Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region. Again, using the center of the half-circle as the origin, the struts are modeled by the equations y=x+8 and y=x-4 . A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart. Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart. 9. Algebraically determine the x -value of where the beam should be placed. 10. Explain where to place the beam

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;

, and

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

Y-coordinate of strut 2 is

y₁ - y₂ = 2

y₁ - y₂ = -

∴ - = 2

 = 2 +

x + 8 = 4 + 4·  + (x - 4)

x + 8 - x + 4 - 4 = 4·  

8 = 4·  

2 =  

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, = √(16) = 4

The coordinate of the location where one end of the beam is placed = (8, 4)

Strut 2, y-coordinate, = √(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)

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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

2

step-by-step explanation: