Then divide both sides by trig functions
#help-49
safe onyx
silent compass
What is the problem, seems like you've got your answer?
safe onyx
$$F = \frac {\mu_smg}{( cos\theta + \mu_s sin\theta ) } $$
grand pondBOT
smeagol
grim vector
What is the problem, seems like you've got your answer?
he probably need a check only
safe onyx
I messed up with signs on the way you guys caught my errors while doing it
grim vector
I messed up with signs on the way you guys caught my errors while doing it
Is denominator always != 0 ?
safe onyx
I originally had - ... instead of +
safe onyx
it's a force
grim vector
if it doesn't change
safe onyx
mu _s is constant too
silent compass
Oh mechanics the bane of my existence
safe onyx
this is the start of physics + calc 😔
thank you all much
i just messed up with signs
.close
midnight plankBOT
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Available help channel!
visual delta
midnight plankBOT
grand pondBOT
Azyrashacorki
visual delta
So square root 36 + 2
rose trout
Yeah. sqrt(36) is 6
twilit coyote
Im asked to solve the inequality:
(I): 2x² - 9x + 6 $\geq$ 0
tranquil zinc
Hi
midnight plankBOT
Im asked to solve the inequality:
(I): 2x² - 9x + 6 $\geq$ 0
grand pondBOT
prodigydude
silent compass
What seems to be the problem?
twilit coyote
i just want to know how the table of signs of 2x² - 9x + 6 will look like
cobalt nest
solve $2x^2 - 9x + 6 = 0$ first
grand pondBOT
Goëtia
midnight plankBOT
@twilit coyote Has your question been resolved?
shrewd elbow
midnight plankBOT
livid python
,rcw
grand pondBOT
shrewd elbow
This is the question
How do i know what length tu and uv are if theyre points arent whole numbers
midnight plankBOT
@shrewd elbow Has your question been resolved?
shrewd elbow
<@&286206848099549185>
urban widget
Does it say u is midpoint
late basin
the transverse road go through K, V
So you could find the equation for that road easily
The first and second roads, the x axis are just simply y = k lines
Plug y = k to the transverse road to get T, U and V
shrewd elbow
Does it say u is midpoint
No
late basin
Then the problem becomes manageable
late basin
And first street is y=1
You forgot that the x axis line is just y = 0
late basin
But what do i do now
Find the intersection of the transverse road with those 3 lines to get T, U, and V
shrewd elbow
Is there a formula the intersection?
sullen jungle
Is there a formula the intersection?
intersection means that the two lines meet at a point so you would need to equate both roads
because they share the same point in common
don't memorize
shrewd elbow
So i make them equal eachother or do i do a simultaneously equation
urban widget
Yes
sullen jungle
So i make them equal eachother or do i do a simultaneously equation
its the same thing
simultaneous equation works
same thing as making the y's equal to each other
(comparison method)
would recommend using simultaneous equations if working with higher dimensions
sullen jungle
what is the problem asking first
shrewd elbow
At the end when i do it out i get an andwer in the form y=mx+c
sullen jungle
sorry didnt read the question was just reading intersection stuff but if you're solving this you need to do something else
eh actually yea nvm what we're doing is correct
thought points were already given so makes sense why you're trying to find intersections
sullen jungle
At the end when i do it out i get an andwer in the form y=mx+c
you get the exact x value and then you need to find the y value
you are already given that y=2
shrewd elbow
Oh yeah the x and y intercepts
sullen jungle
yeah
you find the point T coordinate and do the same for U
V is already given (4,0)
just find the distances and thats it
shrewd elbow
Umm how do i find the x intercept again
sullen jungle
x and y intercepts mean something different than what you're thinking
it means where it meets the x and y axis
sullen jungle
Y=2
Y=3/2x+6(equation for transverse road)
you just solve this simultaneous equation
to find the x coordinate of the point
shrewd elbow
I solved it and got y=3x+4
sullen jungle
what did you exactly do?
do you remember how to solve simultaneous equations? if no i'd recommend to revise them
shrewd elbow
You have to get rid of one of the variables
Either x or y
Y+y=2y,3/2x+0and 6+2
2y=3/2x+8
Divide 2 of both sides
y=3x+4
sullen jungle
You have to get rid of one of the variables
correct, but you are not getting rid of neither of them
you are just finding another true equation
shrewd elbow
But one of the equations doesnt have a 2nd variable
sullen jungle
instead of adding both equations you can either subtract one of the two
or you can confront them
shrewd elbow
Its just y=2
sullen jungle
or you can substitute
sullen jungle
But one of the equations doesnt have a 2nd variable
y = 2
shrewd elbow
Ye
sullen jungle
and y = -(3/2)x + 6
if you know that y = 2
you can substitute it in the second equation
2 = -(3/2)x + 6
this is substitution method
you can also just subtract both equations
y = 2
. - (y = -(3/2)x + 6)
0 = -(-(3/2)x + 6) + 2
or you can confront them which happens to be the same thing as substituting
first y = second y
2 = -(3/2)x + 6
you should revise how to solve simultaneous equations
do not memorize otherwise you will struggle a lot later on
think about it logically
shrewd elbow
How so i revise without memorise
sullen jungle
understand why you are doing something in the first place
if you do not understand why you are doing it ask the teacher
dont just accept that it's just this way
this applies to everything
history for example, people don't attack other countries for no reason
land expansion? money? position?
shrewd elbow
well i guess im doing maths to pass exams
sullen jungle
you will have a much easier time understanding the thought process behind than memorizing 300 different things
- you might even need these things in real life applications
simultaneous equations are everywhere
maybe some other stuff doesn't appear but you can find these everywhere
sullen jungle
still in highschool but i will be in september
shrewd elbow
In america right?
shrewd elbow
How does one obtain this level of wisdom in high school
So your only like 2 years older than me
sullen jungle
How does one obtain this level of wisdom in high school
just personal experience in subjects that are not maths 💀
also mostly comes from laziness because my ahh cannot bother memorizing and i also find it fascinating to discover the reason behind stuff
shrewd elbow
Alright well thanks for the help
sullen jungle
np!
shrewd elbow
.close
carmine void
Let X,Y,Z be three random variables such that for their corellation p = p(X,Y) = p(X,Z) = p(Y,Z) holds. Which values can p have?
midnight plankBOT
Let X,Y,Z be three random variables such that for their corellation p = p(X,Y) =...
