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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Chlorine is frequently used to disinfect swimming pools. The chlorine concentration should remain between 1.5 and 2.5 parts per million. On warm sunny days with many swimmers agitating the water, 30% of the chlorine can dissipate into the air or combine with other chemicals each day.(a) Find C and
Explain how to solve the equation Cax = k symbolically for x. Demonstrate your method.
The Richter scale is used to measure the intensity of earthquakes, where intensity cor- responds to the amount of energy released by an earthquake. If an earthquake has an intensity of x, then its magnitude, as computed by the Richter scale, is given by R(x) = log(x/I0), where I0 is the intensity
Explain how linear and exponential functions differ. Give examples.
If the intensity x of an earthquake increases by a factor of 10, by how much does the Richter number R increase? Generalize your results.
For all types of animals, the percentage that survive into the next year decreases. In one study, the survival rate of a sample of reindeer was modeled by S(t) = 100(0.999993)t5. The function S outputs the percentage of reindeer that survive t years. (a) Evaluate S(4) and S(15). Interpret the
Find the hydrogen ion concentration for the following pH levels of acid rain.(a) 4.92 (pH of rain at Amsterdam Islands) (b) 3.9 (pH of some rain in the eastern U.S.)
The formula D = 160 + 10 log x can be used to calculate loudness of a sound in decibels. Solve the equation for x.
Air pollutants frequently cause acid rain. A measure of the acidity is pH, which ranges between 1 and 14. Pure water is neutral and has a pH of 7. Acidic solutions have a pH less than 7, whereas alkaline solutions have a pH greater than 7. A pH value can be computed by pH = -logx, where x
The faster a locomotive travels, the more horsepower is needed. The formula H(x) = 0.157(1.033)x calculates this horsepower for a level track. The input x is in miles per hour and the output H(x) is the horsepower required per ton of cargo.(a) Evaluate H(30) and interpret the result. (b)
The formula A = P(1 +r/n)nt can be used to calculate the future value of an investment. Solve the equation for t.
Estimate the maximum weight of a plane that can take off from a runway that is 5 thousand feet long.
Heavier aircraft require runways with thicker pavement for landings and takeoffs. A pavement 6 inches thick can accommodate an aircraft weighing 80,000 pounds, whereas a 12-inch-thick pavement is necessary for a 350,000-pound plane. The relation between pavement thickness / in inches and gross
When fossil fuels are burned, carbon is released into the atmosphere. Governments could reduce carbon emissions by placing a tax on fossil fuels. The cost-benefit equation In (1-P) = -0.0034 - 0.0053.x estimates the relationship between a tax of x dollars per ton of carbon and the percent P
There is a relation between an air-plane's weight x and the runway length L required for takeoff. For some airplanes the minimum runway length L in thousands of feet is given by L(x) = 3log.x, where x is measured in thousands of pounds.(a) Evaluate L(100) and interpret the result. (b) If the
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. x + y = 500 -x=y=-500
The figure represents a system of linear equations. Classify the system as consistent or inconsistent. Solve the system graphically and symbolically, if possible. -1 3 x+y=4 3 2x - y = 2
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. 2x - y = -4 -4x + 2y = 8
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. x - 2y = -6 -2x + y = 6
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. - 2x − 3y = 1 x + y = −2
The figure represents a system of linear equations. Classify the system as consistent or inconsistent. Solve the system graphically and symbolically, if possible. 2x+y=-4 2 -x + 2y = 2 ➤X
The figure represents a system of linear equations. Classify the system as consistent or inconsistent. Solve the system graphically and symbolically, if possible. 3x-2y=-2 77 3 3x-2y = 6 X
