Newton's law of cooling says the rate of change of temperature is proportional to the difference between the object's temperature and the temperature of the environment.
Here, the object starts out at 200 °F, which is 133 °F greater than the environment temperature. 10 minutes later, the object is 195 °F, so is 128 °F greater than the environment. In other words, the temperature difference has decayed by a factor of 128/133 in 10 minutes.
The solution to the differential equation described by Newton's Law of Cooling can be written as the equation
T(t) = 67 + 133*(128/133)^(t/10)
where T is the object's temperature in °F and t is the time in minutes from when the object was placed in the 67 °F environment.
The equation
T(t) = 180
can be solved analytically, but it can be a bit easier to solve it graphically. A graphing calculator shows it takes
42.528 minutes for the temperature of the coffee to reach 180 °F.
Answer:
Step-by-step explanation:
Air pressure is measured in pascals. For a professional American football game, the ball should be inflated to about 90,000 pascals. Scientists studied the effects of air temperature on the pressure inside American footballs by taking these steps:
1. Prepare 100 footballs.
2. Measure each football's air pressure.
3. Divide footballs into 10 groups.
4. Place the groups in different lockers cooled to different air temperatures.
5. After 12 hours, remove the footballs from lockers.
6. Measure each football’s pressure again.
7. Compare the new pressures to the starting pressures.
What two terms best describe the variable "air pressure inside the football" in this experiment?
independent, qualitative
independent, quantitative
dependent, qualitative
dependent, quantitative
Answer:
−25x^2+5x−1/2
Step-by-step explanation: