Precalculus Enhanced with Graphing Utilities Plus MyLab Math with Pearson eText - Access Card Package (7th Edition) (Sullivan & Sullivan Precalculus Titles)
7th Edition
ISBN: 9780134265148
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Textbook Question
Chapter 8.4, Problem 42AE
Geometry See the figure, which shows a circle of radius with center at . Find the area of the shaded region as a function of the central angle .
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Precalculus Enhanced with Graphing Utilities Plus MyLab Math with Pearson eText - Access Card Package (7th Edition) (Sullivan & Sullivan Precalculus Titles)
Ch. 8.1 - In a right triangle, if the length of the...Ch. 8.1 - If is an acute angle, solve the equation tan= 1 2...Ch. 8.1 - If is an acute angle, solve the equation sin= 1 2...Ch. 8.1 - True or False sin 52 =cos 48Ch. 8.1 - The sum of the measures of the two acute angles in...Ch. 8.1 - When you look up at an object, the acute angle...Ch. 8.1 - True or False In a right triangle, if two sides...Ch. 8.1 - True or False In a right triangle, if we know the...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...
Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - Prob. 16SBCh. 8.1 - Prob. 17SBCh. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - Prob. 19SBCh. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - Prob. 21SBCh. 8.1 - Prob. 22SBCh. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 19-28, find the exact value of each...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - Geometry The hypotenuse of a right triangle is 5...Ch. 8.1 - Geometry The hypotenuse of a right triangle is 3...Ch. 8.1 - Geometry A right triangle has a hypotenuse of...Ch. 8.1 - Geometry A right triangle has a hypotenuse of...Ch. 8.1 - Geometry A right triangle contains a 25 angle. (a)...Ch. 8.1 - Geometry A right triangle contains an angle of 8...Ch. 8.1 - Finding the Width of a Gorge Find the distance...Ch. 8.1 - Finding the Distance across a Pond Find the...Ch. 8.1 - The Eiffel Tower The tallest tower built before...Ch. 8.1 - Finding the Distance of a Ship from Shore A person...Ch. 8.1 - Finding the Distance to a Plateau Suppose that you...Ch. 8.1 - Finding the Reach of a Ladder A 22-foot extension...Ch. 8.1 - Finding the Angle of Elevation of the Sun At 10 AM...Ch. 8.1 - Directing a Laser Beam A laser beam is to be...Ch. 8.1 - Finding the Speed of a Truck A state trooper is...Ch. 8.1 - Security A security camera in a neighborhood bank...Ch. 8.1 - Parallax One method of measuring the distance from...Ch. 8.1 - Parallax See Problem 59. 61 Cygni, sometimes...Ch. 8.1 - Washington Monument The angle of elevation of the...Ch. 8.1 - Finding the Length of a Mountain Trail A straight...Ch. 8.1 - Finding the Bearing of an Aircraft A DC-9 aircraft...Ch. 8.1 - Prob. 64AECh. 8.1 - Niagara Falls Incline Railway Situated between...Ch. 8.1 - Willis Tower Willis Tower in Chicago is the second...Ch. 8.1 - Constructing a Highway A highway whose primary...Ch. 8.1 - Photography A camera is mounted on a tripod 4 feet...Ch. 8.1 - Finding the Distance between Two Objects A blimp,...Ch. 8.1 - Hot-Air Balloon While taking a ride in a hot-air...Ch. 8.1 - Mt. Rushmore To measure the height of Lincoln’s...Ch. 8.1 - The CN Tower The CN Tower, located in Toronto,...Ch. 8.1 - Chicago Skyscrapers The angle of inclination from...Ch. 8.1 - Estimating the Width of the Mississippi River A...Ch. 8.1 - Finding the Pitch of a Roof A carpenter is...Ch. 8.1 - Shooting Free Throws in Basketball The eyes of a...Ch. 8.1 - Geometry Find the value of the angle in degrees...Ch. 8.1 - Surveillance Satellites A surveillance satellite...Ch. 8.1 - Calculating Pool Shots A pool player located at X...Ch. 8.1 - One World Trade Center One World Trade Center...Ch. 8.1 - Explain how you would measure the width of the...Ch. 8.1 - Explain how you would measure the height of a TV...Ch. 8.1 - The Gibb’s Hill Lighthouse, Southampton, Bermuda...Ch. 8.1 - Determine whether x3 is a factor of x 4 +2 x 3 21...Ch. 8.1 - Find the exact value of sin15 . Hint: 15=4530Ch. 8.1 - Prob. 86RYKCh. 8.1 - Solve 2 sin 2 sin1=0 for 02 .Ch. 8.2 - The difference formula for the sine function is...Ch. 8.2 - If is an acute angle, solve the equation cos= 3 2...Ch. 8.2 - The two triangles shown are similar. Find the...Ch. 8.2 - If none of the angles of a triangle is a right...Ch. 8.2 - For a triangle with sides a, b, c and opposite...Ch. 8.2 - True or False An oblique triangle in which two...Ch. 8.2 - True or False The Law of Sines can be used to...Ch. 8.2 - Triangles for which two sides and the angle...Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 9-16, solve each triangle.Ch. 8.2 - In Problems 17-24, solve each triangle. A= 40 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. A= 50 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. B= 70 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. A= 70 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. A= 110 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. B= 10 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. A= 40 ,...Ch. 8.2 - In Problems 17-24, solve each triangle. B= 20 ,...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - Finding the Length of a Ski Lift Consult the...Ch. 8.2 - Finding the Height of a Mountain Use the...Ch. 8.2 - Finding the Height of an Airplane An aircraft is...Ch. 8.2 - Finding the Height of the Bridge over the Royal...Ch. 8.2 - Land Dimensions A triangular plot of land has one...Ch. 8.2 - Distance between Runners Two runners in a marathon...Ch. 8.2 - Landscaping Pat needs to determine the height of a...Ch. 8.2 - Construction A loading ramp 10 feet long that...Ch. 8.2 - Prob. 45AECh. 8.2 - Prob. 46AECh. 8.2 - Rescue at Sea Coast Guard Station Able is located...Ch. 8.2 - Prob. 48AECh. 8.2 - Finding the Lean of the Leaning Tower of Pisa The...Ch. 8.2 - Crankshafts on Cars On a certain automobile, the...Ch. 8.2 - Constructing a Highway A highway whose primary...Ch. 8.2 - Calculating Distances at Sea The navigator of a...Ch. 8.2 - Designing an Awning An awning that covers a...Ch. 8.2 - Finding Distances A forest ranger is walking on a...Ch. 8.2 - Prob. 55AECh. 8.2 - Determining the Height of an Aircraft Two sensors...Ch. 8.2 - The Original Ferris Wheel George Washington Gale...Ch. 8.2 - Mollweides Formula For any triangle, Mollweides...Ch. 8.2 - Mollweides Formula Another form of Mollweides...Ch. 8.2 - For any triangle, derive the formula a=bcosC+ccosB...Ch. 8.2 - Law of Tangents For any triangle, derive the Law...Ch. 8.2 - Prob. 64AECh. 8.2 - Make up three problems involving oblique...Ch. 8.2 - What do you do first if you are asked to solve a...Ch. 8.2 - What do you do first if you are asked to solve a...Ch. 8.2 - Solve Example 6 using right-triangle geometry....Ch. 8.2 - Solve: 3 x 3 +4 x 2 27x36=0Ch. 8.2 - Find the exact distance between P 1 =( 1,7 ) and P...Ch. 8.2 - Find the exact value of tan[ cos 1 ( 7 8 ) ] .Ch. 8.2 - Graph y=4sin( 1 2 x ) . Show at least two periods.Ch. 8.3 - Write the formula for the distance d from P 1 =( x...Ch. 8.3 - If is an acute angle, solve the equation cos= 2 2...Ch. 8.3 - If three sides of a triangle are given, the Law of...Ch. 8.3 - If one side and two angles of a triangle are...Ch. 8.3 - If two sides and the included angle of a triangle...Ch. 8.3 - True or False Given only the three sides of a...Ch. 8.3 - True or False The Law of Cosines states that the...Ch. 8.3 - True or False A special case of the Law of Cosines...Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 9-16, solve each triangle.Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , b=4...Ch. 8.3 - In Problems 17-32, solve each triangle. a=2 , c=1...Ch. 8.3 - In Problems 17-32, solve each triangle. b=1 , c=3...Ch. 8.3 - In Problems 17-32, solve each triangle. a=6 , b=4...Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , c=2...Ch. 8.3 - In Problems 17-32, solve each triangle. b=4 , c=1...Ch. 8.3 - In Problems 17-32, solve each triangle. a=2 , b=2...Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , c=2...Ch. 8.3 - In Problems 17-32, solve each triangle. a=12 ,...Ch. 8.3 - In Problems 17-32, solve each triangle. a=4 , b=5...Ch. 8.3 - In Problems 17-32, solve each triangle. a=2 , b=2...Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , b=3...Ch. 8.3 - In Problems 17-32, solve each triangle. a=5 , b=8...Ch. 8.3 - In Problems 17-32, solve each triangle. a=4 , b=3...Ch. 8.3 - In Problems 17-32, solve each triangle. a=10 , b=8...Ch. 8.3 - In Problems 17-32, solve each triangle. a=9 , b=7...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - Distance to the Green A golfer hits an errant tee...Ch. 8.3 - Navigation An airplane flies due north from Ft....Ch. 8.3 - Avoiding a Tropical Storm A cruise ship maintains...Ch. 8.3 - Revising a Flight Plan In attempting to fly from...Ch. 8.3 - Major League Baseball Field A major league...Ch. 8.3 - Little League Baseball Field According to Little...Ch. 8.3 - Finding the Length of a Guy Wire The height of a...Ch. 8.3 - Finding the Length of a Guy Wire A radio tower 500...Ch. 8.3 - Identifying Remains The Purkait triangle, located...Ch. 8.3 - Identifying Remains Like the Purkait triangle in...Ch. 8.3 - Soccer Angles A soccer goal is 8 yards wide....Ch. 8.3 - Wrigley Field, Home of the Chicago Cubs The...Ch. 8.3 - Little League Baseball The distance from home...Ch. 8.3 - Building a Swing Set Clint is building a wooden...Ch. 8.3 - Rods and Pistons Rod OA rotates about the fixed...Ch. 8.3 - Geometry Show that the length d of a chord of a...Ch. 8.3 - Prob. 60AECh. 8.3 - For any triangle, show that sin c 2 = ( sa )( sb )...Ch. 8.3 - Use the law of Cosines to prove the identity cosA...Ch. 8.3 - What do you do first if you are asked to solve a...Ch. 8.3 - What do you do first if you are asked to solve a...Ch. 8.3 - Make up an applied problem that requires using the...Ch. 8.3 - Write down your strategy for solving an oblique...Ch. 8.3 - State the Law of Cosines in words.Ch. 8.3 - Graph: R( x )= 2x+1 x3Ch. 8.3 - Solve 4 x =3 x+1 . If the solution is irrational,...Ch. 8.3 - Given tan= 2 6 5 and cos= 5 7 , find the exact...Ch. 8.3 - Find an equation for the graph.Ch. 8.4 - The area K of a triangle whose base is b and whose...Ch. 8.4 - If two sides a and b and the included angle C are...Ch. 8.4 - The area K of a triangle with sides a , b , and c...Ch. 8.4 - True or False The area of a triangle equals...Ch. 8.4 - Given two sides of a triangle, b and c , and the...Ch. 8.4 - Heron's Formula is used to find the area of...Ch. 8.4 - Prob. 7SBCh. 8.4 - Prob. 8SBCh. 8.4 - Prob. 9SBCh. 8.4 - Prob. 10SBCh. 8.4 - Prob. 11SBCh. 8.4 - Prob. 12SBCh. 8.4 - Prob. 13SBCh. 8.4 - Prob. 14SBCh. 8.4 - Prob. 15SBCh. 8.4 - Prob. 16SBCh. 8.4 - Prob. 17SBCh. 8.4 - Prob. 18SBCh. 8.4 - Prob. 19SBCh. 8.4 - Prob. 20SBCh. 8.4 - Prob. 21SBCh. 8.4 - Prob. 22SBCh. 8.4 - In Problems 15-26, find the area of each triangle....Ch. 8.4 - Prob. 24SBCh. 8.4 - Prob. 25SBCh. 8.4 - In Problems 15-26, find the area of each triangle....Ch. 8.4 - Area of an ASA Triangle If two angles and the...Ch. 8.4 - Area of a Triangle Prove the two other forms of...Ch. 8.4 - In Problems 29-34, use the results of Problem 27...Ch. 8.4 - In Problems 29-34, use the results of Problem 27...Ch. 8.4 - In Problems 29-34, use the results of Problem 27...Ch. 8.4 - In Problems 29-34, use the results of Problem 27...Ch. 8.4 - In Problems 29-34, use the results of Problem 27...Ch. 8.4 - In Problems 29-34, use the results of Problem 27...Ch. 8.4 - Area of a Segment Find the area of the segment...Ch. 8.4 - Area of a Segment Find the area of the segment of...Ch. 8.4 - Cost of a Triangular Lot The dimensions of a...Ch. 8.4 - Amount of Material to Make a Tent A cone-shaped...Ch. 8.4 - Prob. 39AECh. 8.4 - Dimensions of Home Plate The dimensions of home...Ch. 8.4 - Computing Areas See the figure. Find the area of...Ch. 8.4 - Geometry See the figure, which shows a circle of...Ch. 8.4 - Approximating the Area of a Lake To approximate...Ch. 8.4 - Bermuda Triangle The Bermuda Triangle is roughly...Ch. 8.4 - The Flatiron Building Completed in 1902 in New...Ch. 8.4 - Area of a Quadrilateral Bretschneider’s Formula...Ch. 8.4 - The Cow Problem A cow is tethered to one corner of...Ch. 8.4 - Perfect Triangles A perfect triangle is one having...Ch. 8.4 - If h 1 , h 2 , and h 3 are the altitudes dropped...Ch. 8.4 - Show that a formula for the altitude h from a...Ch. 8.4 - Inscribed Circle For Problems 55-58, the lines...Ch. 8.4 - Inscribed Circle For Problems 55-58, the lines...Ch. 8.4 - Inscribed Circle For Problems 55-58, the lines...Ch. 8.4 - Inscribed Circle For Problems 55-58, the lines...Ch. 8.4 - A triangle has vertices A( 0,0 ) , B( 1,0 ) , and...Ch. 8.4 - What do you do first if you are asked to find the...Ch. 8.4 - What do you do first if you are asked to find the...Ch. 8.4 - State the area of an SAS triangle in words.Ch. 8.4 - Without graphing, determine whether the quadratic...Ch. 8.4 - Solve the inequality: x+1 x 2 9 0Ch. 8.4 - P=( 7 3 , 2 3 ) is the point on the unit circle...Ch. 8.4 - Establish the identity: cscsin=coscotCh. 8.5 - The amplitude A and period T of f( x )=5sin( 4x )...Ch. 8.5 - The motion of an object obeys the equation d=4cos(...Ch. 8.5 - When a mass hanging from a spring is pulled down...Ch. 8.5 - True or False If the distance d of an object from...Ch. 8.5 - In Problems 5-8, an object attached to a coiled...Ch. 8.5 - In Problems 5-8, an object attached to a coiled...Ch. 8.5 - In Problems 5-8, an object attached to a coiled...Ch. 8.5 - In Problems 5-8, an object attached to a coiled...Ch. 8.5 - Rework Problem 5 under the same conditions, except...Ch. 8.5 - Rework Problem 6 under the same conditions, except...Ch. 8.5 - Rework Problem 7 under the same conditions, except...Ch. 8.5 - Rework Problem 8 under the same conditions, except...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 13-20, the displacement d (in meters)...Ch. 8.5 - In Problems 21-24, graph each damped vibration...Ch. 8.5 - In Problems 21-24, graph each damped vibration...Ch. 8.5 - In Problems 21-24, graph each damped vibration...Ch. 8.5 - In Problems 21-24, graph each damped vibration...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 25-32, use the method of adding...Ch. 8.5 - In Problems 33-38, (a) use the Product-to-Sum...Ch. 8.5 - In Problems 33-38, (a) use the Product-to-Sum...Ch. 8.5 - In Problems 33-38, (a) use the Product-to-Sum...Ch. 8.5 - In Problems 33-38, (a) use the Product-to-Sum...Ch. 8.5 - In Problems 33-38, (a) use the Product-to-Sum...Ch. 8.5 - In Problems 3338, (a) use the ProducttoSum...Ch. 8.5 - In Problems 39-44, an object of mass m (in grams)...Ch. 8.5 - In Problems 39-44, an object of mass m (in grams)...Ch. 8.5 - In Problems 39-44, an object of mass m (in grams)...Ch. 8.5 - In Problems 39-44, an object of mass m (in grams)...Ch. 8.5 - In Problems 39-44, an object of mass m (in grams)...Ch. 8.5 - In Problems 39-44, an object of mass m (in grams)...Ch. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - Loudspeaker A loudspeaker diaphragm is oscillating...Ch. 8.5 - Colossus Added to Six Flags St. Louis in 1986, the...Ch. 8.5 - Tuning Fork The end of a tuning fork moves in...Ch. 8.5 - Tuning Fork The end of a tuning fork moves in...Ch. 8.5 - Charging a Capacitor See the illustration. If a...Ch. 8.5 - The Sawtooth Curve An oscilloscope often displays...Ch. 8.5 - Touch-Tone Phones On a Touch-Tone phone, each...Ch. 8.5 - Use a graphing utility to graph the sound emitted...Ch. 8.5 - Use a graphing utility to graph the function f( x...Ch. 8.5 - Use a graphing utility to graph y=xsinx,y= x 2...Ch. 8.5 - Use a graphing utility to graph y= 1 x sinx,y= 1 x...Ch. 8.5 - How would you explain to a friend what simple...Ch. 8.5 - Problems 65-68 are based on material learned...Ch. 8.5 - Problems 65-68 are based on material learned...Ch. 8.5 - Problems 65-68 are based on material learned...Ch. 8.R - In Problems 1 and 2, find the exact value of the...Ch. 8.R - In Problems 1 and 2, find the exact value of the...Ch. 8.R - In Problems 3-5, find the exact value of each...Ch. 8.R - In Problems 3-5, find the exact value of each...Ch. 8.R - In Problems 3-5, find the exact value of each...Ch. 8.R - In Problems 6 and 7, solve each triangle.Ch. 8.R - In Problems 6 and 7, solve each triangle.Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 8-20, find the remaining angle(s) and...Ch. 8.R - In Problems 21-25, find the area of each triangle....Ch. 8.R - In Problems 21-25, find the area of each triangle....Ch. 8.R - In Problems 21-25, find the area of each triangle....Ch. 8.R - In Problems 21-25, find the area of each triangle....Ch. 8.R - In Problems 21-25, find the area of each triangle....Ch. 8.R - Area of a Segment Find the area of the segment of...Ch. 8.R - Geometry The hypotenuse of a right triangle is 12...Ch. 8.R - Finding the Width of a River Find the distance...Ch. 8.R - Finding the Distance to Shore The Willis Tower in...Ch. 8.R - Finding the speed of a Glider From a glider 200...Ch. 8.R - Finding the Grade of a Mountain Trail A straight...Ch. 8.R - Finding the Height of a Helicopter Two observers...Ch. 8.R - Constructing a Highway A highway whose primary...Ch. 8.R - Prob. 34RE
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- Geometry A trough for feeding cattle is 4 meters long and its cross sections are isosceles triangles with the two equal sides being 12 meter (see figure). The angle between the two sides is . (a) Write the volume of the trough as a function of /2. (b) Write the volume of the trough as a function of and determine the value of such that the volume is maximized.arrow_forwardGeometry The length of each of the two equal sides of an isosceles triangle is 10 meters (see figure). The angle between the two sides is . (a) Write the area of the triangle as a function of /2. (b) Write the area of the triangle as a function of . Determine the value of such that the area is a maximum.arrow_forwardArea A sprinkler on a golf green is set to spray water over a distance of 15 meters and to rotate through an angle of 150°. Draw a diagram that shows the region that can be irrigated with the sprinkler. Find the area of the region.arrow_forward
