Explanation

(a) \(y = (2x + 3)^{7} + \frac{x - 1}{2x - 1}\)

\(\frac{\mathrm d y}{\mathrm d x} = 7(2x + 3)^{6}. 2 + \frac{(2x - 1).1 - (x - 1).2}{(2x - 1)^{2}}\)

= \(14(2x + 3)^{6} + \frac{2x - 1 - 2x + 2}{(2x - 1)^{2}}\)

= \(14(2x + 3)^{6} + \frac{1}{(2x - 1)^{2}}\)

At x = -1, \(\frac{\mathrm d y}{\mathrm d x} = 14(-1)^{6} + \frac{1}{(2(-1) - 1)^{2}}\)

= \(\frac{\mathrm d y}{\mathrm d x} = 14 + \frac{1}{9} = 14\frac{1}{9}\)

(b) \(\int_{1} ^{2} \frac{x - 1}{(x + 2)^{4}} \mathrm d x\)

\( u = x + 2 \implies \mathrm d u = \mathrm d x\)

If x = 1, u = 1 + 2 = 3; x = 2, u = 2 + 2 = 4.

\(\int_{1} ^{2} \frac{x - 1}{(x + 2)^{4}} \mathrm d x = \int_{3} ^{4} \frac{u - 3}{u^{4}}\)

= \(\int_{3} ^{4} (\frac{u}{u^{4}} - \frac{3}{u^{4}}) \mathrm d u\)

= \(\int_{3} ^{4} (u^{-3} - 3u^{-4}) \mathrm d u\)

= \([\frac{u^{-2}}{-2} + u^{-3}]_{3} ^{4}\)

= \([\frac{1}{u^{3}} - \frac{1}{2u^{2}}]_{3} ^{4}\)

= \((\frac{1}{4^{3}} - \frac{1}{2(4^{2})}) - (\frac{1}{3^{3}} - \frac{1}{2(3^{2})})\)

= \(\frac{1}{64} - \frac{1}{32} - \frac{1}{27} + \frac{1}{18}\)

= \(\frac{5}{1728}\).

Correct Answer: C. state governments

Explanation

Any area not covered in the Constitution is considered to be within the states' powers to make laws and is called a residual power.

Correct Answer: D. off

Correct Answer: C. 6.0\(ms^{-1}\)

Explanation

Given that \(u = 0ms^{-1}, a = 2ms^{-2}, s = 9m\)

We can use the equation, \(v^{2}=u^{2} +2as\) so that we have,

\(v^{2} = 0^{2} + 2\times 2\times 9\)

\(v^{2} = 36; v= 6.0ms^{-1}\)

Note; u = Initial velocity

v = final velocity

a = acceleration

s = distance covered

Correct Answer: D. XXand XY

Correct Answer: D) Christians should be encouraged to work

Explanation

This Christian Religious Knowledge question is asking about the meaning of the charge that he who does not work should not eat. The options given are A, B, C, D,

Option A suggests that Christians must not give food to people to eat, which is incorrect. As Christians, we are called to love and care for our neighbors, and this includes providing food for those in need.

Option B suggests that Christians must give food to working people only, which is also incorrect. While it is important to encourage and support hard work, Christians should not withhold food from those who are not currently employed.

Option C suggests that Christians should be taught to walk, which is unrelated to the question. This option can be ignored.

Option D is the correct answer. The charge that he who does not work should not eat is a biblical principle that encourages Christians to be productive and contribute to society. It does not mean that Christians should withhold food from those who are currently unable to work, but rather that able-bodied individuals should strive to work and be self-sufficient.

In summary, the correct answer to this question is option D, which suggests that Christians should be encouraged to work and be productive members of society while still caring for those in need.

Correct Answer: A. penetration of European merchants capital into Nigeria

Explanation

Penetration of European merchants capital into Nigeria is the correct answer. As slave trade was abolished, legitimate trade started and this encouraged the European merchants agenda for imperialism (i.e to establish industries, extract and trade natural resources) to smoothly penetrate Nigeria.

Correct Answer: C. 4.02g

Correct Answer: C. Privy council

Explanation

The Supreme court become the highest court in 1963, but before then, the Privy council in London sees to dispute settlement and matters adjudication.

Correct Answer: C. Germany