Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) Now re-parametrize the same curve by arc length. • If start at the point (-4,0,0) and follow this curve for 11 units of length, where will you be? • Find the curvature of this curve.

Q: Evaluate dxdy √√3x + 4y over the rectangle [0,3] × [0,4].

A: We find required integral by using Fubinis method.

Q: Let E = {e₁,e₂, e3} be the standard basis for R³, B = {b₁,b₂, b3} be a basis for a vector space V,…

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Q: 8.4.8. At what values of m does the integral verge? 8.4.9. Prove that the integral diverges if k 1.…

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Q: Determine all the primes p such that p^2 77 has exactly 5 positive divisors.

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Q: - The helix curve is (d) Find the torsion 7. 3 a(t) = (cost, sint, 2). 2 (e) Find the curvature k.

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Q: A person has a weekly salary of X dollars, and gets a raise of 16% which is worth $ 41, calculate x,…

A: Solution :- Given weekly salary = X dollars Getting raise of 16 % , which is equal to 41

Q: Use lower and upper sums (left end and right end sums) to approximate the area of the region under…

A: Note: We know that area of rectangle is = length*width. There are two rectangles for each of lower…

Q: WHAT OBJECTIVE/CONSTRAINTS DO YOU PUT INTO SOLVER?

A: As from the given problem, we have the following rough sketch data as already mentioned.

Q: Let 1, Z₁, Z2, Z3, ..., Z-1 be the nth roots of unity. Then prove that (1-z₁)(1-z₂) ... (1-Zn-1) =…

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Q: Using the hypothesis method, Solve the following equation: 2 (D²₁ (D³²-1) Y = x ²

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Q: If w and af are the nonreal cube roots of unity and [1/(a + c)] + [1/(b + c)] + [1/(c + a)] = 20²…

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Q: Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C². 45 -54…

A: Given, The matrix A = 45-54   We have to find the eigen values and eigenspaces.

Q: Example (1): Find the Fourier Series of the following periodic function; f(t)=t+2 -π<t<T

A: The given problem is to find the Fourier series representation of the given periodic function…

Q: A particle moves along line segments from the origin to the points (2, 0, 0), (2, 4, 1), (0, 4, 1),…

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Q: Let B be the standard basis of the space P2 of polynomials.Use coordinate vectors to test whether…

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Q: 1. Let m € Z'. Show that = 721 is an equivalence relation on Z.

A: For m∈ℤ+, The given relation is congruence modulo m. To Prove: the relation is an equivalence…

Q: ∑ sin2(3n+2) / (2n2-3) ii. ∑ 1 / (n - 2π) iii. ∑ (n + 1) / (n3 + 2)

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Q: 5.18 The following equations arise in the analysis of nonlinear equations in population biology…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Using Stoke's Theorem, evaluate c where C is any closed surface enclosing a square region of the xz…

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Q: Let A and B be sets, let R and S be relations on A and B, respectively, and let f: A -> B be a…

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Q: A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. A…

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Q: Let E be the solid bound by the cylinder y²+z²=4, the yz plane, and the plane y=2x with y 20.…

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Q: The plane II contains the points (1, 2, 3), (0, 1, 2) and (2, 3, 0). The line L passes through the…

A: Since you have posted a question with multiple subparts, we will provide the solution only to the…

Q: 8 In the diagram to the right, AD and BE are altitudes of AABC intersecting at P. Let a, b, c and p…

A: Given that in ∆ABC AD and BE are altitudes intersecting at P.       The position vectors of…

Q: Consider the following vectors: -9 -6 THE a= C= -6 -7 -6 For each of the following vectors,…

A: a→=3312, b→=-9-6-6-5, c→=-90-7-6

Q: If D= find a complete solution of: d dt (2D-1)x+ Dy = et 3Dx + (2D + 1)y = t

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Q: Find an orthogonal basis for the column space of the matrix to the right. An orthogonal basis for…

A: The given problem is to find the orthogonal basis for the column space of the given matrix.

Q: Find O d² cot 1 ¹x dx2 -2x (1+x²)² 2x (1+x²)² -1 (1+x²)² -2 (1+x²)²

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Q: 3. Use Variation of Parameter to find a particular solution for y" - 4y - 12y = x.

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Q: (0.4) (2) ODN (0) Jo 0<- 0 1 172

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: The inductive step of an inductive proof shows that for k > 0, if Στo 2 = 2k+1 – 1, then Σ± 20 =…

A: Mathematical induction proof consists of two steps: 1. The base case : prove that the statement…

Q: Consider the following fifth-order linear homogeneous initial value problem with constant…

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Q: Find the range and domain @ f(x,y) = x 1Ⓒ fcx, y) = √x== y X-J x+y 3 f(x, y) = y (XI 1@ f(x, y, z) =…

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Q: w that : The degree of Q(√√2, √√5) ove least 35. The degree of (√√2, V5) ove most 35. The polynomial…

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Q: Solve the IVP y" + 2y + y = 8(t-2), y(0)=0, y'(0) = 1

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: x' + 3x = 88 (1-2) Initial Conditions: x(0) = 0 8 = the Dirac Delta function (Note the above…

A: Solution :- x'+3x=8·δt-2Apply laplace Transform :-sxs+3xs=8e-2sxs=8e-2ss+3

Q: Consider the following double integral: 1 1 √y cos(y) dy dx x² If you need to use any theorems…

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Q: Define the Taylor series of the functions below, up to fifth degree: a. y = sin x @x₁ = 0 b. y =…

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Q: A curve is drawn on a sphere of radius a and the principal normal at a point P makes an angle 0 with…

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Q: In Problems 31 and 32, solve the given initial-value problem. 2 4 (_² ) x. -1 (0 31. X'= -(-3) X,…

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Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the…

A: Given, The temperature varies between 73 and 87 degrees during the day. The average daily…

Q: Q) The Sum of three numbers is 6 If we multiply the third numbers by 2 and add the first number to…

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Q: Let G be a group and H < G. Show that for all x∈G, x-1Hx is a subgroup of G of the same…

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Q: 1) Find the third vertex of an equilateral triangle whose other two vertars are AC1,2,1), BC2,-1,0).…

A: The given vertex of an equilateral triangle are A1,2,1 and B2,-1,0. Let Cx,y,z be third vertex of…

Q: A spring gun at ground level fires a golf ball at an angle of 45%. The ball lands 14 m away. The…

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Q: Obtain the Taylor series of the given function about z-a, and give its radius of convergence R. a)…

A: The main objective is to find the Taylor series of the given function about z=a. And also need to…

Q: 11:2 +¸µ¹¹:¹² + z ¹¹12 Prove that x12 denote differentiation w.r.t.s. = 1 p² 0² + 1+p²². 04 11 1 R²…

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Q: P(0) = {0} P(A) \ {0} P(A) ACB iff P(A) CP(B).

A: According to guideline we need to solve first three question. Rest of the question should be…