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Q: b 2 1+(- dx dy² dx, X y= e у3е ,0<x<1 а Use COMPOSITE Simpson 1/3 rule. Use nine nodes

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Q: Prove: n! > 2"- for any positive integer n that is greater than 2.

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Q: Use the tabular method to evaluate the integral |(* + 2x – 1) cos(4x)dx

A: Given:∫(x3+2x-1)cos(4x)dx

Q: 3 -2 -51 X2 X3 -1 5 7 -11 8. -5 -9 1 6 8 - 3 7 4 A. Solve for the unknown values using Direct…

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

Q: Solve the following differential equation: dy x2 + y2 %3D dx 2хy

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Q: Q16: What's mean by a nilpotent element of a ring R? Find all nilpotent elements of Zg.

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Q: Use the main theorem on primitive roots to show 12 must be a primitive root mod 25 (don't take…

A: We first state the theorem (Theorem 10.6 in Apostols Analytic Number Theory) and then use the…

Q: A company's marginal costs (in hundreds of dollars per year) over a certain period are shown in the…

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Q: An example of cissoid of Diocles is r = sin 0 tan 0 whose graph is below. Show this curve has the…

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Q: each of the following O Abelian group b) Integral domain ring c) Principal ideal =) Sylow p-group.

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Q: Show that the function f defined by 1, f(r, y) = { r2 + y (x, y) = (1, –1) (x, y) # (1, –1) is not…

A: We have to show that  f(x, y)  is not continuous at  (1, -1)

Q: By fixed-Point Iteration, evaluate f(x) =x² -x- e*starting at x1 = 0.

A: The given function is fx=x2-x-e-x To find: the root of the equation.

Q: If A and B are finite sets, then A ∪ B is also a finite set

A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

Q: Question 3.1. Let's think of the set of n-by-n matrices as R by using the matrix entries as…

A: Given: A set of n by n matrix in Rn2 D⊂Rn2 be the subset whose matrices have zero determinants.…

Q: Use the tabular method to evaluate the integral - 2x – 1) cos(4x)dx

A: Introduction: Tabular integration is a technique for quickly integrating many parts in a row. One of…

Q: Determine the Laurengies expansions of f(2) = in the regions: z(1+2²)(4 – 2²) c) |z| > 2. b) 1<|z| <…

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Q: The Education Department will apportion a budget of P1,300,000 to six state universities based on…

A: Standard divisor = Total student populationTotal budget = 97,4501,300,000 = 0.075 (rounds to three…

Q: Q3: Prove that, there is no simple group of order 200.

A: Here we use sylow theorem to prove this.

Q: Find the Zero and order off the Lineartransformation T:RCC)->C identifier aS I (asta,x)=29-1a,

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Q: -a (1) Let a, b, t E R, and a + b # 0. A = a b What is the expression of e4t? What are the…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: A12. Consider the equation cos"(z) – 1 = 0. (a) Show graphically that (1) has a unique solution z…

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Q: Apply the rank one correction algorithm to minimize the function f(X) = 15x + 2x - 2x1x2 -x1 - 5x2 -…

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Q: Q1: what's the relation between prime and semiprime ideals.

A: To Explain: Relations between prime and semi-prime Ideals.

Q: Q32: what's the relation between prime and semiprime ideals?

A: Solution

Q: e" + 3x 08. lim, e' + 0.5x ,2

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Q: = Define maximal ideal, prime ideal.

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Q: is there a trail that is not a walk?

A: Every trail is a walk but every walk is not a trail as in a walk edges may repeated but in a trail…

Q: 1 20 В -2 1 x = с 3 –10 X, 1 3 a) Calculate the pseudoinverse B* . X1 for Bx = c, call it x. X2 b)…

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Q: Let F be a continuous and differentiable vector field. Suppose, for every value of r, the total flux…

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

Q: 1. Given below, find the values of x and y using partial pivoting and also prove that PA=LU. j0 1 4|…

A: Given, A=014122313 LU decomposition, by following the below steps: R3=R3-3R1 R3=R3+5R2 we get…

Q: 28: What is the difference between homomorphism and isomorphism?

A: Let G,∘ and G',* be two groups. A mapping ∅:G→G' is said to be a homomorphism if ∅a∘b=∅a*∅a for all…

Q: 18, where 1, 2, 5. Consider the solutions are there uation 2i Eg + Tg + Tar uovenba (a) if z1, r2,…

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Q: (B) Explain the relationship between each of th a) Field and integral domain. b)

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Q: Q12: Define the concept of field. Is Z a field?

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Q: Q4: prove or disprove each of the following a) Every group has one generator. b) Every group of…

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Q: Locate the vertex, the focus and ends of the latus rectum and find the equation of the directrix,…

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Q: 1. 2x – 5x+ 2 = 0 is an algebraic equation. a. Find the value of x+: b. Find the value of x* + c.…

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Q: Evaluate the following. (2-14)(3-i) 1+i 2 (1-i)(2+i3)(2-i4) (1-4)+(-)

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Q: A space X is locally connected if and only if for every open set U of X, each comj

A: Suppose that X is locally connected. Let U be an open set in X and let C be a component of U. If x…

Q: - Let R=(Z,t9 ,.9). Find 1. Char(R) 2. Nilpotent ideals of R 3. Prime ideals of R.

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Q: 2. The third term of an arithmetic sequence is x and a, = 19x + 6. Find the twelfth term. 3. Php…

A: given

Q: For every item given below, determine which kind of algebraic structure it is, and give at least one…

A: No-7) Given  G=Z+  defined by (a*b) =min(a,b)a      where ... is absolute value. First check about…

Q: A subspace of a completely regular space is completely regular.

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Q: 3 Let I be an ideal of the ring R and define the set ann (1)= {rER raso, VAEI} Prove that ann (I)…

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Q: 1. There is no simple group of ord er 200. 2. Every group of index 2 is normal.

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Q: 15. (a) Find the quadratic approximation for the function f(x) = x3/2 centered at a = 4. (b) Use…

A: 15a Given function is fx=x32. We have to find the quadratic approximation for the given function…

Q: D: Define nilpotent element. Are 1 and 3 nilpotent elements of Z11?

A: Solution

Q: Q21. Give an example for a not commutative ring with identity. Q. 22 True/ false 2 and 3 have…

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Q: (B) Let I be a maximal proper ideal of commutative ring with identity R. Prove that R/I is a field.

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Q: For Problems 4 – 6, compute the indicated power. 4. (-v6 + iv2)* 5. [vZ (cos + isin ) +i sin- 6. (-…

A: #4 and #5 evaluating by polar form, and #6 is solve by Cartesian