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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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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.arrow_forwardThe path of a projectile that is launched h feet above the ground with an initial velocity of vo feet per second and at an angle 0 with the horizontal is given by the parametric equations shown below, where t is the time, in seconds, after the projectile was launched. x= (vo cos 0) t, y=h+ (Vo sin 0) t-16t2 Use a graphing utility to obtain the path of a projectile launched from the ground (h=0) at an angle of 0 = 65° and initial velocity of v = 130 feet per second. Use the graph to determine the maximum height of the projectile and the time at which it reaches this height, as well as the range of the projectile and the time it hits the ground. Choose the correct graph of the path of the projectile. OA. Q G OB. ○ C. O D. Q Q E G [0,1000]x[0,300] [0,1000] x [0,300] [0,1000]x[0,300] What is the maximum height of the projectile? feet (Type an integer or decimal rounded to the nearest tenth as needed.) At what time does the projectile reach this maximum height? seconds (Type an integer or…arrow_forwardConsider 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_forward
- Help4arrow_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. y y -1.5 -1.0 -0.5 -1.5 -1.0 1.5 1.0 0.5 -0.5 -0.5 -1.0 -1.5 y 1.5 1.0 0.5 0.5 1.0 1.5 0.5 1.0 - X 1.5 X -1.5 -1.0 -0.5 -1.5 -1.0 -0.5 1.5 1.0 0.5 -0.5 -1.0 -1.5 1.5 y 1.0 0.5 0.5 0.5 1.0 1.5 0.5 1.0 1.5 X Xarrow_forwardExplain step by steparrow_forward
- part the with parametric equations This shows curve a=tant, y= sin2t %3D 2. a) Find the gradient of the curve at the point P where t= 3. the curve oat b) Find an equation of the normal to the curve at p equation of the normal point c) Find to the a curve an at the where 4.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_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_forward
- Using Derivatives of trigonometrical and inverse trigonometrical functionsarrow_forwardMatch equation graph with its parametric equation. Not all equations will be used. All graphs shown for -5arrow_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning