MML PRECALCULUS ENHANCED
7th Edition
ISBN: 9780134119250
Author: Sullivan
Publisher: INTER PEAR
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Textbook Question
Chapter 8.3, Problem 49AE
Finding the Length of a Guy Wire The height of a radi tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of (see the figure).
a. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the slope side 100 feet from the base of the tower?
b. How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a positio 100 feet from the baseon the flat side?
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Chapter 8 Solutions
MML PRECALCULUS ENHANCED
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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- == 1. A separable differential equation can be written in the form hy) = g(a) where h(y) is a function of y only, and g(x) is a function of r only. All of the equations below are separable. Rewrite each of these in the form h(y) = g(x), then find a general solution by integrating both sides. Determine whether the solutions you found are explicit (functions) or implicit (curves but not functions) (a) 1' = — 1/3 (b) y' = = --- Y (c) y = x(1+ y²)arrow_forwardA circle of radius r centered at the point (0,r) in the plane will intersect the y-axis at the origin and the point A=(0,2r), as pictured below. A line passes through the point A and the point C=(11/2,0) on the x-axis. In this problem, we will investigate the coordinates of the intersection point B between the circle and the line, as 1 → ∞ A=(0,2r) B (0,0) (a) The line through A and C has equation: y= 2 117 x+27 (b) The x-coordinate of the point B is 4472 121,2 +4 40 (c) The y-coordinate of the point B is +27 121 44 (d) The limit as r→ ∞ of the x-coordinate of B is 121 (if your answer is oo, write infinity).arrow_forward1. Show that the vector field F(x, y, z) = (2x sin ye³)ix² cos yj + (3xe³ +5)k satisfies the necessary conditions for a conservative vector field, and find a potential function for F.arrow_forward
- 7. Let F(x1, x2) (F₁(x1, x2), F2(x1, x2)), where = X2 F1(x1, x2) X1 F2(x1, x2) x+x (i) Using the definition, calculate the integral LF.dy, where (t) = (cos(t), sin(t)) and t = [0,2]. [5 Marks] (ii) Explain why Green's Theorem cannot be used to find the integral in part (i). [5 Marks]arrow_forward6. Sketch the trace of the following curve on R², п 3п (t) = (t2 sin(t), t2 cos(t)), tЄ 22 [3 Marks] Find the length of this curve. [7 Marks]arrow_forwardTotal marks 10 Total marks on naner: 80 7. Let DCR2 be a bounded domain with the boundary OD which can be represented as a smooth closed curve : [a, b] R2, oriented in the anticlock- wise direction. Use Green's Theorem to justify that the area of the domain D can be computed by the formula 1 Area(D) = ½ (−y, x) · dy. [5 Marks] (ii) Use the area formula in (i) to find the area of the domain D enclosed by the ellipse y(t) = (10 cos(t), 5 sin(t)), t = [0,2π]. [5 Marks]arrow_forward
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