${A = \frac{1}{2}bh \implies \frac{\dd A}{\dd t} = \frac{1}{2}b\frac{\dd h}{\dd t} + \frac{1}{2}h \frac{\dd b}{\dd t}}$
#help-13
slender ginkgo
wraith daggerBOT
k
ocean robin
Base is bottom part of triangle right?
slender ginkgo
yes
ocean robin
Okay, I think I got this
<@&286206848099549185> How did they pull 2 out of their ass?
Wait nvm
cedar kilnBOT
Available help channel!
craggy stratus
Hi, I'm not entirely sure I follow what's happening here and was hoping I could get some clarification
craggy stratus
So originally the question is as follows;
find the greatest and smallest values of the function
and then in the answers they do the following
I see that this is the partial derivatives of x^2-xy+y^2 in the top row and x^2+y^2 in the bottom row, but why does this work?
What is it that we're actually doing??
They've done the same for similar questions and I feel quite lost, like with this one
when
so why does this work?
cedar kilnBOT
@craggy stratus Has your question been resolved?
craggy stratus
.close
rose cedar
is the proof for problem 3 correct and how would i go about doing 4?
rose cedar
can i just use contradiction for 4?
say that the empty set is a subset of the cartesian product of A and the empty set and isnt one, a contradiction?
solid juniper
this is a weird way to say what you're trying to say
rose cedar
i can shorten it?
solid juniper
you could say something like
let m \in S_1 \times S_2. so m = (x,y) with x \in S_1 and y \in S_2
rose cedar
let $m \in S_1 \times S_2. so m = (x,y) with x \in S_1 and y \in S_2$
wraith daggerBOT
bugmi
solid juniper
this is also kinda awkward
you could put like "we have" or something after the commas
rose cedar
oh ok
solid juniper
anyway yea the idea is right
rose cedar
what ab for 4?
solid juniper
right
A\times \emptyset is the pairs of form (a,b) with a in A and b in the empty set
solid juniper
there is no such tuple
rose cedar
oh so the idea is that we cant write any ordered pairs?
solid juniper
sure or like
rose cedar
and since we cant write any ordered pairs we just write the empty set?
solid juniper
if there was an element (a,b) in A\times \emptyset, then we would have b in the empty set
solid juniper
A\times \emptyset is the pairs of form (a,b) with a in A and b in the empty set
by this
rose cedar
so id just say a line similar to that and then say "but b cannot be an element of the empty set as the empty set has no elements" or smth?
solid juniper
sure
rose cedar
so is this fine?
im assuming that the whole subset stuff is pretty pointless
cuz we know A x emptyset is just empty anyway lol
cedar kilnBOT
@rose cedar Has your question been resolved?
maiden hornet
cedar kilnBOT
plucky knoll
Wah haobin
Need help ah
I come teach you
@maiden hornet I thought kumon prepares you for life
maiden hornet
yo jayden
plucky knoll
Sup
plucky knoll
Binomial?
maiden hornet
i will chop of my dick if u know how to do
maiden hornet
shut the fuck up
plucky knoll
N choose R
maiden hornet
wrong
plucky knoll
Not funny
plucky knoll
I’ll let you crust
You calculate the x^2 x^4
Like
uh how do I type it out
2x times power of what equal x^2
N n^n-2 (2x)^2
2
X^2
It’s 2^2
So it’s
N n^n-2 2^2
2
How do I type the formula out
cedar kilnBOT
@maiden hornet Has your question been resolved?
unborn gull
cedar kilnBOT
unborn gull
knowing that $0 \leq p_n(x) \leq \sqrt{x}$
wraith daggerBOT
💎𝔞𝔷𝔢𝔡𝔡𝔦𝔫𝔢💎
unborn gull
@celest ledge
celest ledge
What is p_n(x)
unborn gull
What is p_n(x)
sorry i forgot
$2p_{n+1}=x+2p_{n}-p_{n}^{2}$
wraith daggerBOT
💎𝔞𝔷𝔢𝔡𝔡𝔦𝔫𝔢💎
unborn gull
And p_1(x) is?
$p_{0}=0$
wraith daggerBOT
💎𝔞𝔷𝔢𝔡𝔡𝔦𝔫𝔢💎
unborn gull
If you have this recursion then use induction
I tried with induction but no result
chilly warren
You mean
$$2p_{n+1}(x)=x+2p_{n}(x)-p_{n}^{2}(x)$$
?
wraith daggerBOT
Xwtek
unborn gull
You mean
$$2p_{n+1}(x)=x+2p_{n}(x)-p_{n}^{2}(x)$$
?
yes
chilly warren
**💎𝔞𝔷𝔢𝔡𝔡𝔦𝔫𝔢💎**
Are you sure about this? $p_2(1)=3\cross 1 - 1^2 = 2$
wraith daggerBOT
Xwtek
chilly warren
Which is larger than $\sqrt{1}=1$
wraith daggerBOT
Xwtek
unborn gull
Are you sure about this? $p_2(1)=3\cross 1 - 1^2 = 2$
in the interval of [0;1]
chilly warren
And 1 is in that interval.
celest ledge
p_2(1)=7/8
unborn gull
And 1 is in that interval.
yes
chilly warren
Wait, I forgot the 2 in $2p_{n+1}(x)$.
wraith daggerBOT
Xwtek
celest ledge
It really is direct calculation
In the end if my calculation is correct it becomes (4n-1)x<=4n^2+12n-2 kind of stuff
It really has nothing to say, direct calculation
cedar kilnBOT
@unborn gull Has your question been resolved?
random fog
Hi, Can I get a help over here on number 10. The topic is all about Rational Equation solving for the value of x.
I've been solving for this equation like for 1hour and 30 mins and I'm getting a decimal answer which x_1 = 3.3085, x_2 = -2.3542, and x_3 is still the same of x_2 (I use calculator)
I'm confused on how to solve the x on this problem because its cubic equation, I try using app Symbolab and it show me the answer (image 3) and it give me only one option answer which that only satisfies to the equation.
I also try the app Sizzle app and it give me a different solution which it gives me a non decimal numbers, and if your going to click image 4 you will see that he factor out -(x+5) which i dont understand why he do that (check image 4 and 5).
Please i need help to find the real answer for this problem is it decimal or an integer. Tysm
cedar kilnBOT
@random fog Has your question been resolved?
stark bough
Ok first take lhs
random fog
<@&286206848099549185>
random fog
Ok first take lhs
Lcd?
stark bough
$(x(x-5) - (x(x+5))/(x-5)(x+5)$
wraith daggerBOT
McApple0214
random fog
Oh okie
random fog
Alr
random fog
Alr wait
stark bough
U get $-10x/x^2 - 25$
wraith daggerBOT
McApple0214
random fog
Mhm
wraith daggerBOT
McApple0214
random fog
Cross multiply?
stark bough
Yes
Then u get quadratic and find using quadratic equation
Lmk what u get answer as
random fog
Alr ima write on a pad
random fog
If I simplify further I will get $-10x^3 - 14x^2 + 50x + 350 = 0$ right?
wraith daggerBOT
nerf.leander
random fog
Yeah through synthetic or rational root theorem
stark bough
**McApple0214**
And substitute the value in this
If it satisfies then that's ur answer
I GTG i reached home
If u have any questions
Ping me
random fog
Yeah i try that earlier using a calculator app, and it gives me only one answer which is x = 3.30856
Which it says it only satisfies the equation
I'm doubting that if its really the answer because it's on decimal result
stark bough
Yeah i try that earlier using a calculator app, and it gives me only one answer ...
This one gave only 1?
It should give 3 values
Cuz it's cubic polynomial
If you give me 1 hour I'll solve it on paper and give u answer
steep badge
real and complex roots maybe
random fog
Actually yeah it gives me 3 solution, I mean it only appear one solution i think its only one that satisfies to the equation when you substitute it
random fog
real and complex roots maybe
Wdym?
random fog
If you give me 1 hour I'll solve it on paper and give u answer
Ummm sure
random fog
Alr tyt budd
stark bough
He prolly doesn't
steep badge
hm
stark bough
I'm trying it
stark bough
@random fog
random fog
Know*
random fog
Wdym by that?
stark bough
Lemme solve wait
random fog
Alr
steep badge
Know*
you have to have a calculator, take initial value as 3
in this case I already know the answer so I took 3
random fog
What is it?
steep badge
Actually yeah it gives me 3 solution, I mean it only appear one solution i think...
this one
random fog
So it is the answer?
random fog
Just tyt
stark bough
You factor out -2 right?
Yep
cedar kilnBOT
cedar kilnBOT
Available help channel!
timber lava
a is even, b is odd, n is even. can a^n + b^n divide (a+b)^n-1?
timber lava
and a relatively first to b
queen ice
a is even, b is odd, n is even. can a^n + b^n divide (a+b)^n-1?
(…)^(n-1) or (…)^n - 1
cedar kilnBOT
@timber lava Has your question been resolved?
queen ice
its (a+b)^(n-1)
n+1 or n-1?
frosty veldt
^ means "to the power of "right ?
frosty veldt
Ok thank you
cedar kilnBOT
@timber lava Has your question been resolved?
timber lava
<@&286206848099549185>
cedar kilnBOT
@timber lava Has your question been resolved?
tiny fjord
Q53
gritty flare
A fabric when washed: "Its length shrinks by
1/3, and it stretches; its width; in 1/5. How many
meters should be purchased? For after
washed, 240 m2 is available. Knowing that the
original width is 60m.
a) 6m b) 15m c) 5m d) 10m e) 20m
tiny fjord
Sorry I’m using this channel
Please use another channel to ask
<@&286206848099549185>
woeful isle
Q53
Start with this
Assume angle BAC to be some Alpha
And angle OAC will be 90- alpha
tiny fjord
Is the altitude of the bottom the midpoint of AC?
woeful isle
Is the altitude of the bottom the midpoint of AC?
