9. [-/8 Points] DETAILS LARHSCALC1 4.AP.009. MY NOTES ASK YOUR TEACHER As a pot of coffee cools down, the temperature of the coffee is modeled by a differentiable function C, for 0 s t s 12, where time t is measured in minutes and the temperature C(t) is measured in degrees Celsius. Selected values of t are shown in the table. (minutes) 3 5 7 12 C(t) (degrees Celsius) 68 59 52 47 45 40 (a) Evaluate "c'(t) dt. Indicate units of measure. 0 . ---Select--- :..... -Select-- Explain the mear .C per minute ver in the context of the problem. minutes The value minutes per "C represents the ---Select--- from t = 0 to t = 12.Explain the meaning of your answer in the context of the problem. 12 : ......................................................... : The value eff C'{t] aft represents the: Se|et:t v from t = D to t = 12. u =' -Select '= average temperature 12 average rate of temperature loss 1 {h} Explain the meaning of C{t} cit in the maaimum rate of temperature I055 12 0 minimum temperature total temperature lost ('1') 1 12 {h} Explain the meaning efE C(t} cit in the context of the problem. I] 1 12 E ......................................................... : The value of _ C(t} tit represents the_ from t = D to t = 12. 12 u " Select average temperature average rate of temperature loss maslmum rate of temperature less Cit} aft. Indicate units I mInImum temperature :| total temperature lost Use a trapezoidal sum with 5 subintervals indicate- Use a trapezoidal sum with 5 subintervals indicated by the table to approximate 1 120 C(t) dt. Indicate units of measure. (Round your answer to one decimal place.) --Select--- :...... -Select- c) Use the data .C "C per minute proximate the rate, in C per minute, at which the temperature is changing at time t = 6. (Round your answer to one decimal place.) minutes minutes per c(c) Use the data in the table to approximate the rate, in "C per minute, at which the temperature is changing at time t = 6. (Round your answer to one decimal place.) .C per minute (d) For 12 s t S 15, the rate of cooling is modeled by C'(t) = -2 cos(0.5t). Based on the model, what is the temperature of the coffee, in .C, when t = 15? Assume C(t) is continuous at t = 12. (Round your answer to two decimal places.) OC