System of linear equations

a) Heckel equation In 1961, Heckel proposed the most widely used equation describing pharmaceutical powder behavior in compaction. It was initially used to study the densification of ceramics and its correlation with pressure. It a first order process where powder pores elimination rate is correlated to the number of pores present. The rate of volume reduction increases as the number of pores decrease. Heckel equation relates the density, pressure and the pore fraction of the powder [16],.…

coefficients expansion in general. After that, I will introduce Jade Mirror of the Four Unknowns written by Zhu Shijie around 14th century AD. My focus will be his idea of using the “four unknowns” to convert a problem into a mathematical system of polynomial equations. Later on, I will also…

Linear Programming: Toy Store In the beginning we were given a linear programming project to do for math class. Linear programming is a method to achieve the best outcome in a mathematical model. We were given an assignment in which we are the owners of a toy store and have 5 different types of toys that we make. The objective of the project is that we need to find out which 2 toy combination will make us the most profit. First we found out that there were 10 different combinations that we…

continuously by the same number, it would be said to be a linear function. Common examples of linear function would be distance traveled over time for objects traveling at constant speed; cost of gas in relation to gallons used. Certain situations are linear or not based on whether or not the rate of change is constant or varies. Linear systems are represented by f(x) = mx + b; the slope (m) and the y-intercept (b). In a table that represents a linear function, the input and out puts will be a…

We discussed the mechanism of the tidal force with its impact on tidal flows. By analyzing the sum and difference of gravitational forces within the Earth-Moon-Sun system, we figured out the changes of tidal force made by stars’ changing positions. On the other hand, we also discussed the formation of tidal flows. Our approach shows how vertical and horizontal tidal forces causing the sea level fluctuations. 1. Introduction The tides are a regular and predictable phenomenon caused by the…

4 The Simplex Method As we have seen, a linear programming problem forms a convex polygon in the best possible scenario. It is imperative to obtain a process that would assist in determining the optimal solution without the need to examine the graphical representation. The need for an algorithm that would perform such process was essential in the early days of the formulations of linear programming problems. Although challenging, the task was accomplished by a mathematician of the twentieth…

Sitting in Algebra II, you may think to yourself: when am I ever going to use any of this in the real world? You are going to use all of the skills you learn in Algebra II more than you will ever realize. Using trigonometry, linear functions, series and sequences, and rational functions are prevalent in everyday life. In this fun, exciting report, you will learn about many situations in which you use Algebra II without even recognizing it! Trigonometry is a widely used math concept in everyday…

called, "System of Linear Equations: Gausssian Elimination". Through this section, I was able to learn how to solve the system of equations for three variables. It took me a few readings to understand the extra variable system. I don't know why, but I feel like it's easier for me to mentally find the answer through process of elimination, than going through the huge process of going by the formulas to find the answer to a three variable system. However, I did notice a weakness, that if the…

that is connected to the vertical board on the top. The first step of this experiment was to turn on the main control valve and to start the flow pump system. Then set the rotameter reading to each of the 5, 10, 15, 20, and 22 that were needed for this experiment. For the 5 and 10 reading, one mass that weighed in at 6 kg was added to the system, and for the rest 12 kg mass was added. The air pump that was used at the scale reading of 5 increased the pressure on the water levels in the tube.…

preferred conformations. in the modern chemistry, where it can lead to significant improvement in the understanding of more complex system. theoretical calculations were proved to give good results for thermodynamic properties [1-3] The determination of the structural parameters of the preferred conformation and…