The total luminosity of the stars in our galaxy isL≈3×1010L. Suppose that the luminosity of our galaxy has been constant for the past 10 Gyrs. How much energy has our galaxy emitted in the form of starlight during that time? Most starsare powered by the fusion of H into4He, with the release of 28.4 MeV for every helium nucleusformed. How many helium nuclei have been created within stars in our galaxy over the course ofthe past 10 Gyrs, assuming that the fusion of H into4He is the only significant energy source? Ifthe baryonic mass of our galaxy isM≈1011M, by what amount has the helium fraction Y ofour galaxy been increased over its primordial valueY4= 0.24?

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.