Mathematics Articles - Page 15 of 26

Introduction A cartesian plane is a two-dimensional plane which is part of a coordinate system. The concept of a cartesian plane is mostly used in Euclidean geometry & algebra. In a two-dimensional plane system, any point can be specified by x-coordinate y-coordinate. Axes on the cartesian plane divided it into 4 equal & infinite parts called quadrants. These quadrants are named quadrant I, quadrant II, quadrant III & quadrant IV. In the case of a circle, a quadrant can be represented by a quarter of the circle. So let's study the topic quadrant of the cartesian plane & circle in ... Read More

Introduction In daily life, we come across various geometrical objects, which are bounded by straight line segments. These are known as polygons. The polygons are categorized into various types based on their number of sides and angles. The rectangle is one type of polygon extensively used in Euclidean geometry. Various objects such as black boards, carrom boards, books, doors, smartphones, beds, etc. These are real-life examples of the rectangle. In this tutorial, we will discuss the meaning, properties, types, and basic formulae related to the rectangle with solved examples. Rectangle A rectangle is a two-dimensional polygon embedded in four ... Read More

Introduction In our daily life, we come across various geometrical objects whose dimensions need to be measured for convenience. In this direction, there are various measuring instruments invented and used. In addition, the measured amount is expressed by various units. In this tutorial, we will discuss the units of measurement of length, metric system, feet system, various units, and their mutual conversion with solved examples. Units of Measurement of Length The measurement of length means to measure the distance between two end-points of the specific object. It is a skill that helps us measure the length of various objects. ... Read More

Introduction Polynomials are mathematical expressions containing variables and coefficients. James Waddell Alexander II invented the concept of the polynomial. There are various terms associated with the polynomial. In this tutorial, we will discuss the meaning of polynomial, various correlations between the zeroes and the coefficients of polynomial equations with solved examples. Polynomials Polynomials are defined as the algebraic expressions containing one or more variable terms multiplied by constant terms. There are two terms associated with a polynomial, such as coefficients (i.e., constants) and variables. For example, $\mathrm{\mathit{f}(p)=p^2+2p+5}$ is an example of a polynomial. The given polynomial is denoted by f(p). ... Read More

Introduction Linear programming or linear optimization is a unique tool used to obtain the optimum (maximum or minimum) value of a mathematical model. It is abbreviated as LP and it is also known as mathematical optimization. In this tutorial, we will learn about linear programming, different methods to solve linear programming problems, and its various types. Linear Programming Linear programming is defined as the mathematical optimization process in which the maxima and minima of the process outcomes are evaluated within specific constraints. In other words, it is a technique to optimize the linear objective function. ... Read More

Introduction The coordinate graph is also called the Coordinate grid or plane. In a coordinate grid, the two perpendicular lines are called the axes. The horizontal axis is called the $\mathrm{x\:-\:axis}$ and the vertical axis is called the $\mathrm{y\:-\:axis}$ In a grid, points are distributed on the number lines, namely, on the $\mathrm{x\:-\:axis}$ and the $\mathrm{y\:-\:axis}$ The points of contact are written in the ordered pair. By reading the latitude and longitude of the coordinate plane, the location of the points on the grid can be found. The points on the $\mathrm{x\:-\:axis}$ is called the ... Read More

Introduction Integers are one of the most important concepts in mathematics, and most of them are relevant to this topic. You can practice this concept by practicing multiple integer worksheets. In mathematics, integers are characterized as numbers with a possible value of either positive, negative, or zero. These figures, however, cannot constitute a fraction. These numbers can be used to carry out a variety of mathematical operations, including addition, subtraction, multiplication, and division, according to the integer worksheet. According to the integer worksheet, examples of integers include 1, 2, 5, 8, -8, - ... Read More

Introduction The scalar triple product is used to find the volume of parallelepiped, which is a 3 dimension of parallelogram. As it is a triple product it deals with the three vectors on the three adjacent edges starting from a common vertex. $\mathrm{volume\:of\:parallelepiped\:=\:\overrightarrow{a}\:.\:(\overrightarrow{b}\:\times\:\overrightarrow{c})}$ We know the area of base of parallelepiped is the area of a parallelogram $\mathrm{=\:l\:\times\:b}$ $\mathrm{Area\:of\:the\:base\:=\:\lvert\:\overrightarrow{b}\:\times\:\overrightarrow{c}\:\rvert}$ To find the height of the Parallelepiped, b × c is a perpendicular line drawn to b and c which is not the actual height of parallelepiped. We first consider the height of the cuboid and convert it into parallelepiped. ... Read More

Introduction Logarithms are just another way of expressing exponents and can be used to solve problems that cannot be solved by the concept of exponents alone. In mathematics, logarithmic function properties are used to solve logarithmic problems. The division takes the final number and determines the count of the addition. Perhaps now you can appreciate how exponents and logarithms are a lot like multiplication and division. You will generally deal with a "base" in exponents and logarithms. The "base" of the exponent will be the same as the base of the logarithm. You have ... Read More

Introduction The link between a right triangle's side ratio and angle is the subject of the mathematical branch of trigonometry. The ratio used to study this relationship is called the trigonometric ratio. That is, sine, cosine, tangent, cotangent, second, cotangent. The hypotenuse, the base (which is adjacent), and the perpendicular are the three sides of a right-angled triangle from which trigonometric ratios in geometry are obtained. The name "trigonometry" is made up of the phrases "Trigonon" and "Metron, " which denote a triangle and a measure, respectively. The ratio of the hypotenuse's length to the neighbouring side's (base) length is ... Read More