奧賽真題amc相關1989aime

p (31)(30)(29)(28)+canbedrawnusingsome(orall)ofthetenpointsasvertices?n

=0.d25d25d25..Ifa<b<c<d<eareconsecutivepositiveintegerssuchthatb+c+disaperfectsquareanda+b+c+d+eisaperfectcube,whatisthesmallestpossiblevalueofc?isnotequalto0andisthesameasthatofgetting

actlytwice.Letj,in secondonastraightlhatmakesa60?anglewithAB.AtthesametimeAllieleavesA,AllieskatebeforemeetingBillie?threeconsecutivetermsofanarithmeticseries.Findk.x1+4x2+9x3+16x4+25x5+36x6+49x7=14x1+9x2+16x3+25x4+36x5+49x6+64x7=129x1+16x2+25x3+36x4+49x5+64x6+81x7=Findthevalueof16x1+25x2+36x3+49x4+64x5+81x6+whentheyshowedtherewasapositiveintegersuchthat1335+1105+845+275=n5.Findthevalueofn.Leta,b,cbethethreesidesofatriangle,andletα,β,γ,betheanglesoppositethem.a2+b2=1989c2,cotα+cot//Thesamplehasauniquemode(mostfrequentvalue).LetDbethedifferencweentherealx,bxcisthegreatestintegerlessthanorequaltox.)LetABCDbeatetrahedronwithAB=41,AC=7,AD=18,BC=36,BD=27,andCD=13,asshowninthefigure.LetdbethedistancweenthemidpointsofedgesABandCD.Findd2.isthelargestnumberofelementsScanhave?Givenapositiveintegern,itcanbeshownthateverycomplexnumberoftheformr+si,1,2,...,n2asdigits.Thatis,theequationr+si=am(?n+i)m+am?1(?n+i)m?1+···+a1(?n+i)+istrueforauniquechoiceofnon-negativeintegermanddigitsa0,a1,...,amchosenfromtheset{0,1,2,...,n2},witham6=0.Wewriter+si=(amam?1...todenotethebase?n+iexpansionofr+si.Thereareonlyfiniymanyintegersk+0ithathavefour-digitexpansionsk= PointPisinside4ABC.LinesegmentsAPD,BPE,andCPFaredrawnwithDonBC,EonAC,andFonAB(seethefigureatright).GiventhatAP=6,BP=9,PD=6,PE=3,andCF=20,findtheareaof4ABC.//1989年(31)(30)(29)(28)1。3n，d10n=0.d25d25d25n4a<b<c<d<ebcd，abcde方數(shù)，那么c的最小可能值是多少？5i0，并且與恰好兩次j53i6 和分別位于A點和B點，在一個寬闊、結冰的湖面上。A和B之間的距離是100米。 離開A，以每秒8米的速度沿與AB成60度角的直線滑行。與此同時，Allie離開A，Billie以每秒7米的速度離開B，并沿著直線路徑，根據(jù)兩個滑冰者的速度，這將是最早可能相遇的路徑。在遇見之前滑了多少米？7k36、300596平方。求k.8x1,x2,...,x7x1+4x2+9x316x425x536x649x7=14x19x216x3+25x4+36x5+49x6+64x7=129x1+16x2+25x3+36x4+49x5+64x6+81x716x125x236x349x464x5