Mathematics Questions and Answers

a = u² - 3y² = (1)² - 3(-1) = -2

b = 2uu + v² + v²

= 2(1)(-1) + (-1)² = -1

∴ 2(2a - b)(a - b∴) = [2(-2) - 1](-2 - (-1)2)

= -3 - 3

= 9

If P = \(\frac{2}{3}\) (\(\frac{1 - r^2}{n^2}\)), find n when r = \(\frac{1}{3}\) and p = 1

p = \(\frac{2(1 - r^2)}{3n^2}\) when r = \(\frac{1}{3}\) and p = 1

1 = \(\frac{2}{3}\) \(\frac{(1 - (\frac{1}{3})^2)}{n^2}\)

n² = \(\frac{2(3 - 1)}{3 \times 3}\)

n² = \(\frac{2 \times 2}{3 \times 3}\)

= \(\frac{4}{9}\)

n = \(\frac{4}{9}\)

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

\(\frac{2\sqrt{14} \times 3\sqrt{21}}{7 \sqrt{24} \times 2\sqrt{98}}\) = \(\frac{6\sqrt{14} \times 3 \times \sqrt{7} \times \sqrt{3}}{7 \times 2 \sqrt{6} \times \sqrt{7} \times \sqrt{14}}\)

= \(\frac{3\sqrt{3}}{14\sqrt{6}}\)

= \(\frac{3\sqrt{3}}{14\sqrt{2} \times \sqrt{3}}\)



= \(\frac{3\sqrt{2}}{28}\)

log\(_2\)6 - log\(_2\)3 = log\(_2\) (\(\frac{6}{3}\))

= log\(_2\)2... A

log\(_2\)8 - 2log\(_2\)\(\frac{1}{2}\)

log\(_2\)8 - log\(_2\)\(\frac{1}{2}\)\(^2\)

log\(_2\)8 - log\(_2\)\(\frac{1}{4}\)

= log\(_2\) 32... B

\(\frac{A}{B}\) = \(\frac{log_22}{log_232}\)

N.B. log\(_2\)2 = 1

= \(\frac{1}{5}\)
 

(0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\) = (8 x 10^-3)10^-3 x (16 x 10^-2)-\(\frac{3}{2}\)

= \(\frac{(2^3)}{10^3}\) - 3 x \(\frac{(2^4)}{10}\) - \(\frac{-3}{2}\)

= \(\frac{625}{8}\)