作业帮如果分别以x,y的半径画同心圆(x>y),所得圆环的面积是100π,那么代数式[8(x+y)^2(x-y)^3]÷[4(x+y)(x-y)^2]^2的值为
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 10:39:07
![如果分别以x,y的半径画同心圆(x>y),所得圆环的面积是100π,那么代数式[8(x+y)^2(x-y)^3]÷[4(x+y)(x-y)^2]^2的值为](/uploads/image/z/5468056-16-6.jpg?t=%E5%A6%82%E6%9E%9C%E5%88%86%E5%88%AB%E4%BB%A5x%2Cy%E7%9A%84%E5%8D%8A%E5%BE%84%E7%94%BB%E5%90%8C%E5%BF%83%E5%9C%86%28x%3Ey%29%2C%E6%89%80%E5%BE%97%E5%9C%86%E7%8E%AF%E7%9A%84%E9%9D%A2%E7%A7%AF%E6%98%AF100%CF%80%2C%E9%82%A3%E4%B9%88%E4%BB%A3%E6%95%B0%E5%BC%8F%5B8%28x%2By%29%5E2%28x-y%29%5E3%5D%C3%B7%5B4%28x%2By%29%28x-y%29%5E2%5D%5E2%E7%9A%84%E5%80%BC%E4%B8%BA)
如果分别以x,y的半径画同心圆(x>y),所得圆环的面积是100π,那么代数式[8(x+y)^2(x-y)^3]÷[4(x+y)(x-y)^2]^2的值为
如果分别以x,y的半径画同心圆(x>y),所得圆环的面积是100π,那么代数式[8(x+y)^2(x-y)^3]÷[4(x+y)(x-y)^2]^2的值为
如果分别以x,y的半径画同心圆(x>y),所得圆环的面积是100π,那么代数式[8(x+y)^2(x-y)^3]÷[4(x+y)(x-y)^2]^2的值为
(x²-y²)π=100π
(x²-y²)=100
[8(x+y)²(x-y)²(x-y)]÷[4(x+y)(x-y)²]²
=[8(x²-y²)²(x-y)]÷[4(x²-y²)(x-y)]²
=1/[2(x-y)]
由圆面积得x^2π－y^2π＝100π
x^2－y^2＝100，即(x+y)(x-y)＝100
根据直角三角形，三边的关系得x=12.5 y=7.5
[8(x+y)^2(x-y)^3]÷[4(x+y)(x-y)^2]^2
=[8(x+y)^2(x-y)^2(x-y)]÷[4^2(x+y)^2(x-y)^2(x-y)^2]
=[8×100^2(x-y)...
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由圆面积得x^2π－y^2π＝100π
x^2－y^2＝100，即(x+y)(x-y)＝100
根据直角三角形，三边的关系得x=12.5 y=7.5
[8(x+y)^2(x-y)^3]÷[4(x+y)(x-y)^2]^2
=[8(x+y)^2(x-y)^2(x-y)]÷[4^2(x+y)^2(x-y)^2(x-y)^2]
=[8×100^2(x-y)]÷[16×100^2(x-y)^2]
=[8×100^2(x-y)]÷[8×100^2(x-y)]×2(x-y)
=1÷[2(x-y)]
=(x+y)÷2(x+y)(x-y)
=(x+y)/200
=20/200
=0.1
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