Challenge yourself (6 points) 4. Global Positioning System (GPS) is a satellite-based navigation system made up of more than 20 satellites. Each satellite transmits a unique signal and orbital parameters that allow GPS devices, such as mobile phones, watches and cars, to compute the precise locations of the devices A GPS receiver uses this information and trilateration to calculate the distances between the receiver and several satellites, and determines a user's position There are three base stations that can send and receive signals from your mobile phone P Suppose that, in a rectangular coordinate system, the locations of the three base stations A. B and C are (0,0), (36.0) and (16,32) respectively (1 unit represents 1km). It is found that the distance between P and the three base stations A. B and C are 29 km, 25 km and 13 km respectively. Assume that A, B. C and P lie on the same horizontal plane. Find the coordinates of the point P. (Hint: find the intersection of the 3 circles) 5. A design for a cooling tower project is shown in the figure. Find the equation of the hyperbola that models the sides of the cooling tower. Assume that the center of the hyperbola-indicated by the intersection of dashed perpendicular lines in the figure-is the origin of the coordinate plane. Round final values to four decimal places. 72 m 79.6 m 60 m page 56 179.6 m se of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting