F(z)=z^4+az^3+〖bz〗^2+cz+d Where a, b, c and d are real constants. Given that -1+2i and 3-i are two roots of the equation f(z)=0 Show all roots of f(z)=0 on a single Argand Diagram -1+2i

a.      Find the values of a, b, c and d

Question 2

Draw the minimum spanning tree using the vertices given in the diagram below

Question 3

By choosing a suitable substitution, find the exact value of

The above diagram shows a sketch of part of the curve C with equation y=x ln x, x>0. The Line l is the normal to C at the point P(e,e)

The region R shown shaded in the diagram, is bounded by the curve C, the line l and the x-axis

Find the exact area of R in terms of e

The exact are of R can be found easily through this

Question 5

1.      Hence, or otherwise, find the value of a

The value of a is only 2 because there are only one variable

2.      Calculate the change in the number of juvenile Chimpanzees in the first year of the study according to this model

According to the given formula, the change in number will be about

3.      Given that the number of juvenile chimpanzees is known to be in decline in the country

Yes, according to the given scenario, the number of chimpanzees are decline. The main reason is that there are different types of factors are affecting the area. Due to this, the rate was declining

4.      Comment on the short-term stability of this model

The short term stability of this model is clear  and accurate. It is also giving proper information about the given model.

Question 6

A college decided to invest in new furniture. There are two type of table available.

The Octo seats 8 people and occupies 7 meter square floor space.

The Quattro seats 4 people and occupies 3 meter square of floor space.

The collage needs seating for at least 480 people

There is 600 meter square of floor space available

There needs to be at least as many Quattros as Octos

There must be at least 30 Octos

a.