Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
11th Edition
ISBN: 9781305283831
Author: Tan
Publisher: Cengage Learning
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Chapter 9.CRQ, Problem 5CRQ
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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)…
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(
=
≈
1. 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.)
Chapter 9 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQCh. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7E
Ch. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - In Exercises 1-10, determine which of the matrices...Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - In Exercises 1518, find X2 the probability...Ch. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Political Polls: Morris Polling conducted a poll 6...Ch. 9.1 - Commuter Trends: In a large metropolitan area, 20...Ch. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - MARKET SHARE OF AUTO MANUFACTURERES In a study of...Ch. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - In Exercises 29 and 30, determine whether the...Ch. 9.1 - Prob. 30ECh. 9.1 - Prob. 1TECh. 9.1 - Prob. 2TECh. 9.1 - Prob. 3TECh. 9.1 - Prob. 4TECh. 9.2 - Prob. 1CQCh. 9.2 - Prob. 2CQCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - COMMUTER TRENDS Within a large metropolitan area,...Ch. 9.2 - Prob. 19ECh. 9.2 - PROFESSIONAL WOMEN From data compiled over a...Ch. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - NETWORK NEWS VIEWERSHIP A television poll was...Ch. 9.2 - Prob. 24ECh. 9.2 - GENETICS In a certain species of roses, a plant...Ch. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 1TECh. 9.2 - Prob. 2TECh. 9.2 - Prob. 3TECh. 9.3 - What is an absorbing stochastic matrix?Ch. 9.3 - Prob. 2CQCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - GAME OF CHANCE Refer to Exercise 26. Suppose Diane...Ch. 9.3 - Prob. 28ECh. 9.3 - COLLEGE GRADUATION RATE The registrar of...Ch. 9.3 - Prob. 30ECh. 9.3 - GENETICS Refer to Example 4. If the offspring are...Ch. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.4 - a. What is the maximin strategy for the row player...Ch. 9.4 - Prob. 2CQCh. 9.4 - Prob. 1ECh. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - GAME OF MATCHING FINGERS Robin and Cathy play a...Ch. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - MARKET SHARE: Rolands Barber Shop and Charleys...Ch. 9.4 - In Exercises 24-26, determine whether the...Ch. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.5 - Prob. 1CQCh. 9.5 - Prob. 2CQCh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - The payoff matrix for a game is [332311121] a....Ch. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - COIN-MATCHING GAME Consider the coin-matching game...Ch. 9.5 - INVESTMENT STRATEGIES As part of their investment...Ch. 9.5 - INVESTMENT STRATEGIES The Maxwells have decided to...Ch. 9.5 - CAMPAIGN STRATEGIES Bella Robinson and Steve...Ch. 9.5 - MARKETING STRATEGIES Two dentists, Lydia Russell...Ch. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.CRQ - Prob. 1CRQCh. 9.CRQ - Prob. 2CRQCh. 9.CRQ - Fill in the blanks. The probabilities in a Markov...Ch. 9.CRQ - Fill in the blanks. A transition matrix associated...Ch. 9.CRQ - Prob. 5CRQCh. 9.CRQ - Prob. 6CRQCh. 9.CRQ - Prob. 7CRQCh. 9.CRQ - Prob. 8CRQCh. 9.CRQ - Prob. 9CRQCh. 9.CRQ - Prob. 10CRQCh. 9.CRE - Prob. 1CRECh. 9.CRE - Prob. 2CRECh. 9.CRE - Prob. 3CRECh. 9.CRE - Prob. 4CRECh. 9.CRE - Prob. 5CRECh. 9.CRE - Prob. 6CRECh. 9.CRE - In Exercises 7-10, determine whether the matrix is...Ch. 9.CRE - Prob. 8CRECh. 9.CRE - Prob. 9CRECh. 9.CRE - Prob. 10CRECh. 9.CRE - In Exercises 11-14, find the steady-state matrix...Ch. 9.CRE - Prob. 12CRECh. 9.CRE - Prob. 13CRECh. 9.CRE - Prob. 14CRECh. 9.CRE - Prob. 15CRECh. 9.CRE - Prob. 16CRECh. 9.CRE - Prob. 17CRECh. 9.CRE - Prob. 18CRECh. 9.CRE - Prob. 19CRECh. 9.CRE - Prob. 20CRECh. 9.CRE - Prob. 21CRECh. 9.CRE - Prob. 22CRECh. 9.CRE - Prob. 23CRECh. 9.CRE - Prob. 24CRECh. 9.CRE - Prob. 25CRECh. 9.CRE - Prob. 26CRECh. 9.CRE - Prob. 27CRECh. 9.CRE - Prob. 28CRECh. 9.CRE - Prob. 29CRECh. 9.CRE - OPTIMIZING DEMAND The management of a divison of...Ch. 9.BMO - The transition matrix for a Markov process is...Ch. 9.BMO - Prob. 2BMOCh. 9.BMO - Prob. 3BMOCh. 9.BMO - Prob. 4BMOCh. 9.BMO - The payoff matrix for a certain game is A=[213234]...Ch. 9.BMO - Prob. 6BMO
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