Pearson eText for Using & Understanding Mathematics: A Quantitative Reasoning Approach -- Instant Access (Pearson+)
7th Edition
ISBN: 9780137553334
Author: Jeffrey Bennett, William Briggs
Publisher: PEARSON+
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Chapter 2.B, Problem 68E
To determine
To calculate:
The purity of a 14-karat gold ring in percentage
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Students have asked these similar questions
Total marks 16
5.
Let (,,P) be a probability space and let X : → R be a random
variable whose probability density function is given by f(x) = }}|x|e¯|×| for
x Є R.
(i)
(ii)
Find the characteristic function of the random variable X.
[8 Marks]
Using the result of (i), calculate the first two moments of the
random variable X, i.e., E(X") for n = 1, 2.
(iii) What is the variance of X?
[6 Marks]
[2 Marks]
Refer to page 12 for a problem on solving a homogeneous differential equation.
Instructions:
• Simplify the equation into a homogeneous form.
Use appropriate substitutions to reduce complexity.
Solve systematically and verify the final result with clear back-substitutions.
Link:
[https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]
Refer to page 36 for solving a bang-bang control problem.
Instructions:
•
Formulate the problem, identifying the control constraints.
•
•
Apply Pontryagin's Maximum Principle to derive the switching conditions.
Clearly illustrate the switching points in the control trajectory. Verify the solution satisfies the
optimality criteria.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
Chapter 2 Solutions
Pearson eText for Using & Understanding Mathematics: A Quantitative Reasoning Approach -- Instant Access (Pearson+)
Ch. 2.A - To end up with units of speed, you need to a....Ch. 2.A - What does the word per mean? divided by multiplied...Ch. 2.A - Which of the following represents 4 square miles?...Ch. 2.A - Thu arc given two pieces of information: (1) the...Ch. 2.A - Which of the following represents 9 square miles?...Ch. 2.A - If you multiply an area in square feet by a height...Ch. 2.A - There are 1760 yards in a mile. Therefore, one...Ch. 2.A - One square foot is equivalent to 12 square inches...Ch. 2.A - You buy apples while traveling in Europe. The...Ch. 2.A - If the current exchange rate is $1.058 per euro,...
Ch. 2.A - Briefly describe the Understand-Solve-Explain...Ch. 2.A - What are units? Describe the meaning of key worxs...Ch. 2.A - Describe the meaning of the key words pre, of,...Ch. 2.A - Explain why a unit conversion really involves just...Ch. 2.A - Explain in words or with a picture why there are 9...Ch. 2.A - Describe how to read and use the currency data in...Ch. 2.A - I drove at a speed of 35 miles for the entire...Ch. 2.A - One dollar is worth about 115 Japanese yen, so 1...Ch. 2.A - I figured out how long the airplane will take to...Ch. 2.A - I have a box with a volume of 2 square feet.Ch. 2.A - I bought the fabric at X-mart, because their price...Ch. 2.A - An actual commercial: “The Goodyear Aquatread tire...Ch. 2.A - 13-20: Math Review. The following exercises...Ch. 2.A - 13-20: Math Review. The following exercises...Ch. 2.A - 13-20: Math Review. The following exercises...Ch. 2.A - 13-20: Math Review. The following exercises...Ch. 2.A - Prob. 17ECh. 2.A - Prob. 18ECh. 2.A - Prob. 19ECh. 2.A - Prob. 20ECh. 2.A - Prob. 21ECh. 2.A - Prob. 22ECh. 2.A - Using Key Words. Write out the three steps of the...Ch. 2.A - Using Key Words. Write out the three steps of the...Ch. 2.A - Area and Volume Calculations. Show clearly your...Ch. 2.A - Area and Volume Calculations. Show clearly your...Ch. 2.A - Prob. 27ECh. 2.A - Prob. 28ECh. 2.A - Prob. 29ECh. 2.A - Prob. 30ECh. 2.A - Prob. 31ECh. 2.A - Prob. 32ECh. 2.A - Prob. 33ECh. 2.A - Working with Units. Write out the three steps of...Ch. 2.A - Working with Units. Write out the three steps of...Ch. 2.A - Working with Units. Write out the three steps of...Ch. 2.A - Working with Units. Write out the three steps of...Ch. 2.A - Working with Units. Write out the three steps of...Ch. 2.A - Working with Units. Write out the three steps of...Ch. 2.A - Working with Units. Write out the three steps of...Ch. 2.A - What Went Wrong? Consider the following exam...Ch. 2.A - What Went Wrong? Consider the following exam...Ch. 2.A - 41-44: What Went Wrong? Consider the following...Ch. 2.A - 41-44: What Went Wrong? Consider the following...Ch. 2.A - 45-52: Unit Conversions. Carry out the following...Ch. 2.A - 45-52: Unit Conversions. Carry out the following...Ch. 2.A - 45-52: Unit Conversions. Carry out the following...Ch. 2.A - 45-52: Unit Conversions. Carry out the following...Ch. 2.A - Unit Conversions. Carry out the following unit...Ch. 2.A - Unit Conversions. Carry out the following unit...Ch. 2.A - Unit Conversions. Carry out the following unit...Ch. 2.A - Unit Conversions. Carry out the following unit...Ch. 2.A - Conversions with Square and Cubic Units. 43.Find a...Ch. 2.A - 43-48: Conversions with Square and Cubic...Ch. 2.A - 53-60: Conversions with Square and Cubic Units....Ch. 2.A - 53-60: Conversions with Square and Cubic Units....Ch. 2.A - 43-48: Conversions with Square and Cubic...Ch. 2.A - 53-60: Conversions with Square and Cubic Units....Ch. 2.A - Conversions with Square and Cubic Units. 59. An...Ch. 2.A - 53-60: Conversions with Square and Cubic Units....Ch. 2.A - Currency Conversions. Use the currency exchange...Ch. 2.A - Currency Conversions. Use the currency exchange...Ch. 2.A - Currency Conversions. Use the currency exchange...Ch. 2.A - Currency Conversions. Use the currency exchange...Ch. 2.A - Currency Conversions. Use the currency exchange...Ch. 2.A - Currency Conversions. Use the currency exchange...Ch. 2.A - More Unit Practice. Use unit analysis to answer...Ch. 2.A - More Unit Practice. Use unit analysis to answer...Ch. 2.A - More Unit Practice. Use unit analysis to answer...Ch. 2.A - More Unit Practice. Use unit analysis to answer...Ch. 2.A - 67-71: More Unit Practice. Use unit analysis to...Ch. 2.A - 72-75: Gas Mileage. Answer the following practical...Ch. 2.A - Prob. 73ECh. 2.A - Prob. 74ECh. 2.A - Prob. 75ECh. 2.A - Prob. 76ECh. 2.A - Full of Hot Air. The average person breathes 6...Ch. 2.A - Busy Reading. Suppose you have a tablet with a...Ch. 2.A - Landscaping Project. Suppose that you are planning...Ch. 2.A - Prob. 80ECh. 2.A - Prob. 81ECh. 2.A - 98. Units on the highway. Next time you are on the...Ch. 2.A - Are the units clear? Find a news story that...Ch. 2.A - South American Adventure. Suppose you are planning...Ch. 2.A - Currency Conversions. Use internet to convert $100...Ch. 2.B - The fact that 1 liter = 1.057 quarts can be...Ch. 2.B - Which is greater, 1200 meters or 3600 feet? a....Ch. 2.B - You are given two pieces of information: (1) the...Ch. 2.B - Which of the following is not a unit of energy? a....Ch. 2.B - You want to know how much total energy is required...Ch. 2.B - New Mexico has a population density of about 12...Ch. 2.B - A temperature of 110°C is a. typical of Phoenix in...Ch. 2.B - The concentration of carbon dioxide in earth’s...Ch. 2.B - The guidelines for a particular drug specify a...Ch. 2.B - A blood alcohol content (BAC) of 0.08gm/100 ml...Ch. 2.B - Prob. 1ECh. 2.B - Prob. 2ECh. 2.B - What is energy? List at least three common units...Ch. 2.B - Prob. 4ECh. 2.B - Prob. 5ECh. 2.B - what do we mean by density? What do we mean by...Ch. 2.B - drank 2 liters of water today.Ch. 2.B - I know a professional bicyclist who weighs 300...Ch. 2.B - My car’s gas tank holds 12 meters of gasoline.Ch. 2.B - My daily food intake gives me about 10 million...Ch. 2.B - Our utility company charges 10$ per watt for the...Ch. 2.B - The beach ball we played with had a density of 10...Ch. 2.B - Prob. 13ECh. 2.B - Prob. 14ECh. 2.B - USCS Units. Answer the following questions...Ch. 2.B - USCS Units. Answer the following questions...Ch. 2.B - USCS Units. Answer the following questions...Ch. 2.B - USCS Units. Answer the following questions...Ch. 2.B - USCS Units. Answer the following questions...Ch. 2.B - USCS Units. Answer the following questions...Ch. 2.B - Price Comparison. In each case, decide which of...Ch. 2.B - Price Comparison. In each case, decide which of...Ch. 2.B - Price Comparison. In each case, decide which of...Ch. 2.B - Price Comparison. In each case, decide which of...Ch. 2.B - Metric Prefixes. Complete the following sentences...Ch. 2.B - Metric Prefixes. Complete the following sentences...Ch. 2.B - Metric Prefixes. Complete the following sentences...Ch. 2.B - Metric Prefixes. Complete the following sentences...Ch. 2.B - Metric Prefixes. Complete the following sentences...Ch. 2.B - Metric Prefixes. Complete the following sentences...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - USCS—Metric Conversions. Convert the following...Ch. 2.B - Greenland ice sheet. The Greenland ice sheet...Ch. 2.B - Volcanic eruption. The greatest volcanic eruption...Ch. 2.B - Prob. 43ECh. 2.B - Prob. 44ECh. 2.B - 45-46: Celsius—Kelvin Conversions. Convert the...Ch. 2.B - 45-46: Celsius—Kelvin Conversions. Convert the...Ch. 2.B - Power Output. In each case, find your average...Ch. 2.B - 47-48. Power Output. In each case, find your...Ch. 2.B - Energy Savings. For these questions, assume that...Ch. 2.B - Energy Savings. For these questions, assume 365...Ch. 2.B - -56: Densities. Compute the following densities...Ch. 2.B - Densities. Compute the following densities using...Ch. 2.B - Densities. Compute the following densities using...Ch. 2.B - Prob. 54ECh. 2.B - Prob. 55ECh. 2.B - 51-56: Densities. Compute the following densities...Ch. 2.B - 51-52. Medication Doses.
