Ok
#help-17
hybrid breach
yes
umbral swift
but could i do it like
hybrid breach
ohh i know what you mean
umbral swift
lets say cos² is f, and (3x) is g?
So i do d/dx(cos²(3x)) which means d/dx cos² * (3x) + cos2 * d/dx (3x)
?
hybrid breach
you committed a sin
umbral swift
💀
hybrid breach
that would work if it was cosx*3x
umbral swift
🥲
hybrid breach
but here it is a function inside another function
odd helm
you might like to write $2\cos^2x = \cos2x + 1$
twin meteorBOT
Xetrov
umbral swift
i get stuck recognizing chain rule and basic derivative
hybrid breach
**Xetrov**
unnecessary
odd helm
if you say so
hybrid breach
i get stuck recognizing chain rule and basic derivative
lots of practice makes the job
umbral swift
ait
odd helm
I'm just saying that it could be a nicer derivative
odd helm
...?
odd helm
whatever ig
odd helm
Tosi, I've given you a form which allows an easy evaluation of the double derivative
why are you not using that
hybrid breach
unnecessary as i said
odd helm
because?
umbral swift
i still get 0/0
hybrid breach
you don need to derivate more
umbral swift
When inserting 0
odd helm
you're making them do a nasty derivative
hybrid breach
do you know what sinx/x as 0 goes to zero does?
hybrid breach
you're making them do a nasty derivative
im not
hybrid breach
do you know what sinx/x as 0 goes to zero does?
.
umbral swift
wait let me translate that real quick
hybrid breach
it's one of the classic limits
hybrid breach
therfore what do we have to do to get that case
umbral swift
maybe sin2x * sinx?
umbral swift
where did you get that /3x from?
hybrid breach
you can multiply on top and bottom by three
and you get yours sin(3x)/3x
which you can eliminate as you know it gives you 1
hybrid breach
what isn't clear
umbral swift
english is the problem
can you write it somewhere or?
i have to translate all the time
umbral swift
Ok
hybrid breach
first of all you can cancel the 2 on the top with the one on the bottom
hybrid breach
dw mister
odd helm
For my lack of foresight
hybrid breach
see it was easier
umbral swift
Where did bro get that -2
hybrid breach
(you could have done it in the first step recalling another identity)
but let's not talk about that
hybrid breach
Where did bro get that -2
which one
umbral swift
in front of sin3x
hybrid breach
you had it aswell
umbral swift
i know where - came from, but 2?
hybrid breach
is it clear
umbral swift
OOOOOOOOOOOOOOO
hybrid breach
where are you from
umbral swift
now i get it
hybrid breach
real moi brat
umbral swift
😂
hybrid breach
italija
umbral swift
ohh
hybrid breach
idk how to spell in your language
hybrid breach
1 am for me aswell
umbral swift
ban this dude
hybrid breach
Gl on monday
for what
umbral swift
Croatia - Italia
plain ledge
Euros
hybrid breach
oh i dont follow that
umbral swift
@plain ledge can you solve this limit for me?
umbral swift
yes
terse cipher
umbral swift
im listening
umbral swift
🥲
terse cipher
umbral swift
I DONT KNOW
terse cipher
HAHAHAH
hybrid breach
wasn't Croatia good
terse cipher
wasn't Croatia good
it was but its ahh now
umbral swift
Seif where you from?
plain ledge
2 words: zlatko dalić
terse cipher
france
umbral swift
ahh
umbral swift
ur team is african
umbral swift
oh💀
hybrid breach
is he that one blonde
umbral swift
yes
hybrid breach
was it the world cup that they won
umbral swift
who?
terse cipher
if thats the case i can solve it
umbral swift
i need to solve this limit
hybrid breach
bro i already solved it
umbral swift
💀
hybrid breach
me and the other guy
hybrid breach
we helped you
terse cipher
it needs to be -9
umbral swift
yes
hybrid breach
yep
umbral swift
what do you guys study btw?
warped cobalt
Amog us
terse cipher
do the hospital rule
twin meteorBOT
Adversing
umbral swift
do the hospital rule
Did it
hybrid breach
|| le persone italiane in sto discord sono n ($n \to 0$) ||
is bro italian
umbral swift
what do you guys study btw?
.
terse cipher
he is sharing ads
wanton thunder
is bro italian
ye
terse cipher
ban him
hybrid breach
ye
ne ho beccato uno il giorno prima della seconda prova di maturità che ho fatto pure io
terse cipher
his name is Advertising
wanton thunder
.
Computer Engineering or Software engineering, it depends by the name it goes in your country
hybrid breach
tell
wanton thunder
his name is Advertising
lmfao
wanton thunder
ne ho beccato uno il giorno prima della seconda prova di maturità che ho fatto p...
figo
wanton thunder
hes from portugal
no, he's from italy
umbral swift
How did bro get rid od cos up?
wanton thunder
I can assure it to you xd
terse cipher
no, he's from italy
hell nah
umbral swift
hybrid breach
How did bro get rid od cos up?
cos0=1
umbral swift
I mean up here
hybrid breach
yes and cos0=1 anyways
terse cipher
tosi where u from
hybrid breach
italy bro
umbral swift
but if he inputs 0 in all xs
umbral swift
Then result is still 0/0
hybrid breach
but the sinx/x goes to 1
umbral swift
Computer Engineering or Software engineering, it depends by the name it goes in ...
Im in civil engineering
hybrid breach
Then result is still 0/0
also limits are multiplicative
umbral swift
mechanics are easier than math ngl
terse cipher
we are 900Km away from each other @hybrid breach
wanton thunder
Im in civil engineering
tough shit
umbral swift
yes
hybrid breach
I'll do pure maths next year
umbral swift
fr
terse cipher
I'll do pure maths next year
guess my dinner
hybrid breach
guess my dinner
jolof rice
wanton thunder
guess my dinner
$\pi$? (🥧)
twin meteorBOT
Adversing
umbral swift
bro integrals are easier than limits fr....
terse cipher
yes pizza
plain ledge
bro integrals are easier than limits fr....
Easier my ass
terse cipher
nah a pizza
hybrid breach
bro integrals are easier than limits fr....
nah man, you never saw elliptic functions
terse cipher
@hybrid breach how old r u
hybrid breach
18
wanton thunder
bro integrals are easier than limits fr....
you say so?
hybrid breach
thanks ig
terse cipher
thats a bad thing
wanton thunder
xd
hybrid breach
you say so?
that just looks scary tbh
plain ledge
you say so?
Trying to find a number here
wanton thunder
that just looks scary tbh
lo farai in Analisi Matematica 2
umbral swift
using numbers in mechanics and statics - 🏝✨️
hybrid breach
lo farai in Analisi Matematica 2
sincero non è difficile
wanton thunder
Trying to find a number here
numbers? what do you mean?
umbral swift
using numbers(letters) in math - 🥲
wanton thunder
what is a number?
umbral swift
Ofc
wanton thunder
(classic calc 2 student)
plain ledge
numbers? what do you mean?
like 0 1 2 3 4 5 6 7 8 9
umbral swift
never heard of those
plain ledge
but ig high level math never heard of that
terse cipher
isnt that just a double integral over a surface
wanton thunder
like 0 1 2 3 4 5 6 7 8 9
yeah I know I was joking
hybrid breach
you stop seeing numbers after a certain point
plain ledge
so am i
wanton thunder
I've reached a level where if I even find a number in an integral I'm blessed
like I have to thank god
umbral swift
bro at my college physics are easier than math
plain ledge
just fail math class like me
terse cipher
but ig high level math never heard of that
alphabets are not higher level math xd
my little brother knows them
umbral swift
physics for me piece of cake ngl
terse cipher
at the age of 8
hybrid breach
like I have to thank god
will you drop out or will you endure
ah no non fai mate pura hai detto
niente
wanton thunder
ah no non fai mate pura hai detto
no non sono così malato
umbral swift
i will drop out if i dont pass this math
hybrid breach
no non sono così malato
io si
hybrid breach
tanto calc 1 e 2 li ho già in mano
umbral swift
I hope so
terse cipher
other than uni
umbral swift
i mean
engineer >>>>>>>>>>>>>>> bacc.
aight bois its been pleasure, thanks for help
croatia win italy 3:1, we win euros, modric retires after
terse cipher
bro
umbral swift
i wish you a loving day
terse cipher
vocal sleetBOT
vocal sleetBOT
Available help channel!
limpid garnet
why are real numbers additionally defined as converging sequences of rational numbers?
vocal sleetBOT
why are real numbers additionally defined as converging sequences of rational nu...
gaunt sparrow
Rational numbers are nice, but they lack a fundamental property for formally defining analysis, and therefore calculus (among others).
That fundamental property is called completeness, i.e. a guarantee that whenever I have sequence whose terms get arbitrarily close to one another (this is called a Cauchy sequence), then the sequence must have a limit within the set we're investigating.
The rational numbers don't have this property. For instance, we can easily approach pi using its decimal expansion, but doing so makes the limit slip out of the rational numbers, since pi isn't rational.
This property is important, because it allows for us to define limits and functions and all the machinery you need for analysis without fear that we get nonsense out of this.
Now as to why we do it that way, it's because by considering converging sequences in Q, we construct a new set, R, that is in some way the "smallest" set that has this property while containing Q.
Note that there are other ways of defining the real numbers, say with Dedekind cuts, or supremum properties.
junior forum
the sequences aren't necessarily converging in Q, (for example pi) they are just cauchy
gaunt sparrow
Yes sorry. I think the point remains mostly the same however. (edit : I've fixed my definition of completeness to reflect the more accurate one you pointed out)
vocal sleetBOT
@limpid garnet Has your question been resolved?
limpid garnet
Yes sorry. I think the point remains mostly the same however. (edit : I've fixed...
Thank you,
Are you a teacher?
gaunt sparrow
No
limpid garnet
interesting
gaunt sparrow
Only, a massive part of my first class in real analysis was about different equivalent definitions of the real numbers, so it somewhat gets carved into your brain hahah
limpid garnet
please excuse me, butI have an additional question, in what order did you (for instance) study formal pure mathematics? I am familiar that there is no concrete order for studying pure math.
limpid garnet
Only, a massive part of my first class in real analysis was about different equi...
I see.
limpid garnet
please excuse me, butI have an additional question, in what order did you (for i...
(I am self tutoring, which is why I ask, and I am sort of a perfectionist)
gaunt sparrow
please excuse me, butI have an additional question, in what order did you (for i...
Yes indeed. Contents of degrees vary quite considerably from curriculum to curriculum, so there is no best way, although I think most of them have the same overarching structure.
That is, most start out say, year 1, with some subjects that force you to do proofs, something like real analysis, group theory. All of that is so that you can then take more advanced classes and be able to come up with proofs on you own.
Self studying is a noble endeavor, although it is significantly harder to test your understanding of the material in a rigorous way, as you would by submitting homework and writing exams.
I personally did :
Y1 : group theory, vector calculus, ODEs, combinatorics, abstract algebra, advanced linear algebra, real analysis
Y2 : differential geometry, topology, complex analysis
Y3 : metric spaces, measure theory, fourier analysis, PDEs, numerical analysis.
Some years were more maths oriented and some less, due to my major being split maths and computer science, but I think it's pretty standard. You might want to look into curricula from other colleges, and maybe look into MIT's open courseware, since you can even get yourself some homework sheets and such.
Sorry that was long
vocal sleetBOT
limpid garnet
.reopen
vocal sleetBOT
✅
gaunt sparrow
You might've seen it, but there's this video from AlephNaught where they describe a good roadmap to most content seen in an undergraduate degree in mathematics, so in case you're interested, this is the link
limpid garnet
You might've seen it, but there's this video from AlephNaught where they describ...
Thank you
vocal sleetBOT
vocal sleetBOT
Available help channel!
crisp zenith
There has to be an easier way to go about this right? does anyone see anywhere I can simplify?
vocal sleetBOT
There has to be an easier way to go about this right? does anyone see anywhere I...
crisp zenith
let me write down the unit tangent I got
wouldn't that be difficult to take the derivative of again to find the unit normal?
I'm wondering if I am approaching this the wrong way
I know if the denominator was like sqrt(3), I'd be able to factor that constant out and take the derivative of the vector with just the numerator, can I still do that?
factoring out the denominator
Are these equivalent?
lime gorge
i remember when i had to do these same problems for calc3 in myopenmath
and yes, they were this long iirc
but if theres an easier way? i dont remember
i remember @pale widget helped me with the TNB frame thing
maybe theres some sort of simplification
crisp zenith
right now im going to try factoring out the denominator and taking deriative of just the numerator and seeing if that works, I know its possible when the denominator is a constant but not sure when its a function
like this
pale widget
You should calculate this using N=BxT instead. That’s why it’s called a TNB frame instead of any other ordering of the letters.
crisp zenith
You should calculate this using N=BxT instead. That’s why it’s called a TNB fram...
is there a formula for just B? we never learned that, we only learned finding T then N and then B = T x N
pale widget
Yes but you’ll have to google it. There are lots of formulas
crisp zenith
ok i'll do that
pale widget
I think it’s r’(t)Xr’’(t) divided by the norm of that quantity off the top of my head but I don’t know
But you should obviously plug in the value of t after you differentiate but before you calculate the cross product and the norm to make it less notationally complex
pale widget
Nope
crisp zenith
im wondering how your tangent is much more simplified than mine
pale widget
Anyway it’s called TNB because you can shift the letters in a circular fashion to get other formulas N=BxT and B=TxN
lime gorge
lime gorge
im wondering how your tangent is much more simplified than mine
well u can simplify all those sin, cos of 5pi/6 right
and maybe its cuz i had pi instead of 5pi/6
vocal sleetBOT
@crisp zenith Has your question been resolved?
vocal sleetBOT
@crisp zenith Has your question been resolved?
vocal sleetBOT
@crisp zenith Has your question been resolved?
harsh gust
What did I do wrong here?
vocal sleetBOT
vocal sleetBOT
proven whale
.reopen
vocal sleetBOT
✅
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
twin meteorBOT
Matchstick
vast shale
i dont know how $P_{O_{2}}$ relates to $P_{N_{2}}$
twin meteorBOT
Matchstick
plain minnow
i dont know how $P_{O_{2}}$ relates to $P_{N_{2}}$
I think they're related by dalton's law
@vast shale do you know dalton's law?
