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A = \(\dfrac{1+5+5^2+5^3+5^4+...+5^{17}}{1+5^2+5^4+...+5^{16}}\)
Đặt tử số là B = 1 + 5 + 52 + 53 + 54 +...+ 517
5B = 5 + 52 + 53 + 54 +...+ 517 + 518
5B - B = 518 - 1
4B = 518 - 1
B = (518 - 1) : 4
Đặt mẫu số là C = 1 + 52 + 54 +...+ 516
52.C = 52 + 54 +...+ 516 + 518
25.C - C = 518 - 1
24C = 518 - 1
C = (518 - 1): 24
A = \(\dfrac{B}{C}\) = \(\dfrac{\dfrac{5^{18}-1}{4}}{\dfrac{5^{18}-1}{24}}\)
A = 6
\(\left(\dfrac{1}{2}-\dfrac{x}{3}\right)^2=\dfrac{36}{49}\\ \Rightarrow\left(\dfrac{1}{2}-\dfrac{x}{3}\right)^2=\left(\dfrac{6}{7}\right)^2\\ \Rightarrow\dfrac{1}{2}-\dfrac{x}{3}=\pm\dfrac{6}{7}\\ \Rightarrow\left[{}\begin{matrix}\dfrac{1}{2}-\dfrac{x}{3}=\dfrac{6}{7}\\\dfrac{1}{2}-\dfrac{x}{3}=-\dfrac{6}{7}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\dfrac{x}{3}=-\dfrac{5}{14}\\\dfrac{x}{3}=\dfrac{19}{14}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{14}\times3\\x=\dfrac{19}{14}\times3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{15}{14}\\x=\dfrac{57}{14}\end{matrix}\right.\)
\(\left(3-\dfrac{2}{3}x\right)^3=-\dfrac{1}{64}\\ \Rightarrow\left(3-\dfrac{2}{3}x\right)^3=\left(-\dfrac{1}{4}\right)^3\\ \Rightarrow3-\dfrac{2}{3}x=-\dfrac{1}{4}\\ \Rightarrow\dfrac{2}{3}x=3-\left(-\dfrac{1}{4}\right)\\ \Rightarrow\dfrac{2}{3}x=\dfrac{13}{4}\\ \Rightarrow x=\dfrac{13}{4}:\dfrac{2}{3}\\ \Rightarrow x=\dfrac{13}{4}\times\dfrac{3}{2}\\ \Rightarrow x=\dfrac{39}{8}\)
Hic 2 câu em làm dr xong tự nhiên thử lung tung rồi lại xóa bài ;-;
a: Chiều dài là x+4
Chu vi là (x+x+4)x2=4x+8(m)
b: Theo đề, ta có; 4x+8=20
=>4x=12
hay x=3(m)
=>Chiều dài là 7(m)
A=\(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...\)
A-\(\frac{1}{5}=\frac{1}{5^2}+\frac{1}{5^3}+...\)
5 -\(\left(A-\frac{1}{5}\right)=5.\left(\frac{1}{5^2}+\frac{1}{5^3}+...1\right)\)
10.\(\left(A-\frac{1}{5}\right)=A\)
\(10A-5=A\)
\(10.A-A=5\)
\(9A=5\)
\(A=\frac{5}{9}\)
T hk pk dung hay sai nha, ma m cu lam ik, co j len t sua
\(a,m\perp AB;n\perp AB\Rightarrow m\text{//}n\)
Thiều hình nên ko làm đc mấy câu kia
\(\frac{3}{13}.\frac{5}{9}+\frac{1}{6}:\frac{13}{3}+1\)
\(=\frac{3}{13}.\frac{5}{9}+\frac{1}{6}.\frac{3}{13}+1\)
\(=\frac{3}{13}.\left(\frac{5}{9}+\frac{1}{6}\right)+1\)
\(=\frac{3}{13}.\left(\frac{30+9}{54}\right)+1\)
\(=\frac{3}{13}.\frac{39}{54}+1\)
\(=\frac{1}{6}+1\)
\(=\frac{7}{6}\)
\(\frac{5}{6}-\frac{7}{9}.\frac{2}{13}-\frac{7}{9}.\frac{11}{13}+\frac{-2}{9}\)
\(=\frac{5}{6}-\frac{7}{9}.\left(\frac{2}{13}-\frac{11}{13}\right)+\frac{-2}{9}\)
\(=\frac{5}{6}-\frac{7}{9}.\frac{-9}{13}-\frac{2}{9}\)
\(=\frac{5}{6}-\frac{-7}{13}-\frac{2}{9}\)
\(\frac{5}{6}-\frac{7}{9}.\frac{2}{13}-\frac{7}{9}.\frac{11}{13}+\frac{-2}{9}\)
\(=\frac{5}{6}-\frac{7}{9}.\left(\frac{2}{13}-\frac{11}{13}\right)+\frac{-2}{9}\)
\(=\frac{5}{6}-\frac{7}{9}.\frac{-9}{13}-\frac{2}{9}\)
\(=\frac{5}{6}-\frac{-7}{13}-\frac{2}{9}\)
\(=\frac{5}{6}+\frac{7}{13}-\frac{2}{9}\)
\(=\frac{195+126-52}{234}\)
\(=\frac{269}{234}\)
\(\frac{3}{13}.\frac{5}{9}+\frac{1}{6}:\frac{13}{3}+1\)
\(=\frac{3}{13}.\frac{5}{9}+\frac{1}{6}.\frac{3}{13}+1\)
\(=\frac{3}{13}.\left(\frac{5}{9}+\frac{1}{6}\right)+1\)
\(=\frac{3}{13}.\left(\frac{30+9}{54}\right)+1\)
\(=\frac{3}{13}.\frac{39}{54}+1\)
\(=\frac{1}{6}+1=\frac{1}{6}+\frac{6}{6}\)
\(=\frac{7}{6}\)
\(\frac{-7}{9}.\frac{2}{13}-\frac{7}{9}.\frac{11}{13}+\frac{-2}{9}\)
\(=\frac{-7}{9}.\frac{2}{13}+\frac{-7}{9}.\frac{11}{13}+\frac{-2}{9}\)
\(=\frac{-7}{9}.\left(\frac{2}{13}+\frac{11}{13}\right)+\frac{-2}{9}\)
\(=\frac{-7}{9}.1+\frac{-2}{9}\)
\(=\frac{-7}{9}+\frac{-2}{9}\)
\(=\frac{-9}{9}=-1\)
\(\frac{2}{13}.\frac{2}{7}.5\)
\(=\frac{2.2.5}{13.7}\)
\(=\frac{20}{91}\)
\(\frac{1}{5}.\frac{11}{12}.\frac{21}{6}\)
\(=\frac{11.21}{5.12.6}\)
\(=\frac{231}{360}=\frac{77}{120}\)
Gọi số học sinh hai lớp 7A, 7B là `a,b` (học sinh) `(a,b in NN^(**))`
Ta có: `a,b` tỉ lệ với `8,9 => a/8=b/9`.
Áp dụng tính chất của dãy tỉ số bằng nhau:
`a/8=b/9=(b-a)/(9-8)=5/1=5`
`=> a=5.8=40`
`b=5.9=45`
Vậy lớp 7A có 40 học sinh, lớp 7B có 45 học sinh.
\(\frac{1}{2}.2^n+4.2^n=9.2^5\)
\(\Rightarrow\left(\frac{1}{2}+4\right).2^n=9.2^5\)
\(\Rightarrow\frac{9}{2}.2^n=9.2^5\)
\(\Rightarrow9.2^{n-1}=9.2^5\)
\(\Rightarrow2^{n-1}=2^5\)
\(\Rightarrow n-1=5\)
\(\Rightarrow n=6\)
cảm ơn bạn chúc bạn hok tốt