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13h
comment Solve differential equation
@Jason yes, indeed
13h
comment Solve differential equation
i think you get $\sin x + \ln |\sec x|$, and must carry the absolute value unless you restrict yourself to the interval where $\cos x \ge 0$...
13h
comment Value of Sine Function from data given
what is your approach to the problem? try to expand tangents into terms with $\sin \alpha, \sin \beta, \cos \alpha, \cos \beta$ and work it out?
14h
comment What does it actually mean if a cost function is differentiable?
@Karnivaurus some derivatives are hard to analytically express :)
17h
comment Polynomial Interpolation and Data Integrity
When you say you evaluate $f$ at $x$, do you mean that $f:\mathbb{R} \to \mathbb{R}$ is a 1-D polynomial and $y_i=f(x_i)$ or that $f:\mathbb{R}^n \to \mathbb{R}^n$ is a vector-valued polynomial which takes $n$ inputs and returns $n$ outputs?
1d
comment How to calculate $P(X_1 < X_2 < X_3…X_n ) $
The problem is symmetric for 2 continuous variables, so your probability there is just $1/2$.
1d
comment In what conditions a quadratic function has an integer value of $f(x)$ where $x$ is also an integer?
$y \in \mathbb{Z}$ iff $a,b,c \in \mathbb{Z}$
1d
comment Is this (funny) combinatorial optimization problem NP-hard ? (cutting numbers and placing them in urns)
lower bound seems to come from the idea that if everything divides evenly you put exactly $$m = \frac{\sum b_i}{nC}$$ in each cell. The problem with that is you may have some numbers $b_i < m$ which would mean you cannot use $m-b_i$ from each such cell. So you "waste" $\sum (m-b_i)^+$ in total...
1d
comment Quick Integration by parts question
it depends. can you bring an example?
1d
comment Is this (funny) combinatorial optimization problem NP-hard ? (cutting numbers and placing them in urns)
another idea: perhaps $$x = \frac{1}{nC} \sum_i b_i$$ can be used to derive a lower bound (I think it is $xC$), which you can improve by adding $\sum (x-b_i)^+$ to it.
2d
comment If independent r.v. converge in probability to a constant, do they converge almost surely?
Do you mean that each element of the sequence be independent, or it is a series of independent terms, which is converging?
2d
comment Is this (funny) combinatorial optimization problem NP-hard ? (cutting numbers and placing them in urns)
At first blush, seems reducible to integer programming, which would make it $\in \mathcal{NP}$. Whether you could reduce something else to it, is a different story. Perhaps by setting $C=1$ you can get a special case like the Knapsack or something like that?
2d
comment How can I tell if two lines will cross using vectors
Not sure what you are asking exactly.
2d
comment Slow convergence simulating log-normal sample from the normal
You are right, it is all about a long tail. I tried it with billion entries, and mean looks ok to 5 digits, but st. dev. is still all over the place. Increasing the mean to 0.05 already matched the st.dev. to 3 digits at 1 mln trials, and doing down to 0.005 with 1 billion trials is not enough... I wonder what the relationship there would be...
2d
comment Algebra 2 help!
I don't think you really taught the OP anything by an answer like that. It would perhaps be better to give him a general hint, or a first step and let the OP figure it out from there.
2d
comment Distribution of test scores calculate cutoff given mean and standard deviation
Hi, welcome to Math.SE! We don't like to do your homework for you :), so could you please update your question with your thoughts/attempts to do the problem and we will be happy to guide you further.
2d
comment Interest Question
I got 70902.58 for the same calculation
2d
comment Interest Question
Also, what is interest "p.a"?
2d
comment Interest Question
Hi, welcome to Math.SE! We don't like to do your homework for you :), so could you please update your question with your thoughts/attempts to do the problem and we will be happy to guide you further
2d
comment Plotting Distance Constrained Points on a Plane
may be an interesting post on StackOverflow, someone with lots of experience in embedding algorithms may be able to contribute