Correct Answer: D. convince the people that he has been sent by God

Correct Answer: A. primary election

Correct Answer: C. Gorges

Correct Answer: D. possessed by the spirit of God

Explanation

n = \(\frac{sin i}{sin r}\)

1.5 = \(\frac{sin \theta}{sin(190 - \theta)} = \frac{sin \theta}{cos theta} = \tan \theta\)

Hence, 0 = tan\(^{-1}\) 1.5 = 56.31\(^o\)

Explanation

(a) Obligations of the employer to the employees are:

(i) The employer has the duty to provide safety tools for the employee.

(ii) He is obliged to pay the employee his remuneration.

(iii) He has the obligation to provide a safe place of work.

(iv) He has the duty to train his new employees such that they can avoid reasonably foreseen able harm which could result from a failure to give them proper instructions and training.

(v) He must give the employee work to keep him busy.

(vi) The employer has a duty to reimburse his employee for any expenses or loss he incurs in the course of the employer's business.

(b) Duties of employee to the employer are:

(i) The employee must perform his duties faithfully and honestly.

(ii) He must not reveal any confidential information regarding his employer.

(iii) The employee must perform the task given to him according to laid down instructions.

(iv) The employee should be loyal.

(v) He must not allow his own interest to conflict with the interest of his employer.

(vi) The employee must show respect to his employer

Explanation

(a) Blackpod disease of cocoa (i) this is fungal disease of cocoa

(ii) causal organism: phytophthora palmivora

(iii) causes heavy yield loss most especially, in areas of high rainfall which helps in the transmission of spores of the causal fungus from the infected pods or soil to other areas of the farm.

(iv) Symptoms: - appearance of brown spots on the pod which covers the entire pod surface. - later turn black. - the disease penetrates the pod into the beans, leading to rottening, thereby, reducing the economic value.

(v) Prevention: Remove unwanted plant canopies and allow light penetration by regular pruning. Plant resistant variety e.g. hybrid. Spray with fungicides like perenox, Caocobre sandox. Remove and burn infected pods.

(b) Leaf Blight of Cassava: (i) This is a bacterial disease.

(ii) Causal organism: Xanthomonas manihotis

(iii) Transmission: Through cassava cuttings obtained from infected ones and may also be transmitted through contaminated farm tools, e.g. cutlass, hoes used for both cutting and planting of cuttings.

(iv) Symptoms: Occurs on young leaves as small spots leading to larger ones to form light brown dead areas. Later, the upper young leaves die and drop. Canker of stem and back of stem die and there is gum exudation from stem.

(v) Prevention: Plant resistant variety; remove and destroy affected plants; practise crop rotation.

Correct Answer: D. tell the rock before their eyes to yield its Water

Explanation

(a) \(\frac{8x^2 + 8x + 9}{(x - 1)(2x + 3)^2}≡\frac{A}{(x - 1)}+\frac{B}{2x + 3}+\frac{C}{(2x + 3)^2}\)

\(\frac{8x^2 + 8x + 9}{(x - 1)(2x + 3)^2}≡\frac{A(2x + 3)2+B(x - 1)(2x + 3)+C(x - 1)}{(x - 1)(2x + 3)^2}\)

\(8x^2+8x+9=A(2x+3)^2+B(x-1)(2x+3)+C(x-1)\)

Put \(x=1\)

\(8(1)^2+8(1)+9=A(2(1)+3)^2+B(1-1)(2(1)+3)+C(1-1)\)

⇒25=25A

=A=\(\frac{25}{25}=1\)

Put \(x=-\frac{3}{2}\)

\(8(-\frac{3}{2})^2+8(-\frac{3}{2})+9=A(2(-\frac{3}{2})+3)^2+B(-\frac{3}{2}-1)(2(-\frac{3}{2})+3)+C(-\frac{3}{2}-1)\)

⇒15=-2.5C

\(=C=-\frac{15}{2.5}=-6\)

Since \(8x^2+8x+9=A(2x+3)^2+B(x-1)(2x+3)+C(x-1)\)

\(⇒8x^2+8x+9=A(4x^2+12x+9)+B(2x^2+x-3)+C(x-1)\)

\(=8x^2+8x+9=4Ax^2+12A+9A+2Bx^2+Bx-3B+Cx-C\)

\(=8x^2+8x+9=4Ax^2+2Bx^2+12Ax+Bx+Cx+9A-3B-C\)

\(=8x^2+8x+9=(4A+2B)x^2+(12A+B+C)x+9A-3B-C\)

By comparing the coefficient of \(x, 8=12A+B+c\)

=8=12(1)+B-6

=8=12+B-6

=8=6+B

=8-6=B

=\(\therefore \frac{8x^2+8x+9}{(x-1)(2x+3)^2}=\frac{1}{x-1}+\frac{2}{2x+3}-\frac{6}{(2x+3)^2}\)

(b) Equation of a circle =\((x - a)^2 + (y - b)^2 = r^2\)

Where "a" and "b" are the coordinate of the center and "r" is the radius

2πr = 6π (given)

∴ r = 3 units

=\( (x - (-2))^2 + (y - 5)^2 = 3^2\)

= \((x + 2)^2 + (y - 5)^2 = 9\)

= \(x^2 + 4x + 4 + y^2 - 10y + 25 = 9\)

= \(x^2 + y^2 + 4x - 10y + 29 - 9 = 0\)

∴ \(x^2 + y^2 + 4x - 10y + 20 = 0\)

Correct Answer: A. ii, iv, i and iii