Applications of algebraic equations and inequalities

The advancements in modern technology are a result of theories presented by scientists and researchers, which they proved on the basis of mathematical models. These models involve the techniques that are the core elements in mathematics which includes calculus, trigonometry, algebra, and geometry. However, all these methods ultimately lead either to the graphical solution or the algebraic equations and inequalities that are solved to provide the best possible outcome. Consequently, these algebraic equations and inequalities include the quadratic and cubic expressions that possess a variety of applications; some of them will be discussed here. Quadratic equations are the most common algebraic expressions that are encountered in daily life. The most common application of this type of equation is the calculations of areas of boxes, lands, and rooms. Consider the preparation of 4 square feet rectangular box as an example, where its length is twice its width; its dimension can be determined by writing a quadratic equation based on the area of a rectangle (2x2 = 4). As a result, it supports determining the parameters of any real world’s geometrical shape from its desired area. Quadratic equations also have a vital role in the field of economics. This kind of equation is employed to calculate the profit or loss of a business. For instance, the number of glasses sold can be determined by the revenue equation 5x2 = 100 to earn a revenue of $100 by selling x number of glasses, and the cost of each glass is $5x. Hence, it helps optimize the quantity of a commodity to earn the maximum revenue. Similarly, another type of algebraic function is quadratic inequalities. The quadratic inequalities are usually used to highlight a limitation within the solution of an unknown variable. For example, if a constraint is added to the equation of the area of the rectangle, such as only a 4 square feet wood is available to prepare the carton, and its length should be twice its width, the area of the rectangle is given by the inequality 2x2 ≤ 4. Therefore, it assists in constructing the best possible design with limited resources. Quadratic inequalities also have an important role, like the quadratic equations, in the field of finances. A limiting constraint can be added to that equation to convert an equation into an inequality. Take the revenue of a lemonade shop as an example; if a limitation is added to it, such as the income should be greater than $100 or the number of glasses sold should be greater than 12, the equation of revenue will be treated as an inequality. Consequently, the quadratic inequality contributes to identifying the maximum revenue or profit, minimum cost or the maximum production. Alternatively, there are cubic equations, which are less common form algebraic functions than quadratic equations. Yet, the simplest application of this category is the determination of volumes of boxes and rooms. Assume the preparation of a 32 cubic feet room as an example, where its length and width are twice its height; its dimension can be determined by writing a cubic equation based on the capacity of the room (4x3 =32). Subsequently, it promotes determining the parameters of any real world’s geometrical shape from its desired volume. In a nutshell, algebraic equations and inequalities are precisely important and truly have many applications in real-world situations. Nevertheless, the utilization of these algebraic expressions has helped in understanding the phenomenon involved in daily activities effectively and efficiently.