If the acceleration vector of a particle is given to be a(t) = (1, 0, −1) and the initial velocity is given to be v(0) = (0, 1, 0) then the velocity of the particle at time t is v(t) = (1, 1, −1) Ov(t) = (t, t, -t) Ov(t) = (1, t, -1) Ov(t) = (t, 1, -t) O None of the above

Q: If r'(t) = (1,21,3r*) and r(0) = (0,1,2) then r(t) equals %3D (a) (1,r°,r'). (b) (1,r",r')+ (0,1,2)…

A:

Q: In the solution of the differential equation. d²x dt² obtained with the +2 +5x3 = 0 condition x=1…

A: Rewrite the equation in a system of ordinary first order differential equations:

Q: general equation of (z-t)dz=(z+t)dt

A:

Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

A:

Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (2, 1, −2), u'(2) = (7, 1, 8), and v(t) = (t,…

A:

Q: 10 Find the maximum rate of change of f at the given point and the direction in which it occurs. (3,…

A:

Q: 5) The position vector of a particle is given by s(t) = 2t2 – 4t + 1.Find the time at which the -…

A:

Q: (b)Find orthogonal trajectory of x'y = c.

A: The given problem is to find the orthogonal trajectories of x2y=c.

Q: The equations ry? + 5zzcos(u) + ye" = 10 and zyz + ze" - 4u = 12 are solved for u and v as functions…

A:

Q: (1,2) 6. Evaluate 0,1 (x²-y) dx + (y² +x) dy along a straight line from (0,1) to (1,1) and then from…

A:

Q: Solve Utt (1,4) Ux (o,t) =o UCX, 0) = 0 KUXX (xst) 0Lxo %3D Ux (1,t) = 0 Ut (x,0)= 2 %3D -1 %3D…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: 6. A particle is travelling along the circular path x² + y² = 100. At the moment when the particle…

A:

Q: (10) Suppose the temperature of a metal plate is given by f (r, y) = the temperature of the metal…

A: The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Use the…

Q: et f(r, y) (-(4r + y)) Then %3D ardy

A: The given differential equation is: f(x,y)=-(4x+y)7

Q: 1. Find a unit vector in the direction in which f increase most rapidly at p. What is the rate of…

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

Q: () Find the solution that satisfies Y(0) 1

A: We will find out the required solution.

Q: Find a solution of x dy = y²-y that passes through the indicated points. dx (a) (0, 1) y = (b) y = 1…

A:

Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: f(2) 1 dt, then f'(z) = ++1

A:

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…

Q: 25. A particle is located at (1, 1,0) at time t = 0 and it follows a path whose velocity vector is…

A: Let's find.

Q: Assume that R (t) + 0. Show that T'(1) = R' (t) – (De||R (t)|)Ť(t) T'(t : ||T (t)||

A: As per the question (and the general conventions in vector calculus) we have a vector valued curve…

Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

Q: If r (t) = (cos(t), sin(t), 2) r(t) = (cos(t), sin(t), 2) , %3D T then fr (t) dt =

A: It is integration using limit problem.

Q: (Calculus) The tangent vector to (x(t), y(t)) is (x'(t), y'(t)). The tangent vector's length ||(x',…

A: Given that the tangent vector to and is the speed of the point along the curve at time t .Here also…

Q: 10. Given R = x7 + y3+ zR, and r = |R show that (a) V x (7 x R) =7 + 7R, (b) (A x V) × R = -27, (c)…

A: Given: be any constant vector.

Q: Jackie and Christine are racing again! We only get some discrete data this time, but we can find the…

A: Sol:- (a) We can plot their movements on the xy-plane as follows:         y-axis         |  C     *…

Q: Find the general solution to the following 3-by-3 linear system: 1 -5 10 2 -4 8 X. dt 3 -5 8.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: [y = = V +2 u?-1] 3 Vx2 + 2 u2+1.

A:

Q: Evaluate the integral. dx 2 (a² + x²)3/21 a>

A:

Q: find the unit vectors T (t) & N (E) from fe() ex 3t r(t) = given T (t) = (141) ₁1 | r¹(t)\ 8 N (t)…

A: