Find a unit normal vector of the surface at the given point P. x² + y² = 25, P: (4, 3,6)

Q: (6) Consider the ODE equations. dt4 = 3y² + y y" +3y". Write it as a system of four first order…

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Q: 4. 5. 2 sinh 6t4t cosh 6t t²e-2t sin 8t

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Q: f(x) = x² - 2x - 15

A: Given Data: Let us consider the given function is, fx=x2-2x-15. (A) rational function that is…

Q: Vector-Valued Function r(t) = (5 sin t, 4t, 5 cos t) O 5 Z 0 oy -5 1.0 0.5 0.0 0.0 -0.5 -1.0 Z 2 5…

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Q: 10. What is the cosine of the angle between the vectors U = (0, 1,0) and V = (2, 2, 1) ? a) 10, b)…

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Q: 0, An experiment starts with an ideal-gas sample in a sealed container with a movable piston at…

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Q: sufficient condition for a curve to be a helix is The necessary and that its curvature and torsion…

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Q: V. Find the third derivative: 1) y = 10 tan(x) - 2 cot(x) 2) y = x³ - x² sin (x) 1 3) y = 2 sin(x)-4…

A: The given problem is to find the 3rd derivative of the given functions.

Q: Let G be a group and let a be a fixed element of G. Show that H = {x E G |xa = ax} is a subgroup of…

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Q: Let vertices of an acute-angled triangle are A(z₁), B(z₂), and C(23). If the origin O is the…

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Q: Use laplace transform to solve the initial value problem: 3rd order IVP : 11 y + 24" y' - 2y = sin…

A: Given the differential equation y'''+2y"-y'-2y=sin3t. After applying the Laplace transforms,…

Q: In the field of the integers modulo 17, 6-¹ is a. 3 b. 6 c. 11 d. 12

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Q: This question concerns the linear transformation t from Question 3, given by t: R³ R³ (x, y, z) (2x,…

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Q: lia f(x) = {x, si03 In(x-2) flor). lina flor). lim f(a)

A: The given function is, fx=xsin1xfor x<0xxfor 0<x≤3sin-1x-33+5x-3lnx-2for x>3 To Find: The…

Q: Prove that for the curve x 31 1²) p=-o= 2 = 31, y = 3 t², z = 2 ³

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Q: 7. It is known that for any function f(x) continuous on [0, 1] the Bernstein polynomials satisfy…

A: Given: Function f(x) is continuous.           maxx∈0,1f(x)-Bnx→0 , n→∞ is satisfied by Berstein…

Q: 2(2) Show, and explain well your calculations. Please find: A) Image of the function given. B)…

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Q: 8. Using Reduction to an equation whose Right Member is zero: (D² + D)y = −cosx

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Q: 6. Use the method of Lagrange multipliers to find the maximum and minimum of f(x,y)=x+y subject to…

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Q: Evaluate • [[ ₁ ² ² + ₁ x² + y² - z dS where S is the part of the cone z² = x² + y² that lies…

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Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

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Q: f(x) = X+1 3

A: The given function is, f(x)=-13x+3. (a) Rational function that is opposite to the given function.…

Q: The shaded region in the image represents a subset R of R² = RX R. State the relation R. It should…

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Q: C 44 2 Pen

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Q: A factorization A PDP is not unique. For A= such that A=P,D,P.¹. -18 -4 P₁-0 (Type an integer or…

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Q: The principal normals to a given curve are also principal normals to another curves. Prove that the…

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Q: -5<x<0 0≤x≤1, ther (11, 1<x<5 If f is the Fourier series of g(x)=9x, f(x) = 0+ ]) cos (152) + (sin…

A: Given: gx=0,-5&lt;x&lt;09x,0≤x&lt;111,1≤x&lt;5 and f is the Fourier series of g(x). We have to find…

Q: Ga. Draw a direction field. b. Find the general solution of the given system of equations and…

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Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: 9. The Lagrange form interpolating polynomial P(x) = (A) (1.0, f(1.2)) (B) (1.3, ƒ(1.3)), (0, 1) (C)…

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Q: The differential equation for which the method of undetermined coefficients can not be used to find…

A: The method of undetermined coefficients can be used only for the non-linear terms involving…

Q: Consider the following parametric equations. x= √t +3, y = 2√t; 0≤t≤ 16 X a. Eliminate the parameter…

A: Given, x = t+3y = 2t0≤t≤16

Q: Let T = W = [5 a) U only, -3 5 3 3 2 -3 2 3³] - Now let U = K Then the inverse o b) C only, c)

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Q: In the first step of substituting the numbers into the formula, where is the 40 coming from in A=…

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Q: Let L be a Lie algebra over an algebraically closed field and let x∈ L. Prove that the subspace of L…

A: Given That : L be a Lie algebra over the algebraically closed field and x∈L. Prove That : The…

Q: The time constant for a first-order system can be described as the time it takes for the system to…

A: Given: The statement about the time constant for a first-order system.We need to tell the percent,…

Q: nd a particular solution to = y" + 8y + 16y= = -15.5e-4t t² + 1

A: Particular integration by shortcut method

Q: 3. Let R be the relation defined on P({1,..., 100}) by ARB if and only if |An B is even. Is R…

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Q: Curvature k and torsion of a helix C are in a constant ratio to the curvature k, of the plane curve…

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Q: Questions 1-10 are concerned with the equation: +6+9y=9x 1. What is the order of the equation? a. 0…

A: 1) The order of the equation is 2 2) the degree of the equation is 1 , since highest term has power…

Q: Find the Laplace transforms of the following functions: 1. cos 4x 2. e-x sin 2x Subject :…

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Q: Solve the equation. 615x63x = 36 The solution set is (Simplify your answer. Use a comma to separate…

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Q: Problem 2. (a) (b) 8 For a matrix A = 0 0 3 2 -10 -8 12 10 Determine if A is diagonalizable by…

A: A=δ320-10-801210

Q: Solve the system, x' = Ax+b A = = [10 4 27]. b = [100] e6 2₁ = 6,0₁ = [¹]

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Q: Find the Laplace transforms of the following functions: 1. -2 cos 6x + 5 sin 6x 2. 4xe-3x

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Q: Consider the matrix A = 0 0 0 Find a non-singular matrix P such that J = -21 1 1 1 1 0 21 0 02 P-¹AP…

A: The given matrix is: A=2-211011100210002 Let λ be an eigen value of the above matrix, therefore:…

Q: -2e -2t 4 3 -3x -16x²-5cos (x√√2) -5cos(x√2) 2 3

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Q: Exercise 16.1.7. Suppose that p is a prime, and g is a generator of U(p). Consider the function h:…

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Q: Express the function f(x) = k/(1+bx)^2 in power series form. then evaluate the series at x = 0.048…

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Q: After looking at the problem explain what you would do first and then second following order of…

A: Given, (2x-3)(3x+5)-(x+1)(2x2-6x+3)