6. A toy on an elastic string is attached to the top of a doorway. It is pulled down and released, allowing it to bounce up and down. The length of the elastic string, L centimetres, is modelled by the function L= 110 + 25 cos cos (2t) where t is time in seconds after release. (a) Find the length of the elastic string after 2 seconds. (b)Find the minimum length of the string. (c) Find the first time after release that the string is 85 cm. (d) What is the period of the motion?

The polar coordinates of a point are given. Find the rectangular coordinates of the point. (-) - 5,- 3 5/3 O A. 1, 5 5/3 Ов. 2' 2 5 -5/3 | OC. 2' 2 - 5/3 O D. 1, 2

The velocity v of blood at a valve in the heart of a certain animal is modeled by the equation v= -2 cos (5xt) + 2, where v is in centimeters per second and t is time in seconds. a. What are the maximum and minimum velocities of the blood at this valve? b. What is the animal's heart rate in beats per minute? a. The maximum velocity of the blood at this valve is cm/sec and the minimum velocity of the blood at this valve is b. The animal's heart rate in beats per minute is cm/sec.

The height of a buoy on a lake is changing during a storm. The height's rate of change can be modeled by r(t) = 0.5 cos(0.2t) feet per second where t is measured in seconds. Is the buoy's height increasing or decreasing at time t = 10 seconds? Why?