Created by T Madas Question 181 (****) y ( y = x − 12 x + 35 ) R L1 Q P O x S L2 The figure above shows the curve with equation ( ) y = x − 12 x + 35 The curve crosses the x axis at the points P ( x1, ) and Q ( x2 ,0 ) , where x2 > x1 The tangent to the curve at Q is the straight line L1 a) Find an equation of L1 The tangent to the curve at the point R is denoted by L2 It is further given that L2 meets L1 at right angles, at the point S b) Find an equation of L2 c) Determine the exact coordinates of S ( C1Q , y = x − , y + x = 31 , S , − 2 Created by T Madas ) Created by T Madas Question 182 (****) y P y = 11 − x − Q x2 S R O y =1 x The figure above shows the curve C with equation y = 11 − x − x2 , x ≠ The straight line with equation y = meets C at the points P , Q , R and S , where R and S have positive x coordinates, as shown in the figure Find the area of the finite region bounded by C and the line segment RS 16 Created by T Madas Created by T Madas Question 183 (****) y x y x The figure above shows the design for an earring consisting of a quarter circle with two identical rectangles attached to either straight edge of the quarter circle The quarter circle has radius x cm and the each of the rectangles measure x cm by y cm The earring is assumed to have negligible thickness and treated as a two dimensional object with area 12.25 cm a) Show that the perimeter, P cm , of the earring is given by P = 2x + 49 2x b) Find the value of x that makes the perimeter of the earring minimum, fully justifying that this value of x produces a minimum perimeter c) Show that for the value of x found in part (b), the corresponding value of y is −π ) 16 ( MP1-H , x = 3.5 Created by T Madas