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 1.1, Problem 30E
27, 21, 16, 12, 9
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A communications tower is located at the top
of a steep hill, as shown. The angle of
inclination of the hill is 77°. A guy wire is to be
attached to the top of the tower and to the
ground, 102 ft downhill from the base of the
tower. The angle formed by the guy wire is 9°.
Find the length of the cable required for the
guy wire.
9°
102 ft
77°
NOTE: The picture is NOT drawn to scale.
length of guy-wire =
ft
Enter your answer as a number; your answer
should be accurate to 2 decimal places.
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Under certain conditions, the number of diseased cells N(t) at time t increases at a rate N'(t) = Aekt, where A is the rate of increase at time 0 (in cells per day) and k is a constant.
(a) Suppose A = 60, and at 3 days, the cells are growing at a rate of 180 per day. Find a formula for the number of cells after t days, given that 200 cells are present at t = 0.
(b) Use your answer from part (a) to find the number of cells present after 8 days.
(a) Find a formula for the number of cells, N(t), after t days.
N(t) =
(Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)
Chapter 1 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 1.1 - The next number in the pattern 2,4,6,8,10 is 12Ch. 1.1 - My dog barked and woke me up at 1:02 a.m., 2:03...Ch. 1.1 - To find the perimeter P of a square with side of...Ch. 1.1 - A company charges a 10% re-stocking fee for...Ch. 1.1 - In Exercises 1-16, determine whether the reasoning...Ch. 1.1 - 6. If you take your medicine, you’ll feel a lot...Ch. 1.1 - It has rained every day for the past six days, and...Ch. 1.1 - 8. Carrie’s first five children were boys. If she...Ch. 1.1 - 9. The 2000 movie Cast Away stars Tom Hanks as the...Ch. 1.1 - 10. If the same number is subtracted from both...
Ch. 1.1 - If you build it, they will come. You build it....Ch. 1.1 - 12. All men are mortal. Socrates is a man....Ch. 1.1 - It is a fact that every student who ever attended...Ch. 1.1 - For the past 126 years, a rare plant has bloomed...Ch. 1.1 - 15. In the sequence 5, 10, 15, 20, 25,..., the...Ch. 1.1 - 16. (This anecdote is adapted from a story by...Ch. 1.1 - 17. Discuss the differences between inductive and...Ch. 1.1 - 18. Give an example of faulty inductive...Ch. 1.1 - Determine the most probable next term in each of...Ch. 1.1 - Determine the most probable next term in each of...Ch. 1.1 - 21. 3, 12, 48, 192, 768
Ch. 1.1 - 32, 16,8,4,2Ch. 1.1 - 3, 6, 9, 15, 24, 39Ch. 1.1 - 13,35,57,79,911Ch. 1.1 - 25.
Ch. 1.1 - 1,4, 9, 16, 25Ch. 1.1 - 27. 1, 8, 27, 64, 125
Ch. 1.1 - 28. 2, 6, 12, 20, 30, 42
Ch. 1.1 - Determine the most probable next term in each of...Ch. 1.1 - 30. 27, 21, 16, 12, 9
Ch. 1.1 - 31. 5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5,...Ch. 1.1 - 8, 2, 8, 2, 2, 8, 2, 2, 2, 8, 2, 2, 2, 2, 8, 2, 2,...Ch. 1.1 - 33. Construct a list of numbers similar to those...Ch. 1.1 - 34. Construct a list of numbers similar to those...Ch. 1.1 - Prob. 35ECh. 1.1 - 36.
Ch. 1.1 - 37.
Ch. 1.1 - 38.
Ch. 1.1 - 39.
Ch. 1.1 - 40.
Ch. 1.1 - 41.
Ch. 1.1 - 42.
Ch. 1.1 - 43.
Ch. 1.1 - 3=3(31)23+9=3(91)23+9+27=3(271)23+9+27+81=3(811)2Ch. 1.1 - 12=11212+14=11412+14+18=11812+14+18+116=1116Ch. 1.1 - 46.
Ch. 1.1 - Prob. 47ECh. 1.1 - 48.
Ch. 1.1 - 1+2+3++800Ch. 1.1 - 1+2+3++2000Ch. 1.1 - Modify the procedure of Gauss to find the sum .
Ch. 1.1 - Explain in your own words how the procedure of...Ch. 1.1 - Prob. 53ECh. 1.1 - 53. Modify the procedure of Gauss to find the sum...Ch. 1.1 - 55. What is the most probable next number in this...Ch. 1.1 - Prob. 56ECh. 1.1 - 57. Choose any three-digit number with all...Ch. 1.1 - 58. Choose any number, and follow these steps.
a....Ch. 1.1 - Complete the following....Ch. 1.1 -
60. Refer to Figures 2 (b)–(e) and Figure 3....Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Use the method of successive differences to...Ch. 1.2 - 3, 14, 31, 54, 83, 118, Use the method of...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Prob. 21ECh. 1.2 - 22. The 1952 film Hans Christian Andersen stars...Ch. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - In Exercises 23-32, several equations are given...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Use the formula S=1(n+1)2 to find each sum....Ch. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Use the formula S=n2 to find each sum (Hint: To...Ch. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - 50. Exercises 48 and 49 are specific cases of the...Ch. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - the ninth pentagonal numbers SCh. 1.2 - 56. the seventh hexagonal number
Ch. 1.2 - 57. the tenth heptagonal number |
Ch. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - 68. The 36th term of 8, 38, 68, 98,...
Ch. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - Prob. 72ECh. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - Prob. 75ECh. 1.2 - Prob. 76ECh. 1.2 - Prob. 77ECh. 1.2 - Prob. 78ECh. 1.2 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.2 - Prob. 81ECh. 1.2 - Prob. 82ECh. 1.3 - Broken Elevator A man enters a building on the...Ch. 1.3 - Use the various problem-solving strategies to...Ch. 1.3 - Do You Have a Match? Move 4 of the matches in the...Ch. 1.3 - Sudoku Sudoku is an puzzle that requires the...Ch. 1.3 - Use the various problem-solving strategies to...Ch. 1.3 - A Real Problem We are given the following...Ch. 1.3 - How Old Is Mommy? A mother has two children whose...Ch. 1.3 - An Alarming Situation You have three alarms in...Ch. 1.3 - Laundry Day Every Monday evening, a mathematics...Ch. 1.3 - Pick an Envelope Three envelopes contain a total...Ch. 1.3 - Class Members A classroom contains an equal number...Ch. 1.3 - Prob. 12ECh. 1.3 - Missing Digit Look for a pattern and find the...Ch. 1.3 - 14. Abundancy An integer is abundant if the sum...Ch. 1.3 - Cross-Country Competition The schools in an...Ch. 1.3 - Gone Fishing Four friends go fishing one day and...Ch. 1.3 - Cutting a Square in Half In how many ways can a...Ch. 1.3 - You Lie! Max, Sam, and Brett were playing...Ch. 1.3 - Bookworm Snack A 26-volume encyclopedia (one for...Ch. 1.3 - Pick a Card, Any Card Three face cards from an...Ch. 1.3 - 21. Catwoman’s Cats If you ask Batman’s nemesis,...Ch. 1.3 - Pencil Collection Bob gave four-fifths of his...Ch. 1.3 - Adding Gasoline The gasoline gauge on a van...Ch. 1.3 - 24. Gasoline Tank Capacity When 6 gallons of...Ch. 1.3 - Number Pattern What is the relationship between...Ch. 1.3 - 26. Locking Boxes You and I each have one lock and...Ch. 1.3 - 27. Number in a Sequence In the sequence 16, 80,...Ch. 1.3 - Unknown Number Cindy was asked by her teacher to...Ch. 1.3 - 29. Unfolding and Folding a Box An unfolded box is...Ch. 1.3 - Prob. 30ECh. 1.3 - Labeling Boxes You are working in a store that has...Ch. 1.3 - Mr. Greens Age At his birthday party, Mr. Green...Ch. 1.3 - 33. Sum of Hidden Dots on Dice Three dice with...Ch. 1.3 - 34. Age of the Bus Driver Today is your first day...Ch. 1.3 - 35. Matching Triangles and Squares How can you...Ch. 1.3 - 36. Forming Perfect Square Sums How must one place...Ch. 1.3 - Difference Triangle Balls numbered 1 through 6 are...Ch. 1.3 - Clock Face By drawing two straight lines, divide...Ch. 1.3 - Alphametric If a, b, and c are digits for which...Ch. 1.3 - Perfect Square Only one of