New stupid questions general thread.
Last stupid questions general thread is autosage.
Older stupid questions general still archive here for now
>>7622225
>>7636900
I'll start off
flat surface can only provide a perpendicular counter force right?
second question is this picture,
I'm supposed to find the angle of the bar at which this construction is in balance but I can't seem to find the right equations to do this
>>7636917
This is a statics questions. You're missing relevent info required to solve it. An angle or another length is required.
>>7636920
no other info is given
if you would make this construction the bar would move itself to a certain angle, I just need to know that damn angle
but I don't see how
>>7636994
just watch the mythbuster episode on it bru
Where I can acquire MatLab for free without torrents?
>>7637607
your dreams
So what exactly are quarks (and other fundamental particles) made of?
>>7636917
anyone?
this should be solvable, solution should be around 54 deg >.<
What books would you recommend to someone who completely missed out on school?
>>7637973
strings.. according to some
>>7638044
school books.
>>7637410
the treadmill clearly didnt mache the planespeed
Would this work? If it does work, is it a good idea/efficient?
1. Build a capsule for astronauts to live in when in space.
2. Attach capsule to a massive contraption.
3. Contraption from #2 is basically a giant hydrogen balloon.
4. Let the hydrogen lift the contraption to a significant height.
5. Once #4 is completed, combine the hydrogen with oxygen and use the resulting combination as rocket fuel to go the rest of the way needed into space.
>>7638302
How the fuck would you arrange it so that you can change the hydrogen from a gas into a liquid? Rockets use H2(l). It's not very dense, even in liquid form. Cooling it significantly would be an issue, as with the presumably rapid transition from balloon into rocket. It's not efficient at all, just a huge pain in the ass to design.
How are 315 degrees and -45 degrees any different? They both point to the same spot on a unit circle, and they both have the same values for sin and cosine.
Sup Nerds,
need some help with set theory again how an I prove or disprove following problems?
Anything to read up on that stuff?
Or any hints from yo site?
Basically I ust have to prove that the following sets are sunsets of the one in the title.
Anyone have a suggestion for material, textbooks, etc dealing with neuroanatomy, neurochemistry, and general neurology?
It'll only ever be casually study, but I already have much of the underlying framework to interpret it. I just need more, and it'd be nice to have it relatively serial and in one place.
Is centripetal force conservative? This is a.matter of life and death.
>>7638625
Hint: See if you can write the sets in part a, b, c, d in their explicit form, e.g., try to write 5Z+1 as {5k+1 | k is a member of Z}
>>7638650
cool thanks will try that in an hour, I'll need to nap first - will let ya know afterwards how it went.
>>7638638
Shameless self bump.
>>7638625
Untegruppe = Subgroup
They are all trivially subsets of [math]\mathbb{Z}[/math] but not all of them are subgroups.
>>7638625
God damn fuck this, would someone be so kind to give me the answer to one of those problems so I can work from there?
How would a nuclear bomb in space blowing up play out? Wouldn't you need oxygen for it to explode? Would it just happen then freeze?
>>7638384
They are the same but who uses negative bearings? Thats just retarded
>>7639021
Let [math](G,+)[/math] be a group. A set [math]H \subset G[/math] forms a subgroup [math](H,+)[/math] iff for all [math]x,y \in H[/math] we have [math]x-y \in H[/math].
a) Let [math]x,y \in 2\mathbb{Z}[/math] then there exists numbers [math]n_1,n_2 \in \mathbb{Z}[/math] with [math]x = 2 n_1[/math] and [math]y = 2 n_2[/math]. Now we have [math] x - y = 2 (n_1 - n_2) \in 2\mathbb{Z}[/math]. Thus [math]2\mathbb{Z}[/math] is a subgroup of [math]\mathbb{Z}[/math].
>>7639055
Wow you must be really fucking stupid. The explosion is because of the sudden release of massive amounts of energy in all directions. There'd be no shockwave because there is no air but there would still be massive amounts of ionising and non ionising radiation.
>>7639077
ok cool I've gotten this far but don't I also have to prove the neutral element and the inverse element
>>7639077
Thanks for helping me out though, I've seen that I got atleast the gist of it
How do I show that the ordered square is Lindelöf? Everywhere I look says that it's compact, and so the Lindelöf property obviously follows, but I can't figure out how to show it's compact either.
>>7639122
Use Heine-Borel
>>7639078
Thanks friend!
>>7639130
Do not use Heine-Borel -- it's the standard topology.
>>7639380
That should say
> It's not the standard topology
Hmm... Well, I've got that the ordered square is [0,1] with the discrete topology (which is not compact or Lindelöf) crossed with [0,1] with the standard, but that doesn't seem to be getting me anywhere
What are some operations/tricks besides limits with the denominator approaching 0, that will make f(x) diverge to infinity with finite x? I really like graphs like this but I'd like some that aren't such simple results.
>If the rest mass m is imaginary this implies that the denominator is imaginary because the total energy is an observable and thus must be real.
What? If we accept that an observable must be real, how can we start from the premise that particles with imaginary mass exist?
And why must observables be real in the first place? Isn't alternating current modeled with complex terms? Is AC not observable?
>>7639590
shiit thanks bru !
yea the weight of the beam is 800N
I just never mentioned it here
Does anyone have any suggestions on how to get my day going after sleeping too much?
I'm normally someone that goes with around 7 hours, and I got 9 last night. Now, I'm basically a zombie. I have a ton of shit to do, and no energy to do anything. Any help would be really appreciated.
>>7639735
cold shower
is there a function such that f'=1-f^2 or such that f'=f^2-1?
>>7639831
What Do you mean with [math]f^2[/math]?
[math]f^2 = f \circ f[/math]
or
[math]f^2 = x \mapsto (f(x))^2[/math]
?
>>7639846
(f(x))^2, likes sin^2(x)
>>7639851
Then yes by the theorem of Peano such a function f exists.
https://en.wikipedia.org/wiki/Peano_existence_theorem
>>7639846
>>7639856
I meant to ask what that function was, if there actually was such a function over the reals. Like (tan(x))'=1+tan^2(x), but I need something in the form of f'(x)=1-(f(x))^2. Wolframalpha gives me solutions that have complex numbers in them, and when I tried to solve it, I also got complex numbers.
>>7639871
nevermind, it's the hyperbolic tangent
What is this supposed to mean?
So if a linear combination is an arbitrary sum of vectors scaled by arbitrary coefficients, what's the pic related got to do with points? The a(i) term I assume to be the coefficients in a linear combination. Where are the points? All in all, what does pic related really mean?
Is there anything like this for computer science?
>>7640032
for the programming part, if you are not interested in all the rigors people go through in college, unlike other areas, it's a very hands on thing
JUST DO IT
unlike others, you get immediate feedback on what you do, you can quickly fix/change things, that sort of thing
some stuff to go through:
the C++ programming language or programming principles and practice by bjarne
if you want algorithms, go for knuth or cormen
hang around /g/dpt
solve euler challenges https://projecteuler.net/
if you want
pic related
how do we measure which slit an electron travels through in the double-slit experiment and predict where it will land on the diffraction pattern
>>7640058
Thanks, I frequent /dpt/ and there's some cool stuff. I'm gonna look at knuth and cormen because I'm more interested in the analysis of things; my biggest concern is that the non-programming classes in my undergraduate are not rigorous enough for graduate programs
>>7639553
Can someone answer this please?
|2x+3| is neither odd or even.
I set f(-x) = |2(-x) + 3|
=|-2x + 3|
= 2x + 3
If the equation is f(-x) = f(x) shouldn't this be even? My book says it's neither even or odd.
has anyone ever used
(-1) | arbitrary function |
?
>>7640238
You need to look for non-rational functions which have singularities. For example, the natural log.
>>7637607
Some coursera courses give out MatLab licenses while you're enrolled in the course
>>7640271
How to construct arbitrary such functions?
>>7640239
|-2x+3| != 2x+3
x = -1.5
>>7640297
I thought the absolute value of a negative was a positive?
What are some good multiple choice test taking strategies? I understand the material well, but I'm simply autistic when it comes to taking the test itself.
How to proof binary relations? I don't post an example because
I want to get a grasp on how to solve my HW and not being accused of faggotry.
Thx in advance.
>inb4 underage b&
>>7639590
anon never made it out of class :(
Is there any supplementary book to go with Peter Lax Linear Algebra and its applications ?
My coursework requires this book. I have a lot of catching up to do with the class work and decided to read the book finally. I feel it is too terse for my liking. Any other books with more examples and covers the similar topics? I am in an abstract linear algebra course. The professor has covered the 1st 5 chapters of the book. If there are any other good university course websites with lots of similar homework (more abstract and theory oriented), that would be helpful too. The second recommended book is Linear Algebra by friedberg, insel and spence. But I want to be sure to cover the same stuff from class. Does that book develop abstract theory or is it more suited for problems requiring calculcations and such? If there are good university course webpages for abstract algebra, that'd be helpful too. Is the book by Shilov good? I saw it in the 4chan sci wikia.
>>7640062
by not observing it
Why should a line and a point in [math] \mathbb P^3 [/math] have a plane between them? Is it because you could take the corresponding line and plane in [math] \mathbb A^3 [/math] and take the 3-dimensional linear subspace spanned by both?
>>7640875
A Line and a point not on the line can be connected by by an surjection from every point on the line to the point. Basically connect each point on the line to the point in question. And you have a plane. For a short segment it is a triangle. E.g. (-1,0) to (1,1) is a segment on the x axis and the point (0,2) is on y. If the segment on x axis is connected to the point (0,2) you get a triangle but when you stretch this short segment to the entire line you get a strip between bounded by the horizontal lines y=0 and y=2
What does the added half cell do to the whole combined cell? It's literally a copy of the middle one. question 2 btw
>>7640827
Started typing to tell this post off but then I read the question all the way and this is literally the answer.
Are we heading towards a breakdown of society just like the mice in the mouse utopia experiment?
If you think about it we've got mgtows (the male mice that didn't breed) homosexual population is on the rise and feminists (the female mice that got aggressive)
Do most people that are advanced in mathematics already have fluency to begin with for some reason? Should a person who couldn't hack algebra 2 even be here or live? How do I improve? It's been almost 6 years since I been in school.
>>7639082
That's the "one-step" subgroup condition. It gives you everything in one go!
If you have any element a (okay so we also require the candidate to be non-empty) then, if you fulfill the one-step subgroup condition, you immediately have a-a = 0 in your group too.
Then, as 0 is in your subgroup, for any element b, by the one-step subgroup condition, we also have 0-b = -b.
>>7640928
I don't think this apparatus would work. The electrons move from Mg to the Iron fork when Mg2+ ions are produced, and then are used with Ag+ ions to form Ag solid. Eventually, a positive charge will build up on the left side because of a lack of electrons, but the NO3- ions from the salt bridge will replenish it. Similarly, on the far right there will be a buildup of electrons but this time there is no salt bridge to replenish it.
The only thing I can think of is electrons moving along the wire to the middle Ag and doing the same process there as it did to the far right one, and then the build up of electric charge can be replenished by the K+, but something about that iron fork kinda throws me off.
>>7639963
Oh, I know this.
So, the idea is that a vector space has an origin, right? And this lets us geometrically interpret addition as tip-to-tail blahblah.
Or, algebraically, vector space addition privileges one particular vector: the zero vector.
But what if I don't want to choose an origin?
Specifically, given some set S which can be made into a vector space over a field (F,+,x) via some scalar multiplication * and vector addition + (overloading the symbol, sorry), there are in fact many ways to do so, each given by a choice of origin (some particular s in S). Once you've done this, you have the usual notion of linear combination, for example.
Without choosing an origin, you can still relate your set S to the the vector space V via a subtraction map S x S -> V which takes two points A and B and gives you a vector BA which, geometrically, joins them, and an analogous addition map S x V -> S which takes a point A and a vector AB and, geometrically, places the tail of the vector AB at A, which points to a unique point B in the set S.
After stipulating various uniqueness and existence properties for these maps, we then have a family of bijections S -> V, one for each element S, which we may interpret as being a choice of origin for S, making it vector-space-isomorphic to V. But this isomorphism isn't unique!
Now I get to the point. It turns out that for any choice of origin and any finite set of points {s_i} and any set of coefficients {a_i} summing to 1, the vector to which (sum a_i s_i) corresponds is unique; there is no freedom.
Example: no matter what vector space addition and scalar multiplication I endow R^2 with, the average of the two points (0,0) and (4,4), i.e.
(1/2)(0,0) + (1/2)(4,4)
will always be (2,2); in contrast, the sum
(0,0) + (4,4)
is free to be pretty much anything.
https://en.wikipedia.org/wiki/Affine_space
http://math.ucr.edu/home/baez/torsors.html
>>7640296
Daisy-chaining together the typical elementary functions via addition (finite and countable), multiplication, and composition should be enough to construct a pretty big family, but if you have enough differential equations strength, you can construct equations which provably have properties of basically whatever you want.
>>7641232
No. They might be predisposed with an ability to grasp concepts faster, but most people tend to overestimate the amount intelligence and underestimate the amount of hard work.
As far as Alg. 2. Yes, you should learn it. Khan Academy is the common suggestion. Also look into getting a textbook, sucking it up, and ploughing through it.
Can someone help a nigga out?
I'm a biology/chemistry major currently fucking confounded by graphing pairs of non-linear equations.
How do I make cynaide gas at home so I can ascend to the great biosphere in the sky?
>>7636900
any microbiologists lurking?
how the living shit do you calculate resistant plasmid frequency/transfer rate (during conjugation ofc)
>>7639553
e^(1/x)
You are given [math]P(A \cup B)=0.7[/math] and [math]P(A \cup B')=0.9[/math]. Calculate [math]P(A)[/math]
>>7641325
taxus baccata is way better and you might just have one in your garden at home. make yourself a nice cup of probably disgusting tea and off you go.
>>7641282
>Daisy-chaining together the typical elementary functions via addition (finite and countable), multiplication, and composition
Sure, but I don't really know strategies for this daisy-chaining that would produce results other than ones with some denominator approaching 0.
What concepts is linear algebra useful in?
>>7635233
Is a black hole the clump of matter after it collapses past it's shwarzschild radius, or is it the space time distortion caused by such an event?
>>7641808
matter is defined as a disturbance or bending of spacetime, so the answer is both.
>>7641770
literally every class that's worth studying
i.e: anything technical
>>7637607
If your ISP gives you shit for tormenting then use a VPN, or a torrent-to-direct-link converter like Zbigz (Zbigz.com) or Boxopus.
Yo but does jelqing work?
>>7641960
bump for science
I need help.
Does the Differential equation xy'(x) -y(x) - x - 1=0
have a series solution?
Mathematica says the solution is y(x)=c_1x + x*ln(x) - 1
>>7641960
What on earth is jelquing?
>>7641986
penis exercising techniques to make it bigger
>>7641640
P(AUB)=P(A)+P(B)-P(A^B), P(AUB')=P(A)+P(B')-P(A^B'), P(B)+P(B')=1, P(A^B)+P(A^B')=P(A). Assuming B' is the complement of B. I'm too lazy for Latexing the shit, so ^ denotes the intersection.
>>7641980
Convert lnx to a taylor series, end of discussion
I get how the Monty Hall problem works, yet something is still bothering me.
Let's imagine the same game except the host doesn't know where's the car.
What is your best option ?
At first I thought changing was still the best.
However I have some doubts :
Let's say there are actually 100 doors : Monty Hall randomly opens 98 doors (he never opens yours).
There are only two doors left, the car being behind one of them.
It seems pretty clear that your door is very likely to be the car's door.
Is it still true with only three doors ? Does your door have slightly more chances to be the car's door ?
>>7642001
If the host doesn't know either, the prob for the player to get the car on first choice is the same as the prob for the host to open the car door, 1/3. This then gives two posibilities, opening the car door and player losing always, or opening the goat door. The latter makes the endgame similar to the one with the host knowing his stuff. The calculations are quite simple after these remarks.
>>7642001
You are describing the Monty Fall problem which always has 50/50 chance.
is cognitive science a fun field to get into? artificial intelligence wasn't right for me.
i'm not worried about how much money i earn later in life, i just want to do research.
>>7641992
I already got it brehski, thanks anyway.
>>7642000
At x=0 there's no Maclaurin Series because ln(0) is undefined, and 1/0 is also undefined.
Also, x*ln(x) also has no series at x=0
And for an arbitrary constant, c_1 there's no series for constants.
So it doesnt have a series solution, Right?
Or is there a series solution where x is not equal to 0(point of singularity)?
>>7641987
Most likely not; if that were the case then having sex would make your penis bigger.
>>7642023
Monty Hall Problem does not have a 50/50 Chance. Your initial Choice was a one out three chance. This means there is a 2/3 chance that the car is behind either one of the other two doors. Opening one of those doors does not change the original 2/3 probability of one of those two doors containing the car. Therefore the chance of it being behind the the remaining door is 2/3.
(x-y)(3x-4y)
Why is x * 4y =4xy and not 4yx.
>>7642112
Commutativity
>>7642112
4xy=4yx
They're literally the same thing.
a(bc)=b(ac)=c(ab)
There's a name for it, commutativity (in which
theorderin which theoperands are taken does not affect theirimageunder the operation.) It only applies for real numbers I think.
It applies to addition as well:
a + b= b+ a
You can verify that 1+ 2 = 2+ 1 = 3
and
2*3*4= 3*2*4 =4*3*2 = 24
>>7642140
it doesn't matter?
http://www.mathwords.com/c/commutative.htm
>>7642112
Well unless you're working with operators (which don't necessarily commute) then x4y=4xy=4yx, the only reason you see it written 4xy more then 4yx is because of the alphabet (ie x comes before y).
>>7642112
x goes first in the alphabet so it goes first in the algebra.
also 4*x*y is the same as 4*y*x so it's irrelevant except for convention.
>>7636900
I'm in the UK and am strongly considering a maths PhD with the intension of going into research.. What should I know about it? Pros/cons?
>>7641980
Self bump.
Yes or no?
>>7642146
If we are talking about the ordinary multiplication of numbers, then it makes no difference. It's the same thing for summation. x+4+y=4+x+y.
