
once you get good at it, you can find squares within 3-4s of 2 digit numbers
warm python
you could write it as the sum of simpler squares like (10+7)^2
desert mantle
well the early ones you can just remember
warm python
and simplify from there
dire gale
I’ve had to use Desmos on the practice problems
tranquil pine
you could write it as the sum of simpler squares like (10+7)^2
there's a better trick
if yall pause for a while i'll cook
dire gale
you could write it as the sum of simpler squares like (10+7)^2
I tried that for 13^2 and it didn’t work so I think I did it wrong
warm python
I tried that for 13^2 and it didn’t work so I think I did it wrong
!show
final saddleBOT
I tried that for 13^2 and it didn’t work so I think I did it wrong
Show your work, and if possible, explain where you are stuck.
dire gale
whole pecan
For 13^2 I just do 13x13 = 13 x 10 + (13 x 3)
dire gale
For 13^2 I just do 13x13 = 13 x 10 + (13 x 3)
Ok
So for the other method I got 109?? Cause 10^2 is 100 and 3^2 is 9
dire gale
Yeah that works and it’s easy
tranquil pine
@dire gale
elder aurora
smart!!!
elder aurora
hey I joind this group because I got a C- in math I am in 8th grade can you guys help me so I can pass
next time
dire gale
hey I joind this group because I got a C- in math I am in 8th grade can you guys...
Imma close mine and you should open one
.close
dull egret
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dull egret
need some help with this one
first, im
not sure why we're using induction for finite domain
and second how we do specificy a choice function for picking which f(i) in H(i)
can we just say any? im not sure
final saddleBOT
@dull egret Has your question been resolved?
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@dull egret Has your question been resolved?
lime shell
Trig simplification help/explanation
final saddleBOT
Trig simplification help/explanation
lime shell
I am attempting to perform an operation and simplify the result. I am given cot x (sec x - tan x). First I identified what identities these belonged to so I did cot x = cos/sin; sec x = 1/cos; tan x = sin/cos, I can get to that point every time. However, the part where I am stuck is when it comes to simplifying all of that. I have the answer which is csc x -1, I guess I am just looking to better understand how they simplify: cos x/sin x (1/cos x * sin x/ cos x) --> csc x -1. I understand that 1/sin x is csc
final saddleBOT
@lime shell Has your question been resolved?
vale reef
For this have they multiplied w transpose and w and (c transpose and c ) separately
final saddleBOT
For this have they multiplied w transpose and w and (c transpose and c ) separa...
vale reef
What’s norm
soft zealotBOT
Denascite
vale reef
What does it mean aswell
Ohhhh
Oh I get ur working
Hm I guess I’ll just learn that
Thanks
.close
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heavy grove
I need to maximize angle beta
final saddleBOT
I need to maximize angle beta
heavy grove
b and a are constants
I can change h
I wrote tan(beta+theta)=(b+a)/h
That’s where I’m stuck
final saddleBOT
@heavy grove Has your question been resolved?
swift lynx
im curious why the answer would turn out to be -10 instead of 0
final saddleBOT
im curious why the answer would turn out to be -10 instead of 0
tiny gorge
what was your reasoning for 0?
swift lynx
so basically the way I did it was by simplifying the expression
$\frac{-(x+5)(x-5)}{x-5}$
soft zealotBOT
OneWhoKnocks
tiny gorge
yep that's fine
tiny gorge
yep
swift lynx
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heavy leaf
im looking at the solution of one homework sheet and i am stuck with one step of the solution. Its about Gauss-Lobatto quadrature
final saddleBOT
im looking at the solution of one homework sheet and i am stuck with one step of...
heavy leaf
With the Gauss quadrature it is possible to calculate integrals over polynomials up to degree 2n + 1
on the interval [-1, 1] exactly. Nevertheless, it can be useful to calculate one or
several quadrature points from the outset. Often the boundary points
are often chosen. This results in the Gauss-Lobatto quadrature. To construct this
quadrature formula, consider a polynomial
of degree 2n - 1 and write
with r, s ∈ R and q2n-3 ∈ P2n-3. One then considers
As in the case of the Gauss quadrature, we can form an orthogonal system with respect to the weight
function
So at first. We proved that
is a scalar product on C([-1, 1]).
Where im stuck is the following question:
Based on this scalar product, construct a quadrature formula that calculates the
following integral exactly:
We also got one Hint: Think about the degree of exactness of the quadrature constructed with the scalar product.
product and apply it at a suitable point. The weights
or supporting points do not have to be calculated explicitly.
So the given answer of this question is:
Let Pn-1 ∈ Pn-1 be an orthogonal polynomial which, with respect to the scalar product (-, -)w is perpendicular to Pn-2
Note: Because w(x) = (1 - x2) this results (except for one prefactor) in the
Gegenbauer polynomial with α = 3/2, i.e. Pn-1 ≡ G3/2
n-1 ≡ L′
n, where the latter is the
derivative of the Legendre polynomial.
