Math Answers

if sinθ and cosθ are the roots of equation ax² -bx+c=0 then ?

For the following decimal numbers, determine its binary representation. (Show full working)

a. 200
b. 300
c. 85
d. 77

which expression is equivalent to 2/3(x+2)-1/3(x-2)

What is the coefficient of (x+1)^3 in the cubic Taylor polynomial about -1 for the function f(x)=e^x. The coefficient of (x+1)^3 is?

On 1 Jan 2014 a bird sanctuary is home to 25 birds. During Jan 2014, 3 more birds are brought into the sanctuary. During each subsequent month, 2 more birds are brought into the sanctuary than were brought in during the previous month. Assuming that no birds die or leave the sanctuary, work out how many birds are in the sanctuary on 31 Dec 2014.

4. a) The Gauss elimination method is used to solve the system of equations
6 x 4x x 1 + 2 + α 3 =
3 2x x 2 x 1 − 2 + α 3 =
5 x 3x x α 1 + 2 + 3 =
Find the value of α for which the system has (i) a unique solution (ii) no solution (iii)
infinitely many solutions.

b) Set up the Gaussi-Jacobi iteration scheme in matrix form for the linear system of equations

4 3
4 2
4 3
2 3
1 2 3
1 2
− + =
− + − =
− =
x x
x x x
x x

Show that the iteration scheme is convergent. Hence find the rate of convergence of this
method.

b) Set up the Gaussi-Jacobi iteration scheme in matrix form for the linear system of equations

4 3
4 2
4 3
2 3
1 2 3
1 2
− + =
− + − =
− =
x x
x x x
x x

2. a) Find by Newton’s method the roots of the following equations correct to three places of
decimals.
i) log .4 772393 x 10 x = near x = 6 .
ii) f (x) = x − 2sin x near x = 2 .