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Solution: In 1–4, find a general solution of the system for

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 1E Chapter 9.6

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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2
Problem 1E

In Problems 1–4, find a general solution of the system 𝐱’(𝘵 ) = A𝐱(𝘵 ) for the given matrix A.

Step-by-Step Solution:
Step 1 of 3

Vocabulary I. Thermoregulation:maintainingbodytemperature II. Homeostasis:Homeostasis—steadystatephysiologicalconditionofthebody III. Osmoregulation:maintainingappropriatewaterbalanceforananimal’senvironment IV. Ectothermic:bodytemperaturedeterminedbyenvironment(mostly) V. Endotherms:canregulatetheirbodytemperaturebyahighmetabolicrate VI. Cryoprotectant:isasubstanceusedtoprotectbiologicaltissuefromfreezingdamage(i.e. thatduetoiceformation). VII. Arteries:haveathickermusclelayerandgreaterelasticitytoaccommodatehighpressureas bloodflowsfromheart VIII. Veins:haveathinnermusclelayerastheyconveybloodbacktotheheartatlowervelocity andpressure IX. Capillary:anyofthefinebranchingbloodvesselsthatformanetworkbetweenthe arteriolesandvenules.Oratubethathasaninternaldiameterofhairlikethinness. X. Erythropoietin:ahormonesecretedbythekidneysthatincreasestherateofproductionof redbloodcellsinresponsetofallinglevelsofoxygeninthetissues. XI. EPO:stimulateproductionsofredbloodcells XII. ADH:helpproduceconcentratedurine XIII. ANF:helptolowerbloodpressure XIV. Insulin:lowersbloodsugar XV. Glucagon:increasesbloodsugar XVI. Growthhormone:stimulatesgrowth XVII. ACTH:initiatesstressresponse XVIII. Epinephrine/norepinephrine:increasebloodpressure,breathingrate,mobilizationof glycogen XIX. Glucocorticoids:suppressimmunityanddigestion XX. Estrogens:femalehormones XXI. ImmuneSystem:systemofbiologicalstructuresandprocessesofanorganismthatprotects againstpathogensanddisease XXII. Pheromones: are chemicals that are secreted in our sweat and other bodily fluids that are believed to influence the behavior of the opposite sex, such as triggering sexual interest and excitement. XXIII. ExamTwoStudyGuide:QuestionsandAnswers 1. Describeandprovideexamplesofkeyprocessesbywhichorganisms’physiologicalsystems interactwiththeenvironment 2. Physicallawsconstrainanimalform I. Surfaceareatovolume! II. Exchangewiththeenvironment 3. Homeostasis 4. Thermoregulation I. Endothermvs.ectothermic 5. Whydon’twehaveanimalslikedragons • Physicallawsconstrainthesizeandshapesofanimalform 6. Diffusion:fromhigherconcentrationtolowerconcentration 2 7. Diffusiontime~distance 8. Single-celledorganismorHighSA:VandlowdiffusiondistanceareEasiertogetmaterialsin andwastesout 9. MulticellularorganismorLowSA:VandhighdiffusiondistanceareEasiertoresistdiffusion andconserveheat 10. Whyaresmallmammalslesscommontowardthepoles(awayfromtheequator.Disthe answer. a. Reducedoxygenavailability b. Predominanceofectoderms c. ExcessiveUV-Bradiation d. HigherSA:Vincreasesheatloss e. LowerSA:Vincreasesheatloss 11. MaintainingHomeostasis:Homeostasis—steadystatephysiologicalconditionofthebody • A.Thermoregulation—maintainingbodytemperature • B.Osmoregulation—maintainingappropriatewaterbalanceforananimal’s environment 12. WhybotherwithHomeostasis Becauseinresponsetochangesinexternalconditions • Animalsregulatetheirinternalenvironment • Facilitateenzymaticactivity(e.g.,digestion) 13. Regulationvarieswithdifferentkindsofanimals.ectothermicandendothermic 14. Ectothermsbodytemperaturedeterminedbyenvironment 15. MostInsectsAlsomostfishes,amphibians 16. Endothermsbodytemperaturecontrolledbyhighmetabolicrate • Exampleallmammalsandbirds 17. Whatislikelyresponsiblefortheobservedtemperaturedifferencewiththethoracicand abdominalregions.Eistherightanswer. a. Slowerheatdiffusiontotheabdomen b. Increasedporosityintheabdomen c. GreaterUVabsorbanceinthethorax d. HigherSA:Vinthethorax e. Greatermuscularcontractionsinthethorax 18. Howishomeostasismaintained • Thenervousandendocrinesystemsexerttheultimatecontrolover homeostasisbecausetheycoordinatethefunctionsofthebody'ssystems. Regulationofbodytemperature,bloodpressure,pH,andglucoseconcentrationare fourexamplesofhowthebodymaintainshomeostasis 19. 20. Hypothalamuscontrols: 1.Constriction/dilation 2.Shivering 3.Sweating 21.Energyexpendituresdependsonendothermvs.ectothermic Endothermiscostlyexpensive 21.Energyexpendituredependsonbodysize,SA:Vratio,andhabitat HighSA:Vratioisexpensive Heatlosswhensmall 22. • It’senergeticallyexpensivetobeanendotherm • Sizealsocontributestometaboliccosts o SAtoVolumeagain 23.woodfrogisfoundinAlaskantundra – InsideArcticCircle • Theycansurvivein – freeze(-1t0-6degc) – Nobreathing – Heartstops – Organsdehydrate • Cryprotectant – Glucose – Urea 24.WhydosizerangesdiffersomuchforlandandaquaticanimalsBecause • landmamalsaremorephysicallyconstrainedatlargesizes • aquaticmamalsaremorephysicallyconstrainedatsmallsizes. 