a b Let A = and let k be a scalar. Find a formula that relates det(kA) to k and det(A) c d

Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

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Q: Verify that (AB)T = B'AT. 1 -2 [ -1 4 1 A = 1. and B = 3 2 0 STEP 1: Find (AB)". (AB)T = STEP 2:…

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Q: If x = sin t and y = cos t then the co-ordinates of the stationary points are a:) (0,1) b) (1,0) c)…

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

Q: Let the differential operators A and B be defined as A =D+3 and B=D – 3 The product AB is equal to A…

A: We have to solve the problem

Q: Given 4'(t) = (-4t +1, -4 sin(t),-e), find the unit tangent vector 4 at t = 0.

A: We need to determine the unit tangent vector at t=0 using the data of A~'(t). The unit tangent…

Q: 5. Let C be the unit square with diagonal corners at –1- i and 1+i. Evaluate O f(z) dz, where f(z)…

A: Cauchy Integral theorem states that if fz is analytic in a simply connected region D then for any…

Q: e (²+1)5 sin f(z) = sin ³ z 2³(2-3i)² # Compute the residue Res(f; zo), where zo is the pole.

A: Given that f(z) = sin 3 zz3(z - 3i)2 e1(z+1)5sin 1z-1

Q: write a in the form a = aTT + aNN at the givenvalue of t without finding T and N. r(t) = (et cos t)i…

A: Given: The given vector equation is r(t) = (et cos t)i + ( et sin t) j + √2 et k,   t = 0    Formula…

Q: The Imaginary part of the complex function f(z) is, v(x, y) = x³ – 3x²y + 2x + 1 + y³ – 3xy² Prove…

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Q: Answer all question 1- Find the vector equation if the F(t)= cos(41) +3 sin(4)j +1'k at t= (+)²

A: Given vector is rt=cos4ti+3sin4tj+t3k At t=π rt=cos4πi+3sin4πj+π3krt=i+0j+π3k

Q: Let I = ,x? cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is: O…

A: The two point Gaussian quadrature formula is ∫abf(x)dx≈c1f(x1)+c2f(x2) . Here,…

Q: (b) The For any X1,...X, and Y1,..., Ym, we have: n п т Cov EXi, -ΣΣCον (X, Y) i=1 j=1 i=1_j=1 Hint:…

A: From the property of covariance,  Assume that X and Y are the random variables. Therefore,  CovX,…

Q: Classify the ODE's according to their linearity. Write th solutions. (e cosxxy)dx 1 dy _ 1 ii) y4 dx…

A: Rearrange the ODE, 1y4dydx-1xy3=x by multiplying both sides by y4 and obtain dydx-yx=xy4. The…

Q: TE: Enter the exact answers in terms of i,j and k. Same direction as – 3i + 5j. u = Oppositely…

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Q: Find i (t), given 7(t) = (5 cos(– 2t + 3), 4te', – 2t In( – t)). %3D F (t) =

A: To find the derivative of the given parametric vector, we need to differentiate each component of…

Q: Let C be the unit square with diagonal corners at -1 – i and 1+i. Evaluate O f(z) dz, where f(z) is…

A: Let C be the unit square with diagonal corners at -1-i and 1+i.Evaluate∮Cfzdz,where fz is given by…

Q: Let C be parametrized by x = 8 sin? t and y = 8 sin t cos t for 0 sts Find the length L of C. L =

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Q: 3.2 Given that A ABC lies on the horizontal plane and that, CB = b, ABD=a,CBD= B and BCD= 0 as shown…

A: Solution 3.2.1 In right angled triangle ∆BAD ADBD=hBD=sinα⇒h=BDsinα              … (1) In triangle…

Q: (c) Prove that 00 eiz = 0. (x+i)3

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Q: EX show that J, (x) 2. sin X %3D zm + Sol:- J CX). = (-) M=D0 m+ LIN

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Q: ACT/SAT In the figure, ZP = LS. Which of the following additional pieces of information would allow…

A: observe picture we will see in next step

Q: ST,¥. xキマ 1. Verify C ノyジ * =ンycO

A: Since, we are asked to solve using Stokes theorem only, we will use theorem to evaluate the integral…

Q: Find r(t) and v(t) if a(t) = 8 cos(t)k, v(0) = 4i + 6j, and r(0) = 7i. v(t) r(t) %3D

A: We have given: at=8cost kv0=4i+6jr0=7i We know that at=dvtdt So, we can write this as: dvt=at…

Q: Find the imaginary component of In(z + w) if z = 16 + 6i and w=7+8i . Round off your final answer in…

A: Complex number, imaginary part

Q: Let the differential operators A and B be defined as A =D+3 and B=D – 3. The product AB is equal to…

A: Product of differential operators

Q: Exercise 3. sin(3z) Let f(z) and C: |z – a| = 1. Then ſ, f(z)dz = %3D z²(z-n) a. 0 b. 2ni C-2ni d.…

A: Evaluate the integral using Cauchy integral formula

Q: Let I = L,x sin(x+ 1) dr. The approximation of I using the two-point Gaussian quadratu %3D formula…

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Q: 5) roțațion 90° counterclockwise about the origin C ID B.

A: Given query is to perform indicated rotation.

Q: Show that if L{f(t)} = F(s) then L{etf(t)} = F(s - k) where k is a constant. Hence find: (a) Leat…

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Q: D. -x-+C C.-r+x+C 2. In S(x+9) dx = =x² +9x +C, what part is the integrand? A. C D.글고 +9x + C B. x+9…

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Q: eat cos(bt) C.

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Q: Yı = e', yɔ = sin2t, y3= cos2t make up a fundamental set of solutions by finding the Wronskian.…

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Q: Find D„f(3, 2), where u = cos(0)i + sin(0)j, using each given value of 0. (i) 4 (ii) 0 3 (iii) 0 3.…

A: Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

Q: a) f(z) = 14/(z2 + 2z + 2) is a complex function, find (1/Tt) S-00° 14/(x²+ 2x + 2)dx

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Q: In evaluating a(4 – x)šdx , if we use the substitution that u = 4 – a, then what will be the…

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Q: Determine all real scalars 2 and non-zero solutions (x), given the ODE φ" () + λφ (*) -0 for 0 < x <…

A: Given : The Ordinary Differential equation φ''(x) + λ φ (x) = 0  for 0 &lt; x &lt; 1 and  the two…

Q: (a) A travelling wave is anything of the form f(x-ct), where x is position, t is time and c is a…

A: Given: A travelling wave is  anything of the form fx-ct where x is position, t is time and c is a…

Q: 59. Prove the general formula 1 I x – a)(x – b) where a, b are constants such that a # b. dx In х —…

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. 1. r(t) =…

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Q: ux v of u = 2i + 3j, v = i + j is O 5i 5k 5j O 5i+5j+5k let u = 3i -2i find the magnitude of *

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

Q: the solia generated Find the volumc af by revolving about the line X =3 the reg ion and y = x² + x…

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Q: e* then the integrand is the same as dx In 4+e¯ 4e* + 1 A) True B) False

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Q: P2: find the Laplacian of the following scalar fields: (a). U = p.z sin (9/4) (b). V = x² + 2y² +…

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Q: eBu – 1 eBau – 1 R(u) = 1B1 |u eBu + q – 1 + y2B2 u e$zu + q – 1

A: Given  Ru=γ1β1u-eβ1u-1eβ1u+q-1+γ2β2u-eβ2u-1eβ2u+q-1                  (i) To find a root of the…

Q: |89. Let w = f(r, 0), r = Vx² + y², and 0 = tan- (y/x). Find dw/dx and dw/ðy and express your…

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Q: Let I = ,x² sin(x + 1) dx. The approximation of I using the two-point Gaussian quadrature formula…

A: Fourth option is correct

Q: 5. Given 7(t) = (sin 2t , – cos 2t , 2) a. Find the vectors T, N and B when t = 2 b. Find the…

A: r→t=&lt;sin2t, -cos2t, 2&gt;

Q: write a in the form a = att +ann at the given value without finding T and N r(t) =(2t+4)i+(t)j…

A: Given, r(t) = (2t+4)i + tj +t2 k, t = -1 and we have to calculate the form a = aTT + aNN at the…

Q: Evaluate the complex integral e19.2.png x+yi Vaz + b dz 0. if a = 10, b = 19, c = 10, x = 1, and y =…

A: To find- Evaluate the complex integral ∫0x+yiaz + b dz if a = 10, b = 19, c = 10, x = 1, and y = 5.…