Question 1 a) The straight line 7y=3x -6intersects with x-axis at point A. Another straight line x+ 3y -18=0 intersects with y-axis at point B. These two straight lines intersect each other at point C. (i) Find the coordinates for points A, B and C. (ii) If O is the origin (0,0), show that line OC is perpendicular to line AB. bj Consider the following equations which represents the relationship between p (price per unit in dollars) and q (number of units sold for a certain product): p=644-6q-q' and p= (q+12) (i) Determine which equation is the demand equation. Give your reason. (ii) Find the equilibrium price and quantity. Question 2 Josh is retiring and has the choice of two benefits options under his company's pension plan. Option A: Receive a guaranteed payment of $2100 at the end of each month for 20 years. Option B: Receive a lump-sum payment equal to the future value of the payments described under option A- (1) Find the sum of the payments under option A. (ii) Find the lump-sum payment under option B assuming that interest rate is 6% compounded monthly. (ili) Which pension plan is the better choice for Josh and why? Question 3 Differentiate each of the following function with respect to x. Simplify the answer. (1) f(x) =(2-x)(5+x) (ii) y=w* and u = 2x]