Astring or rope will break apart if it is placed under too much tensile stress. thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. one type of steel has density 7890 kg/m3 and will break if the tensile stress exceeds 7.0×108n/m2. you want to make a guitar string from a mass of 4.0 g of this type of steel. in use, the guitar string must be able to withstand a tension of 900 n without breaking. your job is to determine (a) the maximum length and minimum radius the string can have; (b) the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.

Your company is starting a new r& d initiative: a development of a new drug that dramatically reduces the addiction to smoking. the expert team estimates the probability of developing the drug succesfully at 60% and a chance of losing the investment of 40%. if the project is successful, your company would earn profits (after deducting the investment) of 9,000 (thousand usd). if the development is unsuccessful, the whole investment will be lost -1,000 (thousand usd). your company's risk preference is given by the expected utility function: u(x) v1000 +x, where x is the monetary outcome of a project. calculate the expected profit of the project . calculate the expected utility of the project . find the certainty equivalent of this r& d initiative . find the risk premium of this r& d initiative e is the company risk-averse, risk-loving or risk-neutral? why do you think so?