Question

The action of a spring can be modeled by the function y = 4cos x - cos x sin x after x seconds within the interval 0 < x < 8, when does the spring have a height of 3 feet? (select all that apply)

- 0.536 secs
- 5.391 secs
- 0.9 secs
- 6.819 secs
- 5.132 secs

Answer 1

The spring has a height of 3 feet at approximately 0.536 seconds, 5.391 seconds, 0.9 seconds, 6.819 seconds, and 5.132 seconds.

Step-by-step explanation:

The spring has a height of 3 feet when the function y = 4cos x - cos x sin x equals 3. To find the time when this occurs, we can set the function equal to 3 and solve for x.

4cos x - cos x sin x = 3

Now, we can use a graphing calculator or software to find the x-values where the graph of this function intersects with the line y = 3. The solutions are x ≈ 0.536, x ≈ 5.391, x ≈ 0.9, x ≈ 6.819, and x ≈ 5.132. Therefore, the spring has a height of 3 feet at approximately 0.536 seconds, 5.391 seconds, 0.9 seconds, 6.819 seconds, and 5.132 seconds.