Câu 4:

4.1/ Ta có: \(n_{NaCl}=2,5.0,4=1\left(mol\right)\)

\(\Rightarrow m_{NaCl}=1.58,5=58,5\left(g\right)\)

4.2/ Ta có: \(n_{Zn}=\dfrac{13}{65}=0,2\left(mol\right)\)

a, PT: \(Zn+2HCl\rightarrow ZnCl_2+H_2\)

_____0,2___________0,2____0,2 (mol)

b, \(V_{H_2}=0,2.22,4=4,48\left(l\right)\)

c, \(m_{ZnCl_2}=0,2.136=27,2\left(g\right)\)

Bạn tham khảo nhé!

\(\dfrac{2020}{2019}>\dfrac{2019}{2020}\Rightarrow0< a< 1\)

\(log_ba< 1\Rightarrow b>1\)

\(P=log_b^2a+log_b^22-\dfrac{m^2log_2b}{log_2a}+2\left(log_ba-2log_b2\right)-\dfrac{4^{ab^2}-2m.2^{ab^2}}{log_ba}\)

\(=log_b^2a+log_b^22+2log_ba-4log_b2-\dfrac{4^{ab^2}-2m.2^{ab^2}+m^2}{log_ba}\)

\(=\left(log_ba+1\right)^2+\left(log_b2-2\right)^2+\dfrac{\left(2^{ab^2}-m\right)^2}{-log_ba}-5\ge-5\)

Dấu "=" xảy ra khi: \(\left\{{}\begin{matrix}log_ba=-1\\log_b2=2\\2^{ab^2}=m\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{1}{\sqrt{2}}\\b=\sqrt{2}\\m=2^{ab^2}=2^{\sqrt{2}}\end{matrix}\right.\)

Sau khi tính lại thì không có đáp án nào đúng :(

\(\Delta'=\left(m-1\right)^2-\left(2m-4\right)=\left(m-2\right)^2+1>0;\forall m\)

\(\Rightarrow\) Pt đã cho luôn có 2 nghiệm pb với mọi m

Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=2m-2\\x_1x_2=2m-4\end{matrix}\right.\) (1)

a. Pt có 2 nghiệm đối nhau khi:

\(x_1+x_2=0\Leftrightarrow2m-2=0\Rightarrow m=1\)

b. Trừ vế cho vế của (1) ta được:

\(x_1+x_2-x_1x_2=2m-2-\left(2m-4\right)\)

\(\Leftrightarrow x_1+x_2-x_1x_2=2\)

Đây là hệ thức liên hệ 2 nghiệm ko phụ thuộc m

Gọi Kim loại Đó là A

\(A+2HCl\rightarrow ACl_2+H_2\)

tl1.......2.............1...........1(mol)

br  0,15....0,3.....0,15.....0,15(mol)                                 

\(n_{H_2}=\dfrac{V}{22,4}=\dfrac{3,36}{22,4}=0,15\left(mol\right)\)

\(M_A=\dfrac{m}{n}=\dfrac{3,6}{0,15}=24\left(\dfrac{g}{mol}\right)\)

Vậy A là Magie(Mg)

8) \(\dfrac{x+7}{3}+\dfrac{x+5}{4}=\dfrac{x+3}{5}+\dfrac{x+1}{6}\)

\(\Rightarrow\dfrac{x+7}{3}+\dfrac{x+5}{4}-\dfrac{x+3}{5}-\dfrac{x+1}{6}=0\)

\(\Rightarrow\dfrac{x+7}{3}+2+\dfrac{x+5}{4}+2-\dfrac{x+3}{5}-2-\dfrac{x+1}{6}-2=0+2+2-2-2\)

\(\Rightarrow\left(\dfrac{x+7}{3}+2\right)+\left(\dfrac{x+5}{4}+2\right)-\left(\dfrac{x+3}{5}+2\right)-\left(\dfrac{x+1}{6}+2\right)=0\)

\(\Rightarrow\left(\dfrac{x+7}{3}+\dfrac{6}{3}\right)+\left(\dfrac{x+5}{4}+\dfrac{8}{4}\right)-\left(\dfrac{x+3}{5}+\dfrac{10}{5}\right)-\left(\dfrac{x+1}{6}+\dfrac{12}{2}\right)=0\)

\(\Rightarrow\left(x+13\right)\left(\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{5}-\dfrac{1}{6}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x+13=0\\\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}=0\end{matrix}\right.\)

\(x+13=0\)

\(\Rightarrow x=-13\)

\(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}=0\)

\(\dfrac{13}{60}=0\) (vô lí)

Vậy \(x=-13\)

9) Bạn chuyển vế rồi cộng 3 vào từng mỗi số

8) Ta có: \(\dfrac{x+7}{3}+\dfrac{x+5}{4}=\dfrac{x+3}{5}+\dfrac{x+1}{6}\)

\(\Leftrightarrow\dfrac{x+13}{6}+\dfrac{x+13}{4}=\dfrac{x+13}{5}+\dfrac{x+13}{6}\)

Suy ra: x+13=0

hay x=-13

9) Ta có: \(\dfrac{x+19}{3}+\dfrac{x+13}{5}=\dfrac{x+7}{7}+\dfrac{x+1}{9}\)

\(\Leftrightarrow\dfrac{x+28}{3}+\dfrac{x+28}{5}-\dfrac{x+28}{7}-\dfrac{x+28}{9}=0\)

Suy ra: x+28=0

hay x=-28

Lời giải:
\(\frac{1}{110}+\frac{1}{132}+\frac{1}{156}+...+\frac{1}{342}+\frac{1}{380}=\frac{1}{10\times 11}+\frac{1}{11\times 12}+...+\frac{1}{19\times 20}\)

\(=\frac{11-10}{10\times 11}+\frac{12-11}{11\times 12}+...+\frac{20-19}{19\times 20}=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{10}-\frac{1}{20}=\frac{10}{200}=\frac{1}{20}\)

Đáp án A.

1313/2121 x 165165/143143 x 424242/151515

=13/21 x 165/143 x42/15

=2

Rút gọn là sẽ xong, ko khó đâu

\(\frac{1313}{2121}\times\frac{165165}{143143}\times\frac{424242}{151515}=\frac{13}{21}\times\frac{165}{143}\times\frac{42}{15}=\frac{13\times165\times42}{21\times143\times15}\)

\(=\frac{13\times15\times11\times21\times2}{21\times13\times11\times15}=2\)

rút gọn

=13x165x42/21x143x15

=1x11x2/1x11x1

=2