Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter 8.D, Problem 17E
The Decibel Scale. Use the decibel scale to answer the questions.
- How many times as loud as the softest audible sound is the sound of ordinary conversation’
- How many rimes as loud as the softest audible sound is the sound of a siren at 30 meters?
- What is the loudness, in decibels, of a sound 10 million times as loud as the softest audible sound?
- What is the loudness, in decibels, of a sound 10 trillion times as loud as the softest audible sound?
- How much louder (mote intense) is a 55-dB sound dun a 10-dB sound?
- Suppose that a sound is 100 times as loud as (more intense than, a whisper What is us loudness in decibels?
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
6. [10 marks]
Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of
T.
(a) How many vertices does BL(T) have?
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Prove that your answers are correct.
Chapter 8 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. 8.A - Prob. 1QQCh. 8.A - Prob. 2QQCh. 8.A - The balance owed your credit card doubles from...Ch. 8.A - The number Of songs in your iPod has increased...Ch. 8.A - Which of the following is in example of...Ch. 8.A - On a chessboard with 64 squares, you place 1 penny...Ch. 8.A - At 11:00 you place a single bacterium in a bottle,...Ch. 8.A - Consider the bacterial population described in...Ch. 8.A - Consider the bacterial population described in...Ch. 8.A - Which of the following is not true of any...
Ch. 8.A - Describe basic differences between linear growth...Ch. 8.A - 2. Briefly explain how repeated doublings...Ch. 8.A - Briefly summarize the Story Of the bacteria in the...Ch. 8.A - Explain the meaning Of the two key facts about...Ch. 8.A - Prob. 5ECh. 8.A - Suppose you had a magic hank account in which your...Ch. 8.A - A small town that grows exponentially can become a...Ch. 8.A - H. Human population has been growing exponentially...Ch. 8.A - Prob. 9ECh. 8.A - Prob. 10ECh. 8.A - Prob. 11ECh. 8.A - Prob. 12ECh. 8.A - Prob. 13ECh. 8.A - Prob. 14ECh. 8.A - Linear or Exponential? State whether the growth...Ch. 8.A - Prob. 16ECh. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Prob. 20ECh. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Prob. 22ECh. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - 29. Human Doubling. Human population in the year...Ch. 8.A - Doubling Time versus Initial Amount. a. Would you...Ch. 8.A - Facebook Users. The table shows the number of...Ch. 8.A - Prob. 32ECh. 8.A - Exponential Growth. Identify at least two news...Ch. 8.A - Prob. 34ECh. 8.A - Prob. 35ECh. 8.B - Prob. 1QQCh. 8.B - Prob. 2QQCh. 8.B - Which of the following is not a good approximation...Ch. 8.B - Prob. 4QQCh. 8.B - Radioactive tritium (hvdrogen-3) has a halt-life...Ch. 8.B - Radioactive uramum-235 has a hall-life of about...Ch. 8.B - Prob. 7QQCh. 8.B - log10108= a.100,000,000 b. 108 c.8Ch. 8.B - A rural popular ion decreases at a rate of 20% per...Ch. 8.B - Prob. 10QQCh. 8.B - What is a doubling tune? Suppose a population has...Ch. 8.B - Prob. 2ECh. 8.B - State the approximate doubting time formula and...Ch. 8.B - Prob. 4ECh. 8.B - Prob. 5ECh. 8.B - 6. State the approximate hall-life formula and the...Ch. 8.B - 7. Briefly describe exact doubling time and...Ch. 8.B - 8. Give an example in which it is important to use...Ch. 8.B - Our town is growing with a doubling time of 25...Ch. 8.B - Our town is growing at a rate of 7% per year, so...Ch. 8.B - A toxic chemical decays with a hall-life of 10...Ch. 8.B - The hall-life of plutomum-239 is about 24,000...Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Prob. 15ECh. 8.B - Prob. 16ECh. 8.B - 13-24: Logarithms. Refer to the Brief Review on p....Ch. 8.B - Prob. 18ECh. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - 13-24: Logarithms. Refer to the Brief Review on p....Ch. 8.B - Prob. 22ECh. 8.B - Prob. 23ECh. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Prob. 25ECh. 8.B - Prob. 26ECh. 8.B - Prob. 27ECh. 8.B - Prob. 28ECh. 8.B - Prob. 29ECh. 8.B - Prob. 30ECh. 8.B - Prob. 31ECh. 8.B - Prob. 32ECh. 8.B - Prob. 33ECh. 8.B - Prob. 34ECh. 8.B - 31. Rabbits. A community of rabbits begins with an...Ch. 8.B - Prob. 36ECh. 8.B - Doubling Time Formula. Use the approximate...Ch. 8.B - Prob. 38ECh. 8.B - Prob. 39ECh. 8.B - Prob. 40ECh. 8.B - Prob. 41ECh. 8.B - Prob. 42ECh. 8.B - Prob. 43ECh. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 45ECh. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 47ECh. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 49ECh. 8.B - 49-52: Half-Life Formula. Use the approximate...Ch. 8.B - Prob. 51ECh. 8.B - 49-52: Half-Life Formula. Use the approximate...Ch. 8.B - Prob. 53ECh. 8.B - Exact Formulas. Compare the doubling times found...Ch. 8.B - Prob. 55ECh. 8.B - Exact Formulas. Compare the doubling times found...Ch. 8.B - Prob. 57ECh. 8.B - 58. Nuclear Weapons. Thermonuclear weapons use...Ch. 8.B - Fossil Fuel Emissions. Total emissions of carbon...Ch. 8.B - Yucca Mountain. The U.S. government spent nearly...Ch. 8.B - Crime Rate. The homicide rate decreases at a rate...Ch. 8.B - 62. Drug Metabolism. A particular antibiotic is...Ch. 8.B - Atmospheric Pressure. The pressure of Earth's...Ch. 8.B - Prob. 64ECh. 8.B - 65. Radioactive Half-Life. Find a news story that...Ch. 8.B - Prob. 66ECh. 8.B - Prob. 67ECh. 8.B - Prob. 68ECh. 8.B - Prob. 69ECh. 8.C - Prob. 1QQCh. 8.C - Prob. 2QQCh. 8.C - The primary reason for the rapid growth of human...Ch. 8.C - The carrying capacity of the Earth is defined as...Ch. 8.C - Which of the billowing would cause estimates of...Ch. 8.C - 6. Recall the bacteria in a bottle example from...Ch. 8.C - When researchers project that human population...Ch. 8.C - Prob. 8QQCh. 8.C - Prob. 9QQCh. 8.C - Prob. 10QQCh. 8.C - Based on Figure 8.3, contrast the changes in human...Ch. 8.C - Prob. 2ECh. 8.C - Haw do today’s birth and death rates compare to...Ch. 8.C - Prob. 4ECh. 8.C - Prob. 5ECh. 8.C - What is overshot and collapse? Under what...Ch. 8.C - Prob. 7ECh. 8.C - 8. If birth rates fall more than death rates, the...Ch. 8.C - The carrying capacity of our planet depends only...Ch. 8.C - to rapid increases in computing technology, we...Ch. 8.C - In the wild, we always expect the population of...Ch. 8.C - Prob. 12ECh. 8.C - Prob. 13ECh. 8.C - Varying Growth Rates. Starting from a 2013...Ch. 8.C - Prob. 15ECh. 8.C - 13-16: Varying Growth Rates. Starting from a 2013...Ch. 8.C - Birth and Death Rates. The following table gives...Ch. 8.C - Prob. 18ECh. 8.C - Prob. 19ECh. 8.C - Prob. 20ECh. 8.C - 21. Logistic Growth. Consider a population that...Ch. 8.C - Logistic Growth. Consider a population that begins...Ch. 8.C - Prob. 23ECh. 8.C - Prob. 24ECh. 8.C - Prob. 25ECh. 8.C - Prob. 26ECh. 8.C - Prob. 27ECh. 8.C - Prob. 28ECh. 8.C - Prob. 29ECh. 8.C - Prob. 30ECh. 8.C - Prob. 31ECh. 8.C - Prob. 32ECh. 8.C - Prob. 33ECh. 8.C - Prob. 34.0ECh. 8.C - Prob. 34.1ECh. 8.C - Population Predictions. Find population...Ch. 8.C - Prob. 36ECh. 8.C - Prob. 37ECh. 8.C - Prob. 38ECh. 8.C - Prob. 39ECh. 8.D - The energy release of a magnitude 7 earthquake is...Ch. 8.D - Prob. 2QQCh. 8.D - 3. What is a 0-decibel sound?
the softest sound...Ch. 8.D - Prob. 4QQCh. 8.D - Prob. 5QQCh. 8.D - Prob. 6QQCh. 8.D - Prob. 7QQCh. 8.D - Prob. 8QQCh. 8.D - Prob. 9QQCh. 8.D - Prob. 10QQCh. 8.D - What is the magnitude scale for earthquakes? What...Ch. 8.D - What is the decibel scale? Describe how it is...Ch. 8.D - What is pH? What pH values define an acid, a base,...Ch. 8.D - What is acid rain? Why is it a serious...Ch. 8.D - 5. An earthquake of magnitude 8 will do twice as...Ch. 8.D - A 120-dB wand is 20% louder than a 100-dB sound.Ch. 8.D - If I double the amount of water in the cup, I'll...Ch. 8.D - The lake water was crystal clear, so It could not...Ch. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - Prob. 10ECh. 8.D - Prob. 11ECh. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - 9-14: Earthquake Magnitudes. Use the earthquake...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - Prob. 20ECh. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - Prob. 22ECh. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - The pH scale. Use the pH scale to answer the...Ch. 8.D - The pH Scale. Use the pH scale to answer the...Ch. 8.D - Prob. 27ECh. 8.D - Prob. 28ECh. 8.D - Prob. 29ECh. 8.D - Prob. 30ECh. 8.D - The pH Scale. Use the pH scale to answer the...Ch. 8.D - 25-32: The pH Scale. Use the pH scale to answer...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - 33-38: Logarithmic Thinking. Briefly describe, in...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - Prob. 37ECh. 8.D - Prob. 38ECh. 8.D - 39. Sound and Distance.
The decibel level for...Ch. 8.D - 40. Variation in Sound with Distance. Suppose that...Ch. 8.D - Toxic Dumping in Acidified Lakes. Consider a...Ch. 8.D - Earthquakes in the News. Find a recent news story...Ch. 8.D - Prob. 43ECh. 8.D - Disasters. Find the death lolls for some of the...Ch. 8.D - Prob. 45E
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