Arc length parameterization Find the description of the following curves that uses arc length as a parameter.
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- Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 3t i + (6 − 4t) j + (8 + 2t) k r(t(s)) =arrow_forwardReparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 3t i + (5− 4t) j + (2 + 2t) karrow_forwardArc length Find the arc length of the following curve. r(t) = ⟨2t9/2, t3⟩, for 0 ≤ t ≤ 2arrow_forward
- Arc length calculations Find the length of the following twoand three-dimensional curve.r(t) = ⟨3t2 - 1, 4t2 + 5⟩, for 0 ≤ t ≤ 1arrow_forward3Express the square of the arc length differential on the surface z=xy. What does it take to find the shortest curve (geodesic) on this surface that reaches from point (1,1,1) to point(2,3,6)?arrow_forwardHow do I find the scale factors for the parabolic coordinates: x = 1/2 * (u^2 + v^2) and y = uv. And how do I find the arclength of the curve given in parabolic coordinatess by u = t and v = 1 where t [0,3]?arrow_forward
- Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 4ti + (5 − 2t)j + (2 + 3t)karrow_forwardFind the arc length of the curve on the given interval. (Round your answer to two decimal places.) Parametric Equations Interval x = e−t cos t, y = e−t sin t 0 ≤ t ≤ π 2arrow_forwardConsider the functinon: r(u) = (et, et sin(t), et cos(t)). Find the length along the curve for the function from u=0 to u=t. Reparameterize the curve in terms of arclength.arrow_forward
- (a) Find the arc length function for the curve y= In (sin x) ,0 < x < pie with starting point ( pie / 2 , 0)arrow_forward2. Find the arc length of the curve y = 2/3x3/2 - 1/2x1/2 on [1, 9]. 3. Find the area of the surface generated when the curve y = √(5x − x2) for 1 ≤ x ≤ 4 is revolved about the x-axis. 4. A spring requires 2 J of work to be stretched 0.1 m from its equilibrium position. How much work is required to stretch the spring 0.4 m from its equilibrium position? Assume Hooke’s law is obeyed.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage