For which values of c is the topological space xc : = {(x, y) € c^2 e: x^2 - y^2 = c} a riemann surface? you do not need to explicitly construct charts, but you do need to prove your answer is correct. (warning: use the implicit function theorem to produce a complex structure. the hardest part is proving that x. is not a manifold for certain values of c. if you get stuck, try drawing a picture.)

Even if a person is in very good shape, applying to be a police officer requires commitment to fitness. applicants must pass a physical fitness test. in order to prepare for the test, janet purchases an activity tracker to court her steps. her goal is to walk 10,000 steps each day. she measures heard average step length to be 30 inches. play janet runs, her average steps length increases to 36 in. how many steps would she have to take to run 1 mile 50280 round to the nearest step