Explanation

(a) Substituting for m and n to get 2(i - j) + 2i + 3j - r = 0 and solving for r to get r = 4i + j

Thus |r| = \(\sqrt{4^2 + 1^2}\) = \(\sqrt{17}\) = 4.1231

(b)(i) Given that S = 3t - \(\frac{r^3}{3}\) + 9, they took the derivative of S with respect to t and equated to zero to obtain \(\frac{d_s}{d_t}\) = 3 - t\(^2\) = 0

Solve to get t = \(\sqrt{3}\) = 1.7321 seconds

(b)(ii) Substituting for (t), the distance covered is S = 3(1.7321) - \(\frac{(1.7321)^3}{3}\) + 9

Therefore; 5.1963 - 1.732198389 + 9

= 12.4641 metres

Correct Answer: A. An earthquake

Correct Answer: D. erection of the image

Explanation

An astronomical telescope produces an inverted image because the objective lens forms a real, inverted image, and the eyepiece then magnifies this inverted image. For astronomical observations, an inverted image is generally not an issue as there's no inherent up or down in space.

However, for terrestrial observations (objects on Earth), an inverted image would be highly inconvenient and confusing. Therefore, a terrestrial telescope incorporates an additional optical component, often called an erecting system (which can be a lens or a set of lenses, or even prisms in binoculars), whose purpose is to re-invert the image produced by the objective lens, thus presenting an upright (erect) image to the observer.

Let's look at the options:

• A. improving the sharpness: While quality lenses contribute to sharpness, the primary function of this *extra* lens is not to improve sharpness itself, but to modify the orientation of the image.

• B. creating an inverted image: This is incorrect. The objective lens already creates an inverted image. The extra lens works to *correct* this inversion.

• C. magnification of the image: Magnification is achieved by the combination of the objective and eyepiece. The extra lens primarily deals with image orientation, not magnification.

• D. erection of the image: This is precisely the function of the extra lens (erecting system) in a terrestrial telescope – to make the image upright.

The final answer is D

Correct Answer: A) Amos

Explanation

The question is asking which book in the Bible emphasizes social justice the most. The options given are Amos, Ezekiel, Hosea, and Isaiah. The correct answer is option A, Amos. Amos is one of the twelve minor prophets in the Old Testament. In his book, he speaks out against social injustices such as oppression of the poor and corrupt practices of the wealthy. He also emphasizes the importance of treating others fairly and justly. Although other books in the Bible also address social justice, Amos is considered to be the most direct and forceful in his message. Ezekiel, Hosea, and Isaiah are also prophets who speak about social justice, but their messages are more varied and not as focused on this topic as Amos' message. It is important for Christians to understand the message of social justice in the Bible and to apply it in their lives. This means treating others with respect and fairness, helping those in need, and standing up against oppression and injustice.

Correct Answer: C) the number of people who are out of work and actively looking for work

Explanation

This Economics question is asking about what the unemployment rate measures as a percentage of the labour force. The options are: A) the number of people in an economy who do not have jobs, B) the number of people in an economy who have jobs, C) the number of people who are out of work and actively looking for work (which is the correct answer), and D) the number of people who are looking for work.

The unemployment rate is a measure of the percentage of the labour force that is unemployed. The labour force includes people who are employed and those who are actively seeking work. Therefore, options A and B are incorrect as they do not take into account the labour force as a whole.

Option C is the correct answer because it refers to the number of people who are out of work and actively looking for work, which is a subset of the labour force. These are people who are willing and able to work, but are currently unable to find employment. By measuring this as a percentage of the labour force, we can get an idea of the level of unemployment in an economy.

Option D is not the correct answer as it is too broad. It includes people who are not actively seeking work, which is not relevant to the unemployment rate.

In summary, the unemployment rate measures the number of people who are out of work and actively looking for work as a percentage of the labour force. This is useful for understanding the level of unemployment in an economy.

Explanation

Reasons why the use of money has replaced the barter system in modern economic transactions:

(i) Barter makes specialization of labour to be limited because barter system encourages self sufficiency.

(ii) Prob-lem of the determination of the rate of exchange between two commodities

(iii) Problem of coincidence of wants: It is difficult to find one who has what you want and wants what you have.

(iv) Many goods cannot be divided into convenient sizes because of their bulkiness and indivisibility.

(v) Barter makes the question of deferred payment difficult because it is not possible to guarantee that the item paid back will be of identical size, state and quantity as the one borrowed.

(vi) The difficulty of storing wealth or value especially where the form of exchange is perishable e.g. oranges, yams etc.

Correct Answer: B. Lenz's law

Correct Answer: C. Kaduna, Sokoto and Jama'are

Correct Answer: D. a soliloquy

Correct Answer: A. convenience goods

Explanation

Convenience goods are those that the customer purchases frequently, immediately, and with minimum effort. Soaps and newspapers are considered convenience goods.