Show that the given set of functions is orthogonal on the indicated interval. find the norm of each function in the set. 1, cos nπ p  x , n = 1, 2, 3, ; [0, p] for m ≠ n p cos nπ p  x cos mπ p  x dx 0 = 1 2 p cos (n − m)π p  x + correct: your answer is correct. dx 0 = correct: your answer is correct. p 0 = correct: your answer is correct. for m = n p cos2 nπ p  x dx 0 = p 1 2 + dx 0 = p 0 = correct: your answer is correct. also p 1 · cos nπ p  x dx 0 = p 0 = and p 12 dx 0 = correct: your answer is correct. p 0 = correct: your answer is correct. so that cos nπ p  x = correct: your answer is correct. and 1 =

Atrain traveled for 1.5 hours to the first station, stopped for 30 minutes, then traveled for 4 hours to the final station where it stopped for 1 hour. the total distance traveled is a function of time. which graph most accurately represents this scenario? a graph is shown with the x-axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the origin and moves upward for 1.5 hours. the line then continues upward at a slow rate until 2 hours. from 2 to 6 hours, the line continues quickly upward. from 6 to 7 hours, it moves downward until it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y axis labeled total distance (in miles). a line is shown beginning at the origin. the line moves upward until 1.5 hours, then is a horizontal line until 2 hours. the line moves quickly upward again until 6 hours, and then is horizontal until 7 hours a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the y-axis where y equals 125. it is horizontal until 1.5 hours, then moves downward until 2 hours where it touches the x-axis. the line moves upward until 6 hours and then moves downward until 7 hours where it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at y equals 125 and is horizontal for 1.5 hours. the line moves downward until 2 hours, then back up until 5.5 hours. the line is horizontal from 5.5 to 7 hours