Determine the solution x(t) of the ordinary differential equations with initial values a. x"(t) - x(t) = tu(t)  with x(0)=0 , x'(0)=2

Q: Consider the following LP problem: minimize z= -x₁ + subject to x2-2x3, X₁ + X₂ + X3 ≤6, -X1 + 2x2 +…

A: Given that: minimize z=-x1+x2-2x3,subject to          x1+x2+x3≤6,…

Q: g) Determine length of the curve r(t) = 2cost î+ 2sint j + 3t k from (2,0,0) to (2,0,67)

A:

Q: Approximate the following integrals using Gaussian quadrature with n = 3 and compare your answers to…

A: As per the policy, we are allowed to solve one question at a time. So, I am answering the first…

Q: Present a second order differential equation. Identify the corresponding auxiliary equation.…

A:

Q: Let n be a nonnegative integer. Express each sum in closed form (without Zor ellipsis) by using…

A: Introduction: The binomial theorem is one of the most important and applicable theorem in classical…

Q: 11. Based on the given graph, determine the zeros of the function and note if multiplicity is odd or…

A:

Q: Find the number zeroes with which the decimal representation of 700! terminates. a (a) 245 O (b) 199…

A:

Q: Which point(s) on the Ferris wheel would have the same horizontal distance to the Vertical Axis as…

A: We have to determine a point on the Ferris wheel which is at the same horizontal distance from the…

Q: Question TWO In the diagram, EFGH is a rectangle having diagonals intersecting at M. M₂ = 60° and L₂…

A: Given figure is where EFGH is a rectangle Diagonal of rectangle intersect at point M, so…

Q: Using Laplace transformation, solve the equation r(t) = tif 1 < t < 2 and 0 otherwise. Y'(0) = 0…

A: By Bartleby policy I have to solve only first one as Q2)a) and Q)2)b) are unrelated and lengthy…

Q: If a projectile is fired straight upward from the ground with an initial speed of 32 feet per…

A: Here h(t)=-16t2+32t ......(1)

Q: Evaluate sinh (5 + j5). a. 23.15-j78.28 b. 21.05-171.16 c. 25.47-j64.69 d. 19.14-j86.11

A: Follow the steps

Q: Question 2 [3 ] Given the function xyex f(x, y) = 2x³ +50y² a) Find the domain of f. b) Find exist.…

A:

Q: The owner of a restaurant decides to poll regular customers to choose which dish she’ll submit to an…

A: Given the data of casting votes to select a dish for an annual competition. The voters give…

Q: 2. Let (2n) and (yn) be Cauchy sequences of real numbers. Define (Tn) to be equivalent to (yn),…

A: Given :  xn and yn be the Cauchy sequences of real numbers. And  (xn) ~ (yn)  if  limn→∞xn-yn = 0 To…

Q: 4. Let U be a subspace of R¹⁰0. Suppose U has 7 lincarly independent vectors and at the same time it…

A: It is given that U is a subspace of ℝ10. The subspace U has 7 linearly independent vectors and the…

Q: 4. (-3x + 2y) dy + (-3y + 2x) dx = 0; y(3)=8. Determine y(5).

A: Sol:-

Q: Using integration, find the area of the triangle with vertices at (2, -5), (6, 2) and (4, 1). Sketch…

A:

Q: Given a vector x, show that the infinity norm defined by |||x|| = max|x|, satisfies the triangular…

A:

Q: Show that if a non-zero element in a normed space X, then there is a bounded linear functional f on…

A:

Q: (b) Sketch the polar curve r = √cos 20 and r= 2 cose. Then find the area of the region that is…

A: Introduction: Each Cartesian curve has a respective polar representation. The most general…

Q: An automorphism of a group G is an isomorphism G→ G. (1) Prove that Aut(G), the set of all the…

A: As per the policy, we are solving 3 subparts of the given question. Please repost the question and…

Q: 2. Circles. Let A = 8 1 0 1 -1 1 2 5 -1 -1 -1 7 1 1 6 -1 Show that A is invertible by Gershgorin

A: We have to solve given problems:

Q: f(x) = x³ - 5ex + 7x Find the first 2 values of the derivative vector when the derivative of the…

A: Given: The function, fx=x3-5ex+7x.   To Find: The first 2 values of the derivative vector when the…

Q: Consider the function f = x->sinx. Compute the value of f(x) at x = 1.2, then find the derivative of…

A:

Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: Evaluate: So SY SY ㅇㅎ 01 21-13 dyde O-3 이용 2 12+y2

A: To Evaluate: ∫03/2∫x/32x-x2dydxx2+y2.

Q: 1. Below is a graph of the derivative of the function g. f a How many solutions to the equation g(x)…

A:

Q: Find the general solution of the system x'(t) = Ax(t) for the given matrix A. 4 A = + 4 5 3

A:

Q: The velocity of a faster asteroid is given as a function of time in this table: Time (second)…

A: Given the velocity of an asteroid at different time intervals. Also the velocity equation is given…

Q: Using matrix algebra techniques, find a general solution to the system. 3x-8y y' = 8x-31y x(t) y(t)…

A:

Q: .Let A= 10 1 1 1 -1 -1 1 O Solve the system Ax=(1 1 1) using the results of part (a).

A:

Q: Q6 Using the Fourier series of f(x) 1 + 1 -+ 2 1 1 1 + = 9 + 1 16 (-π< x < π) Prove that 1 π² 6 + 25…

A: The given problem is to find summation of series by using the Fourier series expansion of the given…

Q: use the knowlegde of the mean value theorem to prove the trignometric identity…

A:

Q: What is the location of the image of P(−8, 1)P(-8, 1) after a counterclockwise rotation of 90°90°…

A: Given: Point P-8, 1. To find: Image of the point P after a counterclockwise rotation of 90° about…

Q: Question 1 [- Let f(x, y) =ln(xy)-50x³y Find fx, fxy and fxyx.

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

Q: The solution of the following non exact differential equation (y + y² cos x) dx + (2x + 3y sin x)dy…

A: e^(logx)=x

Q: Q4 a) Using Gamma function evaluate b) x6e-3x dx. tre (xe"*, x>0 0, x < 0 Find the Fourier…

A:

Q: Q5 a) b) (x > 0,k > 0) Find the Fourier cosine integral of f(x) = e-kx Find the Fourier series of…

A:

Q: ) ) Given a set of data points (t.. yi) as below ty 1 10 2 5.49 3 0.89 -0.14 5 -1.07 6 0.84 The…

A: Given that: Set of data points=ti,yi, t y 1 10 2 5.49 3 0.89 4 -0.14 5 -1.07 6 0.84…

Q: takes one great sword unsheathe attack, one full spirit long sword combo, f light bow gun and five…

A: Gauss Siedel method: In numerical algebra, the Gauss-Seidel method also referred to as the Liebmann…

Q: Find the limit, if it exists, or show that the limit does not exist. x² - 3y² lim (x,y) (0,0) x² +…

A:

Q: 3.1.P15 Let n ≥ 2, let x, y € C" be given nonzero vectors, and let A = xy*. (a) Show if y*x #0 and 0…

A:

Q: Use the method of undetermined coefficients to determine only the form of a particular solution for…

A:

Q: Use an appropriate test to determine whether the series converges. 9 3 Ink Σ k=3

A: The given series can be written as ∑k=3∞3ln k.  We know the inequality,  lnk&lt;k. ∀k&gt;1…

Q: Question function r(t) = (1+ In 1, ¹3,-3e-3¹). Find the integral / r(t)dt. Consider the curve which…

A:

Q: اعه W = {4; [0₁+0) IR is absolutely continuous what is absolutely continuous ?

A:

Q: 3. Graph a rectangular prism with edge length of 6 units, width of 8, and height of 10. Be sure to…

A: To graph a rectangular prism with the edges as, Length=6 unitsBreadth=8 unitsHeight=10 units

Q: The figure shows a vector field F and two curves C₁ and C₂. Are the line integrals of F over C₁ and…

A: Consider the given vector field figure,

Q: 2. Country X decides to run a simulation to determine what we to war with country Y. Both are small…

A: A differential equation is a relation between an unknown function and its derivatives. Such…