Correct Answer: D. Asia

Correct Answer: A) debited to trading account and shown as a current liability

Explanation

(a) In John's gospel, Jesus describes himself as the door and .the good shepherd. He says the shepherd must pass through the door whenever he wants to feed his sheep or take them out for grazing. He says that the sheep recognize their owner and the owner of the sheep calls them by name and they recognize his voice. The sheep would run away from the hired man for they do not know him. The thief would come through the window. For he is not the owner. The sheep would run away from him. Jesus expects all good shepherd to enter through the door and not to jump in through the window., whoever does that is a thief. The sheep would not follow the person whom they do not known. They would run away from such a person. Jesus equally says that He is the door to the sheep. All those who came before Him are thieves, the sheep did not listen to them nor follow them. He goes on further to say that He is the door, if anybody enters by Him he will be saved. The thief comes to steal. Jesus comes to give abundant life so that they may have it abundantly.

(b) This teaching relates to leadership role among Christians in the following ways:

(i) The teaching illustrates the fact that leadership involves taking risks to help those being led.

(ii) Jesus as the lamb, makes a great sacrifice for the sake of others. So Christian leaders should be ready to help others without counting the cost.

Explanation

R = \(U\sqrt{\frac{2H}{g}}\)

= 0.4 \(\sqrt{\frac{2 \times 20}{10}}\)

= 0.8m

Correct Answer: A. market towns amd commercial centers

Correct Answer: B. Q

Correct Answer: B. 1

Correct Answer: A) the business has a bank overdraft

Explanation

(a) \(m = (6i + 8j) ; n = (-8i + \frac{7}{3}j)\)

(i) \(|m| = \sqrt{6^{2} + 8^{2}} = \sqrt{36 + 64}\)

= 10 units.

Direction of m: \(\tan \alpha = \frac{8}{6} = 1.333\)

\(\alpha = 53.13°\)

\(|n| = \sqrt{(-8)^{2} + (\frac{7}{3})^{2}} = \sqrt{64 + \frac{49}{9}}\)

= \(\sqrt{\frac{625}{9}} = \frac{25}{3} units\)

Direction of n :

\(\tan \beta = \frac{\frac{7}{3}}{-8}\)

= \(-\frac{7}{24} = -0.2917\)

\(\beta = \tan^{-1} (-0.2917) = -16.26°\)

(ii) Let the angle between m and n be \(\theta\).

\(m \cdot n = |m||n| \cos \theta\)

\(\cos \theta = \frac{m \cdot n}{|m||n|}\)

\(m \cdot n = (6i + 8j) \cdot (-8i + \frac{7}{3}j)\)

= \(-48 + \frac{56}{3}\)

= \(\frac{-88}{3}\)

\(\cos \theta = \frac{-\frac{88}{3}}{10 \times \frac{25}{3}}\)

= \(\frac{-88}{250}\)

\(\cos \theta = -0.352\)

\(\theta = \cos^{-1} (-0.352) = 110.61°\)

(b) For PQ to be perpendicular to RS, the angle between them should be 90°. That is, \(\cos \theta = 0\).

\(\overrightarrow{PQ} = \begin{pmatrix} 10 \\ 4 \end{pmatrix} - \begin{pmatrix} -2 \\ 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 1 \end{pmatrix}\)

\(\overrightarrow{RS} = \begin{pmatrix} 4 \\ 0 \end{pmatrix} - \begin{pmatrix} 3 \\ 12 \end{pmatrix} = \begin{pmatrix} 1 \\ -12 \end{pmatrix}\)

\(|PQ| = \sqrt{12^{2} + 1^{2}} = \sqrt{144 + 1} = \sqrt{145}\)

\(|RS| = \sqrt{1^{2} + (-12)^{2}} = \sqrt{1 + 144} = \sqrt{145}\)

\(\overrightarrow{PQ} \cdot \overrightarrow{RS} = (12i + j) \cdot (i - 12j)\)

= \(0\)

\(\overrightarrow{PQ} \cdot \overrightarrow{RS} = |PQ||RS| \cos \theta\)

\(\cos \theta = \frac{0}{(\sqrt{145})(\sqrt{145})} = 0\)

Correct Answer: C) J.J Thomson

Explanation

In 1898, JJ Thomson proposed a structure for the atom which had a positively charges spheres (+) in which negatively charged electrons (-) were embedded. Thomson knew that atoms had an overall neutral charge. Therefore, he reasoned that there must be a source of positive charge within the atom to counterbalance the negative charge on the electrons. This led Thomson to propose that atoms could be described as negative particles floating within a soup of diffuse positive charge. This model is often called the plum pudding model of the atom, due to the fact that its description is very similar to plum pudding, a popular English dessert