2023-2024学年云南省高二期末模拟考试卷(24-579B)试题(数学)

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2023-2024学年云南省高二期末模拟考试卷(24-579B)试题(数学)试卷答案

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Bycontrollingthefrequencyandstrengthoftheelectriccurrent,theresearcherscanstimulateeithersourness,saltinessorbitterness.Theysayupto80%ofpeopleexperiencechangesinsaltinessandsournesswiththedevicesand70%cansensechangesinbitterness.DrRanasinghesaidhewasalsoworkingonwaysofimitatingsweetnessandspicinessbyrapidlyheatingandcoolingthetongue.Itcouldleadtoaspoonthatallowsdessertstotastesweetwhilehavinglowersugarlevelsoraforkthatcangiveacurryextraheatwithouttheneedforextrachilies().DrRanasinghesaid:"Wehavesomecarlyfindingsofimitatingswectness,amint-coolsensationandhotorspicysensations."28.Whatscasoningcutleryhasbeendeveloped?A.Chopsticks.B.Knives.C.Forks.D.Spoons,29.Howdocstheseasoningcutlerywork?A.Itcutsdownsaltinfood.B.Itaddsextraseasoninginfood.C.Itdeliversanelectricshocktothetongue.D.Itweakensourtastesensationinourmind.30.Whatdoestheunderlinedword"relinquishing"inParagraphImean?A.Removing.B.AttractingC.Acquiring.D.Compromising.31.Whatdoesthetextmainlywanttotellus?A.GiveyourselfanelectricshocktomaketakeawayshealthyB.Trytoeatathomeinsteadofhavingtake-outfoodtostayhealthy.C.Makeyourfoodtastesaltierbyusingapairofelectricchopsticks.D.Reducetheamountofsaltinyourfoodtoavoidhealthproblems.0LastyearCongressissuedamoralcalltoactionwhenitorderedtheNationalInstitutesofHealthtoreevaluateitsethicaloversight(伦理上的疏忽)ofgovernment---fundedprimate(灵长类)research.Althoughthescientificcommunitywidelyseesnonhumanprimatesasessentialforadvancesinbiomedicine(theyhavecausedmajorgainsinthefightsagainstAIDSandncurologicaldiseasessuchasParkinson's,forexamplc),rescarchersagreemorccanbedonetotreattheanimalsmorehumanelyandconductresearchlesswastefully.Tothatend,theNIHgatheredfamousscientistslastSeptembertodiscussthefutureofprimate-basedrescarch-andtheyagreedthatdatasharingisthewayforward.Researcherscouldreduceexperimentsonnonhumanprimatesbystudyingdatathathavealrcadybeencollectedtoanswernewquestions,saysDavidO'Connor,apathologistattheUniversityofWisconsin-Madison.O'Connoriswalkingthewalk:hislaboratorystudiestheZikavirusinprimates,andheimmediatelypostsalltheresultsonline.ThegoalistofigureoutwaystofightZikaasquicklyaspossiblewithoutplacinganundue(burdenonresearchprimates.TheSeattle-basedAllenInstituteforBrainScience,whichusesrhesusmacaques,smallSouthAsianmonkeys,tostudythemolecularbasisofbraindevelopment,alsomakesallresultspublic.O'Connorsaysthispracticeshouldbemorewidespreadsothat"researcherswhoareusingthisscarcebutvitalresourcecanlearnasmuchaspossiblefromasfewanimalsasnecessary."Still,heisskepticalthatdatasharingwillcatchonbecauseitwouldrequireachangein"normativebehavior"-science'sstrongcultureofsecrecy,inwhich

分析设A、B点坐标分别为（x₁，y₁），（x₂，y₂），由直线垂直的性质得x₁x₂+y₁y₂=0，由$\left\{\begin{array}{l}{x+2y-3=0}\\{{x}^{2}+{y}^{2}+x-2cy+c=0}\end{array}\right.$，得5y²-（2c+14）y+c+12=0，由此利用韦达定理能求出实数c的值．

解答解：设A、B点坐标分别为（x₁，y₁），（x₂，y₂），
由OA⊥OB，得k_OA•k_OB=-1，即$\frac{{y}_{1}}{{x}_{1}}•\frac{{y}_{2}}{{x}_{2}}$=-1，
∴x₁x₂+y₁y₂=0，①
由$\left\{\begin{array}{l}{x+2y-3=0}\\{{x}^{2}+{y}^{2}+x-2cy+c=0}\end{array}\right.$，
得5y²-（2c+14）y+c+12=0，
则${y}_{1}+{y}_{2}=\frac{1}{5}（2c+14）y+c+12=0$，②
又x₁x₂=（3-2y₁）（3-2y₂）=9-6（y₁+y₂）+4y₁y₂，
代入①，得9-6（y₁+y₂）+5y₁y₂=0，③
联立②③，解得c=3．
∴实数c的值为3．

点评本题考查直线中参数值的求法，是中档题，解题时要认真审题，注意直线垂直的性质、韦达定理的合理运用．