these numbers is a...Ch. 1.3 - Sleeping on the Way to Grandmas House While...Ch. 1.3 - Buckets of Water You have brought two unmarked...Ch. 1.3 - Counting Puzzle (Rectangles) How many rectangles...Ch. 1.3 - Digit Puzzle Place each of the digits 1, 2, 3, 4,...Ch. 1.3 - 45. Palindromic Number (Note: A palindromic number...Ch. 1.3 - 46. How Much Is That Doggie in the Window? A man...Ch. 1.3 - Final Digits of a Power of 7 What are the final...Ch. 1.3 - 48. Units Digit of a Power of 3 If you raise 3 to...Ch. 1.3 - Summing the Digits When 10 - 50 is expressed as a...Ch. 1.3 - 50. Frog Climbing up a Well A frog is at the...Ch. 1.3 - 51. Units Digit of a Power of 7 What is the units...Ch. 1.3 - Prob. 52ECh. 1.3 - Going Postal Joanie wants to mail a package that...Ch. 1.3 - 54. Counting Puzzle (Squares) How many squares are...Ch. 1.3 - Matching Socks A drawer contains 20 black socks...Ch. 1.3 - Prob. 56ECh. 1.3 - 57. Perfect Number A perfect number is a counting...Ch. 1.3 - Naming Children Beckys mother has three daughters....Ch. 1.3 - 59. Growth of a Lily Pad A lily pad grows so that...Ch. 1.3 - Prob. 60ECh. 1.3 - Prob. 61ECh. 1.3 - Prob. 62ECh. 1.3 - Adam and Eves Assets Eve said to Adam, If you give...Ch. 1.3 - Prob. 64ECh. 1.3 - Prob. 65ECh. 1.3 - Prob. 66ECh. 1.3 - Prob. 67ECh. 1.3 - Prob. 68ECh. 1.3 - 69. Pitches in a Baseball Game What is the minimum...Ch. 1.3 - 70. Weighing Coins You have eight coins. Seven are...Ch. 1.3 - 71. Geometry Puzzle When the diagram shown is...Ch. 1.3 - Prob. 72ECh. 1.3 - Prob. 73ECh. 1.3 - Prob. 74ECh. 1.3 - 75. Paying for a Mint Brian has an unlimited...Ch. 1.3 - Prob. 76ECh. 1.3 - Prob. 77ECh. 1.3 - Prob. 78ECh. 1.3 - Prob. 79ECh. 1.3 - Prob. 80ECh. 1.3 - Prob. 81ECh. 1.3 - Making Change Webster has some pennies, dimes, and...Ch. 1.4 - 39.7+(8.24.1)Ch. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - 5.765Ch. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Find the decimal representation of 16 on your...Ch. 1.4 - Prob. 34ECh. 1.4 - 35. Choose any digit except 0. Multiply it by 429....Ch. 1.4 - Prob. 36ECh. 1.4 - 37. Pages to Store Trading Cards A plastic page...Ch. 1.4 - Prob. 38ECh. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Price per Acre of Land To build a millennium clock...Ch. 1.4 - Prob. 42ECh. 1.4 - In Exercises 41-46, use estimation to determine...Ch. 1.4 - 44. Revolutions of Mercury The planet Mercury...Ch. 1.4 - Reception Average In 2013, A. J. Green of the...Ch. 1.4 - Prob. 46ECh. 1.4 - Foreign-Born Americans Approximately 37.5 million...Ch. 1.4 - Prob. 48ECh. 1.4 - Prob. 49ECh. 1.4 - Prob. 50ECh. 1.4 - Prob. 51ECh. 1.4 - Prob. 52ECh. 1.4 - Prob. 53ECh. 1.4 - Describe the change from 2004 to 2010. U.S. Car...Ch. 1.4 - Prob. 55ECh. 1.4 - Prob. 56ECh. 1.4 - Prob. 57ECh. 1.4 - Prob. 58ECh. 1.4 - Prob. 59ECh. 1.4 - The Simpsons The longest-running animated...Ch. 1.4 - Donald in Mathmagic Land One of the most popular...Ch. 1.4 - Prob. 62ECh. 1 - In Exercises 1 and 2 decide whether the reasoning...Ch. 1 - In Exercises 1 and 2, decide whether the reasoning...Ch. 1 - Counting Puzzle (Rectangles) How many rectangles...Ch. 1 - Use the list of equations and inductive reasoning...Ch. 1 - Use the method of successive differences to find...Ch. 1 - Find the sum 1+2+3++250.Ch. 1 - 7 Consider the following equations, where the left...Ch. 1 - Use the result of Exercise 7 and the method of...Ch. 1 - 9 Describe the pattern used to obtain the terms of...Ch. 1 - Use problem-solving strategies to solve each...Ch. 1 - Units Digit of a Power of 9 What is the units...Ch. 1 - Counting Puzzle (Triangles) How many triangles are...Ch. 1 - Make Them Equal Consider the following...Ch. 1 - Prob. 14TCh. 1 - 15 Units Digit of a Sum Find the units digit (ones...Ch. 1 - Prob. 16TCh. 1 - Prob. 17TCh. 1 - Use your calculator to evaluate each of the...Ch. 1 - Prob. 19TCh. 1 - Unemployment Rate The line graph shows the overall...
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