Question

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 slingshot attraction is modeled by y = –3x2 + 48x – 30. Which attraction reaches a greater height, and what does it represent in terms of the context?
The slingshot reaches a greater height at 162 feet, which is the vertex of the parabola.
The Ferris wheel reaches a greater height at 175 feet, which is the highest point of the circle.
The slingshot reaches a greater height at 144 feet, which is the vertex of the parabola.
The Ferris wheel reaches a greater height at 145 feet, which is the highest point on the circle.

Answer 1

The attraction which reaches a greater height with what it represent in terms of the context are:

• The slingshot reaches a greater height at 162 feet, which is the vertex of the parabola.
• The Ferris wheel reaches a greater height at 145 feet, which is the highest point on the circle.

What is the equation of a circle?

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²     ......equation 1.

Where:

• h and k represents the coordinates at the center.
• r represents the radius of a circle.

From the question, we have the following information:

(x – 100)² + (y – 75)² = 4,900    .....equation 2.

By comparing equation 1 and equation 2, we have the following parameters:

Center of circle, (h, k) = (100, 75) feet.

Radius, r = √4,900 = 70 feet.

Therefore, the height of the highest point on this circle is given by:

Highest point = r + k

Highest point = 70 + 75

Highest point = 145 feet.

For the slingshot, we have:

y = –3x² + 48x – 30.

The vertex of a parabola occurs when x = -b/2a;

x = -48/2(-3)

x = 48/6

x = 8.

When x = 8, the vertex of this parabola is given by:

y max = –3x² + 48x – 30.

y max = –3(8)² + 48(8) – 30.

y max = -192 + 384 - 30

y max = 162 feet.

Read more on height here: brainly.com/question/27928407

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