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Using the usual notations for a triangle (see the figure at the upper right), where a, b, c are the lengths of the three sides, A, B, C are the vertices opposite those three respective sides, α, β, γ are the corresponding angles at those vertices, s is the semiperimeter, that is, s = a + b + c / 2 , and r is the radius of the inscribed circle, the law of cotangents states that
In projectile motion, the horizontal motion and the vertical motion are independent of each other; that is, neither motion affects the other. This is the principle of compound motion established by Galileo in 1638, [ 1 ] and used by him to prove the parabolic form of projectile motion.
In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate in a prescribed way. In particular, if the vertex set of the graph is V , one should be able to choose a word w over the alphabet V such that letters a and b alternate in w if and only if the ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The surface of the projectile also must be considered: a smooth projectile will face less air resistance than a rough-surfaced one, and irregularities on the surface of a projectile may change its trajectory if they create more drag on one side of the projectile than on the other. However, certain irregularities such as dimples on a golf ball ...
(However, as directed graphs, tournaments are not complete: complete directed graphs have two edges, in both directions, between each two vertices. [1]) The name tournament comes from interpreting the graph as the outcome of a round-robin tournament, a game where each player is paired against every other exactly once. In a tournament, the ...
Next, thrust in an inward and upward motion on the diaphragm. This will force air out of the lungs and remove the blockage. ... "Type the numbers ‘9-1-1’ into the ‘to’ or ‘recipient ...
The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.
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