51. The antihistamine...Ch. 2.B - 51-52. Medication Doses.
52. Suppose a dose of...Ch. 2.B - Blood Alcohol Content: Wine. A typical glass of...Ch. 2.B - Prob. 60ECh. 2.B - The Metric Mile. Consider the following world...Ch. 2.B - Prob. 62ECh. 2.B - Currency Conversions. Answer the following...Ch. 2.B - Prob. 64ECh. 2.B - Prob. 65ECh. 2.B - Prob. 66ECh. 2.B - 67-70: Gems and Gold. Use carats and karats, as...Ch. 2.B - 67-70: Gems and Gold. Use carats and karats, as...Ch. 2.B - 67-70: Gems and Gold. Use carats and karats, as...Ch. 2.B - Prob. 70ECh. 2.B - Prob. 71ECh. 2.B - The Star of Africa. The Star of Africa was cut...Ch. 2.B - Prob. 73ECh. 2.B - Prob. 74ECh. 2.B - Prob. 75ECh. 2.B - Prob. 76ECh. 2.B - Prob. 77ECh. 2.B - Prob. 78ECh. 2.B - Fertilizing Winter Wheat. Guidelines for the...Ch. 2.B - 80. Metric Area. When the metric system was first...Ch. 2.B - 69-70: Electric Bills. Consider the following...Ch. 2.B - 69-70: Electric Bills. Consider the following...Ch. 2.B - Prob. 83ECh. 2.B - Prob. 84ECh. 2.B - Prob. 85ECh. 2.B - Prob. 86ECh. 2.B - Prob. 87ECh. 2.B - Prob. 88ECh. 2.B - Wind Power: One Turbine. Modern wind energy...Ch. 2.B - Prob. 90ECh. 2.B - 62-67: Drug Dosing.
