Given u and v as follows, calculate u + v, u – v, and v – u. 2 (a) u (b) и %3D 4 -3- 21

Q: a²f af af and əx' əy :f(x, y) = (x+ y)(2x + y)² Compute se дхду

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Q: [1 Given that A 1 1/3 and A = -I, d %3D C What is the value of C?

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Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i + 2j − k, v = i + j + 2k

A: Given vectors are (a)

Q: Given F(r, s, t) = r(3s4 – 6t°), compute: Frst

A: This is a partial differential problem

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A: Introduction: The formula for differentiation of product of two functions is given by,…

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Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and dv S…

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Q: (a) Calculate the p-value for Hạ: o² # 20, n = 13, x = 27.5. %3D 32, n = 29, x = 34.5. %3D < p <…

A: Provided information is: (a) Ha:σ2≠20, n=13, χ2=27.5 The p value of the test statistic can be…

Q: Given z=4+5i , What is arg z ? o -0.896+2kTt, k = 0, ± 1, ± 2,... o 0.896 + 2kt, k = 0, ± 1, ± 2,...…

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Q: Find the joint CDF, F(t, s) for all t e R and s E R.

A: Given joint density function of x and y , we need to find cumulative distribution function CDF .

Q: dx The evaluation of S is Vx+1 -Vx 3

A: First we have to do rationalisation of the given expression.

Q: Find the following. (0, 1), v = (5, -3) (a) u|| (b) ||v|| (c) |u + || (d) |ll M (e) u+ v (f) |u+ v

A: Given  u = 0, 1, v = 5, -3

Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: 0.6 a1 f A = (0.2 0.7) and Ak: a2 hen And find the value of a1, a3 O a. a2 = 0.6 O b. a2 = 0.2 %3D O…

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Q: If u = a + j13 and v = -11 – jb, calculate the value of Re ().

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Q: a) Are Y1 and Y2 independent? b) Find V(Y1 – 2Y2), if we know that E(Y,) = E(Y 2) =}.

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Q: If u = a +j13 and v = -11 – jb, calculate the value of Re

A: Given, u=a+j13v=-11-jb

Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: S = {(x, Y, z) E R³ : 2? = x² + y², 0 < z < 4}. Evaluate e*dS.

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Q: The joint pmf of X and Y are given in the table below: Y X 4 2 1 15 15 2 15 3 3 15 15 上面00

A: Solution-: We have following table: X Y 0 2 4 1 0 2/15 1/15 2 3/15 6/15 0 3 3/15 0 0…

Q: Refer to the figure below to find the components of u.

A: When a vector u makes an angle θ with an axis; the magnitude of the component of the vector along…

Q: Evaluate (7x+2vy) ds where C is given in the accompanying figure. (1,1) 1- y =x y=x2 (0,0)

A: To evaluate: ∫C 7x+2y ds  where C  is the region bounded by y=x   and   y =x2

Q: Given u= i -4 j and v = -4 i -4 j, calculate u

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Q: FInd the following. (0, 1), v = (5, –2) u = (a) |삐 (b) ||v|| (c) |u + v|| (d) (e) u + v (f)

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Q: A A -(RA¬S) v ¬R B -(¬RVS) V R B © -(¬RVS) = ¬R (RA-S)V¬R

A: (R∧¬S)⇒¬R

Q: Find the following. u = 3(4, 9) %3D (a) u|| (b) v|| (c) |u+ v|| (d) (e) (f)

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Q: (b) F. dr = 1 |(가를 -16+ 를) C2: r(t) - Ostsi %3D

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Q: Ir If z = f(x- y), then of df дх ду 1 -1 12 O 5

A: → Use chain rule of differentiation.             ∂(f(g(x)))∂x=∂(f(g(x)))∂(f(x))×∂(f(x))∂x→While…

Q: xa, ya, + za Let A = (x² + y? + )3/2 i show that V X A = 0.

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Q: let R = (-2, 7). Calculate the following: The components of u = PŔ, where P = (1, 2)

A: Given,               R=(-2, 7)   and   P= (1, 2).    The components  of u=PR⇀=?

Q: i) (i × j). k = 2.

A: This can't be equal to 2.

Q: Which of the following symbols denotes the operation of antidifferentiation? A) C) E B) F'(x) D)

A: In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or…

Q: g(x, y, z)

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Q: The expression for Absorption law is given by Select one: a. A + AB = B b. A + AB %3D А с. А + В %3D…

A: Here I am attaching image so that you understand each and every step.

Q: The joint pmf of X and Y are given in the table below: Y X 2 4 1 15 15 3 15 3 15 15

A: Solution-: We have following table of joint pmf of x and Y: X Y 0 2 4 1 0 2/15 1/15 2 3/15…

Q: Find and a and дхду f(x,y) = x2 - y2 + 6xy + 4x – 8y + 2 a. b. f(x, y) = e*y + xy

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Q: S g find Ju u and av Write the anuser in terms of U ty D Using the chain rele and V 2 to

A: Answer

Q: H.W: Given the following table find x3, fo Af₁,Af₂, A² fo j xj Afo A² fo 0 fo 30 A² fo 4 20 Af₁ 2 14…

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Q: You are told that Vf(2,3) =. %3D Given ü =, compute Düf(2,3).

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: (b) Evaluate at the point (s, t) = (1, 2). Əsət

A: As per requirement, we we solve part b) only Given function is z=fst-3,s2+t3 f1-1,9=3, f2-1,9=7,…

Q: Evaluate |(2x + 5Vy) ds where C is given in the accompanying figure. (1,1) y =x (0,0)

A: Here we use line integral of a scalar function . 1. ∫cfx,yds=∫cfx)t,ytdsdt  where   dsdt = dxdt2…

Q: (E,E2 – k)z(k, l) = 0, - (E1 – kE,')z(k, l) = 0. -

A: The given operator form is: E1E2-kzk,l=0             (1)

Q: a) W(2) = %3D b) W (10) = %3D c) If w(t) = 12, then what is t? and

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Q: wx + yz = bc, for z II

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Q: 1 f (t) = t – bet) (aeº а-b (ае&t — eat – beat)

A: This is the problem of Laplace transform.

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = 2i + k, v = i + 3k

A: Given that, the two vectors u = 2i + k, v = i + 3k To find the following (a) u × v, (b) v × u, and…

Q: The joint pmf of X and Y are given in the table below: Y X 2 4 2 15 6 15 1 15 3 2 15 3 15

A: Here we have to find the variance V(Y) from the given joint distribution table

Q: Given A E R3X3, 1 = |1|,02= 1 , V3 = 0, w2 = -2 1 2 -4 Av1 = 01, Av2 = w2, Au3 = 03. %3D %3D %3D

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