Explanation Procedure used: Addition or Subtraction of Rational Numbers (Fraction) with unlike denominators: 1. Compute the LCD of the denominators. 2. Write fraction with the LCD as the denominator. 3. Add or subtract the numerators and write the result over the common denominator. 4. Write the result in lowest terms. “ Finding the lowest common denominator ( LCD ) : 1. Find the prime factors of each denominator. 2. For each different prime factor that appears, note the highest power to which it is raised in any one of the denominators. 3. Form the product of all the different prime factors, each raised to the power found in step 2. This product is called the lowest common denominator.” Calculation: From Exercise 57, the given expression is x + 1 x + 1 x 2 − 1 x . Consider the numerator of the expression x + 1 x + 1 . To make the denominators of the fractions equivalent, find the LCD of the denominators. The factors to be considered are 1 and x . Thus, the LCD of the denominators of each fraction is the product of 1 and x . That is, the required LCD is x . To make the resulting denominator in each fraction the LCD, multiply and divide the fraction by the proper quantity. x + 1 x + 1 = x ⋅ 1 + 1 x ⋅ 1 + 1 ⋅ 1 = x ⋅ x x + 1 x ⋅ 1 + 1 ⋅ x x = x 2 x + 1 x + x x Since the denominators of the fractions are same, add the numerators and keep the denominator as it is. x + 1 x + 1 = x 2 + 1 + x x = x 2 + x + 1 x Consider the denominator of the given expression x 2 − 1 x . To make the denominators of the fractions equivalent, find the LCD of the denominators. The factors to be considered are 1 and x . Thus, the LCD of the denominators of each fractions is the product of 1 and x . That is, the required LCD is x . To make the resulting denominator in each fraction equal to the LCD, multiply and divide the fraction by the proper quantity. x 2 − 1 x = x 2 ⋅ 1 − 1 x = x 2 ⋅ x x − 1 x = x 3 x − 1 x Since the denominators of the fractions are same, subtract the numerators and keep the denominator as it is

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6, Problem 73RE

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To perform: The indicated operations in the expression x+1x+1x2−1x and simplify it; check the result by using graphing calculator.

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Chapter 6, Problem 72RE

Chapter 6, Problem 74RE

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The accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Develop line charts for each variable and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). What is the line chart for the variable Fossil Fuels Production?

The accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year Fossil Fuels Production Fossil Fuels Consumption Total Energy Consumption1949 28.748 29.002 31.9821950 32.563 31.632 34.6161951 35.792 34.008 36.9741952 34.977 33.800 36.7481953 35.349 34.826 37.6641954 33.764 33.877 36.6391955 37.364 37.410 40.2081956 39.771 38.888 41.7541957 40.133 38.926 41.7871958 37.216 38.717 41.6451959 39.045 40.550 43.4661960 39.869 42.137 45.0861961 40.307 42.758 45.7381962 41.732 44.681 47.8261963 44.037 46.509 49.6441964 45.789 48.543 51.8151965 47.235 50.577 54.0151966 50.035 53.514 57.0141967 52.597 55.127 58.9051968 54.306 58.502 62.4151969 56.286…

For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Month PercentApr 1972 4.97May 1972 5.00Jun 1972 5.04Jul 1972 5.25Aug 1972 5.27Sep 1972 5.50Oct 1972 5.73Nov 1972 5.75Dec 1972 5.79Jan 1973 6.00Feb 1973 6.02Mar 1973 6.30Apr 1973 6.61May 1973 7.01Jun 1973 7.49Jul 1973 8.30Aug 1973 9.23Sep 1973 9.86Oct 1973 9.94Nov 1973 9.75Dec 1973 9.75Jan 1974 9.73Feb 1974 9.21Mar 1974 8.85Apr 1974 10.02May 1974 11.25Jun 1974 11.54Jul 1974 11.97Aug 1974 12.00Sep 1974 12.00Oct 1974 11.68Nov 1974 10.83Dec 1974 10.50Jan 1975 10.05Feb 1975 8.96Mar 1975 7.93Apr 1975 7.50May 1975 7.40Jun 1975 7.07Jul 1975 7.15Aug 1975 7.66Sep 1975 7.88Oct 1975 7.96Nov 1975 7.53Dec 1975 7.26Jan 1976 7.00Feb 1976 6.75Mar 1976 6.75Apr 1976 6.75May 1976…

Chapter 6 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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To perform: The indicated operations in the expression x + 1 x + 1 x 2 − 1 x and simplify it; check the result by using graphing calculator.

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To perform: The indicated operations in the expression x+1x+1x2−1x and simplify it; check the result by using graphing calculator.

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Chapter 6 Solutions