(本小题满分14分)某城市自西向东和自南向北的两条主干道的东南方位有一块空地市规划部门计划利用它建设一个供市民休闲健身的小型绿化广场,如下图所示是步行小道设计方案示意图,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232326058294063.jpg)
其中,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232605845500.png)
分别表示自西向东,自南向北的两条主干道.设计方案是自主干道交汇点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232605860271.png)
处修一条步行小道,小道为抛物线
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232605891416.png)
的一段,在小道上依次以点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232326060631330.png)
为圆心,修一系列圆型小道,这些圆型小道与主干道
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606157330.png)
相切,且任意相邻的两圆彼此外切,若
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606172318.png)
(单位:百米)且
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606203436.png)
.
(1)记以
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606250315.png)
为圆心的圆与主干道
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606157330.png)
切于
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606453342.png)
点,证明:数列
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606469442.png)
是等差数列,并求
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606562450.png)
关于
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606656271.png)
的表达式;
(2)记
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606671350.png)
的面积为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606703343.png)
,根据以往施工经验可知,面积为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606718290.png)
的圆型小道的施工工时为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606734400.png)
(单位:周).试问5周时间内能否完成前
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232606656271.png)
个圆型小道的修建?请说明你的理由.