chung minh rang
\(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+\dfrac{4}{3^4}+....+\dfrac{100}{3^{100}}\) < \(\dfrac{3}{4}\)
giup minh nhe minh dang can gap
tim x
\(\dfrac{5}{6}x-\dfrac{3}{4}=\dfrac{-1}{4}+\dfrac{2}{3}\)
\(-1\dfrac{1}{2}-\dfrac{2}{3}x=\dfrac{5}{6}-\left(\dfrac{-2}{5}\right)\)
\(\left(\dfrac{4}{5}:x+1,5\right):\dfrac{2}{3}=-1,5\)
\(\dfrac{4}{3}x-\dfrac{2}{3}=\dfrac{1}{4}-x\)
giup minh nhe minh dang can gap
\(\dfrac{5}{6}x-\dfrac{3}{4}=\dfrac{-1}{4}+\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{5}{6}x=\dfrac{7}{6}\)
\(\Rightarrow x=\dfrac{7}{5}\)
b) \(-1\dfrac{1}{2}-\dfrac{2}{3}x=\dfrac{5}{6}-\left(\dfrac{-2}{5}\right)\)
\(\Leftrightarrow\dfrac{2}{3}x=-\dfrac{41}{15}\)
\(\Rightarrow x=-\dfrac{41}{10}\)
c) \(\left(\dfrac{4}{5}:x+1,5\right):\dfrac{2}{3}=-1,5\)
\(\Leftrightarrow\dfrac{8+15x}{10x}.\dfrac{3}{2}=\dfrac{-3}{2}\)
\(\Leftrightarrow\dfrac{24+45x}{20x}=\dfrac{-3}{2}\)
\(\Leftrightarrow-60x=48+90x\)
\(\Rightarrow x=-0,32\)
d) \(\dfrac{4}{3}x-\dfrac{2}{3}=\dfrac{1}{4}-x\)
\(\Leftrightarrow\dfrac{4x-2}{3}=\dfrac{1-4x}{4}\)
\(\Rightarrow16x-8=3-12x\)
\(\Rightarrow x=\dfrac{11}{28}\)
tinh nhanh
A=\(\dfrac{1}{3}-\dfrac{3}{4}-\left(\dfrac{-3}{5}\right)+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\)
B=\(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{3}+\dfrac{13}{15}+\dfrac{11}{15}-\dfrac{9}{11}+\dfrac{7}{9}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{3}-\dfrac{1}{3}\)
giup minh nhe minh dang can gap
\(A=\left(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}\right)-\left(\dfrac{3}{4}+\dfrac{2}{9}+\dfrac{1}{36}\right)+\dfrac{1}{64}\)
\(=\dfrac{5+9+1}{15}-\dfrac{27+8+1}{36}+\dfrac{1}{64}\)
=1/64
tinh nhanh
A=\dfrac{1}{3}-\dfrac{3}{4}-\left(\dfrac{-3}{5}\right)+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}
B=\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{3}+\dfrac{13}{15}+\dfrac{11}{15}-\dfrac{9}{11}+\dfrac{7}{9}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{3}-\dfrac{1}{3}
giup minh nhe minh dang can gap
tim x
a, \(2,75\div x=0,4\div1,5\)
b, \(3\dfrac{1}{2}\div\left(2x-3\right)=\dfrac{-3}{4}\div0,2\)
c, \(\dfrac{3x+2}{27}=\dfrac{3}{3x+2}\)
d ,\(\dfrac{5-x}{4}=\dfrac{2x+3}{2}\)
giup minh nhe minh dang can gap
a: \(\dfrac{2.75}{x}=\dfrac{0.4}{1.5}=\dfrac{4}{15}\)
\(\Leftrightarrow x=\dfrac{11}{4}\cdot\dfrac{15}{4}=\dfrac{165}{16}\)
b: \(3\dfrac{1}{2}:\left(2x-3\right)=\dfrac{-3}{4}:0.2\)
\(\Leftrightarrow\dfrac{7}{2}:\left(2x-3\right)=\dfrac{-3}{4}:\dfrac{1}{5}=\dfrac{-15}{4}\)
\(\Leftrightarrow2x-3=\dfrac{7}{2}:\dfrac{-15}{4}=\dfrac{-7}{2}\cdot\dfrac{4}{15}=\dfrac{-28}{30}=\dfrac{-14}{15}\)
=>2x=-14/15+3=45/45-14/15=31/45
=>x=31/90
c: \(\dfrac{3x+2}{27}=\dfrac{3}{3x+2}\)
\(\Leftrightarrow\left(3x+2\right)^2=81\)
=>3x+2=9 hoặc 3x+2=-9
=>3x=7 hoặc 3x=-11
=>x=7/3 hoặc x=-11/3
d: \(\dfrac{5-x}{4}=\dfrac{2x+3}{2}\)
=>10-2x=8x+12
=>-10x=2
hay x=-1/5
tim x
\dfrac{5}{6}x-\dfrac{3}{4}=\dfrac{-1}{4}+\dfrac{2}{3}65x−43=4−1+32
-1\dfrac{1}{2}-\dfrac{2}{3}x=\dfrac{5}{6}-\left(\dfrac{-2}{5}\right)−121−32x=65−(5−2)
\left(\dfrac{4}{5}:x+1,5\right):\dfrac{2}{3}=-1,5(54:x+1,5):32=−1,5
\dfrac{4}{3}x-\dfrac{2}{3}=\dfrac{1}{4}-x34x−32=41−x
giup minh nhe minh dang can gap
☹➞cac ban giup minh cau nay voi
☛ tinh tong
M = 1+\(\dfrac{1}{5}\)+\(\dfrac{3}{35}\)+...\(\dfrac{3}{9603}\)+\(\dfrac{3}{9999}\)
➜giup minh nhanh nhe minh dang can gap lam moi nguoi a
➞thank you cac ban ❕
\(M=1+\dfrac{1}{5}+\dfrac{3}{35}+...+\dfrac{3}{9999}\\ =\dfrac{3}{3}+\dfrac{3}{15}+\dfrac{3}{35}+...+\dfrac{3}{9999}\\ =\dfrac{3}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{99\cdot101}\right)\\ =\dfrac{3}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\\ =\dfrac{3}{2}\left(1-\dfrac{1}{101}\right)=\dfrac{3}{2}\cdot\dfrac{100}{101}=\dfrac{150}{101}\)
cho A = 3a - 4ab + 5b . tinh gia tri cua A khi
a, \(\left|a\right|=\dfrac{3}{4},b=\dfrac{-5}{6}\)
b,\(a=\dfrac{-2}{3},b=\dfrac{4}{5}\)
giup minh nhe minh dang can gap
a) Vì |a|=\(\dfrac{3}{4}\)=>a=\(\dfrac{3}{4}\).Thay vào ta sẽ có:
A=3.\(\dfrac{3}{4}\)-4.\(\dfrac{3}{4}\).(\(\dfrac{-5}{6}\))+5.(\(\dfrac{-5}{6}\))
A=\(\dfrac{9}{4}-\left(\dfrac{-5}{2}\right)+\left(\dfrac{-25}{6}\right)\)
A=\(\dfrac{19}{4}\)-\(\dfrac{25}{6}\)
A=\(\dfrac{14}{24}\)=\(\dfrac{7}{12}\)
b, Thay vào, ta sẽ có:
A=3.\(\left(\dfrac{-2}{3}\right)-4.\left(\dfrac{-2}{3}\right).\dfrac{4}{5}+5.\dfrac{4}{5}\)
A=-2-\(\left(\dfrac{-32}{15}\right)\)+4
A=\(\dfrac{2}{15}\)+4
A=\(\dfrac{62}{15}\)
cho \(\dfrac{3x-2}{4}=\dfrac{5y+3}{6}=\dfrac{2z-1}{3}\) va \(5x^2-7=38\) tinh
a ,3x - 4y + 2z
b , -x - 3y + 5z
c , 2x - 5y - 4z
giup minh nhe minh dang can gap
5x2 - 7 = 38 => x2 = 9 => x = \(\pm\)3
Từ đây thay x vào \(\dfrac{3x-2}{4}\) để tìm y,z
tim x, y biet
a ,\(\dfrac{x}{2}=\dfrac{y}{5}\) va x . y = 3,6
b , \(\dfrac{x}{3}=\dfrac{y}{4}\) va x . y =108
giup minh nhe minh dang can gap
a)Ta có :
\(\dfrac{x}{2}=\dfrac{y}{5}=k\)
Mà x.y=3,6 => 2k+5k=3,6=>7k=3,6
Vậy k = \(\dfrac{18}{35}\)
\(x=2k\Rightarrow x=\dfrac{36}{35}\)
\(y=5k\Rightarrow y=\dfrac{18}{7}\)
\(a,\dfrac{x}{2}=\dfrac{y}{5}\)
\(\rightarrow\)\(x.5=y.2\)
\(x.x.5=y.x.2\)
\(x^2.5=3,6.2\)
\(x^2.5=7,2\)
\(x^2=1,44\)
\(\rightarrow x=1,2\) hoặc \(x=-1,2\)
Ý b bạn làm tường tự nha