
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 16, Problem 4E
Using set notation, write out the
experiments:
a. Three runners (A, B, and C) are running in a race (assume that there are no ties).
The observation is the order in which the three runners cross the finish line.
b. Four runners (A, B, C, and D) are running in a qualifying race (assume that there
are no ties). The top two finishers qualify for the finals. The observation is the pair
of runners that qualify for the finals.
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
No chatgpt pls will upvote
(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
Ꮖ
(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
Chapter 16 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - The board of directors of Fibber Corporation has...Ch. 16 - You reach into a large jar containing jelly beans...Ch. 16 - In Exerxises 7 through 10, the sample spaces are...Ch. 16 - In Exerxises 7 through 10, the sample spaces are...Ch. 16 - Prob. 9ECh. 16 - In Exerxises 7 through 10, the sample spaces are...
Ch. 16 - A coin is tossed three times in a row The...Ch. 16 - A student randomly guesses the answers to a...Ch. 16 - A pair of dice is rolled. The observation is the...Ch. 16 - A card is drawn out of a standard deck of 52...Ch. 16 - A coin is tossed 10 times in a row. The...Ch. 16 - Five candidates (A,B,C,D,andE) have a chance to be...Ch. 16 - A California license plate starts with a digit...Ch. 16 - A computer password consists of four letters A...Ch. 16 - Jack packs two pairs of shoes, one pair of boots,...Ch. 16 - A French restaurant offers a menu consisting of...Ch. 16 - A set of reference books consists of eight volumes...Ch. 16 - Nine people four men and five women line up at a...Ch. 16 - 7. Nine people four men and five women line up at...Ch. 16 - Prob. 24ECh. 16 - Determine the number of outcomes N in each sample...Ch. 16 - Determine the number of outcomes N in each sample...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - A major league baseball team roster consists of 40...Ch. 16 - Bob has 20 different dress shirts in his wardrobe....Ch. 16 - Consider the sample space S={o1,o2,o3,o4,o5}....Ch. 16 - Consider the sample space S={o1,o2,o3,o4}. Suppose...Ch. 16 - Four candidates are running for mayor of...Ch. 16 - Seven horses A, B, C, D, E, F, and G are running...Ch. 16 - An honest coin is tossed three times in a row....Ch. 16 - A student randomly guesses the answers to a...Ch. 16 - A pair of honest dice is rolled. Find the...Ch. 16 - A card is drawn at random out of a well-shuffled...Ch. 16 - An honest coin is tossed 10 times in a row. Find...Ch. 16 - Five candidates A, B, C, D, and E have a chance to...Ch. 16 - A student takes a 10-question true-or-false quiz...Ch. 16 - Suppose that the probability of giving birth to a...Ch. 16 - The Tasmania State University glee club has 15...Ch. 16 - Ten professional basketball teams are...Ch. 16 - An honest coin is tossed 10 times in a row. The...Ch. 16 - Imagine a game in which you roll an honest die...Ch. 16 - Find the odds of each of the following events. a....Ch. 16 - Find the odds of each of the following events. a....Ch. 16 - In each case, find the probability of an event E...Ch. 16 - In each case, find the probability of an event E...Ch. 16 - Prob. 53ECh. 16 - Table 16-19 shows the aggregate scores of a golf...Ch. 16 - At Thomas Jefferson High School, the student body...Ch. 16 - In 2005 the Middletown Zoo averaged 4000 visitors...Ch. 16 - Prob. 57ECh. 16 - A basketball player shoots two consecutive free...Ch. 16 - Prob. 59ECh. 16 - A pair of honest dice is rolled once. Find the...Ch. 16 - Suppose that you roll a pair of honest dice. If...Ch. 16 - On an American roulette wheel, there are 18 red...Ch. 16 - On an American roulette wheel, there are 38...Ch. 16 - Suppose that you roll a single die. If an odd...Ch. 16 - Prob. 65ECh. 16 - Jackie is buying a new MP3 player from Better Buy....Ch. 16 - The service history of the Prego SUV is as...Ch. 16 - An insurance company plans to sell a 250,000...Ch. 16 - The ski club at Tasmania State University has 35...Ch. 16 - Prob. 70ECh. 16 - Prob. 71ECh. 16 - Two teams call them X and Y play against each...Ch. 16 - An urn contains seven red balls and three blue...Ch. 16 - Prob. 74ECh. 16 - Prob. 75ECh. 16 - A draw poker hand consists of 5 cards taken from a...Ch. 16 - Prob. 77ECh. 16 - Prob. 78ECh. 16 - Yahtzee. Yahtzee is a dice game in which five...Ch. 16 - In head-to-head, 7-card stud poker you make your...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- (6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward(10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward
- (9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward(8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward
- (4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward(2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forward
- Answer the following questions related to the following matrix A = 3 ³).arrow_forward(5) (10 points) Let D be the parallelogram in the xy-plane with vertices (0, 0), (1, 1), (1, 1), (0, -2). Let f(x,y) = xy/2. Use the linear change of variables T(u, v)=(u,u2v) = (x, y) 1 to calculate the integral f(x,y) dA= 0 ↓ The domain of T is a rectangle R. What is R? |ǝ(x, y) du dv. |ð(u, v)|arrow_forward2 Anot ined sove in peaper PV+96252 Q3// Find the volume of the region between the cylinder z = y2 and the xy- plane that is bounded by the planes x=1, x=2,y=-2,andy=2. vertical rect a Q4// Draw and Evaluate Soxy-2sin (ny2)dydx D Lake tarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL

College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning

Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL


Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY