The system 4х + 20 y 19 z 1 %3D 5х + 26 y 27 z 4 %3D 4 x + 20 y 20 z 4 = has the solution x = , y = , Z = + +

Q: Determine the curl of the vector field A = pz sin o ap + 3pz cos o ao at (5, ,1)

A: Here we have given the vector field A=ρzsinϕaρ+3ρz2cosϕaϕ. it is required to find the curl of the…

Q: Find area inside out Side r=2c0s6 ra I

A: Given polar equations are r=2cosθ and r=1 Consider first polar equation r=2cosθ Multiply with r on…

Q: rmine whether the following series converges or di If the series converges, determine the sum. n/2 1…

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Q: Let B = {b1, b2} and C = {C1, c2} be two bases for a vector space V. You are given that b1 = 5c1 +…

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Q: 6. Using Second Theorem of Pappus, calculate the volume of solid of revolution when the area of the…

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Q: Question 15 You are given the data points (i, Yi) for i = 1, 2, 3: (2, 3), (1, –8), (2,9). If y = a…

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Q: 14x10 14x10-2100f v is given in m/s and t is given in seconds. At t=16 s and using At= 2 s, The…

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Q: Q2) Solve the D.E dy + (xy – xy²)dx = 0

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Q: Question 10 Consider the linear transformation T : P2 → M22 given by [4a + c T(a + bx + ca2) : You…

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Q: Question 16 -37 25 For A = 1. 0| and 6 = a least-squar es solution of Ax 1 4 [10 What is the…

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Q: +00 7. It is known that for allzER, cos r%D Find a power series representation for (2n)! n=0 +00 I…

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Q: Consider the following graph. 5- 4- Let u,(t) = u(t – 7) be the unit step function shifted 7 units…

A: Given: A graph To find: Express the function in the above graph in the form of y=f(t)uat+g(t)ubt.

Q: Let H = Span{1 +x²,1+x,1+x + a²,1+2x – 2x²}.What is dim H?

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Q: 2ラ(エトリ) = C)

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Q: 3. 37 Consider the orthogonal basis B = -3 10 of R3. 3 1 5 Let v = -64 15 a If vB =|b|, what is the…

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Q: Question 18 Let B = {1+x, 1 – x2, x + 2x} and p(a) = 7+ 10x + 11a?. You are given that B is a basis…

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Q: Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) =…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 – x from above inside x = y? ,x = 4 .

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Q: by (E)- HA (). [6 11 If B = is a basis for R such that T|B is a diagonal ma %3D then the value of a…

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Q: Find inside r=2sine out side area rI era

A: Area bounded by polar curves

Q: 1 2 -2 76. 1 0 -2 3 01 2 2 -4 10 8 0 1 0 2 0 1.A= 0 1 0 2 2 =B 0 0 0 0 1 -2 2 4 -2 6 0 0 0 0 0 a. Is…

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Q: Solve for the laplace transform x(t) = (t+3) sin(t-6)

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Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

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Q: Find the sum of the following convergent series: [tan(2n – 1) – tan-(2n + 3)]. n=0

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Q: Evaluate triple integral S*dz dx dy.

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Q: (i) Use the IVT to show that there is some number t in (1, 2) such that 3(t? +1)? = 20t. 1. Use part…

A: Let us solve the Intermediate Value Theorem  related problem and The Mean value Theorem related…

Q: Let f be on [aib] and differentiable on Caib), Prove that continuous If azo, then there are if X3…

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Q: Let f(x) = sin(x). Suppose that h and k are two functions such that W (x) = cos(x), k'(x) = f(x +…

A: Let us solve the differentiation and integration based problem in the next steps.

Q: [2 0] [26] For A = 1 3 and b = , a least-squares solution of Ax = bis 3 1 5 What is the…

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Q: -B-B- 1 and W =Span{u1, U2, Uz}. For Let U1 %3D , U2 = Uz = 0. 2 -2 in W ? what value of t is the…

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Q: Question 30 Consider the linear transformation T : M22 → P2 given by a T ) = (a +ŏ+e+ 5d) + (a + b…

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Q: [2 1 1 V2 = 3 1 V4 1 Let Vj = , V3 1 4 1 2 8 For what value of t is the set {v1, V2, V3, V4} NOT a…

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Q: Q4) Find plane area inside the polar function r = 2 and outside the polar function = sin - 0) +1 in…

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Q: You are given that B = {1 – x², 1+ x, 2x + 3x²} is a basis for P2 and - 2 [p(x)]B= |3. If p(x) = a +…

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Q: Question 12 -9 The eigenvalues of 1 are and

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Q: 2* If ODE of 2nd order and y. 2 x + 3 e-2x, the suggested y, is: C e2x + c2 e3x Yp = Yp = a, x + a2…

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Q: Given the matrix G = and do =|Then do and dị are G – conjugate if dį is given by 1.5 O A Non of…

A: We know that,  Two vectors u and v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0

Q: -3 5 11 M = N = -6 2 Find MN ii) Solve the Linear System using Cramer's Rule (or otherwise) -11x + y…

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Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

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Q: 1.1 Show that if |z| < 1. then lim z" = 0. %3D 1.2 Show that lim Vn = 1.

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Q: Question 20 2 0 0] Let A = |0 0 4 1 4 1 Which of the following statements is TRUE about the…

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Q: Question 32 f 3 4 - Let S = 1 3 -7 1 8 -17 Which of the following statements describes the set S?…

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Q: -2-X Q1) Evaluate the integral S* dy dx using polar coordinate

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Q: Let Y C R² be the set {(x, y)|0 < x < 1,0 < y < 1 and y E Q if x # 0} endowed with the dictionary…

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Q: A model created by an engineer is represented by the following multivariable functions w = ze*y¸ I…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 - x from above inside x = y2 ,x = 4.

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Q: 1 37 a Let A 1 1 Find a QR-factorization of A. If R = then the 1 value of a is , the value of b is…

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Q: dx (1 – e²)² -1

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Q: 2 cVy Q3) Evaluate triple integral N S dz dx dy. x-y

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Q: Question 17 Suppose that is an eigenvector of a matrix A with corresponding eigenvalue ó. Then x is…

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