And their placement
#help-0
uncut mauve
ionic jewel
^
its absolutely worth learning
im a computer science student and I use it daily
i take notes, do hw, all that in latex
manic quail
You could learn it yourself quite easily though, so a class probably isn't necessary.
ionic jewel
^
manic quail
^
gaunt magnet
who can help me
manic quail
Just ask the question, then we can try helping you.
gaunt magnet
Describe the transformation or series of transformations that must be applied to the base function y = 2 x to obtain each given function.
these 3 questions
manic quail
Describing is hard
the 5 makes it steeper and changes th y intersect
the x-1 shifts it to the right by 1
gaunt magnet
the x-1 shifts it to the right by 1
so u gotta list the transformation
viscid wren
I have no idea what I’m doing here
viscid wren
could i hop in a voice channel and ask a question?
spring harbor
It’s 2 am for me so I cannot
viscid wren
could i use a a tan half angle formula and then find the csc of that?
spring harbor
You’re dealing with arctan and not tan
limpid spade
Ga slapen
spring harbor
Wait you should use sin(x/2) = sqrt((1-cos(x))/2) to get sin
viscid wren
he never showed us an example similar to this so im trying to understand the process, thank you though.
spring harbor
Hm okay no worries
spring harbor
I think you can also do it with a right triangle but it has been a while so I can’t remember well
viscid wren
so use a sin half angle formula?
spring harbor
Yeah
viscid wren
but make it csc
spring harbor
Cos(arctanx) = 1/sqrt(1+x^2)
.
viscid wren
i tried it initially but got caught up when i showed my work
viscid wren
i got the sqrt 8/3
viscid wren
instead of using the sin half angle formula my professor taught us to flip the 2 and 1-cos to make it into csc
so it would be 2/1-cos
he said its easier than using a reciprocal of a half angle formula
spring harbor
That might work, regardless you should get same answer as I did if you did it correctly
viscid wren
i even plugged it into symbolab to verify so im a little stuck
spring harbor
,calc csc(arctan(sqrt(15)/2))
ocean sealBOT
The following error occured while calculating:
Error: (intermediate value)(intermediate value)(intermediate value) is not a function
viscid wren
just wondering what did you plug into cos for the formula?
spring harbor
just wondering what did you plug into cos for the formula?
First I used the half angle sin formula
Then used cos(arctanx) formula
viscid wren
alright yeah i need to scroll back up and work it that way then
we got the same answer
ur answer is just an expanded sqrt 8/3
ocean sealBOT
spring harbor
,w calc (sqrt8 )/3
ocean sealBOT
spring harbor
Hm ok as long as you think it is correct
viscid wren
its the same decimal i think you aren't including both numerator and denominator in the radical
trail hamlet
for alternating series, how does the divergence test workk? Do you just ignore the (-1)^n and take the limit as n --> infinit
mossy stream
I got part a done, I was just having issues with b. I found that both F(x,y) and (with ß being the symbol for partial derivative) ßF(x,y)/ßy are continuous but I don’t know how to turn that into bounds, which upon graphing and solving this differential I’m pretty sure are 1 & 2
<@&286206848099549185>
vale wigeon
do you know how to evaluate a function at a point?
junior relic
i do not
vale wigeon
so if i asked you to calculate just f(-5) you couldn't do it?
junior relic
I could not
vale wigeon
do you know what "f(x) = 3x+6" even means, then?
junior relic
I do not
vale wigeon
...do you know what a function is?
junior relic
No.
vale wigeon
bruh
junior relic
bruh indeed
junior relic
my teacher has been on maternity leave
vale wigeon
like even at the most basic level of "a function is an object that takes numbers as input and returns numbers as output according to a predetermined rule"
(also like how the hell are you getting assigned homework on things you have not been taught if that's the case)
junior relic
okay no I understand functions, I was being stupid. I don't know how to solve the question I sent. What do I do to find the answer
vale wigeon
...
okay so
let's go back to where i started
if i asked you for the value of f(-5) would you be able to find it
i.e. plug -5 into f
junior relic
yes
vale wigeon
okay great can you do that
like right here and now
and ping me once you have the answer
junior relic
would the answer to my problem be 233?
vale wigeon
i guess my hint was enough for you to do the whole thing even though i was gonna take you through it step by step
vale wigeon
yw
faint zinc
is dis occupied
vale wigeon
@mossy stream sorry i know your question got buried but the gist is that your solution curve can't cross y=1 nor y=2 as it doing so would violate uniqueness at the crossing point. if you need me to elaborate you can ping me here or in #multivariable-calculus
@faint zinc this channel is free atm you can post your question
vale wigeon
post your question
faint zinc
ii just need help on how to subtract/divide/add/and multiply
mystic sinew
I got a question is (ab)^x = a^x * b^x
vale wigeon
@mystic sinew yes. but this channel is busy.
mystic sinew
ok nice thanks
vale wigeon
@faint zinc so you want a crash course in fraction arithmetic?
