Question

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

Answer 1

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