An apple with mass 0.4 kg is hanging at rest from the lower end of a light vertical rope. A dart of mass 0.1 kg is shot vertically upward, strikes the bottom of the apple, and remains embedded in it.

a) If the speed of the dart is 5 m/s just before it strikes the apple, what is the speed of the apple just after the collision?

b) How much energy was dissipated during the strike?

c) How high does the apple move upward because of its collision with the dart?

A firm has generated $150 million in earnings before interest and taxes last year and expects these earnings to grow 10% a year for the next 3 years. The firm is expected to generate a return on capital of 20% on new investments for the next 3 years, and there is no efficiency growth. After year 3, the firm will be in stable growth, growing 3% a year in perpetuity, with a return on capital of 12% and a cost of capital of 10%. The corporate tax rate is 30%. Estimate the terminal value of the company at the end of year 3

Consider a firm with an EBIT of $10,900,000. The firm finances its assets with $50,800,000 debt (costing 6.9 percent) and 10,400,000 shares of stock selling at $10.00 per share. The firm is considering increasing its debt by $25,400,000, using the proceeds to buy back shares of stock. The firm is in the 40 percent tax bracket. The change in capital structure will have no effect on the operations of the firm. Thus, EBIT will remain at $10,900,000.

Calculate the EPS before and after the change in capital structure and indicate changes in EPS.

An air bottle used for scuba diving breathing apparatus has a volume of 30 l. After it has been used, the pressure and temperature of the remaining air in the bottle are 0.3 MPa and 24 ◦C. Before the apparatus is used again, it is charged with air at temperature of 50 ◦C until the pressure in the bottle reaches 6 MPa. The charging processes is fast, and can be assumed to be adiabatic.

Questions: (a) Calculate the mass of air to be added to the bottle.

(b) What is the temperature of the air in the bottle at the end of the charging process?

Question 1.

Describe in detail how a protein-encoding gene in a eukaryote is transcribed as mRNA, and what events happen to the mRNA before it can be translated into a protein.

Question 2.

You want to investigate the effect of a probiotic on your gut microbiome- the population of bacteria living in your digestive tract. You collect faecal samples prior to and after consumption of the probiotic. Describe in detail how you would sequence the metagenome of the bacteria in these faecal samples and what bioinformatic analyses you would undertake.

A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.6 kg and 2.3 kg, and the length of the wire is 1.21 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

A mass is moving at 10 m/s in the +x direction and it collides in a perfectly elastic collision with a mass of 4 kg moving in the -x direction. The collision takes places in 0.22 seconds and after the collision the mass that was moving in the +x direction is moving in the -x direction at 8 m/s and the mass that was moving in the -x direction is moving in the +x direction at 14 m/s. What is the magnitude of the average force, in Newtons, on the first mass which was originally moving in the +x direction before the collision?

A mass is moving at 10 m/s in the +x direction and it collides in a perfectly elastic collision with a mass of 2 kg moving in the -x direction. The collision takes places in 0.21 seconds and after the collision the mass that was moving in the +x direction is moving in the -x direction at 9 m/s and the mass that was moving in the -x direction is moving in the +x direction at 13 m/s. What is the magnitude of the average force, in Newtons, on the first mass which was originally moving in the +x direction before the collision?

                                  
   Paired Observation                              
                                  
   Try this paired observation at 5% significance.                              
                                  
   After   310   305   284   305   291   288   291   297
   Before   285   290   278   298   284   285   288   295
                                  
                                  
   Ho: μd = 0                              
   Ha: μd = 0                              
                                  
                                  
                                  
   Using the calculator, find standard deviation of the differences.                              
       sample standard deviation =                           
                                  
                                  
two tail, 0.05, df=7      

tcrit =? alpha =?   
                                  
       tstat =? pvalue =?   
           Reject       Reject              
                                  
                                  
   tstat =    dbar - μd =?   
       sd / √n                          
                                  
   Decision:                                

Section C. Arc Consistency

Consider the following constraint network.

10. If the variables A, B and C each have the domain {1,2,3,4} before arc consistency is run, indicate what their domains will be after arc consistency has finished:

A = {               }

B = {    }

C = {                         }

11. If we have just considered the edge <B, A < B> and reduce the domain of B as a result, do we need to add any arcs back to the To-Do Arcs list? If not, why not? If so, which edges?