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All Textbook Solutions for Calculus: An Applied Approach (MindTap Course List)

Plotting Points in the Cartesian Plane In Exercises 1 and 2, plot the points in the Cartesian plane. (2,3),(0,6),(5,1),(4,3),(3,1)Plotting Points in the Cartesian Plane In Exercises 1 and 2, plot the points in the Cartesian plane. (3,4),(1,2),(6,5),(2,0),(5,5)3RE 4RE 5RE 6RE 7RE 8RE 9RE Finding the Midpoint of a Line Segment In Exercises 9-14, find the midpoint of the line segment joining the two points. (-7, 0), (3, 6)11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE 19RE 20RE 21RE 22RE 23RE 24RE 25RE 26RE 27RE 28RE 29RE 30RE 31RE 32RE 33RE 34RE 35RE 36RE 37RE 38RE Finding Points of Intersection In Exercises 37-40, find the point(s) of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y=x3,y=x Finding Points of Intersection In Exercises 37-40, find the point(s) of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y=x3+4x23,y=2x2+27x3 Break-Even Analysis A student organization wants to raise money by having a T-shirt sale. Each shirt costs $8. The silk screening costs $200 for the design, plus $2 per shirt. Each shirt will sell for $14. (a) Find equations for the total cost C and the total revenue R for x shirts. (b) Find the break-even point. (c) How many units would yield a profit of $600?42RE Supply and Demand The demand and supply equations for a cordless screwdriver are given by p=91.40.009xDemandequationp=6.440.008xSupplyequation where p is the price in dollars and x represents the number of units. Find the equilibrium point for this market.Wind Energy The table shows the annual amounts of U.S. consumption W (in trillion Btu) of wind energy for the years 2008 through 2013. (Source: U.S. Energy Information Administration) Year 2008 2009 2010 Consumption 546 721 923 Year 2011 2012 2013 Consumption 1168 1340 1595 Spreadsheet at LarsonAppliedCalculus.com A mathematical model for the data is given by W=0.630t3+24.83t2100.2t+77 where t represents the year, with t=8 corresponding to 2008. (a) Use a graph and a table to compare the actual consumptions with the model. (b) Use the model to predict the consumption in 2019.45RE 46RE 47RE 48RE 49RE 50RE 51RE 52RE 53RE 54RE 55RE 56RE 57RE 58RE 59RE 60RE 61RE 62RE 63RE 64RE 65RE Finding Parallel and Perpendicular Lines In Exercises 65 and 66, find an equation of the line passing through the given point and satisfying the given condition. Point: (1,3) (a) Parallel to the x-axis (b) Perpendicular to the x-axis (c) Parallel to the line 4x+5y=3 (d) Perpendicular to the line 5x2y=3 Demand When a wholesaler sold a product at $32 per unit, sales were 750 units per week. After a price increase of $5 per unit, the sales dropped to 700 units per week. Assume that the relationship between the price p and the units sold per week x is linear. (a) Write a linear equation expressing x in terms of p. (b) Predict the number of units sold per week at a price of $34.50 per unit. (c) Predict the number of units sold per week at a price of $42 per unit.Linear Depreciation A printing company purchases an advanced color copier/printer for $117,000. After 9 years, the equipment will be obsolete and have no value. (a) Write a linear equation giving the value v (in dollars) of the equipment in terms of the time t (in years), 0t9. (b) Use a graphing utility to graph the equation. (c) Move the cursor along the graph and estimate (to two-decimal-place accuracy) the value of the equipment after 4 years. (d) Move the cursor along the graph and estimate (to two-decimal-place accuracy) the time when the value of the equipment will be $84,000.69RE 70RE 71RE 72RE 73RE 74RE 75RE 76RE 77RE 78RE 79RE 80RE 81RE 82RE 83RE 84RE 85RE 86RE 87RE 88RE 89RE 90RE 91RE 92RE 93RE 94RE 95RE 96RE 97RE 98RE 99RE 100RE 101RE 102RE 103RE 104RE 105RE 106RE 107RE 108RE 109RE 110RE 111RE 112RE 113RE 114RE 115RE Determining Continuity In Exercises 111122, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied. f(x)=x+12x+2 117RE 118RE 119RE 120RE 121RE 122RE 123RE 124RE 125RE Salary Contract A union contract guarantees a 3.5% yearly salary increase for 2 years. For a current salary of $40,000, the salaries S for the next 3 years are given by S(t)={ 41,400,1t242,849,2t340,000,0t1 where t = 0 represents the present year. Does the limit of S exist as t approaches 2? Explain your reasoning.127RE 128RE 1TYS 2TYS 3TYS The demand and supply equations for a product are p = 65 2.1x and p = 43 + 1.9x, respectively, where p is the price (in dollars) and x represents the number of units (in thousands). Find the equilibrium point for this market.5TYS 6TYS 7TYS 8TYS 9TYS 10TYS 11TYS 12TYS 13TYS 14TYS 15TYS 16TYS 17TYS 18TYS 19TYS 20TYS 21TYS 22TYS Plot the points (3,2),(4,2),(3,1),(0,2),and(1,2). iStockphoto.com/Gradyreese The numbers E (in thousands of people) of employees in the consumer lending industry in the United States from 2005 through 2013 are shown in the table, where t represents the year. Sketch a scatter plot of the data. (Source: U.S. Bureau of Labor Statistics) t 2005 2006 2007 2008 2009 2010 2011 2012 2013 E 113 118 119 110 97 91 87 91 95 Spreadsheet at Larson Applied Calulus.com Find the distance between the points (-2, 1) and (2, 4).Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.com Use the Distance Formula to show that the points (2, 1), (5, 5), and (6, 3) are vertices of a right triangle. The figures provided with Examples 3 and 4 were not really essential to the solution. Nevertheless, it is strongly recommended that you develop the habit of including sketches with your solutionseven when they are not required.Checkpoint 5 Worked-out solution available at LarsonAppliedCalculus.com A quarterback throws a pass from the 10-yard line, 10 yards from one sideline. The pass is caught by a wide receiver on the 30-yard line, 25 yards from the same sideline. How long is the pass?Checkpoint 5 Worked-out solution available at LarsonAppliedCalculus.com Find the midpoint of the line segment joining the points (-6, 2) and (2, 8).Checkpoint 5 Worked-out solution available at LarsonAppliedCalculus.com Kellogg Company had annual sales of about $13.2 billion in 2011 and about $14.8 billion in 2013. Without knowing any additional information, estimate the 2012 annual sales. (Source: Kellogg Co.)Find the vertices of the parallelogram in Example 8 after it has been translated two units to the left and four units down.In Exercises 1-6, simplify the expression. 5+(4)2 In Exercises 1-6, simplify the expression. 3+(1)2 In Exercises 1-6, simplify the expression. (36)2+[ 1(5) ]2 4SWU In Exercises 1-6, simplify the expression. 27+12 6SWU In Exercises 7-10, solve for x or y. x+(5)2=7 8SWU In Exercises 7-10, solve for x or y. (3x)2+(74)2=45 10SWU Plotting Points in the Cartesian Plane In Exercises 1 and 2, plot the plot the points in the Cartesian plane. See Example 1. (5,3),(1,1),(2,4),(2,0),(1,4)Plotting Points in the Cartesian Plane In Exercises 1 and 2, plot the points in the Cartesian plane. See Example 1. (0,4),(5,1),(3,5),(2,2),(6,1)Finding a Distance and the Midpoint of a Line Segment In Exercises 3-12, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. See Examples 1, 3 and 6. (3,1),(5,5)4E 5E 6E Findding a Distance and the Midpoint of a Line Segment In Exercises 3-12, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. See Examples 1, 3 and 6. (2,12),(8,4)8E Findding a Distance and the Midpoint of a Line Segment In Exercises 3-12, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. See Examples 1, 3 and 6. (12,1), (32,5)Finding a Distance and the Midpoint of a Line Segment In Exercises 3-12, (a) plot the points, (b) find the distance between the points, (b) find the distance between the point, and (c) find the midpoint of the line segment joining the points. See Examples 1, 3, and 6. (23,13),(56,1)11E Finding a Distance and the Midpoint of a Line Segment In Exercises 3-12, (a) plot the points, (b) find the distance between the points, (b) find the distance between the point, and (c) find the midpoint of the line segment joining the points. See Examples 1, 3, and 6. (5.2,6.4),(2.7,1.8)Verifying a Right Triangle In Exercises 13-16, (a) find the length of each side of the right triangle and (b) show that these lengths satisfy the Pythagorean Theorem. See Example 4.14E Verifying a Right Triangle In Exercises 13-16, (a) find the length of each side of the right triangle and (b) show that these lengths satisfy the Pythagorean Theorem. See Example 4.Verifying a Right Triangle In Exercises 13-16, (a) find the length of each side of the right triangle and (b) show that these lengths satisfy the Pythagorean Theorem. See Example 4.Verifying a Polygon In Exercises 1720, show that the points form the vertices of the indicated polygon. (A rhombus is a quadrilateral whose sides have the same length.) Right triangle: (0, 1), (3, 7), (4, -1)Verifying a Polygon In Exercises 1720, show that the points form the vertices of the indicated polygon. (A rhombus is a quadrilateral whose sides have the same length.) Isosceles triangle: (1, -3), (3, 2), (-2, 4)19E 20E Finding Values In Exercises 21 and 22, find the value(s) of x such that the distance between the points is 5. (1,0),(x,4)Finding Values In Exercises 21 and 22, find the value(s) of x such that the distance between the points is 5. (2,1),(x,2)Finding Values In Exercises 23 and 24, find the value(s) of y such that the distance between the points is 8. (3,0),(5,y)24E Sports A soccer player passes the ball from a point that is 18 yards from an endline and 12 yards from a sideline. The pass is received by a teammate who is 42 yards from the same endline and 50 yards from the same sideline, as shown in the figure. How long is the pass?Sports The first soccer player in Exercise 25 passes the ball to another teammate who is 37 yards from the same endline and 33 yards from the same sideline. How long is the pass?27E 28E Dow Jones Industrial Average The graph shows the Dow Jones Industrial Average for common stocks. (Source: SP Dow Jones Indices LLC) (a) Estimate the Dow Jones Industrial Average for March 2013, July 2013, and July 2014. (b) Estimate the percent increase or decrease in the Dow Jones Industrial Average from December 2013 to January 2014.Home Sales The graph shows the median sales prices (in thousands of dollars) of existing one-family homes sold in the United States from 2006 through 2013. (Source: National Association of Realtors) (a) Estimate the median sales prices of existing one-family homes for 2007, 2009, and 2012. (b) Estimate the percent increase or decrease in the median value of existing one-family homes from 2011 to 2012.Revenue and Profit The revenues and profits of Buffalo Wild Wings for 2011 and 2013 are shown in the table. (a) Use the Midpoint Formula to estimate the revenue and profit in 2012. (b) Then use your schools library, the Internet, or some other reference source to find the actual revenue and profit for 2012. (c) Did the revenue and profit increase in a linear pattern from 2011 to 2013? Explain your reasoning. (d) What were the expenses during each of the given years? (e) How would you rate the growth of Buffalo Wild Wings from 2011 to 2013? (Source: Buffalo Wild Wings, Inc.) Year 2011 2012 2013 Revenue (millions of $) 784.5 1266.7 Profit (millions of $) 50.4 71.6 Revenue and Profit The revenues and profits of Walt Disney Company for 2011 and 2013 are shown in the table. (a) Use the Midpoint Formula to estimate the revenue and profit in 2012. (b) Then use your schools library, the Internet, or some other reference source to find the actual revenue and profit for 2012. (c) Did the revenue and profit increase in a linear pattern from 2011 to 2013? Explain your reasoning. (d) What were the expenses during each of the given years? (e) How would you rate the growth of Walt Disney Company from 2011 to 2013? (Source: Walt Disney Company) Year 2011 2012 2013 Revenue (billions of $) 40.9 45.0 Profit (billions of $) 4.8 6.1 33E 34E 35E 36E Using the Midpoint Formula Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining (x1, y1) and (x2, y2) into four equal parts.Using the Midpoint Formula Use Exercise 37 to find the points that divide the line segment joining the given points into four equal parts. (a) (1,2),(4,1) (b) (2,3),(0,0)Using the Midpoint Formula Show that (13[ 2x1+x2 ],13[ 2y1+y2 ]) is one of the points of trisection of the line segment joining (x1,y1) and (x2,y2) Then, find the second point of trisection by finding the midpoint of the line segment joining (13[ 2x1+x2 ],13[ 2y1+y2 ]) and (x2,y2)Using the Midpoint Formula Use Exercise 39 to find the points of trisection of the line segment joining the given points. (a) (1,2),(4,1) (b) (2,3),(0,0)Sketch the graph of y=2x1.2CP 3CP 4CP How many units must the company in Example 5 sell to break even when the selling price is $1.45 per unit?The demand and supply equations for a streaming-media device are p=1133.5xDemandequationp=89+2.5xSupplyequation where p is the price in dollars and x represents the number of units in millions. Find the equilibrium point for this market.7CP 1SWU 2SWU 3SWU 4SWU 5SWU 6SWU 7SWU 8SWU In Exercises 7-10, evaluate the expression for the given value of x. ExpressionxValuey=4x27x=0.5 10SWU 11SWU 12SWU 13SWU 14SWU Matching In Exercises 1-6, match the equation with its graph. [The graphs are labeled (a)-(f).] y=x2 2E Matching In Exercises 1-6, match the equation with its graph. (The graphs are labeled (a)-(f).] y=x2+2x 4E Matching In Exercises 1-6, match the equation with its graph. (The graphs are labeled (a)-(f).] y=| x |2 6E 7E 8E 9E Sketching the Graph of an Equation in Exercises 7-22, sketch the graph of the equation. Use a graphing utility to verify your results. See Examples 1 and 2. y=x2+6 11E 12E 13E 14E 15E Sketching the Graph of an Equation In Exercises 7-22, sketch the graph of the equation. Use a graphing utility to verify your results. See Examples 1 and 2. y=x+4 17E 18E Sketching the Graph of an Equation in Exercises 7-22, sketch the graph of the equation. Use a graphing utility to verify your results. See Examples 1 and 2. y=1x3 20E 21E 22E 23E 24E Finding x- and y-Intercepts In Exercises 2332, find the x- and y-intercepts of the graph of the equation. See Example 3. y=x2+x2 26E 27E 28E Finding x- and y-Intercepts In Exercises 2332, find the x- and y-intercepts of the graph of the equation. See Example 3. y=x24x2 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E Finding Points of Intersection In Exercises 41-48, find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y=x+2,y=2x1 Finding Points of Intersection In Exercises 41-48, find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y=x+7,y=32x8 Finding Points of Intersection In Exercises 41-48, find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y=x2+15,y=3x+11 44E 45E Finding Points of Intersection In Exercises 41-48, find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y=x,y=x Finding Points of Intersection In Exercises 41-48, find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y=x42x2+1,y=1x2 48E Finding a Break-Even Point In Exercises 49-54, C represents the total cost (in dollars) of producing x units of a product and R represents the total revenue (in dollars) from the sale of X units. How many units must the company sell to break even? See Example 5. C=0.85x+35,000,R=1.55x 50E Finding a Break-Even Point In Exercises 49-54, C represents the total cost (in dollars) of producing x units of a product and R represents the total revenue (in dollars) from the sale of X units. How many units must the company sell to break even? See Example 5. C=8650x+250,000,R=9950x 52E 53E 54E Break-Even Analysis You are setting up a part-time business with an initial investment of $21,000. The unit cost of the product is $11.50, and the selling price is $19.90. (a) Find equations for the total cost C (in dollars) and total revenue R (in dollars) for x units. (b) Find the break-even point by finding the point of intersection of the cost and revenue equations. (c) How many units would yield a profit of $1000?Break-Even Analysis A 2015 Toyota Camry costs $33,500 with a gasoline engine. A 2015 Toyota Avalon costs $36,775 with a hybrid engine. The Camry gets 31 miles per gallon of gasoline and the Avalon gets 39 miles per gallon of gasoline. Assume that the price of gasoline is $2.759. (Source: Toyota Motor Sales, U.S.A., Inc. and U.S. Energy Information Administration) (a) Show that the cost Cg (in dollars) of driving the Toyota Camry x miles is Cg=33,500+2.759x31 and the cost Ch (in dollars) of driving the Toyota Avalon x miles is Ch=36,775+2.759x39 (b) Find the break-even point. That is, find the mileage at which the hybrid-powered Toyota Avalon becomes more economical than the gasoline- powered Toyota Camry.Supply and Demand The demand and supply equations for an MP3 player are given by p=2054xDemandequationp=1353xSupplyequation where p is the price (in dollars) and x represents the number of units (in hundreds of thousands). Find the equilibrium point for this market.Supply and Demand The demand and supply equations for an MP3 player are given by p=19015xDemandequationp=75+8xSupplyequation where p is the price (in dollars) and x represents the number of units (in hundreds of thousands). Find the equilibrium point for this market.E-Book Revenue The table shows the annual revenues (in billions of dollars) of e-books in the United States from 2009 through 2013. (Source: Statista) Year 2009 2010 2011 2012 2013 Revenue 0.82 1.52 2.31 3.35 4.52 A mathematical model for the data is given by y=0.00333t30.0250t2+0.252t1.85, where y is the annual revenue (in billions of dollars) and t is the year, with t = 9 corresponding to 2009. (a) Use a graph and a table to compare the data with the model. (b) Use the model to predict the revenue in 2018.HOW DO YOU SEE IT? The graph shows the cost and revenue equations for a product. (a) For what number of units sold does the company break even? (b) For what numbers of units sold is there a loss for the company? (c) For what numbers of units sold is there a profit for the company?Making a Conjecture Use a graphing utility to graph the equation y=cx+1forc=1,2,3,4, and 5. Then make a conjecture about the x-coefficient and the graph of the equation.64E 65E 66E 67E 68E 69E Finding Intercepts In Exercises 6570, use a graphing utility to graph the equation and approximate the x- and y-intercepts of the graph. y=0.4x5.30.4x2+5.3 Sketch the graph of each linear equation. a. y=4x2 b. x=1 c. 2x+y=6 The business in Example 2 installs a second ramp that rises 27 inches over a horizontal length of 26 feet. Is the ramp steeper than recommended?A small business determines that the value of a digital copier t years after its purchase is V = 300t + 1500. Describe the practical significance of the y-intercept and slope of the line given by this equation.

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