Consider the vector-valued function R (t) = ( 8/3 t 3− t, 2t2 , 2 − 2t2 ) - Find II R(t) II (Simplify the answer please) - Find the distance traveled by a particle moving along the curve from the point where t = −1 to the point where t = 2

Q: Find the positive t when the vector r r(t) = (3t, 4t², 10t² - 4) is perpendicular to r'(t). t =

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Q: Determine the domain of the vector function r() = cos(4t) i + 7in(t - 5) J - 10 Evaluate if the…

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Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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Q: Find r'(t)'r" (t) given the following vector function. r(t) = 3cos(t)i+ 4sin(t)j cost sint -25cost…

A: Given vector function is, r(t)=3cost i+4sint j

Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

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Q: At time t=0, a particle is located at the point (3,9,4). It travels in a straight line to the point…

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Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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Q: Consider the vector-valued function. (a) Show that is continuous at t = -1. (b) Evaluate (R. RY(2).…

A: Like a scalar function, features like continuity and differentiability are also demonstrated by…

Q: 1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b)…

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

Q: *Suppose U := (0, 1) c R and a smooth enough function u : U × R, → R satisfies Un – Uxx = f(x, t)…

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Q: Find the velocity vector v(t) and the acceleration vector a(t) of the straight line motion given by…

A: Consider the given question,The velocity vector v(t) from the given position vector is find as,