A spring with an 8 kg mass is kept stretched 0.4 m beyond its natural length by a force of 32 N. The spring starts at its equilibrium position and is given an initial velocity of 5 m/s. Find the position (in m) of the mass at any time t. x(t) = 1.5811 sin(√10 t) X m

Q: Use the basic building block = Σa", |z| < 1, together with the properties stated in n=0 this section…

A:

Q: (c) Show that if is continuously differentiable in a given region V and on its boundary S, then Lods…

A: Consider the the vector function   f=ϕa   ,  where ϕ is a scalar function and a is constant vector.…

Q: Bsinh lan da bs dx C√x 0 using the first four terms of the series if a = 2, b = 10, c = 6, k = 0.63,…

A: We know  sinhx=x+x33!+x55!+x77!+... ∫0kbsinhaxncxdx=∫0kbaxn+axn33!+axn55!+axn77!cxdx…

Q: om the surface. By applying an appropriate integral theorem, evaluate the following integrals. (F).…

A: Stokes theorem is used to find the surface integral

Q: (a) Verify Green's theorem in the plane for f(3x2 - 8y2) dx + (4y - 6xy) dy, where C is the boundary…

A:

Q: Find a power series representation for the function. (Give your power series representation centered…

A:

Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

A:

Q: Find the mass and the center of mass of the following solid: The tetrahedron bounded by the planes…

A: The given problem is to find mass and center of mass of the given solid tetrahedron bounded by given…

Q: 1. You are going to build a giant Ferris wheel near Limketkai Mall. Given two endpoints of a…

A:

Q: Problem 1. Let V, W be vector spaces over F, and let TEL(V, W). Suppose U₁, U2, Uk E V are such that…

A:

Q: X a) Sketch the graphs of y = + 1 and y = ²2/4 + 1 on the following axes.

A: (a). Given,                     y=x2+1, and y=2x+1.

Q: Evaluate the Riemann sum, iπ 2n n 1 lim Σcos( n→∞ N i=1

A:

Q: In Z7, evaluate the following expressions. 3- (2 x 5) 2 × 3 × 4 5 x 3 3+4+5 3² +4² 1. 1 2. 2 3. 3 4.…

A:

Q: Your client has been given a trust fund valued at $1.64 million. She cannot access the money until…

A: The trust fund valued $1.64 million. The money will be available from 65 years old after 15 years.…

Q: Question 2: Given the function f(x, y) = sin(x + y), at the point P(π/3, π/4), What unit direction…

A:

Q: Find a 3 x 3 matrix A that has eigenvalues 3, 5 and -4 with -3 -3 1 2 and ][- E Number Number Number…

A: For a matrix A with eigenvalues λ1, λ2, λ3 and eigenvectors v1, v2, v3 , matrix A can be written as…

Q: (a) Verify Green's theorem in the plane for f(3x² - 8y²) dx + (4y - 6xy) dy, where C is the boundary…

A: Since there are many problems, therefore find the solution of first (a) part.

Q: Find an SVD of the indicated matrix.

A: Given: A=111111 To find the SVD of the indicated matrix.

Q: Verify Stokes theorem ㅋ F² = (2x²-y)=² - y²²} - y²zk, where -y s is of and the the с upper sphere.…

A: Given: F=2x-yi-yz2j-y2zk where S is the upper half surface of sphere x2+y2+z2=1 and C is its…

Q: X6n+1 = T X6n-4 = X6n-3 = X6n-2 = Ibn = n-1 f3i+2p+f3i+3h) II f3i+3p+f3i+4h, i=0 h II i=0 n-1 k II…

A: Given: The information that leads to the required proof.We need to show the equations marked in…

Q: # show that 18 x +11y = 1188 has solution Since (18₁111 = 1188

A:

Q: Verify Green's theorem in the plane for f(3x²-8y2) dx + (4y - 6xy) dy, where C is the boundary of…

A: Given integral is: ∫C3x2-8y2dx+4y-6xydy. Where C is the boundary of the region y=x and y=x2. We have…

Q: 11. The equation A5,000(1.035) describes the dollar amount of an investment after years. a) What is…

A:

Q: x(t) = Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where -4 ^-[33] -4…

A: This is an homogeneous linear differential system. We will solve by this using eigenvalues and…

Q: (b) Find a formula for adj (adj A).

A:

Q: Using Riemann sums, prove that (3x² - 2)dx= 22 1

A:

Q: A house on a hill is enclosed by a circular fence with center at the front door. The fence is made…

A: According to question, The fence is described by x2+y2=80 with origin at the center of the circle.…

Q: Let G be solid in the first octant bounded by the paraboloid z = x^2 +y^2, and the planes z = 2, y =…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Consider the set of vectors B = {(1, 0, 2), (2, 1, -1), (3, 0, 7)} (1) Is 3 linearly independent?…

A:

Q: Complete the truth table for the given statement: (p vrq) v p. rq руга (pvq) p 1 1 0 0 q 1 0 1 0 г…

A:

Q: Let f(x,y) = xy, g(s, t) (2s + 3t, 4s+t), and F(s, t) = (ƒ 0 g)(s, t). Evaluate DF(s, t) both…

A:

Q: SSR(2+cos6(x)sin³(y)- 6x³y²ex4)dxdy

A:

Q: (c) Let S be a surface described by x² + y² + 3z² = 1, z ≤ 0, and let F(x, y, z)= yi aj+zx³y²k.…

A:

Q: 3. Let B be an m x n matrix and let AB be a k x n matrix. If rank B = rank (AB), show that null (A)…

A:

Q: A ballast is dropped from a stationary hot-air balloon that is hovering at an altitude of 340 ft.…

A: A ballast is dropped from a stationary hot-air balloon that is hovering at an altitude of 340 ft.…

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

A:

Q: (a) Let U = 3i -j- 4k and V = -2i+4j-3k. Show that U. V is commutative but U x V is not. (b) For any…

A: ( a) U=3i-j-4kV=-2i+4j-3kU·V=3i-j-4k·-2i+4j-3k        =-6-4+12         =2V·U=-2i+4j-3k·3i-j-4k…

Q: Problem 1: Use an LU-factorization of the coefficient matrix to solve the linear system 2x1 -2x1 +…

A: Write the given system of equations in matrix form, that is, in the form AX=B.…

Q: X6n-4 = h X6n-3 = n-1 f3i+29-f3ik h II (J3i+1p-fat-sh) (136429 - fak) f3i-1p-f3i-3h, i=0 X6n-2 = n-1…

A: Given: The information that leads to the required proof.We need to show the equations marked in…

Q: 1. Let f(x,y) = x² + y², g(t) = (3t+1, 2t − 3), and F(t) = (fog)(t). Evaluate F'(t) both directly…

A: 1. Given,              f(x, y)=x2+y2, g(t)=3t+1, 2t-3 and F(t)=f∘gt.

Q: 2 Obtain a power series solution of the equation (1+x²)y" - 3xy' - 5y = 0 up to and including the…

A: Given the equation is                         1+x2y''-3xy'-5y=0.

Q: Bob makes his first $600 deposit into an IRA earning 7.2% compounded annually on his 24th birthday…

A: Consider the case where deposits are made, Periodic deposit amount R is $600. he makes a total 20…

Q: (b) Assume that F(x, y, z)= ei+zej + (z + 1)ek is a vector field defined on a smooth curve C given…

A: This is the question from the vector calculus.

Q: Set up the simplex tableau. Do not solve Maximize z=135x1 + 255x2 85x1 + 64x2≤530 75x1 + 37x2≤130…

A: Given Linear programming problem is: Maximize z=135x1+255x2 85x1+64x2≤53075x1+37x2≤13024x1+12x2≤92…

Q: 10. In 2013, the population of a city was 715,000, with an annual growth rate of 0.013% a) Find a…

A:

Q: 2. Consider the sequence defined by the recursive rule x₁ = = 1, ₂ = 7, Xn+1 = 7xn 12xn-1. Using…

A: The sequence is defined recursive rule x1=1, x2=7, xn+1=7xn-12xn-1. Using induction, we have to…

Q: "S[. 10. 10 2x-1 16 S[cate 7XH - 21 7² dx = 5 In (2x-1) - 3 -зе + 7x+1 15 Cos (2x+3) B (2x+1)+ - 8…

A:

Q: 3. Let f(x, y, z) = xyz, g(s, t) = (3s + st, s, t), and F(s, t) = (fog)(s, t). Evaluate DF(s, t)…

A:

Q: Given a matrix below as A-AI= 0. Find the Eigen values A. A = 1 0 0 1 3 -1 1

A:

Q: A colony of an animal begins with one pair of mature animals, which will produce a pair of offspring…

A: