Correct Answer: C. 3.6m3

Explanation

Before Jesus arrived Bethany, Lazarus had been buried for four days. Martha heard of Jesus' arrival and went to meet him. She told Jesus that if he (Jesus) had been around, his brother would not have died. She said that whatever Jesus asked of God, God would do it for him. Jesus replied that his brother (Lazarus) would rise again. Martha said she knew that her brother would resurrect in the last days. It was at this point that Jesus said. I am the resurrection and the life. He said that whoever believes in him, though he dies, yet shall live and whoever lives and believes in him shall never die. In another encounter, Jesus said to Thomas that in his father's house, there are many rooms and that if this were not so, he would not have said that he was going to prepare a place for them. After this, Jesus said that he would come again and take them to himself. He then said that they knew where he was going, but, Thomas replied that they did not, how then could they know the way. Jesus replied, I am the way and the truth, and the life; no one comes to the father, but by me .

Correct Answer: A. through representatives

Correct Answer: B. Transformation

Correct Answer: D. excise duties

Explanation

(a) \(a = \begin{pmatrix} 8 \\ 3 \end{pmatrix} ; b = \begin{pmatrix} 6 \\ -5 \end{pmatrix} ; c = \begin{pmatrix} 2 \\ -3 \end{pmatrix} ; |d| = \sqrt{41}\)

\(p = a + b - 2c\)

= \(\begin{pmatrix} 8 \\ 3 \end{pmatrix} + \begin{pmatrix} 6 \\ -5 \end{pmatrix} + 2\begin{pmatrix} 2 \\ -3 \end{pmatrix}\)

= \(\begin{pmatrix} 8 + 6 + 4 \\ 3 - 5 - 6 \end{pmatrix}\)

= \(\begin{pmatrix} 10 \\ -8 \end{pmatrix}\)

\(|p| = \sqrt{10^{2} + (-8)^{2}} = \sqrt{164}\)

\(|p| = 2\sqrt{41}\)

\(|d| = \frac{1}{2} |p|\)

\(\therefore d = \frac{1}{2} p = \frac{1}{2} \begin{pmatrix} 10 \\ -8 \end{pmatrix}\)

= \(\begin{pmatrix} 5 \\ -4 \end{pmatrix}\)

(b) A(3, 4) ; B(3, n).

\(OA = 3i + 4j ; OB = 3i + nj\)

\(OA \cdot OB = |OA||OB| \cos \theta\)

\((3i + 4j) \cdot (3i + nj) = |3i + 4j||3i + nj| \cos 30\)

\(9 + 4n = 5 (\sqrt{9 + n^{2}}) (\sqrt{3}{2})\)

\(2(9 + 4n) = 5(\sqrt{3(9 + n^{2})})\)

\(18 + 8n = 5\sqrt{27 + 3n^{2}}\)

Squaring both sides,

\(324 + 288n + 64n^{2} = 25(27 + 3n^{2})\)

\(324 + 288n + 64n^{2} = 675 + 75n^{2}\)

\(75n^{2} - 64n^{2} - 288n + 675 - 324 = 0\)

\(11n^{2} - 288n + 351 = 0\)

\(n = \frac{-(-288) \pm \sqrt{(-288)^{2} - 4(11)(351)}}{2(11)}\)

\(n = \frac{288 \pm \sqrt{82944 - 15444}}{22}\)

\(n = \frac{288 \pm \sqrt{67500}}{22}\)

\(n = \frac{288 \pm 259.81}{22}\)

\(n = \frac{288 + 259.81}{22} ; n = \frac{288 - 259.81}{22}\)

\(n = \frac{547.81}{22} ; n = \frac{28.19}{22}\)

\(n = 24.9 ; n = 1.28\)

Correct Answer: C. ii

Correct Answer: A. Virus

Correct Answer: C. fused ovaries

Correct Answer: A. healed Aeneas