vast shale
<@456226577798135808> do you know dalton's law?
the one that talks of partial pressure summation?
plain minnow
the one that talks of partial pressure summation?
yeah?
vast shale
i cannot recall any further than that
plain minnow
i cannot recall any further than that
P1 + P2 + P3 = P(total)
where 1,2,3 are ideal gasses
vast shale
yes
plain minnow
so you can right it in a useful form
vast shale
do i use ideal gas equation to proceed further?
plain minnow
,,P_1 = X_i P_t
twin meteorBOT
Wither
plain minnow
X1 is mole fraction of gas
vast shale
X1 is mole fraction of gas
is there a way to do that?
vocal sleetBOT
@vast shale Has your question been resolved?
plain minnow
but i know percentage by volume
volume percent is same as mole percent
because of avogadro's law
vast shale
OH YES
plain minnow
I think you can do it now @vast shale
vast shale
.close
vocal sleetBOT
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Available help channel!
tulip temple
vocal sleetBOT
wanton thunder
you could use the tangent addition rule
$\tan{(A+B)} = \frac{\tan{A} + tan{B}}{1-\tan{A}\tan{B}}$
$\tan{(A-B)} = \frac{\tan{A} - tan{B}}{1+\tan{A}\tan{B}}$
twin meteorBOT
Adversing
wanton thunder
I forgot the 1 lmao
tulip temple
can you try it please:C
wanton thunder
yes, now I'll try it
tulip temple
on skibidi
vocal sleetBOT
@tulip temple Has your question been resolved?
tulip temple
you know you are cooked when it takes 5 quattuordecillion yearsto type it out
vocal sleetBOT
tulip temple
NO WAIT
wanton thunder
.reopen
tulip temple
ah yes thank gawd
wanton thunder
ok now starting from what I wrote you should have
$$ \frac{\tan{A} + \tan{B}}{1-\tan{A}\tan{B}} = n \cdot \frac{\tan{A} - \tan{B}}{1+\tan{A}\tan{B}} $$
Then I'd multiply both sides by $(1-\tan{A}\tan{B})(1+\tan{A}\tan{B})$ so we obtain:
$$
(\tan{A} + \tan{B})(1+\tan{A}\tan{B}) = n(\tan{A} - \tan{B})(1-\tan{A}\tan{B})
$$
Once you get here and simplify to find both $\tan{A}$ and $\tan{B}$, you should get something like this:
$$
\tan{A} + \tan{B} + \tan{A}^{2}\tan{B} + \tan{A}\tan{B}^2 = n(\tan{A} - \tan{B} - \tan{A}^{2}\tan{B} + \tan{A}\tan{B}^2)
$$
Here I'm going to use the $\sin{(2\theta)}$ identity ($\sin{(2\theta)} = 2\sin{(\theta)}\cos{(\theta)}$) for both $A$ and $B$. As a consequence of this step, you get:
$$
\frac{\sin{(2A)}}{\sin{(2B)}} = \frac{2\sin{A}\cos{A}}{2\sin{B}\cos{B}} = \frac{\sin{A}\cos{A}}{\sin{B}\cos{B}}
$$
jesus I hate LaTeX
one sec
tulip temple
ong
vocal sleetBOT
Available help channel!
tulip temple
no
twin meteorBOT
Adversing
wanton thunder
$$
\tan{A} + \tan{B} + \tan{A}^{2}\tan{B} + \tan{A}\tan{B}^2 = n(\tan{A} - \tan{B} - \tan{A}^{2}\tan{B} + \tan{A}\tan{B}^2)
$$
twin meteorBOT
Adversing
wanton thunder
**Adversing**
it's too long
wanton thunder
you mean in the end?
where you obtain
$$
\frac{\sin{(2A)}}{\sin{(2B)}} = \frac{2\sin{A}\cos{A}}{2\sin{B}\cos{B}} = \frac{\sin{A}\cos{A}}{\sin{B}\cos{B}}
$$
?
twin meteorBOT
Adversing
tulip temple
wait do you even obtain that
where did the n go
in the equation
what im asking is when you simplify tan(A+B) = ntan(A-B) what do you get
wanton thunder
you have to distribute $n$ on the right-hand side combining the terms, solving then for $\tan{A}$ and $\tan{B}$
twin meteorBOT
Adversing
tulip temple
so you cross multiply?
wanton thunder
$$
\tan{A} + \tan{B} + \tan{A}^{2}\tan{B} + \tan{A}\tan{B}^2 = n(\tan{A} - \tan{...
the expansion is this, but since it's too long to be rendered I suggest you to copy-paste my message and render it by yourself
tulip temple
i get that
what
do u do after that
is my question
how do you get tan and tan b induvidually
wanton thunder
after that you rearrange to solve for tan(A) and tan(B)
vocal sleetBOT
vocal sleetBOT
Available help channel!
tender pilot
Hi! I was reading an article by Abraham Wald called "method of Estimating Plane Vulnerability Based on Damage of Survivor". https://apps.dtic.mil/sti/tr/pdf/ADA091073.pdf But I didn't really understand the pages 6 and 7 where he makes a hypothetical scenario in which " dummy bullets would have been used" in order to find equation (26) and use it later in the article. He sets the random variable yi as bi - ai. If I am right, yi seems to refer to the proportion of "planes that would have potentially been downed if real bullets had been used". But I have trouble understanding why making a hypothetical scenario in which dummy bullets would have been used helps to provide information about the missing planes? And why set the variable yi = bi - ai when it clearly looks equal to the random variable xi = Ni - ai (the number of planes shot down with i bullet holes is equal to the total number of planes with i bullet holes minus the number of planes with i bullet holes that survived)?
vocal sleetBOT
Hi! I was reading an article by Abraham Wald called "method of Estimating Plane ...
@tender pilot Has your question been resolved?
nova willow
to reply to your first question imagine you use pretend bullets that don't break the planes. With pretend bullets, every plane, whether hit a lot or a little, makes it back to the hangar because they don’t get broken. By comparing the number of hits with pretend bullets (where all planes come back) to the number of hits with real bullets (where some planes don’t come back), you can guess how many planes got hit but didn’t make it back. So, the pretend bullets help you understand the total number of planes that got hit by giving you a way to see what would have happened if no planes were "broken." This helps you figure out the number of planes that are missing because they were hit too much.
i could be wrong or shit at explaining, this is what i think
(note that i skimmed through it)
to the second question, you use yi = bi - ai because xi = Ni - ai directly represents the number of planes shot down with i bullet holes. It is a straightforward count of the planes that didn’t make it back. On the other hand, yi = bi - ai s not just a direct count of missing planes. Instead, it represents the difference between the hypothetical total hits and the actual observed hits is used to estimate the total number of planes that would have been observed if none were shot down.
@tender pilot
dont take everything i said as truth😭
specifically they are different because, xi directly gives you the count of missing planes but doesn’t help in estimating the total distribution of hits. yi and bi helps you estimate the total hit distribution by considering a hypothetical scenario where no planes are shot down. This helps in understanding the overall picture of plane vulnerability. xi is used to identify how many planes are missing. yi helps to understand how many planes would have been hit in a complete dataset (if no planes were shot down).
this is actually really interesting i'll look into it more
thanks
vocal sleetBOT
@tender pilot Has your question been resolved?
nova willow
well rip wrote an essay for nun😭 DM me if you have questions again @tender pilot
fiery maple
Lets see question b) find area of shaded region
My question is when I integrate from -1 to 0 do I have to put a modulus?
fiery maple
Because in the answer scheme I had to put a modulus integration of 0 to -1 added with the integration of 0 to 3
To get the correct answer
I dont know in what condition should I put modulus in
rough spruce
area under curve question so ans cannot be negative
cus its an area
otherwise dont mind it
fiery maple
But cant i integrate from -1 to 3 tho
fiery maple
If I integrate from -1 to 3 I dont get the correct answer
It has to be modulus 0 to -1 added with 0 to 3
rough spruce
the b one ?
fiery maple
yeah
rough spruce
oh yeah
rough spruce
It has to be modulus 0 to -1 added with 0 to 3
just do this one
and if the ans is negative then just modulus it
fiery maple
Thing is idk when should i split when should I not split them
fiery maple
If I integrate from -1 to 3 I dont get the correct answer
Because this answer is positive
So does that mean the area from 0 to 1 i have to put a modulus for question a)
vocal sleetBOT
@fiery maple Has your question been resolved?
fiery maple
<@&286206848099549185>
heavy fiber
So does that mean the area from 0 to 1 i have to put a modulus for question a)
What is the question?
fiery maple
For a)
Find the area of the shaded region
Do i have to put modulus if the area is below the x-axis?
somber yew
Yes, split the integral and apply absolute value to each negative outcome
sudden compass
If I integrate from -1 to 3 I dont get the correct answer
show work
vocal sleetBOT
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Available help channel!
vagrant sable
Sin(xy)= 1/2
vocal sleetBOT
Sin(xy)= 1/2
scenic ravine
so (xy)=?
scenic ravine
oh, you want to differentiate it
vagrant sable
oh, you want to differentiate it
Yes
brittle cipher
sin(anything real) is always between -1 and 1, never 30
scenic ravine
ok $cos(xy)(y + \frac{xdy}{dx})=0$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
vagrant sable
sin(anything real) is always between -1 and 1, never 30
Yes i fixed it
scenic ravine
can you do it from here?
scenic ravine
what is $-30x^{-2}$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
vagrant sable
XY=30
scenic ravine
yes
vagrant sable
**ƒ(Why am. I here)=I don't Know**
=
scenic ravine
,w differentiate sin(xy)=1/2 with respect to x
twin meteorBOT
scenic ravine
**ƒ(Why am. I here)=I don't Know**
I think this is the derivative only $\in [ 0, \frac {\pi}{2}]$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
scenic ravine
I could be wrong though
scenic ravine
ping helpers in 5 minutes
vagrant sable
I will
<@&286206848099549185>
I call upon you
RISE
RISE GREAT HELPERS RISE
Yall should pay me for this intro
vagrant sable
can we have the original question though
Sin(xy)=1/2
digital lake
w
viral copper
Is this paraphrasing or exactly what you've been given
viral copper
what
vagrant sable
Is this paraphrasing or exactly what you've been given
Not really
scenic ravine
Xy= 30 says otgerwise
not only 30
drifting terrace
youre trying to do what?
viral copper
[ \left ( x\dv{y}{x} + y\right )\cos(xy) = 0 ]
drifting terrace
sin(xy)=1/2, find dy/dx for when xy=30?
twin meteorBOT
Bob l'éponge
viral copper
Okay I get what you mean now
vagrant sable
sin(xy)=1/2, find dy/dx for when xy=30?
No, from sin(xy)=1/2 we can conclude that xy=30
viral copper
no
vagrant sable
Why
drifting terrace
No, from sin(xy)=1/2 we can conclude that xy=30
not necessarily
also thats in degrees
vagrant sable
not necessarily
One of the values
vagrant sable
assuming you're in degrees
Wdym
vagrant sable
what is your question
Why does it have two different answers
Or- why doesnt eork eith degrees
viral copper
what has two different answers
It does it's just that degrees don't work that well when you're working on the xy plane
vagrant sable
what has two different answers
Dy/dx (sin(xy)= 1/2)
viral copper
Relegate degrees to physics
viral copper
Dy/dx (sin(xy)= 1/2)
???
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
vagrant sable
not sure why youre trying ro solve sin(xy)=1/2
Differentiate it 😭
Does it maje sense now?
drifting terrace
what are you trying to differentiate tho
viral copper
**Bob l'éponge**
then this is what you get
drifting terrace
Indeed xy=30°+360k° or 150°+360k° for integer k, but that has nothing to do with the question and theres nothing to differentiate
vagrant sable
what are you trying to differentiate tho
Sin(xy)=1/2but thats not my question- i was just wondering why differentiating xy=30 gives us a different solution
drifting terrace
Sin(xy)=1/2but thats not my question- i was just wondering why differentiating x...
d/dx (xy=30) also gives
x dy/dx + y = 0
then dy/dx = -y/x
scenic ravine
or alternatively $y=30/x$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
scenic ravine
differentaiting that gives a different answer
vagrant sable
or alternatively $y=30/x$
Yes
scenic ravine
I think that's the question
vagrant sable
Yes tgats tge question
drifting terrace
ah well
viral copper
btw you're under the impression that sin(xy) = 30 gives you one curve, you get a family of infinitely many curves
drifting terrace
d/dx (30/x) = -30/x^2 = -(30/x)/x = -y/x
vagrant sable
btw you're under the impression that sin(xy) = 30 gives you one curve, you get a...
Hmm not really i just gave out one of tge possible values
vagrant sable
d/dx (30/x) = -30/x^2 = -(30/x)/x = -y/x
OH
Okay
Nice
See 😭 that was tge answer
drifting terrace
lol sorry i didnt get it
vagrant sable
Idk i feel like everything got so complicated
vagrant sable
lol sorry i didnt get it
Nah its my fault i didnt deliever the question properly
Anyways ty u 3
drifting terrace
doesn't that imply y=30 <:thonkzoom:533366356536721418>
30/x
drifting terrace
lol
vagrant sable
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bold scarab
I’m stuck on question 4
vocal sleetBOT
I’m stuck on question 4
tawny hollow
!status
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
tawny hollow
Are you aware how to do (AB)^-1 ?
bold scarab
It’s b-1 and a-1
tawny hollow
So expressed as an equation what would it look like?
tawny hollow
Are you aware how to do (AB)^-1 ?
i mean this
tawny hollow
yea!
bold scarab
-1 being the exponent
tawny hollow
So given the hint in your original question, we have that
(ABC)^-1 = (XC)^-1
correct?
tawny hollow
X is AB
bold scarab
But ab inverse is b-1 a-1?
bold scarab
Sorry about that
tawny hollow
so to reiterate, it seems youve got this; but to make sure.
How would the RHS of this equation look like (XC)^-1 = ?
bold scarab
C-1 X-1 which would be c-1 b-1 a-1
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wary mantle
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signal blaze
white acorn
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untold arrow
$A=[a_1,a_2,a_3,a_4], a_1,a_2,a_3,a_3$ are all 4 dim col vectors, a1,a2 are linear indep. If $b=a_1+2a_2-a_3=a_1+a_2+a_3+a_4=a_1+3a_2+a_3+2a_4$, what's the genaral solution of $Ax=b$?
vocal sleetBOT
$A=[a_1,a_2,a_3,a_4], a_1,a_2,a_3,a_3$ are all 4 dim col vectors, a1,a2 are line...
twin meteorBOT
nino
vocal sleetBOT
@untold arrow Has your question been resolved?
untold arrow
<@&286206848099549185> any hints?
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@untold arrow Has your question been resolved?
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@untold arrow Has your question been resolved?
normal heath
$A=[a_1,a_2,a_3,a_4], a_1,a_2,a_3,a_3$ are all 4 dim col vectors, a1,a2 are line...
i guess try to simplify the b = ... = ... = ... as it gives relations between the column vectors, try to find a3 and a4 in terms of a1 and a2
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still summit
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still summit
how would i put these on a number line
civic otter
You mean how to graph (on the number line) the solutions to those inequalities?
still summit
yeah
civic otter
Ok, so first of all we need to solve them, do you agree?
vocal sleetBOT
@still summit Has your question been resolved?
vast shale
First one is null coz mod of something is always more than or eq to 0
Try the 2nd one urself if u can
frail dew
how?
wheat garnet
sorry u can take this
vocal sleetBOT
whole oasis
1 + 1/4 = 5/4
then:
5/4 + x^2/4 = 1/4 * (5 + x^2)
taking a sqrt of 1/4 you'll get 1/2
and that's all
frail dew
yes
frail dew
oh right
dude my brain is cooked
thanks
i guess this channel is already closed so no need to close it...
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waxen bough
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waxen bough
I am unable to figure out the two functions for this. I've tried a number of combinations and messed with it on desmos but i just don't know how to solve it; i tried working it out with my tutor but no luck, they're not sure how to find the two functions that cover all the bases
shadow raft
f(2)=g(2) and f'(2)=g'(2)=1.23
atomic forum
What a strange question
waxen bough
every one of my assignments has a question about Rod at the end and it's always nonsensical 😭
atomic forum
every one of my assignments has a question about Rod at the end and it's always ...
I found a stupid example
waxen bough
id be happy to hear it!
atomic forum
Wait they don't even have the rate of change
ugh
Here
Ughhh i forgot the y intercept
hang on
i think this works
waxen bough
how would you prove that it has an instantaneous rate of change of 1.23?
twin meteorBOT
Pseudonium
atomic forum
np
waxen bough
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kisnar
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kisnar
kisnar
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kisnar
kisnar
kisnar
hard atlas
yes
twin meteorBOT
kisnar
hard atlas
yes
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mental wedge
Hey friends. Just a question about writing maths.
Is it ok to start a series of biconditional statements with the words 'if and only if', then continue by using the symbol, like I've done in the highlighted part on the screenshot? Does that make sense?
pale perch
i dont know if i can necessarily fault it but it feels iffy to me nonetheless
mental wedge
i dont know if i can necessarily fault it but it feels iffy to me nonetheless
Hey, yeah I know what you mean. Can I ask, how would you write the same thing? Would you write "The sum above is equal to tan(x) if and only if the following equation holds: "?
Anyone else have an opinion? It's just I struggle to start off series of "if and only if" statements, and I'm trying to figure out how to do it right?
<@&286206848099549185>?
Hey. Is anybody else able to help, please? 🙂
whole oasis
Well, for me it's understandable, I wouldn't look for a problem here
mental wedge
Well, for me it's understandable, I wouldn't look for a problem here
Ok, thanks. I think it's understandable, but I'm not sure if it's technically correct
whole oasis
I'd say so, usage of a symbol "if and only if" after the highlighted part only tells us they're equivalent transformations
It'd clear even without them, that's not a mathematical logic let's be honest
mental wedge
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desert edge
Difference between these and if any other options I missed
vocal sleetBOT
Difference between these and if any other options I missed
desert edge
I guess the left one is the confusing one to me
I get that it’s order of operations but
Hmm I guess that’s it really
desert edge
Yeah that might be why I’m confused tbh idk
formal pond
You rarely see the right one
desert edge
I’m doing linear algebra and calculus but for some reason my fundamental order of operations and stuff have gone to hell
For no reason lol
formal pond
You will be fine
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coral tide
Hello! I need some help with a probability problem.
I have a set "P" with a bunch of discrete elements. These constitute all of the items in existence.
I also have a very large dataset of multisets, each multiset containing elements from "P".
Given an existing multiset "B", and an item "I", how can I predict the probability of "I" being added as the "next" item in the multiset?
half imp
Not enough information to say anything
coral tide
What information can I add for clarity?
half imp
how are objects being selected, what does it mean that we have a multiset with only some items filled out
like, I'm supposed to determine which object is next based on which objects are already in there?
which factors are relevant to the probability
vocal sleetBOT
@coral tide Has your question been resolved?
coral tide
Okay, apologies for the vagueness. Also apologies if any of my terminologies are incorrectly used. I'm essentially doing a fun project on trying to improve deck building for trading card games (Pokemon, MTG, Yugioh, etc). I am trying to find a way to calculate optimal weights of cards in a particular deck. I am looking at using variations of decks (different distributions of card types). At a beginning of a game, we draw five random cards off the top of a deck.
So deck variations are the multiset "B", where cards are "P"
vocal sleetBOT
half imp
.reopen
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half imp
click the X next time bot asks if the question is resolved or it'll close again
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@coral tide Has your question been resolved?
stuck hawk
Do i just have to write to get help ?
vocal sleetBOT
Do i just have to write to get help ?
stuck hawk
ok i see
we have two simple interest formulas: Ct=C0(1+i×t) and I = co x i x t why not just use the following formula: Ct=C0+I after using the formula to find the interest?
weary sentinel
we have two simple interest formulas: Ct=C0(1+i×t) and I = co x i x t why not ju...
they are the same thing
stuck hawk
so i can feel free to use what i want ?
weary sentinel
also, this looks like chatgpt, which you should not use (because it does things like this, with unclear explanations)
what they did is start with the calculation for simple interest
add it to the initial cost, to get total cost
then rewrite total cost
stuck hawk
ye
weary sentinel
there was no actual computation happening.
weary sentinel
when you ask "why not just use the following formula" the answer is they are the same formula
one just has an extra level of abstraction, by using the variable I
stuck hawk
hahaha i see thanks my mind was blowing up thx mate and do you know the formula for the compound interest
weary sentinel
depends, continuous or based on a period of time?
stuck hawk
based on a period of time
i mean wdym by continuous ? like untill i take back the money ?
weary sentinel
[C_t=C_0(1 + i)^{\frac{t}{p}}]
twin meteorBOT
Astral
weary sentinel
for t multiple of period p
alternatively you can say floor(t) instead of just t
continuous means instead of interest accruing regularly in one bunch at a time, at the end of every period
stuck hawk
p= exemple 365 days
stuck hawk
thx
weary sentinel
in red we have interest that accrues every 1 unit of x
it jumps up in increasingly large steps
in blue, we have the continuous interest equivalent in rate to periodic interest
which accrues at every moment of time
stuck hawk
oh i see thanks mate
may i ask another question i mean no relation to this
let me just write it
the probability that today will be a sunny day is 1/3 if it's sunny today the probability that it will rain tomorrow is 1/2 if it's raining today the probability that it will rain tomorrow is 2/3 : the probability of having two days of rain, for example? how do I find that out?
weary sentinel
take it one step at a time
logically, the two components to whether it will rain on day 1 and day 2, are the odds it will rain on day 1, and the odds it will rain on day 2
hmm if this is not over the course of a very constrained number of days then I can't help you
stuck hawk
the probability that today will be a sunny day is 1/3 if it's sunny today the pr...
we can't find a probability with these information?
to find the probability of having two days of rain
weary sentinel
are you talking about these two days both being rainy, yes. If you are talking about any two days in a row of a larger sequence, I have no idea
stuck hawk
are you talking about these two days both being rainy, yes. If you are talking a...
these two days being rainy
weary sentinel
then it's the odds of the first day being rainy, combined with the odds of the second day being rainy if the first day is rainy, no?
why are you confused
weary sentinel
you can write it as a fraction
stuck hawk
yes thats what i want to know how can i do that if you don't mind sir
weary sentinel
what are the odds that the first day will be rainy?
stuck hawk
1/3
weary sentinel
.... no
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safe wharf
You have to divide n in the denominator by n^2 as well
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shrewd jacinth
How do i find out the range of the logarithmic function, whats the way, the answer was option B
vocal sleetBOT
How do i find out the range of the logarithmic function, whats the way, the answ...
surreal basin
How do i find out the range of the logarithmic function, whats the way, the answ...
do you know the range of x^2 + 1?
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wanton shuttle
I tried to do this but i stuck at this part
vocal sleetBOT
I tried to do this but i stuck at this part
shrewd jacinth
.reopen
wanton shuttle
?
digital lake
factorize it
digital lake
oh gawd that handwriting
wanton shuttle
and for the other one is (x-3)(x-3)
yeah
my handwriting is bad
I think the common factor is (x-3)(x-3)
But it can't be
Beacuse the factor for 4
Is x(x-3)
Even chatgpt got it wrong
digital lake
it should be 4/x(x + 3)
digital lake
nvm
digital lake
thats right
wanton shuttle
Oh
digital lake
ok then transform the equation and reduce it
digital lake
let em see
undone aurora
ur suppose to show that LHS is equal to RHS?
digital lake
what
digital lake
yea i got 2 answers
digital lake
wait let me reduce the equation
wanton shuttle
ok
digital lake
my method
wanton shuttle
mhm
wanton shuttle
so you did the Multiplication crossover
oh yep thats what i did
but i got it wrong
digital lake
oh