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[10] A tournament (with more than two vertices) is Hamiltonian if and only if it is strongly connected. The number of different Hamiltonian cycles in a complete undirected graph on n vertices is (n – 1)! / 2 and in a complete directed graph on n vertices is (n – 1)!. These counts assume that cycles that are the same apart from their ...
The weight of the object in the fluid is reduced, because of the force acting on it, which is called upthrust. In simple terms, the principle states that the buoyant force (F b) on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume (V) times the gravity (g) [1] [3]
However, the names of all SI mass units are based on gram, rather than on kilogram; thus 10 3 kg is a megagram (10 6 g), not a *kilokilogram. The tonne (t) is an SI-compatible unit of mass equal to a megagram (Mg), or 10 3 kg. The unit is in common use for masses above about 10 3 kg and is often used with SI prefixes.
A one-kilogram mass is still a one-kilogram mass (as mass is an intrinsic property of the object) but the downward force due to gravity, and therefore its weight, is only one-sixth of what the object would have on Earth. So a man of mass 180 pounds weighs only about 30 pounds-force when visiting the Moon. If an object with a mass of one hundred ...
A more complex version has twelve coins, eleven of twelve of which are identical. If one is different, we don't know whether it is heavier or lighter than the others. This time the balance may be used three times to determine if there is a unique coin—and if there is, to isolate it and determine its weight relative to the others.
The planetary problem is the n-body problem in the case that one of the masses is much larger than all the others. A prototypical example of a planetary problem is the Sun–Jupiter–Saturn system, where the mass of the Sun is about 1000 times larger than the masses of Jupiter or Saturn. [18]
Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than 100 kilograms.
For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten (about 3.162). For example, the nearest order of magnitude for 1.7 × 10 8 is 8, whereas the nearest order of magnitude for 3.7 × 10 8 is 9.