32
36
48
64
Correct answer is A
Reacting force - Weight = Net force
R = W + ma = mg + ma
480 = 10p + 5p
480 = 15p
p = 32 kg
\(\begin{pmatrix} 3 \\ -1 \end{pmatrix}\)
\(\begin{pmatrix} -5 \\ -1 \end{pmatrix}\)
\(\begin{pmatrix} -5 \\ 1 \end{pmatrix}\)
\(\begin{pmatrix} -5 \\ -9 \end{pmatrix}\)
Correct answer is B
\(4 \begin{pmatrix} 3 \\ 2 \end{pmatrix} + 3 \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\)
\(\begin{pmatrix} 12 \\ 8 \end{pmatrix} + \begin{pmatrix} 3x \\ 3y \end{pmatrix} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\)
\(\begin{pmatrix} 3x \\ 3y \end{pmatrix} = \begin{pmatrix} -3 - 12 \\ 5 - 8 \end{pmatrix}\)
\(\begin{pmatrix} 3x \\ 3y \end{pmatrix} = \begin{pmatrix} -15 \\ -3 \end{pmatrix}\)
\(\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -5 \\ -1 \end{pmatrix}\)
12
11
10
8
Correct answer is A
\(Mean : \frac{x + 4 + z + t}{4} = 5 \implies x + 4 + z + t = 20\)
\(\implies x + z + t = 16 ... (1)\)
\(Median : \frac{4 + z}{2} = z \implies 4 + z = 2z\)
\(4 = z\)
From 1,
\(\implies x + 4 + t = 16 \)
\(x + t = 12\)
Find, in surd form, the value of \(\cos 165\).
\(\frac{1}{4}(\sqrt{6} + \sqrt{2})\)
\(\frac{1}{4}(\sqrt{6} - \sqrt{2})\)
\(-\frac{1}{4}(\sqrt{6} - \sqrt{2})\)
\(-\frac{1}{4}(\sqrt{6} + \sqrt{2})\)
Correct answer is D
\(\cos 165 = -\cos (180 - 165) = -\cos 15\)
\(\cos 15 = \cos (45 - 30)\)
\(\cos (x - y) = \cos x \cos y + \sin x \sin y\)
\(\cos (45 - 30) = \cos 45 \cos 30 + \sin 45 \sin 30\)
= \((\frac{\sqrt{2}}{2})(\frac{\sqrt{3}}{2}) + (\frac{\sqrt{2}}{2})(\frac{1}{2})\)
= \(\frac{1}{4}(\sqrt{6} + \sqrt{2})\)
\(\therefore \cos 165 = -\frac{1}{4}(\sqrt{6} + \sqrt{2})\)
\((-1, 5)\)
\((-\frac{1}{2}, 3\frac{1}{2})\)
\((0, 4\frac{1}{2})\)
\((1\frac{1}{2}, 5)\)
Correct answer is C
No explanation has been provided for this answer.