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问题 解答题

在△ABC中，a、b、c分别是角A、B、C所对的边，满足a2+c2-b2=ac．

（1）求角B的大小；

（2）若x∈[0，π），求函数f（x）=sin（x-B）+sinx的值域．

答案

（1）在△ABC中，由余弦定理得cosB=

a2+c2-b2
2ac
=
1
2

又∵B∈(0，π)，∴B=

π
3
；

（2）f(x)=sin(x-

π
3
)+sinx=
3
2
sinx-
3
2
cosx=
3
sin(x-
π
6
)

∵0≤x＜π，则-

π
6
≤x-
π
6
＜
5π
6

∴sin(x-

π
6
)∈[-
1
2
，1]

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单项选择题

Young girls at high risk for depression appear to have a malfunctioning reward system in their brains, a new study suggests. The finding comes from research that (1) a high-risk group of 13 girls, aged 10 to 14, who were not depressed but had mothers who (2) recurrent depression and a low-risk group of 13 girls with no (3) or family history of depression. Both groups were given MRI brain (4) while completing a task that could (5) either reward or punishment.

(6) with girls in the low-risk group, those in the high-risk group had (7) neural responses during both anticipation and receipt of the reward. (8) , the high-risk girls showed no (9) in an area of the brain called the dorsal anterior cingulated cortex (背侧前扣带皮质), believed to play a role in (10) past experiences to assist learning.

The high-risk girls did have greater activation of this brain area (11) receiving punishment, compared with the other girls. The researchers said that this suggests that high-risk girls have easier time (12) information about loss and punishment than information about reward and pleasure.

"Considered together with reduced activation in the striatal (纹状体的) areas commonly observed (13) reward, it seems that the reward-processing system is critically (14) in daughters who are at elevated risk for depression, (15) they have not yet experienced a depressive (16) ," wrote Ian H. Gotlib, of Stanford University, and his colleagues. " (17) , longitudinal studies are needed to determine whether the anomalous activations (18) in this study during the processing of (19) and losses are associated with the (20) onset of depression," they concluded. The study was published in the April of the Archives of General Psychiatry.

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