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Q: 1. Let p be a prime and let g be a primitive root modulo p. Let a be an integer which is relatively…

A: This is an if and only if question and so has two parts. We use the definition of a primitive and…

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Q: Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z…

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Q: SEPARATION OF VARIABLES 12.46. Solve each of the following boundary-value problems by the method of…

A: The given problem is to find the solution for the given partial differential equation with given…

Q: 39 Find the sum of the series sin x + 3 sin 3x +5 sin 5x +...+(2k − 1) sin (2k-1)x

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Q: Solve the problem. The radial flow field of an incompressible fluid is shown below. For which of the…

A: To Examine: For which of the curves the circulation of incompressible flow is not necessarily.

Q: Integrating Factors found by inspection y(x²y²m)dx + x (x²y²+n)dy=0 when x = e, y = 1 y(x² + y²-1)dx…

A: Multiplying by a function to each Equation, which is called integrating factor.

Q: Question 12 Compute the product or state that it is undefined. 5-3 || Undefined -3 4 -3 8 2 -4 8 [-2…

A: Remark: Let A and B are matrices of order m*n and n*p. Then multiplication of A and B is possible…

Q: Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z…

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Q: Consider the following matrices: d₁1 d21 0 0 0 0 d12 d22 0 0 0 0 0 0 с 0 0 0 0 0 0 0 0 €11 €12 €13 0…

A: We can check whether the statement is true or not.

Q: Solve dx dt x² + x t² + 1 °

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Q: Find the gradient field F of the function f. f(x, y, z) = x4e9x +y6₂⁹ OF = (4 + 9x)x3e9xi + 6y5z9;…

A: Given function f  f(x,y,z) = x4e9x + y6z9  We need to find the gradient field F for the given…

Q: Consider the planes P₁: 3x+y-2zm 7 and P₂ : x+2y+z=4. Give a parametrization for the line of…

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Q: 08(3-j2) 7245

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Q: Use the Divergence Theorem to calculate the flux of the vector fields F₁ = −4zi + 4xk and F₂ = −4zi…

A: Given That : Vector Fields are F1→=-4zi^+4xk^ and F2→=-4zi^+1-4yj^+4xk^  To Find : Using the…

Q: 5. Find the transfer function and poles of the system represented in state space form: [010] [03] A…

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Q: Calculate the flux of the field F across the closed plane curve C. F = yi - xj; the curve C is the…

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Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F =…

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Q: Newton's law of cooling and warming states that the temperature T(t) of an object at time & follows…

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Q: Applying the Fundamental Theorem of Line IntegralsSuppose the vector field F is continuous on ℝ2, F…

A: Given:  F=f, g =∇φφ1, 2=7 , φ3, 6, φ6, 4 To find: ∮CF·dr

Q: Using Lagrange interpolation, find the value of y at x = 8 Given y(0) = 18, y(1) = 42, y(7) = 57 and…

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Q: Please explain a, b, & c in a readable way

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Q: prove that any two linearly independent eigenvectors must have different eigenvalues

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Q: Calculate the flow or line integral in the field F along the path C. F = y²i+zj + xk; C is the curve…

A: Given, F=y2i+zj+xk;C is the curve r(t) = (-2+4t)i+3tj-4tk;  0≤t≤1

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

A: The cylinder is x2-6x+z=4 Cuts the plane y=1, y=4 and z=0 F→x,y,z=xy,3xz2,yz

Q: press the improper rational transform: 3 X(z) + 1 + z 8 ms of a polynomial and a proper function N

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Q: 1-i<z-i<3-i 12+(-1)2<z-i<32+(-1)2 2<z-i<10 I  dont understand this

A: As you didn't understand the line so, i rewrite in below step.

Q: Please help me answer 4Di, and 9

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Q: (c) u-8v-2w=1 u+v+5w = 4 3u-v+w=-2

A: u-8v-2w=1u+v+5w=43u-v+w=-2

Q: Question 2 Find the work done by F over the curve in the direction of increasing t. F = -9yi + 9xj +…

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Q: Suppose W₁, W₂ are subspaces of a finite-dimensional inner product space. Prove the following: (a)…

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Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward-pointing…

A: Solving the above question of stokes theorem

Q: From the 7 choices, select all that apply span{ |} + { 1 C -4 } span{ span{ span{ 1 O {0} 1 -1}+{0}…

A: Subspace must contains zero vector with respect to addition. Affine subspace is not consider here.…

Q: Evaluate. The differential is exact. (4,4,5) (1, 1, 1) .. O In 80 O In 13 0 80 In ܫܘܐܐܘܠܐܘܐ X dx + 1…

A: In the given problem we have to find the value of the integration . Where the differential is exact.…

Q: Current Attempt in Progress If f (x) x² and g(x) = (x + 2) (x - 1)(x − 3), find all x for which f(x)…

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Q: 125 people were surveyed on the types of volunteering in which they participate. They were asked…

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Q: Find the work done by F over the curve in the direction of increasing t. 1 F = ti + ½ j + k ; C:…

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Q: eff(V x F) · ds where M is the hemisphere a² + y² + z² = 4, x ≥ 0, with the normal in . M Use…

A: The given problem is to evaluate the given surface integral of the given vector field over the given…

Q: the sequence a1, A2, A3,... Ans. is an A.P., then prove th 2 n ²-a² + a²-a²+ + a²n-1-a²n -(a₁ - a₂n)…

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Q: TRUE OR FALSE 1. Under deterministic approach (one which investments are not subject to financial…

A: Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: f (a+bx)e¹/x = x, show t bod 12

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Q: = Write the form of a particular solution without determining the coefficients given that yh C₁ C₂e…

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Q: Let P be an elliptic paraboloid whose vertex is at (0,0, 12) and which intersects the zy-plane in a…

A: We will start with a general standard elliptical paraboloid and then adjust it to satisfy given…

Q: Let F= . Use Stokes' Theorem to evaluate LF C F. dr, where C is the curve of intersection of the…

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Q: Given the first order initial value problem, choose all correct answers dy (x) (2)-6y-12(x) (²/3)=0.…

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Q: Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed…

A: Given That : The Vector field around any smooth, closed curve C is as follows: F→=∇3xy2z-2sinx2z+9…

Q: For the game and mixed strategies, find the expected value. 4 5 (1) 5 2 G=(², 1), - ( + ) r = -3 Let…

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Q: Question 13 Evaluate. The differential is exact. (4, 2, 6) SAA (0, 0, 0) (8x + 1)e8x dx + z dy + y…

A: Given the differential is exact. We need to solve the given integral

Q: Two oil tankers crash in the Pacific Ocean. The spreading oil slick has a circular shape, and the…

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Q: Given f(t) = sin tfor π/2 < t < π, show the representation of f(t) using unit step functions.

A: Formula :                                ft = f0if   0 ≤t ≤af1if   a≤t≤bf2if    t≥b…