Estimate the area of a circle with R = 1m using the finite element method concept using the upper bound approach and simple triangle element. Plot the mesh convergence. Compare the upper- and lower-bound approaches' sensitivity analysis (mesh convergence). Find the number of elements that would result in an optimum answer.

Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. The following table shows the closing prices on September 22, 2015, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day. Tech Stocks Close Change AAPL (Apple) $113.40 -1.81 ADBE (Adobe Systems) $84.66 1.34 EBAY (eBay) $25.61 -0.31 MSFT (Microsoft) $3.90 -0.21 S (Sprint) $4.40 0.02 WIFI (Boingo Wireless) $8.51 0.56 Non-Tech Stocks ANF (Abercrombie & Fitch) $21.81 -0.02 в (Воeing) $133.99 -2.03 F (Ford Motor Co.) $13.91 -0.40 GE (General Electric) $25.10 0.01 GIS (General Mills) $57.12 0.33 JNJ (Johnson & Johnson) $93.26 0.13 On the morning of September 22, 2015, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. (a) How many possible collections are possible?…

Rain is designing a new bottle for Luscious Curls shampoo. The bottle should have a volume of 450 cm³. The company they work for wants to minimize the amount of plastic used per bottle, however the company would like to have a choice between two B3 of three shapes; a cylinder, triangular prism, or rectangular prism. Help Rain to determine the most efficient dimensions of the two most efficient shapes for the bottle with the minimum surface area.Also calculate the surface area of the shapes. Show your work. Bottle choice 1 Bottle choice 2 Bottle choice 1 Bottle choice 2 show your work here Shape and dimensions Shape and surface area