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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 Functions (MindTap Course List)
- Sketch 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_forwardUse the parameter t to write parametric equations representing the given curve. Line passing through (0, 2) and (3, 1)arrow_forwardplz provide accurate solutionarrow_forward
- plz provide accurate solutionarrow_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_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
- 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_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_forwardAnswer all partsarrow_forward
- 5: 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_forwardLearning activity: Plot the points (x,y) and draw a smooth curve defined by the parametric equation: x = t2 , y = t+1arrow_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
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