The formula
#help-0
unique dune
tender shard
btw do they both have the same height
unique dune
Yes
tender shard
oh right I need to find their middle too
unique dune
Now find area of the bottom one using the formula
tender shard
108?
ocean sealBOT
Result:
140
Result:
48
,calc 7/4 * 48
ocean sealBOT
Result:
84
84???
unique dune
Wdym
tender shard
both of them are getting multiplied by 1/2
unique dune
if 5k/2*h is 60 isn't 9k/2*h 108
The former equation is solely responsible for giving the value of kh
Because the latter one is based on it
lone heartBOT
tender shard
if 7h/4h = 60 then 9h/h4 is?
unique dune
How is it timed out
lone heartBOT
✅
unique dune
if 7h/4*h = 60 then 9h/h*4 is?
?
unique dune
??
Essentially here’s our flowchart
Find area 1 = 60 -> find kh -> Fond area 2 -> use kh in finding area 2
unique dune
Yup
tender shard
14kh/4?
tender shard
9kh/4
unique dune
Huh
tender shard
the bottom part's area
tender shard
thats the upper part
unique dune
Wdym upper part
tender shard
it's split into 2 pieces
tender shard
isn't that the middle part
unique dune
tender shard
how do you know half of CB is k
unique dune
Half of cb is 3k/2
The middle red line
Top red line is k
Bottom red line is 2k
It’s the average between k and 2k
lone heartBOT
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wispy plaza
is a vector field just a vector valued function where the input space is the same dimension as the output space?
wispy plaza
What if the input space is greater than the output space (example, F(x,y,z) = <Q(x,y,z), P(x,y,z)>)
is this still a vector field?
summer dirge
is a vector field just a vector valued function where the input space is the sam...
a vector field in R^n is a function from a subset of R^n to R^n, so yeah
summer dirge
What if the input space is greater than the output space (example, F(x,y,z) = <Q...
no, this is a real valued function
F goes from R^3 to R
wispy plaza
no, this is a real valued function
sorry for the delayed response
could you explain a bit more
summer dirge
oh wait, you're using < > to denote a vector?
wispy plaza
by F(x,y,z) = <Q(x,y,z), P(x,y,z)>, I meant F(x,y,z) = Q(x,y,z)i + P(x,y,z)j
wispy plaza
sorry for the confusion
summer dirge
anyways, F is going from R^3 to R^2 still, so it's not a vector field 
wispy plaza
I don't know how to plot fancy math symbols and the other notation seemed a bit more readable
wispy plaza
anyways, F is going from R^3 to R^2 still, so it's not a vector field <:sadcatth...
is there a special term for it?
summer dirge
the point of a vector field is to look like a swarm of vectors in space
if your codomain is R^2, then the vectors don't live in the space of the domain, so to speak
so you aren't attaching a vectors to points in R^3 anymore
wispy plaza
the point of a vector field is to look like a swarm of vectors in space
I see. This makes sense given that vector fields are functions from Rn to Rn
summer dirge
is there a special term for it?
there's no special name for an arbitrary map from R^3 to R^2, I don't think 
wispy plaza
there's no special name for an arbitrary map from R^3 to R^2, I don't think <:ca...
damn
summer dirge
I mean, why would there be? 
wispy plaza
I mean, vector fields get a special name
summer dirge
yeah because they have an easy visualization 
wispy plaza
so, from R^m to R^n, where n > m would also not be vector field
summer dirge
indeed
wispy plaza
is there a special name for this?
summer dirge
there's no special name for any map that goes from R^m to R^n without any other special properties
summer dirge
well, we give names to interesting things
not to boring things or things with no special properties
summer dirge
well, we give names to interesting things
we do have names for some functions going from R^m to R^n
(for example, if the total derivative of f: R^m to R^n is surjective at each point, we call f a smooth submersion)
(if it's injective everywhere, f is a smooth immersion)
but these kinds of functions have much stronger conditions imposed on them
an arbitrary map from R^m to R^n is not even necessarily bounded or continuous
wispy plaza
These words are beyond my understanding
summer dirge
so there's not much use to naming them
wispy plaza
Lowkey did not pass my intro to proofs class
summer dirge
an arbitrary map from R^m to R^n is not even necessarily bounded or continuous
without these minimal conditions, the functions are just really boring and not worth studying, let alone naming
summer dirge
These words are beyond my understanding
I just wanted to throw those two terms out there so you believe me when I say that some functions from R^m to R^n are interesting enough to name :p
I wasn't expecting you to know what they were
wispy plaza
anyways, thank you
lone heartBOT
summer dirge
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wispy plaza
for functions F(x(t), y(t)) is it possible to have y(t) = g(x(t)) and use F(x, g(x))
wispy plaza
F(x, g(x)) = some function of x, and we can find the derivative dF/dx
I didn't even realize I'm using the same help channel I just used like 3 minutes ago (this is an irrelavant comment)
proven leaf
from the multivariate chain rule (\frac{dF}{dt}=\frac{\partial F}{\partial x}\frac{dx}{dt}+\frac{\partial F}{\partial y}\frac{dy}{dt}) if we have (y(t)=g(x(t))) and (x(t)=x) then (\frac{dy}{dt}=g'(x)\frac{dx}{dt}) but (\frac{dx}{dt}=1) so then we reduce to (\frac{dF}{dx}=\frac{\partial F}{\partial x}\cdot 1+\frac{\partial F}{\partial y}\frac{dg}{dx})
but if we have that F depending on x and g(x) one would be better off using chain rule normally
ocean sealBOT
PajamaMamaLlama
wispy plaza
**PajamaMamaLlama**
what if x(t) didn't equal t
proven leaf
for functions F(x(t), y(t)) is it possible to have y(t) = g(x(t)) and use F(x, g...
but here you've made x no longer depend on t
wispy plaza
My question is probably poorly worded, I barely understand what I'm even asking
proven leaf
no worries, no question is a bad question :) were you trying to say if you have a function depending on g(x) and x then can you succinctly write the derivative expression?
wispy plaza
I suppose my question is, if you can get a function F(x(t), y(t)), where y(t) = g(x(t)), we have F(x(t), g(x(t))) we could find dF/dx instead of dF/dt
I think I'm confused becuase I don't really understand what it means to take a derivate of a function with respect to a function
proven leaf
well the way I like to visualize when I was first doing it was to draw a tree diagram with F then branch off into however many variables F depends upon (in this case that is x and y) then for each branch repeat
so x depends on t and y depends on t
so we have (\frac{df}{dt}=\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}) for (f(x(t),y(t)))
ocean sealBOT
PajamaMamaLlama
proven leaf
and we for taking the derivative of a "function" that's where the partial derivative is important, that fancy looking d. this symbol means to treat all other variables as constants
wispy plaza
if we're able to repersent y as a function of x
then there is no need for a partial derivative
visually thinking, is this the same as projecting the line repersenting F(x(t),y(t)) in R^3 to the xz plane and taking the derivative of that?
where the line can be repersented by the vector valued funcion r(t) = <x(t), y(t), F(x(t),y(t))>
keen plinth
are you asking for the derivative of F(x, y(x))?
wispy plaza
I don't think so, I'm not sure
This is the question I'm asking "if you can get a function F(x(t), y(t)), where y(t) = g(x(t)), we have F(x(t), g(x(t))) we could find dF/dx instead of dF/dt"
keen plinth
but they'll be related
wispy plaza
I'm not asking if they're equivalent, I'm simply asking I can take dF/dx if i choose to
keen plinth
well you can do anything you choose to
wispy plaza
where the line can be repersented by the vector valued funcion r(t) = <x(t), y(t...
and also
tacit arch
r/technicallythetruth
keen plinth
but within a certain context you need to choose to something that's relevant
if i ask for dF/dt and you answer with dF/dx
you can certainly choose to do that
and i can certainly choose to tell you you've not done what i've asked
keen plinth
visually thinking, is this the same as projecting the line repersenting F(x(t),y...
this seems reasonable
wispy plaza
if i ask for dF/dt and you answer with dF/dx
I mean, maybe in some scenarios finding dF/dx(dx/dt) may be easier than finding (partial dF/dx) (dx/dt) and (partial dF/dy) (dy/dt)
keen plinth
that's a true statement
wispy plaza
how would I project r(t) onto the xz plane?
keen plinth
kill y
wispy plaza
like simply have r(t) = <x(t), 0, F(x(t), g(x(t)))> where g(x(t)) = y(t)
keen plinth
yes
wispy plaza
thanks
I think I understand the relashonship between partial and normal derivatives a bit better now
.close
lone heartBOT
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
hard harness
But let’s see
wispy plaza
did bro come back with an alt acount?
hard harness
did bro come back with an alt acount?
Who?
wispy plaza
also, what's with that tag 
sly mantle
@timber carbon thanks for mute evading. the alt and original account will be banned
hard harness
…oh
slate vortex
💀
hard harness
that tag is crazy
My tag?
slate vortex
no that guy's tag
wispy plaza
no
slate vortex
said "NAZI"
hard harness
Sorry, I’m very confused
strange schooner
said "NAZI"
Still does bruh
hard harness
said "NAZI"
…oh
strange schooner
Wht
lone heartBOT
hard harness
Well, that just happened 
wispy plaza
imagine bro comes back with a third alt
hard harness
This is literally the first I’m hearing about this dude
strange schooner
Bro just could NOT accept people not helping him
wispy plaza
This is literally the first I’m hearing about this dude
he was was cuasing a ruckus like literally 3 minutes earlier. I've never seen them either
sly mantle
ive closed the channel, lets clear out
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foggy nest
Guys, I have a task to represent a graph with an automorphism in Z3. I kind of found it, but I don't know how to prove it reasonably. Can someone write and I'll check in the morning (it's my night now) .you will save me 🙏
lone heartBOT
Guys, I have a task to represent a graph with an automorphism in Z3. I kind of f...
