1. Longitude and Latitude:

A ship is located at a point with coordinates 30°N, 45°E. If the ship sails 100 km due north, calculate the new coordinates of the ship. Assume the Earth is a perfect sphere and use the approximation that 1 degree of latitude is approximately 111 km.

2. Logarithm:

Given the logarithm table, if log₁₀(2) ≈ 0.301 and log₁₀(5) ≈ 0.699, calculate log₁₀(20) using the properties of logarithms.

3. Simultaneous Equations (Elimination Method):

Solve the following simultaneous equations using the elimination method:

3x + 4y = 10
2x - 5y = -4

4. Simultaneous Equations (Substitution Method):

Solve the following simultaneous equations using the substitution method:

x + 2y = 7
3x - y = 8

5. Matrix Method (2x2 and 3x3):

a) Solve the simultaneous equations using a matrix method:

x + 2y = 3
2x + 3y = 5

b) Solve the following system of equations using a 3x3 matrix:

x + y + z = 6
2x - y + 3z = 14
-x + 4y + z = 2