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a) 11 3 − 2 3 ≤ x ≤ 15 9 − − 39 9
⇔ 3 ≤ x ≤ 6 ⇒ x ∈ 3 ; 4 ; 5 ; 6
b) − 5 17 + 3 17 ≤ x 17 ≤ 13 17 + − 11 17
⇔ − 2 17 ≤ x 17 ≤ 2 17 ⇔ − 2 ≤ x ≤ 2 ⇒ x ∈ − 2 ; − 1 ; 0 ; 1 ; 2
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\(3\frac{1}{1117}.\frac{4}{1119}-1\frac{1116}{1117}.5\frac{1118}{1119}-\frac{5}{1119}\)
\(=\frac{3352}{1117}.\frac{4}{1119}-\frac{2233}{1117}.\frac{6713}{1119}-\frac{5}{1119}\)
\(=\frac{1}{1119}\left(\frac{3352}{1117}.4-\frac{2233}{1117}.6713-5\right)\)
\(=\frac{1}{1119}\left(\frac{13408}{1117}-\frac{14990129}{1117}-\frac{5585}{1117}\right)\)
\(=\frac{1}{1119}.\frac{-14982306}{1117}\)
\(=\frac{-14982306}{1249923}\)
Đặt \(x=\frac{1}{1117}\) ,\(y=\frac{1}{1119}\)
Khi đó biểu thức có dạng \((3+x).4y-\left(1+1-x\right).\left(5+1-y\right)-5.y\)
\(=12y+4xy-\left(2-x\right)\left(6-y\right)-5y\)
\(=12y+4xy-\left(12-6x-2y+xy\right)-5y\)
\(=9y+3xy-12+6x\)
\(=\frac{9}{1119}+\frac{3}{1117.1119}-12+\frac{6}{1117}\)
\(=\frac{9.1117+3-12.1117.1119+6.1119}{1117.1119}\)
Ưm đến đây tự tính nha =)
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Đáp án cần chọn là: B
E = ( − 3 31 + − 6 17 + 1 25 ) + ( − 28 31 + − 11 17 + − 1 5 ) E = − 3 31 + − 6 17 + 1 25 + − 28 31 + − 6 17 + − 1 5 E = ( − 3 31 + − 28 31 ) + ( − 6 17 + − 6 17 ) + ( 1 25 + − 1 5 ) E = − 3 31 + − 6 17 + 1 25 + − 28 31 + − 11 17 + − 1 5 E = − 3 31 + − 6 17 + 1 25 + − 28 31 + − 11 17 + − 1 5 E = − 3 31 + − 28 31 + − 6 17 + − 11 17 + 1 25 + − 1 5 E = − 1 − 1 − 4 25 E = − 54 25
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18.
Do D thuộc trục hoành nên tọa độ có dạng: \(D\left(a;0;0\right)\)
\(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AD}=\left(a-3;4;0\right)\\\overrightarrow{BC}=\left(4;0;-3\right)\end{matrix}\right.\)
\(AD=BC\Leftrightarrow\left(a-3\right)^2+4^2=4^2+\left(-3\right)^2\)
\(\Rightarrow\left(a-3\right)^2=9\Rightarrow\left[{}\begin{matrix}a=0\\a=6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}D\left(0;0;0\right)\\D\left(6;0;0\right)\end{matrix}\right.\)
19.
\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{2.\left(-1\right)+1.0+0.\left(-2\right)}{\sqrt{2^2+1^2+0^2}.\sqrt{\left(-1\right)^2+0^2+\left(-2\right)^2}}=-\dfrac{2}{5}\)
20.
\(\overrightarrow{OA}=\left(2;2;1\right)\Rightarrow OA=\sqrt{2^2+2^2+1^2}=3\)
1117 : x = 8
x = 1117 :8
x = 139,625
1117 : x = 8
x = 8 x 1117
x = 8936