@foggy nest Has your question been resolved?
lone heartBOT
@foggy nest Has your question been resolved?
lone heartBOT
@foggy nest Has your question been resolved?
glad cradle
lone heartBOT
mossy reef
cuz the ceiling of a func is the floor + 1 i got g(x)=f(x)+1 but that is wrong
What happens if x is a natural number?
lone heartBOT
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alpine sable
im js tired give me this bs answer
lone heartBOT
im js tired give me this bs answer
raw jetty
!noans
lone heartBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
alpine sable
fine in stuck on the fraction part and im so tired
restive owl
for improper fractions
multiply the denominator by the whole number
and add the numerator to that value
tacit arch
im js tired give me this bs answer
Oh you're in 5th grade? Are you almost 11 years old yet?
restive owl
do for both, multiply by a factor to both the denominator and numerator
tacit arch
gang its my brothers lol
Oh just tell your brother to join then
Much more efficient to help him
So you don't have to learn
alpine sable
hes 4th grade amp and hes gonna be in 5th grade amp and he has to do this
he doenst have dc
hes 10
slate vortex
Btw you don't (and shouldn't) need to convert these to improper fractions
Get a common denominator in the fractions
vale wigeon
@alpine sable show your little brother these and perhaps encourage him to go to khanacademy (it's free and has practice questions too but without the stakes of homework)
if you're unable to do this question yourself maybe you would benefit from doing the same :P
hybrid ravine
hi for part b, to find the displacement-time function i would need to figure out whether to take the positive or negative v (from rooting v^2 from part a). How do I know which one to take?
hybrid ravine
and integrate
no like I already did part a
i need help determining positive or negative v for part b
tranquil thistle
u can do it by maxima minima concept
of differentiation
vel < 0 initially
find the point where == 0
next points vel > 0
hybrid ravine
next points vel > 0
wait how do ik whether to take positive or negative v tho
mental salmon
i believe you'd take the negative values of v given that the initial velocity is negative. also, given that the solution for part a is ||v² = 2x³||, we'd assume negative values for a new x in terms of the derivative we should have studied previously in that v = dx/dt. i'd say we start working with ||v = -sqrt(2x³)||
hope it helps!
hybrid ravine
i believe you'd take the negative values of v given that the initial velocity is...
wait so if the initial velocity is negative, how do ik it doesnt turn positive
mental salmon
i think you`d have to make a general function to describe the position in function of time, i assumed the following: ||x(t)=2/(t+sqrt(2)²||. for t = 0, we have the initial x condition of 1. you'll find v(t) by differtentiating x(t) and, finally, testing for t = 0 and finding the first value of v. it gives the following equation: ||v(t) = −4(t+ 2)^-3||, so the velocity is always in the negatives.
sorry i'm taking so long, i've been juggling keyboards here lol
hybrid ravine
sorry i'm taking so long, i've been juggling keyboards here lol
all good i got it thanks :)
.close
lone heartBOT
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errant flower
Yo I just wanted to see if I’m on the right track w this (I had a lot of messy work which I crossed out hence why everything’s cropped)
hushed scroll
Factorisation is wrong
tawdry lily
Yo I just wanted to see if I’m on the right track w this (I had a lot of messy w...
You flipped the factorizations
mental salmon
so, your first factor is wrong for a² -a-2
errant flower
You flipped the factorizations
Which photo is this?
mental salmon
it should be (a-2)(a+1)
mental salmon
Which photo is this?
1st one!
tawdry lily
Which photo is this?
hushed scroll
(a²-a-2)/(a²+2a-8).
Try factor it again and compare it with what you did in 2nd photo.
errant flower
Okay
mental salmon
yeah! i'd say youre doing good tho, the other factors in pic 1 are all correct!
errant flower
Aside from the literal answers I get from calculating, am I doing the right approach? If that makes sense
mental salmon
Aside from the literal answers I get from calculating, am I doing the right appr...
yep! i'd say so!
tawdry lily
Aside from the literal answers I get from calculating, am I doing the right appr...
Yep
errant flower
yep! i'd say so!
Okay that’s good
I’ll fix the tiny mistake I made and see how it is
Thanks everyone
mental salmon
good luck!
errant flower
good luck!
Thanks
tawdry lily
If you want to know how to factor trinomials simple yet quick, watch this video I saw on youtube: https://youtube.com/shorts/kZjBy2OOCR0?si=VSzzTVBDT_xYO1D2
midnight carbon
they are just headache if put wrong
mental salmon
^
errant flower
If you want to know how to factor trinomials simple yet quick, watch this video ...
Yo thanks dude
tawdry lily
Yo thanks dude
No worries
errant flower
I’ve just been using the ac method as you can see cus it’s the only one which makes sense to me
mental salmon
there's also the classic refactoring after spliting it
tawdry lily
For me using the tic-tac-toe method is the most efficient method yet
mental salmon
it takes more time but its a failsafe method honeslty
hushed scroll
For me using the tic-tac-toe method is the most efficient method yet
What is this method?
midnight carbon
For me using the tic-tac-toe method is the most efficient method yet
what is that method never heard about it
tawdry lily
If you want to know how to factor trinomials simple yet quick, watch this video ...
Here
mental salmon
its a solid one tbh!
royal forge
splitting the middle term is an easy method/trick to check if the factorisation is correct
tawdry lily
its a solid one tbh!
I agree
midnight carbon
splitting the middle term is an easy method/trick to check if the factorisation ...
yeah it was the first method that is ever taught
royal forge
yeah it was the first method that is ever taught
yea
tawdry lily
splitting the middle term is an easy method/trick to check if the factorisation ...
Otherwise, just solve for x and then replug x to the factors and the trinomial itself
midnight carbon
i usually just do it by head and refactor to see if im insane or correct
lol
royal forge
if ax^2 + bx +c = 0
then multiply a and c
and split the middle term b so that its sum is equal to ac
errant flower
Okay I think I can solve it from here, y’all take this discussion to gen now
royal forge
Otherwise, just solve for x and then replug x to the factors and the trinomial i...
umm isnt that kind long?
errant flower
.close
tawdry lily
umm isnt that kind long?
Nah
lone heartBOT
midnight carbon
if ax^2 + bx +c = 0
then multiply a and c
and split the middle term b so that ...
nostalgis
hushed scroll
For me directly using formula is best to solve quadratic
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hushed scroll
Others are too much guessing
lone heartBOT
Others are too much guessing
hushed scroll
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tawdry lily
For me directly using formula is best to solve quadratic
Quadratic equation is a different thing it's not for factoring it's for solving for x
midnight carbon
For me directly using formula is best to solve quadratic
its like sometime using a sword to stitch a button eg x^2-1
hushed scroll
Quadratic equation is a different thing it's not for factoring it's for solving ...
We can factor after getting x
royal forge
as the eq we made was equal to 0
tawdry lily
We can factor after getting x
I guess
midnight carbon
it was in algebraic equations
oh yeah maybe i dont have that good of a memory
royal forge
and find x easily
royal forge
oh yeah maybe i dont have that good of a memory
lol
hushed scroll
royal forge
alr
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devout ermine
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uneven jewel
!status
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
tawdry lily
You can treat these like normal quadratic equations
unique dune
Assuming the derivation is correct
Use the second bracket to find p= something
Then pr = pp = p^2
2a(p+q) = -2bq
p+q = -(bq)/a
p= -(bq)/a - q
,w expand (p+2q+r)(p-r)
junior vigil
note that p and r are both roots of f(x)=a(x+q)^2+2bqx+c
ocean sealBOT
devout ermine
what
devout ermine
2a(p+q) = -2bq
how
junior vigil
note that p and r are both roots of f(x)=a(x+q)^2+2bqx+c
then you can either use vietta formula or just multiply both solutions of quadratic formula to get same result
devout ermine
note that p and r are both roots of f(x)=a(x+q)^2+2bqx+c
how did u get this polynomial
junior vigil
replace instances of p and r with x in each respective equation
devout ermine
why
devout ermine
why did u put x in place or r
junior vigil
why did u put x in place or r
because polynomials have nice properties...
glad iron
why did u put x in place or r
Because the equations are symmetric
devout ermine
im not getting
junior vigil
do you see how the first equation is f(p)=0
devout ermine
are they quadratic ply
glad iron
Had they not been symmetric you'd have to try some sort of algebraic manipulation
devout ermine
is th epolynomial in p or q
junior vigil
you can still use algebraic manipulation
devout ermine
do you see how the first equation is f(p)=0
no
junior vigil
is th epolynomial in p or q
the polynomial is in terms of x, but we're plugging p into it
devout ermine
how would i know that
junior vigil
note that p and r are both roots of f(x)=a(x+q)^2+2bqx+c
if you replace x with p here you'll get the first equation
junior vigil
how would i know that
because p and r are in the same place in each respective equation
a(q+r)^2, a(q+p)^2
devout ermine
can you tell from starting what i need to do
junior vigil
2bqp,2bqr
devout ermine
i can see that
glad iron
If you have a quadratic ax^2+bx+c=0 and x1 and x2 are roots then x1 and x2 satisfy ax1^2+bx1+c=0, ax2^2+bx2+c=0, conversely if x1 and x2 satisfy the above equations then you have a quadratic namely ax^2+bx+c=0 which has roots x1 and x2
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foggy nest
Guys, I have a task to represent a graph with an automorphism in Z3. I kind of found it, but I don't know how to prove it reasonably. Can someone write
lone heartBOT
Guys, I have a task to represent a graph with an automorphism in Z3. I kind of f...
@foggy nest Has your question been resolved?
lone heartBOT
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visual hedge
does anyone know how I got the mass of the object for this (7)
lavish cave
does anyone know how I got the mass of the object for this (7)
you have $mg \sin \theta = 26$ and $mg \cos \theta = 58$
ocean sealBOT
south
visual hedge
honestly i might be tweaking my teacher did this a while ago but I'm so confused
lavish cave
ah wait there's a coefficient of friction
visual hedge
26?
lavish cave
nah that still shouldn't affect it though
lavish cave
the question is broken ....
yeah
visual hedge
damn ok but thanks anyway cause I have an understanding for this now
ocean sealBOT
south
lavish cave
damn ok but thanks anyway cause I have an understanding for this now
no worries!
visual hedge
.close
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vast harbor
sorry for the image not being clear , i know this is a basic questino , im trying to find the equation of every linear line , e.g the first line have B=-2mt , but the second line is where i got abit confused
vast harbor
the y axis is B(mt) , the x axis is t(ms)
the slope of the line is 0.6
B=mt + p
cant find p
i know how to get it usually , cuz its the point that the graph intersect y axis at , but our graph doesnt intersect y axis
im so good at complicating things
my question is just how to get p when you dont have a full graph of a line
p as in y=mx + p
alpine sable
You know the m right?
vast harbor
i got a formula for it anyways $p=y_1 - mx_1$
ocean sealBOT
<rajel />
lone heartBOT
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devout ermine
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north rover
<@&268886789983436800> Username.
alpine sable
Request a nickname bruh
north rover
Try graphing it.
ocean sealBOT
Lucifer
clever folio
You need to change your username + pronouns. Dm the modmail after you do and we can unmute you.
alpine sable
Graph 'em
north rover
Oh, he’s muted. 
clever folio
Yeah sorry, screwed up writing the ticket. They should see your suggestions/pings either way I think.
