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#help-0
vernal ether
hi hi, a part of getting started on my project is to create an equation from a graph about an environmental issue. I can't figure it out though
vernal ether
here's the graph i'm supposed to work on
i can hover over the line and view the points specifically, but inputting them and trying to make an equation just isn't working
vernal ether
yep
vernal ether
the few lessons before were all about logarithmic, so i thought that might be it?
plain flame
,w graph ln(x)
ocean sealBOT
vernal ether
uhh
plain flame
what is the ratio between 1970 and 1980?
and what is the ratio between 1990 and 2000?
vernal ether
like, the points ?
plain flame
the ratio between the waste in 1980 and 1970
vernal ether
(1970 , 249 mil) and (1980 , 798 mil) ?
ocean sealBOT
Result:
3.2048192771084
hmm
i hoped the ratio would stay constant
that does kind of change it
well anyways, a function that keeps increasing more
what types of that do you know
vernal ether
exponential ?
plain flame
yes thats possible
but exponential curves have a constant ratio between them]
so if its 3.2 between 1970 and 1980 aand its 1.95 between 1990 and 2000 then it cant quite be exponential
so do you know any other lines that curve upwards
vernal ether
well quadratic but it cant be that
plain flame
why not
vernal ether
the steps to this project are super broad, hold on a moment
do you think even an "average" of the rate of growth would be allowed ?
it's asking basically to predict outcomes
plain flame
yeah it should be exponential
but the rate of growth should be constant
could you check some more ratios
vernal ether
yea im stumped
i think ill write an equation that basically predicts an outcome, not pinpoints it down to the decimal
because i really just need an idea of where this function will go if it continues
vernal ether
alright thank you
vernal ether
aaggghhhh
vernal ether
closer
plain flame
one second i will do multiple linear regression
lone heartBOT
@vernal ether Has your question been resolved?
lone heartBOT
@vernal ether Has your question been resolved?
vernal ether
<@&286206848099549185>
noble turtle
hi this is the first time posting
lone heartBOT
hi this is the first time posting
noble turtle
so i want to have three points
let's say you have point m and n
each of them has x and y coords
but i want to know what is the point in the line between them that has the same x coordinates as point u
it is not an equation to just plug in the x axis
its just two points and im connecting them
this will be used in a code
whoops i missread it
im sorry i thought im supposed to ping
remote heron
let's say you have point m and n
each of them has x and y coords
but i want to k...
midpoint formula, probably
tacit arch
let's say you have point m and n
each of them has x and y coords
but i want to k...
do you know the x, y coordinates of u?
noble turtle
yes
noble turtle
midpoint formula, probably
well its not middle
tacit arch
you can construct the equation of the line connecting m and n and just plug the x coordinate of u into the line
tacit arch
can you tell us all the information
noble turtle
i am trying to render a cube
so the points of the cube are moving around alot
point m and n are just vertecies
i want to intercept them with the x coordinates of u
im sorry if this is vague but its such a weird problem never had to think about lol
remote heron
i want to intercept them with the x coordinates of u
well if its not the middle then youd have to be more clear about where you want it to be
tacit arch
i am trying to render a cube
cubes live in 3 dimensions
remote heron
finding the point in the middle of 2 points in 2d or 3d space is pretty straightforward
remote heron
what makes u position where it is
remote heron
im not sure i follow
noble turtle
one second let me try to draw it
remote heron
theres a thing called uh
perspective projection
but it may be overkill for what you need to know
remote heron
hmm
id have to think its some kind of projection but im not sure, sorry
maybe i should have let @tacit arch take it 
noble turtle
lol its ok ive been scratching my head at this for quite a bit
tacit arch
the problem isn't even well formulated yet
noble turtle
lol my bad
i have very little to explain its a weird problem
ok actually here is another question i am not sure if this would make it better
what if you had four points
m and n
u and v
m is connected to n
and u is connected to v
is there a way to see where they intercept
considering that there is no set equation for the lines since they move constantly
lone heartBOT
@noble turtle Has your question been resolved?
fallow wadi
lone heartBOT
fallow wadi
Without lhopital
vale wigeon
taylor
fallow wadi
I am actually insanely smart
vale wigeon
fallow wadi
No taylor isnt allowed
vale wigeon
vale wigeon
-1+1
waxen flame
Split it into two limits? 🤔
keen plinth
fallow wadi
Wont help, you gotta do it by +-1
ocean sealBOT
desert tendon
Ah yes the first thing that comes to sight
keen plinth
,w expand (1 + 5x)^3 - (x + 1)^2
keen plinth
now just evaluate at x=0
long axle
What did u even do, what is that
ocean sealBOT
keen plinth
theres probably a more efficient way but 
long axle
Wow
ocean sealBOT
riemann
ruby current
theres probably a more efficient way but <:catshrug:563818735085944843>
wow how did you know that the numerator would have an x term, so the x on the bottom would cancel, and that the resulting limit wouldn't be 0/0?
keen plinth
taylor
modern topaz
lone heartBOT
@fallow wadi Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
zenith tide
I'm struggling for some reason with this question (this isn't homework btw, it's self-study). It seems to me that the "vision" of the ant is given at any point on the curve by the equation y - y_0 = -2(x- x_0). Plugging in the values we have for the top of the cell phone tower, we get y - 1100 = -2x. Solving for y, we get x=-550. Plugging that into the original equation to get the height, I get y= -301500 which is weird because the ants starts climbing at y=0. What have I done wrong?
lone heartBOT
zenith tide
.reopen
lone heartBOT
✅
zenith tide
nvm I have no idea what to do
high rapids
Best to draw the scenario.
My instinct is this has something to do with angle of elevation.
zenith tide
I have it drawn out in my notebook, and I've translated this problem into "At which x does the tangent to f(x) intersect (0, 1100)
I have one point and a gradient (-2x) so I should be able to figure out the equation of the line but for some reason im really struggling with it
y - y_0 = m(x-x_0) Is the general equation for a line
plugging in the points I know
I get y - 1100 = -2(x-0)
But that leads nowhere
lone heartBOT
@zenith tide Has your question been resolved?
lone heartBOT
@zenith tide Has your question been resolved?
gusty gorge
I have it drawn out in my notebook, and I've translated this problem into "At wh...
this is correct
gusty gorge
I have one point and a gradient (-2x) so I should be able to figure out the equa...
you're getting your xs mixed up
Let's say that x' is the desired point, where you can just see the top of the cell phone tower.
If you're standing at x', what is y', your elevation?
(in terms of x')
leaden crater
I need help with what set is a feasible solution or not.
lone heartBOT
I need help with what set is a feasible solution or not.
lone heartBOT
@leaden crater Has your question been resolved?
tribal haven
this might depend on the OR course but step 1 is rearranging the columns of A such that you can form a partition A=[N|B] where N is your non-basic variables, and B is a square matrix containing your basic variables
leaden crater
Thank you so much. i just figured it out after staring at it for an hour
I appreciate the response
lone heartBOT
@leaden crater Has your question been resolved?
viral crater
lone heartBOT
pseudo ice
Try being negative 
viral crater
doesn't it have to work for all numbers positive and negative?
so if i lets say set n as 2 then if m is 1 that's false right
or is that not how I am supposed to do it
pseudo ice
...there exists an integer n, such that for all integers m, n<m^2
You don't need all possible choices of n to be like that, just at least one
viral crater
so if i satisfy just 1 n that satisfies the entire statement?
pseudo ice
Picking n to be a[ny] strictly negative number should do it
strange meadow
it works
pseudo ice
so if i satisfy just 1 n that satisfies the entire statement?
Yep 
strange meadow
statement is true 😉
viral crater
.close
steady basin
When converting an equation from polar form to Cartesian , is ur aim to always get rid of all the rs, cos thetas and sin thetas?
steady basin
And just get it in x and y?
tacit arch
Yes. That is the definition of Cartesian
last onyx
how do i solve this primitive throguh parts
lone heartBOT
how do i solve this primitive throguh parts
tribal haven
state the integration by parts formula
pliant oak
Substitution then integral by parts
last onyx
the problem is we can only use parts
wary stream
like the formula it self
Pretty sure that's what IV wants
last onyx
i said integral when i really wanted to say primitive sorry
pliant oak
You can also directly do IBP
Let u=ln(x²+1)
wary stream
i said integral when i really wanted to say primitive sorry
Wtf is "primitive through parts"?
Are you trying to do $\int xln(x^2 +1)$?
ocean sealBOT
dldh06
last onyx
yes
wary stream
That's still an integral
last onyx
well we call them primitives in my language so sorry for the confusion
wary stream
You can also directly do IBP
Let u=ln(x²+1)
Also this u sub doesn't really help much
wary stream
You can u sub to make it easier then do integral by parts
wary stream
You can still u sub to make it easier
devout hollow
profs really like to handicap their students 💀
last onyx
least sadistic uni prof
tribal haven
im just telling you state the integration by parts formula
wary stream
I'm pretty sure that no where in the instructions states that you can't use u sub to make life easier
tribal haven
an usub makes your life slightly easier but it's not necessary
last onyx
the question it self is more above but its in another language
so how would do this with sub then?
burnt imp
u=x^2 +1?
