We can use this power series to approximate the constant  . a) First, evaluate arctan(1) . (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for  . (The answer will be just a series – not a power series.) c) Verify that the series you found in part (b) converges. d) Use your convergent series from part (b) to approximate  with |error| < 0.5. e) How many terms would you need to approximate  with |error| < 0.001?

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

Match each whole number with a rational, exponential expression 3 square root 27^2find the domain and range of the exponential function h(x)=125^x. explain your findings. as x decreases does h increase or decrease? explain. as x increases does h increase or decrease? explain.

Which is the graph of the linear equation x – 2y = 6?