I'm gonna close this channel for now.
.close
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north rover
What’s the exact solution?
alpine sable
I'd suspect one
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tight matrix
lone heartBOT
tight matrix
im actually so lost help a brotha out 😭
undone knot
Did you snip the top of the blue curve? 👀
tight matrix
nah its like that in the problem
undone knot
Do you get what the question is asking?
tight matrix
i understand what its asking i just cant seem to understand which one is what
for q1
question 1
undone knot
Look at places where the slope is 0
undone knot
Yaur :3
ebon granite
Curve b is the derivative of curve c
tight matrix
ahhh
ebon granite
The other one is more... complex (pun intended)
rustic jungle
Hey guys, im really stucked to understand this problem in probability. I made a python program to verify that i got the correct answer but i dont know why is it true. I want to know the expected gain of a slot machine, supposing that you dont have to pay for playing.
the machine has 3 different reels: r1 r2 and r3, placed from left to right. Every reel show 3 icons in vertical, meaning that you can see 3x3 grid in your screen.
r 1 : A,B,C,D total of 4 faces
r 2: A,B,C,D,u, u,u 7 faces
r 3: A,B,C,u,u,u,D 7 faces as well
for instance, you can get:
A u u
B u D
C A A
A,B,C,D are ordinary figures and the u is the universal figures (wild card), which can serve as any figure of A,B,C,D (prioritize bigger prize if there are many). Every horizontal line can win you a prize (horizontal payline), so you can win up to 3 different prizes. The rules to determine if you get a prize or not in a given row are the following: suppose that in this row you have these 3 icons from left to right (x,y,z), here the order matter.
+0 if x!=y, i.e. the first two figures dont match
+1 if the first two figures match but the 3rd figure is different to them
+2 if all figures are the same
in the previous example:
+2 prize for the first row because you can get A A A by choosing u=A
+1 for the second row because you can pick u=B but the third figure is D, which prevents you from getting a +2
+0 for the third row because C!=A.
Assuming that every reel has equal probability to stop at any face as their first figure. Whats the expected gain?
rustic jungle
what ive done is supposing that every row has same expected gain because i believe that there is a symmetry, eventhough i dont know where is it
so i can just multiply by 3 to the expected gain of the first row to get the total gain
for computing the expected gain of a single row, what ive done is to classify every possible outcome with respect to their number of universal figures (the u figure)
Lets say we have these 3 figures in the first row (f1,f2,f3)
If we have zero wildcards: f1, f2, f3 are regular figures(4x4x4 = 64 scenarios)
+0: if f1 != f2 → 4x3x4 = 48 possibilities
+1: if f1 = f2 != f3 → 4x1x3 = 12 possibilities
+2: if f1 = f2 = f3 → 4x1x1 = 4 possibilities
If we have exactly 1 wildcard:
f2 = wildcard and f1, f3 are regular figures(4x3x4 = 48 scenarios)
+0: impossible, 0 possible scenarios
+1: if f3 != f1 → 4x3x3 = 36 possibilities
+2: if f3 = f1 → 4x3x1 = 12 possibilities
f3 = wildcard and f1, f2 are regular figures(4x4x3 = 48 scenarios)
+0: if f1 != f2 → 4x3x3 = 36 possibilities
+1: impossible, 0 possibilities
+2: if f1 = f2 → 4x1x3 = 12 possibilities
If we have exactly 2 wildcards (4x3x3 = 36 scenarios)
+0: impossible
+1: impossible
+2: always → 4x3x3 = 36 possibilities
so we get that in the first row, our expected gain is
[+2x(4+12+12+36)+1x(12+36+0+0)+0*(48+0+36+0)] / 196 =176/196
which is approximately 0.898
and the expected gain per game is 3 times that number, which is around 2.694
the experimental result is also around 2.69
so i think this is the correct answer, but i dont know how do you see the symmetry in the first step, so you can legally say the total expected gain is 3 times the expected gain of a single line
lone heartBOT
@rustic jungle Has your question been resolved?
lone heartBOT
@rustic jungle Has your question been resolved?
tropic thistle
I think if you restate your question in a more readable format, maybe with some simplifications, it would be easier for someone to help you.
lone heartBOT
@rustic jungle Has your question been resolved?
coarse elm
lone heartBOT
coarse elm
Determine the solution to each system
I think im just a little bit confused because with other examples, id just make them equal
so x + y + x = x + y + z
but that gets me nowhere
since its the same plane
coarse elm
So I need to create two parameters instead?
coarse elm
ya its the same thing
visual ocean
soooo the answer is
visual ocean
no
visual ocean
really?
visual ocean
even for planes that are multiples of each other?
coarse elm
x = 1 - y - z
bc i thought its this idk
north rover
What happens in a system of equations when two lines have the same equation?
coarse elm
isnt there no solution
visual ocean
isnt there no solution
no
visual ocean
there are solutions
coarse elm
its 1 solution
visual ocean
no
north rover
Rather, all real x.
north rover
The parametrization doesn’t even matter. You’re just describing the line.
visual ocean
The parametrization doesn’t even matter. You’re just describing the line.
yeah exactly
coarse elm
no i already did that in the other question
i need to do it in parametric form
So it does matter because I dont even know how to do it
visual ocean
I don't see why you would need to put it in parametric form
north rover
no i already did that in the other question
coarse elm
I don't see why you would need to put it in parametric form
because this is what we learned bruhh lol
it's on the test
visual ocean
is this like a school assignment?
visual ocean
damn
coarse elm
so do u know how to do it
visual ocean
no lmao
visual ocean
wait show me the answer again
coarse elm
north rover
Okay, do you realize there are infinite amounts of ways you can put this in parametric form? There is not a singular answer.
visual ocean
Ig just do what they did here
visual ocean
set y and z as some parametric variables
coarse elm
u pick a variable as a parameter
visual ocean
then solve for x in terms of these parameters
north rover
A plane needs 2.
coarse elm
...
north rover
A plane is in the form $\Pi=(a, b, c)+\lambda(d, e, f)+\mu(g, h, i)$.
ocean sealBOT
;(
coarse elm
Here I don’t I just use Z as t so only using one parameter
north rover
Again, it really doesn’t matter.
It’s just for convienience that they put that answer there.
visual ocean
lmao @coarse elm atp just follow what the answer key says
undone knot
Here I don’t I just use Z as t so only using one parameter
Ig in that case they intersect on a line so you only need one parameter
Kinda like there’s only one way you can move along a line
coarse elm
oh
undone knot
Whereas you can move along a plane in “2”
north rover
Whereas you can move along a plane in “2”
You mean there are 2 direction vectors, yes.
coarse elm
LOL
the only thing yall had to tell me is that
when the planes are coincident, you use two parameters
I would have understood it right away
@undone knot LOL thank you
😭
undone knot
I only got that from reading the conversation XD
north rover
when the planes are coincident, you use two parameters
Because...you’re describing one plane.
I said this.
coarse elm
But thanks to everyone else too!!
north rover
A plane needs 2.
^
visual ocean
But thanks to everyone else too!!
I didn't do much but gl on your exam 🙏
coarse elm
Yeah like, two planes that are coincident
I thought you meant any two planes intersecting need two
lone heartBOT
lone heartBOT
Available help channel!
ebon meadow
explain if this is an onto function or not.
$f(m,n) = m^2 - n^2$ where the domain and co-domain is the set of all integers
ocean sealBOT
joseph
ebon meadow
by inspection, i can tell that it isnt since the difference of squares doesnt satisfy all integers
but how do i prove that?
like for a counterexample, we can do:
$m^2 - n^2 = 2$
ocean sealBOT
joseph
ebon meadow
but how do i show that there are no integers that satisfy w/o exhaustion?
twilit dome
what do you think of when you see m^2-n^2
ebon meadow
(m+n)(m-n) is what immediately comes to mind
buoyant saddle
m and n are integers so their sum and difference must also be which means what about the possible values of m + n and m - n
if it equals 2
twilit dome
so, the factors of 2 are 1, 2, -1, -2, right
ebon meadow
m and n are integers so their sum and difference must also be which means what a...
ohhhh
ok so we let a = (m+n) and b = (m-n)
wait nvm
buoyant saddle
so, the factors of 2 are 1, 2, -1, -2, right
^
buoyant saddle
now what should you do
ebon meadow
now what should you do
im not sure
buoyant saddle
use factorization of 2
twilit dome
imo it should be a knee-jerk reaction to think m=a+b/2, n=a-b/2 when you see a = (m+n) and b = (m-n)
ebon meadow
and m would only be an integer if (a+b) is an integer divisible by 2?
so that means its not arbitrary
twilit dome
so, no matter the choice of m and n, m+n will be equal to 3 or -3, which is odd.
ebon meadow
.close
unborn burrow
What is the purpose of D? Why are they mentioning it?
lone heartBOT
What is the purpose of D? Why are they mentioning it?
unborn burrow
I believe I understand what the set is but I dont see why they are mentioning it or its importance
wait actually im not sure I fully understand what this set is
let me take another look
unborn burrow
what is E? and X'?
E in this section is treated at the universe
X' is their way of saying the complement of X
So X' = {x in E: x not in X}
summer dirge
I see
well, if they're mentioning it here, they ought to use it later on, yeah?
D is just the collection of all subsets of E whose complements are also in E
whether or not this has a use depends on what the author does with it later :p
hybrid ravine
Hi how do I find the constant
lone heartBOT
Hi how do I find the constant
summer dirge
why do you need to find it? 
also, you can't find it with the information given
the point is just to have it there as part of the function defining the force F
the greatest height will be in terms of k
hybrid ravine
the greatest height will be in terms of k
wait but how do i prove part a then?
because the equation i got isn't the same as what they got
summer dirge
wait but how do i prove part a then?
the first thing you ought to do is find what C is by using the initial condition
hybrid ravine
wait i thought u said you can't find it
summer dirge
then use the fact that at the highest point, v = 0
summer dirge
the first thing you ought to do is find what C is by using the initial condition
anyhow yeah
you'll use the fact that velocity = u when t = 0 to find C
hybrid ravine
I apologize
nono its ok
hybrid ravine
you'll use the fact that velocity = u when t = 0 to find C
oh ok
wait is my current equation right
so far
im a bit sus
of it
summer dirge
it looks okay to me
hybrid ravine
kk
summer dirge
the only thing is that you can get rid of the negatives in the natural log
because they reside inside an absolute value
but that's an aesthetics choice
summer dirge
then use the fact that at the highest point, v = 0 <:MenheraSalute4:103310002861...
