Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Chapter 5, Problem 20T
To determine
To calculate: The eighth term of a Fibonacci-type sequence with the first term 1 and second term 4.
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Problem1
We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
Chapter 5 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 5.1 - Decide whether each statement is true or false
1....Ch. 5.1 - Decide whether each statement is true or false. If...Ch. 5.1 - Decide whether each statement is true or false....Ch. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Decide whether each statement is true or false.
7....Ch. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Find all natural number factors of each...
Ch. 5.1 - Find all natural number factors of each number. 28Ch. 5.1 - Find all natural number factors of each number. 72Ch. 5.1 - Use divisibility tests to decide whether the given...Ch. 5.1 - Use divisibility tests to decide whether the given...Ch. 5.1 - Use divisibility tests to decide whether the given...Ch. 5.1 - Prob. 16ECh. 5.1 - (a) In constructing the Sieve of Eratosthenes for...Ch. 5.1 - (a) Continue the Sieve of Eratosthenes in Table 1...Ch. 5.1 - In your list for Exercise 18(a). consider the six...Ch. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Find the prime factorization of each composite...Ch. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Here is a divisibility test for 7.
(a) Double the...Ch. 5.1 - Here is a divisibility test for 7. (a)Double the...Ch. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Here is a divisibility test for 11. (a) Starting...Ch. 5.1 - Prob. 36ECh. 5.1 - Here is a divisibility test for 11.
(a) Starting...Ch. 5.1 - Prob. 38ECh. 5.1 - 39. Consider the divisibility test for the...Ch. 5.1 - 40. Give two factorizations of the number 75 that...Ch. 5.1 - Prob. 41ECh. 5.1 - Determine all possible digit replacements for x so...Ch. 5.1 - Determine all possible digit replacements for x so...Ch. 5.1 - Determine all possible digit replacements for x so...Ch. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Leap years occur when the year number is divisible...Ch. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Leap years occur when the year number is divisible...Ch. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - 58. Choose any 6-digit number consisting of three...Ch. 5.1 - One of the authors has three sons who were born....Ch. 5.1 -
Ore of the authors has three sons who were born,...Ch. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - Prob. 4ECh. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - 15. (a) Evaluate the Fermat number for .
(b) In...Ch. 5.2 - 16. (a) Verify the value given in the text for the...Ch. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - 19. Why do you suppose it normally takes up to a...Ch. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - 22. Explain n your own words the proof by Euclid...Ch. 5.2 - 23. For the composite number , find
Ch. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Explain why large prime numbers are important in...Ch. 5.2 - 30. Describe the difference between Mersenne...Ch. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - Prob. 2ECh. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - Prob. 5ECh. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - It has been proved that the reciprocals of all the...Ch. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - 21. There are four abundant numbers between 1 and...Ch. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - 25. The proper divisors of 1184 are 1.2. 4. 8, 16,...Ch. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - The first four perfect numbers were identified in...Ch. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - 47. Explain why the primorial formula does not...Ch. 5.3 - Prob. 48ECh. 5.3 - 49. Choose the correct completion: The primorial...Ch. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.4 - Decide whether each statement is true or false. No...Ch. 5.4 - Decide whether each statement is true or false.
2....Ch. 5.4 - Decide whether each statement is true or false. If...Ch. 5.4 - Decide whether each statement is true or false.
4....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false.
9....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the formula given in the text on page 203and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Explain in your own words how to find the greatest...Ch. 5.4 - 48, Explain in your own words how to find the...Ch. 5.4 - If p. q, and r and different primes, and a. b, and...Ch. 5.4 - Find (a) the greatest common factor and (b) the...Ch. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - It is possible to extend the Euclidean algorithm...Ch. 5.4 - Prob. 55ECh. 5.4 - Suppose that the least common multiple of p and q...Ch. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Refer to Examples 9 and 10 to solve each problem....Ch. 5.4 - Refer to Examples 9 and 10 to solve each...Ch. 5.4 - Refer to Examples 9 and 10 to solve each...Ch. 5.4 - Prob. 63ECh. 5.4 - Refer to Examples 9 and 10 to solve each problem....Ch. 5.5 - Answer each question concerning the Fibonacci...Ch. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - It has been shown that if m divides n, then Fm is...Ch. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Recall (lie Pythagorean theorem from geometry: If...Ch. 5.5 - Recall (lie Pythagorean theorem from geometry: If...Ch. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5 - In Exercises 1-6, decide whether each statement is...Ch. 5 - In Exercises 1-6, decide whether each statement is...Ch. 5 - Prob. 3TCh. 5 - In Exercises 1-6, decide whether each statement is...Ch. 5 - Prob. 5TCh. 5 - Prob. 6TCh. 5 - Use divisibility tests to determine whether the...Ch. 5 - Prob. 8TCh. 5 - Prob. 9TCh. 5 - Prob. 10TCh. 5 - Prob. 11TCh. 5 - Prob. 12TCh. 5 - Give a pair of twin primes between 60 and 80.Ch. 5 - Prob. 14TCh. 5 - Prob. 15TCh. 5 - Prob. 16TCh. 5 - Prob. 17TCh. 5 - Prob. 18TCh. 5 - Prob. 19TCh. 5 - Prob. 20TCh. 5 - 21. Choose any term after the first in the...Ch. 5 - 22. Which one of the following is the exact value...
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- 5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forward
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