- Graphical Reasoning Use the formulas for the area of a circular sector and arc length given in Section 1.1. (a) For =0.8, write the area and arc length as functions of r. What is the domain of each function? Use a graphing utility to graph the functions. Use the graphs to determine which function changes more rapidly as r increases. Explain. (b) For r=10 centimeters, write the area and arc length as functions of . What is the domain of each function? Use the graphing utility to graph the functions.arrow_forwardView from a Satellite The figures on the next page indicate that the higher the orbit of satellite, the more of the earth the satellite can see. Let ,s, and h be as in the figure, and assume that the earth is a sphere of radius 3960 mi. a Express the angle as a function of h. b Express the distance s as a function of . c Express the distance s as a function of h. Hint: Find the composition of the functions in parts a and b. d If the satellite is 100 mi above the earth, what is the distance s that it can see? e How high does the satellite have to be to see both Los Angeles and New York, 2450 mi apart?arrow_forwardUsing the Unit Circle Use the unit circle to verify that the cosine and secant functions are even and that the sine, cosecant, tangent, and cotangent functions are odd.arrow_forward
- The designers of a water park have sketched a preliminary drawing of a new slide (see figure). (a) Find the height h of the slide. (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance d a rider travels. (c) Safety restrictions require the angle of depression to be no less than 25 and no more than 30. Find an interval for how far a rider travels horizontally.arrow_forwardAn Aluminum Can The cost of making a can is determined by how much aluminum A, in square inches, is needed to make it. This in turn depends on the radius r and the height h of the can, both measured in inches. You will need some basic facts about cans. See Figure 2.107. The surface of a can may be modeled as consisting of three parts: two circles of radius r and the surface of a cylinder of radius r and height h. The area of each circle is r2. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. a. Explain why the height of any can that holds a volume of 15 cubic inches is given by h=15r2 b. Make a graph of the height h as a function of r, and explain what the graph is showing. c. Is there a value of r that gives the least height h? Explain. d. If A is the amount of aluminum needed to make the can, explain why A=2r2+2rh. e. Using the formula for h from part a, explain why we may also write A as A=2r2+30r.arrow_forwardAngle of Depression A cellular telephone tower that is 120 feet tall is placed on top of a mountain that is 1200 feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 400 feet above sea level?arrow_forward
- Belts and Pulleys A thin belt of length L surrounds two pulleys of radii R and r, as shown in the figure (1). aShow that the angle in rad where the belt crosses itself satisfies the equation +2cot2=LR+r Hint: Express L in terms of R, r, and by adding up the lengths of the curved and straight parts of the belt. bSuppose that R=2.42ft, r=1.21ft, and L=27.78ft. Find by solving the equation in part a graphically. Express your answer both in radians and in degrees. Figure (1)arrow_forwardDistance A plane flying at an altitude of 7 miles above a radar antenna passes directly over the radar antenna (see figure). Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. ( d is positive as the plane approaches the antenna.) Write d as a function of x and graph the function over the interval 0x.arrow_forwardForce The force F (in pounds) on a person’s back when he or she bends over at an angle from an upright position is modeled by F=0.6Wsin+90sin12 where W represents the person’s weight (in pounds). (a) Simplify the model. (b) Use a graphing utility to graph the model, where W=185and090. (c) At what angle is the force maximized? At what angle is the force minimized?arrow_forward
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