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问题 填空题

△ABC中，a、b、c分别是角A、B、C的对边，若a2-c2=2b，且sinB=6cosA•sinC，则b的值为______．

答案

△ABC中，∵sinB=6cosA•sinC，∴由正弦定理可得 b=6c•cosA=6c•

b2+c2-a2
2bc
=3×
b2+c2-a2
b
．

∵a2-c2=2b，∴b=3•

b2-2b
b
，化简可得 b（b-3）=0，由此可得 b=3，

故答案为 3．

阅读理解

任务型阅读。

     Hello! My name is Tina. I come from America, but I love China very much, because my mother is

Chinese. Today (今天) is October 18th-my birthday. In the morning, my parents take me(A) _____ a

store and buy a red skirt for me,(B) for I like red very much. In the afternoon, we go to Disneyland

(迪士尼乐园) I have fun there.(C) In the evening, we have a birthday party at home. My friends all

come to mu party and we eat a big cake(蛋糕). Thank my parents and friends for giving me a happy

birthday!

根据短文内容，完成下列任务。

1. 请写出A处所缺的单词：

    _____________

2. 猜一猜B处划线单词的意思：

    _____________

3. 请将C处的句子翻译成汉语：

    _____________

4. What do they eat in the evening?

    _____________

5. Is Tina happy today?  

    _____________
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解答题
已知向量
a
=（cos
3
2
x，sin
3
2
x），
b
=（cos
x
2
，-sin
x
2
），且x∈[0，
π
2
]；
（I）求
a
•
b
及|
a
+
b
|；
（II）若f（x）=
a
•
b
-
3
|
a
+
b
|sinx，求f（x）的最大值与最小值．
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