Find the velocity, acceleration, and speed of a particle with the given position function r(t) = ti + t2j+ 2 k v(t) i+ 2t + 5 = a(t) 2j |v(t)| V 41 +1 II

Q: The orthogonal trajectories of the family of curves y = cx² is A x=ky² B C x²+2y²=k 2x² + y² = k

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A: Given: Consider the given, x'(t)+3x(t)+y'(t)-4y(t)=-3z(t) --→ (1)y'(t)-y(t)+x''(t)=0…

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Q: Consider a particle moving along the x-axis where x(t) is the position of the particle at time t,…

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Q: (a) Given that F(t) = 3t²i +t*j+tk and G(t) = t*i+ 2t²j. Calculate: |d²F| |at2\t=1 ii. [E(t) • G(e)]

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Q: Consider a particle moving along the x-axis, where x(t) is the position of the particle at time t,…

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Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

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Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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Q: The velocity of a particle moving along the x-axis is v(t)=3t+2.At t = 0, its position is 3.  What…

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Q: The velocity of a moving praticle in three space is given by : v(t) = - 3t i- 3t j-3t k , t>0 %3D…

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Q: The orthogonal trajectories of the family of curves y= cx2 is A x=ky? B x? +2y? =k © x2 = ky? D…

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Q: Consider a particle moving along the x-axis where x(t) is the position of the particle at time t,…

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Q: The orthogonal trajectories of the family of curves y = cx2 is A x=ky? B x²=ky² © 2x2+y²=k D…

A: Solution

Q: Consider a particle moving along the x-axis where x(t) is the position of the particle at time t,…

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Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

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Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

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Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: A particle moves with position function F(t) = (t In t)i +tj+ ek, a) Find the velocity, speed, and…

A: Given : distance vector , r(t)→ To find : 1. Velocity , v(t) →= dr(t)→dt 2. Speed = v(t)→ 3.…

Q: 2L, - 2L <I< 0 f(z) = f(x) %3D 2L- r, 0SI< 2L

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Q: Find the orthogonal trajectories of the family of curves y = ce^x. Select the correct response: x^2…

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Q: The orthogonal trajectories of y = 9ax is where a is an arbitrary constant y + = 4c 2 Oy +x2 = 9 O…

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Q: 3. Find V x F for F(x, y, z) = -xZ x² + y² i+ -yz x² + y² =j+ x² + y²k.

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Q: A water storage tank takes 12 hours to drain by opening the valve at the bottom. The depth y of…

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Q: Finding the orthogonal trajectories of y? = x² (1 – cx)

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) =…

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Q: 1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

A: Given that: f(x, y, z)=x3y+4z3y2-xyz+x2-z53               NOTE: As per our answering guidelines, we…

Q: A particle moves along the x axis so that its velocity at the t is given by…

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Q: (a) Use Euler's method to derive a new iterative numeric approximation to the velocity of the…

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Q: The Linear approximation (linearization) of f(x) = at æ = 2 is 1 %3D %3D (A) y = - (B) y = - (x – 2)…

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Q: 2. The position of a particle is i (t) = (2.0or² i+ 6.0j – 6.0t k) m. a. Determine its velocity and…

A: To find Velocity and acceleration vectors from the given position vectors.

Q: The function f (x,y) = y2-3ay+2r2 is homogeneous of what degree? A - 1 2 D

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Q: 2. A particle moves along the x-axis with velocity v(t) = t2 – 3t – 4, t 2 0. Find and interpret…

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Q: Find the orthogonal trajectories of x2 + y? – 2cy = 0

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