Yes
Cos (90-aplha) = ((4400)^1/2)/2/r
woeful isle
woeful isle
noble fiber
||30^2+(50-x)^2=x^2
⇔x^2-(50-x)^2=30^2
⇔(50-x+x)(2x-50)=900
⇔2x-50=90/5=18
⇔2x=68
∴x=34,B||
woeful isle
Equate
noble fiber
30²+50²=900+2500=3400
tiny fjord
Digesting
tiny fjord
Oh so you need to cos again
Ok I understand two methods
Thank Q guys
Have a good day
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
surreal girder
this might not be worded correctly or i am very stupid but i dont understand what my prof is sayinng rn
surreal girder
is there a point 0,2000 in the equation
why would t= 0 but also be 2000?
if t is the time
dire geode
P(0) = population in year 2000
cedar bluff
You could see t as the amount of years that has passed since 2000
surreal girder
oh so 2000 dosent matter in the quation its just lore
dire geode
yes
surreal girder
ok i think i get it
thank you
sorry for askinng here but i used up all my chat gpts and test tmrw
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
spiral cairn
i just wanna check if i understand this right. If im wrong tell me why, if im right tell me if there is anything else i should know
3
Σ 6
1
rare vault
this is not a question
rare vault
this doesn't make any sense. Your "math" looks like $\sum_{1}^36$ which is an expression not an equation. it has no concept of trueness
wraith daggerBOT
spiral cairn
this doesn't make any sense. Your "math" looks like $\sum_{1}^36$ which is an ex...
let me specify, i want to check if its a correct use of the greek letter "sigma" me teacher told me that its the (number below + number above + every number between)
so
3
Σ 6
1
would be (1+2+3=6)
rare vault
ah, it's close but not quite. you still need the equal sign. the correct form is $\sum_{n=1}^{3}n=6$, which reads "the sum from n=1 to 3 of n is six"
wraith daggerBOT
spiral cairn
so the use of SIGMA is correct but im just missing the equal sign?
rare vault
the stuff below is where you "start", the stuff above is where you "end" and the stuff next to the sum/sigma is what you are adding each time
rare vault
so the use of SIGMA is correct but im just missing the equal sign?
no, you need the variable as I did
spiral cairn
oh so
3
Σ n =6
n=1
rare vault
yes, that's correct
spiral cairn
thank you
rare vault
as a test, what's $\sum_{n=2}^{4} (n+1)$?
wraith daggerBOT
rare vault
very close
rare vault
it means that instead of adding just the number n, we are adding one more than that (n+1)
so it's (2+1)+(3+1)+(4+1)
rare vault
yes it is 12
spiral cairn
ooooohhh
rare vault
would you like another to try?
spiral cairn
and if it was (n+2) it would be (2+2) (3+2) (4+2)
spiral cairn
would you like another to try?
yes
rare vault
$\sum_{q=3}^{6} (2q-1)$
spiral cairn
alright give me a moment
wraith daggerBOT
spiral cairn
2q would mean (2 * q) and (q=3) would mean (q=(3 * 2)) so its ((3 * 2)-1) ((4 * 2)-1) and so on
rare vault
yes
spiral cairn
alright, thank you very much i think i get it now
rare vault
also, I used q here, but in general people almost always use n or i
spiral cairn
imma take some notes so i dont forget this, thank you very much for helping me
rare vault
so use one of those, but know that any are possible
rare vault
2q would mean (2 * q) and (q=3) would mean (q=(3 * 2)) so its ((3 * 2)-1) ((4 * ...
specifically it's 5+7+9+11 = 32
spiral cairn
do i always have to use variables? or can i dumb it down to just
3
Σ 6
1
wraith daggerBOT
spiral cairn
ooohhh
rare vault
but you should use the variable for clarity
spiral cairn
ok ok got it
rare vault
the sigma also has a bunch of other possible notation but you won't see it for long enough that you shouldn't learn it now
the basic variable iteration is the one you want
spiral cairn
i know it can be a synonym for sum, like in excel
rare vault
yes it basically means "sum from n = lower bound to upper bound of inside stuff"
it always means sum, there's just different ways to use it sometimes
spiral cairn
you have been very helpful, thank you again
elder echo
A 60 mg liquid has 1/3 of its potency after 15 months what is the rate of decay rounded to the nearest tenth.
is the equation for this problem 20= 60(b)^15
divide by 60
1/3=b^15
15th root
making the rate of change (nearest tenth) 7.1%?
prime sparrow
12
hard thistle
A 60 mg liquid has 1/3 of its potency after 15 months what is the rate of decay ...