@carmine void Has your question been resolved?
fallow scarab
Correlation is proportional to inner product and inner product has a Cauchy Schwarz inequality
carmine void
Correlation is proportional to inner product and inner product has a Cauchy Schw...
Thanks for the hint! You're probably referring to $Cov(X,Y) \leq Var X \cdot Var Y$ aren't you? I have thought about it, but didn't see how I can apply this
grand pondBOT
Error5506
nova yoke
what's your definition of correlation, is it cov(x,y) / sqrt(var(x)var(y)) ?
honest urchin
I think without loss of generality you can assume E[X] = E[Y] = E[Z] = 0 and E[X²] = E[Y²] = E[Z²] = 1.
After that the corellation coincides with the inner product.
What values can an inner product take if there are three vectors taking the same inner product?
carmine void
I think without loss of generality you can assume E[X] = E[Y] = E[Z] = 0 and E[X...
That's very smart. Even though I unfortunately can't follow the second one...
honest urchin
I think you can further assume this vector spacxe is 3 dimensional by rotation.
At this point you have an equation.
honest urchin
That's very smart. Even though I unfortunately can't follow the second one...
can you just do:
carmine void
Oh, no
honest urchin
X' = (X - E[X])/sqrt(Var(X))
honest urchin
Is it not what Bungo said
carmine void
Is it not what Bungo said
Yes, somehow I squared the numerator and didn't square the denominator
carmine void
Is it not what Bungo said
So it is either 0 or 1?
grim vector
I've been working with an wrongly defined p(X,Y) the whole time
Outstanding move
carmine void
Outstanding move
honest urchin
What is the angle formula?
honest urchin
why not in the unit sphere?
length 1 that's all
carmine void
why not in the unit sphere?
That's a good point
glass dome
anyway i get that p >= -1/2 by considering the variance of X+Y+Z
i'm not sure how to do better
carmine void
anyway i get that p >= -1/2 by considering the variance of X+Y+Z
Did you ask gtp by any chance?
Because it gave me a bs argument for -1/2
honest urchin
Geometrically I am now thinking p > = 0 might be a better option
glass dome
no?
i mean
var(X+Y+Z) = var(X) + var(Y) + var(Z) + 2cov(X, Y) + 2cov(X, Z) + 2cov(Y, Z) = 3 + 6p
but variance >= 0
so 6p + 3 >= 0, so p >= -1/2
carmine void
var(X+Y+Z) = var(X) + var(Y) + var(Z) + 2cov(X, Y) + 2cov(X, Z) + 2cov(Y, Z) = 3...
Wow, that's cool
honest urchin
but geometrically it is obvious 3 vectors at the same angle to each other can exist
glass dome
if very vaguely we consider the unit sphere
then it seems intuitive that the maximum angle between three points on the sphere would be 120
which would correspond to p = -1/2
so maybe actually every value from -1/2 to 1 is okay
honest urchin
but variance >= 0
so the proof is this + construction for all cases
glass dome
i'm not sure how we can rigorously actually compare the random variables to vectors in R^n
honest urchin
i'm not sure how we can rigorously actually compare the random variables to vect...
ehm
I think I described that part
you just reduce to unit variance case
then you pick an orthongal 3 dimensional basis for the span of them and map over to R³
honest urchin
L2 random variables live already in Hilbert space.
carmine void
Huge thank you @honest urchin and @glass dome for your help! 
honest urchin
For an explicit construction, you might want to consider a single random variable taking the values 0, 1 and 2 with equal probability and then finding 3 functions mapping 0 , 1 and 2 to some values for X, Y and Z.
honest urchin
Huge thank you <@295654938741309443> and <@209767680100663296> for your help! <:...
Happy to help, this question was intruiging.
midnight plankBOT
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Available help channel!
undone heath
Need help
undone heath
Is my proof for the intermediate value theorem correct?
It assumed a bit knowledge since I tried to write it on one page though
@dawn dagger help me 😭
dawn dagger
i appreciate the effort and even colors wow, but like i have no idea
undone heath
😭😭😭
nova yoke
is this U_i defined somewhere?
undone heath
is this U_i defined somewhere?
No space for the page so I just defined it briefly so it’s an over cover of [a,b]
Since I only really need to argue the bounded property of f on [a,b] such that its sign over the interval is preserved
nova yoke
i haven't read the whole thing but my general concern is that you seem to be relying on compactness (since you use the heine-borel theorem) and i don't see any use of connectedness. But the intermediate value theorem isn't necessarily true on a compact set that is not connected
of course [a,b] is both compact and connected, but you need to use the latter fact somehow
undone heath
i haven't read the whole thing but my general concern is that you seem to be rel...
