Basic Technical Mathematics with Calculus (11th Edition)
11th Edition
ISBN: 9780134437736
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 4, Problem 95RE
To determine
The time taken to reach the beach.
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1. Let W, U, and S be graphs defined as follows:
• V(W) is the set of countries in the world;
• V(U) is the set of countries in the European Union;
V(S) is the set of countries in the Schengen Area;
● for X = {W,U,S}, E(X) is the set of pairs of countries in V(X) that share a
land border.
Recall that land borders between countries in the Schengen Area are special in that
they can be crossed without a passport.
(a) The notions of a country and a land border are somewhat ambiguous. Explain
the notions you will use to get a precise definition of the graphs W, U, and S.
(b) Is S a subgraph of U? Is U an induced subgraph of W? Justify your answers.
(c) Using non-mathematical language, explain what it means for a country x if
VEV(S) and dw (v) = 0. Give all such countries.
Let A = {v Є V(W) \V(S) such that |Nw(v)| > 0 and Nw (v) ≤ V(S)}.
(d) Using non-mathematical language, explain what the set A represents in terms
of countries and land borders. Give a specific element of A or explain why A…
3. A spreadsheet consists of cells indexed by a row and a column. Each cell contains
either a value or a formula that depends on the values of other cells.
(a) Describe a graph, digraph, or network that models an arbitrary spreadsheet
and allows you to answer the remaining parts of this question.
(b) Explain, by referring to the graph, digraph, or network, when it is possible to
change the value of cell x without changing the value of cell y.
(c) Explain, by referring to the graph, digraph, or network, when it is possible to
calculate the values of all cells in the spreadsheet.
Consider the following spreadsheet with 5 rows, 7 columns, and 35 cells. For exam-
ple, cell el contains a value, whereas cell al contains a formula that depends on the
values cells el and 95.
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b
с
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el+g5
al-c5 110
al+cl 180
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a2+c4 240
a2+c2 120
f5-e2
e3+e5
3
a2+b2 a3-c3 100
a3+c1 200
f5-e3
f1+f2
4 a3+b3 a4+c2 220
a4+c2 100 f5-e4
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130 a5+c5 120 g3+g4 gl+g2
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Chapter 4 Solutions
Basic Technical Mathematics with Calculus (11th Edition)
Ch. 4.1 - Change 17°24′ to decimal form.
Ch. 4.1 - Prob. 2PECh. 4.1 - Prob. 3PECh. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7E
Ch. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - In Exercises 15–18, by means of the definition of...Ch. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - In Exercises 19–22, use a calculator conversion...Ch. 4.1 - In Exercises 19–22, use a calculator conversion...Ch. 4.1 - In Exercises 19–22, use a calculator conversion...Ch. 4.1 - Prob. 22ECh. 4.1 - In Exercises 23–26, use a calculator conversion...Ch. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - In Exercises 31–34, change the given angles to...Ch. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - In Exercises 35–42, draw angles in standard...Ch. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - A windmill rotates 15.6 revolutions in a...Ch. 4.2 - In Example 2, change (3, 4) to (4, 3) and then...Ch. 4.2 - Prob. 2PECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - In Exercises 3–18, find values of the...Ch. 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 - In Exercises 19–26, find the values of the...Ch. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - In Exercises 19–26, find the values of the...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - In Exercises 27-30, each given point is on the...Ch. 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. 4.3 - Find the value of sin 12.5°.
Ch. 4.3 - Find θ if tan θ = 1.039.
Ch. 4.3 - Find the values of cot 56.4°.
Ch. 4.3 - Prob. 4PECh. 4.3 - Prob. 1ECh. 4.3 - In Example 5, change sec 27.82° to csc 27.82° and...Ch. 4.3 - In Exercises 1–4, make the given changes in the...Ch. 4.3 -
In Exercises 1–4, make the given changes in the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - In Exercises 5–20, find the values of the...Ch. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - In Exercises 21–36, find θ for each of the given...Ch. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - In Exercises 41–44, use a calculator to verify the...Ch. 4.3 - Prob. 42ECh. 4.3 - In Exercises 41–44, use a calculator to verify the...Ch. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - In Exercises 51–54, find the values of the...Ch. 4.3 - In Exercises 51–54, find the values of the...Ch. 4.3 - In Exercises 51–54, find the values of the...Ch. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - In Exercises 55–60, solve the given problems.
