Let R be the region bounded by the graph of y = -x- + 4 and the x-axis. A solid is generated when R is revolved around the horizontal line y = -1. What is the definite integral that gives the volume of this solid? O TT [2, [(-x2 +5)2 -1] dx O-x / 2 2( - x 2 + 5 ) 2 dx On 1 2,[(-x 2 + 4 ) 2 - 1] dx O- IT / 2 ( - x 2 + 4 ) 2 OxThe amount of water in a baby pool at noon is 137 gallons. Over the next 12 hours, the amount of water changes at a rate modeled by the differentiable function P, where P(t) is measured in gallons per hour and time t is measured in hours since noon. Which of the following is the best interpretation of [. P(t) dt? O The change in the amount of water in the pool, in gallons, between noon and 4 p.m. O The rate at which the amount of water is changing, in gallons per hour, at 4 p.m. O The amount of water in the pool, in gallons, at 4 p.m. The average amount of water in the pool, in gallons, between noon and 4 p.m.The region R is bounded by the graph of y = x- and the line y = 4. What is the volume of the solid formed by revolving R around the line y = 4? O 16AT 3 O 3 O 25610 15 5121 15At the time a cup of chili is served, its temperature is 170 degrees Fahrenheit. The chili's temperature is modeled by the function C, where C(t) is measured in degrees Fahrenheit and t is measured in minutes. The rate at which the temperature of the chili is decreasing is given by C(t) = 22e-0.05. According to the model, what is the approximate temperature of the cup of chili at t = 5 minutes? O 166.848 .F 97.328 -F 92.733 -F 0 77.267 . FThe base of a solid is the region in the rst quadrant between the graph of y = 1?, the line it = 4, and the xaxis. For each solid, each cross section perpendicular to the xaxis is an equilateral triangle. What is the volume of the solid? 02 5-17 256 O 5:: 64 O?J