\(3\sqrt{10}\)
\(\sqrt{82}\)
15
\(2\sqrt{5}\)
Correct answer is A
\(V = \begin{pmatrix} -2 \\ 4 \end{pmatrix}\) and \(U = \begin{pmatrix} -1 \\ 5 \end{pmatrix}\)
\(U + V = \begin{pmatrix} -1 - 2 \\ 5 + 4 \end{pmatrix} = \begin{pmatrix} -3 \\ 9 \end{pmatrix}\)
\(|U + V| = \sqrt{(-3)^{2} + 9^{2}} = \sqrt{9 + 81} = \sqrt{90}\)
= \(sqrt{9 \times 10} = 3\sqrt{10}\)
Calculate the mean deviation of 1, 2, 3, 4, 5, 5, 6, 7, 8, 9.
2
3
4
5
Correct answer is A
| x | 1 | 2 | 3 | 4 | 5 | 5 | 6 | 7 | 8 | 9 | Total |
| \(x - \bar{x}\) | -4 | -3 | -2 | -1 | 0 | 0 | 1 | 2 | 3 | 4 | |
| \(|x - \bar{x}|\) | 4 | 3 | 2 | 1 | 0 | 0 | 1 | 2 | 3 | 4 | 20 |
Mean (\(\bar{x}\)) = \(\frac{1+2+3+4+5+5+6+7+8+9}{10} = \frac{50}{10} = 5\)
\(MD = \frac{\sum |x - \bar{x}|}{n} = \frac{20}{10} = 2\)
If \(g(x) = \frac{x + 1}{x - 2}, x \neq -2\), find \(g^{-1}(2)\).
3
2
\(\frac{3}{4}\)
-3
Correct answer is D
\(g(x) = \frac{x + 1}{x + 2}, x \neq 2\)
Let y = x, then \(g(y) = \frac{y + 1}{y + 2}\)
Let x = g(y), so that \(x = \frac{y + 1}{y + 2}\)
\(x(y + 2) = y + 1\)
\(xy + 2x = y + 1 \implies xy - y = 1 - 2x\)
\(y(x - 1) = 1 - 2x \implies y = \frac{1 - 2x}{x - 1}\)
\(y = g^{-1}(x) = \frac{1 - 2x}{x - 1}\)
\(g^{-1}(2) = \frac{1 - 2(2)}{2 - 1} = -3\)
N3,173,032
N3,048,000
N1,084,730
N8555,600
Correct answer is C
No explanation has been provided for this answer.
P and Q are the points (3, 1) and (7, 4) respectively. Find the unit vector along PQ.
\(\begin{pmatrix} 4 \\ 3 \end{pmatrix}\)
\(\begin{pmatrix} 0.6 \\ 0.8 \end{pmatrix}\)
\(\begin{pmatrix} 0.8 \\ 0.6 \end{pmatrix}\)
\(\begin{pmatrix} -0.8 \\ 0.6 \end{pmatrix}\)
Correct answer is C
\(PQ = \begin{pmatrix} 7 - 3 \\ 4 - 1 \end{pmatrix}\)
\(= \begin{pmatrix} 4 \\ 3 \end{pmatrix}\)
\(\hat{n} = \frac{\overrightarrow{PQ}}{|PQ|} \)
\(|PQ| = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5\)
\(\hat{n} = \frac{1}{5}\begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} 0.8 \\ 0.6 \end{pmatrix}\)