Derivatives

As business becomes more globalized and trade continues to expand internationally, companies need to understand and reduce the risk associated with international business. Though there are many risks faced by companies when operating internationally, including political, financial, and cultural, this paper will specifically discuss the financial risk associated with exchange rates and how companies mitigate this risk through currency hedging. Foreign Exchange Risks Foreign exchange risk is “the…

If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…

Answers: 1. Segment A (Position-Time on Ramp): The graph is a curve. On any graph that curves, the slope or steepness of the graph changes from one point on the graph to another. Since the slope is constantly changing, the velocity is non-constant. Also, as the graph lies above the x-axis and its slope is increasing, the velocity of the object is also increasing (speeding up) in a positive left direction. Segment B (Position-Time on Flat Surface): The graph is a straight line, which represents…

The handy helper I choose was a video from Khan Academy. This video was about the Cartesian Coordinate System. I naturally gravitated to the Khan Academy link because I was already accustomed to the website while using it to get spun back up before this class. The Kahn Academy site contains similar math videos and you learn from watching their videos and practicing math problems that relate to the video. This particular video consists of a guy explaining math while at the same time visually…

Francisco Gutierrez 03.03 Linear Functions 1. The equation we have is 2x+3y=1200. The first thing you would need to do in the equation is subtract 2x to both sides. 2x cancels out and now we subtract 2x and 1200. You would end up getting 3y=2x-1200. Then finally, you would have to divide everything by -3. Your final answer for this question is y=-2/3x+400. Your slope is -2/3 and your y-intercept is 400. 2. So we know that our slope is -2/3 and the y-intercept is 400. You have one point on the…

The solution of the Frank and Doris race problem looked to be simple at first. Although Doris speed began faster, Frank gained speed and passed her and thus seemed to be the winner of the race. After looking more closely at the problem I discovered this was not quite the case. I first sketched Frank and Doris given values onto the one Velocity-Time graph. Originally looking at this graph, it looks as if Frank passes Doris at 10 seconds, because that is when his speed becomes greater than Doris’s…

There are several areas in the natural world where the process of exponential decay arises from random processes. Whenever a material decays at a rate in proportion to its amount, this material represents the process of exponential decay. Exponential decay can be described using the mathematical model y=a×e^(-bx). A prominent example of naturally occurring random exponential decay is the process of radioactive decay. Some isotopes of nature are considered radioactive due to a specific…

The Mandelbrot and Filled Julia Sets The Mandelbrot and Filled Julia Sets are sets of numbers that are composed of complex numbers that do not diverge for varying conditions of the function fc(z)=z²+c. For the Mandelbrot set, the function is iterated from z=0. The filled Julia set holds c constant for any complex number to look at the behavior of the iterated functions for each value of z in the complex plane. Both sets are derived from the iterations of simple functions in the complex plane,…

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…

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