Michael and his friend Justine enjoy hiking. Michael started up a mountain before Justine, so he’s closer to the top when Justine starts hiking. Michael is 320 yards from the top and hikes 80 yards per hour. Justine is 390 yards from the top. But she doesn’t know how many yards she hikes per hour. So every half hour, she writes down the yards left to hike in a table, as shown here. Part A Start by finding points for Michael’s function. What are two points you could use to graph Michael’s function for the yards left to hike in terms of the time he’s spent hiking since Justine started?

Part B What are two points that represent Justine’s function for the yards left to hike in terms of the hours she’s spent hiking?

Part C Could you graph the two functions from the information in the two previous parts? Explain your answer.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12