MYLAB W/ETEXT FOR MATHEMATICS ALL AROUN
6th Edition
ISBN: 9780135902783
Author: Pirnot
Publisher: PEARSON
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Textbook Question
Chapter 3.5, Problem 34E
In each of your drawings for Exercises 31 – 33, state a condition in your drawing that is not present in the statement that you are trying to illustrate.
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Please solving problem2
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 3 Solutions
MYLAB W/ETEXT FOR MATHEMATICS ALL AROUN
Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...Ch. 3.1 - Sharpening Your Skills In Exercise 110, determine...
Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - In Exercise 1120, identify each statement as...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: g: Global...Ch. 3.1 - Consider the following statements: t: The radial...Ch. 3.1 - Prob. 26ECh. 3.1 - Consider the following statements: t: The radial...Ch. 3.1 - Consider the following statements: t: The radial...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - In Exercises 2934, negate each quantified...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Applying What Youve Learned Use the following...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - Consider the happy and sad faces below. Determine...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - In Exercises 4548, examine each statement to...Ch. 3.1 - Because the English language is so complex, it is...Ch. 3.1 - Because the English language is so complex, it is...Ch. 3.1 - Because the English language is so complex, it is...Ch. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - In 1937, Claude Shannon showed that computer...Ch. 3.1 - Prob. 57ECh. 3.1 - In 1937, Claude Shannon showed that computer...Ch. 3.1 - In Exercises 5962, determine if the following...Ch. 3.1 - In Exercises 5962, determine if the following...Ch. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - 6772. In symbolic logic, the form of statements is...Ch. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 3.1 - 6772. In symbolic logic, the form of statements is...Ch. 3.1 - Think of real-life situation that you might want...Ch. 3.1 - Provide arguments for or against the view that...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - Prob. 8ECh. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - In Exercise 1-10, assume that p is true, q is...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - State whether the numbers given in Exercise 11-14...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 15-24, construct a truth table for...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 25-28, determine whether we are using...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 29-34, use DeMorgans laws to rewrite...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - In Exercise 35-42, determine whether the pair of...Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Exercise 43-48, deal with three-valued logic....Ch. 3.2 - Applying What Youve Learned Use the following...Ch. 3.2 - Applying What Youve Learned Use the following...Ch. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Use this graph based on data from the National Pet...Ch. 3.2 - Prob. 64ECh. 3.2 - In Section 3.1 page 94, we showed how to represent...Ch. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - What advantage do you see in using truth tables to...Ch. 3.2 - Prob. 71ECh. 3.2 - The and connective is necessary in the sense that...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.2 - The stroke connective has the following truth...Ch. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Assume that you begin with a statement of the form...Ch. 3.3 - Prob. 30ECh. 3.3 - Assume that you begin with a statement of the form...Ch. 3.3 - Assume that you begin with a statement of the form...Ch. 3.3 - In Exercises 3336, write the indicated statement...Ch. 3.3 - In Exercises 3336, write the indicated statement...Ch. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - In Exercises 3740, determine which pairs of...Ch. 3.3 - In Exercises 3740, determine which pairs of...Ch. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - In Exercises 4148, rewrite each statement using...Ch. 3.3 - Prob. 42ECh. 3.3 - In Exercises 4148, rewrite each statement using...Ch. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - In Exercises 4148, rewrite each statement using...Ch. 3.3 - Prob. 48ECh. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Find the truth value for each statement in...Ch. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - According to an Accountemps survey appearing in...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - Perhaps you have heard the term helicopter...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - In Exercises 6568, write the converse, inverse, or...Ch. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - Communicating Mathematics Give an example of a...Ch. 3.3 - Communicating Mathematics Is it possible to have a...Ch. 3.3 - Communicating Mathematics Explain why it is...Ch. 3.3 - Communicating Mathematics Why is it reasonable to...Ch. 3.3 - In Exercises 75 and 76, assume that a credit card...Ch. 3.3 - In Exercises 75 and 76, assume that a credit card...Ch. 3.3 - Challenge Yourself In Exercises 79 and 80, use...Ch. 3.3 - Challenge Yourself In Exercises 79 and 80, use...Ch. 3.3 - Prob. 81ECh. 3.3 - Prob. 82ECh. 3.3 - Prob. 83ECh. 3.3 - Prob. 84ECh. 3.3 - Exercises 85 and 86 are based on the exercise sets...Ch. 3.3 - Exercises 85 and 86 are based on the exercise sets...Ch. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - We have emphasized that the form of a logical...Ch. 3.4 - Challenge Yourself Exercises 49-52 are puzzles...Ch. 3.4 - Challenge Yourself Exercises 49-52 are puzzles...Ch. 3.4 - Challenge Yourself Exercises 49-52 are puzzles...Ch. 3.4 - In a complicated argument with many variables, it...Ch. 3.4 - In a complicated argument with many variables, it...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.4 - In addition to the argument forms that you studies...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 116, determine whether each syllogism...Ch. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 18ECh. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 20ECh. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 22ECh. 3.5 - In Exercise 1724, complete each syllogism so that...Ch. 3.5 - Prob. 24ECh. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - In Exercises 25 28, write two syllogisms that can...Ch. 3.5 - Give an example of a valid syllogism that has a...Ch. 3.5 - Give an example of a invalid syllogism that has a...Ch. 3.5 - Draw an Euler diagram for the statements All As...Ch. 3.5 - Draw an Euler diagram for the statements Some As...Ch. 3.5 - Draw an Euler diagram for the statements No As are...Ch. 3.5 - In each of your drawings for Exercises 31 33,...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In Exercises 1-8, assign a truth value between 0...Ch. 3.6 - In a Exercises 9-12, calculate the truth value of...Ch. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - In a Exercises 9-12, calculate the truth value of...Ch. 3.6 - In Exercises 13-16, consider the following fuzzy...Ch. 3.6 - In Exercises 13-16, consider the following fuzzy...Ch. 3.6 - In Exercise 13-16, consider the following fuzzy...Ch. 3.6 - In Exercise 13-16, consider the following fuzzy...Ch. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - Prob. 19ECh. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - In Exercises 17-24, assume that p has a truth...Ch. 3.6 - Prob. 24ECh. 3.6 - In exercises 25-28, use the method described in...Ch. 3.6 - Prob. 26ECh. 3.6 - In exercises 25-28, use the method described in...Ch. 3.6 - In exercises 25-28, use the method described in...Ch. 3.6 - How are the rules for computing the truth tables...Ch. 3.6 - Discuss some situations in which using fuzzy logic...Ch. 3.6 - Choose a situation you will face in which you must...Ch. 3.6 - Do you have any criticisms of the decision-making...Ch. 3.CR - Prob. 1CRCh. 3.CR - Let v represent the statement I will buy a new...Ch. 3.CR - Let f represent Antonio is fluent in Spanish and...Ch. 3.CR - Negate each quantified statement and then rewrite...Ch. 3.CR - Let p represent some true statement, q represent...Ch. 3.CR - How many rows will be in the table for each...Ch. 3.CR - Construct a truth table for each statement. a....Ch. 3.CR - Negate each statement and then rewrite the...Ch. 3.CR - Which pairs of statements are logically...Ch. 3.CR - Assume we are dealing with three- valued logic and...Ch. 3.CR - Assume that p represent a true statement, q a...Ch. 3.CR - Construct a truth table for each statement. a. pq...Ch. 3.CR - Prob. 13CRCh. 3.CR - Rewrite each statement using the words if then. a....Ch. 3.CR - Section 3.4 15. Identify the form of each...Ch. 3.CR - Determine whether the form represents a valid...Ch. 3.CR - Use a truth table to determine whether the...Ch. 3.CR - In Exercises 18 and 19, use Euler diagrams to...Ch. 3.CR - In Exercises 18 and 19, use Euler diagrams to...Ch. 3.CR - Assume that p and q are fuzzy statements having...Ch. 3.CT - Which of the following are statements? a. New York...Ch. 3.CT - Negate each quantified statement and then rewrite...Ch. 3.CT - Let p represent the statement I will pass my...Ch. 3.CT - Let t represent The Tigers will win the series and...Ch. 3.CT - Prob. 5CTCh. 3.CT - If p is false and q is true and r is false, what...Ch. 3.CT - Prob. 7CTCh. 3.CT - Construct a truth table for each statement. a....Ch. 3.CT - Prob. 9CTCh. 3.CT - Negate each statement and then rewrite the...Ch. 3.CT - Determine whether the following pairs of...Ch. 3.CT - Write in words the converse, inverse, and...Ch. 3.CT - If p is true, q is false, and r is true, what is...Ch. 3.CT - Assume we are dealing with three-valued logic and...Ch. 3.CT - Prob. 15CTCh. 3.CT - Determine whether the form represents a valid...Ch. 3.CT - Identify the form of each argument. If it aint...Ch. 3.CT - In fuzzy logic, we replaced the conditional pq by...Ch. 3.CT - Use a truth table to determine if the argument is...Ch. 3.CT - Use an Euler diagram to determine whether the...
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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
- Problem 1.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%. 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.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forwardWhat is the standard scores associated to the left of z is 0.1446arrow_forward2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forward
- 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. 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(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forwardConsider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forwardNote: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…arrow_forward
- 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forwardThe general solution X'=Ax is given. Discuss the nature of the solutions in a neighborhood of (0,0) -2-2 (²) |a) A = (23) X(A) = (₁ (fi)e* + (2 (2) eht -2-5arrow_forward
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