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The elements of an arithmetico-geometric sequence () are the products of the elements of an arithmetic progression (in blue) with initial value and common difference , = + (), with the corresponding elements of a geometric progression (in green) with initial value and common ratio , =, so that [4]
A set of points is said to guard a polygon if, for every point in the polygon, there is some such that the line segment between and does not leave the polygon. The art gallery problem can be applied in several domains such as in robotics , when artificial intelligences (AI) need to execute movements depending on their surroundings.
A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set. An equation may be solved either numerically or symbolically. Solving an equation numerically means that only numbers are admitted as solutions.
For example, the solution set for the above equation is a line, since a point in the solution set can be chosen by specifying the value of the parameter z. An infinite solution of higher order may describe a plane, or higher-dimensional set. Different choices for the free variables may lead to different descriptions of the same solution set.
In mathematics, the solution set of a system of equations or inequality is the set of all its solutions, that is the values that satisfy all equations and inequalities. [1] Also, the solution set or the truth set of a statement or a predicate is the set of all values that satisfy it. If there is no solution, the solution set is the empty set. [2]
Let the system of equations be written in matrix form as = where is the coefficient matrix, is the vector of unknowns, and is an vector of constants. In which case, if the system is indeterminate, then the infinite solution set is the set of all vectors generated by [4]
At least five drone shows have been canceled or have paused the use of the systems, after several drones struck a crowd at a holiday show in Orlando on December 21.
Since z = 1 − x, the solution of the hypergeometric equation at x = 1 is the same as the solution for this equation at z = 0. But the solution at z = 0 is identical to the solution we obtained for the point x = 0, if we replace each γ by α + β − γ + 1. Hence, to get the solutions, we just make this substitution in the previous results.