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cold crow
help
glossy valveBOT
knief
lime ether
yes that works
in general do the first term + (n-1)d where d is the difference so here that becomes 7 + (n-1)(6) = 6n + 1
cold crow
in general do the first term + (n-1)d where d is the difference so here that bec...
o yea
y know for this one
do you just sub the -58 into the n
i havent revised maths in a long time
lime ether
do you just sub the -58 into the n
no you’d set -58 = 8 - 6n and see if this returns an integer value for n (positive integer of course and maybe you include 0)
cold crow
so u find n on its own?
lime ether
i don’t know what that means
cold crow
cold crow
no you’d set -58 = 8 - 6n and see if this returns an integer value for n (positi...
is that wht u trying to do here
yea i got 11
lime ether
if it returns an positive integer value then it’s in the sequence
lime ether
yea i got 11
then it’s the 11th term
cold crow
oh ok
lime ether
2, -4, -10, -16, -22, -28, -34, -40, -46, -52, -58
if we start at n = 1 being 2
i guess if we start with 8 then it’s the 12th term
lime ether
what did you do so far
lime ether
no ideas?
lime ether
yes you need to find the area of his garden
then find out how many bags you need to cover the entire garden
then multiply it by the cost per bag
lime ether
it’s a quarter of a circle
lime ether
mhm
cold crow
38.48451
lime ether
what is that area for?
cold crow
afo
lime ether
you can’t just throw numbers out
cold crow
i did pi x 7^2 /4
lime ether
,w (pi)(49)/4
glossy valveBOT
lime ether
yes that’s a good idea
lime ether
yes just leave it as 49pi/4
lime ether
yep
cold crow
i got 99m^2
lime ether
what’s the formula for the area of a triangle?
lime ether
now add em all up
cold crow
what i added now is the total area no?
lime ether
what i added now is the total area no?
yes
lime ether
so would u divide it by 14
yes
glossy valveBOT
glossy valveBOT
Result:
186.15
17x10.95
lime ether
nice
cold crow
that is a pretty decent 5 marker tbh
could you explain this one?
i believe its something about sohcahtoa?
.close
tulip abyss
Decide a and b so f is continually and Differentiable in x =2
tulip abyss
think its translated differentiable.
no
the pic is wrong holdon
its supposed to be ax^2 + b , x>2
not 1x^2 + 1
hoary wyvern
Alright
tulip abyss
ok so ik i have to find the limits from both 2- and 2+ first but then im stuck.
hoary wyvern
Oh great you know it
Where you get stuck?
tulip abyss
so basically ik i have to find the limits first but idk where to go after
if that makes sense
hoary wyvern
You need to solve it then lol
You mean you have less equations then the unknowns?
tulip abyss
the limits so ik its continuing but idk about the Differentiable part
hoary wyvern
the limits so ik its continuing but idk about the Differentiable part
Just differentiate both of them and then limit them to x=2
You will get the second equation
keen moth
can you write down what those limits should be for this specific function to be continuos at x=2?
tulip abyss
okok give me a sec. ill grab my phone to take a pic
keen moth
sure
tulip abyss
my phone was dead i had to take the pic w my laptop sorry
idk what to do after this.
the task itself is this but its in norwegian i tried to translate it over
Decide a and b so f is continually and Differentiable in x =2
keen moth
a bit..
tulip abyss
hjelp meg.
keen moth
i can't actually see whats in here
tulip abyss
that e^1/2 *2 = e
like when i replaced the x with 2
i'm genuinly royally screwed for my exam on friday
keen moth
hmm, for continuity what do we need to compared this right-hand limit to? what the other limit do we need to consider, and what should they be equal to for the function to be continuity at x=2?
keen moth
super close
keen moth
you're right that for continuity, we need to equate the limits
you've correctly calculated the right-hand limit as 4a + b
keen moth
yes
so back to the limits for continuity
You've got the right-hand limit
lim (x-> 2+) f(x) = 4a + b
now what about the left-hand limit
tulip abyss
THE E
EULERS NU;BER
e
the natural logarhythm number e.
ok im sorry im slow and it's probably annoying to help me
keen moth
haha no worries
tulip abyss
ok lim (x->2-) f(x) = e
and lim(x->2+) f(x) = 4a + b
and these needs to be fulfilled for the continuicy part now how do decide what a and b is so that f is differanntial in x =2
keen moth
ok lim (x->2-) f(x) = e
and lim(x->2+) f(x) = 4a + b
and these needs to be fulf...
almost there, but be a tiny bit more precise
tulip abyss
that is as precise it gets.
keen moth
when x approaches 2 from the left, we are using the function e^(½x) so we need to plug in x=2 into e^(½x) to get the left-hand limit
tulip abyss
I DID
keen moth
what do you get when you substitute x = 2 into e^(½x)? it's not just 'e'... it's 'e' raised some power
keen moth
you are absolutely right
my apologies
i might have been a little unclear in my previous hint
sorry about that
tulip abyss
no worries
am i allowed to swear in here or no cs im so fucking lost no idea what to do now
keen moth
am i allowed to swear in here or no cs im so fucking lost no idea what to do now
haha, it's okay to vent a little
keen moth
sure
just like continuity required the limits from both sides to match, differentiability requires the derivatives from both sides to match at x=2
think about it: for the function to be "smooth" (differentiable) at x=2, the slopes of the two pieces of the function must also connect smoothly at that point
and the slope is given by the derivative
keen moth
let me see
tulip abyss
a = (1/8) e and b= (1/2) e
i regret taking advanced maht
im not even onna educate myself into smt that needs math.
tulip abyss
how so
i am not wrong. refuse to believe that
i found a and put it in there basically
(1/8)e *4 + b = e
seperated b
and found B.
earlier after finding the limits it gave:
e = 4a + b
i put in a
e = 4* (1/8) e + b
then swapped e with b
- b = 4*1/8 e - e
got
-b = 4/8 e - e
then multiplied with -(1) on both sides
WHAT DO U MEANNN
keen moth
tulip abyss
no
Youre wrong.
i'm about to math your ass holdon.
Im gonna prove my point and stand my ground youre not taking this win from me.
give me 5 mins and i will show you.
keen moth
brukeren antok a = 1/8e basert på en feil i derivasjonsformelen den korrekte verdien for a er negativ, og b følger derav
tulip abyss
hør her gi meg 5 min og jeg skal bevise at det jeg har gjort er riktig. punktum finale.
i want more opinions on this.
tulip abyss
thank u for ur patience
keen moth
tulip abyss
are u ready for this.
keen moth
...
keen moth
hm.
tulip abyss
No
tulip abyss
Youre not hming me i KNOW IM RIGHT
keen moth
i'm gonna SHOW YOU
tulip abyss
and ur NOT taking this WIN FROM ME
I ALREADY SHOWED U
EVERYTHING IS SHOWN
YOU CANT GO MORE IN DEPHT ON IT
is it appropirate to ask u what youre taking your degree in.
graduating from
ping me when youve returned to face your defeat.
idk abt u but this debate has been going on for over an hour
tulip abyss
no.
i dont trust these ai generated ass math explainations
YOU explain it to me. U prove me wrong
gritty rose
i dont trust these ai generated ass math explainations
hard to follow the whole conversation, but if you want to start over and ignore him, just open a new channel with the original image and your work so someone who doesn't speak your language can help
tulip abyss
no i know im right.
tulip abyss
i did this shit on a pc program earlier today
keen moth
continuity you got this part
gritty rose
no i know im right.
then close?
tulip abyss
and why
gritty rose
because you said you're right so done with your question?
keen moth
4a + b = e
a = -1/8e
4 * (-1/8)e + b = e
(4/8)e + b = e
(1/2)e + b = e
add (1/2)e to both sides
b = e +(1/2)e = (1 + 1/2e) = (3/2)e
tulip abyss
shouldnt one of those thigs go negative when u swap sides of the =
keen moth
let's start again
tulip abyss
ohmydays
keen moth
tulip abyss
ok idc atp did this stuff on a pc program earlier w the teachre and got what i got.
keen moth
the right-hnd limit as x pproaches 2
lim x -> 2 f(x) = a * 2² + b = 4a + b
these limits must be equal
4a + b = e
tulip abyss
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dapper lynx
True or False:
The median in a categorical frequency table is the same as the average.
dapper lynx
It´s false right?
nimble crane
I'm inclined to agree
dapper lynx
I'm inclined to agree
with me?
nimble crane
yes
dapper lynx
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safe trench
What was the original question even
It's confusing
Did they ask for in general or your specific example?
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@dapper lynx Has your question been resolved?
rapid rain
im getting the same...
The median is not always the same as the average
they can be equal
but they're definitely not always equal
for example
dapper lynx
but in this case?
rapid rain
median vs average of : 1 2 4
rapid rain
but in this case?
in some cases you can have them be equal
dapper lynx
but in this
rapid rain
"The median in a categorical frequency table is the same as the average"
in that statement
it's asked whether it's true for ANY (every) categorical frequency table
the answer is: false, it's not true for every frequency table
rapid rain
here, in THIS table, yes, they are equal
rapid rain
median vs average of : 1 2 4
doesn't mean it's true for every table
dapper lynx
here, in THIS table, yes, they are equal
Can you give me a formula for median for frequency table?
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unreal cliff
HOW DO YOU FACTOR THIS IM TWEAKING
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HOW DO YOU FACTOR THIS IM TWEAKING
next sail
HOW DO YOU FACTOR THIS IM TWEAKING
factor theorem
unreal cliff
factor theorem
what is that !!!!!
next sail
look it up
unreal cliff
dawg i just did
we never learned that in class
yet this is a practice problem for my midterm tomorrow
hot lily
This problem is cruel 😦
sudden condor
Fr
hot lily
,w complex roots of a polynomial
glossy valveBOT
charred scarab
Isn't that just algebra theory or whatever it's called
hot lily
Where did 1 - 5x + x^3 come from
sudden condor
,w complex roots of a polynomial
It’s says factors doesn’t want sols
charred scarab
Group them, get GCF, and then do the rest of the theory right?
hot lily
It’s says factors doesn’t want sols
Have you ever dealt with complex roots before
sudden condor
Have you ever dealt with complex roots before
Yea
hot lily
Have you ever dealt with complex roots before
@unreal cliff
unreal cliff
Have you ever dealt with complex roots before
no idk
unreal cliff
Well only way is grouping
how do you group something with 5 terms
sudden condor
how do you group something with 5 terms
it’s quartic can be grouped to 2 quadratic trinomials
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unreal cliff
Then the problem likely has a typo
how do you do this guys
hot lily
how do you do this guys
Expand, combine like terms just like normal
unreal cliff
Expand, combine like terms just like normal
how do i find m(n+p) tho
tropic bridge
I’ve done everything accurately but I have no idea how to get the 2nd time value for 11.4 because its a sinusoidal function so 11.4 has to be reached twice every cycle
tropic bridge
i rotated it for ease sake
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@tropic bridge Has your question been resolved?
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charred geode
how to go from the first line to the second
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how to go from the first line to the second
charred geode
I'm thinking of smth like substituting $z=\sin \theta$ and doing each term separately but how to do it faster?
glossy valveBOT
Hamdy Hisham
torn gust
I'm thinking of smth like substituting $z=\sin \theta$ and doing each term separ...
that integral is the formula for a half-circle
so just like a special case of integral
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@charred geode Has your question been resolved?
modest yoke
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charred geode
that integral is the formula for a half-circle
How ?
umbral dome
what part are you having trouble with?
torn gust
How ?
unit circle is x^2+y^2=1 so y=sqrt(1-x^2)
oh maybe I misread and it's completely different
charred geode
unit circle is x^2+y^2=1 so y=sqrt(1-x^2)
what about the numerator
torn gust
yea nvm it's just the definition for arcsin
charred geode
more like c - d actually
what's the frequency of SHM
charred geode
angular frequency over 2pi
and what's the angular frequency
charred geode
yea nvm it's just the definition for arcsin
yes but what about the numerator
charred geode
if i beat u at a chess game would u tell me
I think we shouldn't give answers here
anyway
charred geode
$\omega_0=\sqrt{\frac{k}{m}}$
glossy valveBOT
Hamdy Hisham
modest yoke
come
charred geode
https://lichess.org/j5kFPQgL
I got banned on lichess and chess.com 7 times
modest yoke
its ok its anon link
charred geode
its ok its anon link
not interested bro
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vocal sonnet
$x^2 + 16y^2 = 16$
Volume about x = 4
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$x^2 + 16y^2 = 16$
Volume about x = 4
glossy valveBOT
smeagol
glossy valveBOT
smeagol
vocal sonnet
,tex Then Area = $\pi r^2 \$
= $\pi (4 - \sqrt{16-y^2})^2$
glossy valveBOT
smeagol
vocal sonnet
Then V = $\pi \int^1_{-1} (4 - \sqrt{16-y^2})^2 dy$
glossy valveBOT
smeagol
vocal sonnet
but this get's me the wrong answer
hollow herald
r = (4 - √(16 - y²)) is AB length, do you see why pi r² would not give you what you're looking for?
note that in the solid thus formed by revolution, B must be in a void space out of the solid, however, when you write your integral, integrating from -1 to 1, it encaptures point B within it
vocal sonnet
r = (4 - √(16 - y²)) is AB length, do you see why pi r² would not give you what ...
am I making the shape like a single sphere or two spheres?
sorry bad sketch
vocal sonnet
note that in the solid thus formed by revolution, B must be in a void space out ...
but I think it shows the difference
hollow herald
r = (4 - √(16 - y²)) is AB length, do you see why pi r² would not give you what ...
It's this. eq 1 is for the sphere x² + 16y² = 16, the other ellipse is just for demonstration when your original ellipse has revolved 180° about x = 4
I'd suggest using this: (2pi)(x)(l) dx
where l is the height of the column
vocal sonnet
r = (4 - √(16 - y²)) is AB length, do you see why pi r² would not give you what ...
so my current radius is too small
hollow herald
no, your current radius accounts for points out of the solid.
vocal sonnet
This is the original question, I'm focusing on the second part right now
hollow herald
Yes I understood you completely
hollow herald
I'd suggest using this: `(2pi)(x)(l) dx`
Try to understand. (√(16 - y²), y) would be point A for some y, and your radius for this point is BA, if you do pi(BA)², you'll have a circle containing B and you're basically doing it for the entirety of the ellipse
however, the solid of revolution will not contain B, so your integral is wrongly set
vocal sonnet
so right now I have the radius being just half the sphere around the point, I need the area of the whole shape being rotate?
hollow herald
"radius being just half the sphere around the point" - what do you mean by that?
Try using the shell method
vocal sonnet
Try using the shell method
I'm not supposed to do shell yet this is before that 🏃
vocal sonnet
"radius being just half the sphere around the point" - what do you mean by that?
so right now I am calculating the area if half the circle spins around, but I need the entire circle going around
sorry I am confused 😅
I want this entire shape around x = 4?
So would solving using this function work?
hollow herald
so right now I am calculating the area if half the circle spins around, but I ne...
No
Right now you're calculating... wait give me a min
hollow herald
No worries
Basically, and this is just a dissection of the solid, you're evaluating the dark red region
Also, the right ellipse is just our ellipse rotated 180°. What I'm trying to show is that you're including volume outside of the solid of revolution
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@vocal sonnet Has your question been resolved?
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@vocal sonnet Has your question been resolved?
hollow herald
@vocal sonnet try (2π)(4π) = 8π² as your answer
It's really only 2π[ int dA ] where dA represents a small area element within your ellipse. You don't need shell or dish washer to write that right?
tranquil plank
undone flint
Can you translate?
undone flint
In english?
Oh I didn't see
hollow herald
b) Similarly as above, draw the line x = y, you're interested in the region above that line within the circle - again, your probability would then be (Area of desired region)[f(..) = 1/π]```I think the area of the small was 1/4
hollow herald
radius of small circle is 1/√2
tranquil plank
But can i really directly assume it like that?
hollow herald
But can i really directly assume it like that?
Assume what?
tranquil plank
Like the area is the probability?
hollow herald
the area is not the probability
area times probability density function is the probability
You're evaluating sort of like a cdf : cumulative distribution function
tranquil plank
Is this circle pdf or cdf
hollow herald
Your pdf is f(x, y) = 1/pi for x² + y² ≤ 1
tranquil plank
But thats this shown circle right?
hollow herald
the circle encompasses your random variables
tranquil plank
I tried to do a. And found the area of the smaller circle. Then divided to the area of bigger circle
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tranquil plank
<@&286206848099549185>
leaden ermine
I tried to do a. And found the area of the smaller circle. Then divided to the a...
Why would you divide it, since the the whole circle has probability 1 anyway because it's a the density function. Also what did you get?
leaden ermine
Do you know how to compute integrals?
tranquil plank
Kind of
leaden ermine
Basically you want to calculate the probability (area) of 1/pi over the circle with radius 1/sqrt(2)
Do you understand this?
tranquil plank
Okay but why the area is probability?
leaden ermine
Ok see it is similar to yesterday
where your density function was 1-dimensional
and you learnt that integrating the density function over some interval, gives you some probability
it is here the same situation, but your density function is 2-dimensional
tranquil plank
I see.
That means i have to integrate 1/pi in range of x2+y2 less than 1/2 condition?
leaden ermine
have you encountered multi variable calculus yet?
leaden ermine
That means i have to integrate 1/pi in range of x2+y2 less than 1/2 condition?
..yea basically..
tranquil plank
Yes but it sounds too complicated to me
We learned a formula with double integral
But it was not on circle
leaden ermine
what is the formula saying
tranquil plank
Double integral on the f(x)
leaden ermine
f(x,y)?
tranquil plank
Integrate the f(x,y) one time under x and one time under y?
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
tranquil plank
Yeahh
leaden ermine
Ok!
See the only hard part is to set up the bounds correctly
integration rules work here the same
tranquil plank
Okay how ?
leaden ermine
Ok so I will show you
but we won't integrate with x and y variables
or do you want to get straight to the integration part?
tranquil plank
but we won't integrate with x and y variables
What do you mean?
tranquil plank
or do you want to get straight to the integration part?
No
leaden ermine
but you encountered multivariable calc?
leaden ermine
What is the name on german
Polarkoordinaten or Zylinderkoordinaten
tranquil plank
I dont know
tranquil plank
Polarkoordinaten or Zylinderkoordinaten
No.
leaden ermine
substitution
tranquil plank
Yes
leaden ermine
essentially we are doing here the very same thing but with two variables
with polar coordinates and why is because it makes integration very easy
tranquil plank
Okay. Let me see it anyways.
leaden ermine
So normally you would look at your region and figure out the bounds for y
since we start with dy
,w plot x^2+y^2 <= 1/2
this is the region
the whole
tranquil plank
Okay.
leaden ermine
your smaller circle looks like this
glossy valveBOT
leaden ermine
and now in order to find the bounds for y
you solve x^2+y^2 <= 1/2 for y
are you able to do that?
leaden ermine
ok well done
tranquil plank
I forgot the =
leaden ermine
yea but dw
the bounds for x are even simpler
you just need to look at which x your circle begins and at which it stops
well your circle has radius r = sqrt(1/2) basically
so what can x be at most
leaden ermine
yea
tranquil plank
leaden ermine
yea
tranquil plank
So now i have to solve it?
tranquil plank
Forgot the minus
leaden ermine
You can also do this
[ 4 \cdot \frac{1}{\pi} \int_{0}^{\frac{1}{\sqrt{2}}} \int_{0}^{ \sqrt{\frac{1}{2}-x^2}} 1 : dy dx ]
because of symmetry.
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
tranquil plank
Why?
tranquil plank
Whatt
leaden ermine
,w plot y = 1/pi from -1 to 1
glossy valveBOT
tranquil plank
Will it affect the result?
leaden ermine
see
it doesnt matter if you integrate from -1 to 1 here or from 0 to 1 but double it
tranquil plank
I see
tranquil plank
So you only integrating right upper corner of the circle and multiplying it by 4?
glossy valveBOT
leaden ermine
and double it
actually yea we are integrating a fourth area and multiply by 4
upper right 🙂
yes
tranquil plank
Understood
leaden ermine
ok now here comes the easiest
as you notice
integrating square root functions
that's ugly
tranquil plank
Yes
leaden ermine
but the good thing is our region is a circle
so we make a substitution
and it works this way
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
leaden ermine
Now I will explain why it's easier
tranquil plank
Does it only work on circle?
leaden ermine
despite looking intimidating
leaden ermine
Does it only work on circle?
ellipses too, but that's another topic
tranquil plank
Now I will explain why it's easier
Okay
leaden ermine
f(x,y) = 1/pi so after your substitiution as shown above your transformed function f(r,theta) = 1/pi still
since it's basically a constant
since there is no x and y really in your function it remains the same
tranquil plank
Okay
leaden ermine
Now you only need to find the bounds
and the cool thing is you don't have to think complicated
you just have to see it geometrically
naturally
you have a circle with radius sqrt(1/2)
so naturally how much should the radius be at most
tranquil plank
Pi/4
leaden ermine
nope
tranquil plank
Pi/2
leaden ermine
again
you have a circle with radius sqrt(1/2)
** radius sqrt(1/2) **
it's practically there
tranquil plank
I dont know
leaden ermine
listen to your gut
tranquil plank
The radius is (1/2)^(1/2)
leaden ermine
yes
tranquil plank
Pi/2 is the area
leaden ermine
stop
tranquil plank
Okay
leaden ermine
really simple
your radius can become at most what
if you have a circle with radius r = sqrt(1/2)
tranquil plank
The radius is (1/2)^(1/2)
?
leaden ermine
yes!
and now the lower bound
naturally or geometrically the radius is never practically negative
so what should be the lowest value for radius
tranquil plank
0
leaden ermine
Yes!
So
0 <= r <= sqrt(1/2)
really simple
ok now theta the angle
for that
i will draw a picture
so you understand
Imagine a clock
a clock has a pointer
but imagine it goes counterclockwise
as it moves
it creates an angle theta with the x-axis
for example
this is where it starts
well the angle between yellow pointer and x-axis is 0
does that make sense
since they are parallel
tranquil plank
Okay
leaden ermine
so now we know 0 <= theta
and as the pointer rotates counterclockwise
the angle becomes greater
right
tranquil plank
Yes
leaden ermine
and for a full circle
it has to do one period
rotate once around
until it's again at where the yellow pointer is
maybe you can tell how much degree this is?
tranquil plank
360?
leaden ermine
if you go around a circle
yes!
360°
which translates to 2pi
so 0 <= theta <= 2pi
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
tranquil plank
Why are we multiplying it by r?
leaden ermine
I won't explain why it's too complicated for now
leaden ermine
**anti\-algebraist 𝔸dωn𝓲²s**
this was the formula.
leaden ermine
or you watch a video and try to understand
tranquil plank
1/2?
leaden ermine
,w Integral[4/pi,{x,0,sqrt(1/2)},{y,0,sqrt(1/2-x^2)]
glossy valveBOT
tranquil plank
Yep
leaden ermine
b) seems again to integrate
your domain is x^2+y^2 <= 1 but you must restrict your region such that x < y
that's basically like a diagonally cutting the disc
,w plot x^2+y^2 <= 1 and x < y
glossy valveBOT
leaden ermine
see!
this is your region that you want to integrate f(x,y) over
you could use again polar coordinates
just need to restrict theta
tranquil plank
Really?
leaden ermine
you can see the pointer
tranquil plank
45 to 225?
leaden ermine
you genius
now in radian
quick formula is to multiply by pi/180
45 is pi/4
225 is 5pi/4
what about the radius?
what do you think
tranquil plank
It wont change?
tranquil plank
So its 1?
leaden ermine
yes
and lowest is 0 again
because it's the whole disk where we only consider a part of it since it was cut
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
tranquil plank
So its 1/2
leaden ermine
So its 1/2
yep
this is how it would look in cartesian coordinates btw
very complicated to set up
tranquil plank
I see. Hope something like this wont come tomorrow
leaden ermine
if it does try to remember the polar thing
leaden ermine
**anti\-algebraist 𝔸dωn𝓲²s**
I would write this in your formelsammlung
with the identity sin^2(theta) + cos^2(theta) = 1
tranquil plank
Formelsammlung is not allowed
leaden ermine
really
tranquil plank
Yes
leaden ermine
tranquil plank
Am i supposed to use transformationssatz or what
leaden ermine
seems like it
tranquil plank
But how?
leaden ermine
also believe it or not the polar coordinates thing is also based on transformationssatz
tranquil plank
I dont want to believe it
leaden ermine
the additional factor r comes from that det determinant thing in the transformationsatz but anyway
Ok so we basically know
or I think it was
,, \mathbb{P}(X \leq x, Y \leq y) = \int_{-\infty}^x \int_{-\infty}^y f(u,v) : du dv
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
leaden ermine
this
tranquil plank
Okay
tranquil plank
leaden ermine
this looks familar to polar coordinates
R = sqrt(X²+Y²) is the distance from the origin
radius R essentially
tranquil plank
Okay.
tranquil plank
No
leaden ermine
well you should know
i mean here it's probably again just a factor r
using polar
tranquil plank
But there is two ramdom variable
leaden ermine
,, \iint f_{X,Y}(x,y) : dydx = \iint f_{R,\Theta}(r,\theta) \cdot \abs{J} : dr d\theta
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
tranquil plank
Is it also only for circle?
leaden ermine
well yea essentially
tranquil plank
What is that big J
leaden ermine
the determinant of the jacobian
tranquil plank
How do i find that?
leaden ermine
linear algebra
well first
since we are in 2 dimension we need 2x2 jacobi matrix which contains the partials
tranquil plank
What is even jacobi
leaden ermine
a matrix that contains the partials of your sub
,, \abs{J} = \left | \det \begin{pmatrix} x_r & x_\theta \ y_r & y_\theta \end{pmatrix} \right | = \abs{ x_ry_\theta - y_r x_\theta }
tranquil plank
What is partial
leaden ermine
partial derivative
I find it funny how i didn't want to explain that complicated thing and now well i am forced
x = rcos(theta) and y = rsin(theta) basically
you differentiate one variable at one time basically
and treat the others as constants
that's partial differentiation basically
leaden ermine
well it is and I think it's no use rn lol
tranquil plank
Why?
leaden ermine
Is there no other way without jacob
that is the very essence of your transformationsatz
tranquil plank
But you should show me the other way too.
leaden ermine
But you should show me the other way too.
there is no other huh
tranquil plank
Really?
leaden ermine
yea
tranquil plank
Sad
leaden ermine
well there is a shortcut
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
leaden ermine
famously, the determinant of that matrix we would have just set up equals r
tranquil plank
What does that even mean
leaden ermine
well how do i explain a concept that takes months to teach in seconds
tranquil plank
We didnt learn anything like that
leaden ermine
you didn't have linear algebra?
tranquil plank
Yeahh i had
leaden ermine
yet you were introduced to such thigns
so you know what a matrix is
and a determinant
leaden ermine
famously, the determinant of that matrix we would have just set up equals *r*
that is a matrix
and i am saying the determinant of that matrix equals r
so |J| = r
tranquil plank
I dont think we had that
leaden ermine
well that cannot be
when you have linear algebra you are certainly introduced to matrices and determinants
it's the very first concepts you study first semester
tranquil plank
Yeahh we learned a lot about matrices and determinants
leaden ermine
so you did what, only vector geometry?
tranquil plank
No matrix
Euklodische geometry
4 or 5 ways to find the determinant of the matrix etc.
leaden ermine
4 or 5 ways to find the determinant of the matrix etc.
so you did that
tranquil plank
Anyways lets go back to our problem
leaden ermine
well that's the problem
leaden ermine
famously, the determinant of that matrix we would have just set up equals *r*
this is basically what you would have
and the determinant is r
tranquil plank
I see
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
leaden ermine
The reason I put ' at the variables is for notation because it's basically illegal to integrate a variable and then have it as a bound too
like
glossy valveBOT
anti-algebraist 𝔸dωn𝓲²s
leaden ermine
I wish you viel Erfolg for tomorrow.
I know you have been studying hard.
You deserve to at least pass.
leaden ermine
toi toi toi
tranquil plank
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wicked zodiac
what does this mean
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what does this mean
sudden condor
what is a discriminat
b^2-4ac
long sky
As seen in the quadratic formula in the sqrt
sudden condor
ryo <:BocchiPlushStare:1162306513843535973>
bocchi
wicked zodiac
As seen in the quadratic formula in the sqrt
so is that a negative one
is that what it means
by negative
wicked zodiac
i see
long sky
If b^2-4ac=0
Then one solution exists
This scenario is also commonly referred to as a double root
sudden condor
If b^2-4ac=0
Then one solution exists
I prefer both solution being a duplicate of each other
(cuz theorem of algebra)
wicked zodiac
If b^2-4ac is negative
is it saying if we olug in the numbers and it gives us a neg?
sudden condor
is it saying if we olug in the numbers and it gives us a neg?
yea
wicked zodiac
i see
sudden condor
they won't give a real sol so no factoring
wicked zodiac
sudden condor
https://tenor.com/view/bocchi-the-rock-bocchi-the-rock-money-bocchi-money-anime-...
I needed that tbh
was changing the string of my 30 basses
sudden condor
done, would you give me money now ?
wicked zodiac
done, would you give me money now ?
no
wicked zodiac
nah
long sky
😭
sudden condor
we doin bocchi the rock refrences now lol
wicked zodiac
💀
sudden condor
bocchi the peak ngl
wicked zodiac
bocchi the peak ngl
true
sudden condor
say something<:BocchiTheGlock:1067601762808246282>
bocchi the glock lol
wicked zodiac
yes
sudden condor
I really need to sleep gn
hoary ember
say something<:BocchiTheGlock:1067601762808246282>
wicked zodiac
I really need to sleep gn
gn
hoary ember
gn
sudden condor
U2
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@wicked zodiac Has your question been resolved?
torn jolt
why am i subtracting Ek2???
full forumBOT
why am i subtracting Ek2???
brazen moth
what's good my dude
brazen moth
anyways
torn jolt
i thought i would add it
brazen moth
do you mean subtracting Ek1?
torn jolt
yeah sorry
brazen moth
think in terms of conservation of energy
the energy of the block starts off with some kinetic energy
torn jolt
OHbecause its the change
brazen moth
yess
torn jolt
it basically has inital and final
brazen moth
exactly
torn jolt
and we are looking for the change inbetween those 2
omg
i understand
Thank you
better than my teacher fr
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whole pivot
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whole pivot
I need help on question 14
What happens to the right angle?
Also forgot to mark the other angles as 90
Nvm I got it
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torn jolt
Why is this wrong even though it was used to get the second answer
thorn sonnet
Why is this wrong even though it was used to get the second answer
who said its wrong?
torn jolt
It is a program, it allows to check answer three times prior to submission.
thorn sonnet
It is a program, it allows to check answer three times prior to submission.
and the program says that f(y) = 1000 * 9.8 * 4 * y is wrong?
thorn sonnet
Why is this wrong even though it was used to get the second answer
how would you use that to get the second answer?
torn jolt
You would take the integral of that function from 5 to 10
thorn sonnet
You would take the integral of that function from 5 to 10
uh
i don't get the logic of that
why don't you just integrate it from 0 to 5 and use the depth?
like 1000 * 9.8 * 4 * (10-y) dy
cuz the formula uses depth in my experience
torn jolt
genius
thorn sonnet
hmm but it seems like they both work
torn jolt
it worked!!!!!!!!!!!!!!
thorn sonnet
it worked!!!!!!!!!!!!!!
ayy
thorn sonnet
genius
how does your way work?
they probably just wanted you to do it the specific way im used to doing it but
torn jolt
I think I mistakely got the anwser
thorn sonnet
I think I mistakely got the anwser
oh 💀
torn jolt
thank you, Im going to close now
thorn sonnet
alr np cya mate
torn jolt
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clever helm
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clever helm
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glossy valveBOT
Kenzo
lime ether
then
clever helm
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lime ether
what techniques do you know
clever helm
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lime ether
what does that do
clever helm
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clever helm
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lime ether
youll literally get the same thing essentially in terms of u if you use that substitution
partial fraction
clever helm
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lime ether
is what you want
clever helm
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glossy valveBOT
Kenzo
lime ether
$\frac{1}{y(1-y)} = \frac{A}{y} + \frac{B}{1-y}$
clever helm
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glossy valveBOT
knief
clever helm
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clever helm
**Kenzo**
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lime ether
you cant just take ln lol
to see why maybe you should differentiate it
$\int \frac{\dd{u}}{u} = \ln|u| + c$
clever helm
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glossy valveBOT
knief
lime ether
is 1 the derivative of y(1-y)?
clever helm
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lime ether
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no
y(1-y) is y - y^2
derivative is 1 - 2y
clever helm
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lime ether
which is not the numerator