An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(
2 answers:
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Answer:
- 7.5 ft
- 32.5 ft, 5 ft
- 10.7 ft
Step-by-step explanation:
a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.
The irrigation system is positioned <u> 7.5 </u> feet above the ground
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b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...
h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet
The spray reaches a maximum height of <u> 32.5 </u> feet at a horizontal distance of <u> 5 </u> feet from the sprinkler head.
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c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.
The spray reaches the ground at about <u> 10.7 </u> feet away.
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