A naval engineer uses the function, P, to analyze the effect of water pressure on submarines. The function of P(d) measures the pressure exerted by water, where d represents the depth of water in meters. Which of the following would be a possible domain? Show your work.
a) d is the set of all integers
b) d is the set of all integers where d>0.
c) d is the set of all rational numbers
d) d is the set of all rational numbers where {0< equal to d < equal to depth of sea floor}
The possible domain for the function P(d) would be:
d) d is the set of all rational numbers where 0 ≤ d ≤ depth of sea floor
This is because the depth of water can vary and can be a rational number, and we need to ensure that the depth is within the range of 0 to the depth of the sea floor.
Show your work
To show that the domain for the function P(d) is the set of all rational numbers where 0 ≤ d ≤ depth of sea floor, we need to consider the restrictions and constraints on the depth of water.
First, we know that d represents the depth of water in meters. Depth is typically a real number and can be positive or negative. However, in this case, we can assume that depth will always be positive since it represents the depth of water. Therefore, we can rule out options a) and b) as they include negative integers or only positive integers.
Next, we consider the constraint that the depth of water cannot exceed the depth of the sea floor. This means that d should be less than or equal to the depth of the sea floor. Additionally, we need to ensure that the depth is non-zero, as there must be some water present. This means that d should be greater than or equal to zero.
Putting these constraints together, the possible domain for the function P(d) is the set of all rational numbers where 0 ≤ d ≤ depth of sea floor.
Therefore, the correct option is d) d is the set of all rational numbers where 0 ≤ d ≤ depth of sea floor.