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. 3x − y = −2 =3x + y = 2 พร
The figure represents a system of linear equations. Classify the system as consistent or inconsistent. Solve the system graphically and symbolically, if possible. - 33x+y=3 1 3x+y=-2 23 X
If possible, solve the system of linear equations and check your answer. x + y = 1 -2x - y = 0
If possible, solve the system of linear equations and check your answer. -2xy = -2 3x + 4y = -7
If possible, solve the system of linear equations and check your answer. x + 3y = 12 3у x-3y = -6
If possible, solve the system of linear equations and check your answer. x + 2y = 0 3x + 7y = 1
If possible, solve the system of linear equations and check your answer. 2x9y-17 8x + 5y = 14
If possible, solve the system of linear equations and check your answer. 3x + 6y = 0 4x - 2y = -5
If possible, solve the system of linear equations and check your answer. 3x - 2y = 5 -6x + 4y = -10
If possible, solve the system of linear equations and check your answer. x - y = -5 x + y =
If possible, solve the system of linear equations and check your answer. -x-=-4 x + 2y = 7 3
If possible, solve the system of linear equations and check your answer. = 끝 - X
If possible, solve the system of linear equations and check your answer. 0.2x 0.1y = 0.5 0.4x + 0.3y = 2.5
If possible, solve the system of linear equations and check your answer. 2x - 7y = 8 -3x+2y = 5
If possible, solve the system of linear equations and check your answer. 100x + 200y = 300 200x + 100y = 0
If possible, solve the system of linear equations and check your answer. 0.6x0.2y = 2 -1.2x + 0.4y = 3
If possible, solve the nonlinear system of equations. x²-y=0 2x + y = 0
If possible, solve the nonlinear system of equations. xy = x + y = 8 6
If possible, solve the nonlinear system of equations. x² - y = 3 x +y = 3
If possible, solve the nonlinear system of equations. 2x - y = 0 2xy = 4
If possible, solve the nonlinear system of equations. x² + y² = 20 y = 2x
If possible, solve the nonlinear system of equations. x² + y² = 9 x +y = 3
If possible, solve the nonlinear system of equations. V √x - 2y = 0 x=y=-2
If possible, solve the nonlinear system of equations. x² - y = 4 x² + y = 4
If possible, solve the nonlinear system of equations. x² + y² = 4 2x² + y = -3
If possible, solve the nonlinear system of equations. 2x² - y = y = 5 -4x² + 2y = -10
If possible, solve the nonlinear system of equations. x² + x = y 2x² - y = 2 =
If possible, solve the nonlinear system of equations. -6√x + 2y = -3 - y = 1 2√x 21
If possible, solve the nonlinear system of equations. x² + y = 4 3x² - y = 0
If possible, solve the nonlinear system of equations. x³ = x= 3y x=y=0
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. x + y = 20 x-y = 8
The area of a rectangle with length 1 and width w is computed by A(1, w) = Iw, and its perimeter is calculated by P(1, w) = 21+ 2w. Assume that I > w and use the method of substitution to solve the system of equations for I and w. A(1, w) = 300 P(1, w) = 70
Write a system of linear equations with two variables whose solution satisfies the problem. State what each variable represents. Then solve the system.The screen of a rectangular television set is 2 inches wider than it is high. If the perimeter of the screen is 38 inches, find its dimensions.
Write a system of linear equations with two variables whose solution satisfies the problem. State what each variable represents. Then solve the system.The sum of two numbers is 300 and their difference is 8. Find the two numbers.
Write a system of linear equations with two variables whose solution satisfies the problem. State what each variable represents. Then solve the system.Admission prices to a movie are $4 for children and $7 for adults. If 75 tickets were sold for $456, how many of each type of ticket were sold?
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. 2x + y = 15 x-y=0
Write a system of linear equations with two variables whose solution satisfies the problem. State what each variable represents. Then solve the system.A sample of 16 dimes and quarters has a value of $2.65. How many of each type of coin are there?
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. 4x + 2y = 10 -2x - y = 10
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. 4x - Зу = 5 3x + 4y = 2
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. 2x + 3y = 5 5x - 2y = 3
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. x + 3y = x-2y = 10 -5
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. 2x + 4y = 7 -x-2y = 5
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. x-3y= 1 2х - бу = 2
Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. Support your results graphically or numerically. 2 2x + 3y = 2 x-2y = -5
Solve the system, if possible. 2x - y = 6 1- = 42 + x²- =
Solve the system, if possible. 2x + 3y = 7 - 3x + 2y = -4
Solve the system, if possible. 7x - 3y = -17 -21x + 9y = 51
Solve the system, if possible. 2х - 3y = 1 3x - 2y = 2
Solve the system, if possible. 5x - 2y = 7 10x - 4y = 6
Use elimination to solve the nonlinear system of equations. x² + y² = 4 2x² + y² = 8
Solve the system, if possible. 7x − 5y = −15 −2x + 3y = -2 F
Solve the system, if possible. x - y = 5 x=y=4
Solve the system, if possible. 0.2x + 0.3y = 8 -0.4x + 0.2y = 0
Use elimination to solve the nonlinear system of equations. x² + y = 12 x² - y = 6 X
Solve the system, if possible. + -2x - 4y = 5
Use elimination to solve the nonlinear system of equations. x² + y² = 4 x² - y² = 4
Use elimination to solve the nonlinear system of equations. x² + 1² = 25 x2 + 7y 37
Approximate, to the nearest thousandth, any solutions to the nonlinear system of equations graphically. x³ - 3x + y = 1 x² + 2y = 3
Use elimination to solve the nonlinear system of equations. x² + 2y = 15 2x² - y = 10
Solve the nonlinear system of equations Symbolically and Graphically. x² + y² = 16 x - y = 0
Solve the nonlinear system of equations Symbolically and Graphically. x² - y = 1 3x + y = -1
Use elimination to solve the nonlinear system of equations. x2 + y² = 36 x2 - бу = 36
Approximate, to the nearest thousandth, any solutions to the nonlinear system of equations graphically. 2x³ - x² = 5y 2-x - y = 0
Solve the nonlinear system of equations Symbolically and Graphically. 12 ху xy = х-у= 4
Approximate, to the nearest thousandth, any solutions to the nonlinear system of equations graphically. x4 - 3x³ = y log x² - y = 0
Approximate, to the nearest thousandth, any solutions to the nonlinear system of equations graphically.x2 + y = 5x + y2 = 6
Approximate, to the nearest thousandth, any solutions to the nonlinear system of equations graphically. e²x + y = 4 In x - 2y = 0
Approximate, to the nearest thousandth, any solutions to the nonlinear system of equations graphically. 3x² + y = 3 (0.3)* + 4y = 1
The weights W1 and W2 exerted on each rafter for the roof truss shown in the figure are determined by the system of linear equations. Solve the system. W₁ + √2W₂ = 300 √3w₁ - √₂w₂ = 0 150 pounds 30° 45° W₂
A box has an open top, rec- tangular sides, and a square base. Its volume is 576 cubic inches, and its outside surface area is 336 square inches. Find the dimensions of the box.
In 2010, the United States consumed 94.58 quadrillion (1015) Btu of energy from renewable and nonrenewable sources. It used 79.44 quadrillion Btu more from nonrenewable sources than from renewable sources.(a) Write a system of equations whose solution gives the consumption of energy from renewable
Break-Even Point The break-even point for a company is where costs equal revenues. Therefore the break-even point is the solution to a system of two equations. For each of the following, C represents cost in dollars to produce x items and R represents revenue in dollars from selling x items.The
The total number of global data breaches involving identity theft in 2014 and 2015 was 1739. There were 95 fewer incidences in 2015 than in 2014.(a) Write a system of equations whose solution represents the incidences of data breaches in each of these years. (b) Solve the system
In 2013, the combined population of Minneapolis/St. Paul, Minnesota, was 695,000. The population of Minneapolis was 105,000 greater than the population of St. Paul.(a) Write a system of equations whose solution gives the population of each city in thousands. (b) Solve the system of
The United States and China together produce 5.9 million tons of e-waste each year. About 0.7 million more tons are produced in the United States than in China. (a) Write a system of equations whose solution represents the amount of e-waste produced in each country. (b) Solve the system
Break-Even Point The break-even point for a company is where costs equal revenues. Therefore the break-even point is the solution to a system of two equa- tions. For each of the following, C represents cost in dollars to produce x items and R represents revenue in dollars from selling x items.C=
Break-Even Point The break-even point for a company is where costs equal revenues. Therefore the break-even point is the solution to a system of two equa- tions. For each of the following, C represents cost in dollars to produce x items and R represents revenue in dollars from selling x items.C =
Find the radius and height of a cylindrical container with a volume of 50 cubic inches and a lateral surface area of 65 square inches.
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