The...Ch. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.4 - Prob. 1PECh. 4.4 - Prob. 2PECh. 4.4 - Prob. 3PECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 13ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 19ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 29ECh. 4.4 - In Exercises 7–30, solve the right triangles with...Ch. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - In Exercises 31–34, find the part of the triangle...Ch. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - In Exercises 35–38, find the indicated part of the...Ch. 4.4 - Prob. 37ECh. 4.4 - In Exercises 35–38, find the indicated part of the...Ch. 4.4 - Prob. 39ECh. 4.4 - In Exercises 39–42, solve the given problems.
40....Ch. 4.4 - In Exercises 39–42, solve the given problems.
41....Ch. 4.4 - Prob. 42ECh. 4.5 - Find θ if the letters in the road are 2.0 m long,...Ch. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 5ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 8ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - In Exercises 3–44, solve the given problems....Ch. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4 - Prob. 1RECh. 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 - Prob. 16RECh. 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 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - In Exercises 23-28, find the indicated...Ch. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - In Exercises 5–20, find the values of the...Ch. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - In Exercises 29–36, find the values of the...Ch. 4 - In Exercises 29–36, find the values of the...Ch. 4 - Prob. 36RECh. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - Prob. 38RECh. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - In Exercises 37–48, find θ for each of the given...Ch. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - In Exercises 49 and 50, assume θ is an acute angle...Ch. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - In Exercises 51–60, solve the right triangles with...Ch. 4 - In Exercises 51–60, solve the right triangles with...Ch. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 -
In Exercises 61–105, solve the given...Ch. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - The apparent power S in an electric circuit in...Ch. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 93RECh. 4 - Prob. 94RECh. 4 - Prob. 95RECh. 4 - Prob. 96RECh. 4 - Prob. 97RECh. 4 - Prob. 98RECh. 4 - Prob. 99RECh. 4 - In Exercises 61–105, solve the given...Ch. 4 - Prob. 101RECh. 4 - Prob. 102RECh. 4 - Prob. 103RECh. 4 - Prob. 104RECh. 4 - In Exercises 61–105, solve the given...Ch. 4 - Prob. 1PTCh. 4 - Prob. 2PTCh. 4 - Prob. 3PTCh. 4 - Prob. 4PTCh. 4 - Prob. 5PTCh. 4 - Find tan θ in fractional form if (assume θ is...Ch. 4 - Find csc θ if tan θ = 1.294 (assume θ is acute).
Ch. 4 - Prob. 8PTCh. 4 - Prob. 9PTCh. 4 - Prob. 10PTCh. 4 - Prob. 11PTCh. 4 - Prob. 12PTCh. 4 - Prob. 13PTCh. 4 - Prob. 14PTCh. 4 - Prob. 15PT
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- (a) Test the hypothesis. Consider the hypothesis test Ho = : against H₁o < 02. Suppose that the sample sizes aren₁ = 7 and n₂ = 13 and that $² = 22.4 and $22 = 28.2. Use α = 0.05. Ho is not ✓ rejected. 9-9 IV (b) Find a 95% confidence interval on of 102. Round your answer to two decimal places (e.g. 98.76).arrow_forwardLet us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force for using ultrasound was 6.4 pounds with standard deviation 0.3 pounds. Assume that the standard deviations are known. Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null hypothesis, 40 = 0. What level of type II error would you recommend here? Round your answer to four decimal places (e.g. 98.7654). Use a = 0.05. β = i What sample size would be required? Assume the sample sizes are to be equal.…arrow_forward= Consider the hypothesis test Ho: μ₁ = μ₂ against H₁ μ₁ μ2. Suppose that sample sizes are n₁ = 15 and n₂ = 15, that x1 = 4.7 and X2 = 7.8 and that s² = 4 and s² = 6.26. Assume that o and that the data are drawn from normal distributions. Use απ 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ẞ = 0.05 if the true difference in means is - 2? Assume that α = 0.05. (a) The null hypothesis is 98.7654). rejected. The P-value is 0.0008 (b) The power is 0.94 . Round your answer to four decimal places (e.g. Round your answer to two decimal places (e.g. 98.76). (c) n₁ = n2 = 1 . Round your answer to the nearest integer.arrow_forward
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