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Two other solutions are x = 3, y = 6, z = 1, and x = 8, y = 9, z = 2. There is a unique plane in three-dimensional space which passes through the three points with these coordinates, and this plane is the set of all points whose coordinates are solutions of the equation.
In 2020, it was announced that Google's AlphaFold, a neural network based on DeepMind artificial intelligence, is capable of predicting a protein's final shape based solely on its amino-acid chain with an accuracy of around 90% on a test sample of proteins used by the team.
[1] The Lotka–Volterra system of equations is an example of a Kolmogorov population model (not to be confused with the better known Kolmogorov equations), [2] [3] [4] which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism.
Kleiber's plot comparing body size to metabolic rate for a variety of species. [1]Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, states, after many observations that, for a vast number of animals, an animal's Basal Metabolic Rate scales to the 3 ⁄ 4 power of the animal's mass.
When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. For linear equations, logical independence is the same as linear independence. The equations x − 2y = −1, 3x + 5y = 8, and 4x + 3y = 7 are linearly dependent. For example ...
The relationship between the solubility of a protein and increasing ionic strength of the solution can be represented by the Cohn equation: = S = solubility of the protein, B is idealized solubility, K is a salt-specific constant and I is the ionic strength of the solution, which is attributed to the added salt.
The Barth surface, shown in the figure is the geometric representation of the solutions of a polynomial system reduced to a single equation of degree 6 in 3 variables. Some of its numerous singular points are visible on the image. They are the solutions of a system of 4 equations of degree 5 in 3 variables.
In the field of computer science, the method is called generate and test (brute force). In elementary algebra, when solving equations, it is called guess and check. [citation needed] This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory.