Bacterial metabolism can be harnessed to generate electricity.

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Please write down the equation that we use to solve for dynamic problems on a piece of paper.  Take a photo of that paper and upload it. 

With the same amount of torque applied, which of the following generates a greater angular acceleration?

Praxilla, who lived in ancient Greece, derives utility from reading poems and from eating cucumbers. Praxilla gets 30 units of marginal utility from her first poem, 27 units of marginal utility from her second poem, 24 units of marginal utility from her third poem, and so on, with marginal utility declining by three units for each additional poem. Praxilla gets six units of marginal utility for each of her first three cucumbers consumed, five units of marginal utility for each of her next three cucumbers consumed, four units of marginal utility for each of the following three cucumbers consumed, and so on, with marginal utility declining by one for every three cucumbers consumed. A poem costs three bronze coins, but a cucumber costs only one bronze coin. Praxilla has 18 bronze coins. Sketch Praxilla’s budget set between poems and cucumbers, placing poems on the vertical axis and cucumbers on the horizontal axis. Start off with the choice of zero poems and 18 cucumbers, and calculate the changes in marginal utility of moving along the budget line to the next choice of one poem and 15 cucumbers. Using this step-by-step process based on marginal utility, create a table and identify Praxilla’s utility-maximizing choice. Compare the marginal utility of the two goods and the relative prices at the optimal choice to see if the expected relationship holds. Hint: Label the table columns: 1) Choice, 2) Marginal Gain from More Poems, 3) Marginal Loss from Fewer Cucumbers, 4) Overall Gain or Loss, 5) Is the previous choice optimal? Label the table rows (underneath the column titles): 1) 0 poems and 18 cucumbers, 2) 1 poem and 15 cucumbers, 3) 2 poems and 12 cucumbers, 4) 3 poems and 9 cucumbers, 5) 4 poems and 6 cucumbers, 6) 5 poems and 3 cucumbers, 7) 6 poems and 0 cucumbers.

Table 15-3The table represents a demand curve faced by a firm in a competitive market.​ Quantity Demanded (Units) Total Revenue (Dollars) 12 132 13 143 14 154 15 165 16 176  Refer to Table 15-3. For this firm, the marginal revenue of the 13th unit is

Which of the following represents the firm’s short-run condition for shutting down?

Education yields positive externalities. For example,

The following table shows the units of output a worker can produce per month in the U.S. and France. Which of the following statements about comparative advantage is true?