Write down the Euler-Lagrange equations associated with the following Lagrangian L(t, x, y, x°, y°) : (a) x°2 + y° 2 − k 2 (x + y) 2 (b) x°2 + y° 2 − k 2 (x − y) 2 (c) x°2 + y° 2 + k 2 (x + y) 2 (d) x°2 − y° 2 + k 2 (x + y) 2

Q: (а) 8а + 2у + 32 %3D 0 (b) z = sin(x) + cos(y) (1) (c) z = sin 2+x2+y? (d) z = ey II 2. 10 2 0- -5…

A:

Q: Evaluate 8(2x + y) dx + 8xy dy on the given curve from (-1, 2) to (2, 5). (-1,2) (-1,0) X (2,5)…

A:

Q: (a) The parametric curve is described by x(t)=e" and y(t)=e, where tER. Compute d'y dx² as a…

A:

Q: ind parametric equations for the tangent line to the curve with the given parametric equations at…

A: In this question, the concept of Parametric Equation is applied. Parametric Equation Parametric…

Q: The equations re + uz – cos(v) - 2 = 0 and u cos(y) + 10x2v – 10yz2 – 1 = 0 can be solved for (u,v)…

A:

Q: b) Given four points A(-2, 0, -3), B (1, -2, 1), C (-2,-³), D (,0). Find the equation of the plane…

A: As per norms, we will be solving only one question. If you need an answer to others then kindly…

Q: (a) termine the root mean square value of this signal between t = 0, and t = 1/2. An electrical…

A: NOTE: Hi! Thank you for your question. As per the honor code, we'll answer the first question since…

Q: For each problem below write an expression in the form ax + by + cz in the first blank, then choose…

A:

Q: Question 3 Express the curve by an equation in x and y given x(1) = sec? (t) + 2 and y(t) = 3 +…

A:

Q: 9. Given the parametric equations x = et and y = te-t, vt. dy (a) Find dx (b) Find dx2 d?y (c) For…

A:

Q: Let z(t) = 5 cos (t) and y(t) = 3 sin(t) ELLIPSE 2- At t = 3, x(3) = -495 -1- y(3) = 0.42 -2- dz…

A:

Q: 3. The points where r = 1 – cos 0 and r= cos 0 intersect are (A) (0,0) (B) (0,0) , (C) (0,0) (D) (E)…

A:

Q: (4) Evaluate sin(yz)dr+xz cos(yz)dy+ry cos(yz)dz, where C is any curve joining the point (0, 0,0) to…

A:

Q: 1.) You and a friend are standing on the surface of hilly terrain described by f(x,y) = cos(x+y).…

A: In the given question we have to find the slope of the surface              f(x,y)=cos(x+y)at the…

Q: Problem 4. Find y as a function of x if r'y" – 5zy + 9y = x°, y(1) = -9, y (1) = 4.

A:

Q: Question 4. Consider the equation и, — ихх — их 3D 0, 0 0 u(0, 1) %3D 0, и(1,1) %3D 1, 1> 0, и(х,0)…

A: Given equation is  ut-uxx-ux=0 , 0<x<1, t>0                 (i) Let us consider…

Q: Chapter 13, Section 13.7, Question 031 Find parametric equations for the tangent line to the curve…

A:

Q: PDE: ) Solve the problem Ut = 16u1 BC: u(0, t)u(1,t) = 0 IC: u(x,0) = 2 sin(2x), u(x, t) = 0 0…

A:

Q: Find parametric equations representing the line segment joining P(-3, 2) to Q(2, -1) as (x(t),…

A:

Q: A company produces two types of solar panels per year. x thousand of type A and y thousand of type…

A:

Q: Utt = 9uxx, u(0, t) = u(1, t) = 0 u(x, 0) = sin 2πX Ut(x, 0) = sin 3πX 0 0

A: