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问题 解答题

在△ABC中，A、B、C的对边分别为a、b、c，且满足acosC-bcosB=bcosB-ccosA．

（1）求B的值；（2）若a=2，c=3，求b．

答案

（1）根据正弦定理a=2rsinA，b=2rsinB，c=2rsinC

∵acosC-bcosB=bcosB-ccosA．

∴sinAcosC-sinBcosB=sinBcosB-sinCcosA

∴sinAcosC+sinCcosA=2sinBcosB

即sin（A+C）=sin2B，A+C=2B

∴A+C+B=3B=180°

∴B=60°

（2）由（1）知B=60°∴cosB=

1
2

根据余弦定理可知，b2=a2+c2-2accosB

将a=2，c=3代入可得b2=7

∴b=

7

填空题

防波堤按结构型式分（）、（）以及（）三类。
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单项选择题

In one sense, we can trace all the problems of the American city back (91) a single starting point: we Americans don’t like our cities very much.
That is, on the (92) of it, absurd. After all, more than three-fourths of us now live in cities, and more are (93) to them every year. We are told that the problems of our cities are (94) more attention in Washington, and scholarship has discovered a whole new (95) in urban studies.
(96) , it is historically true: in the American psychology, the city has been a basically suspect institution, (97) with the corruption of Europe, totally lacking that sense of spaciousness and innocence of the (98) and the rural landscape.
I don’t pretend to be a scholar on the history of the city in American life. But my thirteen years in public (99) , first as an officer of the U. S. Department of Justice, then as Congressman, and now as Mayor of the biggest city in America have taught me (100) too well the fact that a p antiurban attitude (101) consistently through the mainstream of American thinking. Much of the (102) behind the settlement of America was in reaction (103) the conditions in European industrial centers and much of the theory (104) the basis of freedom in America was linked directly to the availability of land and the perfectibility of man outside the corrupt influences of the city.
What has this to do with the predicament of the modern city I think it has (105) to do with it. For the fact is that the United States (106) the federal government, which has historically established our national priorities, has simply never thought that the American city was "worthy" of (107) —at least not to the (108) of expending any basic resources on it.
Antipathy to the city predates the American experience. When industrialization (109) the European working man into the major cities of the continent, books and pamphlets appeared (110) the city as a source of crime, corruption, filth, disease, vice, licentiousness, subversion, and high prices.

A．many

B．much

C．lots

D．great
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