The operation otimes is defined for all nonzero numbers by aotimes b =fraca^2b. Determine [(1otimes 2)otimes 3]-[1otimes (2otimes 3)].

AMC 8 2000 Problem 17

AMC8 2000 年第 17 题

表达式与运算★★★☆☆

The operation

\otimes

is defined for all nonzero numbers by

\displaystyle a\otimes b =\frac{a^2}b

. Determine

[(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)]

对于所有非零数，定义.. 。求的值。 Problem 18 Consider these two geoboard quadrilaterals. Which of the following statements is true? 考虑下面几何画板上的两个四边形。下面哪句话是对的？（A）The area of quadrilateral I is more than the area of quadrilateral II. | 四边形 I 的面积大于四边形 II 的面积. （B）The area of quadrilateral I is less than the area of quadrilateral II. | 四边形 I 的面积小于四边形 II 的面积. （C）The quadrilaterals have the same area and the same perimeter. | 这两个四边形的面积相同. （D）The quadrilaterals have the same area, but the perimeter of I is more than theperimeter of II．| 这 2 个四边形有相同的面积，但是 I 的周长大于 II 的周长。（E）The quadrilaterals have the same area,but the perimeter of I is less than theperimeter ofII． | 这 2 个四边形有相同的面积，但是 I 的周长小于 II 的周长

A. $\displaystyle -\frac{2}{3}$
B. $\displaystyle -\frac{1}{4}$
C.0
D. $\displaystyle \frac{1}{4}$
E. $\displaystyle \frac{2}{3}$

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