Find all the roots of the given function. Use preliminary analysis and graphing to find good initial approximations. f(x) = cos (5x)-4x² + 9x The function has a root when x (Do not round until the final answer. Then round to six decimal places as needed. Use a comma to separate answers as needed.)

Tell if the function f(x) = −2 sin (10x)−4 is increasing, constant, or decreasing at x = −(1/2) and at x = (1/2).

Determine the amplitude, range, period, and phase shift and then sketch the graph of the function using the quarter points. y=-2 sin (-2x+3)-3 Which of the following functions is equivalent to y = - 2 sin (x - 17 ) - 3 O A. y 4 sin x- O C. y=-2 sin |2x - π n ( - 2x + 737) - 3² 3? 3 O B. y = -2 sin 2 sin (2x + 3) +3 O D. y=2 sin 2x- - 3

During a year, the length of a day, from sunrise to sunset, in Taloga, Oklahoma, varies from the shortest day of approximately 9.6 hours to the longest day of approximately 14.4 hours, while in Montreal, the day lengths vary from 8.3 hours to 15.7 hours. 2л For each location, determine a function L(t) = 12 + A sin t that approximates the length of a day, in hours, where t 365 represents the day of the year assuming t = 0 is the spring equinox on March 21. Define LT (t) as the equation for Taloga and LM (t) as the equation for Montreal. (Express numbers in exact form. Use symbolic notation and fractions where needed. LT (t) = LM (t) =