Second derivative test

direction. Then, the difference between the accelerations would be that one is negative and the other is positive, meaning one is slowing down and one is increasing. 3. At one second, the instantaneous velocity of the car is, negative 0.869800824m/s right while the data from Logger Pro calculated the velocity of the car at one second to be negative 0.759364334m/s right. Therefore, the slope of the instantaneous velocity is steeper and therefore states the car accelerates more quickly than what…

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…

looks as if Frank passes Doris at 10 seconds, because that is when his speed becomes greater than Doris’s speed. This was not true. Sure, Frank’s speed was now faster than Doris, but it did not tell me anything about the previous distances they had traveled, so I could not assume that Frank passed Doris at ten seconds. Then I realized it might be beneficial…

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…

Global business today is subject to various kinds of risks. One risk that global business needs to handle is the foreign exchange risk. Foreign exchange risk is the risk that companies face a potential gain or loss due to the fluctuation of an exchange rate change. Companies could be subject to a significant financial loss even with a small change in the exchange rate. Thus, the primary purpose of managing foreign exchange risk is to mitigate potential currency losses. There are at least…

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The Cost-of-Carry Model In the commodity market the Cost of Carry model is used to price the futures and forwards contracts based on the spot price of the traded asset. The cost of carry is all the costs to carry an asset from the present until a certain future period, those are the cost to finance the asset (the interest), the storage costs, the transportation cost, and the insurance costs. The cost of carry model looks at the price of the future or forwardcontract as a function of the spot…