I don't see what the problem is, I get at least 4 digits correct If I evaluate the sum for n<=13 and 10 digits correct for n<=32. (I don't think n=0 should count).
Because \frac{2k x^2}{(2k+1)(1+x^2)} is smaller than 1/2 for all x, the error must halve for each increase of n.
I used the...
Most psysics books will only talk about 2 cases, the adiabatic case, where you move the piston so quickly that no heat is transferred or the isothermal case where the piston is moved so slowly that the temperature stays equal to the surroundings.
Anything in between means the heat capacity...
The equation for the intensity with single slit diffraction is
\frac { \frac {\pi d} {\lambda} sin(\phi) } { \frac {\pi d} {\lambda} }
your equation is produced if d = \frac {\lambda} { 2 \pi} . d is obviously too small here to get destructive interference at any angle. For the light to...
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Does this mean that if you had a rectangle where only the top right corner was missing, you'd say that there were 126 - 2! = 124 paths? That answer is wrong.
If the output voltage of the transistor is greater than 3V the capacitor will charge. If the output voltage goes below 3V the capacitor will discharge and act like a voltage source itself, with its positive side on the left and the negative side on the right.
To measure the the output of the solar cell you have to connect a load and measure the current that goes through it and the voltage across it. You have to try different resistances as load to see what the value of the load resistance is that maximizes the power.
Energy = Power * Time, so you...
you made a mistake somewhere doing this.
The easiest way to do it is to start by calculating the acceleration of all the blocks by using F = m*a for all of them together
It's not that difficult. If the map was a complete 4x5 rectangle there would be 9C4 = 9!/(4!5!) = 126 paths. Only one path goes through the upper left point, and 6C1 = 6 paths going through the point 3 left of the football stadium.
The total number is 9C4 - 1 - 6C1 = 119
conservation of momentum doesn't hold here because momentum can be exchanged with the Earth by friction on the floor. What is conserved is angular momentum around the point where the feet touch the floor. Wobbling and swaying your arms cannot change that. (but gravity can if the center of mass...