\(4(6 + 5\pi)\)
\(4(6 + 2\pi)\)
\(4(3 + 3\pi)\)
\(4(3 + 5\pi)\)
Correct answer is A
The angle subtended by the minor arc = \(\frac{\pi}{3} radians\)
The angle subtended by the major arc = \(2\pi - \frac{\pi}{3} = \frac{5\pi}{3}\)
Perimeter of the major arc = \(r\theta + 2r\)
= \(12 \times \frac{5\pi}{3} + 2(12) = 20\pi + 24\)
= \(4(5\pi + 6)\)
\((5\frac{2}{3}, \frac{2}{5})\)
\((\frac{2}{5}, 5\frac{2}{5})\)
\((\frac{2}{5}, 2\frac{2}{5})\)
\((\frac{-2}{5}, 5\frac{2}{5})\)
Correct answer is B
\((x = \frac{nx_{1} + mx_{2}}{n + m}, y = \frac{ny_{1} + my_{2}}{n + m})\)
Given P(-2, 3) and Q(4, 9),
\((\frac{2(4) + 3(-2)}{2 + 3}, \frac{2(9) + 3(3)}{2 + 3})\)
= \((\frac{2}{5}, \frac{27}{5})\)
= \((\frac{2}{5}, 5\frac{2}{5})\)
Evaluate \(\int_{0}^{2} (8x - 4x^{2}) \mathrm {d} x\).
\(-16\)
\(\frac{-16}{3}\)
\(\frac{16}{3}\)
\(16\)
Correct answer is C
\(\int_{0}^{2} (8x - 4x^{2}) \mathrm {d} x = (\frac{8x^{1 + 1}}{2} - \frac{4x^{2+1}}{3})|_{0}^{2}\)
= \((4x^{2} - \frac{4x^{3}}{3}) |_{0}^{2}\)
= \((4(2^2) - \frac{4(2^3)}{3})\)
= \(16 - \frac{32}{3} = \frac{16}{3}\)
0 and 1
0 and 4
0 and 5
1 and 4
Correct answer is D
\(s = ut + \frac{at^{2}}{2}\)
This movement is against gravity, so it is negative.
\(s = ut - \frac{gt^{2}}{2}\)
\(s = 20m, u = 25ms^{-1}\)
\(20 = 25t - \frac{10t^{2}}{2} \implies 20 = 25t - 5t^{2}\)
\(5t^{2} - 25t + 20 = 0 \)
\(5t^{2} - 5t - 20t + 20 = 0 \implies 5t(t - 1) - 20(t - 1) = 0\)
\(5t - 20 = \text{0 or t - 1 = 0}\)
\(t = \text{1 or 4}\)
-4
-3
-1
2
Correct answer is B
\(P = begin{pmatrix} y - 2 & y - 1 \\ y - 4 & y + 2 \end{pmatrix}\)
\(|P| = (y - 2)(y + 2) - (y - 1)(y - 4) = (y^{2} - 4) - (y^{2} - 5y + 4) = -23\)
\(5y - 8 = -23 \implies 5y = -23 + 8 = -15\)
\(y = \frac{-15}{5} = -3\)