Answers from an expert in as fast as 30 minutes! 57SECTION 3-1 | Inductive and Deductive ReinoningWe started with 3 nd followed the pocedere to produce 20. Starting withs 6 as ouroriginal number produces atinal resuli of 24 Starting with 100 produces a final result of40 Starting with 100 produces a final result of 400 In each of these cases the resultingmumber is four times the original tumber. We eimjecture that tattewing the given yeocedure produces a nuniber that is four times the orginal numberjc exam-TAKE NOTEe Exumple 5, we will e wedoctive method to verify thatthe procedire in Exampde 2eteneSields a reilt thuat is fourimes the original mber.oning isConsider the following procedure: Picka amber.CHECK YOUR PROGRESSMultiply the number by 9, add 15 to the product, divide the wim by 3, and subtra 5.Complete the above procedure for several different numbers, Use inductive reasoning to make a conjecture about the relationship between the size of the teulting nunberand the size of the original number,ingang toScientists often use inductive reasoning For instance, Galileo Galilei (1564-1642) used inductive reasoning to discover that the time rcquired for a pendulum to complete one swing, called the period of the pendulum, depends on the length of the pendu-lum. Galileo did not have a dock, so he masured the periods of pendulums in "heartbeatsThe following table shows some results obtained for petndulums of various lengtha. Forthe sake of convenience, a length of 10 inches has been designated as I unit.HISTORICAL NOTEGalileo Galifei(gar-lae)entered the Un-versity of Pisa tostudy medicineat the age of 17,but he soon real-zed that he was more interestedin the study of astronomy and thephysical scences. Galeo's study ofpendulums assisted in the develop-Length of pendulum, Period of pendulum,in heartheatsIn units4ment of pendulum clocks16259.36The period of a pendulum is the time ittakes for the pendulum to swing from leftto cight and back to its original position.EXAMPLEUse Inductive Reasoning to Solve an ApplicationUse the data in the above table and inductive reasoning to answer each of the followingquestions.a. If a pendulum has a length of 49 units, what is its period?b. If the length of a pendulum is quadrupled, what happens to its period?Solutiona. In the table, cach pendulum has a period that is the square root of its length. Thuswe conjecture that a pendulum with a length of 49 units will have a period of7 heartbeats.b. In the table, a pendulum with a length of 4 units has a period that is twice thatof a pendulum with a length of I unit. A pendulum with a length of 16 units hasa period that is twice that of a pendulum with a length of 4 units. It appears thatquadrupling the length of a pendulum doubles its period.Velocityof tsunami,in feet per secondHeightof tsunami,in feetCHECK YOUR PROGRESS S A tsunami is a sea wave produced by an under-water earthquake. The height of a tsunami as it approaches land depends on the velocityof the tsunami. Use the table at the left and inductive reasoning to answer each of thefollowing questions,4.9.162536121518a. What happens to the height of a tsunami when its velocity is doubled?49b. What should be the height of a tsunami if its velocity is 30 feet per second?212464 A tsunami is a sea wave produced by an underwater earthquake. The height of a tsunamias it approaches land depends on the velocity of the tsunami. Use the table below andinductive reasoning to answer each of the following questions.Velocity of tsunami, Height of tsunami,in feet per secondin feet649912161525183621492464a. What happens to the height of tsunami when its velocity is doubled?b. What should be the height of tsunami if its velocity is 30 feet per second?

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Answers from an expert in as fast as 30 minutes! 57SECTION 3-1 | Inductive and Deductive ReinoningWe started with 3 nd followed the pocedere to produce 20. Starting withs 6 as ouroriginal number produces atinal resuli of 24 Starting with 100 produces a final result of40 Starting with 100 produces a final result of 400 In each of these cases the resultingmumber is four times the original tumber. We eimjecture that tattewing the given yeocedure produces a nuniber that is four times the orginal numberjc exam-TAKE NOTEe Exumple 5, we will e wedoctive method to verify thatthe procedire in Exampde 2eteneSields a reilt thuat is fourimes the original mber.oning isConsider the following procedure: Picka amber.CHECK YOUR PROGRESSMultiply the number by 9, add 15 to the product, divide the wim by 3, and subtra 5.Complete the above procedure for several different numbers, Use inductive reasoning to make a conjecture about the relationship between the size of the teulting nunberand the size of the original number,ingang toScientists often use inductive reasoning For instance, Galileo Galilei (1564-1642) used inductive reasoning to discover that the time rcquired for a pendulum to complete one swing, called the period of the pendulum, depends on the length of the pendu-lum. Galileo did not have a dock, so he masured the periods of pendulums in &#34;heartbeatsThe following table shows some results obtained for petndulums of various lengtha. Forthe sake of convenience, a length of 10 inches has been designated as I unit.HISTORICAL NOTEGalileo Galifei(gar-lae)entered the Un-versity of Pisa tostudy medicineat the age of 17,but he soon real-zed that he was more interestedin the study of astronomy and thephysical scences. Galeo's study ofpendulums assisted in the develop-Length of pendulum, Period of pendulum,in heartheatsIn units4ment of pendulum clocks16259.36The period of a pendulum is the time ittakes for the pendulum to swing from leftto cight and back to its original position.EXAMPLEUse Inductive Reasoning to Solve an ApplicationUse the data in the above table and inductive reasoning to answer each of the followingquestions.a. If a pendulum has a length of 49 units, what is its period?b. If the length of a pendulum is quadrupled, what happens to its period?Solutiona. In the table, cach pendulum has a period that is the square root of its length. Thuswe conjecture that a pendulum with a length of 49 units will have a period of7 heartbeats.b. In the table, a pendulum with a length of 4 units has a period that is twice thatof a pendulum with a length of I unit. A pendulum with a length of 16 units hasa period that is twice that of a pendulum with a length of 4 units. It appears thatquadrupling the length of a pendulum doubles its period.Velocityof tsunami,in feet per secondHeightof tsunami,in feetCHECK YOUR PROGRESS S A tsunami is a sea wave produced by an under-water earthquake. The height of a tsunami as it approaches land depends on the velocityof the tsunami. Use the table at the left and inductive reasoning to answer each of thefollowing questions,4.9.162536121518a. What happens to the height of a tsunami when its velocity is doubled?49b. What should be the height of a tsunami if its velocity is 30 feet per second?212464 A tsunami is a sea wave produced by an underwater earthquake. The height of a tsunamias it approaches land depends on the velocity of the tsunami. Use the table below andinductive reasoning to answer each of the following questions.Velocity of tsunami, Height of tsunami,in feet per secondin feet649912161525183621492464a. What happens to the height of tsunami when its velocity is doubled?b. What should be the height of tsunami if its velocity is 30 feet per second?

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