Question

Olivia would now like to compare the climate of Johannesburg. South Africa, to the climates of the other 3 cities. She collects data for the month of the year m and the average daily high temperature H in degrees Celsius. As before, m 0 represents the first day of January, and mI1 represents the first day of December. 9 可250 25.1- 24.0 21.1-18.9 T16.0 16,7 ㄒㄧ-228T238|242|252 Use your graphing calculator to perform a sinusoidal regression on the data. Write the fuaction in the form a sin(bm+c)+ d. Round off a, b,c, and d to 4 decimal places. 29. 30. Circle the letter(s) of all statements that would accurately describe the climate of Johannesburg in comparison to the other cities. Remember that in the Southern Hemisphere. summer is during the months of December, January, and February and winter is during the months of June, July, and August. A. Winters are cooler than all of the other 3 cities. B. Summers are hotter than all of the other 3 cities. C. More variable than Rio de Janeiro, but less variable than Hong Kong. D. Cooler than Rio de Janeiro in the summer, and significantly cooler in winter E. During April, it will have about the same temperature as Havana. F None of these is accurate. 31. What if Johannesburg's function had the same midline as Havana's, and its climate were as variable as Hong Kong's? Rewrite the function for Johannesburg to account for these new parameters, and complete the missing values in the table. Give temperatures to the nearest tenth of a degree H(m): 1m

complete 29-31 and show correct work please

Answer 1

Use your Graphing calculator to perform a sinusoidal regression on the data As m = 0 represents the first day of January presents the first day of December Given data is To write the function in the form a sin (bm + c) + d using the least squares best fit, we get y = 2.79329 sin x -1.03849 co x + 21.2022 \r\n y = 2.980089 [(2.79329/2.980089) sin x - (2.79329/2.980089) cos x] + 21.2022 y = 2.980089 [sin x cos theta - sin theta cos x] + 21.2022 y = 2.980089 [sin (x - theta)] + 21.2022 where theta = 0.3559 Therefore This equation will be y = 2.980089(sin (x -0.355945)] + 21.2022 y = 2.980089 [sin(x + (-0.355945))] + 21.2022 on comparing this with y = a sin (bm + c) + d where = 2.980089, b = 1, c = -0.355945 and d = 21.2022