A hamster wheel is in a cage on top of a table. The height of the hamster above the table in centimeters as it runs on the wheel can be modelled by the function h(t) = -6 cos(4πt) + 10 Where t represent time in seconds. a) What is the period of the function? What does the period represent in the context of this problem? b) Determine the height, to the nearest tenth of a centimeter, of the hamster after 32 seconds.

4) Find the amplitude, period, frequency, and sketch one cycle of the displacement of an object moving in simple harmonic motion given by y = -2.3 sin(0.5nt), where y is in meters and t in seconds.

Determine the value of 0, in radians, to two decimal places, if: sec(0) = 1.33, for 0< 0< 27.

1. The average monthly temperature, y, in degrees Fahrenheit, for Alaska, can be modeled by 2n y = 16 sin (x -#) + 40, where x is the month of the year (January = 1, February = 2, ..). Find the amplitude and explain what it means in relation to this problem. (4 points) b. Find the period and explain what it means in relation to this problem. (4 points) C. Graph the function for 1 S x < 12. (4 points) d. What is the highest average monthly temperature? In which month does this occur? (4 points) a. 2. Sketch a reasonable graph that models the motion of a diving board vibrating 13 inches in each direction per second just after someone has dived off. (4 points)