Answer:
The beam should be placed 8 feet from the center.
Step-by-step explanation:
The struts are y = √(x + 8) and y = √(x − 4). The struts are 2 feet apart at the location of the beam:
√(x + 8) − √(x − 4) = 2
Solving:
√(x + 8) = 2 + √(x − 4)
x + 8 = 4 + 4√(x − 4) + x − 4
8 = 4√(x − 4)
2 = √(x − 4)
x − 4 = 4
x = 8
The reinforcement beam have a vertical orientation, therefore, the distance
between the struts is given by the difference between the given function.
The correct responses are;
Reasons:
The given function for the struts are;
[tex]y = \sqrt{x + 8}[/tex], and [tex]y = \sqrt{x - 4}[/tex]
The distance between the beam where the struts is placed = 2 feet
The orientation of the struts = Vertically
Solution:
We have, the vertical distance between the two struts where the beam is
placed = 2 feet.
The function of the struts give their distance from the x-axis.
When struts are 2 feet apart, we have;
Y-coordinate of strut 1 - Y-coordinate of strut 2
Y-coordinate of strut 1 is [tex]y_1 = \sqrt{x + 8}[/tex]
Y-coordinate of strut 2 is [tex]y_2 = \sqrt{x - 4}[/tex]
y₁ - y₂ = 2
y₁ - y₂ = [tex]\sqrt{x + 8}[/tex] - [tex]\sqrt{x - 4}[/tex]
∴ [tex]\sqrt{x + 8}[/tex] - [tex]\sqrt{x - 4}[/tex] = 2
[tex]\sqrt{x + 8}[/tex] = 2 + [tex]\sqrt{x - 4}[/tex]
x + 8 = 4 + 4· [tex]\sqrt{x - 4}[/tex] + (x - 4)
x + 8 - x + 4 - 4 = 4· [tex]\sqrt{x - 4}[/tex]
8 = 4· [tex]\sqrt{x - 4}[/tex]
2 = [tex]\sqrt{x - 4}[/tex]
4 = x - 4
x = 4 + 4 = 8
x = 8
The x-value of where the beam should be placed is x = 8
The y-coordinates of the point where the beam is placed are;
Strut 1, y-coordinate, [tex]y_1 = \sqrt{8 + 8}[/tex] = √(16) = 4
The coordinate of the location where one end of the beam is placed = (8, 4)
Strut 2, y-coordinate, [tex]y_2 = \sqrt{8 - 4}[/tex] = √(4) = 2
The coordinate of the location where the other point of the beam is placed = (2, 4)
The beam extends from (2, 4) to (8, 4)
Learn more here:
https://brainly.com/question/14479555
