Math Problem Solver

QUESTION ONE

Use the Given the equations below to answer the questions that follow:

5w + 4x + 3y + 2z = 30

2x + w + 3y + 4z = 30

6w + 3y - 2x – 2z = 3

4w + 3x + 4y – 4z = 6

(a) From the above system of simultaneous equations form a matrix (A) to represent the above information.

(b) Find the determinant of the matrix A above

(c) Find the inverse of the matrix A above showing all your workings.

(d) Using the inverse method of matrix operations, solve the simultaneous equations above and show the values of “w, x, y & z’

QUESTION TWO

Gatheru and Karibu Certified Public Accountants have recently started to give business advice to their clients. Acting as consultants, they have estimated the demand curve of a client’s firm to be;

AR = 200 – Q

Where AR is average revenue in millions of shillings and Q is the output in units.

Investigations of the client’s firm’s cost profile shows that marginal cost (MC) is given by:

MC = Q2 – 28Q + 211 (in millions of shillings)

Further investigations have shown that the firm’s cost when not producing output is Sh.10 million.

Required:

i) The equation of total cost. ii) The equation of total revenue iii) An expression for profit iv) The level of output that maximizes profit.

v) The equation of marginal revenue.

QUESTION THREE

a) Differentiate the following functions:

(i) Y= 2x3 + 4

(3x + 7)2

(ii) P = (6q4 + 4q2 + 5q + 7)5

b) Evaluate the following:

(i) ʃ(x1/4 + x- ½+ x6)

(ii)  5 (x + 16) dx

0

e) Factorize the following:

i. 15x4 +10x3 + 25 x2 ii. 9x2 - 25y2