vale wigeon
we might do better to move to #prealg-and-algebra for less risk of being interrupted since this is gonna be a long convo
faint zinc
ok
tight locust
question
algebraically speaking: why does
$(\sum\limits_{n=0}^\infty \frac{1}{n!})^x = \sum\limits_{n=0}^\infty \frac{x^n}{n!}$
ocean sealBOT
EndTimes
tight locust
that's not a rule of arithmetic is it?
tight locust
<@&286206848099549185>
cosmic plover
Question:
Find the 3-digit numbers that can be formed from the given digits: 1, 2, 3, 4 and 5 assuming that
a) digits can be repeated.
b) digits are not allowed to be repeated.
coral pagoda
that's not a rule of arithmetic is it?
no, those are certainly not the same thing
tight locust
idk i just think it's weird how you just put x^n in the top of the fraction to get the exponential
that doesn't seem right
is there something special about e that makes it so
coral pagoda
The first property should be more surpising.
the second side is simply just the Maclaurin series of e^x
gritty aspen
https://www.wolframalpha.com/input/?i=sum+from+0+to+10+of+%28-10000%29%5En%2Fn%2...
maybe coz you summed it from 0 to 10?
tight locust
it's clearly diverging
even when i choose an odd limit it just keeps oscillating from inf to -inf
the maclaurin series is supposed to be true for all x
tight locust
it should be going to 0
especially after 100 terms
huh you're right
the infinite sum goes to 0
gritty aspen
mhm yeah
gritty aspen
hmmm
zenith fog
The slide was 5m tall, from the end of the slide the stairs were 4m away. The stairs were also 1m taller then the end of the slide, how tall are the stairs?
tight locust
it doesn't converge to 0
gritty aspen
The slide was 5m tall, from the end of the slide the stairs were 4m away. The st...
mate channel is busy
zenith fog
Srry
gritty aspen
npp
gritty aspen
it doesn't converge to 0
youre right it doesnt
but does the maclaurin series need to?
the value is still equivalent rightA?
?*
gritty aspen
that's literally the definition of e^x
wai can u send the link of what you got on wolfram
stray raven
can anyone please help me with proportion exam questions (roughly 10) in pms please - thanks in advance.
tight locust
ok
gritty aspen
https://www.wolframalpha.com/input/?i=sum+from+0+to+111+of+%28-10000%29%5En%2Fn%...
hm maybe ask a helper?
solar cradle
@tight locust It won't converge to zero, it will converge to e^{-10000}. Also the partial sums of a Taylor series approximate the function locally, so for it to start finding values near e^{-10000} you'll need a very high n
tight locust
@solar cradle right, it won't be 0 but just some small real. that's not what i'm getting
also how high?
specifically
solar cradle
@tight locust I'm not sure, that's an interesting question though
Probably higher than something Wolffram alpha can do easily
At least for the case x=-10000
tight locust
hmm
that's a good point actually
let me try -1
just 10 terms:
and here's what i was getting before with x=-100
coral pagoda
it doesn't converge to 0
Yes it does. The further away your value is from the center point (0), the longer it will take to converge
There should be an exact form/more decimals button somewhere. Click it
tight locust
this is actually a really interesting concept but i'm not sure how to phrase it right
is there a way to actually determine the amount of terms for a maclaurin series evaluated at x to converge within a certain interval of its true value?
what do you call that
solar cradle
Yeah, you're essentially talking about minimizing the error that is f(x) - (partial sum) < y to the point where y is negligible . I'm not really sure how it can be done, but I'm sure it has. It will definitely depend on the function
fossil tapir
coral pagoda
Yeah, you're essentially talking about minimizing the error that is f(x) - (part...
This is the Taylor series inequality. Given $|f^{n+1}(x)|\leq M$ for $|x-a|\leq R$, then
[|R_n(x)|\leq\frac{M|x-a|^{n+1}}{(n+1)!}]
ocean sealBOT
dackid
coral pagoda
Now, unfortunately for you, if we considered$ x=10,000$ for $e^x$, then
[|f^{n+1}(x)|\leq 10,000^ne^{10,000}]
tight locust
-10000
solar cradle
@coral pagoda gotcha, yeah I think I remember seeing that poppin up for like a week in calc 2 lol
ocean sealBOT
dackid
coral pagoda
-10000
Nope! 10,000 here
Because we are looking at the interval $-10,000\leq x\leq 10,000$
ocean sealBOT
dackid
coral pagoda
**dackid**
So the bound for the derivative is what we see here
Which is absolutely gigantic!!
It takes an extremely long time to minimize the error efficiently when choosing such a large number for x
coral pagoda
R_n(x) is the remainder
tight locust
true value - partial sum?
ocean sealBOT
dackid
tight locust
so uh what does that mean in terms of the number of terms
so the (n+1) derivative of f(x) < 10000^n*e^10000
how many terms is that
coral pagoda
Well, n refers to the n^th term
ocean sealBOT
dackid
coral pagoda
There is going to be a value of n where the denominator will eventually be bigger than the denominator, but it is an absolutely gigantic number
tight locust
ahh i see
so it relies on the fact that exponentials will always be slower than factorials
coral pagoda
Yeppers
tight locust
so lim x-> inf (really large real)^x/x! is 0
coral pagoda
In this scenario, use n!, not x!
There is extension of factorials onto the positive real numbers, but that's probably not something you've learned yet
coral pagoda
That is the one
So let's just consider the integer factorials
So lim (really large number)^n/n!=0
ocean sealBOT
dackid
solar cradle
Better yet $$\lim\limits_{n \rightarrow \infty} \frac{\frac{n^{n}}{e^{n}}\sqrt{2 \pi n}}{n!} = 1 $$
ocean sealBOT
Billy Clintorus
coral pagoda
That's one I can't see right away 🤔
solar cradle
It's just Stirling's formula lol, I don't remember the proof either but I feel like I use it twice a week
coral pagoda
It's quite the non-trivial limit
fast wave
jagged imp
a letter
gray isle
gonna need more context
nimble matrix
If that's Area then it might be the length
inner hemlock
oh my bad oops
gray isle
in the context of dealing with a cone,
that'll give you the curved surface area
where d is the diameter and L is the slant height
vale wigeon
it's the area of the surface without the base
gray isle
no its not
vale wigeon
it is not, and even unrolling it will not yield a triangle
it'll yield a circular sector
inner hemlock
what does d stand for? diameter of base?
vale wigeon
presumably yes
vale wigeon
what's the problem
finding when a parametric curve has vertical and horizontal tangents?
waxen pendant
Yes
vale wigeon
are you familiar with thinking of a parametric curve as the trajectory of a particle, with the parameter thought of as time
waxen pendant
yes
waxen pendant
okay so what I know is
that u find the derivative
of the x and y
then set them equal to 0
vale wigeon
so for a horizontal tangent you want dy/dt to be 0 and dx/dt to not be 0
vice versa for vertical
vale wigeon
don't call me bro, please
if they're both 0 the particle comes to a stop, so there may not even be a tangent
jagged imp
dont call me bro
thanks man
waxen pendant
man isnt bro
jovial knoll
hello i have a question if I want to learn linear algebra where do I start?
and if I am learning it to better understand quantum mechanics is there a specific video or book i should take a look at?
vale wigeon
i've heard good things said about the book "linear algebra done wrong"
jovial knoll
preferably a video
vale wigeon
also for quantum you will probably need a good understanding of PDEs and physics in general
there's a video series by 3b1b called Essence of Linear Algebra but it's not a self contained course
vale wigeon
@waxen pendant "dawg" is fine i guess.
waxen pendant
I will just call u ann
its okay
if u dont like nicknames
hey for 23 why is there no vertical tangent
So i took the derivative of cos which is -sin and -sin is 0 at 0
vale wigeon
dy/dθ = -3sin(3θ)
waxen pendant
is it because that is also 0
vale wigeon
that's not the opposite of what i said
vale wigeon
sin(θ)=0 has solutions θ=0 and θ=π
for theta between 0 and 2pi anyway
sin(3θ)=0 has solutions θ=0, π/3, 2π/3, π, 4π/3, 5π/3
jovial knoll
wait so what exactly do I need to learn before learning quantum mechanics?
other than understanding PDEs and physics
is there anything else?
vale wigeon
well... linalg i guess
multivar calculus too but that's a prereq for pde
mb also statistics to some extent
waxen pendant
why dont u try going to community college @jovial knoll
they have a lot of classes for those subjects
vale wigeon
and how do you get the honorable rank?
it's complicated
jovial knoll
ok
jovial knoll
why dont u try going to community college <@!825085776839573504>
yeah ik i should but corona virus is really bad where I live so i cant really leave the house
jovial knoll
there's a video series by 3b1b called Essence of Linear Algebra but it's not a s...
he is really good at explaining
waxen pendant
@vale wigeon would u help me wiht this question please
I found dx as -sint
and dy as cos^2t-sin^2t
but idk what to do from there
vale wigeon
dx**/dt**
waxen pendant
im not concerned with the graphing part
vale wigeon
anyway
waxen pendant
just the finding the tangents
vale wigeon
you should first find at what times the particle goes through (0,0)
and calculate x' and y' at those times
vale wigeon
no!
at t=0 the particle is at (1,0)
you should set x and y themselves to zero.
the position. not the velocity!
waxen pendant
but when Im finding tangents u use x' and y'
vale wigeon
...
look
how are you gonna find the values of dx/dt and dy/dt, and hence the slope of your tangents at (0,0), if you don't know what values of t to plug into them?
waxen pendant
ann go easy on me please im trying my best
vale wigeon
i'm trying to rectify your misconceptions here
waxen pendant
thank you
okay
so
like u said
I found the t values
for when x and y are 0
so x is 0 at pi/2
vale wigeon
you should have ||t = π/2 and t = 3π/2||
waxen pendant
and y is 0 at pi/2 and 0 and pi
vale wigeon
who said t only goes from 0 to pi tho
waxen pendant
yes
vale wigeon
you need x and y to be zero simultaneously
vale wigeon
yes, x=0 implies y=0 in our case.
vale wigeon
yes there we go
vale wigeon
now we know when the particle passes through the origin.
