###### Answer: a. (opens to the left)

In mathematics the graph of a function f is the set of ordered pairs (x y) where f(x) = y.In the common case where x and f(x) are real numbers these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.. …

In geometry the unit hyperbola is the set of points (x y) in the Cartesian plane that satisfy the implicit equation − = In the study of indefinite orthogonal groups the unit hyperbola forms the basis for an alternative radial length = −. Whereas the unit circle surrounds …

Linear equation – Wikipedia

Linear equation – Wikipedia

Heat equation – Wikipedia

If b ≠ 0 the equation + + = is a linear equation in the single variable y for every value of x.It has therefore a unique solution for y which is given by = − −. This defines a function.The graph of this function is a line with slope − and y-intercept −. The …

The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes.It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity.Equivalently in polar coordinates (r θ) it can be described by the equation

Mon Jan 06 2003 13:30:00 GMT-0500 (Eastern Standard Time) · The function u above represents temperature of a body. Alternatively … (Perona & Malik 1990) and in machine-learning as the driving theory behind scale-space or graph Laplacian methods. The heat equation can be efficiently solved numerically using the implicit Crank–Nicolson method of (Crank & Nicolson 1947). This method can be extended to many of the models with no closed form solution …

An n × m rook’s graph represents the moves of a rook on an n × m chessboard. Its vertices m…