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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Use the graph of f to determine each of the following. Where applicable, use interval notation.a. the domain of fb. the range of fc. the x-interceptsd. the y-intercepte. interval(s) where f is increasingf. interval(s) where f is decreasingg. the number at which f has a relative maximumh. the
In Exercises 53–54, make a rough sketch in a rectangular coordinate system of the graphs representing the equations in each system.The system, whose graphs are a line with negative slope and a parabola whose equation has a negative leading coefficient, has one solution.
Explain how to find the partial fraction decomposition of a rational expression with a repeated linear factor in the denominator.
In Exercises 87–88, we used the data in a bar graph to develop linear functions that modeled the percentage of never-married American females and males, ages 25–29. For this group exercise, you might find it helpful to pattern your work after Exercises 87 and 88. Group members should begin by
In Exercises 53–54, make a rough sketch in a rectangular coordinate system of the graphs representing the equations in each system.The system, whose graphs are a line with positive slope and a parabola whose equation has a positive leading coefficient, has two solutions.
Find ln 2 using a calculator. Then calculate each of the following: 1-; 1 - + - + 3 1+1-1/2 + 1 - 1 ; .... Describe what you observe.
Explain how to find the partial fraction decomposition of a rational expression with distinct linear factors in the denominator.
Find (f ° g)(x) and (g ° f )(x).
If g(x) = Vx [√x-3 if x ≥ 3 13 - x if x < 3' find g(-1) and g(7).
Research applications of logarithmic functions as mathematical models and plan a seminar based on your group’s research. Each group member should research one of the following areas or any other area of interest: pH (acidity of solutions), intensity of sound (decibels), brightness of stars, human
In Exercises 105–108, evaluate each expression without using a calculator.log2(log3 81)
This group exercise involves exploring the way we grow. Group members should create a graph for the function that models the percentage of adult height attained by a boy who is x years old, f(x) = 29 + 48.8 log(x + 1). Let x = 5, 6, 7,......, 15, find function values, and connect the resulting
In Exercises 135–138, determine whether each statement makes sense or does not make sense, and explain your reasoning.I estimate that log8 16 lies between 1 and 2 because 81 = 8 and 82 = 64.
In Exercises 17–19, use the graph to determinea. The function’s domain;b. The function’s range;c. The x-intercepts, if any;d. The y-intercept, if there is one;e. Intervals on which the function is increasing, decreasing, or constant;f. The missing function values, indicated by question marks,
In Exercises 105–108, evaluate each expression without using a calculator.log(ln e)
Exercises 97–99 will help you prepare for the material covered in the next section.What problem do you encounter when using the switch and- solve strategy to find the inverse of f(x) = 2x ?
In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement.ln e = 0
In Exercises 38–41, determine whether each statement makes sense or does not make sense, and explain your reasoning.According to the Blitzer Bonus on page 278, calculus studies change by analyzing slopes of secant lines over successively shorter intervals.
Each group member should research one situation that provides two different pricing options. These can involve areas such as public transportation options (with or without discount passes), cellphone plans, long-distance telephone plans, or anything of interest. Be sure to bring in all the details
In all exercises, other than Φ, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 1 X 2 V 4
An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The price at which supply and
Perform the operations and write the result in standard form: -20 + √-32 10
An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The price at which supply and
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the x-variable and the y-variable is at most 3. The y-variable added to the product of 4 and the x-variable does not exceed 6.
The graphs show per capita consumption of soda and bottled water in the United States, in gallons, from 2000 through 2015.a. Write the slope-intercept equation of the line that models soda consumption per capita, y, in gallons, x years after 2000.b. Write the slope-intercept equation of the line
The graphs show changing attitudes toward gay marriage for the period from 2001 through 2015.a. Write the slope-intercept equation of the line that models the percentage of the U.S. public that supported gay marriage, y, x years after 2001. Round the value of the slope, m, to one decimal place. If
Find the partial fraction decomposition of 4x² + 5x9 3- 6x-9
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 3 and the x-variable does not exceed 6.
Explain how to solve a nonlinear system using the addition method. Use x2 - y2 = 5 and 3x2 - 2y2 = 19 to illustrate your explanation.
The graphs of solution sets of systems of inequalities involve finding the intersection of the solution sets of two or more inequalities. By contrast, in Exercises 71–72, you will be graphing the union of the solution sets of two inequalities.Graph the union of y > 3/2 x - 2 and y < 4.
Exercises 69–71 will help you prepare for the material covered in the next section.Graph x - y = 3 and (x - 2)2 + (y + 3)2 = 4 in the same rectangular coordinate system. What are the two intersection points? Show that each of these ordered pairs satisfies both equations.
In Exercises 69–72, determine whether each statement makes sense or does not make sense, and explain your reasoning.Without using any algebra, it’s obvious that the nonlinear system consisting of x2 + y2 = 4 and x2 + y2 = 25 does not have real-number solutions.
Exercises 69–71 will help you prepare for the material covered in the next section.Solve by the addition method: 2x + 4y = -4 (3x + 5y = -3.
In Exercises 69–72, determine whether each statement makes sense or does not make sense, and explain your reasoning.I graphed a nonlinear system that modeled the orbits of Earth and Mars, and the graphs indicated the system had a solution with a real ordered pair.
