Solve each of the following problems using the problem-solving strategies discussed in this section. Include what type of strategy was used in solving the problem.Note: Lesson in the Photo attached 15. A group of mathematicians were at a conference. Each mathematician exchangedhis/her business card with every other mathematician who was present.a. If there were 20 mathematicians, how many business cards were exchanged?b. If there was a total of 1200 business cards exchanged, how many mathematicianswere at the meeting? 8:00cdn.fbsbx.comMathematics in the Modern WorldHand OutsDoneProblem Solving and ReasoningProblem-solving has been an integral part of the mathematics curriculum that mustbe taught alongside the various mathematical concepts and skills necessary for success inschool and in real life. Most occupations require good problem-solving skills. This sectionaims to help you become a better problem solver and to show that problem-solving can bean enjoyable experience.In cognitive psychology, problem-solving refers to the mental process people gothrough to discover, analyze, and solve problems. George Polya (1877-1985) defines it as anact to find a way out of difficulty, find a way around an obstacle, find a way where none isknown, and attain a desired end that is not immediately attainable by direct means.Problem-solving involves all of the steps in the problem process, including thediscovery of the problem, the decision to tackle the issue, understanding the problem,researching the available options and taking actions to achieve your goals.Common Problem-Solving Strategies/HeuristicsHeuristics are procedures or strategies that do not guarantee a solution to a problembut provide a more highly probable method for discovering the solution to a problem.There are many reasonable ways to solve problems. You will find choosing a strategyincreasingly easy. Here is a partial list of problem-solving strategies:1. Working backwards - This strategy is used to solve problems is used to solve problemsthat include a number of linked factors or events, where some of the information has notbeen provided, usually at the beginning of the problem. This entails starting with the endresults and reversing the steps you need to get those results to figure out the answer to theproblem.2. Guess and Check - Often referred to as "Trial and Error", it is important to recognizethat an error really isn't a mistake at all, it helps to guide the problem solver to the nextattempt at the answer. The following are the essential features of the guess and checkstrategy:a. Make an "educated" guess at the solution.b. Check the guess against the conditions of the problem.c. Use the information obtained in checking to make a better guess.d. Continue this procedure until the correct answer is obtained3. Make a Diagram - Drawing a diagram is the most common problem-solving strategy.Very often, a problem solver needs to draw a diagram just to understand the meaning of theproblem. The diagram represents the problem in a way we can see it, understand it, andthink about it while looking for the next step. When you draw a diagram, you organizedinformation spatially, which then allows the visual part of your brain to become moreinvolved in the problem-solving process.4. Make a List - Making a list is a systematic method of organizing information in rowsand/or columns. By putting the given information in an organized list, you can clearlyanalyze this information and then solve the problem by completing the list. By making asystematic list, one will see every possible combination.5. Look for a Pattern - This strategy entails looking for patterns in the data in order tosolve the problem, that is, the solver looks for items or numbers that are repeated or at

Given a group of mathematicians were at conference. Each mathematician exchanged his/her business…

15. A group of mathematicians were at a conference. Each mathematician exchanged his/her business card with every other mathematician who was present. a. If there were 20 mathematicians, how many business cards were exchanged? b. If there was a total of 1200 business cards exchanged, how many mathematicians were at the meeting?

15. A group of mathematicians were at a conference. Each mathematician exchanged his/her business card with every other mathematician who was present. a. If there were 20 mathematicians, how many business cards were exchanged? b. If there was a total of 1200 business cards exchanged, how many mathematicians were at the meeting?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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