Is it to argue that if for two points in the closed set such that their distance smaller than delta then it’s covered by one open set
frozen hazel
emma did you state the intermediate value theorem
undone heath
Then the sign of the function is preserved since the limit point is bounded locally
undone heath
emma did you state the intermediate value theorem
Bcs I wanted to make it on one paper so very briefly as I assumed the negation of it, so the reversed of the assumption is the ivt
Since we have f(a)f(b)<0 so their signs must differ, however the local limit is bounded, since exist the delta neighborhood which forms an open cover for the closed interval which is the basic idea here
frozen hazel
where was the contradiction
undone heath
I must show that for two points with the property their distance is less than delta that they are covered in one open set of the family which will preserve the sign leading to contradiction
That f(a)f(b)<0 such that there isn’t any x_0 such that f(x_0)=0
frozen hazel
I'm not following where you showed that led to a contradiction
undone heath
Because their sign is preserved in this open sets
We have literally shown that f(a)f(b)=f(x)f(x_0)>0 which is absurd because that f(a)f(b)<0
frozen hazel
right, give me a moment to think about it
normally the theorem's proven a little differently
undone heath
Yes bcs I was proving these theorem interchangeably and I thought that ivt must be a part of completeness too so I did some research, and found the corollary and gave it a try
frozen hazel
normally you can prove it by directly appealing to the completeness of R
nova yoke
why is f(a)f(b)=f(x)f(x_0)>0
undone heath
Here are the others ones so I feel it must be provable using heine Borel theorem for ivt
undone heath
*why* is f(a)f(b)=f(x)f(x_0)>0
Because of that [a,b] is compact so we have a finite subcovering that each of the x’ x’’ satisfies their distance is less than delta
undone heath
By our corollary that the two points are in the one of the open set of the family
nova yoke
Because of that [a,b] is compact so we have a finite subcovering that each of th...
but what is delta, and how does it relate to how much f can vary on an interval with length less than delta?
undone heath
It’s by the corollary..
I will type the fuller version of the last line
frozen hazel
(a quick tip on terms, normally corollaries are quick to prove. The word you probably meant to put was lemma. I think that lemma is usually referred to as the lebesgue number lemma or something like that)
undone heath
Since that for all x_k in the partitions such that the distance of x_k and x_{k+1} satisfies their distance less than delta’ and since their sign is preserved and our corollary that the two points are contained in one of the cover in U_I hence we derived the contradiction that f(a)f(b)=f(x)f(x_0)> 0 which is absurd hence the ivt is proven
undone heath
(a quick tip on terms, normally corollaries are quick to prove. The word you pro...
Yes indeed Lebesgue number
frozen hazel
How do you know f is bounded on that set
undone heath
How do you know f is bounded on that set
Limit of f at every point is bounded locally
That in the epsilon neighborhood the sign is preserved
frozen hazel
ok i see
nova yoke
i don't see how boundedness of f helps, of course it's bounded on every subset of [a,b] because it's bounded on [a,b] itself
undone heath
ok i see
This is the most crucial argument of the proof alongside the corollary or lemma but since I am not a math student this doesn’t matter to me… that the sign is preserved thanks to that f is bounded locally in the epsilon neighborhood
nova yoke
you are just asserting things without any justification, how does local boundedness give you a contradiction?
undone heath
Because that all of these delta neighborhood will give me an open cover
Of the entirety of the set
undone heath
And each of the neighborhood the sign is preserved and all the points are contained of each of the neighborhoods
So the sign is preserved throughout the interval
nova yoke
observe that for example if instead of [a,b] we had a union of two compact intervals such as A = [-1, -1/2] U [1/2, 1] and we defined f(x) = x, then there's no point with f(x) = 0 even though f(-1) < 0 and f(1) > 0 and A is compact
so compactness alone isn't gonna prove this for you
undone heath
observe that for example if instead of [a,b] we had a union of two compact inter...
But that’s a union, and the function isn’t continuous
nova yoke
it is continuous
undone heath
Here I stated f is of class C0
undone heath
Every x_k and x_k-1 is smaller than delta there’s no discontinuity
nova yoke
i can take A = [-1, -delta/10000], [delta/10000, 1]
since you haven't said what delta is
frozen hazel
delta is the number produced by the lebesgue number lemma. It is the lebesgue number of the open covering. Edit: maybe I misinterpreted
undone heath
I definitely said delta>0 be arbitrary somewhere I think but I forgot detail very often 😭😭
I will have to fix it a bit 😭😭😭
Or maybe it’s just wrong
nova yoke
Every x_k and x_k-1 is smaller than delta there’s no discontinuity
this isn't what the lebesgue number lemma says though
it says that if two points are separated by less than delta then there's some open set in the cover that contains both
frozen hazel
you can use connectedness
nova yoke
yea in fact you must use connectedness i believe
because the IVT is not necessarily true on non-connected sets
undone heath
How about I plug the boundary point in the partition will it imply the connectedness?
frozen hazel
basically you can show that the continuous image of a connected set is connected, and that if we had f(a)<0<f(b) with no c where f(c)=0, we'd have a separation of the image of [a,b]
nova yoke
and btw, the IVT holds if the domain is connected, even if it's not compact
so i don't think open covers are really relevant to this
undone heath
Then I think I made it seemingly too easy 😭
But I am quite certain since one of my friend mentions that all the property of completeness implies one another
nova yoke
the usual proof is actually quite simple, suppose there's some point with f(x) > 0 and another with f(x) < 0, but that there's no point with f(x) = 0. Then consider the two sets A = f^-1(-infty,0) and B = f^-1(0,\infty)
A and B are both open since f is continuous
and they're both nonempty since there are points with f>0 and points with f<0
and the domain of f is A U B since there's no point with f(x) = 0
thus the domain of f is not connected
undone heath
Does ivt holds on disconnected set?!
nova yoke
what we're showing here is that if f changes sign but "skips" zero as a value, then its domain must be disconnected
so the contrapositive is, if the domain is connected, then f can't skip values
undone heath
But what I wanted to prove is simple
That if f is continuous then it attains all values
nova yoke
well it attains all values between f(a) and f(b) yes
undone heath
That’s it… and I have never learned connected and implication of ivt😭😭
nova yoke
the above argument works if you replace 0 with any value between f(a) and f(b)
undone heath
Yes I think I was proving a simpler statement that a continuous function with connected images must attain 0 if f(a)f(b)<0
Again I am not a math student and am quite dumb😭
You’re right if this disconnectedness is in play then it’s probably not savable anymore
I was proving a much simpler version I think 😭😭
nova yoke
if you're not familiar with connectedness it's ok, just use the equivalent statement: we have shown that the domain D of f is the disjoint union of two nonempty sets which are both open relative to D
and the key fact you need is that this can't happen with an interval in R
which btw is a nontrivial fact, it takes a bit of work to prove
what's the context here, are you asked to prove the IVT as part of your coursework? and if so, what machinery do you have available?
undone heath
what's the context here, are you asked to prove the IVT as part of your coursewo...
I enrolled a comb of real analysis with Ross s analysis and folland analysis in a row in next year’s spring and am so nervous since the book of folland is so hard and I have no courage to prepare it and have limit YouTube channels teaching those concepts
And I feel so nervous I don’t know I could prepare in relatively thorough manner to be fully prepared
nova yoke
folland's "real analysis"? or "advanced calculus"? two different books at different levels, real analysis is much harder
undone heath
So I am actively proving different things to make knowledge reserve
undone heath
folland's "real analysis"? or "advanced calculus"? two different books at differ...
Follands modern applications of real analysis and another real analysis using Ross book two course I enrolled in a row starting the spring next year 2026
so basically I don’t have much experience of analysis and am panicking for a while now
nova yoke
which ross book? "elementary analysis"? there's a big big gap between that and folland
undone heath
Yes
nova yoke
gap in sophistication that is
undone heath
Very hug
nova yoke
not necessarily in content
undone heath
Very very big
nova yoke
do you know the book "understanding analysis" by abbott?
i think it would be very useful for you right now
undone heath
I finished all exercises of Ross and some on Abbott and now find rudins a bit easier but still
I have been panicking since I saw the content of that folland’s book
nova yoke
oh good, if you have abbott you should check this section:
undone heath
Yes I was proving this version though, but I didn’t know that the connectedness comes into play here…
nova yoke
yea fundamentally connectedness is going to be involved for any version of the IVT that i am aware of
for example it's false if you consider intervals of the form [a,b] in the space of rational numbers (as opposed to real numbers)
undone heath
True, I must be missing a lot of stuff since I was not revising every detail of it I believe…
Now I am even more panicking
nova yoke
well you still have a while, not until next year?
that's a good amount of time to prepare
undone heath
True… I shall study again and again.. and my current study is quite easy.. i will revise the book of Abbott again and alongside some exercise of rudins maybe this is better
nova yoke
yea that would be very helpful
undone heath
And I rely quite heavily on certain argument type, so sometimes it’s not very flexible..
nova yoke
another book that i recommend to help prepare for folland (the measure theory/lebesgue integration part) would be axler's "Measure, Integration & Real Analysis"
undone heath
I will definitely buy it, since I am quite kinda shy person and I definitely don’t want to fail my promise to fail this comb…
I literally have many many analysis books alongside many calculus books, doing puzzles but maybe I forgot to read the theorem in depth which is probably a result of panic
In some degree
I just hope I can do this…
And yes I will order that book
dawn dagger
I just hope I can do this…
you are doing really great, your understanding is exceeding exponentially
undone heath
you are doing really great, your understanding is exceeding exponentially
That follands’ book is a monster I didn’t even have the courage to prepare for it 😭
nova yoke
folland is a fairly hard read even by the standards of analysis books
but i assume you'll have an instructor?
undone heath
but i assume you'll have an instructor?
No I am not even in the department of mathematics, i enrolled the courses of next years fully as my option.. which led to problems like lack of resources and introductory course was still fine many videos are available on YouTube and I would say I can even pass the exam of the course using Ross s book (I have studied by myself for five months already)
But follands, it’s too absurdly complicated and I always felt my foundation isn’t sophisticated enough
nova yoke
i mean next year when you take the course, that will have an instructor right?
undone heath
Probably going to be more anxious since no more down to earth video available anymore..
sleek cloud
You should try Principa Mathematica. Really vital for math majors
nova yoke
their job is to make this stuff accessible to some degree
undone heath
i mean next year when you take the course, that will have an instructor right?
Yes probably, alongside the lectures I will have some discussions sessions
sleek cloud
Probably going to be more anxious since no more down to earth video available an...
Check our organic chemistry tutor
nova yoke
Probably going to be more anxious since no more down to earth video available an...
yea i don't know of any good video lectures at the level of folland, unfortunately
undone heath
yea i don't know of any good video lectures at the level of folland, unfortunate...
That I could’ve studied this analysis independently is primarily a result of these YouTube videos…
Anyways thanks for clarifying that concepts to me or I would even think it’s correct 😭😭😭 I must work harder and thankfully my study is like basically nothing to do
nova yoke
That I could’ve studied this analysis independently is primarily a result of the...
sometimes people organize reading groups on this server, there was a folland one recently in fact, but it was fairly fast paced and i'm not sure it would have been all that useful for you
but keep an eye out, maybe there will be another
sleek cloud
I have multivariable exam on Monday and right now binge watching professors videos on YouTube. The only problem is they are monetized. Can't use add blocks in mobile app
undone heath
sometimes people organize reading groups on this server, there was a folland one...
Thanks so much you helped me so much…. I will go and grab some dinner!! And please have a wonderful day !! Thanks so much again 🥰🥰🥰
nova yoke
Thanks so much you helped me so much…. I will go and grab some dinner!! And plea...
yw, good luck! feel free to ask in these channels anytime
midnight plankBOT
@undone heath Has your question been resolved?
midnight plankBOT
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Available help channel!
dusty portal
so uh...are they speaking in alien or what? (context: i've completed the first chapter of this textbook which is first order equations but apparently when going to second order they start spewing gibberish!) pls help me understand this
midnight plankBOT
so uh...are they speaking in alien or what? (context: i've completed the first c...
fallow scarab
so uh...are they speaking in alien or what? (context: i've completed the first c...
