(Modeling) Height of a Satellite Artificial satellites that orbit Earth of...

(Modeling) Height of a Satellite Artificial satellites that orbit Earth often use VHF signals to communicate with the ground. VHF signals travel in straight lines. The height h of the satellite above Earth and the time T that the satellite can communicate with a fixed location on the ground are related by the model

where R = 3955 mi is the radius of Earth and P is the period for the satellite to orbit Earth. (Source: Schlosser, W., T. Schmidt-Kaler, and E. Milone, Challenges of Astronomy, Springer-Verlag.)

(a) Find h to the nearest mile when T = 25 min and P = 140 min. (Evaluate the cosine function in degree mode.)

(b) What is the value of h to the nearest mile if T is increased to 30 min?