A Ferris wheel at an amusement park is modeled by (x – 100)2 + (y – 75)2 = 4,900, where the measurements are in feet. A slingsho
t attraction is modeled by y = –3x2 + 48x – 30. Which attraction reaches a greater height, and what does it represent in terms of the context?
1 answer:
The attraction that reaches a greater height and what it represent in terms of the context is:
- The slingshot reaches a greater height at 162 ft, which is the vertex of the parabola.
- The Ferris wheel reaches a greater height at 145 ft, which is the highest point on the circle.
<h3>Height</h3>
Ferris wheel
(x – 100)2 + (y – 75)2 = 4,900
y max= 75+70
y max=145 ft
Sling shot
y = –3x² + 48x – 30
dy/dx=-6+48=0
x=48/6
x=8
Hence:
y max = –3(8)² + 48(8) – 30
y max = –3×64+48(8)-30
y max = –192+384-30
y max =162 ft
Therefore slingshot reaches a greater height at 162 ft and Ferris wheel reaches a greater height at 145 ft.
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