For integers m, n, p, q E Z, n, q0, use this and the field axioms (a) Prove m + P 9 mq+np and m. 2 mp nq nq n 9 (b) Show that the field axioms also hold for rational numbers Q. (c) Prove < mq> np for n <0,q> 0. 9 (d) Show that the sum a rational number and an irrational number is always irrational.

Q: 8 If S has a maximum and a minimum then S is compact.

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A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: (B) Prove that: 1. Every Boolean ring is commutative. 2. Every field is integral domain.

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Q: постолни тяло beens его вдо колкот - Solue nan-ty ay = nаy - yan и 2 +у2 в (res) 14:09

A: The solution is given as

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Q: Question 5. Given a metric spaceX,p> (c) True or false? Justify your answer. If (n)neN is a bounded…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: QUESTION 6 Solve the following boundary value problems a. y"+4y= 0, y(0)=-2, y (7) = 5 6 b. y"+3y=0,…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Let f and g be functions which are differentiable on R. For each of the following statements,…

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Q: Example 9.2. From y = A2" + B(-3), derive a difference equation by eliminating the constants.

A: Given yn=A2n+B(-3)n......(1) We derive a difference equation by eliminating the constants.

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Q: Problem 4. (. Let C be the curve given by parametric equations y(t) = 2t, z(t) = lnt, te (-∞0, +00).…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: 1. Let A be an m X n real matrix with full column rank. Show that the Gram matrix AT A associated…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

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A: This question from complex number.

Q: Find the generalized union and intersection: 1. A = {1,2,3,...} 2+1 Q-(무)

A: Let us find the generalized union and intersection of the given indexed set in the next step.

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Q: 3. Use Laplace transforms to solve y+3y=1351 24 y(0) = 6

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Q: Consider the curve C which is the intersection of the surfaces shown in the attached figure.

A: To evaluate the below integral. ∫Cx−y−2zds

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Q: Example 8.8. From the table below, for what value of x, y is minimum? Also find this value of y. **…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: directional derivativ e this information to

A: Given as, f1,2=3, i+j=0.7

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = 1², y(t) = 2t, z(t) = ln t, t€…

A: Since you have posted multipart question and we can answer three subparts. So, answered the first…

Q: eff curl(F). ds. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of the paraboloid z = 9 - x² -…

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Q: 18. 20. 13 22° 9 57° 125° X 32% X 19. 21. 34° X 3.1° X 26 70° 66° 9

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Q: Example 9.13. Solve Yx+1-yx + xyx+1 Yx = 0 given y₁ = 2.

A: Let us solve the given problem in the next step.

Q: 2 x ² d ² y dx² 2. 2x dy x= + dx + (x² +1)y=0

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Q: A population P obeys the logistic model. It satisfies the equation 5 dP P(7-P) for P >0. dt 700 (a)…

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Q: 2. Let A € M₂ (R) be given. (a) If AA¹ = 0, prove that A = On. Does this hold if A € M₁ (C)? (b)…

A: This is a problem of Linear Algebra.

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A: 3.

Q: In Exercises 1-3, find the general se S 1. d²y ,dy dt² dt +6- +8y=2e-3t

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Obtain using Jacob's method, all the eigen values and eigen vectors of the following matrices: (a) 1…

A: We see that the given matrix is symmetric, that is aij=aji∀i,j A=110.5110.250.50.252 The largest…

Q: (a) Find the infimum and supremum of the set S=2- n² EN} (b) Prove or disprove: If a set SCR has a…

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Q: $0.5 Josh (sin x) d dx using Romberg's method, correct 30 Example 8.20. Evaluate the integral to 3…

A: Solution :-

Q: Question 9. (a) Given a continuous function f: RR and a connected subset S € R, is f¹(S) connected?…

A: Thank you for the question. As per guidelines, we will solve the first question. Kindly repost the…

Q: erential equations 1. y - xy = 0; M(1,1). 2. y4y² = 1; M(1,0). 3. y 4. yy' - ry³ = 0; M(1,1). 1=1/4

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Q: Let f and g be functions which are differentiable on R. For each of the following statements,…

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Q: Determine the Fourier Series of the function f(x)= |x|, -3 ≤ x ≤ 3, f(x) = f(x+6).

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Q: Consider the sequence 4, 8, 16, 32, ... Give a closed formula for the nth term of the sequence (in…

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Q: The longer base of an isosceles trapezoid is one more than 1/3 of the shorter base. If the altitude…

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