Question

Which function expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters?

1) y = (12/π) * arcsin((x - 35)/0.6)
2) y = (12/π) * arcsin((x + 35)/0.6)
3) y = (π/12) * arcsin(x/0.6) - 35
4) y = (π/12) * arcsin(x/0.6) + 35

Answer 1

The function that expresses the number of seconds since the bird left the branch, y, as a function of the height of the bird in meters, x, is y = (12/π) * arcsin((x - 35)/0.6).

Step-by-step explanation:

The function that expresses the number of seconds since the bird left the branch, y, as a function of the height of the bird in meters, x, is:

y = (12/π) * arcsin((x - 35)/0.6)

This function represents the inverse sine function of the height of the bird, with a scaling factor of (12/π) and a shift of 35 meters. The arcsin function returns values in radians, so it converts the height of the bird in meters to an angle in radians. The result is the number of seconds since the bird left the branch.