waxen pendant
do dy/dx
vale wigeon
now you need to find dy/dx at those points yes
vale wigeon
i'm... a university student in the final year of my undergrad degree
fading zephyr
10.04.2021 at 10:53 AM is the (or rather, just another) moment in which i, as someone doing an engineering phd, feel supremely compelled to flush my past degrees down the toilet
vale wigeon
?!
waxen pendant
im doing engineering undergrad
fading zephyr
just reveling once more in the knowledge that it took me 7 years to learn less math than any mathematician learns in 1 or 2 years haha
mad props to everyone studying maths
vale wigeon
depending on how you count it could've taken me like... 4 years to get to where i am currently
vale wigeon
don't put yourself down to praise others
fading zephyr
that's a valid point
dusky oar
@vale wigeon I have a question
ocean sealBOT
sullen nova
wtf is that?
vale wigeon
tanh is hyperbolic tangent, if that's what you're asking.
ocean sealBOT
sullen nova
,w dy/dx = 2x(1+y^2)
ocean sealBOT
sullen nova
,w dy/dx = 2x(1+(y)^(2))
ocean sealBOT
vale wigeon
why does the ans looks complicated?
it happens sometimes with ODEs. you're lucky you even have a formula in the first place!
sullen nova
how to solve that
vale wigeon
do you know how to solve separable ODEs?
what you've presented here so far has all been separable.
sullen nova
the latter
sullen nova
what is ODEs
urban hearth
yes
jagged imp
its seperable.
sullen nova
What does that mean?
jagged imp
look up how to solve seperable differential equations
fervent wind
hey guys, there was something I was wondering regarding vectors. So like, I know that cosine similarity measures direction not magnitude. For Mean Squared Error, does it measure direction or magnitude of a vector?
fading zephyr
magnitude
alpine sable
Simplify (a^2) + (a^2) + (a^2) + (b * a)
fading zephyr
it's the magnitude squared of the error
fervent wind
it's the magnitude squared of the error
I was also wondering, have you heard of the Mahalanobis distance?
fading zephyr
i have
fervent wind
so you know the part of about dividing the covariance right?
fading zephyr
mhm
alpine sable
Simplify (a^2) + (a^2) + (a^2) + (b * a)
can someone explain me why this is 3a^2 + b * a and not something like this:
3a^6 + b * a
a^6 + b * a
fading zephyr
shaky, go to an empty channel
fervent wind
so that's what I don't quite understand..why does dividing the covariance take away it's collinearity?
alpine sable
nah I'll just wait
fading zephyr
what do you mean by collinearity, for starters?
fervent wind
the correlation I mean haha
fervent wind
because apparently that's what Mahalanobis distance takes away right
yeh more correlation haha
fading zephyr
it decorrelates the data
think of it this way
normally, there is no reason for the columns of a matrix to be orthonormal
so the pairwise dot product of columns will not be 0, and the dot product of a column with itself will not be 1
this means the correlation matrix is not an identity matrix
fervent wind
ok?
fading zephyr
some variables will be weighted more heavily than others because of this
since the eigenvalues of the covariance matrix (the 0-centered correlation matrix) will not be 1
some variables are weighted more heavily than others
and this depends on how large the correlation between columns is
if you put the inverse covariance matrix in between two vectors you're taking the dot product of, this will normalize the weights of the variables
they will now correspond to orthonormal eigenvectors, with eigenvalues of 1
so now all the variables have the same importance
this is also known as a "whitening operation"
or a whitening filter, or preconditioning
it's the same as doing a change of basis, too
to a basis that does not preferentially enlarge some dimensions
worldly crane
waht is the derivative of e=mc^2?
fervent wind
oh ok I kinda understand now, basically the inverse covariance matrix normalizes the correlated weights which will then correspond to orthonormal eigenvectors resulting in 1.
So is minusing one matrix from the other same as taking the dot product? Because I remember in the formula it used minus instead of dot product. However I do remember that Cosine similarity uses dot product instead, so wonder what the difference is between minus and dot product.
fading zephyr
none, off the top of my head
i doubt it uses a subtraction instead of a dot product
fervent wind
this is the formula..
[(xB – xA)T * C -1 * (xB – xA)]0.5
but yeh I understand better now tq
fading zephyr
the dot product is still there
fervent wind
where?
fading zephyr
(xB - xA)^T (xB - xA) is the same as the dot product of xB - xA with itself
C is a symmetric matrix, so it can be factored into some D^T D, and so can its inverse
so you can rewrite this as the 2-norm squared of some D (xA - xB)
which is its dot product with itself
D is a "whitening matrix"
a "square root factor" of the inverse covariance
so you're taking the difference between xA and xB
then you change it into a basis in which the variables all have the same weight, i.e. you decorrelate them
and you consider the length of that decorrelated error
you can also see that if the variables are already decorrelated, the covariance C is an identity, and so is its inverse, and so are its factors D and D^T
so the mahalanobis distance becomes equivalent to the MSE
which is a dot product
so the mahalanobis dist. is also a dot product
or a quadratic form or conjugate product
same thing
fervent wind
ok I can see clearer now, but I don't fully understand the D part, like how is the covariance related to D? i.e. the 2nd and 3rd lines
fading zephyr
say C is the covariance, and it's symmetric and invertible
then it can be factored into some E^T E, with E invertible
fervent wind
oh so like split
fading zephyr
C^-1 is also symmetric, and then it can also be factored into D^T D
then D (xA - xB) is some vector w
and the mahalanobis distance becomes w^T w
which is a dot product
fervent wind
oh ok I understand now. thank you very much.
