INJECTIVE AND SURJECTIVE FUNCTIONS
One-one Functions Let A and B be sets and f is a function from A to B. The function f is called a one-one function or an injective function if the following holds: f(a) = f(b) ⇒ a =Read More
LEVELS OF MEASUREMENT
There are four levels of measurement. Sequentially from the lowest to the highest, they are: 1) nominal measurement, 2) ordinal measurement, 3) interval measurement, 4) ratio measurement. Data with nominal or ordinal measurement are qualitative, while that of interval orRead More
ELEMENTARY THEORETICAL PROBABILITIES
There are several approaches to determine the probability of an event. One of them is what we call the classical or theoretical probability. Mathematically, the theoretical probability is obtained by dividing the number of the elements of the set calledRead More
HOW TO DETERMINE THE EQUATIONS OF LINES USING FAMILY OF LINES
Every line in the Cartesian plane can be expressed in the general form Ax + By + C = 0. Suppose that the lines g and h have equations A1x + B1y + C1 = 0 and A2x + B2yRead More
SKETCHING THE GRAPHS OF SINE AND COSINE FUNCTIONS
How to graph the function for 0 ≤ x ≤ 2π? If we already know the graph of y = sin x, then with the techniques provided below, the graph of the function can be easily drawn. Let’s first lookRead More
THE THEOREM OF TOTAL PROBABILITY AND BAYES’ RULE
Case Study In a certain assembly plant, three machines, M1, M2, and M3, make 20%, 30%, and 50%, respectively, of the products. It is known from past experience that 4%, 3%, and 5% of the products made by each machine,Read More
THE EQUATION OF THE POLAR OF A POINT WITH RESPECT TO A CIRCLE (2)
In the article The Equation of The Polar of A Point with Respect to A Circle (1), it is shown that the equation of the polar of the point K(x1,y1) with respect to the circle (x – α)2 + (yRead More
THE EQUATION OF THE POLAR OF A POINT WITH RESPECT TO A CIRCLE (1)
This post introduces the concept of polars. There are several approaches to understanding the concept. The approach adopted in this article is through the points of tangency on a circle. [Regarding the notion of the points of tangency, the readersRead More
THE EQUATIONS OF THE TANGENT LINES TO A CIRCLE (2)
In the previous post The Equations of The Tangent Lines to A Circle (1), it is discussed how to determine the equations of the tangent lines to a circle on condition that the slopes of the lines are given. Now,Read More
THE EQUATIONS OF THE TANGENT LINES TO A CIRCLE (1)
If a line and a circle are placed on a plane, there are three possibilities in terms of the number of points of intersection between them. First, the line intersects the circle at two distinct points. (See Figure 1 below.)Read More