Correct Answer: A. 045°

Correct Answer: (c) 7hrs 45mins

Correct Answer: B. 25

Correct Answer: C. 2, 3

Explanation

Let the no. be x and x + 1

x + (x + 1) = \(\frac{5}{6}\) of x(x + 1)

2x + 1 = \(\frac{5}{6}\) x(x + 1)

6(2x + 1) = 5x² + 5x

12x + 6 = 5x² + 5x

5x² + 5x - 12x - 6 = 0

5x² - 7x - 6 = 0

5x² - 10x + 3x - 6 = 0

5x(x - 2) + 3(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3) = 0

x - 2 = 0

for (5x + 3) = 0

5x = -3

x = \(\frac{-3}{5}\) (Imposible since x is a whole number)

x - 2 = 0

x = 2

x = \(\frac{-3}{5}\)(Impossible since x is a whole number)

x - 2 = 0

x = 2

The numbers are x = 2

x + 1 = 2 + 1

= 3

Explanation

(a) Using the two- point form,

\(\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}\)

\(\frac{y - 5}{-7 - 5} = \frac{x - 2}{-4 - 2}\)

\(\frac{y - 5}{- 12} = \frac{x - 2}{- 6}\)

\(y - 5 = 2(x - 2)\)

\(y - 5 = 2x - 4 \implies y - 2x = -4 + 5 = 1\)

\(Equation : y = 2x + 1\)

(b) (i)

In \(\Delta PQR, <QPR = 60° + 30° = 90°\). PQR is a right- angled triangle.

(ii) (1) In \(\Delta PQR, |QR|^{2} = 5^{2} + 8^{2}\)

\(25 + 64 = 89\)

\(|QR| = \sqrt{89} = 9.434 km \approxeq 9.43 km\)

(2) In the diagram above, the bearing of R from Q is the obtuse angle NQR.

But \(\tan \alpha = \frac{8}{5} = 1.6\)

\(\alpha = \tan^{-1} (1.6) = 58°\)

Hence, angle NQR = 360° - (a + 60° + 90°)

= 360° - (58° + 60° + 90°)

= 360° - 208°

= 152°

Correct Answer: A. -2

Explanation

(a)

(b)(i) \(Speed = \frac{distance}{time}\)

\(950 = \frac{d}{4} \implies d = 950 \times 4\)

\(d = 3800km\)

\(d = \frac{\theta}{360} \times 2\pi r\)

\(3800 = \frac{\theta}{360} \times 2 \times \frac{22}{7} \times 6400\)

\(3800 = \frac{\theta \times 281600}{2520}\)

\(\theta = \frac{2520 \times 3800}{281600}\)

\(\theta = 34.01°\)

\(\theta = 34°N\) (to the nearest degree)

(ii) Distance between P and Q, correct to four significant figures.

Longitude difference = 65° - 15° = 50°

Using, \(d = \frac{\theta}{360} \times 2 \pi r\)

where \(r = R \cos \theta\)

\(d = \frac{\theta}{360} \times 2 \pi R \cos \theta\)

= \(\frac{50}{360} \times 2 \times \frac{22}{7} \times 6400 \cos 34.01°\)

= \(4631.53 km\)

\(\approxeq 4632km\) (to 4 significant figures).

Explanation

u = 40j m/s ; v = 30i m/s,

Change in momentum : \(m(v - u)\)

= \(0.1 (30i - 40j)\)

= \(3i - 4j\)

Magnitude : \(\sqrt{3^{2} + 4^{2}}\)

= \(\sqrt{25}\)

= \(5 Ns^{-1}\)

Correct Answer: A. \(x > 1\)

Explanation

2x + 3 < 5x

-3x < -3

X > 1

Correct Answer: D. \(\cos^{2} \theta\)

Explanation

\((1 + \sin \theta)(1 - \sin \theta) = 1 - \sin \theta + \sin \theta - \sin^{2} \theta\)

\(= 1 - \sin^{2} \theta\)

Recall, \(\cos^{2} \theta + \sin^{2} \theta = 1\)

\(\therefore 1 - \sin^{2} \theta = \cos^{2} \theta\).