A dead body was found within a closed room of a house where the temperature was a constant 70° F. At the time of discovery the core temperature of the body was determined to be 85° F. One hour later a second measurement showed that the core temperature of the body was 80° F. Assume that the time of death corresponds to t = 0 and that the core temperature at the time was 98.6° F. Determine how many hours elapsed before the body was found. [Hint: Let t1 > 0 denote the time that the body was discovered.]

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Chapter87: An Introduction To G- And M-codes For Cnc Programming
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1. A dead body was found within a closed room of a house where the temperature was a constant 70° F. At the time
of discovery the core temperature of the body was determined to be 85° F. One hour later a second measurement
showed that the core temperature of the body was 80° F. Assume that the time of death corresponds to t = 0
and that the core temperature at the time was 98.6° F. Determine how many hours elapsed before the body was
found. [Hint: Let ti > 0 denote the time that the body was discovered.]
2. The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification
of Newton's Law of Cooling is
dT
= kS(T – Tm),
dt
where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time.
Initially, the temperature of the coffee is 200° F. The exposed surface area of the coffee in cup B is twice the
surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 120° F. If Tm = 70°
F, then what is the temperature of the coffee in cup B after 30 min?
(Turn Over)
3. A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. ASsuming
air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone.
4. The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming
Transcribed Image Text:3:51 Search Done Written Assignment 3-1 (1... 1. A dead body was found within a closed room of a house where the temperature was a constant 70° F. At the time of discovery the core temperature of the body was determined to be 85° F. One hour later a second measurement showed that the core temperature of the body was 80° F. Assume that the time of death corresponds to t = 0 and that the core temperature at the time was 98.6° F. Determine how many hours elapsed before the body was found. [Hint: Let ti > 0 denote the time that the body was discovered.] 2. The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of Newton's Law of Cooling is dT = kS(T – Tm), dt where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 200° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 120° F. If Tm = 70° F, then what is the temperature of the coffee in cup B after 30 min? (Turn Over) 3. A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. ASsuming air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone. 4. The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming
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