The field of a new soccer stadium is watered by three individual sprinkler systems, as shown by the A, B, and C regions in the figure below. Each sprinkler system is controlled by exactly one of three on-off valves in an underground maintenance room, and each sprinkler system can be turned on without turning on the other two systems. Each of the valves is presently in the off position, and the field is dry. The valves have not been labeled, so you do not know which valve controls which sprinkler system. You want to correctly label the valves as A, B, and C. you also want to do it by making only one trip up

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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2) The field of a new soccer stadium is watered by three individual sprinkler systems, as
shown by the A, B, and C regions in the figure below. Each sprinkler system is controlled
by exactly one of three on-off valves in an underground maintenance room, and each
sprinkler system can be turned on without turning on the other two systems. Each of the
valves is presently in the off position, and the field is dry. The valves have not been
labeled, so you do not know which valve controls which sprinkler system. You want to
correctly label the valves as A, B, and C. you also want to do it by making only one trip up
to the field. You cannot see the field from the
maintenance room, and no one is available to
help you. What procedure can you use to
determine how to correctly label the valves?
Assume that all of the valves and all of the
sprinkler systems are operating properly. Also
that
the sprinklers
are
either
completely off or completely on. Explain your
reasoning.
Transcribed Image Text:2) The field of a new soccer stadium is watered by three individual sprinkler systems, as shown by the A, B, and C regions in the figure below. Each sprinkler system is controlled by exactly one of three on-off valves in an underground maintenance room, and each sprinkler system can be turned on without turning on the other two systems. Each of the valves is presently in the off position, and the field is dry. The valves have not been labeled, so you do not know which valve controls which sprinkler system. You want to correctly label the valves as A, B, and C. you also want to do it by making only one trip up to the field. You cannot see the field from the maintenance room, and no one is available to help you. What procedure can you use to determine how to correctly label the valves? Assume that all of the valves and all of the sprinkler systems are operating properly. Also that the sprinklers are either completely off or completely on. Explain your reasoning.
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