Homework 4
35 points
Complete your homework and submit it to your instructor.
Each problem is worth 5 points.
- The average temperature, in °F, for Atlanta, GA is modeled by the sinusoidal function
where t is the time in months and January is t = 1.
What is the average temperature for the month of February? - Using the same equation from problem 1, what is the average temperature in Atlanta, GA, for the month of June?
- The following is a table for the maximum temperature per month, for Boulder, CO (www.wordclimate.com):
Month Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec °F
45.1 48.2 53.8 62.8 71.6 81.5 87.4 85.1 76.6 66.7 52.9 45.5
Find the sinusoidal function that models this data. - What is the amplitude, period, phase shift, and vertical shift of the function found in problem 3?
- A carnival Ferris wheel with a radius of 7 m makes one complete revolution every 16 seconds. The bottom of the wheel is 1.5 m above the ground. The ride starts at the bottom. Find the sinusoidal function that models this Ferris wheel in terms of time (t) in seconds.
- What is the amplitude, period, phase shift, and vertical shift of the function found in problem 5?
- The diagram below shows a mass, a spring, and a near-frictionless surface. If you pull the mass back 10 cm and then release it, the mass starts to oscillate. The distance of the mass from the wall is modeled by the equation
cm, where t is the time in seconds.
Where is the mass when t = 2 seconds?
