v(t) = (3 t² + 2 t+1) î +t² ĵ +6t² Â then after 2 minutes the particle will be at the point: 1) (16, 8, 19) 3) (14, 4, 16 ) 2) (17, 8, 24) 4) (16, 8, 13)

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

A:

Q: If a particle moves in the xy-plane so that at time t > 0 its position vector is (In (t2 + 2t) ,…

A: As we know that the expression for the velocity is; v=dstdt Given position vector is:…

Q: 1. Use an antiderivative to show that for every contour C extending from a point z₁ to a point 22, 1…

A:

Q: Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

A:

Q: 8. Find the orthogonal trajectories of vy = cx

A:

Q: (c(2z+y), %3D ue of c in the joi F of W.

A:

Q: 8. Find the orthogonal trajectories of Vy = cx

A:

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: What is the equation of the orthogonal trajectories of 4x + 5y = C? (1) 4х + 5у %3D k (2) 4х — 5у…

A: Given : Equation 4x + 5y = C To find : Orthogonal trajectories for the given equation?

Q: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

A:

Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: 2. Calculate the divergence of D = (÷)[10xyzảy + 5x²zãy + (2z3 – 5x²y)ã,] at P(-2,3,5).

A:

Q: Use the composite trapezoidal rule to find approximations to I = (t- cost) dt with n= 1, 2, 4, and…

A: The composite trapezoid rule: ∫abf(x)dx=h2f(a)+2∑i=1n-1fxi+f(b), where h=b-an,xi=a+ih,i=0,...,n The…

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: The divergence of the vector G=i+siny j + 3k is :- -8y x3 + siny -8y x3 + cosy Option 1 Option 3…

A:

Q: (a) 3y' In (u) dy

A: We will use the ILATE rule in this example to solve the integral and for solving we use the formula…

Q: Suppose that a duck is swimr - perature is given by the formı v²sin x. Find dT/dt in two chain rule…

A: Given query is to find the derivative of function T.

Q: 1. Find a vector which is tangent to the curve of intersection of the surfaces z = x2 – y? and xyz +…

A:

Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

A:

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A:

Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

A:

Q: dz - Prove that : Iz%3D2 %3D z%3D2 z+1 2in.

A:

Q: 2. At time t sec, the positions of two particles A andB on a horizontal coordinate line are sA = 3t3…

A:

Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1,…

A: Given that

Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

A:

Q: Identify the transacation of point P x + 3, y + 1). ddf2d92a ddf892d342a ddf892d342a dd1892d342a…

A:

Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

A:

Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2.1,7",e-7) from 0 to…

A: The detailed solution of the problem is given in the next steps.

Q: Let y = v2x. Determine the point (x, y) that is closest to the point (5, 0). That is, deteremine the…

A: find the minimum distance from a point

Q: 2. If a particle moves in the xy-plane so that at any time t > 0, its position vector is (In(r² +…

A: Solution-

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: (4) Find the orthogonal trajectories of the family of curves z +y 2C?, where C being %3D a…

A: Note:-    as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

A:

Q: Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1,…

A:

Q: Find the dircctional deriu atrue Du f(-3,-1,3) for the function f Cxiy,2) =xy + yz +ZX in the…

A:

Q: What is the equation of the orthogonal trajectories of 4x + 5y = C? (1) 4x + 5y = k (2) 4х — 5у 3Dk…

A:

Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

A:

Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

A:

Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2 t, e",e-) from 0 to…

A:

Q: Prove that the vector T'(t) = 0 for moving in a straight line

A: Note that, the object's path is rt=xti+ytj. yt=mxt+b, where m and b are constant. It is known that,…

Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

A:

Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

A:

Q: 6. Suppose that the temperature T at point (x, y,z) is given by the function T = 2x2 – y? + 4z², and…

A: Given temperature function is: T=2x2-y2+4z2 The tiny bug is at point 1,-2,1 Now, to find in which…

Q: d) must be done using Vector Calculus and the Lagrange multiplier. Optimize: the function f(x, y) =…

A: Given: The function fx,y=49-x2-y2 subject to the constraint x+3y=10. To optimize the function we'll…