Find two unit vectors orthogonal to both (2,3,1) and (-1,1,0). (smaller i value) (larger i value) the answer is not -127,127 .

Q: 1 2n+3 - whether an C. Is the sequence bounded? is increasing, decreasing or not

A: a sequence {a_n} is called bounded if there exists two real numbers m and n such that…

Q: Let B be a subset of R4. Which of the following statements are correct? DIf |B| = 3, then B is…

A: Consider a vector space ℝ4. Since the basis of ℝ4 must be set of 4 vectors.  Any vector span ℝ4 will…

Q: Fill in the blank. (Enter your answer in terms of t.) {} 1 (s-4)³

A: We want to find Laplace inverse of 1(s-4)3.

Q: 3 Compute eta for A = 3 3 4 1 2 1 -1 -3 -2

A: Given: A=334121-1-3-2 We have to find etA

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: Let F = Z, [x] (x³ + 3x + 2) and α=x+ (x+3x+. (x³+3x+2) €F. Find a³.

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Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1, 1) to (1, 1.0) and C₂ is…

A: As you have asked more than one different question, we shall solve first question only.

Q: Determine the value of the interquartile range for the following data set: 42, 62, 22, 74, 12, 34, 2…

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Q: Problem 1. Let L be the line (2t, t, t — 1), t € R, and A the point (1, 1,-1). Let P be the plane…

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Q: Show the final answers using EXACT values only, not calculator-based values. Show complete…

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Q: hot (1603).png hot (1597).png Determine (without solving the problem) an interval in which the…

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Q: Consider the following initial-value problem. y' - y = 2 cos(3t), y(0) = 0 Find L{f(t)} for f(t) = 2…

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Q: V. Let C be the curve represented by R(t) = (cos 2t, 2√3t, 5 - sin 2t). ㅠ 1. Determine the curvature…

A: Introduction: In general, a curve's curvature can be thought of as the speed at which the curve is…

Q: 3.45. The density (d) of a liquid is calculated by measuring its depth (c) in a calibrated…

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Q: Find the general solution of the differential equation ㅠ y" + 16y= 13 sec² (4t), 0 <t<! 8 NOTE: Use…

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Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

A: Correct answer is f(x)= Sin(x) which is infinitely many times continuously differentiable but it is…

Q: (a) Calculate the inverse Fourier transform h(x) of h(k), where h(k)= 0 for b for -b for 0 for ka,…

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Q: 31 36 41 46 f(x) 0.515 0.588 0.656 0.719 8 51 0.777 56 0.829

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Q: Describe the graph of the equation. r = 17 sin 5ti + 17 cos 5t j O It is a circle of radius 5 in the…

A: Given parametric equation r(t)=17sin(5t)i+17cos(5t)j In cartesian expression r(t)=x(t)i+y(t)j

Q: Consider the equation y"-y-2y = 0. Assume that y₁ (1) = ¹ and y₂(1) = e² form a fundamental set of…

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Q: Let U(n) be the group of units in Zn. If n > 2, prove that there is an element k EU (n) such chat k²…

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Q: 1. Consider the curve C = C₁ U C2, where C₁ is the line segment from (0, 1, 1) to (1, 1.0) and C₂ is…

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Q: 4. a) Prove that i) V=1 ¡¡) fx+nh = Σk=0 I A I+A 1+A (1) Ak fx.

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Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1.1) to (1,1,0) and C₂ is…

A: Given Data: The given curve is C=C1∪C2, where C1 is the line segment from 0,1,1 to 1,1,0 and C2 is…

Q: Determine the vector field of F. F(x, y) = yi - xj

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Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1, 1) to (1,1,0) and C₂ is…

A: Here we have given that the force is, F→x,y,z=ez-y,x-z2,y3 and the curve C=C1∪C2. where C1 is the…

Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A:

Q: (b) A linear system has the form dy dt y(0) = (1,0,0) Suppose the eigenvalues of A are 2₁ = -1,2₂ =…

A: Given: The linear system, dydt=Ay, y0=1,0,0T. The eigen values of A are λ1=-1, λ2=-12+2i and…

Q: 4. Let S be the triangular region in R3 with vertices at (2,0,0), (0,6,0), and (0, 0, 3) with upward…

A: Given: Let us consider the given, surface S with vertices, 2,0,0,0,6,0, and 0,0,3 Let's determine,…

Q: Consider the phase plane for a system of differential equations below, which plots x(t) versus y(t).…

A: As per the question we are given a vector field plot of a linear dynamic system with dynamic…

Q: Consider the diagram below in a two dimensional Cartesian x-y plane. The parabola is given by the…

A: we will use symmetry of given figure about y-axis and condition of quadratic equation to find…

Q: (0-2) dy do With initial value problem // (0) = -1 - 2X - = 3 (8-2) seco tano

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Q: or each function.m 6. P(-2)=x4 + 3x³+x²+x+3 7. P(3)=2x³+4x²-x-9; 8. P 9. P(1) -- 4 P(3)=2x³ +…

A: Solution :-

Q: 9 4 y² 2. Let C₁ be the ellipse + = 1 traced counterclockwise and C₂ be the paral- lelogram with…

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Q: Solve the following equations. tan² x + 2sec x - 7=0 if x = [0, 2π)

A: Use tan2x+1=sec2x to generate a quadratic equation in secx

Q: Using the D'Alembert method solve Utt = guxx u(x,0) = sin(2x), and u₂(x,0) = sin(31x). 0 0,

A: This is a problem of the partial differential equation.

Q: Suppose that demographic studies show that each year about 8% of a city's population moves to the…

A: Let the percentage of people who lived in the city be x% and the per of people who lived in the…

Q: A a 5x5 real matrix & v₁,..., v5 linearly independent real vectors in 5 dimensional space: Av₁ = 4v₁…

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Q: ACTURE QUISION, IS DESCRIBED BY THE EQUATION y = COSH x WHERE X e Y ARE HORIZONTAL AND VERTICAL…

A: (i)  y=cosh(104/60)=  2.9181

Q: VIII. Evaluate the following definite integrals. (a) ₁²√³-5da

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Q: Evaluate: f(1) Given: F(s)-(s+1)³/54 5.67

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Q: Find the positive integer A such that t²x" +tx' + t²x = λx has a nontrivial solution satisfying x(0)…

A: Hint: Substitute t=ey , t2x''=D(D-1), tx'=D-1in the given equation and calculate to obtain the…

Q: Given a triangle with interior angles a, ß, y, and opposite sides with lengths a, b, c respectively,…

A: For the given triangle value of angle α= 30 degree

Q: 5. Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) = [0, 1]…

A: Given :             R→u ,v =u2 , v2  ,uvF→x , y ,z =z, z , xy To Find : ∫02∫01F→.Ru→×Rv→du dv

Q: Q.8 (a) Find the eigenvalues and eigenfunctions of the integral equation g(x)=2(2xt-4x²)g(1) dt

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Q: Determine whether the sequence converges or diverges. 3+5n² a. an n+n² b. - cos² n 2n

A: a.  Given an = 3 + 5n2n + n2 Here limn→∞an = limn→∞3 + 5n2n + n2              = limn→∞3n2 + 51n + 1…

Q: 2. Each individual in a random sample of 1349 high school and college students (from a research…

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Q: 5. Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) = [0, 1]…

A: Given That : R(u,v) →=u2,v2,uvF(x.y,z)→=z,z,xy Find : Double integral which is equal to the flux of…

Q: 1. Consider the curve C = C₁ UC2, where C₁ is the line segment from (0, 1.1) to (1,1,0) and C₂ is…

A: Given: Let us consider the given curve, C=C1∪C2 Here C1 is the line segment from the points (0,1,1)…

Q: Show that the polynomial x³-x+2 over the finite field F3 is irreducible check that, if a is any root…

A: We know that a point x=a is a root of the function fx if fa=0 i.e., if the point satisfies the…