Select your answer If the hours of daylight on a given day in Stockholm can be modeled using the function \( I(d)= \) \( 6.2 \sin \left(0.017 d-\frac{\pi}{2}\right)+12.2 \) in which \( I(d) \) represents the length of the day and \( d \) stands for the day of the year, what is the approximate length of the day on June \( 30 ? \) -6.0 hours -9.5 hours -12.0 hours -15.5 hours -18.5 hours

To find the length of the day on June 30, we need to substitute the day number for June 30 into the function. Step 1. Determine the day number for June 30: • January has 31 days. • February has 28 days. • March has 31 days. • April has 30 days. • May has 31 days. Adding them up: 31 + 28 + 31 + 30 + 31 = 151 days by the end of May. Since June 30 is the 30th day of June, the day number d = 151 + 30 = 181. Step 2. Substitute d = 181 into the function:   I(d) = 6.2 sin(0.017d – π/2) + 12.2   I(181) = 6.2 sin(0.017×181 – π/2) + 12.2 Step 3. Calculate the argument of the sine function:   0.017 × 181 = 3.077   Now, 3.077 – π/2 ≈ 3.077 – 1.571 = 1.506 Step 4. Find the sine:   sin(1.506) is almost sin(π/2), which is approximately 1 (more precisely, about 0.997). Step 5. Evaluate I(181):   I(181) ≈ 6.2 × 0.997 + 12.2   ≈ 6.18 + 12.2   ≈ 18.38 hours Rounding this value gives approximately 18.5 hours. Among the provided options, the answer is 18.5 hours.