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From top to bottom: x 1/8, x 1/4, x 1/2, x 1, x 2, x 4, x 8. If x is a nonnegative real number, and n is a positive integer, / or denotes the unique positive real n th root of x, that is, the unique positive real number y such that =.
[2] [7] [8] The 2019 revision of the SI now defines the kelvin in terms of energy by setting the Boltzmann constant to exactly 1.380 649 × 10 −23 joules per kelvin; [2] every 1 K change of thermodynamic temperature corresponds to a thermal energy change of exactly 1.380 649 × 10 −23 J.
For an ideal absorber/emitter or black body, the Stefan–Boltzmann law states that the total energy radiated per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the black body's temperature, T: The constant of proportionality, , is called the Stefan–Boltzmann constant.
If its temperature is allowed to change by 1 °C, its mass changes by 1.5 picograms (1 pg = 1 × 10 −12 g). [note 5] A spinning ball has greater mass than when it is not spinning. Its increase of mass is exactly the equivalent of the mass of energy of rotation, which is itself the sum of the kinetic energies of all the moving parts of the ball.
A type Ia supernova explosion gives off 1– 2 × 10 44 joules of energy, which is about 2.4–4.8 hundred billion yottatons (24–48 octillion (2.4– 4.8 × 10 28) megatons) of TNT, equivalent to the explosive force of a quantity of TNT over a trillion (10 12) times the mass of the planet Earth.
Average full-size passenger cars have a drag area of roughly 8 sq ft (0.74 m 2). Reported drag areas range from the 1999 Honda Insight at 5.1 sq ft (0.47 m 2) to the 2003 Hummer H2 at 26.5 sq ft (2.46 m 2). The drag area of a bicycle (and rider) is also in the range of 6.5–7.5 sq ft (0.60–0.70 m 2). [5]
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
According to rules of thumb, this approximation is good if n ≥ 20 and p ≤ 0.05 [36] such that np ≤ 1, or if n > 50 and p < 0.1 such that np < 5, [37] or if n ≥ 100 and np ≤ 10. [38] [39] Concerning the accuracy of Poisson approximation, see Novak, [40] ch. 4, and references therein.