If V is a linear space and S is a proper subset of V, and we define a relation on V via v1 ~ v2 iff v1 - v2 are in S, a subspace of V. We are given ~ is an equivalence relation, show that the set of equivalence classes, V/S, is a vector space as well, where the typical element of V/S is v + s, where v is any element of V.

Briefly describe the main similarities and differences between the threshold phenomena for the stochastic general epidemic model and the deterministic general epidemic model.

(Topic: Epidemics)

Pls explain in a simple way to understand. Thxs

Write a MATLAB code to obtain the following. Keep your code commented whenever required. Copy your source code and command widow outcomes and screen shots of any plots in your solution.

Develop three functions for temperature-conversion.

• Create a function called F_to_K that converts and return temperatures in Fahrenheit to Kelvin and store results in ‘F_to_K2.txt’.
• Create a function called C_to_R that converts and return temperatures in Celsius to Rankine and store results in ‘C_to_R2.txt’.
• Create a function called C_to_F that converts and return temperatures in Celsius to Fahrenheit and store results in ‘C_to_F2.txt’.

Use the following equations to achieve these conversions.

1 degree Fahrenheit =255.928 Kelvin

1 degree Celsius =493.47 Rankine

1 degree Celsius =33.8 degrees Fahrenheit

• Write an appropriate MATLAB code to collectively call and test these functions.
  • It should import data from ‘Tempr2.txt’ and convey it to each of the above mentioned user defined functions. ‘Tempr2.txt’ is available on BlackBoard under the folder Final_Exam.
  • It should display on the command window one conversion table for each case while displaying first 20 inputs and converted values.
  • It should also display a table on the command window, which presents the mean, median, variance and standard deviation values according to the following Table.

There are 12 students in a party. Five of them are girls. In how many ways can these 12 students be arranged in a row if (i) there are no restrictions? (ii) the 5 girls must be together (forming a block) (iii) no two girls are adjacent? (iv) two particular boys A and B, there are no boys but exactly 3 girls?

question 1:

The total revenue received from the sale of x units of a product is given by

TRx= -3x^5 + 3/2 x^4+ x/4+ 12square x+ 6y

Find the

1. 1. Average revenue AR.
2. 2. Marginal revenue MR.
3. 3. MR at x = 4.      
4. 4. The actual revenue from selling10^th item.
5. 5. Write down different rule of derivative.

question 2 :

1. Calculate the principle amount borrowed from the bank for 20 months at a rate of 7 3/4 % per annum with interest of 2250 RO. Also find the total amount to be paid back to the bank .

2. Find the rate of interest required for an investment of 2000 RO to earn 320 RO interest over a period of 18 months.

3. A family spends 30 % of their income on mortgage installments of 500 RO per month. Calculate the monthly income of the family.

4. Find the sale price of a car if its cost price is 5500 RO and % loss is 15%.

5. The price of a PC decreases from 60 RO to 55 RO. Express this decrease as a % decrease.

Determine whether or not W is a subspace of V. Justify your answer.

W = {p(x) ∈ P(R)|p(1) = −p(−1)}, V = P(R)

Prove the following test: Let {x_n} be a sequence and lim |X_n| ^1/n = L

1. If L< 1 then {x_n} is convergent to zero

2. If L> 1 then {x_n} is divergent

Solve the differential equation. x''(t)+2x'(t)+5x(t) = 2

Find the power series solution for the equation y'' + (sinx)y = x; y(0) = 0; y'(0) = 1

Provide the recurrence relation for the coefficients and derive at least 3 non-zero terms of the solution.

Let

f(x, y) = x²y(2 − x + y²)⁵ − 4x²(1 + x + y)⁷ + x³y²(1 − 3x − y)⁸.

Find the coefficient of x⁵y³ in the expansion of f(x, y)

A mass of 50 g stretches a spring 3.828125 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 10 cm/s, and if there is no damping, determine the position u of the mass at any time t.

Enclose arguments of functions in parentheses. For example, sin(2x).

Assume g=9.8 ms2. Enter an exact answer.

Prove that rect(x)*rect(x) = tri(x)

Notes 2.7 Using CRT notation, show what is going on for all the combinations you considered in Notes 2.6. Explain why gcd(s + t, 35) sometimes gave you a factor, and it sometimes did not

Notes 2.6 is:

Notes 2.6 Consider all the possible sets of two square roots s, t of 1 (mod 35) where s ≢ t (mod 35) (there are six of them, since addition is commutative (mod 35).

For all possible combinations, compute gcd(s + t, 35). Which combinations give you a single prime factor of 35?

1.) Prove that Z+, the set of positive integers, can be expressed as a countably infinite union of disjoint countably infinite sets.

2.) Let A and B be two sets. Suppose that A and B are both countably infinite sets. Prove that there is a one-to-one correspondence between A and B.

Please show all steps. Thank you!

(I rate all answered questions)