第6章_课后习题答案1006

Solutions Chapter 6Attributes must be separated by commas. Thus here B is an alias of A.6.1.2a)SELECT address AS Studio_AddressFROM StudioWHERE NAME = 'MGM';b)SELECT birthdate AS Star_BirthdateFROM MovieStarWHERE name = 'Sandra Bullock';c)SELECT starNameFROM StarsInWHERE movieYear = 1980OR movieTitle LIKE '%Love%';However, above query will also return words that have the substring Love e.g. Lover. Below query will only return movies that have title containing the word Love.SELECT starNameFROM StarsInWHERE movieYear = 1980OR movieTitle LIKE 'Love %'OR movieTitle LIKE '% Love %'OR movieTitle LIKE '% Love'OR movieTitle = 'Love';d)SELECT name AS Exec_NameFROM MovieExecWHERE netWorth >= 10000000;e)SELECT name AS Star_NameFROM movieStarWHERE gender = 'M'OR address LIKE '% Malibu %';a)SELECT model,speed,hdFROM PCWHERE price < 1000 ;MODEL SPEED HD----- ---------- ------1002 2.10 2501003 1.42 801004 2.80 2501005 3.20 2501007 2.20 2001008 2.20 2501009 2.00 2501010 2.80 3001011 1.86 1601012 2.80 1601013 3.06 8011 record(s) selected.b)SELECT model ,speed AS gigahertz,hd AS gigabytesFROM PCWHERE price < 1000 ;MODEL GIGAHERTZ GIGABYTES ----- ---------- ---------1002 2.10 2501003 1.42 801004 2.80 2501005 3.20 2501007 2.20 2001008 2.20 2501009 2.00 2501010 2.80 3001011 1.86 1601012 2.80 1601013 3.06 8011 record(s) selected.c)SELECT makerFROM ProductWHERE TYPE = 'printer' ; MAKER-----DDEEEHH7 record(s) selected.d)SELECT model,ram ,screenFROM LaptopWHERE price > 1500 ; MODEL RAM SCREEN ----- ------ -------2001 2048 20.12005 1024 17.02006 2048 15.42010 2048 15.44 record(s) selected.e)SELECT *FROM PrinterWHERE color ;MODEL CASE TYPE PRICE----- ----- -------- ------3001 TRUE ink-jet 993003 TRUE laser 9993004 TRUE ink-jet 1203006 TRUE ink-jet 1003007 TRUE laser 2005 record(s) selected.Note: Implementation of Boolean type is optional in SQL standard (feature IDT031). PostgreSQL has implementation similar to above example. Other DBMS provide equivalent support. E.g. In DB2 the column type can be declare as SMALLINT with CONSTRAINT that the value can be 0 or 1. The result can be returned as Boolean type CHAR using CASE.CREATE TABLE Printer(model CHAR(4) UNIQUE NOT NULL,color SMALLINT ,type VARCHAR(8) ,price SMALLINT ,CONSTRAINT Printer_ISCOLOR CHECK(color IN(0,1)));SELECT model,CASE colorWHEN 1THEN 'TRUE'WHEN 0THEN 'FALSE'ELSE 'ERROR'END CASE ,type,priceFROM PrinterWHERE color = 1;f)SELECT model,hdFROM PCWHERE speed = 3.2AND price < 2000;MODEL HD----- ------1005 2501006 3202 record(s) selected.6.1.4a)SELECT class,countryFROM ClassesWHERE numGuns >= 10 ; CLASS COUNTRY------------------ ------------ Tennessee USA1 record(s) selected.b)SELECT name AS shipName FROM ShipsWHERE launched < 1918 ; SHIPNAME------------------HarunaHieiKirishimaKongoRamilliesRenownRepulseResolutionRevengeRoyal OakRoyal Sovereign11 record(s) selected.c)SELECT ship AS shipName, battleFROM OutcomesWHERE result = 'sunk' ; SHIPNAME BATTLE------------------ ------------------ Arizona Pearl Harbor Bismark Denmark Strait Fuso Surigao Strait Hood Denmark Strait Kirishima Guadalcanal Scharnhorst North Cape Yamashiro Surigao Strait 7 record(s) selected.d)SELECT name AS shipNameFROM ShipsWHERE name = class ;SHIPNAME------------------IowaKongoNorth CarolinaRenownRevengeYamato6 record(s) selected.e)SELECT name AS shipNameFROM ShipsWHERE name LIKE 'R%';SHIPNAME------------------RamilliesRenownRepulseResolutionRevengeRoyal OakRoyal Sovereign7 record(s) selected.Note: As mentioned in exercise 2.4.3, there are some dangling pointers and to retrieve all ships a UNION of Ships and Outcomes is required.Below query returns 8 rows including ship named Rodney.SELECT name AS shipNameFROM ShipsWHERE name LIKE 'R%'UNIONSELECT ship AS shipNameFROM OutcomesWHERE ship LIKE 'R%';f) Only using a filter like '% % %' will incorrectly match name such as ' a b ' since % can match any sequence of 0 or more characters.SELECT name AS shipNameFROM ShipsWHERE name LIKE '_% _% _%' ;SHIPNAME------------------0 record(s) selected.Note: As in (e), UNION with results from Outcomes.SELECT name AS shipNameFROM ShipsWHERE name LIKE '_% _% _%'UNIONSELECT ship AS shipNameFROM OutcomesWHERE ship LIKE '_% _% _%' ;SHIPNAME------------------Duke of YorkKing George VPrince of Wales3 record(s) selected.6.1.5a)The resulting expression is false when neither of (a=10) or (b=20) is TRUE.a = 10b = 20 a = 10 OR b = 20NULL TRUE TRUETRUE NULL TRUEFALSE TRUE TRUETRUE FALSE TRUETRUE TRUE TRUEb)The resulting expression is only TRUE when both (a=10) and (b=20) are TRUE.a = 10b = 20 a = 10 AND b = 20TRUE TRUE TRUEThe expression is always TRUE unless a is NULL.a < 10 a >= 10 a = 10 ANDb = 20TRUE FALSE TRUEFALSE TRUE TRUEd)The expression is TRUE when a=b except when the values are NULL.a b a = bNOT NULL NOT NULL TRUE when a=b; else FALSEe)Like in (d), the expression is TRUE when a<=b except when the values are NULL.a b a <= bNOT NULL NOT NULL TRUE when a<=b; else FALSE6.1.6SELECT *FROM MoviesWHERE LENGTH IS NOT NULL;6.2.1a)SELECT AS starNameFROM MovieStar M,StarsIn SWHERE = S.starNameAND S.movieTitle = 'Titanic'AND M.gender = 'M';b)SELECT S.starNameFROM Movies M ,StarsIn S,Studios TWHERE ='MGM'AND M.year = 1995AND M.title = S.movieTitleAND M.studioName = ;SELECT AS presidentName FROM MovieExec X,Studio TWHERE X.cert# = T.presC#AND = 'MGM';d)SELECT M1.titleFROM Movies M1,Movies M2WHERE M1.length > M2.lengthAND M2.title ='Gone With the Wind' ;e)SELECT AS execNameFROM MovieExec X1,MovieExec X2WHERE Worth > WorthAND = 'Merv Griffin' ;6.2.2a)SELECT R.maker AS manufacturer,L.speed AS gigahertzFROM Product R,Laptop LWHERE L.hd >= 30AND R.model = L.model ; MANUFACTURER GIGAHERTZ------------ ----------A 2.00A 2.16A 2.00B 1.83E 2.00E 1.73E 1.80F 1.60F 1.60G 2.0010 record(s) selected.SELECT R.model,P.priceFROM Product R,PC PWHERE R.maker = 'B'AND R.model = P.model UNIONSELECT R.model,L.priceFROM Product R,Laptop LWHERE R.maker = 'B'AND R.model = L.model UNIONSELECT R.model,T.priceFROM Product R,Printer TWHERE R.maker = 'B'AND R.model = T.model ; MODEL PRICE----- ------1004 6491005 6301006 10492007 14294 record(s) selected.c)SELECT R.makerFROM Product R,Laptop LWHERE R.model = L.model EXCEPTSELECT R.makerFROM Product R,PC PWHERE R.model = P.model ; MAKER-----FG2 record(s) selected.SELECT DISTINCT P1.hd FROM PC P1,PC P2WHERE P1.hd =P2.hdAND P1.model > P2.model ; Alternate Answer:SELECT DISTINCT P.hdFROM PC PGROUP BY P.hdHAVING COUNT(P.model) >= 2 ;e)SELECT P1.model,P2.modelFROM PC P1,PC P2WHERE P1.speed = P2.speed AND P1.ram = P2.ramAND P1.model < P2.model ; MODEL MODEL----- -----1004 10121 record(s) selected.f)SELECT M.makerFROM(SELECT maker,R.modelFROM PC P,Product RWHERE SPEED >= 3.0AND P.model=R.modelUNIONSELECT maker,R.modelFROM Laptop L,Product RWHERE speed >= 3.0AND L.model=R.model) MGROUP BY M.makerHAVING COUNT(M.model) >= 2 ; MAKER-----B1 record(s) selected.6.2.3a)SELECT FROM Ships S,Classes CWHERE S.class = C.classAND C.displacement > 35000;NAME------------------IowaMissouriMusashiNew JerseyNorth CarolinaWashingtonWisconsinYamato8 record(s) selected.b)SELECT ,C.displacement,C.numGunsFROM Ships S ,Outcomes O,Classes CWHERE = O.shipAND S.class = C.classAND O.battle = 'Guadalcanal' ;NAME DISPLACEMENT NUMGUNS------------------ ------------ -------Kirishima 32000 8Washington 37000 92 record(s) selected.Note:South Dakota was also engaged in battle of Guadalcanal but not chosen since it is not in Ships table(Hence, no information regarding it's Class isavailable).SELECT name shipName FROM ShipsUNIONSELECT ship shipName FROM Outcomes ; SHIPNAME------------------ArizonaBismarkCaliforniaDuke of YorkFusoHarunaHieiHoodIowaKing George VKirishimaKongoMissouriMusashiNew JerseyNorth CarolinaPrince of Wales RamilliesRenownRepulseResolutionRevengeRodneyRoyal OakRoyal Sovereign ScharnhorstSouth DakotaTenneseeTennesseeWashingtonWest VirginiaWisconsinYamashiroYamato34 record(s) selected.SELECT C1.countryFROM Classes C1,Classes C2WHERE C1.country = C2.country AND C1.type = 'bb'AND C2.type = 'bc' ; COUNTRY------------Gt. BritainJapan2 record(s) selected.e)SELECT O1.shipFROM Outcomes O1,Battles B1WHERE O1.battle = AND O1.result = 'damaged'AND EXISTS(SELECT B2.dateFROM Outcomes O2,Battles B2WHERE O2.battle= AND O1.ship = O2.shipAND B1.date < B2.date) ;SHIP------------------0 record(s) selected.f)SELECT O.battleFROM Outcomes O,Ships S ,Classes CWHERE O.ship = AND S.class = C.class GROUP BY C.country,O.battleHAVING COUNT(O.ship) > 3; SELECT O.battleFROM Ships S ,Classes C,Outcomes OWHERE C.Class = S.classAND O.ship = GROUP BY C.country,O.battleHAVING COUNT(O.ship) >= 3;6.2.4Since tuple variables are not guaranteed to be unique, every relation Ri should be renamed using an alias. Every tuple variable should be qualified with the alias. Tuple variables for repeating relations will also be distinctlyidentified this way.Thus the query will be likeSELECT A1.COLL1,A1.COLL2,A2.COLL1,…FROM R1 A1,R2 A2,…,Rn AnWH ERE A1.COLL1=A2.COLC2,…6.2.5Again, create a tuple variable for every Ri, i=1,2,...,nThat is, the FROM clause isFROM R1 A1, R2 A2,...,Rn An.Now, build the WHERE clause from C by replacing every reference to some attribute COL1 of Ri by Ai.COL1. In addition apply Natural Join i.e. add condition to check equality of common attribute names between Ri and Ri+1 for all i from 0 to n-1. Also, build the SELECT clause from list of attributes L by replacing every attribute COLj of Ri by Ai.COLj.6.3.1a)SELECT DISTINCT makerFROM ProductWHERE model IN(SELECT modelFROM PCWHERE speed >= 3.0);SELECT DISTINCT R.makerFROM Product RWHERE EXISTS(SELECT P.modelFROM PC PWHERE P.speed >= 3.0AND P.model =R.model);SELECT P1.modelFROM Printer P1WHERE P1.price >= ALL(SELECT P2.priceFROM Printer P2) ;SELECT P1.modelFROM Printer P1WHERE P1.price IN(SELECT MAX(P2.price)FROM Printer P2) ;c)SELECT L.modelFROM Laptop LWHERE L.speed < ANY(SELECT P.speedFROM PC P) ;SELECT L.modelFROM Laptop LWHERE EXISTS(SELECT P.speedFROM PC PWHERE P.speed >= L.speed ) ;SELECT modelFROM(SELECT model,priceFROM PCUNIONSELECT model,priceFROM LaptopUNIONSELECT model,priceFROM Printer) M1WHERE M1.price >= ALL (SELECT priceFROM PCUNIONSELECT priceFROM LaptopUNIONSELECT priceFROM Printer) ;(d) – contd --SELECT modelFROM(SELECT model,priceFROM PCUNIONSELECT model,priceFROM LaptopUNIONSELECT model,priceFROM Printer) M1WHERE M1.price IN(SELECT MAX(price)FROM(SELECT priceFROM PCUNIONSELECT priceFROM LaptopUNIONSELECT priceFROM Printer) M2) ;e)SELECT R.makerFROM Product R,Printer TWHERE R.model =T.model AND T.price <= ALL(SELECT MIN(price)FROM Printer);SELECT R.makerFROM Product R,Printer T1WHERE R.model =T1.model AND T1.price IN(SELECT MIN(T2.price) FROM Printer T2);f)SELECT R1.makerFROM Product R1,PC P1WHERE R1.model=P1.modelAND P1.ram IN(SELECT MIN(ram)FROM PC)AND P1.speed >= ALL(SELECT P1.speedFROM Product R1,PC P1WHERE R1.model=P1.model AND P1.ram IN(SELECT MIN(ram)FROM PC));SELECT R1.makerFROM Product R1,PC P1WHERE R1.model=P1.modelAND P1.ram =(SELECT MIN(ram)FROM PC)AND P1.speed IN(SELECT MAX(P1.speed)FROM Product R1,PC P1WHERE R1.model=P1.model AND P1.ram IN(SELECT MIN(ram)FROM PC));6.3.2a)SELECT C.countryFROM Classes CWHERE numGuns IN(SELECT MAX(numGuns)FROM Classes);SELECT C.countryFROM Classes CWHERE numGuns >= ALL(SELECT numGunsFROM Classes);b)SELECT DISTINCT C.class FROM Classes C,Ships SWHERE C.class = S.classAND EXISTS(SELECT shipFROM Outcomes OWHERE O.result='sunk' AND O.ship = ) ;SELECT DISTINCT C.class FROM Classes C,Ships SWHERE C.class = S.classAND IN(SELECT shipFROM Outcomes OWHERE O.result='sunk' ) ;c)SELECT FROM Ships SWHERE S.class IN(SELECT classFROM Classes CWHERE bore=16) ;SELECT FROM Ships SWHERE EXISTS(SELECT classFROM Classes CWHERE bore =16AND C.class = S.class );SELECT O.battleFROM Outcomes OWHERE O.ship IN(SELECT nameFROM Ships SWHERE S.Class ='Kongo' );SELECT O.battleFROM Outcomes OWHERE EXISTS(SELECT nameFROM Ships SWHERE S.Class ='Kongo' AND = O.ship );SELECT FROM Ships S,Classes CWHERE S.Class = C.ClassAND numGuns >= ALL(SELECT numGunsFROM Ships S2,Classes C2WHERE S2.Class = C2.Class AND C2.bore = C.bore) ;SELECT FROM Ships S,Classes CWHERE S.Class = C.ClassAND numGuns IN(SELECT MAX(numGuns)FROM Ships S2,Classes C2WHERE S2.Class = C2.Class AND C2.bore = C.bore) ;Better answer;SELECT FROM Ships S,Classes CWHERE S.Class = C.ClassAND numGuns >= ALL(SELECT numGunsFROM Classes C2WHERE C2.bore = C.bore) ;SELECT FROM Ships S,Classes CWHERE S.Class = C.ClassAND numGuns IN(SELECT MAX(numGuns)FROM Classes C2WHERE C2.bore = C.bore) ;6.3.3SELECT titleFROM MoviesGROUP BY titleHAVING COUNT(title) > 1 ;6.3.4SELECT FROM Ships S,Classes CWHERE S.Class = C.Class ;Assumption: In R1 join R2, the rows of R2 are unique on the joining columns. SELECT COLL12,COLL13,COLL14FROM R1WHERE COLL12 IN(SELECT COL22FROM R2)AND COLL13 IN(SELECT COL33FROM R3)AND COLL14 IN(SELECT COL44FROM R4) ...6.3.5(a)SELECT ,S.addressFROM MovieStar S,MovieExec EWHERE S.gender ='F'AND Worth > 10000000AND = AND S.address = E.address ;Note: As mentioned previously in the book, the names of stars are unique. However no such restriction exists for executives. Thus, both name and address are required as join columns.Alternate solution:SELECT name,addressFROM MovieStarWHERE gender = 'F'AND (name, address) IN(SELECT name,addressFROM MovieExecWHERE netWorth > 10000000) ;(b)SELECT name,addressFROM MovieStarWHERE (name,address) NOT IN(SELECT name addressFROM MovieExec) ;6.3.6By replacing the column in subquery with a constant and using IN subquery forthe constant, statement equivalent to EXISTS can be found.i.e. replace "WHERE EXISTS (SELECT C1 FROM R1..)" by "WHERE 1 IN (SELECT 1 FROM R1...)"Example:SELECT DISTINCT R.makerFROM Product RWHERE EXISTS(SELECT P.modelFROM PC PWHERE P.speed >= 3.0AND P.model =R.model) ;Above statement can be transformed to below statement.SELECT DISTINCT R.makerFROM Product RWHERE 1 IN(SELECT 1FROM PC PWHERE P.speed >= 3.0AND P.model =R.model) ;6.3.7(a)n*m tuples are returned where there are n studios and m executives. Each studiowill appear m times; once for every exec.(b)There are no common attributes between StarsIn and MovieStar; hence no tuplesare returned.(c)There will be at least one tuple corresponding to each star in MovieStar. Theunemployed stars will appear once with null values for StarsIn. All employedstars will appear as many times as the number of movies they are working in. Inother words, for each tuple in StarsIn(starName), the correspoding tuple fromMovieStar(name)) is joined and returned. For tuples in MovieStar that do nothave a corresponding entry in StarsIn, the MovieStar tuple is returned with nullvalues for StarsIn columns.6.3.8Since model numbers are unique, a full natural outer join of PC, Laptop andPrinter will return one row for each model. We want all information about PCs,Laptops and Printers even if the model does not appear in Product but vice versais not true. Thus a left natural outer join between Product and result above isrequired. The type attribute from Product must be renamed since Printer has atype attribute as well and the two attributes are different.(SELECT maker,model,type AS productTypeFROM Product) RIGHT NATURAL OUTER JOIN ((PC FULL NATURAL OUTER JOIN Laptop) FULL NATURAL OUTER JOIN Printer);Alternately, the Product relation can be joined individually with each ofPC,Laptop and Printer and the three results can be Unioned together. Forattributes that do not exist in one relation, a constant such as 'NA' or 0.0 canbe used. Below is an example of this approach using PC and Laptop.SELECT R.MAKER ,R.MODEL ,R.TYPE ,P.SPEED ,P.RAM ,P.HD ,0.0 AS SCREEN,P.PRICEFROM PRODUCT R,PC PWHERE R.MODEL = P.MODELUNIONSELECT R.MAKER ,R.MODEL ,R.TYPE ,L.SPEED ,L.RAM ,L.HD ,L.SCREEN,L.PRICEFROM PRODUCT R,LAPTOP LWHERE R.MODEL = L.MODEL;6.3.9SELECT *FROM Classes RIGHT NATURALOUTER JOIN Ships ;6.3.10SELECT *FROM Classes RIGHT NATURALOUTER JOIN ShipsUNION(SELECT C2.class ,C2.type ,C2.country ,C2.numguns ,C2.bore ,C2.displacement,C2.class NAME ,FROM Classes C2,Ships S2WHERE C2.Class NOT IN(SELECT ClassFROM Ships)) ;6.3.11(a)SELECT *FROM R,S ;(b)Let Attr consist ofAttrR = attributes unique to RAttrS = attributes unique to SAttrU = attributes common to R and SThus in Attr, attributes common to R and S are not repeated. SELECT AttrFROM R,SWHERE R.AttrU1 = S.AttrU1AND R.AttrU2 = S.AttrU2 ...AND R.AttrUi = S.AttrUi ;(c)SELECT *FROM R,SWHERE C ;6.4.1(a)DISTINCT keyword is not required here since each model only occurs once in PC relation.SELECT modelFROM PCWHERE speed >= 3.0 ;(b)SELECT DISTINCT R.makerFROM Product R,Laptop LWHERE R.model = L.modelAND L.hd > 100 ;(c)SELECT R.model,P.priceFROM Product R,PC PWHERE R.model = P.modelAND R.maker = 'B'UNIONSELECT R.model,L.priceFROM Product R,Laptop LWHERE R.model = L.modelAND R.maker = 'B'UNIONSELECT R.model,T.priceFROM Product R,Printer TWHERE R.model = T.modelAND R.maker = 'B' ;SELECT modelFROM PrinterWHERE color=TRUEAND type ='laser' ;(e)SELECT DISTINCT R.makerFROM Product R,Laptop LWHERE R.model = L.modelAND R.maker NOT IN(SELECT R1.makerFROM Product R1,PC PWHERE R1.model = P.model) ;better:SELECT DISTINCT R.makerFROM Product RWHERE R.type = 'laptop'AND R.maker NOT IN(SELECT R.makerFROM Product RWHERE R.type = 'pc') ;(f)With GROUP BY hd, DISTINCT keyword is not required. SELECT hdFROM PCGROUP BY hdHAVING COUNT(hd) > 1 ;(g)SELECT P1.model,P2.modelFROM PC P1,PC P2WHERE P1.speed = P2.speedAND P1.ram = P2.ramAND P1.model < P2.model ;SELECT R.makerFROM Product RWHERE R.model IN(SELECT P.modelFROM PC PWHERE P.speed >= 2.8)OR R.model IN(SELECT L.modelFROM Laptop LWHERE L.speed >= 2.8)GROUP BY R.makerHAVING COUNT(R.model) > 1 ;(i)After finding the maximum speed, an IN subquery can provide the manufacturer name.SELECT MAX(M.speed)FROM(SELECT speedFROM PCUNIONSELECT speedFROM Laptop) M ;SELECT R.makerFROM Product R,PC PWHERE R.model = P.modelAND P.speed IN(SELECT MAX(M.speed)FROM(SELECT speedFROM PCUNIONSELECT speedFROM Laptop) M)UNIONSELECT R2.makerFROM Product R2,Laptop LWHERE R2.model = L.modelAND L.speed IN(SELECT MAX(N.speed)FROM(SELECT speedFROM PCUNIONSELECT speedFROM Laptop) N) ;Alternately,SELECT COALESCE(MAX(P2.speed),MAX(L2.speed),0) SPEED FROM PC P2FULL OUTER JOIN Laptop L2ON P2.speed = L2.speed ;SELECT R.makerFROM Product R,PC PWHERE R.model = P.modelAND P.speed IN(SELECT COALESCE(MAX(P2.speed),MAX(L2.speed),0) SPEED FROM PC P2FULL OUTER JOIN Laptop L2ON P2.speed = L2.speed)UNIONSELECT R2.makerFROM Product R2,Laptop LWHERE R2.model = L.modelAND L.speed IN(SELECT COALESCE(MAX(P2.speed),MAX(L2.speed),0) SPEED FROM PC P2FULL OUTER JOIN Laptop L2ON P2.speed = L2.speed)SELECT R.makerFROM Product R,PC PWHERE R.model = P.modelGROUP BY R.makerHAVING COUNT(DISTINCT speed) >= 3 ;(k)SELECT R.makerFROM Product R,PC PWHERE R.model = P.modelGROUP BY R.makerHAVING COUNT(R.model) = 3 ;better;SELECT R.makerFROM Product RWHERE R.type='pc'GROUP BY R.makerHAVING COUNT(R.model) = 3 ;6.4.2(a)We can assume that class is unique in Classes and DISTINCT keyword is not required.SELECT class,countryFROM ClassesWHERE bore >= 16 ;(b)Ship names are not unique (In absence of hull codes, year of launch can help distinguish ships).SELECT DISTINCT name AS Ship_NameFROM ShipsWHERE launched < 1921 ;(c)SELECT DISTINCT ship AS Ship_NameFROM OutcomesWHERE battle = 'Denmark Strait'AND result = 'sunk' ;(d)SELECT DISTINCT AS Ship_NameFROM Ships S,Classes CWHERE S.class = C.classAND C.displacement > 35000 ;SELECT DISTINCT O.ship AS Ship_Name,C.displacement ,C.numGunsFROM Classes C ,Outcomes O,Ships SWHERE C.class = S.classAND = O.shipAND O.battle = 'Guadalcanal' ;SHIP_NAME DISPLACEMENT NUMGUNS------------------ ------------ -------Kirishima 32000 8Washington 37000 92 record(s) selected.Note: South Dakota was also in Guadalcanal but its class information is not available. Below query will return name of all ships that were in Guadalcanal even if no other information is available (shown as NULL). The above query is modified from INNER joins to LEFT OUTER joins.SELECT DISTINCT O.ship AS Ship_Name,C.displacement ,C.numGunsFROM Outcomes OLEFT JOIN Ships SON = O.shipLEFT JOIN Classes CON C.class = S.classWHERE O.battle = 'Guadalcanal' ;SHIP_NAME DISPLACEMENT NUMGUNS------------------ ------------ -------Kirishima 32000 8South Dakota - -Washington 37000 93 record(s) selected.(f)The Set opearator UNION guarantees unique results.SELECT ship AS Ship_NameFROM OutcomesUNIONSELECT name AS Ship_NameFROM Ships ;(g)SELECT C.classFROM Classes C,Ships SWHERE C.class = S.classGROUP BY C.classHAVING COUNT() = 1 ;better:SELECT S.classFROM Ships SGROUP BY S.classHAVING COUNT() = 1 ;(h)The Set opearator INTERSECT guarantees unique results.SELECT C.countryFROM Classes CWHERE C.type='bb'INTERSECTSELECT C2.countryFROM Classes C2WHERE C2.type='bc' ;However, above query does not account for classes without any ships belonging to them.SELECT C.countryFROM Classes C,Ships SWHERE C.class = S.classAND C.type ='bb'INTERSECTSELECT C2.countryFROM Classes C2,Ships S2WHERE C2.class = S2.classAND C2.type ='bc' ;SELECT O2.ship AS Ship_Name FROM Outcomes O2,Battles B2WHERE O2.battle = AND B2.date > ANY(SELECT B.dateFROM Outcomes O,Battles BWHERE O.battle = AND O.result ='damaged' AND O.ship = O2.ship);6.4.3a)SELECT DISTINCT R.maker FROM Product R,PC PWHERE R.model = P.modelAND P.speed >= 3.0;b)Models are unique.SELECT P1.modelFROM Printer P1LEFT OUTER JOIN Printer P2 ON (P1.price < P2.price) WHERE P2.model IS NULL ;c)SELECT DISTINCT L.model FROM Laptop L,PC PWHERE L.speed < P.speed ;Due to set operator UNION, unique results are returned.It is difficult to completely avoid a subquery here. One option is to use Views. CREATE VIEW AllProduct ASSELECT model,priceFROM PCUNIONSELECT model,priceFROM LaptopUNIONSELECT model,priceFROM Printer ;SELECT A1.modelFROM AllProduct A1LEFT OUTER JOIN AllProduct A2ON (A1.price < A2.price)WHERE A2.model IS NULL ;But if we replace the View, the query contains a FROM subquery. SELECT A1.modelFROM(SELECT model,priceFROM PCUNIONSELECT model,priceFROM LaptopUNIONSELECT model,priceFROM Printer) A1LEFT OUTER JOIN(SELECT model,priceFROM PCUNIONSELECT model,priceFROM LaptopUNIONSELECT model,priceFROM Printer) A2ON (A1.price < A2.price) WHERE A2.model IS NULL ;e)SELECT DISTINCT R.makerFROM Product R,Printer TWHERE R.model =T.modelAND T.price <= ALL(SELECT MIN(price)FROM Printer);f)SELECT DISTINCT R1.makerFROM Product R1,PC P1WHERE R1.model=P1.modelAND P1.ram IN(SELECT MIN(ram)FROM PC)AND P1.speed >= ALL(SELECT P1.speedFROM Product R1,PC P1WHERE R1.model=P1.modelAND P1.ram IN(SELECT MIN(ram)FROM PC));6.4.4a)SELECT DISTINCT C1.countryFROM Classes C1LEFT OUTER JOIN Classes C2 ON (C1.numGuns < C2.numGuns) WHERE C2.country IS NULL ;。

第2讲 等差数列及前n 项和考纲展示 命题探究1 等差数列的定义一般地，如果一个数列从第2项起，每一项与它的前一项的差等于同一个常数，那么这个数列就叫做等差数列，这个常数叫做等差数列的公差，公差通常用字母d 表示，定义的表达式为a n ＋1－a n ＝d ，d 为常数．2 等差中项如果a ，A ，b 成等差数列，那么A 叫做a 与b 的等差中项，且A ＝a ＋b 2.3 等差数列的通项公式及其变形通项公式：a n ＝a 1＋(n －1)d ，其中a 1是首项，d 是公差．通项公式的变形：a n ＝a m ＋(n －m )d ，m ，n ∈N *.4 等差数列的前n 项和等差数列的前n 项和公式：S n ＝n (a 1＋a n )2＝na 1＋n (n －1)2d . 5 等差数列的单调性当d >0时，数列{a n }为递增数列；当d <0时，数列{a n }为递减数列；当d ＝0时，数列{a n }为常数列．注意点 定义法证明等差数列时的注意事项(1)证明等差数列时，切忌只通过计算数列的a 2－a 1，a 3－a 2，a 4－a 3等有限的几个项的差后，发现它们都等于同一个常数，就断言数列{a n }为等差数列．(2)用定义法证明等差数列时，常采用a n ＋1－a n ＝d ，若采用a n －a n －1＝d ，则n ≥2，否则n ＝1时无意义.1．思维辨析(1)若一个数列从第2项起每一项与它的前一项的差都是常数，则这个数列是等差数列．( )(2)数列{a n }为等差数列的充要条件是对任意n ∈N *，都有2a n ＋1＝a n ＋a n ＋2.( )(3)等差数列{a n }的单调性是由公差d 决定的．( )(4)数列{a n }为等差数列的充要条件是其通项公式为n 的一次函数．( )(5)等差数列的前n 项和公式是常数项为0的二次函数．( ) 答案 (1)× (2)√ (3)√ (4)× (5)×2．等差数列{a n }的前n 项和为S n ，且S 3＝6，a 3＝4，则公差d 等于( )A ．1 B.53 C ．2D ．3答案 C解析 因为S 3＝(a 1＋a 3)×32＝6，而a 3＝4.所以a 1＝0，所以d ＝a 3－a 12＝2.3．等差数列{a n }的前n 项和为S n ，若a 1＝2，S 3＝12，则a 6等于( )A ．8B ．10C ．12D ．14 答案 C解析 ∵S 3＝3(a 1＋a 3)2＝3a 2＝12，∴a 2＝4. ∵a 1＝2，∴d ＝a 2－a 1＝4－2＝2.∴a 6＝a 1＋5d ＝12.故选C.[考法综述] 等差数列的定义，通项公式及前n 项和公式是高考中常考内容，用定义判断或证明等差数列，由n ，a n ，S n ，a 1，d 五个量之间的关系考查基本运算能力．命题法1 等差数列的基本运算典例1 等差数列{a n }的前n 项和记为S n .已知a 10＝30，a 20＝50.(1)求通项a n ；(2)若S n ＝242，求n .[解] (1)由a n ＝a 1＋(n －1)d ，a 10＝30，a 20＝50，得方程组⎩⎪⎨⎪⎧a 1＋9d ＝30，a 1＋19d ＝50. 解得a 1＝12，d ＝2.所以a n ＝2n ＋10；(2)由S n ＝na 1＋n (n －1)2d ，S n ＝242，得方程12n ＋n (n －1)2×2＝242，解得n ＝11或n ＝－22(舍去)．【解题法】 等差数列计算中的两个技巧(1)等差数列的通项公式及前n 项和公式，共涉及五个量a 1，a n ，d ，n ，S n ，知其中三个就能求另外两个，体现了用方程的思想解决问题．(2)数列的通项公式和前n 项和公式在解题中起到变量代换作用，而a 1和d 是等差数列的两个基本量，用它们表示已知和未知是常用方法．命题法2 等差数列的判定与证明典例2 数列{a n }满足a 1＝1，a 2＝2，a n ＋2＝2a n ＋1－a n ＋2.(1)设b n ＝a n ＋1－a n ，证明{b n }是等差数列；(2)求{a n }的通项公式．[解] (1)证明：∵a n ＋2＝2a n ＋1－a n ＋2，∴b n ＋1－b n ＝a n ＋2－a n ＋1－(a n ＋1－a n )＝2a n ＋1－a n ＋2－2a n ＋1＋a n ＝2.∴{b n }是以1为首项，2为公差的等差数列．(2)由(1)得b n ＝1＋2(n －1)，即a n ＋1－a n ＝2n －1，∴a 2－a 1＝1，a 3－a 2＝3，a 4－a 3＝5，…，a n －a n －1＝2n －3，累加法可得a n －a 1＝1＋3＋5＋…＋(2n －3)＝(n －1)2，∴a n ＝n 2－2n ＋2.【解题法】 等差数列的判定方法(1)定义法：对于n ≥2的任意自然数，验证a n －a n －1为同一常数．(2)等差中项法：验证2a n －1＝a n ＋a n －2(n ≥3，n ∈N *)成立．(3)通项公式法：验证a n ＝pn ＋q .(4)前n 项和公式法：验证S n ＝An 2＋Bn .1．在等差数列{a n }中，若a 2＝4，a 4＝2，则a 6＝( )A ．－1B ．0C ．1D ．6答案 B解析 设数列{a n }的公差为d ，由a 4＝a 2＋2d ，a 2＝4，a 4＝2，得2＝4＋2d ，d ＝－1，∴a 6＝a 4＋2d ＝0.故选B.2.已知{a n }是等差数列，公差d 不为零，前n 项和是S n .若a 3，a 4，a 8成等比数列，则( )扫一扫·听名师解题A ．a 1d >0，dS 4>0B ．a 1d <0，dS 4<0C ．a 1d >0，dS 4<0D ．a 1d <0，dS 4>0答案 B解析 由a 24＝a 3a 8，得(a 1＋2d )(a 1＋7d )＝(a 1＋3d )2，整理得d (5d ＋3a 1)＝0，又d ≠0，∴a 1＝－53d ，则a 1d ＝－53d 2<0，又∵S 4＝4a 1＋6d ＝－23d ，∴dS 4＝－23d 2<0，故选B.3．设{a n }是首项为a 1，公差为－1的等差数列，S n 为其前n 项和．若S 1，S 2，S 4成等比数列，则a 1的值为________．答案 －12解析由已知得S1＝a1，S2＝a1＋a2＝2a1－1，S4＝4a1＋4×32×(－1)＝4a1－6，而S1，S2，S4成等比数列，所以(2a1－1)2＝a1(4a1－6)，整理得2a1＋1＝0，解得a1＝－1 2.4.已知数列{a n}的前n项和为S n，a1＝1，a n≠0，a n a n＋1＝λS n－1，其中λ为常数．(1)证明：a n＋2－a n＝λ；(2)是否存在λ，使得{a n}为等差数列？并说明理由．解(1)证明：由题设，a n a n＋1＝λS n－1，a n＋1a n＋2＝λS n＋1－1.两式相减得a n＋1(a n＋2－a n)＝λa n＋1.由于a n＋1≠0，所以a n＋2－a n＝λ.(2)由题设，a1＝1，a1a2＝λS1－1，可得a2＝λ－1.由(1)知，a3＝λ＋1.令2a2＝a1＋a3，解得λ＝4.故a n＋2－a n＝4，由此可得{a2n－1}是首项为1，公差为4的等差数列，a2n－1＝4n－3；{a2n}是首项为3，公差为4的等差数列，a2n＝4n－1.所以a n＝2n－1，a n＋1－a n＝2.因此存在λ＝4，使得数列{a n}为等差数列．等差数列及其前n项和的性质已知{a n}为等差数列，d为公差，S n为该数列的前n项和．(1)有穷等差数列中与首末两项等距离的两项的和相等，即a1＋a n＝a2＋a n－1＝a3＋a n－2＝…＝a k＋a n－k＋1＝….(2)等差数列{a n}中，当m＋n＝p＋q时，a m＋a n＝a p＋a q(m，n，p，q∈N*)．特别地，若m＋n＝2p，则2a p＝a m＋a n(m，n，p∈N*)．(3)相隔等距离的项组成的数列是等差数列，即a k，a k＋m，a k＋2m，…仍是等差数列，公差为md(k，m∈N*)．(4)S n，S2n－S n，S3n－S2n，…也成等差数列，公差为n2d.(5)⎩⎨⎧⎭⎬⎫S n n 也成等差数列，其首项与{a n }首项相同，公差是{a n }的公差的12.(6)在等差数列{a n }中，①若项数为偶数2n ，则S 2n ＝n (a 1＋a 2n )＝n (a n ＋a n ＋1)；S 偶－S 奇＝nd ；S 奇S 偶＝a n a n ＋1. ②若项数为奇数2n －1，则S 2n －1＝(2n －1)a n ；S 奇－S 偶＝a n ；S 奇S 偶＝n n －1. (7)若数列{a n }与{b n }均为等差数列，且前n 项和分别是S n 和T n ，则S 2m －1T 2m －1＝a m b m. (8)若数列{a n }，{b n }是公差分别为d 1，d 2的等差数列，则数列{pa n }，{a n ＋p }，{pa n ＋qb n }都是等差数列(p ，q 都是常数)，且公差分别为pd 1，d 1，pd 1＋qd 2.注意点 前n 项和性质的理解等差数列{a n }中，设前n 项和为S n ，则S n ，S 2n ，S 3n 的关系为2(S 2n －S n )＝S n ＋(S 3n －S 2n )不要理解为2S 2n ＝S n ＋S 3n .1．思维辨析(1)等差数列{a n }中，有a 1＋a 7＝a 2＋a 6.( )(2)若已知四个数成等差数列，则这四个数可设为a －2d ，a －d ，a ＋d ，a ＋2d .( )(3)若三个数成等差数列，则这三个数可设为：a －d ，a ，a ＋d .( )(4)求等差数列的前n 项和的最值时，只需将它的前n 项和进行配方，即得顶点为其最值处．( )答案 (1)√ (2)× (3)√ (4)×2．若S n 是等差数列{a n }的前n 项和，a 2＋a 10＝4，则S 11的值为( )A ．12B ．18C ．22D ．44答案 C 解析 由题可知S 11＝11(a 1＋a 11)2＝11(a 2＋a 10)2＝11×42＝22，故选C.3．在等差数列{a n }中，若a 4＋a 6＋a 8＋a 10＋a 12＝90，则a 10－13a 14的值为( )A ．12B ．14C ．16D ．18答案 A解析 由题意知5a 8＝90，a 8＝18，a 10－13a 14＝a 1＋9d －13(a 1＋13d )＝23a 8＝12，选A 项．[考法综述] 等差数列的性质是高考中的常考内容，灵活应用由概念推导出的重要性质，在解题过程中可以达到避繁就简的目的．命题法1 等差数列性质的应用典例1 等差数列{a n }中，如果a 1＋a 4＋a 7＝39，a 3＋a 6＋a 9＝27，则数列{a n }前9项的和为( )A ．297B ．144C ．99D ．66[解析] 由a 1＋a 4＋a 7＝39，得3a 4＝39，a 4＝13.由a 3＋a 6＋a 9＝27，得3a 6＝27，a 6＝9.所以S 9＝9(a 1＋a 9)2＝9(a 4＋a 6)2＝9×(13＋9)2＝9×11＝99，故选C.[答案] C【解题法】 应用等差数列性质应注意(1)要注意等差数列通项公式及前n 项和公式的灵活应用，如a n＝a m ＋(n －m )d ，d ＝a n －a m n －m，S 2n －1＝(2n －1)a n ，S n ＝n (a 1＋a n )2＝n (a 2＋a n －1)2(n ，m ∈N *)等． (2)如果{a n }为等差数列，m ＋n ＝p ＋q ，则a m ＋a n ＝a p ＋a q ( m ，n ，p ，q ∈N *)．一般地，a m ＋a n ≠a m ＋n ，必须是两项相加，当然也可以是a m －n ＋a m ＋n ＝2a m .因此，若出现a m －n ，a m ，a m ＋n 等项时，可以利用此性质将已知条件转化为与a m (或其他项)有关的条件．命题法2 与等差数列前n 项和有关的最值问题典例2 等差数列{a n }中，设S n 为其前n 项和，且a 1>0，S 3＝S 11，则当n 为多少时，S n 最大？[解] 解法一：由S 3＝S 11得3a 1＋3×22d ＝11a 1＋11×102d ，则d＝－213a 1.从而S n ＝d 2n 2＋⎝ ⎛⎭⎪⎫a 1－d 2n ＝－a 113(n －7)2＋4913a 1，又a 1>0，所以－a 113<0.故当n ＝7时，S n 最大．解法二：由于S n ＝an 2＋bn 是关于n 的二次函数，由S 3＝S 11，可知S n ＝an 2＋bn 的图象关于n ＝3＋112＝7对称．由解法一可知a ＝－a 113<0，故当n ＝7时，S n 最大．解法三：由解法一可知，d ＝－213a 1.要使S n 最大，则有⎩⎪⎨⎪⎧ a n ≥0，a n ＋1≤0， 即⎩⎪⎨⎪⎧ a 1＋(n －1)⎝ ⎛⎭⎪⎫－213a 1≥0，a 1＋n ⎝ ⎛⎭⎪⎫－213a 1≤0，≤n ≤n ＝7时，S n 最大．解法四：由S 3＝S 11，可得2a 1＋13d ＝0，即(a 1＋6d )＋(a 1＋7d )＝0，故a 7＋a 8＝0，又由a 1>0，S 3＝S 11可知d <0，所以a 7>0，a 8<0，所以当n ＝7时，S n 最大．【解题法】 求等差数列前n 项和的最值的方法(1)二次函数法：用求二次函数最值的方法(配方法)求其前n 项和的最值，但要注意n ∈N *.(2)图象法：利用二次函数图象的对称性来确定n 的值，使S n 取得最值．(3)项的符号法：当a 1>0，d <0时，满足⎩⎪⎨⎪⎧ a n ≥0a n ＋1≤0的项数n ，使S n 取最大值；当a 1<0，d >0时，满足⎩⎪⎨⎪⎧a n ≤0，a n ＋1 ≥0的项数n ，使S n 取最小值，即正项变负项处最大，负项变正项处最小，若有零项，则使S n 取最值的n 有两个．1．设{a n }是等差数列．下列结论中正确的是( )A ．若a 1＋a 2>0，则a 2＋a 3>0B ．若a 1＋a 3<0，则a 1＋a 2<0C ．若0<a 1<a 2，则a 2>a 1a 3D ．若a 1<0，则(a 2－a 1)(a 2－a 3)>0答案 C解析 若{a n }是递减的等差数列，则选项A 、B 都不一定正确．若{a n }为公差为0的等差数列，则选项D 不正确．对于C 选项，由条件可知{a n }为公差不为0的正项数列，由等差中项的性质得a 2＝a 1＋a 32，由基本不等式得a 1＋a 32>a 1a 3，所以C 正确．2．在等差数列{a n }中，a 1>0，a 2012＋a 2013>0，a 2012·a 2013<0，则使S n >0成立的最大自然数n 是( )A ．4025B ．4024C ．4023D ．4022答案 B解析 ∵等差数列{a n }的首项a 1>0，a 2012＋a 2013>0，a 2012·a 2013<0，假设a 2012<0<a 2013，则d >0，而a 1>0，可得a 2012＝a 1＋2011d >0，矛盾，故不可能．∴a 2012>0，a 2013<0.再根据S 4024＝4024(a 1＋a 4024)2＝2012(a 2012＋a 2013)>0， 而S 4025＝4025a 2013<0，因此使前n 项和S n >0成立的最大自然数n 为4024.3.已知等差数列{a n }，{b n }的前n 项和分别为S n ，T n ，若S n T n＝2n 3n ＋1，则a n b n＝( ) A.23B.2n －13n －1C.2n ＋13n ＋1D.2n －13n ＋4 答案 B解析 a n b n ＝2a n 2b n＝2n －12(a 1＋a 2n －1)2n －12(b 1＋b 2n －1)＝S 2n －1T 2n －1＝2(2n －1)3(2n －1)＋1＝2n －13n －1.故选B.4．在等差数列{a n }中，若a 3＋a 4＋a 5＋a 6＋a 7＝25，则a 2＋a 8＝________.答案 10解析 由a 3＋a 4＋a 5＋a 6＋a 7＝25，得5a 5＝25，所以a 5＝5，故a 2＋a 8＝2a 5＝10.5．中位数为1010的一组数构成等差数列，其末项为2015，则该数列的首项为________．答案 5解析 设等差数列的首项为a 1，根据等差数列的性质可得，a 1＋2015＝2×1010，解得a 1＝5.6．在等差数列{a n }中，a 1＝7，公差为d ，前n 项和为S n ，当且仅当n ＝8时S n 取得最大值，则d 的取值范围为________．答案 ⎝ ⎛⎭⎪⎫－1，－78 解析 由题意知d <0且⎩⎪⎨⎪⎧ a 8>0，a 9<0，即⎩⎪⎨⎪⎧7＋7d >0，7＋8d <0，解得－1<d <－78.7.若等差数列{a n }满足a 7＋a 8＋a 9>0，a 7＋a 10<0，则当n ＝________时，{a n }的前n 项和最大．答案 8解析 根据题意知a 7＋a 8＋a 9＝3a 8>0，即a 8>0.又a 8＋a 9＝a 7＋a 10<0，∴a 9<0，∴当n ＝8时，{a n }的前n 项和最大．8．已知公差大于零的等差数列{a n }的前n 项和为S n ，且满足a 3·a 4＝117，a 2＋a 5＝22.(1)求通项a n ； (2)求S n 的最小值；(3)若数列{b n }是等差数列，且b n ＝S nn ＋c ，求非零常数c .解 (1)因为数列{a n }为等差数列， 所以a 3＋a 4＝a 2＋a 5＝22. 又a 3·a 4＝117，所以a 3，a 4是方程x 2－22x ＋117＝0的两实根， 又公差d >0，所以a 3<a 4， 所以a 3＝9，a 4＝13，所以⎩⎪⎨⎪⎧ a 1＋2d ＝9，a 1＋3d ＝13，所以⎩⎪⎨⎪⎧a 1＝1，d ＝4.所以通项a n ＝4n －3. (2)由(1)知a 1＝1，d ＝4.所以S n ＝na 1＋n (n －1)2×d ＝2n 2－n ＝2⎝ ⎛⎭⎪⎫n －142－18.所以当n ＝1时，S n 最小，最小值为S 1＝a 1＝1.(3)由(2)知S n ＝2n 2－n ，所以b n ＝S n n ＋c ＝2n 2－n n ＋c，所以b 1＝11＋c ，b 2＝62＋c ，b 3＝153＋c .因为数列{b n }是等差数列， 所以2b 2＝b 1＋b 3， 即62＋c ×2＝11＋c ＋153＋c ， 所以2c 2＋c ＝0，所以c ＝－12或c ＝0(舍去)， 故c ＝－12.已知等差数列{a n }的前n 项和为S n ，且a 5＝9，S 5＝15，则使其前n 项和S n 取得最小值时的n ＝________.[错解][错因分析] 等差数列的前n 项和最值问题，可以通过找对称轴来确定，本题只关注到n ∈N *，并未关注到n ＝1与n ＝2时，S 1＝S 2，导致错误．[正解] ∵a 5＝9，S 5＝15，∴a 1＝－3，d ＝3. ∴a n ＝3n －6，S n ＝32n 2－92n .把S n 看作是关于n 的二次函数，其对称轴为n ＝32. ∴当n ＝1或n ＝2时，S 1＝S 2且最小． [心得体会]………………………………………………………………………………………………时间：60分钟基础组1.[2016·冀州中学猜题]已知等差数列{a n }中，a 7＋a 9＝16，S 11＝992，则a 12的值是( )A ．15B ．30C ．31D ．64答案 A解析 由题意可知2a 8＝a 7＋a 9＝16⇒a 8＝8，S 11＝11(a 1＋a 11)2＝11×2a 62＝11a 6＝992，a 6＝92，则d ＝a 8－a 62＝74，所以a 12＝a 8＋4d ＝15，故选A.2．[2016·武邑中学仿真]已知S n 表示数列{a n }的前n 项和，若对任意的n ∈N *满足a n ＋1＝a n ＋a 2，且a 3＝2，则S 2014＝( )A ．1006×2013B ．1006×2014C ．1007×2013D ．1007×2014答案 C解析 在a n ＋1＝a n ＋a 2中，令n ＝1，则a 2＝a 1＋a 2，a 1＝0，令n ＝2，则a 3＝2＝2a 2，a 2＝1，于是a n ＋1－a n ＝1，故数列{a n }是首项为0，公差为1的等差数列，S 2014＝2014×20132＝1007×2013.故选C. 3．[2016·冀州中学期末]在数列{a n }中，若a 1＝1，a 2＝12，2a n ＋1＝1a n ＋1a n ＋2(n ∈N *)，则该数列的通项为( ) A ．a n ＝1n B ．a n ＝2n ＋1C ．a n ＝2n ＋2D ．a n ＝3n答案 A 解析 由已知式2a n ＋1＝1a n ＋1a n ＋2可得1a n ＋1－1a n ＝1a n ＋2－1a n ＋1，知⎩⎨⎧⎭⎬⎫1a n是首项为1a 1＝1，公差为1a 2－1a 1＝2－1＝1的等差数列，所以1a n ＝n ，即a n ＝1n .4．[2016·衡水中学预测]设等差数列{a n }的前n 项和为S n ，若S 3＝9，S 6＝36，则a 7＋a 8＋a 9＝( )A ．63B ．45C ．36D ．27答案 B解析 S 3＝9，S 6－S 3＝36－9＝27，根据S 3，S 6－S 3，S 9－S 6成等差数列，S 9－S 6＝45，S 9－S 6＝a 7＋a 8＋a 9＝45，故选B.5．[2016·衡水二中期中]已知等差数列{a n }中，前四项和为60，最后四项和为260，且S n ＝520，则a 7＝( )A ．20B ．40C ．60D ．80答案 B解析 前四项的和是60，后四项的和是260，若有偶数项，则中间两项的和是(60＋260)÷4＝80.S n ＝520,520÷80不能整除，说明没有偶数项，有奇数项，则中间项是(60＋260)÷8＝40.所以共有520÷40＝13项，因此a 7是中间项，所以a 7＝40.6．[2016·枣强中学模拟]已知等差数列{a n }的前n 项和为S n ，且S 4S2＝4，则S 6S 4＝( )A.94B.32C.53 D ．4答案 A解析 由S 4S 2＝4，可设S 2＝x ，S 4＝4x .∵S 2，S 4－S 2，S 6－S 4成等差数列，∴2(S 4－S 2)＝S 2＋(S 6－S 4)．则S 6＝3S 4－3S 2＝12x －3x ＝9x ，因此，S 6S 4＝9x 4x ＝94.7．[2016·衡水二中热身]设等差数列{a n }的前n 项和为S n ，若a 1＝－3，a k ＋1＝32，S k ＝－12，则正整数k ＝______.答案 13解析 由S k ＋1＝S k ＋a k ＋1＝－12＋32＝－212，又S k ＋1＝(k ＋1)(a 1＋a k ＋1)2＝(k ＋1)⎝ ⎛⎭⎪⎫－3＋322＝－212，解得k ＝13.8.[2016·武邑中学期末]设正项数列{a n }的前n 项和是S n ，若{a n }和{S n }都是等差数列，且公差相等，则a 1＝________.答案 14解析 设等差数列{a n }的公差为d ， 则S n ＝d 2n 2＋(a 1－d2)n ， ∴S n ＝d 2n 2＋⎝⎛⎭⎪⎫a 1－d 2n ，数列{S n }是等差数列，则S n 是关于n 的一次函数(或者是常数)，则a 1－d2＝0，S n ＝d2n ，从而数列{S n }的公差是d2，那么有d 2＝d ，d ＝0(舍去)或d ＝12，故a 1＝14.9．[2016·衡水中学周测]已知等差数列{a n }的前n 项和为S n ，若S 2＝10，S 5＝55，则a 10＝________.答案 39解析 设等差数列{a n }的公差为d ，由题意可得⎩⎨⎧a 1＋(a 1＋d )＝10，5a 1＋5×42d ＝55，即⎩⎪⎨⎪⎧2a 1＋d ＝10，a 1＋2d ＝11，解得a 1＝3，d ＝4，a 10＝a 1＋(10－1)d ＝39.10．[2016·冀州中学月考]设数列{a n }为等差数列，数列{b n }为等比数列．若a 1<a 2，b 1<b 2，且b i ＝a 2i (i ＝1,2,3)，则数列{b n }的公比为________．答案 3＋2 2解析 设a 1，a 2，a 3分别为a －d ，a ，a ＋d ，因为a 1<a 2，所以d >0，又b 22＝b 1b 3，所以a 4＝(a －d )2(a ＋d )2＝(a 2－d 2)2，则a 2＝d 2－a 2或a 2＝a 2－d 2(舍)，则d ＝±2a .若d ＝－2a ，则q ＝b 2b 1＝⎝ ⎛⎭⎪⎫a 2a 12＝(1－2)2＝3－22<1，舍去；若d ＝2a ，则q ＝⎝ ⎛⎭⎪⎫a 2a 12＝3＋2 2.11．[2016·衡水中学模拟]等差数列{a n }的前n 项和为S n .已知a 1＝10，a 2为整数，且S n ≤S 4.(1)求{a n }的通项公式；(2)设b n ＝1a n a n ＋1，求数列{b n }的前n 项和T n .解 (1)由a 1＝10，a 2为整数知，等差数列{a n }的公差d 为整数，又S n ≤S 4，故a 4≥0，a 5≤0，于是10＋3d ≥0,10＋4d ≤0.解得－103≤d ≤－52.因此d ＝－3.数列{a n }的通项公式为a n ＝13－3n . (2)b n ＝1(13－3n )(10－3n )＝13⎝ ⎛⎭⎪⎫110－3n －113－3n .于是T n ＝b 1＋b 2＋…＋b n＝13⎣⎢⎢⎡⎦⎥⎥⎤⎝ ⎛⎭⎪⎫17－110＋⎝ ⎛⎭⎪⎫14－17＋…＋⎝ ⎛ 110－3n －⎭⎪⎫113－3n ＝13⎝ ⎛⎭⎪⎫110－3n －110＝n 10(10－3n ). 12．[2016·冀州中学期中]已知数列{a n }的前n 项和为S n ，且满足：a n ＋2S n S n －1＝0(n ≥2，n ∈N *)，a 1＝12，判断{a n }是否为等差数列，并说明你的理由．解 数列{a n }不是等差数列，a n ＝S n －S n －1(n ≥2)，a n ＋2S n S n －1＝0， ∴S n －S n －1＋2S n S n －1＝0(n ≥2)， ∴1S n－1S n －1＝2(n ≥2)，又S 1＝a 1＝12，∴⎩⎨⎧⎭⎬⎫1S n 是以2为首项，2为公差的等差数列． ∴1S n＝2＋(n －1)×2＝2n ，故S n ＝12n .∴当n ≥2时，a n ＝S n －S n －1＝12n －12(n －1)＝－12n (n －1)，∴a n ＋1＝－12n (n ＋1)，而a n ＋1－a n ＝－12n (n ＋1)－－12n (n －1)＝－12n⎝ ⎛⎭⎪⎫1n ＋1－1n －1＝1n (n －1)(n ＋1). ∴当n ≥2时，a n ＋1－a n 的值不是一个与n 无关的常数，故数列{a n }不是一个等差数列．能力组13.[2016·衡水中学猜题]已知正项数列{a n }中，a 1＝1，a 2＝2,2a 2n ＝a 2n ＋1＋a 2n －1(n ≥2)，则a 6等于( )A ．16B ．8C ．2 2D ．4答案 D解析 由2a 2n ＝a 2n ＋1＋a 2n －1(n ≥2)可得，数列{a 2n }是首项为a 21＝1，公差为a 22－a 21＝3的等差数列，由此可得a 2n ＝1＋3(n －1)＝3n －2，即得a n ＝3n －2，∴a 6＝3×6－2＝4，故应选D.14.[2016·衡水中学一轮检测]已知数列{a n }为等差数列，若a 11a 10<－1，且它们的前n 项和S n 有最大值，则使S n >0的n 的最大值为( )A ．11B ．19C ．20D ．21答案 B解析 ∵a 11a 10<－1，且S n 有最大值，∴a 10>0，a 11<0，且a 10＋a 11<0， ∴S 19＝19(a 1＋a 19)2＝19·a 10>0， S 20＝20(a 1＋a 20)2＝10(a 10＋a 11)<0， 故使得S n >0的n 的最大值为19.15.[2016·武邑中学猜题]已知等差数列{a n }中，a 5＝12，a 20＝－18. (1)求数列{a n }的通项公式； (2)求数列{|a n |}的前n 项和S n . 解 (1)设数列{a n }的公差为d ，依题意得⎩⎪⎨⎪⎧a 5＝a 1＋4d ＝12a 20＝a 1＋19d ＝－18，解得⎩⎪⎨⎪⎧a 1＝20d ＝－2，∴a n ＝20＋(n －1)×(－2)＝－2n ＋22.(2)由(1)知|a n |＝|－2n ＋22|＝⎩⎪⎨⎪⎧－2n ＋22，n ≤112n －22，n >11，∴当n ≤11时，S n ＝20＋18＋…＋(－2n ＋22)＝n (20－2n ＋22)2＝(21－n )n ；当n >11时，S n ＝S 11＋2＋4＋…＋(2n －22)＝110＋(n －11)(2＋2n －22)2＝n 2－21n ＋220. 综上所述，S n ＝⎩⎪⎨⎪⎧(21－n )n ，n ≤11n 2－21n ＋220，n >11.16．[2016·冀州中学仿真]已知数列{a n }的各项均为正数，前n 项和为S n ，且满足2S n ＝a 2n ＋n －4.(1)求证{a n }为等差数列； (2)求{a n }的通项公式． 解 (1)证明：当n ＝1时，有2a 1＝a 21＋1－4，即a 21－2a 1－3＝0，解得a 1＝3(a 1＝－1舍去)． 当n ≥2时，有2S n －1＝a 2n －1＋n －5，又2S n ＝a 2n ＋n －4，两式相减得2a n ＝a 2n －a 2n －1＋1， 即a 2n －2a n ＋1＝a 2n －1，也即(a n －1)2＝a 2n －1，因此a n －1＝a n －1或a n －1＝－a n －1. 若a n －1＝－a n －1，则a n ＋a n －1＝1， 而a 1＝3，所以a 2＝－2，这与数列{a n }的各项均为正数相矛盾， 所以a n －1＝a n －1，即a n －a n －1＝1， 因此{a n }为等差数列．(2)由(1)知a 1＝3，d ＝1，所以数列{a n }的通项公式a n ＝3＋(n －1)＝n ＋2，即a n ＝n ＋2.。

选词填空第一单元1)Average students who work hard usually do better than clever students who are（idle）.刻苦学习的一般学生通常成绩比懒惰的聪明学生好。

2) Mrs. Parker had her car windows smashed by a gang（wielding）baseball bats.帕克太太的车窗被一群手持棒球拍的犯罪团伙打碎了。

3) The world will be different, and we will have to be prepared to（adapt）to the change.世界会变得不同，我们不得不准备好去适应这种变化。

4) It seems that more and more people are willing to（donate）their organs for use after death.似乎越来越多的人愿意死后捐献器官。

5）Ralph got（scratched）all over when he was running through the bushes.拉尔夫在灌木丛中跑时浑身刮伤。

6) The idle young man lit a cigarette and sat on the end of the table, one leg（swingin）.这个懒散的年轻人点上一支烟，晃着一条腿坐在桌子一头。

7) If you would move（sideways）to the left, I can get everyone on the picture.你往左边斜一点，我就可以把所有人拍进照片了。

8) We’ve（plotted）our projected costs for the coming year, and they show a big increase.我们绘制了明年的预计成本，显示增长很大。

第一章 概 论第二章 1.1 解：按1mol 干空气计算，空气中各组分摩尔比即体积比，故n N2=0.781mol ，n O2=0.209mol ，n Ar =0.00934mol ，n CO2=0.00033mol 。

质量百分数为%51.75%100197.2801.28781.0%2=⨯⨯⨯=N ，%08.23%100197.2800.32209.0%2=⨯⨯⨯=O ； %29.1%100197.2894.3900934.0%=⨯⨯⨯=Ar ，%05.0%100197.2801.4400033.0%2=⨯⨯⨯=CO 。

1.2 解：由我国《环境空气质量标准》二级标准查得三种污染物日平均浓度限值如下：SO2：0.15mg/m 3，NO2：0.12mg/m 3，CO ：4.00mg/m 3。

按标准状态下1m 3干空气计算，其摩尔数为mol643.444.221013=⨯。

故三种污染物体积百分数分别为： SO 2：ppm 052.0643.44641015.03=⨯⨯-，NO 2：ppm058.0643.44461012.03=⨯⨯- CO ：ppm20.3643.44281000.43=⨯⨯-。

1.3 解：1）ρ（g/m 3N ）334/031.1104.221541050.1Nm g =⨯⨯⨯=--c （mol/m 3N ）3334/1070.6104.221050.1Nm mol ---⨯=⨯⨯=。

2）每天流经管道的CCl 4质量为1.031×10×3600×24×10－3kg=891kg 1.4 解：每小时沉积量200×（500×15×60×10－6）×0.12g μ=10.8g μ 1.5 解：由《大气污染控制工程》P14 （1－1），取M=2102369.0105.19102.22102422=⨯⨯⨯==--∝O p p M Hb O COHb ，COHb 饱和度%15.192369.012369.0/1/222=+=+=+=Hb O COHb Hb O COHb Hb O COHb COHb CO ρ1.6 解：含氧总量为mL960100204800=⨯。

Unit11. An imbalance between the rich and poor is the oldest and most fatal ailment of republics贫富不均乃共和政体最致命的宿疾2. Their poverty is a temporary misfortune, if they are poor and meek, they eventually will inherit the earth他们的贫穷只是一种暂时性的不幸，如果他们贫穷但却温顺，他们最终将成为世界的主人3.Couples in love should repair to R H Macy’s not their bedroom热恋的夫妇应该在梅西百货商店过夜，而不是他们的新房4.The American beauty rose can be produced in the splendor and fragrance which bring cheer to its beholder only by sacrificing the early buds which grow up around it.and so is in economic life. It’s merely the working out of the a law of the nature and a law of god美国这朵玫瑰花以其华贵与芳香让观众倾倒，赞不绝口，而她之所以能被培植就是因为在早期其周围的花蕾被插掉了，在经济生活中情况亦是如此。

这是自然规律和上帝的意志在起作用5. (It has become) an economically not unrewarding enterprise. （它已成为）经济上收入不菲的行业6.There is…no form of oppression that is quiet so great, no constriction on thought and effort quiet so comprehensive, as that which come from having no money at all 没有哪种压迫比身无分文更厉害，也没有哪种对思想和行为的束缚比一无所有来得更全面彻底7. Freedom we rightly cherish, cherishing it, we should not use it as a cover for denying freedom to those in need.我们珍惜自由式对的。

Unit 6Preview1. Listen to the recording of the text and choose the statement that best reflects your understanding.1. D2. C3. A4. C5. DVocabulary1. Become familiar with the rules of word formation.1. Give the corresponding nouns for the following verbs.1. strain 7. realization 13. assurance2. teasing/tease 8. burial 14. astonishment3. dawn 9. scattering/scatter 15. expectation4. Death 10. grasp 16.insurance5. leak 11. appreciation 17. reflection6. inspection 12. flight 18. belief2. Give the corresponding verbs for the following nouns.1. stream 6. Accept2. state 7. encounter3. relate 8. Collect4. form 9. radiate5. recognize 10. identify3. Decide whether the missing letter is e, o or a.（注意：在不发音的e结尾的动词后面加er, or或ar时，应先删去该字母e；在以重读闭音节结尾的动词后面加er, or或ar时，如结尾只有一个辅音，则该辅音必须双写。

）1. reporter 10. supporter 19. composer2. professor 11. visitor 20. interpreter3．Editor 12.1iar 21.beggar4．Adviser 13. seller 22. sailor5．Robber 14. murderer 23. announcer6. actor 15.traveler 24. manager7. aggressor 16. scholar 25. invader8. beginner 17. author 26. creator9. passenger 18. successor 27. dealer4. Translate the following expressions, paying attention to the different use of the suffix “-ful”.1．令人羞愧的结果 10.带着哭腔；声泪俱下地2．满满一碗米饭 11.吃一大口3．色彩鲜艳的衣服 12.一厢情愿的想法4．一个令人快乐的人 13.有希望的形势5．满满一篮子的苹果 14.一屋子的客人6．满满一盒巧克力 15.一调羹油7．一小撮人 16.一大捧书8．一条有帮助的建议 17.痛苦的记忆9．一个有害的习惯 18.活泼的性格5. Fill in the blanks with correct forms of the appropriate words listed below.1 acceptance2 occurrence3 astonishing, unrecognizable4 appreciative, expectations5 identical, identify, identifications2. Give corresponding synonyms and antonyms for the following words.SynonymsAntonyms3. Fill in the blanks with the correct forms of the appropriate phrases and expressions listed below. Note that some of them may be used more than once.1. After all, regarded as2. regarded as / in a sense, consists of3. for ages, at once4. were astonished at, After all5. calls for, on their part/ in turn6. dawned on, in case, melt into7. reflect on, in relation to, calls for8. cut, in, on their part/ in turn, work out4. Fill in the blanks with the correct prepositions or adverbs.1 off/ out2 off3 out/through4 through5 to, through6 to7 with8 on9 to 10 with5.Translate the following sentences into English using the words and expressions listed below.1. 当我们到达目的地时，我们发现这块地上已经没有任何建筑，只有一些石头散落在地上。

6.1 节的练习为下面的表达式构造DAG((x+y)-((x+y)*(x-y)))+((x+y)*(x-y))解答为下列表达式构造DAG，且指出他们每个子表达式的值编码。

假定+ 是左结合的。

1a+b+(a+b)2a+b+a+b3a+a+(a+a+a+(a+a+a+a))解答a+b+(a+b)1 id a2 id b3 + 1 24 + 3 3 a+b+a+b1 id a2 id b3 + 1 24 + 3 15 + 4 2 a+a+(a+a+a+(a+a+a+a))1 id a2 + 1 13 + 2 14 + 3 15 + 3 46 + 2 56.2 节的练习6.2.1将算数表达式a+-(b+c) 翻译成4抽象语法树5四元式序列6三元式序列7间接三元式序列解答抽象语法树四元式序列op arg1 arg20 + b c t11 minus t1 t22 + a t2 t3三元式序列op arg10 + b c1 minus (0)2 + a (1) 间接三元式序列op arg10 + b c1 minus (0)2 + a (1)instruction0 (0)1 (1)2 (2)参考间接三元式更详细的讲解6.2.2对下列赋值语句重复练习6.2.18 a = b[i] + c[j]9a[i] = b*c - b*d10x = f(y+1) + 211x = *p + &y解答a = b[i] + c[j]四元式0) =[] b i t11) =[] c j t22) + t1 t2 t33) = t3 a三元式0) =[] b i1) =[] c j2) + (0) (1)3) = a (2)间接三元式0) =[] b i1) =[] c j2) + (0) (1)3) = a (2)0）1）2）3）a[i] = b*c - b*d四元式0) * b c t11) * b d t22) - t1 t2 t33) []= a i t44) = t3 t4三元式0) * b c1) * b d2) - (0) (1)3) []= a i4) = (3) (2)间接三元式0) * b c 1) * b d 2) - (0) (1) 3) []= a i 4) = (3) (2) 0) 1) 2) 3) 4)x = f(y+1) + 2四元式0) + y 1 t11) param t12) call f 1 t23) + t2 2 t34) = t3 x三元式0) + y 11) param (0)2) call f 13) + (2) 24) = x (3)间接三元式0) + y 11) param (0)2) call f 13) + (2) 24) = x (3)0)1)2)3)4)参考数组元素的取值和赋值6.2.3 !说明如何对一个三地址代码序列进行转换，使得每个被定值的变量都有唯一的变量名。

第6章 习题解答6-1 指出下列各类型的触发器中那些能组成移位寄存器，哪些不能组成移位寄存器，如果能够，在（）内打√，否则打×。

（1）基本RS 触发器 （ ）； （2）同步RS 触发器 （ ）； （3）主从结构触发器 （ ）； （4）维持阻塞触发器 （ ）；（5）用CMOS 传输门的边沿触发器 （ ）；（6）利用传输延迟时间的边沿触发器（ ）。

解答：（1）×；（2）×；（3）√；（4）√；（5）√；（6）√；6-2 试分析图6-79所示时序电路的逻辑功能，写出电路的驱动方程、状态方程和输出方程，画出电路的状态转换图，并且说明电路能够自启动。

解答： 驱动方程：113J K Q ==；221J K Q ==；312J Q Q =、33K Q = 状态方程：111111313113n Q J Q K Q Q Q Q Q Q Q +=+=+=e 122222121212n Q J Q K Q Q Q QQ Q Q +=+=+=⊕13333312333123n Q J Q K Q QQ Q Q Q QQ Q +=+=+=输出方程：123CO QQ Q =状态转换表如下：5 100 000 1 101 011 1 110 010 11110011状态转换图如下：此电路为能自启动的同步五进制加法计数器。

6-3 试分析图6-80所示时序电路的逻辑功能，写出电路的驱动方程、状态方程和输出方程，画出电路的状态转换图。

A 为输入逻辑变量。

解答： 驱动方程：12D AQ =；21212()D AQ Q A Q Q ==+ 状态方程：1112n Q D AQ +==12212()n Q D A Q Q +==+输出方程：12CO AQQ = 状态转换表如下：脉冲数 A 初态21Q Q次态1121n n Q Q ++输出CO1 0 00 00 02 0 01 00 03 0 10 00 04 0 11 00 0100011 01 11 0 1 11 10 1110101状态转换图如下：此电路为串行数据检测器，当输入4个或4个以上的1时输出为1，其他输入情况下输出为0。

