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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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- Use a graphing utility to graph each set of parametric equations. x = t − sin t, y = 1 − cos t, 0 ≤ t ≤ 2π x = 2t − sin(2t), y = 1 − cos(2t), 0 ≤ t ≤ π (a) Compare the graphs of the two sets of parametric equations in earlier part. When the curve represents the motion of a particle and t is time, what can you infer about the average speeds of the particle on the paths represented by the two sets of parametric equations?arrow_forwardSunDose cac à mortar is fired from ground level at an angle of 45° with an initials need of 200 ft/sec. Choose a coordinace system with the origin at the point of launcn. Part: 0 / 5 Part 1 of 5 la) Write parametric equations to define the pan of the mortar as a function of the time? In sec). The parametric equacions are x = Part: 1/5 Part 2 of 5 and= 10) What is the range of the mortar? That is, what is the norizontal distance traveled from the point of launch to the point where the mortar lands? Give an exact answer. Do not round intermediace cak ulacions. The mortar traveled ft. Part: 2 / 5 Part 3 of 5 Ic) What are che coordinates of the mortar als maximum neign? Give an exact answer. Do not round Intermediace calculacions. The coordinaces are ·C.D. סםarrow_forward(b) How do you sketch a parametric curve?arrow_forward
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- Please help me.arrow_forwardplz provide accurate solutionarrow_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_forward
- Find parametric equations for the line segment joining the first point to the second point. (0,0,0) and (1,7,5) The parametric equations are x= y = forarrow_forwardAnswer all partsarrow_forwardMatch equation graph with its parametric equation. Not all equations will be used. All graphs shown for -5arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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