Let S be the flat-bottomed solid whose base is the region of the xy plane delimited by the curves y=ex, y=-2, x-1 and x-3, and whose sections perpendicular to the x-axis are semicircles whose diameter lies in the xy plane. a) Determine the area A(x) of the section of S by the plane of the abscissa points x . A(x)= b) Determine the volume of S to within 10.01. #6- *** 5 m 6 m 2 m A tank has the shape of a right prism whose parallel extremities are isosceles triangles, as in the figure above. It is 5m high, 2m wide and 6m long, and it is filled with water. We want to calculate the work required to pump all of its water through the pipe 3 m above the tank. (i) Let x be the height in meters measured from the bottom of the reservoir. The weight of a thin layer of water between heights x and x+Ax is approximately P(x)^x What is P(x)? P(x)= Preview Change entry mode Express the answer with a formula. We recall that the density of water is p=1000Kg/m3 and that the gravitational acceleration at the surface of the earth is g=9.8m/s2. (ii) The work in Joules required to pump this thin layer of water 3 m above the reservoir is approximately w(x)Ax. What is w(x)? W(x)= Preview Change entry mode Express the answer with a formula. (iii) Using the previous results, determine the work required to pump all the water 3 m above the reservoir. Give its numerical value to within 3 significant digits. #7-A cable that weighs 5 N/m is used to raise 80 N of ore from the bottom of a shaft 80 meters below. (i) Suppose that at some point x meters of cable have been brought to the surface. Then the work to go up Ax meters more is about w(x)Ax. What is w(x)? W(x)= Express your answer with a formula. (ii) What, in Joules, is the work required to bring the ore to the surface?