I won't like block the queue anymore haha. Shaky or anyone else you guys can ask your questions.
fading zephyr
aight, GG
autumn lantern
i don't understand what "sum of decimal digits" mean
jagged imp
as in like, the sum of the decimal digits of 12345678910 is 1+2+3+4+5+6+7+8+9+1+0
autumn lantern
ohhhh thanks! sorry i might have been just overthinking it hahaha so i should probably use modulo arithmetic to find the prime number greater than +k right?
pale cargo
@vale wigeon if you would be so kind
vale wigeon
bruh
pale cargo
^^
jagged imp
ohhhh thanks! sorry i might have been just overthinking it hahaha so i should pr...
yeah idk sorry. I don't see what mod arithmetic could have to do with it but i am a known dumbfuck.
autumn lantern
yeah idk sorry. I don't see what mod arithmetic could have to do with it but i a...
it's okay! you've helped out a lot already!! though, do you have a diff way to show that the statement holds even if it doesn't use mod arithmetic?
jagged imp
nope
autumn lantern
thanks tho!!
ocean sealBOT
pale cargo
sullen nova
spring harbor
How can you calculate the integral of $\sqrt{\left|4x\right|}$
ocean sealBOT
Echo
alpine sable
:( i asked a question
alpine sable
Can i express a point like (2/3) as f(2)=3
.
spring harbor
Can i express a point like (2/3) as f(2)=3
(x,y), the 2 is x and 3 is y
spring harbor
Yeah
alpine sable
great thanks
spring harbor
How can you calculate the integral of $\sqrt{\left|4x\right|}$
ocean sealBOT
Echo
spring harbor
hwo to solve this
use u=1+x substitution and split the fraction in two parts
alpine sable
all the modulus is doing is extending the domain
what's that star role you got
Edit: k I just realised I have one
spring harbor
all the modulus is doing is extending the domain
Not sure what modulus is
gritty aspen
what's that star role you got
Edit: k I just realised I have one
lmfao
gritty aspen
Not sure what modulus is
the absolute value
wai
graphing the fn makes it clearer
lemme send u wha i mean
spring harbor
I graphed it
I need to calculate the area between y=4 and that function
I got integral from -4 to 4
but I need to integrate it now
obsidian crane
Replace modulus with square and square root
I don't have a paper nearby to solve it
gritty aspen
Replace modulus with square and square root
how would that change anything except the domain again tho?
obsidian crane
That's the only way to deal with the modulus (to remove it)
It won't change the domain ofc
And changing the domain is not our goal either
obsidian crane
The new square root is combined with the older square root
Sec
Well it's frustrating I don't have a paper
Just try it
spring harbor
I get that it's equal to 2* (2x^(3/2)/3)
But if I use -4 in it I get the sqrt of a negative number
So I must be doing something wrong
obsidian crane
Do you have any hint what's the correct answer ?
I tried it in my head (might be wrong) it can be 4/3 * x^3/2
gritty aspen
mhm see what i was saying is, to approach it graphtically
wait
area between
y = 4
gritty aspen
what do u mean given integral?
gritty aspen
wait can u send a snip of what the q exactly says
spring harbor
It's in dutch.
spring harbor
What is the area of the area above the graph of the function f with f (x) = (see above) and below the horizontal line with equation y = 4?
gritty aspen
Ohhhh
gritty aspen
Yepppp
gritty aspen
nppp
gritty aspen
what was your integral fn
spring harbor
2*(I(2sqrtx)) = 2 * 2 * [2/3 * x^(3/2)]
from 4 to 0
$$4\left(\frac{2x^{\frac{3}{2}}}{3}\right)$$
gritty aspen
2*(I(2sqrtx)) = 2 * 2 * [2/3 * x^(3/2)]
how did u get this?
ocean sealBOT
Echo
quick surge
gritty aspen
@quick surge channel is busy
gritty aspen
Did I do it wrong ;-;
see jus
quick surge
i need to find the value a and b, i know how to find a but i dont know how to find b, oh sorry
spring harbor
thats what i did..
gritty aspen
hm then
integrating root(x) gives
(1/1.5)*x^1.5 right?
mutliply that w root 4
and ull get
(2/1.5)*x^1.5
spring harbor
Well wait
I think I did it right
but we just have to do it from 0 -> 4
and not -4 -> 4
spring harbor
because 32/3 is an option, which is half of what I got
spring harbor
no I didn't
I did 2
but like I said
I multiplied it by 2 since there are two sides
nevermind I got the answer somehow right but they did this:
gritty aspen
nevermind I got the answer somehow right but they did this:
oh
spring harbor
but yeah they are both correct I believe
gritty aspen
Ohhhh
wai no
lmfao we jus integrated
2*root(x)
we frgt the subtract the functions first
and then integrate
gritty aspen
nevermind I got the answer somehow right but they did this:
yep this is correct
spring harbor
Do you have to do that?
gritty aspen
Yess
spring harbor
For every function?
gritty aspen
because
otherwise
they represent diff areas
nono see
they want the area in between
y = 4
and
y = root(4x)
so we need to do
integ( 4 - root(4x))
gritty aspen
For every function?
for calculating the area between any two functions, we need to do this yes
spring harbor
But let's say I need to calculate the area between x^2 and y=5, I thought we first calculate the intersections between the two lines, set those as the boundaries and integrate x^2
so we get integral of x^2 from -sqrt5 -> sqrt5 in this example
spring harbor
Fill in x=6 in the original equation and check yourself
alpine sable
wait would it still be correct if i did the other way first
spring harbor
you multiplied everything by 3
that's also fine
but you can't say 2x/3 + 1 = 5 <=> 2x + 1 = 15
spring harbor
You multiplied both sides by 3
Some people tend to multiply only one side by 3 and leave some values out
which gets them the wrong result
alpine sable
0iq
ocean sealBOT
sullen nova
how
come
<@&286206848099549185>
ya
why C is not negative
My calculation says it's suppose to be negative
-1/y = x+c
=> y = 1/(-x-c)
C is negative
vale wigeon
"negative" does not mean "has a minus sign in front"
also, C is an arbitrary constant. it can absorb nonzero multipliers.
you could write $\int 2x \dd{x} = x^2 - C$ just as easily as $\int 2x \dd{x} = x^2 + C$, with absolutely no issue.
ocean sealBOT
Ann
sullen nova
they give x=3 and y=-1 to find C
sullen nova
it doesn't matter
sullen nova
yes
vale wigeon
are you asked for C itself, directly?
or are you asked to solve the initial value problem?
vale wigeon
answer my question
sullen nova
I'll send you the problem
sullen nova
I did but it's not 100% full
vale wigeon
send the problem.
vale wigeon
see ok
youre not asked for C
the C stays in your own internal calculations
it doesnt form part of the answer
not directly anyway
sullen nova
so what's the general solution
vale wigeon
if you wish i can present to you a solution the IVP with your form and with WA's form just to demonstrate that you get the same thing in both cases
sullen nova
in order to find the general solution, you will have to find C
sullen nova
why it can be both negative and positive
pine lake
Helu
severe latch
Hello guys, can anyone help in discrete math?
noble sinew
1st: 5 * pens= 3 * pencils
2nd: pens+pencils=notebooks
3rd: Technically doesn't say he wants to spend all his money, so the actual 3rd equation would be 5 * pens + 3 * pencils + 9 * notebooks <= 102, however it only have 1 positive integer solution
pine lake
sullen nova
Before I started to learn calculus, I can describe the world as algebra but after learning calculus, I just can't see the world in calculus like I do with algebra.
spring harbor
Calculus is used more in real life situations but we just don't notice it as much
sullen nova
just can't see it
round nova
you'll see when you do more advanced physics
gritty aspen
#help-1 message
Literally the exact same as what i said here, but alright if you needed an extra hour to write it down.
round nova
you use it everywhere
gritty aspen
Not only physics but chemistry and biology as well
And econ and finance
pine lake
https://discord.com/channels/268882317391429632/269573202018041856/8303966122651...
Bruh i did other questions
Because u said u were not sure
sullen nova
how do you even use those derivative or integral or differential in real world
gritty aspen
Because u said u were not sure
click the link i posted and see whether i actually said that lmao, because i didn't, i literally said the answer. But lmfao it is chill, i was just pointing that out.
spring harbor
how do you even use those derivative or integral or differential in real world
Acceleration/speed/time relationship for example
limpid spade
Jigger, your name is very close to a ban.
ionic sedge
with ti-83 plus CE-t is there a way to quickly scrol to a certain n in the table with sequence mode?!
stark terrace
how do i do a
pine lake
click the link i posted and see whether i actually said that lmao, because i did...
Bruh
I found the ans without inequality
stark terrace
<@&286206848099549185>
gray gorge
At most two means: either zero, one, or two
Calculate those cases separately and add them up
gritty aspen
I found the ans without inequality
mhm yes, i told u technically it shld be an inequality based on the wording of the q
i never said u had to treat it like an inequality to get the answer
the q also said a system of equations
so
yeah jus having three eqs shldve been enough
rapid nova
Prove that
$$
\sum_{k = 0}^n \binom{n}{k} \frac{(-1)^k}{2k + 1} = \frac{(2n)!!}{(2n+1)!!}
$$
ocean sealBOT
rept1d
alpine sable
,w prove \sum_{k = 0}^n \binom{n}{k} \frac{(-1)^k}{2k + 1} = \frac{(2n)!!}{(2n+1)!!}
ocean sealBOT
alpine sable
proof by wolfram
alpine sable
Prove that
$$
\sum_{k = 0}^n \binom{n}{k} \frac{(-1)^k}{2k + 1} = \frac{(2n)!!}{...
first thing that comes to mind is using induction, ill work it out and let you know if i get anywhere with it
rapid nova
Ok
alpine sable
its 50% right?
since if you take one gold ball that means there are only 2 options left
please ask your question in an unoccupied channel
its unoccupied
no, the other guy is still waiting for an answer to his question
oh
rapid nova
@alpine sable https://en.wikipedia.org/wiki/Bertrand's_box_paradox
alpine sable
thx
maiden dagger
alpine sable
What's your question?
maiden dagger
a and b
alpine sable
What did you try
alpine sable
Do you know what Col B means?
alpine sable
Do you have notes?
alpine sable
to see what you know?
alpine sable
do you know matrix multiplication?
alpine sable
by what kind of column matrices can you multiply that matrix on the right?
maiden dagger
3*1
right?
im confused
as long as it isnts the numbers in A
It should be fine right?
I just need to go backwards
alpine sable
matrix multiplication is not commutative
alpine sable
thing is, matrices can be viewed as linear maps, but i don't know if you're familiar with that
alpine sable
if you multiply a (properly sized) column on the right of that matrix, what do you get
alpine sable
do you always get 0 0 0?
maiden dagger
no
alpine sable
the set of possible values you get
is called the column space of the matrix B
and represented as Col B
is your pfp kali linux logo lol
alpine sable
aight, so what they're asking is for vectors (3x1 column matrices in this case) of the form BX for some 3x1 column X that are not columns of the matrix B
alpine sable
thank you too
quartz ermine
I'm having a lot of trouble figured out how to graph this, I feel like it should be trivial though. On Desmos, given an origin and a an angle, a, graph a ray starting at the origin point and traveling only in the direction of that angle, not backward
I can easily accomplish this at (0,0) with two lines, limiting the first to all positive x and the second to all negative x, but I'd like to use just one line
vale wigeon
on desmos? so you're allowed to use parametric equations?
quartz ermine
Yea
vale wigeon
$(x_0 + t\cos(a), y_0 + t \sin(a))$ for $0 \leq t \leq \mbox{[large number]}$
ocean sealBOT
Ann
quartz ermine
Could you also help me with the non-parametric version? One using y=mx+b with a domain condition?
alpine sable
i don't understandwhy you need two lines if you can restrict the domain
quartz ermine
I can't really think of a domain restriction that would limit the line to only the direction of the angle, if that makes sense
I know one exists, and that's what I'm asking for help with
vale wigeon
you can restrict the domain but the restriction might have to depend on the value of a in a way that's hard to put into desmos.
quartz ermine
Haha that's exactly what I was afraid of
turbid sleet
How would you go about solving probability problems, for example: A farm has 7 horses and 9 cows. What is the probability of picking at least 3 horses out of a group of 5 animals?
I understand it's a combination problem because the order doesn't matter
but I get confused on what choose what * what choose what...etc.
would it look something like this?
[ (7 3)(9 2) + (7 4)(9 1) + (7 5)(9 0) ] / (16 5)
cursive flax
can someone explain to me how to solve these kind of questions
eg: This year 40 more children joined a football league than joined last year.children in this year’s league is 110% of the number in last year’s league.
manic quail
$c+40=c \cdot \frac{110}{100}$
ocean sealBOT
veryhappyperson
cursive flax
.
manic quail
c are the children from the previous year
Do you understand the equation?
the fraction just means 110%
cursive flax
i understand everything except the Cdot
manic quail
that means multiplication
cursive flax
oh
manic quail
Are you American? I have the feeling like that most Americans use the "x" as multiplication instead xD
cursive flax
no im bhutanese;-;
manic quail
Ahh okay. Do you also use the "x" as multiplication?
cursive flax
yes.
velvet pelican
@turbid sleet I think your answer is correct (you can look at the hypergeometric distribution as a more general case)
junior wadi
which exponent rule has been applied here?
manic quail
take $log_3(...)$ on both sides
ocean sealBOT
veryhappyperson
tired creek
$\frac{1}{3}=3^{-1}$ and $9=3^2$
ocean sealBOT
the one n only
junior wadi
thank you, the only problem is I don't know how that works
I am terrible and logs haha
manic quail
Log is a great function, and because it is so great, you can put both sides of an equation in there and it is still fine.
$\log_3{9^{3x-6}}=\log_3{(\frac{1}{3})^y}$
ocean sealBOT
veryhappyperson
junior wadi
I know how they are usually used to remove a power, but I've only just started learning about them
manic quail
And because logarithms are so incredibly great, you may also pull out the exponent: $(3x-6)\log_3{9}=y\log_3{\frac{1}{3}}$
ocean sealBOT
veryhappyperson
tired creek
dont think u need logs for this
junior wadi
I see
tired creek
by exponent laws they meant equating the powers
junior wadi
Bruh, I am dumb, sorry <@!630381088404930560>
Not as much as me :)
manic quail
You can just bring them to the same base.
junior wadi
This is way too confusing for me, I not going to lie, I have no idea how to do that
I really am a lost cause
alpine sable
I dont understand why one would use ln(100)? and is it a poisson process becaues of the avereaged probability?
manic quail
@junior wadi have you solved it yet?
alpine sable
sorry i thought the room was free cuz there wer enothing for 20 mins
manic quail
No worries, might be free after all, it all depends on whether JawGBoi has already resigned xD
@alpine sable what don't you get? They just wanted to isolate $\mu$, hence they used the log.
ocean sealBOT
veryhappyperson
alpine sable
<@456226577798135808> what don't you get? They just wanted to isolate $\mu$, hen...
