Quantitative Methods Answers

find the number of years it would take for 748 to increase by 72 percent if invested at interest rate 7.9 percent per annum, compounded semi-annually

a company in the wholesale trade selling sportswear and stocks two brands, a and b, of football kit, each consisting of a shirt, a pair of shorts and a pair of socks. the costs for brand a are sh.50 for a shirt, sh 30 for a pair of shorts and sh10 for a pair of socks and those for brand b are sh.60.25 for a shirt, sh.40 for a pair of shorts and sh.10 for a pair of socks. three customers x, y, z demand the following combinations of brands; x, 36 kits of brand a and 48 kits of brand b y, 24 kits of brand a and 72 kits of brand b z, 60 kits of branda required:i) express the costs of brands a and b in matrix form, then the demands of the customers, x,y and z in matrix form. (5 marks)ii) by forming the product of the two matrices that you obtain in the previous part, deduce the detailed costs to each of the customers. (5 marks)

The second divided difference f[xo, x1, x2]

can be written as 

f[xo, x1, x2] = af(x0) + bf(x1) + cf(x2). 

Find the expressions for a, b, c. 

if "f(3)" =5 and "f(5)" =3, what is the form of "f(x)" by lagrange's formula

Perform three iteration of the bisection method compute the positive root of

the equation f(x) = x² – 5x + 2

Find a root of the following equations correct to three decimals using Newton's raphson method: x³ -5x +3=0

Use simpson's method to approximate

8

∫ (x^2-x+3)dx with 8 sub-interval

Use the Newton’s method to approximate the real solution of xcube-2x-2=0 in the interval [1,2]

Find the negative root of the equation x^3 - 2x + 5 =0

Find the real roots of the equation x^3 + x^2 - 100= 0 by the iteration method