Final answer:
The height of the inclined pipe in inches, d feet away from the shut-off valve is calculated by the equation h = 3d + 24. None of the provided options in the question match this equation.
Step-by-step explanation:
The connection to the shut-off valve is 2 feet off the ground, and the pipe rises 3 inches for each foot away from the valve. To write an equation to determine the height, h, of the top of an inclined pipe d feet from a shut-off valve, we need to take into account the initial height and the increase in height per foot.
Since the initial height is 2 feet and there are 12 inches in a foot, we convert this initial height into inches to be consistent with the units for the rise of the pipe, which is given in inches. Thus, the initial height is 2 feet * 12 inches/foot = 24 inches. We know that the pipe rises by 3 inches for each foot away from the valve, so for every foot d, we add an additional 3 inches to the initial height.
The equation to represent the height h in inches, d feet from the shut-off valve, is:
h = 3d + 24
However, none of the given options match this equation exactly, suggesting a possible error in the question options. For this reason, none of the provided options (A, B, C, or D) are correct.