.
lone heartBOT
summer dirge
viral mist
are you following me around to say hi to me? <:giggle:1317870990998638592>
Yeah
We can play games if you are free
lone heartBOT
Available help channel!
keen niche
Need help with this discrete math problem
lone heartBOT
Need help with this discrete math problem
lone heartBOT
@keen niche Has your question been resolved?
lone heartBOT
gray isle
lone heartBOT
vale wigeon
<@&268886789983436800> spam
lone heartBOT
Available help channel!
odd hedge
How do i do this question?
lone heartBOT
How do i do this question?
odd hedge
the angles are outside of the triangle so idk what to do
alpine sable
I know how to get x alone for inequality’s but that’s it I don’t know how to decide what’s the right answer from what I solved. how do I know how to pick my answer after I solved for x?
buoyant saddle
I know how to get x alone for inequality’s but that’s it I don’t know how to dec...
you’re done
it’s an or statement
you take the union of the two intervals
buoyant saddle
So it would be the first option on the left?
yea
alpine sable
For or statements do I always include both results for x as my final answer ? Or will theyll be times where only one x from one inequality is wrong?
tidal lintel
ok
reef wren
For or statements do I always include both results for x as my final answer ? Or...
the statement matters in the same question if the statement was AND instead of OR then there wouldn't be any solutions
alpine sable
And that’s because for an AND statement both would have to work for x rather than either x solution for an OR statement?
reef wren
And that’s because for an AND statement both would have to work for x rather tha...
yep
OR if one of them or both statements are true then it is
true
AND if both them are true then it is true
other than that it is false
alpine sable
Oh ahahah that makes me feel better, to check if the x’s work I plug in both solutions to my problems before?
reef wren
yep simple
OR you take the union of the sets
AND you take the intersection of sets
and yep you could check for some values of x
lone heartBOT
tidal lintel
1233463909187376218321e76163216812373627638165315713-2232r762181322362464874864715e
lone heartBOT
Available help channel!
worthy lichen
Will it be something like — if the ball is dropped from the top of a building, it will rise to the same height as the building, i.e., 20 meters? Or could something else happen? I feel it’s not necessary that the ball will rise exactly up to the height of the building. So then, what should I take as x?
worthy lichen
to find the t
lusty laurel
lemme see
height is 20m
ok
u = 10
put 20 in place of x
then its done
@worthy lichen
cuz displacement is 20m
u doing it right
worthy lichen
Ahh
lusty laurel
even if you throw upwards, the displacement will be 20 right?
worthy lichen
Will it be something like — if the ball is dropped from the top of a building, i...
.
Disp of the ball?
Till the turning point?
lusty laurel
Disp of the ball?
in your diagram the ball was thrown upward and fell to the ground right?
worthy lichen
Yes
lusty laurel
and you need to calculate time
worthy lichen
Yes
worthy lichen
Yep
lusty laurel
a = -10
worthy lichen
actually point I can't understand is
lusty laurel
yes
worthy lichen
Why the rising height of ball is 20m before it turns down
lusty laurel
Why the rising height of ball is 20m before it turns down
does it matter?
what is displacement?
tell me what is displacement
worthy lichen
Distance between final and initial point
lusty laurel
Distance between final and initial point
so what is the distance between initiala dn final point here
this is the speciality of laws of motion
however curved the path is, it will always give the displacement
20m right? from top to bottom?
worthy lichen
Im not asking that
lusty laurel
top of building is initial point and boottom is final point
so do 20 = 10t - 1/2 x 10 x t^2
youll get the time
worthy lichen
I need to understand
I am asking why we take height of building as the displacement (x) before it turns
At v = 0
worthy lichen
Im not
mellow bluff
cuz building doesnt movwe
worthy lichen
Bruh
worthy lichen
why I should take x = 20
lusty laurel
why I should take x = 20
because in 2nd equation, you put displacement
and displacement here is 20
mellow bluff
why I should take x = 20
cuz in second equation, you put displacement
and displacement here is 20
worthy lichen
from top of building to this point?
lusty laurel
doesnt matter
worthy lichen
Why
worthy lichen
In real life is it necessary that ball will displace same as the height of my house
mellow bluff
newton's equations only works on displacement
can u like not copy me
lusty laurel
In real life is it necessary that ball will displace same as the height of my ho...
yes
always
lusty laurel
if you throwing from house's height
lusty laurel
vertically upwards
vale wigeon
can u like not copy me
you're the copycat mate
mellow bluff
you're the copycat mate
my wifi is slow
vale wigeon
mellow bluff
its because of my wifi
vale wigeon
i call BS. <@&268886789983436800> yall might wanna look at this
vale wigeon
mellow bluff
i call BS. <@&268886789983436800> yall might wanna look at this
nah why
lusty laurel
Explain why no
sigh, becuase the initial point is your house's top and final point is your house's bottom
worthy lichen
If i throw really slowly will it really go far as my houses height
sly mantle
@mellow bluff stop
mellow bluff
alr
lusty laurel
If i throw really slowly will it really go far as my houses height
now youre throwing the ball from ground?
worthy lichen
Wait wait
lusty laurel
even if you throw the ball slowly it will be acted upon by gravity and reach ground right?
worthy lichen
I am thinking ur taking the initial point from where ball is throw to the bottom point of house
I am not talking about top to bottom
lusty laurel
i think this is helpful
was it necessary to derive the formula
turbid narwhal
**I am thinking ur taking the initial point from where ball is throw to the bott...
yep
lusty laurel
**I am thinking ur taking the initial point from where ball is throw to the bott...
yes
worthy lichen
No no
lusty laurel
I am not talking about top to bottom
THAT is displacement
turbid narwhal
I am not talking about that
so
turbid narwhal
I am taking about this
this equation will solve through differentiation
sly mantle
@mellow bluff sucks ur having a bad time but that doesnt belong in a help channel. pls take a day off to sort urself out
lusty laurel
newton's equation will always give you the correct answer with disp
lusty laurel
that time will automatically will be taken
the time where the ball goes up and down will automatically be taken
that's the power of equations of motio
n
turbid narwhal
that's the power of equations of motio
yep buddy
worthy lichen
@lusty laurel can you ask me a similar question to test that I understand or not
worthy lichen
I doubt tho
lusty laurel
🙂
you know, if you just drop the ball with 0 force and throw it upwards , both will take the same time to reach ground
try it yourself from your house's roof
worthy lichen
What exactly to do?
turbid narwhal
What exactly to do?
find maximum value of this equation
lusty laurel
find maximum value of this equation
bro he is having difficulty with just the equation, why differentiate
turbid narwhal
i mean value of x where it is maximum
turbid narwhal
How do I know how high it will go
put value of t bro in the equation
worthy lichen
Do you think I am overthinking this?
lusty laurel
Do you think I am overthinking this?
come in vc i will explain it by speaking, can you speak hindi?
turbid narwhal
Do you think I am overthinking this?
yep because is kinda basic topic of equation of motion
lusty laurel
damn there is no vc here
worthy lichen
I got it
lusty laurel
what will happen to you in rotation?
worthy lichen
nothing it will be easy
lusty laurel
nothing it will be easy
GOOD!
lusty laurel
Not actually
it is easy bruh
turbid narwhal
what will happen to you in rotation?
it is pretty dangerous
turbid narwhal
nothing it will be easy
easy brohhh
lusty laurel
it is pretty dangerous
nah bro, just remember work, power energy and force, youll be cool
for me, fluids feel more difficult than rotation
lone heartBOT
turbid narwhal
for me, fluids feel more difficult than rotation
nahh thats simple some concepts are use in it like force on base particles surface tension and force on wall etc
lusty laurel
nahh thats simple some concepts are use in it like force on base particles surfa...
acceleration and rotation of fluids man
that throws me off
turbid narwhal
Everything is doable tho
yep but if you didn't did the high level question then you say this that rotation is easy
lusty laurel
like find the equation of the parabola formed on the liquid surface when the liquid rotates with certain omega
bernoulli's also has some tough scenarious
turbid narwhal
like find the equation of the parabola formed on the liquid surface when the liq...
i think every chapter is hard enough it depends on our practise
lusty laurel
i think every chapter is hard enough it depends on our practise
for me , only fluid i=was tough, rest was easy
i mean not tough, requires revision
turbid narwhal
like i totally wasted my 11th but now some topics i recall these seems like easy
worthy lichen
@lusty laurel
lusty laurel
like i totally wasted my 11th but now some topics i recall these seems like easy
maine backlog nahi kiya
🎉
turbid narwhal
i mean not tough, requires revision
yep are you guys in 12th or 11th
lusty laurel
<@1258036511333552259>
yes?
worthy lichen
As the ball rises and turns down and at the height of building again it's displacement is 0 and the leftover displacement it has to cover is 20m
Easy
turbid narwhal
maine backlog nahi kiya
thats the good thing buddy due to many reasons or ya ye bol lo mereko JEE wagera ke bare ma nhi pta tha to
lusty laurel
As the ball rises and turns down and at the height of building again it's displa...
PRECISEELY!
IT COMES BACK TO ITS INITIAL POSITION
AND THEN GOES DOWN
worthy lichen
😀
lusty laurel
turbid narwhal
i think some these mini topics builds critical thinking
lusty laurel
i think some these mini topics builds critical thinking
in thermodynamics very much
worthy lichen
you done projectile?
I have studied it but not practice problems yet
lusty laurel
accidentally i still calculate enthalpy in physics
turbid narwhal
in thermodynamics very much
yes are youu preparing for jee also
lusty laurel
lusty laurel
yes are youu preparing for jee also
yep
worthy lichen
The height on going down will be +20m? Right
lusty laurel
The height on going down will be +20m? Right
-20
lusty laurel
dam do you tried this year jee questions
yep
all conics in advcance done
ITF one as well
binomial one as well