Question

The town of coldwater had a sudden winter storm that caused temperatures to plummet during the storm the temperature T in degrees fahrenheit could be modeled by the function T(x) = 0.8x^2 - 16x + 60 where x is the number of hours since the storm began at noon. If the temperature as the storm began was 60f and the lowest temperature of the storm occurred at 10 what was the minimum temperature?

Answer 1

Answer: The average rate of change of temperature from 0 to 1.5 hours after the storm began is -3.445 degrees F per hour. The average temperature during the first 1.5 hours of the storm was 75.834 degrees F.To calculate the average rate of change of temperature, we need to find the change in temperature during the first 1.5 hours, which is the integral of the rate of change of temperature from 0 to 1.5. Thus,Average rate of change = (1/1.5) * ∫[0,1.5] t(h)dh= (1/1.5) * [2.34 - 8.64 + 13.3775 - 9.99]= -3.445 degrees F per hourTo calculate the average temperature during the first 1.5 hours, we need to find the average value of the temperature from 0 to 1.5 hours. Thus,Average temperature = (1/1.5) * ∫[0,1.5] [80 + t(h)] dh= (1/1.5) * [120 + 3.9 - 6.48 + 7.62 - 4.995]= 75.834 degrees FTherefore, The average temperature during the first 1.5 hours of the storm was 75.834 degrees F.

Step-by-step explanation: