#help-10
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dude i dont know how to
Yeah ^^" get your s.a. right ✓
Now, write S.A. in terms of one variable
oh i already did all that stuff
show me
h = 8/(pi * r^2)
plug that into the equation im minimizing
and when simplified i get
16/r + 2pi*r^2
so thats my final equation of S.A
and next i get the derivative
can you confirm taht is correct
(@_@;)
$S(r) = \frac{2(\pi r^3 + 8)}{r}$
Ansh
nope it's correct
lastly what's the third equation!?
what
hmm
R u high!? lmao
nah this just doesnt make sense
Minimum or maximum occurs when first derivative is 0
obv
HOW EXACTLY
there's only 1 critical point
4(-4/r^2 + pi*r)
= 0
im not quite sure how to make that portion in parentheses = 0
yes correct
im not sure how to make it equal -
0*
bruh equate to zero!?
$-\frac{4}{r^2} + \pi r = 0$
Ansh
⁉️
would you
move pi*r to other side
so its
- 4/r^2 = - pi*r
and then simplify from there..?
true
1 sec lemme figure it out
is it
cbrt(4/pi)
is that the crit pt
@raven spire
oh srry.. I meant: except possibly you :o
Since you'd rather figure the c.p. on one side than use the equation
and yes.
I just equate to zero and get the critical point rather than messing with only one side of the derivative
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Find the volume of the solid whose base is bounded by the given graph and the cross sections perpendicular to the x-axis are squares. a) x^2+y^2=9
hello! i'm not quite sure what the question is talking about. what does it mean by cross sections perpendicular to the x-axis are squares?
is it like riemann sum?
A cross section is the 2D shape made by cutting your solid
Like, if you look directly into the cut
So any cut will give you a square cross section
So the base is a circle, but a vertical cut gives a square cross section
Definitely an odd solid, but it is possible
haha i guess i just cant wrap my head around it
It's kind of like a semi-sphere except it has two corners on the top
so if i want to find the area
And the walls are vertical
So area of a square is the square of the side length
yes
And the volume of the solid is the integral of "all such areas"
uh huh
So, if you take a cut at x, what's the area of the cross section?
x is where we're cutting, not the length of the side
Though it is definitely related
You're on the right track. Good intuition, the height of the circle is exactly what we need
,w graph sqrt(9 - x^2)
Basically that's half of the length of the square, no matter where we cut
The square's length is given by:
2√[9 - x²]
The area of the square is then:
4(9 - x²)
Finally, the volume is given by:
∫ 4(9 - x²) dx
can i ask why it is half
Nice picture of the solid btw, where's that from?
i just found it on google 🙂
The graph I made is only half of the base, since I made a semi-circle
The whole base is the whole circle
OHHHHH
i get it now
this makes a lot of sense
that helps a bunch
thank you so much
Np, feel free to ask if you have anything else!
okie imma try solving this!
haha sorry i have another question
what would the intervals be?
would it be [-3, 3]?
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<@&286206848099549185>
What is your question?
What do you think it should be? Which factors have you not yet accounted for with the parts that are already filled in?
There's also a 1/x factor, where did it go?
and also, after putting (14/9x) into the equation, the denominator became 9n!
yea i dont know where it went
i dont know where the x in the denomionator went
Can you combine (1/x) with x^n?
if you have
14 * x^n
does the n get distributed to the 14
making it 14^n?
i dont think so ....
No, that would be true if it was (14 * x)^n
yea okay
But with 14 * x^n, the n is only applied to the x.
OK, and what are you left with?
im left with just 14
When you divide x^n by x
Nope
Deep Hariya
$\frac{x^n} {x} = x^n * x^{-1}$
$\frac{x^n} {x} = x^n * x^{-1}= x^{n-1}$
Deep Hariya
Get it?
Get it?
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tysm @copper latch
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I got Q = (7,11) for question C but when I use that for question D, i dont end up with the same lenght
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i havent learned about this "mod" thing yet and my teacher still told me to find the value of this equation
is that a screenshot of the question exactly as it was given to you by the teacher
yeah
cause this seems not to make much sense at all
how??
is that "how??" as in "how does this not make any sense??" or "how do i solve it??"
how does this not make any sense??
also idk how to solve it since i havent learned this
both i guess
well ok like, assuming mod is meant in the operational sense, i.e. a mod b is interpreted as "the remainder of a on division by b, lying between 0 and b-1 inclusive"
then 6 mod 28 = 6 and 32 mod 431 = 32
so you have 6 + 32 = x + 7
which just makes this an incredibly obtuse way to write down a simple linear equation
if you're so desperate for an "answer", then that'd have to be it.
