Find the magnitude of the vectors represented 5 3 1 by (a) (b) |³| (c) 12 4 3 LO 5 1

Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6).

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Q: Compare the phase shift and amplitude of y=-cos(x-180∘) and y=-2sin(x-90∘). Which of the following…

A: Given: y=-cos(x-180°) and y=-2sin(x-90°) To find: Correct comparison between phase shift and…

Q: If mx = 1 (mod n) has a solution, then nx = 1 (mod m) has no a solution. Select one: True False

A: We know the definition of Congruence ,  Suppose m be a positive integer , we say that integers a and…

Q: Let f [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

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Q: Which of the following sets of polynomials form a basis for P₂? (i) P₁ = 1 + 4x + 6x², P2 3+x = (ii)…

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Q: Consider the following table. X f(x) X f(x) 0.0 6.5 2.0 7.9 0.4 6.1 2.4 8.5 0.8 6.4 2.8 8.6 1.2 6.6…

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Q: d) 2log4128-5

A: Introduction: To make it less hard or difficult; to make it simpler or easier To condense an…

Q: 8: [1 The matrix A = 4 L3 O True O False -2 31 1 -1 - 2 is a positive definite matrix. 21

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Q: C e

A: Given: Graph with 6 vertices To find: Euler's trail or explain why the graph does not have an Euler…

Q: = 2. Find the Fourier series of the function f(x) -4, 4, - π < x < 0 0 < x < π

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Q: The function f is defined as follows. X if x #0 f(x) = 2 if x = 0 (a) Find the domain of the…

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Q: The values of b and c for which the identity f(x + 1) - f(x) = 8x + 3 is satisfied, where f(x) = bx²…

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Q: 2. y = ln(x² - 1), 2 ≤ x ≤3 ;y-axis

A: The given problem is to find the area of surface of revolution generated when the given curve is…

Q: 2. Given the following sets, where U is the universal set, and A, B and C are three sets in the…

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Q: Find the determinant of by cofactor expansion. 5 0 7 0 1 -7 - 4 0 0 6 -8 0 0 0 3 0 0 - 20 -54 0 1 0…

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Q: 12: Apply Newton's method with line search for f(x) = x₁-x2 + 2x² + 2x₁x₂ + x2 with a starting point…

A: We have f(X) = x1-x2+2x12+2x1x2+x22

Q: Solve the system of differential equations. 2x + 2y - 17x + y' 4y x (0) = -2, y(0) = -17 =

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Q: Find arc length: r(t) = 3 cos ti + 3 sin tj + 5tzk

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Q: 12. Solving the y(t) = sen (54) - 25(u)du with y(0) = 0, we get the convolution y(t)=sen (5t)g(t)…

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Q: In each of Problems 34 through 37, construct a first order linear differential equation whose…

A: To find- Construct a first order linear differential equation whose solutions have the required…

Q: Suppose that a numerical method is used to approximate the solution of an initial -value problem…

A: Given: Interval=1,5 To find: a) Runge Kutta method b) Runge- mid point method c) Euler method

Q: 19 1. The expression -1 n is equal to n=1 9 O 45 O 50 O 362880

A: I have given the answer in the next step. Hope you understand that

Q: (b) Find the following integrals: i. f(4x³+ sin x) dx. ii. ₁²(x²+)dx.

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Q: 2. Minimize: Z = 20X₁ + 10X₂ + 80X3 Subject to: X₁ + X₂ + X3 ≥ 6 : 2X₁ + 4X₂ + X3 = 20 2X₁ + X₂ ≤ 5…

A: We have to find the solution to the given problem.

Q: Find each indicated quantity if it exists. Let f(x)=

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Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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Q: mperature T of a heated circular plate with the origin being at th 64 T(x, y): = x² + y² + 2 point…

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Q: ay Consider the linear system = AY with A = dt Find the corresponding straight-line solutions Y₁ (t)…

A: Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: A necessary condition for a function to be unimodal on the interval [a, b] is that strictly convex…

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Q: The Hessian matrix for f(x) = x³x3 + x2x3 at the point [1 2 3] is given by: [6 0 31 [18 0 31 [3 0 6]…

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Q: 1. Rotation 180° clockwise about the origin 3 A J →X

A: The linear transformation is very useful in different types of transformation. The important kinds…

Q: C d e a f Figure 12: An undirected graph has 6 vertices, a through f. 5 vertices are in the form of…

A: Given: Graph with 6 vertices. To find: Euler's trail

Q: 6: [1 The rank of the matrix A = 4 15 True O False 2 2 5 7 31 6 is equal to 3. 9

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Q: Q3. Find the cross product of the vectors and .

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Q: 2: A necessary condition for a function to be unimodal on the interval [a, b] is that strictly…

A: Statement: A necessary condition for a function to be a unimodal on the interval [a,b] is that…

Q: 6: The function f(x) = x + x² - 16x₁ - 4x₂ has minimizers points at A: [] and [2] B: [2] and [4] C:…

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Q: 2: The function f(x) = x² + 2x² + 3x² + 4x₁x₂ + 5x₂x3 + 6x₁x3 can be written in the form f(x) XTQX…

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Q: One of the following is a general solution of the homogeneous differential equation y" - y' - 2y = 0…

A: To find the given solution :-

Q: 9. Find the numerical Integration of cos(x) + sin (x) where n = 4 using trapezoidal rule.

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Q: 1. A system is composed of a rod and a disk, as shown at t = 0 below: 6 -6 4 6 -2 -4 -6 The axes…

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Q: One section of a suspension bridge hangs between two towers that are 50 feet above the surface and…

A: To find: The equation of the parabola that is shown in the given figure.

Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0,…

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Q: 1. Some graphing calculator only accepts common logarithms, then the equivalent equation a student…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: (a) For each of the following linear transformations, write down its matrix and describe its type.…

A: (a) To find: the transformation matrices. Please post the multiple questions separately. Here I…

Q: Find the arc length of r(t) = 3 cos ti + 3 sin tj + 5t^(7/2) k

A: The given vector is r→t=3 cost i^+3 sint j^+5t72 k^....(1) To find: the arc length of the vector.

Q: 3: The cubic interpolation method with two points has converge rate with order three. True False

A: Solution

Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At 1:0,…

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Q: Z is a complex number

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Q: 17: Which of the following directions is descent direction for f(x) = 2x1 + x² - 2x₁x₂ + 4 where Xo…

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Q: 6. Check the convergence of the following series: 8 n (a) (1+-!-)" 2

A: As per the company guidelines we are allow to solve one question at a time so i am solving first one…