Math Answers

b) Evaluate the 2^nd order partial derivatives 62 u

6𝑥2

62 u

and 6𝑦2 if

𝑢 = 2𝑥³+3𝑥² 𝑦 + 𝑥𝑦³+𝑦³.

1.    Find the derivatives of the following functions with respect to x.

𝑥³ + 𝑦³ = 3   

𝑦 = (sin 𝑥)^{𝑡𝑎𝑛𝑥}

The following information relates to stocks X, Y and Z on 1 July 2020:

Stock Number of Shares Price (Sh.)

X 60,000 30

Y 200,000 25

Z 90,000 65

During the year, stock X undertook a reverse stock split of one for two. On 1 July 2021 the prices of stock X, Y and Z were Sh. 40, Sh. 35 and Sh. 70 respectively

Required:

a) Construct a price weighted index for the three stocks and compute the percentage change in the index (3 mks)

b) Construct a value weighted index for the three stocks and compute the percentage change in the index (3 mks)

c) Discuss four key market anomalies (2 mks)

d) Discuss four costs incurred by investors for exclusion of financial services (2 mks)

A-ONE publisher and sells books. The management is in the process of printing a new book to be marked. 

The book may be bound by either cloth or paperback. Each cloth bound book sold out bring a profit of Rs 

60 and each paper bound book contributes Rs 35. It takes 10 minutes to bind a cloth cover and 8 minutes 

to bind a paperback. The total available time for binding is 20 hours. After considerable market surrey, it is 

predicated that the cloth cover sales will not exceed 800 copies and the paperback sales will be no more 

than 1200 copies. Formulate as an LP model with an appropriate objective function and constraints.

Question 1:  A portfolio consists of four stocks along. The table below shows the number of shares held in each stock, the price per share paid for each stock and the expected return on each stock. Calculate the expected return on the portfolio. All three steps of calculations must be shown, or marks will be deducted.                                                                                                                

A spring is such that a 16 lb weight stretches it by 1.5 in. The weight is pulled down to a point

4 in below the equilibrium point and given an initial downward velocity of 4 ft/sec. An impressed

force of F(t) = 2 cos 74t is acting on the spring. Describe the motion.

A spring is such that a 2 lb weight stretches it by 6 in. An impressed force of F(t) = ¼ sin 8t is

acting on the spring. If the 2-lb weight is released from a point 3 in below the equilibrium point,

describe the motion.

A spring is such that it would be stretched 15.36 in by a 40 lb weight. Let the weight be attached

to a spring and pulled down 6.5 in below the equilibrium point. If the weight is started with an

upward velocity of 7 flt/sec, describe the motion. No damping force but an impressed force of

F(t) = 10lb is present.

A spring with constant 1.5lb/ft, lies on a long smooth (frictionless) table. An 8 lb weight is

attached to the spring and is at rest at equilibrium position. A 6 lb force is applied to the support

along the line of action of the spring for 5 secs and is removed. Discuss the motion.

A spring is such that it would be stretched 8 in by a 20 lb weight. Let the weight be attached to

a spring and pulled down 5 in below the equilibrium point. If the weight is started with an upward

velocity of 4 flt/sec, describe the motion. No damping force or impressed force is present.