题目内容
电灯可在点A与桌面的垂直线上移动(如图),在桌面上另一点B离垂足O的距离为a,为使点B处有最大的照度(照度I与sin∠OBA成正比,与r2成反比,且比例系数均为正的常数),则电灯A与点O的距离为( )
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A.![]() | B.![]() | C.![]() | D.![]() |
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B
设
到
的距离为
,则
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于是
,
.
当
时,即方程
的根为
(舍)与
,在我们讨论的半闭区间
内,所以函数
在点
取极大值,也是最大值。即当电灯与
点距离为
时,点
的照度
为最大.
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于是
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当
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