>>7641980
>>7642201
yes it does. The solution of a DE with variable coefficients of the powers of x will always have a solution of the form [eqn] y= \sum_{n=0}^{\infty} c_nx^n [/eqn] This can easily be seen because y and it's derivatives are powers of x, and in order for all the dimensions to match up the derivatives must be multiplied by a power of x (y=x^2 is multiplied by 1, y'=2x must be multiplied by x, y''=2 must be multiplied by x^2 so that all of the dimensions are consistent).
>>7642236
Thanks, anon.
Is there a condition(s) where a DE does not have series solutions at all?
guy im tripping hard.
if you have an integral xsqrt(x^2 +1) dx
do you just use U substitution or trig?
I had this question on an exam yesterday and I just went with U substitution, but idk if I'm right....
>>7641657
How to combine a finite number of elementary functions that don't diverge with finite x, or have a function describing the combination of a finite number of finite elements, so that the result will diverge with finite x?
>>7642236
To solve something like xy'-y-x-1=0, we need to take the derivative of the solution given above. [eqn] y= \sum_{n=1}^{\infty} nc_nx^{n-1} [/eqn] Now we substitute the two forms into the DE. Remember x*x^(n-1)=x^n, so we get: [eqn] -x-1+ \sum_{n=1}^{\infty} nc_nx^n- \sum_{n=0}^{\infty} c_nx^n=0 [/eqn] Since they have the same power of x, we can combine the two summations as long as we pull out the n=0 term from the second one. [eqn] -x-1-c_0+ \sum_{n=1}^{\infty} c_nx^n(n-1)=0 [/eqn] Both terms need to be 0, so. [math] c_0=-x-1 [/math] and [eqn] \sum_{n=1}^{\infty} c_nx^n(n-1)=0 [/eqn] x^n can't equal 0 as n>=1, so c_n(n-1)=0. When n=1, c_1 can be anything we want it to. But for n>1, c_n=0. This means the series terminates. When we substitute these c values into the original form given above, we get (-x-1)+c_1*x, or (c_1-1)x-1. c_1 absorbs the 1 that's subtracted from it and leaves c_1x-1. This is only have the answer though, not the general solution. y1=x, which is the essence of the solution found without any of the junk like c_1 or -1. to find a second linearly independent solution we can use reduction of order which I won't do because I'm running out of space but you end up getting y2=x*lnx. So add the two solutions and you'll get what mathematica gave to you (although there should be a c_2 in front of the x*lnx).
>>7642401
u sub should be fine its a function to a power with its derivative you would have used trig if no x on the outside sqrt
>>7638384
They indicate the same place on the unit circle, but they represent different means of getting to that point.
>>7642365
I'm not far enough ahead in my DE class to have an answer for that, but I'd guess something like sec(x)y''-e^(1/x)y'+3y=cosh(x) would be really hard to solve with a series solution. That doesn't necessarily mean it doesn't have one though. Maybe someone else can answer that one.
>>7642145
It does not only apply to real numbers. Abelian groups are objects in which addition is commutative, and commutative rings are objects in which addition asks multiplication commute (e.g. the real numbers). Commutative rings are a fascinating subject.
>>7642365
I don't know the conditions but I believe there are plenty of nonlinear ODEs even at second order that don't have series solutions
>>7642465
Even first ODE like
x * y'(x) = 1
don't have a series solution.
Can anyone give an example of a regulated function that is not continuous almost everywhere?
>>7642540
Nah, they are all continuous almost everywhere (the set of discontinuities is countable)
>>7642592
So how is the regulated integral more general than the Riemann integral?
>>7642602
I don't think it is (unless we're not talking about the same thing), the regulated functions are a subset of the Riemann-integrable functions
>>7638236
well...
>>7642612
Regulated functions are uniform limits of step function sequences (or equivalently, functions that have a left and right limit everywhere).
>>7642717
That's what I thought. Then, they are all Riemann-integrable but the set of Riemann-integrable functions is strictly greater than that of regulated functions (consider the function f defined on [0,1] by f(0)=0 and f(x) = sin(1/x) otherwise)
>>7642421
Isn't reduction of order for second order differential equations?
If I use y1(x)=x...
First I assumed a solution y2(x)=v(x) y1(x) then for this problem y2(x)= x*v(x) y2'(x) = xv' +v
Substituting it into the original equation:
xy'-x-y-1=0 gives:
[math]x^{2}*v' -x -1=0[/math]
The solution for that D.E is v(x) = c_1 -1/x+ ln(x)
For the question in the image, does this proof make sense?
The n-sphere is compact because of Heine-Borel (closed and bounded).
The map from the n-sphere to the quotient space is continuous by definition, call this map M.
As the n-sphere is compact M maps a compact set to a compact set. Therefore quotient space is compact, which is defined as the real projective plane, so the real project plane is compact.
>>7643107
Makes sense to me. Just a little thing, though. That's the real projective (n-)space, the plane is the case n=2. Just said this so that you don't get any complaints about it.
>>7643364
Cool, thanks!
>>7642896
Interesting, when you multiply v(x)*x to get y2 it ends up being c_1x-1+xlnx, the exact solution that mathematica gave. I just thought that y2=ln(x)*x, and I think that would be the case if there is no input function. Usually the procedure is to find the solution of the homogeneous equation first and then from there we can find the particular solution, then the general solution is just their sum. I'm not sure exactly what we did but we ended up with the right answer.
I don't understand this question:
In modeling the number of claims filed by an individual under an automobile policy during a three-year period, an actuary makes the simplifying assumption that for all integers [math]n \geq 0[/math], [math]p(n + 1) = 0.2 p(n)[/math] where p(n) represents the probability that the policyholder files n claims during the period.
Under this assumption, calculate the probability that a policyholder files more than one claim during the period.
To me, (a math undergrad noob), it looks like a recursive function, where we can calculate the probability of [math]n+1[/math] claims, given the probability of [math]n[/math] claims. But we're not given the probability of 1 claim during this period, so how does this really work?
>>7643387
probabilities sum to 1
Are any fields of science immune to this runaway affirmative action/feminist insanity that's going around lately?
Where do they draw the line? At what point do skills and human lives become more important that idiots feelings?
>>7643383
>y1
>y2
This is a first order D.E
Shouldn't there be just one answer?
>>7643411
Yeah I guess you're right. I've been doing second order DE's so long I got everything all confused and shit. Fuck.
>>7643433
Bummer.
You can't help me solve it?
>>7643401
Say it again
>>7643446
Not the same guy but let's see: You want to see if the equation has a power series solution
Now I don't know what you know about differential equations but here are some facts:
Let's say you want to solve an equation of the form ay' + by + c = 0 on an interval I where a,b,c continuous functions on I:
1. If a vanishes somewhere in I, then you are *not* in the linear case (ie. you may have any number of solutions: a finite number, none at all, infinitely many)
2. To solve this, you need to solve the equation on each interval where a doesn't vanish (on each of these the equation is linear and you can easily find the solutions) and then see if you can patch up the solutions in such a way that the resulting functions are continuously differentiable (this is where things can go wrong)
Now how does this help us ?
We want to solve this equation on [math][0,+\infty)[/math]. We see that x vanishes at 0 so the equation is not linear. Therefore, we need to find the solutions on [math](0,+\infty)[/math] and then see if they are differentiable at 0.
On [math](0,+\infty)[/math], we easily see that the solutions are indeed exactly the ones given by mathematica (notice that x -> x*ln(x) -1 is a solution and then notice that the solutions to the homogenous equation are exactly the x -> c*x).
Now, we need to see if any of these functions is differentiable at x=0. Note that they all continuous at 0 since they all converge to -1 as x goes to 0.
Now let f be the function [math]x \to c x + x \ln x -1[/math] extended to [math][0,+\infty)[/math] by setting f(0) = -1.
We see that [math]\frac{f(x)-f(0)}{x} = c x + \ln x[/math] which goes to infinity as x goes to 0, therefore f is not differentiable at 0. In particular, it doesn't have a Taylor series expansion at x = 0.
To conclude, the equation doesn't have a power series solution (actually, it doesn't have a solution at all on any interval containing 0)
>>7643401
Right now I have this:
[eqn]
P(n>1) + P(1) + P(0) = 1 \\
P(n) = 0.2^{n}P(0) \\
P(n>1) = \sum_{n>1}0.2^{n}P(0)
[/eqn]
wut do
>>7643693
[eqn]2 P(0) = P(0)\sum_{n \ge 0} \frac{1}{2^n} = \sum_{n \ge 0} P(n) = 1[/eqn]
So [math] P(0) = \frac{1}{2}[/math]
>>7643710
I'm pretty dumb, care to explain how you came up with the whole [math]\frac{1}{2^{n}}[/math] part?
>>7638625
bist du behindert?
ganz im ernst lies es einfach im skript nach spast
Hast wahrscheinlich noch nicht mal 10 Std seit Semesterbeginn gelernt
>>7643717
Shit, my bad, it should have read [math]\frac{1}{5^n}[/math] (I replaced 0.2 by 1/2 instead of 1/5.. mad arithmetic skills)
So finally you get [math] P(0) \sum_{n \ge 0} \frac{1}{5^n} = 1[/math] so [math]P(0) = \frac{4}{5}[/math]
>>7643717
Not him, but [math]sum_{n \geq 0}\frac{1}{2^n}=2[/math] is just the geometric series.
>>7643735
Thank you anon
>>7638244
and what are strings made of and what are they made of and what are they made of, you can as deep and tiny as you want, noone can answer this question lol
>>7643636
You need to ask more precise questions. It's hard to know how to help you beyond just giving you the definition of an inductive set.
>>7643680
Thank you, based anon.
Is there a name for the property that some shapes, such as parabolas or catenaries, are "unique", in the sense that stretching it out horizontally or vertically is the same as zooming in or out?
logbase_2(x) = logbase_x(2)
how do you get 0.5 as solution?
I did
sqrt(x) = 2^(1/x)
and got x = 2
but 0.5 is a valid solution too
I know psychology isn't exactly "science and math" but I think you guys are the most capable of answering this.
When I was a small child I drew charts with numbers all the time. Things like prime numbers, powers of x and other patterns, while other kids drew observable stuff like houses, trees, cars etc. My notebook(s) were filled with it.
Do I have legitimate autism or was I just "interested in math"? I was also a social outcast all my life if that helps.
>>7644480
I doubt a child having the age at which it draws cars and trees has the capability to understand prime numbers
Are there materials through which the speed of sound is greater than the speed of light in the same material?
Is it theoretically possible for the speed of sound in a material of finite density to be equal to the speed of light in a vacuum?
>>7644492
My parents taught me about numbers before 1st grade. When I was in 1st grade I already knew about the 4 main operations. Prime numbers aren't that hard to grasp when you know how division works.
Children at elementary school draw stuff all the time. At least where I'm from they did.
does anyone know any books to help understand the tuition behind:
levi-civeta symbols and their application
einstein summation convention
dirac delta application
>>7644503
intuition*
>>7642901
>It also does not apply for complex numbers
Of course it does. The complex numbers are a field.
>>7641980
Dude, you know the solution:
y(x)=c_1x + x*ln(x) - 1
does that function have a series? Sure, say around x=1.
>>7644457
A equation an have more than one answer.
For example, polynomials: for a polynomial of n degrees there are n solutions; a polynomial of the second degree will have 2 solutions; that of 3rd degree will have 3 solutions, etc.
You can draw a graph of the equation to see how many roots it has.
The graph of your equation is PIC related.
You can clearly see it has two roots: one at 0.5, another at 2.
If you want to solve it analytically use the fact that logbase_a (b) = log(b) / log(a)
Applying it to your equation, the LHS can be written as: log(2)/ log(x) and the RHS can be written as log(x)/log(2)
Combining you get:
log(2)/log(x) = log(x)/log(2)
log(2)/log(x) - log(x)/log(2) = 0
If you substitute y = -log(x) and expand you'll get:
[math]y^{2} - log^{2} (2) = 0[/math]
Use the identity a^{2} - b^{2} = (a+b)(a-b)
(y + log(2)) * (y - log(2)) = 0
Equating both sides to 0
y + log(2) = 0, y - log(2) = 0
On the RHS y = log(2)
Recall that y = -log(x)
-log(x) = log(2)
log(x) = -log(2)
Something else you should know: -log(a) = log(1/a)
So we can rewrite that as:
log(x) = log(1/2)
x= 1/2
If you solve the other part of the equation you'll get y= -log(2)
-log(x) = -log(2)
log(x) = log(2)
x= 2
Therefore, x=2, x= 1/2.
