1. A pendulum is connected to a rope 3m long, which is connected to a ceiling 4m high. The angle between its widest swing and vertical hanging position is pi/3. If the pendulum swings out to its widest position for 2 seconds, model the horizontal displacement of the pendulum using a sine function, considering vertical to be x=0.
2. The tides at Cape Capstan change the depth of the water in the harbour. On one day in September, the tides have a high point of approximately 13m at 3 pm and 1.6m at 9 pm. The sailboat has a draft of 2.5m deep. The captain of the sailboat plans to exit the harbourer at 8:30 pm.
a.Write a cosine trigonometric equation that represents the situation described.
b.Plot an accurate graph 1 cycle.
c.Determine whether the sailboat can exit the harbour safely.
3. The average number of customers, c, at a 24-hour sandwich shop per hour is modeled roughly by the equation c(h)=-5cos[pih/12]+12, with h=0 representing midnight.
a. How many hours per day are there 13 customers per hour, to the nearest hour?
b. What is the maximum number of customers?
c. What time of day is peak(max) business?
4. A 3m ladder is leaning against a vertical wall such that the angle between the ground and the ladder is pi/3. What is the exact height that the ladder reaches up the wall?
Please show all steps. Thank you.
Here is the identical set of questions answered by oobleck
www.jiskha.com/questions/1879992/1-a-pendulum-is-connected-to-a-rope-3m-long-which-is-connected-to-a-ceiling-4m-high-the
The Cape Capstan question has been recycled for years with the teacher just changing the data values. Here is one going back all the way to 2010
All you have to do is change your data values and follow the same steps
www.jiskha.com/questions/458326/the-tides-at-cape-capstan-new-brunswick-change-the-depth-of-the-water-in-the-harbour-on
For each case copy-and-paste the URLs