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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
The quadratic formula is exactly correct when performed using the idealized arithmetic of real numbers, but when approximate arithmetic is used instead, for example pen-and-paper arithmetic carried out to a fixed number of decimal places or the floating-point binary arithmetic available on computers, the limitations of the number representation ...
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
In this context, the quadratic formula is not completely stable. This occurs when the roots have different order of magnitude, or, equivalently, when b 2 and b 2 − 4ac are close in magnitude. In this case, the subtraction of two nearly equal numbers will cause loss of significance or catastrophic cancellation in the smaller root.
A2.1 A2.2 B1 B2 C1 C2 Korean: Test of Proficiency in Korean [77] Level 1 Level 2 Level 3 Level 4 Level 5–Level 6 Luxembourgish: Institut National des Langues [78] A2 B1 B2 C1 Norwegian: Norskprøve [79] A1 A2 B1 B2 C1 – høyere akademisk nivå (advanced academic level) [80] Polish: Egzaminy Certyfikatowe z Języka Polskiego jako Obcego [81]
If c = p e is a prime power, there exists a primitive Pythagorean triple a 2 + b 2 = c 2 if and only if the prime p has the form 4n + 1; this triple is unique up to the exchange of a and b. More generally, a positive integer c is the hypotenuse of a primitive Pythagorean triple if and only if each prime factor of c is congruent to 1 modulo 4 ...
The B2 scenarios are of a world more divided, but more ecologically friendly. The B2 scenarios are characterized by: Continuously increasing population, but at a slower rate than in A2. Emphasis on local rather than global solutions to economic, social and environmental stability. Intermediate levels of economic development.
Alternatively the final velocity of a particle, v 2 (v A2 or v B2) is expressed by: = (+) Where: e is the coefficient of restitution. v CoM is the velocity of the center of mass of the system of two particles: = + +