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Jan
26
comment (beginner question) How to find points where a series stops being flat, or becomes flat?
Could you give us some example series to work with? In general, you can look at a(n)-a(n-1) or something of that nature.
Jan
26
comment Another version of connecting ropes problem
I'm probably missing something, but there's a (N-1)/N chance your second rope will be different from your first (assuming we're allowing self-looping), (N-2)/N that the next one will be different, (N-3)/N that third one will be, etc. Thus, it seems the answer would be N!/(N^N). This may be equal to what you wrote down, but I don't think it is.
Jan
26
comment Calculating Down Range and Cross Range Coordinates
Why r = z/sind(-el). That would r negative when el is between 0 and 90 degrees (which occurs in case 2). I think you mean r= |z/sind(el)| don't you, where |x| is the absolute value of x.
Jan
24
comment (Non-continuous) solutions to $f(f(x))=kx$ and $f(x^2)=xf(x)$
More of a hint: f(x) = x*Sqrt[k] for x in set S, and f(x) = x*-Sqrt[k] for x outside of S. Just choose S carefully.
Jan
24
comment (Non-continuous) solutions to $f(f(x))=kx$ and $f(x^2)=xf(x)$
Hint: the function can jump between two values and still satisfy f(f(x))=kx for example. Note that this is just a hint, not a solution. You need to carefully choose which subsets have which value.
Jan
24
comment How to know if a two variable function is increasing?
You might be thinking of partial derivatives?
Jan
24
comment Prove that the series is monotonic and converging
Wild guess: what is S(n+1)-S(n) and U(n+1)-U(n)?
Jan
24
comment Draw Regions On the Complex Plane that Satisfy this Relation
Beat me to it. My hint was going to be: if a complex number has imaginary part zero, it's argument must also be 0.
Jan
23
comment Financial Mathematics, interest problem
If you don't know the interest rate, how did you get A(0)=200?
Jan
21
comment Eccentricity is invariant for ellipse defined by intersection between plane and ellipsoid [can't be correct]??
OK, yes, that's the point I was making. However, I haven't been able to prove my point, so I'm no longer sure it's true.
Jan
21
comment Eccentricity is invariant for ellipse defined by intersection between plane and ellipsoid [can't be correct]??
Actually, I'm not sure I have a point, since the figure I drew above isn't an ellipse. Presumably, 'tilted ellipses' do exist and there are formulas for them, but I haven't been able to find one.
Jan
20
comment Tangent line of Lissajous curve?
WA will give you an exact solution too, but it's the arctangent of a root of an irreducible 5th degree polynomial, so that's not really helpful. Are you allowed to graph the function to determine the number of roots (note that they don't ask for the values of the roots, just the number) and/or use numerical approximation techniques?
Jan
20
comment Tangent line of Lissajous curve?
Yes, but two of those roots are outside [-Pi,Pi]. Actually, there are an infinite number of roots, but they only correspond to a finite number of points since both sin and cos are sinusoidal.
Jan
20
comment Tangent line of Lissajous curve?
Well, yes, but that's because of the chain rule: dy/dx = (dy/dt)/(dx/dt)
Jan
20
answered Tangent line of Lissajous curve?
Jan
19
answered Eccentricity is invariant for ellipse defined by intersection between plane and ellipsoid [can't be correct]??
Jan
18
revised Expected value and a variance of a die sequence
general solution
Jan
17
answered Expected value and a variance of a die sequence
Jan
17
comment Hypothesis test given $\bar{x},s,\mu,\sigma$
Hint: if you have n tests, what is the sample standard deviation?
Jan
17
comment Solving $x^2 + y^2 = 1 + z^4$ with (x,y,z) = 1 and z < x < y
x^2 - 1 = z^4 - y^2 is a difference of square on both sides. Not sure if this helps, just a random thought.