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如图1,在平面直角坐标系中,有一矩形ABCD,其三个顶点的坐标分别为A(2,0)、B(8,0)、C(8,3).将直线l:y=-3x-3以每秒3个单位的速度向右运动,设运动时间为t秒.

(1)当t=_________时,直线l经过点A.(直接填写答案)
(2)设直线l扫过矩形ABCD的面积为S,试求S>0时S与t的函数关系式.
(3)在第一象限有一半径为3、且与两坐标轴恰好都相切的⊙M,在直线l出发的同时,⊙M以每秒2个单位的速度向右运动,如图2所示,则当t为何值时,直线l与⊙M相切?

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答案(点此获取答案解析)

(1)y=-3x-3与x轴交点坐标是(-1,0),直线l经过点A(2,0),故向右平移3个单位长度,直线l:y=-3x-3以每秒3个单位的速度向右运动,所以t=1;(2)由题意,可知矩形ABCD顶点D的坐标为(2,3).由一次函数的性质可知,当t由小到大变化时,直线l:y=﹣3(x﹣3t)-3=﹣3x+9t﹣3向右平移,依次扫过矩形ABCD的不同部分.可得当直线经过A(2,0)时,t=1;当直线经过D(2,3)时,t=

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