25.Whichoftheseisanexampleofnegativefeedback A. Asabloodclotbeginstoform,theprocessofitsformationgetsfasterandfaster. B. thegenerationofanervesignal,wheresodiumionsmovingthroughsodium channelsinthecellmembranecauseadditionalsodiumchannelstoopenup C. D. the"thermostat"inthehypothalamusofmammalsshutsoffshiveringonce normalbodytemperatureisreached E. F. Thedigestiveenzymepepsinogenisconvertedtopepsinbytheactionof G. hydrochloricacid;pepsinitselfcanthenconvertpepsinogenintopepsin. H. Oncelaborduringchildbirthbegins,uterinecontractionsincreaseinfrequency I. andintensitytopushthebabyout 26.Matchthefollowingskullswiththeirdigestivesystems Iiiiii ABC a) Herbivore=Ia,carnivore=IIb,omnivore=IIIc b) Herbivore=IIa,carnivore=Ic,omnivore=IIIb c) Herbivore=IIIc,carnivore=Ib,omnivore=IIa d) Herbivore=IIIa,carnivore=IIb,omnivore=Ic e) Herbivore=IIIa,carnivore=Ib,omnivore=IIc 27.mutationoccursinwhichaperson’sgastrinisnolongeraffectedbyH+willpredict Largebuild-upofpepsin 28.Whyisn’tpepsinusedinthesmallintestinebecauseThepHofthesmallintestineistoo high 29.Carbondioxideentersthebloodatthecapillariesofmostbodytissues(includinghead,hind limbs,forelimbs,andabdominalorgans) 30.TheCapillarieshas/havethethinnestwalls. 31.BloodpressureishighestintheAorta 32.Whichofthefollowingfeaturesdoallgasexchangesystemshaveincommon exchangesurfacesaremoist 33.Whichlungstructureisatinysacthatfunctionsasaninterfaceforgasexchangebetween airandbloodAlveolus 34.Thebodyregulatesbreathinginresponseto: CarbondioxidelevelsandbloodpH 35.AllarecharacteristicsofredbloodcellsEXCEPT: Mostnumerousbloodcells Containhemoglobin Initiateclotting Highsurfaceareatovolumeratio Don'tcontainnucleiormitochondriawhenmature 36.Manymarineanimals,includingseaturtlesanddolphins,haveadaptationsthatallowthem toregulateheatgainandloss.Incoolerwater,thecountercurrentheatexchangerinthesea turtle'sflipperstransfersheatfromarteriestoveins,resultinginheatretentioninthebodyand coolertemperaturesintheflippers. Inadditiontocountercurrentheatexchangersinitsflippers,amaledolphin'stesteshavea countercurrentheatexchangertohelpkeepthemcool.Thetestesaresurroundedby abdominalmusclethatwarmswithactivity,suchasvigorousswimming.Becausehigh temperaturescandamagesperm,acountercurrentheatexchangertransfersheatfromthe arteriesnearthetestestoveinscarryingcoolerbloodfromthetail.Inthisway,thetestesare keptcoolenoughtoprotectthespermfromdamage,andheatisretainedinthebodycore. 37.Whichofthefollowingstatementsaboutdiffusionacrossacellmembraneistrue TheanswerisB WhyistheanswerBLet'sgothrougheachoption... A.Ittakeslongerforparticlestodiffusethroughoutlargecellsincomparisontosmall cellsbecauseofthelargersurfaceareaofthecellmembrane. -largersurfaceareasaregreatforallowingparticlestodiffuseinandoutofacell!The reasonthatittakeslongerhastodowiththeincreaseinvolumerelativetosurface area.Thesmallcellactuallyhasalargersurfaceareatovolume(SA/V)whichallows particlestomoveinandoutfaster(seeanswerforB). B.Thesurfaceareaofthemembranedetermineshowmanymoleculescanenterand exitacellatonce. -thisistrue!Thebiggerthearea,themoreparticlescanmoveinandoutofthecell! Butanincreaseinvolumewillaffecthowlongittakesforaparticle(sayO2)togetto whereitneedstogoandforparticles,sayCO2,togetoutofthecells.Buthowcanyou separatevolumeandsurfaceareaThinkaboutapancakethathasalargeSA/Vratio andbasketballthathasasmallerSA/Vratio.Ifaparticleenteredeither,whichwouldit exitfirst C.Smallcellsandlargecellshavesimilarabilitiestobalancetherateofoxygenuptake withtherateofoxygenconsumption. -becauseofthelargerSA/Vratio,ittakeslesstimeforaparticletoenterasmallcell,to gettowhereitisneeded,anddiffusebackout(perhapsassomeproduct). D.Thespeedofdiffusingparticlesisslowerinlargecellsthaninsmallcells. -Theparticlespeeddoesnotchange!Theparticlesmoveatthesamerate,theyjustgo inandoutofacellatdifferentrates,dependingontheSA/Vratioofthecell! 38.Whentryingtoexchangematerials(likenutirents)intooroutofcellsmostefficiently,what relationshipbetweensurfaceareaandvolumeismostbeneficial • Maximizesurfaceareaandminimizevolume. 39.WhichisNOTconsistentwithwhatyouknowaboutchangesinsurfacetovolumeratios • Assurfaceareaincreases,volumeincreasesatthesamerate 40.Duringdigestion,hydrochloricacid(HCl)lowersthestomach'spHandthiscausesthe enzymepepsinogentobeconvertedtoitsactiveform,calledpepsin.Pepsinisaproteolytic enzyme,whichmeansitcleaves(breaks)peptidebondsassocciatedwithfoodparticles.The enzymepepsincanalsocleavepepsinogenintopepsin,andthiscausestherateatwhich pepsinogenisconvertedtopepsintoincrease.Thisisanexampleof • apositivefeedbackloop 41.whichisfalse A. Carbohydratesaredigestedbyenzymesinthemouthandsmallintestine,andare absorbedonlyinthesmallintestine B. Proteinsaremechanicallydigestedinthemouthandstomach,andarechemically digestedandabsorbedinthestomachonly C. Fatsaredigestedbyenzymesinthesmallintestine,andareabsorbedonlyinthe smallintestine D. Differentenzymesareinvolvedinthebreakdownofcarbohydrates,proteins,and fats E. Alloftheaboveareactuallycorrect. 42.Whichwouldbethebestbodyplanforamammaladaptedforlifeinacoldclimateto minimizeheatloss A. Largesize,sphericalbody,longears B. Largesize,elongatedbody,shortears C. Largesize,sphericalbody,shortears D. Smallsize,elongatedbody,longears E. Smallsize,sphericalshape,shortears 43.Basedonyourknowledgeofsizeandmetabolicdemand,inwhichgroup(s)ofanimalsyou expecttofindaclosedcirculatorysystem • Birdsandcephalopods(octopus,squid,etc.) 44.Thecapillariesallowformaterialexchange(e.g.,oxygen,nutrients,wasteproducts).Why doesn’tthisoccurinthearteriesandveins • ThebloodisflowingtoofastandThewallsofarteriesandveinsaretoothick 45.AllarefunctionsoftheimmunesystemEXCEPT: A. Distinguish"self"cellsfrom"non-self"cells B. Protectagainstrepeatedencounterswithspecificpathogens C. Targeteddestructionofforeigncellsandmolecules D. Preventpathogensfromenteringthebody A. E. MaintainbloodpHhomeostasis B. 46.Majorhistocompatibilitycomplex(MHC)isinvolvedwith:antigenpresentationand recognition. 47.Thebestdefinitionofanantigenis:foreignmoleculethattriggersthegenerationof antibodies 48..Thebody'sinnate(non-specific)defensesagainstpathogensincludeallofthefollowing except: A. mucousmembranes B. naturalkillercells C. macrophages D. antimicrobialmolecules E. T-lymphocytes 49.Whatarethemaincellsinvolvedinthespecificimmuneresponse A. selfcellsandnon-selfcells B. B-lymphocytesandT-lymphocytes C. antigensandantibodies D. naturalkillercellsandmacrophages 50.Blymphocytesrespondtoantigensbyproducingantibodies whilecytotoxicTlymphocytesrespondtoantigensbydirectattackonthepathogen 51.WhichofthefollowingisatruedifferencebetweenTcellsandBcells • Tcells,butnotBcells,candirectlyattackanddestroyinfectedcells 52.Whatistheprimaryfunctionofantibody-mediatedimmunity itproducesantibodiesthatcirculateinthebody 55.WhichofthefollowingfeaturesisNOTanadaptationformaximizinggasexchangeinthe alveoliofthelungs A. Highsurfacearea B. Moistexchangesurface C. Shortdiffusiondistancebetweenalveoliandbloodvessels D. Largenumberofalveoli E. Specializedtransportproteinsembeddedinalveolarcells 56.Whichstatementabouthumanbloodvesselsiscorrect A. Allarteriescarryoxygenatedblood,allveinscarrydeoxygenatedblood B. Veinstransportbloodfromthehearttothecapillaries C. Arteriescarrybloodtowardtheatriaoftheheart D. Pulmonaryveinscarryoxygenatedbloodtotheheart E. Thediameterofarteriesislargerthanthatofveins F. 57.Whichsequenceofbloodflowwouldbeobservedinamammal A.B. leftventricle--aorta--lungs--outtothebodytissues D. rightatrium--pulmonaryartery--leftatrium--rightventricle C. E.F. veins--rightatrium--rightventricle--pulmonaryartery--lungs GH. . pulmonaryveins--leftatrium--leftventricle--outtothelungs I. rightventricle--pulmonaryvein--leftventricle--outtothe bodytissues 58.Whichorganismisn'tcorrectlymatchedwithitscirculationtype: flatworm—diffusion A. dragonfly--opencirculation bird--closedcirculation,2chamberedheart B. octopus--closedcirculation C. mammal--closedcirculation,4chamberedheart 58.WhichbarriermustO2andCO2crosstopassbetweenairandbloodinsidethe lungs: D. extracellularfluid,epithelialcells,capillarywall 59.Countercurrentexchangeinthefishgillhelpstomaximize: • Diffusionofoxygenintotheblood 60.Whichstatementaboutthemammalianheartiscorrect • Intheadultheart,bloodintherightchambersoftheheartcannotentertheleftchamberswithout passingthroughthelungs 61.Whichbloodcomponentismatchedincorrectlywithitsfunction • whitebloodcells(leukocytes)--transportcarbondioxideandregulatebloodpH 62.Whichstatementaboutgas(O2andCO2)transportinhumansiscorrect • whitebloodcells(leukocytes)--transportcarbondioxideandregulatebloodpH 63. weeatfornutritionalrequirementsandadaptationamonganimals. 64. whatdoweneedtosurvive,growandstoreenergy • Energy(ATPproduction) a. Monomersofprotein,carbs,fat b. Cellularrespiration 65. Biosynthesis (growth, reproduction) • Carbon and nitrogen • Storage b) Essentialnutrientsare 1)Aminoacids:proteinassembly 2)Fattyacids:membranesandhormones 3)Vitamins:co-enzymes 4)Inorganicminerals:bones,hemoglobin 66.Matchthefollowingskullswiththeirdigestivesystems: a) Herbivore=Ia,carnivore=IIb,omnivore=IIIc b) Herbivore=IIa,carnivore=Ic,omnivore=IIIb c) Herbivore=IIIc,carnivore=Ib,omnivore=IIa d) Herbivore=IIIa,carnivore=IIb,omnivore=Ic e) Herbivore=IIIa,carnivore=Ib,omnivore=IIc 67.4stagesoffoodprocessing. 1) Ingestioniseating(mechanicaldigestion) • CHEWING:Mechanicalbreak-downoffoodintosmallerparticlesEsophageal sphinctercontrolsmovementoffoodintoesophagus 2) Digestionischemicallybreakdownfoodintomoleculesusablebycells. • Parasympatheticnervoussystem(PNS) a)BeginswithSalivainmouth—salivaryamylasebreaksdownstarchand glycogen( smallcarbohydrates) b)Then,stomach—enzymes,e.g.,pepsin,andgastricjuice(veryacidic)whichare importantinproteindigestion.Stomachalsostoresfood. -H++ PNS GASTRIN PEPSINOGEN PEPSIN MUCUS 3) Absorptioniscellstakeupdigestedmaterialandallowsittobeprocessed 1) Aminoacids,sugars,fattyacids,nitrogenousbases • AbsorptionOccursinsmallintestine—digestedmoleculesmustenterthebody viaDIFFUSION • Smallintestinehasahighsurfaceareaandlowdiffusiondistancetoaccomplish this. --Villi --Microvilli 4) Eliminationisexcessdigestedmaterialleavesthebody(getridoftherest) • Waterbalance 90%ofwater“borrowed”fromcirculatorysystem -Diarrhea(dehydration) -Constipation • Feces • Smell:bacteriainlargeintestine • Color:Bile,bilirubins,andiron(breakdownofred-bloodcells) Summary:FoodProcessing Goal:breakdownandabsorbuseablemonomers Ingestion Digestion Absorption Elimination yesandsome yessalivary Mouth mechanical Amylase(carbs) digestion Stomach Yespepsinproteins Yescarbsproteins Smallintestine nucleicacidsand Yesmaineventishere fats Yes,andwater Largeintestine reabsorption 68.foodprocessingDigestion(continued)thesmallintestineisalsoveryimportant Smallintestine—inhumansisabout6meterslong.Mostdigestionoccurshere(and absorption) 69.FoodProcessingorDigestion—RoleofotherOrgans • Pancreas(enzymesupplyhouse!) – Producesdigestiveenzymes • Trypsin,chymotrypsin,carboxypeptidase(polypeptides aminoacids) • Nuclease(nucleicacid nucleotides) • Amylase(polysaccharides disaccharides) • Lipase(fatdroplets glycerol,fattyacids) • Liver – Detoxifyalcoholandothertoxins – Productionofbilesalts(breakupfatglobules) – Gallbladderstoresbile 70.Whyisn’tpepsinusedinthesmallintestine a) Digestiondoesnotoccurinthesmallintestine b) Proteinsarenotdigestedinthesmallintestine c) ThepHofthesmallintestineistoohigh d) AandB e) Pepsinisusedinthesmallintestine Ulcerscausesare 1. RapidEatingandStress • Immunesuppression 2.Bacteria—Helicobacterpylori Preventsstomachcellsfromsecretingmucus 3.Firsttreatmentforulcersisanantibiotic. 71.Ifamutationoccursinwhichaperson’sgastrinisnolongeraffectedbyH+,predictwhat wouldhappen a) Accumulationofpepsinogenwithoutconversiontopepsin b) FailuretoproduceH+inthefirstplace c) Failuretoproducepepsin d) Largebuild-upofpepsin e) AandC 72.Nutritionanddigestion. • Animalseattoobtainenergy,growandtoacquireessentialnutrients – Adaptationsvaryamongherbivores,carnivores,andomnivores(dentition, cecum,intestinallength) • Foodprocessinginvolvesfouressentialsteps – Ingestion,Digestion,Absorbtion,Elimination – Mouth,stomach,small&largeintestine • HelpfromPancreasandLiver • Keythemes:compartmentalization,feedbackloops,andSA:V 73.Howhasfoodaffectedprimateevolution • Brainsareenergeticallyexpensive 74.Whatdoesthecirculatorysystemdo • FUNDAMENTALCHALLENGES – Getthegoodstuffdistributedtoallcellsinthebody • Oxygen,essentialnutrientsandmonomers – Getthebadstuffoutofbody’scellsandintoexcretorysystem • CO 2wasteproducts • Closelytiedtotherespiratory(orgasexchange)systeminmanyanimals(nextlecture) 75.TypesofCirculatorySystems. 1)Diffusionalone Occursinverysmallorganisms:single-celledorsmallmulticellularorganisms --Singlecelledprotists --Fewcelllayeredanimals Cheapbutsufferslimitations Diffusiontime~distance 2 2)OpenCirculatorySystem Arthropodsandmostmolluscs Bathestheorgansdirectlyandisnotconfinedtovessels --Hemolymph --NOTtransportoxygen Advantages:cheaptobuildandmaintain --noextensivebloodvessels --nohighpressuresystem 3)ClosedCirculatorySystem • Bloodcontainedinextensivevesselnetworks – Arteries,veins,capillaries – Earthworms,somemolluscs,allvertebrates • Advantages:highbloodpressureallowsforgreatermetabolicdemands – Larger,moreactiveanimals – Mostendotherms – EXPENSIVE 76.Arterieshaveathickermusclelayerandgreaterelasticitytoaccommodatehighpressureas bloodflowsfromheart 77.Veinshaveathinnermusclelayerastheyconveybloodbacktotheheartatlowervelocity andpressure 78.Thecapillariesallowformaterialexchange(e.g.,oxygen,nutrients,wasteproducts).Why doesn’tthisoccurinthearteriesandveins a) Thebloodisflowingtoofast b) Thewallsofarteriesandveinsaretoothick c) Thenecessarymaterialsarenotinarteriesandveins d) AandB e) Alloftheabove(A,B,&C) 79.Howdocapillariesfacilitatematerialexchange 1.Thin-walled 2.Closeproximity 3.Slowflow *Facilitatediffusion! Thisallowsoxygen,nutrientsandwastetoflowtoandfromtissues 80.Blood • RedBloodCells—havehemoglobin,nonucleus • WhiteBloodCells—roleinimmunefunction Platelets—aidinbloodclotting,nonucleus • 81.synthesis. • Redbloodcells – Biconcavedisks • HighSA:V(exchange) • 25trillioninabody(5L) – Nonucleusormitochondria • Morespaceforhemoglobin • CSI–howgetDNA – Producedinbonemarrow • Erythropoietin(EPO) • Circulatorysystem=transportsystem – Function:oxygenandnutrientstotissues,CO2andwasteproductsout • Typesofsystemsvaryamongorganisms – Diffusionvs.openvs.closed • Humancirculatorysystem – Heart,bloodvessels,blood – Physics&diffusionplaykeyrolesinthisprocess 82.Capillarieshaveamuchnarrowerdiameterthanarteriesorveins.However,bloodflows slower–notfaster–whenincapillaries.Why a) Capillarywallsarenotthinenoughtoallowoxygenexchangewithcells b) Capillariesarefarfromtheheart,andbloodslowswithdistancefromheart c) Diastolicbloodpressureistoolowtodeliverbloodtocapillariesatahighflow rate d) Systemiccapillariesaresuppliedbytheleftventricle,whichhasaloweroutput thantherightventricle e) Thetotalsurfaceareaofthecapillariesislargerthanthetotalsurfaceareaof arteries 83.Capillarieshaveamuchnarrowerdiameterthanarteriesorveins.However,bloodflows slower–notfaster–whenincapillaries.Why a) Increasedconcentrationofredbloodcellsinthecapillariesslowsdowntheflow rate b) Capillariesarefarfromtheheart,andbloodslowswithdistancefromheart c) Diastolicbloodpressureistoolowtodeliverbloodtocapillariesatahighflow rate d) Systemiccapillariesaresuppliedbytheleftventricle,whichhasaloweroutput thantherightventricle e) Thecombineddiameterofallthecapillariesislargerthanthecombined diameterofarteries 84.Respiratorysysteminfluencedbymetabolicdemands 1) Totalmetabolismisproportionaltobodymass 1) Endothermyvs.ectothermy 2) Becausemassincreasesfasterthansurfacearea,it’sharderforbiggeranimalsto acquiresufficientoxygenbydiffusionfromtheexteriortotheinterioroftheanimal. 1) SA:Vdecreasesbutmetabolicdemandincreases 3) Thus,respiratorygasexchangesurfacemustscalewithbodyvolumeinsteadofbody surfacearea. Inhumans,thelungsurfaceis100m ,whereasthebodysurfaceis2m . 2 • 85.Considertwocube-shapedorganisms.Bothareendothermic.Onehasdimensionsof2x2x 2cm.Theotheris4x4x4cm.Ifthesmallercubehasalungsurfaceareaof10,whatisthe estimatedlungsurfaceareaofthelargercube 2 A. 40cm 2 B. 2.5cm C. 1.5cm 2 D. 80cm 2 2 E. 1.25cm • Surfaceareaofacube:6xLxW Volumeofacube:LxWxH 86.4TypesofGasTransferMechanisms: 1) Bodysurface(diffusiononly) 1) NeedhighSAtoV 2) Lowmetabolicdemand Examples:Protists,flatworms,cnidarians 2) Gills(aquatic) Aquaticanimals Challenge:oxygencontentofwater(1%)isMUCHlowerthanair(20%) 1)HighSA:gillsurfaceareacanexceedbodysurfacearea 2)Ventilation:Waterismovedpastgillsbymuscularactivity WaterisDENSERthanair 3)Countercurrentexchange 3) TrachealSystem(branchednetwork) Insectshaveanopencirculatorysystem(notinvolvedingasexchange) Trachealsystem(onland) --Oxygentransportedasagas! --MustkeepwetwithhighSA 4) Lungs Mammals,birds,reptilesandmanyamphibians Lungsarehighlyvascularizedwithhighsurfaceareaandlowdiffusiondistance • Dependsonwhereyouliveandyourmetabolicdemands 87.Whyisgasexchangemoredifficultforaquaticanimalswithgillsthanforterrestrialanimals withlungs a) Waterisdenserthanair b) WatercontainslessO2thanairperunitvolume c) Diffusionissloweracrosstheair-waterinterface d) AandB e) A,BandC 88.Howdoesyourbodyknowwhenandhowfasttobreathe a) Yourbrainmonitorsoxygenconcentrationsinyourblood b) Yourlungsmonitoroxygenconcentrationsinyourblood c) Yourbrainmonitorstheratioofoxygentocarbondioxideinyourblood d) Yourlungsmonitortheratioofoxygentocarbondioxideinyourblood e) Yourbrainmonitorscarbondioxideconcentrationsinyourblood 89.Howcontrolbreathing MedullamonitorsCO l2velsusingchangesinpH. CO 2reactswithwatertoformcarbonicacid. LowerpH=higherCO 2 So,breathingrateincreases 90.Howtransportoxygen • O2transportinbloodisincreased70xbyhemoglobin – Aproteinwith4subunits – Oxyhemoglobin • Bindsoxygenreversibly – ConformationverysensitivetopH • HighCO changesbloodpH hemoglobinreleasesmoreoxygen. 2 – HighpHinducesbinding – LowpHinducesrelease 91.MatchthelocationsinthebodywiththelocalbloodpHandhemoglobin(Hb)activity a.I.HbbindingO2,pHlow;II.HbreleasingO2,pHhigh a. I.HbbindingO2,pHhigh;II.HbreleasingO2,pHlow b. I.HbreleasingO2,pHlow;II.HbbindingO2,pHhigh c. I.HbreleasingO2,pHhigh;II.HbbindingO2,pHlow 92.Respiration:obtainoxygenandexpelCO 2 – Closelylinkedtocirculation • Physicalstructureconstrainsrespiratorystructures – Endothermyvs.ectothermy,aquaticvs.terrestrial – Skin,gills,trachea,lungs – Surfaceareaanddiffusiondistance • Humanrespiration – TheroleofpH – Chemicalbindingofoxygen • Hemoglobingreatlyenhancesoxygentransport 93.AltitudeandRespiration • Arefeweroxygenmoleculesperbreathathighaltitude • Resultsinhypoxia(lowlevelsofoxygen): – Sleeplessness – Headachesandvomiting – Inabilitytomaintainsustainedactivity • Within2weeks,producemoreRBCs 94.Whatdoestheimmunesystemdo • FUNDAMENTALCHALLENGES o Defense:keepthebadguysoutBacteria,viruses,&multicellularparasites DESTROY o Multiplelinesofdefense • Precisionwarfare o Differentiateselffrom“non-self” o Differentiatehealthyselffrom“infectedself” DESTROY o Preventre-infection • Oneofmostsophisticatedandelaborateorgansystemsinthebody 95.therearetwotypesofImmunity 1. Innate(Non-specific)Immunity Providesgeneralprotectionagainstanythingforeignthatmightencounterorenterthe body. --Broadspectrum I.Skinandmucousmembranes PhysicalBARRIER Alsoprovideschemicaldefenses—e.g.,sweat,whichmakestheskinveryacidic, andantimicrobialproteins Injurycreatesopening II.Phagocyticcells—engulforingestinvaders “Phagocytosis”(eat‘em) Whitebloodcells— Macrophages(‘bigeaters’)etc. neutrophils(firstresponders) eosinophils(dealwithmacroparasites) III.Antimicrobialproteins—proteinsthatchemicallyattackpathogens&communicateto othercells ComplementSystem(>30proteins) Complexcascadeàproteinsthatattackinvaders Interferons—usedintreatmentofviralinfectionsandcancer IV.Inflammatoryresponse(localized) Chemicalandcellularresponsetoinjuryorlocalizedinfection àEliminatessourceofinfection àPromoteswoundhealing V.Naturalkillercells Cellsthatdestroyvirus-infectedcellsorcancerouscells LackofMHCproteinsoncell surfacetriggerNKC Lyse(=breakopen)thecellsinsteadofengulfingthem 96.Whichofthefollowinghelpsyourbodyrecognize“self”from“non-self”whenfighting pathogens A.Inflammatoryresponse B.Complementsystem C.Majorhistocompatibilitycomplex D.Phagocytes E.A,BandC 97.Immunedefensesystem I. Innateimmunesystem(non-specific) I. Skin(protectivebarrier) II. Phagocytes(eat‘em) III. Antimicrobialpeptides(kill‘em) IV. Inflammation V. Naturalkillers(dissolve‘em) II. Acquiredimmunesystem(specific) I. Antibody-mediatedresponse(Bcells&antibodies) I. Primaryandsecondaryresponses II. Cell-mediatedresponse(Tcells) I. Dealingwithintracellularinfections 98.RoleofLymphocytesinAcquiredImmunity(Whitebloodcells=Lymphocytes) • B-cells—involvedinantibody-mediatedresponseinwhichantibodiesare produced. • T-cells—involvedincell-mediatedimmunityinwhichTcellsattackinfectedcells 99.whitebloodcellsproduced InnateImmunesystem -Macrophages -Naturalkillercells Acquiredimmunesystem Lymphocytes -TandB-cells 100.LymphocytesRecognizeAntigens Mustbeabletodifferentiateselffromnon-self! Antigensaretypicallyforeignproteinsorcomplexsugars(orpiecesthereof) --isolatedmolecules,toxins,orfragmentsfrombacteria,fungi,viruses, protozoaandparasites --“Antigen”fromAntibodyGenerator Antigensarerecognizedbyspecificantigenreceptors ProducedbyBcells Receptorsveryspecifictocertainantigens 101.Howdoesyourbodyproduceantibodies Antibodies(immunoglobins) Oncethoughttobe“madetoorder”in responsetoinvasionbyantigens NowknownthatdiverseantibodiesareproducedinfetaltissuebydifferentiationofB lymphocytes. --Millionsofvarietiescirculating! --Attempttoanticipateeverypossibleantigen Thesecellsremaindormantuntilneeded --CLONALSELECTION 102.ClonalSelectionare2typesofcells EffectorCells(=plasmacells) • Short-livedcellsthatcombattheantigen • Initialdefense(primaryresponse) – 2000antibodiespersecond! MemoryCells(secondaryresponse) • Long-livedcellsthatbindtothesameantigen • Canrespondrapidlyandstronglytothesecondexposuretotheantigen 2.Acquired(Specific)Immunity Allowstheorganismtoresistaspecificpathogenafterexposure. --Targeteddestruction 103.Vaccineshelptheacquiredimmunesystembecomeprimedsothatitcanrapidlyrespond toanactualattackbyagivenpathogen.Whatcanwemakevaccinesoutof A.Componentsofnon-functionalviruses B.Componentsofnon-livingbacteria C.Toxinsproducedbybacteria D.AandB E.A,BandC 104.Cell-mediatedImmunity Tcellsrespondtoantigenfragmentspresentedonsurfaceofbody’scells Indicateintracellularinfection Viruses,cancercells,etc. 1)HelperTcells Firstresponsetoantigen-presentingbodycells StimulatesproliferationofBcellsandcytotoxicTcells 2)CytotoxicTcells Identifyanddestroyinfectedcells Exposepathogentorestimmunesystem 105.Youaccidentallyexposeyourselftoanintracellularvirus.Whichofthefollowing“linesof defense”inyourimmunesystemwouldyouexpecttorespond a) interferons b) cytotoxicTcells c) helperTcells d) aandb e) a,bandc 106.Osmoticequilibrium 1. Gainionsfromtheoutsideenvironment Hypertonicenvironment 2. Losewatertotheoutsideenvironment “Dryout”inwater 107.Whatdoestheexcretorysystemdo • FUNDAMENTALCHALLENGES – Homeostasis(steadystatephysiologicalcondition) • Osmoregulation:maintainingdesiredwaterandionbalance • Movementofwaterandsolutes(substancesdissolvedinwater) – Keepthegoodstuff,getridofthebadstuff • Water,nutrients,vitamins,salts,nitrogenouswaste • Variesbyhabitat:fresh-vs.saltwater;landvs.water • Howdothisefficiently 108.dealingwithwater • Marineenvironments – Hypertonicenvironmentformostvertebrates • Drinkalotofwater • Concentratedurinewithlotsofsalt,littlewater • Freshwaterenvironments – Hypotonicenvironment • Peealot(diluteurinewithfewsalts) • Terrestrialenvironments – Desiccationenvironment • Conservewateratallcosts • Skin,exoskeleton,waxycuticle,shells,etc. 109.Nitrogenouswastes • Byproductsofbreakingdownproteinsandaminoacids. • Whatyouexcretedependsonyourhabitat --Ammonia --Urea --Uricacid Toproducethosedependsonwhereyoulive. 110Nitrogenouswastes 1.Ammonia—averysmallandtoxicmolecule(NH ) 3 Solubleinwater Excretedbyanimalswithaccesstowater(dilute) Fishesandaquaticinsects 2)Urea—detoxifiesammonia Lowtoxicity Mammals,turtles,adultamphibians(land) Energeticallyexpensive Why Because 3)Uricacid—“saltsnot” Lowtoxicitythanurea Insects,birds,reptiles Notsolubleinwater --Semi-solidpaste! --Conservewater Mostenergeticallyexpensive 111.Ananimalhasthefollowingcharacteristics:aterrestriallifestyleandendothermy(anda highmetabolicdemand).Youpredicttheanimalalsohas: I.Ureaasitsnitrogenouswaste II.Lungs III.Aclosedcirculatorysystem a)Ionly b)IandIIonly c)IIandIIIonly d)I,II,andIII e)IIIonly 112.Osmoregulation Kidney—filtersblood,producesurine Ureter—carriesurineproducedbykidneystobladder Bladder—storageofurine Urethra—carriesurineoutofthebody 113.whyweneedkidney Allowslifeondryland Approximately1500litersofbloodperdayarefilteredbythekidneys. --Eliminatestoxicwasteproducts --99%ofwater,vitamins,sugar,etc.retained Yourbloodisfiltered250+timesperday Metabolicallyexpensive 114.kidneystructure Consistsofrepeatingunitscallednephrons 80kmoftubules! 1.Filtrationofblood 2.Reabsorbtion/secretion 3.Excretion 115.Anatomyofanephron–Bowman’scapsule Filtration:removingwastefromthebloodànephron Glomerulus—aballofcapillaries Bowman’scapsule—entryintothenephron,waterandsolutestransferredherefrom blood(nobloodcells) 116.LoopofHenle Descendingandascending‘limbs‘WaterandsolutesreabsorbedAllowsyouto generateconcentratedurine 117.MatchtheLoopsofHenleshowninthediagramtothemammalsthatpossessthem. (Thesedrawingshavebeenscaledtobodysize). I. Kangaroorat(desertrodent) II. Beaver(aquaticmammal) III. Human a)rat,beaver,human b)human,beaver,rat c)rat,human,beaver d)beaver,human,rat e)beaver,rat,human 118.HormonalcontroloftheKidney Kidneysareveryflexible Versatility!(50to1200mOsm/L) ADH—Antidiuretichormone helpsconcentrateurine Effectsofalcohol 119.UrineTrouble…(orEverythingyouwantedtoknowabouturine) • Truckerbombs–growingepidemic! • Color – Yellow:bilirubin'sagain(hemoglobin) – Black:alkaptonuria(geneticdisease) – Bloody:kidneyproblems,parasites,etc. • Urea – Cigaretteadditive 120.drinkingsaltwater • Urine:50to1400mOsm/kg • Blood:300mOsm/kg • Seawater:2000mOsm/kg – 1Lintake,1.7Lloss – Water,watereverywhere… • Noranydroptodrink… • Boilit,condensetheevaporatedwater. 121.vampirebats • vampirebat – 3speciesSouthAmerica – Feedonsleepingmammals • Saliva – draculin(anticoagulant) – Drink–notsuck–blood • Excretorysystem – 20g(1ozofblood)in20minutes – 40ganimal! – diluteurinemostlyplasma – Concentratedurinebackincave • kiss! – Bloodtransfusions 122.TheHangover.(Veisalgia) • Alcoholisadiuretic(blocksADH) – 250mlalcoholà1000mlwaterloss! • Dehydration – Brainshrinksfromskull;drymouth – Thenthehangoverwillcome • Liverdetoxification – Reduceglycogen(storedglucose) – Musclefatigue,mentalexhaustion – Alcoholwithtoxins,impuritiesàmoresevere 123.Toomuchwater • Waterintoxication – ToomuchwatercalledHyponatremia • Saltconcentrationofblooddecreases – Impairbrain,heart,musclefunction – Marathonrunners – Ecstasyusers • 2006:“HoldyourweeforaWii” – Radiostationcontestkillswoman • 2014:5-yrdiesafterforcedtodrinksoda 124.Somediseasesanddisordersoftheexcretorysystem Kidneystones—usuallymadeofcalciumoxalate(80%)(genetics,diet,andhydration) 125.ExcretorySystem • Osmoregulationisprocessbywhichfluidandionbalancesaremaintained – Homeostasis – Challengesvarywithenvironment • Howmuchandwhichformsofnitrogenouswastesareproducedvariesamonganimals – Ammonia,ureaanduricacid – Landvs.water,freshwatervs.saltwater • Inhumans,nephronswithinthekidneyplayavitalroleinosmoregulation – Filtration,reabsorption/secretionandexcretion – Versatilityofthekidney! 126.Inwhatpartofthenephronismostofthesodiumchlorideremovedfromthefiltrate(i.e., whereisthetubulemembraneselectivelypermeabletosaltbutnottowater) a)glomerulus b)Bowman’scapsule c)proximaltubule d)ascendinglimboftheLoopofHenle e)descendinglimboftheLoopofHenle 127.ChemicalSignalinginAnimals ChemicalSignalsproducedbyglands Exocrine—theexternalenvironment--affecttheinteractionoforganisms(e.g., pheromones) Endocrine--theinternalenvironment--affectinternalfunctioningoforgans 128.Evidenceforhumanpheromones • Menstrualsynchrony • Lapdancing!! – 5300lapdances – 60dayperiod • Dancers: – Ovulating:$70 – Non-ovulating:$50 – Birthcontrol:$35 129.TheEndocrineSystem • Asetofglandsthatproducehormones • Hormones—arechemicalmessengersinbloodsstream – Producedbyglandsinthebody – Secretedintothebloodstream – Effectiveatverylowconcentrations • Hormonesreachallpartsofthebody,butonlycertaincellsrespond 130.HowdotheNervousandEndocrineSystemsDiffer • Hormones – Moreslowlyacting • minutestoyears – Specializedglands – Travelthroughoutbloodstream – Examples– • Growth • Puberty • Metabolism • Aging • Neurotransmitters – Rapidacting • secondstominutes – Releasedbyneurons – Crosssynapses – Examples– • Heartrate • Respiration • Voluntarymusclecontractions 131.NeurotransmittersandHormonesare–e.g.,Norepinephrine 132.Hormonalsignaling—3events 1. Receptionofasignal—bindingtoareceptor 1. Maybepositiveornegativedependingonreceptor 2. Receptorpresence&abundancemodulatessignalstrength! 2. Signaltransduction—triggeringofchangeswithinacell 3. Responseofthecell—e.g.,productionofaprotein 133.WhichofthefollowingisNOTtrueofhormones a)hormonestravelinthebloodstream b)hormonesareeffectiveatlowconcentrations c)hormonescanbeusedtocommunicatewithotherindividuals d)aandb e)ALLofthesearetrueofhormones 134.PartsoftheEndocrineSystem • Hypothalamus:producehormones,regulatepituitarysystem – Specializedbloodandnerveconnectionswithpituitary • Pituitarygland: – producehormones,regulateperipheralglands • Peripheralglands – Heart:bloodpressure – Pancreas:bloodglucose – Adrenal:stress,osmoregulation – Ovaries/testes:sex&reproduction 135.PituitaryGland ADH–Anti-diuretic Hormone Regulatesbloodosmolarityandwaterreabsorbtion AtrialNaturiaticFactor --ANFinterfereswithADH 136.Somemalfunctionsofthe EndocrineSystemare PituitaryGland GrowthHormone(toomuch)àGigantism GrowthHormone(toolittle)àdwarfism Dutch:tallestpeople Males:6’1” Females:5’7” 137.Pancreas • Producesthehormonesinsulinandglucagon—regulatebloodglucosethroughnegative feedbacks – Insulin—lowersbloodglucose – Glucagon—raisesbloodglucose • Homeostasis:blood-sugarlevels TypeIDiabetes(children) • Autoimmunedisorder—immunesystemdestroysbetacells(insulinproducingcells) TypeII(“Adult-onsetDiabetes”) • Deficiencyofinsulinorreducedresponsivenessoftargetcells – Lossofsugarinurine • USA:Emergingepidemic(20millioncases) – Age,activity,bodyweight – Amputation,blindness 138.Anorganismissufferingfromdiabetes.Whymightthisalsoleadtofrequenturinationand dehydration a)insulininterfereswiththeproductionofADH b)saltisnotbeingexcretedaroundtheloopofHenle c)thebodymustuseextrawatertoexcretethesugar d)itspancreasisnolongerproducingenoughglucagon e)itsADHreceptorshavebeenup-regulated(moresensitizedtoADH) 139.AdrenalGland—2parts • AdrenalMedulla – Producesepinephrine+norepinephrine – Increasedbloodflowtoheartandlungs,acceleratedheartbeat,increasedblood pressure,etc. • Adrenalcortex – Producescorticosteroidssuchasglucocorticoidswhichaffectlong-term responsestostress 140.TheLowTControversy • Hypogonadisminmen – Decreasingtestosteroneproduction(andropause) – Depression,fatigue,sexualdysfunction,muscleloss • 2002:$324million • 2013:$2.2billion • Feb2014 • RisksofTtreatment • Heartattack,stroke,death 142.IfapersonhasmemoryBcellsagainstanantigenonthemeaslesvirus,thatperson: ismuchlesslikelytodevelopmeaslesasecond time 143.Whichofthefollowingstatementsabout clonalselectionisFALSE macrophagesundergoclonalselection 144.WhichistrueabouttheBplasmacells involvedinclonalselection plasmacellsareclonesofB-cellsthathave encounteredandrespondedtothepresenceof anantigen 145.Whichofthefollowingcellscanengulf (phagocytize)apathogen Macrophages 146.Whichofthefollowingeventsdoesn'toccur aspartoftheinflammatoryresponsetoabreak intheskin Bcellssecreteantibodiestomarkpathogens fordestruction 147.Whichstatementbestdescribesthe differenceinresponsesofBcellsandcytotoxicT cells Bcellssecreteantibodiesagainstapathogen; cytotoxicTcellskillpathogen-infectedhost cells 148.WhichisNOTanexampleofacellor moleculethattheimmunesystemiscapableof recognizingandrepsondingto Noneoftheabove(allofthesecellsand moleculescanberecognizedbytheimmune system) 149.Whichisnotpartoftheinnateimmune system cytotoxicTcells 150.Antigensare foreignmoleculesthattriggerthegenerationof antibodies.

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Chapter 9.6, Problem 1E is Solved
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Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

Since the solution to 1E from 9.6 chapter was answered, more than 316 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. The answer to “?In 1–4, find a general solution of the system ????’(???? ) = A????(???? ) for the given matrix A.” is broken down into a number of easy to follow steps, and 19 words. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This full solution covers the following key subjects: Find, general, given, Matrix, solution. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. The full step-by-step solution to problem: 1E from chapter: 9.6 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM.

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Solution: In 1–4, find a general solution of the system for