2. The course of a river is modelled by the curve r(z) =-x4 + 12x3-54x2 + 110x-85. A straight highway is built that intersects the river at two points, whose x-coordinates are x-3/2 and x-9/2. Let L...
2. The course of a river is modelled by the curve r(z) =-x4 + 12x3-54x2 + 110x-85. A straight highway is built that intersects the river at two points, whose x-coordinates are x-3/2 and x-9/2. Let L denote the land which now lies enclosed between the river and the highway. A straight railway is proposed that will meet the river at two points with x-coordinates x = 3 and x = 34/3 + 6). This will divide L into two pieces, L1 and L2, where Lı is the piece containing the point (3,0) (a) Find the equation h(r) for the route of the highway. b) Find the equation R(r) for the proposed route of the railway. (c) Find a relation for the points in L1 and a separate relation for the points in L2 (d) Find the area of Li and the area of L2. Which is larger?
2. The course of a river is modelled by the curve r(z) =-x4 + 12x3-54x2 + 110x-85. A straight highway is built that intersects the river at two points, whose x-coordinates are x-3/2 and x-9/2. Let L denote the land which now lies enclosed between the river and the highway. A straight railway is proposed that will meet the river at two points with x-coordinates x = 3 and x = 34/3 + 6). This will divide L into two pieces, L1 and L2, where Lı is the piece containing the point (3,0) (a) Find the equation h(r) for the route of the highway. b) Find the equation R(r) for the proposed route of the railway. (c) Find a relation for the points in L1 and a separate relation for the points in L2 (d) Find the area of Li and the area of L2. Which is larger?