广东省2024-2025学年七年级开学测试试题(数学)

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广东省2024-2025学年七年级开学测试试题(数学)试卷答案

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阅读下列短文,从每题所给的A、B、C、D四个选项中选出最佳选项

AYellowstoneNationalParkYellowstoneisopenyear-roundtovisitors,thoughexperiencesdifferdependingontheseasonyouvisit.March-May:SnowcancontinuctofallintoMarchandmanyoftheroadsmayremainclosed,withploughingusuallybeginningsometimeinApril.Hikingconditionsatthistimearewet.Youwon'tfindmanycrowds,forgoodreason.June-August:ThebusiesttimeofyearintheparkisJulyandAugust,asfamiliesarriveintheirdrovesandtemperaturesriseupintothemid-20s(C).Backcountrytrailsarefullyopenandthisistheidealtimetogohiking.September-October:BySeptember,theweatherisprettymild(highsof19CinSeptember).Bearscanbespottedbyroadsideastheytrydesperatelytofattenupbeforewinter.November-February:Temperaturcscandropbelowzcro,butthisalsoyicldssomeuniquccxperiences.Elkandbisonarealreadymigratinginimpressiveherdsandthisisagreattimeforwolfspotting-theirdarkcoatsaremucheasiertoseeagainstawhitebackdropofsnow.Wolf-trackingtripsareamust.CostoftravelEntrancefeesforYellowstoneareE16forindividualsandanadditionalf30foracar.Campsitesvaryinprice,costingaslittleasE12.50pernight.AccommodationDuringthepeaksummermonths,pricesriseandroomsarebookeduplonginadvance.Inwinterjustahandfulofthepark'slodgesremainopen21.Whereisthistextprobablytakenfrom?A.Arescarchreport.B.Asciencenewspaper.C.Atravelbrochure.D.Ageographytextbook.22.WhichmonthismostsuitableforhikinginYellowstoneNationalPark?A.July.B.April.C.October.D.November.23.Howmuchshouldacoupledrivingacarpayforentrancefees?A.f46.B.f44.5.C.32.D.f62.BFromhisuptownManhattanhome,SamirKumarcanusuallyseeskyscrapersdowntown.Butthisweck,assmokefromwildfiresraginginthewesternUnitedStatesandCanadastretchedallthewaytotheEastCoast,thecityskylinewasinvisible.

分析先求出圆的参数方程,利用参数方程结合三角函数的性质能求出x2+y2的最大值.

解答解:∵实数x,y满足x2+y2-6x+8y+24=0,
x2+y2-6x+8y+24=0圆,圆心为(3,-4),半径为:r=$\frac{1}{2}\sqrt{36+64-96}$=1,
∴$\left\{\begin{array}{l}{x=3+cosθ}\\{y=-4+sinθ}\end{array}\right.$,0≤θ<2π,
∴x2+y2=(3+cosθ)2+(-4+sinθ)2=-8sinθ+6cosθ+26=10sin(θ+α)+26,
∴x2+y2的最大值为36.
故答案为:36.

点评本题考查代数式的最大值的求法,是基础题,解题时要认真审题,注意圆的参数方程的合理运用.