In addition to being computed directly, the following integrals may be computed by applying one or more of the following theorems. (a) −0.1 r · d r c where c is the line segment from (3, 0, 8) to (−2, 7, 1). which of the following theorems can be used? select all that apply. fundamental theorem of line integrals green's theorem divergence theorem stokes' theorem (b) 2x i + 4y j + 18z k · d a s where s is the sphere of radius 4 centered at (0, 5, −4). which of the following theorems can be used? select all that apply. fundamental theorem of line integrals green's theorem divergence theorem stokes' theorem (c) (−9x+20y) i + (7x−8y) j · d r c where c is a square of side 8 in the xy-plane, traversed counterclockwise with center at (3, 5, 0). which of the following theorems can be used? select all that apply. fundamental theorem of line integrals green's theorem divergence theorem stokes' theorem

Sketch one cycle if the cosine function y=2cos2theta

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? )

Which graph of a hyperbola represents the equation 16x^2-y^2=16