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30120001MATHEMATICSINPRACTICEANDTHEORYVol130No11Jan.2000:11%,100;11%,100.404!5,.,,,;,,,,.:[1]1()1,,1993.[2]1Mathematica1,,1998.[3]1()1,,1996.MathematicalModelofheaped-upGangueZHAOYi2rong,CHENWei,SUNDong2jie(JimeiUniversity,Xiamen361021)Synopsis:Thispaperdiscussestheexpenditureofheapingupgangueincoalfieldandanalyzesdifferentland2purchasewaysandtheheaping2upnumber,fromwhichitcomestoaconclusionasfollows:Theleastexpenditureisneededonlyinthecasethatalllandarepurchasedonceatthebeginningofcoalextraction,andthatalltheganguemetalsarepiledinoneheap.Also,forthedifferentgangueproductionrate,amathematialwayoffiguringoutthetotalexpendituremen2tionedaboveisgiven.Lastbutnotleast,basedonthedifferentgangueproductionrate,aformu2laofworkingoutthelowestannualaverageexpenditureisaccordinglyprovided.1,2(1.,030024)(21,100084):,,.CD.C.:,.,,.,.,,,.,,.1111::(1);(2);(3)100ö;(4),;(5),,;(6)20().,,.11211A-SBOD,A-BCD,SOB.h=A0,C=OSB,sinC=hötgAhötgB=tgBtgA]C=19SOBSODOBCD,S=h2cosCtgBtgA+C+Pö2tg2A=2.345h2(m2)(1)S(h)=1.1S=2.587h2(m2)(2)V(h)=Shö3=0.784h3(m3)(3)21p,q=pö(1-p),300q(107kg),c=2(103kgöm3)1.5q(106m3),tV(t)=1.5qt(106m3)(4)2930(3)(4)h(t)=124.1(qt)1ö3(m)(5)(5)(2)tS(T)=59.77(qt)2ö3()(6),20h(20)=337.1q1ö3(m),S(20)=440.4q2ö3().,p=011,h(20)=162(m),s(20)=102().3110%5%,,.p=011,Q=8102=816().11311l,l=xösinB(x),G(x)=0.3(1-0.02)1ö10=0.30.98xö10sinB=0.3e-0.00478x(7)21J(h)=h0cxgG(x)dV(x)(8)(3)(7)g=9.8(mös2),J(h)=1.537h0x3e0.00478xdx(105)(9)(9):h0x3ebxdx=[(h3b3-3h2b2+6hb-6)ebh+b]öb4(10)3.1()=316106015ö,(10)(5)t.p=011,t=1t=20k(t)():T12345678910k(t)8.5014.2518.0021.0923.8226.3228.6430.8332.9234.93t11121314151617181920k(t)36.8638.7340.5542.3344.0745.7747.4449.0850.6952.28,5%.20KSK=20t=1K(t)1.05t-1=404(),S=10020t=111.05t-1=1269()(11)KQ1220(),S.4.10%20102,,391:,20.10%,11%,,.,20.,,.:,10,,5132=1026(),1852=370(),1396(),1220().,.211.(3),p=q,p=10%10%,,.21,.:.,.,,.,.31,.,,:(1)v0,v1,v20,21,:ij=min{i+k,20}(i=0,1,,19;k=1,2,,20)vivj;(2)Wij,Wij=ij();(3)v0v20,.,,.41,,,.,550540530,.3,,.,.,.114930,,,.,.,,.,.,.,.,:c3sin2BcosBctgAcos[arcsin(tgBctgA)].,,.,.,,,.,,.,,.,,.,.21,,,,..,,.,,..,.31,GB7713-87,:.,,,.,,,,,.,,.,,.,,,..,.,,.591:AnswerstotheQuestiononPilingofGangueandIntroducedReflectionJIAXiao2feng1,TANGYun2(1.TaiyuanUniversityofTechnology,Taiyuan030024)(2.TsinghuaUniversity,Beijing100084)Abstract:Inthispaperfirstareferenceanswertothequestiononpilingofgangueisprovid2ed.Thenvariousanswersderivedbystudentsfromtheirdifferentunderstandingoftheratioofganguetotherawcoalandofthewaytorentthelandareintroduced.Finallybasedontheanal2ysesofshortageandmistakesdiscoveredfromtheanswersofstudentssomesuggestionandproblemstobeconsideredintheeducationofmathematicalmodelingareproposed.Keywords:Pilingofgangue;Mathematicalmodeling7,720008,().:3;3;3;3;3;3.2001810(ICTMA10).,:3(),,2000;3,,1998;3,V.19(2000),No.1,.20003,.:csiam.edu.cn:100084:(010)627817856930