Rate of electromagnetic radiation

A nearby star that was recently discovered and found to have a surface temperature of 3,042 K and a radius of 15.4% of the Sun’s radius. After continuous observations, scientists observed periodic dips in the light of the star and determined that a planet was orbiting around it at 48.57 mAU.

a) Calculate the rate of electromagnetic radiation from the surface of this star.   [3 pts]

b) Calculate the radiation flux at the planet’s distance.   [3 pts]

c) Calculate the surface temperature of the planet. You may assume that it acts as a blackbody and that it radiates as much thermal radiation as it receives.   [2 pts]

d) Calculate the maximum frequency corresponding to the radiated spectrum produced by the star based on the temperature.