The mod does nothing cause the number on the right is larger then the left
i am confused
Ikr
so your teacher is either unable or unwilling to communicate what she wants from you.
or she's intentionally setting you up for failure.
wha
im a failure
my life
so
is the answer "0" possible
like
in any way
that u can do this
and get 0
nope
just to be clear, i was not calling you a failure and did not intend for my message to be read as such.
if if u reverse 28 % 6 | 431 % 32
still u cant
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good news
since you asked so brazenly: no
why be so noob and complain
yayyyyyyyyyyyyyyyyyy
wut
she is getting fired tomorrow
ok thats all
lol stop making this kind of shit up and close the channel Lol
Wow thats great!
yes
but very unfortunate that I didnt ask
no need to be rude
anyways have a bad day
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5x(y-3) - 3xy - 3y(x+3)=
so yea
i am not sure on how i should solve this
i thought
it would be 5xy-15x-3xy-3yx+9y=
but then i dont even know if i got this right
and i cant make it up in my head
After adding +15x to other side you can factor out y
What
You can solve for y.
2xy-15x+9y=0
Add 15x to other side
2xy+9y=15x
Factor out y
??? 6x?
?
Oh my bad
isnt 2xy just 6x then?
I didn't even saw 3yx lmao
it makes it so much harder tbh
You want to seperate the variables
how do i do that then
You can do this by using the distributive property of addition and multiplication
Lets say for example you have 2xy +3x+ 4y
=0
Lets use the commutative propertie to rearrange the terms
what words are you using lmao
commutative propertie is
a+b=b+a
basically you can rearrange the terms because that wouldnt change the result
so with rearrangement
2xy +4y +3x= 0
but often of the times i mess it up with the "+" and "-"
what do you mean
Xy and yx same
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$x_{1,n} = 1000x_{3,n-1}\ x_{2,n}=0.02x_{1,n-1}\ x_{3,n}=0.05*x_{2,n-1}$ did i get the right difference equations for this?
fall
@long roost Has your question been resolved?
<@&286206848099549185>
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Do my equations look right for the question?
Seems about right
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shouldnt it be -x^3 in the fourth line
im pretty sure this solution is wrong because if you simply use the calculator you get a different answer
@restive turret Has your question been resolved?
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Suppose g is an even function and f is any function. Show that "f o g" is an even function.
welp
what's an even function?
f is even if f(x)=f(-x)
It's prolly not the right convention
nah adding a couple lines introducing f and g would've been okay but
the math part's there
so it seems reasonable?
mhmm
is that a yes lmao
yeah
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I’m confused on how to do this
,rotate
this is not about roots
No?
No.
indeed
Be patient.
finding inverses:
Swap x and y
solve for y.
That is what I was doing
The double variable
In one term
I don’t know how to proceed with that
ok you didn't switch x and y.
And then swap
the order of those steps don't matter but sure
How would you solve a linear equation
Solve for the variable
I don’t know how to move the 2x to the other side
subtract from both sides...
If I multiply or divide, I still have an x
again, like any other linear equation
The process of isolating for a variable doesn't magically change like you think it does.
Now I can’t get rid of the y
Oh wait
I think I have it
I got the inverse
What do I do with it?
range of f is the domain of its inverse
Ok
so find the values not in the range of f
...
.
Domain of y I think is all real numbers
Domain of the function is clearly not all of R.
No
I don’t know
You are right
So 1/2 is not in the range of the original function?
It was wrong
Yeah
I don’t know what to do
what did you get for the inverse......
Or is posting your work still something you're adverse to?
y=(-3x+1)/(2x+1)
yes, so what's not in the domain of the inverse?
-1/2
Remember what you want to do in the original question. I ask you to find an x for my y. When is this not possible?
^ just so you can make sense of this entire process
When the root is the same for both the num and denom
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"This was the answer last time, so it must be the answer this time, cause every question is the exact same"
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Hello, and thanks in advance for helping
TL;DR
I have a group of points, and need to find circles with radius r that have x points inside it. How do I find these circles?
Context:
I'm working on a project for a simulation of people, cars, and other entities, and need a function to determine an area where the density of entities is above a certain value; for example, Find where 3 people are within 3 metres of each other, and then put a ball on the place so they are all inside the ball. Input radius = r, input amount of ppl = p
For this, my approach is to find possible areas first, then determine the centre point of the circle.
Finding possible areas:
I think of looking around each person and see if it can find other persons in a radius of r. These build possible groups where I then can try to find an area inside.
Finding point of circle:
This is the tricky part, and the one my question entails.
Solution attempt and also problem:
Within the area where I suspect a possible circle:
I am thinking of using the intersection of circles, gradually adding the circle of a person to the already processed group of circles, until I either can't add the circle because there would be no intersection, or every circle has been added. The problem then remains in determining the area of the intersection. Once I have the area, I can just use the middle point or something like that. But I don't know how to describe the area on the coordinate system, and then keep using it for potential intersection.
