选择章节

若\(x,y\)满足约束条件\(\begin{cases} & x-y\geqslant 0, \\ & x+y-2\leqslant 0, \\ & y\geqslant 0, \end{cases}\)则\(z=3x-4y\)的最小值为_________．

已知实数\(x\)，\(y\)满足\(\begin{cases} & x+2y-2\geqslant 0 \\ & 2x+y-4\leqslant 0 \\ & y\leqslant x+1 \end{cases}\)，且\(m=\dfrac{x+3y+4}{x+1}\)，则实数\(m\)的取值范围_____．

已知\(x\)、\(y\)满足约束条件\(\begin{cases} & x-y+5\geqslant 0 \\ & x+y\geqslant 0 \\ & x\leqslant 3 \end{cases}\)，则\(z=2x+4y\)的最小值为 _________

\((1)\)若实数\(x\)，\(y\)满足约束条件\(\begin{cases} y-x\leqslant 1 \\ x+y\leqslant 3 \\ y\geqslant 1 \end{cases},\)则\(z=x+3y\)的最大值为____．

\((2)\)已知等差数列^{\(\left\{{a}_{n}\right\} \)}的前项和为\(S_{n}\)，若\(a_{3}+a_{4}=18-a_{6}-a_{5}\)，则\(S_{8}=\)________．

\((3)\)若向量\(\overset{⇀}{a} \)，\(\overset{⇀}{b} \)夹角为\(\dfrac{\pi }{3}\)，且\(\left| \overset{⇀}{a}\right|=2,\left| \overset{⇀}{b}\right|=1 \)，则\(\overset{⇀}{a} \)与\(\overset{⇀}{a} +2\overset{⇀}{b} \)的夹角为_________ 

\((4)\)已知实数\(a,b\)满足\(\ln \left( b+1 \right)+a-3b=0\)，实数\(c,d\)满足\(2d-c+\sqrt{5}=0\)，则\({{\left( a-c \right)}^{2}}+{{\left( b-d \right)}^{2}}\)的最小值为_________

若\(x\)，\(y\)满足约束条件\(\begin{cases} & x+y-2\leqslant 0, \\ & x-2y+2\leqslant 0, \\ & x-y+2\geqslant 0, \end{cases}\)，则\(z=3x+y\)的最大值为________________．

若实数\(x{,}y\)满足\(\begin{cases} x{+}y{-}1{\geqslant }0 \\ x{-}y{-}2{\leqslant }0 \\ y{\leqslant }1 \end{cases}\)，则\(z{=-}\dfrac{1}{3}x{+}y\)的最小值为______ ．