Answer:
A) Yes you are totally safe
Step-by-step explanation:
The function that models the height of the curved arch in feet, f(x) = -0.0009·x² + 1.24·x + 1.65
The height of the platform = 2 feet + The maximum height of the arch
The amount of stretch of the bungee before retracting = 420 feet
The vertex of the parabola is the point x = (-b/2·a), from which we get;
At the maximum height of the arch, x = -1.24/(2 × -0.0009) = 6,200/9 = 688.[tex]\overline 8[/tex]
The maximum height of the arch = f(688.[tex]\overline 8[/tex]), therefore, we have;
f(688.[tex]\overline 8[/tex]) = -0.0009×(688.[tex]\overline 8[/tex])² + 1.24 × (688.[tex]\overline 8[/tex]) + 1.65 = 428.76[tex]\overline 1[/tex]
The maximum height of the arch = 428.76[tex]\overline 1[/tex] feet
The height of the platform above the ground = 2 ft. + 428.76[tex]\overline 1[/tex] ft. = 430.76[tex]\overline 1[/tex] ft.
Therefore;
The height of the platform above the ground = 430.76[tex]\overline 1[/tex] feet > The amount the bungee will stretch before retracting = 420 ft.
430.76[tex]\overline 1[/tex] ft, > 420 ft.
Therefore, the jumper is totally safe.
