Evaluate \((2^{0} + 4^{-\frac{1}{2}})^{2}\)
\(\frac{1}{4}\)
\(\frac{5}{4}\)
\(\frac{9}{4}\)
4
9
Correct answer is C
\((2^{0} + 4^{-\frac{1}{2}})^{2}\)
= \((1 + (\frac{1}{4})^{\frac{1}{2}})^{2}\)
= \((1 + \frac{1}{2})^{2}\)
= \((\frac{3}{2})^{2} = \frac{9}{4}\)
Write down the number 0.0052048 correct to three significant figures
0.005
0.0052
0.00520
5.2048
5204
Correct answer is C
0.0052048 = 0.00520
Find, correct to three significant figures, the value of \(\sqrt{41830}\).
205
647
2050
6470
64.7
Correct answer is A
\(\sqrt{41830} = 204.5238\)
\(\approxeq 205\) (to three significant figures)
p< 0
p\(\geq\) 0
p \(\leq\) 0
p < 1
p > 0
Correct answer is E
\(\frac{k}{k + 1}\) + \(\frac{k + 1}{k}\)
= \(\frac{k^2 + (k + 1)^2}{k(k + 10}\)
= \(\frac{2k^2 + 2k + 1}{k(k + 1}\)
let k = \(\frac{1}{2}\)
p = \(\frac{10}{3}\)
p > 0
Solve the given equation \((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)
27
9
\(\frac{1}{27}\)
18
81
Correct answer is A
\((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)
Let \(\log_{3} x = a\).
\(a^{2} - 6a + 9 = 0\)
\(a^{2} - 3a - 3a + 9 = 0\)
\(a(a - 3) - 3(a - 3) = 0\)
\((a - 3)(a - 3) = 0\)
\(\implies a = 3 (twice)\)
\(\log_{3} x = 3 \implies x = 3^{3} = 27\)