The zeros x1, . . . , xn-1 of Pn-1 are simple, real
and lie in (-1, 1). With ˜w1, . . . , ˜wn-1 we denote the corresponding weights
of the weighted quadrature Iw,n-2. According to Jacobi's quadrature theorem, the
degree of exactness of Iw,n-2 is just 2(n - 2) + 1 = 2n - 3, and in particular
Insert results in
now my question is the last equation of the pic above
why is the wn and w0 the two weights
the original homework is in german. I can also send a pic when someone can help
final saddleBOT
@heavy leaf Has your question been resolved?
final saddleBOT
@heavy leaf Has your question been resolved?
final saddleBOT
@heavy leaf Has your question been resolved?
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@heavy leaf Has your question been resolved?
final saddleBOT
@heavy leaf Has your question been resolved?
tranquil pine
I'm trying to understand the significance of determining the linear independence of functions outside of considering vectors explicitly. Say, for example, we want to determine if the functions [
f_1(t) = 1 \q f_2(t) = t \q f_3(t) = t^2
]
are linearly independent on some interval $I$. Usually in linear algebra, if we have a set of linearly independent vectors that implies that they span $\R^n$ with $n$ being the amount of vectors we have, but how does that extend when considering the linear independence of functions rather?
final saddleBOT
I'm trying to understand the significance of determining the linear independence...
soft zealotBOT
tranquil pine
These span *some function space*
oh i had no clue of the existence of such thing
are they similar to a vector space
royal gust
Fair, my bad I shouldn't have thrown in that wording without making myself clear
It is just a regular vector space
Well, at least we can consider it as a vector space
tranquil pine
(just so this isnt some weird XY i ask because of this)
royal gust
You'll see "function space", "eigenfunction" etc when we are considering functions as vectors.
But these are really just vectors
tranquil pine
okay thats very interesting
so how do you go about determining the linear independence here
i mean usually with vectors u Gaussian reduce or check if det is nonzero
royal gust
So any solution to a linear, homogenous DE is a vector space. The dimension of that vector space is the same as the order of the DE
tranquil pine
assuming linear independence i suppose?
royal gust
Like, you want to see a proof of theorem 4.1.3?
tranquil pine
if it isnt too insane i don't mind, but i guess i also would like to see how it can be applied
royal gust
I mean theorem 4.1.3 isn't telling you what the basis vectors are, just that they exist
It's up to you to find a set that's linearly independent and prove it
tranquil pine
i mean I think the (->) case is simple
it being a fundamental set og solutions implies that the Wronskian is nonzero by definition
so the system must only really have the trivial solution
Well im skipping proving thr part where a nonzero determinant implies linear independence lmao
royal gust
Sorry, I should have read closer before. I think I am confused. What's a "fundamental set of solutions", if not a linearly independent set of solutions?
tranquil pine
let me fish out the proper definition but im pretty sure it's said in the way it is because the book doesn't expect you to have linear algebra knowledge
this "theorem" is very funny to me because it's just like using the identity 
but yeah i guess thats it 
royal gust
The fact that solutions to DEs form a vector space isn't that crazy. The derivative is linear, so it's pretty natural that solutions add to make solutions
The dimension of the space being the order of the DE is nuts to me, though
tranquil pine
is it?
royal gust
Tells you exactly when you're done finding solutions
tranquil pine
oh i mean i guess that's a consequence of the existence and uniqueness theorem?
royal gust
You know what? I actually don't know why this works. Probably something-something factoring out solutions
I think I'll look
royal gust
This answer seems strong
https://math.stackexchange.com/questions/2659254/why-a-n-th-order-linear-homogeneous-ode-has-exactly-n-linearly-independent-solut?rq=1
worldly vale
Heuristically it's not too surprising that the dimension is n. If we "integrate n times" we'll have n constants I.e. degrees of freedom
But I wouldn't know how to prove it in general just vibes
tranquil pine
aight that solution is understandable
for me at least
but okay back to the topic
tranquil pine
how do u verify that those functions span the interval -infty < t < infty
for eaxmple
.close
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tranquil pine
(i think its ok now thanks yall)
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Available help channel!
azure dew
hiya, im needing to do a little math for a program im making and can't figure out how to get it to work the way i'd like it to.
ive got a list of chances (not % but just a list of numbers like [ 1, 2, 4, 8, 16, 32, 64 ]), and i need to have the lower and higher numbers tend towards the midpoint while having a "multiplier" that would make it more quickly tend towards the midpoint, i'd also like it if the numbers further from the midpoint tended towards it quicker
final saddleBOT
hiya, im needing to do a little math for a program im making and can't figure ou...
@azure dew Has your question been resolved?
azure dew
<@&286206848099549185>
neat oyster
Sounds like simple harmonic motion
elder halo
Sounds like simple harmonic motion
Ikr
neat oyster
Lol we have force etc in physics which helps in determing accelerations and the end points...the farther you are more is the acceleration guided towards centre. But I don't really have any i dea how could be based completely on mathematics
Perhaps this hought process may help you a bit
neat oyster
Can you eplain a bit?
elder halo
Like if uk
The momentum
U can fig out distance
But it won't be applicable to this question ig
neat oyster
Aghh..Yeah I understand it...but I don't think it will help here
neat oyster
<@&286206848099549185>
You should tag again I feel, maybe someone else may help you betterr
azure dew
i think honestly i can do something just with sin and map the list of numbers within the bounds of pi
elder halo
Which lv question is it
elder halo
i think honestly i can do something just with sin and map the list of numbers wi...
?
Like high school uni etc
azure dew
uhhh its sorta just a personal programming project im working on, but i can't figure out the math for how to get it to work properly
elder halo
def adjust_list(numbers, midpoint, multiplier):
adjusted_numbers = []
for num in numbers:
distance_to_midpoint = abs(num - midpoint)
adjustment = distance_to_midpoint * multiplier
if num < midpoint:
adjusted_num = num + adjustment
else:
adjusted_num = num - adjustment
adjusted_numbers.append(adjusted_num)
return adjusted_numbers
numbers = [1, 2, 4, 8, 16, 32, 64]
midpoint = sum(numbers) / len(numbers) # Calculate the midpoint
multiplier = 0.1 # Adjust this value to control the rate of convergence
adjusted_numbers = adjust_list(numbers, midpoint, multiplier)
print(adjusted_numbers)
Maybe this might help
Chat gpt 😅
elder halo
uhhh its sorta just a personal programming project im working on, but i can't fi...
Which language
azure dew
writing it in ts aha
elder halo
Turbo script
azure dew
im meant to be learning java and python in uni as well but... they're a bit slow at teaching first years
azure dew
c++ is fun but i only ever use it to write game cheats
elder halo
c++ is fun but i only ever use it to write game cheats
Genius 🤣 i learned c++ for almost a yr and all ik at most is looping programm and till Matrix idk how to even make the most basic game like snake and ladder
neat oyster
Well I wanted to clarify, universities are after 12th grade correct?
elder halo
Yea
azure dew
ya
neat oyster
So colleges and unis are diff?
azure dew
but i don't do much maths doing a cs degree
elder halo
I just finished 11 rn so I can't be blamed for not knowing and shit we were recommending physics and chem for programming
elder halo
So colleges and unis are diff?
That what I never knew the diff
neat oyster
I just finished 11 rn so I can't be blamed for not knowing and shit we were reco...
Same heree!!
azure dew
So colleges and unis are diff?
depends on where you are, in the US colleges just don't have masters/phd
neat oyster
depends on where you are, in the US colleges just don't have masters/phd
Oh I seee... good to know
azure dew
in the UK, where i live, we only have universities and college is pre-uni (year 12 and 13)
elder halo
Same heree!!
Damn bro which state
neat oyster
Damn bro which state
I am from India
elder halo
I am from India
Yea which state
neat oyster
in the UK, where i live, we only have universities and college is pre-uni (year ...
Ohhh
elder halo
in the UK, where i live, we only have universities and college is pre-uni (year ...
12 and 13 grade or old
azure dew
grade
neat oyster
Yea which state
Maharasthra, Mumbai
elder halo
Ohhh
elder halo
She genius
azure dew
So you are doing your degree in Computer science?
yep
elder halo
Cs are the top course in every uni tho idk abt un it's hard asf to get into it in india
neat oyster
Cs are the top course in every uni tho idk abt un it's hard asf to get into it i...
Ikr...Infact talking about JEE.. you need to get above 200 rank to get into the best insitute for cs, competing with almost 21-22 lacks ppl
elder halo
Ikr...Infact talking about JEE.. you need to get above 200 rank to get into the ...
Yea
azure dew
well, i've been programming independent from academic study for 5 years now so everything they teach me is really easy and even 3rd year knowledge is... quite easy
neat oyster
well, i've been programming independent from academic study for 5 years now so e...
Ayoo that;s something cool...
elder halo
well, i've been programming independent from academic study for 5 years now so e...
Future ethical hacker prolly
azure dew
ethical if they give me money 
neat oyster
ethical if they give me money <:A_HuTaoWink:792067911728234507>
😂😂😂😂 Or else we k
neat oyster
Sent ya friend req!
elder halo
Where does hacking stand in coding
Can u tell me the ans
Like i learned c++ but idk how to hack
Is it a different concept or something
azure dew
hacking is an extremely broad term and within the cyber security community its not really called hacking
elder halo
Then
azure dew
usually we call it reverse engineering since we're taking apart programs and finding vulnerabilities in them
azure dew
i've found a couple vulnerabilities in games but usually the higher paid ones are within game companies main infrastructure, not the game
elder halo
My cs man told like 2-3 months are needed to find loopholes and all
azure dew
How long it usually takes
well, coming across a new AAA game, i could find a vulnerability of some sort in about 2-3 weeks if im seriously looking for one?
neat oyster
usually we call it reverse engineering since we're taking apart programs and fin...
This sounded way more cool and logical ngl
azure dew
i actually have a vulnerability that i haven't disclosed to the papermc development team for a movement exploit aha
its been in thir server software for about 3-4 years?
elder halo
i actually have a vulnerability that i haven't disclosed to the papermc developm...
U get payed for finding vulnerability?
neat oyster
I have very less interest in coding or computer related stuffs😂. Ya'll continue..I'll join you later!
azure dew
U get payed for finding vulnerability?
nah i was just writing some cheats and found it
elder halo
Oo
azure dew
im doing more ethical stuff with minecraft development recently though
elder halo
U can sell it then right
azure dew
yeah i could sell them
elder halo
I got a nice business plan
Which lang do think got the most amt of prospect in future
azure dew
honestly that doesn't really matter too much for me, i've learnt enough langs now that i can transfer most of the skills from each if i just spend a month or two learning a different lang
elder halo
honestly that doesn't really matter too much for me, i've learnt enough langs no...
But for a beginner like me ?
I don't wanna be clean slate when i go to uni gotta flex when I reach there
azure dew
realistically no lang is the best, it depends on what you want to go into and what the industry uses
java is massively used just because its old (even if its not that good)
anyway we should probs stop using the help channel for non-help things 😛
.close
final saddleBOT
elder halo
java is massively used just because its old (even if its not that good)
Oo ok
elder halo
anyway we should probs stop using the help channel for non-help things 😛
This channel been occupied for too long now 
final saddleBOT
Available help channel!
tranquil pine
im trying to solve the ODE [
2y'' + (x+1)y' + 3y = 0, \q x_0 = 2
]
tranquil pine
So so our recurrence relation has conditions $a_2 = 0, a_1 = 0, a_0 = 0$ and then the recurrence relation itself is [
2(n+2)(n+1)a_{n+2} + 3(n+1)a_{n+1} +(3+n)a_n = 0
]
So how do I evaluate this?
soft zealotBOT
tranquil pine
u dont have to look at this, I just put it there in case my recurrence relation is sus
rustic wedge
try a_n = r^n ig
pliant shore
Yep you will get a quadratic equation for your characteristic equation
tranquil pine
But like this is nonlinear no?
rustic wedge
But like this is nonlinear no?
not really ig? i forgot what nonlinear is
pliant shore
Wolfram Alpha also gives me an answer using erfi(x) for your original ODE
rustic wedge
https://www.wolframalpha.com/input?i=2%28n+%2B+2%29%28n+%2B+1%29x%5E2+%2B+3%28n+...
shet
tranquil pine
Wolfram Alpha also gives me an answer using erfi(x) for your original ODE
well i am trying to find a series solution
pliant shore
Fair enough
rustic wedge
try umbral calculus might be easier 🙂
tranquil pine
not really ig? i forgot what nonlinear is
its linear if you have something like [
c_na_n + c_{n-1}a_{n-1} + \dots + a_0 = 0
]
aka a linear combination of the terms afaik
soft zealotBOT
rustic wedge
bruh u have linear too then no
rustic wedge
then why did u put c_n bruh
hollow iron
@tranquil pine are u learning from a book?
tranquil pine
then why did u put c_n bruh
Because u said you dont know what nonlinear means
so i answered that by showing what linear is
hollow iron
if you're gonna get a nonlinear weird recurrence every question, surely there's a way you are supposed to solve them
tranquil pine
if you're gonna get a nonlinear weird recurrence every question, surely there's ...
maybe
rustic wedge
Because u said you dont know what nonlinear means
no i mean i thought c_n meant a sequence of constants dependent on n
tranquil pine
the solution steps are pretty much the same in the sense u retreieve a recurrence relation and solve it
its 11
hollow iron
Wronskian??
what kind of secrets are you keeping from us
so there IS a method to solve these or what
tranquil pine
the wronskian is just to verify if our solutions are linearly independent so dont worry about that
like
the steps are the same i can show an example if u want
hollow iron
ok show
rustic wedge
qylo try this:
$$ \mathcal \frac{df}{dx} = \sum_{k=1}^{\infty} \frac{(-1)^{k-1}}{k}f^k(x)$$
hazy hemlock
..
rustic wedge
<@&268886789983436800>
rustic wedge
(this is called method of generating function iirc)
tranquil pine
what book is this, if you're okay to share?
"Elementary differential equations and boundary value problems" and no i invert the colour using my PDF viewer
nova iron
"Elementary differential equations and boundary value problems" and no i invert ...
oh okay i guess i was interested in the inverting color more than the book then 
thanks
soft zealotBOT
rak³en
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rustic wedge
wtf i happening to my latex
hollow iron
tf
nova iron
tf
inland kettle
heh?
solar glade
$q$
soft zealotBOT
Samuel
rustic wedge
$\frac{df}{dx}$
soft zealotBOT
rak³en
soft zealotBOT
rak³en
solar glade
Lol
rustic wedge
shouldnt have used \mathcal
hollow iron
where did you get this from
rustic wedge
where did you get this from
operational calculus 🙂
tranquil pine
Something is iffy here. a_2 shouldnt be an independent term
rustic wedge
**rak³en**
btw this might not work because convergence
tranquil pine
ah actually maybe its fine
soft zealotBOT
hollow iron
oh ok
tranquil pine
thats our actual condition, but like, you need to
decide on what are the independent terms
hollow iron
well all I can say is that I think you're supposed to just find the pattern
tranquil pine
aight will do
and yeah i guess u express it as
a_2 = -3/4 a_1 - 3/4 a_0
so like
a_1 and a_0 are independet
and the terms are expressable using those
so we like
,, a_n = \4{-3(n-1)a_{n-1} - (n+1)a_{n-2}}{2n(n-1)}, \q n \ge 3
soft zealotBOT
rustic wedge
btw qylo solving for a_n and putting it into ur definition of y, u dont get the standard series for erfi
rustic wedge
i doubt that gives u the erfi series expansion
tranquil pine
you dont?
rustic wedge
you dont?
nope, standard series involves n!, urs doesnt
some manipulation might be at play tho
tranquil pine
i mean it doesnt seem to be JUST erfi so i can see why the series solution might differ from what erfi(x)'s series alone looks like?
rustic wedge
there doesnt seem to be anything that could get rid of the n! in the denominator of erfi(x) from that..
rustic wedge
https://www.wolframalpha.com/input?i=2%28n+%2B+2%29%28n+%2B+1%29x%5E2+%2B+3%28n+...
this might be wrong btw
pliant shore
Anyways WA sometimes writes stuff in a very weird form
rustic wedge
Anyways WA sometimes writes stuff in a very weird form
u missed r = x^n in the quadratic u put in WA
nvm am just being dumb
tranquil pine
the first few terms of the solution seem like they coincide
idk how to make WA give u series solutions
it gives something messed up because its trying to calculate it explicitly
rustic wedge
coefficients differ
rustic wedge
it gives something messed up because its trying to calculate it explicitly
ask nlp thingy to give u series solution
pulsar wind
How do they know that fn converges to f point wise?
final saddleBOT
How do they know that fn converges to f point wise?
final saddleBOT
@pulsar wind Has your question been resolved?
desert mantle
well they are a bit imprecise
when doing measure theory you basically always mean a.e.
null sets dont matter
pulsar wind
converging mu-a.e. means pointwise a.e.
Do you mind elaborating, I’m quite confused as to why this is true? Are you saying semantically they’re the same thing
desert mantle
well reread the second paragraph
pulsar wind
Oh yes, I kept thinking to normal point wise convergence not pointwise a.e
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bronze oxide
Main issue is how do I rotate, scale factor, reflect etc from a point not in the triangle.
final saddleBOT
Main issue is how do I rotate, scale factor, reflect etc from a point not in the...
bronze oxide
Also what's the x+y = 6 line
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@bronze oxide Has your question been resolved?
bronze oxide
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stable inlet
Did i answer this question correctly
final saddleBOT
Did i answer this question correctly
stable inlet
crisp epoch
the 2pi(k)/5 part seems about right
haven't learned about the second half of the problem though
final saddleBOT
@stable inlet Has your question been resolved?
rose pulsar
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rose pulsar
I am having trouble finding the u, whether it be 3x or cos^2(3x)
royal gust
You'll need to open up your trig identities for this integral
rose pulsar
You'll need to open up your trig identities for this integral
sin^2 (3x)
royal gust
I wouldn't go with that identity, since now you need another identity
Try an identity that removes the ²
rose pulsar
I wouldn't go with that identity, since now you need another identity
(1-cos(2x))/2
final saddleBOT
@rose pulsar Has your question been resolved?
cloud portal
How do i take the derivative of this
final saddleBOT
How do i take the derivative of this
rotund badge
How do i take the derivative of this
product rule?
rotund badge
You suffer
cloud portal
Aight thanks
and with a fourth and fifth and so on the same logic?
rotund badge
you can think of a(x)b(x)c(x) as a(x)d(x) where d(x) = b(x)c(x)
So the derivative would be a'(x)d(x) + a(x)d'(x)
but then d'(x) = b'(x)c(x) + b(x)c'(x)
and so it keeps being recursive
final saddleBOT
cloud portal
Why do derivatives work
I get what they do and that there are different rules achieve it with but can someone please explain
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obtuse pagoda
final saddleBOT
obtuse pagoda
Could someone help
lucid marsh
whats the question
obtuse pagoda
lucid marsh
my approach to this would be
- angle adding formula
- black magic algebra and trig identities
- get answer
not sure what the answer is tho
rotund badge
I would just bring out the table and see what angle gives you cos = 2sin lmao
obtuse pagoda
I tried the angle adding formula but get stuck 💀
broken dock
In the first step you're using the double angle identity, but there's no "double angle" here.
broken dock
Just apply the angle sum identity to both sides and simplify.
final saddleBOT
@obtuse pagoda Has your question been resolved?
fleet cove
Any help with part c?
fleet cove
<@&286206848099549185>
cedar bobcat
<@&286206848099549185>
doesn't GAC look like a right triangle to you
fleet cove
@unkempt moon
jolly tapir
i think i need to find h
the fact that the shape is a "cuboid" is a pretty big clue
the face AEHD is a square and so is BFGC
jolly tapir
i alr considered that
how have you considered it and not know how to find h
what exactly did you consider
fleet cove
that this shape is a cuboid
fleet cove
earlier u said AEHD is a square
it's not a square
idk the relationship between GC and AD
jolly tapir
wait a minute
can we assume the information given from the first question applies to the second
jolly tapir
you can now solve for the volume of the paperweight
and given that a and b are still the same you can find the third edge
fleet cove
The volume of the paperweight will be $2ab^2 + \frac{1}{2} \pi a^2b$
soft zealotBOT
hoax
fleet cove
Volume = $2(6\sqrt{5})(10\sqrt{3} - 6\sqrt{5})^2 + \frac{1}{2} \pi (6\sqrt{5})^2(10\sqrt{3} - 6\sqrt{5})$
soft zealotBOT
hoax
fleet cove
now what?
