Câu này hơi khó ai nhanh sẽ đc 10 k
(×-1/3) ngũ 2 -1/9=5/3
Nhanh nhất sẽ đc 10 k nhá😉
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Tìm x nha bn!
\(\left(9x^2+1\right)\left(3x-\frac{1}{2}\right)=0\)
\(\text{Vì tích trên bằng 0 nên 1 trong 2 số hạng phải bằng 0 mà }9x^2+1\text{ chắc chắn lớn hơn 0}\)
\(\Rightarrow3x-\frac{1}{2}=0\)
\(\Leftrightarrow3x=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{1}{6}\)
\(-7x-\frac{1}{2}=-2x-\frac{1}{2}\)
\(\Leftrightarrow-7x+2x=-\frac{1}{2}+\frac{1}{2}\)
\(\Leftrightarrow-5x=0\)
\(\Rightarrow x=0\)
Ta thấy:
\(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{17\cdot19}\)
\(=\frac{1}{2}\cdot\frac{2}{3\cdot5}+\frac{1}{2}\cdot\frac{2}{5\cdot7}+...+\frac{1}{2}\cdot\frac{2}{17\cdot19}\)
\(=\frac{1}{2}\cdot\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{17\cdot19}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\right)\)
\(=\frac{1}{2}\cdot\left[\frac{1}{3}-\left(\frac{1}{5}-\frac{1}{5}\right)-\left(\frac{1}{7}-\frac{1}{7}\right)-...-\left(\frac{1}{17}-\frac{1}{17}\right)-\frac{1}{19}\right]\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-0-0-...-0-\frac{1}{19}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{19}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{19}{57}-\frac{3}{57}\right)\)
\(=\frac{1}{2}\cdot\frac{16}{57}\)
\(=\frac{1\cdot16}{2\cdot57}\)
\(=\frac{8}{57}\)
Khi đó:
\(\left(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{17\cdot19}\right)\cdot114-0,2\cdot\left(x-1\right)=10\)
\(\Rightarrow\frac{8}{57}\cdot114-\frac{1}{5}\cdot\left(x-1\right)=10\)
\(\Rightarrow8\cdot2-\left(x-1\right)\cdot\frac{1}{5}=10\)
\(\Rightarrow16-\frac{x-1}{5}=10\)
\(\Rightarrow\frac{x-1}{5}=16-10\)
\(\Rightarrow\frac{x-1}{5}=6\)
\(\Rightarrow x-1=6\cdot5\)
\(\Rightarrow x-1=30\)
\(\Rightarrow x=30+1\)
\(\Rightarrow x=31\)
Vậy x = 31
2.
Ba thùng to đụng số lít dầu là :
238 x 3 = 714 ( lít )
Bốn thùng nhỏ đựng số lít dầu là :
42 x 4 = 160 ( lít )
Trung bình mỗi thùng đựng số lít dầu là :
( 714 + 160 ) : 2 = 437 ( lít )
Đáp số 437 lít
h mình nha :))
Số phần bể chưa có nước là:
1-3/8-2/5=9/40(bể)
Đ/S: 9/40 bể
Phân số chỉ số phần bể chưa có nước là:
\(1-\frac{3}{8}-\frac{2}{5}=\frac{9}{40}\) ( bể )
Đáp số: \(\frac{9}{40}\)bể
\(\left(8+9+1+2\right).100\)
\(=20.100\)
\(=2000\)
chuc bn hoc gioi!!
nhae
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(2A=1-\frac{1}{3^{100}}\)
\(A=\frac{1-\frac{1}{3^{100}}}{2}\)
\(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(3B=\frac{5.3}{4.7}+\frac{5.3}{7.10}+\frac{5.3}{10.13}+...+\frac{5.3}{25.28}\)
\(3B=5\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
\(3B=5\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(3B=5\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(3B=5\cdot\frac{3}{14}=\frac{15}{14}\)
\(B=\frac{15}{14}:3=\frac{5}{14}\)
a) \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)
\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)
\(2A=1-\frac{1}{3^{100}}\)
\(\Rightarrow A=\frac{1-\frac{1}{3^{100}}}{2}\)
b) \(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{5}{3}.\left(\frac{1}{7}-\frac{1}{10}\right)+\frac{5}{3}.\left(\frac{1}{10}-\frac{1}{13}\right)+...+\frac{5}{3}.\left(\frac{1}{25}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(B=\frac{5}{3}.\frac{3}{14}\)
\(\Rightarrow B=\frac{5}{14}\)
TBR , ta có :
\((x-\frac{1}{3})^2\)\(-\frac{1}{9}\)\(=\frac{5}{3}\)
\(\Rightarrow(x-\frac{1}{3})^2=\frac{5}{3}+\frac{1}{9}=\frac{16}{9}\)
\(\Rightarrow(x-\frac{1}{3})^2=(\frac{4}{9})^2\)
\(\Rightarrow x-\frac{1}{3}=\frac{4}{9}\)
\(\Rightarrow x=\frac{4}{9}+\frac{1}{3}\)
\(\Rightarrow x=\frac{7}{9}\)
K cho mình nha
( x -1/3 )^2 - 1/9 = 5/3
( x -1/3 )^2 = 5/3 + 1/9
( x - 1/3 )^2 = 15/9 + 1/9
( x - 1/3 )^2 = 16/9
( x - 1/3 ) = -4/3 hoặc x -1/3 = 4/3
=> x = -4/3 + 1/3 hoặc x = 4/3 + 1/3
=> x = -3/3 = -1 hoặc x = 5/3
Vậy x = -1 hoặc x = 5/3
Chúc học giỏi !!!