In Exercises 69–70, rewrite each inequality in the system without absolute value bars. Then graph the rewritten system in rectangular coordinates. f|x ≤ 1 X y ≤ 2
Harsh, mandatory minimum sentences for drug offenses account for more than half the population in U.S. federal prisons. The bar graph shows the number of inmates in federal prisons, in thousands, for drug offenses and all other crimes in 1998 and 2010. (Other crimes include murder, robbery, fraud,
Does x2 + y = 10 define y as a function of x?
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the x-variable and the y-variable is no more than 2. The y-variable is no less than the difference between the square of the x-variable and 4.
The bar graph indicates that fewer U.S. adults are getting married.a. Use these models to determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately what percentage of Americans,
Write a system of equations, one equation whose graph is a line and the other whose graph is a parabola, that has no ordered pairs that are real numbers in its solution set. Graph the equations using a graphing utility and verify that you are correct.
68. Given f(x) = 6x + 5 and g(x) = x2 - 3x + 2, find each of the following:a. ( f ° g) (x)b. (g ° f ) (x)c. ( f ° g) (-1).
In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system.The sum of the squares of the x-variable and the y-variable is no more than 25. The sum of twice the y-variable and the x-variable is no less than 5.
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. V/0.64
Evaluate the expression by hand. Check your result with a calculator. -3)³
Use grouping to factor the polynomial. 424 +42³ +2²+ =
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate. a = 60 feet, b = 11 feet
Find the partial fraction decomposition for the rational expression. 3x² + x³ + 5x² - x +4 (x - 1)(x² + 1)²
Evaluate the expression by hand. Check your result with a calculator.
Use grouping to factor the polynomial. 2x³ 3x² + 2x - 3 -
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate. a = 21 feet, b = 11 yards
Find the partial fraction decomposition for the rational expression. -x²8x² + 3x - 10 (x + 2)(x² + 4)²
Find the partial fraction decomposition for the rational expression. -1
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. VII
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. V/0.36
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate. a = 5 centimeters, c = 13 centimeters
Use grouping to factor the polynomial. 8x³2x² + 12x - 3
Evaluate the expression by hand. Check your result with a calculator. 104
Find an exponential model f(x) that describes each situation.A sample of 152 birds decreases in number by 3.4% per week.
Find the partial fraction decomposition for the rational expression. 5x + 10x15x³+4x²+ 13x - 9 x³ + 2x²-3x
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. 16 25
Find the opposite of the polynomial. 7x³
Use grouping to factor the polynomial. 2x²x³ + 4x - 2
Evaluate the expression by hand. Check your result with a calculator. 뚜
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 8(1.12)
Use grouping to factor the polynomial. 2x²5x³+ 10x - 25 -
Evaluate the expression by hand. Check your result with a calculator. 뚜
Find an exponential model f(x) that describes each situation.A mutual fund account contains $2500 and increases by 2.1% per year.
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate. a = 6 meters, c = 15 meters
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 9(1.005)*
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate. b = 7 millimeters, c = 10 millimeters
Find the partial fraction decomposition for the rational expression. 3+5 + 3x² + 3x + рив + F2 X
Find the opposite of the polynomial. -38
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number.
Find an exponential model f(x) that describes each situation.A mutual fund account contains $2500 and increases by 2.1% per year.
Use grouping to factor the polynomial. ab - 3a + 2b - 6
Evaluate the expression by hand. Check your result with a calculator.
Find the opposite of the polynomial. 1925 - 52² + 3z
Use the Pythagorean theorem to find the missing side of the right triangle with legs a and b and hypotenuse c. Then calculate the perimeter. Approximate values to the nearest tenth when appropriate. b = 1.2 miles, c = 2 miles
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x)= 1.5(0.35)*
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. -16
Use grouping to factor the polynomial. 2ax 6bxay + 3by -
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x)= 100(1.23)*
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. -64
Find the opposite of the polynomial. -x²-x+6 9
Find the area of the right triangle that satisfies the conditions. Approximate values to the nearest tenth when appropriate. Legs with lengths 3 feet and 6 feet
Factor the expression completely. x² + 7x + 10
Evaluate the expression by hand. Check your result with a calculator.
Find the opposite of the polynomial. 4- ? - 9
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 0.55*
Find the area of the right triangle that satisfies the conditions. Approximate values to the nearest tenth when appropriate. Hypotenuse 10 inches and leg 6 inches
Factor the expression completely. x² + 3x - 10
Evaluate the expression by hand. Check your result with a calculator. 01
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. 27
Find the opposite of the polynomial. 1 - 8x + 6x²-x³
Factor the expression completely. x² + 8x + 12
For the given f(x), state the initial value, the growth or decay factor, and percent change for each unit increase in x. f(x) = 0.4*
Find the area of the right triangle that satisfies the conditions. Approximate values to the nearest tenth when appropriate. Hypotenuse 15 inches and leg 11 inches
If possible, simplify the expression by hand. If you cannot, approximate the answer to the nearest hundredth. Variables represent any real number. 64
Use the product rule to simplify. -9 .
Subtract the polynomials. (5x-3) (2x + 4)
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