111. To find out how long a person could remain in air at the same temperature, we can use the information given that the cold water removes body heat 25 times faster than air at the same temperature. So if a person has between 30 and 90 seconds to get out of the water, we can divide this range by 25 to find the equivalent range for air.
If we divide 30 seconds by 25, we get 1.2 seconds, and if we divide 90 seconds by 25, we get 3.6 seconds.
Therefore, a person could remain in air at the same temperature for anywhere between 1.2 seconds and 3.6 seconds.
81. According to Albert Einstein's theory of relativity, if a person travels at nearly the speed of light, time slows down significantly. The formula to calculate the time dilation is given as follows:
T(v) = To * sqrt(1 - (v/c)^2)
In the formula, T(v) represents the time experienced by the twin in the spaceship, To represents the time experienced by the twin on Earth, v represents the velocity of the spaceship, and c represents the speed of light.
To find out how much the twin in the spaceship ages, we need to know the value of v. Without that information, we cannot calculate the specific age.
21. To analyze whether the given model represents the data in the table exactly, we need to substitute the values from the table into the given equation and check if it matches.
Plugging in the provided values:
For t = 0, P(t) = - (1/300)(0)^2 + (53/30)(0) + 100 = 100
For t = 20, P(t) = - (1/300)(20)^2 + (53/30)(20) + 100 ≈ 134
For t = 30, P(t) = - (1/300)(30)^2 + (53/30)(30) + 100 ≈ 150
For t = 50, P(t) = - (1/300)(50)^2 + (53/30)(50) + 100 ≈ 180
Comparing these calculated values with the data in the table, we can see that the model does fit the data exactly.
(b) P*(60) refers to the value of P(t) when t is equal to 60 seconds. In this situation, it would represent the heart rate of the athlete 60 seconds into the race. The significance of this value would depend on the context and purpose of the analysis.
The domain of P, in this case, would be the range of values of t that are meaningful in the given situation. Since the race lasts 50 seconds, the domain of P would likely be from 0 to 50 seconds.
69. To find the number of motor vehicle deaths in each of the two years, we can set up a proportion based on the given information.
Let x represent the number of deaths in 1912.
Then, the number of deaths in 2003 would be 13.75x.
According to the given information, the number of deaths in 2003 is 39,525 more than in 1912. So we can set up the equation:
13.75x - x = 39,525
Simplifying the equation:
12.75x = 39,525
Dividing both sides by 12.75:
x = 3,100
Therefore, the number of motor vehicle deaths in 1912 was 3,100, and in 2003 it was 13.75 * 3,100 = 42,625.