please tell me how to write proofs for diophantine equation

5. Of the 9-letter passwords formed by rearranging the letters AAAABBCCC (4 A’s, 2 B’s, and 3 C’s), I select one at random. Determine the following probabilities.

(a) Prob (my word is a palindrome and has no two C’s next to each other).

(b) Prob (my word has two C’s next to each other and the other C not next to them).

(c) Prob (my word has the three C’s next to each other and the B’s apart from each other). Leave your probabilities with factorials in them.

Let . If we use Accelerated Newton-Raphson method to approximate the root of the equation , which of the following(s) is/are ture:

(I)  is multiple root of order

(II) Accelerated Newton-Raphson formula is :

(III) The sequence  obtained by the Accelerated Newton-Raphson method converge to the root  quadratically.

Find the constants a, b, and c such that the function f(z)=ax^2-bxy+2y^2+i(x^2+cxy+dy^2) is entire?

f\left(z\right)=ax^2-bxy+2y^2+i\left(x^2+cxy+dy^2\right)

Write out the first 4 terms of y1 and y2:

( x+2 ) y" - 3y' + 2xy = 0 ; x0 = 3

For countable set G, H = {f : N → G : f is injective} where N is the natural numbers. What is the cardinality of H. Prove it.

The line k goes through the point Q(-3,5) and is perpendicular to the line g: x - 3y - 22 = 0. Where do the angle bisectors of lines g and k intersect the line AB when A = (-3,3) and B = (10,3)?

For the following relations on S = {0,1,2,3}, specify which of the properties (R), (AR), (AS), and (T) the relations satisfy.

(R) = reflexive

(AR) = anti reflexive

(AS) = anti symmetric

(T) = transitive

b.) (m,n) in the domain of R2 if m - n is even

c.) (m,n) in the domain of R3 if m less than or equal to n

d.) (m,n) in the domain of R4 if m + n is less than or equal to 4

e.) (m,n) in the domain of R5 if max{m,n} = 3

y''-3y'+2y=1+cost+e^-t

NOL Carryback and Carryforward, Valuation Account versus No Valuation Account)

(LO 3) Spamela Hamderson Inc. reports the following pretax income (loss) for both financial reporting purposes and tax purposes. (Assume the carryback provision is used for a net operating loss.)

The tax rates listed were all enacted by the beginning of 2015.

Instructions

(a)  

Prepare the journal entries for the years 2015-2018 to record income tax expense (benefit) and income taxes payable (refundable) and the tax effects of the loss carryback and carryforward, assuming that at the end of 2017 the benefits of the loss carryforward are judged more likely than not to be realized in the future.

(b)  

Using the assumption in (a), prepare the income tax section of the 2017 income statement beginning with the line “Operating loss before income taxes.”

(c)  

Prepare the journal entries for 2017 and 2018, assuming that based on the weight of available evidence, it is more likely than not that one-fourth of the benefits of the loss carryforward will not be realized.

(d)  

Using the assumption in (c), prepare the income tax section of the 2017 income statement beginning with the line “Operating loss before income taxes.”

The management of Cal Supermarkets has determined that the quantity demanded per week of their 90% lean ground sirloin, x, and the quantity demanded per week of their 80% ground beef, y (both measured in pounds), are related to their unit prices p and q (in dollars), respectively, by the equations x = 6800 − 600p − 400q and y = 5200 − 400p − 600q. (a) What is the total revenue function R(p, q)? Hint: R(p, q) = xp + yq R(p, q) = (b) What price should Cal Supermarkets charge for each product to maximize its weekly revenue? (p, q) = How many pounds of each product will then be sold? (x, y) = What is the maximum revenue? $ Incorrect: Your answer is incorrect.

3) Find the Fourier series of ?(?), which is assumed to have the period 2?. Specify the relationships for Fourier coefficients, and illustrate the pattern for the first several terms within the series ?(?). You may use software to solve for the integrals, but show the complete result and illustrate the simplification process to a reduced form. [35 pts]   

?(?) = ?²    (0 < ? < 2?)   

Formulate the situation as a system of inequalities. (Let x represent the number of goats the farmer can raise and y represent the number of llamas.) A rancher raises goats and llamas on his 800-acre ranch. Each goat needs 4 acres of land and requires $70 of veterinary care per year, while each llama needs 10 acres of land and requires $56 of veterinary care per year. If the rancher can afford no more than $9,240 for veterinary care this year, how many of each animal can he raise?Find the vertices. (Order your answers from smallest to largest x, then from smallest to largest y.)