The point P(9, −2) lies on the curve y = 2/(8 − x). (a) If Q is the point (x, 2/(8 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 8.9 mPQ = (ii) 8.99 mPQ = (iii) 8.999 mPQ = (iv) 8.9999 mPQ = (v) 9.1 mPQ = (vi) 9.01 mPQ = (vii) 9.001 mPQ = (viii) 9.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(9, −2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(9, −2).

896.31 cm= km 100cm = 1m 1000m = 1km a) 0.0089631 b) 0.0089631 c) 8.9631 d) 89.631

Determine the difference: 3.2 × 1010 – 1.1 × 1010. write your answer in scientific notation.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.