Please show your work.

C. Let's say we wanted to observe this star from a small telescope with a V limit of 10 mag. Could we do it? {3pts) D. What is the distance to the star forming region that hosts this star? (3pts) 5. Let's say that star in Question 4 explodes as a supernova increasing its luminosity by a factor of 50,000 and the supernova remnant. A. What are the new values of the intrinsic apparent and absolute magnitudes? {10pts) B. If the angular resolution of the Hubble Space Telescope was 0.05 arc seconds (Note this similar to the James Webb Space Telescope), how fast would the ejecta have to move in order to see it after only 2 days? Is this a reasonable speed? {10pt) 4. A star in the night sky has the stellar type 05V has an intrinsic color index of (B-V)0 = -0.32 and a magnitude of V0 = 4, MV,0 = -5.7 and is embedded in a young, dusty, star forming region with an E(B-V) = 0.20 mag