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Mathematics Articles
Page 18 of 21
Quotient
Introduction Division is splitting (dividend) into equal parts by a known number of parts (divisor). Division is used everywhere in real life. When a number is divided by the same number the result is 1. Example: 4\/4 = 1. When a number is divided by 1 the result is the same number. Example:15/1=15 . When 0 is divided by a number, the result is 0. Example: 0÷14 = 0. When a number is divided by 0, the result doesn't have any value. Example: 7÷0 = undefined. Division Algorithm To divide a number there are two steps to follow − ...
Read MoreIntercept
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 MoreScalar triple product
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 MoreSec 0
Introduction The notion of trigonometry was developed by the Greek mathematician Hipparchus, while the name trigonometry is a 16th-century Latin derivative. Trigonometry is one of the most important branches of mathematics. The name "trigonometry" is made up of the phrases "Trigonon" and "Metron, " which denote a triangle and a measure, respectively. It is the study of the relationship between the sides and angles of a right-angled triangle. The ratio of the hypotenuse's length to the neighbouring side's (base) length is known as the sec of an angle in a right triangle. The angle 0° for sec 0 degrees is ...
Read MoreSec 60
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 MoreProperties of Logarithms
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 MoreDeterminant
Introduction We studied in the previous classes that the system of two linear equations in two variables namely $\mathrm{a_{1}x\:+\:b_{1}y\:=\:c_{1}\:and\:a_{2}x\:+\:b_{2}y\:=\:c_{2}}$ will have unique solution if $\mathrm{\frac{a_{1}}{b_{1}}\:\neq\:\frac{a_{2}}{b_{2}}\:i.e.\:a_{1}b_{2}\:-\:b_{1}a_{2}\:\neq\:0}$. Thus, $\mathrm{(a_{1}b_{2}\:-\:b_{1}a_{2})}$ is the determining factor for the system of two linear equations. We define $\mathrm{a_{1}b_{2}\:-\:b_{1}a_{2}}$ to be the determinant of the square matrix of order 2. In this tutorial we define the determinant of the square matrix of order 2 and 3 and understand the properties of determinants along with some solved examples. Determinant To every square matrix $\mathrm{A\:=\:[a_{ij}]}$ of order 𝑛, we can associate a real or complex number called ...
Read MoreDifferential Equations
Introduction We need to develop various mathematical models to establish relationships between multiple variables in real life. In this direction, differential equations play an important role. These are applied parts of mathematics and used in calculus. In this tutorial, we will discuss the meaning, order, degree, and types of differential equations with solved examples. Differential Equations Differential equations are mathematical statements containing functions and their derivatives. It describes the relationship between the variables with their rate of change. It is used in engineering, science, biology, finance, etc. The differential equations contain at least one ordinary derivative or partial derivative term. ...
Read MoreFundamental principle of counting
Introduction You go shopping on a bright sunny day. You chose nice jeans and decided to pay with a credit card. But suddenly you realized that you couldn't remember your PIN. What a tragedy! Now what you can think of is to list all possible combinations to understand your pin. How many combinations are possible? If you list and count all possible combinations, the answer to this question will be difficult. In these situations, the basic principle of counting or the principle of multiplication is useful. Number system A number system is defined as a system of writing to ...
Read MorePoisson Distribution
Introduction Poisson distributions are frequently used to comprehend various events that take place continuously over a predetermined period of time. The Poisson distribution is a discrete function , therefore the variable can only take values from a list of (possibly infinite) numbers. The Poisson distribution is used in probability and statistics concepts of mathematics. It is a discrete probability distribution used in probability theory and statistics to express the chances of happening that a given number of events will happen within a given time period and regardless of the amount of time that has passed since the last outcome. Definition ...
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