Assignment:
Q1. Solve for x algebraically.
log3x + log3(x + 6) = 3
Q2. Find the vertex, focus, and directrix of the parabola given by the equation.
(x - 2)2 = 8(y + 3)
Q3. Solve the system of equations.
x2 - 2y2 = 8
x2 + 3y2 = 28
Q4. Maximize C = 6x +7y with the constraints:
x + 2y < 16
5x + 3y < 45
Provide complete and step by step solution for the question and show calculations and use formulas.