Topology
2nd Edition
ISBN: 9780134689517
Author: Munkres, James R.
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 2.17, Problem 9E
Let
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The Course Name Real Analysis please Solve questions by Real Analysis
part 3 of the question is:
A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
2. The duration of the ride is 15 min.
(a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris
wheel?
(b) What is the position of that passenger when the ride ends?
Chapter 2 Solutions
Topology
Ch. 2.13 - Prob. 1ECh. 2.13 - Consider the nine topologies on the set X=a,b,c...Ch. 2.13 - Show that the collection Tc given in Example 4 of...Ch. 2.13 - a If {T} is a family of topologies on X, show that...Ch. 2.13 - Show that if A is a basis for a topology on X,...Ch. 2.13 - Show that the topologies of l and K are not...Ch. 2.13 - Consider the following topologies on : T1 = the...Ch. 2.13 - a Apply Lemma 13.2 to show that the countable...Ch. 2.16 - Show that if Y is a subspace of X, and A is a...Ch. 2.16 - If and are topologies on X and is strictly...
Ch. 2.16 - Consider the set Y=[1,1] as a subspace of .Which...Ch. 2.16 - A map f:XY is said to be an open map if for every...Ch. 2.16 - Let X and X denote a single set in the topologies ...Ch. 2.16 - Exercises Show that the countable collection...Ch. 2.16 - Prob. 7ECh. 2.16 - Exercises If L is a straight line in the plane,...Ch. 2.16 - Exercises Show that the dictionary order topology...Ch. 2.16 - Exercises Let I=[0,1]. Compare the product...Ch. 2.17 - Let C be a collection of subsets of the set X....Ch. 2.17 - Show that if A is closed in Y and Y is closed in...Ch. 2.17 - Show that if A is closed in X and B is closed in...Ch. 2.17 - Show that if U is open in X and A is closed in X,...Ch. 2.17 - Let X be an ordered set in the order topology....Ch. 2.17 - Prob. 6.1ECh. 2.17 - Prob. 6.2ECh. 2.17 - Let A, B, and A denote subsets of a space X. Prove...Ch. 2.17 - Prob. 7ECh. 2.17 - Let A, B, and A denote subsets of a space X....Ch. 2.17 - Let A, B, and A denote subsets of a space X....Ch. 2.17 - Let A, B, and A denote subsets of a space X....Ch. 2.17 - Let AX and BY. Show that in the space XY, AB=AB.Ch. 2.17 - Show that every order topology is Hausdorff.Ch. 2.17 - Show that the product of two Hausdorff spaces is...Ch. 2.17 - Show that a subspace of a Hausdorff space is...Ch. 2.17 - Show that X is Hausdorff if and only if the...Ch. 2.17 - Prob. 14ECh. 2.17 - Show the T1 axiom is equivalent to the condition...Ch. 2.17 - Prob. 16.1ECh. 2.17 - Consider the five topologies on given in Exercise...Ch. 2.17 - Consider the lower limit topology on and the...Ch. 2.17 - Prob. 19ECh. 2.18 - Prove that for functions f:, the definition of...Ch. 2.18 - Prob. 2ECh. 2.18 - Let X and X denote a single set in the two...Ch. 2.18 - Let X and X denote a single set in the two...Ch. 2.18 - Given x0X and y0Y, show that the maps f:XXY and...Ch. 2.18 - Show that subspace (a,b) of is homeomorphic with...Ch. 2.18 - Prob. 6ECh. 2.18 - (a) Suppose that f: is continuous from the right,...Ch. 2.18 - Let Y be an ordered set in the order topology. Let...Ch. 2.18 - Let {A} be a collection of subsets of X; let X=A....Ch. 2.18 - Let f:AB and g:CD be continuous functions. Let us...Ch. 2.18 - Prob. 11ECh. 2.19 - Prove Theorem 19.2. Theorem 19.2. Suppose the...Ch. 2.19 - Prove Theorem 19.3. Theorem 19.3. Let A be a...Ch. 2.19 - Prove Theorem 19.4. Theorem 19.4. If each space X...Ch. 2.19 - Show that (X1Xn1)Xn is homeomorphic with X1Xn.Ch. 2.19 - One of the implications stated in Theorem 19.6...Ch. 2.19 - Let be the subset of consisting of all sequences...Ch. 2.19 - Given sequences (a1,a2,...) and (b1,b2,...) of...Ch. 2.19 - Show that the choice axiom is equivalent to the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- 3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its resting position. The pendulum's furthest distance to either side was 6 in. Graph the function that represents the pendulum's displacement as a function of time. Answer: f(t) (a) Write an equation to represent the displacement of the pendulum as a function of time. (b) Graph the function. 10 9 8 7 6 5 4 3 2 1 0 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -1 -5. -6 -7 -8 -9 -10-arrow_forwardA power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. (a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. (b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forwardThe Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride. Height of Passenger in Ferris Wheel 180 160 140- €120 Height, h (ft) 100 80 60 40 20 0 ך 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time of operation, t (min) Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel. Answer:arrow_forward
- 1. Graph the function f(x)=sin(x) −2¸ Answer: y -2π 一元 1 −1 -2 -3 -4+ 元 2πarrow_forward3. Graph the function f(x) = −(x-2)²+4 Answer: f(x) 6 5 4 3 2+ 1 -6-5 -4-3-2-1 × 1 2 3 4 5 6 -1 -2+ ရာ -3+ -4+ -5 -6arrow_forward2. Graph the function f(x) = cos(2x)+1 Answer: -2π 一元 y 3 2- 1 -1 -2+ ရာ -3- Π 2πarrow_forward
- 2. Graph the function f(x) = |x+1+2 Answer: -6-5-4-3-2-1 f(x) 6 5 4 3 2 1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6arrow_forward1. The table shows values of a function f(x). What is the average rate of change of f(x) over the interval from x = 5 to x = 9? Show your work. X 4 f(x) LO 5 6 7 8 9 10 -2 8 10 11 14 18arrow_forward• Find a real-world situation that can be represented by a sinusoidal function. You may find something online that represents a sinusoidal graph or you can create a sinusoidal graph yourself with a measuring tape and a rope. • Provide a graph complete with labels and units for the x- and y-axes. • Describe the amplitude, period, and vertical shift in terms of the real-world situation.arrow_forward
- f(x) = 4x²+6x 2. Given g(x) = 2x² +13x+15 and find 41 (4)(x) Show your work.arrow_forwardf(x) = x² − 6x + 8 3. Given and g(x) = x -2 solve f(x) = g(x) using a table of values. Show your work.arrow_forward1. Graph the function f(x) = 3√x-2 Answer: -6-5 -4-3-2 -1 6 LO 5 f(x) 4 3 2+ 1 1 2 3 4 5 6 -1 -2+ -3 -4 -5 -6- 56arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
What is a Relation? | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=hV1_wvsdJCE;License: Standard YouTube License, CC-BY
RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY