Question

the texas star has: middle height: 106 feet radius: 101 feet below type an expression for the height of a person after starting from the bottom and turning any number of degrees(x) (hint: type what you have been typing in the calculator, but instead of the degrees turned type x ) attempts: 0 submit

Explanation:

Step1: Recall the formula for height in a circular motion

The general formula for the height \(h\) of an object in circular motion (like a Fer - ris wheel) is \(h = h_0+r - r\cos(x)\), where \(h_0\) is the middle - height (vertical shift), \(r\) is the radius (amplitude), and \(x\) is the angle of rotation.

Step2: Substitute the given values

We are given that \(h_0 = 106\) (middle height) and \(r = 101\) (radius).
Substituting these values into the formula \(h=h_0 + r-r\cos(x)\), we get \(h = 106+101 - 101\cos(x)\).
Simplifying the constant terms \(106 + 101\) (but note that the middle - height is already accounted for in the formula structure). The formula for the height of a person on the Texas Star (a Fer - ris wheel) after turning \(x\) degrees is \(106-101\cos(x)\) (since starting from the bottom, when \(x = 0\), \(\cos(0)=1\) and \(h=106 - 101\times1=5\) (which is consistent with the general position of the bottom of a Fer - ris wheel relative to the middle - height)).

Answer:

\(106 - 101\cos(x)\)