Prove the necessary and sufficient conditions for a curve to be a straight line isbthat the curvature k=0 at all points of the curve.

Q: Let f(r) be a measurable function. Is the function g(x) = f(x) + c also measurable for any constant…

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Q: s3-2s2+5s-9 R(s) s2 (s+3)(s+1) 3s+10 W(s) %D s(s-8)(s-6)²

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Q: help with

A: Given,           v→=w-yi→+xj→

Q: dz (b) Determine the by using the Chain rule with the following information: ds z = cos (rªy^) – sin…

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Q: find a basis. 8. Consider the subset S = { [x, y, z] | x - 3y – z = 0}. Decide if it is a vector…

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Q: Unit 2: Linear inequalities and Applications Consider the following problem: "A chocolate…

A: Solution :  Given data                        type A     type B    Total Milk           :     1…

Q: (-1)"n (xn) = п+2

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Q: Compute the integral f(x)dx, where the graph of f is the red curve given in the following figure.…

A: We have to compute the integral ∫-19fxdx

Q: 6. For each of the following series determine if the series converges or diverges using the…

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Q: In 150 words explain the role of Mathematics in your field?

A: Mathematics is a fundamental part of human thought and logic, and integral to attempts at…

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i+11…

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Q: How many positive integers greater than 5 and less than 2020 are divisible by 7? are divisible by…

A: 1) Here , 2020/7 = 288.57 So 288 multiples of 7 are there between 5 to 2020 So , 288 integers are…

Q: Practice Exercise: Find the differential equations of the following by eliminating the arbitrary…

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Q: Prove that following sequences converges to zero. 2n Xn n² + Tt

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Q: 6. For each of the following series determine if the series converges or diverges using the…

A: Given the series are (a) ∑n=0∞-1n-23n+3n let     bn=13n+3n⇒bn+1=13n+1+3n+1≤13n+3n bn hence bn is…

Q: Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by…

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Q: y = Ce * + C2e 2x + C3e * + e 2x

A: y=c1e-x+c2e-2x+c3e-x+e2xy=c1+c3e-x+c2e-2x+e2x Here, complimentary solution is  y=c1+c3e-x+c2e-2x…

Q: 16 e).y" + 2y = 48(t – 2n) ; y(0) = 3 and y'(0) = 0

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Q: Use diagonalization to find the 3 × 3 orthogonal projection matrix P whose 1-eigenspace is W = Span…

A: Given  W=Span-101,0-11 and null space is W⊥=Span111

Q: 5, i, Evaluate the first and second derivatives of the function z-2x4+3x3+2x-5 when x = 4.

A: We have to find the first and second derivative of the function z=2x4+3x3+2x-5 when x=4.

Q: The accumulated value of one at time t (where 0 < t < 1) is given by a second degree polynomial in…

A: We are given that, The accumulated value of $1 at time t is at2+bt+c, a≠0 We have two information…

Q: If the boy has 10 T-shirts, 6 pants, and 4 pairs of shoes. How many possibilities can he dress…

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Q: . Solve the following problem with insulated boundaries: Uz = Uxx Ju,(0, t) = 0 lu(1, t) = 0 u(x, 0)…

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Q: 5. Find the solution for the following differential equations a) y =1+x+y+ xy. b) x'y'+2y= e*, y(1)…

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Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

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Q: 3. Show that if x is an eigenvector of the matrix product AB and Bx # 0, then Bx is an eigenvector…

A: 3) Let , A and B two matrices. Let , x  be an eigenvector of the matrix product  AB , and Bx ≠ 0. We…

Q: -3 -2 -1 1. -8642 -2 3 * 6 4 2 0 2 46 8 10 2 2- -8-6 -4 -2 8 4 2 -2 4 -6 5 Determine whether these…

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Q: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round…

A: Given that sin2θ=6 cos2θ Now, we have to find the solutions.

Q: 2 2 Find a non-zero vector in R* which is orthogonal to 3 1 3 and 1 2

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Q: x-1 y+3 12-z Consider the following lines defined by I,: and l2: 9. =- %D 7 x = 2t + 10, y = 5t, z…

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Q: Which of the following graphs have Euler circults or Euler trals? OA: Has Euler trail. DA: Has Euler…

A: Solution: Given that

Q: What is the contour map of the function using the given values of k? t(x, y) = 1 1 1 %3D x2 + y? k =…

A: contour map for a function t(x, y)=f(x, y) is t(x, y)=k

Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

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Q: 1. (20%) Use least-squares regression to fit the following data to 6. 2 4. 11 12 15 17 19 6 6 9 8 7…

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Q: If f(x)= x - 4 and g(x)= Vx-2; which of the following is equal to х — 2 Option 1 – 4(SF 2) X - х — 2…

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Q: Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude.…

A: We have to find the upper bound for  error.

Q: A "periodic function" is given by a function which O satisfies f(t+T) = -f(t) O satisfies f(t+T) =…

A: Definition of  Periodic function : A function y= f(t) is said to be a periodic function if there…

Q: Solve the questions given below using the Fundamental Theorem of Calculus. r9(x) If f(x) = 1 rcos a…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that y and z are twice-differentiable functions of x. Show that d y dx y'

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Q: 5. Suppose A = PDP¯1, where P is 2 × 2 and D = 9I. Let B = 51 – 3A+ A². Show that B is…

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Q: Find the fluid force on the vertical side of the tank, where the dimensions are given in feet.…

A: To find the fluid force on the vertical side of the tank, where dimensions are given in feet.

Q: 1- 3s Find the Inverse Laplace Transform of G (s) =- s2+ 8s + 21

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Q: 16. Integrate f(x, y, z) = x + Vy – z? over the path from (0, 0, 0) to (1, 1, 1) (see accompanying…

A: We have to integrate the given function over the path C1 and C2

Q: Let G be simple connected planar graph. If G has 8 vertices and 11 edges, in how many regions will…

A: Euler formula for planar graph: Let G be a connected planar graph, and let n, e and f denote,…

Q: Consider the following system of two nonlinear equations: y = -x +x+ 0.75 y+ 5xy = x² Employ initial…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs…

Q: 3. Find a basis among the vectors [1, 2, 3], [2, 6, 10], [0, –3, –6],[-1,-3,-5] (which are surely…

A: Q3 asked and answered.

Q: dz (b) by using the Chain rule with the following information: ds Determine the z = cos (x"y^) – sin…

A: We have to find dz/ds using chain rule of differentiation.

Q: 21 There is a family that has two children. Suppose that girls and boys are equally likely, what is…

A: The probability of an event given A given event B is: PA/B=PA∩BPB Now, we have that event A is that…

Q: Laurent

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Q: Describe the graph of the equation. r = -9i+¿j + (r² – 1) k O It is a parabola in the x = –9 plane,…

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