两县城A和B相距20km,现计划在两城外以AB为直径的半圆弧
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上选择一点C建造垃圾处理厂,其对城市的影响度与所选地点到城市的距离有关,对城A和城B的总影响度为城A与城B的影响度之和,记C点到城A的距离为x km,建在C处的垃圾处理厂对城A和城B的总影响度为y,统计调查表明:垃圾处理厂对城A的影响度与所选地点到城A的距离的平方成反比,比例系数为4;对城B的影响度与所选地点到城B的距离的平方成反比,比例系数为k,当垃圾处理厂建在
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的中点时,对城A和城B的总影响度为0.065.
(1)按下列要求建立函数关系式:
①设∠CAB=θ(rad),将θ表示成y 的函数;并写出函数的定义域.
②设AC=x(km),将x表示成y的函数;并写出函数的定义域.
(2)请你选用(1)中的一个函数关系确定垃圾处理厂的位置,使建在此处的垃圾处理厂对城A和城B的总影响度最小?
考点分析:
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