Explanation

Ghusl becomes obligatory for seven causes, and theghusl for each of these different causes has different names:

• Ghusl Janabat isghusl performed after sexual intercourse or ejaculation.
• Ghusl Hayd is following menstruation.
• Ghusl Nifas is following lochia.
• Ghusl Mayyit isghusl performed on a dead Muslim.

In some denominations, two further categories obligate ghusl:

• Ghusl Istihada is for irregular bleeding (in women).
• Ghusl Mas-hil Mayyit becomes obligatory if one directly touches a dead body.
• Ghusl also becomes obligatory following a vow or oath to perform it.

Correct Answer: C. no lungs

Correct Answer: C) CHCl₃

Correct Answer: A) Abishai

Explanation

The question is asking which person made the statement God has given your enemy into your hand this day, now, therefore, let me pin him to the earth with one stroke of the spear, and I will not strike him twice to David. The options are Abishai, Abner, Ahimelech, and David's armour bearer.

The correct option is A, Abishai. In 1 Samuel 26:8-9, Abishai said this to David when they came across Saul sleeping in the camp. David had the opportunity to kill Saul but he chose not to, and instead took Saul's spear and water jug as proof that he could have killed him.

This statement by Abishai shows his eagerness to help David defeat his enemy, Saul. It also highlights the importance of mercy and forgiveness, which are values that Christians are encouraged to uphold.

In summary, Abishai made the statement God has given your enemy into your hand this day, now, therefore, let me pin him to the earth with one stroke of the spear, and I will not strike him twice to David. This shows his eagerness to help David defeat Saul, but David chose not to kill Saul, instead opting to show mercy and forgiveness.

Correct Answer: D. conurbation

Correct Answer: A. neglects the log in his own eyes

Correct Answer: B. Ration

Correct Answer: A. deceased

Correct Answer: D. Presence of vascular system

Explanation

(a) \(p = (4i - 3j) ; q = (-i + 5j)\)

\(2p + 3q = \begin{pmatrix} 8i - 3i \\ -6j + 15j \end{pmatrix}\)

= \(\begin{pmatrix} 5i \\ 9j \end{pmatrix}\)

Let \(r = k \begin{pmatrix} 5i \\ 9j \end{pmatrix} = \begin{pmatrix} 5ki \\ 9kj \end{pmatrix}\)

\(|r| = \sqrt{(5k)^{2} + (9k)^{2}} = 15\)

\(\sqrt{25k^{2} + 81k^{2}} = 15 \implies 25k^{2} + 81k^{2} = 225\)

\(106k^{2} = 225 \implies k^{2} = \frac{225}{106} = 2.123\)

\(k = \sqrt{2.123} = 1.457\)

\(\therefore r = \begin{pmatrix} 5i \times 1.457 \\ 9j \times 1.457 \end{pmatrix}\)

= \(\begin{pmatrix} 7.285i \\ 13.113j \end{pmatrix}\)

(b)(i)

Resolve the forces along the x and y- axis.

Let \(F_{1} = \begin{pmatrix} 8 \cos 120° \\ 8 \sin 120° \end{pmatrix}\)

\(F_{2} = \begin{pmatrix} 6 \cos 90° \\ 6 \sin 90° \end{pmatrix}\)

\(F_{3} = \begin{pmatrix} 4 \cos 30° \\ 4 \sin 30° \end{pmatrix}\)

\(R = F_{1} + F_{2} + F_{3}\)

= \(\begin{pmatrix} 8 \cos 120° \\ 8 \sin 120° \end{pmatrix} + \begin{pmatrix} 6 \cos 90° \\ 6 \sin 90° \end{pmatrix} + \begin{pmatrix} 4 \cos 30° \\ 4 \sin 30° \end{pmatrix}\)

= \(\begin{pmatrix} -8 \cos 60° \\ 8 \sin 60 \end{pmatrix} + \begin{pmatrix} 6 \cos 90° \\ 6 \sin 90° \end{pmatrix} + \begin{pmatrix} 4 \cos 30° \\ 4 \sin 30° \end{pmatrix}\)

= \(\begin{pmatrix} -8 \times 0.5 \\ 8 \times 0.866 \end{pmatrix} + \begin{pmatrix} 6 \times 0 \\ 6 \times 1 \end{pmatrix} + \begin{pmatrix} 4 \times 0.866 \\ 4 \times 0.5 \end{pmatrix}\)

= \(\begin{pmatrix} -4 + 0 + 3.464 \\ 6.928 + 6 + 2 \end{pmatrix}\)

= \(\begin{pmatrix} -0.536 \\ 14.928 \end{pmatrix}\)

\(|R| = \sqrt{(-0.536)^{2} + (14.928)^{2}} = \sqrt{0.2873 + 222.8452}\)

= \(\sqrt{223.1325} = 14.94N\)

(ii)Direction \(\theta\)

\(\tan \theta = \frac{14.928}{-0.536} = -27.851\)

\(\theta = -87.9° = 92.1°\)

The direction is N 02.1° W or a bearing of 267.9°.