One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wearing upon the structure; ice flows striking the structure; the forces the current creates caused by river traffic flowing beneath the bridge; height of the bridge and the wind force. The bridge also has to be designed to withstand the constant flow of traffic on the bridge and to bear its weight. Graphing parabolas and hyperbolas can be used to illustrate some of these design issues.
1. How does the graph of a parabola differ from the graph of one branch of a hyperbola? Identify some real world applications and mathematical examples of parabolas and hyperbolas (other than civil engineering).
2. Search the internet to find and discuss at least two practice uses of probability today. Be sure to cite your sources.
Probability is where history is used in an attempt to determine or tell one what will happen in the future. (web6.duc.auburn.edu, 2005) This is found throughout various aspects of business and everyday life. For instance, individuals play the lottery, bet on horse races or gamble in Las Vegas based on historical knowledge. This in turn provides them the information as to where they place their desired bets. So if one went to a horse race that had a horse and/or jockey that had won three out of the past four races individuals would in turn place it on their tickets. As one would feel it would have a higher probability of being successful within this race than the others due to its history. (http://mathforum.org/library/drmath/view/56701.html) However to increase ones understanding let me provide an example which should affect almost all individuals which is that of automobile insurance. After all, everyone pays this premium either monthly or annually and feels their rates are too high. Insurance companies utilize probabilities to forecast the likelihood for claims or accidents for specific genders or age brackets of individuals. This forecasting allows the company to set the rates for these individuals, pay the claims anticipated and other various aspects. For example, the statisticians at the insurance company calculate that male drivers under the age of 25 during a one-year period will have a .25 probability of having an accident The company in which we are discussing insures 10,000 male drivers within that age bracket so the financial manager based on the probability figures will forecast that 2,500 of the company's policyholders under the age of 25 will have an accident during the coming year. http://www.cob.ohio-state.edu/fin/Autumn2005/640_Class%203.ppt
Real-Life Applications of Parabolas, Hyperbolas and Probability are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.