Pearson eText for Thinking Mathematically -- Instant Access (Pearson+)
7th Edition
ISBN: 9780137502240
Author: ROBERT BLITZER
Publisher: PEARSON+
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Chapter 4.3, Problem 13E
To determine
To calculate: The value after subtraction of two numbers,
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Question 1. (10 points)
A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by
dV
=
1.45V(2 In(V+1)).
dt
(a) (4 pts) Find all the equilibria and determine their stability using the stability condition.
(b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of
f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable.
(c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain
in biological terms what happens to the size of each of these tumours at time progresses.
For the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.
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Chapter 4 Solutions
Pearson eText for Thinking Mathematically -- Instant Access (Pearson+)
Ch. 4.1 - CHECK POINT 1 Write each of the following in...Ch. 4.1 - CHECK POINT 2 Express each expanded form as a...Ch. 4.1 - CHECK POINT 3 Write each Babylonian numeral as a...Ch. 4.1 - CHECK POINT 4 Write each Mayan numeral as a...Ch. 4.1 - Q.1. A number addresses the question “how many?” A...Ch. 4.1 - Q.2. Our number system is called the __________...Ch. 4.1 - Prob. 3CVCCh. 4.1 - Q.4. When we write 547 as, , we are using an...Ch. 4.1 - Prob. 5CVCCh. 4.1 - The Hindu Arabic numeration system uses power of...
Ch. 4.1 - Prob. 7CVCCh. 4.1 - Using ∨ for 1 and < for 10, the expanded from < ...Ch. 4.1 - Q.9. The place value in the Mayan numeration...Ch. 4.1 - Q.10.
= = .
...Ch. 4.1 - In Exercises 1-8, evaluate the expression.
1.
Ch. 4.1 - In Exercises 1-8, evaluate the expression.
2.
Ch. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - In Exercises 1-8, evaluate the expression. 3 4Ch. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - In Exercises 9-22, write each Hindu-Arabic numeral...Ch. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - In Exercises 23-32, express each expanded form as...Ch. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - In Exercises 34-46, use Table 4.1 on page 215 to...Ch. 4.1 - In Exercises 34-46, use Table 4.1 on page 215 to...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - In Exercises 34-46, use Table 4.1 on page 215 to...Ch. 4.1 - Prob. 46ECh. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - In Exercises 47-60, use Table 4.2 on page 216 to...Ch. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Prob. 77ECh. 4.1 - Prob. 78ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 81ECh. 4.1 - Explain how to write a Hindu-Arabic numeral in...Ch. 4.1 - 83. Describe one way that the Babylonian system is...Ch. 4.1 - 84. Describe one way that the Mayan system is...Ch. 4.1 - Research activity Write a report on the history of...Ch. 4.1 - Prob. 86ECh. 4.1 - Prob. 87ECh. 4.1 - Prob. 88ECh. 4.1 - Make Sense? In Exercises 86-89, determine whether...Ch. 4.1 - Prob. 90ECh. 4.1 - Prob. 91ECh. 4.1 - Use Babylonian numerals to write the numeral that...Ch. 4.2 - CHECK POINT 1 Convert to base ten.
Ch. 4.2 - CHECK POINT 2 Convert to base ten.
Ch. 4.2 - CHECK POINT 3 Convert to base ten.
Ch. 4.2 - CHECK POINT 4 Convert the base ten numeral 6 to a...Ch. 4.2 - CHECK POINT 5 Convert the base ten numeral 365 to...Ch. 4.2 - CHECK POINT 6 Convert the base ten numeral 51 to a...Ch. 4.2 - CHECK POINT 7 Convert the base ten numeral 2763 to...Ch. 4.2 - In the numeral 324 five , the base is _____. In...Ch. 4.2 - 324 five = ( 3 × _ _ ) + ( 2 × _ _ ) + ( 4 × _ _ )Ch. 4.2 - Prob. 3CVCCh. 4.2 - Prob. 4CVCCh. 4.2 - Prob. 5CVCCh. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Prob. 7CVCCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - In Exercises 1-18, convert the numeral to a...Ch. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - In Exercises 19-32, mentally convert each base ten...Ch. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - In Exercises 33-48, convert each base ten numeral...Ch. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - In Exercises 49-52, use Table 4.1 on page 215 to...Ch. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - In Exercises 53-56, use Table 4.2 on page 216 to...Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - 59. Convert to base eight.
Ch. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Read the Blitzer Bonus on page 222. Then use the...Ch. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Make Sense? In Exercises 73-76, determine whether...Ch. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - In Exercises 77-78, write, in the indicated base,...Ch. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.2 - Prob. 80ECh. 4.2 - Prob. 81ECh. 4.2 - Prob. 82ECh. 4.2 - The following topics are appropriate for either...Ch. 4.2 - The following topics are appropriate for either...Ch. 4.3 - CHECK POINT 1 Add: 32 five + 44 five . _Ch. 4.3 - Prob. 2CPCh. 4.3 - Prob. 3CPCh. 4.3 - Prob. 4CPCh. 4.3 - Prob. 5CPCh. 4.3 - Prob. 6CPCh. 4.3 - Prob. 1CVCCh. 4.3 - Prob. 2CVCCh. 4.3 - Consider the following addition in base eight: ...Ch. 4.3 - Prob. 4CVCCh. 4.3 - Prob. 5CVCCh. 4.3 - 6. We can use products in base three to perform...Ch. 4.3 - 7. True or False: Computation in bases other than...Ch. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - 342 five + 413 five _Ch. 4.3 - Prob. 6ECh. 4.3 - In Exercises 1-12, add in the indicated base. 645...Ch. 4.3 - In Exercises 1-12, add in the indicated base. 632...Ch. 4.3 - In Exercises 1-12, add in the indicated base. 6784...Ch. 4.3 - In Exercises 1-12, add in the indicated base.
10....Ch. 4.3 - In Exercises 1-12, add in the indicated base....Ch. 4.3 - In Exercises 1-12, add in the indicated base. 53 B...Ch. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - 475 eight − 267 eight _ _ _ _ _ _ _ _ _ _ _ _ _ _...Ch. 4.3 - In Exercises 13-24, subtract in the indicated...Ch. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - Prob. 30ECh. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - In Exercises 25-34, multiply in the indicated...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - In Exercises 35-38, use the multiplication tables...Ch. 4.3 - In Exercises 35-38, use the multiplication tables...Ch. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - In Exercises 39-46, perform the indicated...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Read the Blitzer Bonus on page 233. Then use the...Ch. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - 56. Describe two difficulties that youngsters...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Make Sense? In Exercises 57-60, determine whether...Ch. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Divide: 31 seven 2426 seven .Ch. 4.3 - 64. Use the Mayan numerals in Table 4.2 on page...Ch. 4.3 - Group members should research various methods that...Ch. 4.3 - 66. Organize a debate. One side represents people...Ch. 4.4 - CHECK POINT 1 Write the following numeral as a...Ch. 4.4 - CHECK POINT 2 Write 2563 as an Egyptian numeral.
Ch. 4.4 - Prob. 3CPCh. 4.4 - CHECK POINT 4 Write MCDXLVII as a Hindu-Arabic...Ch. 4.4 - Prob. 5CPCh. 4.4 - Prob. 6CPCh. 4.4 - Prob. 7CPCh. 4.4 - Prob. 1CVCCh. 4.4 - Prob. 2CVCCh. 4.4 - True or False: Like the system in Exercises 1-2,...Ch. 4.4 - Exercises 4-7 involve Roman numerals. Roman...Ch. 4.4 - Prob. 5CVCCh. 4.4 - Prob. 6CVCCh. 4.4 - Exercises 4-7 involve Roman numerals. Roman...Ch. 4.4 - Prob. 8CVCCh. 4.4 - Prob. 9CVCCh. 4.4 - Prob. 10CVCCh. 4.4 - Prob. 11CVCCh. 4.4 - Fill in the blank so that the resulting statement...Ch. 4.4 - Use Table 4.6 on page 236 to solve Exercises 1-12....Ch. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - In Exercises 13-28, write each Roman numeral as a...Ch. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - In Exercise 29-36, write each Hindu-Arabic numeral...Ch. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - In Exercises 43-48, write each Hindu-Arabic...Ch. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - In Exercises 49-52, write each Ionic Greek numeral...Ch. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Describe how a number is represented in the...Ch. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Make Sense? In Exercises 76-79, determine whether...Ch. 4.4 - Make Sense? In Exercises 76-79, determine whether...Ch. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4 - In Exercises 1-2, evaluate the expression 11 2Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - In Exercises 13-18, convert the numeral to a...Ch. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - In Exercises 25-28, add in the indicated base.
25....Ch. 4 - In Exercises 25-28, add in the indicated base.
26....Ch. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - In Exercises 29-32, subtract in the indicated...Ch. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - 44. Describe how the Egyptian system or the system...Ch. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Use Table 4.8 on page 239 to solve Exercises...Ch. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Describe how the Chinese system or the system in...Ch. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - In Exercises 62-63, write each Hindu-Arabic...Ch. 4 - In Exercises 62-63, write each Hindu-Arabic...Ch. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - 4. Express as a Hindu-Arabic numeral:
Ch. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - 7. Explain why a symbol for zero is needed in a...Ch. 4 - Prob. 8TCh. 4 - 9. Place values in the Mayan system are
Use the...Ch. 4 - In Exercises 10-12, convert the numeral to a...Ch. 4 - In Exercises 10-12, convert the numeral to a...Ch. 4 - In Exercises 10-12, convert the numeral to a...Ch. 4 - In Exercises 13-15, convert each base ten numeral...Ch. 4 - In Exercises 13-15, convert each base ten numeral...Ch. 4 - In Exercises 13-15, convert each base ten numeral...Ch. 4 - Prob. 16TCh. 4 - In Exercises 16-18, perform the indicated...Ch. 4 - In Exercises 16-18, perform the indicated...Ch. 4 - Prob. 19TCh. 4 - Prob. 20TCh. 4 - Use the symbols in the table shown below to solve...Ch. 4 - Prob. 22TCh. 4 - Use the symbols in the table shown below to solve...Ch. 4 - Prob. 24T
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