62. Solution Concentrations....Ch. 2.B - 62-67: Drug Dosing.
64. Infusion Rates for...Ch. 2.B - 62-67: Drug Dosing.
65. Infusion Rates for...Ch. 2.B - Prob. 95ECh. 2.B - Drug Dosing. 67. Administering Penicillin. A...Ch. 2.B - Prob. 97ECh. 2.B - Prob. 98ECh. 2.B - Should the United States Go Metric? Research the...Ch. 2.B - Prob. 100ECh. 2.B - Utility Bill. Analyze a utility bill. Explain all...Ch. 2.B - Prob. 102ECh. 2.B - 84. Air Pollution. Investigate the average...Ch. 2.B - Alcohol Poisoning. Research some aspects of the...Ch. 2.C - 1. A quantitative problem from daily life
a....Ch. 2.C - Prob. 2QQCh. 2.C - Prob. 3QQCh. 2.C - Prob. 4QQCh. 2.C - Prob. 5QQCh. 2.C - Prob. 6QQCh. 2.C - 7. When confronted with a complex problem, why can...Ch. 2.C - 8. Forty balls numbered 1 through 40 are mixed up...Ch. 2.C - 9. Karen arrives at the subway station every day...Ch. 2.C - Prob. 10QQCh. 2.C - Summarize the strategic hints for problem solving...Ch. 2.C - 2. Give an example of a problem that has more than...Ch. 2.C - 3. My simple problem-solving recioe will work for...Ch. 2.C - 4. Whether it’s a problem in mathematics or...Ch. 2.C - Mathematics requires precison, so approximations...Ch. 2.C - Prob. 6ECh. 2.C - A Toll Booth. A toll collector on a highway...Ch. 2.C - Prob. 8ECh. 2.C - A Second Race. Jordan and Amari run a 200-meter...Ch. 2.C - Prob. 10ECh. 2.C - Mixing Marbles. Consider the case in which each of...Ch. 2.C - 12. Coiling Problems. Eight turns of a wire are...Ch. 2.C - 13 Bowed Rail. Suppose a railroad rail is 1...Ch. 2.C - 14. China’s Population. To convince yourself that...Ch. 2.C - Alternative Thinking: The Monk and the Mountain. A...Ch. 2.C - 16. Crossing a Moat. A castle is surrounded by a...Ch. 2.C - Prob. 17ECh. 2.C - Prob. 18ECh. 2.C - Prob. 19ECh. 2.C - Prob. 20ECh. 2.C - Prob. 21ECh. 2.C - Prob. 22ECh. 2.C - Prob. 23ECh. 2.C - Prob. 24ECh. 2.C - Prob. 25ECh. 2.C - Puzzle Problems. The following puzzle problems...Ch. 2.C - 20-39: Puzzle Problems. The following puzzle...Ch. 2.C - 20-39: Puzzle Problems. The following puzzle...Ch. 2.C - Puzzle Problems. The following puzzle problems...Ch. 2.C - Prob. 30ECh. 2.C - Puzzle Problems. The following puzzle problems...Ch. 2.C - Puzzle Problems. The following puzzle problems...Ch. 2.C - Prob. 33ECh. 2.C - Prob. 34ECh. 2.C - Prob. 35ECh. 2.C - Prob. 36ECh. 2.C - Prob. 37ECh. 2.C - Prob. 38ECh. 2.C - Prob. 39ECh. 2.C - 40. You are planning to have a child. How much...Ch. 2.C - 49. Textbook Analysis. Although research shows...Ch. 2.C - 52. Multiple Solutions. Find an example of a real...Ch. 2.C - 53. Multiple Strategies. Find an example of a real...Ch. 2.C - Prob. 44E
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- Total marks 16 5. Let (N,F,P) be a probability space and let X : N → R be a random variable such that the probability density function is given by f(x)=ex for x € R. (i) Find the characteristic function of the random variable X. [8 Marks] (ii) Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1,2. (iii) What is the variance of X. [6 Marks] [2 Marks]arrow_forward6. Let P be the standard normal distribution, i.e., P is the proba- bility measure on (R, B(R)) given by 1 dP(x) = 를 = e dx. √2πT Consider the random variables 21 fn(x) = (1 + x²) en+2, x Є R, n Є N. Using the dominated convergence theorem, prove that the limit Total marks 9 exists and find it. lim E(fn) n∞ [9 Marks]arrow_forwardRefer to page 38 for solving an optimal control problem using dynamic programming. Instructions: • Define the value function and derive the Hamilton-Jacobi-Bellman (HJB) equation. • Solve the HJB equation explicitly, showing all intermediate steps and justifications. Verify the solution satisfies the boundary conditions and optimality. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
- Refer to page 18 for solving a second-order linear non-homogeneous differential equation. Instructions: Solve the associated homogeneous equation first. Use either the method of undetermined coefficients or variation of parameters for the particular solution. • Provide detailed steps for combining solutions into the general solution. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward6. Let X be a random variable taking values in (0,∞) with proba- bility density function fx(u) = 5e5u u > 0. Total marks 8 Let Y = X2. Find the probability density function of Y. [8 Marks]arrow_forward5. Let a probability measure P on ([0,3], B([0,3])) be given by 1 dP(s): = ½ s² ds. 9 Consider a random variable X : [0,3] → R given by X(s) = s², sc [0,3]. S Total marks 7 Find the distribution of X. [7 Marks]arrow_forward
- Refer to page 24 for solving a differential equation using Laplace transforms. Instructions: Take the Laplace transform of the given equation, applying initial conditions appropriately. ⚫ Solve the resulting algebraic equation and find the inverse transform. Provide step-by-step solutions with intermediate results and final verification. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 30 for deriving the Euler-Lagrange equation for an optimal control problem. Instructions: • Use the calculus of variations to derive the Euler-Lagrange equation. Clearly define the functional being minimized or maximized. Provide step-by-step derivations, including all necessary boundary conditions. Avoid skipping critical explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 32 for solving a linear-quadratic regulator (LQR) problem. Instructions: • Formulate the cost functional and state-space representation. • Derive the Riccati equation and solve it step-by-step. Clearly explain how the optimal control law is obtained. Ensure all matrix algebra is shown in detail. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
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