Do you have a more specific question
dusty portal
Do you have a more specific question
help me understand it
floral apex
which one
dusty portal
like what is a "wronskian" for example
grand pondBOT
dusty portal
it makes no sense
floral apex
its just a definition
dusty portal
.close
mint ravine
Please help
midnight plankBOT
Please help
mint ravine
I know that there are 12 squares with two vertices in the set
but the question says "two or more vertices"
so idk what to do with that
unique stream
but the question says "two or more vertices"
at least two corners meet
corners = vertices
if you take any two vertices from among ABCD
and try to construct a square
you'll end up with either one or two possibilities
violet storm
I know that there are 12 squares with two vertices in the set
are you sure about that number 12? are all those squares actually distinct?
mint ravine
are you sure about that number 12? are all those squares actually distinct?
yeah there are 4 choose 2 ways to choose two points from the set
and then you multiply by two to count every option
unique stream
yeah there are 4 choose 2 ways to choose two points from the set
wait why
select two points
and try to construct a square
you don't have many options
violet storm
again, are you sure that the squares are distinct for each combination of two points? draw them on paper and see
unique stream
if you take two adjacent ones
you can only either construct the square itself
or a mirror image of it
so with adjacent corners
we have 5 squares
now take diagonal corner pairs into account
for both pairs you have two options
violet storm
yeah, but try to let the helpee think through the problem instead of just doing it for them :p
mint ravine
i got 9 squares
unique stream
Si I skipped to the conclusion :D
unique stream
i got 9 squares
yoppa
violet storm
i got 9 squares
yeah, thats for when you pick combination of 2 points, now if you are forced to use 3 or 4 of the points, what do you end up with?
mint ravine
if you have 4 points, you can only make one square
violet storm
and is it a new one compared to the 9 we came up with already?
mint ravine
no
violet storm
and with 3 points?
mint ravine
1 square too
violet storm
and same one for any combination of 3 you pick, the original square formed by the 4 points, so again nothing new
so final total is?
mint ravine
9
violet storm
ya so you pretty much had the right idea from the start but just had to check for the fact you were counting the central square multiple times
violet storm
mint ravine
is aops wrong or smth
violet storm
what's aops, the website?
viral dagger
isnt that alcumus
mint ravine
isnt that alcumus
the challenge homework thing
viral dagger
o
violet storm
9 seems right to me, @viral dagger ?
violet storm
try 12 in case whoever wrote the problem double countered the central square...
or 5
but you pretty much know those are wrong
mint ravine
maybe try 5
doesn't work
violet storm
midnight plankBOT
violet storm
thanks for helping!
just to be clear that question is wrong :p you should bring it up to the teacher or whoever
mint ravine
just to be clear that question is wrong :p you should bring it up to the teacher...
oh ok
violet storm
ohhh ok i stand humbled
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gritty holly
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gritty holly
okay i know that integral of sec(x)tan(x)= sec(x) +C but i dont know what to do with the -1
fading ore
okay i know that integral of sec(x)tan(x)= sec(x) +C but i dont know what to do ...
it just makes the integral negative
$\int c f(x) \dd x = c \int f(x) \dd x$
grand pondBOT
hiidostuff
fading ore
like this?
mhm
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last slate
can someone tell me how to solve this using synthetic division
midnight plankBOT
can someone tell me how to solve this using synthetic division
last slate
is it ok for the x to be a negative
heady plume
yes
last slate
so when i do synthetic division how do i plug in
heady plume
just not the value of x for which the denom goes 0
last slate
or should i do long division? idk
heady plume
would be better for you to write -f(x) = ..., and give the minus back to right side after you're done simplifying
$-f(x) = \frac{x^2-5x+6}{x+1}$
grand pondBOT
Arya
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thick sparrow
How do i find out how many tokes are currently held by people ?
midnight plankBOT
How do i find out how many tokes are currently held by people ?
olive yew
How do i find out how many tokes are currently held by people ?
I think it should be circulating supply because that is the number of coin that is available to the public
thick sparrow
I think it should be circulating supply because that is the number of coin that ...
Yeah but this is fixed number its been set from h
The start on this number isnt changing
olive yew
Yeah but this is fixed number its been set from h
The start on this number isnt ...
I don't understand crypto too much maybe check it on google
wind oxide
How do i find out how many tokes are currently held by people ?
'tokes'?
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slate lark
Have a problem with ellipse integral formula execution in mathematica.
It takes too much time and formula doesn't seem to work.
midnight plankBOT
Have a problem with ellipse integral formula execution in mathematica.
It takes ...
@slate lark Has your question been resolved?
midnight plankBOT
@slate lark Has your question been resolved?
midnight plankBOT
@slate lark Has your question been resolved?
midnight plankBOT
@slate lark Has your question been resolved?
midnight plankBOT
@slate lark Has your question been resolved?
queen herald
Have a problem with ellipse integral formula execution in mathematica.
It takes ...
I think you forgot a colon
Should've been matC[a_, b_] := Integrate[...]
mint ravine
I got 12 but the thing said I was wrong
midnight plankBOT
I got 12 but the thing said I was wrong
mint ravine
Can someone please help
Here was my work on how I got 12:
First, I know there are 4! or 24 total arrangements of the numbers
and I also know that if you switch the two middle numbers, the sum will remain constant
while if you switch any other numbers, there would be a new, unique sum
so there are 3!*2 or 12 middle numbers that end up with the same sum
and then I just subtracted 24-12 to get 12 unique final sums
but I think I am missing some, but idk what they are
please help
<@&286206848099549185>
please help someone
.close
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obtuse totem
midnight plankBOT
obtuse totem
Just wondering if it’s valid to write out the computations like this (with the divide symbol) cause the last computation, you can’t do 54/81=0 r54…
How do I say it’s not like exact division?
