1. For 0 S t S 12 particles A and B move along the the az-axis. The position of particle A at time t is given by scA(t) = gsin (7;). The velocity of particle B at time t is given by 113(13): cos (71%). Both particles are at position :0 = 0 at time t = 0. a) For 0 S t S 12, when is the particle A moving to the left? b) Find the displacement and the total distance travelled by the particle A during the time interval 0 S t S 12. c) For 0 S t S 12, nd all times t during which the two particles A and B travel in the same direction. d) Find all the time intervals Within 0 S t S 12 when both particles A and B are speeding up (i.e. when speed functions of both particles are increasing in time) or both slowing down (i.e. speed functions of both particles are decreasing in time). Explain your reasoning. 2. A factory produces smartphone processors, its output is measured in hundreds of processors. The daily cost of producing a: hundred units of output is C, in thousands of dollars, where C(m) = 0.12:3 1.2.132 + 9.62: + 3. Furthermore, when a: = 7 the daily output is increasing at the rate of 10 processors per day. a) Find the rate at which the daily cost is changing when at = 7. Indicate the units of measure. b) The wholesale price of each processor is $110. Assuming that all of them are sold at this price, what is the daily revenue R generated by the factory when m = 7? c) Find the rate at which the daily revenue is changing when so = 7. Indicate the units of measure. d) Prot is dened as \"revenue minus costs\". Is the daily prot increasing or decreasing when .7: = 7? 3. A collection of geometrical problems on related rates. a) The volume of a cube is decreasing at the rate of 10 m3/hr. How fast is the total surface area decreasing when the surface area is 54 m2? b) Rachael is blowing up a balloon so that the diameter increases at the rate of 10 cm/sec. At what rate must she blow air into the balloon when the diameter measures 4 cm? c) The area of an equilateral triangle is increasing at the rate of 5 m2 / hr. Find the rate at which the height is changing when the area is 64x/g/3 m2. 4. The trough shown below is 5 feet long and its vertical cross sections are inverted isosceles triangles with base 2 feet and height 3 feet. Water is being siphoned out of the trough at the rate of 2 cubic feet per minute. At any time 15, let h be the depth and V be the volume of water in the trough. a) Find V when the trough is full. 1 b) What is the rate of change in h at time t = t1 when the trough is 21 full by volume? c) What is the rate of change in the area of the surface of the water at t = t1