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六、（每小题7分，共14分） 25．（本题7分）
解：设南瓜亩产量的增长率为x，则种植面积的增长率为2x． ········································ 1分 根据题意，得
··················································································· 4分 10(1?2x)?2 000(1?x)?60 000．·
解这个方程，得x1?0.5，x2??2（不合题意，舍去）． ·················································· 6分 答：南瓜亩产量的增长率为50％． ······················································································ 7分
26．（本题7分） 解：（1）在梯形ABCD中，AD∥BC，
AB?DC?AD?6，∠ABC?60?， ?∠A?∠D?120?，
?∠AEB?∠ABE?180??120??60?． ?∠BEF?120?，
?∠AEB?∠DEF?180??120??60?，
?∠ABE?∠DEF．
········································································································· 2分 ?△ABE∽△DEF． ·
AEAB． ······················································································································ 3分 ??DFDE?AE?x，DF?y，
?x6． ························································································································ 4分 ?y6?x?y与x的函数表达式是
11····························································································· 5分 y??x(6?x)??x2?x； ·
6612（2）y??x?x
613·············································································································· 6分 ??(x?3)2?． ·
623········································································ 7分 ?当x?3时，y有最大值，最大值为． ·2七、（本题10分）
27．解：（1）①2，60； ···································································································· 2分 ②2； ······································································································································ 4分
?△AO1O2经过旋转相似变换A(2，45)，（2）得到△ABI，此时，线段O1O2变为线段BI；
? ································································································· 6分
?2??，45△CIB经过旋转相似变换C???2?，得到△CAO2，此时，线段BI变为线段AO1． ?? ····································································································· 8分
?2?2?1，45??45??90?， 2?O1O2?AO2，O1O2?AO2． ························································································ 10分
八、（本题7分） 28．（1）画法一：以点A为圆心，大于点A到直线l的距离长为半径画弧，与直线l交于B，C两点，则点B，C即为所求． ································································································ 1分 A l
C B
画图正确． ······························································································································ 2分 画法二：在直线l上任取一点B，以点B为圆心，AB长为半径画弧，与直线l交于点C，则点B，C即为所求． ··········································································································· 1分 A
l C B
画图正确． ······························································································································ 2分 （2）画法：
在直线l上任取B，C两点，以点A为圆心，BC长为半径画弧，以点C为圆心，AB长为半径画弧，两弧交于点P．则点P即为所求． ···································································· 5分
P A
l C B
画图正确． ······························································································································ 7分
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