>>7644495
Nothing can be faster than the speed of light.
Sound is a mechanical wave meaning it needs material for its propagation and it increases in speed the denser the material.
Still not up to the speed of light though.
>>7636900
if i have 3 separate pieces of land and a 1/3 chance to strike oil on each of them, what's the probability that ill have some oil?
>>7644570
(2/3)^3
>>7644536
Mistake.
I was considering quaternions as part of complex numbers.
I forgot quaternions extended the complex numbers.
>>7644574
since this is stupid question thread and im stupid, can u explain how?
>>7644582
First ask yourself: What is the chance not to get oil on the first island? It's obviously 2/3. Now what is the chance of getting 2 empty islands in a row? (2/3)*(2/3)
Actually I made a mistake. It's 1-(2/3)^3, in other words "1 minus the chance of getting no oil".
>>7644570
What's the chance of getting no oil at all? That's (2/3)^3, right? Now we use the complementary rule: P(having oil somewhere) = P(not having no oil anywhere) = 1 - P(not having oil anywhere).
P(having some oil) = 1 - (2/3)^3 = 19/27
>>7636900
is it a dumb idea to go a university and study something in a language that isn't your own?
like your third language
>>7644599
>>7644600
that clears it up, thank u guize, and just one more question. suppose theres a game where you roll a fair die and if you get a 4, you win and lose otherwise. someone named A made a special die where the probablity of getting 4 is 1/2. she keeps this die along with two other fair dice in her purse, meaning she uses the illegal die with probability 1/3. given that A wins the game, whats the probability she cheated? i know its bayes theorem but im having trouble setting it up because again im stupid
>>7644555
shiiit, thnx anon
>substitute y = -log(x) and expand
how did you expand those fractions
I don't see it desu
>>7644622
nvmd, I got it
could you explain why
sqrt(x) = 2^(1/x)
only renders one solution?
I did something similar on a test once and the teacher showed my why but I can't recall it
Is em drive real?
>>7644616
>if the university is located in your own country
>yes it's dumb since nothing will prove you followed all classes in another language (I think)
>if the university is located in another country
>no, you can prove you studied abroad and know another language well
>>7644700
oh I've been living here for 3 years, enough to manage the written language without a hitch. I meant like attending lectures is still a bit if a problem since I have to focus on translating and understanding what's being said- kinda dumb.
oh well, what's done is done
Reviewing how to graph sin and cos waves, and I can't figure out how to graph y = sin(pi*x) from (0,2pi) to save my life even though I can do most of the other problems. The whole pi is really throwing me off.
>>7643410
I think you have misunderstood. Plans like affirmative action etc don't give spots to other deservedly people. They invest time pre-selection giving marginalised individuals the training and advantage they otherwise would not have received due to not being in a place of privilege. It won't hold back science or anything brah, all good. If anything it will increase the likelihood of finding shit out.
How would you find the height of the object on the right, where radius = r?
Each segment is composed of 1/8th of the circle.
God I'm dumb
Undergrad here, haven't taken any proof-based courses yet.
When writing a proof, are there any rules or conventions on using a stronger/ weaker theorem or axiom? Like should you use the strongest axiom you can, or the weakest axiom that still proves the point? Is it better to cover several bases with one powerful theorem, or split it up amongst a chain of weaker theorems?
>>7636900
If force = power/velocity, what happens when velocity is 0? Does that mean that for a given amount of power, force is undefined? Or is there some other equation that applies at v = 0?
>>7645213
How exactly is height defined? Do they mean the difference between the lowest point and the highest point on the Y axis, even though there isn't any actual vertical line connecting them? If that's the case couldn't you just find the vertical component of one "half" of the inner line and multiply it by two?
>>7645364
sorry for not being clear,
height refers to the distance between the bottom of the curve on the left and the top of the curve on the right
not sure if that helps
I think I figured it out though
height = (2r)cos45 - (2)(2rcos45-r)
tell me if im wrong
Hey guys can you help me with my ODE homework?
the question goes:
Solve the given differential equation
y'' - 2xy' + 8y = 0 ; subject to initial conditions: y(0) = 3 ; y'(0) = 0
what do? it would be greatly appreciated
>>7645675
Looks like a problem you can solve by using a characteristic equation
>>7645694
but what about that x in the coefficient of y' ?
>>7636900
if there is always an infinite number of dividing points between 2 objects, (some distance), then how do i get from home to work and back?
i know this sounds like a troll, but i really want an answer, even if it is that the guys who said "infinite division... blah blah" was stupid
>>7636917
Which function is this?
>>7645866
[math]x \mapsto -x \mathrm{e}^{- x^2}[/math]
>>7645871
Thank you so much anon <3
guys, regarding infinite series and test for convergence.
I'm trying to figure out when I should use a direct comparison test v. limit compared test?
I mean, can't you just use DCT instead of LCT?
by p-series you can find if its convergent or not, no? Having trouble figure it out...
>>7645793
that doesn't really help anon..
>>7645364
Say the power is fixed. If we gradually decrease the velocity, the fraction as a whole increases and as such so does the force. By having a force be applied for a certain power with a very low velocity, the force must be extremely high. If the velocity is 0, the fraction is undefined (dividing by zero).
Think of it this way: v = s/t. If we take an extremely small timeframe and keep s, the distance traveled, fixed, the velocity goes to infinity. This is analogous to F = P/v but more intuitive.
>>7645338
Well it's a matter of taste but yeah, if you have a big theorem that proves a result but see that a weaker property still proves it, then you should use the weaker theorem because it shows that you really understand what makes that result work (instead of using the stronger theorem as a black box).
