2.
[tex]a)ma = \frac{6 + 54}{2} = \frac{60}{2} = 30 \\ mg = \sqrt{6 \times 54} = \sqrt{324} = 18 \\ mh = \frac{2 \times 6 \times 54}{6 + 54} = \frac{648}{60} = 10.8[/tex]
[tex]b)ma = \frac{ \frac{1}{4} + \frac{1}{9} }{2} = \frac{ \frac{9 + 4}{36} }{2} = \frac{ \frac{13}{36} }{2} = \frac{13}{36} \times \frac{1}{2} = \frac{13}{72} = 0.18 \\ mg = \sqrt{ \frac{1}{4} \times \frac{1}{9} } = \sqrt{ \frac{1}{36} } = \frac{1}{6} = 0.166 \\ mh = \frac{2 \times \frac{1}{4} \times \frac{1}{9} }{ \frac{1}{4} + \frac{1}{9} } = \frac{ \frac{1}{2} \times \frac{1}{9} }{ \frac{13}{36} } = \frac{ \frac{1}{18} }{ \frac{13}{36} } = \frac{1}{18} \times \frac{36}{13} = \frac{2}{13} = 0.153[/tex]
[tex]c)ma = \frac{5 + 7.2}{2} = \frac{12.2}{2} = 6.1 \\ mg = \sqrt{5 \times 7.2} = \sqrt{36} = 6 \\ mh = \frac{2 \times 5 \times 7.2}{5 + 7.2} = \frac{72}{12.2} = 5.9[/tex]
[tex]d)ma = \frac{25 \sqrt{3} + 12 \sqrt{3} }{2} = \frac{37 \sqrt{3} }{2} = 18.5 \sqrt{3} \\ mg = \sqrt{25 \sqrt{3} \times 12 \sqrt{3} } = \sqrt{25 \times 12 \times 3} = \sqrt{900} = 30 \\ mh = \frac{2 \times 25 \sqrt{3 } \times 12 \sqrt{3} }{25 \sqrt{3} + 12 \sqrt{3} } = \frac{2 \times 25 \times 12 \times 3}{37 \sqrt{3} } = \frac{1800}{37 \sqrt{3} } = \frac{1800 \sqrt{3} }{111} = 16.21 \sqrt{3} [/tex]
3.
[tex]a)mg = \sqrt{9 \times b} = 18 = \sqrt{324} \\ 9 \times b = 324 = > \\ = > b = \frac{324}{9} = 36[/tex]
[tex]d)mg = \sqrt{0.1 \times b} = 0.11 = \sqrt{0.0121} \\ = > 0.1 \times b = 0.0121 = > \\ = > b = \frac{0.0121}{0.1} = 0.121[/tex]
