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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
- A 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_forwardA 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_forwardQuestion vector equation a) Let C be a curve defined by the r(t)=. Show that the point P(-5, 11,) lies on the curve C. b) Find parametric equations for the tangent line to the curve C at the point P.arrow_forward
- Determine the parametric equationarrow_forwardUse a graphing utility to graph the curve represented by the parametric equations Cycloid: x = θ + sin θ, y = 1 − cos θ. Indicate the orientation of the curve. Identify any points at which the curve is not smooth.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_forward
- Determine the Following Graph of the parametric curve with direction Initial and Terminal points The Cartesian quation The domain of the cartesian equationarrow_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_forwardUsing parametric equations, find an equation of the line tangent to the curve at the point corresponding to the given value t.arrow_forward
- Road 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_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_forwardUse 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_forward
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