However, there is also the imperative of conciseness so I would say: use the weaker theorem if both proofs are of comparable length, otherwise use the stronger one (sometimes, when trying to solve a problem using the weaker property, you wind up re-proving the big theorem in a special case, which is a good exercise but ultimately useless if your goal is just to solve the problem).
>>7636900
Sup /sci/
I've tried asking /g/ but no one seemed to know.
I'm making fractal renderer and want to use fixed-point arithmetic to have as much precision as I need. However it require lot's of operation on integers.
The question is: will GPU be better at computing fixed point arithmetic or should I do it on CPU in asm? GPU works nicely on floats(pic related) but I've heard it's not that fast when operating on integers. Streaming from CPU to GPU is not a problem, I can stream full HD in 200 fps using only one thread.
Wtf is a "mixed derivative"?
You have a function [math]f(x, y)[/math], and you can calculate partial derivatives [math]f_x(x, y)[/math] and [math]f_y(x, y)[/math].
[math]f_x(x,y) = [/math] Derivative of f(x,y) if y is constant.
[math]f_y(x,y) = [/math] Derivative of f(x,y) if x is constant.
But wtf is [math]f_xy(x, y)[/math]?
So apparently my engineering department offers an MEng and MSci in electrical engineering. Is there any difference, practically speaking, between the two? Because getting above 3.4 GPA as an undergrad guarantees entry into the MEng but not MSci for some reason.
>>7640306
You're right
>>7645974
Interpret it as [eqn] \frac{ \partial }{ \partial y} \left( \frac{ \partial f}{ \partial x} \right) [/eqn] Since mixed derivatives are equal the same interpretation holds if we swap x and y around.
>>7646018
Is it somehow different with total derivative?
Is total derivative a synonym for mixed derivative?
>>7645974
It's a partial derivative of order two: It's the partial derivative relative to y of [math]f_x[/math]
I have a geology class project worth around 25% of my grade that I should have started like a month ago and I'm running out of time. It involves taking field data and using gis software, but since I have started so late my field data isn't going to give useful information so I won't have much to write my paper about. The sad part is I am a math major and I took this sophomore geology class for fun and its probably going to lower my 3.9 gpa because I didn't take this project seriously....
I feel like I'm going to die, how do I deal with the stress associated with unavoidable failure? Well I probably won't fail the class but I am most likely going to make a C or a B if I get lucky.
How could I show that SL(n, R) (nxn matrices with determinant equal to 1) is differential manifold?
>>7646108
[math]SL_n(\mathbb R)[/math] is the inverse image of 1 by the smooth function [math]\det: \mathcal M_n(\mathbb R) \to \mathbb R[/math].
To prove that it is a submanifold of [math]M_n(\mathbb R) [/math], you just need to prove that the gradient of the determinant is nonzero at every point in [math]SL_n[/math].
But you can check that for any matrix M, you have the identity [math]\mathrm{grad}_M \det = \mathrm{com}(M)[/math] (it's kinda tedious but it follows from the expansion [math]\det(M+H) = \sum_{\sigma \in \mathfrak{S}_n} \epsilon(\sigma)\prod_{i=1}^n(M_{i \sigma(i)}+ H_{i \sigma(i)})[/math]).
In particular, if M is in [math]SL_n[/math], then [math]\mathrm{grad}_M \det = ^t M^{-1}[/math], therefore it is nonzero at every point.
>>7646018
Be careful that in general only holds if the function if has continuous second partial derivatives (by Schwarz' theorem).
>>7646148
Could you tell me what [math]com[/math] function is? And what do you mean writing: [math]=^{t}M^{-1}[/math].
>>7646039
Anybody? Are they the same?
How can I find B at point p?
I know you use superposition since it's a hole. But I can't seem to get the right answer and end up getting
[math]B=\frac{I\mu_0}{2(R^2-a^2)}[/math]
When it should also have
[math]\frac{R}{2}-\frac{a^2}{2(R+B)}[/math]
So what am I doing wrong?
Imagine that you have to cover a rectangular area of 3 dm width and 4 dm height
using a set of 12 quadratic tiles of area 1 dm^2
. In how many ways can you cover the rectangle if
you have
(a) 9 white tiles and 3 black tiles,
(b) 4 white tiles, 2 black tiles, 3 blue tiles and 3 red tiles?
We assume that tiles of the same colour are identical such that two coverages that result from
exchanging two tiles of the same colour are considered equal.
Can someone explain to me how to solve this, i feel really stupid atm.
>>7646327
got answered on math.stackexchange.com
don't just post your question on a bunch of forums and then bail out
physics question I don't really get.
>>7646419
I haven't really done anything like this for awhile, but I looked up some shit online that might help. [math] W_{net} = \frac{1}{2} I \omega_f^2 - \frac{1}{2} I \omega_i^2 [/math] and I is defined as the mass times the distance from the axis in question. So for the first one, W=9*1*(2.6^2)/2. The second one is 2.5*2*(2.6^2)/2. The third one should be the addition of these two.
While we're posting hw questions, I might as well ask how the fuck do I do this?
Unretard me, I can't see why this statement is false.
[math] ( \exists m \in \N ) ( \forall n \in \N ) (m=n+1) [/math]
To me, this reads "there exists a natural number n+1 for all natural numbers n", how is that false?
>>7646468
it reads : "there exist an integer m, such that m = n+1 for all n".
meaning "there is a integer which is the successor of any given integer."
which is false.
A correct statement would be "for all n, exists m s.t. m=n+1" or equivalently "any integer has a successor."
>>7646445
1st one was right
30J
2nd
I got wrong which ended up being 34J
really not sure about it
3rd
30+34= 64J
thanks man
>>7646484
Thanks man... I am now unretarded.
>>7646484
Integers are Q
So I applied for fall semester for CP Pomona, SDSU, and CSU Long Beach for Computer Engineering.
Spring semester:
Physics I (4 credits)
Chemistry 101 (5 credits)
Intro to Biology (4 credits)
Classes I also need:
History (3 credits)
Discrete Mathematics (3 credits) (Pomona doesn't take it)
I was thinking of just taking non-specific GE and fullfill them instead of taking certain specific major classes since not all of the universities take those classes. I need Physics I, Chemistry 101, and Intro to Biology just for the chance of getting into one of these universities. After this semester, I'll be done with Differential Equations which is the last Math class that I'll need. I'm also taking C++, Oral Communication, and Critical Thinking this semester. Should I just take these three classes and hope I'll pass, or should I also take the History class and maybe a fullfillment for Area E which is something stupid like Nutrition?
>>7646411
I see, i found it on math exchange too now thanks for the tip. This is a question for a lecture with over a hundred people so it is possible that other people from there asked somewhere aswell.
I usually only ask /sci/ when i have a math related problem.
if im on a ship moving 0.5*c in one direction and another ship is moving 0.6*c in the opposite direction, am i not moving faster than the speed of light relative to the ship i am not standing on
>>7646513
aight cool anon
you can bookmark his profile and stalk him so you read solutions to questions you might have too
>>7646518
no, because velocities add differently near light speed. [math] v'= \frac{v+u}{1+ \frac{vu}{c^2} } [math] so v'=.85c
>>7646536
[math] v'= \frac{v+u}{1+ \frac{vu}{c^2} } [/math]
How would you define a probability of 1 ?
An event that has a probability of 0 to happen isn't necessarily the empty set :
for instance if i choose a random positive integer there is a probability of 0 that i choose number 5, yet {5} is not the empty set.
There is a probability of 1 that i choose a number that is greater than 10, yet [10, infinite] is not the universe N, and there is still a possibility that i choose the number 4, although the probability is 0.
It is clear that having a probability of 1 isn't exactly the same thing as "happening everytime", so how would you define a probability of 1 ?
>>7646511
>taking Physics, Chemistry, and Biology in one semester
Good luck, friend.
>>7646605
It means that if you plot a graph of n/N vs. N (N = no of trials, n = no of successes), you'll notice that the ratio approaches 1 as N approaches infinity
>>7646611
>Physics 1
>Chem 1
>Bio 1
I'd say you have a better chance of failing that history course
>>7644820
Bls resbond
Physics and mechE's:
I'm trying to figure out how the torque of a motor is affected by weight on (parallel to) the axis of rotation. Is there a quick and dirty estimate I can use in the manner of a coefficient of friction to calculate this, or am on the wrong track here.
I'm building a pan and tilt turret and I don't want my motor to stall or snap under the weight of my gun assembly.
Already asked in /diy, no dice
What's the difference between these intervals in the unit circle?
[-180, 180] degrees
and
[0, 380] degrees
I'm trying to find angles that satisfy a certain trigonometric value.
>>7646688
why are you letting the journal bearing of the motor hold weight? build a gear train, don't connect directly to shaft.
>>7646687
just plug in numbers and see what happens. when x=0, sin(pi*0)=0. when x=1, sin(pi*1)=0, when x= 1/2, sin(pi/2)=1. It's just gonna be the sin curve but instead of repeating every 2pi it repeats every 2.
>>7646732
-180 and 180
the direction you travel 2 it
>>7646751
Oh, that's it. Thanks.
>>7646744
because it would make things much simpler if I could mount the tilt servo directly on the pan servo.
>>7646769
>mount the tilt servo directly on the pan servo.
no. don't do that. you are going to snap your shit up. never load the journal bearing of a motor with anything that weighs more than the motor itself.
offset the pan servo and link with a spur gear on a secondary shaft. mount your tilt servo on that second shaft.
How in the hell would I go about proving this? I understand what it's saying, but I really don't know how to prove it. Can I appeal to the Completeness Axiom in some way?
pretty stupid, but what are the steps to produce the complex root formula?
>>7641312
Where did you get this question from? University? Just curious.
>>7647076
If there weren't such an a then [math]\sup A - \epsilon[/math] would be an upper bound of A which is strictly lesser than [math]\sup A[/math]
>>7647076
The question is not well-formed. Is [math]A[/math] supposed to be a subset of the reals?
>>7643364
It's not. The relation does not [math]x\sim\lambda x[/math] for all [math]\lambda\in\mathbb R\setminus\{0\}[/math] but just [math]x\sim-x[/math]...
>>7647129
I-I think I understand. Guessing that I should just assume that a doesn't exist and derive a contradiction to the assignment.
>>7647150
Here's the rest of the page
>>7646205
Woops sorry, I thought it was a standard notation but apparently it's just french.
What I denote by [math]com(M)[/math] is the matrix of the cofactors (ie. the coefficient of index (i,j) is the determinant of the matrix obtained from M by removing the i-th row and the j-th column), we call it "comatrice".
And what I meant by [math] ^t M^{-1}[/math] was the transpose of the inverse of M (maybe you write [math](M^{-1})^T[/math] ?)
I need some help regarding higher order linear difference equations
(I excuse the weird notation, as I only know of the German notation):
I have the equation
y_n+2 - 7y_n+1 + 10y_n = 3^n, with the initial values of y_0 = 0, and y_1 = 1
the solution will be of the form y_n^(i) = y_n^(h) + y_n^(s)
first the homogeneous solution is necessary ,
so we solve X2 - 7X + 10 = 0
and we get the solution X_1 = 2, X_2 = 5.
so y_n = c1*2^n + c2*5^n (here is what I am not sure of)
we acquire the special solution through assuming
y_n^(s) = c*3^n
after solving we get
y_n^(s) = 1/5 * 3^n
From then I don't know how to proceed.
Can anyone help me out?
>>7647187
made a mistake with the special solution, it's
1/2 * 3^n,
so the general solution seems to be:
y_n^(i) = c1*2^n + c2*5^n + 1/2 * 3^n.
Still I don't know how to proceed.
I cannot figure out the values for a three equation system.
I have x = 4 and y = -19, which are both the correct values.
Now, the two equations I could plug them into are
y-4z = 10, which would not work because the correct answer is supposed to be a whole number, not a decimal or fraction.
Then, there is
x - 2y + z = - 9
thus
4 + 38 + z = - 9
42 + z = - 9
z = -51, which apparently is not the correct answer
I know 100% that I have the x and y values correct.
So am I just going retarded or something?
As you may guess, I'm a bio/chem major, not a math guy.
>>7647303
your equations are wrong, it's as simple as that
