A vector in the direction of vector i -23 + 2k that has magnitude 15 is î-2j + 2k 3 O 5 -10 + 10k O 15i - 30j + 30k O i - 2j+15k

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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: 2) Traceable. Which of the following graphs are traceable, and why? ☆

A: Given graphs are: We have to tell which of the given graph is traceable.

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Q: Use Bisection method to find the root of the function: f(x) = ln (0.5+x2) on the interval [0.3,…

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Q: 8. Which of the following are orthonormal s 1 A = {U₁ = (₂0₁2), U₂=(2,0, B = { U₁ = (2,0, ₂2), U₂ =…

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Q: A fluid has density 600 kg/m³ and flows with velocity = x + yj + zk, where x, y, and z are measured…

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Q: 1. Solve the initial value problem: y" - 6y' +9y = 11e³x 43 y(0) 27/1/₁y'(0) = 24/12/2 == 2. Find…

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Q: Problem 4. Given a scalar a, the exponential eº can be expanded by Taylor series as: (b) eª 1 =1+a+…

A: Given: A=111010012 and A is diagonalizable. To Do: (a) Express eA by eD. (b) Compute eA.

Q: Solve it on paper!  f'(x)=e^-x (x-1) Part D: Let h be the function defined by h(x) = −2f(x)g(x).…

A: Define the function g(x) in the interval [-3 , 0]

Q: For the systems below, find and classify the critical points. -x+x²7 (2) [1] - [-*+²²]. () []=[v-2²₂…

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Q: f(x, y) = x² - 9xy + y² + 7y+1

A: Find the saddle points for both functions below. Enter each point as an ordered triple, e.g.,…

Q: Problem 3. (a) e (c) Let A be an n x n matrix with characteristic polynomial: f(t) = (-1)" t" +…

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Q: Given V = -2 10 2 -6 -6 1 8-9 and -4 -2 -10 find the closest point to in the subspace W spanned by

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Q: 2. The system of the equation is has a) No solution, c) A unique solution, 2x + y + z = 9 -3x + 4y +…

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Q: Suppose y Σan" on an open interval I that contains the origin. Express the following as a n=0…

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Q: please provide the correct answer

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Q: *← X = →* Find the least-squares solution of the system -7 -13 -7

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Q: Consider the following matrix: 0 0 2 0 -3 18 -18 0 0 3 -3 0 0 A = 5 0 -3 -3 0 0 0 -15 0 5-15-2 a)…

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Q: Prove that fo f = Idom f iff f-¹ is a function from ran f to dom f.

A: Prove That : f-1of=Idom iff f-1is a function from ran f to dom f.

Q: Prove the following for any given sets A, B, C and D. 3. ACB iff P(A) CP(B). 4. ACB if and only if…

A: Let P(A) denotes the power set of set A, that contains all the subsets of set A.

Q: Take the function defined by the series f(t) = 2+1 cos(nat). Find the antiderivative which is in the…

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Q: Evaluate • [[F · ds, where F = and S is the helicoid with vector equation , 0≤ u ≤ 2, 0≤ v≤ with…

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Q: Can you answer d,e, and f pl

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Q: 2.    Consider a linear system below: 2x − y + z = 2 x + 2y − z = 5 3x + y + 2z = 5 (a)    For the…

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Q: For given data (xi,yi), i = 1, 2..., n, the solution of equations a ac Σlyi - (cx; + d)]² = 0 i=1 od…

A: Look inside the summation its like summing up square of distances of y to some fixed cx+d.Least…

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Q: . Given the set of data points: X y 6 5 10 2 1 3 Set up and solve a direct interpolation polynomial…

A: Interpolation is the finding of the value between two points on a line or on a curve. For the…

Q: 3. Solve (2 + 3x)² + 3(2 + 3x) -36y= ax² + bx + 1 + 2 sin ln(2 + 3x). dx²

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Q: Let T be the linear transformation that is reflection across the line y = √√8x in R² followed by a…

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Q: 11. The derivative of cos 3x² is: a. -6x sin 3x² cos 3x² b. - sin 3x² c. -6x cos 3x² d. -6x sin 3x²…

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Q: 10 0 0 1 a 1 1 -1 0 2,

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Q: Suppose that E is the splitting field for some polynomial over GF(p).If Gal(E/GF(p)) = p6, how many…

A: Given: E is the splitting field for some polynomials over GF(p). And Gal(E/GF(p)) = p6. We have to…

Q: Find the approximate value of A using differentials if A = 80.4. Round off the final answer to five…

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Q: Which of the following is true about the quadratic fit to the three points: (1,0), (3,2) and (5,3).…

A: There are given three points (1, 0), (3, 2), and (5, 3). our goal is to find the quadratic equation…

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

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Q: Let F . te [F Use Stokes' Theorem to evaluate F. dr, where C' is the triangle with vertices…

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Q: Use Fourier series to evaluate the following infinite sums 1 1 1 4₁=1++: + + ...8 8 27 64 1 1 1 1₂ =…

A: We will be using the Fourier series to evaluate the following infinite sum.…

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

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Q: Which of the following are true regarding the second derivative of the function f(x) = cos √xatx=2?…

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Q: 3. If M(x,y) is homogeneous of degree 3 and homogeneous, then N(x,y) is homogen (A) y (B) 0 (C) 3…

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Q: Use the method of undetermined coefficients to find a general solution to the system x'(t)= 0-30 A=…

A: Here, we use eigenvalues and eigenvector method to find solution.