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Arc Length In Exercises 49-54, find the arc length of the curve on the given interval.
Parametric Equations Interval
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CALCULUS: EARLY TRANSCENDENTAL FUNCTIO
- (b) How do you sketch a parametric curve?arrow_forwardGraph the curve with parametric equations x = sin(t), y = 2 sin(2t), z = sin(3t). And Find the total length of this curve correct to four decimal places. Calculus 3arrow_forwardSketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter x-2, y-t ++ -1 0.5 05 05- -05- 0.5 + --05arrow_forward
- Consider the parametric curve C defined by x = x ( t ) and y = y ( t ) . (a) Explain how to determine the location of the horizontal tangent line(s) of C. (b) Explain how to determine the location of the vertical tangent line(s) of C Use complete sentences to answer this question. All math in your solution must be appropriately typeset.arrow_forward5: A potato cannon launches a potato straight up from a height of 5 feet with an initial velocity of 128 ft/sec. The horizontal distance from the cannon launch and the vertical height from the ground, in feet, are modeled by a set of parametric equations. . Write a set of parametric equations that will model the height of the potato as a function of time, t. . Find the average rate of change in horizontal position over the first two seconds. Show your work and units. What is the average rate of change in vertical motion over the first two seconds? Show your work and units.arrow_forwardUse calculus to determine all points on the curve where ther is a horizontal and veriticle tangent line Find the equation of the tangent line at the orgin (0,0) in the form y=mx + barrow_forward
- Learning activity: Plot the points (x,y) and draw a smooth curve defined by the parametric equation: x = t2 , y = t+1arrow_forwardDynamics of rigid bodies. Write down the derivation of formula and describe each variable of "Curvilinear Motion:Normal and Tangential Components"arrow_forwardConsider the parametric curve = cos(t) sin(t) and y sin²(t) on the domain () < t < π. = Find the values of t for which this function has a horizontal tangent line. Find the values of t for which this function has a vertical tangent line. Question Help: Message instructor Submit Questionarrow_forward
- Answer all partsarrow_forwardA pair of parametric equations is given. x = sin²(t), y = sin⭑(t) (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases. -1.5 -1.0 -0.5 1.5 1.0ㅏ 0.5 -0.5 -1.0- -1.5 y 1.5 1.0 0.5 y 1.5 1.0 0.5 x x 0.5 1.0 1.5 -1.5 -1.0 -0.5 2.5 1.0 1.5 -0.5 -1.0 -1.5 y 1.5 1.0 0.5 -1.5 -1.0 -0% 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.5 1.0 1.5 -0.5 -0.5 -1.0 -1.5 (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. . where [ sxs -1.0 -1.5arrow_forwardFind a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = x² + y², z = 16 - y, (4, -1, 17) Need Help? Read It harrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning