Question

The height, in inches, of a point on a bicycle wheel moving at a constant speed is modeled by the function h(t) = 12sin(4πx) + 12. In this function, t represents the amount of time in seconds since the wheel began moving.

Part A
Create a table and evaluate the function at 0.125-second intervals from 0 through 1 seconds.

Answer 1

Answer: Explanation below.

Explanation:

To evaluate the function at 0.125-second intervals from 0 through 1 seconds, we need to substitute the values of t = 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, and 1 in the given function and calculate the corresponding values of h(t).

Using the function h(t) = 12sin(4πx) + 12, we get:

At t = 0 seconds, h(0) = 12sin(4π(0)) + 12 = 12sin(0) + 12 = 12 + 0 = 12

At t = 0.125 seconds, h(0.125) = 12sin(4π(0.125)) + 12 ≈ 18.99

At t = 0.25 seconds, h(0.25) = 12sin(4π(0.25)) + 12 ≈ 23.39

At t = 0.375 seconds, h(0.375) = 12sin(4π(0.375)) + 12 ≈ 24.73

At t = 0.5 seconds, h(0.5) = 12sin(4π(0.5)) + 12 = 12sin(2π) + 12 = 12 + 0 = 12

At t = 0.625 seconds, h(0.625) = 12sin(4π(0.625)) + 12 ≈ 4.60

At t = 0.75 seconds, h(0.75) = 12sin(4π(0.75)) + 12 ≈ -0.80

At t = 0.875 seconds, h(0.875) = 12sin(4π(0.875)) + 12 ≈ -3.91

At t = 1 second, h(1) = 12sin(4π(1)) + 12 = 12sin(4π) + 12 = 12 + 0 = 12

Thus, the table of values for h(t) at 0.125-second intervals from 0 through 1 seconds is:

t | h(t)

___________

0 12

0.125 18.99

0.25 23.39

0.375 24.73

0.5 12

0.625 4.60

0.75 -0.80

0.875 -3.91

1 12