A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin string, four beats are heard every second. Next, a bit of tape is put onto each tine of the tuning fork, and the tuning fork now produces five beats per second with the same mandolin string. What is the frequency of the string?

The average atmospheric pressure on earth is approximated as a function of altitude by the relation patm = 101.325 (1 − 0.02256z)5.256, where patm is the atmospheric pressure in kpa, and z is the altitude in km with z = 0 at sea level. determine the approximate atmospheric pressures at atlanta (z = 306 m), denver (z = 1610 m), mexico city (z = 2309 m), and the top of mount everest (z = 8848 m).