Antonio's toy boat is bobbing in the water under a dock. The vertical distance HHH (in \text{cm}cmstart text, c, m, end text) between the dock and the top of the boat's mast ttt seconds after its first peak is modeled by the following function. Here, ttt is entered in radians. H(t) = {5}\cos\left({\dfrac{2\pi}{3}}t\rig ht) - {35.5}H(t)=5cos( 3 2π t)−35.5H, left parenthesis, t, right parenthesis, equals, 5, cosine, left parenthesis, start fraction, 2, pi, divided by, 3, end fraction, t, right parenthesis, minus, 35, point, 5 How long does it take the toy boat to bob down from its peak to a height of -35\text{ cm}−35 cmminus, 35, start text, space, c, m, end text? Round your final answer to the nearest tenth of a second.

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a.what is the independent and dependent variables? b.find the amplitude and the period of the function. c.create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.