Log
hard thistle
Is my answer correct
Yes it is correct
elder echo
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
quick flume
cedar kilnBOT
dire geode
,w plot cos(2(x-pi/4)) + 2 for 0 < x < 2pi
wraith daggerBOT
cedar kilnBOT
@quick flume Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
spice canopy
The problem i am solving is to simplify this :
cedar kilnBOT
The problem i am solving is to simplify this :
dire geode
cancel one power of a+b
spice canopy
Okay so the above will just be : b * (a+b)?
dire geode
if by above you mean numerator yes
spice canopy
exactly, im from Sweden so i dont know what its called in english unfortunately
So how will that affect the equation on the bottom? It should affect it right?
4a in the bottom?
by removing 1b from each side and a from the left
acoustic portal
cedar kilnBOT
acoustic portal
I have A_2 = (0,2) U (16, infinity)
and claim that the inf(A2) is 0 and sup(A2) is infinity
Im not sure how to go about proving that inf(A2) is 0
cedar kilnBOT
@acoustic portal Has your question been resolved?
acoustic portal
I understand to prove that the A2 isnt bounded from above I can take some real value and suppose that it is a bound
by the archimedian property, there exists some integer n that is in A2 that is greater than this value
but I do not know how to prove the inf
I have started with supposing that there exists some value alpha which is real and is greater than 0 such that alpha is a lower bound
grand shale
Im not sure how to go about proving that inf(A2) is 0
assume its not
acoustic portal
assume its not
yeah I have contradicted the statement
grand shale
then ur done?
grand shale
how am I done sorry
inf => greatest lower bound
assume theres a bound greater than 0
and u contradicted the satatement
u proved 0 is a LB
and there is no lower bound greater than 0
this implies 0 is inf
acoustic portal
yeah but 0 isnt a part of the set
grand shale
so?
acoustic portal
dont we want some element in the set thats less than this new value to show that this new value isnt a bound?
grand shale
does it say that you find a infimum IN the set?
it doesnt
infimum can be outside the set
acoustic portal
well no but I thought to show a value isnt a bound we find some value in the set that is less than it
acoustic portal
well no but I thought to show a value isnt a bound we find some value in the set...
I do understand that and thank you for helping but I thought it was this?
cedar kilnBOT
safe dragon
Was 15 done incorrectly
cedar kilnBOT
Available help channel!
cedar kilnBOT
soft lark
Okay my writing is message asf
But I'll let you see what I started by doing
So I added LCD to the top to make it so I can cancel the denominator
Then I get this
But wtf I do here
.close
soft lark
cedar kilnBOT
soft lark
3d
Okay what did I do wrong
I factored
Found LCD to make it so I could cross out to get rid of denominator
And now I have (x^2+x+2)(x-1) as my first thing, this would foil and create x^3 and a bunch of stuff
soft lark
And ik at my level these questions aren't suppost to have cubed
soft lark
and hard to readf
Bro I can't fix that srry
plucky magnet
I understand everything
aight death note pfp
soft lark
Can someone just help man
hard thistle
if i could read it...
plucky magnet
if i could read it...
same
hard thistle
well i can its just timeconsuminger
soft lark
if i could read it...
Bro which part can't you read
hard thistle
ill read it ig but itll be nonchalant
plucky magnet
<@1210477727828934668> <@885323755700777050> rewrote it slow asf so it's neat as...
wait what do you need help with again
hard thistle
you are doing d right
plucky magnet
I wrote it up there
notice how if you expand the stuff on the right and left
the x^3 terms cancel out
hard thistle
lol it ends up as 3
soft lark
Okay
soft lark
lol it ends up as 3
I'll let you know if I have other issues
hard thistle
horrifying amounts of factoring in this one lol
cedar kilnBOT
@soft lark Has your question been resolved?
void dew
uhh, I wanna get into "Infinite set theory" I also am dumb as hell, not a fast learner, and don't know much
cedar kilnBOT
uhh, I wanna get into "Infinite set theory" I also am dumb as hell, not a fast l...
@void dew Has your question been resolved?
cedar kilnBOT
@void dew Has your question been resolved?
cedar kilnBOT
@void dew Has your question been resolved?
rancid prairie
How would I do this problem?
cedar kilnBOT
How would I do this problem?
rancid prairie
This is my work so far
dusk goblet
well
for block b
we have T = mbg
and block a
we have T = fs
= mus Fn = mus mag
it seems like you don’t have any numbers
dusk goblet
we have T = mbg
so id just use ^
rancid prairie
we have T = fs
why would block a have this?
dusk goblet
why would block a have this?
two horizontal forces for block A
rancid prairie
2?
dusk goblet
tension to the right, and friction to the left
dusk goblet
what does fs stand for then?
static friction
i just didn’t feel like typing it with latex sorry
rancid prairie
okok
Wait so I'm lot
wouldn't the equation be Fs = Fn (Mu) ?
This is what I got
I’m so lost 😭
@dusk goblet
wraith daggerBOT
knief
rancid prairie
Okok I got it
So the magnitude is mbg since the objects are at rest it makes that force the only active force
dusk goblet
So the magnitude is mbg since the objects are at rest it makes that force the on...
wdym
yes mbg
i thought you said mag
my fault
rancid prairie
ur good haha
dusk goblet
So the magnitude is mbg since the objects are at rest it makes that force the on...
yes those are the only two forces acting on B which is at rest so they must be equal in magnitude
as per newtons sexond law
a = 0
hence F_net = 0
cedar kilnBOT
@rancid prairie Has your question been resolved?
cedar kilnBOT
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Available help channel!
nova stag
hello can i ask my question here?
cedar kilnBOT
hello can i ask my question here?
solid juniper
yep
nova stag
the answer to the first question is 1.45. i need the answer for second question
steady pivot
solid juniper
cedar kilnBOT
@nova stag Has your question been resolved?
nova stag
the answer to the first question is 1.45. i need the answer for second question
heyo <@&286206848099549185>
cedar kilnBOT
@nova stag Has your question been resolved?
nova stag
...
cedar kilnBOT
@nova stag Has your question been resolved?
proven jacinth
i need help with laplace transform 🥲
cedar kilnBOT
i need help with laplace transform 🥲
proven jacinth
anyone ?
slate lintel
might help if you were more specific and followed the guidelines given to you in the green message above
cedar kilnBOT
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cedar kilnBOT
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fading garden
I would end up with 2 triple integrals for the total mass.
One with bounds 0<p<R. arccos(-h/R)<φ<arccos(h/R). 0<θ<2pi.
The second with bounds 0<p<R. arccos(h/R)<φ<pi/2. 0<θ<2pi.
cedar kilnBOT
I would end up with 2 triple integrals for the total mass.
One with bounds 0<p<R...
@fading garden Has your question been resolved?
nova stag
.reopen
fading garden
Or are these bounds just wrong?
cedar kilnBOT
@fading garden Has your question been resolved?
fading garden
I would end up with 2 triple integrals for the total mass.
One with bounds 0<p<R...
should they instead be:
One with bounds 0<p<R. arccos(-h/R)<φ<pi. 0<θ<2pi?
The second with bounds 0<p<R. 0<φ<arccos(-h/R). 0<θ<2pi?
cedar kilnBOT
@fading garden Has your question been resolved?
mortal grove
should they instead be:
One with bounds 0<p<R. arccos(-h/R)<φ<pi. 0<θ<2pi?
The ...
where are you getting -h/R?
you should have cos(phi) = h/R
otherwise that's mostly correct, just realize that doesn't account for the entire volume of the sphere. you'll need to add the volume of a cone to "fill in" the rest of the sphere up to a height of h
fading garden
I got -h/R because its -R<z<h
fading garden
otherwise that's mostly correct, just realize that doesn't account for the entir...
dont the two triple integrals i gave combined make a sphere?
mortal grove
dont the two triple integrals i gave combined make a sphere?
yes, but the density depends on the height of the sphere, not phi
mortal grove
I got -h/R because its -R<z<h
phi starts at the top of the sphere. if you calculate cos(phi), you should get h/R
fading garden
hm
i thought phi started from the center?
so how would I fix my bounds then?
or is it not something that can be solved by changing the bounds?
mortal grove
so how would I fix my bounds then?
your bounds are all fine except for phi
for the top part, you should have 0 < phi < arccos(h/R)
for the bottom, you should have arccos(h/R) < phi < pi
then account for the cone missing and you're fine, it'll be a pain though
fading garden
I still don’t really understand the missing cone thing
fading garden
your bounds are all fine except for phi
for the top part, you should have 0 < p...
When I try and graph this, the graph doesn’t exist
Oh wait
Yes it does
mortal grove
I still don’t really understand the missing cone thing
when you do phi from 0 to arccos(h/R), you're getting a region like this blue one here
but you want the region above that dark blue line
fading garden
when you do phi from 0 to arccos(h/R), you're getting a region like this blue on...
So how do we handle that then?
Oh wait hang on
It’s a cone
I think I’ve done a similar problem earlier
fading garden
So. Am I gonna need to make 2 more triple integrals? Or could I maybe integrate some kind of function to make this correct?
fading garden
I think I’ve done a similar problem earlier
no no i have not
fading garden
ok yeah i dunno how to do this lol
can i get a hand with this <@&286206848099549185>?
fading garden
at this point, im honestly not certain that the cone can be gotten in spherical coordinates
dreamy void
at this point, im honestly not certain that the cone can be gotten in spherical ...
use polar
dreamy void
it's like stacking up discs with increasing radius but as radius increases so does the z component too
linearly
wraith daggerBOT
bacc (unhelpful)
dreamy void
when you do phi from 0 to arccos(h/R), you're getting a region like this blue on...
the purple length is h-r and then use pythagoras and solve for r to find the upper bound
fading garden
the purple length is h-r and then use pythagoras and solve for r to find the upp...
purple?
dreamy void
d
fading garden
oh that
mortal grove
you don't need spherical coords to find the volume of the cone, just use the fact that the volume of a cone is
(1/3)pir^2*h, where h is the height of the cone and r is the radius of the base
fading garden
you don't need spherical coords to find the volume of the cone, just use the fac...
wouldnt that mess up the center of mass calculation though?
mortal grove
it shouldn't mess anything up, you can find the center of mass of the cone and the center of mass of the stuff with spherical coords
then average them and you'll get the correct center of mass
now that i think about it actually, you don't even need 3 dimensions 🤔
since z is the only thing that matters, you should just be able to project the entire problem onto a plane
fading garden
but if the cone isnt in spherical coords, how would i get the center of mass using spherical coords?
or are you just telling me to solve the triple integrals i have right now, add them up, and then divide by the total mass?
or would i take that formula you gave me, and plug in the spherical coordinate equivalent of z for h, and (x^2+y^2) for r^2?
that feels wrong
actually yeah that doesnt work
mortal grove
I would simplify this to the plane to make your life way easier
and use polar coordinates instead
it'll be 10x easier computationally
fading garden
how would i do that then?
fading garden
how though lmao
i dont think i understand what you mean when you say that i can do it in polar coordinates on a plane
fading garden
Well i came up with an idea for an integral for the cone in spherical coordinates. But it’ll be absolutely awful to solve so I’d rather not if I can help it
And that’s assuming it even actually is the cone
Ok yeah, that’s absolutely disgusting
Anyway, the bounds I came up with for it are:
0<p<hsec(φ). 0<φ<arccos(h/R). 0<θ<2pi.
I’ll try and graph it if I can, and see if it is the cone
And not just some goofy shape
yeah actually, that looks like a cone
still dont want to integrate it though
fading garden
after all that mess. i ended up with my center of mass being 0 for x, 0 for y
(no i didnt actually calculate this, i just knew it was 0 becasue symmetry)
and as for my z coordinate i got this beautiful equation:
cedar kilnBOT
@fading garden Has your question been resolved?
carmine bronze
Fairly sure the regions should look like this.
cedar kilnBOT
@fading garden Has your question been resolved?
jovial marlin
Woah
cedar kilnBOT
cedar kilnBOT
Available help channel!
gleaming falcon
gleaming falcon
am I typing it wrong?
or is it just wrong
I dont belive I did anything incorrectly
help me someone please
steep atlas
astral smelt
given that that line actually hits 15 at 9, then it seems right
gleaming falcon
but for those 2 it didn't
gleaming falcon
given that that line actually hits 15 at 9, then it seems right
yeah but
It doesn't check
as if I type it wrong
or in a incorrect form
<@&286206848099549185>
mossy cloud
look
when the curves goes 5 to the right
how much does it go down
@gleaming falcon
astral smelt
Right yeah the arrow doesn't hit 15 at 9
idle crystal
when the curves goes 5 to the right
(in the original image it was 4.5 to the right) i think
mossy cloud
when the curves goes 5 to the right
how much does it go down
astral smelt
Just look at the intercept at x=5 instead and it should work'
mossy cloud
when the curves goes 5 to the right
how much does it go down
gleaming falcon
uhh
gleaming falcon
np
mossy cloud
the slope is -1/5
learn your goddamn formulas if you dont understand why the slope is -1/5
gleaming falcon
I just made this phonk
mossy cloud
this explains it well
mossy cloud
I just made this phonk
you should focus on your math instead of killing my ears
normal cipher
I just made this phonk
what.
gleaming falcon
headphone warning ngl
normal cipher
ouch my ears
gleaming falcon
you should focus on your math instead of killing my ears
my bad
I forgot to type it
gleaming falcon
you should focus on your math instead of killing my ears
sorry
normal cipher
eek
gleaming falcon
b is the y intercept
gleaming falcon
ok i'll give you a question
bet
normal cipher
find the slope at (4,16) of the equation y = x^2
gleaming falcon
8
normal cipher
ok
gleaming falcon
nice slope
mossy cloud
nice slope
answer my question
gleaming falcon
It's easy
mossy cloud
read this
gleaming falcon
but I forget it right after
mossy cloud
death quit
mossy cloud
I am currently
well focus on it
close discord
and read it and UNDERSTAND it
dont just read
mossy cloud
the one I'm solving?
yes
normal cipher
bro what is your teaching method
astral smelt
Proof by intimidation
normal cipher
😂
mossy cloud
Proof by intimidation
blud said the slope was -2 💀💀
astral smelt
I mean i did misread the arrow, but incase it actually hit y=15, at x= 9 then the slope would've been -2/3
gleaming falcon
MUHAHAAHAHAA
I AM
THE MAIN CHARACTER
HAHAHAHAHAHHAAHA
RYOIKI TENKAI
graphs are ez bro
cedar kilnBOT
@gleaming falcon Has your question been resolved?
gleaming falcon
no
crimson sedge
Just need someone to quickly look over, see if this makes sense
crimson sedge
Wait let me rotate
normal cipher
,rccw
wraith daggerBOT
crimson sedge
Ooo thank you
normal cipher
sry i cant solve question tho 😭
crimson sedge
Lolol that’s fine
void sage
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
solemn quail
You just said that y was in the image of A minus image of C
you don't need to repeat it
you might put 4 or 5 words to justify why x is not in C
but it's probably fine either way
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
ah, okay, thankyou, ill make those edits
alpine gulch
if there is a correlation between A and B, and also a correlation between B and C, can i say there is a correlation between A and C^
mental trail
if there is a correlation between A and B, and also a correlation between B and ...
what are A,B,C? Random variables? events? and what is the def of correlation?
alpine gulch
im not the best with terminology, but it would be like saying screen time (A) affects sleeping (B), and (B) affects memorization (C)
i guess causation would be more appropriate, not correlation
mental trail
so you mean transitivity of causation
if A implies B (everytime) and B implies C (everytime), then A implies C (everytime)
that statement is true
however there is no transitivity of correlation
alpine gulch
right that makes sense
i know this may be less mathemtical and weird to say, but if you replace (everytime) with (sometimes), would it still work?
obtuse mango
if there is a correlation between A and B, and also a correlation between B and ...
in maths u'll often be able to find monstrous counterexamples to statements that you think are true
mental trail
no, that's literally becoming correlation
mental trail
i know this may be less mathemtical and weird to say, but if you replace (everyt...
if for example A implies B half of the time and B implies C half of the time
It might be that A implies C 75% of the time
or that A implies C half of the time
obtuse mango
if there is a correlation between A and B, and also a correlation between B and ...
but i think if ur talking more abt real like, then i think it generally is true that if there's some vague correlation between A & B and there's some correlation between B&C, then there'll be "some correlation" between A&C
mental trail
or that A implies C 25% of the time
alpine gulch
no, that's literally becoming correlation
oh i see, i didn't view it like that
alpine gulch
but i think if ur talking more abt real like, then i think it generally is true ...
yes exactly
ok i'm satisfied, thanks both of you for the help
mental trail
but i think if ur talking more abt real like, then i think it generally is true ...
not sure
like for example take X and Y independent variables
then X and X+Y will have some correlation
since whenever X changes, the X part of X+Y changes too
X+Y and Y have some correlation the same way
but do X and Y have any correlation?
obtuse mango
not sure
i mean i was thinking more like strictly IRL like the example he gave or like "climate change is causing the sea level to rise" and "climate change is causing more natural disasters" therefore there's some loose correlation between the sea level and natural disasters
mental trail
i mean i was thinking more like strictly IRL like the example he gave or like "c...
again that's not applicable
obtuse mango
ofc u can construct mathematical examples but i feel like unless you're doing something maths-related, u'll never randomly encounter independent r.v.s X&Y in the wild
twilit escarp
Chocolate makes ppl smart
mental trail
do cats relate to bubble bath makers?
obtuse mango
do cats relate to bubble bath makers?
nah but it could be like correlated cus u have money
like if u bought stuff, that implies you have money etc.
mental trail
?
I don't follow you anymore
what does correlation mean to you?
because if in your head it means "caused by a similar thing" then no
obtuse mango
like those events follow similar trends basically
anyway yeah this discussion isn't really mathematical
mental trail
like those events follow similar trends basically
do cats and bubble bath makers follow similar trends?
I know I'm putting the conversation to the extreme
but correlation of A and B + correlation of B and C doesn't mean correlation of A and C in the MAJORITY of cases
mathematically or IRL
obtuse mango
do cats and bubble bath makers follow similar trends?
well as in like there's like some loose connection but like i feel like if someone's asking about XYZ irl-y then they're probably thinking of stuff like "CO2 emmisions correlate to sea level rising" etc.
mental trail
well as in like there's like some *loose* connection but like i feel like if som...
in that case isn't there a loose connection between literally everything?
then what's the point of talking about correlation
obtuse mango
do cats and bubble bath makers follow similar trends?
but like i mentioned above you could think of it as if someone's got enough money to take care of a cat, then they'll also probably have enough money to buy a bubble bath maker cus that's not smth ppl normally buy
obtuse mango
in that case isn't there a loose connection between literally everything?
yh true
alpine gulch
.close
cobalt scarab
Why doesn’t this work?
cedar kilnBOT
Why doesn’t this work?
cobalt scarab
It’s when the derivative it 0 and the graph changes from going downwards to going upwards and vice veranda
Verse
twilit escarp
It’s when the derivative it 0 and the graph changes from going downwards to goin...
Second derivative*
cobalt scarab
How do I see the second derivative on the graph
twilit escarp
When the tangent goes from bottom to top of function and vice versa
You have inflexion point
cobalt scarab
What does that look like
twilit escarp
When it goes from concave up to concave down
cobalt scarab
Isn’t it just when the line is flat
twilit escarp
Isn’t it just when the line is flat
Nah this is a local extrema
Take example on x²
It has a flat line in 0,0
cobalt scarab
I know how to do with with the numbers
twilit escarp
But no inflexion point
cobalt scarab
I don’t know how to do it when it’s a graph
twilit escarp
Click and see a point where, before, the line is under/above the curve and after the line is above/under the curve
twilit escarp
Changes what ?
cobalt scarab
From going down to going up
twilit escarp
From going down to going up
This is a local extremum, not an inflexion point
twilit escarp
But you have to check the line derivative
cobalt scarab
I thought it starts on the maximum minimum points
That’s how it with when it’s in interval notation
twilit escarp
Not neccessarly
cobalt scarab
(-inf,5) for example
5 would be the maxima/minima
Then the graph would change direction
That’s how it’s been so far at least
twilit escarp
(-inf,5) for example
You talking about range right ?
twilit escarp
But extremum are using simple derivatives here we need the second one
cobalt scarab
It still worked when I did it with the second one
I just used the third derivative to calculate
I just don’t know what to do when it’s a graph
No idea where to put the point
cedar kilnBOT
@cobalt scarab Has your question been resolved?
clear laurel
Hello! Im stuck on what to do with this, i feel like i dont have the complete information or something. I know once i figure out how to do the first angle everything else will come after. Also ive looked at trajectory calculators to see if im doing the right work and my answer always differ especially for time. im just stuck here
The first image is the problem and second is the work ive done so far(ive undone alot of work bc i was on the wrong track )
cedar kilnBOT
@clear laurel Has your question been resolved?
clear laurel
<@&286206848099549185>
near snow
It’s physics
But anyways
Do you know 1-D kinematics?
Because a projectile motion is just 2 independent motions across different axes
It’s a combinations of two linear motions which doesn’t affect each other.
There is no acceleration across x-axis, so the horizontal velocity moves with a constant velocity.
$a_x = 0$
$v_x(t) = V_x$
$x(t) = X + V_x t$
wraith daggerBOT
timuko
near snow
On the other hand, there is a constant acceleration across y-axis of $-g$. Now, let’s use the formulas for the movement with constant acceleration.
wraith daggerBOT
timuko
near snow
\begin{align*}
a_y &= -g\
v_y(t) &= V_y - gt \
y(t) &= Y + V_y t - \frac{1}{2}gt^2
\end{align*}
wraith daggerBOT
timuko
near snow
Now express velocities $V_x$ and $V_y$ in terms of the initial velocity $v_0$ and the launch angle $\theta$
wraith daggerBOT
timuko
cedar kilnBOT
@clear laurel Has your question been resolved?
clear laurel
Because a projectile motion is just 2 independent motions across different axes
Im just confused on how time plays into this too because im used to position time graphs, is time the x?
clear laurel
And how ever i do time i end up getting different answers than before
How am i supposed to get 5 points of one line if i dont know how to get the slope too
Im sorry for the follow ups 😞
A more specific question i have is what variable should i try to find first? Distance, time, or something else?
digital cliff
the two functions are x(t) and y(t)
so one point would be ( x(0), y(0) )
another could be ( x(7), y(7) )
etc
you would first want to find the functions x(t, theta) and y(t, theta)
clear laurel
Theta is the angle correct which in this case the velocity for x and y ?
So i have to find their positons at certain times in the x and y or am i not getting it
Like id find the time for the projectiles entire path and use formulas to find their position at other times
fringe mauve
do u want to do this the mathw ay or the phys way
clear laurel
Im not sure the difference sorry
fringe mauve
also ur assuming for air res right
clear laurel
No resistence
fringe mauve
Im not sure the difference sorry
the onyl difference is that u derive the kinematic formula from scratch
if ht e math way before using htem
it helps a bit with understanding how they work
or i can just give htem to u
and u can use tem
fringe mauve
aight calm
so u have ur intival speed
well call U = 40
and ur differnet angles
and u just need to plot the cruve
of their projectile right?
clear laurel
Yup
clear laurel
Yes
fringe mauve
ok so since there is not air res
ax = o
so ur fromulas are this
X(t) = 40cos(theta)t
fringe mauve
**timuko**
.
yt is given here
but where assuming the projectile starts from (0,0)
so that big capital y is also 0
clear laurel
Mhm
But if both x and t are unknown in that formula id use a diff one to get one of the variables right? Or do i have x
clear laurel
Ohhh like f(x)