Hello I need some help with these 4 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. A window has the shape of a rectangle, topped by a semicircle, as shown. The perimeter of the window is 8 m. Determine an O equation that could be used to express the area of the window in terms of its width. Express this as a function, A(w). You need not solve the problem. O O 2. An oil pipeline will connect points A and B which are 3 km apart and on opposite banks of a 1 km wide river. From point A to point C on the opposite bank, the pipeline will run under the water. From point C to point B the pipeline will run above ground. The cost of running the pipeline under water is three times the cost 3 km of running it above ground. Determine an equation that can be used to minimize the cost. You need not solve the problem. Determining Boundaries 3. A wire 60 cm long is to be cut into two pieces. One of the pieces will be bent into the shape of a square and the other into the shape of an equilateral triangle, as shown in the diagram below: 60 cm x cm 60 - xcm 60- X & cm -cm The wire is to be cut in order that the sum of the areas of the square and the triangle is to be a maximum. An equation that can be used to model the sum of the areas is A (x = V3 (60-x) 36 Determine the boundaries and the corresponding areas. You need not solve further. 4. A cylindrical tank is to have a capacity of 1000 m3. It is to fit into a foundry that is 12 m wide with a height of 11 m. The base of the tank will cost half as much as the top. The metal for the side of the tank will cost four fifths as much as the top. An equation that can be used to model the cost of the tank is C(r) = zar2 + 1600 Determine any restrictions on r. You need not solve further