Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Chapter 10.4, Problem 1E
Read each combination value directly from Pascal's triangle.
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2. A tank with a capacity of 650 gal. originally contains 200 gal of water with 100 lb. of salt in
solution. Water containing 1 lb. of salt per gallon is entering at a rate of 4 gal/min, and the
mixture is allowed to flow out of the tank at a rate of 3 gal/min.
a. Find the amount of salt in the tank at any time prior to the instant when the tank
begins to overflow (650 gallons).
b. Find the concentration (in pounds per gallon) of salt in the tank when the tank hits
400 gallons.
D.E. for mixture problems:
dv
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dA
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dy
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a. What are the equilibrium solutions for the differential equation?
b. Where is the differential equation increasing or decreasing? Show how you know.
Showing them on the drawing is not enough.
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d. Consider the slope field for the differential equation. Draw solution curves given the
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i. y(0) = -5
ii. y(0) = -1
iii. y(0) = 2
Chapter 10 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Electing Officers of a Club Refer to Examples 1...Ch. 10.1 - Appointing Committees List and count the ways club...Ch. 10.1 - Appointing Committees List and count the ways club...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...
Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Refer to Table 2 (the product table for rolling...Ch. 10.1 - Construct a product table showing all possible...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Of the sixteen numbers in the product table for...Ch. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Determine the number of triangles (of any size) in...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - Consider only the smallest individual cubes and...Ch. 10.1 - 49. Find the number of paths from A to B in the...Ch. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Work each problem.
52. Shaking Hands in a Group A...Ch. 10.1 - Work each problem. Number of Games in a Chess...Ch. 10.1 - Work each problem. Sums of Digits How many...Ch. 10.1 - Work each problem. Sums of Digits How many...Ch. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Work each problem. Selecting Dinner Items Michael...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Setting Options on a Computer Printer For...Ch. 10.1 - Work each problem. Building Numbers from Sets of...Ch. 10.1 - Work each problem. Lattice Points on a Line...Ch. 10.1 - Work each problem.
64. Lengths of Segments Joining...Ch. 10.1 - Work each problem. Patterns in Floor Tiling A...Ch. 10.1 - Work each problem, Counting Matchsticks in a Grid...Ch. 10.1 - Prob. 67ECh. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Prob. 9ECh. 10.2 - Evaluate each expression without using a...Ch. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - For the given values of n and r, evaluate (a)...Ch. 10.2 - For the given values of n and r, evaluate (a)...Ch. 10.2 - For the given values of n and r, evaluate
(a) and...Ch. 10.2 - For the given values of n and r, evaluate
(a) and...Ch. 10.2 - Use a calculator to evaluate each expression. 10!Ch. 10.2 - Use a calculator to evaluate each expression.
18....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression.
23....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression....Ch. 10.2 - Use a calculator to evaluate each expression.
26. ...Ch. 10.2 - Use a calculator to evaluate each expression.
27. ...Ch. 10.2 - Use a calculator to evaluate each expression.
28. ...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Arranging Letters Find the number of...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Prob. 34ECh. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Prob. 36ECh. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Settings on a Switch Panel A panel containing...Ch. 10.2 - Matching Club Members with Tasks Recall the club...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Matching Club Members with Tasks Recall the...Ch. 10.2 - Building Numbers with Specified Digits In...Ch. 10.2 - Building Numbers with Specified Digits In...Ch. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Selecting Dinner Items The Gourmet de Coeur...Ch. 10.2 - Selecting Dinner Items The Gourmet de Coeur...Ch. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Prob. 54ECh. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Selecting a College Class Schedule Jessica's class...Ch. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - 62. Listing Phone Numbers Raj keeps the phone...Ch. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Seating Arrangements at a Theater In Exercises...Ch. 10.2 - Prob. 67ECh. 10.2 - Seating Arrangements at a Theater In Exercises...Ch. 10.2 - Prob. 69ECh. 10.2 - Work each problem. Palindromes How many of the...Ch. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.3 - Evaluate each expression. 9P3Ch. 10.3 - Evaluate each expression.
2.
Ch. 10.3 - Evaluate each expression.
3.
Ch. 10.3 - Evaluate each expression. 11P3Ch. 10.3 - Evaluate each expression.
5.
Ch. 10.3 - Evaluate each expression.
6.
Ch. 10.3 - Evaluate each expression. 10C8Ch. 10.3 - Evaluate each expression.
8.
Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of permutations...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Determine the number of combinations (subsets) of...Ch. 10.3 - Use a calculator to evaluate each expression. 22P9Ch. 10.3 - Use a calculator to evaluate each expression....Ch. 10.3 - Use a calculator to evaluate each expression.
19....Ch. 10.3 - Use a calculator to evaluate each expression.
20....Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Prob. 25ECh. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Decide whether each object is a permutation or a...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Exercises 29-36 can be solved using permutations...Ch. 10.3 - Prob. 36ECh. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - Exercises 37-44 can be solved using combinations...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Prob. 67ECh. 10.3 - Prob. 68ECh. 10.3 - Prob. 69ECh. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - In Exercises 45-72, use permutations,...Ch. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Prob. 4ECh. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Read each combination value directly from Pascal's...Ch. 10.4 - Prob. 8ECh. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Selecting Committees of Congressmembers A...Ch. 10.4 - Prob. 12ECh. 10.4 - Tossing Coins Suppose eight fair coins are tossed....Ch. 10.4 - Prob. 14ECh. 10.4 - Tossing Coins Suppose eight fair coins are tossed....Ch. 10.4 - Prob. 16ECh. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Selecting Classrooms Diana is searching for her...Ch. 10.4 - Prob. 20ECh. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - For a set of five objects, find the number of...Ch. 10.4 - How many subsets (of any size) are there for a set...Ch. 10.4 - 28. For a given row in Pascal's triangle, let n be...Ch. 10.4 - 29. Which rows of Pascal's triangle have a single...Ch. 10.4 - 30. What is the least four-digit number in...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Patterns in Pascal's Triangle Over the years, many...Ch. 10.4 - Tartaglia's Rectangle More than a century before...Ch. 10.4 - Tartaglia's Rectangle The triangle that Pascal...Ch. 10.4 - Tartaglia's Rectangle The triangle that Pascal...Ch. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.5 - How many proper subsets are there of each set?
1....Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Tossing Coins If you toss seven fair coins, in how...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Rolling Dice If you roll two fair dice (say red...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Drawing Cards If you draw a single card from a...Ch. 10.5 - Identifying Properties of Counting Numbers Flow...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Identifying Properties of Counting Numbers How...Ch. 10.5 - Choosing Country Music Albums Jeanne's collection...Ch. 10.5 - Choosing Broadway Hits The ten longest Broadway...Ch. 10.5 - 23. Choosing Days of the Week How many different...Ch. 10.5 - Choosing School Assignments tor Completion Diona...Ch. 10.5 - Selecting Restaurants Jason wants to dine at four...Ch. 10.5 - Selecting Restaurants Jason wants to dine at four...Ch. 10.5 - Seating Arrangements on an Airliner Refer to...Ch. 10.5 - 28. Identifying Properties of Counting Numbers...Ch. 10.5 - 29. Counting Radio Call Letters Radio stations in...Ch. 10.5 - 30. Selecting Faculty Committees A committee of...Ch. 10.5 - Selecting Search-and-Rescue Teams A Civil Air...Ch. 10.5 - Choosing Team Members Three students from a class...Ch. 10.5 - Prob. 33ECh. 10.5 - Drawing Cards If a single card is drawn from a...Ch. 10.5 - Prob. 35ECh. 10.5 - Drawing Cards If a single card is drawn from a...Ch. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Prob. 39ECh. 10.5 - Choosing Senators The table categorizes 20...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Counting Card Hands Among the 2,598,960 possible...Ch. 10.5 - Prob. 45ECh. 10.5 - Counting Card Hands Among the 2,598,960possible...Ch. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Three-digit Numbers If only the digits 0,...Ch. 10 - Counting Triangles in a Figure Determine the...Ch. 10 - Tossing Coins Construct a tree diagram showing all...Ch. 10 - 7. Sums of Digits How many nonrepeating four-digit...Ch. 10 - 8. Arranging Children Yeo has invited her sister...Ch. 10 - Evaluate each expression. 6!Ch. 10 - Evaluate each expression. 8!6!Ch. 10 - Evaluate each expression.
11.
Ch. 10 - Evaluate each expression.
12.
Ch. 10 - Building Words from Sets of Letters How many...Ch. 10 - Building Words from Sets of Letters Using the...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Scheduling Assignments Eileen has seven homework...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball PlayersIf there are...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Selecting Groups of Basketball Players If there...Ch. 10 - Prob. 23TCh. 10 - Prob. 24TCh. 10 - Prob. 25TCh. 10 - Prob. 26TCh. 10 - Prob. 27TCh. 10 - Prob. 28TCh. 10 - Prob. 29TCh. 10 - Prob. 30TCh. 10 - Prob. 31TCh. 10 - Prob. 32TCh. 10 - Prob. 33TCh. 10 - Prob. 34TCh. 10 - Prob. 35TCh. 10 - Prob. 36T
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- 5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I purposefully removed the units- don't worry about them. Assume no conversions are needed.) a) Find the equation for the displacement of the spring mass at time t. b) Write the equation for the displacement of the spring mass in phase-mode form. c) Characterize the damping of the spring mass system as overdamped, underdamped or critically damped. Explain how you know. D.E. for Spring Mass Systems k m* g = kLo y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo m 2 A₁ = √c₁² + C₂² Q = tan-1arrow_forward4. Given the following information determine the appropriate trial solution to find yp. Do not solve the differential equation. Do not find the constants. a) (D-4)2(D+ 2)y = 4e-2x b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3xarrow_forward9.7 Given the equations 0.5x₁-x2=-9.5 1.02x₁ - 2x2 = -18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system's condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a modified slightly to 0.52. Interpret your results.arrow_forward
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