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Rationalize each denominator. See Examples 1 through 3.23

Intermediate Algebra | 6th Edition | ISBN: 9780321785046 | Authors: Elayn El Martin-Gay ISBN: 9780321785046 180

Solution for problem 27 Chapter 7.5

Intermediate Algebra | 6th Edition

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Intermediate Algebra | 6th Edition | ISBN: 9780321785046 | Authors: Elayn El Martin-Gay

Intermediate Algebra | 6th Edition

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Problem 27

Rationalize each denominator. See Examples 1 through 3.23 2y223 9x2

Step-by-Step Solution:
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Exam3Review(AlltheNotes) TheShoulderComplex ShoulderGirdle Havefourarticulations: • Sternoclavicular • Acromioclavicular • Coracoclavicular • Scapulothoracic Sternoclavicular(SC)Articulation Articulationbetweenthesternumandclavicle – Ball-and-socketjoint – Freelymobileinfrontalandtransverseplane – Limitedsagittalmovement Siteofmostmovementofshouldergirdle – Elevation:depression(shruggingshoulders,60°) – Protraction:retraction(rowing,30°) – Anterior:posteriorrotation(raisingyourhand,30-45°) Ligamentoussupport – Anteriorsternoclavicularligament – Posteriorsternoclavicularligament – Costoclavicular&interclavicularligaments Anterior Posterior Acromioclavicular(AC)Articulation Articulationbetweentheacromionprocessanddistalendofclavicle Motionmostnoticeableduringarmelevation(shoulderabduction) Ligamentoussupport – Superioracromioclavicularligament – Inferioracromioclavicularligament – Coracoacromialligament Coracoclavicular(CC)Articulation Articulationbetweencoracoidprocessofscapulaandclavicle AssistsinreinforcementoftheweakACarticulation Ligamentoussupport – Coracoclavicularligaments i.e.,conoid&trapezoid ScapulothoracicArticulation • “articulation”betweentheanteriorsurfaceofthescapula(scapularfossa) andthethoracicwall – supporteddynamicallybymuscles – noligamentoussupport • actstostabilizeshoulderregionduringlifting(shrugging)-e.g.pickingupa suitcase • facilitatesoverheadmovementsthroughelevationandupwardrotationof theglenohumeraljoint Clavicle • Roles: – Helpsfacilitatescapularmotion – Siteofmuscularattachment – Providesabarriertoprotectunderlyingstructures – Actsstruttostabilizetheshoulderandpreventmedialdisplacement whenthemusclescontract – Preventsaninferiormigrationoftheshouldergirdle. Scapula Primaryfunctionistoprovidemuscleattachmentsitesforshouldermuscles. ShoulderGirdleMovements Abduction(protraction) scapulamoveslaterallyawayfromspinalcolumn Adduction(retraction) scapulamovesmediallytowardspinalcolumn Downwardrotation returninginferiorangleinferomedially Upwardrotation towardspinalcolumn&glenoidfossato turningglenoidfossaupward&moving normalposition inferioranglesuperolaterallyawayfrom spinalcolumn Elevation upwardorsuperiormovement Depression i.e.,shruggingshoulders downwardorinferiormovement i.e.,returningtonormalposition • Shouldergirdlemuscles – Stabilizescapula • maintainscapulainarelativelystaticpositionduringshoulder jointactions • Providestablebaseforshouldermusclestomovehumerus – Moveshouldergirdle • enhancemovementofupperextremitywhenshouldergoes throughextremerangesofmotion • Synergywithmusclesofglenohumeraljoint – Attheextremerangesofmotion: • Scapularmusclesmoveshouldergirdletopositionglenoid fossa • Allowshumerusmoremobility – Withouttheaccompanyingscapulamovementhumeruscanonlybe o raisedintoapproximately90 oftotalshoulderabduction&flexion. – Synergybetweenscapula&shoulderjointmusclesenhances movementofentireupperextremity ScapulohumeralRhythm scapularrotationtofacilitateshoulderabduction 1st30 ofabduction littlescapularrotation e.g.,shoulder=30 ,scapula≈6 o beyond30 o forevery2 ofshouldermovement,scapularotates1 o 2:1ratio FivePrimaryMuscleInvolvedinShoulderGirdleMovement 1. levatorscapulae 2. trapezius 3. rhomboids 4. serratusanterior 5. pectoralisminor ShoulderGirdleMuscles Rhomboids Rhomboids Trapezius Trapezius Levator Levator Scapulae Scapulae Trapezius Pectoralis Minor SerratusAnterior PectoralisMinor Rhomboids PectoralisMinor Trapezius LevatorScapulae SerratusAnterior Trapeziusmuscle Upperfibers: elevation upwardrotation Middlefibers: elevation retraction Lowerfibers: depression upwardrotation retraction Levatorscapulaemuscle elevation downwardrotation Rhomboidmuscles-major&minor retraction elevation downwardrotation PectoralisMinorMuscle depression protraction downwardrotation SerratusAnteriorMuscle SubclaviusMuscle protraction Stabilization&protectionofSCjoint upwardrotation depression protraction ScapulaProtraction(abduction) Scapulamovinglaterallyawayfromspinousprocesseswithoutrotation e.g.,Push-up&benchpress(upwardphase) Agonists ScapulaRetraction(adduction) Pectoralisminor Serratusanterior Scapulamovingmedialtowardthespinousprocesseswithoutrotation(i.e,return fromabduction) Agonists e.g.,rowing Middletrapezius Rhomboids ScapulaUpwardRotation Lateral&upwardmovement e.g.,reachingarmoverhead ScapulaDownwardRotation Downward&MedialMovement GlenoidFossaisrotateddownwardwhendownwardmovementofshoulderjoint occurs Agonists e.g.,latpulldowns Pectoralisminor ScapulaElevation Rhomboid Superiormovementofthescapulawithoutrotation e.g.,Shouldershrugs Agonists Rhomboid Levatorscapula Uppertrapezius ScapulaDepression Inferiormovementofthescapulawithoutrotation Agonists Lowertrapezius Pectoralisminor ShoulderJoint Glenohumeral(GH)articulation – Articulationofthehumerusandglenoidfossa – Designedformobility(Mostmobileinbody) – Lacksbonyandligamentoussupport – Shallowglenoidfossa – Half-sphericalhumeralhead • Widerangeofmotionoftheshoulderjointinmanydifferentplanesrequires asignificantamountoflaxity • Commontohaveinstabilityproblems – Rotatorcuffimpingement – Subluxations&dislocations • Thepriceofmobilityisreducedstability • Themoremobileajointis,thelessstableitis&themorestableitis,theless mobile StabilityofGH – Passive,Staticstabilizers- • articularsurface,glenoidlabrum,jointcapsuleandligaments. – Fullysealed,whichprovidessuctionandresistsadislocatingforceat lowerloads. – Dynamicsupport • occursmostlyatmidrangeofmotionandisprovidedbythe musclesastheycontractinacoordinatedpatterntocompress thehumeralheadintheglenoidcavity. – PosteriorStability • Theposteriorrotatorcuffmuscles – AnteriorStability • Subscapularis • Longheadofthebiceps(superiorhumeralheadtranslation) – TheDeltoidandtheotherscapulothoracicmusclespositionthe scapulatoprovidemaximumGHstability. Supportingstructuresforshoulder Glenoidfossais¼-⅓sizeofhumeralhead Glenoidlabrum – Lipofcartilagesurroundingthejoint – Increaseswidthanddepthoffossa – Assistsinholdingthehumerusinplace Coracohumeralligament – Stabilizesthehumerusagainstsuperiorandlateraldisplacement Glenohumeralligament – Stabilizesthehumerusagainstanteriordisplacement – Superior – Middle – Inferior ShoulderJointMovements Abduction Adduction superior&lateral inferior&medial movementofhumerus movementofhumerus awayfrombody Extension towardbody movementofhumerus straightposteriorly Horizontaladduction Flexion aka-transverseflexion movementofhumerus movementofhumerusin straightanteriorly transverseplanetoward&across chest Horizontalabduction aka-transverseextension movementofhumerusintransverseplane awayfromchest Internal(medial)rotation movementofhumerus External(lateral)rotation mediallyarounditslongaxis movementofhumeruslaterally arounditslongaxisawayfrommidline towardmidline ShoulderJoint ShoulderGirdle Abduction Upwardrotation Adduction DownwardRotation Flexion Elevations&UpwardRotation Extension Depression&DownwardsRotation InternalRotation Protraction ExternalRotation Retraction HorizontalAdduction Protraction HorizontalAbduction Retraction Glenohumeralinternalrotationdeficit(GIRD) – differenceininternalrotationrangeofmotionbetweenan individual’sthrowing&nonthrowingshoulders – overheadathleteswithaGIRDofgreaterthan20%hadahigherrisk ofinjury – stretchingexercisesrecommendedto regaininternalrotation • improveperformance • reducelikelihoodofinjury MusclesthatAttachorCrosstheGlenohumeral 1. Deltoid 2. Coracobrachialis 3. Teresmajor 4. Subscapularis 5. Supraspinatus 6. Infraspinatus 7. Teresminor 8. latissimusdorsi 9. pectoralismajor RotatorCuffMuscles Supraspinatus Infraspinatus Teresminor Subscapularis Deltoid CoracobrachialisMuscle Posteriorfibers: abduction horizontaladduction flexion extension adduction horizontalabduction externalrotation TeresMajorMuscle internalrotation extension adduction Latissimusdorsi’s“littlehelper” Onlyeffectivewhenrhomboidsstabilizescapula PectoralisMajorMuscle Clavicularhead: Sternalhead: flexion(upto60 )o extension horizontaladduction horizontaladduction internalrotation internalrotation adduction(<90 ) o adduction abduction(>90 ) o LatissimusDorsiMuscle adduction extension internalrotation horizontalabduction downwardrotationofthescapula GlenohumeralFlexion Agonists Anteriordeltoid Pectoralismajor(clavicularhead) GlenohumeralExtension Agonists Teresmajor Latissimusdorsi Pectoralismajor(sternalhead) Deltoid GlenohumeralAbduction Agonists Deltoid Supraspinatus Pectoralismajor(clavicularhead) GlenohumeralAdduction Agonists Latissimusdorsi Teresmajor Pectoralismajor(sternalhead) GlenohumeralInternalRotation Agonists Latissimusdorsi Teresmajor Subscapularis Pectoralismajor(sternalhead) GlenohumeralExternalRotation Agonists Infraspinatus Teresminor GlenohumeralHorizontalAbduction Agonists Posteriordeltoid Infraspinatus Teresminor GlenohumeralHorizontalAdduction Agonists Anteriordeltoid Pectoralismajor Coracobrachialis ElbowComplex Distalhumerus Medialepicondyle • Attachmentsitefor: Olecranonfossa Jointcapsule • Deepdepressiononposteriorsurface ofdistalhumerus Ulnarcollateralligament Superficialflexormusclesoftheforearm • Proximaltothetrochlea • Olecranonprocess(ulna)fitsinto Lateralepicondyle thisnotchwhenelbowisextended • Attachmentsitefor: Radialcollateralligament Superficialextensormusclesoftheforearm Capitulum • Hemisphericshape • Situatedonanterioranddistalaspectofhumerus • Doesnotextendposteriorly Trochlea • Pulley-shapedsurface • 330 surfacearea Radial&coronoidfossae • Shallowdepressionsonanteriorsurfaceofdistalhumerus • Proximaltothecapitulumandtrochlea,respectively • Allowcloseapproximationbetweenhumerusandtheradiusandulnaduring maximumelbowflexion • (RadialHead–RadialFossa,CoronoidProcessofUlna–CoronoidFossa) ProximalUlna Largerthandistalend Olecranonprocess • Hooklikeprojection • Extendsproximallyandanteriorly Coronoidprocess • Superiorsurfaceformsflooroftrochlearnotch • Lateralaspectisasmoothovalfacet,i.e.,radialnotch Trochlearnotch • Articulateswithtrochleaofthehumerus Radialnotch • Articulateswithheadoftheradius Smallerthandistalend Radialhead • Disc-shapedexpansionofproximalendoftheradius • Proximalendisconcave(fovea)Articulateswiththecapitulum (Humerus) • Rimarticulateswithradialnotch(Ulna) ElbowJoint Hinge-typejoint(Uni-Axial) Allowsonlyflexion&extension 2interrelatedjoints -Humeroulnararticulation -Humeroradialarticulation ElbowLigaments Radial(lateral)andulnar(medial)collateralligaments:supportforthesidesofthe joint. Annularligament:holdstheproximalradioulnarjointtogether UlnohumeralJoint • Thejointisaunionbetweenthetrochleaonthedistalendofthehumerus andthetrochlearnotchontheulna. • Onthefrontoftheulnaisthecoronoidprocesswhichmakescontactinthe coronoidfossaofthehumerus,limitingflexionintheterminalstagesof motion • Ontheposteriorsideistheolecranonprocess,whichmakescontactwiththe olecranonfossaonthehumerus,terminatingextension. RadialCollateralLigament • Provideslateralstability • Resistsvarustorques • Preventselbowadduction • Rarelyinjured UlnarCollateralLigament • Providesmedialsupport • Resistsvalgustorques • Preventelbowabduction • Manycontactsports&throwingactivitiesplacestressonmedial aspectofjoint,resultingininjury ProximalRadioulnarArticulation • Pivot-typejoint(uni-axial) • Minimalbonysupport • Annularligamentmaintainsradialheadinitsjoint RadioUnlarjoint • Astheradiuscrossesovertheulnainpronation,thedistalendoftheulna moveslaterally. • Interosseusmembraneisthesiteformuscularattachmentandensuresthat theradiusandulnamaintainaspecificrelationshiptoeachother. LateralEpicondylitis “TennisElbow” – inflammation,sorenessorpainontheoutside(lateral)sideofthe upperarmnearelbow. MOI=repetitivemicrotraumatoinsertionofwristextensormuscles RiskFactors – Repetitivegripping&twisting – Poororimpropertechnique – Poororimproperequipment MedialEpicondylitis “Golfer’sElbow” – inflammation,sorenessorpainontheinside(medial)sideofthe upperarmnearelbow. MOI=repeatedforcefulwristflexionandextremevalgustorqueontheelbow Medialstrain – initialforwardphaseofthrow – handandelbowlagbehindtrunkandshoulder ElbowMovements Flexion movementofforearmtoshoulderbybendingtheelbowtodecreaseitsangle Extension movementofforearmawayfromshoulderbystraighteningtheelbowtoincreaseits angle Pronation internalrotarymovementofradiusonulnathatresultsinhandmovingfrompalm- uptopalm-downposition Supination externalrotarymovementofradiusonulnathatresultsinhandmovingfrompalm- downtopalm-upposition MusclesoftheElbow Flexion • BicepsBrachii • Brachialis • Brachioradialis • PronatorTeres Extension • TricepsBrachii • Anconeus Supination • BicepsBrachii • Supinator • Brachioradialis Pronation • PronatorTeres • PronatorQuadratus • Brachioradialis TheWristComplex Bones 29bones,includingradius&ulna 8carpalbones In2rowsof4bones Formwrist 5metacarpalbones Numbered1-5fromthumbtolittlefinger Jointhewristbones 14phalanges(digits) 3foreachfingeracceptthethumb,whichhasonly2 Proximal,middle,&distal – Thumbhasasesamoidboneinitsflexortendon – Othersesamoidsmayoccurinjointsoffingers – FlexorCarpiUlnarisgainssomeofitspowerbyencasing thepisiformboneandusingitasasesamoidboneto increaseMA. DistalRadius Dorsaltubercle • Groovedoneithersideforextensortendons • Servesaspulleytoredirectthepullofextensorpollicislongis Radialstyloidprocess Ulnar(sigmoid)notch Distalsurface • Articulateswiththescaphoidandlunate • Biconcave,continuousarticularsurface • 10-15 anteriortilt • 15-25 medialtilt • Decreasesshearforcesonthedistalradius DistalUlna Seatoftheulna • Articulationwithradius • ⅔-¾ofperimetercoveredwitharticularcartilage Ulnarstyloidprocess Fovea • Attachmentforapexoffibrocartilaginousdisc Pole • U-shapedarticularsurface • Articulationwithfibrocartilaginousdisc Carpus Comprisedof8carpalbones • Proximalrow scaphoid(boat-shaped) lunate(moon-shaped) triquetrum(three-cornered) pisiform(pea-shaped) • Distalrow trapezium(greatermultangular) trapezoid(lessermultangular) capitate(head-shaped) hamate(hooked) Metacarpals Miniaturelongbones – Proximalbase • Thumb:saddle-shapedfacet • Longfingershaveflattenedfacets • Littlefingersomewhatsaddle-shape • Variationsallowdistinctdifferencesinmobilityof carpometacarpal(CMC)articulations – Distalhead • Almostperfectlyround • Articularcartilagecoversanterioranddistalsurfacesand extendslightlyontheposteriorsurface • Allowsslighthyperextensionatmetacarpophalangeal(MCP) joints. Phalanges 14phalangesinthehand – 3ineachfinger,2inthumb – prominentcentralgrooveonheadofproximalandmiddlephalanges – Affectsthedirectionofflexion/extension – Fingersconvergetowardsthebaseofthethumbduringflexion SesamoidBones – Typicallyfoundintendonsoftheflexorpollicisbrevisandadductor pollicis – LesscommoninthetendonsdistaltotheMCPjointsofthefingers DistalRadioulnarArticulation • Pivot-typejoint • Minimalbonysupport – Theulnamakesnoactualcontactwiththecarpalsandisseparatedby afibrocartilagedisc. • Jointcapsuleandtriangularfibrocartilagecomplex(TFCC)providesupport • TFCC Triangularfibrocartilage Dorsalradioulnarligament Volarradioulnarligament Ulnarcollateralligamentcomplex Meniscushomologue • Thisarrangementisimportantsothattheulnacanglideonthediscin pronationandsupinationwhilenotinfluencingwristorcarpalmovements. TriangularFibrocartilageComplex • Triangularfibrocartilagedisc – fillsthespacebetweenulnaandcarpus • Dorsalradioulnarligament – tightinpronation • Volarradioulnarligament – tightinsupination • Ulnarcollateralligamentcomplex – insertsonpisiformandbaseof5 metacarpal • Meniscushomologue – softtissuethatrunsfromdorsalborderoftheradiusmediallytothe volarsurfaceofthemedialaspectofthetriquetrum RadiocarpalJoint: Articulationbetweentheradiusandproximalrowofcarpalbones Onlyscaphoidandlunatearticulatedirectlywiththeradius Triquetrumarticulateswithdistalsurfaceoftriangularfibrocartilage Jointcapsuleencloseallsurfaces MidcarpalJoint: Junctionbetweentheproximalanddistalrowsofcarpalbones Medialcompartment Proximalconcavity: scaphoid,lunateandtriquetrum Distalconvexity: capitateandhamate Lateralcompartment Distalscaphoid,trapeziumandtrapezoid Ligamentsmainsourceofsupport IntercarpalJoints Articulationsbetweenadjacentcarpalboneswithineachrow Stabilizedbyjointcapsuleandextrinsicandintrinsicligaments Transversecarpalligament – Supportsentirecarpalarch – Tautinmaxpronationandsupination – Carpaltunnelsyndrome • Contentsofcarpaltunnelarecompressed JointsoftheFingers Metacarpophalangeal(MCP)joints • Condyloid Proximalinterphalangeal(PIP)joints • Hingejoint Distalinterphalangeal(DIP)joints • Hingejoint ThumbJoint • Hingejoint • Metacarpophalangeal • Thethumbdetermineswhetherafineprecisionpositionorpowerpositionis generated. WristMovements • Wrist – Flexion&extension – Abduction&adduction • Fingers – Flexion&extension – MCPjointsalsoabduct&adduct Abduction&Adduction Middlephalangeisreferencepointtodifferentiateabduction&adduction Abduction: Movementofthethumb,index&middlefingerslaterallytowardradialsideofhand Movementofthering&littlefingersmediallytowardulnarsideofhand Adduction: Medialmovementofthumb,index&middlefingerstowardulnarsideofhand Lateralmovementofring&littlefingertowardradialsideofhandisadduction SpecialMovements Opposition: movementofthumbacross(palmar)aspecttoopposeanyorallofthephalanges Reposition: movementofthumbasitreturnstoanatomicalpositionfromoppositionwithhand and/orfingers Muscle Extrinsicmusclesofwrist&handgroupedaccordingtofunction&location 6musclesmovewristbutnotfingers&thumb – 3wristflexors • flexorcarpiradialis • flexorcarpiulnaris • palmarislongus*Variable(13%Missing) – 3wristextensors • extensorcarpiradialislongus • extensorcarpiradialisbrevis • extensorcarpiulnaris 9musclesprimarymoversofphalanges – Alsoinvolvedinwristjointactions – Generallyweakerintheirwristactions – Flexors • Flexordigitorumsuperficialis • Flexordigitorumprofundus • Flexorpollicislongus(thumbflexor) – Extensors • Extensordigitorum • Extensorindicis • Extensordigitiminimi • Extensorpollicislongus(thumbextensor) • Extensorpollicisbrevis(thumbextensor) – Abductorofthumb&wrist • Abductorpollicislongus IntrinsicMusclesoftheHand Thenareminence-muscularpadonpalmarsurfaceof1 metacarpalt Hypothenareminence-muscularpadthatformsulnarborderonpalmarsurface

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Chapter 7.5, Problem 27 is Solved
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Textbook: Intermediate Algebra
Edition: 6
Author: Elayn El Martin-Gay
ISBN: 9780321785046

This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. The full step-by-step solution to problem: 27 from chapter: 7.5 was answered by , our top Math solution expert on 12/23/17, 04:59PM. Since the solution to 27 from 7.5 chapter was answered, more than 237 students have viewed the full step-by-step answer. The answer to “Rationalize each denominator. See Examples 1 through 3.23 2y223 9x2” is broken down into a number of easy to follow steps, and 10 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 90 chapters, and 8410 solutions. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046.

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Rationalize each denominator. See Examples 1 through 3.23