Dust particles are trapped on a surface. There are two energy levels particles can be in: absorbed on a surface with zero energy, and wiggling with energy E=3/2kT. However, since the surface area is limited, not all particles can be in any state. There are 1000 particles and 1...
Rotating cylinders are not just physical abstractions: for example, they can turn a flow of the air, thus creating lift as the airplane wings. Historically people have even used rotating cylinders to power ships (although with little efficiency). NASA wrote more about this her...
i mean f^(5)(x)=f(f(f(f(f(x))))).
Define the function f(x)=2x/(1−x^2). Find the number of distinct real solutions of the equation f^(5)(x)=x.
Determine how many 1000 digit numbers A have the following property: When any digit of A, aside from the first, is deleted to form a 999 digit number B, then B divides A.
A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius R=4 cm. The plane of the coin is tilted at an angle of θ=45∘ with respect to the horizontal plane (see the figure below). Find the coin's period T in...
A wire is bent into the shape of an planar Archimedean spiral which in polar coordinates is described by the equation r=bθ. The spiral has N=100 turns and outer radius R=10 cm (R is the distance from point O to point T). Note that in the figure below we show a spiral havi...
Yeah it is !
Our muscles atrophy when there is no gravitational force. On long space flights this is a problem, which is why astronauts exercise. On very long space flights it might be advisable to simulate gravity. Your space ship is a long cylinder of radius 100 m that spins about its ax...
Data Structures and Algorithms
how can i give the link ??