Alternative:
The alternative is to just see if all the circles intersect, and then bruteforce my way towards it once I know a solution MUST exist. As in, I create a circle, and slightly nudge it until it finds the point. This is bruteforce and inefficient.
I am open to other implementations, this is just what I thought of during the past hour(s)
There is also a problem with finding the radius around the people
Because using the radius of the circle means that I might miss things like this
And using 2r I might have too many circles
You could do it entity by entity ig
This is why I need to find the intersection of the circles after this initial guess
That is my current attempt. Yes.
The problem is that I need the intersections and I don't know how to determine that area
I'd just use the distance
If it's less than your radius sample size thing then +1
Then see if numInside/size is worse than max dens
What do you mean
I'm sorry, I don't think I follow
Are you saying to uhh
Split up the map into blocks based on the radius
Then check the amount of entities in each?
Or are you saying to do distance around each entity
Because that's basically what I'm trying to do here but I don't know how to calculate the intersection of the circles based on the entities that are out of distance, but still within a possible area
center M for r cannot be determined unless I create triangle OR
Draw a circle around each entity
Find where every circle intersects
And choose a point from the intersection
I just don't know how to calculate that intersection, and am asking if i.e. you know any way to calculate it
Because suddenly there are 3 circles instead of 2
Added obligatory r
look into BVHs and quadtrees
What does BVHs stand for? I'm getting unrelated google results
A bounding volume hierarchy (BVH) is a tree structure on a set of geometric objects. All geometric objects are wrapped in bounding volumes that form the leaf nodes of the tree. These nodes are then grouped as small sets and enclosed within larger bounding volumes. These, in turn, are also grouped and enclosed within other larger bounding volumes...
this would allow you to search efficiently for bounds with x points
Looks promising
I need time to read through stuff
Though on further thinking... A bit scary, because the entities are moving
So I'd need one where you can insert and remove relatively fast
yes and thats one of its strengths as well
since things dont move very far per frame
this is common for resolving collisions in physics sims
It looks promising
I'm just still unsure about the actual implementation
From the way I understand it
You set a bounding shape, i.e. a square
I guess that's what you use the quadtree for
To determine the squares and find squares with entites inside
you can construct a bounding sphere around N points by (arbitrarily) choosing a center C, sorting all points by distance to C and choosing the Nth as the radius for the sphere
I mean I think we can also do squares, I would have to worry less about circles intersecting then
absolutely
so you want a box that contains N points? i think BVH will serve you well
Yeah, except for the BVH it doesn't look like they save the distance themselves
THey are just sorted based on distance
do you want a sphere or box?
Whatever is easier to implement / run
I'm still worried about performance
But I think this is already more efficient than my previous attempt
This does look pretty good. I just am worried that the map is too big
Ya, I think this is solved for now
Thank you very much!
np
Completely forgot about this in the context of the other thing
Wanna chat a bit or should I close now
bvh doesn't care how big your map is, only how many objects there are
Ok, means I still slightly misunderstood it but I now have somewhere to look at
its great
And do research and ask ppl about
u can close
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Hello
Am counfused sorry
im asking you to tell me what happens if i put in the input x in f(g(x))
f o g means f(g(x))
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not a question from there but a general question
e.g for b
distribution Y, what would the new expectation be?
i know that var(2x) = 4var(x) so ik the answer
so for distribution Y
would the expectation be 2*expectation(x)
do 1/6(n^2-1)
Can you prove it?
oh wait i think it would be
it would be 1/n sum from 1 to n of 2r
right?
which would just be 2 x e(x)
Right
ok so for part 3
expectation(x) = n+1/2
so for n=100
expectation(x) = 50.5
so expectation of Y should = 101 right?
mark scheme says 57.73 though idk where they got that from
this is true only for $X = r$ and $2X = 2r$
riemann
i dont understand what that means
Your $Y$ is a little more complicated
riemann
$X = {1,2,3, \ldots, n}$ Your statement would be true for $2X = {2,4,6, \ldots, 2n}$
riemann
But your $Y \neq 2X$
riemann
oh the -1
so expectation of (2x-1) = 2ex(x) -1 ???
doesn't that mean expectation is 100
oh, as it should be. i read somethign slightly wrong
aha that works
so back to this question
p(100-57.75k <= Y <= 100+57.73k) = 1
so the probability of y being between a number and another number is 100%
which means y is between the lowest value and highest value of the distribution?
which is 1 and 199?
omg
its that easy?
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@mint hazel Has your question been resolved?
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Hi, I'm not sure if this is the right way to do this, I need to find angle AOC, so I imagine a 360° circle inside the triangle and do some basic math.
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cause you follow the slopes
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There are 10k lockers the first person opens all of them the second person opens every second locker and the third does the opposite for every third locker, how many lockers are opened and closed
Please don't occupy multiple help channels.
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k
the first and second person are just opening lockers?
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Hello!
Which 1a and 1b?
seriously?
is is that hard?
i asked so many people
no one is able to help
lol
ty tho, tysm
I don't do geometry
no also other
ppl
10k ppl
@mental grove Has your question been resolved?
I think I can help
SERIOUSLY?
damn- ty
so the easiest angle to find first on 1a is the complementary angle to 116 degrees
do you know how to find htat?
thats completely fair
ty
tryna figure out how to explain this, it's been a few years
do you at least know which angle I'm referring to
yeah
Yeah
alrighty
82
Oh sweet it does give you that
I meant left
alright
I'm invested in this now
lol
my guy anakin has been waiting for over half an hour
even changed your pfp
watch an idiot struggle
my gf forced me to :(
I am stuck as well 
sorry its taking me so long, I'm tryna figure it out myself
yeah
furthest I got was a = 34 - b
not sure where to go from there
so I haven't figured out how to solve it yet, but do you know the sum of interior angles of a square
I DID
I JUST DID
I KNOW WHAT A IS
A IS
180-64
because opposite angles
in an inscribed shape
form 180
that's a thing? huh
right?
I thought those angles only worked if the lines are parallel
apparently yes
yeah same lol
kinda wack
ok
1b
do you know this
ye
what
If you add all the interior angles (angles inside the square), how many degrees do you get
360..
wait listen
Alright i'm listening
the other part of the b
is 98
because
180-82
and then
180-98
giving you 82
i think i'm on to something for this one
ye?
what does that tell you?
nothing.
lol
if you rotate a triangle
i am a dumb piece of useless shit.
does that change the angles?
idk, does it?
hey you basically solved 1a by yourself
lol i couldnt solve 1a for some reason either
I THINK I GOT IT
srsly?
Ok ok so you know how I was talking about parallel lines
ye?
do you know the rule for that
how is that useful though....
okay
yep
in lenght
No
they are tangents
I considered that, but they don't have to be equal I don't think
the picture disagrees 👁️👁️
yeah ok so
well darn, that makes this problem way easier
;-;
I was pretty proud of the way I found it out
haha
me? either games or school stuff
sit in the math discord server and help other dumb shits like me?
then im lucky
Oh don't get me wrong I could use the help
But people don't help with calc 4 all that often
makes sense
Do you know how to solve it now
nah
;-;
Ok so sum of angles in a triangle is 180
yee
If the 2 side lengths are equal, then so are the 2 angles touching the non-equal side
whats dat?
isosceles triangle, it's what you got
yep
it is.
i might be
its isosceles
so you can find angle alpha in this diagram (alpha being the weird a with two tails)
how tf do i find it lmfao
180 = 52 + alpha + alpha
ye
ye
so you can find out d
yessir
is d 64?
YEEEE
FINALLY
alr
now i can get c
53
52*
c is 52
i said it from the start
uhh maybe idk i haven't done it yet
lemme verify that
the answer is right there
the triangle
to the right
is the same
as the inscribed one
i think
someone said it earlier
uhhhhh
is that right?
still working on it
still trucking along?
lmao
which sucks because i have to take a quiz
what time is it for ya
this is a warmup
6 pm
fun
1 am 13 minutes
tbh
mood
i dont care all that much, i dont like my cousin thaaat much
this isnt even my homework lmfao
BRuh
wait then what even is it?!?
my cousins homework
I-
and i thought it was complete bullshit
wyd then, just have them do it
I feel betrayed
yeah
so i challenged him i could do it faster than him
bruh
this is the most tragic plot twist of the century
gl
you too
ty
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how do i do 0,4³
@outer widget Is this $0.4^3$
sills
$x^3 = x \cdot x \cdot x$
sills
Multiply normally, ignoring the decimal points.
Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.
yes
ok thx
i know i'm in 9th grade but teachers in brazil are wild
thank you so much
.close
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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@lone shore Call the width x and the length y, then convert the two sentences into equations
so x2 - 150?
Im so confused
perimeter is 2 * length + 2 * width
maybe draw a rectangle and label the sides x and y, for example
it's not going to help
so 6 will be x and y for the width
but how tf am I going to find the length
if theres no width
<@&286206848099549185>
@lone shore Has your question been resolved?
@lone shore Do you still need help?
yes
Okay
P = 2W + 2L correct?
So you might be thinking
150 = 2W + 2L
We know L in terms of W
Because of how the problem explains the length
the length of a rectangle is 6m less than twice its width
@lone shore
@lone shore Has your question been resolved?
