摘要: 中...cm.长为1cm的线段在的边上沿方向以1cm/s的速度向点运动(运动前点与点重合).过分别作的垂线交直角边于两点.线段运动的时间为s. (1)若的面积为.写出与的函数关系式(写出自变量的取值范围), (2)线段运动过程中.四边形有可能成为矩形吗?若有可能.求出此时的值,若不可能.说明理由, (3)为何值时.以为顶点的三角形与相似? 解:(1)当点在上时... .········································································ 2分 当点在上时.. .·················································· 4分 (2)... .········································································ 6分 由条件知.若四边形为矩形.需.即. . 当s时.四边形为矩形.································································· 8分 知.当s时.四边形为矩形.此时. .··························································································· 9分 除此之外.当时..此时. ...····························· 10分 .. 又..········································ 11分 .. 当s或s时.以为顶点的三角形与相似.··················· 12分
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(2011山东济宁,18,6分)观察下面的变形规律:
=1-
;
=
-
;
=
-
;……
解答下面的问题:
(1)若n为正整数,请你猜想
= ;
(2)证明你猜想的结论;
(3)求和:
+
+
+…+
.