Find the length of the following two-dimensional curve. 兀 r(t) = (9 cos t + 9t sin t 9 sin t-9t cos t. for 0sts 2. LD (Type an exact answer, using t as needed.)

Q: b. A curve is given by the equations, where t is a parameter: x = 3t2 + 4t y = sin2t i. Find in…

A: A curve is given by the equations                                    x=3t2+4t…

Q: What curves are represented by the following? Sketch them. [cos t, sin 2t, 0]

A: To Sketch: The curves represented by the parametric form [cos t, sin2t, 0].

Q: Find the exact length of the curve x =t-2sint, y =1-2 cost 0<t<4r.

A: The answer of the question is given below.

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

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Q: Given the curves r1 = 1 + 3 cos(θ), 0 ≤ θ ≤ 2π, and r2 = 3sin(2θ), 0 ≤ θ ≤ 2π a.   Plot both curves…

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Q: Find the length of the curve (t) = (4 cos(5t), 4 sin(5t), 5t) for -3 ≤ t ≤9 Give your answer to two…

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Q: Find the lengths of the following curves: e. x = 8cos t + 8t sin t and y = 8 sin t – 8t cos t,…

A: Solution:Givenx=8 cost+ 8t sinty= 8 sint -8t cost,   0≤t≤π2To find the length Formulaarc…

Q: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

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Q: A polar curve is given by r = 5 (3-cos(e)) What is the slope of the tangent line to the curve at 0 =…

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Q: Find the unit to the - tangent r = (a cos t, a sin t. h t) − ∞ 0 and equation of tangent complete…

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Q: e2x2 f (y) dy +g (y). C) u (x, y) =e2.2 f (y) dy +g (x). The solutions of the PDE Uyx - 4xuy = 0…

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Q: Which one of the following could be the graph of the curve given parametrically by x(t) = sin(t +…

A: Here we have to draw the graph of given parametric equations. We have x(t)=sint+sin(t)…