soft zealotBOT
hoax
jolly tapir
assuming the volume of the new shape is equal to that
find the third edge by division
(i really hope when they said "melted down" they meant retains the same volume, otherwise I'm not sure how you'd solve this)
fleet cove
oh yea
i could try that
originally, by "melted down"
i thought they just like melted away a piece of the original shape
as if they completely removed the semi-cylinder
and a small portion of the cuboid
jolly tapir
they probably could've clarified it but that's what they meant i think
otherwise its back to me assuming it's a square cuz how else would you find h
fleet cove
that means the design of the question is poor, no?
jolly tapir
just a little bit yea 
fleet cove
so i get h being 14cm
and i get angle GAC being about 28 degrees
thx for the help
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boreal robin
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boreal robin
Need help solving this integral
lavish river
take the sub u = (x-2)/2
use 1 + (sinh u)^2 = (cosh u)^2
finally use the def: cosh u = (e^u + e^-u)/2
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@boreal robin Has your question been resolved?
boreal robin
take the sub u = (x-2)/2
use 1 + (sinh u)^2 = (cosh u)^2
finally use the def: co...
thx
ill try that
lavish river
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raven obsidian
Hi, when testing the rational root theorem with synthetic divison and none of the rational roots give a remainder of zero (remainder theorem stating r= 0 means k from x- k is a factor), how do i find the real numbers?
final saddleBOT
Hi, when testing the rational root theorem with synthetic divison and none of th...
raven obsidian
my head genuinely hurts testing all positive and negative numbers that i cant recall other ways to do this
grand kiln
Hi, when testing the rational root theorem with synthetic divison and none of th...
what numbers have you tried
raven obsidian
+-{1, 2, 4, 7, 8, 14, 28, 56}
I started by putting them in for f(x), since the theorem states that k of (x-k) is a factor, so if the answer results in 0, it works
but none of them worked
grand kiln
I graphed it and some of them work
raven obsidian
watching the given guide video isnt helping because they have numbers that work
raven obsidian
I graphed it and some of them work
.-.
grand kiln
maybe your arithmetic was wrong somewhere
raven obsidian
give me a point/x-value that worked for you so i can try it again
grand kiln
-2 and -4 should work
raven obsidian
no way it worked, where tf did i go wrong
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carmine thistle
Log Proofs;
If a^x=b^y=c^z=d^w=K , (a does not equal 1) , show that log(base a)abcd=x(1/x+1/y+1/z+1/w)
I have first solved for a,b,c, and d. a=k^1/x , b=k^1/y , c=k^1/z , d=k^1/w . I've tried substituing some things into different places, but I really just need some help on the next step, where to take the equation next.
final saddleBOT
Log Proofs;
If a^x=b^y=c^z=d^w=K , (a does not equal 1) , show that log(base a)...
dry light
Where did the x come from
I mean lemme tjink
Because I know a^x b^y c^z d^w = K^4
Oh wait I'm dumb I see where the x is from lol
Lemme cook
Actually well
Hold on
Eh nvm
spring haven
.tex log rules
dry light
i was thinking and then I didn't
spring haven
I forgot the command
dry light
,tex log rules
spring haven
Guess I’ll have to write this out by hand
soft zealotBOT
Peter Griffin
dry light
Fuck man
spring haven
No
spring haven
$\log_a(abcd)=\frac{\log_k(abcd)}{\log_k(a)}$
soft zealotBOT
kheerii
spring haven
Use this
dry light
Log Proofs;
If a^x=b^y=c^z=d^w=K , (a does not equal 1) , show that log(base a)...
Hm what happens if you solve for log_a(k)
Or ln(k)
dry light
Because I know a^x b^y c^z d^w = K^4
Following up on this:
$e^{x \ln(a) + y \ln(b) + z \ln(c) + w \ln(d)} = e^{4 ln(K)}$
soft zealotBOT
Peter Griffin
carmine thistle
huh
dry light
Actually this should work with what you've also been doing
spring haven
They just took the log on both sides
carmine thistle
and my teacher has really just been giving us problems to tinker with one side or the other so that the given looks like the proved
Im trying to digest what those text thigns are
take the log on both sides
that is a familiar thing
dry light
Well I'm just trying different things
I'm legit lying in bed lol so like i cannot grab paper and pencil
carmine thistle
Im thinking i substitute what i have for a b c and d into the log_a(Abcd)
but im not sure what good that would do me
My teacher generally wants us to solve the equations step by step, by doing something to one side of the equation until it looks like what we are trying to prove
dry light
Hm
carmine thistle
**kheerii**
less using formulas like this
dry light
Well let's look at what you've done so far
a = K^(1/x), etc etc
What i am seeing is that if you take the log base A of both sides
For all four
You get
spring haven
less using formulas like this
This is just base change
You can’t really do this without it
I mean, you can
But it’ll be more complicated
spring haven
Write $abcd=K^{1/x+1/y+1/z+1/w}$
soft zealotBOT
kheerii
carmine thistle
spring haven
You already got the answer on the second last line
Just take an x common from all the terms
spring haven
You got 1+x/y+x/z+x/w
carmine thistle
and im also not entirely sure how i got there
So 1 + x/y + x/z +x/w = x(1/x+1/y+1/z+1/w)?
wow
im very tired
and the more i look at this problem the less i understnad
and im not really solving
im proving something is equal to something else
why is a#1 important
final saddleBOT
@carmine thistle Has your question been resolved?
ivory vessel
i have a doubt
final saddleBOT
i have a doubt
ivory vessel
does there exist a formula that can calculate the length of a sine wave
i tried deriving it myself but im stumped, i can only calculate the area, but not the length
terse siren
length?
ivory vessel
yes
terse siren
as in line integral?
ivory vessel
is that what its called?
distant ridge
arc length?
ivory vessel
arc length?
yes
formal trail
arc length of a curve $y = f(x)$ between $x=a$ and $x=b$ is [ L(a,b) = \int_a^b \sqrt{1+(f'(x))^2} , dx]
soft zealotBOT
pnoןɔ
formal trail
unfortunately such an integral is not elementary
it falls into a category called "elliptic integrals" (named because they can arise from calculating the arc length of ellipses)
,w arc length of sin(x) between 0 and pi
soft zealotBOT
ivory vessel
holy hell
formal trail
where E is given as follows https://mathworld.wolfram.com/CompleteEllipticIntegraloftheSecondKind.html
ivory vessel
i see thank you sir for resolving my doubt
god i fucking wish my math sirs taught me arc lengths for hours
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sacred lynx
F(g(x)+3)=g(f(x)-3) need to solve this equation if f(x)=3x+1 and g(x)=2-x
lunar skiff
F(g(x)+3)=g(f(x)-3) need to solve this equation if f(x)=3x+1 and g(x)=2-x
plug the functions,
remove each f(smth)
and put (3 * smth + 1)
lunar skiff
plug the functions,
remove each f(smth)
and put (3 * smth + 1)
the same way with g(x)
sacred lynx
Ok wait il let you know what i get
So far i got f(5-x) and g(3x-2)
Do i need to remove f and g now?
@lunar skiff
Wait i think its wrong
lunar skiff
So far i got f(5-x) and g(3x-2)
thats right
lunar skiff
Do i need to remove f and g now?
yes, as u did before
lunar skiff
g(6-3x-2)?
where are u getting the 6?
sacred lynx
no wait let me rewrite it
lunar skiff
g(f(x) -3) = g((3x+1) -3)
= g(3x -2)
sacred lynx
g(x)=2-x this
lunar skiff
this is what u ended up with ,right
f(5-x) = g(3x -2)
lets try the left hand side, the f part
lunar skiff
plug the functions,
remove each f(smth)
and put (3 * smth + 1)
what will it be based on what i told u?
sacred lynx
16-3x
sacred lynx
and 4-3x
lunar skiff
F(g(x)+3)=g(f(x)-3) need to solve this equation if f(x)=3x+1 and g(x)=2-x
u sure about the question itself?
sacred lynx
yes
lunar skiff
F(g(x)+3)=g(f(x)-3) need to solve this equation if f(x)=3x+1 and g(x)=2-x
wait, is it f or F on the left side?
sacred lynx
its the same
lunar skiff
no its different, f and F is different things
lunar skiff
maybe, if u ended up with a true equation like 4 = 4, with no x in it, we would say that there is an infinite number of solutions
but instead we got 16 = 4 which is not correct
so here there is no solution
lunar skiff
alright
it would be easier if u could send a picture of the question, instead of just typing the whole thing
sacred lynx
the pool using the first pipe fills up in 30 minutes with the second pipe it fills up in 20 minutes . what time would the amount of water be the same if we turn the first one ate 9 am and the second one ate 9.05 am
sacred lynx
it would be easier if u could send a picture of the question, instead of just ty...
its in another language
you wouldnt udnerstand
lunar skiff
the pool using the first pipe fills up in 30 minutes with the second pipe it fi...
alright, lets analyse the question, the first pipe fills in 30m which means that how much of the poill it can fill in 1m?
sacred lynx
30/x?
sacred lynx
second is x/20
lunar skiff
second is x/20
yes
now since the two pipes didnt start at the same time
we have first to know how much the poll is filled during the first 5 minutes
sacred lynx
how?
lunar skiff
x/30?
using what u have just come up with
x/30, tells u how much of the pool is filled during x minutes
sacred lynx
5/30
sacred lynx
1/6
lunar skiff
1/6
soryy, 1/6 correct
now we need to know hiw much time is needed to fill up the rest of the pool using the two pipes together
what the equation that tell u how much is filled using the two pipes?
sacred lynx
add them
lunar skiff
x/30+x/20=1?
like that, but that would tell u how much time to fill the whole pool
cuz x/30 and x/20 is how much is filled in x minutes
and when u add them up u get the total amount
sacred lynx
do i need to replace x with something?
lunar skiff
x/30+x/20=1?
and also it will not equal 1
sacred lynx
5/6
lunar skiff
yes
sacred lynx
x is 10
sacred lynx
so thast the answer
lunar skiff
so thast the answer
no
look, u have two stages, the first is when u have 1 pipe only, and the second u have 2 pipes
u need to get the time of each stage and add them up
sacred lynx
there are no 2 pipes
its always seperate
fist one we turn on at 9am ans the second one in a seperate pool ate 9.05
lunar skiff
the pool using the first pipe fills up in 30 minutes with the second pipe it fi...
"what time would the amount of water be the same" these are two pools then?
sacred lynx
Yea 2 pools
lunar skiff
in this case its the same approach
we stll know that the first pool would fill up to 1/6 of its volume in 5 minutes
so one has 1/6 and the other is still empty
so for the first one, it would be 1/6 +x/30
and the empty one x/20
lunar skiff
u need to know when they are equal
lunar skiff
so for the first one, it would be 1/6 +x/30
so if this is how much is the first pool is filled
sacred lynx
5/6+x/20?
lunar skiff
5/6+x/20?
?
do u understand what x/30 means?
x/30 is the percentage of how much the pool is filled in x minutes
lets forget about the x for a sec, 1/30 is how much the pool is filled in 1 minute, right?
sacred lynx
yes
lunar skiff
so after t minutes how much the pool will be filled?
sacred lynx
t/30
sacred lynx
yes
lunar skiff
alright so t/30 is how much is filled after t minutes
ok, that for the first pipe
for the second it will be t/20, ok?
sacred lynx
yea
lunar skiff
then lets see, the first is filled for 5 minutes
so we want to know how much is filled in these 5 mins
lunar skiff
alright so t/30 is how much is filled after t minutes
based on what we got.
sacred lynx
1/6
lunar skiff
so 1/6 of the pool will be filled
sacred lynx
of the first one in 5 mins yea
lunar skiff
now what will be the amount of water in the first pool then after t minutes?
after u fill it up with 1/6
sacred lynx
t/30+1/6
sacred lynx
t/20
lunar skiff
t/20
good so far
now u know the amount of water in the two pool after t minutes
and we need to know when they will equal each other
sacred lynx
mhhh when?
lunar skiff
u just equal them
lunar skiff
mhhh when?
thats the question!
lunar skiff
well t is still 10
and whats the problem with that :-\
sacred lynx
was the first one we did not correct?
lunar skiff
was the first one we did not correct?
yeah, but that doesn't mean the second is incorrect
its just a coincidence
sacred lynx
ok so what was the point of doing the second one?
lunar skiff
ok so what was the point of doing the second one?
cuz the approache is wrong for the first one
i thought it was the same pool
sacred lynx
but now i need what time would they have the same amount of water
so what time would it be
sacred lynx
9.30 and 9.25
sacred lynx
first one starrts at 9.00 and i t needs 30 mins no?
lunar skiff
30 minutes??
lunar skiff
nooo, thats when they will completely be filled up
he asks about when they will be the same level
sacred lynx
yea
lunar skiff
i mean obviously they will be the same level when they are filled up
but thats not a question
thats easy
but they will have the same level befor even they are filled up
sacred lynx
but they will have the same level befor even they are filled up
yea but how do i finds that?
lunar skiff
yea but how do i finds that?
then what was i trying to explain to you
sacred lynx
ok explain
lunar skiff
what dose the 10 mins that we get means?
lunar skiff
well t is still 10
.
sacred lynx
amount of water
lunar skiff
10 is the amount of water?
lunar skiff
already, im gonna go through it, but dont let me go over a point that u don't with out interrupting me
if u dont understand type a massage dont take too much time to respond if u can
okay?
sacred lynx
ok
lunar skiff
so, u understand the 1/6 part?
the amount of water in the first pool after the first 5 mins
sacred lynx
yes
lunar skiff
so u know that since the first pool already has 1/6 of water, then the amount of water in it after will be 1/6 + the water coming from the pipe
so it will be 1/6 + t/30
sacred lynx
ok
lunar skiff
and for the second since its still empty it will be just t/20
now we have the amount of water in each pool after t minutes (which is (1/6 + t/30) and (t/20)) , and we need to know when they will be equal
agree?
lunar skiff
nope, t is not seperate
they are the same t
t is the minutes passed after the start time which is 9:05
sacred lynx
ok
lunar skiff
so we need when they are equal
literally u make the two equations equal to each other
sacred lynx
ok i get this so far
but how do i find at what time like 9.....?
what AM would they be equal
lunar skiff
no wait
lunar skiff
t is the minutes passed after the start time which is 9:05
this
lunar skiff
correct
sacred lynx
ok thanks
sorry to ask but do you got time for just 1 more problem its a geometri one
lunar skiff
in this case i'd prefer if u close this help and open a new one
this this one is old and down in the help chats
so if u one new one it will top up and people will be able to see ur question, cuz i need to do something
sacred lynx
.close
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