7 (a) The variables x and y are connected by the equation y=3 +x - x^2/2. Some corresponding values of x and y are given in the table below. (i) Complete the table. (ii) Using a scale of 2 cm to 1 unit, draw a horizontal x-axis for -3 =< x =< 5. Using a scale of 1 cm to 1 unit, draw a vertical y-axis for -5 =< y =< 5. Draw the graph of y=3 +x - x^2/2 for -3 =< x =< 5. (iii) By drawing a tangent, estimate the gradient of the curve at (3, 1.5). (iv) The points of intersection of the graph of y=3 +x - x^2/2 and the line y = k are the solutions of the equation 10 + 2x - x^2 = 0. (a) Find the value of k. (b) By drawing the line y = k on your graph, find the solutions of the equation 10 + 2x - x^2 = 0. (b) This is a sketch of the graph of y = pa^x, where a > 0. The graph passes through the points (0, 4) and (2, 36). (i) Write down the value of p. (ii) Find the value of a. (iii) The graph passes through the point (4, q). Find the value of q.