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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
- 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_forwardA pair of parametric equations is given. x = Vt, y = 1 - t (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases.arrow_forwardDetermine the Following Graph of the parametric curve with direction Initial and Terminal points The Cartesian quation The domain of the cartesian equationarrow_forward
- 1 Trace the curve r = sinecose. 2arrow_forwardA wheel with radius 2 cm is being pushed up a ramp at a rate of 7 cm per second. The ramp is 790 cm long, and 250 cm tall at the end. A point P is marked on the circle as shown (picture is not to scale). P 790 cm 250 cm Write parametric equations for the position of the point P as a function of t, time in seconds after the ball starts rolling up the ramp. Both x and y are measured in centimeters. I = y = You will have a radical expression for part of the horizontal component. It's best to use the exact radical expression even though the answer that WAMAP shows will have a decimal approximation.arrow_forwardRoad turn having the shape of the plane curve (x - 1)² + (y + 3)² = 500 7 (where x, y are measured in metres) is banked at an angle 0 = tan ¹0) Find the Rated speed of the turn in kilometres per hour. You may assume that the gravitational acceleration is 9.8 m/s².arrow_forward
- A pair of parametric equations is given. x = 2t, y = t + 4 (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases.arrow_forwardDetermine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain.arrow_forwardUse a graphing utility to graph the curve represented by the parametric equationsHypocycloid: x = 3 cos3 θ, y = 3 sin3 θ . Indicate the orientation of the curve. Identify any points at which the curve is not smooth.arrow_forward
- (b) How do you sketch a parametric curve?arrow_forwardrewrite the parametric equations in cartesian form. graph the curve; include an arrow to show the direction of the curve: x(t)=3cos^2t, y(t)=-3sin t answer options provided in photoarrow_forwardA pair of parametric equations is given. x = 10t − 6, y = 5t, t ≥ 0 (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases.arrow_forward
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