Precalculus
11th Edition
ISBN: 9780135189405
Author: Michael Sullivan
Publisher: PEARSON
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Textbook Question
Chapter 8.2, Problem 45AYU
Landscaping Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is , and from a second position 40 feet farther along this path it is . What is the height of the tree?
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Chapter 8 Solutions
Precalculus
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 - Prob. 5AYUCh. 8.1 - When you look up at an object, the acute angle...Ch. 8.1 - Prob. 7AYUCh. 8.1 - Prob. 8AYUCh. 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. 16AYUCh. 8.1 - In Problems 9-18, find the exact value of the six...Ch. 8.1 - Prob. 18AYUCh. 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 - Prob. 22AYUCh. 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 - Prob. 32AYUCh. 8.1 - In Problems 29-42, use the right triangle shown...Ch. 8.1 - Prob. 34AYUCh. 8.1 - Prob. 35AYUCh. 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 - Prob. 38AYUCh. 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 - Prob. 41AYUCh. 8.1 - Prob. 42AYUCh. 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. 64AYUCh. 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 - Challenge Problem Drive Wheel of an Engine The...Ch. 8.1 - Challenge Problem Rework Problem if the belt is...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 - Prob. 86AYUCh. 8.1 - Find the exact value of .
Ch. 8.1 - Prob. 88AYUCh. 8.1 - Solve 2sin2sin+5=6for02.Ch. 8.1 - Prob. 90AYUCh. 8.1 - Prob. 91AYUCh. 8.1 - Prob. 92AYUCh. 8.1 - Prob. 93AYUCh. 8.1 - Prob. 94AYUCh. 8.1 - Prob. 95AYUCh. 8.2 - The difference formula for the sine function is...Ch. 8.2 - Prob. 2AYUCh. 8.2 - Approximate sin40andsin80.Ch. 8.2 - Prob. 4AYUCh. 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 - Multiple Choice If two angles of a triangle...Ch. 8.2 - Prob. 8AYUCh. 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 , solve each triangle.
Ch. 8.2 - In Problems 17-24, solve each triangle. A= 50 ,...Ch. 8.2 - In Problems 1926, solve each triangle....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 2738, two sides and an angle are...Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems , two sides and an angle are given....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 , two sides and an angle are given....Ch. 8.2 - In Problems 25-36, two sides and an angle are...Ch. 8.2 - In Problems 2738, 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. 47AYUCh. 8.2 - Prob. 48AYUCh. 8.2 - Rescue at Sea Coast Guard Station Able is located...Ch. 8.2 - Prob. 50AYUCh. 8.2 - Finding the Lean of the Leaning Tower of Pisa The...Ch. 8.2 - Prob. 52AYUCh. 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. 57AYUCh. 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. 66AYUCh. 8.2 - Make up three problems involving oblique...Ch. 8.2 - Prob. 68AYUCh. 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 - Prob. 71AYUCh. 8.2 - Find the exact distance between P 1 =( 1,7 ) and P...Ch. 8.2 - Prob. 73AYUCh. 8.2 - Prob. 74AYUCh. 8.2 - Write the equation in logarithmic form.
Ch. 8.2 - Prob. 76AYUCh. 8.2 - Prob. 77AYUCh. 8.2 - Find the equation of line perpendicular to y=23x+7...Ch. 8.2 - Prob. 79AYUCh. 8.2 - Prob. 80AYUCh. 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 1732, solve each triangle....Ch. 8.3 - In Problems 17-32, solve each triangle. a=6 , b=4...Ch. 8.3 - In Problems solve each triangle.
Ch. 8.3 - In Problems 17-32, solve each triangle. b=4 , c=1...Ch. 8.3 - In Problems solve each triangle.
Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , c=2...Ch. 8.3 - In Problems solve each triangle.
