Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137400126
Author: Raymond Barnett, Michael Ziegler
Publisher: PEARSON+
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Chapter 8.2, Problem 17E
In Problems 9–24, find the exact value of each expression without using a calculator.
17.
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Question 1:
If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p =
13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the
column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts)
Solution:
A barometer works based on the principle that the pressure exerted by the liquid column
balances atmospheric pressure. The pressure is given by:
P = pgh
Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the
liquid column is inversely proportional to its density:
Step 1: Given Data
PHg
hol=hgx
Poil
• Density of mercury: PHg = 13.6 g/cm³
Density of oil: Poil = 0.92 g/cm³
• Standard height of mercury at 1.00 atm: hμg
Step 2: Compute Height of Oil
= 760 mm = 0.760 m
13.6
hoil
= 0.760 x
0.92
hoil
= 0.760 × 14.78
hoil
= 11.23 m
Step 3: Compare Heights
Since oil is less dense than mercury, the column of oil must be much taller than that of
mercury. The factor by which it is taller is:
Final…
Chapter 8 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
Ch. 8.1 - Find the degree measure of 1 rad.Ch. 8.1 - Without using a calculator, find: (A)cot 45 (B)cos...Ch. 8.1 - Solve the right triangle in Figure 14. Round side...Ch. 8.1 - Solve the right triangle in Figure 16. Round...Ch. 8.1 - Repeat Example 5 assuming that the man is standing...Ch. 8.1 - Prob. 1EDCh. 8.1 - Prob. 1ECh. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...
Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - In Problems 916, find the trigonometric ratio by...Ch. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - In Problems 916, find the trigonometric ratio by...Ch. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - In Problems 1724, find the exact value without...Ch. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - In Problems 1724, find the exact value without...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - In Problems 3742, use a calculator to find the...Ch. 8.1 - Prob. 40ECh. 8.1 - In Problems 3742, use a calculator to find the...Ch. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Digital display. An 8-foot-tall digital display...Ch. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - An angle above the horizontal is called an angle...Ch. 8.1 - An angle above the horizontal is called an angle...Ch. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.2 - Referring to Figure 2, find (A) sin 180(B)...Ch. 8.2 - Find the exact values without using a calculator....Ch. 8.2 - Find the exact values without using a calculator....Ch. 8.2 - Refer to Example 4. (A)Find the exact value of...Ch. 8.2 - Prob. 1EDCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 4ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 6ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 30ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 33ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 39ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - Prob. 48ECh. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - Prob. 50ECh. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - Find the domain of the tangent function.Ch. 8.2 - Find the domain of the cotangent function.Ch. 8.2 - Find the domain of the secant function.Ch. 8.2 - Prob. 62ECh. 8.2 - Explain why the range of the cosecant function is...Ch. 8.2 - Explain why the range of the secant function is...Ch. 8.2 - Explain why the range of the cotangent function is...Ch. 8.2 - Explain why the range of the tangent function is...Ch. 8.2 - Seasonal business cycle. Suppose that profits on...Ch. 8.2 - Seasonal business cycle. Revenues from sales of a...Ch. 8.2 - Prob. 69ECh. 8.2 - Pollution. In a large city, the amount of sulfur...Ch. 8.2 - Prob. 71ECh. 8.3 - Find each of the following derivatives:...Ch. 8.3 - Find the slope of the graph of f(x) = cos x at...Ch. 8.3 - Find ddxcscx.Ch. 8.3 - Suppose that revenues from the sale of ski jackets...Ch. 8.3 - Prob. 1EDCh. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Prob. 22ECh. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Prob. 26ECh. 8.3 - Find the slope of the graph of f(x) = sin x at x =...Ch. 8.3 - Find the slope of the graph of f(x) = cos x at x =...Ch. 8.3 - Prob. 29ECh. 8.3 - From the graph of y = f'(x) on the next page,...Ch. 8.3 - Prob. 31ECh. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - In Problems 39 and 40, find f(x). 39.f(x) = ex sin...Ch. 8.3 - Prob. 40ECh. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - Prob. 43ECh. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - Profit. Suppose that profits on the sale of...Ch. 8.3 - Revenue. Revenues from sales of a soft drink over...Ch. 8.3 - Physiology. A normal seated adult inhales and...Ch. 8.3 - Pollution. In a large city, the amount of sulfur...Ch. 8.4 - Find the area under the cosine curve y = cos x...Ch. 8.4 - Find cos20tdt.Ch. 8.4 - Find sinxcosxdx.Ch. 8.4 - Prob. 4MPCh. 8.4 - Suppose that revenues from the sale of ski jackets...Ch. 8.4 - Prob. 1ECh. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - Prob. 8ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Prob. 13ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Prob. 18ECh. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Find the shaded area under the cosine curve in the...Ch. 8.4 - Find the shaded area under the sine curve in the...Ch. 8.4 - Use a calculator to evaluate the definite...Ch. 8.4 - Prob. 26ECh. 8.4 - Use a calculator to evaluate the definite...Ch. 8.4 - Prob. 28ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Given the definite integral I=03exsinxdx (A)Graph...Ch. 8.4 - Given the definite integral I=03excosxdx (A)Graph...Ch. 8.4 - Seasonal business cycle. Suppose that profits on...Ch. 8.4 - Seasonal business cycle. Revenues from sales of a...Ch. 8.4 - Pollution. In a large city, the amount of sulfur...Ch. 8 - Convert to radian measure in terms of : (A) 30(B)...Ch. 8 - Evaluate without using a calculator: (A) cos (B)...Ch. 8 - In Problems 36, find each derivative or integral....Ch. 8 - In Problems 36, find each derivative or integral....Ch. 8 - Prob. 5RECh. 8 - In Problems 36, find each derivative or integral....Ch. 8 - Convert to degree measure: (A) /6(B) /4(C) /3(D)...Ch. 8 - Evaluate without using a calculator: (A) sin6(B)...Ch. 8 - Evaluate with the use of a calculator: (A) cos...Ch. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - In Problems 1218, find each derivative or...Ch. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 15RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 17RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 19RECh. 8 - Find the area under the sine curve y = sin x from...Ch. 8 - Given the definite integral I=15sinxxdx (A)Graph...Ch. 8 - Convert 15 to radian measure.Ch. 8 - Evaluate without using a calculator: (A) sin32 (B)...Ch. 8 - Prob. 24RECh. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RE
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