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Hence, the water leaked is (N – 1) × T – τ, which because the leak is one unit per second, took exactly (N – 1) × T – τ seconds to leak. Thus the shortest time in which all N packets can arrive and conform is ( N – 1) × T – τ seconds, which is exactly τ less than the time it would have taken if the packets had been arriving ...
The radius vector, , is the distance from the charged particle's position at the retarded time to the point of observation of the electromagnetic fields at the present time, is the charge's velocity divided by , ˙ is the charge's acceleration divided by , and = /.
The following is a list of notable unsolved problems grouped into broad areas of physics. [1] Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.
[1] The concept of Archimedes' principle is that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. [2] The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV.
The unit of activity is the becquerel (symbol Bq), which is defined equivalent to reciprocal seconds (symbol s −1). The older, non-SI unit of activity is the curie (Ci), which is 3.7 × 10 10 radioactive decays per second. Another unit of activity is the rutherford, which is defined as 1 × 10 6 radioactive decays per second.
Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function and the Fourier coefficients of the J-invariant (OEIS: A000521): ∑ n = − 1 ∞ j n q n = 256 ( 1 − z + z 2 ) 3 z 2 ( 1 − z ) 2 , {\displaystyle \sum _{n=-1}^{\infty }\mathrm {j} _{n}q^{n}=256{\dfrac {(1-z+z^{2})^{3}}{z ...
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.