In order to create a function from this, we need to quantify the date into "day of year", beginning with January 1, whic

[answerhappygod]

In Order To Create A Function From This We Need To Quantify The Date Into Day Of Year Beginning With January 1 Whic 1 (90.74 KiB) Viewed 25 times

In Order To Create A Function From This We Need To Quantify The Date Into Day Of Year Beginning With January 1 Whic 2 (69.46 KiB) Viewed 25 times

In Order To Create A Function From This We Need To Quantify The Date Into Day Of Year Beginning With January 1 Whic 3 (15.23 KiB) Viewed 25 times

In Order To Create A Function From This We Need To Quantify The Date Into Day Of Year Beginning With January 1 Whic 4 (20.74 KiB) Viewed 25 times

In order to create a function from this, we need to quantify the date into "day of year", beginning with January 1, which we will call "Day 1" (we can assume I corresponds to 11:59 PM on January 1, so we'll think of the New Year beginning at x = 0). This becomes our independent variable. We also turn the amount of time between sunrise and sunset into "hours of daylight", which becomes our dependent variable. Date Day of Sunrise Sunset Minutes of Hours of Year Daylight Daylight 1/3 3 7:20 4:43 563 9.38 1/10 10 7:20 4:49 569 9.48 1/17 17 7:17 4:57 580 9.67 1/24 24 7:13 5:05 592 9.87 1/31 31 7:08 5:14 606 10.1 2/7 38 7:01 5:22 621 10.35 2/14 45 6:52 5:31 639 10.65 2/21 52 6:43 5:39 656 10.93 2/28 59 6:33 5:47 674 11.23 3/7 66 6:22 5:55 693 11.55 3/14 73 6:11 6:02 711 11.85 3/21 80 6:00 6:10 730 12.17 3/28 87 5:48 6:17 749 12.48 4/4 5:37 6:24 767 12.78 4/11 101 5:25 6:31 786 13.1 4/18 108 5:15 6:38 13.38 4/25 115 5:05 6:46 821 13.68 S/2 122 4:56 6:53 837 13.95 5/9 129 4:48 7:00 852 14.2 5/16 136 4:41 7:07 866 14.43 5/23 143 4:35 7:13 878 14.63 5/30 150 4:31 7:19 888 14.8 6/6 157 4:28 7:24 896 14.93 6/13 164 4:27 7:28 901 15.02 6/20 171 4:27 7:30 903 15.05 6/27 178 4:29 7:31 902 15.03 7/4 185 4:32 7:31 899 14.98 7/11 192 4:37 7:28 891 14.85 7/18 4:42 7:25 883 14.72 7/25 206 4:48 7:19 871 14.52 8/1 213 4:55 7:13 858 14.3 8/8 220 5:01 7:05 844 14.07 8/15 227 5:08 6:56 828 13.8 8/22 234 5:15 6:46 811 13.52 8/29 241 5:22 6:35 793 13.22 9/5 248 5:28 6:24 776 12.93 94 803 199

9/12 9/19 9/26 10/3 10/10 10/17 10/24 10/31 11/7 11/14 11/22 11/29 12/6 12/13 12/20 12/27 255 262 269 276 283 290 297 304 311 318 326 333 340 347 354 361 5:35 5:42 5:48 5:55 6:02 6:10 6:17 6:25 6:34 6:42 6:50 6:58 7:05 7:12 7:16 7:19 6:13 6:01 5:49 5:37 5:26 5:15 5:05 4:56 4:48 4:42 4:34 4:31 4:30 4:32 4:34 4:37 758 739 721 702 684 665 648 631 614 600 588 573 565 560 558 558 12.63 12.32 12.02 11.7 11.4 11.08 10.8 10.52 10.23 10 9.8 9.55 9.42 9.33 9.3 9.3 The sinusoidal function that can be used to model this data is f(x) = 2.836 sin(0.0172(x - 80))+12.164, where x is the day of the year, and f(x) gives the number of hours of daylight on day x. Y-

7. a. For which value of x is the amount of daylight increasing the fastest? For which x-value is it decreasing the fastest? Then find the dates that correspond to these X-values. b. Determine the intervals where the function is concave up and concave down.

11. Another option to estimate the total amount of daylight for the year is to integrate the sinusoidal model. Write the definite integral that would need to be evaluated below and use Maple to find its value. Write your final answer accurate to 6 decimal places. 12. Are the values from the Riemann sums and the definite integral fairly close? What factors account for the differences?