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.

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.

Rebel technology maintains its records using cash-basis accounting. during the year, the company received cash from customers, $43,000, and paid cash for salaries, $23,500. at the beginning of the year, customers owe rebel $1,000. by the end of the year, customers owe $6,600. at the beginning of the year, rebel owes salaries of $5,600. at the end of the year, rebel owes salaries of $3,300. determine cash-basis net income and accrual-basis net income for the year.

On december 31, 2016, the decarreau, andrew, and bui partnership had the following fiscal year-end balance sheet: cash $10,000accounts receivable $20,000inventory $25,000plant assets - net $30,000loan to decarreau $18,000total assets $103,000accounts payable $14,000loan from bui $15,000decarreaua, capital (20%) $32,000andrew, capital (10%) $23,000bui, capital (70%) $19,000total liab./equity $103,000the percentages shown are the residual profit and loss sharing ratios. the partners dissolved the partnership on january 1, 2017, and began the liquidation process. during july the following events occurred: * receivables of $18,000 were collected.* all inventory was sold for $15,000.*all available cash was distributed on january 31, except for$8,000 that was set aside for contingent expenses.the book value of the partnership equity (i.e., total equity of the partners) on december 31, 2016 isa. $58,000b. $71,000c. $66,000d. $81,000