光的衍射习题答案第六章光的衍射6－1求矩形夫琅和费衍射图样中，沿图样对角线方向第一个次极大和第二个次极大相对于图样中心的强度。

解：对角线上第一个次极大对应于1.43，其相对强度为：II0inin2in1.430.00221.4324对角线上第二个次极大对应于2.46，其相对强度为：II0inin2in2.460.000292.46246－2由氩离子激光器发出波长488nm的蓝色平面光，垂直照射在一不透明屏的水平矩形孔上，此矩形孔尺寸为0.75mm某0.25mm。

在位于矩形孔附近正透镜（f2.5m）焦平面处的屏上观察衍射图样，试求中央亮斑的尺寸。

解：中央亮斑边缘的坐标为：某fafb2500488100.752500488100.25661.63mm2某3.26mmy4.88mm2y9.76mm∴中央亮斑是尺寸为3.26mm某9.76mm的竖直矩形6－3一天文望远镜的物镜直径D＝100mm，人眼瞳孔的直径d＝2mm，求对于发射波长为0.5μm光的物体的角分辨极限。

为充分利用物镜的分辨本领，该望远镜的放大率应选多大？解：当望远镜的角分辨率为：1.22D1.220.510100100.510210636.1106rad人眼的最小分辨角为：e1.22ed61.2233.05104rad∴望远镜的放大率应为：MDd506－4一个使用汞绿光（546nm）的微缩制版照相物镜的相对孔径（D/f）为1:4，问用分辨率为每毫米380条线的底片来记录物镜的像是否合适？解：照相物镜的最大分辨本领为：N1D11.225461061.22f14375/mm∵380>375∴可以选用每毫米380条线的底片。

6－5若要使照相机感光胶片能分辨2m的线距，问（1）光胶片的分辨本领至少是每毫米多少线？（2）照相机镜头的相对孔径D/f至少有多大？解：（1）由于相机感光胶片能分辨2m的线距，则分辨本领至少为：N10.002＝500线/毫米（2）可见光一般取中心波长550nm计算，则相机的相对孔径至少为：Df1.22N1.225501065001:2.986－6借助于直径为2m的反射式望远镜，将地球上的一束激光（600nm）聚焦在月球上某处。

大气污染控制工程课后作业习题解答第一章 概 论1。

1 解：按1mol 干空气计算，空气中各组分摩尔比即体积比,故n N2=0。

781mol ，n O2=0。

209mol ，n Ar =0。

00934mol ，n CO2=0.00033mol 。

质量百分数为%51.75%100197.2801.28781.0%2=⨯⨯⨯=N ，%08.23%100197.2800.32209.0%2=⨯⨯⨯=O ；%29.1%100197.2894.3900934.0%=⨯⨯⨯=Ar ,%05.0%100197.2801.4400033.0%2=⨯⨯⨯=CO 。

1。

2 解：由我国《环境空气质量标准》二级标准查得三种污染物日平均浓度限值如下：SO2:0。

15mg/m 3,NO2：0。

12mg/m 3，CO ：4.00mg/m 3。

按标准状态下1m 3干空气计算，其摩尔数为mol 643.444.221013=⨯。

故三种污染物体积百分数分别为： SO 2：ppm 052.0643.44641015.03=⨯⨯-，NO 2：ppm 058.0643.44461012.03=⨯⨯- CO:ppm 20.3643.44281000.43=⨯⨯-。

1。

3 解： 1）ρ(g/m 3N )334/031.1104.221541050.1N m g =⨯⨯⨯=-- c （mol/m 3N ）3334/1070.6104.221050.1N m mol ---⨯=⨯⨯=。

2）每天流经管道的CCl 4质量为1.031×10×3600×24×10－3kg=891kg1.4 解：每小时沉积量200×（500×15×60×10－6）×0。

12g μ=10。

8g μ1.5 解:由《大气污染控制工程》P14 （1－1）,取M=2102369.0105.19102.22102422=⨯⨯⨯==--∝O p p M Hb O COHb ， COHb 饱和度%15.192369.012369.0/1/222=+=+=+=Hb O COHb Hb O COHb Hb O COHb COHb CO ρ1。

第六章 分子动理论6-1 一立方容器，每边长20cm 其中贮有，的气体，当把气体加热到时，容器每个壁所受到的压力为多大？解：根据理想气体状态方程NkT pV =得11kT Vp N =。

所以221111N/cm 5.13N/m 135100101325300400==⨯====p T T V kT kT V p V NkT p6-2 一氧气瓶的容积是 ，其中氧气的压强是 ，规定瓶内氧气压强降到时就得充气，以免混入其他气体而需洗瓶，今有一玻璃室，每天需用氧气，问一瓶氧气能用几天。

解：一瓶氧的摩尔数为RT pV =ν，用完后瓶中还剩氧气的摩尔数为RTVp '='ν，实际能用的摩尔数为RT p p )(-'-='=ννν∆.每天所用氧气的摩尔数为RTV p ''''=''ν。

一瓶氧气能用的天数为)d (6.940032110132)(=⨯-='''''-=''=V p V p p n νν∆ 6-3 有一水银气压计，当水银柱为0.76m 高时，管顶离水银柱液面0.12m ，管的截面积为2.0×10-4m 2，当有少量氦(He)混入水银管内顶部，水银柱高下降为0.6m ，此时温度为27℃，试计算有多少质量氦气在管顶(He 的摩尔质量为0.004kg ·mol -1)?解：当压强计顶部中混入氦气，其压强为)(21h h g p -=ρ，由理想气体状态方程得氦气的质量为kg1095.1004.030031.8100.2)16.012.0()6.076.0(546.13)(6421--⨯=⨯⨯⨯⨯+⨯-⨯=-==RTV h h g RT pVM ρμ 6-4 在常温下(例如27℃)，气体分子的平均平动能等于多少ev?在多高的温度下，气体分子的平均平动能等于1000ev?解：23.8810ev -⨯ ，301Ki N 21 4 682)s m (1-⋅i V10.020.030.040.050.0解：s /m 7.2141==υs /25.6m s /m 1.656410.5020.4080.3060.2040.1021222222==⨯+⨯+⨯+⨯+⨯=υ6-6 下列系统各有多少个自由度：(1)在一平面上滑动的粒子；(2)可以在一平面上滑动并可围绕垂直于平面的轴转动的硬币； (3)一弯成三角形的金属棒在空间自由运动． 解：（1）确定平面上运动的粒子需要2个独立坐标，所以自由度数为2；（2）确定硬币的平动需要两个独立坐标，确定转动需要一个坐标，确定硬币位置共需3个坐标，所以自由度数为3；（3）这是一个自由刚体，有6个自由度，其中3个平动自由度和3个转动自由度。

习题目录6.1 (3)6.2 (3)6.3 (4)6.4 (6)6.5 (7)6.6 (7)6.7 (7)6.8 (8)6.9 (10)6.10 (11)6.11 (11)6.12 (12)6.13 (13)6.14 (13)6.15 (14)6.16 (15)6.17 (15)6.18 (16)6.19 (16)6.20 (16)6.21 (16)6.22 (17)6.23 (18)6.24 (19)6.25 (19)6.26 (19)6.27 (20)6.28 (20)6.29 (20)6.30 (21)6.31 (22)6.32 (22)6.33 (22)6.34 (23)6.35 (24)6.36 .................................................................................................................... 错误!未定义书签。

6.37 (25)6.38 (26)6.39 (26)6.40 (27)6.41 (27)6.42 (28)6.43 .................................................................................................................... 错误!未定义书签。

6.44 .................................................................................................................... 错误!未定义书签。

6.45 (32)6.46 (35)输入序列的101的最后一个“1”，输出Z=1。

其余情况下输出为“0”。

（1） （2）解：1）S 0：起始状态，或收到101序列后重新开始检测。

Lesson 11.An imbalance between the rich and poor is the oldest and most fatal ailment of republics.贫富不均乃共和政体最致命疾.2. Their poverty is a temporary misfortune, if they are poor and meek, they eventually will inherit the earth.他们的贫穷只是一种暂时性的不幸，如果他们贫穷但却温顺，他们最终将成为世界的主人.3.Couples in love should repair to R H Macy’s not their bedrooms.热恋的夫妇应该在梅西百货商店过夜,而不是他们的新房.4.The American beauty rose can be produced in the splendor and fragrance which bring cheer to its beholder only by sacrificing the early buds which grow up around it. And so is in economic life. It’s merely the working out of a law of the nature and a law of God.美国这朵玫瑰花以其华贵与芳香让观众倾倒，赞不绝口，而她之所以能被培植就是因为在早期其周围的花蕾被插掉了，在经济生活中情况亦是如此。

这是自然规律和上帝的意志在起作用.5.(It has become) an economically not unrewarding enterprise.（它已成为）经济上收入不菲的行业.6. There is...no form of oppression that is quiet so great, no constriction on thought and effort quiet so comprehensive, as that which come from having no money at all.没有哪种压迫比身无分文更厉害，也没有哪种对思想和行为的束缚比一无所有来得更全面彻底7.Freedom we rightly cherish. Cherishing it, we should not use it as a cover for denying freedom to those in need.我们珍惜自由式对的。

6.5 习题6.1 将一个列表的数据复制到另一个列表中。

程序分析：使用列表[:]。

程序源代码：a = [1, 2, 3]b = a[:]print(b)6.2 写代码，有如下列表，利用切片实现每一个功能。

li = [1, 3, 2, "a", 4, "b", 5,"c"]1)通过对li列表的切片形成新的列表l1,l1 = [1,3,2]2)通过对li列表的切片形成新的列表l2,l2 = ["a",4,"b"]3)通过对li列表的切片形成新的列表l3,l3 = ["1,2,4,5]4)通过对li列表的切片形成新的列表l4,l4 = [3,"a","b"]5)通过对li列表的切片形成新的列表l5,l5 = ["c"]6)通过对li列表的切片形成新的列表l6,l6 = ["b","a",3]l1=li[0:3]l2=li[3:6]l3=li[::2]l4=li[1:-2:2]l5=li[-1]print(l1,l2,l3,l4,l5)6.3 使用while和for循环分别打印字符串s="asdfer"中每个元素。

#while循环s="asdfer"count=0while count<len(s):print(s[count])count+=1#for循环for i in s:print(i)1216.4 利用for循环和range从100~10，倒序将所有的偶数添加到一个新列表中，然后对列表的元素进行筛选，将能被4整除的数留下来。

li = []for i in range(100,9,-1):if i%4==0:li.append(i)print(li)6.5 利用for循环和range，将1-30的数字一次添加到一个列表中，并循环这个列表，将能被3整除的数改成*。