This is a problem in batch processing of materials using a mixing tank. The mixing tank has inflow and outflow tubes and a stirrer that keeps the concentration uniform at all points in the tank. The tank is initially filled by a volume V of solution, formed by dissolving a given solute in a solvent, with concentration C0 (measured in kg/l); The inflow tube carries a solution of different concentration Cin than the initial concentration; the volumetric flowrate is Qin The outflow flowrate is Qout and, due to the well-mixed assumption, the outflow concentration has the same concentration as the instantaneous concentration of the tank. (i) Derive the differential equation governing the instantaneous concentration in the tank.

Need help with (c) and (d) Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m3): x 88 177 182 354 369 442 970 y 0.39 0.60 0.50 0.66 0.61 0.69 0.92 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy?   (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.)   (c) The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a…

I got an answer but I think I did something wrong because my answer seems quite astronomical in pricing.

After coming back from the sets of “Nailed it!" Jacques decided to bake a pyramid shaped gradient chocolate cake. A gradient cake is where the chocolate is not homogeneously mixed, rather the density of the chocolate is different at different layers. Suppose the square-base of the pyramid has length 4 inches and the height of the pyramid is 8 inches. The density of the chocolate is given by the function f (y) =% 8/in³, where y is the height of the layer measured from the bottom of the cake. Find the total amount of chocolate that Jacques will need to bake his cake. 8