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Ymorist [56]
2 years ago
5

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation ℎ(

)=−2+10+9.5 h ( x ) = − x 2 + 10 x + 9.5 , where x is the number of feet away from the sprinkler head (along the ground) the spray is.
Mathematics
1 answer:
maw [93]2 years ago
8 0
  1. The irrigation system is positioned 9.5 feet above the ground to start.
  2. The spray reaches a maximum height of <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> away from the sprinkler head.
  3. The spray reaches all the way to the ground at about 10.87 feet away​

<h3>How to determine the position?</h3>

Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

<h3>How to determine the maximum height?</h3>

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -10/2(-1)

Xmax = 5.

Thus, the maximum height on the vertical axis is given by:

h(x) = -x² + 10x + 9.5

h(5) = -(5)² + 10(5) + 9.5

h(5) = -25 + 50 + 9.5

h(5) = 34.5 feet.

Therefore, the spray reaches a maximum height of <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> away from the sprinkler head.

Also, the spray reaches all the way to the ground at about:

Maximum distance = √34.5 + 5

Maximum distance = 10.87 feet.

Read more on maximum height here: brainly.com/question/24288300

#SPJ1

<u>Complete Question:</u>

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away​

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