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- https://math.libretexts.org/Courses/Highline_College/Math_142%3A_Precalculus_II/06%3A_Vectors/6.01%3A_Vectors_from_a_Geometric_Point_of_ViewThere are some quantities that require only a number to describe them. We call this number the magnitude of the quantity. One such example is temperature since we describe this with only a number such...There are some quantities that require only a number to describe them. We call this number the magnitude of the quantity. One such example is temperature since we describe this with only a number such as 68 degrees Fahrenheit. Other such quantities are length, area, and mass. These types of quantities are often called scalar quantities. However, there are other quantities that require both a magnitude and a direction. One such example is force, and another is velocity.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/08%3A_Conic_Sections/8.01%3A_Distance_Midpoint_and_the_ParabolaA conic section is a curve obtained from the intersection of a right circular cone and a plane. The conic sections are the parabola, circle, ellipse, and hyperbola.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/01%3A_Analytic_Geometry/1.03%3A_Distance_Between_Two_Points_CirclesThe actual (positive) distance from one point to the other is the length of the hypotenuse of a right triangle with legs |Δx| and |Δy|. The Pythagorean theorem then says that the distance between th...The actual (positive) distance from one point to the other is the length of the hypotenuse of a right triangle with legs |Δx| and |Δy|. The Pythagorean theorem then says that the distance between the two points is the square root of the sum of the squares of the horizontal and vertical sides.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/03%3A_Triangles_and_Vectors/3.05%3A_Vectors_from_a_Geometric_Point_of_ViewThere are some quantities that require only a number to describe them. We call this number the magnitude of the quantity. One such example is temperature since we describe this with only a number such...There are some quantities that require only a number to describe them. We call this number the magnitude of the quantity. One such example is temperature since we describe this with only a number such as 68 degrees Fahrenheit. Other such quantities are length, area, and mass. These types of quantities are often called scalar quantities. However, there are other quantities that require both a magnitude and a direction. One such example is force, and another is velocity.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/11%3A_Appendix_-_Prerequisite_Function_Material/11.01%3A_Sets_of_Real_Numbers_and_the_Cartesian_Coordinate_PlaneThis section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and...This section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and explains how to plot points and graph equations on the Cartesian plane. The section also discusses intervals and the distance formula, providing foundational knowledge for working with functions and graphs in Algebra.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_(Lecture_Notes)/01%3A_Functions/1.02%3A_Domain_and_RangeFinding the Domain of a Function Defined by an Equation Examples Domain and range of a set of data points. Domain of a quadratic, simple rational, and shifted square root function. Note You will likel...Finding the Domain of a Function Defined by an Equation Examples Domain and range of a set of data points. Domain of a quadratic, simple rational, and shifted square root function. Note You will likely have to review interval notation. Definitions Set-builder notation Finding Domain and Range from Graphs Do one. Finding Domains and Ranges of the Toolkit Functions Graphing Piecewise-Defined Functions Definition Piecewise function Example Graph a piecewise involving raw toolkit functions only.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/06%3A_Orthogonality/6.03%3A_Orthogonal_ProjectionThis page explains the orthogonal decomposition of vectors concerning subspaces in Rn, detailing how to compute orthogonal projections using matrix representations. It includes methods f...This page explains the orthogonal decomposition of vectors concerning subspaces in Rn, detailing how to compute orthogonal projections using matrix representations. It includes methods for deriving projection matrices, with an emphasis on linear transformations and their properties. The text outlines the relationship between a subspace and its orthogonal complement, utilizing examples to illustrate projection calculations and reflections across subspaces.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/10%3A_Vectors/10.01%3A_Introduction_to_Cartesian_Coordinates_in_SpaceIn this section we introduce Cartesian coordinates in space and explore basic surfaces. This will lay a foundation for much of what we do in the remainder of the text. Each point P in space can be r...In this section we introduce Cartesian coordinates in space and explore basic surfaces. This will lay a foundation for much of what we do in the remainder of the text. Each point P in space can be represented with an ordered triple, P=(a,b,c), where a,b and c represent the relative position of PP along the x, y and z -axes, respectively. Each axis is perpendicular to the other two.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.01%3A_Sets_of_Real_Numbers_and_the_Cartesian_Coordinate_PlaneThis section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and...This section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and explains how to plot points and graph equations on the Cartesian plane. The section also discusses intervals and the distance formula, providing foundational knowledge for working with functions and graphs in Algebra.
