David L. Johnson, Jr. v. State of Indiana
5
pages
English
Documents
Le téléchargement nécessite un accès à la bibliothèque YouScribe Tout savoir sur nos offres
5
pages
English
Documents
Le téléchargement nécessite un accès à la bibliothèque YouScribe Tout savoir sur nos offres
- exposé - matière potentielle : on a mental health assessment
- exposé - matière potentielle : the law
- exposé - matière potentielle : the case
- revision
- exposé
- exposé - matière potentielle : on the mental health assessment
- redaction
- a.j.
- a. j.
- felony charge of neglect
- johnson
- johnson to an executed term of forty years
- trial court
- jury
- evidence
Then You added, subtracted, and multiplied radical expressions. (Lesson 103)
Now Solve radical equations. Solve radical equations with extraneous solutions.
NewVocabulary radical equations extraneous solutions
Math Online glencoe.com Extra Examples Personal Tutor SelfCheck Quiz Homework Help
Radical Equations Why? The waterline length of a sailboat is the length of the line made by the water’s edge when the boat is full. A sailboat’s hull speed is the fastest speed that it can travel. You can estimate hull speedhby using the formulah=1.34√, whereis the length of the sailboat’s waterline.
Radical Equations Equations that contain variables in the radicand, likeh=1.34√, are calledradical equations. To solve, isolate the desired variable on one side of the equation first. Then square each side of the equation to eliminate the radical.
For Your
EXAMPLE 1Variable as a Radicand SAILINGIdris and Sebastian are sailing in a friend’s sailboat. They measure the hull speed at 9 nautical miles per hour. Find the length of the sailboat’s waterline. Round to the nearest foot. UnderstandYou know how fast the boat will travel and that it relates to the length. PlanThe boat travels at 9 nautical miles per hour. The formula for hull speed ish=1.34√. Solveh=1.34√Formula for hull speed __9=1.34√Substitute 9 forh. √ 9 1.34 =Divide each side by 1.34. 1.34 1.34 6.71641791=√Simplify. 2 2 (6.716417912)=(√)Square each side of the equation. 45.11026954≈Simplify. The sailboat’s waterline length is about 45 feet. CheckCheck the results by substituting your estimate back into the original formula. Remember that your result should be about 9. h=1.34√Formula for hull speed 91.3445h=9 and=45 √ 91.34(6.708203932√45=6.708203932 ) 9≈8.98899327Multiply. 62410 Chapter Radical Functions and Geometry
Watch Out! Squaring Each Side Remember that when you square each side of the equation, you must square the entire side of the equation, even if there is more than one term on the side.
StudyTip Extraneous SolutionsWhen checking solutions for extraneous solutions, we are only interested in principal roots. For example, while √1=±1, we are only interested in 1.
✓Check Your Progress 1.DRIVINGThe equationv=√2.5r represents the maximum velocity that a car can travel safely on an unbanked curve whenvis the maximum velocity in miles per hour andris the radius of the turn in feet. If a road is designed for a maximum speed of 65 miles per hour, what is the radius of the turn?
Personal Tutorglencoe.com
When a radicand is an expression, isolate the radical first. Then square both sides of the equation.
EXAMPLE 2Expression as a Radicand Solve√a+5+7=12. √a+5+7=12Original equation 22 √a+5=5Subtract 7 from each side. (√a+5)=5Square each side. a+5=25Simplify. a=20Subtract 5 from each side. ✓Check Your ProgressSolve each equation. 2A.√c-3-2=4 2B.4+√h+1=14 Personal Tutorglencoe.com
Extraneous SolutionsSquaring each side of an equation sometimes produces a solution that is not a solution of the original equation. These are calledextraneous solutions. Therefore, you must check all solutions in the original equation.
EXAMPLE 3Variable on Each Side Solve√k+1=k-1. Check your solution. √k+1=k-1Original equation 2 22kplify. 2 (√k+1)=(k-1)Square each side. k+1=k- +1Sim 2 0=k-3kSubtractkand 1 from each side. 0=k(k-3)Factor. k=0 ork-3=0Zero Product Property k=3Solve. CHECK√k+1=k-1Original equation√k+1=k-1Original equation √0+10-1k=0√3+13-1k=3 √1-1Simplify.√42Simplify. 1≠-1✘False2=2True Since 0 does not satisfy the original equation, 3 is the only solution. ✓Check Your Progress Solve each equation. Check your solution. 3A.√t+5=t+3 3B.x-3=√x-1 Personal Tutorglencoe.com Lesson 10-4 Radical Equations 625
✓ Check Your Understanding Example 11. GEOMETRYThe surface area of a basketball isxsquare inches. What is the radius 2 p. 624 of the basketball if the formula for the surface area of a sphere isSA= 4πr? Examples 2 and 3Solve each equation. Check your solution. p. 625 2.√10h+1=21 3.√7r+2+3=7 4.5+√g-3=6 5.√3x-5=x-5 6.√2n+3=n 7.√a-2+4=a
=StepbyStep Solutionsbegin on page R12. Practice and Problem Solving Extra Practicebegins on page 815. p. 624√_7Example 19.8 8. EXERCISESuppose the functionS=π,whereSrepresents speed in meters per second andis the leg length of a person in meters, can approximate the maximum speed that a person can run. a.speed of a person with a leg length ofWhat is the maximum running 1.1 meters to the nearest tenth of a meter? b.What is the leg length of a person with a running speed of 2.7 meters per second to the nearest tenth of a meter? c.person’s leg length increases, does their speed increase or decrease?As a Explain. Examples 2 and 3Solve each equation. Check your solution. p. 625 √a+11=21 10.√t√ -4=7 11.n-3=6 9 12.√c+10=4 13.√h-5=2√3 14.√k+7=3√2 15.y=√12-y 16.√u+6=u 17.√r+3=r-3 8.√2t=1+t 19.5√a-3+4=14 20.2√x-11-8=4 11-21.The amount of timet, in seconds, that it takes a simple pendulum to complete a full swing is called the period of the pendulum. It is given by t=2π√_,whereis the length of the pendulum, in feet. 32 a.The Giant Swing completes a period in about 8 seconds. About how long is the pendulum’s arm? Round to the nearest foot. b.Does increasing the length of the pendulum increase or decrease the period? Explain. Solve each equation. Check your solution. 4 22.√6a-6=a+1 23.√x+9x+15=x+524.6√_-3=0 25k DollarCityinBransSoinlv,er25._-10=4 26.√2a-121=a 27.√5x-9=2x5y 2 2 √6 The Giant Swing at 28. GEOMETRYThe formula for the slant heightcof a cone is reaches a height ofthe radius of its base. Find the height of the cone if therh Missouri, swings riders at 2 2 c=√h+r ,wherehis the height of the cone andris 45 miles per hour and 7 stories.slant height is 4 and the radius is 2. Round to the nearest tenth. Source:Silver Dollar City Amusement Park 626 Chapter10 Radical Functions and Geometry
Packaging has several objectives, including physical protection, information transmission, marketing, convenience, security, and portion control.C Source:Packaging World
MULTIPLE REPRESENTATIONSIn this problem, you will solve a radical equation by 29 graphing. Consider the equation√2x-7=x-7. a. GRAPHICALClear theY=list. Enter the left side of the equation as PressGRAPH.Y1=√2x-7. Enter the right side of the equation asY2=x-7. b. GRAPHICALSketch what is shown on the screen. c. ANALYTICALUse theintersectfeature on theCALCmenu to find the point of intersection. d. ANALYTICALSolve the radical equation algebraically. How does your solution compare to the solution from the graph? 30.CKAGINGA cylindrical container of chocolate drink mix has a volume of 162 cubic inches. The radiusrof the container can be found by using the formula r=_,whereVis the volume of the container andhis the height. V √ πh a.If the radius is 2.5 inches, find the height of the container. Round your answer to the nearest hundredth. b.If the height of the container is 10 inches, find the radius of the container. Round to the nearest hundredth
H.O.T. ProblemsUseHigherOrderThinking Skills 31. FIND THE ERRORJada and Fina solved√6-b=√b+10. Is either of them correct? Explain. JadaFia 22 210)(√6–b)= (√b+ 10) √6-b=√b+ 10√6–b=√b +106 – b = b + 10 2 (√6–b)=(√b + 6 – b = b + 10 2b = 4 b = 2 –2b = 4 b = –2Chk√6–(2)√(2)+ 10no sOlutôN √4≠√12✘ √(–2) +10Check√6 – (–2) √8=√8✔ 32. REASONINGWhich equation has the same solution set as√4=√x+2? Explain A.√4=√x+√2 B.4=x+2 C.2-√2=√x 33. REASONINGExplain how solving the equation 5=√x+1 is different from solving the equation 5=√x+1. 34. OPEN ENDEDWrite a radical equation with a variable on each side. Then solve the equation. 35. REASONINGIs the following equationsometimes,alwaysornevertrue? Explain. 2 √(x-2)=x-2 x+9=36. CHALLENGESolve√√3+√x. 37. WRITING IN MATHWrite some general rules about how to solve radical equations. Demonstrate your rules by solving a radical equation. Lesson 10-4 Radical Equations 627
Standardized Test Practice
38. SHORTRESPONSEZack needs to drill a hole40.What is the slope of a line that is parallel at each of the pointsA,B,C,D, andEon tothe line? circleP. y $ % # 1 0x 110° " & If Zack drills holes so thatm∠APE=110° F-3 H3 and the other four angles are equal in measure, what ism∠CPD?_ _ 1 1 G-J3 3 39.Which expression is undefined whenw=3? w_+1w2-3w41.What are the solutions of w-3w+1 A C√x+3-1=x-4?_ _w2 A1, 6 C1 2 w-3w3w B D3w B-1,-6 D6 3
Spiral Review 42.ELECTRICITYThe voltageVrequired for a circuit is given byV=√PR, wherePis the power in watts andRis the resistance in ohms. How many more volts are needed to light a 100-watt light bulb than a 75-watt light bulb if the resistance of both is 110 ohms?(Lesson 103) Simplifyeachexpression.(Lesson 102) 43.√6∙√8 44.√3∙√6 45.7√3∙2√6 27 5c49.P96HYfeSIeCt.AL(LSesCsIoEtnNs9Ce5Ec)Arpjoceitelissisvisghdnobenyhot=9t6rsatig-ht up2Itel.(s)ofhevaluergmorfveldnuotshtnehheiwghhi_,s 3 46._ 47.√_5 48.2 2 5 √9xy√ 2 a 4d √16xyin feet, after16t. Find t Factor each trinomial, if possible. If the trinomial cannot be factored using integers, writeprime.(Lesson 84) 2 2 2 50.2x+7x+5 51.6p+5p-6 52.5d+6d-8 2 2 2 53.8k-19k+9 54.9g-12g+4 55.2a-9a-18 Determine whether each expression is a monomial. Writeyesorno. Explain.(Lesson 71) 3x1_14 x 58.a-2b 59.4n+5p 60._25 56.12 57.4 61.abcy
Skills Review
Simplify.(Lesson 11) 2 6 62.9 63.10
5 2 64.4 65.(8v)
628 Chapter10 Radical Functions and Geometry
66._)32 w( 9
3 2 67.(10y)
