Mr. Green’s hobby was restoring old houses. He recently purchased an old rundown house that needed a lot of repair, especially with the plumbing. The kitchen faucet dripped all day and night. It intrigued Mr. Green how much water dripped from this faucet in one day, but he surely didn’t want to sit and watch the faucet drip all day. So he figured that if he could discover how much water dripped within a certain time span, he could calculate the dripping rate for any time span. In his first observation he noted that 6 ounces of water dripped in 10 minutes. A) Using Mr. Green’s observation, can you help him figure out how much water would have dripped in only 5 minutes?

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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