In spite of = Due to + Ving/N, S + V

= In spite of/Due to + the fact that + S + V, S + V

=Although + S + V, S + V

Nghĩa: Mặc dù, biểu thị 2 hành động trái ngược nhau

a, PT: \(Fe+H_2SO_4\rightarrow FeSO_4+H_2\)

b, Ta có: \(n_{Fe}=\dfrac{19,6}{56}=0,35\left(mol\right)\)

Theo PT: \(n_{H_2}=n_{Fe}=0,35\left(mol\right)\Rightarrow V_{H_2}=0,35.22,4=7,84\left(l\right)\)

c, \(n_{H_2SO_4}=n_{Fe}=0,35\left(mol\right)\Rightarrow C_{M_{H_2SO_4}}=\dfrac{0,35}{0,2}=1,75\left(M\right)\)

d, \(n_{FeSO_4}=n_{Fe}=0,35\left(mol\right)\Rightarrow m_{FeSO_4}=0,35.152=53,2\left(g\right)\)

e, \(C_{M_{FeSO_4}}=\dfrac{0,35}{0,2}=1,75\left(M\right)\)

d, \(n_{H_2SO_4}=0,25.1,6=0,4\left(mol\right)\)

Xét tỉ lệ: \(\dfrac{n_{Fe}}{1}< \dfrac{n_{H_2SO_4}}{1}\), ta được H₂SO₄ dư.

Theo PT: \(n_{H_2SO_4\left(pư\right)}=n_{Fe}=0,35\left(mol\right)\)

\(\Rightarrow n_{H_2SO_4\left(dư\right)}=0,4-0,35=0,05\left(mol\right)\)

\(\Rightarrow m_{H_2SO_4\left(dư\right)}=0,05.98=4,9\left(g\right)\)

Đề bài phải sửa thành AN=NC mới c/m được

A B C D

MA=MB (gt)

AN=NC (gt)

=> MN là đường trung bình của tg ABC

=> MN//BC và \(MN=\dfrac{BC}{2}\)

Ta có

\(BC\perp AB\) mà MN//BC => \(MN\perp AB\) (1)

Ta có

\(BC=AB\Rightarrow MN=\dfrac{AB}{2}\)

Mà \(MA=MB=\dfrac{AB}{2}\)

=> MN = MA (2)

Từ (1) và (2) => tg AMN vuông cân tại M

\(\sqrt{2}\)\(\times\)\(\sqrt{4}\) - \(\sqrt{15}\) = 2\(\sqrt{2}\) - \(\sqrt{15}\)

Đáp án mà em chọn là sai rồi em  nhé.

Em chọn đáp án: (\(\sqrt{7x}\) + \(\sqrt{5}\))²

Đáp án đúng phải là: (\(\sqrt{7}\)\(x\) + \(\sqrt{5}\))²

                  \(\sqrt{7x}\) và \(\sqrt{7}\)\(x\) khác nhau hoàn toàn em nhé

              vì    \(\sqrt{7x}\) = \(\sqrt{7}\) \(\times\) \(\sqrt{x}\)

                 \(\sqrt{7}\)\(x\) = \(\sqrt{7}\) \(\times\) \(x\)

               Nên \(\sqrt{7x}\) \(\ne\) \(\sqrt{7}\)\(x\)

Đáp án của em chọn là sai. 

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 Ta thấy 1 cặp tam giác đồng dạng quen thuộc là \(\Delta HAB~\Delta HCA\), từ đó suy ra \(\dfrac{S_{HAB}}{S_{HCA}}=\left(\dfrac{AB}{AC}\right)^2\). Mà ta lại có \(\dfrac{S_{HAB}}{S_{HCA}}=\dfrac{HB}{HC}\) (2 tam giác có chung đường cao hạ từ A) nên suy ra đpcm.

\(\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+2\sqrt{3}+\sqrt{4^2-2.4.\sqrt{2}+\sqrt{2^2}}}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+2\sqrt{3}+\sqrt{\left(4-\sqrt{2}\right)^2}}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+2\sqrt{3}+\left|4-\sqrt{2}\right|}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+2\sqrt{3}+4-\sqrt{2}}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{4+2\sqrt{3}}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\left(\sqrt{3}+1\right)^2}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{3}-1}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}\sqrt{2-\sqrt{3}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\left|\sqrt{3}-1\right|}\)

\(=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{3}-2}\)

\(=\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)

\(=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)\)

\(=\sqrt{3^2}-1^2\\ =3-1\\ =2\)

\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left|2+\sqrt{3}\right|}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{3}-20}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{5^2-2.5.\sqrt{3}+\sqrt{3^2}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\left|5-\sqrt{3}\right|}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+25-5\sqrt{3}}}\)

\(=\sqrt{4+\sqrt{25}}\)

\(=\sqrt{4+5}\)

\(=\sqrt{9}\\ =3\)

 \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10.|2+\sqrt{3}|}}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10.\left(2+\sqrt{3}\right)}}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-20-10\sqrt{3}}}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5.|5-\sqrt{3}|}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+5.\left(5-\sqrt{3}\right)}}\)

= \(\sqrt{4+\sqrt{5\sqrt{3}+25-5\sqrt{3}}}\)

= \(\sqrt{4+\sqrt{25}}\)

= \(\sqrt{4+5}\)

= \(\sqrt{9}\)

= \(3\)

\(e,\dfrac{\sqrt{4x-1}}{\sqrt{7-2x}-2}\) có nghĩa \(\Leftrightarrow\left[{}\begin{matrix}4x-1\ge0\\7-2x\ne4\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\ge\dfrac{1}{4}\\x\ne-\dfrac{3}{2}\end{matrix}\right.\) \(\Leftrightarrow x\ge\dfrac{1}{4}\)

\(d,\dfrac{\sqrt{2x-1}}{\sqrt{2x+17}+1}\) có nghĩa \(\Leftrightarrow\left[{}\begin{matrix}2x-1\ge0\\2x+17\ge0\end{matrix}\right.\)  \(\Leftrightarrow\left[{}\begin{matrix}x\ge\dfrac{1}{2}\\x\ge-\dfrac{17}{2}\end{matrix}\right.\) \(\Leftrightarrow x\ge\dfrac{1}{2}\)

 \(b,c,\dfrac{3}{\sqrt{2x-17}}\) có nghĩa \(\Leftrightarrow2x-17>0\Leftrightarrow x>\dfrac{17}{2}\)

\(a,\sqrt{2-5x}\) có nghĩa \(\Leftrightarrow2-5x\ge0\Leftrightarrow x\le\dfrac{2}{5}\)