a) The distance d that can be seen from horizon to horizon from an airplane varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950 m, find d for h = 5250 m.
b) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If V = 250 cm^{3 }when T = 200° C and P = 130 kPa, what is the volume when T = 170°C and P = 130 kPa?
c) The acceleration of gravity g on a satellite in orbit around the earth varies inversely as the square of its distance r from the center of the earth.
If g = 8.7 m/s^{2} for a satellite at an altitude of 400 km above the surface of the earth, find g if it is 1000 km above the surface.
The radius of the earth is 6 6.4×10 m.