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A=ghi laị biểu thức
A=(0,8*7+0,8*0,8)*(1,25*7-1,25*4/5)+31,64
A=[0,8*(7+0,8)]*[1,25*(7-4/5)]+31,64
A=(0,8*7,8)*(1,25*6,2)+31,+31,64
A=6,24*7,75+31,64
A=48,36+31,64
A=80
Lời giải:
Ta có:
\(\cos (\overrightarrow{a}, \overrightarrow{b})=\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}||\overrightarrow{b}|}=\frac{2.6+(-3).4}{\sqrt{2^2+(-3)^2}.\sqrt{6^2+4^2}}\)
\(=0\)
\(\Rightarrow \angle (\overrightarrow{a}; \overrightarrow{b})=\frac{\pi}{2}\)
1.
\(\overrightarrow{AB}=\left(6;2\right)\) ; \(\overrightarrow{AC}=\left(1;-3\right)\)
\(\Rightarrow\overrightarrow{AB}.\overrightarrow{AC}=6.1+2.\left(-3\right)=0\)
\(\Rightarrow AB\perp AC\Rightarrow\Delta ABC\) vuông tại A (ko phải tại B như đề bài ghi)
\(AB=\sqrt[]{6^2+2^2}=2\sqrt{10}\) ; \(AC=\sqrt{1^2+\left(-3\right)^2}=\sqrt{10}\)
\(S_{ABC}=\dfrac{1}{2}AB.AC=10\)
2.
Pt có 2 nghiệm cùng dấu khi:
\(\left\{{}\begin{matrix}\Delta'=16-\left(m+5\right)\ge0\\x_1x_2=m+5>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\le11\\m>-5\end{matrix}\right.\)
\(\Rightarrow-5< m\le11\)
cos(\(\dfrac{3a}{2}\))*cos(\(\dfrac{a}{2}\))=\(\dfrac{1}{2}\left(cos\left(\dfrac{3a}{2}+\dfrac{a}{2}\right)+cos\left(\dfrac{3a}{2}-\dfrac{a}{2}\right)\right)\)=\(\dfrac{1}{2}\left(cos\left(2a\right)+cos\left(a\right)\right)\)=\(\dfrac{1}{2}\left(2cos^2a-1+cosa\right)\)=\(\dfrac{1}{2}\left(2\cdot\left(\dfrac{3}{4}\right)^2-1+\dfrac{3}{4}\right)=\dfrac{7}{16}\)
đề bài tính "A" :
\(\left\{{}\begin{matrix}\dfrac{x}{x^2-x+1}=a\\A=\dfrac{x^2}{x^4+x^2+1}\end{matrix}\right.\) \(\begin{matrix}\left(1\right)\\\\\left(2\right)\end{matrix}\)
\(x=0;a=0;A=0\)
\(x\ne0;\left(1\right)\Leftrightarrow\dfrac{1}{a}=\dfrac{x^2-x+1}{x}=x+\dfrac{1}{x}-1\)
\(\left(2\right)\Leftrightarrow\dfrac{1}{A}=\dfrac{x^4+x^2+1}{x^2}=x^2+\dfrac{1}{x^2}+1=\left(x+\dfrac{1}{x}\right)^2-1=\left(x+\dfrac{1}{x}-1\right)\left(x+\dfrac{1}{x}+1\right)\)
\(\dfrac{1}{A}=\dfrac{1}{a}\left(\dfrac{1}{a}+2\right)=\dfrac{2a+1}{a^2}\)
\(a=\dfrac{-1}{2}\Leftrightarrow\left(x^2+x+1\right)=0;voN_0\)
a khác -1/2 mọi x
\(A=\dfrac{a^2}{2a+1}\)
\(\overrightarrow{AB}\cdot\overrightarrow{CB}=4\)
=>AB*CB*cosB=4
=>AB*CB*AB/BC=4
=>BA^2=4
=>AB=2
\(\overrightarrow{AC}\cdot\overrightarrow{BC}=9\)
=>AC*BC*cosC=9
=>AC*BC*AC/BC=9
=>AC=3
=>\(BC=\sqrt{13}\)
A = ( 0,87 +6,4 ).(1,25.7 - 4/5.1,25)+31,64
A= 7,2.7,75+31,64
A=55,8+31,64
A=87,44
(0,87 + 6,4) . (1,25 . 7 - 4/5 . 1,25) + 31,64
= 7,27 . (8,75 - 1) + 31,64
= 7,27 . 7,75 + 31,64
= 56,3425 + 31,64
= 87,9825