Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 7.4, Problem 49E
To determine
The odd about Pythagoras’ most famous result.
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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 7 Solutions
Mathematics: A Practical Odyssey
Ch. 7.1 - In Exercises 120, write the given number in...Ch. 7.1 - In Exercises 120, write the given number in...Ch. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - In Exercises 21-48, convert the given number to...Ch. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Prob. 70ECh. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - Prob. 81ECh. 7.1 - Prob. 82ECh. 7.1 - Prob. 83ECh. 7.1 - Prob. 84ECh. 7.1 - Prob. 85ECh. 7.1 - Prob. 86ECh. 7.1 - Prob. 87ECh. 7.1 - Prob. 88ECh. 7.1 - Prob. 89ECh. 7.1 - Prob. 90ECh. 7.1 - Prob. 91ECh. 7.1 - Prob. 92ECh. 7.1 - a. What digits does base eleven use? b. What are...Ch. 7.1 - Prob. 94ECh. 7.1 - Prob. 95ECh. 7.1 - Prob. 96ECh. 7.1 - Prob. 97ECh. 7.1 - Prob. 98ECh. 7.1 - Prob. 99ECh. 7.1 - Prob. 100ECh. 7.1 - Prob. 101ECh. 7.1 - Prob. 103ECh. 7.1 - Prob. 104ECh. 7.1 - Prob. 105ECh. 7.1 - What was the subject matter of Mohammed ibn Musa...Ch. 7.1 - Prob. 107ECh. 7.1 - Prob. 108ECh. 7.1 - Prob. 109ECh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - In Exercises112, perform the given computation,...Ch. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - In Exercises 18, perform the given computation,...Ch. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Is 65 abundant, perfect, or deficient?Why?Ch. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Answer the following, using complete sentences and...Ch. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.5 - Exercise 1 and 2 refer to Henry Dudenys version of...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - How many great-great-great grandparents does a...Ch. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Carefully draw the Fibonacci spiral composed of...Ch. 7.5 - 10. Carefully draw the Fibonacci spiral composed...Ch. 7.5 - BinetsFormula states that the nth Fibonacci number...Ch. 7.5 - a. Use Binets Formula see Exercise 11 to find the...Ch. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Prob. 24ECh. 7.5 - Prob. 27ECh. 7.CR - Prob. 1CRCh. 7.CR - In Exercises 1-18, write the given number in...Ch. 7.CR - Prob. 3CRCh. 7.CR - Prob. 4CRCh. 7.CR - Prob. 5CRCh. 7.CR - Prob. 6CRCh. 7.CR - Prob. 7CRCh. 7.CR - Prob. 8CRCh. 7.CR - Prob. 9CRCh. 7.CR - Prob. 10CRCh. 7.CR - Prob. 11CRCh. 7.CR - Prob. 12CRCh. 7.CR - Prob. 13CRCh. 7.CR - Prob. 14CRCh. 7.CR - Prob. 15CRCh. 7.CR - Prob. 16CRCh. 7.CR - Prob. 17CRCh. 7.CR - Prob. 18CRCh. 7.CR - Prob. 19CRCh. 7.CR - Prob. 20CRCh. 7.CR - Prob. 21CRCh. 7.CR - Prob. 22CRCh. 7.CR - Prob. 23CRCh. 7.CR - Prob. 24CRCh. 7.CR - Prob. 25CRCh. 7.CR - Prob. 26CRCh. 7.CR - Prob. 27CRCh. 7.CR - Prob. 28CRCh. 7.CR - Prob. 29CRCh. 7.CR - Prob. 30CRCh. 7.CR - Prob. 31CRCh. 7.CR - Prob. 32CRCh. 7.CR - Prob. 33CRCh. 7.CR - Prob. 34CRCh. 7.CR - Prob. 35CRCh. 7.CR - Prob. 36CRCh. 7.CR - Prob. 37CRCh. 7.CR - Prob. 38CRCh. 7.CR - Prob. 39CRCh. 7.CR - Prob. 40CRCh. 7.CR - Prob. 41CRCh. 7.CR - Prob. 42CRCh. 7.CR - Prob. 43CRCh. 7.CR - Prob. 44CRCh. 7.CR - Prob. 45CRCh. 7.CR - Prob. 46CRCh. 7.CR - Prob. 47CRCh. 7.CR - Prob. 48CRCh. 7.CR - Prob. 49CRCh. 7.CR - Prob. 50CRCh. 7.CR - Prob. 51CRCh. 7.CR - Prob. 52CRCh. 7.CR - Prob. 53CRCh. 7.CR - Prob. 54CRCh. 7.CR - Prob. 55CRCh. 7.CR - Prob. 56CRCh. 7.CR - Prob. 57CRCh. 7.CR - Prob. 58CRCh. 7.CR - Prob. 59CRCh. 7.CR - Prob. 60CRCh. 7.CR - Prob. 61CRCh. 7.CR - Prob. 62CRCh. 7.CR - Prob. 63CRCh. 7.CR - Prob. 64CRCh. 7.CR - Prob. 65CRCh. 7.CR - Prob. 66CRCh. 7.CR - Prob. 67CRCh. 7.CR - Prob. 68CRCh. 7.CR - Prob. 69CRCh. 7.CR - Prob. 70CRCh. 7.CR - Prob. 71CRCh. 7.CR - Prob. 72CRCh. 7.CR - Prob. 73CRCh. 7.CR - Prob. 74CRCh. 7.CR - Prob. 75CRCh. 7.CR - Prob. 76CRCh. 7.CR - Prob. 77CRCh. 7.CR - Prob. 78CRCh. 7.CR - Prob. 79CRCh. 7.CR - Prob. 80CRCh. 7.CR - Prob. 81CRCh. 7.CR - Prob. 82CRCh. 7.CR - Prob. 83CRCh. 7.CR - Prob. 84CRCh. 7.CR - Prob. 85CRCh. 7.CR - Prob. 86CRCh. 7.CR - Prob. 87CRCh. 7.CR - Prob. 88CRCh. 7.CR - Prob. 89CRCh. 7.CR - Prob. 90CRCh. 7.CR - Prob. 91CRCh. 7.CR - 2171 is a Mersenne prime. Find the perfect number...Ch. 7.CR - Prob. 93CRCh. 7.CR - Referring to Henry Dudenys version of Fibonaccis...Ch. 7.CR - How many great-great grandparents does a drone bee...Ch. 7.CR - Prob. 96CRCh. 7.CR - Prob. 97CRCh. 7.CR - Prob. 98CRCh. 7.CR - Binets Formula states that nth Fibonacci number...Ch. 7.CR - Give six different examples of the presence of...Ch. 7.CR - Prob. 101CRCh. 7.CR - Prob. 102CRCh. 7.CR - Prob. 103CRCh. 7.CR - Give an example of a building that uses a golden...Ch. 7.CR - Prob. 105CRCh. 7.CR - Prob. 106CRCh. 7.CR - Prob. 107CRCh. 7.CR - Prob. 108CRCh. 7.CR - Prob. 109CRCh. 7.CR - Prob. 110CRCh. 7.CR - Prob. 111CRCh. 7.CR - Prob. 112CRCh. 7.CR - Answer the following, using complete sentences and...Ch. 7.CR - Prob. 114CRCh. 7.CR - Prob. 115CRCh. 7.CR - Answer the following, using complete sentences and...Ch. 7.CR - Prob. 117CRCh. 7.CR - Prob. 118CR
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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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