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 1732, solve each triangle....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 - Prob. 36AYUCh. 8.3 - Prob. 37AYUCh. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - Mixed Practice In Problems 3344, solve each...Ch. 8.3 - Prob. 40AYUCh. 8.3 - Prob. 41AYUCh. 8.3 - Prob. 42AYUCh. 8.3 - Prob. 43AYUCh. 8.3 - Prob. 44AYUCh. 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 - Prob. 54AYUCh. 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 - Prob. 58AYUCh. 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 - Prob. 61AYUCh. 8.3 - Prob. 62AYUCh. 8.3 - For any triangle, show that sin c 2 = ( sa )( sb )...Ch. 8.3 - Prob. 64AYUCh. 8.3 - Prob. 65AYUCh. 8.3 - Prob. 66AYUCh. 8.3 - Prob. 67AYUCh. 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 - Prob. 71AYUCh. 8.3 - Given tan= 2 6 5 and cos= 5 7 , find the exact...Ch. 8.3 - Prob. 73AYUCh. 8.3 - Prob. 74AYUCh. 8.3 - Prob. 75AYUCh. 8.3 - Prob. 76AYUCh. 8.3 - Prob. 77AYUCh. 8.3 - Convert 96 to radians.Ch. 8.3 - Prob. 79AYUCh. 8.4 - The area K of a triangle whose base is b and whose...Ch. 8.4 - Prob. 2AYUCh. 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 - Find the area of the right triangle whose legs are...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. 9AYUCh. 8.4 - Prob. 10AYUCh. 8.4 - Prob. 11AYUCh. 8.4 - Prob. 12AYUCh. 8.4 - Prob. 13AYUCh. 8.4 - Prob. 14AYUCh. 8.4 - Prob. 15AYUCh. 8.4 - Prob. 16AYUCh. 8.4 - Prob. 17AYUCh. 8.4 - Prob. 18AYUCh. 8.4 - Prob. 19AYUCh. 8.4 - Prob. 20AYUCh. 8.4 - Prob. 21AYUCh. 8.4 - Prob. 22AYUCh. 8.4 - Prob. 23AYUCh. 8.4 - Prob. 24AYUCh. 8.4 - Prob. 25AYUCh. 8.4 - Prob. 26AYUCh. 8.4 - Prob. 27AYUCh. 8.4 - Prob. 28AYUCh. 8.4 - Prob. 29AYUCh. 8.4 - Prob. 30AYUCh. 8.4 - Prob. 31AYUCh. 8.4 - Prob. 32AYUCh. 8.4 - Prob. 33AYUCh. 8.4 - Prob. 34AYUCh. 8.4 - Prob. 35AYUCh. 8.4 - Prob. 36AYUCh. 8.4 - Prob. 37AYUCh. 8.4 - Prob. 38AYUCh. 8.4 - Cost of a Triangular Lot The dimensions of a...Ch. 8.4 - Prob. 40AYUCh. 8.4 - Prob. 41AYUCh. 8.4 - Prob. 42AYUCh. 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 - The Flatiron Building Completed in 1902 in New...Ch. 8.4 - Bermuda Triangle The Bermuda Triangle is roughly...Ch. 8.4 - Bretschneiders Formula There is a Heron-type...Ch. 8.4 - Perfect Triangles A perfect triangle is one having...Ch. 8.4 - Prob. 56AYUCh. 8.4 - Show that a formula for the altitude h from a...Ch. 8.4 - Prob. 58AYUCh. 8.4 - Inscribed Circle For Problems 55-58, the lines...Ch. 8.4 - Prob. 60AYUCh. 8.4 - Prob. 61AYUCh. 8.4 - Prob. 62AYUCh. 8.4 - Prob. 63AYUCh. 8.4 - Prob. 64AYUCh. 8.4 - Prob. 65AYUCh. 8.4 - Prob. 66AYUCh. 8.4 - Prob. 67AYUCh. 8.4 - Prob. 68AYUCh. 8.4 - Establish the identity: cscsin=coscotCh. 8.4 - Prob. 70AYUCh. 8.4 - Prob. 71AYUCh. 8.4 - Prob. 72AYUCh. 8.4 - Prob. 73AYUCh. 8.4 - Solve: x(x7)=18Ch. 8.4 - Prob. 75AYUCh. 8.5 - The amplitude A and period T of f( x )=5sin( 4x )...Ch. 8.5 - Prob. 2AYUCh. 8.5 - Prob. 3AYUCh. 8.5 - Prob. 4AYUCh. 8.5 - Prob. 5AYUCh. 8.5 - Prob. 6AYUCh. 8.5 - Prob. 7AYUCh. 8.5 - Prob. 8AYUCh. 8.5 - Prob. 9AYUCh. 8.5 - Prob. 10AYUCh. 8.5 - Rework Problem 7 under the same conditions, except...Ch. 8.5 - Prob. 12AYUCh. 8.5 - Rework Problem 9 under the same conditions, except...Ch. 8.5 - Rework Problem 10 under the same conditions,...Ch. 8.5 - Prob. 15AYUCh. 8.5 - Prob. 16AYUCh. 8.5 - Prob. 17AYUCh. 8.5 - Prob. 18AYUCh. 8.5 - In Problems 15-22, the displacement (in meters) of...Ch. 8.5 - Prob. 20AYUCh. 8.5 - Prob. 21AYUCh. 8.5 - Prob. 22AYUCh. 8.5 - Prob. 23AYUCh. 8.5 - Prob. 24AYUCh. 8.5 - Prob. 25AYUCh. 8.5 - Prob. 26AYUCh. 8.5 - Prob. 27AYUCh. 8.5 - Prob. 28AYUCh. 8.5 - Prob. 29AYUCh. 8.5 - Prob. 30AYUCh. 8.5 - Prob. 31AYUCh. 8.5 - Prob. 32AYUCh. 8.5 - Prob. 33AYUCh. 8.5 - Prob. 34AYUCh. 8.5 - Prob. 35AYUCh. 8.5 - Prob. 36AYUCh. 8.5 - Prob. 37AYUCh. 8.5 - Prob. 38AYUCh. 8.5 - Prob. 39AYUCh. 8.5 - Prob. 40AYUCh. 8.5 - Prob. 41AYUCh. 8.5 - Prob. 42AYUCh. 8.5 - Prob. 43AYUCh. 8.5 - Prob. 44AYUCh. 8.5 - Prob. 45AYUCh. 8.5 - Prob. 46AYUCh. 8.5 - Prob. 47AYUCh. 8.5 - Prob. 48AYUCh. 8.5 - Prob. 49AYUCh. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - Prob. 51AYUCh. 8.5 - Prob. 52AYUCh. 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 - A Clock Signal A clock signal is a non-sinusoidal...Ch. 8.5 - Non-Sinusoidal Waves Both the sawtooth and square...Ch. 8.5 - Graph the sound emitted by the * key on a...Ch. 8.5 - Challenge Problem Beats When two sinusoidal waves...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 - Prob. 71AYUCh. 8.5 - Prob. 72AYUCh. 8.5 - Prob. 73AYUCh. 8.5 - Prob. 74AYUCh. 8.5 - Prob. 75AYUCh. 8.5 - Prob. 76AYUCh. 8.5 - Prob. 77AYUCh. 8.5 - Prob. 78AYUCh. 8 - In Problems 1 and 2, find the exact value of the...Ch. 8 - In Problems 1 and 2, find the exact value of the...Ch. 8 - In Problems 3-5, find the exact value of each...Ch. 8 - In Problems 3-5, find the exact value of each...Ch. 8 - In Problems 3-5, find the exact value of each...Ch. 8 - In Problems 6 and 7, solve each triangle.Ch. 8 - In Problems 6 and 7, solve each triangle.Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - Prob. 14RECh. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - Prob. 18RECh. 8 - In Problems 8-20, find the remaining angle(s) and...Ch. 8 - Prob. 20RECh. 8 - In Problems 21-25, find the area of each triangle....Ch. 8 - Prob. 22RECh. 8 - In Problems 21-25, find the area of each triangle....Ch. 8 - Prob. 24RECh. 8 - In Problems 21-25, find the area of each triangle....Ch. 8 - Area of a Segment Find the area of the segment of...Ch. 8 - Prob. 27RECh. 8 - Finding the Width of a River Find the distance...Ch. 8 - Finding the Distance to Shore The Willis Tower in...Ch. 8 - Prob. 30RECh. 8 - Finding the Grade of a Mountain Trail A straight...Ch. 8 - Finding the Height of a Helicopter Two observers...Ch. 8 - Prob. 33RECh. 8 - Approximating the Area of a Lake To approximate...Ch. 8 - Finding the Bearing of a Ship The Majesty leaves...Ch. 8 - Frictional Force A box sitting on a flat surface...Ch. 8 - Frictional Force (See Problem 37.) Once the box...Ch. 8 - Prob. 39RECh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - In Problem, use the given information to determine...Ch. 8 - Prob. 4CTCh. 8 - In Problem 35, use the given information to...Ch. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CTCh. 8 - 10. Find the area of the triangle described in...Ch. 8 - Prob. 11CTCh. 8 - A hot- air balloon is flying at a height of 600...Ch. 8 - Find the area of the shaded region enclosed in a...Ch. 8 - 14. Find the area of the quadrilateral shown.
Ch. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Graph each of the following functions...Ch. 8 - Solve the triangle for which side a is 20, side c...Ch. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Suppose that f(x)=4x+5 and g(x)=x2+5x24. Solve...
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- 2. Find the equation of the tangent line to the graph of the given function at the given point. f(x)=(x+3)(2x²-6) at (1,-16)arrow_forward6. Researchers who have been studying the alarming rate at which the level of the Dead Sea has been dropping have shown that the density d (x) (in g per cm³) of the Dead Sea brine during evaporation can be estimated by the function d(x)=1.66 0.90x+0.47x², where x is the fraction of the remaining brine, 0≤x≤1. a) Estimate the density of the brine when 60% of the brine remains. b) Find and interpret the instantaneous rate of change of the density when 60% of the brine remains.arrow_forward5. If g'(5) 10 and h'(5)=-4, find f'(5) for f(x)=4g(x)-2h(x)+3.arrow_forward
- 2. Find each derivative. Write answers with positive exponents. a) Dx 9x -3 [97] b) f'(3) if f(x) = x²-5x² 8arrow_forwardA ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.arrow_forwardTwo cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dtarrow_forward
- An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ Noarrow_forward4.1 Basic Rules of Differentiation. 1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with appropriate derivative notation. a) y=8x-5x3 4 X b) y=-50 √x+11x -5 c) p(x)=-10x²+6x3³arrow_forwardPlease refer belowarrow_forward
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