Two people are headed towards each other on skateboards and experience very little friction or airresistance. One person has massm1= 40 kg and one has mass m2= 80 kg. If they are going equal velocities(v = 3 m/s)before the collision, which direction will they be going afterward? How fast?What if we allow the lighter person to start off on a hill of height h. What should h be so that after the collision both skateboarders have stopped?

1. Create a Binary Search Tree for the following data and do In-order, Preorder and Post-order traversal of the tree.

50, 60, 25, 40, 30, 70, 35, 10, 55, 65, 5

1. Write an algorithm to delete a node in Singly Linked List                            [12
2. Write an algorithm of Binary Search                                                              [10]
3. Write a program in ‘C’ to generate Fibonacci series using recursion            [8]

The length of time junior high school students sleep per night follows an approximate uniform distribution from seven to eleven hours. Suppose we randomly select a junior high student.

1. Find the probability that the randomly selected student sleeps less than 8 1/2 hours per night.

A. 0. 375

B. 0. 4705

C. 0. 7727

D. . 2143

2. On average, how long does a junior high school student sleep per night ?

A. 9 hours

B. 8 hours

C. 4 hours

D. 11 hours

3. Find the probability that the randomly selected student sleeps eight to twelve hours per night?

A. 0. 4705

B. 0. 375

C. 0. 7727

D. . 2143

4. 65 % of junior high school students sleep at least how many hours ?

A. 8. 4 hours

B. 7. 8 hours

C. 6. 5 hours

D. 9. 6 hours

You have saved $10,000 for a down payment on the purchase of a new car, however, since you plan to buy the car one year from today, you need to decide how to invest the money for one year. You are limited to one of two choices:

1. A Bond Fund with an expected return of 3%/year

2. A Stock Fund with an expected return of 7%/year.

Which fund is best? Explain why!

To make a phrase/words, solve the 18 application of derivatives below.  Then replace each numbered blank with the letter corresponding to the answer for that problem. Show all solutions on the answers given below.

"   __ __ __ __ __ __ __       __ __ __ __      __ __ __ __ __ __ __      __ __ __ __ __      __ __ __ __ __"       

"__ __ __ __ __ __ __      __ __      __      __ __ __ __ __ __ __      __ __ __ __ __      __ __ __ ."     

Derivative Application Problems:      

1.  Find the equation of the line normal to the curve  f(x) = x³ – 3x²  at the point (1, -2).          

2.  Find the equation of the line tangent to the curve  x² y – x = y³ – 8  at the point where x = 0.          

3.  Determine the point(s) of inflection of  f(x) = x³ – 5x² + 3x + 6.         

4.  Determine the relative minimum point(s) of  f(x) = x⁴ – 4x³.        

5.  A particle moves along a line according to the law s = 2t³ – 9t² + 12t – 4, where t≥0 .  Determine the total distance traveled between t = 0 and t = 4.             

6.  A particle moves along a line according to the law s = t⁴ – 4t³, where t≥0.    Determine the total distance traveled between t = 0 and t = 4.        

7.  If one leg, AB, of a right triangle increases at the rate of  2 inches per second, while the other   leg, AC,  decreases at 3 inches per second, determine how fast the hypotenuse is   changing (in feet per second) when AB = 6 feet and AC = 8 feet.     

8.  The diameter and height of a paper cup in the shape of a cone are both 4 inches, and water is leaking   out at the rate of ½ cubic inch per second.  Determine the rate (in inches per second) at which  the water level is dropping when the diameter of the surface is 2 inches.     

9.  For what value of y is the tangent to the curve  y² – xy + 9 = 0 vertical?        

10.  For what value of  k  is the line  y = 3x + k tangent to the curve  y = x³ ?        

11.  Determine the slopes of the two tangents that can be drawn from the point (3, 5) to the parabola    y = x² .              

12.  Determine the area of the largest rectangle that can be drawn with one side along the x-axis and  

two vertices on the curve  y = e^-x2

13.  A tangent drawn to the parabola  y = 4 – x²  at the point (1, 3)  forms a right triangle with the   coordinate axes.  What is the area of this triangle?         

14.  If the cylinder of largest possible volume is inscribed in a given sphere, determine the ratio of the   volume of the sphere to that of the cylinder.

15.  Determine the first quadrant point on the curve  y²x = 18 which is closest to the point  (2, 0).     

16.  Two cars are traveling along perpendicular roads, car A at 40 mph, car B at 60 mph.  At noon when   car A reaches the intersection, car B is 90 miles away, and moving toward it.  At 1PM, what is   the rate, in miles per hour, at which the distance between the cars is changing?

1. Zenith Corporation is deciding between the introduction of two new automobiles: a traditional gasoline-powered model, or a hydrogen fuel-cell model. Incremental cash flows in millions are estimated to be:

Assume end-of-year cash flows, and that the appropriate discount rate for NPV analysis is 12%.

(a) Compute each project’s payback period.

(b) What is each project’s internal rate of return?

(c) Compute each project’s net present value.

(d) Assuming Zenith's goal is to maximize firm value, which project should be taken? Support your answer, including a short statement of which evaluation criterion was most relevant, which were less relevant, and why.   

Shred, Inc. manufactures two types of paper shredders, Mini and Deluxe. Here are data for the current month:

Mini shredder Deluxe shredder

Selling price $240 per unit $480 per unit

Variable costs $160 per unit $370 per unit

Shred can manufacture 40 Mini shredders per hour but only 20 Deluxe shredders per hour. Fixed costs are $1.2 million per month and Shred’s maximum operating capacity is 600 hours per month. Fixed costs are unaffected by the mix of products produced. Monthly demand is 17,000 Mini shredders and 10,000 Deluxe shredders.

a. What is Shred’s operating income if it allocates the 600 operating hours 50-50 between Mini and Deluxe shredders? __________

b. What is Shred’s operating income if it emphasizes the product with the highest contribution margin per unit of constraint? ________

1) A thermocouple element when taken from a liquid at 50 degrees Celsius and plunged into a liquid at 100 degrees celsius at time equal to zero gave the following e.m.f. values. Determine the 95% response time. Time 0 20 40 60 80 100 120 e.m.f. (mV) 2.5 3.8 4.5 4.8 4.9 5.0 5.0

2) What are the advantages and disadvantages of a plastic film type of potentiometer and when compared with the wired-wound potentiometer.

3) A shaft encoder is to be used with a 50 mm radius tracking wheel to monitor the linear displacement. If the encoder produces 256 pluses per revolution, what will be the number of pulses produced by a linear displacement of 300 mm?.

4) Suggest a sensor that could be used, as part of a control system, to determine the difference in level between two containers. The output is to provide an electrical signal for the control system.

Question 36

There are two firms: Firm U and Firm L. Both firms have $50M total assets and $8M EBIT (earnings before interest and taxes). Firm U is an unleveraged firm without debt. Firm L is a leveraged firm with 50% of debt and 50% of common equity. The pre-tax cost of debt for Firm L is 10%. Both firms have 40% corporate tax rate. Calculate the return on equity (ROE) for firm U.

Question 37

Based on the information from Question 36, what’s the return on equity (ROE) for firm L

Question 38

Based on the information from Question 36, what’s the difference of the total dollars paid to all investors in Firm L and Firm U?