So to not interpret as 54/81=0.666666
Or reduce to fraction
Maybe I’m thinking too much but here I’m just assuming the grader will know it’s division w remainder
runic hamlet
you can always write it as 54=0*81+54
but it should be fine to just write 54/81=0 R 54 etc
I want to note that your life could be easier if you replaced some of those numbers with the negatives
eg -7 instead of 74, -10 instead of 71
heady plume
that, or you could wrap your expression with a [ . ] to show gif
so something like [27/8] becomes 3, and you can write R = 3
obtuse totem
eg -7 instead of 74, -10 instead of 71
can you show me how to do it that way?
heady plume
However, I'd advise against such method of computation ._.
obtuse totem
what do you mean by that
runic hamlet
instead of computing 74*71, compute (-7)(-10) and then take the remainder mod 81
heady plume
Notice 18*21 = 27*14 So your equation in a sense is 27k = 81m + r and so 27 divides your "r", rewriting r = 27n, will make your life much easier as you're only left to check k = 3m + n or k (mod 3) = n
obtuse totem
instead of computing 74*71, compute (-7)(-10) and then take the remainder mod ...
where are you getting -7 and -10
how does this work tho
you cant reduce the remainder to a negative?
runic hamlet
sure
obtuse totem
wait you can do that?
runic hamlet
yes
midnight plankBOT
@obtuse totem Has your question been resolved?
obtuse totem
i dont rlly see how it makes it easier
I still have to do a bunch of multiplying and dividing..
oh wait i shouldve just kept 70 as is
easy multiplication w 0
what about this question
is it faster to multiply the powers out?
whats the fastest method
i was thinking i multiply 7(7) first and reduce that
or I can match 5 and 7
so i have a bunch of r=35(mod31)s
Like this
wind oxide
is it faster to multiply the powers out?
if ur fast enough with numbers, it doesnt really matter
heady plume
Yes, what you've written essentially reduces as easily as: 7^3 5^5 3^4 = (7*5)^3 (25) * 27 * 3 = (4)^3 (-6)(-4)(3) = (64)(24*3) = 2*10 = 20
midnight plankBOT
@obtuse totem Has your question been resolved?
obtuse totem
sht
maybe i should learn abacus
is it worth it
now😭
multiplying takes too long
midnight plankBOT
@obtuse totem Has your question been resolved?
midnight plankBOT
@obtuse totem Has your question been resolved?
obtuse totem
Is there a faster method
This takes so long to do
I’m using fast modular exponential method
obtuse totem
you cant reduce the remainder to a negative?
@runic hamlet you can reduce remainder to negative, but if you have a = b(modm), then a has to be within 0 and m-1 tho, right?
<@&286206848099549185>
dawn dagger
I might have an idea
obtuse totem
ok
grand pondBOT
anti-algebraist 𝔸dωn𝓲²s
dawn dagger
If I recall it relates to the Chinese remainder theorem
grand pondBOT
anti-algebraist 𝔸dωn𝓲²s
obtuse totem
ok
obtuse totem
yea, cause rn im concerned about a bigger problem
am I trippin or did I just learn the wrong computing method
@dawn dagger https://youtu.be/8r4-5k-o1QE?si=xMoqvWs-5rWbKyzy
this doesnt work for 3^5(mod7)?
am I trippin??
im so confused
dawn dagger
this doesnt work for 3^5(mod7)?
how so?
dawn dagger
which is not right
You forgot a crucial step
In the 3rd column your binary digit is 1 not 0 so it requires two steps
Also the value in the 2nd column is incorrect.
3² mod 7 = 2
Then 2nd columns has 2
Now you need two steps since the binary is 1 in column 3
Take the 2 and square it mod 7 so 2² mod 7 = 4 and now next step take 4 and multiply it by the base mod 7.
4 * 3 mod 7 = 12 mod 7 = 5
The last column contains the solution which is indeed 5.
@obtuse totem
violet lion
Euler's totient function
Oh wait, I think CRT would be more suitable
$37^{31} \equiv 1^{31} = 1 \pmod{4}$
grand pondBOT
timuko
obtuse totem
<@781226352724410398>
hello! sorry i’m here
lmaooo went to get mcdonald’s😂
lmao it’s ok junk food for one day
thank you all!
I’ll look at this again later
gonna sleep now
gn!
heady plume
thank you all!
Also, 37³¹ = 1 (mod 4). Now the only number in {0, ..., 99} with these characteristics is 13, so 37³¹ = 13 (mod 100)```||algebraist gave the same sol. it seems, I'll still leave it tho cuz mine's not very technical||
charred shuttle
Hello. how can i know what the question is for the definite integral? I try setting (5/3) y = sqrt(1+y^2) but then i only get 1 solution 0.75 (-0.75 is extraneous) so how to find the 2 values to take for indefinite integral?
midnight plankBOT
Hello. how can i know what the question is for the definite integral? I try sett...
heady plume
$\frac{5y}{3} = \sqrt{1 + y^2}$
grand pondBOT
Arya
heady plume
is a quadratic. solve
charred shuttle
Yea i solved but u only get 1 solution
gaunt nimbus
,w 5y/3 = sqrt{1+y^2}
grand pondBOT
gaunt nimbus
oh
charred shuttle
So how to find the lower number for definite integral
heady plume
Hello. how can i know what the question is for the definite integral? I try sett...
the other bound is y = 0
charred shuttle
But that one doesnt work for the equation
heady plume
? y = 0 bound isn't working?
gaunt nimbus
why is this?
charred shuttle
for equation 5y/3 = sqrt(1+y^2) 0 doesnt work i mean
gaunt nimbus
no no
heady plume
why'd you solve for that, there's not even any intersection
you're solving area bounded by 3 different curves
gaunt nimbus
the bounds need not be the intersections of the two
heady plume
(or rather, 2 lines and a curve)
charred shuttle
So the definite integral will be from 0 to 0.75?
gaunt nimbus
yes
gaunt nimbus
sqrt(1+y^2) - 5/3y
the curve is more positive
,w integral from 0 to 0.75 of sqrt(1+y^2) - 5/3y dy
grand pondBOT
last slate
midnight plankBOT
last slate
i was going through the answers again
granite cipher
I'm stuck
granite cipher
fallow scarab
ie
x1 + x2 means scoring one point per heads on each of the two fair coins
while 2x means tossing only one fair coin but scoring two points if it shows heads
and these two are not the same
and his variance calculation should be Var(x1) + Var(x2) + Var(y)
granite cipher
ie
x1 + x2 means scoring one point per heads on each of the two fair coins
while...
I got 0.13
But isn't the coin supposed to be more biased to heads
No wait nvm
13 is prime
@fallow scarab
fallow scarab
tell him what he's got now is a quadratic equation in p
it will have two roots, one above 0.5 and one below -- he wants to go for the bigger one
granite cipher
it will have two roots, one above 0.5 and one below -- he wants to go for the bi...
Ahhh sweet
Thanks
.close
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midnight plankBOT
round parcel
@dark locust There's no question shown. It's just a table and a description of what's in the table.
radiant roost
the question might be elsewhere
sometimes at the beginning it'll say something like "for problems 1 through 3, do such-and-such..."
midnight plankBOT
@dark locust Has your question been resolved?
dark locust
Ohh, thank you guyss !!
boreal parrot
How do I solve this
midnight plankBOT
How do I solve this
boreal parrot
I would do u= cos^-1 (2x) and it would work but its 3x unfortunately
midnight plankBOT
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boreal parrot
<@&286206848099549185>
heady plume
hmmmmmm
molten solstice
🟥🔴🔺
boreal parrot
start with u = arccos 3x
I find du/dx of that ?
heady plume
do I have to explain how substitution works?
I can only suggest to go along with u = arccos 3x
boreal parrot
do I have to explain how substitution works?
I know how it works
boreal parrot
I can only suggest to go along with u = arccos 3x
Okay lemme do it rq
3/sqrt (1-9x²)
heady plume
$= -\int e^u \frac{\sin u}{\sqrt{9-4\cos^2 u}} \dd u$
grand pondBOT
Arya
boreal parrot
Yes but I haven't reached that step yet
heady plume
try IBP on this or something ... I gtg. If you reach a wall, hit the helpers
heady plume
Huh, u = arccos 3x => 3x = cos(u)
@boreal parrotwhat you doing !
plug x in terms of u
boreal parrot
X²=cos²u/9 ?
heady plume
btw when integrating it is not compulsory to progress in only one direction
heady plume
X²=cos²u/9 ?
yes indeed
heady plume
btw when integrating **it is not compulsory to progress in only one direction**
after reaching the last step I wrote, try differentiating $e^u sin^{-1} \left(\frac{2\cos u}{3}\right)$
grand pondBOT
Arya
heady plume
you'll notice that you'll get something + 3*your integrand
boreal parrot
**Arya**
I'm not able to get the denominator as u
The numerator is clear from the sqrt of 1-cos²u
In denominator I have
heady plume
In denominator I have
good. now differentiate the term I gave you
in a seperate line,
neatly
boreal parrot
good. now differentiate the term I gave you
Am asking for help coz I can't do these things by myself 🥲
Could u like workout it out and show me the steps and I follow through coz that's kind of easier for me
heady plume
heady plume
Could u like workout it out and show me the steps and I follow through coz that'...
$\left[e^u \sin^{-1} \left(\frac{2\cos u}{3}\right)\right]' = e^u \sin^{-1} \left(\frac{2\cos u}{3}\right) - \frac{2e^u \sin u}{3\sqrt{1 - \frac{4\cos^2 u}{9}}}$
grand pondBOT
Arya
heady plume
if you look with your eyes open, the right-most part of the equation is your integral
so if you could expand arcsin(2cosu/3) in terms of u, you'd be mostly done [altho Idk if that'd be easy]
I would've surely looked for the easiest way out but I'm at the deadline of my own hw :p
boreal parrot
OK but how did u come up with differentiating this coz I couldn't see it in the terms earlier
boreal parrot
I would've surely looked for the easiest way out but I'm at the deadline of my o...
It's okay
heady plume
How do I solve this
oh btw, it looks like this is not a calculable integral
so you were probably given this as a definite integral or a prank ._>
!xy
midnight plankBOT
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.
boreal parrot
so you were probably given this as a definite integral or a prank ._>
It was indefinite I think it just had an error
Coz the others were quite direct except it
midnight plankBOT
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inland patio
My linear algebra is a bit rusty, so excuse me if this is obvious. I'm reading this answer on the polar decomposition of a real matrix. I'm a tiny bit confused by the sentence where the author says M^tM being positive definite and hence has the unique positive semi-definite square root P=sqrt(M^tM). Isn't it more precise to say that P is also positive definite instead of positive semi-definite?
midnight plankBOT
My linear algebra is a bit rusty, so excuse me if this is obvious. I'm reading [...
hard umbra
yes
midnight plankBOT
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dawn dagger
||algebraist gave the same sol. it seems, I'll still leave it tho cuz mine's not...
I did and got ignored lol
midnight plankBOT
I did and got ignored lol
dawn dagger
.close
midnight plankBOT
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tidal turret
midnight plankBOT
tidal turret
odd solar
What have you done so far
odd solar
What do you need acceleration for
tidal turret
since is a uniformly accelerated motion
tidal turret
What do you need acceleration for
we dont?
tidal turret
What does it mean for A and B to ‘meet’ again?
well
they are the same place
at some time
odd solar
Yeah
So their position on the line is the same
And how do you get position from velocity?
tidal turret
And how do you get position from velocity?
integration?
odd solar
Yes
tidal turret
And how do you get position from velocity?
I dont know
odd solar
So how would you formulate the question mathematically
tidal turret
wait wait wait
is better if we use kinematic equations
idk if intwgration is necessary
and maybe we are using a hammer to kill a wasp
odd solar
You can do, I haven’t used suvat in a long time so it didn’t come to mind
odd solar
Yeah in the UK they are known as SUVAT equations
tidal turret
tidal turret
Yeah in the UK they are known as SUVAT equations
problem is which one I use
tidal turret
reason and motive
tidal turret
Since the others require final velocity, which you can’t get
hmm
tidal turret
Since the others require final velocity, which you can’t get
A: vi = -2 m/s
A : vf = 0 m/s
A : t = 3s
B : vi = 4m/s
B : vf = 0m/s
B : t = 12s
aA: (0-(-2))/3 = 2/3 m/s^2
aB: (0-4)/12 = -1/3 m/s^2
odd solar
Where is vf = 0 coming from
tidal turret
from the graph
odd solar
How so
last slate
hello.
tidal turret
for A, v1 is -2m/s when t = 0s
for A, v2 is 0m/s when t = 3s
odd solar
That’s initial velocity
tidal turret
That’s initial velocity
edited, still wrong?
odd solar
And you’re saying v2 is final velocity?
odd solar
But how do you know they meet at t=3s?
tidal turret
they don't,we are calculating acceleration
since the graph is linear, acceleration is constant
odd solar
Ooh ok right
tidal turret
I havent used suvat yet
odd solar
So you agree we can’t use the equations that have final vel in them
tidal turret
also, we need second eq in suvat because we don't have vf of A
tidal turret
So you agree we can’t use the equations that have final vel in them
ye
odd solar
Yeah, we’re on the same page now
tidal turret
so now what?
odd solar
You get the u and a for both A and B, then you will have to solve simultaneously since t is also unknown
odd solar
Or set them equal to each other, solve for t, then find position at that t
tidal turret
uA = -2m/s
uB = 4m/s
tidal turret
Or set them equal to each other, solve for t, then find position at that t
exactly
tidal turret
Or set them equal to each other, solve for t, then find position at that t
nice bro
s = ut + (1/2)(at^2)
A: s = (-2)t + (1/2)(2/3 . t^2)
B: s = 4t + (1/2)(-1/3 . t^2)
(-2)t + (1/2)(2/3 . t^2) = 4t + (1/2)(-1/3 . t^2)
-4t + (2/3)t^2 = 8t -(1/3)t^2
-12t + 2t^2 = 24t -t^2
3t^2 -36t = 0
t(3t -36) = 0
t1 = 0s
3t = 36
t2 = 12s
odd solar
So they meet again after 12s
tidal turret
,calc 12 * 12
grand pondBOT
Result:
144
A: s = (-2)(12) + (1/2)(2/3 . 144)
A: s = -24 + (2/6 . 144)
,calc -24 + (2/6 * 144)
grand pondBOT
Result:
24
?
tidal turret
Result:
```
24
```
they meet at 0m and after 24meters
odd solar
tidal turret
You could just get the area under velocity time graph of B
wdym
base x height x 1/2
tidal turret
,calc 1/2 * 4 * 12
grand pondBOT
Result:
24
broo how does that work
the integral is the area under the curve
odd solar
The area is base * height
Which is seconds * (metres/seconds)
The seconds cancel giving you metres
odd solar
the integral is the area under the curve
Yeah, which is why I initially suggested equating the integrals
tidal turret
interesting
we can do it with definite integrals
is just too complicated for me tho
tidal turret
Yeah in the UK they are known as SUVAT equations
bloody hell mate
odd solar
Nice one weon
tidal turret
Nice one weon
ty for the helppp
odd solar
Your linear algebra questions are more interesting cl
midnight plankBOT
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cosmic cobalt
i do not know how to solve htis
midnight plankBOT
i do not know how to solve htis
cosmic cobalt
i know only the equation of an eclipse
carmine sigil
This is not a question about ellipses per se
This is a question on how well you are able to read and interpret a diagram.
carmine sigil
It's asking you to find the value a
Using the diagram
Where is "a" on the diagram?
cosmic cobalt
this
carmine sigil
Yes.
Then on the bottom you have a bunch of things, are those adding to make 2a or multiplying?
cosmic cobalt
there is no multiplying in the answer choices
carmine sigil
True
cosmic cobalt
wait dont tell me that the questions is just this silly?
i do 2a = aall the values down?
carmine sigil
So can you write out an equation that begins with "2a ="
carmine sigil
Yeah, ecpc
cosmic cobalt
can i ask for help in something else
cosmic cobalt
i guess this is more math than physics, I chose B
carmine sigil
!1q
midnight plankBOT
It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.
carmine sigil
So you have:
0.2 E1 = E2
cosmic cobalt
yes
carmine sigil
Where E1 is the kinetic energy of the small mass
cosmic cobalt
yes
cosmic cobalt
.2(1/2m x v^2)=(1/2M x v^2)
cosmic cobalt
i mean by x , multiply
carmine sigil
.2(1/2m x v^2)=(1/2M x v^2)
This is not quite correct
cosmic cobalt
why
carmine sigil
Because M is the bigger Rock so M has more kinetic energy
cosmic cobalt
yes
carmine sigil
In other words you have 0.2 small = large
cosmic cobalt
but what is wrong in the equation
carmine sigil
But really it's 0.2 large = small
cosmic cobalt
but D doesnt make sense , how is the the big mass is 0.2 of small mass
cosmic cobalt
But really it's 0.2 large = small
that is what am thinking about
so the question is wrong?
carmine sigil
This problem actually has a lot of problems going on
carmine sigil
i guess this is more math than physics, I chose B
This is the wrong M for instance
cosmic cobalt
this is their explanation
carmine sigil
I think they just got everything mixed up
cosmic cobalt
but it doesnt make sense to say big stone is 0.2 of small stone
carmine sigil
You're correct. Just a broken problem
cosmic cobalt
do you know physics? may i ask a physics problem
carmine sigil
I do, and go ahead
cosmic cobalt
newtons law
ok so i said Fy net = ma
so F tension - F weight = ma
50 - 10(4) = 4a
10 = 4a
a = 2.5
non of the answer choices give me that
i do not understand why this did the pythegorean theorem
what is Fa
carmine sigil
Oh
cosmic cobalt
there is no applied force
cosmic cobalt
why
carmine sigil
Ok so
silver bluff
i do not understand why this did the pythegorean theorem
for vector addition
carmine sigil
The total length of the vector is not the length of the x direction plus the length of the y direction