The acceleration of certain objects is studied in an experimental test track for automobiles. The distance traveled by an object L is measured as a function of time t to yield the following:
t (s) 0.1 0.2 0.5 1.0 1.5 1.8 2.0 3.0

L (m) 0.26 0.55 1.56 3.90 7.41 10.28 12.6 30.

Obtain a best fit to this data, considering first-, second, and third-order polynomials. Using these polynomials, calculate the values of the dependent variable L at the time intervals employed for the given data to evaluate the accuracy of the polynomial representations. Discuss the results obtained.

Q] The historical actual sales of an item purchased by a factory is given below. What would have been the forecast had the manager a) used 3 period moving average to make the forecast in the past, and b) used exponential smoothing with alpha=0.2 to make the forecast in the past. Show all calculations. PLEASE PROVIDE TABULATED EXCEL CALCULATIONS.

Sub: Material Science

A child of mass 50 kg is standing at the edge of a playground merry-go-round of diameter 3 m. Other children push the merry-go-round faster and faster until the first child's feet begin to slip. (a) If the coefficient of friction between the shoes and the rotating surface is 0.2, how long does it take the merry-go-round to make one revolution? (b) How fast is the first child traveling when he begins to slip? (c) What is the angle between the first child's body and a vertical line before he begins to slip?

A ten grams ball glides to the left at a speed of 0.4 meters per second on a frictionless flat surface at the OC fair skating rink. The ball collides head-on, elastically, with another larger ball with mass 30 grams which was gliding to the right with a speed of 0.2 meters per second.

A. After the collision, what is the final velocity of each ball.

B. What is the change in momentum for each ball? How do they compare to each other?

C. What is the change in kinetic energy for each ball? How do they compare to each other?

Suppose you have the following information on the Fed’s and the European Central Bank’s (ECB) policy rules: Fed real interest rate =0.5 (inflation rate -2) ECB real interest rate= 0.2 * (inflation rate-2) +1

Graph these policy rules. If the inflation rate is 2 percent in each, what will be the real interest rate in the U.S. and the ECB area?

Some argue that Europe has a much lower tolerance for inflation than the United States. Can you tell—either from the diagram or from the equations—whether this is true?

a.) Develop equations for X and S as a function of dilution rate for a continuous cell culture system. Assuming that the kinetics are governed by an uncompetetive inhibition model.

b.) Plot X, S and "yield of cell mass (g cells/l) per time" versus dilution rate and recommend a dilution rate to operate the reactor at if:

So = 20 g/l

Ks = 1 g/l

I = 0.08 g/l

Y x/s = 0.2 g cells/g substrate

Xo= 0

KI = .02 g/l

m = 0.75 h-1

.    A package of Chips Ahoy Cereal is marked “Net Wt. 12 oz.” The actual weight is normally distributed

       with a mean of 12 oz. and a standard deviation of 0.2 oz. In each of the following, provide sketches

      of the normal distribution curve with appropriate labels and formulas used.

a.     What percent of boxes would be expected to weigh more than 11.75 oz.?                          

b.   In a sample of 2,000 packages, how many would be expected to weigh more than 12.3 oz.?                                                                                                                                                  

c.    What is the probability that a random package would weigh between 11.8 and 12.1 oz.?       

25. If the following waves are superposed y1 = A Cos[k x – w t] and y2 = A Cos[k x + w t] where A = 0.2 cm, f = 10 Hz and c = 10 m/s. (a) Sketch the waveform at time t = 0 and t = 1/40 s. (b) What is the distance between the nodes. (c) Determine the kinetic and potential energy contained within the string section between the a node and an antinode. (d) Show that the total energy between the node and antinode is a constant in time. Why is this physically reasonable?

A 10 g bullet is fired with 450 m/s into a 10 kg block that sits at rest on a wooden table 20 cm from the edge of the table. The bullet gets embedded in the block (perfectly inelastic collision). The block, with the embedded bullet, then slides to the edge of the table and drops down with some initial velocity while leaving the edge of the table. The coefficient of kinetic friction between the block and the surface of the table is k = 0.2. If the table is 1 m high, how far from the point directly below the table’s edge does the block land?

Installing Tesla solar panels in a house costs $18,000. It is expected that the average monthly savings will be 1,000 kWh per month. Assuming that the utility company charges 0.2 per $/kWhr.

1. What is the Present worth of this investment for i=6% and N=15 years?
2. A different approach could be to install energy efficient windows and enhance the insulation for $12,000, which would yield average monthly savings of 700 kWh per month. Assuming the same interest rate and time span. What is the present worth of this alternative?
3. Which option would you choose? Why?