Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
In each problem, show three examples and make a correct conjecture. a) Describe the product of odd number and even integers. What conjecture can you form? (Recall: Integers are positive or negative whole numbers, including zero (...-2,-1,0,1,2...) b) Describe the product of two consecutive numbers. Give your conjecture. c) Think of a number. Add it to 5, multiply 2 and then subtract 7. What is the result? Note: The picture has been attached is the reference.

In each problem, show three examples and make a correct conjecture. a) Describe the product of odd number and even integers. What conjecture can you form? (Recall: Integers are positive or negative whole numbers, including zero (...-2,-1,0,1,2...) b) Describe the product of two consecutive numbers. Give your conjecture. c) Think of a number. Add it to 5, multiply 2 and then subtract 7. What is the result? Note: The picture has been attached is the reference.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%

In each problem, show three examples and make a correct conjecture.

a) Describe the product of odd number and even integers. What conjecture can you form? (Recall: Integers are positive or negative whole numbers, including zero (...-2,-1,0,1,2...)

b) Describe the product of two consecutive numbers. Give your conjecture.

c) Think of a number. Add it to 5, multiply 2 and then subtract 7. What is the result?

Note:

The picture has been attached is the reference.

 

В. Аnalysis The five things that you listed serve as 'examples' and based from these, you generated an impression or conclusion about that person. This process is called as INDUCTIVE REASONING. Your conclusion may be right or wrong, thus you are just making a CONJECTURE. So to prove the validity of your conjecture, that person may give further details to support your conclusion if it is true or give examples contrary to it which are called COUNTEREAMPLES. INDUCTIVE REASONING - a process of making general conclusions based from examples. CONJECTURE – the conclusion formed; ideas based on incomplete information which may be true or false. COUNTER EXAMPLES – used to prove the validity of conjectures; statements contradicting the claims or conjectures. Examples: 1. What is the next number in the sequence: 4,8, 12, 16 Conjecture: The next number is identified by adding 4 to the preceding number. Thus, the next number will be 20. 2. 1,6, 16, 31, 51, Conjecture: The first two numbers have a difference of 5. The second and third numbers have a difference of 10. Continuing the process, the difference of two consecutive numbers is a multiple of 5. Therefore, the next number in the list is 76. 3. Ms. Jen is pretty. She is a Math teacher. Conjecture: Therefore, all math teachers are pretty. 4. EDSA is a major thoroughfare which has a speed limit of 60kph. Conjecture: Therefore, all major thoroughfares have a speed limit of 60 kph.
Transcribed Image Text:В. Аnalysis The five things that you listed serve as 'examples' and based from these, you generated an impression or conclusion about that person. This process is called as INDUCTIVE REASONING. Your conclusion may be right or wrong, thus you are just making a CONJECTURE. So to prove the validity of your conjecture, that person may give further details to support your conclusion if it is true or give examples contrary to it which are called COUNTEREAMPLES. INDUCTIVE REASONING - a process of making general conclusions based from examples. CONJECTURE – the conclusion formed; ideas based on incomplete information which may be true or false. COUNTER EXAMPLES – used to prove the validity of conjectures; statements contradicting the claims or conjectures. Examples: 1. What is the next number in the sequence: 4,8, 12, 16 Conjecture: The next number is identified by adding 4 to the preceding number. Thus, the next number will be 20. 2. 1,6, 16, 31, 51, Conjecture: The first two numbers have a difference of 5. The second and third numbers have a difference of 10. Continuing the process, the difference of two consecutive numbers is a multiple of 5. Therefore, the next number in the list is 76. 3. Ms. Jen is pretty. She is a Math teacher. Conjecture: Therefore, all math teachers are pretty. 4. EDSA is a major thoroughfare which has a speed limit of 60kph. Conjecture: Therefore, all major thoroughfares have a speed limit of 60 kph.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS