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.)

What power can you write to represent the volume of the cube shown? write the power as an expression with a base and an exponent and then find the volume of the cube

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.

From the beginning of the day the temperature rose 15 degrees so that by 4 pm it was 87 degrees. what was the temperature at the start of the day