If you prove by strong induction a statement of the form ∀ n ≥ 1P(n), the inductive step proves the following implications (multiple correct answers are possible):

a) (P(1) ∧ P(2)) => P(3)

b) (P(1) ∧ P(2) ∧ P(3)) => P(4)

c) P(1) => P(2)

This assignment requires using the Excel add-in called Solver.

Sam manufacturing company produces two types of tires: Economy tires and Premium tires. The manufacturing time and the profit contribution per tire are given in the following table.

Answer the following assuming that the company is interested in maximizing the total profit contribution.

1. What is the linear programming model for this problem?
2. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Gatson manufacture?
3. What is the total profit contribution Gatson can earn with the optimal production quantities?

4 parts following these instructions

Find the critical numbers for f and the open intervals on which f is increasing (decreasing)

For the first question, your answer should be a comma-separated list of x values or the word "none". For the other two, your answer should either be a single interval, such as (0,1), a comma-separated list of intervals, such as (-inf, 2), (3,4), or the word "none".

answeres needed for each part

part 1)

Let f(x)=18+3x−x^2

part 2)

let f(x)= 5+2x-x^3

part 3)

let f(x)=6x-6

part 4)

let f(x)= 6x^2-8x^4

Descartes' Rule of signs Use Descartes' Rule positive and how of Signs to determine how many negative real zeros of the polynomial can have. Then determine the possible total number of real zeros.

P(x) = x^3 - x^2 - x - 3

P(x) = 2x^3 - x^2 + 4x -7

P(x) = 2x^6 + 5x^4 - x^3 -5x -1

P(x) = x^4 + x^3 + x^2 + x + 12

P(x) = x^5 + 4x^3 - x^2 + 6x

P(x) = x^8 - x^5 + x^4 - x^3 + x^2 - x + 1

*** Please explain to me very detaily***

Thank you very much.

1. a) Calculate the volume of 2.00 X 10^-3 M SCN^- required to prepare 50 mL of 2.00 X 10^-4 M SCN^-.

b) Calculate [FeSCN^2+] for each standard solution:

Assume that all SCN^- ions react (mol SCN^- = mol FeSCN^2+ ). Thus the calculation of [FeSCN^2+] is: mol FeSCN^2+ / L of total solution.

Write as a script in the editor window of Matlab:

Concession stand. Write a program, ConcessionStand.m, that uses vector-matrix multiplication to tabulate and display the cost of each of the following orders. Assume that a hot dog costs $3.00, a brat costs $3.50, and a Coke costs $2.50.

----------------------------------------------------

  hot dogs brats cokes

order 1    2 1 3

order 2 1 0 2

order 3 2 2 2

order 4 0 5 1

In Java!!

Problem 2 – Compute the sum of the series (19%)

The natural logarithm of 2, ln(2), is an irrational number, and can be calculated by using the following series:

1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + ... 1/n

The result is an approximation of ln(2). The result is more accurate when the number n goes larger.
Compute the natural logarithm of 2, by adding up to n terms in the series, where n is a positive integer and input by user.

Requirements:

1. Use either for or while loop to display the number pattern.

1. In 3 to 4 sentences, come up with your own personal ethical principle/philosophy
which upholds over the years.
2. What other ethical principle/philosophy you want to embrace as ypu grow older?
State it in 2 to 4 sentences.

1)Why we want to choose 1-2 heat exchange
2) Benefits of using many tubes in the heat exchange
3) material use for tube
4)shell tube
5) why we use 1 inch two pass
6) the length of tube we use is 6ft
7)U tube - Coose BEU and AEU
8)tube sheet
9) buffle