THE CIRCUMRADIUS OF A CONCYCLIC QUADRILATERAL
Suppose that a quadrilateral ABCD be given with the following lengths of sides: AB = 3 cm, BC = 8 cm, CD = 6 cm and AD = 5 cm. (See Figure 1.) What is the radius of the circumcircleRead More
FINDING THE EQUATION OF A TANGENT LINE
Let f be a function defined on to and C be the curve whose equation is y = f (x). This article shows us how to determine the equation of the tangent line to C at the point K(a,b) whereRead More
BIJECTIVE FUNCTIONS
In the article Injective and Surjective Functions, the concepts of injective functions and surjective functions are discussed separately. Some functions are injective but not surjective while others are surjective but not injective. In fact, It is possible for a functionRead More
CRAMER’S RULE
This article elaborates on how to solve systems of linear equations by applying a theorem called the Cramer’s rule. This rule is an alternative to the elimination and substitution techniques. At the first stage of applying the rule, we haveRead More
TECHNIQUES FOR SOLVING SYSTEMS OF LINEAR EQUATIONS IN TWO UNKNOWNS
An arbitrary system of m linear equations in n unknowns has the following general form: where x1, x2, …, xn are the unknowns and the subscripted a’s and b’s denote constants. As with the systems of linear equations inRead More
THE ABSOLUTE VALUE FUNCTION
Let f be a function on to given by: The function just-defined is called the absolute value function. For every x ∈ the image of x under f is denoted by |x|. Thus, The graph of the absolute value functionRead More
HALF IS AS MUCH AS A WHOLE … HOW COME?
The set of all natural numbers, , is a countably infinite set. In fact, . Now, let G be the set of all even natural numbers. Thus, G = {2, 4, 6, 8, 10, 12, …}. Note that G isRead More
THE EQUATION OF ANGLE BISECTOR
In this article, we’ll learn how to determine the equation of the bisector of the angle between two lines whose equations are given. For example, suppose that the equations of lines g and h are and , respectively. As FigureRead More
POWERS AND EXPONENTIAL FUNCTIONS
The readers may find that literatures on mathematics provide various definitions of powers. Some authors do not distinguish the term power from index/exponent. Throughout this article, a power is a mathematical expression in the form of br where . The numberRead More
THE LOGARITHMS
Definition Let , a, b > 0 and b ≠ 1. The logarithm of a to base b, denoted by , is defined as follows. if and only if The number b is called the base of the logarithm, andRead More