Problem 4. Suppose a line segment is divided into two pieces, the longer of length a and the shorter of length b. ,then this ratio is known as the golden ratio or golden mean, denoted 1.618034. (It doesn't a +b If a a +b a matter what a and b are; as long as the ratio will equal .) See the figure below: a a+b (a) Show that is a solution to the equation x2 – x – 1 = 0, and find an exact (non-decimal) expression for e. a + b (Hint: In the equation a let b = 1 and a = x, so b' = x = 4.) b (b) Consider the sequence an defined in the following way: 1 a2 = 1+ 1 1 1 a1 = 1+1, a4 = 1 + 1+ az = 1+ az = 1+ 1 1+ 1+1 1+1 1 1 1+ 1 1+ 1+1 1 1+ 1 1+1 This sequence has a limit (you do not need to prove this), given by 1 L = 1+ 1 1+ 1 1+ 1+ 1+.. What is this limit? (Hint: First explain why L = 1+
Problem 4. Suppose a line segment is divided into two pieces, the longer of length a and the shorter of length b. ,then this ratio is known as the golden ratio or golden mean, denoted 1.618034. (It doesn't a +b If a a +b a matter what a and b are; as long as the ratio will equal .) See the figure below: a a+b (a) Show that is a solution to the equation x2 – x – 1 = 0, and find an exact (non-decimal) expression for e. a + b (Hint: In the equation a let b = 1 and a = x, so b' = x = 4.) b (b) Consider the sequence an defined in the following way: 1 a2 = 1+ 1 1 1 a1 = 1+1, a4 = 1 + 1+ az = 1+ az = 1+ 1 1+ 1+1 1+1 1 1 1+ 1 1+ 1+1 1 1+ 1 1+1 This sequence has a limit (you do not need to prove this), given by 1 L = 1+ 1 1+ 1 1+ 1+ 1+.. What is this limit? (Hint: First explain why L = 1+
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter7: Equations And Inequalities In Two Variables
Section7.3: Distance And Slope
Problem 70PS
Related questions
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
4 till 8
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning