A naval engineer uses the function, P, to analyze the effects of water pressure on submarines. The function 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?
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 ≤ d ≤ depth of sea floor}.
D d is the set of all rational numbers where { 0 ≤ d ≤ depth of sea floor}.
can you explain more
Certainly!
In this case, the function P(d) represents the pressure exerted by water at a certain depth d. The depth of water can be any rational number within a certain range, as water pressure increases with depth.
The depth of water cannot be negative or zero, as negative depths do not make sense in this context and zero depth would mean the submarine is on the surface.
Therefore, the possible domain of d would be all rational numbers such that 0 ≤ d ≤ depth of sea floor. This limits the depth to a non-negative value up to the depth of the sea floor.
So, the correct answer is D: d is the set of all rational numbers where { 0 ≤ d ≤ depth of sea floor}.