Factorize completely 81a\(^4\) - 16b\(^4\)
(3a + 2b)(2a - 3b)(9a2 + 4b2)
(3a - 2b)(2a - 3b)(4a2 - 9b2)
(3a - 2b)(3a + 2b)(9a2 + 4b2)
(6a - 2b)(8a - 3b)(4a3 - 9b2)
Correct answer is C
81a\(^4\) - 16b\(^4\) = (9a\(^2\))\(^2\) - (4b\(^2\))\(^2\)
= (9a\(^2\) + 4b\(^2\))(9a\(^2\) - 4b\(^2\))
N:B 9a\(^2\) - 4b\(^2\) = (3a - 2b)(3a + 2b)
Without using tables find the numerical value of log749 + log7(\(\frac{1}{7}\))
1
2
3
7
9
Correct answer is A
log749 + log7\(\frac{1}{7}\)
= log77
= 1
If \((\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}\), find the values of m and n.
m = 4, n = 2
m = -4, n = -2
m = -4, n =2
m = 4, n = -2
m = -2, n = 4
Correct answer is D
(\(\frac{2}{3}\))m (\(\frac{3}{4}\))n = \(\frac{256}{729}\)
\(\frac{2^m}{4^n}\) x \(\frac{3^n}{3^m}\) = \(\frac{2^{8}}{3^{6}}\)
\(2^{m} \div 2^{2n} = 2^{8}; 3^{n} \div 3^{m} = 3^{-6}\)
m - 2n = 8........(i)
-m + n = -6........(ii)
Solving the equations simultaneously
m = 4, n = -2
55
10
5
4
2
Correct answer is E
% error = \(\frac{\text{Actual error}}{\text{real value}}\) x 100
= \(\frac{5}{250}\) x 100
= 2%
4.46
4.48
4.47
4.49
4.50
Correct answer is C
59.81798 = 59.8(3 s.f)
0.0746829 = 0.0747
59.8 x 0.0747 = 4.46706
= 4.47(3s.f)