1. A wire is parametrized by (t, 5t – 3,3 – t2) from 0 st<1. (a) The density of the wire is given by p(x, y, z) = Vī g/cm. What is the total mass of the wire? (b) An electric field is given by E(x, y, z) = (y+ 3, 2x, 2ar + z). What is the work done by the field on an electron moving along the parametrization?

Q: An object starts its motion at x=0 with an initial speed v(0) = 8. Assume that the velocity follows…

A:

Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

A:

Q: Flux of F(x,y) = 5 x î +3 y ĵ across the circle x? + y? = 1 (anticlockwise) is - 8 T Can not find.

A: Use the Gauss’ Divergence theorem,: Use the Gauss’ Divergence theorem,

Q: Given: R(t) = (cos t +tsin t) i + (sin t –t cos t) j + t?k^ ,t>0 What is the acceleration at t = EIN

A:

Q: Are the following functions homogeneous? If they are, determined their order. (a) f(y, t) = t^y² +…

A:

Q: dz Z 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using direct…

A:

Q: Consider w = F(x,y,z) = x2 + yz3 Find the equation of the tangent when x= 3, y = 2, z = 1.  At…

A: The given surface is Fx,y,z=x2+yz3. (1) The given point is x=3,y=2, z=1. We know that the equation…

Q: 8. Use change of variables to find: a) The Jacobian if x=(u+3v), y =; -(v- 2u).

A: We will use concept of change of variables.

Q: Given r"(t) = (e^t, sint, cost),  r(0) = (1, 0, 1),  r'(0) = (0, 2, 2),  solve for r(t).

A:

Q: Form a DE with respect to t: x = Acos (In t) + Bsin(In t).

A: Sol

Q: 4. Perform the following (a) A gold-plated plate D is defined by the rectangle enclosed by the lines…

A: Part (a)Part (b)           Dear  student if you have any question than comment in comment box.

Q: Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set…

A:

Q: An electric dipole with dipole moment p = 6 x 105 Cm sets up an electric field (in newtons per…

A:

Q: Calculate distance between two Points Space 2: 2 x² + y² +2²³ - R² r = R₂0₂0 € 3

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: What is the integrating factor of the linear De of order one y'= 1+ 3ytanx ? A B с D sec ³x cos³x *…

A:

Q: (iii) The moment of inertia I of an annulus of inner radius 'a' outer radius 'b' and mass 'm' is…

A:

Q: Q₁) Find $dz 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using…

A:

Q: (7) Determine the upward flux of ▼ × F through the part of the elliptical cone C = {(x, y, z)|z = 2…

A:

Q: 3) A beam of square cross section of the dimensions shown below is subjected to a shear force of V=8…

A: Solution:-

Q: V(x, y) = 80-20xe ²+₁²

A: Note the following facts about a function f(x, y):   (i) The maximum rate of change is ∇f  (ii) The…

Q: A bug is located at the point (9,0) at time t=0 and crawls at the rate of 6 units/minute in the…

A: Given data is: A bug is located at the point (9,0) at time t=0 Crawls at the rate of 6 units/minute…

Q: Suppose the divergence of the electric field in some spherical region is found to be V E = 5kr³.…

A: as given,   the divergence of electric field in some spherical region is ∇·E=5kr3 claim- to find the…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = t2i 1,3K 4tj + %3D (a) r'(t) (b) r"(t)…

A: