A trough has a trapezoidal cross section with a height of T T m and horizontal sides of width 5 m and 7 m. Assume the length of the trough is 12 m. See the figure to the right. Complete parts (a) and (b) below. a. How much work is required to pump the water out of the trough (to the level of the top of the trough) when it is full? Use 1000 kgrm3 for the density of water and 9.8 mrs2 for the acceleration due to gravity. Draw a y-axis in the vertical direction (parallel to gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For 0 5 y s 7, find the cross-sectional area My) in terms of y. Am = D (Simplify your answer. Use integers or fractions for any numbers in the expression.) A water tank, shown to the right, is shaped like an inverted cone with height 6 m and base radius 1-51\" 1.5 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank -. /[ and out of the tank? Use 1000 kg,'m3 forthe density of water and 9.8 meQ for the acceleration due ,r 6 m to gravity. b. Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain. a. Draw a y-axis in the vertical direction (parallel to gravity) and choose the bottom of the tank as the origin. For 0 s y s 6, find the cross-sectional area My) in terms of y. Y2 ' TE N?) = W (Simplify your answer. Type an exact answer, using it as needed. Use integers or fractions for any numbers in the expression.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of A 50-m-Iong chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and that the chain has a density of 4 kgfm. Use 9.8 mi's2 for the acceleration due to gravity. a. How much work is required to wind the entire chain onto the cylinder using the winch? b. How much work is required to wind the chain onto the cylinder if a 25-kg block is attached to the end of the chain? a. Set up the integral that gives the work required to wind the entire chain onto the cylinder using the winch. Use increasing limits of integration. Judy (Type exact answers.) Suppose a force of 60 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, nd the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position? c. How much work is required to stretch the spring 0.6 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. k = (Type an integer or a decimal.) Find the mass of the thin bar with the given density function. p(x) = 1 + sin x; for SXS 4 The mass of the thin bar is units. (Type an exact answer.)Find the area of the surface generated when the given curve is revolved about the x-axis. x3 1 1.: