2. Determine the position function of the motion of a particle, if the velocity vector is 3 1 7' (t) = 2(t+1)/zi + e^²)++ k, e^¹²j t 1 r' With initial condition r(0) = k

Q: X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the…

A: Directional derivative of the function

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

A:

Q: Find the directional derivative of f(x, y) = (xy)^1/2  at P(6, 6) in the direction from P to Q(9, 2)

A: The directional derivative (D.D) of function f at point P in the direction of vector a is given by,

Q: An object is moving in the air (defying gravity) so that its height after t seconds is given by…

A: Answer :- A)Answer

Q: 3 Find the velocity and position vectors for the particle whose acceleration is given by a' (t) =…

A:

Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

A:

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

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

Q: along the following paths C:(a) x=2t^2, y=t, z=t^3 from t=0 to t=1; (b) the straight lines that A ·…

A: We will use parameterization to find line integral

Q: Find the equation of the tangent line to y = = at x = 1. y - V2 = - V7 (x - 1) A) E (x - 1) -- x y -…

A: The solution is given as

Q: 2) A particle is moving along the path given by ~c(t) = (t^4 − 4t, t^3 + t). (a) Compute the…

A:

Q: Find the equation of the tangent plane to z=e^y+x+x^2+10 at the point (2,0,17).

A:

Q: 5.- Determine the tangential and normal components of the acceleration for the vector function:…

A: Step 1:Step 2:

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: ) y = -3 ln x + 3x

A:

Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Subject = Discrete Structures In a group of 9 people is it possible for each person to have exactly…

A: It is not possible,  Imagine constructing an acquaintance graph in which each of the 9 people are…

Q: This question is about gradients and directional derivatives. How can you tell the differences…

A: Gradient: Points in the direction of steepest ascent of a scalar field.Directional Derivative:…

Q: Find f. f ''(t) = 9/ squareroot t,    f(4) = 31,    f '(4) = 12

A:

Q: 2. If a particle's position is given by r(t) = <t ₁2 cost, sint), find the IN velocity,…

A: Given: particle position, r→t=t, 2 cos t, sin t We have to find the velocity, acceleration and speed…

Q: gravity and wind.

A:

Q: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: Let c(t) = (t^3 + 1, t^2 − 4t). Find:(a) An equation of the tangent line at t = 3

A: c(t)=t3+1 , t2-4t

Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Find the derivative of the function T(z) = az + b cz + d' numbers such that ad – bc ‡ 0. When is…

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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: Consider a particle moving along a curve so that it is at position f(t) = (2t³, 2+²) at time t. Then…

A: Given, A particle is moving along a curve such that its position is at ft=2t3,2t2 at time t.

Q: What's the value of the closed integral (Z + 2z) / (z - 1) dz within the closed curve /z/ = 4 а. 6πί…

A: