Question

You are riding a Ferris Wheel at the fair that is modeled by the equationy=50sin(π40x−20)+65, where y is the height above the ground and x is the time in seconds. Determine the first time after the ride starts that you are 96 feet above ground . Round your answers to ONE decimal place.

Answer 1

To determine the first time after the ride starts that you are 96 feet above the ground, substitute the value of y into the given height equation and solve for x.

Step-by-step explanation:

To determine the first time after the ride starts that you are 96 feet above the ground, we need to set up an equation using the given height equation.

Given: y = 50sin(π40x−20)+65 and y = 96

Substitute the value of y into the equation:

96 = 50sin(π40x−20)+65

Now, solve for x:

31 = 50sin(π40x−20)

Sin(π40x−20) = 31/50

Take the inverse sin of both sides:

π40x−20 = sin⁻¹(31/50)

40x−20 = π⁻¹sin⁻¹(31/50)

40x−20 = 0.615

40x = 20.615

x = 0.515 seconds