that we do not carry out the mission, it leaves us with a sense of emptiness at the end of our day. With that I will analyze this problem by specifically looking at job involvement and Perceived Organization Support. Good introductory paragraph helps follow the discussion Job Involvement Job involvement is defined as the degree to which a person identifies with a job, actively participates in it, and considers performance important to self-worth. Because of the sensitive nature and pure destructive power of the weapons that we work with, there are strict guidelines that ICBM operators have to adhere to. These guidelines are written as step by step instructions on how perform a task which range from launching a missile to something as simple as opening a door. This in my opinion drives job involvement down because as officers we are trained to be problem solvers. However, we are not given the opportunity to solve any problems by any other means then examining status received from the missiles and following a checklist. This then leaves many of us having a low level of psychological empowerment which is the belief in the degree of work put forward will have on their work environment (Robbins & Judge, 2009). These two factors make it extremely tough to go to work each day knowing that the core philosophy of the job is “read a step, do a step” and explained in such a manner that with just a basic understanding of the weapon system any one could perform the day…
In a polynomial equation, if a number # if (x-#) is a factor of g(x), then # is a zero/root of the polynomial. If the group of three wants to prove that the binomial (x+2) is a factor of the g(x) equation, one option they could explore is using long division with the binomial in the divisor position. Essentially, no one was wrong. Prof. McCory and Ms. Guerra were in the green. 3. Dr. Collier summons you over to his table. He wants to demonstrate the graph of a fourth-degree polynomial function,…
In 1540, a man by the name of Lodovico Ferrari, please be aware that I don’t think his name has anything to do with the sports car, was an Italian mathematician known for discovering the solutions to quartic functions. A quartic function is a function of the form ax^4 + bx^3 +cx^2 +dx+e, where a is a nonzero, which is defined by a polynomial raised to the fourth degree, called quartic polynomial. We will probably go more in depth about these quartic polynomials soon in class. My quartic…
Like many other truly great mathematicians Nikolai Ivanovich Lobachevsky came from a humble background, worked hard to raise himself to be highly renowned and died before the significance of his works could be truly accepted and appreciated. Lobachevsky was a rector and a professor of mathematics at Kazan University for nineteen years, devised a method for finding roots of a polynomial and published a plethora of material on algebra, numerical analysis, astronomy and probability. His most…
There's a really interesting way to see that the converse is false (not every number congruent to 5 modulo 6 is prime). You could of course just find a counterexample, but this is a special case of a more general phenomenon, described below. Claim: There is no polynomial P in Z[x] of positive degree such that the values P(0), P(1), ... are all prime. Proof: Suppose otherwise, so P(0) = p for some prime p. Then the constant term of P is p, so p | P(kp) for k >= 1 an integer. Since these…
units” of algebra [Allen]. These concepts undoubtedly, integrated and related many areas of mathematics, amongst these, topology, theory and analysis [Allen]. The Fundamental Theorem of Algebra As the study of algebra became more expansive and necessary, it became of extreme importance to many other disciplines as well. And as remarkable mathematicians made new discoveries, algebra developed and progressed as a mathematical science. Prodigious individuals such as Descartes and Fermat were…
Introducing a polynomial description of the displacements in thickness direction, he opened the door for shell models that match the three-dimensional theory with arbitrary exactness. Nevertheless, these shear-deformable shell models are commonly called shells with Reissner-Mindlin kinematics due to the origin of the assumption of shear-deformable cross-sections. Following the naming of Bischoff [Bis1999], the pure displacement-based shell formulations with shear deformation are called…
1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number? Answer: If the equation is 7th degree then it has 7 roots. Those roots can be complex or real. Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi. If at least one root were complex, then we would have a…
publication for engineering, and mechanics than mathematics. L’arithmétique, which means Arithmetic was also published in 1585. This publication is the opinion that all numbers, even squares, square roots, negative, and irrational numbers were all the same. This statement is an opinion that is not often shared by other mathematicians, but he found to be supported through the development of algebra. Algebra is the study of of mathematics where letters are introduced to represent numbers, or…
Introduction I’m going to start this paper with introducing the history of Pascal’s Triangle, time ranging from 2nd century BC to 18th century AD. Among all the academic works by ancient mathematicians, I’m going to focus on Jiu Zhang Suan Shu [Nine Chapters on the Mathematical Art] composed by Chinese scholars around 2nd century BC-10th century AD. I will use the binomial expansions derived from Pascal’s triangle as an example and then illustrate the coefficients expansion in general. After…