If a u2 - 3v2 and b = 2uv + v2 evaluate (2a - b)(a - b2), when u = 1 and v = -1
9
15
27
33
Correct answer is A
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
\(\frac{3}{2}\)
\(\frac{1}{3}\)
3
\(\frac{2}{3}\)
Correct answer is D
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 = \(\frac{4}{9}\)
= \(\frac{2}{3}\)
Simplify without using tables \(\frac{2\sqrt{14} \times 3\sqrt{21}}{7\sqrt{24} \times 2\sqrt{98}}\)
\frac{3\sqrt{14}}{4}\)
\(\frac{3\sqrt{2}}{4}\)
\(\frac{3\sqrt{14}}{28}\)
\(\frac{3\sqrt{2}}{28}\)
Correct answer is D
\(\frac{2\sqrt{14} \times 3\sqrt{21}}{7 \sqrt{24} \times 2\sqrt{98}}\) = \(\frac{6\sqrt{14} \times 3 \times \sqrt{7} \times \sqrt{3}}{7 \times 2 \sqrt{6} \times \sqrt{7} \times \sqrt{14}}\)
= \(\frac{3\sqrt{3}}{14\sqrt{6}}\)
= \(\frac{3\sqrt{3}}{14\sqrt{2} \times \sqrt{3}}\)
= \(\frac{3\sqrt{2}}{28}\)
Simplify without using tables \(\frac{log_26}{log_28}\) - \(\frac{log_23}{2log_2\frac{1}{2}}\)
\(\frac{1}{5}\)
\(\frac{1}{2}\)
\(\frac{-1}{2}\)
(\frac{log_23}{log_27}\)
Correct answer is A
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
= \(\frac{1}{5}\)
Evaluate without using tables (0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\)
\(\frac{625}{8}\)
\(\frac{8}{625}\)
\(\frac{1}{8}\)
8
Correct answer is A
(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 \(\frac{(2^4)}{10}\) - \(\frac{-3}{2}\)
= \(\frac{625}{8}\)