Q:  What is the average apparent magnitude in the K filter for
              RR Lyrae stars in the cluster M3?

            The average of the K-band apparent magnitudes is about

                   m(K)  =  14.70



  Q:  The absolute magnitude of RR Lyrae stars in the K filter is approximately
              M(K) = -0.35

              What is the distance to the cluster M3?


           First, we compute the difference between apparent and absolute
           magnitudes, which is called the "distance modulus"

                   m(K) - M(K)  =  14.70 - (-0.35)  = 15.05  mag


           Next, we use the distance modulus formula to calculate the
           distance to the cluster:

                   (m - M)  =  15.05  =  5*log(d) - 5

                    5*log(d)  =  20.05

                      log(d)  =   4.01

                       d      =   10^(4.01)  =  10,200 pc