Use the following information to answer the next question. The sunrise time for a particular Alberta city can be modelled by the sinuscidal regression function S=1.51sin(0.0172d+1.51)+7.00 where S is the sunrise time in hours after midnight, and d is the number of days since the beginning of the year (January I=1 January 2=2 etc.) 24. According to the sinusoidal regression function, determine the sunrise time on August 15 (day 227) to the nearest hundredth of an hour, after midnight.

Question

Use the following information to answer the next question. The sunrise time for a particular Alberta city can be modelled by the sinuscidal regression function S=1.51sin(0.0172d+1.51)+7.00 where S is the sunrise time in hours after midnight, and d is the number of days since the beginning of the year (January I=1 January 2=2 etc.) 24. According to the sinusoidal regression function, determine the sunrise time on August 15 (day 227) to the nearest hundredth of an hour, after midnight.

Answer 1

Here's how to determine the sunrise time on August 15th (day 227):1. **Substitute the value of 'd' into the equation:** d = 227 S = 1.51sin(0.0172 * 227 + 1.51) + 7.002. **Calculate the value inside the sine function:** 0.0172 * 227 = 3.9044 3.9044 + 1.51 = 5.41443. **Calculate the sine value:** sin(5.4144) ≈ -0.77 (Make sure your calculator is in radian mode)4. **Complete the calculation:** S = 1.51 * (-0.77) + 7.00 S = -1.1627 + 7.00 S ≈ 5.84Therefore, the sunrise time on August 15th is approximately 5.84 hours after midnight. This translates to 5:50 am (0.84 hours * 60 minutes/hour ≈ 50 minutes).

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