Final answer:
The length of the day on June 30 in Stockholm can be approximated by substituting 181 into the sinusoidal function and solving for l(181). The correct answer is option (c).
Step-by-step explanation:
The question is asking us to determine the approximate length of the day in Stockholm on June 30 using the given sinusoidal function l(d) = 6.2sin(0.017d - π /2) + 12.2, where l(d) represents the length of the day and d stands for the day of the year. Since June 30 is the 181st day of the year, we plug in d = 181 into the function to find l(181).
By substituting d with 181, the equation becomes l(181) = 6.2sin(0.017(181) - π /2) + 12.2. Calculating the sine part gives us sin(3.077 - π /2), which is approximately sin(0.078). The sine of a small angle is approximately equal to the angle itself (in radians), hence sin(0.078) ≈ 0.078. Now, multiply that by 6.2 to get 0.4836 and then add 12.2 to find the approximate length of day, which is about 12.6836 hours.
The closest answer option to our result is 12.0 hours, so option c would be the correct choice for the approximate length of the day on June 30 in Stockholm.