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The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
This method was frowned upon by my high school math teacher by the fact that it can cause confusion and errors when answer expression with positive/negative numbers. ie. (x + 3)(x - 7) = the answer could be incorrect by the confusion of the minus sign. I think there should be some articles that explains the negative aspect of this rule.
[1] [2] When n = 2, it is easy to see why this is incorrect: (x + y) 2 can be correctly computed as x 2 + 2xy + y 2 using distributivity (commonly known by students in the United States as the FOIL method). For larger positive integer values of n, the correct result is given by the binomial theorem.
The FOIL algorithm is as follows: Input List of examples and predicate to be learned Output A set of first-order Horn clauses FOIL(Pred, Pos, Neg) Let Pos be the positive examples Let Pred be the predicate to be learned Until Pos is empty do: Let Neg be the negative examples Set Body to empty Call LearnClauseBody Add Pred ← Body to the rule
Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.
The foil thickness homogeneity is of more importance for the detector energy resolution than the absolute thickness. [1] If heavy ions are used and detected, the effect of energy loss straggling will be easily surpassed by the energy loss variation, which is a direct consequence of different foil thicknesses.
Hybrid Reverse Monte Carlo (HRMC) [19] [20] is a code capable of fitting both the pair correlation function and structure factor along with bond angle and coordination distributions. Unique to this code is the implementation of a number of empirical interatomic potentials for carbon (EDIP), silicon (EDIP [ 21 ] and Stillinger-Weber [ 22 ] ) and ...
For the metal foil, they tested a variety of metals, but favoured gold because they could make the foil very thin, as gold is the most malleable metal. [16]: 127 As a source of alpha particles, Rutherford's substance of choice was radium, which is thousands of times more radioactive than uranium. [17]