Explanation

In \(\Delta\) BPY, \(\tan 35° = \frac{h}{x}\)

\(h = x \tan 35 = 0.7 x ... (1)\)

In \(\Delta\) BPX, \(\frac{h}{x + 4000} = \tan 15\)

\(\frac{h}{x + 4000} = 0.3\)

\(h = 0.3 (x + 4000) = 0.3x + 1200 ... (2)\)

Equating (1) and (2) as the values of h, we have

\(0.7x = 0.3x + 1200 \implies 0.7x - 0.3x = 1200\)

\(0.4x = 1200 \times x = \frac{1200}{0.4} = 3000m\)

\(\therefore h = 0.7x = 0.7 (3000) = 2100m\)

\(\text{The total height = } 5200m + 2100m = 7300m\)

Explanation

(a)(i) < PQR = (180° - 130°) + 50° = 100°

\(PR^{2} = PQ^{2} + QR^{2} - 2(PQ)(QR) \cos < PQR\)

= \(8^{2} + 13^{2} - 2(8)(13) \cos 100\)

= \(233 + 36.118\)

\(PR^{2} = 269.118\)

\(PR = 16.405 m \approxeq 16.4 m\)

(ii) \(\frac{QR}{\sin < QPR} = \frac{PR}{\sin < PQR}\)

\(\frac{13}{\sin < QPR} = \frac{16.4}{\sin 100}\)

\(\sin < QPR = \frac{13 \times \sin 100}{16.4}\)

\(\sin < QPR = 0.7806\)

\(< QPR = 51.32° \approxeq 51.3°\)

The bearing of R from P = 50° + 51.3° = 101.3°

\(\approxeq\) 101°.

(b)

In \(\Delta PQD\),

\(\frac{h}{8} = \sin 51.3\)

\(h = 8 \sin 51.3\)

= \(6.243 m \)

\(\approxeq 6.24 m\)

Area of \(\Delta PQR = \frac{1}{2} \times PR \times h\)

\(\frac{1}{2} \times 6.24 \times 16.4 = 51.166 m^{2}\)

\(\approxeq 51.2 m^{2}\)

Correct Answer: (b) 100/3%

Explanation

P(y) = 2y + 3, q(y) = y\(^2\) - 2

q \(\cap\) p = qp(y)

= q(2y + 3)

= (2y + 3)\(^3\) - 2

= 4xy\(^2\) + 12y + 9 - 2

= 4y\(^2\) + 12y + 7

(b)

No. of ways = 2 x 5 x 5 x 5

= 250 ways

Correct Answer: B.. x=5,y=9

Explanation

The set is already in increasing order. We have six numbers in the set and we need to ensure the set will have a median of 6. When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. The two middle numbers represent x and 7. Let's set up an equation. x+7/2=6. The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by 2, and subtract 7 on both sides, we get x to be 5. Finally, to find y, we need a number that is greater than or equal to 9 and less than or equal to 10. Answer x=5, y=9 satisfies all conditions.

Correct Answer: (a) #10,000

Correct Answer: B. SE55S5

Correct Answer: A. \(\frac{\pi r}{3}\)

Correct Answer: C. \(\begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)

Explanation

\(u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}\)

\(a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}; t = 3 secs\)

\(v = u + at \implies v = \begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 3 \\ -4 \end{pmatrix} \times 3\)

= \(\begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 9 \\ -12 \end{pmatrix} = \begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)\)

Correct Answer: B. 9

Explanation

\(\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}\)

= \(\frac{3^n * 3^n * 3^1 * - 3^2 * 3^2}{3^n * 3^1 - 3^n}\)

= \(\frac{3^n (3^2 * 3^1)}{3^n (3^1 - 1)}\)

= \(\frac{27-9}{3-1}\)

= \(\frac{18}{2}\)

= 9