Mathematics Questions and Answers

\(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\)

When x = 4,

\(\log_{2} y = 3 - \log_{2} 4^{\frac{3}{2}}\)

\(\log_{2} y = 3 - \log_{2} 2^{3}\)

\(\log_{2} y = 3 - 3 \log_{2} 2 = 3 - 3 = 0\)

\(\log_{2} y = 0 \implies y = 2^{0} = 1\)

Let XW = a, a :7

\(\frac{a}{5 - a}\) = \(\frac{3}{7}\)

7a = 15 - 3a

10a = 15

a = \(\frac{15}{10}\)

= \(\frac{3}{2}\)

= 1.5cm

\(\frac{1}{x + 1}\) - \(\frac{1}{x + 3}\) = \(\frac{1}{4}\)

\(\frac{x + 3 - x - 1}{(x + 1)(x + 3)}\) = \(\frac{1}{4}\)

\(\frac{2}{x^2 + 4x + 3}\) = \(\frac{1}{4}\)

= x2 + 4x + 3 = 8

x2 + 4x - 5 = 0

= (x - 1)(x + 5) = 0

x = 1 or -5

\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{3 - 2}{\sqrt{3} + \sqrt{2}}\)

\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) = \(\frac{\sqrt{2}}{\sqrt{3}}\) - \(\frac{x}{\sqrt{2}}\)

\(\frac{\sqrt{3} + \sqrt{2}}{3 + \sqrt{2}}\) = \(\sqrt{6}\) + 2

\(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) = \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) x \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)

= 5 - 2\(\sqrt{6}\)

\(\sqrt{6}\) + 2 - (5 - 2 \(\sqrt{6}\)) = \(\sqrt{6}\) + 2 - 5 + 2\(\sqrt{6}\)

= 3\(\sqrt{6}\) - 3

= 3(\(\sqrt{6}\) - 1)

1 hr = 60 mins, 60 mins = 360°

30 mins = \(\frac{360^o}{1}\) × \(\frac{30}{60}\)

= 180°

90 mins = 360° + 180°

= 540°