1. Let g(s) = √ s. Find a simple function f so that f(g(s)) = 0. Hint: see Methods of computing square roots on Wikipedia. Use Newton’s method to estimate √ 2. Start with 3 different (and interesting) initial values of your choice and report the number of iterations it takes to obtain an accuracy of at least 4 digits.

In python.

y'' + 16y = (8)(cos(4t)) y(0)=y'(0)= 0

Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

Sec 5.4

-find the payment necessary to amortize a 12% loan of $2100 compounded quarterly with 15 quarterly payments

-find the monthly house payments necessary to amortize a 10.8% loan of 162,200 over 25 years

-find the payment made by ordinary annuity with the present value.

-77,822; monthly payments for 24 years; interest rate 4.3%, compounded monthly

-287,938; quarterly payments for 29 years; interest rate 6%, compounded quarterly

give an example of the divergence theorem and the greens theorem

Big Chill, Inc. sells portable dehumidifier units at the current price of $183. Unit variable costs are $75. Fixed costs, made up primarily of salaries, rent, insurance and advertising, are $4,018,000. Calculate breakeven sales for Big Chill, Inc. Round your answer to the nearest whole number.

A manufacturer is considering a switch from manufacturers’ representatives to an internal sales force. The following cost estimates are available. Manufacturers’ reps are paid 8.7% commission and incur $610,000 in fixed costs, while an internal sales force has fixed costs projected at $2,150,000 and would receive 2.7% commission. Assume that sales revenue is double the breakeven volume or the point at which the manufacturer would be indifference between reps and an internal sales force. At this volume, how much would the manufacturer save, assuming the company had switched to an internal sales force? Report your answer in dollars.

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2

Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

y'' + 16y = (8)(cos(4t)) y0)= 0 y'(0)= 8

Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

1) Show the absolute value function f(x) = |x| is continuous at every point.

2) Suppose A and B are sets then define the cartesian product A * B

Please answer both the questions.

1.) (10pts) Consider the following differential equation: (x^2)(dy/dx)=2x(sqrt(y))+(x^3)(sqrt(y))

a)Determine whether the equation is separable (S), linear (L), autonomous (A), or non-linear (N). (An equation could be more than one of these types.)

b)Identify the region of the plane where the Chapter 1 Existence and Uniqueness Theorem guarantees a unique solution exists at an initial condition (x0, y0).

2.(12pts) Consider the IVP: y'+y=y/t , y(2) = 0

For each of the functions y₁(t)and y₂(t) below, decide if it is a solution of the IVP. (Answer is Yes or No, but show, or explain, briefly how you decided for each.)

(a) y₁(t)=te^-1

(b) y₂(t)= t-2

The table below shows a dataset representing the ages of employees working for three different districts. Assuming a minimum working age of 18 and a mandatory retirement age of 65:

1. What is the possible age range for each district?
2. What is the possible age range for all districts combined?
3. What is the computed age range for each district?
4. What is the computed age range for all districts combined?
5. What does the computed versus actual age range tell you about the dispersion computed in questions 1-4?
6. What is the standard deviation for age in each district?
7. What does the standard deviation tell you about the dispersion of age in each district?
8. What is the standard deviation of age in all districts combined?
9. What is the variance in age in each district?
10. What is the variance in age when all districts are combined?

Let f be a one-to-one function from A into b with B countable. Prove that A is countable.

Section on Cardinality

Find the distinct sixth roots of -64

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 2x³ + xy² + 5x² + y²

Local Maximum Value(s) = 125/27

Local Minimum Value(s) = ?

Saddle Point(s) (x,y,f) = ?

.

2. Find the indicated partial derivative.

f(x, y) = sqrt 2x + 5y ; f_y(5, 3)

f_y(5, 3) =

Please calculate the questions below:

10 portions or 1.45 ltr of finished pumpkin soup

320 g pumpkin, peeled

110 g onions cleaned and washed

1100 ml chicken stock

300 ml heavy cream

Please calculate the following

1. How much pumpkin peeled is needed for 165 portions at 135 ml per portion
2. How much onions cleaned is needed for 290 portions at 160 ml per portion
3. How much chicken stock needs to be prepared for 329 portions at 140 ml per portions?

A kilo pumpkin costs P 48 and after trimming there are only 720g pumpkin, peeled available

4. Please calculate the multiplication factor for the pumpkin to pumpkin peeled
5. How much pumpkin needs to be purchased to serve 165 portions of soup at 135 ml?