I really dont understand much of what is going on tbh
I dont understand how the average can be 4.6 raisins in one cookie to have 99% average that there is at least 1 raisin
why not 1 raisin in every cookie?
manic quail
Sorry, I hate statistics and probability and I am terrible at it xD I thought you were just confused about the log.
rich heath
Express each of the following statements in algebraic form
Z decreased by 3x is equal to y
alpine sable
Sorry, I hate statistics and probability and I am terrible at it xD I thought yo...
no need for the sorry, im the one who is sorry for bothering you. thanks for your help and yeah probability sucks
alpine sable
Express each of the following statements in algebraic form
Z decreased by 3x is...
sorry room is busy
What does any of this stuff mean?
rich heath
sorry room is busy
Okay np!
alpine sable
What does any of this stuff mean?
Which?
All of it.
I don't understand a single thing.
Well, some of it I do.
Just lots to see.
thats why im asking i dont understand either
rapid nova
first thing that comes to mind is using induction, ill work it out and let you k...
Hey, have you succeed?
alpine sable
<@&286206848099549185>
alpine sable
I dont understand why one would use ln(100)? and is it a poisson process becaue...
Yes. it's the probability distribution of poisson process (i.e. an exponential distribution ) since the question assumes an average rate. The rate equals the number of raisins per cookie, which we assume is unchanging. The question is then is to determine this very rate given the information P(X>=1) >= 0.99 . We simply replace the LHS by 1 minus the cumulative distribution function of the exponential distrbution.
P(X>=1) = 1 - P(X<1) = 1-CDF(1) = 1- (1-exp(1*rate))
yes but why is 4.6 raisins need in every cookie to be make sure that there on average is at least on 1 raisin in every cookie?
and thank you!
alpine sable
yes but why is 4.6 raisins need in every cookie to be make sure that there on a...
well i am not sure why you say "on average" here. The question is for a cookie containing at least 1 raisin with a very high probability (99%) !
We need as much as 4.6 raisins to "ensure" this high probabilty
Yes correct, my bad, but still why is the answer 5 raisins? Why not 1 raisin in every cookie? its seems... not logical for me at least.
if you have 1 raisin in every cookie then you also have a 100% probability?
alpine sable
Yes correct, my bad, but still why is the answer 5 raisins? Why not 1 raisin in ...
well the actual number of raisins per cookie is not supposed constant, it's the average rate that is constant. And because of that the best value that gives results closer to this rate is 4.6, as our calculations show. If we had instead 1 raisin as you suggest, then the actual number of raisins per cookie will vary widely around this value, and can be thus close to 0 (no raisin in a cookie)
MAKES SENSE!!! THANK YOU SO MUCH 🙏 🙏
alpine sable
if you have 1 raisin in every cookie then you also have a 100% probability?
Always keep in mind the diffrence between actual values of X and the parameters of the distribution of X like the average rate of raisins per cookie in our case
alpine sable
MAKES SENSE!!! THANK YOU SO MUCH 🙏 🙏
You're welcome. I'm glad!
alpine sable
You're welcome. I'm glad!
I really appericate it and thanks again for your very nice explaniation and tips. I will write it down now!
Youre welcome buddy
rich basin
Say you are a bakery and you have dough with raisins in it. That dough is baked into cookies, and no matter how much raisins you put in the dough, there is always a risk of some cookies coming out having no raisins in them.
thorn kindle
ok.
alpine sable
Say you are a bakery and you have dough with raisins in it. That dough is baked ...
good analogy! thanks !
hearty orbit
Does anyone know if I have to set my calculator on rad or deg for calculating the roots if D < 0?
alpine sable
Does anyone know if I have to set my calculator on rad or deg for calculating th...
both settings yield correct results. The formula is independent of the unit of angular measure
vale wigeon
@hearty orbit if you aren't doing trig, deg vs rad doesn't matter.
hearty orbit
So in this case it doesn't matter? @vale wigeon
vale wigeon
i mean ok let's put it this way
the only thing that's actually happening to angles is division by 3
which it doesn't matter if they're in radians or degrees
jade belfry
I have the SAT coming up on tuesday, are there any math formulas outside of area formulas, pythag theorem, and quadratic equation that I should know for the SAT?
alpine sable
hi since no ones is using this I'll ask
Can someone help me with equations
explain the whole thing
And constructing of fomulae
hearty orbit
which it doesn't matter if they're in radians or degrees
@vale wigeon In the picture I send you can see the part 3 * sqrt(3) * q, but is it 3 * sqrt(3) * q or 3 * sqrt(3 * q). Its located in the formule to calculate the 3 roots if D <0