Section P.3, problem 94.
In the solutions guide, the sentence..."If p = 65, x = 45 units." Should be "If p = 655, x = 45 units."
Section P.4, problems 65 and 66.
A factorization is not reasonably possible so skip the algebraic solution and solve the equation by graphing.
Section P.4, problem 74.
In the solutions guide, the technique used in factoring is not one that is known at this time. Please omit the problem.
Section P.4, problem 80.
The method for solving the system of equations algebraically is presented later in the textbook, so please omit that part of the problem.
Section P.5, problem 54(b).
Please omit this problem. To this point, students have not learned a method that can be used to factor the resulting polynomial and a method that can be used is not presented until later in the textbook.
Chapter P Review Exercises, #100.
The answers are correct but the factorization in the third step in the solutions guide is incorrect. Here are all the steps.
216x4 - x = 0
x(216x3 - 1) = 0
x(6x - 1)(36x2 + 6x + 1) = 0
x = 0,1/6
Section 1.4, #86.
In the solutions guide, replace the equal sign under the radical with a plus sign.
Chapter 1 Test, #7.
Omit this problem from the test because it contains a trick that I would not expect students to catch. The trick has to do with window settings necessary to see the curves in the graph. Here are the window settings that work.
Xmin = -1
Xmax = 1
and here's the real kicker ...
Ymin = -.1
Ymax = .1
Chapter 1 Test, #14.
Omit the problem because there is a mistake in the solutions guide and because there were no examples containing this degree of sophistication.
Chapter 1 Test, #21.
The domain should be 0 < x ≤ 25 because when x is greater than 25 it will no longer be the shortest side of the rectangle.
Section 2.4, #77.
There is a mistake beginning with the third term in the sequence. The steps below describe how to generate the third term.
Each term is generated using the idea...
(previous term)2 + (previous term)
The previous term is -3/16 + (1/4)i which I write as -3/16 + i/4 to make the calculations easier. The next term is...
(-3/16 + i/4)2 + (-3/16 + i/4)
9/256 + 2(-3/16)(i/4) + i2/16 - 3/16 + i/4
9/256 + 2(-3/16)(i/4) - 1/16 - 3/16 + i/4
Put like terms next to each other to see the collections easier...
9/256 - 1/16 - 3/16 - 3i/32 + i/4
9/256 - 4/16 - 3i/32 + i/4
9/256 - 64/256 - 3i/32 + 8i/32
-55/256 + 5i/32
Section 2.5, #40.
In the solutions guide, the exponent on the first binomial should be understood 1 rather than 2.
Chapter 2 Review Exercises, problem 5.
In the solutions guide, the sign in the binomial squared should be plus rather than minus and the first-coordinate of the vertex should be -5/2 rather than 5/2.
Section 3.2, #72.
In the solutions guide, the answer should be 21,351 ft-lb rather than 21,351 ft-16.
Section 3.5, #67.
Change the coefficient of the given formula from -1.0 to -2.5 so that the problem in the text corresponds with the solution in the solutions guide.
Chapter 3 Test, problem 1.
The problem may be counted correct if the student describes a transformation graphically in which the graph of 2^x is reflected in the y-axis, moved one unit to the left, and moved down 3 units. Those transformations seem to be indicated by the function.
However, that is not the correct interpretation. We did not study the combination of reflection in the y-axis and horizontal shift in the same problem so an incorrect interpretation is likely.
A correct interpretation is possible by manipulating the exponent from -x + 1 to -(x-1). In that form the thought process for transformations is
1. Consider 2^x.
2. 2^(x-1) moves the graph one unit to the right.
3. 2^[-(x-1)] reflects the y-axis.
4. 2^[-(x-1)] - 3 moves the graph down 3.
Cumulative Test for Chapters 1-3, #22.
The function listed should be f(x) = 2x4 + 5x3 + 5x2 + 20x - 20.
Section 4.4, #124.
The problem does not appear in the solutions manual.
Draw a right triangle and label one of the acute angles theta.
Since cos θ = 2/9, label the side adjacent to theta 2 and the hypotenuse 9. Use the Pythagorean Theorem to solve for the third side. It turns out to be the square root of 77. Label the side opposite theta the square root of 77.
sin θ = sqrt 77 / 9
tan θ = sqrt 77 / 2
cot θ = 2 / sqrt 77
sec θ = 9 / 2
csc θ = 9 / sqrt 77
Section 4.5, problem 83.
In the solutions guide, the equation listed is incorrect. The regression equation is of the form
y = a sin(bx + c) + d
a = 2.445783614
b = 0.4786424479
c = 1.579779881
d = 3.364812504
Section 4.8, problem 25.
In the solutions guide, the problem is solved incorrectly. The length of the hypotenuse (denominator) should be 13,800 miles rather than 4,150 miles. The angle theta should be 16.85 degrees and the angle alpha should be 73.15 degrees.
Section 5.4, problem 65.
The answer in the solutions guide is not the same as the suggested answer in the text. The answer in the solutions guide should contain t in the first fraction and 2x in the second fraction.
Section 6.3, problem 2.
In the solutions guide, the coordinates of the terminal point should be used first in the calculations of u and v.
Chapter 6, Practice Test in the Solutions Guide (page 590), #8.
The answer should read 109.442 mi. rather than 190.442 mi.
Chapter 4-6 Cumulative Test in the Solutions Guide (page 639).
The problem listed as #47 should be #46. There is no problem number 47.
Section 7.2, problem 65.
In the Solutions Guide, the second equation should begin with a factor of 3 rather than 6.
Section 7.2, problem 66.
There are actually two mistakes in the solutions guide, one mistake in each equation. In equation one, notice that both variable terms become negative in the second group of equations, but only the x-term should be negative.
The second equation is set up incorrectly. Since the airplanes are traveling in opposite directions, it is the sum of their distances which will be 3200 miles after 2 hours. Therefore, the second equation should be 2x + 1.5y = 3200.
Section 7.2, even-numbered problems from #70-78.
All of these problems are set up incorrectly in the solutions guide. Just a quick glance at the first equation in each problem reveals they are set up as differences when, in fact, they should all be sums. Please select the odd-numbered problems only in this group.
Section 7.2, problems from #90-93.
Page 598 Textbook, Advanced Applications. These problems are optional. These system of equations are from a course in differential equations, which is Calculus IV in college. Problems 90 and 92 are not supported on pages 988 and 989 in the solutions guide. But problems 91 and 93 are supported in the solutions guide on pages 348-349.
Section 7.2, problems from #94-108.
Page 508 Textbook, Review. The solutions for these textbook problems are reflected in the solutions guide as a problem number that is two less than the number in the textbook. For example, Precalculus 7.2, problem 96 in the textbook is supported as problem 94 in the solutions guide etc. This continues through textbook section 7.2, where problem 108 is supported as problem 106 in the solutions guide.
Section 7.4, problem 11.
Notice that once A and B are replaced with expressions, the two fractions are the same no matter how you decide to work it. The order of the fractions may be different, but the overall problem is the same so it doesn't matter whether A is over x, or over 2x + 1.
Section 10.6, problem 78.
Change the word "some" in the problem to "any" and in the solutions guide the answer should be true.
Cumulative Test, Chapters 7-10, problems 27 and 39.
>>problem 27. In the solutions guide, the values of A and C are listed incorrectly. The correct values are A=1 and C=2.
>>problem 39. The second vertex should be (-2, 0) rather than (2, pi).
Chapter 11 Test, problem 16.
Please omit the problem unless you have a calculator capable of 3-dimensional graphing.
Section 11.2, problems 56,58,60,62.
In the solutions guide, equal signs have been replaced with plus signs.
Section 11.3, problems 2,4,6,8.
In the solutions guide, equal signs have been replaced with plus signs.
Section 12.3, problem 39.
In the solutions guide, the answers to parts (b) and (c) should be in dollars and not billions of dollars.
You may use the calculator anytime for most of the problems. However, there will be times when answers will need to be in "exact form", which means that radicals should not be estimated using a calculator.