2. (a) Find the values of a and b such that the eigenvalues of A = |a 1 are 2 and -5. (b) Find the values of a, b and c such that the eigenvalues of A = | 0 1 0 | 0 0 1 | a b c are 3, -2, and 5.

b 1|

1A) Use surface integral to evaluate the flux of
F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2

1B) Use the Divergence Theorem to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3>

across the cylinder x^2+y^2=1, 0<=z<=2

A bacterial population is found to increase 50% every 24 hours. We want to answer the question: why
how much does the population multiply in a week? Establish and solve an initial value problem to express the population of bacteria as a function of time and graph this function.

dx/dt = -5x + y , dy/dt = 4x - 2y

Research will be conducted for a reason or set of reasons. As a result of research actions will generally be taken, although, in some instances research will show that no action needs to be taken. Explain how a community service organisation which is using research results to implement changes to practice can ensure that the changes are made with as little disruption to the workplace as possible. (350 words)

Discuss the roles that Green, Thomson, and Stokes played in discovering these theorems and making them widely known.

Let R=R+. Define:

a+b = ab ; a*b = a^(lnb)

1. Is (R+, +, *) a ring?

2. If so is it commutative?

3. Does it have an identity?

Prove that every natural number is odd or even.

A basis of a vector space V is a maximal linearly independent set of vectors in V . Similarly, one can view it as a minimal spanning set of vectors in V . Prove that any set S ⊆ V spanning a finite-dimensional vector space V contains a basis of V .

what is the code to solve and graph the following function in matlab

dv/dt=80.5(1-e^(.4t))

Write a user-defined MATLAB function that converts real numbers in decimal form to binary form. Name the function b = deciTObina (d), where the input argument d is the number to be converted and the output argument b is a 30-element-long vector with 1s and 0s that represents the number in binary form. The first 15 elements of b store the digits to the left of the decimal point, and the last 15 elements of b store the digits to the right of the decimal point. If more than 15 positions are required in the binary form for the digits to the right of the decimal point, the digits should be chopped. If the number that is entered as d is larger than can be stored in b, the function should display an error message. Use the deciTObina in the Command Window to convert the numbers 85.321, 0.00671, and 3006.42.

USING MATLAB....

a.) Create anonymous functions:

fa(x)=sin(x^2)

fb(x)=sin^2(x)

b.) Evaluate them both at x=1/2 pi

c.)Evaluate them both at x=(0,1,2,...,10)^T

d.) Calculate fa(fb(2)) and fb(fa(2))

Prove that equation have a unique solution through the point (0,1). With the knowledge acquired can you exhibit explicitly that unique solution for a and b?

(a) y' = y - y^2

(b) y' = y^2 - y^3

Joni is considering job offers from two companies. Company A offered her a starting salary of $63,160 with a 3.4% raise at the end of each year. Company B offered her a starting salary of $45,900 with a raise of $1800 at the end of each year.

1. What is the ratio of Joni's salary one year compared to her salary in the previous year for Company A?

      

2. If Joni works for Company A, her salary for any year is  % of her salary from the previous year.   

3. Define a function, ff, that expresses Joni's varying salary at Company A in terms of the varying number of years, nn, since she accepted the position.

      

4. Define a function, gg, that expresses Joni's varying salary at Company B in terms of the varying number of years, nn, since she accepted the position.

      

5. Determine Joni's projected salary at each company after working for 3 years.

   1. Joni's salary at Company A after 3 years: $   
   2. Joni's salary at Company B after 3 years: $   

6. Use function notation to represent the change in Joni's projected salary at Company A as the number of years she works increases from 4 to 10.

      

Use one MATLAB statement to generate each of the following scalars and vectors. (These parts are sequential)

a.) Generate the vector x=(sin5,sin10,sin15,...,sin200) but dont print

b.)Find the Max value in X and which index has this value. Print both the index and the value using Disp (so you can use 2 statements)

c.)Find the minimum value x and which index has this value. Print both the index and the value using Disp (so you can use 2 statements)

d.)Find the difference between the max and min values

e.) find the sum of all the elements of x

f.)find the sum of the absolute value of all the succesive elements of x

g.) find the differences between all the successive elements of x

h.)Find the absolute differences between all the successive elements of x

k.) sort all these elements in increasing order. print this out in two columns. The first containing the values and the second containing the indicies in x where these values occur (so you can use 2 statements.)

l.) Print out the product of all the elements in x, the mean value of these elemnets and their srtandard deviation, and only 1 statement is allowed.