如图,某农业研究所要在一个矩形试验田ABCD内种植三种农作物,三种农作物分别种植在并排排列的三个形状相同、大小相等的矩形中.试验田四周和三个种植区域之间设有1米宽的非种植区.已知种植区的占地面积为800平方米,问:应怎样设计试验田ABCD的长与宽,才能使其占地面积最小?最小占地面积是多少?
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已知函数f(x)=cosx(sinx+cosx),x∈R.
(1)请指出函数f(x)的奇偶性,并给予证明;
(2)当
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时,求f(x)的取值范围.
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以下四个命题中,真命题的个数为( )
①集合{a
1,a
2,a
3,a
4}的真子集的个数为15;
②平面内两条直线的夹角等于它们的方向向量的夹角;
③设z
1,z
2∈C,若
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,则z
1=0且z
2=0;
④设无穷数列{a
n}的前n项和为S
n,若{S
n}是等差数列,则{a
n}一定是常数列.
A.0
B.1
C.2
D.3
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已知向量
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,
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满足:
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,且
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(k>0).则向量
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与向量
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的夹角的最大值为( )
A.
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B.
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C.
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D.
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曲线x
2+y
2-6x=0(y>0)与直线y=k(x+2)有公共点的充要条件是( )
A.
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B.
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C.
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D.
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设函数
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则方程f(x)=x
2+1的实数解的个数为
.
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