At what time t does the speed of a particle moving in 3-space with position function r(t) = ti+tj+ (t² – 20t) k - have its minimum value?

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

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Q: The curve crosses the x axis at A(2, 0) and at the point B(10, 0). The curve has a minimum at M(3,…

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Q: A particle moves along the curve *= 21² , y = t² – 4t and = = 31 – 5 where t is the time . Find the…

A: Given: Position vector is given as, r→=2t2i^+(t2-4t)j^+(3t-5)k^ The objective is to find the…

Q: 6. A particle moves with position function S(t) = – 2? + 31, t0 [T:3] a) Determine the velocity of…

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Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

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 following is the acceleration function for a particle moving in. a straight line: a(t) = 212 -…

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Q: Determine the NATURAL cubic spline S(x) that interpolates the data f (1) = 1, f (2) = 1, and f (3) =…

A: The given data  is x0=1 , x1=2 , x2=3 and fx0=1 , fx1=1 , fx2=0. The spline polynomial will consist…

Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. Find the orthogonal trajectories of the family of curve a2+3y2 = cy ,where c is an arbitrary…

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Q: 2. A particle moves along the x-axis so that its position at any time t≥ 0 is given by x(t) = x³ -…

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Q: 5. A particle moves in a linear motion along the x-axis. The function s(t) = t3-4t2 +3t-2 gives the…

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Q: (6) Find the orthogonal trajectories for the given families of curves 2x2 – 7y = c.

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Q: Find the orthogonal trajectories of

A: Given,          y=ax2+4ax+4a, where a being paarameter.

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: (a) A particle is moving in the vertical plane and the height of the particle is given by…

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Q: Determine the minimum speed of a particle moving in 3-space with position function r(t) = ti+ 4t j +…

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Q: 18 The curve y = (x + 2)2 has a minimum point at A (0, 4). B (4, 0). (0, -2). (-2, 0).

A: for minimum point put f'(x)=0and solve the question.

Q: ? ? ? 1. f(t) = 4t² + 28t, g(t) = 4t² - 28t 2. f(0) cos(30), = g(0) = -8 cos³ (0) + 6 cos (0) 3.…

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