wary stream
There's too many people now, I'm leaving. And @pliant oak Are you typing like an essay? Or trying to give the full solution because you shouldn't do that
pliant oak
u=ln(x²+1),dv=xdx
You just take v as the function of x²+1
Then you can directly do the integral by IBP
tribal haven
it's been 20 minutes and i just wanted the guy to give the integration by parts formula and it's not been given
it's important to drill the formula into your head so when you have something to ibp you can immediately recall the formula and identify the correct substitution
last onyx
thx
pliant oak
Abbreviation of Integral by parts
last onyx
<:thinkies:827642567775748163>it's been 20 minutes and i just wanted the guy to ...
i know the formula
what i dont know is how to solve this particular itegral
tribal haven
well i wouldn't know, if you know the formula and can identify a substitution then you won't be needing help
so either you struggle with the formula or identifying the correct u/v, gotta cover both grounds
last onyx
so after the sub you should stay with just ln(x²+1) right?
tribal haven
it doesn't matter if you do the u-sub, you'll get the same answer, but you might find it slightly easier with the u-sub
pliant oak
u=ln(x²+1),dv=xdx
You just take v as the function of x²+1
Then you can directly...
∫udv=uv-∫vdu
Take the value of v as the function of (x²+1) to cancel the denominator then you can directly do ∫vdu
wary stream
∫udv=uv-∫vdu
Take the value of v as the function of (x²+1) to cancel the denomi...
First you said u = ln(x^2 + 1) then v to be x^2 + 1?
last onyx
this is the answer
pliant oak
First you said u = ln(x^2 + 1) then v to be x^2 + 1?
No v≠x²+1 because d(x²+1)=2xdx≠xdx=dv
last onyx
I got $xln(x^2 +1)-2x+2arctan(x)+C$
ocean sealBOT
Sir
wary stream
I got $xln(x^2 +1)-2x+2arctan(x)+C$
First post your work
last onyx
pliant oak
I mean dv=xdx
Then Integral two sides to get v
This step is indeterminate Integral
So you can choose certain constant C to make v as the function of x²+1
last onyx
@wary stream
pliant oak
IBP:∫udv=uv-∫vdu
I take u=ln(x²+1),dv=xdx
So ∫xln(x²+1)dx=∫udv
Then apply IBP
If what the problem required is "only" using IBP,take the value of v as the function of (x²+1)
Otherwise,using substitution then IBP is easier to understand
last onyx
can you elaborate if you dont mind
pliant oak
In IBP
We first choose u and dv
I have chosen the right u and dv for you
You just find du and v precisely
last onyx
but here u cant be either one can it?
pliant oak
What do you mean?
u=x? It doesn’t work,too
last onyx
i mean i can use it but at least from what i know, i wont get very far and will just complicate it no?
oh nvm it works
i got it
thx giys
.close
lone heartBOT
lone heartBOT
Available help channel!
stone solstice
Hey
stone solstice
Would ab=-ba be equal vectors
Or opposite vectore
My teacher said opposite
But wouldnmt they also be equal?
tacit arch
Would ab=-ba be equal vectors
What are a and b
placid zinc
AB (the vector starting at point A and ending at point B)
And -BA (the vector ending at point B and starting at point A)
are the same vector
naive valley
the vector from a to b and the vector from b to a are opposites
if you put a - sign on one of them then they're the same vector, not opposite
placid zinc
The - is doing a lot of work here
burnt imp
better picture?
naive valley
it wouldn't be the first time an answer key was wrong, alas
stone solstice
So would the andwer be “ab and ba are opposite vectors”
naive valley
yep that's one valid pair
spare rune
lone heartBOT
spare rune
help
tacit arch
do you know how to plug in n/4 into 4n-1 ?
lone heartBOT
@spare rune Has your question been resolved?
lunar phoenix
lone heartBOT
lunar phoenix
I get the answer C for this question, but on brainly it says the answer is D
im confused on how its not C, can someone explain?
abstract fractal
im confused on how its not C, can someone explain?
I would say it's because D is completely random, minimizing the chance of any interference. In addition, it specifies to do each combo multiple times, while C doesn't specify that
lunar phoenix
but i thought that through randomization there could be repeats
which would jeopardize the experiment, no?
so there has to be a way to ensure that every combination happens
or is my logic wrong
idk
abstract fractal
I'm interpreting it, not as "select a random combo each time," rather "go through the combos in a random order."
lunar phoenix
oh ok
so you mean that its best to randomize order of which the weights and gas are
so if it were chronological its not good
is that what youre saying?
lone heartBOT
@lunar phoenix Has your question been resolved?
Available help channel!
Available help channel!
next bridge
lone heartBOT
next bridge
lowkey confused aff
raven haven
on how to multiply those?
next bridge
on how to multiply those?
It’s simplifying and multiplying i thhink
next bridge
naw
last ether
Well you have to follow exponent laws
You do multiply the numerators together and denominators together, yes
next bridge
Well you have to follow exponent laws
ya im stuck on that. it gets confuding
last ether
$$a^b \cdot a^c = a^{b+c}$$
$$\frac{a^b}{a^c} = a^{b-c}$$
ocean sealBOT
Umbraleviathan
next bridge
one sec
raven haven
was gonna add the divide one, thanks.
last ether
Sure
last ether
Well yeah. You need still need to to multiply the rest of the factors
next bridge
Well yeah. You need still need to to multiply the rest of the factors
like the exponents?
ocean sealBOT
Umbraleviathan
last ether
You still have to simplify that
next bridge
You still have to simplify that
an i add the exponenets?
last ether
Yeah, for factors whose bases are the same
next bridge
Do the same for the denominator
i got 42wy^-4
last ether
$\frac{84w^6y^{-1}}{42wy^4}$
ocean sealBOT
Umbraleviathan
last ether
Simplify this
next bridge
**Umbraleviathan**
i got 2w5y3
it was THAT easy?? wtf
@last ether
why my mom and teachers make it so complicated
tacit arch
Teaching math is hard
last ether
Yeah ... helping my classmates is also hard
Try explaining that you don't add all 4 numbers to do determinants
But then they end up doing division instead of some stupid shit
tacit arch
Yeah ... helping my classmates is also hard
But easiest $20
last ether
LOL that was fuckijg hilarious
"<0,2> is a zero vector" and a bad mind is one way to lose 20
lone heartBOT
@next bridge Has your question been resolved?
dense plover
try simplifying the two fractions by themselves first then multiplying
keen plinth
bad maths keeping umbral up at night
steel sapphire
Yo im doing test corrections rn and one of the questions I think I’m doing incorrectly. The question gives me f f’ and f’’ and is asking for the critical values. I left it black because I was on a time crunch and didn’t know what a critical value was.
tribal oxide
Yo im doing test corrections rn and one of the questions I think I’m doing incor...
critical value are all the points in the domain of the original function where the derivative is 0 or does not exist, but it cant be an endpoint
steel sapphire
So a critical point?
tribal oxide
Wait does critical value mean something other than a critical point?
If it does then idk😎
steel sapphire
That’s what I’m trying to figure out
steel sapphire
Earlier it said find the critical points so I did
steel sapphire
Now it says critical value and I’m confused
I don’t believe we ever went over a “critical value” just a critical point
Or I was just absent lol
tribal oxide
Now it says critical value and I’m confused
Maybe they want the value of the function for the x coordinate?
raven haven
I'm going to guess that
a critical value is an x such that
f(x) = y
where (x, y) gives the critical point
steel sapphire
So would I be correct or
steel sapphire
I have no idea
raven haven
could you pull it up?
steel sapphire
I’ve only ever seen critical value on the test
I only see references to critical points
No critical values
I asked during math help and they just said it was a critical number
steel sapphire
Critical points is when f’(x) = 0 or is undefined
steel sapphire
So…
1 and -1
For that equation
Yea?
Wait no
It would be when f’(x) is 0 not f’’(x) = 0
Wait
I think I’m confusing myself
It said critical values of f’’ for f’
Use f’’ to find critical values of f’
So you can basically remove one prime from each and it would be normal
steel sapphire
Lol
Basically all I have to do is set double prime to 0
And solve
Which I did
Right?
raven haven
I guess?
craggy cloak
hey
craggy cloak
i need help with this question
The angles of a quadrilateral are in the ratio 1:1:3:4. Find the measures of all the angles.
.close
subtle birch
Let m be the smallest positive integer such that m^2+(m+1)^2+......(m+10)^2 is the square of a positive integer n. Find m and n
alpine sable
well calculate the sum first
vale wigeon
^
rose sigil
i think he already did that from something he posted elsewhere
but did not share it here for whatever reason lol
tacit arch
Let m be the smallest positive integer such that m^2+(m+1)^2+......(m+10)^2 is t...
Show your progress
subtle birch
Show your progress
I got upto 11(m²+10m+35)=n²
Couldn't get further
rose sigil
not sure if it helps but m^2 + 10m + 35 needs to be divisible by 11
so that should reduce your possible m's but not sure by how much or how much work that will take
i have no good tricks
twin nimbus
Well, I found the answer with a calculator, but I also don't have a good trick.
rose sigil
chatgpt was not so helpful
tribal haven
11[(m+5)²+10] = n²
how do you get (m+5)² = 1 mod 11 without bruteforcing
keen plinth
(m+5-1)(m+5+1) = 0
twin nimbus
Oh hey, that is a decent trick.
From there you can check like 4 or 5 values by hand until you find one which happens to be square.
But that is still not very satisfying
Much better than having to check well over a dozen though
tribal haven
oh yeah that's a thing
i just mentally checked my way to m=5 and got lucky
twin nimbus
||m=18|| was the solution I found. m=5 gives n^2 = 110, which is not a square.
rose sigil
yea i checked it with brute force and got the same (as omnipotententity)
tribal haven
oh that doesn't even work, that's only divisibility by 11
yikes
rose sigil
divisibility by 11 is just a necessary condition
rose sigil
it works
keen plinth
okay so thats literally the first candidate
twin nimbus
And 18 works. Nice. @subtle birch you still around?
How did you arrive at the 0,2 mod 3 and the 0,2 mod 4 constraint, btw?
ocean sealBOT
keen plinth
,w Table[m^2 + 10m + 35 mod 4, {m, 0, 3}]
ocean sealBOT
twin nimbus
Oh cool, I don't think I would have seen that
keen plinth
you can try mod 5 too but since the coeffs are already multiples of 5 it doesnt do anything
tribal haven
i guess it's to make the bruteforce part less garbage if just checking mod11 didn't get a solution fast enough 🫠
subtle birch
not sure if it helps but m^2 + 10m + 35 needs to be divisible by 11
Wait, thanks It actually helped
That means we have to check for values of n which are divisible by 11 like 11,22,33 so it narrows the search
rose sigil
hmm that's another way 
keen plinth
subtle birch
And 18 works. Nice. <@773731789113786399> you still around?
Yes
rose sigil
but longer than snow's method i imagine
alpine sable
Wait, thanks It actually helped
That means we have to check for values of n whic...
22,33 won't make perfect squares
check for 11,44,99 and so on
subtle birch
22,33 won't make perfect squares
Ik I mean we have to only search for numbers divisible by 11 so 77 is one
rose sigil
Wait, thanks It actually helped
That means we have to check for values of n whic...
gonna add that's not rly what i was saying but still right and a good observation
subtle birch
.close
lone heartBOT
devout summit
Read about Pell equation
lone heartBOT
Available help channel!
reef parrot
could anyone explain what's going on in this step to me?
lone heartBOT
could anyone explain what's going on in this step to me?
fading mauve
I've got the first part solved, idk what to answer for the second part
viral crater
lone heartBOT
viral crater
how do i turn this into explicit form?
ik k^2 is (n+1)(2n+1)/6 and k is n(n+1)/2
but what do i do with that -3
rose sigil
do you know a formula for sums of cubes?
ocean sealBOT
keen plinth
something like that
viral crater
does -3k^2 cound as ar^n-1
keen plinth
no
viral crater
wait not -1
keen plinth
,w expand 1/4 ((k+1/2)^4 - (k-1/2)^4) - 1/8((k+1/2)^2 - (k-1/2)^2) - ((k+1/2)^3 - (k-1/2)^3)
viral crater
so itll be k^3 - 3k^2
keen plinth
yes
keen plinth
or would i just work with k^2
no you'll need something like the sum of cubes formula
rose sigil
and that -3k^2 i can just apply this?
sounds totally off track :c
viral crater
mmm
ocean sealBOT
keen plinth
rose sigil
ms snow what are you doing
keen plinth
im reverse engineering the telescope
viral crater
rose sigil
tribal oxide
1 to 20 - 1 to 9 should work right?
viral crater
im confused whats going on
ocean sealBOT
woven plaza
1 to 20 - 1 to 9 should work right?
Yea
rose sigil
rice is still hung up on sums of cubes i think
keen plinth
sum of cubes should be doable
,w expand 1/4 ((k+1/2)^4 - (k-1/2)^4) - 1/8((k+1/2)^2 - (k-1/2)^2)
keen plinth
so now you can sum
ocean sealBOT
keen plinth
and the RHS telescopes
keen plinth
but like
if you just look up the sum of cubes formula
you can use these to piece together your sum
viral crater
can i do something like n^2(n+1)^2/4 -3((n+1)(2n+1)/6)?
keen plinth
yes
wheat crystal
lone heartBOT
wheat crystal
idk what to do at all 😦
its like use summation formula
but how do i find the amount of terms cuz this is geometric
pliant cedar
what is the general term of a geometric series
wheat crystal
a_n = a_1(1-r^n) divided by 1-r
pliant cedar
this is the sum
wheat crystal
oh shoot
pliant cedar
of the first n terms
wheat crystal
54
wheat crystal
2/81
wheat crystal
1/3
pliant cedar
yes
wheat crystal
how do i simplify that tho
pliant cedar
and findn
wheat crystal
do i multiply both sides by 1/54
pliant cedar
i mean multiply both sides by 1/54
ivory igloo
= 54 + 54/3 + 54/3^2 + 54/3^3 + ... + 54/3^7
pliant cedar
that gets rid of 54 in the right hand side
pliant cedar
= 54 + 54/3 + 54/3^2 + 54/3^3 + ... + 54/3^7
maybe write 81 as a power of 3 first
pliant cedar
1/2187 = (1/3)^n-1
i meant to reply to this sorry
ivory igloo
oh k
wheat crystal
what
pliant cedar
= 54 + 54/3 + 54/3^2 + 54/3^3 + ... + 54/3^7
so ur left hand side is 2/81 right
ivory igloo
??
pliant cedar
lol sorry i keep replying to u
wheat crystal
yes it is
pliant cedar
can u write 81 as a power of 3
wheat crystal
3^4
ivory igloo
wdym
pliant cedar
now write 54 as a multiple of a power of 3
wheat crystal
i feel like its not supposed to be this complicated
pliant cedar
now write 54 as a multiple of a power of 3
54 = 9 * 6 = 3 * 3 * 3 * 2 = 3^3 * 2
so when u multiply both sides by 1/54, u get 2/(81*54) = 2/(3^4 * 3^3 * 2)
the 2 cancels
and u get 1/(3^4 * 3^4) = 1/3^7
and this is what equals (1/3)^n-1 = 1/(3^n-1)
ivory igloo
= 54 + 54/3 + 54/3^2 + 54/3^3 + ... + 54/3^7
= 54(1 + 1/3 + 1/3^2 + ... + 1/3^7)
= 54(3^7/3^7 + 3^6/3^7 + ... + 1/3^7)
= 54(3^7 + 3^6 + ... + 1)/3^7
Now the hard part is finding 3^7 + 3^6 + ... + 1
If you think its very painful to calculate this, then there is a formula to find it:
P + P^2 + P^3 + ... + P^n = (P^(n+1)-1)/P-1
3 + 3^2 + 3^3 + ... + 3^7 = (3^8-1)/3-1 = (6561-1)/2 = 3280
Putting it in:
= 54(3280)/3^7
= 177120/3^4
= 6560/3^4 = 6560/81
@wheat crystal
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alpine sable
Hey, LP problem. I have solved problems without using a single subtraction, but now I have to deal with fixed, and variable costs. How do I start?
alpine sable
This is what I got right now, but I do not understand how I implement the aspect of costs, revenue, and profit.
thanks in advance
<@&286206848099549185>
lone heartBOT
@alpine sable Has your question been resolved?
noble sinew
Choosing to use book 1 you then have profit is 12000 * 1_{x_1>0}+(40-19) * x_1
alpine sable
hey
noble sinew
for 0<=x_1<=9000
alpine sable
right right
so what would the objective function be then, because usually its just 500x1 + 600x2 + 700x3 etc
but now i have to take into account that I have costs
And if i don't publish a book, i wouldnt have to pay the costs
noble sinew
Choosing to use book 1 you then have profit is 12000 * 1_{x_1>0}+(40-19) * x_1
You can write a function to be maximzed doing the same like here for the rest
alpine sable
thank you, isnt there some kind of bot who simplifies this into perspective
im not really used to typing out equations and functions and stuff haha
noble sinew
What?
alpine sable
Texit bot its called
because i dont fully understand the things you typed out for me
i just joined this server lol
noble sinew
$12000 \cdot \bf{1}_{x_1>0}+(40-19) \cdot x_1$
alpine sable
ahhhh
ocean sealBOT
ScapeProf
alpine sable
i appreciate it!
so the objective function will then be that
and then +
and then the same, but for the other books right
noble sinew
yep
noble sinew
last year of bachelor
alpine sable
cool what major
noble sinew
math
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grave solar
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grave solar
Can anyone please help me with this
rose sigil
can you use stirling’s formula?
pseudo ice
+ looks like AM/GM might help, maybe? [edit: it doesn't]
grave solar
can you use stirling’s formula?
I dont know that... so no i cant use it
grave solar
~~+ looks like AM/GM might help, maybe?~~ [edit: it doesn't]
How
warm vector
wait I thought help 0 is where you're supposed to ask your question
grave solar
That is what i did
pseudo ice
How
Cause that limit is the geometric mean of something... It's just a thought atm, haven't yet validated, but then you could probably sandwich it
No it doesn't, I don't think
rose sigil
i think it easily goes off to inf by stirling
naive valley
what about taking the log of the expression, you'll get (1/n) times the sum of log(1) through log(n), which sounds riemann sum-ish
hmm, scratch that, the spacing between the points doesn't shrink
you do something similar when proving stirling's formula
grave solar
hmm, scratch that, the spacing between the points doesn't shrink
Hmm
Layla can you teach me
Whats stirling
Or rather give me a bit of hint
rose sigil
it’s an approximation (good enough to use for limits) for factorial that’s often more algebra friendly than a product of integers
but if you haven’t seen it i doubt you cn use it
grave solar
Does it infers that the solution to this question would be https://goo.gl/search/Infinity
Infinity,
keen plinth
,w lim n to inf of (n!)^(1/n)
ocean sealBOT
rose sigil
i think it easily goes off to inf by stirling
i already said that ms snow
keen plinth
i didnt 
grave solar
Oh its good but cn any one suggest me an alternative method for this
keen plinth
maybe theres a bounding argument from below
rose sigil
alternate method 1
keen plinth
but what you can do is riemann sums
ocean sealBOT
keen plinth
for the first term
keen plinth
and that diverges which is slightly 
but
you can use that in some kind of bounding argument from below
rose sigil
maybe there’s something simple because the bound can be really terrible
and doesn’t need to be like stirling level powerful
grave solar
🙏
naive valley
Maybe try showing that no positive integer k is a bound for the sequence. For n > k , you have n! = [n(n-1)...(k+1)][k!] >= k^(n-k) k! = k^n (k! k^-k) = c k^n, where c depends on k but not on n. Therefore (n!)^(1/n) > c^(1/n) k. Now c^(1/n) -> 1, so the liminf of (n!)^(1/n) is greater than k
grave solar
Mathematical induction?
alpine sable
Is there a Geometric intuitive proof of why Moment of Inertia about any axis that lie in the plane of square is equal
alpine sable
here is the definition of moment of inertia for proof
where Ri is just magnitude of radius vector from axis of rotation
and Mi is mass of the tiny part of square
raven haven
this is literally a physics law lol
plain flame
i dont think physicists like proofs
just write something half coherent and they will accept 🙂
raven haven
Proof: mathematica said so should be fine
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
i dont think physicists like proofs
i am not a physicist ..i am a curious person who wants to know what kinda symmetry in math leads to this property of square's moment of inertia ..which is also just a formula you know ...i don't see any physics here
raven haven
alpine sable
https://en.wikipedia.org/wiki/Noether%27s_theorem have fun
i dont see moment of inertia here are you trolling ??
raven haven
no im not
alpine sable
when ur friend started comparing mathematician vs physict
raven haven
I mean you can try the physics server
alpine sable
Is there a Geometric intuitive proof of why Moment of Inertia about any axis tha...
^
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@alpine sable Has your question been resolved?
alpine sable
Hello, got an LP problem in Excel: I want to solve it, but I'm having trouble with calculating the Total fixed cost per book, i'd like it to be matching the fixed cost (since its fixed) IF the amount of books that are being produced is greater than 0 (because then I would have to produce the books, which will result in fixed cost) Could someone tell me which function I have to use for this, and or/if I'm doing it al wrong.
alpine sable
this is the problem
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185> a
mossy dagger
@alpine sable I believe what you are looking for is =IF(Cond, IfTrue, IfFalse).
alpine sable
hey
alright
so
id like it to be
If the amount of the books produced is > 0, then i want the fixed cost to display in this cell, if its not > 0, then id like it to stay 0
is that possible?
mossy dagger
is that possible?
Almost anything is possible in Excell. What you are looking for is an If statement.
For your example, Cond would be D5=0, IfTrue would be 0, and IfFalse would be 12000.
=IF(D5=0,0,12000).
Try this, and play with the various values to understand what it does.
Well, might be better to use the cell D11 rather than hard coding in 12000.
mossy dagger
That's good.
alpine sable
i hope so lmao
mossy dagger
I always recommend looking up Excel functions.
mossy dagger
mossy dagger
Appreciate the help Skallos :))
No problem!
Thanks!
alpine sable
.close
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native hare
I need help on this missed school for 2 weeks from being sick 
austere frigate
The angle of a line is 180, and if you cross two lines the angle is the same on opposite sides
Pretty much all you need to know to solve the problem, not exactly sure of the names for the properties though
lone heartBOT
@native hare Has your question been resolved?
rocky grove
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@native hare Has your question been resolved?
iron fiber
Anyone that can help me get in the right direction?
lone heartBOT
Anyone that can help me get in the right direction?
mortal trellis
well assume it has a cycle {x1, x2} of length 2
then x1 R x2 and x2 R x1
why does that not work
merry depot
is it just me or is that definition missing something? Or am I reading it weird.
if and only if xi R x(i+1) what?
iron fiber
why does that not work
Then they would be the same? If x1 >= x2 and x2 >= x1?
iron fiber
is it just me or is that definition missing something? Or am I reading it weird.
No idea, this is the only text included in this question.
mortal trellis
if and only if xi R x(i+1) what?
xi R x(i+1) means xi and x(i+1) are related. because R is supposed to be a partial order you could equivalently write xi <= x(i+1)
mortal trellis
Then they would be the same? If x1 >= x2 and x2 >= x1?
yes
but they are supposed to be distinct to actually form a cycle. so that can't work
merry depot
xi R x(i+1) means xi and x(i+1) are related. because R is supposed to be a parti...
Ah, I was reading that as a coset notation haha
iron fiber
but they are supposed to be distinct to actually form a cycle. so that can't wor...
If x1 <= x2 and x2 <= x1, would they always have to be the same, isnt a back and forth path possible?
Just trying to imagine it in my head.
mortal trellis
remember the definition of a partial order
iron fiber
Oh so with the antisymmetric, if (a,b) and (b,a), a must be b, is that what you are referring to?
Yeah I get it, if its a partial order, this isnt possible that (a,b) and (b,a) and a and b are distinct.
otherwise it wouldnt be a partial order
mortal trellis
yes
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sterile idol
Hello. I have this question
lone heartBOT
Hello. I have this question
languid bolt
slow moat
whats 2+2
hazy ferry
xd
sterile idol
I translated the question
- Give the definition: let f'(x) is the derivative of the function y = f(x), f"(x) is the number of derivatives of the function y = f'(x), if the equation
f"(x) = 0 has a real solution x = x0, it is said that (x_0, f(x_0)) for the function y=f(x) "inflection point" after the study found that there are three functions
f(x) = ax^3+bx^2+cx+d have an "inflection point", and the "inflection point" is also the center of symmetry of the image of the function y = f(x), if the function
This just provided some information
But the question is
If f(x) = x^3 - 3x^2 then f(1/2021) + f(2/2021) + ... + f(4040/2021) + f(4041/2021) =
Now I know how to find the answer, it's pretty simple
2022/2021 = 2 - 2020/2021 and so on till 4041/2021 and then we can simply tell f(x) = -f(2-x)-4
So most of the terms cancel out leaving us with f(2021/2021) - 4 - 4 - 4 ... - 4 = -2 - 4(2020) = -2 - 8080 = -8082
But that's not my question
sterile idol
8. Give the definition: let f'(x) is the derivative of the function y = f(x), f"...
My question is whether the information given here can be used somehow to solve this question
I feel like if it's symmetrical at a point then somehow its possible to know which terms can cancel out
Sorry for making it long
<@&286206848099549185>
limpid turret
Your second derivative will give you your intelection point 2
That's how you find that x=2 is your symmetry point and deduce that most points will cancel
lone heartBOT
@sterile idol Has your question been resolved?
warped topaz
lone heartBOT
https://gyazo.com/f2c3951a8b1fe49a485030b3311bfcaa.png
warped topaz
I dont even know how to start this one
warped topaz
but theres still 2 unknowns?
slate jolt
try to work a bit more
you get a² log(b) =0
so either a=0
or log(b)=0
but can a=0?
warped topaz
so b = 1?
warped topaz
Awesome
just wondering
Is there any way I could solve this buy using the graph
cause they dont usually give me a graph
so I assumed I would need it
slate jolt
no
warped topaz
slate jolt
you need information about the value of the function
warped topaz
yeye but to help
slate jolt
either a graph
warped topaz
like is there a different method
slate jolt
or something that tells you some values
like theres not info in just this
not enough*
warped topaz
.close
next tundra
Hello, a weird question but
lone heartBOT
Hello, a weird question but
winter nacelle
what is it
next tundra
Hello wasn't done typing hit enter by accident, it's like a whole paragraph so give me a sec
There's a character in League of Legends whos ability scales off attack speed, meaning that the cooldown of the ability gets lower as the attack speed gets higher.
The cooldown of the ability starts at 4 seconds and the lowest possible is 1.33 seconds 66% reduction.
The lowest cooldown is achieved at 114 attack speed.
prime badge
who's that
next tundra
I want to know if you could graph the relationship between attack speed and cooldown reduction
olive trout
who's that
yasuo
limpid turret
We would need to know if the relation is linear
Or perhaps related in any other way
I would guess linear, but no guarantee yet
next tundra
I believe the the equation for cooldown reduction is x/1.72 = y where x is attack speed and y is cooldown reduction
limpid turret
What is the initial attack speed?
next tundra
Attack speed is referring to bonus attack speed in the equation so it would be 0