Homework Answers

In the mid-1990s, time magazine reported that 27% of the US Congress supported a tax cut as a means of stimulating the economy and increasing Tax revenues. Suppose at that time five members of congress were randomly selected for an interview and asked whether they supported the tax cut to stimulate the economy.

Find the probability that:

2.1 At least three of the five members were in favour of a tax cut. (6)

2.2 Less than five members were in favour of a tax cut. (6)

2.3 Not more than 3 members were in favour of the tax. (6)

2.4 Find the mean of the above distribution (6)

2.5 Find the variance and standard deviation of the above distribution (6)

1.If a=(i+3j-k) , b=(7i-2j+4k), find the area of the Parallelogram.

2. If 2x - 4y =3, 5y = (-3)x + 10 are two functions. Evaluate the x, y values using graphical method.

3. Evaluate the surfaces in ³ that are represented by the following equations.

i. y = 4

ii. z = 5

4.Following figure shows a Tetrahedron.

Construct an equation to find the volume of the given Tetrahedron using vector methods and if the vectors of the Tetrahedron are a=(i+4j-2k) , b=(3i-5j+k) and c=(-4i+3j+6k), find the volume of the Tetrahedron using the above constructed equation.

Solve True / False by giving reasons for your answers.

a) The integrating factor of the differential equation

xdx + ydy = m(xdy + ydx) is .

1/xy. ?

b) The equation (δ^2 z)/ ( δ^2 x) + x^2 × (( δ^2 z) / ( δ y^2)) = 0

is hyperbolic. ?

c) The solution of the differential equation

( D^3 + D^2 D' - DD'^2 - D'^3 ) is

z = θ1 ( y + x ) + θ2 ( y - x ) + x^2 θ3 (y-x ) ?

d) The Pfaffian differential equation

a^2× y^2 × z^2 dx + b^2 × z^2 × x ^2 dy + c^2 × x ^2 ×y ^2 dz = 0 is Integrable. ?

e) The general solution of the equation x ^2 × y'' + xy'- y = 0,

defined in [0,1] is given

y = c1 × x + c2 × x^-1 ?