Recent content by nickek

Sorry, I missed the equal sign in the problem statement and have now rewritten the post with mathematical typesetting.

Rewrite the given equation, attempt 1: ##2\sin(x)\cos(x) + 2\sin(x) + 2\cos(x) = 0## ##\sin(x)\cos(x) + \sin(x) + \cos(x) = 0## ##\sin(x)(\cos(x) + 1) + \cos(x) = 0##, naaah, can't get any relevant out from here. Attempt 2: ##2\sin(x)\cos(x) + 2\sqrt{2}*\sin(x + \pi/4) = 0## ##\sin(x)\cos(x) +...

Great! Actually what I looked for.

Thank you. Yes, the number of paths should be C(n+m,m). I will think more about the extension. Tanks again!

Hi! If I have points A and B in a lattice in the plane, and the closest path between them is n + m steps (for example 4 steps upwards and 5 steps to the right), there are C(9,(5-4)) = 9 combinations of paths between them. I have to choose the 4 ways upwards (or the 5 ways to the right) of the 9...

Thank you. Maybe the position thing. About the acceleration axes, I just used the z-values (positive upward).

Hi! I have just performed some experiments with my phones accelerometer, and plotted the acceleration as a function of time from the raw data. The experiments I did was: jumping down from a chair jumping from the floor and up let the device fall toward a bed When I analyze the graphs, I think...

Thank you. My failure was that I not included the values held as constants in the product of each measure when I plotted the graph...

Hi! I have performed an experiment measure force on a wire with electric current in a magnetic field. I got 3 graphs: Force as function of length (L) of wire, Force as function of current (I) and Force as function of magnetic field (B). In all cases, I got approximately a straight line through...

Hi! I have two questions regarding spectral lines, in the optical wavelengths. Every line has a width. One reason is the uncertinity in energy of the atomic states according to Heisenberg uncertinity relation. But this is just a very small part of the width, I think. Are there other causes to...

Hi! Many students know that A\sin(x) + B\cos(x) =\sqrt{A^2+B^2} \sin{(x+\arctan \frac{B}{A})}. I have seen just one deduction of that relation, showed by set up a system of two equations, solving for amplitude and phase shift. Is it possible to deduce the relation in a vectorial way, or in...

Hi! I came across a toy, formed as a rod. When spinning that rod counterclockwise, the behavior is as expected. But turn the direction to clockwise spinning, it immediately slows down and ends up spinning counterclockwise. See this YouTube clip. Anyone who has an explantation of this...

Thanks for answers, everyone. Now I have a starting point for curious students asking about this task.

Hi! In a book, there is stated that the least detectable object by a bat is when the object is λ/2 of the sound wavelength emitted by the bat. I know there is resolution criteria for light microscopes too, which concerns the wavelength of the light. My question is: Are these criteria about...

Ah, these answers together solved my quandary. Thanks Bill_K and mfb!